Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(1.02602\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.02602 | 0.592374 | 0.296187 | − | 0.955130i | \(-0.404285\pi\) | ||||
0.296187 | + | 0.955130i | \(0.404285\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.02602 | −0.418872 | ||||||||
\(7\) | −3.81201 | −1.44081 | −0.720403 | − | 0.693556i | \(-0.756043\pi\) | ||||
−0.720403 | + | 0.693556i | \(0.756043\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.94728 | −0.649093 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.83918 | −0.856046 | −0.428023 | − | 0.903768i | \(-0.640790\pi\) | ||||
−0.428023 | + | 0.903768i | \(0.640790\pi\) | |||||||
\(12\) | 1.02602 | 0.296187 | ||||||||
\(13\) | −0.0600620 | −0.0166582 | −0.00832909 | − | 0.999965i | \(-0.502651\pi\) | ||||
−0.00832909 | + | 0.999965i | \(0.502651\pi\) | |||||||
\(14\) | 3.81201 | 1.01880 | ||||||||
\(15\) | 1.02602 | 0.264918 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.05914 | −1.22702 | −0.613511 | − | 0.789686i | \(-0.710244\pi\) | ||||
−0.613511 | + | 0.789686i | \(0.710244\pi\) | |||||||
\(18\) | 1.94728 | 0.458978 | ||||||||
\(19\) | −4.22523 | −0.969334 | −0.484667 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484667 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.91121 | −0.853496 | ||||||||
\(22\) | 2.83918 | 0.605316 | ||||||||
\(23\) | 8.19324 | 1.70841 | 0.854204 | − | 0.519938i | \(-0.174045\pi\) | ||||
0.854204 | + | 0.519938i | \(0.174045\pi\) | |||||||
\(24\) | −1.02602 | −0.209436 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.0600620 | 0.0117791 | ||||||||
\(27\) | −5.07602 | −0.976880 | ||||||||
\(28\) | −3.81201 | −0.720403 | ||||||||
\(29\) | −4.58061 | −0.850599 | −0.425299 | − | 0.905053i | \(-0.639831\pi\) | ||||
−0.425299 | + | 0.905053i | \(0.639831\pi\) | |||||||
\(30\) | −1.02602 | −0.187325 | ||||||||
\(31\) | 9.54004 | 1.71344 | 0.856721 | − | 0.515780i | \(-0.172498\pi\) | ||||
0.856721 | + | 0.515780i | \(0.172498\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.91306 | −0.507099 | ||||||||
\(34\) | 5.05914 | 0.867636 | ||||||||
\(35\) | −3.81201 | −0.644348 | ||||||||
\(36\) | −1.94728 | −0.324547 | ||||||||
\(37\) | 7.17604 | 1.17973 | 0.589867 | − | 0.807501i | \(-0.299180\pi\) | ||||
0.589867 | + | 0.807501i | \(0.299180\pi\) | |||||||
\(38\) | 4.22523 | 0.685422 | ||||||||
\(39\) | −0.0616249 | −0.00986788 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.87566 | −0.449102 | −0.224551 | − | 0.974462i | \(-0.572092\pi\) | ||||
−0.224551 | + | 0.974462i | \(0.572092\pi\) | |||||||
\(42\) | 3.91121 | 0.603513 | ||||||||
\(43\) | 0.707096 | 0.107831 | 0.0539156 | − | 0.998545i | \(-0.482830\pi\) | ||||
0.0539156 | + | 0.998545i | \(0.482830\pi\) | |||||||
\(44\) | −2.83918 | −0.428023 | ||||||||
\(45\) | −1.94728 | −0.290283 | ||||||||
\(46\) | −8.19324 | −1.20803 | ||||||||
\(47\) | −0.230248 | −0.0335851 | −0.0167925 | − | 0.999859i | \(-0.505345\pi\) | ||||
−0.0167925 | + | 0.999859i | \(0.505345\pi\) | |||||||
\(48\) | 1.02602 | 0.148093 | ||||||||
\(49\) | 7.53145 | 1.07592 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −5.19079 | −0.726856 | ||||||||
\(52\) | −0.0600620 | −0.00832909 | ||||||||
\(53\) | 2.37088 | 0.325666 | 0.162833 | − | 0.986654i | \(-0.447937\pi\) | ||||
0.162833 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(54\) | 5.07602 | 0.690758 | ||||||||
\(55\) | −2.83918 | −0.382835 | ||||||||
\(56\) | 3.81201 | 0.509402 | ||||||||
\(57\) | −4.33518 | −0.574208 | ||||||||
\(58\) | 4.58061 | 0.601464 | ||||||||
\(59\) | 8.52669 | 1.11008 | 0.555040 | − | 0.831824i | \(-0.312703\pi\) | ||||
0.555040 | + | 0.831824i | \(0.312703\pi\) | |||||||
\(60\) | 1.02602 | 0.132459 | ||||||||
\(61\) | 6.74990 | 0.864236 | 0.432118 | − | 0.901817i | \(-0.357766\pi\) | ||||
0.432118 | + | 0.901817i | \(0.357766\pi\) | |||||||
\(62\) | −9.54004 | −1.21159 | ||||||||
\(63\) | 7.42306 | 0.935217 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0600620 | −0.00744977 | ||||||||
\(66\) | 2.91306 | 0.358573 | ||||||||
\(67\) | −11.8218 | −1.44427 | −0.722134 | − | 0.691753i | \(-0.756839\pi\) | ||||
−0.722134 | + | 0.691753i | \(0.756839\pi\) | |||||||
\(68\) | −5.05914 | −0.613511 | ||||||||
\(69\) | 8.40644 | 1.01202 | ||||||||
\(70\) | 3.81201 | 0.455623 | ||||||||
\(71\) | 10.1208 | 1.20112 | 0.600560 | − | 0.799580i | \(-0.294945\pi\) | ||||
0.600560 | + | 0.799580i | \(0.294945\pi\) | |||||||
\(72\) | 1.94728 | 0.229489 | ||||||||
\(73\) | 3.63271 | 0.425177 | 0.212588 | − | 0.977142i | \(-0.431811\pi\) | ||||
0.212588 | + | 0.977142i | \(0.431811\pi\) | |||||||
\(74\) | −7.17604 | −0.834197 | ||||||||
\(75\) | 1.02602 | 0.118475 | ||||||||
\(76\) | −4.22523 | −0.484667 | ||||||||
\(77\) | 10.8230 | 1.23340 | ||||||||
\(78\) | 0.0616249 | 0.00697764 | ||||||||
\(79\) | −4.99070 | −0.561498 | −0.280749 | − | 0.959781i | \(-0.590583\pi\) | ||||
−0.280749 | + | 0.959781i | \(0.590583\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0.633735 | 0.0704149 | ||||||||
\(82\) | 2.87566 | 0.317563 | ||||||||
\(83\) | 7.41435 | 0.813830 | 0.406915 | − | 0.913466i | \(-0.366604\pi\) | ||||
0.406915 | + | 0.913466i | \(0.366604\pi\) | |||||||
\(84\) | −3.91121 | −0.426748 | ||||||||
\(85\) | −5.05914 | −0.548741 | ||||||||
\(86\) | −0.707096 | −0.0762482 | ||||||||
\(87\) | −4.69981 | −0.503872 | ||||||||
\(88\) | 2.83918 | 0.302658 | ||||||||
\(89\) | −3.81665 | −0.404564 | −0.202282 | − | 0.979327i | \(-0.564836\pi\) | ||||
−0.202282 | + | 0.979327i | \(0.564836\pi\) | |||||||
\(90\) | 1.94728 | 0.205261 | ||||||||
\(91\) | 0.228957 | 0.0240012 | ||||||||
\(92\) | 8.19324 | 0.854204 | ||||||||
\(93\) | 9.78829 | 1.01500 | ||||||||
\(94\) | 0.230248 | 0.0237482 | ||||||||
\(95\) | −4.22523 | −0.433499 | ||||||||
\(96\) | −1.02602 | −0.104718 | ||||||||
\(97\) | 15.1842 | 1.54172 | 0.770862 | − | 0.637003i | \(-0.219826\pi\) | ||||
0.770862 | + | 0.637003i | \(0.219826\pi\) | |||||||
\(98\) | −7.53145 | −0.760791 | ||||||||
\(99\) | 5.52868 | 0.555653 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.8094 | 1.37409 | 0.687044 | − | 0.726616i | \(-0.258908\pi\) | ||||
0.687044 | + | 0.726616i | \(0.258908\pi\) | |||||||
\(102\) | 5.19079 | 0.513965 | ||||||||
\(103\) | 1.91094 | 0.188290 | 0.0941452 | − | 0.995558i | \(-0.469988\pi\) | ||||
0.0941452 | + | 0.995558i | \(0.469988\pi\) | |||||||
\(104\) | 0.0600620 | 0.00588956 | ||||||||
\(105\) | −3.91121 | −0.381695 | ||||||||
\(106\) | −2.37088 | −0.230281 | ||||||||
\(107\) | −12.7904 | −1.23650 | −0.618249 | − | 0.785982i | \(-0.712158\pi\) | ||||
−0.618249 | + | 0.785982i | \(0.712158\pi\) | |||||||
\(108\) | −5.07602 | −0.488440 | ||||||||
\(109\) | 13.5187 | 1.29485 | 0.647427 | − | 0.762128i | \(-0.275845\pi\) | ||||
0.647427 | + | 0.762128i | \(0.275845\pi\) | |||||||
\(110\) | 2.83918 | 0.270705 | ||||||||
\(111\) | 7.36277 | 0.698843 | ||||||||
\(112\) | −3.81201 | −0.360201 | ||||||||
\(113\) | 7.59117 | 0.714118 | 0.357059 | − | 0.934082i | \(-0.383780\pi\) | ||||
0.357059 | + | 0.934082i | \(0.383780\pi\) | |||||||
