Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.69277 | −1.55467 | −0.777336 | − | 0.629086i | \(-0.783429\pi\) | ||||
−0.777336 | + | 0.629086i | \(0.783429\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.930791 | 0.416262 | 0.208131 | − | 0.978101i | \(-0.433262\pi\) | ||||
0.208131 | + | 0.978101i | \(0.433262\pi\) | |||||||
\(6\) | 2.69277 | 1.09932 | ||||||||
\(7\) | −2.75733 | −1.04217 | −0.521087 | − | 0.853503i | \(-0.674473\pi\) | ||||
−0.521087 | + | 0.853503i | \(0.674473\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.25101 | 1.41700 | ||||||||
\(10\) | −0.930791 | −0.294342 | ||||||||
\(11\) | 1.87937 | 0.566652 | 0.283326 | − | 0.959024i | \(-0.408562\pi\) | ||||
0.283326 | + | 0.959024i | \(0.408562\pi\) | |||||||
\(12\) | −2.69277 | −0.777336 | ||||||||
\(13\) | −1.88739 | −0.523468 | −0.261734 | − | 0.965140i | \(-0.584294\pi\) | ||||
−0.261734 | + | 0.965140i | \(0.584294\pi\) | |||||||
\(14\) | 2.75733 | 0.736929 | ||||||||
\(15\) | −2.50640 | −0.647151 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.64409 | −0.883823 | −0.441911 | − | 0.897059i | \(-0.645699\pi\) | ||||
−0.441911 | + | 0.897059i | \(0.645699\pi\) | |||||||
\(18\) | −4.25101 | −1.00197 | ||||||||
\(19\) | −3.78639 | −0.868657 | −0.434329 | − | 0.900754i | \(-0.643014\pi\) | ||||
−0.434329 | + | 0.900754i | \(0.643014\pi\) | |||||||
\(20\) | 0.930791 | 0.208131 | ||||||||
\(21\) | 7.42487 | 1.62024 | ||||||||
\(22\) | −1.87937 | −0.400684 | ||||||||
\(23\) | −1.94353 | −0.405254 | −0.202627 | − | 0.979256i | \(-0.564948\pi\) | ||||
−0.202627 | + | 0.979256i | \(0.564948\pi\) | |||||||
\(24\) | 2.69277 | 0.549659 | ||||||||
\(25\) | −4.13363 | −0.826726 | ||||||||
\(26\) | 1.88739 | 0.370148 | ||||||||
\(27\) | −3.36868 | −0.648303 | ||||||||
\(28\) | −2.75733 | −0.521087 | ||||||||
\(29\) | −10.1187 | −1.87899 | −0.939496 | − | 0.342561i | \(-0.888706\pi\) | ||||
−0.939496 | + | 0.342561i | \(0.888706\pi\) | |||||||
\(30\) | 2.50640 | 0.457605 | ||||||||
\(31\) | −9.02661 | −1.62123 | −0.810614 | − | 0.585581i | \(-0.800866\pi\) | ||||
−0.810614 | + | 0.585581i | \(0.800866\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.06072 | −0.880958 | ||||||||
\(34\) | 3.64409 | 0.624957 | ||||||||
\(35\) | −2.56650 | −0.433818 | ||||||||
\(36\) | 4.25101 | 0.708502 | ||||||||
\(37\) | −0.0607967 | −0.00999492 | −0.00499746 | − | 0.999988i | \(-0.501591\pi\) | ||||
−0.00499746 | + | 0.999988i | \(0.501591\pi\) | |||||||
\(38\) | 3.78639 | 0.614233 | ||||||||
\(39\) | 5.08231 | 0.813821 | ||||||||
\(40\) | −0.930791 | −0.147171 | ||||||||
\(41\) | −6.84750 | −1.06940 | −0.534700 | − | 0.845042i | \(-0.679575\pi\) | ||||
−0.534700 | + | 0.845042i | \(0.679575\pi\) | |||||||
\(42\) | −7.42487 | −1.14568 | ||||||||
\(43\) | 9.48945 | 1.44713 | 0.723564 | − | 0.690257i | \(-0.242503\pi\) | ||||
0.723564 | + | 0.690257i | \(0.242503\pi\) | |||||||
\(44\) | 1.87937 | 0.283326 | ||||||||
\(45\) | 3.95680 | 0.589845 | ||||||||
\(46\) | 1.94353 | 0.286558 | ||||||||
\(47\) | 8.53876 | 1.24551 | 0.622753 | − | 0.782419i | \(-0.286014\pi\) | ||||
0.622753 | + | 0.782419i | \(0.286014\pi\) | |||||||
\(48\) | −2.69277 | −0.388668 | ||||||||
\(49\) | 0.602891 | 0.0861272 | ||||||||
\(50\) | 4.13363 | 0.584583 | ||||||||
\(51\) | 9.81271 | 1.37405 | ||||||||
\(52\) | −1.88739 | −0.261734 | ||||||||
\(53\) | −1.06001 | −0.145603 | −0.0728015 | − | 0.997346i | \(-0.523194\pi\) | ||||
−0.0728015 | + | 0.997346i | \(0.523194\pi\) | |||||||
\(54\) | 3.36868 | 0.458419 | ||||||||
\(55\) | 1.74930 | 0.235876 | ||||||||
\(56\) | 2.75733 | 0.368464 | ||||||||
\(57\) | 10.1959 | 1.35048 | ||||||||
\(58\) | 10.1187 | 1.32865 | ||||||||
\(59\) | −5.02007 | −0.653557 | −0.326779 | − | 0.945101i | \(-0.605963\pi\) | ||||
−0.326779 | + | 0.945101i | \(0.605963\pi\) | |||||||
\(60\) | −2.50640 | −0.323575 | ||||||||
\(61\) | −7.43945 | −0.952524 | −0.476262 | − | 0.879303i | \(-0.658009\pi\) | ||||
−0.476262 | + | 0.879303i | \(0.658009\pi\) | |||||||
\(62\) | 9.02661 | 1.14638 | ||||||||
\(63\) | −11.7215 | −1.47676 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.75677 | −0.217900 | ||||||||
\(66\) | 5.06072 | 0.622931 | ||||||||
\(67\) | 6.67092 | 0.814983 | 0.407492 | − | 0.913209i | \(-0.366404\pi\) | ||||
0.407492 | + | 0.913209i | \(0.366404\pi\) | |||||||
\(68\) | −3.64409 | −0.441911 | ||||||||
\(69\) | 5.23348 | 0.630037 | ||||||||
\(70\) | 2.56650 | 0.306755 | ||||||||
\(71\) | −11.3277 | −1.34435 | −0.672175 | − | 0.740393i | \(-0.734640\pi\) | ||||
−0.672175 | + | 0.740393i | \(0.734640\pi\) | |||||||
\(72\) | −4.25101 | −0.500986 | ||||||||
\(73\) | 1.49471 | 0.174943 | 0.0874714 | − | 0.996167i | \(-0.472121\pi\) | ||||
0.0874714 | + | 0.996167i | \(0.472121\pi\) | |||||||
\(74\) | 0.0607967 | 0.00706747 | ||||||||
\(75\) | 11.1309 | 1.28529 | ||||||||
\(76\) | −3.78639 | −0.434329 | ||||||||
\(77\) | −5.18206 | −0.590550 | ||||||||
\(78\) | −5.08231 | −0.575459 | ||||||||
\(79\) | −5.20048 | −0.585100 | −0.292550 | − | 0.956250i | \(-0.594504\pi\) | ||||
−0.292550 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(80\) | 0.930791 | 0.104066 | ||||||||
\(81\) | −3.68195 | −0.409105 | ||||||||
\(82\) | 6.84750 | 0.756179 | ||||||||
\(83\) | −1.01903 | −0.111853 | −0.0559265 | − | 0.998435i | \(-0.517811\pi\) | ||||
−0.0559265 | + | 0.998435i | \(0.517811\pi\) | |||||||
\(84\) | 7.42487 | 0.810119 | ||||||||
\(85\) | −3.39189 | −0.367902 | ||||||||
\(86\) | −9.48945 | −1.02327 | ||||||||
\(87\) | 27.2473 | 2.92121 | ||||||||
\(88\) | −1.87937 | −0.200342 | ||||||||
\(89\) | −6.26525 | −0.664115 | −0.332057 | − | 0.943259i | \(-0.607743\pi\) | ||||
−0.332057 | + | 0.943259i | \(0.607743\pi\) | |||||||
\(90\) | −3.95680 | −0.417083 | ||||||||
\(91\) | 5.20417 | 0.545545 | ||||||||
\(92\) | −1.94353 | −0.202627 | ||||||||
\(93\) | 24.3066 | 2.52048 | ||||||||
\(94\) | −8.53876 | −0.880705 | ||||||||
\(95\) | −3.52434 | −0.361589 | ||||||||
\(96\) | 2.69277 | 0.274830 | ||||||||
\(97\) | −3.11516 | −0.316297 | −0.158148 | − | 0.987415i | \(-0.550552\pi\) | ||||
−0.158148 | + | 0.987415i | \(0.550552\pi\) | |||||||
\(98\) | −0.602891 | −0.0609012 | ||||||||
\(99\) | 7.98923 | 0.802948 | ||||||||
\(100\) | −4.13363 | −0.413363 | ||||||||
\(101\) | 9.71379 | 0.966558 | 0.483279 | − | 0.875466i | \(-0.339446\pi\) | ||||
0.483279 | + | 0.875466i | \(0.339446\pi\) | |||||||
\(102\) | −9.81271 | −0.971603 | ||||||||
\(103\) | −7.53370 | −0.742318 | −0.371159 | − | 0.928569i | \(-0.621039\pi\) | ||||
−0.371159 | + | 0.928569i | \(0.621039\pi\) | |||||||
\(104\) | 1.88739 | 0.185074 | ||||||||
\(105\) | 6.91099 | 0.674444 | ||||||||
\(106\) | 1.06001 | 0.102957 | ||||||||
\(107\) | 1.13067 | 0.109306 | 0.0546529 | − | 0.998505i | \(-0.482595\pi\) | ||||
0.0546529 | + | 0.998505i | \(0.482595\pi\) | |||||||
\(108\) | −3.36868 | −0.324151 | ||||||||
\(109\) | 18.5114 | 1.77307 | 0.886537 | − | 0.462659i | \(-0.153104\pi\) | ||||
0.886537 | + | 0.462659i | \(0.153104\pi\) | |||||||
\(110\) | −1.74930 | −0.166789 | ||||||||
\(111\) | 0.163712 | 0.0155388 | ||||||||
\(112\) | −2.75733 | −0.260544 | ||||||||
