Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.66 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.81437 | 1.99006 | 0.995030 | − | 0.0995765i | \(-0.0317488\pi\) | ||||
0.995030 | + | 0.0995765i | \(0.0317488\pi\) | |||||||
\(3\) | −0.650611 | −0.375630 | −0.187815 | − | 0.982204i | \(-0.560141\pi\) | ||||
−0.187815 | + | 0.982204i | \(0.560141\pi\) | |||||||
\(4\) | 5.92068 | 2.96034 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.83106 | −0.747527 | ||||||||
\(7\) | 2.61686 | 0.989079 | 0.494540 | − | 0.869155i | \(-0.335337\pi\) | ||||
0.494540 | + | 0.869155i | \(0.335337\pi\) | |||||||
\(8\) | 11.0342 | 3.90119 | ||||||||
\(9\) | −2.57671 | −0.858902 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41331 | 1.63217 | 0.816087 | − | 0.577929i | \(-0.196139\pi\) | ||||
0.816087 | + | 0.577929i | \(0.196139\pi\) | |||||||
\(12\) | −3.85206 | −1.11199 | ||||||||
\(13\) | −1.23017 | −0.341187 | −0.170593 | − | 0.985342i | \(-0.554568\pi\) | ||||
−0.170593 | + | 0.985342i | \(0.554568\pi\) | |||||||
\(14\) | 7.36481 | 1.96833 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.2131 | 4.80326 | ||||||||
\(17\) | 3.00034 | 0.727691 | 0.363845 | − | 0.931459i | \(-0.381464\pi\) | ||||
0.363845 | + | 0.931459i | \(0.381464\pi\) | |||||||
\(18\) | −7.25180 | −1.70927 | ||||||||
\(19\) | −6.30332 | −1.44608 | −0.723041 | − | 0.690805i | \(-0.757256\pi\) | ||||
−0.723041 | + | 0.690805i | \(0.757256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70256 | −0.371528 | ||||||||
\(22\) | 15.2351 | 3.24812 | ||||||||
\(23\) | 4.83187 | 1.00752 | 0.503758 | − | 0.863845i | \(-0.331950\pi\) | ||||
0.503758 | + | 0.863845i | \(0.331950\pi\) | |||||||
\(24\) | −7.17899 | −1.46541 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.46214 | −0.678982 | ||||||||
\(27\) | 3.62827 | 0.698260 | ||||||||
\(28\) | 15.4936 | 2.92801 | ||||||||
\(29\) | −0.808277 | −0.150093 | −0.0750466 | − | 0.997180i | \(-0.523911\pi\) | ||||
−0.0750466 | + | 0.997180i | \(0.523911\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.46822 | −0.802516 | −0.401258 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401258 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(32\) | 32.0042 | 5.65759 | ||||||||
\(33\) | −3.52196 | −0.613094 | ||||||||
\(34\) | 8.44408 | 1.44815 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.2558 | −2.54264 | ||||||||
\(37\) | −3.55882 | −0.585066 | −0.292533 | − | 0.956255i | \(-0.594498\pi\) | ||||
−0.292533 | + | 0.956255i | \(0.594498\pi\) | |||||||
\(38\) | −17.7399 | −2.87779 | ||||||||
\(39\) | 0.800360 | 0.128160 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.83696 | −0.286884 | −0.143442 | − | 0.989659i | \(-0.545817\pi\) | ||||
−0.143442 | + | 0.989659i | \(0.545817\pi\) | |||||||
\(42\) | −4.79162 | −0.739364 | ||||||||
\(43\) | 3.25301 | 0.496079 | 0.248039 | − | 0.968750i | \(-0.420214\pi\) | ||||
0.248039 | + | 0.968750i | \(0.420214\pi\) | |||||||
\(44\) | 32.0504 | 4.83179 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.5987 | 2.00502 | ||||||||
\(47\) | −9.92958 | −1.44838 | −0.724189 | − | 0.689602i | \(-0.757786\pi\) | ||||
−0.724189 | + | 0.689602i | \(0.757786\pi\) | |||||||
\(48\) | −12.5002 | −1.80425 | ||||||||
\(49\) | −0.152052 | −0.0217218 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.95206 | −0.273343 | ||||||||
