Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,2,Mod(1,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.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: | \(15.3712023891\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.311108 | −0.219986 | −0.109993 | − | 0.993932i | \(-0.535083\pi\) | ||||
−0.109993 | + | 0.993932i | \(0.535083\pi\) | |||||||
\(3\) | 2.21432 | 1.27844 | 0.639219 | − | 0.769025i | \(-0.279258\pi\) | ||||
0.639219 | + | 0.769025i | \(0.279258\pi\) | |||||||
\(4\) | −1.90321 | −0.951606 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.688892 | −0.281239 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.21432 | 0.429327 | ||||||||
\(9\) | 1.90321 | 0.634404 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.21432 | −1.21657 | ||||||||
\(13\) | 2.21432 | 0.614142 | 0.307071 | − | 0.951687i | \(-0.400651\pi\) | ||||
0.307071 | + | 0.951687i | \(0.400651\pi\) | |||||||
\(14\) | 0.311108 | 0.0831471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.42864 | 0.857160 | ||||||||
\(17\) | −4.21432 | −1.02212 | −0.511061 | − | 0.859544i | \(-0.670748\pi\) | ||||
−0.511061 | + | 0.859544i | \(0.670748\pi\) | |||||||
\(18\) | −0.592104 | −0.139560 | ||||||||
\(19\) | 7.80642 | 1.79092 | 0.895458 | − | 0.445146i | \(-0.146848\pi\) | ||||
0.895458 | + | 0.445146i | \(0.146848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.21432 | −0.483204 | ||||||||
\(22\) | −0.311108 | −0.0663284 | ||||||||
\(23\) | −2.90321 | −0.605362 | −0.302681 | − | 0.953092i | \(-0.597882\pi\) | ||||
−0.302681 | + | 0.953092i | \(0.597882\pi\) | |||||||
\(24\) | 2.68889 | 0.548868 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.688892 | −0.135103 | ||||||||
\(27\) | −2.42864 | −0.467392 | ||||||||
\(28\) | 1.90321 | 0.359673 | ||||||||
\(29\) | 0.755569 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.11753 | 1.27835 | 0.639173 | − | 0.769063i | \(-0.279277\pi\) | ||||
0.639173 | + | 0.769063i | \(0.279277\pi\) | |||||||
\(32\) | −3.49532 | −0.617890 | ||||||||
\(33\) | 2.21432 | 0.385464 | ||||||||
\(34\) | 1.31111 | 0.224853 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.62222 | −0.603703 | ||||||||
\(37\) | 6.28100 | 1.03259 | 0.516295 | − | 0.856411i | \(-0.327311\pi\) | ||||
0.516295 | + | 0.856411i | \(0.327311\pi\) | |||||||
\(38\) | −2.42864 | −0.393977 | ||||||||
\(39\) | 4.90321 | 0.785142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.54617 | −0.866166 | −0.433083 | − | 0.901354i | \(-0.642574\pi\) | ||||
−0.433083 | + | 0.901354i | \(0.642574\pi\) | |||||||
\(42\) | 0.688892 | 0.106298 | ||||||||
\(43\) | 4.14764 | 0.632510 | 0.316255 | − | 0.948674i | \(-0.397575\pi\) | ||||
0.316255 | + | 0.948674i | \(0.397575\pi\) | |||||||
\(44\) | −1.90321 | −0.286920 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.903212 | 0.133171 | ||||||||
\(47\) | −1.03011 | −0.150257 | −0.0751286 | − | 0.997174i | \(-0.523937\pi\) | ||||
−0.0751286 | + | 0.997174i | \(0.523937\pi\) | |||||||
\(48\) | 7.59210 | 1.09583 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.33185 | −1.30672 | ||||||||
\(52\) | −4.21432 | −0.584421 | ||||||||
\(53\) | 6.57628 | 0.903322 | 0.451661 | − | 0.892190i | \(-0.350832\pi\) | ||||
0.451661 | + | 0.892190i | \(0.350832\pi\) | |||||||
\(54\) | 0.755569 | 0.102820 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.21432 | −0.162270 | ||||||||
\(57\) | 17.2859 | 2.28958 | ||||||||
\(58\) | −0.235063 | −0.0308653 | ||||||||
\(59\) | 2.68889 | 0.350064 | 0.175032 | − | 0.984563i | \(-0.443997\pi\) | ||||
0.175032 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.79060 | 1.12552 | 0.562761 | − | 0.826620i | \(-0.309739\pi\) | ||||
0.562761 | + | 0.826620i | \(0.309739\pi\) | |||||||
\(62\) | −2.21432 | −0.281219 | ||||||||
\(63\) | −1.90321 | −0.239782 | ||||||||
\(64\) | −5.76986 | −0.721232 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.688892 | −0.0847968 | ||||||||
\(67\) | −1.52543 | −0.186361 | −0.0931803 | − | 0.995649i | \(-0.529703\pi\) | ||||
−0.0931803 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(68\) | 8.02074 | 0.972658 | ||||||||
\(69\) | −6.42864 | −0.773917 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.61285 | 0.903479 | 0.451739 | − | 0.892150i | \(-0.350804\pi\) | ||||
0.451739 | + | 0.892150i | \(0.350804\pi\) | |||||||
\(72\) | 2.31111 | 0.272367 | ||||||||
\(73\) | 12.2143 | 1.42958 | 0.714789 | − | 0.699340i | \(-0.246523\pi\) | ||||
0.714789 | + | 0.699340i | \(0.246523\pi\) | |||||||
\(74\) | −1.95407 | −0.227156 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.8573 | −1.70425 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −1.52543 | −0.172721 | ||||||||
\(79\) | 3.52543 | 0.396642 | 0.198321 | − | 0.980137i | \(-0.436451\pi\) | ||||
0.198321 | + | 0.980137i | \(0.436451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0874 | −1.23194 | ||||||||
\(82\) | 1.72546 | 0.190545 | ||||||||
\(83\) | 2.13335 | 0.234166 | 0.117083 | − | 0.993122i | \(-0.462646\pi\) | ||||
0.117083 | + | 0.993122i | \(0.462646\pi\) | |||||||
\(84\) | 4.21432 | 0.459820 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.29036 | −0.139144 | ||||||||
\(87\) | 1.67307 | 0.179372 | ||||||||
\(88\) | 1.21432 | 0.129447 | ||||||||
\(89\) | 17.2859 | 1.83230 | 0.916152 | − | 0.400831i | \(-0.131279\pi\) | ||||
0.916152 | + | 0.400831i | \(0.131279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.21432 | −0.232124 | ||||||||
\(92\) | 5.52543 | 0.576066 | ||||||||
\(93\) | 15.7605 | 1.63429 | ||||||||
\(94\) | 0.320476 | 0.0330545 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.73975 | −0.789935 | ||||||||
\(97\) | −5.28592 | −0.536704 | −0.268352 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268352 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(98\) | −0.311108 | −0.0314266 | ||||||||
\(99\) | 1.90321 | 0.191280 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.1082 | 1.80183 | 0.900915 | − | 0.433996i | \(-0.142897\pi\) | ||||
0.900915 | + | 0.433996i | \(0.142897\pi\) | |||||||
\(102\) | 2.90321 | 0.287461 | ||||||||
\(103\) | −16.7447 | −1.64990 | −0.824951 | − | 0.565205i | \(-0.808797\pi\) | ||||
−0.824951 | + | 0.565205i | \(0.808797\pi\) | |||||||
\(104\) | 2.68889 | 0.263668 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.04593 | −0.198719 | ||||||||
\(107\) | 0.561993 | 0.0543299 | 0.0271649 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271649 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(108\) | 4.62222 | 0.444773 | ||||||||
\(109\) | −3.93978 | −0.377362 | −0.188681 | − | 0.982038i | \(-0.560421\pi\) | ||||
−0.188681 | + | 0.982038i | \(0.560421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.9081 | 1.32010 | ||||||||
\(112\) | −3.42864 | −0.323976 | ||||||||
\(113\) | −11.2859 | −1.06169 | −0.530845 | − | 0.847469i | \(-0.678125\pi\) | ||||
