Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.70235 | −0.982854 | −0.491427 | − | 0.870919i | \(-0.663525\pi\) | ||||
−0.491427 | + | 0.870919i | \(0.663525\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.07630 | 1.82298 | 0.911489 | − | 0.411325i | \(-0.134934\pi\) | ||||
0.911489 | + | 0.411325i | \(0.134934\pi\) | |||||||
\(6\) | 1.70235 | 0.694983 | ||||||||
\(7\) | 1.03752 | 0.392146 | 0.196073 | − | 0.980589i | \(-0.437181\pi\) | ||||
0.196073 | + | 0.980589i | \(0.437181\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.101993 | −0.0339977 | ||||||||
\(10\) | −4.07630 | −1.28904 | ||||||||
\(11\) | −1.31126 | −0.395361 | −0.197680 | − | 0.980267i | \(-0.563341\pi\) | ||||
−0.197680 | + | 0.980267i | \(0.563341\pi\) | |||||||
\(12\) | −1.70235 | −0.491427 | ||||||||
\(13\) | 2.37232 | 0.657963 | 0.328982 | − | 0.944336i | \(-0.393295\pi\) | ||||
0.328982 | + | 0.944336i | \(0.393295\pi\) | |||||||
\(14\) | −1.03752 | −0.277289 | ||||||||
\(15\) | −6.93930 | −1.79172 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.13379 | −1.24513 | −0.622564 | − | 0.782569i | \(-0.713909\pi\) | ||||
−0.622564 | + | 0.782569i | \(0.713909\pi\) | |||||||
\(18\) | 0.101993 | 0.0240400 | ||||||||
\(19\) | 4.46798 | 1.02503 | 0.512513 | − | 0.858680i | \(-0.328715\pi\) | ||||
0.512513 | + | 0.858680i | \(0.328715\pi\) | |||||||
\(20\) | 4.07630 | 0.911489 | ||||||||
\(21\) | −1.76623 | −0.385423 | ||||||||
\(22\) | 1.31126 | 0.279562 | ||||||||
\(23\) | 0.760254 | 0.158524 | 0.0792619 | − | 0.996854i | \(-0.474744\pi\) | ||||
0.0792619 | + | 0.996854i | \(0.474744\pi\) | |||||||
\(24\) | 1.70235 | 0.347491 | ||||||||
\(25\) | 11.6162 | 2.32325 | ||||||||
\(26\) | −2.37232 | −0.465250 | ||||||||
\(27\) | 5.28069 | 1.01627 | ||||||||
\(28\) | 1.03752 | 0.196073 | ||||||||
\(29\) | 5.15882 | 0.957969 | 0.478984 | − | 0.877823i | \(-0.341005\pi\) | ||||
0.478984 | + | 0.877823i | \(0.341005\pi\) | |||||||
\(30\) | 6.93930 | 1.26694 | ||||||||
\(31\) | −0.698242 | −0.125408 | −0.0627040 | − | 0.998032i | \(-0.519972\pi\) | ||||
−0.0627040 | + | 0.998032i | \(0.519972\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.23223 | 0.388582 | ||||||||
\(34\) | 5.13379 | 0.880438 | ||||||||
\(35\) | 4.22925 | 0.714874 | ||||||||
\(36\) | −0.101993 | −0.0169988 | ||||||||
\(37\) | −7.91187 | −1.30070 | −0.650352 | − | 0.759633i | \(-0.725379\pi\) | ||||
−0.650352 | + | 0.759633i | \(0.725379\pi\) | |||||||
\(38\) | −4.46798 | −0.724802 | ||||||||
\(39\) | −4.03853 | −0.646682 | ||||||||
\(40\) | −4.07630 | −0.644520 | ||||||||
\(41\) | 3.27999 | 0.512249 | 0.256124 | − | 0.966644i | \(-0.417554\pi\) | ||||
0.256124 | + | 0.966644i | \(0.417554\pi\) | |||||||
\(42\) | 1.76623 | 0.272535 | ||||||||
\(43\) | 5.83497 | 0.889824 | 0.444912 | − | 0.895574i | \(-0.353235\pi\) | ||||
0.444912 | + | 0.895574i | \(0.353235\pi\) | |||||||
\(44\) | −1.31126 | −0.197680 | ||||||||
\(45\) | −0.415754 | −0.0619770 | ||||||||
\(46\) | −0.760254 | −0.112093 | ||||||||
\(47\) | −2.17474 | −0.317219 | −0.158610 | − | 0.987341i | \(-0.550701\pi\) | ||||
−0.158610 | + | 0.987341i | \(0.550701\pi\) | |||||||
\(48\) | −1.70235 | −0.245714 | ||||||||
\(49\) | −5.92355 | −0.846221 | ||||||||
\(50\) | −11.6162 | −1.64278 | ||||||||
\(51\) | 8.73953 | 1.22378 | ||||||||
\(52\) | 2.37232 | 0.328982 | ||||||||
\(53\) | −0.495898 | −0.0681169 | −0.0340584 | − | 0.999420i | \(-0.510843\pi\) | ||||
−0.0340584 | + | 0.999420i | \(0.510843\pi\) | |||||||
\(54\) | −5.28069 | −0.718611 | ||||||||
\(55\) | −5.34510 | −0.720734 | ||||||||
\(56\) | −1.03752 | −0.138645 | ||||||||
\(57\) | −7.60608 | −1.00745 | ||||||||
\(58\) | −5.15882 | −0.677386 | ||||||||
\(59\) | −1.42763 | −0.185862 | −0.0929309 | − | 0.995673i | \(-0.529624\pi\) | ||||
−0.0929309 | + | 0.995673i | \(0.529624\pi\) | |||||||
\(60\) | −6.93930 | −0.895860 | ||||||||
\(61\) | −10.1785 | −1.30323 | −0.651613 | − | 0.758551i | \(-0.725908\pi\) | ||||
−0.651613 | + | 0.758551i | \(0.725908\pi\) | |||||||
\(62\) | 0.698242 | 0.0886768 | ||||||||
\(63\) | −0.105820 | −0.0133321 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.67029 | 1.19945 | ||||||||
\(66\) | −2.23223 | −0.274769 | ||||||||
\(67\) | 15.5856 | 1.90408 | 0.952042 | − | 0.305966i | \(-0.0989794\pi\) | ||||
0.952042 | + | 0.305966i | \(0.0989794\pi\) | |||||||
\(68\) | −5.13379 | −0.622564 | ||||||||
\(69\) | −1.29422 | −0.155806 | ||||||||
\(70\) | −4.22925 | −0.505492 | ||||||||
\(71\) | −7.14382 | −0.847815 | −0.423907 | − | 0.905706i | \(-0.639342\pi\) | ||||
−0.423907 | + | 0.905706i | \(0.639342\pi\) | |||||||
\(72\) | 0.101993 | 0.0120200 | ||||||||
\(73\) | −8.35550 | −0.977937 | −0.488969 | − | 0.872301i | \(-0.662627\pi\) | ||||
−0.488969 | + | 0.872301i | \(0.662627\pi\) | |||||||
\(74\) | 7.91187 | 0.919737 | ||||||||
\(75\) | −19.7749 | −2.28341 | ||||||||
\(76\) | 4.46798 | 0.512513 | ||||||||
\(77\) | −1.36046 | −0.155039 | ||||||||
\(78\) | 4.03853 | 0.457273 | ||||||||
\(79\) | 6.98878 | 0.786299 | 0.393150 | − | 0.919475i | \(-0.371385\pi\) | ||||
0.393150 | + | 0.919475i | \(0.371385\pi\) | |||||||
\(80\) | 4.07630 | 0.455744 | ||||||||
\(81\) | −8.68362 | −0.964846 | ||||||||
\(82\) | −3.27999 | −0.362215 | ||||||||
\(83\) | 9.52981 | 1.04603 | 0.523016 | − | 0.852323i | \(-0.324807\pi\) | ||||
0.523016 | + | 0.852323i | \(0.324807\pi\) | |||||||
\(84\) | −1.76623 | −0.192711 | ||||||||
\(85\) | −20.9269 | −2.26984 | ||||||||
\(86\) | −5.83497 | −0.629201 | ||||||||
\(87\) | −8.78213 | −0.941543 | ||||||||
\(88\) | 1.31126 | 0.139781 | ||||||||
\(89\) | 15.9239 | 1.68792 | 0.843962 | − | 0.536402i | \(-0.180217\pi\) | ||||
0.843962 | + | 0.536402i | \(0.180217\pi\) | |||||||
\(90\) | 0.415754 | 0.0438244 | ||||||||
\(91\) | 2.46133 | 0.258018 | ||||||||
\(92\) | 0.760254 | 0.0792619 | ||||||||
\(93\) | 1.18865 | 0.123258 | ||||||||
\(94\) | 2.17474 | 0.224308 | ||||||||
\(95\) | 18.2128 | 1.86860 | ||||||||
\(96\) | 1.70235 | 0.173746 | ||||||||
\(97\) | 6.80293 | 0.690733 | 0.345367 | − | 0.938468i | \(-0.387755\pi\) | ||||
0.345367 | + | 0.938468i | \(0.387755\pi\) | |||||||
\(98\) | 5.92355 | 0.598369 | ||||||||
\(99\) | 0.133740 | 0.0134413 | ||||||||
\(100\) | 11.6162 | 1.16162 | ||||||||
\(101\) | 10.7348 | 1.06815 | 0.534076 | − | 0.845436i | \(-0.320660\pi\) | ||||
0.534076 | + | 0.845436i | \(0.320660\pi\) | |||||||
\(102\) | −8.73953 | −0.865342 | ||||||||
\(103\) | −8.94582 | −0.881458 | −0.440729 | − | 0.897640i | \(-0.645280\pi\) | ||||
−0.440729 | + | 0.897640i | \(0.645280\pi\) | |||||||
\(104\) | −2.37232 | −0.232625 | ||||||||
\(105\) | −7.19968 | −0.702617 | ||||||||
\(106\) | 0.495898 | 0.0481659 | ||||||||
\(107\) | −1.15600 | −0.111755 | −0.0558776 | − | 0.998438i | \(-0.517796\pi\) | ||||
−0.0558776 | + | 0.998438i | \(0.517796\pi\) | |||||||
\(108\) | 5.28069 | 0.508134 | ||||||||
\(109\) | 11.5722 | 1.10842 | 0.554208 | − | 0.832378i | \(-0.313021\pi\) | ||||
0.554208 | + | 0.832378i | \(0.313021\pi\) | |||||||
\(110\) | 5.34510 | 0.509636 | ||||||||
\(111\) | 13.4688 | 1.27840 | ||||||||
\(112\) | 1.03752 | 0.0980366 | ||||||||
\(113\) | 12.7261 | 1.19717 | 0.598584 | − | 0.801060i | \(-0.295730\pi\) | ||||
