Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(1,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.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: | \(1.92439468871\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.49073\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 241.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.49073 | 1.76121 | 0.880604 | − | 0.473852i | \(-0.157137\pi\) | ||||
0.880604 | + | 0.473852i | \(0.157137\pi\) | |||||||
\(3\) | 1.22208 | 0.705566 | 0.352783 | − | 0.935705i | \(-0.385235\pi\) | ||||
0.352783 | + | 0.935705i | \(0.385235\pi\) | |||||||
\(4\) | 4.20371 | 2.10186 | ||||||||
\(5\) | −3.14843 | −1.40802 | −0.704011 | − | 0.710189i | \(-0.748610\pi\) | ||||
−0.704011 | + | 0.710189i | \(0.748610\pi\) | |||||||
\(6\) | 3.04385 | 1.24265 | ||||||||
\(7\) | 0.136122 | 0.0514495 | 0.0257247 | − | 0.999669i | \(-0.491811\pi\) | ||||
0.0257247 | + | 0.999669i | \(0.491811\pi\) | |||||||
\(8\) | 5.48885 | 1.94060 | ||||||||
\(9\) | −1.50653 | −0.502177 | ||||||||
\(10\) | −7.84189 | −2.47982 | ||||||||
\(11\) | −0.905365 | −0.272978 | −0.136489 | − | 0.990642i | \(-0.543582\pi\) | ||||
−0.136489 | + | 0.990642i | \(0.543582\pi\) | |||||||
\(12\) | 5.13726 | 1.48300 | ||||||||
\(13\) | −0.123706 | −0.0343099 | −0.0171549 | − | 0.999853i | \(-0.505461\pi\) | ||||
−0.0171549 | + | 0.999853i | \(0.505461\pi\) | |||||||
\(14\) | 0.339044 | 0.0906133 | ||||||||
\(15\) | −3.84762 | −0.993452 | ||||||||
\(16\) | 5.26378 | 1.31595 | ||||||||
\(17\) | 1.26034 | 0.305678 | 0.152839 | − | 0.988251i | \(-0.451158\pi\) | ||||
0.152839 | + | 0.988251i | \(0.451158\pi\) | |||||||
\(18\) | −3.75236 | −0.884439 | ||||||||
\(19\) | −2.13460 | −0.489710 | −0.244855 | − | 0.969560i | \(-0.578740\pi\) | ||||
−0.244855 | + | 0.969560i | \(0.578740\pi\) | |||||||
\(20\) | −13.2351 | −2.95946 | ||||||||
\(21\) | 0.166352 | 0.0363010 | ||||||||
\(22\) | −2.25502 | −0.480771 | ||||||||
\(23\) | 6.64978 | 1.38657 | 0.693287 | − | 0.720661i | \(-0.256162\pi\) | ||||
0.693287 | + | 0.720661i | \(0.256162\pi\) | |||||||
\(24\) | 6.70778 | 1.36922 | ||||||||
\(25\) | 4.91264 | 0.982528 | ||||||||
\(26\) | −0.308118 | −0.0604269 | ||||||||
\(27\) | −5.50732 | −1.05988 | ||||||||
\(28\) | 0.572220 | 0.108139 | ||||||||
\(29\) | 5.36862 | 0.996928 | 0.498464 | − | 0.866911i | \(-0.333898\pi\) | ||||
0.498464 | + | 0.866911i | \(0.333898\pi\) | |||||||
\(30\) | −9.58338 | −1.74968 | ||||||||
\(31\) | −9.78467 | −1.75738 | −0.878689 | − | 0.477395i | \(-0.841581\pi\) | ||||
−0.878689 | + | 0.477395i | \(0.841581\pi\) | |||||||
\(32\) | 2.13295 | 0.377055 | ||||||||
\(33\) | −1.10642 | −0.192604 | ||||||||
\(34\) | 3.13917 | 0.538363 | ||||||||
\(35\) | −0.428573 | −0.0724420 | ||||||||
\(36\) | −6.33303 | −1.05550 | ||||||||
\(37\) | 5.76688 | 0.948070 | 0.474035 | − | 0.880506i | \(-0.342797\pi\) | ||||
0.474035 | + | 0.880506i | \(0.342797\pi\) | |||||||
\(38\) | −5.31669 | −0.862481 | ||||||||
\(39\) | −0.151178 | −0.0242079 | ||||||||
\(40\) | −17.2813 | −2.73241 | ||||||||
\(41\) | 6.43642 | 1.00520 | 0.502600 | − | 0.864519i | \(-0.332377\pi\) | ||||
0.502600 | + | 0.864519i | \(0.332377\pi\) | |||||||
\(42\) | 0.414337 | 0.0639336 | ||||||||
\(43\) | −3.18712 | −0.486032 | −0.243016 | − | 0.970022i | \(-0.578137\pi\) | ||||
−0.243016 | + | 0.970022i | \(0.578137\pi\) | |||||||
\(44\) | −3.80590 | −0.573761 | ||||||||
\(45\) | 4.74322 | 0.707077 | ||||||||
\(46\) | 16.5628 | 2.44205 | ||||||||
\(47\) | 12.9849 | 1.89404 | 0.947022 | − | 0.321168i | \(-0.104075\pi\) | ||||
0.947022 | + | 0.321168i | \(0.104075\pi\) | |||||||
\(48\) | 6.43274 | 0.928486 | ||||||||
\(49\) | −6.98147 | −0.997353 | ||||||||
\(50\) | 12.2360 | 1.73044 | ||||||||
\(51\) | 1.54023 | 0.215676 | ||||||||
\(52\) | −0.520025 | −0.0721145 | ||||||||
\(53\) | 3.90862 | 0.536890 | 0.268445 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268445 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(54\) | −13.7172 | −1.86668 | ||||||||
\(55\) | 2.85048 | 0.384359 | ||||||||
\(56\) | 0.747155 | 0.0998429 | ||||||||
\(57\) | −2.60864 | −0.345522 | ||||||||
\(58\) | 13.3718 | 1.75580 | ||||||||
\(59\) | 8.15085 | 1.06115 | 0.530575 | − | 0.847638i | \(-0.321976\pi\) | ||||
0.530575 | + | 0.847638i | \(0.321976\pi\) | |||||||
\(60\) | −16.1743 | −2.08809 | ||||||||
\(61\) | −14.3712 | −1.84004 | −0.920021 | − | 0.391870i | \(-0.871828\pi\) | ||||
−0.920021 | + | 0.391870i | \(0.871828\pi\) | |||||||
\(62\) | −24.3709 | −3.09511 | ||||||||
\(63\) | −0.205073 | −0.0258368 | ||||||||
\(64\) | −5.21498 | −0.651873 | ||||||||
\(65\) | 0.389481 | 0.0483091 | ||||||||
\(66\) | −2.75580 | −0.339216 | ||||||||
\(67\) | −4.89534 | −0.598062 | −0.299031 | − | 0.954243i | \(-0.596663\pi\) | ||||
−0.299031 | + | 0.954243i | \(0.596663\pi\) | |||||||
\(68\) | 5.29812 | 0.642491 | ||||||||
\(69\) | 8.12653 | 0.978319 | ||||||||
\(70\) | −1.06746 | −0.127586 | ||||||||
\(71\) | 4.32869 | 0.513720 | 0.256860 | − | 0.966449i | \(-0.417312\pi\) | ||||
0.256860 | + | 0.966449i | \(0.417312\pi\) | |||||||
\(72\) | −8.26912 | −0.974525 | ||||||||
\(73\) | 5.64935 | 0.661206 | 0.330603 | − | 0.943770i | \(-0.392748\pi\) | ||||
0.330603 | + | 0.943770i | \(0.392748\pi\) | |||||||
\(74\) | 14.3637 | 1.66975 | ||||||||
\(75\) | 6.00362 | 0.693238 | ||||||||
\(76\) | −8.97323 | −1.02930 | ||||||||
\(77\) | −0.123241 | −0.0140446 | ||||||||
\(78\) | −0.376543 | −0.0426351 | ||||||||
\(79\) | 1.43490 | 0.161439 | 0.0807195 | − | 0.996737i | \(-0.474278\pi\) | ||||
0.0807195 | + | 0.996737i | \(0.474278\pi\) | |||||||
\(80\) | −16.5727 | −1.85288 | ||||||||
\(81\) | −2.21077 | −0.245641 | ||||||||
\(82\) | 16.0314 | 1.77037 | ||||||||
\(83\) | −11.7625 | −1.29110 | −0.645549 | − | 0.763718i | \(-0.723372\pi\) | ||||
−0.645549 | + | 0.763718i | \(0.723372\pi\) | |||||||
\(84\) | 0.699296 | 0.0762994 | ||||||||
\(85\) | −3.96811 | −0.430402 | ||||||||
\(86\) | −7.93825 | −0.856004 | ||||||||
\(87\) | 6.56086 | 0.703398 | ||||||||
\(88\) | −4.96941 | −0.529741 | ||||||||
\(89\) | −13.7381 | −1.45624 | −0.728118 | − | 0.685452i | \(-0.759605\pi\) | ||||
−0.728118 | + | 0.685452i | \(0.759605\pi\) | |||||||
\(90\) | 11.8141 | 1.24531 | ||||||||
\(91\) | −0.0168392 | −0.00176523 | ||||||||
\(92\) | 27.9538 | 2.91438 | ||||||||
\(93\) | −11.9576 | −1.23995 | ||||||||
\(94\) | 32.3419 | 3.33581 | ||||||||
\(95\) | 6.72063 | 0.689522 | ||||||||
\(96\) | 2.60662 | 0.266037 | ||||||||
\(97\) | 13.6204 | 1.38294 | 0.691472 | − | 0.722404i | \(-0.256963\pi\) | ||||
0.691472 | + | 0.722404i | \(0.256963\pi\) | |||||||
\(98\) | −17.3889 | −1.75655 | ||||||||
\(99\) | 1.36396 | 0.137083 | ||||||||
\(100\) | 20.6513 | 2.06513 | ||||||||
\(101\) | −0.0787660 | −0.00783751 | −0.00391876 | − | 0.999992i | \(-0.501247\pi\) | ||||
−0.00391876 | + | 0.999992i | \(0.501247\pi\) | |||||||
\(102\) | 3.83630 | 0.379850 | ||||||||
\(103\) | −6.36701 | −0.627360 | −0.313680 | − | 0.949529i | \(-0.601562\pi\) | ||||
−0.313680 | + | 0.949529i | \(0.601562\pi\) | |||||||
\(104\) | −0.679004 | −0.0665818 | ||||||||
\(105\) | −0.523748 | −0.0511126 | ||||||||
\(106\) | 9.73529 | 0.945575 | ||||||||
\(107\) | −1.99570 | −0.192932 | −0.0964660 | − | 0.995336i | \(-0.530754\pi\) | ||||
