Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77677 | −1.96347 | −0.981737 | − | 0.190244i | \(-0.939072\pi\) | ||||
−0.981737 | + | 0.190244i | \(0.939072\pi\) | |||||||
\(3\) | −3.10732 | −1.79401 | −0.897007 | − | 0.442016i | \(-0.854263\pi\) | ||||
−0.897007 | + | 0.442016i | \(0.854263\pi\) | |||||||
\(4\) | 5.71046 | 2.85523 | ||||||||
\(5\) | −0.966106 | −0.432056 | −0.216028 | − | 0.976387i | \(-0.569310\pi\) | ||||
−0.216028 | + | 0.976387i | \(0.569310\pi\) | |||||||
\(6\) | 8.62833 | 3.52250 | ||||||||
\(7\) | 4.66578 | 1.76350 | 0.881750 | − | 0.471717i | \(-0.156366\pi\) | ||||
0.881750 | + | 0.471717i | \(0.156366\pi\) | |||||||
\(8\) | −10.3031 | −3.64269 | ||||||||
\(9\) | 6.65546 | 2.21849 | ||||||||
\(10\) | 2.68266 | 0.848330 | ||||||||
\(11\) | 0.00376926 | 0.00113648 | 0.000568238 | − | 1.00000i | \(-0.499819\pi\) | ||||
0.000568238 | 1.00000i | \(0.499819\pi\) | ||||||||
\(12\) | −17.7442 | −5.12232 | ||||||||
\(13\) | 6.25341 | 1.73438 | 0.867192 | − | 0.497974i | \(-0.165922\pi\) | ||||
0.867192 | + | 0.497974i | \(0.165922\pi\) | |||||||
\(14\) | −12.9558 | −3.46259 | ||||||||
\(15\) | 3.00200 | 0.775114 | ||||||||
\(16\) | 17.1884 | 4.29711 | ||||||||
\(17\) | 4.19620 | 1.01773 | 0.508864 | − | 0.860847i | \(-0.330066\pi\) | ||||
0.508864 | + | 0.860847i | \(0.330066\pi\) | |||||||
\(18\) | −18.4807 | −4.35594 | ||||||||
\(19\) | 2.54249 | 0.583288 | 0.291644 | − | 0.956527i | \(-0.405798\pi\) | ||||
0.291644 | + | 0.956527i | \(0.405798\pi\) | |||||||
\(20\) | −5.51691 | −1.23362 | ||||||||
\(21\) | −14.4981 | −3.16374 | ||||||||
\(22\) | −0.0104664 | −0.00223144 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 32.0151 | 6.53505 | ||||||||
\(25\) | −4.06664 | −0.813328 | ||||||||
\(26\) | −17.3643 | −3.40542 | ||||||||
\(27\) | −11.3587 | −2.18598 | ||||||||
\(28\) | 26.6438 | 5.03520 | ||||||||
\(29\) | 2.76292 | 0.513061 | 0.256531 | − | 0.966536i | \(-0.417421\pi\) | ||||
0.256531 | + | 0.966536i | \(0.417421\pi\) | |||||||
\(30\) | −8.33588 | −1.52192 | ||||||||
\(31\) | −1.73444 | −0.311515 | −0.155758 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155758 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(32\) | −27.1221 | −4.79456 | ||||||||
\(33\) | −0.0117123 | −0.00203885 | ||||||||
\(34\) | −11.6519 | −1.99828 | ||||||||
\(35\) | −4.50764 | −0.761930 | ||||||||
\(36\) | 38.0057 | 6.33429 | ||||||||
\(37\) | 9.51286 | 1.56390 | 0.781952 | − | 0.623338i | \(-0.214224\pi\) | ||||
0.781952 | + | 0.623338i | \(0.214224\pi\) | |||||||
\(38\) | −7.05992 | −1.14527 | ||||||||
\(39\) | −19.4314 | −3.11151 | ||||||||
\(40\) | 9.95389 | 1.57385 | ||||||||
\(41\) | −2.36385 | −0.369172 | −0.184586 | − | 0.982816i | \(-0.559094\pi\) | ||||
−0.184586 | + | 0.982816i | \(0.559094\pi\) | |||||||
\(42\) | 40.2579 | 6.21193 | ||||||||
\(43\) | −5.09898 | −0.777588 | −0.388794 | − | 0.921325i | \(-0.627108\pi\) | ||||
−0.388794 | + | 0.921325i | \(0.627108\pi\) | |||||||
\(44\) | 0.0215242 | 0.00324490 | ||||||||
\(45\) | −6.42988 | −0.958510 | ||||||||
\(46\) | −2.77677 | −0.409413 | ||||||||
\(47\) | −7.55988 | −1.10272 | −0.551361 | − | 0.834267i | \(-0.685891\pi\) | ||||
−0.551361 | + | 0.834267i | \(0.685891\pi\) | |||||||
\(48\) | −53.4100 | −7.70907 | ||||||||
\(49\) | 14.7695 | 2.10993 | ||||||||
\(50\) | 11.2921 | 1.59695 | ||||||||
\(51\) | −13.0390 | −1.82582 | ||||||||
\(52\) | 35.7099 | 4.95207 | ||||||||
\(53\) | 11.8266 | 1.62451 | 0.812254 | − | 0.583304i | \(-0.198240\pi\) | ||||
0.812254 | + | 0.583304i | \(0.198240\pi\) | |||||||
\(54\) | 31.5405 | 4.29212 | ||||||||
\(55\) | −0.00364151 | −0.000491021 0 | ||||||||
\(56\) | −48.0720 | −6.42389 | ||||||||
\(57\) | −7.90034 | −1.04643 | ||||||||
\(58\) | −7.67200 | −1.00738 | ||||||||
\(59\) | 9.51316 | 1.23851 | 0.619254 | − | 0.785191i | \(-0.287435\pi\) | ||||
0.619254 | + | 0.785191i | \(0.287435\pi\) | |||||||
\(60\) | 17.1428 | 2.21313 | ||||||||
\(61\) | −11.2164 | −1.43611 | −0.718053 | − | 0.695988i | \(-0.754967\pi\) | ||||
−0.718053 | + | 0.695988i | \(0.754967\pi\) | |||||||
\(62\) | 4.81615 | 0.611652 | ||||||||
\(63\) | 31.0529 | 3.91230 | ||||||||
\(64\) | 40.9351 | 5.11689 | ||||||||
\(65\) | −6.04146 | −0.749351 | ||||||||
\(66\) | 0.0325224 | 0.00400323 | ||||||||
\(67\) | 3.65836 | 0.446940 | 0.223470 | − | 0.974711i | \(-0.428262\pi\) | ||||
0.223470 | + | 0.974711i | \(0.428262\pi\) | |||||||
\(68\) | 23.9622 | 2.90585 | ||||||||
\(69\) | −3.10732 | −0.374078 | ||||||||
\(70\) | 12.5167 | 1.49603 | ||||||||
\(71\) | 2.25856 | 0.268042 | 0.134021 | − | 0.990979i | \(-0.457211\pi\) | ||||
0.134021 | + | 0.990979i | \(0.457211\pi\) | |||||||
\(72\) | −68.5718 | −8.08127 | ||||||||
\(73\) | 1.57815 | 0.184709 | 0.0923545 | − | 0.995726i | \(-0.470561\pi\) | ||||
0.0923545 | + | 0.995726i | \(0.470561\pi\) | |||||||
\(74\) | −26.4150 | −3.07069 | ||||||||
\(75\) | 12.6364 | 1.45912 | ||||||||
\(76\) | 14.5188 | 1.66542 | ||||||||
\(77\) | 0.0175866 | 0.00200417 | ||||||||
\(78\) | 53.9565 | 6.10937 | ||||||||
\(79\) | 0.604109 | 0.0679676 | 0.0339838 | − | 0.999422i | \(-0.489181\pi\) | ||||
0.0339838 | + | 0.999422i | \(0.489181\pi\) | |||||||
\(80\) | −16.6058 | −1.85659 | ||||||||
\(81\) | 15.3288 | 1.70319 | ||||||||
\(82\) | 6.56388 | 0.724859 | ||||||||
\(83\) | −15.9342 | −1.74900 | −0.874500 | − | 0.485025i | \(-0.838810\pi\) | ||||
−0.874500 | + | 0.485025i | \(0.838810\pi\) | |||||||
\(84\) | −82.7908 | −9.03321 | ||||||||
\(85\) | −4.05398 | −0.439715 | ||||||||
\(86\) | 14.1587 | 1.52677 | ||||||||
\(87\) | −8.58529 | −0.920439 | ||||||||
\(88\) | −0.0388351 | −0.00413983 | ||||||||
\(89\) | −3.32964 | −0.352941 | −0.176471 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176471 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(90\) | 17.8543 | 1.88201 | ||||||||
\(91\) | 29.1771 | 3.05859 | ||||||||
\(92\) | 5.71046 | 0.595357 | ||||||||
\(93\) | 5.38948 | 0.558863 | ||||||||
\(94\) | 20.9921 | 2.16516 | ||||||||
\(95\) | −2.45632 | −0.252013 | ||||||||
\(96\) | 84.2772 | 8.60151 | ||||||||
\(97\) | 10.5025 | 1.06636 | 0.533182 | − | 0.846000i | \(-0.320996\pi\) | ||||
0.533182 | + | 0.846000i | \(0.320996\pi\) | |||||||
\(98\) | −41.0116 | −4.14280 | ||||||||
\(99\) | 0.0250862 | 0.00252126 | ||||||||
\(100\) | −23.2224 | −2.32224 | ||||||||
\(101\) | 7.22212 | 0.718627 | 0.359314 | − | 0.933217i | \(-0.383011\pi\) | ||||
0.359314 | + | 0.933217i | \(0.383011\pi\) | |||||||
\(102\) | 36.2062 | 3.58495 | ||||||||
\(103\) | 13.3741 | 1.31779 | 0.658895 | − | 0.752235i | \(-0.271024\pi\) | ||||
0.658895 | + | 0.752235i | \(0.271024\pi\) | |||||||
\(104\) | −64.4295 | −6.31783 | ||||||||
\(105\) | 14.0067 | 1.36691 | ||||||||
\(106\) | −32.8398 | −3.18968 | ||||||||
\(107\) | −3.71905 | −0.359534 | −0.179767 | − | 0.983709i | \(-0.557534\pi\) | ||||
−0.179767 | + | 0.983709i | \(0.557534\pi\) | |||||||
\(108\) | −64.8633 | −6.24148 | ||||||||
\(109\) | −8.34626 | −0.799426 | −0.399713 | − | 0.916640i | \(-0.630890\pi\) | ||||
−0.399713 | + | 0.916640i | \(0.630890\pi\) | |||||||
\(110\) | 0.0101116 | 0.000964107 0 | ||||||||
