Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89706 | −1.34143 | −0.670713 | − | 0.741717i | \(-0.734012\pi\) | ||||
−0.670713 | + | 0.741717i | \(0.734012\pi\) | |||||||
\(3\) | −1.32001 | −0.762108 | −0.381054 | − | 0.924553i | \(-0.624439\pi\) | ||||
−0.381054 | + | 0.924553i | \(0.624439\pi\) | |||||||
\(4\) | 1.59885 | 0.799423 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.50414 | 1.02231 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.761013 | 0.269059 | ||||||||
\(9\) | −1.25758 | −0.419192 | ||||||||
\(10\) | −1.89706 | −0.599904 | ||||||||
\(11\) | −4.27013 | −1.28749 | −0.643746 | − | 0.765239i | \(-0.722621\pi\) | ||||
−0.643746 | + | 0.765239i | \(0.722621\pi\) | |||||||
\(12\) | −2.11049 | −0.609247 | ||||||||
\(13\) | 6.67988 | 1.85267 | 0.926333 | − | 0.376705i | \(-0.122943\pi\) | ||||
0.926333 | + | 0.376705i | \(0.122943\pi\) | |||||||
\(14\) | 1.89706 | 0.507011 | ||||||||
\(15\) | −1.32001 | −0.340825 | ||||||||
\(16\) | −4.64138 | −1.16035 | ||||||||
\(17\) | 3.66894 | 0.889849 | 0.444925 | − | 0.895568i | \(-0.353230\pi\) | ||||
0.444925 | + | 0.895568i | \(0.353230\pi\) | |||||||
\(18\) | 2.38570 | 0.562315 | ||||||||
\(19\) | −8.31367 | −1.90729 | −0.953643 | − | 0.300940i | \(-0.902700\pi\) | ||||
−0.953643 | + | 0.300940i | \(0.902700\pi\) | |||||||
\(20\) | 1.59885 | 0.357513 | ||||||||
\(21\) | 1.32001 | 0.288050 | ||||||||
\(22\) | 8.10070 | 1.72708 | ||||||||
\(23\) | 4.46641 | 0.931310 | 0.465655 | − | 0.884966i | \(-0.345819\pi\) | ||||
0.465655 | + | 0.884966i | \(0.345819\pi\) | |||||||
\(24\) | −1.00454 | −0.205052 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −12.6722 | −2.48521 | ||||||||
\(27\) | 5.62004 | 1.08158 | ||||||||
\(28\) | −1.59885 | −0.302154 | ||||||||
\(29\) | 2.61057 | 0.484771 | 0.242385 | − | 0.970180i | \(-0.422070\pi\) | ||||
0.242385 | + | 0.970180i | \(0.422070\pi\) | |||||||
\(30\) | 2.50414 | 0.457191 | ||||||||
\(31\) | −1.94181 | −0.348759 | −0.174379 | − | 0.984679i | \(-0.555792\pi\) | ||||
−0.174379 | + | 0.984679i | \(0.555792\pi\) | |||||||
\(32\) | 7.28297 | 1.28746 | ||||||||
\(33\) | 5.63661 | 0.981207 | ||||||||
\(34\) | −6.96021 | −1.19367 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.01067 | −0.335112 | ||||||||
\(37\) | −5.68944 | −0.935338 | −0.467669 | − | 0.883904i | \(-0.654906\pi\) | ||||
−0.467669 | + | 0.883904i | \(0.654906\pi\) | |||||||
\(38\) | 15.7715 | 2.55848 | ||||||||
\(39\) | −8.81751 | −1.41193 | ||||||||
\(40\) | 0.761013 | 0.120327 | ||||||||
\(41\) | 8.33873 | 1.30229 | 0.651145 | − | 0.758953i | \(-0.274289\pi\) | ||||
0.651145 | + | 0.758953i | \(0.274289\pi\) | |||||||
\(42\) | −2.50414 | −0.386397 | ||||||||
\(43\) | −12.2885 | −1.87398 | −0.936988 | − | 0.349362i | \(-0.886398\pi\) | ||||
−0.936988 | + | 0.349362i | \(0.886398\pi\) | |||||||
\(44\) | −6.82728 | −1.02925 | ||||||||
\(45\) | −1.25758 | −0.187468 | ||||||||
\(46\) | −8.47305 | −1.24928 | ||||||||
\(47\) | 4.28551 | 0.625106 | 0.312553 | − | 0.949900i | \(-0.398816\pi\) | ||||
0.312553 | + | 0.949900i | \(0.398816\pi\) | |||||||
\(48\) | 6.12667 | 0.884308 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.89706 | −0.268285 | ||||||||
\(51\) | −4.84304 | −0.678161 | ||||||||
\(52\) | 10.6801 | 1.48106 | ||||||||
\(53\) | −0.475367 | −0.0652967 | −0.0326483 | − | 0.999467i | \(-0.510394\pi\) | ||||
−0.0326483 | + | 0.999467i | \(0.510394\pi\) | |||||||
\(54\) | −10.6616 | −1.45086 | ||||||||
\(55\) | −4.27013 | −0.575784 | ||||||||
\(56\) | −0.761013 | −0.101695 | ||||||||
\(57\) | 10.9741 | 1.45356 | ||||||||
\(58\) | −4.95241 | −0.650284 | ||||||||
\(59\) | 7.05293 | 0.918213 | 0.459107 | − | 0.888381i | \(-0.348170\pi\) | ||||
0.459107 | + | 0.888381i | \(0.348170\pi\) | |||||||
\(60\) | −2.11049 | −0.272463 | ||||||||
\(61\) | 2.30152 | 0.294680 | 0.147340 | − | 0.989086i | \(-0.452929\pi\) | ||||
0.147340 | + | 0.989086i | \(0.452929\pi\) | |||||||
\(62\) | 3.68373 | 0.467834 | ||||||||
\(63\) | 1.25758 | 0.158440 | ||||||||
\(64\) | −4.53348 | −0.566685 | ||||||||
\(65\) | 6.67988 | 0.828538 | ||||||||
\(66\) | −10.6930 | −1.31622 | ||||||||
\(67\) | 2.86284 | 0.349751 | 0.174876 | − | 0.984591i | \(-0.444048\pi\) | ||||
0.174876 | + | 0.984591i | \(0.444048\pi\) | |||||||
\(68\) | 5.86608 | 0.711366 | ||||||||
\(69\) | −5.89570 | −0.709758 | ||||||||
\(70\) | 1.89706 | 0.226742 | ||||||||
\(71\) | 5.04155 | 0.598322 | 0.299161 | − | 0.954203i | \(-0.403293\pi\) | ||||
0.299161 | + | 0.954203i | \(0.403293\pi\) | |||||||
\(72\) | −0.957032 | −0.112787 | ||||||||
\(73\) | −11.5287 | −1.34934 | −0.674668 | − | 0.738121i | \(-0.735713\pi\) | ||||
−0.674668 | + | 0.738121i | \(0.735713\pi\) | |||||||
\(74\) | 10.7932 | 1.25469 | ||||||||
\(75\) | −1.32001 | −0.152422 | ||||||||
\(76\) | −13.2923 | −1.52473 | ||||||||
\(77\) | 4.27013 | 0.486626 | ||||||||
\(78\) | 16.7274 | 1.89400 | ||||||||
\(79\) | 3.32995 | 0.374649 | 0.187324 | − | 0.982298i | \(-0.440018\pi\) | ||||
0.187324 | + | 0.982298i | \(0.440018\pi\) | |||||||
\(80\) | −4.64138 | −0.518922 | ||||||||
\(81\) | −3.64577 | −0.405086 | ||||||||
\(82\) | −15.8191 | −1.74693 | ||||||||
\(83\) | −15.7266 | −1.72622 | −0.863112 | − | 0.505013i | \(-0.831488\pi\) | ||||
−0.863112 | + | 0.505013i | \(0.831488\pi\) | |||||||
\(84\) | 2.11049 | 0.230274 | ||||||||
\(85\) | 3.66894 | 0.397953 | ||||||||
\(86\) | 23.3120 | 2.51380 | ||||||||
\(87\) | −3.44598 | −0.369447 | ||||||||
\(88\) | −3.24962 | −0.346411 | ||||||||
\(89\) | −4.88159 | −0.517448 | −0.258724 | − | 0.965951i | \(-0.583302\pi\) | ||||
−0.258724 | + | 0.965951i | \(0.583302\pi\) | |||||||
\(90\) | 2.38570 | 0.251475 | ||||||||
\(91\) | −6.67988 | −0.700242 | ||||||||
\(92\) | 7.14110 | 0.744511 | ||||||||
\(93\) | 2.56320 | 0.265792 | ||||||||
\(94\) | −8.12988 | −0.838533 | ||||||||
\(95\) | −8.31367 | −0.852964 | ||||||||
\(96\) | −9.61358 | −0.981182 | ||||||||
\(97\) | 11.4440 | 1.16197 | 0.580983 | − | 0.813916i | \(-0.302668\pi\) | ||||
0.580983 | + | 0.813916i | \(0.302668\pi\) | |||||||
\(98\) | −1.89706 | −0.191632 | ||||||||
\(99\) | 5.37001 | 0.539706 | ||||||||
\(100\) | 1.59885 | 0.159885 | ||||||||
\(101\) | −9.76565 | −0.971719 | −0.485859 | − | 0.874037i | \(-0.661493\pi\) | ||||
−0.485859 | + | 0.874037i | \(0.661493\pi\) | |||||||
\(102\) | 9.18755 | 0.909703 | ||||||||
\(103\) | −3.44731 | −0.339674 | −0.169837 | − | 0.985472i | \(-0.554324\pi\) | ||||
−0.169837 | + | 0.985472i | \(0.554324\pi\) | |||||||
\(104\) | 5.08348 | 0.498476 | ||||||||
\(105\) | 1.32001 | 0.128820 | ||||||||
\(106\) | 0.901801 | 0.0875907 | ||||||||
\(107\) | −15.1976 | −1.46921 | −0.734603 | − | 0.678497i | \(-0.762631\pi\) | ||||
−0.734603 | + | 0.678497i | \(0.762631\pi\) | |||||||
\(108\) | 8.98558 | 0.864638 | ||||||||
\(109\) | −2.44588 | −0.234273 | −0.117136 | − | 0.993116i | \(-0.537371\pi\) | ||||
−0.117136 | + | 0.993116i | \(0.537371\pi\) | |||||||
\(110\) | 8.10070 | 0.772372 | ||||||||
\(111\) | 7.51011 | 0.712829 | ||||||||
\(112\) | 4.64138 | 0.438569 | ||||||||
\(113\) | 16.7433 | 1.57508 | 0.787538 | − | 0.616266i | \(-0.211355\pi\) | ||||