−0.530845 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(114\) | −5.37778 | −0.503676 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.43801 | −0.133516 | ||||||||
\(117\) | 4.21432 | 0.389614 | ||||||||
\(118\) | −0.836535 | −0.0770093 | ||||||||
\(119\) | 4.21432 | 0.386326 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.73483 | −0.247599 | ||||||||
\(123\) | −12.2810 | −1.10734 | ||||||||
\(124\) | −13.5462 | −1.21648 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.592104 | 0.0527488 | ||||||||
\(127\) | 12.9906 | 1.15273 | 0.576366 | − | 0.817192i | \(-0.304470\pi\) | ||||
0.576366 | + | 0.817192i | \(0.304470\pi\) | |||||||
\(128\) | 8.78568 | 0.776552 | ||||||||
\(129\) | 9.18421 | 0.808624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.47013 | −0.740038 | −0.370019 | − | 0.929024i | \(-0.620649\pi\) | ||||
−0.370019 | + | 0.929024i | \(0.620649\pi\) | |||||||
\(132\) | −4.21432 | −0.366809 | ||||||||
\(133\) | −7.80642 | −0.676903 | ||||||||
\(134\) | 0.474572 | 0.0409968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.11753 | −0.438825 | ||||||||
\(137\) | 11.1383 | 0.951607 | 0.475804 | − | 0.879552i | \(-0.342157\pi\) | ||||
0.475804 | + | 0.879552i | \(0.342157\pi\) | |||||||
\(138\) | 2.00000 | 0.170251 | ||||||||
\(139\) | −8.04149 | −0.682070 | −0.341035 | − | 0.940051i | \(-0.610777\pi\) | ||||
−0.341035 | + | 0.940051i | \(0.610777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.28100 | −0.192095 | ||||||||
\(142\) | −2.36842 | −0.198753 | ||||||||
\(143\) | 2.21432 | 0.185171 | ||||||||
\(144\) | 6.52543 | 0.543786 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.79997 | −0.314488 | ||||||||
\(147\) | 2.21432 | 0.182634 | ||||||||
\(148\) | −11.9541 | −0.982618 | ||||||||
\(149\) | −6.13335 | −0.502464 | −0.251232 | − | 0.967927i | \(-0.580836\pi\) | ||||
−0.251232 | + | 0.967927i | \(0.580836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1476 | 0.825803 | 0.412902 | − | 0.910776i | \(-0.364515\pi\) | ||||
0.412902 | + | 0.910776i | \(0.364515\pi\) | |||||||
\(152\) | 9.47949 | 0.768889 | ||||||||
\(153\) | −8.02074 | −0.648439 | ||||||||
\(154\) | 0.311108 | 0.0250698 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.33185 | −0.747146 | ||||||||
\(157\) | 21.7146 | 1.73301 | 0.866505 | − | 0.499168i | \(-0.166361\pi\) | ||||
0.866505 | + | 0.499168i | \(0.166361\pi\) | |||||||
\(158\) | −1.09679 | −0.0872558 | ||||||||
\(159\) | 14.5620 | 1.15484 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.90321 | 0.228805 | ||||||||
\(162\) | 3.44938 | 0.271009 | ||||||||
\(163\) | 8.01429 | 0.627728 | 0.313864 | − | 0.949468i | \(-0.398376\pi\) | ||||
0.313864 | + | 0.949468i | \(0.398376\pi\) | |||||||
\(164\) | 10.5555 | 0.824249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.663703 | −0.0515133 | ||||||||
\(167\) | −15.1240 | −1.17033 | −0.585165 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585165 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(168\) | −2.68889 | −0.207453 | ||||||||
\(169\) | −8.09679 | −0.622830 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8573 | 1.13616 | ||||||||
\(172\) | −7.89384 | −0.601900 | ||||||||
\(173\) | −19.6938 | −1.49729 | −0.748646 | − | 0.662969i | \(-0.769296\pi\) | ||||
−0.748646 | + | 0.662969i | \(0.769296\pi\) | |||||||
\(174\) | −0.520505 | −0.0394594 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.42864 | 0.258443 | ||||||||
\(177\) | 5.95407 | 0.447535 | ||||||||
\(178\) | −5.37778 | −0.403082 | ||||||||
\(179\) | 5.53972 | 0.414058 | 0.207029 | − | 0.978335i | \(-0.433621\pi\) | ||||
0.207029 | + | 0.978335i | \(0.433621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9081 | −1.47976 | −0.739880 | − | 0.672739i | \(-0.765118\pi\) | ||||
−0.739880 | + | 0.672739i | \(0.765118\pi\) | |||||||
\(182\) | 0.688892 | 0.0510641 | ||||||||
\(183\) | 19.4652 | 1.43891 | ||||||||
\(184\) | −3.52543 | −0.259898 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.90321 | −0.359521 | ||||||||
\(187\) | −4.21432 | −0.308182 | ||||||||
\(188\) | 1.96052 | 0.142986 | ||||||||
\(189\) | 2.42864 | 0.176658 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8988 | −1.51218 | −0.756091 | − | 0.654467i | \(-0.772893\pi\) | ||||
−0.756091 | + | 0.654467i | \(0.772893\pi\) | |||||||
\(192\) | −12.7763 | −0.922051 | ||||||||
\(193\) | 13.6271 | 0.980903 | 0.490451 | − | 0.871469i | \(-0.336832\pi\) | ||||
0.490451 | + | 0.871469i | \(0.336832\pi\) | |||||||
\(194\) | 1.64449 | 0.118068 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.90321 | −0.135944 | ||||||||
\(197\) | −15.7003 | −1.11860 | −0.559299 | − | 0.828966i | \(-0.688930\pi\) | ||||
−0.559299 | + | 0.828966i | \(0.688930\pi\) | |||||||
\(198\) | −0.592104 | −0.0420790 | ||||||||
\(199\) | −23.9146 | −1.69526 | −0.847630 | − | 0.530588i | \(-0.821971\pi\) | ||||
−0.847630 | + | 0.530588i | \(0.821971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.37778 | −0.238251 | ||||||||
\(202\) | −5.63359 | −0.396378 | ||||||||
\(203\) | −0.755569 | −0.0530305 | ||||||||
\(204\) | 17.7605 | 1.24348 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.20940 | 0.362956 | ||||||||
\(207\) | −5.52543 | −0.384044 | ||||||||
\(208\) | 7.59210 | 0.526418 | ||||||||
\(209\) | 7.80642 | 0.539982 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4795 | 0.790281 | 0.395141 | − | 0.918621i | \(-0.370696\pi\) | ||||
0.395141 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(212\) | −12.5161 | −0.859607 | ||||||||
\(213\) | 16.8573 | 1.15504 | ||||||||
\(214\) | −0.174840 | −0.0119518 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.94914 | −0.200664 | ||||||||
\(217\) | −7.11753 | −0.483170 | ||||||||
\(218\) | 1.22570 | 0.0830146 | ||||||||
\(219\) | 27.0464 | 1.82763 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.33185 | −0.627728 | ||||||||
\(222\) | −4.32693 | −0.290404 | ||||||||
\(223\) | −19.7669 | −1.32369 | −0.661846 | − | 0.749640i | \(-0.730227\pi\) | ||||
−0.661846 | + | 0.749640i | \(0.730227\pi\) | |||||||
\(224\) | 3.49532 | 0.233541 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.51114 | 0.233557 | ||||||||
\(227\) | −3.61285 | −0.239793 | −0.119897 | − | 0.992786i | \(-0.538256\pi\) | ||||
−0.119897 | + | 0.992786i | \(0.538256\pi\) | |||||||
\(228\) | −32.8988 | −2.17877 | ||||||||
\(229\) | −18.7239 | −1.23731 | −0.618656 | − | 0.785662i | \(-0.712322\pi\) | ||||
−0.618656 | + | 0.785662i | \(0.712322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.21432 | −0.145692 | ||||||||
\(232\) | 0.917502 | 0.0602370 | ||||||||
\(233\) | −7.00492 | −0.458908 | −0.229454 | − | 0.973320i | \(-0.573694\pi\) | ||||
−0.229454 | + | 0.973320i | \(0.573694\pi\) | |||||||
\(234\) | −1.31111 | −0.0857098 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.11753 | −0.333123 | ||||||||
\(237\) | 7.80642 | 0.507082 | ||||||||
\(238\) | −1.31111 | −0.0849865 | ||||||||
