Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.32 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74833 | 1.94336 | 0.971682 | − | 0.236293i | \(-0.0759327\pi\) | ||||
0.971682 | + | 0.236293i | \(0.0759327\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.55332 | 2.77666 | ||||||||
\(5\) | 0.373803 | 0.167170 | 0.0835849 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835849 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(6\) | −2.74833 | −1.12200 | ||||||||
\(7\) | −2.56695 | −0.970218 | −0.485109 | − | 0.874454i | \(-0.661220\pi\) | ||||
−0.485109 | + | 0.874454i | \(0.661220\pi\) | |||||||
\(8\) | 9.76571 | 3.45270 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.02733 | 0.324872 | ||||||||
\(11\) | 5.33080 | 1.60730 | 0.803648 | − | 0.595104i | \(-0.202889\pi\) | ||||
0.803648 | + | 0.595104i | \(0.202889\pi\) | |||||||
\(12\) | −5.55332 | −1.60311 | ||||||||
\(13\) | 1.62873 | 0.451729 | 0.225864 | − | 0.974159i | \(-0.427479\pi\) | ||||
0.225864 | + | 0.974159i | \(0.427479\pi\) | |||||||
\(14\) | −7.05484 | −1.88549 | ||||||||
\(15\) | −0.373803 | −0.0965155 | ||||||||
\(16\) | 15.7328 | 3.93319 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 2.74833 | 0.647788 | ||||||||
\(19\) | 6.40751 | 1.46998 | 0.734992 | − | 0.678076i | \(-0.237186\pi\) | ||||
0.734992 | + | 0.678076i | \(0.237186\pi\) | |||||||
\(20\) | 2.07585 | 0.464174 | ||||||||
\(21\) | 2.56695 | 0.560155 | ||||||||
\(22\) | 14.6508 | 3.12356 | ||||||||
\(23\) | −8.29053 | −1.72870 | −0.864348 | − | 0.502894i | \(-0.832268\pi\) | ||||
−0.864348 | + | 0.502894i | \(0.832268\pi\) | |||||||
\(24\) | −9.76571 | −1.99342 | ||||||||
\(25\) | −4.86027 | −0.972054 | ||||||||
\(26\) | 4.47629 | 0.877873 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −14.2551 | −2.69397 | ||||||||
\(29\) | 7.11963 | 1.32208 | 0.661041 | − | 0.750350i | \(-0.270115\pi\) | ||||
0.661041 | + | 0.750350i | \(0.270115\pi\) | |||||||
\(30\) | −1.02733 | −0.187565 | ||||||||
\(31\) | −0.319404 | −0.0573666 | −0.0286833 | − | 0.999589i | \(-0.509131\pi\) | ||||
−0.0286833 | + | 0.999589i | \(0.509131\pi\) | |||||||
\(32\) | 23.7074 | 4.19091 | ||||||||
\(33\) | −5.33080 | −0.927973 | ||||||||
\(34\) | −2.74833 | −0.471335 | ||||||||
\(35\) | −0.959535 | −0.162191 | ||||||||
\(36\) | 5.55332 | 0.925554 | ||||||||
\(37\) | −9.68955 | −1.59295 | −0.796477 | − | 0.604669i | \(-0.793305\pi\) | ||||
−0.796477 | + | 0.604669i | \(0.793305\pi\) | |||||||
\(38\) | 17.6100 | 2.85671 | ||||||||
\(39\) | −1.62873 | −0.260806 | ||||||||
\(40\) | 3.65045 | 0.577187 | ||||||||
\(41\) | 10.6895 | 1.66941 | 0.834707 | − | 0.550694i | \(-0.185637\pi\) | ||||
0.834707 | + | 0.550694i | \(0.185637\pi\) | |||||||
\(42\) | 7.05484 | 1.08859 | ||||||||
\(43\) | −2.22479 | −0.339277 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(44\) | 29.6037 | 4.46292 | ||||||||
\(45\) | 0.373803 | 0.0557233 | ||||||||
\(46\) | −22.7851 | −3.35948 | ||||||||
\(47\) | −1.32238 | −0.192889 | −0.0964447 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964447 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(48\) | −15.7328 | −2.27083 | ||||||||
\(49\) | −0.410745 | −0.0586778 | ||||||||
\(50\) | −13.3576 | −1.88905 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 9.04487 | 1.25430 | ||||||||
\(53\) | 0.149084 | 0.0204782 | 0.0102391 | − | 0.999948i | \(-0.496741\pi\) | ||||
0.0102391 | + | 0.999948i | \(0.496741\pi\) | |||||||
\(54\) | −2.74833 | −0.374000 | ||||||||
\(55\) | 1.99267 | 0.268691 | ||||||||
\(56\) | −25.0681 | −3.34987 | ||||||||
\(57\) | −6.40751 | −0.848696 | ||||||||
\(58\) | 19.5671 | 2.56929 | ||||||||
\(59\) | 0.248068 | 0.0322957 | 0.0161479 | − | 0.999870i | \(-0.494860\pi\) | ||||
0.0161479 | + | 0.999870i | \(0.494860\pi\) | |||||||
\(60\) | −2.07585 | −0.267991 | ||||||||
\(61\) | 10.9718 | 1.40480 | 0.702400 | − | 0.711782i | \(-0.252112\pi\) | ||||
0.702400 | + | 0.711782i | \(0.252112\pi\) | |||||||
\(62\) | −0.877828 | −0.111484 | ||||||||
\(63\) | −2.56695 | −0.323406 | ||||||||
\(64\) | 33.6903 | 4.21128 | ||||||||
\(65\) | 0.608824 | 0.0755154 | ||||||||
\(66\) | −14.6508 | −1.80339 | ||||||||
\(67\) | 6.82788 | 0.834158 | 0.417079 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417079 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(68\) | −5.55332 | −0.673439 | ||||||||
\(69\) | 8.29053 | 0.998063 | ||||||||
\(70\) | −2.63712 | −0.315196 | ||||||||
\(71\) | −9.62623 | −1.14242 | −0.571211 | − | 0.820803i | \(-0.693526\pi\) | ||||
−0.571211 | + | 0.820803i | \(0.693526\pi\) | |||||||
\(72\) | 9.76571 | 1.15090 | ||||||||
\(73\) | 1.57803 | 0.184695 | 0.0923473 | − | 0.995727i | \(-0.470563\pi\) | ||||
0.0923473 | + | 0.995727i | \(0.470563\pi\) | |||||||
\(74\) | −26.6301 | −3.09569 | ||||||||
\(75\) | 4.86027 | 0.561216 | ||||||||
\(76\) | 35.5830 | 4.08165 | ||||||||
\(77\) | −13.6839 | −1.55943 | ||||||||
\(78\) | −4.47629 | −0.506840 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 5.88095 | 0.657510 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 29.3782 | 3.24428 | ||||||||
\(83\) | 17.5951 | 1.93132 | 0.965658 | − | 0.259817i | \(-0.0836624\pi\) | ||||
0.965658 | + | 0.259817i | \(0.0836624\pi\) | |||||||
\(84\) | 14.2551 | 1.55536 | ||||||||
\(85\) | −0.373803 | −0.0405446 | ||||||||
\(86\) | −6.11445 | −0.659338 | ||||||||
\(87\) | −7.11963 | −0.763305 | ||||||||
\(88\) | 52.0590 | 5.54951 | ||||||||
\(89\) | 14.4784 | 1.53471 | 0.767354 | − | 0.641223i | \(-0.221573\pi\) | ||||
0.767354 | + | 0.641223i | \(0.221573\pi\) | |||||||
\(90\) | 1.02733 | 0.108291 | ||||||||
\(91\) | −4.18088 | −0.438275 | ||||||||
\(92\) | −46.0400 | −4.80000 | ||||||||
\(93\) | 0.319404 | 0.0331206 | ||||||||
\(94\) | −3.63435 | −0.374854 | ||||||||
\(95\) | 2.39515 | 0.245737 | ||||||||
\(96\) | −23.7074 | −2.41963 | ||||||||
\(97\) | −15.6399 | −1.58799 | −0.793993 | − | 0.607927i | \(-0.792001\pi\) | ||||
−0.793993 | + | 0.607927i | \(0.792001\pi\) | |||||||
\(98\) | −1.12886 | −0.114032 | ||||||||
\(99\) | 5.33080 | 0.535766 | ||||||||
\(100\) | −26.9907 | −2.69907 | ||||||||
\(101\) | −17.8744 | −1.77857 | −0.889286 | − | 0.457352i | \(-0.848798\pi\) | ||||
−0.889286 | + | 0.457352i | \(0.848798\pi\) | |||||||
\(102\) | 2.74833 | 0.272125 | ||||||||
\(103\) | 8.14100 | 0.802156 | 0.401078 | − | 0.916044i | \(-0.368636\pi\) | ||||
0.401078 | + | 0.916044i | \(0.368636\pi\) | |||||||
\(104\) | 15.9057 | 1.55968 | ||||||||
\(105\) | 0.959535 | 0.0936410 | ||||||||
\(106\) | 0.409731 | 0.0397966 | ||||||||
\(107\) | −0.591829 | −0.0572143 | −0.0286071 | − | 0.999591i | \(-0.509107\pi\) | ||||
−0.0286071 | + | 0.999591i | \(0.509107\pi\) | |||||||
\(108\) | −5.55332 | −0.534369 | ||||||||
\(109\) | −8.27027 | −0.792148 | −0.396074 | − | 0.918219i | \(-0.629628\pi\) | ||||
−0.396074 | + | 0.918219i | \(0.629628\pi\) | |||||||
\(110\) | 5.47651 | 0.522165 | ||||||||
\(111\) | 9.68955 | 0.919692 | ||||||||
\(112\) | −40.3853 | −3.81605 | ||||||||
\(113\) | −2.16838 | −0.203984 | −0.101992 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101992 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(114\) | −17.6100 | −1.64932 | ||||||||
