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: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 | ||||||||
\(3\) | −2.64782 | −1.52872 | −0.764359 | − | 0.644790i | \(-0.776945\pi\) | ||||
−0.764359 | + | 0.644790i | \(0.776945\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.675974 | −0.302305 | −0.151152 | − | 0.988510i | \(-0.548298\pi\) | ||||
−0.151152 | + | 0.988510i | \(0.548298\pi\) | |||||||
\(6\) | −2.64782 | −1.08097 | ||||||||
\(7\) | −0.999289 | −0.377696 | −0.188848 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188848 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.01094 | 1.33698 | ||||||||
\(10\) | −0.675974 | −0.213762 | ||||||||
\(11\) | −1.77569 | −0.535391 | −0.267695 | − | 0.963504i | \(-0.586262\pi\) | ||||
−0.267695 | + | 0.963504i | \(0.586262\pi\) | |||||||
\(12\) | −2.64782 | −0.764359 | ||||||||
\(13\) | 1.00412 | 0.278492 | 0.139246 | − | 0.990258i | \(-0.455532\pi\) | ||||
0.139246 | + | 0.990258i | \(0.455532\pi\) | |||||||
\(14\) | −0.999289 | −0.267071 | ||||||||
\(15\) | 1.78986 | 0.462139 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.24084 | −0.786019 | −0.393009 | − | 0.919534i | \(-0.628566\pi\) | ||||
−0.393009 | + | 0.919534i | \(0.628566\pi\) | |||||||
\(18\) | 4.01094 | 0.945389 | ||||||||
\(19\) | −3.17784 | −0.729047 | −0.364523 | − | 0.931194i | \(-0.618768\pi\) | ||||
−0.364523 | + | 0.931194i | \(0.618768\pi\) | |||||||
\(20\) | −0.675974 | −0.151152 | ||||||||
\(21\) | 2.64594 | 0.577391 | ||||||||
\(22\) | −1.77569 | −0.378578 | ||||||||
\(23\) | 8.40714 | 1.75301 | 0.876505 | − | 0.481392i | \(-0.159869\pi\) | ||||
0.876505 | + | 0.481392i | \(0.159869\pi\) | |||||||
\(24\) | −2.64782 | −0.540484 | ||||||||
\(25\) | −4.54306 | −0.908612 | ||||||||
\(26\) | 1.00412 | 0.196924 | ||||||||
\(27\) | −2.67680 | −0.515150 | ||||||||
\(28\) | −0.999289 | −0.188848 | ||||||||
\(29\) | 4.15832 | 0.772181 | 0.386090 | − | 0.922461i | \(-0.373825\pi\) | ||||
0.386090 | + | 0.922461i | \(0.373825\pi\) | |||||||
\(30\) | 1.78986 | 0.326782 | ||||||||
\(31\) | −2.23231 | −0.400934 | −0.200467 | − | 0.979700i | \(-0.564246\pi\) | ||||
−0.200467 | + | 0.979700i | \(0.564246\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.70171 | 0.818462 | ||||||||
\(34\) | −3.24084 | −0.555799 | ||||||||
\(35\) | 0.675494 | 0.114179 | ||||||||
\(36\) | 4.01094 | 0.668491 | ||||||||
\(37\) | 1.52693 | 0.251026 | 0.125513 | − | 0.992092i | \(-0.459942\pi\) | ||||
0.125513 | + | 0.992092i | \(0.459942\pi\) | |||||||
\(38\) | −3.17784 | −0.515514 | ||||||||
\(39\) | −2.65872 | −0.425737 | ||||||||
\(40\) | −0.675974 | −0.106881 | ||||||||
\(41\) | 7.13965 | 1.11503 | 0.557513 | − | 0.830168i | \(-0.311756\pi\) | ||||
0.557513 | + | 0.830168i | \(0.311756\pi\) | |||||||
\(42\) | 2.64594 | 0.408277 | ||||||||
\(43\) | 2.77622 | 0.423369 | 0.211685 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211685 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(44\) | −1.77569 | −0.267695 | ||||||||
\(45\) | −2.71130 | −0.404176 | ||||||||
\(46\) | 8.40714 | 1.23957 | ||||||||
\(47\) | 11.0813 | 1.61638 | 0.808189 | − | 0.588923i | \(-0.200448\pi\) | ||||
0.808189 | + | 0.588923i | \(0.200448\pi\) | |||||||
\(48\) | −2.64782 | −0.382180 | ||||||||
\(49\) | −6.00142 | −0.857346 | ||||||||
\(50\) | −4.54306 | −0.642486 | ||||||||
\(51\) | 8.58115 | 1.20160 | ||||||||
\(52\) | 1.00412 | 0.139246 | ||||||||
\(53\) | −8.39649 | −1.15335 | −0.576673 | − | 0.816975i | \(-0.695649\pi\) | ||||
−0.576673 | + | 0.816975i | \(0.695649\pi\) | |||||||
\(54\) | −2.67680 | −0.364266 | ||||||||
\(55\) | 1.20032 | 0.161851 | ||||||||
\(56\) | −0.999289 | −0.133536 | ||||||||
\(57\) | 8.41435 | 1.11451 | ||||||||
\(58\) | 4.15832 | 0.546014 | ||||||||
\(59\) | −3.93445 | −0.512222 | −0.256111 | − | 0.966647i | \(-0.582441\pi\) | ||||
−0.256111 | + | 0.966647i | \(0.582441\pi\) | |||||||
\(60\) | 1.78986 | 0.231070 | ||||||||
\(61\) | −1.97459 | −0.252821 | −0.126410 | − | 0.991978i | \(-0.540346\pi\) | ||||
−0.126410 | + | 0.991978i | \(0.540346\pi\) | |||||||
\(62\) | −2.23231 | −0.283503 | ||||||||
\(63\) | −4.00809 | −0.504972 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.678759 | −0.0841896 | ||||||||
\(66\) | 4.70171 | 0.578740 | ||||||||
\(67\) | −11.2348 | −1.37256 | −0.686278 | − | 0.727340i | \(-0.740757\pi\) | ||||
−0.686278 | + | 0.727340i | \(0.740757\pi\) | |||||||
\(68\) | −3.24084 | −0.393009 | ||||||||
\(69\) | −22.2606 | −2.67986 | ||||||||
\(70\) | 0.675494 | 0.0807370 | ||||||||
\(71\) | 0.753276 | 0.0893974 | 0.0446987 | − | 0.999001i | \(-0.485767\pi\) | ||||
0.0446987 | + | 0.999001i | \(0.485767\pi\) | |||||||
\(72\) | 4.01094 | 0.472694 | ||||||||
\(73\) | 0.958508 | 0.112185 | 0.0560925 | − | 0.998426i | \(-0.482136\pi\) | ||||
0.0560925 | + | 0.998426i | \(0.482136\pi\) | |||||||
\(74\) | 1.52693 | 0.177502 | ||||||||
\(75\) | 12.0292 | 1.38901 | ||||||||
\(76\) | −3.17784 | −0.364523 | ||||||||
\(77\) | 1.77443 | 0.202215 | ||||||||
\(78\) | −2.65872 | −0.301041 | ||||||||
\(79\) | 8.32703 | 0.936864 | 0.468432 | − | 0.883500i | \(-0.344819\pi\) | ||||
0.468432 | + | 0.883500i | \(0.344819\pi\) | |||||||
\(80\) | −0.675974 | −0.0755762 | ||||||||
\(81\) | −4.94516 | −0.549462 | ||||||||
\(82\) | 7.13965 | 0.788442 | ||||||||
\(83\) | 12.0952 | 1.32762 | 0.663811 | − | 0.747900i | \(-0.268938\pi\) | ||||
0.663811 | + | 0.747900i | \(0.268938\pi\) | |||||||
\(84\) | 2.64594 | 0.288695 | ||||||||
\(85\) | 2.19072 | 0.237617 | ||||||||
\(86\) | 2.77622 | 0.299367 | ||||||||
\(87\) | −11.0105 | −1.18045 | ||||||||
\(88\) | −1.77569 | −0.189289 | ||||||||
\(89\) | 0.663771 | 0.0703596 | 0.0351798 | − | 0.999381i | \(-0.488800\pi\) | ||||
0.0351798 | + | 0.999381i | \(0.488800\pi\) | |||||||
\(90\) | −2.71130 | −0.285796 | ||||||||
\(91\) | −1.00341 | −0.105185 | ||||||||
\(92\) | 8.40714 | 0.876505 | ||||||||
\(93\) | 5.91074 | 0.612916 | ||||||||
\(94\) | 11.0813 | 1.14295 | ||||||||
\(95\) | 2.14814 | 0.220394 | ||||||||
\(96\) | −2.64782 | −0.270242 | ||||||||
\(97\) | 12.5368 | 1.27292 | 0.636458 | − | 0.771311i | \(-0.280399\pi\) | ||||
0.636458 | + | 0.771311i | \(0.280399\pi\) | |||||||
\(98\) | −6.00142 | −0.606235 | ||||||||
\(99\) | −7.12219 | −0.715807 | ||||||||
\(100\) | −4.54306 | −0.454306 | ||||||||
\(101\) | −0.820120 | −0.0816050 | −0.0408025 | − | 0.999167i | \(-0.512991\pi\) | ||||
−0.0408025 | + | 0.999167i | \(0.512991\pi\) | |||||||
\(102\) | 8.58115 | 0.849661 | ||||||||
\(103\) | −19.6474 | −1.93591 | −0.967956 | − | 0.251122i | \(-0.919201\pi\) | ||||
−0.967956 | + | 0.251122i | \(0.919201\pi\) | |||||||
\(104\) | 1.00412 | 0.0984619 | ||||||||
\(105\) | −1.78859 | −0.174548 | ||||||||
\(106\) | −8.39649 | −0.815539 | ||||||||
\(107\) | 2.18068 | 0.210814 | 0.105407 | − | 0.994429i | \(-0.466385\pi\) | ||||
0.105407 | + | 0.994429i | \(0.466385\pi\) | |||||||
\(108\) | −2.67680 | −0.257575 | ||||||||
\(109\) | 0.957011 | 0.0916651 | 0.0458325 | − | 0.998949i | \(-0.485406\pi\) | ||||
0.0458325 | + | 0.998949i | \(0.485406\pi\) | |||||||
\(110\) | 1.20032 | 0.114446 | ||||||||
\(111\) | −4.04303 | −0.383747 | ||||||||
\(112\) | −0.999289 | −0.0944240 | ||||||||
