Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3645,2,Mod(1,3645)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3645, 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("3645.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3645 = 3^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3645.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: | \(29.1054715368\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 3 x^{14} - 15 x^{13} + 47 x^{12} + 84 x^{11} - 279 x^{10} - 219 x^{9} + 783 x^{8} + 279 x^{7} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.300859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3645.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.300859 | −0.212739 | −0.106370 | − | 0.994327i | \(-0.533923\pi\) | ||||
−0.106370 | + | 0.994327i | \(0.533923\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.90948 | −0.954742 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.28937 | −1.62123 | −0.810615 | − | 0.585580i | \(-0.800867\pi\) | ||||
−0.810615 | + | 0.585580i | \(0.800867\pi\) | |||||||
\(8\) | 1.17620 | 0.415851 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.300859 | −0.0951400 | ||||||||
\(11\) | −1.77263 | −0.534467 | −0.267233 | − | 0.963632i | \(-0.586109\pi\) | ||||
−0.267233 | + | 0.963632i | \(0.586109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.04481 | 1.12183 | 0.560914 | − | 0.827874i | \(-0.310450\pi\) | ||||
0.560914 | + | 0.827874i | \(0.310450\pi\) | |||||||
\(14\) | 1.29050 | 0.344899 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.46510 | 0.866274 | ||||||||
\(17\) | 3.90428 | 0.946928 | 0.473464 | − | 0.880813i | \(-0.343003\pi\) | ||||
0.473464 | + | 0.880813i | \(0.343003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.11369 | 0.255498 | 0.127749 | − | 0.991807i | \(-0.459225\pi\) | ||||
0.127749 | + | 0.991807i | \(0.459225\pi\) | |||||||
\(20\) | −1.90948 | −0.426974 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.533311 | 0.113702 | ||||||||
\(23\) | −8.62555 | −1.79855 | −0.899276 | − | 0.437383i | \(-0.855906\pi\) | ||||
−0.899276 | + | 0.437383i | \(0.855906\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.21692 | −0.238657 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.19048 | 1.54786 | ||||||||
\(29\) | −0.598345 | −0.111110 | −0.0555549 | − | 0.998456i | \(-0.517693\pi\) | ||||
−0.0555549 | + | 0.998456i | \(0.517693\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.62890 | 0.292560 | 0.146280 | − | 0.989243i | \(-0.453270\pi\) | ||||
0.146280 | + | 0.989243i | \(0.453270\pi\) | |||||||
\(32\) | −3.39491 | −0.600141 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.17464 | −0.201449 | ||||||||
\(35\) | −4.28937 | −0.725036 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.21715 | 0.857694 | 0.428847 | − | 0.903377i | \(-0.358920\pi\) | ||||
0.428847 | + | 0.903377i | \(0.358920\pi\) | |||||||
\(38\) | −0.335064 | −0.0543545 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.17620 | 0.185974 | ||||||||
\(41\) | −0.756985 | −0.118221 | −0.0591106 | − | 0.998251i | \(-0.518826\pi\) | ||||
−0.0591106 | + | 0.998251i | \(0.518826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.20963 | −1.09946 | −0.549729 | − | 0.835343i | \(-0.685269\pi\) | ||||
−0.549729 | + | 0.835343i | \(0.685269\pi\) | |||||||
\(44\) | 3.38480 | 0.510278 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.59507 | 0.382623 | ||||||||
\(47\) | 11.7489 | 1.71376 | 0.856880 | − | 0.515516i | \(-0.172400\pi\) | ||||
0.856880 | + | 0.515516i | \(0.172400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3987 | 1.62838 | ||||||||
\(50\) | −0.300859 | −0.0425479 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.72349 | −1.07106 | ||||||||
\(53\) | −3.97724 | −0.546316 | −0.273158 | − | 0.961969i | \(-0.588068\pi\) | ||||
−0.273158 | + | 0.961969i | \(0.588068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.77263 | −0.239021 | ||||||||
\(56\) | −5.04517 | −0.674189 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.180017 | 0.0236374 | ||||||||
\(59\) | 13.8195 | 1.79915 | 0.899576 | − | 0.436764i | \(-0.143876\pi\) | ||||
0.899576 | + | 0.436764i | \(0.143876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48018 | −1.08578 | −0.542888 | − | 0.839805i | \(-0.682669\pi\) | ||||
−0.542888 | + | 0.839805i | \(0.682669\pi\) | |||||||
\(62\) | −0.490070 | −0.0622390 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.90880 | −0.738600 | ||||||||
\(65\) | 4.04481 | 0.501696 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.83466 | 0.957156 | 0.478578 | − | 0.878045i | \(-0.341152\pi\) | ||||
0.478578 | + | 0.878045i | \(0.341152\pi\) | |||||||
\(68\) | −7.45517 | −0.904072 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.29050 | 0.154244 | ||||||||
\(71\) | 5.18353 | 0.615172 | 0.307586 | − | 0.951520i | \(-0.400479\pi\) | ||||
0.307586 | + | 0.951520i | \(0.400479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.37528 | −0.512088 | −0.256044 | − | 0.966665i | \(-0.582419\pi\) | ||||
−0.256044 | + | 0.966665i | \(0.582419\pi\) | |||||||
\(74\) | −1.56963 | −0.182465 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.12657 | −0.243935 | ||||||||
\(77\) | 7.60345 | 0.866493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8907 | −1.45032 | −0.725159 | − | 0.688582i | \(-0.758234\pi\) | ||||
−0.725159 | + | 0.688582i | \(0.758234\pi\) | |||||||
\(80\) | 3.46510 | 0.387410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.227746 | 0.0251503 | ||||||||
\(83\) | −7.90723 | −0.867932 | −0.433966 | − | 0.900929i | \(-0.642886\pi\) | ||||
−0.433966 | + | 0.900929i | \(0.642886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.90428 | 0.423479 | ||||||||
\(86\) | 2.16908 | 0.233898 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.08497 | −0.222258 | ||||||||
\(89\) | 3.25566 | 0.345100 | 0.172550 | − | 0.985001i | \(-0.444799\pi\) | ||||
0.172550 | + | 0.985001i | \(0.444799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3497 | −1.81874 | ||||||||
\(92\) | 16.4703 | 1.71715 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.53478 | −0.364584 | ||||||||
\(95\) | 1.11369 | 0.114262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.99171 | −0.202227 | −0.101114 | − | 0.994875i | \(-0.532241\pi\) | ||||
−0.101114 | + | 0.994875i | \(0.532241\pi\) | |||||||
\(98\) | −3.42940 | −0.346422 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.90948 | −0.190948 | ||||||||
\(101\) | −9.16732 | −0.912183 | −0.456091 | − | 0.889933i | \(-0.650751\pi\) | ||||
−0.456091 | + | 0.889933i | \(0.650751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.81293 | 0.178633 | 0.0893165 | − | 0.996003i | \(-0.471532\pi\) | ||||
0.0893165 | + | 0.996003i | \(0.471532\pi\) | |||||||
\(104\) | 4.75751 | 0.466513 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.19659 | 0.116223 | ||||||||