\(239\) | 20.9906 | 1.35777 | 0.678886 | − | 0.734244i | \(-0.262463\pi\) | ||||
0.678886 | + | 0.734244i | \(0.262463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7491 | 0.692411 | 0.346206 | − | 0.938159i | \(-0.387470\pi\) | ||||
0.346206 | + | 0.938159i | \(0.387470\pi\) | |||||||
\(242\) | −0.311108 | −0.0199988 | ||||||||
\(243\) | −17.2652 | −1.10756 | ||||||||
\(244\) | −16.7304 | −1.07105 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.82071 | 0.243600 | ||||||||
\(247\) | 17.2859 | 1.09988 | ||||||||
\(248\) | 8.64296 | 0.548828 | ||||||||
\(249\) | 4.72393 | 0.299367 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.30174 | −0.397762 | −0.198881 | − | 0.980024i | \(-0.563731\pi\) | ||||
−0.198881 | + | 0.980024i | \(0.563731\pi\) | |||||||
\(252\) | 3.62222 | 0.228178 | ||||||||
\(253\) | −2.90321 | −0.182523 | ||||||||
\(254\) | −4.04149 | −0.253585 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.80642 | 0.550401 | ||||||||
\(257\) | −26.2766 | −1.63909 | −0.819543 | − | 0.573018i | \(-0.805773\pi\) | ||||
−0.819543 | + | 0.573018i | \(0.805773\pi\) | |||||||
\(258\) | −2.85728 | −0.177886 | ||||||||
\(259\) | −6.28100 | −0.390282 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.43801 | 0.0890104 | ||||||||
\(262\) | 2.63512 | 0.162798 | ||||||||
\(263\) | −12.7239 | −0.784591 | −0.392295 | − | 0.919839i | \(-0.628319\pi\) | ||||
−0.392295 | + | 0.919839i | \(0.628319\pi\) | |||||||
\(264\) | 2.68889 | 0.165490 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.42864 | 0.148909 | ||||||||
\(267\) | 38.2766 | 2.34249 | ||||||||
\(268\) | 2.90321 | 0.177342 | ||||||||
\(269\) | −14.1017 | −0.859796 | −0.429898 | − | 0.902877i | \(-0.641451\pi\) | ||||
−0.429898 | + | 0.902877i | \(0.641451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.28592 | −0.321097 | −0.160548 | − | 0.987028i | \(-0.551326\pi\) | ||||
−0.160548 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(272\) | −14.4494 | −0.876123 | ||||||||
\(273\) | −4.90321 | −0.296756 | ||||||||
\(274\) | −3.46520 | −0.209341 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.2351 | 0.736464 | ||||||||
\(277\) | −15.1798 | −0.912064 | −0.456032 | − | 0.889963i | \(-0.650730\pi\) | ||||
−0.456032 | + | 0.889963i | \(0.650730\pi\) | |||||||
\(278\) | 2.50177 | 0.150046 | ||||||||
\(279\) | 13.5462 | 0.810988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.8671 | 1.96069 | 0.980344 | − | 0.197295i | \(-0.0632158\pi\) | ||||
0.980344 | + | 0.197295i | \(0.0632158\pi\) | |||||||
\(282\) | 0.709636 | 0.0422582 | ||||||||
\(283\) | 8.94914 | 0.531971 | 0.265986 | − | 0.963977i | \(-0.414303\pi\) | ||||
0.265986 | + | 0.963977i | \(0.414303\pi\) | |||||||
\(284\) | −14.4889 | −0.859756 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.688892 | −0.0407350 | ||||||||
\(287\) | 5.54617 | 0.327380 | ||||||||
\(288\) | −6.65233 | −0.391992 | ||||||||
\(289\) | 0.760491 | 0.0447348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7047 | −0.686142 | ||||||||
\(292\) | −23.2464 | −1.36039 | ||||||||
\(293\) | 22.9195 | 1.33897 | 0.669486 | − | 0.742825i | \(-0.266514\pi\) | ||||
0.669486 | + | 0.742825i | \(0.266514\pi\) | |||||||
\(294\) | −0.688892 | −0.0401770 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.62714 | 0.443318 | ||||||||
\(297\) | −2.42864 | −0.140924 | ||||||||
\(298\) | 1.90813 | 0.110535 | ||||||||
\(299\) | −6.42864 | −0.371778 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.14764 | −0.239066 | ||||||||
\(302\) | −3.15701 | −0.181666 | ||||||||
\(303\) | 40.0973 | 2.30353 | ||||||||
\(304\) | 26.7654 | 1.53510 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.49532 | 0.142648 | ||||||||
\(307\) | 18.2953 | 1.04417 | 0.522084 | − | 0.852894i | \(-0.325155\pi\) | ||||
0.522084 | + | 0.852894i | \(0.325155\pi\) | |||||||
\(308\) | 1.90321 | 0.108446 | ||||||||
\(309\) | −37.0781 | −2.10930 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.54617 | −0.314495 | −0.157247 | − | 0.987559i | \(-0.550262\pi\) | ||||
−0.157247 | + | 0.987559i | \(0.550262\pi\) | |||||||
\(312\) | 5.95407 | 0.337083 | ||||||||
\(313\) | 23.8064 | 1.34562 | 0.672809 | − | 0.739816i | \(-0.265087\pi\) | ||||
0.672809 | + | 0.739816i | \(0.265087\pi\) | |||||||
\(314\) | −6.75557 | −0.381239 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.70964 | −0.377447 | ||||||||
\(317\) | −10.5906 | −0.594826 | −0.297413 | − | 0.954749i | \(-0.596124\pi\) | ||||
−0.297413 | + | 0.954749i | \(0.596124\pi\) | |||||||
\(318\) | −4.53035 | −0.254049 | ||||||||
\(319\) | 0.755569 | 0.0423037 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.24443 | 0.0694574 | ||||||||
\(322\) | −0.903212 | −0.0503340 | ||||||||
\(323\) | −32.8988 | −1.83054 | ||||||||
\(324\) | 21.1017 | 1.17232 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.49331 | −0.138092 | ||||||||
\(327\) | −8.72393 | −0.482434 | ||||||||
\(328\) | −6.73483 | −0.371869 | ||||||||
\(329\) | 1.03011 | 0.0567919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.1146 | 1.65525 | 0.827625 | − | 0.561282i | \(-0.189692\pi\) | ||||
0.827625 | + | 0.561282i | \(0.189692\pi\) | |||||||
\(332\) | −4.06022 | −0.222834 | ||||||||
\(333\) | 11.9541 | 0.655079 | ||||||||
\(334\) | 4.70519 | 0.257457 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.59210 | −0.414183 | ||||||||
\(337\) | 30.4558 | 1.65904 | 0.829518 | − | 0.558481i | \(-0.188615\pi\) | ||||
0.829518 | + | 0.558481i | \(0.188615\pi\) | |||||||
\(338\) | 2.51897 | 0.137014 | ||||||||
\(339\) | −24.9906 | −1.35730 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.11753 | 0.385436 | ||||||||
\(342\) | −4.62222 | −0.249941 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.03657 | 0.271553 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.12690 | 0.329384 | ||||||||
\(347\) | 28.3511 | 1.52196 | 0.760982 | − | 0.648772i | \(-0.224717\pi\) | ||||
0.760982 | + | 0.648772i | \(0.224717\pi\) | |||||||
\(348\) | −3.18421 | −0.170691 | ||||||||
\(349\) | −32.5654 | −1.74319 | −0.871593 | − | 0.490231i | \(-0.836912\pi\) | ||||
−0.871593 | + | 0.490231i | \(0.836912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.37778 | −0.287045 | ||||||||
\(352\) | −3.49532 | −0.186301 | ||||||||
\(353\) | 24.2766 | 1.29211 | 0.646055 | − | 0.763291i | \(-0.276418\pi\) | ||||
0.646055 | + | 0.763291i | \(0.276418\pi\) | |||||||
\(354\) | −1.85236 | −0.0984517 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −32.8988 | −1.74363 | ||||||||
\(357\) | 9.33185 | 0.493894 | ||||||||
\(358\) | −1.72345 | −0.0910871 | ||||||||
\(359\) | 16.4746 | 0.869495 | 0.434747 | − | 0.900552i | \(-0.356838\pi\) | ||||
0.434747 | + | 0.900552i | \(0.356838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.9403 | 2.20738 | ||||||||
\(362\) | 6.19358 | 0.325527 | ||||||||
\(363\) | 2.21432 | 0.116222 | ||||||||
