Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61749 | −1.14374 | −0.571868 | − | 0.820346i | \(-0.693781\pi\) | ||||
−0.571868 | + | 0.820346i | \(0.693781\pi\) | |||||||
\(3\) | 2.78278 | 1.60664 | 0.803319 | − | 0.595549i | \(-0.203065\pi\) | ||||
0.803319 | + | 0.595549i | \(0.203065\pi\) | |||||||
\(4\) | 0.616262 | 0.308131 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.50111 | −1.83757 | ||||||||
\(7\) | −5.17171 | −1.95472 | −0.977362 | − | 0.211573i | \(-0.932141\pi\) | ||||
−0.977362 | + | 0.211573i | \(0.932141\pi\) | |||||||
\(8\) | 2.23818 | 0.791315 | ||||||||
\(9\) | 4.74386 | 1.58129 | ||||||||
\(10\) | −1.61749 | −0.511494 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.71492 | 0.495055 | ||||||||
\(13\) | −1.96466 | −0.544899 | −0.272450 | − | 0.962170i | \(-0.587834\pi\) | ||||
−0.272450 | + | 0.962170i | \(0.587834\pi\) | |||||||
\(14\) | 8.36518 | 2.23569 | ||||||||
\(15\) | 2.78278 | 0.718510 | ||||||||
\(16\) | −4.85275 | −1.21319 | ||||||||
\(17\) | −1.20619 | −0.292545 | −0.146273 | − | 0.989244i | \(-0.546728\pi\) | ||||
−0.146273 | + | 0.989244i | \(0.546728\pi\) | |||||||
\(18\) | −7.67313 | −1.80857 | ||||||||
\(19\) | 1.46585 | 0.336290 | 0.168145 | − | 0.985762i | \(-0.446222\pi\) | ||||
0.168145 | + | 0.985762i | \(0.446222\pi\) | |||||||
\(20\) | 0.616262 | 0.137800 | ||||||||
\(21\) | −14.3917 | −3.14054 | ||||||||
\(22\) | 1.61749 | 0.344849 | ||||||||
\(23\) | 5.25760 | 1.09628 | 0.548142 | − | 0.836385i | \(-0.315335\pi\) | ||||
0.548142 | + | 0.836385i | \(0.315335\pi\) | |||||||
\(24\) | 6.22835 | 1.27136 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.17781 | 0.623220 | ||||||||
\(27\) | 4.85277 | 0.933917 | ||||||||
\(28\) | −3.18713 | −0.602311 | ||||||||
\(29\) | −3.23003 | −0.599802 | −0.299901 | − | 0.953970i | \(-0.596954\pi\) | ||||
−0.299901 | + | 0.953970i | \(0.596954\pi\) | |||||||
\(30\) | −4.50111 | −0.821786 | ||||||||
\(31\) | 4.38231 | 0.787085 | 0.393543 | − | 0.919306i | \(-0.371249\pi\) | ||||
0.393543 | + | 0.919306i | \(0.371249\pi\) | |||||||
\(32\) | 3.37289 | 0.596249 | ||||||||
\(33\) | −2.78278 | −0.484420 | ||||||||
\(34\) | 1.95100 | 0.334594 | ||||||||
\(35\) | −5.17171 | −0.874179 | ||||||||
\(36\) | 2.92346 | 0.487243 | ||||||||
\(37\) | 1.24419 | 0.204543 | 0.102272 | − | 0.994757i | \(-0.467389\pi\) | ||||
0.102272 | + | 0.994757i | \(0.467389\pi\) | |||||||
\(38\) | −2.37100 | −0.384626 | ||||||||
\(39\) | −5.46722 | −0.875456 | ||||||||
\(40\) | 2.23818 | 0.353887 | ||||||||
\(41\) | 0.338077 | 0.0527987 | 0.0263994 | − | 0.999651i | \(-0.491596\pi\) | ||||
0.0263994 | + | 0.999651i | \(0.491596\pi\) | |||||||
\(42\) | 23.2784 | 3.59194 | ||||||||
\(43\) | 0.413393 | 0.0630418 | 0.0315209 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315209 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(44\) | −0.616262 | −0.0929050 | ||||||||
\(45\) | 4.74386 | 0.707173 | ||||||||
\(46\) | −8.50409 | −1.25386 | ||||||||
\(47\) | −3.40991 | −0.497386 | −0.248693 | − | 0.968582i | \(-0.580001\pi\) | ||||
−0.248693 | + | 0.968582i | \(0.580001\pi\) | |||||||
\(48\) | −13.5041 | −1.94915 | ||||||||
\(49\) | 19.7466 | 2.82095 | ||||||||
\(50\) | −1.61749 | −0.228747 | ||||||||
\(51\) | −3.35657 | −0.470014 | ||||||||
\(52\) | −1.21075 | −0.167900 | ||||||||
\(53\) | 5.96665 | 0.819582 | 0.409791 | − | 0.912179i | \(-0.365602\pi\) | ||||
0.409791 | + | 0.912179i | \(0.365602\pi\) | |||||||
\(54\) | −7.84930 | −1.06815 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −11.5752 | −1.54680 | ||||||||
\(57\) | 4.07914 | 0.540296 | ||||||||
\(58\) | 5.22453 | 0.686015 | ||||||||
\(59\) | 7.57994 | 0.986824 | 0.493412 | − | 0.869796i | \(-0.335749\pi\) | ||||
0.493412 | + | 0.869796i | \(0.335749\pi\) | |||||||
\(60\) | 1.71492 | 0.221395 | ||||||||
\(61\) | 11.2671 | 1.44261 | 0.721305 | − | 0.692617i | \(-0.243543\pi\) | ||||
0.721305 | + | 0.692617i | \(0.243543\pi\) | |||||||
\(62\) | −7.08832 | −0.900218 | ||||||||
\(63\) | −24.5339 | −3.09098 | ||||||||
\(64\) | 4.24988 | 0.531235 | ||||||||
\(65\) | −1.96466 | −0.243686 | ||||||||
\(66\) | 4.50111 | 0.554048 | ||||||||
\(67\) | 2.61273 | 0.319195 | 0.159598 | − | 0.987182i | \(-0.448980\pi\) | ||||
0.159598 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(68\) | −0.743332 | −0.0901422 | ||||||||
\(69\) | 14.6307 | 1.76133 | ||||||||
\(70\) | 8.36518 | 0.999830 | ||||||||
\(71\) | −12.8357 | −1.52332 | −0.761661 | − | 0.647975i | \(-0.775616\pi\) | ||||
−0.761661 | + | 0.647975i | \(0.775616\pi\) | |||||||
\(72\) | 10.6176 | 1.25130 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | −2.01245 | −0.233943 | ||||||||
\(75\) | 2.78278 | 0.321328 | ||||||||
\(76\) | 0.903349 | 0.103621 | ||||||||
\(77\) | 5.17171 | 0.589372 | ||||||||
\(78\) | 8.84315 | 1.00129 | ||||||||
\(79\) | −4.74712 | −0.534092 | −0.267046 | − | 0.963684i | \(-0.586048\pi\) | ||||
−0.267046 | + | 0.963684i | \(0.586048\pi\) | |||||||
\(80\) | −4.85275 | −0.542553 | ||||||||
\(81\) | −0.727378 | −0.0808198 | ||||||||
\(82\) | −0.546834 | −0.0603878 | ||||||||
\(83\) | 9.19417 | 1.00919 | 0.504596 | − | 0.863356i | \(-0.331642\pi\) | ||||
0.504596 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(84\) | −8.86908 | −0.967696 | ||||||||
\(85\) | −1.20619 | −0.130830 | ||||||||
\(86\) | −0.668658 | −0.0721032 | ||||||||
\(87\) | −8.98847 | −0.963665 | ||||||||
\(88\) | −2.23818 | −0.238591 | ||||||||
\(89\) | 10.4557 | 1.10831 | 0.554153 | − | 0.832415i | \(-0.313042\pi\) | ||||
0.554153 | + | 0.832415i | \(0.313042\pi\) | |||||||
\(90\) | −7.67313 | −0.808819 | ||||||||
\(91\) | 10.1607 | 1.06513 | ||||||||
\(92\) | 3.24006 | 0.337799 | ||||||||
\(93\) | 12.1950 | 1.26456 | ||||||||
\(94\) | 5.51548 | 0.568878 | ||||||||
\(95\) | 1.46585 | 0.150393 | ||||||||
\(96\) | 9.38602 | 0.957957 | ||||||||
\(97\) | 14.7591 | 1.49856 | 0.749278 | − | 0.662256i | \(-0.230401\pi\) | ||||
0.749278 | + | 0.662256i | \(0.230401\pi\) | |||||||
\(98\) | −31.9399 | −3.22642 | ||||||||
\(99\) | −4.74386 | −0.476776 | ||||||||
\(100\) | 0.616262 | 0.0616262 | ||||||||
\(101\) | 3.81148 | 0.379256 | 0.189628 | − | 0.981856i | \(-0.439272\pi\) | ||||
0.189628 | + | 0.981856i | \(0.439272\pi\) | |||||||
\(102\) | 5.42921 | 0.537572 | ||||||||
\(103\) | −13.4112 | −1.32144 | −0.660721 | − | 0.750631i | \(-0.729749\pi\) | ||||
−0.660721 | + | 0.750631i | \(0.729749\pi\) | |||||||
\(104\) | −4.39726 | −0.431187 | ||||||||
\(105\) | −14.3917 | −1.40449 | ||||||||
\(106\) | −9.65098 | −0.937386 | ||||||||
\(107\) | −4.48228 | −0.433318 | −0.216659 | − | 0.976247i | \(-0.569516\pi\) | ||||
−0.216659 | + | 0.976247i | \(0.569516\pi\) | |||||||
\(108\) | 2.99058 | 0.287769 | ||||||||
\(109\) | 5.50832 | 0.527601 | 0.263800 | − | 0.964577i | \(-0.415024\pi\) | ||||
0.263800 | + | 0.964577i | \(0.415024\pi\) | |||||||
\(110\) | 1.61749 | 0.154221 | ||||||||
\(111\) | 3.46230 | 0.328627 | ||||||||
\(112\) | 25.0970 | 2.37144 | ||||||||
\(113\) | −18.1196 | −1.70455 | −0.852276 | − | 0.523093i | \(-0.824778\pi\) | ||||
−0.852276 | + | 0.523093i | \(0.824778\pi\) | |||||||