\(107\) | −3.71297 | −0.358946 | −0.179473 | − | 0.983763i | \(-0.557439\pi\) | ||||
−0.179473 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.24138 | −0.310468 | −0.155234 | − | 0.987878i | \(-0.549613\pi\) | ||||
−0.155234 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(110\) | 0.533311 | 0.0508492 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.8631 | −1.40443 | ||||||||
\(113\) | −12.2993 | −1.15702 | −0.578509 | − | 0.815676i | \(-0.696365\pi\) | ||||
−0.578509 | + | 0.815676i | \(0.696365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.62555 | −0.804336 | ||||||||
\(116\) | 1.14253 | 0.106081 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.15774 | −0.382751 | ||||||||
\(119\) | −16.7469 | −1.53519 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.85780 | −0.714345 | ||||||||
\(122\) | 2.55134 | 0.230987 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.11037 | −0.279319 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0119 | −0.977144 | −0.488572 | − | 0.872523i | \(-0.662482\pi\) | ||||
−0.488572 | + | 0.872523i | \(0.662482\pi\) | |||||||
\(128\) | 8.56754 | 0.757271 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.21692 | −0.106731 | ||||||||
\(131\) | −17.5454 | −1.53295 | −0.766475 | − | 0.642275i | \(-0.777991\pi\) | ||||
−0.766475 | + | 0.642275i | \(0.777991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.77703 | −0.414221 | ||||||||
\(134\) | −2.35713 | −0.203625 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.59223 | 0.393781 | ||||||||
\(137\) | −0.356723 | −0.0304769 | −0.0152385 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152385 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.49122 | −0.126483 | −0.0632416 | − | 0.997998i | \(-0.520144\pi\) | ||||
−0.0632416 | + | 0.997998i | \(0.520144\pi\) | |||||||
\(140\) | 8.19048 | 0.692222 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.55951 | −0.130871 | ||||||||
\(143\) | −7.16993 | −0.599579 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.598345 | −0.0496898 | ||||||||
\(146\) | 1.31634 | 0.108941 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.96206 | −0.818876 | ||||||||
\(149\) | 18.0992 | 1.48274 | 0.741372 | − | 0.671094i | \(-0.234175\pi\) | ||||
0.741372 | + | 0.671094i | \(0.234175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2099 | −1.72603 | −0.863017 | − | 0.505174i | \(-0.831428\pi\) | ||||
−0.863017 | + | 0.505174i | \(0.831428\pi\) | |||||||
\(152\) | 1.30993 | 0.106249 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.28757 | −0.184337 | ||||||||
\(155\) | 1.62890 | 0.130837 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.47578 | −0.437015 | −0.218507 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218507 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(158\) | 3.87828 | 0.308540 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.39491 | −0.268391 | ||||||||
\(161\) | 36.9982 | 2.91586 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9869 | −1.40884 | −0.704420 | − | 0.709783i | \(-0.748793\pi\) | ||||
−0.704420 | + | 0.709783i | \(0.748793\pi\) | |||||||
\(164\) | 1.44545 | 0.112871 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.37896 | 0.184643 | ||||||||
\(167\) | −19.9377 | −1.54283 | −0.771415 | − | 0.636333i | \(-0.780450\pi\) | ||||
−0.771415 | + | 0.636333i | \(0.780450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.36045 | 0.258496 | ||||||||
\(170\) | −1.17464 | −0.0900907 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.7667 | 1.04970 | ||||||||
\(173\) | −6.76573 | −0.514389 | −0.257194 | − | 0.966360i | \(-0.582798\pi\) | ||||
−0.257194 | + | 0.966360i | \(0.582798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.28937 | −0.324246 | ||||||||
\(176\) | −6.14232 | −0.462995 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.979495 | −0.0734163 | ||||||||
\(179\) | −9.43971 | −0.705557 | −0.352778 | − | 0.935707i | \(-0.614763\pi\) | ||||
−0.352778 | + | 0.935707i | \(0.614763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.13240 | 0.0841709 | 0.0420855 | − | 0.999114i | \(-0.486600\pi\) | ||||
0.0420855 | + | 0.999114i | \(0.486600\pi\) | |||||||
\(182\) | 5.21980 | 0.386917 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.1454 | −0.747929 | ||||||||
\(185\) | 5.21715 | 0.383572 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92084 | −0.506102 | ||||||||
\(188\) | −22.4344 | −1.63620 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.335064 | −0.0243081 | ||||||||
\(191\) | 23.6241 | 1.70938 | 0.854689 | − | 0.519141i | \(-0.173748\pi\) | ||||
0.854689 | + | 0.519141i | \(0.173748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.71596 | −0.195499 | −0.0977497 | − | 0.995211i | \(-0.531164\pi\) | ||||
−0.0977497 | + | 0.995211i | \(0.531164\pi\) | |||||||
\(194\) | 0.599223 | 0.0430217 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.7656 | −1.55469 | ||||||||
\(197\) | 14.2743 | 1.01700 | 0.508501 | − | 0.861061i | \(-0.330200\pi\) | ||||
0.508501 | + | 0.861061i | \(0.330200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2703 | 1.50781 | 0.753905 | − | 0.656983i | \(-0.228168\pi\) | ||||
0.753905 | + | 0.656983i | \(0.228168\pi\) | |||||||
\(200\) | 1.17620 | 0.0831701 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.75807 | 0.194057 | ||||||||
\(203\) | 2.56652 | 0.180134 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.756985 | −0.0528701 | ||||||||
\(206\) | −0.545436 | −0.0380023 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.0156 | 0.971810 | ||||||||
\(209\) | −1.97416 | −0.136555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1444 | −1.38680 | −0.693400 | − | 0.720553i | \(-0.743888\pi\) | ||||
−0.693400 | + | 0.720553i | \(0.743888\pi\) | |||||||
\(212\) | 7.59447 | 0.521591 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.11708 | 0.0763619 | ||||||||
\(215\) | −7.20963 | −0.491693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.98697 | −0.474306 | ||||||||
\(218\) | 0.975197 | 0.0660487 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.38480 | 0.228203 | ||||||||
\(221\) | 15.7921 | 1.06229 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.78299 | −0.387258 | −0.193629 | − | 0.981075i | \(-0.562026\pi\) | ||||
−0.193629 | + | 0.981075i | \(0.562026\pi\) | |||||||
\(224\) | 14.5620 | 0.972967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.70035 | 0.246144 | ||||||||
\(227\) | −15.3090 | −1.01610 | −0.508048 | − | 0.861329i | \(-0.669633\pi\) | ||||
−0.508048 | + | 0.861329i | \(0.669633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.46710 | 0.163030 | 0.0815152 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815152 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(230\) | 2.59507 | 0.171114 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.703775 | −0.0462051 | ||||||||
