Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2209,4,Mod(1,2209)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2209, 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("2209.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2209 = 47^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2209.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: | \(130.335219203\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 47) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.43163\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2209.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.51882 | 0.536983 | 0.268491 | − | 0.963282i | \(-0.413475\pi\) | ||||
0.268491 | + | 0.963282i | \(0.413475\pi\) | |||||||
\(3\) | −5.95044 | −1.14516 | −0.572582 | − | 0.819848i | \(-0.694058\pi\) | ||||
−0.572582 | + | 0.819848i | \(0.694058\pi\) | |||||||
\(4\) | −5.69320 | −0.711649 | ||||||||
\(5\) | 6.17438 | 0.552253 | 0.276127 | − | 0.961121i | \(-0.410949\pi\) | ||||
0.276127 | + | 0.961121i | \(0.410949\pi\) | |||||||
\(6\) | −9.03763 | −0.614933 | ||||||||
\(7\) | −3.35636 | −0.181226 | −0.0906132 | − | 0.995886i | \(-0.528883\pi\) | ||||
−0.0906132 | + | 0.995886i | \(0.528883\pi\) | |||||||
\(8\) | −20.7975 | −0.919126 | ||||||||
\(9\) | 8.40778 | 0.311399 | ||||||||
\(10\) | 9.37775 | 0.296550 | ||||||||
\(11\) | −20.2172 | −0.554155 | −0.277077 | − | 0.960848i | \(-0.589366\pi\) | ||||
−0.277077 | + | 0.960848i | \(0.589366\pi\) | |||||||
\(12\) | 33.8770 | 0.814955 | ||||||||
\(13\) | 5.57597 | 0.118961 | 0.0594807 | − | 0.998229i | \(-0.481056\pi\) | ||||
0.0594807 | + | 0.998229i | \(0.481056\pi\) | |||||||
\(14\) | −5.09770 | −0.0973155 | ||||||||
\(15\) | −36.7403 | −0.632420 | ||||||||
\(16\) | 13.9580 | 0.218094 | ||||||||
\(17\) | −26.5077 | −0.378180 | −0.189090 | − | 0.981960i | \(-0.560554\pi\) | ||||
−0.189090 | + | 0.981960i | \(0.560554\pi\) | |||||||
\(18\) | 12.7699 | 0.167216 | ||||||||
\(19\) | 25.3539 | 0.306136 | 0.153068 | − | 0.988216i | \(-0.451085\pi\) | ||||
0.153068 | + | 0.988216i | \(0.451085\pi\) | |||||||
\(20\) | −35.1519 | −0.393011 | ||||||||
\(21\) | 19.9718 | 0.207534 | ||||||||
\(22\) | −30.7062 | −0.297572 | ||||||||
\(23\) | 90.2723 | 0.818395 | 0.409197 | − | 0.912446i | \(-0.365809\pi\) | ||||
0.409197 | + | 0.912446i | \(0.365809\pi\) | |||||||
\(24\) | 123.754 | 1.05255 | ||||||||
\(25\) | −86.8770 | −0.695016 | ||||||||
\(26\) | 8.46888 | 0.0638802 | ||||||||
\(27\) | 110.632 | 0.788560 | ||||||||
\(28\) | 19.1084 | 0.128970 | ||||||||
\(29\) | 123.275 | 0.789368 | 0.394684 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394684 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(30\) | −55.8018 | −0.339599 | ||||||||
\(31\) | −129.587 | −0.750789 | −0.375395 | − | 0.926865i | \(-0.622493\pi\) | ||||
−0.375395 | + | 0.926865i | \(0.622493\pi\) | |||||||
\(32\) | 187.579 | 1.03624 | ||||||||
\(33\) | 120.301 | 0.634598 | ||||||||
\(34\) | −40.2604 | −0.203076 | ||||||||
\(35\) | −20.7234 | −0.100083 | ||||||||
\(36\) | −47.8671 | −0.221607 | ||||||||
\(37\) | −213.578 | −0.948972 | −0.474486 | − | 0.880263i | \(-0.657366\pi\) | ||||
−0.474486 | + | 0.880263i | \(0.657366\pi\) | |||||||
\(38\) | 38.5079 | 0.164390 | ||||||||
\(39\) | −33.1795 | −0.136230 | ||||||||
\(40\) | −128.411 | −0.507591 | ||||||||
\(41\) | 124.700 | 0.474995 | 0.237498 | − | 0.971388i | \(-0.423673\pi\) | ||||
0.237498 | + | 0.971388i | \(0.423673\pi\) | |||||||
\(42\) | 30.3336 | 0.111442 | ||||||||
\(43\) | 424.723 | 1.50627 | 0.753135 | − | 0.657866i | \(-0.228541\pi\) | ||||
0.753135 | + | 0.657866i | \(0.228541\pi\) | |||||||
\(44\) | 115.100 | 0.394364 | ||||||||
\(45\) | 51.9128 | 0.171971 | ||||||||
\(46\) | 137.107 | 0.439464 | ||||||||
\(47\) | 0 | 0 | ||||||||
\(48\) | −83.0566 | −0.249754 | ||||||||
\(49\) | −331.735 | −0.967157 | ||||||||
\(50\) | −131.950 | −0.373212 | ||||||||
\(51\) | 157.733 | 0.433078 | ||||||||
\(52\) | −31.7451 | −0.0846588 | ||||||||
\(53\) | 361.680 | 0.937370 | 0.468685 | − | 0.883365i | \(-0.344728\pi\) | ||||
0.468685 | + | 0.883365i | \(0.344728\pi\) | |||||||
\(54\) | 168.030 | 0.423443 | ||||||||
\(55\) | −124.828 | −0.306034 | ||||||||
\(56\) | 69.8038 | 0.166570 | ||||||||
\(57\) | −150.867 | −0.350576 | ||||||||
\(58\) | 187.233 | 0.423877 | ||||||||
\(59\) | 836.472 | 1.84575 | 0.922876 | − | 0.385097i | \(-0.125832\pi\) | ||||
0.922876 | + | 0.385097i | \(0.125832\pi\) | |||||||
\(60\) | 209.170 | 0.450062 | ||||||||
\(61\) | −194.845 | −0.408973 | −0.204486 | − | 0.978869i | \(-0.565552\pi\) | ||||
−0.204486 | + | 0.978869i | \(0.565552\pi\) | |||||||
\(62\) | −196.818 | −0.403161 | ||||||||
\(63\) | −28.2195 | −0.0564338 | ||||||||
\(64\) | 173.234 | 0.338348 | ||||||||
\(65\) | 34.4282 | 0.0656968 | ||||||||
\(66\) | 182.715 | 0.340768 | ||||||||
\(67\) | −902.163 | −1.64503 | −0.822513 | − | 0.568746i | \(-0.807429\pi\) | ||||
−0.822513 | + | 0.568746i | \(0.807429\pi\) | |||||||
\(68\) | 150.914 | 0.269132 | ||||||||
\(69\) | −537.160 | −0.937196 | ||||||||
\(70\) | −31.4751 | −0.0537428 | ||||||||
\(71\) | 690.711 | 1.15454 | 0.577270 | − | 0.816553i | \(-0.304118\pi\) | ||||
0.577270 | + | 0.816553i | \(0.304118\pi\) | |||||||
\(72\) | −174.860 | −0.286215 | ||||||||
\(73\) | 698.209 | 1.11944 | 0.559720 | − | 0.828682i | \(-0.310909\pi\) | ||||
0.559720 | + | 0.828682i | \(0.310909\pi\) | |||||||
\(74\) | −324.386 | −0.509582 | ||||||||
\(75\) | 516.957 | 0.795907 | ||||||||
\(76\) | −144.345 | −0.217862 | ||||||||
\(77\) | 67.8561 | 0.100427 | ||||||||
\(78\) | −50.3936 | −0.0731533 | ||||||||
\(79\) | −449.718 | −0.640471 | −0.320235 | − | 0.947338i | \(-0.603762\pi\) | ||||
−0.320235 | + | 0.947338i | \(0.603762\pi\) | |||||||
\(80\) | 86.1823 | 0.120443 | ||||||||
\(81\) | −885.319 | −1.21443 | ||||||||
\(82\) | 189.396 | 0.255064 | ||||||||
\(83\) | −543.425 | −0.718659 | −0.359329 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(84\) | −113.704 | −0.147691 | ||||||||
\(85\) | −163.669 | −0.208851 | ||||||||
\(86\) | 645.076 | 0.808841 | ||||||||
\(87\) | −733.543 | −0.903955 | ||||||||
\(88\) | 420.465 | 0.509338 | ||||||||
\(89\) | 725.592 | 0.864187 | 0.432093 | − | 0.901829i | \(-0.357775\pi\) | ||||
0.432093 | + | 0.901829i | \(0.357775\pi\) | |||||||
\(90\) | 78.8461 | 0.0923456 | ||||||||
\(91\) | −18.7150 | −0.0215589 | ||||||||
\(92\) | −513.938 | −0.582410 | ||||||||
\(93\) | 771.099 | 0.859776 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 156.545 | 0.169065 | ||||||||
\(96\) | −1116.18 | −1.18666 | ||||||||
\(97\) | −214.741 | −0.224780 | −0.112390 | − | 0.993664i | \(-0.535851\pi\) | ||||
−0.112390 | + | 0.993664i | \(0.535851\pi\) | |||||||
\(98\) | −503.844 | −0.519347 | ||||||||
\(99\) | −169.981 | −0.172563 | ||||||||
\(100\) | 494.608 | 0.494608 | ||||||||
\(101\) | 1390.95 | 1.37034 | 0.685171 | − | 0.728382i | \(-0.259727\pi\) | ||||
0.685171 | + | 0.728382i | \(0.259727\pi\) | |||||||
\(102\) | 239.567 | 0.232556 | ||||||||
\(103\) | −1545.53 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(104\) | −115.966 | −0.109340 | ||||||||
\(105\) | 123.314 | 0.114611 | ||||||||
\(106\) | 549.326 | 0.503351 | ||||||||
\(107\) | 1327.49 | 1.19938 | 0.599688 | − | 0.800234i | \(-0.295291\pi\) | ||||
