Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.0566801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.0566801 | −0.0327243 | −0.0163621 | − | 0.999866i | \(-0.505208\pi\) | ||||
−0.0163621 | + | 0.999866i | \(0.505208\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.0566801 | −0.0231396 | ||||||||
\(7\) | 5.00659 | 1.89231 | 0.946157 | − | 0.323708i | \(-0.104930\pi\) | ||||
0.946157 | + | 0.323708i | \(0.104930\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.99679 | −0.998929 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.22584 | 0.671116 | 0.335558 | − | 0.942019i | \(-0.391075\pi\) | ||||
0.335558 | + | 0.942019i | \(0.391075\pi\) | |||||||
\(12\) | −0.0566801 | −0.0163621 | ||||||||
\(13\) | −2.99679 | −0.831160 | −0.415580 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415580 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(14\) | 5.00659 | 1.33807 | ||||||||
\(15\) | 0.0566801 | 0.0146347 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.17205 | 0.284265 | 0.142132 | − | 0.989848i | \(-0.454604\pi\) | ||||
0.142132 | + | 0.989848i | \(0.454604\pi\) | |||||||
\(18\) | −2.99679 | −0.706350 | ||||||||
\(19\) | −7.27464 | −1.66892 | −0.834459 | − | 0.551071i | \(-0.814220\pi\) | ||||
−0.834459 | + | 0.551071i | \(0.814220\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.283774 | −0.0619246 | ||||||||
\(22\) | 2.22584 | 0.474551 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −0.0566801 | −0.0115698 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.99679 | −0.587719 | ||||||||
\(27\) | 0.339899 | 0.0654135 | ||||||||
\(28\) | 5.00659 | 0.946157 | ||||||||
\(29\) | 2.78953 | 0.518002 | 0.259001 | − | 0.965877i | \(-0.416607\pi\) | ||||
0.259001 | + | 0.965877i | \(0.416607\pi\) | |||||||
\(30\) | 0.0566801 | 0.0103483 | ||||||||
\(31\) | 7.90982 | 1.42065 | 0.710323 | − | 0.703876i | \(-0.248549\pi\) | ||||
0.710323 | + | 0.703876i | \(0.248549\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.126161 | −0.0219618 | ||||||||
\(34\) | 1.17205 | 0.201005 | ||||||||
\(35\) | −5.00659 | −0.846269 | ||||||||
\(36\) | −2.99679 | −0.499465 | ||||||||
\(37\) | 0.498984 | 0.0820324 | 0.0410162 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410162 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(38\) | −7.27464 | −1.18010 | ||||||||
\(39\) | 0.169858 | 0.0271991 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 5.54398 | 0.865824 | 0.432912 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432912 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(42\) | −0.283774 | −0.0437873 | ||||||||
\(43\) | 10.3763 | 1.58236 | 0.791182 | − | 0.611580i | \(-0.209466\pi\) | ||||
0.791182 | + | 0.611580i | \(0.209466\pi\) | |||||||
\(44\) | 2.22584 | 0.335558 | ||||||||
\(45\) | 2.99679 | 0.446735 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.15586 | 0.606194 | 0.303097 | − | 0.952960i | \(-0.401979\pi\) | ||||
0.303097 | + | 0.952960i | \(0.401979\pi\) | |||||||
\(48\) | −0.0566801 | −0.00818107 | ||||||||
\(49\) | 18.0660 | 2.58085 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.0664321 | −0.00930236 | ||||||||
\(52\) | −2.99679 | −0.415580 | ||||||||
\(53\) | 2.72827 | 0.374757 | 0.187379 | − | 0.982288i | \(-0.440001\pi\) | ||||
0.187379 | + | 0.982288i | \(0.440001\pi\) | |||||||
\(54\) | 0.339899 | 0.0462543 | ||||||||
\(55\) | −2.22584 | −0.300132 | ||||||||
\(56\) | 5.00659 | 0.669034 | ||||||||
\(57\) | 0.412328 | 0.0546141 | ||||||||
\(58\) | 2.78953 | 0.366283 | ||||||||
\(59\) | −1.61972 | −0.210870 | −0.105435 | − | 0.994426i | \(-0.533624\pi\) | ||||
−0.105435 | + | 0.994426i | \(0.533624\pi\) | |||||||
\(60\) | 0.0566801 | 0.00731737 | ||||||||
\(61\) | −5.58655 | −0.715285 | −0.357642 | − | 0.933859i | \(-0.616419\pi\) | ||||
−0.357642 | + | 0.933859i | \(0.616419\pi\) | |||||||
\(62\) | 7.90982 | 1.00455 | ||||||||
\(63\) | −15.0037 | −1.89029 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.99679 | 0.371706 | ||||||||
\(66\) | −0.126161 | −0.0155293 | ||||||||
\(67\) | 6.27410 | 0.766504 | 0.383252 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383252 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(68\) | 1.17205 | 0.142132 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.00659 | −0.598402 | ||||||||
\(71\) | 9.80578 | 1.16373 | 0.581866 | − | 0.813285i | \(-0.302323\pi\) | ||||
0.581866 | + | 0.813285i | \(0.302323\pi\) | |||||||
\(72\) | −2.99679 | −0.353175 | ||||||||
\(73\) | 1.68505 | 0.197220 | 0.0986102 | − | 0.995126i | \(-0.468560\pi\) | ||||
0.0986102 | + | 0.995126i | \(0.468560\pi\) | |||||||
\(74\) | 0.498984 | 0.0580057 | ||||||||
\(75\) | −0.0566801 | −0.00654486 | ||||||||
\(76\) | −7.27464 | −0.834459 | ||||||||
\(77\) | 11.1439 | 1.26996 | ||||||||
\(78\) | 0.169858 | 0.0192327 | ||||||||
\(79\) | 11.0622 | 1.24459 | 0.622296 | − | 0.782782i | \(-0.286200\pi\) | ||||
0.622296 | + | 0.782782i | \(0.286200\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.97110 | 0.996789 | ||||||||
\(82\) | 5.54398 | 0.612230 | ||||||||
\(83\) | −1.37389 | −0.150804 | −0.0754021 | − | 0.997153i | \(-0.524024\pi\) | ||||
−0.0754021 | + | 0.997153i | \(0.524024\pi\) | |||||||
\(84\) | −0.283774 | −0.0309623 | ||||||||
\(85\) | −1.17205 | −0.127127 | ||||||||
\(86\) | 10.3763 | 1.11890 | ||||||||
\(87\) | −0.158111 | −0.0169512 | ||||||||
\(88\) | 2.22584 | 0.237275 | ||||||||
\(89\) | −16.2240 | −1.71974 | −0.859871 | − | 0.510512i | \(-0.829456\pi\) | ||||
−0.859871 | + | 0.510512i | \(0.829456\pi\) | |||||||
\(90\) | 2.99679 | 0.315889 | ||||||||
\(91\) | −15.0037 | −1.57282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.448330 | −0.0464896 | ||||||||
\(94\) | 4.15586 | 0.428644 | ||||||||
\(95\) | 7.27464 | 0.746363 | ||||||||
\(96\) | −0.0566801 | −0.00578489 | ||||||||
\(97\) | −4.93548 | −0.501122 | −0.250561 | − | 0.968101i | \(-0.580615\pi\) | ||||
−0.250561 | + | 0.968101i | \(0.580615\pi\) | |||||||
\(98\) | 18.0660 | 1.82494 | ||||||||
\(99\) | −6.67037 | −0.670398 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.55146 | −0.253879 | −0.126940 | − | 0.991910i | \(-0.540515\pi\) | ||||
−0.126940 | + | 0.991910i | \(0.540515\pi\) | |||||||
\(102\) | −0.0664321 | −0.00657776 | ||||||||
\(103\) | −16.4581 | −1.62166 | −0.810831 | − | 0.585281i | \(-0.800984\pi\) | ||||
−0.810831 | + | 0.585281i | \(0.800984\pi\) | |||||||
\(104\) | −2.99679 | −0.293860 | ||||||||
\(105\) | 0.283774 | 0.0276935 | ||||||||
\(106\) | 2.72827 | 0.264993 | ||||||||
\(107\) | 19.4802 | 1.88322 | 0.941612 | − | 0.336699i | \(-0.109310\pi\) | ||||
0.941612 | + | 0.336699i | \(0.109310\pi\) | |||||||
\(108\) | 0.339899 | 0.0327068 | ||||||||
\(109\) | −2.83881 | −0.271909 | −0.135954 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135954 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(110\) | −2.22584 | −0.212226 | ||||||||
\(111\) | −0.0282824 | −0.00268445 | ||||||||
\(112\) | 5.00659 | 0.473079 | ||||||||
\(113\) | −8.88945 | −0.836249 | −0.418125 | − | 0.908390i | \(-0.637313\pi\) | ||||
−0.418125 | + | 0.908390i | \(0.637313\pi\) | |||||||
\(114\) | 0.412328 | 0.0386180 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.78953 | 0.259001 | ||||||||
