Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8049,2,Mod(1,8049)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8049, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8049.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8049 = 3 \cdot 2683 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8049.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: | \(64.2715885869\) |
Analytic rank: | \(0\) |
Dimension: | \(129\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8049.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82087 | −1.99465 | −0.997327 | − | 0.0730622i | \(-0.976723\pi\) | ||||
−0.997327 | + | 0.0730622i | \(0.976723\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.95730 | 2.97865 | ||||||||
\(5\) | 1.28710 | 0.575611 | 0.287805 | − | 0.957689i | \(-0.407074\pi\) | ||||
0.287805 | + | 0.957689i | \(0.407074\pi\) | |||||||
\(6\) | −2.82087 | −1.15161 | ||||||||
\(7\) | 2.58338 | 0.976426 | 0.488213 | − | 0.872724i | \(-0.337649\pi\) | ||||
0.488213 | + | 0.872724i | \(0.337649\pi\) | |||||||
\(8\) | −11.1630 | −3.94672 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.63075 | −1.14814 | ||||||||
\(11\) | 5.50374 | 1.65944 | 0.829721 | − | 0.558179i | \(-0.188500\pi\) | ||||
0.829721 | + | 0.558179i | \(0.188500\pi\) | |||||||
\(12\) | 5.95730 | 1.71972 | ||||||||
\(13\) | 5.71159 | 1.58411 | 0.792054 | − | 0.610451i | \(-0.209012\pi\) | ||||
0.792054 | + | 0.610451i | \(0.209012\pi\) | |||||||
\(14\) | −7.28738 | −1.94763 | ||||||||
\(15\) | 1.28710 | 0.332329 | ||||||||
\(16\) | 19.5748 | 4.89369 | ||||||||
\(17\) | 4.87983 | 1.18353 | 0.591766 | − | 0.806110i | \(-0.298431\pi\) | ||||
0.591766 | + | 0.806110i | \(0.298431\pi\) | |||||||
\(18\) | −2.82087 | −0.664885 | ||||||||
\(19\) | 5.71437 | 1.31097 | 0.655484 | − | 0.755209i | \(-0.272465\pi\) | ||||
0.655484 | + | 0.755209i | \(0.272465\pi\) | |||||||
\(20\) | 7.66766 | 1.71454 | ||||||||
\(21\) | 2.58338 | 0.563740 | ||||||||
\(22\) | −15.5253 | −3.31001 | ||||||||
\(23\) | −3.55185 | −0.740613 | −0.370306 | − | 0.928910i | \(-0.620747\pi\) | ||||
−0.370306 | + | 0.928910i | \(0.620747\pi\) | |||||||
\(24\) | −11.1630 | −2.27864 | ||||||||
\(25\) | −3.34336 | −0.668672 | ||||||||
\(26\) | −16.1116 | −3.15975 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 15.3900 | 2.90843 | ||||||||
\(29\) | −8.92701 | −1.65771 | −0.828853 | − | 0.559467i | \(-0.811006\pi\) | ||||
−0.828853 | + | 0.559467i | \(0.811006\pi\) | |||||||
\(30\) | −3.63075 | −0.662882 | ||||||||
\(31\) | −7.74680 | −1.39137 | −0.695683 | − | 0.718349i | \(-0.744898\pi\) | ||||
−0.695683 | + | 0.718349i | \(0.744898\pi\) | |||||||
\(32\) | −32.8918 | −5.81451 | ||||||||
\(33\) | 5.50374 | 0.958079 | ||||||||
\(34\) | −13.7654 | −2.36074 | ||||||||
\(35\) | 3.32508 | 0.562042 | ||||||||
\(36\) | 5.95730 | 0.992883 | ||||||||
\(37\) | 8.26151 | 1.35818 | 0.679092 | − | 0.734053i | \(-0.262374\pi\) | ||||
0.679092 | + | 0.734053i | \(0.262374\pi\) | |||||||
\(38\) | −16.1195 | −2.61493 | ||||||||
\(39\) | 5.71159 | 0.914586 | ||||||||
\(40\) | −14.3680 | −2.27177 | ||||||||
\(41\) | −5.39003 | −0.841782 | −0.420891 | − | 0.907111i | \(-0.638282\pi\) | ||||
−0.420891 | + | 0.907111i | \(0.638282\pi\) | |||||||
\(42\) | −7.28738 | −1.12447 | ||||||||
\(43\) | −8.03917 | −1.22596 | −0.612981 | − | 0.790097i | \(-0.710030\pi\) | ||||
−0.612981 | + | 0.790097i | \(0.710030\pi\) | |||||||
\(44\) | 32.7874 | 4.94289 | ||||||||
\(45\) | 1.28710 | 0.191870 | ||||||||
\(46\) | 10.0193 | 1.47727 | ||||||||
\(47\) | 7.41995 | 1.08231 | 0.541155 | − | 0.840923i | \(-0.317987\pi\) | ||||
0.541155 | + | 0.840923i | \(0.317987\pi\) | |||||||
\(48\) | 19.5748 | 2.82538 | ||||||||
\(49\) | −0.326141 | −0.0465916 | ||||||||
\(50\) | 9.43118 | 1.33377 | ||||||||
\(51\) | 4.87983 | 0.683313 | ||||||||
\(52\) | 34.0256 | 4.71850 | ||||||||
\(53\) | 1.41138 | 0.193869 | 0.0969343 | − | 0.995291i | \(-0.469096\pi\) | ||||
0.0969343 | + | 0.995291i | \(0.469096\pi\) | |||||||
\(54\) | −2.82087 | −0.383871 | ||||||||
\(55\) | 7.08390 | 0.955192 | ||||||||
\(56\) | −28.8383 | −3.85368 | ||||||||
\(57\) | 5.71437 | 0.756887 | ||||||||
\(58\) | 25.1819 | 3.30655 | ||||||||
\(59\) | −1.88343 | −0.245201 | −0.122601 | − | 0.992456i | \(-0.539123\pi\) | ||||
−0.122601 | + | 0.992456i | \(0.539123\pi\) | |||||||
\(60\) | 7.66766 | 0.989891 | ||||||||
\(61\) | 4.49047 | 0.574946 | 0.287473 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287473 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(62\) | 21.8527 | 2.77529 | ||||||||
\(63\) | 2.58338 | 0.325475 | ||||||||
\(64\) | 53.6340 | 6.70425 | ||||||||
\(65\) | 7.35141 | 0.911830 | ||||||||
\(66\) | −15.5253 | −1.91104 | ||||||||
\(67\) | −3.11381 | −0.380412 | −0.190206 | − | 0.981744i | \(-0.560916\pi\) | ||||
−0.190206 | + | 0.981744i | \(0.560916\pi\) | |||||||
\(68\) | 29.0706 | 3.52533 | ||||||||
\(69\) | −3.55185 | −0.427593 | ||||||||
\(70\) | −9.37962 | −1.12108 | ||||||||
\(71\) | 4.39590 | 0.521698 | 0.260849 | − | 0.965380i | \(-0.415998\pi\) | ||||
0.260849 | + | 0.965380i | \(0.415998\pi\) | |||||||
\(72\) | −11.1630 | −1.31557 | ||||||||
\(73\) | 5.03934 | 0.589810 | 0.294905 | − | 0.955527i | \(-0.404712\pi\) | ||||
0.294905 | + | 0.955527i | \(0.404712\pi\) | |||||||
\(74\) | −23.3046 | −2.70911 | ||||||||
\(75\) | −3.34336 | −0.386058 | ||||||||
\(76\) | 34.0422 | 3.90491 | ||||||||
\(77\) | 14.2183 | 1.62032 | ||||||||
\(78\) | −16.1116 | −1.82428 | ||||||||
\(79\) | 17.2533 | 1.94115 | 0.970575 | − | 0.240798i | \(-0.0774091\pi\) | ||||
0.970575 | + | 0.240798i | \(0.0774091\pi\) | |||||||
\(80\) | 25.1948 | 2.81686 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.2046 | 1.67906 | ||||||||
\(83\) | −8.55662 | −0.939211 | −0.469606 | − | 0.882876i | \(-0.655604\pi\) | ||||
−0.469606 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(84\) | 15.3900 | 1.67918 | ||||||||
\(85\) | 6.28085 | 0.681254 | ||||||||
\(86\) | 22.6774 | 2.44537 | ||||||||
\(87\) | −8.92701 | −0.957076 | ||||||||
\(88\) | −61.4383 | −6.54935 | ||||||||
\(89\) | −12.1637 | −1.28934 | −0.644672 | − | 0.764459i | \(-0.723006\pi\) | ||||
−0.644672 | + | 0.764459i | \(0.723006\pi\) | |||||||
\(90\) | −3.63075 | −0.382715 | ||||||||
\(91\) | 14.7552 | 1.54677 | ||||||||
\(92\) | −21.1594 | −2.20602 | ||||||||
\(93\) | −7.74680 | −0.803305 | ||||||||
\(94\) | −20.9307 | −2.15884 | ||||||||
\(95\) | 7.35500 | 0.754607 | ||||||||
\(96\) | −32.8918 | −3.35701 | ||||||||
\(97\) | −0.748112 | −0.0759593 | −0.0379796 | − | 0.999279i | \(-0.512092\pi\) | ||||
−0.0379796 | + | 0.999279i | \(0.512092\pi\) | |||||||
\(98\) | 0.920002 | 0.0929342 | ||||||||
\(99\) | 5.50374 | 0.553147 | ||||||||
\(100\) | −19.9174 | −1.99174 | ||||||||
\(101\) | −0.176176 | −0.0175302 | −0.00876509 | − | 0.999962i | \(-0.502790\pi\) | ||||
−0.00876509 | + | 0.999962i | \(0.502790\pi\) | |||||||
\(102\) | −13.7654 | −1.36297 | ||||||||
\(103\) | −8.81068 | −0.868143 | −0.434071 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434071 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(104\) | −63.7585 | −6.25203 | ||||||||
\(105\) | 3.32508 | 0.324495 | ||||||||