\(113\) | −15.6071 | −1.46819 | −0.734096 | − | 0.679046i | \(-0.762394\pi\) | ||||
−0.734096 | + | 0.679046i | \(0.762394\pi\) | |||||||
\(114\) | 8.41435 | 0.788076 | ||||||||
\(115\) | −5.68301 | −0.529944 | ||||||||
\(116\) | 4.15832 | 0.386090 | ||||||||
\(117\) | 4.02746 | 0.372339 | ||||||||
\(118\) | −3.93445 | −0.362195 | ||||||||
\(119\) | 3.23854 | 0.296876 | ||||||||
\(120\) | 1.78986 | 0.163391 | ||||||||
\(121\) | −7.84692 | −0.713357 | ||||||||
\(122\) | −1.97459 | −0.178771 | ||||||||
\(123\) | −18.9045 | −1.70456 | ||||||||
\(124\) | −2.23231 | −0.200467 | ||||||||
\(125\) | 6.45086 | 0.576983 | ||||||||
\(126\) | −4.00809 | −0.357069 | ||||||||
\(127\) | 11.2992 | 1.00264 | 0.501322 | − | 0.865261i | \(-0.332847\pi\) | ||||
0.501322 | + | 0.865261i | \(0.332847\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.35092 | −0.647213 | ||||||||
\(130\) | −0.678759 | −0.0595311 | ||||||||
\(131\) | −5.39567 | −0.471422 | −0.235711 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235711 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(132\) | 4.70171 | 0.409231 | ||||||||
\(133\) | 3.17558 | 0.275358 | ||||||||
\(134\) | −11.2348 | −0.970543 | ||||||||
\(135\) | 1.80945 | 0.155732 | ||||||||
\(136\) | −3.24084 | −0.277900 | ||||||||
\(137\) | 22.0525 | 1.88407 | 0.942036 | − | 0.335511i | \(-0.108909\pi\) | ||||
0.942036 | + | 0.335511i | \(0.108909\pi\) | |||||||
\(138\) | −22.2606 | −1.89495 | ||||||||
\(139\) | 5.75164 | 0.487848 | 0.243924 | − | 0.969794i | \(-0.421565\pi\) | ||||
0.243924 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(140\) | 0.675494 | 0.0570897 | ||||||||
\(141\) | −29.3414 | −2.47099 | ||||||||
\(142\) | 0.753276 | 0.0632135 | ||||||||
\(143\) | −1.78300 | −0.149102 | ||||||||
\(144\) | 4.01094 | 0.334245 | ||||||||
\(145\) | −2.81092 | −0.233434 | ||||||||
\(146\) | 0.958508 | 0.0793267 | ||||||||
\(147\) | 15.8907 | 1.31064 | ||||||||
\(148\) | 1.52693 | 0.125513 | ||||||||
\(149\) | 8.06859 | 0.661005 | 0.330502 | − | 0.943805i | \(-0.392782\pi\) | ||||
0.330502 | + | 0.943805i | \(0.392782\pi\) | |||||||
\(150\) | 12.0292 | 0.982180 | ||||||||
\(151\) | −0.119283 | −0.00970714 | −0.00485357 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485357 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(152\) | −3.17784 | −0.257757 | ||||||||
\(153\) | −12.9988 | −1.05089 | ||||||||
\(154\) | 1.77443 | 0.142988 | ||||||||
\(155\) | 1.50898 | 0.121204 | ||||||||
\(156\) | −2.65872 | −0.212868 | ||||||||
\(157\) | −10.7447 | −0.857520 | −0.428760 | − | 0.903418i | \(-0.641049\pi\) | ||||
−0.428760 | + | 0.903418i | \(0.641049\pi\) | |||||||
\(158\) | 8.32703 | 0.662463 | ||||||||
\(159\) | 22.2324 | 1.76314 | ||||||||
\(160\) | −0.675974 | −0.0534405 | ||||||||
\(161\) | −8.40117 | −0.662105 | ||||||||
\(162\) | −4.94516 | −0.388528 | ||||||||
\(163\) | 2.11664 | 0.165788 | 0.0828940 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828940 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(164\) | 7.13965 | 0.557513 | ||||||||
\(165\) | −3.17823 | −0.247425 | ||||||||
\(166\) | 12.0952 | 0.938771 | ||||||||
\(167\) | −22.9250 | −1.77399 | −0.886994 | − | 0.461780i | \(-0.847211\pi\) | ||||
−0.886994 | + | 0.461780i | \(0.847211\pi\) | |||||||
\(168\) | 2.64594 | 0.204139 | ||||||||
\(169\) | −11.9917 | −0.922442 | ||||||||
\(170\) | 2.19072 | 0.168021 | ||||||||
\(171\) | −12.7461 | −0.974722 | ||||||||
\(172\) | 2.77622 | 0.211685 | ||||||||
\(173\) | 18.6550 | 1.41831 | 0.709155 | − | 0.705052i | \(-0.249077\pi\) | ||||
0.709155 | + | 0.705052i | \(0.249077\pi\) | |||||||
\(174\) | −11.0105 | −0.834702 | ||||||||
\(175\) | 4.53983 | 0.343179 | ||||||||
\(176\) | −1.77569 | −0.133848 | ||||||||
\(177\) | 10.4177 | 0.783043 | ||||||||
\(178\) | 0.663771 | 0.0497517 | ||||||||
\(179\) | −10.4922 | −0.784221 | −0.392111 | − | 0.919918i | \(-0.628255\pi\) | ||||
−0.392111 | + | 0.919918i | \(0.628255\pi\) | |||||||
\(180\) | −2.71130 | −0.202088 | ||||||||
\(181\) | −18.9162 | −1.40603 | −0.703015 | − | 0.711175i | \(-0.748163\pi\) | ||||
−0.703015 | + | 0.711175i | \(0.748163\pi\) | |||||||
\(182\) | −1.00341 | −0.0743774 | ||||||||
\(183\) | 5.22837 | 0.386492 | ||||||||
\(184\) | 8.40714 | 0.619783 | ||||||||
\(185\) | −1.03216 | −0.0758862 | ||||||||
\(186\) | 5.91074 | 0.433397 | ||||||||
\(187\) | 5.75472 | 0.420827 | ||||||||
\(188\) | 11.0813 | 0.808189 | ||||||||
\(189\) | 2.67490 | 0.194570 | ||||||||
\(190\) | 2.14814 | 0.155842 | ||||||||
\(191\) | 3.11891 | 0.225677 | 0.112838 | − | 0.993613i | \(-0.464006\pi\) | ||||
0.112838 | + | 0.993613i | \(0.464006\pi\) | |||||||
\(192\) | −2.64782 | −0.191090 | ||||||||
\(193\) | 3.51877 | 0.253287 | 0.126643 | − | 0.991948i | \(-0.459580\pi\) | ||||
0.126643 | + | 0.991948i | \(0.459580\pi\) | |||||||
\(194\) | 12.5368 | 0.900088 | ||||||||
\(195\) | 1.79723 | 0.128702 | ||||||||
\(196\) | −6.00142 | −0.428673 | ||||||||
\(197\) | −18.2977 | −1.30365 | −0.651827 | − | 0.758368i | \(-0.725997\pi\) | ||||
−0.651827 | + | 0.758368i | \(0.725997\pi\) | |||||||
\(198\) | −7.12219 | −0.506152 | ||||||||
\(199\) | −6.62886 | −0.469908 | −0.234954 | − | 0.972007i | \(-0.575494\pi\) | ||||
−0.234954 | + | 0.972007i | \(0.575494\pi\) | |||||||
\(200\) | −4.54306 | −0.321243 | ||||||||
\(201\) | 29.7478 | 2.09825 | ||||||||
\(202\) | −0.820120 | −0.0577034 | ||||||||
\(203\) | −4.15536 | −0.291649 | ||||||||
\(204\) | 8.58115 | 0.600801 | ||||||||
\(205\) | −4.82622 | −0.337078 | ||||||||
\(206\) | −19.6474 | −1.36890 | ||||||||
\(207\) | 33.7206 | 2.34374 | ||||||||
\(208\) | 1.00412 | 0.0696231 | ||||||||
\(209\) | 5.64286 | 0.390325 | ||||||||
\(210\) | −1.78859 | −0.123424 | ||||||||
\(211\) | 11.7326 | 0.807703 | 0.403852 | − | 0.914825i | \(-0.367671\pi\) | ||||
0.403852 | + | 0.914825i | \(0.367671\pi\) | |||||||
\(212\) | −8.39649 | −0.576673 | ||||||||
\(213\) | −1.99454 | −0.136663 | ||||||||
\(214\) | 2.18068 | 0.149068 | ||||||||
\(215\) | −1.87665 | −0.127987 | ||||||||
\(216\) | −2.67680 | −0.182133 | ||||||||
\(217\) | 2.23072 | 0.151431 | ||||||||
\(218\) | 0.957011 | 0.0648170 | ||||||||
\(219\) | −2.53796 | −0.171499 | ||||||||
\(220\) | 1.20032 | 0.0809256 | ||||||||
\(221\) | −3.25419 | −0.218900 | ||||||||
\(222\) | −4.04303 | −0.271350 | ||||||||
\(223\) | −0.662036 | −0.0443332 | −0.0221666 | − | 0.999754i | \(-0.507056\pi\) | ||||
−0.0221666 | + | 0.999754i | \(0.507056\pi\) | |||||||
\(224\) | −0.999289 | −0.0667678 | ||||||||
\(225\) | −18.2220 | −1.21480 | ||||||||
\(226\) | −15.6071 | −1.03817 | ||||||||
\(227\) | 10.0944 | 0.669991 | 0.334996 | − | 0.942220i | \(-0.391265\pi\) | ||||
0.334996 | + | 0.942220i | \(0.391265\pi\) | |||||||
\(228\) | 8.41435 | 0.557254 | ||||||||
\(229\) | 7.12675 | 0.470949 | 0.235475 | − | 0.971881i | \(-0.424336\pi\) | ||||
0.235475 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(230\) | −5.68301 | −0.374727 | ||||||||
\(231\) | −4.69836 | −0.309130 | ||||||||
\(232\) | 4.15832 | 0.273007 | ||||||||
\(233\) | −3.11727 | −0.204219 | −0.102110 | − | 0.994773i | \(-0.532559\pi\) | ||||
−0.102110 | + | 0.994773i | \(0.532559\pi\) | |||||||
