Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.806301 | 0.465518 | 0.232759 | − | 0.972534i | \(-0.425225\pi\) | ||||
0.232759 | + | 0.972534i | \(0.425225\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.48458 | 0.663923 | 0.331961 | − | 0.943293i | \(-0.392290\pi\) | ||||
0.331961 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70067 | 1.02076 | 0.510378 | − | 0.859950i | \(-0.329505\pi\) | ||||
0.510378 | + | 0.859950i | \(0.329505\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.34988 | −0.783293 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.03911 | −1.51935 | −0.759674 | − | 0.650304i | \(-0.774641\pi\) | ||||
−0.759674 | + | 0.650304i | \(0.774641\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.37759 | 1.49148 | 0.745738 | − | 0.666239i | \(-0.232097\pi\) | ||||
0.745738 | + | 0.666239i | \(0.232097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19702 | 0.309068 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.13412 | 1.00267 | 0.501336 | − | 0.865253i | \(-0.332842\pi\) | ||||
0.501336 | + | 0.865253i | \(0.332842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17755 | 0.475181 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.14061 | 1.48892 | 0.744460 | − | 0.667667i | \(-0.232707\pi\) | ||||
0.744460 | + | 0.667667i | \(0.232707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79603 | −0.559207 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.31361 | −0.830155 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.01825 | 1.11756 | 0.558780 | − | 0.829316i | \(-0.311270\pi\) | ||||
0.558780 | + | 0.829316i | \(0.311270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.76160 | 1.03481 | 0.517407 | − | 0.855740i | \(-0.326897\pi\) | ||||
0.517407 | + | 0.855740i | \(0.326897\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.06304 | −0.707284 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00935 | 0.677703 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46239 | 0.569213 | 0.284607 | − | 0.958644i | \(-0.408137\pi\) | ||||
0.284607 | + | 0.958644i | \(0.408137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.33596 | 0.694309 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.81340 | 1.53260 | 0.766298 | − | 0.642486i | \(-0.222097\pi\) | ||||
0.766298 | + | 0.642486i | \(0.222097\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.87461 | −1.35337 | −0.676683 | − | 0.736275i | \(-0.736583\pi\) | ||||
−0.676683 | + | 0.736275i | \(0.736583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.48857 | −0.520046 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.7688 | −1.86253 | −0.931264 | − | 0.364345i | \(-0.881293\pi\) | ||||
−0.931264 | + | 0.364345i | \(0.881293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.293600 | 0.0419428 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.33335 | 0.466762 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.901754 | −0.123865 | −0.0619327 | − | 0.998080i | \(-0.519726\pi\) | ||||
−0.0619327 | + | 0.998080i | \(0.519726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.48094 | −1.00873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.806301 | −0.106797 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.24773 | −0.292630 | −0.146315 | − | 0.989238i | \(-0.546741\pi\) | ||||
−0.146315 | + | 0.989238i | \(0.546741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.43729 | −0.312063 | −0.156032 | − | 0.987752i | \(-0.549870\pi\) | ||||
−0.156032 | + | 0.987752i | \(0.549870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.34624 | −0.799551 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.98345 | 0.990225 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66268 | 0.203129 | 0.101565 | − | 0.994829i | \(-0.467615\pi\) | ||||
0.101565 | + | 0.994829i | \(0.467615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.75749 | 0.693120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0535198 | 0.00635163 | 0.00317581 | − | 0.999995i | \(-0.498989\pi\) | ||||
0.00317581 | + | 0.999995i | \(0.498989\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.80260 | 0.210978 | 0.105489 | − | 0.994420i | \(-0.466359\pi\) | ||||
0.105489 | + | 0.994420i | \(0.466359\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.25444 | −0.260321 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.6089 | −1.55088 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.57156 | 0.396840 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.75299 | 0.521709 | 0.260854 | − | 0.965378i | \(-0.415996\pi\) | ||||
0.260854 | + | 0.965378i | \(0.415996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.13742 | 0.665697 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.85252 | 0.520245 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.5468 | 1.75396 | 0.876979 | − | 0.480530i | \(-0.159556\pi\) | ||||
0.876979 | + | 0.480530i | \(0.159556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.5231 | 1.52243 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.64558 | 0.481725 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.48458 | −0.152314 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.23091 | 0.734188 | 0.367094 | − | 0.930184i | \(-0.380353\pi\) | ||||
0.367094 | + | 0.930184i | \(0.380353\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.8413 | 1.19009 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.8263 | −1.57478 | −0.787388 | − | 0.616458i | \(-0.788567\pi\) | ||||
−0.787388 | + | 0.616458i | \(0.788567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9089 | 1.07489 | 0.537445 | − | 0.843299i | \(-0.319390\pi\) | ||||
0.537445 | + | 0.843299i | \(0.319390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.23274 | 0.315483 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5069 | 1.59579 | 0.797893 | − | 0.602799i | \(-0.205948\pi\) | ||||