\(106\) | −3.98133 | −0.386701 | ||||||||
\(107\) | 13.0834 | 1.26482 | 0.632411 | − | 0.774633i | \(-0.282065\pi\) | ||||
0.632411 | + | 0.774633i | \(0.282065\pi\) | |||||||
\(108\) | 5.95730 | 0.573241 | ||||||||
\(109\) | 10.8167 | 1.03605 | 0.518025 | − | 0.855365i | \(-0.326667\pi\) | ||||
0.518025 | + | 0.855365i | \(0.326667\pi\) | |||||||
\(110\) | −19.9827 | −1.90528 | ||||||||
\(111\) | 8.26151 | 0.784148 | ||||||||
\(112\) | 50.5691 | 4.77833 | ||||||||
\(113\) | 19.4323 | 1.82803 | 0.914016 | − | 0.405677i | \(-0.132964\pi\) | ||||
0.914016 | + | 0.405677i | \(0.132964\pi\) | |||||||
\(114\) | −16.1195 | −1.50973 | ||||||||
\(115\) | −4.57161 | −0.426305 | ||||||||
\(116\) | −53.1809 | −4.93772 | ||||||||
\(117\) | 5.71159 | 0.528036 | ||||||||
\(118\) | 5.31289 | 0.489091 | ||||||||
\(119\) | 12.6065 | 1.15563 | ||||||||
\(120\) | −14.3680 | −1.31161 | ||||||||
\(121\) | 19.2912 | 1.75375 | ||||||||
\(122\) | −12.6670 | −1.14682 | ||||||||
\(123\) | −5.39003 | −0.486003 | ||||||||
\(124\) | −46.1499 | −4.14439 | ||||||||
\(125\) | −10.7388 | −0.960506 | ||||||||
\(126\) | −7.28738 | −0.649211 | ||||||||
\(127\) | −3.45101 | −0.306228 | −0.153114 | − | 0.988209i | \(-0.548930\pi\) | ||||
−0.153114 | + | 0.988209i | \(0.548930\pi\) | |||||||
\(128\) | −85.5107 | −7.55815 | ||||||||
\(129\) | −8.03917 | −0.707810 | ||||||||
\(130\) | −20.7374 | −1.81879 | ||||||||
\(131\) | 6.18630 | 0.540500 | 0.270250 | − | 0.962790i | \(-0.412894\pi\) | ||||
0.270250 | + | 0.962790i | \(0.412894\pi\) | |||||||
\(132\) | 32.7874 | 2.85378 | ||||||||
\(133\) | 14.7624 | 1.28006 | ||||||||
\(134\) | 8.78364 | 0.758791 | ||||||||
\(135\) | 1.28710 | 0.110776 | ||||||||
\(136\) | −54.4736 | −4.67107 | ||||||||
\(137\) | −7.63340 | −0.652166 | −0.326083 | − | 0.945341i | \(-0.605729\pi\) | ||||
−0.326083 | + | 0.945341i | \(0.605729\pi\) | |||||||
\(138\) | 10.0193 | 0.852900 | ||||||||
\(139\) | 12.4241 | 1.05379 | 0.526897 | − | 0.849929i | \(-0.323355\pi\) | ||||
0.526897 | + | 0.849929i | \(0.323355\pi\) | |||||||
\(140\) | 19.8085 | 1.67412 | ||||||||
\(141\) | 7.41995 | 0.624872 | ||||||||
\(142\) | −12.4003 | −1.04061 | ||||||||
\(143\) | 31.4351 | 2.62874 | ||||||||
\(144\) | 19.5748 | 1.63123 | ||||||||
\(145\) | −11.4900 | −0.954193 | ||||||||
\(146\) | −14.2153 | −1.17647 | ||||||||
\(147\) | −0.326141 | −0.0268997 | ||||||||
\(148\) | 49.2162 | 4.04555 | ||||||||
\(149\) | −8.42534 | −0.690231 | −0.345115 | − | 0.938560i | \(-0.612160\pi\) | ||||
−0.345115 | + | 0.938560i | \(0.612160\pi\) | |||||||
\(150\) | 9.43118 | 0.770053 | ||||||||
\(151\) | −11.2229 | −0.913305 | −0.456652 | − | 0.889645i | \(-0.650952\pi\) | ||||
−0.456652 | + | 0.889645i | \(0.650952\pi\) | |||||||
\(152\) | −63.7896 | −5.17402 | ||||||||
\(153\) | 4.87983 | 0.394511 | ||||||||
\(154\) | −40.1079 | −3.23198 | ||||||||
\(155\) | −9.97094 | −0.800885 | ||||||||
\(156\) | 34.0256 | 2.72423 | ||||||||
\(157\) | −3.06391 | −0.244527 | −0.122263 | − | 0.992498i | \(-0.539015\pi\) | ||||
−0.122263 | + | 0.992498i | \(0.539015\pi\) | |||||||
\(158\) | −48.6693 | −3.87193 | ||||||||
\(159\) | 1.41138 | 0.111930 | ||||||||
\(160\) | −42.3353 | −3.34690 | ||||||||
\(161\) | −9.17579 | −0.723154 | ||||||||
\(162\) | −2.82087 | −0.221628 | ||||||||
\(163\) | −2.33880 | −0.183189 | −0.0915944 | − | 0.995796i | \(-0.529196\pi\) | ||||
−0.0915944 | + | 0.995796i | \(0.529196\pi\) | |||||||
\(164\) | −32.1100 | −2.50737 | ||||||||
\(165\) | 7.08390 | 0.551481 | ||||||||
\(166\) | 24.1371 | 1.87340 | ||||||||
\(167\) | −15.7238 | −1.21674 | −0.608372 | − | 0.793652i | \(-0.708177\pi\) | ||||
−0.608372 | + | 0.793652i | \(0.708177\pi\) | |||||||
\(168\) | −28.8383 | −2.22492 | ||||||||
\(169\) | 19.6222 | 1.50940 | ||||||||
\(170\) | −17.7175 | −1.35887 | ||||||||
\(171\) | 5.71437 | 0.436989 | ||||||||
\(172\) | −47.8917 | −3.65171 | ||||||||
\(173\) | −1.27131 | −0.0966557 | −0.0483279 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483279 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(174\) | 25.1819 | 1.90904 | ||||||||
\(175\) | −8.63718 | −0.652909 | ||||||||
\(176\) | 107.735 | 8.12080 | ||||||||
\(177\) | −1.88343 | −0.141567 | ||||||||
\(178\) | 34.3121 | 2.57180 | ||||||||
\(179\) | 26.0073 | 1.94388 | 0.971938 | − | 0.235239i | \(-0.0755872\pi\) | ||||
0.971938 | + | 0.235239i | \(0.0755872\pi\) | |||||||
\(180\) | 7.66766 | 0.571514 | ||||||||
\(181\) | 3.15225 | 0.234305 | 0.117153 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117153 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(182\) | −41.6225 | −3.08526 | ||||||||
\(183\) | 4.49047 | 0.331945 | ||||||||
\(184\) | 39.6494 | 2.92299 | ||||||||
\(185\) | 10.6334 | 0.781785 | ||||||||
\(186\) | 21.8527 | 1.60232 | ||||||||
\(187\) | 26.8573 | 1.96400 | ||||||||
\(188\) | 44.2028 | 3.22382 | ||||||||
\(189\) | 2.58338 | 0.187913 | ||||||||
\(190\) | −20.7475 | −1.50518 | ||||||||
\(191\) | −14.0165 | −1.01420 | −0.507099 | − | 0.861888i | \(-0.669282\pi\) | ||||
−0.507099 | + | 0.861888i | \(0.669282\pi\) | |||||||
\(192\) | 53.6340 | 3.87070 | ||||||||
\(193\) | −3.72039 | −0.267800 | −0.133900 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133900 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(194\) | 2.11033 | 0.151513 | ||||||||
\(195\) | 7.35141 | 0.526445 | ||||||||
\(196\) | −1.94292 | −0.138780 | ||||||||
\(197\) | 16.7597 | 1.19408 | 0.597039 | − | 0.802212i | \(-0.296344\pi\) | ||||
0.597039 | + | 0.802212i | \(0.296344\pi\) | |||||||
\(198\) | −15.5253 | −1.10334 | ||||||||
\(199\) | 14.6221 | 1.03653 | 0.518267 | − | 0.855219i | \(-0.326577\pi\) | ||||
0.518267 | + | 0.855219i | \(0.326577\pi\) | |||||||
\(200\) | 37.3220 | 2.63906 | ||||||||
\(201\) | −3.11381 | −0.219631 | ||||||||
\(202\) | 0.496970 | 0.0349667 | ||||||||
\(203\) | −23.0619 | −1.61863 | ||||||||
\(204\) | 29.0706 | 2.03535 | ||||||||
\(205\) | −6.93754 | −0.484539 | ||||||||
\(206\) | 24.8538 | 1.73164 | ||||||||
\(207\) | −3.55185 | −0.246871 | ||||||||
\(208\) | 111.803 | 7.75214 | ||||||||
\(209\) | 31.4505 | 2.17547 | ||||||||
\(210\) | −9.37962 | −0.647255 | ||||||||
\(211\) | −18.1465 | −1.24925 | −0.624627 | − | 0.780923i | \(-0.714749\pi\) | ||||
−0.624627 | + | 0.780923i | \(0.714749\pi\) | |||||||
\(212\) | 8.40804 | 0.577466 | ||||||||
\(213\) | 4.39590 | 0.301202 | ||||||||
\(214\) | −36.9066 | −2.52288 | ||||||||
\(215\) | −10.3473 | −0.705677 | ||||||||
\(216\) | −11.1630 | −0.759546 | ||||||||
\(217\) | −20.0129 | −1.35857 | ||||||||
\(218\) | −30.5125 | −2.06656 | ||||||||
\(219\) | 5.03934 | 0.340527 | ||||||||
\(220\) | 42.2009 | 2.84518 | ||||||||
\(221\) | 27.8716 | 1.87484 | ||||||||
\(222\) | −23.3046 | −1.56410 | ||||||||
\(223\) | −12.0369 | −0.806050 | −0.403025 | − | 0.915189i | \(-0.632041\pi\) | ||||
−0.403025 | + | 0.915189i | \(0.632041\pi\) | |||||||
\(224\) | −84.9722 | −5.67744 | ||||||||
\(225\) | −3.34336 | −0.222891 | ||||||||
\(226\) | −54.8158 | −3.64629 | ||||||||
\(227\) | 21.6411 | 1.43637 | 0.718184 | − | 0.695853i | \(-0.244973\pi\) | ||||
0.718184 | + | 0.695853i | \(0.244973\pi\) | |||||||
\(228\) | 34.0422 | 2.25450 | ||||||||
