Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89473 | −1.33978 | −0.669890 | − | 0.742460i | \(-0.733659\pi\) | ||||
−0.669890 | + | 0.742460i | \(0.733659\pi\) | |||||||
\(3\) | −0.654571 | −0.377917 | −0.188959 | − | 0.981985i | \(-0.560511\pi\) | ||||
−0.188959 | + | 0.981985i | \(0.560511\pi\) | |||||||
\(4\) | 1.59002 | 0.795010 | ||||||||
\(5\) | 2.95213 | 1.32023 | 0.660116 | − | 0.751164i | \(-0.270507\pi\) | ||||
0.660116 | + | 0.751164i | \(0.270507\pi\) | |||||||
\(6\) | 1.24024 | 0.506326 | ||||||||
\(7\) | −2.97686 | −1.12515 | −0.562574 | − | 0.826747i | \(-0.690189\pi\) | ||||
−0.562574 | + | 0.826747i | \(0.690189\pi\) | |||||||
\(8\) | 0.776803 | 0.274641 | ||||||||
\(9\) | −2.57154 | −0.857179 | ||||||||
\(10\) | −5.59350 | −1.76882 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.04078 | −0.300448 | ||||||||
\(13\) | −2.31439 | −0.641897 | −0.320949 | − | 0.947097i | \(-0.604002\pi\) | ||||
−0.320949 | + | 0.947097i | \(0.604002\pi\) | |||||||
\(14\) | 5.64036 | 1.50745 | ||||||||
\(15\) | −1.93238 | −0.498938 | ||||||||
\(16\) | −4.65188 | −1.16297 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 4.87238 | 1.14843 | ||||||||
\(19\) | 8.06990 | 1.85136 | 0.925682 | − | 0.378304i | \(-0.123492\pi\) | ||||
0.925682 | + | 0.378304i | \(0.123492\pi\) | |||||||
\(20\) | 4.69394 | 1.04960 | ||||||||
\(21\) | 1.94857 | 0.425212 | ||||||||
\(22\) | −1.89473 | −0.403959 | ||||||||
\(23\) | 1.76109 | 0.367213 | 0.183606 | − | 0.983000i | \(-0.441223\pi\) | ||||
0.183606 | + | 0.983000i | \(0.441223\pi\) | |||||||
\(24\) | −0.508473 | −0.103792 | ||||||||
\(25\) | 3.71506 | 0.743012 | ||||||||
\(26\) | 4.38516 | 0.860001 | ||||||||
\(27\) | 3.64697 | 0.701859 | ||||||||
\(28\) | −4.73327 | −0.894504 | ||||||||
\(29\) | −4.64475 | −0.862509 | −0.431255 | − | 0.902230i | \(-0.641929\pi\) | ||||
−0.431255 | + | 0.902230i | \(0.641929\pi\) | |||||||
\(30\) | 3.66135 | 0.668467 | ||||||||
\(31\) | −2.51028 | −0.450859 | −0.225430 | − | 0.974259i | \(-0.572379\pi\) | ||||
−0.225430 | + | 0.974259i | \(0.572379\pi\) | |||||||
\(32\) | 7.26047 | 1.28348 | ||||||||
\(33\) | −0.654571 | −0.113946 | ||||||||
\(34\) | 1.89473 | 0.324944 | ||||||||
\(35\) | −8.78807 | −1.48546 | ||||||||
\(36\) | −4.08879 | −0.681466 | ||||||||
\(37\) | −7.64717 | −1.25719 | −0.628593 | − | 0.777734i | \(-0.716369\pi\) | ||||
−0.628593 | + | 0.777734i | \(0.716369\pi\) | |||||||
\(38\) | −15.2903 | −2.48042 | ||||||||
\(39\) | 1.51494 | 0.242584 | ||||||||
\(40\) | 2.29322 | 0.362590 | ||||||||
\(41\) | −0.808864 | −0.126323 | −0.0631617 | − | 0.998003i | \(-0.520118\pi\) | ||||
−0.0631617 | + | 0.998003i | \(0.520118\pi\) | |||||||
\(42\) | −3.69202 | −0.569691 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.59002 | 0.239705 | ||||||||
\(45\) | −7.59151 | −1.13167 | ||||||||
\(46\) | −3.33680 | −0.491984 | ||||||||
\(47\) | −0.805861 | −0.117547 | −0.0587734 | − | 0.998271i | \(-0.518719\pi\) | ||||
−0.0587734 | + | 0.998271i | \(0.518719\pi\) | |||||||
\(48\) | 3.04499 | 0.439506 | ||||||||
\(49\) | 1.86170 | 0.265957 | ||||||||
\(50\) | −7.03906 | −0.995473 | ||||||||
\(51\) | 0.654571 | 0.0916583 | ||||||||
\(52\) | −3.67993 | −0.510315 | ||||||||
\(53\) | 11.2784 | 1.54920 | 0.774602 | − | 0.632449i | \(-0.217950\pi\) | ||||
0.774602 | + | 0.632449i | \(0.217950\pi\) | |||||||
\(54\) | −6.91004 | −0.940337 | ||||||||
\(55\) | 2.95213 | 0.398065 | ||||||||
\(56\) | −2.31243 | −0.309012 | ||||||||
\(57\) | −5.28233 | −0.699662 | ||||||||
\(58\) | 8.80058 | 1.15557 | ||||||||
\(59\) | 8.88704 | 1.15699 | 0.578497 | − | 0.815684i | \(-0.303639\pi\) | ||||
0.578497 | + | 0.815684i | \(0.303639\pi\) | |||||||
\(60\) | −3.07252 | −0.396661 | ||||||||
\(61\) | −0.148551 | −0.0190200 | −0.00951001 | − | 0.999955i | \(-0.503027\pi\) | ||||
−0.00951001 | + | 0.999955i | \(0.503027\pi\) | |||||||
\(62\) | 4.75631 | 0.604052 | ||||||||
\(63\) | 7.65510 | 0.964453 | ||||||||
\(64\) | −4.45290 | −0.556613 | ||||||||
\(65\) | −6.83239 | −0.847453 | ||||||||
\(66\) | 1.24024 | 0.152663 | ||||||||
\(67\) | −8.30785 | −1.01497 | −0.507483 | − | 0.861662i | \(-0.669424\pi\) | ||||
−0.507483 | + | 0.861662i | \(0.669424\pi\) | |||||||
\(68\) | −1.59002 | −0.192818 | ||||||||
\(69\) | −1.15276 | −0.138776 | ||||||||
\(70\) | 16.6511 | 1.99018 | ||||||||
\(71\) | 1.70595 | 0.202459 | 0.101230 | − | 0.994863i | \(-0.467722\pi\) | ||||
0.101230 | + | 0.994863i | \(0.467722\pi\) | |||||||
\(72\) | −1.99758 | −0.235417 | ||||||||
\(73\) | 12.9783 | 1.51900 | 0.759499 | − | 0.650509i | \(-0.225444\pi\) | ||||
0.759499 | + | 0.650509i | \(0.225444\pi\) | |||||||
\(74\) | 14.4894 | 1.68435 | ||||||||
\(75\) | −2.43177 | −0.280797 | ||||||||
\(76\) | 12.8313 | 1.47185 | ||||||||
\(77\) | −2.97686 | −0.339245 | ||||||||
\(78\) | −2.87040 | −0.325009 | ||||||||
\(79\) | −10.0903 | −1.13524 | −0.567622 | − | 0.823289i | \(-0.692137\pi\) | ||||
−0.567622 | + | 0.823289i | \(0.692137\pi\) | |||||||
\(80\) | −13.7329 | −1.53539 | ||||||||
\(81\) | 5.32741 | 0.591934 | ||||||||
\(82\) | 1.53258 | 0.169245 | ||||||||
\(83\) | 13.0959 | 1.43746 | 0.718731 | − | 0.695288i | \(-0.244723\pi\) | ||||
0.718731 | + | 0.695288i | \(0.244723\pi\) | |||||||
\(84\) | 3.09826 | 0.338048 | ||||||||
\(85\) | −2.95213 | −0.320203 | ||||||||
\(86\) | −1.89473 | −0.204315 | ||||||||
\(87\) | 3.04032 | 0.325957 | ||||||||
\(88\) | 0.776803 | 0.0828075 | ||||||||
\(89\) | −7.73489 | −0.819897 | −0.409949 | − | 0.912109i | \(-0.634453\pi\) | ||||
−0.409949 | + | 0.912109i | \(0.634453\pi\) | |||||||
\(90\) | 14.3839 | 1.51620 | ||||||||
\(91\) | 6.88963 | 0.722229 | ||||||||
\(92\) | 2.80017 | 0.291938 | ||||||||
\(93\) | 1.64316 | 0.170387 | ||||||||
\(94\) | 1.52689 | 0.157487 | ||||||||
\(95\) | 23.8234 | 2.44423 | ||||||||
\(96\) | −4.75249 | −0.485049 | ||||||||
\(97\) | −13.9630 | −1.41773 | −0.708866 | − | 0.705343i | \(-0.750793\pi\) | ||||
−0.708866 | + | 0.705343i | \(0.750793\pi\) | |||||||
\(98\) | −3.52742 | −0.356324 | ||||||||
\(99\) | −2.57154 | −0.258449 | ||||||||
\(100\) | 5.90702 | 0.590702 | ||||||||
\(101\) | −12.4410 | −1.23793 | −0.618964 | − | 0.785419i | \(-0.712447\pi\) | ||||
−0.618964 | + | 0.785419i | \(0.712447\pi\) | |||||||
\(102\) | −1.24024 | −0.122802 | ||||||||
\(103\) | 12.7577 | 1.25706 | 0.628528 | − | 0.777787i | \(-0.283658\pi\) | ||||
0.628528 | + | 0.777787i | \(0.283658\pi\) | |||||||
\(104\) | −1.79783 | −0.176292 | ||||||||
\(105\) | 5.75242 | 0.561379 | ||||||||
\(106\) | −21.3695 | −2.07559 | ||||||||
\(107\) | 4.30060 | 0.415755 | 0.207877 | − | 0.978155i | \(-0.433344\pi\) | ||||
0.207877 | + | 0.978155i | \(0.433344\pi\) | |||||||
\(108\) | 5.79875 | 0.557985 | ||||||||
\(109\) | 1.16601 | 0.111683 | 0.0558416 | − | 0.998440i | \(-0.482216\pi\) | ||||
0.0558416 | + | 0.998440i | \(0.482216\pi\) | |||||||
\(110\) | −5.59350 | −0.533319 | ||||||||
\(111\) | 5.00562 | 0.475112 | ||||||||
\(112\) | 13.8480 | 1.30851 | ||||||||
\(113\) | 7.02879 | 0.661213 | 0.330606 | − | 0.943769i | \(-0.392747\pi\) | ||||
0.330606 | + | 0.943769i | \(0.392747\pi\) | |||||||
\(114\) | 10.0086 | 0.937393 | ||||||||