\(111\) | −29.5595 | −2.80567 | ||||||||
\(112\) | 80.1975 | 7.57795 | ||||||||
\(113\) | 19.5324 | 1.83746 | 0.918728 | − | 0.394891i | \(-0.129218\pi\) | ||||
0.918728 | + | 0.394891i | \(0.129218\pi\) | |||||||
\(114\) | 21.9374 | 2.05463 | ||||||||
\(115\) | −0.966106 | −0.0900899 | ||||||||
\(116\) | 15.7775 | 1.46491 | ||||||||
\(117\) | 41.6193 | 3.84771 | ||||||||
\(118\) | −26.4159 | −2.43178 | ||||||||
\(119\) | 19.5786 | 1.79476 | ||||||||
\(120\) | −30.9299 | −2.82350 | ||||||||
\(121\) | −11.0000 | −0.999999 | ||||||||
\(122\) | 31.1452 | 2.81976 | ||||||||
\(123\) | 7.34525 | 0.662299 | ||||||||
\(124\) | −9.90447 | −0.889447 | ||||||||
\(125\) | 8.75934 | 0.783459 | ||||||||
\(126\) | −86.2269 | −7.68170 | ||||||||
\(127\) | 3.50952 | 0.311419 | 0.155710 | − | 0.987803i | \(-0.450234\pi\) | ||||
0.155710 | + | 0.987803i | \(0.450234\pi\) | |||||||
\(128\) | −59.4232 | −5.25232 | ||||||||
\(129\) | 15.8442 | 1.39500 | ||||||||
\(130\) | 16.7758 | 1.47133 | ||||||||
\(131\) | −2.74298 | −0.239655 | −0.119827 | − | 0.992795i | \(-0.538234\pi\) | ||||
−0.119827 | + | 0.992795i | \(0.538234\pi\) | |||||||
\(132\) | −0.0668827 | −0.00582139 | ||||||||
\(133\) | 11.8627 | 1.02863 | ||||||||
\(134\) | −10.1584 | −0.877554 | ||||||||
\(135\) | 10.9737 | 0.944466 | ||||||||
\(136\) | −43.2339 | −3.70727 | ||||||||
\(137\) | 7.87604 | 0.672895 | 0.336448 | − | 0.941702i | \(-0.390774\pi\) | ||||
0.336448 | + | 0.941702i | \(0.390774\pi\) | |||||||
\(138\) | 8.62833 | 0.734492 | ||||||||
\(139\) | 15.8297 | 1.34266 | 0.671330 | − | 0.741159i | \(-0.265723\pi\) | ||||
0.671330 | + | 0.741159i | \(0.265723\pi\) | |||||||
\(140\) | −25.7407 | −2.17549 | ||||||||
\(141\) | 23.4910 | 1.97830 | ||||||||
\(142\) | −6.27150 | −0.526292 | ||||||||
\(143\) | 0.0235708 | 0.00197109 | ||||||||
\(144\) | 114.397 | 9.53307 | ||||||||
\(145\) | −2.66927 | −0.221671 | ||||||||
\(146\) | −4.38217 | −0.362671 | ||||||||
\(147\) | −45.8937 | −3.78525 | ||||||||
\(148\) | 54.3228 | 4.46531 | ||||||||
\(149\) | 12.7538 | 1.04483 | 0.522415 | − | 0.852691i | \(-0.325031\pi\) | ||||
0.522415 | + | 0.852691i | \(0.325031\pi\) | |||||||
\(150\) | −35.0883 | −2.86495 | ||||||||
\(151\) | −18.5514 | −1.50969 | −0.754844 | − | 0.655904i | \(-0.772287\pi\) | ||||
−0.754844 | + | 0.655904i | \(0.772287\pi\) | |||||||
\(152\) | −26.1955 | −2.12474 | ||||||||
\(153\) | 27.9276 | 2.25782 | ||||||||
\(154\) | −0.0488339 | −0.00393514 | ||||||||
\(155\) | 1.67566 | 0.134592 | ||||||||
\(156\) | −110.962 | −8.88408 | ||||||||
\(157\) | 16.1506 | 1.28896 | 0.644481 | − | 0.764620i | \(-0.277074\pi\) | ||||
0.644481 | + | 0.764620i | \(0.277074\pi\) | |||||||
\(158\) | −1.67747 | −0.133453 | ||||||||
\(159\) | −36.7491 | −2.91439 | ||||||||
\(160\) | 26.2029 | 2.07152 | ||||||||
\(161\) | 4.66578 | 0.367715 | ||||||||
\(162\) | −42.5644 | −3.34418 | ||||||||
\(163\) | 10.7399 | 0.841216 | 0.420608 | − | 0.907243i | \(-0.361817\pi\) | ||||
0.420608 | + | 0.907243i | \(0.361817\pi\) | |||||||
\(164\) | −13.4987 | −1.05407 | ||||||||
\(165\) | 0.0113153 | 0.000880898 0 | ||||||||
\(166\) | 44.2455 | 3.43412 | ||||||||
\(167\) | 13.6364 | 1.05522 | 0.527609 | − | 0.849487i | \(-0.323089\pi\) | ||||
0.527609 | + | 0.849487i | \(0.323089\pi\) | |||||||
\(168\) | 149.375 | 11.5246 | ||||||||
\(169\) | 26.1052 | 2.00809 | ||||||||
\(170\) | 11.2570 | 0.863370 | ||||||||
\(171\) | 16.9214 | 1.29402 | ||||||||
\(172\) | −29.1175 | −2.22019 | ||||||||
\(173\) | 12.8624 | 0.977912 | 0.488956 | − | 0.872308i | \(-0.337378\pi\) | ||||
0.488956 | + | 0.872308i | \(0.337378\pi\) | |||||||
\(174\) | 23.8394 | 1.80726 | ||||||||
\(175\) | −18.9741 | −1.43430 | ||||||||
\(176\) | 0.0647877 | 0.00488356 | ||||||||
\(177\) | −29.5605 | −2.22190 | ||||||||
\(178\) | 9.24566 | 0.692991 | ||||||||
\(179\) | 21.2095 | 1.58527 | 0.792637 | − | 0.609693i | \(-0.208707\pi\) | ||||
0.792637 | + | 0.609693i | \(0.208707\pi\) | |||||||
\(180\) | −36.7176 | −2.73677 | ||||||||
\(181\) | −16.4164 | −1.22022 | −0.610110 | − | 0.792317i | \(-0.708875\pi\) | ||||
−0.610110 | + | 0.792317i | \(0.708875\pi\) | |||||||
\(182\) | −81.0180 | −6.00546 | ||||||||
\(183\) | 34.8528 | 2.57640 | ||||||||
\(184\) | −10.3031 | −0.759554 | ||||||||
\(185\) | −9.19043 | −0.675694 | ||||||||
\(186\) | −14.9653 | −1.09731 | ||||||||
\(187\) | 0.0158166 | 0.00115662 | ||||||||
\(188\) | −43.1704 | −3.14852 | ||||||||
\(189\) | −52.9972 | −3.85498 | ||||||||
\(190\) | 6.82063 | 0.494820 | ||||||||
\(191\) | 9.12693 | 0.660401 | 0.330201 | − | 0.943911i | \(-0.392884\pi\) | ||||
0.330201 | + | 0.943911i | \(0.392884\pi\) | |||||||
\(192\) | −127.199 | −9.17977 | ||||||||
\(193\) | 16.3956 | 1.18018 | 0.590091 | − | 0.807337i | \(-0.299092\pi\) | ||||
0.590091 | + | 0.807337i | \(0.299092\pi\) | |||||||
\(194\) | −29.1630 | −2.09378 | ||||||||
\(195\) | 18.7728 | 1.34435 | ||||||||
\(196\) | 84.3408 | 6.02434 | ||||||||
\(197\) | −5.22362 | −0.372168 | −0.186084 | − | 0.982534i | \(-0.559580\pi\) | ||||
−0.186084 | + | 0.982534i | \(0.559580\pi\) | |||||||
\(198\) | −0.0696586 | −0.00495042 | ||||||||
\(199\) | −7.55778 | −0.535757 | −0.267879 | − | 0.963453i | \(-0.586323\pi\) | ||||
−0.267879 | + | 0.963453i | \(0.586323\pi\) | |||||||
\(200\) | 41.8990 | 2.96270 | ||||||||
\(201\) | −11.3677 | −0.801816 | ||||||||
\(202\) | −20.0542 | −1.41101 | ||||||||
\(203\) | 12.8912 | 0.904784 | ||||||||
\(204\) | −74.4584 | −5.21313 | ||||||||
\(205\) | 2.28373 | 0.159503 | ||||||||
\(206\) | −37.1369 | −2.58745 | ||||||||
\(207\) | 6.65546 | 0.462586 | ||||||||
\(208\) | 107.486 | 7.45283 | ||||||||
\(209\) | 0.00958332 | 0.000662892 0 | ||||||||
\(210\) | −38.8934 | −2.68390 | ||||||||
\(211\) | −16.3145 | −1.12314 | −0.561570 | − | 0.827429i | \(-0.689802\pi\) | ||||
−0.561570 | + | 0.827429i | \(0.689802\pi\) | |||||||
\(212\) | 67.5353 | 4.63834 | ||||||||
\(213\) | −7.01807 | −0.480870 | ||||||||
\(214\) | 10.3270 | 0.705936 | ||||||||
\(215\) | 4.92616 | 0.335961 | ||||||||
\(216\) | 117.030 | 7.96286 | ||||||||
\(217\) | −8.09253 | −0.549357 | ||||||||
\(218\) | 23.1756 | 1.56965 | ||||||||
\(219\) | −4.90384 | −0.331370 | ||||||||
\(220\) | −0.0207947 | −0.00140198 | ||||||||
\(221\) | 26.2406 | 1.76513 | ||||||||
\(222\) | 82.0801 | 5.50885 | ||||||||
\(223\) | 10.5430 | 0.706009 | 0.353004 | − | 0.935622i | \(-0.385160\pi\) | ||||
0.353004 | + | 0.935622i | \(0.385160\pi\) | |||||||
\(224\) | −126.546 | −8.45521 | ||||||||
\(225\) | −27.0653 | −1.80436 | ||||||||
\(226\) | −54.2371 | −3.60780 | ||||||||
\(227\) | −21.8618 | −1.45102 | −0.725508 | − | 0.688214i | \(-0.758395\pi\) | ||||
−0.725508 | + | 0.688214i | \(0.758395\pi\) | |||||||
\(228\) | −45.1146 | −2.98779 | ||||||||
\(229\) | 6.79922 | 0.449305 | 0.224653 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224653 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(230\) | 2.68266 | 0.176889 | ||||||||
\(231\) | −0.0546471 | −0.00359552 | ||||||||
\(232\) | −28.4666 | −1.86893 | ||||||||
\(233\) | −24.7658 | −1.62246 | −0.811231 | − | 0.584726i | \(-0.801202\pi\) | ||||
−0.811231 | + | 0.584726i | \(0.801202\pi\) | |||||||