\(52\) | −7.28342 | −1.01003 | ||||||||
\(53\) | −4.28280 | −0.588288 | −0.294144 | − | 0.955761i | \(-0.595034\pi\) | ||||
−0.294144 | + | 0.955761i | \(0.595034\pi\) | |||||||
\(54\) | 10.2113 | 1.38958 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 28.8750 | 3.85859 | ||||||||
\(57\) | 4.10101 | 0.543192 | ||||||||
\(58\) | −2.27479 | −0.298695 | ||||||||
\(59\) | 8.63214 | 1.12381 | 0.561904 | − | 0.827202i | \(-0.310069\pi\) | ||||
0.561904 | + | 0.827202i | \(0.310069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.96432 | −0.507579 | −0.253790 | − | 0.967259i | \(-0.581677\pi\) | ||||
−0.253790 | + | 0.967259i | \(0.581677\pi\) | |||||||
\(62\) | −12.5752 | −1.59706 | ||||||||
\(63\) | −6.74287 | −0.849522 | ||||||||
\(64\) | 51.6455 | 6.45568 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.91209 | −1.22009 | ||||||||
\(67\) | 1.74963 | 0.213751 | 0.106876 | − | 0.994272i | \(-0.465915\pi\) | ||||
0.106876 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(68\) | 17.7641 | 2.15421 | ||||||||
\(69\) | −3.14367 | −0.378453 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.96965 | −0.827145 | −0.413573 | − | 0.910471i | \(-0.635719\pi\) | ||||
−0.413573 | + | 0.910471i | \(0.635719\pi\) | |||||||
\(72\) | −28.4320 | −3.35074 | ||||||||
\(73\) | 14.4128 | 1.68689 | 0.843444 | − | 0.537216i | \(-0.180524\pi\) | ||||
0.843444 | + | 0.537216i | \(0.180524\pi\) | |||||||
\(74\) | −10.0158 | −1.16432 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.3199 | −4.28089 | ||||||||
\(77\) | 14.1659 | 1.61435 | ||||||||
\(78\) | 2.25251 | 0.255046 | ||||||||
\(79\) | 3.91235 | 0.440174 | 0.220087 | − | 0.975480i | \(-0.429366\pi\) | ||||
0.220087 | + | 0.975480i | \(0.429366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.36953 | 0.596614 | ||||||||
\(82\) | −5.16987 | −0.570917 | ||||||||
\(83\) | 2.24169 | 0.246058 | 0.123029 | − | 0.992403i | \(-0.460739\pi\) | ||||
0.123029 | + | 0.992403i | \(0.460739\pi\) | |||||||
\(84\) | −10.0803 | −1.09985 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.15517 | 0.987227 | ||||||||
\(87\) | 0.525874 | 0.0563796 | ||||||||
\(88\) | 59.7317 | 6.36742 | ||||||||
\(89\) | −0.00669658 | −0.000709836 0 | −0.000354918 | − | 1.00000i | \(-0.500113\pi\) | ||||
−0.000354918 | 1.00000i | \(0.500113\pi\) | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.21917 | −0.337461 | ||||||||
\(92\) | 28.6080 | 2.98259 | ||||||||
\(93\) | 2.90707 | 0.301449 | ||||||||
\(94\) | −27.9455 | −2.88236 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20.8223 | −2.12516 | ||||||||
\(97\) | −11.4628 | −1.16387 | −0.581934 | − | 0.813236i | \(-0.697704\pi\) | ||||
−0.581934 | + | 0.813236i | \(0.697704\pi\) | |||||||
\(98\) | −0.427931 | −0.0432276 | ||||||||
\(99\) | −13.9485 | −1.40188 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2533 | −1.51776 | −0.758879 | − | 0.651231i | \(-0.774253\pi\) | ||||
−0.758879 | + | 0.651231i | \(0.774253\pi\) | |||||||
\(102\) | −5.49381 | −0.543968 | ||||||||
\(103\) | −10.6257 | −1.04698 | −0.523490 | − | 0.852032i | \(-0.675370\pi\) | ||||
−0.523490 | + | 0.852032i | \(0.675370\pi\) | |||||||
\(104\) | −13.5739 | −1.33103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0534 | −1.17073 | ||||||||