\(364\) | 4.21432 | 0.220890 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.05578 | −0.316541 | ||||||||
\(367\) | −6.71609 | −0.350577 | −0.175289 | − | 0.984517i | \(-0.556086\pi\) | ||||
−0.175289 | + | 0.984517i | \(0.556086\pi\) | |||||||
\(368\) | −9.95407 | −0.518892 | ||||||||
\(369\) | −10.5555 | −0.549499 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.57628 | −0.341424 | ||||||||
\(372\) | −29.9956 | −1.55520 | ||||||||
\(373\) | −10.5477 | −0.546139 | −0.273070 | − | 0.961994i | \(-0.588039\pi\) | ||||
−0.273070 | + | 0.961994i | \(0.588039\pi\) | |||||||
\(374\) | 1.31111 | 0.0677958 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25088 | −0.0645095 | ||||||||
\(377\) | 1.67307 | 0.0861675 | ||||||||
\(378\) | −0.755569 | −0.0388623 | ||||||||
\(379\) | −33.0607 | −1.69821 | −0.849107 | − | 0.528221i | \(-0.822859\pi\) | ||||
−0.849107 | + | 0.528221i | \(0.822859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.7654 | 1.47370 | ||||||||
\(382\) | 6.50177 | 0.332659 | ||||||||
\(383\) | 17.3067 | 0.884329 | 0.442165 | − | 0.896934i | \(-0.354211\pi\) | ||||
0.442165 | + | 0.896934i | \(0.354211\pi\) | |||||||
\(384\) | 19.4543 | 0.992773 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.23951 | −0.215785 | ||||||||
\(387\) | 7.89384 | 0.401267 | ||||||||
\(388\) | 10.0602 | 0.510730 | ||||||||
\(389\) | −33.1842 | −1.68251 | −0.841253 | − | 0.540642i | \(-0.818182\pi\) | ||||
−0.841253 | + | 0.540642i | \(0.818182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2351 | 0.618754 | ||||||||
\(392\) | 1.21432 | 0.0613324 | ||||||||
\(393\) | −18.7556 | −0.946093 | ||||||||
\(394\) | 4.88448 | 0.246076 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.62222 | −0.182023 | ||||||||
\(397\) | −10.6637 | −0.535196 | −0.267598 | − | 0.963531i | \(-0.586230\pi\) | ||||
−0.267598 | + | 0.963531i | \(0.586230\pi\) | |||||||
\(398\) | 7.44002 | 0.372934 | ||||||||
\(399\) | −17.2859 | −0.865378 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5906 | −0.528868 | −0.264434 | − | 0.964404i | \(-0.585185\pi\) | ||||
−0.264434 | + | 0.964404i | \(0.585185\pi\) | |||||||
\(402\) | 1.05086 | 0.0524119 | ||||||||
\(403\) | 15.7605 | 0.785086 | ||||||||
\(404\) | −34.4637 | −1.71463 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.235063 | 0.0116660 | ||||||||
\(407\) | 6.28100 | 0.311337 | ||||||||
\(408\) | −11.3319 | −0.561010 | ||||||||
\(409\) | 11.8829 | 0.587574 | 0.293787 | − | 0.955871i | \(-0.405084\pi\) | ||||
0.293787 | + | 0.955871i | \(0.405084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.6637 | 1.21657 | ||||||||
\(412\) | 31.8687 | 1.57006 | ||||||||
\(413\) | −2.68889 | −0.132312 | ||||||||
\(414\) | 1.71900 | 0.0844844 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.73975 | −0.379472 | ||||||||
\(417\) | −17.8064 | −0.871984 | ||||||||
\(418\) | −2.42864 | −0.118789 | ||||||||
\(419\) | −2.61576 | −0.127788 | −0.0638942 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638942 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5254 | −1.04909 | −0.524543 | − | 0.851384i | \(-0.675764\pi\) | ||||
−0.524543 | + | 0.851384i | \(0.675764\pi\) | |||||||
\(422\) | −3.57136 | −0.173851 | ||||||||
\(423\) | −1.96052 | −0.0953238 | ||||||||
\(424\) | 7.98571 | 0.387820 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.24443 | −0.254094 | ||||||||
\(427\) | −8.79060 | −0.425407 | ||||||||
\(428\) | −1.06959 | −0.0517006 | ||||||||
\(429\) | 4.90321 | 0.236729 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.0464 | −0.917433 | −0.458717 | − | 0.888583i | \(-0.651691\pi\) | ||||
−0.458717 | + | 0.888583i | \(0.651691\pi\) | |||||||
\(432\) | −8.32693 | −0.400630 | ||||||||
\(433\) | −18.6953 | −0.898441 | −0.449220 | − | 0.893421i | \(-0.648298\pi\) | ||||
−0.449220 | + | 0.893421i | \(0.648298\pi\) | |||||||
\(434\) | 2.21432 | 0.106291 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.49823 | 0.359100 | ||||||||
\(437\) | −22.6637 | −1.08415 | ||||||||
\(438\) | −8.41435 | −0.402053 | ||||||||
\(439\) | −0.990632 | −0.0472803 | −0.0236401 | − | 0.999721i | \(-0.507526\pi\) | ||||
−0.0236401 | + | 0.999721i | \(0.507526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.90321 | 0.0906291 | ||||||||
\(442\) | 2.90321 | 0.138092 | ||||||||
\(443\) | −20.3511 | −0.966908 | −0.483454 | − | 0.875370i | \(-0.660618\pi\) | ||||
−0.483454 | + | 0.875370i | \(0.660618\pi\) | |||||||
\(444\) | −26.4701 | −1.25622 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.14965 | 0.291194 | ||||||||
\(447\) | −13.5812 | −0.642369 | ||||||||
\(448\) | 5.76986 | 0.272600 | ||||||||
\(449\) | −29.1383 | −1.37512 | −0.687560 | − | 0.726127i | \(-0.741318\pi\) | ||||
−0.687560 | + | 0.726127i | \(0.741318\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.54617 | −0.261159 | ||||||||
\(452\) | 21.4795 | 1.01031 | ||||||||
\(453\) | 22.4701 | 1.05574 | ||||||||
\(454\) | 1.12399 | 0.0527512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.9906 | 0.982976 | ||||||||
\(457\) | −31.3131 | −1.46477 | −0.732383 | − | 0.680893i | \(-0.761592\pi\) | ||||
−0.732383 | + | 0.680893i | \(0.761592\pi\) | |||||||
\(458\) | 5.82516 | 0.272192 | ||||||||
\(459\) | 10.2351 | 0.477732 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.9017 | 0.554317 | 0.277158 | − | 0.960824i | \(-0.410607\pi\) | ||||
0.277158 | + | 0.960824i | \(0.410607\pi\) | |||||||
\(462\) | 0.688892 | 0.0320502 | ||||||||
\(463\) | −3.89384 | −0.180962 | −0.0904811 | − | 0.995898i | \(-0.528840\pi\) | ||||
−0.0904811 | + | 0.995898i | \(0.528840\pi\) | |||||||
\(464\) | 2.59057 | 0.120264 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.17929 | 0.100953 | ||||||||
\(467\) | 21.3985 | 0.990206 | 0.495103 | − | 0.868834i | \(-0.335130\pi\) | ||||
0.495103 | + | 0.868834i | \(0.335130\pi\) | |||||||
\(468\) | −8.02074 | −0.370759 | ||||||||
\(469\) | 1.52543 | 0.0704377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.0830 | 2.21555 | ||||||||
\(472\) | 3.26517 | 0.150292 | ||||||||
\(473\) | 4.14764 | 0.190709 | ||||||||
\(474\) | −2.42864 | −0.111551 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.02074 | −0.367630 | ||||||||
\(477\) | 12.5161 | 0.573071 | ||||||||
\(478\) | −6.53035 | −0.298691 | ||||||||
\(479\) | −11.9813 | −0.547438 | −0.273719 | − | 0.961810i | \(-0.588254\pi\) | ||||
−0.273719 | + | 0.961810i | \(0.588254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9081 | 0.634156 | ||||||||
\(482\) | −3.34413 | −0.152321 | ||||||||
\(483\) | 6.42864 | 0.292513 | ||||||||
\(484\) | −1.90321 | −0.0865096 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.37133 | 0.243649 | ||||||||
\(487\) | 16.5892 | 0.751728 | 0.375864 | − | 0.926675i | \(-0.377346\pi\) | ||||
0.375864 | + | 0.926675i | \(0.377346\pi\) | |||||||
\(488\) | 10.6746 | 0.483217 | ||||||||
\(489\) | 17.7462 | 0.802511 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.2400 | −1.86113 | −0.930567 | − | 0.366121i | \(-0.880686\pi\) | ||||
