Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19545 | 1.55242 | 0.776210 | − | 0.630474i | \(-0.217140\pi\) | ||||
0.776210 | + | 0.630474i | \(0.217140\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.82002 | 1.41001 | ||||||||
\(5\) | 4.21837 | 1.88651 | 0.943257 | − | 0.332063i | \(-0.107745\pi\) | ||||
0.943257 | + | 0.332063i | \(0.107745\pi\) | |||||||
\(6\) | −2.19545 | −0.896290 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.80031 | 0.636504 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.26124 | 2.92866 | ||||||||
\(11\) | −1.86322 | −0.561782 | −0.280891 | − | 0.959740i | \(-0.590630\pi\) | ||||
−0.280891 | + | 0.959740i | \(0.590630\pi\) | |||||||
\(12\) | −2.82002 | −0.814068 | ||||||||
\(13\) | 7.10449 | 1.97043 | 0.985215 | − | 0.171324i | \(-0.0548043\pi\) | ||||
0.985215 | + | 0.171324i | \(0.0548043\pi\) | |||||||
\(14\) | 2.19545 | 0.586760 | ||||||||
\(15\) | −4.21837 | −1.08918 | ||||||||
\(16\) | −1.68754 | −0.421886 | ||||||||
\(17\) | 3.10077 | 0.752047 | 0.376023 | − | 0.926610i | \(-0.377291\pi\) | ||||
0.376023 | + | 0.926610i | \(0.377291\pi\) | |||||||
\(18\) | 2.19545 | 0.517473 | ||||||||
\(19\) | −0.529760 | −0.121535 | −0.0607676 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607676 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(20\) | 11.8959 | 2.66000 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −4.09061 | −0.872122 | ||||||||
\(23\) | 3.54125 | 0.738403 | 0.369201 | − | 0.929349i | \(-0.379631\pi\) | ||||
0.369201 | + | 0.929349i | \(0.379631\pi\) | |||||||
\(24\) | −1.80031 | −0.367486 | ||||||||
\(25\) | 12.7947 | 2.55894 | ||||||||
\(26\) | 15.5976 | 3.05893 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.82002 | 0.532933 | ||||||||
\(29\) | −7.75844 | −1.44071 | −0.720353 | − | 0.693608i | \(-0.756020\pi\) | ||||
−0.720353 | + | 0.693608i | \(0.756020\pi\) | |||||||
\(30\) | −9.26124 | −1.69086 | ||||||||
\(31\) | 5.88019 | 1.05611 | 0.528056 | − | 0.849209i | \(-0.322921\pi\) | ||||
0.528056 | + | 0.849209i | \(0.322921\pi\) | |||||||
\(32\) | −7.30553 | −1.29145 | ||||||||
\(33\) | 1.86322 | 0.324345 | ||||||||
\(34\) | 6.80759 | 1.16749 | ||||||||
\(35\) | 4.21837 | 0.713035 | ||||||||
\(36\) | 2.82002 | 0.470003 | ||||||||
\(37\) | −7.96976 | −1.31022 | −0.655110 | − | 0.755533i | \(-0.727378\pi\) | ||||
−0.655110 | + | 0.755533i | \(0.727378\pi\) | |||||||
\(38\) | −1.16306 | −0.188674 | ||||||||
\(39\) | −7.10449 | −1.13763 | ||||||||
\(40\) | 7.59436 | 1.20077 | ||||||||
\(41\) | 3.04195 | 0.475074 | 0.237537 | − | 0.971379i | \(-0.423660\pi\) | ||||
0.237537 | + | 0.971379i | \(0.423660\pi\) | |||||||
\(42\) | −2.19545 | −0.338766 | ||||||||
\(43\) | 0.508504 | 0.0775461 | 0.0387730 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387730 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(44\) | −5.25431 | −0.792117 | ||||||||
\(45\) | 4.21837 | 0.628838 | ||||||||
\(46\) | 7.77466 | 1.14631 | ||||||||
\(47\) | 3.71913 | 0.542490 | 0.271245 | − | 0.962510i | \(-0.412565\pi\) | ||||
0.271245 | + | 0.962510i | \(0.412565\pi\) | |||||||
\(48\) | 1.68754 | 0.243576 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 28.0901 | 3.97254 | ||||||||
\(51\) | −3.10077 | −0.434194 | ||||||||
\(52\) | 20.0348 | 2.77832 | ||||||||
\(53\) | −2.38571 | −0.327703 | −0.163851 | − | 0.986485i | \(-0.552392\pi\) | ||||
−0.163851 | + | 0.986485i | \(0.552392\pi\) | |||||||
\(54\) | −2.19545 | −0.298763 | ||||||||
\(55\) | −7.85976 | −1.05981 | ||||||||
\(56\) | 1.80031 | 0.240576 | ||||||||
\(57\) | 0.529760 | 0.0701684 | ||||||||
\(58\) | −17.0333 | −2.23658 | ||||||||
\(59\) | −1.30798 | −0.170285 | −0.0851424 | − | 0.996369i | \(-0.527135\pi\) | ||||
−0.0851424 | + | 0.996369i | \(0.527135\pi\) | |||||||
\(60\) | −11.8959 | −1.53575 | ||||||||
\(61\) | 3.47580 | 0.445031 | 0.222516 | − | 0.974929i | \(-0.428573\pi\) | ||||
0.222516 | + | 0.974929i | \(0.428573\pi\) | |||||||
\(62\) | 12.9097 | 1.63953 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −12.6639 | −1.58298 | ||||||||
\(65\) | 29.9694 | 3.71724 | ||||||||
\(66\) | 4.09061 | 0.503520 | ||||||||
\(67\) | −4.11826 | −0.503126 | −0.251563 | − | 0.967841i | \(-0.580945\pi\) | ||||
−0.251563 | + | 0.967841i | \(0.580945\pi\) | |||||||
\(68\) | 8.74421 | 1.06039 | ||||||||
\(69\) | −3.54125 | −0.426317 | ||||||||
\(70\) | 9.26124 | 1.10693 | ||||||||
\(71\) | −12.8448 | −1.52440 | −0.762200 | − | 0.647342i | \(-0.775881\pi\) | ||||
−0.762200 | + | 0.647342i | \(0.775881\pi\) | |||||||
\(72\) | 1.80031 | 0.212168 | ||||||||
\(73\) | −7.58629 | −0.887908 | −0.443954 | − | 0.896050i | \(-0.646425\pi\) | ||||
−0.443954 | + | 0.896050i | \(0.646425\pi\) | |||||||
\(74\) | −17.4972 | −2.03401 | ||||||||
\(75\) | −12.7947 | −1.47740 | ||||||||
\(76\) | −1.49393 | −0.171366 | ||||||||
\(77\) | −1.86322 | −0.212334 | ||||||||
\(78\) | −15.5976 | −1.76608 | ||||||||
\(79\) | −4.42542 | −0.497899 | −0.248949 | − | 0.968516i | \(-0.580085\pi\) | ||||
−0.248949 | + | 0.968516i | \(0.580085\pi\) | |||||||
\(80\) | −7.11869 | −0.795894 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.67847 | 0.737514 | ||||||||
\(83\) | −5.10705 | −0.560571 | −0.280286 | − | 0.959917i | \(-0.590429\pi\) | ||||
−0.280286 | + | 0.959917i | \(0.590429\pi\) | |||||||
\(84\) | −2.82002 | −0.307689 | ||||||||
\(85\) | 13.0802 | 1.41875 | ||||||||
\(86\) | 1.11640 | 0.120384 | ||||||||
\(87\) | 7.75844 | 0.831792 | ||||||||
\(88\) | −3.35437 | −0.357577 | ||||||||
\(89\) | 4.45620 | 0.472356 | 0.236178 | − | 0.971710i | \(-0.424105\pi\) | ||||
0.236178 | + | 0.971710i | \(0.424105\pi\) | |||||||
\(90\) | 9.26124 | 0.976221 | ||||||||
\(91\) | 7.10449 | 0.744752 | ||||||||
\(92\) | 9.98639 | 1.04115 | ||||||||
\(93\) | −5.88019 | −0.609747 | ||||||||
\(94\) | 8.16517 | 0.842173 | ||||||||
\(95\) | −2.23472 | −0.229278 | ||||||||
\(96\) | 7.30553 | 0.745618 | ||||||||
\(97\) | 9.35481 | 0.949837 | 0.474919 | − | 0.880030i | \(-0.342477\pi\) | ||||
0.474919 | + | 0.880030i | \(0.342477\pi\) | |||||||
\(98\) | 2.19545 | 0.221774 | ||||||||
\(99\) | −1.86322 | −0.187261 | ||||||||
\(100\) | 36.0812 | 3.60812 | ||||||||
\(101\) | −14.5347 | −1.44626 | −0.723128 | − | 0.690714i | \(-0.757296\pi\) | ||||
−0.723128 | + | 0.690714i | \(0.757296\pi\) | |||||||
\(102\) | −6.80759 | −0.674052 | ||||||||
\(103\) | 18.0813 | 1.78160 | 0.890800 | − | 0.454396i | \(-0.150145\pi\) | ||||
0.890800 | + | 0.454396i | \(0.150145\pi\) | |||||||
\(104\) | 12.7902 | 1.25419 | ||||||||
\(105\) | −4.21837 | −0.411671 | ||||||||
\(106\) | −5.23772 | −0.508732 | ||||||||
\(107\) | −3.56618 | −0.344756 | −0.172378 | − | 0.985031i | \(-0.555145\pi\) | ||||
−0.172378 | + | 0.985031i | \(0.555145\pi\) | |||||||
\(108\) | −2.82002 | −0.271356 | ||||||||
\(109\) | 18.7449 | 1.79544 | 0.897720 | − | 0.440567i | \(-0.145223\pi\) | ||||
0.897720 | + | 0.440567i | \(0.145223\pi\) | |||||||
\(110\) | −17.2557 | −1.64527 | ||||||||
\(111\) | 7.96976 | 0.756456 | ||||||||
\(112\) | −1.68754 | −0.159458 | ||||||||
\(113\) | 1.73057 | 0.162798 | 0.0813990 | − | 0.996682i | \(-0.474061\pi\) | ||||