\(233\) | −8.42853 | −0.552171 | −0.276086 | − | 0.961133i | \(-0.589037\pi\) | ||||
−0.276086 | + | 0.961133i | \(0.589037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7489 | 0.766417 | ||||||||
\(236\) | −26.3882 | −1.71773 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.03846 | 0.326595 | ||||||||
\(239\) | 15.2495 | 0.986409 | 0.493204 | − | 0.869914i | \(-0.335826\pi\) | ||||
0.493204 | + | 0.869914i | \(0.335826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.650803 | −0.0419219 | −0.0209610 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209610 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(242\) | 2.36409 | 0.151969 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.1928 | 1.03664 | ||||||||
\(245\) | 11.3987 | 0.728236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50466 | 0.286625 | ||||||||
\(248\) | 1.91592 | 0.121661 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.300859 | −0.0190280 | ||||||||
\(251\) | −6.15859 | −0.388727 | −0.194364 | − | 0.980930i | \(-0.562264\pi\) | ||||
−0.194364 | + | 0.980930i | \(0.562264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.2899 | 0.961266 | ||||||||
\(254\) | 3.31302 | 0.207877 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.23998 | 0.577499 | ||||||||
\(257\) | −7.01222 | −0.437410 | −0.218705 | − | 0.975791i | \(-0.570183\pi\) | ||||
−0.218705 | + | 0.975791i | \(0.570183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3783 | −1.39052 | ||||||||
\(260\) | −7.72349 | −0.478991 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.27869 | 0.326119 | ||||||||
\(263\) | −19.4528 | −1.19951 | −0.599756 | − | 0.800183i | \(-0.704736\pi\) | ||||
−0.599756 | + | 0.800183i | \(0.704736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.97724 | −0.244320 | ||||||||
\(266\) | 1.43721 | 0.0881211 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.9602 | −0.913837 | ||||||||
\(269\) | −10.1856 | −0.621026 | −0.310513 | − | 0.950569i | \(-0.600501\pi\) | ||||
−0.310513 | + | 0.950569i | \(0.600501\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.87083 | −0.417373 | −0.208687 | − | 0.977983i | \(-0.566919\pi\) | ||||
−0.208687 | + | 0.977983i | \(0.566919\pi\) | |||||||
\(272\) | 13.5287 | 0.820299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.107323 | 0.00648365 | ||||||||
\(275\) | −1.77263 | −0.106893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.5635 | 1.59604 | 0.798022 | − | 0.602628i | \(-0.205880\pi\) | ||||
0.798022 | + | 0.602628i | \(0.205880\pi\) | |||||||
\(278\) | 0.448646 | 0.0269080 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.04517 | −0.301507 | ||||||||
\(281\) | 23.9246 | 1.42722 | 0.713611 | − | 0.700543i | \(-0.247059\pi\) | ||||
0.713611 | + | 0.700543i | \(0.247059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5016 | −0.802588 | −0.401294 | − | 0.915949i | \(-0.631439\pi\) | ||||
−0.401294 | + | 0.915949i | \(0.631439\pi\) | |||||||
\(284\) | −9.89786 | −0.587330 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.15714 | 0.127554 | ||||||||
\(287\) | 3.24699 | 0.191664 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.75656 | −0.103327 | ||||||||
\(290\) | 0.180017 | 0.0105710 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.35453 | 0.488912 | ||||||||
\(293\) | 5.51414 | 0.322140 | 0.161070 | − | 0.986943i | \(-0.448506\pi\) | ||||
0.161070 | + | 0.986943i | \(0.448506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8195 | 0.804605 | ||||||||
\(296\) | 6.13643 | 0.356673 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.44531 | −0.315438 | ||||||||
\(299\) | −34.8887 | −2.01766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.9248 | 1.78247 | ||||||||
\(302\) | 6.38118 | 0.367196 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.85904 | 0.221331 | ||||||||
\(305\) | −8.48018 | −0.485574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.76721 | 0.272079 | 0.136039 | − | 0.990703i | \(-0.456563\pi\) | ||||
0.136039 | + | 0.990703i | \(0.456563\pi\) | |||||||
\(308\) | −14.5187 | −0.827278 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.490070 | −0.0278341 | ||||||||
\(311\) | −10.8755 | −0.616691 | −0.308345 | − | 0.951274i | \(-0.599775\pi\) | ||||
−0.308345 | + | 0.951274i | \(0.599775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4182 | −0.701916 | −0.350958 | − | 0.936391i | \(-0.614144\pi\) | ||||
−0.350958 | + | 0.936391i | \(0.614144\pi\) | |||||||
\(314\) | 1.64744 | 0.0929703 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.6146 | 1.38468 | ||||||||
\(317\) | 11.0331 | 0.619678 | 0.309839 | − | 0.950789i | \(-0.399725\pi\) | ||||
0.309839 | + | 0.950789i | \(0.399725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.06064 | 0.0593845 | ||||||||
\(320\) | −5.90880 | −0.330312 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.1312 | −0.620319 | ||||||||
\(323\) | 4.34816 | 0.241938 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.04481 | 0.224365 | ||||||||
\(326\) | 5.41151 | 0.299716 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.890368 | −0.0491623 | ||||||||
\(329\) | −50.3956 | −2.77840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.02600 | 0.111359 | 0.0556796 | − | 0.998449i | \(-0.482267\pi\) | ||||
0.0556796 | + | 0.998449i | \(0.482267\pi\) | |||||||
\(332\) | 15.0987 | 0.828651 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.99845 | 0.328221 | ||||||||
\(335\) | 7.83466 | 0.428053 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.3801 | −0.837806 | −0.418903 | − | 0.908031i | \(-0.637585\pi\) | ||||
−0.418903 | + | 0.908031i | \(0.637585\pi\) | |||||||
\(338\) | −1.01102 | −0.0549923 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.45517 | −0.404313 | ||||||||
\(341\) | −2.88744 | −0.156364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8676 | −1.01875 | ||||||||
\(344\) | −8.48000 | −0.457211 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.03553 | 0.109431 | ||||||||
\(347\) | −1.15918 | −0.0622280 | −0.0311140 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311140 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.16380 | −0.276412 | −0.138206 | − | 0.990404i | \(-0.544134\pi\) | ||||
−0.138206 | + | 0.990404i | \(0.544134\pi\) | |||||||
\(350\) | 1.29050 | 0.0689799 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.01791 | 0.320756 | ||||||||
\(353\) | 12.1424 | 0.646277 | 0.323138 | − | 0.946352i | \(-0.395262\pi\) | ||||
0.323138 | + | 0.946352i | \(0.395262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.18353 | 0.275113 | ||||||||
\(356\) | −6.21663 | −0.329481 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.84002 | 0.150100 | ||||||||
\(359\) | −8.89415 | −0.469415 | −0.234708 | − | 0.972066i | \(-0.575413\pi\) | ||||