\(115\) | −3.09903 | −0.288986 | ||||||||
\(116\) | 39.5376 | 3.67098 | ||||||||
\(117\) | 1.62873 | 0.150576 | ||||||||
\(118\) | 0.681773 | 0.0627623 | ||||||||
\(119\) | 2.56695 | 0.235312 | ||||||||
\(120\) | −3.65045 | −0.333239 | ||||||||
\(121\) | 17.4174 | 1.58340 | ||||||||
\(122\) | 30.1543 | 2.73004 | ||||||||
\(123\) | −10.6895 | −0.963837 | ||||||||
\(124\) | −1.77375 | −0.159288 | ||||||||
\(125\) | −3.68580 | −0.329668 | ||||||||
\(126\) | −7.05484 | −0.628495 | ||||||||
\(127\) | 17.9434 | 1.59222 | 0.796110 | − | 0.605152i | \(-0.206888\pi\) | ||||
0.796110 | + | 0.605152i | \(0.206888\pi\) | |||||||
\(128\) | 45.1772 | 3.99314 | ||||||||
\(129\) | 2.22479 | 0.195882 | ||||||||
\(130\) | 1.67325 | 0.146754 | ||||||||
\(131\) | 17.8875 | 1.56284 | 0.781420 | − | 0.624005i | \(-0.214496\pi\) | ||||
0.781420 | + | 0.624005i | \(0.214496\pi\) | |||||||
\(132\) | −29.6037 | −2.57667 | ||||||||
\(133\) | −16.4478 | −1.42620 | ||||||||
\(134\) | 18.7653 | 1.62107 | ||||||||
\(135\) | −0.373803 | −0.0321718 | ||||||||
\(136\) | −9.76571 | −0.837403 | ||||||||
\(137\) | 1.72142 | 0.147071 | 0.0735355 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735355 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(138\) | 22.7851 | 1.93960 | ||||||||
\(139\) | −8.00475 | −0.678954 | −0.339477 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339477 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(140\) | −5.32861 | −0.450350 | ||||||||
\(141\) | 1.32238 | 0.111365 | ||||||||
\(142\) | −26.4561 | −2.22014 | ||||||||
\(143\) | 8.68244 | 0.726062 | ||||||||
\(144\) | 15.7328 | 1.31106 | ||||||||
\(145\) | 2.66134 | 0.221012 | ||||||||
\(146\) | 4.33695 | 0.358929 | ||||||||
\(147\) | 0.410745 | 0.0338777 | ||||||||
\(148\) | −53.8092 | −4.42309 | ||||||||
\(149\) | −18.5362 | −1.51854 | −0.759271 | − | 0.650775i | \(-0.774444\pi\) | ||||
−0.759271 | + | 0.650775i | \(0.774444\pi\) | |||||||
\(150\) | 13.3576 | 1.09065 | ||||||||
\(151\) | 3.63863 | 0.296107 | 0.148054 | − | 0.988979i | \(-0.452699\pi\) | ||||
0.148054 | + | 0.988979i | \(0.452699\pi\) | |||||||
\(152\) | 62.5739 | 5.07541 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −37.6079 | −3.03053 | ||||||||
\(155\) | −0.119394 | −0.00958997 | ||||||||
\(156\) | −9.04487 | −0.724169 | ||||||||
\(157\) | 8.19091 | 0.653706 | 0.326853 | − | 0.945075i | \(-0.394012\pi\) | ||||
0.326853 | + | 0.945075i | \(0.394012\pi\) | |||||||
\(158\) | 2.74833 | 0.218645 | ||||||||
\(159\) | −0.149084 | −0.0118231 | ||||||||
\(160\) | 8.86189 | 0.700594 | ||||||||
\(161\) | 21.2814 | 1.67721 | ||||||||
\(162\) | 2.74833 | 0.215929 | ||||||||
\(163\) | −5.79651 | −0.454018 | −0.227009 | − | 0.973893i | \(-0.572895\pi\) | ||||
−0.227009 | + | 0.973893i | \(0.572895\pi\) | |||||||
\(164\) | 59.3621 | 4.63540 | ||||||||
\(165\) | −1.99267 | −0.155129 | ||||||||
\(166\) | 48.3572 | 3.75325 | ||||||||
\(167\) | 9.67616 | 0.748763 | 0.374382 | − | 0.927275i | \(-0.377855\pi\) | ||||
0.374382 | + | 0.927275i | \(0.377855\pi\) | |||||||
\(168\) | 25.0681 | 1.93405 | ||||||||
\(169\) | −10.3472 | −0.795941 | ||||||||
\(170\) | −1.02733 | −0.0787929 | ||||||||
\(171\) | 6.40751 | 0.489995 | ||||||||
\(172\) | −12.3550 | −0.942057 | ||||||||
\(173\) | −18.4489 | −1.40265 | −0.701323 | − | 0.712843i | \(-0.747407\pi\) | ||||
−0.701323 | + | 0.712843i | \(0.747407\pi\) | |||||||
\(174\) | −19.5671 | −1.48338 | ||||||||
\(175\) | 12.4761 | 0.943104 | ||||||||
\(176\) | 83.8682 | 6.32180 | ||||||||
\(177\) | −0.248068 | −0.0186459 | ||||||||
\(178\) | 39.7915 | 2.98250 | ||||||||
\(179\) | 11.9693 | 0.894626 | 0.447313 | − | 0.894377i | \(-0.352381\pi\) | ||||
0.447313 | + | 0.894377i | \(0.352381\pi\) | |||||||
\(180\) | 2.07585 | 0.154725 | ||||||||
\(181\) | −19.5566 | −1.45363 | −0.726815 | − | 0.686833i | \(-0.759000\pi\) | ||||
−0.726815 | + | 0.686833i | \(0.759000\pi\) | |||||||
\(182\) | −11.4904 | −0.851728 | ||||||||
\(183\) | −10.9718 | −0.811062 | ||||||||
\(184\) | −80.9629 | −5.96867 | ||||||||
\(185\) | −3.62198 | −0.266294 | ||||||||
\(186\) | 0.877828 | 0.0643654 | ||||||||
\(187\) | −5.33080 | −0.389827 | ||||||||
\(188\) | −7.34362 | −0.535589 | ||||||||
\(189\) | 2.56695 | 0.186718 | ||||||||
\(190\) | 6.58266 | 0.477556 | ||||||||
\(191\) | −15.7826 | −1.14199 | −0.570993 | − | 0.820955i | \(-0.693442\pi\) | ||||
−0.570993 | + | 0.820955i | \(0.693442\pi\) | |||||||
\(192\) | −33.6903 | −2.43138 | ||||||||
\(193\) | 8.56277 | 0.616362 | 0.308181 | − | 0.951328i | \(-0.400280\pi\) | ||||
0.308181 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(194\) | −42.9835 | −3.08603 | ||||||||
\(195\) | −0.608824 | −0.0435988 | ||||||||
\(196\) | −2.28100 | −0.162929 | ||||||||
\(197\) | −11.6567 | −0.830507 | −0.415253 | − | 0.909706i | \(-0.636307\pi\) | ||||
−0.415253 | + | 0.909706i | \(0.636307\pi\) | |||||||
\(198\) | 14.6508 | 1.04119 | ||||||||
\(199\) | −17.5984 | −1.24752 | −0.623760 | − | 0.781616i | \(-0.714396\pi\) | ||||
−0.623760 | + | 0.781616i | \(0.714396\pi\) | |||||||
\(200\) | −47.4640 | −3.35621 | ||||||||
\(201\) | −6.82788 | −0.481602 | ||||||||
\(202\) | −49.1248 | −3.45641 | ||||||||
\(203\) | −18.2758 | −1.28271 | ||||||||
\(204\) | 5.55332 | 0.388810 | ||||||||
\(205\) | 3.99575 | 0.279076 | ||||||||
\(206\) | 22.3742 | 1.55888 | ||||||||
\(207\) | −8.29053 | −0.576232 | ||||||||
\(208\) | 25.6244 | 1.77673 | ||||||||
\(209\) | 34.1572 | 2.36270 | ||||||||
\(210\) | 2.63712 | 0.181979 | ||||||||
\(211\) | −24.6862 | −1.69947 | −0.849733 | − | 0.527213i | \(-0.823237\pi\) | ||||
−0.849733 | + | 0.527213i | \(0.823237\pi\) | |||||||
\(212\) | 0.827910 | 0.0568611 | ||||||||
\(213\) | 9.62623 | 0.659578 | ||||||||
\(214\) | −1.62654 | −0.111188 | ||||||||
\(215\) | −0.831632 | −0.0567169 | ||||||||
\(216\) | −9.76571 | −0.664472 | ||||||||
\(217\) | 0.819895 | 0.0556581 | ||||||||
\(218\) | −22.7294 | −1.53943 | ||||||||
\(219\) | −1.57803 | −0.106633 | ||||||||
\(220\) | 11.0659 | 0.746065 | ||||||||
\(221\) | −1.62873 | −0.109560 | ||||||||
\(222\) | 26.6301 | 1.78730 | ||||||||
\(223\) | −6.86018 | −0.459391 | −0.229696 | − | 0.973263i | \(-0.573773\pi\) | ||||
−0.229696 | + | 0.973263i | \(0.573773\pi\) | |||||||
\(224\) | −60.8558 | −4.06610 | ||||||||
\(225\) | −4.86027 | −0.324018 | ||||||||
\(226\) | −5.95944 | −0.396416 | ||||||||
\(227\) | −9.87021 | −0.655109 | −0.327554 | − | 0.944832i | \(-0.606224\pi\) | ||||
−0.327554 | + | 0.944832i | \(0.606224\pi\) | |||||||
\(228\) | −35.5830 | −2.35654 | ||||||||
\(229\) | −14.7541 | −0.974976 | −0.487488 | − | 0.873130i | \(-0.662087\pi\) | ||||
−0.487488 | + | 0.873130i | \(0.662087\pi\) | |||||||
\(230\) | −8.51715 | −0.561604 | ||||||||
\(231\) | 13.6839 | 0.900336 | ||||||||
\(232\) | 69.5282 | 4.56475 | ||||||||
\(233\) | −16.1279 | −1.05658 | −0.528289 | − | 0.849065i | \(-0.677166\pi\) | ||||
−0.528289 | + | 0.849065i | \(0.677166\pi\) | |||||||
\(234\) | 4.47629 | 0.292624 | ||||||||
\(235\) | −0.494311 | −0.0322453 | ||||||||