−0.0964660 | + | 0.995336i | \(0.530754\pi\) | |||||||
\(108\) | −23.1512 | −2.22773 | ||||||||
\(109\) | 14.8223 | 1.41972 | 0.709861 | − | 0.704341i | \(-0.248758\pi\) | ||||
0.709861 | + | 0.704341i | \(0.248758\pi\) | |||||||
\(110\) | 7.09977 | 0.676937 | ||||||||
\(111\) | 7.04756 | 0.668925 | ||||||||
\(112\) | 0.716519 | 0.0677047 | ||||||||
\(113\) | −12.3669 | −1.16338 | −0.581690 | − | 0.813410i | \(-0.697608\pi\) | ||||
−0.581690 | + | 0.813410i | \(0.697608\pi\) | |||||||
\(114\) | −6.49740 | −0.608537 | ||||||||
\(115\) | −20.9364 | −1.95233 | ||||||||
\(116\) | 22.5681 | 2.09540 | ||||||||
\(117\) | 0.186367 | 0.0172296 | ||||||||
\(118\) | 20.3015 | 1.86891 | ||||||||
\(119\) | 0.171561 | 0.0157270 | ||||||||
\(120\) | −21.1190 | −1.92789 | ||||||||
\(121\) | −10.1803 | −0.925483 | ||||||||
\(122\) | −35.7947 | −3.24070 | ||||||||
\(123\) | 7.86579 | 0.709234 | ||||||||
\(124\) | −41.1319 | −3.69376 | ||||||||
\(125\) | 0.275046 | 0.0246009 | ||||||||
\(126\) | −0.510780 | −0.0455039 | ||||||||
\(127\) | 15.9678 | 1.41691 | 0.708456 | − | 0.705754i | \(-0.249392\pi\) | ||||
0.708456 | + | 0.705754i | \(0.249392\pi\) | |||||||
\(128\) | −17.2550 | −1.52514 | ||||||||
\(129\) | −3.89491 | −0.342927 | ||||||||
\(130\) | 0.970089 | 0.0850824 | ||||||||
\(131\) | −12.1390 | −1.06059 | −0.530293 | − | 0.847814i | \(-0.677918\pi\) | ||||
−0.530293 | + | 0.847814i | \(0.677918\pi\) | |||||||
\(132\) | −4.65109 | −0.404826 | ||||||||
\(133\) | −0.290566 | −0.0251953 | ||||||||
\(134\) | −12.1930 | −1.05331 | ||||||||
\(135\) | 17.3394 | 1.49234 | ||||||||
\(136\) | 6.91783 | 0.593199 | ||||||||
\(137\) | 0.846052 | 0.0722831 | 0.0361416 | − | 0.999347i | \(-0.488493\pi\) | ||||
0.0361416 | + | 0.999347i | \(0.488493\pi\) | |||||||
\(138\) | 20.2410 | 1.72302 | ||||||||
\(139\) | 15.6472 | 1.32717 | 0.663587 | − | 0.748099i | \(-0.269033\pi\) | ||||
0.663587 | + | 0.748099i | \(0.269033\pi\) | |||||||
\(140\) | −1.80160 | −0.152263 | ||||||||
\(141\) | 15.8685 | 1.33637 | ||||||||
\(142\) | 10.7816 | 0.904769 | ||||||||
\(143\) | 0.111999 | 0.00936584 | ||||||||
\(144\) | −7.93006 | −0.660838 | ||||||||
\(145\) | −16.9027 | −1.40370 | ||||||||
\(146\) | 14.0710 | 1.16452 | ||||||||
\(147\) | −8.53188 | −0.703698 | ||||||||
\(148\) | 24.2423 | 1.99271 | ||||||||
\(149\) | −0.542212 | −0.0444198 | −0.0222099 | − | 0.999753i | \(-0.507070\pi\) | ||||
−0.0222099 | + | 0.999753i | \(0.507070\pi\) | |||||||
\(150\) | 14.9534 | 1.22094 | ||||||||
\(151\) | 8.53046 | 0.694199 | 0.347100 | − | 0.937828i | \(-0.387167\pi\) | ||||
0.347100 | + | 0.937828i | \(0.387167\pi\) | |||||||
\(152\) | −11.7165 | −0.950331 | ||||||||
\(153\) | −1.89875 | −0.153505 | ||||||||
\(154\) | −0.306958 | −0.0247354 | ||||||||
\(155\) | 30.8064 | 2.47443 | ||||||||
\(156\) | −0.635510 | −0.0508815 | ||||||||
\(157\) | −16.2204 | −1.29453 | −0.647263 | − | 0.762267i | \(-0.724086\pi\) | ||||
−0.647263 | + | 0.762267i | \(0.724086\pi\) | |||||||
\(158\) | 3.57394 | 0.284328 | ||||||||
\(159\) | 4.77662 | 0.378811 | ||||||||
\(160\) | −6.71544 | −0.530902 | ||||||||
\(161\) | 0.905184 | 0.0713385 | ||||||||
\(162\) | −5.50641 | −0.432625 | ||||||||
\(163\) | 1.36363 | 0.106808 | 0.0534039 | − | 0.998573i | \(-0.482993\pi\) | ||||
0.0534039 | + | 0.998573i | \(0.482993\pi\) | |||||||
\(164\) | 27.0569 | 2.11279 | ||||||||
\(165\) | 3.48351 | 0.271191 | ||||||||
\(166\) | −29.2971 | −2.27389 | ||||||||
\(167\) | 13.4045 | 1.03727 | 0.518636 | − | 0.854995i | \(-0.326440\pi\) | ||||
0.518636 | + | 0.854995i | \(0.326440\pi\) | |||||||
\(168\) | 0.913080 | 0.0704457 | ||||||||
\(169\) | −12.9847 | −0.998823 | ||||||||
\(170\) | −9.88346 | −0.758027 | ||||||||
\(171\) | 3.21584 | 0.245921 | ||||||||
\(172\) | −13.3978 | −1.02157 | ||||||||
\(173\) | −13.6007 | −1.03404 | −0.517022 | − | 0.855972i | \(-0.672959\pi\) | ||||
−0.517022 | + | 0.855972i | \(0.672959\pi\) | |||||||
\(174\) | 16.3413 | 1.23883 | ||||||||
\(175\) | 0.668721 | 0.0505505 | ||||||||
\(176\) | −4.76565 | −0.359224 | ||||||||
\(177\) | 9.96096 | 0.748711 | ||||||||
\(178\) | −34.2179 | −2.56474 | ||||||||
\(179\) | 23.9070 | 1.78689 | 0.893445 | − | 0.449172i | \(-0.148281\pi\) | ||||
0.893445 | + | 0.449172i | \(0.148281\pi\) | |||||||
\(180\) | 19.9391 | 1.48617 | ||||||||
\(181\) | −11.6044 | −0.862545 | −0.431273 | − | 0.902222i | \(-0.641935\pi\) | ||||
−0.431273 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(182\) | −0.0419418 | −0.00310893 | ||||||||
\(183\) | −17.5627 | −1.29827 | ||||||||
\(184\) | 36.4996 | 2.69079 | ||||||||
\(185\) | −18.1567 | −1.33490 | ||||||||
\(186\) | −29.7831 | −2.18380 | ||||||||
\(187\) | −1.14107 | −0.0834433 | ||||||||
\(188\) | 54.5849 | 3.98101 | ||||||||
\(189\) | −0.749670 | −0.0545305 | ||||||||
\(190\) | 16.7393 | 1.21439 | ||||||||
\(191\) | −4.85929 | −0.351606 | −0.175803 | − | 0.984425i | \(-0.556252\pi\) | ||||
−0.175803 | + | 0.984425i | \(0.556252\pi\) | |||||||
\(192\) | −6.37310 | −0.459939 | ||||||||
\(193\) | 25.6451 | 1.84597 | 0.922987 | − | 0.384831i | \(-0.125740\pi\) | ||||
0.922987 | + | 0.384831i | \(0.125740\pi\) | |||||||
\(194\) | 33.9247 | 2.43565 | ||||||||
\(195\) | 0.475975 | 0.0340852 | ||||||||
\(196\) | −29.3481 | −2.09629 | ||||||||
\(197\) | 1.46990 | 0.104726 | 0.0523629 | − | 0.998628i | \(-0.483325\pi\) | ||||
0.0523629 | + | 0.998628i | \(0.483325\pi\) | |||||||
\(198\) | 3.39725 | 0.241432 | ||||||||
\(199\) | 7.46714 | 0.529332 | 0.264666 | − | 0.964340i | \(-0.414738\pi\) | ||||
0.264666 | + | 0.964340i | \(0.414738\pi\) | |||||||
\(200\) | 26.9647 | 1.90669 | ||||||||
\(201\) | −5.98248 | −0.421972 | ||||||||
\(202\) | −0.196185 | −0.0138035 | ||||||||
\(203\) | 0.730790 | 0.0512914 | ||||||||
\(204\) | 6.47470 | 0.453320 | ||||||||
\(205\) | −20.2646 | −1.41534 | ||||||||
\(206\) | −15.8585 | −1.10491 | ||||||||
\(207\) | −10.0181 | −0.696306 | ||||||||
\(208\) | −0.651162 | −0.0451500 | ||||||||
\(209\) | 1.93259 | 0.133680 | ||||||||
\(210\) | −1.30451 | −0.0900200 | ||||||||
\(211\) | −20.1549 | −1.38752 | −0.693759 | − | 0.720208i | \(-0.744047\pi\) | ||||
−0.693759 | + | 0.720208i | \(0.744047\pi\) | |||||||
\(212\) | 16.4307 | 1.12847 | ||||||||
\(213\) | 5.28998 | 0.362463 | ||||||||
\(214\) | −4.97075 | −0.339793 | ||||||||
\(215\) | 10.0345 | 0.684344 | ||||||||
\(216\) | −30.2288 | −2.05681 | ||||||||
\(217\) | −1.33191 | −0.0904162 | ||||||||
\(218\) | 36.9184 | 2.50043 | ||||||||
\(219\) | 6.90393 | 0.466524 | ||||||||
\(220\) | 11.9826 | 0.807868 | ||||||||
\(221\) | −0.155912 | −0.0104878 | ||||||||
\(222\) | 17.5535 | 1.17812 | ||||||||
\(223\) | −8.91317 | −0.596870 | −0.298435 | − | 0.954430i | \(-0.596465\pi\) | ||||
−0.298435 | + | 0.954430i | \(0.596465\pi\) | |||||||
\(224\) | 0.290342 | 0.0193993 | ||||||||
\(225\) | −7.40105 | −0.493403 | ||||||||
\(226\) | −30.8026 | −2.04896 | ||||||||
\(227\) | −17.2725 | −1.14642 | −0.573209 | − | 0.819409i | \(-0.694302\pi\) | ||||
−0.573209 | + | 0.819409i | \(0.694302\pi\) | |||||||
\(228\) | −10.9660 | −0.726239 | ||||||||
\(229\) | −12.9392 | −0.855044 | −0.427522 | − | 0.904005i | \(-0.640613\pi\) | ||||
−0.427522 | + | 0.904005i | \(0.640613\pi\) | |||||||