0.797893 | + | 0.602799i | \(0.205948\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.23324 | 0.692819 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.79173 | 0.264979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.09683 | −0.761686 | −0.380843 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6008 | 0.988528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.6367 | −1.16826 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1649 | 1.02348 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3926 | 1.30842 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.91256 | 0.713451 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5738 | −1.03519 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.52754 | 0.401754 | 0.200877 | − | 0.979616i | \(-0.435621\pi\) | ||||
0.200877 | + | 0.979616i | \(0.435621\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.15561 | −0.630016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2696 | −1.24674 | −0.623371 | − | 0.781926i | \(-0.714237\pi\) | ||||
−0.623371 | + | 0.781926i | \(0.714237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.70067 | −0.234177 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.40389 | −0.551159 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.202571 | 0.0173068 | 0.00865342 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865342 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.15719 | −0.267789 | −0.133895 | − | 0.990996i | \(-0.542748\pi\) | ||||
−0.133895 | + | 0.990996i | \(0.542748\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.2955 | −0.867041 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.0983 | −2.26607 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.93455 | 0.741974 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.236730 | 0.0195251 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3866 | 1.42437 | 0.712184 | − | 0.701993i | \(-0.247706\pi\) | ||||
0.712184 | + | 0.701993i | \(0.247706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.92205 | 0.319172 | 0.159586 | − | 0.987184i | \(-0.448984\pi\) | ||||
0.159586 | + | 0.987184i | \(0.448984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.71468 | −0.785386 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.55353 | 0.687036 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.83804 | 0.465926 | 0.232963 | − | 0.972486i | \(-0.425158\pi\) | ||||
0.232963 | + | 0.972486i | \(0.425158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.727086 | −0.0576617 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.2844 | 1.51982 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.771769 | −0.0604496 | −0.0302248 | − | 0.999543i | \(-0.509622\pi\) | ||||
−0.0302248 | + | 0.999543i | \(0.509622\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.03189 | −0.469582 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.6899 | 1.36888 | 0.684442 | − | 0.729067i | \(-0.260046\pi\) | ||||
0.684442 | + | 0.729067i | \(0.260046\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.9185 | 1.22450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34988 | 0.179700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3702 | 1.47269 | 0.736345 | − | 0.676606i | \(-0.236550\pi\) | ||||
0.736345 | + | 0.676606i | \(0.236550\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.55115 | −0.570813 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.81235 | −0.136225 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.802564 | 0.0599864 | 0.0299932 | − | 0.999550i | \(-0.490451\pi\) | ||||
0.0299932 | + | 0.999550i | \(0.490451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.95188 | −0.516729 | −0.258364 | − | 0.966048i | \(-0.583184\pi\) | ||||
−0.258364 | + | 0.966048i | \(0.583184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.96519 | −0.145271 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.14018 | 0.377914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.8323 | −1.52341 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.6496 | −0.847386 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9890 | 0.939854 | 0.469927 | − | 0.882705i | \(-0.344280\pi\) | ||||
0.469927 | + | 0.882705i | \(0.344280\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0398276 | 0.00286686 | 0.00143343 | − | 0.999999i | \(-0.499544\pi\) | ||||
0.00143343 | + | 0.999999i | \(0.499544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.43706 | 0.460968 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.26601 | 0.375188 | 0.187594 | − | 0.982247i | \(-0.439931\pi\) | ||||
0.187594 | + | 0.982247i | \(0.439931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5497 | −1.10229 | −0.551146 | − | 0.834409i | \(-0.685809\pi\) | ||||
−0.551146 | + | 0.834409i | \(0.685809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.34062 | 0.0945604 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.2533 | 1.14076 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.5687 | 1.01753 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.7796 | −1.16626 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.03911 | 0.348562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8583 | −1.22942 | −0.614709 | − | 0.788754i | \(-0.710727\pi\) | ||||
−0.614709 | + | 0.788754i | \(0.710727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0431531 | 0.00295680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.1750 | −0.898530 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5602 | 1.05629 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.45344 | 0.0982141 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.2316 | 1.49546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.86018 | −0.325462 | −0.162731 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162731 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.57034 | 0.438022 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9183 | 1.18928 | 0.594640 | − | 0.803992i | \(-0.297294\pi\) | ||||
0.594640 | + | 0.803992i | \(0.297294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.4287 | −1.15172 | −0.575860 | − | 0.817548i | \(-0.695333\pi\) | ||||
−0.575860 | + | 0.817548i | \(0.695333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9729 | −0.721965 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.49941 | 0.491303 | 0.245651 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245651 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.9563 | −1.23657 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.806301 | −0.0523749 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9505 | −1.41986 | −0.709931 | − | 0.704271i | \(-0.751274\pi\) | ||||