0.0813990 | + | 0.996682i | \(0.474061\pi\) | |||||||
\(114\) | 1.16306 | 0.108931 | ||||||||
\(115\) | 14.9383 | 1.39301 | ||||||||
\(116\) | −21.8789 | −2.03141 | ||||||||
\(117\) | 7.10449 | 0.656810 | ||||||||
\(118\) | −2.87161 | −0.264354 | ||||||||
\(119\) | 3.10077 | 0.284247 | ||||||||
\(120\) | −7.59436 | −0.693267 | ||||||||
\(121\) | −7.52841 | −0.684401 | ||||||||
\(122\) | 7.63097 | 0.690875 | ||||||||
\(123\) | −3.04195 | −0.274284 | ||||||||
\(124\) | 16.5822 | 1.48913 | ||||||||
\(125\) | 32.8809 | 2.94095 | ||||||||
\(126\) | 2.19545 | 0.195587 | ||||||||
\(127\) | −4.30518 | −0.382023 | −0.191012 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191012 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(128\) | −13.1919 | −1.16601 | ||||||||
\(129\) | −0.508504 | −0.0447712 | ||||||||
\(130\) | 65.7964 | 5.77072 | ||||||||
\(131\) | −6.14930 | −0.537267 | −0.268634 | − | 0.963242i | \(-0.586572\pi\) | ||||
−0.268634 | + | 0.963242i | \(0.586572\pi\) | |||||||
\(132\) | 5.25431 | 0.457329 | ||||||||
\(133\) | −0.529760 | −0.0459360 | ||||||||
\(134\) | −9.04145 | −0.781063 | ||||||||
\(135\) | −4.21837 | −0.363060 | ||||||||
\(136\) | 5.58233 | 0.478681 | ||||||||
\(137\) | 9.25062 | 0.790334 | 0.395167 | − | 0.918609i | \(-0.370687\pi\) | ||||
0.395167 | + | 0.918609i | \(0.370687\pi\) | |||||||
\(138\) | −7.77466 | −0.661823 | ||||||||
\(139\) | 8.43552 | 0.715491 | 0.357746 | − | 0.933819i | \(-0.383545\pi\) | ||||
0.357746 | + | 0.933819i | \(0.383545\pi\) | |||||||
\(140\) | 11.8959 | 1.00539 | ||||||||
\(141\) | −3.71913 | −0.313207 | ||||||||
\(142\) | −28.2002 | −2.36651 | ||||||||
\(143\) | −13.2372 | −1.10695 | ||||||||
\(144\) | −1.68754 | −0.140629 | ||||||||
\(145\) | −32.7280 | −2.71791 | ||||||||
\(146\) | −16.6553 | −1.37841 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −22.4748 | −1.84742 | ||||||||
\(149\) | −12.2995 | −1.00761 | −0.503807 | − | 0.863816i | \(-0.668068\pi\) | ||||
−0.503807 | + | 0.863816i | \(0.668068\pi\) | |||||||
\(150\) | −28.0901 | −2.29355 | ||||||||
\(151\) | −20.0132 | −1.62865 | −0.814326 | − | 0.580407i | \(-0.802893\pi\) | ||||
−0.814326 | + | 0.580407i | \(0.802893\pi\) | |||||||
\(152\) | −0.953729 | −0.0773577 | ||||||||
\(153\) | 3.10077 | 0.250682 | ||||||||
\(154\) | −4.09061 | −0.329631 | ||||||||
\(155\) | 24.8048 | 1.99237 | ||||||||
\(156\) | −20.0348 | −1.60406 | ||||||||
\(157\) | −0.146577 | −0.0116982 | −0.00584908 | − | 0.999983i | \(-0.501862\pi\) | ||||
−0.00584908 | + | 0.999983i | \(0.501862\pi\) | |||||||
\(158\) | −9.71581 | −0.772948 | ||||||||
\(159\) | 2.38571 | 0.189199 | ||||||||
\(160\) | −30.8175 | −2.43634 | ||||||||
\(161\) | 3.54125 | 0.279090 | ||||||||
\(162\) | 2.19545 | 0.172491 | ||||||||
\(163\) | −8.85854 | −0.693854 | −0.346927 | − | 0.937892i | \(-0.612775\pi\) | ||||
−0.346927 | + | 0.937892i | \(0.612775\pi\) | |||||||
\(164\) | 8.57836 | 0.669857 | ||||||||
\(165\) | 7.85976 | 0.611882 | ||||||||
\(166\) | −11.2123 | −0.870242 | ||||||||
\(167\) | 21.0526 | 1.62910 | 0.814551 | − | 0.580092i | \(-0.196983\pi\) | ||||
0.814551 | + | 0.580092i | \(0.196983\pi\) | |||||||
\(168\) | −1.80031 | −0.138897 | ||||||||
\(169\) | 37.4737 | 2.88259 | ||||||||
\(170\) | 28.7170 | 2.20249 | ||||||||
\(171\) | −0.529760 | −0.0405117 | ||||||||
\(172\) | 1.43399 | 0.109341 | ||||||||
\(173\) | −15.1654 | −1.15301 | −0.576503 | − | 0.817095i | \(-0.695583\pi\) | ||||
−0.576503 | + | 0.817095i | \(0.695583\pi\) | |||||||
\(174\) | 17.0333 | 1.29129 | ||||||||
\(175\) | 12.7947 | 0.967187 | ||||||||
\(176\) | 3.14427 | 0.237008 | ||||||||
\(177\) | 1.30798 | 0.0983140 | ||||||||
\(178\) | 9.78338 | 0.733295 | ||||||||
\(179\) | −2.26726 | −0.169463 | −0.0847313 | − | 0.996404i | \(-0.527003\pi\) | ||||
−0.0847313 | + | 0.996404i | \(0.527003\pi\) | |||||||
\(180\) | 11.8959 | 0.886667 | ||||||||
\(181\) | 13.6000 | 1.01088 | 0.505441 | − | 0.862861i | \(-0.331330\pi\) | ||||
0.505441 | + | 0.862861i | \(0.331330\pi\) | |||||||
\(182\) | 15.5976 | 1.15617 | ||||||||
\(183\) | −3.47580 | −0.256939 | ||||||||
\(184\) | 6.37534 | 0.469996 | ||||||||
\(185\) | −33.6194 | −2.47175 | ||||||||
\(186\) | −12.9097 | −0.946583 | ||||||||
\(187\) | −5.77742 | −0.422486 | ||||||||
\(188\) | 10.4880 | 0.764916 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −4.90623 | −0.355936 | ||||||||
\(191\) | −10.5010 | −0.759823 | −0.379912 | − | 0.925023i | \(-0.624046\pi\) | ||||
−0.379912 | + | 0.925023i | \(0.624046\pi\) | |||||||
\(192\) | 12.6639 | 0.913936 | ||||||||
\(193\) | 7.47587 | 0.538125 | 0.269063 | − | 0.963123i | \(-0.413286\pi\) | ||||
0.269063 | + | 0.963123i | \(0.413286\pi\) | |||||||
\(194\) | 20.5381 | 1.47455 | ||||||||
\(195\) | −29.9694 | −2.14615 | ||||||||
\(196\) | 2.82002 | 0.201430 | ||||||||
\(197\) | 8.06293 | 0.574460 | 0.287230 | − | 0.957862i | \(-0.407266\pi\) | ||||
0.287230 | + | 0.957862i | \(0.407266\pi\) | |||||||
\(198\) | −4.09061 | −0.290707 | ||||||||
\(199\) | −15.5487 | −1.10222 | −0.551108 | − | 0.834434i | \(-0.685795\pi\) | ||||
−0.551108 | + | 0.834434i | \(0.685795\pi\) | |||||||
\(200\) | 23.0343 | 1.62877 | ||||||||
\(201\) | 4.11826 | 0.290480 | ||||||||
\(202\) | −31.9102 | −2.24520 | ||||||||
\(203\) | −7.75844 | −0.544536 | ||||||||
\(204\) | −8.74421 | −0.612218 | ||||||||
\(205\) | 12.8321 | 0.896233 | ||||||||
\(206\) | 39.6966 | 2.76579 | ||||||||
\(207\) | 3.54125 | 0.246134 | ||||||||
\(208\) | −11.9891 | −0.831296 | ||||||||
\(209\) | 0.987059 | 0.0682763 | ||||||||
\(210\) | −9.26124 | −0.639087 | ||||||||
\(211\) | 24.3290 | 1.67488 | 0.837439 | − | 0.546531i | \(-0.184052\pi\) | ||||
0.837439 | + | 0.546531i | \(0.184052\pi\) | |||||||
\(212\) | −6.72774 | −0.462063 | ||||||||
\(213\) | 12.8448 | 0.880113 | ||||||||
\(214\) | −7.82938 | −0.535206 | ||||||||
\(215\) | 2.14506 | 0.146292 | ||||||||
\(216\) | −1.80031 | −0.122495 | ||||||||
\(217\) | 5.88019 | 0.399173 | ||||||||
\(218\) | 41.1536 | 2.78728 | ||||||||
\(219\) | 7.58629 | 0.512634 | ||||||||
\(220\) | −22.1647 | −1.49434 | ||||||||
\(221\) | 22.0294 | 1.48186 | ||||||||
\(222\) | 17.4972 | 1.17434 | ||||||||
\(223\) | −14.6404 | −0.980394 | −0.490197 | − | 0.871612i | \(-0.663075\pi\) | ||||
−0.490197 | + | 0.871612i | \(0.663075\pi\) | |||||||
\(224\) | −7.30553 | −0.488122 | ||||||||
\(225\) | 12.7947 | 0.852979 | ||||||||
\(226\) | 3.79938 | 0.252731 | ||||||||
\(227\) | −24.4756 | −1.62450 | −0.812251 | − | 0.583308i | \(-0.801758\pi\) | ||||
−0.812251 | + | 0.583308i | \(0.801758\pi\) | |||||||
\(228\) | 1.49393 | 0.0989380 | ||||||||
\(229\) | 16.7245 | 1.10519 | 0.552594 | − | 0.833451i | \(-0.313638\pi\) | ||||
0.552594 | + | 0.833451i | \(0.313638\pi\) | |||||||
\(230\) | 32.7964 | 2.16253 | ||||||||
\(231\) | 1.86322 | 0.122591 | ||||||||
\(232\) | −13.9676 | −0.917015 | ||||||||
\(233\) | −24.1742 | −1.58371 | −0.791853 | − | 0.610712i | \(-0.790884\pi\) | ||||
−0.791853 | + | 0.610712i | \(0.790884\pi\) | |||||||
\(234\) | 15.5976 | 1.01964 | ||||||||
\(235\) | 15.6887 | 1.02342 | ||||||||
\(236\) | −3.68853 | −0.240103 | ||||||||