\(230\) | −52.1468 | −3.43846 | ||||||||
\(231\) | −0.150609 | −0.00990936 | ||||||||
\(232\) | 29.4675 | 1.93464 | ||||||||
\(233\) | −24.8301 | −1.62668 | −0.813338 | − | 0.581791i | \(-0.802352\pi\) | ||||
−0.813338 | + | 0.581791i | \(0.802352\pi\) | |||||||
\(234\) | 0.464189 | 0.0303450 | ||||||||
\(235\) | −40.8822 | −2.66686 | ||||||||
\(236\) | 34.2639 | 2.23039 | ||||||||
\(237\) | 1.75356 | 0.113906 | ||||||||
\(238\) | 0.427311 | 0.0276985 | ||||||||
\(239\) | 7.52122 | 0.486507 | 0.243254 | − | 0.969963i | \(-0.421785\pi\) | ||||
0.243254 | + | 0.969963i | \(0.421785\pi\) | |||||||
\(240\) | −20.2531 | −1.30733 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −25.3564 | −1.62997 | ||||||||
\(243\) | 13.8202 | 0.886569 | ||||||||
\(244\) | −60.4123 | −3.86750 | ||||||||
\(245\) | 21.9807 | 1.40430 | ||||||||
\(246\) | 19.5915 | 1.24911 | ||||||||
\(247\) | 0.264062 | 0.0168019 | ||||||||
\(248\) | −53.7065 | −3.41037 | ||||||||
\(249\) | −14.3746 | −0.910955 | ||||||||
\(250\) | 0.685064 | 0.0433272 | ||||||||
\(251\) | −30.0279 | −1.89534 | −0.947671 | − | 0.319250i | \(-0.896569\pi\) | ||||
−0.947671 | + | 0.319250i | \(0.896569\pi\) | |||||||
\(252\) | −0.862068 | −0.0543052 | ||||||||
\(253\) | −6.02048 | −0.378504 | ||||||||
\(254\) | 39.7714 | 2.49548 | ||||||||
\(255\) | −4.84932 | −0.303677 | ||||||||
\(256\) | −32.5475 | −2.03422 | ||||||||
\(257\) | −9.93458 | −0.619702 | −0.309851 | − | 0.950785i | \(-0.600279\pi\) | ||||
−0.309851 | + | 0.950785i | \(0.600279\pi\) | |||||||
\(258\) | −9.70114 | −0.603967 | ||||||||
\(259\) | 0.785002 | 0.0487777 | ||||||||
\(260\) | 1.63726 | 0.101539 | ||||||||
\(261\) | −8.08800 | −0.500634 | ||||||||
\(262\) | −30.2348 | −1.86791 | ||||||||
\(263\) | 18.4575 | 1.13814 | 0.569069 | − | 0.822290i | \(-0.307304\pi\) | ||||
0.569069 | + | 0.822290i | \(0.307304\pi\) | |||||||
\(264\) | −6.07300 | −0.373767 | ||||||||
\(265\) | −12.3060 | −0.755953 | ||||||||
\(266\) | −0.723721 | −0.0443742 | ||||||||
\(267\) | −16.7890 | −1.02747 | ||||||||
\(268\) | −20.5786 | −1.25704 | ||||||||
\(269\) | −1.14902 | −0.0700569 | −0.0350285 | − | 0.999386i | \(-0.511152\pi\) | ||||
−0.0350285 | + | 0.999386i | \(0.511152\pi\) | |||||||
\(270\) | 43.1878 | 2.62833 | ||||||||
\(271\) | 12.2034 | 0.741303 | 0.370651 | − | 0.928772i | \(-0.379134\pi\) | ||||
0.370651 | + | 0.928772i | \(0.379134\pi\) | |||||||
\(272\) | 6.63417 | 0.402256 | ||||||||
\(273\) | −0.0205787 | −0.00124548 | ||||||||
\(274\) | 2.10728 | 0.127306 | ||||||||
\(275\) | −4.44773 | −0.268208 | ||||||||
\(276\) | 34.1616 | 2.05629 | ||||||||
\(277\) | −4.31327 | −0.259159 | −0.129580 | − | 0.991569i | \(-0.541363\pi\) | ||||
−0.129580 | + | 0.991569i | \(0.541363\pi\) | |||||||
\(278\) | 38.9728 | 2.33743 | ||||||||
\(279\) | 14.7409 | 0.882515 | ||||||||
\(280\) | −2.35237 | −0.140581 | ||||||||
\(281\) | −17.1399 | −1.02248 | −0.511240 | − | 0.859438i | \(-0.670814\pi\) | ||||
−0.511240 | + | 0.859438i | \(0.670814\pi\) | |||||||
\(282\) | 39.5242 | 2.35363 | ||||||||
\(283\) | 13.8905 | 0.825704 | 0.412852 | − | 0.910798i | \(-0.364533\pi\) | ||||
0.412852 | + | 0.910798i | \(0.364533\pi\) | |||||||
\(284\) | 18.1966 | 1.07977 | ||||||||
\(285\) | 8.21312 | 0.486503 | ||||||||
\(286\) | 0.278959 | 0.0164952 | ||||||||
\(287\) | 0.876142 | 0.0517170 | ||||||||
\(288\) | −3.21335 | −0.189349 | ||||||||
\(289\) | −15.4115 | −0.906561 | ||||||||
\(290\) | −42.1001 | −2.47220 | ||||||||
\(291\) | 16.6452 | 0.975757 | ||||||||
\(292\) | 23.7482 | 1.38976 | ||||||||
\(293\) | −0.325090 | −0.0189920 | −0.00949598 | − | 0.999955i | \(-0.503023\pi\) | ||||
−0.00949598 | + | 0.999955i | \(0.503023\pi\) | |||||||
\(294\) | −21.2506 | −1.23936 | ||||||||
\(295\) | −25.6624 | −1.49412 | ||||||||
\(296\) | 31.6535 | 1.83982 | ||||||||
\(297\) | 4.98614 | 0.289325 | ||||||||
\(298\) | −1.35050 | −0.0782325 | ||||||||
\(299\) | −0.822618 | −0.0475732 | ||||||||
\(300\) | 25.2375 | 1.45709 | ||||||||
\(301\) | −0.433839 | −0.0250061 | ||||||||
\(302\) | 21.2470 | 1.22263 | ||||||||
\(303\) | −0.0962580 | −0.00552988 | ||||||||
\(304\) | −11.2360 | −0.644432 | ||||||||
\(305\) | 45.2467 | 2.59082 | ||||||||
\(306\) | −4.72926 | −0.270354 | ||||||||
\(307\) | −14.3600 | −0.819566 | −0.409783 | − | 0.912183i | \(-0.634396\pi\) | ||||
−0.409783 | + | 0.912183i | \(0.634396\pi\) | |||||||
\(308\) | −0.518068 | −0.0295197 | ||||||||
\(309\) | −7.78096 | −0.442644 | ||||||||
\(310\) | 76.7302 | 4.35798 | ||||||||
\(311\) | −11.2072 | −0.635502 | −0.317751 | − | 0.948174i | \(-0.602928\pi\) | ||||
−0.317751 | + | 0.948174i | \(0.602928\pi\) | |||||||
\(312\) | −0.829794 | −0.0469778 | ||||||||
\(313\) | 19.3860 | 1.09576 | 0.547879 | − | 0.836557i | \(-0.315435\pi\) | ||||
0.547879 | + | 0.836557i | \(0.315435\pi\) | |||||||
\(314\) | −40.4005 | −2.27993 | ||||||||
\(315\) | 0.645658 | 0.0363787 | ||||||||
\(316\) | 6.03191 | 0.339322 | ||||||||
\(317\) | 5.19578 | 0.291824 | 0.145912 | − | 0.989298i | \(-0.453388\pi\) | ||||
0.145912 | + | 0.989298i | \(0.453388\pi\) | |||||||
\(318\) | 11.8973 | 0.667165 | ||||||||
\(319\) | −4.86056 | −0.272139 | ||||||||
\(320\) | 16.4190 | 0.917852 | ||||||||
\(321\) | −2.43890 | −0.136126 | ||||||||
\(322\) | 2.25457 | 0.125642 | ||||||||
\(323\) | −2.69032 | −0.149693 | ||||||||
\(324\) | −9.29343 | −0.516302 | ||||||||
\(325\) | −0.607724 | −0.0337104 | ||||||||
\(326\) | 3.39643 | 0.188111 | ||||||||
\(327\) | 18.1140 | 1.00171 | ||||||||
\(328\) | 35.3285 | 1.95069 | ||||||||
\(329\) | 1.76754 | 0.0974476 | ||||||||
\(330\) | 8.67646 | 0.477623 | ||||||||
\(331\) | 0.0173250 | 0.000952268 0 | 0.000476134 | − | 1.00000i | \(-0.499848\pi\) | ||||
0.000476134 | 1.00000i | \(0.499848\pi\) | ||||||||
\(332\) | −49.4461 | −2.71371 | ||||||||
\(333\) | −8.68799 | −0.476099 | ||||||||
\(334\) | 33.3869 | 1.82685 | ||||||||
\(335\) | 15.4127 | 0.842084 | ||||||||
\(336\) | 0.875641 | 0.0477701 | ||||||||
\(337\) | 0.347899 | 0.0189513 | 0.00947563 | − | 0.999955i | \(-0.496984\pi\) | ||||
0.00947563 | + | 0.999955i | \(0.496984\pi\) | |||||||
\(338\) | −32.3413 | −1.75914 | ||||||||
\(339\) | −15.1133 | −0.820841 | ||||||||
\(340\) | −16.6808 | −0.904642 | ||||||||
\(341\) | 8.85870 | 0.479725 | ||||||||
\(342\) | 8.00976 | 0.433118 | ||||||||
\(343\) | −1.90319 | −0.102763 | ||||||||
\(344\) | −17.4936 | −0.943194 | ||||||||
\(345\) | −25.5858 | −1.37750 | ||||||||
\(346\) | −33.8756 | −1.82117 | ||||||||
\(347\) | 6.37601 | 0.342282 | 0.171141 | − | 0.985247i | \(-0.445255\pi\) | ||||
0.171141 | + | 0.985247i | \(0.445255\pi\) | |||||||
\(348\) | 27.5800 | 1.47844 | ||||||||
\(349\) | −0.970720 | −0.0519614 | −0.0259807 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259807 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(350\) | 1.66560 | 0.0890301 | ||||||||
\(351\) | 0.681289 | 0.0363645 | ||||||||
\(352\) | −1.93110 | −0.102928 | ||||||||
\(353\) | 30.5488 | 1.62595 | 0.812975 | − | 0.582299i | \(-0.197847\pi\) | ||||
0.812975 | + | 0.582299i | \(0.197847\pi\) | |||||||
\(354\) | 24.8100 | 1.31864 | ||||||||
\(355\) | −13.6286 | −0.723330 | ||||||||
\(356\) | −57.7511 | −3.06080 | ||||||||
\(357\) | 0.209660 | 0.0110964 | ||||||||