\(236\) | 1.37760 | 0.0896742 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 7.05484 | 0.457297 | ||||||||
\(239\) | −30.8739 | −1.99706 | −0.998532 | − | 0.0541703i | \(-0.982749\pi\) | ||||
−0.998532 | + | 0.0541703i | \(0.982749\pi\) | |||||||
\(240\) | −5.88095 | −0.379614 | ||||||||
\(241\) | 7.78762 | 0.501645 | 0.250822 | − | 0.968033i | \(-0.419299\pi\) | ||||
0.250822 | + | 0.968033i | \(0.419299\pi\) | |||||||
\(242\) | 47.8689 | 3.07713 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 60.9302 | 3.90066 | ||||||||
\(245\) | −0.153538 | −0.00980916 | ||||||||
\(246\) | −29.3782 | −1.87308 | ||||||||
\(247\) | 10.4361 | 0.664034 | ||||||||
\(248\) | −3.11921 | −0.198070 | ||||||||
\(249\) | −17.5951 | −1.11505 | ||||||||
\(250\) | −10.1298 | −0.640664 | ||||||||
\(251\) | 17.3058 | 1.09233 | 0.546167 | − | 0.837676i | \(-0.316086\pi\) | ||||
0.546167 | + | 0.837676i | \(0.316086\pi\) | |||||||
\(252\) | −14.2551 | −0.897989 | ||||||||
\(253\) | −44.1952 | −2.77853 | ||||||||
\(254\) | 49.3144 | 3.09426 | ||||||||
\(255\) | 0.373803 | 0.0234085 | ||||||||
\(256\) | 56.7814 | 3.54883 | ||||||||
\(257\) | 4.96971 | 0.310002 | 0.155001 | − | 0.987914i | \(-0.450462\pi\) | ||||
0.155001 | + | 0.987914i | \(0.450462\pi\) | |||||||
\(258\) | 6.11445 | 0.380669 | ||||||||
\(259\) | 24.8726 | 1.54551 | ||||||||
\(260\) | 3.38100 | 0.209681 | ||||||||
\(261\) | 7.11963 | 0.440694 | ||||||||
\(262\) | 49.1608 | 3.03717 | ||||||||
\(263\) | −27.5432 | −1.69839 | −0.849193 | − | 0.528083i | \(-0.822911\pi\) | ||||
−0.849193 | + | 0.528083i | \(0.822911\pi\) | |||||||
\(264\) | −52.0590 | −3.20401 | ||||||||
\(265\) | 0.0557279 | 0.00342334 | ||||||||
\(266\) | −45.2040 | −2.77163 | ||||||||
\(267\) | −14.4784 | −0.886064 | ||||||||
\(268\) | 37.9174 | 2.31618 | ||||||||
\(269\) | 10.1279 | 0.617509 | 0.308755 | − | 0.951142i | \(-0.400088\pi\) | ||||
0.308755 | + | 0.951142i | \(0.400088\pi\) | |||||||
\(270\) | −1.02733 | −0.0625216 | ||||||||
\(271\) | −1.32119 | −0.0802568 | −0.0401284 | − | 0.999195i | \(-0.512777\pi\) | ||||
−0.0401284 | + | 0.999195i | \(0.512777\pi\) | |||||||
\(272\) | −15.7328 | −0.953938 | ||||||||
\(273\) | 4.18088 | 0.253038 | ||||||||
\(274\) | 4.73103 | 0.285812 | ||||||||
\(275\) | −25.9091 | −1.56238 | ||||||||
\(276\) | 46.0400 | 2.77128 | ||||||||
\(277\) | 0.795932 | 0.0478229 | 0.0239115 | − | 0.999714i | \(-0.492388\pi\) | ||||
0.0239115 | + | 0.999714i | \(0.492388\pi\) | |||||||
\(278\) | −21.9997 | −1.31945 | ||||||||
\(279\) | −0.319404 | −0.0191222 | ||||||||
\(280\) | −9.37054 | −0.559997 | ||||||||
\(281\) | 11.6674 | 0.696020 | 0.348010 | − | 0.937491i | \(-0.386858\pi\) | ||||
0.348010 | + | 0.937491i | \(0.386858\pi\) | |||||||
\(282\) | 3.63435 | 0.216422 | ||||||||
\(283\) | −28.7465 | −1.70880 | −0.854400 | − | 0.519616i | \(-0.826075\pi\) | ||||
−0.854400 | + | 0.519616i | \(0.826075\pi\) | |||||||
\(284\) | −53.4575 | −3.17212 | ||||||||
\(285\) | −2.39515 | −0.141876 | ||||||||
\(286\) | 23.8622 | 1.41100 | ||||||||
\(287\) | −27.4394 | −1.61969 | ||||||||
\(288\) | 23.7074 | 1.39697 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.31424 | 0.429507 | ||||||||
\(291\) | 15.6399 | 0.916824 | ||||||||
\(292\) | 8.76332 | 0.512834 | ||||||||
\(293\) | 1.52782 | 0.0892559 | 0.0446280 | − | 0.999004i | \(-0.485790\pi\) | ||||
0.0446280 | + | 0.999004i | \(0.485790\pi\) | |||||||
\(294\) | 1.12886 | 0.0658366 | ||||||||
\(295\) | 0.0927286 | 0.00539887 | ||||||||
\(296\) | −94.6254 | −5.49999 | ||||||||
\(297\) | −5.33080 | −0.309324 | ||||||||
\(298\) | −50.9435 | −2.95108 | ||||||||
\(299\) | −13.5030 | −0.780901 | ||||||||
\(300\) | 26.9907 | 1.55831 | ||||||||
\(301\) | 5.71093 | 0.329172 | ||||||||
\(302\) | 10.0002 | 0.575444 | ||||||||
\(303\) | 17.8744 | 1.02686 | ||||||||
\(304\) | 100.808 | 5.78172 | ||||||||
\(305\) | 4.10131 | 0.234840 | ||||||||
\(306\) | −2.74833 | −0.157112 | ||||||||
\(307\) | −18.2538 | −1.04180 | −0.520900 | − | 0.853618i | \(-0.674404\pi\) | ||||
−0.520900 | + | 0.853618i | \(0.674404\pi\) | |||||||
\(308\) | −75.9912 | −4.33000 | ||||||||
\(309\) | −8.14100 | −0.463125 | ||||||||
\(310\) | −0.328135 | −0.0186368 | ||||||||
\(311\) | 28.4096 | 1.61096 | 0.805479 | − | 0.592624i | \(-0.201908\pi\) | ||||
0.805479 | + | 0.592624i | \(0.201908\pi\) | |||||||
\(312\) | −15.9057 | −0.900483 | ||||||||
\(313\) | −9.69798 | −0.548162 | −0.274081 | − | 0.961707i | \(-0.588374\pi\) | ||||
−0.274081 | + | 0.961707i | \(0.588374\pi\) | |||||||
\(314\) | 22.5113 | 1.27039 | ||||||||
\(315\) | −0.959535 | −0.0540637 | ||||||||
\(316\) | 5.55332 | 0.312399 | ||||||||
\(317\) | 21.1700 | 1.18902 | 0.594512 | − | 0.804087i | \(-0.297345\pi\) | ||||
0.594512 | + | 0.804087i | \(0.297345\pi\) | |||||||
\(318\) | −0.409731 | −0.0229766 | ||||||||
\(319\) | 37.9533 | 2.12498 | ||||||||
\(320\) | 12.5935 | 0.703999 | ||||||||
\(321\) | 0.591829 | 0.0330327 | ||||||||
\(322\) | 58.4884 | 3.25943 | ||||||||
\(323\) | −6.40751 | −0.356524 | ||||||||
\(324\) | 5.55332 | 0.308518 | ||||||||
\(325\) | −7.91607 | −0.439105 | ||||||||
\(326\) | −15.9307 | −0.882321 | ||||||||
\(327\) | 8.27027 | 0.457347 | ||||||||
\(328\) | 104.390 | 5.76398 | ||||||||
\(329\) | 3.39450 | 0.187145 | ||||||||
\(330\) | −5.47651 | −0.301472 | ||||||||
\(331\) | −21.6099 | −1.18779 | −0.593895 | − | 0.804543i | \(-0.702410\pi\) | ||||
−0.593895 | + | 0.804543i | \(0.702410\pi\) | |||||||
\(332\) | 97.7114 | 5.36261 | ||||||||
\(333\) | −9.68955 | −0.530984 | ||||||||
\(334\) | 26.5933 | 1.45512 | ||||||||
\(335\) | 2.55228 | 0.139446 | ||||||||
\(336\) | 40.3853 | 2.20320 | ||||||||
\(337\) | −29.5121 | −1.60763 | −0.803813 | − | 0.594882i | \(-0.797199\pi\) | ||||
−0.803813 | + | 0.594882i | \(0.797199\pi\) | |||||||
\(338\) | −28.4376 | −1.54680 | ||||||||
\(339\) | 2.16838 | 0.117770 | ||||||||
\(340\) | −2.07585 | −0.112579 | ||||||||
\(341\) | −1.70268 | −0.0922052 | ||||||||
\(342\) | 17.6100 | 0.952238 | ||||||||
\(343\) | 19.0230 | 1.02715 | ||||||||
\(344\) | −21.7266 | −1.17142 | ||||||||
\(345\) | 3.09903 | 0.166846 | ||||||||
\(346\) | −50.7038 | −2.72585 | ||||||||
\(347\) | −20.7743 | −1.11522 | −0.557612 | − | 0.830101i | \(-0.688282\pi\) | ||||
−0.557612 | + | 0.830101i | \(0.688282\pi\) | |||||||
\(348\) | −39.5376 | −2.11944 | ||||||||
\(349\) | −25.9885 | −1.39113 | −0.695567 | − | 0.718462i | \(-0.744847\pi\) | ||||
−0.695567 | + | 0.718462i | \(0.744847\pi\) | |||||||
\(350\) | 34.2884 | 1.83279 | ||||||||
\(351\) | −1.62873 | −0.0869352 | ||||||||
\(352\) | 126.379 | 6.73604 | ||||||||
\(353\) | 2.38009 | 0.126679 | 0.0633397 | − | 0.997992i | \(-0.479825\pi\) | ||||
0.0633397 | + | 0.997992i | \(0.479825\pi\) | |||||||
\(354\) | −0.681773 | −0.0362358 | ||||||||
\(355\) | −3.59831 | −0.190979 | ||||||||
\(356\) | 80.4033 | 4.26137 | ||||||||
\(357\) | −2.56695 | −0.135858 | ||||||||
\(358\) | 32.8956 | 1.73858 | ||||||||
\(359\) | 20.0137 | 1.05628 | 0.528141 | − | 0.849157i | \(-0.322889\pi\) | ||||
0.528141 | + | 0.849157i | \(0.322889\pi\) | |||||||
\(360\) | 3.65045 | 0.192396 | ||||||||
\(361\) | 22.0562 | 1.16085 | ||||||||
