Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(2.41044\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | 1.41044 | 0.814318 | 0.407159 | − | 0.913357i | \(-0.366519\pi\) | ||||
0.407159 | + | 0.913357i | \(0.366519\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.41044 | 0.575810 | ||||||||
\(7\) | −3.15104 | −1.19098 | −0.595490 | − | 0.803363i | \(-0.703042\pi\) | ||||
−0.595490 | + | 0.803363i | \(0.703042\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.01066 | −0.336885 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.04069 | −0.313780 | −0.156890 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156890 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(12\) | 1.41044 | 0.407159 | ||||||||
\(13\) | −3.01659 | −0.836653 | −0.418326 | − | 0.908297i | \(-0.637383\pi\) | ||||
−0.418326 | + | 0.908297i | \(0.637383\pi\) | |||||||
\(14\) | −3.15104 | −0.842150 | ||||||||
\(15\) | 1.41044 | 0.364174 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.09209 | 0.507406 | 0.253703 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253703 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(18\) | −1.01066 | −0.238214 | ||||||||
\(19\) | 3.54717 | 0.813778 | 0.406889 | − | 0.913478i | \(-0.366614\pi\) | ||||
0.406889 | + | 0.913478i | \(0.366614\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −4.44435 | −0.969837 | ||||||||
\(22\) | −1.04069 | −0.221876 | ||||||||
\(23\) | −1.80458 | −0.376281 | −0.188141 | − | 0.982142i | \(-0.560246\pi\) | ||||
−0.188141 | + | 0.982142i | \(0.560246\pi\) | |||||||
\(24\) | 1.41044 | 0.287905 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.01659 | −0.591603 | ||||||||
\(27\) | −5.65679 | −1.08865 | ||||||||
\(28\) | −3.15104 | −0.595490 | ||||||||
\(29\) | −0.429786 | −0.0798093 | −0.0399047 | − | 0.999203i | \(-0.512705\pi\) | ||||
−0.0399047 | + | 0.999203i | \(0.512705\pi\) | |||||||
\(30\) | 1.41044 | 0.257510 | ||||||||
\(31\) | −9.55437 | −1.71602 | −0.858008 | − | 0.513637i | \(-0.828298\pi\) | ||||
−0.858008 | + | 0.513637i | \(0.828298\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.46783 | −0.255517 | ||||||||
\(34\) | 2.09209 | 0.358790 | ||||||||
\(35\) | −3.15104 | −0.532622 | ||||||||
\(36\) | −1.01066 | −0.168443 | ||||||||
\(37\) | 7.40717 | 1.21773 | 0.608866 | − | 0.793273i | \(-0.291625\pi\) | ||||
0.608866 | + | 0.793273i | \(0.291625\pi\) | |||||||
\(38\) | 3.54717 | 0.575428 | ||||||||
\(39\) | −4.25473 | −0.681302 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.28453 | −1.45000 | −0.725000 | − | 0.688749i | \(-0.758160\pi\) | ||||
−0.725000 | + | 0.688749i | \(0.758160\pi\) | |||||||
\(42\) | −4.44435 | −0.685778 | ||||||||
\(43\) | −7.43486 | −1.13381 | −0.566903 | − | 0.823785i | \(-0.691858\pi\) | ||||
−0.566903 | + | 0.823785i | \(0.691858\pi\) | |||||||
\(44\) | −1.04069 | −0.156890 | ||||||||
\(45\) | −1.01066 | −0.150660 | ||||||||
\(46\) | −1.80458 | −0.266071 | ||||||||
\(47\) | −10.5989 | −1.54601 | −0.773006 | − | 0.634399i | \(-0.781248\pi\) | ||||
−0.773006 | + | 0.634399i | \(0.781248\pi\) | |||||||
\(48\) | 1.41044 | 0.203580 | ||||||||
\(49\) | 2.92903 | 0.418433 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.95077 | 0.413190 | ||||||||
\(52\) | −3.01659 | −0.418326 | ||||||||
\(53\) | −7.88673 | −1.08333 | −0.541663 | − | 0.840596i | \(-0.682205\pi\) | ||||
−0.541663 | + | 0.840596i | \(0.682205\pi\) | |||||||
\(54\) | −5.65679 | −0.769792 | ||||||||
\(55\) | −1.04069 | −0.140327 | ||||||||
\(56\) | −3.15104 | −0.421075 | ||||||||
\(57\) | 5.00308 | 0.662674 | ||||||||
\(58\) | −0.429786 | −0.0564337 | ||||||||
\(59\) | 3.06070 | 0.398469 | 0.199235 | − | 0.979952i | \(-0.436154\pi\) | ||||
0.199235 | + | 0.979952i | \(0.436154\pi\) | |||||||
\(60\) | 1.41044 | 0.182087 | ||||||||
\(61\) | −4.36339 | −0.558675 | −0.279337 | − | 0.960193i | \(-0.590115\pi\) | ||||
−0.279337 | + | 0.960193i | \(0.590115\pi\) | |||||||
\(62\) | −9.55437 | −1.21341 | ||||||||
\(63\) | 3.18461 | 0.401224 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.01659 | −0.374162 | ||||||||
\(66\) | −1.46783 | −0.180678 | ||||||||
\(67\) | 11.1448 | 1.36155 | 0.680774 | − | 0.732493i | \(-0.261643\pi\) | ||||
0.680774 | + | 0.732493i | \(0.261643\pi\) | |||||||
\(68\) | 2.09209 | 0.253703 | ||||||||
\(69\) | −2.54525 | −0.306413 | ||||||||
\(70\) | −3.15104 | −0.376621 | ||||||||
\(71\) | 8.28515 | 0.983266 | 0.491633 | − | 0.870802i | \(-0.336400\pi\) | ||||
0.491633 | + | 0.870802i | \(0.336400\pi\) | |||||||
\(72\) | −1.01066 | −0.119107 | ||||||||
\(73\) | −5.43760 | −0.636423 | −0.318212 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318212 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(74\) | 7.40717 | 0.861066 | ||||||||
\(75\) | 1.41044 | 0.162864 | ||||||||
\(76\) | 3.54717 | 0.406889 | ||||||||
\(77\) | 3.27926 | 0.373706 | ||||||||
\(78\) | −4.25473 | −0.481753 | ||||||||
\(79\) | 9.01031 | 1.01374 | 0.506869 | − | 0.862023i | \(-0.330803\pi\) | ||||
0.506869 | + | 0.862023i | \(0.330803\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −4.94661 | −0.549623 | ||||||||
\(82\) | −9.28453 | −1.02531 | ||||||||
\(83\) | 8.94926 | 0.982309 | 0.491154 | − | 0.871073i | \(-0.336575\pi\) | ||||
0.491154 | + | 0.871073i | \(0.336575\pi\) | |||||||
\(84\) | −4.44435 | −0.484918 | ||||||||
\(85\) | 2.09209 | 0.226919 | ||||||||
\(86\) | −7.43486 | −0.801721 | ||||||||
\(87\) | −0.606188 | −0.0649902 | ||||||||
\(88\) | −1.04069 | −0.110938 | ||||||||
\(89\) | −8.34070 | −0.884112 | −0.442056 | − | 0.896987i | \(-0.645751\pi\) | ||||
−0.442056 | + | 0.896987i | \(0.645751\pi\) | |||||||
\(90\) | −1.01066 | −0.106533 | ||||||||
\(91\) | 9.50540 | 0.996436 | ||||||||
\(92\) | −1.80458 | −0.188141 | ||||||||
\(93\) | −13.4759 | −1.39738 | ||||||||
\(94\) | −10.5989 | −1.09320 | ||||||||
\(95\) | 3.54717 | 0.363932 | ||||||||
\(96\) | 1.41044 | 0.143953 | ||||||||
\(97\) | 6.35468 | 0.645220 | 0.322610 | − | 0.946532i | \(-0.395440\pi\) | ||||
0.322610 | + | 0.946532i | \(0.395440\pi\) | |||||||
\(98\) | 2.92903 | 0.295877 | ||||||||
\(99\) | 1.05178 | 0.105708 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −4.10281 | −0.408245 | −0.204122 | − | 0.978945i | \(-0.565434\pi\) | ||||
−0.204122 | + | 0.978945i | \(0.565434\pi\) | |||||||
\(102\) | 2.95077 | 0.292170 | ||||||||
\(103\) | −8.66854 | −0.854136 | −0.427068 | − | 0.904219i | \(-0.640454\pi\) | ||||
−0.427068 | + | 0.904219i | \(0.640454\pi\) | |||||||
\(104\) | −3.01659 | −0.295801 | ||||||||
\(105\) | −4.44435 | −0.433724 | ||||||||
\(106\) | −7.88673 | −0.766027 | ||||||||
\(107\) | −15.3045 | −1.47954 | −0.739770 | − | 0.672860i | \(-0.765066\pi\) | ||||
−0.739770 | + | 0.672860i | \(0.765066\pi\) | |||||||
\(108\) | −5.65679 | −0.544325 | ||||||||
\(109\) | −13.5541 | −1.29825 | −0.649126 | − | 0.760681i | \(-0.724865\pi\) | ||||
−0.649126 | + | 0.760681i | \(0.724865\pi\) | |||||||
\(110\) | −1.04069 | −0.0992261 | ||||||||
\(111\) | 10.4474 | 0.991621 | ||||||||
\(112\) | −3.15104 | −0.297745 | ||||||||
\(113\) | 16.1227 | 1.51670 | 0.758349 | − | 0.651849i | \(-0.226006\pi\) | ||||