\(107\) | −12.1123 | −1.17094 | −0.585472 | − | 0.810693i | \(-0.699091\pi\) | ||||
−0.585472 | + | 0.810693i | \(0.699091\pi\) | |||||||
\(108\) | 21.4818 | 2.06709 | ||||||||
\(109\) | 15.2837 | 1.46392 | 0.731959 | − | 0.681349i | \(-0.238606\pi\) | ||||
0.731959 | + | 0.681349i | \(0.238606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.31541 | 0.219769 | ||||||||
\(112\) | 50.2778 | 4.75081 | ||||||||
\(113\) | −20.2175 | −1.90190 | −0.950951 | − | 0.309341i | \(-0.899891\pi\) | ||||
−0.950951 | + | 0.309341i | \(0.899891\pi\) | |||||||
\(114\) | 11.5418 | 1.08099 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.78555 | −0.444327 | ||||||||
\(117\) | 3.16978 | 0.293046 | ||||||||
\(118\) | 24.2940 | 2.23645 | ||||||||
\(119\) | 7.85148 | 0.719744 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3039 | 1.66399 | ||||||||
\(122\) | −11.1571 | −1.01011 | ||||||||
\(123\) | 1.19514 | 0.107762 | ||||||||
\(124\) | −26.4549 | −2.37572 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −18.9769 | −1.69060 | ||||||||
\(127\) | 10.7914 | 0.957583 | 0.478791 | − | 0.877929i | \(-0.341075\pi\) | ||||
0.478791 | + | 0.877929i | \(0.341075\pi\) | |||||||
\(128\) | 81.3411 | 7.18960 | ||||||||
\(129\) | −2.11644 | −0.186342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.42934 | 0.386993 | 0.193497 | − | 0.981101i | \(-0.438017\pi\) | ||||
0.193497 | + | 0.981101i | \(0.438017\pi\) | |||||||
\(132\) | −20.8524 | −1.81497 | ||||||||
\(133\) | −16.4949 | −1.43029 | ||||||||
\(134\) | 4.92410 | 0.425378 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.1065 | 2.83886 | ||||||||
\(137\) | 5.24958 | 0.448502 | 0.224251 | − | 0.974531i | \(-0.428006\pi\) | ||||
0.224251 | + | 0.974531i | \(0.428006\pi\) | |||||||
\(138\) | −8.84745 | −0.753145 | ||||||||
\(139\) | 6.16732 | 0.523105 | 0.261553 | − | 0.965189i | \(-0.415765\pi\) | ||||
0.261553 | + | 0.965189i | \(0.415765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.46029 | 0.544055 | ||||||||
\(142\) | −19.6152 | −1.64607 | ||||||||
\(143\) | −6.65927 | −0.556876 | ||||||||
\(144\) | −49.5064 | −4.12553 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 40.5629 | 3.35701 | ||||||||
\(147\) | 0.0989269 | 0.00815935 | ||||||||
\(148\) | −21.0706 | −1.73199 | ||||||||
\(149\) | 10.5225 | 0.862034 | 0.431017 | − | 0.902344i | \(-0.358155\pi\) | ||||
0.431017 | + | 0.902344i | \(0.358155\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.7257 | −1.68663 | −0.843315 | − | 0.537420i | \(-0.819399\pi\) | ||||
−0.843315 | + | 0.537420i | \(0.819399\pi\) | |||||||
\(152\) | −69.5523 | −5.64144 | ||||||||
\(153\) | −7.73100 | −0.625015 | ||||||||
\(154\) | 39.8680 | 3.21265 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.73867 | 0.379397 | ||||||||
\(157\) | 17.8432 | 1.42404 | 0.712019 | − | 0.702160i | \(-0.247781\pi\) | ||||
0.712019 | + | 0.702160i | \(0.247781\pi\) | |||||||
\(158\) | 11.0108 | 0.875972 | ||||||||
\(159\) | 2.78644 | 0.220979 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.6443 | 0.996513 | ||||||||
\(162\) | 15.1118 | 1.18730 | ||||||||
\(163\) | 4.59778 | 0.360126 | 0.180063 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180063 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(164\) | −10.8760 | −0.849275 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.30895 | 0.489670 | ||||||||