0.599688 | + | 0.800234i | \(0.295291\pi\) | |||||||
\(108\) | −629.849 | −0.561179 | ||||||||
\(109\) | 973.505 | 0.855457 | 0.427729 | − | 0.903907i | \(-0.359314\pi\) | ||||
0.427729 | + | 0.903907i | \(0.359314\pi\) | |||||||
\(110\) | −189.591 | −0.164335 | ||||||||
\(111\) | 1270.88 | 1.08673 | ||||||||
\(112\) | −46.8482 | −0.0395245 | ||||||||
\(113\) | 365.992 | 0.304687 | 0.152343 | − | 0.988328i | \(-0.451318\pi\) | ||||
0.152343 | + | 0.988328i | \(0.451318\pi\) | |||||||
\(114\) | −229.139 | −0.188253 | ||||||||
\(115\) | 557.375 | 0.451961 | ||||||||
\(116\) | −701.831 | −0.561753 | ||||||||
\(117\) | 46.8816 | 0.0370445 | ||||||||
\(118\) | 1270.45 | 0.991137 | ||||||||
\(119\) | 88.9695 | 0.0685363 | ||||||||
\(120\) | 764.105 | 0.581274 | ||||||||
\(121\) | −922.266 | −0.692912 | ||||||||
\(122\) | −295.934 | −0.219611 | ||||||||
\(123\) | −742.018 | −0.543947 | ||||||||
\(124\) | 737.763 | 0.534299 | ||||||||
\(125\) | −1308.21 | −0.936078 | ||||||||
\(126\) | −42.8603 | −0.0303040 | ||||||||
\(127\) | 1034.31 | 0.722682 | 0.361341 | − | 0.932434i | \(-0.382319\pi\) | ||||
0.361341 | + | 0.932434i | \(0.382319\pi\) | |||||||
\(128\) | −1237.52 | −0.854552 | ||||||||
\(129\) | −2527.29 | −1.72493 | ||||||||
\(130\) | 52.2901 | 0.0352780 | ||||||||
\(131\) | −98.9237 | −0.0659771 | −0.0329885 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329885 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(132\) | −684.898 | −0.451611 | ||||||||
\(133\) | −85.0968 | −0.0554799 | ||||||||
\(134\) | −1370.22 | −0.883351 | ||||||||
\(135\) | 683.084 | 0.435485 | ||||||||
\(136\) | 551.293 | 0.347596 | ||||||||
\(137\) | 1607.67 | 1.00257 | 0.501286 | − | 0.865282i | \(-0.332860\pi\) | ||||
0.501286 | + | 0.865282i | \(0.332860\pi\) | |||||||
\(138\) | −815.848 | −0.503258 | ||||||||
\(139\) | −3175.56 | −1.93775 | −0.968875 | − | 0.247549i | \(-0.920375\pi\) | ||||
−0.968875 | + | 0.247549i | \(0.920375\pi\) | |||||||
\(140\) | 117.983 | 0.0712239 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1049.06 | 0.619968 | ||||||||
\(143\) | −112.730 | −0.0659230 | ||||||||
\(144\) | 117.356 | 0.0679145 | ||||||||
\(145\) | 761.149 | 0.435931 | ||||||||
\(146\) | 1060.45 | 0.601120 | ||||||||
\(147\) | 1973.97 | 1.10755 | ||||||||
\(148\) | 1215.94 | 0.675336 | ||||||||
\(149\) | −1155.85 | −0.635509 | −0.317754 | − | 0.948173i | \(-0.602929\pi\) | ||||
−0.317754 | + | 0.948173i | \(0.602929\pi\) | |||||||
\(150\) | 785.163 | 0.427389 | ||||||||
\(151\) | 1941.03 | 1.04608 | 0.523042 | − | 0.852307i | \(-0.324797\pi\) | ||||
0.523042 | + | 0.852307i | \(0.324797\pi\) | |||||||
\(152\) | −527.297 | −0.281378 | ||||||||
\(153\) | −222.871 | −0.117765 | ||||||||
\(154\) | 103.061 | 0.0539278 | ||||||||
\(155\) | −800.118 | −0.414626 | ||||||||
\(156\) | 188.898 | 0.0969481 | ||||||||
\(157\) | −1023.76 | −0.520414 | −0.260207 | − | 0.965553i | \(-0.583791\pi\) | ||||
−0.260207 | + | 0.965553i | \(0.583791\pi\) | |||||||
\(158\) | −683.038 | −0.343922 | ||||||||
\(159\) | −2152.16 | −1.07344 | ||||||||
\(160\) | 1158.19 | 0.572267 | ||||||||
\(161\) | −302.986 | −0.148315 | ||||||||
\(162\) | −1344.64 | −0.652128 | ||||||||
\(163\) | −728.517 | −0.350073 | −0.175036 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175036 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(164\) | −709.939 | −0.338030 | ||||||||
\(165\) | 742.784 | 0.350459 | ||||||||
\(166\) | −825.363 | −0.385907 | ||||||||
\(167\) | 1594.21 | 0.738706 | 0.369353 | − | 0.929289i | \(-0.379579\pi\) | ||||
0.369353 | + | 0.929289i | \(0.379579\pi\) | |||||||
\(168\) | −415.363 | −0.190750 | ||||||||
\(169\) | −2165.91 | −0.985848 | ||||||||
\(170\) | −248.583 | −0.112150 | ||||||||
\(171\) | 213.170 | 0.0953306 | ||||||||
\(172\) | −2418.03 | −1.07194 | ||||||||
\(173\) | −1111.94 | −0.488665 | −0.244332 | − | 0.969692i | \(-0.578569\pi\) | ||||
−0.244332 | + | 0.969692i | \(0.578569\pi\) | |||||||
\(174\) | −1114.12 | −0.485408 | ||||||||
\(175\) | 291.591 | 0.125955 | ||||||||
\(176\) | −282.192 | −0.120858 | ||||||||
\(177\) | −4977.38 | −2.11369 | ||||||||
\(178\) | 1102.04 | 0.464053 | ||||||||
\(179\) | −924.477 | −0.386026 | −0.193013 | − | 0.981196i | \(-0.561826\pi\) | ||||
−0.193013 | + | 0.981196i | \(0.561826\pi\) | |||||||
\(180\) | −295.550 | −0.122383 | ||||||||
\(181\) | −1695.96 | −0.696462 | −0.348231 | − | 0.937409i | \(-0.613217\pi\) | ||||
−0.348231 | + | 0.937409i | \(0.613217\pi\) | |||||||
\(182\) | −28.4246 | −0.0115768 | ||||||||
\(183\) | 1159.41 | 0.468340 | ||||||||
\(184\) | −1877.43 | −0.752208 | ||||||||
\(185\) | −1318.71 | −0.524073 | ||||||||
\(186\) | 1171.16 | 0.461685 | ||||||||
\(187\) | 535.911 | 0.209570 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −371.321 | −0.142908 | ||||||||
\(190\) | 237.763 | 0.0907848 | ||||||||
\(191\) | −1985.24 | −0.752079 | −0.376039 | − | 0.926604i | \(-0.622714\pi\) | ||||
−0.376039 | + | 0.926604i | \(0.622714\pi\) | |||||||
\(192\) | −1030.82 | −0.387464 | ||||||||
\(193\) | −172.859 | −0.0644696 | −0.0322348 | − | 0.999480i | \(-0.510262\pi\) | ||||
−0.0322348 | + | 0.999480i | \(0.510262\pi\) | |||||||
\(194\) | −326.152 | −0.120703 | ||||||||
\(195\) | −204.863 | −0.0752335 | ||||||||
\(196\) | 1888.63 | 0.688277 | ||||||||
\(197\) | 18.9634 | 0.00685829 | 0.00342915 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00342915 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(198\) | −258.171 | −0.0926636 | ||||||||
\(199\) | −2200.21 | −0.783762 | −0.391881 | − | 0.920016i | \(-0.628176\pi\) | ||||
−0.391881 | + | 0.920016i | \(0.628176\pi\) | |||||||
\(200\) | 1806.82 | 0.638808 | ||||||||
\(201\) | 5368.27 | 1.88382 | ||||||||
\(202\) | 2112.60 | 0.735850 | ||||||||
\(203\) | −413.757 | −0.143054 | ||||||||
\(204\) | −898.003 | −0.308200 | ||||||||
\(205\) | 769.943 | 0.262318 | ||||||||
\(206\) | −2347.37 | −0.793928 | ||||||||
\(207\) | 758.990 | 0.254848 | ||||||||
\(208\) | 77.8297 | 0.0259448 | ||||||||
\(209\) | −512.584 | −0.169647 | ||||||||
\(210\) | 187.291 | 0.0615443 | ||||||||
\(211\) | −236.491 | −0.0771599 | −0.0385800 | − | 0.999256i | \(-0.512283\pi\) | ||||
−0.0385800 | + | 0.999256i | \(0.512283\pi\) | |||||||
\(212\) | −2059.12 | −0.667079 | ||||||||
\(213\) | −4110.04 | −1.32214 | ||||||||
\(214\) | 2016.21 | 0.644044 | ||||||||
\(215\) | 2622.40 | 0.831843 | ||||||||
\(216\) | −2300.86 | −0.724787 | ||||||||
\(217\) | 434.940 | 0.136063 | ||||||||
\(218\) | 1478.58 | 0.459366 | ||||||||
\(219\) | −4154.65 | −1.28194 | ||||||||
\(220\) | 710.673 | 0.217789 | ||||||||
\(221\) | −147.806 | −0.0449888 | ||||||||
\(222\) | 1930.24 | 0.583555 | ||||||||
\(223\) | −1396.42 | −0.419334 | −0.209667 | − | 0.977773i | \(-0.567238\pi\) | ||||
−0.209667 | + | 0.977773i | \(0.567238\pi\) | |||||||
\(224\) | −629.584 | −0.187794 | ||||||||
\(225\) | −730.443 | −0.216428 | ||||||||
\(226\) | 555.874 | 0.163612 | ||||||||
\(227\) | −3034.35 | −0.887211 | −0.443605 | − | 0.896222i | \(-0.646301\pi\) | ||||
−0.443605 | + | 0.896222i | \(0.646301\pi\) | |||||||
\(228\) | 858.915 | 0.249487 | ||||||||
\(229\) | −4938.80 | −1.42517 | −0.712587 | − | 0.701584i | \(-0.752477\pi\) | ||||
−0.712587 | + | 0.701584i | \(0.752477\pi\) | |||||||