−0.234708 | + | 0.972066i | \(0.575413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7597 | −0.934721 | ||||||||
\(362\) | −0.340694 | −0.0179065 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.1289 | 1.73643 | ||||||||
\(365\) | −4.37528 | −0.229013 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.6276 | −1.44215 | −0.721075 | − | 0.692857i | \(-0.756352\pi\) | ||||
−0.721075 | + | 0.692857i | \(0.756352\pi\) | |||||||
\(368\) | −29.8884 | −1.55804 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.56963 | −0.0816010 | ||||||||
\(371\) | 17.0598 | 0.885703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.8466 | −1.59718 | −0.798589 | − | 0.601877i | \(-0.794420\pi\) | ||||
−0.798589 | + | 0.601877i | \(0.794420\pi\) | |||||||
\(374\) | 2.08220 | 0.107668 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.8192 | 0.712668 | ||||||||
\(377\) | −2.42019 | −0.124646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0219 | −1.07982 | −0.539911 | − | 0.841722i | \(-0.681542\pi\) | ||||
−0.539911 | + | 0.841722i | \(0.681542\pi\) | |||||||
\(380\) | −2.12657 | −0.109091 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.10751 | −0.363652 | ||||||||
\(383\) | 21.5253 | 1.09989 | 0.549945 | − | 0.835201i | \(-0.314649\pi\) | ||||
0.549945 | + | 0.835201i | \(0.314649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.60345 | 0.387508 | ||||||||
\(386\) | 0.817122 | 0.0415904 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.80313 | 0.193075 | ||||||||
\(389\) | −13.4127 | −0.680050 | −0.340025 | − | 0.940416i | \(-0.610435\pi\) | ||||
−0.340025 | + | 0.940416i | \(0.610435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.6766 | −1.70310 | ||||||||
\(392\) | 13.4072 | 0.677165 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.29455 | −0.216357 | ||||||||
\(395\) | −12.8907 | −0.648602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0060 | −0.853506 | −0.426753 | − | 0.904368i | \(-0.640343\pi\) | ||||
−0.426753 | + | 0.904368i | \(0.640343\pi\) | |||||||
\(398\) | −6.39935 | −0.320771 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.46510 | 0.173255 | ||||||||
\(401\) | −6.23973 | −0.311597 | −0.155799 | − | 0.987789i | \(-0.549795\pi\) | ||||
−0.155799 | + | 0.987789i | \(0.549795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.58860 | 0.328201 | ||||||||
\(404\) | 17.5049 | 0.870899 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.772161 | −0.0383217 | ||||||||
\(407\) | −9.24805 | −0.458409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.60027 | 0.474703 | 0.237351 | − | 0.971424i | \(-0.423721\pi\) | ||||
0.237351 | + | 0.971424i | \(0.423721\pi\) | |||||||
\(410\) | 0.227746 | 0.0112476 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.46176 | −0.170548 | ||||||||
\(413\) | −59.2771 | −2.91684 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.90723 | −0.388151 | ||||||||
\(416\) | −13.7318 | −0.673255 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.593943 | 0.0290507 | ||||||||
\(419\) | −15.0053 | −0.733058 | −0.366529 | − | 0.930407i | \(-0.619454\pi\) | ||||
−0.366529 | + | 0.930407i | \(0.619454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.0390 | 1.80517 | 0.902584 | − | 0.430513i | \(-0.141667\pi\) | ||||
0.902584 | + | 0.430513i | \(0.141667\pi\) | |||||||
\(422\) | 6.06064 | 0.295027 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.67804 | −0.227186 | ||||||||
\(425\) | 3.90428 | 0.189386 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.3746 | 1.76029 | ||||||||
\(428\) | 7.08985 | 0.342701 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.16908 | 0.104602 | ||||||||
\(431\) | 14.3326 | 0.690378 | 0.345189 | − | 0.938533i | \(-0.387815\pi\) | ||||
0.345189 | + | 0.938533i | \(0.387815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4669 | 0.695233 | 0.347616 | − | 0.937637i | \(-0.386991\pi\) | ||||
0.347616 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(434\) | 2.10209 | 0.100904 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.18936 | 0.296416 | ||||||||
\(437\) | −9.60619 | −0.459526 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9516 | −0.713601 | −0.356801 | − | 0.934181i | \(-0.616132\pi\) | ||||
−0.356801 | + | 0.934181i | \(0.616132\pi\) | |||||||
\(440\) | −2.08497 | −0.0993970 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.75119 | −0.225991 | ||||||||
\(443\) | 34.6483 | 1.64619 | 0.823094 | − | 0.567905i | \(-0.192246\pi\) | ||||
0.823094 | + | 0.567905i | \(0.192246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.25566 | 0.154333 | ||||||||
\(446\) | 1.73986 | 0.0823850 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.3450 | 1.19744 | ||||||||
\(449\) | 25.5553 | 1.20603 | 0.603015 | − | 0.797730i | \(-0.293966\pi\) | ||||
0.603015 | + | 0.797730i | \(0.293966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.34185 | 0.0631853 | ||||||||
\(452\) | 23.4853 | 1.10465 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.60586 | 0.216164 | ||||||||
\(455\) | −17.3497 | −0.813365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2167 | −0.898919 | −0.449459 | − | 0.893301i | \(-0.648383\pi\) | ||||
−0.449459 | + | 0.893301i | \(0.648383\pi\) | |||||||
\(458\) | −0.742248 | −0.0346830 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.4703 | 0.767934 | ||||||||
\(461\) | 11.2073 | 0.521976 | 0.260988 | − | 0.965342i | \(-0.415952\pi\) | ||||
0.260988 | + | 0.965342i | \(0.415952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7319 | −0.591703 | −0.295852 | − | 0.955234i | \(-0.595603\pi\) | ||||
−0.295852 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(464\) | −2.07332 | −0.0962516 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.53580 | 0.117469 | ||||||||
\(467\) | 32.9377 | 1.52417 | 0.762087 | − | 0.647475i | \(-0.224175\pi\) | ||||
0.762087 | + | 0.647475i | \(0.224175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.6057 | −1.55177 | ||||||||
\(470\) | −3.53478 | −0.163047 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.2546 | 0.748179 | ||||||||
\(473\) | 12.7800 | 0.587624 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.11369 | 0.0510996 | ||||||||
\(476\) | 31.9780 | 1.46571 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.58795 | −0.209848 | ||||||||
\(479\) | 22.1599 | 1.01251 | 0.506255 | − | 0.862384i | \(-0.331029\pi\) | ||||
0.506255 | + | 0.862384i | \(0.331029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.1023 | 0.962184 | ||||||||
\(482\) | 0.195800 | 0.00891845 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.0043 | 0.682015 | ||||||||
\(485\) | −1.99171 | −0.0904388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7072 | −0.711761 | −0.355881 | − | 0.934531i | \(-0.615819\pi\) | ||||
−0.355881 | + | 0.934531i | \(0.615819\pi\) | |||||||