\(113\) | 8.73109 | 0.821352 | 0.410676 | − | 0.911781i | \(-0.365293\pi\) | ||||
0.410676 | + | 0.911781i | \(0.365293\pi\) | |||||||
\(114\) | −10.1959 | −0.954931 | ||||||||
\(115\) | −1.80902 | −0.168692 | ||||||||
\(116\) | −10.1187 | −0.939496 | ||||||||
\(117\) | −8.02332 | −0.741756 | ||||||||
\(118\) | 5.02007 | 0.462135 | ||||||||
\(119\) | 10.0480 | 0.921097 | ||||||||
\(120\) | 2.50640 | 0.228802 | ||||||||
\(121\) | −7.46796 | −0.678905 | ||||||||
\(122\) | 7.43945 | 0.673536 | ||||||||
\(123\) | 18.4387 | 1.66256 | ||||||||
\(124\) | −9.02661 | −0.810614 | ||||||||
\(125\) | −8.50150 | −0.760397 | ||||||||
\(126\) | 11.7215 | 1.04423 | ||||||||
\(127\) | −17.2044 | −1.52664 | −0.763321 | − | 0.646020i | \(-0.776432\pi\) | ||||
−0.763321 | + | 0.646020i | \(0.776432\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −25.5529 | −2.24981 | ||||||||
\(130\) | 1.75677 | 0.154079 | ||||||||
\(131\) | −1.57465 | −0.137578 | −0.0687890 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687890 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(132\) | −5.06072 | −0.440479 | ||||||||
\(133\) | 10.4403 | 0.905292 | ||||||||
\(134\) | −6.67092 | −0.576280 | ||||||||
\(135\) | −3.13554 | −0.269864 | ||||||||
\(136\) | 3.64409 | 0.312478 | ||||||||
\(137\) | 3.48450 | 0.297701 | 0.148851 | − | 0.988860i | \(-0.452443\pi\) | ||||
0.148851 | + | 0.988860i | \(0.452443\pi\) | |||||||
\(138\) | −5.23348 | −0.445504 | ||||||||
\(139\) | 7.78296 | 0.660142 | 0.330071 | − | 0.943956i | \(-0.392927\pi\) | ||||
0.330071 | + | 0.943956i | \(0.392927\pi\) | |||||||
\(140\) | −2.56650 | −0.216909 | ||||||||
\(141\) | −22.9929 | −1.93635 | ||||||||
\(142\) | 11.3277 | 0.950599 | ||||||||
\(143\) | −3.54711 | −0.296625 | ||||||||
\(144\) | 4.25101 | 0.354251 | ||||||||
\(145\) | −9.41837 | −0.782153 | ||||||||
\(146\) | −1.49471 | −0.123703 | ||||||||
\(147\) | −1.62345 | −0.133900 | ||||||||
\(148\) | −0.0607967 | −0.00499746 | ||||||||
\(149\) | −4.30914 | −0.353019 | −0.176509 | − | 0.984299i | \(-0.556481\pi\) | ||||
−0.176509 | + | 0.984299i | \(0.556481\pi\) | |||||||
\(150\) | −11.1309 | −0.908835 | ||||||||
\(151\) | −8.76686 | −0.713437 | −0.356718 | − | 0.934212i | \(-0.616104\pi\) | ||||
−0.356718 | + | 0.934212i | \(0.616104\pi\) | |||||||
\(152\) | 3.78639 | 0.307117 | ||||||||
\(153\) | −15.4911 | −1.25238 | ||||||||
\(154\) | 5.18206 | 0.417582 | ||||||||
\(155\) | −8.40189 | −0.674856 | ||||||||
\(156\) | 5.08231 | 0.406911 | ||||||||
\(157\) | −19.0598 | −1.52114 | −0.760568 | − | 0.649258i | \(-0.775080\pi\) | ||||
−0.760568 | + | 0.649258i | \(0.775080\pi\) | |||||||
\(158\) | 5.20048 | 0.413728 | ||||||||
\(159\) | 2.85435 | 0.226365 | ||||||||
\(160\) | −0.930791 | −0.0735855 | ||||||||
\(161\) | 5.35897 | 0.422346 | ||||||||
\(162\) | 3.68195 | 0.289281 | ||||||||
\(163\) | −18.1259 | −1.41973 | −0.709864 | − | 0.704339i | \(-0.751244\pi\) | ||||
−0.709864 | + | 0.704339i | \(0.751244\pi\) | |||||||
\(164\) | −6.84750 | −0.534700 | ||||||||
\(165\) | −4.71047 | −0.366710 | ||||||||
\(166\) | 1.01903 | 0.0790920 | ||||||||
\(167\) | 16.7561 | 1.29663 | 0.648313 | − | 0.761374i | \(-0.275475\pi\) | ||||
0.648313 | + | 0.761374i | \(0.275475\pi\) | |||||||
\(168\) | −7.42487 | −0.572841 | ||||||||
\(169\) | −9.43775 | −0.725981 | ||||||||
\(170\) | 3.39189 | 0.260146 | ||||||||
\(171\) | −16.0960 | −1.23089 | ||||||||
\(172\) | 9.48945 | 0.723564 | ||||||||
\(173\) | −0.220686 | −0.0167784 | −0.00838921 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838921 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(174\) | −27.2473 | −2.06561 | ||||||||
\(175\) | 11.3978 | 0.861592 | ||||||||
\(176\) | 1.87937 | 0.141663 | ||||||||
\(177\) | 13.5179 | 1.01607 | ||||||||
\(178\) | 6.26525 | 0.469600 | ||||||||
\(179\) | −16.7066 | −1.24871 | −0.624356 | − | 0.781140i | \(-0.714639\pi\) | ||||
−0.624356 | + | 0.781140i | \(0.714639\pi\) | |||||||
\(180\) | 3.95680 | 0.294922 | ||||||||
\(181\) | 5.62445 | 0.418062 | 0.209031 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209031 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(182\) | −5.20417 | −0.385759 | ||||||||
\(183\) | 20.0327 | 1.48086 | ||||||||
\(184\) | 1.94353 | 0.143279 | ||||||||
\(185\) | −0.0565890 | −0.00416051 | ||||||||
\(186\) | −24.3066 | −1.78225 | ||||||||
\(187\) | −6.84861 | −0.500820 | ||||||||
\(188\) | 8.53876 | 0.622753 | ||||||||
\(189\) | 9.28858 | 0.675645 | ||||||||
\(190\) | 3.52434 | 0.255682 | ||||||||
\(191\) | −11.8780 | −0.859464 | −0.429732 | − | 0.902956i | \(-0.641392\pi\) | ||||
−0.429732 | + | 0.902956i | \(0.641392\pi\) | |||||||
\(192\) | −2.69277 | −0.194334 | ||||||||
\(193\) | −11.5145 | −0.828835 | −0.414418 | − | 0.910087i | \(-0.636015\pi\) | ||||
−0.414418 | + | 0.910087i | \(0.636015\pi\) | |||||||
\(194\) | 3.11516 | 0.223656 | ||||||||
\(195\) | 4.73057 | 0.338763 | ||||||||
\(196\) | 0.602891 | 0.0430636 | ||||||||
\(197\) | −20.8984 | −1.48895 | −0.744473 | − | 0.667653i | \(-0.767299\pi\) | ||||
−0.744473 | + | 0.667653i | \(0.767299\pi\) | |||||||
\(198\) | −7.98923 | −0.567770 | ||||||||
\(199\) | 17.6607 | 1.25193 | 0.625966 | − | 0.779851i | \(-0.284705\pi\) | ||||
0.625966 | + | 0.779851i | \(0.284705\pi\) | |||||||
\(200\) | 4.13363 | 0.292292 | ||||||||
\(201\) | −17.9633 | −1.26703 | ||||||||
\(202\) | −9.71379 | −0.683460 | ||||||||
\(203\) | 27.9006 | 1.95824 | ||||||||
\(204\) | 9.81271 | 0.687027 | ||||||||
\(205\) | −6.37358 | −0.445150 | ||||||||
\(206\) | 7.53370 | 0.524898 | ||||||||
\(207\) | −8.26197 | −0.574247 | ||||||||
\(208\) | −1.88739 | −0.130867 | ||||||||
\(209\) | −7.11604 | −0.492227 | ||||||||
\(210\) | −6.91099 | −0.476904 | ||||||||
\(211\) | 22.4666 | 1.54666 | 0.773331 | − | 0.634003i | \(-0.218589\pi\) | ||||
0.773331 | + | 0.634003i | \(0.218589\pi\) | |||||||
\(212\) | −1.06001 | −0.0728015 | ||||||||
\(213\) | 30.5029 | 2.09002 | ||||||||
\(214\) | −1.13067 | −0.0772909 | ||||||||
\(215\) | 8.83269 | 0.602385 | ||||||||
\(216\) | 3.36868 | 0.229210 | ||||||||
\(217\) | 24.8894 | 1.68960 | ||||||||
\(218\) | −18.5114 | −1.25375 | ||||||||
\(219\) | −4.02492 | −0.271979 | ||||||||
\(220\) | 1.74930 | 0.117938 | ||||||||
\(221\) | 6.87783 | 0.462653 | ||||||||
\(222\) | −0.163712 | −0.0109876 | ||||||||
\(223\) | 21.9951 | 1.47290 | 0.736450 | − | 0.676492i | \(-0.236501\pi\) | ||||
0.736450 | + | 0.676492i | \(0.236501\pi\) | |||||||
\(224\) | 2.75733 | 0.184232 | ||||||||
\(225\) | −17.5721 | −1.17147 | ||||||||
\(226\) | −8.73109 | −0.580783 | ||||||||
\(227\) | −26.4944 | −1.75849 | −0.879246 | − | 0.476368i | \(-0.841953\pi\) | ||||
−0.879246 | + | 0.476368i | \(0.841953\pi\) | |||||||
\(228\) | 10.1959 | 0.675238 | ||||||||
\(229\) | 0.892211 | 0.0589589 | 0.0294795 | − | 0.999565i | \(-0.490615\pi\) | ||||
0.0294795 | + | 0.999565i | \(0.490615\pi\) | |||||||
\(230\) | 1.80902 | 0.119283 | ||||||||
\(231\) | 13.9541 | 0.918112 | ||||||||
\(232\) | 10.1187 | 0.664324 | ||||||||
\(233\) | −10.8204 | −0.708869 | −0.354435 | − | 0.935081i | \(-0.615327\pi\) | ||||
−0.354435 | + | 0.935081i | \(0.615327\pi\) | |||||||
\(234\) | 8.02332 | 0.524501 | ||||||||