\(230\) | 846.551 | 0.242695 | ||||||||
\(231\) | −403.774 | −0.115006 | ||||||||
\(232\) | −2563.81 | −0.725529 | ||||||||
\(233\) | −4759.80 | −1.33831 | −0.669153 | − | 0.743125i | \(-0.733343\pi\) | ||||
−0.669153 | + | 0.743125i | \(0.733343\pi\) | |||||||
\(234\) | 71.2045 | 0.0198922 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4762.20 | −1.31353 | ||||||||
\(237\) | 2676.02 | 0.733443 | ||||||||
\(238\) | 135.128 | 0.0368028 | ||||||||
\(239\) | 3666.84 | 0.992419 | 0.496210 | − | 0.868203i | \(-0.334725\pi\) | ||||
0.496210 | + | 0.868203i | \(0.334725\pi\) | |||||||
\(240\) | −512.823 | −0.137927 | ||||||||
\(241\) | 6119.79 | 1.63573 | 0.817864 | − | 0.575412i | \(-0.195158\pi\) | ||||
0.817864 | + | 0.575412i | \(0.195158\pi\) | |||||||
\(242\) | −1400.75 | −0.372082 | ||||||||
\(243\) | 2280.98 | 0.602160 | ||||||||
\(244\) | 1109.29 | 0.291045 | ||||||||
\(245\) | −2048.26 | −0.534116 | ||||||||
\(246\) | −1126.99 | −0.292090 | ||||||||
\(247\) | 141.373 | 0.0364183 | ||||||||
\(248\) | 2695.07 | 0.690070 | ||||||||
\(249\) | 3233.62 | 0.822982 | ||||||||
\(250\) | −1986.93 | −0.502658 | ||||||||
\(251\) | −4257.22 | −1.07057 | −0.535285 | − | 0.844671i | \(-0.679796\pi\) | ||||
−0.535285 | + | 0.844671i | \(0.679796\pi\) | |||||||
\(252\) | 160.659 | 0.0401611 | ||||||||
\(253\) | −1825.05 | −0.453517 | ||||||||
\(254\) | 1570.93 | 0.388068 | ||||||||
\(255\) | 973.901 | 0.239169 | ||||||||
\(256\) | −3265.45 | −0.797228 | ||||||||
\(257\) | 6251.15 | 1.51726 | 0.758630 | − | 0.651522i | \(-0.225869\pi\) | ||||
0.758630 | + | 0.651522i | \(0.225869\pi\) | |||||||
\(258\) | −3838.49 | −0.926255 | ||||||||
\(259\) | 716.844 | 0.171979 | ||||||||
\(260\) | −196.006 | −0.0467531 | ||||||||
\(261\) | 1036.47 | 0.245809 | ||||||||
\(262\) | −150.247 | −0.0354286 | ||||||||
\(263\) | −5008.06 | −1.17418 | −0.587091 | − | 0.809521i | \(-0.699727\pi\) | ||||
−0.587091 | + | 0.809521i | \(0.699727\pi\) | |||||||
\(264\) | −2501.96 | −0.583276 | ||||||||
\(265\) | 2233.15 | 0.517665 | ||||||||
\(266\) | −129.247 | −0.0297918 | ||||||||
\(267\) | −4317.60 | −0.989635 | ||||||||
\(268\) | 5136.19 | 1.17068 | ||||||||
\(269\) | 4565.07 | 1.03471 | 0.517356 | − | 0.855770i | \(-0.326916\pi\) | ||||
0.517356 | + | 0.855770i | \(0.326916\pi\) | |||||||
\(270\) | 1037.48 | 0.233848 | ||||||||
\(271\) | 3111.82 | 0.697526 | 0.348763 | − | 0.937211i | \(-0.386602\pi\) | ||||
0.348763 | + | 0.937211i | \(0.386602\pi\) | |||||||
\(272\) | −369.996 | −0.0824790 | ||||||||
\(273\) | 111.362 | 0.0246885 | ||||||||
\(274\) | 2441.75 | 0.538364 | ||||||||
\(275\) | 1756.41 | 0.385147 | ||||||||
\(276\) | 3058.16 | 0.666955 | ||||||||
\(277\) | −4349.10 | −0.943364 | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||||
−0.471682 | + | 0.881769i | \(0.656353\pi\) | |||||||
\(278\) | −4823.09 | −1.04054 | ||||||||
\(279\) | −1089.54 | −0.233795 | ||||||||
\(280\) | 430.995 | 0.0919888 | ||||||||
\(281\) | 1640.50 | 0.348271 | 0.174135 | − | 0.984722i | \(-0.444287\pi\) | ||||
0.174135 | + | 0.984722i | \(0.444287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6268.38 | −1.31667 | −0.658333 | − | 0.752727i | \(-0.728738\pi\) | ||||
−0.658333 | + | 0.752727i | \(0.728738\pi\) | |||||||
\(284\) | −3932.36 | −0.821628 | ||||||||
\(285\) | −931.510 | −0.193607 | ||||||||
\(286\) | −171.217 | −0.0353995 | ||||||||
\(287\) | −418.537 | −0.0860817 | ||||||||
\(288\) | 1577.13 | 0.322684 | ||||||||
\(289\) | −4210.34 | −0.856980 | ||||||||
\(290\) | 1156.05 | 0.234087 | ||||||||
\(291\) | 1277.80 | 0.257410 | ||||||||
\(292\) | −3975.04 | −0.796649 | ||||||||
\(293\) | −4720.69 | −0.941248 | −0.470624 | − | 0.882334i | \(-0.655971\pi\) | ||||
−0.470624 | + | 0.882334i | \(0.655971\pi\) | |||||||
\(294\) | 2998.10 | 0.594737 | ||||||||
\(295\) | 5164.69 | 1.01932 | ||||||||
\(296\) | 4441.88 | 0.872226 | ||||||||
\(297\) | −2236.66 | −0.436984 | ||||||||
\(298\) | −1755.52 | −0.341257 | ||||||||
\(299\) | 503.356 | 0.0973573 | ||||||||
\(300\) | −2943.14 | −0.566407 | ||||||||
\(301\) | −1425.52 | −0.272976 | ||||||||
\(302\) | 2948.07 | 0.561729 | ||||||||
\(303\) | −8276.76 | −1.56927 | ||||||||
\(304\) | 353.891 | 0.0667666 | ||||||||
\(305\) | −1203.05 | −0.225856 | ||||||||
\(306\) | −338.500 | −0.0632378 | ||||||||
\(307\) | −9475.50 | −1.76155 | −0.880774 | − | 0.473536i | \(-0.842977\pi\) | ||||
−0.880774 | + | 0.473536i | \(0.842977\pi\) | |||||||
\(308\) | −386.318 | −0.0714692 | ||||||||
\(309\) | 9196.57 | 1.69312 | ||||||||
\(310\) | −1215.23 | −0.222647 | ||||||||
\(311\) | −7724.72 | −1.40845 | −0.704227 | − | 0.709975i | \(-0.748706\pi\) | ||||
−0.704227 | + | 0.709975i | \(0.748706\pi\) | |||||||
\(312\) | 690.050 | 0.125213 | ||||||||
\(313\) | 7719.80 | 1.39409 | 0.697043 | − | 0.717029i | \(-0.254499\pi\) | ||||
0.697043 | + | 0.717029i | \(0.254499\pi\) | |||||||
\(314\) | −1554.91 | −0.279454 | ||||||||
\(315\) | −174.238 | −0.0311657 | ||||||||
\(316\) | 2560.33 | 0.455791 | ||||||||
\(317\) | −10756.5 | −1.90583 | −0.952914 | − | 0.303241i | \(-0.901931\pi\) | ||||
−0.952914 | + | 0.303241i | \(0.901931\pi\) | |||||||
\(318\) | −3268.73 | −0.576420 | ||||||||
\(319\) | −2492.28 | −0.437432 | ||||||||
\(320\) | 1069.61 | 0.186854 | ||||||||
\(321\) | −7899.15 | −1.37348 | ||||||||
\(322\) | −460.181 | −0.0796425 | ||||||||
\(323\) | −672.074 | −0.115775 | ||||||||
\(324\) | 5040.30 | 0.864248 | ||||||||
\(325\) | −484.424 | −0.0826801 | ||||||||
\(326\) | −1106.48 | −0.187983 | ||||||||
\(327\) | −5792.79 | −0.979638 | ||||||||
\(328\) | −2593.43 | −0.436581 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1128.15 | 0.188190 | ||||||||
\(331\) | 3699.02 | 0.614250 | 0.307125 | − | 0.951669i | \(-0.400633\pi\) | ||||
0.307125 | + | 0.951669i | \(0.400633\pi\) | |||||||
\(332\) | 3093.83 | 0.511433 | ||||||||
\(333\) | −1795.72 | −0.295509 | ||||||||
\(334\) | 2421.32 | 0.396672 | ||||||||
\(335\) | −5570.30 | −0.908471 | ||||||||
\(336\) | 278.768 | 0.0452620 | ||||||||
\(337\) | 9917.45 | 1.60308 | 0.801540 | − | 0.597942i | \(-0.204015\pi\) | ||||
0.801540 | + | 0.597942i | \(0.204015\pi\) | |||||||
\(338\) | −3289.62 | −0.529384 | ||||||||
\(339\) | −2177.81 | −0.348916 | ||||||||
\(340\) | 931.798 | 0.148629 | ||||||||
\(341\) | 2619.88 | 0.416053 | ||||||||
\(342\) | 323.766 | 0.0511909 | ||||||||
\(343\) | 2264.65 | 0.356501 | ||||||||
\(344\) | −8833.15 | −1.38445 | ||||||||
\(345\) | −3316.63 | −0.517569 | ||||||||
\(346\) | −1688.83 | −0.262405 | ||||||||
\(347\) | −7738.48 | −1.19719 | −0.598593 | − | 0.801054i | \(-0.704273\pi\) | ||||
−0.598593 | + | 0.801054i | \(0.704273\pi\) | |||||||
\(348\) | 4176.21 | 0.643299 | ||||||||
\(349\) | 8939.40 | 1.37110 | 0.685552 | − | 0.728024i | \(-0.259561\pi\) | ||||
0.685552 | + | 0.728024i | \(0.259561\pi\) | |||||||
\(350\) | 442.873 | 0.0676358 | ||||||||
\(351\) | 616.881 | 0.0938082 | ||||||||
\(352\) | −3792.32 | −0.574237 | ||||||||
\(353\) | 7812.51 | 1.17795 | 0.588977 | − | 0.808150i | \(-0.299531\pi\) | ||||
0.588977 | + | 0.808150i | \(0.299531\pi\) | |||||||
\(354\) | −7559.73 | −1.13501 | ||||||||
\(355\) | 4264.71 | 0.637599 | ||||||||
\(356\) | −4130.94 | −0.614998 | ||||||||
\(357\) | −529.408 | −0.0784852 | ||||||||