\(234\) | 4.02746 | 0.263284 | ||||||||
\(235\) | −7.49069 | −0.488639 | ||||||||
\(236\) | −3.93445 | −0.256111 | ||||||||
\(237\) | −22.0485 | −1.43220 | ||||||||
\(238\) | 3.23854 | 0.209923 | ||||||||
\(239\) | 15.8275 | 1.02380 | 0.511898 | − | 0.859046i | \(-0.328943\pi\) | ||||
0.511898 | + | 0.859046i | \(0.328943\pi\) | |||||||
\(240\) | 1.78986 | 0.115535 | ||||||||
\(241\) | −17.6675 | −1.13806 | −0.569032 | − | 0.822316i | \(-0.692682\pi\) | ||||
−0.569032 | + | 0.822316i | \(0.692682\pi\) | |||||||
\(242\) | −7.84692 | −0.504419 | ||||||||
\(243\) | 21.1243 | 1.35512 | ||||||||
\(244\) | −1.97459 | −0.126410 | ||||||||
\(245\) | 4.05681 | 0.259180 | ||||||||
\(246\) | −18.9045 | −1.20531 | ||||||||
\(247\) | −3.19093 | −0.203034 | ||||||||
\(248\) | −2.23231 | −0.141752 | ||||||||
\(249\) | −32.0259 | −2.02956 | ||||||||
\(250\) | 6.45086 | 0.407988 | ||||||||
\(251\) | −15.0190 | −0.947992 | −0.473996 | − | 0.880527i | \(-0.657189\pi\) | ||||
−0.473996 | + | 0.880527i | \(0.657189\pi\) | |||||||
\(252\) | −4.00809 | −0.252486 | ||||||||
\(253\) | −14.9285 | −0.938546 | ||||||||
\(254\) | 11.2992 | 0.708976 | ||||||||
\(255\) | −5.80064 | −0.363250 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2957 | −0.766987 | −0.383494 | − | 0.923544i | \(-0.625279\pi\) | ||||
−0.383494 | + | 0.923544i | \(0.625279\pi\) | |||||||
\(258\) | −7.35092 | −0.457649 | ||||||||
\(259\) | −1.52584 | −0.0948113 | ||||||||
\(260\) | −0.678759 | −0.0420948 | ||||||||
\(261\) | 16.6788 | 1.03239 | ||||||||
\(262\) | −5.39567 | −0.333346 | ||||||||
\(263\) | 22.7772 | 1.40450 | 0.702250 | − | 0.711931i | \(-0.252179\pi\) | ||||
0.702250 | + | 0.711931i | \(0.252179\pi\) | |||||||
\(264\) | 4.70171 | 0.289370 | ||||||||
\(265\) | 5.67581 | 0.348662 | ||||||||
\(266\) | 3.17558 | 0.194707 | ||||||||
\(267\) | −1.75755 | −0.107560 | ||||||||
\(268\) | −11.2348 | −0.686278 | ||||||||
\(269\) | −18.8576 | −1.14977 | −0.574885 | − | 0.818234i | \(-0.694953\pi\) | ||||
−0.574885 | + | 0.818234i | \(0.694953\pi\) | |||||||
\(270\) | 1.80945 | 0.110119 | ||||||||
\(271\) | 12.2942 | 0.746819 | 0.373410 | − | 0.927667i | \(-0.378189\pi\) | ||||
0.373410 | + | 0.927667i | \(0.378189\pi\) | |||||||
\(272\) | −3.24084 | −0.196505 | ||||||||
\(273\) | 2.65684 | 0.160799 | ||||||||
\(274\) | 22.0525 | 1.33224 | ||||||||
\(275\) | 8.06706 | 0.486462 | ||||||||
\(276\) | −22.2606 | −1.33993 | ||||||||
\(277\) | −29.6731 | −1.78288 | −0.891441 | − | 0.453136i | \(-0.850305\pi\) | ||||
−0.891441 | + | 0.453136i | \(0.850305\pi\) | |||||||
\(278\) | 5.75164 | 0.344961 | ||||||||
\(279\) | −8.95366 | −0.536041 | ||||||||
\(280\) | 0.675494 | 0.0403685 | ||||||||
\(281\) | 5.55595 | 0.331440 | 0.165720 | − | 0.986173i | \(-0.447005\pi\) | ||||
0.165720 | + | 0.986173i | \(0.447005\pi\) | |||||||
\(282\) | −29.3414 | −1.74725 | ||||||||
\(283\) | −32.7588 | −1.94731 | −0.973655 | − | 0.228025i | \(-0.926773\pi\) | ||||
−0.973655 | + | 0.228025i | \(0.926773\pi\) | |||||||
\(284\) | 0.753276 | 0.0446987 | ||||||||
\(285\) | −5.68788 | −0.336921 | ||||||||
\(286\) | −1.78300 | −0.105431 | ||||||||
\(287\) | −7.13458 | −0.421141 | ||||||||
\(288\) | 4.01094 | 0.236347 | ||||||||
\(289\) | −6.49697 | −0.382175 | ||||||||
\(290\) | −2.81092 | −0.165063 | ||||||||
\(291\) | −33.1951 | −1.94593 | ||||||||
\(292\) | 0.958508 | 0.0560925 | ||||||||
\(293\) | −29.2191 | −1.70700 | −0.853500 | − | 0.521093i | \(-0.825525\pi\) | ||||
−0.853500 | + | 0.521093i | \(0.825525\pi\) | |||||||
\(294\) | 15.8907 | 0.926763 | ||||||||
\(295\) | 2.65959 | 0.154847 | ||||||||
\(296\) | 1.52693 | 0.0887509 | ||||||||
\(297\) | 4.75316 | 0.275807 | ||||||||
\(298\) | 8.06859 | 0.467401 | ||||||||
\(299\) | 8.44177 | 0.488200 | ||||||||
\(300\) | 12.0292 | 0.694506 | ||||||||
\(301\) | −2.77425 | −0.159905 | ||||||||
\(302\) | −0.119283 | −0.00686398 | ||||||||
\(303\) | 2.17153 | 0.124751 | ||||||||
\(304\) | −3.17784 | −0.182262 | ||||||||
\(305\) | 1.33478 | 0.0764290 | ||||||||
\(306\) | −12.9988 | −0.743093 | ||||||||
\(307\) | −14.8070 | −0.845082 | −0.422541 | − | 0.906344i | \(-0.638862\pi\) | ||||
−0.422541 | + | 0.906344i | \(0.638862\pi\) | |||||||
\(308\) | 1.77443 | 0.101107 | ||||||||
\(309\) | 52.0226 | 2.95946 | ||||||||
\(310\) | 1.50898 | 0.0857044 | ||||||||
\(311\) | −12.9873 | −0.736443 | −0.368222 | − | 0.929738i | \(-0.620033\pi\) | ||||
−0.368222 | + | 0.929738i | \(0.620033\pi\) | |||||||
\(312\) | −2.65872 | −0.150521 | ||||||||
\(313\) | −26.2368 | −1.48299 | −0.741495 | − | 0.670959i | \(-0.765883\pi\) | ||||
−0.741495 | + | 0.670959i | \(0.765883\pi\) | |||||||
\(314\) | −10.7447 | −0.606358 | ||||||||
\(315\) | 2.70937 | 0.152656 | ||||||||
\(316\) | 8.32703 | 0.468432 | ||||||||
\(317\) | −17.8514 | −1.00263 | −0.501317 | − | 0.865264i | \(-0.667151\pi\) | ||||
−0.501317 | + | 0.865264i | \(0.667151\pi\) | |||||||
\(318\) | 22.2324 | 1.24673 | ||||||||
\(319\) | −7.38389 | −0.413418 | ||||||||
\(320\) | −0.675974 | −0.0377881 | ||||||||
\(321\) | −5.77405 | −0.322276 | ||||||||
\(322\) | −8.40117 | −0.468179 | ||||||||
\(323\) | 10.2989 | 0.573044 | ||||||||
\(324\) | −4.94516 | −0.274731 | ||||||||
\(325\) | −4.56177 | −0.253042 | ||||||||
\(326\) | 2.11664 | 0.117230 | ||||||||
\(327\) | −2.53399 | −0.140130 | ||||||||
\(328\) | 7.13965 | 0.394221 | ||||||||
\(329\) | −11.0735 | −0.610499 | ||||||||
\(330\) | −3.17823 | −0.174956 | ||||||||
\(331\) | 33.2198 | 1.82593 | 0.912964 | − | 0.408040i | \(-0.133788\pi\) | ||||
0.912964 | + | 0.408040i | \(0.133788\pi\) | |||||||
\(332\) | 12.0952 | 0.663811 | ||||||||
\(333\) | 6.12443 | 0.335616 | ||||||||
\(334\) | −22.9250 | −1.25440 | ||||||||
\(335\) | 7.59447 | 0.414930 | ||||||||
\(336\) | 2.64594 | 0.144348 | ||||||||
\(337\) | −6.51251 | −0.354759 | −0.177379 | − | 0.984143i | \(-0.556762\pi\) | ||||
−0.177379 | + | 0.984143i | \(0.556762\pi\) | |||||||
\(338\) | −11.9917 | −0.652265 | ||||||||
\(339\) | 41.3248 | 2.24445 | ||||||||
\(340\) | 2.19072 | 0.118809 | ||||||||
\(341\) | 3.96388 | 0.214656 | ||||||||
\(342\) | −12.7461 | −0.689232 | ||||||||
\(343\) | 12.9922 | 0.701512 | ||||||||
\(344\) | 2.77622 | 0.149684 | ||||||||
\(345\) | 15.0476 | 0.810135 | ||||||||
\(346\) | 18.6550 | 1.00290 | ||||||||
\(347\) | −34.6642 | −1.86087 | −0.930437 | − | 0.366453i | \(-0.880572\pi\) | ||||
−0.930437 | + | 0.366453i | \(0.880572\pi\) | |||||||
\(348\) | −11.0105 | −0.590223 | ||||||||
\(349\) | −19.6558 | −1.05215 | −0.526074 | − | 0.850439i | \(-0.676337\pi\) | ||||
−0.526074 | + | 0.850439i | \(0.676337\pi\) | |||||||
\(350\) | 4.53983 | 0.242664 | ||||||||
\(351\) | −2.68782 | −0.143465 | ||||||||
\(352\) | −1.77569 | −0.0946446 | ||||||||
\(353\) | −24.3355 | −1.29525 | −0.647624 | − | 0.761960i | \(-0.724237\pi\) | ||||
−0.647624 | + | 0.761960i | \(0.724237\pi\) | |||||||
\(354\) | 10.4177 | 0.553695 | ||||||||
\(355\) | −0.509195 | −0.0270253 | ||||||||
\(356\) | 0.663771 | 0.0351798 | ||||||||
\(357\) | −8.57505 | −0.453840 | ||||||||
\(358\) | −10.4922 | −0.554528 | ||||||||
\(359\) | −1.38190 | −0.0729337 | −0.0364669 | − | 0.999335i | \(-0.511610\pi\) | ||||
−0.0364669 | + | 0.999335i | \(0.511610\pi\) | |||||||
