Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.33092\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33092 | −0.941100 | −0.470550 | − | 0.882373i | \(-0.655945\pi\) | ||||
−0.470550 | + | 0.882373i | \(0.655945\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.228660 | −0.114330 | ||||||||
\(5\) | −2.36819 | −1.05909 | −0.529544 | − | 0.848283i | \(-0.677637\pi\) | ||||
−0.529544 | + | 0.848283i | \(0.677637\pi\) | |||||||
\(6\) | 1.33092 | 0.543345 | ||||||||
\(7\) | −2.92169 | −1.10430 | −0.552148 | − | 0.833746i | \(-0.686192\pi\) | ||||
−0.552148 | + | 0.833746i | \(0.686192\pi\) | |||||||
\(8\) | 2.96616 | 1.04870 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.15187 | 0.996708 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.228660 | 0.0660085 | ||||||||
\(13\) | 4.67063 | 1.29540 | 0.647700 | − | 0.761895i | \(-0.275731\pi\) | ||||
0.647700 | + | 0.761895i | \(0.275731\pi\) | |||||||
\(14\) | 3.88853 | 1.03925 | ||||||||
\(15\) | 2.36819 | 0.611464 | ||||||||
\(16\) | −3.49039 | −0.872599 | ||||||||
\(17\) | −3.08651 | −0.748589 | −0.374294 | − | 0.927310i | \(-0.622115\pi\) | ||||
−0.374294 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(18\) | −1.33092 | −0.313700 | ||||||||
\(19\) | −5.01988 | −1.15164 | −0.575820 | − | 0.817577i | \(-0.695317\pi\) | ||||
−0.575820 | + | 0.817577i | \(0.695317\pi\) | |||||||
\(20\) | 0.541511 | 0.121086 | ||||||||
\(21\) | 2.92169 | 0.637566 | ||||||||
\(22\) | −1.33092 | −0.283752 | ||||||||
\(23\) | −4.73072 | −0.986423 | −0.493212 | − | 0.869909i | \(-0.664177\pi\) | ||||
−0.493212 | + | 0.869909i | \(0.664177\pi\) | |||||||
\(24\) | −2.96616 | −0.605465 | ||||||||
\(25\) | 0.608331 | 0.121666 | ||||||||
\(26\) | −6.21622 | −1.21910 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.668075 | 0.126254 | ||||||||
\(29\) | −2.14373 | −0.398081 | −0.199040 | − | 0.979991i | \(-0.563782\pi\) | ||||
−0.199040 | + | 0.979991i | \(0.563782\pi\) | |||||||
\(30\) | −3.15187 | −0.575449 | ||||||||
\(31\) | 1.22908 | 0.220750 | 0.110375 | − | 0.993890i | \(-0.464795\pi\) | ||||
0.110375 | + | 0.993890i | \(0.464795\pi\) | |||||||
\(32\) | −1.28690 | −0.227494 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 4.10789 | 0.704497 | ||||||||
\(35\) | 6.91913 | 1.16955 | ||||||||
\(36\) | −0.228660 | −0.0381100 | ||||||||
\(37\) | −5.71888 | −0.940178 | −0.470089 | − | 0.882619i | \(-0.655778\pi\) | ||||
−0.470089 | + | 0.882619i | \(0.655778\pi\) | |||||||
\(38\) | 6.68104 | 1.08381 | ||||||||
\(39\) | −4.67063 | −0.747900 | ||||||||
\(40\) | −7.02444 | −1.11066 | ||||||||
\(41\) | −9.30697 | −1.45350 | −0.726752 | − | 0.686900i | \(-0.758971\pi\) | ||||
−0.726752 | + | 0.686900i | \(0.758971\pi\) | |||||||
\(42\) | −3.88853 | −0.600013 | ||||||||
\(43\) | −3.00386 | −0.458084 | −0.229042 | − | 0.973417i | \(-0.573559\pi\) | ||||
−0.229042 | + | 0.973417i | \(0.573559\pi\) | |||||||
\(44\) | −0.228660 | −0.0344718 | ||||||||
\(45\) | −2.36819 | −0.353029 | ||||||||
\(46\) | 6.29619 | 0.928323 | ||||||||
\(47\) | −1.19144 | −0.173789 | −0.0868944 | − | 0.996218i | \(-0.527694\pi\) | ||||
−0.0868944 | + | 0.996218i | \(0.527694\pi\) | |||||||
\(48\) | 3.49039 | 0.503795 | ||||||||
\(49\) | 1.53629 | 0.219470 | ||||||||
\(50\) | −0.809639 | −0.114500 | ||||||||
\(51\) | 3.08651 | 0.432198 | ||||||||
\(52\) | −1.06799 | −0.148103 | ||||||||
\(53\) | −4.66301 | −0.640514 | −0.320257 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320257 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(54\) | 1.33092 | 0.181115 | ||||||||
\(55\) | −2.36819 | −0.319327 | ||||||||
\(56\) | −8.66621 | −1.15807 | ||||||||
\(57\) | 5.01988 | 0.664899 | ||||||||
\(58\) | 2.85313 | 0.374634 | ||||||||
\(59\) | −8.94746 | −1.16486 | −0.582430 | − | 0.812881i | \(-0.697898\pi\) | ||||
−0.582430 | + | 0.812881i | \(0.697898\pi\) | |||||||
\(60\) | −0.541511 | −0.0699088 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −1.63581 | −0.207747 | ||||||||
\(63\) | −2.92169 | −0.368099 | ||||||||
\(64\) | 8.69354 | 1.08669 | ||||||||
\(65\) | −11.0609 | −1.37194 | ||||||||
\(66\) | 1.33092 | 0.163825 | ||||||||
\(67\) | 8.99807 | 1.09929 | 0.549645 | − | 0.835398i | \(-0.314763\pi\) | ||||
0.549645 | + | 0.835398i | \(0.314763\pi\) | |||||||
\(68\) | 0.705762 | 0.0855862 | ||||||||
\(69\) | 4.73072 | 0.569512 | ||||||||
\(70\) | −9.20879 | −1.10066 | ||||||||
\(71\) | 14.8610 | 1.76368 | 0.881838 | − | 0.471553i | \(-0.156306\pi\) | ||||
0.881838 | + | 0.471553i | \(0.156306\pi\) | |||||||
\(72\) | 2.96616 | 0.349565 | ||||||||
\(73\) | 9.79980 | 1.14698 | 0.573490 | − | 0.819213i | \(-0.305589\pi\) | ||||
0.573490 | + | 0.819213i | \(0.305589\pi\) | |||||||
\(74\) | 7.61136 | 0.884802 | ||||||||
\(75\) | −0.608331 | −0.0702441 | ||||||||
\(76\) | 1.14785 | 0.131667 | ||||||||
\(77\) | −2.92169 | −0.332958 | ||||||||
\(78\) | 6.21622 | 0.703849 | ||||||||
\(79\) | 11.9696 | 1.34669 | 0.673343 | − | 0.739331i | \(-0.264858\pi\) | ||||
0.673343 | + | 0.739331i | \(0.264858\pi\) | |||||||
\(80\) | 8.26592 | 0.924158 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.3868 | 1.36789 | ||||||||
\(83\) | 12.9510 | 1.42156 | 0.710781 | − | 0.703414i | \(-0.248342\pi\) | ||||
0.710781 | + | 0.703414i | \(0.248342\pi\) | |||||||
\(84\) | −0.668075 | −0.0728929 | ||||||||
\(85\) | 7.30945 | 0.792821 | ||||||||
\(86\) | 3.99788 | 0.431103 | ||||||||
\(87\) | 2.14373 | 0.229832 | ||||||||
\(88\) | 2.96616 | 0.316194 | ||||||||
\(89\) | −0.425469 | −0.0450997 | −0.0225498 | − | 0.999746i | \(-0.507178\pi\) | ||||
−0.0225498 | + | 0.999746i | \(0.507178\pi\) | |||||||
\(90\) | 3.15187 | 0.332236 | ||||||||
\(91\) | −13.6462 | −1.43051 | ||||||||
\(92\) | 1.08173 | 0.112778 | ||||||||
\(93\) | −1.22908 | −0.127450 | ||||||||
\(94\) | 1.58570 | 0.163553 | ||||||||
\(95\) | 11.8880 | 1.21969 | ||||||||
\(96\) | 1.28690 | 0.131344 | ||||||||
\(97\) | 5.28118 | 0.536222 | 0.268111 | − | 0.963388i | \(-0.413601\pi\) | ||||
0.268111 | + | 0.963388i | \(0.413601\pi\) | |||||||
\(98\) | −2.04467 | −0.206543 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.139101 | −0.0139101 | ||||||||
\(101\) | −18.0972 | −1.80074 | −0.900368 | − | 0.435130i | \(-0.856703\pi\) | ||||
−0.900368 | + | 0.435130i | \(0.856703\pi\) | |||||||
\(102\) | −4.10789 | −0.406742 | ||||||||
\(103\) | 5.40800 | 0.532867 | 0.266433 | − | 0.963853i | \(-0.414155\pi\) | ||||
0.266433 | + | 0.963853i | \(0.414155\pi\) | |||||||
\(104\) | 13.8538 | 1.35848 | ||||||||
\(105\) | −6.91913 | −0.675238 | ||||||||
\(106\) | 6.20608 | 0.602788 | ||||||||
\(107\) | −5.18077 | −0.500844 | −0.250422 | − | 0.968137i | \(-0.580569\pi\) | ||||
−0.250422 | + | 0.968137i | \(0.580569\pi\) | |||||||
\(108\) | 0.228660 | 0.0220028 | ||||||||
\(109\) | −11.1822 | −1.07106 | −0.535530 | − | 0.844516i | \(-0.679888\pi\) | ||||
−0.535530 | + | 0.844516i | \(0.679888\pi\) | |||||||
\(110\) | 3.15187 | 0.300519 | ||||||||
\(111\) | 5.71888 | 0.542812 | ||||||||
\(112\) | 10.1979 | 0.963607 | ||||||||
\(113\) | −8.56972 | −0.806172 | −0.403086 | − | 0.915162i | \(-0.632062\pi\) | ||||
−0.403086 | + | 0.915162i | \(0.632062\pi\) | |||||||