0.758349 | + | 0.651849i | \(0.226006\pi\) | |||||||
\(114\) | 5.00308 | 0.468581 | ||||||||
\(115\) | −1.80458 | −0.168278 | ||||||||
\(116\) | −0.429786 | −0.0399047 | ||||||||
\(117\) | 3.04874 | 0.281856 | ||||||||
\(118\) | 3.06070 | 0.281760 | ||||||||
\(119\) | −6.59225 | −0.604311 | ||||||||
\(120\) | 1.41044 | 0.128755 | ||||||||
\(121\) | −9.91696 | −0.901542 | ||||||||
\(122\) | −4.36339 | −0.395043 | ||||||||
\(123\) | −13.0953 | −1.18076 | ||||||||
\(124\) | −9.55437 | −0.858008 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.18461 | 0.283708 | ||||||||
\(127\) | 12.6071 | 1.11870 | 0.559351 | − | 0.828931i | \(-0.311050\pi\) | ||||
0.559351 | + | 0.828931i | \(0.311050\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.4864 | −0.923278 | ||||||||
\(130\) | −3.01659 | −0.264573 | ||||||||
\(131\) | 9.23835 | 0.807158 | 0.403579 | − | 0.914945i | \(-0.367766\pi\) | ||||
0.403579 | + | 0.914945i | \(0.367766\pi\) | |||||||
\(132\) | −1.46783 | −0.127759 | ||||||||
\(133\) | −11.1773 | −0.969193 | ||||||||
\(134\) | 11.1448 | 0.962760 | ||||||||
\(135\) | −5.65679 | −0.486859 | ||||||||
\(136\) | 2.09209 | 0.179395 | ||||||||
\(137\) | −22.3754 | −1.91166 | −0.955829 | − | 0.293925i | \(-0.905038\pi\) | ||||
−0.955829 | + | 0.293925i | \(0.905038\pi\) | |||||||
\(138\) | −2.54525 | −0.216666 | ||||||||
\(139\) | −14.1367 | −1.19906 | −0.599529 | − | 0.800353i | \(-0.704646\pi\) | ||||
−0.599529 | + | 0.800353i | \(0.704646\pi\) | |||||||
\(140\) | −3.15104 | −0.266311 | ||||||||
\(141\) | −14.9492 | −1.25895 | ||||||||
\(142\) | 8.28515 | 0.695274 | ||||||||
\(143\) | 3.13935 | 0.262525 | ||||||||
\(144\) | −1.01066 | −0.0842214 | ||||||||
\(145\) | −0.429786 | −0.0356918 | ||||||||
\(146\) | −5.43760 | −0.450019 | ||||||||
\(147\) | 4.13122 | 0.340738 | ||||||||
\(148\) | 7.40717 | 0.608866 | ||||||||
\(149\) | −7.35152 | −0.602260 | −0.301130 | − | 0.953583i | \(-0.597364\pi\) | ||||
−0.301130 | + | 0.953583i | \(0.597364\pi\) | |||||||
\(150\) | 1.41044 | 0.115162 | ||||||||
\(151\) | 16.3564 | 1.33107 | 0.665533 | − | 0.746368i | \(-0.268204\pi\) | ||||
0.665533 | + | 0.746368i | \(0.268204\pi\) | |||||||
\(152\) | 3.54717 | 0.287714 | ||||||||
\(153\) | −2.11438 | −0.170938 | ||||||||
\(154\) | 3.27926 | 0.264250 | ||||||||
\(155\) | −9.55437 | −0.767425 | ||||||||
\(156\) | −4.25473 | −0.340651 | ||||||||
\(157\) | −7.76589 | −0.619785 | −0.309893 | − | 0.950772i | \(-0.600293\pi\) | ||||
−0.309893 | + | 0.950772i | \(0.600293\pi\) | |||||||
\(158\) | 9.01031 | 0.716822 | ||||||||
\(159\) | −11.1238 | −0.882172 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.68630 | 0.448143 | ||||||||
\(162\) | −4.94661 | −0.388642 | ||||||||
\(163\) | 15.3338 | 1.20104 | 0.600519 | − | 0.799610i | \(-0.294961\pi\) | ||||
0.600519 | + | 0.799610i | \(0.294961\pi\) | |||||||
\(164\) | −9.28453 | −0.725000 | ||||||||
\(165\) | −1.46783 | −0.114271 | ||||||||
\(166\) | 8.94926 | 0.694597 | ||||||||
\(167\) | −20.5909 | −1.59337 | −0.796686 | − | 0.604393i | \(-0.793416\pi\) | ||||
−0.796686 | + | 0.604393i | \(0.793416\pi\) | |||||||
\(168\) | −4.44435 | −0.342889 | ||||||||
\(169\) | −3.90016 | −0.300012 | ||||||||
\(170\) | 2.09209 | 0.160456 | ||||||||
\(171\) | −3.58497 | −0.274150 | ||||||||
\(172\) | −7.43486 | −0.566903 | ||||||||
\(173\) | 9.79839 | 0.744958 | 0.372479 | − | 0.928041i | \(-0.378508\pi\) | ||||
0.372479 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(174\) | −0.606188 | −0.0459550 | ||||||||
\(175\) | −3.15104 | −0.238196 | ||||||||
\(176\) | −1.04069 | −0.0784451 | ||||||||
\(177\) | 4.31694 | 0.324481 | ||||||||
\(178\) | −8.34070 | −0.625162 | ||||||||
\(179\) | 11.9994 | 0.896877 | 0.448439 | − | 0.893814i | \(-0.351980\pi\) | ||||
0.448439 | + | 0.893814i | \(0.351980\pi\) | |||||||
\(180\) | −1.01066 | −0.0753299 | ||||||||
\(181\) | 0.246164 | 0.0182972 | 0.00914860 | − | 0.999958i | \(-0.497088\pi\) | ||||
0.00914860 | + | 0.999958i | \(0.497088\pi\) | |||||||
\(182\) | 9.50540 | 0.704587 | ||||||||
\(183\) | −6.15430 | −0.454939 | ||||||||
\(184\) | −1.80458 | −0.133035 | ||||||||
\(185\) | 7.40717 | 0.544586 | ||||||||
\(186\) | −13.4759 | −0.988099 | ||||||||
\(187\) | −2.17722 | −0.159214 | ||||||||
\(188\) | −10.5989 | −0.773006 | ||||||||
\(189\) | 17.8248 | 1.29656 | ||||||||
\(190\) | 3.54717 | 0.257339 | ||||||||
\(191\) | 20.4010 | 1.47617 | 0.738084 | − | 0.674709i | \(-0.235731\pi\) | ||||
0.738084 | + | 0.674709i | \(0.235731\pi\) | |||||||
\(192\) | 1.41044 | 0.101790 | ||||||||
\(193\) | 2.54753 | 0.183375 | 0.0916875 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916875 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(194\) | 6.35468 | 0.456240 | ||||||||
\(195\) | −4.25473 | −0.304687 | ||||||||
\(196\) | 2.92903 | 0.209216 | ||||||||
\(197\) | −3.59037 | −0.255803 | −0.127901 | − | 0.991787i | \(-0.540824\pi\) | ||||
−0.127901 | + | 0.991787i | \(0.540824\pi\) | |||||||
\(198\) | 1.05178 | 0.0747469 | ||||||||
\(199\) | −22.6077 | −1.60262 | −0.801308 | − | 0.598251i | \(-0.795862\pi\) | ||||
−0.801308 | + | 0.598251i | \(0.795862\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.7190 | 1.10873 | ||||||||
\(202\) | −4.10281 | −0.288673 | ||||||||
\(203\) | 1.35427 | 0.0950513 | ||||||||
\(204\) | 2.95077 | 0.206595 | ||||||||
\(205\) | −9.28453 | −0.648460 | ||||||||
\(206\) | −8.66854 | −0.603966 | ||||||||
\(207\) | 1.82381 | 0.126764 | ||||||||
\(208\) | −3.01659 | −0.209163 | ||||||||
\(209\) | −3.69152 | −0.255348 | ||||||||
\(210\) | −4.44435 | −0.306689 | ||||||||
\(211\) | −0.563633 | −0.0388021 | −0.0194011 | − | 0.999812i | \(-0.506176\pi\) | ||||
−0.0194011 | + | 0.999812i | \(0.506176\pi\) | |||||||
\(212\) | −7.88673 | −0.541663 | ||||||||
\(213\) | 11.6857 | 0.800692 | ||||||||
\(214\) | −15.3045 | −1.04619 | ||||||||
\(215\) | −7.43486 | −0.507053 | ||||||||
\(216\) | −5.65679 | −0.384896 | ||||||||
\(217\) | 30.1062 | 2.04374 | ||||||||
\(218\) | −13.5541 | −0.918002 | ||||||||
\(219\) | −7.66942 | −0.518251 | ||||||||
\(220\) | −1.04069 | −0.0701634 | ||||||||
\(221\) | −6.31099 | −0.424523 | ||||||||
\(222\) | 10.4474 | 0.701182 | ||||||||
\(223\) | −9.19193 | −0.615537 | −0.307769 | − | 0.951461i | \(-0.599582\pi\) | ||||
−0.307769 | + | 0.951461i | \(0.599582\pi\) | |||||||
\(224\) | −3.15104 | −0.210537 | ||||||||
\(225\) | −1.01066 | −0.0673771 | ||||||||
\(226\) | 16.1227 | 1.07247 | ||||||||
\(227\) | −4.76633 | −0.316353 | −0.158176 | − | 0.987411i | \(-0.550561\pi\) | ||||
−0.158176 | + | 0.987411i | \(0.550561\pi\) | |||||||
\(228\) | 5.00308 | 0.331337 | ||||||||
\(229\) | −11.9104 | −0.787060 | −0.393530 | − | 0.919312i | \(-0.628746\pi\) | ||||
−0.393530 | + | 0.919312i | \(0.628746\pi\) | |||||||
\(230\) | −1.80458 | −0.118991 | ||||||||
\(231\) | 4.62520 | 0.304316 | ||||||||
\(232\) | −0.429786 | −0.0282169 | ||||||||
\(233\) | 15.3681 | 1.00680 | 0.503398 | − | 0.864055i | \(-0.332083\pi\) | ||||
0.503398 | + | 0.864055i | \(0.332083\pi\) | |||||||
\(234\) | 3.04874 | 0.199302 | ||||||||
\(235\) | −10.5989 | −0.691398 | ||||||||
\(236\) | 3.06070 | 0.199235 | ||||||||