\(234\) | −115.567 | −7.55487 | ||||||||
\(235\) | 7.30364 | 0.476437 | ||||||||
\(236\) | 54.3245 | 3.53622 | ||||||||
\(237\) | −1.87716 | −0.121935 | ||||||||
\(238\) | −54.3652 | −3.52397 | ||||||||
\(239\) | 14.5875 | 0.943584 | 0.471792 | − | 0.881710i | \(-0.343607\pi\) | ||||
0.471792 | + | 0.881710i | \(0.343607\pi\) | |||||||
\(240\) | 51.5997 | 3.33075 | ||||||||
\(241\) | −4.10431 | −0.264382 | −0.132191 | − | 0.991224i | \(-0.542201\pi\) | ||||
−0.132191 | + | 0.991224i | \(0.542201\pi\) | |||||||
\(242\) | 30.5444 | 1.96347 | ||||||||
\(243\) | −13.5553 | −0.869574 | ||||||||
\(244\) | −64.0505 | −4.10041 | ||||||||
\(245\) | −14.2689 | −0.911609 | ||||||||
\(246\) | −20.3961 | −1.30041 | ||||||||
\(247\) | 15.8992 | 1.01164 | ||||||||
\(248\) | 17.8701 | 1.13475 | ||||||||
\(249\) | 49.5126 | 3.13773 | ||||||||
\(250\) | −24.3227 | −1.53830 | ||||||||
\(251\) | −19.9574 | −1.25970 | −0.629850 | − | 0.776716i | \(-0.716884\pi\) | ||||
−0.629850 | + | 0.776716i | \(0.716884\pi\) | |||||||
\(252\) | 177.326 | 11.1705 | ||||||||
\(253\) | 0.00376926 | 0.000236972 0 | ||||||||
\(254\) | −9.74513 | −0.611464 | ||||||||
\(255\) | 12.5970 | 0.788856 | ||||||||
\(256\) | 83.1344 | 5.19590 | ||||||||
\(257\) | −26.6907 | −1.66492 | −0.832460 | − | 0.554086i | \(-0.813068\pi\) | ||||
−0.832460 | + | 0.554086i | \(0.813068\pi\) | |||||||
\(258\) | −43.9957 | −2.73905 | ||||||||
\(259\) | 44.3849 | 2.75795 | ||||||||
\(260\) | −34.4995 | −2.13957 | ||||||||
\(261\) | 18.3885 | 1.13822 | ||||||||
\(262\) | 7.61662 | 0.470556 | ||||||||
\(263\) | −15.6514 | −0.965105 | −0.482553 | − | 0.875867i | \(-0.660290\pi\) | ||||
−0.482553 | + | 0.875867i | \(0.660290\pi\) | |||||||
\(264\) | 0.120673 | 0.00742692 | ||||||||
\(265\) | −11.4258 | −0.701878 | ||||||||
\(266\) | −32.9400 | −2.01968 | ||||||||
\(267\) | 10.3463 | 0.633182 | ||||||||
\(268\) | 20.8909 | 1.27612 | ||||||||
\(269\) | 5.45580 | 0.332646 | 0.166323 | − | 0.986071i | \(-0.446811\pi\) | ||||
0.166323 | + | 0.986071i | \(0.446811\pi\) | |||||||
\(270\) | −30.4715 | −1.85443 | ||||||||
\(271\) | −11.3918 | −0.692006 | −0.346003 | − | 0.938233i | \(-0.612461\pi\) | ||||
−0.346003 | + | 0.938233i | \(0.612461\pi\) | |||||||
\(272\) | 72.1261 | 4.37329 | ||||||||
\(273\) | −90.6626 | −5.48715 | ||||||||
\(274\) | −21.8700 | −1.32121 | ||||||||
\(275\) | −0.0153282 | −0.000924327 0 | ||||||||
\(276\) | −17.7442 | −1.06808 | ||||||||
\(277\) | −15.3705 | −0.923524 | −0.461762 | − | 0.887004i | \(-0.652783\pi\) | ||||
−0.461762 | + | 0.887004i | \(0.652783\pi\) | |||||||
\(278\) | −43.9555 | −2.63628 | ||||||||
\(279\) | −11.5435 | −0.691092 | ||||||||
\(280\) | 46.4427 | 2.77548 | ||||||||
\(281\) | −24.2522 | −1.44677 | −0.723383 | − | 0.690447i | \(-0.757414\pi\) | ||||
−0.723383 | + | 0.690447i | \(0.757414\pi\) | |||||||
\(282\) | −65.2291 | −3.88434 | ||||||||
\(283\) | −15.0284 | −0.893345 | −0.446673 | − | 0.894697i | \(-0.647391\pi\) | ||||
−0.446673 | + | 0.894697i | \(0.647391\pi\) | |||||||
\(284\) | 12.8974 | 0.765320 | ||||||||
\(285\) | 7.63257 | 0.452114 | ||||||||
\(286\) | −0.0654506 | −0.00387017 | ||||||||
\(287\) | −11.0292 | −0.651034 | ||||||||
\(288\) | −180.510 | −10.6367 | ||||||||
\(289\) | 0.608105 | 0.0357709 | ||||||||
\(290\) | 7.41197 | 0.435246 | ||||||||
\(291\) | −32.6346 | −1.91307 | ||||||||
\(292\) | 9.01199 | 0.527387 | ||||||||
\(293\) | −17.3221 | −1.01197 | −0.505983 | − | 0.862543i | \(-0.668870\pi\) | ||||
−0.505983 | + | 0.862543i | \(0.668870\pi\) | |||||||
\(294\) | 127.436 | 7.43224 | ||||||||
\(295\) | −9.19072 | −0.535104 | ||||||||
\(296\) | −98.0119 | −5.69683 | ||||||||
\(297\) | −0.0428139 | −0.00248431 | ||||||||
\(298\) | −35.4143 | −2.05150 | ||||||||
\(299\) | 6.25341 | 0.361644 | ||||||||
\(300\) | 72.1594 | 4.16613 | ||||||||
\(301\) | −23.7908 | −1.37128 | ||||||||
\(302\) | 51.5129 | 2.96423 | ||||||||
\(303\) | −22.4415 | −1.28923 | ||||||||
\(304\) | 43.7014 | 2.50645 | ||||||||
\(305\) | 10.8362 | 0.620478 | ||||||||
\(306\) | −77.5487 | −4.43316 | ||||||||
\(307\) | 28.5097 | 1.62713 | 0.813567 | − | 0.581471i | \(-0.197523\pi\) | ||||
0.813567 | + | 0.581471i | \(0.197523\pi\) | |||||||
\(308\) | 0.100427 | 0.00572238 | ||||||||
\(309\) | −41.5577 | −2.36413 | ||||||||
\(310\) | −4.65291 | −0.264268 | ||||||||
\(311\) | −17.0880 | −0.968972 | −0.484486 | − | 0.874799i | \(-0.660993\pi\) | ||||
−0.484486 | + | 0.874799i | \(0.660993\pi\) | |||||||
\(312\) | 200.203 | 11.3343 | ||||||||
\(313\) | −3.60663 | −0.203859 | −0.101929 | − | 0.994792i | \(-0.532502\pi\) | ||||
−0.101929 | + | 0.994792i | \(0.532502\pi\) | |||||||
\(314\) | −44.8467 | −2.53084 | ||||||||
\(315\) | −30.0004 | −1.69033 | ||||||||
\(316\) | 3.44974 | 0.194063 | ||||||||
\(317\) | 24.7512 | 1.39017 | 0.695084 | − | 0.718929i | \(-0.255367\pi\) | ||||
0.695084 | + | 0.718929i | \(0.255367\pi\) | |||||||
\(318\) | 102.044 | 5.72233 | ||||||||
\(319\) | 0.0104142 | 0.000583082 0 | ||||||||
\(320\) | −39.5477 | −2.21078 | ||||||||
\(321\) | 11.5563 | 0.645009 | ||||||||
\(322\) | −12.9558 | −0.721999 | ||||||||
\(323\) | 10.6688 | 0.593628 | ||||||||
\(324\) | 87.5342 | 4.86301 | ||||||||
\(325\) | −25.4304 | −1.41062 | ||||||||
\(326\) | −29.8223 | −1.65170 | ||||||||
\(327\) | 25.9345 | 1.43418 | ||||||||
\(328\) | 24.3550 | 1.34478 | ||||||||
\(329\) | −35.2727 | −1.94465 | ||||||||
\(330\) | −0.0314201 | −0.00172962 | ||||||||
\(331\) | −12.4592 | −0.684821 | −0.342410 | − | 0.939550i | \(-0.611243\pi\) | ||||
−0.342410 | + | 0.939550i | \(0.611243\pi\) | |||||||
\(332\) | −90.9913 | −4.99380 | ||||||||
\(333\) | 63.3125 | 3.46950 | ||||||||
\(334\) | −37.8652 | −2.07189 | ||||||||
\(335\) | −3.53436 | −0.193103 | ||||||||
\(336\) | −249.199 | −13.5949 | ||||||||
\(337\) | −3.12830 | −0.170409 | −0.0852046 | − | 0.996363i | \(-0.527154\pi\) | ||||
−0.0852046 | + | 0.996363i | \(0.527154\pi\) | |||||||
\(338\) | −72.4881 | −3.94283 | ||||||||
\(339\) | −60.6936 | −3.29642 | ||||||||
\(340\) | −23.1501 | −1.25549 | ||||||||
\(341\) | −0.00653757 | −0.000354029 0 | ||||||||
\(342\) | −46.9870 | −2.54077 | ||||||||
\(343\) | 36.2509 | 1.95737 | ||||||||
\(344\) | 52.5353 | 2.83252 | ||||||||
\(345\) | 3.00200 | 0.161622 | ||||||||
\(346\) | −35.7160 | −1.92011 | ||||||||
\(347\) | 35.7568 | 1.91953 | 0.959763 | − | 0.280812i | \(-0.0906038\pi\) | ||||
0.959763 | + | 0.280812i | \(0.0906038\pi\) | |||||||
\(348\) | −49.0259 | −2.62807 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | 52.6866 | 2.81622 | ||||||||
\(351\) | −71.0306 | −3.79133 | ||||||||
\(352\) | −0.102230 | −0.00544890 | ||||||||
\(353\) | 13.8709 | 0.738272 | 0.369136 | − | 0.929375i | \(-0.379654\pi\) | ||||
0.369136 | + | 0.929375i | \(0.379654\pi\) | |||||||
\(354\) | 82.0826 | 4.36264 | ||||||||
\(355\) | −2.18201 | −0.115809 | ||||||||
\(356\) | −19.0138 | −1.00773 | ||||||||
\(357\) | −60.8369 | −3.21983 | ||||||||
\(358\) | −58.8940 | −3.11265 | ||||||||
\(359\) | −3.68549 | −0.194513 | −0.0972563 | − | 0.995259i | \(-0.531007\pi\) | ||||
−0.0972563 | + | 0.995259i | \(0.531007\pi\) | |||||||