\(114\) | −6.68104 | −0.625737 | ||||||||
\(115\) | 11.2033 | 1.04471 | ||||||||
\(116\) | 0.490186 | 0.0455126 | ||||||||
\(117\) | 4.67063 | 0.431800 | ||||||||
\(118\) | 11.9083 | 1.09625 | ||||||||
\(119\) | 9.01784 | 0.826664 | ||||||||
\(120\) | 7.02444 | 0.641241 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.33092 | 0.120496 | ||||||||
\(123\) | 9.30697 | 0.839181 | ||||||||
\(124\) | −0.281042 | −0.0252383 | ||||||||
\(125\) | 10.4003 | 0.930232 | ||||||||
\(126\) | 3.88853 | 0.346418 | ||||||||
\(127\) | 0.489906 | 0.0434721 | 0.0217361 | − | 0.999764i | \(-0.493081\pi\) | ||||
0.0217361 | + | 0.999764i | \(0.493081\pi\) | |||||||
\(128\) | −8.99659 | −0.795193 | ||||||||
\(129\) | 3.00386 | 0.264475 | ||||||||
\(130\) | 14.7212 | 1.29114 | ||||||||
\(131\) | −4.25776 | −0.372002 | −0.186001 | − | 0.982550i | \(-0.559553\pi\) | ||||
−0.186001 | + | 0.982550i | \(0.559553\pi\) | |||||||
\(132\) | 0.228660 | 0.0199023 | ||||||||
\(133\) | 14.6665 | 1.27175 | ||||||||
\(134\) | −11.9757 | −1.03454 | ||||||||
\(135\) | 2.36819 | 0.203821 | ||||||||
\(136\) | −9.15509 | −0.785042 | ||||||||
\(137\) | −20.9037 | −1.78592 | −0.892961 | − | 0.450134i | \(-0.851376\pi\) | ||||
−0.892961 | + | 0.450134i | \(0.851376\pi\) | |||||||
\(138\) | −6.29619 | −0.535968 | ||||||||
\(139\) | 10.2136 | 0.866307 | 0.433153 | − | 0.901320i | \(-0.357401\pi\) | ||||
0.433153 | + | 0.901320i | \(0.357401\pi\) | |||||||
\(140\) | −1.58213 | −0.133714 | ||||||||
\(141\) | 1.19144 | 0.100337 | ||||||||
\(142\) | −19.7788 | −1.65980 | ||||||||
\(143\) | 4.67063 | 0.390578 | ||||||||
\(144\) | −3.49039 | −0.290866 | ||||||||
\(145\) | 5.07676 | 0.421602 | ||||||||
\(146\) | −13.0427 | −1.07942 | ||||||||
\(147\) | −1.53629 | −0.126711 | ||||||||
\(148\) | 1.30768 | 0.107491 | ||||||||
\(149\) | −13.3117 | −1.09054 | −0.545268 | − | 0.838262i | \(-0.683572\pi\) | ||||
−0.545268 | + | 0.838262i | \(0.683572\pi\) | |||||||
\(150\) | 0.809639 | 0.0661067 | ||||||||
\(151\) | −14.1469 | −1.15126 | −0.575628 | − | 0.817711i | \(-0.695243\pi\) | ||||
−0.575628 | + | 0.817711i | \(0.695243\pi\) | |||||||
\(152\) | −14.8898 | −1.20772 | ||||||||
\(153\) | −3.08651 | −0.249530 | ||||||||
\(154\) | 3.88853 | 0.313347 | ||||||||
\(155\) | −2.91070 | −0.233793 | ||||||||
\(156\) | 1.06799 | 0.0855074 | ||||||||
\(157\) | 15.2651 | 1.21829 | 0.609144 | − | 0.793059i | \(-0.291513\pi\) | ||||
0.609144 | + | 0.793059i | \(0.291513\pi\) | |||||||
\(158\) | −15.9305 | −1.26737 | ||||||||
\(159\) | 4.66301 | 0.369801 | ||||||||
\(160\) | 3.04762 | 0.240936 | ||||||||
\(161\) | 13.8217 | 1.08930 | ||||||||
\(162\) | −1.33092 | −0.104567 | ||||||||
\(163\) | 18.0609 | 1.41464 | 0.707321 | − | 0.706892i | \(-0.249903\pi\) | ||||
0.707321 | + | 0.706892i | \(0.249903\pi\) | |||||||
\(164\) | 2.12813 | 0.166179 | ||||||||
\(165\) | 2.36819 | 0.184363 | ||||||||
\(166\) | −17.2368 | −1.33783 | ||||||||
\(167\) | −18.8759 | −1.46066 | −0.730329 | − | 0.683096i | \(-0.760633\pi\) | ||||
−0.730329 | + | 0.683096i | \(0.760633\pi\) | |||||||
\(168\) | 8.66621 | 0.668613 | ||||||||
\(169\) | 8.81480 | 0.678061 | ||||||||
\(170\) | −9.72827 | −0.746124 | ||||||||
\(171\) | −5.01988 | −0.383880 | ||||||||
\(172\) | 0.686863 | 0.0523728 | ||||||||
\(173\) | 20.7395 | 1.57680 | 0.788398 | − | 0.615165i | \(-0.210911\pi\) | ||||
0.788398 | + | 0.615165i | \(0.210911\pi\) | |||||||
\(174\) | −2.85313 | −0.216295 | ||||||||
\(175\) | −1.77736 | −0.134356 | ||||||||
\(176\) | −3.49039 | −0.263098 | ||||||||
\(177\) | 8.94746 | 0.672532 | ||||||||
\(178\) | 0.566264 | 0.0424433 | ||||||||
\(179\) | 10.9017 | 0.814834 | 0.407417 | − | 0.913242i | \(-0.366430\pi\) | ||||
0.407417 | + | 0.913242i | \(0.366430\pi\) | |||||||
\(180\) | 0.541511 | 0.0403619 | ||||||||
\(181\) | 9.68426 | 0.719825 | 0.359913 | − | 0.932986i | \(-0.382806\pi\) | ||||
0.359913 | + | 0.932986i | \(0.382806\pi\) | |||||||
\(182\) | 18.1619 | 1.34625 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −14.0321 | −1.03446 | ||||||||
\(185\) | 13.5434 | 0.995731 | ||||||||
\(186\) | 1.63581 | 0.119943 | ||||||||
\(187\) | −3.08651 | −0.225708 | ||||||||
\(188\) | 0.272434 | 0.0198693 | ||||||||
\(189\) | 2.92169 | 0.212522 | ||||||||
\(190\) | −15.8220 | −1.14785 | ||||||||
\(191\) | −10.8157 | −0.782597 | −0.391298 | − | 0.920264i | \(-0.627974\pi\) | ||||
−0.391298 | + | 0.920264i | \(0.627974\pi\) | |||||||
\(192\) | −8.69354 | −0.627402 | ||||||||
\(193\) | −6.19562 | −0.445970 | −0.222985 | − | 0.974822i | \(-0.571580\pi\) | ||||
−0.222985 | + | 0.974822i | \(0.571580\pi\) | |||||||
\(194\) | −7.02881 | −0.504639 | ||||||||
\(195\) | 11.0609 | 0.792091 | ||||||||
\(196\) | −0.351288 | −0.0250920 | ||||||||
\(197\) | −1.14995 | −0.0819308 | −0.0409654 | − | 0.999161i | \(-0.513043\pi\) | ||||
−0.0409654 | + | 0.999161i | \(0.513043\pi\) | |||||||
\(198\) | −1.33092 | −0.0945841 | ||||||||
\(199\) | 13.8061 | 0.978687 | 0.489344 | − | 0.872091i | \(-0.337236\pi\) | ||||
0.489344 | + | 0.872091i | \(0.337236\pi\) | |||||||
\(200\) | 1.80441 | 0.127591 | ||||||||
\(201\) | −8.99807 | −0.634675 | ||||||||
\(202\) | 24.0858 | 1.69467 | ||||||||
\(203\) | 6.26332 | 0.439599 | ||||||||
\(204\) | −0.705762 | −0.0494132 | ||||||||
\(205\) | 22.0407 | 1.53939 | ||||||||
\(206\) | −7.19760 | −0.501481 | ||||||||
\(207\) | −4.73072 | −0.328808 | ||||||||
\(208\) | −16.3023 | −1.13036 | ||||||||
\(209\) | −5.01988 | −0.347232 | ||||||||
\(210\) | 9.20879 | 0.635467 | ||||||||
\(211\) | 8.67180 | 0.596991 | 0.298496 | − | 0.954411i | \(-0.403515\pi\) | ||||
0.298496 | + | 0.954411i | \(0.403515\pi\) | |||||||
\(212\) | 1.06624 | 0.0732300 | ||||||||
\(213\) | −14.8610 | −1.01826 | ||||||||
\(214\) | 6.89518 | 0.471345 | ||||||||
\(215\) | 7.11371 | 0.485151 | ||||||||
\(216\) | −2.96616 | −0.201822 | ||||||||
\(217\) | −3.59100 | −0.243773 | ||||||||
\(218\) | 14.8826 | 1.00797 | ||||||||
\(219\) | −9.79980 | −0.662209 | ||||||||
\(220\) | 0.541511 | 0.0365087 | ||||||||
\(221\) | −14.4160 | −0.969722 | ||||||||
\(222\) | −7.61136 | −0.510841 | ||||||||
\(223\) | 0.540497 | 0.0361944 | 0.0180972 | − | 0.999836i | \(-0.494239\pi\) | ||||
0.0180972 | + | 0.999836i | \(0.494239\pi\) | |||||||
\(224\) | 3.75992 | 0.251220 | ||||||||
\(225\) | 0.608331 | 0.0405554 | ||||||||
\(226\) | 11.4056 | 0.758688 | ||||||||
\(227\) | 5.60176 | 0.371802 | 0.185901 | − | 0.982568i | \(-0.440480\pi\) | ||||
0.185901 | + | 0.982568i | \(0.440480\pi\) | |||||||
\(228\) | −1.14785 | −0.0760180 | ||||||||
\(229\) | −12.8413 | −0.848578 | −0.424289 | − | 0.905527i | \(-0.639476\pi\) | ||||
−0.424289 | + | 0.905527i | \(0.639476\pi\) | |||||||
\(230\) | −14.9106 | −0.983176 | ||||||||
\(231\) | 2.92169 | 0.192233 | ||||||||
\(232\) | −6.35865 | −0.417466 | ||||||||
\(233\) | 26.1667 | 1.71423 | 0.857117 | − | 0.515121i | \(-0.172253\pi\) | ||||
0.857117 | + | 0.515121i | \(0.172253\pi\) | |||||||
\(234\) | −6.21622 | −0.406367 | ||||||||
\(235\) | 2.82155 | 0.184058 | ||||||||
\(236\) | 2.04593 | 0.133179 | ||||||||
\(237\) | −11.9696 | −0.777509 | ||||||||
\(238\) | −12.0020 | −0.777974 | ||||||||