\(114\) | 4.33518 | 0.406026 | ||||||||
\(115\) | 8.19324 | 0.764023 | ||||||||
\(116\) | −4.58061 | −0.425299 | ||||||||
\(117\) | 0.116957 | 0.0108127 | ||||||||
\(118\) | −8.52669 | −0.784945 | ||||||||
\(119\) | 19.2855 | 1.76790 | ||||||||
\(120\) | −1.02602 | −0.0936625 | ||||||||
\(121\) | −2.93905 | −0.267186 | ||||||||
\(122\) | −6.74990 | −0.611107 | ||||||||
\(123\) | −2.95049 | −0.266036 | ||||||||
\(124\) | 9.54004 | 0.856721 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.42306 | −0.661298 | ||||||||
\(127\) | −7.71307 | −0.684424 | −0.342212 | − | 0.939623i | \(-0.611176\pi\) | ||||
−0.342212 | + | 0.939623i | \(0.611176\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.725496 | 0.0638764 | ||||||||
\(130\) | 0.0600620 | 0.00526778 | ||||||||
\(131\) | 14.9284 | 1.30430 | 0.652148 | − | 0.758092i | \(-0.273868\pi\) | ||||
0.652148 | + | 0.758092i | \(0.273868\pi\) | |||||||
\(132\) | −2.91306 | −0.253550 | ||||||||
\(133\) | 16.1066 | 1.39662 | ||||||||
\(134\) | 11.8218 | 1.02125 | ||||||||
\(135\) | −5.07602 | −0.436874 | ||||||||
\(136\) | 5.05914 | 0.433818 | ||||||||
\(137\) | −15.8192 | −1.35152 | −0.675762 | − | 0.737120i | \(-0.736185\pi\) | ||||
−0.675762 | + | 0.737120i | \(0.736185\pi\) | |||||||
\(138\) | −8.40644 | −0.715604 | ||||||||
\(139\) | −5.17609 | −0.439030 | −0.219515 | − | 0.975609i | \(-0.570448\pi\) | ||||
−0.219515 | + | 0.975609i | \(0.570448\pi\) | |||||||
\(140\) | −3.81201 | −0.322174 | ||||||||
\(141\) | −0.236239 | −0.0198949 | ||||||||
\(142\) | −10.1208 | −0.849319 | ||||||||
\(143\) | 0.170527 | 0.0142602 | ||||||||
\(144\) | −1.94728 | −0.162273 | ||||||||
\(145\) | −4.58061 | −0.380399 | ||||||||
\(146\) | −3.63271 | −0.300645 | ||||||||
\(147\) | 7.72743 | 0.637348 | ||||||||
\(148\) | 7.17604 | 0.589867 | ||||||||
\(149\) | 6.58195 | 0.539214 | 0.269607 | − | 0.962970i | \(-0.413106\pi\) | ||||
0.269607 | + | 0.962970i | \(0.413106\pi\) | |||||||
\(150\) | −1.02602 | −0.0837743 | ||||||||
\(151\) | 19.1521 | 1.55857 | 0.779287 | − | 0.626667i | \(-0.215581\pi\) | ||||
0.779287 | + | 0.626667i | \(0.215581\pi\) | |||||||
\(152\) | 4.22523 | 0.342711 | ||||||||
\(153\) | 9.85157 | 0.796452 | ||||||||
\(154\) | −10.8230 | −0.872142 | ||||||||
\(155\) | 9.54004 | 0.766275 | ||||||||
\(156\) | −0.0616249 | −0.00493394 | ||||||||
\(157\) | 1.25197 | 0.0999181 | 0.0499590 | − | 0.998751i | \(-0.484091\pi\) | ||||
0.0499590 | + | 0.998751i | \(0.484091\pi\) | |||||||
\(158\) | 4.99070 | 0.397039 | ||||||||
\(159\) | 2.43258 | 0.192916 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −31.2327 | −2.46148 | ||||||||
\(162\) | −0.633735 | −0.0497909 | ||||||||
\(163\) | 1.40366 | 0.109943 | 0.0549715 | − | 0.998488i | \(-0.482493\pi\) | ||||
0.0549715 | + | 0.998488i | \(0.482493\pi\) | |||||||
\(164\) | −2.87566 | −0.224551 | ||||||||
\(165\) | −2.91306 | −0.226782 | ||||||||
\(166\) | −7.41435 | −0.575465 | ||||||||
\(167\) | 8.87085 | 0.686447 | 0.343224 | − | 0.939254i | \(-0.388481\pi\) | ||||
0.343224 | + | 0.939254i | \(0.388481\pi\) | |||||||
\(168\) | 3.91121 | 0.301756 | ||||||||
\(169\) | −12.9964 | −0.999723 | ||||||||
\(170\) | 5.05914 | 0.388019 | ||||||||
\(171\) | 8.22770 | 0.629188 | ||||||||
\(172\) | 0.707096 | 0.0539156 | ||||||||
\(173\) | −10.2824 | −0.781756 | −0.390878 | − | 0.920442i | \(-0.627829\pi\) | ||||
−0.390878 | + | 0.920442i | \(0.627829\pi\) | |||||||
\(174\) | 4.69981 | 0.356292 | ||||||||
\(175\) | −3.81201 | −0.288161 | ||||||||
\(176\) | −2.83918 | −0.214011 | ||||||||
\(177\) | 8.74857 | 0.657583 | ||||||||
\(178\) | 3.81665 | 0.286070 | ||||||||
\(179\) | 3.08332 | 0.230458 | 0.115229 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115229 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(180\) | −1.94728 | −0.145142 | ||||||||
\(181\) | 10.7889 | 0.801929 | 0.400965 | − | 0.916094i | \(-0.368675\pi\) | ||||
0.400965 | + | 0.916094i | \(0.368675\pi\) | |||||||
\(182\) | −0.228957 | −0.0169714 | ||||||||
\(183\) | 6.92555 | 0.511951 | ||||||||
\(184\) | −8.19324 | −0.604013 | ||||||||
\(185\) | 7.17604 | 0.527593 | ||||||||
\(186\) | −9.78829 | −0.717712 | ||||||||
\(187\) | 14.3638 | 1.05039 | ||||||||
\(188\) | −0.230248 | −0.0167925 | ||||||||
\(189\) | 19.3498 | 1.40749 | ||||||||
\(190\) | 4.22523 | 0.306530 | ||||||||
\(191\) | 22.1217 | 1.60067 | 0.800337 | − | 0.599551i | \(-0.204654\pi\) | ||||
0.800337 | + | 0.599551i | \(0.204654\pi\) | |||||||
\(192\) | 1.02602 | 0.0740467 | ||||||||
\(193\) | −16.6942 | −1.20167 | −0.600836 | − | 0.799372i | \(-0.705166\pi\) | ||||
−0.600836 | + | 0.799372i | \(0.705166\pi\) | |||||||
\(194\) | −15.1842 | −1.09016 | ||||||||
\(195\) | −0.0616249 | −0.00441305 | ||||||||
\(196\) | 7.53145 | 0.537961 | ||||||||
\(197\) | −21.6286 | −1.54097 | −0.770486 | − | 0.637457i | \(-0.779986\pi\) | ||||
−0.770486 | + | 0.637457i | \(0.779986\pi\) | |||||||
\(198\) | −5.52868 | −0.392906 | ||||||||
\(199\) | −5.08690 | −0.360601 | −0.180300 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180300 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −12.1295 | −0.855547 | ||||||||
\(202\) | −13.8094 | −0.971627 | ||||||||
\(203\) | 17.4614 | 1.22555 | ||||||||
\(204\) | −5.19079 | −0.363428 | ||||||||
\(205\) | −2.87566 | −0.200845 | ||||||||
\(206\) | −1.91094 | −0.133141 | ||||||||
\(207\) | −15.9545 | −1.10892 | ||||||||
\(208\) | −0.0600620 | −0.00416455 | ||||||||
\(209\) | 11.9962 | 0.829794 | ||||||||
\(210\) | 3.91121 | 0.269899 | ||||||||
\(211\) | 10.6499 | 0.733167 | 0.366583 | − | 0.930385i | \(-0.380527\pi\) | ||||
0.366583 | + | 0.930385i | \(0.380527\pi\) | |||||||
\(212\) | 2.37088 | 0.162833 | ||||||||
\(213\) | 10.3842 | 0.711512 | ||||||||
\(214\) | 12.7904 | 0.874336 | ||||||||
\(215\) | 0.707096 | 0.0482236 | ||||||||
\(216\) | 5.07602 | 0.345379 | ||||||||
\(217\) | −36.3668 | −2.46874 | ||||||||
\(218\) | −13.5187 | −0.915600 | ||||||||
\(219\) | 3.72724 | 0.251864 | ||||||||
\(220\) | −2.83918 | −0.191418 | ||||||||
\(221\) | 0.303862 | 0.0204400 | ||||||||
\(222\) | −7.36277 | −0.494157 | ||||||||
\(223\) | −0.372245 | −0.0249274 | −0.0124637 | − | 0.999922i | \(-0.503967\pi\) | ||||
−0.0124637 | + | 0.999922i | \(0.503967\pi\) | |||||||
\(224\) | 3.81201 | 0.254701 | ||||||||
\(225\) | −1.94728 | −0.129819 | ||||||||
\(226\) | −7.59117 | −0.504957 | ||||||||
\(227\) | −4.26913 | −0.283352 | −0.141676 | − | 0.989913i | \(-0.545249\pi\) | ||||
−0.141676 | + | 0.989913i | \(0.545249\pi\) | |||||||
\(228\) | −4.33518 | −0.287104 | ||||||||
\(229\) | −11.1730 | −0.738332 | −0.369166 | − | 0.929363i | \(-0.620357\pi\) | ||||
−0.369166 | + | 0.929363i | \(0.620357\pi\) | |||||||
\(230\) | −8.19324 | −0.540246 | ||||||||
\(231\) | 11.1046 | 0.730631 | ||||||||
\(232\) | 4.58061 | 0.300732 | ||||||||
\(233\) | 2.91303 | 0.190839 | 0.0954194 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954194 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(234\) | −0.116957 | −0.00764574 | ||||||||
\(235\) | −0.230248 | −0.0150197 | ||||||||
\(236\) | 8.52669 | 0.555040 | ||||||||