\(114\) | −6.59796 | −0.617955 | ||||||||
\(115\) | 5.25760 | 0.490273 | ||||||||
\(116\) | −1.99055 | −0.184818 | ||||||||
\(117\) | −9.32008 | −0.861642 | ||||||||
\(118\) | −12.2604 | −1.12867 | ||||||||
\(119\) | 6.23809 | 0.571845 | ||||||||
\(120\) | 6.22835 | 0.568568 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −18.2245 | −1.64996 | ||||||||
\(123\) | 0.940793 | 0.0848284 | ||||||||
\(124\) | 2.70065 | 0.242525 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 39.6832 | 3.53526 | ||||||||
\(127\) | 1.42881 | 0.126786 | 0.0633932 | − | 0.997989i | \(-0.479808\pi\) | ||||
0.0633932 | + | 0.997989i | \(0.479808\pi\) | |||||||
\(128\) | −13.6199 | −1.20384 | ||||||||
\(129\) | 1.15038 | 0.101285 | ||||||||
\(130\) | 3.17781 | 0.278713 | ||||||||
\(131\) | 14.9359 | 1.30496 | 0.652478 | − | 0.757808i | \(-0.273730\pi\) | ||||
0.652478 | + | 0.757808i | \(0.273730\pi\) | |||||||
\(132\) | −1.71492 | −0.149265 | ||||||||
\(133\) | −7.58097 | −0.657353 | ||||||||
\(134\) | −4.22605 | −0.365075 | ||||||||
\(135\) | 4.85277 | 0.417660 | ||||||||
\(136\) | −2.69968 | −0.231495 | ||||||||
\(137\) | 19.4229 | 1.65941 | 0.829705 | − | 0.558202i | \(-0.188508\pi\) | ||||
0.829705 | + | 0.558202i | \(0.188508\pi\) | |||||||
\(138\) | −23.6650 | −2.01450 | ||||||||
\(139\) | 15.6235 | 1.32517 | 0.662586 | − | 0.748986i | \(-0.269459\pi\) | ||||
0.662586 | + | 0.748986i | \(0.269459\pi\) | |||||||
\(140\) | −3.18713 | −0.269362 | ||||||||
\(141\) | −9.48902 | −0.799120 | ||||||||
\(142\) | 20.7616 | 1.74228 | ||||||||
\(143\) | 1.96466 | 0.164293 | ||||||||
\(144\) | −23.0207 | −1.91839 | ||||||||
\(145\) | −3.23003 | −0.268240 | ||||||||
\(146\) | 1.61749 | 0.133864 | ||||||||
\(147\) | 54.9505 | 4.53224 | ||||||||
\(148\) | 0.766745 | 0.0630260 | ||||||||
\(149\) | 16.4438 | 1.34713 | 0.673564 | − | 0.739129i | \(-0.264763\pi\) | ||||
0.673564 | + | 0.739129i | \(0.264763\pi\) | |||||||
\(150\) | −4.50111 | −0.367514 | ||||||||
\(151\) | 20.1213 | 1.63744 | 0.818722 | − | 0.574190i | \(-0.194683\pi\) | ||||
0.818722 | + | 0.574190i | \(0.194683\pi\) | |||||||
\(152\) | 3.28084 | 0.266111 | ||||||||
\(153\) | −5.72202 | −0.462598 | ||||||||
\(154\) | −8.36518 | −0.674085 | ||||||||
\(155\) | 4.38231 | 0.351995 | ||||||||
\(156\) | −3.36924 | −0.269755 | ||||||||
\(157\) | −3.60715 | −0.287882 | −0.143941 | − | 0.989586i | \(-0.545978\pi\) | ||||
−0.143941 | + | 0.989586i | \(0.545978\pi\) | |||||||
\(158\) | 7.67840 | 0.610860 | ||||||||
\(159\) | 16.6039 | 1.31677 | ||||||||
\(160\) | 3.37289 | 0.266651 | ||||||||
\(161\) | −27.1908 | −2.14293 | ||||||||
\(162\) | 1.17652 | 0.0924365 | ||||||||
\(163\) | 24.8027 | 1.94270 | 0.971350 | − | 0.237654i | \(-0.0763783\pi\) | ||||
0.971350 | + | 0.237654i | \(0.0763783\pi\) | |||||||
\(164\) | 0.208344 | 0.0162689 | ||||||||
\(165\) | −2.78278 | −0.216639 | ||||||||
\(166\) | −14.8715 | −1.15425 | ||||||||
\(167\) | 6.22933 | 0.482040 | 0.241020 | − | 0.970520i | \(-0.422518\pi\) | ||||
0.241020 | + | 0.970520i | \(0.422518\pi\) | |||||||
\(168\) | −32.2113 | −2.48515 | ||||||||
\(169\) | −9.14010 | −0.703085 | ||||||||
\(170\) | 1.95100 | 0.149635 | ||||||||
\(171\) | 6.95380 | 0.531770 | ||||||||
\(172\) | 0.254758 | 0.0194251 | ||||||||
\(173\) | −5.79410 | −0.440517 | −0.220258 | − | 0.975442i | \(-0.570690\pi\) | ||||
−0.220258 | + | 0.975442i | \(0.570690\pi\) | |||||||
\(174\) | 14.5387 | 1.10218 | ||||||||
\(175\) | −5.17171 | −0.390945 | ||||||||
\(176\) | 4.85275 | 0.365789 | ||||||||
\(177\) | 21.0933 | 1.58547 | ||||||||
\(178\) | −16.9120 | −1.26761 | ||||||||
\(179\) | 0.408017 | 0.0304966 | 0.0152483 | − | 0.999884i | \(-0.495146\pi\) | ||||
0.0152483 | + | 0.999884i | \(0.495146\pi\) | |||||||
\(180\) | 2.92346 | 0.217902 | ||||||||
\(181\) | 16.8460 | 1.25215 | 0.626076 | − | 0.779762i | \(-0.284660\pi\) | ||||
0.626076 | + | 0.779762i | \(0.284660\pi\) | |||||||
\(182\) | −16.4347 | −1.21822 | ||||||||
\(183\) | 31.3540 | 2.31775 | ||||||||
\(184\) | 11.7674 | 0.867507 | ||||||||
\(185\) | 1.24419 | 0.0914744 | ||||||||
\(186\) | −19.7252 | −1.44632 | ||||||||
\(187\) | 1.20619 | 0.0882057 | ||||||||
\(188\) | −2.10140 | −0.153260 | ||||||||
\(189\) | −25.0972 | −1.82555 | ||||||||
\(190\) | −2.37100 | −0.172010 | ||||||||
\(191\) | −21.3403 | −1.54413 | −0.772064 | − | 0.635545i | \(-0.780775\pi\) | ||||
−0.772064 | + | 0.635545i | \(0.780775\pi\) | |||||||
\(192\) | 11.8265 | 0.853502 | ||||||||
\(193\) | 16.3527 | 1.17709 | 0.588547 | − | 0.808463i | \(-0.299700\pi\) | ||||
0.588547 | + | 0.808463i | \(0.299700\pi\) | |||||||
\(194\) | −23.8726 | −1.71395 | ||||||||
\(195\) | −5.46722 | −0.391516 | ||||||||
\(196\) | 12.1691 | 0.869221 | ||||||||
\(197\) | −2.50342 | −0.178361 | −0.0891806 | − | 0.996015i | \(-0.528425\pi\) | ||||
−0.0891806 | + | 0.996015i | \(0.528425\pi\) | |||||||
\(198\) | 7.67313 | 0.545305 | ||||||||
\(199\) | 1.96225 | 0.139100 | 0.0695499 | − | 0.997578i | \(-0.477844\pi\) | ||||
0.0695499 | + | 0.997578i | \(0.477844\pi\) | |||||||
\(200\) | 2.23818 | 0.158263 | ||||||||
\(201\) | 7.27064 | 0.512831 | ||||||||
\(202\) | −6.16501 | −0.433769 | ||||||||
\(203\) | 16.7048 | 1.17245 | ||||||||
\(204\) | −2.06853 | −0.144826 | ||||||||
\(205\) | 0.338077 | 0.0236123 | ||||||||
\(206\) | 21.6924 | 1.51138 | ||||||||
\(207\) | 24.9413 | 1.73354 | ||||||||
\(208\) | 9.53400 | 0.661064 | ||||||||
\(209\) | −1.46585 | −0.101395 | ||||||||
\(210\) | 23.2784 | 1.60637 | ||||||||
\(211\) | 6.77598 | 0.466478 | 0.233239 | − | 0.972419i | \(-0.425068\pi\) | ||||
0.233239 | + | 0.972419i | \(0.425068\pi\) | |||||||
\(212\) | 3.67702 | 0.252539 | ||||||||
\(213\) | −35.7190 | −2.44743 | ||||||||
\(214\) | 7.25002 | 0.495601 | ||||||||
\(215\) | 0.413393 | 0.0281932 | ||||||||
\(216\) | 10.8614 | 0.739023 | ||||||||
\(217\) | −22.6640 | −1.53854 | ||||||||
\(218\) | −8.90963 | −0.603436 | ||||||||
\(219\) | −2.78278 | −0.188043 | ||||||||
\(220\) | −0.616262 | −0.0415484 | ||||||||
\(221\) | 2.36976 | 0.159408 | ||||||||
\(222\) | −5.60022 | −0.375862 | ||||||||
\(223\) | −8.18519 | −0.548121 | −0.274060 | − | 0.961712i | \(-0.588367\pi\) | ||||
−0.274060 | + | 0.961712i | \(0.588367\pi\) | |||||||
\(224\) | −17.4436 | −1.16550 | ||||||||
\(225\) | 4.74386 | 0.316257 | ||||||||
\(226\) | 29.3082 | 1.94956 | ||||||||
\(227\) | −2.00813 | −0.133284 | −0.0666422 | − | 0.997777i | \(-0.521229\pi\) | ||||
−0.0666422 | + | 0.997777i | \(0.521229\pi\) | |||||||
\(228\) | 2.51382 | 0.166482 | ||||||||
\(229\) | 2.02799 | 0.134013 | 0.0670067 | − | 0.997753i | \(-0.478655\pi\) | ||||
0.0670067 | + | 0.997753i | \(0.478655\pi\) | |||||||
\(230\) | −8.50409 | −0.560743 | ||||||||
\(231\) | 14.3917 | 0.946907 | ||||||||
\(232\) | −7.22939 | −0.474632 | ||||||||
\(233\) | −3.39690 | −0.222538 | −0.111269 | − | 0.993790i | \(-0.535492\pi\) | ||||
−0.111269 | + | 0.993790i | \(0.535492\pi\) | |||||||
\(234\) | 15.0751 | 0.985490 | ||||||||
\(235\) | −3.40991 | −0.222438 | ||||||||
\(236\) | 4.67123 | 0.304071 | ||||||||
\(237\) | −13.2102 | −0.858093 | ||||||||
\(238\) | −10.0900 | −0.654040 | ||||||||