\(239\) | 17.1822 | 1.11142 | 0.555711 | − | 0.831376i | \(-0.312446\pi\) | ||||
0.555711 | + | 0.831376i | \(0.312446\pi\) | |||||||
\(240\) | −8.26592 | −0.533563 | ||||||||
\(241\) | 20.5527 | 1.32392 | 0.661959 | − | 0.749540i | \(-0.269725\pi\) | ||||
0.661959 | + | 0.749540i | \(0.269725\pi\) | |||||||
\(242\) | −1.33092 | −0.0855546 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.228660 | 0.0146385 | ||||||||
\(245\) | −3.63823 | −0.232438 | ||||||||
\(246\) | −12.3868 | −0.789754 | ||||||||
\(247\) | −23.4460 | −1.49183 | ||||||||
\(248\) | 3.64565 | 0.231499 | ||||||||
\(249\) | −12.9510 | −0.820739 | ||||||||
\(250\) | −13.8420 | −0.875442 | ||||||||
\(251\) | 22.6512 | 1.42973 | 0.714865 | − | 0.699262i | \(-0.246488\pi\) | ||||
0.714865 | + | 0.699262i | \(0.246488\pi\) | |||||||
\(252\) | 0.668075 | 0.0420848 | ||||||||
\(253\) | −4.73072 | −0.297418 | ||||||||
\(254\) | −0.652024 | −0.0409116 | ||||||||
\(255\) | −7.30945 | −0.457735 | ||||||||
\(256\) | −5.41338 | −0.338336 | ||||||||
\(257\) | −12.2924 | −0.766778 | −0.383389 | − | 0.923587i | \(-0.625243\pi\) | ||||
−0.383389 | + | 0.923587i | \(0.625243\pi\) | |||||||
\(258\) | −3.99788 | −0.248897 | ||||||||
\(259\) | 16.7088 | 1.03824 | ||||||||
\(260\) | 2.52920 | 0.156854 | ||||||||
\(261\) | −2.14373 | −0.132694 | ||||||||
\(262\) | 5.66672 | 0.350091 | ||||||||
\(263\) | 11.9232 | 0.735219 | 0.367609 | − | 0.929980i | \(-0.380176\pi\) | ||||
0.367609 | + | 0.929980i | \(0.380176\pi\) | |||||||
\(264\) | −2.96616 | −0.182555 | ||||||||
\(265\) | 11.0429 | 0.678360 | ||||||||
\(266\) | −19.5200 | −1.19684 | ||||||||
\(267\) | 0.425469 | 0.0260383 | ||||||||
\(268\) | −2.05750 | −0.125682 | ||||||||
\(269\) | −8.16149 | −0.497615 | −0.248807 | − | 0.968553i | \(-0.580039\pi\) | ||||
−0.248807 | + | 0.968553i | \(0.580039\pi\) | |||||||
\(270\) | −3.15187 | −0.191816 | ||||||||
\(271\) | 27.6984 | 1.68256 | 0.841278 | − | 0.540602i | \(-0.181804\pi\) | ||||
0.841278 | + | 0.540602i | \(0.181804\pi\) | |||||||
\(272\) | 10.7731 | 0.653218 | ||||||||
\(273\) | 13.6462 | 0.825903 | ||||||||
\(274\) | 27.8211 | 1.68073 | ||||||||
\(275\) | 0.608331 | 0.0366838 | ||||||||
\(276\) | −1.08173 | −0.0651123 | ||||||||
\(277\) | −1.78976 | −0.107536 | −0.0537681 | − | 0.998553i | \(-0.517123\pi\) | ||||
−0.0537681 | + | 0.998553i | \(0.517123\pi\) | |||||||
\(278\) | −13.5935 | −0.815281 | ||||||||
\(279\) | 1.22908 | 0.0735832 | ||||||||
\(280\) | 20.5233 | 1.22650 | ||||||||
\(281\) | −11.9883 | −0.715164 | −0.357582 | − | 0.933882i | \(-0.616399\pi\) | ||||
−0.357582 | + | 0.933882i | \(0.616399\pi\) | |||||||
\(282\) | −1.58570 | −0.0944272 | ||||||||
\(283\) | −18.0687 | −1.07407 | −0.537035 | − | 0.843560i | \(-0.680456\pi\) | ||||
−0.537035 | + | 0.843560i | \(0.680456\pi\) | |||||||
\(284\) | −3.39812 | −0.201641 | ||||||||
\(285\) | −11.8880 | −0.704186 | ||||||||
\(286\) | −6.21622 | −0.367573 | ||||||||
\(287\) | 27.1921 | 1.60510 | ||||||||
\(288\) | −1.28690 | −0.0758312 | ||||||||
\(289\) | −7.47345 | −0.439615 | ||||||||
\(290\) | −6.75675 | −0.396770 | ||||||||
\(291\) | −5.28118 | −0.309588 | ||||||||
\(292\) | −2.24082 | −0.131134 | ||||||||
\(293\) | 23.4090 | 1.36757 | 0.683784 | − | 0.729684i | \(-0.260333\pi\) | ||||
0.683784 | + | 0.729684i | \(0.260333\pi\) | |||||||
\(294\) | 2.04467 | 0.119248 | ||||||||
\(295\) | 21.1893 | 1.23369 | ||||||||
\(296\) | −16.9631 | −0.985962 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 17.7168 | 1.02630 | ||||||||
\(299\) | −22.0954 | −1.27781 | ||||||||
\(300\) | 0.139101 | 0.00803101 | ||||||||
\(301\) | 8.77635 | 0.505860 | ||||||||
\(302\) | 18.8283 | 1.08345 | ||||||||
\(303\) | 18.0972 | 1.03966 | ||||||||
\(304\) | 17.5214 | 1.00492 | ||||||||
\(305\) | 2.36819 | 0.135602 | ||||||||
\(306\) | 4.10789 | 0.234832 | ||||||||
\(307\) | 8.48031 | 0.483997 | 0.241998 | − | 0.970277i | \(-0.422197\pi\) | ||||
0.241998 | + | 0.970277i | \(0.422197\pi\) | |||||||
\(308\) | 0.668075 | 0.0380671 | ||||||||
\(309\) | −5.40800 | −0.307651 | ||||||||
\(310\) | 3.87390 | 0.220023 | ||||||||
\(311\) | −16.1743 | −0.917160 | −0.458580 | − | 0.888653i | \(-0.651642\pi\) | ||||
−0.458580 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(312\) | −13.8538 | −0.784320 | ||||||||
\(313\) | 0.716595 | 0.0405044 | 0.0202522 | − | 0.999795i | \(-0.493553\pi\) | ||||
0.0202522 | + | 0.999795i | \(0.493553\pi\) | |||||||
\(314\) | −20.3166 | −1.14653 | ||||||||
\(315\) | 6.91913 | 0.389849 | ||||||||
\(316\) | −2.73697 | −0.153967 | ||||||||
\(317\) | −2.26108 | −0.126995 | −0.0634974 | − | 0.997982i | \(-0.520225\pi\) | ||||
−0.0634974 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(318\) | −6.20608 | −0.348020 | ||||||||
\(319\) | −2.14373 | −0.120026 | ||||||||
\(320\) | −20.5880 | −1.15090 | ||||||||
\(321\) | 5.18077 | 0.289162 | ||||||||
\(322\) | −18.3955 | −1.02514 | ||||||||
\(323\) | 15.4939 | 0.862104 | ||||||||
\(324\) | −0.228660 | −0.0127033 | ||||||||
\(325\) | 2.84129 | 0.157607 | ||||||||
\(326\) | −24.0376 | −1.33132 | ||||||||
\(327\) | 11.1822 | 0.618377 | ||||||||
\(328\) | −27.6060 | −1.52429 | ||||||||
\(329\) | 3.48101 | 0.191914 | ||||||||
\(330\) | −3.15187 | −0.173505 | ||||||||
\(331\) | −11.8409 | −0.650836 | −0.325418 | − | 0.945570i | \(-0.605505\pi\) | ||||
−0.325418 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(332\) | −2.96139 | −0.162527 | ||||||||
\(333\) | −5.71888 | −0.313393 | ||||||||
\(334\) | 25.1222 | 1.37463 | ||||||||
\(335\) | −21.3092 | −1.16424 | ||||||||
\(336\) | −10.1979 | −0.556339 | ||||||||
\(337\) | 30.4451 | 1.65845 | 0.829225 | − | 0.558915i | \(-0.188782\pi\) | ||||
0.829225 | + | 0.558915i | \(0.188782\pi\) | |||||||
\(338\) | −11.7318 | −0.638124 | ||||||||
\(339\) | 8.56972 | 0.465443 | ||||||||
\(340\) | −1.67138 | −0.0906433 | ||||||||
\(341\) | 1.22908 | 0.0665585 | ||||||||
\(342\) | 6.68104 | 0.361269 | ||||||||
\(343\) | 15.9633 | 0.861936 | ||||||||
\(344\) | −8.90993 | −0.480391 | ||||||||
\(345\) | −11.2033 | −0.603163 | ||||||||
\(346\) | −27.6026 | −1.48392 | ||||||||
\(347\) | 12.9041 | 0.692728 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(348\) | −0.490186 | −0.0262767 | ||||||||
\(349\) | −18.0493 | −0.966159 | −0.483080 | − | 0.875576i | \(-0.660482\pi\) | ||||
−0.483080 | + | 0.875576i | \(0.660482\pi\) | |||||||
\(350\) | 2.36552 | 0.126442 | ||||||||
\(351\) | −4.67063 | −0.249300 | ||||||||
\(352\) | −1.28690 | −0.0685919 | ||||||||
\(353\) | 11.3839 | 0.605903 | 0.302951 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302951 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(354\) | −11.9083 | −0.632921 | ||||||||
\(355\) | −35.1937 | −1.86789 | ||||||||
\(356\) | 0.0972879 | 0.00515625 | ||||||||
\(357\) | −9.01784 | −0.477275 | ||||||||
\(358\) | −14.5093 | −0.766841 | ||||||||
\(359\) | 3.51661 | 0.185599 | 0.0927997 | − | 0.995685i | \(-0.470418\pi\) | ||||
0.0927997 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(360\) | −7.02444 | −0.370220 | ||||||||
\(361\) | 6.19918 | 0.326273 | ||||||||
\(362\) | −12.8889 | −0.677428 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 3.12033 | 0.163550 | ||||||||