\(115\) | 5.19896 | 0.484806 | ||||||||
\(116\) | −7.38525 | −0.685704 | ||||||||
\(117\) | 5.95155 | 0.550221 | ||||||||
\(118\) | −16.8386 | −1.55012 | ||||||||
\(119\) | 2.97686 | 0.272888 | ||||||||
\(120\) | −1.50108 | −0.137029 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.281465 | 0.0254826 | ||||||||
\(123\) | 0.529459 | 0.0477397 | ||||||||
\(124\) | −3.99139 | −0.358438 | ||||||||
\(125\) | −3.79330 | −0.339283 | ||||||||
\(126\) | −14.5044 | −1.29215 | ||||||||
\(127\) | −4.02695 | −0.357334 | −0.178667 | − | 0.983910i | \(-0.557179\pi\) | ||||
−0.178667 | + | 0.983910i | \(0.557179\pi\) | |||||||
\(128\) | −6.08386 | −0.537742 | ||||||||
\(129\) | −0.654571 | −0.0576318 | ||||||||
\(130\) | 12.9456 | 1.13540 | ||||||||
\(131\) | 5.25164 | 0.458838 | 0.229419 | − | 0.973328i | \(-0.426317\pi\) | ||||
0.229419 | + | 0.973328i | \(0.426317\pi\) | |||||||
\(132\) | −1.04078 | −0.0905884 | ||||||||
\(133\) | −24.0230 | −2.08306 | ||||||||
\(134\) | 15.7412 | 1.35983 | ||||||||
\(135\) | 10.7663 | 0.926617 | ||||||||
\(136\) | −0.776803 | −0.0666103 | ||||||||
\(137\) | 3.88496 | 0.331915 | 0.165957 | − | 0.986133i | \(-0.446929\pi\) | ||||
0.165957 | + | 0.986133i | \(0.446929\pi\) | |||||||
\(138\) | 2.18417 | 0.185929 | ||||||||
\(139\) | 2.69022 | 0.228182 | 0.114091 | − | 0.993470i | \(-0.463604\pi\) | ||||
0.114091 | + | 0.993470i | \(0.463604\pi\) | |||||||
\(140\) | −13.9732 | −1.18095 | ||||||||
\(141\) | 0.527493 | 0.0444230 | ||||||||
\(142\) | −3.23232 | −0.271251 | ||||||||
\(143\) | −2.31439 | −0.193539 | ||||||||
\(144\) | 11.9625 | 0.996872 | ||||||||
\(145\) | −13.7119 | −1.13871 | ||||||||
\(146\) | −24.5905 | −2.03512 | ||||||||
\(147\) | −1.21861 | −0.100510 | ||||||||
\(148\) | −12.1591 | −0.999476 | ||||||||
\(149\) | 11.1826 | 0.916118 | 0.458059 | − | 0.888922i | \(-0.348545\pi\) | ||||
0.458059 | + | 0.888922i | \(0.348545\pi\) | |||||||
\(150\) | 4.60757 | 0.376206 | ||||||||
\(151\) | −15.0744 | −1.22674 | −0.613368 | − | 0.789797i | \(-0.710186\pi\) | ||||
−0.613368 | + | 0.789797i | \(0.710186\pi\) | |||||||
\(152\) | 6.26873 | 0.508461 | ||||||||
\(153\) | 2.57154 | 0.207896 | ||||||||
\(154\) | 5.64036 | 0.454513 | ||||||||
\(155\) | −7.41066 | −0.595239 | ||||||||
\(156\) | 2.40878 | 0.192857 | ||||||||
\(157\) | −1.80903 | −0.144376 | −0.0721881 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721881 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(158\) | 19.1184 | 1.52098 | ||||||||
\(159\) | −7.38250 | −0.585471 | ||||||||
\(160\) | 21.4338 | 1.69449 | ||||||||
\(161\) | −5.24252 | −0.413168 | ||||||||
\(162\) | −10.0940 | −0.793061 | ||||||||
\(163\) | −23.8752 | −1.87005 | −0.935026 | − | 0.354579i | \(-0.884624\pi\) | ||||
−0.935026 | + | 0.354579i | \(0.884624\pi\) | |||||||
\(164\) | −1.28611 | −0.100428 | ||||||||
\(165\) | −1.93238 | −0.150436 | ||||||||
\(166\) | −24.8133 | −1.92588 | ||||||||
\(167\) | −10.7819 | −0.834325 | −0.417162 | − | 0.908832i | \(-0.636975\pi\) | ||||
−0.417162 | + | 0.908832i | \(0.636975\pi\) | |||||||
\(168\) | 1.51365 | 0.116781 | ||||||||
\(169\) | −7.64358 | −0.587968 | ||||||||
\(170\) | 5.59350 | 0.429002 | ||||||||
\(171\) | −20.7521 | −1.58695 | ||||||||
\(172\) | 1.59002 | 0.121238 | ||||||||
\(173\) | 4.05113 | 0.308002 | 0.154001 | − | 0.988071i | \(-0.450784\pi\) | ||||
0.154001 | + | 0.988071i | \(0.450784\pi\) | |||||||
\(174\) | −5.76061 | −0.436711 | ||||||||
\(175\) | −11.0592 | −0.835999 | ||||||||
\(176\) | −4.65188 | −0.350648 | ||||||||
\(177\) | −5.81720 | −0.437248 | ||||||||
\(178\) | 14.6556 | 1.09848 | ||||||||
\(179\) | 6.86119 | 0.512829 | 0.256415 | − | 0.966567i | \(-0.417459\pi\) | ||||
0.256415 | + | 0.966567i | \(0.417459\pi\) | |||||||
\(180\) | −12.0706 | −0.899693 | ||||||||
\(181\) | −13.2319 | −0.983522 | −0.491761 | − | 0.870730i | \(-0.663647\pi\) | ||||
−0.491761 | + | 0.870730i | \(0.663647\pi\) | |||||||
\(182\) | −13.0540 | −0.967628 | ||||||||
\(183\) | 0.0972373 | 0.00718799 | ||||||||
\(184\) | 1.36802 | 0.100852 | ||||||||
\(185\) | −22.5754 | −1.65978 | ||||||||
\(186\) | −3.11335 | −0.228282 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −1.28133 | −0.0934509 | ||||||||
\(189\) | −10.8565 | −0.789695 | ||||||||
\(190\) | −45.1390 | −3.27473 | ||||||||
\(191\) | 2.34918 | 0.169981 | 0.0849905 | − | 0.996382i | \(-0.472914\pi\) | ||||
0.0849905 | + | 0.996382i | \(0.472914\pi\) | |||||||
\(192\) | 2.91474 | 0.210354 | ||||||||
\(193\) | −18.2046 | −1.31040 | −0.655198 | − | 0.755457i | \(-0.727415\pi\) | ||||
−0.655198 | + | 0.755457i | \(0.727415\pi\) | |||||||
\(194\) | 26.4563 | 1.89945 | ||||||||
\(195\) | 4.47229 | 0.320267 | ||||||||
\(196\) | 2.96014 | 0.211438 | ||||||||
\(197\) | 24.9465 | 1.77736 | 0.888681 | − | 0.458526i | \(-0.151622\pi\) | ||||
0.888681 | + | 0.458526i | \(0.151622\pi\) | |||||||
\(198\) | 4.87238 | 0.346265 | ||||||||
\(199\) | −9.70404 | −0.687901 | −0.343951 | − | 0.938988i | \(-0.611765\pi\) | ||||
−0.343951 | + | 0.938988i | \(0.611765\pi\) | |||||||
\(200\) | 2.88587 | 0.204062 | ||||||||
\(201\) | 5.43808 | 0.383573 | ||||||||
\(202\) | 23.5724 | 1.65855 | ||||||||
\(203\) | 13.8268 | 0.970450 | ||||||||
\(204\) | 1.04078 | 0.0728693 | ||||||||
\(205\) | −2.38787 | −0.166776 | ||||||||
\(206\) | −24.1725 | −1.68418 | ||||||||
\(207\) | −4.52871 | −0.314767 | ||||||||
\(208\) | 10.7663 | 0.746507 | ||||||||
\(209\) | 8.06990 | 0.558207 | ||||||||
\(210\) | −10.8993 | −0.752124 | ||||||||
\(211\) | −16.9711 | −1.16834 | −0.584168 | − | 0.811633i | \(-0.698579\pi\) | ||||
−0.584168 | + | 0.811633i | \(0.698579\pi\) | |||||||
\(212\) | 17.9328 | 1.23163 | ||||||||
\(213\) | −1.11667 | −0.0765127 | ||||||||
\(214\) | −8.14850 | −0.557020 | ||||||||
\(215\) | 2.95213 | 0.201333 | ||||||||
\(216\) | 2.83298 | 0.192760 | ||||||||
\(217\) | 7.47275 | 0.507283 | ||||||||
\(218\) | −2.20927 | −0.149631 | ||||||||
\(219\) | −8.49524 | −0.574055 | ||||||||
\(220\) | 4.69394 | 0.316466 | ||||||||
\(221\) | 2.31439 | 0.155683 | ||||||||
\(222\) | −9.48432 | −0.636546 | ||||||||
\(223\) | −28.1230 | −1.88326 | −0.941629 | − | 0.336653i | \(-0.890705\pi\) | ||||
−0.941629 | + | 0.336653i | \(0.890705\pi\) | |||||||
\(224\) | −21.6134 | −1.44411 | ||||||||
\(225\) | −9.55342 | −0.636895 | ||||||||
\(226\) | −13.3177 | −0.885879 | ||||||||
\(227\) | −2.12293 | −0.140904 | −0.0704519 | − | 0.997515i | \(-0.522444\pi\) | ||||
−0.0704519 | + | 0.997515i | \(0.522444\pi\) | |||||||
\(228\) | −8.39901 | −0.556238 | ||||||||
\(229\) | 26.4793 | 1.74980 | 0.874900 | − | 0.484304i | \(-0.160927\pi\) | ||||
0.874900 | + | 0.484304i | \(0.160927\pi\) | |||||||
\(230\) | −9.85065 | −0.649533 | ||||||||
\(231\) | 1.94857 | 0.128206 | ||||||||
\(232\) | −3.60806 | −0.236881 | ||||||||
\(233\) | 23.1464 | 1.51637 | 0.758184 | − | 0.652040i | \(-0.226087\pi\) | ||||
0.758184 | + | 0.652040i | \(0.226087\pi\) | |||||||
\(234\) | −11.2766 | −0.737175 | ||||||||
\(235\) | −2.37900 | −0.155189 | ||||||||
\(236\) | 14.1306 | 0.919822 | ||||||||
\(237\) | 6.60480 | 0.429028 | ||||||||
\(238\) | −5.64036 | −0.365610 | ||||||||