\(360\) | −2.71130 | −0.142898 | ||||||||
\(361\) | −8.90133 | −0.468491 | ||||||||
\(362\) | −18.9162 | −0.994214 | ||||||||
\(363\) | 20.7772 | 1.09052 | ||||||||
\(364\) | −1.00341 | −0.0525927 | ||||||||
\(365\) | −0.647927 | −0.0339140 | ||||||||
\(366\) | 5.22837 | 0.273291 | ||||||||
\(367\) | 30.4033 | 1.58704 | 0.793519 | − | 0.608545i | \(-0.208246\pi\) | ||||
0.793519 | + | 0.608545i | \(0.208246\pi\) | |||||||
\(368\) | 8.40714 | 0.438253 | ||||||||
\(369\) | 28.6367 | 1.49077 | ||||||||
\(370\) | −1.03216 | −0.0536597 | ||||||||
\(371\) | 8.39052 | 0.435614 | ||||||||
\(372\) | 5.91074 | 0.306458 | ||||||||
\(373\) | 32.0524 | 1.65961 | 0.829806 | − | 0.558052i | \(-0.188451\pi\) | ||||
0.829806 | + | 0.558052i | \(0.188451\pi\) | |||||||
\(374\) | 5.75472 | 0.297570 | ||||||||
\(375\) | −17.0807 | −0.882044 | ||||||||
\(376\) | 11.0813 | 0.571476 | ||||||||
\(377\) | 4.17545 | 0.215046 | ||||||||
\(378\) | 2.67490 | 0.137582 | ||||||||
\(379\) | 25.8904 | 1.32990 | 0.664950 | − | 0.746888i | \(-0.268453\pi\) | ||||
0.664950 | + | 0.746888i | \(0.268453\pi\) | |||||||
\(380\) | 2.14814 | 0.110197 | ||||||||
\(381\) | −29.9183 | −1.53276 | ||||||||
\(382\) | 3.11891 | 0.159578 | ||||||||
\(383\) | −21.0970 | −1.07800 | −0.539002 | − | 0.842304i | \(-0.681198\pi\) | ||||
−0.539002 | + | 0.842304i | \(0.681198\pi\) | |||||||
\(384\) | −2.64782 | −0.135121 | ||||||||
\(385\) | −1.19947 | −0.0611306 | ||||||||
\(386\) | 3.51877 | 0.179101 | ||||||||
\(387\) | 11.1353 | 0.566037 | ||||||||
\(388\) | 12.5368 | 0.636458 | ||||||||
\(389\) | −7.11805 | −0.360900 | −0.180450 | − | 0.983584i | \(-0.557755\pi\) | ||||
−0.180450 | + | 0.983584i | \(0.557755\pi\) | |||||||
\(390\) | 1.79723 | 0.0910063 | ||||||||
\(391\) | −27.2462 | −1.37790 | ||||||||
\(392\) | −6.00142 | −0.303118 | ||||||||
\(393\) | 14.2868 | 0.720672 | ||||||||
\(394\) | −18.2977 | −0.921822 | ||||||||
\(395\) | −5.62886 | −0.283219 | ||||||||
\(396\) | −7.12219 | −0.357904 | ||||||||
\(397\) | −27.9275 | −1.40164 | −0.700822 | − | 0.713337i | \(-0.747183\pi\) | ||||
−0.700822 | + | 0.713337i | \(0.747183\pi\) | |||||||
\(398\) | −6.62886 | −0.332275 | ||||||||
\(399\) | −8.40837 | −0.420945 | ||||||||
\(400\) | −4.54306 | −0.227153 | ||||||||
\(401\) | −10.0662 | −0.502680 | −0.251340 | − | 0.967899i | \(-0.580871\pi\) | ||||
−0.251340 | + | 0.967899i | \(0.580871\pi\) | |||||||
\(402\) | 29.7478 | 1.48369 | ||||||||
\(403\) | −2.24150 | −0.111657 | ||||||||
\(404\) | −0.820120 | −0.0408025 | ||||||||
\(405\) | 3.34280 | 0.166105 | ||||||||
\(406\) | −4.15536 | −0.206227 | ||||||||
\(407\) | −2.71135 | −0.134397 | ||||||||
\(408\) | 8.58115 | 0.424830 | ||||||||
\(409\) | −27.3491 | −1.35232 | −0.676162 | − | 0.736753i | \(-0.736358\pi\) | ||||
−0.676162 | + | 0.736753i | \(0.736358\pi\) | |||||||
\(410\) | −4.82622 | −0.238350 | ||||||||
\(411\) | −58.3910 | −2.88022 | ||||||||
\(412\) | −19.6474 | −0.967956 | ||||||||
\(413\) | 3.93165 | 0.193464 | ||||||||
\(414\) | 33.7206 | 1.65728 | ||||||||
\(415\) | −8.17605 | −0.401347 | ||||||||
\(416\) | 1.00412 | 0.0492310 | ||||||||
\(417\) | −15.2293 | −0.745782 | ||||||||
\(418\) | 5.64286 | 0.276001 | ||||||||
\(419\) | 0.124193 | 0.00606723 | 0.00303362 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303362 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(420\) | −1.78859 | −0.0872740 | ||||||||
\(421\) | −14.8032 | −0.721463 | −0.360732 | − | 0.932670i | \(-0.617473\pi\) | ||||
−0.360732 | + | 0.932670i | \(0.617473\pi\) | |||||||
\(422\) | 11.7326 | 0.571132 | ||||||||
\(423\) | 44.4466 | 2.16107 | ||||||||
\(424\) | −8.39649 | −0.407769 | ||||||||
\(425\) | 14.7233 | 0.714186 | ||||||||
\(426\) | −1.99454 | −0.0966357 | ||||||||
\(427\) | 1.97319 | 0.0954894 | ||||||||
\(428\) | 2.18068 | 0.105407 | ||||||||
\(429\) | 4.72107 | 0.227935 | ||||||||
\(430\) | −1.87665 | −0.0905002 | ||||||||
\(431\) | 1.54029 | 0.0741932 | 0.0370966 | − | 0.999312i | \(-0.488189\pi\) | ||||
0.0370966 | + | 0.999312i | \(0.488189\pi\) | |||||||
\(432\) | −2.67680 | −0.128787 | ||||||||
\(433\) | −26.4020 | −1.26880 | −0.634400 | − | 0.773005i | \(-0.718753\pi\) | ||||
−0.634400 | + | 0.773005i | \(0.718753\pi\) | |||||||
\(434\) | 2.23072 | 0.107078 | ||||||||
\(435\) | 7.44280 | 0.356855 | ||||||||
\(436\) | 0.957011 | 0.0458325 | ||||||||
\(437\) | −26.7166 | −1.27803 | ||||||||
\(438\) | −2.53796 | −0.121268 | ||||||||
\(439\) | 1.28084 | 0.0611312 | 0.0305656 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305656 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(440\) | 1.20032 | 0.0572231 | ||||||||
\(441\) | −24.0714 | −1.14626 | ||||||||
\(442\) | −3.25419 | −0.154786 | ||||||||
\(443\) | −16.4162 | −0.779956 | −0.389978 | − | 0.920824i | \(-0.627517\pi\) | ||||
−0.389978 | + | 0.920824i | \(0.627517\pi\) | |||||||
\(444\) | −4.04303 | −0.191874 | ||||||||
\(445\) | −0.448692 | −0.0212700 | ||||||||
\(446\) | −0.662036 | −0.0313483 | ||||||||
\(447\) | −21.3642 | −1.01049 | ||||||||
\(448\) | −0.999289 | −0.0472120 | ||||||||
\(449\) | 36.2018 | 1.70847 | 0.854234 | − | 0.519889i | \(-0.174027\pi\) | ||||
0.854234 | + | 0.519889i | \(0.174027\pi\) | |||||||
\(450\) | −18.2220 | −0.858991 | ||||||||
\(451\) | −12.6778 | −0.596975 | ||||||||
\(452\) | −15.6071 | −0.734096 | ||||||||
\(453\) | 0.315840 | 0.0148395 | ||||||||
\(454\) | 10.0944 | 0.473755 | ||||||||
\(455\) | 0.678276 | 0.0317981 | ||||||||
\(456\) | 8.41435 | 0.394038 | ||||||||
\(457\) | 42.1247 | 1.97051 | 0.985256 | − | 0.171087i | \(-0.0547278\pi\) | ||||
0.985256 | + | 0.171087i | \(0.0547278\pi\) | |||||||
\(458\) | 7.12675 | 0.333011 | ||||||||
\(459\) | 8.67507 | 0.404917 | ||||||||
\(460\) | −5.68301 | −0.264972 | ||||||||
\(461\) | −16.4873 | −0.767888 | −0.383944 | − | 0.923356i | \(-0.625434\pi\) | ||||
−0.383944 | + | 0.923356i | \(0.625434\pi\) | |||||||
\(462\) | −4.69836 | −0.218588 | ||||||||
\(463\) | 10.5166 | 0.488747 | 0.244374 | − | 0.969681i | \(-0.421418\pi\) | ||||
0.244374 | + | 0.969681i | \(0.421418\pi\) | |||||||
\(464\) | 4.15832 | 0.193045 | ||||||||
\(465\) | −3.99551 | −0.185287 | ||||||||
\(466\) | −3.11727 | −0.144405 | ||||||||
\(467\) | −35.4620 | −1.64098 | −0.820492 | − | 0.571658i | \(-0.806300\pi\) | ||||
−0.820492 | + | 0.571658i | \(0.806300\pi\) | |||||||
\(468\) | 4.02746 | 0.186170 | ||||||||
\(469\) | 11.2269 | 0.518409 | ||||||||
\(470\) | −7.49069 | −0.345520 | ||||||||
\(471\) | 28.4500 | 1.31091 | ||||||||
\(472\) | −3.93445 | −0.181098 | ||||||||
\(473\) | −4.92970 | −0.226668 | ||||||||
\(474\) | −22.0485 | −1.01272 | ||||||||
\(475\) | 14.4371 | 0.662420 | ||||||||
\(476\) | 3.23854 | 0.148438 | ||||||||
\(477\) | −33.6778 | −1.54200 | ||||||||
\(478\) | 15.8275 | 0.723933 | ||||||||
\(479\) | −29.1676 | −1.33270 | −0.666351 | − | 0.745638i | \(-0.732145\pi\) | ||||
−0.666351 | + | 0.745638i | \(0.732145\pi\) | |||||||
\(480\) | 1.78986 | 0.0816954 | ||||||||
\(481\) | 1.53322 | 0.0699087 | ||||||||
\(482\) | −17.6675 | −0.804732 | ||||||||
\(483\) | 22.2448 | 1.01217 | ||||||||
\(484\) | −7.84692 | −0.356678 | ||||||||
\(485\) | −8.47453 | −0.384809 | ||||||||