\(117\) | 8.98075 | 0.830270 | ||||||||
\(118\) | −1.61972 | −0.149108 | ||||||||
\(119\) | 5.86799 | 0.537918 | ||||||||
\(120\) | 0.0566801 | 0.00517416 | ||||||||
\(121\) | −6.04563 | −0.549603 | ||||||||
\(122\) | −5.58655 | −0.505783 | ||||||||
\(123\) | −0.314233 | −0.0283335 | ||||||||
\(124\) | 7.90982 | 0.710323 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −15.0037 | −1.33664 | ||||||||
\(127\) | 3.43426 | 0.304741 | 0.152371 | − | 0.988323i | \(-0.451309\pi\) | ||||
0.152371 | + | 0.988323i | \(0.451309\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.588128 | −0.0517817 | ||||||||
\(130\) | 2.99679 | 0.262836 | ||||||||
\(131\) | 19.1282 | 1.67124 | 0.835618 | − | 0.549311i | \(-0.185110\pi\) | ||||
0.835618 | + | 0.549311i | \(0.185110\pi\) | |||||||
\(132\) | −0.126161 | −0.0109809 | ||||||||
\(133\) | −36.4212 | −3.15812 | ||||||||
\(134\) | 6.27410 | 0.542000 | ||||||||
\(135\) | −0.339899 | −0.0292538 | ||||||||
\(136\) | 1.17205 | 0.100503 | ||||||||
\(137\) | −17.0162 | −1.45379 | −0.726897 | − | 0.686747i | \(-0.759038\pi\) | ||||
−0.726897 | + | 0.686747i | \(0.759038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.94931 | 0.334976 | 0.167488 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167488 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(140\) | −5.00659 | −0.423134 | ||||||||
\(141\) | −0.235554 | −0.0198373 | ||||||||
\(142\) | 9.80578 | 0.822883 | ||||||||
\(143\) | −6.67038 | −0.557805 | ||||||||
\(144\) | −2.99679 | −0.249732 | ||||||||
\(145\) | −2.78953 | −0.231657 | ||||||||
\(146\) | 1.68505 | 0.139456 | ||||||||
\(147\) | −1.02398 | −0.0844565 | ||||||||
\(148\) | 0.498984 | 0.0410162 | ||||||||
\(149\) | 18.6998 | 1.53195 | 0.765975 | − | 0.642871i | \(-0.222257\pi\) | ||||
0.765975 | + | 0.642871i | \(0.222257\pi\) | |||||||
\(150\) | −0.0566801 | −0.00462791 | ||||||||
\(151\) | 18.3668 | 1.49467 | 0.747336 | − | 0.664447i | \(-0.231333\pi\) | ||||
0.747336 | + | 0.664447i | \(0.231333\pi\) | |||||||
\(152\) | −7.27464 | −0.590051 | ||||||||
\(153\) | −3.51239 | −0.283960 | ||||||||
\(154\) | 11.1439 | 0.897999 | ||||||||
\(155\) | −7.90982 | −0.635332 | ||||||||
\(156\) | 0.169858 | 0.0135996 | ||||||||
\(157\) | −12.4944 | −0.997162 | −0.498581 | − | 0.866843i | \(-0.666145\pi\) | ||||
−0.498581 | + | 0.866843i | \(0.666145\pi\) | |||||||
\(158\) | 11.0622 | 0.880059 | ||||||||
\(159\) | −0.154639 | −0.0122637 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.97110 | 0.704836 | ||||||||
\(163\) | 3.37214 | 0.264127 | 0.132063 | − | 0.991241i | \(-0.457840\pi\) | ||||
0.132063 | + | 0.991241i | \(0.457840\pi\) | |||||||
\(164\) | 5.54398 | 0.432912 | ||||||||
\(165\) | 0.126161 | 0.00982162 | ||||||||
\(166\) | −1.37389 | −0.106635 | ||||||||
\(167\) | 19.9217 | 1.54159 | 0.770793 | − | 0.637086i | \(-0.219860\pi\) | ||||
0.770793 | + | 0.637086i | \(0.219860\pi\) | |||||||
\(168\) | −0.283774 | −0.0218937 | ||||||||
\(169\) | −4.01924 | −0.309173 | ||||||||
\(170\) | −1.17205 | −0.0898924 | ||||||||
\(171\) | 21.8006 | 1.66713 | ||||||||
\(172\) | 10.3763 | 0.791182 | ||||||||
\(173\) | −17.0776 | −1.29839 | −0.649194 | − | 0.760623i | \(-0.724894\pi\) | ||||
−0.649194 | + | 0.760623i | \(0.724894\pi\) | |||||||
\(174\) | −0.158111 | −0.0119863 | ||||||||
\(175\) | 5.00659 | 0.378463 | ||||||||
\(176\) | 2.22584 | 0.167779 | ||||||||
\(177\) | 0.0918062 | 0.00690058 | ||||||||
\(178\) | −16.2240 | −1.21604 | ||||||||
\(179\) | −13.0442 | −0.974967 | −0.487483 | − | 0.873132i | \(-0.662085\pi\) | ||||
−0.487483 | + | 0.873132i | \(0.662085\pi\) | |||||||
\(180\) | 2.99679 | 0.223367 | ||||||||
\(181\) | −6.10807 | −0.454009 | −0.227005 | − | 0.973894i | \(-0.572893\pi\) | ||||
−0.227005 | + | 0.973894i | \(0.572893\pi\) | |||||||
\(182\) | −15.0037 | −1.11215 | ||||||||
\(183\) | 0.316646 | 0.0234072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.498984 | −0.0366860 | ||||||||
\(186\) | −0.448330 | −0.0328731 | ||||||||
\(187\) | 2.60880 | 0.190775 | ||||||||
\(188\) | 4.15586 | 0.303097 | ||||||||
\(189\) | 1.70173 | 0.123783 | ||||||||
\(190\) | 7.27464 | 0.527758 | ||||||||
\(191\) | −2.56505 | −0.185600 | −0.0928001 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928001 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(192\) | −0.0566801 | −0.00409054 | ||||||||
\(193\) | 11.1506 | 0.802637 | 0.401318 | − | 0.915939i | \(-0.368552\pi\) | ||||
0.401318 | + | 0.915939i | \(0.368552\pi\) | |||||||
\(194\) | −4.93548 | −0.354347 | ||||||||
\(195\) | −0.169858 | −0.0121638 | ||||||||
\(196\) | 18.0660 | 1.29043 | ||||||||
\(197\) | −7.61900 | −0.542831 | −0.271416 | − | 0.962462i | \(-0.587492\pi\) | ||||
−0.271416 | + | 0.962462i | \(0.587492\pi\) | |||||||
\(198\) | −6.67037 | −0.474043 | ||||||||
\(199\) | 15.8779 | 1.12555 | 0.562777 | − | 0.826609i | \(-0.309733\pi\) | ||||
0.562777 | + | 0.826609i | \(0.309733\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.355617 | −0.0250833 | ||||||||
\(202\) | −2.55146 | −0.179520 | ||||||||
\(203\) | 13.9660 | 0.980222 | ||||||||
\(204\) | −0.0664321 | −0.00465118 | ||||||||
\(205\) | −5.54398 | −0.387208 | ||||||||
\(206\) | −16.4581 | −1.14669 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.99679 | −0.207790 | ||||||||
\(209\) | −16.1922 | −1.12004 | ||||||||
\(210\) | 0.283774 | 0.0195823 | ||||||||
\(211\) | −1.50006 | −0.103268 | −0.0516341 | − | 0.998666i | \(-0.516443\pi\) | ||||
−0.0516341 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(212\) | 2.72827 | 0.187379 | ||||||||
\(213\) | −0.555793 | −0.0380823 | ||||||||
\(214\) | 19.4802 | 1.33164 | ||||||||
\(215\) | −10.3763 | −0.707655 | ||||||||
\(216\) | 0.339899 | 0.0231272 | ||||||||
\(217\) | 39.6013 | 2.68831 | ||||||||
\(218\) | −2.83881 | −0.192269 | ||||||||
\(219\) | −0.0955089 | −0.00645389 | ||||||||
\(220\) | −2.22584 | −0.150066 | ||||||||
\(221\) | −3.51240 | −0.236270 | ||||||||
\(222\) | −0.0282824 | −0.00189819 | ||||||||
\(223\) | −8.90770 | −0.596504 | −0.298252 | − | 0.954487i | \(-0.596404\pi\) | ||||
−0.298252 | + | 0.954487i | \(0.596404\pi\) | |||||||
\(224\) | 5.00659 | 0.334517 | ||||||||
\(225\) | −2.99679 | −0.199786 | ||||||||
\(226\) | −8.88945 | −0.591318 | ||||||||
\(227\) | −4.29484 | −0.285059 | −0.142529 | − | 0.989791i | \(-0.545524\pi\) | ||||
−0.142529 | + | 0.989791i | \(0.545524\pi\) | |||||||
\(228\) | 0.412328 | 0.0273071 | ||||||||
\(229\) | −17.8967 | −1.18265 | −0.591324 | − | 0.806434i | \(-0.701395\pi\) | ||||
−0.591324 | + | 0.806434i | \(0.701395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.631636 | −0.0415586 | ||||||||
\(232\) | 2.78953 | 0.183141 | ||||||||
\(233\) | 27.2662 | 1.78627 | 0.893134 | − | 0.449790i | \(-0.148501\pi\) | ||||
0.893134 | + | 0.449790i | \(0.148501\pi\) | |||||||
\(234\) | 8.98075 | 0.587090 | ||||||||
\(235\) | −4.15586 | −0.271098 | ||||||||
\(236\) | −1.61972 | −0.105435 | ||||||||
\(237\) | −0.627005 | −0.0407284 | ||||||||
\(238\) | 5.86799 | 0.380366 | ||||||||
\(239\) | −13.8416 | −0.895341 | −0.447671 | − | 0.894198i | \(-0.647746\pi\) | ||||