0.598584 | + | 0.801060i | \(0.295730\pi\) | |||||||
\(114\) | 7.60608 | 0.712375 | ||||||||
\(115\) | 3.09902 | 0.288985 | ||||||||
\(116\) | 5.15882 | 0.478984 | ||||||||
\(117\) | −0.241960 | −0.0223692 | ||||||||
\(118\) | 1.42763 | 0.131424 | ||||||||
\(119\) | −5.32642 | −0.488272 | ||||||||
\(120\) | 6.93930 | 0.633469 | ||||||||
\(121\) | −9.28059 | −0.843690 | ||||||||
\(122\) | 10.1785 | 0.921521 | ||||||||
\(123\) | −5.58371 | −0.503466 | ||||||||
\(124\) | −0.698242 | −0.0627040 | ||||||||
\(125\) | 26.9697 | 2.41225 | ||||||||
\(126\) | 0.105820 | 0.00942720 | ||||||||
\(127\) | 15.6377 | 1.38762 | 0.693811 | − | 0.720157i | \(-0.255930\pi\) | ||||
0.693811 | + | 0.720157i | \(0.255930\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.93318 | −0.874567 | ||||||||
\(130\) | −9.67029 | −0.848141 | ||||||||
\(131\) | 9.26329 | 0.809338 | 0.404669 | − | 0.914463i | \(-0.367387\pi\) | ||||
0.404669 | + | 0.914463i | \(0.367387\pi\) | |||||||
\(132\) | 2.23223 | 0.194291 | ||||||||
\(133\) | 4.63563 | 0.401960 | ||||||||
\(134\) | −15.5856 | −1.34639 | ||||||||
\(135\) | 21.5257 | 1.85264 | ||||||||
\(136\) | 5.13379 | 0.440219 | ||||||||
\(137\) | −0.0402046 | −0.00343491 | −0.00171746 | − | 0.999999i | \(-0.500547\pi\) | ||||
−0.00171746 | + | 0.999999i | \(0.500547\pi\) | |||||||
\(138\) | 1.29422 | 0.110171 | ||||||||
\(139\) | −19.9509 | −1.69221 | −0.846105 | − | 0.533016i | \(-0.821058\pi\) | ||||
−0.846105 | + | 0.533016i | \(0.821058\pi\) | |||||||
\(140\) | 4.22925 | 0.357437 | ||||||||
\(141\) | 3.70218 | 0.311780 | ||||||||
\(142\) | 7.14382 | 0.599496 | ||||||||
\(143\) | −3.11074 | −0.260133 | ||||||||
\(144\) | −0.101993 | −0.00849942 | ||||||||
\(145\) | 21.0289 | 1.74635 | ||||||||
\(146\) | 8.35550 | 0.691506 | ||||||||
\(147\) | 10.0840 | 0.831712 | ||||||||
\(148\) | −7.91187 | −0.650352 | ||||||||
\(149\) | −12.8354 | −1.05152 | −0.525760 | − | 0.850633i | \(-0.676219\pi\) | ||||
−0.525760 | + | 0.850633i | \(0.676219\pi\) | |||||||
\(150\) | 19.7749 | 1.61462 | ||||||||
\(151\) | −16.1459 | −1.31393 | −0.656967 | − | 0.753919i | \(-0.728161\pi\) | ||||
−0.656967 | + | 0.753919i | \(0.728161\pi\) | |||||||
\(152\) | −4.46798 | −0.362401 | ||||||||
\(153\) | 0.523611 | 0.0423314 | ||||||||
\(154\) | 1.36046 | 0.109629 | ||||||||
\(155\) | −2.84624 | −0.228616 | ||||||||
\(156\) | −4.03853 | −0.323341 | ||||||||
\(157\) | 12.0959 | 0.965358 | 0.482679 | − | 0.875797i | \(-0.339664\pi\) | ||||
0.482679 | + | 0.875797i | \(0.339664\pi\) | |||||||
\(158\) | −6.98878 | −0.555998 | ||||||||
\(159\) | 0.844194 | 0.0669490 | ||||||||
\(160\) | −4.07630 | −0.322260 | ||||||||
\(161\) | 0.788780 | 0.0621646 | ||||||||
\(162\) | 8.68362 | 0.682249 | ||||||||
\(163\) | 1.88880 | 0.147942 | 0.0739709 | − | 0.997260i | \(-0.476433\pi\) | ||||
0.0739709 | + | 0.997260i | \(0.476433\pi\) | |||||||
\(164\) | 3.27999 | 0.256124 | ||||||||
\(165\) | 9.09925 | 0.708376 | ||||||||
\(166\) | −9.52981 | −0.739657 | ||||||||
\(167\) | 6.55728 | 0.507418 | 0.253709 | − | 0.967281i | \(-0.418349\pi\) | ||||
0.253709 | + | 0.967281i | \(0.418349\pi\) | |||||||
\(168\) | 1.76623 | 0.136268 | ||||||||
\(169\) | −7.37210 | −0.567085 | ||||||||
\(170\) | 20.9269 | 1.60502 | ||||||||
\(171\) | −0.455703 | −0.0348485 | ||||||||
\(172\) | 5.83497 | 0.444912 | ||||||||
\(173\) | 9.61367 | 0.730914 | 0.365457 | − | 0.930828i | \(-0.380913\pi\) | ||||
0.365457 | + | 0.930828i | \(0.380913\pi\) | |||||||
\(174\) | 8.78213 | 0.665772 | ||||||||
\(175\) | 12.0521 | 0.911053 | ||||||||
\(176\) | −1.31126 | −0.0988402 | ||||||||
\(177\) | 2.43033 | 0.182675 | ||||||||
\(178\) | −15.9239 | −1.19354 | ||||||||
\(179\) | 10.3741 | 0.775400 | 0.387700 | − | 0.921786i | \(-0.373270\pi\) | ||||
0.387700 | + | 0.921786i | \(0.373270\pi\) | |||||||
\(180\) | −0.415754 | −0.0309885 | ||||||||
\(181\) | −5.78228 | −0.429793 | −0.214897 | − | 0.976637i | \(-0.568941\pi\) | ||||
−0.214897 | + | 0.976637i | \(0.568941\pi\) | |||||||
\(182\) | −2.46133 | −0.182446 | ||||||||
\(183\) | 17.3274 | 1.28088 | ||||||||
\(184\) | −0.760254 | −0.0560466 | ||||||||
\(185\) | −32.2512 | −2.37115 | ||||||||
\(186\) | −1.18865 | −0.0871564 | ||||||||
\(187\) | 6.73175 | 0.492274 | ||||||||
\(188\) | −2.17474 | −0.158610 | ||||||||
\(189\) | 5.47883 | 0.398526 | ||||||||
\(190\) | −18.2128 | −1.32130 | ||||||||
\(191\) | 8.94259 | 0.647063 | 0.323532 | − | 0.946217i | \(-0.395130\pi\) | ||||
0.323532 | + | 0.946217i | \(0.395130\pi\) | |||||||
\(192\) | −1.70235 | −0.122857 | ||||||||
\(193\) | −17.8248 | −1.28305 | −0.641527 | − | 0.767100i | \(-0.721699\pi\) | ||||
−0.641527 | + | 0.767100i | \(0.721699\pi\) | |||||||
\(194\) | −6.80293 | −0.488422 | ||||||||
\(195\) | −16.4623 | −1.17889 | ||||||||
\(196\) | −5.92355 | −0.423111 | ||||||||
\(197\) | 18.6669 | 1.32996 | 0.664982 | − | 0.746859i | \(-0.268439\pi\) | ||||
0.664982 | + | 0.746859i | \(0.268439\pi\) | |||||||
\(198\) | −0.133740 | −0.00950447 | ||||||||
\(199\) | 13.4208 | 0.951375 | 0.475687 | − | 0.879614i | \(-0.342199\pi\) | ||||
0.475687 | + | 0.879614i | \(0.342199\pi\) | |||||||
\(200\) | −11.6162 | −0.821392 | ||||||||
\(201\) | −26.5322 | −1.87144 | ||||||||
\(202\) | −10.7348 | −0.755298 | ||||||||
\(203\) | 5.35239 | 0.375664 | ||||||||
\(204\) | 8.73953 | 0.611889 | ||||||||
\(205\) | 13.3702 | 0.933818 | ||||||||
\(206\) | 8.94582 | 0.623285 | ||||||||
\(207\) | −0.0775406 | −0.00538944 | ||||||||
\(208\) | 2.37232 | 0.164491 | ||||||||
\(209\) | −5.85870 | −0.405255 | ||||||||
\(210\) | 7.19968 | 0.496825 | ||||||||
\(211\) | −3.72585 | −0.256498 | −0.128249 | − | 0.991742i | \(-0.540936\pi\) | ||||
−0.128249 | + | 0.991742i | \(0.540936\pi\) | |||||||
\(212\) | −0.495898 | −0.0340584 | ||||||||
\(213\) | 12.1613 | 0.833278 | ||||||||
\(214\) | 1.15600 | 0.0790228 | ||||||||
\(215\) | 23.7851 | 1.62213 | ||||||||
\(216\) | −5.28069 | −0.359305 | ||||||||
\(217\) | −0.724441 | −0.0491783 | ||||||||
\(218\) | −11.5722 | −0.783768 | ||||||||
\(219\) | 14.2240 | 0.961170 | ||||||||
\(220\) | −5.34510 | −0.360367 | ||||||||
\(221\) | −12.1790 | −0.819248 | ||||||||
\(222\) | −13.4688 | −0.903967 | ||||||||
\(223\) | −3.81823 | −0.255688 | −0.127844 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127844 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(224\) | −1.03752 | −0.0693223 | ||||||||
\(225\) | −1.18477 | −0.0789850 | ||||||||
\(226\) | −12.7261 | −0.846526 | ||||||||
\(227\) | 15.3243 | 1.01711 | 0.508554 | − | 0.861030i | \(-0.330180\pi\) | ||||
0.508554 | + | 0.861030i | \(0.330180\pi\) | |||||||
\(228\) | −7.60608 | −0.503725 | ||||||||
\(229\) | 19.0411 | 1.25827 | 0.629136 | − | 0.777295i | \(-0.283409\pi\) | ||||
0.629136 | + | 0.777295i | \(0.283409\pi\) | |||||||
\(230\) | −3.09902 | −0.204344 | ||||||||
\(231\) | 2.31599 | 0.152381 | ||||||||
\(232\) | −5.15882 | −0.338693 | ||||||||
\(233\) | −12.6530 | −0.828928 | −0.414464 | − | 0.910066i | \(-0.636031\pi\) | ||||
−0.414464 | + | 0.910066i | \(0.636031\pi\) | |||||||
\(234\) | 0.241960 | 0.0158174 | ||||||||
\(235\) | −8.86491 | −0.578283 | ||||||||
\(236\) | −1.42763 | −0.0929309 | ||||||||