\(358\) | 59.5457 | 3.14709 | ||||||||
\(359\) | 8.22124 | 0.433901 | 0.216950 | − | 0.976183i | \(-0.430389\pi\) | ||||
0.216950 | + | 0.976183i | \(0.430389\pi\) | |||||||
\(360\) | 26.0348 | 1.37215 | ||||||||
\(361\) | −14.4435 | −0.760184 | ||||||||
\(362\) | −28.9033 | −1.51912 | ||||||||
\(363\) | −12.4411 | −0.652989 | ||||||||
\(364\) | −0.0707871 | −0.00371025 | ||||||||
\(365\) | −17.7866 | −0.930994 | ||||||||
\(366\) | −43.7438 | −2.28652 | ||||||||
\(367\) | 25.1108 | 1.31077 | 0.655387 | − | 0.755294i | \(-0.272506\pi\) | ||||
0.655387 | + | 0.755294i | \(0.272506\pi\) | |||||||
\(368\) | 35.0030 | 1.82466 | ||||||||
\(369\) | −9.69667 | −0.504789 | ||||||||
\(370\) | −45.2232 | −2.35104 | ||||||||
\(371\) | 0.532051 | 0.0276227 | ||||||||
\(372\) | −50.2663 | −2.60619 | ||||||||
\(373\) | −27.0231 | −1.39920 | −0.699601 | − | 0.714534i | \(-0.746639\pi\) | ||||
−0.699601 | + | 0.714534i | \(0.746639\pi\) | |||||||
\(374\) | −2.84209 | −0.146961 | ||||||||
\(375\) | 0.336127 | 0.0173575 | ||||||||
\(376\) | 71.2722 | 3.67558 | ||||||||
\(377\) | −0.664131 | −0.0342045 | ||||||||
\(378\) | −1.86722 | −0.0960396 | ||||||||
\(379\) | 22.9961 | 1.18123 | 0.590616 | − | 0.806953i | \(-0.298885\pi\) | ||||
0.590616 | + | 0.806953i | \(0.298885\pi\) | |||||||
\(380\) | 28.2516 | 1.44928 | ||||||||
\(381\) | 19.5139 | 0.999725 | ||||||||
\(382\) | −12.1032 | −0.619252 | ||||||||
\(383\) | 3.72670 | 0.190425 | 0.0952126 | − | 0.995457i | \(-0.469647\pi\) | ||||
0.0952126 | + | 0.995457i | \(0.469647\pi\) | |||||||
\(384\) | −21.0869 | −1.07609 | ||||||||
\(385\) | 0.388015 | 0.0197751 | ||||||||
\(386\) | 63.8749 | 3.25115 | ||||||||
\(387\) | 4.80151 | 0.244074 | ||||||||
\(388\) | 57.2563 | 2.90675 | ||||||||
\(389\) | 4.72525 | 0.239580 | 0.119790 | − | 0.992799i | \(-0.461778\pi\) | ||||
0.119790 | + | 0.992799i | \(0.461778\pi\) | |||||||
\(390\) | 1.18552 | 0.0600312 | ||||||||
\(391\) | 8.38100 | 0.423845 | ||||||||
\(392\) | −38.3202 | −1.93546 | ||||||||
\(393\) | −14.8347 | −0.748313 | ||||||||
\(394\) | 3.66111 | 0.184444 | ||||||||
\(395\) | −4.51769 | −0.227310 | ||||||||
\(396\) | 5.73370 | 0.288129 | ||||||||
\(397\) | 32.2227 | 1.61721 | 0.808606 | − | 0.588350i | \(-0.200222\pi\) | ||||
0.808606 | + | 0.588350i | \(0.200222\pi\) | |||||||
\(398\) | 18.5986 | 0.932264 | ||||||||
\(399\) | −0.355094 | −0.0177769 | ||||||||
\(400\) | 25.8591 | 1.29295 | ||||||||
\(401\) | −6.02370 | −0.300809 | −0.150405 | − | 0.988625i | \(-0.548058\pi\) | ||||
−0.150405 | + | 0.988625i | \(0.548058\pi\) | |||||||
\(402\) | −14.9007 | −0.743180 | ||||||||
\(403\) | 1.21042 | 0.0602955 | ||||||||
\(404\) | −0.331110 | −0.0164733 | ||||||||
\(405\) | 6.96045 | 0.345868 | ||||||||
\(406\) | 1.82020 | 0.0903349 | ||||||||
\(407\) | −5.22113 | −0.258802 | ||||||||
\(408\) | 8.45411 | 0.418541 | ||||||||
\(409\) | 18.5405 | 0.916767 | 0.458384 | − | 0.888754i | \(-0.348429\pi\) | ||||
0.458384 | + | 0.888754i | \(0.348429\pi\) | |||||||
\(410\) | −50.4737 | −2.49272 | ||||||||
\(411\) | 1.03394 | 0.0510005 | ||||||||
\(412\) | −26.7651 | −1.31862 | ||||||||
\(413\) | 1.10951 | 0.0545956 | ||||||||
\(414\) | −24.9523 | −1.22634 | ||||||||
\(415\) | 37.0334 | 1.81790 | ||||||||
\(416\) | −0.263858 | −0.0129367 | ||||||||
\(417\) | 19.1220 | 0.936409 | ||||||||
\(418\) | 4.81355 | 0.235438 | ||||||||
\(419\) | 29.7394 | 1.45286 | 0.726432 | − | 0.687238i | \(-0.241177\pi\) | ||||
0.726432 | + | 0.687238i | \(0.241177\pi\) | |||||||
\(420\) | −2.20169 | −0.107431 | ||||||||
\(421\) | 2.65516 | 0.129405 | 0.0647023 | − | 0.997905i | \(-0.479390\pi\) | ||||
0.0647023 | + | 0.997905i | \(0.479390\pi\) | |||||||
\(422\) | −50.2002 | −2.44371 | ||||||||
\(423\) | −19.5622 | −0.951146 | ||||||||
\(424\) | 21.4538 | 1.04189 | ||||||||
\(425\) | 6.19161 | 0.300337 | ||||||||
\(426\) | 13.1759 | 0.638374 | ||||||||
\(427\) | −1.95624 | −0.0946691 | ||||||||
\(428\) | −8.38937 | −0.405515 | ||||||||
\(429\) | 0.136871 | 0.00660822 | ||||||||
\(430\) | 24.9931 | 1.20527 | ||||||||
\(431\) | 27.9512 | 1.34636 | 0.673181 | − | 0.739478i | \(-0.264927\pi\) | ||||
0.673181 | + | 0.739478i | \(0.264927\pi\) | |||||||
\(432\) | −28.9893 | −1.39475 | ||||||||
\(433\) | 13.5815 | 0.652687 | 0.326344 | − | 0.945251i | \(-0.394183\pi\) | ||||
0.326344 | + | 0.945251i | \(0.394183\pi\) | |||||||
\(434\) | −3.31743 | −0.159242 | ||||||||
\(435\) | −20.6564 | −0.990400 | ||||||||
\(436\) | 62.3089 | 2.98405 | ||||||||
\(437\) | −14.1946 | −0.679019 | ||||||||
\(438\) | 17.1958 | 0.821647 | ||||||||
\(439\) | 27.3113 | 1.30350 | 0.651748 | − | 0.758435i | \(-0.274036\pi\) | ||||
0.651748 | + | 0.758435i | \(0.274036\pi\) | |||||||
\(440\) | 15.6459 | 0.745887 | ||||||||
\(441\) | 10.5178 | 0.500848 | ||||||||
\(442\) | −0.388334 | −0.0184712 | ||||||||
\(443\) | 4.06001 | 0.192897 | 0.0964484 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964484 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(444\) | 29.6259 | 1.40599 | ||||||||
\(445\) | 43.2535 | 2.05041 | ||||||||
\(446\) | −22.2003 | −1.05121 | ||||||||
\(447\) | −0.662624 | −0.0313410 | ||||||||
\(448\) | −0.709876 | −0.0335385 | ||||||||
\(449\) | −1.53571 | −0.0724746 | −0.0362373 | − | 0.999343i | \(-0.511537\pi\) | ||||
−0.0362373 | + | 0.999343i | \(0.511537\pi\) | |||||||
\(450\) | −18.4340 | −0.868986 | ||||||||
\(451\) | −5.82731 | −0.274397 | ||||||||
\(452\) | −51.9869 | −2.44526 | ||||||||
\(453\) | 10.4249 | 0.489803 | ||||||||
\(454\) | −43.0211 | −2.01908 | ||||||||
\(455\) | 0.0530171 | 0.00248548 | ||||||||
\(456\) | −14.3184 | −0.670521 | ||||||||
\(457\) | −4.50705 | −0.210831 | −0.105415 | − | 0.994428i | \(-0.533617\pi\) | ||||
−0.105415 | + | 0.994428i | \(0.533617\pi\) | |||||||
\(458\) | −32.2279 | −1.50591 | ||||||||
\(459\) | −6.94111 | −0.323983 | ||||||||
\(460\) | −88.0106 | −4.10352 | ||||||||
\(461\) | 17.5820 | 0.818875 | 0.409438 | − | 0.912338i | \(-0.365725\pi\) | ||||
0.409438 | + | 0.912338i | \(0.365725\pi\) | |||||||
\(462\) | −0.375126 | −0.0174525 | ||||||||
\(463\) | −42.1082 | −1.95693 | −0.978466 | − | 0.206407i | \(-0.933823\pi\) | ||||
−0.978466 | + | 0.206407i | \(0.933823\pi\) | |||||||
\(464\) | 28.2592 | 1.31190 | ||||||||
\(465\) | 37.6477 | 1.74587 | ||||||||
\(466\) | −61.8451 | −2.86492 | ||||||||
\(467\) | 10.6368 | 0.492210 | 0.246105 | − | 0.969243i | \(-0.420849\pi\) | ||||
0.246105 | + | 0.969243i | \(0.420849\pi\) | |||||||
\(468\) | 0.783434 | 0.0362143 | ||||||||
\(469\) | −0.666367 | −0.0307699 | ||||||||
\(470\) | −101.826 | −4.69689 | ||||||||
\(471\) | −19.8225 | −0.913373 | ||||||||
\(472\) | 44.7388 | 2.05927 | ||||||||
\(473\) | 2.88551 | 0.132676 | ||||||||
\(474\) | 4.36763 | 0.200612 | ||||||||
\(475\) | −10.4865 | −0.481154 | ||||||||
\(476\) | 0.721193 | 0.0330558 | ||||||||
\(477\) | −5.88845 | −0.269614 | ||||||||
\(478\) | 18.7333 | 0.856841 | ||||||||
\(479\) | 24.3303 | 1.11168 | 0.555839 | − | 0.831290i | \(-0.312397\pi\) | ||||
0.555839 | + | 0.831290i | \(0.312397\pi\) | |||||||
\(480\) | −8.20678 | −0.374586 | ||||||||
\(481\) | −0.713398 | −0.0325282 | ||||||||
\(482\) | 2.49073 | 0.113449 | ||||||||
\(483\) | 1.10620 | 0.0503340 | ||||||||
\(484\) | −42.7951 | −1.94523 | ||||||||