\(358\) | −1404.11 | −0.207289 | ||||||||
\(359\) | −4671.36 | −0.686754 | −0.343377 | − | 0.939198i | \(-0.611571\pi\) | ||||
−0.343377 | + | 0.939198i | \(0.611571\pi\) | |||||||
\(360\) | −1079.65 | −0.158063 | ||||||||
\(361\) | −6216.18 | −0.906281 | ||||||||
\(362\) | −2575.85 | −0.373988 | ||||||||
\(363\) | 5487.89 | 0.793498 | ||||||||
\(364\) | 106.548 | 0.0153424 | ||||||||
\(365\) | 4311.00 | 0.618214 | ||||||||
\(366\) | 1760.94 | 0.251491 | ||||||||
\(367\) | 2391.88 | 0.340204 | 0.170102 | − | 0.985426i | \(-0.445590\pi\) | ||||
0.170102 | + | 0.985426i | \(0.445590\pi\) | |||||||
\(368\) | 1260.03 | 0.178487 | ||||||||
\(369\) | 1048.45 | 0.147913 | ||||||||
\(370\) | −2002.88 | −0.281418 | ||||||||
\(371\) | −1213.93 | −0.169876 | ||||||||
\(372\) | −4390.02 | −0.611859 | ||||||||
\(373\) | −13119.4 | −1.82117 | −0.910583 | − | 0.413326i | \(-0.864367\pi\) | ||||
−0.910583 | + | 0.413326i | \(0.864367\pi\) | |||||||
\(374\) | 813.950 | 0.112536 | ||||||||
\(375\) | 7784.43 | 1.07196 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 687.380 | 0.0939042 | ||||||||
\(378\) | −563.968 | −0.0767391 | ||||||||
\(379\) | −8968.11 | −1.21546 | −0.607732 | − | 0.794142i | \(-0.707920\pi\) | ||||
−0.607732 | + | 0.794142i | \(0.707920\pi\) | |||||||
\(380\) | −891.239 | −0.120315 | ||||||||
\(381\) | −6154.63 | −0.827589 | ||||||||
\(382\) | −3015.22 | −0.403853 | ||||||||
\(383\) | −10643.6 | −1.42001 | −0.710005 | − | 0.704197i | \(-0.751307\pi\) | ||||
−0.710005 | + | 0.704197i | \(0.751307\pi\) | |||||||
\(384\) | 7363.82 | 0.978602 | ||||||||
\(385\) | 418.969 | 0.0554614 | ||||||||
\(386\) | −262.541 | −0.0346191 | ||||||||
\(387\) | 3570.98 | 0.469051 | ||||||||
\(388\) | 1222.56 | 0.159964 | ||||||||
\(389\) | 4554.56 | 0.593639 | 0.296819 | − | 0.954934i | \(-0.404074\pi\) | ||||
0.296819 | + | 0.954934i | \(0.404074\pi\) | |||||||
\(390\) | −311.149 | −0.0403991 | ||||||||
\(391\) | −2392.91 | −0.309501 | ||||||||
\(392\) | 6899.24 | 0.888939 | ||||||||
\(393\) | 588.640 | 0.0755546 | ||||||||
\(394\) | 28.8019 | 0.00368278 | ||||||||
\(395\) | −2776.73 | −0.353702 | ||||||||
\(396\) | 967.738 | 0.122805 | ||||||||
\(397\) | −2676.50 | −0.338362 | −0.169181 | − | 0.985585i | \(-0.554112\pi\) | ||||
−0.169181 | + | 0.985585i | \(0.554112\pi\) | |||||||
\(398\) | −3341.71 | −0.420867 | ||||||||
\(399\) | 506.364 | 0.0635336 | ||||||||
\(400\) | −1212.63 | −0.151579 | ||||||||
\(401\) | −2570.96 | −0.320169 | −0.160084 | − | 0.987103i | \(-0.551177\pi\) | ||||
−0.160084 | + | 0.987103i | \(0.551177\pi\) | |||||||
\(402\) | 8153.42 | 1.01158 | ||||||||
\(403\) | −722.572 | −0.0893149 | ||||||||
\(404\) | −7918.94 | −0.975203 | ||||||||
\(405\) | −5466.30 | −0.670673 | ||||||||
\(406\) | −628.420 | −0.0768177 | ||||||||
\(407\) | 4317.94 | 0.525878 | ||||||||
\(408\) | −3280.44 | −0.398054 | ||||||||
\(409\) | 2904.50 | 0.351145 | 0.175572 | − | 0.984467i | \(-0.443822\pi\) | ||||
0.175572 | + | 0.984467i | \(0.443822\pi\) | |||||||
\(410\) | 1169.40 | 0.140860 | ||||||||
\(411\) | −9566.34 | −1.14811 | ||||||||
\(412\) | 8798.99 | 1.05217 | ||||||||
\(413\) | −2807.50 | −0.334499 | ||||||||
\(414\) | 1152.77 | 0.136849 | ||||||||
\(415\) | −3355.31 | −0.396882 | ||||||||
\(416\) | 1045.94 | 0.123272 | ||||||||
\(417\) | 18896.0 | 2.21904 | ||||||||
\(418\) | −778.521 | −0.0910974 | ||||||||
\(419\) | 10586.1 | 1.23428 | 0.617141 | − | 0.786852i | \(-0.288291\pi\) | ||||
0.617141 | + | 0.786852i | \(0.288291\pi\) | |||||||
\(420\) | −702.049 | −0.0815630 | ||||||||
\(421\) | −8155.31 | −0.944098 | −0.472049 | − | 0.881572i | \(-0.656486\pi\) | ||||
−0.472049 | + | 0.881572i | \(0.656486\pi\) | |||||||
\(422\) | −359.187 | −0.0414336 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7522.03 | −0.861561 | ||||||||
\(425\) | 2302.91 | 0.262842 | ||||||||
\(426\) | −6242.40 | −0.709965 | ||||||||
\(427\) | 653.969 | 0.0741166 | ||||||||
\(428\) | −7557.65 | −0.853535 | ||||||||
\(429\) | 670.796 | 0.0754926 | ||||||||
\(430\) | 3982.94 | 0.446685 | ||||||||
\(431\) | 170.047 | 0.0190043 | 0.00950217 | − | 0.999955i | \(-0.496975\pi\) | ||||
0.00950217 | + | 0.999955i | \(0.496975\pi\) | |||||||
\(432\) | 1544.21 | 0.171981 | ||||||||
\(433\) | 8139.98 | 0.903424 | 0.451712 | − | 0.892164i | \(-0.350814\pi\) | ||||
0.451712 | + | 0.892164i | \(0.350814\pi\) | |||||||
\(434\) | 660.594 | 0.0730634 | ||||||||
\(435\) | −4529.17 | −0.499212 | ||||||||
\(436\) | −5542.35 | −0.608786 | ||||||||
\(437\) | 2288.76 | 0.250540 | ||||||||
\(438\) | −6310.15 | −0.688381 | ||||||||
\(439\) | −9489.42 | −1.03168 | −0.515838 | − | 0.856686i | \(-0.672519\pi\) | ||||
−0.515838 | + | 0.856686i | \(0.672519\pi\) | |||||||
\(440\) | 2596.11 | 0.281284 | ||||||||
\(441\) | −2789.15 | −0.301172 | ||||||||
\(442\) | −224.491 | −0.0241582 | ||||||||
\(443\) | 8297.13 | 0.889862 | 0.444931 | − | 0.895565i | \(-0.353228\pi\) | ||||
0.444931 | + | 0.895565i | \(0.353228\pi\) | |||||||
\(444\) | −7235.39 | −0.773370 | ||||||||
\(445\) | 4480.08 | 0.477250 | ||||||||
\(446\) | −2120.91 | −0.225175 | ||||||||
\(447\) | 6877.81 | 0.727761 | ||||||||
\(448\) | −581.437 | −0.0613176 | ||||||||
\(449\) | −3521.42 | −0.370125 | −0.185063 | − | 0.982727i | \(-0.559249\pi\) | ||||
−0.185063 | + | 0.982727i | \(0.559249\pi\) | |||||||
\(450\) | −1109.41 | −0.116218 | ||||||||
\(451\) | −2521.07 | −0.263221 | ||||||||
\(452\) | −2083.66 | −0.216830 | ||||||||
\(453\) | −11550.0 | −1.19794 | ||||||||
\(454\) | −4608.62 | −0.476417 | ||||||||
\(455\) | −115.553 | −0.0119060 | ||||||||
\(456\) | 3137.65 | 0.322223 | ||||||||
\(457\) | −2750.17 | −0.281504 | −0.140752 | − | 0.990045i | \(-0.544952\pi\) | ||||
−0.140752 | + | 0.990045i | \(0.544952\pi\) | |||||||
\(458\) | −7501.13 | −0.765294 | ||||||||
\(459\) | −2932.60 | −0.298218 | ||||||||
\(460\) | −3173.25 | −0.321638 | ||||||||
\(461\) | 4820.72 | 0.487035 | 0.243518 | − | 0.969896i | \(-0.421699\pi\) | ||||
0.243518 | + | 0.969896i | \(0.421699\pi\) | |||||||
\(462\) | −613.258 | −0.0617562 | ||||||||
\(463\) | −12993.3 | −1.30422 | −0.652108 | − | 0.758126i | \(-0.726115\pi\) | ||||
−0.652108 | + | 0.758126i | \(0.726115\pi\) | |||||||
\(464\) | 1720.68 | 0.172157 | ||||||||
\(465\) | 4761.06 | 0.474814 | ||||||||
\(466\) | −7229.27 | −0.718647 | ||||||||
\(467\) | −2516.52 | −0.249359 | −0.124679 | − | 0.992197i | \(-0.539790\pi\) | ||||
−0.124679 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(468\) | −266.906 | −0.0263627 | ||||||||
\(469\) | 3027.99 | 0.298122 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6091.83 | 0.595959 | ||||||||
\(472\) | −17396.5 | −1.69648 | ||||||||
\(473\) | −8586.69 | −0.834707 | ||||||||
\(474\) | 4064.38 | 0.393847 | ||||||||
\(475\) | −2202.67 | −0.212770 | ||||||||
\(476\) | −506.521 | −0.0487738 | ||||||||
\(477\) | 3040.93 | 0.291896 | ||||||||
\(478\) | 5569.26 | 0.532912 | ||||||||
\(479\) | 9282.30 | 0.885426 | 0.442713 | − | 0.896663i | \(-0.354016\pi\) | ||||
0.442713 | + | 0.896663i | \(0.354016\pi\) | |||||||
\(480\) | −6891.72 | −0.655339 | ||||||||
\(481\) | −1190.90 | −0.112891 | ||||||||
\(482\) | 9294.84 | 0.878357 | ||||||||
\(483\) | 1802.90 | 0.169845 | ||||||||
\(484\) | 5250.64 | 0.493111 | ||||||||
\(485\) | −1325.89 | −0.124135 | ||||||||