−0.709931 | + | 0.704271i | \(0.751274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.728320 | −0.0469152 | −0.0234576 | − | 0.999725i | \(-0.507467\pi\) | ||||
−0.0234576 | + | 0.999725i | \(0.507467\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.8206 | 1.01489 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.435871 | 0.0278468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.37759 | −0.342168 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.83234 | 0.242865 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.93064 | 0.437458 | 0.218729 | − | 0.975786i | \(-0.429809\pi\) | ||||
0.218729 | + | 0.975786i | \(0.429809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.9823 | −2.26219 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.94861 | 0.309894 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7320 | 1.16847 | 0.584236 | − | 0.811583i | \(-0.301394\pi\) | ||||
0.584236 | + | 0.811583i | \(0.301394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.35076 | 0.581028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.1421 | −0.875377 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.5991 | 1.39352 | 0.696762 | − | 0.717303i | \(-0.254624\pi\) | ||||
0.696762 | + | 0.717303i | \(0.254624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.33872 | −0.0822371 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.3417 | 0.816499 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2505 | −0.624986 | −0.312493 | − | 0.949920i | \(-0.601164\pi\) | ||||
−0.312493 | + | 0.949920i | \(0.601164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6351 | −1.25350 | −0.626748 | − | 0.779222i | \(-0.715614\pi\) | ||||
−0.626748 | + | 0.779222i | \(0.715614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.7100 | 0.708720 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.0895 | 0.849629 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9656 | 1.07945 | 0.539724 | − | 0.841842i | \(-0.318529\pi\) | ||||
0.539724 | + | 0.841842i | \(0.318529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.5391 | −0.810562 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.00345 | −0.477446 | −0.238723 | − | 0.971088i | \(-0.576729\pi\) | ||||
−0.238723 | + | 0.971088i | \(0.576729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3963 | 1.45021 | 0.725105 | − | 0.688638i | \(-0.241791\pi\) | ||||
0.725105 | + | 0.688638i | \(0.241791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.19702 | −0.0709051 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.5027 | 1.56441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0909650 | 0.00535088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.83029 | 0.341778 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.5340 | −1.78382 | −0.891908 | − | 0.452217i | \(-0.850633\pi\) | ||||
−0.891908 | + | 0.452217i | \(0.850633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.33693 | −0.194284 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.7368 | 1.26129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 38.3993 | 2.22069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.9674 | −1.38146 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.7608 | −0.733087 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.61835 | −0.207186 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.7976 | −1.58649 | −0.793247 | − | 0.608900i | \(-0.791611\pi\) | ||||
−0.793247 | + | 0.608900i | \(0.791611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.79589 | 0.500381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5560 | 0.711985 | 0.355992 | − | 0.934489i | \(-0.384143\pi\) | ||||
0.355992 | + | 0.934489i | \(0.384143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.63902 | −0.262213 | −0.131106 | − | 0.991368i | \(-0.541853\pi\) | ||||
−0.131106 | + | 0.991368i | \(0.541853\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.42148 | −0.530840 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6434 | −0.710123 | −0.355061 | − | 0.934843i | \(-0.615540\pi\) | ||||
−0.355061 | + | 0.934843i | \(0.615540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.3266 | −1.69796 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.3096 | 0.742867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.13412 | −0.230029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0359 | −0.834043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.83217 | 0.322520 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.4844 | −1.90119 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.893865 | 0.0491313 | 0.0245656 | − | 0.999698i | \(-0.492180\pi\) | ||||
0.0245656 | + | 0.999698i | \(0.492180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.13619 | −0.445861 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.46838 | 0.134862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.698634 | 0.0380570 | 0.0190285 | − | 0.999819i | \(-0.493943\pi\) | ||||
0.0190285 | + | 0.999819i | \(0.493943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.52848 | −0.354579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0333 | −1.57224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1118 | −0.977943 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.54743 | 0.460178 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.3726 | −1.20102 | −0.600511 | − | 0.799616i | \(-0.705036\pi\) | ||||
−0.600511 | + | 0.799616i | \(0.705036\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3093 | 0.873017 | 0.436509 | − | 0.899700i | \(-0.356215\pi\) | ||||
0.436509 | + | 0.899700i | \(0.356215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.1969 | −1.23816 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.6027 | 1.41592 | 0.707961 | − | 0.706252i | \(-0.249615\pi\) | ||||
0.707961 | + | 0.706252i | \(0.249615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0794542 | 0.00421699 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.00226 | 0.476450 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.05161 | 0.266614 | 0.133307 | − | 0.991075i | \(-0.457440\pi\) | ||||
