Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78468 | −1.26196 | −0.630979 | − | 0.775800i | \(-0.717347\pi\) | ||||
−0.630979 | + | 0.775800i | \(0.717347\pi\) | |||||||
\(3\) | −2.38377 | −1.37627 | −0.688134 | − | 0.725583i | \(-0.741570\pi\) | ||||
−0.688134 | + | 0.725583i | \(0.741570\pi\) | |||||||
\(4\) | 1.18508 | 0.592538 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.25426 | 1.73679 | ||||||||
\(7\) | 4.23911 | 1.60223 | 0.801116 | − | 0.598509i | \(-0.204240\pi\) | ||||
0.801116 | + | 0.598509i | \(0.204240\pi\) | |||||||
\(8\) | 1.45438 | 0.514199 | ||||||||
\(9\) | 2.68235 | 0.894116 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.490889 | −0.148009 | −0.0740043 | − | 0.997258i | \(-0.523578\pi\) | ||||
−0.0740043 | + | 0.997258i | \(0.523578\pi\) | |||||||
\(12\) | −2.82495 | −0.815492 | ||||||||
\(13\) | −4.16199 | −1.15433 | −0.577165 | − | 0.816628i | \(-0.695841\pi\) | ||||
−0.577165 | + | 0.816628i | \(0.695841\pi\) | |||||||
\(14\) | −7.56544 | −2.02195 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.96575 | −1.24144 | ||||||||
\(17\) | −2.03619 | −0.493850 | −0.246925 | − | 0.969035i | \(-0.579420\pi\) | ||||
−0.246925 | + | 0.969035i | \(0.579420\pi\) | |||||||
\(18\) | −4.78713 | −1.12834 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.1050 | −2.20510 | ||||||||
\(22\) | 0.876080 | 0.186781 | ||||||||
\(23\) | 4.39525 | 0.916472 | 0.458236 | − | 0.888830i | \(-0.348481\pi\) | ||||
0.458236 | + | 0.888830i | \(0.348481\pi\) | |||||||
\(24\) | −3.46689 | −0.707677 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.42782 | 1.45672 | ||||||||
\(27\) | 0.757211 | 0.145725 | ||||||||
\(28\) | 5.02367 | 0.949384 | ||||||||
\(29\) | 3.26270 | 0.605869 | 0.302934 | − | 0.953011i | \(-0.402034\pi\) | ||||
0.302934 | + | 0.953011i | \(0.402034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.08833 | −0.734285 | −0.367143 | − | 0.930165i | \(-0.619664\pi\) | ||||
−0.367143 | + | 0.930165i | \(0.619664\pi\) | |||||||
\(32\) | 5.95351 | 1.05244 | ||||||||
\(33\) | 1.17017 | 0.203700 | ||||||||
\(34\) | 3.63395 | 0.623218 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.17879 | 0.529798 | ||||||||
\(37\) | 2.14440 | 0.352538 | 0.176269 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176269 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.92123 | 1.58867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.36602 | −0.681857 | −0.340929 | − | 0.940089i | \(-0.610741\pi\) | ||||
−0.340929 | + | 0.940089i | \(0.610741\pi\) | |||||||
\(42\) | 18.0343 | 2.78275 | ||||||||
\(43\) | 10.6241 | 1.62015 | 0.810077 | − | 0.586324i | \(-0.199425\pi\) | ||||
0.810077 | + | 0.586324i | \(0.199425\pi\) | |||||||
\(44\) | −0.581742 | −0.0877008 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.84410 | −1.15655 | ||||||||
\(47\) | 2.62142 | 0.382373 | 0.191187 | − | 0.981554i | \(-0.438766\pi\) | ||||
0.191187 | + | 0.981554i | \(0.438766\pi\) | |||||||
\(48\) | 11.8372 | 1.70855 | ||||||||
\(49\) | 10.9700 | 1.56715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.85381 | 0.679670 | ||||||||
\(52\) | −4.93228 | −0.683985 | ||||||||
\(53\) | −11.4341 | −1.57059 | −0.785296 | − | 0.619121i | \(-0.787489\pi\) | ||||
−0.785296 | + | 0.619121i | \(0.787489\pi\) | |||||||
\(54\) | −1.35138 | −0.183899 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.16526 | 0.823867 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.82287 | −0.764581 | ||||||||
\(59\) | 0.542306 | 0.0706022 | 0.0353011 | − | 0.999377i | \(-0.488761\pi\) | ||||
0.0353011 | + | 0.999377i | \(0.488761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6423 | −1.74671 | −0.873356 | − | 0.487083i | \(-0.838061\pi\) | ||||
−0.873356 | + | 0.487083i | \(0.838061\pi\) | |||||||
\(62\) | 7.29635 | 0.926637 | ||||||||
\(63\) | 11.3708 | 1.43258 | ||||||||
\(64\) | −0.693606 | −0.0867007 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.08837 | −0.257061 | ||||||||
\(67\) | 7.15699 | 0.874365 | 0.437182 | − | 0.899373i | \(-0.355976\pi\) | ||||
0.437182 | + | 0.899373i | \(0.355976\pi\) | |||||||
\(68\) | −2.41305 | −0.292625 | ||||||||
\(69\) | −10.4772 | −1.26131 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.03858 | −0.716647 | −0.358324 | − | 0.933597i | \(-0.616652\pi\) | ||||
−0.358324 | + | 0.933597i | \(0.616652\pi\) | |||||||
\(72\) | 3.90114 | 0.459754 | ||||||||
\(73\) | 2.05419 | 0.240425 | 0.120212 | − | 0.992748i | \(-0.461642\pi\) | ||||
0.120212 | + | 0.992748i | \(0.461642\pi\) | |||||||
\(74\) | −3.82707 | −0.444888 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.08093 | −0.237144 | ||||||||
\(78\) | −17.7062 | −2.00483 | ||||||||
\(79\) | −5.34029 | −0.600830 | −0.300415 | − | 0.953809i | \(-0.597125\pi\) | ||||
−0.300415 | + | 0.953809i | \(0.597125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.85206 | −1.09467 | ||||||||
\(82\) | 7.79193 | 0.860475 | ||||||||
\(83\) | 8.11578 | 0.890823 | 0.445411 | − | 0.895326i | \(-0.353057\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353057\pi\) | |||||||
\(84\) | −11.9753 | −1.30661 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18.9605 | −2.04457 | ||||||||
\(87\) | −7.77752 | −0.833838 | ||||||||
\(88\) | −0.713937 | −0.0761060 | ||||||||
\(89\) | 4.34099 | 0.460144 | 0.230072 | − | 0.973174i | \(-0.426104\pi\) | ||||
0.230072 | + | 0.973174i | \(0.426104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.6431 | −1.84950 | ||||||||
\(92\) | 5.20871 | 0.543045 | ||||||||
\(93\) | 9.74562 | 1.01057 | ||||||||
\(94\) | −4.67839 | −0.482539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.1918 | −1.44844 | ||||||||
\(97\) | −5.64669 | −0.573335 | −0.286667 | − | 0.958030i | \(-0.592547\pi\) | ||||
−0.286667 | + | 0.958030i | \(0.592547\pi\) | |||||||
\(98\) | −19.5780 | −1.97768 | ||||||||
\(99\) | −1.31674 | −0.132337 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.30082 | −0.328444 | −0.164222 | − | 0.986423i | \(-0.552511\pi\) | ||||
−0.164222 | + | 0.986423i | \(0.552511\pi\) | |||||||
\(102\) | −8.66250 | −0.857715 | ||||||||
\(103\) | 3.41567 | 0.336556 | 0.168278 | − | 0.985740i | \(-0.446179\pi\) | ||||
0.168278 | + | 0.985740i | \(0.446179\pi\) | |||||||
\(104\) | −6.05310 | −0.593556 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.4062 | 1.98202 | ||||||||
\(107\) | 1.75252 | 0.169422 | 0.0847110 | − | 0.996406i | \(-0.473003\pi\) | ||||
0.0847110 | + | 0.996406i | \(0.473003\pi\) | |||||||
\(108\) | 0.897354 | 0.0863479 | ||||||||
\(109\) | 3.51923 | 0.337081 | 0.168541 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168541 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.11176 | −0.485186 | ||||||||
\(112\) | −21.0503 | −1.98907 | ||||||||
\(113\) | −13.2583 | −1.24723 | −0.623616 | − | 0.781731i | \(-0.714337\pi\) | ||||
−0.623616 | + | 0.781731i | \(0.714337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.86655 | 0.359000 | ||||||||
