Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.461317 | −0.206307 | −0.103154 | − | 0.994665i | \(-0.532893\pi\) | ||||
−0.103154 | + | 0.994665i | \(0.532893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.07386 | −1.16181 | −0.580905 | − | 0.813971i | \(-0.697301\pi\) | ||||
−0.580905 | + | 0.813971i | \(0.697301\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.13061 | −1.54694 | −0.773469 | − | 0.633834i | \(-0.781480\pi\) | ||||
−0.773469 | + | 0.633834i | \(0.781480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.80493 | 1.88735 | 0.943673 | − | 0.330878i | \(-0.107345\pi\) | ||||
0.943673 | + | 0.330878i | \(0.107345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.461317 | 0.119112 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.28513 | 0.311690 | 0.155845 | − | 0.987781i | \(-0.450190\pi\) | ||||
0.155845 | + | 0.987781i | \(0.450190\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.12411 | 1.40497 | 0.702484 | − | 0.711700i | \(-0.252074\pi\) | ||||
0.702484 | + | 0.711700i | \(0.252074\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.07386 | 0.670771 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.36756 | −1.74476 | −0.872379 | − | 0.488831i | \(-0.837424\pi\) | ||||
−0.872379 | + | 0.488831i | \(0.837424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78719 | −0.957437 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.615911 | 0.114372 | 0.0571859 | − | 0.998364i | \(-0.481787\pi\) | ||||
0.0571859 | + | 0.998364i | \(0.481787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.68978 | −0.662704 | −0.331352 | − | 0.943507i | \(-0.607505\pi\) | ||||
−0.331352 | + | 0.943507i | \(0.607505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.13061 | 0.893125 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41803 | 0.239690 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6984 | 1.75881 | 0.879403 | − | 0.476078i | \(-0.157942\pi\) | ||||
0.879403 | + | 0.476078i | \(0.157942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.80493 | −1.08966 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.4321 | −1.62922 | −0.814612 | − | 0.580006i | \(-0.803050\pi\) | ||||
−0.814612 | + | 0.580006i | \(0.803050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.274161 | −0.0418091 | −0.0209045 | − | 0.999781i | \(-0.506655\pi\) | ||||
−0.0209045 | + | 0.999781i | \(0.506655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.461317 | −0.0687691 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.41573 | 1.08169 | 0.540847 | − | 0.841121i | \(-0.318104\pi\) | ||||
0.540847 | + | 0.841121i | \(0.318104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44862 | 0.349803 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.28513 | −0.179955 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.05978 | −0.832374 | −0.416187 | − | 0.909279i | \(-0.636634\pi\) | ||||
−0.416187 | + | 0.909279i | \(0.636634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.36684 | 0.319145 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.12411 | −0.811158 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1942 | −1.71774 | −0.858870 | − | 0.512194i | \(-0.828833\pi\) | ||||
−0.858870 | + | 0.512194i | \(0.828833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.72241 | 0.604642 | 0.302321 | − | 0.953206i | \(-0.402239\pi\) | ||||
0.302321 | + | 0.953206i | \(0.402239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.07386 | −0.387270 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.13923 | −0.389374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.57481 | 1.04758 | 0.523790 | − | 0.851847i | \(-0.324518\pi\) | ||||
0.523790 | + | 0.851847i | \(0.324518\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.36756 | 1.00734 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.71053 | −1.15243 | −0.576214 | − | 0.817299i | \(-0.695471\pi\) | ||||
−0.576214 | + | 0.817299i | \(0.695471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1190 | −1.41842 | −0.709211 | − | 0.704996i | \(-0.750949\pi\) | ||||
−0.709211 | + | 0.704996i | \(0.750949\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.78719 | 0.552777 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.7708 | 1.79725 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4083 | −1.17103 | −0.585513 | − | 0.810663i | \(-0.699107\pi\) | ||||
−0.585513 | + | 0.810663i | \(0.699107\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.536826 | −0.0589244 | −0.0294622 | − | 0.999566i | \(-0.509379\pi\) | ||||
−0.0294622 | + | 0.999566i | \(0.509379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.592854 | −0.0643040 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.615911 | −0.0660326 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.8744 | 1.47068 | 0.735342 | − | 0.677696i | \(-0.237021\pi\) | ||||
0.735342 | + | 0.677696i | \(0.237021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.9174 | −2.19274 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.68978 | 0.382612 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82516 | −0.289855 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.4725 | 1.36792 | 0.683960 | − | 0.729519i | \(-0.260256\pi\) | ||||
0.683960 | + | 0.729519i | \(0.260256\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.13061 | −0.515646 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.25530 | −0.323915 | −0.161957 | − | 0.986798i | \(-0.551781\pi\) | ||||
−0.161957 | + | 0.986798i | \(0.551781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.08644 | 0.402649 | 0.201324 | − | 0.979525i | \(-0.435475\pi\) | ||||
0.201324 | + | 0.979525i | \(0.435475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41803 | −0.138385 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2673 | 1.18592 | 0.592960 | − | 0.805232i | \(-0.297959\pi\) | ||||
0.592960 | + | 0.805232i | \(0.297959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.40696 | 0.134762 | 0.0673811 | − | 0.997727i | \(-0.478536\pi\) | ||||
0.0673811 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6984 | −1.01545 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.51084 | −0.424344 | −0.212172 | − | 0.977232i | \(-0.568054\pi\) | ||||