\(486\) | 21.1243 | 0.958217 | ||||||||
\(487\) | −19.6810 | −0.891830 | −0.445915 | − | 0.895075i | \(-0.647122\pi\) | ||||
−0.445915 | + | 0.895075i | \(0.647122\pi\) | |||||||
\(488\) | −1.97459 | −0.0893857 | ||||||||
\(489\) | −5.60448 | −0.253443 | ||||||||
\(490\) | 4.05681 | 0.183268 | ||||||||
\(491\) | −14.4946 | −0.654132 | −0.327066 | − | 0.945002i | \(-0.606060\pi\) | ||||
−0.327066 | + | 0.945002i | \(0.606060\pi\) | |||||||
\(492\) | −18.9045 | −0.852281 | ||||||||
\(493\) | −13.4764 | −0.606948 | ||||||||
\(494\) | −3.19093 | −0.143567 | ||||||||
\(495\) | 4.81442 | 0.216392 | ||||||||
\(496\) | −2.23231 | −0.100234 | ||||||||
\(497\) | −0.752741 | −0.0337650 | ||||||||
\(498\) | −32.0259 | −1.43512 | ||||||||
\(499\) | 18.5198 | 0.829060 | 0.414530 | − | 0.910036i | \(-0.363946\pi\) | ||||
0.414530 | + | 0.910036i | \(0.363946\pi\) | |||||||
\(500\) | 6.45086 | 0.288491 | ||||||||
\(501\) | 60.7012 | 2.71193 | ||||||||
\(502\) | −15.0190 | −0.670332 | ||||||||
\(503\) | −26.5307 | −1.18294 | −0.591472 | − | 0.806325i | \(-0.701453\pi\) | ||||
−0.591472 | + | 0.806325i | \(0.701453\pi\) | |||||||
\(504\) | −4.00809 | −0.178535 | ||||||||
\(505\) | 0.554380 | 0.0246696 | ||||||||
\(506\) | −14.9285 | −0.663652 | ||||||||
\(507\) | 31.7520 | 1.41015 | ||||||||
\(508\) | 11.2992 | 0.501322 | ||||||||
\(509\) | −34.9885 | −1.55084 | −0.775418 | − | 0.631448i | \(-0.782461\pi\) | ||||
−0.775418 | + | 0.631448i | \(0.782461\pi\) | |||||||
\(510\) | −5.80064 | −0.256857 | ||||||||
\(511\) | −0.957827 | −0.0423718 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.50644 | 0.375568 | ||||||||
\(514\) | −12.2957 | −0.542342 | ||||||||
\(515\) | 13.2811 | 0.585235 | ||||||||
\(516\) | −7.35092 | −0.323606 | ||||||||
\(517\) | −19.6770 | −0.865394 | ||||||||
\(518\) | −1.52584 | −0.0670417 | ||||||||
\(519\) | −49.3950 | −2.16820 | ||||||||
\(520\) | −0.678759 | −0.0297655 | ||||||||
\(521\) | 7.75607 | 0.339800 | 0.169900 | − | 0.985461i | \(-0.445656\pi\) | ||||
0.169900 | + | 0.985461i | \(0.445656\pi\) | |||||||
\(522\) | 16.6788 | 0.730011 | ||||||||
\(523\) | −2.93779 | −0.128461 | −0.0642304 | − | 0.997935i | \(-0.520459\pi\) | ||||
−0.0642304 | + | 0.997935i | \(0.520459\pi\) | |||||||
\(524\) | −5.39567 | −0.235711 | ||||||||
\(525\) | −12.0206 | −0.524624 | ||||||||
\(526\) | 22.7772 | 0.993131 | ||||||||
\(527\) | 7.23454 | 0.315142 | ||||||||
\(528\) | 4.70171 | 0.204615 | ||||||||
\(529\) | 47.6801 | 2.07305 | ||||||||
\(530\) | 5.67581 | 0.246541 | ||||||||
\(531\) | −15.7809 | −0.684831 | ||||||||
\(532\) | 3.17558 | 0.137679 | ||||||||
\(533\) | 7.16906 | 0.310526 | ||||||||
\(534\) | −1.75755 | −0.0760564 | ||||||||
\(535\) | −1.47408 | −0.0637302 | ||||||||
\(536\) | −11.2348 | −0.485272 | ||||||||
\(537\) | 27.7814 | 1.19885 | ||||||||
\(538\) | −18.8576 | −0.813010 | ||||||||
\(539\) | 10.6567 | 0.459015 | ||||||||
\(540\) | 1.80945 | 0.0778662 | ||||||||
\(541\) | −14.4463 | −0.621096 | −0.310548 | − | 0.950558i | \(-0.600513\pi\) | ||||
−0.310548 | + | 0.950558i | \(0.600513\pi\) | |||||||
\(542\) | 12.2942 | 0.528081 | ||||||||
\(543\) | 50.0867 | 2.14943 | ||||||||
\(544\) | −3.24084 | −0.138950 | ||||||||
\(545\) | −0.646915 | −0.0277108 | ||||||||
\(546\) | 2.65684 | 0.113702 | ||||||||
\(547\) | −22.4181 | −0.958530 | −0.479265 | − | 0.877670i | \(-0.659097\pi\) | ||||
−0.479265 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(548\) | 22.0525 | 0.942036 | ||||||||
\(549\) | −7.91999 | −0.338017 | ||||||||
\(550\) | 8.06706 | 0.343981 | ||||||||
\(551\) | −13.2145 | −0.562956 | ||||||||
\(552\) | −22.2606 | −0.947474 | ||||||||
\(553\) | −8.32111 | −0.353850 | ||||||||
\(554\) | −29.6731 | −1.26069 | ||||||||
\(555\) | 2.73298 | 0.116009 | ||||||||
\(556\) | 5.75164 | 0.243924 | ||||||||
\(557\) | −3.95791 | −0.167702 | −0.0838510 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838510 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(558\) | −8.95366 | −0.379039 | ||||||||
\(559\) | 2.78765 | 0.117905 | ||||||||
\(560\) | 0.675494 | 0.0285448 | ||||||||
\(561\) | −15.2375 | −0.643326 | ||||||||
\(562\) | 5.55595 | 0.234363 | ||||||||
\(563\) | 28.2418 | 1.19025 | 0.595125 | − | 0.803633i | \(-0.297102\pi\) | ||||
0.595125 | + | 0.803633i | \(0.297102\pi\) | |||||||
\(564\) | −29.3414 | −1.23549 | ||||||||
\(565\) | 10.5500 | 0.443842 | ||||||||
\(566\) | −32.7588 | −1.37696 | ||||||||
\(567\) | 4.94164 | 0.207530 | ||||||||
\(568\) | 0.753276 | 0.0316068 | ||||||||
\(569\) | −6.40748 | −0.268616 | −0.134308 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134308 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(570\) | −5.68788 | −0.238239 | ||||||||
\(571\) | 17.7442 | 0.742570 | 0.371285 | − | 0.928519i | \(-0.378917\pi\) | ||||
0.371285 | + | 0.928519i | \(0.378917\pi\) | |||||||
\(572\) | −1.78300 | −0.0745511 | ||||||||
\(573\) | −8.25832 | −0.344996 | ||||||||
\(574\) | −7.13458 | −0.297791 | ||||||||
\(575\) | −38.1941 | −1.59281 | ||||||||
\(576\) | 4.01094 | 0.167123 | ||||||||
\(577\) | 0.388267 | 0.0161637 | 0.00808187 | − | 0.999967i | \(-0.497427\pi\) | ||||
0.00808187 | + | 0.999967i | \(0.497427\pi\) | |||||||
\(578\) | −6.49697 | −0.270238 | ||||||||
\(579\) | −9.31707 | −0.387204 | ||||||||
\(580\) | −2.81092 | −0.116717 | ||||||||
\(581\) | −12.0866 | −0.501437 | ||||||||
\(582\) | −33.1951 | −1.37598 | ||||||||
\(583\) | 14.9096 | 0.617491 | ||||||||
\(584\) | 0.958508 | 0.0396634 | ||||||||
\(585\) | −2.72246 | −0.112560 | ||||||||
\(586\) | −29.2191 | −1.20703 | ||||||||
\(587\) | −13.5651 | −0.559891 | −0.279946 | − | 0.960016i | \(-0.590316\pi\) | ||||
−0.279946 | + | 0.960016i | \(0.590316\pi\) | |||||||
\(588\) | 15.8907 | 0.655320 | ||||||||
\(589\) | 7.09391 | 0.292300 | ||||||||
\(590\) | 2.65959 | 0.109493 | ||||||||
\(591\) | 48.4489 | 1.99292 | ||||||||
\(592\) | 1.52693 | 0.0627564 | ||||||||
\(593\) | 21.4715 | 0.881728 | 0.440864 | − | 0.897574i | \(-0.354672\pi\) | ||||
0.440864 | + | 0.897574i | \(0.354672\pi\) | |||||||
\(594\) | 4.75316 | 0.195025 | ||||||||
\(595\) | −2.18917 | −0.0897471 | ||||||||
\(596\) | 8.06859 | 0.330502 | ||||||||
\(597\) | 17.5520 | 0.718357 | ||||||||
\(598\) | 8.44177 | 0.345210 | ||||||||
\(599\) | 23.2629 | 0.950495 | 0.475247 | − | 0.879852i | \(-0.342359\pi\) | ||||
0.475247 | + | 0.879852i | \(0.342359\pi\) | |||||||
\(600\) | 12.0292 | 0.491090 | ||||||||
\(601\) | 28.3956 | 1.15828 | 0.579141 | − | 0.815227i | \(-0.303388\pi\) | ||||
0.579141 | + | 0.815227i | \(0.303388\pi\) | |||||||
\(602\) | −2.77425 | −0.113070 | ||||||||
\(603\) | −45.0624 | −1.83508 | ||||||||
\(604\) | −0.119283 | −0.00485357 | ||||||||
\(605\) | 5.30432 | 0.215651 | ||||||||
\(606\) | 2.17153 | 0.0882123 | ||||||||
\(607\) | 30.7963 | 1.24998 | 0.624991 | − | 0.780632i | \(-0.285103\pi\) | ||||
0.624991 | + | 0.780632i | \(0.285103\pi\) | |||||||
\(608\) | −3.17784 | −0.128878 | ||||||||
\(609\) | 11.0027 | 0.445850 | ||||||||
\(610\) | 1.33478 | 0.0540435 | ||||||||
\(611\) | 11.1270 | 0.450149 | ||||||||
\(612\) | −12.9988 | −0.525446 | ||||||||
\(613\) | −18.2003 | −0.735103 | −0.367552 | − | 0.930003i | \(-0.619804\pi\) | ||||
