Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11520 | −1.49567 | −0.747835 | − | 0.663885i | \(-0.768907\pi\) | ||||
−0.747835 | + | 0.663885i | \(0.768907\pi\) | |||||||
\(3\) | 0.824774 | 0.476184 | 0.238092 | − | 0.971243i | \(-0.423478\pi\) | ||||
0.238092 | + | 0.971243i | \(0.423478\pi\) | |||||||
\(4\) | 2.47406 | 1.23703 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.74456 | −0.712213 | ||||||||
\(7\) | 0.827865 | 0.312903 | 0.156452 | − | 0.987686i | \(-0.449994\pi\) | ||||
0.156452 | + | 0.987686i | \(0.449994\pi\) | |||||||
\(8\) | −1.00272 | −0.354515 | ||||||||
\(9\) | −2.31975 | −0.773249 | ||||||||
\(10\) | 2.11520 | 0.668884 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.04054 | 0.589052 | ||||||||
\(13\) | 6.12707 | 1.69934 | 0.849671 | − | 0.527313i | \(-0.176800\pi\) | ||||
0.849671 | + | 0.527313i | \(0.176800\pi\) | |||||||
\(14\) | −1.75110 | −0.468000 | ||||||||
\(15\) | −0.824774 | −0.212956 | ||||||||
\(16\) | −2.82716 | −0.706790 | ||||||||
\(17\) | 2.24003 | 0.543286 | 0.271643 | − | 0.962398i | \(-0.412433\pi\) | ||||
0.271643 | + | 0.962398i | \(0.412433\pi\) | |||||||
\(18\) | 4.90672 | 1.15653 | ||||||||
\(19\) | −1.94946 | −0.447237 | −0.223619 | − | 0.974677i | \(-0.571787\pi\) | ||||
−0.223619 | + | 0.974677i | \(0.571787\pi\) | |||||||
\(20\) | −2.47406 | −0.553216 | ||||||||
\(21\) | 0.682802 | 0.149000 | ||||||||
\(22\) | −2.11520 | −0.450961 | ||||||||
\(23\) | −4.61905 | −0.963139 | −0.481569 | − | 0.876408i | \(-0.659933\pi\) | ||||
−0.481569 | + | 0.876408i | \(0.659933\pi\) | |||||||
\(24\) | −0.827018 | −0.168814 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −12.9599 | −2.54166 | ||||||||
\(27\) | −4.38759 | −0.844392 | ||||||||
\(28\) | 2.04818 | 0.387070 | ||||||||
\(29\) | 1.17583 | 0.218347 | 0.109173 | − | 0.994023i | \(-0.465180\pi\) | ||||
0.109173 | + | 0.994023i | \(0.465180\pi\) | |||||||
\(30\) | 1.74456 | 0.318511 | ||||||||
\(31\) | −7.54708 | −1.35550 | −0.677748 | − | 0.735295i | \(-0.737044\pi\) | ||||
−0.677748 | + | 0.735295i | \(0.737044\pi\) | |||||||
\(32\) | 7.98544 | 1.41164 | ||||||||
\(33\) | 0.824774 | 0.143575 | ||||||||
\(34\) | −4.73809 | −0.812576 | ||||||||
\(35\) | −0.827865 | −0.139935 | ||||||||
\(36\) | −5.73918 | −0.956531 | ||||||||
\(37\) | 2.15280 | 0.353918 | 0.176959 | − | 0.984218i | \(-0.443374\pi\) | ||||
0.176959 | + | 0.984218i | \(0.443374\pi\) | |||||||
\(38\) | 4.12349 | 0.668919 | ||||||||
\(39\) | 5.05345 | 0.809199 | ||||||||
\(40\) | 1.00272 | 0.158544 | ||||||||
\(41\) | −5.98039 | −0.933980 | −0.466990 | − | 0.884263i | \(-0.654662\pi\) | ||||
−0.466990 | + | 0.884263i | \(0.654662\pi\) | |||||||
\(42\) | −1.44426 | −0.222854 | ||||||||
\(43\) | −6.75944 | −1.03081 | −0.515403 | − | 0.856948i | \(-0.672358\pi\) | ||||
−0.515403 | + | 0.856948i | \(0.672358\pi\) | |||||||
\(44\) | 2.47406 | 0.372978 | ||||||||
\(45\) | 2.31975 | 0.345808 | ||||||||
\(46\) | 9.77020 | 1.44054 | ||||||||
\(47\) | 0.151070 | 0.0220358 | 0.0110179 | − | 0.999939i | \(-0.496493\pi\) | ||||
0.0110179 | + | 0.999939i | \(0.496493\pi\) | |||||||
\(48\) | −2.33177 | −0.336562 | ||||||||
\(49\) | −6.31464 | −0.902091 | ||||||||
\(50\) | −2.11520 | −0.299134 | ||||||||
\(51\) | 1.84752 | 0.258704 | ||||||||
\(52\) | 15.1587 | 2.10213 | ||||||||
\(53\) | −10.7003 | −1.46980 | −0.734898 | − | 0.678177i | \(-0.762770\pi\) | ||||
−0.734898 | + | 0.678177i | \(0.762770\pi\) | |||||||
\(54\) | 9.28062 | 1.26293 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −0.830117 | −0.110929 | ||||||||
\(57\) | −1.60787 | −0.212967 | ||||||||
\(58\) | −2.48712 | −0.326575 | ||||||||
\(59\) | 4.22161 | 0.549607 | 0.274804 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274804 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(60\) | −2.04054 | −0.263432 | ||||||||
\(61\) | 3.88540 | 0.497474 | 0.248737 | − | 0.968571i | \(-0.419984\pi\) | ||||
0.248737 | + | 0.968571i | \(0.419984\pi\) | |||||||
\(62\) | 15.9636 | 2.02737 | ||||||||
\(63\) | −1.92044 | −0.241952 | ||||||||
\(64\) | −11.2365 | −1.40456 | ||||||||
\(65\) | −6.12707 | −0.759969 | ||||||||
\(66\) | −1.74456 | −0.214740 | ||||||||
\(67\) | 8.84825 | 1.08099 | 0.540493 | − | 0.841349i | \(-0.318238\pi\) | ||||
0.540493 | + | 0.841349i | \(0.318238\pi\) | |||||||
\(68\) | 5.54195 | 0.672060 | ||||||||
\(69\) | −3.80967 | −0.458631 | ||||||||
\(70\) | 1.75110 | 0.209296 | ||||||||
\(71\) | 9.01270 | 1.06961 | 0.534805 | − | 0.844975i | \(-0.320385\pi\) | ||||
0.534805 | + | 0.844975i | \(0.320385\pi\) | |||||||
\(72\) | 2.32606 | 0.274129 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −4.55360 | −0.529345 | ||||||||
\(75\) | 0.824774 | 0.0952367 | ||||||||
\(76\) | −4.82308 | −0.553245 | ||||||||
\(77\) | 0.827865 | 0.0943440 | ||||||||
\(78\) | −10.6890 | −1.21029 | ||||||||
\(79\) | 8.75713 | 0.985254 | 0.492627 | − | 0.870240i | \(-0.336037\pi\) | ||||
0.492627 | + | 0.870240i | \(0.336037\pi\) | |||||||
\(80\) | 2.82716 | 0.316086 | ||||||||
\(81\) | 3.34047 | 0.371164 | ||||||||
\(82\) | 12.6497 | 1.39693 | ||||||||
\(83\) | −0.0896414 | −0.00983942 | −0.00491971 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00491971 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(84\) | 1.68929 | 0.184317 | ||||||||
\(85\) | −2.24003 | −0.242965 | ||||||||
\(86\) | 14.2976 | 1.54174 | ||||||||
\(87\) | 0.969798 | 0.103973 | ||||||||
\(88\) | −1.00272 | −0.106890 | ||||||||
\(89\) | −15.0105 | −1.59111 | −0.795556 | − | 0.605880i | \(-0.792821\pi\) | ||||
−0.795556 | + | 0.605880i | \(0.792821\pi\) | |||||||
\(90\) | −4.90672 | −0.517214 | ||||||||
\(91\) | 5.07238 | 0.531730 | ||||||||
\(92\) | −11.4278 | −1.19143 | ||||||||
\(93\) | −6.22464 | −0.645465 | ||||||||
\(94\) | −0.319543 | −0.0329583 | ||||||||
\(95\) | 1.94946 | 0.200011 | ||||||||
\(96\) | 6.58618 | 0.672200 | ||||||||
\(97\) | 15.6292 | 1.58690 | 0.793452 | − | 0.608633i | \(-0.208282\pi\) | ||||
0.793452 | + | 0.608633i | \(0.208282\pi\) | |||||||
\(98\) | 13.3567 | 1.34923 | ||||||||
\(99\) | −2.31975 | −0.233143 | ||||||||
\(100\) | 2.47406 | 0.247406 | ||||||||
\(101\) | −16.1945 | −1.61141 | −0.805705 | − | 0.592317i | \(-0.798213\pi\) | ||||
−0.805705 | + | 0.592317i | \(0.798213\pi\) | |||||||
\(102\) | −3.90786 | −0.386936 | ||||||||
\(103\) | −8.60944 | −0.848314 | −0.424157 | − | 0.905589i | \(-0.639429\pi\) | ||||
−0.424157 | + | 0.905589i | \(0.639429\pi\) | |||||||
\(104\) | −6.14374 | −0.602443 | ||||||||
\(105\) | −0.682802 | −0.0666346 | ||||||||
\(106\) | 22.6332 | 2.19833 | ||||||||
\(107\) | −11.8020 | −1.14094 | −0.570469 | − | 0.821319i | \(-0.693238\pi\) | ||||
−0.570469 | + | 0.821319i | \(0.693238\pi\) | |||||||
\(108\) | −10.8551 | −1.04454 | ||||||||
\(109\) | 13.1159 | 1.25627 | 0.628136 | − | 0.778104i | \(-0.283818\pi\) | ||||
0.628136 | + | 0.778104i | \(0.283818\pi\) | |||||||
\(110\) | 2.11520 | 0.201676 | ||||||||
\(111\) | 1.77558 | 0.168530 | ||||||||
\(112\) | −2.34051 | −0.221157 | ||||||||
\(113\) | 0.612633 | 0.0576317 | 0.0288158 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288158 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(114\) | 3.40095 | 0.318528 | ||||||||
