Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81586 | −1.99112 | −0.995558 | − | 0.0941512i | \(-0.969986\pi\) | ||||
−0.995558 | + | 0.0941512i | \(0.969986\pi\) | |||||||
\(3\) | 1.36738 | 0.789458 | 0.394729 | − | 0.918798i | \(-0.370838\pi\) | ||||
0.394729 | + | 0.918798i | \(0.370838\pi\) | |||||||
\(4\) | 5.92908 | 2.96454 | ||||||||
\(5\) | −2.81839 | −1.26042 | −0.630211 | − | 0.776424i | \(-0.717032\pi\) | ||||
−0.630211 | + | 0.776424i | \(0.717032\pi\) | |||||||
\(6\) | −3.85036 | −1.57190 | ||||||||
\(7\) | −0.890414 | −0.336545 | −0.168272 | − | 0.985741i | \(-0.553819\pi\) | ||||
−0.168272 | + | 0.985741i | \(0.553819\pi\) | |||||||
\(8\) | −11.0638 | −3.91163 | ||||||||
\(9\) | −1.13027 | −0.376756 | ||||||||
\(10\) | 7.93620 | 2.50965 | ||||||||
\(11\) | −5.19095 | −1.56513 | −0.782565 | − | 0.622569i | \(-0.786089\pi\) | ||||
−0.782565 | + | 0.622569i | \(0.786089\pi\) | |||||||
\(12\) | 8.10732 | 2.34038 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.50728 | 0.670100 | ||||||||
\(15\) | −3.85382 | −0.995051 | ||||||||
\(16\) | 19.2959 | 4.82397 | ||||||||
\(17\) | 6.81972 | 1.65402 | 0.827012 | − | 0.562184i | \(-0.190039\pi\) | ||||
0.827012 | + | 0.562184i | \(0.190039\pi\) | |||||||
\(18\) | 3.18268 | 0.750164 | ||||||||
\(19\) | 4.77719 | 1.09596 | 0.547981 | − | 0.836491i | \(-0.315397\pi\) | ||||
0.547981 | + | 0.836491i | \(0.315397\pi\) | |||||||
\(20\) | −16.7105 | −3.73658 | ||||||||
\(21\) | −1.21754 | −0.265688 | ||||||||
\(22\) | 14.6170 | 3.11635 | ||||||||
\(23\) | −3.65966 | −0.763092 | −0.381546 | − | 0.924350i | \(-0.624608\pi\) | ||||
−0.381546 | + | 0.924350i | \(0.624608\pi\) | |||||||
\(24\) | −15.1284 | −3.08807 | ||||||||
\(25\) | 2.94333 | 0.588666 | ||||||||
\(26\) | −2.81586 | −0.552236 | ||||||||
\(27\) | −5.64765 | −1.08689 | ||||||||
\(28\) | −5.27934 | −0.997701 | ||||||||
\(29\) | −3.09025 | −0.573845 | −0.286922 | − | 0.957954i | \(-0.592632\pi\) | ||||
−0.286922 | + | 0.957954i | \(0.592632\pi\) | |||||||
\(30\) | 10.8518 | 1.98126 | ||||||||
\(31\) | −9.56903 | −1.71865 | −0.859324 | − | 0.511431i | \(-0.829116\pi\) | ||||
−0.859324 | + | 0.511431i | \(0.829116\pi\) | |||||||
\(32\) | −32.2070 | −5.69345 | ||||||||
\(33\) | −7.09801 | −1.23560 | ||||||||
\(34\) | −19.2034 | −3.29335 | ||||||||
\(35\) | 2.50953 | 0.424189 | ||||||||
\(36\) | −6.70145 | −1.11691 | ||||||||
\(37\) | 3.83986 | 0.631269 | 0.315635 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315635 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(38\) | −13.4519 | −2.18219 | ||||||||
\(39\) | 1.36738 | 0.218956 | ||||||||
\(40\) | 31.1820 | 4.93031 | ||||||||
\(41\) | −1.36139 | −0.212613 | −0.106306 | − | 0.994333i | \(-0.533902\pi\) | ||||
−0.106306 | + | 0.994333i | \(0.533902\pi\) | |||||||
\(42\) | 3.42841 | 0.529016 | ||||||||
\(43\) | −3.24758 | −0.495251 | −0.247626 | − | 0.968856i | \(-0.579650\pi\) | ||||
−0.247626 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(44\) | −30.7776 | −4.63989 | ||||||||
\(45\) | 3.18553 | 0.474871 | ||||||||
\(46\) | 10.3051 | 1.51940 | ||||||||
\(47\) | 2.91161 | 0.424702 | 0.212351 | − | 0.977194i | \(-0.431888\pi\) | ||||
0.212351 | + | 0.977194i | \(0.431888\pi\) | |||||||
\(48\) | 26.3848 | 3.80832 | ||||||||
\(49\) | −6.20716 | −0.886738 | ||||||||
\(50\) | −8.28801 | −1.17210 | ||||||||
\(51\) | 9.32516 | 1.30578 | ||||||||
\(52\) | 5.92908 | 0.822216 | ||||||||
\(53\) | 9.64024 | 1.32419 | 0.662095 | − | 0.749420i | \(-0.269668\pi\) | ||||
0.662095 | + | 0.749420i | \(0.269668\pi\) | |||||||
\(54\) | 15.9030 | 2.16413 | ||||||||
\(55\) | 14.6301 | 1.97272 | ||||||||
\(56\) | 9.85133 | 1.31644 | ||||||||
\(57\) | 6.53224 | 0.865217 | ||||||||
\(58\) | 8.70171 | 1.14259 | ||||||||
\(59\) | −5.16660 | −0.672633 | −0.336317 | − | 0.941749i | \(-0.609181\pi\) | ||||
−0.336317 | + | 0.941749i | \(0.609181\pi\) | |||||||
\(60\) | −22.8496 | −2.94987 | ||||||||
\(61\) | −6.62776 | −0.848598 | −0.424299 | − | 0.905522i | \(-0.639479\pi\) | ||||
−0.424299 | + | 0.905522i | \(0.639479\pi\) | |||||||
\(62\) | 26.9451 | 3.42203 | ||||||||
\(63\) | 1.00641 | 0.126795 | ||||||||
\(64\) | 52.0988 | 6.51235 | ||||||||
\(65\) | −2.81839 | −0.349578 | ||||||||
\(66\) | 19.9870 | 2.46023 | ||||||||
\(67\) | −10.0518 | −1.22802 | −0.614010 | − | 0.789298i | \(-0.710445\pi\) | ||||
−0.614010 | + | 0.789298i | \(0.710445\pi\) | |||||||
\(68\) | 40.4347 | 4.90342 | ||||||||
\(69\) | −5.00415 | −0.602429 | ||||||||
\(70\) | −7.06651 | −0.844609 | ||||||||
\(71\) | 7.71839 | 0.916005 | 0.458002 | − | 0.888951i | \(-0.348565\pi\) | ||||
0.458002 | + | 0.888951i | \(0.348565\pi\) | |||||||
\(72\) | 12.5050 | 1.47373 | ||||||||
\(73\) | 4.11268 | 0.481353 | 0.240677 | − | 0.970605i | \(-0.422631\pi\) | ||||
0.240677 | + | 0.970605i | \(0.422631\pi\) | |||||||
\(74\) | −10.8125 | −1.25693 | ||||||||
\(75\) | 4.02466 | 0.464727 | ||||||||
\(76\) | 28.3244 | 3.24903 | ||||||||
\(77\) | 4.62209 | 0.526736 | ||||||||
\(78\) | −3.85036 | −0.435967 | ||||||||
\(79\) | −5.30061 | −0.596365 | −0.298183 | − | 0.954509i | \(-0.596380\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596380\pi\) | |||||||
\(80\) | −54.3833 | −6.08024 | ||||||||
\(81\) | −4.33170 | −0.481300 | ||||||||
\(82\) | 3.83348 | 0.423337 | ||||||||
\(83\) | −10.5174 | −1.15444 | −0.577218 | − | 0.816590i | \(-0.695862\pi\) | ||||
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(84\) | −7.21887 | −0.787644 | ||||||||
\(85\) | −19.2206 | −2.08477 | ||||||||
\(86\) | 9.14474 | 0.986102 | ||||||||
\(87\) | −4.22555 | −0.453026 | ||||||||
\(88\) | 57.4314 | 6.12221 | ||||||||
\(89\) | 1.60169 | 0.169779 | 0.0848893 | − | 0.996390i | \(-0.472946\pi\) | ||||
0.0848893 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(90\) | −8.97003 | −0.945524 | ||||||||
\(91\) | −0.890414 | −0.0933407 | ||||||||
\(92\) | −21.6984 | −2.26222 | ||||||||
\(93\) | −13.0845 | −1.35680 | ||||||||
\(94\) | −8.19869 | −0.845630 | ||||||||
\(95\) | −13.4640 | −1.38138 | ||||||||
\(96\) | −44.0393 | −4.49474 | ||||||||
\(97\) | −1.11488 | −0.113199 | −0.0565996 | − | 0.998397i | \(-0.518026\pi\) | ||||
−0.0565996 | + | 0.998397i | \(0.518026\pi\) | |||||||
\(98\) | 17.4785 | 1.76560 | ||||||||
\(99\) | 5.86716 | 0.589671 | ||||||||
\(100\) | 17.4512 | 1.74512 | ||||||||
\(101\) | −14.3178 | −1.42468 | −0.712338 | − | 0.701836i | \(-0.752364\pi\) | ||||
−0.712338 | + | 0.701836i | \(0.752364\pi\) | |||||||
\(102\) | −26.2584 | −2.59997 | ||||||||
\(103\) | −0.233744 | −0.0230315 | −0.0115157 | − | 0.999934i | \(-0.503666\pi\) | ||||
−0.0115157 | + | 0.999934i | \(0.503666\pi\) | |||||||
\(104\) | −11.0638 | −1.08489 | ||||||||
\(105\) | 3.43149 | 0.334879 | ||||||||
\(106\) | −27.1456 | −2.63661 | ||||||||
\(107\) | −18.4949 | −1.78797 | −0.893983 | − | 0.448100i | \(-0.852101\pi\) | ||||
−0.893983 | + | 0.448100i | \(0.852101\pi\) | |||||||
\(108\) | −33.4854 | −3.22213 | ||||||||
\(109\) | 17.7624 | 1.70133 | 0.850665 | − | 0.525708i | \(-0.176200\pi\) | ||||
0.850665 | + | 0.525708i | \(0.176200\pi\) | |||||||
\(110\) | −41.1964 | −3.92792 | ||||||||