\(237\) | 12.7085 | 0.825506 | ||||||||
\(238\) | −6.59225 | −0.427312 | ||||||||
\(239\) | −8.67620 | −0.561217 | −0.280608 | − | 0.959822i | \(-0.590536\pi\) | ||||
−0.280608 | + | 0.959822i | \(0.590536\pi\) | |||||||
\(240\) | 1.41044 | 0.0910436 | ||||||||
\(241\) | −11.9235 | −0.768063 | −0.384031 | − | 0.923320i | \(-0.625465\pi\) | ||||
−0.384031 | + | 0.923320i | \(0.625465\pi\) | |||||||
\(242\) | −9.91696 | −0.637486 | ||||||||
\(243\) | 9.99349 | 0.641082 | ||||||||
\(244\) | −4.36339 | −0.279337 | ||||||||
\(245\) | 2.92903 | 0.187129 | ||||||||
\(246\) | −13.0953 | −0.834925 | ||||||||
\(247\) | −10.7004 | −0.680849 | ||||||||
\(248\) | −9.55437 | −0.606703 | ||||||||
\(249\) | 12.6224 | 0.799912 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −11.7240 | −0.740015 | −0.370008 | − | 0.929029i | \(-0.620645\pi\) | ||||
−0.370008 | + | 0.929029i | \(0.620645\pi\) | |||||||
\(252\) | 3.18461 | 0.200612 | ||||||||
\(253\) | 1.87801 | 0.118070 | ||||||||
\(254\) | 12.6071 | 0.791042 | ||||||||
\(255\) | 2.95077 | 0.184784 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.6262 | 1.03712 | 0.518558 | − | 0.855042i | \(-0.326469\pi\) | ||||
0.518558 | + | 0.855042i | \(0.326469\pi\) | |||||||
\(258\) | −10.4864 | −0.652856 | ||||||||
\(259\) | −23.3403 | −1.45029 | ||||||||
\(260\) | −3.01659 | −0.187081 | ||||||||
\(261\) | 0.434366 | 0.0268866 | ||||||||
\(262\) | 9.23835 | 0.570747 | ||||||||
\(263\) | 17.0636 | 1.05219 | 0.526094 | − | 0.850426i | \(-0.323656\pi\) | ||||
0.526094 | + | 0.850426i | \(0.323656\pi\) | |||||||
\(264\) | −1.46783 | −0.0903390 | ||||||||
\(265\) | −7.88673 | −0.484478 | ||||||||
\(266\) | −11.1773 | −0.685323 | ||||||||
\(267\) | −11.7641 | −0.719949 | ||||||||
\(268\) | 11.1448 | 0.680774 | ||||||||
\(269\) | −7.54805 | −0.460213 | −0.230106 | − | 0.973165i | \(-0.573907\pi\) | ||||
−0.230106 | + | 0.973165i | \(0.573907\pi\) | |||||||
\(270\) | −5.65679 | −0.344262 | ||||||||
\(271\) | 2.98704 | 0.181450 | 0.0907249 | − | 0.995876i | \(-0.471082\pi\) | ||||
0.0907249 | + | 0.995876i | \(0.471082\pi\) | |||||||
\(272\) | 2.09209 | 0.126852 | ||||||||
\(273\) | 13.4068 | 0.811417 | ||||||||
\(274\) | −22.3754 | −1.35175 | ||||||||
\(275\) | −1.04069 | −0.0627561 | ||||||||
\(276\) | −2.54525 | −0.153206 | ||||||||
\(277\) | −0.626895 | −0.0376665 | −0.0188332 | − | 0.999823i | \(-0.505995\pi\) | ||||
−0.0188332 | + | 0.999823i | \(0.505995\pi\) | |||||||
\(278\) | −14.1367 | −0.847862 | ||||||||
\(279\) | 9.65618 | 0.578101 | ||||||||
\(280\) | −3.15104 | −0.188310 | ||||||||
\(281\) | 23.0483 | 1.37495 | 0.687473 | − | 0.726210i | \(-0.258720\pi\) | ||||
0.687473 | + | 0.726210i | \(0.258720\pi\) | |||||||
\(282\) | −14.9492 | −0.890209 | ||||||||
\(283\) | 1.83831 | 0.109276 | 0.0546381 | − | 0.998506i | \(-0.482599\pi\) | ||||
0.0546381 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(284\) | 8.28515 | 0.491633 | ||||||||
\(285\) | 5.00308 | 0.296357 | ||||||||
\(286\) | 3.13935 | 0.185633 | ||||||||
\(287\) | 29.2559 | 1.72692 | ||||||||
\(288\) | −1.01066 | −0.0595535 | ||||||||
\(289\) | −12.6232 | −0.742539 | ||||||||
\(290\) | −0.429786 | −0.0252379 | ||||||||
\(291\) | 8.96291 | 0.525415 | ||||||||
\(292\) | −5.43760 | −0.318212 | ||||||||
\(293\) | −11.1006 | −0.648504 | −0.324252 | − | 0.945971i | \(-0.605113\pi\) | ||||
−0.324252 | + | 0.945971i | \(0.605113\pi\) | |||||||
\(294\) | 4.13122 | 0.240938 | ||||||||
\(295\) | 3.06070 | 0.178201 | ||||||||
\(296\) | 7.40717 | 0.430533 | ||||||||
\(297\) | 5.88698 | 0.341597 | ||||||||
\(298\) | −7.35152 | −0.425862 | ||||||||
\(299\) | 5.44369 | 0.314817 | ||||||||
\(300\) | 1.41044 | 0.0814318 | ||||||||
\(301\) | 23.4275 | 1.35034 | ||||||||
\(302\) | 16.3564 | 0.941206 | ||||||||
\(303\) | −5.78677 | −0.332441 | ||||||||
\(304\) | 3.54717 | 0.203444 | ||||||||
\(305\) | −4.36339 | −0.249847 | ||||||||
\(306\) | −2.11438 | −0.120871 | ||||||||
\(307\) | 10.5173 | 0.600255 | 0.300128 | − | 0.953899i | \(-0.402971\pi\) | ||||
0.300128 | + | 0.953899i | \(0.402971\pi\) | |||||||
\(308\) | 3.27926 | 0.186853 | ||||||||
\(309\) | −12.2265 | −0.695539 | ||||||||
\(310\) | −9.55437 | −0.542652 | ||||||||
\(311\) | 9.81794 | 0.556725 | 0.278362 | − | 0.960476i | \(-0.410208\pi\) | ||||
0.278362 | + | 0.960476i | \(0.410208\pi\) | |||||||
\(312\) | −4.25473 | −0.240877 | ||||||||
\(313\) | 26.9734 | 1.52463 | 0.762314 | − | 0.647208i | \(-0.224063\pi\) | ||||
0.762314 | + | 0.647208i | \(0.224063\pi\) | |||||||
\(314\) | −7.76589 | −0.438254 | ||||||||
\(315\) | 3.18461 | 0.179433 | ||||||||
\(316\) | 9.01031 | 0.506869 | ||||||||
\(317\) | 9.77743 | 0.549155 | 0.274578 | − | 0.961565i | \(-0.411462\pi\) | ||||
0.274578 | + | 0.961565i | \(0.411462\pi\) | |||||||
\(318\) | −11.1238 | −0.623790 | ||||||||
\(319\) | 0.447275 | 0.0250426 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −21.5861 | −1.20482 | ||||||||
\(322\) | 5.68630 | 0.316885 | ||||||||
\(323\) | 7.42101 | 0.412916 | ||||||||
\(324\) | −4.94661 | −0.274811 | ||||||||
\(325\) | −3.01659 | −0.167331 | ||||||||
\(326\) | 15.3338 | 0.849262 | ||||||||
\(327\) | −19.1173 | −1.05719 | ||||||||
\(328\) | −9.28453 | −0.512653 | ||||||||
\(329\) | 33.3976 | 1.84127 | ||||||||
\(330\) | −1.46783 | −0.0808016 | ||||||||
\(331\) | 9.21802 | 0.506668 | 0.253334 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253334 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(332\) | 8.94926 | 0.491154 | ||||||||
\(333\) | −7.48610 | −0.410236 | ||||||||
\(334\) | −20.5909 | −1.12668 | ||||||||
\(335\) | 11.1448 | 0.608903 | ||||||||
\(336\) | −4.44435 | −0.242459 | ||||||||
\(337\) | −3.83268 | −0.208779 | −0.104390 | − | 0.994536i | \(-0.533289\pi\) | ||||
−0.104390 | + | 0.994536i | \(0.533289\pi\) | |||||||
\(338\) | −3.90016 | −0.212141 | ||||||||
\(339\) | 22.7401 | 1.23508 | ||||||||
\(340\) | 2.09209 | 0.113460 | ||||||||
\(341\) | 9.94316 | 0.538452 | ||||||||
\(342\) | −3.58497 | −0.193853 | ||||||||
\(343\) | 12.8278 | 0.692635 | ||||||||
\(344\) | −7.43486 | −0.400861 | ||||||||
\(345\) | −2.54525 | −0.137032 | ||||||||
\(346\) | 9.79839 | 0.526765 | ||||||||
\(347\) | 28.8686 | 1.54975 | 0.774875 | − | 0.632115i | \(-0.217813\pi\) | ||||
0.774875 | + | 0.632115i | \(0.217813\pi\) | |||||||
\(348\) | −0.606188 | −0.0324951 | ||||||||
\(349\) | 26.4828 | 1.41759 | 0.708795 | − | 0.705414i | \(-0.249239\pi\) | ||||
0.708795 | + | 0.705414i | \(0.249239\pi\) | |||||||
\(350\) | −3.15104 | −0.168430 | ||||||||
\(351\) | 17.0643 | 0.910822 | ||||||||
\(352\) | −1.04069 | −0.0554691 | ||||||||
\(353\) | −17.6764 | −0.940818 | −0.470409 | − | 0.882449i | \(-0.655894\pi\) | ||||
−0.470409 | + | 0.882449i | \(0.655894\pi\) | |||||||
\(354\) | 4.31694 | 0.229443 | ||||||||
\(355\) | 8.28515 | 0.439730 | ||||||||
\(356\) | −8.34070 | −0.442056 | ||||||||
\(357\) | −9.29798 | −0.492101 | ||||||||
\(358\) | 11.9994 | 0.634188 | ||||||||
\(359\) | −17.0247 | −0.898528 | −0.449264 | − | 0.893399i | \(-0.648314\pi\) | ||||
−0.449264 | + | 0.893399i | \(0.648314\pi\) | |||||||
\(360\) | −1.01066 | −0.0532663 | ||||||||
