Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,4,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(42.7763847542\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.27399\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63099 | −0.576643 | −0.288322 | − | 0.957534i | \(-0.593097\pi\) | ||||
−0.288322 | + | 0.957534i | \(0.593097\pi\) | |||||||
\(3\) | −9.87991 | −1.90139 | −0.950695 | − | 0.310128i | \(-0.899628\pi\) | ||||
−0.950695 | + | 0.310128i | \(0.899628\pi\) | |||||||
\(4\) | −5.33986 | −0.667483 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 16.1141 | 1.09642 | ||||||||
\(7\) | −5.21997 | −0.281852 | −0.140926 | − | 0.990020i | \(-0.545008\pi\) | ||||
−0.140926 | + | 0.990020i | \(0.545008\pi\) | |||||||
\(8\) | 21.7572 | 0.961543 | ||||||||
\(9\) | 70.6126 | 2.61528 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.55158 | −0.234400 | −0.117200 | − | 0.993108i | \(-0.537392\pi\) | ||||
−0.117200 | + | 0.993108i | \(0.537392\pi\) | |||||||
\(12\) | 52.7573 | 1.26914 | ||||||||
\(13\) | 11.3429 | 0.241996 | 0.120998 | − | 0.992653i | \(-0.461391\pi\) | ||||
0.120998 | + | 0.992653i | \(0.461391\pi\) | |||||||
\(14\) | 8.51374 | 0.162528 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.23299 | 0.113016 | ||||||||
\(17\) | −68.4740 | −0.976904 | −0.488452 | − | 0.872591i | \(-0.662438\pi\) | ||||
−0.488452 | + | 0.872591i | \(0.662438\pi\) | |||||||
\(18\) | −115.169 | −1.50808 | ||||||||
\(19\) | 6.93014 | 0.0836780 | 0.0418390 | − | 0.999124i | \(-0.486678\pi\) | ||||
0.0418390 | + | 0.999124i | \(0.486678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 51.5728 | 0.535910 | ||||||||
\(22\) | 13.9476 | 0.135165 | ||||||||
\(23\) | 132.042 | 1.19708 | 0.598538 | − | 0.801095i | \(-0.295749\pi\) | ||||
0.598538 | + | 0.801095i | \(0.295749\pi\) | |||||||
\(24\) | −214.959 | −1.82827 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −18.5001 | −0.139545 | ||||||||
\(27\) | −430.889 | −3.07128 | ||||||||
\(28\) | 27.8739 | 0.188131 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.419319 | −0.00242941 | −0.00121471 | − | 0.999999i | \(-0.500387\pi\) | ||||
−0.00121471 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(32\) | −185.855 | −1.02671 | ||||||||
\(33\) | 84.4888 | 0.445685 | ||||||||
\(34\) | 111.681 | 0.563325 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −377.061 | −1.74565 | ||||||||
\(37\) | −395.483 | −1.75722 | −0.878609 | − | 0.477542i | \(-0.841528\pi\) | ||||
−0.878609 | + | 0.477542i | \(0.841528\pi\) | |||||||
\(38\) | −11.3030 | −0.0482524 | ||||||||
\(39\) | −112.067 | −0.460128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −447.209 | −1.70347 | −0.851736 | − | 0.523971i | \(-0.824450\pi\) | ||||
−0.851736 | + | 0.523971i | \(0.824450\pi\) | |||||||
\(42\) | −84.1150 | −0.309029 | ||||||||
\(43\) | −184.132 | −0.653020 | −0.326510 | − | 0.945194i | \(-0.605873\pi\) | ||||
−0.326510 | + | 0.945194i | \(0.605873\pi\) | |||||||
\(44\) | 45.6642 | 0.156458 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −215.360 | −0.690285 | ||||||||
\(47\) | 97.2612 | 0.301851 | 0.150926 | − | 0.988545i | \(-0.451775\pi\) | ||||
0.150926 | + | 0.988545i | \(0.451775\pi\) | |||||||
\(48\) | −71.4613 | −0.214886 | ||||||||
\(49\) | −315.752 | −0.920559 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 676.516 | 1.85748 | ||||||||
\(52\) | −60.5693 | −0.161528 | ||||||||
\(53\) | 209.547 | 0.543086 | 0.271543 | − | 0.962426i | \(-0.412466\pi\) | ||||
0.271543 | + | 0.962426i | \(0.412466\pi\) | |||||||
\(54\) | 702.776 | 1.77103 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −113.572 | −0.271013 | ||||||||
\(57\) | −68.4691 | −0.159105 | ||||||||
\(58\) | 47.2988 | 0.107080 | ||||||||
\(59\) | 45.9651 | 0.101426 | 0.0507131 | − | 0.998713i | \(-0.483851\pi\) | ||||
0.0507131 | + | 0.998713i | \(0.483851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 427.655 | 0.897634 | 0.448817 | − | 0.893624i | \(-0.351846\pi\) | ||||
0.448817 | + | 0.893624i | \(0.351846\pi\) | |||||||
\(62\) | 0.683906 | 0.00140091 | ||||||||
\(63\) | −368.596 | −0.737122 | ||||||||
\(64\) | 245.264 | 0.479031 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −137.801 | −0.257001 | ||||||||
\(67\) | 405.055 | 0.738588 | 0.369294 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369294 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(68\) | 365.641 | 0.652067 | ||||||||
\(69\) | −1304.57 | −2.27611 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −557.971 | −0.932662 | −0.466331 | − | 0.884610i | \(-0.654424\pi\) | ||||
−0.466331 | + | 0.884610i | \(0.654424\pi\) | |||||||
\(72\) | 1536.33 | 2.51470 | ||||||||
\(73\) | 381.988 | 0.612443 | 0.306222 | − | 0.951960i | \(-0.400935\pi\) | ||||
0.306222 | + | 0.951960i | \(0.400935\pi\) | |||||||
\(74\) | 645.031 | 1.01329 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.0060 | −0.0558536 | ||||||||
\(77\) | 44.6390 | 0.0660660 | ||||||||
\(78\) | 182.780 | 0.265330 | ||||||||
\(79\) | 577.208 | 0.822038 | 0.411019 | − | 0.911627i | \(-0.365173\pi\) | ||||
0.411019 | + | 0.911627i | \(0.365173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2350.60 | 3.22442 | ||||||||
\(82\) | 729.396 | 0.982296 | ||||||||
\(83\) | 353.745 | 0.467813 | 0.233907 | − | 0.972259i | \(-0.424849\pi\) | ||||
0.233907 | + | 0.972259i | \(0.424849\pi\) | |||||||
\(84\) | −275.392 | −0.357711 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 300.318 | 0.376560 | ||||||||
\(87\) | 286.517 | 0.353079 | ||||||||
\(88\) | −186.059 | −0.225385 | ||||||||
\(89\) | −277.871 | −0.330947 | −0.165473 | − | 0.986214i | \(-0.552915\pi\) | ||||
−0.165473 | + | 0.986214i | \(0.552915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −59.2095 | −0.0682070 | ||||||||
\(92\) | −705.088 | −0.799027 | ||||||||
\(93\) | 4.14283 | 0.00461926 | ||||||||
\(94\) | −158.632 | −0.174060 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1836.23 | 1.95218 | ||||||||
\(97\) | −677.917 | −0.709609 | −0.354804 | − | 0.934941i | \(-0.615453\pi\) | ||||
−0.354804 | + | 0.934941i | \(0.615453\pi\) | |||||||
\(98\) | 514.989 | 0.530834 | ||||||||
\(99\) | −603.849 | −0.613022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 567.816 | 0.559404 | 0.279702 | − | 0.960087i | \(-0.409764\pi\) | ||||
0.279702 | + | 0.960087i | \(0.409764\pi\) | |||||||
\(102\) | −1103.39 | −1.07110 | ||||||||
\(103\) | −319.205 | −0.305362 | −0.152681 | − | 0.988276i | \(-0.548791\pi\) | ||||
−0.152681 | + | 0.988276i | \(0.548791\pi\) | |||||||
\(104\) | 246.789 | 0.232689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −341.771 | −0.313167 | ||||||||
\(107\) | 79.6547 | 0.0719674 | 0.0359837 | − | 0.999352i | \(-0.488544\pi\) | ||||
0.0359837 | + | 0.999352i | \(0.488544\pi\) | |||||||
\(108\) | 2300.88 | 2.05003 | ||||||||
\(109\) | −1708.43 | −1.50126 | −0.750632 | − | 0.660721i | \(-0.770251\pi\) | ||||