\(167\) | −17.5052 | −1.35459 | −0.677297 | − | 0.735710i | \(-0.736849\pi\) | ||||
−0.677297 | + | 0.735710i | \(0.736849\pi\) | |||||||
\(168\) | −18.7864 | −1.44940 | ||||||||
\(169\) | −11.4867 | −0.883592 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.2418 | 1.24204 | ||||||||
\(172\) | 19.2600 | 1.46856 | ||||||||
\(173\) | 7.56238 | 0.574957 | 0.287478 | − | 0.957787i | \(-0.407183\pi\) | ||||
0.287478 | + | 0.957787i | \(0.407183\pi\) | |||||||
\(174\) | 1.48000 | 0.112199 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 104.006 | 7.83976 | ||||||||
\(177\) | −5.61616 | −0.422137 | ||||||||
\(178\) | −0.0188467 | −0.00141262 | ||||||||
\(179\) | 18.9722 | 1.41805 | 0.709024 | − | 0.705184i | \(-0.249136\pi\) | ||||
0.709024 | + | 0.705184i | \(0.249136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4516 | 1.74314 | 0.871572 | − | 0.490268i | \(-0.163101\pi\) | ||||
0.871572 | + | 0.490268i | \(0.163101\pi\) | |||||||
\(182\) | −9.05994 | −0.671567 | ||||||||
\(183\) | 2.57923 | 0.190662 | ||||||||
\(184\) | 53.3160 | 3.93051 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.18158 | 0.599902 | ||||||||
\(187\) | 16.2418 | 1.18772 | ||||||||
\(188\) | −58.7898 | −4.28769 | ||||||||
\(189\) | 9.49466 | 0.690635 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.45986 | 0.105632 | 0.0528159 | − | 0.998604i | \(-0.483180\pi\) | ||||
0.0528159 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(192\) | −33.6011 | −2.42495 | ||||||||
\(193\) | −0.501079 | −0.0360684 | −0.0180342 | − | 0.999837i | \(-0.505741\pi\) | ||||
−0.0180342 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(194\) | −32.2605 | −2.31617 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.900253 | −0.0643038 | ||||||||
\(197\) | 3.38682 | 0.241301 | 0.120650 | − | 0.992695i | \(-0.461502\pi\) | ||||
0.120650 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(198\) | −39.2562 | −2.78982 | ||||||||
\(199\) | −8.11615 | −0.575339 | −0.287669 | − | 0.957730i | \(-0.592880\pi\) | ||||
−0.287669 | + | 0.957730i | \(0.592880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.13833 | −0.0802914 | ||||||||
\(202\) | −42.9284 | −3.02043 | ||||||||
\(203\) | −2.11515 | −0.148454 | ||||||||
\(204\) | −11.5575 | −0.809187 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −29.9046 | −2.08355 | ||||||||
\(207\) | −12.4503 | −0.865357 | ||||||||
\(208\) | −23.6353 | −1.63881 | ||||||||
\(209\) | −34.1218 | −2.36026 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3941 | −1.33514 | −0.667571 | − | 0.744546i | \(-0.732666\pi\) | ||||
−0.667571 | + | 0.744546i | \(0.732666\pi\) | |||||||
\(212\) | −25.3571 | −1.74153 | ||||||||
\(213\) | 4.53453 | 0.310701 | ||||||||
\(214\) | −34.0886 | −2.33025 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 40.0351 | 2.72405 | ||||||||
\(217\) | −11.6927 | −0.793752 | ||||||||
\(218\) | 43.0141 | 2.91328 | ||||||||
\(219\) | −9.37712 | −0.633647 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.69092 | −0.248278 | ||||||||
\(222\) | 6.51641 | 0.437353 | ||||||||
\(223\) | 10.0804 | 0.675036 | 0.337518 | − | 0.941319i | \(-0.390413\pi\) | ||||
0.337518 | + | 0.941319i | \(0.390413\pi\) | |||||||
\(224\) | 83.7504 | 5.59581 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −56.8995 | −3.78490 | ||||||||