\(115\) | 4.61905 | 0.430729 | ||||||||
\(116\) | 2.90908 | 0.270101 | ||||||||
\(117\) | −14.2132 | −1.31402 | ||||||||
\(118\) | −8.92954 | −0.822031 | ||||||||
\(119\) | 1.85444 | 0.169996 | ||||||||
\(120\) | 0.827018 | 0.0754961 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.21838 | −0.744057 | ||||||||
\(123\) | −4.93247 | −0.444746 | ||||||||
\(124\) | −18.6719 | −1.67679 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.06210 | 0.361881 | ||||||||
\(127\) | −4.88916 | −0.433843 | −0.216921 | − | 0.976189i | \(-0.569602\pi\) | ||||
−0.216921 | + | 0.976189i | \(0.569602\pi\) | |||||||
\(128\) | 7.79643 | 0.689113 | ||||||||
\(129\) | −5.57502 | −0.490853 | ||||||||
\(130\) | 12.9599 | 1.13666 | ||||||||
\(131\) | −13.3123 | −1.16310 | −0.581549 | − | 0.813511i | \(-0.697553\pi\) | ||||
−0.581549 | + | 0.813511i | \(0.697553\pi\) | |||||||
\(132\) | 2.04054 | 0.177606 | ||||||||
\(133\) | −1.61389 | −0.139942 | ||||||||
\(134\) | −18.7158 | −1.61680 | ||||||||
\(135\) | 4.38759 | 0.377624 | ||||||||
\(136\) | −2.24612 | −0.192603 | ||||||||
\(137\) | −14.1345 | −1.20759 | −0.603796 | − | 0.797139i | \(-0.706346\pi\) | ||||
−0.603796 | + | 0.797139i | \(0.706346\pi\) | |||||||
\(138\) | 8.05821 | 0.685960 | ||||||||
\(139\) | 18.3988 | 1.56057 | 0.780284 | − | 0.625425i | \(-0.215074\pi\) | ||||
0.780284 | + | 0.625425i | \(0.215074\pi\) | |||||||
\(140\) | −2.04818 | −0.173103 | ||||||||
\(141\) | 0.124599 | 0.0104931 | ||||||||
\(142\) | −19.0636 | −1.59978 | ||||||||
\(143\) | 6.12707 | 0.512371 | ||||||||
\(144\) | 6.55830 | 0.546525 | ||||||||
\(145\) | −1.17583 | −0.0976477 | ||||||||
\(146\) | −2.11520 | −0.175055 | ||||||||
\(147\) | −5.20815 | −0.429561 | ||||||||
\(148\) | 5.32615 | 0.437807 | ||||||||
\(149\) | −4.23845 | −0.347227 | −0.173614 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173614 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(150\) | −1.74456 | −0.142443 | ||||||||
\(151\) | −5.08106 | −0.413491 | −0.206745 | − | 0.978395i | \(-0.566287\pi\) | ||||
−0.206745 | + | 0.978395i | \(0.566287\pi\) | |||||||
\(152\) | 1.95477 | 0.158552 | ||||||||
\(153\) | −5.19629 | −0.420095 | ||||||||
\(154\) | −1.75110 | −0.141107 | ||||||||
\(155\) | 7.54708 | 0.606196 | ||||||||
\(156\) | 12.5025 | 1.00100 | ||||||||
\(157\) | 0.401127 | 0.0320134 | 0.0160067 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160067 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(158\) | −18.5231 | −1.47362 | ||||||||
\(159\) | −8.82532 | −0.699893 | ||||||||
\(160\) | −7.98544 | −0.631304 | ||||||||
\(161\) | −3.82395 | −0.301369 | ||||||||
\(162\) | −7.06575 | −0.555138 | ||||||||
\(163\) | −8.12504 | −0.636402 | −0.318201 | − | 0.948023i | \(-0.603079\pi\) | ||||
−0.318201 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(164\) | −14.7958 | −1.15536 | ||||||||
\(165\) | −0.824774 | −0.0642086 | ||||||||
\(166\) | 0.189609 | 0.0147165 | ||||||||
\(167\) | 6.95319 | 0.538054 | 0.269027 | − | 0.963133i | \(-0.413298\pi\) | ||||
0.269027 | + | 0.963133i | \(0.413298\pi\) | |||||||
\(168\) | −0.684659 | −0.0528226 | ||||||||
\(169\) | 24.5409 | 1.88777 | ||||||||
\(170\) | 4.73809 | 0.363395 | ||||||||
\(171\) | 4.52226 | 0.345826 | ||||||||
\(172\) | −16.7232 | −1.27514 | ||||||||
\(173\) | −24.3172 | −1.84880 | −0.924401 | − | 0.381421i | \(-0.875435\pi\) | ||||
−0.924401 | + | 0.381421i | \(0.875435\pi\) | |||||||
\(174\) | −2.05131 | −0.155510 | ||||||||
\(175\) | 0.827865 | 0.0625807 | ||||||||
\(176\) | −2.82716 | −0.213105 | ||||||||
\(177\) | 3.48188 | 0.261714 | ||||||||
\(178\) | 31.7502 | 2.37978 | ||||||||
\(179\) | 9.69553 | 0.724678 | 0.362339 | − | 0.932046i | \(-0.381978\pi\) | ||||
0.362339 | + | 0.932046i | \(0.381978\pi\) | |||||||
\(180\) | 5.73918 | 0.427774 | ||||||||
\(181\) | −15.8353 | −1.17703 | −0.588515 | − | 0.808487i | \(-0.700287\pi\) | ||||
−0.588515 | + | 0.808487i | \(0.700287\pi\) | |||||||
\(182\) | −10.7291 | −0.795293 | ||||||||
\(183\) | 3.20458 | 0.236889 | ||||||||
\(184\) | 4.63162 | 0.341447 | ||||||||
\(185\) | −2.15280 | −0.158277 | ||||||||
\(186\) | 13.1663 | 0.965402 | ||||||||
\(187\) | 2.24003 | 0.163807 | ||||||||
\(188\) | 0.373756 | 0.0272589 | ||||||||
\(189\) | −3.63233 | −0.264213 | ||||||||
\(190\) | −4.12349 | −0.299150 | ||||||||
\(191\) | −6.10008 | −0.441386 | −0.220693 | − | 0.975343i | \(-0.570832\pi\) | ||||
−0.220693 | + | 0.975343i | \(0.570832\pi\) | |||||||
\(192\) | −9.26754 | −0.668827 | ||||||||
\(193\) | 4.08667 | 0.294165 | 0.147082 | − | 0.989124i | \(-0.453012\pi\) | ||||
0.147082 | + | 0.989124i | \(0.453012\pi\) | |||||||
\(194\) | −33.0588 | −2.37348 | ||||||||
\(195\) | −5.05345 | −0.361885 | ||||||||
\(196\) | −15.6228 | −1.11591 | ||||||||
\(197\) | −5.86681 | −0.417993 | −0.208996 | − | 0.977916i | \(-0.567020\pi\) | ||||
−0.208996 | + | 0.977916i | \(0.567020\pi\) | |||||||
\(198\) | 4.90672 | 0.348706 | ||||||||
\(199\) | 16.6657 | 1.18140 | 0.590701 | − | 0.806891i | \(-0.298851\pi\) | ||||
0.590701 | + | 0.806891i | \(0.298851\pi\) | |||||||
\(200\) | −1.00272 | −0.0709031 | ||||||||
\(201\) | 7.29781 | 0.514748 | ||||||||
\(202\) | 34.2545 | 2.41014 | ||||||||
\(203\) | 0.973432 | 0.0683215 | ||||||||
\(204\) | 4.57086 | 0.320024 | ||||||||
\(205\) | 5.98039 | 0.417689 | ||||||||
\(206\) | 18.2107 | 1.26880 | ||||||||
\(207\) | 10.7150 | 0.744746 | ||||||||
\(208\) | −17.3222 | −1.20108 | ||||||||
\(209\) | −1.94946 | −0.134847 | ||||||||
\(210\) | 1.44426 | 0.0996634 | ||||||||
\(211\) | 2.50375 | 0.172365 | 0.0861826 | − | 0.996279i | \(-0.472533\pi\) | ||||
0.0861826 | + | 0.996279i | \(0.472533\pi\) | |||||||
\(212\) | −26.4731 | −1.81818 | ||||||||
\(213\) | 7.43344 | 0.509331 | ||||||||
\(214\) | 24.9634 | 1.70647 | ||||||||
\(215\) | 6.75944 | 0.460990 | ||||||||
\(216\) | 4.39953 | 0.299350 | ||||||||
\(217\) | −6.24796 | −0.424139 | ||||||||
\(218\) | −27.7426 | −1.87897 | ||||||||
\(219\) | 0.824774 | 0.0557331 | ||||||||
\(220\) | −2.47406 | −0.166801 | ||||||||
\(221\) | 13.7248 | 0.923229 | ||||||||
\(222\) | −3.75569 | −0.252065 | ||||||||
\(223\) | −22.6474 | −1.51658 | −0.758289 | − | 0.651918i | \(-0.773965\pi\) | ||||
−0.758289 | + | 0.651918i | \(0.773965\pi\) | |||||||
\(224\) | 6.61086 | 0.441707 | ||||||||
\(225\) | −2.31975 | −0.154650 | ||||||||
\(226\) | −1.29584 | −0.0861979 | ||||||||
\(227\) | 16.7119 | 1.10921 | 0.554603 | − | 0.832115i | \(-0.312870\pi\) | ||||
0.554603 | + | 0.832115i | \(0.312870\pi\) | |||||||
\(228\) | −3.97795 | −0.263446 | ||||||||
\(229\) | −7.76788 | −0.513316 | −0.256658 | − | 0.966502i | \(-0.582621\pi\) | ||||
−0.256658 | + | 0.966502i | \(0.582621\pi\) | |||||||
\(230\) | −9.77020 | −0.644228 | ||||||||
\(231\) | 0.682802 | 0.0449250 | ||||||||
\(232\) | −1.17903 | −0.0774073 | ||||||||
\(233\) | −28.6401 | −1.87627 | −0.938137 | − | 0.346266i | \(-0.887450\pi\) | ||||
−0.938137 | + | 0.346266i | \(0.887450\pi\) | |||||||
\(234\) | 30.0638 | 1.96533 | ||||||||
\(235\) | −0.151070 | −0.00985472 | ||||||||
\(236\) | 10.4445 | 0.679879 | ||||||||
\(237\) | 7.22266 | 0.469162 | ||||||||