\(111\) | 5.25055 | 0.498361 | ||||||||
\(112\) | −17.1813 | −1.62348 | ||||||||
\(113\) | −14.5875 | −1.37228 | −0.686140 | − | 0.727470i | \(-0.740696\pi\) | ||||
−0.686140 | + | 0.727470i | \(0.740696\pi\) | |||||||
\(114\) | −18.3939 | −1.72275 | ||||||||
\(115\) | 10.3144 | 0.961819 | ||||||||
\(116\) | −18.3223 | −1.70119 | ||||||||
\(117\) | −1.13027 | −0.104493 | ||||||||
\(118\) | 14.5484 | 1.33929 | ||||||||
\(119\) | −6.07237 | −0.556653 | ||||||||
\(120\) | 42.6377 | 3.89227 | ||||||||
\(121\) | 15.9459 | 1.44963 | ||||||||
\(122\) | 18.6629 | 1.68966 | ||||||||
\(123\) | −1.86154 | −0.167849 | ||||||||
\(124\) | −56.7356 | −5.09501 | ||||||||
\(125\) | 5.79650 | 0.518455 | ||||||||
\(126\) | −2.83390 | −0.252464 | ||||||||
\(127\) | 20.4899 | 1.81818 | 0.909091 | − | 0.416599i | \(-0.136778\pi\) | ||||
0.909091 | + | 0.416599i | \(0.136778\pi\) | |||||||
\(128\) | −82.2890 | −7.27339 | ||||||||
\(129\) | −4.44068 | −0.390980 | ||||||||
\(130\) | 7.93620 | 0.696051 | ||||||||
\(131\) | 12.5531 | 1.09677 | 0.548385 | − | 0.836226i | \(-0.315243\pi\) | ||||
0.548385 | + | 0.836226i | \(0.315243\pi\) | |||||||
\(132\) | −42.0847 | −3.66300 | ||||||||
\(133\) | −4.25368 | −0.368840 | ||||||||
\(134\) | 28.3044 | 2.44513 | ||||||||
\(135\) | 15.9173 | 1.36994 | ||||||||
\(136\) | −75.4517 | −6.46993 | ||||||||
\(137\) | −20.9783 | −1.79230 | −0.896150 | − | 0.443752i | \(-0.853647\pi\) | ||||
−0.896150 | + | 0.443752i | \(0.853647\pi\) | |||||||
\(138\) | 14.0910 | 1.19951 | ||||||||
\(139\) | 1.09302 | 0.0927085 | 0.0463543 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463543 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(140\) | 14.8792 | 1.25753 | ||||||||
\(141\) | 3.98128 | 0.335284 | ||||||||
\(142\) | −21.7339 | −1.82387 | ||||||||
\(143\) | −5.19095 | −0.434089 | ||||||||
\(144\) | −21.8095 | −1.81746 | ||||||||
\(145\) | 8.70953 | 0.723287 | ||||||||
\(146\) | −11.5808 | −0.958430 | ||||||||
\(147\) | −8.48756 | −0.700042 | ||||||||
\(148\) | 22.7669 | 1.87142 | ||||||||
\(149\) | −5.91776 | −0.484801 | −0.242401 | − | 0.970176i | \(-0.577935\pi\) | ||||
−0.242401 | + | 0.970176i | \(0.577935\pi\) | |||||||
\(150\) | −11.3329 | −0.925326 | ||||||||
\(151\) | 6.71847 | 0.546742 | 0.273371 | − | 0.961909i | \(-0.411861\pi\) | ||||
0.273371 | + | 0.961909i | \(0.411861\pi\) | |||||||
\(152\) | −52.8537 | −4.28700 | ||||||||
\(153\) | −7.70810 | −0.623163 | ||||||||
\(154\) | −13.0152 | −1.04879 | ||||||||
\(155\) | 26.9693 | 2.16622 | ||||||||
\(156\) | 8.10732 | 0.649105 | ||||||||
\(157\) | −9.07044 | −0.723900 | −0.361950 | − | 0.932197i | \(-0.617889\pi\) | ||||
−0.361950 | + | 0.932197i | \(0.617889\pi\) | |||||||
\(158\) | 14.9258 | 1.18743 | ||||||||
\(159\) | 13.1819 | 1.04539 | ||||||||
\(160\) | 90.7719 | 7.17615 | ||||||||
\(161\) | 3.25861 | 0.256815 | ||||||||
\(162\) | 12.1975 | 0.958323 | ||||||||
\(163\) | 2.18550 | 0.171181 | 0.0855907 | − | 0.996330i | \(-0.472722\pi\) | ||||
0.0855907 | + | 0.996330i | \(0.472722\pi\) | |||||||
\(164\) | −8.07178 | −0.630300 | ||||||||
\(165\) | 20.0050 | 1.55738 | ||||||||
\(166\) | 29.6156 | 2.29862 | ||||||||
\(167\) | 7.54304 | 0.583698 | 0.291849 | − | 0.956464i | \(-0.405729\pi\) | ||||
0.291849 | + | 0.956464i | \(0.405729\pi\) | |||||||
\(168\) | 13.4705 | 1.03927 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 54.1227 | 4.15102 | ||||||||
\(171\) | −5.39950 | −0.412910 | ||||||||
\(172\) | −19.2552 | −1.46819 | ||||||||
\(173\) | 21.7276 | 1.65192 | 0.825959 | − | 0.563731i | \(-0.190634\pi\) | ||||
0.825959 | + | 0.563731i | \(0.190634\pi\) | |||||||
\(174\) | 11.8986 | 0.902028 | ||||||||
\(175\) | −2.62078 | −0.198112 | ||||||||
\(176\) | −100.164 | −7.55013 | ||||||||
\(177\) | −7.06471 | −0.531016 | ||||||||
\(178\) | −4.51014 | −0.338049 | ||||||||
\(179\) | −1.68407 | −0.125874 | −0.0629368 | − | 0.998018i | \(-0.520047\pi\) | ||||
−0.0629368 | + | 0.998018i | \(0.520047\pi\) | |||||||
\(180\) | 18.8873 | 1.40778 | ||||||||
\(181\) | −7.49746 | −0.557282 | −0.278641 | − | 0.960395i | \(-0.589884\pi\) | ||||
−0.278641 | + | 0.960395i | \(0.589884\pi\) | |||||||
\(182\) | 2.50728 | 0.185852 | ||||||||
\(183\) | −9.06268 | −0.669933 | ||||||||
\(184\) | 40.4896 | 2.98493 | ||||||||
\(185\) | −10.8222 | −0.795666 | ||||||||
\(186\) | 36.8442 | 2.70155 | ||||||||
\(187\) | −35.4008 | −2.58876 | ||||||||
\(188\) | 17.2632 | 1.25905 | ||||||||
\(189\) | 5.02875 | 0.365788 | ||||||||
\(190\) | 37.9127 | 2.75048 | ||||||||
\(191\) | −22.0653 | −1.59659 | −0.798295 | − | 0.602266i | \(-0.794265\pi\) | ||||
−0.798295 | + | 0.602266i | \(0.794265\pi\) | |||||||
\(192\) | 71.2389 | 5.14123 | ||||||||
\(193\) | 7.27390 | 0.523587 | 0.261793 | − | 0.965124i | \(-0.415686\pi\) | ||||
0.261793 | + | 0.965124i | \(0.415686\pi\) | |||||||
\(194\) | 3.13936 | 0.225393 | ||||||||
\(195\) | −3.85382 | −0.275978 | ||||||||
\(196\) | −36.8028 | −2.62877 | ||||||||
\(197\) | −15.9931 | −1.13946 | −0.569731 | − | 0.821831i | \(-0.692953\pi\) | ||||
−0.569731 | + | 0.821831i | \(0.692953\pi\) | |||||||
\(198\) | −16.5211 | −1.17410 | ||||||||
\(199\) | −11.9028 | −0.843766 | −0.421883 | − | 0.906650i | \(-0.638631\pi\) | ||||
−0.421883 | + | 0.906650i | \(0.638631\pi\) | |||||||
\(200\) | −32.5643 | −2.30264 | ||||||||
\(201\) | −13.7446 | −0.969471 | ||||||||
\(202\) | 40.3170 | 2.83670 | ||||||||
\(203\) | 2.75160 | 0.193124 | ||||||||
\(204\) | 55.2896 | 3.87105 | ||||||||
\(205\) | 3.83692 | 0.267982 | ||||||||
\(206\) | 0.658190 | 0.0458583 | ||||||||
\(207\) | 4.13639 | 0.287499 | ||||||||
\(208\) | 19.2959 | 1.33793 | ||||||||
\(209\) | −24.7981 | −1.71532 | ||||||||
\(210\) | −9.66261 | −0.666784 | ||||||||
\(211\) | 19.5185 | 1.34371 | 0.671854 | − | 0.740683i | \(-0.265498\pi\) | ||||
0.671854 | + | 0.740683i | \(0.265498\pi\) | |||||||
\(212\) | 57.1578 | 3.92562 | ||||||||
\(213\) | 10.5540 | 0.723148 | ||||||||
\(214\) | 52.0790 | 3.56005 | ||||||||
\(215\) | 9.15295 | 0.624226 | ||||||||
\(216\) | 62.4843 | 4.25152 | ||||||||
\(217\) | 8.52040 | 0.578402 | ||||||||
\(218\) | −50.0165 | −3.38755 | ||||||||
\(219\) | 5.62361 | 0.380008 | ||||||||
\(220\) | 86.7432 | 5.84823 | ||||||||
\(221\) | 6.81972 | 0.458744 | ||||||||
\(222\) | −14.7848 | −0.992294 | ||||||||
\(223\) | 20.0607 | 1.34337 | 0.671683 | − | 0.740838i | \(-0.265572\pi\) | ||||
0.671683 | + | 0.740838i | \(0.265572\pi\) | |||||||
\(224\) | 28.6776 | 1.91610 | ||||||||
\(225\) | −3.32675 | −0.221783 | ||||||||
\(226\) | 41.0765 | 2.73237 | ||||||||
\(227\) | −1.00059 | −0.0664113 | −0.0332057 | − | 0.999449i | \(-0.510572\pi\) | ||||
−0.0332057 | + | 0.999449i | \(0.510572\pi\) | |||||||
\(228\) | 38.7302 | 2.56497 | ||||||||
\(229\) | −1.96655 | −0.129953 | −0.0649765 | − | 0.997887i | \(-0.520697\pi\) | ||||
−0.0649765 | + | 0.997887i | \(0.520697\pi\) | |||||||
\(230\) | −29.0438 | −1.91509 | ||||||||
\(231\) | 6.32016 | 0.415836 | ||||||||
\(232\) | 34.1898 | 2.24467 | ||||||||
\(233\) | −11.8398 | −0.775649 | −0.387825 | − | 0.921733i | \(-0.626773\pi\) | ||||