\(227\) | −18.2708 | −1.21267 | −0.606337 | − | 0.795208i | \(-0.707362\pi\) | ||||
−0.606337 | + | 0.795208i | \(0.707362\pi\) | |||||||
\(228\) | 24.2808 | 1.60803 | ||||||||
\(229\) | 8.47594 | 0.560106 | 0.280053 | − | 0.959985i | \(-0.409648\pi\) | ||||
0.280053 | + | 0.959985i | \(0.409648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.21646 | −0.606399 | ||||||||
\(232\) | −8.91872 | −0.585542 | ||||||||
\(233\) | −6.84820 | −0.448640 | −0.224320 | − | 0.974516i | \(-0.572016\pi\) | ||||
−0.224320 | + | 0.974516i | \(0.572016\pi\) | |||||||
\(234\) | 8.92092 | 0.583179 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 51.1081 | 3.32685 | ||||||||
\(237\) | −2.54542 | −0.165343 | ||||||||
\(238\) | 22.0970 | 1.43233 | ||||||||
\(239\) | 22.5107 | 1.45609 | 0.728047 | − | 0.685527i | \(-0.240428\pi\) | ||||
0.728047 | + | 0.685527i | \(0.240428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 51.5140 | 3.31144 | ||||||||
\(243\) | −14.3783 | −0.922366 | ||||||||
\(244\) | −23.4715 | −1.50261 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.36358 | 0.214454 | ||||||||
\(247\) | 7.75414 | 0.493384 | ||||||||
\(248\) | −49.3034 | −3.13077 | ||||||||
\(249\) | −1.45847 | −0.0924268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1052 | −1.01655 | −0.508276 | − | 0.861194i | \(-0.669717\pi\) | ||||
−0.508276 | + | 0.861194i | \(0.669717\pi\) | |||||||
\(252\) | −39.9224 | −2.51487 | ||||||||
\(253\) | 26.1564 | 1.64444 | ||||||||
\(254\) | 30.3710 | 1.90565 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 125.633 | 7.85206 | ||||||||
\(257\) | 10.7289 | 0.669251 | 0.334626 | − | 0.942351i | \(-0.391390\pi\) | ||||
0.334626 | + | 0.942351i | \(0.391390\pi\) | |||||||
\(258\) | −5.95645 | −0.370832 | ||||||||
\(259\) | −9.31293 | −0.578677 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.08269 | 0.128915 | ||||||||
\(262\) | 12.4658 | 0.770140 | ||||||||
\(263\) | −21.5665 | −1.32985 | −0.664924 | − | 0.746911i | \(-0.731536\pi\) | ||||
−0.664924 | + | 0.746911i | \(0.731536\pi\) | |||||||
\(264\) | −38.8621 | −2.39180 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −46.4228 | −2.84636 | ||||||||
\(267\) | 0.00435687 | 0.000266636 0 | ||||||||
\(268\) | 10.3590 | 0.632776 | ||||||||
\(269\) | 2.92655 | 0.178435 | 0.0892174 | − | 0.996012i | \(-0.471563\pi\) | ||||
0.0892174 | + | 0.996012i | \(0.471563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.75309 | −0.106493 | −0.0532463 | − | 0.998581i | \(-0.516957\pi\) | ||||
−0.0532463 | + | 0.998581i | \(0.516957\pi\) | |||||||
\(272\) | 57.6458 | 3.49529 | ||||||||
\(273\) | 2.09443 | 0.126761 | ||||||||
\(274\) | 14.7743 | 0.892546 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.6127 | −1.12035 | ||||||||
\(277\) | 9.59302 | 0.576389 | 0.288194 | − | 0.957572i | \(-0.406945\pi\) | ||||
0.288194 | + | 0.957572i | \(0.406945\pi\) | |||||||
\(278\) | 17.3571 | 1.04101 | ||||||||
\(279\) | 11.5133 | 0.689283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.01836 | −0.120406 | −0.0602028 | − | 0.998186i | \(-0.519175\pi\) | ||||
−0.0602028 | + | 0.998186i | \(0.519175\pi\) | |||||||
\(282\) | 18.1817 | 1.08270 | ||||||||
\(283\) | −1.20732 | −0.0717678 | −0.0358839 | − | 0.999356i | \(-0.511425\pi\) | ||||