\(365\) | −23.2078 | −1.21475 | ||||||||
\(366\) | −1.33092 | −0.0695681 | ||||||||
\(367\) | −6.46554 | −0.337498 | −0.168749 | − | 0.985659i | \(-0.553973\pi\) | ||||
−0.168749 | + | 0.985659i | \(0.553973\pi\) | |||||||
\(368\) | 16.5121 | 0.860751 | ||||||||
\(369\) | −9.30697 | −0.484502 | ||||||||
\(370\) | −18.0252 | −0.937083 | ||||||||
\(371\) | 13.6239 | 0.707317 | ||||||||
\(372\) | 0.281042 | 0.0145713 | ||||||||
\(373\) | 4.51638 | 0.233849 | 0.116925 | − | 0.993141i | \(-0.462696\pi\) | ||||
0.116925 | + | 0.993141i | \(0.462696\pi\) | |||||||
\(374\) | 4.10789 | 0.212414 | ||||||||
\(375\) | −10.4003 | −0.537070 | ||||||||
\(376\) | −3.53399 | −0.182252 | ||||||||
\(377\) | −10.0126 | −0.515674 | ||||||||
\(378\) | −3.88853 | −0.200004 | ||||||||
\(379\) | −26.1477 | −1.34312 | −0.671558 | − | 0.740952i | \(-0.734375\pi\) | ||||
−0.671558 | + | 0.740952i | \(0.734375\pi\) | |||||||
\(380\) | −2.71832 | −0.139447 | ||||||||
\(381\) | −0.489906 | −0.0250986 | ||||||||
\(382\) | 14.3948 | 0.736502 | ||||||||
\(383\) | −23.3062 | −1.19089 | −0.595445 | − | 0.803396i | \(-0.703024\pi\) | ||||
−0.595445 | + | 0.803396i | \(0.703024\pi\) | |||||||
\(384\) | 8.99659 | 0.459105 | ||||||||
\(385\) | 6.91913 | 0.352631 | ||||||||
\(386\) | 8.24585 | 0.419703 | ||||||||
\(387\) | −3.00386 | −0.152695 | ||||||||
\(388\) | −1.20760 | −0.0613064 | ||||||||
\(389\) | 19.3335 | 0.980249 | 0.490125 | − | 0.871652i | \(-0.336951\pi\) | ||||
0.490125 | + | 0.871652i | \(0.336951\pi\) | |||||||
\(390\) | −14.7212 | −0.745437 | ||||||||
\(391\) | 14.6014 | 0.738425 | ||||||||
\(392\) | 4.55688 | 0.230157 | ||||||||
\(393\) | 4.25776 | 0.214775 | ||||||||
\(394\) | 1.53049 | 0.0771051 | ||||||||
\(395\) | −28.3463 | −1.42626 | ||||||||
\(396\) | −0.228660 | −0.0114906 | ||||||||
\(397\) | 8.98364 | 0.450876 | 0.225438 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225438 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(398\) | −18.3748 | −0.921043 | ||||||||
\(399\) | −14.6665 | −0.734246 | ||||||||
\(400\) | −2.12332 | −0.106166 | ||||||||
\(401\) | −6.20996 | −0.310110 | −0.155055 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155055 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(402\) | 11.9757 | 0.597293 | ||||||||
\(403\) | 5.74059 | 0.285959 | ||||||||
\(404\) | 4.13810 | 0.205878 | ||||||||
\(405\) | −2.36819 | −0.117676 | ||||||||
\(406\) | −8.33596 | −0.413707 | ||||||||
\(407\) | −5.71888 | −0.283474 | ||||||||
\(408\) | 9.15509 | 0.453244 | ||||||||
\(409\) | 27.1966 | 1.34478 | 0.672392 | − | 0.740196i | \(-0.265267\pi\) | ||||
0.672392 | + | 0.740196i | \(0.265267\pi\) | |||||||
\(410\) | −29.3343 | −1.44872 | ||||||||
\(411\) | 20.9037 | 1.03110 | ||||||||
\(412\) | −1.23660 | −0.0609227 | ||||||||
\(413\) | 26.1417 | 1.28635 | ||||||||
\(414\) | 6.29619 | 0.309441 | ||||||||
\(415\) | −30.6705 | −1.50556 | ||||||||
\(416\) | −6.01063 | −0.294695 | ||||||||
\(417\) | −10.2136 | −0.500162 | ||||||||
\(418\) | 6.68104 | 0.326780 | ||||||||
\(419\) | 17.1176 | 0.836250 | 0.418125 | − | 0.908389i | \(-0.362687\pi\) | ||||
0.418125 | + | 0.908389i | \(0.362687\pi\) | |||||||
\(420\) | 1.58213 | 0.0772000 | ||||||||
\(421\) | −16.4220 | −0.800357 | −0.400179 | − | 0.916437i | \(-0.631052\pi\) | ||||
−0.400179 | + | 0.916437i | \(0.631052\pi\) | |||||||
\(422\) | −11.5414 | −0.561829 | ||||||||
\(423\) | −1.19144 | −0.0579296 | ||||||||
\(424\) | −13.8312 | −0.671705 | ||||||||
\(425\) | −1.87762 | −0.0910780 | ||||||||
\(426\) | 19.7788 | 0.958284 | ||||||||
\(427\) | 2.92169 | 0.141391 | ||||||||
\(428\) | 1.18464 | 0.0572615 | ||||||||
\(429\) | −4.67063 | −0.225500 | ||||||||
\(430\) | −9.46776 | −0.456576 | ||||||||
\(431\) | 39.0693 | 1.88190 | 0.940951 | − | 0.338542i | \(-0.109934\pi\) | ||||
0.940951 | + | 0.338542i | \(0.109934\pi\) | |||||||
\(432\) | 3.49039 | 0.167932 | ||||||||
\(433\) | 20.6507 | 0.992409 | 0.496205 | − | 0.868206i | \(-0.334727\pi\) | ||||
0.496205 | + | 0.868206i | \(0.334727\pi\) | |||||||
\(434\) | 4.77932 | 0.229415 | ||||||||
\(435\) | −5.07676 | −0.243412 | ||||||||
\(436\) | 2.55692 | 0.122454 | ||||||||
\(437\) | 23.7476 | 1.13600 | ||||||||
\(438\) | 13.0427 | 0.623205 | ||||||||
\(439\) | −36.3101 | −1.73299 | −0.866493 | − | 0.499189i | \(-0.833631\pi\) | ||||
−0.866493 | + | 0.499189i | \(0.833631\pi\) | |||||||
\(440\) | −7.02444 | −0.334877 | ||||||||
\(441\) | 1.53629 | 0.0731567 | ||||||||
\(442\) | 19.1864 | 0.912606 | ||||||||
\(443\) | 3.64725 | 0.173286 | 0.0866430 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866430 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(444\) | −1.30768 | −0.0620598 | ||||||||
\(445\) | 1.00759 | 0.0477645 | ||||||||
\(446\) | −0.719357 | −0.0340625 | ||||||||
\(447\) | 13.3117 | 0.629621 | ||||||||
\(448\) | −25.3999 | −1.20003 | ||||||||
\(449\) | 38.3189 | 1.80838 | 0.904191 | − | 0.427129i | \(-0.140475\pi\) | ||||
0.904191 | + | 0.427129i | \(0.140475\pi\) | |||||||
\(450\) | −0.809639 | −0.0381667 | ||||||||
\(451\) | −9.30697 | −0.438248 | ||||||||
\(452\) | 1.95955 | 0.0921697 | ||||||||
\(453\) | 14.1469 | 0.664679 | ||||||||
\(454\) | −7.45548 | −0.349903 | ||||||||
\(455\) | 32.3167 | 1.51503 | ||||||||
\(456\) | 14.8898 | 0.697277 | ||||||||
\(457\) | 10.6266 | 0.497093 | 0.248547 | − | 0.968620i | \(-0.420047\pi\) | ||||
0.248547 | + | 0.968620i | \(0.420047\pi\) | |||||||
\(458\) | 17.0907 | 0.798597 | ||||||||
\(459\) | 3.08651 | 0.144066 | ||||||||
\(460\) | −2.56174 | −0.119442 | ||||||||
\(461\) | −24.2727 | −1.13049 | −0.565246 | − | 0.824923i | \(-0.691219\pi\) | ||||
−0.565246 | + | 0.824923i | \(0.691219\pi\) | |||||||
\(462\) | −3.88853 | −0.180911 | ||||||||
\(463\) | 5.27536 | 0.245167 | 0.122583 | − | 0.992458i | \(-0.460882\pi\) | ||||
0.122583 | + | 0.992458i | \(0.460882\pi\) | |||||||
\(464\) | 7.48246 | 0.347365 | ||||||||
\(465\) | 2.91070 | 0.134980 | ||||||||
\(466\) | −34.8256 | −1.61327 | ||||||||
\(467\) | 5.97949 | 0.276698 | 0.138349 | − | 0.990384i | \(-0.455820\pi\) | ||||
0.138349 | + | 0.990384i | \(0.455820\pi\) | |||||||
\(468\) | −1.06799 | −0.0493677 | ||||||||
\(469\) | −26.2896 | −1.21394 | ||||||||
\(470\) | −3.75525 | −0.173217 | ||||||||
\(471\) | −15.2651 | −0.703379 | ||||||||
\(472\) | −26.5396 | −1.22158 | ||||||||
\(473\) | −3.00386 | −0.138118 | ||||||||
\(474\) | 15.9305 | 0.731714 | ||||||||
\(475\) | −3.05375 | −0.140116 | ||||||||
\(476\) | −2.06202 | −0.0945125 | ||||||||
\(477\) | −4.66301 | −0.213505 | ||||||||
\(478\) | −22.8680 | −1.04596 | ||||||||
\(479\) | −10.7587 | −0.491579 | −0.245790 | − | 0.969323i | \(-0.579047\pi\) | ||||
−0.245790 | + | 0.969323i | \(0.579047\pi\) | |||||||
\(480\) | −3.04762 | −0.139104 | ||||||||
\(481\) | −26.7108 | −1.21791 | ||||||||
\(482\) | −27.3540 | −1.24594 | ||||||||
\(483\) | −13.8217 | −0.628910 | ||||||||
\(484\) | −0.228660 | −0.0103936 | ||||||||
\(485\) | −12.5068 | −0.567907 | ||||||||
\(486\) | 1.33092 | 0.0603716 | ||||||||
\(487\) | 27.3853 | 1.24095 | 0.620474 | − | 0.784227i | \(-0.286940\pi\) | ||||
0.620474 | + | 0.784227i | \(0.286940\pi\) | |||||||