\(238\) | −3.92250 | −0.254258 | ||||||||
\(239\) | 5.65644 | 0.365885 | 0.182942 | − | 0.983124i | \(-0.441438\pi\) | ||||
0.182942 | + | 0.983124i | \(0.441438\pi\) | |||||||
\(240\) | 2.33177 | 0.150515 | ||||||||
\(241\) | −1.17445 | −0.0756531 | −0.0378266 | − | 0.999284i | \(-0.512043\pi\) | ||||
−0.0378266 | + | 0.999284i | \(0.512043\pi\) | |||||||
\(242\) | −2.11520 | −0.135970 | ||||||||
\(243\) | 15.9179 | 1.02113 | ||||||||
\(244\) | 9.61269 | 0.615390 | ||||||||
\(245\) | 6.31464 | 0.403428 | ||||||||
\(246\) | 10.4331 | 0.665193 | ||||||||
\(247\) | −11.9445 | −0.760009 | ||||||||
\(248\) | 7.56761 | 0.480544 | ||||||||
\(249\) | −0.0739339 | −0.00468537 | ||||||||
\(250\) | 2.11520 | 0.133777 | ||||||||
\(251\) | 20.2478 | 1.27803 | 0.639016 | − | 0.769194i | \(-0.279342\pi\) | ||||
0.639016 | + | 0.769194i | \(0.279342\pi\) | |||||||
\(252\) | −4.75127 | −0.299302 | ||||||||
\(253\) | −4.61905 | −0.290397 | ||||||||
\(254\) | 10.3415 | 0.648886 | ||||||||
\(255\) | −1.84752 | −0.115696 | ||||||||
\(256\) | 5.98194 | 0.373871 | ||||||||
\(257\) | −0.371738 | −0.0231884 | −0.0115942 | − | 0.999933i | \(-0.503691\pi\) | ||||
−0.0115942 | + | 0.999933i | \(0.503691\pi\) | |||||||
\(258\) | 11.7923 | 0.734154 | ||||||||
\(259\) | 1.78223 | 0.110742 | ||||||||
\(260\) | −15.1587 | −0.940103 | ||||||||
\(261\) | −2.72764 | −0.168837 | ||||||||
\(262\) | 28.1581 | 1.73961 | ||||||||
\(263\) | −4.68370 | −0.288810 | −0.144405 | − | 0.989519i | \(-0.546127\pi\) | ||||
−0.144405 | + | 0.989519i | \(0.546127\pi\) | |||||||
\(264\) | −0.827018 | −0.0508995 | ||||||||
\(265\) | 10.7003 | 0.657313 | ||||||||
\(266\) | 3.41370 | 0.209307 | ||||||||
\(267\) | −12.3803 | −0.757661 | ||||||||
\(268\) | 21.8911 | 1.33721 | ||||||||
\(269\) | −9.45147 | −0.576266 | −0.288133 | − | 0.957590i | \(-0.593035\pi\) | ||||
−0.288133 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(270\) | −9.28062 | −0.564800 | ||||||||
\(271\) | −12.7498 | −0.774493 | −0.387246 | − | 0.921976i | \(-0.626574\pi\) | ||||
−0.387246 | + | 0.921976i | \(0.626574\pi\) | |||||||
\(272\) | −6.33291 | −0.383989 | ||||||||
\(273\) | 4.18357 | 0.253201 | ||||||||
\(274\) | 29.8972 | 1.80616 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −9.42534 | −0.567339 | ||||||||
\(277\) | 5.66400 | 0.340317 | 0.170159 | − | 0.985417i | \(-0.445572\pi\) | ||||
0.170159 | + | 0.985417i | \(0.445572\pi\) | |||||||
\(278\) | −38.9171 | −2.33410 | ||||||||
\(279\) | 17.5073 | 1.04814 | ||||||||
\(280\) | 0.830117 | 0.0496090 | ||||||||
\(281\) | 0.0361771 | 0.00215815 | 0.00107907 | − | 0.999999i | \(-0.499657\pi\) | ||||
0.00107907 | + | 0.999999i | \(0.499657\pi\) | |||||||
\(282\) | −0.263551 | −0.0156942 | ||||||||
\(283\) | −24.8316 | −1.47608 | −0.738042 | − | 0.674755i | \(-0.764249\pi\) | ||||
−0.738042 | + | 0.674755i | \(0.764249\pi\) | |||||||
\(284\) | 22.2979 | 1.32314 | ||||||||
\(285\) | 1.60787 | 0.0952417 | ||||||||
\(286\) | −12.9599 | −0.766338 | ||||||||
\(287\) | −4.95096 | −0.292246 | ||||||||
\(288\) | −18.5242 | −1.09155 | ||||||||
\(289\) | −11.9823 | −0.704840 | ||||||||
\(290\) | 2.48712 | 0.146049 | ||||||||
\(291\) | 12.8906 | 0.755658 | ||||||||
\(292\) | 2.47406 | 0.144783 | ||||||||
\(293\) | −3.94204 | −0.230297 | −0.115148 | − | 0.993348i | \(-0.536734\pi\) | ||||
−0.115148 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(294\) | 11.0163 | 0.642482 | ||||||||
\(295\) | −4.22161 | −0.245792 | ||||||||
\(296\) | −2.15866 | −0.125469 | ||||||||
\(297\) | −4.38759 | −0.254594 | ||||||||
\(298\) | 8.96515 | 0.519337 | ||||||||
\(299\) | −28.3012 | −1.63670 | ||||||||
\(300\) | 2.04054 | 0.117810 | ||||||||
\(301\) | −5.59591 | −0.322543 | ||||||||
\(302\) | 10.7474 | 0.618445 | ||||||||
\(303\) | −13.3568 | −0.767327 | ||||||||
\(304\) | 5.51144 | 0.316103 | ||||||||
\(305\) | −3.88540 | −0.222477 | ||||||||
\(306\) | 10.9912 | 0.628324 | ||||||||
\(307\) | 8.69983 | 0.496526 | 0.248263 | − | 0.968693i | \(-0.420140\pi\) | ||||
0.248263 | + | 0.968693i | \(0.420140\pi\) | |||||||
\(308\) | 2.04818 | 0.116706 | ||||||||
\(309\) | −7.10085 | −0.403953 | ||||||||
\(310\) | −15.9636 | −0.906669 | ||||||||
\(311\) | 18.4221 | 1.04462 | 0.522311 | − | 0.852755i | \(-0.325070\pi\) | ||||
0.522311 | + | 0.852755i | \(0.325070\pi\) | |||||||
\(312\) | −5.06720 | −0.286873 | ||||||||
\(313\) | 14.4041 | 0.814168 | 0.407084 | − | 0.913391i | \(-0.366546\pi\) | ||||
0.407084 | + | 0.913391i | \(0.366546\pi\) | |||||||
\(314\) | −0.848461 | −0.0478814 | ||||||||
\(315\) | 1.92044 | 0.108204 | ||||||||
\(316\) | 21.6656 | 1.21879 | ||||||||
\(317\) | −1.64194 | −0.0922203 | −0.0461101 | − | 0.998936i | \(-0.514683\pi\) | ||||
−0.0461101 | + | 0.998936i | \(0.514683\pi\) | |||||||
\(318\) | 18.6673 | 1.04681 | ||||||||
\(319\) | 1.17583 | 0.0658341 | ||||||||
\(320\) | 11.2365 | 0.628137 | ||||||||
\(321\) | −9.73394 | −0.543296 | ||||||||
\(322\) | 8.08840 | 0.450749 | ||||||||
\(323\) | −4.36684 | −0.242978 | ||||||||
\(324\) | 8.26451 | 0.459140 | ||||||||
\(325\) | 6.12707 | 0.339869 | ||||||||
\(326\) | 17.1861 | 0.951847 | ||||||||
\(327\) | 10.8176 | 0.598216 | ||||||||
\(328\) | 5.99666 | 0.331110 | ||||||||
\(329\) | 0.125066 | 0.00689509 | ||||||||
\(330\) | 1.74456 | 0.0960348 | ||||||||
\(331\) | −2.62836 | −0.144468 | −0.0722340 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722340 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(332\) | −0.221778 | −0.0121716 | ||||||||
\(333\) | −4.99396 | −0.273667 | ||||||||
\(334\) | −14.7074 | −0.804751 | ||||||||
\(335\) | −8.84825 | −0.483431 | ||||||||
\(336\) | −1.93039 | −0.105311 | ||||||||
\(337\) | 4.00470 | 0.218150 | 0.109075 | − | 0.994034i | \(-0.465211\pi\) | ||||
0.109075 | + | 0.994034i | \(0.465211\pi\) | |||||||
\(338\) | −51.9089 | −2.82347 | ||||||||
\(339\) | 0.505284 | 0.0274433 | ||||||||
\(340\) | −5.54195 | −0.300554 | ||||||||
\(341\) | −7.54708 | −0.408697 | ||||||||
\(342\) | −9.56547 | −0.517241 | ||||||||
\(343\) | −11.0227 | −0.595171 | ||||||||
\(344\) | 6.77784 | 0.365436 | ||||||||
\(345\) | 3.80967 | 0.205106 | ||||||||
\(346\) | 51.4357 | 2.76520 | ||||||||
\(347\) | −25.0253 | −1.34343 | −0.671715 | − | 0.740810i | \(-0.734442\pi\) | ||||
−0.671715 | + | 0.740810i | \(0.734442\pi\) | |||||||
\(348\) | 2.39933 | 0.128618 | ||||||||
\(349\) | −35.4360 | −1.89685 | −0.948424 | − | 0.317004i | \(-0.897323\pi\) | ||||
−0.948424 | + | 0.317004i | \(0.897323\pi\) | |||||||
\(350\) | −1.75110 | −0.0936001 | ||||||||
\(351\) | −26.8831 | −1.43491 | ||||||||
\(352\) | 7.98544 | 0.425625 | ||||||||
\(353\) | −18.8403 | −1.00277 | −0.501385 | − | 0.865224i | \(-0.667176\pi\) | ||||
−0.501385 | + | 0.865224i | \(0.667176\pi\) | |||||||
\(354\) | −7.36485 | −0.391437 | ||||||||
\(355\) | −9.01270 | −0.478344 | ||||||||
\(356\) | −37.1369 | −1.96825 | ||||||||
\(357\) | 1.52949 | 0.0809493 | ||||||||
\(358\) | −20.5079 | −1.08388 | ||||||||
\(359\) | 27.9176 | 1.47343 | 0.736716 | − | 0.676202i | \(-0.236375\pi\) | ||||
0.736716 | + | 0.676202i | \(0.236375\pi\) | |||||||
\(360\) | −2.32606 | −0.122594 | ||||||||