\(229\) | 0.382159 | 0.0252538 | 0.0126269 | − | 0.999920i | \(-0.495981\pi\) | ||||
0.0126269 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(230\) | 12.8959 | 0.850330 | ||||||||
\(231\) | 14.2183 | 0.935494 | ||||||||
\(232\) | 99.6523 | 6.54250 | ||||||||
\(233\) | −23.4617 | −1.53703 | −0.768513 | − | 0.639834i | \(-0.779003\pi\) | ||||
−0.768513 | + | 0.639834i | \(0.779003\pi\) | |||||||
\(234\) | −16.1116 | −1.05325 | ||||||||
\(235\) | 9.55025 | 0.622990 | ||||||||
\(236\) | −11.2201 | −0.730368 | ||||||||
\(237\) | 17.2533 | 1.12072 | ||||||||
\(238\) | −35.5612 | −2.30509 | ||||||||
\(239\) | 7.62569 | 0.493265 | 0.246633 | − | 0.969109i | \(-0.420676\pi\) | ||||
0.246633 | + | 0.969109i | \(0.420676\pi\) | |||||||
\(240\) | 25.1948 | 1.62632 | ||||||||
\(241\) | −13.1669 | −0.848152 | −0.424076 | − | 0.905627i | \(-0.639401\pi\) | ||||
−0.424076 | + | 0.905627i | \(0.639401\pi\) | |||||||
\(242\) | −54.4179 | −3.49812 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 26.7511 | 1.71256 | ||||||||
\(245\) | −0.419778 | −0.0268186 | ||||||||
\(246\) | 15.2046 | 0.969408 | ||||||||
\(247\) | 32.6381 | 2.07671 | ||||||||
\(248\) | 86.4775 | 5.49133 | ||||||||
\(249\) | −8.55662 | −0.542254 | ||||||||
\(250\) | 30.2927 | 1.91588 | ||||||||
\(251\) | 9.18538 | 0.579776 | 0.289888 | − | 0.957061i | \(-0.406382\pi\) | ||||
0.289888 | + | 0.957061i | \(0.406382\pi\) | |||||||
\(252\) | 15.3900 | 0.969477 | ||||||||
\(253\) | −19.5485 | −1.22900 | ||||||||
\(254\) | 9.73485 | 0.610819 | ||||||||
\(255\) | 6.28085 | 0.393322 | ||||||||
\(256\) | 133.946 | 8.37165 | ||||||||
\(257\) | −18.4091 | −1.14833 | −0.574164 | − | 0.818740i | \(-0.694673\pi\) | ||||
−0.574164 | + | 0.818740i | \(0.694673\pi\) | |||||||
\(258\) | 22.6774 | 1.41184 | ||||||||
\(259\) | 21.3426 | 1.32617 | ||||||||
\(260\) | 43.7945 | 2.71602 | ||||||||
\(261\) | −8.92701 | −0.552568 | ||||||||
\(262\) | −17.4507 | −1.07811 | ||||||||
\(263\) | −28.5947 | −1.76322 | −0.881611 | − | 0.471976i | \(-0.843541\pi\) | ||||
−0.881611 | + | 0.471976i | \(0.843541\pi\) | |||||||
\(264\) | −61.4383 | −3.78127 | ||||||||
\(265\) | 1.81660 | 0.111593 | ||||||||
\(266\) | −41.6428 | −2.55328 | ||||||||
\(267\) | −12.1637 | −0.744403 | ||||||||
\(268\) | −18.5499 | −1.13311 | ||||||||
\(269\) | −7.31009 | −0.445704 | −0.222852 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222852 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(270\) | −3.63075 | −0.220961 | ||||||||
\(271\) | 3.50290 | 0.212786 | 0.106393 | − | 0.994324i | \(-0.466070\pi\) | ||||
0.106393 | + | 0.994324i | \(0.466070\pi\) | |||||||
\(272\) | 95.5216 | 5.79185 | ||||||||
\(273\) | 14.7552 | 0.893025 | ||||||||
\(274\) | 21.5328 | 1.30085 | ||||||||
\(275\) | −18.4010 | −1.10962 | ||||||||
\(276\) | −21.1594 | −1.27365 | ||||||||
\(277\) | −1.50911 | −0.0906738 | −0.0453369 | − | 0.998972i | \(-0.514436\pi\) | ||||
−0.0453369 | + | 0.998972i | \(0.514436\pi\) | |||||||
\(278\) | −35.0466 | −2.10196 | ||||||||
\(279\) | −7.74680 | −0.463788 | ||||||||
\(280\) | −37.1179 | −2.21822 | ||||||||
\(281\) | 17.4136 | 1.03881 | 0.519405 | − | 0.854528i | \(-0.326154\pi\) | ||||
0.519405 | + | 0.854528i | \(0.326154\pi\) | |||||||
\(282\) | −20.9307 | −1.24640 | ||||||||
\(283\) | −17.7691 | −1.05627 | −0.528133 | − | 0.849162i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849162i | \(0.677108\pi\) | |||||||
\(284\) | 26.1877 | 1.55395 | ||||||||
\(285\) | 7.35500 | 0.435672 | ||||||||
\(286\) | −88.6743 | −5.24342 | ||||||||
\(287\) | −13.9245 | −0.821938 | ||||||||
\(288\) | −32.8918 | −1.93817 | ||||||||
\(289\) | 6.81275 | 0.400750 | ||||||||
\(290\) | 32.4118 | 1.90329 | ||||||||
\(291\) | −0.748112 | −0.0438551 | ||||||||
\(292\) | 30.0208 | 1.75684 | ||||||||
\(293\) | −15.8907 | −0.928346 | −0.464173 | − | 0.885745i | \(-0.653648\pi\) | ||||
−0.464173 | + | 0.885745i | \(0.653648\pi\) | |||||||
\(294\) | 0.920002 | 0.0536556 | ||||||||
\(295\) | −2.42417 | −0.141140 | ||||||||
\(296\) | −92.2233 | −5.36037 | ||||||||
\(297\) | 5.50374 | 0.319360 | ||||||||
\(298\) | 23.7668 | 1.37677 | ||||||||
\(299\) | −20.2867 | −1.17321 | ||||||||
\(300\) | −19.9174 | −1.14993 | ||||||||
\(301\) | −20.7682 | −1.19706 | ||||||||
\(302\) | 31.6583 | 1.82173 | ||||||||
\(303\) | −0.176176 | −0.0101211 | ||||||||
\(304\) | 111.858 | 6.41547 | ||||||||
\(305\) | 5.77971 | 0.330945 | ||||||||
\(306\) | −13.7654 | −0.786913 | ||||||||
\(307\) | −28.3786 | −1.61965 | −0.809825 | − | 0.586672i | \(-0.800438\pi\) | ||||
−0.809825 | + | 0.586672i | \(0.800438\pi\) | |||||||
\(308\) | 84.7024 | 4.82637 | ||||||||
\(309\) | −8.81068 | −0.501222 | ||||||||
\(310\) | 28.1267 | 1.59749 | ||||||||
\(311\) | −12.8537 | −0.728869 | −0.364435 | − | 0.931229i | \(-0.618738\pi\) | ||||
−0.364435 | + | 0.931229i | \(0.618738\pi\) | |||||||
\(312\) | −63.7585 | −3.60961 | ||||||||
\(313\) | 26.4270 | 1.49374 | 0.746872 | − | 0.664967i | \(-0.231555\pi\) | ||||
0.746872 | + | 0.664967i | \(0.231555\pi\) | |||||||
\(314\) | 8.64288 | 0.487746 | ||||||||
\(315\) | 3.32508 | 0.187347 | ||||||||
\(316\) | 102.783 | 5.78200 | ||||||||
\(317\) | −24.0540 | −1.35101 | −0.675503 | − | 0.737357i | \(-0.736074\pi\) | ||||
−0.675503 | + | 0.737357i | \(0.736074\pi\) | |||||||
\(318\) | −3.98133 | −0.223262 | ||||||||
\(319\) | −49.1320 | −2.75086 | ||||||||
\(320\) | 69.0326 | 3.85904 | ||||||||
\(321\) | 13.0834 | 0.730246 | ||||||||
\(322\) | 25.8837 | 1.44244 | ||||||||
\(323\) | 27.8852 | 1.55157 | ||||||||
\(324\) | 5.95730 | 0.330961 | ||||||||
\(325\) | −19.0959 | −1.05925 | ||||||||
\(326\) | 6.59744 | 0.365398 | ||||||||
\(327\) | 10.8167 | 0.598164 | ||||||||
\(328\) | 60.1690 | 3.32228 | ||||||||
\(329\) | 19.1686 | 1.05680 | ||||||||
\(330\) | −19.9827 | −1.10001 | ||||||||
\(331\) | 11.7313 | 0.644811 | 0.322405 | − | 0.946602i | \(-0.395509\pi\) | ||||
0.322405 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(332\) | −50.9743 | −2.79758 | ||||||||
\(333\) | 8.26151 | 0.452728 | ||||||||
\(334\) | 44.3547 | 2.42698 | ||||||||
\(335\) | −4.00780 | −0.218969 | ||||||||
\(336\) | 50.5691 | 2.75877 | ||||||||
\(337\) | −8.12339 | −0.442509 | −0.221255 | − | 0.975216i | \(-0.571015\pi\) | ||||
−0.221255 | + | 0.975216i | \(0.571015\pi\) | |||||||
\(338\) | −55.3516 | −3.01073 | ||||||||
\(339\) | 19.4323 | 1.05542 | ||||||||
\(340\) | 37.4169 | 2.02922 | ||||||||
\(341\) | −42.6364 | −2.30889 | ||||||||
\(342\) | −16.1195 | −0.871642 | ||||||||
\(343\) | −18.9262 | −1.02192 | ||||||||
\(344\) | 89.7413 | 4.83853 | ||||||||
\(345\) | −4.57161 | −0.246127 | ||||||||
\(346\) | 3.58619 | 0.192795 | ||||||||
\(347\) | 13.7414 | 0.737678 | 0.368839 | − | 0.929493i | \(-0.379755\pi\) | ||||
0.368839 | + | 0.929493i | \(0.379755\pi\) | |||||||
\(348\) | −53.1809 | −2.85079 | ||||||||
\(349\) | 22.7269 | 1.21654 | 0.608271 | − | 0.793729i | \(-0.291863\pi\) | ||||
0.608271 | + | 0.793729i | \(0.291863\pi\) | |||||||
\(350\) | 24.3643 | 1.30233 | ||||||||
\(351\) | 5.71159 | 0.304862 | ||||||||
\(352\) | −181.028 | −9.64884 | ||||||||
\(353\) | 4.28109 | 0.227859 | 0.113930 | − | 0.993489i | \(-0.463656\pi\) | ||||
0.113930 | + | 0.993489i | \(0.463656\pi\) | |||||||