\(486\) | 3464.39 | 0.323350 | ||||||||
\(487\) | 10070.8 | 0.937063 | 0.468532 | − | 0.883447i | \(-0.344783\pi\) | ||||
0.468532 | + | 0.883447i | \(0.344783\pi\) | |||||||
\(488\) | 4052.28 | 0.375897 | ||||||||
\(489\) | 4335.00 | 0.400890 | ||||||||
\(490\) | −3110.93 | −0.286811 | ||||||||
\(491\) | −8493.09 | −0.780627 | −0.390313 | − | 0.920682i | \(-0.627633\pi\) | ||||
−0.390313 | + | 0.920682i | \(0.627633\pi\) | |||||||
\(492\) | 4224.45 | 0.387100 | ||||||||
\(493\) | −3267.75 | −0.298523 | ||||||||
\(494\) | 214.719 | 0.0195560 | ||||||||
\(495\) | −1049.53 | −0.0952987 | ||||||||
\(496\) | −1808.78 | −0.163743 | ||||||||
\(497\) | −2318.28 | −0.209233 | ||||||||
\(498\) | 4911.28 | 0.441927 | ||||||||
\(499\) | 11520.7 | 1.03354 | 0.516769 | − | 0.856125i | \(-0.327134\pi\) | ||||
0.516769 | + | 0.856125i | \(0.327134\pi\) | |||||||
\(500\) | 7447.89 | 0.666160 | ||||||||
\(501\) | −9486.27 | −0.845939 | ||||||||
\(502\) | −6465.93 | −0.574878 | ||||||||
\(503\) | −15802.2 | −1.40077 | −0.700385 | − | 0.713766i | \(-0.746988\pi\) | ||||
−0.700385 | + | 0.713766i | \(0.746988\pi\) | |||||||
\(504\) | 586.895 | 0.0518698 | ||||||||
\(505\) | 8588.25 | 0.756776 | ||||||||
\(506\) | −2771.92 | −0.243531 | ||||||||
\(507\) | 12888.1 | 1.12896 | ||||||||
\(508\) | −5888.56 | −0.514296 | ||||||||
\(509\) | 18133.1 | 1.57905 | 0.789525 | − | 0.613718i | \(-0.210327\pi\) | ||||
0.789525 | + | 0.613718i | \(0.210327\pi\) | |||||||
\(510\) | 1479.18 | 0.128430 | ||||||||
\(511\) | −2343.44 | −0.202872 | ||||||||
\(512\) | 4940.58 | 0.426454 | ||||||||
\(513\) | 2804.95 | 0.241407 | ||||||||
\(514\) | 9494.35 | 0.814742 | ||||||||
\(515\) | −9542.67 | −0.816506 | ||||||||
\(516\) | 14388.3 | 1.22754 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1088.75 | 0.0923497 | ||||||||
\(519\) | 6616.52 | 0.559601 | ||||||||
\(520\) | −716.019 | −0.0603836 | ||||||||
\(521\) | 1617.14 | 0.135985 | 0.0679926 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679926 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(522\) | 1574.21 | 0.131995 | ||||||||
\(523\) | 7545.61 | 0.630873 | 0.315436 | − | 0.948947i | \(-0.397849\pi\) | ||||
0.315436 | + | 0.948947i | \(0.397849\pi\) | |||||||
\(524\) | 563.192 | 0.0469526 | ||||||||
\(525\) | −1735.09 | −0.144239 | ||||||||
\(526\) | −7606.32 | −0.630516 | ||||||||
\(527\) | 3435.05 | 0.283934 | ||||||||
\(528\) | 1679.17 | 0.138402 | ||||||||
\(529\) | −4017.91 | −0.330230 | ||||||||
\(530\) | 3391.75 | 0.277977 | ||||||||
\(531\) | 7032.87 | 0.574766 | ||||||||
\(532\) | 484.473 | 0.0394823 | ||||||||
\(533\) | 695.322 | 0.0565061 | ||||||||
\(534\) | −6557.64 | −0.531417 | ||||||||
\(535\) | 8196.42 | 0.662359 | ||||||||
\(536\) | 18762.7 | 1.51199 | ||||||||
\(537\) | 5501.05 | 0.442063 | ||||||||
\(538\) | 6933.51 | 0.555622 | ||||||||
\(539\) | 6706.74 | 0.535955 | ||||||||
\(540\) | −3888.93 | −0.309913 | ||||||||
\(541\) | 12142.0 | 0.964923 | 0.482461 | − | 0.875917i | \(-0.339743\pi\) | ||||
0.482461 | + | 0.875917i | \(0.339743\pi\) | |||||||
\(542\) | 4726.28 | 0.374560 | ||||||||
\(543\) | 10091.7 | 0.797562 | ||||||||
\(544\) | −4972.30 | −0.391885 | ||||||||
\(545\) | 6010.79 | 0.472429 | ||||||||
\(546\) | 169.139 | 0.0132573 | ||||||||
\(547\) | −17852.1 | −1.39543 | −0.697715 | − | 0.716375i | \(-0.745800\pi\) | ||||
−0.697715 | + | 0.716375i | \(0.745800\pi\) | |||||||
\(548\) | −9152.77 | −0.713480 | ||||||||
\(549\) | −1638.21 | −0.127354 | ||||||||
\(550\) | 2667.66 | 0.206817 | ||||||||
\(551\) | 3125.51 | 0.241654 | ||||||||
\(552\) | 11171.6 | 0.861401 | ||||||||
\(553\) | 1509.41 | 0.116070 | ||||||||
\(554\) | −6605.48 | −0.506570 | ||||||||
\(555\) | 7846.91 | 0.600149 | ||||||||
\(556\) | 18079.1 | 1.37900 | ||||||||
\(557\) | −10350.7 | −0.787388 | −0.393694 | − | 0.919242i | \(-0.628803\pi\) | ||||
−0.393694 | + | 0.919242i | \(0.628803\pi\) | |||||||
\(558\) | −1654.81 | −0.125544 | ||||||||
\(559\) | 2368.24 | 0.179188 | ||||||||
\(560\) | −289.259 | −0.0218275 | ||||||||
\(561\) | −3188.91 | −0.239992 | ||||||||
\(562\) | 2491.62 | 0.187015 | ||||||||
\(563\) | 12353.6 | 0.924761 | 0.462380 | − | 0.886682i | \(-0.346995\pi\) | ||||
0.462380 | + | 0.886682i | \(0.346995\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2259.77 | 0.168264 | ||||||||
\(566\) | −9520.52 | −0.707027 | ||||||||
\(567\) | 2971.45 | 0.220087 | ||||||||
\(568\) | −14365.0 | −1.06117 | ||||||||
\(569\) | 24894.7 | 1.83416 | 0.917081 | − | 0.398700i | \(-0.130539\pi\) | ||||
0.917081 | + | 0.398700i | \(0.130539\pi\) | |||||||
\(570\) | −1414.79 | −0.103963 | ||||||||
\(571\) | 10062.0 | 0.737442 | 0.368721 | − | 0.929540i | \(-0.379796\pi\) | ||||
0.368721 | + | 0.929540i | \(0.379796\pi\) | |||||||
\(572\) | 641.796 | 0.0469141 | ||||||||
\(573\) | 11813.1 | 0.861253 | ||||||||
\(574\) | −635.681 | −0.0462244 | ||||||||
\(575\) | −7842.59 | −0.568798 | ||||||||
\(576\) | 1456.52 | 0.105361 | ||||||||
\(577\) | −4187.40 | −0.302121 | −0.151060 | − | 0.988525i | \(-0.548269\pi\) | ||||
−0.151060 | + | 0.988525i | \(0.548269\pi\) | |||||||
\(578\) | −6394.74 | −0.460183 | ||||||||
\(579\) | 1028.59 | 0.0738283 | ||||||||
\(580\) | −4333.37 | −0.310230 | ||||||||
\(581\) | 1823.93 | 0.130240 | ||||||||
\(582\) | 1940.75 | 0.138224 | ||||||||
\(583\) | −7312.14 | −0.519448 | ||||||||
\(584\) | −14521.0 | −1.02891 | ||||||||
\(585\) | 289.465 | 0.0204579 | ||||||||
\(586\) | −7169.86 | −0.505434 | ||||||||
\(587\) | 4333.47 | 0.304704 | 0.152352 | − | 0.988326i | \(-0.451315\pi\) | ||||
0.152352 | + | 0.988326i | \(0.451315\pi\) | |||||||
\(588\) | −11238.2 | −0.788189 | ||||||||
\(589\) | −3285.53 | −0.229844 | ||||||||
\(590\) | 7844.22 | 0.547359 | ||||||||
\(591\) | −112.840 | −0.00785386 | ||||||||
\(592\) | −2981.13 | −0.206966 | ||||||||
\(593\) | 6152.44 | 0.426055 | 0.213027 | − | 0.977046i | \(-0.431668\pi\) | ||||
0.213027 | + | 0.977046i | \(0.431668\pi\) | |||||||
\(594\) | −3397.08 | −0.234653 | ||||||||
\(595\) | 549.331 | 0.0378494 | ||||||||
\(596\) | 6580.47 | 0.452259 | ||||||||
\(597\) | 13092.2 | 0.897536 | ||||||||
\(598\) | 764.506 | 0.0522792 | ||||||||
\(599\) | 7257.67 | 0.495059 | 0.247529 | − | 0.968880i | \(-0.420381\pi\) | ||||
0.247529 | + | 0.968880i | \(0.420381\pi\) | |||||||
\(600\) | −10751.4 | −0.731539 | ||||||||
\(601\) | −15872.7 | −1.07731 | −0.538654 | − | 0.842527i | \(-0.681067\pi\) | ||||
−0.538654 | + | 0.842527i | \(0.681067\pi\) | |||||||
\(602\) | −2165.11 | −0.146583 | ||||||||
\(603\) | −7585.19 | −0.512260 | ||||||||
\(604\) | −11050.7 | −0.744445 | ||||||||
\(605\) | −5694.42 | −0.382663 | ||||||||
\(606\) | −12570.9 | −0.842669 | ||||||||
\(607\) | 15068.0 | 1.00757 | 0.503783 | − | 0.863830i | \(-0.331941\pi\) | ||||
0.503783 | + | 0.863830i | \(0.331941\pi\) | |||||||
\(608\) | 4755.87 | 0.317230 | ||||||||
\(609\) | 2462.04 | 0.163821 | ||||||||
\(610\) | −1827.21 | −0.121281 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1268.85 | 0.0838075 | ||||||||
\(613\) | 12024.1 | 0.792252 | 0.396126 | − | 0.918196i | \(-0.370354\pi\) | ||||
0.396126 | + | 0.918196i | \(0.370354\pi\) | |||||||
\(614\) | −14391.6 | −0.945921 | ||||||||
\(615\) | −4581.50 | −0.300397 | ||||||||
\(616\) | −1411.23 | −0.0923056 | ||||||||
