Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
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([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.17 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16473 | 0.765347 | 0.382673 | − | 0.923884i | \(-0.375003\pi\) | ||||
0.382673 | + | 0.923884i | \(0.375003\pi\) | |||||||
\(3\) | − 9.14133i | − 1.75925i | −0.475668 | − | 0.879625i | \(-0.657794\pi\) | ||||
0.475668 | − | 0.879625i | \(-0.342206\pi\) | |||||||
\(4\) | −3.31395 | −0.414244 | ||||||||
\(5\) | − 16.2298i | − 1.45164i | −0.687886 | − | 0.725819i | \(-0.741461\pi\) | ||||
0.687886 | − | 0.725819i | \(-0.258539\pi\) | |||||||
\(6\) | − 19.7885i | − 1.34644i | ||||||||
\(7\) | 12.2246i | 0.660065i | 0.943970 | + | 0.330032i | \(0.107060\pi\) | ||||
−0.943970 | + | 0.330032i | \(0.892940\pi\) | |||||||
\(8\) | −24.4916 | −1.08239 | ||||||||
\(9\) | −56.5639 | −2.09496 | ||||||||
\(10\) | − 35.1331i | − 1.11101i | ||||||||
\(11\) | − 11.1761i | − 0.306338i | −0.988200 | − | 0.153169i | \(-0.951052\pi\) | ||||
0.988200 | − | 0.153169i | \(-0.0489480\pi\) | |||||||
\(12\) | 30.2939i | 0.728759i | ||||||||
\(13\) | 28.9000 | 0.616570 | 0.308285 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308285 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(14\) | 26.4629i | 0.505178i | ||||||||
\(15\) | −148.362 | −2.55379 | ||||||||
\(16\) | −26.5061 | −0.414158 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −122.445 | −1.60337 | ||||||||
\(19\) | 79.5850 | 0.960950 | 0.480475 | − | 0.877009i | \(-0.340464\pi\) | ||||
0.480475 | + | 0.877009i | \(0.340464\pi\) | |||||||
\(20\) | 53.7848i | 0.601332i | ||||||||
\(21\) | 111.749 | 1.16122 | ||||||||
\(22\) | − 24.1932i | − 0.234455i | ||||||||
\(23\) | − 45.0447i | − 0.408368i | −0.978933 | − | 0.204184i | \(-0.934546\pi\) | ||||
0.978933 | − | 0.204184i | \(-0.0654541\pi\) | |||||||
\(24\) | 223.886i | 1.90419i | ||||||||
\(25\) | −138.406 | −1.10725 | ||||||||
\(26\) | 62.5606 | 0.471890 | ||||||||
\(27\) | 270.253i | 1.92631i | ||||||||
\(28\) | − 40.5117i | − 0.273428i | ||||||||
\(29\) | − 20.3774i | − 0.130482i | −0.997870 | − | 0.0652411i | \(-0.979218\pi\) | ||||
0.997870 | − | 0.0652411i | \(-0.0207817\pi\) | |||||||
\(30\) | −321.163 | −1.95454 | ||||||||
\(31\) | − 1.03839i | − 0.00601613i | −0.999995 | − | 0.00300806i | \(-0.999043\pi\) | ||||
0.999995 | − | 0.00300806i | \(-0.000957498\pi\) | |||||||
\(32\) | 138.555 | 0.765413 | ||||||||
\(33\) | −102.164 | −0.538926 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 198.402 | 0.958175 | ||||||||
\(36\) | 187.450 | 0.867824 | ||||||||
\(37\) | 219.921i | 0.977159i | 0.872520 | + | 0.488579i | \(0.162485\pi\) | ||||
−0.872520 | + | 0.488579i | \(0.837515\pi\) | |||||||
\(38\) | 172.280 | 0.735460 | ||||||||
\(39\) | − 264.184i | − 1.08470i | ||||||||
\(40\) | 397.494i | 1.57123i | ||||||||
\(41\) | − 310.992i | − 1.18460i | −0.805716 | − | 0.592302i | \(-0.798219\pi\) | ||||
0.805716 | − | 0.592302i | \(-0.201781\pi\) | |||||||
\(42\) | 241.906 | 0.888735 | ||||||||
\(43\) | −483.760 | −1.71564 | −0.857822 | − | 0.513947i | \(-0.828183\pi\) | ||||
−0.857822 | + | 0.513947i | \(0.828183\pi\) | |||||||
\(44\) | 37.0371i | 0.126899i | ||||||||
\(45\) | 918.020i | 3.04112i | ||||||||
\(46\) | − 97.5095i | − 0.312543i | ||||||||
\(47\) | −632.422 | −1.96273 | −0.981364 | − | 0.192156i | \(-0.938452\pi\) | ||||
−0.981364 | + | 0.192156i | \(0.938452\pi\) | |||||||
\(48\) | 242.301i | 0.728606i | ||||||||
\(49\) | 193.560 | 0.564315 | ||||||||
\(50\) | −299.612 | −0.847431 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −95.7732 | −0.255411 | ||||||||
\(53\) | −490.172 | −1.27038 | −0.635192 | − | 0.772354i | \(-0.719079\pi\) | ||||
−0.635192 | + | 0.772354i | \(0.719079\pi\) | |||||||
\(54\) | 585.024i | 1.47429i | ||||||||
\(55\) | −181.386 | −0.444692 | ||||||||
\(56\) | − 299.400i | − 0.714446i | ||||||||
\(57\) | − 727.512i | − 1.69055i | ||||||||
\(58\) | − 44.1115i | − 0.0998642i | ||||||||
\(59\) | −147.956 | −0.326478 | −0.163239 | − | 0.986587i | \(-0.552194\pi\) | ||||
−0.163239 | + | 0.986587i | \(0.552194\pi\) | |||||||
\(60\) | 491.665 | 1.05789 | ||||||||
\(61\) | 176.395i | 0.370246i | 0.982715 | + | 0.185123i | \(0.0592684\pi\) | ||||
−0.982715 | + | 0.185123i | \(0.940732\pi\) | |||||||
\(62\) | − 2.24783i | − 0.00460442i | ||||||||
\(63\) | − 691.469i | − 1.38281i | ||||||||
\(64\) | 511.982 | 0.999964 | ||||||||
\(65\) | − 469.041i | − 0.895037i | ||||||||
\(66\) | −221.158 | −0.412465 | ||||||||
\(67\) | 809.312 | 1.47572 | 0.737860 | − | 0.674954i | \(-0.235836\pi\) | ||||
0.737860 | + | 0.674954i | \(0.235836\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −411.768 | −0.718421 | ||||||||
\(70\) | 429.487 | 0.733336 | ||||||||
\(71\) | − 714.189i | − 1.19378i | −0.802322 | − | 0.596892i | \(-0.796402\pi\) | ||||
0.802322 | − | 0.596892i | \(-0.203598\pi\) | |||||||
\(72\) | 1385.34 | 2.26756 | ||||||||
\(73\) | − 780.184i | − 1.25087i | −0.780276 | − | 0.625436i | \(-0.784921\pi\) | ||||
0.780276 | − | 0.625436i | \(-0.215079\pi\) | |||||||
\(74\) | 476.070i | 0.747865i | ||||||||
\(75\) | 1265.22i | 1.94793i | ||||||||
\(76\) | −263.741 | −0.398068 | ||||||||
\(77\) | 136.623 | 0.202203 | ||||||||
\(78\) | − 571.887i | − 0.830172i | ||||||||
\(79\) | − 230.265i | − 0.327935i | −0.986466 | − | 0.163968i | \(-0.947571\pi\) | ||||
0.986466 | − | 0.163968i | \(-0.0524293\pi\) | |||||||
\(80\) | 430.188i | 0.601207i | ||||||||
\(81\) | 943.248 | 1.29389 | ||||||||
\(82\) | − 673.213i | − 0.906633i | ||||||||
\(83\) | −236.046 | −0.312161 | −0.156080 | − | 0.987744i | \(-0.549886\pi\) | ||||
−0.156080 | + | 0.987744i | \(0.549886\pi\) | |||||||
\(84\) | −370.330 | −0.481028 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1047.21 | −1.31306 | ||||||||
\(87\) | −186.276 | −0.229551 | ||||||||
\(88\) | 273.721i | 0.331577i | ||||||||
\(89\) | −688.557 | −0.820078 | −0.410039 | − | 0.912068i | \(-0.634485\pi\) | ||||
−0.410039 | + | 0.912068i | \(0.634485\pi\) | |||||||
\(90\) | 1987.26i | 2.32751i | ||||||||
\(91\) | 353.290i | 0.406976i | ||||||||
\(92\) | 149.276i | 0.169164i | ||||||||
\(93\) | −9.49224 | −0.0105839 | ||||||||
\(94\) | −1369.02 | −1.50217 | ||||||||
\(95\) | − 1291.65i | − 1.39495i | ||||||||
\(96\) | − 1266.57i | − 1.34655i | ||||||||
\(97\) | 1846.11i | 1.93241i | 0.257775 | + | 0.966205i | \(0.417011\pi\) | ||||
−0.257775 | + | 0.966205i | \(0.582989\pi\) | |||||||
\(98\) | 419.004 | 0.431896 | ||||||||
\(99\) | 632.164i | 0.641766i | ||||||||
\(100\) | 458.672 | 0.458672 | ||||||||
\(101\) | −735.748 | −0.724848 | −0.362424 | − | 0.932013i | \(-0.618051\pi\) | ||||
−0.362424 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 387.334 | 0.370535 | 0.185268 | − | 0.982688i | \(-0.440685\pi\) | ||||
0.185268 | + | 0.982688i | \(0.440685\pi\) | |||||||
\(104\) | −707.808 | −0.667368 | ||||||||
\(105\) | − 1813.66i | − 1.68567i | ||||||||
\(106\) | −1061.09 | −0.972284 | ||||||||
\(107\) | − 793.424i | − 0.716852i | −0.933558 | − | 0.358426i | \(-0.883314\pi\) | ||||
0.933558 | − | 0.358426i | \(-0.116686\pi\) | |||||||
\(108\) | − 895.606i | − 0.797961i | ||||||||
\(109\) | − 1709.67i | − 1.50236i | −0.660100 | − | 0.751178i | \(-0.729486\pi\) | ||||