\(360\) | 66.2477 | 3.49156 | ||||||||
\(361\) | −12.5357 | −0.659776 | ||||||||
\(362\) | 45.5845 | 2.39587 | ||||||||
\(363\) | 34.1805 | 1.79401 | ||||||||
\(364\) | 166.614 | 8.73297 | ||||||||
\(365\) | −1.52466 | −0.0798046 | ||||||||
\(366\) | −96.7784 | −5.05869 | ||||||||
\(367\) | −10.0369 | −0.523920 | −0.261960 | − | 0.965079i | \(-0.584369\pi\) | ||||
−0.261960 | + | 0.965079i | \(0.584369\pi\) | |||||||
\(368\) | 17.1884 | 0.896009 | ||||||||
\(369\) | −15.7325 | −0.819002 | ||||||||
\(370\) | 25.5197 | 1.32671 | ||||||||
\(371\) | 55.1803 | 2.86482 | ||||||||
\(372\) | 30.7764 | 1.59568 | ||||||||
\(373\) | 12.2772 | 0.635692 | 0.317846 | − | 0.948142i | \(-0.397041\pi\) | ||||
0.317846 | + | 0.948142i | \(0.397041\pi\) | |||||||
\(374\) | −0.0439190 | −0.00227100 | ||||||||
\(375\) | −27.2181 | −1.40554 | ||||||||
\(376\) | 77.8901 | 4.01688 | ||||||||
\(377\) | 17.2777 | 0.889846 | ||||||||
\(378\) | 147.161 | 7.56915 | ||||||||
\(379\) | 19.6035 | 1.00696 | 0.503481 | − | 0.864006i | \(-0.332052\pi\) | ||||
0.503481 | + | 0.864006i | \(0.332052\pi\) | |||||||
\(380\) | −14.0267 | −0.719554 | ||||||||
\(381\) | −10.9052 | −0.558691 | ||||||||
\(382\) | −25.3434 | −1.29668 | ||||||||
\(383\) | −2.26773 | −0.115876 | −0.0579378 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579378 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(384\) | 184.647 | 9.42273 | ||||||||
\(385\) | −0.0169905 | −0.000865915 0 | ||||||||
\(386\) | −45.5269 | −2.31726 | ||||||||
\(387\) | −33.9361 | −1.72507 | ||||||||
\(388\) | 59.9739 | 3.04471 | ||||||||
\(389\) | 9.45152 | 0.479211 | 0.239606 | − | 0.970870i | \(-0.422982\pi\) | ||||
0.239606 | + | 0.970870i | \(0.422982\pi\) | |||||||
\(390\) | −52.1277 | −2.63959 | ||||||||
\(391\) | 4.19620 | 0.212211 | ||||||||
\(392\) | −152.172 | −7.68584 | ||||||||
\(393\) | 8.52331 | 0.429944 | ||||||||
\(394\) | 14.5048 | 0.730741 | ||||||||
\(395\) | −0.583634 | −0.0293658 | ||||||||
\(396\) | 0.143254 | 0.00719876 | ||||||||
\(397\) | 29.5184 | 1.48149 | 0.740743 | − | 0.671789i | \(-0.234474\pi\) | ||||
0.740743 | + | 0.671789i | \(0.234474\pi\) | |||||||
\(398\) | 20.9862 | 1.05195 | ||||||||
\(399\) | −36.8613 | −1.84537 | ||||||||
\(400\) | −69.8991 | −3.49496 | ||||||||
\(401\) | 28.7987 | 1.43814 | 0.719070 | − | 0.694937i | \(-0.244568\pi\) | ||||
0.719070 | + | 0.694937i | \(0.244568\pi\) | |||||||
\(402\) | 31.5655 | 1.57434 | ||||||||
\(403\) | −10.8462 | −0.540287 | ||||||||
\(404\) | 41.2416 | 2.05185 | ||||||||
\(405\) | −14.8092 | −0.735875 | ||||||||
\(406\) | −35.7959 | −1.77652 | ||||||||
\(407\) | 0.0358565 | 0.00177734 | ||||||||
\(408\) | 134.342 | 6.65090 | ||||||||
\(409\) | −25.3140 | −1.25169 | −0.625847 | − | 0.779945i | \(-0.715247\pi\) | ||||
−0.625847 | + | 0.779945i | \(0.715247\pi\) | |||||||
\(410\) | −6.34140 | −0.313179 | ||||||||
\(411\) | −24.4734 | −1.20718 | ||||||||
\(412\) | 76.3723 | 3.76259 | ||||||||
\(413\) | 44.3863 | 2.18411 | ||||||||
\(414\) | −18.4807 | −0.908276 | ||||||||
\(415\) | 15.3941 | 0.755666 | ||||||||
\(416\) | −169.606 | −8.31561 | ||||||||
\(417\) | −49.1881 | −2.40875 | ||||||||
\(418\) | −0.0266107 | −0.00130157 | ||||||||
\(419\) | −2.74753 | −0.134225 | −0.0671127 | − | 0.997745i | \(-0.521379\pi\) | ||||
−0.0671127 | + | 0.997745i | \(0.521379\pi\) | |||||||
\(420\) | 79.9847 | 3.90285 | ||||||||
\(421\) | 0.573424 | 0.0279470 | 0.0139735 | − | 0.999902i | \(-0.495552\pi\) | ||||
0.0139735 | + | 0.999902i | \(0.495552\pi\) | |||||||
\(422\) | 45.3018 | 2.20526 | ||||||||
\(423\) | −50.3144 | −2.44637 | ||||||||
\(424\) | −121.851 | −5.91759 | ||||||||
\(425\) | −17.0644 | −0.827747 | ||||||||
\(426\) | 19.4876 | 0.944176 | ||||||||
\(427\) | −52.3331 | −2.53257 | ||||||||
\(428\) | −21.2375 | −1.02655 | ||||||||
\(429\) | −0.0732419 | −0.00353615 | ||||||||
\(430\) | −13.6788 | −0.659651 | ||||||||
\(431\) | −19.3644 | −0.932750 | −0.466375 | − | 0.884587i | \(-0.654440\pi\) | ||||
−0.466375 | + | 0.884587i | \(0.654440\pi\) | |||||||
\(432\) | −195.238 | −9.39339 | ||||||||
\(433\) | −13.3963 | −0.643787 | −0.321893 | − | 0.946776i | \(-0.604319\pi\) | ||||
−0.321893 | + | 0.946776i | \(0.604319\pi\) | |||||||
\(434\) | 22.4711 | 1.07865 | ||||||||
\(435\) | 8.29430 | 0.397681 | ||||||||
\(436\) | −47.6610 | −2.28255 | ||||||||
\(437\) | 2.54249 | 0.121624 | ||||||||
\(438\) | 13.6168 | 0.650637 | ||||||||
\(439\) | −9.02989 | −0.430973 | −0.215487 | − | 0.976507i | \(-0.569134\pi\) | ||||
−0.215487 | + | 0.976507i | \(0.569134\pi\) | |||||||
\(440\) | 0.0375188 | 0.00178864 | ||||||||
\(441\) | 98.2980 | 4.68086 | ||||||||
\(442\) | −72.8641 | −3.46579 | ||||||||
\(443\) | −26.0447 | −1.23742 | −0.618712 | − | 0.785618i | \(-0.712345\pi\) | ||||
−0.618712 | + | 0.785618i | \(0.712345\pi\) | |||||||
\(444\) | −168.799 | −8.01082 | ||||||||
\(445\) | 3.21679 | 0.152490 | ||||||||
\(446\) | −29.2754 | −1.38623 | ||||||||
\(447\) | −39.6301 | −1.87444 | ||||||||
\(448\) | 190.994 | 9.02363 | ||||||||
\(449\) | −13.9042 | −0.656181 | −0.328090 | − | 0.944646i | \(-0.606405\pi\) | ||||
−0.328090 | + | 0.944646i | \(0.606405\pi\) | |||||||
\(450\) | 75.1543 | 3.54281 | ||||||||
\(451\) | −0.00890998 | −0.000419555 0 | ||||||||
\(452\) | 111.539 | 5.24636 | ||||||||
\(453\) | 57.6451 | 2.70840 | ||||||||
\(454\) | 60.7051 | 2.84903 | ||||||||
\(455\) | −28.1881 | −1.32148 | ||||||||
\(456\) | 81.3980 | 3.81181 | ||||||||
\(457\) | −6.47558 | −0.302915 | −0.151457 | − | 0.988464i | \(-0.548397\pi\) | ||||
−0.151457 | + | 0.988464i | \(0.548397\pi\) | |||||||
\(458\) | −18.8799 | −0.882199 | ||||||||
\(459\) | −47.6634 | −2.22474 | ||||||||
\(460\) | −5.51691 | −0.257227 | ||||||||
\(461\) | −15.1618 | −0.706157 | −0.353078 | − | 0.935594i | \(-0.614865\pi\) | ||||
−0.353078 | + | 0.935594i | \(0.614865\pi\) | |||||||
\(462\) | 0.151743 | 0.00705970 | ||||||||
\(463\) | 19.1112 | 0.888171 | 0.444086 | − | 0.895984i | \(-0.353529\pi\) | ||||
0.444086 | + | 0.895984i | \(0.353529\pi\) | |||||||
\(464\) | 47.4903 | 2.20468 | ||||||||
\(465\) | −5.20681 | −0.241460 | ||||||||
\(466\) | 68.7690 | 3.18566 | ||||||||
\(467\) | 15.7093 | 0.726938 | 0.363469 | − | 0.931606i | \(-0.381592\pi\) | ||||
0.363469 | + | 0.931606i | \(0.381592\pi\) | |||||||
\(468\) | 237.665 | 10.9861 | ||||||||
\(469\) | 17.0691 | 0.788178 | ||||||||
\(470\) | −20.2805 | −0.935472 | ||||||||
\(471\) | −50.1853 | −2.31242 | ||||||||
\(472\) | −98.0150 | −4.51150 | ||||||||
\(473\) | −0.0192194 | −0.000883710 0 | ||||||||
\(474\) | 5.21245 | 0.239416 | ||||||||
\(475\) | −10.3394 | −0.474404 | ||||||||
\(476\) | 111.803 | 5.12446 | ||||||||
\(477\) | 78.7115 | 3.60395 | ||||||||
\(478\) | −40.5060 | −1.85270 | ||||||||
\(479\) | −38.0748 | −1.73968 | −0.869840 | − | 0.493334i | \(-0.835778\pi\) | ||||
−0.869840 | + | 0.493334i | \(0.835778\pi\) | |||||||
\(480\) | −81.4208 | −3.71633 | ||||||||
\(481\) | 59.4878 | 2.71241 | ||||||||
\(482\) | 11.3967 | 0.519106 | ||||||||
\(483\) | −14.4981 | −0.659686 | ||||||||
\(484\) | −62.8150 | −2.85523 | ||||||||
\(485\) | −10.1465 | −0.460729 | ||||||||
\(486\) | 37.6400 | 1.70739 | ||||||||