\(617\) | 4814.15 | 0.314117 | 0.157059 | − | 0.987589i | \(-0.449799\pi\) | ||||
0.157059 | + | 0.987589i | \(0.449799\pi\) | |||||||
\(618\) | 13967.9 | 0.909178 | ||||||||
\(619\) | −9575.51 | −0.621764 | −0.310882 | − | 0.950448i | \(-0.600624\pi\) | ||||
−0.310882 | + | 0.950448i | \(0.600624\pi\) | |||||||
\(620\) | 4555.23 | 0.295068 | ||||||||
\(621\) | 9987.00 | 0.645354 | ||||||||
\(622\) | −11732.4 | −0.756315 | ||||||||
\(623\) | −2435.35 | −0.156613 | ||||||||
\(624\) | −463.121 | −0.0297110 | ||||||||
\(625\) | 2782.25 | 0.178064 | ||||||||
\(626\) | 11725.0 | 0.748600 | ||||||||
\(627\) | 3050.10 | 0.194273 | ||||||||
\(628\) | 5828.47 | 0.370353 | ||||||||
\(629\) | 5661.46 | 0.358883 | ||||||||
\(630\) | −264.636 | −0.0167355 | ||||||||
\(631\) | −21583.8 | −1.36171 | −0.680855 | − | 0.732418i | \(-0.738392\pi\) | ||||
−0.680855 | + | 0.732418i | \(0.738392\pi\) | |||||||
\(632\) | 9352.98 | 0.588673 | ||||||||
\(633\) | 1407.23 | 0.0883607 | ||||||||
\(634\) | −16337.2 | −1.02340 | ||||||||
\(635\) | 6386.25 | 0.399103 | ||||||||
\(636\) | 12252.7 | 0.763914 | ||||||||
\(637\) | −1849.75 | −0.115054 | ||||||||
\(638\) | −3785.31 | −0.234893 | ||||||||
\(639\) | 5807.35 | 0.359523 | ||||||||
\(640\) | −7640.94 | −0.471929 | ||||||||
\(641\) | 11164.6 | 0.687951 | 0.343975 | − | 0.938979i | \(-0.388226\pi\) | ||||
0.343975 | + | 0.938979i | \(0.388226\pi\) | |||||||
\(642\) | −11997.4 | −0.737536 | ||||||||
\(643\) | 8679.03 | 0.532298 | 0.266149 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266149 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(644\) | 1724.96 | 0.105548 | ||||||||
\(645\) | −15604.4 | −0.952596 | ||||||||
\(646\) | −1020.76 | −0.0621690 | ||||||||
\(647\) | 9386.78 | 0.570374 | 0.285187 | − | 0.958472i | \(-0.407944\pi\) | ||||
0.285187 | + | 0.958472i | \(0.407944\pi\) | |||||||
\(648\) | 18412.4 | 1.11621 | ||||||||
\(649\) | −16911.1 | −1.02283 | ||||||||
\(650\) | −735.752 | −0.0443978 | ||||||||
\(651\) | −2588.08 | −0.155814 | ||||||||
\(652\) | 4147.59 | 0.249129 | ||||||||
\(653\) | 25776.8 | 1.54475 | 0.772376 | − | 0.635166i | \(-0.219068\pi\) | ||||
0.772376 | + | 0.635166i | \(0.219068\pi\) | |||||||
\(654\) | −8798.18 | −0.526049 | ||||||||
\(655\) | −610.792 | −0.0364361 | ||||||||
\(656\) | 1740.56 | 0.103594 | ||||||||
\(657\) | 5870.38 | 0.348593 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −176.671 | −0.0104433 | −0.00522164 | − | 0.999986i | \(-0.501662\pi\) | ||||
−0.00522164 | + | 0.999986i | \(0.501662\pi\) | |||||||
\(660\) | −4228.82 | −0.249404 | ||||||||
\(661\) | 443.366 | 0.0260892 | 0.0130446 | − | 0.999915i | \(-0.495848\pi\) | ||||
0.0130446 | + | 0.999915i | \(0.495848\pi\) | |||||||
\(662\) | 5618.14 | 0.329842 | ||||||||
\(663\) | 879.514 | 0.0515196 | ||||||||
\(664\) | 11301.9 | 0.660538 | ||||||||
\(665\) | −525.420 | −0.0306390 | ||||||||
\(666\) | −2727.36 | −0.158683 | ||||||||
\(667\) | 11128.4 | 0.646014 | ||||||||
\(668\) | −9076.16 | −0.525700 | ||||||||
\(669\) | 8309.34 | 0.480206 | ||||||||
\(670\) | −8460.26 | −0.487833 | ||||||||
\(671\) | 3939.21 | 0.226634 | ||||||||
\(672\) | 3746.30 | 0.215055 | ||||||||
\(673\) | 33702.8 | 1.93038 | 0.965192 | − | 0.261544i | \(-0.0842316\pi\) | ||||
0.965192 | + | 0.261544i | \(0.0842316\pi\) | |||||||
\(674\) | 15062.8 | 0.860826 | ||||||||
\(675\) | −9611.38 | −0.548062 | ||||||||
\(676\) | 12330.9 | 0.701578 | ||||||||
\(677\) | −7298.49 | −0.414334 | −0.207167 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207167 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(678\) | −3307.70 | −0.187362 | ||||||||
\(679\) | 720.748 | 0.0407360 | ||||||||
\(680\) | 3403.89 | 0.191961 | ||||||||
\(681\) | 18055.7 | 1.01600 | ||||||||
\(682\) | 3979.11 | 0.223414 | ||||||||
\(683\) | 27754.4 | 1.55490 | 0.777448 | − | 0.628948i | \(-0.216514\pi\) | ||||
0.777448 | + | 0.628948i | \(0.216514\pi\) | |||||||
\(684\) | −1213.62 | −0.0678419 | ||||||||
\(685\) | 9926.35 | 0.553674 | ||||||||
\(686\) | 3439.59 | 0.191435 | ||||||||
\(687\) | 29388.0 | 1.63206 | ||||||||
\(688\) | 5928.30 | 0.328509 | ||||||||
\(689\) | 2016.72 | 0.111511 | ||||||||
\(690\) | −5037.36 | −0.277926 | ||||||||
\(691\) | −19119.2 | −1.05257 | −0.526287 | − | 0.850307i | \(-0.676416\pi\) | ||||
−0.526287 | + | 0.850307i | \(0.676416\pi\) | |||||||
\(692\) | 6330.48 | 0.347758 | ||||||||
\(693\) | 570.519 | 0.0312731 | ||||||||
\(694\) | −11753.3 | −0.642868 | ||||||||
\(695\) | −19607.1 | −1.07013 | ||||||||
\(696\) | 15255.8 | 0.830849 | ||||||||
\(697\) | −3305.50 | −0.179634 | ||||||||
\(698\) | 13577.3 | 0.736259 | ||||||||
\(699\) | 28322.9 | 1.53258 | ||||||||
\(700\) | −1660.08 | −0.0896360 | ||||||||
\(701\) | 29188.2 | 1.57264 | 0.786322 | − | 0.617817i | \(-0.211983\pi\) | ||||
0.786322 | + | 0.617817i | \(0.211983\pi\) | |||||||
\(702\) | 936.929 | 0.0503734 | ||||||||
\(703\) | −5415.03 | −0.290515 | ||||||||
\(704\) | −3502.30 | −0.187497 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11865.8 | 0.632541 | ||||||||
\(707\) | −4668.53 | −0.248342 | ||||||||
\(708\) | 28337.2 | 1.50420 | ||||||||
\(709\) | −11377.0 | −0.602639 | −0.301320 | − | 0.953523i | \(-0.597427\pi\) | ||||
−0.301320 | + | 0.953523i | \(0.597427\pi\) | |||||||
\(710\) | 6477.32 | 0.342380 | ||||||||
\(711\) | −3781.13 | −0.199442 | ||||||||
\(712\) | −15090.5 | −0.794297 | ||||||||
\(713\) | −11698.1 | −0.614442 | ||||||||
\(714\) | −804.073 | −0.0421452 | ||||||||
\(715\) | −696.040 | −0.0364062 | ||||||||
\(716\) | 5263.23 | 0.274715 | ||||||||
\(717\) | −21819.3 | −1.13648 | ||||||||
\(718\) | −7094.93 | −0.368775 | ||||||||
\(719\) | −8170.53 | −0.423796 | −0.211898 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211898 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(720\) | 724.602 | 0.0375060 | ||||||||
\(721\) | 5187.35 | 0.267943 | ||||||||
\(722\) | −9441.24 | −0.486657 | ||||||||
\(723\) | −36415.5 | −1.87318 | ||||||||
\(724\) | 9655.42 | 0.495637 | ||||||||
\(725\) | −10709.8 | −0.548623 | ||||||||
\(726\) | 8335.11 | 0.426095 | ||||||||
\(727\) | −19612.6 | −1.00054 | −0.500270 | − | 0.865870i | \(-0.666766\pi\) | ||||
−0.500270 | + | 0.865870i | \(0.666766\pi\) | |||||||
\(728\) | 389.224 | 0.0198154 | ||||||||
\(729\) | 10330.8 | 0.524858 | ||||||||
\(730\) | 6547.63 | 0.331971 | ||||||||
\(731\) | −11258.4 | −0.569642 | ||||||||
\(732\) | −6600.77 | −0.333294 | ||||||||
\(733\) | −16619.4 | −0.837451 | −0.418725 | − | 0.908113i | \(-0.637523\pi\) | ||||
−0.418725 | + | 0.908113i | \(0.637523\pi\) | |||||||
\(734\) | 3632.82 | 0.182684 | ||||||||
\(735\) | 12188.0 | 0.611650 | ||||||||
\(736\) | 16933.2 | 0.848053 | ||||||||
\(737\) | 18239.2 | 0.911599 | ||||||||
\(738\) | 1592.40 | 0.0794268 | ||||||||
\(739\) | −19520.6 | −0.971686 | −0.485843 | − | 0.874046i | \(-0.661487\pi\) | ||||
−0.485843 | + | 0.874046i | \(0.661487\pi\) | |||||||
\(740\) | 7507.68 | 0.372956 | ||||||||
\(741\) | −841.231 | −0.0417050 | ||||||||
\(742\) | −1843.74 | −0.0912206 | ||||||||
\(743\) | −162.092 | −0.00800345 | −0.00400172 | − | 0.999992i | \(-0.501274\pi\) | ||||
−0.00400172 | + | 0.999992i | \(0.501274\pi\) | |||||||
\(744\) | −16036.9 | −0.790243 | ||||||||
\(745\) | −7136.65 | −0.350962 | ||||||||