\(239\) | −7.14075 | −0.461897 | −0.230948 | − | 0.972966i | \(-0.574183\pi\) | ||||
−0.230948 | + | 0.972966i | \(0.574183\pi\) | |||||||
\(240\) | 8.98919 | 0.580250 | ||||||||
\(241\) | −6.85523 | −0.441584 | −0.220792 | − | 0.975321i | \(-0.570864\pi\) | ||||
−0.220792 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(242\) | −1.89473 | −0.121798 | ||||||||
\(243\) | −14.4281 | −0.925561 | ||||||||
\(244\) | −0.236199 | −0.0151211 | ||||||||
\(245\) | 5.49597 | 0.351125 | ||||||||
\(246\) | −1.00319 | −0.0639607 | ||||||||
\(247\) | −18.6769 | −1.18838 | ||||||||
\(248\) | −1.94999 | −0.123825 | ||||||||
\(249\) | −8.57221 | −0.543241 | ||||||||
\(250\) | 7.18730 | 0.454565 | ||||||||
\(251\) | 4.30264 | 0.271581 | 0.135790 | − | 0.990738i | \(-0.456643\pi\) | ||||
0.135790 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(252\) | 12.1718 | 0.766749 | ||||||||
\(253\) | 1.76109 | 0.110719 | ||||||||
\(254\) | 7.63001 | 0.478749 | ||||||||
\(255\) | 1.93238 | 0.121010 | ||||||||
\(256\) | 20.4331 | 1.27707 | ||||||||
\(257\) | 6.48342 | 0.404425 | 0.202212 | − | 0.979342i | \(-0.435187\pi\) | ||||
0.202212 | + | 0.979342i | \(0.435187\pi\) | |||||||
\(258\) | 1.24024 | 0.0772139 | ||||||||
\(259\) | 22.7645 | 1.41452 | ||||||||
\(260\) | −10.8636 | −0.673734 | ||||||||
\(261\) | 11.9442 | 0.739325 | ||||||||
\(262\) | −9.95047 | −0.614742 | ||||||||
\(263\) | −3.23554 | −0.199512 | −0.0997559 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997559 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(264\) | −0.508473 | −0.0312944 | ||||||||
\(265\) | 33.2952 | 2.04531 | ||||||||
\(266\) | 45.5172 | 2.79084 | ||||||||
\(267\) | 5.06304 | 0.309853 | ||||||||
\(268\) | −13.2097 | −0.806908 | ||||||||
\(269\) | −2.61337 | −0.159340 | −0.0796699 | − | 0.996821i | \(-0.525387\pi\) | ||||
−0.0796699 | + | 0.996821i | \(0.525387\pi\) | |||||||
\(270\) | −20.3993 | −1.24146 | ||||||||
\(271\) | 21.3015 | 1.29397 | 0.646986 | − | 0.762501i | \(-0.276029\pi\) | ||||
0.646986 | + | 0.762501i | \(0.276029\pi\) | |||||||
\(272\) | 4.65188 | 0.282061 | ||||||||
\(273\) | −4.50975 | −0.272943 | ||||||||
\(274\) | −7.36098 | −0.444693 | ||||||||
\(275\) | 3.71506 | 0.224027 | ||||||||
\(276\) | −1.83291 | −0.110328 | ||||||||
\(277\) | −8.21199 | −0.493411 | −0.246705 | − | 0.969091i | \(-0.579348\pi\) | ||||
−0.246705 | + | 0.969091i | \(0.579348\pi\) | |||||||
\(278\) | −5.09726 | −0.305713 | ||||||||
\(279\) | 6.45527 | 0.386467 | ||||||||
\(280\) | −6.82660 | −0.407968 | ||||||||
\(281\) | 17.5590 | 1.04748 | 0.523741 | − | 0.851877i | \(-0.324536\pi\) | ||||
0.523741 | + | 0.851877i | \(0.324536\pi\) | |||||||
\(282\) | −0.999460 | −0.0595170 | ||||||||
\(283\) | 3.39288 | 0.201686 | 0.100843 | − | 0.994902i | \(-0.467846\pi\) | ||||
0.100843 | + | 0.994902i | \(0.467846\pi\) | |||||||
\(284\) | 2.71250 | 0.160957 | ||||||||
\(285\) | −15.5941 | −0.923716 | ||||||||
\(286\) | 4.38516 | 0.259300 | ||||||||
\(287\) | 2.40788 | 0.142132 | ||||||||
\(288\) | −18.6706 | −1.10017 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 25.9804 | 1.52562 | ||||||||
\(291\) | 9.13981 | 0.535785 | ||||||||
\(292\) | 20.6358 | 1.20762 | ||||||||
\(293\) | 10.0153 | 0.585099 | 0.292550 | − | 0.956250i | \(-0.405496\pi\) | ||||
0.292550 | + | 0.956250i | \(0.405496\pi\) | |||||||
\(294\) | 2.30895 | 0.134661 | ||||||||
\(295\) | 26.2357 | 1.52750 | ||||||||
\(296\) | −5.94034 | −0.345275 | ||||||||
\(297\) | 3.64697 | 0.211619 | ||||||||
\(298\) | −21.1881 | −1.22740 | ||||||||
\(299\) | −4.07585 | −0.235713 | ||||||||
\(300\) | −3.86657 | −0.223236 | ||||||||
\(301\) | −2.97686 | −0.171583 | ||||||||
\(302\) | 28.5620 | 1.64356 | ||||||||
\(303\) | 8.14354 | 0.467834 | ||||||||
\(304\) | −37.5402 | −2.15308 | ||||||||
\(305\) | −0.438542 | −0.0251108 | ||||||||
\(306\) | −4.87238 | −0.278535 | ||||||||
\(307\) | 15.9995 | 0.913141 | 0.456570 | − | 0.889687i | \(-0.349078\pi\) | ||||
0.456570 | + | 0.889687i | \(0.349078\pi\) | |||||||
\(308\) | −4.73327 | −0.269703 | ||||||||
\(309\) | −8.35085 | −0.475063 | ||||||||
\(310\) | 14.0412 | 0.797489 | ||||||||
\(311\) | −22.3221 | −1.26577 | −0.632884 | − | 0.774247i | \(-0.718129\pi\) | ||||
−0.632884 | + | 0.774247i | \(0.718129\pi\) | |||||||
\(312\) | 1.17681 | 0.0666236 | ||||||||
\(313\) | 1.76777 | 0.0999200 | 0.0499600 | − | 0.998751i | \(-0.484091\pi\) | ||||
0.0499600 | + | 0.998751i | \(0.484091\pi\) | |||||||
\(314\) | 3.42763 | 0.193432 | ||||||||
\(315\) | 22.5989 | 1.27330 | ||||||||
\(316\) | −16.0437 | −0.902531 | ||||||||
\(317\) | −24.2100 | −1.35977 | −0.679884 | − | 0.733320i | \(-0.737970\pi\) | ||||
−0.679884 | + | 0.733320i | \(0.737970\pi\) | |||||||
\(318\) | 13.9879 | 0.784402 | ||||||||
\(319\) | −4.64475 | −0.260056 | ||||||||
\(320\) | −13.1455 | −0.734858 | ||||||||
\(321\) | −2.81505 | −0.157121 | ||||||||
\(322\) | 9.93318 | 0.553555 | ||||||||
\(323\) | −8.06990 | −0.449022 | ||||||||
\(324\) | 8.47068 | 0.470594 | ||||||||
\(325\) | −8.59812 | −0.476938 | ||||||||
\(326\) | 45.2372 | 2.50546 | ||||||||
\(327\) | −0.763234 | −0.0422070 | ||||||||
\(328\) | −0.628328 | −0.0346936 | ||||||||
\(329\) | 2.39893 | 0.132258 | ||||||||
\(330\) | 3.66135 | 0.201550 | ||||||||
\(331\) | −6.08229 | −0.334313 | −0.167156 | − | 0.985930i | \(-0.553458\pi\) | ||||
−0.167156 | + | 0.985930i | \(0.553458\pi\) | |||||||
\(332\) | 20.8228 | 1.14280 | ||||||||
\(333\) | 19.6650 | 1.07763 | ||||||||
\(334\) | 20.4288 | 1.11781 | ||||||||
\(335\) | −24.5259 | −1.33999 | ||||||||
\(336\) | −9.06450 | −0.494509 | ||||||||
\(337\) | −16.8355 | −0.917086 | −0.458543 | − | 0.888672i | \(-0.651629\pi\) | ||||
−0.458543 | + | 0.888672i | \(0.651629\pi\) | |||||||
\(338\) | 14.4826 | 0.787748 | ||||||||
\(339\) | −4.60084 | −0.249883 | ||||||||
\(340\) | −4.69394 | −0.254565 | ||||||||
\(341\) | −2.51028 | −0.135939 | ||||||||
\(342\) | 39.3196 | 2.12616 | ||||||||
\(343\) | 15.2960 | 0.825907 | ||||||||
\(344\) | 0.776803 | 0.0418824 | ||||||||
\(345\) | −3.40309 | −0.183216 | ||||||||
\(346\) | −7.67581 | −0.412654 | ||||||||
\(347\) | 15.2068 | 0.816344 | 0.408172 | − | 0.912905i | \(-0.366166\pi\) | ||||
0.408172 | + | 0.912905i | \(0.366166\pi\) | |||||||
\(348\) | 4.83418 | 0.259139 | ||||||||
\(349\) | 13.8219 | 0.739870 | 0.369935 | − | 0.929058i | \(-0.379380\pi\) | ||||
0.369935 | + | 0.929058i | \(0.379380\pi\) | |||||||
\(350\) | 20.9543 | 1.12005 | ||||||||
\(351\) | −8.44052 | −0.450522 | ||||||||
\(352\) | 7.26047 | 0.386984 | ||||||||
\(353\) | 35.9828 | 1.91517 | 0.957586 | − | 0.288148i | \(-0.0930395\pi\) | ||||
0.957586 | + | 0.288148i | \(0.0930395\pi\) | |||||||
\(354\) | 11.0221 | 0.585816 | ||||||||
\(355\) | 5.03618 | 0.267293 | ||||||||
\(356\) | −12.2986 | −0.651827 | ||||||||
\(357\) | −1.94857 | −0.103129 | ||||||||
\(358\) | −13.0001 | −0.687078 | ||||||||
\(359\) | −26.5807 | −1.40287 | −0.701437 | − | 0.712731i | \(-0.747458\pi\) | ||||
−0.701437 | + | 0.712731i | \(0.747458\pi\) | |||||||
\(360\) | −5.89711 | −0.310805 | ||||||||
\(361\) | 46.1234 | 2.42755 | ||||||||
\(362\) | 25.0710 | 1.31770 | ||||||||