−0.0358839 | + | 0.999356i | \(0.511425\pi\) | |||||||
\(284\) | −41.2650 | −2.44863 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.7416 | −1.10822 | ||||||||
\(287\) | −4.80705 | −0.283751 | ||||||||
\(288\) | −82.4653 | −4.85932 | ||||||||
\(289\) | −7.99793 | −0.470467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.45780 | 0.437184 | ||||||||
\(292\) | 85.3334 | 4.99376 | ||||||||
\(293\) | −11.5977 | −0.677547 | −0.338774 | − | 0.940868i | \(-0.610012\pi\) | ||||
−0.338774 | + | 0.940868i | \(0.610012\pi\) | |||||||
\(294\) | 0.278417 | 0.0162376 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.2688 | −2.28246 | ||||||||
\(297\) | 19.6409 | 1.13968 | ||||||||
\(298\) | 29.6141 | 1.71550 | ||||||||
\(299\) | −5.94401 | −0.343751 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.51266 | 0.490662 | ||||||||
\(302\) | −58.3297 | −3.35649 | ||||||||
\(303\) | 9.92395 | 0.570116 | ||||||||
\(304\) | −121.106 | −6.94591 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.7579 | −1.24382 | ||||||||
\(307\) | −29.1382 | −1.66301 | −0.831503 | − | 0.555520i | \(-0.812519\pi\) | ||||
−0.831503 | + | 0.555520i | \(0.812519\pi\) | |||||||
\(308\) | 83.8715 | 4.77902 | ||||||||
\(309\) | 6.91319 | 0.393278 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.98179 | 0.395901 | 0.197950 | − | 0.980212i | \(-0.436571\pi\) | ||||
0.197950 | + | 0.980212i | \(0.436571\pi\) | |||||||
\(312\) | 8.83136 | 0.499977 | ||||||||
\(313\) | −16.8525 | −0.952560 | −0.476280 | − | 0.879294i | \(-0.658015\pi\) | ||||
−0.476280 | + | 0.879294i | \(0.658015\pi\) | |||||||
\(314\) | 50.2172 | 2.83392 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.1637 | 1.30306 | ||||||||
\(317\) | −10.8529 | −0.609562 | −0.304781 | − | 0.952423i | \(-0.598583\pi\) | ||||
−0.304781 | + | 0.952423i | \(0.598583\pi\) | |||||||
\(318\) | 7.84206 | 0.439761 | ||||||||
\(319\) | −4.37545 | −0.244978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.88042 | 0.439842 | ||||||||
\(322\) | 35.5858 | 1.98312 | ||||||||
\(323\) | −18.9121 | −1.05230 | ||||||||
\(324\) | 31.7912 | 1.76618 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.9399 | 0.716672 | ||||||||
\(327\) | −9.94377 | −0.549892 | ||||||||
\(328\) | −20.2694 | −1.11919 | ||||||||
\(329\) | −25.9843 | −1.43256 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0540 | −0.717512 | −0.358756 | − | 0.933431i | \(-0.616799\pi\) | ||||
−0.358756 | + | 0.933431i | \(0.616799\pi\) | |||||||
\(332\) | 13.2723 | 0.728414 | ||||||||
\(333\) | 9.17003 | 0.502515 | ||||||||
\(334\) | −49.2661 | −2.69572 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −32.7113 | −1.78455 | ||||||||
\(337\) | 21.4023 | 1.16586 | 0.582929 | − | 0.812523i | \(-0.301907\pi\) | ||||
0.582929 | + | 0.812523i | \(0.301907\pi\) | |||||||
\(338\) | −32.3278 | −1.75840 | ||||||||
\(339\) | 13.1537 | 0.714412 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.1879 | −1.30985 | ||||||||
\(342\) | 45.7105 | 2.47174 | ||||||||
\(343\) | −18.7159 | −1.01056 | ||||||||
\(344\) | 35.8944 | 1.93530 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.2833 | 1.14420 | ||||||||
\(347\) | −16.0213 | −0.860066 | −0.430033 | − | 0.902813i | \(-0.641498\pi\) | ||||
−0.430033 | + | 0.902813i | \(0.641498\pi\) | |||||||
\(348\) | 3.11353 | 0.166903 | ||||||||