0.787538 | + | 0.616266i | \(0.211355\pi\) | |||||||
\(114\) | −20.8186 | −1.94984 | ||||||||
\(115\) | 4.46641 | 0.416495 | ||||||||
\(116\) | 4.17390 | 0.387537 | ||||||||
\(117\) | −8.40046 | −0.776623 | ||||||||
\(118\) | −13.3798 | −1.23171 | ||||||||
\(119\) | −3.66894 | −0.336331 | ||||||||
\(120\) | −1.00454 | −0.0917019 | ||||||||
\(121\) | 7.23400 | 0.657636 | ||||||||
\(122\) | −4.36614 | −0.395291 | ||||||||
\(123\) | −11.0072 | −0.992485 | ||||||||
\(124\) | −3.10465 | −0.278806 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.38570 | −0.212535 | ||||||||
\(127\) | 16.8355 | 1.49391 | 0.746953 | − | 0.664877i | \(-0.231516\pi\) | ||||
0.746953 | + | 0.664877i | \(0.231516\pi\) | |||||||
\(128\) | −5.96564 | −0.527293 | ||||||||
\(129\) | 16.2209 | 1.42817 | ||||||||
\(130\) | −12.6722 | −1.11142 | ||||||||
\(131\) | −2.43588 | −0.212823 | −0.106412 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106412 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(132\) | 9.01207 | 0.784400 | ||||||||
\(133\) | 8.31367 | 0.720886 | ||||||||
\(134\) | −5.43098 | −0.469165 | ||||||||
\(135\) | 5.62004 | 0.483696 | ||||||||
\(136\) | 2.79211 | 0.239422 | ||||||||
\(137\) | 13.6639 | 1.16739 | 0.583693 | − | 0.811975i | \(-0.301607\pi\) | ||||
0.583693 | + | 0.811975i | \(0.301607\pi\) | |||||||
\(138\) | 11.1845 | 0.952088 | ||||||||
\(139\) | 9.24299 | 0.783980 | 0.391990 | − | 0.919969i | \(-0.371787\pi\) | ||||
0.391990 | + | 0.919969i | \(0.371787\pi\) | |||||||
\(140\) | −1.59885 | −0.135127 | ||||||||
\(141\) | −5.65691 | −0.476398 | ||||||||
\(142\) | −9.56414 | −0.802604 | ||||||||
\(143\) | −28.5240 | −2.38529 | ||||||||
\(144\) | 5.83689 | 0.486408 | ||||||||
\(145\) | 2.61057 | 0.216796 | ||||||||
\(146\) | 21.8707 | 1.81003 | ||||||||
\(147\) | −1.32001 | −0.108873 | ||||||||
\(148\) | −9.09654 | −0.747731 | ||||||||
\(149\) | −18.2824 | −1.49775 | −0.748876 | − | 0.662710i | \(-0.769406\pi\) | ||||
−0.748876 | + | 0.662710i | \(0.769406\pi\) | |||||||
\(150\) | 2.50414 | 0.204462 | ||||||||
\(151\) | 8.96584 | 0.729630 | 0.364815 | − | 0.931080i | \(-0.381132\pi\) | ||||
0.364815 | + | 0.931080i | \(0.381132\pi\) | |||||||
\(152\) | −6.32681 | −0.513172 | ||||||||
\(153\) | −4.61397 | −0.373018 | ||||||||
\(154\) | −8.10070 | −0.652773 | ||||||||
\(155\) | −1.94181 | −0.155970 | ||||||||
\(156\) | −14.0978 | −1.12873 | ||||||||
\(157\) | 11.3997 | 0.909797 | 0.454899 | − | 0.890543i | \(-0.349675\pi\) | ||||
0.454899 | + | 0.890543i | \(0.349675\pi\) | |||||||
\(158\) | −6.31713 | −0.502564 | ||||||||
\(159\) | 0.627489 | 0.0497631 | ||||||||
\(160\) | 7.28297 | 0.575769 | ||||||||
\(161\) | −4.46641 | −0.352002 | ||||||||
\(162\) | 6.91626 | 0.543393 | ||||||||
\(163\) | 22.6807 | 1.77649 | 0.888247 | − | 0.459367i | \(-0.151924\pi\) | ||||
0.888247 | + | 0.459367i | \(0.151924\pi\) | |||||||
\(164\) | 13.3323 | 1.04108 | ||||||||
\(165\) | 5.63661 | 0.438809 | ||||||||
\(166\) | 29.8344 | 2.31560 | ||||||||
\(167\) | −17.3959 | −1.34613 | −0.673067 | − | 0.739581i | \(-0.735024\pi\) | ||||
−0.673067 | + | 0.739581i | \(0.735024\pi\) | |||||||
\(168\) | 1.00454 | 0.0775023 | ||||||||
\(169\) | 31.6209 | 2.43237 | ||||||||
\(170\) | −6.96021 | −0.533824 | ||||||||
\(171\) | 10.4551 | 0.799519 | ||||||||
\(172\) | −19.6474 | −1.49810 | ||||||||
\(173\) | −20.2634 | −1.54060 | −0.770299 | − | 0.637683i | \(-0.779893\pi\) | ||||
−0.770299 | + | 0.637683i | \(0.779893\pi\) | |||||||
\(174\) | 6.53723 | 0.495586 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 19.8193 | 1.49394 | ||||||||
\(177\) | −9.30993 | −0.699777 | ||||||||
\(178\) | 9.26068 | 0.694118 | ||||||||
\(179\) | −7.63870 | −0.570943 | −0.285472 | − | 0.958387i | \(-0.592150\pi\) | ||||
−0.285472 | + | 0.958387i | \(0.592150\pi\) | |||||||
\(180\) | −2.01067 | −0.149867 | ||||||||
\(181\) | −24.3992 | −1.81358 | −0.906790 | − | 0.421583i | \(-0.861474\pi\) | ||||
−0.906790 | + | 0.421583i | \(0.861474\pi\) | |||||||
\(182\) | 12.6722 | 0.939323 | ||||||||
\(183\) | −3.03803 | −0.224578 | ||||||||
\(184\) | 3.39899 | 0.250577 | ||||||||
\(185\) | −5.68944 | −0.418296 | ||||||||
\(186\) | −4.86256 | −0.356540 | ||||||||
\(187\) | −15.6669 | −1.14567 | ||||||||
\(188\) | 6.85187 | 0.499724 | ||||||||
\(189\) | −5.62004 | −0.408798 | ||||||||
\(190\) | 15.7715 | 1.14419 | ||||||||
\(191\) | 15.9255 | 1.15233 | 0.576166 | − | 0.817333i | \(-0.304548\pi\) | ||||
0.576166 | + | 0.817333i | \(0.304548\pi\) | |||||||
\(192\) | 5.98423 | 0.431875 | ||||||||
\(193\) | −3.08991 | −0.222417 | −0.111208 | − | 0.993797i | \(-0.535472\pi\) | ||||
−0.111208 | + | 0.993797i | \(0.535472\pi\) | |||||||
\(194\) | −21.7101 | −1.55869 | ||||||||
\(195\) | −8.81751 | −0.631435 | ||||||||
\(196\) | 1.59885 | 0.114203 | ||||||||
\(197\) | 24.1934 | 1.72371 | 0.861854 | − | 0.507157i | \(-0.169303\pi\) | ||||
0.861854 | + | 0.507157i | \(0.169303\pi\) | |||||||
\(198\) | −10.1872 | −0.723976 | ||||||||
\(199\) | −10.2745 | −0.728343 | −0.364172 | − | 0.931332i | \(-0.618648\pi\) | ||||
−0.364172 | + | 0.931332i | \(0.618648\pi\) | |||||||
\(200\) | 0.761013 | 0.0538118 | ||||||||
\(201\) | −3.77897 | −0.266548 | ||||||||
\(202\) | 18.5261 | 1.30349 | ||||||||
\(203\) | −2.61057 | −0.183226 | ||||||||
\(204\) | −7.74327 | −0.542138 | ||||||||
\(205\) | 8.33873 | 0.582402 | ||||||||
\(206\) | 6.53977 | 0.455647 | ||||||||
\(207\) | −5.61685 | −0.390398 | ||||||||
\(208\) | −31.0039 | −2.14973 | ||||||||
\(209\) | 35.5004 | 2.45562 | ||||||||
\(210\) | −2.50414 | −0.172802 | ||||||||
\(211\) | −4.67557 | −0.321879 | −0.160940 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160940 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(212\) | −0.760039 | −0.0521997 | ||||||||
\(213\) | −6.65489 | −0.455986 | ||||||||
\(214\) | 28.8308 | 1.97083 | ||||||||
\(215\) | −12.2885 | −0.838067 | ||||||||
\(216\) | 4.27692 | 0.291008 | ||||||||
\(217\) | 1.94181 | 0.131818 | ||||||||
\(218\) | 4.63999 | 0.314260 | ||||||||
\(219\) | 15.2180 | 1.02834 | ||||||||
\(220\) | −6.82728 | −0.460295 | ||||||||
\(221\) | 24.5081 | 1.64859 | ||||||||
\(222\) | −14.2472 | −0.956207 | ||||||||
\(223\) | −2.11945 | −0.141929 | −0.0709644 | − | 0.997479i | \(-0.522608\pi\) | ||||
−0.0709644 | + | 0.997479i | \(0.522608\pi\) | |||||||
\(224\) | −7.28297 | −0.486614 | ||||||||
\(225\) | −1.25758 | −0.0838384 | ||||||||
\(226\) | −31.7631 | −2.11285 | ||||||||
\(227\) | 19.7057 | 1.30791 | 0.653957 | − | 0.756532i | \(-0.273108\pi\) | ||||
0.653957 | + | 0.756532i | \(0.273108\pi\) | |||||||
\(228\) | 17.5459 | 1.16201 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −8.47305 | −0.558697 | ||||||||
\(231\) | −5.63661 | −0.370862 | ||||||||
\(232\) | 1.98668 | 0.130432 | ||||||||
\(233\) | −16.2231 | −1.06281 | −0.531405 | − | 0.847118i | \(-0.678336\pi\) | ||||
−0.531405 | + | 0.847118i | \(0.678336\pi\) | |||||||
\(234\) | 15.9362 | 1.04178 | ||||||||
\(235\) | 4.28551 | 0.279556 | ||||||||
\(236\) | 11.2766 | 0.734041 | ||||||||
\(237\) | −4.39557 | −0.285523 | ||||||||
\(238\) | 6.96021 | 0.451164 | ||||||||