0.660100 | − | 0.751178i | \(-0.270514\pi\) | |||||||
\(110\) | −392.651 | −0.340344 | ||||||||
\(111\) | 2010.37 | 1.71907 | ||||||||
\(112\) | − 324.025i | − 0.273371i | ||||||||
\(113\) | 42.1279i | 0.0350713i | 0.999846 | + | 0.0175357i | \(0.00558206\pi\) | ||||
−0.999846 | + | 0.0175357i | \(0.994418\pi\) | |||||||
\(114\) | − 1574.87i | − 1.29386i | ||||||||
\(115\) | −731.066 | −0.592802 | ||||||||
\(116\) | 67.5297i | 0.0540515i | ||||||||
\(117\) | −1634.70 | −1.29169 | ||||||||
\(118\) | −320.284 | −0.249869 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3633.63 | 2.76419 | ||||||||
\(121\) | 1206.09 | 0.906157 | ||||||||
\(122\) | 381.846i | 0.283367i | ||||||||
\(123\) | −2842.88 | −2.08401 | ||||||||
\(124\) | 3.44117i | 0.00249215i | ||||||||
\(125\) | 217.583i | 0.155690i | ||||||||
\(126\) | − 1496.84i | − 1.05833i | ||||||||
\(127\) | 1536.78 | 1.07376 | 0.536878 | − | 0.843660i | \(-0.319603\pi\) | ||||
0.536878 | + | 0.843660i | \(0.319603\pi\) | |||||||
\(128\) | −0.135867 | −9.38207e−5 0 | ||||||||
\(129\) | 4422.21i | 3.01825i | ||||||||
\(130\) | − 1015.35i | − 0.685013i | ||||||||
\(131\) | 264.718i | 0.176554i | 0.996096 | + | 0.0882768i | \(0.0281360\pi\) | ||||
−0.996096 | + | 0.0882768i | \(0.971864\pi\) | |||||||
\(132\) | 338.568 | 0.223247 | ||||||||
\(133\) | 972.892i | 0.634289i | ||||||||
\(134\) | 1751.94 | 1.12944 | ||||||||
\(135\) | 4386.15 | 2.79630 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 686.450 | 0.428083 | 0.214042 | − | 0.976825i | \(-0.431337\pi\) | ||||
0.214042 | + | 0.976825i | \(0.431337\pi\) | |||||||
\(138\) | −891.366 | −0.549841 | ||||||||
\(139\) | 43.2364i | 0.0263832i | 0.999913 | + | 0.0131916i | \(0.00419914\pi\) | ||||
−0.999913 | + | 0.0131916i | \(0.995801\pi\) | |||||||
\(140\) | −657.496 | −0.396918 | ||||||||
\(141\) | 5781.18i | 3.45293i | ||||||||
\(142\) | − 1546.02i | − 0.913659i | ||||||||
\(143\) | − 322.989i | − 0.188879i | ||||||||
\(144\) | 1499.29 | 0.867643 | ||||||||
\(145\) | −330.721 | −0.189413 | ||||||||
\(146\) | − 1688.89i | − 0.957350i | ||||||||
\(147\) | − 1769.39i | − 0.992770i | ||||||||
\(148\) | − 728.810i | − 0.404782i | ||||||||
\(149\) | 335.407 | 0.184413 | 0.0922067 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922067 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(150\) | 2738.85i | 1.49084i | ||||||||
\(151\) | 2432.29 | 1.31084 | 0.655421 | − | 0.755264i | \(-0.272491\pi\) | ||||
0.655421 | + | 0.755264i | \(0.272491\pi\) | |||||||
\(152\) | −1949.17 | −1.04012 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 295.752 | 0.154756 | ||||||||
\(155\) | −16.8528 | −0.00873324 | ||||||||
\(156\) | 875.494i | 0.449331i | ||||||||
\(157\) | 2706.98 | 1.37605 | 0.688026 | − | 0.725686i | \(-0.258477\pi\) | ||||
0.688026 | + | 0.725686i | \(0.258477\pi\) | |||||||
\(158\) | − 498.462i | − 0.250984i | ||||||||
\(159\) | 4480.83i | 2.23492i | ||||||||
\(160\) | − 2248.71i | − 1.11110i | ||||||||
\(161\) | 550.652 | 0.269549 | ||||||||
\(162\) | 2041.87 | 0.990277 | ||||||||
\(163\) | − 190.765i | − 0.0916678i | −0.998949 | − | 0.0458339i | \(-0.985405\pi\) | ||||
0.998949 | − | 0.0458339i | \(-0.0145945\pi\) | |||||||
\(164\) | 1030.61i | 0.490715i | ||||||||
\(165\) | 1658.11i | 0.782325i | ||||||||
\(166\) | −510.974 | −0.238911 | ||||||||
\(167\) | − 2757.18i | − 1.27759i | −0.769379 | − | 0.638793i | \(-0.779434\pi\) | ||||
0.769379 | − | 0.638793i | \(-0.220566\pi\) | |||||||
\(168\) | −2736.91 | −1.25689 | ||||||||
\(169\) | −1361.79 | −0.619841 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4501.63 | −2.01315 | ||||||||
\(172\) | 1603.16 | 0.710696 | ||||||||
\(173\) | − 1453.00i | − 0.638554i | −0.947661 | − | 0.319277i | \(-0.896560\pi\) | ||||
0.947661 | − | 0.319277i | \(-0.103440\pi\) | |||||||
\(174\) | −403.238 | −0.175686 | ||||||||
\(175\) | − 1691.96i | − 0.730858i | ||||||||
\(176\) | 296.235i | 0.126872i | ||||||||
\(177\) | 1352.51i | 0.574356i | ||||||||
\(178\) | −1490.54 | −0.627644 | ||||||||
\(179\) | 1171.47 | 0.489160 | 0.244580 | − | 0.969629i | \(-0.421350\pi\) | ||||
0.244580 | + | 0.969629i | \(0.421350\pi\) | |||||||
\(180\) | − 3042.28i | − 1.25977i | ||||||||
\(181\) | − 2737.41i | − 1.12414i | −0.827089 | − | 0.562072i | \(-0.810005\pi\) | ||||
0.827089 | − | 0.562072i | \(-0.189995\pi\) | |||||||
\(182\) | 764.776i | 0.311478i | ||||||||
\(183\) | 1612.48 | 0.651355 | ||||||||
\(184\) | 1103.22i | 0.442012i | ||||||||
\(185\) | 3569.28 | 1.41848 | ||||||||
\(186\) | −20.5481 | −0.00810033 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2095.82 | 0.813049 | ||||||||
\(189\) | −3303.73 | −1.27149 | ||||||||
\(190\) | − 2796.07i | − 1.06762i | ||||||||
\(191\) | −1345.56 | −0.509744 | −0.254872 | − | 0.966975i | \(-0.582033\pi\) | ||||
−0.254872 | + | 0.966975i | \(0.582033\pi\) | |||||||
\(192\) | − 4680.19i | − 1.75919i | ||||||||
\(193\) | − 3787.61i | − 1.41263i | −0.707896 | − | 0.706317i | \(-0.750355\pi\) | ||||
0.707896 | − | 0.706317i | \(-0.249645\pi\) | |||||||
\(194\) | 3996.32i | 1.47896i | ||||||||
\(195\) | −4287.66 | −1.57459 | ||||||||
\(196\) | −641.448 | −0.233764 | ||||||||
\(197\) | − 72.4095i | − 0.0261876i | −0.999914 | − | 0.0130938i | \(-0.995832\pi\) | ||||
0.999914 | − | 0.0130938i | \(-0.00416801\pi\) | |||||||
\(198\) | 1368.46i | 0.491174i | ||||||||
\(199\) | 2703.59i | 0.963077i | 0.876425 | + | 0.481539i | \(0.159922\pi\) | ||||
−0.876425 | + | 0.481539i | \(0.840078\pi\) | |||||||
\(200\) | 3389.80 | 1.19847 | ||||||||
\(201\) | − 7398.19i | − 2.59616i | ||||||||
\(202\) | −1592.69 | −0.554760 | ||||||||
\(203\) | 249.105 | 0.0861267 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5047.33 | −1.71962 | ||||||||
\(206\) | 838.472 | 0.283588 | ||||||||
\(207\) | 2547.90i | 0.855514i | ||||||||
\(208\) | −766.025 | −0.255357 | ||||||||
\(209\) | − 889.450i | − 0.294376i | ||||||||
\(210\) | − 3926.08i | − 1.29012i | ||||||||
\(211\) | 2338.29i | 0.762911i | 0.924387 | + | 0.381456i | \(0.124577\pi\) | ||||
−0.924387 | + | 0.381456i | \(0.875423\pi\) | |||||||
\(212\) | 1624.41 | 0.526249 | ||||||||
\(213\) | −6528.64 | −2.10016 | ||||||||
\(214\) | − 1717.55i | − 0.548640i | ||||||||
\(215\) | 7851.33i | 2.49049i | ||||||||
\(216\) | − 6618.94i | − 2.08501i | ||||||||
\(217\) | 12.6938 | 0.00397103 | ||||||||
\(218\) | − 3700.97i | − 1.14982i | ||||||||
\(219\) | −7131.91 | −2.20059 | ||||||||
\(220\) | 601.105 | 0.184211 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4351.91 | 1.31568 | ||||||||
\(223\) | −1737.70 | −0.521815 | −0.260908 | − | 0.965364i | \(-0.584022\pi\) | ||||
−0.260908 | + | 0.965364i | \(0.584022\pi\) | |||||||
\(224\) | 1693.77i | 0.505222i | ||||||||
\(225\) | 7828.80 | 2.31965 | ||||||||
\(226\) | 91.1954i | 0.0268417i | ||||||||
\(227\) | 4480.83i | 1.31015i | 0.755565 | + | 0.655073i | \(0.227362\pi\) | ||||
−0.755565 | + | 0.655073i | \(0.772638\pi\) | |||||||
\(228\) | 2410.94i | 0.700301i | ||||||||
\(229\) | 3917.73 | 1.13053 | 0.565264 | − | 0.824910i | \(-0.308774\pi\) | ||||
0.565264 | + | 0.824910i | \(0.308774\pi\) | |||||||
\(230\) | −1582.56 | −0.453699 | ||||||||
\(231\) | − 1248.92i | − 0.355726i | ||||||||
\(232\) | 499.075i | 0.141232i | ||||||||
\(233\) | − 4166.02i | − 1.17135i | −0.810546 | − | 0.585675i | \(-0.800829\pi\) | ||||