−0.750632 | + | 0.660721i | \(0.770251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3907.34 | 3.34116 | ||||||||
\(112\) | −37.7560 | −0.0318536 | ||||||||
\(113\) | −1050.31 | −0.874383 | −0.437191 | − | 0.899369i | \(-0.644027\pi\) | ||||
−0.437191 | + | 0.899369i | \(0.644027\pi\) | |||||||
\(114\) | 111.673 | 0.0917465 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 154.856 | 0.123948 | ||||||||
\(117\) | 800.950 | 0.632887 | ||||||||
\(118\) | −74.9687 | −0.0584867 | ||||||||
\(119\) | 357.432 | 0.275342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1257.87 | −0.945057 | ||||||||
\(122\) | −697.503 | −0.517615 | ||||||||
\(123\) | 4418.39 | 3.23896 | ||||||||
\(124\) | 2.23910 | 0.00162159 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 601.177 | 0.425057 | ||||||||
\(127\) | −366.926 | −0.256373 | −0.128187 | − | 0.991750i | \(-0.540916\pi\) | ||||
−0.128187 | + | 0.991750i | \(0.540916\pi\) | |||||||
\(128\) | 1086.81 | 0.750482 | ||||||||
\(129\) | 1819.21 | 1.24165 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2310.86 | 1.54123 | 0.770614 | − | 0.637302i | \(-0.219950\pi\) | ||||
0.770614 | + | 0.637302i | \(0.219950\pi\) | |||||||
\(132\) | −451.158 | −0.297487 | ||||||||
\(133\) | −36.1751 | −0.0235848 | ||||||||
\(134\) | −660.643 | −0.425902 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1489.80 | −0.939335 | ||||||||
\(137\) | −1899.65 | −1.18466 | −0.592329 | − | 0.805696i | \(-0.701791\pi\) | ||||
−0.592329 | + | 0.805696i | \(0.701791\pi\) | |||||||
\(138\) | 2127.74 | 1.31250 | ||||||||
\(139\) | 1309.49 | 0.799061 | 0.399531 | − | 0.916720i | \(-0.369173\pi\) | ||||
0.399531 | + | 0.916720i | \(0.369173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −960.932 | −0.573937 | ||||||||
\(142\) | 910.047 | 0.537813 | ||||||||
\(143\) | −96.9994 | −0.0567238 | ||||||||
\(144\) | 510.740 | 0.295567 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −623.020 | −0.353161 | ||||||||
\(147\) | 3119.60 | 1.75034 | ||||||||
\(148\) | 2111.83 | 1.17291 | ||||||||
\(149\) | 1782.98 | 0.980320 | 0.490160 | − | 0.871632i | \(-0.336938\pi\) | ||||
0.490160 | + | 0.871632i | \(0.336938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1631.96 | −0.879515 | −0.439758 | − | 0.898116i | \(-0.644936\pi\) | ||||
−0.439758 | + | 0.898116i | \(0.644936\pi\) | |||||||
\(152\) | 150.781 | 0.0804600 | ||||||||
\(153\) | −4835.12 | −2.55488 | ||||||||
\(154\) | −72.8059 | −0.0380965 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 598.420 | 0.307128 | ||||||||
\(157\) | −852.817 | −0.433517 | −0.216759 | − | 0.976225i | \(-0.569548\pi\) | ||||
−0.216759 | + | 0.976225i | \(0.569548\pi\) | |||||||
\(158\) | −941.422 | −0.474022 | ||||||||
\(159\) | −2070.31 | −1.03262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −689.257 | −0.337398 | ||||||||
\(162\) | −3833.81 | −1.85934 | ||||||||
\(163\) | −3280.24 | −1.57625 | −0.788123 | − | 0.615518i | \(-0.788947\pi\) | ||||
−0.788123 | + | 0.615518i | \(0.788947\pi\) | |||||||
\(164\) | 2388.04 | 1.13704 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −576.955 | −0.269761 | ||||||||
\(167\) | 1682.26 | 0.779504 | 0.389752 | − | 0.920920i | \(-0.372561\pi\) | ||||
0.389752 | + | 0.920920i | \(0.372561\pi\) | |||||||
\(168\) | 1122.08 | 0.515301 | ||||||||
\(169\) | −2068.34 | −0.941438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 489.355 | 0.218842 | ||||||||
\(172\) | 983.239 | 0.435879 | ||||||||
\(173\) | 1590.22 | 0.698854 | 0.349427 | − | 0.936964i | \(-0.386376\pi\) | ||||
0.349427 | + | 0.936964i | \(0.386376\pi\) | |||||||
\(174\) | −467.308 | −0.203601 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −61.8535 | −0.0264908 | ||||||||
\(177\) | −454.131 | −0.192851 | ||||||||
\(178\) | 453.206 | 0.190838 | ||||||||
\(179\) | −1794.60 | −0.749356 | −0.374678 | − | 0.927155i | \(-0.622247\pi\) | ||||
−0.374678 | + | 0.927155i | \(0.622247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2353.41 | 0.966450 | 0.483225 | − | 0.875496i | \(-0.339465\pi\) | ||||
0.483225 | + | 0.875496i | \(0.339465\pi\) | |||||||
\(182\) | 96.5702 | 0.0393311 | ||||||||
\(183\) | −4225.20 | −1.70675 | ||||||||
\(184\) | 2872.88 | 1.15104 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.75693 | −0.00266367 | ||||||||
\(187\) | 585.560 | 0.228986 | ||||||||
\(188\) | −519.361 | −0.201480 | ||||||||
\(189\) | 2249.23 | 0.865646 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2184.35 | −0.827508 | −0.413754 | − | 0.910389i | \(-0.635783\pi\) | ||||
−0.413754 | + | 0.910389i | \(0.635783\pi\) | |||||||
\(192\) | −2423.19 | −0.910825 | ||||||||
\(193\) | 3109.71 | 1.15980 | 0.579901 | − | 0.814687i | \(-0.303091\pi\) | ||||
0.579901 | + | 0.814687i | \(0.303091\pi\) | |||||||
\(194\) | 1105.68 | 0.409191 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1686.07 | 0.614457 | ||||||||
\(197\) | −923.756 | −0.334086 | −0.167043 | − | 0.985950i | \(-0.553422\pi\) | ||||
−0.167043 | + | 0.985950i | \(0.553422\pi\) | |||||||
\(198\) | 984.874 | 0.353495 | ||||||||
\(199\) | 4548.71 | 1.62035 | 0.810174 | − | 0.586189i | \(-0.199372\pi\) | ||||
0.810174 | + | 0.586189i | \(0.199372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4001.91 | −1.40434 | ||||||||
\(202\) | −926.103 | −0.322576 | ||||||||
\(203\) | 151.379 | 0.0523386 | ||||||||
\(204\) | −3612.50 | −1.23983 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 520.622 | 0.176085 | ||||||||
\(207\) | 9323.85 | 3.13069 | ||||||||
\(208\) | 82.0429 | 0.0273493 | ||||||||
\(209\) | −59.2636 | −0.0196141 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −318.664 | −0.103970 | −0.0519851 | − | 0.998648i | \(-0.516555\pi\) | ||||
−0.0519851 | + | 0.998648i | \(0.516555\pi\) | |||||||
\(212\) | −1118.95 | −0.362500 | ||||||||
\(213\) | 5512.70 | 1.77335 | ||||||||
\(214\) | −129.916 | −0.0414995 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9374.94 | −2.95317 | ||||||||
\(217\) | 2.18883 | 0.000684735 0 | ||||||||
\(218\) | 2786.44 | 0.865694 | ||||||||
\(219\) | −3774.01 | −1.16449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −776.691 | −0.236407 | ||||||||
\(222\) | −6372.85 | −1.92666 | ||||||||
\(223\) | −1706.70 | −0.512509 | −0.256254 | − | 0.966609i | \(-0.582488\pi\) | ||||
−0.256254 | + | 0.966609i | \(0.582488\pi\) | |||||||
\(224\) | 970.157 | 0.289381 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1713.06 | 0.504207 | ||||||||
\(227\) | −3043.63 | −0.889925 | −0.444962 | − | 0.895549i | \(-0.646783\pi\) | ||||
−0.444962 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(228\) | 365.616 | 0.106199 | ||||||||
\(229\) | −2621.57 | −0.756500 | −0.378250 | − | 0.925704i | \(-0.623474\pi\) | ||||
−0.378250 | + | 0.925704i | \(0.623474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −441.029 | −0.125617 | ||||||||
\(232\) | −630.960 | −0.178554 | ||||||||
\(233\) | 2778.73 | 0.781291 | 0.390646 | − | 0.920541i | \(-0.372252\pi\) | ||||