\(361\) | −15.1996 | −0.799979 | ||||||||
\(362\) | 33.4948 | 1.76045 | ||||||||
\(363\) | 0.824774 | 0.0432894 | ||||||||
\(364\) | 12.5494 | 0.657765 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −6.77831 | −0.354308 | ||||||||
\(367\) | −14.6189 | −0.763100 | −0.381550 | − | 0.924348i | \(-0.624610\pi\) | ||||
−0.381550 | + | 0.924348i | \(0.624610\pi\) | |||||||
\(368\) | 13.0588 | 0.680737 | ||||||||
\(369\) | 13.8730 | 0.722199 | ||||||||
\(370\) | 4.55360 | 0.236730 | ||||||||
\(371\) | −8.85839 | −0.459905 | ||||||||
\(372\) | −15.4001 | −0.798458 | ||||||||
\(373\) | 7.39667 | 0.382985 | 0.191493 | − | 0.981494i | \(-0.438667\pi\) | ||||
0.191493 | + | 0.981494i | \(0.438667\pi\) | |||||||
\(374\) | −4.73809 | −0.245001 | ||||||||
\(375\) | −0.824774 | −0.0425912 | ||||||||
\(376\) | −0.151481 | −0.00781204 | ||||||||
\(377\) | 7.20441 | 0.371046 | ||||||||
\(378\) | 7.68309 | 0.395176 | ||||||||
\(379\) | −5.83226 | −0.299583 | −0.149792 | − | 0.988718i | \(-0.547860\pi\) | ||||
−0.149792 | + | 0.988718i | \(0.547860\pi\) | |||||||
\(380\) | 4.82308 | 0.247419 | ||||||||
\(381\) | −4.03245 | −0.206589 | ||||||||
\(382\) | 12.9029 | 0.660168 | ||||||||
\(383\) | −17.6802 | −0.903418 | −0.451709 | − | 0.892165i | \(-0.649186\pi\) | ||||
−0.451709 | + | 0.892165i | \(0.649186\pi\) | |||||||
\(384\) | 6.43029 | 0.328144 | ||||||||
\(385\) | −0.827865 | −0.0421919 | ||||||||
\(386\) | −8.64411 | −0.439974 | ||||||||
\(387\) | 15.6802 | 0.797070 | ||||||||
\(388\) | 38.6675 | 1.96304 | ||||||||
\(389\) | 6.51062 | 0.330101 | 0.165051 | − | 0.986285i | \(-0.447221\pi\) | ||||
0.165051 | + | 0.986285i | \(0.447221\pi\) | |||||||
\(390\) | 10.6890 | 0.541260 | ||||||||
\(391\) | −10.3468 | −0.523260 | ||||||||
\(392\) | 6.33182 | 0.319805 | ||||||||
\(393\) | −10.9796 | −0.553848 | ||||||||
\(394\) | 12.4094 | 0.625179 | ||||||||
\(395\) | −8.75713 | −0.440619 | ||||||||
\(396\) | −5.73918 | −0.288405 | ||||||||
\(397\) | 1.69173 | 0.0849056 | 0.0424528 | − | 0.999098i | \(-0.486483\pi\) | ||||
0.0424528 | + | 0.999098i | \(0.486483\pi\) | |||||||
\(398\) | −35.2513 | −1.76699 | ||||||||
\(399\) | −1.33110 | −0.0666381 | ||||||||
\(400\) | −2.82716 | −0.141358 | ||||||||
\(401\) | 18.8440 | 0.941023 | 0.470511 | − | 0.882394i | \(-0.344069\pi\) | ||||
0.470511 | + | 0.882394i | \(0.344069\pi\) | |||||||
\(402\) | −15.4363 | −0.769892 | ||||||||
\(403\) | −46.2415 | −2.30345 | ||||||||
\(404\) | −40.0660 | −1.99336 | ||||||||
\(405\) | −3.34047 | −0.165989 | ||||||||
\(406\) | −2.05900 | −0.102186 | ||||||||
\(407\) | 2.15280 | 0.106710 | ||||||||
\(408\) | −1.85254 | −0.0917145 | ||||||||
\(409\) | −4.28795 | −0.212025 | −0.106013 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106013 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(410\) | −12.6497 | −0.624724 | ||||||||
\(411\) | −11.6578 | −0.575035 | ||||||||
\(412\) | −21.3002 | −1.04939 | ||||||||
\(413\) | 3.49492 | 0.171974 | ||||||||
\(414\) | −22.6644 | −1.11389 | ||||||||
\(415\) | 0.0896414 | 0.00440032 | ||||||||
\(416\) | 48.9273 | 2.39886 | ||||||||
\(417\) | 15.1749 | 0.743117 | ||||||||
\(418\) | 4.12349 | 0.201687 | ||||||||
\(419\) | −4.03059 | −0.196907 | −0.0984536 | − | 0.995142i | \(-0.531390\pi\) | ||||
−0.0984536 | + | 0.995142i | \(0.531390\pi\) | |||||||
\(420\) | −1.68929 | −0.0824289 | ||||||||
\(421\) | −33.1294 | −1.61463 | −0.807315 | − | 0.590121i | \(-0.799080\pi\) | ||||
−0.807315 | + | 0.590121i | \(0.799080\pi\) | |||||||
\(422\) | −5.29592 | −0.257802 | ||||||||
\(423\) | −0.350444 | −0.0170392 | ||||||||
\(424\) | 10.7294 | 0.521066 | ||||||||
\(425\) | 2.24003 | 0.108657 | ||||||||
\(426\) | −15.7232 | −0.761791 | ||||||||
\(427\) | 3.21659 | 0.155661 | ||||||||
\(428\) | −29.1987 | −1.41137 | ||||||||
\(429\) | 5.05345 | 0.243983 | ||||||||
\(430\) | −14.2976 | −0.689489 | ||||||||
\(431\) | −19.0881 | −0.919440 | −0.459720 | − | 0.888064i | \(-0.652050\pi\) | ||||
−0.459720 | + | 0.888064i | \(0.652050\pi\) | |||||||
\(432\) | 12.4044 | 0.596808 | ||||||||
\(433\) | 25.5852 | 1.22955 | 0.614774 | − | 0.788703i | \(-0.289247\pi\) | ||||
0.614774 | + | 0.788703i | \(0.289247\pi\) | |||||||
\(434\) | 13.2157 | 0.634372 | ||||||||
\(435\) | −0.969798 | −0.0464982 | ||||||||
\(436\) | 32.4494 | 1.55404 | ||||||||
\(437\) | 9.00466 | 0.430751 | ||||||||
\(438\) | −1.74456 | −0.0833583 | ||||||||
\(439\) | 10.7910 | 0.515026 | 0.257513 | − | 0.966275i | \(-0.417097\pi\) | ||||
0.257513 | + | 0.966275i | \(0.417097\pi\) | |||||||
\(440\) | 1.00272 | 0.0478028 | ||||||||
\(441\) | 14.6484 | 0.697541 | ||||||||
\(442\) | −29.0306 | −1.38085 | ||||||||
\(443\) | −3.42386 | −0.162673 | −0.0813363 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813363 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(444\) | 4.39287 | 0.208476 | ||||||||
\(445\) | 15.0105 | 0.711567 | ||||||||
\(446\) | 47.9036 | 2.26830 | ||||||||
\(447\) | −3.49576 | −0.165344 | ||||||||
\(448\) | −9.30226 | −0.439491 | ||||||||
\(449\) | 4.68094 | 0.220907 | 0.110454 | − | 0.993881i | \(-0.464770\pi\) | ||||
0.110454 | + | 0.993881i | \(0.464770\pi\) | |||||||
\(450\) | 4.90672 | 0.231305 | ||||||||
\(451\) | −5.98039 | −0.281606 | ||||||||
\(452\) | 1.51569 | 0.0712920 | ||||||||
\(453\) | −4.19073 | −0.196897 | ||||||||
\(454\) | −35.3489 | −1.65901 | ||||||||
\(455\) | −5.07238 | −0.237797 | ||||||||
\(456\) | 1.61224 | 0.0755001 | ||||||||
\(457\) | 6.87059 | 0.321392 | 0.160696 | − | 0.987004i | \(-0.448626\pi\) | ||||
0.160696 | + | 0.987004i | \(0.448626\pi\) | |||||||
\(458\) | 16.4306 | 0.767751 | ||||||||
\(459\) | −9.82831 | −0.458746 | ||||||||
\(460\) | 11.4278 | 0.532823 | ||||||||
\(461\) | −20.0665 | −0.934591 | −0.467296 | − | 0.884101i | \(-0.654772\pi\) | ||||
−0.467296 | + | 0.884101i | \(0.654772\pi\) | |||||||
\(462\) | −1.44426 | −0.0671930 | ||||||||
\(463\) | 7.57643 | 0.352106 | 0.176053 | − | 0.984381i | \(-0.443667\pi\) | ||||
0.176053 | + | 0.984381i | \(0.443667\pi\) | |||||||
\(464\) | −3.32427 | −0.154325 | ||||||||
\(465\) | 6.22464 | 0.288661 | ||||||||
\(466\) | 60.5794 | 2.80628 | ||||||||
\(467\) | −17.3491 | −0.802818 | −0.401409 | − | 0.915899i | \(-0.631479\pi\) | ||||
−0.401409 | + | 0.915899i | \(0.631479\pi\) | |||||||
\(468\) | −35.1644 | −1.62547 | ||||||||
\(469\) | 7.32515 | 0.338244 | ||||||||
\(470\) | 0.319543 | 0.0147394 | ||||||||
\(471\) | 0.330839 | 0.0152442 | ||||||||
\(472\) | −4.23310 | −0.194844 | ||||||||
\(473\) | −6.75944 | −0.310800 | ||||||||
\(474\) | −15.2773 | −0.701711 | ||||||||
\(475\) | −1.94946 | −0.0894474 | ||||||||
\(476\) | 4.58798 | 0.210290 | ||||||||
\(477\) | 24.8220 | 1.13652 | ||||||||
\(478\) | −11.9645 | −0.547243 | ||||||||
\(479\) | −8.28398 | −0.378505 | −0.189252 | − | 0.981928i | \(-0.560606\pi\) | ||||
−0.189252 | + | 0.981928i | \(0.560606\pi\) | |||||||
\(480\) | −6.58618 | −0.300617 | ||||||||
\(481\) | 13.1904 | 0.601429 | ||||||||
\(482\) | 2.48420 | 0.113152 | ||||||||
\(483\) | −3.15389 | −0.143507 | ||||||||
\(484\) | 2.47406 | 0.112457 | ||||||||
\(485\) | −15.6292 | −0.709685 | ||||||||
\(486\) | −33.6695 | −1.52728 | ||||||||