\(354\) | 5.31289 | 0.282377 | ||||||||
\(355\) | 5.65799 | 0.300295 | ||||||||
\(356\) | −72.4625 | −3.84050 | ||||||||
\(357\) | 12.6065 | 0.667205 | ||||||||
\(358\) | −73.3631 | −3.87736 | ||||||||
\(359\) | 27.7077 | 1.46236 | 0.731178 | − | 0.682186i | \(-0.238971\pi\) | ||||
0.731178 | + | 0.682186i | \(0.238971\pi\) | |||||||
\(360\) | −14.3680 | −0.757258 | ||||||||
\(361\) | 13.6541 | 0.718635 | ||||||||
\(362\) | −8.89209 | −0.467358 | ||||||||
\(363\) | 19.2912 | 1.01253 | ||||||||
\(364\) | 87.9011 | 4.60727 | ||||||||
\(365\) | 6.48616 | 0.339501 | ||||||||
\(366\) | −12.6670 | −0.662116 | ||||||||
\(367\) | 4.00823 | 0.209228 | 0.104614 | − | 0.994513i | \(-0.466639\pi\) | ||||
0.104614 | + | 0.994513i | \(0.466639\pi\) | |||||||
\(368\) | −69.5267 | −3.62433 | ||||||||
\(369\) | −5.39003 | −0.280594 | ||||||||
\(370\) | −29.9955 | −1.55939 | ||||||||
\(371\) | 3.64615 | 0.189298 | ||||||||
\(372\) | −46.1499 | −2.39276 | ||||||||
\(373\) | −33.8094 | −1.75059 | −0.875293 | − | 0.483593i | \(-0.839332\pi\) | ||||
−0.875293 | + | 0.483593i | \(0.839332\pi\) | |||||||
\(374\) | −75.7610 | −3.91751 | ||||||||
\(375\) | −10.7388 | −0.554548 | ||||||||
\(376\) | −82.8289 | −4.27158 | ||||||||
\(377\) | −50.9874 | −2.62598 | ||||||||
\(378\) | −7.28738 | −0.374822 | ||||||||
\(379\) | −9.95169 | −0.511184 | −0.255592 | − | 0.966785i | \(-0.582270\pi\) | ||||
−0.255592 | + | 0.966785i | \(0.582270\pi\) | |||||||
\(380\) | 43.8159 | 2.24771 | ||||||||
\(381\) | −3.45101 | −0.176801 | ||||||||
\(382\) | 39.5387 | 2.02298 | ||||||||
\(383\) | −33.6597 | −1.71993 | −0.859965 | − | 0.510354i | \(-0.829515\pi\) | ||||
−0.859965 | + | 0.510354i | \(0.829515\pi\) | |||||||
\(384\) | −85.5107 | −4.36370 | ||||||||
\(385\) | 18.3004 | 0.932675 | ||||||||
\(386\) | 10.4947 | 0.534168 | ||||||||
\(387\) | −8.03917 | −0.408654 | ||||||||
\(388\) | −4.45673 | −0.226256 | ||||||||
\(389\) | 16.1923 | 0.820980 | 0.410490 | − | 0.911865i | \(-0.365358\pi\) | ||||
0.410490 | + | 0.911865i | \(0.365358\pi\) | |||||||
\(390\) | −20.7374 | −1.05008 | ||||||||
\(391\) | −17.3324 | −0.876539 | ||||||||
\(392\) | 3.64072 | 0.183884 | ||||||||
\(393\) | 6.18630 | 0.312058 | ||||||||
\(394\) | −47.2768 | −2.38177 | ||||||||
\(395\) | 22.2068 | 1.11735 | ||||||||
\(396\) | 32.7874 | 1.64763 | ||||||||
\(397\) | 25.1385 | 1.26166 | 0.630832 | − | 0.775920i | \(-0.282714\pi\) | ||||
0.630832 | + | 0.775920i | \(0.282714\pi\) | |||||||
\(398\) | −41.2470 | −2.06753 | ||||||||
\(399\) | 14.7624 | 0.739045 | ||||||||
\(400\) | −65.4455 | −3.27228 | ||||||||
\(401\) | −8.75459 | −0.437184 | −0.218592 | − | 0.975816i | \(-0.570146\pi\) | ||||
−0.218592 | + | 0.975816i | \(0.570146\pi\) | |||||||
\(402\) | 8.78364 | 0.438088 | ||||||||
\(403\) | −44.2465 | −2.20407 | ||||||||
\(404\) | −1.04953 | −0.0522162 | ||||||||
\(405\) | 1.28710 | 0.0639568 | ||||||||
\(406\) | 65.0545 | 3.22860 | ||||||||
\(407\) | 45.4692 | 2.25383 | ||||||||
\(408\) | −54.4736 | −2.69684 | ||||||||
\(409\) | −5.87867 | −0.290682 | −0.145341 | − | 0.989382i | \(-0.546428\pi\) | ||||
−0.145341 | + | 0.989382i | \(0.546428\pi\) | |||||||
\(410\) | 19.5699 | 0.966487 | ||||||||
\(411\) | −7.63340 | −0.376528 | ||||||||
\(412\) | −52.4878 | −2.58589 | ||||||||
\(413\) | −4.86561 | −0.239421 | ||||||||
\(414\) | 10.0193 | 0.492422 | ||||||||
\(415\) | −11.0133 | −0.540620 | ||||||||
\(416\) | −187.865 | −9.21082 | ||||||||
\(417\) | 12.4241 | 0.608409 | ||||||||
\(418\) | −88.7176 | −4.33932 | ||||||||
\(419\) | −7.24945 | −0.354159 | −0.177079 | − | 0.984197i | \(-0.556665\pi\) | ||||
−0.177079 | + | 0.984197i | \(0.556665\pi\) | |||||||
\(420\) | 19.8085 | 0.966556 | ||||||||
\(421\) | 36.9107 | 1.79892 | 0.899459 | − | 0.437005i | \(-0.143961\pi\) | ||||
0.899459 | + | 0.437005i | \(0.143961\pi\) | |||||||
\(422\) | 51.1888 | 2.49183 | ||||||||
\(423\) | 7.41995 | 0.360770 | ||||||||
\(424\) | −15.7553 | −0.765145 | ||||||||
\(425\) | −16.3150 | −0.791395 | ||||||||
\(426\) | −12.4003 | −0.600794 | ||||||||
\(427\) | 11.6006 | 0.561393 | ||||||||
\(428\) | 77.9418 | 3.76746 | ||||||||
\(429\) | 31.4351 | 1.51770 | ||||||||
\(430\) | 29.1882 | 1.40758 | ||||||||
\(431\) | 28.2983 | 1.36308 | 0.681540 | − | 0.731781i | \(-0.261311\pi\) | ||||
0.681540 | + | 0.731781i | \(0.261311\pi\) | |||||||
\(432\) | 19.5748 | 0.941792 | ||||||||
\(433\) | 21.7269 | 1.04413 | 0.522065 | − | 0.852906i | \(-0.325162\pi\) | ||||
0.522065 | + | 0.852906i | \(0.325162\pi\) | |||||||
\(434\) | 56.4538 | 2.70987 | ||||||||
\(435\) | −11.4900 | −0.550904 | ||||||||
\(436\) | 64.4382 | 3.08603 | ||||||||
\(437\) | −20.2966 | −0.970919 | ||||||||
\(438\) | −14.2153 | −0.679233 | ||||||||
\(439\) | −12.1015 | −0.577574 | −0.288787 | − | 0.957393i | \(-0.593252\pi\) | ||||
−0.288787 | + | 0.957393i | \(0.593252\pi\) | |||||||
\(440\) | −79.0776 | −3.76988 | ||||||||
\(441\) | −0.326141 | −0.0155305 | ||||||||
\(442\) | −78.6220 | −3.73967 | ||||||||
\(443\) | 11.0435 | 0.524694 | 0.262347 | − | 0.964974i | \(-0.415504\pi\) | ||||
0.262347 | + | 0.964974i | \(0.415504\pi\) | |||||||
\(444\) | 49.2162 | 2.33570 | ||||||||
\(445\) | −15.6559 | −0.742161 | ||||||||
\(446\) | 33.9545 | 1.60779 | ||||||||
\(447\) | −8.42534 | −0.398505 | ||||||||
\(448\) | 138.557 | 6.54621 | ||||||||
\(449\) | 6.23074 | 0.294047 | 0.147023 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147023 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(450\) | 9.43118 | 0.444590 | ||||||||
\(451\) | −29.6654 | −1.39689 | ||||||||
\(452\) | 115.764 | 5.44507 | ||||||||
\(453\) | −11.2229 | −0.527297 | ||||||||
\(454\) | −61.0466 | −2.86506 | ||||||||
\(455\) | 18.9915 | 0.890335 | ||||||||
\(456\) | −63.7896 | −2.98722 | ||||||||
\(457\) | −21.6536 | −1.01291 | −0.506455 | − | 0.862266i | \(-0.669044\pi\) | ||||
−0.506455 | + | 0.862266i | \(0.669044\pi\) | |||||||
\(458\) | −1.07802 | −0.0503726 | ||||||||
\(459\) | 4.87983 | 0.227771 | ||||||||
\(460\) | −27.2344 | −1.26981 | ||||||||
\(461\) | 39.4092 | 1.83547 | 0.917735 | − | 0.397193i | \(-0.130016\pi\) | ||||
0.917735 | + | 0.397193i | \(0.130016\pi\) | |||||||
\(462\) | −40.1079 | −1.86599 | ||||||||
\(463\) | 21.3620 | 0.992776 | 0.496388 | − | 0.868101i | \(-0.334659\pi\) | ||||
0.496388 | + | 0.868101i | \(0.334659\pi\) | |||||||
\(464\) | −174.744 | −8.11230 | ||||||||
\(465\) | −9.97094 | −0.462391 | ||||||||
\(466\) | 66.1823 | 3.06584 | ||||||||
\(467\) | 20.9324 | 0.968636 | 0.484318 | − | 0.874892i | \(-0.339068\pi\) | ||||
0.484318 | + | 0.874892i | \(0.339068\pi\) | |||||||
\(468\) | 34.0256 | 1.57283 | ||||||||
\(469\) | −8.04416 | −0.371445 | ||||||||
\(470\) | −26.9400 | −1.24265 | ||||||||
\(471\) | −3.06391 | −0.141177 | ||||||||
\(472\) | 21.0247 | 0.967740 | ||||||||
\(473\) | −44.2456 | −2.03441 | ||||||||
\(474\) | −48.6693 | −2.23546 | ||||||||
\(475\) | −19.1052 | −0.876607 | ||||||||
\(476\) | 75.1004 | 3.44222 | ||||||||
\(477\) | 1.41138 | 0.0646229 | ||||||||
\(478\) | −21.5111 | −0.983894 | ||||||||
\(479\) | 10.9268 | 0.499259 | 0.249629 | − | 0.968341i | \(-0.419691\pi\) | ||||
0.249629 | + | 0.968341i | \(0.419691\pi\) | |||||||