\(488\) | −2.96616 | −0.134272 | ||||||||
\(489\) | −18.0609 | −0.816744 | ||||||||
\(490\) | 4.84218 | 0.218747 | ||||||||
\(491\) | −12.9998 | −0.586672 | −0.293336 | − | 0.956009i | \(-0.594765\pi\) | ||||
−0.293336 | + | 0.956009i | \(0.594765\pi\) | |||||||
\(492\) | −2.12813 | −0.0959437 | ||||||||
\(493\) | 6.61665 | 0.297999 | ||||||||
\(494\) | 31.2047 | 1.40396 | ||||||||
\(495\) | −2.36819 | −0.106442 | ||||||||
\(496\) | −4.28998 | −0.192626 | ||||||||
\(497\) | −43.4193 | −1.94762 | ||||||||
\(498\) | 17.2368 | 0.772398 | ||||||||
\(499\) | −18.5160 | −0.828889 | −0.414444 | − | 0.910075i | \(-0.636024\pi\) | ||||
−0.414444 | + | 0.910075i | \(0.636024\pi\) | |||||||
\(500\) | −2.37814 | −0.106354 | ||||||||
\(501\) | 18.8759 | 0.843311 | ||||||||
\(502\) | −30.1469 | −1.34552 | ||||||||
\(503\) | 19.8385 | 0.884556 | 0.442278 | − | 0.896878i | \(-0.354170\pi\) | ||||
0.442278 | + | 0.896878i | \(0.354170\pi\) | |||||||
\(504\) | −8.66621 | −0.386024 | ||||||||
\(505\) | 42.8576 | 1.90714 | ||||||||
\(506\) | 6.29619 | 0.279900 | ||||||||
\(507\) | −8.81480 | −0.391479 | ||||||||
\(508\) | −0.112022 | −0.00497017 | ||||||||
\(509\) | −9.34304 | −0.414123 | −0.207061 | − | 0.978328i | \(-0.566390\pi\) | ||||
−0.207061 | + | 0.978328i | \(0.566390\pi\) | |||||||
\(510\) | 9.72827 | 0.430775 | ||||||||
\(511\) | −28.6320 | −1.26661 | ||||||||
\(512\) | 25.1979 | 1.11360 | ||||||||
\(513\) | 5.01988 | 0.221633 | ||||||||
\(514\) | 16.3601 | 0.721615 | ||||||||
\(515\) | −12.8072 | −0.564352 | ||||||||
\(516\) | −0.686863 | −0.0302374 | ||||||||
\(517\) | −1.19144 | −0.0523993 | ||||||||
\(518\) | −22.2380 | −0.977084 | ||||||||
\(519\) | −20.7395 | −0.910364 | ||||||||
\(520\) | −32.8086 | −1.43875 | ||||||||
\(521\) | −18.6247 | −0.815961 | −0.407980 | − | 0.912991i | \(-0.633767\pi\) | ||||
−0.407980 | + | 0.912991i | \(0.633767\pi\) | |||||||
\(522\) | 2.85313 | 0.124878 | ||||||||
\(523\) | 7.84831 | 0.343183 | 0.171591 | − | 0.985168i | \(-0.445109\pi\) | ||||
0.171591 | + | 0.985168i | \(0.445109\pi\) | |||||||
\(524\) | 0.973579 | 0.0425310 | ||||||||
\(525\) | 1.77736 | 0.0775703 | ||||||||
\(526\) | −15.8688 | −0.691915 | ||||||||
\(527\) | −3.79357 | −0.165251 | ||||||||
\(528\) | 3.49039 | 0.151900 | ||||||||
\(529\) | −0.620292 | −0.0269692 | ||||||||
\(530\) | −14.6972 | −0.638405 | ||||||||
\(531\) | −8.94746 | −0.388287 | ||||||||
\(532\) | −3.35365 | −0.145399 | ||||||||
\(533\) | −43.4694 | −1.88287 | ||||||||
\(534\) | −0.566264 | −0.0245047 | ||||||||
\(535\) | 12.2691 | 0.530438 | ||||||||
\(536\) | 26.6897 | 1.15282 | ||||||||
\(537\) | −10.9017 | −0.470445 | ||||||||
\(538\) | 10.8623 | 0.468305 | ||||||||
\(539\) | 1.53629 | 0.0661727 | ||||||||
\(540\) | −0.541511 | −0.0233029 | ||||||||
\(541\) | −28.4103 | −1.22145 | −0.610726 | − | 0.791842i | \(-0.709122\pi\) | ||||
−0.610726 | + | 0.791842i | \(0.709122\pi\) | |||||||
\(542\) | −36.8642 | −1.58345 | ||||||||
\(543\) | −9.68426 | −0.415591 | ||||||||
\(544\) | 3.97203 | 0.170299 | ||||||||
\(545\) | 26.4816 | 1.13435 | ||||||||
\(546\) | −18.1619 | −0.777257 | ||||||||
\(547\) | −30.5691 | −1.30704 | −0.653520 | − | 0.756909i | \(-0.726708\pi\) | ||||
−0.653520 | + | 0.756909i | \(0.726708\pi\) | |||||||
\(548\) | 4.77984 | 0.204185 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −0.809639 | −0.0345231 | ||||||||
\(551\) | 10.7613 | 0.458445 | ||||||||
\(552\) | 14.0321 | 0.597245 | ||||||||
\(553\) | −34.9715 | −1.48714 | ||||||||
\(554\) | 2.38202 | 0.101202 | ||||||||
\(555\) | −13.5434 | −0.574886 | ||||||||
\(556\) | −2.33544 | −0.0990449 | ||||||||
\(557\) | 28.3132 | 1.19967 | 0.599835 | − | 0.800124i | \(-0.295233\pi\) | ||||
0.599835 | + | 0.800124i | \(0.295233\pi\) | |||||||
\(558\) | −1.63581 | −0.0692492 | ||||||||
\(559\) | −14.0299 | −0.593402 | ||||||||
\(560\) | −24.1505 | −1.02054 | ||||||||
\(561\) | 3.08651 | 0.130313 | ||||||||
\(562\) | 15.9555 | 0.673041 | ||||||||
\(563\) | 35.6071 | 1.50066 | 0.750331 | − | 0.661063i | \(-0.229894\pi\) | ||||
0.750331 | + | 0.661063i | \(0.229894\pi\) | |||||||
\(564\) | −0.272434 | −0.0114715 | ||||||||
\(565\) | 20.2947 | 0.853806 | ||||||||
\(566\) | 24.0479 | 1.01081 | ||||||||
\(567\) | −2.92169 | −0.122700 | ||||||||
\(568\) | 44.0801 | 1.84956 | ||||||||
\(569\) | −14.0979 | −0.591015 | −0.295507 | − | 0.955340i | \(-0.595489\pi\) | ||||
−0.295507 | + | 0.955340i | \(0.595489\pi\) | |||||||
\(570\) | 15.8220 | 0.662710 | ||||||||
\(571\) | −21.3065 | −0.891648 | −0.445824 | − | 0.895121i | \(-0.647089\pi\) | ||||
−0.445824 | + | 0.895121i | \(0.647089\pi\) | |||||||
\(572\) | −1.06799 | −0.0446548 | ||||||||
\(573\) | 10.8157 | 0.451832 | ||||||||
\(574\) | −36.1904 | −1.51056 | ||||||||
\(575\) | −2.87785 | −0.120014 | ||||||||
\(576\) | 8.69354 | 0.362231 | ||||||||
\(577\) | 33.3841 | 1.38980 | 0.694900 | − | 0.719107i | \(-0.255449\pi\) | ||||
0.694900 | + | 0.719107i | \(0.255449\pi\) | |||||||
\(578\) | 9.94654 | 0.413722 | ||||||||
\(579\) | 6.19562 | 0.257481 | ||||||||
\(580\) | −1.16085 | −0.0482018 | ||||||||
\(581\) | −37.8390 | −1.56982 | ||||||||
\(582\) | 7.02881 | 0.291354 | ||||||||
\(583\) | −4.66301 | −0.193122 | ||||||||
\(584\) | 29.0678 | 1.20283 | ||||||||
\(585\) | −11.0609 | −0.457314 | ||||||||
\(586\) | −31.1554 | −1.28702 | ||||||||
\(587\) | 7.08280 | 0.292338 | 0.146169 | − | 0.989260i | \(-0.453306\pi\) | ||||
0.146169 | + | 0.989260i | \(0.453306\pi\) | |||||||
\(588\) | 0.351288 | 0.0144869 | ||||||||
\(589\) | −6.16984 | −0.254224 | ||||||||
\(590\) | −28.2012 | −1.16103 | ||||||||
\(591\) | 1.14995 | 0.0473028 | ||||||||
\(592\) | 19.9612 | 0.820398 | ||||||||
\(593\) | −24.1694 | −0.992519 | −0.496260 | − | 0.868174i | \(-0.665294\pi\) | ||||
−0.496260 | + | 0.868174i | \(0.665294\pi\) | |||||||
\(594\) | 1.33092 | 0.0546082 | ||||||||
\(595\) | −21.3560 | −0.875509 | ||||||||
\(596\) | 3.04385 | 0.124681 | ||||||||
\(597\) | −13.8061 | −0.565045 | ||||||||
\(598\) | 29.4072 | 1.20255 | ||||||||
\(599\) | 15.8654 | 0.648242 | 0.324121 | − | 0.946016i | \(-0.394932\pi\) | ||||
0.324121 | + | 0.946016i | \(0.394932\pi\) | |||||||
\(600\) | −1.80441 | −0.0736647 | ||||||||
\(601\) | −21.4050 | −0.873128 | −0.436564 | − | 0.899673i | \(-0.643805\pi\) | ||||
−0.436564 | + | 0.899673i | \(0.643805\pi\) | |||||||
\(602\) | −11.6806 | −0.476065 | ||||||||
\(603\) | 8.99807 | 0.366430 | ||||||||
\(604\) | 3.23483 | 0.131623 | ||||||||
\(605\) | −2.36819 | −0.0962807 | ||||||||
\(606\) | −24.0858 | −0.978420 | ||||||||
\(607\) | 37.9016 | 1.53838 | 0.769189 | − | 0.639021i | \(-0.220660\pi\) | ||||
0.769189 | + | 0.639021i | \(0.220660\pi\) | |||||||
\(608\) | 6.46007 | 0.261991 | ||||||||
\(609\) | −6.26332 | −0.253803 | ||||||||
\(610\) | −3.15187 | −0.127615 | ||||||||
\(611\) | −5.56476 | −0.225126 | ||||||||
\(612\) | 0.705762 | 0.0285287 | ||||||||
\(613\) | −5.28282 | −0.213371 | −0.106686 | − | 0.994293i | \(-0.534024\pi\) | ||||
−0.106686 | + | 0.994293i | \(0.534024\pi\) | |||||||
\(614\) | −11.2866 | −0.455489 | ||||||||
\(615\) | −22.0407 | −0.888766 | ||||||||
\(616\) | −8.66621 | −0.349172 | ||||||||