\(487\) | −22.0963 | −1.00128 | −0.500640 | − | 0.865656i | \(-0.666902\pi\) | ||||
−0.500640 | + | 0.865656i | \(0.666902\pi\) | |||||||
\(488\) | −3.89597 | −0.176362 | ||||||||
\(489\) | −6.70132 | −0.303044 | ||||||||
\(490\) | −13.3567 | −0.603394 | ||||||||
\(491\) | −31.6243 | −1.42718 | −0.713592 | − | 0.700561i | \(-0.752933\pi\) | ||||
−0.713592 | + | 0.700561i | \(0.752933\pi\) | |||||||
\(492\) | −12.2032 | −0.550163 | ||||||||
\(493\) | 2.63390 | 0.118625 | ||||||||
\(494\) | 25.2649 | 1.13672 | ||||||||
\(495\) | 2.31975 | 0.104265 | ||||||||
\(496\) | 21.3368 | 0.958051 | ||||||||
\(497\) | 7.46129 | 0.334685 | ||||||||
\(498\) | 0.156385 | 0.00700777 | ||||||||
\(499\) | 16.1613 | 0.723478 | 0.361739 | − | 0.932279i | \(-0.382183\pi\) | ||||
0.361739 | + | 0.932279i | \(0.382183\pi\) | |||||||
\(500\) | −2.47406 | −0.110643 | ||||||||
\(501\) | 5.73481 | 0.256213 | ||||||||
\(502\) | −42.8281 | −1.91151 | ||||||||
\(503\) | −3.09687 | −0.138083 | −0.0690413 | − | 0.997614i | \(-0.521994\pi\) | ||||
−0.0690413 | + | 0.997614i | \(0.521994\pi\) | |||||||
\(504\) | 1.92566 | 0.0857758 | ||||||||
\(505\) | 16.1945 | 0.720644 | ||||||||
\(506\) | 9.77020 | 0.434338 | ||||||||
\(507\) | 20.2407 | 0.898923 | ||||||||
\(508\) | −12.0961 | −0.536676 | ||||||||
\(509\) | −37.6697 | −1.66968 | −0.834840 | − | 0.550492i | \(-0.814440\pi\) | ||||
−0.834840 | + | 0.550492i | \(0.814440\pi\) | |||||||
\(510\) | 3.90786 | 0.173043 | ||||||||
\(511\) | 0.827865 | 0.0366226 | ||||||||
\(512\) | −28.2458 | −1.24830 | ||||||||
\(513\) | 8.55344 | 0.377644 | ||||||||
\(514\) | 0.786299 | 0.0346821 | ||||||||
\(515\) | 8.60944 | 0.379377 | ||||||||
\(516\) | −13.7929 | −0.607198 | ||||||||
\(517\) | 0.151070 | 0.00664405 | ||||||||
\(518\) | −3.76976 | −0.165634 | ||||||||
\(519\) | −20.0562 | −0.880370 | ||||||||
\(520\) | 6.14374 | 0.269421 | ||||||||
\(521\) | 5.26003 | 0.230446 | 0.115223 | − | 0.993340i | \(-0.463242\pi\) | ||||
0.115223 | + | 0.993340i | \(0.463242\pi\) | |||||||
\(522\) | 5.76949 | 0.252524 | ||||||||
\(523\) | 35.8193 | 1.56627 | 0.783135 | − | 0.621852i | \(-0.213620\pi\) | ||||
0.783135 | + | 0.621852i | \(0.213620\pi\) | |||||||
\(524\) | −32.9353 | −1.43879 | ||||||||
\(525\) | 0.682802 | 0.0297999 | ||||||||
\(526\) | 9.90695 | 0.431964 | ||||||||
\(527\) | −16.9056 | −0.736422 | ||||||||
\(528\) | −2.33177 | −0.101477 | ||||||||
\(529\) | −1.66437 | −0.0723639 | ||||||||
\(530\) | −22.6332 | −0.983123 | ||||||||
\(531\) | −9.79307 | −0.424983 | ||||||||
\(532\) | −3.99286 | −0.173112 | ||||||||
\(533\) | −36.6423 | −1.58715 | ||||||||
\(534\) | 26.1867 | 1.13321 | ||||||||
\(535\) | 11.8020 | 0.510243 | ||||||||
\(536\) | −8.87232 | −0.383226 | ||||||||
\(537\) | 7.99662 | 0.345080 | ||||||||
\(538\) | 19.9917 | 0.861904 | ||||||||
\(539\) | −6.31464 | −0.271991 | ||||||||
\(540\) | 10.8551 | 0.467131 | ||||||||
\(541\) | −26.0702 | −1.12085 | −0.560424 | − | 0.828206i | \(-0.689362\pi\) | ||||
−0.560424 | + | 0.828206i | \(0.689362\pi\) | |||||||
\(542\) | 26.9683 | 1.15839 | ||||||||
\(543\) | −13.0606 | −0.560482 | ||||||||
\(544\) | 17.8876 | 0.766924 | ||||||||
\(545\) | −13.1159 | −0.561822 | ||||||||
\(546\) | −8.84907 | −0.378705 | ||||||||
\(547\) | −16.4087 | −0.701584 | −0.350792 | − | 0.936453i | \(-0.614088\pi\) | ||||
−0.350792 | + | 0.936453i | \(0.614088\pi\) | |||||||
\(548\) | −34.9695 | −1.49382 | ||||||||
\(549\) | −9.01315 | −0.384672 | ||||||||
\(550\) | −2.11520 | −0.0901923 | ||||||||
\(551\) | −2.29224 | −0.0976529 | ||||||||
\(552\) | 3.82004 | 0.162592 | ||||||||
\(553\) | 7.24972 | 0.308290 | ||||||||
\(554\) | −11.9805 | −0.509002 | ||||||||
\(555\) | −1.77558 | −0.0753690 | ||||||||
\(556\) | 45.5197 | 1.93047 | ||||||||
\(557\) | 15.6256 | 0.662076 | 0.331038 | − | 0.943617i | \(-0.392601\pi\) | ||||
0.331038 | + | 0.943617i | \(0.392601\pi\) | |||||||
\(558\) | −37.0314 | −1.56766 | ||||||||
\(559\) | −41.4156 | −1.75169 | ||||||||
\(560\) | 2.34051 | 0.0989044 | ||||||||
\(561\) | 1.84752 | 0.0780022 | ||||||||
\(562\) | −0.0765218 | −0.00322788 | ||||||||
\(563\) | −34.7228 | −1.46339 | −0.731695 | − | 0.681632i | \(-0.761271\pi\) | ||||
−0.731695 | + | 0.681632i | \(0.761271\pi\) | |||||||
\(564\) | 0.308264 | 0.0129803 | ||||||||
\(565\) | −0.612633 | −0.0257737 | ||||||||
\(566\) | 52.5237 | 2.20773 | ||||||||
\(567\) | 2.76546 | 0.116138 | ||||||||
\(568\) | −9.03722 | −0.379193 | ||||||||
\(569\) | 29.0364 | 1.21727 | 0.608635 | − | 0.793450i | \(-0.291717\pi\) | ||||
0.608635 | + | 0.793450i | \(0.291717\pi\) | |||||||
\(570\) | −3.40095 | −0.142450 | ||||||||
\(571\) | −12.0731 | −0.505244 | −0.252622 | − | 0.967565i | \(-0.581293\pi\) | ||||
−0.252622 | + | 0.967565i | \(0.581293\pi\) | |||||||
\(572\) | 15.1587 | 0.633817 | ||||||||
\(573\) | −5.03119 | −0.210181 | ||||||||
\(574\) | 10.4722 | 0.437103 | ||||||||
\(575\) | −4.61905 | −0.192628 | ||||||||
\(576\) | 26.0657 | 1.08607 | ||||||||
\(577\) | 6.18071 | 0.257306 | 0.128653 | − | 0.991690i | \(-0.458935\pi\) | ||||
0.128653 | + | 0.991690i | \(0.458935\pi\) | |||||||
\(578\) | 25.3449 | 1.05421 | ||||||||
\(579\) | 3.37058 | 0.140077 | ||||||||
\(580\) | −2.90908 | −0.120793 | ||||||||
\(581\) | −0.0742110 | −0.00307879 | ||||||||
\(582\) | −27.2661 | −1.13021 | ||||||||
\(583\) | −10.7003 | −0.443160 | ||||||||
\(584\) | −1.00272 | −0.0414929 | ||||||||
\(585\) | 14.2132 | 0.587646 | ||||||||
\(586\) | 8.33820 | 0.344448 | ||||||||
\(587\) | −37.1615 | −1.53382 | −0.766909 | − | 0.641756i | \(-0.778206\pi\) | ||||
−0.766909 | + | 0.641756i | \(0.778206\pi\) | |||||||
\(588\) | −12.8853 | −0.531379 | ||||||||
\(589\) | 14.7127 | 0.606228 | ||||||||
\(590\) | 8.92954 | 0.367623 | ||||||||
\(591\) | −4.83879 | −0.199041 | ||||||||
\(592\) | −6.08631 | −0.250146 | ||||||||
\(593\) | −44.0427 | −1.80862 | −0.904308 | − | 0.426881i | \(-0.859612\pi\) | ||||
−0.904308 | + | 0.426881i | \(0.859612\pi\) | |||||||
\(594\) | 9.28062 | 0.380788 | ||||||||
\(595\) | −1.85444 | −0.0760246 | ||||||||
\(596\) | −10.4862 | −0.429530 | ||||||||
\(597\) | 13.7455 | 0.562564 | ||||||||
\(598\) | 59.8627 | 2.44797 | ||||||||
\(599\) | 4.93228 | 0.201528 | 0.100764 | − | 0.994910i | \(-0.467871\pi\) | ||||
0.100764 | + | 0.994910i | \(0.467871\pi\) | |||||||
\(600\) | −0.827018 | −0.0337629 | ||||||||
\(601\) | 13.3427 | 0.544260 | 0.272130 | − | 0.962260i | \(-0.412272\pi\) | ||||
0.272130 | + | 0.962260i | \(0.412272\pi\) | |||||||
\(602\) | 11.8364 | 0.482417 | ||||||||
\(603\) | −20.5257 | −0.835871 | ||||||||
\(604\) | −12.5708 | −0.511499 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 28.2522 | 1.14767 | ||||||||
\(607\) | −32.8901 | −1.33497 | −0.667485 | − | 0.744623i | \(-0.732629\pi\) | ||||
−0.667485 | + | 0.744623i | \(0.732629\pi\) | |||||||
\(608\) | −15.5673 | −0.631338 | ||||||||
\(609\) | 0.802861 | 0.0325336 | ||||||||
\(610\) | 8.21838 | 0.332753 | ||||||||
\(611\) | 0.925616 | 0.0374464 | ||||||||
\(612\) | −12.8559 | −0.519670 | ||||||||
\(613\) | 29.0716 | 1.17419 | 0.587095 | − | 0.809518i | \(-0.300272\pi\) | ||||
0.587095 | + | 0.809518i | \(0.300272\pi\) | |||||||