−0.447671 | + | 0.894198i | \(0.647746\pi\) | |||||||
\(240\) | 0.0566801 | 0.00365869 | ||||||||
\(241\) | 15.1156 | 0.973680 | 0.486840 | − | 0.873491i | \(-0.338149\pi\) | ||||
0.486840 | + | 0.873491i | \(0.338149\pi\) | |||||||
\(242\) | −6.04563 | −0.388628 | ||||||||
\(243\) | −1.52818 | −0.0980327 | ||||||||
\(244\) | −5.58655 | −0.357642 | ||||||||
\(245\) | −18.0660 | −1.15419 | ||||||||
\(246\) | −0.314233 | −0.0200348 | ||||||||
\(247\) | 21.8006 | 1.38714 | ||||||||
\(248\) | 7.90982 | 0.502274 | ||||||||
\(249\) | 0.0778723 | 0.00493496 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 19.6466 | 1.24008 | 0.620040 | − | 0.784570i | \(-0.287116\pi\) | ||||
0.620040 | + | 0.784570i | \(0.287116\pi\) | |||||||
\(252\) | −15.0037 | −0.945144 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.43426 | 0.215484 | ||||||||
\(255\) | 0.0664321 | 0.00416014 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.35642 | 0.0846110 | 0.0423055 | − | 0.999105i | \(-0.486530\pi\) | ||||
0.0423055 | + | 0.999105i | \(0.486530\pi\) | |||||||
\(258\) | −0.588128 | −0.0366152 | ||||||||
\(259\) | 2.49821 | 0.155231 | ||||||||
\(260\) | 2.99679 | 0.185853 | ||||||||
\(261\) | −8.35961 | −0.517447 | ||||||||
\(262\) | 19.1282 | 1.18174 | ||||||||
\(263\) | 9.35101 | 0.576608 | 0.288304 | − | 0.957539i | \(-0.406909\pi\) | ||||
0.288304 | + | 0.957539i | \(0.406909\pi\) | |||||||
\(264\) | −0.126161 | −0.00776467 | ||||||||
\(265\) | −2.72827 | −0.167597 | ||||||||
\(266\) | −36.4212 | −2.23313 | ||||||||
\(267\) | 0.919579 | 0.0562773 | ||||||||
\(268\) | 6.27410 | 0.383252 | ||||||||
\(269\) | 19.9733 | 1.21779 | 0.608897 | − | 0.793250i | \(-0.291612\pi\) | ||||
0.608897 | + | 0.793250i | \(0.291612\pi\) | |||||||
\(270\) | −0.339899 | −0.0206856 | ||||||||
\(271\) | 22.3390 | 1.35700 | 0.678499 | − | 0.734602i | \(-0.262631\pi\) | ||||
0.678499 | + | 0.734602i | \(0.262631\pi\) | |||||||
\(272\) | 1.17205 | 0.0710662 | ||||||||
\(273\) | 0.850412 | 0.0514693 | ||||||||
\(274\) | −17.0162 | −1.02799 | ||||||||
\(275\) | 2.22584 | 0.134223 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2078 | −1.09400 | −0.547000 | − | 0.837132i | \(-0.684230\pi\) | ||||
−0.547000 | + | 0.837132i | \(0.684230\pi\) | |||||||
\(278\) | 3.94931 | 0.236864 | ||||||||
\(279\) | −23.7041 | −1.41912 | ||||||||
\(280\) | −5.00659 | −0.299201 | ||||||||
\(281\) | 10.7438 | 0.640919 | 0.320459 | − | 0.947262i | \(-0.396163\pi\) | ||||
0.320459 | + | 0.947262i | \(0.396163\pi\) | |||||||
\(282\) | −0.235554 | −0.0140271 | ||||||||
\(283\) | −10.7171 | −0.637067 | −0.318533 | − | 0.947912i | \(-0.603190\pi\) | ||||
−0.318533 | + | 0.947912i | \(0.603190\pi\) | |||||||
\(284\) | 9.80578 | 0.581866 | ||||||||
\(285\) | −0.412328 | −0.0244242 | ||||||||
\(286\) | −6.67038 | −0.394428 | ||||||||
\(287\) | 27.7564 | 1.63841 | ||||||||
\(288\) | −2.99679 | −0.176587 | ||||||||
\(289\) | −15.6263 | −0.919194 | ||||||||
\(290\) | −2.78953 | −0.163807 | ||||||||
\(291\) | 0.279744 | 0.0163989 | ||||||||
\(292\) | 1.68505 | 0.0986102 | ||||||||
\(293\) | −17.1056 | −0.999320 | −0.499660 | − | 0.866222i | \(-0.666542\pi\) | ||||
−0.499660 | + | 0.866222i | \(0.666542\pi\) | |||||||
\(294\) | −1.02398 | −0.0597198 | ||||||||
\(295\) | 1.61972 | 0.0943040 | ||||||||
\(296\) | 0.498984 | 0.0290028 | ||||||||
\(297\) | 0.756560 | 0.0439001 | ||||||||
\(298\) | 18.6998 | 1.08325 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.0566801 | −0.00327243 | ||||||||
\(301\) | 51.9497 | 2.99433 | ||||||||
\(302\) | 18.3668 | 1.05689 | ||||||||
\(303\) | 0.144617 | 0.00830802 | ||||||||
\(304\) | −7.27464 | −0.417229 | ||||||||
\(305\) | 5.58655 | 0.319885 | ||||||||
\(306\) | −3.51239 | −0.200790 | ||||||||
\(307\) | 5.94744 | 0.339438 | 0.169719 | − | 0.985492i | \(-0.445714\pi\) | ||||
0.169719 | + | 0.985492i | \(0.445714\pi\) | |||||||
\(308\) | 11.1439 | 0.634982 | ||||||||
\(309\) | 0.932845 | 0.0530677 | ||||||||
\(310\) | −7.90982 | −0.449248 | ||||||||
\(311\) | −20.0565 | −1.13730 | −0.568650 | − | 0.822580i | \(-0.692534\pi\) | ||||
−0.568650 | + | 0.822580i | \(0.692534\pi\) | |||||||
\(312\) | 0.169858 | 0.00961634 | ||||||||
\(313\) | 20.8169 | 1.17664 | 0.588320 | − | 0.808628i | \(-0.299790\pi\) | ||||
0.588320 | + | 0.808628i | \(0.299790\pi\) | |||||||
\(314\) | −12.4944 | −0.705100 | ||||||||
\(315\) | 15.0037 | 0.845362 | ||||||||
\(316\) | 11.0622 | 0.622296 | ||||||||
\(317\) | −13.5804 | −0.762750 | −0.381375 | − | 0.924420i | \(-0.624549\pi\) | ||||
−0.381375 | + | 0.924420i | \(0.624549\pi\) | |||||||
\(318\) | −0.154639 | −0.00867172 | ||||||||
\(319\) | 6.20904 | 0.347640 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −1.10414 | −0.0616272 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.52627 | −0.474414 | ||||||||
\(324\) | 8.97110 | 0.498394 | ||||||||
\(325\) | −2.99679 | −0.166232 | ||||||||
\(326\) | 3.37214 | 0.186766 | ||||||||
\(327\) | 0.160904 | 0.00889802 | ||||||||
\(328\) | 5.54398 | 0.306115 | ||||||||
\(329\) | 20.8067 | 1.14711 | ||||||||
\(330\) | 0.126161 | 0.00694493 | ||||||||
\(331\) | −18.1061 | −0.995200 | −0.497600 | − | 0.867407i | \(-0.665785\pi\) | ||||
−0.497600 | + | 0.867407i | \(0.665785\pi\) | |||||||
\(332\) | −1.37389 | −0.0754021 | ||||||||
\(333\) | −1.49535 | −0.0819445 | ||||||||
\(334\) | 19.9217 | 1.09007 | ||||||||
\(335\) | −6.27410 | −0.342791 | ||||||||
\(336\) | −0.283774 | −0.0154812 | ||||||||
\(337\) | −19.2644 | −1.04940 | −0.524699 | − | 0.851288i | \(-0.675822\pi\) | ||||
−0.524699 | + | 0.851288i | \(0.675822\pi\) | |||||||
\(338\) | −4.01924 | −0.218618 | ||||||||
\(339\) | 0.503855 | 0.0273657 | ||||||||
\(340\) | −1.17205 | −0.0635635 | ||||||||
\(341\) | 17.6060 | 0.953419 | ||||||||
\(342\) | 21.8006 | 1.17884 | ||||||||
\(343\) | 55.4028 | 2.99147 | ||||||||
\(344\) | 10.3763 | 0.559450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.0776 | −0.918099 | ||||||||
\(347\) | −3.92813 | −0.210873 | −0.105436 | − | 0.994426i | \(-0.533624\pi\) | ||||
−0.105436 | + | 0.994426i | \(0.533624\pi\) | |||||||
\(348\) | −0.158111 | −0.00847562 | ||||||||
\(349\) | 13.6354 | 0.729884 | 0.364942 | − | 0.931030i | \(-0.381089\pi\) | ||||
0.364942 | + | 0.931030i | \(0.381089\pi\) | |||||||
\(350\) | 5.00659 | 0.267614 | ||||||||
\(351\) | −1.01861 | −0.0543691 | ||||||||
\(352\) | 2.22584 | 0.118638 | ||||||||
\(353\) | 0.968813 | 0.0515647 | 0.0257823 | − | 0.999668i | \(-0.491792\pi\) | ||||
0.0257823 | + | 0.999668i | \(0.491792\pi\) | |||||||
\(354\) | 0.0918062 | 0.00487944 | ||||||||
\(355\) | −9.80578 | −0.520437 | ||||||||
\(356\) | −16.2240 | −0.859871 | ||||||||
\(357\) | −0.332599 | −0.0176030 | ||||||||
\(358\) | −13.0442 | −0.689406 | ||||||||
\(359\) | 14.2017 | 0.749536 | 0.374768 | − | 0.927119i | \(-0.377722\pi\) | ||||
0.374768 | + | 0.927119i | \(0.377722\pi\) | |||||||
\(360\) | 2.99679 | 0.157945 | ||||||||
\(361\) | 33.9204 | 1.78528 | ||||||||
\(362\) | −6.10807 | −0.321033 | ||||||||
\(363\) | 0.342667 | 0.0179854 | ||||||||
\(364\) | −15.0037 | −0.786408 | ||||||||
\(365\) | −1.68505 | −0.0881996 | ||||||||
\(366\) | 0.316646 | 0.0165514 | ||||||||