0.133307 | + | 0.991075i | \(0.457440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.6048 | 0.609093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.67609 | 0.140073 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4420 | 0.910466 | 0.455233 | − | 0.890372i | \(-0.349556\pi\) | ||||
0.455233 | + | 0.890372i | \(0.349556\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.0603 | −1.20047 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.43534 | −0.126436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6958 | −0.709142 | −0.354571 | − | 0.935029i | \(-0.615373\pi\) | ||||
−0.354571 | + | 0.935029i | \(0.615373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.33198 | −0.481901 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.3637 | 1.66681 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.51884 | 0.386217 | 0.193108 | − | 0.981177i | \(-0.438143\pi\) | ||||
0.193108 | + | 0.981177i | \(0.438143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.65056 | 0.187024 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00434 | −0.306807 | −0.153404 | − | 0.988164i | \(-0.549023\pi\) | ||||
−0.153404 | + | 0.988164i | \(0.549023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.2035 | −1.02967 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.8543 | 1.06008 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.38695 | −0.425235 | −0.212618 | − | 0.977135i | \(-0.568199\pi\) | ||||
−0.212618 | + | 0.977135i | \(0.568199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.5202 | 1.49290 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5056 | −0.580381 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.48458 | −0.0746972 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.4410 | −0.524019 | −0.262009 | − | 0.965065i | \(-0.584385\pi\) | ||||
−0.262009 | + | 0.965065i | \(0.584385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.17755 | −0.109014 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3891 | 0.568746 | 0.284373 | − | 0.958714i | \(-0.408215\pi\) | ||||
0.284373 | + | 0.958714i | \(0.408215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.9835 | 1.54340 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.30226 | 0.263471 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4473 | −0.864833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6248 | −0.673704 | −0.336852 | − | 0.941558i | \(-0.609362\pi\) | ||||
−0.336852 | + | 0.941558i | \(0.609362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.163334 | 0.00805665 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.07038 | −0.298704 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.05618 | 0.346374 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.54564 | −0.124661 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.77773 | 0.282260 | 0.141130 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141130 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.9535 | −1.36237 | −0.681186 | − | 0.732110i | \(-0.738535\pi\) | ||||
−0.681186 | + | 0.732110i | \(0.738535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.0052 | 1.45890 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5591 | −0.560701 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.58231 | −0.318540 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.8494 | −1.05490 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7140 | −0.997759 | −0.498880 | − | 0.866671i | \(-0.666255\pi\) | ||||
−0.498880 | + | 0.866671i | \(0.666255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.33174 | 0.256227 | 0.128113 | − | 0.991760i | \(-0.459108\pi\) | ||||
0.128113 | + | 0.991760i | \(0.459108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.20394 | 0.345402 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.14061 | −0.341582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.4985 | 1.88516 | 0.942581 | − | 0.333978i | \(-0.108391\pi\) | ||||
0.942581 | + | 0.333978i | \(0.108391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.689923 | −0.0328535 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.29356 | 0.346527 | 0.173264 | − | 0.984875i | \(-0.444569\pi\) | ||||
0.173264 | + | 0.984875i | \(0.444569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.5650 | 1.16449 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0189 | 0.663069 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.19330 | 0.339473 | 0.169736 | − | 0.985489i | \(-0.445708\pi\) | ||||
0.169736 | + | 0.985489i | \(0.445708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −49.4508 | −2.32855 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.16236 | 0.148580 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.5606 | 1.01078 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.34387 | −0.437088 | −0.218544 | − | 0.975827i | \(-0.570131\pi\) | ||||
−0.218544 | + | 0.975827i | \(0.570131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.8330 | −0.832373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.4003 | 1.22958 | 0.614791 | − | 0.788690i | \(-0.289240\pi\) | ||||
0.614791 | + | 0.788690i | \(0.289240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8286 | −1.15389 | −0.576943 | − | 0.816785i | \(-0.695754\pi\) | ||||
−0.576943 | + | 0.816785i | \(0.695754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.89673 | 0.319828 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0703 | 1.11384 | 0.556921 | − | 0.830566i | \(-0.311983\pi\) | ||||
0.556921 | + | 0.830566i | \(0.311983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.49036 | 0.207345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.70722 | 0.216897 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.7201 | 2.05623 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.79603 | 0.128291 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.11901 | 0.0970229 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4110 | −0.567073 | −0.283536 | − | 0.958961i | \(-0.591508\pi\) | ||||
−0.283536 | + | 0.958961i | \(0.591508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6193 | 0.848968 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.5490 | 0.707506 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.7348 | 0.487444 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.9883 | 1.76673 | 0.883365 | − | 0.468686i | \(-0.155273\pi\) | ||||