\(349\) | −3.02544 | −0.161948 | −0.0809740 | − | 0.996716i | \(-0.525803\pi\) | ||||
−0.0809740 | + | 0.996716i | \(0.525803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.46337 | −0.238237 | ||||||||
\(352\) | 173.248 | 9.23417 | ||||||||
\(353\) | −17.6346 | −0.938593 | −0.469297 | − | 0.883041i | \(-0.655492\pi\) | ||||
−0.469297 | + | 0.883041i | \(0.655492\pi\) | |||||||
\(354\) | −15.8060 | −0.840077 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0396483 | −0.00210135 | ||||||||
\(357\) | −5.10826 | −0.270358 | ||||||||
\(358\) | 53.3948 | 2.82200 | ||||||||
\(359\) | 28.6242 | 1.51073 | 0.755363 | − | 0.655307i | \(-0.227461\pi\) | ||||
0.755363 | + | 0.655307i | \(0.227461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7319 | 1.09115 | ||||||||
\(362\) | 66.0015 | 3.46896 | ||||||||
\(363\) | −11.9087 | −0.625046 | ||||||||
\(364\) | −19.0597 | −0.998998 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.25891 | 0.379429 | ||||||||
\(367\) | 3.90612 | 0.203898 | 0.101949 | − | 0.994790i | \(-0.467492\pi\) | ||||
0.101949 | + | 0.994790i | \(0.467492\pi\) | |||||||
\(368\) | 92.8350 | 4.83936 | ||||||||
\(369\) | 4.73329 | 0.246405 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2075 | −0.581863 | ||||||||
\(372\) | 17.2118 | 0.892392 | ||||||||
\(373\) | −7.22326 | −0.374006 | −0.187003 | − | 0.982359i | \(-0.559877\pi\) | ||||
−0.187003 | + | 0.982359i | \(0.559877\pi\) | |||||||
\(374\) | 45.7104 | 2.36363 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −109.565 | −5.65040 | ||||||||
\(377\) | 0.994315 | 0.0512098 | ||||||||
\(378\) | 26.7215 | 1.37440 | ||||||||
\(379\) | −9.64189 | −0.495271 | −0.247635 | − | 0.968853i | \(-0.579654\pi\) | ||||
−0.247635 | + | 0.968853i | \(0.579654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.02101 | −0.359697 | ||||||||
\(382\) | 4.10859 | 0.210214 | ||||||||
\(383\) | 32.2148 | 1.64610 | 0.823050 | − | 0.567969i | \(-0.192271\pi\) | ||||
0.823050 | + | 0.567969i | \(0.192271\pi\) | |||||||
\(384\) | −52.9214 | −2.70063 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.41022 | −0.0717783 | ||||||||
\(387\) | −8.38204 | −0.426083 | ||||||||
\(388\) | −67.8673 | −3.44544 | ||||||||
\(389\) | −28.7781 | −1.45911 | −0.729554 | − | 0.683923i | \(-0.760272\pi\) | ||||
−0.729554 | + | 0.683923i | \(0.760272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4973 | 0.733159 | ||||||||
\(392\) | −1.67778 | −0.0847407 | ||||||||
\(393\) | −2.88178 | −0.145366 | ||||||||
\(394\) | 9.53176 | 0.480203 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −82.5846 | −4.15003 | ||||||||
\(397\) | −16.4418 | −0.825188 | −0.412594 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412594 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(398\) | −22.8418 | −1.14496 | ||||||||
\(399\) | 10.7318 | 0.537260 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.9686 | 1.89606 | 0.948030 | − | 0.318180i | \(-0.103072\pi\) | ||||
0.948030 | + | 0.318180i | \(0.103072\pi\) | |||||||
\(402\) | −3.20367 | −0.159785 | ||||||||
\(403\) | 5.49666 | 0.273808 | ||||||||
\(404\) | −90.3097 | −4.49308 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.95280 | −0.295433 | ||||||||
\(407\) | −19.2650 | −0.954930 | ||||||||
\(408\) | −21.5395 | −1.06636 | ||||||||
