Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.34399 | −1.35330 | −0.676651 | − | 0.736304i | \(-0.736570\pi\) | ||||
−0.676651 | + | 0.736304i | \(0.736570\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.04947 | 0.469339 | 0.234670 | − | 0.972075i | \(-0.424599\pi\) | ||||
0.234670 | + | 0.972075i | \(0.424599\pi\) | |||||||
\(6\) | 2.34399 | 0.956930 | ||||||||
\(7\) | −2.18495 | −0.825834 | −0.412917 | − | 0.910769i | \(-0.635490\pi\) | ||||
−0.412917 | + | 0.910769i | \(0.635490\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.49429 | 0.831428 | ||||||||
\(10\) | −1.04947 | −0.331873 | ||||||||
\(11\) | −1.41075 | −0.425358 | −0.212679 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212679 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(12\) | −2.34399 | −0.676651 | ||||||||
\(13\) | 1.55513 | 0.431316 | 0.215658 | − | 0.976469i | \(-0.430810\pi\) | ||||
0.215658 | + | 0.976469i | \(0.430810\pi\) | |||||||
\(14\) | 2.18495 | 0.583953 | ||||||||
\(15\) | −2.45996 | −0.635158 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.65650 | −1.37190 | −0.685951 | − | 0.727647i | \(-0.740614\pi\) | ||||
−0.685951 | + | 0.727647i | \(0.740614\pi\) | |||||||
\(18\) | −2.49429 | −0.587909 | ||||||||
\(19\) | −3.08363 | −0.707434 | −0.353717 | − | 0.935352i | \(-0.615082\pi\) | ||||
−0.353717 | + | 0.935352i | \(0.615082\pi\) | |||||||
\(20\) | 1.04947 | 0.234670 | ||||||||
\(21\) | 5.12150 | 1.11760 | ||||||||
\(22\) | 1.41075 | 0.300774 | ||||||||
\(23\) | −7.68050 | −1.60150 | −0.800748 | − | 0.599002i | \(-0.795564\pi\) | ||||
−0.800748 | + | 0.599002i | \(0.795564\pi\) | |||||||
\(24\) | 2.34399 | 0.478465 | ||||||||
\(25\) | −3.89860 | −0.779721 | ||||||||
\(26\) | −1.55513 | −0.304987 | ||||||||
\(27\) | 1.18539 | 0.228128 | ||||||||
\(28\) | −2.18495 | −0.412917 | ||||||||
\(29\) | −9.05297 | −1.68109 | −0.840547 | − | 0.541738i | \(-0.817767\pi\) | ||||
−0.840547 | + | 0.541738i | \(0.817767\pi\) | |||||||
\(30\) | 2.45996 | 0.449124 | ||||||||
\(31\) | 0.0306546 | 0.00550573 | 0.00275286 | − | 0.999996i | \(-0.499124\pi\) | ||||
0.00275286 | + | 0.999996i | \(0.499124\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.30679 | 0.575638 | ||||||||
\(34\) | 5.65650 | 0.970082 | ||||||||
\(35\) | −2.29305 | −0.387596 | ||||||||
\(36\) | 2.49429 | 0.415714 | ||||||||
\(37\) | −3.29992 | −0.542504 | −0.271252 | − | 0.962508i | \(-0.587438\pi\) | ||||
−0.271252 | + | 0.962508i | \(0.587438\pi\) | |||||||
\(38\) | 3.08363 | 0.500231 | ||||||||
\(39\) | −3.64522 | −0.583702 | ||||||||
\(40\) | −1.04947 | −0.165936 | ||||||||
\(41\) | −7.01221 | −1.09512 | −0.547561 | − | 0.836766i | \(-0.684444\pi\) | ||||
−0.547561 | + | 0.836766i | \(0.684444\pi\) | |||||||
\(42\) | −5.12150 | −0.790265 | ||||||||
\(43\) | −4.37246 | −0.666795 | −0.333397 | − | 0.942786i | \(-0.608195\pi\) | ||||
−0.333397 | + | 0.942786i | \(0.608195\pi\) | |||||||
\(44\) | −1.41075 | −0.212679 | ||||||||
\(45\) | 2.61769 | 0.390222 | ||||||||
\(46\) | 7.68050 | 1.13243 | ||||||||
\(47\) | 9.27923 | 1.35351 | 0.676757 | − | 0.736206i | \(-0.263385\pi\) | ||||
0.676757 | + | 0.736206i | \(0.263385\pi\) | |||||||
\(48\) | −2.34399 | −0.338326 | ||||||||
\(49\) | −2.22599 | −0.317999 | ||||||||
\(50\) | 3.89860 | 0.551346 | ||||||||
\(51\) | 13.2588 | 1.85660 | ||||||||
\(52\) | 1.55513 | 0.215658 | ||||||||
\(53\) | −3.22734 | −0.443310 | −0.221655 | − | 0.975125i | \(-0.571146\pi\) | ||||
−0.221655 | + | 0.975125i | \(0.571146\pi\) | |||||||
\(54\) | −1.18539 | −0.161311 | ||||||||
\(55\) | −1.48055 | −0.199637 | ||||||||
\(56\) | 2.18495 | 0.291976 | ||||||||
\(57\) | 7.22800 | 0.957373 | ||||||||
\(58\) | 9.05297 | 1.18871 | ||||||||
\(59\) | 6.66120 | 0.867215 | 0.433608 | − | 0.901102i | \(-0.357240\pi\) | ||||
0.433608 | + | 0.901102i | \(0.357240\pi\) | |||||||
\(60\) | −2.45996 | −0.317579 | ||||||||
\(61\) | −8.75759 | −1.12129 | −0.560647 | − | 0.828055i | \(-0.689448\pi\) | ||||
−0.560647 | + | 0.828055i | \(0.689448\pi\) | |||||||
\(62\) | −0.0306546 | −0.00389314 | ||||||||
\(63\) | −5.44989 | −0.686621 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.63207 | 0.202434 | ||||||||
\(66\) | −3.30679 | −0.407038 | ||||||||
\(67\) | −4.41171 | −0.538976 | −0.269488 | − | 0.963004i | \(-0.586855\pi\) | ||||
−0.269488 | + | 0.963004i | \(0.586855\pi\) | |||||||
\(68\) | −5.65650 | −0.685951 | ||||||||
\(69\) | 18.0030 | 2.16731 | ||||||||
\(70\) | 2.29305 | 0.274072 | ||||||||
\(71\) | 5.29311 | 0.628176 | 0.314088 | − | 0.949394i | \(-0.398301\pi\) | ||||
0.314088 | + | 0.949394i | \(0.398301\pi\) | |||||||
\(72\) | −2.49429 | −0.293954 | ||||||||
\(73\) | −15.4311 | −1.80608 | −0.903040 | − | 0.429557i | \(-0.858670\pi\) | ||||
−0.903040 | + | 0.429557i | \(0.858670\pi\) | |||||||
\(74\) | 3.29992 | 0.383608 | ||||||||
\(75\) | 9.13829 | 1.05520 | ||||||||
\(76\) | −3.08363 | −0.353717 | ||||||||
\(77\) | 3.08243 | 0.351275 | ||||||||
\(78\) | 3.64522 | 0.412739 | ||||||||
\(79\) | 11.0534 | 1.24361 | 0.621803 | − | 0.783173i | \(-0.286400\pi\) | ||||
0.621803 | + | 0.783173i | \(0.286400\pi\) | |||||||
\(80\) | 1.04947 | 0.117335 | ||||||||
\(81\) | −10.2614 | −1.14016 | ||||||||
\(82\) | 7.01221 | 0.774369 | ||||||||
\(83\) | −5.20435 | −0.571252 | −0.285626 | − | 0.958341i | \(-0.592202\pi\) | ||||
−0.285626 | + | 0.958341i | \(0.592202\pi\) | |||||||
\(84\) | 5.12150 | 0.558801 | ||||||||
\(85\) | −5.93635 | −0.643887 | ||||||||
\(86\) | 4.37246 | 0.471495 | ||||||||
\(87\) | 21.2201 | 2.27503 | ||||||||
\(88\) | 1.41075 | 0.150387 | ||||||||
\(89\) | 12.0123 | 1.27330 | 0.636649 | − | 0.771153i | \(-0.280320\pi\) | ||||
0.636649 | + | 0.771153i | \(0.280320\pi\) | |||||||
\(90\) | −2.61769 | −0.275928 | ||||||||
\(91\) | −3.39789 | −0.356196 | ||||||||
\(92\) | −7.68050 | −0.800748 | ||||||||
\(93\) | −0.0718540 | −0.00745091 | ||||||||
\(94\) | −9.27923 | −0.957079 | ||||||||
\(95\) | −3.23619 | −0.332026 | ||||||||
\(96\) | 2.34399 | 0.239232 | ||||||||
\(97\) | −8.28067 | −0.840775 | −0.420388 | − | 0.907345i | \(-0.638106\pi\) | ||||
−0.420388 | + | 0.907345i | \(0.638106\pi\) | |||||||
\(98\) | 2.22599 | 0.224859 | ||||||||
\(99\) | −3.51882 | −0.353655 | ||||||||
\(100\) | −3.89860 | −0.389860 | ||||||||
\(101\) | −4.82528 | −0.480133 | −0.240067 | − | 0.970756i | \(-0.577169\pi\) | ||||
−0.240067 | + | 0.970756i | \(0.577169\pi\) | |||||||
\(102\) | −13.2588 | −1.31281 | ||||||||
\(103\) | −5.80979 | −0.572456 | −0.286228 | − | 0.958162i | \(-0.592401\pi\) | ||||
−0.286228 | + | 0.958162i | \(0.592401\pi\) | |||||||
\(104\) | −1.55513 | −0.152493 | ||||||||
\(105\) | 5.37488 | 0.524535 | ||||||||
\(106\) | 3.22734 | 0.313467 | ||||||||
\(107\) | 3.60050 | 0.348073 | 0.174037 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174037 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(108\) | 1.18539 | 0.114064 | ||||||||
\(109\) | 7.46909 | 0.715409 | 0.357704 | − | 0.933835i | \(-0.383560\pi\) | ||||
0.357704 | + | 0.933835i | \(0.383560\pi\) | |||||||
\(110\) | 1.48055 | 0.141165 | ||||||||
\(111\) | 7.73498 | 0.734172 | ||||||||
\(112\) | −2.18495 | −0.206458 | ||||||||