0.810546 | − | 0.585675i | \(-0.199171\pi\) | |||||||
\(234\) | −3538.67 | −0.988590 | ||||||||
\(235\) | 10264.1i | 2.84917i | ||||||||
\(236\) | 490.318 | 0.135242 | ||||||||
\(237\) | −2104.93 | −0.576920 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1780.06 | −0.481768 | −0.240884 | − | 0.970554i | \(-0.577437\pi\) | ||||
−0.240884 | + | 0.970554i | \(0.577437\pi\) | |||||||
\(240\) | 3932.49 | 1.05767 | ||||||||
\(241\) | − 2469.12i | − 0.659958i | −0.943988 | − | 0.329979i | \(-0.892958\pi\) | ||||
0.943988 | − | 0.329979i | \(-0.107042\pi\) | |||||||
\(242\) | 2610.87 | 0.693524 | ||||||||
\(243\) | − 1325.70i | − 0.349975i | ||||||||
\(244\) | − 584.563i | − 0.153372i | ||||||||
\(245\) | − 3141.44i | − 0.819180i | ||||||||
\(246\) | −6154.06 | −1.59499 | ||||||||
\(247\) | 2300.00 | 0.592493 | ||||||||
\(248\) | 25.4318i | 0.00651178i | ||||||||
\(249\) | 2157.77i | 0.549169i | ||||||||
\(250\) | 471.009i | 0.119157i | ||||||||
\(251\) | −4824.05 | −1.21311 | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||||
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(252\) | 2291.50i | 0.572820i | ||||||||
\(253\) | −503.424 | −0.125099 | ||||||||
\(254\) | 3326.71 | 0.821796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4096.15 | −1.00004 | ||||||||
\(257\) | −5558.77 | −1.34921 | −0.674604 | − | 0.738180i | \(-0.735686\pi\) | ||||
−0.674604 | + | 0.738180i | \(0.735686\pi\) | |||||||
\(258\) | 9572.88i | 2.31000i | ||||||||
\(259\) | −2688.45 | −0.644988 | ||||||||
\(260\) | 1554.38i | 0.370764i | ||||||||
\(261\) | 1152.62i | 0.273355i | ||||||||
\(262\) | 573.043i | 0.135125i | ||||||||
\(263\) | 3172.23 | 0.743757 | 0.371878 | − | 0.928281i | \(-0.378714\pi\) | ||||
0.371878 | + | 0.928281i | \(0.378714\pi\) | |||||||
\(264\) | 2502.17 | 0.583326 | ||||||||
\(265\) | 7955.40i | 1.84414i | ||||||||
\(266\) | 2106.05i | 0.485451i | ||||||||
\(267\) | 6294.33i | 1.44272i | ||||||||
\(268\) | −2682.02 | −0.611309 | ||||||||
\(269\) | − 2849.92i | − 0.645959i | −0.946406 | − | 0.322979i | \(-0.895316\pi\) | ||||
0.946406 | − | 0.322979i | \(-0.104684\pi\) | |||||||
\(270\) | 9494.83 | 2.14014 | ||||||||
\(271\) | −2565.11 | −0.574980 | −0.287490 | − | 0.957784i | \(-0.592821\pi\) | ||||
−0.287490 | + | 0.957784i | \(0.592821\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3229.54 | 0.715973 | ||||||||
\(274\) | 1485.98 | 0.327632 | ||||||||
\(275\) | 1546.84i | 0.339194i | ||||||||
\(276\) | 1364.58 | 0.297602 | ||||||||
\(277\) | − 6260.95i | − 1.35806i | −0.734108 | − | 0.679032i | \(-0.762400\pi\) | ||||
0.734108 | − | 0.679032i | \(-0.237600\pi\) | |||||||
\(278\) | 93.5951i | 0.0201923i | ||||||||
\(279\) | 58.7352i | 0.0126035i | ||||||||
\(280\) | −4859.20 | −1.03712 | ||||||||
\(281\) | 1807.59 | 0.383744 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(282\) | 12514.7i | 2.64269i | ||||||||
\(283\) | − 1264.09i | − 0.265521i | −0.991148 | − | 0.132761i | \(-0.957616\pi\) | ||||
0.991148 | − | 0.132761i | \(-0.0423841\pi\) | |||||||
\(284\) | 2366.79i | 0.494518i | ||||||||
\(285\) | −11807.4 | −2.45407 | ||||||||
\(286\) | − 699.184i | − 0.144558i | ||||||||
\(287\) | 3801.74 | 0.781915 | ||||||||
\(288\) | −7837.18 | −1.60351 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −715.921 | −0.144967 | ||||||||
\(291\) | 16875.9 | 3.39959 | ||||||||
\(292\) | 2585.49i | 0.518166i | ||||||||
\(293\) | 3708.40 | 0.739410 | 0.369705 | − | 0.929149i | \(-0.379459\pi\) | ||||
0.369705 | + | 0.929149i | \(0.379459\pi\) | |||||||
\(294\) | − 3830.26i | − 0.759813i | ||||||||
\(295\) | 2401.29i | 0.473927i | ||||||||
\(296\) | − 5386.24i | − 1.05766i | ||||||||
\(297\) | 3020.38 | 0.590101 | ||||||||
\(298\) | 726.065 | 0.141140 | ||||||||
\(299\) | − 1301.79i | − 0.251788i | ||||||||
\(300\) | − 4192.88i | − 0.806919i | ||||||||
\(301\) | − 5913.76i | − 1.13244i | ||||||||
\(302\) | 5265.25 | 1.00325 | ||||||||
\(303\) | 6725.71i | 1.27519i | ||||||||
\(304\) | −2109.49 | −0.397985 | ||||||||
\(305\) | 2862.85 | 0.537463 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4689.47 | 0.871799 | 0.435899 | − | 0.899995i | \(-0.356430\pi\) | ||||
0.435899 | + | 0.899995i | \(0.356430\pi\) | |||||||
\(308\) | −452.763 | −0.0837615 | ||||||||
\(309\) | − 3540.75i | − 0.651864i | ||||||||
\(310\) | −36.4818 | −0.00668396 | ||||||||
\(311\) | 2725.79i | 0.496995i | 0.968633 | + | 0.248497i | \(0.0799368\pi\) | ||||
−0.968633 | + | 0.248497i | \(0.920063\pi\) | |||||||
\(312\) | 6470.30i | 1.17407i | ||||||||
\(313\) | − 1406.42i | − 0.253980i | −0.991904 | − | 0.126990i | \(-0.959468\pi\) | ||||
0.991904 | − | 0.126990i | \(-0.0405316\pi\) | |||||||
\(314\) | 5859.87 | 1.05316 | ||||||||
\(315\) | −11222.4 | −2.00734 | ||||||||
\(316\) | 763.089i | 0.135845i | ||||||||
\(317\) | − 836.717i | − 0.148248i | −0.997249 | − | 0.0741241i | \(-0.976384\pi\) | ||||
0.997249 | − | 0.0741241i | \(-0.0236161\pi\) | |||||||
\(318\) | 9699.77i | 1.71049i | ||||||||
\(319\) | −227.740 | −0.0399717 | ||||||||
\(320\) | − 8309.36i | − 1.45159i | ||||||||
\(321\) | −7252.95 | −1.26112 | ||||||||
\(322\) | 1192.01 | 0.206299 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3125.88 | −0.535987 | ||||||||
\(325\) | −3999.94 | −0.682698 | ||||||||
\(326\) | − 412.954i | − 0.0701577i | ||||||||
\(327\) | −15628.7 | −2.64302 | ||||||||
\(328\) | 7616.70i | 1.28220i | ||||||||
\(329\) | − 7731.09i | − 1.29553i | ||||||||
\(330\) | 3589.35i | 0.598750i | ||||||||
\(331\) | −2544.99 | −0.422614 | −0.211307 | − | 0.977420i | \(-0.567772\pi\) | ||||
−0.211307 | + | 0.977420i | \(0.567772\pi\) | |||||||
\(332\) | 782.244 | 0.129311 | ||||||||
\(333\) | − 12439.6i | − 2.04711i | ||||||||
\(334\) | − 5968.54i | − 0.977796i | ||||||||
\(335\) | − 13135.0i | − 2.14221i | ||||||||
\(336\) | −2962.02 | −0.480927 | ||||||||
\(337\) | 9258.04i | 1.49649i | 0.663422 | + | 0.748246i | \(0.269104\pi\) | ||||
−0.663422 | + | 0.748246i | \(0.730896\pi\) | |||||||
\(338\) | −2947.91 | −0.474393 | ||||||||
\(339\) | 385.105 | 0.0616992 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6051 | −0.00184297 | ||||||||
\(342\) | −9744.81 | −1.54076 | ||||||||
\(343\) | 6559.21i | 1.03255i | ||||||||
\(344\) | 11848.1 | 1.85699 | ||||||||
\(345\) | 6682.92i | 1.04289i | ||||||||
\(346\) | − 3145.36i | − 0.488716i | ||||||||
\(347\) | 11972.3i | 1.85217i | 0.377310 | + | 0.926087i | \(0.376849\pi\) | ||||
−0.377310 | + | 0.926087i | \(0.623151\pi\) | |||||||
\(348\) | 617.311 | 0.0950901 | ||||||||
\(349\) | −1887.57 | −0.289511 | −0.144755 | − | 0.989467i | \(-0.546240\pi\) | ||||
−0.144755 | + | 0.989467i | \(0.546240\pi\) | |||||||
\(350\) | − 3662.63i | − 0.559360i | ||||||||
\(351\) | 7810.31i | 1.18770i | ||||||||
\(352\) | − 1548.50i | − 0.234475i | ||||||||
\(353\) | 7441.02 | 1.12194 | 0.560971 | − | 0.827836i | \(-0.310428\pi\) | ||||
0.560971 | + | 0.827836i | \(0.310428\pi\) | |||||||
\(354\) | 2927.82i | 0.439581i | ||||||||
\(355\) | −11591.1 | −1.73294 | ||||||||
\(356\) | 2281.85 | 0.339712 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2535.91 | 0.374377 | ||||||||
\(359\) | −11518.8 | −1.69342 | −0.846711 | − | 0.532052i | \(-0.821421\pi\) | ||||
−0.846711 | + | 0.532052i | \(0.821421\pi\) | |||||||