0.883365 | + | 0.468686i | \(0.155273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.622278 | −0.0281404 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.97418 | −0.404999 | −0.202499 | − | 0.979282i | \(-0.564906\pi\) | ||||
−0.202499 | + | 0.979282i | \(0.564906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.8802 | 1.12055 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.5793 | 0.790131 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.144539 | 0.00648346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.3058 | −0.595651 | −0.297826 | − | 0.954620i | \(-0.596261\pi\) | ||||
−0.297826 | + | 0.954620i | \(0.596261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.2634 | 0.637241 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.0571 | −1.78606 | −0.893028 | − | 0.450001i | \(-0.851424\pi\) | ||||
−0.893028 | + | 0.450001i | \(0.851424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.4954 | −1.04553 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8351 | 0.570027 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9829 | −0.531134 | −0.265567 | − | 0.964092i | \(-0.585559\pi\) | ||||
−0.265567 | + | 0.964092i | \(0.585559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.86821 | 0.215357 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.31361 | 0.190451 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.1952 | 0.713644 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 64.3436 | 2.82983 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6182 | 0.685564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3214 | 0.583622 | 0.291811 | − | 0.956476i | \(-0.405742\pi\) | ||||
0.291811 | + | 0.956476i | \(0.405742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0507 | −0.833027 | −0.416513 | − | 0.909130i | \(-0.636748\pi\) | ||||
−0.416513 | + | 0.909130i | \(0.636748\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.08850 | −0.265724 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.8192 | 1.03758 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9884 | 1.21688 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.28190 | 0.229215 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.7725 | 2.28583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.5058 | 1.05948 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.647108 | 0.0279248 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.47948 | −0.0637257 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.78993 | 0.420902 | 0.210451 | − | 0.977604i | \(-0.432507\pi\) | ||||
0.210451 | + | 0.977604i | \(0.432507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.60531 | −0.240547 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.7383 | 0.459978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.2331 | −1.50646 | −0.753230 | − | 0.657757i | \(-0.771505\pi\) | ||||
−0.753230 | + | 0.657757i | \(0.771505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.72734 | 0.244437 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.01825 | −0.256386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.70067 | −0.114844 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.14453 | 0.175926 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.3016 | −1.49578 | −0.747889 | − | 0.663824i | \(-0.768933\pi\) | ||||
−0.747889 | + | 0.663824i | \(0.768933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.7241 | −2.01851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.7971 | −0.709174 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7994 | −0.876589 | −0.438294 | − | 0.898831i | \(-0.644417\pi\) | ||||
−0.438294 | + | 0.898831i | \(0.644417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0204 | −0.505701 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.64560 | 0.405077 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.4346 | −1.19204 | −0.596020 | − | 0.802970i | \(-0.703252\pi\) | ||||
−0.596020 | + | 0.802970i | \(0.703252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1303 | 0.758728 | 0.379364 | − | 0.925247i | \(-0.376143\pi\) | ||||
0.379364 | + | 0.925247i | \(0.376143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4731 | 0.437519 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.9654 | −0.832614 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.4651 | −1.10176 | −0.550879 | − | 0.834585i | \(-0.685707\pi\) | ||||
−0.550879 | + | 0.834585i | \(0.685707\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0321131 | 0.00133457 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8362 | 0.532537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.54404 | 0.188195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.7601 | −0.775636 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.8325 | 1.85043 | 0.925217 | − | 0.379439i | \(-0.123883\pi\) | ||||
0.925217 | + | 0.379439i | \(0.123883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.76160 | −0.237403 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.24599 | 0.174657 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.3793 | 1.32966 | 0.664829 | − | 0.746996i | \(-0.268505\pi\) | ||||
0.664829 | + | 0.746996i | \(0.268505\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.5751 | 0.679514 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.5378 | −0.513137 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.3023 | 0.666092 | 0.333046 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333046 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.18880 | 0.374819 | 0.187410 | − | 0.982282i | \(-0.439991\pi\) | ||||
0.187410 | + | 0.982282i | \(0.439991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.90711 | −0.159110 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3669 | 0.868689 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9964 | −0.852219 | −0.426110 | − | 0.904672i | \(-0.640116\pi\) | ||||
−0.426110 | + | 0.904672i | \(0.640116\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.1050 | 0.531043 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −68.6657 | −2.77792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.21357 | 0.129795 | 0.0648974 | − | 0.997892i | \(-0.479328\pi\) | ||||