−0.930567 | + | 0.366121i | \(0.880686\pi\) | |||||||
\(492\) | 23.3733 | 1.05375 | ||||||||
\(493\) | −3.18421 | −0.143410 | ||||||||
\(494\) | −5.37778 | −0.241958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.4035 | 1.09575 | ||||||||
\(497\) | −7.61285 | −0.341483 | ||||||||
\(498\) | −1.46965 | −0.0658566 | ||||||||
\(499\) | −32.3783 | −1.44945 | −0.724725 | − | 0.689038i | \(-0.758033\pi\) | ||||
−0.724725 | + | 0.689038i | \(0.758033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.4893 | −1.49619 | ||||||||
\(502\) | 1.96052 | 0.0875023 | ||||||||
\(503\) | −33.4795 | −1.49278 | −0.746388 | − | 0.665511i | \(-0.768214\pi\) | ||||
−0.746388 | + | 0.665511i | \(0.768214\pi\) | |||||||
\(504\) | −2.31111 | −0.102945 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.903212 | 0.0401527 | ||||||||
\(507\) | −17.9289 | −0.796249 | ||||||||
\(508\) | −24.7239 | −1.09695 | ||||||||
\(509\) | −8.79706 | −0.389923 | −0.194961 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194961 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2143 | −0.540330 | ||||||||
\(512\) | −20.3111 | −0.897633 | ||||||||
\(513\) | −18.9590 | −0.837060 | ||||||||
\(514\) | 8.17484 | 0.360577 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17.4795 | −0.769492 | ||||||||
\(517\) | −1.03011 | −0.0453043 | ||||||||
\(518\) | 1.95407 | 0.0858568 | ||||||||
\(519\) | −43.6084 | −1.91420 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4415 | 1.24605 | 0.623023 | − | 0.782203i | \(-0.285904\pi\) | ||||
0.623023 | + | 0.782203i | \(0.285904\pi\) | |||||||
\(522\) | −0.447375 | −0.0195811 | ||||||||
\(523\) | 3.80642 | 0.166443 | 0.0832216 | − | 0.996531i | \(-0.473479\pi\) | ||||
0.0832216 | + | 0.996531i | \(0.473479\pi\) | |||||||
\(524\) | 16.1204 | 0.704225 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.95851 | 0.172599 | ||||||||
\(527\) | −29.9956 | −1.30663 | ||||||||
\(528\) | 7.59210 | 0.330404 | ||||||||
\(529\) | −14.5714 | −0.633537 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.11753 | 0.222082 | ||||||||
\(532\) | 14.8573 | 0.644145 | ||||||||
\(533\) | −12.2810 | −0.531949 | ||||||||
\(534\) | −11.9081 | −0.515315 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.85236 | −0.0800096 | ||||||||
\(537\) | 12.2667 | 0.529347 | ||||||||
\(538\) | 4.38715 | 0.189144 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2351 | 1.38589 | 0.692947 | − | 0.720989i | \(-0.256312\pi\) | ||||
0.692947 | + | 0.720989i | \(0.256312\pi\) | |||||||
\(542\) | 1.64449 | 0.0706369 | ||||||||
\(543\) | −44.0830 | −1.89178 | ||||||||
\(544\) | 14.7304 | 0.631560 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.52543 | 0.0652823 | ||||||||
\(547\) | −19.3876 | −0.828955 | −0.414478 | − | 0.910060i | \(-0.636036\pi\) | ||||
−0.414478 | + | 0.910060i | \(0.636036\pi\) | |||||||
\(548\) | −21.1985 | −0.905555 | ||||||||
\(549\) | 16.7304 | 0.714035 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.89829 | 0.251276 | ||||||||
\(552\) | −7.80642 | −0.332263 | ||||||||
\(553\) | −3.52543 | −0.149916 | ||||||||
\(554\) | 4.72254 | 0.200642 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.3047 | 0.649062 | ||||||||
\(557\) | 1.58565 | 0.0671862 | 0.0335931 | − | 0.999436i | \(-0.489305\pi\) | ||||
0.0335931 | + | 0.999436i | \(0.489305\pi\) | |||||||
\(558\) | −4.21432 | −0.178406 | ||||||||
\(559\) | 9.18421 | 0.388451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.33185 | −0.393991 | ||||||||
\(562\) | −10.2252 | −0.431325 | ||||||||
\(563\) | −28.8069 | −1.21407 | −0.607033 | − | 0.794677i | \(-0.707640\pi\) | ||||
−0.607033 | + | 0.794677i | \(0.707640\pi\) | |||||||
\(564\) | 4.34122 | 0.182798 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.78415 | −0.117027 | ||||||||
\(567\) | 11.0874 | 0.465628 | ||||||||
\(568\) | 9.24443 | 0.387888 | ||||||||
\(569\) | −14.6953 | −0.616061 | −0.308030 | − | 0.951376i | \(-0.599670\pi\) | ||||
−0.308030 | + | 0.951376i | \(0.599670\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3368 | −0.516278 | −0.258139 | − | 0.966108i | \(-0.583109\pi\) | ||||
−0.258139 | + | 0.966108i | \(0.583109\pi\) | |||||||
\(572\) | −4.21432 | −0.176210 | ||||||||
\(573\) | −46.2766 | −1.93323 | ||||||||
\(574\) | −1.72546 | −0.0720192 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.9813 | −0.457553 | ||||||||
\(577\) | 8.13335 | 0.338596 | 0.169298 | − | 0.985565i | \(-0.445850\pi\) | ||||
0.169298 | + | 0.985565i | \(0.445850\pi\) | |||||||
\(578\) | −0.236595 | −0.00984104 | ||||||||
\(579\) | 30.1748 | 1.25402 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.13335 | −0.0885064 | ||||||||
\(582\) | 3.64143 | 0.150942 | ||||||||
\(583\) | 6.57628 | 0.272362 | ||||||||
\(584\) | 14.8321 | 0.613756 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.13044 | −0.294556 | ||||||||
\(587\) | −2.30619 | −0.0951865 | −0.0475932 | − | 0.998867i | \(-0.515155\pi\) | ||||
−0.0475932 | + | 0.998867i | \(0.515155\pi\) | |||||||
\(588\) | −4.21432 | −0.173796 | ||||||||
\(589\) | 55.5625 | 2.28941 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.7654 | −1.43006 | ||||||||
\(592\) | 21.5353 | 0.885094 | ||||||||
\(593\) | 25.7067 | 1.05565 | 0.527824 | − | 0.849354i | \(-0.323008\pi\) | ||||
0.527824 | + | 0.849354i | \(0.323008\pi\) | |||||||
\(594\) | 0.755569 | 0.0310014 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.6731 | 0.478148 | ||||||||
\(597\) | −52.9545 | −2.16729 | ||||||||
\(598\) | 2.00000 | 0.0817861 | ||||||||
\(599\) | 27.5210 | 1.12448 | 0.562238 | − | 0.826975i | \(-0.309940\pi\) | ||||
0.562238 | + | 0.826975i | \(0.309940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1175 | 0.698239 | 0.349119 | − | 0.937078i | \(-0.386481\pi\) | ||||
0.349119 | + | 0.937078i | \(0.386481\pi\) | |||||||
\(602\) | 1.29036 | 0.0525913 | ||||||||
\(603\) | −2.90321 | −0.118228 | ||||||||
\(604\) | −19.3131 | −0.785840 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.4746 | −0.506745 | ||||||||
\(607\) | 21.4291 | 0.869781 | 0.434890 | − | 0.900483i | \(-0.356787\pi\) | ||||
0.434890 | + | 0.900483i | \(0.356787\pi\) | |||||||
\(608\) | −27.2859 | −1.10659 | ||||||||
\(609\) | −1.67307 | −0.0677962 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.28100 | −0.0922792 | ||||||||
\(612\) | 15.2652 | 0.617058 | ||||||||
\(613\) | 40.3037 | 1.62785 | 0.813927 | − | 0.580968i | \(-0.197326\pi\) | ||||
0.813927 | + | 0.580968i | \(0.197326\pi\) | |||||||
\(614\) | −5.69181 | −0.229703 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.21432 | −0.0489263 | ||||||||
\(617\) | 15.0553 | 0.606104 | 0.303052 | − | 0.952974i | \(-0.401994\pi\) | ||||
0.303052 | + | 0.952974i | \(0.401994\pi\) | |||||||
\(618\) | 11.5353 | 0.464017 | ||||||||
\(619\) | 14.6702 | 0.589643 | 0.294822 | − | 0.955552i | \(-0.404740\pi\) | ||||