\(237\) | −5.12057 | −0.332617 | ||||||||
\(238\) | −19.2855 | −1.25010 | ||||||||
\(239\) | −18.7629 | −1.21367 | −0.606834 | − | 0.794828i | \(-0.707561\pi\) | ||||
−0.606834 | + | 0.794828i | \(0.707561\pi\) | |||||||
\(240\) | 1.02602 | 0.0662294 | ||||||||
\(241\) | 5.17217 | 0.333169 | 0.166584 | − | 0.986027i | \(-0.446726\pi\) | ||||
0.166584 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(242\) | 2.93905 | 0.188929 | ||||||||
\(243\) | 15.8783 | 1.01859 | ||||||||
\(244\) | 6.74990 | 0.432118 | ||||||||
\(245\) | 7.53145 | 0.481167 | ||||||||
\(246\) | 2.95049 | 0.188116 | ||||||||
\(247\) | 0.253775 | 0.0161473 | ||||||||
\(248\) | −9.54004 | −0.605793 | ||||||||
\(249\) | 7.60728 | 0.482092 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −1.37020 | −0.0864865 | −0.0432433 | − | 0.999065i | \(-0.513769\pi\) | ||||
−0.0432433 | + | 0.999065i | \(0.513769\pi\) | |||||||
\(252\) | 7.42306 | 0.467609 | ||||||||
\(253\) | −23.2621 | −1.46247 | ||||||||
\(254\) | 7.71307 | 0.483961 | ||||||||
\(255\) | −5.19079 | −0.325060 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.3103 | −1.64119 | −0.820595 | − | 0.571510i | \(-0.806358\pi\) | ||||
−0.820595 | + | 0.571510i | \(0.806358\pi\) | |||||||
\(258\) | −0.725496 | −0.0451674 | ||||||||
\(259\) | −27.3552 | −1.69977 | ||||||||
\(260\) | −0.0600620 | −0.00372488 | ||||||||
\(261\) | 8.91973 | 0.552118 | ||||||||
\(262\) | −14.9284 | −0.922277 | ||||||||
\(263\) | −7.70166 | −0.474905 | −0.237452 | − | 0.971399i | \(-0.576312\pi\) | ||||
−0.237452 | + | 0.971399i | \(0.576312\pi\) | |||||||
\(264\) | 2.91306 | 0.179287 | ||||||||
\(265\) | 2.37088 | 0.145642 | ||||||||
\(266\) | −16.1066 | −0.987561 | ||||||||
\(267\) | −3.91597 | −0.239653 | ||||||||
\(268\) | −11.8218 | −0.722134 | ||||||||
\(269\) | 11.2857 | 0.688103 | 0.344052 | − | 0.938951i | \(-0.388201\pi\) | ||||
0.344052 | + | 0.938951i | \(0.388201\pi\) | |||||||
\(270\) | 5.07602 | 0.308917 | ||||||||
\(271\) | −23.5557 | −1.43091 | −0.715453 | − | 0.698661i | \(-0.753780\pi\) | ||||
−0.715453 | + | 0.698661i | \(0.753780\pi\) | |||||||
\(272\) | −5.05914 | −0.306756 | ||||||||
\(273\) | 0.234915 | 0.0142177 | ||||||||
\(274\) | 15.8192 | 0.955671 | ||||||||
\(275\) | −2.83918 | −0.171209 | ||||||||
\(276\) | 8.40644 | 0.506008 | ||||||||
\(277\) | 21.2834 | 1.27880 | 0.639399 | − | 0.768875i | \(-0.279183\pi\) | ||||
0.639399 | + | 0.768875i | \(0.279183\pi\) | |||||||
\(278\) | 5.17609 | 0.310441 | ||||||||
\(279\) | −18.5771 | −1.11218 | ||||||||
\(280\) | 3.81201 | 0.227811 | ||||||||
\(281\) | 7.77606 | 0.463881 | 0.231941 | − | 0.972730i | \(-0.425493\pi\) | ||||
0.231941 | + | 0.972730i | \(0.425493\pi\) | |||||||
\(282\) | 0.236239 | 0.0140678 | ||||||||
\(283\) | −4.40338 | −0.261754 | −0.130877 | − | 0.991399i | \(-0.541779\pi\) | ||||
−0.130877 | + | 0.991399i | \(0.541779\pi\) | |||||||
\(284\) | 10.1208 | 0.600560 | ||||||||
\(285\) | −4.33518 | −0.256794 | ||||||||
\(286\) | −0.170527 | −0.0100835 | ||||||||
\(287\) | 10.9620 | 0.647069 | ||||||||
\(288\) | 1.94728 | 0.114745 | ||||||||
\(289\) | 8.59495 | 0.505585 | ||||||||
\(290\) | 4.58061 | 0.268983 | ||||||||
\(291\) | 15.5793 | 0.913277 | ||||||||
\(292\) | 3.63271 | 0.212588 | ||||||||
\(293\) | −22.7215 | −1.32740 | −0.663702 | − | 0.747997i | \(-0.731016\pi\) | ||||
−0.663702 | + | 0.747997i | \(0.731016\pi\) | |||||||
\(294\) | −7.72743 | −0.450673 | ||||||||
\(295\) | 8.52669 | 0.496443 | ||||||||
\(296\) | −7.17604 | −0.417099 | ||||||||
\(297\) | 14.4117 | 0.836254 | ||||||||
\(298\) | −6.58195 | −0.381282 | ||||||||
\(299\) | −0.492102 | −0.0284590 | ||||||||
\(300\) | 1.02602 | 0.0592374 | ||||||||
\(301\) | −2.69546 | −0.155364 | ||||||||
\(302\) | −19.1521 | −1.10208 | ||||||||
\(303\) | 14.1688 | 0.813974 | ||||||||
\(304\) | −4.22523 | −0.242333 | ||||||||
\(305\) | 6.74990 | 0.386498 | ||||||||
\(306\) | −9.85157 | −0.563177 | ||||||||
\(307\) | 13.1709 | 0.751705 | 0.375852 | − | 0.926680i | \(-0.377350\pi\) | ||||
0.375852 | + | 0.926680i | \(0.377350\pi\) | |||||||
\(308\) | 10.8230 | 0.616698 | ||||||||
\(309\) | 1.96067 | 0.111538 | ||||||||
\(310\) | −9.54004 | −0.541838 | ||||||||
\(311\) | 2.88029 | 0.163327 | 0.0816633 | − | 0.996660i | \(-0.473977\pi\) | ||||
0.0816633 | + | 0.996660i | \(0.473977\pi\) | |||||||
\(312\) | 0.0616249 | 0.00348882 | ||||||||
\(313\) | −9.85746 | −0.557177 | −0.278588 | − | 0.960411i | \(-0.589866\pi\) | ||||
−0.278588 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(314\) | −1.25197 | −0.0706528 | ||||||||
\(315\) | 7.42306 | 0.418242 | ||||||||
\(316\) | −4.99070 | −0.280749 | ||||||||
\(317\) | −16.8840 | −0.948297 | −0.474149 | − | 0.880445i | \(-0.657244\pi\) | ||||
−0.474149 | + | 0.880445i | \(0.657244\pi\) | |||||||
\(318\) | −2.43258 | −0.136412 | ||||||||
\(319\) | 13.0052 | 0.728151 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −13.1233 | −0.732469 | ||||||||
\(322\) | 31.2327 | 1.74053 | ||||||||
\(323\) | 21.3760 | 1.18939 | ||||||||
\(324\) | 0.633735 | 0.0352075 | ||||||||
\(325\) | −0.0600620 | −0.00333164 | ||||||||
\(326\) | −1.40366 | −0.0777415 | ||||||||
\(327\) | 13.8704 | 0.767038 | ||||||||
\(328\) | 2.87566 | 0.158782 | ||||||||
\(329\) | 0.877708 | 0.0483896 | ||||||||
\(330\) | 2.91306 | 0.160359 | ||||||||
\(331\) | −20.8767 | −1.14749 | −0.573743 | − | 0.819035i | \(-0.694509\pi\) | ||||
−0.573743 | + | 0.819035i | \(0.694509\pi\) | |||||||
\(332\) | 7.41435 | 0.406915 | ||||||||
\(333\) | −13.9737 | −0.765757 | ||||||||
\(334\) | −8.87085 | −0.485391 | ||||||||
\(335\) | −11.8218 | −0.645896 | ||||||||
\(336\) | −3.91121 | −0.213374 | ||||||||
\(337\) | 25.3229 | 1.37943 | 0.689714 | − | 0.724082i | \(-0.257736\pi\) | ||||
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(338\) | 12.9964 | 0.706911 | ||||||||
\(339\) | 7.78871 | 0.423025 | ||||||||
\(340\) | −5.05914 | −0.274371 | ||||||||
\(341\) | −27.0859 | −1.46678 | ||||||||
\(342\) | −8.22770 | −0.444903 | ||||||||
\(343\) | −2.02590 | −0.109388 | ||||||||
\(344\) | −0.707096 | −0.0381241 | ||||||||
\(345\) | 8.40644 | 0.452587 | ||||||||
\(346\) | 10.2824 | 0.552785 | ||||||||
\(347\) | −1.92580 | −0.103382 | −0.0516911 | − | 0.998663i | \(-0.516461\pi\) | ||||
−0.0516911 | + | 0.998663i | \(0.516461\pi\) | |||||||
\(348\) | −4.69981 | −0.251936 | ||||||||
\(349\) | 6.70738 | 0.359038 | 0.179519 | − | 0.983755i | \(-0.442546\pi\) | ||||
0.179519 | + | 0.983755i | \(0.442546\pi\) | |||||||
\(350\) | 3.81201 | 0.203761 | ||||||||
\(351\) | 0.304875 | 0.0162730 | ||||||||
\(352\) | 2.83918 | 0.151329 | ||||||||
\(353\) | −30.5721 | −1.62719 | −0.813595 | − | 0.581432i | \(-0.802493\pi\) | ||||
−0.813595 | + | 0.581432i | \(0.802493\pi\) | |||||||
\(354\) | −8.74857 | −0.464981 | ||||||||
\(355\) | 10.1208 | 0.537157 | ||||||||
\(356\) | −3.81665 | −0.202282 | ||||||||
\(357\) | 19.7874 | 1.04726 | ||||||||
\(358\) | −3.08332 | −0.162959 | ||||||||
\(359\) | 21.5773 | 1.13880 | 0.569402 | − | 0.822059i | \(-0.307175\pi\) | ||||
0.569402 | + | 0.822059i | \(0.307175\pi\) | |||||||
\(360\) | 1.94728 | 0.102631 | ||||||||