\(113\) | 8.83095 | 0.830746 | 0.415373 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415373 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(114\) | −7.22800 | −0.676965 | ||||||||
\(115\) | −8.06049 | −0.751644 | ||||||||
\(116\) | −9.05297 | −0.840547 | ||||||||
\(117\) | 3.87895 | 0.358609 | ||||||||
\(118\) | −6.66120 | −0.613214 | ||||||||
\(119\) | 12.3592 | 1.13296 | ||||||||
\(120\) | 2.45996 | 0.224562 | ||||||||
\(121\) | −9.00978 | −0.819070 | ||||||||
\(122\) | 8.75759 | 0.792875 | ||||||||
\(123\) | 16.4365 | 1.48203 | ||||||||
\(124\) | 0.0306546 | 0.00275286 | ||||||||
\(125\) | −9.33885 | −0.835293 | ||||||||
\(126\) | 5.44989 | 0.485515 | ||||||||
\(127\) | −13.0920 | −1.16173 | −0.580863 | − | 0.814001i | \(-0.697285\pi\) | ||||
−0.580863 | + | 0.814001i | \(0.697285\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.2490 | 0.902375 | ||||||||
\(130\) | −1.63207 | −0.143142 | ||||||||
\(131\) | −20.3025 | −1.77383 | −0.886917 | − | 0.461928i | \(-0.847158\pi\) | ||||
−0.886917 | + | 0.461928i | \(0.847158\pi\) | |||||||
\(132\) | 3.30679 | 0.287819 | ||||||||
\(133\) | 6.73759 | 0.584223 | ||||||||
\(134\) | 4.41171 | 0.381114 | ||||||||
\(135\) | 1.24404 | 0.107070 | ||||||||
\(136\) | 5.65650 | 0.485041 | ||||||||
\(137\) | 13.6218 | 1.16379 | 0.581894 | − | 0.813265i | \(-0.302312\pi\) | ||||
0.581894 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(138\) | −18.0030 | −1.53252 | ||||||||
\(139\) | −11.2288 | −0.952415 | −0.476207 | − | 0.879333i | \(-0.657989\pi\) | ||||
−0.476207 | + | 0.879333i | \(0.657989\pi\) | |||||||
\(140\) | −2.29305 | −0.193798 | ||||||||
\(141\) | −21.7504 | −1.83172 | ||||||||
\(142\) | −5.29311 | −0.444188 | ||||||||
\(143\) | −2.19391 | −0.183464 | ||||||||
\(144\) | 2.49429 | 0.207857 | ||||||||
\(145\) | −9.50086 | −0.789003 | ||||||||
\(146\) | 15.4311 | 1.27709 | ||||||||
\(147\) | 5.21770 | 0.430349 | ||||||||
\(148\) | −3.29992 | −0.271252 | ||||||||
\(149\) | 11.6635 | 0.955510 | 0.477755 | − | 0.878493i | \(-0.341451\pi\) | ||||
0.477755 | + | 0.878493i | \(0.341451\pi\) | |||||||
\(150\) | −9.13829 | −0.746138 | ||||||||
\(151\) | 17.4128 | 1.41703 | 0.708517 | − | 0.705694i | \(-0.249365\pi\) | ||||
0.708517 | + | 0.705694i | \(0.249365\pi\) | |||||||
\(152\) | 3.08363 | 0.250116 | ||||||||
\(153\) | −14.1089 | −1.14064 | ||||||||
\(154\) | −3.08243 | −0.248389 | ||||||||
\(155\) | 0.0321712 | 0.00258405 | ||||||||
\(156\) | −3.64522 | −0.291851 | ||||||||
\(157\) | 18.7650 | 1.49761 | 0.748804 | − | 0.662792i | \(-0.230629\pi\) | ||||
0.748804 | + | 0.662792i | \(0.230629\pi\) | |||||||
\(158\) | −11.0534 | −0.879363 | ||||||||
\(159\) | 7.56486 | 0.599932 | ||||||||
\(160\) | −1.04947 | −0.0829682 | ||||||||
\(161\) | 16.7815 | 1.32257 | ||||||||
\(162\) | 10.2614 | 0.806212 | ||||||||
\(163\) | −15.4664 | −1.21142 | −0.605709 | − | 0.795686i | \(-0.707110\pi\) | ||||
−0.605709 | + | 0.795686i | \(0.707110\pi\) | |||||||
\(164\) | −7.01221 | −0.547561 | ||||||||
\(165\) | 3.47039 | 0.270170 | ||||||||
\(166\) | 5.20435 | 0.403936 | ||||||||
\(167\) | −17.5983 | −1.36180 | −0.680900 | − | 0.732377i | \(-0.738411\pi\) | ||||
−0.680900 | + | 0.732377i | \(0.738411\pi\) | |||||||
\(168\) | −5.12150 | −0.395132 | ||||||||
\(169\) | −10.5816 | −0.813966 | ||||||||
\(170\) | 5.93635 | 0.455297 | ||||||||
\(171\) | −7.69146 | −0.588181 | ||||||||
\(172\) | −4.37246 | −0.333397 | ||||||||
\(173\) | −8.61548 | −0.655023 | −0.327511 | − | 0.944847i | \(-0.606210\pi\) | ||||
−0.327511 | + | 0.944847i | \(0.606210\pi\) | |||||||
\(174\) | −21.2201 | −1.60869 | ||||||||
\(175\) | 8.51826 | 0.643920 | ||||||||
\(176\) | −1.41075 | −0.106340 | ||||||||
\(177\) | −15.6138 | −1.17360 | ||||||||
\(178\) | −12.0123 | −0.900358 | ||||||||
\(179\) | −0.878161 | −0.0656368 | −0.0328184 | − | 0.999461i | \(-0.510448\pi\) | ||||
−0.0328184 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(180\) | 2.61769 | 0.195111 | ||||||||
\(181\) | 9.61659 | 0.714796 | 0.357398 | − | 0.933952i | \(-0.383664\pi\) | ||||
0.357398 | + | 0.933952i | \(0.383664\pi\) | |||||||
\(182\) | 3.39789 | 0.251868 | ||||||||
\(183\) | 20.5277 | 1.51745 | ||||||||
\(184\) | 7.68050 | 0.566214 | ||||||||
\(185\) | −3.46318 | −0.254618 | ||||||||
\(186\) | 0.0718540 | 0.00526859 | ||||||||
\(187\) | 7.97992 | 0.583550 | ||||||||
\(188\) | 9.27923 | 0.676757 | ||||||||
\(189\) | −2.59002 | −0.188396 | ||||||||
\(190\) | 3.23619 | 0.234778 | ||||||||
\(191\) | 20.8588 | 1.50929 | 0.754645 | − | 0.656133i | \(-0.227809\pi\) | ||||
0.754645 | + | 0.656133i | \(0.227809\pi\) | |||||||
\(192\) | −2.34399 | −0.169163 | ||||||||
\(193\) | −18.7552 | −1.35003 | −0.675014 | − | 0.737805i | \(-0.735862\pi\) | ||||
−0.675014 | + | 0.737805i | \(0.735862\pi\) | |||||||
\(194\) | 8.28067 | 0.594518 | ||||||||
\(195\) | −3.82556 | −0.273954 | ||||||||
\(196\) | −2.22599 | −0.158999 | ||||||||
\(197\) | −21.2499 | −1.51399 | −0.756997 | − | 0.653419i | \(-0.773334\pi\) | ||||
−0.756997 | + | 0.653419i | \(0.773334\pi\) | |||||||
\(198\) | 3.51882 | 0.250072 | ||||||||
\(199\) | 14.3586 | 1.01785 | 0.508927 | − | 0.860810i | \(-0.330042\pi\) | ||||
0.508927 | + | 0.860810i | \(0.330042\pi\) | |||||||
\(200\) | 3.89860 | 0.275673 | ||||||||
\(201\) | 10.3410 | 0.729398 | ||||||||
\(202\) | 4.82528 | 0.339506 | ||||||||
\(203\) | 19.7803 | 1.38830 | ||||||||
\(204\) | 13.2588 | 0.928300 | ||||||||
\(205\) | −7.35913 | −0.513984 | ||||||||
\(206\) | 5.80979 | 0.404788 | ||||||||
\(207\) | −19.1574 | −1.33153 | ||||||||
\(208\) | 1.55513 | 0.107829 | ||||||||
\(209\) | 4.35025 | 0.300913 | ||||||||
\(210\) | −5.37488 | −0.370902 | ||||||||
\(211\) | 0.948037 | 0.0652656 | 0.0326328 | − | 0.999467i | \(-0.489611\pi\) | ||||
0.0326328 | + | 0.999467i | \(0.489611\pi\) | |||||||
\(212\) | −3.22734 | −0.221655 | ||||||||
\(213\) | −12.4070 | −0.850113 | ||||||||
\(214\) | −3.60050 | −0.246125 | ||||||||
\(215\) | −4.58879 | −0.312953 | ||||||||
\(216\) | −1.18539 | −0.0806556 | ||||||||
\(217\) | −0.0669787 | −0.00454681 | ||||||||
\(218\) | −7.46909 | −0.505870 | ||||||||
\(219\) | 36.1704 | 2.44417 | ||||||||
\(220\) | −1.48055 | −0.0998186 | ||||||||
\(221\) | −8.79661 | −0.591724 | ||||||||
\(222\) | −7.73498 | −0.519138 | ||||||||
\(223\) | 1.73412 | 0.116125 | 0.0580625 | − | 0.998313i | \(-0.481508\pi\) | ||||
0.0580625 | + | 0.998313i | \(0.481508\pi\) | |||||||
\(224\) | 2.18495 | 0.145988 | ||||||||
\(225\) | −9.72423 | −0.648282 | ||||||||
\(226\) | −8.83095 | −0.587426 | ||||||||
\(227\) | 21.5834 | 1.43254 | 0.716271 | − | 0.697822i | \(-0.245848\pi\) | ||||
0.716271 | + | 0.697822i | \(0.245848\pi\) | |||||||
\(228\) | 7.22800 | 0.478686 | ||||||||
\(229\) | −13.5664 | −0.896493 | −0.448246 | − | 0.893910i | \(-0.647951\pi\) | ||||
−0.448246 | + | 0.893910i | \(0.647951\pi\) | |||||||
\(230\) | 8.06049 | 0.531493 | ||||||||
\(231\) | −7.22517 | −0.475381 | ||||||||
\(232\) | 9.05297 | 0.594357 | ||||||||
\(233\) | −26.1818 | −1.71522 | −0.857612 | − | 0.514297i | \(-0.828053\pi\) | ||||
−0.857612 | + | 0.514297i | \(0.828053\pi\) | |||||||
\(234\) | −3.87895 | −0.253575 | ||||||||
\(235\) | 9.73831 | 0.635257 | ||||||||