0.390646 | + | 0.920541i | \(0.372252\pi\) | |||||||
\(234\) | −1306.34 | −0.364950 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −245.447 | −0.0677002 | ||||||||
\(237\) | −5702.76 | −1.56301 | ||||||||
\(238\) | −582.969 | −0.158774 | ||||||||
\(239\) | 4722.67 | 1.27818 | 0.639088 | − | 0.769133i | \(-0.279312\pi\) | ||||
0.639088 | + | 0.769133i | \(0.279312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4704.13 | −1.25734 | −0.628672 | − | 0.777671i | \(-0.716401\pi\) | ||||
−0.628672 | + | 0.777671i | \(0.716401\pi\) | |||||||
\(242\) | 2051.58 | 0.544961 | ||||||||
\(243\) | −11589.7 | −3.05959 | ||||||||
\(244\) | −2283.62 | −0.599155 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7206.36 | −1.86773 | ||||||||
\(247\) | 78.6076 | 0.0202497 | ||||||||
\(248\) | −9.12321 | −0.00233599 | ||||||||
\(249\) | −3494.96 | −0.889496 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4449.07 | 1.11882 | 0.559408 | − | 0.828893i | \(-0.311029\pi\) | ||||
0.559408 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(252\) | 1968.25 | 0.492016 | ||||||||
\(253\) | −1129.17 | −0.280594 | ||||||||
\(254\) | 598.454 | 0.147836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3734.70 | −0.911792 | ||||||||
\(257\) | −7226.68 | −1.75404 | −0.877019 | − | 0.480456i | \(-0.840471\pi\) | ||||
−0.877019 | + | 0.480456i | \(0.840471\pi\) | |||||||
\(258\) | −2967.11 | −0.715986 | ||||||||
\(259\) | 2064.41 | 0.495275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2047.77 | −0.485646 | ||||||||
\(262\) | −3769.00 | −0.888739 | ||||||||
\(263\) | 4789.59 | 1.12296 | 0.561481 | − | 0.827490i | \(-0.310232\pi\) | ||||
0.561481 | + | 0.827490i | \(0.310232\pi\) | |||||||
\(264\) | 1838.24 | 0.428545 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 59.0014 | 0.0136000 | ||||||||
\(267\) | 2745.34 | 0.629259 | ||||||||
\(268\) | −2162.94 | −0.492995 | ||||||||
\(269\) | −47.0448 | −0.0106631 | −0.00533154 | − | 0.999986i | \(-0.501697\pi\) | ||||
−0.00533154 | + | 0.999986i | \(0.501697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7721.78 | 1.73087 | 0.865433 | − | 0.501025i | \(-0.167044\pi\) | ||||
0.865433 | + | 0.501025i | \(0.167044\pi\) | |||||||
\(272\) | −495.272 | −0.110405 | ||||||||
\(273\) | 584.984 | 0.129688 | ||||||||
\(274\) | 3098.32 | 0.683125 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6966.20 | 1.51926 | ||||||||
\(277\) | 7554.66 | 1.63868 | 0.819342 | − | 0.573305i | \(-0.194339\pi\) | ||||
0.819342 | + | 0.573305i | \(0.194339\pi\) | |||||||
\(278\) | −2135.77 | −0.460773 | ||||||||
\(279\) | −29.6092 | −0.00635360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2094.83 | −0.444723 | −0.222361 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222361 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(282\) | 1567.27 | 0.330957 | ||||||||
\(283\) | 8200.83 | 1.72257 | 0.861287 | − | 0.508119i | \(-0.169659\pi\) | ||||
0.861287 | + | 0.508119i | \(0.169659\pi\) | |||||||
\(284\) | 2979.49 | 0.622536 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 158.205 | 0.0327094 | ||||||||
\(287\) | 2334.42 | 0.480127 | ||||||||
\(288\) | −13123.7 | −2.68514 | ||||||||
\(289\) | −224.318 | −0.0456580 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6697.76 | 1.34924 | ||||||||
\(292\) | −2039.76 | −0.408795 | ||||||||
\(293\) | −3518.87 | −0.701620 | −0.350810 | − | 0.936447i | \(-0.614094\pi\) | ||||
−0.350810 | + | 0.936447i | \(0.614094\pi\) | |||||||
\(294\) | −5088.05 | −1.00932 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8604.62 | −1.68964 | ||||||||
\(297\) | 3684.78 | 0.719907 | ||||||||
\(298\) | −2908.03 | −0.565295 | ||||||||
\(299\) | 1497.74 | 0.289687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 961.163 | 0.184055 | ||||||||
\(302\) | 2661.71 | 0.507167 | ||||||||
\(303\) | −5609.97 | −1.06364 | ||||||||
\(304\) | 50.1256 | 0.00945691 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7886.06 | 1.47325 | ||||||||
\(307\) | 8725.36 | 1.62209 | 0.811046 | − | 0.584982i | \(-0.198898\pi\) | ||||
0.811046 | + | 0.584982i | \(0.198898\pi\) | |||||||
\(308\) | −238.366 | −0.0440979 | ||||||||
\(309\) | 3153.72 | 0.580611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2640.09 | 0.481370 | 0.240685 | − | 0.970603i | \(-0.422628\pi\) | ||||
0.240685 | + | 0.970603i | \(0.422628\pi\) | |||||||
\(312\) | −2438.26 | −0.442433 | ||||||||
\(313\) | 1938.00 | 0.349976 | 0.174988 | − | 0.984571i | \(-0.444011\pi\) | ||||
0.174988 | + | 0.984571i | \(0.444011\pi\) | |||||||
\(314\) | 1390.94 | 0.249985 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3082.21 | −0.548696 | ||||||||
\(317\) | 5546.11 | 0.982651 | 0.491326 | − | 0.870976i | \(-0.336512\pi\) | ||||
0.491326 | + | 0.870976i | \(0.336512\pi\) | |||||||
\(318\) | 3376.66 | 0.595452 | ||||||||
\(319\) | 247.996 | 0.0435270 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −786.981 | −0.136838 | ||||||||
\(322\) | 1124.17 | 0.194558 | ||||||||
\(323\) | −474.534 | −0.0817454 | ||||||||
\(324\) | −12551.9 | −2.15224 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5350.04 | 0.908931 | ||||||||
\(327\) | 16879.1 | 2.85449 | ||||||||
\(328\) | −9730.04 | −1.63796 | ||||||||
\(329\) | −507.701 | −0.0850773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 185.492 | 0.0308023 | 0.0154012 | − | 0.999881i | \(-0.495097\pi\) | ||||
0.0154012 | + | 0.999881i | \(0.495097\pi\) | |||||||
\(332\) | −1888.95 | −0.312257 | ||||||||
\(333\) | −27926.1 | −4.59562 | ||||||||
\(334\) | −2743.76 | −0.449496 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 373.026 | 0.0605662 | ||||||||
\(337\) | 8508.32 | 1.37530 | 0.687652 | − | 0.726040i | \(-0.258641\pi\) | ||||
0.687652 | + | 0.726040i | \(0.258641\pi\) | |||||||
\(338\) | 3373.45 | 0.542874 | ||||||||
\(339\) | 10377.0 | 1.66254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.58584 | 0.000569454 0 | ||||||||
\(342\) | −798.135 | −0.126194 | ||||||||
\(343\) | 3438.67 | 0.541313 | ||||||||
\(344\) | −4006.20 | −0.627906 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2593.63 | −0.402990 | ||||||||
\(347\) | −7853.53 | −1.21498 | −0.607492 | − | 0.794326i | \(-0.707824\pi\) | ||||
−0.607492 | + | 0.794326i | \(0.707824\pi\) | |||||||
\(348\) | −1529.96 | −0.235674 | ||||||||
\(349\) | 6328.33 | 0.970624 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4887.51 | −0.743237 | ||||||||
\(352\) | 1589.35 | 0.240661 | ||||||||
\(353\) | 7973.45 | 1.20222 | 0.601111 | − | 0.799166i | \(-0.294725\pi\) | ||||
0.601111 | + | 0.799166i | \(0.294725\pi\) | |||||||
\(354\) | 740.684 | 0.111206 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1483.79 | 0.220901 | ||||||||
\(357\) | −3531.40 | −0.523533 | ||||||||
\(358\) | 2926.98 | 0.432111 | ||||||||
\(359\) | −10059.4 | −1.47887 | −0.739435 | − | 0.673228i | \(-0.764907\pi\) | ||||
−0.739435 | + | 0.673228i | \(0.764907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6810.97 | −0.992998 | ||||||||