\(237\) | 4.42542 | 0.287462 | ||||||||
\(238\) | 6.80759 | 0.441271 | ||||||||
\(239\) | 14.0472 | 0.908635 | 0.454317 | − | 0.890840i | \(-0.349883\pi\) | ||||
0.454317 | + | 0.890840i | \(0.349883\pi\) | |||||||
\(240\) | 7.11869 | 0.459509 | ||||||||
\(241\) | 6.30449 | 0.406108 | 0.203054 | − | 0.979168i | \(-0.434913\pi\) | ||||
0.203054 | + | 0.979168i | \(0.434913\pi\) | |||||||
\(242\) | −16.5283 | −1.06248 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.80182 | 0.627497 | ||||||||
\(245\) | 4.21837 | 0.269502 | ||||||||
\(246\) | −6.67847 | −0.425804 | ||||||||
\(247\) | −3.76367 | −0.239477 | ||||||||
\(248\) | 10.5861 | 0.672220 | ||||||||
\(249\) | 5.10705 | 0.323646 | ||||||||
\(250\) | 72.1884 | 4.56560 | ||||||||
\(251\) | −3.95090 | −0.249379 | −0.124689 | − | 0.992196i | \(-0.539793\pi\) | ||||
−0.124689 | + | 0.992196i | \(0.539793\pi\) | |||||||
\(252\) | 2.82002 | 0.177644 | ||||||||
\(253\) | −6.59814 | −0.414821 | ||||||||
\(254\) | −9.45183 | −0.593061 | ||||||||
\(255\) | −13.0802 | −0.819114 | ||||||||
\(256\) | −3.63440 | −0.227150 | ||||||||
\(257\) | 8.93082 | 0.557089 | 0.278545 | − | 0.960423i | \(-0.410148\pi\) | ||||
0.278545 | + | 0.960423i | \(0.410148\pi\) | |||||||
\(258\) | −1.11640 | −0.0695038 | ||||||||
\(259\) | −7.96976 | −0.495217 | ||||||||
\(260\) | 84.5141 | 5.24134 | ||||||||
\(261\) | −7.75844 | −0.480235 | ||||||||
\(262\) | −13.5005 | −0.834064 | ||||||||
\(263\) | −2.99783 | −0.184854 | −0.0924271 | − | 0.995719i | \(-0.529463\pi\) | ||||
−0.0924271 | + | 0.995719i | \(0.529463\pi\) | |||||||
\(264\) | 3.35437 | 0.206447 | ||||||||
\(265\) | −10.0638 | −0.618216 | ||||||||
\(266\) | −1.16306 | −0.0713119 | ||||||||
\(267\) | −4.45620 | −0.272715 | ||||||||
\(268\) | −11.6136 | −0.709411 | ||||||||
\(269\) | 10.1308 | 0.617684 | 0.308842 | − | 0.951113i | \(-0.400059\pi\) | ||||
0.308842 | + | 0.951113i | \(0.400059\pi\) | |||||||
\(270\) | −9.26124 | −0.563621 | ||||||||
\(271\) | −22.6698 | −1.37709 | −0.688546 | − | 0.725193i | \(-0.741751\pi\) | ||||
−0.688546 | + | 0.725193i | \(0.741751\pi\) | |||||||
\(272\) | −5.23268 | −0.317278 | ||||||||
\(273\) | −7.10449 | −0.429983 | ||||||||
\(274\) | 20.3093 | 1.22693 | ||||||||
\(275\) | −23.8393 | −1.43756 | ||||||||
\(276\) | −9.98639 | −0.601110 | ||||||||
\(277\) | −11.1878 | −0.672209 | −0.336104 | − | 0.941825i | \(-0.609109\pi\) | ||||
−0.336104 | + | 0.941825i | \(0.609109\pi\) | |||||||
\(278\) | 18.5198 | 1.11074 | ||||||||
\(279\) | 5.88019 | 0.352038 | ||||||||
\(280\) | 7.59436 | 0.453850 | ||||||||
\(281\) | −21.3543 | −1.27389 | −0.636947 | − | 0.770908i | \(-0.719803\pi\) | ||||
−0.636947 | + | 0.770908i | \(0.719803\pi\) | |||||||
\(282\) | −8.16517 | −0.486229 | ||||||||
\(283\) | 6.26470 | 0.372398 | 0.186199 | − | 0.982512i | \(-0.440383\pi\) | ||||
0.186199 | + | 0.982512i | \(0.440383\pi\) | |||||||
\(284\) | −36.2226 | −2.14942 | ||||||||
\(285\) | 2.23472 | 0.132374 | ||||||||
\(286\) | −29.0617 | −1.71845 | ||||||||
\(287\) | 3.04195 | 0.179561 | ||||||||
\(288\) | −7.30553 | −0.430483 | ||||||||
\(289\) | −7.38524 | −0.434426 | ||||||||
\(290\) | −71.8528 | −4.21934 | ||||||||
\(291\) | −9.35481 | −0.548389 | ||||||||
\(292\) | −21.3934 | −1.25196 | ||||||||
\(293\) | 11.9972 | 0.700882 | 0.350441 | − | 0.936585i | \(-0.386032\pi\) | ||||
0.350441 | + | 0.936585i | \(0.386032\pi\) | |||||||
\(294\) | −2.19545 | −0.128041 | ||||||||
\(295\) | −5.51756 | −0.321245 | ||||||||
\(296\) | −14.3480 | −0.833961 | ||||||||
\(297\) | 1.86322 | 0.108115 | ||||||||
\(298\) | −27.0030 | −1.56424 | ||||||||
\(299\) | 25.1588 | 1.45497 | ||||||||
\(300\) | −36.0812 | −2.08315 | ||||||||
\(301\) | 0.508504 | 0.0293097 | ||||||||
\(302\) | −43.9381 | −2.52835 | ||||||||
\(303\) | 14.5347 | 0.834996 | ||||||||
\(304\) | 0.893992 | 0.0512740 | ||||||||
\(305\) | 14.6622 | 0.839558 | ||||||||
\(306\) | 6.80759 | 0.389164 | ||||||||
\(307\) | −1.50840 | −0.0860890 | −0.0430445 | − | 0.999073i | \(-0.513706\pi\) | ||||
−0.0430445 | + | 0.999073i | \(0.513706\pi\) | |||||||
\(308\) | −5.25431 | −0.299392 | ||||||||
\(309\) | −18.0813 | −1.02861 | ||||||||
\(310\) | 54.4578 | 3.09300 | ||||||||
\(311\) | −13.3690 | −0.758088 | −0.379044 | − | 0.925379i | \(-0.623747\pi\) | ||||
−0.379044 | + | 0.925379i | \(0.623747\pi\) | |||||||
\(312\) | −12.7902 | −0.724105 | ||||||||
\(313\) | 2.88428 | 0.163029 | 0.0815146 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815146 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(314\) | −0.321804 | −0.0181604 | ||||||||
\(315\) | 4.21837 | 0.237678 | ||||||||
\(316\) | −12.4798 | −0.702041 | ||||||||
\(317\) | 18.2840 | 1.02693 | 0.513465 | − | 0.858111i | \(-0.328362\pi\) | ||||
0.513465 | + | 0.858111i | \(0.328362\pi\) | |||||||
\(318\) | 5.23772 | 0.293717 | ||||||||
\(319\) | 14.4557 | 0.809363 | ||||||||
\(320\) | −53.4210 | −2.98632 | ||||||||
\(321\) | 3.56618 | 0.199045 | ||||||||
\(322\) | 7.77466 | 0.433265 | ||||||||
\(323\) | −1.64266 | −0.0914002 | ||||||||
\(324\) | 2.82002 | 0.156668 | ||||||||
\(325\) | 90.8996 | 5.04220 | ||||||||
\(326\) | −19.4485 | −1.07715 | ||||||||
\(327\) | −18.7449 | −1.03660 | ||||||||
\(328\) | 5.47645 | 0.302386 | ||||||||
\(329\) | 3.71913 | 0.205042 | ||||||||
\(330\) | 17.2557 | 0.949897 | ||||||||
\(331\) | 29.7199 | 1.63355 | 0.816776 | − | 0.576954i | \(-0.195759\pi\) | ||||
0.816776 | + | 0.576954i | \(0.195759\pi\) | |||||||
\(332\) | −14.4020 | −0.790410 | ||||||||
\(333\) | −7.96976 | −0.436740 | ||||||||
\(334\) | 46.2201 | 2.52905 | ||||||||
\(335\) | −17.3724 | −0.949154 | ||||||||
\(336\) | 1.68754 | 0.0920630 | ||||||||
\(337\) | −11.9817 | −0.652683 | −0.326341 | − | 0.945252i | \(-0.605816\pi\) | ||||
−0.326341 | + | 0.945252i | \(0.605816\pi\) | |||||||
\(338\) | 82.2718 | 4.47499 | ||||||||
\(339\) | −1.73057 | −0.0939914 | ||||||||
\(340\) | 36.8864 | 2.00044 | ||||||||
\(341\) | −10.9561 | −0.593305 | ||||||||
\(342\) | −1.16306 | −0.0628912 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.915462 | 0.0493584 | ||||||||
\(345\) | −14.9383 | −0.804253 | ||||||||
\(346\) | −33.2950 | −1.78995 | ||||||||
\(347\) | −24.1315 | −1.29545 | −0.647724 | − | 0.761875i | \(-0.724279\pi\) | ||||
−0.647724 | + | 0.761875i | \(0.724279\pi\) | |||||||
\(348\) | 21.8789 | 1.17283 | ||||||||
\(349\) | −3.28839 | −0.176024 | −0.0880118 | − | 0.996119i | \(-0.528051\pi\) | ||||
−0.0880118 | + | 0.996119i | \(0.528051\pi\) | |||||||
\(350\) | 28.0901 | 1.50148 | ||||||||
\(351\) | −7.10449 | −0.379209 | ||||||||
\(352\) | 13.6118 | 0.725513 | ||||||||
\(353\) | 2.81282 | 0.149711 | 0.0748557 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748557 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(354\) | 2.87161 | 0.152625 | ||||||||
\(355\) | −54.1843 | −2.87580 | ||||||||
\(356\) | 12.5666 | 0.666026 | ||||||||
\(357\) | −3.10077 | −0.164110 | ||||||||
\(358\) | −4.97765 | −0.263077 | ||||||||
\(359\) | −5.81349 | −0.306824 | −0.153412 | − | 0.988162i | \(-0.549026\pi\) | ||||
−0.153412 | + | 0.988162i | \(0.549026\pi\) | |||||||