0.0648974 | + | 0.997892i | \(0.479328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.7468 | 0.473677 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.6397 | −1.23351 | −0.616753 | − | 0.787157i | \(-0.711552\pi\) | ||||
−0.616753 | + | 0.787157i | \(0.711552\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.35627 | −0.0947064 | −0.0473532 | − | 0.998878i | \(-0.515079\pi\) | ||||
−0.0473532 | + | 0.998878i | \(0.515079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.8018 | −1.23604 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.6874 | 1.79036 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.20204 | −0.128082 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.06304 | 0.162262 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.3139 | 0.570734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.9916 | −0.955089 | −0.477545 | − | 0.878607i | \(-0.658473\pi\) | ||||
−0.477545 | + | 0.878607i | \(0.658473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.3992 | −0.572317 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.72148 | 0.266734 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.57886 | 0.0625567 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.125765 | −0.00497518 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.0351 | −0.909833 | −0.454916 | − | 0.890534i | \(-0.650331\pi\) | ||||
−0.454916 | + | 0.890534i | \(0.650331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.3109 | −1.03760 | −0.518801 | − | 0.854895i | \(-0.673622\pi\) | ||||
−0.518801 | + | 0.854895i | \(0.673622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.6231 | −0.418282 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.51126 | 0.216670 | 0.108335 | − | 0.994114i | \(-0.465448\pi\) | ||||
0.108335 | + | 0.994114i | \(0.465448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3266 | 0.444607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.5462 | 0.491723 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.82044 | −0.227772 | −0.113886 | − | 0.993494i | \(-0.536330\pi\) | ||||
−0.113886 | + | 0.993494i | \(0.536330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.1843 | −0.827741 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.23588 | −0.165258 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.0908 | 1.05531 | 0.527654 | − | 0.849460i | \(-0.323072\pi\) | ||||
0.527654 | + | 0.849460i | \(0.323072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9044 | 0.463029 | 0.231514 | − | 0.972831i | \(-0.425632\pi\) | ||||
0.231514 | + | 0.972831i | \(0.425632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.9254 | 0.696164 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00935 | −0.155476 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.9740 | 1.66396 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.91877 | −0.151508 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.2818 | 0.474133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.68644 | 0.142102 | 0.0710510 | − | 0.997473i | \(-0.477365\pi\) | ||||
0.0710510 | + | 0.997473i | \(0.477365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0610 | 0.464228 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.7172 | 1.75705 | 0.878527 | − | 0.477693i | \(-0.158527\pi\) | ||||
0.878527 | + | 0.477693i | \(0.158527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.5283 | 0.749427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4476 | 0.553632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.5355 | 1.09188 | 0.545939 | − | 0.837825i | \(-0.316173\pi\) | ||||
0.545939 | + | 0.837825i | \(0.316173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.300733 | 0.0114904 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0528 | −0.536147 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.84927 | −0.184742 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.2935 | −1.60892 | −0.804460 | − | 0.594007i | \(-0.797545\pi\) | ||||
−0.804460 | + | 0.594007i | \(0.797545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.9794 | 1.21480 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.68709 | −0.177791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.5698 | 1.53669 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.04678 | 0.228710 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.2244 | −1.44371 | −0.721857 | − | 0.692042i | \(-0.756711\pi\) | ||||
−0.721857 | + | 0.692042i | \(0.756711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.46239 | −0.130586 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.2845 | −0.575648 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.7416 | −1.60746 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.1321 | −1.09408 | −0.547039 | − | 0.837107i | \(-0.684245\pi\) | ||||
−0.547039 | + | 0.837107i | \(0.684245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34988 | 0.0881273 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.1413 | 1.54076 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.2295 | −1.50450 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.6987 | −0.660972 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.13411 | −0.266057 | −0.133029 | − | 0.991112i | \(-0.542470\pi\) | ||||
−0.133029 | + | 0.991112i | \(0.542470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.4614 | 1.09720 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.587246 | −0.0218399 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.8272 | −0.624947 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8284 | −1.36589 | −0.682945 | − | 0.730470i | \(-0.739301\pi\) | ||||
−0.682945 | + | 0.730470i | \(0.739301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.04148 | 0.0756104 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.6887 | −1.35698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.2173 | 1.70708 | 0.853538 | − | 0.521031i | \(-0.174452\pi\) | ||||
0.853538 | + | 0.521031i | \(0.174452\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.351443 | 0.0129632 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.37845 | −0.308624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.8933 | −1.68821 | −0.844106 | − | 0.536176i | \(-0.819868\pi\) | ||||
−0.844106 | + | 0.536176i | \(0.819868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.33596 | −0.159285 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5619 | 0.827715 | 0.413858 | − | 0.910342i | \(-0.364181\pi\) | ||||