\(361\) | −1.14745 | −0.0603922 | ||||||||
\(362\) | −10.7889 | −0.567050 | ||||||||
\(363\) | −3.01553 | −0.158274 | ||||||||
\(364\) | 0.228957 | 0.0120006 | ||||||||
\(365\) | 3.63271 | 0.190145 | ||||||||
\(366\) | −6.92555 | −0.362004 | ||||||||
\(367\) | 37.3989 | 1.95221 | 0.976105 | − | 0.217301i | \(-0.0697254\pi\) | ||||
0.976105 | + | 0.217301i | \(0.0697254\pi\) | |||||||
\(368\) | 8.19324 | 0.427102 | ||||||||
\(369\) | 5.59971 | 0.291509 | ||||||||
\(370\) | −7.17604 | −0.373064 | ||||||||
\(371\) | −9.03785 | −0.469222 | ||||||||
\(372\) | 9.78829 | 0.507499 | ||||||||
\(373\) | −6.26345 | −0.324309 | −0.162155 | − | 0.986765i | \(-0.551844\pi\) | ||||
−0.162155 | + | 0.986765i | \(0.551844\pi\) | |||||||
\(374\) | −14.3638 | −0.742736 | ||||||||
\(375\) | 1.02602 | 0.0529835 | ||||||||
\(376\) | 0.230248 | 0.0118741 | ||||||||
\(377\) | 0.275121 | 0.0141694 | ||||||||
\(378\) | −19.3498 | −0.995249 | ||||||||
\(379\) | 20.6983 | 1.06320 | 0.531600 | − | 0.846996i | \(-0.321591\pi\) | ||||
0.531600 | + | 0.846996i | \(0.321591\pi\) | |||||||
\(380\) | −4.22523 | −0.216750 | ||||||||
\(381\) | −7.91377 | −0.405435 | ||||||||
\(382\) | −22.1217 | −1.13185 | ||||||||
\(383\) | 33.2733 | 1.70019 | 0.850093 | − | 0.526633i | \(-0.176546\pi\) | ||||
0.850093 | + | 0.526633i | \(0.176546\pi\) | |||||||
\(384\) | −1.02602 | −0.0523590 | ||||||||
\(385\) | 10.8230 | 0.551591 | ||||||||
\(386\) | 16.6942 | 0.849711 | ||||||||
\(387\) | −1.37691 | −0.0699925 | ||||||||
\(388\) | 15.1842 | 0.770862 | ||||||||
\(389\) | 6.30931 | 0.319895 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(390\) | 0.0616249 | 0.00312050 | ||||||||
\(391\) | −41.4508 | −2.09626 | ||||||||
\(392\) | −7.53145 | −0.380396 | ||||||||
\(393\) | 15.3168 | 0.772631 | ||||||||
\(394\) | 21.6286 | 1.08963 | ||||||||
\(395\) | −4.99070 | −0.251110 | ||||||||
\(396\) | 5.52868 | 0.277827 | ||||||||
\(397\) | 32.9865 | 1.65555 | 0.827773 | − | 0.561063i | \(-0.189607\pi\) | ||||
0.827773 | + | 0.561063i | \(0.189607\pi\) | |||||||
\(398\) | 5.08690 | 0.254983 | ||||||||
\(399\) | 16.5258 | 0.827322 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 12.1295 | 0.604963 | ||||||||
\(403\) | −0.572994 | −0.0285428 | ||||||||
\(404\) | 13.8094 | 0.687044 | ||||||||
\(405\) | 0.633735 | 0.0314905 | ||||||||
\(406\) | −17.4614 | −0.866593 | ||||||||
\(407\) | −20.3741 | −1.00991 | ||||||||
\(408\) | 5.19079 | 0.256983 | ||||||||
\(409\) | −11.5782 | −0.572506 | −0.286253 | − | 0.958154i | \(-0.592410\pi\) | ||||
−0.286253 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(410\) | 2.87566 | 0.142019 | ||||||||
\(411\) | −16.2308 | −0.800607 | ||||||||
\(412\) | 1.91094 | 0.0941452 | ||||||||
\(413\) | −32.5039 | −1.59941 | ||||||||
\(414\) | 15.9545 | 0.784122 | ||||||||
\(415\) | 7.41435 | 0.363956 | ||||||||
\(416\) | 0.0600620 | 0.00294478 | ||||||||
\(417\) | −5.31078 | −0.260070 | ||||||||
\(418\) | −11.9962 | −0.586753 | ||||||||
\(419\) | 12.1502 | 0.593575 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(420\) | −3.91121 | −0.190847 | ||||||||
\(421\) | 14.7818 | 0.720422 | 0.360211 | − | 0.932871i | \(-0.382705\pi\) | ||||
0.360211 | + | 0.932871i | \(0.382705\pi\) | |||||||
\(422\) | −10.6499 | −0.518427 | ||||||||
\(423\) | 0.448357 | 0.0217998 | ||||||||
\(424\) | −2.37088 | −0.115140 | ||||||||
\(425\) | −5.05914 | −0.245405 | ||||||||
\(426\) | −10.3842 | −0.503115 | ||||||||
\(427\) | −25.7307 | −1.24520 | ||||||||
\(428\) | −12.7904 | −0.618249 | ||||||||
\(429\) | 0.174964 | 0.00844735 | ||||||||
\(430\) | −0.707096 | −0.0340992 | ||||||||
\(431\) | 11.2478 | 0.541786 | 0.270893 | − | 0.962610i | \(-0.412681\pi\) | ||||
0.270893 | + | 0.962610i | \(0.412681\pi\) | |||||||
\(432\) | −5.07602 | −0.244220 | ||||||||
\(433\) | 26.4507 | 1.27114 | 0.635570 | − | 0.772043i | \(-0.280765\pi\) | ||||
0.635570 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(434\) | 36.3668 | 1.74566 | ||||||||
\(435\) | −4.69981 | −0.225339 | ||||||||
\(436\) | 13.5187 | 0.647427 | ||||||||
\(437\) | −34.6183 | −1.65602 | ||||||||
\(438\) | −3.72724 | −0.178095 | ||||||||
\(439\) | 31.2270 | 1.49039 | 0.745193 | − | 0.666849i | \(-0.232357\pi\) | ||||
0.745193 | + | 0.666849i | \(0.232357\pi\) | |||||||
\(440\) | 2.83918 | 0.135353 | ||||||||
\(441\) | −14.6658 | −0.698373 | ||||||||
\(442\) | −0.303862 | −0.0144532 | ||||||||
\(443\) | 10.1216 | 0.480892 | 0.240446 | − | 0.970663i | \(-0.422706\pi\) | ||||
0.240446 | + | 0.970663i | \(0.422706\pi\) | |||||||
\(444\) | 7.36277 | 0.349422 | ||||||||
\(445\) | −3.81665 | −0.180927 | ||||||||
\(446\) | 0.372245 | 0.0176263 | ||||||||
\(447\) | 6.75322 | 0.319416 | ||||||||
\(448\) | −3.81201 | −0.180101 | ||||||||
\(449\) | −18.1971 | −0.858776 | −0.429388 | − | 0.903120i | \(-0.641271\pi\) | ||||
−0.429388 | + | 0.903120i | \(0.641271\pi\) | |||||||
\(450\) | 1.94728 | 0.0917956 | ||||||||
\(451\) | 8.16451 | 0.384452 | ||||||||
\(452\) | 7.59117 | 0.357059 | ||||||||
\(453\) | 19.6505 | 0.923259 | ||||||||
\(454\) | 4.26913 | 0.200360 | ||||||||
\(455\) | 0.228957 | 0.0107337 | ||||||||
\(456\) | 4.33518 | 0.203013 | ||||||||
\(457\) | −42.1368 | −1.97108 | −0.985539 | − | 0.169450i | \(-0.945801\pi\) | ||||
−0.985539 | + | 0.169450i | \(0.945801\pi\) | |||||||
\(458\) | 11.1730 | 0.522080 | ||||||||
\(459\) | 25.6803 | 1.19865 | ||||||||
\(460\) | 8.19324 | 0.382012 | ||||||||
\(461\) | 14.6396 | 0.681833 | 0.340917 | − | 0.940094i | \(-0.389263\pi\) | ||||
0.340917 | + | 0.940094i | \(0.389263\pi\) | |||||||
\(462\) | −11.1046 | −0.516634 | ||||||||
\(463\) | 30.1478 | 1.40109 | 0.700543 | − | 0.713610i | \(-0.252941\pi\) | ||||
0.700543 | + | 0.713610i | \(0.252941\pi\) | |||||||
\(464\) | −4.58061 | −0.212650 | ||||||||
\(465\) | 9.78829 | 0.453921 | ||||||||
\(466\) | −2.91303 | −0.134943 | ||||||||
\(467\) | −12.6979 | −0.587590 | −0.293795 | − | 0.955869i | \(-0.594918\pi\) | ||||
−0.293795 | + | 0.955869i | \(0.594918\pi\) | |||||||
\(468\) | 0.116957 | 0.00540636 | ||||||||
\(469\) | 45.0650 | 2.08091 | ||||||||
\(470\) | 0.230248 | 0.0106205 | ||||||||
\(471\) | 1.28455 | 0.0591889 | ||||||||
\(472\) | −8.52669 | −0.392473 | ||||||||
\(473\) | −2.00757 | −0.0923084 | ||||||||
\(474\) | 5.12057 | 0.235196 | ||||||||
\(475\) | −4.22523 | −0.193867 | ||||||||
\(476\) | 19.2855 | 0.883951 | ||||||||
\(477\) | −4.61677 | −0.211388 | ||||||||
\(478\) | 18.7629 | 0.858193 | ||||||||
\(479\) | 23.6094 | 1.07874 | 0.539371 | − | 0.842068i | \(-0.318662\pi\) | ||||
0.539371 | + | 0.842068i | \(0.318662\pi\) | |||||||
\(480\) | −1.02602 | −0.0468313 | ||||||||
\(481\) | −0.431007 | −0.0196522 | ||||||||
\(482\) | −5.17217 | −0.235586 | ||||||||
\(483\) | −32.0455 | −1.45812 | ||||||||
\(484\) | −2.93905 | −0.133593 | ||||||||
\(485\) | 15.1842 | 0.689480 | ||||||||
\(486\) | −15.8783 | −0.720253 | ||||||||
\(487\) | 32.6718 | 1.48050 | 0.740250 | − | 0.672332i | \(-0.234707\pi\) | ||||
0.740250 | + | 0.672332i | \(0.234707\pi\) | |||||||
\(488\) | −6.74990 | −0.305554 | ||||||||
\(489\) | 1.44018 | 0.0651274 | ||||||||