\(360\) | 7.59436 | 0.400258 | ||||||||
\(361\) | −18.7194 | −0.985229 | ||||||||
\(362\) | 29.8583 | 1.56931 | ||||||||
\(363\) | 7.52841 | 0.395139 | ||||||||
\(364\) | 20.0348 | 1.05011 | ||||||||
\(365\) | −32.0018 | −1.67505 | ||||||||
\(366\) | −7.63097 | −0.398877 | ||||||||
\(367\) | −1.74954 | −0.0913254 | −0.0456627 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456627 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(368\) | −5.97602 | −0.311522 | ||||||||
\(369\) | 3.04195 | 0.158358 | ||||||||
\(370\) | −73.8099 | −3.83719 | ||||||||
\(371\) | −2.38571 | −0.123860 | ||||||||
\(372\) | −16.5822 | −0.859748 | ||||||||
\(373\) | −10.2564 | −0.531055 | −0.265528 | − | 0.964103i | \(-0.585546\pi\) | ||||
−0.265528 | + | 0.964103i | \(0.585546\pi\) | |||||||
\(374\) | −12.6840 | −0.655876 | ||||||||
\(375\) | −32.8809 | −1.69796 | ||||||||
\(376\) | 6.69557 | 0.345297 | ||||||||
\(377\) | −55.1197 | −2.83881 | ||||||||
\(378\) | −2.19545 | −0.112922 | ||||||||
\(379\) | 25.8315 | 1.32687 | 0.663437 | − | 0.748232i | \(-0.269097\pi\) | ||||
0.663437 | + | 0.748232i | \(0.269097\pi\) | |||||||
\(380\) | −6.30196 | −0.323284 | ||||||||
\(381\) | 4.30518 | 0.220561 | ||||||||
\(382\) | −23.0544 | −1.17956 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 13.1919 | 0.673195 | ||||||||
\(385\) | −7.85976 | −0.400571 | ||||||||
\(386\) | 16.4129 | 0.835396 | ||||||||
\(387\) | 0.508504 | 0.0258487 | ||||||||
\(388\) | 26.3807 | 1.33928 | ||||||||
\(389\) | 17.8373 | 0.904387 | 0.452193 | − | 0.891920i | \(-0.350642\pi\) | ||||
0.452193 | + | 0.891920i | \(0.350642\pi\) | |||||||
\(390\) | −65.7964 | −3.33173 | ||||||||
\(391\) | 10.9806 | 0.555313 | ||||||||
\(392\) | 1.80031 | 0.0909292 | ||||||||
\(393\) | 6.14930 | 0.310191 | ||||||||
\(394\) | 17.7018 | 0.891803 | ||||||||
\(395\) | −18.6681 | −0.939293 | ||||||||
\(396\) | −5.25431 | −0.264039 | ||||||||
\(397\) | 21.1747 | 1.06273 | 0.531364 | − | 0.847143i | \(-0.321680\pi\) | ||||
0.531364 | + | 0.847143i | \(0.321680\pi\) | |||||||
\(398\) | −34.1364 | −1.71110 | ||||||||
\(399\) | 0.529760 | 0.0265212 | ||||||||
\(400\) | −21.5916 | −1.07958 | ||||||||
\(401\) | 20.5743 | 1.02743 | 0.513716 | − | 0.857961i | \(-0.328269\pi\) | ||||
0.513716 | + | 0.857961i | \(0.328269\pi\) | |||||||
\(402\) | 9.04145 | 0.450947 | ||||||||
\(403\) | 41.7757 | 2.08100 | ||||||||
\(404\) | −40.9881 | −2.03923 | ||||||||
\(405\) | 4.21837 | 0.209613 | ||||||||
\(406\) | −17.0333 | −0.845348 | ||||||||
\(407\) | 14.8494 | 0.736059 | ||||||||
\(408\) | −5.58233 | −0.276367 | ||||||||
\(409\) | −12.1648 | −0.601510 | −0.300755 | − | 0.953701i | \(-0.597239\pi\) | ||||
−0.300755 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(410\) | 28.1723 | 1.39133 | ||||||||
\(411\) | −9.25062 | −0.456300 | ||||||||
\(412\) | 50.9894 | 2.51207 | ||||||||
\(413\) | −1.30798 | −0.0643616 | ||||||||
\(414\) | 7.77466 | 0.382104 | ||||||||
\(415\) | −21.5434 | −1.05753 | ||||||||
\(416\) | −51.9021 | −2.54471 | ||||||||
\(417\) | −8.43552 | −0.413089 | ||||||||
\(418\) | 2.16704 | 0.105994 | ||||||||
\(419\) | −6.99551 | −0.341753 | −0.170876 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170876 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(420\) | −11.8959 | −0.580460 | ||||||||
\(421\) | −5.99266 | −0.292064 | −0.146032 | − | 0.989280i | \(-0.546650\pi\) | ||||
−0.146032 | + | 0.989280i | \(0.546650\pi\) | |||||||
\(422\) | 53.4132 | 2.60011 | ||||||||
\(423\) | 3.71913 | 0.180830 | ||||||||
\(424\) | −4.29501 | −0.208584 | ||||||||
\(425\) | 39.6733 | 1.92444 | ||||||||
\(426\) | 28.2002 | 1.36630 | ||||||||
\(427\) | 3.47580 | 0.168206 | ||||||||
\(428\) | −10.0567 | −0.486108 | ||||||||
\(429\) | 13.2372 | 0.639099 | ||||||||
\(430\) | 4.70938 | 0.227106 | ||||||||
\(431\) | −1.59618 | −0.0768851 | −0.0384426 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384426 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(432\) | 1.68754 | 0.0811920 | ||||||||
\(433\) | 9.73971 | 0.468061 | 0.234030 | − | 0.972229i | \(-0.424808\pi\) | ||||
0.234030 | + | 0.972229i | \(0.424808\pi\) | |||||||
\(434\) | 12.9097 | 0.619684 | ||||||||
\(435\) | 32.7280 | 1.56919 | ||||||||
\(436\) | 52.8610 | 2.53158 | ||||||||
\(437\) | −1.87601 | −0.0897419 | ||||||||
\(438\) | 16.6553 | 0.795823 | ||||||||
\(439\) | −39.8533 | −1.90209 | −0.951047 | − | 0.309046i | \(-0.899990\pi\) | ||||
−0.951047 | + | 0.309046i | \(0.899990\pi\) | |||||||
\(440\) | −14.1500 | −0.674574 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 48.3644 | 2.30046 | ||||||||
\(443\) | 11.5291 | 0.547764 | 0.273882 | − | 0.961763i | \(-0.411692\pi\) | ||||
0.273882 | + | 0.961763i | \(0.411692\pi\) | |||||||
\(444\) | 22.4748 | 1.06661 | ||||||||
\(445\) | 18.7979 | 0.891107 | ||||||||
\(446\) | −32.1423 | −1.52198 | ||||||||
\(447\) | 12.2995 | 0.581746 | ||||||||
\(448\) | −12.6639 | −0.598312 | ||||||||
\(449\) | 22.1935 | 1.04737 | 0.523687 | − | 0.851911i | \(-0.324556\pi\) | ||||
0.523687 | + | 0.851911i | \(0.324556\pi\) | |||||||
\(450\) | 28.0901 | 1.32418 | ||||||||
\(451\) | −5.66783 | −0.266888 | ||||||||
\(452\) | 4.88022 | 0.229546 | ||||||||
\(453\) | 20.0132 | 0.940303 | ||||||||
\(454\) | −53.7350 | −2.52191 | ||||||||
\(455\) | 29.9694 | 1.40499 | ||||||||
\(456\) | 0.953729 | 0.0446625 | ||||||||
\(457\) | −11.4603 | −0.536092 | −0.268046 | − | 0.963406i | \(-0.586378\pi\) | ||||
−0.268046 | + | 0.963406i | \(0.586378\pi\) | |||||||
\(458\) | 36.7179 | 1.71571 | ||||||||
\(459\) | −3.10077 | −0.144731 | ||||||||
\(460\) | 42.1263 | 1.96415 | ||||||||
\(461\) | 25.6597 | 1.19509 | 0.597545 | − | 0.801835i | \(-0.296143\pi\) | ||||
0.597545 | + | 0.801835i | \(0.296143\pi\) | |||||||
\(462\) | 4.09061 | 0.190313 | ||||||||
\(463\) | 31.0692 | 1.44391 | 0.721953 | − | 0.691942i | \(-0.243245\pi\) | ||||
0.721953 | + | 0.691942i | \(0.243245\pi\) | |||||||
\(464\) | 13.0927 | 0.607813 | ||||||||
\(465\) | −24.8048 | −1.15030 | ||||||||
\(466\) | −53.0734 | −2.45858 | ||||||||
\(467\) | −15.5283 | −0.718562 | −0.359281 | − | 0.933229i | \(-0.616978\pi\) | ||||
−0.359281 | + | 0.933229i | \(0.616978\pi\) | |||||||
\(468\) | 20.0348 | 0.926107 | ||||||||
\(469\) | −4.11826 | −0.190164 | ||||||||
\(470\) | 34.4437 | 1.58877 | ||||||||
\(471\) | 0.146577 | 0.00675393 | ||||||||
\(472\) | −2.35477 | −0.108387 | ||||||||
\(473\) | −0.947454 | −0.0435640 | ||||||||
\(474\) | 9.71581 | 0.446262 | ||||||||
\(475\) | −6.77811 | −0.311001 | ||||||||
\(476\) | 8.74421 | 0.400790 | ||||||||
\(477\) | −2.38571 | −0.109234 | ||||||||
\(478\) | 30.8399 | 1.41058 | ||||||||
\(479\) | 24.3080 | 1.11066 | 0.555331 | − | 0.831629i | \(-0.312591\pi\) | ||||
0.555331 | + | 0.831629i | \(0.312591\pi\) | |||||||
\(480\) | 30.8175 | 1.40662 | ||||||||
\(481\) | −56.6210 | −2.58170 | ||||||||
\(482\) | 13.8412 | 0.630450 | ||||||||
\(483\) | −3.54125 | −0.161133 | ||||||||
\(484\) | −21.2302 | −0.965010 | ||||||||
\(485\) | 39.4621 | 1.79188 | ||||||||
\(486\) | −2.19545 | −0.0995878 | ||||||||
\(487\) | −24.0735 | −1.09087 | −0.545436 | − | 0.838152i | \(-0.683636\pi\) | ||||