\(746\) | −19925.9 | −0.977935 | ||||||||
\(747\) | −4569.00 | −0.223790 | ||||||||
\(748\) | −3051.04 | −0.149141 | ||||||||
\(749\) | −4455.53 | −0.217359 | ||||||||
\(750\) | 11823.1 | 0.575625 | ||||||||
\(751\) | −30012.2 | −1.45827 | −0.729135 | − | 0.684370i | \(-0.760077\pi\) | ||||
−0.729135 | + | 0.684370i | \(0.760077\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25332.3 | 1.22598 | ||||||||
\(754\) | 1044.00 | 0.0504250 | ||||||||
\(755\) | 11984.7 | 0.577704 | ||||||||
\(756\) | 2114.00 | 0.101700 | ||||||||
\(757\) | 25232.6 | 1.21148 | 0.605742 | − | 0.795661i | \(-0.292876\pi\) | ||||
0.605742 | + | 0.795661i | \(0.292876\pi\) | |||||||
\(758\) | −13620.9 | −0.652683 | ||||||||
\(759\) | 10859.9 | 0.519351 | ||||||||
\(760\) | −3255.73 | −0.155392 | ||||||||
\(761\) | −26393.1 | −1.25723 | −0.628613 | − | 0.777719i | \(-0.716377\pi\) | ||||
−0.628613 | + | 0.777719i | \(0.716377\pi\) | |||||||
\(762\) | −9347.76 | −0.444401 | ||||||||
\(763\) | −3267.43 | −0.155031 | ||||||||
\(764\) | 11302.4 | 0.535217 | ||||||||
\(765\) | −1376.09 | −0.0650362 | ||||||||
\(766\) | −16165.7 | −0.762521 | ||||||||
\(767\) | 4664.15 | 0.219573 | ||||||||
\(768\) | 19430.9 | 0.912956 | ||||||||
\(769\) | −12734.0 | −0.597140 | −0.298570 | − | 0.954388i | \(-0.596510\pi\) | ||||
−0.298570 | + | 0.954388i | \(0.596510\pi\) | |||||||
\(770\) | 636.337 | 0.0297818 | ||||||||
\(771\) | −37197.1 | −1.73751 | ||||||||
\(772\) | 984.118 | 0.0458798 | ||||||||
\(773\) | 29097.4 | 1.35389 | 0.676947 | − | 0.736032i | \(-0.263303\pi\) | ||||
0.676947 | + | 0.736032i | \(0.263303\pi\) | |||||||
\(774\) | 5423.66 | 0.251873 | ||||||||
\(775\) | 11258.1 | 0.521811 | ||||||||
\(776\) | 4466.06 | 0.206601 | ||||||||
\(777\) | −4265.54 | −0.196944 | ||||||||
\(778\) | 6917.55 | 0.318774 | ||||||||
\(779\) | 3161.62 | 0.145413 | ||||||||
\(780\) | 1166.33 | 0.0535399 | ||||||||
\(781\) | −13964.2 | −0.639794 | ||||||||
\(782\) | −3634.40 | −0.166197 | ||||||||
\(783\) | 13638.2 | 0.622464 | ||||||||
\(784\) | −4630.37 | −0.210932 | ||||||||
\(785\) | −6321.09 | −0.287401 | ||||||||
\(786\) | 894.036 | 0.0405715 | ||||||||
\(787\) | 4595.00 | 0.208124 | 0.104062 | − | 0.994571i | \(-0.466816\pi\) | ||||
0.104062 | + | 0.994571i | \(0.466816\pi\) | |||||||
\(788\) | −107.962 | −0.00488070 | ||||||||
\(789\) | 29800.2 | 1.34463 | ||||||||
\(790\) | −4217.34 | −0.189932 | ||||||||
\(791\) | −1228.40 | −0.0552173 | ||||||||
\(792\) | 3535.18 | 0.158608 | ||||||||
\(793\) | −1086.45 | −0.0486519 | ||||||||
\(794\) | −4065.12 | −0.181695 | ||||||||
\(795\) | −13288.2 | −0.592811 | ||||||||
\(796\) | 12526.2 | 0.557764 | ||||||||
\(797\) | 29030.2 | 1.29021 | 0.645107 | − | 0.764092i | \(-0.276813\pi\) | ||||
0.645107 | + | 0.764092i | \(0.276813\pi\) | |||||||
\(798\) | 769.074 | 0.0341164 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −16296.3 | −0.720203 | ||||||||
\(801\) | 6100.62 | 0.269107 | ||||||||
\(802\) | −3904.82 | −0.171925 | ||||||||
\(803\) | −14115.8 | −0.620343 | ||||||||
\(804\) | −30562.6 | −1.34062 | ||||||||
\(805\) | −1870.75 | −0.0819073 | ||||||||
\(806\) | −1097.46 | −0.0479606 | ||||||||
\(807\) | −27164.2 | −1.18491 | ||||||||
\(808\) | −28928.2 | −1.25952 | ||||||||
\(809\) | 25943.4 | 1.12747 | 0.563734 | − | 0.825957i | \(-0.309364\pi\) | ||||
0.563734 | + | 0.825957i | \(0.309364\pi\) | |||||||
\(810\) | −8302.30 | −0.360140 | ||||||||
\(811\) | 18828.1 | 0.815222 | 0.407611 | − | 0.913156i | \(-0.366362\pi\) | ||||
0.407611 | + | 0.913156i | \(0.366362\pi\) | |||||||
\(812\) | 2355.60 | 0.101805 | ||||||||
\(813\) | −18516.7 | −0.798782 | ||||||||
\(814\) | 6558.15 | 0.282387 | ||||||||
\(815\) | −4498.14 | −0.193329 | ||||||||
\(816\) | 2201.64 | 0.0944520 | ||||||||
\(817\) | 10768.4 | 0.461124 | ||||||||
\(818\) | 4411.40 | 0.188559 | ||||||||
\(819\) | −157.351 | −0.00671344 | ||||||||
\(820\) | −4383.43 | −0.186678 | ||||||||
\(821\) | −23631.4 | −1.00456 | −0.502278 | − | 0.864706i | \(-0.667505\pi\) | ||||
−0.502278 | + | 0.864706i | \(0.667505\pi\) | |||||||
\(822\) | −14529.5 | −0.616515 | ||||||||
\(823\) | −37638.6 | −1.59417 | −0.797084 | − | 0.603868i | \(-0.793625\pi\) | ||||
−0.797084 | + | 0.603868i | \(0.793625\pi\) | |||||||
\(824\) | 32143.0 | 1.35893 | ||||||||
\(825\) | −10451.4 | −0.441056 | ||||||||
\(826\) | −4264.08 | −0.179620 | ||||||||
\(827\) | 3452.86 | 0.145185 | 0.0725924 | − | 0.997362i | \(-0.476873\pi\) | ||||
0.0725924 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(828\) | −4321.08 | −0.181362 | ||||||||
\(829\) | 2949.59 | 0.123575 | 0.0617875 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617875 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(830\) | −5096.11 | −0.213119 | ||||||||
\(831\) | 25879.1 | 1.08031 | ||||||||
\(832\) | 965.950 | 0.0402503 | ||||||||
\(833\) | 8793.53 | 0.365760 | ||||||||
\(834\) | 28699.5 | 1.19159 | ||||||||
\(835\) | 9843.27 | 0.407953 | ||||||||
\(836\) | 2918.24 | 0.120729 | ||||||||
\(837\) | −14336.4 | −0.592043 | ||||||||
\(838\) | 16078.3 | 0.662789 | ||||||||
\(839\) | 21099.3 | 0.868212 | 0.434106 | − | 0.900862i | \(-0.357064\pi\) | ||||
0.434106 | + | 0.900862i | \(0.357064\pi\) | |||||||
\(840\) | −2564.61 | −0.105342 | ||||||||
\(841\) | −9192.18 | −0.376899 | ||||||||
\(842\) | −12386.4 | −0.506965 | ||||||||
\(843\) | −9761.70 | −0.398827 | ||||||||
\(844\) | 1346.39 | 0.0549108 | ||||||||
\(845\) | −13373.1 | −0.544438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3095.46 | 0.125574 | ||||||||
\(848\) | 5048.35 | 0.204435 | ||||||||
\(849\) | 37299.7 | 1.50780 | ||||||||
\(850\) | 3497.70 | 0.141141 | ||||||||
\(851\) | −19280.2 | −0.776634 | ||||||||
\(852\) | 23399.3 | 0.940898 | ||||||||
\(853\) | −5832.07 | −0.234099 | −0.117049 | − | 0.993126i | \(-0.537344\pi\) | ||||
−0.117049 | + | 0.993126i | \(0.537344\pi\) | |||||||
\(854\) | 993.260 | 0.0397994 | ||||||||
\(855\) | 1316.19 | 0.0526466 | ||||||||
\(856\) | −27608.4 | −1.10238 | ||||||||
\(857\) | 3182.86 | 0.126866 | 0.0634331 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634331 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(858\) | 1018.82 | 0.0405382 | ||||||||
\(859\) | −34773.9 | −1.38122 | −0.690610 | − | 0.723227i | \(-0.742658\pi\) | ||||
−0.690610 | + | 0.723227i | \(0.742658\pi\) | |||||||
\(860\) | −14929.8 | −0.591980 | ||||||||
\(861\) | 2490.48 | 0.0985776 | ||||||||
\(862\) | 258.270 | 0.0102050 | ||||||||
\(863\) | −13655.6 | −0.538636 | −0.269318 | − | 0.963051i | \(-0.586798\pi\) | ||||
−0.269318 | + | 0.963051i | \(0.586798\pi\) | |||||||
\(864\) | 20752.3 | 0.817137 | ||||||||
\(865\) | −6865.52 | −0.269867 | ||||||||
\(866\) | 12363.1 | 0.485123 | ||||||||
\(867\) | 25053.4 | 0.981382 | ||||||||
\(868\) | −2476.20 | −0.0968290 | ||||||||
\(869\) | 9092.01 | 0.354920 | ||||||||
\(870\) | −6878.98 | −0.268068 | ||||||||
\(871\) | −5030.44 | −0.195695 | ||||||||
\(872\) | −20246.4 | −0.786273 | ||||||||
\(873\) | −1805.49 | −0.0699962 | ||||||||
\(874\) | 3476.20 | 0.134536 | ||||||||
\(875\) | 4390.82 | 0.169642 | ||||||||
\(876\) | 23653.2 | 0.912293 | ||||||||
\(877\) | 43458.4 | 1.67330 | 0.836651 | − | 0.547736i | \(-0.184510\pi\) | ||||
0.836651 | + | 0.547736i | \(0.184510\pi\) | |||||||