\(361\) | −6.41755 | −0.337766 | ||||||||
\(362\) | 0.246164 | 0.0129381 | ||||||||
\(363\) | −13.9873 | −0.734142 | ||||||||
\(364\) | 9.50540 | 0.498218 | ||||||||
\(365\) | −5.43760 | −0.284617 | ||||||||
\(366\) | −6.15430 | −0.321691 | ||||||||
\(367\) | −36.4460 | −1.90247 | −0.951233 | − | 0.308474i | \(-0.900182\pi\) | ||||
−0.951233 | + | 0.308474i | \(0.900182\pi\) | |||||||
\(368\) | −1.80458 | −0.0940703 | ||||||||
\(369\) | 9.38347 | 0.488484 | ||||||||
\(370\) | 7.40717 | 0.385080 | ||||||||
\(371\) | 24.8514 | 1.29022 | ||||||||
\(372\) | −13.4759 | −0.698692 | ||||||||
\(373\) | −15.9187 | −0.824239 | −0.412119 | − | 0.911130i | \(-0.635211\pi\) | ||||
−0.412119 | + | 0.911130i | \(0.635211\pi\) | |||||||
\(374\) | −2.17722 | −0.112581 | ||||||||
\(375\) | 1.41044 | 0.0728349 | ||||||||
\(376\) | −10.5989 | −0.546598 | ||||||||
\(377\) | 1.29649 | 0.0667727 | ||||||||
\(378\) | 17.8248 | 0.916807 | ||||||||
\(379\) | −9.80431 | −0.503614 | −0.251807 | − | 0.967778i | \(-0.581025\pi\) | ||||
−0.251807 | + | 0.967778i | \(0.581025\pi\) | |||||||
\(380\) | 3.54717 | 0.181966 | ||||||||
\(381\) | 17.7816 | 0.910980 | ||||||||
\(382\) | 20.4010 | 1.04381 | ||||||||
\(383\) | −9.63675 | −0.492415 | −0.246207 | − | 0.969217i | \(-0.579184\pi\) | ||||
−0.246207 | + | 0.969217i | \(0.579184\pi\) | |||||||
\(384\) | 1.41044 | 0.0719763 | ||||||||
\(385\) | 3.27926 | 0.167126 | ||||||||
\(386\) | 2.54753 | 0.129666 | ||||||||
\(387\) | 7.51408 | 0.381962 | ||||||||
\(388\) | 6.35468 | 0.322610 | ||||||||
\(389\) | 10.6926 | 0.542137 | 0.271069 | − | 0.962560i | \(-0.412623\pi\) | ||||
0.271069 | + | 0.962560i | \(0.412623\pi\) | |||||||
\(390\) | −4.25473 | −0.215447 | ||||||||
\(391\) | −3.77534 | −0.190927 | ||||||||
\(392\) | 2.92903 | 0.147938 | ||||||||
\(393\) | 13.0301 | 0.657284 | ||||||||
\(394\) | −3.59037 | −0.180880 | ||||||||
\(395\) | 9.01031 | 0.453358 | ||||||||
\(396\) | 1.05178 | 0.0528540 | ||||||||
\(397\) | 3.69620 | 0.185507 | 0.0927534 | − | 0.995689i | \(-0.470433\pi\) | ||||
0.0927534 | + | 0.995689i | \(0.470433\pi\) | |||||||
\(398\) | −22.6077 | −1.13322 | ||||||||
\(399\) | −15.7649 | −0.789232 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 2.95099 | 0.147366 | 0.0736828 | − | 0.997282i | \(-0.476525\pi\) | ||||
0.0736828 | + | 0.997282i | \(0.476525\pi\) | |||||||
\(402\) | 15.7190 | 0.783994 | ||||||||
\(403\) | 28.8217 | 1.43571 | ||||||||
\(404\) | −4.10281 | −0.204122 | ||||||||
\(405\) | −4.94661 | −0.245799 | ||||||||
\(406\) | 1.35427 | 0.0672114 | ||||||||
\(407\) | −7.70858 | −0.382100 | ||||||||
\(408\) | 2.95077 | 0.146085 | ||||||||
\(409\) | 34.2197 | 1.69205 | 0.846027 | − | 0.533141i | \(-0.178988\pi\) | ||||
0.846027 | + | 0.533141i | \(0.178988\pi\) | |||||||
\(410\) | −9.28453 | −0.458530 | ||||||||
\(411\) | −31.5591 | −1.55670 | ||||||||
\(412\) | −8.66854 | −0.427068 | ||||||||
\(413\) | −9.64438 | −0.474569 | ||||||||
\(414\) | 1.82381 | 0.0896354 | ||||||||
\(415\) | 8.94926 | 0.439302 | ||||||||
\(416\) | −3.01659 | −0.147901 | ||||||||
\(417\) | −19.9390 | −0.976416 | ||||||||
\(418\) | −3.69152 | −0.180558 | ||||||||
\(419\) | −29.3149 | −1.43213 | −0.716064 | − | 0.698035i | \(-0.754058\pi\) | ||||
−0.716064 | + | 0.698035i | \(0.754058\pi\) | |||||||
\(420\) | −4.44435 | −0.216862 | ||||||||
\(421\) | −11.7698 | −0.573623 | −0.286812 | − | 0.957987i | \(-0.592595\pi\) | ||||
−0.286812 | + | 0.957987i | \(0.592595\pi\) | |||||||
\(422\) | −0.563633 | −0.0274372 | ||||||||
\(423\) | 10.7119 | 0.520829 | ||||||||
\(424\) | −7.88673 | −0.383013 | ||||||||
\(425\) | 2.09209 | 0.101481 | ||||||||
\(426\) | 11.6857 | 0.566175 | ||||||||
\(427\) | 13.7492 | 0.665370 | ||||||||
\(428\) | −15.3045 | −0.739770 | ||||||||
\(429\) | 4.42786 | 0.213779 | ||||||||
\(430\) | −7.43486 | −0.358541 | ||||||||
\(431\) | 17.6035 | 0.847932 | 0.423966 | − | 0.905678i | \(-0.360638\pi\) | ||||
0.423966 | + | 0.905678i | \(0.360638\pi\) | |||||||
\(432\) | −5.65679 | −0.272163 | ||||||||
\(433\) | 19.7338 | 0.948348 | 0.474174 | − | 0.880431i | \(-0.342747\pi\) | ||||
0.474174 | + | 0.880431i | \(0.342747\pi\) | |||||||
\(434\) | 30.1062 | 1.44514 | ||||||||
\(435\) | −0.606188 | −0.0290645 | ||||||||
\(436\) | −13.5541 | −0.649126 | ||||||||
\(437\) | −6.40116 | −0.306209 | ||||||||
\(438\) | −7.66942 | −0.366459 | ||||||||
\(439\) | −20.8591 | −0.995553 | −0.497776 | − | 0.867305i | \(-0.665850\pi\) | ||||
−0.497776 | + | 0.867305i | \(0.665850\pi\) | |||||||
\(440\) | −1.04069 | −0.0496130 | ||||||||
\(441\) | −2.96024 | −0.140964 | ||||||||
\(442\) | −6.31099 | −0.300183 | ||||||||
\(443\) | −21.5858 | −1.02557 | −0.512785 | − | 0.858517i | \(-0.671386\pi\) | ||||
−0.512785 | + | 0.858517i | \(0.671386\pi\) | |||||||
\(444\) | 10.4474 | 0.495810 | ||||||||
\(445\) | −8.34070 | −0.395387 | ||||||||
\(446\) | −9.19193 | −0.435251 | ||||||||
\(447\) | −10.3689 | −0.490432 | ||||||||
\(448\) | −3.15104 | −0.148872 | ||||||||
\(449\) | 15.1846 | 0.716608 | 0.358304 | − | 0.933605i | \(-0.383355\pi\) | ||||
0.358304 | + | 0.933605i | \(0.383355\pi\) | |||||||
\(450\) | −1.01066 | −0.0476428 | ||||||||
\(451\) | 9.66234 | 0.454982 | ||||||||
\(452\) | 16.1227 | 0.758349 | ||||||||
\(453\) | 23.0698 | 1.08391 | ||||||||
\(454\) | −4.76633 | −0.223695 | ||||||||
\(455\) | 9.50540 | 0.445620 | ||||||||
\(456\) | 5.00308 | 0.234291 | ||||||||
\(457\) | 10.6088 | 0.496257 | 0.248129 | − | 0.968727i | \(-0.420184\pi\) | ||||
0.248129 | + | 0.968727i | \(0.420184\pi\) | |||||||
\(458\) | −11.9104 | −0.556536 | ||||||||
\(459\) | −11.8345 | −0.552388 | ||||||||
\(460\) | −1.80458 | −0.0841390 | ||||||||
\(461\) | −3.89885 | −0.181588 | −0.0907938 | − | 0.995870i | \(-0.528940\pi\) | ||||
−0.0907938 | + | 0.995870i | \(0.528940\pi\) | |||||||
\(462\) | 4.62520 | 0.215184 | ||||||||
\(463\) | 3.98126 | 0.185025 | 0.0925125 | − | 0.995712i | \(-0.470510\pi\) | ||||
0.0925125 | + | 0.995712i | \(0.470510\pi\) | |||||||
\(464\) | −0.429786 | −0.0199523 | ||||||||
\(465\) | −13.4759 | −0.624929 | ||||||||
\(466\) | 15.3681 | 0.711912 | ||||||||
\(467\) | 12.8211 | 0.593291 | 0.296646 | − | 0.954988i | \(-0.404132\pi\) | ||||
0.296646 | + | 0.954988i | \(0.404132\pi\) | |||||||
\(468\) | 3.04874 | 0.140928 | ||||||||
\(469\) | −35.1175 | −1.62158 | ||||||||
\(470\) | −10.5989 | −0.488892 | ||||||||
\(471\) | −10.9533 | −0.504703 | ||||||||
\(472\) | 3.06070 | 0.140880 | ||||||||
\(473\) | 7.73740 | 0.355766 | ||||||||
\(474\) | 12.7085 | 0.583721 | ||||||||
\(475\) | 3.54717 | 0.162756 | ||||||||
\(476\) | −6.59225 | −0.302155 | ||||||||
\(477\) | 7.97077 | 0.364956 | ||||||||
\(478\) | −8.67620 | −0.396840 | ||||||||
\(479\) | −21.5439 | −0.984367 | −0.492184 | − | 0.870491i | \(-0.663801\pi\) | ||||
−0.492184 | + | 0.870491i | \(0.663801\pi\) | |||||||
\(480\) | 1.41044 | 0.0643775 | ||||||||
\(481\) | −22.3444 | −1.01882 | ||||||||
\(482\) | −11.9235 | −0.543103 | ||||||||
\(483\) | 8.02019 | 0.364931 | ||||||||
\(484\) | −9.91696 | −0.450771 | ||||||||
\(485\) | 6.35468 | 0.288551 | ||||||||
\(486\) | 9.99349 | 0.453314 | ||||||||