−0.545436 | + | 0.838152i | \(0.683636\pi\) | |||||||
\(488\) | 6.25751 | 0.283264 | ||||||||
\(489\) | 8.85854 | 0.400597 | ||||||||
\(490\) | 9.26124 | 0.418380 | ||||||||
\(491\) | 11.9019 | 0.537125 | 0.268563 | − | 0.963262i | \(-0.413451\pi\) | ||||
0.268563 | + | 0.963262i | \(0.413451\pi\) | |||||||
\(492\) | −8.57836 | −0.386742 | ||||||||
\(493\) | −24.0571 | −1.08348 | ||||||||
\(494\) | −8.26296 | −0.371768 | ||||||||
\(495\) | −7.85976 | −0.353270 | ||||||||
\(496\) | −9.92307 | −0.445559 | ||||||||
\(497\) | −12.8448 | −0.576169 | ||||||||
\(498\) | 11.2123 | 0.502434 | ||||||||
\(499\) | 26.3987 | 1.18177 | 0.590884 | − | 0.806756i | \(-0.298779\pi\) | ||||
0.590884 | + | 0.806756i | \(0.298779\pi\) | |||||||
\(500\) | 92.7246 | 4.14677 | ||||||||
\(501\) | −21.0526 | −0.940563 | ||||||||
\(502\) | −8.67403 | −0.387141 | ||||||||
\(503\) | −32.0683 | −1.42985 | −0.714927 | − | 0.699199i | \(-0.753540\pi\) | ||||
−0.714927 | + | 0.699199i | \(0.753540\pi\) | |||||||
\(504\) | 1.80031 | 0.0801920 | ||||||||
\(505\) | −61.3128 | −2.72838 | ||||||||
\(506\) | −14.4859 | −0.643977 | ||||||||
\(507\) | −37.4737 | −1.66427 | ||||||||
\(508\) | −12.1407 | −0.538656 | ||||||||
\(509\) | 27.4241 | 1.21555 | 0.607777 | − | 0.794108i | \(-0.292062\pi\) | ||||
0.607777 | + | 0.794108i | \(0.292062\pi\) | |||||||
\(510\) | −28.7170 | −1.27161 | ||||||||
\(511\) | −7.58629 | −0.335598 | ||||||||
\(512\) | 18.4046 | 0.813376 | ||||||||
\(513\) | 0.529760 | 0.0233895 | ||||||||
\(514\) | 19.6072 | 0.864836 | ||||||||
\(515\) | 76.2735 | 3.36101 | ||||||||
\(516\) | −1.43399 | −0.0631278 | ||||||||
\(517\) | −6.92955 | −0.304761 | ||||||||
\(518\) | −17.4972 | −0.768784 | ||||||||
\(519\) | 15.1654 | 0.665689 | ||||||||
\(520\) | 53.9540 | 2.36604 | ||||||||
\(521\) | 9.43897 | 0.413529 | 0.206764 | − | 0.978391i | \(-0.433707\pi\) | ||||
0.206764 | + | 0.978391i | \(0.433707\pi\) | |||||||
\(522\) | −17.0333 | −0.745527 | ||||||||
\(523\) | −24.1311 | −1.05518 | −0.527590 | − | 0.849499i | \(-0.676904\pi\) | ||||
−0.527590 | + | 0.849499i | \(0.676904\pi\) | |||||||
\(524\) | −17.3411 | −0.757551 | ||||||||
\(525\) | −12.7947 | −0.558406 | ||||||||
\(526\) | −6.58160 | −0.286971 | ||||||||
\(527\) | 18.2331 | 0.794246 | ||||||||
\(528\) | −3.14427 | −0.136837 | ||||||||
\(529\) | −10.4595 | −0.454762 | ||||||||
\(530\) | −22.0946 | −0.959730 | ||||||||
\(531\) | −1.30798 | −0.0567616 | ||||||||
\(532\) | −1.49393 | −0.0647701 | ||||||||
\(533\) | 21.6115 | 0.936099 | ||||||||
\(534\) | −9.78338 | −0.423368 | ||||||||
\(535\) | −15.0435 | −0.650386 | ||||||||
\(536\) | −7.41413 | −0.320242 | ||||||||
\(537\) | 2.26726 | 0.0978393 | ||||||||
\(538\) | 22.2416 | 0.958906 | ||||||||
\(539\) | −1.86322 | −0.0802546 | ||||||||
\(540\) | −11.8959 | −0.511917 | ||||||||
\(541\) | 13.5717 | 0.583493 | 0.291747 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291747 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(542\) | −49.7705 | −2.13782 | ||||||||
\(543\) | −13.6000 | −0.583634 | ||||||||
\(544\) | −22.6528 | −0.971230 | ||||||||
\(545\) | 79.0731 | 3.38712 | ||||||||
\(546\) | −15.5976 | −0.667514 | ||||||||
\(547\) | −31.2410 | −1.33577 | −0.667885 | − | 0.744265i | \(-0.732800\pi\) | ||||
−0.667885 | + | 0.744265i | \(0.732800\pi\) | |||||||
\(548\) | 26.0869 | 1.11438 | ||||||||
\(549\) | 3.47580 | 0.148344 | ||||||||
\(550\) | −52.3381 | −2.23170 | ||||||||
\(551\) | 4.11011 | 0.175096 | ||||||||
\(552\) | −6.37534 | −0.271353 | ||||||||
\(553\) | −4.42542 | −0.188188 | ||||||||
\(554\) | −24.5622 | −1.04355 | ||||||||
\(555\) | 33.6194 | 1.42707 | ||||||||
\(556\) | 23.7883 | 1.00885 | ||||||||
\(557\) | 14.9481 | 0.633373 | 0.316687 | − | 0.948530i | \(-0.397430\pi\) | ||||
0.316687 | + | 0.948530i | \(0.397430\pi\) | |||||||
\(558\) | 12.9097 | 0.546510 | ||||||||
\(559\) | 3.61266 | 0.152799 | ||||||||
\(560\) | −7.11869 | −0.300820 | ||||||||
\(561\) | 5.77742 | 0.243923 | ||||||||
\(562\) | −46.8825 | −1.97762 | ||||||||
\(563\) | −10.5860 | −0.446148 | −0.223074 | − | 0.974801i | \(-0.571609\pi\) | ||||
−0.223074 | + | 0.974801i | \(0.571609\pi\) | |||||||
\(564\) | −10.4880 | −0.441624 | ||||||||
\(565\) | 7.30017 | 0.307121 | ||||||||
\(566\) | 13.7539 | 0.578117 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −23.1246 | −0.970287 | ||||||||
\(569\) | −31.6259 | −1.32583 | −0.662913 | − | 0.748697i | \(-0.730680\pi\) | ||||
−0.662913 | + | 0.748697i | \(0.730680\pi\) | |||||||
\(570\) | 4.90623 | 0.205499 | ||||||||
\(571\) | −23.0662 | −0.965292 | −0.482646 | − | 0.875815i | \(-0.660324\pi\) | ||||
−0.482646 | + | 0.875815i | \(0.660324\pi\) | |||||||
\(572\) | −37.3292 | −1.56081 | ||||||||
\(573\) | 10.5010 | 0.438684 | ||||||||
\(574\) | 6.67847 | 0.278754 | ||||||||
\(575\) | 45.3092 | 1.88953 | ||||||||
\(576\) | −12.6639 | −0.527661 | ||||||||
\(577\) | 32.3531 | 1.34688 | 0.673439 | − | 0.739243i | \(-0.264816\pi\) | ||||
0.673439 | + | 0.739243i | \(0.264816\pi\) | |||||||
\(578\) | −16.2139 | −0.674411 | ||||||||
\(579\) | −7.47587 | −0.310687 | ||||||||
\(580\) | −92.2934 | −3.83228 | ||||||||
\(581\) | −5.10705 | −0.211876 | ||||||||
\(582\) | −20.5381 | −0.851330 | ||||||||
\(583\) | 4.44511 | 0.184097 | ||||||||
\(584\) | −13.6576 | −0.565157 | ||||||||
\(585\) | 29.9694 | 1.23908 | ||||||||
\(586\) | 26.3392 | 1.08806 | ||||||||
\(587\) | 11.4343 | 0.471946 | 0.235973 | − | 0.971760i | \(-0.424172\pi\) | ||||
0.235973 | + | 0.971760i | \(0.424172\pi\) | |||||||
\(588\) | −2.82002 | −0.116295 | ||||||||
\(589\) | −3.11509 | −0.128355 | ||||||||
\(590\) | −12.1135 | −0.498707 | ||||||||
\(591\) | −8.06293 | −0.331665 | ||||||||
\(592\) | 13.4493 | 0.552763 | ||||||||
\(593\) | −43.1524 | −1.77206 | −0.886029 | − | 0.463629i | \(-0.846547\pi\) | ||||
−0.886029 | + | 0.463629i | \(0.846547\pi\) | |||||||
\(594\) | 4.09061 | 0.167840 | ||||||||
\(595\) | 13.0802 | 0.536236 | ||||||||
\(596\) | −34.6848 | −1.42074 | ||||||||
\(597\) | 15.5487 | 0.636364 | ||||||||
\(598\) | 55.2350 | 2.25873 | ||||||||
\(599\) | −8.46508 | −0.345874 | −0.172937 | − | 0.984933i | \(-0.555326\pi\) | ||||
−0.172937 | + | 0.984933i | \(0.555326\pi\) | |||||||
\(600\) | −23.0343 | −0.940373 | ||||||||
\(601\) | 40.0122 | 1.63213 | 0.816066 | − | 0.577958i | \(-0.196150\pi\) | ||||
0.816066 | + | 0.577958i | \(0.196150\pi\) | |||||||
\(602\) | 1.11640 | 0.0455009 | ||||||||
\(603\) | −4.11826 | −0.167709 | ||||||||
\(604\) | −56.4376 | −2.29641 | ||||||||
\(605\) | −31.7576 | −1.29113 | ||||||||
\(606\) | 31.9102 | 1.29627 | ||||||||
\(607\) | −17.9548 | −0.728762 | −0.364381 | − | 0.931250i | \(-0.618719\pi\) | ||||
−0.364381 | + | 0.931250i | \(0.618719\pi\) | |||||||
\(608\) | 3.87018 | 0.156956 | ||||||||
\(609\) | 7.75844 | 0.314388 | ||||||||
\(610\) | 32.1903 | 1.30335 | ||||||||
\(611\) | 26.4225 | 1.06894 | ||||||||
\(612\) | 8.74421 | 0.353464 | ||||||||
\(613\) | 45.1445 | 1.82337 | 0.911685 | − | 0.410890i | \(-0.134782\pi\) | ||||
0.911685 | + | 0.410890i | \(0.134782\pi\) | |||||||
\(614\) | −3.31163 | −0.133646 | ||||||||