−0.387825 | + | 0.921733i | \(0.626773\pi\) | |||||||
\(234\) | 3.18268 | 0.208058 | ||||||||
\(235\) | −8.20605 | −0.535304 | ||||||||
\(236\) | −30.6332 | −1.99405 | ||||||||
\(237\) | −7.24796 | −0.470805 | ||||||||
\(238\) | 17.0990 | 1.10836 | ||||||||
\(239\) | 8.05869 | 0.521273 | 0.260637 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260637 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(240\) | −74.3628 | −4.80010 | ||||||||
\(241\) | −9.81208 | −0.632052 | −0.316026 | − | 0.948751i | \(-0.602349\pi\) | ||||
−0.316026 | + | 0.948751i | \(0.602349\pi\) | |||||||
\(242\) | −44.9015 | −2.88638 | ||||||||
\(243\) | 11.0199 | 0.706925 | ||||||||
\(244\) | −39.2966 | −2.51570 | ||||||||
\(245\) | 17.4942 | 1.11766 | ||||||||
\(246\) | 5.24183 | 0.334207 | ||||||||
\(247\) | 4.77719 | 0.303965 | ||||||||
\(248\) | 105.869 | 6.72272 | ||||||||
\(249\) | −14.3813 | −0.911379 | ||||||||
\(250\) | −16.3222 | −1.03230 | ||||||||
\(251\) | 1.01801 | 0.0642562 | 0.0321281 | − | 0.999484i | \(-0.489772\pi\) | ||||
0.0321281 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(252\) | 5.96706 | 0.375890 | ||||||||
\(253\) | 18.9971 | 1.19434 | ||||||||
\(254\) | −57.6966 | −3.62021 | ||||||||
\(255\) | −26.2819 | −1.64584 | ||||||||
\(256\) | 127.517 | 7.96981 | ||||||||
\(257\) | −5.00999 | −0.312514 | −0.156257 | − | 0.987716i | \(-0.549943\pi\) | ||||
−0.156257 | + | 0.987716i | \(0.549943\pi\) | |||||||
\(258\) | 12.5043 | 0.778487 | ||||||||
\(259\) | −3.41906 | −0.212450 | ||||||||
\(260\) | −16.7105 | −1.03634 | ||||||||
\(261\) | 3.49280 | 0.216199 | ||||||||
\(262\) | −35.3478 | −2.18380 | ||||||||
\(263\) | 15.3038 | 0.943672 | 0.471836 | − | 0.881686i | \(-0.343591\pi\) | ||||
0.471836 | + | 0.881686i | \(0.343591\pi\) | |||||||
\(264\) | 78.5307 | 4.83323 | ||||||||
\(265\) | −27.1700 | −1.66904 | ||||||||
\(266\) | 11.9778 | 0.734404 | ||||||||
\(267\) | 2.19012 | 0.134033 | ||||||||
\(268\) | −59.5978 | −3.64052 | ||||||||
\(269\) | −21.9523 | −1.33845 | −0.669227 | − | 0.743058i | \(-0.733375\pi\) | ||||
−0.669227 | + | 0.743058i | \(0.733375\pi\) | |||||||
\(270\) | −44.8209 | −2.72771 | ||||||||
\(271\) | −30.8855 | −1.87616 | −0.938079 | − | 0.346422i | \(-0.887397\pi\) | ||||
−0.938079 | + | 0.346422i | \(0.887397\pi\) | |||||||
\(272\) | 131.592 | 7.97896 | ||||||||
\(273\) | −1.21754 | −0.0736886 | ||||||||
\(274\) | 59.0721 | 3.56868 | ||||||||
\(275\) | −15.2787 | −0.921338 | ||||||||
\(276\) | −29.6700 | −1.78593 | ||||||||
\(277\) | −13.7135 | −0.823965 | −0.411982 | − | 0.911192i | \(-0.635163\pi\) | ||||
−0.411982 | + | 0.911192i | \(0.635163\pi\) | |||||||
\(278\) | −3.07779 | −0.184593 | ||||||||
\(279\) | 10.8156 | 0.647511 | ||||||||
\(280\) | −27.7649 | −1.65927 | ||||||||
\(281\) | −6.15411 | −0.367124 | −0.183562 | − | 0.983008i | \(-0.558763\pi\) | ||||
−0.183562 | + | 0.983008i | \(0.558763\pi\) | |||||||
\(282\) | −11.2107 | −0.667590 | ||||||||
\(283\) | 16.7963 | 0.998436 | 0.499218 | − | 0.866477i | \(-0.333621\pi\) | ||||
0.499218 | + | 0.866477i | \(0.333621\pi\) | |||||||
\(284\) | 45.7630 | 2.71554 | ||||||||
\(285\) | −18.4104 | −1.09054 | ||||||||
\(286\) | 14.6170 | 0.864321 | ||||||||
\(287\) | 1.21220 | 0.0715538 | ||||||||
\(288\) | 36.4025 | 2.14504 | ||||||||
\(289\) | 29.5085 | 1.73580 | ||||||||
\(290\) | −24.5248 | −1.44015 | ||||||||
\(291\) | −1.52447 | −0.0893661 | ||||||||
\(292\) | 24.3844 | 1.42699 | ||||||||
\(293\) | −13.2050 | −0.771443 | −0.385722 | − | 0.922615i | \(-0.626047\pi\) | ||||
−0.385722 | + | 0.922615i | \(0.626047\pi\) | |||||||
\(294\) | 23.8998 | 1.39387 | ||||||||
\(295\) | 14.5615 | 0.847803 | ||||||||
\(296\) | −42.4833 | −2.46929 | ||||||||
\(297\) | 29.3167 | 1.70113 | ||||||||
\(298\) | 16.6636 | 0.965296 | ||||||||
\(299\) | −3.65966 | −0.211644 | ||||||||
\(300\) | 23.8625 | 1.37770 | ||||||||
\(301\) | 2.89169 | 0.166674 | ||||||||
\(302\) | −18.9183 | −1.08863 | ||||||||
\(303\) | −19.5779 | −1.12472 | ||||||||
\(304\) | 92.1800 | 5.28689 | ||||||||
\(305\) | 18.6796 | 1.06959 | ||||||||
\(306\) | 21.7050 | 1.24079 | ||||||||
\(307\) | 12.6903 | 0.724275 | 0.362137 | − | 0.932125i | \(-0.382047\pi\) | ||||
0.362137 | + | 0.932125i | \(0.382047\pi\) | |||||||
\(308\) | 27.4048 | 1.56153 | ||||||||
\(309\) | −0.319617 | −0.0181824 | ||||||||
\(310\) | −75.9418 | −4.31320 | ||||||||
\(311\) | 9.47046 | 0.537021 | 0.268510 | − | 0.963277i | \(-0.413469\pi\) | ||||
0.268510 | + | 0.963277i | \(0.413469\pi\) | |||||||
\(312\) | −15.1284 | −0.856476 | ||||||||
\(313\) | −29.6412 | −1.67542 | −0.837711 | − | 0.546114i | \(-0.816107\pi\) | ||||
−0.837711 | + | 0.546114i | \(0.816107\pi\) | |||||||
\(314\) | 25.5411 | 1.44137 | ||||||||
\(315\) | −2.83644 | −0.159816 | ||||||||
\(316\) | −31.4278 | −1.76795 | ||||||||
\(317\) | 4.35475 | 0.244587 | 0.122294 | − | 0.992494i | \(-0.460975\pi\) | ||||
0.122294 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(318\) | −37.1184 | −2.08150 | ||||||||
\(319\) | 16.0413 | 0.898141 | ||||||||
\(320\) | −146.835 | −8.20831 | ||||||||
\(321\) | −25.2896 | −1.41153 | ||||||||
\(322\) | −9.17581 | −0.511348 | ||||||||
\(323\) | 32.5791 | 1.81275 | ||||||||
\(324\) | −25.6830 | −1.42683 | ||||||||
\(325\) | 2.94333 | 0.163267 | ||||||||
\(326\) | −6.15406 | −0.340842 | ||||||||
\(327\) | 24.2880 | 1.34313 | ||||||||
\(328\) | 15.0621 | 0.831663 | ||||||||
\(329\) | −2.59254 | −0.142931 | ||||||||
\(330\) | −56.3312 | −3.10093 | ||||||||
\(331\) | 30.7960 | 1.69270 | 0.846351 | − | 0.532626i | \(-0.178795\pi\) | ||||
0.846351 | + | 0.532626i | \(0.178795\pi\) | |||||||
\(332\) | −62.3586 | −3.42238 | ||||||||
\(333\) | −4.34007 | −0.237834 | ||||||||
\(334\) | −21.2402 | −1.16221 | ||||||||
\(335\) | 28.3298 | 1.54782 | ||||||||
\(336\) | −23.4934 | −1.28167 | ||||||||
\(337\) | 22.6814 | 1.23553 | 0.617766 | − | 0.786362i | \(-0.288038\pi\) | ||||
0.617766 | + | 0.786362i | \(0.288038\pi\) | |||||||
\(338\) | −2.81586 | −0.153163 | ||||||||
\(339\) | −19.9467 | −1.08336 | ||||||||
\(340\) | −113.961 | −6.18039 | ||||||||
\(341\) | 49.6723 | 2.68991 | ||||||||
\(342\) | 15.2042 | 0.822152 | ||||||||
\(343\) | 11.7598 | 0.634972 | ||||||||
\(344\) | 35.9304 | 1.93724 | ||||||||
\(345\) | 14.1037 | 0.759316 | ||||||||
\(346\) | −61.1819 | −3.28916 | ||||||||
\(347\) | 10.8949 | 0.584871 | 0.292435 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292435 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(348\) | −25.0536 | −1.34302 | ||||||||
\(349\) | 14.5526 | 0.778985 | 0.389492 | − | 0.921030i | \(-0.372650\pi\) | ||||
0.389492 | + | 0.921030i | \(0.372650\pi\) | |||||||
\(350\) | 7.37976 | 0.394465 | ||||||||
\(351\) | −5.64765 | −0.301449 | ||||||||
\(352\) | 167.185 | 8.91098 | ||||||||
\(353\) | 29.5581 | 1.57322 | 0.786609 | − | 0.617452i | \(-0.211835\pi\) | ||||
0.786609 | + | 0.617452i | \(0.211835\pi\) | |||||||
\(354\) | 19.8933 | 1.05731 | ||||||||
\(355\) | −21.7535 | −1.15455 | ||||||||
\(356\) | 9.49655 | 0.503316 | ||||||||
\(357\) | −8.30325 | −0.439455 | ||||||||
\(358\) | 4.74212 | 0.250629 | ||||||||