\(614\) | −18.4018 | −0.742638 | ||||||||
\(615\) | 4.93247 | 0.198896 | ||||||||
\(616\) | −0.830117 | −0.0334464 | ||||||||
\(617\) | −19.6068 | −0.789341 | −0.394670 | − | 0.918823i | \(-0.629141\pi\) | ||||
−0.394670 | + | 0.918823i | \(0.629141\pi\) | |||||||
\(618\) | 15.0197 | 0.604180 | ||||||||
\(619\) | −33.4922 | −1.34616 | −0.673082 | − | 0.739568i | \(-0.735030\pi\) | ||||
−0.673082 | + | 0.739568i | \(0.735030\pi\) | |||||||
\(620\) | 18.6719 | 0.749881 | ||||||||
\(621\) | 20.2665 | 0.813267 | ||||||||
\(622\) | −38.9664 | −1.56241 | ||||||||
\(623\) | −12.4267 | −0.497864 | ||||||||
\(624\) | −14.2869 | −0.571934 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.4675 | −1.21773 | ||||||||
\(627\) | −1.60787 | −0.0642120 | ||||||||
\(628\) | 0.992409 | 0.0396014 | ||||||||
\(629\) | 4.82233 | 0.192279 | ||||||||
\(630\) | −4.06210 | −0.161838 | ||||||||
\(631\) | 26.3470 | 1.04886 | 0.524429 | − | 0.851454i | \(-0.324279\pi\) | ||||
0.524429 | + | 0.851454i | \(0.324279\pi\) | |||||||
\(632\) | −8.78096 | −0.349288 | ||||||||
\(633\) | 2.06503 | 0.0820775 | ||||||||
\(634\) | 3.47302 | 0.137931 | ||||||||
\(635\) | 4.88916 | 0.194020 | ||||||||
\(636\) | −21.8343 | −0.865787 | ||||||||
\(637\) | −38.6902 | −1.53296 | ||||||||
\(638\) | −2.48712 | −0.0984660 | ||||||||
\(639\) | −20.9072 | −0.827075 | ||||||||
\(640\) | −7.79643 | −0.308181 | ||||||||
\(641\) | 22.0437 | 0.870676 | 0.435338 | − | 0.900267i | \(-0.356629\pi\) | ||||
0.435338 | + | 0.900267i | \(0.356629\pi\) | |||||||
\(642\) | 20.5892 | 0.812591 | ||||||||
\(643\) | −48.6260 | −1.91762 | −0.958810 | − | 0.284047i | \(-0.908323\pi\) | ||||
−0.958810 | + | 0.284047i | \(0.908323\pi\) | |||||||
\(644\) | −9.46066 | −0.372802 | ||||||||
\(645\) | 5.57502 | 0.219516 | ||||||||
\(646\) | 9.23673 | 0.363414 | ||||||||
\(647\) | −5.07076 | −0.199352 | −0.0996762 | − | 0.995020i | \(-0.531781\pi\) | ||||
−0.0996762 | + | 0.995020i | \(0.531781\pi\) | |||||||
\(648\) | −3.34956 | −0.131583 | ||||||||
\(649\) | 4.22161 | 0.165713 | ||||||||
\(650\) | −12.9599 | −0.508331 | ||||||||
\(651\) | −5.15316 | −0.201968 | ||||||||
\(652\) | −20.1018 | −0.787247 | ||||||||
\(653\) | 5.86630 | 0.229566 | 0.114783 | − | 0.993391i | \(-0.463383\pi\) | ||||
0.114783 | + | 0.993391i | \(0.463383\pi\) | |||||||
\(654\) | −22.8814 | −0.894733 | ||||||||
\(655\) | 13.3123 | 0.520154 | ||||||||
\(656\) | 16.9075 | 0.660128 | ||||||||
\(657\) | −2.31975 | −0.0905020 | ||||||||
\(658\) | −0.264538 | −0.0103128 | ||||||||
\(659\) | 31.8713 | 1.24153 | 0.620766 | − | 0.783996i | \(-0.286822\pi\) | ||||
0.620766 | + | 0.783996i | \(0.286822\pi\) | |||||||
\(660\) | −2.04054 | −0.0794278 | ||||||||
\(661\) | 13.8474 | 0.538603 | 0.269302 | − | 0.963056i | \(-0.413207\pi\) | ||||
0.269302 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(662\) | 5.55951 | 0.216076 | ||||||||
\(663\) | 11.3198 | 0.439627 | ||||||||
\(664\) | 0.0898853 | 0.00348823 | ||||||||
\(665\) | 1.61389 | 0.0625840 | ||||||||
\(666\) | 10.5632 | 0.409316 | ||||||||
\(667\) | −5.43124 | −0.210298 | ||||||||
\(668\) | 17.2026 | 0.665588 | ||||||||
\(669\) | −18.6789 | −0.722170 | ||||||||
\(670\) | 18.7158 | 0.723054 | ||||||||
\(671\) | 3.88540 | 0.149994 | ||||||||
\(672\) | 5.45247 | 0.210334 | ||||||||
\(673\) | −28.3566 | −1.09307 | −0.546534 | − | 0.837437i | \(-0.684053\pi\) | ||||
−0.546534 | + | 0.837437i | \(0.684053\pi\) | |||||||
\(674\) | −8.47074 | −0.326281 | ||||||||
\(675\) | −4.38759 | −0.168878 | ||||||||
\(676\) | 60.7157 | 2.33522 | ||||||||
\(677\) | 12.1492 | 0.466931 | 0.233466 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233466 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(678\) | −1.06877 | −0.0410460 | ||||||||
\(679\) | 12.9389 | 0.496548 | ||||||||
\(680\) | 2.24612 | 0.0861348 | ||||||||
\(681\) | 13.7835 | 0.528186 | ||||||||
\(682\) | 15.9636 | 0.611276 | ||||||||
\(683\) | −8.78586 | −0.336182 | −0.168091 | − | 0.985772i | \(-0.553760\pi\) | ||||
−0.168091 | + | 0.985772i | \(0.553760\pi\) | |||||||
\(684\) | 11.1883 | 0.427796 | ||||||||
\(685\) | 14.1345 | 0.540051 | ||||||||
\(686\) | 23.3152 | 0.890179 | ||||||||
\(687\) | −6.40674 | −0.244433 | ||||||||
\(688\) | 19.1100 | 0.728563 | ||||||||
\(689\) | −65.5613 | −2.49769 | ||||||||
\(690\) | −8.05821 | −0.306771 | ||||||||
\(691\) | 16.7245 | 0.636230 | 0.318115 | − | 0.948052i | \(-0.396950\pi\) | ||||
0.318115 | + | 0.948052i | \(0.396950\pi\) | |||||||
\(692\) | −60.1621 | −2.28702 | ||||||||
\(693\) | −1.92044 | −0.0729514 | ||||||||
\(694\) | 52.9335 | 2.00933 | ||||||||
\(695\) | −18.3988 | −0.697907 | ||||||||
\(696\) | −0.972436 | −0.0368601 | ||||||||
\(697\) | −13.3962 | −0.507418 | ||||||||
\(698\) | 74.9542 | 2.83706 | ||||||||
\(699\) | −23.6216 | −0.893450 | ||||||||
\(700\) | 2.04818 | 0.0774141 | ||||||||
\(701\) | 8.71755 | 0.329257 | 0.164629 | − | 0.986356i | \(-0.447357\pi\) | ||||
0.164629 | + | 0.986356i | \(0.447357\pi\) | |||||||
\(702\) | 56.8629 | 2.14615 | ||||||||
\(703\) | −4.19680 | −0.158285 | ||||||||
\(704\) | −11.2365 | −0.423490 | ||||||||
\(705\) | −0.124599 | −0.00469266 | ||||||||
\(706\) | 39.8510 | 1.49981 | ||||||||
\(707\) | −13.4068 | −0.504216 | ||||||||
\(708\) | 8.61436 | 0.323747 | ||||||||
\(709\) | −13.7876 | −0.517803 | −0.258902 | − | 0.965904i | \(-0.583361\pi\) | ||||
−0.258902 | + | 0.965904i | \(0.583361\pi\) | |||||||
\(710\) | 19.0636 | 0.715445 | ||||||||
\(711\) | −20.3143 | −0.761847 | ||||||||
\(712\) | 15.0514 | 0.564074 | ||||||||
\(713\) | 34.8603 | 1.30553 | ||||||||
\(714\) | −3.23518 | −0.121073 | ||||||||
\(715\) | −6.12707 | −0.229139 | ||||||||
\(716\) | 23.9873 | 0.896447 | ||||||||
\(717\) | 4.66529 | 0.174228 | ||||||||
\(718\) | −59.0511 | −2.20377 | ||||||||
\(719\) | 34.4490 | 1.28473 | 0.642366 | − | 0.766398i | \(-0.277953\pi\) | ||||
0.642366 | + | 0.766398i | \(0.277953\pi\) | |||||||
\(720\) | −6.55830 | −0.244413 | ||||||||
\(721\) | −7.12746 | −0.265440 | ||||||||
\(722\) | 32.1501 | 1.19650 | ||||||||
\(723\) | −0.968658 | −0.0360248 | ||||||||
\(724\) | −39.1774 | −1.45602 | ||||||||
\(725\) | 1.17583 | 0.0436694 | ||||||||
\(726\) | −1.74456 | −0.0647467 | ||||||||
\(727\) | 49.8027 | 1.84708 | 0.923540 | − | 0.383503i | \(-0.125282\pi\) | ||||
0.923540 | + | 0.383503i | \(0.125282\pi\) | |||||||
\(728\) | −5.08618 | −0.188507 | ||||||||
\(729\) | 3.10726 | 0.115084 | ||||||||
\(730\) | 2.11520 | 0.0782869 | ||||||||
\(731\) | −15.1413 | −0.560022 | ||||||||
\(732\) | 7.92830 | 0.293038 | ||||||||
\(733\) | −33.6374 | −1.24243 | −0.621213 | − | 0.783642i | \(-0.713360\pi\) | ||||
−0.621213 | + | 0.783642i | \(0.713360\pi\) | |||||||
\(734\) | 30.9218 | 1.14135 | ||||||||
\(735\) | 5.20815 | 0.192106 | ||||||||
\(736\) | −36.8852 | −1.35960 | ||||||||
\(737\) | 8.84825 | 0.325929 | ||||||||
\(738\) | −29.3441 | −1.08017 | ||||||||
\(739\) | 0.276253 | 0.0101621 | 0.00508106 | − | 0.999987i | \(-0.498383\pi\) | ||||
0.00508106 | + | 0.999987i | \(0.498383\pi\) | |||||||
\(740\) | −5.32615 | −0.195793 | ||||||||
\(741\) | −9.85150 | −0.361904 | ||||||||
\(742\) | 18.7372 | 0.687865 | ||||||||