\(487\) | 31.2923 | 1.41799 | 0.708994 | − | 0.705215i | \(-0.249149\pi\) | ||||
0.708994 | + | 0.705215i | \(0.249149\pi\) | |||||||
\(488\) | −4.36339 | −0.197521 | ||||||||
\(489\) | 21.6275 | 0.978028 | ||||||||
\(490\) | 2.92903 | 0.132320 | ||||||||
\(491\) | 16.7735 | 0.756978 | 0.378489 | − | 0.925606i | \(-0.376444\pi\) | ||||
0.378489 | + | 0.925606i | \(0.376444\pi\) | |||||||
\(492\) | −13.0953 | −0.590381 | ||||||||
\(493\) | −0.899152 | −0.0404958 | ||||||||
\(494\) | −10.7004 | −0.481433 | ||||||||
\(495\) | 1.05178 | 0.0472741 | ||||||||
\(496\) | −9.55437 | −0.429004 | ||||||||
\(497\) | −26.1068 | −1.17105 | ||||||||
\(498\) | 12.6224 | 0.565623 | ||||||||
\(499\) | 10.5285 | 0.471320 | 0.235660 | − | 0.971836i | \(-0.424275\pi\) | ||||
0.235660 | + | 0.971836i | \(0.424275\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −29.0423 | −1.29751 | ||||||||
\(502\) | −11.7240 | −0.523270 | ||||||||
\(503\) | 6.54465 | 0.291811 | 0.145906 | − | 0.989299i | \(-0.453390\pi\) | ||||
0.145906 | + | 0.989299i | \(0.453390\pi\) | |||||||
\(504\) | 3.18461 | 0.141854 | ||||||||
\(505\) | −4.10281 | −0.182573 | ||||||||
\(506\) | 1.87801 | 0.0834878 | ||||||||
\(507\) | −5.50094 | −0.244305 | ||||||||
\(508\) | 12.6071 | 0.559351 | ||||||||
\(509\) | 16.4367 | 0.728545 | 0.364272 | − | 0.931292i | \(-0.381318\pi\) | ||||
0.364272 | + | 0.931292i | \(0.381318\pi\) | |||||||
\(510\) | 2.95077 | 0.130662 | ||||||||
\(511\) | 17.1341 | 0.757967 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −20.0656 | −0.885920 | ||||||||
\(514\) | 16.6262 | 0.733352 | ||||||||
\(515\) | −8.66854 | −0.381981 | ||||||||
\(516\) | −10.4864 | −0.461639 | ||||||||
\(517\) | 11.0302 | 0.485108 | ||||||||
\(518\) | −23.3403 | −1.02551 | ||||||||
\(519\) | 13.8201 | 0.606633 | ||||||||
\(520\) | −3.01659 | −0.132286 | ||||||||
\(521\) | 31.6137 | 1.38502 | 0.692510 | − | 0.721408i | \(-0.256505\pi\) | ||||
0.692510 | + | 0.721408i | \(0.256505\pi\) | |||||||
\(522\) | 0.434366 | 0.0190117 | ||||||||
\(523\) | −11.3152 | −0.494781 | −0.247390 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247390 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(524\) | 9.23835 | 0.403579 | ||||||||
\(525\) | −4.44435 | −0.193967 | ||||||||
\(526\) | 17.0636 | 0.744009 | ||||||||
\(527\) | −19.9886 | −0.870717 | ||||||||
\(528\) | −1.46783 | −0.0638793 | ||||||||
\(529\) | −19.7435 | −0.858413 | ||||||||
\(530\) | −7.88673 | −0.342578 | ||||||||
\(531\) | −3.09332 | −0.134239 | ||||||||
\(532\) | −11.1773 | −0.484596 | ||||||||
\(533\) | 28.0077 | 1.21315 | ||||||||
\(534\) | −11.7641 | −0.509081 | ||||||||
\(535\) | −15.3045 | −0.661671 | ||||||||
\(536\) | 11.1448 | 0.481380 | ||||||||
\(537\) | 16.9244 | 0.730344 | ||||||||
\(538\) | −7.54805 | −0.325420 | ||||||||
\(539\) | −3.04822 | −0.131296 | ||||||||
\(540\) | −5.65679 | −0.243430 | ||||||||
\(541\) | −35.4631 | −1.52468 | −0.762338 | − | 0.647179i | \(-0.775949\pi\) | ||||
−0.762338 | + | 0.647179i | \(0.775949\pi\) | |||||||
\(542\) | 2.98704 | 0.128304 | ||||||||
\(543\) | 0.347199 | 0.0148998 | ||||||||
\(544\) | 2.09209 | 0.0896976 | ||||||||
\(545\) | −13.5541 | −0.580596 | ||||||||
\(546\) | 13.4068 | 0.573758 | ||||||||
\(547\) | 11.7442 | 0.502147 | 0.251073 | − | 0.967968i | \(-0.419216\pi\) | ||||
0.251073 | + | 0.967968i | \(0.419216\pi\) | |||||||
\(548\) | −22.3754 | −0.955829 | ||||||||
\(549\) | 4.40989 | 0.188209 | ||||||||
\(550\) | −1.04069 | −0.0443753 | ||||||||
\(551\) | −1.52453 | −0.0649471 | ||||||||
\(552\) | −2.54525 | −0.108333 | ||||||||
\(553\) | −28.3918 | −1.20734 | ||||||||
\(554\) | −0.626895 | −0.0266342 | ||||||||
\(555\) | 10.4474 | 0.443466 | ||||||||
\(556\) | −14.1367 | −0.599529 | ||||||||
\(557\) | 6.71231 | 0.284410 | 0.142205 | − | 0.989837i | \(-0.454581\pi\) | ||||
0.142205 | + | 0.989837i | \(0.454581\pi\) | |||||||
\(558\) | 9.65618 | 0.408779 | ||||||||
\(559\) | 22.4279 | 0.948601 | ||||||||
\(560\) | −3.15104 | −0.133156 | ||||||||
\(561\) | −3.07084 | −0.129651 | ||||||||
\(562\) | 23.0483 | 0.972233 | ||||||||
\(563\) | −3.19238 | −0.134543 | −0.0672713 | − | 0.997735i | \(-0.521429\pi\) | ||||
−0.0672713 | + | 0.997735i | \(0.521429\pi\) | |||||||
\(564\) | −14.9492 | −0.629473 | ||||||||
\(565\) | 16.1227 | 0.678288 | ||||||||
\(566\) | 1.83831 | 0.0772699 | ||||||||
\(567\) | 15.5869 | 0.654590 | ||||||||
\(568\) | 8.28515 | 0.347637 | ||||||||
\(569\) | −40.2457 | −1.68719 | −0.843593 | − | 0.536983i | \(-0.819564\pi\) | ||||
−0.843593 | + | 0.536983i | \(0.819564\pi\) | |||||||
\(570\) | 5.00308 | 0.209556 | ||||||||
\(571\) | −9.96583 | −0.417057 | −0.208529 | − | 0.978016i | \(-0.566867\pi\) | ||||
−0.208529 | + | 0.978016i | \(0.566867\pi\) | |||||||
\(572\) | 3.13935 | 0.131263 | ||||||||
\(573\) | 28.7745 | 1.20207 | ||||||||
\(574\) | 29.2559 | 1.22112 | ||||||||
\(575\) | −1.80458 | −0.0752562 | ||||||||
\(576\) | −1.01066 | −0.0421107 | ||||||||
\(577\) | −29.0788 | −1.21057 | −0.605284 | − | 0.796010i | \(-0.706940\pi\) | ||||
−0.605284 | + | 0.796010i | \(0.706940\pi\) | |||||||
\(578\) | −12.6232 | −0.525054 | ||||||||
\(579\) | 3.59314 | 0.149326 | ||||||||
\(580\) | −0.429786 | −0.0178459 | ||||||||
\(581\) | −28.1994 | −1.16991 | ||||||||
\(582\) | 8.96291 | 0.371524 | ||||||||
\(583\) | 8.20765 | 0.339926 | ||||||||
\(584\) | −5.43760 | −0.225010 | ||||||||
\(585\) | 3.04874 | 0.126050 | ||||||||
\(586\) | −11.1006 | −0.458562 | ||||||||
\(587\) | 6.93147 | 0.286092 | 0.143046 | − | 0.989716i | \(-0.454310\pi\) | ||||
0.143046 | + | 0.989716i | \(0.454310\pi\) | |||||||
\(588\) | 4.13122 | 0.170369 | ||||||||
\(589\) | −33.8910 | −1.39646 | ||||||||
\(590\) | 3.06070 | 0.126007 | ||||||||
\(591\) | −5.06400 | −0.208305 | ||||||||
\(592\) | 7.40717 | 0.304433 | ||||||||
\(593\) | −40.2143 | −1.65140 | −0.825701 | − | 0.564108i | \(-0.809220\pi\) | ||||
−0.825701 | + | 0.564108i | \(0.809220\pi\) | |||||||
\(594\) | 5.88698 | 0.241546 | ||||||||
\(595\) | −6.59225 | −0.270256 | ||||||||
\(596\) | −7.35152 | −0.301130 | ||||||||
\(597\) | −31.8868 | −1.30504 | ||||||||
\(598\) | 5.44369 | 0.222609 | ||||||||
\(599\) | 39.7203 | 1.62293 | 0.811464 | − | 0.584402i | \(-0.198671\pi\) | ||||
0.811464 | + | 0.584402i | \(0.198671\pi\) | |||||||
\(600\) | 1.41044 | 0.0575810 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 23.4275 | 0.954834 | ||||||||
\(603\) | −11.2635 | −0.458686 | ||||||||
\(604\) | 16.3564 | 0.665533 | ||||||||
\(605\) | −9.91696 | −0.403182 | ||||||||
\(606\) | −5.78677 | −0.235071 | ||||||||
\(607\) | −1.07765 | −0.0437405 | −0.0218702 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218702 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(608\) | 3.54717 | 0.143857 | ||||||||
\(609\) | 1.91012 | 0.0774020 | ||||||||
\(610\) | −4.36339 | −0.176668 | ||||||||
\(611\) | 31.9727 | 1.29348 | ||||||||
\(612\) | −2.11438 | −0.0854689 | ||||||||
\(613\) | 16.2193 | 0.655091 | 0.327546 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327546 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(614\) | 10.5173 | 0.424444 | ||||||||
\(615\) | −13.0953 | −0.528053 | ||||||||