−0.212172 | + | 0.977232i | \(0.568054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.86010 | 0.359956 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.80493 | 0.629116 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.95032 | −0.362125 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3232 | 1.39302 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.4321 | 0.940633 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.51500 | 0.403834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.67912 | −0.592676 | −0.296338 | − | 0.955083i | \(-0.595765\pi\) | ||||
−0.296338 | + | 0.955083i | \(0.595765\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.274161 | 0.0241385 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.22326 | 0.106877 | 0.0534383 | − | 0.998571i | \(-0.482982\pi\) | ||||
0.0534383 | + | 0.998571i | \(0.482982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.8247 | −1.63231 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.461317 | 0.0397039 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0509 | 1.11502 | 0.557508 | − | 0.830171i | \(-0.311757\pi\) | ||||
0.557508 | + | 0.830171i | \(0.311757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6783 | 0.990545 | 0.495272 | − | 0.868738i | \(-0.335068\pi\) | ||||
0.495272 | + | 0.868738i | \(0.335068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.41573 | −0.624517 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.9134 | −2.91961 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.284130 | −0.0235957 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.44862 | −0.201959 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.05393 | 0.741727 | 0.370863 | − | 0.928687i | \(-0.379062\pi\) | ||||
0.370863 | + | 0.928687i | \(0.379062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.35196 | −0.598294 | −0.299147 | − | 0.954207i | \(-0.596702\pi\) | ||||
−0.299147 | + | 0.954207i | \(0.596702\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.28513 | 0.103897 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.70216 | 0.136721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.62422 | −0.768097 | −0.384048 | − | 0.923313i | \(-0.625470\pi\) | ||||
−0.384048 | + | 0.923313i | \(0.625470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.05978 | 0.480571 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.7207 | 2.02708 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6560 | 1.85288 | 0.926441 | − | 0.376439i | \(-0.122852\pi\) | ||||
0.926441 | + | 0.376439i | \(0.122852\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.36684 | −0.184258 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.71310 | −0.596857 | −0.298429 | − | 0.954432i | \(-0.596463\pi\) | ||||
−0.298429 | + | 0.954432i | \(0.596463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.3070 | 2.56208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.12411 | 0.468322 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.79746 | −0.288716 | −0.144358 | − | 0.989526i | \(-0.546112\pi\) | ||||
−0.144358 | + | 0.989526i | \(0.546112\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.7151 | 1.11236 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1942 | 0.991737 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5568 | 1.08803 | 0.544014 | − | 0.839076i | \(-0.316904\pi\) | ||||
0.544014 | + | 0.839076i | \(0.316904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0492 | 1.49025 | 0.745124 | − | 0.666927i | \(-0.232391\pi\) | ||||
0.745124 | + | 0.666927i | \(0.232391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.72241 | −0.349090 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.93536 | −0.362855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.59352 | −0.482166 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.07386 | 0.223590 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.1938 | 1.31646 | 0.658230 | − | 0.752817i | \(-0.271305\pi\) | ||||
0.658230 | + | 0.752817i | \(0.271305\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.34471 | −0.600665 | −0.300333 | − | 0.953835i | \(-0.597098\pi\) | ||||
−0.300333 | + | 0.953835i | \(0.597098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.13923 | 0.224805 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4128 | 1.09812 | 0.549059 | − | 0.835784i | \(-0.314986\pi\) | ||||
0.549059 | + | 0.835784i | \(0.314986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3584 | −1.51406 | −0.757030 | − | 0.653380i | \(-0.773350\pi\) | ||||
−0.757030 | + | 0.653380i | \(0.773350\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.57481 | −0.604820 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.89322 | −0.132878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.81252 | 0.336121 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.36756 | −0.581586 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.4204 | −2.17340 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.36018 | 0.644382 | 0.322191 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322191 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.71053 | 0.665355 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.126475 | 0.00862553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3419 | 0.769936 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.1190 | 0.818926 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.74523 | 0.588268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8101 | 1.46051 | 0.730256 | − | 0.683174i | \(-0.239401\pi\) | ||||
0.730256 | + | 0.683174i | \(0.239401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.78719 | −0.319146 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.8387 | 1.38311 | 0.691555 | − | 0.722323i | \(-0.256926\pi\) | ||||
0.691555 | + | 0.722323i | \(0.256926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.84901 | −0.386513 | −0.193257 | − | 0.981148i | \(-0.561905\pi\) | ||||
−0.193257 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.7708 | −1.03764 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.7228 | 1.48862 | 0.744309 | − | 0.667835i | \(-0.232779\pi\) | ||||