\(490\) | −7.53145 | −0.340236 | ||||||||
\(491\) | 15.6896 | 0.708061 | 0.354031 | − | 0.935234i | \(-0.384811\pi\) | ||||
0.354031 | + | 0.935234i | \(0.384811\pi\) | |||||||
\(492\) | −2.95049 | −0.133018 | ||||||||
\(493\) | 23.1740 | 1.04370 | ||||||||
\(494\) | −0.253775 | −0.0114179 | ||||||||
\(495\) | 5.52868 | 0.248496 | ||||||||
\(496\) | 9.54004 | 0.428361 | ||||||||
\(497\) | −38.5807 | −1.73058 | ||||||||
\(498\) | −7.60728 | −0.340890 | ||||||||
\(499\) | 17.9501 | 0.803559 | 0.401779 | − | 0.915736i | \(-0.368392\pi\) | ||||
0.401779 | + | 0.915736i | \(0.368392\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 9.10169 | 0.406633 | ||||||||
\(502\) | 1.37020 | 0.0611552 | ||||||||
\(503\) | −23.0559 | −1.02801 | −0.514006 | − | 0.857786i | \(-0.671839\pi\) | ||||
−0.514006 | + | 0.857786i | \(0.671839\pi\) | |||||||
\(504\) | −7.42306 | −0.330649 | ||||||||
\(505\) | 13.8094 | 0.614511 | ||||||||
\(506\) | 23.2621 | 1.03413 | ||||||||
\(507\) | −13.3346 | −0.592210 | ||||||||
\(508\) | −7.71307 | −0.342212 | ||||||||
\(509\) | −13.0484 | −0.578361 | −0.289181 | − | 0.957275i | \(-0.593383\pi\) | ||||
−0.289181 | + | 0.957275i | \(0.593383\pi\) | |||||||
\(510\) | 5.19079 | 0.229852 | ||||||||
\(511\) | −13.8480 | −0.612597 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.4473 | 0.946923 | ||||||||
\(514\) | 26.3103 | 1.16050 | ||||||||
\(515\) | 1.91094 | 0.0842061 | ||||||||
\(516\) | 0.725496 | 0.0319382 | ||||||||
\(517\) | 0.653715 | 0.0287504 | ||||||||
\(518\) | 27.3552 | 1.20192 | ||||||||
\(519\) | −10.5500 | −0.463092 | ||||||||
\(520\) | 0.0600620 | 0.00263389 | ||||||||
\(521\) | 9.36957 | 0.410488 | 0.205244 | − | 0.978711i | \(-0.434201\pi\) | ||||
0.205244 | + | 0.978711i | \(0.434201\pi\) | |||||||
\(522\) | −8.91973 | −0.390406 | ||||||||
\(523\) | 15.6961 | 0.686343 | 0.343172 | − | 0.939273i | \(-0.388499\pi\) | ||||
0.343172 | + | 0.939273i | \(0.388499\pi\) | |||||||
\(524\) | 14.9284 | 0.652148 | ||||||||
\(525\) | −3.91121 | −0.170699 | ||||||||
\(526\) | 7.70166 | 0.335808 | ||||||||
\(527\) | −48.2645 | −2.10243 | ||||||||
\(528\) | −2.91306 | −0.126775 | ||||||||
\(529\) | 44.1291 | 1.91866 | ||||||||
\(530\) | −2.37088 | −0.102985 | ||||||||
\(531\) | −16.6038 | −0.720545 | ||||||||
\(532\) | 16.1066 | 0.698311 | ||||||||
\(533\) | 0.172718 | 0.00748123 | ||||||||
\(534\) | 3.91597 | 0.169460 | ||||||||
\(535\) | −12.7904 | −0.552979 | ||||||||
\(536\) | 11.8218 | 0.510626 | ||||||||
\(537\) | 3.16355 | 0.136517 | ||||||||
\(538\) | −11.2857 | −0.486562 | ||||||||
\(539\) | −21.3832 | −0.921038 | ||||||||
\(540\) | −5.07602 | −0.218437 | ||||||||
\(541\) | 3.97637 | 0.170957 | 0.0854786 | − | 0.996340i | \(-0.472758\pi\) | ||||
0.0854786 | + | 0.996340i | \(0.472758\pi\) | |||||||
\(542\) | 23.5557 | 1.01180 | ||||||||
\(543\) | 11.0696 | 0.475042 | ||||||||
\(544\) | 5.05914 | 0.216909 | ||||||||
\(545\) | 13.5187 | 0.579076 | ||||||||
\(546\) | −0.234915 | −0.0100534 | ||||||||
\(547\) | 12.2263 | 0.522760 | 0.261380 | − | 0.965236i | \(-0.415822\pi\) | ||||
0.261380 | + | 0.965236i | \(0.415822\pi\) | |||||||
\(548\) | −15.8192 | −0.675762 | ||||||||
\(549\) | −13.1439 | −0.560970 | ||||||||
\(550\) | 2.83918 | 0.121063 | ||||||||
\(551\) | 19.3541 | 0.824514 | ||||||||
\(552\) | −8.40644 | −0.357802 | ||||||||
\(553\) | 19.0246 | 0.809010 | ||||||||
\(554\) | −21.2834 | −0.904246 | ||||||||
\(555\) | 7.36277 | 0.312532 | ||||||||
\(556\) | −5.17609 | −0.219515 | ||||||||
\(557\) | 37.1608 | 1.57455 | 0.787276 | − | 0.616601i | \(-0.211491\pi\) | ||||
0.787276 | + | 0.616601i | \(0.211491\pi\) | |||||||
\(558\) | 18.5771 | 0.786433 | ||||||||
\(559\) | −0.0424696 | −0.00179627 | ||||||||
\(560\) | −3.81201 | −0.161087 | ||||||||
\(561\) | 14.7376 | 0.622222 | ||||||||
\(562\) | −7.77606 | −0.328013 | ||||||||
\(563\) | −28.5033 | −1.20127 | −0.600635 | − | 0.799523i | \(-0.705086\pi\) | ||||
−0.600635 | + | 0.799523i | \(0.705086\pi\) | |||||||
\(564\) | −0.236239 | −0.00994747 | ||||||||
\(565\) | 7.59117 | 0.319363 | ||||||||
\(566\) | 4.40338 | 0.185088 | ||||||||
\(567\) | −2.41580 | −0.101454 | ||||||||
\(568\) | −10.1208 | −0.424660 | ||||||||
\(569\) | 7.96596 | 0.333950 | 0.166975 | − | 0.985961i | \(-0.446600\pi\) | ||||
0.166975 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(570\) | 4.33518 | 0.181581 | ||||||||
\(571\) | 32.7160 | 1.36912 | 0.684560 | − | 0.728956i | \(-0.259994\pi\) | ||||
0.684560 | + | 0.728956i | \(0.259994\pi\) | |||||||
\(572\) | 0.170527 | 0.00713008 | ||||||||
\(573\) | 22.6974 | 0.948197 | ||||||||
\(574\) | −10.9620 | −0.457547 | ||||||||
\(575\) | 8.19324 | 0.341682 | ||||||||
\(576\) | −1.94728 | −0.0811366 | ||||||||
\(577\) | 10.7239 | 0.446441 | 0.223220 | − | 0.974768i | \(-0.428343\pi\) | ||||
0.223220 | + | 0.974768i | \(0.428343\pi\) | |||||||
\(578\) | −8.59495 | −0.357503 | ||||||||
\(579\) | −17.1286 | −0.711839 | ||||||||
\(580\) | −4.58061 | −0.190200 | ||||||||
\(581\) | −28.2636 | −1.17257 | ||||||||
\(582\) | −15.5793 | −0.645784 | ||||||||
\(583\) | −6.73137 | −0.278785 | ||||||||
\(584\) | −3.63271 | −0.150323 | ||||||||
\(585\) | 0.116957 | 0.00483559 | ||||||||
\(586\) | 22.7215 | 0.938617 | ||||||||
\(587\) | 43.9953 | 1.81588 | 0.907940 | − | 0.419101i | \(-0.137655\pi\) | ||||
0.907940 | + | 0.419101i | \(0.137655\pi\) | |||||||
\(588\) | 7.72743 | 0.318674 | ||||||||
\(589\) | −40.3089 | −1.66090 | ||||||||
\(590\) | −8.52669 | −0.351038 | ||||||||
\(591\) | −22.1914 | −0.912831 | ||||||||
\(592\) | 7.17604 | 0.294933 | ||||||||
\(593\) | −5.95594 | −0.244581 | −0.122291 | − | 0.992494i | \(-0.539024\pi\) | ||||
−0.122291 | + | 0.992494i | \(0.539024\pi\) | |||||||
\(594\) | −14.4117 | −0.591321 | ||||||||
\(595\) | 19.2855 | 0.790630 | ||||||||
\(596\) | 6.58195 | 0.269607 | ||||||||
\(597\) | −5.21927 | −0.213611 | ||||||||
\(598\) | 0.492102 | 0.0201235 | ||||||||
\(599\) | −38.3330 | −1.56624 | −0.783122 | − | 0.621868i | \(-0.786374\pi\) | ||||
−0.783122 | + | 0.621868i | \(0.786374\pi\) | |||||||
\(600\) | −1.02602 | −0.0418872 | ||||||||
\(601\) | −11.9060 | −0.485655 | −0.242828 | − | 0.970069i | \(-0.578075\pi\) | ||||
−0.242828 | + | 0.970069i | \(0.578075\pi\) | |||||||
\(602\) | 2.69546 | 0.109859 | ||||||||
\(603\) | 23.0204 | 0.937464 | ||||||||
\(604\) | 19.1521 | 0.779287 | ||||||||
\(605\) | −2.93905 | −0.119489 | ||||||||
\(606\) | −14.1688 | −0.575567 | ||||||||
\(607\) | 20.0404 | 0.813417 | 0.406708 | − | 0.913558i | \(-0.366677\pi\) | ||||
0.406708 | + | 0.913558i | \(0.366677\pi\) | |||||||
\(608\) | 4.22523 | 0.171356 | ||||||||
\(609\) | 17.9157 | 0.725982 | ||||||||
\(610\) | −6.74990 | −0.273296 | ||||||||
\(611\) | 0.0138291 | 0.000559467 0 | ||||||||
\(612\) | 9.85157 | 0.398226 | ||||||||
\(613\) | −34.0665 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(614\) | −13.1709 | −0.531536 | ||||||||
\(615\) | −2.95049 | −0.118975 | ||||||||
\(616\) | −10.8230 | −0.436071 | ||||||||
\(617\) | −20.1106 | −0.809621 | −0.404811 | − | 0.914401i | \(-0.632663\pi\) | ||||