\(363\) | −0.654571 | −0.0343561 | ||||||||
\(364\) | 10.9546 | 0.574179 | ||||||||
\(365\) | 38.3137 | 2.00543 | ||||||||
\(366\) | −0.184239 | −0.00963032 | ||||||||
\(367\) | −11.7561 | −0.613661 | −0.306831 | − | 0.951764i | \(-0.599269\pi\) | ||||
−0.306831 | + | 0.951764i | \(0.599269\pi\) | |||||||
\(368\) | −8.19237 | −0.427057 | ||||||||
\(369\) | 2.08002 | 0.108282 | ||||||||
\(370\) | 42.7744 | 2.22374 | ||||||||
\(371\) | −33.5742 | −1.74308 | ||||||||
\(372\) | 2.61265 | 0.135460 | ||||||||
\(373\) | 31.2902 | 1.62015 | 0.810073 | − | 0.586329i | \(-0.199427\pi\) | ||||
0.810073 | + | 0.586329i | \(0.199427\pi\) | |||||||
\(374\) | 1.89473 | 0.0979744 | ||||||||
\(375\) | 2.48299 | 0.128221 | ||||||||
\(376\) | −0.625995 | −0.0322832 | ||||||||
\(377\) | 10.7498 | 0.553642 | ||||||||
\(378\) | 20.5702 | 1.05802 | ||||||||
\(379\) | −22.7386 | −1.16801 | −0.584003 | − | 0.811752i | \(-0.698514\pi\) | ||||
−0.584003 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(380\) | 37.8797 | 1.94319 | ||||||||
\(381\) | 2.63593 | 0.135043 | ||||||||
\(382\) | −4.45108 | −0.227737 | ||||||||
\(383\) | −19.4061 | −0.991606 | −0.495803 | − | 0.868435i | \(-0.665126\pi\) | ||||
−0.495803 | + | 0.868435i | \(0.665126\pi\) | |||||||
\(384\) | 3.98232 | 0.203222 | ||||||||
\(385\) | −8.78807 | −0.447882 | ||||||||
\(386\) | 34.4929 | 1.75564 | ||||||||
\(387\) | −2.57154 | −0.130719 | ||||||||
\(388\) | −22.2015 | −1.12711 | ||||||||
\(389\) | −33.6127 | −1.70423 | −0.852116 | − | 0.523353i | \(-0.824681\pi\) | ||||
−0.852116 | + | 0.523353i | \(0.824681\pi\) | |||||||
\(390\) | −8.47379 | −0.429087 | ||||||||
\(391\) | −1.76109 | −0.0890621 | ||||||||
\(392\) | 1.44617 | 0.0730428 | ||||||||
\(393\) | −3.43757 | −0.173403 | ||||||||
\(394\) | −47.2669 | −2.38127 | ||||||||
\(395\) | −29.7878 | −1.49879 | ||||||||
\(396\) | −4.08879 | −0.205470 | ||||||||
\(397\) | −1.48876 | −0.0747186 | −0.0373593 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373593 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(398\) | 18.3866 | 0.921636 | ||||||||
\(399\) | 15.7248 | 0.787223 | ||||||||
\(400\) | −17.2820 | −0.864101 | ||||||||
\(401\) | −30.0796 | −1.50210 | −0.751051 | − | 0.660244i | \(-0.770453\pi\) | ||||
−0.751051 | + | 0.660244i | \(0.770453\pi\) | |||||||
\(402\) | −10.3037 | −0.513903 | ||||||||
\(403\) | 5.80977 | 0.289405 | ||||||||
\(404\) | −19.7815 | −0.984165 | ||||||||
\(405\) | 15.7272 | 0.781490 | ||||||||
\(406\) | −26.1981 | −1.30019 | ||||||||
\(407\) | −7.64717 | −0.379056 | ||||||||
\(408\) | 0.508473 | 0.0251732 | ||||||||
\(409\) | −16.7006 | −0.825792 | −0.412896 | − | 0.910778i | \(-0.635483\pi\) | ||||
−0.412896 | + | 0.910778i | \(0.635483\pi\) | |||||||
\(410\) | 4.52438 | 0.223443 | ||||||||
\(411\) | −2.54299 | −0.125436 | ||||||||
\(412\) | 20.2850 | 0.999373 | ||||||||
\(413\) | −26.4555 | −1.30179 | ||||||||
\(414\) | 8.58070 | 0.421718 | ||||||||
\(415\) | 38.6608 | 1.89778 | ||||||||
\(416\) | −16.8036 | −0.823863 | ||||||||
\(417\) | −1.76094 | −0.0862338 | ||||||||
\(418\) | −15.2903 | −0.747874 | ||||||||
\(419\) | −20.8018 | −1.01623 | −0.508116 | − | 0.861288i | \(-0.669658\pi\) | ||||
−0.508116 | + | 0.861288i | \(0.669658\pi\) | |||||||
\(420\) | 9.14647 | 0.446302 | ||||||||
\(421\) | −18.5118 | −0.902210 | −0.451105 | − | 0.892471i | \(-0.648970\pi\) | ||||
−0.451105 | + | 0.892471i | \(0.648970\pi\) | |||||||
\(422\) | 32.1557 | 1.56531 | ||||||||
\(423\) | 2.07230 | 0.100759 | ||||||||
\(424\) | 8.76108 | 0.425476 | ||||||||
\(425\) | −3.71506 | −0.180207 | ||||||||
\(426\) | 2.11579 | 0.102510 | ||||||||
\(427\) | 0.442216 | 0.0214003 | ||||||||
\(428\) | 6.83804 | 0.330529 | ||||||||
\(429\) | 1.51494 | 0.0731418 | ||||||||
\(430\) | −5.59350 | −0.269743 | ||||||||
\(431\) | 12.2863 | 0.591813 | 0.295906 | − | 0.955217i | \(-0.404378\pi\) | ||||
0.295906 | + | 0.955217i | \(0.404378\pi\) | |||||||
\(432\) | −16.9652 | −0.816241 | ||||||||
\(433\) | 27.7426 | 1.33322 | 0.666612 | − | 0.745405i | \(-0.267744\pi\) | ||||
0.666612 | + | 0.745405i | \(0.267744\pi\) | |||||||
\(434\) | −14.1589 | −0.679648 | ||||||||
\(435\) | 8.97543 | 0.430339 | ||||||||
\(436\) | 1.85397 | 0.0887892 | ||||||||
\(437\) | 14.2118 | 0.679844 | ||||||||
\(438\) | 16.0962 | 0.769107 | ||||||||
\(439\) | −9.60314 | −0.458333 | −0.229167 | − | 0.973387i | \(-0.573600\pi\) | ||||
−0.229167 | + | 0.973387i | \(0.573600\pi\) | |||||||
\(440\) | 2.29322 | 0.109325 | ||||||||
\(441\) | −4.78742 | −0.227973 | ||||||||
\(442\) | −4.38516 | −0.208581 | ||||||||
\(443\) | 12.9279 | 0.614223 | 0.307112 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307112 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(444\) | 7.95903 | 0.377719 | ||||||||
\(445\) | −22.8344 | −1.08245 | ||||||||
\(446\) | 53.2857 | 2.52315 | ||||||||
\(447\) | −7.31984 | −0.346216 | ||||||||
\(448\) | 13.2557 | 0.626272 | ||||||||
\(449\) | −28.4481 | −1.34255 | −0.671273 | − | 0.741210i | \(-0.734252\pi\) | ||||
−0.671273 | + | 0.741210i | \(0.734252\pi\) | |||||||
\(450\) | 18.1012 | 0.853298 | ||||||||
\(451\) | −0.808864 | −0.0380879 | ||||||||
\(452\) | 11.1759 | 0.525671 | ||||||||
\(453\) | 9.86726 | 0.463604 | ||||||||
\(454\) | 4.02239 | 0.188780 | ||||||||
\(455\) | 20.3391 | 0.953510 | ||||||||
\(456\) | −4.10333 | −0.192156 | ||||||||
\(457\) | −0.348114 | −0.0162841 | −0.00814205 | − | 0.999967i | \(-0.502592\pi\) | ||||
−0.00814205 | + | 0.999967i | \(0.502592\pi\) | |||||||
\(458\) | −50.1712 | −2.34435 | ||||||||
\(459\) | −3.64697 | −0.170226 | ||||||||
\(460\) | 8.26645 | 0.385425 | ||||||||
\(461\) | −31.0780 | −1.44744 | −0.723722 | − | 0.690091i | \(-0.757570\pi\) | ||||
−0.723722 | + | 0.690091i | \(0.757570\pi\) | |||||||
\(462\) | −3.69202 | −0.171768 | ||||||||
\(463\) | 5.12662 | 0.238254 | 0.119127 | − | 0.992879i | \(-0.461990\pi\) | ||||
0.119127 | + | 0.992879i | \(0.461990\pi\) | |||||||
\(464\) | 21.6068 | 1.00307 | ||||||||
\(465\) | 4.85081 | 0.224951 | ||||||||
\(466\) | −43.8562 | −2.03160 | ||||||||
\(467\) | −12.2535 | −0.567026 | −0.283513 | − | 0.958968i | \(-0.591500\pi\) | ||||
−0.283513 | + | 0.958968i | \(0.591500\pi\) | |||||||
\(468\) | 9.46308 | 0.437431 | ||||||||
\(469\) | 24.7313 | 1.14199 | ||||||||
\(470\) | 4.50758 | 0.207919 | ||||||||
\(471\) | 1.18414 | 0.0545622 | ||||||||
\(472\) | 6.90348 | 0.317758 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −12.5144 | −0.574803 | ||||||||
\(475\) | 29.9802 | 1.37559 | ||||||||
\(476\) | 4.73327 | 0.216949 | ||||||||
\(477\) | −29.0028 | −1.32794 | ||||||||
\(478\) | 13.5298 | 0.618840 | ||||||||
\(479\) | −37.7632 | −1.72545 | −0.862723 | − | 0.505677i | \(-0.831243\pi\) | ||||
−0.862723 | + | 0.505677i | \(0.831243\pi\) | |||||||
\(480\) | −14.0300 | −0.640378 | ||||||||
\(481\) | 17.6985 | 0.806984 | ||||||||
\(482\) | 12.9889 | 0.591626 | ||||||||
\(483\) | 3.43160 | 0.156143 | ||||||||
\(484\) | 1.59002 | 0.0722736 | ||||||||
\(485\) | −41.2207 | −1.87174 | ||||||||
\(486\) | 27.3374 | 1.24005 | ||||||||
\(487\) | 30.6830 | 1.39038 | 0.695190 | − | 0.718826i | \(-0.255320\pi\) | ||||