\(117\) | −11.1639 | −1.03210 | ||||||||
\(118\) | −0.967842 | −0.0890971 | ||||||||
\(119\) | −8.63165 | −0.791262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7590 | −0.978093 | ||||||||
\(122\) | 24.3470 | 2.20428 | ||||||||
\(123\) | 10.4076 | 0.938419 | ||||||||
\(124\) | −4.84498 | −0.435092 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −20.2931 | −1.80786 | ||||||||
\(127\) | 19.8082 | 1.75769 | 0.878846 | − | 0.477105i | \(-0.158314\pi\) | ||||
0.878846 | + | 0.477105i | \(0.158314\pi\) | |||||||
\(128\) | −10.6692 | −0.943029 | ||||||||
\(129\) | −25.3253 | −2.22977 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.43004 | −0.299684 | −0.149842 | − | 0.988710i | \(-0.547876\pi\) | ||||
−0.149842 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(132\) | 1.38674 | 0.120700 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.7729 | −1.10341 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.96139 | −0.253937 | ||||||||
\(137\) | 0.608296 | 0.0519702 | 0.0259851 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259851 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(138\) | 18.6985 | 1.59172 | ||||||||
\(139\) | −8.45799 | −0.717397 | −0.358699 | − | 0.933453i | \(-0.616779\pi\) | ||||
−0.358699 | + | 0.933453i | \(0.616779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24885 | −0.526248 | ||||||||
\(142\) | 10.7769 | 0.904379 | ||||||||
\(143\) | 2.04308 | 0.170851 | ||||||||
\(144\) | −13.3199 | −1.10999 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.66607 | −0.303406 | ||||||||
\(147\) | −26.1500 | −2.15682 | ||||||||
\(148\) | 2.54128 | 0.208892 | ||||||||
\(149\) | −4.63735 | −0.379907 | −0.189953 | − | 0.981793i | \(-0.560834\pi\) | ||||
−0.189953 | + | 0.981793i | \(0.560834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2109 | −1.15646 | −0.578232 | − | 0.815872i | \(-0.696257\pi\) | ||||
−0.578232 | + | 0.815872i | \(0.696257\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.46178 | −0.441559 | ||||||||
\(154\) | 3.71380 | 0.299266 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.7574 | 0.941347 | ||||||||
\(157\) | 10.7281 | 0.856194 | 0.428097 | − | 0.903733i | \(-0.359184\pi\) | ||||
0.428097 | + | 0.903733i | \(0.359184\pi\) | |||||||
\(158\) | 9.53071 | 0.758222 | ||||||||
\(159\) | 27.2562 | 2.16156 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.6319 | 1.46840 | ||||||||
\(162\) | 17.5828 | 1.38143 | ||||||||
\(163\) | −16.9366 | −1.32658 | −0.663289 | − | 0.748363i | \(-0.730840\pi\) | ||||
−0.663289 | + | 0.748363i | \(0.730840\pi\) | |||||||
\(164\) | −5.17406 | −0.404027 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4841 | −1.12418 | ||||||||
\(167\) | −16.2567 | −1.25798 | −0.628991 | − | 0.777412i | \(-0.716532\pi\) | ||||
−0.628991 | + | 0.777412i | \(0.716532\pi\) | |||||||
\(168\) | −14.6965 | −1.13386 | ||||||||
\(169\) | 4.32219 | 0.332476 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5903 | 0.960003 | ||||||||
\(173\) | −8.59112 | −0.653171 | −0.326585 | − | 0.945168i | \(-0.605898\pi\) | ||||
−0.326585 | + | 0.945168i | \(0.605898\pi\) | |||||||
\(174\) | 13.8804 | 1.05227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.43763 | 0.183743 | ||||||||
\(177\) | −1.29273 | −0.0971677 | ||||||||
\(178\) | −7.74728 | −0.580683 | ||||||||
\(179\) | 23.5276 | 1.75853 | 0.879267 | − | 0.476330i | \(-0.158033\pi\) | ||||
0.879267 | + | 0.476330i | \(0.158033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6135 | 1.23487 | 0.617434 | − | 0.786623i | \(-0.288172\pi\) | ||||
0.617434 | + | 0.786623i | \(0.288172\pi\) | |||||||
\(182\) | 31.4873 | 2.33400 | ||||||||
\(183\) | 32.5200 | 2.40394 | ||||||||
\(184\) | 6.39234 | 0.471250 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −17.3928 | −1.27530 | ||||||||
\(187\) | 0.999546 | 0.0730941 | ||||||||
\(188\) | 3.10658 | 0.226571 | ||||||||
\(189\) | 3.20990 | 0.233486 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8109 | −0.926965 | −0.463482 | − | 0.886106i | \(-0.653400\pi\) | ||||
−0.463482 | + | 0.886106i | \(0.653400\pi\) | |||||||
\(192\) | 1.65339 | 0.119323 | ||||||||
\(193\) | −9.63983 | −0.693890 | −0.346945 | − | 0.937885i | \(-0.612781\pi\) | ||||
−0.346945 | + | 0.937885i | \(0.612781\pi\) | |||||||
\(194\) | 10.0775 | 0.723525 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0003 | 0.928596 | ||||||||
\(197\) | 3.10241 | 0.221038 | 0.110519 | − | 0.993874i | \(-0.464749\pi\) | ||||
0.110519 | + | 0.993874i | \(0.464749\pi\) | |||||||
\(198\) | 2.34995 | 0.167004 | ||||||||
\(199\) | 0.524290 | 0.0371659 | 0.0185830 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185830 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0606 | −1.20336 | ||||||||
\(202\) | 5.89091 | 0.414483 | ||||||||
\(203\) | 13.8309 | 0.970742 | ||||||||
\(204\) | 5.75214 | 0.402731 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.09586 | −0.424719 | ||||||||
\(207\) | 11.7896 | 0.819432 | ||||||||
\(208\) | 20.6674 | 1.43303 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0637 | 1.31240 | 0.656201 | − | 0.754586i | \(-0.272162\pi\) | ||||
0.656201 | + | 0.754586i | \(0.272162\pi\) | |||||||
\(212\) | −13.5503 | −0.930636 | ||||||||
\(213\) | 14.3946 | 0.986299 | ||||||||
\(214\) | −3.12768 | −0.213804 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.10127 | 0.0749319 | ||||||||
\(217\) | −17.3309 | −1.17650 | ||||||||
\(218\) | −6.28069 | −0.425382 | ||||||||
\(219\) | −4.89671 | −0.330889 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.47463 | 0.570065 | ||||||||
\(222\) | 9.12284 | 0.612285 | ||||||||
\(223\) | 3.16283 | 0.211799 | 0.105899 | − | 0.994377i | \(-0.466228\pi\) | ||||
0.105899 | + | 0.994377i | \(0.466228\pi\) | |||||||
\(224\) | 25.2376 | 1.68626 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.6617 | 1.57395 | ||||||||
\(227\) | 9.04654 | 0.600440 | 0.300220 | − | 0.953870i | \(-0.402940\pi\) | ||||
0.300220 | + | 0.953870i | \(0.402940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.8920 | −1.18234 | −0.591168 | − | 0.806549i | \(-0.701333\pi\) | ||||
−0.591168 | + | 0.806549i | \(0.701333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.96046 | 0.326374 | ||||||||
\(232\) | 4.74519 | 0.311537 | ||||||||
\(233\) | 6.44330 | 0.422114 | 0.211057 | − | 0.977474i | \(-0.432309\pi\) | ||||
0.211057 | + | 0.977474i | \(0.432309\pi\) | |||||||
\(234\) | 19.9240 | 1.30247 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.642674 | 0.0418345 | ||||||||
\(237\) | 12.7300 | 0.826903 | ||||||||
\(238\) | 15.4047 | 0.998539 | ||||||||
\(239\) | −13.4742 | −0.871571 | −0.435785 | − | 0.900051i | \(-0.643529\pi\) | ||||
−0.435785 | + | 0.900051i | \(0.643529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6351 | 1.13598 | 0.567990 | − | 0.823036i | \(-0.307721\pi\) | ||||