−0.404811 | + | 0.914401i | \(0.632663\pi\) | |||||||
\(618\) | −1.96067 | −0.0788695 | ||||||||
\(619\) | 40.3475 | 1.62170 | 0.810852 | − | 0.585251i | \(-0.199004\pi\) | ||||
0.810852 | + | 0.585251i | \(0.199004\pi\) | |||||||
\(620\) | 9.54004 | 0.383137 | ||||||||
\(621\) | −41.5890 | −1.66891 | ||||||||
\(622\) | −2.88029 | −0.115489 | ||||||||
\(623\) | 14.5491 | 0.582898 | ||||||||
\(624\) | −0.0616249 | −0.00246697 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.85746 | 0.393983 | ||||||||
\(627\) | 12.3084 | 0.491548 | ||||||||
\(628\) | 1.25197 | 0.0499590 | ||||||||
\(629\) | −36.3046 | −1.44756 | ||||||||
\(630\) | −7.42306 | −0.295742 | ||||||||
\(631\) | 18.2878 | 0.728024 | 0.364012 | − | 0.931394i | \(-0.381407\pi\) | ||||
0.364012 | + | 0.931394i | \(0.381407\pi\) | |||||||
\(632\) | 4.99070 | 0.198520 | ||||||||
\(633\) | 10.9270 | 0.434309 | ||||||||
\(634\) | 16.8840 | 0.670548 | ||||||||
\(635\) | −7.71307 | −0.306084 | ||||||||
\(636\) | 2.43258 | 0.0964580 | ||||||||
\(637\) | −0.452354 | −0.0179229 | ||||||||
\(638\) | −13.0052 | −0.514881 | ||||||||
\(639\) | −19.7080 | −0.779638 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −45.6341 | −1.80244 | −0.901218 | − | 0.433365i | \(-0.857326\pi\) | ||||
−0.901218 | + | 0.433365i | \(0.857326\pi\) | |||||||
\(642\) | 13.1233 | 0.517934 | ||||||||
\(643\) | −38.6173 | −1.52292 | −0.761458 | − | 0.648214i | \(-0.775516\pi\) | ||||
−0.761458 | + | 0.648214i | \(0.775516\pi\) | |||||||
\(644\) | −31.2327 | −1.23074 | ||||||||
\(645\) | 0.725496 | 0.0285664 | ||||||||
\(646\) | −21.3760 | −0.841029 | ||||||||
\(647\) | −43.8955 | −1.72571 | −0.862855 | − | 0.505451i | \(-0.831326\pi\) | ||||
−0.862855 | + | 0.505451i | \(0.831326\pi\) | |||||||
\(648\) | −0.633735 | −0.0248954 | ||||||||
\(649\) | −24.2088 | −0.950279 | ||||||||
\(650\) | 0.0600620 | 0.00235582 | ||||||||
\(651\) | −37.3131 | −1.46242 | ||||||||
\(652\) | 1.40366 | 0.0549715 | ||||||||
\(653\) | −3.12228 | −0.122184 | −0.0610922 | − | 0.998132i | \(-0.519458\pi\) | ||||
−0.0610922 | + | 0.998132i | \(0.519458\pi\) | |||||||
\(654\) | −13.8704 | −0.542377 | ||||||||
\(655\) | 14.9284 | 0.583299 | ||||||||
\(656\) | −2.87566 | −0.112275 | ||||||||
\(657\) | −7.07391 | −0.275979 | ||||||||
\(658\) | −0.877708 | −0.0342166 | ||||||||
\(659\) | 25.4076 | 0.989738 | 0.494869 | − | 0.868968i | \(-0.335216\pi\) | ||||
0.494869 | + | 0.868968i | \(0.335216\pi\) | |||||||
\(660\) | −2.91306 | −0.113391 | ||||||||
\(661\) | −26.9407 | −1.04787 | −0.523936 | − | 0.851758i | \(-0.675537\pi\) | ||||
−0.523936 | + | 0.851758i | \(0.675537\pi\) | |||||||
\(662\) | 20.8767 | 0.811395 | ||||||||
\(663\) | 0.311769 | 0.0121081 | ||||||||
\(664\) | −7.41435 | −0.287732 | ||||||||
\(665\) | 16.1066 | 0.624588 | ||||||||
\(666\) | 13.9737 | 0.541472 | ||||||||
\(667\) | −37.5301 | −1.45317 | ||||||||
\(668\) | 8.87085 | 0.343224 | ||||||||
\(669\) | −0.381932 | −0.0147663 | ||||||||
\(670\) | 11.8218 | 0.456718 | ||||||||
\(671\) | −19.1642 | −0.739826 | ||||||||
\(672\) | 3.91121 | 0.150878 | ||||||||
\(673\) | 16.0826 | 0.619939 | 0.309970 | − | 0.950746i | \(-0.399681\pi\) | ||||
0.309970 | + | 0.950746i | \(0.399681\pi\) | |||||||
\(674\) | −25.3229 | −0.975403 | ||||||||
\(675\) | −5.07602 | −0.195376 | ||||||||
\(676\) | −12.9964 | −0.499861 | ||||||||
\(677\) | 11.3254 | 0.435269 | 0.217635 | − | 0.976030i | \(-0.430166\pi\) | ||||
0.217635 | + | 0.976030i | \(0.430166\pi\) | |||||||
\(678\) | −7.78871 | −0.299124 | ||||||||
\(679\) | −57.8824 | −2.22132 | ||||||||
\(680\) | 5.05914 | 0.194009 | ||||||||
\(681\) | −4.38022 | −0.167850 | ||||||||
\(682\) | 27.0859 | 1.03717 | ||||||||
\(683\) | −25.3062 | −0.968314 | −0.484157 | − | 0.874981i | \(-0.660874\pi\) | ||||
−0.484157 | + | 0.874981i | \(0.660874\pi\) | |||||||
\(684\) | 8.22770 | 0.314594 | ||||||||
\(685\) | −15.8192 | −0.604420 | ||||||||
\(686\) | 2.02590 | 0.0773492 | ||||||||
\(687\) | −11.4637 | −0.437369 | ||||||||
\(688\) | 0.707096 | 0.0269578 | ||||||||
\(689\) | −0.142400 | −0.00542501 | ||||||||
\(690\) | −8.40644 | −0.320028 | ||||||||
\(691\) | −41.2801 | −1.57037 | −0.785185 | − | 0.619262i | \(-0.787432\pi\) | ||||
−0.785185 | + | 0.619262i | \(0.787432\pi\) | |||||||
\(692\) | −10.2824 | −0.390878 | ||||||||
\(693\) | −21.0754 | −0.800588 | ||||||||
\(694\) | 1.92580 | 0.0731023 | ||||||||
\(695\) | −5.17609 | −0.196340 | ||||||||
\(696\) | 4.69981 | 0.178146 | ||||||||
\(697\) | 14.5484 | 0.551058 | ||||||||
\(698\) | −6.70738 | −0.253878 | ||||||||
\(699\) | 2.98883 | 0.113048 | ||||||||
\(700\) | −3.81201 | −0.144081 | ||||||||
\(701\) | 10.8088 | 0.408242 | 0.204121 | − | 0.978946i | \(-0.434566\pi\) | ||||
0.204121 | + | 0.978946i | \(0.434566\pi\) | |||||||
\(702\) | −0.304875 | −0.0115068 | ||||||||
\(703\) | −30.3204 | −1.14356 | ||||||||
\(704\) | −2.83918 | −0.107006 | ||||||||
\(705\) | −0.236239 | −0.00889728 | ||||||||
\(706\) | 30.5721 | 1.15060 | ||||||||
\(707\) | −52.6417 | −1.97979 | ||||||||
\(708\) | 8.74857 | 0.328791 | ||||||||
\(709\) | 37.1722 | 1.39603 | 0.698016 | − | 0.716082i | \(-0.254066\pi\) | ||||
0.698016 | + | 0.716082i | \(0.254066\pi\) | |||||||
\(710\) | −10.1208 | −0.379827 | ||||||||
\(711\) | 9.71829 | 0.364465 | ||||||||
\(712\) | 3.81665 | 0.143035 | ||||||||
\(713\) | 78.1638 | 2.92726 | ||||||||
\(714\) | −19.7874 | −0.740524 | ||||||||
\(715\) | 0.170527 | 0.00637734 | ||||||||
\(716\) | 3.08332 | 0.115229 | ||||||||
\(717\) | −19.2511 | −0.718946 | ||||||||
\(718\) | −21.5773 | −0.805256 | ||||||||
\(719\) | −22.8945 | −0.853820 | −0.426910 | − | 0.904294i | \(-0.640398\pi\) | ||||
−0.426910 | + | 0.904294i | \(0.640398\pi\) | |||||||
\(720\) | −1.94728 | −0.0725708 | ||||||||
\(721\) | −7.28453 | −0.271290 | ||||||||
\(722\) | 1.14745 | 0.0427037 | ||||||||
\(723\) | 5.30676 | 0.197360 | ||||||||
\(724\) | 10.7889 | 0.400965 | ||||||||
\(725\) | −4.58061 | −0.170120 | ||||||||
\(726\) | 3.01553 | 0.111917 | ||||||||
\(727\) | 30.7558 | 1.14067 | 0.570334 | − | 0.821413i | \(-0.306814\pi\) | ||||
0.570334 | + | 0.821413i | \(0.306814\pi\) | |||||||
\(728\) | −0.228957 | −0.00848571 | ||||||||
\(729\) | 14.3903 | 0.532972 | ||||||||
\(730\) | −3.63271 | −0.134453 | ||||||||
\(731\) | −3.57730 | −0.132311 | ||||||||
\(732\) | 6.92555 | 0.255976 | ||||||||
\(733\) | 8.99157 | 0.332111 | 0.166056 | − | 0.986116i | \(-0.446897\pi\) | ||||
0.166056 | + | 0.986116i | \(0.446897\pi\) | |||||||
\(734\) | −37.3989 | −1.38042 | ||||||||
\(735\) | 7.72743 | 0.285031 | ||||||||
\(736\) | −8.19324 | −0.302007 | ||||||||
\(737\) | 33.5644 | 1.23636 | ||||||||
\(738\) | −5.59971 | −0.206128 | ||||||||
\(739\) | 10.2220 | 0.376023 | 0.188012 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188012 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(740\) | 7.17604 | 0.263796 | ||||||||
\(741\) | 0.260379 | 0.00956527 | ||||||||
\(742\) | 9.03785 | 0.331790 | ||||||||
\(743\) | −24.5826 | −0.901849 | −0.450924 | − | 0.892562i | \(-0.648906\pi\) | ||||
−0.450924 | + | 0.892562i | \(0.648906\pi\) | |||||||
\(744\) | −9.78829 | −0.358856 | ||||||||