\(488\) | −9.97442 | −0.451521 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.42940 | −0.154924 | ||||||||
\(491\) | 26.5847 | 1.19975 | 0.599874 | − | 0.800094i | \(-0.295217\pi\) | ||||
0.599874 | + | 0.800094i | \(0.295217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.33611 | −0.105213 | ||||||||
\(494\) | −1.35527 | −0.0609764 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.64431 | 0.253437 | ||||||||
\(497\) | −22.2341 | −0.997334 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.11487 | −0.0946747 | −0.0473374 | − | 0.998879i | \(-0.515074\pi\) | ||||
−0.0473374 | + | 0.998879i | \(0.515074\pi\) | |||||||
\(500\) | −1.90948 | −0.0853947 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.85287 | 0.0826976 | ||||||||
\(503\) | −9.60052 | −0.428066 | −0.214033 | − | 0.976826i | \(-0.568660\pi\) | ||||
−0.214033 | + | 0.976826i | \(0.568660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.16732 | −0.407941 | ||||||||
\(506\) | −4.60010 | −0.204499 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.0270 | 0.932921 | ||||||||
\(509\) | 3.94762 | 0.174975 | 0.0874876 | − | 0.996166i | \(-0.472116\pi\) | ||||
0.0874876 | + | 0.996166i | \(0.472116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.7672 | 0.830212 | ||||||||
\(512\) | −19.9150 | −0.880128 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.10969 | 0.0930544 | ||||||||
\(515\) | 1.81293 | 0.0798871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.8265 | −0.915948 | ||||||||
\(518\) | 6.73271 | 0.295818 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.75751 | 0.208631 | ||||||||
\(521\) | 25.3238 | 1.10946 | 0.554729 | − | 0.832031i | \(-0.312822\pi\) | ||||
0.554729 | + | 0.832031i | \(0.312822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5210 | −0.678687 | −0.339344 | − | 0.940662i | \(-0.610205\pi\) | ||||
−0.339344 | + | 0.940662i | \(0.610205\pi\) | |||||||
\(524\) | 33.5027 | 1.46357 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.85256 | 0.255184 | ||||||||
\(527\) | 6.35970 | 0.277033 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.4001 | 2.23479 | ||||||||
\(530\) | 1.19659 | 0.0519765 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.12166 | 0.395474 | ||||||||
\(533\) | −3.06185 | −0.132624 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.71297 | −0.160525 | ||||||||
\(536\) | 9.21515 | 0.398034 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.06443 | 0.132117 | ||||||||
\(539\) | −20.2056 | −0.870317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7630 | 0.505730 | 0.252865 | − | 0.967502i | \(-0.418627\pi\) | ||||
0.252865 | + | 0.967502i | \(0.418627\pi\) | |||||||
\(542\) | 2.06715 | 0.0887918 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.2547 | −0.568291 | ||||||||
\(545\) | −3.24138 | −0.138845 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.0335 | 0.771059 | 0.385529 | − | 0.922696i | \(-0.374019\pi\) | ||||
0.385529 | + | 0.922696i | \(0.374019\pi\) | |||||||
\(548\) | 0.681158 | 0.0290976 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.533311 | 0.0227404 | ||||||||
\(551\) | −0.666371 | −0.0283883 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.2930 | 2.35130 | ||||||||
\(554\) | −7.99186 | −0.339542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.84745 | 0.120759 | ||||||||
\(557\) | −9.90891 | −0.419854 | −0.209927 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209927 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.1616 | −1.23340 | ||||||||
\(560\) | −14.8631 | −0.628080 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.19793 | −0.303626 | ||||||||
\(563\) | 1.16407 | 0.0490598 | 0.0245299 | − | 0.999699i | \(-0.492191\pi\) | ||||
0.0245299 | + | 0.999699i | \(0.492191\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2993 | −0.517435 | ||||||||
\(566\) | 4.06208 | 0.170742 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.09688 | 0.255820 | ||||||||
\(569\) | 5.12125 | 0.214694 | 0.107347 | − | 0.994222i | \(-0.465764\pi\) | ||||
0.107347 | + | 0.994222i | \(0.465764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8341 | −0.620786 | −0.310393 | − | 0.950608i | \(-0.600461\pi\) | ||||
−0.310393 | + | 0.950608i | \(0.600461\pi\) | |||||||
\(572\) | 13.6909 | 0.572444 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.976885 | −0.0407744 | ||||||||
\(575\) | −8.62555 | −0.359710 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.5634 | −1.31400 | −0.657001 | − | 0.753890i | \(-0.728175\pi\) | ||||
−0.657001 | + | 0.753890i | \(0.728175\pi\) | |||||||
\(578\) | 0.528478 | 0.0219818 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.14253 | 0.0474410 | ||||||||
\(581\) | 33.9170 | 1.40712 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.05016 | 0.291988 | ||||||||
\(584\) | −5.14622 | −0.212952 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.65898 | −0.0685318 | ||||||||
\(587\) | −17.0065 | −0.701935 | −0.350967 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350967 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.81409 | 0.0747485 | ||||||||
\(590\) | −4.15774 | −0.171171 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.0779 | 0.742998 | ||||||||
\(593\) | −42.7865 | −1.75703 | −0.878517 | − | 0.477712i | \(-0.841466\pi\) | ||||
−0.878517 | + | 0.477712i | \(0.841466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.7469 | −0.686557 | ||||||||
\(596\) | −34.5601 | −1.41564 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.4966 | 0.429237 | ||||||||
\(599\) | 1.93853 | 0.0792062 | 0.0396031 | − | 0.999215i | \(-0.487391\pi\) | ||||
0.0396031 | + | 0.999215i | \(0.487391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7131 | −0.804113 | −0.402056 | − | 0.915615i | \(-0.631704\pi\) | ||||
−0.402056 | + | 0.915615i | \(0.631704\pi\) | |||||||
\(602\) | −9.30400 | −0.379203 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 40.4999 | 1.64792 | ||||||||
\(605\) | −7.85780 | −0.319465 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5487 | −0.468746 | −0.234373 | − | 0.972147i | \(-0.575304\pi\) | ||||
−0.234373 | + | 0.972147i | \(0.575304\pi\) | |||||||
\(608\) | −3.78088 | −0.153335 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.55134 | 0.103301 | ||||||||
\(611\) | 47.5222 | 1.92254 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9028 | 0.480748 | 0.240374 | − | 0.970680i | \(-0.422730\pi\) | ||||
0.240374 | + | 0.970680i | \(0.422730\pi\) | |||||||
\(614\) | −1.43426 | −0.0578819 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.94320 | 0.360332 | ||||||||
\(617\) | −28.9392 | −1.16505 | −0.582525 | − | 0.812813i | \(-0.697935\pi\) | ||||
−0.582525 | + | 0.812813i | \(0.697935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.87633 | −0.236190 | −0.118095 | − | 0.993002i | \(-0.537679\pi\) | ||||