\(487\) | 10.0164 | 0.453885 | 0.226942 | − | 0.973908i | \(-0.427127\pi\) | ||||
0.226942 | + | 0.973908i | \(0.427127\pi\) | |||||||
\(488\) | 115.563 | 5.23130 | ||||||||
\(489\) | −33.3724 | −1.50915 | ||||||||
\(490\) | 39.6216 | 1.78992 | ||||||||
\(491\) | −20.0866 | −0.906495 | −0.453248 | − | 0.891385i | \(-0.649735\pi\) | ||||
−0.453248 | + | 0.891385i | \(0.649735\pi\) | |||||||
\(492\) | 41.9448 | 1.89102 | ||||||||
\(493\) | 11.5938 | 0.522157 | ||||||||
\(494\) | −44.1486 | −1.98634 | ||||||||
\(495\) | −0.0242359 | −0.00108932 | ||||||||
\(496\) | −29.8123 | −1.33861 | ||||||||
\(497\) | 10.5379 | 0.472691 | ||||||||
\(498\) | −137.485 | −6.16085 | ||||||||
\(499\) | −27.1958 | −1.21745 | −0.608725 | − | 0.793382i | \(-0.708319\pi\) | ||||
−0.608725 | + | 0.793382i | \(0.708319\pi\) | |||||||
\(500\) | 50.0198 | 2.23695 | ||||||||
\(501\) | −42.3728 | −1.89308 | ||||||||
\(502\) | 55.4172 | 2.47339 | ||||||||
\(503\) | −12.6464 | −0.563875 | −0.281938 | − | 0.959433i | \(-0.590977\pi\) | ||||
−0.281938 | + | 0.959433i | \(0.590977\pi\) | |||||||
\(504\) | −319.941 | −14.2513 | ||||||||
\(505\) | −6.97733 | −0.310487 | ||||||||
\(506\) | −0.0104664 | −0.000465287 0 | ||||||||
\(507\) | −81.1172 | −3.60254 | ||||||||
\(508\) | 20.0410 | 0.889174 | ||||||||
\(509\) | 31.2951 | 1.38713 | 0.693566 | − | 0.720393i | \(-0.256039\pi\) | ||||
0.693566 | + | 0.720393i | \(0.256039\pi\) | |||||||
\(510\) | −34.9790 | −1.54890 | ||||||||
\(511\) | 7.36332 | 0.325734 | ||||||||
\(512\) | −111.999 | −4.94969 | ||||||||
\(513\) | −28.8794 | −1.27506 | ||||||||
\(514\) | 74.1139 | 3.26903 | ||||||||
\(515\) | −12.9208 | −0.569359 | ||||||||
\(516\) | 90.4776 | 3.98306 | ||||||||
\(517\) | −0.0284952 | −0.00125322 | ||||||||
\(518\) | −123.247 | −5.41516 | ||||||||
\(519\) | −39.9677 | −1.75439 | ||||||||
\(520\) | 62.2457 | 2.72966 | ||||||||
\(521\) | 39.1149 | 1.71366 | 0.856828 | − | 0.515603i | \(-0.172432\pi\) | ||||
0.856828 | + | 0.515603i | \(0.172432\pi\) | |||||||
\(522\) | −51.0607 | −2.23486 | ||||||||
\(523\) | −9.51402 | −0.416019 | −0.208010 | − | 0.978127i | \(-0.566699\pi\) | ||||
−0.208010 | + | 0.978127i | \(0.566699\pi\) | |||||||
\(524\) | −15.6637 | −0.684270 | ||||||||
\(525\) | 58.9585 | 2.57316 | ||||||||
\(526\) | 43.4603 | 1.89496 | ||||||||
\(527\) | −7.27807 | −0.317038 | ||||||||
\(528\) | −0.201316 | −0.00876117 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 31.7267 | 1.37812 | ||||||||
\(531\) | 63.3144 | 2.74761 | ||||||||
\(532\) | 67.7415 | 2.93697 | ||||||||
\(533\) | −14.7821 | −0.640286 | ||||||||
\(534\) | −28.7292 | −1.24324 | ||||||||
\(535\) | 3.59300 | 0.155339 | ||||||||
\(536\) | −37.6924 | −1.62806 | ||||||||
\(537\) | −65.9049 | −2.84401 | ||||||||
\(538\) | −15.1495 | −0.653142 | ||||||||
\(539\) | 0.0556702 | 0.00239789 | ||||||||
\(540\) | 62.6649 | 2.69667 | ||||||||
\(541\) | −16.1246 | −0.693250 | −0.346625 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346625 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(542\) | 31.6326 | 1.35873 | ||||||||
\(543\) | 51.0110 | 2.18909 | ||||||||
\(544\) | −113.810 | −4.87956 | ||||||||
\(545\) | 8.06337 | 0.345397 | ||||||||
\(546\) | 251.749 | 10.7739 | ||||||||
\(547\) | 12.5283 | 0.535673 | 0.267836 | − | 0.963464i | \(-0.413691\pi\) | ||||
0.267836 | + | 0.963464i | \(0.413691\pi\) | |||||||
\(548\) | 44.9758 | 1.92127 | ||||||||
\(549\) | −74.6500 | −3.18598 | ||||||||
\(550\) | 0.0425630 | 0.00181489 | ||||||||
\(551\) | 7.02470 | 0.299262 | ||||||||
\(552\) | 32.0151 | 1.36265 | ||||||||
\(553\) | 2.81864 | 0.119861 | ||||||||
\(554\) | 42.6804 | 1.81332 | ||||||||
\(555\) | 28.5577 | 1.21220 | ||||||||
\(556\) | 90.3950 | 3.83360 | ||||||||
\(557\) | −5.87314 | −0.248853 | −0.124427 | − | 0.992229i | \(-0.539709\pi\) | ||||
−0.124427 | + | 0.992229i | \(0.539709\pi\) | |||||||
\(558\) | 32.0537 | 1.35694 | ||||||||
\(559\) | −31.8861 | −1.34864 | ||||||||
\(560\) | −77.4793 | −3.27410 | ||||||||
\(561\) | −0.0491472 | −0.00207500 | ||||||||
\(562\) | 67.3428 | 2.84069 | ||||||||
\(563\) | 34.6058 | 1.45846 | 0.729231 | − | 0.684267i | \(-0.239878\pi\) | ||||
0.729231 | + | 0.684267i | \(0.239878\pi\) | |||||||
\(564\) | 134.144 | 5.64849 | ||||||||
\(565\) | −18.8704 | −0.793884 | ||||||||
\(566\) | 41.7304 | 1.75406 | ||||||||
\(567\) | 71.5206 | 3.00358 | ||||||||
\(568\) | −23.2701 | −0.976393 | ||||||||
\(569\) | −15.4399 | −0.647273 | −0.323637 | − | 0.946181i | \(-0.604906\pi\) | ||||
−0.323637 | + | 0.946181i | \(0.604906\pi\) | |||||||
\(570\) | −21.1939 | −0.887715 | ||||||||
\(571\) | 44.4391 | 1.85972 | 0.929858 | − | 0.367918i | \(-0.119929\pi\) | ||||
0.929858 | + | 0.367918i | \(0.119929\pi\) | |||||||
\(572\) | 0.134600 | 0.00562790 | ||||||||
\(573\) | −28.3603 | −1.18477 | ||||||||
\(574\) | 30.6256 | 1.27829 | ||||||||
\(575\) | −4.06664 | −0.169591 | ||||||||
\(576\) | 272.442 | 11.3517 | ||||||||
\(577\) | −37.5616 | −1.56371 | −0.781855 | − | 0.623460i | \(-0.785726\pi\) | ||||
−0.781855 | + | 0.623460i | \(0.785726\pi\) | |||||||
\(578\) | −1.68857 | −0.0702352 | ||||||||
\(579\) | −50.9465 | −2.11726 | ||||||||
\(580\) | −15.2428 | −0.632922 | ||||||||
\(581\) | −74.3453 | −3.08436 | ||||||||
\(582\) | 90.6187 | 3.75627 | ||||||||
\(583\) | 0.0445776 | 0.00184621 | ||||||||
\(584\) | −16.2599 | −0.672838 | ||||||||
\(585\) | −40.2087 | −1.66242 | ||||||||
\(586\) | 48.0995 | 1.98697 | ||||||||
\(587\) | 6.98871 | 0.288455 | 0.144227 | − | 0.989545i | \(-0.453930\pi\) | ||||
0.144227 | + | 0.989545i | \(0.453930\pi\) | |||||||
\(588\) | −262.074 | −10.8078 | ||||||||
\(589\) | −4.40981 | −0.181703 | ||||||||
\(590\) | 25.5205 | 1.05066 | ||||||||
\(591\) | 16.2315 | 0.667674 | ||||||||
\(592\) | 163.511 | 6.72027 | ||||||||
\(593\) | 41.4073 | 1.70039 | 0.850197 | − | 0.526465i | \(-0.176483\pi\) | ||||
0.850197 | + | 0.526465i | \(0.176483\pi\) | |||||||
\(594\) | 0.118884 | 0.00487789 | ||||||||
\(595\) | −18.9150 | −0.775438 | ||||||||
\(596\) | 72.8299 | 2.98323 | ||||||||
\(597\) | 23.4845 | 0.961156 | ||||||||
\(598\) | −17.3643 | −0.710079 | ||||||||
\(599\) | 2.15507 | 0.0880539 | 0.0440270 | − | 0.999030i | \(-0.485981\pi\) | ||||
0.0440270 | + | 0.999030i | \(0.485981\pi\) | |||||||
\(600\) | −130.194 | −5.31513 | ||||||||
\(601\) | −30.3806 | −1.23925 | −0.619625 | − | 0.784898i | \(-0.712715\pi\) | ||||
−0.619625 | + | 0.784898i | \(0.712715\pi\) | |||||||
\(602\) | 66.0615 | 2.69247 | ||||||||
\(603\) | 24.3481 | 0.991529 | ||||||||
\(604\) | −105.937 | −4.31051 | ||||||||
\(605\) | 10.6272 | 0.432055 | ||||||||
\(606\) | 62.3148 | 2.53137 | ||||||||
\(607\) | 23.1999 | 0.941653 | 0.470827 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470827 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(608\) | −68.9578 | −2.79661 | ||||||||
\(609\) | −40.0571 | −1.62320 | ||||||||
\(610\) | −30.0896 | −1.21829 | ||||||||
\(611\) | −47.2750 | −1.91254 | ||||||||
\(612\) | 159.480 | 6.44658 | ||||||||
\(613\) | 26.2793 | 1.06141 | 0.530706 | − | 0.847556i | \(-0.321927\pi\) | ||||
0.530706 | + | 0.847556i | \(0.321927\pi\) | |||||||