0.744309 | + | 0.667835i | \(0.232779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.42100 | −0.223162 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4083 | 0.676092 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.60578 | 0.168554 | 0.0842768 | − | 0.996442i | \(-0.473142\pi\) | ||||
0.0842768 | + | 0.996442i | \(0.473142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7532 | −0.757090 | −0.378545 | − | 0.925583i | \(-0.623576\pi\) | ||||
−0.378545 | + | 0.925583i | \(0.623576\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.12959 | −0.0721669 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.6741 | 2.65166 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.536826 | 0.0340200 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6050 | 1.80553 | 0.902764 | − | 0.430135i | \(-0.141534\pi\) | ||||
0.902764 | + | 0.430135i | \(0.141534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.9307 | 2.69903 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.592854 | 0.0371260 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.8951 | −1.42816 | −0.714079 | − | 0.700065i | \(-0.753154\pi\) | ||||
−0.714079 | + | 0.700065i | \(0.753154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.8854 | −2.04340 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.615911 | 0.0381239 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.7911 | 0.912057 | 0.456029 | − | 0.889965i | \(-0.349271\pi\) | ||||
0.456029 | + | 0.889965i | \(0.349271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.79548 | 0.171725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.8744 | −0.849100 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.32434 | 0.263660 | 0.131830 | − | 0.991272i | \(-0.457915\pi\) | ||||
0.131830 | + | 0.991272i | \(0.457915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.47343 | 0.453979 | 0.226989 | − | 0.973897i | \(-0.427112\pi\) | ||||
0.226989 | + | 0.973897i | \(0.427112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.9174 | 1.26598 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.5612 | 1.48110 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.6405 | −1.78093 | −0.890463 | − | 0.455055i | \(-0.849620\pi\) | ||||
−0.890463 | + | 0.455055i | \(0.849620\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.68978 | −0.220901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1234 | 0.603913 | 0.301956 | − | 0.953322i | \(-0.402360\pi\) | ||||
0.301956 | + | 0.953322i | \(0.402360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0125 | −0.714071 | −0.357036 | − | 0.934091i | \(-0.616213\pi\) | ||||
−0.357036 | + | 0.934091i | \(0.616213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82516 | 0.167348 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.0669 | 1.89285 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3484 | −0.902849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4725 | −0.789769 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.6680 | 1.03217 | 0.516087 | − | 0.856536i | \(-0.327388\pi\) | ||||
0.516087 | + | 0.856536i | \(0.327388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.08672 | 0.354382 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.13061 | 0.297708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −56.9406 | −3.29296 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.842731 | 0.0485742 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.25530 | 0.187012 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.17853 | −0.124742 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.32687 | −0.475240 | −0.237620 | − | 0.971358i | \(-0.576367\pi\) | ||||
−0.237620 | + | 0.971358i | \(0.576367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.08644 | −0.232469 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.53924 | −0.257397 | −0.128698 | − | 0.991684i | \(-0.541080\pi\) | ||||
−0.128698 | + | 0.991684i | \(0.541080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.70186 | −0.378811 | −0.189406 | − | 0.981899i | \(-0.560656\pi\) | ||||
−0.189406 | + | 0.981899i | \(0.560656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41803 | 0.0798967 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3726 | −0.919574 | −0.459787 | − | 0.888029i | \(-0.652074\pi\) | ||||
−0.459787 | + | 0.888029i | \(0.652074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16000 | −0.176926 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2673 | −0.684691 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.87029 | 0.437915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.5764 | −1.80702 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.40696 | −0.0778050 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.7949 | −1.25672 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0668 | −1.76255 | −0.881276 | − | 0.472602i | \(-0.843315\pi\) | ||||
−0.881276 | + | 0.472602i | \(0.843315\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.6984 | 0.586269 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.95571 | −0.216123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.75418 | −0.422397 | −0.211199 | − | 0.977443i | \(-0.567737\pi\) | ||||
−0.211199 | + | 0.977443i | \(0.567737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.51084 | 0.244995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.9308 | 1.02516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.9903 | 0.755406 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.86010 | −0.207821 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1726 | 1.08292 | 0.541461 | − | 0.840726i | \(-0.317871\pi\) | ||||
0.541461 | + | 0.840726i | \(0.317871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7203 | 0.948548 | 0.474274 | − | 0.880377i | \(-0.342711\pi\) | ||||
0.474274 | + | 0.880377i | \(0.342711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.80493 | −0.363220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.7886 | −1.05324 | −0.526620 | − | 0.850101i | \(-0.676541\pi\) | ||||
−0.526620 | + | 0.850101i | \(0.676541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.47964 | 0.237754 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.95032 | 0.209073 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.4867 | 1.71458 | 0.857291 | − | 0.514833i | \(-0.172146\pi\) | ||||