0.567990 | + | 0.823036i | \(0.307721\pi\) | |||||||
\(242\) | 19.2014 | 1.23431 | ||||||||
\(243\) | 21.2134 | 1.36084 | ||||||||
\(244\) | −16.1671 | −1.03499 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.5742 | −1.18424 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.94596 | −0.377569 | ||||||||
\(249\) | −19.3461 | −1.22601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7326 | 1.11927 | 0.559636 | − | 0.828738i | \(-0.310941\pi\) | ||||
0.559636 | + | 0.828738i | \(0.310941\pi\) | |||||||
\(252\) | 13.4752 | 0.848859 | ||||||||
\(253\) | −2.15758 | −0.135646 | ||||||||
\(254\) | −35.3513 | −2.21813 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.4282 | 1.27676 | ||||||||
\(257\) | −27.7475 | −1.73084 | −0.865421 | − | 0.501046i | \(-0.832949\pi\) | ||||
−0.865421 | + | 0.501046i | \(0.832949\pi\) | |||||||
\(258\) | 45.1975 | 2.81387 | ||||||||
\(259\) | 9.09035 | 0.564847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.75170 | 0.541716 | ||||||||
\(262\) | 6.12152 | 0.378189 | ||||||||
\(263\) | −5.56032 | −0.342864 | −0.171432 | − | 0.985196i | \(-0.554839\pi\) | ||||
−0.171432 | + | 0.985196i | \(0.554839\pi\) | |||||||
\(264\) | 1.70186 | 0.104742 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3479 | −0.633282 | ||||||||
\(268\) | 8.48158 | 0.518095 | ||||||||
\(269\) | 4.62765 | 0.282153 | 0.141076 | − | 0.989999i | \(-0.454944\pi\) | ||||
0.141076 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.60838 | −0.462176 | −0.231088 | − | 0.972933i | \(-0.574229\pi\) | ||||
−0.231088 | + | 0.972933i | \(0.574229\pi\) | |||||||
\(272\) | 10.1112 | 0.613083 | ||||||||
\(273\) | 42.0571 | 2.54541 | ||||||||
\(274\) | −1.08561 | −0.0655843 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.4163 | −0.747376 | ||||||||
\(277\) | −7.53544 | −0.452761 | −0.226380 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226380 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(278\) | 15.0948 | 0.905325 | ||||||||
\(279\) | −10.9663 | −0.656536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2549 | 1.08900 | 0.544499 | − | 0.838762i | \(-0.316720\pi\) | ||||
0.544499 | + | 0.838762i | \(0.316720\pi\) | |||||||
\(282\) | 11.1522 | 0.664103 | ||||||||
\(283\) | 30.9333 | 1.83880 | 0.919398 | − | 0.393328i | \(-0.128676\pi\) | ||||
0.919398 | + | 0.393328i | \(0.128676\pi\) | |||||||
\(284\) | −7.15618 | −0.424641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.64624 | −0.215607 | ||||||||
\(287\) | −18.5080 | −1.09249 | ||||||||
\(288\) | 15.9694 | 0.941004 | ||||||||
\(289\) | −12.8539 | −0.756112 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.4604 | 0.789063 | ||||||||
\(292\) | 2.43437 | 0.142461 | ||||||||
\(293\) | 21.8992 | 1.27937 | 0.639683 | − | 0.768639i | \(-0.279066\pi\) | ||||
0.639683 | + | 0.768639i | \(0.279066\pi\) | |||||||
\(294\) | 46.6694 | 2.72181 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.11877 | 0.181275 | ||||||||
\(297\) | −0.371707 | −0.0215686 | ||||||||
\(298\) | 8.27618 | 0.479426 | ||||||||
\(299\) | −18.2930 | −1.05791 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45.0365 | 2.59586 | ||||||||
\(302\) | 25.3618 | 1.45941 | ||||||||
\(303\) | 7.86840 | 0.452028 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.74752 | 0.557229 | ||||||||
\(307\) | −5.45543 | −0.311358 | −0.155679 | − | 0.987808i | \(-0.549757\pi\) | ||||
−0.155679 | + | 0.987808i | \(0.549757\pi\) | |||||||
\(308\) | −2.46607 | −0.140517 | ||||||||
\(309\) | −8.14215 | −0.463191 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.69721 | 0.379764 | 0.189882 | − | 0.981807i | \(-0.439189\pi\) | ||||
0.189882 | + | 0.981807i | \(0.439189\pi\) | |||||||
\(312\) | 14.4292 | 0.816892 | ||||||||
\(313\) | −4.58279 | −0.259035 | −0.129517 | − | 0.991577i | \(-0.541343\pi\) | ||||
−0.129517 | + | 0.991577i | \(0.541343\pi\) | |||||||
\(314\) | −19.1462 | −1.08048 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.32866 | −0.356015 | ||||||||
\(317\) | −27.6794 | −1.55463 | −0.777314 | − | 0.629113i | \(-0.783418\pi\) | ||||
−0.777314 | + | 0.629113i | \(0.783418\pi\) | |||||||
\(318\) | −48.6435 | −2.72779 | ||||||||
\(319\) | −1.60163 | −0.0896738 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.17759 | −0.233170 | ||||||||
\(322\) | −33.2520 | −1.85306 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.6754 | −0.648636 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.2264 | 1.67409 | ||||||||
\(327\) | −8.38903 | −0.463914 | ||||||||
\(328\) | −6.34983 | −0.350611 | ||||||||
\(329\) | 11.1125 | 0.612651 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1302 | 0.776665 | 0.388332 | − | 0.921519i | \(-0.373051\pi\) | ||||
0.388332 | + | 0.921519i | \(0.373051\pi\) | |||||||
\(332\) | 9.61782 | 0.527847 | ||||||||
\(333\) | 5.75203 | 0.315209 | ||||||||
\(334\) | 29.0130 | 1.58752 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 50.1791 | 2.73749 | ||||||||
\(337\) | 14.9974 | 0.816962 | 0.408481 | − | 0.912767i | \(-0.366059\pi\) | ||||
0.408481 | + | 0.912767i | \(0.366059\pi\) | |||||||
\(338\) | −7.71372 | −0.419571 | ||||||||
\(339\) | 31.6046 | 1.71653 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00692 | 0.108681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8294 | 0.908703 | ||||||||
\(344\) | 15.4514 | 0.833082 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.3324 | 0.824274 | ||||||||
\(347\) | 20.9133 | 1.12268 | 0.561342 | − | 0.827584i | \(-0.310285\pi\) | ||||
0.561342 | + | 0.827584i | \(0.310285\pi\) | |||||||
\(348\) | −9.21696 | −0.494081 | ||||||||
\(349\) | −3.13055 | −0.167574 | −0.0837872 | − | 0.996484i | \(-0.526702\pi\) | ||||
−0.0837872 | + | 0.996484i | \(0.526702\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.15151 | −0.168215 | ||||||||
\(352\) | −2.92251 | −0.155771 | ||||||||
\(353\) | −8.04538 | −0.428212 | −0.214106 | − | 0.976810i | \(-0.568684\pi\) | ||||
−0.214106 | + | 0.976810i | \(0.568684\pi\) | |||||||
\(354\) | 2.30711 | 0.122622 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.14441 | 0.272653 | ||||||||
\(357\) | 20.5758 | 1.08899 | ||||||||
\(358\) | −41.9891 | −2.21920 | ||||||||
\(359\) | 30.5842 | 1.61417 | 0.807087 | − | 0.590432i | \(-0.201043\pi\) | ||||
0.807087 | + | 0.590432i | \(0.201043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −29.6497 | −1.55835 | ||||||||
\(363\) | 25.6470 | 1.34612 | ||||||||
\(364\) | −20.9085 | −1.09590 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −58.0377 | −3.03368 | ||||||||
\(367\) | 9.95175 | 0.519477 | 0.259739 | − | 0.965679i | \(-0.416364\pi\) | ||||
0.259739 | + | 0.965679i | \(0.416364\pi\) | |||||||
\(368\) | −21.8257 | −1.13774 | ||||||||
\(369\) | −11.7112 | −0.609659 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.4703 | −2.51645 | ||||||||
\(372\) | 11.5493 | 0.598804 | ||||||||
\(373\) | −9.27611 | −0.480299 | −0.240149 | − | 0.970736i | \(-0.577196\pi\) | ||||