\(359\) | 34.1868 | 1.80431 | 0.902154 | − | 0.431414i | \(-0.141985\pi\) | ||||
0.902154 | + | 0.431414i | \(0.141985\pi\) | |||||||
\(360\) | −35.2440 | −1.85752 | ||||||||
\(361\) | 3.82154 | 0.201133 | ||||||||
\(362\) | 21.1118 | 1.10961 | ||||||||
\(363\) | 21.8042 | 1.14442 | ||||||||
\(364\) | −5.27934 | −0.276713 | ||||||||
\(365\) | −11.5911 | −0.606709 | ||||||||
\(366\) | 25.5193 | 1.33391 | ||||||||
\(367\) | −19.5711 | −1.02160 | −0.510802 | − | 0.859698i | \(-0.670652\pi\) | ||||
−0.510802 | + | 0.859698i | \(0.670652\pi\) | |||||||
\(368\) | −70.6163 | −3.68113 | ||||||||
\(369\) | 1.53873 | 0.0801031 | ||||||||
\(370\) | 30.4739 | 1.58426 | ||||||||
\(371\) | −8.58381 | −0.445649 | ||||||||
\(372\) | −77.5792 | −4.02230 | ||||||||
\(373\) | −0.741225 | −0.0383792 | −0.0191896 | − | 0.999816i | \(-0.506109\pi\) | ||||
−0.0191896 | + | 0.999816i | \(0.506109\pi\) | |||||||
\(374\) | 99.6838 | 5.15452 | ||||||||
\(375\) | 7.92603 | 0.409299 | ||||||||
\(376\) | −32.2133 | −1.66128 | ||||||||
\(377\) | −3.09025 | −0.159156 | ||||||||
\(378\) | −14.1603 | −0.728325 | ||||||||
\(379\) | 23.4901 | 1.20660 | 0.603302 | − | 0.797512i | \(-0.293851\pi\) | ||||
0.603302 | + | 0.797512i | \(0.293851\pi\) | |||||||
\(380\) | −79.8291 | −4.09515 | ||||||||
\(381\) | 28.0175 | 1.43538 | ||||||||
\(382\) | 62.1329 | 3.17900 | ||||||||
\(383\) | −7.85307 | −0.401273 | −0.200637 | − | 0.979666i | \(-0.564301\pi\) | ||||
−0.200637 | + | 0.979666i | \(0.564301\pi\) | |||||||
\(384\) | −112.520 | −5.74204 | ||||||||
\(385\) | −13.0269 | −0.663910 | ||||||||
\(386\) | −20.4823 | −1.04252 | ||||||||
\(387\) | 3.67063 | 0.186589 | ||||||||
\(388\) | −6.61024 | −0.335584 | ||||||||
\(389\) | 29.9332 | 1.51767 | 0.758837 | − | 0.651280i | \(-0.225768\pi\) | ||||
0.758837 | + | 0.651280i | \(0.225768\pi\) | |||||||
\(390\) | 10.8518 | 0.549503 | ||||||||
\(391\) | −24.9578 | −1.26217 | ||||||||
\(392\) | 68.6746 | 3.46859 | ||||||||
\(393\) | 17.1649 | 0.865854 | ||||||||
\(394\) | 45.0344 | 2.26880 | ||||||||
\(395\) | 14.9392 | 0.751672 | ||||||||
\(396\) | 34.7869 | 1.74811 | ||||||||
\(397\) | −13.4144 | −0.673249 | −0.336625 | − | 0.941639i | \(-0.609285\pi\) | ||||
−0.336625 | + | 0.941639i | \(0.609285\pi\) | |||||||
\(398\) | 33.5166 | 1.68004 | ||||||||
\(399\) | −5.81640 | −0.291184 | ||||||||
\(400\) | 56.7941 | 2.83971 | ||||||||
\(401\) | 22.1318 | 1.10521 | 0.552605 | − | 0.833443i | \(-0.313634\pi\) | ||||
0.552605 | + | 0.833443i | \(0.313634\pi\) | |||||||
\(402\) | 38.7030 | 1.93033 | ||||||||
\(403\) | −9.56903 | −0.476667 | ||||||||
\(404\) | −84.8916 | −4.22351 | ||||||||
\(405\) | 12.2084 | 0.606641 | ||||||||
\(406\) | −7.74813 | −0.384533 | ||||||||
\(407\) | −19.9325 | −0.988018 | ||||||||
\(408\) | −103.171 | −5.10774 | ||||||||
\(409\) | −15.9103 | −0.786715 | −0.393358 | − | 0.919386i | \(-0.628687\pi\) | ||||
−0.393358 | + | 0.919386i | \(0.628687\pi\) | |||||||
\(410\) | −10.8042 | −0.533583 | ||||||||
\(411\) | −28.6854 | −1.41495 | ||||||||
\(412\) | −1.38589 | −0.0682777 | ||||||||
\(413\) | 4.60041 | 0.226371 | ||||||||
\(414\) | −11.6475 | −0.572444 | ||||||||
\(415\) | 29.6422 | 1.45508 | ||||||||
\(416\) | −32.2070 | −1.57908 | ||||||||
\(417\) | 1.49457 | 0.0731895 | ||||||||
\(418\) | 69.8281 | 3.41541 | ||||||||
\(419\) | 33.4699 | 1.63511 | 0.817555 | − | 0.575850i | \(-0.195329\pi\) | ||||
0.817555 | + | 0.575850i | \(0.195329\pi\) | |||||||
\(420\) | 20.3456 | 0.992764 | ||||||||
\(421\) | −29.9163 | −1.45803 | −0.729016 | − | 0.684496i | \(-0.760022\pi\) | ||||
−0.729016 | + | 0.684496i | \(0.760022\pi\) | |||||||
\(422\) | −54.9614 | −2.67548 | ||||||||
\(423\) | −3.29089 | −0.160009 | ||||||||
\(424\) | −106.657 | −5.17974 | ||||||||
\(425\) | 20.0727 | 0.973668 | ||||||||
\(426\) | −29.7186 | −1.43987 | ||||||||
\(427\) | 5.90145 | 0.285591 | ||||||||
\(428\) | −109.658 | −5.30050 | ||||||||
\(429\) | −7.09801 | −0.342695 | ||||||||
\(430\) | −25.7734 | −1.24291 | ||||||||
\(431\) | 7.46140 | 0.359403 | 0.179702 | − | 0.983721i | \(-0.442487\pi\) | ||||
0.179702 | + | 0.983721i | \(0.442487\pi\) | |||||||
\(432\) | −108.976 | −5.24313 | ||||||||
\(433\) | −17.1887 | −0.826037 | −0.413019 | − | 0.910723i | \(-0.635526\pi\) | ||||
−0.413019 | + | 0.910723i | \(0.635526\pi\) | |||||||
\(434\) | −23.9923 | −1.15167 | ||||||||
\(435\) | 11.9093 | 0.571005 | ||||||||
\(436\) | 105.315 | 5.04367 | ||||||||
\(437\) | −17.4829 | −0.836320 | ||||||||
\(438\) | −15.8353 | −0.756640 | ||||||||
\(439\) | −1.75209 | −0.0836229 | −0.0418114 | − | 0.999126i | \(-0.513313\pi\) | ||||
−0.0418114 | + | 0.999126i | \(0.513313\pi\) | |||||||
\(440\) | −161.864 | −7.71657 | ||||||||
\(441\) | 7.01575 | 0.334083 | ||||||||
\(442\) | −19.2034 | −0.913412 | ||||||||
\(443\) | 34.4167 | 1.63519 | 0.817593 | − | 0.575797i | \(-0.195308\pi\) | ||||
0.817593 | + | 0.575797i | \(0.195308\pi\) | |||||||
\(444\) | 31.1310 | 1.47741 | ||||||||
\(445\) | −4.51419 | −0.213993 | ||||||||
\(446\) | −56.4883 | −2.67480 | ||||||||
\(447\) | −8.09183 | −0.382731 | ||||||||
\(448\) | −46.3895 | −2.19170 | ||||||||
\(449\) | 11.8819 | 0.560742 | 0.280371 | − | 0.959892i | \(-0.409543\pi\) | ||||
0.280371 | + | 0.959892i | \(0.409543\pi\) | |||||||
\(450\) | 9.36767 | 0.441596 | ||||||||
\(451\) | 7.06689 | 0.332767 | ||||||||
\(452\) | −86.4907 | −4.06818 | ||||||||
\(453\) | 9.18672 | 0.431630 | ||||||||
\(454\) | 2.81752 | 0.132233 | ||||||||
\(455\) | 2.50953 | 0.117649 | ||||||||
\(456\) | −72.2712 | −3.38441 | ||||||||
\(457\) | −29.8747 | −1.39748 | −0.698740 | − | 0.715376i | \(-0.746255\pi\) | ||||
−0.698740 | + | 0.715376i | \(0.746255\pi\) | |||||||
\(458\) | 5.53753 | 0.258752 | ||||||||
\(459\) | −38.5154 | −1.79774 | ||||||||
\(460\) | 61.1547 | 2.85135 | ||||||||
\(461\) | 3.65956 | 0.170443 | 0.0852215 | − | 0.996362i | \(-0.472840\pi\) | ||||
0.0852215 | + | 0.996362i | \(0.472840\pi\) | |||||||
\(462\) | −17.7967 | −0.827978 | ||||||||
\(463\) | −19.6029 | −0.911026 | −0.455513 | − | 0.890229i | \(-0.650544\pi\) | ||||
−0.455513 | + | 0.890229i | \(0.650544\pi\) | |||||||
\(464\) | −59.6290 | −2.76821 | ||||||||
\(465\) | 36.8773 | 1.71014 | ||||||||
\(466\) | 33.3392 | 1.54441 | ||||||||
\(467\) | 20.8779 | 0.966114 | 0.483057 | − | 0.875589i | \(-0.339526\pi\) | ||||
0.483057 | + | 0.875589i | \(0.339526\pi\) | |||||||
\(468\) | −6.70145 | −0.309775 | ||||||||
\(469\) | 8.95024 | 0.413284 | ||||||||
\(470\) | 23.1071 | 1.06585 | ||||||||
\(471\) | −12.4028 | −0.571489 | ||||||||
\(472\) | 57.1620 | 2.63109 | ||||||||
\(473\) | 16.8580 | 0.775132 | ||||||||
\(474\) | 20.4092 | 0.937428 | ||||||||
\(475\) | 14.0608 | 0.645156 | ||||||||
\(476\) | −36.0036 | −1.65022 | ||||||||
\(477\) | −10.8960 | −0.498896 | ||||||||
\(478\) | −22.6922 | −1.03792 | ||||||||
\(479\) | 43.1723 | 1.97259 | 0.986296 | − | 0.164985i | \(-0.0527574\pi\) | ||||
0.986296 | + | 0.164985i | \(0.0527574\pi\) | |||||||
\(480\) | 124.120 | 5.66527 | ||||||||
\(481\) | 3.83986 | 0.175083 | ||||||||
\(482\) | 27.6295 | 1.25849 | ||||||||
\(483\) | 4.45577 | 0.202744 | ||||||||