\(615\) | −12.8321 | −0.517440 | ||||||||
\(616\) | −3.35437 | −0.135151 | ||||||||
\(617\) | −25.8436 | −1.04042 | −0.520212 | − | 0.854037i | \(-0.674147\pi\) | ||||
−0.520212 | + | 0.854037i | \(0.674147\pi\) | |||||||
\(618\) | −39.6966 | −1.59683 | ||||||||
\(619\) | −1.13065 | −0.0454447 | −0.0227223 | − | 0.999742i | \(-0.507233\pi\) | ||||
−0.0227223 | + | 0.999742i | \(0.507233\pi\) | |||||||
\(620\) | 69.9500 | 2.80926 | ||||||||
\(621\) | −3.54125 | −0.142106 | ||||||||
\(622\) | −29.3511 | −1.17687 | ||||||||
\(623\) | 4.45620 | 0.178534 | ||||||||
\(624\) | 11.9891 | 0.479949 | ||||||||
\(625\) | 74.7304 | 2.98922 | ||||||||
\(626\) | 6.33231 | 0.253090 | ||||||||
\(627\) | −0.987059 | −0.0394193 | ||||||||
\(628\) | −0.413351 | −0.0164945 | ||||||||
\(629\) | −24.7124 | −0.985347 | ||||||||
\(630\) | 9.26124 | 0.368977 | ||||||||
\(631\) | −17.7609 | −0.707051 | −0.353526 | − | 0.935425i | \(-0.615017\pi\) | ||||
−0.353526 | + | 0.935425i | \(0.615017\pi\) | |||||||
\(632\) | −7.96711 | −0.316915 | ||||||||
\(633\) | −24.3290 | −0.966991 | ||||||||
\(634\) | 40.1416 | 1.59423 | ||||||||
\(635\) | −18.1609 | −0.720692 | ||||||||
\(636\) | 6.72774 | 0.266772 | ||||||||
\(637\) | 7.10449 | 0.281490 | ||||||||
\(638\) | 31.7368 | 1.25647 | ||||||||
\(639\) | −12.8448 | −0.508133 | ||||||||
\(640\) | −55.6483 | −2.19969 | ||||||||
\(641\) | 17.6206 | 0.695970 | 0.347985 | − | 0.937500i | \(-0.386866\pi\) | ||||
0.347985 | + | 0.937500i | \(0.386866\pi\) | |||||||
\(642\) | 7.82938 | 0.309001 | ||||||||
\(643\) | −33.5938 | −1.32481 | −0.662404 | − | 0.749146i | \(-0.730464\pi\) | ||||
−0.662404 | + | 0.749146i | \(0.730464\pi\) | |||||||
\(644\) | 9.98639 | 0.393519 | ||||||||
\(645\) | −2.14506 | −0.0844616 | ||||||||
\(646\) | −3.60639 | −0.141891 | ||||||||
\(647\) | 15.4941 | 0.609137 | 0.304568 | − | 0.952490i | \(-0.401488\pi\) | ||||
0.304568 | + | 0.952490i | \(0.401488\pi\) | |||||||
\(648\) | 1.80031 | 0.0707227 | ||||||||
\(649\) | 2.43706 | 0.0956630 | ||||||||
\(650\) | 199.566 | 7.82762 | ||||||||
\(651\) | −5.88019 | −0.230463 | ||||||||
\(652\) | −24.9812 | −0.978340 | ||||||||
\(653\) | 43.1742 | 1.68954 | 0.844769 | − | 0.535131i | \(-0.179738\pi\) | ||||
0.844769 | + | 0.535131i | \(0.179738\pi\) | |||||||
\(654\) | −41.1536 | −1.60923 | ||||||||
\(655\) | −25.9401 | −1.01356 | ||||||||
\(656\) | −5.13343 | −0.200427 | ||||||||
\(657\) | −7.58629 | −0.295969 | ||||||||
\(658\) | 8.16517 | 0.318311 | ||||||||
\(659\) | 3.18102 | 0.123915 | 0.0619576 | − | 0.998079i | \(-0.480266\pi\) | ||||
0.0619576 | + | 0.998079i | \(0.480266\pi\) | |||||||
\(660\) | 22.1647 | 0.862758 | ||||||||
\(661\) | −26.4654 | −1.02939 | −0.514693 | − | 0.857375i | \(-0.672094\pi\) | ||||
−0.514693 | + | 0.857375i | \(0.672094\pi\) | |||||||
\(662\) | 65.2486 | 2.53596 | ||||||||
\(663\) | −22.0294 | −0.855550 | ||||||||
\(664\) | −9.19425 | −0.356806 | ||||||||
\(665\) | −2.23472 | −0.0866589 | ||||||||
\(666\) | −17.4972 | −0.678004 | ||||||||
\(667\) | −27.4746 | −1.06382 | ||||||||
\(668\) | 59.3688 | 2.29705 | ||||||||
\(669\) | 14.6404 | 0.566031 | ||||||||
\(670\) | −38.1402 | −1.47349 | ||||||||
\(671\) | −6.47619 | −0.250011 | ||||||||
\(672\) | 7.30553 | 0.281817 | ||||||||
\(673\) | −48.6421 | −1.87501 | −0.937507 | − | 0.347967i | \(-0.886872\pi\) | ||||
−0.937507 | + | 0.347967i | \(0.886872\pi\) | |||||||
\(674\) | −26.3052 | −1.01324 | ||||||||
\(675\) | −12.7947 | −0.492467 | ||||||||
\(676\) | 105.676 | 4.06448 | ||||||||
\(677\) | 28.8193 | 1.10762 | 0.553808 | − | 0.832644i | \(-0.313174\pi\) | ||||
0.553808 | + | 0.832644i | \(0.313174\pi\) | |||||||
\(678\) | −3.79938 | −0.145914 | ||||||||
\(679\) | 9.35481 | 0.359005 | ||||||||
\(680\) | 23.5484 | 0.903038 | ||||||||
\(681\) | 24.4756 | 0.937906 | ||||||||
\(682\) | −24.0536 | −0.921059 | ||||||||
\(683\) | −30.9062 | −1.18259 | −0.591296 | − | 0.806455i | \(-0.701383\pi\) | ||||
−0.591296 | + | 0.806455i | \(0.701383\pi\) | |||||||
\(684\) | −1.49393 | −0.0571219 | ||||||||
\(685\) | 39.0226 | 1.49098 | ||||||||
\(686\) | 2.19545 | 0.0838228 | ||||||||
\(687\) | −16.7245 | −0.638080 | ||||||||
\(688\) | −0.858122 | −0.0327156 | ||||||||
\(689\) | −16.9492 | −0.645715 | ||||||||
\(690\) | −32.7964 | −1.24854 | ||||||||
\(691\) | 6.82756 | 0.259733 | 0.129866 | − | 0.991532i | \(-0.458545\pi\) | ||||
0.129866 | + | 0.991532i | \(0.458545\pi\) | |||||||
\(692\) | −42.7668 | −1.62575 | ||||||||
\(693\) | −1.86322 | −0.0707779 | ||||||||
\(694\) | −52.9796 | −2.01108 | ||||||||
\(695\) | 35.5842 | 1.34978 | ||||||||
\(696\) | 13.9676 | 0.529439 | ||||||||
\(697\) | 9.43240 | 0.357278 | ||||||||
\(698\) | −7.21951 | −0.273262 | ||||||||
\(699\) | 24.1742 | 0.914353 | ||||||||
\(700\) | 36.0812 | 1.36374 | ||||||||
\(701\) | 7.48764 | 0.282804 | 0.141402 | − | 0.989952i | \(-0.454839\pi\) | ||||
0.141402 | + | 0.989952i | \(0.454839\pi\) | |||||||
\(702\) | −15.5976 | −0.588692 | ||||||||
\(703\) | 4.22206 | 0.159238 | ||||||||
\(704\) | 23.5956 | 0.889292 | ||||||||
\(705\) | −15.6887 | −0.590869 | ||||||||
\(706\) | 6.17542 | 0.232415 | ||||||||
\(707\) | −14.5347 | −0.546633 | ||||||||
\(708\) | 3.68853 | 0.138623 | ||||||||
\(709\) | −26.0860 | −0.979680 | −0.489840 | − | 0.871812i | \(-0.662945\pi\) | ||||
−0.489840 | + | 0.871812i | \(0.662945\pi\) | |||||||
\(710\) | −118.959 | −4.46445 | ||||||||
\(711\) | −4.42542 | −0.165966 | ||||||||
\(712\) | 8.02252 | 0.300657 | ||||||||
\(713\) | 20.8232 | 0.779836 | ||||||||
\(714\) | −6.80759 | −0.254768 | ||||||||
\(715\) | −55.8396 | −2.08828 | ||||||||
\(716\) | −6.39370 | −0.238944 | ||||||||
\(717\) | −14.0472 | −0.524601 | ||||||||
\(718\) | −12.7632 | −0.476320 | ||||||||
\(719\) | −47.8781 | −1.78555 | −0.892776 | − | 0.450501i | \(-0.851246\pi\) | ||||
−0.892776 | + | 0.450501i | \(0.851246\pi\) | |||||||
\(720\) | −7.11869 | −0.265298 | ||||||||
\(721\) | 18.0813 | 0.673381 | ||||||||
\(722\) | −41.0975 | −1.52949 | ||||||||
\(723\) | −6.30449 | −0.234466 | ||||||||
\(724\) | 38.3523 | 1.42535 | ||||||||
\(725\) | −99.2667 | −3.68667 | ||||||||
\(726\) | 16.5283 | 0.613422 | ||||||||
\(727\) | 48.3818 | 1.79438 | 0.897191 | − | 0.441643i | \(-0.145604\pi\) | ||||
0.897191 | + | 0.441643i | \(0.145604\pi\) | |||||||
\(728\) | 12.7902 | 0.474038 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −70.2585 | −2.60038 | ||||||||
\(731\) | 1.57675 | 0.0583183 | ||||||||
\(732\) | −9.80182 | −0.362286 | ||||||||
\(733\) | 10.7771 | 0.398062 | 0.199031 | − | 0.979993i | \(-0.436221\pi\) | ||||
0.199031 | + | 0.979993i | \(0.436221\pi\) | |||||||
\(734\) | −3.84104 | −0.141775 | ||||||||
\(735\) | −4.21837 | −0.155597 | ||||||||
\(736\) | −25.8708 | −0.953609 | ||||||||
\(737\) | 7.67323 | 0.282647 | ||||||||
\(738\) | 6.67847 | 0.245838 | ||||||||
\(739\) | −53.9406 | −1.98424 | −0.992119 | − | 0.125302i | \(-0.960010\pi\) | ||||
−0.992119 | + | 0.125302i | \(0.960010\pi\) | |||||||
\(740\) | −94.8073 | −3.48519 | ||||||||
\(741\) | 3.76367 | 0.138262 | ||||||||
\(742\) | −5.23772 | −0.192283 | ||||||||