−0.240149 | + | 0.970736i | \(0.577196\pi\) | |||||||
\(374\) | −1.78387 | −0.0922416 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.81253 | 0.196616 | ||||||||
\(377\) | −13.5793 | −0.699372 | ||||||||
\(378\) | −5.72864 | −0.294649 | ||||||||
\(379\) | 21.1472 | 1.08626 | 0.543129 | − | 0.839649i | \(-0.317239\pi\) | ||||
0.543129 | + | 0.839649i | \(0.317239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −47.2181 | −2.41906 | ||||||||
\(382\) | 22.8634 | 1.16979 | ||||||||
\(383\) | −15.1501 | −0.774136 | −0.387068 | − | 0.922051i | \(-0.626512\pi\) | ||||
−0.387068 | + | 0.922051i | \(0.626512\pi\) | |||||||
\(384\) | 25.4328 | 1.29786 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.2040 | 0.875660 | ||||||||
\(387\) | 28.4974 | 1.44860 | ||||||||
\(388\) | −6.69177 | −0.339723 | ||||||||
\(389\) | −31.4483 | −1.59449 | −0.797247 | − | 0.603653i | \(-0.793711\pi\) | ||||
−0.797247 | + | 0.603653i | \(0.793711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94958 | −0.452600 | ||||||||
\(392\) | 15.9546 | 0.805827 | ||||||||
\(393\) | 8.17642 | 0.412446 | ||||||||
\(394\) | −5.53681 | −0.278940 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.56043 | −0.0784147 | ||||||||
\(397\) | 9.38559 | 0.471049 | 0.235525 | − | 0.971868i | \(-0.424319\pi\) | ||||
0.235525 | + | 0.971868i | \(0.424319\pi\) | |||||||
\(398\) | −0.935689 | −0.0469019 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.16049 | −0.307640 | −0.153820 | − | 0.988099i | \(-0.549158\pi\) | ||||
−0.153820 | + | 0.988099i | \(0.549158\pi\) | |||||||
\(402\) | 30.4477 | 1.51859 | ||||||||
\(403\) | 17.0156 | 0.847607 | ||||||||
\(404\) | −3.91173 | −0.194616 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.6838 | −1.22504 | ||||||||
\(407\) | −1.05266 | −0.0521786 | ||||||||
\(408\) | 7.05927 | 0.349486 | ||||||||
\(409\) | −2.28482 | −0.112977 | −0.0564885 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564885 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.45004 | −0.0715250 | ||||||||
\(412\) | 4.04783 | 0.199422 | ||||||||
\(413\) | 2.29889 | 0.113121 | ||||||||
\(414\) | −21.0406 | −1.03409 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.7785 | −1.21486 | ||||||||
\(417\) | 20.1619 | 0.987332 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.6494 | −1.10649 | −0.553247 | − | 0.833017i | \(-0.686611\pi\) | ||||
−0.553247 | + | 0.833017i | \(0.686611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.9969 | 1.12080 | 0.560400 | − | 0.828222i | \(-0.310647\pi\) | ||||
0.560400 | + | 0.828222i | \(0.310647\pi\) | |||||||
\(422\) | −34.0226 | −1.65620 | ||||||||
\(423\) | 7.03155 | 0.341886 | ||||||||
\(424\) | −16.6294 | −0.807597 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −25.6897 | −1.24467 | ||||||||
\(427\) | −57.8310 | −2.79864 | ||||||||
\(428\) | 2.07687 | 0.100389 | ||||||||
\(429\) | −4.87022 | −0.235137 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6319 | −1.23465 | −0.617323 | − | 0.786710i | \(-0.711783\pi\) | ||||
−0.617323 | + | 0.786710i | \(0.711783\pi\) | |||||||
\(432\) | −3.76012 | −0.180909 | ||||||||
\(433\) | −2.36330 | −0.113573 | −0.0567864 | − | 0.998386i | \(-0.518085\pi\) | ||||
−0.0567864 | + | 0.998386i | \(0.518085\pi\) | |||||||
\(434\) | 30.9300 | 1.48469 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.17056 | 0.199734 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.73906 | 0.417568 | ||||||||
\(439\) | 6.31659 | 0.301474 | 0.150737 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150737 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.4254 | 1.40121 | ||||||||
\(442\) | −15.1245 | −0.719399 | ||||||||
\(443\) | 31.5246 | 1.49778 | 0.748890 | − | 0.662694i | \(-0.230587\pi\) | ||||
0.748890 | + | 0.662694i | \(0.230587\pi\) | |||||||
\(444\) | −6.05782 | −0.287492 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.64463 | −0.267281 | ||||||||
\(447\) | 11.0544 | 0.522854 | ||||||||
\(448\) | −2.94027 | −0.138915 | ||||||||
\(449\) | 15.0828 | 0.711803 | 0.355902 | − | 0.934523i | \(-0.384174\pi\) | ||||
0.355902 | + | 0.934523i | \(0.384174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.14323 | 0.100921 | ||||||||
\(452\) | −15.7121 | −0.739033 | ||||||||
\(453\) | 33.8754 | 1.59161 | ||||||||
\(454\) | −16.1452 | −0.757730 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1347 | 0.941861 | 0.470930 | − | 0.882170i | \(-0.343918\pi\) | ||||
0.470930 | + | 0.882170i | \(0.343918\pi\) | |||||||
\(458\) | 31.9314 | 1.49206 | ||||||||
\(459\) | −1.54183 | −0.0719664 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.48489 | −0.348606 | −0.174303 | − | 0.984692i | \(-0.555767\pi\) | ||||
−0.174303 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(462\) | −8.85283 | −0.411871 | ||||||||
\(463\) | −21.5973 | −1.00371 | −0.501855 | − | 0.864952i | \(-0.667349\pi\) | ||||
−0.501855 | + | 0.864952i | \(0.667349\pi\) | |||||||
\(464\) | −16.2017 | −0.752147 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.4992 | −0.532691 | ||||||||
\(467\) | −27.0503 | −1.25174 | −0.625870 | − | 0.779927i | \(-0.715256\pi\) | ||||
−0.625870 | + | 0.779927i | \(0.715256\pi\) | |||||||
\(468\) | −13.2301 | −0.611561 | ||||||||
\(469\) | 30.3392 | 1.40094 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.5732 | −1.17835 | ||||||||
\(472\) | 0.788717 | 0.0363036 | ||||||||
\(473\) | −5.21524 | −0.239797 | ||||||||
\(474\) | −22.7190 | −1.04352 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.2292 | −0.468853 | ||||||||
\(477\) | −30.6702 | −1.40429 | ||||||||
\(478\) | 24.0470 | 1.09989 | ||||||||
\(479\) | −38.0534 | −1.73870 | −0.869352 | − | 0.494193i | \(-0.835464\pi\) | ||||
−0.869352 | + | 0.494193i | \(0.835464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.92499 | −0.406944 | ||||||||
\(482\) | −31.4731 | −1.43356 | ||||||||
\(483\) | −44.4142 | −2.02092 | ||||||||
\(484\) | −12.7503 | −0.579558 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −37.8591 | −1.71732 | ||||||||
\(487\) | 18.3353 | 0.830851 | 0.415426 | − | 0.909627i | \(-0.363633\pi\) | ||||
0.415426 | + | 0.909627i | \(0.363633\pi\) | |||||||
\(488\) | −19.8410 | −0.898158 | ||||||||
\(489\) | 40.3730 | 1.82573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0675 | −0.679986 | −0.339993 | − | 0.940428i | \(-0.610425\pi\) | ||||
−0.339993 | + | 0.940428i | \(0.610425\pi\) | |||||||
\(492\) | 12.3338 | 0.556049 | ||||||||
\(493\) | −6.64350 | −0.299208 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.3016 | 0.911568 | ||||||||
\(497\) | −25.5982 | −1.14824 | ||||||||
\(498\) | 34.5266 | 1.54717 | ||||||||
\(499\) | 34.5299 | 1.54577 | 0.772886 | − | 0.634545i | \(-0.218812\pi\) | ||||
0.772886 | + | 0.634545i | \(0.218812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.7522 | 1.73132 | ||||||||
\(502\) | −31.6470 | −1.41247 | ||||||||