\(745\) | 6.58195 | 0.241144 | ||||||||
\(746\) | 6.26345 | 0.229321 | ||||||||
\(747\) | −14.4378 | −0.528252 | ||||||||
\(748\) | 14.3638 | 0.525194 | ||||||||
\(749\) | 48.7573 | 1.78155 | ||||||||
\(750\) | −1.02602 | −0.0374650 | ||||||||
\(751\) | 43.0736 | 1.57178 | 0.785888 | − | 0.618369i | \(-0.212206\pi\) | ||||
0.785888 | + | 0.618369i | \(0.212206\pi\) | |||||||
\(752\) | −0.230248 | −0.00839627 | ||||||||
\(753\) | −1.40586 | −0.0512324 | ||||||||
\(754\) | −0.275121 | −0.0100193 | ||||||||
\(755\) | 19.1521 | 0.697016 | ||||||||
\(756\) | 19.3498 | 0.703747 | ||||||||
\(757\) | −3.24488 | −0.117937 | −0.0589685 | − | 0.998260i | \(-0.518781\pi\) | ||||
−0.0589685 | + | 0.998260i | \(0.518781\pi\) | |||||||
\(758\) | −20.6983 | −0.751795 | ||||||||
\(759\) | −23.8674 | −0.866332 | ||||||||
\(760\) | 4.22523 | 0.153265 | ||||||||
\(761\) | 13.6532 | 0.494927 | 0.247464 | − | 0.968897i | \(-0.420403\pi\) | ||||
0.247464 | + | 0.968897i | \(0.420403\pi\) | |||||||
\(762\) | 7.91377 | 0.286686 | ||||||||
\(763\) | −51.5334 | −1.86563 | ||||||||
\(764\) | 22.1217 | 0.800337 | ||||||||
\(765\) | 9.85157 | 0.356184 | ||||||||
\(766\) | −33.2733 | −1.20221 | ||||||||
\(767\) | −0.512129 | −0.0184919 | ||||||||
\(768\) | 1.02602 | 0.0370234 | ||||||||
\(769\) | 38.8276 | 1.40016 | 0.700080 | − | 0.714064i | \(-0.253147\pi\) | ||||
0.700080 | + | 0.714064i | \(0.253147\pi\) | |||||||
\(770\) | −10.8230 | −0.390034 | ||||||||
\(771\) | −26.9949 | −0.972198 | ||||||||
\(772\) | −16.6942 | −0.600836 | ||||||||
\(773\) | −48.6195 | −1.74872 | −0.874362 | − | 0.485275i | \(-0.838720\pi\) | ||||
−0.874362 | + | 0.485275i | \(0.838720\pi\) | |||||||
\(774\) | 1.37691 | 0.0494922 | ||||||||
\(775\) | 9.54004 | 0.342688 | ||||||||
\(776\) | −15.1842 | −0.545081 | ||||||||
\(777\) | −28.0670 | −1.00690 | ||||||||
\(778\) | −6.30931 | −0.226200 | ||||||||
\(779\) | 12.1503 | 0.435330 | ||||||||
\(780\) | −0.0616249 | −0.00220652 | ||||||||
\(781\) | −28.7348 | −1.02821 | ||||||||
\(782\) | 41.4508 | 1.48228 | ||||||||
\(783\) | 23.2513 | 0.830933 | ||||||||
\(784\) | 7.53145 | 0.268980 | ||||||||
\(785\) | 1.25197 | 0.0446847 | ||||||||
\(786\) | −15.3168 | −0.546333 | ||||||||
\(787\) | −12.4110 | −0.442404 | −0.221202 | − | 0.975228i | \(-0.570998\pi\) | ||||
−0.221202 | + | 0.975228i | \(0.570998\pi\) | |||||||
\(788\) | −21.6286 | −0.770486 | ||||||||
\(789\) | −7.90207 | −0.281321 | ||||||||
\(790\) | 4.99070 | 0.177561 | ||||||||
\(791\) | −28.9377 | −1.02890 | ||||||||
\(792\) | −5.52868 | −0.196453 | ||||||||
\(793\) | −0.405412 | −0.0143966 | ||||||||
\(794\) | −32.9865 | −1.17065 | ||||||||
\(795\) | 2.43258 | 0.0862747 | ||||||||
\(796\) | −5.08690 | −0.180300 | ||||||||
\(797\) | −16.8737 | −0.597695 | −0.298848 | − | 0.954301i | \(-0.596602\pi\) | ||||
−0.298848 | + | 0.954301i | \(0.596602\pi\) | |||||||
\(798\) | −16.5258 | −0.585005 | ||||||||
\(799\) | 1.16486 | 0.0412097 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 7.43209 | 0.262600 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −10.3139 | −0.363971 | ||||||||
\(804\) | −12.1295 | −0.427773 | ||||||||
\(805\) | −31.2327 | −1.10081 | ||||||||
\(806\) | 0.572994 | 0.0201828 | ||||||||
\(807\) | 11.5794 | 0.407614 | ||||||||
\(808\) | −13.8094 | −0.485814 | ||||||||
\(809\) | −3.13494 | −0.110219 | −0.0551093 | − | 0.998480i | \(-0.517551\pi\) | ||||
−0.0551093 | + | 0.998480i | \(0.517551\pi\) | |||||||
\(810\) | −0.633735 | −0.0222672 | ||||||||
\(811\) | 40.7686 | 1.43158 | 0.715790 | − | 0.698315i | \(-0.246067\pi\) | ||||
0.715790 | + | 0.698315i | \(0.246067\pi\) | |||||||
\(812\) | 17.4614 | 0.612774 | ||||||||
\(813\) | −24.1687 | −0.847632 | ||||||||
\(814\) | 20.3741 | 0.714111 | ||||||||
\(815\) | 1.40366 | 0.0491680 | ||||||||
\(816\) | −5.19079 | −0.181714 | ||||||||
\(817\) | −2.98764 | −0.104524 | ||||||||
\(818\) | 11.5782 | 0.404823 | ||||||||
\(819\) | −0.445843 | −0.0155790 | ||||||||
\(820\) | −2.87566 | −0.100422 | ||||||||
\(821\) | 11.8701 | 0.414268 | 0.207134 | − | 0.978313i | \(-0.433586\pi\) | ||||
0.207134 | + | 0.978313i | \(0.433586\pi\) | |||||||
\(822\) | 16.2308 | 0.566115 | ||||||||
\(823\) | −5.66292 | −0.197397 | −0.0986986 | − | 0.995117i | \(-0.531468\pi\) | ||||
−0.0986986 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(824\) | −1.91094 | −0.0665707 | ||||||||
\(825\) | −2.91306 | −0.101420 | ||||||||
\(826\) | 32.5039 | 1.13095 | ||||||||
\(827\) | 26.7734 | 0.931004 | 0.465502 | − | 0.885047i | \(-0.345874\pi\) | ||||
0.465502 | + | 0.885047i | \(0.345874\pi\) | |||||||
\(828\) | −15.9545 | −0.554458 | ||||||||
\(829\) | −19.4425 | −0.675266 | −0.337633 | − | 0.941278i | \(-0.609626\pi\) | ||||
−0.337633 | + | 0.941278i | \(0.609626\pi\) | |||||||
\(830\) | −7.41435 | −0.257356 | ||||||||
\(831\) | 21.8373 | 0.757526 | ||||||||
\(832\) | −0.0600620 | −0.00208227 | ||||||||
\(833\) | −38.1027 | −1.32018 | ||||||||
\(834\) | 5.31078 | 0.183897 | ||||||||
\(835\) | 8.87085 | 0.306989 | ||||||||
\(836\) | 11.9962 | 0.414897 | ||||||||
\(837\) | −48.4254 | −1.67383 | ||||||||
\(838\) | −12.1502 | −0.419721 | ||||||||
\(839\) | 31.7180 | 1.09503 | 0.547513 | − | 0.836797i | \(-0.315575\pi\) | ||||
0.547513 | + | 0.836797i | \(0.315575\pi\) | |||||||
\(840\) | 3.91121 | 0.134950 | ||||||||
\(841\) | −8.01798 | −0.276482 | ||||||||
\(842\) | −14.7818 | −0.509415 | ||||||||
\(843\) | 7.97841 | 0.274791 | ||||||||
\(844\) | 10.6499 | 0.366583 | ||||||||
\(845\) | −12.9964 | −0.447089 | ||||||||
\(846\) | −0.448357 | −0.0154148 | ||||||||
\(847\) | 11.2037 | 0.384963 | ||||||||
\(848\) | 2.37088 | 0.0814165 | ||||||||
\(849\) | −4.51796 | −0.155056 | ||||||||
\(850\) | 5.05914 | 0.173527 | ||||||||
\(851\) | 58.7950 | 2.01547 | ||||||||
\(852\) | 10.3842 | 0.355756 | ||||||||
\(853\) | 50.8955 | 1.74263 | 0.871314 | − | 0.490726i | \(-0.163268\pi\) | ||||
0.871314 | + | 0.490726i | \(0.163268\pi\) | |||||||
\(854\) | 25.7307 | 0.880487 | ||||||||
\(855\) | 8.22770 | 0.281381 | ||||||||
\(856\) | 12.7904 | 0.437168 | ||||||||
\(857\) | 1.65949 | 0.0566872 | 0.0283436 | − | 0.999598i | \(-0.490977\pi\) | ||||
0.0283436 | + | 0.999598i | \(0.490977\pi\) | |||||||
\(858\) | −0.174964 | −0.00597318 | ||||||||
\(859\) | −30.3290 | −1.03481 | −0.517405 | − | 0.855740i | \(-0.673102\pi\) | ||||
−0.517405 | + | 0.855740i | \(0.673102\pi\) | |||||||
\(860\) | 0.707096 | 0.0241118 | ||||||||
\(861\) | 11.2473 | 0.383307 | ||||||||
\(862\) | −11.2478 | −0.383100 | ||||||||
\(863\) | 45.8012 | 1.55909 | 0.779545 | − | 0.626346i | \(-0.215450\pi\) | ||||
0.779545 | + | 0.626346i | \(0.215450\pi\) | |||||||
\(864\) | 5.07602 | 0.172690 | ||||||||
\(865\) | −10.2824 | −0.349612 | ||||||||
\(866\) | −26.4507 | −0.898832 | ||||||||
\(867\) | 8.81860 | 0.299495 | ||||||||
\(868\) | −36.3668 | −1.23437 | ||||||||
\(869\) | 14.1695 | 0.480668 | ||||||||
\(870\) | 4.69981 | 0.159338 | ||||||||
\(871\) | 0.710043 | 0.0240589 | ||||||||
\(872\) | −13.5187 | −0.457800 | ||||||||
\(873\) | −29.5679 | −1.00072 | ||||||||
\(874\) | 34.6183 | 1.17098 | ||||||||