\(237\) | −11.8974 | −0.772818 | ||||||||
\(238\) | 5.32642 | 0.345261 | ||||||||
\(239\) | −3.96287 | −0.256337 | −0.128169 | − | 0.991752i | \(-0.540910\pi\) | ||||
−0.128169 | + | 0.991752i | \(0.540910\pi\) | |||||||
\(240\) | −6.93930 | −0.447930 | ||||||||
\(241\) | −20.3938 | −1.31368 | −0.656841 | − | 0.754029i | \(-0.728108\pi\) | ||||
−0.656841 | + | 0.754029i | \(0.728108\pi\) | |||||||
\(242\) | 9.28059 | 0.596579 | ||||||||
\(243\) | −1.05948 | −0.0679656 | ||||||||
\(244\) | −10.1785 | −0.651613 | ||||||||
\(245\) | −24.1462 | −1.54264 | ||||||||
\(246\) | 5.58371 | 0.356004 | ||||||||
\(247\) | 10.5995 | 0.674429 | ||||||||
\(248\) | 0.698242 | 0.0443384 | ||||||||
\(249\) | −16.2231 | −1.02810 | ||||||||
\(250\) | −26.9697 | −1.70572 | ||||||||
\(251\) | 25.6553 | 1.61935 | 0.809674 | − | 0.586880i | \(-0.199644\pi\) | ||||
0.809674 | + | 0.586880i | \(0.199644\pi\) | |||||||
\(252\) | −0.105820 | −0.00666603 | ||||||||
\(253\) | −0.996893 | −0.0626741 | ||||||||
\(254\) | −15.6377 | −0.981196 | ||||||||
\(255\) | 35.6249 | 2.23092 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.0779 | −1.31480 | −0.657402 | − | 0.753540i | \(-0.728345\pi\) | ||||
−0.657402 | + | 0.753540i | \(0.728345\pi\) | |||||||
\(258\) | 9.93318 | 0.618413 | ||||||||
\(259\) | −8.20874 | −0.510066 | ||||||||
\(260\) | 9.67029 | 0.599726 | ||||||||
\(261\) | −0.526164 | −0.0325687 | ||||||||
\(262\) | −9.26329 | −0.572288 | ||||||||
\(263\) | 15.9581 | 0.984019 | 0.492009 | − | 0.870590i | \(-0.336263\pi\) | ||||
0.492009 | + | 0.870590i | \(0.336263\pi\) | |||||||
\(264\) | −2.23223 | −0.137384 | ||||||||
\(265\) | −2.02143 | −0.124176 | ||||||||
\(266\) | −4.63563 | −0.284229 | ||||||||
\(267\) | −27.1080 | −1.65898 | ||||||||
\(268\) | 15.5856 | 0.952042 | ||||||||
\(269\) | −7.34367 | −0.447752 | −0.223876 | − | 0.974618i | \(-0.571871\pi\) | ||||
−0.223876 | + | 0.974618i | \(0.571871\pi\) | |||||||
\(270\) | −21.5257 | −1.31001 | ||||||||
\(271\) | −3.56307 | −0.216441 | −0.108221 | − | 0.994127i | \(-0.534515\pi\) | ||||
−0.108221 | + | 0.994127i | \(0.534515\pi\) | |||||||
\(272\) | −5.13379 | −0.311282 | ||||||||
\(273\) | −4.19006 | −0.253594 | ||||||||
\(274\) | 0.0402046 | 0.00242885 | ||||||||
\(275\) | −15.2319 | −0.918520 | ||||||||
\(276\) | −1.29422 | −0.0779029 | ||||||||
\(277\) | −6.73812 | −0.404855 | −0.202427 | − | 0.979297i | \(-0.564883\pi\) | ||||
−0.202427 | + | 0.979297i | \(0.564883\pi\) | |||||||
\(278\) | 19.9509 | 1.19657 | ||||||||
\(279\) | 0.0712158 | 0.00426358 | ||||||||
\(280\) | −4.22925 | −0.252746 | ||||||||
\(281\) | −24.8932 | −1.48501 | −0.742503 | − | 0.669843i | \(-0.766361\pi\) | ||||
−0.742503 | + | 0.669843i | \(0.766361\pi\) | |||||||
\(282\) | −3.70218 | −0.220462 | ||||||||
\(283\) | 5.60601 | 0.333243 | 0.166621 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166621 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(284\) | −7.14382 | −0.423907 | ||||||||
\(285\) | −31.0047 | −1.83656 | ||||||||
\(286\) | 3.11074 | 0.183942 | ||||||||
\(287\) | 3.40306 | 0.200877 | ||||||||
\(288\) | 0.101993 | 0.00601000 | ||||||||
\(289\) | 9.35582 | 0.550342 | ||||||||
\(290\) | −21.0289 | −1.23486 | ||||||||
\(291\) | −11.5810 | −0.678890 | ||||||||
\(292\) | −8.35550 | −0.488969 | ||||||||
\(293\) | 2.56147 | 0.149643 | 0.0748214 | − | 0.997197i | \(-0.476161\pi\) | ||||
0.0748214 | + | 0.997197i | \(0.476161\pi\) | |||||||
\(294\) | −10.0840 | −0.588109 | ||||||||
\(295\) | −5.81946 | −0.338822 | ||||||||
\(296\) | 7.91187 | 0.459868 | ||||||||
\(297\) | −6.92437 | −0.401793 | ||||||||
\(298\) | 12.8354 | 0.743537 | ||||||||
\(299\) | 1.80356 | 0.104303 | ||||||||
\(300\) | −19.7749 | −1.14171 | ||||||||
\(301\) | 6.05391 | 0.348941 | ||||||||
\(302\) | 16.1459 | 0.929092 | ||||||||
\(303\) | −18.2744 | −1.04984 | ||||||||
\(304\) | 4.46798 | 0.256256 | ||||||||
\(305\) | −41.4907 | −2.37575 | ||||||||
\(306\) | −0.523611 | −0.0299329 | ||||||||
\(307\) | 6.62710 | 0.378228 | 0.189114 | − | 0.981955i | \(-0.439438\pi\) | ||||
0.189114 | + | 0.981955i | \(0.439438\pi\) | |||||||
\(308\) | −1.36046 | −0.0775196 | ||||||||
\(309\) | 15.2289 | 0.866344 | ||||||||
\(310\) | 2.84624 | 0.161656 | ||||||||
\(311\) | 14.4722 | 0.820643 | 0.410321 | − | 0.911941i | \(-0.365417\pi\) | ||||
0.410321 | + | 0.911941i | \(0.365417\pi\) | |||||||
\(312\) | 4.03853 | 0.228637 | ||||||||
\(313\) | −30.8995 | −1.74655 | −0.873273 | − | 0.487232i | \(-0.838007\pi\) | ||||
−0.873273 | + | 0.487232i | \(0.838007\pi\) | |||||||
\(314\) | −12.0959 | −0.682611 | ||||||||
\(315\) | −0.431354 | −0.0243041 | ||||||||
\(316\) | 6.98878 | 0.393150 | ||||||||
\(317\) | −11.4870 | −0.645175 | −0.322588 | − | 0.946540i | \(-0.604553\pi\) | ||||
−0.322588 | + | 0.946540i | \(0.604553\pi\) | |||||||
\(318\) | −0.844194 | −0.0473401 | ||||||||
\(319\) | −6.76457 | −0.378743 | ||||||||
\(320\) | 4.07630 | 0.227872 | ||||||||
\(321\) | 1.96793 | 0.109839 | ||||||||
\(322\) | −0.788780 | −0.0439570 | ||||||||
\(323\) | −22.9377 | −1.27629 | ||||||||
\(324\) | −8.68362 | −0.482423 | ||||||||
\(325\) | 27.5574 | 1.52861 | ||||||||
\(326\) | −1.88880 | −0.104611 | ||||||||
\(327\) | −19.7000 | −1.08941 | ||||||||
\(328\) | −3.27999 | −0.181107 | ||||||||
\(329\) | −2.25634 | −0.124396 | ||||||||
\(330\) | −9.09925 | −0.500897 | ||||||||
\(331\) | 9.23886 | 0.507814 | 0.253907 | − | 0.967229i | \(-0.418284\pi\) | ||||
0.253907 | + | 0.967229i | \(0.418284\pi\) | |||||||
\(332\) | 9.52981 | 0.523016 | ||||||||
\(333\) | 0.806956 | 0.0442209 | ||||||||
\(334\) | −6.55728 | −0.358799 | ||||||||
\(335\) | 63.5316 | 3.47110 | ||||||||
\(336\) | −1.76623 | −0.0963557 | ||||||||
\(337\) | 10.4779 | 0.570767 | 0.285384 | − | 0.958413i | \(-0.407879\pi\) | ||||
0.285384 | + | 0.958413i | \(0.407879\pi\) | |||||||
\(338\) | 7.37210 | 0.400989 | ||||||||
\(339\) | −21.6643 | −1.17664 | ||||||||
\(340\) | −20.9269 | −1.13492 | ||||||||
\(341\) | 0.915579 | 0.0495814 | ||||||||
\(342\) | 0.455703 | 0.0246416 | ||||||||
\(343\) | −13.4085 | −0.723989 | ||||||||
\(344\) | −5.83497 | −0.314600 | ||||||||
\(345\) | −5.27563 | −0.284030 | ||||||||
\(346\) | −9.61367 | −0.516834 | ||||||||
\(347\) | 13.3901 | 0.718818 | 0.359409 | − | 0.933180i | \(-0.382978\pi\) | ||||
0.359409 | + | 0.933180i | \(0.382978\pi\) | |||||||
\(348\) | −8.78213 | −0.470772 | ||||||||
\(349\) | 28.3325 | 1.51660 | 0.758301 | − | 0.651905i | \(-0.226030\pi\) | ||||
0.758301 | + | 0.651905i | \(0.226030\pi\) | |||||||
\(350\) | −12.0521 | −0.644211 | ||||||||
\(351\) | 12.5275 | 0.668667 | ||||||||
\(352\) | 1.31126 | 0.0698906 | ||||||||
\(353\) | 7.38649 | 0.393143 | 0.196572 | − | 0.980489i | \(-0.437019\pi\) | ||||
0.196572 | + | 0.980489i | \(0.437019\pi\) | |||||||
\(354\) | −2.43033 | −0.129171 | ||||||||
\(355\) | −29.1203 | −1.54555 | ||||||||
\(356\) | 15.9239 | 0.843962 | ||||||||
\(357\) | 9.06745 | 0.479900 | ||||||||
\(358\) | −10.3741 | −0.548291 | ||||||||
\(359\) | −17.7601 | −0.937341 | −0.468670 | − | 0.883373i | \(-0.655267\pi\) | ||||
−0.468670 | + | 0.883373i | \(0.655267\pi\) | |||||||
\(360\) | 0.415754 | 0.0219122 | ||||||||