\(485\) | −42.8830 | −1.94722 | ||||||||
\(486\) | 34.4224 | 1.56143 | ||||||||
\(487\) | 15.1777 | 0.687768 | 0.343884 | − | 0.939012i | \(-0.388257\pi\) | ||||
0.343884 | + | 0.939012i | \(0.388257\pi\) | |||||||
\(488\) | −78.8812 | −3.57079 | ||||||||
\(489\) | 1.66646 | 0.0753598 | ||||||||
\(490\) | 54.7479 | 2.47326 | ||||||||
\(491\) | 10.0194 | 0.452169 | 0.226084 | − | 0.974108i | \(-0.427408\pi\) | ||||
0.226084 | + | 0.974108i | \(0.427408\pi\) | |||||||
\(492\) | 33.0655 | 1.49071 | ||||||||
\(493\) | 6.76630 | 0.304739 | ||||||||
\(494\) | 0.657707 | 0.0295916 | ||||||||
\(495\) | −4.29434 | −0.193016 | ||||||||
\(496\) | −51.5044 | −2.31261 | ||||||||
\(497\) | 0.589231 | 0.0264306 | ||||||||
\(498\) | −35.8032 | −1.60438 | ||||||||
\(499\) | −7.82989 | −0.350514 | −0.175257 | − | 0.984523i | \(-0.556076\pi\) | ||||
−0.175257 | + | 0.984523i | \(0.556076\pi\) | |||||||
\(500\) | 1.15621 | 0.0517075 | ||||||||
\(501\) | 16.3813 | 0.731863 | ||||||||
\(502\) | −74.7911 | −3.33809 | ||||||||
\(503\) | −7.39455 | −0.329707 | −0.164853 | − | 0.986318i | \(-0.552715\pi\) | ||||
−0.164853 | + | 0.986318i | \(0.552715\pi\) | |||||||
\(504\) | −1.12561 | −0.0501388 | ||||||||
\(505\) | 0.247990 | 0.0110354 | ||||||||
\(506\) | −14.9954 | −0.666625 | ||||||||
\(507\) | −15.8683 | −0.704735 | ||||||||
\(508\) | 67.1241 | 2.97815 | ||||||||
\(509\) | 13.7526 | 0.609572 | 0.304786 | − | 0.952421i | \(-0.401415\pi\) | ||||
0.304786 | + | 0.952421i | \(0.401415\pi\) | |||||||
\(510\) | −12.0783 | −0.534838 | ||||||||
\(511\) | 0.769003 | 0.0340187 | ||||||||
\(512\) | −46.5568 | −2.05754 | ||||||||
\(513\) | 11.7559 | 0.519036 | ||||||||
\(514\) | −24.7443 | −1.09143 | ||||||||
\(515\) | 20.0461 | 0.883337 | ||||||||
\(516\) | −16.3731 | −0.720784 | ||||||||
\(517\) | −11.7561 | −0.517032 | ||||||||
\(518\) | 1.95523 | 0.0859077 | ||||||||
\(519\) | −16.6211 | −0.729585 | ||||||||
\(520\) | 2.13780 | 0.0937487 | ||||||||
\(521\) | −14.2825 | −0.625730 | −0.312865 | − | 0.949798i | \(-0.601289\pi\) | ||||
−0.312865 | + | 0.949798i | \(0.601289\pi\) | |||||||
\(522\) | −20.1450 | −0.881722 | ||||||||
\(523\) | −29.4674 | −1.28852 | −0.644260 | − | 0.764806i | \(-0.722835\pi\) | ||||
−0.644260 | + | 0.764806i | \(0.722835\pi\) | |||||||
\(524\) | −51.0287 | −2.22920 | ||||||||
\(525\) | 0.817227 | 0.0356667 | ||||||||
\(526\) | 45.9726 | 2.00450 | ||||||||
\(527\) | −12.3320 | −0.537192 | ||||||||
\(528\) | −5.82398 | −0.253456 | ||||||||
\(529\) | 21.2195 | 0.922589 | ||||||||
\(530\) | −30.6509 | −1.33139 | ||||||||
\(531\) | −12.2795 | −0.532886 | ||||||||
\(532\) | −1.22146 | −0.0529569 | ||||||||
\(533\) | −0.796224 | −0.0344883 | ||||||||
\(534\) | −41.8168 | −1.80959 | ||||||||
\(535\) | 6.28334 | 0.271653 | ||||||||
\(536\) | −26.8698 | −1.16060 | ||||||||
\(537\) | 29.2161 | 1.26077 | ||||||||
\(538\) | −2.86189 | −0.123385 | ||||||||
\(539\) | 6.32078 | 0.272255 | ||||||||
\(540\) | 72.8901 | 3.13669 | ||||||||
\(541\) | 31.6583 | 1.36110 | 0.680549 | − | 0.732703i | \(-0.261741\pi\) | ||||
0.680549 | + | 0.732703i | \(0.261741\pi\) | |||||||
\(542\) | 30.3953 | 1.30559 | ||||||||
\(543\) | −14.1814 | −0.608582 | ||||||||
\(544\) | 2.68824 | 0.115257 | ||||||||
\(545\) | −46.6672 | −1.99900 | ||||||||
\(546\) | −0.0512560 | −0.00219355 | ||||||||
\(547\) | −31.5186 | −1.34764 | −0.673820 | − | 0.738896i | \(-0.735348\pi\) | ||||
−0.673820 | + | 0.738896i | \(0.735348\pi\) | |||||||
\(548\) | 3.55656 | 0.151929 | ||||||||
\(549\) | 21.6506 | 0.924027 | ||||||||
\(550\) | −11.0781 | −0.472371 | ||||||||
\(551\) | −11.4598 | −0.488205 | ||||||||
\(552\) | 44.6053 | 1.89853 | ||||||||
\(553\) | 0.195322 | 0.00830595 | ||||||||
\(554\) | −10.7432 | −0.456434 | ||||||||
\(555\) | −22.1888 | −0.941862 | ||||||||
\(556\) | 65.7762 | 2.78953 | ||||||||
\(557\) | −32.3589 | −1.37109 | −0.685545 | − | 0.728030i | \(-0.740436\pi\) | ||||
−0.685545 | + | 0.728030i | \(0.740436\pi\) | |||||||
\(558\) | 36.7156 | 1.55429 | ||||||||
\(559\) | 0.394267 | 0.0166757 | ||||||||
\(560\) | −2.25591 | −0.0953298 | ||||||||
\(561\) | −1.39447 | −0.0588747 | ||||||||
\(562\) | −42.6907 | −1.80080 | ||||||||
\(563\) | 20.8428 | 0.878419 | 0.439209 | − | 0.898385i | \(-0.355259\pi\) | ||||
0.439209 | + | 0.898385i | \(0.355259\pi\) | |||||||
\(564\) | 66.7068 | 2.80886 | ||||||||
\(565\) | 38.9364 | 1.63807 | ||||||||
\(566\) | 34.5974 | 1.45424 | ||||||||
\(567\) | −0.300935 | −0.0126381 | ||||||||
\(568\) | 23.7595 | 0.996926 | ||||||||
\(569\) | 26.6787 | 1.11843 | 0.559215 | − | 0.829022i | \(-0.311103\pi\) | ||||
0.559215 | + | 0.829022i | \(0.311103\pi\) | |||||||
\(570\) | 20.4566 | 0.856834 | ||||||||
\(571\) | 0.500659 | 0.0209519 | 0.0104760 | − | 0.999945i | \(-0.496665\pi\) | ||||
0.0104760 | + | 0.999945i | \(0.496665\pi\) | |||||||
\(572\) | 0.470813 | 0.0196857 | ||||||||
\(573\) | −5.93842 | −0.248081 | ||||||||
\(574\) | 2.18223 | 0.0910844 | ||||||||
\(575\) | 32.6680 | 1.36235 | ||||||||
\(576\) | 7.85654 | 0.327356 | ||||||||
\(577\) | −9.59281 | −0.399354 | −0.199677 | − | 0.979862i | \(-0.563989\pi\) | ||||
−0.199677 | + | 0.979862i | \(0.563989\pi\) | |||||||
\(578\) | −38.3859 | −1.59664 | ||||||||
\(579\) | 31.3402 | 1.30246 | ||||||||
\(580\) | −71.0543 | −2.95037 | ||||||||
\(581\) | −1.60114 | −0.0664263 | ||||||||
\(582\) | 41.4586 | 1.71851 | ||||||||
\(583\) | −3.53873 | −0.146559 | ||||||||
\(584\) | 31.0084 | 1.28314 | ||||||||
\(585\) | −0.586765 | −0.0242597 | ||||||||
\(586\) | −0.809710 | −0.0334488 | ||||||||
\(587\) | 19.6676 | 0.811770 | 0.405885 | − | 0.913924i | \(-0.366963\pi\) | ||||
0.405885 | + | 0.913924i | \(0.366963\pi\) | |||||||
\(588\) | −35.8656 | −1.47907 | ||||||||
\(589\) | 20.8863 | 0.860605 | ||||||||
\(590\) | −63.9181 | −2.63146 | ||||||||
\(591\) | 1.79632 | 0.0738909 | ||||||||
\(592\) | 30.3556 | 1.24761 | ||||||||
\(593\) | 35.9622 | 1.47679 | 0.738394 | − | 0.674369i | \(-0.235584\pi\) | ||||
0.738394 | + | 0.674369i | \(0.235584\pi\) | |||||||
\(594\) | 12.4191 | 0.509562 | ||||||||
\(595\) | −0.540148 | −0.0221439 | ||||||||
\(596\) | −2.27931 | −0.0933640 | ||||||||
\(597\) | 9.12541 | 0.373478 | ||||||||
\(598\) | −2.04892 | −0.0837864 | ||||||||
\(599\) | −8.60123 | −0.351437 | −0.175718 | − | 0.984440i | \(-0.556225\pi\) | ||||
−0.175718 | + | 0.984440i | \(0.556225\pi\) | |||||||
\(600\) | 32.9529 | 1.34530 | ||||||||
\(601\) | 36.8567 | 1.50342 | 0.751708 | − | 0.659496i | \(-0.229230\pi\) | ||||
0.751708 | + | 0.659496i | \(0.229230\pi\) | |||||||
\(602\) | −1.08057 | −0.0440409 | ||||||||
\(603\) | 7.37499 | 0.300333 | ||||||||
\(604\) | 35.8596 | 1.45911 | ||||||||
\(605\) | 32.0521 | 1.30310 | ||||||||
\(606\) | −0.239752 | −0.00973927 | ||||||||
\(607\) | −38.6665 | −1.56942 | −0.784712 | − | 0.619861i | \(-0.787189\pi\) | ||||
−0.784712 | + | 0.619861i | \(0.787189\pi\) | |||||||
\(608\) | −4.55298 | −0.184648 | ||||||||
\(609\) | 0.893080 | 0.0361894 | ||||||||
\(610\) | 112.697 | 4.56298 | ||||||||
\(611\) | −1.60631 | −0.0649845 | ||||||||
\(612\) | −7.98179 | −0.322645 | ||||||||
\(613\) | −38.3341 | −1.54830 | −0.774150 | − | 0.633002i | \(-0.781822\pi\) | ||||
−0.774150 | + | 0.633002i | \(0.781822\pi\) | |||||||