\(236\) | 6.66120 | 0.433608 | ||||||||
\(237\) | −25.9091 | −1.68298 | ||||||||
\(238\) | −12.3592 | −0.801126 | ||||||||
\(239\) | −6.51518 | −0.421432 | −0.210716 | − | 0.977547i | \(-0.567580\pi\) | ||||
−0.210716 | + | 0.977547i | \(0.567580\pi\) | |||||||
\(240\) | −2.45996 | −0.158789 | ||||||||
\(241\) | −16.3552 | −1.05353 | −0.526766 | − | 0.850010i | \(-0.676595\pi\) | ||||
−0.526766 | + | 0.850010i | \(0.676595\pi\) | |||||||
\(242\) | 9.00978 | 0.579170 | ||||||||
\(243\) | 20.4964 | 1.31485 | ||||||||
\(244\) | −8.75759 | −0.560647 | ||||||||
\(245\) | −2.33612 | −0.149249 | ||||||||
\(246\) | −16.4365 | −1.04796 | ||||||||
\(247\) | −4.79546 | −0.305128 | ||||||||
\(248\) | −0.0306546 | −0.00194657 | ||||||||
\(249\) | 12.1989 | 0.773077 | ||||||||
\(250\) | 9.33885 | 0.590641 | ||||||||
\(251\) | 12.0030 | 0.757624 | 0.378812 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378812 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(252\) | −5.44989 | −0.343311 | ||||||||
\(253\) | 10.8353 | 0.681209 | ||||||||
\(254\) | 13.0920 | 0.821464 | ||||||||
\(255\) | 13.9147 | 0.871375 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5817 | −1.22147 | −0.610737 | − | 0.791833i | \(-0.709127\pi\) | ||||
−0.610737 | + | 0.791833i | \(0.709127\pi\) | |||||||
\(258\) | −10.2490 | −0.638075 | ||||||||
\(259\) | 7.21016 | 0.448018 | ||||||||
\(260\) | 1.63207 | 0.101217 | ||||||||
\(261\) | −22.5807 | −1.39771 | ||||||||
\(262\) | 20.3025 | 1.25429 | ||||||||
\(263\) | 17.7616 | 1.09523 | 0.547614 | − | 0.836731i | \(-0.315536\pi\) | ||||
0.547614 | + | 0.836731i | \(0.315536\pi\) | |||||||
\(264\) | −3.30679 | −0.203519 | ||||||||
\(265\) | −3.38701 | −0.208062 | ||||||||
\(266\) | −6.73759 | −0.413108 | ||||||||
\(267\) | −28.1566 | −1.72316 | ||||||||
\(268\) | −4.41171 | −0.269488 | ||||||||
\(269\) | −1.39786 | −0.0852288 | −0.0426144 | − | 0.999092i | \(-0.513569\pi\) | ||||
−0.0426144 | + | 0.999092i | \(0.513569\pi\) | |||||||
\(270\) | −1.24404 | −0.0757096 | ||||||||
\(271\) | −8.65894 | −0.525993 | −0.262996 | − | 0.964797i | \(-0.584711\pi\) | ||||
−0.262996 | + | 0.964797i | \(0.584711\pi\) | |||||||
\(272\) | −5.65650 | −0.342976 | ||||||||
\(273\) | 7.96461 | 0.482040 | ||||||||
\(274\) | −13.6218 | −0.822922 | ||||||||
\(275\) | 5.49997 | 0.331661 | ||||||||
\(276\) | 18.0030 | 1.08365 | ||||||||
\(277\) | −0.130566 | −0.00784498 | −0.00392249 | − | 0.999992i | \(-0.501249\pi\) | ||||
−0.00392249 | + | 0.999992i | \(0.501249\pi\) | |||||||
\(278\) | 11.2288 | 0.673459 | ||||||||
\(279\) | 0.0764613 | 0.00457762 | ||||||||
\(280\) | 2.29305 | 0.137036 | ||||||||
\(281\) | −17.5677 | −1.04800 | −0.524002 | − | 0.851717i | \(-0.675561\pi\) | ||||
−0.524002 | + | 0.851717i | \(0.675561\pi\) | |||||||
\(282\) | 21.7504 | 1.29522 | ||||||||
\(283\) | −7.59996 | −0.451770 | −0.225885 | − | 0.974154i | \(-0.572527\pi\) | ||||
−0.225885 | + | 0.974154i | \(0.572527\pi\) | |||||||
\(284\) | 5.29311 | 0.314088 | ||||||||
\(285\) | 7.58560 | 0.449332 | ||||||||
\(286\) | 2.19391 | 0.129729 | ||||||||
\(287\) | 15.3213 | 0.904389 | ||||||||
\(288\) | −2.49429 | −0.146977 | ||||||||
\(289\) | 14.9960 | 0.882117 | ||||||||
\(290\) | 9.50086 | 0.557910 | ||||||||
\(291\) | 19.4098 | 1.13782 | ||||||||
\(292\) | −15.4311 | −0.903040 | ||||||||
\(293\) | 10.7354 | 0.627168 | 0.313584 | − | 0.949560i | \(-0.398470\pi\) | ||||
0.313584 | + | 0.949560i | \(0.398470\pi\) | |||||||
\(294\) | −5.21770 | −0.304303 | ||||||||
\(295\) | 6.99076 | 0.407018 | ||||||||
\(296\) | 3.29992 | 0.191804 | ||||||||
\(297\) | −1.67229 | −0.0970363 | ||||||||
\(298\) | −11.6635 | −0.675647 | ||||||||
\(299\) | −11.9442 | −0.690751 | ||||||||
\(300\) | 9.13829 | 0.527599 | ||||||||
\(301\) | 9.55362 | 0.550661 | ||||||||
\(302\) | −17.4128 | −1.00199 | ||||||||
\(303\) | 11.3104 | 0.649766 | ||||||||
\(304\) | −3.08363 | −0.176859 | ||||||||
\(305\) | −9.19086 | −0.526267 | ||||||||
\(306\) | 14.1089 | 0.806553 | ||||||||
\(307\) | −12.9018 | −0.736346 | −0.368173 | − | 0.929757i | \(-0.620017\pi\) | ||||
−0.368173 | + | 0.929757i | \(0.620017\pi\) | |||||||
\(308\) | 3.08243 | 0.175638 | ||||||||
\(309\) | 13.6181 | 0.774706 | ||||||||
\(310\) | −0.0321712 | −0.00182720 | ||||||||
\(311\) | −5.19578 | −0.294626 | −0.147313 | − | 0.989090i | \(-0.547062\pi\) | ||||
−0.147313 | + | 0.989090i | \(0.547062\pi\) | |||||||
\(312\) | 3.64522 | 0.206370 | ||||||||
\(313\) | −6.42747 | −0.363302 | −0.181651 | − | 0.983363i | \(-0.558144\pi\) | ||||
−0.181651 | + | 0.983363i | \(0.558144\pi\) | |||||||
\(314\) | −18.7650 | −1.05897 | ||||||||
\(315\) | −5.71952 | −0.322258 | ||||||||
\(316\) | 11.0534 | 0.621803 | ||||||||
\(317\) | 12.2775 | 0.689573 | 0.344787 | − | 0.938681i | \(-0.387951\pi\) | ||||
0.344787 | + | 0.938681i | \(0.387951\pi\) | |||||||
\(318\) | −7.56486 | −0.424216 | ||||||||
\(319\) | 12.7715 | 0.715067 | ||||||||
\(320\) | 1.04947 | 0.0586674 | ||||||||
\(321\) | −8.43953 | −0.471049 | ||||||||
\(322\) | −16.7815 | −0.935197 | ||||||||
\(323\) | 17.4426 | 0.970531 | ||||||||
\(324\) | −10.2614 | −0.570078 | ||||||||
\(325\) | −6.06285 | −0.336306 | ||||||||
\(326\) | 15.4664 | 0.856602 | ||||||||
\(327\) | −17.5075 | −0.968165 | ||||||||
\(328\) | 7.01221 | 0.387184 | ||||||||
\(329\) | −20.2747 | −1.11778 | ||||||||
\(330\) | −3.47039 | −0.191039 | ||||||||
\(331\) | 7.40674 | 0.407111 | 0.203556 | − | 0.979063i | \(-0.434750\pi\) | ||||
0.203556 | + | 0.979063i | \(0.434750\pi\) | |||||||
\(332\) | −5.20435 | −0.285626 | ||||||||
\(333\) | −8.23094 | −0.451053 | ||||||||
\(334\) | 17.5983 | 0.962938 | ||||||||
\(335\) | −4.62998 | −0.252963 | ||||||||
\(336\) | 5.12150 | 0.279401 | ||||||||
\(337\) | −6.15145 | −0.335091 | −0.167545 | − | 0.985864i | \(-0.553584\pi\) | ||||
−0.167545 | + | 0.985864i | \(0.553584\pi\) | |||||||
\(338\) | 10.5816 | 0.575561 | ||||||||
\(339\) | −20.6996 | −1.12425 | ||||||||
\(340\) | −5.93635 | −0.321944 | ||||||||
\(341\) | −0.0432461 | −0.00234191 | ||||||||
\(342\) | 7.69146 | 0.415907 | ||||||||
\(343\) | 20.1583 | 1.08845 | ||||||||
\(344\) | 4.37246 | 0.235747 | ||||||||
\(345\) | 18.8937 | 1.01720 | ||||||||
\(346\) | 8.61548 | 0.463171 | ||||||||
\(347\) | −3.12435 | −0.167724 | −0.0838620 | − | 0.996477i | \(-0.526725\pi\) | ||||
−0.0838620 | + | 0.996477i | \(0.526725\pi\) | |||||||
\(348\) | 21.2201 | 1.13752 | ||||||||
\(349\) | −33.7342 | −1.80575 | −0.902876 | − | 0.429900i | \(-0.858549\pi\) | ||||
−0.902876 | + | 0.429900i | \(0.858549\pi\) | |||||||
\(350\) | −8.51826 | −0.455320 | ||||||||
\(351\) | 1.84344 | 0.0983955 | ||||||||
\(352\) | 1.41075 | 0.0751934 | ||||||||
\(353\) | 10.1358 | 0.539476 | 0.269738 | − | 0.962934i | \(-0.413063\pi\) | ||||
0.269738 | + | 0.962934i | \(0.413063\pi\) | |||||||
\(354\) | 15.6138 | 0.829864 | ||||||||
\(355\) | 5.55498 | 0.294828 | ||||||||
\(356\) | 12.0123 | 0.636649 | ||||||||
\(357\) | −28.9698 | −1.53324 | ||||||||
\(358\) | 0.878161 | 0.0464123 | ||||||||
\(359\) | −22.2355 | −1.17355 | −0.586773 | − | 0.809752i | \(-0.699602\pi\) | ||||
−0.586773 | + | 0.809752i | \(0.699602\pi\) | |||||||