\(367\) | 12.9049 | 0.673633 | 0.336816 | − | 0.941570i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941570i | \(0.390650\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.6141 | −0.864897 | ||||||||
\(370\) | −0.498984 | −0.0259409 | ||||||||
\(371\) | 13.6594 | 0.709158 | ||||||||
\(372\) | −0.448330 | −0.0232448 | ||||||||
\(373\) | −30.5092 | −1.57970 | −0.789852 | − | 0.613297i | \(-0.789843\pi\) | ||||
−0.789852 | + | 0.613297i | \(0.789843\pi\) | |||||||
\(374\) | 2.60880 | 0.134898 | ||||||||
\(375\) | 0.0566801 | 0.00292695 | ||||||||
\(376\) | 4.15586 | 0.214322 | ||||||||
\(377\) | −8.35962 | −0.430543 | ||||||||
\(378\) | 1.70173 | 0.0875277 | ||||||||
\(379\) | −6.87704 | −0.353250 | −0.176625 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176625 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(380\) | 7.27464 | 0.373181 | ||||||||
\(381\) | −0.194654 | −0.00997243 | ||||||||
\(382\) | −2.56505 | −0.131239 | ||||||||
\(383\) | −14.0395 | −0.717383 | −0.358692 | − | 0.933456i | \(-0.616777\pi\) | ||||
−0.358692 | + | 0.933456i | \(0.616777\pi\) | |||||||
\(384\) | −0.0566801 | −0.00289245 | ||||||||
\(385\) | −11.1439 | −0.567945 | ||||||||
\(386\) | 11.1506 | 0.567550 | ||||||||
\(387\) | −31.0954 | −1.58067 | ||||||||
\(388\) | −4.93548 | −0.250561 | ||||||||
\(389\) | 7.36683 | 0.373513 | 0.186756 | − | 0.982406i | \(-0.440202\pi\) | ||||
0.186756 | + | 0.982406i | \(0.440202\pi\) | |||||||
\(390\) | −0.169858 | −0.00860112 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.0660 | 0.912469 | ||||||||
\(393\) | −1.08419 | −0.0546900 | ||||||||
\(394\) | −7.61900 | −0.383840 | ||||||||
\(395\) | −11.0622 | −0.556598 | ||||||||
\(396\) | −6.67037 | −0.335199 | ||||||||
\(397\) | −25.4128 | −1.27543 | −0.637715 | − | 0.770273i | \(-0.720120\pi\) | ||||
−0.637715 | + | 0.770273i | \(0.720120\pi\) | |||||||
\(398\) | 15.8779 | 0.795886 | ||||||||
\(399\) | 2.06436 | 0.103347 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −15.3171 | −0.764898 | −0.382449 | − | 0.923977i | \(-0.624919\pi\) | ||||
−0.382449 | + | 0.923977i | \(0.624919\pi\) | |||||||
\(402\) | −0.355617 | −0.0177366 | ||||||||
\(403\) | −23.7041 | −1.18078 | ||||||||
\(404\) | −2.55146 | −0.126940 | ||||||||
\(405\) | −8.97110 | −0.445777 | ||||||||
\(406\) | 13.9660 | 0.693122 | ||||||||
\(407\) | 1.11066 | 0.0550533 | ||||||||
\(408\) | −0.0664321 | −0.00328888 | ||||||||
\(409\) | −0.156293 | −0.00772821 | −0.00386410 | − | 0.999993i | \(-0.501230\pi\) | ||||
−0.00386410 | + | 0.999993i | \(0.501230\pi\) | |||||||
\(410\) | −5.54398 | −0.273798 | ||||||||
\(411\) | 0.964481 | 0.0475743 | ||||||||
\(412\) | −16.4581 | −0.810831 | ||||||||
\(413\) | −8.10930 | −0.399033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.37389 | 0.0674416 | ||||||||
\(416\) | −2.99679 | −0.146930 | ||||||||
\(417\) | −0.223848 | −0.0109619 | ||||||||
\(418\) | −16.1922 | −0.791986 | ||||||||
\(419\) | −22.0543 | −1.07743 | −0.538713 | − | 0.842490i | \(-0.681089\pi\) | ||||
−0.538713 | + | 0.842490i | \(0.681089\pi\) | |||||||
\(420\) | 0.283774 | 0.0138468 | ||||||||
\(421\) | −30.1447 | −1.46916 | −0.734581 | − | 0.678521i | \(-0.762621\pi\) | ||||
−0.734581 | + | 0.678521i | \(0.762621\pi\) | |||||||
\(422\) | −1.50006 | −0.0730217 | ||||||||
\(423\) | −12.4542 | −0.605545 | ||||||||
\(424\) | 2.72827 | 0.132497 | ||||||||
\(425\) | 1.17205 | 0.0568529 | ||||||||
\(426\) | −0.555793 | −0.0269282 | ||||||||
\(427\) | −27.9696 | −1.35354 | ||||||||
\(428\) | 19.4802 | 0.941612 | ||||||||
\(429\) | 0.378078 | 0.0182538 | ||||||||
\(430\) | −10.3763 | −0.500388 | ||||||||
\(431\) | −2.39601 | −0.115412 | −0.0577058 | − | 0.998334i | \(-0.518379\pi\) | ||||
−0.0577058 | + | 0.998334i | \(0.518379\pi\) | |||||||
\(432\) | 0.339899 | 0.0163534 | ||||||||
\(433\) | −30.5472 | −1.46801 | −0.734003 | − | 0.679146i | \(-0.762350\pi\) | ||||
−0.734003 | + | 0.679146i | \(0.762350\pi\) | |||||||
\(434\) | 39.6013 | 1.90092 | ||||||||
\(435\) | 0.158111 | 0.00758082 | ||||||||
\(436\) | −2.83881 | −0.135954 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.0955089 | −0.00456359 | ||||||||
\(439\) | 5.72872 | 0.273417 | 0.136709 | − | 0.990611i | \(-0.456348\pi\) | ||||
0.136709 | + | 0.990611i | \(0.456348\pi\) | |||||||
\(440\) | −2.22584 | −0.106113 | ||||||||
\(441\) | −54.1399 | −2.57809 | ||||||||
\(442\) | −3.51240 | −0.167068 | ||||||||
\(443\) | 26.3379 | 1.25135 | 0.625677 | − | 0.780082i | \(-0.284823\pi\) | ||||
0.625677 | + | 0.780082i | \(0.284823\pi\) | |||||||
\(444\) | −0.0282824 | −0.00134223 | ||||||||
\(445\) | 16.2240 | 0.769092 | ||||||||
\(446\) | −8.90770 | −0.421792 | ||||||||
\(447\) | −1.05991 | −0.0501320 | ||||||||
\(448\) | 5.00659 | 0.236539 | ||||||||
\(449\) | 10.8553 | 0.512293 | 0.256147 | − | 0.966638i | \(-0.417547\pi\) | ||||
0.256147 | + | 0.966638i | \(0.417547\pi\) | |||||||
\(450\) | −2.99679 | −0.141270 | ||||||||
\(451\) | 12.3400 | 0.581069 | ||||||||
\(452\) | −8.88945 | −0.418125 | ||||||||
\(453\) | −1.04103 | −0.0489121 | ||||||||
\(454\) | −4.29484 | −0.201567 | ||||||||
\(455\) | 15.0037 | 0.703385 | ||||||||
\(456\) | 0.412328 | 0.0193090 | ||||||||
\(457\) | −1.74876 | −0.0818035 | −0.0409018 | − | 0.999163i | \(-0.513023\pi\) | ||||
−0.0409018 | + | 0.999163i | \(0.513023\pi\) | |||||||
\(458\) | −17.8967 | −0.836259 | ||||||||
\(459\) | 0.398379 | 0.0185948 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.58259 | −0.399731 | −0.199865 | − | 0.979823i | \(-0.564051\pi\) | ||||
−0.199865 | + | 0.979823i | \(0.564051\pi\) | |||||||
\(462\) | −0.631636 | −0.0293864 | ||||||||
\(463\) | 2.90364 | 0.134944 | 0.0674718 | − | 0.997721i | \(-0.478507\pi\) | ||||
0.0674718 | + | 0.997721i | \(0.478507\pi\) | |||||||
\(464\) | 2.78953 | 0.129500 | ||||||||
\(465\) | 0.448330 | 0.0207908 | ||||||||
\(466\) | 27.2662 | 1.26308 | ||||||||
\(467\) | 20.5715 | 0.951935 | 0.475967 | − | 0.879463i | \(-0.342098\pi\) | ||||
0.475967 | + | 0.879463i | \(0.342098\pi\) | |||||||
\(468\) | 8.98075 | 0.415135 | ||||||||
\(469\) | 31.4119 | 1.45047 | ||||||||
\(470\) | −4.15586 | −0.191695 | ||||||||
\(471\) | 0.708184 | 0.0326314 | ||||||||
\(472\) | −1.61972 | −0.0745539 | ||||||||
\(473\) | 23.0959 | 1.06195 | ||||||||
\(474\) | −0.627005 | −0.0287993 | ||||||||
\(475\) | −7.27464 | −0.333783 | ||||||||
\(476\) | 5.86799 | 0.268959 | ||||||||
\(477\) | −8.17606 | −0.374356 | ||||||||
\(478\) | −13.8416 | −0.633102 | ||||||||
\(479\) | 3.72487 | 0.170194 | 0.0850969 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850969 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(480\) | 0.0566801 | 0.00258708 | ||||||||
\(481\) | −1.49535 | −0.0681821 | ||||||||
\(482\) | 15.1156 | 0.688496 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.04563 | −0.274801 | ||||||||
\(485\) | 4.93548 | 0.224109 | ||||||||
\(486\) | −1.52818 | −0.0693196 | ||||||||
\(487\) | 24.8257 | 1.12496 | 0.562481 | − | 0.826810i | \(-0.309847\pi\) | ||||
0.562481 | + | 0.826810i | \(0.309847\pi\) | |||||||
\(488\) | −5.58655 | −0.252891 | ||||||||
\(489\) | −0.191133 | −0.00864335 | ||||||||
\(490\) | −18.0660 | −0.816137 | ||||||||