\(878\) | −14412.7 | −0.553992 | ||||||||
\(879\) | 28090.2 | 1.07788 | ||||||||
\(880\) | −1742.36 | −0.0667443 | ||||||||
\(881\) | −26874.5 | −1.02772 | −0.513862 | − | 0.857873i | \(-0.671786\pi\) | ||||
−0.513862 | + | 0.857873i | \(0.671786\pi\) | |||||||
\(882\) | −4236.21 | −0.161724 | ||||||||
\(883\) | −9065.53 | −0.345503 | −0.172752 | − | 0.984965i | \(-0.555266\pi\) | ||||
−0.172752 | + | 0.984965i | \(0.555266\pi\) | |||||||
\(884\) | 841.491 | 0.0320163 | ||||||||
\(885\) | −30732.2 | −1.16729 | ||||||||
\(886\) | 12601.8 | 0.477840 | ||||||||
\(887\) | −42928.3 | −1.62502 | −0.812510 | − | 0.582947i | \(-0.801899\pi\) | ||||
−0.812510 | + | 0.582947i | \(0.801899\pi\) | |||||||
\(888\) | −26431.1 | −0.998841 | ||||||||
\(889\) | −3471.53 | −0.130969 | ||||||||
\(890\) | 6804.42 | 0.256275 | ||||||||
\(891\) | 17898.6 | 0.672982 | ||||||||
\(892\) | 7950.11 | 0.298419 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 10446.1 | 0.390795 | ||||||||
\(895\) | −5708.07 | −0.213184 | ||||||||
\(896\) | 4153.58 | 0.154867 | ||||||||
\(897\) | −2995.19 | −0.111490 | ||||||||
\(898\) | −5348.39 | −0.198751 | ||||||||
\(899\) | −15974.9 | −0.592649 | ||||||||
\(900\) | 4158.56 | 0.154021 | ||||||||
\(901\) | −9587.32 | −0.354495 | ||||||||
\(902\) | −3829.05 | −0.141345 | ||||||||
\(903\) | 8482.49 | 0.312602 | ||||||||
\(904\) | −7611.70 | −0.280046 | ||||||||
\(905\) | −10471.5 | −0.384623 | ||||||||
\(906\) | −17542.3 | −0.643272 | ||||||||
\(907\) | −13748.8 | −0.503330 | −0.251665 | − | 0.967814i | \(-0.580978\pi\) | ||||
−0.251665 | + | 0.967814i | \(0.580978\pi\) | |||||||
\(908\) | 17275.1 | 0.631383 | ||||||||
\(909\) | 11694.8 | 0.426724 | ||||||||
\(910\) | −175.504 | −0.00639331 | ||||||||
\(911\) | −15009.6 | −0.545874 | −0.272937 | − | 0.962032i | \(-0.587995\pi\) | ||||
−0.272937 | + | 0.962032i | \(0.587995\pi\) | |||||||
\(912\) | −2105.81 | −0.0764586 | ||||||||
\(913\) | 10986.5 | 0.398248 | ||||||||
\(914\) | −4177.00 | −0.151163 | ||||||||
\(915\) | 7158.66 | 0.258643 | ||||||||
\(916\) | 28117.5 | 1.01422 | ||||||||
\(917\) | 332.023 | 0.0119568 | ||||||||
\(918\) | −4454.08 | −0.160138 | ||||||||
\(919\) | −40518.6 | −1.45439 | −0.727195 | − | 0.686431i | \(-0.759177\pi\) | ||||
−0.727195 | + | 0.686431i | \(0.759177\pi\) | |||||||
\(920\) | −11592.0 | −0.415409 | ||||||||
\(921\) | 56383.4 | 2.01726 | ||||||||
\(922\) | 7321.79 | 0.261530 | ||||||||
\(923\) | 3851.39 | 0.137346 | ||||||||
\(924\) | 2298.76 | 0.0818439 | ||||||||
\(925\) | 18555.0 | 0.659551 | ||||||||
\(926\) | −19734.5 | −0.700341 | ||||||||
\(927\) | −12994.5 | −0.460403 | ||||||||
\(928\) | 23123.9 | 0.817974 | ||||||||
\(929\) | 14399.3 | 0.508531 | 0.254265 | − | 0.967135i | \(-0.418166\pi\) | ||||
0.254265 | + | 0.967135i | \(0.418166\pi\) | |||||||
\(930\) | 7231.17 | 0.254967 | ||||||||
\(931\) | −8410.77 | −0.296082 | ||||||||
\(932\) | 27098.5 | 0.952404 | ||||||||
\(933\) | 45965.5 | 1.61291 | ||||||||
\(934\) | −3822.13 | −0.133901 | ||||||||
\(935\) | 3308.92 | 0.115736 | ||||||||
\(936\) | −975.017 | −0.0340486 | ||||||||
\(937\) | 48380.8 | 1.68680 | 0.843400 | − | 0.537286i | \(-0.180550\pi\) | ||||
0.843400 | + | 0.537286i | \(0.180550\pi\) | |||||||
\(938\) | 4598.95 | 0.160087 | ||||||||
\(939\) | −45936.3 | −1.59646 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31933.6 | −1.10628 | −0.553139 | − | 0.833089i | \(-0.686570\pi\) | ||||
−0.553139 | + | 0.833089i | \(0.686570\pi\) | |||||||
\(942\) | 9252.38 | 0.320020 | ||||||||
\(943\) | 11256.9 | 0.388734 | ||||||||
\(944\) | 11675.5 | 0.402548 | ||||||||
\(945\) | −2292.67 | −0.0789214 | ||||||||
\(946\) | −13041.6 | −0.448223 | ||||||||
\(947\) | −50096.9 | −1.71904 | −0.859519 | − | 0.511103i | \(-0.829237\pi\) | ||||
−0.859519 | + | 0.511103i | \(0.829237\pi\) | |||||||
\(948\) | −15235.1 | −0.521955 | ||||||||
\(949\) | 3893.19 | 0.133170 | ||||||||
\(950\) | −3345.46 | −0.114254 | ||||||||
\(951\) | 64006.2 | 2.18248 | ||||||||
\(952\) | −1850.34 | −0.0629935 | ||||||||
\(953\) | −12685.9 | −0.431205 | −0.215602 | − | 0.976481i | \(-0.569171\pi\) | ||||
−0.215602 | + | 0.976481i | \(0.569171\pi\) | |||||||
\(954\) | 4618.61 | 0.156743 | ||||||||
\(955\) | −12257.6 | −0.415338 | ||||||||
\(956\) | −20876.0 | −0.706255 | ||||||||
\(957\) | 14830.2 | 0.500931 | ||||||||
\(958\) | 14098.1 | 0.475458 | ||||||||
\(959\) | −5395.91 | −0.181693 | ||||||||
\(960\) | −6364.68 | −0.213978 | ||||||||
\(961\) | −12998.3 | −0.436316 | ||||||||
\(962\) | −1808.77 | −0.0606205 | ||||||||
\(963\) | 11161.2 | 0.373485 | ||||||||
\(964\) | −34841.2 | −1.16406 | ||||||||
\(965\) | −1067.30 | −0.0356036 | ||||||||
\(966\) | 2738.28 | 0.0912036 | ||||||||
\(967\) | 35048.9 | 1.16556 | 0.582780 | − | 0.812630i | \(-0.301965\pi\) | ||||
0.582780 | + | 0.812630i | \(0.301965\pi\) | |||||||
\(968\) | 19180.8 | 0.636874 | ||||||||
\(969\) | 3999.14 | 0.132581 | ||||||||
\(970\) | −2013.79 | −0.0666585 | ||||||||
\(971\) | −29484.5 | −0.974462 | −0.487231 | − | 0.873273i | \(-0.661993\pi\) | ||||
−0.487231 | + | 0.873273i | \(0.661993\pi\) | |||||||
\(972\) | −12986.1 | −0.428527 | ||||||||
\(973\) | 10658.3 | 0.351172 | ||||||||
\(974\) | 15295.6 | 0.503187 | ||||||||
\(975\) | 2882.54 | 0.0946822 | ||||||||
\(976\) | −2719.65 | −0.0891946 | ||||||||
\(977\) | −25899.3 | −0.848100 | −0.424050 | − | 0.905639i | \(-0.639392\pi\) | ||||
−0.424050 | + | 0.905639i | \(0.639392\pi\) | |||||||
\(978\) | 6584.07 | 0.215271 | ||||||||
\(979\) | −14669.4 | −0.478893 | ||||||||
\(980\) | 11661.1 | 0.380103 | ||||||||
\(981\) | 8185.02 | 0.266389 | ||||||||
\(982\) | −12899.4 | −0.419183 | ||||||||
\(983\) | −20316.8 | −0.659210 | −0.329605 | − | 0.944119i | \(-0.606916\pi\) | ||||
−0.329605 | + | 0.944119i | \(0.606916\pi\) | |||||||
\(984\) | 15432.1 | 0.499956 | ||||||||
\(985\) | 117.087 | 0.00378751 | ||||||||
\(986\) | −4963.11 | −0.160302 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −804.863 | −0.0259171 | ||||||||
\(989\) | 38340.7 | 1.23272 | ||||||||
\(990\) | −1594.04 | −0.0511738 | ||||||||
\(991\) | 52179.6 | 1.67259 | 0.836297 | − | 0.548276i | \(-0.184716\pi\) | ||||
0.836297 | + | 0.548276i | \(0.184716\pi\) | |||||||
\(992\) | −24307.8 | −0.777997 | ||||||||
\(993\) | −22010.8 | −0.703417 | ||||||||
\(994\) | −3521.04 | −0.112355 | ||||||||
\(995\) | −13584.9 | −0.432835 | ||||||||
\(996\) | −18409.6 | −0.585675 | ||||||||
\(997\) | −13574.2 | −0.431193 | −0.215596 | − | 0.976483i | \(-0.569170\pi\) | ||||
−0.215596 | + | 0.976483i | \(0.569170\pi\) | |||||||
\(998\) | 17497.8 | 0.554993 | ||||||||
\(999\) | −23628.5 | −0.748322 |
(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 | 2209.4.a.a.1.3 | 3 | ||
47.46 | odd | 2 | 47.4.a.a.1.3 | ✓ | 3 | ||
141.140 | even | 2 | 423.4.a.b.1.1 | 3 | |||
188.187 | even | 2 | 752.4.a.c.1.3 | 3 | |||
235.234 | odd | 2 | 1175.4.a.a.1.1 | 3 | |||
329.328 | even | 2 | 2303.4.a.a.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
47.4.a.a.1.3 | ✓ | 3 | 47.46 | odd | 2 | ||
423.4.a.b.1.1 | 3 | 141.140 | even | 2 | |||
752.4.a.c.1.3 | 3 | 188.187 | even | 2 | |||
1175.4.a.a.1.1 | 3 | 235.234 | odd | 2 | |||
2209.4.a.a.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2303.4.a.a.1.3 | 3 | 329.328 | even | 2 |