\(503\) | −30.8704 | −1.37644 | −0.688221 | − | 0.725501i | \(-0.741608\pi\) | ||||
−0.688221 | + | 0.725501i | \(0.741608\pi\) | |||||||
\(504\) | 16.5374 | 0.736632 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.85059 | 0.171179 | ||||||||
\(507\) | −10.3031 | −0.457577 | ||||||||
\(508\) | 23.4742 | 1.04150 | ||||||||
\(509\) | −10.1777 | −0.451118 | −0.225559 | − | 0.974230i | \(-0.572421\pi\) | ||||
−0.225559 | + | 0.974230i | \(0.572421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.70794 | 0.385217 | ||||||||
\(512\) | −15.1195 | −0.668194 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 49.5204 | 2.18425 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −30.0124 | −1.32122 | ||||||||
\(517\) | −1.28683 | −0.0565946 | ||||||||
\(518\) | −16.2234 | −0.712813 | ||||||||
\(519\) | 20.4792 | 0.898938 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5423 | −0.724732 | −0.362366 | − | 0.932036i | \(-0.618031\pi\) | ||||
−0.362366 | + | 0.932036i | \(0.618031\pi\) | |||||||
\(522\) | −15.6190 | −0.683624 | ||||||||
\(523\) | 7.99801 | 0.349729 | 0.174864 | − | 0.984593i | \(-0.444051\pi\) | ||||
0.174864 | + | 0.984593i | \(0.444051\pi\) | |||||||
\(524\) | −4.06486 | −0.177574 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.92338 | 0.432680 | ||||||||
\(527\) | 8.32463 | 0.362626 | ||||||||
\(528\) | −5.81075 | −0.252880 | ||||||||
\(529\) | −3.68180 | −0.160078 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.45465 | 0.0631266 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.1713 | 0.787088 | ||||||||
\(534\) | 18.4677 | 0.799176 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.4089 | 0.449598 | ||||||||
\(537\) | −56.0843 | −2.42021 | ||||||||
\(538\) | −8.25886 | −0.356065 | ||||||||
\(539\) | −5.38507 | −0.231952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20048 | 0.223586 | 0.111793 | − | 0.993732i | \(-0.464341\pi\) | ||||
0.111793 | + | 0.993732i | \(0.464341\pi\) | |||||||
\(542\) | 13.5785 | 0.583247 | ||||||||
\(543\) | −39.6026 | −1.69951 | ||||||||
\(544\) | −12.1225 | −0.519748 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −75.0585 | −3.21221 | ||||||||
\(547\) | −11.0339 | −0.471777 | −0.235889 | − | 0.971780i | \(-0.575800\pi\) | ||||
−0.235889 | + | 0.971780i | \(0.575800\pi\) | |||||||
\(548\) | 0.720878 | 0.0307944 | ||||||||
\(549\) | −36.5933 | −1.56176 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −15.2379 | −0.648566 | ||||||||
\(553\) | −22.6381 | −0.962669 | ||||||||
\(554\) | 13.4483 | 0.571365 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0234 | −0.425086 | ||||||||
\(557\) | −21.2817 | −0.901735 | −0.450867 | − | 0.892591i | \(-0.648885\pi\) | ||||
−0.450867 | + | 0.892591i | \(0.648885\pi\) | |||||||
\(558\) | 19.5713 | 0.828521 | ||||||||
\(559\) | −44.2173 | −1.87019 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.38269 | −0.100597 | ||||||||
\(562\) | −32.5792 | −1.37427 | ||||||||
\(563\) | −14.7072 | −0.619833 | −0.309917 | − | 0.950764i | \(-0.600301\pi\) | ||||
−0.309917 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(564\) | −7.40537 | −0.311822 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −55.2061 | −2.32048 | ||||||||
\(567\) | −41.7639 | −1.75392 | ||||||||
\(568\) | −8.78236 | −0.368500 | ||||||||
\(569\) | −40.6551 | −1.70435 | −0.852174 | − | 0.523258i | \(-0.824716\pi\) | ||||
−0.852174 | + | 0.523258i | \(0.824716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3240 | −1.01793 | −0.508964 | − | 0.860788i | \(-0.669972\pi\) | ||||
−0.508964 | + | 0.860788i | \(0.669972\pi\) | |||||||
\(572\) | 2.42120 | 0.101236 | ||||||||
\(573\) | 30.5382 | 1.27575 | ||||||||
\(574\) | 33.0308 | 1.37868 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.86049 | −0.0775204 | ||||||||
\(577\) | 33.6876 | 1.40243 | 0.701216 | − | 0.712949i | \(-0.252641\pi\) | ||||
0.701216 | + | 0.712949i | \(0.252641\pi\) | |||||||
\(578\) | 22.9401 | 0.954182 | ||||||||
\(579\) | 22.9791 | 0.954979 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.4037 | 1.42730 | ||||||||
\(582\) | −24.0225 | −0.995764 | ||||||||
\(583\) | 5.61287 | 0.232461 | ||||||||
\(584\) | 2.98757 | 0.123626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.0830 | −1.61451 | ||||||||
\(587\) | −2.24977 | −0.0928580 | −0.0464290 | − | 0.998922i | \(-0.514784\pi\) | ||||
−0.0464290 | + | 0.998922i | \(0.514784\pi\) | |||||||
\(588\) | −30.9898 | −1.27800 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.39543 | −0.304207 | ||||||||
\(592\) | −10.6486 | −0.437653 | ||||||||
\(593\) | −31.3871 | −1.28891 | −0.644457 | − | 0.764640i | \(-0.722917\pi\) | ||||
−0.644457 | + | 0.764640i | \(0.722917\pi\) | |||||||
\(594\) | 0.663377 | 0.0272187 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.49562 | −0.225109 | ||||||||
\(597\) | −1.24979 | −0.0511503 | ||||||||
\(598\) | 32.6471 | 1.33504 | ||||||||
\(599\) | −10.4068 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.29592 | 0.0528616 | 0.0264308 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264308 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(602\) | −80.3757 | −3.27587 | ||||||||
\(603\) | 19.1975 | 0.781783 | ||||||||
\(604\) | −16.8410 | −0.685249 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0426 | −0.570440 | ||||||||
\(607\) | −5.50902 | −0.223604 | −0.111802 | − | 0.993730i | \(-0.535662\pi\) | ||||
−0.111802 | + | 0.993730i | \(0.535662\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.9698 | −1.33600 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.9103 | −0.441385 | ||||||||
\(612\) | −6.47263 | −0.261641 | ||||||||
\(613\) | −40.6727 | −1.64275 | −0.821376 | − | 0.570386i | \(-0.806793\pi\) | ||||
−0.821376 | + | 0.570386i | \(0.806793\pi\) | |||||||
\(614\) | 9.73619 | 0.392921 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.02646 | −0.121939 | ||||||||
\(617\) | 30.5053 | 1.22810 | 0.614049 | − | 0.789268i | \(-0.289540\pi\) | ||||
0.614049 | + | 0.789268i | \(0.289540\pi\) | |||||||
\(618\) | 14.5311 | 0.584527 | ||||||||
\(619\) | 5.80411 | 0.233287 | 0.116643 | − | 0.993174i | \(-0.462787\pi\) | ||||
0.116643 | + | 0.993174i | \(0.462787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.32813 | 0.133553 | ||||||||
\(622\) | −11.9524 | −0.479246 | ||||||||
\(623\) | 18.4019 | 0.737258 | ||||||||
\(624\) | −49.2663 | −1.97223 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.17881 | 0.326891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.7136 | 0.507328 | ||||||||
\(629\) | −4.36642 | −0.174101 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.3642 | −0.930116 | −0.465058 | − | 0.885280i | \(-0.653967\pi\) | ||||
−0.465058 | + | 0.885280i | \(0.653967\pi\) | |||||||
\(632\) | −7.76679 | −0.308946 | ||||||||
\(633\) | −45.4435 | −1.80622 | ||||||||
\(634\) | 49.3987 | 1.96187 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 32.3007 | 1.28080 | ||||||||