−0.367552 | + | 0.930003i | \(0.619804\pi\) | |||||||
\(614\) | −14.8070 | −0.597564 | ||||||||
\(615\) | 12.7790 | 0.515297 | ||||||||
\(616\) | 1.77443 | 0.0714938 | ||||||||
\(617\) | 9.74973 | 0.392509 | 0.196255 | − | 0.980553i | \(-0.437122\pi\) | ||||
0.196255 | + | 0.980553i | \(0.437122\pi\) | |||||||
\(618\) | 52.0226 | 2.09266 | ||||||||
\(619\) | 40.2360 | 1.61722 | 0.808610 | − | 0.588345i | \(-0.200220\pi\) | ||||
0.808610 | + | 0.588345i | \(0.200220\pi\) | |||||||
\(620\) | 1.50898 | 0.0606022 | ||||||||
\(621\) | −22.5042 | −0.903063 | ||||||||
\(622\) | −12.9873 | −0.520744 | ||||||||
\(623\) | −0.663299 | −0.0265745 | ||||||||
\(624\) | −2.65872 | −0.106434 | ||||||||
\(625\) | 18.3547 | 0.734187 | ||||||||
\(626\) | −26.2368 | −1.04863 | ||||||||
\(627\) | −14.9413 | −0.596697 | ||||||||
\(628\) | −10.7447 | −0.428760 | ||||||||
\(629\) | −4.94853 | −0.197311 | ||||||||
\(630\) | 2.70937 | 0.107944 | ||||||||
\(631\) | 46.6381 | 1.85663 | 0.928316 | − | 0.371791i | \(-0.121256\pi\) | ||||
0.928316 | + | 0.371791i | \(0.121256\pi\) | |||||||
\(632\) | 8.32703 | 0.331231 | ||||||||
\(633\) | −31.0657 | −1.23475 | ||||||||
\(634\) | −17.8514 | −0.708970 | ||||||||
\(635\) | −7.63798 | −0.303104 | ||||||||
\(636\) | 22.2324 | 0.881571 | ||||||||
\(637\) | −6.02614 | −0.238764 | ||||||||
\(638\) | −7.38389 | −0.292331 | ||||||||
\(639\) | 3.02135 | 0.119523 | ||||||||
\(640\) | −0.675974 | −0.0267202 | ||||||||
\(641\) | −10.1262 | −0.399960 | −0.199980 | − | 0.979800i | \(-0.564088\pi\) | ||||
−0.199980 | + | 0.979800i | \(0.564088\pi\) | |||||||
\(642\) | −5.77405 | −0.227884 | ||||||||
\(643\) | −24.6692 | −0.972857 | −0.486428 | − | 0.873720i | \(-0.661701\pi\) | ||||
−0.486428 | + | 0.873720i | \(0.661701\pi\) | |||||||
\(644\) | −8.40117 | −0.331052 | ||||||||
\(645\) | 4.96904 | 0.195656 | ||||||||
\(646\) | 10.2989 | 0.405203 | ||||||||
\(647\) | −34.7003 | −1.36421 | −0.682105 | − | 0.731254i | \(-0.738935\pi\) | ||||
−0.682105 | + | 0.731254i | \(0.738935\pi\) | |||||||
\(648\) | −4.94516 | −0.194264 | ||||||||
\(649\) | 6.98636 | 0.274239 | ||||||||
\(650\) | −4.56177 | −0.178927 | ||||||||
\(651\) | −5.90654 | −0.231496 | ||||||||
\(652\) | 2.11664 | 0.0828940 | ||||||||
\(653\) | −4.13867 | −0.161959 | −0.0809793 | − | 0.996716i | \(-0.525805\pi\) | ||||
−0.0809793 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(654\) | −2.53399 | −0.0990870 | ||||||||
\(655\) | 3.64734 | 0.142513 | ||||||||
\(656\) | 7.13965 | 0.278756 | ||||||||
\(657\) | 3.84452 | 0.149989 | ||||||||
\(658\) | −11.0735 | −0.431688 | ||||||||
\(659\) | −5.05728 | −0.197004 | −0.0985019 | − | 0.995137i | \(-0.531405\pi\) | ||||
−0.0985019 | + | 0.995137i | \(0.531405\pi\) | |||||||
\(660\) | −3.17823 | −0.123713 | ||||||||
\(661\) | 40.0109 | 1.55624 | 0.778121 | − | 0.628114i | \(-0.216173\pi\) | ||||
0.778121 | + | 0.628114i | \(0.216173\pi\) | |||||||
\(662\) | 33.2198 | 1.29113 | ||||||||
\(663\) | 8.61650 | 0.334637 | ||||||||
\(664\) | 12.0952 | 0.469385 | ||||||||
\(665\) | −2.14661 | −0.0832420 | ||||||||
\(666\) | 6.12443 | 0.237317 | ||||||||
\(667\) | 34.9596 | 1.35364 | ||||||||
\(668\) | −22.9250 | −0.886994 | ||||||||
\(669\) | 1.75295 | 0.0677730 | ||||||||
\(670\) | 7.59447 | 0.293400 | ||||||||
\(671\) | 3.50627 | 0.135358 | ||||||||
\(672\) | 2.64594 | 0.102069 | ||||||||
\(673\) | 42.9421 | 1.65530 | 0.827649 | − | 0.561246i | \(-0.189678\pi\) | ||||
0.827649 | + | 0.561246i | \(0.189678\pi\) | |||||||
\(674\) | −6.51251 | −0.250852 | ||||||||
\(675\) | 12.1608 | 0.468071 | ||||||||
\(676\) | −11.9917 | −0.461221 | ||||||||
\(677\) | −38.7697 | −1.49004 | −0.745021 | − | 0.667041i | \(-0.767560\pi\) | ||||
−0.745021 | + | 0.667041i | \(0.767560\pi\) | |||||||
\(678\) | 41.3248 | 1.58707 | ||||||||
\(679\) | −12.5279 | −0.480775 | ||||||||
\(680\) | 2.19072 | 0.0840104 | ||||||||
\(681\) | −26.7282 | −1.02423 | ||||||||
\(682\) | 3.96388 | 0.151785 | ||||||||
\(683\) | −44.1884 | −1.69082 | −0.845412 | − | 0.534115i | \(-0.820645\pi\) | ||||
−0.845412 | + | 0.534115i | \(0.820645\pi\) | |||||||
\(684\) | −12.7461 | −0.487361 | ||||||||
\(685\) | −14.9069 | −0.569564 | ||||||||
\(686\) | 12.9922 | 0.496044 | ||||||||
\(687\) | −18.8704 | −0.719949 | ||||||||
\(688\) | 2.77622 | 0.105842 | ||||||||
\(689\) | −8.43107 | −0.321198 | ||||||||
\(690\) | 15.0476 | 0.572852 | ||||||||
\(691\) | −31.7649 | −1.20839 | −0.604196 | − | 0.796836i | \(-0.706506\pi\) | ||||
−0.604196 | + | 0.796836i | \(0.706506\pi\) | |||||||
\(692\) | 18.6550 | 0.709155 | ||||||||
\(693\) | 7.11713 | 0.270358 | ||||||||
\(694\) | −34.6642 | −1.31584 | ||||||||
\(695\) | −3.88796 | −0.147479 | ||||||||
\(696\) | −11.0105 | −0.417351 | ||||||||
\(697\) | −23.1384 | −0.876431 | ||||||||
\(698\) | −19.6558 | −0.743982 | ||||||||
\(699\) | 8.25396 | 0.312194 | ||||||||
\(700\) | 4.53983 | 0.171589 | ||||||||
\(701\) | 16.8264 | 0.635524 | 0.317762 | − | 0.948170i | \(-0.397069\pi\) | ||||
0.317762 | + | 0.948170i | \(0.397069\pi\) | |||||||
\(702\) | −2.68782 | −0.101445 | ||||||||
\(703\) | −4.85234 | −0.183009 | ||||||||
\(704\) | −1.77569 | −0.0669238 | ||||||||
\(705\) | 19.8340 | 0.746992 | ||||||||
\(706\) | −24.3355 | −0.915879 | ||||||||
\(707\) | 0.819537 | 0.0308219 | ||||||||
\(708\) | 10.4177 | 0.391522 | ||||||||
\(709\) | −46.1542 | −1.73336 | −0.866679 | − | 0.498866i | \(-0.833750\pi\) | ||||
−0.866679 | + | 0.498866i | \(0.833750\pi\) | |||||||
\(710\) | −0.509195 | −0.0191098 | ||||||||
\(711\) | 33.3992 | 1.25257 | ||||||||
\(712\) | 0.663771 | 0.0248759 | ||||||||
\(713\) | −18.7673 | −0.702842 | ||||||||
\(714\) | −8.57505 | −0.320913 | ||||||||
\(715\) | 1.20526 | 0.0450743 | ||||||||
\(716\) | −10.4922 | −0.392111 | ||||||||
\(717\) | −41.9084 | −1.56510 | ||||||||
\(718\) | −1.38190 | −0.0515719 | ||||||||
\(719\) | −43.8635 | −1.63583 | −0.817916 | − | 0.575337i | \(-0.804871\pi\) | ||||
−0.817916 | + | 0.575337i | \(0.804871\pi\) | |||||||
\(720\) | −2.71130 | −0.101044 | ||||||||
\(721\) | 19.6334 | 0.731186 | ||||||||
\(722\) | −8.90133 | −0.331273 | ||||||||
\(723\) | 46.7803 | 1.73978 | ||||||||
\(724\) | −18.9162 | −0.703015 | ||||||||
\(725\) | −18.8915 | −0.701612 | ||||||||
\(726\) | 20.7772 | 0.771116 | ||||||||
\(727\) | −45.1451 | −1.67434 | −0.837169 | − | 0.546944i | \(-0.815791\pi\) | ||||
−0.837169 | + | 0.546944i | \(0.815791\pi\) | |||||||
\(728\) | −1.00341 | −0.0371887 | ||||||||
\(729\) | −41.0978 | −1.52214 | ||||||||
\(730\) | −0.647927 | −0.0239809 | ||||||||
\(731\) | −8.99727 | −0.332776 | ||||||||
\(732\) | 5.22837 | 0.193246 | ||||||||
\(733\) | 11.6790 | 0.431372 | 0.215686 | − | 0.976463i | \(-0.430801\pi\) | ||||
0.215686 | + | 0.976463i | \(0.430801\pi\) | |||||||
\(734\) | 30.4033 | 1.12221 | ||||||||
\(735\) | −10.7417 | −0.396213 | ||||||||
\(736\) | 8.40714 | 0.309891 | ||||||||
\(737\) | 19.9496 | 0.734853 | ||||||||
\(738\) | 28.6367 | 1.05413 | ||||||||
\(739\) | 33.6614 | 1.23825 | 0.619127 | − | 0.785291i | \(-0.287487\pi\) | ||||
0.619127 | + | 0.785291i | \(0.287487\pi\) | |||||||
\(740\) | −1.03216 | −0.0379431 | ||||||||
\(741\) | 8.44900 | 0.310382 | ||||||||
\(742\) | 8.39052 | 0.308026 | ||||||||