0.857291 | + | 0.514833i | \(0.172146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5047 | 0.973933 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3232 | −0.804259 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.59071 | 0.292631 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.28220 | 0.119130 | 0.0595649 | − | 0.998224i | \(-0.481029\pi\) | ||||
0.0595649 | + | 0.998224i | \(0.481029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.4321 | −0.543075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.6269 | 0.967061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.60328 | −0.341905 | −0.170953 | − | 0.985279i | \(-0.554684\pi\) | ||||
−0.170953 | + | 0.985279i | \(0.554684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.51500 | −0.233154 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.19123 | 0.215859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.3031 | 1.04290 | 0.521451 | − | 0.853281i | \(-0.325391\pi\) | ||||
0.521451 | + | 0.853281i | \(0.325391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.67912 | 0.342181 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −38.9538 | −1.99045 | −0.995223 | − | 0.0976309i | \(-0.968874\pi\) | ||||
−0.995223 | + | 0.0976309i | \(0.968874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.27534 | −0.370786 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.274161 | −0.0139364 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.74843 | 0.291457 | 0.145729 | − | 0.989325i | \(-0.453447\pi\) | ||||
0.145729 | + | 0.989325i | \(0.453447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.7534 | −0.543824 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.22326 | −0.0617053 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.80153 | 0.241591 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6885 | 0.586628 | 0.293314 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293314 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.8247 | 0.942412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2400 | 0.860925 | 0.430462 | − | 0.902609i | \(-0.358351\pi\) | ||||
0.430462 | + | 0.902609i | \(0.358351\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.1087 | −1.25075 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.461317 | −0.0229230 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54.8894 | −2.72077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3836 | 0.711225 | 0.355613 | − | 0.934633i | \(-0.384272\pi\) | ||||
0.355613 | + | 0.934633i | \(0.384272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.0509 | −0.643755 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.5572 | 1.99569 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.247647 | 0.0121565 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.6783 | −0.571891 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.3061 | −1.43170 | −0.715848 | − | 0.698256i | \(-0.753960\pi\) | ||||
−0.715848 | + | 0.698256i | \(0.753960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8552 | 0.772734 | 0.386367 | − | 0.922345i | \(-0.373730\pi\) | ||||
0.386367 | + | 0.922345i | \(0.373730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.41573 | 0.360565 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.15217 | −0.298424 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5160 | −0.702480 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.9134 | 1.68564 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.7460 | −0.758459 | −0.379230 | − | 0.925303i | \(-0.623811\pi\) | ||||
−0.379230 | + | 0.925303i | \(0.623811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.5465 | −1.03546 | −0.517730 | − | 0.855544i | \(-0.673223\pi\) | ||||
−0.517730 | + | 0.855544i | \(0.673223\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.284130 | 0.0136230 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −51.2439 | −2.45133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.7705 | 0.657228 | 0.328614 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328614 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.44862 | 0.116601 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1748 | −1.48116 | −0.740580 | − | 0.671968i | \(-0.765449\pi\) | ||||
−0.740580 | + | 0.671968i | \(0.765449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.40051 | −0.303413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.05393 | −0.428236 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.9758 | −0.942716 | −0.471358 | − | 0.881942i | \(-0.656236\pi\) | ||||
−0.471358 | + | 0.881942i | \(0.656236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.5232 | 2.52031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.35196 | 0.345425 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.64956 | 0.452378 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5948 | 1.29083 | 0.645415 | − | 0.763832i | \(-0.276684\pi\) | ||||
0.645415 | + | 0.763832i | \(0.276684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.28513 | −0.0599849 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2912 | 1.41080 | 0.705400 | − | 0.708809i | \(-0.250767\pi\) | ||||
0.705400 | + | 0.708809i | \(0.250767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1019 | 1.44543 | 0.722714 | − | 0.691147i | \(-0.242894\pi\) | ||||
0.722714 | + | 0.691147i | \(0.242894\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.70216 | −0.0789357 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.6015 | −0.768225 | −0.384113 | − | 0.923286i | \(-0.625493\pi\) | ||||
−0.384113 | + | 0.923286i | \(0.625493\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.3578 | −1.21709 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.62422 | 0.443461 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.40661 | 0.0646761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.3173 | −1.34517 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.05978 | −0.277458 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.2558 | 1.93072 | 0.965358 | − | 0.260929i | \(-0.0840288\pi\) | ||||
0.965358 | + | 0.260929i | \(0.0840288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 72.8018 | 3.31948 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.7207 | −1.17033 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.21508 | −0.282212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0611 | 1.45283 | 0.726414 | − | 0.687258i | \(-0.241186\pi\) | ||||