0.413858 | + | 0.910342i | \(0.364181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.8118 | 0.945670 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1689 | −0.408650 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.5797 | 1.62891 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.1881 | 1.06509 | 0.532544 | − | 0.846402i | \(-0.321236\pi\) | ||||
0.532544 | + | 0.846402i | \(0.321236\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.58819 | 0.203645 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.82259 | 0.211906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1022 | 0.876010 | 0.438005 | − | 0.898973i | \(-0.355685\pi\) | ||||
0.438005 | + | 0.898973i | \(0.355685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.0126 | −1.05309 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6661 | −0.930395 | −0.465198 | − | 0.885207i | \(-0.654017\pi\) | ||||
−0.465198 | + | 0.885207i | \(0.654017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.5346 | 0.707199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.4222 | −0.521435 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0874 | −0.436450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.1872 | −1.08858 | −0.544288 | − | 0.838898i | \(-0.683200\pi\) | ||||
−0.544288 | + | 0.838898i | \(0.683200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.1037 | 0.543945 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.7509 | 1.68151 | 0.840756 | − | 0.541414i | \(-0.182111\pi\) | ||||
0.840756 | + | 0.541414i | \(0.182111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.1096 | −0.578675 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.53953 | 0.270479 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.81340 | −0.351602 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.269692 | −0.00965033 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.9604 | −0.927749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.66701 | 0.309339 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.7504 | −1.23872 | −0.619360 | − | 0.785107i | \(-0.712608\pi\) | ||||
−0.619360 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.2217 | 0.648710 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.8668 | −0.777495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1068 | −0.465435 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.07941 | −0.0382829 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.7235 | 0.521534 | 0.260767 | − | 0.965402i | \(-0.416025\pi\) | ||||
0.260767 | + | 0.965402i | \(0.416025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.7880 | −1.86750 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.8830 | −1.37386 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.08348 | −0.320549 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.6292 | 1.00905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.26502 | −0.290943 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.5316 | −1.28438 | −0.642191 | − | 0.766545i | \(-0.721974\pi\) | ||||
−0.642191 | + | 0.766545i | \(0.721974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.46592 | −0.156820 | −0.0784099 | − | 0.996921i | \(-0.524984\pi\) | ||||
−0.0784099 | + | 0.996921i | \(0.524984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.6381 | −0.583525 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.14575 | −0.0401339 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.87461 | 0.310483 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −34.1275 | −1.19251 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9756 | −0.941453 | −0.470727 | − | 0.882279i | \(-0.656008\pi\) | ||||
−0.470727 | + | 0.882279i | \(0.656008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.716195 | −0.0249650 | −0.0124825 | − | 0.999922i | \(-0.503973\pi\) | ||||
−0.0124825 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.3604 | 0.395518 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.21881 | −0.146703 | −0.0733513 | − | 0.997306i | \(-0.523369\pi\) | ||||
−0.0733513 | + | 0.997306i | \(0.523369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.3513 | −0.359517 | −0.179759 | − | 0.983711i | \(-0.557532\pi\) | ||||
−0.179759 | + | 0.983711i | \(0.557532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.4857 | 0.502503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.21378 | 0.0420549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2620 | 0.908834 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.8533 | −0.859056 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.1440 | −1.48950 | −0.744748 | − | 0.667345i | \(-0.767430\pi\) | ||||
−0.744748 | + | 0.667345i | \(0.767430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.21929 | 0.248941 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.45320 | −0.222260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.6322 | 0.812974 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.8696 | 1.33558 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.6708 | 0.675099 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.7236 | 0.847513 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.18391 | −0.0405362 | −0.0202681 | − | 0.999795i | \(-0.506452\pi\) | ||||
−0.0202681 | + | 0.999795i | \(0.506452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.48857 | 0.119307 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.08937 | 0.242168 | 0.121084 | − | 0.992642i | \(-0.461363\pi\) | ||||
0.121084 | + | 0.992642i | \(0.461363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.6682 | −1.52406 | −0.762030 | − | 0.647542i | \(-0.775797\pi\) | ||||
−0.762030 | + | 0.647542i | \(0.775797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.3692 | 0.728260 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.5011 | −1.48079 | −0.740397 | − | 0.672170i | \(-0.765362\pi\) | ||||