\(360\) | − 22483.8i | − 3.29167i | ||||||||
\(361\) | −525.233 | −0.0765757 | ||||||||
\(362\) | − 5925.74i | − 0.860359i | ||||||||
\(363\) | − 11025.3i | − 1.59416i | ||||||||
\(364\) | − 1170.79i | − 0.168588i | ||||||||
\(365\) | −12662.2 | −1.81581 | ||||||||
\(366\) | 3490.58 | 0.498513 | ||||||||
\(367\) | − 702.580i | − 0.0999302i | −0.998751 | − | 0.0499651i | \(-0.984089\pi\) | ||||
0.998751 | − | 0.0499651i | \(-0.0159110\pi\) | |||||||
\(368\) | 1193.96i | 0.169129i | ||||||||
\(369\) | 17590.9i | 2.48170i | ||||||||
\(370\) | 7726.52 | 1.08563 | ||||||||
\(371\) | − 5992.15i | − 0.838536i | ||||||||
\(372\) | 31.4569 | 0.00438431 | ||||||||
\(373\) | 8797.32 | 1.22120 | 0.610600 | − | 0.791939i | \(-0.290928\pi\) | ||||
0.610600 | + | 0.791939i | \(0.290928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1989.00 | 0.273897 | ||||||||
\(376\) | 15489.0 | 2.12443 | ||||||||
\(377\) | − 588.906i | − 0.0804515i | ||||||||
\(378\) | −7151.67 | −0.973128 | ||||||||
\(379\) | 3113.75i | 0.422012i | 0.977485 | + | 0.211006i | \(0.0676740\pi\) | ||||
−0.977485 | + | 0.211006i | \(0.932326\pi\) | |||||||
\(380\) | 4280.46i | 0.577850i | ||||||||
\(381\) | − 14048.2i | − 1.88901i | ||||||||
\(382\) | −2912.77 | −0.390131 | ||||||||
\(383\) | 9735.60 | 1.29887 | 0.649434 | − | 0.760418i | \(-0.275006\pi\) | ||||
0.649434 | + | 0.760418i | \(0.275006\pi\) | |||||||
\(384\) | 1.24200i | 0 0.000165054i | ||||||||
\(385\) | − 2217.37i | − 0.293526i | ||||||||
\(386\) | − 8199.15i | − 1.08115i | ||||||||
\(387\) | 27363.3 | 3.59420 | ||||||||
\(388\) | − 6117.91i | − 0.800490i | ||||||||
\(389\) | 1772.22 | 0.230990 | 0.115495 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115495 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(390\) | −9281.61 | −1.20511 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4740.60 | −0.610807 | ||||||||
\(393\) | 2419.88 | 0.310602 | ||||||||
\(394\) | − 156.747i | − 0.0200426i | ||||||||
\(395\) | −3737.16 | −0.476043 | ||||||||
\(396\) | − 2094.96i | − 0.265848i | ||||||||
\(397\) | 1201.80i | 0.151931i | 0.997110 | + | 0.0759653i | \(0.0242038\pi\) | ||||
−0.997110 | + | 0.0759653i | \(0.975796\pi\) | |||||||
\(398\) | 5852.54i | 0.737088i | ||||||||
\(399\) | 8893.53 | 1.11587 | ||||||||
\(400\) | 3668.61 | 0.458576 | ||||||||
\(401\) | − 13633.2i | − 1.69778i | −0.528566 | − | 0.848892i | \(-0.677270\pi\) | ||||
0.528566 | − | 0.848892i | \(-0.322730\pi\) | |||||||
\(402\) | − 16015.1i | − 1.98696i | ||||||||
\(403\) | − 30.0094i | − 0.00370937i | ||||||||
\(404\) | 2438.23 | 0.300264 | ||||||||
\(405\) | − 15308.7i | − 1.87826i | ||||||||
\(406\) | 539.244 | 0.0659168 | ||||||||
\(407\) | 2457.87 | 0.299341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7345.95 | 0.888103 | 0.444051 | − | 0.896001i | \(-0.353541\pi\) | ||||
0.444051 | + | 0.896001i | \(0.353541\pi\) | |||||||
\(410\) | −10926.1 | −1.31610 | ||||||||
\(411\) | − 6275.07i | − 0.753105i | ||||||||
\(412\) | −1283.61 | −0.153492 | ||||||||
\(413\) | − 1808.69i | − 0.215496i | ||||||||
\(414\) | 5515.51i | 0.654765i | ||||||||
\(415\) | 3830.97i | 0.453145i | ||||||||
\(416\) | 4004.23 | 0.471931 | ||||||||
\(417\) | 395.238 | 0.0464146 | ||||||||
\(418\) | − 1925.42i | − 0.225300i | ||||||||
\(419\) | − 3293.55i | − 0.384011i | −0.981394 | − | 0.192005i | \(-0.938501\pi\) | ||||
0.981394 | − | 0.192005i | \(-0.0614991\pi\) | |||||||
\(420\) | 6010.39i | 0.698278i | ||||||||
\(421\) | −9775.57 | −1.13167 | −0.565834 | − | 0.824519i | \(-0.691446\pi\) | ||||
−0.565834 | + | 0.824519i | \(0.691446\pi\) | |||||||
\(422\) | 5061.75i | 0.583892i | ||||||||
\(423\) | 35772.2 | 4.11184 | ||||||||
\(424\) | 12005.1 | 1.37505 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14132.7 | −1.60735 | ||||||||
\(427\) | −2156.35 | −0.244386 | ||||||||
\(428\) | 2629.37i | 0.296952i | ||||||||
\(429\) | −2952.55 | −0.332286 | ||||||||
\(430\) | 16996.0i | 1.90609i | ||||||||
\(431\) | 7842.98i | 0.876527i | 0.898847 | + | 0.438263i | \(0.144406\pi\) | ||||
−0.898847 | + | 0.438263i | \(0.855594\pi\) | |||||||
\(432\) | − 7163.35i | − 0.797794i | ||||||||
\(433\) | 5178.49 | 0.574740 | 0.287370 | − | 0.957820i | \(-0.407219\pi\) | ||||
0.287370 | + | 0.957820i | \(0.407219\pi\) | |||||||
\(434\) | 27.4787 | 0.00303922 | ||||||||
\(435\) | 3023.23i | 0.333225i | ||||||||
\(436\) | 5665.77i | 0.622342i | ||||||||
\(437\) | − 3584.88i | − 0.392421i | ||||||||
\(438\) | −15438.7 | −1.68422 | ||||||||
\(439\) | − 5661.88i | − 0.615550i | −0.951459 | − | 0.307775i | \(-0.900416\pi\) | ||||
0.951459 | − | 0.307775i | \(-0.0995845\pi\) | |||||||
\(440\) | 4442.44 | 0.481329 | ||||||||
\(441\) | −10948.5 | −1.18222 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3020.29 | −0.323924 | −0.161962 | − | 0.986797i | \(-0.551782\pi\) | ||||
−0.161962 | + | 0.986797i | \(0.551782\pi\) | |||||||
\(444\) | −6662.29 | −0.712113 | ||||||||
\(445\) | 11175.1i | 1.19046i | ||||||||
\(446\) | −3761.64 | −0.399370 | ||||||||
\(447\) | − 3066.06i | − 0.324429i | ||||||||
\(448\) | 6258.76i | 0.660041i | ||||||||
\(449\) | − 13308.6i | − 1.39883i | −0.714718 | − | 0.699413i | \(-0.753445\pi\) | ||||
0.714718 | − | 0.699413i | \(-0.246555\pi\) | |||||||
\(450\) | 16947.2 | 1.77533 | ||||||||
\(451\) | −3475.68 | −0.362890 | ||||||||
\(452\) | − 139.610i | − 0.0145281i | ||||||||
\(453\) | − 22234.4i | − 2.30610i | ||||||||
\(454\) | 9699.78i | 1.00272i | ||||||||
\(455\) | 5733.82 | 0.590782 | ||||||||
\(456\) | 17818.0i | 1.82983i | ||||||||
\(457\) | −7260.23 | −0.743150 | −0.371575 | − | 0.928403i | \(-0.621182\pi\) | ||||
−0.371575 | + | 0.928403i | \(0.621182\pi\) | |||||||
\(458\) | 8480.83 | 0.865247 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2422.72 | 0.245565 | ||||||||
\(461\) | 2580.20 | 0.260677 | 0.130338 | − | 0.991470i | \(-0.458394\pi\) | ||||
0.130338 | + | 0.991470i | \(0.458394\pi\) | |||||||
\(462\) | − 2703.56i | − 0.272254i | ||||||||
\(463\) | 14392.8 | 1.44469 | 0.722345 | − | 0.691533i | \(-0.243064\pi\) | ||||
0.722345 | + | 0.691533i | \(0.243064\pi\) | |||||||
\(464\) | 540.125i | 0.0540402i | ||||||||
\(465\) | 154.057i | 0.0153639i | ||||||||
\(466\) | − 9018.29i | − 0.896490i | ||||||||
\(467\) | 11696.0 | 1.15894 | 0.579471 | − | 0.814993i | \(-0.303259\pi\) | ||||
0.579471 | + | 0.814993i | \(0.303259\pi\) | |||||||
\(468\) | 5417.30 | 0.535075 | ||||||||
\(469\) | 9893.50i | 0.974071i | ||||||||
\(470\) | 22218.9i | 2.18060i | ||||||||
\(471\) | − 24745.4i | − 2.42082i | ||||||||
\(472\) | 3623.68 | 0.353375 | ||||||||
\(473\) | 5406.55i | 0.525568i | ||||||||
\(474\) | −4556.61 | −0.441544 | ||||||||
\(475\) | −11015.1 | −1.06401 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27726.0 | 2.66140 | ||||||||
\(478\) | −3853.35 | −0.368720 | ||||||||
\(479\) | − 13997.5i | − 1.33520i | −0.744521 | − | 0.667599i | \(-0.767322\pi\) | ||||
0.744521 | − | 0.667599i | \(-0.232678\pi\) | |||||||
\(480\) | −20556.2 | −1.95471 | ||||||||
\(481\) | 6355.73i | 0.602487i | ||||||||
\(482\) | − 5344.97i | − 0.505097i | ||||||||
\(483\) | − 5033.69i | − 0.474205i | ||||||||
\(484\) | −3996.94 | −0.375370 | ||||||||
\(485\) | 29961.9 | 2.80516 | ||||||||
\(486\) | − 2869.78i | − 0.267852i | ||||||||