\(362\) | −53.7480 | −2.82493 | ||||||||
\(363\) | −17.4174 | −0.914178 | ||||||||
\(364\) | −23.2178 | −1.21694 | ||||||||
\(365\) | 0.589873 | 0.0308754 | ||||||||
\(366\) | −30.1543 | −1.57619 | ||||||||
\(367\) | 17.7943 | 0.928855 | 0.464427 | − | 0.885611i | \(-0.346260\pi\) | ||||
0.464427 | + | 0.885611i | \(0.346260\pi\) | |||||||
\(368\) | −130.433 | −6.79928 | ||||||||
\(369\) | 10.6895 | 0.556471 | ||||||||
\(370\) | −9.95441 | −0.517505 | ||||||||
\(371\) | −0.382691 | −0.0198683 | ||||||||
\(372\) | 1.77375 | 0.0919648 | ||||||||
\(373\) | 1.70830 | 0.0884525 | 0.0442262 | − | 0.999022i | \(-0.485918\pi\) | ||||
0.0442262 | + | 0.999022i | \(0.485918\pi\) | |||||||
\(374\) | −14.6508 | −0.757575 | ||||||||
\(375\) | 3.68580 | 0.190334 | ||||||||
\(376\) | −12.9140 | −0.665989 | ||||||||
\(377\) | 11.5960 | 0.597222 | ||||||||
\(378\) | 7.05484 | 0.362862 | ||||||||
\(379\) | −5.47785 | −0.281378 | −0.140689 | − | 0.990054i | \(-0.544932\pi\) | ||||
−0.140689 | + | 0.990054i | \(0.544932\pi\) | |||||||
\(380\) | 13.3010 | 0.682328 | ||||||||
\(381\) | −17.9434 | −0.919269 | ||||||||
\(382\) | −43.3757 | −2.21929 | ||||||||
\(383\) | −23.6109 | −1.20646 | −0.603230 | − | 0.797567i | \(-0.706120\pi\) | ||||
−0.603230 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(384\) | −45.1772 | −2.30544 | ||||||||
\(385\) | −5.11509 | −0.260689 | ||||||||
\(386\) | 23.5333 | 1.19781 | ||||||||
\(387\) | −2.22479 | −0.113092 | ||||||||
\(388\) | −86.8531 | −4.40930 | ||||||||
\(389\) | 20.5160 | 1.04020 | 0.520101 | − | 0.854105i | \(-0.325894\pi\) | ||||
0.520101 | + | 0.854105i | \(0.325894\pi\) | |||||||
\(390\) | −1.67325 | −0.0847284 | ||||||||
\(391\) | 8.29053 | 0.419270 | ||||||||
\(392\) | −4.01121 | −0.202597 | ||||||||
\(393\) | −17.8875 | −0.902306 | ||||||||
\(394\) | −32.0365 | −1.61398 | ||||||||
\(395\) | 0.373803 | 0.0188081 | ||||||||
\(396\) | 29.6037 | 1.48764 | ||||||||
\(397\) | 14.9466 | 0.750150 | 0.375075 | − | 0.926994i | \(-0.377617\pi\) | ||||
0.375075 | + | 0.926994i | \(0.377617\pi\) | |||||||
\(398\) | −48.3663 | −2.42438 | ||||||||
\(399\) | 16.4478 | 0.823419 | ||||||||
\(400\) | −76.4654 | −3.82327 | ||||||||
\(401\) | 6.18443 | 0.308836 | 0.154418 | − | 0.988006i | \(-0.450650\pi\) | ||||
0.154418 | + | 0.988006i | \(0.450650\pi\) | |||||||
\(402\) | −18.7653 | −0.935927 | ||||||||
\(403\) | −0.520223 | −0.0259142 | ||||||||
\(404\) | −99.2624 | −4.93849 | ||||||||
\(405\) | 0.373803 | 0.0185744 | ||||||||
\(406\) | −50.2279 | −2.49277 | ||||||||
\(407\) | −51.6531 | −2.56035 | ||||||||
\(408\) | 9.76571 | 0.483475 | ||||||||
\(409\) | 2.32025 | 0.114729 | 0.0573645 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573645 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(410\) | 10.9817 | 0.542345 | ||||||||
\(411\) | −1.72142 | −0.0849114 | ||||||||
\(412\) | 45.2096 | 2.22732 | ||||||||
\(413\) | −0.636779 | −0.0313339 | ||||||||
\(414\) | −22.7851 | −1.11983 | ||||||||
\(415\) | 6.57711 | 0.322858 | ||||||||
\(416\) | 38.6130 | 1.89316 | ||||||||
\(417\) | 8.00475 | 0.391994 | ||||||||
\(418\) | 93.8752 | 4.59159 | ||||||||
\(419\) | 3.12902 | 0.152863 | 0.0764313 | − | 0.997075i | \(-0.475647\pi\) | ||||
0.0764313 | + | 0.997075i | \(0.475647\pi\) | |||||||
\(420\) | 5.32861 | 0.260009 | ||||||||
\(421\) | 5.74274 | 0.279884 | 0.139942 | − | 0.990160i | \(-0.455308\pi\) | ||||
0.139942 | + | 0.990160i | \(0.455308\pi\) | |||||||
\(422\) | −67.8458 | −3.30268 | ||||||||
\(423\) | −1.32238 | −0.0642965 | ||||||||
\(424\) | 1.45591 | 0.0707051 | ||||||||
\(425\) | 4.86027 | 0.235758 | ||||||||
\(426\) | 26.4561 | 1.28180 | ||||||||
\(427\) | −28.1642 | −1.36296 | ||||||||
\(428\) | −3.28662 | −0.158865 | ||||||||
\(429\) | −8.68244 | −0.419192 | ||||||||
\(430\) | −2.28560 | −0.110221 | ||||||||
\(431\) | 17.9769 | 0.865916 | 0.432958 | − | 0.901414i | \(-0.357470\pi\) | ||||
0.432958 | + | 0.901414i | \(0.357470\pi\) | |||||||
\(432\) | −15.7328 | −0.756942 | ||||||||
\(433\) | −0.911900 | −0.0438231 | −0.0219116 | − | 0.999760i | \(-0.506975\pi\) | ||||
−0.0219116 | + | 0.999760i | \(0.506975\pi\) | |||||||
\(434\) | 2.25334 | 0.108164 | ||||||||
\(435\) | −2.66134 | −0.127601 | ||||||||
\(436\) | −45.9275 | −2.19953 | ||||||||
\(437\) | −53.1217 | −2.54116 | ||||||||
\(438\) | −4.33695 | −0.207228 | ||||||||
\(439\) | 9.84132 | 0.469701 | 0.234850 | − | 0.972032i | \(-0.424540\pi\) | ||||
0.234850 | + | 0.972032i | \(0.424540\pi\) | |||||||
\(440\) | 19.4598 | 0.927711 | ||||||||
\(441\) | −0.410745 | −0.0195593 | ||||||||
\(442\) | −4.47629 | −0.212915 | ||||||||
\(443\) | 29.2452 | 1.38948 | 0.694740 | − | 0.719261i | \(-0.255519\pi\) | ||||
0.694740 | + | 0.719261i | \(0.255519\pi\) | |||||||
\(444\) | 53.8092 | 2.55367 | ||||||||
\(445\) | 5.41207 | 0.256557 | ||||||||
\(446\) | −18.8540 | −0.892764 | ||||||||
\(447\) | 18.5362 | 0.876730 | ||||||||
\(448\) | −86.4813 | −4.08586 | ||||||||
\(449\) | 10.8120 | 0.510249 | 0.255125 | − | 0.966908i | \(-0.417884\pi\) | ||||
0.255125 | + | 0.966908i | \(0.417884\pi\) | |||||||
\(450\) | −13.3576 | −0.629685 | ||||||||
\(451\) | 56.9834 | 2.68324 | ||||||||
\(452\) | −12.0417 | −0.566396 | ||||||||
\(453\) | −3.63863 | −0.170958 | ||||||||
\(454\) | −27.1266 | −1.27311 | ||||||||
\(455\) | −1.56282 | −0.0732663 | ||||||||
\(456\) | −62.5739 | −2.93029 | ||||||||
\(457\) | −8.60055 | −0.402317 | −0.201158 | − | 0.979559i | \(-0.564471\pi\) | ||||
−0.201158 | + | 0.979559i | \(0.564471\pi\) | |||||||
\(458\) | −40.5490 | −1.89473 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −17.2099 | −0.802415 | ||||||||
\(461\) | −36.5940 | −1.70435 | −0.852177 | − | 0.523254i | \(-0.824718\pi\) | ||||
−0.852177 | + | 0.523254i | \(0.824718\pi\) | |||||||
\(462\) | 37.6079 | 1.74968 | ||||||||
\(463\) | −7.77200 | −0.361195 | −0.180598 | − | 0.983557i | \(-0.557803\pi\) | ||||
−0.180598 | + | 0.983557i | \(0.557803\pi\) | |||||||
\(464\) | 112.011 | 5.20000 | ||||||||
\(465\) | 0.119394 | 0.00553677 | ||||||||
\(466\) | −44.3249 | −2.05331 | ||||||||
\(467\) | 1.56128 | 0.0722474 | 0.0361237 | − | 0.999347i | \(-0.488499\pi\) | ||||
0.0361237 | + | 0.999347i | \(0.488499\pi\) | |||||||
\(468\) | 9.04487 | 0.418099 | ||||||||
\(469\) | −17.5269 | −0.809315 | ||||||||
\(470\) | −1.35853 | −0.0626643 | ||||||||
\(471\) | −8.19091 | −0.377417 | ||||||||
\(472\) | 2.42256 | 0.111507 | ||||||||
\(473\) | −11.8599 | −0.545319 | ||||||||
\(474\) | −2.74833 | −0.126235 | ||||||||
\(475\) | −31.1422 | −1.42890 | ||||||||
\(476\) | 14.2551 | 0.653383 | ||||||||
\(477\) | 0.149084 | 0.00682607 | ||||||||
\(478\) | −84.8516 | −3.88102 | ||||||||
\(479\) | 5.06415 | 0.231387 | 0.115693 | − | 0.993285i | \(-0.463091\pi\) | ||||
0.115693 | + | 0.993285i | \(0.463091\pi\) | |||||||
\(480\) | −8.86189 | −0.404488 | ||||||||
\(481\) | −15.7817 | −0.719583 | ||||||||
\(482\) | 21.4030 | 0.974878 | ||||||||
\(483\) | −21.2814 | −0.968338 | ||||||||
\(484\) | 96.7247 | 4.39658 | ||||||||
\(485\) | −5.84622 | −0.265463 | ||||||||
\(486\) | −2.74833 | −0.124667 | ||||||||