\(239\) | −24.3285 | −1.57368 | −0.786839 | − | 0.617158i | \(-0.788284\pi\) | ||||
−0.786839 | + | 0.617158i | \(0.788284\pi\) | |||||||
\(240\) | 6.12667 | 0.395475 | ||||||||
\(241\) | 3.66169 | 0.235870 | 0.117935 | − | 0.993021i | \(-0.462373\pi\) | ||||
0.117935 | + | 0.993021i | \(0.462373\pi\) | |||||||
\(242\) | −13.7233 | −0.882170 | ||||||||
\(243\) | −12.0477 | −0.772858 | ||||||||
\(244\) | 3.67978 | 0.235574 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 20.8813 | 1.33135 | ||||||||
\(247\) | −55.5343 | −3.53357 | ||||||||
\(248\) | −1.47774 | −0.0938366 | ||||||||
\(249\) | 20.7593 | 1.31557 | ||||||||
\(250\) | −1.89706 | −0.119981 | ||||||||
\(251\) | −23.4662 | −1.48117 | −0.740587 | − | 0.671961i | \(-0.765452\pi\) | ||||
−0.740587 | + | 0.671961i | \(0.765452\pi\) | |||||||
\(252\) | 2.01067 | 0.126660 | ||||||||
\(253\) | −19.0721 | −1.19905 | ||||||||
\(254\) | −31.9379 | −2.00396 | ||||||||
\(255\) | −4.84304 | −0.303283 | ||||||||
\(256\) | 20.3842 | 1.27401 | ||||||||
\(257\) | 30.3879 | 1.89554 | 0.947772 | − | 0.318950i | \(-0.103330\pi\) | ||||
0.947772 | + | 0.318950i | \(0.103330\pi\) | |||||||
\(258\) | −30.7721 | −1.91579 | ||||||||
\(259\) | 5.68944 | 0.353525 | ||||||||
\(260\) | 10.6801 | 0.662352 | ||||||||
\(261\) | −3.28299 | −0.203212 | ||||||||
\(262\) | 4.62101 | 0.285487 | ||||||||
\(263\) | −6.66038 | −0.410697 | −0.205348 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205348 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(264\) | 4.28953 | 0.264002 | ||||||||
\(265\) | −0.475367 | −0.0292016 | ||||||||
\(266\) | −15.7715 | −0.967016 | ||||||||
\(267\) | 6.44374 | 0.394351 | ||||||||
\(268\) | 4.57724 | 0.279599 | ||||||||
\(269\) | 12.7827 | 0.779378 | 0.389689 | − | 0.920947i | \(-0.372583\pi\) | ||||
0.389689 | + | 0.920947i | \(0.372583\pi\) | |||||||
\(270\) | −10.6616 | −0.648842 | ||||||||
\(271\) | 29.0040 | 1.76187 | 0.880933 | − | 0.473241i | \(-0.156916\pi\) | ||||
0.880933 | + | 0.473241i | \(0.156916\pi\) | |||||||
\(272\) | −17.0290 | −1.03253 | ||||||||
\(273\) | 8.81751 | 0.533660 | ||||||||
\(274\) | −25.9213 | −1.56596 | ||||||||
\(275\) | −4.27013 | −0.257498 | ||||||||
\(276\) | −9.42631 | −0.567397 | ||||||||
\(277\) | 13.5153 | 0.812055 | 0.406028 | − | 0.913861i | \(-0.366914\pi\) | ||||
0.406028 | + | 0.913861i | \(0.366914\pi\) | |||||||
\(278\) | −17.5345 | −1.05165 | ||||||||
\(279\) | 2.44197 | 0.146197 | ||||||||
\(280\) | −0.761013 | −0.0454792 | ||||||||
\(281\) | −22.9233 | −1.36749 | −0.683746 | − | 0.729721i | \(-0.739650\pi\) | ||||
−0.683746 | + | 0.729721i | \(0.739650\pi\) | |||||||
\(282\) | 10.7315 | 0.639052 | ||||||||
\(283\) | −18.4144 | −1.09462 | −0.547312 | − | 0.836929i | \(-0.684349\pi\) | ||||
−0.547312 | + | 0.836929i | \(0.684349\pi\) | |||||||
\(284\) | 8.06066 | 0.478312 | ||||||||
\(285\) | 10.9741 | 0.650051 | ||||||||
\(286\) | 54.1117 | 3.19969 | ||||||||
\(287\) | −8.33873 | −0.492220 | ||||||||
\(288\) | −9.15889 | −0.539693 | ||||||||
\(289\) | −3.53886 | −0.208168 | ||||||||
\(290\) | −4.95241 | −0.290816 | ||||||||
\(291\) | −15.1062 | −0.885543 | ||||||||
\(292\) | −18.4327 | −1.07869 | ||||||||
\(293\) | −26.6080 | −1.55445 | −0.777227 | − | 0.629221i | \(-0.783374\pi\) | ||||
−0.777227 | + | 0.629221i | \(0.783374\pi\) | |||||||
\(294\) | 2.50414 | 0.146044 | ||||||||
\(295\) | 7.05293 | 0.410637 | ||||||||
\(296\) | −4.32974 | −0.251661 | ||||||||
\(297\) | −23.9983 | −1.39252 | ||||||||
\(298\) | 34.6828 | 2.00912 | ||||||||
\(299\) | 29.8351 | 1.72541 | ||||||||
\(300\) | −2.11049 | −0.121849 | ||||||||
\(301\) | 12.2885 | 0.708296 | ||||||||
\(302\) | −17.0088 | −0.978745 | ||||||||
\(303\) | 12.8907 | 0.740554 | ||||||||
\(304\) | 38.5869 | 2.21311 | ||||||||
\(305\) | 2.30152 | 0.131785 | ||||||||
\(306\) | 8.75300 | 0.500376 | ||||||||
\(307\) | −19.8881 | −1.13507 | −0.567537 | − | 0.823348i | \(-0.692104\pi\) | ||||
−0.567537 | + | 0.823348i | \(0.692104\pi\) | |||||||
\(308\) | 6.82728 | 0.389020 | ||||||||
\(309\) | 4.55048 | 0.258868 | ||||||||
\(310\) | 3.68373 | 0.209222 | ||||||||
\(311\) | −17.9149 | −1.01586 | −0.507930 | − | 0.861398i | \(-0.669589\pi\) | ||||
−0.507930 | + | 0.861398i | \(0.669589\pi\) | |||||||
\(312\) | −6.71024 | −0.379892 | ||||||||
\(313\) | 12.6009 | 0.712243 | 0.356121 | − | 0.934440i | \(-0.384099\pi\) | ||||
0.356121 | + | 0.934440i | \(0.384099\pi\) | |||||||
\(314\) | −21.6260 | −1.22043 | ||||||||
\(315\) | 1.25758 | 0.0708564 | ||||||||
\(316\) | 5.32408 | 0.299503 | ||||||||
\(317\) | −0.408604 | −0.0229495 | −0.0114747 | − | 0.999934i | \(-0.503653\pi\) | ||||
−0.0114747 | + | 0.999934i | \(0.503653\pi\) | |||||||
\(318\) | −1.19039 | −0.0667535 | ||||||||
\(319\) | −11.1475 | −0.624138 | ||||||||
\(320\) | −4.53348 | −0.253429 | ||||||||
\(321\) | 20.0609 | 1.11969 | ||||||||
\(322\) | 8.47305 | 0.472185 | ||||||||
\(323\) | −30.5024 | −1.69720 | ||||||||
\(324\) | −5.82903 | −0.323835 | ||||||||
\(325\) | 6.67988 | 0.370533 | ||||||||
\(326\) | −43.0268 | −2.38303 | ||||||||
\(327\) | 3.22859 | 0.178541 | ||||||||
\(328\) | 6.34588 | 0.350393 | ||||||||
\(329\) | −4.28551 | −0.236268 | ||||||||
\(330\) | −10.6930 | −0.588630 | ||||||||
\(331\) | −18.0303 | −0.991037 | −0.495518 | − | 0.868598i | \(-0.665022\pi\) | ||||
−0.495518 | + | 0.868598i | \(0.665022\pi\) | |||||||
\(332\) | −25.1445 | −1.37998 | ||||||||
\(333\) | 7.15491 | 0.392086 | ||||||||
\(334\) | 33.0011 | 1.80574 | ||||||||
\(335\) | 2.86284 | 0.156414 | ||||||||
\(336\) | −6.12667 | −0.334237 | ||||||||
\(337\) | 1.14623 | 0.0624392 | 0.0312196 | − | 0.999513i | \(-0.490061\pi\) | ||||
0.0312196 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(338\) | −59.9867 | −3.26285 | ||||||||
\(339\) | −22.1013 | −1.20038 | ||||||||
\(340\) | 5.86608 | 0.318133 | ||||||||
\(341\) | 8.29177 | 0.449024 | ||||||||
\(342\) | −19.8339 | −1.07250 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −9.35169 | −0.504210 | ||||||||
\(345\) | −5.89570 | −0.317414 | ||||||||
\(346\) | 38.4409 | 2.06660 | ||||||||
\(347\) | −27.5656 | −1.47980 | −0.739900 | − | 0.672717i | \(-0.765127\pi\) | ||||
−0.739900 | + | 0.672717i | \(0.765127\pi\) | |||||||
\(348\) | −5.50959 | −0.295345 | ||||||||
\(349\) | 26.9794 | 1.44418 | 0.722088 | − | 0.691801i | \(-0.243183\pi\) | ||||
0.722088 | + | 0.691801i | \(0.243183\pi\) | |||||||
\(350\) | 1.89706 | 0.101402 | ||||||||
\(351\) | 37.5412 | 2.00380 | ||||||||
\(352\) | −31.0992 | −1.65759 | ||||||||
\(353\) | 0.537640 | 0.0286157 | 0.0143078 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143078 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(354\) | 17.6615 | 0.938699 | ||||||||
\(355\) | 5.04155 | 0.267578 | ||||||||
\(356\) | −7.80491 | −0.413660 | ||||||||
\(357\) | 4.84304 | 0.256321 | ||||||||
\(358\) | 14.4911 | 0.765878 | ||||||||
\(359\) | −5.51693 | −0.291172 | −0.145586 | − | 0.989346i | \(-0.546507\pi\) | ||||
−0.145586 | + | 0.989346i | \(0.546507\pi\) | |||||||
\(360\) | −0.957032 | −0.0504400 | ||||||||
\(361\) | 50.1171 | 2.63774 | ||||||||
\(362\) | 46.2868 | 2.43278 | ||||||||