\(614\) | −79.1649 | −3.19484 | ||||||||
\(615\) | −7.09629 | −0.286150 | ||||||||
\(616\) | −0.181196 | −0.00730060 | ||||||||
\(617\) | 8.59311 | 0.345946 | 0.172973 | − | 0.984927i | \(-0.444663\pi\) | ||||
0.172973 | + | 0.984927i | \(0.444663\pi\) | |||||||
\(618\) | 115.396 | 4.64192 | ||||||||
\(619\) | 47.5426 | 1.91090 | 0.955448 | − | 0.295159i | \(-0.0953725\pi\) | ||||
0.955448 | + | 0.295159i | \(0.0953725\pi\) | |||||||
\(620\) | 9.56877 | 0.384291 | ||||||||
\(621\) | −11.3587 | −0.455809 | ||||||||
\(622\) | 47.4495 | 1.90255 | ||||||||
\(623\) | −15.5354 | −0.622412 | ||||||||
\(624\) | −333.995 | −13.3705 | ||||||||
\(625\) | 11.8707 | 0.474830 | ||||||||
\(626\) | 10.0148 | 0.400271 | ||||||||
\(627\) | −0.0297785 | −0.00118924 | ||||||||
\(628\) | 92.2276 | 3.68028 | ||||||||
\(629\) | 39.9179 | 1.59163 | ||||||||
\(630\) | 83.3043 | 3.31892 | ||||||||
\(631\) | −36.5823 | −1.45632 | −0.728160 | − | 0.685408i | \(-0.759624\pi\) | ||||
−0.728160 | + | 0.685408i | \(0.759624\pi\) | |||||||
\(632\) | −6.22419 | −0.247585 | ||||||||
\(633\) | 50.6946 | 2.01493 | ||||||||
\(634\) | −68.7285 | −2.72956 | ||||||||
\(635\) | −3.39057 | −0.134551 | ||||||||
\(636\) | −209.854 | −8.32126 | ||||||||
\(637\) | 92.3599 | 3.65943 | ||||||||
\(638\) | −0.0289178 | −0.00114487 | ||||||||
\(639\) | 15.0317 | 0.594646 | ||||||||
\(640\) | 57.4091 | 2.26929 | ||||||||
\(641\) | −7.49147 | −0.295895 | −0.147948 | − | 0.988995i | \(-0.547267\pi\) | ||||
−0.147948 | + | 0.988995i | \(0.547267\pi\) | |||||||
\(642\) | −32.0892 | −1.26646 | ||||||||
\(643\) | 8.82930 | 0.348193 | 0.174097 | − | 0.984729i | \(-0.444299\pi\) | ||||
0.174097 | + | 0.984729i | \(0.444299\pi\) | |||||||
\(644\) | 26.6438 | 1.04991 | ||||||||
\(645\) | −15.3072 | −0.602719 | ||||||||
\(646\) | −29.6248 | −1.16557 | ||||||||
\(647\) | 47.8933 | 1.88288 | 0.941439 | − | 0.337182i | \(-0.109474\pi\) | ||||
0.941439 | + | 0.337182i | \(0.109474\pi\) | |||||||
\(648\) | −157.934 | −6.20422 | ||||||||
\(649\) | 0.0358576 | 0.00140753 | ||||||||
\(650\) | 70.6143 | 2.76972 | ||||||||
\(651\) | 25.1461 | 0.985554 | ||||||||
\(652\) | 61.3299 | 2.40186 | ||||||||
\(653\) | 27.8575 | 1.09015 | 0.545074 | − | 0.838388i | \(-0.316502\pi\) | ||||
0.545074 | + | 0.838388i | \(0.316502\pi\) | |||||||
\(654\) | −72.0142 | −2.81598 | ||||||||
\(655\) | 2.65001 | 0.103544 | ||||||||
\(656\) | −40.6309 | −1.58637 | ||||||||
\(657\) | 10.5033 | 0.409774 | ||||||||
\(658\) | 97.9443 | 3.81827 | ||||||||
\(659\) | 14.8348 | 0.577882 | 0.288941 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288941 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(660\) | 0.0646158 | 0.00251517 | ||||||||
\(661\) | 8.31497 | 0.323415 | 0.161707 | − | 0.986839i | \(-0.448300\pi\) | ||||
0.161707 | + | 0.986839i | \(0.448300\pi\) | |||||||
\(662\) | 34.5964 | 1.34463 | ||||||||
\(663\) | −81.5380 | −3.16667 | ||||||||
\(664\) | 164.171 | 6.37107 | ||||||||
\(665\) | −11.4606 | −0.444425 | ||||||||
\(666\) | −175.804 | −6.81228 | ||||||||
\(667\) | 2.76292 | 0.106981 | ||||||||
\(668\) | 77.8702 | 3.01289 | ||||||||
\(669\) | −32.7604 | −1.26659 | ||||||||
\(670\) | 9.81412 | 0.379152 | ||||||||
\(671\) | −0.0422774 | −0.00163210 | ||||||||
\(672\) | 393.219 | 15.1688 | ||||||||
\(673\) | −13.4063 | −0.516774 | −0.258387 | − | 0.966041i | \(-0.583191\pi\) | ||||
−0.258387 | + | 0.966041i | \(0.583191\pi\) | |||||||
\(674\) | 8.68657 | 0.334594 | ||||||||
\(675\) | 46.1917 | 1.77792 | ||||||||
\(676\) | 149.072 | 5.73356 | ||||||||
\(677\) | −2.56649 | −0.0986382 | −0.0493191 | − | 0.998783i | \(-0.515705\pi\) | ||||
−0.0493191 | + | 0.998783i | \(0.515705\pi\) | |||||||
\(678\) | 168.532 | 6.47244 | ||||||||
\(679\) | 49.0022 | 1.88053 | ||||||||
\(680\) | 41.7685 | 1.60175 | ||||||||
\(681\) | 67.9316 | 2.60314 | ||||||||
\(682\) | 0.0181533 | 0.000695127 0 | ||||||||
\(683\) | −22.5405 | −0.862488 | −0.431244 | − | 0.902235i | \(-0.641925\pi\) | ||||
−0.431244 | + | 0.902235i | \(0.641925\pi\) | |||||||
\(684\) | 96.6292 | 3.69471 | ||||||||
\(685\) | −7.60909 | −0.290728 | ||||||||
\(686\) | −100.661 | −3.84324 | ||||||||
\(687\) | −21.1274 | −0.806060 | ||||||||
\(688\) | −87.6435 | −3.34138 | ||||||||
\(689\) | 73.9566 | 2.81752 | ||||||||
\(690\) | −8.33588 | −0.317342 | ||||||||
\(691\) | 6.49505 | 0.247083 | 0.123542 | − | 0.992339i | \(-0.460575\pi\) | ||||
0.123542 | + | 0.992339i | \(0.460575\pi\) | |||||||
\(692\) | 73.4504 | 2.79216 | ||||||||
\(693\) | 0.117047 | 0.00444623 | ||||||||
\(694\) | −99.2884 | −3.76894 | ||||||||
\(695\) | −15.2932 | −0.580104 | ||||||||
\(696\) | 88.4551 | 3.35288 | ||||||||
\(697\) | −9.91920 | −0.375716 | ||||||||
\(698\) | 2.77677 | 0.105102 | ||||||||
\(699\) | 76.9553 | 2.91072 | ||||||||
\(700\) | −108.351 | −4.09527 | ||||||||
\(701\) | 15.9523 | 0.602511 | 0.301256 | − | 0.953543i | \(-0.402594\pi\) | ||||
0.301256 | + | 0.953543i | \(0.402594\pi\) | |||||||
\(702\) | 197.236 | 7.44418 | ||||||||
\(703\) | 24.1864 | 0.912206 | ||||||||
\(704\) | 0.154295 | 0.00581522 | ||||||||
\(705\) | −22.6948 | −0.854735 | ||||||||
\(706\) | −38.5162 | −1.44958 | ||||||||
\(707\) | 33.6968 | 1.26730 | ||||||||
\(708\) | −168.804 | −6.34403 | ||||||||
\(709\) | 14.1416 | 0.531098 | 0.265549 | − | 0.964097i | \(-0.414447\pi\) | ||||
0.265549 | + | 0.964097i | \(0.414447\pi\) | |||||||
\(710\) | 6.05893 | 0.227388 | ||||||||
\(711\) | 4.02062 | 0.150785 | ||||||||
\(712\) | 34.3056 | 1.28566 | ||||||||
\(713\) | −1.73444 | −0.0649554 | ||||||||
\(714\) | 168.930 | 6.32206 | ||||||||
\(715\) | −0.0227718 | −0.000851619 0 | ||||||||
\(716\) | 121.116 | 4.52632 | ||||||||
\(717\) | −45.3279 | −1.69280 | ||||||||
\(718\) | 10.2338 | 0.381920 | ||||||||
\(719\) | 31.9387 | 1.19111 | 0.595557 | − | 0.803313i | \(-0.296931\pi\) | ||||
0.595557 | + | 0.803313i | \(0.296931\pi\) | |||||||
\(720\) | −110.520 | −4.11882 | ||||||||
\(721\) | 62.4007 | 2.32392 | ||||||||
\(722\) | 34.8089 | 1.29545 | ||||||||
\(723\) | 12.7534 | 0.474304 | ||||||||
\(724\) | −93.7450 | −3.48401 | ||||||||
\(725\) | −11.2358 | −0.417287 | ||||||||
\(726\) | −94.9115 | −3.52250 | ||||||||
\(727\) | −22.3862 | −0.830258 | −0.415129 | − | 0.909762i | \(-0.636264\pi\) | ||||
−0.415129 | + | 0.909762i | \(0.636264\pi\) | |||||||
\(728\) | −300.614 | −11.1415 | ||||||||
\(729\) | −3.86550 | −0.143167 | ||||||||
\(730\) | 4.23364 | 0.156694 | ||||||||
\(731\) | −21.3964 | −0.791373 | ||||||||
\(732\) | 199.026 | 7.35620 | ||||||||
\(733\) | −3.63197 | −0.134150 | −0.0670750 | − | 0.997748i | \(-0.521367\pi\) | ||||
−0.0670750 | + | 0.997748i | \(0.521367\pi\) | |||||||
\(734\) | 27.8701 | 1.02870 | ||||||||
\(735\) | 44.3382 | 1.63544 | ||||||||
\(736\) | −27.1221 | −0.999735 | ||||||||
\(737\) | 0.0137893 | 0.000507936 0 | ||||||||
\(738\) | 43.6856 | 1.60809 | ||||||||
\(739\) | 3.00310 | 0.110471 | 0.0552355 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552355 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(740\) | −52.4816 | −1.92926 | ||||||||
\(741\) | −49.4041 | −1.81490 | ||||||||
\(742\) | −153.223 | −5.62500 | ||||||||