\(487\) | −16.7417 | −0.758638 | −0.379319 | − | 0.925266i | \(-0.623842\pi\) | ||||
−0.379319 | + | 0.925266i | \(0.623842\pi\) | |||||||
\(488\) | 107.148 | 4.85035 | ||||||||
\(489\) | 5.79651 | 0.262127 | ||||||||
\(490\) | −0.421972 | −0.0190628 | ||||||||
\(491\) | −14.3112 | −0.645856 | −0.322928 | − | 0.946424i | \(-0.604667\pi\) | ||||
−0.322928 | + | 0.946424i | \(0.604667\pi\) | |||||||
\(492\) | −59.3621 | −2.67625 | ||||||||
\(493\) | −7.11963 | −0.320652 | ||||||||
\(494\) | 28.6819 | 1.29046 | ||||||||
\(495\) | 1.99267 | 0.0895638 | ||||||||
\(496\) | −5.02510 | −0.225634 | ||||||||
\(497\) | 24.7101 | 1.10840 | ||||||||
\(498\) | −48.3572 | −2.16694 | ||||||||
\(499\) | 39.9530 | 1.78854 | 0.894270 | − | 0.447528i | \(-0.147695\pi\) | ||||
0.894270 | + | 0.447528i | \(0.147695\pi\) | |||||||
\(500\) | −20.4684 | −0.915376 | ||||||||
\(501\) | −9.67616 | −0.432299 | ||||||||
\(502\) | 47.5621 | 2.12280 | ||||||||
\(503\) | 33.3391 | 1.48652 | 0.743258 | − | 0.669005i | \(-0.233280\pi\) | ||||
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(504\) | −25.0681 | −1.11662 | ||||||||
\(505\) | −6.68151 | −0.297323 | ||||||||
\(506\) | −121.463 | −5.39969 | ||||||||
\(507\) | 10.3472 | 0.459537 | ||||||||
\(508\) | 99.6455 | 4.42106 | ||||||||
\(509\) | −31.5900 | −1.40020 | −0.700101 | − | 0.714044i | \(-0.746862\pi\) | ||||
−0.700101 | + | 0.714044i | \(0.746862\pi\) | |||||||
\(510\) | 1.02733 | 0.0454911 | ||||||||
\(511\) | −4.05073 | −0.179194 | ||||||||
\(512\) | 65.6996 | 2.90354 | ||||||||
\(513\) | −6.40751 | −0.282899 | ||||||||
\(514\) | 13.6584 | 0.602446 | ||||||||
\(515\) | 3.04313 | 0.134096 | ||||||||
\(516\) | 12.3550 | 0.543897 | ||||||||
\(517\) | −7.04936 | −0.310031 | ||||||||
\(518\) | 68.3583 | 3.00349 | ||||||||
\(519\) | 18.4489 | 0.809818 | ||||||||
\(520\) | 5.94560 | 0.260732 | ||||||||
\(521\) | −20.7956 | −0.911072 | −0.455536 | − | 0.890217i | \(-0.650552\pi\) | ||||
−0.455536 | + | 0.890217i | \(0.650552\pi\) | |||||||
\(522\) | 19.5671 | 0.856429 | ||||||||
\(523\) | 6.58581 | 0.287977 | 0.143989 | − | 0.989579i | \(-0.454007\pi\) | ||||
0.143989 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(524\) | 99.3352 | 4.33948 | ||||||||
\(525\) | −12.4761 | −0.544501 | ||||||||
\(526\) | −75.6978 | −3.30058 | ||||||||
\(527\) | 0.319404 | 0.0139135 | ||||||||
\(528\) | −83.8682 | −3.64989 | ||||||||
\(529\) | 45.7329 | 1.98839 | ||||||||
\(530\) | 0.153159 | 0.00665279 | ||||||||
\(531\) | 0.248068 | 0.0107652 | ||||||||
\(532\) | −91.3399 | −3.96009 | ||||||||
\(533\) | 17.4103 | 0.754122 | ||||||||
\(534\) | −39.7915 | −1.72195 | ||||||||
\(535\) | −0.221227 | −0.00956450 | ||||||||
\(536\) | 66.6791 | 2.88010 | ||||||||
\(537\) | −11.9693 | −0.516513 | ||||||||
\(538\) | 27.8348 | 1.20005 | ||||||||
\(539\) | −2.18960 | −0.0943127 | ||||||||
\(540\) | −2.07585 | −0.0893303 | ||||||||
\(541\) | 31.9817 | 1.37500 | 0.687501 | − | 0.726184i | \(-0.258708\pi\) | ||||
0.687501 | + | 0.726184i | \(0.258708\pi\) | |||||||
\(542\) | −3.63108 | −0.155968 | ||||||||
\(543\) | 19.5566 | 0.839254 | ||||||||
\(544\) | −23.7074 | −1.01645 | ||||||||
\(545\) | −3.09145 | −0.132423 | ||||||||
\(546\) | 11.4904 | 0.491745 | ||||||||
\(547\) | 4.25604 | 0.181975 | 0.0909875 | − | 0.995852i | \(-0.470998\pi\) | ||||
0.0909875 | + | 0.995852i | \(0.470998\pi\) | |||||||
\(548\) | 9.55961 | 0.408366 | ||||||||
\(549\) | 10.9718 | 0.468267 | ||||||||
\(550\) | −71.2069 | −3.03627 | ||||||||
\(551\) | 45.6191 | 1.94344 | ||||||||
\(552\) | 80.9629 | 3.44601 | ||||||||
\(553\) | −2.56695 | −0.109158 | ||||||||
\(554\) | 2.18748 | 0.0929373 | ||||||||
\(555\) | 3.62198 | 0.153745 | ||||||||
\(556\) | −44.4530 | −1.88523 | ||||||||
\(557\) | −17.8387 | −0.755849 | −0.377925 | − | 0.925836i | \(-0.623362\pi\) | ||||
−0.377925 | + | 0.925836i | \(0.623362\pi\) | |||||||
\(558\) | −0.877828 | −0.0371614 | ||||||||
\(559\) | −3.62358 | −0.153261 | ||||||||
\(560\) | −15.0961 | −0.637928 | ||||||||
\(561\) | 5.33080 | 0.225067 | ||||||||
\(562\) | 32.0659 | 1.35262 | ||||||||
\(563\) | −35.5431 | −1.49796 | −0.748982 | − | 0.662591i | \(-0.769457\pi\) | ||||
−0.748982 | + | 0.662591i | \(0.769457\pi\) | |||||||
\(564\) | 7.34362 | 0.309222 | ||||||||
\(565\) | −0.810548 | −0.0341000 | ||||||||
\(566\) | −79.0048 | −3.32082 | ||||||||
\(567\) | −2.56695 | −0.107802 | ||||||||
\(568\) | −94.0069 | −3.94444 | ||||||||
\(569\) | −33.9869 | −1.42481 | −0.712403 | − | 0.701770i | \(-0.752393\pi\) | ||||
−0.712403 | + | 0.701770i | \(0.752393\pi\) | |||||||
\(570\) | −6.58266 | −0.275717 | ||||||||
\(571\) | 29.5150 | 1.23516 | 0.617582 | − | 0.786506i | \(-0.288112\pi\) | ||||
0.617582 | + | 0.786506i | \(0.288112\pi\) | |||||||
\(572\) | 48.2164 | 2.01603 | ||||||||
\(573\) | 15.7826 | 0.659326 | ||||||||
\(574\) | −75.4125 | −3.14766 | ||||||||
\(575\) | 40.2942 | 1.68039 | ||||||||
\(576\) | 33.6903 | 1.40376 | ||||||||
\(577\) | 0.756942 | 0.0315119 | 0.0157560 | − | 0.999876i | \(-0.494985\pi\) | ||||
0.0157560 | + | 0.999876i | \(0.494985\pi\) | |||||||
\(578\) | 2.74833 | 0.114315 | ||||||||
\(579\) | −8.56277 | −0.355857 | ||||||||
\(580\) | 14.7793 | 0.613676 | ||||||||
\(581\) | −45.1659 | −1.87380 | ||||||||
\(582\) | 42.9835 | 1.78172 | ||||||||
\(583\) | 0.794735 | 0.0329146 | ||||||||
\(584\) | 15.4106 | 0.637695 | ||||||||
\(585\) | 0.608824 | 0.0251718 | ||||||||
\(586\) | 4.19894 | 0.173457 | ||||||||
\(587\) | 1.94843 | 0.0804202 | 0.0402101 | − | 0.999191i | \(-0.487197\pi\) | ||||
0.0402101 | + | 0.999191i | \(0.487197\pi\) | |||||||
\(588\) | 2.28100 | 0.0940668 | ||||||||
\(589\) | −2.04658 | −0.0843280 | ||||||||
\(590\) | 0.254849 | 0.0104920 | ||||||||
\(591\) | 11.6567 | 0.479493 | ||||||||
\(592\) | −152.443 | −6.26538 | ||||||||
\(593\) | 8.41287 | 0.345475 | 0.172737 | − | 0.984968i | \(-0.444739\pi\) | ||||
0.172737 | + | 0.984968i | \(0.444739\pi\) | |||||||
\(594\) | −14.6508 | −0.601130 | ||||||||
\(595\) | 0.959535 | 0.0393371 | ||||||||
\(596\) | −102.937 | −4.21648 | ||||||||
\(597\) | 17.5984 | 0.720256 | ||||||||
\(598\) | −37.1108 | −1.51758 | ||||||||
\(599\) | −27.4110 | −1.11998 | −0.559991 | − | 0.828499i | \(-0.689195\pi\) | ||||
−0.559991 | + | 0.828499i | \(0.689195\pi\) | |||||||
\(600\) | 47.4640 | 1.93771 | ||||||||
\(601\) | 7.09004 | 0.289209 | 0.144604 | − | 0.989490i | \(-0.453809\pi\) | ||||
0.144604 | + | 0.989490i | \(0.453809\pi\) | |||||||
\(602\) | 15.6955 | 0.639702 | ||||||||
\(603\) | 6.82788 | 0.278053 | ||||||||
\(604\) | 20.2065 | 0.822190 | ||||||||
\(605\) | 6.51069 | 0.264697 | ||||||||
\(606\) | 49.1248 | 1.99556 | ||||||||
\(607\) | 4.23643 | 0.171951 | 0.0859757 | − | 0.996297i | \(-0.472599\pi\) | ||||
0.0859757 | + | 0.996297i | \(0.472599\pi\) | |||||||
\(608\) | 151.905 | 6.16058 | ||||||||
\(609\) | 18.2758 | 0.740572 | ||||||||
\(610\) | 11.2717 | 0.456380 | ||||||||
\(611\) | −2.15381 | −0.0871337 | ||||||||
\(612\) | −5.55332 | −0.224480 | ||||||||
\(613\) | 38.2966 | 1.54678 | 0.773392 | − | 0.633928i | \(-0.218558\pi\) | ||||
0.773392 | + | 0.633928i | \(0.218558\pi\) | |||||||
\(614\) | −50.1675 | −2.02460 | ||||||||