\(363\) | −9.54894 | −0.501189 | ||||||||
\(364\) | −10.6801 | −0.559790 | ||||||||
\(365\) | −11.5287 | −0.603441 | ||||||||
\(366\) | 5.76334 | 0.301255 | ||||||||
\(367\) | 7.90978 | 0.412887 | 0.206444 | − | 0.978458i | \(-0.433811\pi\) | ||||
0.206444 | + | 0.978458i | \(0.433811\pi\) | |||||||
\(368\) | −20.7303 | −1.08064 | ||||||||
\(369\) | −10.4866 | −0.545910 | ||||||||
\(370\) | 10.7932 | 0.561113 | ||||||||
\(371\) | 0.475367 | 0.0246798 | ||||||||
\(372\) | 4.09817 | 0.212480 | ||||||||
\(373\) | 12.0211 | 0.622427 | 0.311214 | − | 0.950340i | \(-0.399264\pi\) | ||||
0.311214 | + | 0.950340i | \(0.399264\pi\) | |||||||
\(374\) | 29.7210 | 1.53684 | ||||||||
\(375\) | −1.32001 | −0.0681650 | ||||||||
\(376\) | 3.26133 | 0.168190 | ||||||||
\(377\) | 17.4383 | 0.898118 | ||||||||
\(378\) | 10.6616 | 0.548372 | ||||||||
\(379\) | 31.9837 | 1.64289 | 0.821447 | − | 0.570285i | \(-0.193167\pi\) | ||||
0.821447 | + | 0.570285i | \(0.193167\pi\) | |||||||
\(380\) | −13.2923 | −0.681880 | ||||||||
\(381\) | −22.2230 | −1.13852 | ||||||||
\(382\) | −30.2117 | −1.54577 | ||||||||
\(383\) | −11.8912 | −0.607613 | −0.303807 | − | 0.952734i | \(-0.598258\pi\) | ||||
−0.303807 | + | 0.952734i | \(0.598258\pi\) | |||||||
\(384\) | 7.87470 | 0.401854 | ||||||||
\(385\) | 4.27013 | 0.217626 | ||||||||
\(386\) | 5.86176 | 0.298356 | ||||||||
\(387\) | 15.4537 | 0.785556 | ||||||||
\(388\) | 18.2973 | 0.928903 | ||||||||
\(389\) | −12.8767 | −0.652876 | −0.326438 | − | 0.945219i | \(-0.605849\pi\) | ||||
−0.326438 | + | 0.945219i | \(0.605849\pi\) | |||||||
\(390\) | 16.7274 | 0.847023 | ||||||||
\(391\) | 16.3870 | 0.828726 | ||||||||
\(392\) | 0.761013 | 0.0384370 | ||||||||
\(393\) | 3.21538 | 0.162194 | ||||||||
\(394\) | −45.8964 | −2.31223 | ||||||||
\(395\) | 3.32995 | 0.167548 | ||||||||
\(396\) | 8.58582 | 0.431454 | ||||||||
\(397\) | −7.14188 | −0.358441 | −0.179220 | − | 0.983809i | \(-0.557357\pi\) | ||||
−0.179220 | + | 0.983809i | \(0.557357\pi\) | |||||||
\(398\) | 19.4915 | 0.977019 | ||||||||
\(399\) | −10.9741 | −0.549393 | ||||||||
\(400\) | −4.64138 | −0.232069 | ||||||||
\(401\) | 36.6474 | 1.83008 | 0.915042 | − | 0.403359i | \(-0.132157\pi\) | ||||
0.915042 | + | 0.403359i | \(0.132157\pi\) | |||||||
\(402\) | 7.16895 | 0.357555 | ||||||||
\(403\) | −12.9710 | −0.646134 | ||||||||
\(404\) | −15.6138 | −0.776815 | ||||||||
\(405\) | −3.64577 | −0.181160 | ||||||||
\(406\) | 4.95241 | 0.245784 | ||||||||
\(407\) | 24.2946 | 1.20424 | ||||||||
\(408\) | −3.68561 | −0.182465 | ||||||||
\(409\) | −11.2138 | −0.554485 | −0.277243 | − | 0.960800i | \(-0.589421\pi\) | ||||
−0.277243 | + | 0.960800i | \(0.589421\pi\) | |||||||
\(410\) | −15.8191 | −0.781249 | ||||||||
\(411\) | −18.0365 | −0.889674 | ||||||||
\(412\) | −5.51172 | −0.271543 | ||||||||
\(413\) | −7.05293 | −0.347052 | ||||||||
\(414\) | 10.6555 | 0.523690 | ||||||||
\(415\) | −15.7266 | −0.771990 | ||||||||
\(416\) | 48.6494 | 2.38523 | ||||||||
\(417\) | −12.2008 | −0.597477 | ||||||||
\(418\) | −67.3465 | −3.29403 | ||||||||
\(419\) | 11.3725 | 0.555585 | 0.277792 | − | 0.960641i | \(-0.410397\pi\) | ||||
0.277792 | + | 0.960641i | \(0.410397\pi\) | |||||||
\(420\) | 2.11049 | 0.102981 | ||||||||
\(421\) | −31.2636 | −1.52370 | −0.761848 | − | 0.647756i | \(-0.775708\pi\) | ||||
−0.761848 | + | 0.647756i | \(0.775708\pi\) | |||||||
\(422\) | 8.86985 | 0.431777 | ||||||||
\(423\) | −5.38935 | −0.262039 | ||||||||
\(424\) | −0.361761 | −0.0175686 | ||||||||
\(425\) | 3.66894 | 0.177970 | ||||||||
\(426\) | 12.6247 | 0.611671 | ||||||||
\(427\) | −2.30152 | −0.111379 | ||||||||
\(428\) | −24.2986 | −1.17452 | ||||||||
\(429\) | 37.6519 | 1.81785 | ||||||||
\(430\) | 23.3120 | 1.12421 | ||||||||
\(431\) | 37.5377 | 1.80813 | 0.904063 | − | 0.427399i | \(-0.140570\pi\) | ||||
0.904063 | + | 0.427399i | \(0.140570\pi\) | |||||||
\(432\) | −26.0848 | −1.25500 | ||||||||
\(433\) | 7.86991 | 0.378204 | 0.189102 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189102 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(434\) | −3.68373 | −0.176825 | ||||||||
\(435\) | −3.44598 | −0.165222 | ||||||||
\(436\) | −3.91059 | −0.187283 | ||||||||
\(437\) | −37.1322 | −1.77627 | ||||||||
\(438\) | −28.8696 | −1.37944 | ||||||||
\(439\) | 26.6791 | 1.27332 | 0.636662 | − | 0.771143i | \(-0.280315\pi\) | ||||
0.636662 | + | 0.771143i | \(0.280315\pi\) | |||||||
\(440\) | −3.24962 | −0.154920 | ||||||||
\(441\) | −1.25758 | −0.0598846 | ||||||||
\(442\) | −46.4934 | −2.21147 | ||||||||
\(443\) | 17.3446 | 0.824069 | 0.412035 | − | 0.911168i | \(-0.364818\pi\) | ||||
0.412035 | + | 0.911168i | \(0.364818\pi\) | |||||||
\(444\) | 12.0075 | 0.569852 | ||||||||
\(445\) | −4.88159 | −0.231410 | ||||||||
\(446\) | 4.02073 | 0.190387 | ||||||||
\(447\) | 24.1329 | 1.14145 | ||||||||
\(448\) | 4.53348 | 0.214187 | ||||||||
\(449\) | −40.9938 | −1.93462 | −0.967308 | − | 0.253605i | \(-0.918384\pi\) | ||||
−0.967308 | + | 0.253605i | \(0.918384\pi\) | |||||||
\(450\) | 2.38570 | 0.112463 | ||||||||
\(451\) | −35.6074 | −1.67669 | ||||||||
\(452\) | 26.7699 | 1.25915 | ||||||||
\(453\) | −11.8350 | −0.556057 | ||||||||
\(454\) | −37.3829 | −1.75447 | ||||||||
\(455\) | −6.67988 | −0.313158 | ||||||||
\(456\) | 8.35145 | 0.391092 | ||||||||
\(457\) | −22.8093 | −1.06697 | −0.533487 | − | 0.845808i | \(-0.679119\pi\) | ||||
−0.533487 | + | 0.845808i | \(0.679119\pi\) | |||||||
\(458\) | 1.89706 | 0.0886439 | ||||||||
\(459\) | 20.6196 | 0.962441 | ||||||||
\(460\) | 7.14110 | 0.332955 | ||||||||
\(461\) | 14.4044 | 0.670878 | 0.335439 | − | 0.942062i | \(-0.391115\pi\) | ||||
0.335439 | + | 0.942062i | \(0.391115\pi\) | |||||||
\(462\) | 10.6930 | 0.497483 | ||||||||
\(463\) | 38.9822 | 1.81166 | 0.905828 | − | 0.423647i | \(-0.139250\pi\) | ||||
0.905828 | + | 0.423647i | \(0.139250\pi\) | |||||||
\(464\) | −12.1167 | −0.562502 | ||||||||
\(465\) | 2.56320 | 0.118866 | ||||||||
\(466\) | 30.7762 | 1.42568 | ||||||||
\(467\) | −0.124066 | −0.00574108 | −0.00287054 | − | 0.999996i | \(-0.500914\pi\) | ||||
−0.00287054 | + | 0.999996i | \(0.500914\pi\) | |||||||
\(468\) | −13.4311 | −0.620851 | ||||||||
\(469\) | −2.86284 | −0.132194 | ||||||||
\(470\) | −8.12988 | −0.375003 | ||||||||
\(471\) | −15.0477 | −0.693363 | ||||||||
\(472\) | 5.36737 | 0.247053 | ||||||||
\(473\) | 52.4734 | 2.41273 | ||||||||
\(474\) | 8.33866 | 0.383008 | ||||||||
\(475\) | −8.31367 | −0.381457 | ||||||||
\(476\) | −5.86608 | −0.268871 | ||||||||
\(477\) | 0.597810 | 0.0273718 | ||||||||
\(478\) | 46.1527 | 2.11097 | ||||||||
\(479\) | 24.0159 | 1.09731 | 0.548657 | − | 0.836047i | \(-0.315139\pi\) | ||||
0.548657 | + | 0.836047i | \(0.315139\pi\) | |||||||
\(480\) | −9.61358 | −0.438798 | ||||||||
\(481\) | −38.0048 | −1.73287 | ||||||||
\(482\) | −6.94646 | −0.316403 | ||||||||
\(483\) | 5.89570 | 0.268263 | ||||||||
\(484\) | 11.5660 | 0.525729 | ||||||||
\(485\) | 11.4440 | 0.519647 | ||||||||
\(486\) | 22.8552 | 1.03673 | ||||||||
\(487\) | −29.7511 | −1.34815 | −0.674076 | − | 0.738662i | \(-0.735458\pi\) | ||||