\(360\) | −2.61769 | −0.137964 | ||||||||
\(361\) | −9.49120 | −0.499537 | ||||||||
\(362\) | −9.61659 | −0.505437 | ||||||||
\(363\) | 21.1188 | 1.10845 | ||||||||
\(364\) | −3.39789 | −0.178098 | ||||||||
\(365\) | −16.1946 | −0.847663 | ||||||||
\(366\) | −20.5277 | −1.07300 | ||||||||
\(367\) | −4.10434 | −0.214245 | −0.107122 | − | 0.994246i | \(-0.534164\pi\) | ||||
−0.107122 | + | 0.994246i | \(0.534164\pi\) | |||||||
\(368\) | −7.68050 | −0.400374 | ||||||||
\(369\) | −17.4904 | −0.910516 | ||||||||
\(370\) | 3.46318 | 0.180042 | ||||||||
\(371\) | 7.05158 | 0.366100 | ||||||||
\(372\) | −0.0718540 | −0.00372546 | ||||||||
\(373\) | 8.90918 | 0.461300 | 0.230650 | − | 0.973037i | \(-0.425915\pi\) | ||||
0.230650 | + | 0.973037i | \(0.425915\pi\) | |||||||
\(374\) | −7.97992 | −0.412632 | ||||||||
\(375\) | 21.8902 | 1.13040 | ||||||||
\(376\) | −9.27923 | −0.478540 | ||||||||
\(377\) | −14.0786 | −0.725084 | ||||||||
\(378\) | 2.59002 | 0.133216 | ||||||||
\(379\) | 19.2351 | 0.988041 | 0.494020 | − | 0.869450i | \(-0.335527\pi\) | ||||
0.494020 | + | 0.869450i | \(0.335527\pi\) | |||||||
\(380\) | −3.23619 | −0.166013 | ||||||||
\(381\) | 30.6875 | 1.57217 | ||||||||
\(382\) | −20.8588 | −1.06723 | ||||||||
\(383\) | −22.5674 | −1.15314 | −0.576569 | − | 0.817048i | \(-0.695609\pi\) | ||||
−0.576569 | + | 0.817048i | \(0.695609\pi\) | |||||||
\(384\) | 2.34399 | 0.119616 | ||||||||
\(385\) | 3.23493 | 0.164867 | ||||||||
\(386\) | 18.7552 | 0.954613 | ||||||||
\(387\) | −10.9062 | −0.554392 | ||||||||
\(388\) | −8.28067 | −0.420388 | ||||||||
\(389\) | −15.7463 | −0.798370 | −0.399185 | − | 0.916870i | \(-0.630707\pi\) | ||||
−0.399185 | + | 0.916870i | \(0.630707\pi\) | |||||||
\(390\) | 3.82556 | 0.193715 | ||||||||
\(391\) | 43.4448 | 2.19710 | ||||||||
\(392\) | 2.22599 | 0.112430 | ||||||||
\(393\) | 47.5888 | 2.40054 | ||||||||
\(394\) | 21.2499 | 1.07056 | ||||||||
\(395\) | 11.6003 | 0.583673 | ||||||||
\(396\) | −3.51882 | −0.176827 | ||||||||
\(397\) | −32.2351 | −1.61783 | −0.808916 | − | 0.587924i | \(-0.799945\pi\) | ||||
−0.808916 | + | 0.587924i | \(0.799945\pi\) | |||||||
\(398\) | −14.3586 | −0.719732 | ||||||||
\(399\) | −15.7928 | −0.790630 | ||||||||
\(400\) | −3.89860 | −0.194930 | ||||||||
\(401\) | −6.38181 | −0.318692 | −0.159346 | − | 0.987223i | \(-0.550939\pi\) | ||||
−0.159346 | + | 0.987223i | \(0.550939\pi\) | |||||||
\(402\) | −10.3410 | −0.515762 | ||||||||
\(403\) | 0.0476720 | 0.00237471 | ||||||||
\(404\) | −4.82528 | −0.240067 | ||||||||
\(405\) | −10.7691 | −0.535119 | ||||||||
\(406\) | −19.7803 | −0.981680 | ||||||||
\(407\) | 4.65537 | 0.230758 | ||||||||
\(408\) | −13.2588 | −0.656407 | ||||||||
\(409\) | 23.1706 | 1.14571 | 0.572855 | − | 0.819657i | \(-0.305836\pi\) | ||||
0.572855 | + | 0.819657i | \(0.305836\pi\) | |||||||
\(410\) | 7.35913 | 0.363441 | ||||||||
\(411\) | −31.9293 | −1.57496 | ||||||||
\(412\) | −5.80979 | −0.286228 | ||||||||
\(413\) | −14.5544 | −0.716175 | ||||||||
\(414\) | 19.1574 | 0.941533 | ||||||||
\(415\) | −5.46183 | −0.268111 | ||||||||
\(416\) | −1.55513 | −0.0762467 | ||||||||
\(417\) | 26.3202 | 1.28891 | ||||||||
\(418\) | −4.35025 | −0.212778 | ||||||||
\(419\) | 20.1679 | 0.985267 | 0.492633 | − | 0.870237i | \(-0.336034\pi\) | ||||
0.492633 | + | 0.870237i | \(0.336034\pi\) | |||||||
\(420\) | 5.37488 | 0.262267 | ||||||||
\(421\) | −0.352628 | −0.0171860 | −0.00859301 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859301 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(422\) | −0.948037 | −0.0461497 | ||||||||
\(423\) | 23.1450 | 1.12535 | ||||||||
\(424\) | 3.22734 | 0.156734 | ||||||||
\(425\) | 22.0525 | 1.06970 | ||||||||
\(426\) | 12.4070 | 0.601121 | ||||||||
\(427\) | 19.1349 | 0.926002 | ||||||||
\(428\) | 3.60050 | 0.174037 | ||||||||
\(429\) | 5.14250 | 0.248282 | ||||||||
\(430\) | 4.58879 | 0.221291 | ||||||||
\(431\) | 17.2506 | 0.830933 | 0.415466 | − | 0.909608i | \(-0.363618\pi\) | ||||
0.415466 | + | 0.909608i | \(0.363618\pi\) | |||||||
\(432\) | 1.18539 | 0.0570321 | ||||||||
\(433\) | 22.2333 | 1.06846 | 0.534232 | − | 0.845338i | \(-0.320601\pi\) | ||||
0.534232 | + | 0.845338i | \(0.320601\pi\) | |||||||
\(434\) | 0.0669787 | 0.00321508 | ||||||||
\(435\) | 22.2699 | 1.06776 | ||||||||
\(436\) | 7.46909 | 0.357704 | ||||||||
\(437\) | 23.6839 | 1.13295 | ||||||||
\(438\) | −36.1704 | −1.72829 | ||||||||
\(439\) | 10.4878 | 0.500557 | 0.250278 | − | 0.968174i | \(-0.419478\pi\) | ||||
0.250278 | + | 0.968174i | \(0.419478\pi\) | |||||||
\(440\) | 1.48055 | 0.0705824 | ||||||||
\(441\) | −5.55226 | −0.264393 | ||||||||
\(442\) | 8.79661 | 0.418412 | ||||||||
\(443\) | −17.4820 | −0.830593 | −0.415297 | − | 0.909686i | \(-0.636322\pi\) | ||||
−0.415297 | + | 0.909686i | \(0.636322\pi\) | |||||||
\(444\) | 7.73498 | 0.367086 | ||||||||
\(445\) | 12.6066 | 0.597609 | ||||||||
\(446\) | −1.73412 | −0.0821128 | ||||||||
\(447\) | −27.3391 | −1.29309 | ||||||||
\(448\) | −2.18495 | −0.103229 | ||||||||
\(449\) | 21.9807 | 1.03733 | 0.518666 | − | 0.854977i | \(-0.326429\pi\) | ||||
0.518666 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(450\) | 9.72423 | 0.458405 | ||||||||
\(451\) | 9.89249 | 0.465819 | ||||||||
\(452\) | 8.83095 | 0.415373 | ||||||||
\(453\) | −40.8154 | −1.91767 | ||||||||
\(454\) | −21.5834 | −1.01296 | ||||||||
\(455\) | −3.56600 | −0.167176 | ||||||||
\(456\) | −7.22800 | −0.338482 | ||||||||
\(457\) | 2.59785 | 0.121522 | 0.0607612 | − | 0.998152i | \(-0.480647\pi\) | ||||
0.0607612 | + | 0.998152i | \(0.480647\pi\) | |||||||
\(458\) | 13.5664 | 0.633916 | ||||||||
\(459\) | −6.70516 | −0.312970 | ||||||||
\(460\) | −8.06049 | −0.375822 | ||||||||
\(461\) | −0.737334 | −0.0343411 | −0.0171705 | − | 0.999853i | \(-0.505466\pi\) | ||||
−0.0171705 | + | 0.999853i | \(0.505466\pi\) | |||||||
\(462\) | 7.22517 | 0.336145 | ||||||||
\(463\) | 26.1869 | 1.21701 | 0.608503 | − | 0.793551i | \(-0.291770\pi\) | ||||
0.608503 | + | 0.793551i | \(0.291770\pi\) | |||||||
\(464\) | −9.05297 | −0.420274 | ||||||||
\(465\) | −0.0754089 | −0.00349701 | ||||||||
\(466\) | 26.1818 | 1.21285 | ||||||||
\(467\) | −26.0862 | −1.20713 | −0.603563 | − | 0.797315i | \(-0.706253\pi\) | ||||
−0.603563 | + | 0.797315i | \(0.706253\pi\) | |||||||
\(468\) | 3.87895 | 0.179304 | ||||||||
\(469\) | 9.63937 | 0.445105 | ||||||||
\(470\) | −9.73831 | −0.449195 | ||||||||
\(471\) | −43.9849 | −2.02672 | ||||||||
\(472\) | −6.66120 | −0.306607 | ||||||||
\(473\) | 6.16847 | 0.283626 | ||||||||
\(474\) | 25.9091 | 1.19004 | ||||||||
\(475\) | 12.0219 | 0.551601 | ||||||||
\(476\) | 12.3592 | 0.566482 | ||||||||
\(477\) | −8.04991 | −0.368580 | ||||||||
\(478\) | 6.51518 | 0.297998 | ||||||||
\(479\) | −29.7741 | −1.36041 | −0.680207 | − | 0.733020i | \(-0.738110\pi\) | ||||
−0.680207 | + | 0.733020i | \(0.738110\pi\) | |||||||
\(480\) | 2.45996 | 0.112281 | ||||||||
\(481\) | −5.13182 | −0.233991 | ||||||||
\(482\) | 16.3552 | 0.744959 | ||||||||
\(483\) | −39.3357 | −1.78984 | ||||||||
\(484\) | −9.00978 | −0.409535 | ||||||||
\(485\) | −8.69035 | −0.394609 | ||||||||
\(486\) | −20.4964 | −0.929737 | ||||||||