\(235\) | 7.94779 | 0.518457 | ||||||||
\(236\) | −5.02007 | −0.326779 | ||||||||
\(237\) | 14.0037 | 0.909638 | ||||||||
\(238\) | −10.0480 | −0.651314 | ||||||||
\(239\) | −16.1783 | −1.04649 | −0.523243 | − | 0.852183i | \(-0.675278\pi\) | ||||
−0.523243 | + | 0.852183i | \(0.675278\pi\) | |||||||
\(240\) | −2.50640 | −0.161788 | ||||||||
\(241\) | 9.39784 | 0.605368 | 0.302684 | − | 0.953091i | \(-0.402117\pi\) | ||||
0.302684 | + | 0.953091i | \(0.402117\pi\) | |||||||
\(242\) | 7.46796 | 0.480058 | ||||||||
\(243\) | 20.0207 | 1.28433 | ||||||||
\(244\) | −7.43945 | −0.476262 | ||||||||
\(245\) | 0.561165 | 0.0358515 | ||||||||
\(246\) | −18.4387 | −1.17561 | ||||||||
\(247\) | 7.14640 | 0.454715 | ||||||||
\(248\) | 9.02661 | 0.573191 | ||||||||
\(249\) | 2.74401 | 0.173895 | ||||||||
\(250\) | 8.50150 | 0.537682 | ||||||||
\(251\) | −7.38830 | −0.466345 | −0.233173 | − | 0.972435i | \(-0.574911\pi\) | ||||
−0.233173 | + | 0.972435i | \(0.574911\pi\) | |||||||
\(252\) | −11.7215 | −0.738382 | ||||||||
\(253\) | −3.65262 | −0.229638 | ||||||||
\(254\) | 17.2044 | 1.07950 | ||||||||
\(255\) | 9.13357 | 0.571967 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.5737 | 1.22097 | 0.610487 | − | 0.792026i | \(-0.290974\pi\) | ||||
0.610487 | + | 0.792026i | \(0.290974\pi\) | |||||||
\(258\) | 25.5529 | 1.59085 | ||||||||
\(259\) | 0.167637 | 0.0104164 | ||||||||
\(260\) | −1.75677 | −0.108950 | ||||||||
\(261\) | −43.0146 | −2.66254 | ||||||||
\(262\) | 1.57465 | 0.0972824 | ||||||||
\(263\) | 3.04083 | 0.187505 | 0.0937527 | − | 0.995596i | \(-0.470114\pi\) | ||||
0.0937527 | + | 0.995596i | \(0.470114\pi\) | |||||||
\(264\) | 5.06072 | 0.311466 | ||||||||
\(265\) | −0.986643 | −0.0606090 | ||||||||
\(266\) | −10.4403 | −0.640138 | ||||||||
\(267\) | 16.8709 | 1.03248 | ||||||||
\(268\) | 6.67092 | 0.407492 | ||||||||
\(269\) | −17.8887 | −1.09069 | −0.545347 | − | 0.838210i | \(-0.683602\pi\) | ||||
−0.545347 | + | 0.838210i | \(0.683602\pi\) | |||||||
\(270\) | 3.13554 | 0.190823 | ||||||||
\(271\) | 19.1775 | 1.16495 | 0.582476 | − | 0.812848i | \(-0.302084\pi\) | ||||
0.582476 | + | 0.812848i | \(0.302084\pi\) | |||||||
\(272\) | −3.64409 | −0.220956 | ||||||||
\(273\) | −14.0136 | −0.848144 | ||||||||
\(274\) | −3.48450 | −0.210507 | ||||||||
\(275\) | −7.76863 | −0.468466 | ||||||||
\(276\) | 5.23348 | 0.315019 | ||||||||
\(277\) | 4.39611 | 0.264137 | 0.132068 | − | 0.991241i | \(-0.457838\pi\) | ||||
0.132068 | + | 0.991241i | \(0.457838\pi\) | |||||||
\(278\) | −7.78296 | −0.466791 | ||||||||
\(279\) | −38.3722 | −2.29728 | ||||||||
\(280\) | 2.56650 | 0.153378 | ||||||||
\(281\) | −17.0653 | −1.01803 | −0.509015 | − | 0.860757i | \(-0.669990\pi\) | ||||
−0.509015 | + | 0.860757i | \(0.669990\pi\) | |||||||
\(282\) | 22.9929 | 1.36921 | ||||||||
\(283\) | 8.83680 | 0.525293 | 0.262647 | − | 0.964892i | \(-0.415405\pi\) | ||||
0.262647 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(284\) | −11.3277 | −0.672175 | ||||||||
\(285\) | 9.49022 | 0.562152 | ||||||||
\(286\) | 3.54711 | 0.209745 | ||||||||
\(287\) | 18.8808 | 1.11450 | ||||||||
\(288\) | −4.25101 | −0.250493 | ||||||||
\(289\) | −3.72058 | −0.218858 | ||||||||
\(290\) | 9.41837 | 0.553066 | ||||||||
\(291\) | 8.38841 | 0.491738 | ||||||||
\(292\) | 1.49471 | 0.0874714 | ||||||||
\(293\) | 16.1859 | 0.945592 | 0.472796 | − | 0.881172i | \(-0.343245\pi\) | ||||
0.472796 | + | 0.881172i | \(0.343245\pi\) | |||||||
\(294\) | 1.62345 | 0.0946813 | ||||||||
\(295\) | −4.67263 | −0.272051 | ||||||||
\(296\) | 0.0607967 | 0.00353374 | ||||||||
\(297\) | −6.33101 | −0.367362 | ||||||||
\(298\) | 4.30914 | 0.249622 | ||||||||
\(299\) | 3.66821 | 0.212138 | ||||||||
\(300\) | 11.1309 | 0.642643 | ||||||||
\(301\) | −26.1656 | −1.50816 | ||||||||
\(302\) | 8.76686 | 0.504476 | ||||||||
\(303\) | −26.1570 | −1.50268 | ||||||||
\(304\) | −3.78639 | −0.217164 | ||||||||
\(305\) | −6.92457 | −0.396500 | ||||||||
\(306\) | 15.4911 | 0.885566 | ||||||||
\(307\) | 28.5524 | 1.62957 | 0.814785 | − | 0.579763i | \(-0.196855\pi\) | ||||
0.814785 | + | 0.579763i | \(0.196855\pi\) | |||||||
\(308\) | −5.18206 | −0.295275 | ||||||||
\(309\) | 20.2865 | 1.15406 | ||||||||
\(310\) | 8.40189 | 0.477195 | ||||||||
\(311\) | 12.8152 | 0.726685 | 0.363342 | − | 0.931656i | \(-0.381636\pi\) | ||||
0.363342 | + | 0.931656i | \(0.381636\pi\) | |||||||
\(312\) | −5.08231 | −0.287729 | ||||||||
\(313\) | −18.4176 | −1.04103 | −0.520513 | − | 0.853854i | \(-0.674259\pi\) | ||||
−0.520513 | + | 0.853854i | \(0.674259\pi\) | |||||||
\(314\) | 19.0598 | 1.07561 | ||||||||
\(315\) | −10.9102 | −0.614721 | ||||||||
\(316\) | −5.20048 | −0.292550 | ||||||||
\(317\) | −32.1260 | −1.80438 | −0.902189 | − | 0.431340i | \(-0.858041\pi\) | ||||
−0.902189 | + | 0.431340i | \(0.858041\pi\) | |||||||
\(318\) | −2.85435 | −0.160064 | ||||||||
\(319\) | −19.0168 | −1.06473 | ||||||||
\(320\) | 0.930791 | 0.0520328 | ||||||||
\(321\) | −3.04463 | −0.169935 | ||||||||
\(322\) | −5.35897 | −0.298643 | ||||||||
\(323\) | 13.7980 | 0.767739 | ||||||||
\(324\) | −3.68195 | −0.204553 | ||||||||
\(325\) | 7.80178 | 0.432765 | ||||||||
\(326\) | 18.1259 | 1.00390 | ||||||||
\(327\) | −49.8470 | −2.75655 | ||||||||
\(328\) | 6.84750 | 0.378090 | ||||||||
\(329\) | −23.5442 | −1.29803 | ||||||||
\(330\) | 4.71047 | 0.259303 | ||||||||
\(331\) | 2.52325 | 0.138690 | 0.0693451 | − | 0.997593i | \(-0.477909\pi\) | ||||
0.0693451 | + | 0.997593i | \(0.477909\pi\) | |||||||
\(332\) | −1.01903 | −0.0559265 | ||||||||
\(333\) | −0.258447 | −0.0141628 | ||||||||
\(334\) | −16.7561 | −0.916853 | ||||||||
\(335\) | 6.20923 | 0.339247 | ||||||||
\(336\) | 7.42487 | 0.405060 | ||||||||
\(337\) | −29.9672 | −1.63242 | −0.816208 | − | 0.577759i | \(-0.803927\pi\) | ||||
−0.816208 | + | 0.577759i | \(0.803927\pi\) | |||||||
\(338\) | 9.43775 | 0.513346 | ||||||||
\(339\) | −23.5108 | −1.27693 | ||||||||
\(340\) | −3.39189 | −0.183951 | ||||||||
\(341\) | −16.9644 | −0.918672 | ||||||||
\(342\) | 16.0960 | 0.870371 | ||||||||
\(343\) | 17.6390 | 0.952415 | ||||||||
\(344\) | −9.48945 | −0.511637 | ||||||||
\(345\) | 4.87128 | 0.262261 | ||||||||
\(346\) | 0.220686 | 0.0118641 | ||||||||
\(347\) | −5.24849 | −0.281754 | −0.140877 | − | 0.990027i | \(-0.544992\pi\) | ||||
−0.140877 | + | 0.990027i | \(0.544992\pi\) | |||||||
\(348\) | 27.2473 | 1.46061 | ||||||||
\(349\) | 16.6418 | 0.890816 | 0.445408 | − | 0.895328i | \(-0.353059\pi\) | ||||
0.445408 | + | 0.895328i | \(0.353059\pi\) | |||||||
\(350\) | −11.3978 | −0.609238 | ||||||||
\(351\) | 6.35802 | 0.339366 | ||||||||
\(352\) | −1.87937 | −0.100171 | ||||||||
\(353\) | −1.92631 | −0.102527 | −0.0512636 | − | 0.998685i | \(-0.516325\pi\) | ||||
−0.0512636 | + | 0.998685i | \(0.516325\pi\) | |||||||
\(354\) | −13.5179 | −0.718468 | ||||||||
\(355\) | −10.5437 | −0.559602 | ||||||||
\(356\) | −6.26525 | −0.332057 | ||||||||
\(357\) | −27.0569 | −1.43200 | ||||||||
\(358\) | 16.7066 | 0.882973 | ||||||||
\(359\) | −7.39255 | −0.390164 | −0.195082 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195082 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(360\) | −3.95680 | −0.208542 | ||||||||