\(617\) | −44.2406 | −1.78106 | −0.890529 | − | 0.454926i | \(-0.849666\pi\) | ||||
−0.890529 | + | 0.454926i | \(0.849666\pi\) | |||||||
\(618\) | 7.19760 | 0.289530 | ||||||||
\(619\) | 23.8962 | 0.960468 | 0.480234 | − | 0.877140i | \(-0.340552\pi\) | ||||
0.480234 | + | 0.877140i | \(0.340552\pi\) | |||||||
\(620\) | 0.665561 | 0.0267296 | ||||||||
\(621\) | 4.73072 | 0.189837 | ||||||||
\(622\) | 21.5266 | 0.863139 | ||||||||
\(623\) | 1.24309 | 0.0498034 | ||||||||
\(624\) | 16.3023 | 0.652616 | ||||||||
\(625\) | −27.6716 | −1.10686 | ||||||||
\(626\) | −0.953729 | −0.0381187 | ||||||||
\(627\) | 5.01988 | 0.200475 | ||||||||
\(628\) | −3.49052 | −0.139287 | ||||||||
\(629\) | 17.6514 | 0.703807 | ||||||||
\(630\) | −9.20879 | −0.366887 | ||||||||
\(631\) | −4.59242 | −0.182821 | −0.0914106 | − | 0.995813i | \(-0.529138\pi\) | ||||
−0.0914106 | + | 0.995813i | \(0.529138\pi\) | |||||||
\(632\) | 35.5038 | 1.41226 | ||||||||
\(633\) | −8.67180 | −0.344673 | ||||||||
\(634\) | 3.00931 | 0.119515 | ||||||||
\(635\) | −1.16019 | −0.0460408 | ||||||||
\(636\) | −1.06624 | −0.0422794 | ||||||||
\(637\) | 7.17544 | 0.284301 | ||||||||
\(638\) | 2.85313 | 0.112956 | ||||||||
\(639\) | 14.8610 | 0.587892 | ||||||||
\(640\) | 21.3056 | 0.842179 | ||||||||
\(641\) | −20.0957 | −0.793731 | −0.396865 | − | 0.917877i | \(-0.629902\pi\) | ||||
−0.396865 | + | 0.917877i | \(0.629902\pi\) | |||||||
\(642\) | −6.89518 | −0.272131 | ||||||||
\(643\) | 25.7989 | 1.01741 | 0.508705 | − | 0.860941i | \(-0.330124\pi\) | ||||
0.508705 | + | 0.860941i | \(0.330124\pi\) | |||||||
\(644\) | −3.16047 | −0.124540 | ||||||||
\(645\) | −7.11371 | −0.280102 | ||||||||
\(646\) | −20.6211 | −0.811327 | ||||||||
\(647\) | −44.0280 | −1.73092 | −0.865460 | − | 0.500977i | \(-0.832974\pi\) | ||||
−0.865460 | + | 0.500977i | \(0.832974\pi\) | |||||||
\(648\) | 2.96616 | 0.116522 | ||||||||
\(649\) | −8.94746 | −0.351219 | ||||||||
\(650\) | −3.78152 | −0.148324 | ||||||||
\(651\) | 3.59100 | 0.140742 | ||||||||
\(652\) | −4.12982 | −0.161736 | ||||||||
\(653\) | −5.99511 | −0.234607 | −0.117303 | − | 0.993096i | \(-0.537425\pi\) | ||||
−0.117303 | + | 0.993096i | \(0.537425\pi\) | |||||||
\(654\) | −14.8826 | −0.581954 | ||||||||
\(655\) | 10.0832 | 0.393982 | ||||||||
\(656\) | 32.4850 | 1.26833 | ||||||||
\(657\) | 9.79980 | 0.382327 | ||||||||
\(658\) | −4.63294 | −0.180611 | ||||||||
\(659\) | 36.8221 | 1.43439 | 0.717193 | − | 0.696874i | \(-0.245426\pi\) | ||||
0.717193 | + | 0.696874i | \(0.245426\pi\) | |||||||
\(660\) | −0.541511 | −0.0210783 | ||||||||
\(661\) | 34.6404 | 1.34736 | 0.673678 | − | 0.739025i | \(-0.264714\pi\) | ||||
0.673678 | + | 0.739025i | \(0.264714\pi\) | |||||||
\(662\) | 15.7593 | 0.612502 | ||||||||
\(663\) | 14.4160 | 0.559869 | ||||||||
\(664\) | 38.4149 | 1.49079 | ||||||||
\(665\) | −34.7332 | −1.34690 | ||||||||
\(666\) | 7.61136 | 0.294934 | ||||||||
\(667\) | 10.1414 | 0.392676 | ||||||||
\(668\) | 4.31616 | 0.166997 | ||||||||
\(669\) | −0.540497 | −0.0208968 | ||||||||
\(670\) | 28.3607 | 1.09567 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −3.75992 | −0.145042 | ||||||||
\(673\) | −35.1235 | −1.35391 | −0.676955 | − | 0.736024i | \(-0.736701\pi\) | ||||
−0.676955 | + | 0.736024i | \(0.736701\pi\) | |||||||
\(674\) | −40.5199 | −1.56077 | ||||||||
\(675\) | −0.608331 | −0.0234147 | ||||||||
\(676\) | −2.01559 | −0.0775228 | ||||||||
\(677\) | 46.6369 | 1.79240 | 0.896200 | − | 0.443650i | \(-0.146317\pi\) | ||||
0.896200 | + | 0.443650i | \(0.146317\pi\) | |||||||
\(678\) | −11.4056 | −0.438029 | ||||||||
\(679\) | −15.4300 | −0.592148 | ||||||||
\(680\) | 21.6810 | 0.831429 | ||||||||
\(681\) | −5.60176 | −0.214660 | ||||||||
\(682\) | −1.63581 | −0.0626382 | ||||||||
\(683\) | −26.3591 | −1.00860 | −0.504301 | − | 0.863528i | \(-0.668250\pi\) | ||||
−0.504301 | + | 0.863528i | \(0.668250\pi\) | |||||||
\(684\) | 1.14785 | 0.0438890 | ||||||||
\(685\) | 49.5039 | 1.89145 | ||||||||
\(686\) | −21.2458 | −0.811169 | ||||||||
\(687\) | 12.8413 | 0.489927 | ||||||||
\(688\) | 10.4846 | 0.399723 | ||||||||
\(689\) | −21.7792 | −0.829722 | ||||||||
\(690\) | 14.9106 | 0.567637 | ||||||||
\(691\) | −43.4335 | −1.65229 | −0.826145 | − | 0.563458i | \(-0.809471\pi\) | ||||
−0.826145 | + | 0.563458i | \(0.809471\pi\) | |||||||
\(692\) | −4.74230 | −0.180275 | ||||||||
\(693\) | −2.92169 | −0.110986 | ||||||||
\(694\) | −17.1743 | −0.651926 | ||||||||
\(695\) | −24.1878 | −0.917494 | ||||||||
\(696\) | 6.35865 | 0.241024 | ||||||||
\(697\) | 28.7261 | 1.08808 | ||||||||
\(698\) | 24.0222 | 0.909253 | ||||||||
\(699\) | −26.1667 | −0.989714 | ||||||||
\(700\) | 0.406411 | 0.0153609 | ||||||||
\(701\) | −29.6826 | −1.12110 | −0.560548 | − | 0.828122i | \(-0.689409\pi\) | ||||
−0.560548 | + | 0.828122i | \(0.689409\pi\) | |||||||
\(702\) | 6.21622 | 0.234616 | ||||||||
\(703\) | 28.7081 | 1.08275 | ||||||||
\(704\) | 8.69354 | 0.327650 | ||||||||
\(705\) | −2.82155 | −0.106266 | ||||||||
\(706\) | −15.1510 | −0.570215 | ||||||||
\(707\) | 52.8744 | 1.98855 | ||||||||
\(708\) | −2.04593 | −0.0768907 | ||||||||
\(709\) | 32.3827 | 1.21616 | 0.608079 | − | 0.793877i | \(-0.291940\pi\) | ||||
0.608079 | + | 0.793877i | \(0.291940\pi\) | |||||||
\(710\) | 46.8399 | 1.75787 | ||||||||
\(711\) | 11.9696 | 0.448895 | ||||||||
\(712\) | −1.26201 | −0.0472959 | ||||||||
\(713\) | −5.81444 | −0.217752 | ||||||||
\(714\) | 12.0020 | 0.449163 | ||||||||
\(715\) | −11.0609 | −0.413656 | ||||||||
\(716\) | −2.49279 | −0.0931600 | ||||||||
\(717\) | −17.1822 | −0.641680 | ||||||||
\(718\) | −4.68031 | −0.174668 | ||||||||
\(719\) | −38.1158 | −1.42148 | −0.710741 | − | 0.703454i | \(-0.751640\pi\) | ||||
−0.710741 | + | 0.703454i | \(0.751640\pi\) | |||||||
\(720\) | 8.26592 | 0.308053 | ||||||||
\(721\) | −15.8005 | −0.588442 | ||||||||
\(722\) | −8.25059 | −0.307055 | ||||||||
\(723\) | −20.5527 | −0.764365 | ||||||||
\(724\) | −2.21440 | −0.0822977 | ||||||||
\(725\) | −1.30410 | −0.0484330 | ||||||||
\(726\) | 1.33092 | 0.0493950 | ||||||||
\(727\) | −32.9791 | −1.22313 | −0.611564 | − | 0.791195i | \(-0.709459\pi\) | ||||
−0.611564 | + | 0.791195i | \(0.709459\pi\) | |||||||
\(728\) | −40.4767 | −1.50017 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.8877 | 1.14320 | ||||||||
\(731\) | 9.27144 | 0.342917 | ||||||||
\(732\) | −0.228660 | −0.00845152 | ||||||||
\(733\) | 22.0044 | 0.812751 | 0.406376 | − | 0.913706i | \(-0.366792\pi\) | ||||
0.406376 | + | 0.913706i | \(0.366792\pi\) | |||||||
\(734\) | 8.60510 | 0.317620 | ||||||||
\(735\) | 3.63823 | 0.134198 | ||||||||
\(736\) | 6.08796 | 0.224405 | ||||||||
\(737\) | 8.99807 | 0.331448 | ||||||||
\(738\) | 12.3868 | 0.455965 | ||||||||
\(739\) | 2.36992 | 0.0871789 | 0.0435894 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435894 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(740\) | −3.09684 | −0.113842 | ||||||||
\(741\) | 23.4460 | 0.861310 | ||||||||
\(742\) | −18.1323 | −0.665656 | ||||||||
\(743\) | 22.5722 | 0.828094 | 0.414047 | − | 0.910255i | \(-0.364115\pi\) | ||||
0.414047 | + | 0.910255i | \(0.364115\pi\) | |||||||