\(491\) | −34.9034 | −1.57517 | −0.787585 | − | 0.616206i | \(-0.788669\pi\) | ||||
−0.787585 | + | 0.616206i | \(0.788669\pi\) | |||||||
\(492\) | −0.314233 | −0.0141667 | ||||||||
\(493\) | 3.26947 | 0.147250 | ||||||||
\(494\) | 21.8006 | 0.980855 | ||||||||
\(495\) | 6.67037 | 0.299811 | ||||||||
\(496\) | 7.90982 | 0.355162 | ||||||||
\(497\) | 49.0935 | 2.20215 | ||||||||
\(498\) | 0.0778723 | 0.00348954 | ||||||||
\(499\) | −13.3137 | −0.596002 | −0.298001 | − | 0.954566i | \(-0.596320\pi\) | ||||
−0.298001 | + | 0.954566i | \(0.596320\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −1.12916 | −0.0504473 | ||||||||
\(502\) | 19.6466 | 0.876870 | ||||||||
\(503\) | −7.23280 | −0.322495 | −0.161247 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161247 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(504\) | −15.0037 | −0.668318 | ||||||||
\(505\) | 2.55146 | 0.113538 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.227811 | 0.0101174 | ||||||||
\(508\) | 3.43426 | 0.152371 | ||||||||
\(509\) | −1.67195 | −0.0741080 | −0.0370540 | − | 0.999313i | \(-0.511797\pi\) | ||||
−0.0370540 | + | 0.999313i | \(0.511797\pi\) | |||||||
\(510\) | 0.0664321 | 0.00294166 | ||||||||
\(511\) | 8.43637 | 0.373203 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.47264 | −0.109170 | ||||||||
\(514\) | 1.35642 | 0.0598290 | ||||||||
\(515\) | 16.4581 | 0.725229 | ||||||||
\(516\) | −0.588128 | −0.0258909 | ||||||||
\(517\) | 9.25028 | 0.406827 | ||||||||
\(518\) | 2.49821 | 0.109765 | ||||||||
\(519\) | 0.967962 | 0.0424888 | ||||||||
\(520\) | 2.99679 | 0.131418 | ||||||||
\(521\) | −11.4822 | −0.503043 | −0.251522 | − | 0.967852i | \(-0.580931\pi\) | ||||
−0.251522 | + | 0.967852i | \(0.580931\pi\) | |||||||
\(522\) | −8.35961 | −0.365890 | ||||||||
\(523\) | 5.27033 | 0.230455 | 0.115228 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115228 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(524\) | 19.1282 | 0.835618 | ||||||||
\(525\) | −0.283774 | −0.0123849 | ||||||||
\(526\) | 9.35101 | 0.407723 | ||||||||
\(527\) | 9.27074 | 0.403840 | ||||||||
\(528\) | −0.126161 | −0.00549045 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −2.72827 | −0.118509 | ||||||||
\(531\) | 4.85397 | 0.210644 | ||||||||
\(532\) | −36.4212 | −1.57906 | ||||||||
\(533\) | −16.6141 | −0.719639 | ||||||||
\(534\) | 0.919579 | 0.0397941 | ||||||||
\(535\) | −19.4802 | −0.842204 | ||||||||
\(536\) | 6.27410 | 0.271000 | ||||||||
\(537\) | 0.739345 | 0.0319051 | ||||||||
\(538\) | 19.9733 | 0.861110 | ||||||||
\(539\) | 40.2120 | 1.73205 | ||||||||
\(540\) | −0.339899 | −0.0146269 | ||||||||
\(541\) | 9.53162 | 0.409796 | 0.204898 | − | 0.978783i | \(-0.434314\pi\) | ||||
0.204898 | + | 0.978783i | \(0.434314\pi\) | |||||||
\(542\) | 22.3390 | 0.959542 | ||||||||
\(543\) | 0.346206 | 0.0148571 | ||||||||
\(544\) | 1.17205 | 0.0502514 | ||||||||
\(545\) | 2.83881 | 0.121601 | ||||||||
\(546\) | 0.850412 | 0.0363943 | ||||||||
\(547\) | −31.5192 | −1.34766 | −0.673832 | − | 0.738884i | \(-0.735353\pi\) | ||||
−0.673832 | + | 0.738884i | \(0.735353\pi\) | |||||||
\(548\) | −17.0162 | −0.726897 | ||||||||
\(549\) | 16.7417 | 0.714519 | ||||||||
\(550\) | 2.22584 | 0.0949102 | ||||||||
\(551\) | −20.2928 | −0.864502 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.3838 | 2.35516 | ||||||||
\(554\) | −18.2078 | −0.773575 | ||||||||
\(555\) | 0.0282824 | 0.00120052 | ||||||||
\(556\) | 3.94931 | 0.167488 | ||||||||
\(557\) | −7.13889 | −0.302485 | −0.151242 | − | 0.988497i | \(-0.548327\pi\) | ||||
−0.151242 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(558\) | −23.7041 | −1.00347 | ||||||||
\(559\) | −31.0955 | −1.31520 | ||||||||
\(560\) | −5.00659 | −0.211567 | ||||||||
\(561\) | −0.147867 | −0.00624296 | ||||||||
\(562\) | 10.7438 | 0.453198 | ||||||||
\(563\) | 44.8946 | 1.89208 | 0.946040 | − | 0.324049i | \(-0.105044\pi\) | ||||
0.946040 | + | 0.324049i | \(0.105044\pi\) | |||||||
\(564\) | −0.235554 | −0.00991863 | ||||||||
\(565\) | 8.88945 | 0.373982 | ||||||||
\(566\) | −10.7171 | −0.450474 | ||||||||
\(567\) | 44.9146 | 1.88624 | ||||||||
\(568\) | 9.80578 | 0.411441 | ||||||||
\(569\) | −19.4266 | −0.814405 | −0.407203 | − | 0.913338i | \(-0.633496\pi\) | ||||
−0.407203 | + | 0.913338i | \(0.633496\pi\) | |||||||
\(570\) | −0.412328 | −0.0172705 | ||||||||
\(571\) | 31.8075 | 1.33110 | 0.665551 | − | 0.746353i | \(-0.268197\pi\) | ||||
0.665551 | + | 0.746353i | \(0.268197\pi\) | |||||||
\(572\) | −6.67038 | −0.278903 | ||||||||
\(573\) | 0.145387 | 0.00607363 | ||||||||
\(574\) | 27.7564 | 1.15853 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.99679 | −0.124866 | ||||||||
\(577\) | −18.4918 | −0.769822 | −0.384911 | − | 0.922954i | \(-0.625768\pi\) | ||||
−0.384911 | + | 0.922954i | \(0.625768\pi\) | |||||||
\(578\) | −15.6263 | −0.649968 | ||||||||
\(579\) | −0.632017 | −0.0262657 | ||||||||
\(580\) | −2.78953 | −0.115829 | ||||||||
\(581\) | −6.87851 | −0.285369 | ||||||||
\(582\) | 0.279744 | 0.0115957 | ||||||||
\(583\) | 6.07271 | 0.251506 | ||||||||
\(584\) | 1.68505 | 0.0697279 | ||||||||
\(585\) | −8.98075 | −0.371308 | ||||||||
\(586\) | −17.1056 | −0.706626 | ||||||||
\(587\) | 34.7498 | 1.43428 | 0.717138 | − | 0.696931i | \(-0.245452\pi\) | ||||
0.717138 | + | 0.696931i | \(0.245452\pi\) | |||||||
\(588\) | −1.02398 | −0.0422283 | ||||||||
\(589\) | −57.5411 | −2.37094 | ||||||||
\(590\) | 1.61972 | 0.0666830 | ||||||||
\(591\) | 0.431846 | 0.0177638 | ||||||||
\(592\) | 0.498984 | 0.0205081 | ||||||||
\(593\) | 36.9329 | 1.51665 | 0.758326 | − | 0.651875i | \(-0.226017\pi\) | ||||
0.758326 | + | 0.651875i | \(0.226017\pi\) | |||||||
\(594\) | 0.756560 | 0.0310420 | ||||||||
\(595\) | −5.86799 | −0.240564 | ||||||||
\(596\) | 18.6998 | 0.765975 | ||||||||
\(597\) | −0.899960 | −0.0368329 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.4422 | −0.508376 | −0.254188 | − | 0.967155i | \(-0.581808\pi\) | ||||
−0.254188 | + | 0.967155i | \(0.581808\pi\) | |||||||
\(600\) | −0.0566801 | −0.00231396 | ||||||||
\(601\) | 35.8127 | 1.46083 | 0.730416 | − | 0.683003i | \(-0.239326\pi\) | ||||
0.730416 | + | 0.683003i | \(0.239326\pi\) | |||||||
\(602\) | 51.9497 | 2.11731 | ||||||||
\(603\) | −18.8022 | −0.765683 | ||||||||
\(604\) | 18.3668 | 0.747336 | ||||||||
\(605\) | 6.04563 | 0.245790 | ||||||||
\(606\) | 0.144617 | 0.00587466 | ||||||||
\(607\) | −23.6933 | −0.961683 | −0.480841 | − | 0.876808i | \(-0.659669\pi\) | ||||
−0.480841 | + | 0.876808i | \(0.659669\pi\) | |||||||
\(608\) | −7.27464 | −0.295026 | ||||||||
\(609\) | −0.791595 | −0.0320771 | ||||||||
\(610\) | 5.58655 | 0.226193 | ||||||||
\(611\) | −12.4542 | −0.503844 | ||||||||
\(612\) | −3.51239 | −0.141980 | ||||||||
\(613\) | 10.8013 | 0.436261 | 0.218131 | − | 0.975920i | \(-0.430004\pi\) | ||||
0.218131 | + | 0.975920i | \(0.430004\pi\) | |||||||
\(614\) | 5.94744 | 0.240019 | ||||||||
\(615\) | 0.314233 | 0.0126711 | ||||||||
\(616\) | 11.1439 | 0.449000 | ||||||||
\(617\) | 31.3128 | 1.26060 | 0.630302 | − | 0.776350i | \(-0.282931\pi\) | ||||
0.630302 | + | 0.776350i | \(0.282931\pi\) | |||||||
\(618\) | 0.932845 | 0.0375245 | ||||||||