\(361\) | 0.962862 | 0.0506770 | ||||||||
\(362\) | 5.78228 | 0.303910 | ||||||||
\(363\) | 15.7988 | 0.829224 | ||||||||
\(364\) | 2.46133 | 0.129009 | ||||||||
\(365\) | −34.0595 | −1.78276 | ||||||||
\(366\) | −17.3274 | −0.905720 | ||||||||
\(367\) | 29.5891 | 1.54454 | 0.772269 | − | 0.635296i | \(-0.219122\pi\) | ||||
0.772269 | + | 0.635296i | \(0.219122\pi\) | |||||||
\(368\) | 0.760254 | 0.0396310 | ||||||||
\(369\) | −0.334536 | −0.0174153 | ||||||||
\(370\) | 32.2512 | 1.67666 | ||||||||
\(371\) | −0.514505 | −0.0267118 | ||||||||
\(372\) | 1.18865 | 0.0616289 | ||||||||
\(373\) | 29.1942 | 1.51162 | 0.755810 | − | 0.654791i | \(-0.227243\pi\) | ||||
0.755810 | + | 0.654791i | \(0.227243\pi\) | |||||||
\(374\) | −6.73175 | −0.348091 | ||||||||
\(375\) | −45.9120 | −2.37089 | ||||||||
\(376\) | 2.17474 | 0.112154 | ||||||||
\(377\) | 12.2384 | 0.630308 | ||||||||
\(378\) | −5.47883 | −0.281801 | ||||||||
\(379\) | 8.17757 | 0.420054 | 0.210027 | − | 0.977696i | \(-0.432645\pi\) | ||||
0.210027 | + | 0.977696i | \(0.432645\pi\) | |||||||
\(380\) | 18.2128 | 0.934299 | ||||||||
\(381\) | −26.6209 | −1.36383 | ||||||||
\(382\) | −8.94259 | −0.457543 | ||||||||
\(383\) | 7.06134 | 0.360818 | 0.180409 | − | 0.983592i | \(-0.442258\pi\) | ||||
0.180409 | + | 0.983592i | \(0.442258\pi\) | |||||||
\(384\) | 1.70235 | 0.0868729 | ||||||||
\(385\) | −5.54566 | −0.282633 | ||||||||
\(386\) | 17.8248 | 0.907256 | ||||||||
\(387\) | −0.595126 | −0.0302520 | ||||||||
\(388\) | 6.80293 | 0.345367 | ||||||||
\(389\) | 4.21852 | 0.213888 | 0.106944 | − | 0.994265i | \(-0.465894\pi\) | ||||
0.106944 | + | 0.994265i | \(0.465894\pi\) | |||||||
\(390\) | 16.4623 | 0.833598 | ||||||||
\(391\) | −3.90298 | −0.197382 | ||||||||
\(392\) | 5.92355 | 0.299184 | ||||||||
\(393\) | −15.7694 | −0.795461 | ||||||||
\(394\) | −18.6669 | −0.940427 | ||||||||
\(395\) | 28.4884 | 1.43341 | ||||||||
\(396\) | 0.133740 | 0.00672067 | ||||||||
\(397\) | 10.9084 | 0.547478 | 0.273739 | − | 0.961804i | \(-0.411740\pi\) | ||||
0.273739 | + | 0.961804i | \(0.411740\pi\) | |||||||
\(398\) | −13.4208 | −0.672723 | ||||||||
\(399\) | −7.89148 | −0.395068 | ||||||||
\(400\) | 11.6162 | 0.580812 | ||||||||
\(401\) | 25.6705 | 1.28192 | 0.640961 | − | 0.767574i | \(-0.278536\pi\) | ||||
0.640961 | + | 0.767574i | \(0.278536\pi\) | |||||||
\(402\) | 26.5322 | 1.32331 | ||||||||
\(403\) | −1.65645 | −0.0825138 | ||||||||
\(404\) | 10.7348 | 0.534076 | ||||||||
\(405\) | −35.3970 | −1.75889 | ||||||||
\(406\) | −5.35239 | −0.265635 | ||||||||
\(407\) | 10.3745 | 0.514247 | ||||||||
\(408\) | −8.73953 | −0.432671 | ||||||||
\(409\) | 27.2787 | 1.34885 | 0.674424 | − | 0.738345i | \(-0.264392\pi\) | ||||
0.674424 | + | 0.738345i | \(0.264392\pi\) | |||||||
\(410\) | −13.3702 | −0.660309 | ||||||||
\(411\) | 0.0684424 | 0.00337602 | ||||||||
\(412\) | −8.94582 | −0.440729 | ||||||||
\(413\) | −1.48120 | −0.0728850 | ||||||||
\(414\) | 0.0775406 | 0.00381091 | ||||||||
\(415\) | 38.8464 | 1.90689 | ||||||||
\(416\) | −2.37232 | −0.116313 | ||||||||
\(417\) | 33.9634 | 1.66320 | ||||||||
\(418\) | 5.85870 | 0.286558 | ||||||||
\(419\) | 11.8089 | 0.576901 | 0.288451 | − | 0.957495i | \(-0.406860\pi\) | ||||
0.288451 | + | 0.957495i | \(0.406860\pi\) | |||||||
\(420\) | −7.19968 | −0.351308 | ||||||||
\(421\) | −38.9584 | −1.89871 | −0.949357 | − | 0.314198i | \(-0.898264\pi\) | ||||
−0.949357 | + | 0.314198i | \(0.898264\pi\) | |||||||
\(422\) | 3.72585 | 0.181371 | ||||||||
\(423\) | 0.221809 | 0.0107847 | ||||||||
\(424\) | 0.495898 | 0.0240830 | ||||||||
\(425\) | −59.6353 | −2.89274 | ||||||||
\(426\) | −12.1613 | −0.589217 | ||||||||
\(427\) | −10.5604 | −0.511056 | ||||||||
\(428\) | −1.15600 | −0.0558776 | ||||||||
\(429\) | 5.29557 | 0.255673 | ||||||||
\(430\) | −23.7851 | −1.14702 | ||||||||
\(431\) | 10.2463 | 0.493547 | 0.246774 | − | 0.969073i | \(-0.420630\pi\) | ||||
0.246774 | + | 0.969073i | \(0.420630\pi\) | |||||||
\(432\) | 5.28069 | 0.254067 | ||||||||
\(433\) | −4.12687 | −0.198325 | −0.0991623 | − | 0.995071i | \(-0.531616\pi\) | ||||
−0.0991623 | + | 0.995071i | \(0.531616\pi\) | |||||||
\(434\) | 0.724441 | 0.0347743 | ||||||||
\(435\) | −35.7986 | −1.71641 | ||||||||
\(436\) | 11.5722 | 0.554208 | ||||||||
\(437\) | 3.39680 | 0.162491 | ||||||||
\(438\) | −14.2240 | −0.679650 | ||||||||
\(439\) | −19.6791 | −0.939233 | −0.469616 | − | 0.882871i | \(-0.655608\pi\) | ||||
−0.469616 | + | 0.882871i | \(0.655608\pi\) | |||||||
\(440\) | 5.34510 | 0.254818 | ||||||||
\(441\) | 0.604161 | 0.0287696 | ||||||||
\(442\) | 12.1790 | 0.579296 | ||||||||
\(443\) | 1.80713 | 0.0858591 | 0.0429296 | − | 0.999078i | \(-0.486331\pi\) | ||||
0.0429296 | + | 0.999078i | \(0.486331\pi\) | |||||||
\(444\) | 13.4688 | 0.639201 | ||||||||
\(445\) | 64.9104 | 3.07705 | ||||||||
\(446\) | 3.81823 | 0.180798 | ||||||||
\(447\) | 21.8505 | 1.03349 | ||||||||
\(448\) | 1.03752 | 0.0490183 | ||||||||
\(449\) | −19.7178 | −0.930540 | −0.465270 | − | 0.885169i | \(-0.654043\pi\) | ||||
−0.465270 | + | 0.885169i | \(0.654043\pi\) | |||||||
\(450\) | 1.18477 | 0.0558508 | ||||||||
\(451\) | −4.30093 | −0.202523 | ||||||||
\(452\) | 12.7261 | 0.598584 | ||||||||
\(453\) | 27.4860 | 1.29141 | ||||||||
\(454\) | −15.3243 | −0.719205 | ||||||||
\(455\) | 10.0331 | 0.470361 | ||||||||
\(456\) | 7.60608 | 0.356188 | ||||||||
\(457\) | 24.0627 | 1.12561 | 0.562804 | − | 0.826591i | \(-0.309723\pi\) | ||||
0.562804 | + | 0.826591i | \(0.309723\pi\) | |||||||
\(458\) | −19.0411 | −0.889733 | ||||||||
\(459\) | −27.1100 | −1.26538 | ||||||||
\(460\) | 3.09902 | 0.144493 | ||||||||
\(461\) | −9.06197 | −0.422058 | −0.211029 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211029 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(462\) | −2.31599 | −0.107750 | ||||||||
\(463\) | −27.5234 | −1.27912 | −0.639560 | − | 0.768741i | \(-0.720883\pi\) | ||||
−0.639560 | + | 0.768741i | \(0.720883\pi\) | |||||||
\(464\) | 5.15882 | 0.239492 | ||||||||
\(465\) | 4.84531 | 0.224696 | ||||||||
\(466\) | 12.6530 | 0.586140 | ||||||||
\(467\) | 3.53732 | 0.163688 | 0.0818438 | − | 0.996645i | \(-0.473919\pi\) | ||||
0.0818438 | + | 0.996645i | \(0.473919\pi\) | |||||||
\(468\) | −0.241960 | −0.0111846 | ||||||||
\(469\) | 16.1704 | 0.746680 | ||||||||
\(470\) | 8.86491 | 0.408908 | ||||||||
\(471\) | −20.5915 | −0.948806 | ||||||||
\(472\) | 1.42763 | 0.0657121 | ||||||||
\(473\) | −7.65118 | −0.351802 | ||||||||
\(474\) | 11.8974 | 0.546465 | ||||||||
\(475\) | 51.9011 | 2.38139 | ||||||||
\(476\) | −5.32642 | −0.244136 | ||||||||
\(477\) | 0.0505782 | 0.00231582 | ||||||||
\(478\) | 3.96287 | 0.181258 | ||||||||
\(479\) | −1.80306 | −0.0823839 | −0.0411919 | − | 0.999151i | \(-0.513116\pi\) | ||||
−0.0411919 | + | 0.999151i | \(0.513116\pi\) | |||||||
\(480\) | 6.93930 | 0.316734 | ||||||||
\(481\) | −18.7695 | −0.855815 | ||||||||
\(482\) | 20.3938 | 0.928913 | ||||||||
\(483\) | −1.34278 | −0.0610987 | ||||||||
\(484\) | −9.28059 | −0.421845 | ||||||||
\(485\) | 27.7308 | 1.25919 | ||||||||
\(486\) | 1.05948 | 0.0480589 | ||||||||
\(487\) | 13.8396 | 0.627131 | 0.313565 | − | 0.949567i | \(-0.398477\pi\) | ||||