\(484\) | 94.5447 | 4.29749 | ||||||||
\(485\) | 3.14218 | 0.142679 | ||||||||
\(486\) | −31.0305 | −1.40757 | ||||||||
\(487\) | −7.06716 | −0.320243 | −0.160122 | − | 0.987097i | \(-0.551189\pi\) | ||||
−0.160122 | + | 0.987097i | \(0.551189\pi\) | |||||||
\(488\) | 73.3280 | 3.31940 | ||||||||
\(489\) | 2.98841 | 0.135141 | ||||||||
\(490\) | −49.2613 | −2.22540 | ||||||||
\(491\) | 9.51917 | 0.429594 | 0.214797 | − | 0.976659i | \(-0.431091\pi\) | ||||
0.214797 | + | 0.976659i | \(0.431091\pi\) | |||||||
\(492\) | −11.0372 | −0.497595 | ||||||||
\(493\) | −21.0746 | −0.949153 | ||||||||
\(494\) | −13.4519 | −0.605230 | ||||||||
\(495\) | −16.5359 | −0.743235 | ||||||||
\(496\) | −184.643 | −8.29071 | ||||||||
\(497\) | −6.87257 | −0.308277 | ||||||||
\(498\) | 40.4958 | 1.81466 | ||||||||
\(499\) | 41.5433 | 1.85974 | 0.929868 | − | 0.367895i | \(-0.119921\pi\) | ||||
0.929868 | + | 0.367895i | \(0.119921\pi\) | |||||||
\(500\) | 34.3680 | 1.53698 | ||||||||
\(501\) | 10.3142 | 0.460805 | ||||||||
\(502\) | −2.86658 | −0.127942 | ||||||||
\(503\) | −30.5253 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738249\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738249\pi\) | |||||||
\(504\) | −11.1346 | −0.495976 | ||||||||
\(505\) | 40.3532 | 1.79569 | ||||||||
\(506\) | −53.4932 | −2.37806 | ||||||||
\(507\) | 1.36738 | 0.0607276 | ||||||||
\(508\) | 121.486 | 5.39007 | ||||||||
\(509\) | −33.2341 | −1.47308 | −0.736538 | − | 0.676396i | \(-0.763541\pi\) | ||||
−0.736538 | + | 0.676396i | \(0.763541\pi\) | |||||||
\(510\) | 74.0063 | 3.27706 | ||||||||
\(511\) | −3.66199 | −0.161997 | ||||||||
\(512\) | −194.492 | −8.59543 | ||||||||
\(513\) | −26.9799 | −1.19119 | ||||||||
\(514\) | 14.1074 | 0.622252 | ||||||||
\(515\) | 0.658781 | 0.0290294 | ||||||||
\(516\) | −26.3292 | −1.15908 | ||||||||
\(517\) | −15.1140 | −0.664713 | ||||||||
\(518\) | 9.62762 | 0.423013 | ||||||||
\(519\) | 29.7099 | 1.30412 | ||||||||
\(520\) | 31.1820 | 1.36742 | ||||||||
\(521\) | 32.4373 | 1.42110 | 0.710552 | − | 0.703644i | \(-0.248445\pi\) | ||||
0.710552 | + | 0.703644i | \(0.248445\pi\) | |||||||
\(522\) | −9.83526 | −0.430478 | ||||||||
\(523\) | 3.01659 | 0.131906 | 0.0659532 | − | 0.997823i | \(-0.478991\pi\) | ||||
0.0659532 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(524\) | 74.4285 | 3.25142 | ||||||||
\(525\) | −3.58361 | −0.156402 | ||||||||
\(526\) | −43.0934 | −1.87896 | ||||||||
\(527\) | −65.2581 | −2.84269 | ||||||||
\(528\) | −136.962 | −5.96052 | ||||||||
\(529\) | −9.60689 | −0.417691 | ||||||||
\(530\) | 76.5069 | 3.32325 | ||||||||
\(531\) | 5.83963 | 0.253418 | ||||||||
\(532\) | −25.2204 | −1.09344 | ||||||||
\(533\) | −1.36139 | −0.0589682 | ||||||||
\(534\) | −6.16708 | −0.266876 | ||||||||
\(535\) | 52.1258 | 2.25359 | ||||||||
\(536\) | 111.211 | 4.80356 | ||||||||
\(537\) | −2.30277 | −0.0993720 | ||||||||
\(538\) | 61.8146 | 2.66502 | ||||||||
\(539\) | 32.2211 | 1.38786 | ||||||||
\(540\) | 94.3750 | 4.06125 | ||||||||
\(541\) | −4.34782 | −0.186927 | −0.0934637 | − | 0.995623i | \(-0.529794\pi\) | ||||
−0.0934637 | + | 0.995623i | \(0.529794\pi\) | |||||||
\(542\) | 86.9692 | 3.73565 | ||||||||
\(543\) | −10.2519 | −0.439951 | ||||||||
\(544\) | −219.643 | −9.41710 | ||||||||
\(545\) | −50.0614 | −2.14440 | ||||||||
\(546\) | 3.42841 | 0.146723 | ||||||||
\(547\) | 25.2797 | 1.08088 | 0.540440 | − | 0.841382i | \(-0.318258\pi\) | ||||
0.540440 | + | 0.841382i | \(0.318258\pi\) | |||||||
\(548\) | −124.382 | −5.31335 | ||||||||
\(549\) | 7.49114 | 0.319714 | ||||||||
\(550\) | 43.0226 | 1.83449 | ||||||||
\(551\) | −14.7627 | −0.628912 | ||||||||
\(552\) | 55.3648 | 2.35648 | ||||||||
\(553\) | 4.71974 | 0.200704 | ||||||||
\(554\) | 38.6154 | 1.64061 | ||||||||
\(555\) | −14.7981 | −0.628145 | ||||||||
\(556\) | 6.48059 | 0.274838 | ||||||||
\(557\) | −6.68514 | −0.283258 | −0.141629 | − | 0.989920i | \(-0.545234\pi\) | ||||
−0.141629 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(558\) | −30.4551 | −1.28927 | ||||||||
\(559\) | −3.24758 | −0.137358 | ||||||||
\(560\) | 48.4237 | 2.04627 | ||||||||
\(561\) | −48.4064 | −2.04372 | ||||||||
\(562\) | 17.3291 | 0.730986 | ||||||||
\(563\) | 9.24535 | 0.389645 | 0.194822 | − | 0.980839i | \(-0.437587\pi\) | ||||
0.194822 | + | 0.980839i | \(0.437587\pi\) | |||||||
\(564\) | 23.6053 | 0.993964 | ||||||||
\(565\) | 41.1134 | 1.72965 | ||||||||
\(566\) | −47.2960 | −1.98800 | ||||||||
\(567\) | 3.85700 | 0.161979 | ||||||||
\(568\) | −85.3945 | −3.58307 | ||||||||
\(569\) | 6.54291 | 0.274293 | 0.137146 | − | 0.990551i | \(-0.456207\pi\) | ||||
0.137146 | + | 0.990551i | \(0.456207\pi\) | |||||||
\(570\) | 51.8412 | 2.17139 | ||||||||
\(571\) | 1.91545 | 0.0801590 | 0.0400795 | − | 0.999196i | \(-0.487239\pi\) | ||||
0.0400795 | + | 0.999196i | \(0.487239\pi\) | |||||||
\(572\) | −30.7776 | −1.28687 | ||||||||
\(573\) | −30.1717 | −1.26044 | ||||||||
\(574\) | −3.41338 | −0.142472 | ||||||||
\(575\) | −10.7716 | −0.449206 | ||||||||
\(576\) | −58.8855 | −2.45356 | ||||||||
\(577\) | 8.03199 | 0.334376 | 0.167188 | − | 0.985925i | \(-0.446531\pi\) | ||||
0.167188 | + | 0.985925i | \(0.446531\pi\) | |||||||
\(578\) | −83.0920 | −3.45617 | ||||||||
\(579\) | 9.94619 | 0.413350 | ||||||||
\(580\) | 51.6395 | 2.14421 | ||||||||
\(581\) | 9.36485 | 0.388520 | ||||||||
\(582\) | 4.29270 | 0.177938 | ||||||||
\(583\) | −50.0420 | −2.07253 | ||||||||
\(584\) | −45.5018 | −1.88288 | ||||||||
\(585\) | 3.18553 | 0.131706 | ||||||||
\(586\) | 37.1834 | 1.53603 | ||||||||
\(587\) | 34.9900 | 1.44419 | 0.722097 | − | 0.691792i | \(-0.243178\pi\) | ||||
0.722097 | + | 0.691792i | \(0.243178\pi\) | |||||||
\(588\) | −50.3235 | −2.07530 | ||||||||
\(589\) | −45.7131 | −1.88357 | ||||||||
\(590\) | −41.0032 | −1.68807 | ||||||||
\(591\) | −21.8687 | −0.899558 | ||||||||
\(592\) | 74.0934 | 3.04522 | ||||||||
\(593\) | 28.0531 | 1.15200 | 0.576001 | − | 0.817449i | \(-0.304612\pi\) | ||||
0.576001 | + | 0.817449i | \(0.304612\pi\) | |||||||
\(594\) | −82.5517 | −3.38714 | ||||||||
\(595\) | 17.1143 | 0.701619 | ||||||||
\(596\) | −35.0869 | −1.43721 | ||||||||
\(597\) | −16.2756 | −0.666118 | ||||||||
\(598\) | 10.3051 | 0.421407 | ||||||||
\(599\) | 27.0572 | 1.10553 | 0.552765 | − | 0.833337i | \(-0.313573\pi\) | ||||
0.552765 | + | 0.833337i | \(0.313573\pi\) | |||||||
\(600\) | −44.5278 | −1.81784 | ||||||||
\(601\) | 32.5369 | 1.32721 | 0.663603 | − | 0.748085i | \(-0.269026\pi\) | ||||
0.663603 | + | 0.748085i | \(0.269026\pi\) | |||||||
\(602\) | −8.14260 | −0.331868 | ||||||||
\(603\) | 11.3612 | 0.462664 | ||||||||
\(604\) | 39.8344 | 1.62084 | ||||||||
\(605\) | −44.9419 | −1.82715 | ||||||||
\(606\) | 55.1288 | 2.23945 | ||||||||
\(607\) | −36.4986 | −1.48143 | −0.740716 | − | 0.671818i | \(-0.765514\pi\) | ||||
−0.740716 | + | 0.671818i | \(0.765514\pi\) | |||||||
\(608\) | −153.859 | −6.23980 | ||||||||
\(609\) | 3.76249 | 0.152464 | ||||||||
\(610\) | −52.5993 | −2.12968 | ||||||||
\(611\) | 2.91161 | 0.117791 | ||||||||
\(612\) | −45.7020 | −1.84739 | ||||||||