−0.118095 | + | 0.993002i | \(0.537679\pi\) | |||||||
\(620\) | −3.11037 | −0.124915 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.27198 | 0.131194 | ||||||||
\(623\) | −13.9647 | −0.559485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.73612 | 0.149325 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4559 | 0.417236 | ||||||||
\(629\) | 20.3692 | 0.812174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2847 | 0.807522 | 0.403761 | − | 0.914864i | \(-0.367703\pi\) | ||||
0.403761 | + | 0.914864i | \(0.367703\pi\) | |||||||
\(632\) | −15.1621 | −0.603116 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.31939 | −0.131830 | ||||||||
\(635\) | −11.0119 | −0.436992 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.1055 | 1.82677 | ||||||||
\(638\) | −0.319104 | −0.0126334 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.56754 | 0.338662 | ||||||||
\(641\) | −9.62261 | −0.380070 | −0.190035 | − | 0.981777i | \(-0.560860\pi\) | ||||
−0.190035 | + | 0.981777i | \(0.560860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.53427 | −0.257686 | −0.128843 | − | 0.991665i | \(-0.541126\pi\) | ||||
−0.128843 | + | 0.991665i | \(0.541126\pi\) | |||||||
\(644\) | −70.6474 | −2.78390 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.30818 | −0.0514698 | ||||||||
\(647\) | 4.88147 | 0.191910 | 0.0959551 | − | 0.995386i | \(-0.469409\pi\) | ||||
0.0959551 | + | 0.995386i | \(0.469409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4969 | −0.961587 | ||||||||
\(650\) | −1.21692 | −0.0477314 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 34.3456 | 1.34508 | ||||||||
\(653\) | −6.27970 | −0.245744 | −0.122872 | − | 0.992423i | \(-0.539210\pi\) | ||||
−0.122872 | + | 0.992423i | \(0.539210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.5454 | −0.685556 | ||||||||
\(656\) | −2.62302 | −0.102412 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.1620 | 0.591075 | ||||||||
\(659\) | −7.21880 | −0.281205 | −0.140602 | − | 0.990066i | \(-0.544904\pi\) | ||||
−0.140602 | + | 0.990066i | \(0.544904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6944 | 1.69951 | 0.849757 | − | 0.527175i | \(-0.176749\pi\) | ||||
0.849757 | + | 0.527175i | \(0.176749\pi\) | |||||||
\(662\) | −0.609541 | −0.0236905 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.30052 | −0.360930 | ||||||||
\(665\) | −4.77703 | −0.185245 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.16105 | 0.199837 | ||||||||
\(668\) | 38.0708 | 1.47300 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.35713 | −0.0910638 | ||||||||
\(671\) | 15.0322 | 0.580311 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4872 | 1.36793 | 0.683965 | − | 0.729514i | \(-0.260254\pi\) | ||||
0.683965 | + | 0.729514i | \(0.260254\pi\) | |||||||
\(674\) | 4.62723 | 0.178234 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.41672 | −0.246797 | ||||||||
\(677\) | −14.3532 | −0.551637 | −0.275818 | − | 0.961210i | \(-0.588949\pi\) | ||||
−0.275818 | + | 0.961210i | \(0.588949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.54317 | 0.327857 | ||||||||
\(680\) | 4.59223 | 0.176104 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.868712 | 0.0332647 | ||||||||
\(683\) | −14.5737 | −0.557646 | −0.278823 | − | 0.960343i | \(-0.589944\pi\) | ||||
−0.278823 | + | 0.960343i | \(0.589944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.356723 | −0.0136297 | ||||||||
\(686\) | 5.67649 | 0.216729 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.9821 | −0.952433 | ||||||||
\(689\) | −16.0872 | −0.612872 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3677 | −1.04112 | −0.520558 | − | 0.853826i | \(-0.674276\pi\) | ||||
−0.520558 | + | 0.853826i | \(0.674276\pi\) | |||||||
\(692\) | 12.9190 | 0.491108 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.348750 | 0.0132384 | ||||||||
\(695\) | −1.49122 | −0.0565650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.95548 | −0.111947 | ||||||||
\(698\) | 1.55357 | 0.0588037 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.19048 | 0.309571 | ||||||||
\(701\) | 30.5667 | 1.15449 | 0.577243 | − | 0.816572i | \(-0.304128\pi\) | ||||
0.577243 | + | 0.816572i | \(0.304128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.81029 | 0.219139 | ||||||||
\(704\) | 10.4741 | 0.394757 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.65316 | −0.137489 | ||||||||
\(707\) | 39.3220 | 1.47886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.8107 | 0.556227 | 0.278113 | − | 0.960548i | \(-0.410291\pi\) | ||||
0.278113 | + | 0.960548i | \(0.410291\pi\) | |||||||
\(710\) | −1.55951 | −0.0585274 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.82932 | 0.143510 | ||||||||
\(713\) | −14.0502 | −0.526184 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.16993 | −0.268140 | ||||||||
\(716\) | 18.0250 | 0.673625 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.67588 | 0.0998631 | ||||||||
\(719\) | −5.24852 | −0.195737 | −0.0978684 | − | 0.995199i | \(-0.531202\pi\) | ||||
−0.0978684 | + | 0.995199i | \(0.531202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.77632 | −0.289605 | ||||||||
\(722\) | 5.34316 | 0.198852 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.16231 | −0.0803615 | ||||||||
\(725\) | −0.598345 | −0.0222220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.4670 | 1.76045 | 0.880226 | − | 0.474555i | \(-0.157391\pi\) | ||||
0.880226 | + | 0.474555i | \(0.157391\pi\) | |||||||
\(728\) | −20.4067 | −0.756324 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.31634 | 0.0487200 | ||||||||
\(731\) | −28.1485 | −1.04111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.7927 | −1.43284 | −0.716421 | − | 0.697668i | \(-0.754221\pi\) | ||||
−0.716421 | + | 0.697668i | \(0.754221\pi\) | |||||||
\(734\) | 8.31202 | 0.306802 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.2830 | 1.07938 | ||||||||
\(737\) | −13.8879 | −0.511568 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4247 | −0.567407 | −0.283704 | − | 0.958912i | \(-0.591563\pi\) | ||||
−0.283704 | + | 0.958912i | \(0.591563\pi\) | |||||||
\(740\) | −9.96206 | −0.366213 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.13261 | −0.188424 | ||||||||
\(743\) | 41.1249 | 1.50873 | 0.754364 | − | 0.656457i | \(-0.227946\pi\) | ||||
0.754364 | + | 0.656457i | \(0.227946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0992 | 0.663103 | ||||||||
\(746\) | 9.28048 | 0.339783 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.2152 | 0.483197 | ||||||||
\(749\) | 15.9263 | 0.581934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.4762 | −1.87839 | −0.939196 | − | 0.343380i | \(-0.888428\pi\) | ||||
−0.939196 | + | 0.343380i | \(0.888428\pi\) | |||||||
\(752\) | 40.7112 | 1.48459 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.728135 | 0.0265171 | ||||||||