\(615\) | −3.99575 | −0.161124 | ||||||||
\(616\) | −133.633 | −5.38423 | ||||||||
\(617\) | −20.6285 | −0.830471 | −0.415236 | − | 0.909714i | \(-0.636301\pi\) | ||||
−0.415236 | + | 0.909714i | \(0.636301\pi\) | |||||||
\(618\) | −22.3742 | −0.900020 | ||||||||
\(619\) | 37.7983 | 1.51924 | 0.759620 | − | 0.650367i | \(-0.225385\pi\) | ||||
0.759620 | + | 0.650367i | \(0.225385\pi\) | |||||||
\(620\) | −0.663034 | −0.0266281 | ||||||||
\(621\) | 8.29053 | 0.332688 | ||||||||
\(622\) | 78.0789 | 3.13068 | ||||||||
\(623\) | −37.1654 | −1.48900 | ||||||||
\(624\) | −25.6244 | −1.02580 | ||||||||
\(625\) | 22.9236 | 0.916944 | ||||||||
\(626\) | −26.6532 | −1.06528 | ||||||||
\(627\) | −34.1572 | −1.36411 | ||||||||
\(628\) | 45.4868 | 1.81512 | ||||||||
\(629\) | 9.68955 | 0.386348 | ||||||||
\(630\) | −2.63712 | −0.105065 | ||||||||
\(631\) | −19.3557 | −0.770538 | −0.385269 | − | 0.922804i | \(-0.625891\pi\) | ||||
−0.385269 | + | 0.922804i | \(0.625891\pi\) | |||||||
\(632\) | 9.76571 | 0.388459 | ||||||||
\(633\) | 24.6862 | 0.981187 | ||||||||
\(634\) | 58.1821 | 2.31070 | ||||||||
\(635\) | 6.70730 | 0.266171 | ||||||||
\(636\) | −0.827910 | −0.0328287 | ||||||||
\(637\) | −0.668993 | −0.0265065 | ||||||||
\(638\) | 104.308 | 4.12961 | ||||||||
\(639\) | −9.62623 | −0.380808 | ||||||||
\(640\) | 16.8874 | 0.667532 | ||||||||
\(641\) | 46.5183 | 1.83736 | 0.918682 | − | 0.394999i | \(-0.129255\pi\) | ||||
0.918682 | + | 0.394999i | \(0.129255\pi\) | |||||||
\(642\) | 1.62654 | 0.0641945 | ||||||||
\(643\) | 31.8736 | 1.25697 | 0.628486 | − | 0.777821i | \(-0.283675\pi\) | ||||
0.628486 | + | 0.777821i | \(0.283675\pi\) | |||||||
\(644\) | 118.183 | 4.65705 | ||||||||
\(645\) | 0.831632 | 0.0327455 | ||||||||
\(646\) | −17.6100 | −0.692855 | ||||||||
\(647\) | 6.15278 | 0.241891 | 0.120945 | − | 0.992659i | \(-0.461407\pi\) | ||||
0.120945 | + | 0.992659i | \(0.461407\pi\) | |||||||
\(648\) | 9.76571 | 0.383633 | ||||||||
\(649\) | 1.32240 | 0.0519088 | ||||||||
\(650\) | −21.7560 | −0.853340 | ||||||||
\(651\) | −0.819895 | −0.0321342 | ||||||||
\(652\) | −32.1899 | −1.26065 | ||||||||
\(653\) | −24.5966 | −0.962538 | −0.481269 | − | 0.876573i | \(-0.659824\pi\) | ||||
−0.481269 | + | 0.876573i | \(0.659824\pi\) | |||||||
\(654\) | 22.7294 | 0.888791 | ||||||||
\(655\) | 6.68641 | 0.261260 | ||||||||
\(656\) | 168.175 | 6.56612 | ||||||||
\(657\) | 1.57803 | 0.0615649 | ||||||||
\(658\) | 9.32920 | 0.363690 | ||||||||
\(659\) | 22.3348 | 0.870042 | 0.435021 | − | 0.900420i | \(-0.356741\pi\) | ||||
0.435021 | + | 0.900420i | \(0.356741\pi\) | |||||||
\(660\) | −11.0659 | −0.430741 | ||||||||
\(661\) | 4.22158 | 0.164200 | 0.0821002 | − | 0.996624i | \(-0.473837\pi\) | ||||
0.0821002 | + | 0.996624i | \(0.473837\pi\) | |||||||
\(662\) | −59.3912 | −2.30831 | ||||||||
\(663\) | 1.62873 | 0.0632547 | ||||||||
\(664\) | 171.829 | 6.66825 | ||||||||
\(665\) | −6.14823 | −0.238418 | ||||||||
\(666\) | −26.6301 | −1.03190 | ||||||||
\(667\) | −59.0255 | −2.28548 | ||||||||
\(668\) | 53.7348 | 2.07906 | ||||||||
\(669\) | 6.86018 | 0.265230 | ||||||||
\(670\) | 7.01452 | 0.270994 | ||||||||
\(671\) | 58.4887 | 2.25793 | ||||||||
\(672\) | 60.8558 | 2.34756 | ||||||||
\(673\) | 29.6046 | 1.14117 | 0.570586 | − | 0.821238i | \(-0.306716\pi\) | ||||
0.570586 | + | 0.821238i | \(0.306716\pi\) | |||||||
\(674\) | −81.1090 | −3.12420 | ||||||||
\(675\) | 4.86027 | 0.187072 | ||||||||
\(676\) | −57.4615 | −2.21006 | ||||||||
\(677\) | −31.7025 | −1.21843 | −0.609213 | − | 0.793007i | \(-0.708514\pi\) | ||||
−0.609213 | + | 0.793007i | \(0.708514\pi\) | |||||||
\(678\) | 5.95944 | 0.228871 | ||||||||
\(679\) | 40.1468 | 1.54069 | ||||||||
\(680\) | −3.65045 | −0.139988 | ||||||||
\(681\) | 9.87021 | 0.378227 | ||||||||
\(682\) | −4.67952 | −0.179188 | ||||||||
\(683\) | −20.2708 | −0.775641 | −0.387821 | − | 0.921735i | \(-0.626772\pi\) | ||||
−0.387821 | + | 0.921735i | \(0.626772\pi\) | |||||||
\(684\) | 35.5830 | 1.36055 | ||||||||
\(685\) | 0.643472 | 0.0245858 | ||||||||
\(686\) | 52.2816 | 1.99612 | ||||||||
\(687\) | 14.7541 | 0.562903 | ||||||||
\(688\) | −35.0020 | −1.33444 | ||||||||
\(689\) | 0.242817 | 0.00925059 | ||||||||
\(690\) | 8.51715 | 0.324242 | ||||||||
\(691\) | 1.09078 | 0.0414953 | 0.0207477 | − | 0.999785i | \(-0.493395\pi\) | ||||
0.0207477 | + | 0.999785i | \(0.493395\pi\) | |||||||
\(692\) | −102.453 | −3.89467 | ||||||||
\(693\) | −13.6839 | −0.519809 | ||||||||
\(694\) | −57.0948 | −2.16729 | ||||||||
\(695\) | −2.99220 | −0.113501 | ||||||||
\(696\) | −69.5282 | −2.63546 | ||||||||
\(697\) | −10.6895 | −0.404892 | ||||||||
\(698\) | −71.4250 | −2.70348 | ||||||||
\(699\) | 16.1279 | 0.610015 | ||||||||
\(700\) | 69.2838 | 2.61868 | ||||||||
\(701\) | −36.0337 | −1.36097 | −0.680487 | − | 0.732760i | \(-0.738232\pi\) | ||||
−0.680487 | + | 0.732760i | \(0.738232\pi\) | |||||||
\(702\) | −4.47629 | −0.168947 | ||||||||
\(703\) | −62.0859 | −2.34162 | ||||||||
\(704\) | 179.596 | 6.76878 | ||||||||
\(705\) | 0.494311 | 0.0186168 | ||||||||
\(706\) | 6.54127 | 0.246184 | ||||||||
\(707\) | 45.8828 | 1.72560 | ||||||||
\(708\) | −1.37760 | −0.0517734 | ||||||||
\(709\) | 7.94892 | 0.298528 | 0.149264 | − | 0.988797i | \(-0.452310\pi\) | ||||
0.149264 | + | 0.988797i | \(0.452310\pi\) | |||||||
\(710\) | −9.88935 | −0.371141 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 141.392 | 5.29889 | ||||||||
\(713\) | 2.64803 | 0.0991695 | ||||||||
\(714\) | −7.05484 | −0.264021 | ||||||||
\(715\) | 3.24552 | 0.121376 | ||||||||
\(716\) | 66.4693 | 2.48407 | ||||||||
\(717\) | 30.8739 | 1.15301 | ||||||||
\(718\) | 55.0043 | 2.05274 | ||||||||
\(719\) | 26.6105 | 0.992404 | 0.496202 | − | 0.868207i | \(-0.334728\pi\) | ||||
0.496202 | + | 0.868207i | \(0.334728\pi\) | |||||||
\(720\) | 5.88095 | 0.219170 | ||||||||
\(721\) | −20.8976 | −0.778266 | ||||||||
\(722\) | 60.6178 | 2.25596 | ||||||||
\(723\) | −7.78762 | −0.289625 | ||||||||
\(724\) | −108.604 | −4.03624 | ||||||||
\(725\) | −34.6033 | −1.28514 | ||||||||
\(726\) | −47.8689 | −1.77658 | ||||||||
\(727\) | −0.269075 | −0.00997942 | −0.00498971 | − | 0.999988i | \(-0.501588\pi\) | ||||
−0.00498971 | + | 0.999988i | \(0.501588\pi\) | |||||||
\(728\) | −40.8292 | −1.51323 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.62117 | 0.0600020 | ||||||||
\(731\) | 2.22479 | 0.0822868 | ||||||||
\(732\) | −60.9302 | −2.25204 | ||||||||
\(733\) | 25.2754 | 0.933568 | 0.466784 | − | 0.884371i | \(-0.345413\pi\) | ||||
0.466784 | + | 0.884371i | \(0.345413\pi\) | |||||||
\(734\) | 48.9046 | 1.80510 | ||||||||
\(735\) | 0.153538 | 0.00566332 | ||||||||
\(736\) | −196.547 | −7.24482 | ||||||||
\(737\) | 36.3981 | 1.34074 | ||||||||
\(738\) | 29.3782 | 1.08143 | ||||||||
\(739\) | 5.68610 | 0.209167 | 0.104583 | − | 0.994516i | \(-0.466649\pi\) | ||||
0.104583 | + | 0.994516i | \(0.466649\pi\) | |||||||
\(740\) | −20.1141 | −0.739407 | ||||||||
\(741\) | −10.4361 | −0.383380 | ||||||||
\(742\) | −1.05176 | −0.0386114 | ||||||||
\(743\) | −4.80201 | −0.176169 | −0.0880843 | − | 0.996113i | \(-0.528074\pi\) | ||||