\(361\) | −4.66326 | −0.245435 | ||||||||
\(362\) | −5.62445 | −0.295615 | ||||||||
\(363\) | 20.1095 | 1.05547 | ||||||||
\(364\) | 5.20417 | 0.272773 | ||||||||
\(365\) | 1.39126 | 0.0728221 | ||||||||
\(366\) | −20.0327 | −1.04713 | ||||||||
\(367\) | 35.2814 | 1.84168 | 0.920838 | − | 0.389945i | \(-0.127506\pi\) | ||||
0.920838 | + | 0.389945i | \(0.127506\pi\) | |||||||
\(368\) | −1.94353 | −0.101314 | ||||||||
\(369\) | −29.1088 | −1.51534 | ||||||||
\(370\) | 0.0565890 | 0.00294192 | ||||||||
\(371\) | 2.92279 | 0.151744 | ||||||||
\(372\) | 24.3066 | 1.26024 | ||||||||
\(373\) | −11.5375 | −0.597387 | −0.298694 | − | 0.954349i | \(-0.596551\pi\) | ||||
−0.298694 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(374\) | 6.84861 | 0.354133 | ||||||||
\(375\) | 22.8926 | 1.18217 | ||||||||
\(376\) | −8.53876 | −0.440353 | ||||||||
\(377\) | 19.0979 | 0.983593 | ||||||||
\(378\) | −9.28858 | −0.477753 | ||||||||
\(379\) | −13.2385 | −0.680015 | −0.340007 | − | 0.940423i | \(-0.610430\pi\) | ||||
−0.340007 | + | 0.940423i | \(0.610430\pi\) | |||||||
\(380\) | −3.52434 | −0.180795 | ||||||||
\(381\) | 46.3274 | 2.37343 | ||||||||
\(382\) | 11.8780 | 0.607733 | ||||||||
\(383\) | −6.63672 | −0.339120 | −0.169560 | − | 0.985520i | \(-0.554235\pi\) | ||||
−0.169560 | + | 0.985520i | \(0.554235\pi\) | |||||||
\(384\) | 2.69277 | 0.137415 | ||||||||
\(385\) | −4.82341 | −0.245824 | ||||||||
\(386\) | 11.5145 | 0.586075 | ||||||||
\(387\) | 40.3398 | 2.05058 | ||||||||
\(388\) | −3.11516 | −0.158148 | ||||||||
\(389\) | −9.73799 | −0.493736 | −0.246868 | − | 0.969049i | \(-0.579401\pi\) | ||||
−0.246868 | + | 0.969049i | \(0.579401\pi\) | |||||||
\(390\) | −4.73057 | −0.239542 | ||||||||
\(391\) | 7.08241 | 0.358173 | ||||||||
\(392\) | −0.602891 | −0.0304506 | ||||||||
\(393\) | 4.24018 | 0.213889 | ||||||||
\(394\) | 20.8984 | 1.05284 | ||||||||
\(395\) | −4.84056 | −0.243555 | ||||||||
\(396\) | 7.98923 | 0.401474 | ||||||||
\(397\) | 19.8725 | 0.997373 | 0.498687 | − | 0.866782i | \(-0.333816\pi\) | ||||
0.498687 | + | 0.866782i | \(0.333816\pi\) | |||||||
\(398\) | −17.6607 | −0.885249 | ||||||||
\(399\) | −28.1134 | −1.40743 | ||||||||
\(400\) | −4.13363 | −0.206681 | ||||||||
\(401\) | −37.2748 | −1.86141 | −0.930707 | − | 0.365765i | \(-0.880807\pi\) | ||||
−0.930707 | + | 0.365765i | \(0.880807\pi\) | |||||||
\(402\) | 17.9633 | 0.895926 | ||||||||
\(403\) | 17.0368 | 0.848661 | ||||||||
\(404\) | 9.71379 | 0.483279 | ||||||||
\(405\) | −3.42712 | −0.170295 | ||||||||
\(406\) | −27.9006 | −1.38468 | ||||||||
\(407\) | −0.114260 | −0.00566364 | ||||||||
\(408\) | −9.81271 | −0.485801 | ||||||||
\(409\) | −40.2143 | −1.98847 | −0.994235 | − | 0.107221i | \(-0.965805\pi\) | ||||
−0.994235 | + | 0.107221i | \(0.965805\pi\) | |||||||
\(410\) | 6.37358 | 0.314769 | ||||||||
\(411\) | −9.38297 | −0.462828 | ||||||||
\(412\) | −7.53370 | −0.371159 | ||||||||
\(413\) | 13.8420 | 0.681121 | ||||||||
\(414\) | 8.26197 | 0.406054 | ||||||||
\(415\) | −0.948503 | −0.0465602 | ||||||||
\(416\) | 1.88739 | 0.0925370 | ||||||||
\(417\) | −20.9577 | −1.02630 | ||||||||
\(418\) | 7.11604 | 0.348057 | ||||||||
\(419\) | 21.5988 | 1.05517 | 0.527586 | − | 0.849502i | \(-0.323097\pi\) | ||||
0.527586 | + | 0.849502i | \(0.323097\pi\) | |||||||
\(420\) | 6.91099 | 0.337222 | ||||||||
\(421\) | −23.6867 | −1.15442 | −0.577209 | − | 0.816596i | \(-0.695858\pi\) | ||||
−0.577209 | + | 0.816596i | \(0.695858\pi\) | |||||||
\(422\) | −22.4666 | −1.09365 | ||||||||
\(423\) | 36.2983 | 1.76489 | ||||||||
\(424\) | 1.06001 | 0.0514784 | ||||||||
\(425\) | 15.0633 | 0.730679 | ||||||||
\(426\) | −30.5029 | −1.47787 | ||||||||
\(427\) | 20.5131 | 0.992696 | ||||||||
\(428\) | 1.13067 | 0.0546529 | ||||||||
\(429\) | 9.55156 | 0.461154 | ||||||||
\(430\) | −8.83269 | −0.425950 | ||||||||
\(431\) | 37.8596 | 1.82363 | 0.911815 | − | 0.410601i | \(-0.134681\pi\) | ||||
0.911815 | + | 0.410601i | \(0.134681\pi\) | |||||||
\(432\) | −3.36868 | −0.162076 | ||||||||
\(433\) | −36.1347 | −1.73652 | −0.868261 | − | 0.496107i | \(-0.834762\pi\) | ||||
−0.868261 | + | 0.496107i | \(0.834762\pi\) | |||||||
\(434\) | −24.8894 | −1.19473 | ||||||||
\(435\) | 25.3615 | 1.21599 | ||||||||
\(436\) | 18.5114 | 0.886537 | ||||||||
\(437\) | 7.35897 | 0.352027 | ||||||||
\(438\) | 4.02492 | 0.192318 | ||||||||
\(439\) | 6.00547 | 0.286625 | 0.143313 | − | 0.989677i | \(-0.454225\pi\) | ||||
0.143313 | + | 0.989677i | \(0.454225\pi\) | |||||||
\(440\) | −1.74930 | −0.0833947 | ||||||||
\(441\) | 2.56289 | 0.122043 | ||||||||
\(442\) | −6.87783 | −0.327145 | ||||||||
\(443\) | 0.145671 | 0.00692106 | 0.00346053 | − | 0.999994i | \(-0.498898\pi\) | ||||
0.00346053 | + | 0.999994i | \(0.498898\pi\) | |||||||
\(444\) | 0.163712 | 0.00776941 | ||||||||
\(445\) | −5.83163 | −0.276446 | ||||||||
\(446\) | −21.9951 | −1.04150 | ||||||||
\(447\) | 11.6035 | 0.548828 | ||||||||
\(448\) | −2.75733 | −0.130272 | ||||||||
\(449\) | 38.5888 | 1.82112 | 0.910558 | − | 0.413380i | \(-0.135652\pi\) | ||||
0.910558 | + | 0.413380i | \(0.135652\pi\) | |||||||
\(450\) | 17.5721 | 0.828357 | ||||||||
\(451\) | −12.8690 | −0.605977 | ||||||||
\(452\) | 8.73109 | 0.410676 | ||||||||
\(453\) | 23.6071 | 1.10916 | ||||||||
\(454\) | 26.4944 | 1.24344 | ||||||||
\(455\) | 4.84399 | 0.227090 | ||||||||
\(456\) | −10.1959 | −0.477466 | ||||||||
\(457\) | 0.169863 | 0.00794587 | 0.00397293 | − | 0.999992i | \(-0.498735\pi\) | ||||
0.00397293 | + | 0.999992i | \(0.498735\pi\) | |||||||
\(458\) | −0.892211 | −0.0416903 | ||||||||
\(459\) | 12.2758 | 0.572985 | ||||||||
\(460\) | −1.80902 | −0.0843460 | ||||||||
\(461\) | 28.2291 | 1.31476 | 0.657379 | − | 0.753560i | \(-0.271665\pi\) | ||||
0.657379 | + | 0.753560i | \(0.271665\pi\) | |||||||
\(462\) | −13.9541 | −0.649203 | ||||||||
\(463\) | −27.8692 | −1.29519 | −0.647595 | − | 0.761985i | \(-0.724225\pi\) | ||||
−0.647595 | + | 0.761985i | \(0.724225\pi\) | |||||||
\(464\) | −10.1187 | −0.469748 | ||||||||
\(465\) | 22.6243 | 1.04918 | ||||||||
\(466\) | 10.8204 | 0.501246 | ||||||||
\(467\) | 23.9808 | 1.10970 | 0.554849 | − | 0.831951i | \(-0.312776\pi\) | ||||
0.554849 | + | 0.831951i | \(0.312776\pi\) | |||||||
\(468\) | −8.02332 | −0.370878 | ||||||||
\(469\) | −18.3940 | −0.849354 | ||||||||
\(470\) | −7.94779 | −0.366604 | ||||||||
\(471\) | 51.3236 | 2.36487 | ||||||||
\(472\) | 5.02007 | 0.231067 | ||||||||
\(473\) | 17.8342 | 0.820018 | ||||||||
\(474\) | −14.0037 | −0.643211 | ||||||||
\(475\) | 15.6515 | 0.718141 | ||||||||
\(476\) | 10.0480 | 0.460549 | ||||||||
\(477\) | −4.50609 | −0.206320 | ||||||||
\(478\) | 16.1783 | 0.739977 | ||||||||
\(479\) | −30.1451 | −1.37737 | −0.688683 | − | 0.725063i | \(-0.741811\pi\) | ||||
−0.688683 | + | 0.725063i | \(0.741811\pi\) | |||||||
\(480\) | 2.50640 | 0.114401 | ||||||||
\(481\) | 0.114747 | 0.00523202 | ||||||||
\(482\) | −9.39784 | −0.428060 | ||||||||
\(483\) | −14.4305 | −0.656609 | ||||||||
\(484\) | −7.46796 | −0.339453 | ||||||||
\(485\) | −2.89956 | −0.131662 | ||||||||
\(486\) | −20.0207 | −0.908156 | ||||||||