\(743\) | −18.2384 | −0.669101 | −0.334550 | − | 0.942378i | \(-0.608584\pi\) | ||||
−0.334550 | + | 0.942378i | \(0.608584\pi\) | |||||||
\(744\) | −55.5283 | −2.03577 | ||||||||
\(745\) | −12.3215 | −0.451425 | ||||||||
\(746\) | −34.0911 | −1.24816 | ||||||||
\(747\) | −106.049 | −3.88013 | ||||||||
\(748\) | 0.0903200 | 0.00330242 | ||||||||
\(749\) | −17.3523 | −0.634039 | ||||||||
\(750\) | 75.5784 | 2.75973 | ||||||||
\(751\) | −28.7223 | −1.04809 | −0.524046 | − | 0.851690i | \(-0.675578\pi\) | ||||
−0.524046 | + | 0.851690i | \(0.675578\pi\) | |||||||
\(752\) | −129.942 | −4.73851 | ||||||||
\(753\) | 62.0141 | 2.25992 | ||||||||
\(754\) | −47.9762 | −1.74719 | ||||||||
\(755\) | 17.9226 | 0.652269 | ||||||||
\(756\) | −302.638 | −11.0068 | ||||||||
\(757\) | −15.7574 | −0.572712 | −0.286356 | − | 0.958123i | \(-0.592444\pi\) | ||||
−0.286356 | + | 0.958123i | \(0.592444\pi\) | |||||||
\(758\) | −54.4344 | −1.97715 | ||||||||
\(759\) | −0.0117123 | −0.000425130 0 | ||||||||
\(760\) | 25.3077 | 0.918006 | ||||||||
\(761\) | −27.0461 | −0.980421 | −0.490210 | − | 0.871604i | \(-0.663080\pi\) | ||||
−0.490210 | + | 0.871604i | \(0.663080\pi\) | |||||||
\(762\) | 30.2813 | 1.09697 | ||||||||
\(763\) | −38.9418 | −1.40979 | ||||||||
\(764\) | 52.1190 | 1.88560 | ||||||||
\(765\) | −26.9811 | −0.975503 | ||||||||
\(766\) | 6.29697 | 0.227519 | ||||||||
\(767\) | 59.4897 | 2.14805 | ||||||||
\(768\) | −258.325 | −9.32151 | ||||||||
\(769\) | 11.8466 | 0.427199 | 0.213600 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213600 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(770\) | 0.0471787 | 0.00170020 | ||||||||
\(771\) | 82.9366 | 2.98689 | ||||||||
\(772\) | 93.6264 | 3.36969 | ||||||||
\(773\) | 30.6942 | 1.10399 | 0.551997 | − | 0.833846i | \(-0.313866\pi\) | ||||
0.551997 | + | 0.833846i | \(0.313866\pi\) | |||||||
\(774\) | 94.2327 | 3.38713 | ||||||||
\(775\) | 7.05335 | 0.253364 | ||||||||
\(776\) | −108.208 | −3.88444 | ||||||||
\(777\) | −137.918 | −4.94779 | ||||||||
\(778\) | −26.2447 | −0.940919 | ||||||||
\(779\) | −6.01007 | −0.215333 | ||||||||
\(780\) | 107.201 | 3.83842 | ||||||||
\(781\) | 0.00851310 | 0.000304623 0 | ||||||||
\(782\) | −11.6519 | −0.416671 | ||||||||
\(783\) | −31.3832 | −1.12154 | ||||||||
\(784\) | 253.865 | 9.06660 | ||||||||
\(785\) | −15.6032 | −0.556903 | ||||||||
\(786\) | −23.6673 | −0.844184 | ||||||||
\(787\) | −22.4534 | −0.800376 | −0.400188 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(788\) | −29.8293 | −1.06262 | ||||||||
\(789\) | 48.6339 | 1.73141 | ||||||||
\(790\) | 1.62062 | 0.0576590 | ||||||||
\(791\) | 91.1340 | 3.24035 | ||||||||
\(792\) | −0.258465 | −0.00918416 | ||||||||
\(793\) | −70.1405 | −2.49076 | ||||||||
\(794\) | −81.9658 | −2.90886 | ||||||||
\(795\) | 35.5035 | 1.25918 | ||||||||
\(796\) | −43.1584 | −1.52971 | ||||||||
\(797\) | −33.1848 | −1.17547 | −0.587733 | − | 0.809055i | \(-0.699979\pi\) | ||||
−0.587733 | + | 0.809055i | \(0.699979\pi\) | |||||||
\(798\) | 102.355 | 3.62334 | ||||||||
\(799\) | −31.7228 | −1.12227 | ||||||||
\(800\) | 110.296 | 3.89955 | ||||||||
\(801\) | −22.1603 | −0.782996 | ||||||||
\(802\) | −79.9675 | −2.82375 | ||||||||
\(803\) | 0.00594848 | 0.000209917 0 | ||||||||
\(804\) | −64.9148 | −2.28937 | ||||||||
\(805\) | −4.50764 | −0.158873 | ||||||||
\(806\) | 30.1174 | 1.06084 | ||||||||
\(807\) | −16.9529 | −0.596772 | ||||||||
\(808\) | −74.4102 | −2.61774 | ||||||||
\(809\) | −34.4832 | −1.21236 | −0.606182 | − | 0.795326i | \(-0.707300\pi\) | ||||
−0.606182 | + | 0.795326i | \(0.707300\pi\) | |||||||
\(810\) | 41.1218 | 1.44487 | ||||||||
\(811\) | −12.2159 | −0.428958 | −0.214479 | − | 0.976729i | \(-0.568805\pi\) | ||||
−0.214479 | + | 0.976729i | \(0.568805\pi\) | |||||||
\(812\) | 73.6146 | 2.58337 | ||||||||
\(813\) | 35.3982 | 1.24147 | ||||||||
\(814\) | −0.0995652 | −0.00348976 | ||||||||
\(815\) | −10.3759 | −0.363452 | ||||||||
\(816\) | −224.119 | −7.84574 | ||||||||
\(817\) | −12.9641 | −0.453557 | ||||||||
\(818\) | 70.2911 | 2.45767 | ||||||||
\(819\) | 194.187 | 6.78543 | ||||||||
\(820\) | 13.0412 | 0.455417 | ||||||||
\(821\) | −11.2220 | −0.391651 | −0.195826 | − | 0.980639i | \(-0.562739\pi\) | ||||
−0.195826 | + | 0.980639i | \(0.562739\pi\) | |||||||
\(822\) | 67.9570 | 2.37027 | ||||||||
\(823\) | 4.48470 | 0.156327 | 0.0781635 | − | 0.996941i | \(-0.475094\pi\) | ||||
0.0781635 | + | 0.996941i | \(0.475094\pi\) | |||||||
\(824\) | −137.795 | −4.80031 | ||||||||
\(825\) | 0.0476298 | 0.00165826 | ||||||||
\(826\) | −123.251 | −4.28844 | ||||||||
\(827\) | 1.94021 | 0.0674679 | 0.0337339 | − | 0.999431i | \(-0.489260\pi\) | ||||
0.0337339 | + | 0.999431i | \(0.489260\pi\) | |||||||
\(828\) | 38.0057 | 1.32079 | ||||||||
\(829\) | 22.3122 | 0.774934 | 0.387467 | − | 0.921884i | \(-0.373350\pi\) | ||||
0.387467 | + | 0.921884i | \(0.373350\pi\) | |||||||
\(830\) | −42.7458 | −1.48373 | ||||||||
\(831\) | 47.7611 | 1.65681 | ||||||||
\(832\) | 255.984 | 8.87465 | ||||||||
\(833\) | 61.9759 | 2.14734 | ||||||||
\(834\) | 136.584 | 4.72952 | ||||||||
\(835\) | −13.1742 | −0.455913 | ||||||||
\(836\) | 0.0547251 | 0.00189271 | ||||||||
\(837\) | 19.7010 | 0.680966 | ||||||||
\(838\) | 7.62925 | 0.263548 | ||||||||
\(839\) | −20.7837 | −0.717533 | −0.358766 | − | 0.933427i | \(-0.616803\pi\) | ||||
−0.358766 | + | 0.933427i | \(0.616803\pi\) | |||||||
\(840\) | −144.312 | −4.97925 | ||||||||
\(841\) | −21.3663 | −0.736768 | ||||||||
\(842\) | −1.59227 | −0.0548731 | ||||||||
\(843\) | 75.3594 | 2.59552 | ||||||||
\(844\) | −93.1635 | −3.20682 | ||||||||
\(845\) | −25.2204 | −0.867607 | ||||||||
\(846\) | 139.712 | 4.80339 | ||||||||
\(847\) | −51.3235 | −1.76350 | ||||||||
\(848\) | 203.281 | 6.98069 | ||||||||
\(849\) | 46.6981 | 1.60267 | ||||||||
\(850\) | 47.3840 | 1.62526 | ||||||||
\(851\) | 9.51286 | 0.326097 | ||||||||
\(852\) | −40.0764 | −1.37299 | ||||||||
\(853\) | −16.5772 | −0.567592 | −0.283796 | − | 0.958885i | \(-0.591594\pi\) | ||||
−0.283796 | + | 0.958885i | \(0.591594\pi\) | |||||||
\(854\) | 145.317 | 4.97264 | ||||||||
\(855\) | −16.3479 | −0.559087 | ||||||||
\(856\) | 38.3177 | 1.30967 | ||||||||
\(857\) | −1.99969 | −0.0683081 | −0.0341540 | − | 0.999417i | \(-0.510874\pi\) | ||||
−0.0341540 | + | 0.999417i | \(0.510874\pi\) | |||||||
\(858\) | 0.203376 | 0.00694315 | ||||||||
\(859\) | −55.5358 | −1.89486 | −0.947428 | − | 0.319969i | \(-0.896327\pi\) | ||||
−0.947428 | + | 0.319969i | \(0.896327\pi\) | |||||||
\(860\) | 28.1306 | 0.959247 | ||||||||
\(861\) | 34.2713 | 1.16796 | ||||||||
\(862\) | 53.7705 | 1.83143 | ||||||||
\(863\) | −52.5776 | −1.78976 | −0.894882 | − | 0.446304i | \(-0.852740\pi\) | ||||
−0.894882 | + | 0.446304i | \(0.852740\pi\) | |||||||
\(864\) | 308.072 | 10.4808 | ||||||||
\(865\) | −12.4265 | −0.422513 | ||||||||
\(866\) | 37.1986 | 1.26406 | ||||||||
\(867\) | −1.88958 | −0.0641735 | ||||||||
\(868\) | −46.2121 | −1.56854 | ||||||||
\(869\) | 0.00227705 | 7.72435e−5 0 | ||||||||
\(870\) | −23.0314 | −0.780837 | ||||||||
\(871\) | 22.8772 | 0.775165 | ||||||||