\(614\) | −35.7667 | −1.44343 | ||||||||
\(615\) | −24.7649 | −0.998618 | ||||||||
\(616\) | −0.676449 | −0.0272549 | ||||||||
\(617\) | −44.3829 | −1.78679 | −0.893395 | − | 0.449272i | \(-0.851683\pi\) | ||||
−0.893395 | + | 0.449272i | \(0.851683\pi\) | |||||||
\(618\) | −19.3802 | −0.779588 | ||||||||
\(619\) | −15.6150 | −0.627619 | −0.313810 | − | 0.949486i | \(-0.601605\pi\) | ||||
−0.313810 | + | 0.949486i | \(0.601605\pi\) | |||||||
\(620\) | 129.501 | 5.20089 | ||||||||
\(621\) | −36.6225 | −1.46961 | ||||||||
\(622\) | −27.9141 | −1.11925 | ||||||||
\(623\) | −1.87007 | −0.0749226 | ||||||||
\(624\) | −0.795769 | −0.0318563 | ||||||||
\(625\) | −25.4292 | −1.01717 | ||||||||
\(626\) | 48.2851 | 1.92986 | ||||||||
\(627\) | 2.36177 | 0.0943200 | ||||||||
\(628\) | −68.1858 | −2.72091 | ||||||||
\(629\) | 7.26825 | 0.289804 | ||||||||
\(630\) | 1.60816 | 0.0640705 | ||||||||
\(631\) | −7.52472 | −0.299555 | −0.149777 | − | 0.988720i | \(-0.547856\pi\) | ||||
−0.149777 | + | 0.988720i | \(0.547856\pi\) | |||||||
\(632\) | 7.87595 | 0.313288 | ||||||||
\(633\) | −24.6307 | −0.978984 | ||||||||
\(634\) | 12.9413 | 0.513963 | ||||||||
\(635\) | −50.2736 | −1.99505 | ||||||||
\(636\) | 20.0796 | 0.796206 | ||||||||
\(637\) | 0.863650 | 0.0342191 | ||||||||
\(638\) | −12.1063 | −0.479294 | ||||||||
\(639\) | −6.52130 | −0.257979 | ||||||||
\(640\) | 54.3262 | 2.14743 | ||||||||
\(641\) | 2.42509 | 0.0957851 | 0.0478926 | − | 0.998852i | \(-0.484749\pi\) | ||||
0.0478926 | + | 0.998852i | \(0.484749\pi\) | |||||||
\(642\) | −6.07463 | −0.239747 | ||||||||
\(643\) | 12.1224 | 0.478061 | 0.239030 | − | 0.971012i | \(-0.423170\pi\) | ||||
0.239030 | + | 0.971012i | \(0.423170\pi\) | |||||||
\(644\) | 3.80514 | 0.149943 | ||||||||
\(645\) | 12.2629 | 0.482850 | ||||||||
\(646\) | −6.70085 | −0.263642 | ||||||||
\(647\) | 12.4628 | 0.489964 | 0.244982 | − | 0.969528i | \(-0.421218\pi\) | ||||
0.244982 | + | 0.969528i | \(0.421218\pi\) | |||||||
\(648\) | −12.1346 | −0.476691 | ||||||||
\(649\) | −7.37950 | −0.289671 | ||||||||
\(650\) | −1.51367 | −0.0593711 | ||||||||
\(651\) | −1.62770 | −0.0637945 | ||||||||
\(652\) | 5.73231 | 0.224495 | ||||||||
\(653\) | −49.4695 | −1.93589 | −0.967945 | − | 0.251163i | \(-0.919187\pi\) | ||||
−0.967945 | + | 0.251163i | \(0.919187\pi\) | |||||||
\(654\) | 45.1171 | 1.76422 | ||||||||
\(655\) | 38.2187 | 1.49333 | ||||||||
\(656\) | 33.8799 | 1.32279 | ||||||||
\(657\) | −8.51092 | −0.332043 | ||||||||
\(658\) | 4.40245 | 0.171626 | ||||||||
\(659\) | 19.5067 | 0.759874 | 0.379937 | − | 0.925012i | \(-0.375946\pi\) | ||||
0.379937 | + | 0.925012i | \(0.375946\pi\) | |||||||
\(660\) | 14.6437 | 0.570004 | ||||||||
\(661\) | 33.2398 | 1.29288 | 0.646439 | − | 0.762966i | \(-0.276258\pi\) | ||||
0.646439 | + | 0.762966i | \(0.276258\pi\) | |||||||
\(662\) | 0.0431518 | 0.00167714 | ||||||||
\(663\) | −0.190536 | −0.00739982 | ||||||||
\(664\) | −64.5624 | −2.50551 | ||||||||
\(665\) | 0.914829 | 0.0354756 | ||||||||
\(666\) | −21.6394 | −0.838510 | ||||||||
\(667\) | 35.7001 | 1.38231 | ||||||||
\(668\) | 56.3487 | 2.18020 | ||||||||
\(669\) | −10.8926 | −0.421131 | ||||||||
\(670\) | 38.3887 | 1.48309 | ||||||||
\(671\) | 13.0112 | 0.502291 | ||||||||
\(672\) | 0.354820 | 0.0136875 | ||||||||
\(673\) | 28.8764 | 1.11310 | 0.556552 | − | 0.830813i | \(-0.312124\pi\) | ||||
0.556552 | + | 0.830813i | \(0.312124\pi\) | |||||||
\(674\) | 0.866521 | 0.0333771 | ||||||||
\(675\) | −27.0555 | −1.04137 | ||||||||
\(676\) | −54.5840 | −2.09938 | ||||||||
\(677\) | 29.4480 | 1.13178 | 0.565889 | − | 0.824482i | \(-0.308533\pi\) | ||||
0.565889 | + | 0.824482i | \(0.308533\pi\) | |||||||
\(678\) | −37.6431 | −1.44567 | ||||||||
\(679\) | 1.85404 | 0.0711517 | ||||||||
\(680\) | −21.7803 | −0.835237 | ||||||||
\(681\) | −21.1083 | −0.808873 | ||||||||
\(682\) | 22.0646 | 0.844897 | ||||||||
\(683\) | 19.6959 | 0.753643 | 0.376821 | − | 0.926286i | \(-0.377017\pi\) | ||||
0.376821 | + | 0.926286i | \(0.377017\pi\) | |||||||
\(684\) | 13.5185 | 0.516891 | ||||||||
\(685\) | −2.66374 | −0.101776 | ||||||||
\(686\) | −4.74033 | −0.180987 | ||||||||
\(687\) | −15.8126 | −0.603289 | ||||||||
\(688\) | −16.7763 | −0.639592 | ||||||||
\(689\) | −0.483520 | −0.0184206 | ||||||||
\(690\) | −63.7273 | −2.42606 | ||||||||
\(691\) | 15.6587 | 0.595683 | 0.297842 | − | 0.954615i | \(-0.403733\pi\) | ||||
0.297842 | + | 0.954615i | \(0.403733\pi\) | |||||||
\(692\) | −57.1735 | −2.17341 | ||||||||
\(693\) | 0.185666 | 0.00705286 | ||||||||
\(694\) | 15.8809 | 0.602830 | ||||||||
\(695\) | −49.2641 | −1.86869 | ||||||||
\(696\) | 36.0115 | 1.36501 | ||||||||
\(697\) | 8.11209 | 0.307267 | ||||||||
\(698\) | −2.41780 | −0.0915149 | ||||||||
\(699\) | −30.3443 | −1.14773 | ||||||||
\(700\) | 2.81111 | 0.106250 | ||||||||
\(701\) | 32.6726 | 1.23403 | 0.617014 | − | 0.786952i | \(-0.288342\pi\) | ||||
0.617014 | + | 0.786952i | \(0.288342\pi\) | |||||||
\(702\) | 1.69690 | 0.0640455 | ||||||||
\(703\) | −12.3100 | −0.464279 | ||||||||
\(704\) | 4.72146 | 0.177947 | ||||||||
\(705\) | −49.9611 | −1.88164 | ||||||||
\(706\) | 76.0887 | 2.86364 | ||||||||
\(707\) | −0.0107218 | −0.000403236 0 | ||||||||
\(708\) | 41.8730 | 1.57368 | ||||||||
\(709\) | −5.63690 | −0.211698 | −0.105849 | − | 0.994382i | \(-0.533756\pi\) | ||||
−0.105849 | + | 0.994382i | \(0.533756\pi\) | |||||||
\(710\) | −33.9451 | −1.27394 | ||||||||
\(711\) | −2.16172 | −0.0810710 | ||||||||
\(712\) | −75.4064 | −2.82597 | ||||||||
\(713\) | −65.0659 | −2.43674 | ||||||||
\(714\) | 0.522207 | 0.0195431 | ||||||||
\(715\) | −0.352622 | −0.0131873 | ||||||||
\(716\) | 100.498 | 3.75579 | ||||||||
\(717\) | 9.19150 | 0.343263 | ||||||||
\(718\) | 20.4769 | 0.764190 | ||||||||
\(719\) | 13.2196 | 0.493006 | 0.246503 | − | 0.969142i | \(-0.420718\pi\) | ||||
0.246503 | + | 0.969142i | \(0.420718\pi\) | |||||||
\(720\) | 24.9673 | 0.930475 | ||||||||
\(721\) | −0.866693 | −0.0322773 | ||||||||
\(722\) | −35.9748 | −1.33884 | ||||||||
\(723\) | 1.22208 | 0.0454495 | ||||||||
\(724\) | −48.7814 | −1.81295 | ||||||||
\(725\) | 26.3741 | 0.979509 | ||||||||
\(726\) | −30.9874 | −1.15005 | ||||||||
\(727\) | 21.6517 | 0.803018 | 0.401509 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401509 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(728\) | −0.0924277 | −0.00342560 | ||||||||
\(729\) | 23.5217 | 0.871173 | ||||||||
\(730\) | −44.3016 | −1.63967 | ||||||||
\(731\) | −4.01687 | −0.148569 | ||||||||
\(732\) | −73.8284 | −2.72878 | ||||||||
\(733\) | −37.5385 | −1.38651 | −0.693257 | − | 0.720690i | \(-0.743825\pi\) | ||||
−0.693257 | + | 0.720690i | \(0.743825\pi\) | |||||||
\(734\) | 62.5441 | 2.30855 | ||||||||
\(735\) | 26.8621 | 0.990823 | ||||||||
\(736\) | 14.1836 | 0.522815 | ||||||||
\(737\) | 4.43208 | 0.163258 | ||||||||
\(738\) | −24.1517 | −0.889038 | ||||||||
\(739\) | −28.8751 | −1.06219 | −0.531093 | − | 0.847313i | \(-0.678219\pi\) | ||||
−0.531093 | + | 0.847313i | \(0.678219\pi\) | |||||||
\(740\) | −76.3254 | −2.80578 | ||||||||
\(741\) | 0.322704 | 0.0118548 | ||||||||
\(742\) | 1.32519 | 0.0486493 | ||||||||
\(743\) | −24.5272 | −0.899817 | −0.449909 | − | 0.893075i | \(-0.648543\pi\) | ||||