\(613\) | −29.3119 | −1.18390 | −0.591949 | − | 0.805975i | \(-0.701641\pi\) | ||||
−0.591949 | + | 0.805975i | \(0.701641\pi\) | |||||||
\(614\) | −35.7342 | −1.44212 | ||||||||
\(615\) | 5.24654 | 0.211561 | ||||||||
\(616\) | −51.1377 | −2.06040 | ||||||||
\(617\) | −1.00000 | −0.0402585 | ||||||||
\(618\) | 0.899998 | 0.0362032 | ||||||||
\(619\) | 13.3805 | 0.537807 | 0.268904 | − | 0.963167i | \(-0.413339\pi\) | ||||
0.268904 | + | 0.963167i | \(0.413339\pi\) | |||||||
\(620\) | 159.903 | 6.42186 | ||||||||
\(621\) | 20.6685 | 0.829398 | ||||||||
\(622\) | −26.6675 | −1.06927 | ||||||||
\(623\) | −1.42617 | −0.0571381 | ||||||||
\(624\) | 26.3848 | 1.05624 | ||||||||
\(625\) | −31.0535 | −1.24214 | ||||||||
\(626\) | 83.4657 | 3.33596 | ||||||||
\(627\) | −33.9085 | −1.35418 | ||||||||
\(628\) | −53.7794 | −2.14603 | ||||||||
\(629\) | 26.1868 | 1.04413 | ||||||||
\(630\) | 7.98704 | 0.318211 | ||||||||
\(631\) | 10.9849 | 0.437301 | 0.218650 | − | 0.975803i | \(-0.429835\pi\) | ||||
0.218650 | + | 0.975803i | \(0.429835\pi\) | |||||||
\(632\) | 58.6447 | 2.33276 | ||||||||
\(633\) | 26.6892 | 1.06080 | ||||||||
\(634\) | −12.2624 | −0.487002 | ||||||||
\(635\) | −57.7484 | −2.29168 | ||||||||
\(636\) | 78.1566 | 3.09911 | ||||||||
\(637\) | −6.20716 | −0.245937 | ||||||||
\(638\) | −45.1701 | −1.78830 | ||||||||
\(639\) | −8.72385 | −0.345110 | ||||||||
\(640\) | 231.923 | 9.16755 | ||||||||
\(641\) | 31.8229 | 1.25693 | 0.628465 | − | 0.777838i | \(-0.283683\pi\) | ||||
0.628465 | + | 0.777838i | \(0.283683\pi\) | |||||||
\(642\) | 71.2119 | 2.81051 | ||||||||
\(643\) | 21.7351 | 0.857149 | 0.428575 | − | 0.903506i | \(-0.359016\pi\) | ||||
0.428575 | + | 0.903506i | \(0.359016\pi\) | |||||||
\(644\) | 19.3206 | 0.761338 | ||||||||
\(645\) | 12.5156 | 0.492800 | ||||||||
\(646\) | −91.7382 | −3.60939 | ||||||||
\(647\) | −4.24628 | −0.166938 | −0.0834692 | − | 0.996510i | \(-0.526600\pi\) | ||||
−0.0834692 | + | 0.996510i | \(0.526600\pi\) | |||||||
\(648\) | 47.9249 | 1.88267 | ||||||||
\(649\) | 26.8195 | 1.05276 | ||||||||
\(650\) | −8.28801 | −0.325083 | ||||||||
\(651\) | 11.6506 | 0.456625 | ||||||||
\(652\) | 12.9580 | 0.507475 | ||||||||
\(653\) | 23.4940 | 0.919392 | 0.459696 | − | 0.888076i | \(-0.347958\pi\) | ||||
0.459696 | + | 0.888076i | \(0.347958\pi\) | |||||||
\(654\) | −68.3917 | −2.67433 | ||||||||
\(655\) | −35.3796 | −1.38239 | ||||||||
\(656\) | −26.2691 | −1.02564 | ||||||||
\(657\) | −4.64843 | −0.181353 | ||||||||
\(658\) | 7.30022 | 0.284592 | ||||||||
\(659\) | −34.7736 | −1.35459 | −0.677294 | − | 0.735713i | \(-0.736847\pi\) | ||||
−0.677294 | + | 0.735713i | \(0.736847\pi\) | |||||||
\(660\) | 118.611 | 4.61693 | ||||||||
\(661\) | 4.53835 | 0.176521 | 0.0882606 | − | 0.996097i | \(-0.471869\pi\) | ||||
0.0882606 | + | 0.996097i | \(0.471869\pi\) | |||||||
\(662\) | −86.7173 | −3.37037 | ||||||||
\(663\) | 9.32516 | 0.362159 | ||||||||
\(664\) | 116.362 | 4.51573 | ||||||||
\(665\) | 11.9885 | 0.464895 | ||||||||
\(666\) | 12.2210 | 0.473555 | ||||||||
\(667\) | 11.3093 | 0.437896 | ||||||||
\(668\) | 44.7233 | 1.73040 | ||||||||
\(669\) | 27.4307 | 1.06053 | ||||||||
\(670\) | −79.7730 | −3.08190 | ||||||||
\(671\) | 34.4044 | 1.32817 | ||||||||
\(672\) | 39.2132 | 1.51268 | ||||||||
\(673\) | −41.7173 | −1.60808 | −0.804042 | − | 0.594573i | \(-0.797321\pi\) | ||||
−0.804042 | + | 0.594573i | \(0.797321\pi\) | |||||||
\(674\) | −63.8676 | −2.46009 | ||||||||
\(675\) | −16.6229 | −0.639816 | ||||||||
\(676\) | 5.92908 | 0.228042 | ||||||||
\(677\) | 2.37370 | 0.0912287 | 0.0456144 | − | 0.998959i | \(-0.485475\pi\) | ||||
0.0456144 | + | 0.998959i | \(0.485475\pi\) | |||||||
\(678\) | 56.1673 | 2.15709 | ||||||||
\(679\) | 0.992708 | 0.0380966 | ||||||||
\(680\) | 212.652 | 8.15485 | ||||||||
\(681\) | −1.36819 | −0.0524290 | ||||||||
\(682\) | −139.870 | −5.35592 | ||||||||
\(683\) | 31.6335 | 1.21042 | 0.605212 | − | 0.796065i | \(-0.293088\pi\) | ||||
0.605212 | + | 0.796065i | \(0.293088\pi\) | |||||||
\(684\) | −32.0141 | −1.22409 | ||||||||
\(685\) | 59.1251 | 2.25905 | ||||||||
\(686\) | −33.1141 | −1.26430 | ||||||||
\(687\) | −2.68902 | −0.102593 | ||||||||
\(688\) | −62.6649 | −2.38908 | ||||||||
\(689\) | 9.64024 | 0.367264 | ||||||||
\(690\) | −39.7140 | −1.51189 | ||||||||
\(691\) | −1.46610 | −0.0557732 | −0.0278866 | − | 0.999611i | \(-0.508878\pi\) | ||||
−0.0278866 | + | 0.999611i | \(0.508878\pi\) | |||||||
\(692\) | 128.825 | 4.89718 | ||||||||
\(693\) | −5.22420 | −0.198451 | ||||||||
\(694\) | −30.6786 | −1.16455 | ||||||||
\(695\) | −3.08055 | −0.116852 | ||||||||
\(696\) | 46.7505 | 1.77207 | ||||||||
\(697\) | −9.28427 | −0.351667 | ||||||||
\(698\) | −40.9782 | −1.55105 | ||||||||
\(699\) | −16.1895 | −0.612343 | ||||||||
\(700\) | −15.5388 | −0.587313 | ||||||||
\(701\) | −11.5812 | −0.437415 | −0.218708 | − | 0.975790i | \(-0.570184\pi\) | ||||
−0.218708 | + | 0.975790i | \(0.570184\pi\) | |||||||
\(702\) | 15.9030 | 0.600221 | ||||||||
\(703\) | 18.3437 | 0.691847 | ||||||||
\(704\) | −270.442 | −10.1927 | ||||||||
\(705\) | −11.2208 | −0.422600 | ||||||||
\(706\) | −83.2315 | −3.13246 | ||||||||
\(707\) | 12.7488 | 0.479467 | ||||||||
\(708\) | −41.8873 | −1.57422 | ||||||||
\(709\) | 22.5602 | 0.847267 | 0.423634 | − | 0.905834i | \(-0.360754\pi\) | ||||
0.423634 | + | 0.905834i | \(0.360754\pi\) | |||||||
\(710\) | 61.2547 | 2.29885 | ||||||||
\(711\) | 5.99110 | 0.224684 | ||||||||
\(712\) | −17.7207 | −0.664111 | ||||||||
\(713\) | 35.0194 | 1.31149 | ||||||||
\(714\) | 23.3808 | 0.875005 | ||||||||
\(715\) | 14.6301 | 0.547135 | ||||||||
\(716\) | −9.98502 | −0.373158 | ||||||||
\(717\) | 11.0193 | 0.411524 | ||||||||
\(718\) | −96.2652 | −3.59259 | ||||||||
\(719\) | 14.4724 | 0.539728 | 0.269864 | − | 0.962898i | \(-0.413021\pi\) | ||||
0.269864 | + | 0.962898i | \(0.413021\pi\) | |||||||
\(720\) | 61.4677 | 2.29076 | ||||||||
\(721\) | 0.208129 | 0.00775112 | ||||||||
\(722\) | −10.7609 | −0.400480 | ||||||||
\(723\) | −13.4169 | −0.498979 | ||||||||
\(724\) | −44.4531 | −1.65209 | ||||||||
\(725\) | −9.09562 | −0.337803 | ||||||||
\(726\) | −61.3976 | −2.27868 | ||||||||
\(727\) | 18.2250 | 0.675927 | 0.337964 | − | 0.941159i | \(-0.390262\pi\) | ||||
0.337964 | + | 0.941159i | \(0.390262\pi\) | |||||||
\(728\) | 9.85133 | 0.365115 | ||||||||
\(729\) | 28.0635 | 1.03939 | ||||||||
\(730\) | 32.6391 | 1.20803 | ||||||||
\(731\) | −22.1476 | −0.819157 | ||||||||
\(732\) | −53.7334 | −1.98604 | ||||||||
\(733\) | 1.12995 | 0.0417358 | 0.0208679 | − | 0.999782i | \(-0.493357\pi\) | ||||
0.0208679 | + | 0.999782i | \(0.493357\pi\) | |||||||
\(734\) | 55.1096 | 2.03413 | ||||||||
\(735\) | 23.9213 | 0.882349 | ||||||||
\(736\) | 117.867 | 4.34462 | ||||||||
\(737\) | 52.1782 | 1.92201 | ||||||||
\(738\) | −4.33285 | −0.159495 | ||||||||
\(739\) | −16.6853 | −0.613780 | −0.306890 | − | 0.951745i | \(-0.599288\pi\) | ||||
−0.306890 | + | 0.951745i | \(0.599288\pi\) | |||||||
\(740\) | −64.1659 | −2.35879 | ||||||||
\(741\) | 6.53224 | 0.239968 | ||||||||