0.313565 | + | 0.949567i | \(0.398477\pi\) | |||||||
\(488\) | 10.1785 | 0.460760 | ||||||||
\(489\) | −3.21540 | −0.145405 | ||||||||
\(490\) | 24.1462 | 1.09081 | ||||||||
\(491\) | 40.3124 | 1.81927 | 0.909636 | − | 0.415406i | \(-0.136360\pi\) | ||||
0.909636 | + | 0.415406i | \(0.136360\pi\) | |||||||
\(492\) | −5.58371 | −0.251733 | ||||||||
\(493\) | −26.4843 | −1.19279 | ||||||||
\(494\) | −10.5995 | −0.476893 | ||||||||
\(495\) | 0.545163 | 0.0245033 | ||||||||
\(496\) | −0.698242 | −0.0313520 | ||||||||
\(497\) | −7.41186 | −0.332468 | ||||||||
\(498\) | 16.2231 | 0.726975 | ||||||||
\(499\) | 32.4731 | 1.45370 | 0.726848 | − | 0.686798i | \(-0.240985\pi\) | ||||
0.726848 | + | 0.686798i | \(0.240985\pi\) | |||||||
\(500\) | 26.9697 | 1.20612 | ||||||||
\(501\) | −11.1628 | −0.498718 | ||||||||
\(502\) | −25.6553 | −1.14505 | ||||||||
\(503\) | −42.9514 | −1.91511 | −0.957553 | − | 0.288257i | \(-0.906924\pi\) | ||||
−0.957553 | + | 0.288257i | \(0.906924\pi\) | |||||||
\(504\) | 0.105820 | 0.00471360 | ||||||||
\(505\) | 43.7583 | 1.94722 | ||||||||
\(506\) | 0.996893 | 0.0443173 | ||||||||
\(507\) | 12.5499 | 0.557361 | ||||||||
\(508\) | 15.6377 | 0.693811 | ||||||||
\(509\) | −34.6615 | −1.53634 | −0.768172 | − | 0.640244i | \(-0.778833\pi\) | ||||
−0.768172 | + | 0.640244i | \(0.778833\pi\) | |||||||
\(510\) | −35.6249 | −1.57750 | ||||||||
\(511\) | −8.66902 | −0.383495 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 23.5940 | 1.04170 | ||||||||
\(514\) | 21.0779 | 0.929706 | ||||||||
\(515\) | −36.4658 | −1.60688 | ||||||||
\(516\) | −9.93318 | −0.437284 | ||||||||
\(517\) | 2.85166 | 0.125416 | ||||||||
\(518\) | 8.20874 | 0.360671 | ||||||||
\(519\) | −16.3659 | −0.718382 | ||||||||
\(520\) | −9.67029 | −0.424070 | ||||||||
\(521\) | 28.1674 | 1.23404 | 0.617019 | − | 0.786949i | \(-0.288340\pi\) | ||||
0.617019 | + | 0.786949i | \(0.288340\pi\) | |||||||
\(522\) | 0.526164 | 0.0230296 | ||||||||
\(523\) | 13.8014 | 0.603492 | 0.301746 | − | 0.953388i | \(-0.402431\pi\) | ||||
0.301746 | + | 0.953388i | \(0.402431\pi\) | |||||||
\(524\) | 9.26329 | 0.404669 | ||||||||
\(525\) | −20.5169 | −0.895432 | ||||||||
\(526\) | −15.9581 | −0.695806 | ||||||||
\(527\) | 3.58463 | 0.156149 | ||||||||
\(528\) | 2.23223 | 0.0971455 | ||||||||
\(529\) | −22.4220 | −0.974870 | ||||||||
\(530\) | 2.02143 | 0.0878053 | ||||||||
\(531\) | 0.145609 | 0.00631887 | ||||||||
\(532\) | 4.63563 | 0.200980 | ||||||||
\(533\) | 7.78119 | 0.337041 | ||||||||
\(534\) | 27.1080 | 1.17308 | ||||||||
\(535\) | −4.71222 | −0.203727 | ||||||||
\(536\) | −15.5856 | −0.673196 | ||||||||
\(537\) | −17.6605 | −0.762105 | ||||||||
\(538\) | 7.34367 | 0.316608 | ||||||||
\(539\) | 7.76733 | 0.334563 | ||||||||
\(540\) | 21.5257 | 0.926318 | ||||||||
\(541\) | 29.4943 | 1.26806 | 0.634030 | − | 0.773309i | \(-0.281400\pi\) | ||||
0.634030 | + | 0.773309i | \(0.281400\pi\) | |||||||
\(542\) | 3.56307 | 0.153047 | ||||||||
\(543\) | 9.84348 | 0.422424 | ||||||||
\(544\) | 5.13379 | 0.220110 | ||||||||
\(545\) | 47.1718 | 2.02062 | ||||||||
\(546\) | 4.19006 | 0.179318 | ||||||||
\(547\) | 12.4292 | 0.531434 | 0.265717 | − | 0.964051i | \(-0.414391\pi\) | ||||
0.265717 | + | 0.964051i | \(0.414391\pi\) | |||||||
\(548\) | −0.0402046 | −0.00171746 | ||||||||
\(549\) | 1.03814 | 0.0443067 | ||||||||
\(550\) | 15.2319 | 0.649492 | ||||||||
\(551\) | 23.0495 | 0.981942 | ||||||||
\(552\) | 1.29422 | 0.0550857 | ||||||||
\(553\) | 7.25101 | 0.308344 | ||||||||
\(554\) | 6.73812 | 0.286275 | ||||||||
\(555\) | 54.9029 | 2.33050 | ||||||||
\(556\) | −19.9509 | −0.846105 | ||||||||
\(557\) | −35.5304 | −1.50547 | −0.752736 | − | 0.658322i | \(-0.771267\pi\) | ||||
−0.752736 | + | 0.658322i | \(0.771267\pi\) | |||||||
\(558\) | −0.0712158 | −0.00301481 | ||||||||
\(559\) | 13.8424 | 0.585472 | ||||||||
\(560\) | 4.22925 | 0.178718 | ||||||||
\(561\) | −11.4598 | −0.483834 | ||||||||
\(562\) | 24.8932 | 1.05006 | ||||||||
\(563\) | −7.98426 | −0.336497 | −0.168248 | − | 0.985745i | \(-0.553811\pi\) | ||||
−0.168248 | + | 0.985745i | \(0.553811\pi\) | |||||||
\(564\) | 3.70218 | 0.155890 | ||||||||
\(565\) | 51.8753 | 2.18241 | ||||||||
\(566\) | −5.60601 | −0.235638 | ||||||||
\(567\) | −9.00944 | −0.378361 | ||||||||
\(568\) | 7.14382 | 0.299748 | ||||||||
\(569\) | −2.21774 | −0.0929727 | −0.0464863 | − | 0.998919i | \(-0.514802\pi\) | ||||
−0.0464863 | + | 0.998919i | \(0.514802\pi\) | |||||||
\(570\) | 31.0047 | 1.29864 | ||||||||
\(571\) | −33.0788 | −1.38431 | −0.692153 | − | 0.721751i | \(-0.743338\pi\) | ||||
−0.692153 | + | 0.721751i | \(0.743338\pi\) | |||||||
\(572\) | −3.11074 | −0.130066 | ||||||||
\(573\) | −15.2235 | −0.635969 | ||||||||
\(574\) | −3.40306 | −0.142041 | ||||||||
\(575\) | 8.83128 | 0.368290 | ||||||||
\(576\) | −0.101993 | −0.00424971 | ||||||||
\(577\) | −36.2739 | −1.51010 | −0.755050 | − | 0.655667i | \(-0.772388\pi\) | ||||
−0.755050 | + | 0.655667i | \(0.772388\pi\) | |||||||
\(578\) | −9.35582 | −0.389151 | ||||||||
\(579\) | 30.3440 | 1.26106 | ||||||||
\(580\) | 21.0289 | 0.873177 | ||||||||
\(581\) | 9.88739 | 0.410198 | ||||||||
\(582\) | 11.5810 | 0.480048 | ||||||||
\(583\) | 0.650253 | 0.0269307 | ||||||||
\(584\) | 8.35550 | 0.345753 | ||||||||
\(585\) | −0.986302 | −0.0407786 | ||||||||
\(586\) | −2.56147 | −0.105813 | ||||||||
\(587\) | 45.8702 | 1.89326 | 0.946632 | − | 0.322315i | \(-0.104461\pi\) | ||||
0.946632 | + | 0.322315i | \(0.104461\pi\) | |||||||
\(588\) | 10.0840 | 0.415856 | ||||||||
\(589\) | −3.11973 | −0.128546 | ||||||||
\(590\) | 5.81946 | 0.239583 | ||||||||
\(591\) | −31.7777 | −1.30716 | ||||||||
\(592\) | −7.91187 | −0.325176 | ||||||||
\(593\) | −26.2469 | −1.07783 | −0.538916 | − | 0.842360i | \(-0.681166\pi\) | ||||
−0.538916 | + | 0.842360i | \(0.681166\pi\) | |||||||
\(594\) | 6.92437 | 0.284110 | ||||||||
\(595\) | −21.7121 | −0.890109 | ||||||||
\(596\) | −12.8354 | −0.525760 | ||||||||
\(597\) | −22.8469 | −0.935062 | ||||||||
\(598\) | −1.80356 | −0.0737533 | ||||||||
\(599\) | −14.9251 | −0.609824 | −0.304912 | − | 0.952381i | \(-0.598627\pi\) | ||||
−0.304912 | + | 0.952381i | \(0.598627\pi\) | |||||||
\(600\) | 19.7749 | 0.807308 | ||||||||
\(601\) | −26.5058 | −1.08120 | −0.540598 | − | 0.841281i | \(-0.681802\pi\) | ||||
−0.540598 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(602\) | −6.05391 | −0.246739 | ||||||||
\(603\) | −1.58962 | −0.0647345 | ||||||||
\(604\) | −16.1459 | −0.656967 | ||||||||
\(605\) | −37.8305 | −1.53803 | ||||||||
\(606\) | 18.2744 | 0.742348 | ||||||||
\(607\) | −24.2897 | −0.985888 | −0.492944 | − | 0.870061i | \(-0.664079\pi\) | ||||
−0.492944 | + | 0.870061i | \(0.664079\pi\) | |||||||
\(608\) | −4.46798 | −0.181201 | ||||||||
\(609\) | −9.11165 | −0.369223 | ||||||||
\(610\) | 41.4907 | 1.67991 | ||||||||
\(611\) | −5.15919 | −0.208718 | ||||||||
\(612\) | 0.523611 | 0.0211657 | ||||||||
\(613\) | 8.53805 | 0.344848 | 0.172424 | − | 0.985023i | \(-0.444840\pi\) | ||||
0.172424 | + | 0.985023i | \(0.444840\pi\) | |||||||
\(614\) | −6.62710 | −0.267448 | ||||||||
\(615\) | −22.7609 | −0.917807 | ||||||||