\(755\) | −21.2099 | −0.771906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.7855 | 1.33699 | 0.668497 | − | 0.743715i | \(-0.266938\pi\) | ||||
0.668497 | + | 0.743715i | \(0.266938\pi\) | |||||||
\(758\) | 6.32463 | 0.229721 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.30993 | 0.0475160 | ||||||||
\(761\) | 23.7062 | 0.859351 | 0.429675 | − | 0.902983i | \(-0.358628\pi\) | ||||
0.429675 | + | 0.902983i | \(0.358628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9035 | 0.503339 | ||||||||
\(764\) | −45.1098 | −1.63201 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.47607 | −0.233990 | ||||||||
\(767\) | 55.8974 | 2.01834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0301 | −0.397756 | −0.198878 | − | 0.980024i | \(-0.563730\pi\) | ||||
−0.198878 | + | 0.980024i | \(0.563730\pi\) | |||||||
\(770\) | −2.28757 | −0.0824382 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.18609 | 0.186651 | ||||||||
\(773\) | −44.2598 | −1.59192 | −0.795958 | − | 0.605352i | \(-0.793032\pi\) | ||||
−0.795958 | + | 0.605352i | \(0.793032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.62890 | 0.0585120 | ||||||||
\(776\) | −2.34265 | −0.0840964 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.03532 | 0.144673 | ||||||||
\(779\) | −0.843046 | −0.0302053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.18846 | −0.328789 | ||||||||
\(782\) | 10.1319 | 0.362316 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 39.4976 | 1.41063 | ||||||||
\(785\) | −5.47578 | −0.195439 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.1437 | −1.46662 | −0.733308 | − | 0.679897i | \(-0.762024\pi\) | ||||
−0.733308 | + | 0.679897i | \(0.762024\pi\) | |||||||
\(788\) | −27.2566 | −0.970975 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.87828 | 0.137983 | ||||||||
\(791\) | 52.7562 | 1.87579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.3007 | −1.21805 | ||||||||
\(794\) | 5.11640 | 0.181574 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40.6153 | −1.43957 | ||||||||
\(797\) | −23.3683 | −0.827748 | −0.413874 | − | 0.910334i | \(-0.635825\pi\) | ||||
−0.413874 | + | 0.910334i | \(0.635825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.8712 | 1.62281 | ||||||||
\(800\) | −3.39491 | −0.120028 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.87728 | 0.0662890 | ||||||||
\(803\) | 7.75574 | 0.273694 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.9982 | 1.30401 | ||||||||
\(806\) | −1.98224 | −0.0698214 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.7826 | −0.379332 | ||||||||
\(809\) | 16.4420 | 0.578070 | 0.289035 | − | 0.957319i | \(-0.406666\pi\) | ||||
0.289035 | + | 0.957319i | \(0.406666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.2346 | 1.72886 | 0.864430 | − | 0.502753i | \(-0.167679\pi\) | ||||
0.864430 | + | 0.502753i | \(0.167679\pi\) | |||||||
\(812\) | −4.90073 | −0.171982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.78236 | 0.0975217 | ||||||||
\(815\) | −17.9869 | −0.630052 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.02930 | −0.280910 | ||||||||
\(818\) | −2.88833 | −0.100988 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.44545 | 0.0504773 | ||||||||
\(821\) | 2.76238 | 0.0964077 | 0.0482039 | − | 0.998838i | \(-0.484650\pi\) | ||||
0.0482039 | + | 0.998838i | \(0.484650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.9929 | −1.15006 | −0.575029 | − | 0.818133i | \(-0.695009\pi\) | ||||
−0.575029 | + | 0.818133i | \(0.695009\pi\) | |||||||
\(824\) | 2.13237 | 0.0742847 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8341 | 0.620526 | ||||||||
\(827\) | 54.7826 | 1.90498 | 0.952489 | − | 0.304574i | \(-0.0985142\pi\) | ||||
0.952489 | + | 0.304574i | \(0.0985142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.0692 | 1.77370 | 0.886852 | − | 0.462053i | \(-0.152887\pi\) | ||||
0.886852 | + | 0.462053i | \(0.152887\pi\) | |||||||
\(830\) | 2.37896 | 0.0825750 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.9000 | −0.828582 | ||||||||
\(833\) | 44.5037 | 1.54196 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.9377 | −0.689974 | ||||||||
\(836\) | 3.76962 | 0.130375 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.51449 | 0.155950 | ||||||||
\(839\) | 41.2173 | 1.42298 | 0.711490 | − | 0.702697i | \(-0.248021\pi\) | ||||
0.711490 | + | 0.702697i | \(0.248021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6420 | −0.987655 | ||||||||
\(842\) | −11.1435 | −0.384031 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.4655 | 1.32404 | ||||||||
\(845\) | 3.36045 | 0.115603 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.7050 | 1.15812 | ||||||||
\(848\) | −13.7815 | −0.473259 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.17464 | −0.0402898 | ||||||||
\(851\) | −45.0008 | −1.54261 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6422 | 0.706776 | 0.353388 | − | 0.935477i | \(-0.385029\pi\) | ||||
0.353388 | + | 0.935477i | \(0.385029\pi\) | |||||||
\(854\) | −10.9436 | −0.374483 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.36720 | −0.149268 | ||||||||
\(857\) | −36.9400 | −1.26185 | −0.630923 | − | 0.775845i | \(-0.717324\pi\) | ||||
−0.630923 | + | 0.775845i | \(0.717324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.6981 | 0.808570 | 0.404285 | − | 0.914633i | \(-0.367520\pi\) | ||||
0.404285 | + | 0.914633i | \(0.367520\pi\) | |||||||
\(860\) | 13.7667 | 0.469440 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.31210 | −0.146871 | ||||||||
\(863\) | −36.6147 | −1.24638 | −0.623189 | − | 0.782072i | \(-0.714163\pi\) | ||||
−0.623189 | + | 0.782072i | \(0.714163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.76573 | −0.230042 | ||||||||
\(866\) | −4.35248 | −0.147903 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.3415 | 0.452840 | ||||||||
\(869\) | 22.8504 | 0.775147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6897 | 1.07376 | ||||||||
\(872\) | −3.81252 | −0.129108 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.89011 | 0.0977594 | ||||||||
\(875\) | −4.28937 | −0.145007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.2122 | 0.817587 | 0.408793 | − | 0.912627i | \(-0.365950\pi\) | ||||
0.408793 | + | 0.912627i | \(0.365950\pi\) | |||||||
\(878\) | 4.49832 | 0.151811 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.14232 | −0.207058 | ||||||||
\(881\) | −26.9469 | −0.907863 | −0.453931 | − | 0.891037i | \(-0.649979\pi\) | ||||
−0.453931 | + | 0.891037i | \(0.649979\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.989181 | 0.0332886 | 0.0166443 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166443 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(884\) | −30.1547 | −1.01421 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.4242 | −0.350209 | ||||||||