\(616\) | 3.27926 | 0.132125 | ||||||||
\(617\) | 35.2021 | 1.41718 | 0.708591 | − | 0.705619i | \(-0.249331\pi\) | ||||
0.708591 | + | 0.705619i | \(0.249331\pi\) | |||||||
\(618\) | −12.2265 | −0.491820 | ||||||||
\(619\) | 39.2335 | 1.57693 | 0.788463 | − | 0.615082i | \(-0.210877\pi\) | ||||
0.788463 | + | 0.615082i | \(0.210877\pi\) | |||||||
\(620\) | −9.55437 | −0.383713 | ||||||||
\(621\) | 10.2081 | 0.409638 | ||||||||
\(622\) | 9.81794 | 0.393664 | ||||||||
\(623\) | 26.2818 | 1.05296 | ||||||||
\(624\) | −4.25473 | −0.170325 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.9734 | 1.07807 | ||||||||
\(627\) | −5.20667 | −0.207934 | ||||||||
\(628\) | −7.76589 | −0.309893 | ||||||||
\(629\) | 15.4965 | 0.617884 | ||||||||
\(630\) | 3.18461 | 0.126878 | ||||||||
\(631\) | 35.7483 | 1.42312 | 0.711558 | − | 0.702628i | \(-0.247990\pi\) | ||||
0.711558 | + | 0.702628i | \(0.247990\pi\) | |||||||
\(632\) | 9.01031 | 0.358411 | ||||||||
\(633\) | −0.794972 | −0.0315973 | ||||||||
\(634\) | 9.77743 | 0.388311 | ||||||||
\(635\) | 12.6071 | 0.500299 | ||||||||
\(636\) | −11.1238 | −0.441086 | ||||||||
\(637\) | −8.83569 | −0.350083 | ||||||||
\(638\) | 0.447275 | 0.0177078 | ||||||||
\(639\) | −8.37344 | −0.331248 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −12.6490 | −0.499604 | −0.249802 | − | 0.968297i | \(-0.580366\pi\) | ||||
−0.249802 | + | 0.968297i | \(0.580366\pi\) | |||||||
\(642\) | −21.5861 | −0.851934 | ||||||||
\(643\) | 17.2681 | 0.680987 | 0.340494 | − | 0.940247i | \(-0.389406\pi\) | ||||
0.340494 | + | 0.940247i | \(0.389406\pi\) | |||||||
\(644\) | 5.68630 | 0.224072 | ||||||||
\(645\) | −10.4864 | −0.412903 | ||||||||
\(646\) | 7.42101 | 0.291976 | ||||||||
\(647\) | −10.9293 | −0.429677 | −0.214838 | − | 0.976650i | \(-0.568922\pi\) | ||||
−0.214838 | + | 0.976650i | \(0.568922\pi\) | |||||||
\(648\) | −4.94661 | −0.194321 | ||||||||
\(649\) | −3.18525 | −0.125032 | ||||||||
\(650\) | −3.01659 | −0.118321 | ||||||||
\(651\) | 42.4630 | 1.66426 | ||||||||
\(652\) | 15.3338 | 0.600519 | ||||||||
\(653\) | −10.2745 | −0.402071 | −0.201036 | − | 0.979584i | \(-0.564431\pi\) | ||||
−0.201036 | + | 0.979584i | \(0.564431\pi\) | |||||||
\(654\) | −19.1173 | −0.747546 | ||||||||
\(655\) | 9.23835 | 0.360972 | ||||||||
\(656\) | −9.28453 | −0.362500 | ||||||||
\(657\) | 5.49555 | 0.214402 | ||||||||
\(658\) | 33.3976 | 1.30197 | ||||||||
\(659\) | −1.44077 | −0.0561245 | −0.0280623 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280623 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(660\) | −1.46783 | −0.0571354 | ||||||||
\(661\) | −15.7992 | −0.614518 | −0.307259 | − | 0.951626i | \(-0.599412\pi\) | ||||
−0.307259 | + | 0.951626i | \(0.599412\pi\) | |||||||
\(662\) | 9.21802 | 0.358268 | ||||||||
\(663\) | −8.90127 | −0.345697 | ||||||||
\(664\) | 8.94926 | 0.347299 | ||||||||
\(665\) | −11.1773 | −0.433436 | ||||||||
\(666\) | −7.48610 | −0.290081 | ||||||||
\(667\) | 0.775584 | 0.0300307 | ||||||||
\(668\) | −20.5909 | −0.796686 | ||||||||
\(669\) | −12.9647 | −0.501244 | ||||||||
\(670\) | 11.1448 | 0.430559 | ||||||||
\(671\) | 4.54094 | 0.175301 | ||||||||
\(672\) | −4.44435 | −0.171445 | ||||||||
\(673\) | 38.0739 | 1.46764 | 0.733821 | − | 0.679343i | \(-0.237735\pi\) | ||||
0.733821 | + | 0.679343i | \(0.237735\pi\) | |||||||
\(674\) | −3.83268 | −0.147629 | ||||||||
\(675\) | −5.65679 | −0.217730 | ||||||||
\(676\) | −3.90016 | −0.150006 | ||||||||
\(677\) | −34.5726 | −1.32873 | −0.664366 | − | 0.747407i | \(-0.731298\pi\) | ||||
−0.664366 | + | 0.747407i | \(0.731298\pi\) | |||||||
\(678\) | 22.7401 | 0.873330 | ||||||||
\(679\) | −20.0238 | −0.768444 | ||||||||
\(680\) | 2.09209 | 0.0802280 | ||||||||
\(681\) | −6.72263 | −0.257612 | ||||||||
\(682\) | 9.94316 | 0.380743 | ||||||||
\(683\) | 30.5658 | 1.16957 | 0.584784 | − | 0.811189i | \(-0.301179\pi\) | ||||
0.584784 | + | 0.811189i | \(0.301179\pi\) | |||||||
\(684\) | −3.58497 | −0.137075 | ||||||||
\(685\) | −22.3754 | −0.854919 | ||||||||
\(686\) | 12.8278 | 0.489767 | ||||||||
\(687\) | −16.7989 | −0.640918 | ||||||||
\(688\) | −7.43486 | −0.283451 | ||||||||
\(689\) | 23.7911 | 0.906367 | ||||||||
\(690\) | −2.54525 | −0.0968962 | ||||||||
\(691\) | −20.9029 | −0.795184 | −0.397592 | − | 0.917562i | \(-0.630154\pi\) | ||||
−0.397592 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(692\) | 9.79839 | 0.372479 | ||||||||
\(693\) | −3.31420 | −0.125896 | ||||||||
\(694\) | 28.8686 | 1.09584 | ||||||||
\(695\) | −14.1367 | −0.536235 | ||||||||
\(696\) | −0.606188 | −0.0229775 | ||||||||
\(697\) | −19.4241 | −0.735739 | ||||||||
\(698\) | 26.4828 | 1.00239 | ||||||||
\(699\) | 21.6758 | 0.819852 | ||||||||
\(700\) | −3.15104 | −0.119098 | ||||||||
\(701\) | −23.0749 | −0.871526 | −0.435763 | − | 0.900061i | \(-0.643521\pi\) | ||||
−0.435763 | + | 0.900061i | \(0.643521\pi\) | |||||||
\(702\) | 17.0643 | 0.644049 | ||||||||
\(703\) | 26.2745 | 0.990962 | ||||||||
\(704\) | −1.04069 | −0.0392226 | ||||||||
\(705\) | −14.9492 | −0.563018 | ||||||||
\(706\) | −17.6764 | −0.665259 | ||||||||
\(707\) | 12.9281 | 0.486211 | ||||||||
\(708\) | 4.31694 | 0.162241 | ||||||||
\(709\) | −38.6734 | −1.45241 | −0.726204 | − | 0.687479i | \(-0.758717\pi\) | ||||
−0.726204 | + | 0.687479i | \(0.758717\pi\) | |||||||
\(710\) | 8.28515 | 0.310936 | ||||||||
\(711\) | −9.10632 | −0.341514 | ||||||||
\(712\) | −8.34070 | −0.312581 | ||||||||
\(713\) | 17.2416 | 0.645704 | ||||||||
\(714\) | −9.29798 | −0.347968 | ||||||||
\(715\) | 3.13935 | 0.117405 | ||||||||
\(716\) | 11.9994 | 0.448439 | ||||||||
\(717\) | −12.2373 | −0.457009 | ||||||||
\(718\) | −17.0247 | −0.635356 | ||||||||
\(719\) | 25.4717 | 0.949935 | 0.474968 | − | 0.880003i | \(-0.342460\pi\) | ||||
0.474968 | + | 0.880003i | \(0.342460\pi\) | |||||||
\(720\) | −1.01066 | −0.0376649 | ||||||||
\(721\) | 27.3149 | 1.01726 | ||||||||
\(722\) | −6.41755 | −0.238837 | ||||||||
\(723\) | −16.8175 | −0.625448 | ||||||||
\(724\) | 0.246164 | 0.00914860 | ||||||||
\(725\) | −0.429786 | −0.0159619 | ||||||||
\(726\) | −13.9873 | −0.519117 | ||||||||
\(727\) | 23.5111 | 0.871977 | 0.435989 | − | 0.899952i | \(-0.356399\pi\) | ||||
0.435989 | + | 0.899952i | \(0.356399\pi\) | |||||||
\(728\) | 9.50540 | 0.352293 | ||||||||
\(729\) | 28.9350 | 1.07167 | ||||||||
\(730\) | −5.43760 | −0.201255 | ||||||||
\(731\) | −15.5544 | −0.575300 | ||||||||
\(732\) | −6.15430 | −0.227470 | ||||||||
\(733\) | −5.37759 | −0.198626 | −0.0993129 | − | 0.995056i | \(-0.531664\pi\) | ||||
−0.0993129 | + | 0.995056i | \(0.531664\pi\) | |||||||
\(734\) | −36.4460 | −1.34525 | ||||||||
\(735\) | 4.13122 | 0.152382 | ||||||||
\(736\) | −1.80458 | −0.0665177 | ||||||||
\(737\) | −11.5983 | −0.427227 | ||||||||
\(738\) | 9.38347 | 0.345410 | ||||||||
\(739\) | −15.8932 | −0.584642 | −0.292321 | − | 0.956320i | \(-0.594427\pi\) | ||||
−0.292321 | + | 0.956320i | \(0.594427\pi\) | |||||||
\(740\) | 7.40717 | 0.272293 | ||||||||
\(741\) | −15.0923 | −0.554428 | ||||||||
\(742\) | 24.8514 | 0.912322 | ||||||||
\(743\) | 12.1988 | 0.447530 | 0.223765 | − | 0.974643i | \(-0.428165\pi\) | ||||