\(743\) | −14.5901 | −0.535260 | −0.267630 | − | 0.963522i | \(-0.586241\pi\) | ||||
−0.267630 | + | 0.963522i | \(0.586241\pi\) | |||||||
\(744\) | −10.5861 | −0.388106 | ||||||||
\(745\) | −51.8839 | −1.90088 | ||||||||
\(746\) | −22.5174 | −0.824421 | ||||||||
\(747\) | −5.10705 | −0.186857 | ||||||||
\(748\) | −16.2924 | −0.595709 | ||||||||
\(749\) | −3.56618 | −0.130305 | ||||||||
\(750\) | −72.1884 | −2.63595 | ||||||||
\(751\) | 15.4981 | 0.565532 | 0.282766 | − | 0.959189i | \(-0.408748\pi\) | ||||
0.282766 | + | 0.959189i | \(0.408748\pi\) | |||||||
\(752\) | −6.27619 | −0.228869 | ||||||||
\(753\) | 3.95090 | 0.143979 | ||||||||
\(754\) | −121.013 | −4.40702 | ||||||||
\(755\) | −84.4232 | −3.07248 | ||||||||
\(756\) | −2.82002 | −0.102563 | ||||||||
\(757\) | −25.5800 | −0.929720 | −0.464860 | − | 0.885384i | \(-0.653895\pi\) | ||||
−0.464860 | + | 0.885384i | \(0.653895\pi\) | |||||||
\(758\) | 56.7118 | 2.05987 | ||||||||
\(759\) | 6.59814 | 0.239497 | ||||||||
\(760\) | −4.02319 | −0.145936 | ||||||||
\(761\) | 1.70694 | 0.0618766 | 0.0309383 | − | 0.999521i | \(-0.490150\pi\) | ||||
0.0309383 | + | 0.999521i | \(0.490150\pi\) | |||||||
\(762\) | 9.45183 | 0.342404 | ||||||||
\(763\) | 18.7449 | 0.678612 | ||||||||
\(764\) | −29.6129 | −1.07136 | ||||||||
\(765\) | 13.0802 | 0.472916 | ||||||||
\(766\) | −2.19545 | −0.0793250 | ||||||||
\(767\) | −9.29254 | −0.335534 | ||||||||
\(768\) | 3.63440 | 0.131145 | ||||||||
\(769\) | −24.2282 | −0.873690 | −0.436845 | − | 0.899537i | \(-0.643904\pi\) | ||||
−0.436845 | + | 0.899537i | \(0.643904\pi\) | |||||||
\(770\) | −17.2557 | −0.621854 | ||||||||
\(771\) | −8.93082 | −0.321636 | ||||||||
\(772\) | 21.0821 | 0.758761 | ||||||||
\(773\) | −20.6755 | −0.743645 | −0.371823 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(774\) | 1.11640 | 0.0401280 | ||||||||
\(775\) | 75.2351 | 2.70252 | ||||||||
\(776\) | 16.8415 | 0.604575 | ||||||||
\(777\) | 7.96976 | 0.285914 | ||||||||
\(778\) | 39.1610 | 1.40399 | ||||||||
\(779\) | −1.61150 | −0.0577382 | ||||||||
\(780\) | −84.5141 | −3.02609 | ||||||||
\(781\) | 23.9327 | 0.856381 | ||||||||
\(782\) | 24.1074 | 0.862080 | ||||||||
\(783\) | 7.75844 | 0.277264 | ||||||||
\(784\) | −1.68754 | −0.0602694 | ||||||||
\(785\) | −0.618319 | −0.0220687 | ||||||||
\(786\) | 13.5005 | 0.481547 | ||||||||
\(787\) | −12.1368 | −0.432629 | −0.216314 | − | 0.976324i | \(-0.569404\pi\) | ||||
−0.216314 | + | 0.976324i | \(0.569404\pi\) | |||||||
\(788\) | 22.7376 | 0.809993 | ||||||||
\(789\) | 2.99783 | 0.106726 | ||||||||
\(790\) | −40.9849 | −1.45818 | ||||||||
\(791\) | 1.73057 | 0.0615318 | ||||||||
\(792\) | −3.35437 | −0.119192 | ||||||||
\(793\) | 24.6938 | 0.876903 | ||||||||
\(794\) | 46.4881 | 1.64980 | ||||||||
\(795\) | 10.0638 | 0.356927 | ||||||||
\(796\) | −43.8475 | −1.55413 | ||||||||
\(797\) | 21.0957 | 0.747247 | 0.373623 | − | 0.927580i | \(-0.378115\pi\) | ||||
0.373623 | + | 0.927580i | \(0.378115\pi\) | |||||||
\(798\) | 1.16306 | 0.0411720 | ||||||||
\(799\) | 11.5322 | 0.407978 | ||||||||
\(800\) | −93.4720 | −3.30473 | ||||||||
\(801\) | 4.45620 | 0.157452 | ||||||||
\(802\) | 45.1699 | 1.59500 | ||||||||
\(803\) | 14.1349 | 0.498811 | ||||||||
\(804\) | 11.6136 | 0.409579 | ||||||||
\(805\) | 14.9383 | 0.526507 | ||||||||
\(806\) | 91.7166 | 3.23058 | ||||||||
\(807\) | −10.1308 | −0.356620 | ||||||||
\(808\) | −26.1669 | −0.920548 | ||||||||
\(809\) | −3.01677 | −0.106064 | −0.0530320 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530320 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(810\) | 9.26124 | 0.325407 | ||||||||
\(811\) | 43.2339 | 1.51815 | 0.759074 | − | 0.651004i | \(-0.225652\pi\) | ||||
0.759074 | + | 0.651004i | \(0.225652\pi\) | |||||||
\(812\) | −21.8789 | −0.767799 | ||||||||
\(813\) | 22.6698 | 0.795064 | ||||||||
\(814\) | 32.6012 | 1.14267 | ||||||||
\(815\) | −37.3686 | −1.30897 | ||||||||
\(816\) | 5.23268 | 0.183180 | ||||||||
\(817\) | −0.269385 | −0.00942458 | ||||||||
\(818\) | −26.7072 | −0.933796 | ||||||||
\(819\) | 7.10449 | 0.248251 | ||||||||
\(820\) | 36.1867 | 1.26370 | ||||||||
\(821\) | 42.1699 | 1.47174 | 0.735870 | − | 0.677123i | \(-0.236773\pi\) | ||||
0.735870 | + | 0.677123i | \(0.236773\pi\) | |||||||
\(822\) | −20.3093 | −0.708369 | ||||||||
\(823\) | −45.9985 | −1.60341 | −0.801704 | − | 0.597721i | \(-0.796073\pi\) | ||||
−0.801704 | + | 0.597721i | \(0.796073\pi\) | |||||||
\(824\) | 32.5518 | 1.13400 | ||||||||
\(825\) | 23.8393 | 0.829978 | ||||||||
\(826\) | −2.87161 | −0.0999163 | ||||||||
\(827\) | −13.9160 | −0.483907 | −0.241954 | − | 0.970288i | \(-0.577788\pi\) | ||||
−0.241954 | + | 0.970288i | \(0.577788\pi\) | |||||||
\(828\) | 9.98639 | 0.347051 | ||||||||
\(829\) | 0.856472 | 0.0297465 | 0.0148733 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148733 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(830\) | −47.2976 | −1.64172 | ||||||||
\(831\) | 11.1878 | 0.388100 | ||||||||
\(832\) | −89.9703 | −3.11916 | ||||||||
\(833\) | 3.10077 | 0.107435 | ||||||||
\(834\) | −18.5198 | −0.641288 | ||||||||
\(835\) | 88.8079 | 3.07332 | ||||||||
\(836\) | 2.78352 | 0.0962701 | ||||||||
\(837\) | −5.88019 | −0.203249 | ||||||||
\(838\) | −15.3583 | −0.530544 | ||||||||
\(839\) | −44.3625 | −1.53156 | −0.765781 | − | 0.643101i | \(-0.777648\pi\) | ||||
−0.765781 | + | 0.643101i | \(0.777648\pi\) | |||||||
\(840\) | −7.59436 | −0.262030 | ||||||||
\(841\) | 31.1934 | 1.07563 | ||||||||
\(842\) | −13.1566 | −0.453406 | ||||||||
\(843\) | 21.3543 | 0.735482 | ||||||||
\(844\) | 68.6082 | 2.36159 | ||||||||
\(845\) | 158.078 | 5.43805 | ||||||||
\(846\) | 8.16517 | 0.280724 | ||||||||
\(847\) | −7.52841 | −0.258679 | ||||||||
\(848\) | 4.02599 | 0.138253 | ||||||||
\(849\) | −6.26470 | −0.215004 | ||||||||
\(850\) | 87.1010 | 2.98754 | ||||||||
\(851\) | −28.2230 | −0.967470 | ||||||||
\(852\) | 36.2226 | 1.24097 | ||||||||
\(853\) | 16.8006 | 0.575243 | 0.287621 | − | 0.957744i | \(-0.407135\pi\) | ||||
0.287621 | + | 0.957744i | \(0.407135\pi\) | |||||||
\(854\) | 7.63097 | 0.261126 | ||||||||
\(855\) | −2.23472 | −0.0764260 | ||||||||
\(856\) | −6.42022 | −0.219438 | ||||||||
\(857\) | 15.1126 | 0.516238 | 0.258119 | − | 0.966113i | \(-0.416897\pi\) | ||||
0.258119 | + | 0.966113i | \(0.416897\pi\) | |||||||
\(858\) | 29.0617 | 0.992150 | ||||||||
\(859\) | 38.3631 | 1.30893 | 0.654466 | − | 0.756091i | \(-0.272893\pi\) | ||||
0.654466 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(860\) | 6.04910 | 0.206273 | ||||||||
\(861\) | −3.04195 | −0.103670 | ||||||||
\(862\) | −3.50433 | −0.119358 | ||||||||
\(863\) | −45.5857 | −1.55176 | −0.775878 | − | 0.630883i | \(-0.782693\pi\) | ||||
−0.775878 | + | 0.630883i | \(0.782693\pi\) | |||||||
\(864\) | 7.30553 | 0.248539 | ||||||||
\(865\) | −63.9735 | −2.17516 | ||||||||
\(866\) | 21.3831 | 0.726627 | ||||||||
\(867\) | 7.38524 | 0.250816 | ||||||||
\(868\) | 16.5822 | 0.562837 | ||||||||
\(869\) | 8.24554 | 0.279711 | ||||||||
\(870\) | 71.8528 | 2.43604 | ||||||||
\(871\) | −29.2581 | −0.991374 | ||||||||
\(872\) | 33.7466 | 1.14280 | ||||||||