\(239\) | −21.4343 | −1.38647 | −0.693234 | − | 0.720713i | \(-0.743815\pi\) | ||||
−0.693234 | + | 0.720713i | \(0.743815\pi\) | |||||||
\(240\) | −13.5041 | −0.871687 | ||||||||
\(241\) | −22.4218 | −1.44432 | −0.722159 | − | 0.691727i | \(-0.756850\pi\) | ||||
−0.722159 | + | 0.691727i | \(0.756850\pi\) | |||||||
\(242\) | −1.61749 | −0.103976 | ||||||||
\(243\) | −16.5825 | −1.06377 | ||||||||
\(244\) | 6.94351 | 0.444513 | ||||||||
\(245\) | 19.7466 | 1.26157 | ||||||||
\(246\) | −1.52172 | −0.0970213 | ||||||||
\(247\) | −2.87990 | −0.183244 | ||||||||
\(248\) | 9.80838 | 0.622833 | ||||||||
\(249\) | 25.5854 | 1.62141 | ||||||||
\(250\) | −1.61749 | −0.102299 | ||||||||
\(251\) | 12.4099 | 0.783308 | 0.391654 | − | 0.920113i | \(-0.371903\pi\) | ||||
0.391654 | + | 0.920113i | \(0.371903\pi\) | |||||||
\(252\) | −15.1193 | −0.952426 | ||||||||
\(253\) | −5.25760 | −0.330542 | ||||||||
\(254\) | −2.31108 | −0.145010 | ||||||||
\(255\) | −3.35657 | −0.210197 | ||||||||
\(256\) | 13.5303 | 0.845641 | ||||||||
\(257\) | −10.1366 | −0.632301 | −0.316150 | − | 0.948709i | \(-0.602390\pi\) | ||||
−0.316150 | + | 0.948709i | \(0.602390\pi\) | |||||||
\(258\) | −1.86073 | −0.115844 | ||||||||
\(259\) | −6.43458 | −0.399825 | ||||||||
\(260\) | −1.21075 | −0.0750873 | ||||||||
\(261\) | −15.3228 | −0.948459 | ||||||||
\(262\) | −24.1586 | −1.49252 | ||||||||
\(263\) | 13.3700 | 0.824428 | 0.412214 | − | 0.911087i | \(-0.364756\pi\) | ||||
0.412214 | + | 0.911087i | \(0.364756\pi\) | |||||||
\(264\) | −6.22835 | −0.383329 | ||||||||
\(265\) | 5.96665 | 0.366528 | ||||||||
\(266\) | 12.2621 | 0.751838 | ||||||||
\(267\) | 29.0960 | 1.78065 | ||||||||
\(268\) | 1.61012 | 0.0983540 | ||||||||
\(269\) | −8.84755 | −0.539444 | −0.269722 | − | 0.962938i | \(-0.586932\pi\) | ||||
−0.269722 | + | 0.962938i | \(0.586932\pi\) | |||||||
\(270\) | −7.84930 | −0.477693 | ||||||||
\(271\) | −9.97716 | −0.606069 | −0.303035 | − | 0.952980i | \(-0.598000\pi\) | ||||
−0.303035 | + | 0.952980i | \(0.598000\pi\) | |||||||
\(272\) | 5.85335 | 0.354912 | ||||||||
\(273\) | 28.2749 | 1.71127 | ||||||||
\(274\) | −31.4163 | −1.89793 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 9.01636 | 0.542721 | ||||||||
\(277\) | −0.0362213 | −0.00217633 | −0.00108816 | − | 0.999999i | \(-0.500346\pi\) | ||||
−0.00108816 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(278\) | −25.2709 | −1.51565 | ||||||||
\(279\) | 20.7890 | 1.24461 | ||||||||
\(280\) | −11.5752 | −0.691751 | ||||||||
\(281\) | 5.16239 | 0.307963 | 0.153981 | − | 0.988074i | \(-0.450790\pi\) | ||||
0.153981 | + | 0.988074i | \(0.450790\pi\) | |||||||
\(282\) | 15.3484 | 0.913982 | ||||||||
\(283\) | 3.77015 | 0.224112 | 0.112056 | − | 0.993702i | \(-0.464256\pi\) | ||||
0.112056 | + | 0.993702i | \(0.464256\pi\) | |||||||
\(284\) | −7.91018 | −0.469383 | ||||||||
\(285\) | 4.07914 | 0.241628 | ||||||||
\(286\) | −3.17781 | −0.187908 | ||||||||
\(287\) | −1.74844 | −0.103207 | ||||||||
\(288\) | 16.0005 | 0.942841 | ||||||||
\(289\) | −15.5451 | −0.914417 | ||||||||
\(290\) | 5.22453 | 0.306795 | ||||||||
\(291\) | 41.0712 | 2.40764 | ||||||||
\(292\) | −0.616262 | −0.0360640 | ||||||||
\(293\) | 22.4755 | 1.31303 | 0.656515 | − | 0.754313i | \(-0.272030\pi\) | ||||
0.656515 | + | 0.754313i | \(0.272030\pi\) | |||||||
\(294\) | −88.8817 | −5.18369 | ||||||||
\(295\) | 7.57994 | 0.441321 | ||||||||
\(296\) | 2.78471 | 0.161858 | ||||||||
\(297\) | −4.85277 | −0.281587 | ||||||||
\(298\) | −26.5976 | −1.54076 | ||||||||
\(299\) | −10.3294 | −0.597364 | ||||||||
\(300\) | 1.71492 | 0.0990110 | ||||||||
\(301\) | −2.13795 | −0.123229 | ||||||||
\(302\) | −32.5459 | −1.87280 | ||||||||
\(303\) | 10.6065 | 0.609328 | ||||||||
\(304\) | −7.11341 | −0.407982 | ||||||||
\(305\) | 11.2671 | 0.645155 | ||||||||
\(306\) | 9.25528 | 0.529089 | ||||||||
\(307\) | −21.1061 | −1.20459 | −0.602293 | − | 0.798275i | \(-0.705746\pi\) | ||||
−0.602293 | + | 0.798275i | \(0.705746\pi\) | |||||||
\(308\) | 3.18713 | 0.181604 | ||||||||
\(309\) | −37.3203 | −2.12308 | ||||||||
\(310\) | −7.08832 | −0.402590 | ||||||||
\(311\) | −7.31842 | −0.414989 | −0.207495 | − | 0.978236i | \(-0.566531\pi\) | ||||
−0.207495 | + | 0.978236i | \(0.566531\pi\) | |||||||
\(312\) | −12.2366 | −0.692761 | ||||||||
\(313\) | −10.8806 | −0.615010 | −0.307505 | − | 0.951546i | \(-0.599494\pi\) | ||||
−0.307505 | + | 0.951546i | \(0.599494\pi\) | |||||||
\(314\) | 5.83451 | 0.329261 | ||||||||
\(315\) | −24.5339 | −1.38233 | ||||||||
\(316\) | −2.92547 | −0.164570 | ||||||||
\(317\) | 5.69923 | 0.320100 | 0.160050 | − | 0.987109i | \(-0.448834\pi\) | ||||
0.160050 | + | 0.987109i | \(0.448834\pi\) | |||||||
\(318\) | −26.8565 | −1.50604 | ||||||||
\(319\) | 3.23003 | 0.180847 | ||||||||
\(320\) | 4.24988 | 0.237576 | ||||||||
\(321\) | −12.4732 | −0.696185 | ||||||||
\(322\) | 43.9807 | 2.45095 | ||||||||
\(323\) | −1.76810 | −0.0983799 | ||||||||
\(324\) | −0.448255 | −0.0249031 | ||||||||
\(325\) | −1.96466 | −0.108980 | ||||||||
\(326\) | −40.1181 | −2.22193 | ||||||||
\(327\) | 15.3284 | 0.847664 | ||||||||
\(328\) | 0.756676 | 0.0417804 | ||||||||
\(329\) | 17.6351 | 0.972253 | ||||||||
\(330\) | 4.50111 | 0.247778 | ||||||||
\(331\) | 32.0185 | 1.75989 | 0.879947 | − | 0.475072i | \(-0.157578\pi\) | ||||
0.879947 | + | 0.475072i | \(0.157578\pi\) | |||||||
\(332\) | 5.66602 | 0.310963 | ||||||||
\(333\) | 5.90225 | 0.323441 | ||||||||
\(334\) | −10.0759 | −0.551326 | ||||||||
\(335\) | 2.61273 | 0.142748 | ||||||||
\(336\) | 69.8394 | 3.81005 | ||||||||
\(337\) | −15.7934 | −0.860319 | −0.430159 | − | 0.902753i | \(-0.641543\pi\) | ||||
−0.430159 | + | 0.902753i | \(0.641543\pi\) | |||||||
\(338\) | 14.7840 | 0.804143 | ||||||||
\(339\) | −50.4229 | −2.73860 | ||||||||
\(340\) | −0.743332 | −0.0403128 | ||||||||
\(341\) | −4.38231 | −0.237315 | ||||||||
\(342\) | −11.2477 | −0.608204 | ||||||||
\(343\) | −65.9220 | −3.55945 | ||||||||
\(344\) | 0.925247 | 0.0498860 | ||||||||
\(345\) | 14.6307 | 0.787692 | ||||||||
\(346\) | 9.37187 | 0.503835 | ||||||||
\(347\) | −0.903324 | −0.0484930 | −0.0242465 | − | 0.999706i | \(-0.507719\pi\) | ||||
−0.0242465 | + | 0.999706i | \(0.507719\pi\) | |||||||
\(348\) | −5.53925 | −0.296935 | ||||||||
\(349\) | −11.4215 | −0.611379 | −0.305689 | − | 0.952131i | \(-0.598887\pi\) | ||||
−0.305689 | + | 0.952131i | \(0.598887\pi\) | |||||||
\(350\) | 8.36518 | 0.447138 | ||||||||
\(351\) | −9.53406 | −0.508891 | ||||||||
\(352\) | −3.37289 | −0.179776 | ||||||||
\(353\) | 19.1505 | 1.01928 | 0.509639 | − | 0.860388i | \(-0.329779\pi\) | ||||
0.509639 | + | 0.860388i | \(0.329779\pi\) | |||||||
\(354\) | −34.1181 | −1.81336 | ||||||||
\(355\) | −12.8357 | −0.681251 | ||||||||
\(356\) | 6.44347 | 0.341503 | ||||||||
\(357\) | 17.3592 | 0.918748 | ||||||||
\(358\) | −0.659961 | −0.0348800 | ||||||||
\(359\) | −21.6269 | −1.14142 | −0.570712 | − | 0.821150i | \(-0.693333\pi\) | ||||
−0.570712 | + | 0.821150i | \(0.693333\pi\) | |||||||
\(360\) | 10.6176 | 0.559597 | ||||||||
\(361\) | −16.8513 | −0.886909 | ||||||||
\(362\) | −27.2482 | −1.43213 | ||||||||