0.695190 | + | 0.718826i | \(0.255320\pi\) | |||||||
\(488\) | −0.115395 | −0.00522368 | ||||||||
\(489\) | 15.6280 | 0.706724 | ||||||||
\(490\) | −10.4134 | −0.470430 | ||||||||
\(491\) | −24.7737 | −1.11802 | −0.559012 | − | 0.829160i | \(-0.688819\pi\) | ||||
−0.559012 | + | 0.829160i | \(0.688819\pi\) | |||||||
\(492\) | 0.841851 | 0.0379536 | ||||||||
\(493\) | 4.64475 | 0.209189 | ||||||||
\(494\) | 35.3878 | 1.59217 | ||||||||
\(495\) | −7.59151 | −0.341213 | ||||||||
\(496\) | 11.6775 | 0.524335 | ||||||||
\(497\) | −5.07838 | −0.227796 | ||||||||
\(498\) | 16.2421 | 0.727824 | ||||||||
\(499\) | −15.7055 | −0.703075 | −0.351538 | − | 0.936174i | \(-0.614341\pi\) | ||||
−0.351538 | + | 0.936174i | \(0.614341\pi\) | |||||||
\(500\) | −6.03142 | −0.269733 | ||||||||
\(501\) | 7.05749 | 0.315306 | ||||||||
\(502\) | −8.15237 | −0.363858 | ||||||||
\(503\) | 20.8092 | 0.927838 | 0.463919 | − | 0.885878i | \(-0.346443\pi\) | ||||
0.463919 | + | 0.885878i | \(0.346443\pi\) | |||||||
\(504\) | 5.94651 | 0.264879 | ||||||||
\(505\) | −36.7275 | −1.63435 | ||||||||
\(506\) | −3.33680 | −0.148339 | ||||||||
\(507\) | 5.00327 | 0.222203 | ||||||||
\(508\) | −6.40294 | −0.284084 | ||||||||
\(509\) | 32.3749 | 1.43499 | 0.717497 | − | 0.696562i | \(-0.245288\pi\) | ||||
0.717497 | + | 0.696562i | \(0.245288\pi\) | |||||||
\(510\) | −3.66135 | −0.162127 | ||||||||
\(511\) | −38.6346 | −1.70910 | ||||||||
\(512\) | −26.5476 | −1.17325 | ||||||||
\(513\) | 29.4307 | 1.29940 | ||||||||
\(514\) | −12.2844 | −0.541840 | ||||||||
\(515\) | 37.6625 | 1.65961 | ||||||||
\(516\) | −1.04078 | −0.0458179 | ||||||||
\(517\) | −0.805861 | −0.0354417 | ||||||||
\(518\) | −43.1328 | −1.89515 | ||||||||
\(519\) | −2.65175 | −0.116399 | ||||||||
\(520\) | −5.30742 | −0.232746 | ||||||||
\(521\) | −4.44136 | −0.194579 | −0.0972897 | − | 0.995256i | \(-0.531017\pi\) | ||||
−0.0972897 | + | 0.995256i | \(0.531017\pi\) | |||||||
\(522\) | −22.6310 | −0.990532 | ||||||||
\(523\) | −19.0302 | −0.832133 | −0.416067 | − | 0.909334i | \(-0.636592\pi\) | ||||
−0.416067 | + | 0.909334i | \(0.636592\pi\) | |||||||
\(524\) | 8.35022 | 0.364781 | ||||||||
\(525\) | 7.23905 | 0.315938 | ||||||||
\(526\) | 6.13049 | 0.267302 | ||||||||
\(527\) | 2.51028 | 0.109349 | ||||||||
\(528\) | 3.04499 | 0.132516 | ||||||||
\(529\) | −19.8986 | −0.865155 | ||||||||
\(530\) | −63.0856 | −2.74026 | ||||||||
\(531\) | −22.8533 | −0.991751 | ||||||||
\(532\) | −38.1970 | −1.65605 | ||||||||
\(533\) | 1.87203 | 0.0810866 | ||||||||
\(534\) | −9.59312 | −0.415135 | ||||||||
\(535\) | 12.6959 | 0.548893 | ||||||||
\(536\) | −6.45357 | −0.278752 | ||||||||
\(537\) | −4.49114 | −0.193807 | ||||||||
\(538\) | 4.95164 | 0.213480 | ||||||||
\(539\) | 1.86170 | 0.0801890 | ||||||||
\(540\) | 17.1187 | 0.736670 | ||||||||
\(541\) | −10.6596 | −0.458290 | −0.229145 | − | 0.973392i | \(-0.573593\pi\) | ||||
−0.229145 | + | 0.973392i | \(0.573593\pi\) | |||||||
\(542\) | −40.3607 | −1.73364 | ||||||||
\(543\) | 8.66125 | 0.371690 | ||||||||
\(544\) | −7.26047 | −0.311290 | ||||||||
\(545\) | 3.44220 | 0.147448 | ||||||||
\(546\) | 8.54479 | 0.365683 | ||||||||
\(547\) | −7.27819 | −0.311193 | −0.155597 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155597 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(548\) | 6.17717 | 0.263876 | ||||||||
\(549\) | 0.382004 | 0.0163036 | ||||||||
\(550\) | −7.03906 | −0.300146 | ||||||||
\(551\) | −37.4827 | −1.59682 | ||||||||
\(552\) | −0.895467 | −0.0381136 | ||||||||
\(553\) | 30.0373 | 1.27732 | ||||||||
\(554\) | 15.5595 | 0.661062 | ||||||||
\(555\) | 14.7772 | 0.627258 | ||||||||
\(556\) | 4.27751 | 0.181407 | ||||||||
\(557\) | 39.0784 | 1.65580 | 0.827901 | − | 0.560874i | \(-0.189535\pi\) | ||||
0.827901 | + | 0.560874i | \(0.189535\pi\) | |||||||
\(558\) | −12.2310 | −0.517781 | ||||||||
\(559\) | −2.31439 | −0.0978884 | ||||||||
\(560\) | 40.8810 | 1.72754 | ||||||||
\(561\) | 0.654571 | 0.0276360 | ||||||||
\(562\) | −33.2697 | −1.40340 | ||||||||
\(563\) | 26.7746 | 1.12841 | 0.564207 | − | 0.825633i | \(-0.309182\pi\) | ||||
0.564207 | + | 0.825633i | \(0.309182\pi\) | |||||||
\(564\) | 0.838725 | 0.0353167 | ||||||||
\(565\) | 20.7499 | 0.872954 | ||||||||
\(566\) | −6.42861 | −0.270215 | ||||||||
\(567\) | −15.8589 | −0.666013 | ||||||||
\(568\) | 1.32519 | 0.0556036 | ||||||||
\(569\) | −8.22951 | −0.344999 | −0.172499 | − | 0.985010i | \(-0.555184\pi\) | ||||
−0.172499 | + | 0.985010i | \(0.555184\pi\) | |||||||
\(570\) | 29.5467 | 1.23758 | ||||||||
\(571\) | −7.11575 | −0.297785 | −0.148892 | − | 0.988853i | \(-0.547571\pi\) | ||||
−0.148892 | + | 0.988853i | \(0.547571\pi\) | |||||||
\(572\) | −3.67993 | −0.153866 | ||||||||
\(573\) | −1.53771 | −0.0642387 | ||||||||
\(574\) | −4.56229 | −0.190426 | ||||||||
\(575\) | 6.54256 | 0.272843 | ||||||||
\(576\) | 11.4508 | 0.477117 | ||||||||
\(577\) | −35.1648 | −1.46393 | −0.731964 | − | 0.681343i | \(-0.761396\pi\) | ||||
−0.731964 | + | 0.681343i | \(0.761396\pi\) | |||||||
\(578\) | −1.89473 | −0.0788106 | ||||||||
\(579\) | 11.9162 | 0.495221 | ||||||||
\(580\) | −21.8022 | −0.905288 | ||||||||
\(581\) | −38.9847 | −1.61736 | ||||||||
\(582\) | −17.3175 | −0.717834 | ||||||||
\(583\) | 11.2784 | 0.467103 | ||||||||
\(584\) | 10.0816 | 0.417179 | ||||||||
\(585\) | 17.5697 | 0.726419 | ||||||||
\(586\) | −18.9763 | −0.783904 | ||||||||
\(587\) | −23.2701 | −0.960459 | −0.480230 | − | 0.877143i | \(-0.659447\pi\) | ||||
−0.480230 | + | 0.877143i | \(0.659447\pi\) | |||||||
\(588\) | −1.93762 | −0.0799062 | ||||||||
\(589\) | −20.2577 | −0.834704 | ||||||||
\(590\) | −49.7097 | −2.04651 | ||||||||
\(591\) | −16.3292 | −0.671695 | ||||||||
\(592\) | 35.5737 | 1.46207 | ||||||||
\(593\) | −25.2457 | −1.03671 | −0.518357 | − | 0.855164i | \(-0.673456\pi\) | ||||
−0.518357 | + | 0.855164i | \(0.673456\pi\) | |||||||
\(594\) | −6.91004 | −0.283522 | ||||||||
\(595\) | 8.78807 | 0.360276 | ||||||||
\(596\) | 17.7806 | 0.728323 | ||||||||
\(597\) | 6.35199 | 0.259970 | ||||||||
\(598\) | 7.72266 | 0.315803 | ||||||||
\(599\) | −43.3602 | −1.77165 | −0.885826 | − | 0.464018i | \(-0.846407\pi\) | ||||
−0.885826 | + | 0.464018i | \(0.846407\pi\) | |||||||
\(600\) | −1.88901 | −0.0771185 | ||||||||
\(601\) | 22.6425 | 0.923608 | 0.461804 | − | 0.886982i | \(-0.347202\pi\) | ||||
0.461804 | + | 0.886982i | \(0.347202\pi\) | |||||||
\(602\) | 5.64036 | 0.229884 | ||||||||
\(603\) | 21.3639 | 0.870007 | ||||||||
\(604\) | −23.9686 | −0.975267 | ||||||||
\(605\) | 2.95213 | 0.120021 | ||||||||
\(606\) | −15.4298 | −0.626795 | ||||||||
\(607\) | −2.29332 | −0.0930831 | −0.0465416 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465416 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(608\) | 58.5913 | 2.37619 | ||||||||
\(609\) | −9.05062 | −0.366750 | ||||||||
\(610\) | 0.830920 | 0.0336430 | ||||||||
\(611\) | 1.86508 | 0.0754530 | ||||||||
\(612\) | 4.08879 | 0.165280 | ||||||||
\(613\) | −15.2958 | −0.617790 | −0.308895 | − | 0.951096i | \(-0.599959\pi\) | ||||
−0.308895 | + | 0.951096i | \(0.599959\pi\) | |||||||
\(614\) | −30.3148 | −1.22341 | ||||||||