−0.0880843 | + | 0.996113i | \(0.528074\pi\) | |||||||
\(744\) | 3.11921 | 0.114356 | ||||||||
\(745\) | −6.92887 | −0.253854 | ||||||||
\(746\) | 4.69498 | 0.171895 | ||||||||
\(747\) | 17.5951 | 0.643772 | ||||||||
\(748\) | −29.6037 | −1.08242 | ||||||||
\(749\) | 1.51920 | 0.0555103 | ||||||||
\(750\) | 10.1298 | 0.369888 | ||||||||
\(751\) | 32.7746 | 1.19596 | 0.597982 | − | 0.801510i | \(-0.295970\pi\) | ||||
0.597982 | + | 0.801510i | \(0.295970\pi\) | |||||||
\(752\) | −20.8047 | −0.758670 | ||||||||
\(753\) | −17.3058 | −0.630659 | ||||||||
\(754\) | 31.8695 | 1.16062 | ||||||||
\(755\) | 1.36013 | 0.0495002 | ||||||||
\(756\) | 14.2551 | 0.518454 | ||||||||
\(757\) | −10.5402 | −0.383090 | −0.191545 | − | 0.981484i | \(-0.561350\pi\) | ||||
−0.191545 | + | 0.981484i | \(0.561350\pi\) | |||||||
\(758\) | −15.0549 | −0.546820 | ||||||||
\(759\) | 44.1952 | 1.60418 | ||||||||
\(760\) | 23.3903 | 0.848456 | ||||||||
\(761\) | 34.4028 | 1.24710 | 0.623550 | − | 0.781783i | \(-0.285690\pi\) | ||||
0.623550 | + | 0.781783i | \(0.285690\pi\) | |||||||
\(762\) | −49.3144 | −1.78647 | ||||||||
\(763\) | 21.2294 | 0.768556 | ||||||||
\(764\) | −87.6456 | −3.17091 | ||||||||
\(765\) | −0.373803 | −0.0135149 | ||||||||
\(766\) | −64.8906 | −2.34459 | ||||||||
\(767\) | 0.404036 | 0.0145889 | ||||||||
\(768\) | −56.7814 | −2.04892 | ||||||||
\(769\) | −10.3263 | −0.372374 | −0.186187 | − | 0.982514i | \(-0.559613\pi\) | ||||
−0.186187 | + | 0.982514i | \(0.559613\pi\) | |||||||
\(770\) | −14.0580 | −0.506614 | ||||||||
\(771\) | −4.96971 | −0.178980 | ||||||||
\(772\) | 47.5518 | 1.71143 | ||||||||
\(773\) | 40.6953 | 1.46371 | 0.731854 | − | 0.681461i | \(-0.238655\pi\) | ||||
0.731854 | + | 0.681461i | \(0.238655\pi\) | |||||||
\(774\) | −6.11445 | −0.219779 | ||||||||
\(775\) | 1.55239 | 0.0557635 | ||||||||
\(776\) | −152.734 | −5.48284 | ||||||||
\(777\) | −24.8726 | −0.892301 | ||||||||
\(778\) | 56.3847 | 2.02149 | ||||||||
\(779\) | 68.4929 | 2.45401 | ||||||||
\(780\) | −3.38100 | −0.121059 | ||||||||
\(781\) | −51.3155 | −1.83621 | ||||||||
\(782\) | 22.7851 | 0.814795 | ||||||||
\(783\) | −7.11963 | −0.254435 | ||||||||
\(784\) | −6.46215 | −0.230791 | ||||||||
\(785\) | 3.06179 | 0.109280 | ||||||||
\(786\) | −49.1608 | −1.75351 | ||||||||
\(787\) | −6.91174 | −0.246377 | −0.123188 | − | 0.992383i | \(-0.539312\pi\) | ||||
−0.123188 | + | 0.992383i | \(0.539312\pi\) | |||||||
\(788\) | −64.7335 | −2.30604 | ||||||||
\(789\) | 27.5432 | 0.980563 | ||||||||
\(790\) | 1.02733 | 0.0365509 | ||||||||
\(791\) | 5.56614 | 0.197909 | ||||||||
\(792\) | 52.0590 | 1.84984 | ||||||||
\(793\) | 17.8702 | 0.634589 | ||||||||
\(794\) | 41.0783 | 1.45781 | ||||||||
\(795\) | −0.0557279 | −0.00197647 | ||||||||
\(796\) | −97.7298 | −3.46394 | ||||||||
\(797\) | −20.4571 | −0.724626 | −0.362313 | − | 0.932056i | \(-0.618013\pi\) | ||||
−0.362313 | + | 0.932056i | \(0.618013\pi\) | |||||||
\(798\) | 45.2040 | 1.60020 | ||||||||
\(799\) | 1.32238 | 0.0467826 | ||||||||
\(800\) | −115.224 | −4.07380 | ||||||||
\(801\) | 14.4784 | 0.511570 | ||||||||
\(802\) | 16.9969 | 0.600180 | ||||||||
\(803\) | 8.41217 | 0.296859 | ||||||||
\(804\) | −37.9174 | −1.33724 | ||||||||
\(805\) | 7.95506 | 0.280379 | ||||||||
\(806\) | −1.42974 | −0.0503606 | ||||||||
\(807\) | −10.1279 | −0.356519 | ||||||||
\(808\) | −174.556 | −6.14087 | ||||||||
\(809\) | −26.2412 | −0.922591 | −0.461295 | − | 0.887247i | \(-0.652615\pi\) | ||||
−0.461295 | + | 0.887247i | \(0.652615\pi\) | |||||||
\(810\) | 1.02733 | 0.0360968 | ||||||||
\(811\) | −13.8119 | −0.485000 | −0.242500 | − | 0.970151i | \(-0.577967\pi\) | ||||
−0.242500 | + | 0.970151i | \(0.577967\pi\) | |||||||
\(812\) | −101.491 | −3.56164 | ||||||||
\(813\) | 1.32119 | 0.0463363 | ||||||||
\(814\) | −141.960 | −4.97569 | ||||||||
\(815\) | −2.16675 | −0.0758980 | ||||||||
\(816\) | 15.7328 | 0.550756 | ||||||||
\(817\) | −14.2554 | −0.498732 | ||||||||
\(818\) | 6.37682 | 0.222960 | ||||||||
\(819\) | −4.18088 | −0.146092 | ||||||||
\(820\) | 22.1897 | 0.774898 | ||||||||
\(821\) | −6.95034 | −0.242568 | −0.121284 | − | 0.992618i | \(-0.538701\pi\) | ||||
−0.121284 | + | 0.992618i | \(0.538701\pi\) | |||||||
\(822\) | −4.73103 | −0.165014 | ||||||||
\(823\) | 11.6523 | 0.406173 | 0.203087 | − | 0.979161i | \(-0.434903\pi\) | ||||
0.203087 | + | 0.979161i | \(0.434903\pi\) | |||||||
\(824\) | 79.5026 | 2.76960 | ||||||||
\(825\) | 25.9091 | 0.902040 | ||||||||
\(826\) | −1.75008 | −0.0608931 | ||||||||
\(827\) | −4.32909 | −0.150537 | −0.0752687 | − | 0.997163i | \(-0.523981\pi\) | ||||
−0.0752687 | + | 0.997163i | \(0.523981\pi\) | |||||||
\(828\) | −46.0400 | −1.60000 | ||||||||
\(829\) | −48.5640 | −1.68670 | −0.843349 | − | 0.537366i | \(-0.819419\pi\) | ||||
−0.843349 | + | 0.537366i | \(0.819419\pi\) | |||||||
\(830\) | 18.0761 | 0.627430 | ||||||||
\(831\) | −0.795932 | −0.0276106 | ||||||||
\(832\) | 54.8724 | 1.90236 | ||||||||
\(833\) | 0.410745 | 0.0142315 | ||||||||
\(834\) | 21.9997 | 0.761788 | ||||||||
\(835\) | 3.61698 | 0.125171 | ||||||||
\(836\) | 189.686 | 6.56042 | ||||||||
\(837\) | 0.319404 | 0.0110402 | ||||||||
\(838\) | 8.59958 | 0.297068 | ||||||||
\(839\) | 6.04404 | 0.208663 | 0.104332 | − | 0.994543i | \(-0.466730\pi\) | ||||
0.104332 | + | 0.994543i | \(0.466730\pi\) | |||||||
\(840\) | 9.37054 | 0.323314 | ||||||||
\(841\) | 21.6892 | 0.747902 | ||||||||
\(842\) | 15.7829 | 0.543916 | ||||||||
\(843\) | −11.6674 | −0.401847 | ||||||||
\(844\) | −137.090 | −4.71884 | ||||||||
\(845\) | −3.86783 | −0.133057 | ||||||||
\(846\) | −3.63435 | −0.124951 | ||||||||
\(847\) | −44.7098 | −1.53625 | ||||||||
\(848\) | 2.34550 | 0.0805446 | ||||||||
\(849\) | 28.7465 | 0.986576 | ||||||||
\(850\) | 13.3576 | 0.458163 | ||||||||
\(851\) | 80.3316 | 2.75373 | ||||||||
\(852\) | 53.4575 | 1.83143 | ||||||||
\(853\) | 17.0646 | 0.584280 | 0.292140 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292140 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(854\) | −77.4046 | −2.64873 | ||||||||
\(855\) | 2.39515 | 0.0819123 | ||||||||
\(856\) | −5.77963 | −0.197544 | ||||||||
\(857\) | −9.99478 | −0.341415 | −0.170708 | − | 0.985322i | \(-0.554605\pi\) | ||||
−0.170708 | + | 0.985322i | \(0.554605\pi\) | |||||||
\(858\) | −23.8622 | −0.814643 | ||||||||
\(859\) | 14.5088 | 0.495035 | 0.247517 | − | 0.968883i | \(-0.420385\pi\) | ||||
0.247517 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(860\) | −4.61832 | −0.157484 | ||||||||
\(861\) | 27.4394 | 0.935131 | ||||||||
\(862\) | 49.4064 | 1.68279 | ||||||||
\(863\) | −26.7850 | −0.911773 | −0.455887 | − | 0.890038i | \(-0.650678\pi\) | ||||
−0.455887 | + | 0.890038i | \(0.650678\pi\) | |||||||
\(864\) | −23.7074 | −0.806542 | ||||||||
\(865\) | −6.89627 | −0.234480 | ||||||||
\(866\) | −2.50620 | −0.0851643 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 4.55314 | 0.154544 | ||||||||
\(869\) | 5.33080 | 0.180835 | ||||||||
\(870\) | −7.31424 | −0.247976 | ||||||||
\(871\) | 11.1208 | 0.376813 | ||||||||
\(872\) | −80.7650 | −2.73505 | ||||||||