\(619\) | −20.9694 | −0.842830 | −0.421415 | − | 0.906868i | \(-0.638466\pi\) | ||||
−0.421415 | + | 0.906868i | \(0.638466\pi\) | |||||||
\(620\) | −7.90982 | −0.317666 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.0565 | −0.804193 | ||||||||
\(623\) | −81.2270 | −3.25429 | ||||||||
\(624\) | 0.169858 | 0.00679978 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 20.8169 | 0.832010 | ||||||||
\(627\) | 0.917776 | 0.0366524 | ||||||||
\(628\) | −12.4944 | −0.498581 | ||||||||
\(629\) | 0.584835 | 0.0233189 | ||||||||
\(630\) | 15.0037 | 0.597761 | ||||||||
\(631\) | −42.5823 | −1.69518 | −0.847588 | − | 0.530655i | \(-0.821946\pi\) | ||||
−0.847588 | + | 0.530655i | \(0.821946\pi\) | |||||||
\(632\) | 11.0622 | 0.440030 | ||||||||
\(633\) | 0.0850235 | 0.00337938 | ||||||||
\(634\) | −13.5804 | −0.539346 | ||||||||
\(635\) | −3.43426 | −0.136284 | ||||||||
\(636\) | −0.154639 | −0.00613183 | ||||||||
\(637\) | −54.1399 | −2.14510 | ||||||||
\(638\) | 6.20904 | 0.245818 | ||||||||
\(639\) | −29.3858 | −1.16249 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 2.40551 | 0.0950120 | 0.0475060 | − | 0.998871i | \(-0.484873\pi\) | ||||
0.0475060 | + | 0.998871i | \(0.484873\pi\) | |||||||
\(642\) | −1.10414 | −0.0435770 | ||||||||
\(643\) | −38.7743 | −1.52911 | −0.764555 | − | 0.644558i | \(-0.777041\pi\) | ||||
−0.764555 | + | 0.644558i | \(0.777041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.588128 | 0.0231575 | ||||||||
\(646\) | −8.52627 | −0.335462 | ||||||||
\(647\) | −0.0464447 | −0.00182593 | −0.000912964 | − | 1.00000i | \(-0.500291\pi\) | ||||
−0.000912964 | 1.00000i | \(0.500291\pi\) | ||||||||
\(648\) | 8.97110 | 0.352418 | ||||||||
\(649\) | −3.60525 | −0.141518 | ||||||||
\(650\) | −2.99679 | −0.117544 | ||||||||
\(651\) | −2.24460 | −0.0879730 | ||||||||
\(652\) | 3.37214 | 0.132063 | ||||||||
\(653\) | 5.95455 | 0.233020 | 0.116510 | − | 0.993190i | \(-0.462829\pi\) | ||||
0.116510 | + | 0.993190i | \(0.462829\pi\) | |||||||
\(654\) | 0.160904 | 0.00629185 | ||||||||
\(655\) | −19.1282 | −0.747400 | ||||||||
\(656\) | 5.54398 | 0.216456 | ||||||||
\(657\) | −5.04974 | −0.197009 | ||||||||
\(658\) | 20.8067 | 0.811129 | ||||||||
\(659\) | 29.7390 | 1.15847 | 0.579234 | − | 0.815161i | \(-0.303352\pi\) | ||||
0.579234 | + | 0.815161i | \(0.303352\pi\) | |||||||
\(660\) | 0.126161 | 0.00491081 | ||||||||
\(661\) | −48.1510 | −1.87286 | −0.936428 | − | 0.350860i | \(-0.885889\pi\) | ||||
−0.936428 | + | 0.350860i | \(0.885889\pi\) | |||||||
\(662\) | −18.1061 | −0.703713 | ||||||||
\(663\) | 0.199083 | 0.00773175 | ||||||||
\(664\) | −1.37389 | −0.0533173 | ||||||||
\(665\) | 36.4212 | 1.41235 | ||||||||
\(666\) | −1.49535 | −0.0579435 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 19.9217 | 0.770793 | ||||||||
\(669\) | 0.504890 | 0.0195202 | ||||||||
\(670\) | −6.27410 | −0.242390 | ||||||||
\(671\) | −12.4348 | −0.480039 | ||||||||
\(672\) | −0.283774 | −0.0109468 | ||||||||
\(673\) | −24.3926 | −0.940266 | −0.470133 | − | 0.882596i | \(-0.655794\pi\) | ||||
−0.470133 | + | 0.882596i | \(0.655794\pi\) | |||||||
\(674\) | −19.2644 | −0.742036 | ||||||||
\(675\) | 0.339899 | 0.0130827 | ||||||||
\(676\) | −4.01924 | −0.154586 | ||||||||
\(677\) | −15.1521 | −0.582344 | −0.291172 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291172 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(678\) | 0.503855 | 0.0193504 | ||||||||
\(679\) | −24.7099 | −0.948280 | ||||||||
\(680\) | −1.17205 | −0.0449462 | ||||||||
\(681\) | 0.243432 | 0.00932834 | ||||||||
\(682\) | 17.6060 | 0.674169 | ||||||||
\(683\) | −27.8748 | −1.06660 | −0.533300 | − | 0.845926i | \(-0.679048\pi\) | ||||
−0.533300 | + | 0.845926i | \(0.679048\pi\) | |||||||
\(684\) | 21.8006 | 0.833565 | ||||||||
\(685\) | 17.0162 | 0.650156 | ||||||||
\(686\) | 55.4028 | 2.11529 | ||||||||
\(687\) | 1.01439 | 0.0387013 | ||||||||
\(688\) | 10.3763 | 0.395591 | ||||||||
\(689\) | −8.17607 | −0.311483 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.9305 | −0.910361 | −0.455180 | − | 0.890399i | \(-0.650425\pi\) | ||||
−0.455180 | + | 0.890399i | \(0.650425\pi\) | |||||||
\(692\) | −17.0776 | −0.649194 | ||||||||
\(693\) | −33.3958 | −1.26860 | ||||||||
\(694\) | −3.92813 | −0.149110 | ||||||||
\(695\) | −3.94931 | −0.149806 | ||||||||
\(696\) | −0.158111 | −0.00599317 | ||||||||
\(697\) | 6.49784 | 0.246123 | ||||||||
\(698\) | 13.6354 | 0.516106 | ||||||||
\(699\) | −1.54545 | −0.0584544 | ||||||||
\(700\) | 5.00659 | 0.189231 | ||||||||
\(701\) | −8.03004 | −0.303291 | −0.151645 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151645 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(702\) | −1.01861 | −0.0384448 | ||||||||
\(703\) | −3.62993 | −0.136905 | ||||||||
\(704\) | 2.22584 | 0.0838896 | ||||||||
\(705\) | 0.235554 | 0.00887150 | ||||||||
\(706\) | 0.968813 | 0.0364617 | ||||||||
\(707\) | −12.7741 | −0.480420 | ||||||||
\(708\) | 0.0918062 | 0.00345029 | ||||||||
\(709\) | −42.3583 | −1.59080 | −0.795400 | − | 0.606085i | \(-0.792739\pi\) | ||||
−0.795400 | + | 0.606085i | \(0.792739\pi\) | |||||||
\(710\) | −9.80578 | −0.368004 | ||||||||
\(711\) | −33.1510 | −1.24326 | ||||||||
\(712\) | −16.2240 | −0.608020 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.332599 | −0.0124472 | ||||||||
\(715\) | 6.67038 | 0.249458 | ||||||||
\(716\) | −13.0442 | −0.487483 | ||||||||
\(717\) | 0.784546 | 0.0292994 | ||||||||
\(718\) | 14.2017 | 0.530002 | ||||||||
\(719\) | −11.2710 | −0.420336 | −0.210168 | − | 0.977665i | \(-0.567401\pi\) | ||||
−0.210168 | + | 0.977665i | \(0.567401\pi\) | |||||||
\(720\) | 2.99679 | 0.111684 | ||||||||
\(721\) | −82.3988 | −3.06869 | ||||||||
\(722\) | 33.9204 | 1.26239 | ||||||||
\(723\) | −0.856753 | −0.0318630 | ||||||||
\(724\) | −6.10807 | −0.227005 | ||||||||
\(725\) | 2.78953 | 0.103600 | ||||||||
\(726\) | 0.342667 | 0.0127176 | ||||||||
\(727\) | −8.89695 | −0.329970 | −0.164985 | − | 0.986296i | \(-0.552758\pi\) | ||||
−0.164985 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(728\) | −15.0037 | −0.556075 | ||||||||
\(729\) | −26.8267 | −0.993580 | ||||||||
\(730\) | −1.68505 | −0.0623665 | ||||||||
\(731\) | 12.1615 | 0.449810 | ||||||||
\(732\) | 0.316646 | 0.0117036 | ||||||||
\(733\) | −30.8068 | −1.13787 | −0.568937 | − | 0.822381i | \(-0.692645\pi\) | ||||
−0.568937 | + | 0.822381i | \(0.692645\pi\) | |||||||
\(734\) | 12.9049 | 0.476330 | ||||||||
\(735\) | 1.02398 | 0.0377701 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.9652 | 0.514413 | ||||||||
\(738\) | −16.6141 | −0.611575 | ||||||||
\(739\) | 0.588418 | 0.0216453 | 0.0108227 | − | 0.999941i | \(-0.496555\pi\) | ||||
0.0108227 | + | 0.999941i | \(0.496555\pi\) | |||||||
\(740\) | −0.498984 | −0.0183430 | ||||||||
\(741\) | −1.23566 | −0.0453931 | ||||||||
\(742\) | 13.6594 | 0.501451 | ||||||||
\(743\) | −7.13026 | −0.261584 | −0.130792 | − | 0.991410i | \(-0.541752\pi\) | ||||
−0.130792 | + | 0.991410i | \(0.541752\pi\) | |||||||
\(744\) | −0.448330 | −0.0164366 | ||||||||
\(745\) | −18.6998 | −0.685109 | ||||||||
\(746\) | −30.5092 | −1.11702 | ||||||||