0.726414 | + | 0.687258i | \(0.241186\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.6560 | −1.06976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2699 | 0.869638 | 0.434819 | − | 0.900518i | \(-0.356812\pi\) | ||||
0.434819 | + | 0.900518i | \(0.356812\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.791527 | 0.0356486 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.36684 | 0.106382 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.8488 | 1.33890 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.8034 | 1.02082 | 0.510410 | − | 0.859931i | \(-0.329494\pi\) | ||||
0.510410 | + | 0.859931i | \(0.329494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.71310 | 0.344596 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.50173 | 0.0668260 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.3070 | −1.47922 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0516 | 0.489855 | 0.244927 | − | 0.969541i | \(-0.421236\pi\) | ||||
0.244927 | + | 0.969541i | \(0.421236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.2521 | 1.64794 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.12411 | −0.270386 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.88515 | −0.0830695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −38.0472 | −1.67332 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79746 | 0.166690 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3139 | 0.583294 | 0.291647 | − | 0.956526i | \(-0.405797\pi\) | ||||
0.291647 | + | 0.956526i | \(0.405797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6565 | 0.684612 | 0.342306 | − | 0.939589i | \(-0.388792\pi\) | ||||
0.342306 | + | 0.939589i | \(0.388792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.7151 | −0.642222 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.74185 | −0.206558 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.0161 | 2.04418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.1942 | −0.572580 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −70.9898 | −3.07491 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.65910 | −0.244664 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.5568 | −0.628173 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.5629 | −0.541124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3601 | 0.617389 | 0.308695 | − | 0.951161i | \(-0.400108\pi\) | ||||
0.308695 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.0492 | −0.860395 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.649054 | −0.0278024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.6563 | 1.73834 | 0.869168 | − | 0.494517i | \(-0.164655\pi\) | ||||
0.869168 | + | 0.494517i | \(0.164655\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.72241 | 0.201547 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.77191 | 0.160689 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.9937 | 1.36051 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.93536 | 0.209494 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.61895 | −0.322825 | −0.161413 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161413 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.86564 | −0.0789083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.59352 | 0.278379 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.7344 | 1.00029 | 0.500143 | − | 0.865943i | \(-0.333281\pi\) | ||||
0.500143 | + | 0.865943i | \(0.333281\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.08093 | 0.0875453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.07386 | −0.129090 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8041 | 0.955998 | 0.477999 | − | 0.878360i | \(-0.341362\pi\) | ||||
0.477999 | + | 0.878360i | \(0.341362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.9778 | 1.71487 | 0.857433 | − | 0.514596i | \(-0.172058\pi\) | ||||
0.857433 | + | 0.514596i | \(0.172058\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1938 | −0.760059 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.0571 | 1.67050 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5156 | 0.770814 | 0.385407 | − | 0.922747i | \(-0.374061\pi\) | ||||
0.385407 | + | 0.922747i | \(0.374061\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.34471 | 0.346794 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.65013 | 0.0684589 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.0904 | 1.28763 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.13923 | −0.129791 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1993 | −1.04009 | −0.520044 | − | 0.854139i | \(-0.674084\pi\) | ||||
−0.520044 | + | 0.854139i | \(0.674084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.5966 | −0.931077 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.4128 | −0.633999 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.4690 | −1.21015 | −0.605073 | − | 0.796170i | \(-0.706856\pi\) | ||||
−0.605073 | + | 0.796170i | \(0.706856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.82235 | 0.0747091 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.3584 | 0.874143 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.9027 | −1.71210 | −0.856050 | − | 0.516893i | \(-0.827088\pi\) | ||||
−0.856050 | + | 0.516893i | \(0.827088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.5334 | −1.93893 | −0.969465 | − | 0.245231i | \(-0.921136\pi\) | ||||
−0.969465 | + | 0.245231i | \(0.921136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.57481 | 0.349193 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.06886 | −0.287390 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.30800 | −0.134267 | −0.0671337 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671337 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.89322 | 0.0767173 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.4635 | 2.04153 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.1428 | −1.45979 | −0.729897 | − | 0.683557i | \(-0.760432\pi\) | ||||