\(637\) | −45.6572 | −1.80901 | ||||||||
\(638\) | 2.85839 | 0.113165 | ||||||||
\(639\) | −16.1976 | −0.640766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3459 | −0.724621 | −0.362311 | − | 0.932057i | \(-0.618012\pi\) | ||||
−0.362311 | + | 0.932057i | \(0.618012\pi\) | |||||||
\(642\) | 7.45565 | 0.294251 | ||||||||
\(643\) | 15.7630 | 0.621633 | 0.310817 | − | 0.950470i | \(-0.399397\pi\) | ||||
0.310817 | + | 0.950470i | \(0.399397\pi\) | |||||||
\(644\) | 22.0803 | 0.870084 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.0443 | −0.984592 | −0.492296 | − | 0.870428i | \(-0.663842\pi\) | ||||
−0.492296 | + | 0.870428i | \(0.663842\pi\) | |||||||
\(648\) | −14.3286 | −0.562880 | ||||||||
\(649\) | −0.266212 | −0.0104497 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.3127 | 1.61917 | ||||||||
\(652\) | −20.0712 | −0.786049 | ||||||||
\(653\) | 2.98852 | 0.116950 | 0.0584749 | − | 0.998289i | \(-0.481376\pi\) | ||||
0.0584749 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(654\) | 14.9717 | 0.585440 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 21.6805 | 0.846482 | ||||||||
\(657\) | 5.51005 | 0.214968 | ||||||||
\(658\) | −19.8322 | −0.773140 | ||||||||
\(659\) | 35.7695 | 1.39338 | 0.696691 | − | 0.717372i | \(-0.254655\pi\) | ||||
0.696691 | + | 0.717372i | \(0.254655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.22147 | −0.125301 | −0.0626503 | − | 0.998036i | \(-0.519955\pi\) | ||||
−0.0626503 | + | 0.998036i | \(0.519955\pi\) | |||||||
\(662\) | −25.2178 | −0.980118 | ||||||||
\(663\) | −20.2015 | −0.784563 | ||||||||
\(664\) | 11.8034 | 0.458061 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.2655 | −0.397781 | ||||||||
\(667\) | 14.3404 | 0.555262 | ||||||||
\(668\) | −19.2655 | −0.745403 | ||||||||
\(669\) | −7.53945 | −0.291492 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.69684 | 0.258529 | ||||||||
\(672\) | −60.1605 | −2.32074 | ||||||||
\(673\) | 0.639706 | 0.0246588 | 0.0123294 | − | 0.999924i | \(-0.496075\pi\) | ||||
0.0123294 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(674\) | −26.7656 | −1.03097 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.12213 | 0.197005 | ||||||||
\(677\) | −25.8005 | −0.991592 | −0.495796 | − | 0.868439i | \(-0.665124\pi\) | ||||
−0.495796 | + | 0.868439i | \(0.665124\pi\) | |||||||
\(678\) | −56.4041 | −2.16618 | ||||||||
\(679\) | −23.9369 | −0.918616 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.5648 | −0.826366 | ||||||||
\(682\) | −3.58170 | −0.137150 | ||||||||
\(683\) | −5.33696 | −0.204213 | −0.102107 | − | 0.994773i | \(-0.532558\pi\) | ||||
−0.102107 | + | 0.994773i | \(0.532558\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −30.0351 | −1.14675 | ||||||||
\(687\) | 42.6503 | 1.62721 | ||||||||
\(688\) | −52.7564 | −2.01132 | ||||||||
\(689\) | 47.5886 | 1.81298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.2507 | 0.504079 | 0.252040 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252040 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(692\) | −10.1811 | −0.387029 | ||||||||
\(693\) | −5.58178 | −0.212034 | ||||||||
\(694\) | −37.3235 | −1.41678 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11.3114 | −0.428759 | ||||||||
\(697\) | 8.89006 | 0.336735 | ||||||||
\(698\) | 5.58702 | 0.211472 | ||||||||
\(699\) | −15.3593 | −0.580943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8699 | 1.54363 | 0.771817 | − | 0.635845i | \(-0.219348\pi\) | ||||
0.771817 | + | 0.635845i | \(0.219348\pi\) | |||||||
\(702\) | 5.62443 | 0.212280 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.340484 | 0.0128325 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.3584 | 0.540386 | ||||||||
\(707\) | −13.9925 | −0.526244 | ||||||||
\(708\) | −1.53199 | −0.0575756 | ||||||||
\(709\) | 7.35745 | 0.276315 | 0.138157 | − | 0.990410i | \(-0.455882\pi\) | ||||
0.138157 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.3245 | −0.537211 | ||||||||
\(712\) | 6.31344 | 0.236606 | ||||||||
\(713\) | −17.9692 | −0.672952 | ||||||||
\(714\) | −36.7213 | −1.37426 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.8820 | 1.04200 | ||||||||
\(717\) | 32.1193 | 1.19952 | ||||||||
\(718\) | −54.5830 | −2.03702 | ||||||||
\(719\) | −31.9597 | −1.19190 | −0.595948 | − | 0.803023i | \(-0.703224\pi\) | ||||
−0.595948 | + | 0.803023i | \(0.703224\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.4794 | 0.539240 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.0381 | −1.56341 | ||||||||
\(724\) | 19.6882 | 0.731707 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −45.7717 | −1.69875 | ||||||||
\(727\) | −29.3883 | −1.08995 | −0.544976 | − | 0.838452i | \(-0.683461\pi\) | ||||
−0.544976 | + | 0.838452i | \(0.683461\pi\) | |||||||
\(728\) | −25.6598 | −0.951014 | ||||||||
\(729\) | −21.0116 | −0.778207 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.6326 | −0.800112 | ||||||||
\(732\) | 38.5387 | 1.42443 | ||||||||
\(733\) | −50.8285 | −1.87739 | −0.938696 | − | 0.344745i | \(-0.887965\pi\) | ||||
−0.938696 | + | 0.344745i | \(0.887965\pi\) | |||||||
\(734\) | −17.7607 | −0.655559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.1671 | 0.964534 | ||||||||
\(737\) | −3.51329 | −0.129414 | ||||||||
\(738\) | 20.9007 | 0.769364 | ||||||||
\(739\) | 14.7245 | 0.541650 | 0.270825 | − | 0.962629i | \(-0.412704\pi\) | ||||
0.270825 | + | 0.962629i | \(0.412704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 86.5039 | 3.17566 | ||||||||
\(743\) | −34.6568 | −1.27144 | −0.635718 | − | 0.771922i | \(-0.719296\pi\) | ||||
−0.635718 | + | 0.771922i | \(0.719296\pi\) | |||||||
\(744\) | 14.1738 | 0.519636 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.5549 | 0.606117 | ||||||||
\(747\) | 21.7693 | 0.796498 | ||||||||
\(748\) | 1.18454 | 0.0433110 | ||||||||
\(749\) | 7.42910 | 0.271453 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.35539 | 0.304893 | 0.152446 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152446 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(752\) | −13.0173 | −0.474692 | ||||||||
\(753\) | −42.2704 | −1.54042 | ||||||||
\(754\) | 24.2348 | 0.882578 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.80398 | 0.138349 | ||||||||
\(757\) | 13.8709 | 0.504146 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(758\) | −37.7410 | −1.37081 | ||||||||
\(759\) | 5.14317 | 0.186685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.3970 | 1.60939 | 0.804696 | − | 0.593687i | \(-0.202328\pi\) | ||||
0.804696 | + | 0.593687i | \(0.202328\pi\) | |||||||
\(762\) | 84.2692 | 3.05275 | ||||||||
\(763\) | 14.9184 | 0.540082 | ||||||||
\(764\) | −15.1819 | −0.549262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.0381 | 0.976927 | ||||||||
\(767\) | −2.25707 | −0.0814983 | ||||||||
\(768\) | −48.6961 | −1.75717 | ||||||||