\(362\) | −3838.39 | −0.557297 | ||||||||
\(363\) | 12427.6 | 1.79692 | ||||||||
\(364\) | 316.170 | 0.0455270 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6891.27 | 0.984187 | ||||||||
\(367\) | 3032.67 | 0.431346 | 0.215673 | − | 0.976466i | \(-0.430805\pi\) | ||||
0.215673 | + | 0.976466i | \(0.430805\pi\) | |||||||
\(368\) | 955.061 | 0.135288 | ||||||||
\(369\) | −31578.6 | −4.45506 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1093.83 | −0.153070 | ||||||||
\(372\) | −22.1221 | −0.00308328 | ||||||||
\(373\) | 11109.4 | 1.54215 | 0.771077 | − | 0.636742i | \(-0.219718\pi\) | ||||
0.771077 | + | 0.636742i | \(0.219718\pi\) | |||||||
\(374\) | −955.045 | −0.132043 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2116.13 | 0.290243 | ||||||||
\(377\) | −328.943 | −0.0449375 | ||||||||
\(378\) | −3668.47 | −0.499169 | ||||||||
\(379\) | 4510.20 | 0.611275 | 0.305638 | − | 0.952148i | \(-0.401130\pi\) | ||||
0.305638 | + | 0.952148i | \(0.401130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3625.20 | 0.487466 | ||||||||
\(382\) | 3562.66 | 0.477177 | ||||||||
\(383\) | −7810.96 | −1.04209 | −0.521047 | − | 0.853528i | \(-0.674458\pi\) | ||||
−0.521047 | + | 0.853528i | \(0.674458\pi\) | |||||||
\(384\) | −10737.6 | −1.42696 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5071.92 | −0.668792 | ||||||||
\(387\) | −13002.0 | −1.70783 | ||||||||
\(388\) | 3619.98 | 0.473652 | ||||||||
\(389\) | 9221.90 | 1.20198 | 0.600989 | − | 0.799258i | \(-0.294774\pi\) | ||||
0.600989 | + | 0.799258i | \(0.294774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9041.46 | −1.16943 | ||||||||
\(392\) | −6869.88 | −0.885157 | ||||||||
\(393\) | −22831.1 | −2.93047 | ||||||||
\(394\) | 1506.64 | 0.192648 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3224.47 | 0.409181 | ||||||||
\(397\) | 10034.3 | 1.26854 | 0.634268 | − | 0.773113i | \(-0.281301\pi\) | ||||
0.634268 | + | 0.773113i | \(0.281301\pi\) | |||||||
\(398\) | −7418.91 | −0.934363 | ||||||||
\(399\) | 357.407 | 0.0448439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8193.64 | −1.02038 | −0.510188 | − | 0.860063i | \(-0.670424\pi\) | ||||
−0.510188 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(402\) | 6527.09 | 0.809805 | ||||||||
\(403\) | −4.75628 | −0.000587908 0 | ||||||||
\(404\) | −3032.06 | −0.373392 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −246.898 | −0.0301807 | ||||||||
\(407\) | 3382.01 | 0.411892 | ||||||||
\(408\) | 14719.1 | 1.78604 | ||||||||
\(409\) | 3921.69 | 0.474120 | 0.237060 | − | 0.971495i | \(-0.423816\pi\) | ||||
0.237060 | + | 0.971495i | \(0.423816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18768.4 | 2.25250 | ||||||||
\(412\) | 1704.51 | 0.203824 | ||||||||
\(413\) | −239.936 | −0.0285872 | ||||||||
\(414\) | −15207.1 | −1.80529 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2108.13 | −0.248460 | ||||||||
\(417\) | −12937.6 | −1.51933 | ||||||||
\(418\) | 96.6586 | 0.0113103 | ||||||||
\(419\) | 3026.66 | 0.352892 | 0.176446 | − | 0.984310i | \(-0.443540\pi\) | ||||
0.176446 | + | 0.984310i | \(0.443540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4823.43 | 0.558384 | 0.279192 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279192 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(422\) | 519.739 | 0.0599538 | ||||||||
\(423\) | 6867.87 | 0.789426 | ||||||||
\(424\) | 4559.17 | 0.522200 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8991.19 | −1.02259 | ||||||||
\(427\) | −2232.35 | −0.253000 | ||||||||
\(428\) | −425.345 | −0.0480370 | ||||||||
\(429\) | 958.346 | 0.107854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2029.51 | −0.226816 | −0.113408 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113408 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(432\) | −3116.61 | −0.347102 | ||||||||
\(433\) | 535.808 | 0.0594672 | 0.0297336 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297336 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(434\) | −3.56997 | −0.000394848 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9122.77 | 1.00207 | ||||||||
\(437\) | 915.072 | 0.100169 | ||||||||
\(438\) | 6155.38 | 0.671497 | ||||||||
\(439\) | 8791.74 | 0.955824 | 0.477912 | − | 0.878408i | \(-0.341394\pi\) | ||||
0.477912 | + | 0.878408i | \(0.341394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22296.1 | −2.40752 | ||||||||
\(442\) | 1266.78 | 0.136322 | ||||||||
\(443\) | −13916.9 | −1.49258 | −0.746291 | − | 0.665619i | \(-0.768167\pi\) | ||||
−0.746291 | + | 0.665619i | \(0.768167\pi\) | |||||||
\(444\) | −20864.7 | −2.23016 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2783.62 | 0.295535 | ||||||||
\(447\) | −17615.7 | −1.86397 | ||||||||
\(448\) | −1280.27 | −0.135016 | ||||||||
\(449\) | 2129.54 | 0.223829 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3824.35 | 0.399294 | ||||||||
\(452\) | 5608.53 | 0.583635 | ||||||||
\(453\) | 16123.6 | 1.67230 | ||||||||
\(454\) | 4964.14 | 0.513169 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1489.70 | −0.152986 | ||||||||
\(457\) | −1932.25 | −0.197783 | −0.0988915 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988915 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(458\) | 4275.77 | 0.436231 | ||||||||
\(459\) | 29504.6 | 3.00035 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16518.3 | −1.66884 | −0.834418 | − | 0.551132i | \(-0.814196\pi\) | ||||
−0.834418 | + | 0.551132i | \(0.814196\pi\) | |||||||
\(462\) | 719.316 | 0.0724364 | ||||||||
\(463\) | −11535.2 | −1.15785 | −0.578926 | − | 0.815380i | \(-0.696528\pi\) | ||||
−0.578926 | + | 0.815380i | \(0.696528\pi\) | |||||||
\(464\) | −209.757 | −0.0209865 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4532.10 | −0.450526 | ||||||||
\(467\) | −15667.8 | −1.55250 | −0.776250 | − | 0.630425i | \(-0.782880\pi\) | ||||
−0.776250 | + | 0.630425i | \(0.782880\pi\) | |||||||
\(468\) | −4276.96 | −0.422441 | ||||||||
\(469\) | −2114.38 | −0.208172 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8425.75 | 0.824285 | ||||||||
\(472\) | 1000.07 | 0.0975255 | ||||||||
\(473\) | 1574.62 | 0.153068 | ||||||||
\(474\) | 9301.17 | 0.901301 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1908.64 | −0.183786 | ||||||||
\(477\) | 14796.7 | 1.42032 | ||||||||
\(478\) | −7702.65 | −0.737052 | ||||||||
\(479\) | 4672.28 | 0.445682 | 0.222841 | − | 0.974855i | \(-0.428467\pi\) | ||||
0.222841 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4485.92 | −0.425239 | ||||||||
\(482\) | 7672.41 | 0.725038 | ||||||||
\(483\) | 6809.80 | 0.641525 | ||||||||
\(484\) | 6716.85 | 0.630809 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18902.8 | 1.76429 | ||||||||
\(487\) | 8465.76 | 0.787722 | 0.393861 | − | 0.919170i | \(-0.371139\pi\) | ||||
0.393861 | + | 0.919170i | \(0.371139\pi\) | |||||||
\(488\) | 9304.60 | 0.863113 | ||||||||