\(747\) | 4.11726 | 0.150643 | ||||||||
\(748\) | 2.60880 | 0.0953873 | ||||||||
\(749\) | 97.5296 | 3.56365 | ||||||||
\(750\) | 0.0566801 | 0.00206967 | ||||||||
\(751\) | −5.32474 | −0.194303 | −0.0971513 | − | 0.995270i | \(-0.530973\pi\) | ||||
−0.0971513 | + | 0.995270i | \(0.530973\pi\) | |||||||
\(752\) | 4.15586 | 0.151549 | ||||||||
\(753\) | −1.11357 | −0.0405808 | ||||||||
\(754\) | −8.35962 | −0.304440 | ||||||||
\(755\) | −18.3668 | −0.668437 | ||||||||
\(756\) | 1.70173 | 0.0618915 | ||||||||
\(757\) | −37.1495 | −1.35022 | −0.675111 | − | 0.737716i | \(-0.735904\pi\) | ||||
−0.675111 | + | 0.737716i | \(0.735904\pi\) | |||||||
\(758\) | −6.87704 | −0.249785 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.27464 | 0.263879 | ||||||||
\(761\) | 25.8794 | 0.938128 | 0.469064 | − | 0.883164i | \(-0.344591\pi\) | ||||
0.469064 | + | 0.883164i | \(0.344591\pi\) | |||||||
\(762\) | −0.194654 | −0.00705157 | ||||||||
\(763\) | −14.2128 | −0.514537 | ||||||||
\(764\) | −2.56505 | −0.0928001 | ||||||||
\(765\) | 3.51239 | 0.126991 | ||||||||
\(766\) | −14.0395 | −0.507266 | ||||||||
\(767\) | 4.85398 | 0.175267 | ||||||||
\(768\) | −0.0566801 | −0.00204527 | ||||||||
\(769\) | −39.2207 | −1.41434 | −0.707168 | − | 0.707045i | \(-0.750028\pi\) | ||||
−0.707168 | + | 0.707045i | \(0.750028\pi\) | |||||||
\(770\) | −11.1439 | −0.401598 | ||||||||
\(771\) | −0.0768819 | −0.00276883 | ||||||||
\(772\) | 11.1506 | 0.401318 | ||||||||
\(773\) | −31.1305 | −1.11969 | −0.559843 | − | 0.828598i | \(-0.689139\pi\) | ||||
−0.559843 | + | 0.828598i | \(0.689139\pi\) | |||||||
\(774\) | −31.0954 | −1.11770 | ||||||||
\(775\) | 7.90982 | 0.284129 | ||||||||
\(776\) | −4.93548 | −0.177173 | ||||||||
\(777\) | −0.141599 | −0.00507982 | ||||||||
\(778\) | 7.36683 | 0.264114 | ||||||||
\(779\) | −40.3305 | −1.44499 | ||||||||
\(780\) | −0.169858 | −0.00608191 | ||||||||
\(781\) | 21.8261 | 0.781000 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.948156 | 0.0338843 | ||||||||
\(784\) | 18.0660 | 0.645213 | ||||||||
\(785\) | 12.4944 | 0.445944 | ||||||||
\(786\) | −1.08419 | −0.0386717 | ||||||||
\(787\) | −10.4888 | −0.373886 | −0.186943 | − | 0.982371i | \(-0.559858\pi\) | ||||
−0.186943 | + | 0.982371i | \(0.559858\pi\) | |||||||
\(788\) | −7.61900 | −0.271416 | ||||||||
\(789\) | −0.530016 | −0.0188691 | ||||||||
\(790\) | −11.0622 | −0.393574 | ||||||||
\(791\) | −44.5059 | −1.58245 | ||||||||
\(792\) | −6.67037 | −0.237021 | ||||||||
\(793\) | 16.7417 | 0.594516 | ||||||||
\(794\) | −25.4128 | −0.901865 | ||||||||
\(795\) | 0.154639 | 0.00548448 | ||||||||
\(796\) | 15.8779 | 0.562777 | ||||||||
\(797\) | 24.9934 | 0.885311 | 0.442656 | − | 0.896692i | \(-0.354036\pi\) | ||||
0.442656 | + | 0.896692i | \(0.354036\pi\) | |||||||
\(798\) | 2.06436 | 0.0730774 | ||||||||
\(799\) | 4.87089 | 0.172320 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 48.6199 | 1.71790 | ||||||||
\(802\) | −15.3171 | −0.540865 | ||||||||
\(803\) | 3.75066 | 0.132358 | ||||||||
\(804\) | −0.355617 | −0.0125416 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.7041 | −0.834941 | ||||||||
\(807\) | −1.13209 | −0.0398514 | ||||||||
\(808\) | −2.55146 | −0.0897599 | ||||||||
\(809\) | 40.3779 | 1.41961 | 0.709805 | − | 0.704398i | \(-0.248783\pi\) | ||||
0.709805 | + | 0.704398i | \(0.248783\pi\) | |||||||
\(810\) | −8.97110 | −0.315212 | ||||||||
\(811\) | −4.58935 | −0.161154 | −0.0805770 | − | 0.996748i | \(-0.525676\pi\) | ||||
−0.0805770 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(812\) | 13.9660 | 0.490111 | ||||||||
\(813\) | −1.26618 | −0.0444068 | ||||||||
\(814\) | 1.11066 | 0.0389285 | ||||||||
\(815\) | −3.37214 | −0.118121 | ||||||||
\(816\) | −0.0664321 | −0.00232559 | ||||||||
\(817\) | −75.4836 | −2.64084 | ||||||||
\(818\) | −0.156293 | −0.00546467 | ||||||||
\(819\) | 44.9629 | 1.57113 | ||||||||
\(820\) | −5.54398 | −0.193604 | ||||||||
\(821\) | −11.6467 | −0.406471 | −0.203236 | − | 0.979130i | \(-0.565146\pi\) | ||||
−0.203236 | + | 0.979130i | \(0.565146\pi\) | |||||||
\(822\) | 0.964481 | 0.0336401 | ||||||||
\(823\) | 54.5971 | 1.90313 | 0.951567 | − | 0.307440i | \(-0.0994725\pi\) | ||||
0.951567 | + | 0.307440i | \(0.0994725\pi\) | |||||||
\(824\) | −16.4581 | −0.573344 | ||||||||
\(825\) | −0.126161 | −0.00439236 | ||||||||
\(826\) | −8.10930 | −0.282159 | ||||||||
\(827\) | 20.8693 | 0.725695 | 0.362848 | − | 0.931849i | \(-0.381805\pi\) | ||||
0.362848 | + | 0.931849i | \(0.381805\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1291 | 0.386529 | 0.193265 | − | 0.981147i | \(-0.438092\pi\) | ||||
0.193265 | + | 0.981147i | \(0.438092\pi\) | |||||||
\(830\) | 1.37389 | 0.0476884 | ||||||||
\(831\) | 1.03202 | 0.0358004 | ||||||||
\(832\) | −2.99679 | −0.103895 | ||||||||
\(833\) | 21.1743 | 0.733645 | ||||||||
\(834\) | −0.223848 | −0.00775121 | ||||||||
\(835\) | −19.9217 | −0.689418 | ||||||||
\(836\) | −16.1922 | −0.560019 | ||||||||
\(837\) | 2.68854 | 0.0929295 | ||||||||
\(838\) | −22.0543 | −0.761855 | ||||||||
\(839\) | −9.25317 | −0.319455 | −0.159727 | − | 0.987161i | \(-0.551062\pi\) | ||||
−0.159727 | + | 0.987161i | \(0.551062\pi\) | |||||||
\(840\) | 0.283774 | 0.00979114 | ||||||||
\(841\) | −21.2185 | −0.731674 | ||||||||
\(842\) | −30.1447 | −1.03886 | ||||||||
\(843\) | −0.608957 | −0.0209736 | ||||||||
\(844\) | −1.50006 | −0.0516341 | ||||||||
\(845\) | 4.01924 | 0.138266 | ||||||||
\(846\) | −12.4542 | −0.428185 | ||||||||
\(847\) | −30.2680 | −1.04002 | ||||||||
\(848\) | 2.72827 | 0.0936893 | ||||||||
\(849\) | 0.607448 | 0.0208475 | ||||||||
\(850\) | 1.17205 | 0.0402011 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.555793 | −0.0190411 | ||||||||
\(853\) | 17.8530 | 0.611276 | 0.305638 | − | 0.952148i | \(-0.401130\pi\) | ||||
0.305638 | + | 0.952148i | \(0.401130\pi\) | |||||||
\(854\) | −27.9696 | −0.957100 | ||||||||
\(855\) | −21.8006 | −0.745563 | ||||||||
\(856\) | 19.4802 | 0.665821 | ||||||||
\(857\) | −4.09253 | −0.139798 | −0.0698992 | − | 0.997554i | \(-0.522268\pi\) | ||||
−0.0698992 | + | 0.997554i | \(0.522268\pi\) | |||||||
\(858\) | 0.378078 | 0.0129074 | ||||||||
\(859\) | −46.0901 | −1.57257 | −0.786287 | − | 0.617862i | \(-0.787999\pi\) | ||||
−0.786287 | + | 0.617862i | \(0.787999\pi\) | |||||||
\(860\) | −10.3763 | −0.353827 | ||||||||
\(861\) | −1.57324 | −0.0536158 | ||||||||
\(862\) | −2.39601 | −0.0816084 | ||||||||
\(863\) | 48.8355 | 1.66238 | 0.831189 | − | 0.555990i | \(-0.187661\pi\) | ||||
0.831189 | + | 0.555990i | \(0.187661\pi\) | |||||||
\(864\) | 0.339899 | 0.0115636 | ||||||||
\(865\) | 17.0776 | 0.580657 | ||||||||
\(866\) | −30.5472 | −1.03804 | ||||||||
\(867\) | 0.885700 | 0.0300799 | ||||||||
\(868\) | 39.6013 | 1.34415 | ||||||||
\(869\) | 24.6226 | 0.835266 | ||||||||
\(870\) | 0.158111 | 0.00536045 | ||||||||
\(871\) | −18.8022 | −0.637088 | ||||||||
\(872\) | −2.83881 | −0.0961343 | ||||||||
\(873\) | 14.7906 | 0.500585 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.00659 | −0.169254 | ||||||||
\(876\) | −0.0955089 | −0.00322695 | ||||||||
\(877\) | 3.55596 | 0.120076 | 0.0600381 | − | 0.998196i | \(-0.480878\pi\) | ||||