\(480\) | −42.3353 | −1.93233 | ||||||||
\(481\) | 47.1863 | 2.15151 | ||||||||
\(482\) | 37.1420 | 1.69177 | ||||||||
\(483\) | −9.17579 | −0.417513 | ||||||||
\(484\) | 114.923 | 5.22379 | ||||||||
\(485\) | −0.962899 | −0.0437230 | ||||||||
\(486\) | −2.82087 | −0.127957 | ||||||||
\(487\) | −9.62579 | −0.436186 | −0.218093 | − | 0.975928i | \(-0.569984\pi\) | ||||
−0.218093 | + | 0.975928i | \(0.569984\pi\) | |||||||
\(488\) | −50.1272 | −2.26915 | ||||||||
\(489\) | −2.33880 | −0.105764 | ||||||||
\(490\) | 1.18414 | 0.0534939 | ||||||||
\(491\) | −8.64578 | −0.390179 | −0.195089 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195089 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(492\) | −32.1100 | −1.44763 | ||||||||
\(493\) | −43.5623 | −1.96195 | ||||||||
\(494\) | −92.0679 | −4.14233 | ||||||||
\(495\) | 7.08390 | 0.318397 | ||||||||
\(496\) | −151.642 | −6.80892 | ||||||||
\(497\) | 11.3563 | 0.509399 | ||||||||
\(498\) | 24.1371 | 1.08161 | ||||||||
\(499\) | 12.4016 | 0.555171 | 0.277585 | − | 0.960701i | \(-0.410466\pi\) | ||||
0.277585 | + | 0.960701i | \(0.410466\pi\) | |||||||
\(500\) | −63.9741 | −2.86101 | ||||||||
\(501\) | −15.7238 | −0.702487 | ||||||||
\(502\) | −25.9108 | −1.15645 | ||||||||
\(503\) | 13.2869 | 0.592432 | 0.296216 | − | 0.955121i | \(-0.404275\pi\) | ||||
0.296216 | + | 0.955121i | \(0.404275\pi\) | |||||||
\(504\) | −28.8383 | −1.28456 | ||||||||
\(505\) | −0.226757 | −0.0100906 | ||||||||
\(506\) | 55.1437 | 2.45144 | ||||||||
\(507\) | 19.6222 | 0.871453 | ||||||||
\(508\) | −20.5587 | −0.912145 | ||||||||
\(509\) | 11.9148 | 0.528116 | 0.264058 | − | 0.964507i | \(-0.414939\pi\) | ||||
0.264058 | + | 0.964507i | \(0.414939\pi\) | |||||||
\(510\) | −17.7175 | −0.784542 | ||||||||
\(511\) | 13.0185 | 0.575906 | ||||||||
\(512\) | −206.824 | −9.14041 | ||||||||
\(513\) | 5.71437 | 0.252296 | ||||||||
\(514\) | 51.9297 | 2.29052 | ||||||||
\(515\) | −11.3403 | −0.499712 | ||||||||
\(516\) | −47.8917 | −2.10832 | ||||||||
\(517\) | 40.8375 | 1.79603 | ||||||||
\(518\) | −60.2047 | −2.64524 | ||||||||
\(519\) | −1.27131 | −0.0558042 | ||||||||
\(520\) | −82.0638 | −3.59874 | ||||||||
\(521\) | −32.6972 | −1.43249 | −0.716246 | − | 0.697848i | \(-0.754141\pi\) | ||||
−0.716246 | + | 0.697848i | \(0.754141\pi\) | |||||||
\(522\) | 25.1819 | 1.10218 | ||||||||
\(523\) | −25.9663 | −1.13543 | −0.567715 | − | 0.823225i | \(-0.692172\pi\) | ||||
−0.567715 | + | 0.823225i | \(0.692172\pi\) | |||||||
\(524\) | 36.8536 | 1.60996 | ||||||||
\(525\) | −8.63718 | −0.376957 | ||||||||
\(526\) | 80.6618 | 3.51702 | ||||||||
\(527\) | −37.8030 | −1.64673 | ||||||||
\(528\) | 107.735 | 4.68855 | ||||||||
\(529\) | −10.3843 | −0.451493 | ||||||||
\(530\) | −5.12439 | −0.222589 | ||||||||
\(531\) | −1.88343 | −0.0817337 | ||||||||
\(532\) | 87.9440 | 3.81286 | ||||||||
\(533\) | −30.7856 | −1.33347 | ||||||||
\(534\) | 34.3121 | 1.48483 | ||||||||
\(535\) | 16.8397 | 0.728046 | ||||||||
\(536\) | 34.7595 | 1.50138 | ||||||||
\(537\) | 26.0073 | 1.12230 | ||||||||
\(538\) | 20.6208 | 0.889025 | ||||||||
\(539\) | −1.79500 | −0.0773161 | ||||||||
\(540\) | 7.66766 | 0.329964 | ||||||||
\(541\) | 20.8169 | 0.894990 | 0.447495 | − | 0.894286i | \(-0.352316\pi\) | ||||
0.447495 | + | 0.894286i | \(0.352316\pi\) | |||||||
\(542\) | −9.88121 | −0.424434 | ||||||||
\(543\) | 3.15225 | 0.135276 | ||||||||
\(544\) | −160.507 | −6.88166 | ||||||||
\(545\) | 13.9222 | 0.596362 | ||||||||
\(546\) | −41.6225 | −1.78128 | ||||||||
\(547\) | 25.3777 | 1.08507 | 0.542536 | − | 0.840032i | \(-0.317464\pi\) | ||||
0.542536 | + | 0.840032i | \(0.317464\pi\) | |||||||
\(548\) | −45.4744 | −1.94257 | ||||||||
\(549\) | 4.49047 | 0.191649 | ||||||||
\(550\) | 51.9068 | 2.21331 | ||||||||
\(551\) | −51.0123 | −2.17320 | ||||||||
\(552\) | 39.6494 | 1.68759 | ||||||||
\(553\) | 44.5719 | 1.89539 | ||||||||
\(554\) | 4.25701 | 0.180863 | ||||||||
\(555\) | 10.6334 | 0.451364 | ||||||||
\(556\) | 74.0138 | 3.13888 | ||||||||
\(557\) | −30.3107 | −1.28431 | −0.642153 | − | 0.766576i | \(-0.721959\pi\) | ||||
−0.642153 | + | 0.766576i | \(0.721959\pi\) | |||||||
\(558\) | 21.8527 | 0.925098 | ||||||||
\(559\) | −45.9164 | −1.94206 | ||||||||
\(560\) | 65.0877 | 2.75046 | ||||||||
\(561\) | 26.8573 | 1.13392 | ||||||||
\(562\) | −49.1215 | −2.07207 | ||||||||
\(563\) | −18.6293 | −0.785132 | −0.392566 | − | 0.919724i | \(-0.628413\pi\) | ||||
−0.392566 | + | 0.919724i | \(0.628413\pi\) | |||||||
\(564\) | 44.2028 | 1.86127 | ||||||||
\(565\) | 25.0113 | 1.05224 | ||||||||
\(566\) | 50.1244 | 2.10688 | ||||||||
\(567\) | 2.58338 | 0.108492 | ||||||||
\(568\) | −49.0715 | −2.05899 | ||||||||
\(569\) | 27.6394 | 1.15870 | 0.579352 | − | 0.815078i | \(-0.303306\pi\) | ||||
0.579352 | + | 0.815078i | \(0.303306\pi\) | |||||||
\(570\) | −20.7475 | −0.869016 | ||||||||
\(571\) | −19.6999 | −0.824417 | −0.412208 | − | 0.911090i | \(-0.635242\pi\) | ||||
−0.412208 | + | 0.911090i | \(0.635242\pi\) | |||||||
\(572\) | 187.268 | 7.83008 | ||||||||
\(573\) | −14.0165 | −0.585548 | ||||||||
\(574\) | 39.2792 | 1.63948 | ||||||||
\(575\) | 11.8751 | 0.495227 | ||||||||
\(576\) | 53.6340 | 2.23475 | ||||||||
\(577\) | 5.90951 | 0.246016 | 0.123008 | − | 0.992406i | \(-0.460746\pi\) | ||||
0.123008 | + | 0.992406i | \(0.460746\pi\) | |||||||
\(578\) | −19.2179 | −0.799358 | ||||||||
\(579\) | −3.72039 | −0.154614 | ||||||||
\(580\) | −68.4493 | −2.84220 | ||||||||
\(581\) | −22.1050 | −0.917071 | ||||||||
\(582\) | 2.11033 | 0.0874758 | ||||||||
\(583\) | 7.76790 | 0.321714 | ||||||||
\(584\) | −56.2542 | −2.32781 | ||||||||
\(585\) | 7.35141 | 0.303943 | ||||||||
\(586\) | 44.8256 | 1.85173 | ||||||||
\(587\) | −1.94760 | −0.0803860 | −0.0401930 | − | 0.999192i | \(-0.512797\pi\) | ||||
−0.0401930 | + | 0.999192i | \(0.512797\pi\) | |||||||
\(588\) | −1.94292 | −0.0801247 | ||||||||
\(589\) | −44.2681 | −1.82403 | ||||||||
\(590\) | 6.83825 | 0.281526 | ||||||||
\(591\) | 16.7597 | 0.689401 | ||||||||
\(592\) | 161.717 | 6.64653 | ||||||||
\(593\) | −18.2732 | −0.750390 | −0.375195 | − | 0.926946i | \(-0.622424\pi\) | ||||
−0.375195 | + | 0.926946i | \(0.622424\pi\) | |||||||
\(594\) | −15.5253 | −0.637012 | ||||||||
\(595\) | 16.2258 | 0.665195 | ||||||||
\(596\) | −50.1922 | −2.05595 | ||||||||
\(597\) | 14.6221 | 0.598443 | ||||||||
\(598\) | 57.2261 | 2.34015 | ||||||||
\(599\) | −29.1238 | −1.18997 | −0.594984 | − | 0.803738i | \(-0.702842\pi\) | ||||
−0.594984 | + | 0.803738i | \(0.702842\pi\) | |||||||
\(600\) | 37.3220 | 1.52366 | ||||||||
\(601\) | −12.9892 | −0.529842 | −0.264921 | − | 0.964270i | \(-0.585346\pi\) | ||||
−0.264921 | + | 0.964270i | \(0.585346\pi\) | |||||||
\(602\) | 58.5845 | 2.38773 | ||||||||
\(603\) | −3.11381 | −0.126804 | ||||||||
\(604\) | −66.8580 | −2.72041 | ||||||||
\(605\) | 24.8298 | 1.00948 | ||||||||
\(606\) | 0.496970 | 0.0201880 | ||||||||
\(607\) | 23.1816 | 0.940911 | 0.470455 | − | 0.882424i | \(-0.344090\pi\) | ||||
0.470455 | + | 0.882424i | \(0.344090\pi\) | |||||||
\(608\) | −187.956 | −7.62263 | ||||||||
\(609\) | −23.0619 | −0.934515 | ||||||||
\(610\) | −16.3038 | −0.660121 | ||||||||