−0.449909 | + | 0.893075i | \(0.648543\pi\) | |||||||
\(744\) | −65.6334 | −2.40624 | ||||||||
\(745\) | 1.70712 | 0.0625440 | ||||||||
\(746\) | −67.3070 | −2.46429 | ||||||||
\(747\) | 17.7205 | 0.648361 | ||||||||
\(748\) | −4.79673 | −0.175386 | ||||||||
\(749\) | −0.271660 | −0.00992624 | ||||||||
\(750\) | 0.837200 | 0.0305702 | ||||||||
\(751\) | 38.3355 | 1.39888 | 0.699442 | − | 0.714689i | \(-0.253432\pi\) | ||||
0.699442 | + | 0.714689i | \(0.253432\pi\) | |||||||
\(752\) | 68.3498 | 2.49246 | ||||||||
\(753\) | −36.6963 | −1.33729 | ||||||||
\(754\) | −1.65417 | −0.0602412 | ||||||||
\(755\) | −26.8576 | −0.977448 | ||||||||
\(756\) | −3.15140 | −0.114615 | ||||||||
\(757\) | 31.6239 | 1.14939 | 0.574694 | − | 0.818368i | \(-0.305121\pi\) | ||||
0.574694 | + | 0.818368i | \(0.305121\pi\) | |||||||
\(758\) | 57.2771 | 2.08040 | ||||||||
\(759\) | −7.35748 | −0.267060 | ||||||||
\(760\) | 36.8885 | 1.33809 | ||||||||
\(761\) | −28.4924 | −1.03285 | −0.516424 | − | 0.856333i | \(-0.672737\pi\) | ||||
−0.516424 | + | 0.856333i | \(0.672737\pi\) | |||||||
\(762\) | 48.6037 | 1.76072 | ||||||||
\(763\) | 2.01765 | 0.0730440 | ||||||||
\(764\) | −20.4271 | −0.739026 | ||||||||
\(765\) | 5.97808 | 0.216138 | ||||||||
\(766\) | 9.28218 | 0.335379 | ||||||||
\(767\) | −1.00831 | −0.0364080 | ||||||||
\(768\) | −39.7755 | −1.43527 | ||||||||
\(769\) | −8.72245 | −0.314539 | −0.157270 | − | 0.987556i | \(-0.550269\pi\) | ||||
−0.157270 | + | 0.987556i | \(0.550269\pi\) | |||||||
\(770\) | 0.966439 | 0.0348280 | ||||||||
\(771\) | −12.1408 | −0.437241 | ||||||||
\(772\) | 107.805 | 3.87997 | ||||||||
\(773\) | −42.2655 | −1.52019 | −0.760093 | − | 0.649814i | \(-0.774847\pi\) | ||||
−0.760093 | + | 0.649814i | \(0.774847\pi\) | |||||||
\(774\) | 11.9592 | 0.429866 | ||||||||
\(775\) | −48.0685 | −1.72667 | ||||||||
\(776\) | 74.7604 | 2.68374 | ||||||||
\(777\) | 0.959332 | 0.0344158 | ||||||||
\(778\) | 11.7693 | 0.421950 | ||||||||
\(779\) | −13.7392 | −0.492256 | ||||||||
\(780\) | 2.00086 | 0.0716423 | ||||||||
\(781\) | −3.91904 | −0.140234 | ||||||||
\(782\) | 20.8748 | 0.746480 | ||||||||
\(783\) | −29.5667 | −1.05663 | ||||||||
\(784\) | −36.7490 | −1.31246 | ||||||||
\(785\) | 51.0687 | 1.82272 | ||||||||
\(786\) | −36.9492 | −1.31794 | ||||||||
\(787\) | 17.5127 | 0.624261 | 0.312130 | − | 0.950039i | \(-0.398957\pi\) | ||||
0.312130 | + | 0.950039i | \(0.398957\pi\) | |||||||
\(788\) | 6.17903 | 0.220119 | ||||||||
\(789\) | 22.5565 | 0.803031 | ||||||||
\(790\) | −11.2523 | −0.400340 | ||||||||
\(791\) | −1.68341 | −0.0598553 | ||||||||
\(792\) | 7.48658 | 0.266024 | ||||||||
\(793\) | 1.77780 | 0.0631316 | ||||||||
\(794\) | 80.2580 | 2.84825 | ||||||||
\(795\) | −15.0389 | −0.533374 | ||||||||
\(796\) | 31.3897 | 1.11258 | ||||||||
\(797\) | −44.6851 | −1.58283 | −0.791413 | − | 0.611281i | \(-0.790654\pi\) | ||||
−0.791413 | + | 0.611281i | \(0.790654\pi\) | |||||||
\(798\) | −0.884442 | −0.0313089 | ||||||||
\(799\) | 16.3654 | 0.578968 | ||||||||
\(800\) | 10.4784 | 0.370467 | ||||||||
\(801\) | 20.6969 | 0.731289 | ||||||||
\(802\) | −15.0034 | −0.529788 | ||||||||
\(803\) | −5.11472 | −0.180495 | ||||||||
\(804\) | −25.1486 | −0.886924 | ||||||||
\(805\) | −2.84991 | −0.100446 | ||||||||
\(806\) | 3.01483 | 0.106193 | ||||||||
\(807\) | −1.40419 | −0.0494297 | ||||||||
\(808\) | −0.432335 | −0.0152095 | ||||||||
\(809\) | 37.7898 | 1.32862 | 0.664309 | − | 0.747458i | \(-0.268726\pi\) | ||||
0.664309 | + | 0.747458i | \(0.268726\pi\) | |||||||
\(810\) | 17.3366 | 0.609145 | ||||||||
\(811\) | 17.5453 | 0.616097 | 0.308049 | − | 0.951371i | \(-0.400324\pi\) | ||||
0.308049 | + | 0.951371i | \(0.400324\pi\) | |||||||
\(812\) | 3.07203 | 0.107807 | ||||||||
\(813\) | 14.9135 | 0.523038 | ||||||||
\(814\) | −13.0044 | −0.455804 | ||||||||
\(815\) | −4.29330 | −0.150388 | ||||||||
\(816\) | 8.10746 | 0.283818 | ||||||||
\(817\) | 6.80322 | 0.238015 | ||||||||
\(818\) | 46.1792 | 1.61462 | ||||||||
\(819\) | 0.0253688 | 0.000886456 0 | ||||||||
\(820\) | −85.1868 | −2.97485 | ||||||||
\(821\) | −21.1741 | −0.738980 | −0.369490 | − | 0.929235i | \(-0.620468\pi\) | ||||
−0.369490 | + | 0.929235i | \(0.620468\pi\) | |||||||
\(822\) | 2.57526 | 0.0898225 | ||||||||
\(823\) | −47.1268 | −1.64274 | −0.821369 | − | 0.570397i | \(-0.806789\pi\) | ||||
−0.821369 | + | 0.570397i | \(0.806789\pi\) | |||||||
\(824\) | −34.9475 | −1.21746 | ||||||||
\(825\) | −5.43547 | −0.189239 | ||||||||
\(826\) | 2.76350 | 0.0961543 | ||||||||
\(827\) | −13.3177 | −0.463103 | −0.231552 | − | 0.972823i | \(-0.574380\pi\) | ||||
−0.231552 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(828\) | −42.1132 | −1.46354 | ||||||||
\(829\) | −41.6063 | −1.44505 | −0.722523 | − | 0.691347i | \(-0.757017\pi\) | ||||
−0.722523 | + | 0.691347i | \(0.757017\pi\) | |||||||
\(830\) | 92.2400 | 3.20170 | ||||||||
\(831\) | −5.27114 | −0.182854 | ||||||||
\(832\) | 0.645125 | 0.0223657 | ||||||||
\(833\) | −8.79904 | −0.304869 | ||||||||
\(834\) | 47.6277 | 1.64921 | ||||||||
\(835\) | −42.2032 | −1.46050 | ||||||||
\(836\) | 8.12405 | 0.280976 | ||||||||
\(837\) | 53.8873 | 1.86262 | ||||||||
\(838\) | 74.0726 | 2.55880 | ||||||||
\(839\) | 20.2863 | 0.700359 | 0.350180 | − | 0.936683i | \(-0.386121\pi\) | ||||
0.350180 | + | 0.936683i | \(0.386121\pi\) | |||||||
\(840\) | −2.87477 | −0.0991891 | ||||||||
\(841\) | −0.177928 | −0.00613546 | ||||||||
\(842\) | 6.61327 | 0.227908 | ||||||||
\(843\) | −20.9462 | −0.721426 | ||||||||
\(844\) | −84.7252 | −2.91636 | ||||||||
\(845\) | 40.8815 | 1.40637 | ||||||||
\(846\) | −48.7240 | −1.67517 | ||||||||
\(847\) | −1.38577 | −0.0476156 | ||||||||
\(848\) | 20.5741 | 0.706518 | ||||||||
\(849\) | 16.9752 | 0.582588 | ||||||||
\(850\) | 15.4216 | 0.528957 | ||||||||
\(851\) | 38.3485 | 1.31457 | ||||||||
\(852\) | 22.2376 | 0.761846 | ||||||||
\(853\) | −26.7153 | −0.914715 | −0.457358 | − | 0.889283i | \(-0.651204\pi\) | ||||
−0.457358 | + | 0.889283i | \(0.651204\pi\) | |||||||
\(854\) | −4.87246 | −0.166732 | ||||||||
\(855\) | −10.1248 | −0.346263 | ||||||||
\(856\) | −10.9541 | −0.374404 | ||||||||
\(857\) | −1.26642 | −0.0432602 | −0.0216301 | − | 0.999766i | \(-0.506886\pi\) | ||||
−0.0216301 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(858\) | 0.340909 | 0.0116385 | ||||||||
\(859\) | −45.0089 | −1.53569 | −0.767843 | − | 0.640638i | \(-0.778670\pi\) | ||||
−0.767843 | + | 0.640638i | \(0.778670\pi\) | |||||||
\(860\) | 42.1820 | 1.43839 | ||||||||
\(861\) | 1.07071 | 0.0364897 | ||||||||
\(862\) | 69.6188 | 2.37122 | ||||||||
\(863\) | 26.1118 | 0.888855 | 0.444428 | − | 0.895815i | \(-0.353407\pi\) | ||||
0.444428 | + | 0.895815i | \(0.353407\pi\) | |||||||
\(864\) | −11.7468 | −0.399635 | ||||||||
\(865\) | 42.8210 | 1.45596 | ||||||||
\(866\) | 33.8279 | 1.14952 | ||||||||
\(867\) | −18.8341 | −0.639638 | ||||||||
\(868\) | −5.59898 | −0.190042 | ||||||||
\(869\) | −1.29911 | −0.0440693 | ||||||||
\(870\) | −51.4495 | −1.74430 | ||||||||
\(871\) | 0.605584 | 0.0205194 | ||||||||
\(872\) | 81.3576 | 2.75511 | ||||||||
\(873\) | −20.5196 | −0.694483 | ||||||||
\(874\) | −35.3548 | −1.19589 | ||||||||
\(875\) | 0.0374399 | 0.00126570 | ||||||||