\(487\) | 9.98926 | 0.452656 | 0.226328 | − | 0.974051i | \(-0.427328\pi\) | ||||
0.226328 | + | 0.974051i | \(0.427328\pi\) | |||||||
\(488\) | 8.75759 | 0.396437 | ||||||||
\(489\) | 36.2530 | 1.63942 | ||||||||
\(490\) | 2.33612 | 0.105535 | ||||||||
\(491\) | 24.9247 | 1.12484 | 0.562418 | − | 0.826853i | \(-0.309871\pi\) | ||||
0.562418 | + | 0.826853i | \(0.309871\pi\) | |||||||
\(492\) | 16.4365 | 0.741016 | ||||||||
\(493\) | 51.2081 | 2.30630 | ||||||||
\(494\) | 4.79546 | 0.215758 | ||||||||
\(495\) | −3.69291 | −0.165984 | ||||||||
\(496\) | 0.0306546 | 0.00137643 | ||||||||
\(497\) | −11.5652 | −0.518769 | ||||||||
\(498\) | −12.1989 | −0.546648 | ||||||||
\(499\) | −10.9537 | −0.490356 | −0.245178 | − | 0.969478i | \(-0.578846\pi\) | ||||
−0.245178 | + | 0.969478i | \(0.578846\pi\) | |||||||
\(500\) | −9.33885 | −0.417646 | ||||||||
\(501\) | 41.2503 | 1.84293 | ||||||||
\(502\) | −12.0030 | −0.535721 | ||||||||
\(503\) | 18.7370 | 0.835444 | 0.417722 | − | 0.908575i | \(-0.362829\pi\) | ||||
0.417722 | + | 0.908575i | \(0.362829\pi\) | |||||||
\(504\) | 5.44989 | 0.242757 | ||||||||
\(505\) | −5.06401 | −0.225345 | ||||||||
\(506\) | −10.8353 | −0.481688 | ||||||||
\(507\) | 24.8031 | 1.10154 | ||||||||
\(508\) | −13.0920 | −0.580863 | ||||||||
\(509\) | 31.9270 | 1.41514 | 0.707570 | − | 0.706643i | \(-0.249791\pi\) | ||||
0.707570 | + | 0.706643i | \(0.249791\pi\) | |||||||
\(510\) | −13.9147 | −0.616155 | ||||||||
\(511\) | 33.7163 | 1.49152 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.65531 | −0.161386 | ||||||||
\(514\) | 19.5817 | 0.863713 | ||||||||
\(515\) | −6.09723 | −0.268676 | ||||||||
\(516\) | 10.2490 | 0.451187 | ||||||||
\(517\) | −13.0907 | −0.575728 | ||||||||
\(518\) | −7.21016 | −0.316796 | ||||||||
\(519\) | 20.1946 | 0.886444 | ||||||||
\(520\) | −1.63207 | −0.0715711 | ||||||||
\(521\) | 43.8688 | 1.92193 | 0.960964 | − | 0.276674i | \(-0.0892324\pi\) | ||||
0.960964 | + | 0.276674i | \(0.0892324\pi\) | |||||||
\(522\) | 22.5807 | 0.988330 | ||||||||
\(523\) | 5.98030 | 0.261500 | 0.130750 | − | 0.991415i | \(-0.458261\pi\) | ||||
0.130750 | + | 0.991415i | \(0.458261\pi\) | |||||||
\(524\) | −20.3025 | −0.886917 | ||||||||
\(525\) | −19.9667 | −0.871418 | ||||||||
\(526\) | −17.7616 | −0.774443 | ||||||||
\(527\) | −0.173398 | −0.00755332 | ||||||||
\(528\) | 3.30679 | 0.143910 | ||||||||
\(529\) | 35.9901 | 1.56479 | ||||||||
\(530\) | 3.38701 | 0.147122 | ||||||||
\(531\) | 16.6149 | 0.721027 | ||||||||
\(532\) | 6.73759 | 0.292111 | ||||||||
\(533\) | −10.9049 | −0.472344 | ||||||||
\(534\) | 28.1566 | 1.21846 | ||||||||
\(535\) | 3.77863 | 0.163364 | ||||||||
\(536\) | 4.41171 | 0.190557 | ||||||||
\(537\) | 2.05840 | 0.0888265 | ||||||||
\(538\) | 1.39786 | 0.0602659 | ||||||||
\(539\) | 3.14033 | 0.135263 | ||||||||
\(540\) | 1.24404 | 0.0535348 | ||||||||
\(541\) | −43.9110 | −1.88788 | −0.943941 | − | 0.330113i | \(-0.892913\pi\) | ||||
−0.943941 | + | 0.330113i | \(0.892913\pi\) | |||||||
\(542\) | 8.65894 | 0.371933 | ||||||||
\(543\) | −22.5412 | −0.967335 | ||||||||
\(544\) | 5.65650 | 0.242520 | ||||||||
\(545\) | 7.83861 | 0.335769 | ||||||||
\(546\) | −7.96461 | −0.340854 | ||||||||
\(547\) | −20.4742 | −0.875415 | −0.437708 | − | 0.899117i | \(-0.644209\pi\) | ||||
−0.437708 | + | 0.899117i | \(0.644209\pi\) | |||||||
\(548\) | 13.6218 | 0.581894 | ||||||||
\(549\) | −21.8439 | −0.932276 | ||||||||
\(550\) | −5.49997 | −0.234519 | ||||||||
\(551\) | 27.9161 | 1.18926 | ||||||||
\(552\) | −18.0030 | −0.766259 | ||||||||
\(553\) | −24.1512 | −1.02701 | ||||||||
\(554\) | 0.130566 | 0.00554724 | ||||||||
\(555\) | 8.11766 | 0.344575 | ||||||||
\(556\) | −11.2288 | −0.476207 | ||||||||
\(557\) | −16.7724 | −0.710668 | −0.355334 | − | 0.934739i | \(-0.615633\pi\) | ||||
−0.355334 | + | 0.934739i | \(0.615633\pi\) | |||||||
\(558\) | −0.0764613 | −0.00323686 | ||||||||
\(559\) | −6.79976 | −0.287599 | ||||||||
\(560\) | −2.29305 | −0.0968990 | ||||||||
\(561\) | −18.7049 | −0.789720 | ||||||||
\(562\) | 17.5677 | 0.741050 | ||||||||
\(563\) | −13.5374 | −0.570532 | −0.285266 | − | 0.958448i | \(-0.592082\pi\) | ||||
−0.285266 | + | 0.958448i | \(0.592082\pi\) | |||||||
\(564\) | −21.7504 | −0.915858 | ||||||||
\(565\) | 9.26785 | 0.389901 | ||||||||
\(566\) | 7.59996 | 0.319450 | ||||||||
\(567\) | 22.4206 | 0.941578 | ||||||||
\(568\) | −5.29311 | −0.222094 | ||||||||
\(569\) | 28.9607 | 1.21409 | 0.607047 | − | 0.794666i | \(-0.292354\pi\) | ||||
0.607047 | + | 0.794666i | \(0.292354\pi\) | |||||||
\(570\) | −7.58560 | −0.317726 | ||||||||
\(571\) | −19.0682 | −0.797978 | −0.398989 | − | 0.916956i | \(-0.630639\pi\) | ||||
−0.398989 | + | 0.916956i | \(0.630639\pi\) | |||||||
\(572\) | −2.19391 | −0.0917320 | ||||||||
\(573\) | −48.8928 | −2.04253 | ||||||||
\(574\) | −15.3213 | −0.639500 | ||||||||
\(575\) | 29.9432 | 1.24872 | ||||||||
\(576\) | 2.49429 | 0.103929 | ||||||||
\(577\) | 10.6521 | 0.443451 | 0.221725 | − | 0.975109i | \(-0.428831\pi\) | ||||
0.221725 | + | 0.975109i | \(0.428831\pi\) | |||||||
\(578\) | −14.9960 | −0.623751 | ||||||||
\(579\) | 43.9619 | 1.82700 | ||||||||
\(580\) | −9.50086 | −0.394502 | ||||||||
\(581\) | 11.3713 | 0.471759 | ||||||||
\(582\) | −19.4098 | −0.804563 | ||||||||
\(583\) | 4.55298 | 0.188565 | ||||||||
\(584\) | 15.4311 | 0.638545 | ||||||||
\(585\) | 4.07085 | 0.168309 | ||||||||
\(586\) | −10.7354 | −0.443475 | ||||||||
\(587\) | −34.9923 | −1.44429 | −0.722144 | − | 0.691743i | \(-0.756843\pi\) | ||||
−0.722144 | + | 0.691743i | \(0.756843\pi\) | |||||||
\(588\) | 5.21770 | 0.215174 | ||||||||
\(589\) | −0.0945275 | −0.00389494 | ||||||||
\(590\) | −6.99076 | −0.287805 | ||||||||
\(591\) | 49.8096 | 2.04889 | ||||||||
\(592\) | −3.29992 | −0.135626 | ||||||||
\(593\) | −14.0327 | −0.576254 | −0.288127 | − | 0.957592i | \(-0.593032\pi\) | ||||
−0.288127 | + | 0.957592i | \(0.593032\pi\) | |||||||
\(594\) | 1.67229 | 0.0686150 | ||||||||
\(595\) | 12.9706 | 0.531744 | ||||||||
\(596\) | 11.6635 | 0.477755 | ||||||||
\(597\) | −33.6564 | −1.37746 | ||||||||
\(598\) | 11.9442 | 0.488435 | ||||||||
\(599\) | 27.6781 | 1.13090 | 0.565448 | − | 0.824784i | \(-0.308703\pi\) | ||||
0.565448 | + | 0.824784i | \(0.308703\pi\) | |||||||
\(600\) | −9.13829 | −0.373069 | ||||||||
\(601\) | 35.6052 | 1.45237 | 0.726184 | − | 0.687500i | \(-0.241292\pi\) | ||||
0.726184 | + | 0.687500i | \(0.241292\pi\) | |||||||
\(602\) | −9.55362 | −0.389376 | ||||||||
\(603\) | −11.0041 | −0.448120 | ||||||||
\(604\) | 17.4128 | 0.708517 | ||||||||
\(605\) | −9.45553 | −0.384422 | ||||||||
\(606\) | −11.3104 | −0.459454 | ||||||||
\(607\) | 5.03024 | 0.204171 | 0.102086 | − | 0.994776i | \(-0.467448\pi\) | ||||
0.102086 | + | 0.994776i | \(0.467448\pi\) | |||||||
\(608\) | 3.08363 | 0.125058 | ||||||||
\(609\) | −46.3648 | −1.87880 | ||||||||
\(610\) | 9.19086 | 0.372127 | ||||||||
\(611\) | 14.4304 | 0.583793 | ||||||||
\(612\) | −14.1089 | −0.570319 | ||||||||
\(613\) | 17.0481 | 0.688567 | 0.344284 | − | 0.938866i | \(-0.388122\pi\) | ||||
0.344284 | + | 0.938866i | \(0.388122\pi\) | |||||||
\(614\) | 12.9018 | 0.520676 | ||||||||