\(611\) | 42.3797 | 1.71450 | ||||||||
\(612\) | 29.0706 | 1.17511 | ||||||||
\(613\) | −28.6397 | −1.15675 | −0.578373 | − | 0.815772i | \(-0.696312\pi\) | ||||
−0.578373 | + | 0.815772i | \(0.696312\pi\) | |||||||
\(614\) | 80.0522 | 3.23064 | ||||||||
\(615\) | −6.93754 | −0.279748 | ||||||||
\(616\) | −158.719 | −6.39496 | ||||||||
\(617\) | −21.5718 | −0.868448 | −0.434224 | − | 0.900805i | \(-0.642977\pi\) | ||||
−0.434224 | + | 0.900805i | \(0.642977\pi\) | |||||||
\(618\) | 24.8538 | 0.999765 | ||||||||
\(619\) | −23.8229 | −0.957521 | −0.478761 | − | 0.877945i | \(-0.658914\pi\) | ||||
−0.478761 | + | 0.877945i | \(0.658914\pi\) | |||||||
\(620\) | −59.3998 | −2.38555 | ||||||||
\(621\) | −3.55185 | −0.142531 | ||||||||
\(622\) | 36.2587 | 1.45384 | ||||||||
\(623\) | −31.4234 | −1.25895 | ||||||||
\(624\) | 111.803 | 4.47570 | ||||||||
\(625\) | 2.89487 | 0.115795 | ||||||||
\(626\) | −74.5472 | −2.97951 | ||||||||
\(627\) | 31.4505 | 1.25601 | ||||||||
\(628\) | −18.2526 | −0.728358 | ||||||||
\(629\) | 40.3148 | 1.60745 | ||||||||
\(630\) | −9.37962 | −0.373693 | ||||||||
\(631\) | −5.22326 | −0.207935 | −0.103967 | − | 0.994581i | \(-0.533154\pi\) | ||||
−0.103967 | + | 0.994581i | \(0.533154\pi\) | |||||||
\(632\) | −192.599 | −7.66118 | ||||||||
\(633\) | −18.1465 | −0.721257 | ||||||||
\(634\) | 67.8531 | 2.69479 | ||||||||
\(635\) | −4.44182 | −0.176268 | ||||||||
\(636\) | 8.40804 | 0.333400 | ||||||||
\(637\) | −1.86278 | −0.0738062 | ||||||||
\(638\) | 138.595 | 5.48702 | ||||||||
\(639\) | 4.39590 | 0.173899 | ||||||||
\(640\) | −110.061 | −4.35055 | ||||||||
\(641\) | −34.6595 | −1.36897 | −0.684484 | − | 0.729028i | \(-0.739972\pi\) | ||||
−0.684484 | + | 0.729028i | \(0.739972\pi\) | |||||||
\(642\) | −36.9066 | −1.45659 | ||||||||
\(643\) | −1.52388 | −0.0600958 | −0.0300479 | − | 0.999548i | \(-0.509566\pi\) | ||||
−0.0300479 | + | 0.999548i | \(0.509566\pi\) | |||||||
\(644\) | −54.6629 | −2.15402 | ||||||||
\(645\) | −10.3473 | −0.407423 | ||||||||
\(646\) | −78.6604 | −3.09485 | ||||||||
\(647\) | 13.7841 | 0.541910 | 0.270955 | − | 0.962592i | \(-0.412661\pi\) | ||||
0.270955 | + | 0.962592i | \(0.412661\pi\) | |||||||
\(648\) | −11.1630 | −0.438524 | ||||||||
\(649\) | −10.3659 | −0.406897 | ||||||||
\(650\) | 53.8670 | 2.11284 | ||||||||
\(651\) | −20.0129 | −0.784368 | ||||||||
\(652\) | −13.9329 | −0.545655 | ||||||||
\(653\) | 42.4086 | 1.65958 | 0.829789 | − | 0.558077i | \(-0.188461\pi\) | ||||
0.829789 | + | 0.558077i | \(0.188461\pi\) | |||||||
\(654\) | −30.5125 | −1.19313 | ||||||||
\(655\) | 7.96242 | 0.311118 | ||||||||
\(656\) | −105.509 | −4.11942 | ||||||||
\(657\) | 5.03934 | 0.196603 | ||||||||
\(658\) | −54.0720 | −2.10794 | ||||||||
\(659\) | 42.1578 | 1.64223 | 0.821117 | − | 0.570760i | \(-0.193351\pi\) | ||||
0.821117 | + | 0.570760i | \(0.193351\pi\) | |||||||
\(660\) | 42.2009 | 1.64267 | ||||||||
\(661\) | −1.19785 | −0.0465909 | −0.0232954 | − | 0.999729i | \(-0.507416\pi\) | ||||
−0.0232954 | + | 0.999729i | \(0.507416\pi\) | |||||||
\(662\) | −33.0925 | −1.28618 | ||||||||
\(663\) | 27.8716 | 1.08244 | ||||||||
\(664\) | 95.5176 | 3.70680 | ||||||||
\(665\) | 19.0008 | 0.736818 | ||||||||
\(666\) | −23.3046 | −0.903036 | ||||||||
\(667\) | 31.7074 | 1.22772 | ||||||||
\(668\) | −93.6712 | −3.62425 | ||||||||
\(669\) | −12.0369 | −0.465373 | ||||||||
\(670\) | 11.3055 | 0.436768 | ||||||||
\(671\) | 24.7144 | 0.954090 | ||||||||
\(672\) | −84.9722 | −3.27787 | ||||||||
\(673\) | 48.3967 | 1.86556 | 0.932779 | − | 0.360450i | \(-0.117377\pi\) | ||||
0.932779 | + | 0.360450i | \(0.117377\pi\) | |||||||
\(674\) | 22.9150 | 0.882653 | ||||||||
\(675\) | −3.34336 | −0.128686 | ||||||||
\(676\) | 116.895 | 4.49597 | ||||||||
\(677\) | −11.9473 | −0.459173 | −0.229586 | − | 0.973288i | \(-0.573737\pi\) | ||||
−0.229586 | + | 0.973288i | \(0.573737\pi\) | |||||||
\(678\) | −54.8158 | −2.10519 | ||||||||
\(679\) | −1.93266 | −0.0741686 | ||||||||
\(680\) | −70.1132 | −2.68872 | ||||||||
\(681\) | 21.6411 | 0.829288 | ||||||||
\(682\) | 120.272 | 4.60544 | ||||||||
\(683\) | −34.8749 | −1.33445 | −0.667225 | − | 0.744857i | \(-0.732518\pi\) | ||||
−0.667225 | + | 0.744857i | \(0.732518\pi\) | |||||||
\(684\) | 34.0422 | 1.30164 | ||||||||
\(685\) | −9.82499 | −0.375393 | ||||||||
\(686\) | 53.3884 | 2.03838 | ||||||||
\(687\) | 0.382159 | 0.0145803 | ||||||||
\(688\) | −157.365 | −5.99949 | ||||||||
\(689\) | 8.06124 | 0.307109 | ||||||||
\(690\) | 12.8959 | 0.490938 | ||||||||
\(691\) | 11.2587 | 0.428302 | 0.214151 | − | 0.976801i | \(-0.431302\pi\) | ||||
0.214151 | + | 0.976801i | \(0.431302\pi\) | |||||||
\(692\) | −7.57355 | −0.287903 | ||||||||
\(693\) | 14.2183 | 0.540107 | ||||||||
\(694\) | −38.7627 | −1.47141 | ||||||||
\(695\) | 15.9911 | 0.606576 | ||||||||
\(696\) | 99.6523 | 3.77731 | ||||||||
\(697\) | −26.3024 | −0.996276 | ||||||||
\(698\) | −64.1096 | −2.42658 | ||||||||
\(699\) | −23.4617 | −0.887402 | ||||||||
\(700\) | −51.4542 | −1.94479 | ||||||||
\(701\) | 13.2909 | 0.501992 | 0.250996 | − | 0.967988i | \(-0.419242\pi\) | ||||
0.250996 | + | 0.967988i | \(0.419242\pi\) | |||||||
\(702\) | −16.1116 | −0.608094 | ||||||||
\(703\) | 47.2093 | 1.78053 | ||||||||
\(704\) | 295.188 | 11.1253 | ||||||||
\(705\) | 9.55025 | 0.359683 | ||||||||
\(706\) | −12.0764 | −0.454501 | ||||||||
\(707\) | −0.455130 | −0.0171169 | ||||||||
\(708\) | −11.2201 | −0.421678 | ||||||||
\(709\) | −16.8315 | −0.632119 | −0.316060 | − | 0.948739i | \(-0.602360\pi\) | ||||
−0.316060 | + | 0.948739i | \(0.602360\pi\) | |||||||
\(710\) | −15.9604 | −0.598984 | ||||||||
\(711\) | 17.2533 | 0.647050 | ||||||||
\(712\) | 135.783 | 5.08868 | ||||||||
\(713\) | 27.5155 | 1.03046 | ||||||||
\(714\) | −35.5612 | −1.33084 | ||||||||
\(715\) | 40.4603 | 1.51313 | ||||||||
\(716\) | 154.933 | 5.79012 | ||||||||
\(717\) | 7.62569 | 0.284787 | ||||||||
\(718\) | −78.1598 | −2.91690 | ||||||||
\(719\) | 4.34534 | 0.162054 | 0.0810269 | − | 0.996712i | \(-0.474180\pi\) | ||||
0.0810269 | + | 0.996712i | \(0.474180\pi\) | |||||||
\(720\) | 25.1948 | 0.938954 | ||||||||
\(721\) | −22.7614 | −0.847677 | ||||||||
\(722\) | −38.5163 | −1.43343 | ||||||||
\(723\) | −13.1669 | −0.489681 | ||||||||
\(724\) | 18.7789 | 0.697913 | ||||||||
\(725\) | 29.8462 | 1.10846 | ||||||||
\(726\) | −54.4179 | −2.01964 | ||||||||
\(727\) | −29.4021 | −1.09046 | −0.545231 | − | 0.838286i | \(-0.683558\pi\) | ||||
−0.545231 | + | 0.838286i | \(0.683558\pi\) | |||||||
\(728\) | −164.712 | −6.10465 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.2966 | −0.677187 | ||||||||
\(731\) | −39.2298 | −1.45097 | ||||||||
\(732\) | 26.7511 | 0.988748 | ||||||||
\(733\) | −18.4629 | −0.681943 | −0.340971 | − | 0.940074i | \(-0.610756\pi\) | ||||
−0.340971 | + | 0.940074i | \(0.610756\pi\) | |||||||
\(734\) | −11.3067 | −0.417337 | ||||||||
\(735\) | −0.419778 | −0.0154837 | ||||||||
\(736\) | 116.827 | 4.30630 | ||||||||
\(737\) | −17.1376 | −0.631272 | ||||||||
\(738\) | 15.2046 | 0.559688 | ||||||||
\(739\) | −35.8149 | −1.31747 | −0.658737 | − | 0.752374i | \(-0.728909\pi\) | ||||
−0.658737 | + | 0.752374i | \(0.728909\pi\) | |||||||