\(873\) | 9.35481 | 0.316612 | ||||||||
\(874\) | −4.11870 | −0.139317 | ||||||||
\(875\) | 32.8809 | 1.11158 | ||||||||
\(876\) | 21.3934 | 0.722818 | ||||||||
\(877\) | 6.90950 | 0.233317 | 0.116659 | − | 0.993172i | \(-0.462782\pi\) | ||||
0.116659 | + | 0.993172i | \(0.462782\pi\) | |||||||
\(878\) | −87.4960 | −2.95285 | ||||||||
\(879\) | −11.9972 | −0.404654 | ||||||||
\(880\) | 13.2637 | 0.447119 | ||||||||
\(881\) | 12.8338 | 0.432381 | 0.216191 | − | 0.976351i | \(-0.430637\pi\) | ||||
0.216191 | + | 0.976351i | \(0.430637\pi\) | |||||||
\(882\) | 2.19545 | 0.0739248 | ||||||||
\(883\) | 23.8492 | 0.802589 | 0.401295 | − | 0.915949i | \(-0.368560\pi\) | ||||
0.401295 | + | 0.915949i | \(0.368560\pi\) | |||||||
\(884\) | 62.1231 | 2.08943 | ||||||||
\(885\) | 5.51756 | 0.185471 | ||||||||
\(886\) | 25.3116 | 0.850360 | ||||||||
\(887\) | −24.8918 | −0.835786 | −0.417893 | − | 0.908496i | \(-0.637231\pi\) | ||||
−0.417893 | + | 0.908496i | \(0.637231\pi\) | |||||||
\(888\) | 14.3480 | 0.481488 | ||||||||
\(889\) | −4.30518 | −0.144391 | ||||||||
\(890\) | 41.2700 | 1.38337 | ||||||||
\(891\) | −1.86322 | −0.0624202 | ||||||||
\(892\) | −41.2862 | −1.38236 | ||||||||
\(893\) | −1.97024 | −0.0659317 | ||||||||
\(894\) | 27.0030 | 0.903115 | ||||||||
\(895\) | −9.56413 | −0.319694 | ||||||||
\(896\) | −13.1919 | −0.440710 | ||||||||
\(897\) | −25.1588 | −0.840028 | ||||||||
\(898\) | 48.7247 | 1.62596 | ||||||||
\(899\) | −45.6211 | −1.52155 | ||||||||
\(900\) | 36.0812 | 1.20271 | ||||||||
\(901\) | −7.39754 | −0.246448 | ||||||||
\(902\) | −12.4435 | −0.414322 | ||||||||
\(903\) | −0.508504 | −0.0169219 | ||||||||
\(904\) | 3.11555 | 0.103622 | ||||||||
\(905\) | 57.3701 | 1.90705 | ||||||||
\(906\) | 43.9381 | 1.45975 | ||||||||
\(907\) | −51.8181 | −1.72059 | −0.860295 | − | 0.509796i | \(-0.829721\pi\) | ||||
−0.860295 | + | 0.509796i | \(0.829721\pi\) | |||||||
\(908\) | −69.0215 | −2.29056 | ||||||||
\(909\) | −14.5347 | −0.482085 | ||||||||
\(910\) | 65.7964 | 2.18113 | ||||||||
\(911\) | −7.60485 | −0.251960 | −0.125980 | − | 0.992033i | \(-0.540208\pi\) | ||||
−0.125980 | + | 0.992033i | \(0.540208\pi\) | |||||||
\(912\) | −0.893992 | −0.0296030 | ||||||||
\(913\) | 9.51556 | 0.314919 | ||||||||
\(914\) | −25.1606 | −0.832240 | ||||||||
\(915\) | −14.6622 | −0.484719 | ||||||||
\(916\) | 47.1634 | 1.55832 | ||||||||
\(917\) | −6.14930 | −0.203068 | ||||||||
\(918\) | −6.80759 | −0.224684 | ||||||||
\(919\) | −44.2742 | −1.46047 | −0.730235 | − | 0.683196i | \(-0.760590\pi\) | ||||
−0.730235 | + | 0.683196i | \(0.760590\pi\) | |||||||
\(920\) | 26.8936 | 0.886655 | ||||||||
\(921\) | 1.50840 | 0.0497035 | ||||||||
\(922\) | 56.3346 | 1.85528 | ||||||||
\(923\) | −91.2558 | −3.00372 | ||||||||
\(924\) | 5.25431 | 0.172854 | ||||||||
\(925\) | −101.971 | −3.35277 | ||||||||
\(926\) | 68.2109 | 2.24155 | ||||||||
\(927\) | 18.0813 | 0.593867 | ||||||||
\(928\) | 56.6795 | 1.86060 | ||||||||
\(929\) | −7.45234 | −0.244503 | −0.122252 | − | 0.992499i | \(-0.539012\pi\) | ||||
−0.122252 | + | 0.992499i | \(0.539012\pi\) | |||||||
\(930\) | −54.4578 | −1.78574 | ||||||||
\(931\) | −0.529760 | −0.0173622 | ||||||||
\(932\) | −68.1717 | −2.23304 | ||||||||
\(933\) | 13.3690 | 0.437682 | ||||||||
\(934\) | −34.0916 | −1.11551 | ||||||||
\(935\) | −24.3713 | −0.797027 | ||||||||
\(936\) | 12.7902 | 0.418062 | ||||||||
\(937\) | −49.7602 | −1.62559 | −0.812797 | − | 0.582547i | \(-0.802056\pi\) | ||||
−0.812797 | + | 0.582547i | \(0.802056\pi\) | |||||||
\(938\) | −9.04145 | −0.295214 | ||||||||
\(939\) | −2.88428 | −0.0941250 | ||||||||
\(940\) | 44.2423 | 1.44302 | ||||||||
\(941\) | −2.32288 | −0.0757238 | −0.0378619 | − | 0.999283i | \(-0.512055\pi\) | ||||
−0.0378619 | + | 0.999283i | \(0.512055\pi\) | |||||||
\(942\) | 0.321804 | 0.0104849 | ||||||||
\(943\) | 10.7723 | 0.350796 | ||||||||
\(944\) | 2.20728 | 0.0718408 | ||||||||
\(945\) | −4.21837 | −0.137224 | ||||||||
\(946\) | −2.08009 | −0.0676296 | ||||||||
\(947\) | 44.8028 | 1.45590 | 0.727948 | − | 0.685632i | \(-0.240474\pi\) | ||||
0.727948 | + | 0.685632i | \(0.240474\pi\) | |||||||
\(948\) | 12.4798 | 0.405324 | ||||||||
\(949\) | −53.8967 | −1.74956 | ||||||||
\(950\) | −14.8810 | −0.482804 | ||||||||
\(951\) | −18.2840 | −0.592898 | ||||||||
\(952\) | 5.58233 | 0.180924 | ||||||||
\(953\) | −55.1203 | −1.78552 | −0.892760 | − | 0.450532i | \(-0.851234\pi\) | ||||
−0.892760 | + | 0.450532i | \(0.851234\pi\) | |||||||
\(954\) | −5.23772 | −0.169577 | ||||||||
\(955\) | −44.2970 | −1.43342 | ||||||||
\(956\) | 39.6132 | 1.28118 | ||||||||
\(957\) | −14.4557 | −0.467286 | ||||||||
\(958\) | 53.3672 | 1.72421 | ||||||||
\(959\) | 9.25062 | 0.298718 | ||||||||
\(960\) | 53.4210 | 1.72415 | ||||||||
\(961\) | 3.57659 | 0.115374 | ||||||||
\(962\) | −124.309 | −4.00788 | ||||||||
\(963\) | −3.56618 | −0.114919 | ||||||||
\(964\) | 17.7787 | 0.572615 | ||||||||
\(965\) | 31.5360 | 1.01518 | ||||||||
\(966\) | −7.77466 | −0.250146 | ||||||||
\(967\) | 24.6199 | 0.791723 | 0.395862 | − | 0.918310i | \(-0.370446\pi\) | ||||
0.395862 | + | 0.918310i | \(0.370446\pi\) | |||||||
\(968\) | −13.5534 | −0.435624 | ||||||||
\(969\) | 1.64266 | 0.0527699 | ||||||||
\(970\) | 86.6372 | 2.78175 | ||||||||
\(971\) | −23.3372 | −0.748928 | −0.374464 | − | 0.927242i | \(-0.622173\pi\) | ||||
−0.374464 | + | 0.927242i | \(0.622173\pi\) | |||||||
\(972\) | −2.82002 | −0.0904520 | ||||||||
\(973\) | 8.43552 | 0.270430 | ||||||||
\(974\) | −52.8522 | −1.69349 | ||||||||
\(975\) | −90.8996 | −2.91112 | ||||||||
\(976\) | −5.86557 | −0.187752 | ||||||||
\(977\) | 54.4539 | 1.74214 | 0.871068 | − | 0.491162i | \(-0.163428\pi\) | ||||
0.871068 | + | 0.491162i | \(0.163428\pi\) | |||||||
\(978\) | 19.4485 | 0.621895 | ||||||||
\(979\) | −8.30288 | −0.265361 | ||||||||
\(980\) | 11.8959 | 0.380000 | ||||||||
\(981\) | 18.7449 | 0.598480 | ||||||||
\(982\) | 26.1301 | 0.833844 | ||||||||
\(983\) | −8.87317 | −0.283010 | −0.141505 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141505 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(984\) | −5.47645 | −0.174583 | ||||||||
\(985\) | 34.0125 | 1.08373 | ||||||||
\(986\) | −52.8163 | −1.68201 | ||||||||
\(987\) | −3.71913 | −0.118381 | ||||||||
\(988\) | −10.6136 | −0.337664 | ||||||||
\(989\) | 1.80074 | 0.0572602 | ||||||||
\(990\) | −17.2557 | −0.548423 | ||||||||
\(991\) | 16.5459 | 0.525599 | 0.262799 | − | 0.964851i | \(-0.415354\pi\) | ||||
0.262799 | + | 0.964851i | \(0.415354\pi\) | |||||||
\(992\) | −42.9579 | −1.36391 | ||||||||
\(993\) | −29.7199 | −0.943132 | ||||||||
\(994\) | −28.2002 | −0.894456 | ||||||||
\(995\) | −65.5901 | −2.07934 | ||||||||
\(996\) | 14.4020 | 0.456343 | ||||||||
\(997\) | 20.8056 | 0.658918 | 0.329459 | − | 0.944170i | \(-0.393134\pi\) | ||||
0.329459 | + | 0.944170i | \(0.393134\pi\) | |||||||
\(998\) | 57.9571 | 1.83460 | ||||||||
\(999\) | 7.96976 | 0.252152 |
(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 | 8043.2.a.t.1.43 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.43 | ✓ | 52 | 1.1 | even | 1 | trivial |