\(487\) | −12.5242 | −0.567524 | −0.283762 | − | 0.958895i | \(-0.591583\pi\) | ||||
−0.283762 | + | 0.958895i | \(0.591583\pi\) | |||||||
\(488\) | 7.43945 | 0.336768 | ||||||||
\(489\) | 48.8088 | 2.20721 | ||||||||
\(490\) | −0.561165 | −0.0253508 | ||||||||
\(491\) | 4.59365 | 0.207308 | 0.103654 | − | 0.994613i | \(-0.466946\pi\) | ||||
0.103654 | + | 0.994613i | \(0.466946\pi\) | |||||||
\(492\) | 18.4387 | 0.831282 | ||||||||
\(493\) | 36.8734 | 1.66070 | ||||||||
\(494\) | −7.14640 | −0.321532 | ||||||||
\(495\) | 7.43630 | 0.334237 | ||||||||
\(496\) | −9.02661 | −0.405307 | ||||||||
\(497\) | 31.2342 | 1.40105 | ||||||||
\(498\) | −2.74401 | −0.122962 | ||||||||
\(499\) | 13.7560 | 0.615802 | 0.307901 | − | 0.951418i | \(-0.400373\pi\) | ||||
0.307901 | + | 0.951418i | \(0.400373\pi\) | |||||||
\(500\) | −8.50150 | −0.380198 | ||||||||
\(501\) | −45.1203 | −2.01583 | ||||||||
\(502\) | 7.38830 | 0.329756 | ||||||||
\(503\) | 39.7287 | 1.77142 | 0.885708 | − | 0.464242i | \(-0.153673\pi\) | ||||
0.885708 | + | 0.464242i | \(0.153673\pi\) | |||||||
\(504\) | 11.7215 | 0.522115 | ||||||||
\(505\) | 9.04151 | 0.402342 | ||||||||
\(506\) | 3.65262 | 0.162379 | ||||||||
\(507\) | 25.4137 | 1.12866 | ||||||||
\(508\) | −17.2044 | −0.763321 | ||||||||
\(509\) | 10.8198 | 0.479577 | 0.239789 | − | 0.970825i | \(-0.422922\pi\) | ||||
0.239789 | + | 0.970825i | \(0.422922\pi\) | |||||||
\(510\) | −9.13357 | −0.404441 | ||||||||
\(511\) | −4.12142 | −0.182321 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.7551 | 0.563153 | ||||||||
\(514\) | −19.5737 | −0.863359 | ||||||||
\(515\) | −7.01230 | −0.308999 | ||||||||
\(516\) | −25.5529 | −1.12490 | ||||||||
\(517\) | 16.0475 | 0.705769 | ||||||||
\(518\) | −0.167637 | −0.00736554 | ||||||||
\(519\) | 0.594256 | 0.0260849 | ||||||||
\(520\) | 1.75677 | 0.0770393 | ||||||||
\(521\) | 6.98607 | 0.306065 | 0.153033 | − | 0.988221i | \(-0.451096\pi\) | ||||
0.153033 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(522\) | 43.0146 | 1.88270 | ||||||||
\(523\) | −10.7300 | −0.469192 | −0.234596 | − | 0.972093i | \(-0.575377\pi\) | ||||
−0.234596 | + | 0.972093i | \(0.575377\pi\) | |||||||
\(524\) | −1.57465 | −0.0687890 | ||||||||
\(525\) | −30.6916 | −1.33949 | ||||||||
\(526\) | −3.04083 | −0.132586 | ||||||||
\(527\) | 32.8938 | 1.43288 | ||||||||
\(528\) | −5.06072 | −0.220240 | ||||||||
\(529\) | −19.2227 | −0.835769 | ||||||||
\(530\) | 0.986643 | 0.0428570 | ||||||||
\(531\) | −21.3404 | −0.926093 | ||||||||
\(532\) | 10.4403 | 0.452646 | ||||||||
\(533\) | 12.9239 | 0.559797 | ||||||||
\(534\) | −16.8709 | −0.730074 | ||||||||
\(535\) | 1.05242 | 0.0454999 | ||||||||
\(536\) | −6.67092 | −0.288140 | ||||||||
\(537\) | 44.9871 | 1.94134 | ||||||||
\(538\) | 17.8887 | 0.771238 | ||||||||
\(539\) | 1.13306 | 0.0488042 | ||||||||
\(540\) | −3.13554 | −0.134932 | ||||||||
\(541\) | 3.40665 | 0.146463 | 0.0732316 | − | 0.997315i | \(-0.476669\pi\) | ||||
0.0732316 | + | 0.997315i | \(0.476669\pi\) | |||||||
\(542\) | −19.1775 | −0.823745 | ||||||||
\(543\) | −15.1454 | −0.649949 | ||||||||
\(544\) | 3.64409 | 0.156239 | ||||||||
\(545\) | 17.2303 | 0.738063 | ||||||||
\(546\) | 14.0136 | 0.599728 | ||||||||
\(547\) | −24.2792 | −1.03810 | −0.519052 | − | 0.854743i | \(-0.673715\pi\) | ||||
−0.519052 | + | 0.854743i | \(0.673715\pi\) | |||||||
\(548\) | 3.48450 | 0.148851 | ||||||||
\(549\) | −31.6252 | −1.34973 | ||||||||
\(550\) | 7.76863 | 0.331256 | ||||||||
\(551\) | 38.3133 | 1.63220 | ||||||||
\(552\) | −5.23348 | −0.222752 | ||||||||
\(553\) | 14.3395 | 0.609776 | ||||||||
\(554\) | −4.39611 | −0.186773 | ||||||||
\(555\) | 0.152381 | 0.00646822 | ||||||||
\(556\) | 7.78296 | 0.330071 | ||||||||
\(557\) | −19.0532 | −0.807308 | −0.403654 | − | 0.914912i | \(-0.632260\pi\) | ||||
−0.403654 | + | 0.914912i | \(0.632260\pi\) | |||||||
\(558\) | 38.3722 | 1.62443 | ||||||||
\(559\) | −17.9103 | −0.757526 | ||||||||
\(560\) | −2.56650 | −0.108454 | ||||||||
\(561\) | 18.4417 | 0.778611 | ||||||||
\(562\) | 17.0653 | 0.719856 | ||||||||
\(563\) | −37.7994 | −1.59306 | −0.796528 | − | 0.604602i | \(-0.793332\pi\) | ||||
−0.796528 | + | 0.604602i | \(0.793332\pi\) | |||||||
\(564\) | −22.9929 | −0.968176 | ||||||||
\(565\) | 8.12681 | 0.341898 | ||||||||
\(566\) | −8.83680 | −0.371438 | ||||||||
\(567\) | 10.1524 | 0.426359 | ||||||||
\(568\) | 11.3277 | 0.475299 | ||||||||
\(569\) | 2.29819 | 0.0963449 | 0.0481725 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481725 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(570\) | −9.49022 | −0.397502 | ||||||||
\(571\) | 3.62670 | 0.151773 | 0.0758863 | − | 0.997116i | \(-0.475821\pi\) | ||||
0.0758863 | + | 0.997116i | \(0.475821\pi\) | |||||||
\(572\) | −3.54711 | −0.148312 | ||||||||
\(573\) | 31.9848 | 1.33618 | ||||||||
\(574\) | −18.8808 | −0.788071 | ||||||||
\(575\) | 8.03384 | 0.335034 | ||||||||
\(576\) | 4.25101 | 0.177125 | ||||||||
\(577\) | −15.3947 | −0.640892 | −0.320446 | − | 0.947267i | \(-0.603833\pi\) | ||||
−0.320446 | + | 0.947267i | \(0.603833\pi\) | |||||||
\(578\) | 3.72058 | 0.154756 | ||||||||
\(579\) | 31.0060 | 1.28857 | ||||||||
\(580\) | −9.41837 | −0.391077 | ||||||||
\(581\) | 2.80981 | 0.116570 | ||||||||
\(582\) | −8.38841 | −0.347711 | ||||||||
\(583\) | −1.99215 | −0.0825062 | ||||||||
\(584\) | −1.49471 | −0.0618516 | ||||||||
\(585\) | −7.46803 | −0.308765 | ||||||||
\(586\) | −16.1859 | −0.668634 | ||||||||
\(587\) | 29.1237 | 1.20207 | 0.601033 | − | 0.799225i | \(-0.294756\pi\) | ||||
0.601033 | + | 0.799225i | \(0.294756\pi\) | |||||||
\(588\) | −1.62345 | −0.0669498 | ||||||||
\(589\) | 34.1783 | 1.40829 | ||||||||
\(590\) | 4.67263 | 0.192369 | ||||||||
\(591\) | 56.2745 | 2.31482 | ||||||||
\(592\) | −0.0607967 | −0.00249873 | ||||||||
\(593\) | 34.8150 | 1.42968 | 0.714840 | − | 0.699288i | \(-0.246500\pi\) | ||||
0.714840 | + | 0.699288i | \(0.246500\pi\) | |||||||
\(594\) | 6.33101 | 0.259764 | ||||||||
\(595\) | 9.35257 | 0.383418 | ||||||||
\(596\) | −4.30914 | −0.176509 | ||||||||
\(597\) | −47.5561 | −1.94634 | ||||||||
\(598\) | −3.66821 | −0.150004 | ||||||||
\(599\) | 18.8411 | 0.769827 | 0.384913 | − | 0.922953i | \(-0.374231\pi\) | ||||
0.384913 | + | 0.922953i | \(0.374231\pi\) | |||||||
\(600\) | −11.1309 | −0.454418 | ||||||||
\(601\) | 0.147052 | 0.00599838 | 0.00299919 | − | 0.999996i | \(-0.499045\pi\) | ||||
0.00299919 | + | 0.999996i | \(0.499045\pi\) | |||||||
\(602\) | 26.1656 | 1.06643 | ||||||||
\(603\) | 28.3582 | 1.15483 | ||||||||
\(604\) | −8.76686 | −0.356718 | ||||||||
\(605\) | −6.95110 | −0.282603 | ||||||||
\(606\) | 26.1570 | 1.06256 | ||||||||
\(607\) | 25.3306 | 1.02814 | 0.514070 | − | 0.857748i | \(-0.328137\pi\) | ||||
0.514070 | + | 0.857748i | \(0.328137\pi\) | |||||||
\(608\) | 3.78639 | 0.153558 | ||||||||
\(609\) | −75.1298 | −3.04441 | ||||||||
\(610\) | 6.92457 | 0.280368 | ||||||||
\(611\) | −16.1160 | −0.651983 | ||||||||
\(612\) | −15.4911 | −0.626190 | ||||||||
\(613\) | 25.4159 | 1.02654 | 0.513269 | − | 0.858228i | \(-0.328434\pi\) | ||||
0.513269 | + | 0.858228i | \(0.328434\pi\) | |||||||