\(615\) | 17.2497 | 0.695576 | ||||||||
\(616\) | −3.08243 | −0.124194 | ||||||||
\(617\) | −0.892886 | −0.0359462 | −0.0179731 | − | 0.999838i | \(-0.505721\pi\) | ||||
−0.0179731 | + | 0.999838i | \(0.505721\pi\) | |||||||
\(618\) | −13.6181 | −0.547800 | ||||||||
\(619\) | −37.8295 | −1.52050 | −0.760249 | − | 0.649632i | \(-0.774923\pi\) | ||||
−0.760249 | + | 0.649632i | \(0.774923\pi\) | |||||||
\(620\) | 0.0321712 | 0.00129203 | ||||||||
\(621\) | −9.10439 | −0.365347 | ||||||||
\(622\) | 5.19578 | 0.208332 | ||||||||
\(623\) | −26.2462 | −1.05153 | ||||||||
\(624\) | −3.64522 | −0.145925 | ||||||||
\(625\) | 9.69214 | 0.387685 | ||||||||
\(626\) | 6.42747 | 0.256893 | ||||||||
\(627\) | −10.1969 | −0.407226 | ||||||||
\(628\) | 18.7650 | 0.748804 | ||||||||
\(629\) | 18.6660 | 0.744262 | ||||||||
\(630\) | 5.71952 | 0.227871 | ||||||||
\(631\) | 15.2056 | 0.605326 | 0.302663 | − | 0.953098i | \(-0.402124\pi\) | ||||
0.302663 | + | 0.953098i | \(0.402124\pi\) | |||||||
\(632\) | −11.0534 | −0.439681 | ||||||||
\(633\) | −2.22219 | −0.0883241 | ||||||||
\(634\) | −12.2775 | −0.487602 | ||||||||
\(635\) | −13.7397 | −0.545243 | ||||||||
\(636\) | 7.56486 | 0.299966 | ||||||||
\(637\) | −3.46171 | −0.137158 | ||||||||
\(638\) | −12.7715 | −0.505629 | ||||||||
\(639\) | 13.2025 | 0.522284 | ||||||||
\(640\) | −1.04947 | −0.0414841 | ||||||||
\(641\) | −28.9376 | −1.14296 | −0.571482 | − | 0.820614i | \(-0.693631\pi\) | ||||
−0.571482 | + | 0.820614i | \(0.693631\pi\) | |||||||
\(642\) | 8.43953 | 0.333082 | ||||||||
\(643\) | −18.3591 | −0.724014 | −0.362007 | − | 0.932175i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932175i | \(0.617908\pi\) | |||||||
\(644\) | 16.7815 | 0.661284 | ||||||||
\(645\) | 10.7561 | 0.423520 | ||||||||
\(646\) | −17.4426 | −0.686269 | ||||||||
\(647\) | −12.9403 | −0.508736 | −0.254368 | − | 0.967108i | \(-0.581867\pi\) | ||||
−0.254368 | + | 0.967108i | \(0.581867\pi\) | |||||||
\(648\) | 10.2614 | 0.403106 | ||||||||
\(649\) | −9.39732 | −0.368877 | ||||||||
\(650\) | 6.06285 | 0.237804 | ||||||||
\(651\) | 0.156997 | 0.00615322 | ||||||||
\(652\) | −15.4664 | −0.605709 | ||||||||
\(653\) | −2.89510 | −0.113294 | −0.0566469 | − | 0.998394i | \(-0.518041\pi\) | ||||
−0.0566469 | + | 0.998394i | \(0.518041\pi\) | |||||||
\(654\) | 17.5075 | 0.684596 | ||||||||
\(655\) | −21.3069 | −0.832530 | ||||||||
\(656\) | −7.01221 | −0.273781 | ||||||||
\(657\) | −38.4897 | −1.50163 | ||||||||
\(658\) | 20.2747 | 0.790388 | ||||||||
\(659\) | 4.04102 | 0.157416 | 0.0787079 | − | 0.996898i | \(-0.474921\pi\) | ||||
0.0787079 | + | 0.996898i | \(0.474921\pi\) | |||||||
\(660\) | 3.47039 | 0.135085 | ||||||||
\(661\) | −4.15409 | −0.161576 | −0.0807878 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807878 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(662\) | −7.40674 | −0.287871 | ||||||||
\(663\) | 20.6192 | 0.800782 | ||||||||
\(664\) | 5.20435 | 0.201968 | ||||||||
\(665\) | 7.07092 | 0.274199 | ||||||||
\(666\) | 8.23094 | 0.318943 | ||||||||
\(667\) | 69.5314 | 2.69227 | ||||||||
\(668\) | −17.5983 | −0.680900 | ||||||||
\(669\) | −4.06475 | −0.157152 | ||||||||
\(670\) | 4.62998 | 0.178872 | ||||||||
\(671\) | 12.3548 | 0.476952 | ||||||||
\(672\) | −5.12150 | −0.197566 | ||||||||
\(673\) | −5.82154 | −0.224404 | −0.112202 | − | 0.993685i | \(-0.535790\pi\) | ||||
−0.112202 | + | 0.993685i | \(0.535790\pi\) | |||||||
\(674\) | 6.15145 | 0.236945 | ||||||||
\(675\) | −4.62137 | −0.177877 | ||||||||
\(676\) | −10.5816 | −0.406983 | ||||||||
\(677\) | −0.719572 | −0.0276554 | −0.0138277 | − | 0.999904i | \(-0.504402\pi\) | ||||
−0.0138277 | + | 0.999904i | \(0.504402\pi\) | |||||||
\(678\) | 20.6996 | 0.794965 | ||||||||
\(679\) | 18.0929 | 0.694340 | ||||||||
\(680\) | 5.93635 | 0.227649 | ||||||||
\(681\) | −50.5913 | −1.93866 | ||||||||
\(682\) | 0.0432461 | 0.00165598 | ||||||||
\(683\) | 42.0362 | 1.60847 | 0.804235 | − | 0.594311i | \(-0.202575\pi\) | ||||
0.804235 | + | 0.594311i | \(0.202575\pi\) | |||||||
\(684\) | −7.69146 | −0.294090 | ||||||||
\(685\) | 14.2957 | 0.546211 | ||||||||
\(686\) | −20.1583 | −0.769649 | ||||||||
\(687\) | 31.7995 | 1.21323 | ||||||||
\(688\) | −4.37246 | −0.166699 | ||||||||
\(689\) | −5.01895 | −0.191207 | ||||||||
\(690\) | −18.8937 | −0.719271 | ||||||||
\(691\) | 0.535871 | 0.0203855 | 0.0101927 | − | 0.999948i | \(-0.496755\pi\) | ||||
0.0101927 | + | 0.999948i | \(0.496755\pi\) | |||||||
\(692\) | −8.61548 | −0.327511 | ||||||||
\(693\) | 7.68845 | 0.292060 | ||||||||
\(694\) | 3.12435 | 0.118599 | ||||||||
\(695\) | −11.7843 | −0.447005 | ||||||||
\(696\) | −21.2201 | −0.804345 | ||||||||
\(697\) | 39.6645 | 1.50240 | ||||||||
\(698\) | 33.7342 | 1.27686 | ||||||||
\(699\) | 61.3698 | 2.32122 | ||||||||
\(700\) | 8.51826 | 0.321960 | ||||||||
\(701\) | 27.0303 | 1.02092 | 0.510461 | − | 0.859901i | \(-0.329475\pi\) | ||||
0.510461 | + | 0.859901i | \(0.329475\pi\) | |||||||
\(702\) | −1.84344 | −0.0695762 | ||||||||
\(703\) | 10.1757 | 0.383786 | ||||||||
\(704\) | −1.41075 | −0.0531698 | ||||||||
\(705\) | −22.8265 | −0.859695 | ||||||||
\(706\) | −10.1358 | −0.381467 | ||||||||
\(707\) | 10.5430 | 0.396510 | ||||||||
\(708\) | −15.6138 | −0.586802 | ||||||||
\(709\) | 44.6754 | 1.67782 | 0.838911 | − | 0.544269i | \(-0.183193\pi\) | ||||
0.838911 | + | 0.544269i | \(0.183193\pi\) | |||||||
\(710\) | −5.55498 | −0.208475 | ||||||||
\(711\) | 27.5704 | 1.03397 | ||||||||
\(712\) | −12.0123 | −0.450179 | ||||||||
\(713\) | −0.235443 | −0.00881740 | ||||||||
\(714\) | 28.9698 | 1.08417 | ||||||||
\(715\) | −2.30245 | −0.0861068 | ||||||||
\(716\) | −0.878161 | −0.0328184 | ||||||||
\(717\) | 15.2715 | 0.570325 | ||||||||
\(718\) | 22.2355 | 0.829822 | ||||||||
\(719\) | 0.144697 | 0.00539630 | 0.00269815 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269815 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(720\) | 2.61769 | 0.0975555 | ||||||||
\(721\) | 12.6941 | 0.472753 | ||||||||
\(722\) | 9.49120 | 0.353226 | ||||||||
\(723\) | 38.3364 | 1.42575 | ||||||||
\(724\) | 9.61659 | 0.357398 | ||||||||
\(725\) | 35.2940 | 1.31078 | ||||||||
\(726\) | −21.1188 | −0.783793 | ||||||||
\(727\) | −33.8738 | −1.25631 | −0.628154 | − | 0.778089i | \(-0.716189\pi\) | ||||
−0.628154 | + | 0.778089i | \(0.716189\pi\) | |||||||
\(728\) | 3.39789 | 0.125934 | ||||||||
\(729\) | −17.2592 | −0.639231 | ||||||||
\(730\) | 16.1946 | 0.599389 | ||||||||
\(731\) | 24.7328 | 0.914777 | ||||||||
\(732\) | 20.5277 | 0.758725 | ||||||||
\(733\) | 29.1531 | 1.07679 | 0.538396 | − | 0.842692i | \(-0.319030\pi\) | ||||
0.538396 | + | 0.842692i | \(0.319030\pi\) | |||||||
\(734\) | 4.10434 | 0.151494 | ||||||||
\(735\) | 5.47584 | 0.201980 | ||||||||
\(736\) | 7.68050 | 0.283107 | ||||||||
\(737\) | 6.22384 | 0.229258 | ||||||||
\(738\) | 17.4904 | 0.643832 | ||||||||
\(739\) | 18.8801 | 0.694516 | 0.347258 | − | 0.937770i | \(-0.387113\pi\) | ||||
0.347258 | + | 0.937770i | \(0.387113\pi\) | |||||||
\(740\) | −3.46318 | −0.127309 | ||||||||
\(741\) | 11.2405 | 0.412930 | ||||||||
\(742\) | −7.05158 | −0.258872 | ||||||||