\(744\) | −3.64565 | −0.133656 | ||||||||
\(745\) | 31.5246 | 1.15497 | ||||||||
\(746\) | −6.01092 | −0.220076 | ||||||||
\(747\) | 12.9510 | 0.473854 | ||||||||
\(748\) | 0.705762 | 0.0258052 | ||||||||
\(749\) | 15.1366 | 0.553080 | ||||||||
\(750\) | 13.8420 | 0.505437 | ||||||||
\(751\) | 4.61181 | 0.168287 | 0.0841437 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841437 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(752\) | 4.15858 | 0.151648 | ||||||||
\(753\) | −22.6512 | −0.825455 | ||||||||
\(754\) | 13.3259 | 0.485301 | ||||||||
\(755\) | 33.5025 | 1.21928 | ||||||||
\(756\) | −0.668075 | −0.0242976 | ||||||||
\(757\) | −2.35032 | −0.0854237 | −0.0427119 | − | 0.999087i | \(-0.513600\pi\) | ||||
−0.0427119 | + | 0.999087i | \(0.513600\pi\) | |||||||
\(758\) | 34.8004 | 1.26401 | ||||||||
\(759\) | 4.73072 | 0.171714 | ||||||||
\(760\) | 35.2618 | 1.27908 | ||||||||
\(761\) | 45.2527 | 1.64041 | 0.820204 | − | 0.572071i | \(-0.193860\pi\) | ||||
0.820204 | + | 0.572071i | \(0.193860\pi\) | |||||||
\(762\) | 0.652024 | 0.0236203 | ||||||||
\(763\) | 32.6709 | 1.18277 | ||||||||
\(764\) | 2.47312 | 0.0894744 | ||||||||
\(765\) | 7.30945 | 0.264274 | ||||||||
\(766\) | 31.0186 | 1.12075 | ||||||||
\(767\) | −41.7903 | −1.50896 | ||||||||
\(768\) | 5.41338 | 0.195338 | ||||||||
\(769\) | −19.5824 | −0.706158 | −0.353079 | − | 0.935594i | \(-0.614865\pi\) | ||||
−0.353079 | + | 0.935594i | \(0.614865\pi\) | |||||||
\(770\) | −9.20879 | −0.331862 | ||||||||
\(771\) | 12.2924 | 0.442699 | ||||||||
\(772\) | 1.41669 | 0.0509878 | ||||||||
\(773\) | −20.2345 | −0.727785 | −0.363892 | − | 0.931441i | \(-0.618552\pi\) | ||||
−0.363892 | + | 0.931441i | \(0.618552\pi\) | |||||||
\(774\) | 3.99788 | 0.143701 | ||||||||
\(775\) | 0.747689 | 0.0268578 | ||||||||
\(776\) | 15.6648 | 0.562335 | ||||||||
\(777\) | −16.7088 | −0.599426 | ||||||||
\(778\) | −25.7313 | −0.922513 | ||||||||
\(779\) | 46.7199 | 1.67391 | ||||||||
\(780\) | −2.52920 | −0.0905598 | ||||||||
\(781\) | 14.8610 | 0.531768 | ||||||||
\(782\) | −19.4333 | −0.694932 | ||||||||
\(783\) | 2.14373 | 0.0766107 | ||||||||
\(784\) | −5.36226 | −0.191509 | ||||||||
\(785\) | −36.1507 | −1.29027 | ||||||||
\(786\) | −5.66672 | −0.202125 | ||||||||
\(787\) | 19.3105 | 0.688344 | 0.344172 | − | 0.938907i | \(-0.388160\pi\) | ||||
0.344172 | + | 0.938907i | \(0.388160\pi\) | |||||||
\(788\) | 0.262949 | 0.00936716 | ||||||||
\(789\) | −11.9232 | −0.424479 | ||||||||
\(790\) | 37.7266 | 1.34225 | ||||||||
\(791\) | 25.0381 | 0.890252 | ||||||||
\(792\) | 2.96616 | 0.105398 | ||||||||
\(793\) | −4.67063 | −0.165859 | ||||||||
\(794\) | −11.9565 | −0.424320 | ||||||||
\(795\) | −11.0429 | −0.391651 | ||||||||
\(796\) | −3.15690 | −0.111893 | ||||||||
\(797\) | 12.0619 | 0.427253 | 0.213627 | − | 0.976915i | \(-0.431472\pi\) | ||||
0.213627 | + | 0.976915i | \(0.431472\pi\) | |||||||
\(798\) | 19.5200 | 0.690999 | ||||||||
\(799\) | 3.67738 | 0.130096 | ||||||||
\(800\) | −0.782861 | −0.0276783 | ||||||||
\(801\) | −0.425469 | −0.0150332 | ||||||||
\(802\) | 8.26494 | 0.291845 | ||||||||
\(803\) | 9.79980 | 0.345827 | ||||||||
\(804\) | 2.05750 | 0.0725625 | ||||||||
\(805\) | −32.7325 | −1.15367 | ||||||||
\(806\) | −7.64024 | −0.269116 | ||||||||
\(807\) | 8.16149 | 0.287298 | ||||||||
\(808\) | −53.6791 | −1.88843 | ||||||||
\(809\) | 35.8603 | 1.26078 | 0.630390 | − | 0.776278i | \(-0.282895\pi\) | ||||
0.630390 | + | 0.776278i | \(0.282895\pi\) | |||||||
\(810\) | 3.15187 | 0.110745 | ||||||||
\(811\) | 43.1282 | 1.51444 | 0.757218 | − | 0.653163i | \(-0.226558\pi\) | ||||
0.757218 | + | 0.653163i | \(0.226558\pi\) | |||||||
\(812\) | −1.43217 | −0.0502594 | ||||||||
\(813\) | −27.6984 | −0.971424 | ||||||||
\(814\) | 7.61136 | 0.266778 | ||||||||
\(815\) | −42.7718 | −1.49823 | ||||||||
\(816\) | −10.7731 | −0.377135 | ||||||||
\(817\) | 15.0790 | 0.527547 | ||||||||
\(818\) | −36.1964 | −1.26558 | ||||||||
\(819\) | −13.6462 | −0.476835 | ||||||||
\(820\) | −5.03983 | −0.175998 | ||||||||
\(821\) | −21.6892 | −0.756957 | −0.378479 | − | 0.925610i | \(-0.623553\pi\) | ||||
−0.378479 | + | 0.925610i | \(0.623553\pi\) | |||||||
\(822\) | −27.8211 | −0.970371 | ||||||||
\(823\) | 6.12406 | 0.213471 | 0.106736 | − | 0.994287i | \(-0.465960\pi\) | ||||
0.106736 | + | 0.994287i | \(0.465960\pi\) | |||||||
\(824\) | 16.0410 | 0.558815 | ||||||||
\(825\) | −0.608331 | −0.0211794 | ||||||||
\(826\) | −34.7925 | −1.21059 | ||||||||
\(827\) | 50.6057 | 1.75973 | 0.879866 | − | 0.475221i | \(-0.157632\pi\) | ||||
0.879866 | + | 0.475221i | \(0.157632\pi\) | |||||||
\(828\) | 1.08173 | 0.0375926 | ||||||||
\(829\) | −15.7599 | −0.547365 | −0.273682 | − | 0.961820i | \(-0.588242\pi\) | ||||
−0.273682 | + | 0.961820i | \(0.588242\pi\) | |||||||
\(830\) | 40.8199 | 1.41688 | ||||||||
\(831\) | 1.78976 | 0.0620861 | ||||||||
\(832\) | 40.6043 | 1.40770 | ||||||||
\(833\) | −4.74178 | −0.164293 | ||||||||
\(834\) | 13.5935 | 0.470703 | ||||||||
\(835\) | 44.7016 | 1.54696 | ||||||||
\(836\) | 1.14785 | 0.0396991 | ||||||||
\(837\) | −1.22908 | −0.0424833 | ||||||||
\(838\) | −22.7821 | −0.786996 | ||||||||
\(839\) | −20.8938 | −0.721334 | −0.360667 | − | 0.932695i | \(-0.617451\pi\) | ||||
−0.360667 | + | 0.932695i | \(0.617451\pi\) | |||||||
\(840\) | −20.5233 | −0.708120 | ||||||||
\(841\) | −24.4044 | −0.841532 | ||||||||
\(842\) | 21.8563 | 0.753217 | ||||||||
\(843\) | 11.9883 | 0.412900 | ||||||||
\(844\) | −1.98290 | −0.0682541 | ||||||||
\(845\) | −20.8751 | −0.718126 | ||||||||
\(846\) | 1.58570 | 0.0545176 | ||||||||
\(847\) | −2.92169 | −0.100391 | ||||||||
\(848\) | 16.2757 | 0.558911 | ||||||||
\(849\) | 18.0687 | 0.620115 | ||||||||
\(850\) | 2.49896 | 0.0857136 | ||||||||
\(851\) | 27.0544 | 0.927414 | ||||||||
\(852\) | 3.39812 | 0.116418 | ||||||||
\(853\) | 19.2873 | 0.660383 | 0.330192 | − | 0.943914i | \(-0.392887\pi\) | ||||
0.330192 | + | 0.943914i | \(0.392887\pi\) | |||||||
\(854\) | −3.88853 | −0.133063 | ||||||||
\(855\) | 11.8880 | 0.406562 | ||||||||
\(856\) | −15.3670 | −0.525233 | ||||||||
\(857\) | 4.94606 | 0.168954 | 0.0844771 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844771 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(858\) | 6.21622 | 0.212218 | ||||||||
\(859\) | −28.0355 | −0.956558 | −0.478279 | − | 0.878208i | \(-0.658739\pi\) | ||||
−0.478279 | + | 0.878208i | \(0.658739\pi\) | |||||||
\(860\) | −1.62662 | −0.0554674 | ||||||||
\(861\) | −27.1921 | −0.926705 | ||||||||
\(862\) | −51.9980 | −1.77106 | ||||||||
\(863\) | −52.8568 | −1.79927 | −0.899634 | − | 0.436645i | \(-0.856167\pi\) | ||||
−0.899634 | + | 0.436645i | \(0.856167\pi\) | |||||||
\(864\) | 1.28690 | 0.0437812 | ||||||||
\(865\) | −49.1152 | −1.66997 | ||||||||
\(866\) | −27.4844 | −0.933957 | ||||||||
\(867\) | 7.47345 | 0.253812 | ||||||||
\(868\) | 0.821118 | 0.0278706 | ||||||||
\(869\) | 11.9696 | 0.406041 | ||||||||
\(870\) | 6.75675 | 0.229075 | ||||||||
\(871\) | 42.0267 | 1.42402 | ||||||||
\(872\) | −33.1682 | −1.12322 | ||||||||
\(873\) | 5.28118 | 0.178741 | ||||||||
\(874\) | −31.6061 | −1.06909 | ||||||||