−0.674076 | + | 0.738662i | \(0.735458\pi\) | |||||||
\(488\) | 1.75149 | 0.0792862 | ||||||||
\(489\) | −29.9388 | −1.35388 | ||||||||
\(490\) | −1.89706 | −0.0857006 | ||||||||
\(491\) | −25.6950 | −1.15960 | −0.579800 | − | 0.814759i | \(-0.696869\pi\) | ||||
−0.579800 | + | 0.814759i | \(0.696869\pi\) | |||||||
\(492\) | −17.5988 | −0.793416 | ||||||||
\(493\) | 9.57803 | 0.431373 | ||||||||
\(494\) | 105.352 | 4.74002 | ||||||||
\(495\) | 5.37001 | 0.241364 | ||||||||
\(496\) | 9.01267 | 0.404681 | ||||||||
\(497\) | −5.04155 | −0.226144 | ||||||||
\(498\) | −39.3817 | −1.76474 | ||||||||
\(499\) | −38.2476 | −1.71220 | −0.856099 | − | 0.516811i | \(-0.827119\pi\) | ||||
−0.856099 | + | 0.516811i | \(0.827119\pi\) | |||||||
\(500\) | 1.59885 | 0.0715026 | ||||||||
\(501\) | 22.9627 | 1.02590 | ||||||||
\(502\) | 44.5169 | 1.98688 | ||||||||
\(503\) | 11.0248 | 0.491573 | 0.245787 | − | 0.969324i | \(-0.420954\pi\) | ||||
0.245787 | + | 0.969324i | \(0.420954\pi\) | |||||||
\(504\) | 0.957032 | 0.0426296 | ||||||||
\(505\) | −9.76565 | −0.434566 | ||||||||
\(506\) | 36.1810 | 1.60844 | ||||||||
\(507\) | −41.7398 | −1.85373 | ||||||||
\(508\) | 26.9173 | 1.19426 | ||||||||
\(509\) | −4.53964 | −0.201216 | −0.100608 | − | 0.994926i | \(-0.532079\pi\) | ||||
−0.100608 | + | 0.994926i | \(0.532079\pi\) | |||||||
\(510\) | 9.18755 | 0.406831 | ||||||||
\(511\) | 11.5287 | 0.510001 | ||||||||
\(512\) | −26.7387 | −1.18170 | ||||||||
\(513\) | −46.7231 | −2.06288 | ||||||||
\(514\) | −57.6477 | −2.54273 | ||||||||
\(515\) | −3.44731 | −0.151907 | ||||||||
\(516\) | 25.9347 | 1.14171 | ||||||||
\(517\) | −18.2997 | −0.804819 | ||||||||
\(518\) | −10.7932 | −0.474227 | ||||||||
\(519\) | 26.7479 | 1.17410 | ||||||||
\(520\) | 5.08348 | 0.222925 | ||||||||
\(521\) | 9.23555 | 0.404617 | 0.202309 | − | 0.979322i | \(-0.435156\pi\) | ||||
0.202309 | + | 0.979322i | \(0.435156\pi\) | |||||||
\(522\) | 6.22804 | 0.272594 | ||||||||
\(523\) | 11.1959 | 0.489561 | 0.244781 | − | 0.969578i | \(-0.421284\pi\) | ||||
0.244781 | + | 0.969578i | \(0.421284\pi\) | |||||||
\(524\) | −3.89459 | −0.170136 | ||||||||
\(525\) | 1.32001 | 0.0576099 | ||||||||
\(526\) | 12.6352 | 0.550919 | ||||||||
\(527\) | −7.12438 | −0.310343 | ||||||||
\(528\) | −26.1617 | −1.13854 | ||||||||
\(529\) | −3.05122 | −0.132662 | ||||||||
\(530\) | 0.901801 | 0.0391717 | ||||||||
\(531\) | −8.86960 | −0.384908 | ||||||||
\(532\) | 13.2923 | 0.576293 | ||||||||
\(533\) | 55.7017 | 2.41271 | ||||||||
\(534\) | −12.2242 | −0.528992 | ||||||||
\(535\) | −15.1976 | −0.657049 | ||||||||
\(536\) | 2.17866 | 0.0941037 | ||||||||
\(537\) | 10.0832 | 0.435120 | ||||||||
\(538\) | −24.2497 | −1.04548 | ||||||||
\(539\) | −4.27013 | −0.183927 | ||||||||
\(540\) | 8.98558 | 0.386678 | ||||||||
\(541\) | 17.1692 | 0.738161 | 0.369081 | − | 0.929397i | \(-0.379673\pi\) | ||||
0.369081 | + | 0.929397i | \(0.379673\pi\) | |||||||
\(542\) | −55.0224 | −2.36341 | ||||||||
\(543\) | 32.2072 | 1.38214 | ||||||||
\(544\) | 26.7208 | 1.14564 | ||||||||
\(545\) | −2.44588 | −0.104770 | ||||||||
\(546\) | −16.7274 | −0.715865 | ||||||||
\(547\) | −0.361961 | −0.0154763 | −0.00773817 | − | 0.999970i | \(-0.502463\pi\) | ||||
−0.00773817 | + | 0.999970i | \(0.502463\pi\) | |||||||
\(548\) | 21.8465 | 0.933235 | ||||||||
\(549\) | −2.89434 | −0.123528 | ||||||||
\(550\) | 8.10070 | 0.345415 | ||||||||
\(551\) | −21.7034 | −0.924596 | ||||||||
\(552\) | −4.48670 | −0.190967 | ||||||||
\(553\) | −3.32995 | −0.141604 | ||||||||
\(554\) | −25.6394 | −1.08931 | ||||||||
\(555\) | 7.51011 | 0.318787 | ||||||||
\(556\) | 14.7781 | 0.626732 | ||||||||
\(557\) | 13.6146 | 0.576868 | 0.288434 | − | 0.957500i | \(-0.406865\pi\) | ||||
0.288434 | + | 0.957500i | \(0.406865\pi\) | |||||||
\(558\) | −4.63257 | −0.196112 | ||||||||
\(559\) | −82.0856 | −3.47185 | ||||||||
\(560\) | 4.64138 | 0.196134 | ||||||||
\(561\) | 20.6804 | 0.873127 | ||||||||
\(562\) | 43.4870 | 1.83439 | ||||||||
\(563\) | −25.3291 | −1.06749 | −0.533747 | − | 0.845644i | \(-0.679217\pi\) | ||||
−0.533747 | + | 0.845644i | \(0.679217\pi\) | |||||||
\(564\) | −9.04453 | −0.380844 | ||||||||
\(565\) | 16.7433 | 0.704395 | ||||||||
\(566\) | 34.9333 | 1.46836 | ||||||||
\(567\) | 3.64577 | 0.153108 | ||||||||
\(568\) | 3.83669 | 0.160984 | ||||||||
\(569\) | 2.08615 | 0.0874561 | 0.0437280 | − | 0.999043i | \(-0.486076\pi\) | ||||
0.0437280 | + | 0.999043i | \(0.486076\pi\) | |||||||
\(570\) | −20.8186 | −0.871995 | ||||||||
\(571\) | −8.54630 | −0.357651 | −0.178826 | − | 0.983881i | \(-0.557230\pi\) | ||||
−0.178826 | + | 0.983881i | \(0.557230\pi\) | |||||||
\(572\) | −45.6054 | −1.90686 | ||||||||
\(573\) | −21.0219 | −0.878201 | ||||||||
\(574\) | 15.8191 | 0.660276 | ||||||||
\(575\) | 4.46641 | 0.186262 | ||||||||
\(576\) | 5.70120 | 0.237550 | ||||||||
\(577\) | 21.2429 | 0.884355 | 0.442178 | − | 0.896927i | \(-0.354206\pi\) | ||||
0.442178 | + | 0.896927i | \(0.354206\pi\) | |||||||
\(578\) | 6.71344 | 0.279242 | ||||||||
\(579\) | 4.07871 | 0.169506 | ||||||||
\(580\) | 4.17390 | 0.173312 | ||||||||
\(581\) | 15.7266 | 0.652451 | ||||||||
\(582\) | 28.6575 | 1.18789 | ||||||||
\(583\) | 2.02988 | 0.0840690 | ||||||||
\(584\) | −8.77351 | −0.363051 | ||||||||
\(585\) | −8.40046 | −0.347316 | ||||||||
\(586\) | 50.4770 | 2.08518 | ||||||||
\(587\) | 4.10742 | 0.169531 | 0.0847656 | − | 0.996401i | \(-0.472986\pi\) | ||||
0.0847656 | + | 0.996401i | \(0.472986\pi\) | |||||||
\(588\) | −2.11049 | −0.0870352 | ||||||||
\(589\) | 16.1435 | 0.665183 | ||||||||
\(590\) | −13.3798 | −0.550840 | ||||||||
\(591\) | −31.9355 | −1.31365 | ||||||||
\(592\) | 26.4069 | 1.08532 | ||||||||
\(593\) | 25.0587 | 1.02904 | 0.514518 | − | 0.857479i | \(-0.327971\pi\) | ||||
0.514518 | + | 0.857479i | \(0.327971\pi\) | |||||||
\(594\) | 45.5263 | 1.86796 | ||||||||
\(595\) | −3.66894 | −0.150412 | ||||||||
\(596\) | −29.2307 | −1.19734 | ||||||||
\(597\) | 13.5625 | 0.555076 | ||||||||
\(598\) | −56.5990 | −2.31451 | ||||||||
\(599\) | 45.3207 | 1.85175 | 0.925877 | − | 0.377825i | \(-0.123328\pi\) | ||||
0.925877 | + | 0.377825i | \(0.123328\pi\) | |||||||
\(600\) | −1.00454 | −0.0410103 | ||||||||
\(601\) | −2.63429 | −0.107455 | −0.0537276 | − | 0.998556i | \(-0.517110\pi\) | ||||
−0.0537276 | + | 0.998556i | \(0.517110\pi\) | |||||||
\(602\) | −23.3120 | −0.950127 | ||||||||
\(603\) | −3.60024 | −0.146613 | ||||||||
\(604\) | 14.3350 | 0.583283 | ||||||||
\(605\) | 7.23400 | 0.294104 | ||||||||
\(606\) | −24.4546 | −0.993398 | ||||||||
\(607\) | 30.3686 | 1.23263 | 0.616313 | − | 0.787502i | \(-0.288626\pi\) | ||||
0.616313 | + | 0.787502i | \(0.288626\pi\) | |||||||
\(608\) | −60.5482 | −2.45555 | ||||||||
\(609\) | 3.44598 | 0.139638 | ||||||||
\(610\) | −4.36614 | −0.176780 | ||||||||
\(611\) | 28.6267 | 1.15811 | ||||||||
\(612\) | −7.37704 | −0.298199 | ||||||||
\(613\) | −4.88769 | −0.197412 | −0.0987059 | − | 0.995117i | \(-0.531470\pi\) | ||||
−0.0987059 | + | 0.995117i | \(0.531470\pi\) | |||||||
\(614\) | 37.7290 | 1.52262 | ||||||||
\(615\) | −11.0072 | −0.443853 | ||||||||