0.294822 | + | 0.955552i | \(0.404740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.05086 | 0.282941 | ||||||||
\(622\) | 1.72546 | 0.0691845 | ||||||||
\(623\) | −17.2859 | −0.692546 | ||||||||
\(624\) | 16.8113 | 0.672992 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.40636 | −0.296018 | ||||||||
\(627\) | 17.2859 | 0.690333 | ||||||||
\(628\) | −41.3274 | −1.64914 | ||||||||
\(629\) | −26.4701 | −1.05543 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.2034 | −0.645048 | −0.322524 | − | 0.946561i | \(-0.604531\pi\) | ||||
−0.322524 | + | 0.946561i | \(0.604531\pi\) | |||||||
\(632\) | 4.28100 | 0.170289 | ||||||||
\(633\) | 25.4193 | 1.01033 | ||||||||
\(634\) | 3.29481 | 0.130854 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −27.7146 | −1.09895 | ||||||||
\(637\) | 2.21432 | 0.0877345 | ||||||||
\(638\) | −0.235063 | −0.00930625 | ||||||||
\(639\) | 14.4889 | 0.573171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.7225 | −1.13447 | −0.567236 | − | 0.823555i | \(-0.691987\pi\) | ||||
−0.567236 | + | 0.823555i | \(0.691987\pi\) | |||||||
\(642\) | −0.387152 | −0.0152797 | ||||||||
\(643\) | 7.87755 | 0.310660 | 0.155330 | − | 0.987863i | \(-0.450356\pi\) | ||||
0.155330 | + | 0.987863i | \(0.450356\pi\) | |||||||
\(644\) | −5.52543 | −0.217732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.2351 | 0.402693 | ||||||||
\(647\) | −29.7540 | −1.16975 | −0.584876 | − | 0.811123i | \(-0.698857\pi\) | ||||
−0.584876 | + | 0.811123i | \(0.698857\pi\) | |||||||
\(648\) | −13.4637 | −0.528903 | ||||||||
\(649\) | 2.68889 | 0.105548 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.7605 | −0.617702 | ||||||||
\(652\) | −15.2529 | −0.597349 | ||||||||
\(653\) | −16.7141 | −0.654073 | −0.327036 | − | 0.945012i | \(-0.606050\pi\) | ||||
−0.327036 | + | 0.945012i | \(0.606050\pi\) | |||||||
\(654\) | 2.71408 | 0.106129 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19.0158 | −0.742443 | ||||||||
\(657\) | 23.2464 | 0.906930 | ||||||||
\(658\) | −0.320476 | −0.0124934 | ||||||||
\(659\) | 1.38223 | 0.0538440 | 0.0269220 | − | 0.999638i | \(-0.491429\pi\) | ||||
0.0269220 | + | 0.999638i | \(0.491429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.723926 | 0.0281575 | 0.0140787 | − | 0.999901i | \(-0.495518\pi\) | ||||
0.0140787 | + | 0.999901i | \(0.495518\pi\) | |||||||
\(662\) | −9.36889 | −0.364132 | ||||||||
\(663\) | −20.6637 | −0.802512 | ||||||||
\(664\) | 2.59057 | 0.100534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.71900 | −0.144108 | ||||||||
\(667\) | −2.19358 | −0.0849356 | ||||||||
\(668\) | 28.7841 | 1.11369 | ||||||||
\(669\) | −43.7703 | −1.69226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.79060 | 0.339357 | ||||||||
\(672\) | 7.73975 | 0.298567 | ||||||||
\(673\) | −27.5254 | −1.06103 | −0.530514 | − | 0.847676i | \(-0.678001\pi\) | ||||
−0.530514 | + | 0.847676i | \(0.678001\pi\) | |||||||
\(674\) | −9.47505 | −0.364965 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.4099 | 0.592689 | ||||||||
\(677\) | 20.4079 | 0.784339 | 0.392170 | − | 0.919893i | \(-0.371725\pi\) | ||||
0.392170 | + | 0.919893i | \(0.371725\pi\) | |||||||
\(678\) | 7.77478 | 0.298589 | ||||||||
\(679\) | 5.28592 | 0.202855 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | −2.21432 | −0.0847907 | ||||||||
\(683\) | 38.5575 | 1.47536 | 0.737682 | − | 0.675149i | \(-0.235920\pi\) | ||||
0.737682 | + | 0.675149i | \(0.235920\pi\) | |||||||
\(684\) | −28.2766 | −1.08118 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.311108 | 0.0118782 | ||||||||
\(687\) | −41.4608 | −1.58183 | ||||||||
\(688\) | 14.2208 | 0.542162 | ||||||||
\(689\) | 14.5620 | 0.554768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.59655 | 0.365070 | 0.182535 | − | 0.983199i | \(-0.441570\pi\) | ||||
0.182535 | + | 0.983199i | \(0.441570\pi\) | |||||||
\(692\) | 37.4815 | 1.42483 | ||||||||
\(693\) | −1.90321 | −0.0722970 | ||||||||
\(694\) | −8.82024 | −0.334812 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.03164 | 0.0770092 | ||||||||
\(697\) | 23.3733 | 0.885328 | ||||||||
\(698\) | 10.1313 | 0.383477 | ||||||||
\(699\) | −15.5111 | −0.586685 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0701 | −1.13573 | −0.567865 | − | 0.823121i | \(-0.692231\pi\) | ||||
−0.567865 | + | 0.823121i | \(0.692231\pi\) | |||||||
\(702\) | 1.67307 | 0.0631460 | ||||||||
\(703\) | 49.0321 | 1.84928 | ||||||||
\(704\) | −5.76986 | −0.217460 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.55262 | −0.284247 | ||||||||
\(707\) | −18.1082 | −0.681028 | ||||||||
\(708\) | −11.3319 | −0.425877 | ||||||||
\(709\) | −4.10171 | −0.154043 | −0.0770215 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770215 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.70964 | 0.251631 | ||||||||
\(712\) | 20.9906 | 0.786657 | ||||||||
\(713\) | −20.6637 | −0.773862 | ||||||||
\(714\) | −2.90321 | −0.108650 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.5433 | −0.394020 | ||||||||
\(717\) | 46.4800 | 1.73583 | ||||||||
\(718\) | −5.12537 | −0.191277 | ||||||||
\(719\) | 19.2696 | 0.718636 | 0.359318 | − | 0.933215i | \(-0.383009\pi\) | ||||
0.359318 | + | 0.933215i | \(0.383009\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.7447 | 0.623604 | ||||||||
\(722\) | −13.0479 | −0.485594 | ||||||||
\(723\) | 23.8020 | 0.885205 | ||||||||
\(724\) | 37.8894 | 1.40815 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.688892 | −0.0255672 | ||||||||
\(727\) | 37.4084 | 1.38740 | 0.693700 | − | 0.720264i | \(-0.255979\pi\) | ||||
0.693700 | + | 0.720264i | \(0.255979\pi\) | |||||||
\(728\) | −2.68889 | −0.0996570 | ||||||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4795 | −0.646502 | ||||||||
\(732\) | −37.0464 | −1.36927 | ||||||||
\(733\) | −4.60147 | −0.169959 | −0.0849796 | − | 0.996383i | \(-0.527083\pi\) | ||||
−0.0849796 | + | 0.996383i | \(0.527083\pi\) | |||||||
\(734\) | 2.08943 | 0.0771222 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.1476 | 0.374047 | ||||||||
\(737\) | −1.52543 | −0.0561898 | ||||||||
\(738\) | 3.28391 | 0.120882 | ||||||||
\(739\) | 35.0420 | 1.28904 | 0.644520 | − | 0.764588i | \(-0.277057\pi\) | ||||
0.644520 | + | 0.764588i | \(0.277057\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.2766 | 1.40612 | ||||||||
\(742\) | 2.04593 | 0.0751086 | ||||||||
\(743\) | −40.7654 | −1.49554 | −0.747769 | − | 0.663959i | \(-0.768875\pi\) | ||||
−0.747769 | + | 0.663959i | \(0.768875\pi\) | |||||||
\(744\) | 19.1383 | 0.701643 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.28147 | 0.120143 | ||||||||
\(747\) | 4.06022 | 0.148556 | ||||||||
\(748\) | 8.02074 | 0.293267 | ||||||||
\(749\) | −0.561993 | −0.0205348 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4286 | 0.891414 | 0.445707 | − | 0.895179i | \(-0.352952\pi\) | ||||
0.445707 | + | 0.895179i | \(0.352952\pi\) | |||||||