−0.740397 | + | 0.672170i | \(0.765362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.7566 | 0.977752 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.0733452 | 0.00249093 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.03911 | 0.170940 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.94124 | 0.302962 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.9918 | −0.575084 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.2570 | −1.05668 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9131 | 1.11140 | 0.555698 | − | 0.831384i | \(-0.312451\pi\) | ||||
0.555698 | + | 0.831384i | \(0.312451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.6196 | −0.830399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2390 | −0.749252 | −0.374626 | − | 0.927176i | \(-0.622229\pi\) | ||||
−0.374626 | + | 0.927176i | \(0.622229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0056 | −0.404022 | −0.202011 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202011 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.69057 | −0.0904426 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.3233 | −1.18604 | −0.593020 | − | 0.805188i | \(-0.702065\pi\) | ||||
−0.593020 | + | 0.805188i | \(0.702065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.2274 | 0.410093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.9975 | −0.602938 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7688 | 0.427293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.19147 | 0.0398264 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.9614 | 1.03377 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.6747 | 1.15647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.72796 | −0.124196 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.3249 | −0.643093 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.3206 | −0.343068 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.15934 | 0.0384954 | 0.0192477 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192477 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.1899 | 1.23351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5361 | −1.21050 | −0.605248 | − | 0.796037i | \(-0.706926\pi\) | ||||
−0.605248 | + | 0.796037i | \(0.706926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.9508 | −0.792657 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.91748 | −0.0964488 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.5375 | −1.27262 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6007 | −0.382672 | −0.191336 | − | 0.981525i | \(-0.561282\pi\) | ||||
−0.191336 | + | 0.981525i | \(0.561282\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.4133 | −0.738542 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.287808 | 0.00947330 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.68095 | −0.318308 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.6347 | −0.841953 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.6131 | 1.00438 | 0.502192 | − | 0.864756i | \(-0.332527\pi\) | ||||
0.502192 | + | 0.864756i | \(0.332527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.293600 | −0.00962234 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.1239 | 0.331442 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.9271 | −1.01142 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3848 | 0.829284 | 0.414642 | − | 0.909985i | \(-0.363907\pi\) | ||||
0.414642 | + | 0.909985i | \(0.363907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.74045 | −0.122065 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.1381 | −1.04767 | −0.523835 | − | 0.851820i | \(-0.675499\pi\) | ||||
−0.523835 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.0737 | 2.28191 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.2948 | −0.562599 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.3415 | 1.21344 | 0.606718 | − | 0.794917i | \(-0.292486\pi\) | ||||
0.606718 | + | 0.794917i | \(0.292486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.69364 | 0.314669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.1944 | −0.330575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4110 | −0.596389 | −0.298195 | − | 0.954505i | \(-0.596384\pi\) | ||||
−0.298195 | + | 0.954505i | \(0.596384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.2832 | 0.623990 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.4524 | −0.790433 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.547078 | 0.0176661 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.19602 | 0.0708395 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.7893 | −1.24997 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0591272 | 0.00190337 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.8004 | 1.24774 | 0.623868 | − | 0.781530i | \(-0.285560\pi\) | ||||
0.623868 | + | 0.781530i | \(0.285560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.33335 | −0.107083 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8198 | −0.603956 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.52651 | −0.273347 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.1235 | −0.388262 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.3647 | 1.35537 | 0.677683 | − | 0.735354i | \(-0.262984\pi\) | ||||
0.677683 | + | 0.735354i | \(0.262984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −83.3811 | −2.66487 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.9972 | −0.542680 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.2497 | 0.837235 | 0.418617 | − | 0.908163i | \(-0.362515\pi\) | ||||
0.418617 | + | 0.908163i | \(0.362515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.81779 | 0.249096 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.8048 | −0.885037 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63.3702 | −2.01505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.8280 | 1.55107 | 0.775536 | − | 0.631304i | \(-0.217480\pi\) | ||||
0.775536 | + | 0.631304i | \(0.217480\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.720724 | 0.0228715 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.0848 | −0.731837 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.5535 | 1.15766 | 0.578831 | − | 0.815448i | \(-0.303509\pi\) | ||||
0.578831 | + | 0.815448i | \(0.303509\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.9354 | −0.472535 |
(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 | 6004.2.a.h.1.20 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.h.1.20 | ✓ | 31 | 1.1 | even | 1 | trivial |