\(487\) | 2888.42i | 0.268761i | 0.990930 | + | 0.134381i | \(0.0429045\pi\) | ||||
−0.990930 | + | 0.134381i | \(0.957095\pi\) | |||||||
\(488\) | − 4320.19i | − 0.400750i | ||||||||
\(489\) | −1743.84 | −0.161267 | ||||||||
\(490\) | − 6800.36i | − 0.626957i | ||||||||
\(491\) | 9420.11 | 0.865832 | 0.432916 | − | 0.901434i | \(-0.357485\pi\) | ||||
0.432916 | + | 0.901434i | \(0.357485\pi\) | |||||||
\(492\) | 9421.17 | 0.863291 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4978.88 | 0.453463 | ||||||||
\(495\) | 10259.9 | 0.931612 | ||||||||
\(496\) | 27.5236i | 0.00249162i | ||||||||
\(497\) | 8730.65 | 0.787975 | ||||||||
\(498\) | 4670.98i | 0.420305i | ||||||||
\(499\) | 713.936i | 0.0640484i | 0.999487 | + | 0.0320242i | \(0.0101954\pi\) | ||||
−0.999487 | + | 0.0320242i | \(0.989805\pi\) | |||||||
\(500\) | − 721.061i | − 0.0644937i | ||||||||
\(501\) | −25204.3 | −2.24759 | ||||||||
\(502\) | −10442.8 | −0.928453 | ||||||||
\(503\) | 17604.4i | 1.56052i | 0.625456 | + | 0.780260i | \(0.284913\pi\) | ||||
−0.625456 | + | 0.780260i | \(0.715087\pi\) | |||||||
\(504\) | 16935.2i | 1.49673i | ||||||||
\(505\) | 11941.0i | 1.05222i | ||||||||
\(506\) | −1089.78 | −0.0957440 | ||||||||
\(507\) | 12448.6i | 1.09046i | ||||||||
\(508\) | −5092.81 | −0.444797 | ||||||||
\(509\) | 12291.2 | 1.07033 | 0.535165 | − | 0.844748i | \(-0.320249\pi\) | ||||
0.535165 | + | 0.844748i | \(0.320249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9537.41 | 0.825656 | ||||||||
\(512\) | −8865.96 | −0.765280 | ||||||||
\(513\) | 21508.1i | 1.85108i | ||||||||
\(514\) | −12033.2 | −1.03261 | ||||||||
\(515\) | − 6286.35i | − 0.537883i | ||||||||
\(516\) | − 14655.0i | − 1.25029i | ||||||||
\(517\) | 7068.02i | 0.601259i | ||||||||
\(518\) | −5819.75 | −0.493639 | ||||||||
\(519\) | −13282.4 | −1.12338 | ||||||||
\(520\) | 11487.6i | 0.968776i | ||||||||
\(521\) | 8736.73i | 0.734670i | 0.930089 | + | 0.367335i | \(0.119730\pi\) | ||||
−0.930089 | + | 0.367335i | \(0.880270\pi\) | |||||||
\(522\) | 2495.12i | 0.209211i | ||||||||
\(523\) | −2513.00 | −0.210107 | −0.105053 | − | 0.994467i | \(-0.533501\pi\) | ||||
−0.105053 | + | 0.994467i | \(0.533501\pi\) | |||||||
\(524\) | − 877.264i | − 0.0731363i | ||||||||
\(525\) | −15466.8 | −1.28576 | ||||||||
\(526\) | 6867.01 | 0.569232 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2707.98 | 0.223200 | ||||||||
\(529\) | 10138.0 | 0.833236 | ||||||||
\(530\) | 17221.3i | 1.41140i | ||||||||
\(531\) | 8368.95 | 0.683957 | ||||||||
\(532\) | − 3224.12i | − 0.262751i | ||||||||
\(533\) | − 8987.66i | − 0.730392i | ||||||||
\(534\) | 13625.5i | 1.10418i | ||||||||
\(535\) | −12877.1 | −1.04061 | ||||||||
\(536\) | −19821.4 | −1.59730 | ||||||||
\(537\) | − 10708.8i | − 0.860554i | ||||||||
\(538\) | − 6169.31i | − 0.494383i | ||||||||
\(539\) | − 2163.25i | − 0.172871i | ||||||||
\(540\) | −14535.5 | −1.15835 | ||||||||
\(541\) | − 9702.15i | − 0.771031i | −0.922701 | − | 0.385516i | \(-0.874024\pi\) | ||||
0.922701 | − | 0.385516i | \(-0.125976\pi\) | |||||||
\(542\) | −5552.77 | −0.440059 | ||||||||
\(543\) | −25023.5 | −1.97765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27747.6 | −2.18088 | ||||||||
\(546\) | 6991.07 | 0.547968 | ||||||||
\(547\) | − 16198.6i | − 1.26618i | −0.774077 | − | 0.633092i | \(-0.781785\pi\) | ||||
0.774077 | − | 0.633092i | \(-0.218215\pi\) | |||||||
\(548\) | −2274.86 | −0.177331 | ||||||||
\(549\) | − 9977.56i | − 0.775650i | ||||||||
\(550\) | 3348.50i | 0.259601i | ||||||||
\(551\) | − 1621.73i | − 0.125387i | ||||||||
\(552\) | 10084.9 | 0.777610 | ||||||||
\(553\) | 2814.90 | 0.216459 | ||||||||
\(554\) | − 13553.2i | − 1.03939i | ||||||||
\(555\) | − 32628.0i | − 2.49546i | ||||||||
\(556\) | − 143.283i | − 0.0109291i | ||||||||
\(557\) | −9873.27 | −0.751066 | −0.375533 | − | 0.926809i | \(-0.622540\pi\) | ||||
−0.375533 | + | 0.926809i | \(0.622540\pi\) | |||||||
\(558\) | 127.146i | 0.00964608i | ||||||||
\(559\) | −13980.7 | −1.05782 | ||||||||
\(560\) | −5258.87 | −0.396835 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3912.95 | 0.293697 | ||||||||
\(563\) | −3283.56 | −0.245801 | −0.122900 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122900 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(564\) | − 19158.6i | − 1.43036i | ||||||||
\(565\) | 683.727 | 0.0509108 | ||||||||
\(566\) | − 2736.42i | − 0.203216i | ||||||||
\(567\) | 11530.8i | 0.854053i | ||||||||
\(568\) | 17491.7i | 1.29214i | ||||||||
\(569\) | 15065.3 | 1.10996 | 0.554982 | − | 0.831862i | \(-0.312725\pi\) | ||||
0.554982 | + | 0.831862i | \(0.312725\pi\) | |||||||
\(570\) | −25559.8 | −1.87821 | ||||||||
\(571\) | − 2567.87i | − 0.188200i | −0.995563 | − | 0.0941000i | \(-0.970003\pi\) | ||||
0.995563 | − | 0.0941000i | \(-0.0299973\pi\) | |||||||
\(572\) | 1070.37i | 0.0782421i | ||||||||
\(573\) | 12300.2i | 0.896767i | ||||||||
\(574\) | 8229.73 | 0.598436 | ||||||||
\(575\) | 6234.47i | 0.452166i | ||||||||
\(576\) | −28959.7 | −2.09488 | ||||||||
\(577\) | −23042.3 | −1.66250 | −0.831249 | − | 0.555900i | \(-0.812374\pi\) | ||||
−0.831249 | + | 0.555900i | \(0.812374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34623.8 | −2.48517 | ||||||||
\(580\) | 1095.99 | 0.0784632 | ||||||||
\(581\) | − 2885.56i | − 0.206046i | ||||||||
\(582\) | 36531.7 | 2.60187 | ||||||||
\(583\) | 5478.22i | 0.389167i | ||||||||
\(584\) | 19108.0i | 1.35393i | ||||||||
\(585\) | 26530.8i | 1.87506i | ||||||||
\(586\) | 8027.68 | 0.565905 | ||||||||
\(587\) | 4094.68 | 0.287914 | 0.143957 | − | 0.989584i | \(-0.454017\pi\) | ||||
0.143957 | + | 0.989584i | \(0.454017\pi\) | |||||||
\(588\) | 5863.69i | 0.411249i | ||||||||
\(589\) | − 82.6401i | − 0.00578120i | ||||||||
\(590\) | 5198.14i | 0.362719i | ||||||||
\(591\) | −661.919 | −0.0460706 | ||||||||
\(592\) | − 5829.26i | − 0.404698i | ||||||||
\(593\) | 25698.4 | 1.77961 | 0.889803 | − | 0.456344i | \(-0.150841\pi\) | ||||
0.889803 | + | 0.456344i | \(0.150841\pi\) | |||||||
\(594\) | 6538.30 | 0.451632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1111.52 | −0.0763922 | ||||||||
\(597\) | 24714.4 | 1.69429 | ||||||||
\(598\) | − 2818.02i | − 0.192705i | ||||||||
\(599\) | 1085.55 | 0.0740472 | 0.0370236 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370236 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(600\) | − 30987.3i | − 2.10842i | ||||||||
\(601\) | − 11163.9i | − 0.757713i | −0.925455 | − | 0.378857i | \(-0.876317\pi\) | ||||
0.925455 | − | 0.378857i | \(-0.123683\pi\) | |||||||
\(602\) | − 12801.7i | − 0.866706i | ||||||||
\(603\) | −45777.8 | −3.09157 | ||||||||
\(604\) | −8060.50 | −0.543008 | ||||||||
\(605\) | − 19574.7i | − 1.31541i | ||||||||
\(606\) | 14559.3i | 0.975961i | ||||||||
\(607\) | 167.486i | 0.0111994i | 0.999984 | + | 0.00559971i | \(0.00178245\pi\) | ||||
−0.999984 | + | 0.00559971i | \(0.998218\pi\) | |||||||
\(608\) | 11026.9 | 0.735524 | ||||||||
\(609\) | − 2277.15i | − 0.151518i | ||||||||
\(610\) | 6197.29 | 0.411346 | ||||||||
\(611\) | −18277.0 | −1.21016 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6533.58 | −0.430487 | −0.215244 | − | 0.976560i | \(-0.569055\pi\) | ||||
−0.215244 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(614\) | 10151.4 | 0.667228 | ||||||||