\(614\) | −28.5524 | −1.15228 | ||||||||
\(615\) | 17.1626 | 0.692063 | ||||||||
\(616\) | 5.18206 | 0.208791 | ||||||||
\(617\) | 42.1789 | 1.69806 | 0.849029 | − | 0.528347i | \(-0.177188\pi\) | ||||
0.849029 | + | 0.528347i | \(0.177188\pi\) | |||||||
\(618\) | −20.2865 | −0.816044 | ||||||||
\(619\) | 12.3983 | 0.498329 | 0.249164 | − | 0.968461i | \(-0.419844\pi\) | ||||
0.249164 | + | 0.968461i | \(0.419844\pi\) | |||||||
\(620\) | −8.40189 | −0.337428 | ||||||||
\(621\) | 6.54714 | 0.262728 | ||||||||
\(622\) | −12.8152 | −0.513844 | ||||||||
\(623\) | 17.2754 | 0.692123 | ||||||||
\(624\) | 5.08231 | 0.203455 | ||||||||
\(625\) | 12.7550 | 0.510201 | ||||||||
\(626\) | 18.4176 | 0.736117 | ||||||||
\(627\) | 19.1619 | 0.765251 | ||||||||
\(628\) | −19.0598 | −0.760568 | ||||||||
\(629\) | 0.221549 | 0.00883373 | ||||||||
\(630\) | 10.9102 | 0.434673 | ||||||||
\(631\) | 7.26420 | 0.289183 | 0.144592 | − | 0.989491i | \(-0.453813\pi\) | ||||
0.144592 | + | 0.989491i | \(0.453813\pi\) | |||||||
\(632\) | 5.20048 | 0.206864 | ||||||||
\(633\) | −60.4973 | −2.40455 | ||||||||
\(634\) | 32.1260 | 1.27589 | ||||||||
\(635\) | −16.0137 | −0.635483 | ||||||||
\(636\) | 2.85435 | 0.113182 | ||||||||
\(637\) | −1.13789 | −0.0450849 | ||||||||
\(638\) | 19.0168 | 0.752881 | ||||||||
\(639\) | −48.1541 | −1.90495 | ||||||||
\(640\) | −0.930791 | −0.0367927 | ||||||||
\(641\) | −3.21485 | −0.126979 | −0.0634894 | − | 0.997983i | \(-0.520223\pi\) | ||||
−0.0634894 | + | 0.997983i | \(0.520223\pi\) | |||||||
\(642\) | 3.04463 | 0.120162 | ||||||||
\(643\) | 15.8284 | 0.624210 | 0.312105 | − | 0.950048i | \(-0.398966\pi\) | ||||
0.312105 | + | 0.950048i | \(0.398966\pi\) | |||||||
\(644\) | 5.35897 | 0.211173 | ||||||||
\(645\) | −23.7844 | −0.936510 | ||||||||
\(646\) | −13.7980 | −0.542873 | ||||||||
\(647\) | 44.6033 | 1.75354 | 0.876768 | − | 0.480913i | \(-0.159695\pi\) | ||||
0.876768 | + | 0.480913i | \(0.159695\pi\) | |||||||
\(648\) | 3.68195 | 0.144641 | ||||||||
\(649\) | −9.43458 | −0.370340 | ||||||||
\(650\) | −7.80178 | −0.306011 | ||||||||
\(651\) | −67.0214 | −2.62678 | ||||||||
\(652\) | −18.1259 | −0.709864 | ||||||||
\(653\) | 0.0506975 | 0.00198395 | 0.000991974 | − | 1.00000i | \(-0.499684\pi\) | ||||
0.000991974 | 1.00000i | \(0.499684\pi\) | ||||||||
\(654\) | 49.8470 | 1.94917 | ||||||||
\(655\) | −1.46567 | −0.0572685 | ||||||||
\(656\) | −6.84750 | −0.267350 | ||||||||
\(657\) | 6.35404 | 0.247895 | ||||||||
\(658\) | 23.5442 | 0.917849 | ||||||||
\(659\) | 16.7782 | 0.653586 | 0.326793 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326793 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(660\) | −4.71047 | −0.183355 | ||||||||
\(661\) | −43.9945 | −1.71119 | −0.855593 | − | 0.517649i | \(-0.826807\pi\) | ||||
−0.855593 | + | 0.517649i | \(0.826807\pi\) | |||||||
\(662\) | −2.52325 | −0.0980688 | ||||||||
\(663\) | −18.5204 | −0.719274 | ||||||||
\(664\) | 1.01903 | 0.0395460 | ||||||||
\(665\) | 9.71777 | 0.376839 | ||||||||
\(666\) | 0.258447 | 0.0100146 | ||||||||
\(667\) | 19.6660 | 0.761469 | ||||||||
\(668\) | 16.7561 | 0.648313 | ||||||||
\(669\) | −59.2277 | −2.28988 | ||||||||
\(670\) | −6.20923 | −0.239884 | ||||||||
\(671\) | −13.9815 | −0.539750 | ||||||||
\(672\) | −7.42487 | −0.286420 | ||||||||
\(673\) | 15.9081 | 0.613213 | 0.306606 | − | 0.951836i | \(-0.400806\pi\) | ||||
0.306606 | + | 0.951836i | \(0.400806\pi\) | |||||||
\(674\) | 29.9672 | 1.15429 | ||||||||
\(675\) | 13.9249 | 0.535969 | ||||||||
\(676\) | −9.43775 | −0.362990 | ||||||||
\(677\) | 19.1096 | 0.734442 | 0.367221 | − | 0.930134i | \(-0.380309\pi\) | ||||
0.367221 | + | 0.930134i | \(0.380309\pi\) | |||||||
\(678\) | 23.5108 | 0.902927 | ||||||||
\(679\) | 8.58954 | 0.329636 | ||||||||
\(680\) | 3.39189 | 0.130073 | ||||||||
\(681\) | 71.3432 | 2.73388 | ||||||||
\(682\) | 16.9644 | 0.649599 | ||||||||
\(683\) | 24.0946 | 0.921956 | 0.460978 | − | 0.887412i | \(-0.347499\pi\) | ||||
0.460978 | + | 0.887412i | \(0.347499\pi\) | |||||||
\(684\) | −16.0960 | −0.615445 | ||||||||
\(685\) | 3.24334 | 0.123922 | ||||||||
\(686\) | −17.6390 | −0.673459 | ||||||||
\(687\) | −2.40252 | −0.0916618 | ||||||||
\(688\) | 9.48945 | 0.361782 | ||||||||
\(689\) | 2.00065 | 0.0762185 | ||||||||
\(690\) | −4.87128 | −0.185446 | ||||||||
\(691\) | 20.8389 | 0.792749 | 0.396375 | − | 0.918089i | \(-0.370268\pi\) | ||||
0.396375 | + | 0.918089i | \(0.370268\pi\) | |||||||
\(692\) | −0.220686 | −0.00838921 | ||||||||
\(693\) | −22.0290 | −0.836812 | ||||||||
\(694\) | 5.24849 | 0.199230 | ||||||||
\(695\) | 7.24430 | 0.274792 | ||||||||
\(696\) | −27.2473 | −1.03281 | ||||||||
\(697\) | 24.9529 | 0.945159 | ||||||||
\(698\) | −16.6418 | −0.629902 | ||||||||
\(699\) | 29.1369 | 1.10206 | ||||||||
\(700\) | 11.3978 | 0.430796 | ||||||||
\(701\) | 16.3691 | 0.618253 | 0.309127 | − | 0.951021i | \(-0.399963\pi\) | ||||
0.309127 | + | 0.951021i | \(0.399963\pi\) | |||||||
\(702\) | −6.35802 | −0.239968 | ||||||||
\(703\) | 0.230200 | 0.00868216 | ||||||||
\(704\) | 1.87937 | 0.0708315 | ||||||||
\(705\) | −21.4016 | −0.806030 | ||||||||
\(706\) | 1.92631 | 0.0724976 | ||||||||
\(707\) | −26.7842 | −1.00732 | ||||||||
\(708\) | 13.5179 | 0.508033 | ||||||||
\(709\) | −17.2049 | −0.646144 | −0.323072 | − | 0.946374i | \(-0.604716\pi\) | ||||
−0.323072 | + | 0.946374i | \(0.604716\pi\) | |||||||
\(710\) | 10.5437 | 0.395698 | ||||||||
\(711\) | −22.1073 | −0.829088 | ||||||||
\(712\) | 6.26525 | 0.234800 | ||||||||
\(713\) | 17.5435 | 0.657010 | ||||||||
\(714\) | 27.0569 | 1.01258 | ||||||||
\(715\) | −3.30162 | −0.123474 | ||||||||
\(716\) | −16.7066 | −0.624356 | ||||||||
\(717\) | 43.5644 | 1.62694 | ||||||||
\(718\) | 7.39255 | 0.275887 | ||||||||
\(719\) | −35.4297 | −1.32130 | −0.660652 | − | 0.750692i | \(-0.729720\pi\) | ||||
−0.660652 | + | 0.750692i | \(0.729720\pi\) | |||||||
\(720\) | 3.95680 | 0.147461 | ||||||||
\(721\) | 20.7729 | 0.773625 | ||||||||
\(722\) | 4.66326 | 0.173548 | ||||||||
\(723\) | −25.3062 | −0.941148 | ||||||||
\(724\) | 5.62445 | 0.209031 | ||||||||
\(725\) | 41.8269 | 1.55341 | ||||||||
\(726\) | −20.1095 | −0.746333 | ||||||||
\(727\) | −8.40604 | −0.311763 | −0.155881 | − | 0.987776i | \(-0.549822\pi\) | ||||
−0.155881 | + | 0.987776i | \(0.549822\pi\) | |||||||
\(728\) | −5.20417 | −0.192879 | ||||||||
\(729\) | −42.8652 | −1.58760 | ||||||||
\(730\) | −1.39126 | −0.0514930 | ||||||||
\(731\) | −34.5805 | −1.27900 | ||||||||
\(732\) | 20.0327 | 0.740431 | ||||||||
\(733\) | −15.3711 | −0.567745 | −0.283873 | − | 0.958862i | \(-0.591619\pi\) | ||||
−0.283873 | + | 0.958862i | \(0.591619\pi\) | |||||||
\(734\) | −35.2814 | −1.30226 | ||||||||
\(735\) | −1.51109 | −0.0557373 | ||||||||
\(736\) | 1.94353 | 0.0716395 | ||||||||
\(737\) | 12.5372 | 0.461812 | ||||||||
\(738\) | 29.1088 | 1.07151 | ||||||||
\(739\) | 8.31178 | 0.305754 | 0.152877 | − | 0.988245i | \(-0.451146\pi\) | ||||
0.152877 | + | 0.988245i | \(0.451146\pi\) | |||||||
\(740\) | −0.0565890 | −0.00208025 | ||||||||
\(741\) | −19.2436 | −0.706932 | ||||||||
\(742\) | −2.92279 | −0.107299 | ||||||||