\(769\) | 19.0001 | 0.685160 | 0.342580 | − | 0.939489i | \(-0.388699\pi\) | ||||
0.342580 | + | 0.939489i | \(0.388699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 66.1436 | 2.38210 | ||||||||
\(772\) | −11.4239 | −0.411157 | ||||||||
\(773\) | 1.86738 | 0.0671650 | 0.0335825 | − | 0.999436i | \(-0.489308\pi\) | ||||
0.0335825 | + | 0.999436i | \(0.489308\pi\) | |||||||
\(774\) | −50.8587 | −1.82808 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.21241 | −0.294808 | ||||||||
\(777\) | −21.6693 | −0.777381 | ||||||||
\(778\) | 56.1252 | 2.01218 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.96427 | 0.106070 | ||||||||
\(782\) | 15.9721 | 0.571162 | ||||||||
\(783\) | 2.47055 | 0.0882904 | ||||||||
\(784\) | −54.4744 | −1.94552 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.5923 | −0.520489 | ||||||||
\(787\) | −12.9689 | −0.462291 | −0.231146 | − | 0.972919i | \(-0.574247\pi\) | ||||
−0.231146 | + | 0.972919i | \(0.574247\pi\) | |||||||
\(788\) | 3.67660 | 0.130973 | ||||||||
\(789\) | 13.2545 | 0.471873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.2032 | −1.99836 | ||||||||
\(792\) | −1.91503 | −0.0680476 | ||||||||
\(793\) | 56.7790 | 2.01628 | ||||||||
\(794\) | −16.7503 | −0.594444 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.621324 | 0.0220222 | ||||||||
\(797\) | 29.9226 | 1.05991 | 0.529956 | − | 0.848025i | \(-0.322209\pi\) | ||||
0.529956 | + | 0.848025i | \(0.322209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.33772 | −0.188835 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6441 | 0.411422 | ||||||||
\(802\) | 10.9945 | 0.388229 | ||||||||
\(803\) | −1.00838 | −0.0355850 | ||||||||
\(804\) | −20.2181 | −0.713038 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.3674 | −1.06964 | ||||||||
\(807\) | −11.0312 | −0.388318 | ||||||||
\(808\) | −4.80064 | −0.168886 | ||||||||
\(809\) | 42.4578 | 1.49274 | 0.746369 | − | 0.665532i | \(-0.231795\pi\) | ||||
0.746369 | + | 0.665532i | \(0.231795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1514 | 1.09387 | 0.546936 | − | 0.837174i | \(-0.315794\pi\) | ||||
0.546936 | + | 0.837174i | \(0.315794\pi\) | |||||||
\(812\) | 16.3907 | 0.575202 | ||||||||
\(813\) | 18.1366 | 0.636079 | ||||||||
\(814\) | 1.87867 | 0.0658472 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −24.1028 | −0.843767 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.07767 | 0.142572 | ||||||||
\(819\) | −47.3250 | −1.65367 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.20740 | −0.216640 | −0.108320 | − | 0.994116i | \(-0.534547\pi\) | ||||
−0.108320 | + | 0.994116i | \(0.534547\pi\) | |||||||
\(822\) | 2.58785 | 0.0902616 | ||||||||
\(823\) | 35.9702 | 1.25384 | 0.626921 | − | 0.779083i | \(-0.284315\pi\) | ||||
0.626921 | + | 0.779083i | \(0.284315\pi\) | |||||||
\(824\) | 4.96766 | 0.173057 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.10279 | −0.142754 | ||||||||
\(827\) | 15.3837 | 0.534945 | 0.267473 | − | 0.963565i | \(-0.413811\pi\) | ||||
0.267473 | + | 0.963565i | \(0.413811\pi\) | |||||||
\(828\) | 13.9716 | 0.485545 | ||||||||
\(829\) | 24.1941 | 0.840295 | 0.420148 | − | 0.907456i | \(-0.361978\pi\) | ||||
0.420148 | + | 0.907456i | \(0.361978\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.9627 | 0.623120 | ||||||||
\(832\) | 2.88678 | 0.100081 | ||||||||
\(833\) | −22.3371 | −0.773936 | ||||||||
\(834\) | −35.9825 | −1.24597 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.09573 | −0.107004 | ||||||||
\(838\) | 40.4218 | 1.39635 | ||||||||
\(839\) | −12.4265 | −0.429012 | −0.214506 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214506 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3548 | −0.632923 | ||||||||
\(842\) | −41.0420 | −1.41440 | ||||||||
\(843\) | −43.5155 | −1.49875 | ||||||||
\(844\) | 22.5920 | 0.777649 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.5491 | −0.431446 | ||||||||
\(847\) | −45.6087 | −1.56713 | ||||||||
\(848\) | 56.7787 | 1.94979 | ||||||||
\(849\) | −73.7379 | −2.53068 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.42518 | 0.323091 | ||||||||
\(852\) | 17.0587 | 0.584420 | ||||||||
\(853\) | −23.1527 | −0.792734 | −0.396367 | − | 0.918092i | \(-0.629729\pi\) | ||||
−0.396367 | + | 0.918092i | \(0.629729\pi\) | |||||||
\(854\) | 103.210 | 3.53176 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.54882 | 0.0871167 | ||||||||
\(857\) | −2.84272 | −0.0971054 | −0.0485527 | − | 0.998821i | \(-0.515461\pi\) | ||||
−0.0485527 | + | 0.998821i | \(0.515461\pi\) | |||||||
\(858\) | 8.69178 | 0.296733 | ||||||||
\(859\) | −25.8715 | −0.882725 | −0.441363 | − | 0.897329i | \(-0.645505\pi\) | ||||
−0.441363 | + | 0.897329i | \(0.645505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.1188 | 1.50356 | ||||||||
\(862\) | 45.7447 | 1.55807 | ||||||||
\(863\) | −38.0032 | −1.29365 | −0.646823 | − | 0.762641i | \(-0.723903\pi\) | ||||
−0.646823 | + | 0.762641i | \(0.723903\pi\) | |||||||
\(864\) | 4.50806 | 0.153367 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.21773 | 0.143324 | ||||||||
\(867\) | 30.6407 | 1.04061 | ||||||||
\(868\) | −20.5384 | −0.697119 | ||||||||
\(869\) | 2.62149 | 0.0889281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7873 | −1.00931 | ||||||||
\(872\) | 5.11828 | 0.173327 | ||||||||
\(873\) | −15.1464 | −0.512628 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.80298 | −0.196065 | ||||||||
\(877\) | 49.0943 | 1.65780 | 0.828898 | − | 0.559400i | \(-0.188968\pi\) | ||||
0.828898 | + | 0.559400i | \(0.188968\pi\) | |||||||
\(878\) | −11.2731 | −0.380448 | ||||||||
\(879\) | −52.2026 | −1.76075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.7494 | −1.87825 | −0.939123 | − | 0.343581i | \(-0.888360\pi\) | ||||
−0.939123 | + | 0.343581i | \(0.888360\pi\) | |||||||
\(882\) | −52.5150 | −1.76827 | ||||||||
\(883\) | 16.6355 | 0.559828 | 0.279914 | − | 0.960025i | \(-0.409694\pi\) | ||||
0.279914 | + | 0.960025i | \(0.409694\pi\) | |||||||
\(884\) | 10.0431 | 0.337786 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.2613 | −1.89014 | ||||||||
\(887\) | 43.3883 | 1.45684 | 0.728418 | − | 0.685133i | \(-0.240256\pi\) | ||||
0.728418 | + | 0.685133i | \(0.240256\pi\) | |||||||
\(888\) | −7.43441 | −0.249483 | ||||||||
\(889\) | 83.9691 | 2.81623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.83627 | 0.162021 | ||||||||
\(892\) | 3.74820 | 0.125499 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −19.7285 | −0.659819 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −45.2277 | −1.51095 | ||||||||
\(897\) | 43.6062 | 1.45597 | ||||||||
\(898\) | −26.9180 | −0.898266 | ||||||||
\(899\) | −13.3390 | −0.444880 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.2820 | 0.775636 | ||||||||
\(902\) | −3.82498 | −0.127358 | ||||||||
\(903\) | −107.357 | −3.57260 | ||||||||
\(904\) | −19.2825 | −0.641326 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −60.4567 | −2.00854 | ||||||||