\(875\) | −30.3865 | −1.02725 | ||||||||
\(876\) | 2.24082 | 0.0757104 | ||||||||
\(877\) | 2.79315 | 0.0943180 | 0.0471590 | − | 0.998887i | \(-0.484983\pi\) | ||||
0.0471590 | + | 0.998887i | \(0.484983\pi\) | |||||||
\(878\) | 48.3257 | 1.63091 | ||||||||
\(879\) | −23.4090 | −0.789566 | ||||||||
\(880\) | 8.26592 | 0.278644 | ||||||||
\(881\) | 21.8113 | 0.734843 | 0.367421 | − | 0.930055i | \(-0.380241\pi\) | ||||
0.367421 | + | 0.930055i | \(0.380241\pi\) | |||||||
\(882\) | −2.04467 | −0.0688478 | ||||||||
\(883\) | −6.55226 | −0.220501 | −0.110251 | − | 0.993904i | \(-0.535165\pi\) | ||||
−0.110251 | + | 0.993904i | \(0.535165\pi\) | |||||||
\(884\) | 3.29635 | 0.110868 | ||||||||
\(885\) | −21.1893 | −0.712271 | ||||||||
\(886\) | −4.85418 | −0.163080 | ||||||||
\(887\) | 17.6112 | 0.591325 | 0.295662 | − | 0.955292i | \(-0.404460\pi\) | ||||
0.295662 | + | 0.955292i | \(0.404460\pi\) | |||||||
\(888\) | 16.9631 | 0.569245 | ||||||||
\(889\) | −1.43135 | −0.0480061 | ||||||||
\(890\) | −1.34102 | −0.0449512 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −0.123590 | −0.00413811 | ||||||||
\(893\) | 5.98087 | 0.200142 | ||||||||
\(894\) | −17.7168 | −0.592537 | ||||||||
\(895\) | −25.8174 | −0.862980 | ||||||||
\(896\) | 26.2853 | 0.878129 | ||||||||
\(897\) | 22.0954 | 0.737745 | ||||||||
\(898\) | −50.9993 | −1.70187 | ||||||||
\(899\) | −2.63482 | −0.0878761 | ||||||||
\(900\) | −0.139101 | −0.00463671 | ||||||||
\(901\) | 14.3924 | 0.479481 | ||||||||
\(902\) | 12.3868 | 0.412435 | ||||||||
\(903\) | −8.77635 | −0.292059 | ||||||||
\(904\) | −25.4192 | −0.845429 | ||||||||
\(905\) | −22.9342 | −0.762358 | ||||||||
\(906\) | −18.8283 | −0.625529 | ||||||||
\(907\) | −31.0718 | −1.03172 | −0.515861 | − | 0.856672i | \(-0.672528\pi\) | ||||
−0.515861 | + | 0.856672i | \(0.672528\pi\) | |||||||
\(908\) | −1.28090 | −0.0425082 | ||||||||
\(909\) | −18.0972 | −0.600245 | ||||||||
\(910\) | −43.0108 | −1.42580 | ||||||||
\(911\) | −3.53312 | −0.117058 | −0.0585288 | − | 0.998286i | \(-0.518641\pi\) | ||||
−0.0585288 | + | 0.998286i | \(0.518641\pi\) | |||||||
\(912\) | −17.5214 | −0.580190 | ||||||||
\(913\) | 12.9510 | 0.428617 | ||||||||
\(914\) | −14.1432 | −0.467815 | ||||||||
\(915\) | −2.36819 | −0.0782900 | ||||||||
\(916\) | 2.93630 | 0.0970180 | ||||||||
\(917\) | 12.4399 | 0.410800 | ||||||||
\(918\) | −4.10789 | −0.135581 | ||||||||
\(919\) | 39.8129 | 1.31331 | 0.656653 | − | 0.754193i | \(-0.271972\pi\) | ||||
0.656653 | + | 0.754193i | \(0.271972\pi\) | |||||||
\(920\) | 33.2307 | 1.09558 | ||||||||
\(921\) | −8.48031 | −0.279436 | ||||||||
\(922\) | 32.3049 | 1.06391 | ||||||||
\(923\) | 69.4102 | 2.28467 | ||||||||
\(924\) | −0.668075 | −0.0219780 | ||||||||
\(925\) | −3.47898 | −0.114388 | ||||||||
\(926\) | −7.02106 | −0.230726 | ||||||||
\(927\) | 5.40800 | 0.177622 | ||||||||
\(928\) | 2.75876 | 0.0905608 | ||||||||
\(929\) | 26.4621 | 0.868193 | 0.434097 | − | 0.900866i | \(-0.357068\pi\) | ||||
0.434097 | + | 0.900866i | \(0.357068\pi\) | |||||||
\(930\) | −3.87390 | −0.127030 | ||||||||
\(931\) | −7.71199 | −0.252750 | ||||||||
\(932\) | −5.98327 | −0.195989 | ||||||||
\(933\) | 16.1743 | 0.529522 | ||||||||
\(934\) | −7.95821 | −0.260401 | ||||||||
\(935\) | 7.30945 | 0.239045 | ||||||||
\(936\) | 13.8538 | 0.452827 | ||||||||
\(937\) | −5.91019 | −0.193077 | −0.0965387 | − | 0.995329i | \(-0.530777\pi\) | ||||
−0.0965387 | + | 0.995329i | \(0.530777\pi\) | |||||||
\(938\) | 34.9893 | 1.14244 | ||||||||
\(939\) | −0.716595 | −0.0233852 | ||||||||
\(940\) | −0.645176 | −0.0210433 | ||||||||
\(941\) | −41.2125 | −1.34349 | −0.671744 | − | 0.740784i | \(-0.734454\pi\) | ||||
−0.671744 | + | 0.740784i | \(0.734454\pi\) | |||||||
\(942\) | 20.3166 | 0.661950 | ||||||||
\(943\) | 44.0287 | 1.43377 | ||||||||
\(944\) | 31.2302 | 1.01646 | ||||||||
\(945\) | −6.91913 | −0.225079 | ||||||||
\(946\) | 3.99788 | 0.129982 | ||||||||
\(947\) | 3.35032 | 0.108871 | 0.0544354 | − | 0.998517i | \(-0.482664\pi\) | ||||
0.0544354 | + | 0.998517i | \(0.482664\pi\) | |||||||
\(948\) | 2.73697 | 0.0888927 | ||||||||
\(949\) | 45.7712 | 1.48580 | ||||||||
\(950\) | 4.06429 | 0.131863 | ||||||||
\(951\) | 2.26108 | 0.0733205 | ||||||||
\(952\) | 26.7484 | 0.866919 | ||||||||
\(953\) | −7.53957 | −0.244231 | −0.122115 | − | 0.992516i | \(-0.538968\pi\) | ||||
−0.122115 | + | 0.992516i | \(0.538968\pi\) | |||||||
\(954\) | 6.20608 | 0.200929 | ||||||||
\(955\) | 25.6137 | 0.828838 | ||||||||
\(956\) | −3.92888 | −0.127069 | ||||||||
\(957\) | 2.14373 | 0.0692970 | ||||||||
\(958\) | 14.3190 | 0.462626 | ||||||||
\(959\) | 61.0741 | 1.97219 | ||||||||
\(960\) | 20.5880 | 0.664474 | ||||||||
\(961\) | −29.4894 | −0.951270 | ||||||||
\(962\) | 35.5498 | 1.14617 | ||||||||
\(963\) | −5.18077 | −0.166948 | ||||||||
\(964\) | −4.69959 | −0.151364 | ||||||||
\(965\) | 14.6724 | 0.472322 | ||||||||
\(966\) | 18.3955 | 0.591867 | ||||||||
\(967\) | −36.1572 | −1.16274 | −0.581369 | − | 0.813640i | \(-0.697483\pi\) | ||||
−0.581369 | + | 0.813640i | \(0.697483\pi\) | |||||||
\(968\) | 2.96616 | 0.0953360 | ||||||||
\(969\) | −15.4939 | −0.497736 | ||||||||
\(970\) | 16.6456 | 0.534457 | ||||||||
\(971\) | −20.8300 | −0.668468 | −0.334234 | − | 0.942490i | \(-0.608478\pi\) | ||||
−0.334234 | + | 0.942490i | \(0.608478\pi\) | |||||||
\(972\) | 0.228660 | 0.00733428 | ||||||||
\(973\) | −29.8410 | −0.956659 | ||||||||
\(974\) | −36.4476 | −1.16786 | ||||||||
\(975\) | −2.84129 | −0.0909942 | ||||||||
\(976\) | 3.49039 | 0.111725 | ||||||||
\(977\) | 23.9880 | 0.767444 | 0.383722 | − | 0.923449i | \(-0.374642\pi\) | ||||
0.383722 | + | 0.923449i | \(0.374642\pi\) | |||||||
\(978\) | 24.0376 | 0.768638 | ||||||||
\(979\) | −0.425469 | −0.0135981 | ||||||||
\(980\) | 0.831918 | 0.0265746 | ||||||||
\(981\) | −11.1822 | −0.357020 | ||||||||
\(982\) | 17.3016 | 0.552117 | ||||||||
\(983\) | −1.23884 | −0.0395129 | −0.0197565 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197565 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(984\) | 27.6060 | 0.880046 | ||||||||
\(985\) | 2.72331 | 0.0867719 | ||||||||
\(986\) | −8.80621 | −0.280447 | ||||||||
\(987\) | −3.48101 | −0.110802 | ||||||||
\(988\) | 5.36117 | 0.170561 | ||||||||
\(989\) | 14.2104 | 0.451865 | ||||||||
\(990\) | 3.15187 | 0.100173 | ||||||||
\(991\) | 2.76799 | 0.0879281 | 0.0439641 | − | 0.999033i | \(-0.486001\pi\) | ||||
0.0439641 | + | 0.999033i | \(0.486001\pi\) | |||||||
\(992\) | −1.58170 | −0.0502191 | ||||||||
\(993\) | 11.8409 | 0.375760 | ||||||||
\(994\) | 57.7874 | 1.83291 | ||||||||
\(995\) | −32.6955 | −1.03652 | ||||||||
\(996\) | 2.96139 | 0.0938351 | ||||||||
\(997\) | 27.1886 | 0.861071 | 0.430536 | − | 0.902574i | \(-0.358325\pi\) | ||||
0.430536 | + | 0.902574i | \(0.358325\pi\) | |||||||
\(998\) | 24.6432 | 0.780068 | ||||||||
\(999\) | 5.71888 | 0.180937 |
(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 | 2013.2.a.e.1.4 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.10 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.4 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.10 | 13 | 3.2 | odd | 2 |