\(743\) | −15.8483 | −0.581416 | −0.290708 | − | 0.956812i | \(-0.593891\pi\) | ||||
−0.290708 | + | 0.956812i | \(0.593891\pi\) | |||||||
\(744\) | −24.3066 | −0.891123 | ||||||||
\(745\) | −4.01091 | −0.146948 | ||||||||
\(746\) | 11.5375 | 0.422417 | ||||||||
\(747\) | −4.33190 | −0.158496 | ||||||||
\(748\) | −6.84861 | −0.250410 | ||||||||
\(749\) | −3.11763 | −0.113916 | ||||||||
\(750\) | −22.8926 | −0.835918 | ||||||||
\(751\) | 29.0199 | 1.05895 | 0.529475 | − | 0.848325i | \(-0.322389\pi\) | ||||
0.529475 | + | 0.848325i | \(0.322389\pi\) | |||||||
\(752\) | 8.53876 | 0.311376 | ||||||||
\(753\) | 19.8950 | 0.725013 | ||||||||
\(754\) | −19.0979 | −0.695505 | ||||||||
\(755\) | −8.16011 | −0.296977 | ||||||||
\(756\) | 9.28858 | 0.337822 | ||||||||
\(757\) | 44.4841 | 1.61680 | 0.808401 | − | 0.588632i | \(-0.200333\pi\) | ||||
0.808401 | + | 0.588632i | \(0.200333\pi\) | |||||||
\(758\) | 13.2385 | 0.480843 | ||||||||
\(759\) | 9.83567 | 0.357012 | ||||||||
\(760\) | 3.52434 | 0.127841 | ||||||||
\(761\) | 40.4438 | 1.46609 | 0.733043 | − | 0.680183i | \(-0.238100\pi\) | ||||
0.733043 | + | 0.680183i | \(0.238100\pi\) | |||||||
\(762\) | −46.3274 | −1.67827 | ||||||||
\(763\) | −51.0422 | −1.84785 | ||||||||
\(764\) | −11.8780 | −0.429732 | ||||||||
\(765\) | −14.4189 | −0.521318 | ||||||||
\(766\) | 6.63672 | 0.239794 | ||||||||
\(767\) | 9.47484 | 0.342117 | ||||||||
\(768\) | −2.69277 | −0.0971670 | ||||||||
\(769\) | −0.856635 | −0.0308910 | −0.0154455 | − | 0.999881i | \(-0.504917\pi\) | ||||
−0.0154455 | + | 0.999881i | \(0.504917\pi\) | |||||||
\(770\) | 4.82341 | 0.173824 | ||||||||
\(771\) | −52.7075 | −1.89821 | ||||||||
\(772\) | −11.5145 | −0.414418 | ||||||||
\(773\) | 35.7972 | 1.28754 | 0.643769 | − | 0.765220i | \(-0.277370\pi\) | ||||
0.643769 | + | 0.765220i | \(0.277370\pi\) | |||||||
\(774\) | −40.3398 | −1.44998 | ||||||||
\(775\) | 37.3127 | 1.34031 | ||||||||
\(776\) | 3.11516 | 0.111828 | ||||||||
\(777\) | −0.451407 | −0.0161942 | ||||||||
\(778\) | 9.73799 | 0.349124 | ||||||||
\(779\) | 25.9273 | 0.928941 | ||||||||
\(780\) | 4.73057 | 0.169382 | ||||||||
\(781\) | −21.2890 | −0.761779 | ||||||||
\(782\) | −7.08241 | −0.253266 | ||||||||
\(783\) | 34.0866 | 1.21816 | ||||||||
\(784\) | 0.602891 | 0.0215318 | ||||||||
\(785\) | −17.7407 | −0.633192 | ||||||||
\(786\) | −4.24018 | −0.151242 | ||||||||
\(787\) | −48.6549 | −1.73436 | −0.867180 | − | 0.497995i | \(-0.834070\pi\) | ||||
−0.867180 | + | 0.497995i | \(0.834070\pi\) | |||||||
\(788\) | −20.8984 | −0.744473 | ||||||||
\(789\) | −8.18825 | −0.291509 | ||||||||
\(790\) | 4.84056 | 0.172219 | ||||||||
\(791\) | −24.0745 | −0.855992 | ||||||||
\(792\) | −7.98923 | −0.283885 | ||||||||
\(793\) | 14.0412 | 0.498616 | ||||||||
\(794\) | −19.8725 | −0.705249 | ||||||||
\(795\) | 2.65680 | 0.0942271 | ||||||||
\(796\) | 17.6607 | 0.625966 | ||||||||
\(797\) | −2.97919 | −0.105528 | −0.0527642 | − | 0.998607i | \(-0.516803\pi\) | ||||
−0.0527642 | + | 0.998607i | \(0.516803\pi\) | |||||||
\(798\) | 28.1134 | 0.995205 | ||||||||
\(799\) | −31.1160 | −1.10081 | ||||||||
\(800\) | 4.13363 | 0.146146 | ||||||||
\(801\) | −26.6336 | −0.941053 | ||||||||
\(802\) | 37.2748 | 1.31622 | ||||||||
\(803\) | 2.80912 | 0.0991318 | ||||||||
\(804\) | −17.9633 | −0.633515 | ||||||||
\(805\) | 4.98807 | 0.175807 | ||||||||
\(806\) | −17.0368 | −0.600094 | ||||||||
\(807\) | 48.1702 | 1.69567 | ||||||||
\(808\) | −9.71379 | −0.341730 | ||||||||
\(809\) | 27.8000 | 0.977397 | 0.488699 | − | 0.872453i | \(-0.337472\pi\) | ||||
0.488699 | + | 0.872453i | \(0.337472\pi\) | |||||||
\(810\) | 3.42712 | 0.120417 | ||||||||
\(811\) | 18.5492 | 0.651349 | 0.325675 | − | 0.945482i | \(-0.394409\pi\) | ||||
0.325675 | + | 0.945482i | \(0.394409\pi\) | |||||||
\(812\) | 27.9006 | 0.979118 | ||||||||
\(813\) | −51.6406 | −1.81112 | ||||||||
\(814\) | 0.114260 | 0.00400480 | ||||||||
\(815\) | −16.8714 | −0.590979 | ||||||||
\(816\) | 9.81271 | 0.343513 | ||||||||
\(817\) | −35.9308 | −1.25706 | ||||||||
\(818\) | 40.2143 | 1.40606 | ||||||||
\(819\) | 22.1230 | 0.773039 | ||||||||
\(820\) | −6.37358 | −0.222575 | ||||||||
\(821\) | 5.69917 | 0.198902 | 0.0994512 | − | 0.995042i | \(-0.468291\pi\) | ||||
0.0994512 | + | 0.995042i | \(0.468291\pi\) | |||||||
\(822\) | 9.38297 | 0.327269 | ||||||||
\(823\) | 39.7512 | 1.38564 | 0.692819 | − | 0.721111i | \(-0.256368\pi\) | ||||
0.692819 | + | 0.721111i | \(0.256368\pi\) | |||||||
\(824\) | 7.53370 | 0.262449 | ||||||||
\(825\) | 20.9191 | 0.728311 | ||||||||
\(826\) | −13.8420 | −0.481625 | ||||||||
\(827\) | −17.8431 | −0.620466 | −0.310233 | − | 0.950661i | \(-0.600407\pi\) | ||||
−0.310233 | + | 0.950661i | \(0.600407\pi\) | |||||||
\(828\) | −8.26197 | −0.287123 | ||||||||
\(829\) | −36.0410 | −1.25175 | −0.625877 | − | 0.779922i | \(-0.715259\pi\) | ||||
−0.625877 | + | 0.779922i | \(0.715259\pi\) | |||||||
\(830\) | 0.948503 | 0.0329230 | ||||||||
\(831\) | −11.8377 | −0.410646 | ||||||||
\(832\) | −1.88739 | −0.0654335 | ||||||||
\(833\) | −2.19699 | −0.0761212 | ||||||||
\(834\) | 20.9577 | 0.725706 | ||||||||
\(835\) | 15.5964 | 0.539736 | ||||||||
\(836\) | −7.11604 | −0.246113 | ||||||||
\(837\) | 30.4078 | 1.05105 | ||||||||
\(838\) | −21.5988 | −0.746119 | ||||||||
\(839\) | −44.7801 | −1.54598 | −0.772991 | − | 0.634417i | \(-0.781240\pi\) | ||||
−0.772991 | + | 0.634417i | \(0.781240\pi\) | |||||||
\(840\) | −6.91099 | −0.238452 | ||||||||
\(841\) | 73.3877 | 2.53061 | ||||||||
\(842\) | 23.6867 | 0.816297 | ||||||||
\(843\) | 45.9529 | 1.58270 | ||||||||
\(844\) | 22.4666 | 0.773331 | ||||||||
\(845\) | −8.78457 | −0.302198 | ||||||||
\(846\) | −36.2983 | −1.24796 | ||||||||
\(847\) | 20.5917 | 0.707538 | ||||||||
\(848\) | −1.06001 | −0.0364007 | ||||||||
\(849\) | −23.7955 | −0.816658 | ||||||||
\(850\) | −15.0633 | −0.516668 | ||||||||
\(851\) | 0.118160 | 0.00405048 | ||||||||
\(852\) | 30.5029 | 1.04501 | ||||||||
\(853\) | −36.0059 | −1.23282 | −0.616410 | − | 0.787426i | \(-0.711413\pi\) | ||||
−0.616410 | + | 0.787426i | \(0.711413\pi\) | |||||||
\(854\) | −20.5131 | −0.701942 | ||||||||
\(855\) | −14.9820 | −0.512373 | ||||||||
\(856\) | −1.13067 | −0.0386455 | ||||||||
\(857\) | 31.3917 | 1.07232 | 0.536160 | − | 0.844116i | \(-0.319874\pi\) | ||||
0.536160 | + | 0.844116i | \(0.319874\pi\) | |||||||
\(858\) | −9.55156 | −0.326085 | ||||||||
\(859\) | −50.0090 | −1.70628 | −0.853142 | − | 0.521679i | \(-0.825306\pi\) | ||||
−0.853142 | + | 0.521679i | \(0.825306\pi\) | |||||||
\(860\) | 8.83269 | 0.301192 | ||||||||
\(861\) | −50.8417 | −1.73268 | ||||||||
\(862\) | −37.8596 | −1.28950 | ||||||||
\(863\) | 36.8503 | 1.25440 | 0.627200 | − | 0.778858i | \(-0.284201\pi\) | ||||
0.627200 | + | 0.778858i | \(0.284201\pi\) | |||||||
\(864\) | 3.36868 | 0.114605 | ||||||||
\(865\) | −0.205412 | −0.00698423 | ||||||||
\(866\) | 36.1347 | 1.22791 | ||||||||
\(867\) | 10.0187 | 0.340252 | ||||||||
\(868\) | 24.8894 | 0.844801 | ||||||||
\(869\) | −9.77364 | −0.331548 | ||||||||
\(870\) | −25.3615 | −0.859835 | ||||||||
\(871\) | −12.5906 | −0.426618 | ||||||||
\(872\) | −18.5114 | −0.626876 | ||||||||