0.223765 | + | 0.974643i | \(0.428165\pi\) | |||||||
\(744\) | −13.4759 | −0.494050 | ||||||||
\(745\) | −7.35152 | −0.269339 | ||||||||
\(746\) | −15.9187 | −0.582825 | ||||||||
\(747\) | −9.04462 | −0.330926 | ||||||||
\(748\) | −2.17722 | −0.0796071 | ||||||||
\(749\) | 48.2250 | 1.76210 | ||||||||
\(750\) | 1.41044 | 0.0515020 | ||||||||
\(751\) | 38.6497 | 1.41035 | 0.705173 | − | 0.709035i | \(-0.250869\pi\) | ||||
0.705173 | + | 0.709035i | \(0.250869\pi\) | |||||||
\(752\) | −10.5989 | −0.386503 | ||||||||
\(753\) | −16.5361 | −0.602608 | ||||||||
\(754\) | 1.29649 | 0.0472154 | ||||||||
\(755\) | 16.3564 | 0.595271 | ||||||||
\(756\) | 17.8248 | 0.648280 | ||||||||
\(757\) | −1.02975 | −0.0374268 | −0.0187134 | − | 0.999825i | \(-0.505957\pi\) | ||||
−0.0187134 | + | 0.999825i | \(0.505957\pi\) | |||||||
\(758\) | −9.80431 | −0.356109 | ||||||||
\(759\) | 2.64883 | 0.0961463 | ||||||||
\(760\) | 3.54717 | 0.128670 | ||||||||
\(761\) | 22.6429 | 0.820806 | 0.410403 | − | 0.911904i | \(-0.365388\pi\) | ||||
0.410403 | + | 0.911904i | \(0.365388\pi\) | |||||||
\(762\) | 17.7816 | 0.644160 | ||||||||
\(763\) | 42.7096 | 1.54619 | ||||||||
\(764\) | 20.4010 | 0.738084 | ||||||||
\(765\) | −2.11438 | −0.0764457 | ||||||||
\(766\) | −9.63675 | −0.348190 | ||||||||
\(767\) | −9.23290 | −0.333381 | ||||||||
\(768\) | 1.41044 | 0.0508949 | ||||||||
\(769\) | 0.211541 | 0.00762835 | 0.00381417 | − | 0.999993i | \(-0.498786\pi\) | ||||
0.00381417 | + | 0.999993i | \(0.498786\pi\) | |||||||
\(770\) | 3.27926 | 0.118176 | ||||||||
\(771\) | 23.4503 | 0.844543 | ||||||||
\(772\) | 2.54753 | 0.0916875 | ||||||||
\(773\) | 6.41109 | 0.230591 | 0.115295 | − | 0.993331i | \(-0.463219\pi\) | ||||
0.115295 | + | 0.993331i | \(0.463219\pi\) | |||||||
\(774\) | 7.51408 | 0.270088 | ||||||||
\(775\) | −9.55437 | −0.343203 | ||||||||
\(776\) | 6.35468 | 0.228120 | ||||||||
\(777\) | −32.9201 | −1.18100 | ||||||||
\(778\) | 10.6926 | 0.383349 | ||||||||
\(779\) | −32.9339 | −1.17998 | ||||||||
\(780\) | −4.25473 | −0.152344 | ||||||||
\(781\) | −8.62229 | −0.308530 | ||||||||
\(782\) | −3.77534 | −0.135006 | ||||||||
\(783\) | 2.43121 | 0.0868845 | ||||||||
\(784\) | 2.92903 | 0.104608 | ||||||||
\(785\) | −7.76589 | −0.277176 | ||||||||
\(786\) | 13.0301 | 0.464770 | ||||||||
\(787\) | 15.8847 | 0.566227 | 0.283114 | − | 0.959086i | \(-0.408633\pi\) | ||||
0.283114 | + | 0.959086i | \(0.408633\pi\) | |||||||
\(788\) | −3.59037 | −0.127901 | ||||||||
\(789\) | 24.0672 | 0.856816 | ||||||||
\(790\) | 9.01031 | 0.320572 | ||||||||
\(791\) | −50.8033 | −1.80636 | ||||||||
\(792\) | 1.05178 | 0.0373734 | ||||||||
\(793\) | 13.1626 | 0.467417 | ||||||||
\(794\) | 3.69620 | 0.131173 | ||||||||
\(795\) | −11.1238 | −0.394519 | ||||||||
\(796\) | −22.6077 | −0.801308 | ||||||||
\(797\) | −20.6779 | −0.732449 | −0.366225 | − | 0.930526i | \(-0.619350\pi\) | ||||
−0.366225 | + | 0.930526i | \(0.619350\pi\) | |||||||
\(798\) | −15.7649 | −0.558071 | ||||||||
\(799\) | −22.1739 | −0.784456 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 8.42958 | 0.297845 | ||||||||
\(802\) | 2.95099 | 0.104203 | ||||||||
\(803\) | 5.65887 | 0.199697 | ||||||||
\(804\) | 15.7190 | 0.554367 | ||||||||
\(805\) | 5.68630 | 0.200416 | ||||||||
\(806\) | 28.8217 | 1.01520 | ||||||||
\(807\) | −10.6461 | −0.374760 | ||||||||
\(808\) | −4.10281 | −0.144336 | ||||||||
\(809\) | −44.6175 | −1.56867 | −0.784334 | − | 0.620339i | \(-0.786995\pi\) | ||||
−0.784334 | + | 0.620339i | \(0.786995\pi\) | |||||||
\(810\) | −4.94661 | −0.173806 | ||||||||
\(811\) | −2.34123 | −0.0822119 | −0.0411059 | − | 0.999155i | \(-0.513088\pi\) | ||||
−0.0411059 | + | 0.999155i | \(0.513088\pi\) | |||||||
\(812\) | 1.35427 | 0.0475257 | ||||||||
\(813\) | 4.21304 | 0.147758 | ||||||||
\(814\) | −7.70858 | −0.270186 | ||||||||
\(815\) | 15.3338 | 0.537121 | ||||||||
\(816\) | 2.95077 | 0.103298 | ||||||||
\(817\) | −26.3727 | −0.922665 | ||||||||
\(818\) | 34.2197 | 1.19646 | ||||||||
\(819\) | −9.60669 | −0.335685 | ||||||||
\(820\) | −9.28453 | −0.324230 | ||||||||
\(821\) | 20.3297 | 0.709510 | 0.354755 | − | 0.934959i | \(-0.384564\pi\) | ||||
0.354755 | + | 0.934959i | \(0.384564\pi\) | |||||||
\(822\) | −31.5591 | −1.10075 | ||||||||
\(823\) | −33.4109 | −1.16463 | −0.582316 | − | 0.812963i | \(-0.697853\pi\) | ||||
−0.582316 | + | 0.812963i | \(0.697853\pi\) | |||||||
\(824\) | −8.66854 | −0.301983 | ||||||||
\(825\) | −1.46783 | −0.0511034 | ||||||||
\(826\) | −9.64438 | −0.335571 | ||||||||
\(827\) | 14.0651 | 0.489092 | 0.244546 | − | 0.969638i | \(-0.421361\pi\) | ||||
0.244546 | + | 0.969638i | \(0.421361\pi\) | |||||||
\(828\) | 1.82381 | 0.0633818 | ||||||||
\(829\) | −27.2410 | −0.946119 | −0.473060 | − | 0.881030i | \(-0.656850\pi\) | ||||
−0.473060 | + | 0.881030i | \(0.656850\pi\) | |||||||
\(830\) | 8.94926 | 0.310633 | ||||||||
\(831\) | −0.884198 | −0.0306725 | ||||||||
\(832\) | −3.01659 | −0.104582 | ||||||||
\(833\) | 6.12779 | 0.212315 | ||||||||
\(834\) | −19.9390 | −0.690430 | ||||||||
\(835\) | −20.5909 | −0.712578 | ||||||||
\(836\) | −3.69152 | −0.127674 | ||||||||
\(837\) | 54.0471 | 1.86814 | ||||||||
\(838\) | −29.3149 | −1.01267 | ||||||||
\(839\) | −24.1273 | −0.832968 | −0.416484 | − | 0.909143i | \(-0.636738\pi\) | ||||
−0.416484 | + | 0.909143i | \(0.636738\pi\) | |||||||
\(840\) | −4.44435 | −0.153345 | ||||||||
\(841\) | −28.8153 | −0.993630 | ||||||||
\(842\) | −11.7698 | −0.405613 | ||||||||
\(843\) | 32.5082 | 1.11964 | ||||||||
\(844\) | −0.563633 | −0.0194011 | ||||||||
\(845\) | −3.90016 | −0.134170 | ||||||||
\(846\) | 10.7119 | 0.368282 | ||||||||
\(847\) | 31.2487 | 1.07372 | ||||||||
\(848\) | −7.88673 | −0.270831 | ||||||||
\(849\) | 2.59283 | 0.0889856 | ||||||||
\(850\) | 2.09209 | 0.0717581 | ||||||||
\(851\) | −13.3668 | −0.458209 | ||||||||
\(852\) | 11.6857 | 0.400346 | ||||||||
\(853\) | −21.3206 | −0.730002 | −0.365001 | − | 0.931007i | \(-0.618931\pi\) | ||||
−0.365001 | + | 0.931007i | \(0.618931\pi\) | |||||||
\(854\) | 13.7492 | 0.470488 | ||||||||
\(855\) | −3.58497 | −0.122604 | ||||||||
\(856\) | −15.3045 | −0.523096 | ||||||||
\(857\) | 37.7178 | 1.28842 | 0.644208 | − | 0.764850i | \(-0.277187\pi\) | ||||
0.644208 | + | 0.764850i | \(0.277187\pi\) | |||||||
\(858\) | 4.42786 | 0.151165 | ||||||||
\(859\) | 21.5115 | 0.733963 | 0.366982 | − | 0.930228i | \(-0.380391\pi\) | ||||
0.366982 | + | 0.930228i | \(0.380391\pi\) | |||||||
\(860\) | −7.43486 | −0.253527 | ||||||||
\(861\) | 41.2637 | 1.40626 | ||||||||
\(862\) | 17.6035 | 0.599578 | ||||||||
\(863\) | 3.67152 | 0.124980 | 0.0624900 | − | 0.998046i | \(-0.480096\pi\) | ||||
0.0624900 | + | 0.998046i | \(0.480096\pi\) | |||||||
\(864\) | −5.65679 | −0.192448 | ||||||||
\(865\) | 9.79839 | 0.333155 | ||||||||
\(866\) | 19.7338 | 0.670583 | ||||||||
\(867\) | −17.8042 | −0.604663 | ||||||||
\(868\) | 30.1062 | 1.02187 | ||||||||
\(869\) | −9.37696 | −0.318091 | ||||||||
\(870\) | −0.606188 | −0.0205517 | ||||||||
\(871\) | −33.6192 | −1.13914 | ||||||||
\(872\) | −13.5541 | −0.459001 | ||||||||