−0.729897 | + | 0.683557i | \(0.760432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.81252 | −0.194060 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.12404 | 0.0452520 | 0.0226260 | − | 0.999744i | \(-0.492797\pi\) | ||||
0.0226260 | + | 0.999744i | \(0.492797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5300 | 0.463429 | 0.231714 | − | 0.972784i | \(-0.425567\pi\) | ||||
0.231714 | + | 0.972784i | \(0.425567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.36756 | 0.335779 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.6480 | −1.70866 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8531 | 0.874123 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.4204 | 1.25481 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.7489 | 0.548203 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5715 | 0.540274 | 0.270137 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270137 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.36018 | −0.372034 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.08119 | 0.122273 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6627 | 0.660200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.71053 | −0.384143 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.9101 | 1.65535 | 0.827675 | − | 0.561207i | \(-0.189663\pi\) | ||||
0.827675 | + | 0.561207i | \(0.189663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6894 | −1.21027 | −0.605135 | − | 0.796123i | \(-0.706881\pi\) | ||||
−0.605135 | + | 0.796123i | \(0.706881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.126475 | −0.00497995 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.5672 | 1.16241 | 0.581204 | − | 0.813758i | \(-0.302582\pi\) | ||||
0.581204 | + | 0.813758i | \(0.302582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.6944 | 2.65724 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3419 | −0.444523 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.892383 | −0.0349217 | −0.0174608 | − | 0.999848i | \(-0.505558\pi\) | ||||
−0.0174608 | + | 0.999848i | \(0.505558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.564311 | −0.0220494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.1190 | −0.472807 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.10258 | 0.0819048 | 0.0409524 | − | 0.999161i | \(-0.486961\pi\) | ||||
0.0409524 | + | 0.999161i | \(0.486961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.25531 | 0.165512 | 0.0827562 | − | 0.996570i | \(-0.473628\pi\) | ||||
0.0827562 | + | 0.996570i | \(0.473628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.74523 | −0.339637 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.68414 | 0.336757 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.15367 | −0.199551 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.8101 | −0.843227 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.2288 | −0.935344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.1845 | −1.66464 | −0.832320 | − | 0.554296i | \(-0.812988\pi\) | ||||
−0.832320 | + | 0.554296i | \(0.812988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.78719 | 0.184259 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3438 | 1.16621 | 0.583103 | − | 0.812398i | \(-0.301839\pi\) | ||||
0.583103 | + | 0.812398i | \(0.301839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.4125 | −1.58926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.8387 | −0.798539 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.0190 | −0.536424 | −0.268212 | − | 0.963360i | \(-0.586433\pi\) | ||||
−0.268212 | + | 0.963360i | \(0.586433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.02062 | −0.230036 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.84901 | 0.223154 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.2363 | −1.57098 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4584 | −0.435900 | −0.217950 | − | 0.975960i | \(-0.569937\pi\) | ||||
−0.217950 | + | 0.975960i | \(0.569937\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.7708 | 0.599083 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.38742 | −0.204357 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.4067 | −0.507814 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.7228 | −0.859454 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.3826 | −1.44969 | −0.724845 | − | 0.688912i | \(-0.758089\pi\) | ||||
−0.724845 | + | 0.688912i | \(0.758089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 65.5182 | 2.47107 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.42100 | 0.128842 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0063 | 0.376327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.6664 | −1.94037 | −0.970186 | − | 0.242364i | \(-0.922077\pi\) | ||||
−0.970186 | + | 0.242364i | \(0.922077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4083 | −0.390342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.8744 | 1.15626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1062 | 0.602337 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.60578 | −0.0973145 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.7992 | 0.775681 | 0.387840 | − | 0.921727i | \(-0.373221\pi\) | ||||
0.387840 | + | 0.921727i | \(0.373221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5612 | −0.467802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.7532 | 0.437106 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.94848 | −0.109504 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4030 | 0.793792 | 0.396896 | − | 0.917864i | \(-0.370087\pi\) | ||||
0.396896 | + | 0.917864i | \(0.370087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.352333 | −0.0130315 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7510 | −1.02501 | −0.512504 | − | 0.858685i | \(-0.671282\pi\) | ||||
−0.512504 | + | 0.858685i | \(0.671282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.12959 | 0.0416656 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.9940 | −1.62054 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3211 | 1.11538 | 0.557690 | − | 0.830050i | \(-0.311688\pi\) | ||||
0.557690 | + | 0.830050i | \(0.311688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.6741 | −1.53094 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.5720 | −1.81862 | −0.909311 | − | 0.416117i | \(-0.863391\pi\) | ||||