\(489\) | 32408.4 | 2.99706 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12302.6 | −1.13077 | −0.565385 | − | 0.824827i | \(-0.691272\pi\) | ||||
−0.565385 | + | 0.824827i | \(0.691272\pi\) | |||||||
\(492\) | −23593.6 | −2.16195 | ||||||||
\(493\) | 1985.74 | 0.181407 | ||||||||
\(494\) | −128.209 | −0.0116769 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.03293 | −0.000274562 0 | ||||||||
\(497\) | 2912.59 | 0.262873 | ||||||||
\(498\) | 5700.26 | 0.512922 | ||||||||
\(499\) | −2781.31 | −0.249516 | −0.124758 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124758 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16620.6 | −1.48214 | ||||||||
\(502\) | −7256.40 | −0.645158 | ||||||||
\(503\) | 13673.9 | 1.21211 | 0.606054 | − | 0.795424i | \(-0.292752\pi\) | ||||
0.606054 | + | 0.795424i | \(0.292752\pi\) | |||||||
\(504\) | −8019.62 | −0.708774 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1841.67 | 0.161803 | ||||||||
\(507\) | 20435.0 | 1.79004 | ||||||||
\(508\) | 1959.33 | 0.171125 | ||||||||
\(509\) | 7431.68 | 0.647158 | 0.323579 | − | 0.946201i | \(-0.395114\pi\) | ||||
0.323579 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1993.97 | −0.172618 | ||||||||
\(512\) | −2603.24 | −0.224704 | ||||||||
\(513\) | −2986.12 | −0.256999 | ||||||||
\(514\) | 11786.7 | 1.01145 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9714.31 | −0.828776 | ||||||||
\(517\) | −831.737 | −0.0707538 | ||||||||
\(518\) | −3367.04 | −0.285597 | ||||||||
\(519\) | −15711.2 | −1.32879 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7797.86 | 0.655721 | 0.327860 | − | 0.944726i | \(-0.393672\pi\) | ||||
0.327860 | + | 0.944726i | \(0.393672\pi\) | |||||||
\(522\) | 3339.89 | 0.280044 | ||||||||
\(523\) | 16670.9 | 1.39382 | 0.696908 | − | 0.717160i | \(-0.254558\pi\) | ||||
0.696908 | + | 0.717160i | \(0.254558\pi\) | |||||||
\(524\) | −12339.7 | −1.02874 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7811.79 | −0.647548 | ||||||||
\(527\) | 28.7124 | 0.00237331 | ||||||||
\(528\) | 611.107 | 0.0503693 | ||||||||
\(529\) | 5268.18 | 0.432990 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3245.71 | 0.265258 | ||||||||
\(532\) | 193.170 | 0.0157425 | ||||||||
\(533\) | −5072.64 | −0.412233 | ||||||||
\(534\) | −4477.63 | −0.362858 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8812.88 | 0.710184 | ||||||||
\(537\) | 17730.5 | 1.42482 | ||||||||
\(538\) | 76.7297 | 0.00614880 | ||||||||
\(539\) | 2700.18 | 0.215779 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13400.1 | 1.06491 | 0.532455 | − | 0.846458i | \(-0.321270\pi\) | ||||
0.532455 | + | 0.846458i | \(0.321270\pi\) | |||||||
\(542\) | −12594.2 | −0.998092 | ||||||||
\(543\) | −23251.5 | −1.83760 | ||||||||
\(544\) | 12726.2 | 1.00300 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −954.105 | −0.0747838 | ||||||||
\(547\) | 17339.4 | 1.35535 | 0.677677 | − | 0.735360i | \(-0.262987\pi\) | ||||
0.677677 | + | 0.735360i | \(0.262987\pi\) | |||||||
\(548\) | 10143.9 | 0.790739 | ||||||||
\(549\) | 30197.9 | 2.34757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −200.974 | −0.0155386 | ||||||||
\(552\) | −28383.7 | −2.18857 | ||||||||
\(553\) | −3013.01 | −0.231693 | ||||||||
\(554\) | −12321.6 | −0.944936 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6992.50 | −0.533360 | ||||||||
\(557\) | 7790.90 | 0.592659 | 0.296330 | − | 0.955086i | \(-0.404237\pi\) | ||||
0.296330 | + | 0.955086i | \(0.404237\pi\) | |||||||
\(558\) | 48.2924 | 0.00366376 | ||||||||
\(559\) | −2088.58 | −0.158028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5785.28 | −0.435392 | ||||||||
\(562\) | 3416.66 | 0.256447 | ||||||||
\(563\) | 21514.2 | 1.61051 | 0.805253 | − | 0.592932i | \(-0.202030\pi\) | ||||
0.805253 | + | 0.592932i | \(0.202030\pi\) | |||||||
\(564\) | 5131.24 | 0.383093 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13375.5 | −0.993311 | ||||||||
\(567\) | −12270.1 | −0.908808 | ||||||||
\(568\) | −12139.9 | −0.896794 | ||||||||
\(569\) | 16993.5 | 1.25203 | 0.626015 | − | 0.779811i | \(-0.284685\pi\) | ||||
0.626015 | + | 0.779811i | \(0.284685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16791.4 | 1.23064 | 0.615321 | − | 0.788277i | \(-0.289027\pi\) | ||||
0.615321 | + | 0.788277i | \(0.289027\pi\) | |||||||
\(572\) | 517.963 | 0.0378621 | ||||||||
\(573\) | 21581.2 | 1.57342 | ||||||||
\(574\) | −3807.42 | −0.276862 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 17318.7 | 1.25280 | ||||||||
\(577\) | −8108.87 | −0.585055 | −0.292527 | − | 0.956257i | \(-0.594496\pi\) | ||||
−0.292527 | + | 0.956257i | \(0.594496\pi\) | |||||||
\(578\) | 365.860 | 0.0263284 | ||||||||
\(579\) | −30723.7 | −2.20524 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1846.54 | −0.131854 | ||||||||
\(582\) | −10924.0 | −0.778032 | ||||||||
\(583\) | −1791.96 | −0.127299 | ||||||||
\(584\) | 8311.00 | 0.588890 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5739.25 | 0.404584 | ||||||||
\(587\) | −16076.3 | −1.13039 | −0.565197 | − | 0.824956i | \(-0.691200\pi\) | ||||
−0.565197 | + | 0.824956i | \(0.691200\pi\) | |||||||
\(588\) | −16658.2 | −1.16832 | ||||||||
\(589\) | −2.90594 | −0.000203289 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9126.63 | 0.635227 | ||||||||
\(592\) | −2860.53 | −0.198593 | ||||||||
\(593\) | 4341.83 | 0.300671 | 0.150335 | − | 0.988635i | \(-0.451965\pi\) | ||||
0.150335 | + | 0.988635i | \(0.451965\pi\) | |||||||
\(594\) | −6009.85 | −0.415130 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9520.88 | −0.654346 | ||||||||
\(597\) | −44940.8 | −3.08091 | ||||||||
\(598\) | −2442.80 | −0.167046 | ||||||||
\(599\) | −10540.1 | −0.718960 | −0.359480 | − | 0.933153i | \(-0.617046\pi\) | ||||
−0.359480 | + | 0.933153i | \(0.617046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16485.6 | 1.11890 | 0.559451 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(602\) | −1567.65 | −0.106134 | ||||||||
\(603\) | 28602.0 | 1.93162 | ||||||||
\(604\) | 8714.43 | 0.587061 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9149.82 | 0.613343 | ||||||||
\(607\) | −13326.5 | −0.891112 | −0.445556 | − | 0.895254i | \(-0.646994\pi\) | ||||
−0.445556 | + | 0.895254i | \(0.646994\pi\) | |||||||
\(608\) | −1288.00 | −0.0859132 | ||||||||
\(609\) | −1495.61 | −0.0995161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1103.22 | 0.0730467 | ||||||||
\(612\) | 25818.9 | 1.70534 | ||||||||
\(613\) | −20459.4 | −1.34804 | −0.674019 | − | 0.738714i | \(-0.735433\pi\) | ||||
−0.674019 | + | 0.738714i | \(0.735433\pi\) | |||||||
\(614\) | −14231.0 | −0.935369 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 971.221 | 0.0635253 | ||||||||
\(617\) | 3108.50 | 0.202826 | 0.101413 | − | 0.994844i | \(-0.467664\pi\) | ||||
0.101413 | + | 0.994844i | \(0.467664\pi\) | |||||||
\(618\) | −5143.70 | −0.334806 | ||||||||
\(619\) | 10426.3 | 0.677012 | 0.338506 | − | 0.940964i | \(-0.390078\pi\) | ||||