\(743\) | 35.2692 | 1.29390 | 0.646950 | − | 0.762532i | \(-0.276044\pi\) | ||||
0.646950 | + | 0.762532i | \(0.276044\pi\) | |||||||
\(744\) | 5.91074 | 0.216698 | ||||||||
\(745\) | −5.45416 | −0.199825 | ||||||||
\(746\) | 32.0524 | 1.17352 | ||||||||
\(747\) | 48.5132 | 1.77501 | ||||||||
\(748\) | 5.75472 | 0.210414 | ||||||||
\(749\) | −2.17913 | −0.0796237 | ||||||||
\(750\) | −17.0807 | −0.623700 | ||||||||
\(751\) | −34.7979 | −1.26979 | −0.634896 | − | 0.772597i | \(-0.718957\pi\) | ||||
−0.634896 | + | 0.772597i | \(0.718957\pi\) | |||||||
\(752\) | 11.0813 | 0.404095 | ||||||||
\(753\) | 39.7677 | 1.44921 | ||||||||
\(754\) | 4.17545 | 0.152061 | ||||||||
\(755\) | 0.0806324 | 0.00293451 | ||||||||
\(756\) | 2.67490 | 0.0972850 | ||||||||
\(757\) | 2.85298 | 0.103693 | 0.0518467 | − | 0.998655i | \(-0.483489\pi\) | ||||
0.0518467 | + | 0.998655i | \(0.483489\pi\) | |||||||
\(758\) | 25.8904 | 0.940381 | ||||||||
\(759\) | 39.5279 | 1.43477 | ||||||||
\(760\) | 2.14814 | 0.0779212 | ||||||||
\(761\) | 27.7116 | 1.00455 | 0.502273 | − | 0.864709i | \(-0.332497\pi\) | ||||
0.502273 | + | 0.864709i | \(0.332497\pi\) | |||||||
\(762\) | −29.9183 | −1.08382 | ||||||||
\(763\) | −0.956331 | −0.0346215 | ||||||||
\(764\) | 3.11891 | 0.112838 | ||||||||
\(765\) | 8.78687 | 0.317690 | ||||||||
\(766\) | −21.0970 | −0.762264 | ||||||||
\(767\) | −3.95066 | −0.142650 | ||||||||
\(768\) | −2.64782 | −0.0955449 | ||||||||
\(769\) | −0.893253 | −0.0322115 | −0.0161058 | − | 0.999870i | \(-0.505127\pi\) | ||||
−0.0161058 | + | 0.999870i | \(0.505127\pi\) | |||||||
\(770\) | −1.19947 | −0.0432258 | ||||||||
\(771\) | 32.5569 | 1.17251 | ||||||||
\(772\) | 3.51877 | 0.126643 | ||||||||
\(773\) | 6.11956 | 0.220105 | 0.110053 | − | 0.993926i | \(-0.464898\pi\) | ||||
0.110053 | + | 0.993926i | \(0.464898\pi\) | |||||||
\(774\) | 11.1353 | 0.400249 | ||||||||
\(775\) | 10.1415 | 0.364293 | ||||||||
\(776\) | 12.5368 | 0.450044 | ||||||||
\(777\) | 4.04016 | 0.144940 | ||||||||
\(778\) | −7.11805 | −0.255195 | ||||||||
\(779\) | −22.6887 | −0.812906 | ||||||||
\(780\) | 1.79723 | 0.0643511 | ||||||||
\(781\) | −1.33758 | −0.0478625 | ||||||||
\(782\) | −27.2462 | −0.974322 | ||||||||
\(783\) | −11.1310 | −0.397789 | ||||||||
\(784\) | −6.00142 | −0.214336 | ||||||||
\(785\) | 7.26314 | 0.259232 | ||||||||
\(786\) | 14.2868 | 0.509592 | ||||||||
\(787\) | 48.9125 | 1.74354 | 0.871771 | − | 0.489913i | \(-0.162972\pi\) | ||||
0.871771 | + | 0.489913i | \(0.162972\pi\) | |||||||
\(788\) | −18.2977 | −0.651827 | ||||||||
\(789\) | −60.3098 | −2.14709 | ||||||||
\(790\) | −5.62886 | −0.200266 | ||||||||
\(791\) | 15.5960 | 0.554530 | ||||||||
\(792\) | −7.12219 | −0.253076 | ||||||||
\(793\) | −1.98273 | −0.0704087 | ||||||||
\(794\) | −27.9275 | −0.991111 | ||||||||
\(795\) | −15.0285 | −0.533007 | ||||||||
\(796\) | −6.62886 | −0.234954 | ||||||||
\(797\) | 26.2257 | 0.928963 | 0.464482 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464482 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(798\) | −8.40837 | −0.297653 | ||||||||
\(799\) | −35.9128 | −1.27050 | ||||||||
\(800\) | −4.54306 | −0.160621 | ||||||||
\(801\) | 2.66235 | 0.0940695 | ||||||||
\(802\) | −10.0662 | −0.355448 | ||||||||
\(803\) | −1.70201 | −0.0600628 | ||||||||
\(804\) | 29.7478 | 1.04913 | ||||||||
\(805\) | 5.67898 | 0.200158 | ||||||||
\(806\) | −2.24150 | −0.0789535 | ||||||||
\(807\) | 49.9316 | 1.75768 | ||||||||
\(808\) | −0.820120 | −0.0288517 | ||||||||
\(809\) | 7.94327 | 0.279270 | 0.139635 | − | 0.990203i | \(-0.455407\pi\) | ||||
0.139635 | + | 0.990203i | \(0.455407\pi\) | |||||||
\(810\) | 3.34280 | 0.117454 | ||||||||
\(811\) | 1.58185 | 0.0555461 | 0.0277731 | − | 0.999614i | \(-0.491158\pi\) | ||||
0.0277731 | + | 0.999614i | \(0.491158\pi\) | |||||||
\(812\) | −4.15536 | −0.145825 | ||||||||
\(813\) | −32.5528 | −1.14168 | ||||||||
\(814\) | −2.71135 | −0.0950328 | ||||||||
\(815\) | −1.43079 | −0.0501185 | ||||||||
\(816\) | 8.58115 | 0.300400 | ||||||||
\(817\) | −8.82238 | −0.308656 | ||||||||
\(818\) | −27.3491 | −0.956237 | ||||||||
\(819\) | −4.02460 | −0.140631 | ||||||||
\(820\) | −4.82622 | −0.168539 | ||||||||
\(821\) | 46.9363 | 1.63809 | 0.819044 | − | 0.573731i | \(-0.194504\pi\) | ||||
0.819044 | + | 0.573731i | \(0.194504\pi\) | |||||||
\(822\) | −58.3910 | −2.03662 | ||||||||
\(823\) | 27.7022 | 0.965637 | 0.482818 | − | 0.875721i | \(-0.339613\pi\) | ||||
0.482818 | + | 0.875721i | \(0.339613\pi\) | |||||||
\(824\) | −19.6474 | −0.684448 | ||||||||
\(825\) | −21.3601 | −0.743664 | ||||||||
\(826\) | 3.93165 | 0.136800 | ||||||||
\(827\) | 2.58119 | 0.0897569 | 0.0448785 | − | 0.998992i | \(-0.485710\pi\) | ||||
0.0448785 | + | 0.998992i | \(0.485710\pi\) | |||||||
\(828\) | 33.7206 | 1.17187 | ||||||||
\(829\) | 24.2908 | 0.843654 | 0.421827 | − | 0.906676i | \(-0.361389\pi\) | ||||
0.421827 | + | 0.906676i | \(0.361389\pi\) | |||||||
\(830\) | −8.17605 | −0.283795 | ||||||||
\(831\) | 78.5689 | 2.72553 | ||||||||
\(832\) | 1.00412 | 0.0348116 | ||||||||
\(833\) | 19.4496 | 0.673890 | ||||||||
\(834\) | −15.2293 | −0.527348 | ||||||||
\(835\) | 15.4967 | 0.536286 | ||||||||
\(836\) | 5.64286 | 0.195162 | ||||||||
\(837\) | 5.97543 | 0.206541 | ||||||||
\(838\) | 0.124193 | 0.00429018 | ||||||||
\(839\) | −43.2157 | −1.49197 | −0.745985 | − | 0.665962i | \(-0.768021\pi\) | ||||
−0.745985 | + | 0.665962i | \(0.768021\pi\) | |||||||
\(840\) | −1.78859 | −0.0617121 | ||||||||
\(841\) | −11.7084 | −0.403737 | ||||||||
\(842\) | −14.8032 | −0.510152 | ||||||||
\(843\) | −14.7111 | −0.506679 | ||||||||
\(844\) | 11.7326 | 0.403852 | ||||||||
\(845\) | 8.10611 | 0.278859 | ||||||||
\(846\) | 44.4466 | 1.52811 | ||||||||
\(847\) | 7.84135 | 0.269432 | ||||||||
\(848\) | −8.39649 | −0.288337 | ||||||||
\(849\) | 86.7395 | 2.97689 | ||||||||
\(850\) | 14.7233 | 0.505006 | ||||||||
\(851\) | 12.8371 | 0.440050 | ||||||||
\(852\) | −1.99454 | −0.0683317 | ||||||||
\(853\) | −40.1372 | −1.37427 | −0.687135 | − | 0.726530i | \(-0.741132\pi\) | ||||
−0.687135 | + | 0.726530i | \(0.741132\pi\) | |||||||
\(854\) | 1.97319 | 0.0675212 | ||||||||
\(855\) | 8.61606 | 0.294663 | ||||||||
\(856\) | 2.18068 | 0.0745341 | ||||||||
\(857\) | 0.933967 | 0.0319037 | 0.0159518 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159518 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(858\) | 4.72107 | 0.161175 | ||||||||
\(859\) | 34.6405 | 1.18192 | 0.590958 | − | 0.806702i | \(-0.298750\pi\) | ||||
0.590958 | + | 0.806702i | \(0.298750\pi\) | |||||||
\(860\) | −1.87665 | −0.0639933 | ||||||||
\(861\) | 18.8911 | 0.643806 | ||||||||
\(862\) | 1.54029 | 0.0524625 | ||||||||
\(863\) | 10.3125 | 0.351040 | 0.175520 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175520 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(864\) | −2.67680 | −0.0910665 | ||||||||
\(865\) | −12.6103 | −0.428762 | ||||||||
\(866\) | −26.4020 | −0.897177 | ||||||||
\(867\) | 17.2028 | 0.584238 | ||||||||
\(868\) | 2.23072 | 0.0757156 | ||||||||
\(869\) | −14.7862 | −0.501588 | ||||||||
\(870\) | 7.44280 | 0.252335 | ||||||||
\(871\) | −11.2811 | −0.382246 | ||||||||