\(742\) | 24.1708 | 0.887339 | ||||||||
\(743\) | 41.3991 | 1.51879 | 0.759394 | − | 0.650632i | \(-0.225496\pi\) | ||||
0.759394 | + | 0.650632i | \(0.225496\pi\) | |||||||
\(744\) | 144.764 | 5.30731 | ||||||||
\(745\) | 16.6786 | 0.611055 | ||||||||
\(746\) | 2.08719 | 0.0764173 | ||||||||
\(747\) | 11.8875 | 0.434940 | ||||||||
\(748\) | −209.894 | −7.67449 | ||||||||
\(749\) | 16.4681 | 0.601731 | ||||||||
\(750\) | −22.3186 | −0.814961 | ||||||||
\(751\) | −42.0670 | −1.53505 | −0.767524 | − | 0.641020i | \(-0.778511\pi\) | ||||
−0.767524 | + | 0.641020i | \(0.778511\pi\) | |||||||
\(752\) | 56.1820 | 2.04875 | ||||||||
\(753\) | 1.39201 | 0.0507276 | ||||||||
\(754\) | 8.70171 | 0.316898 | ||||||||
\(755\) | −18.9353 | −0.689126 | ||||||||
\(756\) | 29.8159 | 1.08439 | ||||||||
\(757\) | −44.7513 | −1.62651 | −0.813257 | − | 0.581904i | \(-0.802308\pi\) | ||||
−0.813257 | + | 0.581904i | \(0.802308\pi\) | |||||||
\(758\) | −66.1449 | −2.40249 | ||||||||
\(759\) | 25.9763 | 0.942880 | ||||||||
\(760\) | 148.962 | 5.40343 | ||||||||
\(761\) | 13.8708 | 0.502817 | 0.251409 | − | 0.967881i | \(-0.419106\pi\) | ||||
0.251409 | + | 0.967881i | \(0.419106\pi\) | |||||||
\(762\) | −78.8933 | −2.85800 | ||||||||
\(763\) | −15.8159 | −0.572574 | ||||||||
\(764\) | −130.827 | −4.73316 | ||||||||
\(765\) | 21.7244 | 0.785449 | ||||||||
\(766\) | 22.1132 | 0.798981 | ||||||||
\(767\) | −5.16660 | −0.186555 | ||||||||
\(768\) | 174.364 | 6.29183 | ||||||||
\(769\) | 46.7759 | 1.68678 | 0.843391 | − | 0.537300i | \(-0.180556\pi\) | ||||
0.843391 | + | 0.537300i | \(0.180556\pi\) | |||||||
\(770\) | 36.6819 | 1.32192 | ||||||||
\(771\) | −6.85057 | −0.246717 | ||||||||
\(772\) | 43.1275 | 1.55219 | ||||||||
\(773\) | −6.50928 | −0.234123 | −0.117061 | − | 0.993125i | \(-0.537347\pi\) | ||||
−0.117061 | + | 0.993125i | \(0.537347\pi\) | |||||||
\(774\) | −10.3360 | −0.371520 | ||||||||
\(775\) | −28.1648 | −1.01171 | ||||||||
\(776\) | 12.3348 | 0.442794 | ||||||||
\(777\) | −4.67517 | −0.167721 | ||||||||
\(778\) | −84.2879 | −3.02187 | ||||||||
\(779\) | −6.50360 | −0.233016 | ||||||||
\(780\) | −22.8496 | −0.818147 | ||||||||
\(781\) | −40.0658 | −1.43367 | ||||||||
\(782\) | 70.2779 | 2.51313 | ||||||||
\(783\) | 17.4526 | 0.623707 | ||||||||
\(784\) | −119.773 | −4.27759 | ||||||||
\(785\) | 25.5641 | 0.912420 | ||||||||
\(786\) | −48.3340 | −1.72402 | ||||||||
\(787\) | −8.41698 | −0.300033 | −0.150016 | − | 0.988684i | \(-0.547933\pi\) | ||||
−0.150016 | + | 0.988684i | \(0.547933\pi\) | |||||||
\(788\) | −94.8246 | −3.37799 | ||||||||
\(789\) | 20.9261 | 0.744990 | ||||||||
\(790\) | −42.0667 | −1.49667 | ||||||||
\(791\) | 12.9889 | 0.461834 | ||||||||
\(792\) | −64.9128 | −2.30658 | ||||||||
\(793\) | −6.62776 | −0.235359 | ||||||||
\(794\) | 37.7731 | 1.34052 | ||||||||
\(795\) | −37.1517 | −1.31764 | ||||||||
\(796\) | −70.5726 | −2.50138 | ||||||||
\(797\) | −7.38839 | −0.261710 | −0.130855 | − | 0.991402i | \(-0.541772\pi\) | ||||
−0.130855 | + | 0.991402i | \(0.541772\pi\) | |||||||
\(798\) | 16.3782 | 0.579781 | ||||||||
\(799\) | 19.8563 | 0.702467 | ||||||||
\(800\) | −94.7958 | −3.35154 | ||||||||
\(801\) | −1.81034 | −0.0639651 | ||||||||
\(802\) | −62.3201 | −2.20060 | ||||||||
\(803\) | −21.3487 | −0.753380 | ||||||||
\(804\) | −81.4930 | −2.87404 | ||||||||
\(805\) | −9.18405 | −0.323695 | ||||||||
\(806\) | 26.9451 | 0.949100 | ||||||||
\(807\) | −30.0171 | −1.05665 | ||||||||
\(808\) | 158.409 | 5.57281 | ||||||||
\(809\) | 29.7531 | 1.04606 | 0.523031 | − | 0.852314i | \(-0.324801\pi\) | ||||
0.523031 | + | 0.852314i | \(0.324801\pi\) | |||||||
\(810\) | −34.3772 | −1.20789 | ||||||||
\(811\) | 52.6864 | 1.85007 | 0.925034 | − | 0.379884i | \(-0.124036\pi\) | ||||
0.925034 | + | 0.379884i | \(0.124036\pi\) | |||||||
\(812\) | 16.3145 | 0.572526 | ||||||||
\(813\) | −42.2322 | −1.48115 | ||||||||
\(814\) | 56.1272 | 1.96726 | ||||||||
\(815\) | −6.15959 | −0.215761 | ||||||||
\(816\) | 179.937 | 6.29906 | ||||||||
\(817\) | −15.5143 | −0.542777 | ||||||||
\(818\) | 44.8013 | 1.56644 | ||||||||
\(819\) | 1.00641 | 0.0351667 | ||||||||
\(820\) | 22.7494 | 0.794444 | ||||||||
\(821\) | −29.4862 | −1.02908 | −0.514538 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514538 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(822\) | 80.7741 | 2.81732 | ||||||||
\(823\) | 26.9336 | 0.938845 | 0.469422 | − | 0.882974i | \(-0.344462\pi\) | ||||
0.469422 | + | 0.882974i | \(0.344462\pi\) | |||||||
\(824\) | 2.58609 | 0.0900906 | ||||||||
\(825\) | −20.8918 | −0.727358 | ||||||||
\(826\) | −12.9541 | −0.450732 | ||||||||
\(827\) | 15.1888 | 0.528166 | 0.264083 | − | 0.964500i | \(-0.414931\pi\) | ||||
0.264083 | + | 0.964500i | \(0.414931\pi\) | |||||||
\(828\) | 24.5250 | 0.852303 | ||||||||
\(829\) | 20.2181 | 0.702205 | 0.351103 | − | 0.936337i | \(-0.385807\pi\) | ||||
0.351103 | + | 0.936337i | \(0.385807\pi\) | |||||||
\(830\) | −83.4684 | −2.89723 | ||||||||
\(831\) | −18.7516 | −0.650486 | ||||||||
\(832\) | 52.0988 | 1.80620 | ||||||||
\(833\) | −42.3311 | −1.46669 | ||||||||
\(834\) | −4.20851 | −0.145729 | ||||||||
\(835\) | −21.2592 | −0.735707 | ||||||||
\(836\) | −147.030 | −5.08515 | ||||||||
\(837\) | 54.0426 | 1.86798 | ||||||||
\(838\) | −94.2466 | −3.25569 | ||||||||
\(839\) | 20.2834 | 0.700260 | 0.350130 | − | 0.936701i | \(-0.386137\pi\) | ||||
0.350130 | + | 0.936701i | \(0.386137\pi\) | |||||||
\(840\) | −37.9652 | −1.30992 | ||||||||
\(841\) | −19.4504 | −0.670702 | ||||||||
\(842\) | 84.2403 | 2.90311 | ||||||||
\(843\) | −8.41502 | −0.289829 | ||||||||
\(844\) | 115.727 | 3.98348 | ||||||||
\(845\) | −2.81839 | −0.0969556 | ||||||||
\(846\) | 9.26670 | 0.318596 | ||||||||
\(847\) | −14.1985 | −0.487865 | ||||||||
\(848\) | 186.017 | 6.38785 | ||||||||
\(849\) | 22.9669 | 0.788223 | ||||||||
\(850\) | −56.5219 | −1.93868 | ||||||||
\(851\) | −14.0526 | −0.481716 | ||||||||
\(852\) | 62.5755 | 2.14380 | ||||||||
\(853\) | −52.2858 | −1.79023 | −0.895117 | − | 0.445832i | \(-0.852908\pi\) | ||||
−0.895117 | + | 0.445832i | \(0.852908\pi\) | |||||||
\(854\) | −16.6177 | −0.568645 | ||||||||
\(855\) | 15.2179 | 0.520441 | ||||||||
\(856\) | 204.623 | 6.99387 | ||||||||
\(857\) | −39.6212 | −1.35344 | −0.676718 | − | 0.736242i | \(-0.736598\pi\) | ||||
−0.676718 | + | 0.736242i | \(0.736598\pi\) | |||||||
\(858\) | 19.9870 | 0.682345 | ||||||||
\(859\) | 23.9547 | 0.817325 | 0.408663 | − | 0.912685i | \(-0.365995\pi\) | ||||
0.408663 | + | 0.912685i | \(0.365995\pi\) | |||||||
\(860\) | 54.2686 | 1.85054 | ||||||||
\(861\) | 1.65754 | 0.0564887 | ||||||||
\(862\) | −21.0103 | −0.715613 | ||||||||
\(863\) | 23.8100 | 0.810503 | 0.405251 | − | 0.914205i | \(-0.367184\pi\) | ||||
0.405251 | + | 0.914205i | \(0.367184\pi\) | |||||||
\(864\) | 181.894 | 6.18816 | ||||||||
\(865\) | −61.2368 | −2.08211 | ||||||||
\(866\) | 48.4011 | 1.64474 | ||||||||
\(867\) | 40.3494 | 1.37034 | ||||||||
\(868\) | 50.5182 | 1.71470 | ||||||||
\(869\) | 27.5152 | 0.933388 | ||||||||
\(870\) | −33.5348 | −1.13694 | ||||||||
\(871\) | −10.0518 | −0.340592 | ||||||||