\(615\) | 1.56303 | 0.0630275 | ||||||||
\(616\) | −2.31243 | −0.0931706 | ||||||||
\(617\) | 21.4378 | 0.863055 | 0.431528 | − | 0.902100i | \(-0.357975\pi\) | ||||
0.431528 | + | 0.902100i | \(0.357975\pi\) | |||||||
\(618\) | 15.8226 | 0.636480 | ||||||||
\(619\) | 7.96311 | 0.320064 | 0.160032 | − | 0.987112i | \(-0.448840\pi\) | ||||
0.160032 | + | 0.987112i | \(0.448840\pi\) | |||||||
\(620\) | −11.7831 | −0.473221 | ||||||||
\(621\) | 6.42264 | 0.257732 | ||||||||
\(622\) | 42.2944 | 1.69585 | ||||||||
\(623\) | 23.0257 | 0.922505 | ||||||||
\(624\) | −7.04729 | −0.282118 | ||||||||
\(625\) | −29.7736 | −1.19094 | ||||||||
\(626\) | −3.34945 | −0.133871 | ||||||||
\(627\) | −5.28233 | −0.210956 | ||||||||
\(628\) | −2.87639 | −0.114781 | ||||||||
\(629\) | 7.64717 | 0.304912 | ||||||||
\(630\) | −42.8188 | −1.70594 | ||||||||
\(631\) | 25.4769 | 1.01422 | 0.507110 | − | 0.861881i | \(-0.330714\pi\) | ||||
0.507110 | + | 0.861881i | \(0.330714\pi\) | |||||||
\(632\) | −7.83816 | −0.311785 | ||||||||
\(633\) | 11.1088 | 0.441534 | ||||||||
\(634\) | 45.8715 | 1.82179 | ||||||||
\(635\) | −11.8881 | −0.471764 | ||||||||
\(636\) | −11.7383 | −0.465455 | ||||||||
\(637\) | −4.30870 | −0.170717 | ||||||||
\(638\) | 8.80058 | 0.348418 | ||||||||
\(639\) | −4.38691 | −0.173544 | ||||||||
\(640\) | −17.9603 | −0.709944 | ||||||||
\(641\) | 32.5634 | 1.28618 | 0.643088 | − | 0.765792i | \(-0.277653\pi\) | ||||
0.643088 | + | 0.765792i | \(0.277653\pi\) | |||||||
\(642\) | 5.33377 | 0.210507 | ||||||||
\(643\) | −34.4178 | −1.35731 | −0.678653 | − | 0.734459i | \(-0.737436\pi\) | ||||
−0.678653 | + | 0.734459i | \(0.737436\pi\) | |||||||
\(644\) | −8.33571 | −0.328473 | ||||||||
\(645\) | −1.93238 | −0.0760874 | ||||||||
\(646\) | 15.2903 | 0.601590 | ||||||||
\(647\) | −17.1473 | −0.674128 | −0.337064 | − | 0.941482i | \(-0.609434\pi\) | ||||
−0.337064 | + | 0.941482i | \(0.609434\pi\) | |||||||
\(648\) | 4.13835 | 0.162570 | ||||||||
\(649\) | 8.88704 | 0.348847 | ||||||||
\(650\) | 16.2911 | 0.638991 | ||||||||
\(651\) | −4.89145 | −0.191711 | ||||||||
\(652\) | −37.9621 | −1.48671 | ||||||||
\(653\) | −15.0431 | −0.588682 | −0.294341 | − | 0.955700i | \(-0.595100\pi\) | ||||
−0.294341 | + | 0.955700i | \(0.595100\pi\) | |||||||
\(654\) | 1.44613 | 0.0565480 | ||||||||
\(655\) | 15.5035 | 0.605773 | ||||||||
\(656\) | 3.76274 | 0.146910 | ||||||||
\(657\) | −33.3742 | −1.30205 | ||||||||
\(658\) | −4.54535 | −0.177196 | ||||||||
\(659\) | 46.9162 | 1.82760 | 0.913798 | − | 0.406170i | \(-0.133136\pi\) | ||||
0.913798 | + | 0.406170i | \(0.133136\pi\) | |||||||
\(660\) | −3.07252 | −0.119598 | ||||||||
\(661\) | −7.78083 | −0.302639 | −0.151320 | − | 0.988485i | \(-0.548352\pi\) | ||||
−0.151320 | + | 0.988485i | \(0.548352\pi\) | |||||||
\(662\) | 11.5243 | 0.447905 | ||||||||
\(663\) | −1.51494 | −0.0588352 | ||||||||
\(664\) | 10.1729 | 0.394787 | ||||||||
\(665\) | −70.9189 | −2.75012 | ||||||||
\(666\) | −37.2599 | −1.44379 | ||||||||
\(667\) | −8.17983 | −0.316724 | ||||||||
\(668\) | −17.1434 | −0.663297 | ||||||||
\(669\) | 18.4085 | 0.711715 | ||||||||
\(670\) | 46.4700 | 1.79529 | ||||||||
\(671\) | −0.148551 | −0.00573475 | ||||||||
\(672\) | 14.1475 | 0.545752 | ||||||||
\(673\) | 14.4691 | 0.557744 | 0.278872 | − | 0.960328i | \(-0.410040\pi\) | ||||
0.278872 | + | 0.960328i | \(0.410040\pi\) | |||||||
\(674\) | 31.8987 | 1.22869 | ||||||||
\(675\) | 13.5487 | 0.521490 | ||||||||
\(676\) | −12.1535 | −0.467440 | ||||||||
\(677\) | −36.5205 | −1.40360 | −0.701799 | − | 0.712375i | \(-0.747619\pi\) | ||||
−0.701799 | + | 0.712375i | \(0.747619\pi\) | |||||||
\(678\) | 8.71738 | 0.334789 | ||||||||
\(679\) | 41.5660 | 1.59516 | ||||||||
\(680\) | −2.29322 | −0.0879411 | ||||||||
\(681\) | 1.38961 | 0.0532499 | ||||||||
\(682\) | 4.75631 | 0.182129 | ||||||||
\(683\) | 5.58282 | 0.213621 | 0.106810 | − | 0.994279i | \(-0.465936\pi\) | ||||
0.106810 | + | 0.994279i | \(0.465936\pi\) | |||||||
\(684\) | −32.9962 | −1.26164 | ||||||||
\(685\) | 11.4689 | 0.438205 | ||||||||
\(686\) | −28.9819 | −1.10653 | ||||||||
\(687\) | −17.3326 | −0.661279 | ||||||||
\(688\) | −4.65188 | −0.177351 | ||||||||
\(689\) | −26.1026 | −0.994430 | ||||||||
\(690\) | 6.44796 | 0.245470 | ||||||||
\(691\) | −14.2933 | −0.543743 | −0.271872 | − | 0.962334i | \(-0.587643\pi\) | ||||
−0.271872 | + | 0.962334i | \(0.587643\pi\) | |||||||
\(692\) | 6.44137 | 0.244864 | ||||||||
\(693\) | 7.65510 | 0.290793 | ||||||||
\(694\) | −28.8129 | −1.09372 | ||||||||
\(695\) | 7.94189 | 0.301253 | ||||||||
\(696\) | 2.36173 | 0.0895213 | ||||||||
\(697\) | 0.808864 | 0.0306379 | ||||||||
\(698\) | −26.1888 | −0.991263 | ||||||||
\(699\) | −15.1509 | −0.573061 | ||||||||
\(700\) | −17.5844 | −0.664627 | ||||||||
\(701\) | 20.6862 | 0.781307 | 0.390653 | − | 0.920538i | \(-0.372249\pi\) | ||||
0.390653 | + | 0.920538i | \(0.372249\pi\) | |||||||
\(702\) | 15.9925 | 0.603600 | ||||||||
\(703\) | −61.7119 | −2.32751 | ||||||||
\(704\) | −4.45290 | −0.167825 | ||||||||
\(705\) | 1.55723 | 0.0586486 | ||||||||
\(706\) | −68.1779 | −2.56591 | ||||||||
\(707\) | 37.0352 | 1.39285 | ||||||||
\(708\) | −9.24947 | −0.347616 | ||||||||
\(709\) | −18.9119 | −0.710251 | −0.355125 | − | 0.934819i | \(-0.615562\pi\) | ||||
−0.355125 | + | 0.934819i | \(0.615562\pi\) | |||||||
\(710\) | −9.54223 | −0.358114 | ||||||||
\(711\) | 25.9475 | 0.973107 | ||||||||
\(712\) | −6.00849 | −0.225178 | ||||||||
\(713\) | −4.42082 | −0.165561 | ||||||||
\(714\) | 3.69202 | 0.138170 | ||||||||
\(715\) | −6.83239 | −0.255517 | ||||||||
\(716\) | 10.9094 | 0.407704 | ||||||||
\(717\) | 4.67413 | 0.174559 | ||||||||
\(718\) | 50.3633 | 1.87954 | ||||||||
\(719\) | −16.5230 | −0.616204 | −0.308102 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308102 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(720\) | 35.3147 | 1.31610 | ||||||||
\(721\) | −37.9780 | −1.41437 | ||||||||
\(722\) | −87.3915 | −3.25238 | ||||||||
\(723\) | 4.48724 | 0.166882 | ||||||||
\(724\) | −21.0390 | −0.781910 | ||||||||
\(725\) | −17.2556 | −0.640855 | ||||||||
\(726\) | 1.24024 | 0.0460296 | ||||||||
\(727\) | 3.86730 | 0.143430 | 0.0717151 | − | 0.997425i | \(-0.477153\pi\) | ||||
0.0717151 | + | 0.997425i | \(0.477153\pi\) | |||||||
\(728\) | 5.35188 | 0.198354 | ||||||||
\(729\) | −6.53801 | −0.242149 | ||||||||
\(730\) | −72.5942 | −2.68683 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 0.154609 | 0.00571452 | ||||||||
\(733\) | −49.5811 | −1.83132 | −0.915661 | − | 0.401952i | \(-0.868332\pi\) | ||||
−0.915661 | + | 0.401952i | \(0.868332\pi\) | |||||||
\(734\) | 22.2746 | 0.822171 | ||||||||
\(735\) | −3.59751 | −0.132696 | ||||||||
\(736\) | 12.7863 | 0.471310 | ||||||||
\(737\) | −8.30785 | −0.306024 | ||||||||
\(738\) | −3.94109 | −0.145074 | ||||||||
\(739\) | 42.7314 | 1.57190 | 0.785950 | − | 0.618291i | \(-0.212175\pi\) | ||||
0.785950 | + | 0.618291i | \(0.212175\pi\) | |||||||
\(740\) | −35.8954 | −1.31954 | ||||||||
\(741\) | 12.2254 | 0.449111 | ||||||||
\(742\) | 63.6141 | 2.33535 | ||||||||
\(743\) | −29.9767 | −1.09974 | −0.549869 | − | 0.835251i | \(-0.685322\pi\) | ||||