\(872\) | 0.957011 | 0.0324085 | ||||||||
\(873\) | 50.2843 | 1.70187 | ||||||||
\(874\) | −26.7166 | −0.903701 | ||||||||
\(875\) | −6.44628 | −0.217924 | ||||||||
\(876\) | −2.53796 | −0.0857496 | ||||||||
\(877\) | −24.8101 | −0.837776 | −0.418888 | − | 0.908038i | \(-0.637580\pi\) | ||||
−0.418888 | + | 0.908038i | \(0.637580\pi\) | |||||||
\(878\) | 1.28084 | 0.0432263 | ||||||||
\(879\) | 77.3670 | 2.60952 | ||||||||
\(880\) | 1.20032 | 0.0404628 | ||||||||
\(881\) | −8.83737 | −0.297738 | −0.148869 | − | 0.988857i | \(-0.547563\pi\) | ||||
−0.148869 | + | 0.988857i | \(0.547563\pi\) | |||||||
\(882\) | −24.0714 | −0.810525 | ||||||||
\(883\) | 0.651910 | 0.0219385 | 0.0109693 | − | 0.999940i | \(-0.496508\pi\) | ||||
0.0109693 | + | 0.999940i | \(0.496508\pi\) | |||||||
\(884\) | −3.25419 | −0.109450 | ||||||||
\(885\) | −7.04211 | −0.236718 | ||||||||
\(886\) | −16.4162 | −0.551512 | ||||||||
\(887\) | 50.6763 | 1.70154 | 0.850772 | − | 0.525535i | \(-0.176135\pi\) | ||||
0.850772 | + | 0.525535i | \(0.176135\pi\) | |||||||
\(888\) | −4.04303 | −0.135675 | ||||||||
\(889\) | −11.2912 | −0.378694 | ||||||||
\(890\) | −0.448692 | −0.0150402 | ||||||||
\(891\) | 8.78107 | 0.294177 | ||||||||
\(892\) | −0.662036 | −0.0221666 | ||||||||
\(893\) | −35.2147 | −1.17841 | ||||||||
\(894\) | −21.3642 | −0.714525 | ||||||||
\(895\) | 7.09244 | 0.237074 | ||||||||
\(896\) | −0.999289 | −0.0333839 | ||||||||
\(897\) | −22.3523 | −0.746321 | ||||||||
\(898\) | 36.2018 | 1.20807 | ||||||||
\(899\) | −9.28264 | −0.309593 | ||||||||
\(900\) | −18.2220 | −0.607399 | ||||||||
\(901\) | 27.2117 | 0.906552 | ||||||||
\(902\) | −12.6778 | −0.422125 | ||||||||
\(903\) | 7.34570 | 0.244450 | ||||||||
\(904\) | −15.6071 | −0.519084 | ||||||||
\(905\) | 12.7869 | 0.425050 | ||||||||
\(906\) | 0.315840 | 0.0104931 | ||||||||
\(907\) | 9.79119 | 0.325111 | 0.162555 | − | 0.986699i | \(-0.448026\pi\) | ||||
0.162555 | + | 0.986699i | \(0.448026\pi\) | |||||||
\(908\) | 10.0944 | 0.334996 | ||||||||
\(909\) | −3.28945 | −0.109104 | ||||||||
\(910\) | 0.678276 | 0.0224846 | ||||||||
\(911\) | −2.61506 | −0.0866409 | −0.0433205 | − | 0.999061i | \(-0.513794\pi\) | ||||
−0.0433205 | + | 0.999061i | \(0.513794\pi\) | |||||||
\(912\) | 8.41435 | 0.278627 | ||||||||
\(913\) | −21.4773 | −0.710797 | ||||||||
\(914\) | 42.1247 | 1.39336 | ||||||||
\(915\) | −3.53424 | −0.116838 | ||||||||
\(916\) | 7.12675 | 0.235475 | ||||||||
\(917\) | 5.39184 | 0.178054 | ||||||||
\(918\) | 8.67507 | 0.286320 | ||||||||
\(919\) | −42.1602 | −1.39074 | −0.695369 | − | 0.718653i | \(-0.744759\pi\) | ||||
−0.695369 | + | 0.718653i | \(0.744759\pi\) | |||||||
\(920\) | −5.68301 | −0.187363 | ||||||||
\(921\) | 39.2064 | 1.29189 | ||||||||
\(922\) | −16.4873 | −0.542979 | ||||||||
\(923\) | 0.756378 | 0.0248965 | ||||||||
\(924\) | −4.69836 | −0.154565 | ||||||||
\(925\) | −6.93693 | −0.228085 | ||||||||
\(926\) | 10.5166 | 0.345596 | ||||||||
\(927\) | −78.8044 | −2.58828 | ||||||||
\(928\) | 4.15832 | 0.136504 | ||||||||
\(929\) | 9.30964 | 0.305439 | 0.152720 | − | 0.988270i | \(-0.451197\pi\) | ||||
0.152720 | + | 0.988270i | \(0.451197\pi\) | |||||||
\(930\) | −3.99551 | −0.131018 | ||||||||
\(931\) | 19.0716 | 0.625045 | ||||||||
\(932\) | −3.11727 | −0.102110 | ||||||||
\(933\) | 34.3881 | 1.12581 | ||||||||
\(934\) | −35.4620 | −1.16035 | ||||||||
\(935\) | −3.89005 | −0.127218 | ||||||||
\(936\) | 4.02746 | 0.131642 | ||||||||
\(937\) | 35.5140 | 1.16019 | 0.580096 | − | 0.814548i | \(-0.303015\pi\) | ||||
0.580096 | + | 0.814548i | \(0.303015\pi\) | |||||||
\(938\) | 11.2269 | 0.366570 | ||||||||
\(939\) | 69.4702 | 2.26707 | ||||||||
\(940\) | −7.49069 | −0.244320 | ||||||||
\(941\) | 2.85485 | 0.0930656 | 0.0465328 | − | 0.998917i | \(-0.485183\pi\) | ||||
0.0465328 | + | 0.998917i | \(0.485183\pi\) | |||||||
\(942\) | 28.4500 | 0.926951 | ||||||||
\(943\) | 60.0241 | 1.95465 | ||||||||
\(944\) | −3.93445 | −0.128055 | ||||||||
\(945\) | −1.80816 | −0.0588195 | ||||||||
\(946\) | −4.92970 | −0.160279 | ||||||||
\(947\) | 7.29759 | 0.237140 | 0.118570 | − | 0.992946i | \(-0.462169\pi\) | ||||
0.118570 | + | 0.992946i | \(0.462169\pi\) | |||||||
\(948\) | −22.0485 | −0.716101 | ||||||||
\(949\) | 0.962456 | 0.0312426 | ||||||||
\(950\) | 14.4371 | 0.468402 | ||||||||
\(951\) | 47.2673 | 1.53275 | ||||||||
\(952\) | 3.23854 | 0.104962 | ||||||||
\(953\) | −30.9193 | −1.00158 | −0.500788 | − | 0.865570i | \(-0.666956\pi\) | ||||
−0.500788 | + | 0.865570i | \(0.666956\pi\) | |||||||
\(954\) | −33.6778 | −1.09036 | ||||||||
\(955\) | −2.10831 | −0.0682232 | ||||||||
\(956\) | 15.8275 | 0.511898 | ||||||||
\(957\) | 19.5512 | 0.632000 | ||||||||
\(958\) | −29.1676 | −0.942363 | ||||||||
\(959\) | −22.0368 | −0.711607 | ||||||||
\(960\) | 1.78986 | 0.0577674 | ||||||||
\(961\) | −26.0168 | −0.839252 | ||||||||
\(962\) | 1.53322 | 0.0494329 | ||||||||
\(963\) | 8.74659 | 0.281855 | ||||||||
\(964\) | −17.6675 | −0.569032 | ||||||||
\(965\) | −2.37860 | −0.0765698 | ||||||||
\(966\) | 22.2448 | 0.715714 | ||||||||
\(967\) | 6.55842 | 0.210905 | 0.105452 | − | 0.994424i | \(-0.466371\pi\) | ||||
0.105452 | + | 0.994424i | \(0.466371\pi\) | |||||||
\(968\) | −7.84692 | −0.252210 | ||||||||
\(969\) | −27.2695 | −0.876023 | ||||||||
\(970\) | −8.47453 | −0.272101 | ||||||||
\(971\) | 28.1034 | 0.901880 | 0.450940 | − | 0.892554i | \(-0.351089\pi\) | ||||
0.450940 | + | 0.892554i | \(0.351089\pi\) | |||||||
\(972\) | 21.1243 | 0.677561 | ||||||||
\(973\) | −5.74755 | −0.184258 | ||||||||
\(974\) | −19.6810 | −0.630619 | ||||||||
\(975\) | 12.0787 | 0.386829 | ||||||||
\(976\) | −1.97459 | −0.0632052 | ||||||||
\(977\) | −21.3900 | −0.684326 | −0.342163 | − | 0.939641i | \(-0.611160\pi\) | ||||
−0.342163 | + | 0.939641i | \(0.611160\pi\) | |||||||
\(978\) | −5.60448 | −0.179211 | ||||||||
\(979\) | −1.17865 | −0.0376699 | ||||||||
\(980\) | 4.05681 | 0.129590 | ||||||||
\(981\) | 3.83852 | 0.122554 | ||||||||
\(982\) | −14.4946 | −0.462541 | ||||||||
\(983\) | 16.1687 | 0.515703 | 0.257851 | − | 0.966185i | \(-0.416985\pi\) | ||||
0.257851 | + | 0.966185i | \(0.416985\pi\) | |||||||
\(984\) | −18.9045 | −0.602653 | ||||||||
\(985\) | 12.3687 | 0.394101 | ||||||||
\(986\) | −13.4764 | −0.429177 | ||||||||
\(987\) | 29.3205 | 0.933282 | ||||||||
\(988\) | −3.19093 | −0.101517 | ||||||||
\(989\) | 23.3401 | 0.742171 | ||||||||
\(990\) | 4.81442 | 0.153012 | ||||||||
\(991\) | −2.44333 | −0.0776150 | −0.0388075 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388075 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(992\) | −2.23231 | −0.0708758 | ||||||||
\(993\) | −87.9601 | −2.79133 | ||||||||
\(994\) | −0.752741 | −0.0238755 | ||||||||
\(995\) | 4.48094 | 0.142055 | ||||||||
\(996\) | −32.0259 | −1.01478 | ||||||||
\(997\) | 29.9719 | 0.949220 | 0.474610 | − | 0.880196i | \(-0.342589\pi\) | ||||
0.474610 | + | 0.880196i | \(0.342589\pi\) | |||||||
\(998\) | 18.5198 | 0.586234 | ||||||||
\(999\) | −4.08728 | −0.129316 |
(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.d.1.11 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.11 | ✓ | 69 | 1.1 | even | 1 | trivial |