\(872\) | 85.9923 | 2.91207 | ||||||||
\(873\) | 69.8988 | 2.36571 | ||||||||
\(874\) | −7.05992 | −0.238805 | ||||||||
\(875\) | 40.8692 | 1.38163 | ||||||||
\(876\) | −28.0032 | −0.946139 | ||||||||
\(877\) | 21.4147 | 0.723122 | 0.361561 | − | 0.932349i | \(-0.382244\pi\) | ||||
0.361561 | + | 0.932349i | \(0.382244\pi\) | |||||||
\(878\) | 25.0739 | 0.846205 | ||||||||
\(879\) | 53.8253 | 1.81548 | ||||||||
\(880\) | −0.0625918 | −0.00210997 | ||||||||
\(881\) | 46.1941 | 1.55632 | 0.778159 | − | 0.628068i | \(-0.216154\pi\) | ||||
0.778159 | + | 0.628068i | \(0.216154\pi\) | |||||||
\(882\) | −272.951 | −9.19074 | ||||||||
\(883\) | −37.3661 | −1.25747 | −0.628734 | − | 0.777620i | \(-0.716427\pi\) | ||||
−0.628734 | + | 0.777620i | \(0.716427\pi\) | |||||||
\(884\) | 149.846 | 5.03986 | ||||||||
\(885\) | 28.5585 | 0.959985 | ||||||||
\(886\) | 72.3203 | 2.42965 | ||||||||
\(887\) | −9.32904 | −0.313238 | −0.156619 | − | 0.987659i | \(-0.550060\pi\) | ||||
−0.156619 | + | 0.987659i | \(0.550060\pi\) | |||||||
\(888\) | 304.555 | 10.2202 | ||||||||
\(889\) | 16.3747 | 0.549188 | ||||||||
\(890\) | −8.93229 | −0.299411 | ||||||||
\(891\) | 0.0577781 | 0.00193564 | ||||||||
\(892\) | 60.2051 | 2.01582 | ||||||||
\(893\) | −19.2209 | −0.643204 | ||||||||
\(894\) | 110.044 | 3.68041 | ||||||||
\(895\) | −20.4907 | −0.684927 | ||||||||
\(896\) | −277.256 | −9.26246 | ||||||||
\(897\) | −19.4314 | −0.648795 | ||||||||
\(898\) | 38.6088 | 1.28839 | ||||||||
\(899\) | −4.79213 | −0.159826 | ||||||||
\(900\) | −154.556 | −5.15185 | ||||||||
\(901\) | 49.6268 | 1.65331 | ||||||||
\(902\) | 0.0247410 | 0.000823784 0 | ||||||||
\(903\) | 73.9256 | 2.46009 | ||||||||
\(904\) | −201.244 | −6.69329 | ||||||||
\(905\) | 15.8600 | 0.527203 | ||||||||
\(906\) | −160.067 | −5.31788 | ||||||||
\(907\) | −34.5079 | −1.14582 | −0.572908 | − | 0.819620i | \(-0.694185\pi\) | ||||
−0.572908 | + | 0.819620i | \(0.694185\pi\) | |||||||
\(908\) | −124.841 | −4.14298 | ||||||||
\(909\) | 48.0665 | 1.59427 | ||||||||
\(910\) | 78.2720 | 2.59469 | ||||||||
\(911\) | 7.67345 | 0.254233 | 0.127116 | − | 0.991888i | \(-0.459428\pi\) | ||||
0.127116 | + | 0.991888i | \(0.459428\pi\) | |||||||
\(912\) | −135.794 | −4.49660 | ||||||||
\(913\) | −0.0600600 | −0.00198770 | ||||||||
\(914\) | 17.9812 | 0.594766 | ||||||||
\(915\) | −33.6715 | −1.11315 | ||||||||
\(916\) | 38.8267 | 1.28287 | ||||||||
\(917\) | −12.7981 | −0.422632 | ||||||||
\(918\) | 132.350 | 4.36821 | ||||||||
\(919\) | 53.5890 | 1.76774 | 0.883868 | − | 0.467736i | \(-0.154930\pi\) | ||||
0.883868 | + | 0.467736i | \(0.154930\pi\) | |||||||
\(920\) | 9.95389 | 0.328170 | ||||||||
\(921\) | −88.5888 | −2.91910 | ||||||||
\(922\) | 42.1009 | 1.38652 | ||||||||
\(923\) | 14.1237 | 0.464887 | ||||||||
\(924\) | −0.312060 | −0.0102660 | ||||||||
\(925\) | −38.6854 | −1.27197 | ||||||||
\(926\) | −53.0673 | −1.74390 | ||||||||
\(927\) | 89.0109 | 2.92350 | ||||||||
\(928\) | −74.9363 | −2.45990 | ||||||||
\(929\) | 17.6799 | 0.580058 | 0.290029 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290029 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(930\) | 14.4581 | 0.474100 | ||||||||
\(931\) | 37.5514 | 1.23070 | ||||||||
\(932\) | −141.424 | −4.63250 | ||||||||
\(933\) | 53.0980 | 1.73835 | ||||||||
\(934\) | −43.6210 | −1.42732 | ||||||||
\(935\) | −0.0152805 | −0.000499726 0 | ||||||||
\(936\) | −428.808 | −14.0160 | ||||||||
\(937\) | −23.6700 | −0.773266 | −0.386633 | − | 0.922234i | \(-0.626362\pi\) | ||||
−0.386633 | + | 0.922234i | \(0.626362\pi\) | |||||||
\(938\) | −47.3970 | −1.54757 | ||||||||
\(939\) | 11.2070 | 0.365725 | ||||||||
\(940\) | 41.7072 | 1.36034 | ||||||||
\(941\) | 8.42218 | 0.274555 | 0.137278 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137278 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(942\) | 139.353 | 4.54037 | ||||||||
\(943\) | −2.36385 | −0.0769776 | ||||||||
\(944\) | 163.516 | 5.32200 | ||||||||
\(945\) | 51.2009 | 1.66557 | ||||||||
\(946\) | 0.0533679 | 0.00173514 | ||||||||
\(947\) | −2.56544 | −0.0833655 | −0.0416827 | − | 0.999131i | \(-0.513272\pi\) | ||||
−0.0416827 | + | 0.999131i | \(0.513272\pi\) | |||||||
\(948\) | −10.7195 | −0.348152 | ||||||||
\(949\) | 9.86885 | 0.320356 | ||||||||
\(950\) | 28.7101 | 0.931480 | ||||||||
\(951\) | −76.9100 | −2.49398 | ||||||||
\(952\) | −201.720 | −6.53778 | ||||||||
\(953\) | 28.2310 | 0.914490 | 0.457245 | − | 0.889341i | \(-0.348836\pi\) | ||||
0.457245 | + | 0.889341i | \(0.348836\pi\) | |||||||
\(954\) | −218.564 | −7.07626 | ||||||||
\(955\) | −8.81758 | −0.285330 | ||||||||
\(956\) | 83.3011 | 2.69415 | ||||||||
\(957\) | −0.0323602 | −0.00104606 | ||||||||
\(958\) | 105.725 | 3.41582 | ||||||||
\(959\) | 36.7479 | 1.18665 | ||||||||
\(960\) | 122.887 | 3.96617 | ||||||||
\(961\) | −27.9917 | −0.902958 | ||||||||
\(962\) | −165.184 | −5.32575 | ||||||||
\(963\) | −24.7520 | −0.797622 | ||||||||
\(964\) | −23.4375 | −0.754870 | ||||||||
\(965\) | −15.8399 | −0.509904 | ||||||||
\(966\) | 40.2579 | 1.29528 | ||||||||
\(967\) | −46.6689 | −1.50077 | −0.750385 | − | 0.661001i | \(-0.770132\pi\) | ||||
−0.750385 | + | 0.661001i | \(0.770132\pi\) | |||||||
\(968\) | 113.334 | 3.64269 | ||||||||
\(969\) | −33.1514 | −1.06498 | ||||||||
\(970\) | 28.1745 | 0.904629 | ||||||||
\(971\) | 21.4465 | 0.688252 | 0.344126 | − | 0.938923i | \(-0.388175\pi\) | ||||
0.344126 | + | 0.938923i | \(0.388175\pi\) | |||||||
\(972\) | −77.4071 | −2.48283 | ||||||||
\(973\) | 73.8580 | 2.36778 | ||||||||
\(974\) | −27.8132 | −0.891191 | ||||||||
\(975\) | 79.0204 | 2.53068 | ||||||||
\(976\) | −192.791 | −6.17110 | ||||||||
\(977\) | 36.1272 | 1.15581 | 0.577906 | − | 0.816104i | \(-0.303870\pi\) | ||||
0.577906 | + | 0.816104i | \(0.303870\pi\) | |||||||
\(978\) | 92.6676 | 2.96318 | ||||||||
\(979\) | −0.0125503 | −0.000401109 0 | ||||||||
\(980\) | −81.4822 | −2.60285 | ||||||||
\(981\) | −55.5482 | −1.77352 | ||||||||
\(982\) | 55.7759 | 1.77988 | ||||||||
\(983\) | 10.8979 | 0.347588 | 0.173794 | − | 0.984782i | \(-0.444397\pi\) | ||||
0.173794 | + | 0.984782i | \(0.444397\pi\) | |||||||
\(984\) | −75.6788 | −2.41255 | ||||||||
\(985\) | 5.04657 | 0.160797 | ||||||||
\(986\) | −32.1933 | −1.02524 | ||||||||
\(987\) | 109.604 | 3.48873 | ||||||||
\(988\) | 90.7920 | 2.88848 | ||||||||
\(989\) | −5.09898 | −0.162138 | ||||||||
\(990\) | 0.0672976 | 0.00213886 | ||||||||
\(991\) | 31.8596 | 1.01205 | 0.506026 | − | 0.862518i | \(-0.331114\pi\) | ||||
0.506026 | + | 0.862518i | \(0.331114\pi\) | |||||||
\(992\) | 47.0418 | 1.49358 | ||||||||
\(993\) | 38.7148 | 1.22858 | ||||||||
\(994\) | −29.2615 | −0.928117 | ||||||||
\(995\) | 7.30162 | 0.231477 | ||||||||
\(996\) | 282.739 | 8.95894 | ||||||||
\(997\) | −7.65486 | −0.242432 | −0.121216 | − | 0.992626i | \(-0.538679\pi\) | ||||
−0.121216 | + | 0.992626i | \(0.538679\pi\) | |||||||
\(998\) | 75.5164 | 2.39043 | ||||||||
\(999\) | −108.054 | −3.41867 |
(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 | 8027.2.a.f.1.3 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.3 | ✓ | 176 | 1.1 | even | 1 | trivial |