\(752\) | −3.53188 | −0.128794 | ||||||||
\(753\) | −13.9541 | −0.508514 | ||||||||
\(754\) | −0.520505 | −0.0189557 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.62222 | −0.168108 | ||||||||
\(757\) | −36.9086 | −1.34147 | −0.670733 | − | 0.741699i | \(-0.734020\pi\) | ||||
−0.670733 | + | 0.741699i | \(0.734020\pi\) | |||||||
\(758\) | 10.2854 | 0.373584 | ||||||||
\(759\) | −6.42864 | −0.233345 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.96190 | −0.143619 | −0.0718094 | − | 0.997418i | \(-0.522877\pi\) | ||||
−0.0718094 | + | 0.997418i | \(0.522877\pi\) | |||||||
\(762\) | −8.94914 | −0.324193 | ||||||||
\(763\) | 3.93978 | 0.142630 | ||||||||
\(764\) | 39.7748 | 1.43900 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.38424 | −0.194540 | ||||||||
\(767\) | 5.95407 | 0.214989 | ||||||||
\(768\) | 19.5002 | 0.703654 | ||||||||
\(769\) | 2.29190 | 0.0826479 | 0.0413239 | − | 0.999146i | \(-0.486842\pi\) | ||||
0.0413239 | + | 0.999146i | \(0.486842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −58.1847 | −2.09547 | ||||||||
\(772\) | −25.9353 | −0.933433 | ||||||||
\(773\) | 11.3047 | 0.406600 | 0.203300 | − | 0.979116i | \(-0.434833\pi\) | ||||
0.203300 | + | 0.979116i | \(0.434833\pi\) | |||||||
\(774\) | −2.45584 | −0.0882732 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.41880 | −0.230421 | ||||||||
\(777\) | −13.9081 | −0.498952 | ||||||||
\(778\) | 10.3239 | 0.370129 | ||||||||
\(779\) | −43.2958 | −1.55123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.61285 | 0.272409 | ||||||||
\(782\) | −3.80642 | −0.136117 | ||||||||
\(783\) | −1.83500 | −0.0655777 | ||||||||
\(784\) | 3.42864 | 0.122451 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.83500 | 0.208128 | ||||||||
\(787\) | −20.2163 | −0.720634 | −0.360317 | − | 0.932830i | \(-0.617332\pi\) | ||||
−0.360317 | + | 0.932830i | \(0.617332\pi\) | |||||||
\(788\) | 29.8809 | 1.06446 | ||||||||
\(789\) | −28.1748 | −1.00305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.2859 | 0.401281 | ||||||||
\(792\) | 2.31111 | 0.0821216 | ||||||||
\(793\) | 19.4652 | 0.691230 | ||||||||
\(794\) | 3.31756 | 0.117736 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.5145 | 1.61322 | ||||||||
\(797\) | −50.4514 | −1.78708 | −0.893540 | − | 0.448984i | \(-0.851786\pi\) | ||||
−0.893540 | + | 0.448984i | \(0.851786\pi\) | |||||||
\(798\) | 5.37778 | 0.190372 | ||||||||
\(799\) | 4.34122 | 0.153581 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.8988 | 1.16242 | ||||||||
\(802\) | 3.29481 | 0.116344 | ||||||||
\(803\) | 12.2143 | 0.431034 | ||||||||
\(804\) | 6.42864 | 0.226721 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.90321 | −0.172708 | ||||||||
\(807\) | −31.2257 | −1.09920 | ||||||||
\(808\) | 21.9891 | 0.773574 | ||||||||
\(809\) | 17.9911 | 0.632534 | 0.316267 | − | 0.948670i | \(-0.397571\pi\) | ||||
0.316267 | + | 0.948670i | \(0.397571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3082 | −1.34518 | −0.672591 | − | 0.740014i | \(-0.734819\pi\) | ||||
−0.672591 | + | 0.740014i | \(0.734819\pi\) | |||||||
\(812\) | 1.43801 | 0.0504642 | ||||||||
\(813\) | −11.7047 | −0.410502 | ||||||||
\(814\) | −1.95407 | −0.0684900 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −31.9956 | −1.12007 | ||||||||
\(817\) | 32.3783 | 1.13277 | ||||||||
\(818\) | −3.69688 | −0.129258 | ||||||||
\(819\) | −4.21432 | −0.147260 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3082 | 0.778561 | 0.389281 | − | 0.921119i | \(-0.372724\pi\) | ||||
0.389281 | + | 0.921119i | \(0.372724\pi\) | |||||||
\(822\) | −7.67307 | −0.267629 | ||||||||
\(823\) | −38.3541 | −1.33694 | −0.668470 | − | 0.743739i | \(-0.733051\pi\) | ||||
−0.668470 | + | 0.743739i | \(0.733051\pi\) | |||||||
\(824\) | −20.3334 | −0.708347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.836535 | 0.0291068 | ||||||||
\(827\) | 30.5446 | 1.06214 | 0.531071 | − | 0.847328i | \(-0.321790\pi\) | ||||
0.531071 | + | 0.847328i | \(0.321790\pi\) | |||||||
\(828\) | 10.5161 | 0.365458 | ||||||||
\(829\) | −52.9215 | −1.83804 | −0.919020 | − | 0.394211i | \(-0.871018\pi\) | ||||
−0.919020 | + | 0.394211i | \(0.871018\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.6128 | −1.16602 | ||||||||
\(832\) | −12.7763 | −0.442939 | ||||||||
\(833\) | −4.21432 | −0.146018 | ||||||||
\(834\) | 5.53972 | 0.191825 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14.8573 | −0.513850 | ||||||||
\(837\) | −17.2859 | −0.597489 | ||||||||
\(838\) | 0.813784 | 0.0281117 | ||||||||
\(839\) | 38.6987 | 1.33603 | 0.668014 | − | 0.744148i | \(-0.267144\pi\) | ||||
0.668014 | + | 0.744148i | \(0.267144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | 6.69673 | 0.230785 | ||||||||
\(843\) | 72.7783 | 2.50662 | ||||||||
\(844\) | −21.8479 | −0.752036 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.609933 | 0.0209699 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 22.5477 | 0.774291 | ||||||||
\(849\) | 19.8163 | 0.680093 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2351 | −0.625090 | ||||||||
\(852\) | −32.0830 | −1.09914 | ||||||||
\(853\) | −29.3352 | −1.00442 | −0.502210 | − | 0.864746i | \(-0.667479\pi\) | ||||
−0.502210 | + | 0.864746i | \(0.667479\pi\) | |||||||
\(854\) | 2.73483 | 0.0935838 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.682439 | 0.0233253 | ||||||||
\(857\) | 21.0627 | 0.719488 | 0.359744 | − | 0.933051i | \(-0.382864\pi\) | ||||
0.359744 | + | 0.933051i | \(0.382864\pi\) | |||||||
\(858\) | −1.52543 | −0.0520772 | ||||||||
\(859\) | 16.9525 | 0.578413 | 0.289207 | − | 0.957267i | \(-0.406609\pi\) | ||||
0.289207 | + | 0.957267i | \(0.406609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2810 | 0.418535 | ||||||||
\(862\) | 5.92549 | 0.201823 | ||||||||
\(863\) | 49.8336 | 1.69636 | 0.848178 | − | 0.529711i | \(-0.177700\pi\) | ||||
0.848178 | + | 0.529711i | \(0.177700\pi\) | |||||||
\(864\) | 8.48886 | 0.288797 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.81627 | 0.197645 | ||||||||
\(867\) | 1.68397 | 0.0571906 | ||||||||
\(868\) | 13.5462 | 0.459787 | ||||||||
\(869\) | 3.52543 | 0.119592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.37778 | −0.114452 | ||||||||
\(872\) | −4.78415 | −0.162012 | ||||||||
\(873\) | −10.0602 | −0.340487 | ||||||||
\(874\) | 7.05086 | 0.238499 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −51.4750 | −1.73918 | ||||||||
\(877\) | −1.29036 | −0.0435725 | −0.0217863 | − | 0.999763i | \(-0.506935\pi\) | ||||
−0.0217863 | + | 0.999763i | \(0.506935\pi\) | |||||||
\(878\) | 0.308193 | 0.0104010 | ||||||||
\(879\) | 50.7511 | 1.71179 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.4380 | 0.789647 | 0.394823 | − | 0.918757i | \(-0.370806\pi\) | ||||
0.394823 | + | 0.918757i | \(0.370806\pi\) | |||||||
\(882\) | −0.592104 | −0.0199372 | ||||||||