\(872\) | −196.519 | −6.65498 | ||||||||
\(873\) | 1.26012 | 0.0426485 | ||||||||
\(874\) | 49.2294 | 1.66521 | ||||||||
\(875\) | −5.16129 | −0.174483 | ||||||||
\(876\) | 33.3428 | 1.12655 | ||||||||
\(877\) | −16.7727 | −0.566374 | −0.283187 | − | 0.959065i | \(-0.591392\pi\) | ||||
−0.283187 | + | 0.959065i | \(0.591392\pi\) | |||||||
\(878\) | 4.93366 | 0.166503 | ||||||||
\(879\) | −18.0562 | −0.609022 | ||||||||
\(880\) | 282.301 | 9.51636 | ||||||||
\(881\) | 6.73851 | 0.227026 | 0.113513 | − | 0.993536i | \(-0.463790\pi\) | ||||
0.113513 | + | 0.993536i | \(0.463790\pi\) | |||||||
\(882\) | −19.7554 | −0.665199 | ||||||||
\(883\) | −1.05387 | −0.0354655 | −0.0177327 | − | 0.999843i | \(-0.505645\pi\) | ||||
−0.0177327 | + | 0.999843i | \(0.505645\pi\) | |||||||
\(884\) | 40.4347 | 1.35997 | ||||||||
\(885\) | 19.9111 | 0.669305 | ||||||||
\(886\) | −96.9126 | −3.25584 | ||||||||
\(887\) | −28.5380 | −0.958212 | −0.479106 | − | 0.877757i | \(-0.659039\pi\) | ||||
−0.479106 | + | 0.877757i | \(0.659039\pi\) | |||||||
\(888\) | −58.0909 | −1.94940 | ||||||||
\(889\) | −18.2445 | −0.611899 | ||||||||
\(890\) | 12.7113 | 0.426085 | ||||||||
\(891\) | 22.4856 | 0.753296 | ||||||||
\(892\) | 118.942 | 3.98247 | ||||||||
\(893\) | 13.9093 | 0.465457 | ||||||||
\(894\) | 22.7855 | 0.762061 | ||||||||
\(895\) | 4.74638 | 0.158654 | ||||||||
\(896\) | 73.2713 | 2.44782 | ||||||||
\(897\) | −5.00415 | −0.167084 | ||||||||
\(898\) | −33.4578 | −1.11650 | ||||||||
\(899\) | 29.5707 | 0.986237 | ||||||||
\(900\) | −19.7246 | −0.657486 | ||||||||
\(901\) | 65.7437 | 2.19024 | ||||||||
\(902\) | −19.8994 | −0.662577 | ||||||||
\(903\) | 3.95404 | 0.131582 | ||||||||
\(904\) | 161.393 | 5.36785 | ||||||||
\(905\) | 21.1308 | 0.702411 | ||||||||
\(906\) | −25.8685 | −0.859425 | ||||||||
\(907\) | 23.2176 | 0.770928 | 0.385464 | − | 0.922723i | \(-0.374041\pi\) | ||||
0.385464 | + | 0.922723i | \(0.374041\pi\) | |||||||
\(908\) | −5.93257 | −0.196879 | ||||||||
\(909\) | 16.1830 | 0.536755 | ||||||||
\(910\) | −7.06651 | −0.234252 | ||||||||
\(911\) | 32.3101 | 1.07048 | 0.535240 | − | 0.844700i | \(-0.320221\pi\) | ||||
0.535240 | + | 0.844700i | \(0.320221\pi\) | |||||||
\(912\) | 126.045 | 4.17378 | ||||||||
\(913\) | 54.5953 | 1.80684 | ||||||||
\(914\) | 84.1231 | 2.78254 | ||||||||
\(915\) | 25.5422 | 0.844399 | ||||||||
\(916\) | −11.6598 | −0.385251 | ||||||||
\(917\) | −11.1775 | −0.369112 | ||||||||
\(918\) | 108.454 | 3.57952 | ||||||||
\(919\) | −35.9112 | −1.18460 | −0.592300 | − | 0.805717i | \(-0.701780\pi\) | ||||
−0.592300 | + | 0.805717i | \(0.701780\pi\) | |||||||
\(920\) | −114.116 | −3.76228 | ||||||||
\(921\) | 17.3525 | 0.571785 | ||||||||
\(922\) | −10.3048 | −0.339372 | ||||||||
\(923\) | 7.71839 | 0.254054 | ||||||||
\(924\) | 37.4728 | 1.23276 | ||||||||
\(925\) | 11.3020 | 0.371607 | ||||||||
\(926\) | 55.1992 | 1.81396 | ||||||||
\(927\) | 0.264193 | 0.00867723 | ||||||||
\(928\) | 99.5276 | 3.26715 | ||||||||
\(929\) | −58.9536 | −1.93420 | −0.967102 | − | 0.254389i | \(-0.918126\pi\) | ||||
−0.967102 | + | 0.254389i | \(0.918126\pi\) | |||||||
\(930\) | −103.841 | −3.40509 | ||||||||
\(931\) | −29.6528 | −0.971831 | ||||||||
\(932\) | −70.1990 | −2.29944 | ||||||||
\(933\) | 12.9497 | 0.423955 | ||||||||
\(934\) | −58.7893 | −1.92365 | ||||||||
\(935\) | 99.7733 | 3.26293 | ||||||||
\(936\) | 12.5050 | 0.408739 | ||||||||
\(937\) | 18.6653 | 0.609770 | 0.304885 | − | 0.952389i | \(-0.401382\pi\) | ||||
0.304885 | + | 0.952389i | \(0.401382\pi\) | |||||||
\(938\) | −25.2027 | −0.822896 | ||||||||
\(939\) | −40.5309 | −1.32268 | ||||||||
\(940\) | −48.6544 | −1.58693 | ||||||||
\(941\) | 12.6138 | 0.411198 | 0.205599 | − | 0.978636i | \(-0.434086\pi\) | ||||
0.205599 | + | 0.978636i | \(0.434086\pi\) | |||||||
\(942\) | 34.9245 | 1.13790 | ||||||||
\(943\) | 4.98221 | 0.162243 | ||||||||
\(944\) | −99.6940 | −3.24476 | ||||||||
\(945\) | −14.1730 | −0.461047 | ||||||||
\(946\) | −47.4698 | −1.54338 | ||||||||
\(947\) | 15.0056 | 0.487615 | 0.243808 | − | 0.969824i | \(-0.421603\pi\) | ||||
0.243808 | + | 0.969824i | \(0.421603\pi\) | |||||||
\(948\) | −42.9737 | −1.39572 | ||||||||
\(949\) | 4.11268 | 0.133503 | ||||||||
\(950\) | −39.5934 | −1.28458 | ||||||||
\(951\) | 5.95461 | 0.193091 | ||||||||
\(952\) | 67.1833 | 2.17742 | ||||||||
\(953\) | −52.0022 | −1.68452 | −0.842258 | − | 0.539074i | \(-0.818774\pi\) | ||||
−0.842258 | + | 0.539074i | \(0.818774\pi\) | |||||||
\(954\) | 30.6818 | 0.993359 | ||||||||
\(955\) | 62.1887 | 2.01238 | ||||||||
\(956\) | 47.7807 | 1.54534 | ||||||||
\(957\) | 21.9346 | 0.709045 | ||||||||
\(958\) | −121.567 | −3.92766 | ||||||||
\(959\) | 18.6794 | 0.603189 | ||||||||
\(960\) | −200.779 | −6.48012 | ||||||||
\(961\) | 60.5664 | 1.95375 | ||||||||
\(962\) | −10.8125 | −0.348610 | ||||||||
\(963\) | 20.9041 | 0.673627 | ||||||||
\(964\) | −58.1767 | −1.87374 | ||||||||
\(965\) | −20.5007 | −0.659940 | ||||||||
\(966\) | −12.5468 | −0.403688 | ||||||||
\(967\) | −45.7973 | −1.47274 | −0.736371 | − | 0.676578i | \(-0.763462\pi\) | ||||
−0.736371 | + | 0.676578i | \(0.763462\pi\) | |||||||
\(968\) | −176.422 | −5.67042 | ||||||||
\(969\) | 44.5480 | 1.43109 | ||||||||
\(970\) | −8.84794 | −0.284090 | ||||||||
\(971\) | 46.7361 | 1.49983 | 0.749916 | − | 0.661533i | \(-0.230094\pi\) | ||||
0.749916 | + | 0.661533i | \(0.230094\pi\) | |||||||
\(972\) | 65.3378 | 2.09571 | ||||||||
\(973\) | −0.973238 | −0.0312006 | ||||||||
\(974\) | 19.9001 | 0.637642 | ||||||||
\(975\) | 4.02466 | 0.128892 | ||||||||
\(976\) | −127.888 | −4.09361 | ||||||||
\(977\) | 31.4383 | 1.00580 | 0.502901 | − | 0.864344i | \(-0.332266\pi\) | ||||
0.502901 | + | 0.864344i | \(0.332266\pi\) | |||||||
\(978\) | −8.41495 | −0.269081 | ||||||||
\(979\) | −8.31428 | −0.265726 | ||||||||
\(980\) | 103.725 | 3.31336 | ||||||||
\(981\) | −20.0763 | −0.640986 | ||||||||
\(982\) | −26.8047 | −0.855372 | ||||||||
\(983\) | 14.8186 | 0.472641 | 0.236320 | − | 0.971675i | \(-0.424058\pi\) | ||||
0.236320 | + | 0.971675i | \(0.424058\pi\) | |||||||
\(984\) | 20.5956 | 0.656563 | ||||||||
\(985\) | 45.0749 | 1.43620 | ||||||||
\(986\) | 59.3432 | 1.88987 | ||||||||
\(987\) | −3.54499 | −0.112838 | ||||||||
\(988\) | 28.3244 | 0.901118 | ||||||||
\(989\) | 11.8850 | 0.377922 | ||||||||
\(990\) | 46.5629 | 1.47987 | ||||||||
\(991\) | −21.8530 | −0.694184 | −0.347092 | − | 0.937831i | \(-0.612831\pi\) | ||||
−0.347092 | + | 0.937831i | \(0.612831\pi\) | |||||||
\(992\) | 308.190 | 9.78504 | ||||||||
\(993\) | 42.1099 | 1.33632 | ||||||||
\(994\) | 19.3522 | 0.613815 | ||||||||
\(995\) | 33.5467 | 1.06350 | ||||||||
\(996\) | −85.2681 | −2.70182 | ||||||||
\(997\) | 48.0583 | 1.52202 | 0.761011 | − | 0.648739i | \(-0.224703\pi\) | ||||
0.761011 | + | 0.648739i | \(0.224703\pi\) | |||||||
\(998\) | −116.980 | −3.70295 | ||||||||
\(999\) | −21.6862 | −0.686121 |
(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 | 8021.2.a.d.1.1 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.d.1.1 | ✓ | 174 | 1.1 | even | 1 | trivial |