−0.549869 | + | 0.835251i | \(0.685322\pi\) | |||||||
\(744\) | 1.27641 | 0.0467954 | ||||||||
\(745\) | 33.0126 | 1.20949 | ||||||||
\(746\) | −59.2867 | −2.17064 | ||||||||
\(747\) | −33.6766 | −1.23216 | ||||||||
\(748\) | −1.59002 | −0.0581369 | ||||||||
\(749\) | −12.8023 | −0.467785 | ||||||||
\(750\) | −4.70460 | −0.171788 | ||||||||
\(751\) | −13.7876 | −0.503116 | −0.251558 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251558 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(752\) | 3.74876 | 0.136703 | ||||||||
\(753\) | −2.81639 | −0.102635 | ||||||||
\(754\) | −20.3680 | −0.741759 | ||||||||
\(755\) | −44.5015 | −1.61958 | ||||||||
\(756\) | −17.2621 | −0.627816 | ||||||||
\(757\) | −8.49848 | −0.308882 | −0.154441 | − | 0.988002i | \(-0.549358\pi\) | ||||
−0.154441 | + | 0.988002i | \(0.549358\pi\) | |||||||
\(758\) | 43.0837 | 1.56487 | ||||||||
\(759\) | −1.15276 | −0.0418425 | ||||||||
\(760\) | 18.5061 | 0.671286 | ||||||||
\(761\) | −26.0583 | −0.944614 | −0.472307 | − | 0.881434i | \(-0.656579\pi\) | ||||
−0.472307 | + | 0.881434i | \(0.656579\pi\) | |||||||
\(762\) | −4.99439 | −0.180928 | ||||||||
\(763\) | −3.47104 | −0.125660 | ||||||||
\(764\) | 3.73525 | 0.135137 | ||||||||
\(765\) | 7.59151 | 0.274471 | ||||||||
\(766\) | 36.7694 | 1.32853 | ||||||||
\(767\) | −20.5681 | −0.742671 | ||||||||
\(768\) | −13.3749 | −0.482626 | ||||||||
\(769\) | 13.6232 | 0.491266 | 0.245633 | − | 0.969363i | \(-0.421004\pi\) | ||||
0.245633 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(770\) | 16.6511 | 0.600063 | ||||||||
\(771\) | −4.24386 | −0.152839 | ||||||||
\(772\) | −28.9457 | −1.04178 | ||||||||
\(773\) | 43.2246 | 1.55468 | 0.777340 | − | 0.629081i | \(-0.216569\pi\) | ||||
0.777340 | + | 0.629081i | \(0.216569\pi\) | |||||||
\(774\) | 4.87238 | 0.175134 | ||||||||
\(775\) | −9.32584 | −0.334994 | ||||||||
\(776\) | −10.8465 | −0.389368 | ||||||||
\(777\) | −14.9010 | −0.534571 | ||||||||
\(778\) | 63.6872 | 2.28330 | ||||||||
\(779\) | −6.52746 | −0.233870 | ||||||||
\(780\) | 7.11102 | 0.254615 | ||||||||
\(781\) | 1.70595 | 0.0610437 | ||||||||
\(782\) | 3.33680 | 0.119324 | ||||||||
\(783\) | −16.9393 | −0.605360 | ||||||||
\(784\) | −8.66039 | −0.309300 | ||||||||
\(785\) | −5.34048 | −0.190610 | ||||||||
\(786\) | 6.51329 | 0.232321 | ||||||||
\(787\) | −26.4697 | −0.943543 | −0.471771 | − | 0.881721i | \(-0.656385\pi\) | ||||
−0.471771 | + | 0.881721i | \(0.656385\pi\) | |||||||
\(788\) | 39.6654 | 1.41302 | ||||||||
\(789\) | 2.11789 | 0.0753989 | ||||||||
\(790\) | 56.4399 | 2.00804 | ||||||||
\(791\) | −20.9237 | −0.743962 | ||||||||
\(792\) | −1.99758 | −0.0709808 | ||||||||
\(793\) | 0.343806 | 0.0122089 | ||||||||
\(794\) | 2.82080 | 0.100106 | ||||||||
\(795\) | −21.7941 | −0.772957 | ||||||||
\(796\) | −15.4296 | −0.546889 | ||||||||
\(797\) | −33.1969 | −1.17589 | −0.587947 | − | 0.808899i | \(-0.700064\pi\) | ||||
−0.587947 | + | 0.808899i | \(0.700064\pi\) | |||||||
\(798\) | −29.7942 | −1.05470 | ||||||||
\(799\) | 0.805861 | 0.0285093 | ||||||||
\(800\) | 26.9731 | 0.953643 | ||||||||
\(801\) | 19.8906 | 0.702798 | ||||||||
\(802\) | 56.9928 | 2.01249 | ||||||||
\(803\) | 12.9783 | 0.457995 | ||||||||
\(804\) | 8.64666 | 0.304944 | ||||||||
\(805\) | −15.4766 | −0.545478 | ||||||||
\(806\) | −11.0080 | −0.387739 | ||||||||
\(807\) | 1.71064 | 0.0602172 | ||||||||
\(808\) | −9.66422 | −0.339986 | ||||||||
\(809\) | 12.3123 | 0.432877 | 0.216439 | − | 0.976296i | \(-0.430556\pi\) | ||||
0.216439 | + | 0.976296i | \(0.430556\pi\) | |||||||
\(810\) | −29.7989 | −1.04703 | ||||||||
\(811\) | 44.6830 | 1.56903 | 0.784517 | − | 0.620108i | \(-0.212911\pi\) | ||||
0.784517 | + | 0.620108i | \(0.212911\pi\) | |||||||
\(812\) | 21.9849 | 0.771518 | ||||||||
\(813\) | −13.9433 | −0.489014 | ||||||||
\(814\) | 14.4894 | 0.507851 | ||||||||
\(815\) | −70.4827 | −2.46890 | ||||||||
\(816\) | −3.04499 | −0.106596 | ||||||||
\(817\) | 8.06990 | 0.282330 | ||||||||
\(818\) | 31.6432 | 1.10638 | ||||||||
\(819\) | −17.7169 | −0.619079 | ||||||||
\(820\) | −3.79676 | −0.132589 | ||||||||
\(821\) | 25.5553 | 0.891887 | 0.445944 | − | 0.895061i | \(-0.352868\pi\) | ||||
0.445944 | + | 0.895061i | \(0.352868\pi\) | |||||||
\(822\) | 4.81828 | 0.168057 | ||||||||
\(823\) | −16.4058 | −0.571869 | −0.285934 | − | 0.958249i | \(-0.592304\pi\) | ||||
−0.285934 | + | 0.958249i | \(0.592304\pi\) | |||||||
\(824\) | 9.91024 | 0.345240 | ||||||||
\(825\) | −2.43177 | −0.0846635 | ||||||||
\(826\) | 50.1261 | 1.74411 | ||||||||
\(827\) | −6.95415 | −0.241820 | −0.120910 | − | 0.992663i | \(-0.538581\pi\) | ||||
−0.120910 | + | 0.992663i | \(0.538581\pi\) | |||||||
\(828\) | −7.20073 | −0.250243 | ||||||||
\(829\) | −41.6877 | −1.44787 | −0.723937 | − | 0.689867i | \(-0.757669\pi\) | ||||
−0.723937 | + | 0.689867i | \(0.757669\pi\) | |||||||
\(830\) | −73.2519 | −2.54261 | ||||||||
\(831\) | 5.37533 | 0.186468 | ||||||||
\(832\) | 10.3058 | 0.357288 | ||||||||
\(833\) | −1.86170 | −0.0645040 | ||||||||
\(834\) | 3.33652 | 0.115534 | ||||||||
\(835\) | −31.8294 | −1.10150 | ||||||||
\(836\) | 12.8313 | 0.443780 | ||||||||
\(837\) | −9.15491 | −0.316440 | ||||||||
\(838\) | 39.4138 | 1.36153 | ||||||||
\(839\) | −49.7722 | −1.71833 | −0.859163 | − | 0.511701i | \(-0.829015\pi\) | ||||
−0.859163 | + | 0.511701i | \(0.829015\pi\) | |||||||
\(840\) | 4.46850 | 0.154178 | ||||||||
\(841\) | −7.42626 | −0.256078 | ||||||||
\(842\) | 35.0750 | 1.20876 | ||||||||
\(843\) | −11.4936 | −0.395862 | ||||||||
\(844\) | −26.9843 | −0.928839 | ||||||||
\(845\) | −22.5648 | −0.776254 | ||||||||
\(846\) | −3.92646 | −0.134994 | ||||||||
\(847\) | −2.97686 | −0.102286 | ||||||||
\(848\) | −52.4656 | −1.80168 | ||||||||
\(849\) | −2.22088 | −0.0762205 | ||||||||
\(850\) | 7.03906 | 0.241438 | ||||||||
\(851\) | −13.4673 | −0.461655 | ||||||||
\(852\) | −1.77552 | −0.0608284 | ||||||||
\(853\) | −7.24125 | −0.247936 | −0.123968 | − | 0.992286i | \(-0.539562\pi\) | ||||
−0.123968 | + | 0.992286i | \(0.539562\pi\) | |||||||
\(854\) | −0.837882 | −0.0286717 | ||||||||
\(855\) | −61.2627 | −2.09514 | ||||||||
\(856\) | 3.34072 | 0.114183 | ||||||||
\(857\) | −8.92241 | −0.304784 | −0.152392 | − | 0.988320i | \(-0.548698\pi\) | ||||
−0.152392 | + | 0.988320i | \(0.548698\pi\) | |||||||
\(858\) | −2.87040 | −0.0979939 | ||||||||
\(859\) | −28.5188 | −0.973048 | −0.486524 | − | 0.873667i | \(-0.661735\pi\) | ||||
−0.486524 | + | 0.873667i | \(0.661735\pi\) | |||||||
\(860\) | 4.69394 | 0.160062 | ||||||||
\(861\) | −1.57613 | −0.0537142 | ||||||||
\(862\) | −23.2794 | −0.792898 | ||||||||
\(863\) | −22.0744 | −0.751421 | −0.375711 | − | 0.926737i | \(-0.622601\pi\) | ||||
−0.375711 | + | 0.926737i | \(0.622601\pi\) | |||||||
\(864\) | 26.4787 | 0.900823 | ||||||||
\(865\) | 11.9594 | 0.406633 | ||||||||
\(866\) | −52.5648 | −1.78623 | ||||||||
\(867\) | −0.654571 | −0.0222304 | ||||||||
\(868\) | 11.8818 | 0.403295 | ||||||||
\(869\) | −10.0903 | −0.342289 | ||||||||
\(870\) | −17.0061 | −0.576559 | ||||||||
\(871\) | 19.2276 | 0.651504 | ||||||||