\(363\) | 2.78278 | 0.146058 | ||||||||
\(364\) | 6.26163 | 0.328199 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −50.7146 | −2.65090 | ||||||||
\(367\) | −10.0892 | −0.526652 | −0.263326 | − | 0.964707i | \(-0.584819\pi\) | ||||
−0.263326 | + | 0.964707i | \(0.584819\pi\) | |||||||
\(368\) | −25.5138 | −1.33000 | ||||||||
\(369\) | 1.60379 | 0.0834899 | ||||||||
\(370\) | −2.01245 | −0.104623 | ||||||||
\(371\) | −30.8578 | −1.60206 | ||||||||
\(372\) | 7.51531 | 0.389651 | ||||||||
\(373\) | −8.23827 | −0.426562 | −0.213281 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213281 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(374\) | −1.95100 | −0.100884 | ||||||||
\(375\) | 2.78278 | 0.143702 | ||||||||
\(376\) | −7.63198 | −0.393589 | ||||||||
\(377\) | 6.34592 | 0.326832 | ||||||||
\(378\) | 40.5943 | 2.08795 | ||||||||
\(379\) | −12.9820 | −0.666838 | −0.333419 | − | 0.942779i | \(-0.608202\pi\) | ||||
−0.333419 | + | 0.942779i | \(0.608202\pi\) | |||||||
\(380\) | 0.903349 | 0.0463408 | ||||||||
\(381\) | 3.97606 | 0.203700 | ||||||||
\(382\) | 34.5176 | 1.76607 | ||||||||
\(383\) | 15.1968 | 0.776522 | 0.388261 | − | 0.921550i | \(-0.373076\pi\) | ||||
0.388261 | + | 0.921550i | \(0.373076\pi\) | |||||||
\(384\) | −37.9012 | −1.93414 | ||||||||
\(385\) | 5.17171 | 0.263575 | ||||||||
\(386\) | −26.4503 | −1.34628 | ||||||||
\(387\) | 1.96108 | 0.0996872 | ||||||||
\(388\) | 9.09544 | 0.461751 | ||||||||
\(389\) | 26.1275 | 1.32472 | 0.662359 | − | 0.749187i | \(-0.269555\pi\) | ||||
0.662359 | + | 0.749187i | \(0.269555\pi\) | |||||||
\(390\) | 8.84315 | 0.447790 | ||||||||
\(391\) | −6.34168 | −0.320713 | ||||||||
\(392\) | 44.1965 | 2.23226 | ||||||||
\(393\) | 41.5633 | 2.09659 | ||||||||
\(394\) | 4.04925 | 0.203998 | ||||||||
\(395\) | −4.74712 | −0.238853 | ||||||||
\(396\) | −2.92346 | −0.146909 | ||||||||
\(397\) | 10.5780 | 0.530896 | 0.265448 | − | 0.964125i | \(-0.414480\pi\) | ||||
0.265448 | + | 0.964125i | \(0.414480\pi\) | |||||||
\(398\) | −3.17391 | −0.159093 | ||||||||
\(399\) | −21.0962 | −1.05613 | ||||||||
\(400\) | −4.85275 | −0.242637 | ||||||||
\(401\) | 14.8349 | 0.740822 | 0.370411 | − | 0.928868i | \(-0.379217\pi\) | ||||
0.370411 | + | 0.928868i | \(0.379217\pi\) | |||||||
\(402\) | −11.7602 | −0.586543 | ||||||||
\(403\) | −8.60975 | −0.428882 | ||||||||
\(404\) | 2.34887 | 0.116861 | ||||||||
\(405\) | −0.727378 | −0.0361437 | ||||||||
\(406\) | −27.0198 | −1.34097 | ||||||||
\(407\) | −1.24419 | −0.0616720 | ||||||||
\(408\) | −7.51260 | −0.371929 | ||||||||
\(409\) | 39.4074 | 1.94857 | 0.974284 | − | 0.225322i | \(-0.0723435\pi\) | ||||
0.974284 | + | 0.225322i | \(0.0723435\pi\) | |||||||
\(410\) | −0.546834 | −0.0270062 | ||||||||
\(411\) | 54.0497 | 2.66607 | ||||||||
\(412\) | −8.26480 | −0.407177 | ||||||||
\(413\) | −39.2013 | −1.92897 | ||||||||
\(414\) | −40.3422 | −1.98271 | ||||||||
\(415\) | 9.19417 | 0.451324 | ||||||||
\(416\) | −6.62660 | −0.324896 | ||||||||
\(417\) | 43.4768 | 2.12907 | ||||||||
\(418\) | 2.37100 | 0.115969 | ||||||||
\(419\) | 26.4856 | 1.29391 | 0.646954 | − | 0.762529i | \(-0.276043\pi\) | ||||
0.646954 | + | 0.762529i | \(0.276043\pi\) | |||||||
\(420\) | −8.86908 | −0.432767 | ||||||||
\(421\) | −5.18173 | −0.252542 | −0.126271 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126271 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(422\) | −10.9601 | −0.533527 | ||||||||
\(423\) | −16.1761 | −0.786510 | ||||||||
\(424\) | 13.3544 | 0.648548 | ||||||||
\(425\) | −1.20619 | −0.0585090 | ||||||||
\(426\) | 57.7751 | 2.79921 | ||||||||
\(427\) | −58.2705 | −2.81991 | ||||||||
\(428\) | −2.76226 | −0.133519 | ||||||||
\(429\) | 5.46722 | 0.263960 | ||||||||
\(430\) | −0.668658 | −0.0322455 | ||||||||
\(431\) | −12.0400 | −0.579946 | −0.289973 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289973 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(432\) | −23.5493 | −1.13302 | ||||||||
\(433\) | −6.02638 | −0.289609 | −0.144805 | − | 0.989460i | \(-0.546255\pi\) | ||||
−0.144805 | + | 0.989460i | \(0.546255\pi\) | |||||||
\(434\) | 36.6588 | 1.75968 | ||||||||
\(435\) | −8.98847 | −0.430964 | ||||||||
\(436\) | 3.39457 | 0.162570 | ||||||||
\(437\) | 7.70686 | 0.368669 | ||||||||
\(438\) | 4.50111 | 0.215071 | ||||||||
\(439\) | −2.84212 | −0.135647 | −0.0678236 | − | 0.997697i | \(-0.521606\pi\) | ||||
−0.0678236 | + | 0.997697i | \(0.521606\pi\) | |||||||
\(440\) | −2.23818 | −0.106701 | ||||||||
\(441\) | 93.6753 | 4.46073 | ||||||||
\(442\) | −3.83306 | −0.182320 | ||||||||
\(443\) | 20.9707 | 0.996348 | 0.498174 | − | 0.867077i | \(-0.334004\pi\) | ||||
0.498174 | + | 0.867077i | \(0.334004\pi\) | |||||||
\(444\) | 2.13368 | 0.101260 | ||||||||
\(445\) | 10.4557 | 0.495649 | ||||||||
\(446\) | 13.2394 | 0.626905 | ||||||||
\(447\) | 45.7594 | 2.16435 | ||||||||
\(448\) | −21.9792 | −1.03842 | ||||||||
\(449\) | 12.4509 | 0.587594 | 0.293797 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293797 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(450\) | −7.67313 | −0.361715 | ||||||||
\(451\) | −0.338077 | −0.0159194 | ||||||||
\(452\) | −11.1664 | −0.525225 | ||||||||
\(453\) | 55.9930 | 2.63078 | ||||||||
\(454\) | 3.24813 | 0.152442 | ||||||||
\(455\) | 10.1607 | 0.476340 | ||||||||
\(456\) | 9.12984 | 0.427544 | ||||||||
\(457\) | −41.7766 | −1.95423 | −0.977114 | − | 0.212715i | \(-0.931770\pi\) | ||||
−0.977114 | + | 0.212715i | \(0.931770\pi\) | |||||||
\(458\) | −3.28025 | −0.153276 | ||||||||
\(459\) | −5.85339 | −0.273213 | ||||||||
\(460\) | 3.24006 | 0.151068 | ||||||||
\(461\) | 38.3701 | 1.78708 | 0.893538 | − | 0.448988i | \(-0.148215\pi\) | ||||
0.893538 | + | 0.448988i | \(0.148215\pi\) | |||||||
\(462\) | −23.2784 | −1.08301 | ||||||||
\(463\) | 33.5022 | 1.55698 | 0.778490 | − | 0.627657i | \(-0.215986\pi\) | ||||
0.778490 | + | 0.627657i | \(0.215986\pi\) | |||||||
\(464\) | 15.6745 | 0.727672 | ||||||||
\(465\) | 12.1950 | 0.565529 | ||||||||
\(466\) | 5.49444 | 0.254525 | ||||||||
\(467\) | −23.3483 | −1.08043 | −0.540216 | − | 0.841526i | \(-0.681658\pi\) | ||||
−0.540216 | + | 0.841526i | \(0.681658\pi\) | |||||||
\(468\) | −5.74361 | −0.265498 | ||||||||
\(469\) | −13.5123 | −0.623939 | ||||||||
\(470\) | 5.51548 | 0.254410 | ||||||||
\(471\) | −10.0379 | −0.462522 | ||||||||
\(472\) | 16.9653 | 0.780889 | ||||||||
\(473\) | −0.413393 | −0.0190078 | ||||||||
\(474\) | 21.3673 | 0.981432 | ||||||||
\(475\) | 1.46585 | 0.0672579 | ||||||||
\(476\) | 3.84430 | 0.176203 | ||||||||
\(477\) | 28.3049 | 1.29599 | ||||||||
\(478\) | 34.6696 | 1.58575 | ||||||||
\(479\) | 15.3855 | 0.702979 | 0.351490 | − | 0.936192i | \(-0.385675\pi\) | ||||
0.351490 | + | 0.936192i | \(0.385675\pi\) | |||||||
\(480\) | 9.38602 | 0.428411 | ||||||||
\(481\) | −2.44441 | −0.111455 | ||||||||
\(482\) | 36.2670 | 1.65192 | ||||||||
\(483\) | −75.6659 | −3.44292 | ||||||||
\(484\) | 0.616262 | 0.0280119 | ||||||||
\(485\) | 14.7591 | 0.670174 | ||||||||
\(486\) | 26.8219 | 1.21667 | ||||||||
\(487\) | −24.1495 | −1.09432 | −0.547159 | − | 0.837028i | \(-0.684291\pi\) | ||||