\(876\) | 29.0222 | 0.980568 | ||||||||
\(877\) | 18.2107 | 0.614931 | 0.307466 | − | 0.951559i | \(-0.400519\pi\) | ||||
0.307466 | + | 0.951559i | \(0.400519\pi\) | |||||||
\(878\) | 68.0249 | 2.29573 | ||||||||
\(879\) | −0.397285 | −0.0134001 | ||||||||
\(880\) | 15.0043 | 0.505796 | ||||||||
\(881\) | 7.40050 | 0.249329 | 0.124665 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124665 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(882\) | 26.1970 | 0.882098 | ||||||||
\(883\) | −1.57266 | −0.0529243 | −0.0264621 | − | 0.999650i | \(-0.508424\pi\) | ||||
−0.0264621 | + | 0.999650i | \(0.508424\pi\) | |||||||
\(884\) | −0.655410 | −0.0220438 | ||||||||
\(885\) | −31.3614 | −1.05420 | ||||||||
\(886\) | 10.1124 | 0.339732 | ||||||||
\(887\) | −1.08367 | −0.0363861 | −0.0181930 | − | 0.999834i | \(-0.505791\pi\) | ||||
−0.0181930 | + | 0.999834i | \(0.505791\pi\) | |||||||
\(888\) | 38.6830 | 1.29812 | ||||||||
\(889\) | 2.17358 | 0.0728994 | ||||||||
\(890\) | 107.733 | 3.61121 | ||||||||
\(891\) | 2.00155 | 0.0670545 | ||||||||
\(892\) | −37.4684 | −1.25453 | ||||||||
\(893\) | −27.7175 | −0.927532 | ||||||||
\(894\) | −1.65042 | −0.0551981 | ||||||||
\(895\) | −75.2695 | −2.51598 | ||||||||
\(896\) | −2.34879 | −0.0784676 | ||||||||
\(897\) | −1.00530 | −0.0335660 | ||||||||
\(898\) | −3.82503 | −0.127643 | ||||||||
\(899\) | −52.5301 | −1.75198 | ||||||||
\(900\) | −31.1119 | −1.03706 | ||||||||
\(901\) | 4.92620 | 0.164115 | ||||||||
\(902\) | −14.5142 | −0.483271 | ||||||||
\(903\) | −0.530184 | −0.0176434 | ||||||||
\(904\) | −67.8801 | −2.25766 | ||||||||
\(905\) | 36.5356 | 1.21448 | ||||||||
\(906\) | 25.9655 | 0.862646 | ||||||||
\(907\) | 39.1868 | 1.30118 | 0.650588 | − | 0.759431i | \(-0.274522\pi\) | ||||
0.650588 | + | 0.759431i | \(0.274522\pi\) | |||||||
\(908\) | −72.6088 | −2.40961 | ||||||||
\(909\) | 0.118664 | 0.00393582 | ||||||||
\(910\) | 0.132051 | 0.00437745 | ||||||||
\(911\) | 11.8818 | 0.393662 | 0.196831 | − | 0.980437i | \(-0.436935\pi\) | ||||
0.196831 | + | 0.980437i | \(0.436935\pi\) | |||||||
\(912\) | −13.7313 | −0.454689 | ||||||||
\(913\) | 10.6493 | 0.352441 | ||||||||
\(914\) | −11.2258 | −0.371317 | ||||||||
\(915\) | 55.2949 | 1.82799 | ||||||||
\(916\) | −54.3925 | −1.79718 | ||||||||
\(917\) | −1.65239 | −0.0545666 | ||||||||
\(918\) | −17.2884 | −0.570602 | ||||||||
\(919\) | −28.1347 | −0.928077 | −0.464039 | − | 0.885815i | \(-0.653600\pi\) | ||||
−0.464039 | + | 0.885815i | \(0.653600\pi\) | |||||||
\(920\) | −114.917 | −3.78869 | ||||||||
\(921\) | −17.5490 | −0.578258 | ||||||||
\(922\) | 43.7919 | 1.44221 | ||||||||
\(923\) | −0.535485 | −0.0176257 | ||||||||
\(924\) | −0.633118 | −0.0208281 | ||||||||
\(925\) | 28.3306 | 0.931505 | ||||||||
\(926\) | −104.880 | −3.44657 | ||||||||
\(927\) | 9.59210 | 0.315046 | ||||||||
\(928\) | 11.4510 | 0.375897 | ||||||||
\(929\) | 59.5689 | 1.95439 | 0.977197 | − | 0.212335i | \(-0.0681068\pi\) | ||||
0.977197 | + | 0.212335i | \(0.0681068\pi\) | |||||||
\(930\) | 93.7701 | 3.07484 | ||||||||
\(931\) | 14.9026 | 0.488413 | ||||||||
\(932\) | −104.379 | −3.41904 | ||||||||
\(933\) | −13.6961 | −0.448389 | ||||||||
\(934\) | 26.4932 | 0.866885 | ||||||||
\(935\) | 3.59259 | 0.117490 | ||||||||
\(936\) | 1.02294 | 0.0334359 | ||||||||
\(937\) | 25.8722 | 0.845209 | 0.422605 | − | 0.906314i | \(-0.361116\pi\) | ||||
0.422605 | + | 0.906314i | \(0.361116\pi\) | |||||||
\(938\) | −1.65974 | −0.0541923 | ||||||||
\(939\) | 23.6911 | 0.773130 | ||||||||
\(940\) | −171.857 | −5.60535 | ||||||||
\(941\) | −43.2143 | −1.40875 | −0.704373 | − | 0.709830i | \(-0.748772\pi\) | ||||
−0.704373 | + | 0.709830i | \(0.748772\pi\) | |||||||
\(942\) | −49.3724 | −1.60864 | ||||||||
\(943\) | 42.8008 | 1.39378 | ||||||||
\(944\) | 42.9043 | 1.39642 | ||||||||
\(945\) | 2.36029 | 0.0767802 | ||||||||
\(946\) | 7.18702 | 0.233670 | ||||||||
\(947\) | −53.0980 | −1.72545 | −0.862726 | − | 0.505672i | \(-0.831245\pi\) | ||||
−0.862726 | + | 0.505672i | \(0.831245\pi\) | |||||||
\(948\) | 7.37145 | 0.239414 | ||||||||
\(949\) | −0.698859 | −0.0226859 | ||||||||
\(950\) | −26.1190 | −0.847412 | ||||||||
\(951\) | 6.34963 | 0.205901 | ||||||||
\(952\) | 0.941672 | 0.0305198 | ||||||||
\(953\) | −28.8397 | −0.934210 | −0.467105 | − | 0.884202i | \(-0.654703\pi\) | ||||
−0.467105 | + | 0.884202i | \(0.654703\pi\) | |||||||
\(954\) | −14.6665 | −0.474846 | ||||||||
\(955\) | 15.2992 | 0.495069 | ||||||||
\(956\) | 31.6171 | 1.02257 | ||||||||
\(957\) | −5.93997 | −0.192012 | ||||||||
\(958\) | 60.6000 | 1.95790 | ||||||||
\(959\) | 0.115167 | 0.00371893 | ||||||||
\(960\) | 20.0653 | 0.647605 | ||||||||
\(961\) | 64.7397 | 2.08838 | ||||||||
\(962\) | −1.77688 | −0.0572889 | ||||||||
\(963\) | 3.00659 | 0.0968860 | ||||||||
\(964\) | 4.20371 | 0.135393 | ||||||||
\(965\) | −80.7419 | −2.59917 | ||||||||
\(966\) | 2.75525 | 0.0886487 | ||||||||
\(967\) | 6.08196 | 0.195583 | 0.0977914 | − | 0.995207i | \(-0.468822\pi\) | ||||
0.0977914 | + | 0.995207i | \(0.468822\pi\) | |||||||
\(968\) | −55.8782 | −1.79599 | ||||||||
\(969\) | −3.28778 | −0.105619 | ||||||||
\(970\) | −106.810 | −3.42945 | ||||||||
\(971\) | 2.57155 | 0.0825251 | 0.0412626 | − | 0.999148i | \(-0.486862\pi\) | ||||
0.0412626 | + | 0.999148i | \(0.486862\pi\) | |||||||
\(972\) | 58.0963 | 1.86344 | ||||||||
\(973\) | 2.12993 | 0.0682824 | ||||||||
\(974\) | 37.8035 | 1.21130 | ||||||||
\(975\) | −0.742684 | −0.0237849 | ||||||||
\(976\) | −75.6468 | −2.42139 | ||||||||
\(977\) | 52.2605 | 1.67196 | 0.835980 | − | 0.548760i | \(-0.184900\pi\) | ||||
0.835980 | + | 0.548760i | \(0.184900\pi\) | |||||||
\(978\) | 4.15069 | 0.132724 | ||||||||
\(979\) | 12.4380 | 0.397520 | ||||||||
\(980\) | 92.4006 | 2.95163 | ||||||||
\(981\) | −22.3303 | −0.712953 | ||||||||
\(982\) | 24.9555 | 0.796363 | ||||||||
\(983\) | 5.96528 | 0.190263 | 0.0951314 | − | 0.995465i | \(-0.469673\pi\) | ||||
0.0951314 | + | 0.995465i | \(0.469673\pi\) | |||||||
\(984\) | 43.1741 | 1.37634 | ||||||||
\(985\) | −4.62787 | −0.147456 | ||||||||
\(986\) | 16.8530 | 0.536709 | ||||||||
\(987\) | 2.16007 | 0.0687557 | ||||||||
\(988\) | 1.11004 | 0.0353152 | ||||||||
\(989\) | −21.1937 | −0.673920 | ||||||||
\(990\) | −10.6960 | −0.339942 | ||||||||
\(991\) | 1.36771 | 0.0434466 | 0.0217233 | − | 0.999764i | \(-0.493085\pi\) | ||||
0.0217233 | + | 0.999764i | \(0.493085\pi\) | |||||||
\(992\) | −20.8702 | −0.662629 | ||||||||
\(993\) | 0.0211725 | 0.000671888 0 | ||||||||
\(994\) | 1.46761 | 0.0465499 | ||||||||
\(995\) | −23.5098 | −0.745311 | ||||||||
\(996\) | −60.4268 | −1.91470 | ||||||||
\(997\) | −17.2016 | −0.544780 | −0.272390 | − | 0.962187i | \(-0.587814\pi\) | ||||
−0.272390 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(998\) | −19.5021 | −0.617329 | ||||||||
\(999\) | −31.7601 | −1.00484 |
(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 | 241.2.a.b.1.11 | ✓ | 12 | |
3.2 | odd | 2 | 2169.2.a.h.1.2 | 12 | |||
4.3 | odd | 2 | 3856.2.a.n.1.5 | 12 | |||
5.4 | even | 2 | 6025.2.a.h.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2169.2.a.h.1.2 | 12 | 3.2 | odd | 2 | |||
3856.2.a.n.1.5 | 12 | 4.3 | odd | 2 | |||
6025.2.a.h.1.2 | 12 | 5.4 | even | 2 |