\(907\) | 19.8364 | 0.658656 | 0.329328 | − | 0.944216i | \(-0.393178\pi\) | ||||
0.329328 | + | 0.944216i | \(0.393178\pi\) | |||||||
\(908\) | 10.7208 | 0.355784 | ||||||||
\(909\) | −8.85395 | −0.293667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4076 | −0.510478 | −0.255239 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255239 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.98395 | −0.131849 | ||||||||
\(914\) | −35.9339 | −1.18859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.2034 | −0.700579 | ||||||||
\(917\) | −14.5403 | −0.480163 | ||||||||
\(918\) | 2.75167 | 0.0908186 | ||||||||
\(919\) | −13.2561 | −0.437278 | −0.218639 | − | 0.975806i | \(-0.570162\pi\) | ||||
−0.218639 | + | 0.975806i | \(0.570162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0045 | 0.428512 | ||||||||
\(922\) | 13.3581 | 0.439926 | ||||||||
\(923\) | 25.1325 | 0.827247 | ||||||||
\(924\) | 5.87853 | 0.193389 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.5442 | 1.26664 | ||||||||
\(927\) | 9.16200 | 0.300920 | ||||||||
\(928\) | 19.4245 | 0.637641 | ||||||||
\(929\) | 31.2016 | 1.02369 | 0.511846 | − | 0.859077i | \(-0.328962\pi\) | ||||
0.511846 | + | 0.859077i | \(0.328962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.63580 | 0.250119 | ||||||||
\(933\) | −15.9646 | −0.522658 | ||||||||
\(934\) | 48.2762 | 1.57964 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.2365 | −0.530707 | ||||||||
\(937\) | 16.2187 | 0.529840 | 0.264920 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264920 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(938\) | −54.1458 | −1.76792 | ||||||||
\(939\) | 10.9243 | 0.356502 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.1748 | −1.14666 | −0.573332 | − | 0.819323i | \(-0.694350\pi\) | ||||
−0.573332 | + | 0.819323i | \(0.694350\pi\) | |||||||
\(942\) | 45.6400 | 1.48703 | ||||||||
\(943\) | −19.1897 | −0.624903 | ||||||||
\(944\) | −2.69295 | −0.0876482 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.30752 | 0.302614 | ||||||||
\(947\) | 22.2784 | 0.723950 | 0.361975 | − | 0.932188i | \(-0.382103\pi\) | ||||
0.361975 | + | 0.932188i | \(0.382103\pi\) | |||||||
\(948\) | 15.0860 | 0.489972 | ||||||||
\(949\) | −8.54953 | −0.277530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65.9811 | 2.13958 | ||||||||
\(952\) | −12.5537 | −0.406866 | ||||||||
\(953\) | −4.25996 | −0.137994 | −0.0689968 | − | 0.997617i | \(-0.521980\pi\) | ||||
−0.0689968 | + | 0.997617i | \(0.521980\pi\) | |||||||
\(954\) | 54.7364 | 1.77216 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.9679 | −0.516439 | ||||||||
\(957\) | 3.81790 | 0.123415 | ||||||||
\(958\) | 67.9131 | 2.19417 | ||||||||
\(959\) | 2.57863 | 0.0832684 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2856 | −0.460825 | ||||||||
\(962\) | 15.9282 | 0.513547 | ||||||||
\(963\) | 4.70085 | 0.151483 | ||||||||
\(964\) | 20.8990 | 0.673111 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 79.2650 | 2.55031 | ||||||||
\(967\) | 1.21906 | 0.0392023 | 0.0196012 | − | 0.999808i | \(-0.493760\pi\) | ||||
0.0196012 | + | 0.999808i | \(0.493760\pi\) | |||||||
\(968\) | −15.6477 | −0.502935 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.34003 | 0.139278 | 0.0696391 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696391 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(972\) | 25.1395 | 0.806349 | ||||||||
\(973\) | −35.8543 | −1.14944 | ||||||||
\(974\) | −32.7226 | −1.04850 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.7440 | 2.16843 | ||||||||
\(977\) | 21.5270 | 0.688710 | 0.344355 | − | 0.938840i | \(-0.388098\pi\) | ||||
0.344355 | + | 0.938840i | \(0.388098\pi\) | |||||||
\(978\) | −72.0527 | −2.30399 | ||||||||
\(979\) | −2.13095 | −0.0681054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.43980 | 0.301389 | ||||||||
\(982\) | 26.8906 | 0.858114 | ||||||||
\(983\) | 14.5998 | 0.465661 | 0.232830 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232830 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(984\) | 15.1365 | 0.482534 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.8565 | 0.377588 | ||||||||
\(987\) | −26.4896 | −0.843172 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.6954 | 1.48483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.9286 | −1.01425 | −0.507123 | − | 0.861874i | \(-0.669291\pi\) | ||||
−0.507123 | + | 0.861874i | \(0.669291\pi\) | |||||||
\(992\) | −24.3399 | −0.772792 | ||||||||
\(993\) | −33.6831 | −1.06890 | ||||||||
\(994\) | 45.6845 | 1.44903 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22.9267 | −0.726459 | ||||||||
\(997\) | −55.1812 | −1.74761 | −0.873803 | − | 0.486280i | \(-0.838353\pi\) | ||||
−0.873803 | + | 0.486280i | \(0.838353\pi\) | |||||||
\(998\) | −61.6248 | −1.95070 | ||||||||
\(999\) | 1.62377 | 0.0513737 |
(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 | 9025.2.a.ct.1.5 | 24 | ||
5.2 | odd | 4 | 1805.2.b.l.1084.5 | 24 | |||
5.3 | odd | 4 | 1805.2.b.l.1084.20 | 24 | |||
5.4 | even | 2 | inner | 9025.2.a.ct.1.20 | 24 | ||
19.14 | odd | 18 | 475.2.l.f.101.7 | 48 | |||
19.15 | odd | 18 | 475.2.l.f.301.7 | 48 | |||
19.18 | odd | 2 | 9025.2.a.cu.1.20 | 24 | |||
95.14 | odd | 18 | 475.2.l.f.101.2 | 48 | |||
95.18 | even | 4 | 1805.2.b.k.1084.5 | 24 | |||
95.33 | even | 36 | 95.2.p.a.44.2 | ✓ | 48 | ||
95.34 | odd | 18 | 475.2.l.f.301.2 | 48 | |||
95.37 | even | 4 | 1805.2.b.k.1084.20 | 24 | |||
95.52 | even | 36 | 95.2.p.a.44.7 | yes | 48 | ||
95.53 | even | 36 | 95.2.p.a.54.7 | yes | 48 | ||
95.72 | even | 36 | 95.2.p.a.54.2 | yes | 48 | ||
95.94 | odd | 2 | 9025.2.a.cu.1.5 | 24 | |||
285.53 | odd | 36 | 855.2.da.b.244.2 | 48 | |||
285.128 | odd | 36 | 855.2.da.b.424.7 | 48 | |||
285.167 | odd | 36 | 855.2.da.b.244.7 | 48 | |||
285.242 | odd | 36 | 855.2.da.b.424.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.2 | ✓ | 48 | 95.33 | even | 36 | ||
95.2.p.a.44.7 | yes | 48 | 95.52 | even | 36 | ||
95.2.p.a.54.2 | yes | 48 | 95.72 | even | 36 | ||
95.2.p.a.54.7 | yes | 48 | 95.53 | even | 36 | ||
475.2.l.f.101.2 | 48 | 95.14 | odd | 18 | |||
475.2.l.f.101.7 | 48 | 19.14 | odd | 18 | |||
475.2.l.f.301.2 | 48 | 95.34 | odd | 18 | |||
475.2.l.f.301.7 | 48 | 19.15 | odd | 18 | |||
855.2.da.b.244.2 | 48 | 285.53 | odd | 36 | |||
855.2.da.b.244.7 | 48 | 285.167 | odd | 36 | |||
855.2.da.b.424.2 | 48 | 285.242 | odd | 36 | |||
855.2.da.b.424.7 | 48 | 285.128 | odd | 36 | |||
1805.2.b.k.1084.5 | 24 | 95.18 | even | 4 | |||
1805.2.b.k.1084.20 | 24 | 95.37 | even | 4 | |||
1805.2.b.l.1084.5 | 24 | 5.2 | odd | 4 | |||
1805.2.b.l.1084.20 | 24 | 5.3 | odd | 4 | |||
9025.2.a.ct.1.5 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.ct.1.20 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.cu.1.5 | 24 | 95.94 | odd | 2 | |||
9025.2.a.cu.1.20 | 24 | 19.18 | odd | 2 |