\(743\) | 42.4345 | 1.55677 | 0.778385 | − | 0.627787i | \(-0.216039\pi\) | ||||
0.778385 | + | 0.627787i | \(0.216039\pi\) | |||||||
\(744\) | 0.0718540 | 0.00263430 | ||||||||
\(745\) | 12.2405 | 0.448458 | ||||||||
\(746\) | −8.90918 | −0.326188 | ||||||||
\(747\) | −12.9811 | −0.474955 | ||||||||
\(748\) | 7.97992 | 0.291775 | ||||||||
\(749\) | −7.86691 | −0.287451 | ||||||||
\(750\) | −21.8902 | −0.799316 | ||||||||
\(751\) | 47.6990 | 1.74056 | 0.870280 | − | 0.492558i | \(-0.163938\pi\) | ||||
0.870280 | + | 0.492558i | \(0.163938\pi\) | |||||||
\(752\) | 9.27923 | 0.338379 | ||||||||
\(753\) | −28.1349 | −1.02529 | ||||||||
\(754\) | 14.0786 | 0.512712 | ||||||||
\(755\) | 18.2743 | 0.665069 | ||||||||
\(756\) | −2.59002 | −0.0941981 | ||||||||
\(757\) | 20.4047 | 0.741621 | 0.370810 | − | 0.928709i | \(-0.379080\pi\) | ||||
0.370810 | + | 0.928709i | \(0.379080\pi\) | |||||||
\(758\) | −19.2351 | −0.698650 | ||||||||
\(759\) | −25.3978 | −0.921882 | ||||||||
\(760\) | 3.23619 | 0.117389 | ||||||||
\(761\) | 29.4965 | 1.06925 | 0.534623 | − | 0.845091i | \(-0.320454\pi\) | ||||
0.534623 | + | 0.845091i | \(0.320454\pi\) | |||||||
\(762\) | −30.6875 | −1.11169 | ||||||||
\(763\) | −16.3196 | −0.590809 | ||||||||
\(764\) | 20.8588 | 0.754645 | ||||||||
\(765\) | −14.8069 | −0.535346 | ||||||||
\(766\) | 22.5674 | 0.815392 | ||||||||
\(767\) | 10.3591 | 0.374044 | ||||||||
\(768\) | −2.34399 | −0.0845814 | ||||||||
\(769\) | −13.8261 | −0.498582 | −0.249291 | − | 0.968429i | \(-0.580198\pi\) | ||||
−0.249291 | + | 0.968429i | \(0.580198\pi\) | |||||||
\(770\) | −3.23493 | −0.116579 | ||||||||
\(771\) | 45.8994 | 1.65302 | ||||||||
\(772\) | −18.7552 | −0.675014 | ||||||||
\(773\) | 31.2558 | 1.12419 | 0.562097 | − | 0.827071i | \(-0.309995\pi\) | ||||
0.562097 | + | 0.827071i | \(0.309995\pi\) | |||||||
\(774\) | 10.9062 | 0.392014 | ||||||||
\(775\) | −0.119510 | −0.00429293 | ||||||||
\(776\) | 8.28067 | 0.297259 | ||||||||
\(777\) | −16.9005 | −0.606304 | ||||||||
\(778\) | 15.7463 | 0.564533 | ||||||||
\(779\) | 21.6231 | 0.774727 | ||||||||
\(780\) | −3.82556 | −0.136977 | ||||||||
\(781\) | −7.46727 | −0.267200 | ||||||||
\(782\) | −43.4448 | −1.55358 | ||||||||
\(783\) | −10.7313 | −0.383506 | ||||||||
\(784\) | −2.22599 | −0.0794997 | ||||||||
\(785\) | 19.6933 | 0.702886 | ||||||||
\(786\) | −47.5888 | −1.69743 | ||||||||
\(787\) | −23.1041 | −0.823572 | −0.411786 | − | 0.911280i | \(-0.635095\pi\) | ||||
−0.411786 | + | 0.911280i | \(0.635095\pi\) | |||||||
\(788\) | −21.2499 | −0.756997 | ||||||||
\(789\) | −41.6330 | −1.48217 | ||||||||
\(790\) | −11.6003 | −0.412719 | ||||||||
\(791\) | −19.2952 | −0.686058 | ||||||||
\(792\) | 3.51882 | 0.125036 | ||||||||
\(793\) | −13.6192 | −0.483632 | ||||||||
\(794\) | 32.2351 | 1.14398 | ||||||||
\(795\) | 7.93912 | 0.281572 | ||||||||
\(796\) | 14.3586 | 0.508927 | ||||||||
\(797\) | 3.27116 | 0.115870 | 0.0579352 | − | 0.998320i | \(-0.481548\pi\) | ||||
0.0579352 | + | 0.998320i | \(0.481548\pi\) | |||||||
\(798\) | 15.7928 | 0.559060 | ||||||||
\(799\) | −52.4880 | −1.85689 | ||||||||
\(800\) | 3.89860 | 0.137836 | ||||||||
\(801\) | 29.9620 | 1.05866 | ||||||||
\(802\) | 6.38181 | 0.225350 | ||||||||
\(803\) | 21.7695 | 0.768230 | ||||||||
\(804\) | 10.3410 | 0.364699 | ||||||||
\(805\) | 17.6118 | 0.620733 | ||||||||
\(806\) | −0.0476720 | −0.00167917 | ||||||||
\(807\) | 3.27656 | 0.115340 | ||||||||
\(808\) | 4.82528 | 0.169753 | ||||||||
\(809\) | −32.9813 | −1.15956 | −0.579780 | − | 0.814773i | \(-0.696862\pi\) | ||||
−0.579780 | + | 0.814773i | \(0.696862\pi\) | |||||||
\(810\) | 10.7691 | 0.378387 | ||||||||
\(811\) | −35.6142 | −1.25058 | −0.625292 | − | 0.780391i | \(-0.715020\pi\) | ||||
−0.625292 | + | 0.780391i | \(0.715020\pi\) | |||||||
\(812\) | 19.7803 | 0.694152 | ||||||||
\(813\) | 20.2965 | 0.711828 | ||||||||
\(814\) | −4.65537 | −0.163171 | ||||||||
\(815\) | −16.2315 | −0.568566 | ||||||||
\(816\) | 13.2588 | 0.464150 | ||||||||
\(817\) | 13.4831 | 0.471713 | ||||||||
\(818\) | −23.1706 | −0.810139 | ||||||||
\(819\) | −8.47530 | −0.296151 | ||||||||
\(820\) | −7.35913 | −0.256992 | ||||||||
\(821\) | 50.6260 | 1.76686 | 0.883429 | − | 0.468564i | \(-0.155229\pi\) | ||||
0.883429 | + | 0.468564i | \(0.155229\pi\) | |||||||
\(822\) | 31.9293 | 1.11366 | ||||||||
\(823\) | −28.8589 | −1.00596 | −0.502979 | − | 0.864298i | \(-0.667763\pi\) | ||||
−0.502979 | + | 0.864298i | \(0.667763\pi\) | |||||||
\(824\) | 5.80979 | 0.202394 | ||||||||
\(825\) | −12.8919 | −0.448837 | ||||||||
\(826\) | 14.5544 | 0.506412 | ||||||||
\(827\) | −23.1180 | −0.803893 | −0.401947 | − | 0.915663i | \(-0.631666\pi\) | ||||
−0.401947 | + | 0.915663i | \(0.631666\pi\) | |||||||
\(828\) | −19.1574 | −0.665764 | ||||||||
\(829\) | −38.4205 | −1.33440 | −0.667200 | − | 0.744879i | \(-0.732507\pi\) | ||||
−0.667200 | + | 0.744879i | \(0.732507\pi\) | |||||||
\(830\) | 5.46183 | 0.189583 | ||||||||
\(831\) | 0.306046 | 0.0106166 | ||||||||
\(832\) | 1.55513 | 0.0539145 | ||||||||
\(833\) | 12.5913 | 0.436264 | ||||||||
\(834\) | −26.3202 | −0.911394 | ||||||||
\(835\) | −18.4690 | −0.639146 | ||||||||
\(836\) | 4.35025 | 0.150456 | ||||||||
\(837\) | 0.0363377 | 0.00125601 | ||||||||
\(838\) | −20.1679 | −0.696689 | ||||||||
\(839\) | 28.3429 | 0.978507 | 0.489253 | − | 0.872142i | \(-0.337269\pi\) | ||||
0.489253 | + | 0.872142i | \(0.337269\pi\) | |||||||
\(840\) | −5.37488 | −0.185451 | ||||||||
\(841\) | 52.9563 | 1.82608 | ||||||||
\(842\) | 0.352628 | 0.0121524 | ||||||||
\(843\) | 41.1786 | 1.41827 | ||||||||
\(844\) | 0.948037 | 0.0326328 | ||||||||
\(845\) | −11.1051 | −0.382026 | ||||||||
\(846\) | −23.1450 | −0.795743 | ||||||||
\(847\) | 19.6859 | 0.676416 | ||||||||
\(848\) | −3.22734 | −0.110827 | ||||||||
\(849\) | 17.8142 | 0.611382 | ||||||||
\(850\) | −22.0525 | −0.756393 | ||||||||
\(851\) | 25.3451 | 0.868817 | ||||||||
\(852\) | −12.4070 | −0.425056 | ||||||||
\(853\) | −2.54129 | −0.0870123 | −0.0435061 | − | 0.999053i | \(-0.513853\pi\) | ||||
−0.0435061 | + | 0.999053i | \(0.513853\pi\) | |||||||
\(854\) | −19.1349 | −0.654782 | ||||||||
\(855\) | −8.07199 | −0.276056 | ||||||||
\(856\) | −3.60050 | −0.123063 | ||||||||
\(857\) | 24.4635 | 0.835659 | 0.417829 | − | 0.908526i | \(-0.362791\pi\) | ||||
0.417829 | + | 0.908526i | \(0.362791\pi\) | |||||||
\(858\) | −5.14250 | −0.175562 | ||||||||
\(859\) | −6.78867 | −0.231627 | −0.115813 | − | 0.993271i | \(-0.536947\pi\) | ||||
−0.115813 | + | 0.993271i | \(0.536947\pi\) | |||||||
\(860\) | −4.58879 | −0.156476 | ||||||||
\(861\) | −35.9130 | −1.22391 | ||||||||
\(862\) | −17.2506 | −0.587558 | ||||||||
\(863\) | −53.4908 | −1.82085 | −0.910424 | − | 0.413676i | \(-0.864245\pi\) | ||||
−0.910424 | + | 0.413676i | \(0.864245\pi\) | |||||||
\(864\) | −1.18539 | −0.0403278 | ||||||||
\(865\) | −9.04172 | −0.307428 | ||||||||
\(866\) | −22.2333 | −0.755519 | ||||||||
\(867\) | −35.1504 | −1.19377 | ||||||||
\(868\) | −0.0669787 | −0.00227341 | ||||||||
\(869\) | −15.5936 | −0.528978 | ||||||||
\(870\) | −22.2699 | −0.755021 | ||||||||
\(871\) | −6.86080 | −0.232469 | ||||||||
\(872\) | −7.46909 | −0.252935 | ||||||||