\(873\) | −6.42240 | −0.217365 | ||||||||
\(874\) | −6.40116 | −0.216523 | ||||||||
\(875\) | −3.15104 | −0.106524 | ||||||||
\(876\) | −7.66942 | −0.259126 | ||||||||
\(877\) | −55.2201 | −1.86465 | −0.932325 | − | 0.361620i | \(-0.882224\pi\) | ||||
−0.932325 | + | 0.361620i | \(0.882224\pi\) | |||||||
\(878\) | −20.8591 | −0.703962 | ||||||||
\(879\) | −15.6568 | −0.528089 | ||||||||
\(880\) | −1.04069 | −0.0350817 | ||||||||
\(881\) | −30.9841 | −1.04388 | −0.521940 | − | 0.852982i | \(-0.674792\pi\) | ||||
−0.521940 | + | 0.852982i | \(0.674792\pi\) | |||||||
\(882\) | −2.96024 | −0.0996765 | ||||||||
\(883\) | −5.21387 | −0.175461 | −0.0877304 | − | 0.996144i | \(-0.527961\pi\) | ||||
−0.0877304 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(884\) | −6.31099 | −0.212261 | ||||||||
\(885\) | 4.31694 | 0.145112 | ||||||||
\(886\) | −21.5858 | −0.725188 | ||||||||
\(887\) | 3.86782 | 0.129869 | 0.0649343 | − | 0.997890i | \(-0.479316\pi\) | ||||
0.0649343 | + | 0.997890i | \(0.479316\pi\) | |||||||
\(888\) | 10.4474 | 0.350591 | ||||||||
\(889\) | −39.7255 | −1.33235 | ||||||||
\(890\) | −8.34070 | −0.279581 | ||||||||
\(891\) | 5.14789 | 0.172461 | ||||||||
\(892\) | −9.19193 | −0.307769 | ||||||||
\(893\) | −37.5962 | −1.25811 | ||||||||
\(894\) | −10.3689 | −0.346787 | ||||||||
\(895\) | 11.9994 | 0.401096 | ||||||||
\(896\) | −3.15104 | −0.105269 | ||||||||
\(897\) | 7.67800 | 0.256361 | ||||||||
\(898\) | 15.1846 | 0.506718 | ||||||||
\(899\) | 4.10634 | 0.136954 | ||||||||
\(900\) | −1.01066 | −0.0336885 | ||||||||
\(901\) | −16.4997 | −0.549686 | ||||||||
\(902\) | 9.66234 | 0.321721 | ||||||||
\(903\) | 33.0431 | 1.09961 | ||||||||
\(904\) | 16.1227 | 0.536234 | ||||||||
\(905\) | 0.246164 | 0.00818276 | ||||||||
\(906\) | 23.0698 | 0.766441 | ||||||||
\(907\) | −46.4004 | −1.54070 | −0.770350 | − | 0.637622i | \(-0.779918\pi\) | ||||
−0.770350 | + | 0.637622i | \(0.779918\pi\) | |||||||
\(908\) | −4.76633 | −0.158176 | ||||||||
\(909\) | 4.14653 | 0.137532 | ||||||||
\(910\) | 9.50540 | 0.315101 | ||||||||
\(911\) | −31.7722 | −1.05266 | −0.526330 | − | 0.850280i | \(-0.676432\pi\) | ||||
−0.526330 | + | 0.850280i | \(0.676432\pi\) | |||||||
\(912\) | 5.00308 | 0.165669 | ||||||||
\(913\) | −9.31342 | −0.308229 | ||||||||
\(914\) | 10.6088 | 0.350907 | ||||||||
\(915\) | −6.15430 | −0.203455 | ||||||||
\(916\) | −11.9104 | −0.393530 | ||||||||
\(917\) | −29.1104 | −0.961309 | ||||||||
\(918\) | −11.8345 | −0.390597 | ||||||||
\(919\) | −38.7173 | −1.27717 | −0.638584 | − | 0.769553i | \(-0.720479\pi\) | ||||
−0.638584 | + | 0.769553i | \(0.720479\pi\) | |||||||
\(920\) | −1.80458 | −0.0594953 | ||||||||
\(921\) | 14.8341 | 0.488799 | ||||||||
\(922\) | −3.89885 | −0.128402 | ||||||||
\(923\) | −24.9929 | −0.822652 | ||||||||
\(924\) | 4.62520 | 0.152158 | ||||||||
\(925\) | 7.40717 | 0.243546 | ||||||||
\(926\) | 3.98126 | 0.130832 | ||||||||
\(927\) | 8.76091 | 0.287746 | ||||||||
\(928\) | −0.429786 | −0.0141084 | ||||||||
\(929\) | −21.4597 | −0.704071 | −0.352035 | − | 0.935987i | \(-0.614510\pi\) | ||||
−0.352035 | + | 0.935987i | \(0.614510\pi\) | |||||||
\(930\) | −13.4759 | −0.441891 | ||||||||
\(931\) | 10.3898 | 0.340511 | ||||||||
\(932\) | 15.3681 | 0.503398 | ||||||||
\(933\) | 13.8476 | 0.453351 | ||||||||
\(934\) | 12.8211 | 0.419520 | ||||||||
\(935\) | −2.17722 | −0.0712027 | ||||||||
\(936\) | 3.04874 | 0.0996512 | ||||||||
\(937\) | 7.45122 | 0.243421 | 0.121710 | − | 0.992566i | \(-0.461162\pi\) | ||||
0.121710 | + | 0.992566i | \(0.461162\pi\) | |||||||
\(938\) | −35.1175 | −1.14663 | ||||||||
\(939\) | 38.0444 | 1.24153 | ||||||||
\(940\) | −10.5989 | −0.345699 | ||||||||
\(941\) | 37.2907 | 1.21564 | 0.607822 | − | 0.794073i | \(-0.292044\pi\) | ||||
0.607822 | + | 0.794073i | \(0.292044\pi\) | |||||||
\(942\) | −10.9533 | −0.356879 | ||||||||
\(943\) | 16.7547 | 0.545608 | ||||||||
\(944\) | 3.06070 | 0.0996174 | ||||||||
\(945\) | 17.8248 | 0.579840 | ||||||||
\(946\) | 7.73740 | 0.251564 | ||||||||
\(947\) | −47.3493 | −1.53865 | −0.769323 | − | 0.638859i | \(-0.779407\pi\) | ||||
−0.769323 | + | 0.638859i | \(0.779407\pi\) | |||||||
\(948\) | 12.7085 | 0.412753 | ||||||||
\(949\) | 16.4030 | 0.532465 | ||||||||
\(950\) | 3.54717 | 0.115086 | ||||||||
\(951\) | 13.7905 | 0.447187 | ||||||||
\(952\) | −6.59225 | −0.213656 | ||||||||
\(953\) | 29.2932 | 0.948899 | 0.474450 | − | 0.880283i | \(-0.342647\pi\) | ||||
0.474450 | + | 0.880283i | \(0.342647\pi\) | |||||||
\(954\) | 7.97077 | 0.258063 | ||||||||
\(955\) | 20.4010 | 0.660162 | ||||||||
\(956\) | −8.67620 | −0.280608 | ||||||||
\(957\) | 0.630855 | 0.0203927 | ||||||||
\(958\) | −21.5439 | −0.696053 | ||||||||
\(959\) | 70.5056 | 2.27674 | ||||||||
\(960\) | 1.41044 | 0.0455218 | ||||||||
\(961\) | 60.2860 | 1.94471 | ||||||||
\(962\) | −22.3444 | −0.720413 | ||||||||
\(963\) | 15.4676 | 0.498436 | ||||||||
\(964\) | −11.9235 | −0.384031 | ||||||||
\(965\) | 2.54753 | 0.0820078 | ||||||||
\(966\) | 8.02019 | 0.258045 | ||||||||
\(967\) | −40.1468 | −1.29103 | −0.645517 | − | 0.763746i | \(-0.723358\pi\) | ||||
−0.645517 | + | 0.763746i | \(0.723358\pi\) | |||||||
\(968\) | −9.91696 | −0.318743 | ||||||||
\(969\) | 10.4669 | 0.336245 | ||||||||
\(970\) | 6.35468 | 0.204037 | ||||||||
\(971\) | 16.4345 | 0.527410 | 0.263705 | − | 0.964603i | \(-0.415056\pi\) | ||||
0.263705 | + | 0.964603i | \(0.415056\pi\) | |||||||
\(972\) | 9.99349 | 0.320541 | ||||||||
\(973\) | 44.5452 | 1.42805 | ||||||||
\(974\) | 31.2923 | 1.00267 | ||||||||
\(975\) | −4.25473 | −0.136260 | ||||||||
\(976\) | −4.36339 | −0.139669 | ||||||||
\(977\) | 35.9031 | 1.14864 | 0.574322 | − | 0.818630i | \(-0.305266\pi\) | ||||
0.574322 | + | 0.818630i | \(0.305266\pi\) | |||||||
\(978\) | 21.6275 | 0.691570 | ||||||||
\(979\) | 8.68010 | 0.277417 | ||||||||
\(980\) | 2.92903 | 0.0935644 | ||||||||
\(981\) | 13.6986 | 0.437362 | ||||||||
\(982\) | 16.7735 | 0.535265 | ||||||||
\(983\) | −23.9468 | −0.763785 | −0.381893 | − | 0.924207i | \(-0.624728\pi\) | ||||
−0.381893 | + | 0.924207i | \(0.624728\pi\) | |||||||
\(984\) | −13.0953 | −0.417462 | ||||||||
\(985\) | −3.59037 | −0.114399 | ||||||||
\(986\) | −0.899152 | −0.0286348 | ||||||||
\(987\) | 47.1053 | 1.49938 | ||||||||
\(988\) | −10.7004 | −0.340425 | ||||||||
\(989\) | 13.4168 | 0.426629 | ||||||||
\(990\) | 1.05178 | 0.0334278 | ||||||||
\(991\) | 37.5903 | 1.19410 | 0.597048 | − | 0.802205i | \(-0.296340\pi\) | ||||
0.597048 | + | 0.802205i | \(0.296340\pi\) | |||||||
\(992\) | −9.55437 | −0.303352 | ||||||||
\(993\) | 13.0015 | 0.412589 | ||||||||
\(994\) | −26.1068 | −0.828057 | ||||||||
\(995\) | −22.6077 | −0.716712 | ||||||||
\(996\) | 12.6224 | 0.399956 | ||||||||
\(997\) | −0.824218 | −0.0261033 | −0.0130516 | − | 0.999915i | \(-0.504155\pi\) | ||||
−0.0130516 | + | 0.999915i | \(0.504155\pi\) | |||||||
\(998\) | 10.5285 | 0.333273 | ||||||||
\(999\) | −41.9008 | −1.32568 |
(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 | 6010.2.a.c.1.14 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.14 | ✓ | 16 | 1.1 | even | 1 | trivial |