−0.547159 | + | 0.837028i | \(0.684291\pi\) | |||||||
\(488\) | 25.2179 | 1.14156 | ||||||||
\(489\) | 69.0205 | 3.12122 | ||||||||
\(490\) | −31.9399 | −1.44290 | ||||||||
\(491\) | 12.7278 | 0.574398 | 0.287199 | − | 0.957871i | \(-0.407276\pi\) | ||||
0.287199 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(492\) | 0.579775 | 0.0261383 | ||||||||
\(493\) | 3.89605 | 0.175469 | ||||||||
\(494\) | 4.65820 | 0.209583 | ||||||||
\(495\) | −4.74386 | −0.213221 | ||||||||
\(496\) | −21.2662 | −0.954881 | ||||||||
\(497\) | 66.3828 | 2.97768 | ||||||||
\(498\) | −41.3840 | −1.85446 | ||||||||
\(499\) | 26.8541 | 1.20215 | 0.601077 | − | 0.799191i | \(-0.294739\pi\) | ||||
0.601077 | + | 0.799191i | \(0.294739\pi\) | |||||||
\(500\) | 0.616262 | 0.0275601 | ||||||||
\(501\) | 17.3349 | 0.774464 | ||||||||
\(502\) | −20.0729 | −0.895897 | ||||||||
\(503\) | −3.42219 | −0.152588 | −0.0762940 | − | 0.997085i | \(-0.524309\pi\) | ||||
−0.0762940 | + | 0.997085i | \(0.524309\pi\) | |||||||
\(504\) | −54.9112 | −2.44594 | ||||||||
\(505\) | 3.81148 | 0.169609 | ||||||||
\(506\) | 8.50409 | 0.378053 | ||||||||
\(507\) | −25.4349 | −1.12960 | ||||||||
\(508\) | 0.880522 | 0.0390668 | ||||||||
\(509\) | −18.8514 | −0.835575 | −0.417787 | − | 0.908545i | \(-0.637194\pi\) | ||||
−0.417787 | + | 0.908545i | \(0.637194\pi\) | |||||||
\(510\) | 5.42921 | 0.240409 | ||||||||
\(511\) | 5.17171 | 0.228783 | ||||||||
\(512\) | 5.35481 | 0.236652 | ||||||||
\(513\) | 7.11345 | 0.314066 | ||||||||
\(514\) | 16.3957 | 0.723185 | ||||||||
\(515\) | −13.4112 | −0.590967 | ||||||||
\(516\) | 0.708936 | 0.0312092 | ||||||||
\(517\) | 3.40991 | 0.149968 | ||||||||
\(518\) | 10.4078 | 0.457294 | ||||||||
\(519\) | −16.1237 | −0.707751 | ||||||||
\(520\) | −4.39726 | −0.192833 | ||||||||
\(521\) | −10.7512 | −0.471017 | −0.235509 | − | 0.971872i | \(-0.575676\pi\) | ||||
−0.235509 | + | 0.971872i | \(0.575676\pi\) | |||||||
\(522\) | 24.7845 | 1.08479 | ||||||||
\(523\) | −12.5296 | −0.547879 | −0.273940 | − | 0.961747i | \(-0.588327\pi\) | ||||
−0.273940 | + | 0.961747i | \(0.588327\pi\) | |||||||
\(524\) | 9.20442 | 0.402097 | ||||||||
\(525\) | −14.3917 | −0.628107 | ||||||||
\(526\) | −21.6257 | −0.942927 | ||||||||
\(527\) | −5.28591 | −0.230258 | ||||||||
\(528\) | 13.5041 | 0.587691 | ||||||||
\(529\) | 4.64231 | 0.201840 | ||||||||
\(530\) | −9.65098 | −0.419212 | ||||||||
\(531\) | 35.9582 | 1.56045 | ||||||||
\(532\) | −4.67186 | −0.202551 | ||||||||
\(533\) | −0.664206 | −0.0287700 | ||||||||
\(534\) | −47.0624 | −2.03659 | ||||||||
\(535\) | −4.48228 | −0.193786 | ||||||||
\(536\) | 5.84774 | 0.252584 | ||||||||
\(537\) | 1.13542 | 0.0489970 | ||||||||
\(538\) | 14.3108 | 0.616982 | ||||||||
\(539\) | −19.7466 | −0.850548 | ||||||||
\(540\) | 2.99058 | 0.128694 | ||||||||
\(541\) | 21.8026 | 0.937368 | 0.468684 | − | 0.883366i | \(-0.344728\pi\) | ||||
0.468684 | + | 0.883366i | \(0.344728\pi\) | |||||||
\(542\) | 16.1379 | 0.693183 | ||||||||
\(543\) | 46.8787 | 2.01176 | ||||||||
\(544\) | −4.06837 | −0.174430 | ||||||||
\(545\) | 5.50832 | 0.235950 | ||||||||
\(546\) | −45.7343 | −1.95725 | ||||||||
\(547\) | −1.26711 | −0.0541776 | −0.0270888 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270888 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(548\) | 11.9696 | 0.511316 | ||||||||
\(549\) | 53.4498 | 2.28118 | ||||||||
\(550\) | 1.61749 | 0.0689698 | ||||||||
\(551\) | −4.73475 | −0.201707 | ||||||||
\(552\) | 32.7462 | 1.39377 | ||||||||
\(553\) | 24.5507 | 1.04400 | ||||||||
\(554\) | 0.0585874 | 0.00248914 | ||||||||
\(555\) | 3.46230 | 0.146966 | ||||||||
\(556\) | 9.62819 | 0.408326 | ||||||||
\(557\) | 35.0295 | 1.48425 | 0.742124 | − | 0.670263i | \(-0.233819\pi\) | ||||
0.742124 | + | 0.670263i | \(0.233819\pi\) | |||||||
\(558\) | −33.6260 | −1.42350 | ||||||||
\(559\) | −0.812177 | −0.0343514 | ||||||||
\(560\) | 25.0970 | 1.06054 | ||||||||
\(561\) | 3.35657 | 0.141715 | ||||||||
\(562\) | −8.35010 | −0.352228 | ||||||||
\(563\) | 3.56704 | 0.150333 | 0.0751664 | − | 0.997171i | \(-0.476051\pi\) | ||||
0.0751664 | + | 0.997171i | \(0.476051\pi\) | |||||||
\(564\) | −5.84772 | −0.246234 | ||||||||
\(565\) | −18.1196 | −0.762298 | ||||||||
\(566\) | −6.09816 | −0.256325 | ||||||||
\(567\) | 3.76179 | 0.157980 | ||||||||
\(568\) | −28.7287 | −1.20543 | ||||||||
\(569\) | 44.4117 | 1.86183 | 0.930917 | − | 0.365230i | \(-0.119010\pi\) | ||||
0.930917 | + | 0.365230i | \(0.119010\pi\) | |||||||
\(570\) | −6.59796 | −0.276358 | ||||||||
\(571\) | −25.4825 | −1.06641 | −0.533206 | − | 0.845986i | \(-0.679013\pi\) | ||||
−0.533206 | + | 0.845986i | \(0.679013\pi\) | |||||||
\(572\) | 1.21075 | 0.0506238 | ||||||||
\(573\) | −59.3852 | −2.48085 | ||||||||
\(574\) | 2.82807 | 0.118041 | ||||||||
\(575\) | 5.25760 | 0.219257 | ||||||||
\(576\) | 20.1608 | 0.840035 | ||||||||
\(577\) | −11.2279 | −0.467426 | −0.233713 | − | 0.972306i | \(-0.575088\pi\) | ||||
−0.233713 | + | 0.972306i | \(0.575088\pi\) | |||||||
\(578\) | 25.1440 | 1.04585 | ||||||||
\(579\) | 45.5060 | 1.89116 | ||||||||
\(580\) | −1.99055 | −0.0826529 | ||||||||
\(581\) | −47.5496 | −1.97269 | ||||||||
\(582\) | −66.4321 | −2.75370 | ||||||||
\(583\) | −5.96665 | −0.247113 | ||||||||
\(584\) | −2.23818 | −0.0926164 | ||||||||
\(585\) | −9.32008 | −0.385338 | ||||||||
\(586\) | −36.3537 | −1.50176 | ||||||||
\(587\) | −28.5203 | −1.17716 | −0.588579 | − | 0.808440i | \(-0.700312\pi\) | ||||
−0.588579 | + | 0.808440i | \(0.700312\pi\) | |||||||
\(588\) | 33.8639 | 1.39652 | ||||||||
\(589\) | 6.42381 | 0.264689 | ||||||||
\(590\) | −12.2604 | −0.504755 | ||||||||
\(591\) | −6.96646 | −0.286562 | ||||||||
\(592\) | −6.03772 | −0.248149 | ||||||||
\(593\) | −41.2072 | −1.69218 | −0.846088 | − | 0.533044i | \(-0.821048\pi\) | ||||
−0.846088 | + | 0.533044i | \(0.821048\pi\) | |||||||
\(594\) | 7.84930 | 0.322061 | ||||||||
\(595\) | 6.23809 | 0.255737 | ||||||||
\(596\) | 10.1337 | 0.415092 | ||||||||
\(597\) | 5.46050 | 0.223483 | ||||||||
\(598\) | 16.7077 | 0.683227 | ||||||||
\(599\) | 1.93477 | 0.0790525 | 0.0395263 | − | 0.999219i | \(-0.487415\pi\) | ||||
0.0395263 | + | 0.999219i | \(0.487415\pi\) | |||||||
\(600\) | 6.22835 | 0.254271 | ||||||||
\(601\) | −45.6035 | −1.86021 | −0.930104 | − | 0.367297i | \(-0.880283\pi\) | ||||
−0.930104 | + | 0.367297i | \(0.880283\pi\) | |||||||
\(602\) | 3.45811 | 0.140942 | ||||||||
\(603\) | 12.3944 | 0.504739 | ||||||||
\(604\) | 12.4000 | 0.504547 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −17.1559 | −0.696910 | ||||||||
\(607\) | 40.0947 | 1.62739 | 0.813697 | − | 0.581289i | \(-0.197451\pi\) | ||||
0.813697 | + | 0.581289i | \(0.197451\pi\) | |||||||
\(608\) | 4.94416 | 0.200512 | ||||||||
\(609\) | 46.4858 | 1.88370 | ||||||||
\(610\) | −18.2245 | −0.737887 | ||||||||
\(611\) | 6.69932 | 0.271025 | ||||||||
\(612\) | −3.52626 | −0.142541 | ||||||||
\(613\) | −25.4550 | −1.02812 | −0.514059 | − | 0.857755i | \(-0.671859\pi\) | ||||
−0.514059 | + | 0.857755i | \(0.671859\pi\) | |||||||
\(614\) | 34.1388 | 1.37773 | ||||||||