\(616\) | 1.36046 | 0.0548147 | ||||||||
\(617\) | −32.7930 | −1.32019 | −0.660097 | − | 0.751180i | \(-0.729485\pi\) | ||||
−0.660097 | + | 0.751180i | \(0.729485\pi\) | |||||||
\(618\) | −15.2289 | −0.612598 | ||||||||
\(619\) | −14.8820 | −0.598158 | −0.299079 | − | 0.954228i | \(-0.596679\pi\) | ||||
−0.299079 | + | 0.954228i | \(0.596679\pi\) | |||||||
\(620\) | −2.84624 | −0.114308 | ||||||||
\(621\) | 4.01466 | 0.161103 | ||||||||
\(622\) | −14.4722 | −0.580282 | ||||||||
\(623\) | 16.5213 | 0.661914 | ||||||||
\(624\) | −4.03853 | −0.161670 | ||||||||
\(625\) | 51.8557 | 2.07423 | ||||||||
\(626\) | 30.8995 | 1.23499 | ||||||||
\(627\) | 9.97358 | 0.398306 | ||||||||
\(628\) | 12.0959 | 0.482679 | ||||||||
\(629\) | 40.6179 | 1.61954 | ||||||||
\(630\) | 0.431354 | 0.0171856 | ||||||||
\(631\) | 29.2178 | 1.16314 | 0.581572 | − | 0.813495i | \(-0.302438\pi\) | ||||
0.581572 | + | 0.813495i | \(0.302438\pi\) | |||||||
\(632\) | −6.98878 | −0.277999 | ||||||||
\(633\) | 6.34271 | 0.252100 | ||||||||
\(634\) | 11.4870 | 0.456208 | ||||||||
\(635\) | 63.7440 | 2.52960 | ||||||||
\(636\) | 0.844194 | 0.0334745 | ||||||||
\(637\) | −14.0526 | −0.556782 | ||||||||
\(638\) | 6.76457 | 0.267812 | ||||||||
\(639\) | 0.728620 | 0.0288237 | ||||||||
\(640\) | −4.07630 | −0.161130 | ||||||||
\(641\) | 1.52056 | 0.0600584 | 0.0300292 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300292 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(642\) | −1.96793 | −0.0776679 | ||||||||
\(643\) | 30.5898 | 1.20634 | 0.603172 | − | 0.797611i | \(-0.293903\pi\) | ||||
0.603172 | + | 0.797611i | \(0.293903\pi\) | |||||||
\(644\) | 0.788780 | 0.0310823 | ||||||||
\(645\) | −40.4906 | −1.59432 | ||||||||
\(646\) | 22.9377 | 0.902471 | ||||||||
\(647\) | 1.90178 | 0.0747669 | 0.0373834 | − | 0.999301i | \(-0.488098\pi\) | ||||
0.0373834 | + | 0.999301i | \(0.488098\pi\) | |||||||
\(648\) | 8.68362 | 0.341125 | ||||||||
\(649\) | 1.87200 | 0.0734825 | ||||||||
\(650\) | −27.5574 | −1.08089 | ||||||||
\(651\) | 1.23325 | 0.0483351 | ||||||||
\(652\) | 1.88880 | 0.0739709 | ||||||||
\(653\) | 24.2031 | 0.947139 | 0.473569 | − | 0.880756i | \(-0.342965\pi\) | ||||
0.473569 | + | 0.880756i | \(0.342965\pi\) | |||||||
\(654\) | 19.7000 | 0.770330 | ||||||||
\(655\) | 37.7600 | 1.47540 | ||||||||
\(656\) | 3.27999 | 0.128062 | ||||||||
\(657\) | 0.852203 | 0.0332476 | ||||||||
\(658\) | 2.25634 | 0.0879615 | ||||||||
\(659\) | 27.2315 | 1.06079 | 0.530395 | − | 0.847751i | \(-0.322044\pi\) | ||||
0.530395 | + | 0.847751i | \(0.322044\pi\) | |||||||
\(660\) | 9.09925 | 0.354188 | ||||||||
\(661\) | 16.3279 | 0.635081 | 0.317541 | − | 0.948245i | \(-0.397143\pi\) | ||||
0.317541 | + | 0.948245i | \(0.397143\pi\) | |||||||
\(662\) | −9.23886 | −0.359079 | ||||||||
\(663\) | 20.7330 | 0.805201 | ||||||||
\(664\) | −9.52981 | −0.369828 | ||||||||
\(665\) | 18.8962 | 0.732764 | ||||||||
\(666\) | −0.806956 | −0.0312689 | ||||||||
\(667\) | 3.92201 | 0.151861 | ||||||||
\(668\) | 6.55728 | 0.253709 | ||||||||
\(669\) | 6.49998 | 0.251304 | ||||||||
\(670\) | −63.5316 | −2.45444 | ||||||||
\(671\) | 13.3467 | 0.515245 | ||||||||
\(672\) | 1.76623 | 0.0681338 | ||||||||
\(673\) | 20.0018 | 0.771012 | 0.385506 | − | 0.922705i | \(-0.374027\pi\) | ||||
0.385506 | + | 0.922705i | \(0.374027\pi\) | |||||||
\(674\) | −10.4779 | −0.403593 | ||||||||
\(675\) | 61.3417 | 2.36104 | ||||||||
\(676\) | −7.37210 | −0.283542 | ||||||||
\(677\) | −15.5543 | −0.597799 | −0.298899 | − | 0.954285i | \(-0.596619\pi\) | ||||
−0.298899 | + | 0.954285i | \(0.596619\pi\) | |||||||
\(678\) | 21.6643 | 0.832011 | ||||||||
\(679\) | 7.05819 | 0.270869 | ||||||||
\(680\) | 20.9269 | 0.802509 | ||||||||
\(681\) | −26.0874 | −0.999670 | ||||||||
\(682\) | −0.915579 | −0.0350593 | ||||||||
\(683\) | −22.9697 | −0.878910 | −0.439455 | − | 0.898265i | \(-0.644828\pi\) | ||||
−0.439455 | + | 0.898265i | \(0.644828\pi\) | |||||||
\(684\) | −0.455703 | −0.0174242 | ||||||||
\(685\) | −0.163886 | −0.00626176 | ||||||||
\(686\) | 13.4085 | 0.511938 | ||||||||
\(687\) | −32.4147 | −1.23670 | ||||||||
\(688\) | 5.83497 | 0.222456 | ||||||||
\(689\) | −1.17643 | −0.0448184 | ||||||||
\(690\) | 5.27563 | 0.200840 | ||||||||
\(691\) | −26.6472 | −1.01371 | −0.506854 | − | 0.862032i | \(-0.669192\pi\) | ||||
−0.506854 | + | 0.862032i | \(0.669192\pi\) | |||||||
\(692\) | 9.61367 | 0.365457 | ||||||||
\(693\) | 0.138758 | 0.00527098 | ||||||||
\(694\) | −13.3901 | −0.508281 | ||||||||
\(695\) | −81.3257 | −3.08486 | ||||||||
\(696\) | 8.78213 | 0.332886 | ||||||||
\(697\) | −16.8388 | −0.637815 | ||||||||
\(698\) | −28.3325 | −1.07240 | ||||||||
\(699\) | 21.5399 | 0.814715 | ||||||||
\(700\) | 12.0521 | 0.455526 | ||||||||
\(701\) | 9.42887 | 0.356124 | 0.178062 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178062 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(702\) | −12.5275 | −0.472819 | ||||||||
\(703\) | −35.3501 | −1.33325 | ||||||||
\(704\) | −1.31126 | −0.0494201 | ||||||||
\(705\) | 15.0912 | 0.568368 | ||||||||
\(706\) | −7.38649 | −0.277994 | ||||||||
\(707\) | 11.1376 | 0.418872 | ||||||||
\(708\) | 2.43033 | 0.0913375 | ||||||||
\(709\) | −31.0011 | −1.16427 | −0.582135 | − | 0.813092i | \(-0.697783\pi\) | ||||
−0.582135 | + | 0.813092i | \(0.697783\pi\) | |||||||
\(710\) | 29.1203 | 1.09287 | ||||||||
\(711\) | −0.712807 | −0.0267324 | ||||||||
\(712\) | −15.9239 | −0.596772 | ||||||||
\(713\) | −0.530841 | −0.0198802 | ||||||||
\(714\) | −9.06745 | −0.339341 | ||||||||
\(715\) | −12.6803 | −0.474216 | ||||||||
\(716\) | 10.3741 | 0.387700 | ||||||||
\(717\) | 6.74621 | 0.251942 | ||||||||
\(718\) | 17.7601 | 0.662800 | ||||||||
\(719\) | 22.9014 | 0.854080 | 0.427040 | − | 0.904233i | \(-0.359556\pi\) | ||||
0.427040 | + | 0.904233i | \(0.359556\pi\) | |||||||
\(720\) | −0.415754 | −0.0154943 | ||||||||
\(721\) | −9.28148 | −0.345660 | ||||||||
\(722\) | −0.962862 | −0.0358340 | ||||||||
\(723\) | 34.7175 | 1.29116 | ||||||||
\(724\) | −5.78228 | −0.214897 | ||||||||
\(725\) | 59.9260 | 2.22560 | ||||||||
\(726\) | −15.7988 | −0.586350 | ||||||||
\(727\) | −26.5340 | −0.984092 | −0.492046 | − | 0.870569i | \(-0.663751\pi\) | ||||
−0.492046 | + | 0.870569i | \(0.663751\pi\) | |||||||
\(728\) | −2.46133 | −0.0912231 | ||||||||
\(729\) | 27.8545 | 1.03165 | ||||||||
\(730\) | 34.0595 | 1.26060 | ||||||||
\(731\) | −29.9555 | −1.10794 | ||||||||
\(732\) | 17.3274 | 0.640441 | ||||||||
\(733\) | 4.32778 | 0.159850 | 0.0799250 | − | 0.996801i | \(-0.474532\pi\) | ||||
0.0799250 | + | 0.996801i | \(0.474532\pi\) | |||||||
\(734\) | −29.5891 | −1.09215 | ||||||||
\(735\) | 41.1053 | 1.51619 | ||||||||
\(736\) | −0.760254 | −0.0280233 | ||||||||
\(737\) | −20.4368 | −0.752800 | ||||||||
\(738\) | 0.334536 | 0.0123145 | ||||||||
\(739\) | 28.1923 | 1.03707 | 0.518536 | − | 0.855056i | \(-0.326477\pi\) | ||||
0.518536 | + | 0.855056i | \(0.326477\pi\) | |||||||
\(740\) | −32.2512 | −1.18558 | ||||||||
\(741\) | −18.0441 | −0.662865 | ||||||||
\(742\) | 0.514505 | 0.0188881 | ||||||||