−0.909311 | + | 0.416117i | \(0.863391\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.17673 | −0.153024 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.536826 | −0.0196415 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.7078 | −1.37781 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.1097 | −0.843286 | −0.421643 | − | 0.906762i | \(-0.638546\pi\) | ||||
−0.421643 | + | 0.906762i | \(0.638546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.6050 | −1.04242 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.39159 | 0.123432 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.6602 | 1.58686 | 0.793429 | − | 0.608663i | \(-0.208294\pi\) | ||||
0.793429 | + | 0.608663i | \(0.208294\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −42.9307 | −1.55829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2561 | −0.951784 | −0.475892 | − | 0.879504i | \(-0.657875\pi\) | ||||
−0.475892 | + | 0.879504i | \(0.657875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.32479 | −0.156568 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.592854 | −0.0214347 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −89.7856 | −3.24197 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.2830 | 1.05597 | 0.527986 | − | 0.849253i | \(-0.322947\pi\) | ||||
0.527986 | + | 0.849253i | \(0.322947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.8951 | 0.824548 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.6109 | 1.06503 | 0.532515 | − | 0.846420i | \(-0.321247\pi\) | ||||
0.532515 | + | 0.846420i | \(0.321247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.6637 | 0.634497 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.8854 | 1.17976 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.8875 | −2.28901 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.8210 | 1.78274 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.615911 | −0.0220109 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.43982 | 0.158464 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.4862 | −1.40753 | −0.703766 | − | 0.710432i | \(-0.748499\pi\) | ||||
−0.703766 | + | 0.710432i | \(0.748499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.7911 | −0.526577 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8657 | 0.493007 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1356 | 1.14117 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.79548 | −0.0991454 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.1648 | 0.785118 | 0.392559 | − | 0.919727i | \(-0.371590\pi\) | ||||
0.392559 | + | 0.919727i | \(0.371590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.53019 | 0.337154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.8744 | 0.490228 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62.1779 | 2.19421 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8654 | −0.418201 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.32434 | −0.152224 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.2730 | −1.16982 | −0.584908 | − | 0.811099i | \(-0.698870\pi\) | ||||
−0.584908 | + | 0.811099i | \(0.698870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.556963 | 0.0195576 | 0.00977881 | − | 0.999952i | \(-0.496887\pi\) | ||||
0.00977881 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.47343 | −0.262105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.9129 | −0.382263 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.67899 | −0.0587404 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.9174 | −0.730913 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00401 | 0.139741 | 0.0698704 | − | 0.997556i | \(-0.477741\pi\) | ||||
0.0698704 | + | 0.997556i | \(0.477741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5663 | 0.438033 | 0.219016 | − | 0.975721i | \(-0.429715\pi\) | ||||
0.219016 | + | 0.975721i | \(0.429715\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.5612 | −0.855111 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9485 | −1.18051 | −0.590253 | − | 0.807218i | \(-0.700972\pi\) | ||||
−0.590253 | + | 0.807218i | \(0.700972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.7090 | 0.684521 | 0.342261 | − | 0.939605i | \(-0.388807\pi\) | ||||
0.342261 | + | 0.939605i | \(0.388807\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6405 | 1.02822 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.14680 | 0.109030 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.55819 | 0.123136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.68978 | 0.127537 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.95135 | 0.343559 | 0.171779 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171779 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6207 | −0.986919 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.1234 | −0.348669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.3651 | −0.528576 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.1014 | −1.61842 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.0125 | 0.412269 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −89.5195 | −3.06869 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.4240 | 1.69224 | 0.846122 | − | 0.532988i | \(-0.178931\pi\) | ||||
0.846122 | + | 0.532988i | \(0.178931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82516 | −0.0966184 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5986 | 0.976909 | 0.488455 | − | 0.872589i | \(-0.337561\pi\) | ||||
0.488455 | + | 0.872589i | \(0.337561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.16739 | −0.108070 | −0.0540349 | − | 0.998539i | \(-0.517208\pi\) | ||||
−0.0540349 | + | 0.998539i | \(0.517208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.0669 | −1.09284 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.5485 | −0.937762 | −0.468881 | − | 0.883261i | \(-0.655343\pi\) | ||||
−0.468881 | + | 0.883261i | \(0.655343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.75184 | 0.0595642 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3484 | 0.521260 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.4010 | 1.81150 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.3509 | 1.97715 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.4725 | 0.455974 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.8785 | −0.469178 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9871 | 0.641149 | 0.320574 | − | 0.947223i | \(-0.396124\pi\) | ||||