\(873\) | −20.6544 | −0.699044 | ||||||||
\(874\) | −23.6839 | −0.801118 | ||||||||
\(875\) | 20.4049 | 0.689813 | ||||||||
\(876\) | 36.1704 | 1.22209 | ||||||||
\(877\) | −5.69700 | −0.192374 | −0.0961871 | − | 0.995363i | \(-0.530665\pi\) | ||||
−0.0961871 | + | 0.995363i | \(0.530665\pi\) | |||||||
\(878\) | −10.4878 | −0.353947 | ||||||||
\(879\) | −25.1636 | −0.848749 | ||||||||
\(880\) | −1.48055 | −0.0499093 | ||||||||
\(881\) | 37.6137 | 1.26724 | 0.633619 | − | 0.773645i | \(-0.281569\pi\) | ||||
0.633619 | + | 0.773645i | \(0.281569\pi\) | |||||||
\(882\) | 5.55226 | 0.186954 | ||||||||
\(883\) | 46.6007 | 1.56824 | 0.784119 | − | 0.620610i | \(-0.213115\pi\) | ||||
0.784119 | + | 0.620610i | \(0.213115\pi\) | |||||||
\(884\) | −8.79661 | −0.295862 | ||||||||
\(885\) | −16.3863 | −0.550818 | ||||||||
\(886\) | 17.4820 | 0.587318 | ||||||||
\(887\) | −8.93349 | −0.299957 | −0.149979 | − | 0.988689i | \(-0.547920\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547920\pi\) | |||||||
\(888\) | −7.73498 | −0.259569 | ||||||||
\(889\) | 28.6053 | 0.959392 | ||||||||
\(890\) | −12.6066 | −0.422573 | ||||||||
\(891\) | 14.4763 | 0.484974 | ||||||||
\(892\) | 1.73412 | 0.0580625 | ||||||||
\(893\) | −28.6137 | −0.957523 | ||||||||
\(894\) | 27.3391 | 0.914356 | ||||||||
\(895\) | −0.921607 | −0.0308059 | ||||||||
\(896\) | 2.18495 | 0.0729941 | ||||||||
\(897\) | 27.9971 | 0.934795 | ||||||||
\(898\) | −21.9807 | −0.733504 | ||||||||
\(899\) | −0.277515 | −0.00925565 | ||||||||
\(900\) | −9.72423 | −0.324141 | ||||||||
\(901\) | 18.2555 | 0.608178 | ||||||||
\(902\) | −9.89249 | −0.329384 | ||||||||
\(903\) | −22.3936 | −0.745211 | ||||||||
\(904\) | −8.83095 | −0.293713 | ||||||||
\(905\) | 10.0924 | 0.335482 | ||||||||
\(906\) | 40.8154 | 1.35600 | ||||||||
\(907\) | −40.3819 | −1.34086 | −0.670430 | − | 0.741973i | \(-0.733890\pi\) | ||||
−0.670430 | + | 0.741973i | \(0.733890\pi\) | |||||||
\(908\) | 21.5834 | 0.716271 | ||||||||
\(909\) | −12.0356 | −0.399196 | ||||||||
\(910\) | 3.56600 | 0.118212 | ||||||||
\(911\) | −42.0164 | −1.39207 | −0.696033 | − | 0.718010i | \(-0.745053\pi\) | ||||
−0.696033 | + | 0.718010i | \(0.745053\pi\) | |||||||
\(912\) | 7.22800 | 0.239343 | ||||||||
\(913\) | 7.34206 | 0.242987 | ||||||||
\(914\) | −2.59785 | −0.0859293 | ||||||||
\(915\) | 21.5433 | 0.712199 | ||||||||
\(916\) | −13.5664 | −0.448246 | ||||||||
\(917\) | 44.3599 | 1.46489 | ||||||||
\(918\) | 6.70516 | 0.221303 | ||||||||
\(919\) | 30.9534 | 1.02106 | 0.510530 | − | 0.859860i | \(-0.329449\pi\) | ||||
0.510530 | + | 0.859860i | \(0.329449\pi\) | |||||||
\(920\) | 8.06049 | 0.265746 | ||||||||
\(921\) | 30.2418 | 0.996500 | ||||||||
\(922\) | 0.737334 | 0.0242828 | ||||||||
\(923\) | 8.23149 | 0.270943 | ||||||||
\(924\) | −7.22517 | −0.237691 | ||||||||
\(925\) | 12.8651 | 0.423001 | ||||||||
\(926\) | −26.1869 | −0.860554 | ||||||||
\(927\) | −14.4913 | −0.475956 | ||||||||
\(928\) | 9.05297 | 0.297178 | ||||||||
\(929\) | 59.5976 | 1.95533 | 0.977666 | − | 0.210163i | \(-0.0673994\pi\) | ||||
0.977666 | + | 0.210163i | \(0.0673994\pi\) | |||||||
\(930\) | 0.0754089 | 0.00247276 | ||||||||
\(931\) | 6.86415 | 0.224963 | ||||||||
\(932\) | −26.1818 | −0.857612 | ||||||||
\(933\) | 12.1789 | 0.398718 | ||||||||
\(934\) | 26.0862 | 0.853567 | ||||||||
\(935\) | 8.37472 | 0.273883 | ||||||||
\(936\) | −3.87895 | −0.126787 | ||||||||
\(937\) | −8.80122 | −0.287523 | −0.143762 | − | 0.989612i | \(-0.545920\pi\) | ||||
−0.143762 | + | 0.989612i | \(0.545920\pi\) | |||||||
\(938\) | −9.63937 | −0.314737 | ||||||||
\(939\) | 15.0659 | 0.491658 | ||||||||
\(940\) | 9.73831 | 0.317629 | ||||||||
\(941\) | −13.1580 | −0.428938 | −0.214469 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214469 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(942\) | 43.9849 | 1.43310 | ||||||||
\(943\) | 53.8573 | 1.75383 | ||||||||
\(944\) | 6.66120 | 0.216804 | ||||||||
\(945\) | −2.71816 | −0.0884217 | ||||||||
\(946\) | −6.16847 | −0.200554 | ||||||||
\(947\) | −43.0408 | −1.39864 | −0.699319 | − | 0.714810i | \(-0.746513\pi\) | ||||
−0.699319 | + | 0.714810i | \(0.746513\pi\) | |||||||
\(948\) | −25.9091 | −0.841488 | ||||||||
\(949\) | −23.9975 | −0.778991 | ||||||||
\(950\) | −12.0219 | −0.390041 | ||||||||
\(951\) | −28.7783 | −0.933201 | ||||||||
\(952\) | −12.3592 | −0.400563 | ||||||||
\(953\) | 16.9703 | 0.549721 | 0.274861 | − | 0.961484i | \(-0.411368\pi\) | ||||
0.274861 | + | 0.961484i | \(0.411368\pi\) | |||||||
\(954\) | 8.04991 | 0.260626 | ||||||||
\(955\) | 21.8908 | 0.708369 | ||||||||
\(956\) | −6.51518 | −0.210716 | ||||||||
\(957\) | −29.9363 | −0.967703 | ||||||||
\(958\) | 29.7741 | 0.961958 | ||||||||
\(959\) | −29.7629 | −0.961095 | ||||||||
\(960\) | −2.45996 | −0.0793947 | ||||||||
\(961\) | −30.9991 | −0.999970 | ||||||||
\(962\) | 5.13182 | 0.165456 | ||||||||
\(963\) | 8.98067 | 0.289398 | ||||||||
\(964\) | −16.3552 | −0.526766 | ||||||||
\(965\) | −19.6831 | −0.633621 | ||||||||
\(966\) | 39.3357 | 1.26561 | ||||||||
\(967\) | 2.30590 | 0.0741527 | 0.0370764 | − | 0.999312i | \(-0.488196\pi\) | ||||
0.0370764 | + | 0.999312i | \(0.488196\pi\) | |||||||
\(968\) | 9.00978 | 0.289585 | ||||||||
\(969\) | −40.8852 | −1.31342 | ||||||||
\(970\) | 8.69035 | 0.279030 | ||||||||
\(971\) | 13.3048 | 0.426973 | 0.213486 | − | 0.976946i | \(-0.431518\pi\) | ||||
0.213486 | + | 0.976946i | \(0.431518\pi\) | |||||||
\(972\) | 20.4964 | 0.657423 | ||||||||
\(973\) | 24.5344 | 0.786536 | ||||||||
\(974\) | −9.98926 | −0.320076 | ||||||||
\(975\) | 14.2113 | 0.455124 | ||||||||
\(976\) | −8.75759 | −0.280324 | ||||||||
\(977\) | −31.6225 | −1.01169 | −0.505847 | − | 0.862623i | \(-0.668820\pi\) | ||||
−0.505847 | + | 0.862623i | \(0.668820\pi\) | |||||||
\(978\) | −36.2530 | −1.15924 | ||||||||
\(979\) | −16.9464 | −0.541608 | ||||||||
\(980\) | −2.33612 | −0.0746247 | ||||||||
\(981\) | 18.6300 | 0.594811 | ||||||||
\(982\) | −24.9247 | −0.795379 | ||||||||
\(983\) | 15.2433 | 0.486185 | 0.243093 | − | 0.970003i | \(-0.421838\pi\) | ||||
0.243093 | + | 0.970003i | \(0.421838\pi\) | |||||||
\(984\) | −16.4365 | −0.523978 | ||||||||
\(985\) | −22.3012 | −0.710576 | ||||||||
\(986\) | −51.2081 | −1.63080 | ||||||||
\(987\) | 47.5236 | 1.51269 | ||||||||
\(988\) | −4.79546 | −0.152564 | ||||||||
\(989\) | 33.5827 | 1.06787 | ||||||||
\(990\) | 3.69291 | 0.117368 | ||||||||
\(991\) | 32.6978 | 1.03868 | 0.519341 | − | 0.854567i | \(-0.326178\pi\) | ||||
0.519341 | + | 0.854567i | \(0.326178\pi\) | |||||||
\(992\) | −0.0306546 | −0.000973284 0 | ||||||||
\(993\) | −17.3613 | −0.550945 | ||||||||
\(994\) | 11.5652 | 0.366825 | ||||||||
\(995\) | 15.0690 | 0.477719 | ||||||||
\(996\) | 12.1989 | 0.386538 | ||||||||
\(997\) | 19.0893 | 0.604565 | 0.302282 | − | 0.953218i | \(-0.402251\pi\) | ||||
0.302282 | + | 0.953218i | \(0.402251\pi\) | |||||||
\(998\) | 10.9537 | 0.346734 | ||||||||
\(999\) | −3.91169 | −0.123761 |
(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 | 8026.2.a.c.1.13 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.c.1.13 | ✓ | 86 | 1.1 | even | 1 | trivial |