\(743\) | 7.65119 | 0.280695 | 0.140348 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140348 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(744\) | −1.18865 | −0.0435782 | ||||||||
\(745\) | −52.3211 | −1.91690 | ||||||||
\(746\) | −29.1942 | −1.06888 | ||||||||
\(747\) | −0.971975 | −0.0355627 | ||||||||
\(748\) | 6.73175 | 0.246137 | ||||||||
\(749\) | −1.19938 | −0.0438244 | ||||||||
\(750\) | 45.9120 | 1.67647 | ||||||||
\(751\) | 37.7778 | 1.37853 | 0.689266 | − | 0.724508i | \(-0.257933\pi\) | ||||
0.689266 | + | 0.724508i | \(0.257933\pi\) | |||||||
\(752\) | −2.17474 | −0.0793048 | ||||||||
\(753\) | −43.6744 | −1.59158 | ||||||||
\(754\) | −12.2384 | −0.445695 | ||||||||
\(755\) | −65.8156 | −2.39527 | ||||||||
\(756\) | 5.47883 | 0.199263 | ||||||||
\(757\) | 1.13336 | 0.0411928 | 0.0205964 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205964 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(758\) | −8.17757 | −0.297023 | ||||||||
\(759\) | 1.69706 | 0.0615995 | ||||||||
\(760\) | −18.2128 | −0.660649 | ||||||||
\(761\) | 1.72037 | 0.0623634 | 0.0311817 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311817 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(762\) | 26.6209 | 0.964373 | ||||||||
\(763\) | 12.0064 | 0.434661 | ||||||||
\(764\) | 8.94259 | 0.323532 | ||||||||
\(765\) | 2.13440 | 0.0771693 | ||||||||
\(766\) | −7.06134 | −0.255137 | ||||||||
\(767\) | −3.38680 | −0.122290 | ||||||||
\(768\) | −1.70235 | −0.0614284 | ||||||||
\(769\) | 30.1413 | 1.08692 | 0.543461 | − | 0.839435i | \(-0.317114\pi\) | ||||
0.543461 | + | 0.839435i | \(0.317114\pi\) | |||||||
\(770\) | 5.54566 | 0.199852 | ||||||||
\(771\) | 35.8820 | 1.29226 | ||||||||
\(772\) | −17.8248 | −0.641527 | ||||||||
\(773\) | 48.2615 | 1.73585 | 0.867924 | − | 0.496698i | \(-0.165454\pi\) | ||||
0.867924 | + | 0.496698i | \(0.165454\pi\) | |||||||
\(774\) | 0.595126 | 0.0213914 | ||||||||
\(775\) | −8.11094 | −0.291354 | ||||||||
\(776\) | −6.80293 | −0.244211 | ||||||||
\(777\) | 13.9742 | 0.501321 | ||||||||
\(778\) | −4.21852 | −0.151241 | ||||||||
\(779\) | 14.6549 | 0.525068 | ||||||||
\(780\) | −16.4623 | −0.589443 | ||||||||
\(781\) | 9.36742 | 0.335193 | ||||||||
\(782\) | 3.90298 | 0.139570 | ||||||||
\(783\) | 27.2421 | 0.973554 | ||||||||
\(784\) | −5.92355 | −0.211555 | ||||||||
\(785\) | 49.3065 | 1.75983 | ||||||||
\(786\) | 15.7694 | 0.562476 | ||||||||
\(787\) | −46.3501 | −1.65220 | −0.826101 | − | 0.563522i | \(-0.809446\pi\) | ||||
−0.826101 | + | 0.563522i | \(0.809446\pi\) | |||||||
\(788\) | 18.6669 | 0.664982 | ||||||||
\(789\) | −27.1663 | −0.967147 | ||||||||
\(790\) | −28.4884 | −1.01357 | ||||||||
\(791\) | 13.2036 | 0.469465 | ||||||||
\(792\) | −0.133740 | −0.00475223 | ||||||||
\(793\) | −24.1467 | −0.857475 | ||||||||
\(794\) | −10.9084 | −0.387125 | ||||||||
\(795\) | 3.44119 | 0.122046 | ||||||||
\(796\) | 13.4208 | 0.475687 | ||||||||
\(797\) | 37.0247 | 1.31148 | 0.655741 | − | 0.754985i | \(-0.272356\pi\) | ||||
0.655741 | + | 0.754985i | \(0.272356\pi\) | |||||||
\(798\) | 7.89148 | 0.279355 | ||||||||
\(799\) | 11.1647 | 0.394978 | ||||||||
\(800\) | −11.6162 | −0.410696 | ||||||||
\(801\) | −1.62412 | −0.0573855 | ||||||||
\(802\) | −25.6705 | −0.906455 | ||||||||
\(803\) | 10.9563 | 0.386638 | ||||||||
\(804\) | −26.5322 | −0.935719 | ||||||||
\(805\) | 3.21530 | 0.113325 | ||||||||
\(806\) | 1.65645 | 0.0583461 | ||||||||
\(807\) | 12.5015 | 0.440075 | ||||||||
\(808\) | −10.7348 | −0.377649 | ||||||||
\(809\) | −10.3362 | −0.363402 | −0.181701 | − | 0.983354i | \(-0.558160\pi\) | ||||
−0.181701 | + | 0.983354i | \(0.558160\pi\) | |||||||
\(810\) | 35.3970 | 1.24373 | ||||||||
\(811\) | 31.7218 | 1.11390 | 0.556951 | − | 0.830545i | \(-0.311971\pi\) | ||||
0.556951 | + | 0.830545i | \(0.311971\pi\) | |||||||
\(812\) | 5.35239 | 0.187832 | ||||||||
\(813\) | 6.06561 | 0.212730 | ||||||||
\(814\) | −10.3745 | −0.363628 | ||||||||
\(815\) | 7.69930 | 0.269695 | ||||||||
\(816\) | 8.73953 | 0.305945 | ||||||||
\(817\) | 26.0705 | 0.912092 | ||||||||
\(818\) | −27.2787 | −0.953779 | ||||||||
\(819\) | −0.251039 | −0.00877201 | ||||||||
\(820\) | 13.3702 | 0.466909 | ||||||||
\(821\) | 0.280146 | 0.00977716 | 0.00488858 | − | 0.999988i | \(-0.498444\pi\) | ||||
0.00488858 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(822\) | −0.0684424 | −0.00238720 | ||||||||
\(823\) | 36.5580 | 1.27433 | 0.637167 | − | 0.770726i | \(-0.280106\pi\) | ||||
0.637167 | + | 0.770726i | \(0.280106\pi\) | |||||||
\(824\) | 8.94582 | 0.311642 | ||||||||
\(825\) | 25.9301 | 0.902771 | ||||||||
\(826\) | 1.48120 | 0.0515375 | ||||||||
\(827\) | 36.4356 | 1.26699 | 0.633495 | − | 0.773747i | \(-0.281620\pi\) | ||||
0.633495 | + | 0.773747i | \(0.281620\pi\) | |||||||
\(828\) | −0.0775406 | −0.00269472 | ||||||||
\(829\) | 1.02705 | 0.0356708 | 0.0178354 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178354 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(830\) | −38.8464 | −1.34838 | ||||||||
\(831\) | 11.4707 | 0.397913 | ||||||||
\(832\) | 2.37232 | 0.0822454 | ||||||||
\(833\) | 30.4103 | 1.05365 | ||||||||
\(834\) | −33.9634 | −1.17606 | ||||||||
\(835\) | 26.7295 | 0.925011 | ||||||||
\(836\) | −5.85870 | −0.202627 | ||||||||
\(837\) | −3.68720 | −0.127448 | ||||||||
\(838\) | −11.8089 | −0.407931 | ||||||||
\(839\) | 12.2991 | 0.424614 | 0.212307 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212307 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(840\) | 7.19968 | 0.248413 | ||||||||
\(841\) | −2.38659 | −0.0822962 | ||||||||
\(842\) | 38.9584 | 1.34259 | ||||||||
\(843\) | 42.3771 | 1.45954 | ||||||||
\(844\) | −3.72585 | −0.128249 | ||||||||
\(845\) | −30.0509 | −1.03378 | ||||||||
\(846\) | −0.221809 | −0.00762594 | ||||||||
\(847\) | −9.62881 | −0.330850 | ||||||||
\(848\) | −0.495898 | −0.0170292 | ||||||||
\(849\) | −9.54342 | −0.327529 | ||||||||
\(850\) | 59.6353 | 2.04547 | ||||||||
\(851\) | −6.01503 | −0.206193 | ||||||||
\(852\) | 12.1613 | 0.416639 | ||||||||
\(853\) | 31.0343 | 1.06260 | 0.531298 | − | 0.847185i | \(-0.321705\pi\) | ||||
0.531298 | + | 0.847185i | \(0.321705\pi\) | |||||||
\(854\) | 10.5604 | 0.361371 | ||||||||
\(855\) | −1.85758 | −0.0635280 | ||||||||
\(856\) | 1.15600 | 0.0395114 | ||||||||
\(857\) | 33.9058 | 1.15820 | 0.579101 | − | 0.815256i | \(-0.303404\pi\) | ||||
0.579101 | + | 0.815256i | \(0.303404\pi\) | |||||||
\(858\) | −5.29557 | −0.180788 | ||||||||
\(859\) | 7.08003 | 0.241568 | 0.120784 | − | 0.992679i | \(-0.461459\pi\) | ||||
0.120784 | + | 0.992679i | \(0.461459\pi\) | |||||||
\(860\) | 23.7851 | 0.811065 | ||||||||
\(861\) | −5.79322 | −0.197432 | ||||||||
\(862\) | −10.2463 | −0.348991 | ||||||||
\(863\) | 5.77788 | 0.196681 | 0.0983406 | − | 0.995153i | \(-0.468647\pi\) | ||||
0.0983406 | + | 0.995153i | \(0.468647\pi\) | |||||||
\(864\) | −5.28069 | −0.179653 | ||||||||
\(865\) | 39.1882 | 1.33244 | ||||||||
\(866\) | 4.12687 | 0.140237 | ||||||||
\(867\) | −15.9269 | −0.540906 | ||||||||
\(868\) | −0.724441 | −0.0245891 | ||||||||
\(869\) | −9.16413 | −0.310872 | ||||||||
\(870\) | 35.7986 | 1.21369 | ||||||||
\(871\) | 36.9740 | 1.25282 | ||||||||
\(872\) | −11.5722 | −0.391884 | ||||||||