\(616\) | 3.24962 | 0.130931 | ||||||||
\(617\) | 40.6460 | 1.63635 | 0.818174 | − | 0.574971i | \(-0.194987\pi\) | ||||
0.818174 | + | 0.574971i | \(0.194987\pi\) | |||||||
\(618\) | −8.63255 | −0.347252 | ||||||||
\(619\) | −3.17161 | −0.127478 | −0.0637388 | − | 0.997967i | \(-0.520302\pi\) | ||||
−0.0637388 | + | 0.997967i | \(0.520302\pi\) | |||||||
\(620\) | −3.10465 | −0.124686 | ||||||||
\(621\) | 25.1014 | 1.00728 | ||||||||
\(622\) | 33.9857 | 1.36270 | ||||||||
\(623\) | 4.88159 | 0.195577 | ||||||||
\(624\) | 40.9254 | 1.63833 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.9046 | −0.955421 | ||||||||
\(627\) | −46.8609 | −1.87144 | ||||||||
\(628\) | 18.2264 | 0.727313 | ||||||||
\(629\) | −20.8742 | −0.832310 | ||||||||
\(630\) | −2.38570 | −0.0950486 | ||||||||
\(631\) | 29.6709 | 1.18118 | 0.590590 | − | 0.806971i | \(-0.298895\pi\) | ||||
0.590590 | + | 0.806971i | \(0.298895\pi\) | |||||||
\(632\) | 2.53414 | 0.100803 | ||||||||
\(633\) | 6.17179 | 0.245307 | ||||||||
\(634\) | 0.775148 | 0.0307850 | ||||||||
\(635\) | 16.8355 | 0.668095 | ||||||||
\(636\) | 1.00326 | 0.0397818 | ||||||||
\(637\) | 6.67988 | 0.264667 | ||||||||
\(638\) | 21.1474 | 0.837235 | ||||||||
\(639\) | −6.34013 | −0.250812 | ||||||||
\(640\) | −5.96564 | −0.235813 | ||||||||
\(641\) | 46.6544 | 1.84274 | 0.921370 | − | 0.388688i | \(-0.127071\pi\) | ||||
0.921370 | + | 0.388688i | \(0.127071\pi\) | |||||||
\(642\) | −38.0569 | −1.50198 | ||||||||
\(643\) | 10.2635 | 0.404752 | 0.202376 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202376 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(644\) | −7.14110 | −0.281399 | ||||||||
\(645\) | 16.2209 | 0.638698 | ||||||||
\(646\) | 57.8649 | 2.27666 | ||||||||
\(647\) | −8.62561 | −0.339108 | −0.169554 | − | 0.985521i | \(-0.554233\pi\) | ||||
−0.169554 | + | 0.985521i | \(0.554233\pi\) | |||||||
\(648\) | −2.77448 | −0.108992 | ||||||||
\(649\) | −30.1169 | −1.18219 | ||||||||
\(650\) | −12.6722 | −0.497043 | ||||||||
\(651\) | −2.56320 | −0.100460 | ||||||||
\(652\) | 36.2630 | 1.42017 | ||||||||
\(653\) | 12.1068 | 0.473774 | 0.236887 | − | 0.971537i | \(-0.423873\pi\) | ||||
0.236887 | + | 0.971537i | \(0.423873\pi\) | |||||||
\(654\) | −6.12483 | −0.239500 | ||||||||
\(655\) | −2.43588 | −0.0951775 | ||||||||
\(656\) | −38.7032 | −1.51111 | ||||||||
\(657\) | 14.4983 | 0.565631 | ||||||||
\(658\) | 8.12988 | 0.316936 | ||||||||
\(659\) | 22.4317 | 0.873813 | 0.436907 | − | 0.899507i | \(-0.356074\pi\) | ||||
0.436907 | + | 0.899507i | \(0.356074\pi\) | |||||||
\(660\) | 9.01207 | 0.350794 | ||||||||
\(661\) | 33.0051 | 1.28375 | 0.641876 | − | 0.766809i | \(-0.278157\pi\) | ||||
0.641876 | + | 0.766809i | \(0.278157\pi\) | |||||||
\(662\) | 34.2047 | 1.32940 | ||||||||
\(663\) | −32.3509 | −1.25641 | ||||||||
\(664\) | −11.9682 | −0.464455 | ||||||||
\(665\) | 8.31367 | 0.322390 | ||||||||
\(666\) | −13.5733 | −0.525955 | ||||||||
\(667\) | 11.6599 | 0.451472 | ||||||||
\(668\) | −27.8134 | −1.07613 | ||||||||
\(669\) | 2.79769 | 0.108165 | ||||||||
\(670\) | −5.43098 | −0.209817 | ||||||||
\(671\) | −9.82780 | −0.379398 | ||||||||
\(672\) | 9.61358 | 0.370852 | ||||||||
\(673\) | −14.5490 | −0.560822 | −0.280411 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280411 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(674\) | −2.17447 | −0.0837575 | ||||||||
\(675\) | 5.62004 | 0.216315 | ||||||||
\(676\) | 50.5569 | 1.94450 | ||||||||
\(677\) | 9.74845 | 0.374663 | 0.187332 | − | 0.982297i | \(-0.440016\pi\) | ||||
0.187332 | + | 0.982297i | \(0.440016\pi\) | |||||||
\(678\) | 41.9275 | 1.61022 | ||||||||
\(679\) | −11.4440 | −0.439182 | ||||||||
\(680\) | 2.79211 | 0.107073 | ||||||||
\(681\) | −26.0117 | −0.996771 | ||||||||
\(682\) | −15.7300 | −0.602333 | ||||||||
\(683\) | −9.72430 | −0.372090 | −0.186045 | − | 0.982541i | \(-0.559567\pi\) | ||||
−0.186045 | + | 0.982541i | \(0.559567\pi\) | |||||||
\(684\) | 16.7161 | 0.639154 | ||||||||
\(685\) | 13.6639 | 0.522071 | ||||||||
\(686\) | 1.89706 | 0.0724302 | ||||||||
\(687\) | 1.32001 | 0.0503615 | ||||||||
\(688\) | 57.0355 | 2.17446 | ||||||||
\(689\) | −3.17540 | −0.120973 | ||||||||
\(690\) | 11.1845 | 0.425787 | ||||||||
\(691\) | 11.7121 | 0.445548 | 0.222774 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222774 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(692\) | −32.3981 | −1.23159 | ||||||||
\(693\) | −5.37001 | −0.203990 | ||||||||
\(694\) | 52.2937 | 1.98504 | ||||||||
\(695\) | 9.24299 | 0.350607 | ||||||||
\(696\) | −2.62243 | −0.0994031 | ||||||||
\(697\) | 30.5943 | 1.15884 | ||||||||
\(698\) | −51.1817 | −1.93726 | ||||||||
\(699\) | 21.4146 | 0.809976 | ||||||||
\(700\) | −1.59885 | −0.0604307 | ||||||||
\(701\) | 33.9656 | 1.28286 | 0.641431 | − | 0.767181i | \(-0.278341\pi\) | ||||
0.641431 | + | 0.767181i | \(0.278341\pi\) | |||||||
\(702\) | −71.2180 | −2.68795 | ||||||||
\(703\) | 47.3001 | 1.78396 | ||||||||
\(704\) | 19.3585 | 0.729602 | ||||||||
\(705\) | −5.65691 | −0.213052 | ||||||||
\(706\) | −1.01994 | −0.0383858 | ||||||||
\(707\) | 9.76565 | 0.367275 | ||||||||
\(708\) | −14.8851 | −0.559418 | ||||||||
\(709\) | 31.9062 | 1.19826 | 0.599131 | − | 0.800651i | \(-0.295513\pi\) | ||||
0.599131 | + | 0.800651i | \(0.295513\pi\) | |||||||
\(710\) | −9.56414 | −0.358936 | ||||||||
\(711\) | −4.18767 | −0.157050 | ||||||||
\(712\) | −3.71495 | −0.139224 | ||||||||
\(713\) | −8.67290 | −0.324803 | ||||||||
\(714\) | −9.18755 | −0.343835 | ||||||||
\(715\) | −28.5240 | −1.06674 | ||||||||
\(716\) | −12.2131 | −0.456425 | ||||||||
\(717\) | 32.1138 | 1.19931 | ||||||||
\(718\) | 10.4660 | 0.390586 | ||||||||
\(719\) | 29.6370 | 1.10527 | 0.552637 | − | 0.833422i | \(-0.313622\pi\) | ||||
0.552637 | + | 0.833422i | \(0.313622\pi\) | |||||||
\(720\) | 5.83689 | 0.217528 | ||||||||
\(721\) | 3.44731 | 0.128385 | ||||||||
\(722\) | −95.0752 | −3.53833 | ||||||||
\(723\) | −4.83347 | −0.179759 | ||||||||
\(724\) | −39.0106 | −1.44982 | ||||||||
\(725\) | 2.61057 | 0.0969541 | ||||||||
\(726\) | 18.1149 | 0.672308 | ||||||||
\(727\) | 13.4931 | 0.500432 | 0.250216 | − | 0.968190i | \(-0.419498\pi\) | ||||
0.250216 | + | 0.968190i | \(0.419498\pi\) | |||||||
\(728\) | −5.08348 | −0.188406 | ||||||||
\(729\) | 26.8403 | 0.994087 | ||||||||
\(730\) | 21.8707 | 0.809472 | ||||||||
\(731\) | −45.0857 | −1.66756 | ||||||||
\(732\) | −4.85735 | −0.179533 | ||||||||
\(733\) | 8.21393 | 0.303388 | 0.151694 | − | 0.988427i | \(-0.451527\pi\) | ||||
0.151694 | + | 0.988427i | \(0.451527\pi\) | |||||||
\(734\) | −15.0054 | −0.553858 | ||||||||
\(735\) | −1.32001 | −0.0486893 | ||||||||
\(736\) | 32.5287 | 1.19902 | ||||||||
\(737\) | −12.2247 | −0.450302 | ||||||||
\(738\) | 19.8937 | 0.732298 | ||||||||
\(739\) | 49.6286 | 1.82562 | 0.912809 | − | 0.408387i | \(-0.133908\pi\) | ||||
0.912809 | + | 0.408387i | \(0.133908\pi\) | |||||||
\(740\) | −9.09654 | −0.334396 | ||||||||
\(741\) | 73.3058 | 2.69296 | ||||||||
\(742\) | −0.901801 | −0.0331062 | ||||||||
\(743\) | 50.2872 | 1.84486 | 0.922429 | − | 0.386167i | \(-0.126201\pi\) | ||||