0.338506 | + | 0.940964i | \(0.390078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −56895.5 | −3.67655 | ||||||||
\(622\) | −4305.97 | −0.277579 | ||||||||
\(623\) | 1450.48 | 0.0932780 | ||||||||
\(624\) | −810.576 | −0.0520016 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3160.87 | −0.201811 | ||||||||
\(627\) | 585.519 | 0.0372941 | ||||||||
\(628\) | 4553.92 | 0.289365 | ||||||||
\(629\) | 27080.3 | 1.71663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18018.2 | 1.13675 | 0.568377 | − | 0.822768i | \(-0.307572\pi\) | ||||
0.568377 | + | 0.822768i | \(0.307572\pi\) | |||||||
\(632\) | 12558.4 | 0.790424 | ||||||||
\(633\) | 3148.37 | 0.197688 | ||||||||
\(634\) | −9045.67 | −0.566639 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11055.2 | 0.689255 | ||||||||
\(637\) | −3581.53 | −0.222772 | ||||||||
\(638\) | −404.479 | −0.0250995 | ||||||||
\(639\) | −39399.8 | −2.43917 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15178.7 | 0.935295 | 0.467648 | − | 0.883915i | \(-0.345102\pi\) | ||||
0.467648 | + | 0.883915i | \(0.345102\pi\) | |||||||
\(642\) | 1283.56 | 0.0789067 | ||||||||
\(643\) | −23957.1 | −1.46932 | −0.734662 | − | 0.678433i | \(-0.762659\pi\) | ||||
−0.734662 | + | 0.678433i | \(0.762659\pi\) | |||||||
\(644\) | 3680.54 | 0.225207 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 773.962 | 0.0471379 | ||||||||
\(647\) | 12835.2 | 0.779915 | 0.389958 | − | 0.920833i | \(-0.372490\pi\) | ||||
0.389958 | + | 0.920833i | \(0.372490\pi\) | |||||||
\(648\) | 51142.5 | 3.10041 | ||||||||
\(649\) | −393.074 | −0.0237743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.6255 | −0.00130195 | ||||||||
\(652\) | 17516.0 | 1.05212 | ||||||||
\(653\) | 4355.97 | 0.261045 | 0.130523 | − | 0.991445i | \(-0.458335\pi\) | ||||
0.130523 | + | 0.991445i | \(0.458335\pi\) | |||||||
\(654\) | −27529.7 | −1.64602 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3234.66 | −0.192519 | ||||||||
\(657\) | 26973.2 | 1.60171 | ||||||||
\(658\) | 828.056 | 0.0490593 | ||||||||
\(659\) | −32704.1 | −1.93319 | −0.966594 | − | 0.256313i | \(-0.917492\pi\) | ||||
−0.966594 | + | 0.256313i | \(0.917492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2839.66 | −0.167095 | −0.0835475 | − | 0.996504i | \(-0.526625\pi\) | ||||
−0.0835475 | + | 0.996504i | \(0.526625\pi\) | |||||||
\(662\) | −302.536 | −0.0177620 | ||||||||
\(663\) | 7673.64 | 0.449501 | ||||||||
\(664\) | 7696.50 | 0.449823 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 45547.3 | 2.65003 | ||||||||
\(667\) | −3829.23 | −0.222291 | ||||||||
\(668\) | −8983.04 | −0.520306 | ||||||||
\(669\) | 16862.1 | 0.974478 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3657.13 | −0.210405 | ||||||||
\(672\) | −9585.06 | −0.550226 | ||||||||
\(673\) | 18569.9 | 1.06362 | 0.531810 | − | 0.846864i | \(-0.321512\pi\) | ||||
0.531810 | + | 0.846864i | \(0.321512\pi\) | |||||||
\(674\) | −13877.0 | −0.793060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11044.6 | 0.628393 | ||||||||
\(677\) | −18106.5 | −1.02790 | −0.513952 | − | 0.857819i | \(-0.671819\pi\) | ||||
−0.513952 | + | 0.857819i | \(0.671819\pi\) | |||||||
\(678\) | −16924.8 | −0.958693 | ||||||||
\(679\) | 3538.71 | 0.200005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30070.8 | 1.69209 | ||||||||
\(682\) | −5.84848 | −0.000328372 0 | ||||||||
\(683\) | 5510.97 | 0.308743 | 0.154371 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(684\) | −2613.09 | −0.146073 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5608.44 | −0.312145 | ||||||||
\(687\) | 25900.9 | 1.43840 | ||||||||
\(688\) | −1331.82 | −0.0738014 | ||||||||
\(689\) | 2376.87 | 0.131425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24652.0 | 1.35717 | 0.678587 | − | 0.734520i | \(-0.262592\pi\) | ||||
0.678587 | + | 0.734520i | \(0.262592\pi\) | |||||||
\(692\) | −8491.53 | −0.466473 | ||||||||
\(693\) | 3152.08 | 0.172781 | ||||||||
\(694\) | 12809.1 | 0.700613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6233.82 | 0.339501 | ||||||||
\(697\) | 30622.2 | 1.66413 | ||||||||
\(698\) | −10321.5 | −0.559704 | ||||||||
\(699\) | −27453.6 | −1.48554 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3399.10 | −0.183142 | −0.0915708 | − | 0.995799i | \(-0.529189\pi\) | ||||
−0.0915708 | + | 0.995799i | \(0.529189\pi\) | |||||||
\(702\) | 7971.50 | 0.428582 | ||||||||
\(703\) | −2740.75 | −0.147041 | ||||||||
\(704\) | −2097.39 | −0.112285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13004.7 | −0.693253 | ||||||||
\(707\) | −2963.98 | −0.157669 | ||||||||
\(708\) | 2424.99 | 0.128724 | ||||||||
\(709\) | 26329.1 | 1.39465 | 0.697327 | − | 0.716753i | \(-0.254373\pi\) | ||||
0.697327 | + | 0.716753i | \(0.254373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40758.2 | 2.14986 | ||||||||
\(712\) | −6045.70 | −0.318219 | ||||||||
\(713\) | −55.3678 | −0.00290819 | ||||||||
\(714\) | 5759.68 | 0.301892 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9582.91 | 0.500182 | ||||||||
\(717\) | −46659.6 | −2.43031 | ||||||||
\(718\) | 16406.8 | 0.852781 | ||||||||
\(719\) | 22345.6 | 1.15904 | 0.579521 | − | 0.814957i | \(-0.303240\pi\) | ||||
0.579521 | + | 0.814957i | \(0.303240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1666.24 | 0.0860668 | ||||||||
\(722\) | 11108.7 | 0.572606 | ||||||||
\(723\) | 46476.4 | 2.39070 | ||||||||
\(724\) | −12566.9 | −0.645089 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −20269.4 | −1.03618 | ||||||||
\(727\) | 29862.8 | 1.52345 | 0.761727 | − | 0.647898i | \(-0.224352\pi\) | ||||
0.761727 | + | 0.647898i | \(0.224352\pi\) | |||||||
\(728\) | −1288.23 | −0.0655839 | ||||||||
\(729\) | 51039.2 | 2.59306 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12608.2 | 0.637938 | ||||||||
\(732\) | 22562.0 | 1.13923 | ||||||||
\(733\) | 987.919 | 0.0497812 | 0.0248906 | − | 0.999690i | \(-0.492076\pi\) | ||||
0.0248906 | + | 0.999690i | \(0.492076\pi\) | |||||||
\(734\) | −4946.27 | −0.248733 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24540.7 | −1.22905 | ||||||||
\(737\) | −3463.86 | −0.173125 | ||||||||
\(738\) | 51504.5 | 2.56898 | ||||||||
\(739\) | −35870.9 | −1.78556 | −0.892782 | − | 0.450489i | \(-0.851250\pi\) | ||||
−0.892782 | + | 0.450489i | \(0.851250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −776.636 | −0.0385026 | ||||||||
\(742\) | 1784.03 | 0.0882667 | ||||||||
\(743\) | −8322.20 | −0.410918 | −0.205459 | − | 0.978666i | \(-0.565869\pi\) | ||||
−0.205459 | + | 0.978666i | \(0.565869\pi\) | |||||||
\(744\) | 90.1365 | 0.00444162 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18119.4 | −0.889273 | ||||||||
\(747\) | 24978.8 | 1.22346 | ||||||||
\(748\) | −3126.81 | −0.152844 | ||||||||
\(749\) | −415.795 | −0.0202841 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20781.2 | 1.00974 | 0.504872 | − | 0.863194i | \(-0.331540\pi\) | ||||