0.320574 | + | 0.947223i | \(0.396124\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.6680 | −0.595926 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.69188 | −0.124383 | −0.0621913 | − | 0.998064i | \(-0.519809\pi\) | ||||
−0.0621913 | + | 0.998064i | \(0.519809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.4959 | 1.59837 | 0.799183 | − | 0.601088i | \(-0.205266\pi\) | ||||
0.799183 | + | 0.601088i | \(0.205266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.08672 | −0.204603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.9946 | 1.00712 | 0.503560 | − | 0.863960i | \(-0.332023\pi\) | ||||
0.503560 | + | 0.863960i | \(0.332023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.5307 | 0.688577 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.13061 | −0.171882 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.4147 | 1.51975 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.71531 | −0.224468 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 56.9406 | 1.90119 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.27257 | −0.0757946 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.78762 | −0.259443 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.842731 | −0.0280443 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.24905 | −0.307449 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.3261 | −1.70425 | −0.852127 | − | 0.523335i | \(-0.824688\pi\) | ||||
−0.852127 | + | 0.523335i | \(0.824688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.25530 | −0.107972 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1307 | 0.600697 | 0.300349 | − | 0.953830i | \(-0.402897\pi\) | ||||
0.300349 | + | 0.953830i | \(0.402897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.75425 | 0.0911523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.17853 | 0.0720199 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.76013 | −0.124170 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.7329 | 1.50859 | 0.754294 | − | 0.656537i | \(-0.227979\pi\) | ||||
0.754294 | + | 0.656537i | \(0.227979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.32687 | 0.274380 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −66.0795 | −2.17503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.2152 | −1.68395 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.08644 | 0.134216 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.4296 | 1.35926 | 0.679630 | − | 0.733555i | \(-0.262140\pi\) | ||||
0.679630 | + | 0.733555i | \(0.262140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.9956 | 0.491462 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.53924 | 0.148608 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.04170 | 0.0994744 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9436 | −0.749534 | −0.374767 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374767 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.70186 | 0.218707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0310 | −0.359602 | −0.179801 | − | 0.983703i | \(-0.557545\pi\) | ||||
−0.179801 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 87.2915 | 2.84260 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41803 | −0.0461284 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.911573 | 0.0296221 | 0.0148111 | − | 0.999890i | \(-0.495285\pi\) | ||||
0.0148111 | + | 0.999890i | \(0.495285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −82.4689 | −2.67705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3726 | 0.530916 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2543 | 0.396955 | 0.198478 | − | 0.980105i | \(-0.436400\pi\) | ||||
0.198478 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.39313 | −0.271595 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.16000 | 0.102148 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.1168 | −1.29544 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3855 | −0.560824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.2673 | 0.395307 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.84956 | 0.123922 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.11612 | −0.164523 | −0.0822617 | − | 0.996611i | \(-0.526214\pi\) | ||||
−0.0822617 | + | 0.996611i | \(0.526214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.87029 | −0.252830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0116 | −0.770567 | −0.385284 | − | 0.922798i | \(-0.625896\pi\) | ||||
−0.385284 | + | 0.922798i | \(0.625896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.8976 | −1.15082 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.5764 | 1.04328 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.4229 | 0.493422 | 0.246711 | − | 0.969089i | \(-0.420650\pi\) | ||||
0.246711 | + | 0.969089i | \(0.420650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −71.1842 | −2.27506 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40696 | 0.0449207 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.9914 | −0.828998 | −0.414499 | − | 0.910050i | \(-0.636043\pi\) | ||||
−0.414499 | + | 0.910050i | \(0.636043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.11020 | −0.226550 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.7949 | 0.725570 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.29406 | 0.0729467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.7510 | 1.77099 | 0.885495 | − | 0.464650i | \(-0.153820\pi\) | ||||
0.885495 | + | 0.464650i | \(0.153820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.0668 | 1.01761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.85302 | 0.312362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9362 | 0.663057 | 0.331528 | − | 0.943445i | \(-0.392436\pi\) | ||||
0.331528 | + | 0.943445i | \(0.392436\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.6984 | −0.338482 |
(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 | 6036.2.a.i.1.11 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.11 | ✓ | 26 | 1.1 | even | 1 | trivial |