0.922429 | + | 0.386167i | \(0.126201\pi\) | |||||||
\(744\) | 1.95063 | 0.0715136 | ||||||||
\(745\) | −18.2824 | −0.669815 | ||||||||
\(746\) | −22.8047 | −0.834940 | ||||||||
\(747\) | 19.7774 | 0.723619 | ||||||||
\(748\) | −25.0489 | −0.915878 | ||||||||
\(749\) | 15.1976 | 0.555307 | ||||||||
\(750\) | 2.50414 | 0.0914383 | ||||||||
\(751\) | 44.8289 | 1.63583 | 0.817915 | − | 0.575339i | \(-0.195130\pi\) | ||||
0.817915 | + | 0.575339i | \(0.195130\pi\) | |||||||
\(752\) | −19.8907 | −0.725339 | ||||||||
\(753\) | 30.9756 | 1.12881 | ||||||||
\(754\) | −33.0816 | −1.20476 | ||||||||
\(755\) | 8.96584 | 0.326300 | ||||||||
\(756\) | −8.98558 | −0.326802 | ||||||||
\(757\) | 5.50860 | 0.200213 | 0.100107 | − | 0.994977i | \(-0.468082\pi\) | ||||
0.100107 | + | 0.994977i | \(0.468082\pi\) | |||||||
\(758\) | −60.6752 | −2.20382 | ||||||||
\(759\) | 25.1754 | 0.913808 | ||||||||
\(760\) | −6.32681 | −0.229498 | ||||||||
\(761\) | 18.9523 | 0.687021 | 0.343510 | − | 0.939149i | \(-0.388384\pi\) | ||||
0.343510 | + | 0.939149i | \(0.388384\pi\) | |||||||
\(762\) | 42.1584 | 1.52724 | ||||||||
\(763\) | 2.44588 | 0.0885469 | ||||||||
\(764\) | 25.4625 | 0.921201 | ||||||||
\(765\) | −4.61397 | −0.166819 | ||||||||
\(766\) | 22.5584 | 0.815068 | ||||||||
\(767\) | 47.1128 | 1.70114 | ||||||||
\(768\) | −26.9073 | −0.970932 | ||||||||
\(769\) | 17.3677 | 0.626296 | 0.313148 | − | 0.949704i | \(-0.398616\pi\) | ||||
0.313148 | + | 0.949704i | \(0.398616\pi\) | |||||||
\(770\) | −8.10070 | −0.291929 | ||||||||
\(771\) | −40.1123 | −1.44461 | ||||||||
\(772\) | −4.94030 | −0.177805 | ||||||||
\(773\) | −45.9153 | −1.65146 | −0.825729 | − | 0.564066i | \(-0.809236\pi\) | ||||
−0.825729 | + | 0.564066i | \(0.809236\pi\) | |||||||
\(774\) | −29.3166 | −1.05376 | ||||||||
\(775\) | −1.94181 | −0.0697518 | ||||||||
\(776\) | 8.70906 | 0.312637 | ||||||||
\(777\) | −7.51011 | −0.269424 | ||||||||
\(778\) | 24.4280 | 0.875785 | ||||||||
\(779\) | −69.3254 | −2.48384 | ||||||||
\(780\) | −14.0978 | −0.504784 | ||||||||
\(781\) | −21.5281 | −0.770335 | ||||||||
\(782\) | −31.0871 | −1.11167 | ||||||||
\(783\) | 14.6715 | 0.524317 | ||||||||
\(784\) | −4.64138 | −0.165764 | ||||||||
\(785\) | 11.3997 | 0.406874 | ||||||||
\(786\) | −6.09977 | −0.217572 | ||||||||
\(787\) | −30.1502 | −1.07474 | −0.537370 | − | 0.843347i | \(-0.680582\pi\) | ||||
−0.537370 | + | 0.843347i | \(0.680582\pi\) | |||||||
\(788\) | 38.6815 | 1.37797 | ||||||||
\(789\) | 8.79176 | 0.312995 | ||||||||
\(790\) | −6.31713 | −0.224753 | ||||||||
\(791\) | −16.7433 | −0.595323 | ||||||||
\(792\) | 4.08665 | 0.145213 | ||||||||
\(793\) | 15.3739 | 0.545944 | ||||||||
\(794\) | 13.5486 | 0.480821 | ||||||||
\(795\) | 0.627489 | 0.0222547 | ||||||||
\(796\) | −16.4274 | −0.582255 | ||||||||
\(797\) | −9.03981 | −0.320206 | −0.160103 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160103 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(798\) | 20.8186 | 0.736970 | ||||||||
\(799\) | 15.7233 | 0.556250 | ||||||||
\(800\) | 7.28297 | 0.257492 | ||||||||
\(801\) | 6.13897 | 0.216910 | ||||||||
\(802\) | −69.5224 | −2.45492 | ||||||||
\(803\) | 49.2292 | 1.73726 | ||||||||
\(804\) | −6.04200 | −0.213085 | ||||||||
\(805\) | −4.46641 | −0.157420 | ||||||||
\(806\) | 24.6069 | 0.866741 | ||||||||
\(807\) | −16.8733 | −0.593970 | ||||||||
\(808\) | −7.43179 | −0.261449 | ||||||||
\(809\) | 32.6004 | 1.14617 | 0.573084 | − | 0.819497i | \(-0.305747\pi\) | ||||
0.573084 | + | 0.819497i | \(0.305747\pi\) | |||||||
\(810\) | 6.91626 | 0.243013 | ||||||||
\(811\) | 2.53557 | 0.0890357 | 0.0445179 | − | 0.999009i | \(-0.485825\pi\) | ||||
0.0445179 | + | 0.999009i | \(0.485825\pi\) | |||||||
\(812\) | −4.17390 | −0.146475 | ||||||||
\(813\) | −38.2855 | −1.34273 | ||||||||
\(814\) | −46.0885 | −1.61540 | ||||||||
\(815\) | 22.6807 | 0.794472 | ||||||||
\(816\) | 22.4784 | 0.786901 | ||||||||
\(817\) | 102.162 | 3.57421 | ||||||||
\(818\) | 21.2732 | 0.743801 | ||||||||
\(819\) | 8.40046 | 0.293536 | ||||||||
\(820\) | 13.3323 | 0.465586 | ||||||||
\(821\) | 23.7993 | 0.830600 | 0.415300 | − | 0.909685i | \(-0.363677\pi\) | ||||
0.415300 | + | 0.909685i | \(0.363677\pi\) | |||||||
\(822\) | 34.2163 | 1.19343 | ||||||||
\(823\) | 17.9706 | 0.626417 | 0.313209 | − | 0.949684i | \(-0.398596\pi\) | ||||
0.313209 | + | 0.949684i | \(0.398596\pi\) | |||||||
\(824\) | −2.62345 | −0.0913922 | ||||||||
\(825\) | 5.63661 | 0.196241 | ||||||||
\(826\) | 13.3798 | 0.465544 | ||||||||
\(827\) | 34.2727 | 1.19178 | 0.595889 | − | 0.803067i | \(-0.296800\pi\) | ||||
0.595889 | + | 0.803067i | \(0.296800\pi\) | |||||||
\(828\) | −8.98047 | −0.312093 | ||||||||
\(829\) | −24.1607 | −0.839134 | −0.419567 | − | 0.907724i | \(-0.637818\pi\) | ||||
−0.419567 | + | 0.907724i | \(0.637818\pi\) | |||||||
\(830\) | 29.8344 | 1.03557 | ||||||||
\(831\) | −17.8403 | −0.618874 | ||||||||
\(832\) | −30.2831 | −1.04988 | ||||||||
\(833\) | 3.66894 | 0.127121 | ||||||||
\(834\) | 23.1457 | 0.801472 | ||||||||
\(835\) | −17.3959 | −0.602010 | ||||||||
\(836\) | 56.7597 | 1.96308 | ||||||||
\(837\) | −10.9130 | −0.377210 | ||||||||
\(838\) | −21.5744 | −0.745276 | ||||||||
\(839\) | 21.1655 | 0.730714 | 0.365357 | − | 0.930867i | \(-0.380947\pi\) | ||||
0.365357 | + | 0.930867i | \(0.380947\pi\) | |||||||
\(840\) | 1.00454 | 0.0346601 | ||||||||
\(841\) | −22.1849 | −0.764997 | ||||||||
\(842\) | 59.3090 | 2.04392 | ||||||||
\(843\) | 30.2590 | 1.04218 | ||||||||
\(844\) | −7.47552 | −0.257318 | ||||||||
\(845\) | 31.6209 | 1.08779 | ||||||||
\(846\) | 10.2239 | 0.351506 | ||||||||
\(847\) | −7.23400 | −0.248563 | ||||||||
\(848\) | 2.20636 | 0.0757667 | ||||||||
\(849\) | 24.3072 | 0.834221 | ||||||||
\(850\) | −6.96021 | −0.238733 | ||||||||
\(851\) | −25.4114 | −0.871090 | ||||||||
\(852\) | −10.6401 | −0.364526 | ||||||||
\(853\) | 34.2244 | 1.17182 | 0.585911 | − | 0.810375i | \(-0.300737\pi\) | ||||
0.585911 | + | 0.810375i | \(0.300737\pi\) | |||||||
\(854\) | 4.36614 | 0.149406 | ||||||||
\(855\) | 10.4551 | 0.357556 | ||||||||
\(856\) | −11.5656 | −0.395303 | ||||||||
\(857\) | −2.56529 | −0.0876287 | −0.0438144 | − | 0.999040i | \(-0.513951\pi\) | ||||
−0.0438144 | + | 0.999040i | \(0.513951\pi\) | |||||||
\(858\) | −71.4280 | −2.43851 | ||||||||
\(859\) | 54.2604 | 1.85134 | 0.925670 | − | 0.378331i | \(-0.123502\pi\) | ||||
0.925670 | + | 0.378331i | \(0.123502\pi\) | |||||||
\(860\) | −19.6474 | −0.669971 | ||||||||
\(861\) | 11.0072 | 0.375124 | ||||||||
\(862\) | −71.2113 | −2.42547 | ||||||||
\(863\) | −19.5129 | −0.664227 | −0.332113 | − | 0.943239i | \(-0.607762\pi\) | ||||
−0.332113 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(864\) | 40.9306 | 1.39249 | ||||||||
\(865\) | −20.2634 | −0.688976 | ||||||||
\(866\) | −14.9297 | −0.507332 | ||||||||
\(867\) | 4.67133 | 0.158647 | ||||||||
\(868\) | 3.10465 | 0.105379 | ||||||||
\(869\) | −14.2193 | −0.482357 | ||||||||
\(870\) | 6.53723 | 0.221633 | ||||||||
\(871\) | 19.1234 | 0.647973 | ||||||||
\(872\) | −1.86135 | −0.0630332 | ||||||||
\(873\) | −14.3917 | −0.487087 | ||||||||