\(873\) | −13.2426 | −0.448194 | ||||||||
\(874\) | −7.35897 | −0.248921 | ||||||||
\(875\) | 23.4415 | 0.792466 | ||||||||
\(876\) | −4.02492 | −0.135989 | ||||||||
\(877\) | 2.94745 | 0.0995284 | 0.0497642 | − | 0.998761i | \(-0.484153\pi\) | ||||
0.0497642 | + | 0.998761i | \(0.484153\pi\) | |||||||
\(878\) | −6.00547 | −0.202675 | ||||||||
\(879\) | −43.5850 | −1.47008 | ||||||||
\(880\) | 1.74930 | 0.0589690 | ||||||||
\(881\) | 12.1401 | 0.409009 | 0.204504 | − | 0.978866i | \(-0.434442\pi\) | ||||
0.204504 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(882\) | −2.56289 | −0.0862971 | ||||||||
\(883\) | 9.43037 | 0.317357 | 0.158679 | − | 0.987330i | \(-0.449277\pi\) | ||||
0.158679 | + | 0.987330i | \(0.449277\pi\) | |||||||
\(884\) | 6.87783 | 0.231327 | ||||||||
\(885\) | 12.5823 | 0.422950 | ||||||||
\(886\) | −0.145671 | −0.00489393 | ||||||||
\(887\) | −8.89817 | −0.298771 | −0.149386 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149386 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(888\) | −0.163712 | −0.00549380 | ||||||||
\(889\) | 47.4382 | 1.59103 | ||||||||
\(890\) | 5.83163 | 0.195477 | ||||||||
\(891\) | −6.91975 | −0.231820 | ||||||||
\(892\) | 21.9951 | 0.736450 | ||||||||
\(893\) | −32.3311 | −1.08192 | ||||||||
\(894\) | −11.6035 | −0.388080 | ||||||||
\(895\) | −15.5504 | −0.519792 | ||||||||
\(896\) | 2.75733 | 0.0921161 | ||||||||
\(897\) | −9.87763 | −0.329805 | ||||||||
\(898\) | −38.5888 | −1.28772 | ||||||||
\(899\) | 91.3374 | 3.04627 | ||||||||
\(900\) | −17.5721 | −0.585737 | ||||||||
\(901\) | 3.86276 | 0.128687 | ||||||||
\(902\) | 12.8690 | 0.428491 | ||||||||
\(903\) | 70.4579 | 2.34469 | ||||||||
\(904\) | −8.73109 | −0.290392 | ||||||||
\(905\) | 5.23519 | 0.174024 | ||||||||
\(906\) | −23.6071 | −0.784294 | ||||||||
\(907\) | 8.66708 | 0.287786 | 0.143893 | − | 0.989593i | \(-0.454038\pi\) | ||||
0.143893 | + | 0.989593i | \(0.454038\pi\) | |||||||
\(908\) | −26.4944 | −0.879246 | ||||||||
\(909\) | 41.2934 | 1.36962 | ||||||||
\(910\) | −4.84399 | −0.160577 | ||||||||
\(911\) | 13.6303 | 0.451590 | 0.225795 | − | 0.974175i | \(-0.427502\pi\) | ||||
0.225795 | + | 0.974175i | \(0.427502\pi\) | |||||||
\(912\) | 10.1959 | 0.337619 | ||||||||
\(913\) | −1.91514 | −0.0633818 | ||||||||
\(914\) | −0.169863 | −0.00561858 | ||||||||
\(915\) | 18.6463 | 0.616427 | ||||||||
\(916\) | 0.892211 | 0.0294795 | ||||||||
\(917\) | 4.34184 | 0.143380 | ||||||||
\(918\) | −12.2758 | −0.405161 | ||||||||
\(919\) | 18.4237 | 0.607741 | 0.303870 | − | 0.952713i | \(-0.401721\pi\) | ||||
0.303870 | + | 0.952713i | \(0.401721\pi\) | |||||||
\(920\) | 1.80902 | 0.0596416 | ||||||||
\(921\) | −76.8850 | −2.53345 | ||||||||
\(922\) | −28.2291 | −0.929675 | ||||||||
\(923\) | 21.3798 | 0.703724 | ||||||||
\(924\) | 13.9541 | 0.459056 | ||||||||
\(925\) | 0.251311 | 0.00826306 | ||||||||
\(926\) | 27.8692 | 0.915838 | ||||||||
\(927\) | −32.0258 | −1.05187 | ||||||||
\(928\) | 10.1187 | 0.332162 | ||||||||
\(929\) | −14.1475 | −0.464165 | −0.232083 | − | 0.972696i | \(-0.574554\pi\) | ||||
−0.232083 | + | 0.972696i | \(0.574554\pi\) | |||||||
\(930\) | −22.6243 | −0.741882 | ||||||||
\(931\) | −2.28278 | −0.0748151 | ||||||||
\(932\) | −10.8204 | −0.354435 | ||||||||
\(933\) | −34.5085 | −1.12976 | ||||||||
\(934\) | −23.9808 | −0.784675 | ||||||||
\(935\) | −6.37462 | −0.208472 | ||||||||
\(936\) | 8.02332 | 0.262250 | ||||||||
\(937\) | −50.5113 | −1.65013 | −0.825067 | − | 0.565035i | \(-0.808863\pi\) | ||||
−0.825067 | + | 0.565035i | \(0.808863\pi\) | |||||||
\(938\) | 18.3940 | 0.600584 | ||||||||
\(939\) | 49.5944 | 1.61845 | ||||||||
\(940\) | 7.94779 | 0.259228 | ||||||||
\(941\) | 35.5256 | 1.15810 | 0.579052 | − | 0.815291i | \(-0.303423\pi\) | ||||
0.579052 | + | 0.815291i | \(0.303423\pi\) | |||||||
\(942\) | −51.3236 | −1.67221 | ||||||||
\(943\) | 13.3083 | 0.433379 | ||||||||
\(944\) | −5.02007 | −0.163389 | ||||||||
\(945\) | 8.64572 | 0.281245 | ||||||||
\(946\) | −17.8342 | −0.579841 | ||||||||
\(947\) | −38.6413 | −1.25567 | −0.627837 | − | 0.778345i | \(-0.716059\pi\) | ||||
−0.627837 | + | 0.778345i | \(0.716059\pi\) | |||||||
\(948\) | 14.0037 | 0.454819 | ||||||||
\(949\) | −2.82111 | −0.0915771 | ||||||||
\(950\) | −15.6515 | −0.507803 | ||||||||
\(951\) | 86.5080 | 2.80522 | ||||||||
\(952\) | −10.0480 | −0.325657 | ||||||||
\(953\) | 7.13924 | 0.231263 | 0.115631 | − | 0.993292i | \(-0.463111\pi\) | ||||
0.115631 | + | 0.993292i | \(0.463111\pi\) | |||||||
\(954\) | 4.50609 | 0.145890 | ||||||||
\(955\) | −11.0560 | −0.357762 | ||||||||
\(956\) | −16.1783 | −0.523243 | ||||||||
\(957\) | 51.2078 | 1.65531 | ||||||||
\(958\) | 30.1451 | 0.973944 | ||||||||
\(959\) | −9.60794 | −0.310257 | ||||||||
\(960\) | −2.50640 | −0.0808939 | ||||||||
\(961\) | 50.4798 | 1.62838 | ||||||||
\(962\) | −0.114747 | −0.00369960 | ||||||||
\(963\) | 4.80648 | 0.154887 | ||||||||
\(964\) | 9.39784 | 0.302684 | ||||||||
\(965\) | −10.7176 | −0.345013 | ||||||||
\(966\) | 14.4305 | 0.464292 | ||||||||
\(967\) | −25.9656 | −0.834996 | −0.417498 | − | 0.908678i | \(-0.637093\pi\) | ||||
−0.417498 | + | 0.908678i | \(0.637093\pi\) | |||||||
\(968\) | 7.46796 | 0.240029 | ||||||||
\(969\) | −37.1547 | −1.19358 | ||||||||
\(970\) | 2.89956 | 0.0930994 | ||||||||
\(971\) | −10.2381 | −0.328556 | −0.164278 | − | 0.986414i | \(-0.552529\pi\) | ||||
−0.164278 | + | 0.986414i | \(0.552529\pi\) | |||||||
\(972\) | 20.0207 | 0.642164 | ||||||||
\(973\) | −21.4602 | −0.687983 | ||||||||
\(974\) | 12.5242 | 0.401300 | ||||||||
\(975\) | −21.0084 | −0.672807 | ||||||||
\(976\) | −7.43945 | −0.238131 | ||||||||
\(977\) | 2.39826 | 0.0767270 | 0.0383635 | − | 0.999264i | \(-0.487786\pi\) | ||||
0.0383635 | + | 0.999264i | \(0.487786\pi\) | |||||||
\(978\) | −48.8088 | −1.56073 | ||||||||
\(979\) | −11.7747 | −0.376322 | ||||||||
\(980\) | 0.561165 | 0.0179258 | ||||||||
\(981\) | 78.6922 | 2.51245 | ||||||||
\(982\) | −4.59365 | −0.146589 | ||||||||
\(983\) | 46.0826 | 1.46981 | 0.734903 | − | 0.678172i | \(-0.237228\pi\) | ||||
0.734903 | + | 0.678172i | \(0.237228\pi\) | |||||||
\(984\) | −18.4387 | −0.587805 | ||||||||
\(985\) | −19.4520 | −0.619792 | ||||||||
\(986\) | −36.8734 | −1.17429 | ||||||||
\(987\) | 63.3991 | 2.01802 | ||||||||
\(988\) | 7.14640 | 0.227357 | ||||||||
\(989\) | −18.4430 | −0.586455 | ||||||||
\(990\) | −7.43630 | −0.236341 | ||||||||
\(991\) | −15.6410 | −0.496854 | −0.248427 | − | 0.968651i | \(-0.579914\pi\) | ||||
−0.248427 | + | 0.968651i | \(0.579914\pi\) | |||||||
\(992\) | 9.02661 | 0.286595 | ||||||||
\(993\) | −6.79453 | −0.215618 | ||||||||
\(994\) | −31.2342 | −0.990689 | ||||||||
\(995\) | 16.4384 | 0.521132 | ||||||||
\(996\) | 2.74401 | 0.0869474 | ||||||||
\(997\) | 57.5113 | 1.82140 | 0.910701 | − | 0.413066i | \(-0.135542\pi\) | ||||
0.910701 | + | 0.413066i | \(0.135542\pi\) | |||||||
\(998\) | −13.7560 | −0.435438 | ||||||||
\(999\) | 0.204805 | 0.00647973 |
(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 | 8002.2.a.e.1.6 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.6 | ✓ | 77 | 1.1 | even | 1 | trivial |