\(872\) | 0.905757 | 0.0306728 | ||||||||
\(873\) | 35.9065 | 1.21525 | ||||||||
\(874\) | −26.9276 | −0.910841 | ||||||||
\(875\) | 11.2921 | 0.381744 | ||||||||
\(876\) | −13.5076 | −0.456379 | ||||||||
\(877\) | −15.6016 | −0.526828 | −0.263414 | − | 0.964683i | \(-0.584849\pi\) | ||||
−0.263414 | + | 0.964683i | \(0.584849\pi\) | |||||||
\(878\) | 18.1954 | 0.614065 | ||||||||
\(879\) | −6.55572 | −0.221119 | ||||||||
\(880\) | −13.7329 | −0.462937 | ||||||||
\(881\) | −3.51153 | −0.118307 | −0.0591533 | − | 0.998249i | \(-0.518840\pi\) | ||||
−0.0591533 | + | 0.998249i | \(0.518840\pi\) | |||||||
\(882\) | 9.07090 | 0.305433 | ||||||||
\(883\) | −11.8415 | −0.398498 | −0.199249 | − | 0.979949i | \(-0.563850\pi\) | ||||
−0.199249 | + | 0.979949i | \(0.563850\pi\) | |||||||
\(884\) | 3.67993 | 0.123770 | ||||||||
\(885\) | −17.1731 | −0.577269 | ||||||||
\(886\) | −24.4949 | −0.822924 | ||||||||
\(887\) | −37.9074 | −1.27281 | −0.636403 | − | 0.771357i | \(-0.719578\pi\) | ||||
−0.636403 | + | 0.771357i | \(0.719578\pi\) | |||||||
\(888\) | 3.88838 | 0.130485 | ||||||||
\(889\) | 11.9877 | 0.402054 | ||||||||
\(890\) | 43.2651 | 1.45025 | ||||||||
\(891\) | 5.32741 | 0.178475 | ||||||||
\(892\) | −44.7162 | −1.49721 | ||||||||
\(893\) | −6.50322 | −0.217622 | ||||||||
\(894\) | 13.8691 | 0.463854 | ||||||||
\(895\) | 20.2551 | 0.677053 | ||||||||
\(896\) | 18.1108 | 0.605039 | ||||||||
\(897\) | 2.66794 | 0.0890798 | ||||||||
\(898\) | 53.9015 | 1.79872 | ||||||||
\(899\) | 11.6596 | 0.388870 | ||||||||
\(900\) | −15.1901 | −0.506338 | ||||||||
\(901\) | −11.2784 | −0.375737 | ||||||||
\(902\) | 1.53258 | 0.0510294 | ||||||||
\(903\) | 1.94857 | 0.0648443 | ||||||||
\(904\) | 5.45998 | 0.181596 | ||||||||
\(905\) | −39.0624 | −1.29848 | ||||||||
\(906\) | −18.6958 | −0.621128 | ||||||||
\(907\) | −32.6679 | −1.08472 | −0.542359 | − | 0.840147i | \(-0.682469\pi\) | ||||
−0.542359 | + | 0.840147i | \(0.682469\pi\) | |||||||
\(908\) | −3.37550 | −0.112020 | ||||||||
\(909\) | 31.9925 | 1.06113 | ||||||||
\(910\) | −38.5371 | −1.27749 | ||||||||
\(911\) | 20.5666 | 0.681403 | 0.340701 | − | 0.940172i | \(-0.389335\pi\) | ||||
0.340701 | + | 0.940172i | \(0.389335\pi\) | |||||||
\(912\) | 24.5727 | 0.813685 | ||||||||
\(913\) | 13.0959 | 0.433411 | ||||||||
\(914\) | 0.659584 | 0.0218171 | ||||||||
\(915\) | 0.287057 | 0.00948981 | ||||||||
\(916\) | 42.1026 | 1.39111 | ||||||||
\(917\) | −15.6334 | −0.516261 | ||||||||
\(918\) | 6.91004 | 0.228065 | ||||||||
\(919\) | 17.2439 | 0.568824 | 0.284412 | − | 0.958702i | \(-0.408202\pi\) | ||||
0.284412 | + | 0.958702i | \(0.408202\pi\) | |||||||
\(920\) | 4.03857 | 0.133148 | ||||||||
\(921\) | −10.4728 | −0.345091 | ||||||||
\(922\) | 58.8845 | 1.93926 | ||||||||
\(923\) | −3.94824 | −0.129958 | ||||||||
\(924\) | 3.09826 | 0.101925 | ||||||||
\(925\) | −28.4097 | −0.934105 | ||||||||
\(926\) | −9.71358 | −0.319208 | ||||||||
\(927\) | −32.8070 | −1.07752 | ||||||||
\(928\) | −33.7231 | −1.10701 | ||||||||
\(929\) | 38.6789 | 1.26901 | 0.634506 | − | 0.772918i | \(-0.281203\pi\) | ||||
0.634506 | + | 0.772918i | \(0.281203\pi\) | |||||||
\(930\) | −9.19100 | −0.301385 | ||||||||
\(931\) | 15.0237 | 0.492383 | ||||||||
\(932\) | 36.8032 | 1.20553 | ||||||||
\(933\) | 14.6114 | 0.478355 | ||||||||
\(934\) | 23.2172 | 0.759690 | ||||||||
\(935\) | −2.95213 | −0.0965449 | ||||||||
\(936\) | 4.62318 | 0.151113 | ||||||||
\(937\) | 13.1333 | 0.429047 | 0.214523 | − | 0.976719i | \(-0.431180\pi\) | ||||
0.214523 | + | 0.976719i | \(0.431180\pi\) | |||||||
\(938\) | −46.8593 | −1.53001 | ||||||||
\(939\) | −1.15713 | −0.0377615 | ||||||||
\(940\) | −3.78266 | −0.123377 | ||||||||
\(941\) | 38.8873 | 1.26769 | 0.633845 | − | 0.773460i | \(-0.281476\pi\) | ||||
0.633845 | + | 0.773460i | \(0.281476\pi\) | |||||||
\(942\) | −2.24363 | −0.0731014 | ||||||||
\(943\) | −1.42448 | −0.0463875 | ||||||||
\(944\) | −41.3414 | −1.34555 | ||||||||
\(945\) | −32.0498 | −1.04258 | ||||||||
\(946\) | −1.89473 | −0.0616031 | ||||||||
\(947\) | 12.7571 | 0.414549 | 0.207274 | − | 0.978283i | \(-0.433541\pi\) | ||||
0.207274 | + | 0.978283i | \(0.433541\pi\) | |||||||
\(948\) | 10.5018 | 0.341082 | ||||||||
\(949\) | −30.0369 | −0.975040 | ||||||||
\(950\) | −56.8045 | −1.84298 | ||||||||
\(951\) | 15.8472 | 0.513879 | ||||||||
\(952\) | 2.31243 | 0.0749464 | ||||||||
\(953\) | −6.74011 | −0.218334 | −0.109167 | − | 0.994023i | \(-0.534818\pi\) | ||||
−0.109167 | + | 0.994023i | \(0.534818\pi\) | |||||||
\(954\) | 54.9525 | 1.77915 | ||||||||
\(955\) | 6.93509 | 0.224414 | ||||||||
\(956\) | −11.3539 | −0.367213 | ||||||||
\(957\) | 3.04032 | 0.0982797 | ||||||||
\(958\) | 71.5513 | 2.31172 | ||||||||
\(959\) | −11.5650 | −0.373453 | ||||||||
\(960\) | 8.60470 | 0.277715 | ||||||||
\(961\) | −24.6985 | −0.796726 | ||||||||
\(962\) | −33.5341 | −1.08118 | ||||||||
\(963\) | −11.0592 | −0.356376 | ||||||||
\(964\) | −10.9000 | −0.351064 | ||||||||
\(965\) | −53.7424 | −1.73003 | ||||||||
\(966\) | −6.50198 | −0.209198 | ||||||||
\(967\) | −44.5197 | −1.43166 | −0.715829 | − | 0.698276i | \(-0.753951\pi\) | ||||
−0.715829 | + | 0.698276i | \(0.753951\pi\) | |||||||
\(968\) | 0.776803 | 0.0249674 | ||||||||
\(969\) | 5.28233 | 0.169693 | ||||||||
\(970\) | 78.1023 | 2.50771 | ||||||||
\(971\) | −36.6867 | −1.17733 | −0.588666 | − | 0.808376i | \(-0.700347\pi\) | ||||
−0.588666 | + | 0.808376i | \(0.700347\pi\) | |||||||
\(972\) | −22.9409 | −0.735831 | ||||||||
\(973\) | −8.00842 | −0.256738 | ||||||||
\(974\) | −58.1361 | −1.86280 | ||||||||
\(975\) | 5.62808 | 0.180243 | ||||||||
\(976\) | 0.691041 | 0.0221197 | ||||||||
\(977\) | 37.5646 | 1.20180 | 0.600899 | − | 0.799325i | \(-0.294809\pi\) | ||||
0.600899 | + | 0.799325i | \(0.294809\pi\) | |||||||
\(978\) | −29.6110 | −0.946855 | ||||||||
\(979\) | −7.73489 | −0.247208 | ||||||||
\(980\) | 8.73871 | 0.279148 | ||||||||
\(981\) | −2.99843 | −0.0957324 | ||||||||
\(982\) | 46.9397 | 1.49791 | ||||||||
\(983\) | 6.96919 | 0.222283 | 0.111141 | − | 0.993805i | \(-0.464549\pi\) | ||||
0.111141 | + | 0.993805i | \(0.464549\pi\) | |||||||
\(984\) | 0.411286 | 0.0131113 | ||||||||
\(985\) | 73.6452 | 2.34653 | ||||||||
\(986\) | −8.80058 | −0.280268 | ||||||||
\(987\) | −1.57027 | −0.0499824 | ||||||||
\(988\) | −29.6967 | −0.944778 | ||||||||
\(989\) | 1.76109 | 0.0559994 | ||||||||
\(990\) | 14.3839 | 0.457150 | ||||||||
\(991\) | −1.47439 | −0.0468356 | −0.0234178 | − | 0.999726i | \(-0.507455\pi\) | ||||
−0.0234178 | + | 0.999726i | \(0.507455\pi\) | |||||||
\(992\) | −18.2258 | −0.578669 | ||||||||
\(993\) | 3.98129 | 0.126342 | ||||||||
\(994\) | 9.62218 | 0.305197 | ||||||||
\(995\) | −28.6476 | −0.908189 | ||||||||
\(996\) | −13.6300 | −0.431882 | ||||||||
\(997\) | 5.43912 | 0.172259 | 0.0861293 | − | 0.996284i | \(-0.472550\pi\) | ||||
0.0861293 | + | 0.996284i | \(0.472550\pi\) | |||||||
\(998\) | 29.7578 | 0.941966 | ||||||||
\(999\) | −27.8890 | −0.882368 |
(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 | 8041.2.a.d.1.13 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.d.1.13 | ✓ | 62 | 1.1 | even | 1 | trivial |