\(887\) | −24.8187 | −0.833331 | −0.416665 | − | 0.909060i | \(-0.636801\pi\) | ||||
−0.416665 | + | 0.909060i | \(0.636801\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.2339 | 1.58418 | ||||||||
\(890\) | −0.979495 | −0.0328328 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.0425 | 0.369731 | ||||||||
\(893\) | 13.0847 | 0.437862 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.43971 | −0.315535 | ||||||||
\(896\) | −36.7493 | −1.22771 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.68854 | −0.256570 | ||||||||
\(899\) | −0.974646 | −0.0325063 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5283 | −0.517322 | ||||||||
\(902\) | −0.403708 | −0.0134420 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.4665 | −0.481147 | ||||||||
\(905\) | 1.13240 | 0.0376424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.27950 | 0.108894 | 0.0544470 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544470 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(908\) | 29.2324 | 0.970110 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.21980 | 0.173035 | ||||||||
\(911\) | 39.4133 | 1.30582 | 0.652910 | − | 0.757435i | \(-0.273548\pi\) | ||||
0.652910 | + | 0.757435i | \(0.273548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0166 | 0.463881 | ||||||||
\(914\) | 5.78151 | 0.191236 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.71088 | −0.155652 | ||||||||
\(917\) | 75.2587 | 2.48526 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.02247 | −0.297624 | −0.148812 | − | 0.988866i | \(-0.547545\pi\) | ||||
−0.148812 | + | 0.988866i | \(0.547545\pi\) | |||||||
\(920\) | −10.1454 | −0.334484 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.37182 | −0.111045 | ||||||||
\(923\) | 20.9664 | 0.690116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21715 | 0.171539 | ||||||||
\(926\) | 3.83052 | 0.125879 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.03133 | 0.0666816 | ||||||||
\(929\) | 24.9112 | 0.817311 | 0.408655 | − | 0.912689i | \(-0.365998\pi\) | ||||
0.408655 | + | 0.912689i | \(0.365998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.6946 | 0.416049 | ||||||||
\(932\) | 16.0941 | 0.527181 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.90959 | −0.324252 | ||||||||
\(935\) | −6.92084 | −0.226336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4029 | −0.829876 | −0.414938 | − | 0.909850i | \(-0.636197\pi\) | ||||
−0.414938 | + | 0.909850i | \(0.636197\pi\) | |||||||
\(938\) | 10.1106 | 0.330122 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −22.4344 | −0.731730 | ||||||||
\(941\) | −24.2416 | −0.790252 | −0.395126 | − | 0.918627i | \(-0.629299\pi\) | ||||
−0.395126 | + | 0.918627i | \(0.629299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.52941 | 0.212627 | ||||||||
\(944\) | 47.8861 | 1.55856 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.84497 | −0.125011 | ||||||||
\(947\) | −10.9166 | −0.354741 | −0.177371 | − | 0.984144i | \(-0.556759\pi\) | ||||
−0.177371 | + | 0.984144i | \(0.556759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.6972 | −0.574474 | ||||||||
\(950\) | −0.335064 | −0.0108709 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.6978 | −0.638409 | ||||||||
\(953\) | 14.5735 | 0.472081 | 0.236040 | − | 0.971743i | \(-0.424150\pi\) | ||||
0.236040 | + | 0.971743i | \(0.424150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.6241 | 0.764457 | ||||||||
\(956\) | −29.1187 | −0.941766 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.66700 | −0.215401 | ||||||||
\(959\) | 1.53012 | 0.0494101 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3467 | −0.914409 | ||||||||
\(962\) | −6.34883 | −0.204695 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.24270 | 0.0400246 | ||||||||
\(965\) | −2.71596 | −0.0874300 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.9194 | −1.54098 | −0.770492 | − | 0.637450i | \(-0.779989\pi\) | ||||
−0.770492 | + | 0.637450i | \(0.779989\pi\) | |||||||
\(968\) | −9.24237 | −0.297061 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.599223 | 0.0192399 | ||||||||
\(971\) | −10.0839 | −0.323608 | −0.161804 | − | 0.986823i | \(-0.551731\pi\) | ||||
−0.161804 | + | 0.986823i | \(0.551731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.39638 | 0.205058 | ||||||||
\(974\) | 4.72565 | 0.151420 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.3846 | −0.940579 | ||||||||
\(977\) | −32.2259 | −1.03100 | −0.515499 | − | 0.856890i | \(-0.672394\pi\) | ||||
−0.515499 | + | 0.856890i | \(0.672394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.77107 | −0.184444 | ||||||||
\(980\) | −21.7656 | −0.695277 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.99823 | −0.255234 | ||||||||
\(983\) | −2.53026 | −0.0807029 | −0.0403514 | − | 0.999186i | \(-0.512848\pi\) | ||||
−0.0403514 | + | 0.999186i | \(0.512848\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2743 | 0.454817 | ||||||||
\(986\) | 0.702839 | 0.0223830 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.60158 | −0.273653 | ||||||||
\(989\) | 62.1870 | 1.97743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.6978 | −1.61047 | −0.805234 | − | 0.592957i | \(-0.797960\pi\) | ||||
−0.805234 | + | 0.592957i | \(0.797960\pi\) | |||||||
\(992\) | −5.52999 | −0.175577 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.68932 | 0.212172 | ||||||||
\(995\) | 21.2703 | 0.674313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9724 | 0.442509 | 0.221254 | − | 0.975216i | \(-0.428985\pi\) | ||||
0.221254 | + | 0.975216i | \(0.428985\pi\) | |||||||
\(998\) | 0.636279 | 0.0201411 | ||||||||
\(999\) | 0 | 0 |
(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 | 3645.2.a.g.1.7 | 15 | ||
3.2 | odd | 2 | 3645.2.a.h.1.9 | 15 | |||
27.2 | odd | 18 | 135.2.k.a.31.3 | ✓ | 30 | ||
27.13 | even | 9 | 405.2.k.a.181.3 | 30 | |||
27.14 | odd | 18 | 135.2.k.a.61.3 | yes | 30 | ||
27.25 | even | 9 | 405.2.k.a.226.3 | 30 | |||
135.2 | even | 36 | 675.2.u.c.274.6 | 60 | |||
135.14 | odd | 18 | 675.2.l.d.601.3 | 30 | |||
135.29 | odd | 18 | 675.2.l.d.301.3 | 30 | |||
135.68 | even | 36 | 675.2.u.c.574.6 | 60 | |||
135.83 | even | 36 | 675.2.u.c.274.5 | 60 | |||
135.122 | even | 36 | 675.2.u.c.574.5 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.k.a.31.3 | ✓ | 30 | 27.2 | odd | 18 | ||
135.2.k.a.61.3 | yes | 30 | 27.14 | odd | 18 | ||
405.2.k.a.181.3 | 30 | 27.13 | even | 9 | |||
405.2.k.a.226.3 | 30 | 27.25 | even | 9 | |||
675.2.l.d.301.3 | 30 | 135.29 | odd | 18 | |||
675.2.l.d.601.3 | 30 | 135.14 | odd | 18 | |||
675.2.u.c.274.5 | 60 | 135.83 | even | 36 | |||
675.2.u.c.274.6 | 60 | 135.2 | even | 36 | |||
675.2.u.c.574.5 | 60 | 135.122 | even | 36 | |||
675.2.u.c.574.6 | 60 | 135.68 | even | 36 | |||
3645.2.a.g.1.7 | 15 | 1.1 | even | 1 | trivial | ||
3645.2.a.h.1.9 | 15 | 3.2 | odd | 2 |