\(743\) | 40.5744 | 1.48853 | 0.744266 | − | 0.667883i | \(-0.232800\pi\) | ||||
0.744266 | + | 0.667883i | \(0.232800\pi\) | |||||||
\(744\) | 6.24157 | 0.228827 | ||||||||
\(745\) | 4.23845 | 0.155285 | ||||||||
\(746\) | −15.6454 | −0.572819 | ||||||||
\(747\) | 0.207945 | 0.00760832 | ||||||||
\(748\) | 5.54195 | 0.202634 | ||||||||
\(749\) | −9.77042 | −0.357003 | ||||||||
\(750\) | 1.74456 | 0.0637023 | ||||||||
\(751\) | −20.5155 | −0.748621 | −0.374311 | − | 0.927303i | \(-0.622121\pi\) | ||||
−0.374311 | + | 0.927303i | \(0.622121\pi\) | |||||||
\(752\) | −0.427099 | −0.0155747 | ||||||||
\(753\) | 16.6999 | 0.608578 | ||||||||
\(754\) | −15.2387 | −0.554963 | ||||||||
\(755\) | 5.08106 | 0.184919 | ||||||||
\(756\) | −8.98659 | −0.326839 | ||||||||
\(757\) | 30.1446 | 1.09563 | 0.547813 | − | 0.836601i | \(-0.315461\pi\) | ||||
0.547813 | + | 0.836601i | \(0.315461\pi\) | |||||||
\(758\) | 12.3364 | 0.448078 | ||||||||
\(759\) | −3.80967 | −0.138282 | ||||||||
\(760\) | −1.95477 | −0.0709068 | ||||||||
\(761\) | −3.93368 | −0.142596 | −0.0712979 | − | 0.997455i | \(-0.522714\pi\) | ||||
−0.0712979 | + | 0.997455i | \(0.522714\pi\) | |||||||
\(762\) | 8.52943 | 0.308989 | ||||||||
\(763\) | 10.8582 | 0.393092 | ||||||||
\(764\) | −15.0919 | −0.546007 | ||||||||
\(765\) | 5.19629 | 0.187872 | ||||||||
\(766\) | 37.3972 | 1.35122 | ||||||||
\(767\) | 25.8661 | 0.933971 | ||||||||
\(768\) | 4.93375 | 0.178031 | ||||||||
\(769\) | 2.96825 | 0.107038 | 0.0535190 | − | 0.998567i | \(-0.482956\pi\) | ||||
0.0535190 | + | 0.998567i | \(0.482956\pi\) | |||||||
\(770\) | 1.75110 | 0.0631051 | ||||||||
\(771\) | −0.306600 | −0.0110419 | ||||||||
\(772\) | 10.1106 | 0.363890 | ||||||||
\(773\) | 26.2479 | 0.944072 | 0.472036 | − | 0.881579i | \(-0.343519\pi\) | ||||
0.472036 | + | 0.881579i | \(0.343519\pi\) | |||||||
\(774\) | −33.1667 | −1.19215 | ||||||||
\(775\) | −7.54708 | −0.271099 | ||||||||
\(776\) | −15.6717 | −0.562582 | ||||||||
\(777\) | 1.46994 | 0.0527337 | ||||||||
\(778\) | −13.7712 | −0.493723 | ||||||||
\(779\) | 11.6585 | 0.417711 | ||||||||
\(780\) | −12.5025 | −0.447662 | ||||||||
\(781\) | 9.01270 | 0.322500 | ||||||||
\(782\) | 21.8855 | 0.782624 | ||||||||
\(783\) | −5.15908 | −0.184370 | ||||||||
\(784\) | 17.8525 | 0.637589 | ||||||||
\(785\) | −0.401127 | −0.0143168 | ||||||||
\(786\) | 23.2240 | 0.828374 | ||||||||
\(787\) | 39.0436 | 1.39175 | 0.695877 | − | 0.718161i | \(-0.255016\pi\) | ||||
0.695877 | + | 0.718161i | \(0.255016\pi\) | |||||||
\(788\) | −14.5148 | −0.517069 | ||||||||
\(789\) | −3.86300 | −0.137526 | ||||||||
\(790\) | 18.5231 | 0.659021 | ||||||||
\(791\) | 0.507177 | 0.0180332 | ||||||||
\(792\) | 2.32606 | 0.0826529 | ||||||||
\(793\) | 23.8061 | 0.845379 | ||||||||
\(794\) | −3.57834 | −0.126991 | ||||||||
\(795\) | 8.82532 | 0.313002 | ||||||||
\(796\) | 41.2319 | 1.46143 | ||||||||
\(797\) | −37.6438 | −1.33341 | −0.666705 | − | 0.745322i | \(-0.732296\pi\) | ||||
−0.666705 | + | 0.745322i | \(0.732296\pi\) | |||||||
\(798\) | 2.81553 | 0.0996686 | ||||||||
\(799\) | 0.338401 | 0.0119718 | ||||||||
\(800\) | 7.98544 | 0.282328 | ||||||||
\(801\) | 34.8206 | 1.23033 | ||||||||
\(802\) | −39.8587 | −1.40746 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 18.0552 | 0.636757 | ||||||||
\(805\) | 3.82395 | 0.134777 | ||||||||
\(806\) | 97.8098 | 3.44520 | ||||||||
\(807\) | −7.79533 | −0.274408 | ||||||||
\(808\) | 16.2385 | 0.571270 | ||||||||
\(809\) | −41.5247 | −1.45993 | −0.729965 | − | 0.683485i | \(-0.760464\pi\) | ||||
−0.729965 | + | 0.683485i | \(0.760464\pi\) | |||||||
\(810\) | 7.06575 | 0.248265 | ||||||||
\(811\) | 22.7405 | 0.798525 | 0.399263 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399263 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(812\) | 2.40832 | 0.0845156 | ||||||||
\(813\) | −10.5157 | −0.368801 | ||||||||
\(814\) | −4.55360 | −0.159604 | ||||||||
\(815\) | 8.12504 | 0.284608 | ||||||||
\(816\) | −5.22322 | −0.182849 | ||||||||
\(817\) | 13.1773 | 0.461015 | ||||||||
\(818\) | 9.06985 | 0.317120 | ||||||||
\(819\) | −11.7666 | −0.411160 | ||||||||
\(820\) | 14.7958 | 0.516692 | ||||||||
\(821\) | −2.19280 | −0.0765293 | −0.0382647 | − | 0.999268i | \(-0.512183\pi\) | ||||
−0.0382647 | + | 0.999268i | \(0.512183\pi\) | |||||||
\(822\) | 24.6585 | 0.860063 | ||||||||
\(823\) | 27.5360 | 0.959844 | 0.479922 | − | 0.877311i | \(-0.340665\pi\) | ||||
0.479922 | + | 0.877311i | \(0.340665\pi\) | |||||||
\(824\) | 8.63287 | 0.300740 | ||||||||
\(825\) | 0.824774 | 0.0287150 | ||||||||
\(826\) | −7.39245 | −0.257216 | ||||||||
\(827\) | 18.8854 | 0.656711 | 0.328355 | − | 0.944554i | \(-0.393506\pi\) | ||||
0.328355 | + | 0.944554i | \(0.393506\pi\) | |||||||
\(828\) | 26.5096 | 0.921272 | ||||||||
\(829\) | 27.0161 | 0.938308 | 0.469154 | − | 0.883116i | \(-0.344559\pi\) | ||||
0.469154 | + | 0.883116i | \(0.344559\pi\) | |||||||
\(830\) | −0.189609 | −0.00658143 | ||||||||
\(831\) | 4.67152 | 0.162053 | ||||||||
\(832\) | −68.8465 | −2.38682 | ||||||||
\(833\) | −14.1450 | −0.490094 | ||||||||
\(834\) | −32.0979 | −1.11146 | ||||||||
\(835\) | −6.95319 | −0.240625 | ||||||||
\(836\) | −4.82308 | −0.166810 | ||||||||
\(837\) | 33.1135 | 1.14457 | ||||||||
\(838\) | 8.52549 | 0.294508 | ||||||||
\(839\) | 18.3076 | 0.632048 | 0.316024 | − | 0.948751i | \(-0.397652\pi\) | ||||
0.316024 | + | 0.948751i | \(0.397652\pi\) | |||||||
\(840\) | 0.684659 | 0.0236230 | ||||||||
\(841\) | −27.6174 | −0.952325 | ||||||||
\(842\) | 70.0752 | 2.41495 | ||||||||
\(843\) | 0.0298380 | 0.00102767 | ||||||||
\(844\) | 6.19442 | 0.213221 | ||||||||
\(845\) | −24.5409 | −0.844234 | ||||||||
\(846\) | 0.741259 | 0.0254850 | ||||||||
\(847\) | 0.827865 | 0.0284458 | ||||||||
\(848\) | 30.2514 | 1.03884 | ||||||||
\(849\) | −20.4804 | −0.702887 | ||||||||
\(850\) | −4.73809 | −0.162515 | ||||||||
\(851\) | −9.94390 | −0.340872 | ||||||||
\(852\) | 18.3907 | 0.630056 | ||||||||
\(853\) | 11.4478 | 0.391965 | 0.195983 | − | 0.980607i | \(-0.437210\pi\) | ||||
0.195983 | + | 0.980607i | \(0.437210\pi\) | |||||||
\(854\) | −6.80371 | −0.232818 | ||||||||
\(855\) | −4.52226 | −0.154658 | ||||||||
\(856\) | 11.8341 | 0.404480 | ||||||||
\(857\) | 17.1362 | 0.585360 | 0.292680 | − | 0.956210i | \(-0.405453\pi\) | ||||
0.292680 | + | 0.956210i | \(0.405453\pi\) | |||||||
\(858\) | −10.6890 | −0.364918 | ||||||||
\(859\) | −33.9076 | −1.15691 | −0.578456 | − | 0.815713i | \(-0.696345\pi\) | ||||
−0.578456 | + | 0.815713i | \(0.696345\pi\) | |||||||
\(860\) | 16.7232 | 0.570258 | ||||||||
\(861\) | −4.08342 | −0.139163 | ||||||||
\(862\) | 40.3750 | 1.37518 | ||||||||
\(863\) | 3.73976 | 0.127303 | 0.0636515 | − | 0.997972i | \(-0.479725\pi\) | ||||
0.0636515 | + | 0.997972i | \(0.479725\pi\) | |||||||
\(864\) | −35.0368 | −1.19198 | ||||||||
\(865\) | 24.3172 | 0.826810 | ||||||||
\(866\) | −54.1178 | −1.83900 | ||||||||
\(867\) | −9.88268 | −0.335633 | ||||||||
\(868\) | −15.4578 | −0.524672 | ||||||||
\(869\) | 8.75713 | 0.297065 | ||||||||
\(870\) | 2.05131 | 0.0695460 | ||||||||
\(871\) | 54.2138 | 1.83696 | ||||||||
\(872\) | −13.1515 | −0.445367 | ||||||||