\(615\) | 46139.3i | 3.02523i | ||||||||
\(616\) | −3346.12 | −0.218862 | ||||||||
\(617\) | − 9073.82i | − 0.592056i | −0.955179 | − | 0.296028i | \(-0.904338\pi\) | ||||
0.955179 | − | 0.296028i | \(-0.0956621\pi\) | |||||||
\(618\) | − 7664.75i | − 0.498902i | ||||||||
\(619\) | 26617.2i | 1.72833i | 0.503212 | + | 0.864163i | \(0.332151\pi\) | ||||
−0.503212 | + | 0.864163i | \(0.667849\pi\) | |||||||
\(620\) | 55.8495 | 0.00361769 | ||||||||
\(621\) | 12173.5 | 0.786641 | ||||||||
\(622\) | 5900.60i | 0.380374i | ||||||||
\(623\) | − 8417.32i | − 0.541304i | ||||||||
\(624\) | 7002.49i | 0.449237i | ||||||||
\(625\) | −13769.5 | −0.881246 | ||||||||
\(626\) | − 3044.52i | − 0.194383i | ||||||||
\(627\) | −8130.76 | −0.517881 | ||||||||
\(628\) | −8970.79 | −0.570022 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −24293.5 | −1.53631 | ||||||||
\(631\) | −5977.98 | −0.377147 | −0.188573 | − | 0.982059i | \(-0.560386\pi\) | ||||
−0.188573 | + | 0.982059i | \(0.560386\pi\) | |||||||
\(632\) | 5639.58i | 0.354953i | ||||||||
\(633\) | 21375.0 | 1.34215 | ||||||||
\(634\) | − 1811.26i | − 0.113461i | ||||||||
\(635\) | − 24941.6i | − 1.55870i | ||||||||
\(636\) | − 14849.2i | − 0.925803i | ||||||||
\(637\) | 5593.88 | 0.347940 | ||||||||
\(638\) | −492.995 | −0.0305922 | ||||||||
\(639\) | 40397.3i | 2.50093i | ||||||||
\(640\) | 2.20509i | 0 0.000136194i | ||||||||
\(641\) | 7927.25i | 0.488467i | 0.969716 | + | 0.244234i | \(0.0785363\pi\) | ||||
−0.969716 | + | 0.244234i | \(0.921464\pi\) | |||||||
\(642\) | −15700.7 | −0.965195 | ||||||||
\(643\) | 9197.33i | 0.564086i | 0.959402 | + | 0.282043i | \(0.0910121\pi\) | ||||
−0.959402 | + | 0.282043i | \(0.908988\pi\) | |||||||
\(644\) | −1824.83 | −0.111659 | ||||||||
\(645\) | 71771.5 | 4.38140 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19035.8 | 1.15669 | 0.578343 | − | 0.815794i | \(-0.303700\pi\) | ||||
0.578343 | + | 0.815794i | \(0.303700\pi\) | |||||||
\(648\) | −23101.7 | −1.40049 | ||||||||
\(649\) | 1653.57i | 0.100013i | ||||||||
\(650\) | −8658.79 | −0.522501 | ||||||||
\(651\) | − 116.039i | − 0.00698604i | ||||||||
\(652\) | 632.186i | 0.0379729i | ||||||||
\(653\) | 19349.6i | 1.15958i | 0.814764 | + | 0.579792i | \(0.196866\pi\) | ||||
−0.814764 | + | 0.579792i | \(0.803134\pi\) | |||||||
\(654\) | −33831.8 | −2.02283 | ||||||||
\(655\) | 4296.32 | 0.256292 | ||||||||
\(656\) | 8243.17i | 0.490613i | ||||||||
\(657\) | 44130.2i | 2.62052i | ||||||||
\(658\) | − 16735.7i | − 0.991528i | ||||||||
\(659\) | 16666.8 | 0.985201 | 0.492600 | − | 0.870256i | \(-0.336046\pi\) | ||||
0.492600 | + | 0.870256i | \(0.336046\pi\) | |||||||
\(660\) | − 5494.90i | − 0.324074i | ||||||||
\(661\) | 6024.30 | 0.354490 | 0.177245 | − | 0.984167i | \(-0.443281\pi\) | ||||
0.177245 | + | 0.984167i | \(0.443281\pi\) | |||||||
\(662\) | −5509.21 | −0.323446 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5781.14 | 0.337879 | ||||||||
\(665\) | 15789.8 | 0.920758 | ||||||||
\(666\) | − 26928.4i | − 1.56675i | ||||||||
\(667\) | −917.893 | −0.0532848 | ||||||||
\(668\) | 9137.16i | 0.529232i | ||||||||
\(669\) | 15884.9i | 0.918003i | ||||||||
\(670\) | − 28433.7i | − 1.63953i | ||||||||
\(671\) | 1971.40 | 0.113421 | ||||||||
\(672\) | 15483.3 | 0.888812 | ||||||||
\(673\) | − 27296.1i | − 1.56343i | −0.623637 | − | 0.781714i | \(-0.714346\pi\) | ||||
0.623637 | − | 0.781714i | \(-0.285654\pi\) | |||||||
\(674\) | 20041.1i | 1.14534i | ||||||||
\(675\) | − 37404.8i | − 2.13290i | ||||||||
\(676\) | 4512.91 | 0.256766 | ||||||||
\(677\) | − 13081.5i | − 0.742632i | −0.928507 | − | 0.371316i | \(-0.878907\pi\) | ||||
0.928507 | − | 0.371316i | \(-0.121093\pi\) | |||||||
\(678\) | 833.647 | 0.0472213 | ||||||||
\(679\) | −22567.9 | −1.27552 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40960.8 | 2.30487 | ||||||||
\(682\) | −25.1220 | −0.00141051 | ||||||||
\(683\) | 15698.0i | 0.879452i | 0.898132 | + | 0.439726i | \(0.144925\pi\) | ||||
−0.898132 | + | 0.439726i | \(0.855075\pi\) | |||||||
\(684\) | 14918.2 | 0.833936 | ||||||||
\(685\) | − 11140.9i | − 0.621422i | ||||||||
\(686\) | 14198.9i | 0.790258i | ||||||||
\(687\) | − 35813.3i | − 1.98888i | ||||||||
\(688\) | 12822.6 | 0.710547 | ||||||||
\(689\) | −14166.0 | −0.783281 | ||||||||
\(690\) | 14466.7i | 0.798170i | ||||||||
\(691\) | 13621.7i | 0.749919i | 0.927041 | + | 0.374959i | \(0.122343\pi\) | ||||
−0.927041 | + | 0.374959i | \(0.877657\pi\) | |||||||
\(692\) | 4815.19i | 0.264517i | ||||||||
\(693\) | −7727.93 | −0.423607 | ||||||||
\(694\) | 25916.7i | 1.41756i | ||||||||
\(695\) | 701.718 | 0.0382988 | ||||||||
\(696\) | 4562.21 | 0.248463 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −4086.08 | −0.221576 | ||||||||
\(699\) | −38082.9 | −2.06070 | ||||||||
\(700\) | 5607.07i | 0.302753i | ||||||||
\(701\) | 5733.01 | 0.308892 | 0.154446 | − | 0.988001i | \(-0.450641\pi\) | ||||
0.154446 | + | 0.988001i | \(0.450641\pi\) | |||||||
\(702\) | 16907.2i | 0.909004i | ||||||||
\(703\) | 17502.4i | 0.939000i | ||||||||
\(704\) | − 5721.96i | − 0.306327i | ||||||||
\(705\) | 93827.4 | 5.01240 | ||||||||
\(706\) | 16107.8 | 0.858674 | ||||||||
\(707\) | − 8994.20i | − 0.478447i | ||||||||
\(708\) | − 4482.16i | − 0.237924i | ||||||||
\(709\) | − 25474.5i | − 1.34939i | −0.738097 | − | 0.674694i | \(-0.764275\pi\) | ||||
0.738097 | − | 0.674694i | \(-0.235725\pi\) | |||||||
\(710\) | −25091.7 | −1.32630 | ||||||||
\(711\) | 13024.7i | 0.687011i | ||||||||
\(712\) | 16863.9 | 0.887642 | ||||||||
\(713\) | −46.7739 | −0.00245679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5242.05 | −0.274184 | ||||||||
\(716\) | −3882.19 | −0.202632 | ||||||||
\(717\) | 16272.1i | 0.847551i | ||||||||
\(718\) | −24935.1 | −1.29606 | ||||||||
\(719\) | − 15508.0i | − 0.804380i | −0.915556 | − | 0.402190i | \(-0.868249\pi\) | ||||
0.915556 | − | 0.402190i | \(-0.131751\pi\) | |||||||
\(720\) | − 24333.1i | − 1.25950i | ||||||||
\(721\) | 4734.99i | 0.244577i | ||||||||
\(722\) | −1136.99 | −0.0586070 | ||||||||
\(723\) | −22571.0 | −1.16103 | ||||||||
\(724\) | 9071.64i | 0.465670i | ||||||||
\(725\) | 2820.36i | 0.144477i | ||||||||
\(726\) | − 23866.8i | − 1.22008i | ||||||||
\(727\) | −32127.0 | −1.63896 | −0.819481 | − | 0.573106i | \(-0.805738\pi\) | ||||
−0.819481 | + | 0.573106i | \(0.805738\pi\) | |||||||
\(728\) | − 8652.65i | − 0.440506i | ||||||||
\(729\) | 13349.0 | 0.678200 | ||||||||
\(730\) | −27410.3 | −1.38973 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5343.68 | −0.269820 | ||||||||
\(733\) | −1723.27 | −0.0868353 | −0.0434177 | − | 0.999057i | \(-0.513825\pi\) | ||||
−0.0434177 | + | 0.999057i | \(0.513825\pi\) | |||||||
\(734\) | − 1520.89i | − 0.0764812i | ||||||||
\(735\) | −28716.9 | −1.44114 | ||||||||
\(736\) | − 6241.15i | − 0.312570i | ||||||||
\(737\) | − 9044.96i | − 0.452070i | ||||||||
\(738\) | 38079.5i | 1.89936i | ||||||||
\(739\) | −22411.5 | −1.11559 | −0.557796 | − | 0.829978i | \(-0.688353\pi\) | ||||
−0.557796 | + | 0.829978i | \(0.688353\pi\) | |||||||
\(740\) | −11828.4 | −0.587597 | ||||||||
\(741\) | − 21025.1i | − 1.04234i | ||||||||
\(742\) | − 12971.4i | − 0.641771i | ||||||||
\(743\) | 23971.3i | 1.18361i | 0.806082 | + | 0.591804i | \(0.201584\pi\) | ||||