\(874\) | 70.4421 | 2.38274 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 24.3313 | 0.822078 | ||||||||
\(877\) | −6.73691 | −0.227489 | −0.113745 | − | 0.993510i | \(-0.536285\pi\) | ||||
−0.113745 | + | 0.993510i | \(0.536285\pi\) | |||||||
\(878\) | −50.6119 | −1.70807 | ||||||||
\(879\) | 35.1227 | 1.18466 | ||||||||
\(880\) | 19.8193 | 0.668108 | ||||||||
\(881\) | −29.0828 | −0.979824 | −0.489912 | − | 0.871772i | \(-0.662971\pi\) | ||||
−0.489912 | + | 0.871772i | \(0.662971\pi\) | |||||||
\(882\) | 2.38570 | 0.0803307 | ||||||||
\(883\) | 12.7617 | 0.429465 | 0.214733 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214733 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(884\) | 39.1847 | 1.31792 | ||||||||
\(885\) | −9.30993 | −0.312950 | ||||||||
\(886\) | −32.9039 | −1.10543 | ||||||||
\(887\) | −1.05298 | −0.0353554 | −0.0176777 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176777 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(888\) | 5.71530 | 0.191793 | ||||||||
\(889\) | −16.8355 | −0.564643 | ||||||||
\(890\) | 9.26068 | 0.310419 | ||||||||
\(891\) | 15.5679 | 0.521545 | ||||||||
\(892\) | −3.38867 | −0.113461 | ||||||||
\(893\) | −35.6283 | −1.19226 | ||||||||
\(894\) | −45.7817 | −1.53117 | ||||||||
\(895\) | −7.63870 | −0.255334 | ||||||||
\(896\) | 5.96564 | 0.199298 | ||||||||
\(897\) | −39.3826 | −1.31495 | ||||||||
\(898\) | 77.7678 | 2.59514 | ||||||||
\(899\) | −5.06922 | −0.169068 | ||||||||
\(900\) | −2.01067 | −0.0670224 | ||||||||
\(901\) | −1.74409 | −0.0581042 | ||||||||
\(902\) | 67.5495 | 2.24915 | ||||||||
\(903\) | −16.2209 | −0.539798 | ||||||||
\(904\) | 12.7419 | 0.423788 | ||||||||
\(905\) | −24.3992 | −0.811057 | ||||||||
\(906\) | 22.4517 | 0.745909 | ||||||||
\(907\) | −8.79195 | −0.291932 | −0.145966 | − | 0.989290i | \(-0.546629\pi\) | ||||
−0.145966 | + | 0.989290i | \(0.546629\pi\) | |||||||
\(908\) | 31.5064 | 1.04558 | ||||||||
\(909\) | 12.2811 | 0.407337 | ||||||||
\(910\) | 12.6722 | 0.420078 | ||||||||
\(911\) | −42.7355 | −1.41589 | −0.707944 | − | 0.706268i | \(-0.750377\pi\) | ||||
−0.707944 | + | 0.706268i | \(0.750377\pi\) | |||||||
\(912\) | −50.9351 | −1.68663 | ||||||||
\(913\) | 67.1548 | 2.22250 | ||||||||
\(914\) | 43.2707 | 1.43127 | ||||||||
\(915\) | −3.03803 | −0.100434 | ||||||||
\(916\) | −1.59885 | −0.0528274 | ||||||||
\(917\) | 2.43588 | 0.0804397 | ||||||||
\(918\) | −39.1167 | −1.29104 | ||||||||
\(919\) | −36.6966 | −1.21051 | −0.605254 | − | 0.796032i | \(-0.706929\pi\) | ||||
−0.605254 | + | 0.796032i | \(0.706929\pi\) | |||||||
\(920\) | 3.39899 | 0.112062 | ||||||||
\(921\) | 26.2525 | 0.865049 | ||||||||
\(922\) | −27.3260 | −0.899933 | ||||||||
\(923\) | 33.6770 | 1.10849 | ||||||||
\(924\) | −9.01207 | −0.296475 | ||||||||
\(925\) | −5.68944 | −0.187068 | ||||||||
\(926\) | −73.9516 | −2.43020 | ||||||||
\(927\) | 4.33526 | 0.142389 | ||||||||
\(928\) | 19.0127 | 0.624122 | ||||||||
\(929\) | −5.26699 | −0.172804 | −0.0864022 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864022 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(930\) | −4.86256 | −0.159450 | ||||||||
\(931\) | −8.31367 | −0.272469 | ||||||||
\(932\) | −25.9382 | −0.849636 | ||||||||
\(933\) | 23.6478 | 0.774195 | ||||||||
\(934\) | 0.235361 | 0.00770124 | ||||||||
\(935\) | −15.6669 | −0.512361 | ||||||||
\(936\) | −6.39286 | −0.208957 | ||||||||
\(937\) | −48.1241 | −1.57214 | −0.786072 | − | 0.618135i | \(-0.787889\pi\) | ||||
−0.786072 | + | 0.618135i | \(0.787889\pi\) | |||||||
\(938\) | 5.43098 | 0.177328 | ||||||||
\(939\) | −16.6332 | −0.542805 | ||||||||
\(940\) | 6.85187 | 0.223483 | ||||||||
\(941\) | 12.7062 | 0.414211 | 0.207106 | − | 0.978319i | \(-0.433596\pi\) | ||||
0.207106 | + | 0.978319i | \(0.433596\pi\) | |||||||
\(942\) | 28.5465 | 0.930096 | ||||||||
\(943\) | 37.2441 | 1.21284 | ||||||||
\(944\) | −32.7353 | −1.06544 | ||||||||
\(945\) | −5.62004 | −0.182820 | ||||||||
\(946\) | −99.5453 | −3.23650 | ||||||||
\(947\) | −11.6901 | −0.379878 | −0.189939 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189939 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(948\) | −7.02784 | −0.228253 | ||||||||
\(949\) | −77.0106 | −2.49987 | ||||||||
\(950\) | 15.7715 | 0.511697 | ||||||||
\(951\) | 0.539361 | 0.0174900 | ||||||||
\(952\) | −2.79211 | −0.0904929 | ||||||||
\(953\) | −45.9722 | −1.48918 | −0.744592 | − | 0.667520i | \(-0.767356\pi\) | ||||
−0.744592 | + | 0.667520i | \(0.767356\pi\) | |||||||
\(954\) | −1.13408 | −0.0367173 | ||||||||
\(955\) | 15.9255 | 0.515338 | ||||||||
\(956\) | −38.8975 | −1.25804 | ||||||||
\(957\) | 14.7148 | 0.475661 | ||||||||
\(958\) | −45.5597 | −1.47197 | ||||||||
\(959\) | −13.6639 | −0.441230 | ||||||||
\(960\) | 5.98423 | 0.193140 | ||||||||
\(961\) | −27.2294 | −0.878367 | ||||||||
\(962\) | 72.0975 | 2.32452 | ||||||||
\(963\) | 19.1121 | 0.615879 | ||||||||
\(964\) | 5.85448 | 0.188560 | ||||||||
\(965\) | −3.08991 | −0.0994678 | ||||||||
\(966\) | −11.1845 | −0.359856 | ||||||||
\(967\) | 28.7114 | 0.923296 | 0.461648 | − | 0.887063i | \(-0.347258\pi\) | ||||
0.461648 | + | 0.887063i | \(0.347258\pi\) | |||||||
\(968\) | 5.50517 | 0.176943 | ||||||||
\(969\) | 40.2634 | 1.29345 | ||||||||
\(970\) | −21.7101 | −0.697068 | ||||||||
\(971\) | 18.0656 | 0.579752 | 0.289876 | − | 0.957064i | \(-0.406386\pi\) | ||||
0.289876 | + | 0.957064i | \(0.406386\pi\) | |||||||
\(972\) | −19.2624 | −0.617841 | ||||||||
\(973\) | −9.24299 | −0.296317 | ||||||||
\(974\) | 56.4397 | 1.80844 | ||||||||
\(975\) | −8.81751 | −0.282386 | ||||||||
\(976\) | −10.6823 | −0.341931 | ||||||||
\(977\) | 17.6273 | 0.563947 | 0.281974 | − | 0.959422i | \(-0.409011\pi\) | ||||
0.281974 | + | 0.959422i | \(0.409011\pi\) | |||||||
\(978\) | 56.7958 | 1.81613 | ||||||||
\(979\) | 20.8450 | 0.666210 | ||||||||
\(980\) | 1.59885 | 0.0510733 | ||||||||
\(981\) | 3.07588 | 0.0982054 | ||||||||
\(982\) | 48.7451 | 1.55552 | ||||||||
\(983\) | 12.8787 | 0.410767 | 0.205383 | − | 0.978682i | \(-0.434156\pi\) | ||||
0.205383 | + | 0.978682i | \(0.434156\pi\) | |||||||
\(984\) | −8.37662 | −0.267037 | ||||||||
\(985\) | 24.1934 | 0.770866 | ||||||||
\(986\) | −18.1701 | −0.578655 | ||||||||
\(987\) | 5.65691 | 0.180061 | ||||||||
\(988\) | −88.7909 | −2.82481 | ||||||||
\(989\) | −54.8853 | −1.74525 | ||||||||
\(990\) | −10.1872 | −0.323772 | ||||||||
\(991\) | −32.8525 | −1.04359 | −0.521797 | − | 0.853070i | \(-0.674738\pi\) | ||||
−0.521797 | + | 0.853070i | \(0.674738\pi\) | |||||||
\(992\) | −14.1421 | −0.449013 | ||||||||
\(993\) | 23.8002 | 0.755276 | ||||||||
\(994\) | 9.56414 | 0.303356 | ||||||||
\(995\) | −10.2745 | −0.325725 | ||||||||
\(996\) | 33.1910 | 1.05170 | ||||||||
\(997\) | 33.3491 | 1.05618 | 0.528088 | − | 0.849190i | \(-0.322909\pi\) | ||||
0.528088 | + | 0.849190i | \(0.322909\pi\) | |||||||
\(998\) | 72.5581 | 2.29679 | ||||||||
\(999\) | −31.9749 | −1.01164 |
(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 | 8015.2.a.m.1.12 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.12 | ✓ | 67 | 1.1 | even | 1 | trivial |