0.0600381 | + | 0.998196i | \(0.480878\pi\) | |||||||
\(878\) | 5.72872 | 0.193335 | ||||||||
\(879\) | 0.969548 | 0.0327020 | ||||||||
\(880\) | −2.22584 | −0.0750331 | ||||||||
\(881\) | −3.70062 | −0.124677 | −0.0623386 | − | 0.998055i | \(-0.519856\pi\) | ||||
−0.0623386 | + | 0.998055i | \(0.519856\pi\) | |||||||
\(882\) | −54.1399 | −1.82298 | ||||||||
\(883\) | 48.9080 | 1.64588 | 0.822942 | − | 0.568125i | \(-0.192331\pi\) | ||||
0.822942 | + | 0.568125i | \(0.192331\pi\) | |||||||
\(884\) | −3.51240 | −0.118135 | ||||||||
\(885\) | −0.0918062 | −0.00308603 | ||||||||
\(886\) | 26.3379 | 0.884841 | ||||||||
\(887\) | 14.2490 | 0.478436 | 0.239218 | − | 0.970966i | \(-0.423109\pi\) | ||||
0.239218 | + | 0.970966i | \(0.423109\pi\) | |||||||
\(888\) | −0.0282824 | −0.000949097 0 | ||||||||
\(889\) | 17.1939 | 0.576666 | ||||||||
\(890\) | 16.2240 | 0.543830 | ||||||||
\(891\) | 19.9682 | 0.668961 | ||||||||
\(892\) | −8.90770 | −0.298252 | ||||||||
\(893\) | −30.2324 | −1.01169 | ||||||||
\(894\) | −1.05991 | −0.0354486 | ||||||||
\(895\) | 13.0442 | 0.436018 | ||||||||
\(896\) | 5.00659 | 0.167259 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8553 | 0.362246 | ||||||||
\(899\) | 22.0647 | 0.735897 | ||||||||
\(900\) | −2.99679 | −0.0998929 | ||||||||
\(901\) | 3.19768 | 0.106530 | ||||||||
\(902\) | 12.3400 | 0.410878 | ||||||||
\(903\) | −2.94451 | −0.0979873 | ||||||||
\(904\) | −8.88945 | −0.295659 | ||||||||
\(905\) | 6.10807 | 0.203039 | ||||||||
\(906\) | −1.04103 | −0.0345860 | ||||||||
\(907\) | 41.9716 | 1.39364 | 0.696822 | − | 0.717244i | \(-0.254597\pi\) | ||||
0.696822 | + | 0.717244i | \(0.254597\pi\) | |||||||
\(908\) | −4.29484 | −0.142529 | ||||||||
\(909\) | 7.64617 | 0.253608 | ||||||||
\(910\) | 15.0037 | 0.497368 | ||||||||
\(911\) | −44.2206 | −1.46509 | −0.732546 | − | 0.680717i | \(-0.761668\pi\) | ||||
−0.732546 | + | 0.680717i | \(0.761668\pi\) | |||||||
\(912\) | 0.412328 | 0.0136535 | ||||||||
\(913\) | −3.05806 | −0.101207 | ||||||||
\(914\) | −1.74876 | −0.0578438 | ||||||||
\(915\) | −0.316646 | −0.0104680 | ||||||||
\(916\) | −17.8967 | −0.591324 | ||||||||
\(917\) | 95.7670 | 3.16250 | ||||||||
\(918\) | 0.398379 | 0.0131485 | ||||||||
\(919\) | 1.40847 | 0.0464612 | 0.0232306 | − | 0.999730i | \(-0.492605\pi\) | ||||
0.0232306 | + | 0.999730i | \(0.492605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.337102 | −0.0111079 | ||||||||
\(922\) | −8.58259 | −0.282652 | ||||||||
\(923\) | −29.3859 | −0.967248 | ||||||||
\(924\) | −0.631636 | −0.0207793 | ||||||||
\(925\) | 0.498984 | 0.0164065 | ||||||||
\(926\) | 2.90364 | 0.0954196 | ||||||||
\(927\) | 49.3213 | 1.61993 | ||||||||
\(928\) | 2.78953 | 0.0915707 | ||||||||
\(929\) | −27.9060 | −0.915565 | −0.457783 | − | 0.889064i | \(-0.651356\pi\) | ||||
−0.457783 | + | 0.889064i | \(0.651356\pi\) | |||||||
\(930\) | 0.448330 | 0.0147013 | ||||||||
\(931\) | −131.423 | −4.30723 | ||||||||
\(932\) | 27.2662 | 0.893134 | ||||||||
\(933\) | 1.13681 | 0.0372173 | ||||||||
\(934\) | 20.5715 | 0.673119 | ||||||||
\(935\) | −2.60880 | −0.0853170 | ||||||||
\(936\) | 8.98075 | 0.293545 | ||||||||
\(937\) | 58.6731 | 1.91677 | 0.958384 | − | 0.285483i | \(-0.0921541\pi\) | ||||
0.958384 | + | 0.285483i | \(0.0921541\pi\) | |||||||
\(938\) | 31.4119 | 1.02563 | ||||||||
\(939\) | −1.17990 | −0.0385047 | ||||||||
\(940\) | −4.15586 | −0.135549 | ||||||||
\(941\) | 4.60998 | 0.150281 | 0.0751406 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751406 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(942\) | 0.708184 | 0.0230739 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.61972 | −0.0527176 | ||||||||
\(945\) | −1.70173 | −0.0553574 | ||||||||
\(946\) | 23.0959 | 0.750913 | ||||||||
\(947\) | −11.0202 | −0.358107 | −0.179054 | − | 0.983839i | \(-0.557304\pi\) | ||||
−0.179054 | + | 0.983839i | \(0.557304\pi\) | |||||||
\(948\) | −0.627005 | −0.0203642 | ||||||||
\(949\) | −5.04975 | −0.163922 | ||||||||
\(950\) | −7.27464 | −0.236021 | ||||||||
\(951\) | 0.769737 | 0.0249604 | ||||||||
\(952\) | 5.86799 | 0.190183 | ||||||||
\(953\) | −16.1839 | −0.524249 | −0.262124 | − | 0.965034i | \(-0.584423\pi\) | ||||
−0.262124 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(954\) | −8.17606 | −0.264710 | ||||||||
\(955\) | 2.56505 | 0.0830029 | ||||||||
\(956\) | −13.8416 | −0.447671 | ||||||||
\(957\) | −0.351929 | −0.0113763 | ||||||||
\(958\) | 3.72487 | 0.120345 | ||||||||
\(959\) | −85.1932 | −2.75103 | ||||||||
\(960\) | 0.0566801 | 0.00182934 | ||||||||
\(961\) | 31.5653 | 1.01824 | ||||||||
\(962\) | −1.49535 | −0.0482120 | ||||||||
\(963\) | −58.3781 | −1.88121 | ||||||||
\(964\) | 15.1156 | 0.486840 | ||||||||
\(965\) | −11.1506 | −0.358950 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.3630 | −1.52309 | −0.761546 | − | 0.648111i | \(-0.775559\pi\) | ||||
−0.761546 | + | 0.648111i | \(0.775559\pi\) | |||||||
\(968\) | −6.04563 | −0.194314 | ||||||||
\(969\) | 0.483270 | 0.0155249 | ||||||||
\(970\) | 4.93548 | 0.158469 | ||||||||
\(971\) | 26.7348 | 0.857960 | 0.428980 | − | 0.903314i | \(-0.358873\pi\) | ||||
0.428980 | + | 0.903314i | \(0.358873\pi\) | |||||||
\(972\) | −1.52818 | −0.0490164 | ||||||||
\(973\) | 19.7726 | 0.633881 | ||||||||
\(974\) | 24.8257 | 0.795468 | ||||||||
\(975\) | 0.169858 | 0.00543982 | ||||||||
\(976\) | −5.58655 | −0.178821 | ||||||||
\(977\) | 57.5025 | 1.83967 | 0.919835 | − | 0.392306i | \(-0.128323\pi\) | ||||
0.919835 | + | 0.392306i | \(0.128323\pi\) | |||||||
\(978\) | −0.191133 | −0.00611177 | ||||||||
\(979\) | −36.1121 | −1.15415 | ||||||||
\(980\) | −18.0660 | −0.577096 | ||||||||
\(981\) | 8.50731 | 0.271618 | ||||||||
\(982\) | −34.9034 | −1.11381 | ||||||||
\(983\) | 7.20561 | 0.229823 | 0.114912 | − | 0.993376i | \(-0.463342\pi\) | ||||
0.114912 | + | 0.993376i | \(0.463342\pi\) | |||||||
\(984\) | −0.314233 | −0.0100174 | ||||||||
\(985\) | 7.61900 | 0.242762 | ||||||||
\(986\) | 3.26947 | 0.104121 | ||||||||
\(987\) | −1.17933 | −0.0375383 | ||||||||
\(988\) | 21.8006 | 0.693569 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.67037 | 0.211998 | ||||||||
\(991\) | −18.9210 | −0.601046 | −0.300523 | − | 0.953775i | \(-0.597161\pi\) | ||||
−0.300523 | + | 0.953775i | \(0.597161\pi\) | |||||||
\(992\) | 7.90982 | 0.251137 | ||||||||
\(993\) | 1.02625 | 0.0325672 | ||||||||
\(994\) | 49.0935 | 1.55715 | ||||||||
\(995\) | −15.8779 | −0.503363 | ||||||||
\(996\) | 0.0778723 | 0.00246748 | ||||||||
\(997\) | 31.2523 | 0.989771 | 0.494885 | − | 0.868958i | \(-0.335210\pi\) | ||||
0.494885 | + | 0.868958i | \(0.335210\pi\) | |||||||
\(998\) | −13.3137 | −0.421437 | ||||||||
\(999\) | 0.169604 | 0.00536603 |
(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 | 5290.2.a.bk.1.8 | 15 | ||
23.9 | even | 11 | 230.2.g.d.81.2 | yes | 30 | ||
23.18 | even | 11 | 230.2.g.d.71.2 | ✓ | 30 | ||
23.22 | odd | 2 | 5290.2.a.bl.1.8 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.g.d.71.2 | ✓ | 30 | 23.18 | even | 11 | ||
230.2.g.d.81.2 | yes | 30 | 23.9 | even | 11 | ||
5290.2.a.bk.1.8 | 15 | 1.1 | even | 1 | trivial | ||
5290.2.a.bl.1.8 | 15 | 23.22 | odd | 2 |