\(740\) | 63.3465 | 2.32866 | ||||||||
\(741\) | 32.6381 | 1.19899 | ||||||||
\(742\) | −10.2853 | −0.377585 | ||||||||
\(743\) | −8.56045 | −0.314052 | −0.157026 | − | 0.987594i | \(-0.550191\pi\) | ||||
−0.157026 | + | 0.987594i | \(0.550191\pi\) | |||||||
\(744\) | 86.4775 | 3.17042 | ||||||||
\(745\) | −10.8443 | −0.397304 | ||||||||
\(746\) | 95.3720 | 3.49182 | ||||||||
\(747\) | −8.55662 | −0.313070 | ||||||||
\(748\) | 159.997 | 5.85007 | ||||||||
\(749\) | 33.7995 | 1.23501 | ||||||||
\(750\) | 30.2927 | 1.10613 | ||||||||
\(751\) | −16.7520 | −0.611290 | −0.305645 | − | 0.952146i | \(-0.598872\pi\) | ||||
−0.305645 | + | 0.952146i | \(0.598872\pi\) | |||||||
\(752\) | 145.244 | 5.29650 | ||||||||
\(753\) | 9.18538 | 0.334734 | ||||||||
\(754\) | 143.829 | 5.23793 | ||||||||
\(755\) | −14.4450 | −0.525708 | ||||||||
\(756\) | 15.3900 | 0.559728 | ||||||||
\(757\) | −41.1103 | −1.49418 | −0.747090 | − | 0.664723i | \(-0.768550\pi\) | ||||
−0.747090 | + | 0.664723i | \(0.768550\pi\) | |||||||
\(758\) | 28.0724 | 1.01964 | ||||||||
\(759\) | −19.5485 | −0.709565 | ||||||||
\(760\) | −82.1039 | −2.97822 | ||||||||
\(761\) | 0.542636 | 0.0196706 | 0.00983528 | − | 0.999952i | \(-0.496869\pi\) | ||||
0.00983528 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(762\) | 9.73485 | 0.352656 | ||||||||
\(763\) | 27.9436 | 1.01163 | ||||||||
\(764\) | −83.5004 | −3.02094 | ||||||||
\(765\) | 6.28085 | 0.227085 | ||||||||
\(766\) | 94.9495 | 3.43067 | ||||||||
\(767\) | −10.7573 | −0.388425 | ||||||||
\(768\) | 133.946 | 4.83338 | ||||||||
\(769\) | −49.6287 | −1.78966 | −0.894829 | − | 0.446410i | \(-0.852702\pi\) | ||||
−0.894829 | + | 0.446410i | \(0.852702\pi\) | |||||||
\(770\) | −51.6230 | −1.86036 | ||||||||
\(771\) | −18.4091 | −0.662988 | ||||||||
\(772\) | −22.1635 | −0.797681 | ||||||||
\(773\) | −25.5809 | −0.920080 | −0.460040 | − | 0.887898i | \(-0.652165\pi\) | ||||
−0.460040 | + | 0.887898i | \(0.652165\pi\) | |||||||
\(774\) | 22.6774 | 0.815124 | ||||||||
\(775\) | 25.9003 | 0.930367 | ||||||||
\(776\) | 8.35118 | 0.299790 | ||||||||
\(777\) | 21.3426 | 0.765662 | ||||||||
\(778\) | −45.6762 | −1.63757 | ||||||||
\(779\) | −30.8007 | −1.10355 | ||||||||
\(780\) | 43.7945 | 1.56810 | ||||||||
\(781\) | 24.1939 | 0.865727 | ||||||||
\(782\) | 48.8925 | 1.74839 | ||||||||
\(783\) | −8.92701 | −0.319025 | ||||||||
\(784\) | −6.38414 | −0.228005 | ||||||||
\(785\) | −3.94357 | −0.140752 | ||||||||
\(786\) | −17.4507 | −0.622447 | ||||||||
\(787\) | −42.1706 | −1.50322 | −0.751610 | − | 0.659608i | \(-0.770722\pi\) | ||||
−0.751610 | + | 0.659608i | \(0.770722\pi\) | |||||||
\(788\) | 99.8423 | 3.55674 | ||||||||
\(789\) | −28.5947 | −1.01800 | ||||||||
\(790\) | −62.6425 | −2.22872 | ||||||||
\(791\) | 50.2009 | 1.78494 | ||||||||
\(792\) | −61.4383 | −2.18312 | ||||||||
\(793\) | 25.6477 | 0.910777 | ||||||||
\(794\) | −70.9123 | −2.51658 | ||||||||
\(795\) | 1.81660 | 0.0644282 | ||||||||
\(796\) | 87.1082 | 3.08747 | ||||||||
\(797\) | 38.7306 | 1.37191 | 0.685954 | − | 0.727645i | \(-0.259385\pi\) | ||||
0.685954 | + | 0.727645i | \(0.259385\pi\) | |||||||
\(798\) | −41.6428 | −1.47414 | ||||||||
\(799\) | 36.2081 | 1.28095 | ||||||||
\(800\) | 109.969 | 3.88800 | ||||||||
\(801\) | −12.1637 | −0.429782 | ||||||||
\(802\) | 24.6956 | 0.872030 | ||||||||
\(803\) | 27.7352 | 0.978755 | ||||||||
\(804\) | −18.5499 | −0.654204 | ||||||||
\(805\) | −11.8102 | −0.416255 | ||||||||
\(806\) | 124.813 | 4.39637 | ||||||||
\(807\) | −7.31009 | −0.257327 | ||||||||
\(808\) | 1.96666 | 0.0691867 | ||||||||
\(809\) | 37.4145 | 1.31542 | 0.657712 | − | 0.753270i | \(-0.271524\pi\) | ||||
0.657712 | + | 0.753270i | \(0.271524\pi\) | |||||||
\(810\) | −3.63075 | −0.127572 | ||||||||
\(811\) | −1.78602 | −0.0627156 | −0.0313578 | − | 0.999508i | \(-0.509983\pi\) | ||||
−0.0313578 | + | 0.999508i | \(0.509983\pi\) | |||||||
\(812\) | −137.386 | −4.82132 | ||||||||
\(813\) | 3.50290 | 0.122852 | ||||||||
\(814\) | −128.263 | −4.49560 | ||||||||
\(815\) | −3.01028 | −0.105445 | ||||||||
\(816\) | 95.5216 | 3.34392 | ||||||||
\(817\) | −45.9388 | −1.60720 | ||||||||
\(818\) | 16.5830 | 0.579809 | ||||||||
\(819\) | 14.7552 | 0.515588 | ||||||||
\(820\) | −41.3289 | −1.44327 | ||||||||
\(821\) | 43.1268 | 1.50514 | 0.752568 | − | 0.658515i | \(-0.228815\pi\) | ||||
0.752568 | + | 0.658515i | \(0.228815\pi\) | |||||||
\(822\) | 21.5328 | 0.751043 | ||||||||
\(823\) | 8.97231 | 0.312755 | 0.156377 | − | 0.987697i | \(-0.450018\pi\) | ||||
0.156377 | + | 0.987697i | \(0.450018\pi\) | |||||||
\(824\) | 98.3537 | 3.42631 | ||||||||
\(825\) | −18.4010 | −0.640641 | ||||||||
\(826\) | 13.7252 | 0.477562 | ||||||||
\(827\) | −0.268351 | −0.00933148 | −0.00466574 | − | 0.999989i | \(-0.501485\pi\) | ||||
−0.00466574 | + | 0.999989i | \(0.501485\pi\) | |||||||
\(828\) | −21.1594 | −0.735341 | ||||||||
\(829\) | 3.22766 | 0.112101 | 0.0560507 | − | 0.998428i | \(-0.482149\pi\) | ||||
0.0560507 | + | 0.998428i | \(0.482149\pi\) | |||||||
\(830\) | 31.0670 | 1.07835 | ||||||||
\(831\) | −1.50911 | −0.0523505 | ||||||||
\(832\) | 306.335 | 10.6203 | ||||||||
\(833\) | −1.59151 | −0.0551427 | ||||||||
\(834\) | −35.0466 | −1.21357 | ||||||||
\(835\) | −20.2382 | −0.700371 | ||||||||
\(836\) | 187.360 | 6.47997 | ||||||||
\(837\) | −7.74680 | −0.267768 | ||||||||
\(838\) | 20.4497 | 0.706424 | ||||||||
\(839\) | 23.5753 | 0.813910 | 0.406955 | − | 0.913448i | \(-0.366591\pi\) | ||||
0.406955 | + | 0.913448i | \(0.366591\pi\) | |||||||
\(840\) | −37.1179 | −1.28069 | ||||||||
\(841\) | 50.6916 | 1.74799 | ||||||||
\(842\) | −104.120 | −3.58822 | ||||||||
\(843\) | 17.4136 | 0.599757 | ||||||||
\(844\) | −108.104 | −3.72109 | ||||||||
\(845\) | 25.2558 | 0.868827 | ||||||||
\(846\) | −20.9307 | −0.719612 | ||||||||
\(847\) | 49.8365 | 1.71240 | ||||||||
\(848\) | 27.6275 | 0.948734 | ||||||||
\(849\) | −17.7691 | −0.609835 | ||||||||
\(850\) | 46.0226 | 1.57856 | ||||||||
\(851\) | −29.3437 | −1.00589 | ||||||||
\(852\) | 26.1877 | 0.897175 | ||||||||
\(853\) | 10.2631 | 0.351401 | 0.175700 | − | 0.984444i | \(-0.443781\pi\) | ||||
0.175700 | + | 0.984444i | \(0.443781\pi\) | |||||||
\(854\) | −32.7238 | −1.11978 | ||||||||
\(855\) | 7.35500 | 0.251536 | ||||||||
\(856\) | −146.050 | −4.99190 | ||||||||
\(857\) | −49.1576 | −1.67919 | −0.839597 | − | 0.543211i | \(-0.817209\pi\) | ||||
−0.839597 | + | 0.543211i | \(0.817209\pi\) | |||||||
\(858\) | −88.6743 | −3.02729 | ||||||||
\(859\) | 11.5065 | 0.392595 | 0.196298 | − | 0.980544i | \(-0.437108\pi\) | ||||
0.196298 | + | 0.980544i | \(0.437108\pi\) | |||||||
\(860\) | −61.6417 | −2.10196 | ||||||||
\(861\) | −13.9245 | −0.474546 | ||||||||
\(862\) | −79.8257 | −2.71887 | ||||||||
\(863\) | 16.3316 | 0.555935 | 0.277967 | − | 0.960590i | \(-0.410339\pi\) | ||||
0.277967 | + | 0.960590i | \(0.410339\pi\) | |||||||
\(864\) | −32.8918 | −1.11900 | ||||||||
\(865\) | −1.63631 | −0.0556361 | ||||||||
\(866\) | −61.2888 | −2.08268 | ||||||||
\(867\) | 6.81275 | 0.231373 | ||||||||
\(868\) | −119.223 | −4.04669 | ||||||||
\(869\) | 94.9579 | 3.22123 | ||||||||
\(870\) | 32.4118 | 1.09886 | ||||||||