\(873\) | −15.6399 | −0.529329 | ||||||||
\(874\) | −145.996 | −4.93839 | ||||||||
\(875\) | 9.46128 | 0.319850 | ||||||||
\(876\) | −8.76332 | −0.296085 | ||||||||
\(877\) | −13.9883 | −0.472351 | −0.236175 | − | 0.971710i | \(-0.575894\pi\) | ||||
−0.236175 | + | 0.971710i | \(0.575894\pi\) | |||||||
\(878\) | 27.0472 | 0.912799 | ||||||||
\(879\) | −1.52782 | −0.0515319 | ||||||||
\(880\) | 31.3502 | 1.05681 | ||||||||
\(881\) | −58.0873 | −1.95701 | −0.978506 | − | 0.206219i | \(-0.933884\pi\) | ||||
−0.978506 | + | 0.206219i | \(0.933884\pi\) | |||||||
\(882\) | −1.12886 | −0.0380108 | ||||||||
\(883\) | −7.78627 | −0.262029 | −0.131014 | − | 0.991380i | \(-0.541823\pi\) | ||||
−0.131014 | + | 0.991380i | \(0.541823\pi\) | |||||||
\(884\) | −9.04487 | −0.304212 | ||||||||
\(885\) | −0.0927286 | −0.00311704 | ||||||||
\(886\) | 80.3754 | 2.70027 | ||||||||
\(887\) | 32.6996 | 1.09794 | 0.548972 | − | 0.835841i | \(-0.315019\pi\) | ||||
0.548972 | + | 0.835841i | \(0.315019\pi\) | |||||||
\(888\) | 94.6254 | 3.17542 | ||||||||
\(889\) | −46.0599 | −1.54480 | ||||||||
\(890\) | 14.8742 | 0.498583 | ||||||||
\(891\) | 5.33080 | 0.178589 | ||||||||
\(892\) | −38.0968 | −1.27557 | ||||||||
\(893\) | −8.47319 | −0.283544 | ||||||||
\(894\) | 50.9435 | 1.70381 | ||||||||
\(895\) | 4.47415 | 0.149554 | ||||||||
\(896\) | −115.968 | −3.87421 | ||||||||
\(897\) | 13.5030 | 0.450854 | ||||||||
\(898\) | 29.7149 | 0.991600 | ||||||||
\(899\) | −2.27404 | −0.0758434 | ||||||||
\(900\) | −26.9907 | −0.899689 | ||||||||
\(901\) | −0.149084 | −0.00496670 | ||||||||
\(902\) | 156.609 | 5.21452 | ||||||||
\(903\) | −5.71093 | −0.190048 | ||||||||
\(904\) | −21.1758 | −0.704297 | ||||||||
\(905\) | −7.31031 | −0.243003 | ||||||||
\(906\) | −10.0002 | −0.332233 | ||||||||
\(907\) | 20.5355 | 0.681870 | 0.340935 | − | 0.940087i | \(-0.389256\pi\) | ||||
0.340935 | + | 0.940087i | \(0.389256\pi\) | |||||||
\(908\) | −54.8124 | −1.81901 | ||||||||
\(909\) | −17.8744 | −0.592857 | ||||||||
\(910\) | −4.29516 | −0.142383 | ||||||||
\(911\) | −32.2160 | −1.06737 | −0.533683 | − | 0.845685i | \(-0.679192\pi\) | ||||
−0.533683 | + | 0.845685i | \(0.679192\pi\) | |||||||
\(912\) | −100.808 | −3.33808 | ||||||||
\(913\) | 93.7961 | 3.10420 | ||||||||
\(914\) | −23.6371 | −0.781847 | ||||||||
\(915\) | −4.10131 | −0.135585 | ||||||||
\(916\) | −81.9341 | −2.70718 | ||||||||
\(917\) | −45.9165 | −1.51630 | ||||||||
\(918\) | 2.74833 | 0.0907084 | ||||||||
\(919\) | 21.1769 | 0.698561 | 0.349280 | − | 0.937018i | \(-0.386426\pi\) | ||||
0.349280 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(920\) | −30.2642 | −0.997781 | ||||||||
\(921\) | 18.2538 | 0.601483 | ||||||||
\(922\) | −100.572 | −3.31218 | ||||||||
\(923\) | −15.6785 | −0.516065 | ||||||||
\(924\) | 75.9912 | 2.49993 | ||||||||
\(925\) | 47.0939 | 1.54844 | ||||||||
\(926\) | −21.3600 | −0.701934 | ||||||||
\(927\) | 8.14100 | 0.267385 | ||||||||
\(928\) | 168.788 | 5.54073 | ||||||||
\(929\) | 4.41948 | 0.144998 | 0.0724992 | − | 0.997368i | \(-0.476903\pi\) | ||||
0.0724992 | + | 0.997368i | \(0.476903\pi\) | |||||||
\(930\) | 0.328135 | 0.0107600 | ||||||||
\(931\) | −2.63185 | −0.0862555 | ||||||||
\(932\) | −89.5637 | −2.93376 | ||||||||
\(933\) | −28.4096 | −0.930087 | ||||||||
\(934\) | 4.29091 | 0.140403 | ||||||||
\(935\) | −1.99267 | −0.0651673 | ||||||||
\(936\) | 15.9057 | 0.519894 | ||||||||
\(937\) | 17.6203 | 0.575630 | 0.287815 | − | 0.957686i | \(-0.407071\pi\) | ||||
0.287815 | + | 0.957686i | \(0.407071\pi\) | |||||||
\(938\) | −48.1696 | −1.57279 | ||||||||
\(939\) | 9.69798 | 0.316481 | ||||||||
\(940\) | −2.74507 | −0.0895342 | ||||||||
\(941\) | 48.3348 | 1.57567 | 0.787835 | − | 0.615886i | \(-0.211202\pi\) | ||||
0.787835 | + | 0.615886i | \(0.211202\pi\) | |||||||
\(942\) | −22.5113 | −0.733459 | ||||||||
\(943\) | −88.6214 | −2.88591 | ||||||||
\(944\) | 3.90279 | 0.127025 | ||||||||
\(945\) | 0.959535 | 0.0312137 | ||||||||
\(946\) | −32.5949 | −1.05975 | ||||||||
\(947\) | −30.4385 | −0.989118 | −0.494559 | − | 0.869144i | \(-0.664670\pi\) | ||||
−0.494559 | + | 0.869144i | \(0.664670\pi\) | |||||||
\(948\) | −5.55332 | −0.180364 | ||||||||
\(949\) | 2.57019 | 0.0834318 | ||||||||
\(950\) | −85.5892 | −2.77688 | ||||||||
\(951\) | −21.1700 | −0.686483 | ||||||||
\(952\) | 25.0681 | 0.812463 | ||||||||
\(953\) | −7.67649 | −0.248666 | −0.124333 | − | 0.992241i | \(-0.539679\pi\) | ||||
−0.124333 | + | 0.992241i | \(0.539679\pi\) | |||||||
\(954\) | 0.409731 | 0.0132655 | ||||||||
\(955\) | −5.89957 | −0.190905 | ||||||||
\(956\) | −171.452 | −5.54517 | ||||||||
\(957\) | −37.9533 | −1.22686 | ||||||||
\(958\) | 13.9180 | 0.449669 | ||||||||
\(959\) | −4.41881 | −0.142691 | ||||||||
\(960\) | −12.5935 | −0.406454 | ||||||||
\(961\) | −30.8980 | −0.996709 | ||||||||
\(962\) | −43.3733 | −1.39841 | ||||||||
\(963\) | −0.591829 | −0.0190714 | ||||||||
\(964\) | 43.2472 | 1.39290 | ||||||||
\(965\) | 3.20079 | 0.103037 | ||||||||
\(966\) | −58.4884 | −1.88183 | ||||||||
\(967\) | 35.4487 | 1.13995 | 0.569977 | − | 0.821660i | \(-0.306952\pi\) | ||||
0.569977 | + | 0.821660i | \(0.306952\pi\) | |||||||
\(968\) | 170.094 | 5.46702 | ||||||||
\(969\) | 6.40751 | 0.205839 | ||||||||
\(970\) | −16.0674 | −0.515892 | ||||||||
\(971\) | 0.843630 | 0.0270734 | 0.0135367 | − | 0.999908i | \(-0.495691\pi\) | ||||
0.0135367 | + | 0.999908i | \(0.495691\pi\) | |||||||
\(972\) | −5.55332 | −0.178123 | ||||||||
\(973\) | 20.5478 | 0.658733 | ||||||||
\(974\) | −46.0117 | −1.47431 | ||||||||
\(975\) | 7.91607 | 0.253517 | ||||||||
\(976\) | 172.617 | 5.52534 | ||||||||
\(977\) | −24.8192 | −0.794036 | −0.397018 | − | 0.917811i | \(-0.629955\pi\) | ||||
−0.397018 | + | 0.917811i | \(0.629955\pi\) | |||||||
\(978\) | 15.9307 | 0.509408 | ||||||||
\(979\) | 77.1815 | 2.46673 | ||||||||
\(980\) | −0.852644 | −0.0272367 | ||||||||
\(981\) | −8.27027 | −0.264049 | ||||||||
\(982\) | −39.3319 | −1.25513 | ||||||||
\(983\) | 17.2037 | 0.548712 | 0.274356 | − | 0.961628i | \(-0.411535\pi\) | ||||
0.274356 | + | 0.961628i | \(0.411535\pi\) | |||||||
\(984\) | −104.390 | −3.32784 | ||||||||
\(985\) | −4.35732 | −0.138836 | ||||||||
\(986\) | −19.5671 | −0.623144 | ||||||||
\(987\) | −3.39450 | −0.108048 | ||||||||
\(988\) | 57.9551 | 1.84380 | ||||||||
\(989\) | 18.4447 | 0.586507 | ||||||||
\(990\) | 5.47651 | 0.174055 | ||||||||
\(991\) | −50.5285 | −1.60509 | −0.802545 | − | 0.596591i | \(-0.796522\pi\) | ||||
−0.802545 | + | 0.596591i | \(0.796522\pi\) | |||||||
\(992\) | −7.57223 | −0.240419 | ||||||||
\(993\) | 21.6099 | 0.685770 | ||||||||
\(994\) | 67.9115 | 2.15402 | ||||||||
\(995\) | −6.57835 | −0.208548 | ||||||||
\(996\) | −97.7114 | −3.09610 | ||||||||
\(997\) | −4.96068 | −0.157106 | −0.0785532 | − | 0.996910i | \(-0.525030\pi\) | ||||
−0.0785532 | + | 0.996910i | \(0.525030\pi\) | |||||||
\(998\) | 109.804 | 3.47578 | ||||||||
\(999\) | 9.68955 | 0.306564 |
(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 | 4029.2.a.l.1.32 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.32 | ✓ | 32 | 1.1 | even | 1 | trivial |