\(615\) | 0.940793 | 0.0379364 | ||||||||
\(616\) | 11.5752 | 0.466379 | ||||||||
\(617\) | 25.8050 | 1.03887 | 0.519434 | − | 0.854510i | \(-0.326143\pi\) | ||||
0.519434 | + | 0.854510i | \(0.326143\pi\) | |||||||
\(618\) | 60.3651 | 2.42824 | ||||||||
\(619\) | 16.9067 | 0.679536 | 0.339768 | − | 0.940509i | \(-0.389651\pi\) | ||||
0.339768 | + | 0.940509i | \(0.389651\pi\) | |||||||
\(620\) | 2.70065 | 0.108461 | ||||||||
\(621\) | 25.5139 | 1.02384 | ||||||||
\(622\) | 11.8374 | 0.474638 | ||||||||
\(623\) | −54.0741 | −2.16643 | ||||||||
\(624\) | 26.5310 | 1.06209 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.5993 | 0.703409 | ||||||||
\(627\) | −4.07914 | −0.162905 | ||||||||
\(628\) | −2.22295 | −0.0887053 | ||||||||
\(629\) | −1.50073 | −0.0598381 | ||||||||
\(630\) | 39.6832 | 1.58102 | ||||||||
\(631\) | 31.9729 | 1.27282 | 0.636410 | − | 0.771351i | \(-0.280419\pi\) | ||||
0.636410 | + | 0.771351i | \(0.280419\pi\) | |||||||
\(632\) | −10.6249 | −0.422635 | ||||||||
\(633\) | 18.8561 | 0.749461 | ||||||||
\(634\) | −9.21842 | −0.366110 | ||||||||
\(635\) | 1.42881 | 0.0567006 | ||||||||
\(636\) | 10.2323 | 0.405738 | ||||||||
\(637\) | −38.7955 | −1.53713 | ||||||||
\(638\) | −5.22453 | −0.206841 | ||||||||
\(639\) | −60.8910 | −2.40881 | ||||||||
\(640\) | −13.6199 | −0.538374 | ||||||||
\(641\) | 36.4576 | 1.43999 | 0.719994 | − | 0.693980i | \(-0.244145\pi\) | ||||
0.719994 | + | 0.693980i | \(0.244145\pi\) | |||||||
\(642\) | 20.1752 | 0.796252 | ||||||||
\(643\) | −48.0124 | −1.89342 | −0.946712 | − | 0.322083i | \(-0.895617\pi\) | ||||
−0.946712 | + | 0.322083i | \(0.895617\pi\) | |||||||
\(644\) | −16.7566 | −0.660304 | ||||||||
\(645\) | 1.15038 | 0.0452962 | ||||||||
\(646\) | 2.85988 | 0.112521 | ||||||||
\(647\) | −47.7463 | −1.87710 | −0.938550 | − | 0.345144i | \(-0.887830\pi\) | ||||
−0.938550 | + | 0.345144i | \(0.887830\pi\) | |||||||
\(648\) | −1.62800 | −0.0639539 | ||||||||
\(649\) | −7.57994 | −0.297539 | ||||||||
\(650\) | 3.17781 | 0.124644 | ||||||||
\(651\) | −63.0690 | −2.47187 | ||||||||
\(652\) | 15.2850 | 0.598606 | ||||||||
\(653\) | −22.7666 | −0.890928 | −0.445464 | − | 0.895300i | \(-0.646961\pi\) | ||||
−0.445464 | + | 0.895300i | \(0.646961\pi\) | |||||||
\(654\) | −24.7935 | −0.969503 | ||||||||
\(655\) | 14.9359 | 0.583594 | ||||||||
\(656\) | −1.64060 | −0.0640547 | ||||||||
\(657\) | −4.74386 | −0.185076 | ||||||||
\(658\) | −28.5245 | −1.11200 | ||||||||
\(659\) | 24.3477 | 0.948452 | 0.474226 | − | 0.880403i | \(-0.342728\pi\) | ||||
0.474226 | + | 0.880403i | \(0.342728\pi\) | |||||||
\(660\) | −1.71492 | −0.0667532 | ||||||||
\(661\) | −7.05610 | −0.274450 | −0.137225 | − | 0.990540i | \(-0.543818\pi\) | ||||
−0.137225 | + | 0.990540i | \(0.543818\pi\) | |||||||
\(662\) | −51.7894 | −2.01285 | ||||||||
\(663\) | 6.59453 | 0.256110 | ||||||||
\(664\) | 20.5782 | 0.798589 | ||||||||
\(665\) | −7.58097 | −0.293977 | ||||||||
\(666\) | −9.54680 | −0.369931 | ||||||||
\(667\) | −16.9822 | −0.657554 | ||||||||
\(668\) | 3.83890 | 0.148531 | ||||||||
\(669\) | −22.7776 | −0.880632 | ||||||||
\(670\) | −4.22605 | −0.163267 | ||||||||
\(671\) | −11.2671 | −0.434963 | ||||||||
\(672\) | −48.5418 | −1.87254 | ||||||||
\(673\) | 30.5927 | 1.17926 | 0.589630 | − | 0.807673i | \(-0.299273\pi\) | ||||
0.589630 | + | 0.807673i | \(0.299273\pi\) | |||||||
\(674\) | 25.5455 | 0.983977 | ||||||||
\(675\) | 4.85277 | 0.186783 | ||||||||
\(676\) | −5.63270 | −0.216642 | ||||||||
\(677\) | −40.7328 | −1.56549 | −0.782744 | − | 0.622344i | \(-0.786181\pi\) | ||||
−0.782744 | + | 0.622344i | \(0.786181\pi\) | |||||||
\(678\) | 81.5584 | 3.13223 | ||||||||
\(679\) | −76.3296 | −2.92926 | ||||||||
\(680\) | −2.69968 | −0.103528 | ||||||||
\(681\) | −5.58819 | −0.214140 | ||||||||
\(682\) | 7.08832 | 0.271426 | ||||||||
\(683\) | 19.5672 | 0.748720 | 0.374360 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374360 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(684\) | 4.28536 | 0.163855 | ||||||||
\(685\) | 19.4229 | 0.742111 | ||||||||
\(686\) | 106.628 | 4.07107 | ||||||||
\(687\) | 5.64345 | 0.215311 | ||||||||
\(688\) | −2.00609 | −0.0764815 | ||||||||
\(689\) | −11.7224 | −0.446590 | ||||||||
\(690\) | −23.6650 | −0.900911 | ||||||||
\(691\) | −7.76507 | −0.295397 | −0.147699 | − | 0.989032i | \(-0.547187\pi\) | ||||
−0.147699 | + | 0.989032i | \(0.547187\pi\) | |||||||
\(692\) | −3.57068 | −0.135737 | ||||||||
\(693\) | 24.5339 | 0.931965 | ||||||||
\(694\) | 1.46111 | 0.0554631 | ||||||||
\(695\) | 15.6235 | 0.592634 | ||||||||
\(696\) | −20.1178 | −0.762563 | ||||||||
\(697\) | −0.407786 | −0.0154460 | ||||||||
\(698\) | 18.4741 | 0.699256 | ||||||||
\(699\) | −9.45283 | −0.357539 | ||||||||
\(700\) | −3.18713 | −0.120462 | ||||||||
\(701\) | −15.3991 | −0.581615 | −0.290807 | − | 0.956782i | \(-0.593924\pi\) | ||||
−0.290807 | + | 0.956782i | \(0.593924\pi\) | |||||||
\(702\) | 15.4212 | 0.582036 | ||||||||
\(703\) | 1.82379 | 0.0687857 | ||||||||
\(704\) | −4.24988 | −0.160173 | ||||||||
\(705\) | −9.48902 | −0.357377 | ||||||||
\(706\) | −30.9757 | −1.16578 | ||||||||
\(707\) | −19.7119 | −0.741341 | ||||||||
\(708\) | 12.9990 | 0.488532 | ||||||||
\(709\) | 19.4906 | 0.731984 | 0.365992 | − | 0.930618i | \(-0.380730\pi\) | ||||
0.365992 | + | 0.930618i | \(0.380730\pi\) | |||||||
\(710\) | 20.7616 | 0.779170 | ||||||||
\(711\) | −22.5197 | −0.844553 | ||||||||
\(712\) | 23.4018 | 0.877019 | ||||||||
\(713\) | 23.0404 | 0.862870 | ||||||||
\(714\) | −28.0783 | −1.05080 | ||||||||
\(715\) | 1.96466 | 0.0734742 | ||||||||
\(716\) | 0.251445 | 0.00939694 | ||||||||
\(717\) | −59.6469 | −2.22755 | ||||||||
\(718\) | 34.9812 | 1.30549 | ||||||||
\(719\) | −20.8639 | −0.778092 | −0.389046 | − | 0.921218i | \(-0.627195\pi\) | ||||
−0.389046 | + | 0.921218i | \(0.627195\pi\) | |||||||
\(720\) | −23.0207 | −0.857932 | ||||||||
\(721\) | 69.3588 | 2.58306 | ||||||||
\(722\) | 27.2567 | 1.01439 | ||||||||
\(723\) | −62.3950 | −2.32050 | ||||||||
\(724\) | 10.3815 | 0.385827 | ||||||||
\(725\) | −3.23003 | −0.119960 | ||||||||
\(726\) | −4.50111 | −0.167052 | ||||||||
\(727\) | 7.67699 | 0.284724 | 0.142362 | − | 0.989815i | \(-0.454530\pi\) | ||||
0.142362 | + | 0.989815i | \(0.454530\pi\) | |||||||
\(728\) | 22.7414 | 0.842852 | ||||||||
\(729\) | −43.9632 | −1.62827 | ||||||||
\(730\) | 1.61749 | 0.0598659 | ||||||||
\(731\) | −0.498632 | −0.0184426 | ||||||||
\(732\) | 19.3223 | 0.714171 | ||||||||
\(733\) | −1.71918 | −0.0634994 | −0.0317497 | − | 0.999496i | \(-0.510108\pi\) | ||||
−0.0317497 | + | 0.999496i | \(0.510108\pi\) | |||||||
\(734\) | 16.3191 | 0.602350 | ||||||||
\(735\) | 54.9505 | 2.02688 | ||||||||
\(736\) | 17.7333 | 0.653659 | ||||||||
\(737\) | −2.61273 | −0.0962410 | ||||||||
\(738\) | −2.59411 | −0.0954903 | ||||||||
\(739\) | 26.1527 | 0.962042 | 0.481021 | − | 0.876709i | \(-0.340266\pi\) | ||||
0.481021 | + | 0.876709i | \(0.340266\pi\) | |||||||
\(740\) | 0.766745 | 0.0281861 | ||||||||
\(741\) | −8.01413 | −0.294407 | ||||||||
\(742\) | 49.9121 | 1.83233 | ||||||||
\(743\) | 11.6118 | 0.425994 | 0.212997 | − | 0.977053i | \(-0.431677\pi\) | ||||