\(871\) | −17.7848 | −0.602614 | ||||||||
\(872\) | −120.747 | −4.08900 | ||||||||
\(873\) | −0.748112 | −0.0253198 | ||||||||
\(874\) | 57.2541 | 1.93665 | ||||||||
\(875\) | −27.7424 | −0.937863 | ||||||||
\(876\) | 30.0208 | 1.01431 | ||||||||
\(877\) | −5.31796 | −0.179575 | −0.0897874 | − | 0.995961i | \(-0.528619\pi\) | ||||
−0.0897874 | + | 0.995961i | \(0.528619\pi\) | |||||||
\(878\) | 34.1368 | 1.15206 | ||||||||
\(879\) | −15.8907 | −0.535981 | ||||||||
\(880\) | 138.666 | 4.67442 | ||||||||
\(881\) | 8.19563 | 0.276118 | 0.138059 | − | 0.990424i | \(-0.455914\pi\) | ||||
0.138059 | + | 0.990424i | \(0.455914\pi\) | |||||||
\(882\) | 0.920002 | 0.0309781 | ||||||||
\(883\) | −0.839517 | −0.0282520 | −0.0141260 | − | 0.999900i | \(-0.504497\pi\) | ||||
−0.0141260 | + | 0.999900i | \(0.504497\pi\) | |||||||
\(884\) | 166.039 | 5.58450 | ||||||||
\(885\) | −2.42417 | −0.0814874 | ||||||||
\(886\) | −31.1523 | −1.04658 | ||||||||
\(887\) | −21.6898 | −0.728271 | −0.364135 | − | 0.931346i | \(-0.618635\pi\) | ||||
−0.364135 | + | 0.931346i | \(0.618635\pi\) | |||||||
\(888\) | −92.2233 | −3.09481 | ||||||||
\(889\) | −8.91528 | −0.299009 | ||||||||
\(890\) | 44.1632 | 1.48035 | ||||||||
\(891\) | 5.50374 | 0.184382 | ||||||||
\(892\) | −71.7074 | −2.40094 | ||||||||
\(893\) | 42.4004 | 1.41887 | ||||||||
\(894\) | 23.7668 | 0.794880 | ||||||||
\(895\) | 33.4741 | 1.11892 | ||||||||
\(896\) | −220.907 | −7.37998 | ||||||||
\(897\) | −20.2867 | −0.677354 | ||||||||
\(898\) | −17.5761 | −0.586522 | ||||||||
\(899\) | 69.1558 | 2.30647 | ||||||||
\(900\) | −19.9174 | −0.663913 | ||||||||
\(901\) | 6.88732 | 0.229450 | ||||||||
\(902\) | 83.6821 | 2.78631 | ||||||||
\(903\) | −20.7682 | −0.691124 | ||||||||
\(904\) | −216.922 | −7.21473 | ||||||||
\(905\) | 4.05728 | 0.134869 | ||||||||
\(906\) | 31.6583 | 1.05177 | ||||||||
\(907\) | 25.8657 | 0.858856 | 0.429428 | − | 0.903101i | \(-0.358715\pi\) | ||||
0.429428 | + | 0.903101i | \(0.358715\pi\) | |||||||
\(908\) | 128.922 | 4.27844 | ||||||||
\(909\) | −0.176176 | −0.00584340 | ||||||||
\(910\) | −53.5725 | −1.77591 | ||||||||
\(911\) | −15.9196 | −0.527439 | −0.263720 | − | 0.964599i | \(-0.584949\pi\) | ||||
−0.263720 | + | 0.964599i | \(0.584949\pi\) | |||||||
\(912\) | 111.858 | 3.70397 | ||||||||
\(913\) | −47.0935 | −1.55857 | ||||||||
\(914\) | 61.0818 | 2.02041 | ||||||||
\(915\) | 5.77971 | 0.191071 | ||||||||
\(916\) | 2.27663 | 0.0752221 | ||||||||
\(917\) | 15.9816 | 0.527758 | ||||||||
\(918\) | −13.7654 | −0.454324 | ||||||||
\(919\) | −33.8725 | −1.11735 | −0.558675 | − | 0.829386i | \(-0.688690\pi\) | ||||
−0.558675 | + | 0.829386i | \(0.688690\pi\) | |||||||
\(920\) | 51.0329 | 1.68250 | ||||||||
\(921\) | −28.3786 | −0.935105 | ||||||||
\(922\) | −111.168 | −3.66113 | ||||||||
\(923\) | 25.1076 | 0.826426 | ||||||||
\(924\) | 84.7024 | 2.78651 | ||||||||
\(925\) | −27.6212 | −0.908180 | ||||||||
\(926\) | −60.2593 | −1.98024 | ||||||||
\(927\) | −8.81068 | −0.289381 | ||||||||
\(928\) | 293.626 | 9.63874 | ||||||||
\(929\) | 16.5466 | 0.542876 | 0.271438 | − | 0.962456i | \(-0.412501\pi\) | ||||
0.271438 | + | 0.962456i | \(0.412501\pi\) | |||||||
\(930\) | 28.1267 | 0.922311 | ||||||||
\(931\) | −1.86369 | −0.0610801 | ||||||||
\(932\) | −139.768 | −4.57826 | ||||||||
\(933\) | −12.8537 | −0.420813 | ||||||||
\(934\) | −59.0475 | −1.93209 | ||||||||
\(935\) | 34.5682 | 1.13050 | ||||||||
\(936\) | −63.7585 | −2.08401 | ||||||||
\(937\) | −40.8563 | −1.33472 | −0.667359 | − | 0.744736i | \(-0.732575\pi\) | ||||
−0.667359 | + | 0.744736i | \(0.732575\pi\) | |||||||
\(938\) | 22.6915 | 0.740904 | ||||||||
\(939\) | 26.4270 | 0.862414 | ||||||||
\(940\) | 56.8937 | 1.85567 | ||||||||
\(941\) | 20.7293 | 0.675755 | 0.337878 | − | 0.941190i | \(-0.390291\pi\) | ||||
0.337878 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(942\) | 8.64288 | 0.281600 | ||||||||
\(943\) | 19.1446 | 0.623434 | ||||||||
\(944\) | −36.8676 | −1.19994 | ||||||||
\(945\) | 3.32508 | 0.108165 | ||||||||
\(946\) | 124.811 | 4.05795 | ||||||||
\(947\) | 45.1600 | 1.46750 | 0.733751 | − | 0.679419i | \(-0.237768\pi\) | ||||
0.733751 | + | 0.679419i | \(0.237768\pi\) | |||||||
\(948\) | 102.783 | 3.33824 | ||||||||
\(949\) | 28.7826 | 0.934323 | ||||||||
\(950\) | 53.8933 | 1.74853 | ||||||||
\(951\) | −24.0540 | −0.780004 | ||||||||
\(952\) | −140.726 | −4.56096 | ||||||||
\(953\) | −14.8596 | −0.481351 | −0.240675 | − | 0.970606i | \(-0.577369\pi\) | ||||
−0.240675 | + | 0.970606i | \(0.577369\pi\) | |||||||
\(954\) | −3.98133 | −0.128900 | ||||||||
\(955\) | −18.0407 | −0.583784 | ||||||||
\(956\) | 45.4285 | 1.46926 | ||||||||
\(957\) | −49.1320 | −1.58821 | ||||||||
\(958\) | −30.8231 | −0.995849 | ||||||||
\(959\) | −19.7200 | −0.636792 | ||||||||
\(960\) | 69.0326 | 2.22802 | ||||||||
\(961\) | 29.0128 | 0.935898 | ||||||||
\(962\) | −133.106 | −4.29152 | ||||||||
\(963\) | 13.0834 | 0.421608 | ||||||||
\(964\) | −78.4389 | −2.52635 | ||||||||
\(965\) | −4.78854 | −0.154148 | ||||||||
\(966\) | 25.8837 | 0.832794 | ||||||||
\(967\) | −43.2454 | −1.39068 | −0.695339 | − | 0.718682i | \(-0.744746\pi\) | ||||
−0.695339 | + | 0.718682i | \(0.744746\pi\) | |||||||
\(968\) | −215.348 | −6.92154 | ||||||||
\(969\) | 27.8852 | 0.895801 | ||||||||
\(970\) | 2.71621 | 0.0872123 | ||||||||
\(971\) | 5.66898 | 0.181926 | 0.0909632 | − | 0.995854i | \(-0.471005\pi\) | ||||
0.0909632 | + | 0.995854i | \(0.471005\pi\) | |||||||
\(972\) | 5.95730 | 0.191080 | ||||||||
\(973\) | 32.0961 | 1.02895 | ||||||||
\(974\) | 27.1531 | 0.870041 | ||||||||
\(975\) | −19.0959 | −0.611558 | ||||||||
\(976\) | 87.9000 | 2.81361 | ||||||||
\(977\) | −9.55493 | −0.305689 | −0.152845 | − | 0.988250i | \(-0.548843\pi\) | ||||
−0.152845 | + | 0.988250i | \(0.548843\pi\) | |||||||
\(978\) | 6.59744 | 0.210963 | ||||||||
\(979\) | −66.9456 | −2.13959 | ||||||||
\(980\) | −2.50074 | −0.0798833 | ||||||||
\(981\) | 10.8167 | 0.345350 | ||||||||
\(982\) | 24.3886 | 0.778272 | ||||||||
\(983\) | −16.4872 | −0.525858 | −0.262929 | − | 0.964815i | \(-0.584689\pi\) | ||||
−0.262929 | + | 0.964815i | \(0.584689\pi\) | |||||||
\(984\) | 60.1690 | 1.91812 | ||||||||
\(985\) | 21.5715 | 0.687324 | ||||||||
\(986\) | 122.884 | 3.91341 | ||||||||
\(987\) | 19.1686 | 0.610142 | ||||||||
\(988\) | 194.435 | 6.18580 | ||||||||
\(989\) | 28.5540 | 0.907963 | ||||||||
\(990\) | −19.9827 | −0.635093 | ||||||||
\(991\) | 19.5328 | 0.620481 | 0.310240 | − | 0.950658i | \(-0.399590\pi\) | ||||
0.310240 | + | 0.950658i | \(0.399590\pi\) | |||||||
\(992\) | 254.806 | 8.09011 | ||||||||
\(993\) | 11.7313 | 0.372282 | ||||||||
\(994\) | −32.0346 | −1.01608 | ||||||||
\(995\) | 18.8202 | 0.596640 | ||||||||
\(996\) | −50.9743 | −1.61518 | ||||||||
\(997\) | −13.3657 | −0.423297 | −0.211649 | − | 0.977346i | \(-0.567883\pi\) | ||||
−0.211649 | + | 0.977346i | \(0.567883\pi\) | |||||||
\(998\) | −34.9832 | −1.10737 | ||||||||
\(999\) | 8.26151 | 0.261383 |
(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 | 8049.2.a.d.1.1 | ✓ | 129 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8049.2.a.d.1.1 | ✓ | 129 | 1.1 | even | 1 | trivial |