−0.806082 | + | 0.591804i | \(0.798416\pi\) | |||||||
\(744\) | 232.481 | 0.0114558 | ||||||||
\(745\) | − 5443.59i | − 0.267701i | ||||||||
\(746\) | 19043.8 | 0.934642 | ||||||||
\(747\) | 13351.7 | 0.653964 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9699.26 | 0.473169 | ||||||||
\(750\) | 4305.64 | 0.209627 | ||||||||
\(751\) | − 26268.1i | − 1.27635i | −0.769892 | − | 0.638175i | \(-0.779690\pi\) | ||||
0.769892 | − | 0.638175i | \(-0.220310\pi\) | |||||||
\(752\) | 16763.0 | 0.812879 | ||||||||
\(753\) | 44098.3i | 2.13417i | ||||||||
\(754\) | − 1274.82i | − 0.0615733i | ||||||||
\(755\) | − 39475.6i | − 1.90287i | ||||||||
\(756\) | 10948.4 | 0.526706 | ||||||||
\(757\) | 345.842 | 0.0166048 | 0.00830239 | − | 0.999966i | \(-0.497357\pi\) | ||||
0.00830239 | + | 0.999966i | \(0.497357\pi\) | |||||||
\(758\) | 6740.42i | 0.322986i | ||||||||
\(759\) | 4601.97i | 0.220080i | ||||||||
\(760\) | 31634.6i | 1.50988i | ||||||||
\(761\) | 28929.2 | 1.37803 | 0.689015 | − | 0.724747i | \(-0.258043\pi\) | ||||
0.689015 | + | 0.724747i | \(0.258043\pi\) | |||||||
\(762\) | − 30410.5i | − 1.44574i | ||||||||
\(763\) | 20900.0 | 0.991652 | ||||||||
\(764\) | 4459.11 | 0.211159 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21074.9 | 0.994084 | ||||||||
\(767\) | −4275.92 | −0.201297 | ||||||||
\(768\) | 37444.2i | 1.75931i | ||||||||
\(769\) | −29320.3 | −1.37492 | −0.687462 | − | 0.726221i | \(-0.741275\pi\) | ||||
−0.687462 | + | 0.726221i | \(0.741275\pi\) | |||||||
\(770\) | − 4799.99i | − 0.224649i | ||||||||
\(771\) | 50814.6i | 2.37359i | ||||||||
\(772\) | 12552.0i | 0.585175i | ||||||||
\(773\) | −25830.3 | −1.20188 | −0.600938 | − | 0.799296i | \(-0.705206\pi\) | ||||
−0.600938 | + | 0.799296i | \(0.705206\pi\) | |||||||
\(774\) | 59234.2 | 2.75081 | ||||||||
\(775\) | 143.720i | 0.00666137i | ||||||||
\(776\) | − 45214.2i | − 2.09162i | ||||||||
\(777\) | 24576.0i | 1.13469i | ||||||||
\(778\) | 3836.37 | 0.176787 | ||||||||
\(779\) | − 24750.3i | − 1.13834i | ||||||||
\(780\) | 14209.1 | 0.652266 | ||||||||
\(781\) | −7981.85 | −0.365702 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5507.05 | 0.251349 | ||||||||
\(784\) | −5130.51 | −0.233715 | ||||||||
\(785\) | − 43933.7i | − 1.99753i | ||||||||
\(786\) | 5238.37 | 0.237718 | ||||||||
\(787\) | − 13639.9i | − 0.617801i | −0.951094 | − | 0.308900i | \(-0.900039\pi\) | ||||
0.951094 | − | 0.308900i | \(-0.0999610\pi\) | |||||||
\(788\) | 239.962i | 0.0108481i | ||||||||
\(789\) | − 28998.4i | − 1.30845i | ||||||||
\(790\) | −8089.94 | −0.364338 | ||||||||
\(791\) | −514.995 | −0.0231493 | ||||||||
\(792\) | − 15482.7i | − 0.694640i | ||||||||
\(793\) | 5097.80i | 0.228283i | ||||||||
\(794\) | 2601.56i | 0.116280i | ||||||||
\(795\) | 72722.9 | 3.24430 | ||||||||
\(796\) | − 8959.57i | − 0.398949i | ||||||||
\(797\) | −35932.1 | −1.59697 | −0.798483 | − | 0.602017i | \(-0.794364\pi\) | ||||
−0.798483 | + | 0.602017i | \(0.794364\pi\) | |||||||
\(798\) | 19252.1 | 0.854030 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −19176.8 | −0.847505 | ||||||||
\(801\) | 38947.5 | 1.71803 | ||||||||
\(802\) | − 29512.3i | − 1.29939i | ||||||||
\(803\) | −8719.42 | −0.383190 | ||||||||
\(804\) | 24517.3i | 1.07544i | ||||||||
\(805\) | − 8936.97i | − 0.391288i | ||||||||
\(806\) | − 64.9622i | − 0.00283895i | ||||||||
\(807\) | −26052.1 | −1.13640 | ||||||||
\(808\) | 18019.7 | 0.784566 | ||||||||
\(809\) | 19296.4i | 0.838598i | 0.907848 | + | 0.419299i | \(0.137724\pi\) | ||||
−0.907848 | + | 0.419299i | \(0.862276\pi\) | |||||||
\(810\) | − 33139.2i | − 1.43752i | ||||||||
\(811\) | 5464.45i | 0.236600i | 0.992978 | + | 0.118300i | \(0.0377445\pi\) | ||||
−0.992978 | + | 0.118300i | \(0.962256\pi\) | |||||||
\(812\) | −825.522 | −0.0356775 | ||||||||
\(813\) | 23448.6i | 1.01153i | ||||||||
\(814\) | 5320.61 | 0.229100 | ||||||||
\(815\) | −3096.08 | −0.133068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38500.0 | −1.64865 | ||||||||
\(818\) | 15902.0 | 0.679707 | ||||||||
\(819\) | − 19983.4i | − 0.852598i | ||||||||
\(820\) | 16726.6 | 0.712341 | ||||||||
\(821\) | − 16693.5i | − 0.709631i | −0.934936 | − | 0.354816i | \(-0.884544\pi\) | ||||
0.934936 | − | 0.354816i | \(-0.115456\pi\) | |||||||
\(822\) | − 13583.8i | − 0.576387i | ||||||||
\(823\) | − 5833.41i | − 0.247072i | −0.992340 | − | 0.123536i | \(-0.960577\pi\) | ||||
0.992340 | − | 0.123536i | \(-0.0394234\pi\) | |||||||
\(824\) | −9486.44 | −0.401063 | ||||||||
\(825\) | 14140.2 | 0.596726 | ||||||||
\(826\) | − 3915.33i | − 0.164930i | ||||||||
\(827\) | − 11048.3i | − 0.464556i | −0.972649 | − | 0.232278i | \(-0.925382\pi\) | ||||
0.972649 | − | 0.232278i | \(-0.0746180\pi\) | |||||||
\(828\) | − 8443.63i | − 0.354392i | ||||||||
\(829\) | −26287.1 | −1.10131 | −0.550657 | − | 0.834732i | \(-0.685623\pi\) | ||||
−0.550657 | + | 0.834732i | \(0.685623\pi\) | |||||||
\(830\) | 8293.01i | 0.346813i | ||||||||
\(831\) | −57233.4 | −2.38917 | ||||||||
\(832\) | 14796.3 | 0.616548 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 855.583 | 0.0355233 | ||||||||
\(835\) | −44748.4 | −1.85459 | ||||||||
\(836\) | 2947.60i | 0.121943i | ||||||||
\(837\) | 280.628 | 0.0115889 | ||||||||
\(838\) | − 7129.64i | − 0.293901i | ||||||||
\(839\) | − 8311.95i | − 0.342027i | −0.985269 | − | 0.171013i | \(-0.945296\pi\) | ||||
0.985269 | − | 0.171013i | \(-0.0547041\pi\) | |||||||
\(840\) | 44419.5i | 1.82455i | ||||||||
\(841\) | 23973.8 | 0.982974 | ||||||||
\(842\) | −21161.5 | −0.866119 | ||||||||
\(843\) | − 16523.8i | − 0.675101i | ||||||||
\(844\) | − 7748.97i | − 0.316032i | ||||||||
\(845\) | 22101.6i | 0.899785i | ||||||||
\(846\) | 77437.2 | 3.14698 | ||||||||
\(847\) | 14744.0i | 0.598122i | ||||||||
\(848\) | 12992.5 | 0.526139 | ||||||||
\(849\) | −11555.5 | −0.467118 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9906.29 | 0.399040 | ||||||||
\(852\) | 21635.6 | 0.869981 | ||||||||
\(853\) | 3875.16i | 0.155549i | 0.996971 | + | 0.0777743i | \(0.0247814\pi\) | ||||
−0.996971 | + | 0.0777743i | \(0.975219\pi\) | |||||||
\(854\) | −4667.91 | −0.187040 | ||||||||
\(855\) | 73060.6i | 2.92236i | ||||||||
\(856\) | 19432.2i | 0.775912i | ||||||||
\(857\) | 31317.9i | 1.24831i | 0.781301 | + | 0.624154i | \(0.214556\pi\) | ||||
−0.781301 | + | 0.624154i | \(0.785444\pi\) | |||||||
\(858\) | −6391.47 | −0.254314 | ||||||||
\(859\) | −35801.6 | −1.42204 | −0.711021 | − | 0.703171i | \(-0.751767\pi\) | ||||
−0.711021 | + | 0.703171i | \(0.751767\pi\) | |||||||
\(860\) | − 26018.9i | − 1.03167i | ||||||||
\(861\) | − 34753.0i | − 1.37558i | ||||||||
\(862\) | 16977.9i | 0.670847i | ||||||||
\(863\) | −5935.67 | −0.234128 | −0.117064 | − | 0.993124i | \(-0.537348\pi\) | ||||
−0.117064 | + | 0.993124i | \(0.537348\pi\) | |||||||
\(864\) | 37444.8i | 1.47442i | ||||||||
\(865\) | −23582.0 | −0.926950 | ||||||||
\(866\) | 11210.0 | 0.439875 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −42.0668 | −0.00164498 | ||||||||
\(869\) | −2573.47 | −0.100459 | ||||||||
\(870\) | 6544.46i | 0.255032i | ||||||||
\(871\) | 23389.1 | 0.909885 | ||||||||
\(872\) | 41872.6i | 1.62613i | ||||||||
\(873\) | − 104423.i | − 4.04832i | ||||||||
\(874\) | − 7760.29i | − 0.300338i | ||||||||
\(875\) | −2659.86 | −0.102765 | ||||||||