\(875\) | −3.81201 | −0.128870 | ||||||||
\(876\) | 3.72724 | 0.125932 | ||||||||
\(877\) | 41.1733 | 1.39032 | 0.695161 | − | 0.718854i | \(-0.255333\pi\) | ||||
0.695161 | + | 0.718854i | \(0.255333\pi\) | |||||||
\(878\) | −31.2270 | −1.05386 | ||||||||
\(879\) | −23.3128 | −0.786320 | ||||||||
\(880\) | −2.83918 | −0.0957088 | ||||||||
\(881\) | 29.8656 | 1.00620 | 0.503099 | − | 0.864229i | \(-0.332193\pi\) | ||||
0.503099 | + | 0.864229i | \(0.332193\pi\) | |||||||
\(882\) | 14.6658 | 0.493824 | ||||||||
\(883\) | −51.6300 | −1.73749 | −0.868744 | − | 0.495261i | \(-0.835072\pi\) | ||||
−0.868744 | + | 0.495261i | \(0.835072\pi\) | |||||||
\(884\) | 0.303862 | 0.0102200 | ||||||||
\(885\) | 8.74857 | 0.294080 | ||||||||
\(886\) | −10.1216 | −0.340042 | ||||||||
\(887\) | −17.2285 | −0.578475 | −0.289238 | − | 0.957257i | \(-0.593402\pi\) | ||||
−0.289238 | + | 0.957257i | \(0.593402\pi\) | |||||||
\(888\) | −7.36277 | −0.247078 | ||||||||
\(889\) | 29.4023 | 0.986122 | ||||||||
\(890\) | 3.81665 | 0.127934 | ||||||||
\(891\) | −1.79929 | −0.0602784 | ||||||||
\(892\) | −0.372245 | −0.0124637 | ||||||||
\(893\) | 0.972849 | 0.0325552 | ||||||||
\(894\) | −6.75322 | −0.225862 | ||||||||
\(895\) | 3.08332 | 0.103064 | ||||||||
\(896\) | 3.81201 | 0.127350 | ||||||||
\(897\) | −0.504907 | −0.0168584 | ||||||||
\(898\) | 18.1971 | 0.607246 | ||||||||
\(899\) | −43.6993 | −1.45745 | ||||||||
\(900\) | −1.94728 | −0.0649093 | ||||||||
\(901\) | −11.9946 | −0.399600 | ||||||||
\(902\) | −8.16451 | −0.271848 | ||||||||
\(903\) | −2.76560 | −0.0920335 | ||||||||
\(904\) | −7.59117 | −0.252479 | ||||||||
\(905\) | 10.7889 | 0.358634 | ||||||||
\(906\) | −19.6505 | −0.652843 | ||||||||
\(907\) | 19.1681 | 0.636466 | 0.318233 | − | 0.948013i | \(-0.396911\pi\) | ||||
0.318233 | + | 0.948013i | \(0.396911\pi\) | |||||||
\(908\) | −4.26913 | −0.141676 | ||||||||
\(909\) | −26.8908 | −0.891911 | ||||||||
\(910\) | −0.228957 | −0.00758985 | ||||||||
\(911\) | −32.6092 | −1.08039 | −0.540195 | − | 0.841540i | \(-0.681650\pi\) | ||||
−0.540195 | + | 0.841540i | \(0.681650\pi\) | |||||||
\(912\) | −4.33518 | −0.143552 | ||||||||
\(913\) | −21.0507 | −0.696676 | ||||||||
\(914\) | 42.1368 | 1.39376 | ||||||||
\(915\) | 6.92555 | 0.228951 | ||||||||
\(916\) | −11.1730 | −0.369166 | ||||||||
\(917\) | −56.9071 | −1.87924 | ||||||||
\(918\) | −25.6803 | −0.847576 | ||||||||
\(919\) | 9.02246 | 0.297624 | 0.148812 | − | 0.988866i | \(-0.452455\pi\) | ||||
0.148812 | + | 0.988866i | \(0.452455\pi\) | |||||||
\(920\) | −8.19324 | −0.270123 | ||||||||
\(921\) | 13.5137 | 0.445290 | ||||||||
\(922\) | −14.6396 | −0.482129 | ||||||||
\(923\) | −0.607876 | −0.0200085 | ||||||||
\(924\) | 11.1046 | 0.365316 | ||||||||
\(925\) | 7.17604 | 0.235947 | ||||||||
\(926\) | −30.1478 | −0.990717 | ||||||||
\(927\) | −3.72113 | −0.122218 | ||||||||
\(928\) | 4.58061 | 0.150366 | ||||||||
\(929\) | 27.0139 | 0.886296 | 0.443148 | − | 0.896448i | \(-0.353862\pi\) | ||||
0.443148 | + | 0.896448i | \(0.353862\pi\) | |||||||
\(930\) | −9.78829 | −0.320971 | ||||||||
\(931\) | −31.8221 | −1.04293 | ||||||||
\(932\) | 2.91303 | 0.0954194 | ||||||||
\(933\) | 2.95525 | 0.0967504 | ||||||||
\(934\) | 12.6979 | 0.415489 | ||||||||
\(935\) | 14.3638 | 0.469748 | ||||||||
\(936\) | −0.116957 | −0.00382287 | ||||||||
\(937\) | −22.8518 | −0.746537 | −0.373269 | − | 0.927723i | \(-0.621763\pi\) | ||||
−0.373269 | + | 0.927723i | \(0.621763\pi\) | |||||||
\(938\) | −45.0650 | −1.47143 | ||||||||
\(939\) | −10.1140 | −0.330057 | ||||||||
\(940\) | −0.230248 | −0.00750985 | ||||||||
\(941\) | −13.8813 | −0.452516 | −0.226258 | − | 0.974067i | \(-0.572649\pi\) | ||||
−0.226258 | + | 0.974067i | \(0.572649\pi\) | |||||||
\(942\) | −1.28455 | −0.0418529 | ||||||||
\(943\) | −23.5609 | −0.767249 | ||||||||
\(944\) | 8.52669 | 0.277520 | ||||||||
\(945\) | 19.3498 | 0.629451 | ||||||||
\(946\) | 2.00757 | 0.0652719 | ||||||||
\(947\) | −13.2755 | −0.431395 | −0.215698 | − | 0.976460i | \(-0.569203\pi\) | ||||
−0.215698 | + | 0.976460i | \(0.569203\pi\) | |||||||
\(948\) | −5.12057 | −0.166308 | ||||||||
\(949\) | −0.218188 | −0.00708268 | ||||||||
\(950\) | 4.22523 | 0.137084 | ||||||||
\(951\) | −17.3233 | −0.561747 | ||||||||
\(952\) | −19.2855 | −0.625048 | ||||||||
\(953\) | −21.0095 | −0.680565 | −0.340283 | − | 0.940323i | \(-0.610523\pi\) | ||||
−0.340283 | + | 0.940323i | \(0.610523\pi\) | |||||||
\(954\) | 4.61677 | 0.149474 | ||||||||
\(955\) | 22.1217 | 0.715843 | ||||||||
\(956\) | −18.7629 | −0.606834 | ||||||||
\(957\) | 13.3436 | 0.431338 | ||||||||
\(958\) | −23.6094 | −0.762786 | ||||||||
\(959\) | 60.3029 | 1.94728 | ||||||||
\(960\) | 1.02602 | 0.0331147 | ||||||||
\(961\) | 60.0124 | 1.93588 | ||||||||
\(962\) | 0.431007 | 0.0138962 | ||||||||
\(963\) | 24.9066 | 0.802602 | ||||||||
\(964\) | 5.17217 | 0.166584 | ||||||||
\(965\) | −16.6942 | −0.537404 | ||||||||
\(966\) | 32.0455 | 1.03105 | ||||||||
\(967\) | 2.28773 | 0.0735683 | 0.0367842 | − | 0.999323i | \(-0.488289\pi\) | ||||
0.0367842 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(968\) | 2.93905 | 0.0944645 | ||||||||
\(969\) | 21.9323 | 0.704566 | ||||||||
\(970\) | −15.1842 | −0.487536 | ||||||||
\(971\) | 24.3149 | 0.780302 | 0.390151 | − | 0.920751i | \(-0.372423\pi\) | ||||
0.390151 | + | 0.920751i | \(0.372423\pi\) | |||||||
\(972\) | 15.8783 | 0.509296 | ||||||||
\(973\) | 19.7313 | 0.632557 | ||||||||
\(974\) | −32.6718 | −1.04687 | ||||||||
\(975\) | −0.0616249 | −0.00197358 | ||||||||
\(976\) | 6.74990 | 0.216059 | ||||||||
\(977\) | 42.1664 | 1.34902 | 0.674511 | − | 0.738265i | \(-0.264355\pi\) | ||||
0.674511 | + | 0.738265i | \(0.264355\pi\) | |||||||
\(978\) | −1.44018 | −0.0460520 | ||||||||
\(979\) | 10.8362 | 0.346325 | ||||||||
\(980\) | 7.53145 | 0.240583 | ||||||||
\(981\) | −26.3246 | −0.840481 | ||||||||
\(982\) | −15.6896 | −0.500675 | ||||||||
\(983\) | 16.1592 | 0.515397 | 0.257699 | − | 0.966225i | \(-0.417036\pi\) | ||||
0.257699 | + | 0.966225i | \(0.417036\pi\) | |||||||
\(984\) | 2.95049 | 0.0940580 | ||||||||
\(985\) | −21.6286 | −0.689143 | ||||||||
\(986\) | −23.1740 | −0.738010 | ||||||||
\(987\) | 0.900547 | 0.0286647 | ||||||||
\(988\) | 0.253775 | 0.00807367 | ||||||||
\(989\) | 5.79341 | 0.184220 | ||||||||
\(990\) | −5.52868 | −0.175713 | ||||||||
\(991\) | −5.51896 | −0.175316 | −0.0876578 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876578 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(992\) | −9.54004 | −0.302897 | ||||||||
\(993\) | −21.4199 | −0.679741 | ||||||||
\(994\) | 38.5807 | 1.22370 | ||||||||
\(995\) | −5.08690 | −0.161266 | ||||||||
\(996\) | 7.60728 | 0.241046 | ||||||||
\(997\) | −39.8092 | −1.26077 | −0.630384 | − | 0.776283i | \(-0.717103\pi\) | ||||
−0.630384 | + | 0.776283i | \(0.717103\pi\) | |||||||
\(998\) | −17.9501 | −0.568202 | ||||||||
\(999\) | −36.4257 | −1.15246 |
(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 | 4010.2.a.m.1.12 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.12 | ✓ | 20 | 1.1 | even | 1 | trivial |