0.504872 | + | 0.863194i | \(0.331540\pi\) | |||||||
\(752\) | 703.489 | 0.0341139 | ||||||||
\(753\) | −43956.4 | −2.12730 | ||||||||
\(754\) | 536.504 | 0.0259129 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12010.6 | −0.577804 | ||||||||
\(757\) | 16424.7 | 0.788596 | 0.394298 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394298 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(758\) | −7356.10 | −0.352488 | ||||||||
\(759\) | 11156.1 | 0.533519 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 416.312 | 0.0198309 | 0.00991543 | − | 0.999951i | \(-0.496844\pi\) | ||||
0.00991543 | + | 0.999951i | \(0.496844\pi\) | |||||||
\(762\) | −5912.67 | −0.281094 | ||||||||
\(763\) | 8917.95 | 0.423134 | ||||||||
\(764\) | 11664.1 | 0.552347 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12739.6 | 0.600916 | ||||||||
\(767\) | 521.376 | 0.0245447 | ||||||||
\(768\) | 36898.5 | 1.73367 | ||||||||
\(769\) | −37129.2 | −1.74111 | −0.870554 | − | 0.492073i | \(-0.836239\pi\) | ||||
−0.870554 | + | 0.492073i | \(0.836239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 71398.9 | 3.33511 | ||||||||
\(772\) | −16605.4 | −0.774148 | ||||||||
\(773\) | 2182.83 | 0.101567 | 0.0507833 | − | 0.998710i | \(-0.483828\pi\) | ||||
0.0507833 | + | 0.998710i | \(0.483828\pi\) | |||||||
\(774\) | 21206.2 | 0.984809 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14749.6 | −0.682319 | ||||||||
\(777\) | −20396.2 | −0.941711 | ||||||||
\(778\) | −15040.9 | −0.693112 | ||||||||
\(779\) | −3099.22 | −0.142543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4771.53 | 0.218616 | ||||||||
\(782\) | 14746.6 | 0.674343 | ||||||||
\(783\) | 12495.8 | 0.570322 | ||||||||
\(784\) | −2283.83 | −0.104037 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 37237.4 | 1.68984 | ||||||||
\(787\) | −7068.15 | −0.320143 | −0.160071 | − | 0.987105i | \(-0.551172\pi\) | ||||
−0.160071 | + | 0.987105i | \(0.551172\pi\) | |||||||
\(788\) | 4932.73 | 0.222996 | ||||||||
\(789\) | −47320.7 | −2.13519 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5482.61 | 0.246446 | ||||||||
\(792\) | −13138.1 | −0.589446 | ||||||||
\(793\) | 4850.84 | 0.217224 | ||||||||
\(794\) | −16365.9 | −0.731493 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24289.5 | −1.08155 | ||||||||
\(797\) | −15086.0 | −0.670482 | −0.335241 | − | 0.942132i | \(-0.608818\pi\) | ||||
−0.335241 | + | 0.942132i | \(0.608818\pi\) | |||||||
\(798\) | −582.928 | −0.0258589 | ||||||||
\(799\) | −6659.86 | −0.294880 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19621.2 | −0.865519 | ||||||||
\(802\) | 13363.8 | 0.588393 | ||||||||
\(803\) | −3266.60 | −0.143557 | ||||||||
\(804\) | 21369.6 | 0.937375 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.75746 | 0.000339013 0 | ||||||||
\(807\) | 464.798 | 0.0202747 | ||||||||
\(808\) | 12354.1 | 0.537890 | ||||||||
\(809\) | −21798.3 | −0.947326 | −0.473663 | − | 0.880706i | \(-0.657069\pi\) | ||||
−0.473663 | + | 0.880706i | \(0.657069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5569.61 | 0.241153 | 0.120577 | − | 0.992704i | \(-0.461526\pi\) | ||||
0.120577 | + | 0.992704i | \(0.461526\pi\) | |||||||
\(812\) | −808.344 | −0.0349351 | ||||||||
\(813\) | −76290.4 | −3.29105 | ||||||||
\(814\) | −5516.03 | −0.237515 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4893.24 | 0.209924 | ||||||||
\(817\) | −1276.06 | −0.0546434 | ||||||||
\(818\) | −6396.25 | −0.273398 | ||||||||
\(819\) | −4180.93 | −0.178381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21281.8 | 0.904676 | 0.452338 | − | 0.891847i | \(-0.350590\pi\) | ||||
0.452338 | + | 0.891847i | \(0.350590\pi\) | |||||||
\(822\) | −30611.1 | −1.29889 | ||||||||
\(823\) | −16799.0 | −0.711514 | −0.355757 | − | 0.934578i | \(-0.615777\pi\) | ||||
−0.355757 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(824\) | −6945.02 | −0.293618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 391.335 | 0.0164846 | ||||||||
\(827\) | −7360.62 | −0.309497 | −0.154748 | − | 0.987954i | \(-0.549457\pi\) | ||||
−0.154748 | + | 0.987954i | \(0.549457\pi\) | |||||||
\(828\) | −49788.1 | −2.08968 | ||||||||
\(829\) | −11634.6 | −0.487438 | −0.243719 | − | 0.969846i | \(-0.578367\pi\) | ||||
−0.243719 | + | 0.969846i | \(0.578367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −74639.4 | −3.11578 | ||||||||
\(832\) | 2782.00 | 0.115924 | ||||||||
\(833\) | 21620.8 | 0.899299 | ||||||||
\(834\) | 21101.2 | 0.876110 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 316.459 | 0.0130921 | ||||||||
\(837\) | 180.680 | 0.00746141 | ||||||||
\(838\) | −4936.46 | −0.203493 | ||||||||
\(839\) | −32151.0 | −1.32297 | −0.661486 | − | 0.749957i | \(-0.730074\pi\) | ||||
−0.661486 | + | 0.749957i | \(0.730074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | −7866.99 | −0.321988 | ||||||||
\(843\) | 20696.7 | 0.845592 | ||||||||
\(844\) | 1701.62 | 0.0693984 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11201.4 | −0.455217 | ||||||||
\(847\) | 6566.05 | 0.266366 | ||||||||
\(848\) | 1515.66 | 0.0613771 | ||||||||
\(849\) | −81023.4 | −3.27528 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52220.6 | −2.10352 | ||||||||
\(852\) | −29437.1 | −1.18368 | ||||||||
\(853\) | −35044.9 | −1.40670 | −0.703349 | − | 0.710844i | \(-0.748313\pi\) | ||||
−0.703349 | + | 0.710844i | \(0.748313\pi\) | |||||||
\(854\) | 3640.95 | 0.145891 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1733.07 | 0.0691997 | ||||||||
\(857\) | −7143.05 | −0.284716 | −0.142358 | − | 0.989815i | \(-0.545468\pi\) | ||||
−0.142358 | + | 0.989815i | \(0.545468\pi\) | |||||||
\(858\) | −1563.06 | −0.0621933 | ||||||||
\(859\) | 33960.3 | 1.34891 | 0.674454 | − | 0.738317i | \(-0.264379\pi\) | ||||
0.674454 | + | 0.738317i | \(0.264379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23063.9 | −0.912909 | ||||||||
\(862\) | 3310.11 | 0.130792 | ||||||||
\(863\) | −45823.4 | −1.80747 | −0.903736 | − | 0.428090i | \(-0.859186\pi\) | ||||
−0.903736 | + | 0.428090i | \(0.859186\pi\) | |||||||
\(864\) | 80082.7 | 3.15332 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −873.900 | −0.0342914 | ||||||||
\(867\) | 2216.24 | 0.0868136 | ||||||||
\(868\) | −11.6881 | −0.000457049 0 | ||||||||
\(869\) | −4936.04 | −0.192685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4594.49 | 0.178735 | ||||||||
\(872\) | −37170.7 | −1.44353 | ||||||||
\(873\) | −47869.5 | −1.85583 | ||||||||
\(874\) | −1492.48 | −0.0577617 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20152.7 | 0.777279 | ||||||||
\(877\) | 21281.3 | 0.819406 | 0.409703 | − | 0.912219i | \(-0.365632\pi\) | ||||
0.409703 | + | 0.912219i | \(0.365632\pi\) | |||||||
\(878\) | −14339.3 | −0.551169 | ||||||||
\(879\) | 34766.1 | 1.33405 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1359.32 | 0.0519826 | 0.0259913 | − | 0.999662i | \(-0.491726\pi\) | ||||
0.0259913 | + | 0.999662i | \(0.491726\pi\) | |||||||