\(873\) | −36.2558 | −1.22707 | ||||||||
\(874\) | −19.0466 | −0.644262 | ||||||||
\(875\) | −0.827865 | −0.0279869 | ||||||||
\(876\) | 2.04054 | 0.0689434 | ||||||||
\(877\) | 59.0975 | 1.99558 | 0.997791 | − | 0.0664334i | \(-0.0211620\pi\) | ||||
0.997791 | + | 0.0664334i | \(0.0211620\pi\) | |||||||
\(878\) | −22.8251 | −0.770309 | ||||||||
\(879\) | −3.25130 | −0.109664 | ||||||||
\(880\) | 2.82716 | 0.0953035 | ||||||||
\(881\) | 43.8484 | 1.47729 | 0.738646 | − | 0.674094i | \(-0.235466\pi\) | ||||
0.738646 | + | 0.674094i | \(0.235466\pi\) | |||||||
\(882\) | −30.9842 | −1.04329 | ||||||||
\(883\) | 53.7796 | 1.80983 | 0.904914 | − | 0.425595i | \(-0.139935\pi\) | ||||
0.904914 | + | 0.425595i | \(0.139935\pi\) | |||||||
\(884\) | 33.9559 | 1.14206 | ||||||||
\(885\) | −3.48188 | −0.117042 | ||||||||
\(886\) | 7.24214 | 0.243304 | ||||||||
\(887\) | −28.4357 | −0.954779 | −0.477389 | − | 0.878692i | \(-0.658417\pi\) | ||||
−0.477389 | + | 0.878692i | \(0.658417\pi\) | |||||||
\(888\) | −1.78041 | −0.0597465 | ||||||||
\(889\) | −4.04756 | −0.135751 | ||||||||
\(890\) | −31.7502 | −1.06427 | ||||||||
\(891\) | 3.34047 | 0.111910 | ||||||||
\(892\) | −56.0308 | −1.87605 | ||||||||
\(893\) | −0.294505 | −0.00985524 | ||||||||
\(894\) | 7.39422 | 0.247300 | ||||||||
\(895\) | −9.69553 | −0.324086 | ||||||||
\(896\) | 6.45439 | 0.215626 | ||||||||
\(897\) | −23.3421 | −0.779371 | ||||||||
\(898\) | −9.90110 | −0.330404 | ||||||||
\(899\) | −8.87411 | −0.295968 | ||||||||
\(900\) | −5.73918 | −0.191306 | ||||||||
\(901\) | −23.9689 | −0.798520 | ||||||||
\(902\) | 12.6497 | 0.421189 | ||||||||
\(903\) | −4.61536 | −0.153590 | ||||||||
\(904\) | −0.614300 | −0.0204313 | ||||||||
\(905\) | 15.8353 | 0.526383 | ||||||||
\(906\) | 8.86421 | 0.294494 | ||||||||
\(907\) | 18.9605 | 0.629575 | 0.314787 | − | 0.949162i | \(-0.398067\pi\) | ||||
0.314787 | + | 0.949162i | \(0.398067\pi\) | |||||||
\(908\) | 41.3461 | 1.37212 | ||||||||
\(909\) | 37.5671 | 1.24602 | ||||||||
\(910\) | 10.7291 | 0.355666 | ||||||||
\(911\) | −28.9288 | −0.958452 | −0.479226 | − | 0.877691i | \(-0.659083\pi\) | ||||
−0.479226 | + | 0.877691i | \(0.659083\pi\) | |||||||
\(912\) | 4.54569 | 0.150523 | ||||||||
\(913\) | −0.0896414 | −0.00296670 | ||||||||
\(914\) | −14.5326 | −0.480697 | ||||||||
\(915\) | −3.20458 | −0.105940 | ||||||||
\(916\) | −19.2182 | −0.634986 | ||||||||
\(917\) | −11.0208 | −0.363938 | ||||||||
\(918\) | 20.7888 | 0.686133 | ||||||||
\(919\) | 6.58834 | 0.217329 | 0.108665 | − | 0.994078i | \(-0.465343\pi\) | ||||
0.108665 | + | 0.994078i | \(0.465343\pi\) | |||||||
\(920\) | −4.63162 | −0.152700 | ||||||||
\(921\) | 7.17539 | 0.236437 | ||||||||
\(922\) | 42.4446 | 1.39784 | ||||||||
\(923\) | 55.2214 | 1.81763 | ||||||||
\(924\) | 1.68929 | 0.0555735 | ||||||||
\(925\) | 2.15280 | 0.0707837 | ||||||||
\(926\) | −16.0256 | −0.526635 | ||||||||
\(927\) | 19.9717 | 0.655958 | ||||||||
\(928\) | 9.38955 | 0.308227 | ||||||||
\(929\) | 49.5992 | 1.62730 | 0.813649 | − | 0.581357i | \(-0.197478\pi\) | ||||
0.813649 | + | 0.581357i | \(0.197478\pi\) | |||||||
\(930\) | −13.1663 | −0.431741 | ||||||||
\(931\) | 12.3101 | 0.403449 | ||||||||
\(932\) | −70.8571 | −2.32100 | ||||||||
\(933\) | 15.1941 | 0.497432 | ||||||||
\(934\) | 36.6967 | 1.20075 | ||||||||
\(935\) | −2.24003 | −0.0732567 | ||||||||
\(936\) | 14.2519 | 0.465839 | ||||||||
\(937\) | −36.0497 | −1.17769 | −0.588847 | − | 0.808245i | \(-0.700418\pi\) | ||||
−0.588847 | + | 0.808245i | \(0.700418\pi\) | |||||||
\(938\) | −15.4941 | −0.505901 | ||||||||
\(939\) | 11.8801 | 0.387693 | ||||||||
\(940\) | −0.373756 | −0.0121906 | ||||||||
\(941\) | 36.4451 | 1.18808 | 0.594039 | − | 0.804436i | \(-0.297533\pi\) | ||||
0.594039 | + | 0.804436i | \(0.297533\pi\) | |||||||
\(942\) | −0.699789 | −0.0228004 | ||||||||
\(943\) | 27.6237 | 0.899552 | ||||||||
\(944\) | −11.9352 | −0.388457 | ||||||||
\(945\) | 3.63233 | 0.118160 | ||||||||
\(946\) | 14.2976 | 0.464854 | ||||||||
\(947\) | −0.638177 | −0.0207380 | −0.0103690 | − | 0.999946i | \(-0.503301\pi\) | ||||
−0.0103690 | + | 0.999946i | \(0.503301\pi\) | |||||||
\(948\) | 17.8693 | 0.580366 | ||||||||
\(949\) | 6.12707 | 0.198893 | ||||||||
\(950\) | 4.12349 | 0.133784 | ||||||||
\(951\) | −1.35423 | −0.0439138 | ||||||||
\(952\) | −1.85948 | −0.0602662 | ||||||||
\(953\) | −36.8738 | −1.19446 | −0.597231 | − | 0.802070i | \(-0.703732\pi\) | ||||
−0.597231 | + | 0.802070i | \(0.703732\pi\) | |||||||
\(954\) | −52.5033 | −1.69986 | ||||||||
\(955\) | 6.10008 | 0.197394 | ||||||||
\(956\) | 13.9944 | 0.452610 | ||||||||
\(957\) | 0.969798 | 0.0313491 | ||||||||
\(958\) | 17.5222 | 0.566118 | ||||||||
\(959\) | −11.7015 | −0.377860 | ||||||||
\(960\) | 9.26754 | 0.299108 | ||||||||
\(961\) | 25.9584 | 0.837368 | ||||||||
\(962\) | −27.9002 | −0.899538 | ||||||||
\(963\) | 27.3775 | 0.882229 | ||||||||
\(964\) | −2.90566 | −0.0935850 | ||||||||
\(965\) | −4.08667 | −0.131555 | ||||||||
\(966\) | 6.67111 | 0.214639 | ||||||||
\(967\) | 5.42617 | 0.174494 | 0.0872470 | − | 0.996187i | \(-0.472193\pi\) | ||||
0.0872470 | + | 0.996187i | \(0.472193\pi\) | |||||||
\(968\) | −1.00272 | −0.0322287 | ||||||||
\(969\) | −3.60166 | −0.115702 | ||||||||
\(970\) | 33.0588 | 1.06145 | ||||||||
\(971\) | −25.7079 | −0.825004 | −0.412502 | − | 0.910957i | \(-0.635345\pi\) | ||||
−0.412502 | + | 0.910957i | \(0.635345\pi\) | |||||||
\(972\) | 39.3818 | 1.26317 | ||||||||
\(973\) | 15.2317 | 0.488307 | ||||||||
\(974\) | 46.7380 | 1.49758 | ||||||||
\(975\) | 5.05345 | 0.161840 | ||||||||
\(976\) | −10.9846 | −0.351610 | ||||||||
\(977\) | −58.6101 | −1.87510 | −0.937552 | − | 0.347845i | \(-0.886913\pi\) | ||||
−0.937552 | + | 0.347845i | \(0.886913\pi\) | |||||||
\(978\) | 14.1746 | 0.453254 | ||||||||
\(979\) | −15.0105 | −0.479738 | ||||||||
\(980\) | 15.6228 | 0.499051 | ||||||||
\(981\) | −30.4255 | −0.971411 | ||||||||
\(982\) | 66.8916 | 2.13460 | ||||||||
\(983\) | −50.1730 | −1.60027 | −0.800136 | − | 0.599819i | \(-0.795239\pi\) | ||||
−0.800136 | + | 0.599819i | \(0.795239\pi\) | |||||||
\(984\) | 4.94589 | 0.157669 | ||||||||
\(985\) | 5.86681 | 0.186932 | ||||||||
\(986\) | −5.57121 | −0.177424 | ||||||||
\(987\) | 0.103151 | 0.00328333 | ||||||||
\(988\) | −29.5513 | −0.940153 | ||||||||
\(989\) | 31.2222 | 0.992809 | ||||||||
\(990\) | −4.90672 | −0.155946 | ||||||||
\(991\) | 33.1541 | 1.05318 | 0.526588 | − | 0.850121i | \(-0.323471\pi\) | ||||
0.526588 | + | 0.850121i | \(0.323471\pi\) | |||||||
\(992\) | −60.2667 | −1.91347 | ||||||||
\(993\) | −2.16781 | −0.0687933 | ||||||||
\(994\) | −15.7821 | −0.500578 | ||||||||
\(995\) | −16.6657 | −0.528339 | ||||||||
\(996\) | −0.182917 | −0.00579593 | ||||||||
\(997\) | 1.97527 | 0.0625574 | 0.0312787 | − | 0.999511i | \(-0.490042\pi\) | ||||
0.0312787 | + | 0.999511i | \(0.490042\pi\) | |||||||
\(998\) | −34.1843 | −1.08208 | ||||||||
\(999\) | −9.44561 | −0.298846 |
(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 | 4015.2.a.f.1.7 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.f.1.7 | ✓ | 31 | 1.1 | even | 1 | trivial |