\(873\) | −0.693852 | −0.0234833 | ||||||||
\(874\) | −3.39680 | −0.114898 | ||||||||
\(875\) | 27.9817 | 0.945954 | ||||||||
\(876\) | 14.2240 | 0.480585 | ||||||||
\(877\) | 49.2301 | 1.66238 | 0.831191 | − | 0.555986i | \(-0.187659\pi\) | ||||
0.831191 | + | 0.555986i | \(0.187659\pi\) | |||||||
\(878\) | 19.6791 | 0.664138 | ||||||||
\(879\) | −4.36053 | −0.147077 | ||||||||
\(880\) | −5.34510 | −0.180183 | ||||||||
\(881\) | 17.9217 | 0.603797 | 0.301899 | − | 0.953340i | \(-0.402380\pi\) | ||||
0.301899 | + | 0.953340i | \(0.402380\pi\) | |||||||
\(882\) | −0.604161 | −0.0203432 | ||||||||
\(883\) | 7.95247 | 0.267622 | 0.133811 | − | 0.991007i | \(-0.457278\pi\) | ||||
0.133811 | + | 0.991007i | \(0.457278\pi\) | |||||||
\(884\) | −12.1790 | −0.409624 | ||||||||
\(885\) | 9.90677 | 0.333012 | ||||||||
\(886\) | −1.80713 | −0.0607116 | ||||||||
\(887\) | −33.8122 | −1.13530 | −0.567652 | − | 0.823269i | \(-0.692148\pi\) | ||||
−0.567652 | + | 0.823269i | \(0.692148\pi\) | |||||||
\(888\) | −13.4688 | −0.451984 | ||||||||
\(889\) | 16.2245 | 0.544151 | ||||||||
\(890\) | −64.9104 | −2.17580 | ||||||||
\(891\) | 11.3865 | 0.381462 | ||||||||
\(892\) | −3.81823 | −0.127844 | ||||||||
\(893\) | −9.71672 | −0.325158 | ||||||||
\(894\) | −21.8505 | −0.730789 | ||||||||
\(895\) | 42.2881 | 1.41354 | ||||||||
\(896\) | −1.03752 | −0.0346612 | ||||||||
\(897\) | −3.07030 | −0.102514 | ||||||||
\(898\) | 19.7178 | 0.657991 | ||||||||
\(899\) | −3.60210 | −0.120137 | ||||||||
\(900\) | −1.18477 | −0.0394925 | ||||||||
\(901\) | 2.54584 | 0.0848142 | ||||||||
\(902\) | 4.30093 | 0.143205 | ||||||||
\(903\) | −10.3059 | −0.342958 | ||||||||
\(904\) | −12.7261 | −0.423263 | ||||||||
\(905\) | −23.5703 | −0.783503 | ||||||||
\(906\) | −27.4860 | −0.913162 | ||||||||
\(907\) | −46.1789 | −1.53335 | −0.766673 | − | 0.642038i | \(-0.778089\pi\) | ||||
−0.766673 | + | 0.642038i | \(0.778089\pi\) | |||||||
\(908\) | 15.3243 | 0.508554 | ||||||||
\(909\) | −1.09487 | −0.0363147 | ||||||||
\(910\) | −10.0331 | −0.332595 | ||||||||
\(911\) | 18.2569 | 0.604877 | 0.302438 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302438 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(912\) | −7.60608 | −0.251863 | ||||||||
\(913\) | −12.4961 | −0.413560 | ||||||||
\(914\) | −24.0627 | −0.795925 | ||||||||
\(915\) | 70.6319 | 2.33502 | ||||||||
\(916\) | 19.0411 | 0.629136 | ||||||||
\(917\) | 9.61087 | 0.317379 | ||||||||
\(918\) | 27.1100 | 0.894762 | ||||||||
\(919\) | −35.1701 | −1.16015 | −0.580077 | − | 0.814562i | \(-0.696977\pi\) | ||||
−0.580077 | + | 0.814562i | \(0.696977\pi\) | |||||||
\(920\) | −3.09902 | −0.102172 | ||||||||
\(921\) | −11.2817 | −0.371743 | ||||||||
\(922\) | 9.06197 | 0.298440 | ||||||||
\(923\) | −16.9474 | −0.557831 | ||||||||
\(924\) | 2.31599 | 0.0761905 | ||||||||
\(925\) | −91.9062 | −3.02186 | ||||||||
\(926\) | 27.5234 | 0.904475 | ||||||||
\(927\) | 0.912411 | 0.0299675 | ||||||||
\(928\) | −5.15882 | −0.169347 | ||||||||
\(929\) | 11.4417 | 0.375389 | 0.187695 | − | 0.982227i | \(-0.439898\pi\) | ||||
0.187695 | + | 0.982227i | \(0.439898\pi\) | |||||||
\(930\) | −4.84531 | −0.158884 | ||||||||
\(931\) | −26.4663 | −0.867398 | ||||||||
\(932\) | −12.6530 | −0.414464 | ||||||||
\(933\) | −24.6368 | −0.806572 | ||||||||
\(934\) | −3.53732 | −0.115745 | ||||||||
\(935\) | 27.4406 | 0.897405 | ||||||||
\(936\) | 0.241960 | 0.00790871 | ||||||||
\(937\) | 29.1310 | 0.951669 | 0.475835 | − | 0.879535i | \(-0.342146\pi\) | ||||
0.475835 | + | 0.879535i | \(0.342146\pi\) | |||||||
\(938\) | −16.1704 | −0.527982 | ||||||||
\(939\) | 52.6019 | 1.71660 | ||||||||
\(940\) | −8.86491 | −0.289142 | ||||||||
\(941\) | −9.40037 | −0.306443 | −0.153222 | − | 0.988192i | \(-0.548965\pi\) | ||||
−0.153222 | + | 0.988192i | \(0.548965\pi\) | |||||||
\(942\) | 20.5915 | 0.670907 | ||||||||
\(943\) | 2.49363 | 0.0812036 | ||||||||
\(944\) | −1.42763 | −0.0464655 | ||||||||
\(945\) | 22.3334 | 0.726504 | ||||||||
\(946\) | 7.65118 | 0.248761 | ||||||||
\(947\) | 55.4521 | 1.80195 | 0.900976 | − | 0.433870i | \(-0.142852\pi\) | ||||
0.900976 | + | 0.433870i | \(0.142852\pi\) | |||||||
\(948\) | −11.8974 | −0.386409 | ||||||||
\(949\) | −19.8219 | −0.643447 | ||||||||
\(950\) | −51.9011 | −1.68389 | ||||||||
\(951\) | 19.5550 | 0.634113 | ||||||||
\(952\) | 5.32642 | 0.172630 | ||||||||
\(953\) | 35.5889 | 1.15284 | 0.576419 | − | 0.817154i | \(-0.304449\pi\) | ||||
0.576419 | + | 0.817154i | \(0.304449\pi\) | |||||||
\(954\) | −0.0505782 | −0.00163753 | ||||||||
\(955\) | 36.4527 | 1.17958 | ||||||||
\(956\) | −3.96287 | −0.128169 | ||||||||
\(957\) | 11.5157 | 0.372249 | ||||||||
\(958\) | 1.80306 | 0.0582542 | ||||||||
\(959\) | −0.0417131 | −0.00134699 | ||||||||
\(960\) | −6.93930 | −0.223965 | ||||||||
\(961\) | −30.5125 | −0.984273 | ||||||||
\(962\) | 18.7695 | 0.605153 | ||||||||
\(963\) | 0.117904 | 0.00379942 | ||||||||
\(964\) | −20.3938 | −0.656841 | ||||||||
\(965\) | −72.6591 | −2.33898 | ||||||||
\(966\) | 1.34278 | 0.0432033 | ||||||||
\(967\) | 42.8153 | 1.37685 | 0.688424 | − | 0.725308i | \(-0.258303\pi\) | ||||
0.688424 | + | 0.725308i | \(0.258303\pi\) | |||||||
\(968\) | 9.28059 | 0.298289 | ||||||||
\(969\) | 39.0481 | 1.25440 | ||||||||
\(970\) | −27.7308 | −0.890382 | ||||||||
\(971\) | 2.86244 | 0.0918601 | 0.0459300 | − | 0.998945i | \(-0.485375\pi\) | ||||
0.0459300 | + | 0.998945i | \(0.485375\pi\) | |||||||
\(972\) | −1.05948 | −0.0339828 | ||||||||
\(973\) | −20.6995 | −0.663594 | ||||||||
\(974\) | −13.8396 | −0.443448 | ||||||||
\(975\) | −46.9125 | −1.50240 | ||||||||
\(976\) | −10.1785 | −0.325807 | ||||||||
\(977\) | −10.5258 | −0.336750 | −0.168375 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168375 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(978\) | 3.21540 | 0.102817 | ||||||||
\(979\) | −20.8804 | −0.667339 | ||||||||
\(980\) | −24.1462 | −0.771321 | ||||||||
\(981\) | −1.18028 | −0.0376836 | ||||||||
\(982\) | −40.3124 | −1.28642 | ||||||||
\(983\) | −9.29329 | −0.296410 | −0.148205 | − | 0.988957i | \(-0.547350\pi\) | ||||
−0.148205 | + | 0.988957i | \(0.547350\pi\) | |||||||
\(984\) | 5.58371 | 0.178002 | ||||||||
\(985\) | 76.0921 | 2.42450 | ||||||||
\(986\) | 26.4843 | 0.843432 | ||||||||
\(987\) | 3.84110 | 0.122263 | ||||||||
\(988\) | 10.5995 | 0.337214 | ||||||||
\(989\) | 4.43606 | 0.141058 | ||||||||
\(990\) | −0.545163 | −0.0173264 | ||||||||
\(991\) | 9.97620 | 0.316904 | 0.158452 | − | 0.987367i | \(-0.449350\pi\) | ||||
0.158452 | + | 0.987367i | \(0.449350\pi\) | |||||||
\(992\) | 0.698242 | 0.0221692 | ||||||||
\(993\) | −15.7278 | −0.499107 | ||||||||
\(994\) | 7.41186 | 0.235090 | ||||||||
\(995\) | 54.7072 | 1.73433 | ||||||||
\(996\) | −16.2231 | −0.514049 | ||||||||
\(997\) | 52.2680 | 1.65535 | 0.827673 | − | 0.561211i | \(-0.189664\pi\) | ||||
0.827673 | + | 0.561211i | \(0.189664\pi\) | |||||||
\(998\) | −32.4731 | −1.02792 | ||||||||
\(999\) | −41.7801 | −1.32187 |
(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 | 8002.2.a.e.1.18 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.18 | ✓ | 77 | 1.1 | even | 1 | trivial |