0.212997 | + | 0.977053i | \(0.431677\pi\) | |||||||
\(744\) | 27.2945 | 1.00067 | ||||||||
\(745\) | 16.4438 | 0.602454 | ||||||||
\(746\) | 13.3253 | 0.487874 | ||||||||
\(747\) | 43.6159 | 1.59582 | ||||||||
\(748\) | 0.743332 | 0.0271789 | ||||||||
\(749\) | 23.1811 | 0.847017 | ||||||||
\(750\) | −4.50111 | −0.164357 | ||||||||
\(751\) | 38.7626 | 1.41447 | 0.707234 | − | 0.706980i | \(-0.249943\pi\) | ||||
0.707234 | + | 0.706980i | \(0.249943\pi\) | |||||||
\(752\) | 16.5474 | 0.603422 | ||||||||
\(753\) | 34.5341 | 1.25849 | ||||||||
\(754\) | −10.2644 | −0.373809 | ||||||||
\(755\) | 20.1213 | 0.732287 | ||||||||
\(756\) | −15.4664 | −0.562509 | ||||||||
\(757\) | −19.5137 | −0.709237 | −0.354619 | − | 0.935011i | \(-0.615389\pi\) | ||||
−0.354619 | + | 0.935011i | \(0.615389\pi\) | |||||||
\(758\) | 20.9981 | 0.762687 | ||||||||
\(759\) | −14.6307 | −0.531062 | ||||||||
\(760\) | 3.28084 | 0.119008 | ||||||||
\(761\) | 5.44925 | 0.197535 | 0.0987676 | − | 0.995111i | \(-0.468510\pi\) | ||||
0.0987676 | + | 0.995111i | \(0.468510\pi\) | |||||||
\(762\) | −6.43123 | −0.232979 | ||||||||
\(763\) | −28.4874 | −1.03131 | ||||||||
\(764\) | −13.1512 | −0.475793 | ||||||||
\(765\) | −5.72202 | −0.206880 | ||||||||
\(766\) | −24.5807 | −0.888135 | ||||||||
\(767\) | −14.8920 | −0.537720 | ||||||||
\(768\) | 37.6517 | 1.35864 | ||||||||
\(769\) | 5.77063 | 0.208094 | 0.104047 | − | 0.994572i | \(-0.466821\pi\) | ||||
0.104047 | + | 0.994572i | \(0.466821\pi\) | |||||||
\(770\) | −8.36518 | −0.301460 | ||||||||
\(771\) | −28.2078 | −1.01588 | ||||||||
\(772\) | 10.0776 | 0.362699 | ||||||||
\(773\) | 19.9927 | 0.719087 | 0.359544 | − | 0.933128i | \(-0.382932\pi\) | ||||
0.359544 | + | 0.933128i | \(0.382932\pi\) | |||||||
\(774\) | −3.17202 | −0.114016 | ||||||||
\(775\) | 4.38231 | 0.157417 | ||||||||
\(776\) | 33.0334 | 1.18583 | ||||||||
\(777\) | −17.9060 | −0.642374 | ||||||||
\(778\) | −42.2609 | −1.51513 | ||||||||
\(779\) | 0.495570 | 0.0177557 | ||||||||
\(780\) | −3.36924 | −0.120638 | ||||||||
\(781\) | 12.8357 | 0.459299 | ||||||||
\(782\) | 10.2576 | 0.366810 | ||||||||
\(783\) | −15.6746 | −0.560165 | ||||||||
\(784\) | −95.8254 | −3.42234 | ||||||||
\(785\) | −3.60715 | −0.128745 | ||||||||
\(786\) | −67.2281 | −2.39795 | ||||||||
\(787\) | −16.0333 | −0.571527 | −0.285763 | − | 0.958300i | \(-0.592247\pi\) | ||||
−0.285763 | + | 0.958300i | \(0.592247\pi\) | |||||||
\(788\) | −1.54276 | −0.0549586 | ||||||||
\(789\) | 37.2057 | 1.32456 | ||||||||
\(790\) | 7.67840 | 0.273185 | ||||||||
\(791\) | 93.7095 | 3.33193 | ||||||||
\(792\) | −10.6176 | −0.377280 | ||||||||
\(793\) | −22.1361 | −0.786077 | ||||||||
\(794\) | −17.1098 | −0.607205 | ||||||||
\(795\) | 16.6039 | 0.588879 | ||||||||
\(796\) | 1.20926 | 0.0428610 | ||||||||
\(797\) | −24.1224 | −0.854459 | −0.427229 | − | 0.904143i | \(-0.640510\pi\) | ||||
−0.427229 | + | 0.904143i | \(0.640510\pi\) | |||||||
\(798\) | 34.1228 | 1.20793 | ||||||||
\(799\) | 4.11301 | 0.145508 | ||||||||
\(800\) | 3.37289 | 0.119250 | ||||||||
\(801\) | 49.6005 | 1.75255 | ||||||||
\(802\) | −23.9953 | −0.847304 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 4.48062 | 0.158019 | ||||||||
\(805\) | −27.1908 | −0.958349 | ||||||||
\(806\) | 13.9262 | 0.490528 | ||||||||
\(807\) | −24.6208 | −0.866692 | ||||||||
\(808\) | 8.53076 | 0.300111 | ||||||||
\(809\) | 12.4127 | 0.436406 | 0.218203 | − | 0.975903i | \(-0.429981\pi\) | ||||
0.218203 | + | 0.975903i | \(0.429981\pi\) | |||||||
\(810\) | 1.17652 | 0.0413388 | ||||||||
\(811\) | −11.2548 | −0.395211 | −0.197606 | − | 0.980282i | \(-0.563317\pi\) | ||||
−0.197606 | + | 0.980282i | \(0.563317\pi\) | |||||||
\(812\) | 10.2945 | 0.361267 | ||||||||
\(813\) | −27.7642 | −0.973734 | ||||||||
\(814\) | 2.01245 | 0.0705365 | ||||||||
\(815\) | 24.8027 | 0.868802 | ||||||||
\(816\) | 16.2886 | 0.570215 | ||||||||
\(817\) | 0.605973 | 0.0212003 | ||||||||
\(818\) | −63.7409 | −2.22865 | ||||||||
\(819\) | 48.2008 | 1.68427 | ||||||||
\(820\) | 0.208344 | 0.00727568 | ||||||||
\(821\) | 16.6170 | 0.579937 | 0.289968 | − | 0.957036i | \(-0.406355\pi\) | ||||
0.289968 | + | 0.957036i | \(0.406355\pi\) | |||||||
\(822\) | −87.4246 | −3.04928 | ||||||||
\(823\) | 5.60946 | 0.195533 | 0.0977667 | − | 0.995209i | \(-0.468830\pi\) | ||||
0.0977667 | + | 0.995209i | \(0.468830\pi\) | |||||||
\(824\) | −30.0166 | −1.04568 | ||||||||
\(825\) | −2.78278 | −0.0968839 | ||||||||
\(826\) | 63.4075 | 2.20623 | ||||||||
\(827\) | −47.4977 | −1.65166 | −0.825829 | − | 0.563921i | \(-0.809292\pi\) | ||||
−0.825829 | + | 0.563921i | \(0.809292\pi\) | |||||||
\(828\) | 15.3704 | 0.534157 | ||||||||
\(829\) | 40.2663 | 1.39851 | 0.699254 | − | 0.714874i | \(-0.253516\pi\) | ||||
0.699254 | + | 0.714874i | \(0.253516\pi\) | |||||||
\(830\) | −14.8715 | −0.516196 | ||||||||
\(831\) | −0.100796 | −0.00349657 | ||||||||
\(832\) | −8.34958 | −0.289469 | ||||||||
\(833\) | −23.8183 | −0.825254 | ||||||||
\(834\) | −70.3232 | −2.43509 | ||||||||
\(835\) | 6.22933 | 0.215575 | ||||||||
\(836\) | −0.903349 | −0.0312430 | ||||||||
\(837\) | 21.2663 | 0.735072 | ||||||||
\(838\) | −42.8401 | −1.47989 | ||||||||
\(839\) | −40.0117 | −1.38136 | −0.690679 | − | 0.723161i | \(-0.742688\pi\) | ||||
−0.690679 | + | 0.723161i | \(0.742688\pi\) | |||||||
\(840\) | −32.2113 | −1.11139 | ||||||||
\(841\) | −18.5669 | −0.640237 | ||||||||
\(842\) | 8.38138 | 0.288842 | ||||||||
\(843\) | 14.3658 | 0.494785 | ||||||||
\(844\) | 4.17578 | 0.143736 | ||||||||
\(845\) | −9.14010 | −0.314429 | ||||||||
\(846\) | 26.1647 | 0.899560 | ||||||||
\(847\) | −5.17171 | −0.177702 | ||||||||
\(848\) | −28.9546 | −0.994306 | ||||||||
\(849\) | 10.4915 | 0.360067 | ||||||||
\(850\) | 1.95100 | 0.0669188 | ||||||||
\(851\) | 6.54143 | 0.224237 | ||||||||
\(852\) | −22.0123 | −0.754128 | ||||||||
\(853\) | −36.2334 | −1.24061 | −0.620303 | − | 0.784362i | \(-0.712990\pi\) | ||||
−0.620303 | + | 0.784362i | \(0.712990\pi\) | |||||||
\(854\) | 94.2517 | 3.22523 | ||||||||
\(855\) | 6.95380 | 0.237815 | ||||||||
\(856\) | −10.0321 | −0.342891 | ||||||||
\(857\) | −16.7745 | −0.573007 | −0.286503 | − | 0.958079i | \(-0.592493\pi\) | ||||
−0.286503 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(858\) | −8.84315 | −0.301900 | ||||||||
\(859\) | −40.6752 | −1.38782 | −0.693911 | − | 0.720061i | \(-0.744114\pi\) | ||||
−0.693911 | + | 0.720061i | \(0.744114\pi\) | |||||||
\(860\) | 0.254758 | 0.00868719 | ||||||||
\(861\) | −4.86551 | −0.165816 | ||||||||
\(862\) | 19.4745 | 0.663305 | ||||||||
\(863\) | 2.64635 | 0.0900828 | 0.0450414 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450414 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(864\) | 16.3679 | 0.556847 | ||||||||
\(865\) | −5.79410 | −0.197005 | ||||||||
\(866\) | 9.74759 | 0.331237 | ||||||||
\(867\) | −43.2586 | −1.46914 | ||||||||
\(868\) | −13.9670 | −0.474070 | ||||||||
\(869\) | 4.74712 | 0.161035 | ||||||||
\(870\) | 14.5387 | 0.492909 | ||||||||
\(871\) | −5.13312 | −0.173929 | ||||||||
\(872\) | 12.3286 | 0.417499 | ||||||||