\(876\) | 23634.8 | 0.911583 | ||||||||
\(877\) | − 43699.3i | − 1.68258i | −0.540585 | − | 0.841290i | \(-0.681797\pi\) | ||||
0.540585 | − | 0.841290i | \(-0.318203\pi\) | |||||||
\(878\) | − 12256.4i | − 0.471110i | ||||||||
\(879\) | − 33899.7i | − 1.30081i | ||||||||
\(880\) | 4807.83 | 0.184173 | ||||||||
\(881\) | 30329.5i | 1.15985i | 0.814671 | + | 0.579924i | \(0.196918\pi\) | ||||
−0.814671 | + | 0.579924i | \(0.803082\pi\) | |||||||
\(882\) | −23700.5 | −0.904805 | ||||||||
\(883\) | 35558.7 | 1.35521 | 0.677603 | − | 0.735428i | \(-0.263019\pi\) | ||||
0.677603 | + | 0.735428i | \(0.263019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21951.0 | 0.833757 | ||||||||
\(886\) | −6538.11 | −0.247914 | ||||||||
\(887\) | − 23689.6i | − 0.896752i | −0.893845 | − | 0.448376i | \(-0.852003\pi\) | ||||
0.893845 | − | 0.448376i | \(-0.147997\pi\) | |||||||
\(888\) | −49237.3 | −1.86069 | ||||||||
\(889\) | 18786.5i | 0.708749i | ||||||||
\(890\) | 24191.1i | 0.911111i | ||||||||
\(891\) | − 10541.8i | − 0.396369i | ||||||||
\(892\) | 5758.65 | 0.216159 | ||||||||
\(893\) | −50331.3 | −1.88608 | ||||||||
\(894\) | − 6637.19i | − 0.248301i | ||||||||
\(895\) | − 19012.7i | − 0.710083i | ||||||||
\(896\) | − 1.66091i | 0 6.19277e-5i | ||||||||
\(897\) | −11900.1 | −0.442957 | ||||||||
\(898\) | − 28809.6i | − 1.07059i | ||||||||
\(899\) | −21.1596 | −0.000784998 0 | ||||||||
\(900\) | −25944.3 | −0.960900 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −7523.90 | −0.277737 | ||||||||
\(903\) | −54059.6 | −1.99224 | ||||||||
\(904\) | − 1031.78i | − 0.0379608i | ||||||||
\(905\) | −44427.6 | −1.63185 | ||||||||
\(906\) | − 48131.4i | − 1.76496i | ||||||||
\(907\) | 12176.0i | 0.445752i | 0.974847 | + | 0.222876i | \(0.0715445\pi\) | ||||
−0.974847 | + | 0.222876i | \(0.928456\pi\) | |||||||
\(908\) | − 14849.3i | − 0.542721i | ||||||||
\(909\) | 41616.8 | 1.51853 | ||||||||
\(910\) | 12412.2 | 0.452153 | ||||||||
\(911\) | 34830.5i | 1.26673i | 0.773855 | + | 0.633363i | \(0.218326\pi\) | ||||
−0.773855 | + | 0.633363i | \(0.781674\pi\) | |||||||
\(912\) | 19283.5i | 0.700154i | ||||||||
\(913\) | 2638.07i | 0.0956269i | ||||||||
\(914\) | −15716.4 | −0.568767 | ||||||||
\(915\) | − 26170.2i | − 0.945531i | ||||||||
\(916\) | −12983.2 | −0.468315 | ||||||||
\(917\) | −3236.07 | −0.116537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15886.7 | −0.570244 | −0.285122 | − | 0.958491i | \(-0.592034\pi\) | ||||
−0.285122 | + | 0.958491i | \(0.592034\pi\) | |||||||
\(920\) | 17905.0 | 0.641642 | ||||||||
\(921\) | − 42868.0i | − 1.53371i | ||||||||
\(922\) | 5585.44 | 0.199508 | ||||||||
\(923\) | − 20640.1i | − 0.736052i | ||||||||
\(924\) | 4138.85i | 0.147357i | ||||||||
\(925\) | − 30438.5i | − 1.08196i | ||||||||
\(926\) | 31156.6 | 1.10569 | ||||||||
\(927\) | −21909.1 | −0.776256 | ||||||||
\(928\) | − 2823.38i | − 0.0998728i | ||||||||
\(929\) | − 14115.7i | − 0.498514i | −0.968437 | − | 0.249257i | \(-0.919814\pi\) | ||||
0.968437 | − | 0.249257i | \(-0.0801864\pi\) | |||||||
\(930\) | 333.492i | 0.0117587i | ||||||||
\(931\) | 15404.5 | 0.542278 | ||||||||
\(932\) | 13806.0i | 0.485225i | ||||||||
\(933\) | 24917.4 | 0.874338 | ||||||||
\(934\) | 25318.6 | 0.886993 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40036.4 | 1.39811 | ||||||||
\(937\) | 39312.3 | 1.37063 | 0.685314 | − | 0.728248i | \(-0.259665\pi\) | ||||
0.685314 | + | 0.728248i | \(0.259665\pi\) | |||||||
\(938\) | 21416.7i | 0.745502i | ||||||||
\(939\) | −12856.6 | −0.446814 | ||||||||
\(940\) | − 34014.7i | − 1.18025i | ||||||||
\(941\) | 30478.0i | 1.05585i | 0.849291 | + | 0.527924i | \(0.177030\pi\) | ||||
−0.849291 | + | 0.527924i | \(0.822970\pi\) | |||||||
\(942\) | − 53567.0i | − 1.85277i | ||||||||
\(943\) | −14008.5 | −0.483754 | ||||||||
\(944\) | 3921.73 | 0.135213 | ||||||||
\(945\) | 53618.8i | 1.84574i | ||||||||
\(946\) | 11703.7i | 0.402242i | ||||||||
\(947\) | − 45331.1i | − 1.55551i | −0.628570 | − | 0.777753i | \(-0.716360\pi\) | ||||
0.628570 | − | 0.777753i | \(-0.283640\pi\) | |||||||
\(948\) | 6975.65 | 0.238986 | ||||||||
\(949\) | − 22547.3i | − 0.771250i | ||||||||
\(950\) | −23844.6 | −0.814339 | ||||||||
\(951\) | −7648.70 | −0.260806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33782.9 | 1.14830 | 0.574152 | − | 0.818748i | \(-0.305332\pi\) | ||||
0.574152 | + | 0.818748i | \(0.305332\pi\) | |||||||
\(954\) | 60019.3 | 2.03690 | ||||||||
\(955\) | 21838.1i | 0.739964i | ||||||||
\(956\) | 5899.04 | 0.199570 | ||||||||
\(957\) | 2081.84i | 0.0703202i | ||||||||
\(958\) | − 30300.7i | − 1.02189i | ||||||||
\(959\) | 8391.56i | 0.282563i | ||||||||
\(960\) | −75958.6 | −2.55370 | ||||||||
\(961\) | 29789.9 | 0.999964 | ||||||||
\(962\) | 13758.4i | 0.461111i | ||||||||
\(963\) | 44879.1i | 1.50178i | ||||||||
\(964\) | 8182.55i | 0.273384i | ||||||||
\(965\) | −61472.2 | −2.05063 | ||||||||
\(966\) | − 10896.6i | − 0.362931i | ||||||||
\(967\) | 45742.7 | 1.52119 | 0.760593 | − | 0.649229i | \(-0.224908\pi\) | ||||
0.760593 | + | 0.649229i | \(0.224908\pi\) | |||||||
\(968\) | −29539.2 | −0.980813 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 64859.5 | 2.14692 | ||||||||
\(971\) | −7001.98 | −0.231415 | −0.115708 | − | 0.993283i | \(-0.536914\pi\) | ||||
−0.115708 | + | 0.993283i | \(0.536914\pi\) | |||||||
\(972\) | 4393.31i | 0.144975i | ||||||||
\(973\) | −528.547 | −0.0174146 | ||||||||
\(974\) | 6252.64i | 0.205696i | ||||||||
\(975\) | 36564.8i | 1.20104i | ||||||||
\(976\) | − 4675.53i | − 0.153340i | ||||||||
\(977\) | −36142.8 | −1.18353 | −0.591767 | − | 0.806109i | \(-0.701569\pi\) | ||||
−0.591767 | + | 0.806109i | \(0.701569\pi\) | |||||||
\(978\) | −3774.95 | −0.123425 | ||||||||
\(979\) | 7695.39i | 0.251221i | ||||||||
\(980\) | 10410.6i | 0.339341i | ||||||||
\(981\) | 96705.6i | 3.14737i | ||||||||
\(982\) | 20392.0 | 0.662662 | ||||||||
\(983\) | 21919.3i | 0.711207i | 0.934637 | + | 0.355603i | \(0.115725\pi\) | ||||
−0.934637 | + | 0.355603i | \(0.884275\pi\) | |||||||
\(984\) | 69626.7 | 2.25571 | ||||||||
\(985\) | −1175.19 | −0.0380150 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70672.4 | −2.27916 | ||||||||
\(988\) | −7622.11 | −0.245437 | ||||||||
\(989\) | 21790.8i | 0.700614i | ||||||||
\(990\) | 22209.9 | 0.713006 | ||||||||
\(991\) | − 19931.0i | − 0.638880i | −0.947607 | − | 0.319440i | \(-0.896505\pi\) | ||||
0.947607 | − | 0.319440i | \(-0.103495\pi\) | |||||||
\(992\) | − 143.873i | − 0.00460482i | ||||||||
\(993\) | 23264.6i | 0.743483i | ||||||||
\(994\) | 18899.5 | 0.603074 | ||||||||
\(995\) | 43878.7 | 1.39804 | ||||||||
\(996\) | − 7150.75i | − 0.227490i | ||||||||
\(997\) | 18298.2i | 0.581253i | 0.956837 | + | 0.290626i | \(0.0938637\pi\) | ||||
−0.956837 | + | 0.290626i | \(0.906136\pi\) | |||||||
\(998\) | 1545.48i | 0.0490193i | ||||||||
\(999\) | −59434.5 | −1.88231 |
(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.b.f.288.17 | 24 | ||
17.4 | even | 4 | 289.4.a.h.1.4 | ✓ | 12 | ||
17.13 | even | 4 | 289.4.a.i.1.4 | yes | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.4 | ✓ | 12 | 17.4 | even | 4 | ||
289.4.a.i.1.4 | yes | 12 | 17.13 | even | 4 | ||
289.4.b.f.288.17 | 24 | 1.1 | even | 1 | trivial | ||
289.4.b.f.288.18 | 24 | 17.16 | even | 2 | inner |