\(882\) | 36364.7 | 1.38828 | ||||||||
\(883\) | 47928.2 | 1.82663 | 0.913313 | − | 0.407257i | \(-0.133515\pi\) | ||||
0.913313 | + | 0.407257i | \(0.133515\pi\) | |||||||
\(884\) | 4147.42 | 0.157797 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22698.5 | 0.860688 | ||||||||
\(887\) | −3100.58 | −0.117370 | −0.0586851 | − | 0.998277i | \(-0.518691\pi\) | ||||
−0.0586851 | + | 0.998277i | \(0.518691\pi\) | |||||||
\(888\) | 85012.9 | 3.21266 | ||||||||
\(889\) | 1915.34 | 0.0722593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20101.3 | −0.755803 | ||||||||
\(892\) | 9113.56 | 0.342090 | ||||||||
\(893\) | 674.033 | 0.0252583 | ||||||||
\(894\) | 28731.1 | 1.07485 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5673.14 | −0.211525 | ||||||||
\(897\) | −14797.5 | −0.550808 | ||||||||
\(898\) | −3473.27 | −0.129070 | ||||||||
\(899\) | 12.1602 | 0.000451131 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14348.5 | −0.530543 | ||||||||
\(902\) | −6237.48 | −0.230250 | ||||||||
\(903\) | −9496.21 | −0.349960 | ||||||||
\(904\) | −22851.9 | −0.840756 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26297.5 | −0.964321 | ||||||||
\(907\) | −23428.1 | −0.857680 | −0.428840 | − | 0.903380i | \(-0.641078\pi\) | ||||
−0.428840 | + | 0.903380i | \(0.641078\pi\) | |||||||
\(908\) | 16252.6 | 0.594009 | ||||||||
\(909\) | 40094.9 | 1.46300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12868.3 | −0.467999 | −0.234000 | − | 0.972237i | \(-0.575181\pi\) | ||||
−0.234000 | + | 0.972237i | \(0.575181\pi\) | |||||||
\(912\) | −495.237 | −0.0179813 | ||||||||
\(913\) | −3025.07 | −0.109655 | ||||||||
\(914\) | 3151.49 | 0.114050 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13998.8 | 0.504950 | ||||||||
\(917\) | −12062.6 | −0.434398 | ||||||||
\(918\) | −48121.9 | −1.73013 | ||||||||
\(919\) | 3938.41 | 0.141367 | 0.0706834 | − | 0.997499i | \(-0.477482\pi\) | ||||
0.0706834 | + | 0.997499i | \(0.477482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −86205.7 | −3.08423 | ||||||||
\(922\) | 26941.2 | 0.962323 | ||||||||
\(923\) | −6328.99 | −0.225700 | ||||||||
\(924\) | 2355.03 | 0.0838473 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18813.8 | 0.667667 | ||||||||
\(927\) | −22539.9 | −0.798607 | ||||||||
\(928\) | 5389.79 | 0.190656 | ||||||||
\(929\) | −15856.7 | −0.560001 | −0.280001 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280001 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2188.20 | −0.0770306 | ||||||||
\(932\) | −14838.0 | −0.521498 | ||||||||
\(933\) | −26083.9 | −0.915271 | ||||||||
\(934\) | 25554.0 | 0.895238 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17426.4 | 0.608548 | ||||||||
\(937\) | 18559.7 | 0.647085 | 0.323542 | − | 0.946214i | \(-0.395126\pi\) | ||||
0.323542 | + | 0.946214i | \(0.395126\pi\) | |||||||
\(938\) | 3448.54 | 0.120041 | ||||||||
\(939\) | −19147.3 | −0.665441 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24125.6 | 0.835785 | 0.417892 | − | 0.908497i | \(-0.362769\pi\) | ||||
0.417892 | + | 0.908497i | \(0.362769\pi\) | |||||||
\(942\) | −13742.4 | −0.475318 | ||||||||
\(943\) | −59050.6 | −2.03919 | ||||||||
\(944\) | 332.465 | 0.0114627 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2568.19 | −0.0882655 | ||||||||
\(947\) | 6883.31 | 0.236196 | 0.118098 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118098 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(948\) | 30452.0 | 1.04328 | ||||||||
\(949\) | 4332.84 | 0.148209 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54795.0 | −1.86840 | ||||||||
\(952\) | 7776.73 | 0.264753 | ||||||||
\(953\) | −37573.8 | −1.27716 | −0.638580 | − | 0.769555i | \(-0.720478\pi\) | ||||
−0.638580 | + | 0.769555i | \(0.720478\pi\) | |||||||
\(954\) | −24133.3 | −0.819020 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25218.4 | −0.853161 | ||||||||
\(957\) | −2450.18 | −0.0827617 | ||||||||
\(958\) | −7620.45 | −0.257000 | ||||||||
\(959\) | 9916.13 | 0.333898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29790.8 | −0.999994 | ||||||||
\(962\) | 7316.50 | 0.245211 | ||||||||
\(963\) | 5624.63 | 0.188215 | ||||||||
\(964\) | 25119.4 | 0.839255 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11106.7 | −0.369931 | ||||||||
\(967\) | 1584.28 | 0.0526856 | 0.0263428 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263428 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(968\) | −27367.8 | −0.908712 | ||||||||
\(969\) | 4688.35 | 0.155430 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36569.1 | 1.20861 | 0.604304 | − | 0.796754i | \(-0.293451\pi\) | ||||
0.604304 | + | 0.796754i | \(0.293451\pi\) | |||||||
\(972\) | 61887.5 | 2.04222 | ||||||||
\(973\) | −6835.50 | −0.225217 | ||||||||
\(974\) | −13807.6 | −0.454234 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3093.23 | 0.101447 | ||||||||
\(977\) | 33583.0 | 1.09971 | 0.549854 | − | 0.835261i | \(-0.314683\pi\) | ||||
0.549854 | + | 0.835261i | \(0.314683\pi\) | |||||||
\(978\) | −52858.0 | −1.72823 | ||||||||
\(979\) | 2376.23 | 0.0775738 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −120637. | −3.92623 | ||||||||
\(982\) | 20065.4 | 0.652051 | ||||||||
\(983\) | 25900.6 | 0.840387 | 0.420193 | − | 0.907435i | \(-0.361962\pi\) | ||||
0.420193 | + | 0.907435i | \(0.361962\pi\) | |||||||
\(984\) | 96131.9 | 3.11440 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3238.74 | −0.104607 | ||||||||
\(987\) | 5016.04 | 0.161765 | ||||||||
\(988\) | −419.754 | −0.0135163 | ||||||||
\(989\) | −24313.2 | −0.781714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29604.3 | 0.948951 | 0.474475 | − | 0.880269i | \(-0.342638\pi\) | ||||
0.474475 | + | 0.880269i | \(0.342638\pi\) | |||||||
\(992\) | 77.9324 | 0.00249431 | ||||||||
\(993\) | −1832.65 | −0.0585672 | ||||||||
\(994\) | −4750.42 | −0.151584 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18662.6 | 0.593723 | ||||||||
\(997\) | −39267.2 | −1.24735 | −0.623673 | − | 0.781685i | \(-0.714360\pi\) | ||||
−0.623673 | + | 0.781685i | \(0.714360\pi\) | |||||||
\(998\) | 4536.30 | 0.143882 | ||||||||
\(999\) | 170409. | 5.39691 |
(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 | 725.4.a.c.1.3 | 5 | ||
5.4 | even | 2 | 29.4.a.b.1.3 | ✓ | 5 | ||
15.14 | odd | 2 | 261.4.a.f.1.3 | 5 | |||
20.19 | odd | 2 | 464.4.a.l.1.1 | 5 | |||
35.34 | odd | 2 | 1421.4.a.e.1.3 | 5 | |||
40.19 | odd | 2 | 1856.4.a.bb.1.5 | 5 | |||
40.29 | even | 2 | 1856.4.a.y.1.1 | 5 | |||
145.144 | even | 2 | 841.4.a.b.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.3 | ✓ | 5 | 5.4 | even | 2 | ||
261.4.a.f.1.3 | 5 | 15.14 | odd | 2 | |||
464.4.a.l.1.1 | 5 | 20.19 | odd | 2 | |||
725.4.a.c.1.3 | 5 | 1.1 | even | 1 | trivial | ||
841.4.a.b.1.3 | 5 | 145.144 | even | 2 | |||
1421.4.a.e.1.3 | 5 | 35.34 | odd | 2 | |||
1856.4.a.y.1.1 | 5 | 40.29 | even | 2 | |||
1856.4.a.bb.1.5 | 5 | 40.19 | odd | 2 |