\(883\) | 31.0366 | 1.04446 | 0.522232 | − | 0.852804i | \(-0.325100\pi\) | ||||
0.522232 | + | 0.852804i | \(0.325100\pi\) | |||||||
\(884\) | 17.7605 | 0.597350 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.33138 | 0.212707 | ||||||||
\(887\) | 1.40636 | 0.0472211 | 0.0236106 | − | 0.999721i | \(-0.492484\pi\) | ||||
0.0236106 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(888\) | 16.8889 | 0.566755 | ||||||||
\(889\) | −12.9906 | −0.435692 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.0874 | −0.371443 | ||||||||
\(892\) | 37.6207 | 1.25963 | ||||||||
\(893\) | −8.04149 | −0.269098 | ||||||||
\(894\) | 4.22522 | 0.141312 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.78568 | −0.293509 | ||||||||
\(897\) | −14.2351 | −0.475295 | ||||||||
\(898\) | 9.06515 | 0.302508 | ||||||||
\(899\) | 5.37778 | 0.179359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.7146 | −0.923306 | ||||||||
\(902\) | 1.72546 | 0.0574514 | ||||||||
\(903\) | −9.18421 | −0.305631 | ||||||||
\(904\) | −13.7047 | −0.455812 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.99063 | −0.232248 | ||||||||
\(907\) | −5.86220 | −0.194651 | −0.0973256 | − | 0.995253i | \(-0.531029\pi\) | ||||
−0.0973256 | + | 0.995253i | \(0.531029\pi\) | |||||||
\(908\) | 6.87601 | 0.228189 | ||||||||
\(909\) | 34.4637 | 1.14309 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.2257 | −0.636976 | −0.318488 | − | 0.947927i | \(-0.603175\pi\) | ||||
−0.318488 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(912\) | 59.2672 | 1.96253 | ||||||||
\(913\) | 2.13335 | 0.0706037 | ||||||||
\(914\) | 9.74176 | 0.322229 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35.6356 | 1.17743 | ||||||||
\(917\) | 8.47013 | 0.279708 | ||||||||
\(918\) | −3.18421 | −0.105095 | ||||||||
\(919\) | 0.520505 | 0.0171699 | 0.00858494 | − | 0.999963i | \(-0.497267\pi\) | ||||
0.00858494 | + | 0.999963i | \(0.497267\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.5116 | 1.33490 | ||||||||
\(922\) | −3.70271 | −0.121942 | ||||||||
\(923\) | 16.8573 | 0.554864 | ||||||||
\(924\) | 4.21432 | 0.138641 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.21141 | 0.0398092 | ||||||||
\(927\) | −31.8687 | −1.04670 | ||||||||
\(928\) | −2.64095 | −0.0866935 | ||||||||
\(929\) | 19.6414 | 0.644414 | 0.322207 | − | 0.946669i | \(-0.395575\pi\) | ||||
0.322207 | + | 0.946669i | \(0.395575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.80642 | 0.255845 | ||||||||
\(932\) | 13.3319 | 0.436699 | ||||||||
\(933\) | −12.2810 | −0.402062 | ||||||||
\(934\) | −6.65725 | −0.217832 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.11753 | 0.167272 | ||||||||
\(937\) | 54.2973 | 1.77382 | 0.886908 | − | 0.461947i | \(-0.152849\pi\) | ||||
0.886908 | + | 0.461947i | \(0.152849\pi\) | |||||||
\(938\) | −0.474572 | −0.0154953 | ||||||||
\(939\) | 52.7150 | 1.72029 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.95206 | 0.0636353 | 0.0318177 | − | 0.999494i | \(-0.489870\pi\) | ||||
0.0318177 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(942\) | −14.9590 | −0.487390 | ||||||||
\(943\) | 16.1017 | 0.524344 | ||||||||
\(944\) | 9.21924 | 0.300061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.29036 | −0.0419534 | ||||||||
\(947\) | 9.39207 | 0.305201 | 0.152601 | − | 0.988288i | \(-0.451235\pi\) | ||||
0.152601 | + | 0.988288i | \(0.451235\pi\) | |||||||
\(948\) | −14.8573 | −0.482542 | ||||||||
\(949\) | 27.0464 | 0.877964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.4509 | −0.760448 | ||||||||
\(952\) | 5.11753 | 0.165860 | ||||||||
\(953\) | 11.2716 | 0.365124 | 0.182562 | − | 0.983194i | \(-0.441561\pi\) | ||||
0.182562 | + | 0.983194i | \(0.441561\pi\) | |||||||
\(954\) | −3.89384 | −0.126068 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −39.9496 | −1.29206 | ||||||||
\(957\) | 1.67307 | 0.0540827 | ||||||||
\(958\) | 3.72746 | 0.120429 | ||||||||
\(959\) | −11.1383 | −0.359674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6593 | 0.634170 | ||||||||
\(962\) | −4.32693 | −0.139506 | ||||||||
\(963\) | 1.06959 | 0.0344671 | ||||||||
\(964\) | −20.4578 | −0.658903 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.00000 | −0.0643489 | ||||||||
\(967\) | −17.3002 | −0.556337 | −0.278169 | − | 0.960532i | \(-0.589727\pi\) | ||||
−0.278169 | + | 0.960532i | \(0.589727\pi\) | |||||||
\(968\) | 1.21432 | 0.0390297 | ||||||||
\(969\) | −72.8484 | −2.34023 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.2928 | 0.907961 | 0.453980 | − | 0.891012i | \(-0.350004\pi\) | ||||
0.453980 | + | 0.891012i | \(0.350004\pi\) | |||||||
\(972\) | 32.8593 | 1.05396 | ||||||||
\(973\) | 8.04149 | 0.257798 | ||||||||
\(974\) | −5.16103 | −0.165370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.1398 | 0.964752 | ||||||||
\(977\) | 45.9782 | 1.47097 | 0.735486 | − | 0.677539i | \(-0.236954\pi\) | ||||
0.735486 | + | 0.677539i | \(0.236954\pi\) | |||||||
\(978\) | −5.52098 | −0.176542 | ||||||||
\(979\) | 17.2859 | 0.552460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.49823 | −0.239400 | ||||||||
\(982\) | 12.8301 | 0.409424 | ||||||||
\(983\) | −1.41726 | −0.0452037 | −0.0226018 | − | 0.999745i | \(-0.507195\pi\) | ||||
−0.0226018 | + | 0.999745i | \(0.507195\pi\) | |||||||
\(984\) | −14.9131 | −0.475411 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.990632 | 0.0315482 | ||||||||
\(987\) | 2.28100 | 0.0726049 | ||||||||
\(988\) | −32.8988 | −1.04665 | ||||||||
\(989\) | −12.0415 | −0.382897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.9906 | −0.920918 | −0.460459 | − | 0.887681i | \(-0.652315\pi\) | ||||
−0.460459 | + | 0.887681i | \(0.652315\pi\) | |||||||
\(992\) | −24.8780 | −0.789878 | ||||||||
\(993\) | 66.6834 | 2.11613 | ||||||||
\(994\) | 2.36842 | 0.0751216 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.99063 | −0.284879 | ||||||||
\(997\) | 5.80843 | 0.183955 | 0.0919774 | − | 0.995761i | \(-0.470681\pi\) | ||||
0.0919774 | + | 0.995761i | \(0.470681\pi\) | |||||||
\(998\) | 10.0731 | 0.318859 | ||||||||
\(999\) | −15.2543 | −0.482624 |
(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 | 1925.2.a.u.1.2 | 3 | ||
5.2 | odd | 4 | 1925.2.b.o.1849.3 | 6 | |||
5.3 | odd | 4 | 1925.2.b.o.1849.4 | 6 | |||
5.4 | even | 2 | 385.2.a.g.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 3465.2.a.ba.1.2 | 3 | |||
20.19 | odd | 2 | 6160.2.a.bj.1.3 | 3 | |||
35.34 | odd | 2 | 2695.2.a.i.1.2 | 3 | |||
55.54 | odd | 2 | 4235.2.a.o.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.a.g.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
1925.2.a.u.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1925.2.b.o.1849.3 | 6 | 5.2 | odd | 4 | |||
1925.2.b.o.1849.4 | 6 | 5.3 | odd | 4 | |||
2695.2.a.i.1.2 | 3 | 35.34 | odd | 2 | |||
3465.2.a.ba.1.2 | 3 | 15.14 | odd | 2 | |||
4235.2.a.o.1.2 | 3 | 55.54 | odd | 2 | |||
6160.2.a.bj.1.3 | 3 | 20.19 | odd | 2 |