\(873\) | 70.0149 | 2.36964 | ||||||||
\(874\) | −12.4657 | −0.421660 | ||||||||
\(875\) | −5.17171 | −0.174836 | ||||||||
\(876\) | −1.71492 | −0.0579418 | ||||||||
\(877\) | 29.6451 | 1.00104 | 0.500522 | − | 0.865724i | \(-0.333142\pi\) | ||||
0.500522 | + | 0.865724i | \(0.333142\pi\) | |||||||
\(878\) | 4.59710 | 0.155144 | ||||||||
\(879\) | 62.5442 | 2.10956 | ||||||||
\(880\) | 4.85275 | 0.163586 | ||||||||
\(881\) | 38.2096 | 1.28732 | 0.643658 | − | 0.765313i | \(-0.277416\pi\) | ||||
0.643658 | + | 0.765313i | \(0.277416\pi\) | |||||||
\(882\) | −151.518 | −5.10189 | ||||||||
\(883\) | −25.9917 | −0.874689 | −0.437345 | − | 0.899294i | \(-0.644081\pi\) | ||||
−0.437345 | + | 0.899294i | \(0.644081\pi\) | |||||||
\(884\) | 1.46040 | 0.0491184 | ||||||||
\(885\) | 21.0933 | 0.709043 | ||||||||
\(886\) | −33.9198 | −1.13956 | ||||||||
\(887\) | 11.4734 | 0.385238 | 0.192619 | − | 0.981274i | \(-0.438302\pi\) | ||||
0.192619 | + | 0.981274i | \(0.438302\pi\) | |||||||
\(888\) | 7.74923 | 0.260047 | ||||||||
\(889\) | −7.38940 | −0.247833 | ||||||||
\(890\) | −16.9120 | −0.566892 | ||||||||
\(891\) | 0.727378 | 0.0243681 | ||||||||
\(892\) | −5.04422 | −0.168893 | ||||||||
\(893\) | −4.99842 | −0.167266 | ||||||||
\(894\) | −74.0153 | −2.47544 | ||||||||
\(895\) | 0.408017 | 0.0136385 | ||||||||
\(896\) | 70.4383 | 2.35318 | ||||||||
\(897\) | −28.7444 | −0.959749 | ||||||||
\(898\) | −20.1391 | −0.672052 | ||||||||
\(899\) | −14.1550 | −0.472095 | ||||||||
\(900\) | 2.92346 | 0.0974487 | ||||||||
\(901\) | −7.19694 | −0.239765 | ||||||||
\(902\) | 0.546834 | 0.0182076 | ||||||||
\(903\) | −5.94944 | −0.197985 | ||||||||
\(904\) | −40.5549 | −1.34884 | ||||||||
\(905\) | 16.8460 | 0.559979 | ||||||||
\(906\) | −90.5679 | −3.00892 | ||||||||
\(907\) | 21.9329 | 0.728271 | 0.364135 | − | 0.931346i | \(-0.381365\pi\) | ||||
0.364135 | + | 0.931346i | \(0.381365\pi\) | |||||||
\(908\) | −1.23754 | −0.0410691 | ||||||||
\(909\) | 18.0811 | 0.599713 | ||||||||
\(910\) | −16.4347 | −0.544806 | ||||||||
\(911\) | −26.8498 | −0.889574 | −0.444787 | − | 0.895636i | \(-0.646721\pi\) | ||||
−0.444787 | + | 0.895636i | \(0.646721\pi\) | |||||||
\(912\) | −19.7950 | −0.655479 | ||||||||
\(913\) | −9.19417 | −0.304283 | ||||||||
\(914\) | 67.5731 | 2.23512 | ||||||||
\(915\) | 31.3540 | 1.03653 | ||||||||
\(916\) | 1.24977 | 0.0412937 | ||||||||
\(917\) | −77.2442 | −2.55083 | ||||||||
\(918\) | 9.46778 | 0.312483 | ||||||||
\(919\) | 4.99711 | 0.164840 | 0.0824198 | − | 0.996598i | \(-0.473735\pi\) | ||||
0.0824198 | + | 0.996598i | \(0.473735\pi\) | |||||||
\(920\) | 11.7674 | 0.387961 | ||||||||
\(921\) | −58.7335 | −1.93534 | ||||||||
\(922\) | −62.0632 | −2.04394 | ||||||||
\(923\) | 25.2179 | 0.830057 | ||||||||
\(924\) | 8.86908 | 0.291771 | ||||||||
\(925\) | 1.24419 | 0.0409086 | ||||||||
\(926\) | −54.1894 | −1.78077 | ||||||||
\(927\) | −63.6207 | −2.08958 | ||||||||
\(928\) | −10.8946 | −0.357631 | ||||||||
\(929\) | 46.6250 | 1.52972 | 0.764859 | − | 0.644198i | \(-0.222809\pi\) | ||||
0.764859 | + | 0.644198i | \(0.222809\pi\) | |||||||
\(930\) | −19.7252 | −0.646816 | ||||||||
\(931\) | 28.9456 | 0.948655 | ||||||||
\(932\) | −2.09338 | −0.0685710 | ||||||||
\(933\) | −20.3655 | −0.666738 | ||||||||
\(934\) | 37.7656 | 1.23573 | ||||||||
\(935\) | 1.20619 | 0.0394468 | ||||||||
\(936\) | −20.8600 | −0.681830 | ||||||||
\(937\) | −10.3738 | −0.338899 | −0.169449 | − | 0.985539i | \(-0.554199\pi\) | ||||
−0.169449 | + | 0.985539i | \(0.554199\pi\) | |||||||
\(938\) | 21.8559 | 0.713621 | ||||||||
\(939\) | −30.2784 | −0.988099 | ||||||||
\(940\) | −2.10140 | −0.0685400 | ||||||||
\(941\) | 45.4065 | 1.48021 | 0.740106 | − | 0.672491i | \(-0.234776\pi\) | ||||
0.740106 | + | 0.672491i | \(0.234776\pi\) | |||||||
\(942\) | 16.2362 | 0.529003 | ||||||||
\(943\) | 1.77747 | 0.0578824 | ||||||||
\(944\) | −36.7835 | −1.19720 | ||||||||
\(945\) | −25.0972 | −0.816411 | ||||||||
\(946\) | 0.668658 | 0.0217399 | ||||||||
\(947\) | 31.9501 | 1.03824 | 0.519120 | − | 0.854701i | \(-0.326260\pi\) | ||||
0.519120 | + | 0.854701i | \(0.326260\pi\) | |||||||
\(948\) | −8.14093 | −0.264405 | ||||||||
\(949\) | 1.96466 | 0.0637756 | ||||||||
\(950\) | −2.37100 | −0.0769253 | ||||||||
\(951\) | 15.8597 | 0.514286 | ||||||||
\(952\) | 13.9620 | 0.452510 | ||||||||
\(953\) | 50.1110 | 1.62325 | 0.811627 | − | 0.584176i | \(-0.198582\pi\) | ||||
0.811627 | + | 0.584176i | \(0.198582\pi\) | |||||||
\(954\) | −45.7829 | −1.48228 | ||||||||
\(955\) | −21.3403 | −0.690555 | ||||||||
\(956\) | −13.2091 | −0.427214 | ||||||||
\(957\) | 8.98847 | 0.290556 | ||||||||
\(958\) | −24.8858 | −0.804022 | ||||||||
\(959\) | −100.450 | −3.24369 | ||||||||
\(960\) | 11.8265 | 0.381698 | ||||||||
\(961\) | −11.7954 | −0.380497 | ||||||||
\(962\) | 3.95379 | 0.127475 | ||||||||
\(963\) | −21.2633 | −0.685200 | ||||||||
\(964\) | −13.8177 | −0.445039 | ||||||||
\(965\) | 16.3527 | 0.526413 | ||||||||
\(966\) | 122.389 | 3.93779 | ||||||||
\(967\) | −39.7754 | −1.27909 | −0.639545 | − | 0.768754i | \(-0.720877\pi\) | ||||
−0.639545 | + | 0.768754i | \(0.720877\pi\) | |||||||
\(968\) | 2.23818 | 0.0719377 | ||||||||
\(969\) | −4.92024 | −0.158061 | ||||||||
\(970\) | −23.8726 | −0.766502 | ||||||||
\(971\) | 26.0383 | 0.835608 | 0.417804 | − | 0.908537i | \(-0.362800\pi\) | ||||
0.417804 | + | 0.908537i | \(0.362800\pi\) | |||||||
\(972\) | −10.2191 | −0.327779 | ||||||||
\(973\) | −80.8005 | −2.59034 | ||||||||
\(974\) | 39.0615 | 1.25161 | ||||||||
\(975\) | −5.46722 | −0.175091 | ||||||||
\(976\) | −54.6766 | −1.75015 | ||||||||
\(977\) | −32.6256 | −1.04379 | −0.521893 | − | 0.853011i | \(-0.674774\pi\) | ||||
−0.521893 | + | 0.853011i | \(0.674774\pi\) | |||||||
\(978\) | −111.640 | −3.56985 | ||||||||
\(979\) | −10.4557 | −0.334167 | ||||||||
\(980\) | 12.1691 | 0.388728 | ||||||||
\(981\) | 26.1307 | 0.834288 | ||||||||
\(982\) | −20.5871 | −0.656959 | ||||||||
\(983\) | −29.9795 | −0.956199 | −0.478099 | − | 0.878306i | \(-0.658674\pi\) | ||||
−0.478099 | + | 0.878306i | \(0.658674\pi\) | |||||||
\(984\) | 2.10566 | 0.0671260 | ||||||||
\(985\) | −2.50342 | −0.0797656 | ||||||||
\(986\) | −6.30180 | −0.200690 | ||||||||
\(987\) | 49.0745 | 1.56206 | ||||||||
\(988\) | −1.77477 | −0.0564631 | ||||||||
\(989\) | 2.17345 | 0.0691118 | ||||||||
\(990\) | 7.67313 | 0.243868 | ||||||||
\(991\) | −21.9158 | −0.696177 | −0.348089 | − | 0.937462i | \(-0.613169\pi\) | ||||
−0.348089 | + | 0.937462i | \(0.613169\pi\) | |||||||
\(992\) | 14.7811 | 0.469299 | ||||||||
\(993\) | 89.1003 | 2.82751 | ||||||||
\(994\) | −107.373 | −3.40567 | ||||||||
\(995\) | 1.96225 | 0.0622074 | ||||||||
\(996\) | 15.7673 | 0.499605 | ||||||||
\(997\) | 3.82514 | 0.121143 | 0.0605717 | − | 0.998164i | \(-0.480708\pi\) | ||||
0.0605717 | + | 0.998164i | \(0.480708\pi\) | |||||||
\(998\) | −43.4361 | −1.37495 | ||||||||
\(999\) | 6.03776 | 0.191026 |
(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 | 4015.2.a.i.1.10 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.i.1.10 | ✓ | 38 | 1.1 | even | 1 | trivial |