\(409\) | 5.16290 | 0.255289 | 0.127644 | − | 0.991820i | \(-0.459258\pi\) | ||||
0.127644 | + | 0.991820i | \(0.459258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.41543 | −0.168471 | ||||||||
\(412\) | −62.9113 | −3.09942 | ||||||||
\(413\) | 22.5891 | 1.11154 | ||||||||
\(414\) | −35.0398 | −1.72211 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −39.3705 | −1.93030 | ||||||||
\(417\) | −4.01253 | −0.196494 | ||||||||
\(418\) | −96.0315 | −4.69705 | ||||||||
\(419\) | −28.7636 | −1.40519 | −0.702597 | − | 0.711588i | \(-0.747976\pi\) | ||||
−0.702597 | + | 0.711588i | \(0.747976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3201 | 0.990343 | 0.495171 | − | 0.868795i | \(-0.335105\pi\) | ||||
0.495171 | + | 0.868795i | \(0.335105\pi\) | |||||||
\(422\) | −54.5820 | −2.65701 | ||||||||
\(423\) | 25.5856 | 1.24401 | ||||||||
\(424\) | −47.2574 | −2.29502 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.7618 | 0.618313 | ||||||||
\(427\) | −10.3741 | −0.502036 | ||||||||
\(428\) | −71.7132 | −3.46639 | ||||||||
\(429\) | 4.33259 | 0.209180 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8735 | −0.571924 | −0.285962 | − | 0.958241i | \(-0.592313\pi\) | ||||
−0.285962 | + | 0.958241i | \(0.592313\pi\) | |||||||
\(432\) | 69.7101 | 3.35393 | ||||||||
\(433\) | 27.7828 | 1.33515 | 0.667577 | − | 0.744540i | \(-0.267331\pi\) | ||||
0.667577 | + | 0.744540i | \(0.267331\pi\) | |||||||
\(434\) | −32.9076 | −1.57961 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 90.4901 | 4.33369 | ||||||||
\(437\) | −30.4569 | −1.45695 | ||||||||
\(438\) | −26.3907 | −1.26100 | ||||||||
\(439\) | 19.8875 | 0.949177 | 0.474589 | − | 0.880208i | \(-0.342597\pi\) | ||||
0.474589 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.391794 | 0.0186569 | ||||||||
\(442\) | −10.3876 | −0.494089 | ||||||||
\(443\) | −12.6572 | −0.601362 | −0.300681 | − | 0.953725i | \(-0.597214\pi\) | ||||
−0.300681 | + | 0.953725i | \(0.597214\pi\) | |||||||
\(444\) | 13.7088 | 0.650590 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.3701 | 1.34336 | ||||||||
\(447\) | −6.84603 | −0.323806 | ||||||||
\(448\) | 135.149 | 6.38518 | ||||||||
\(449\) | −16.8009 | −0.792882 | −0.396441 | − | 0.918060i | \(-0.629755\pi\) | ||||
−0.396441 | + | 0.918060i | \(0.629755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.94401 | −0.468245 | ||||||||
\(452\) | −119.701 | −5.63027 | ||||||||
\(453\) | 13.4843 | 0.633550 | ||||||||
\(454\) | −51.4207 | −2.41329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 45.2515 | 2.11910 | ||||||||
\(457\) | −25.2275 | −1.18009 | −0.590047 | − | 0.807369i | \(-0.700891\pi\) | ||||
−0.590047 | + | 0.807369i | \(0.700891\pi\) | |||||||
\(458\) | 23.8544 | 1.11464 | ||||||||
\(459\) | 10.8860 | 0.508117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.43924 | 0.253331 | 0.126665 | − | 0.991946i | \(-0.459573\pi\) | ||||
0.126665 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(462\) | −25.9385 | −1.20677 | ||||||||
\(463\) | −7.84739 | −0.364699 | −0.182350 | − | 0.983234i | \(-0.558370\pi\) | ||||
−0.182350 | + | 0.983234i | \(0.558370\pi\) | |||||||
\(464\) | −15.5295 | −0.720938 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.2734 | −0.892821 | ||||||||
\(467\) | −21.2589 | −0.983744 | −0.491872 | − | 0.870668i | \(-0.663687\pi\) | ||||
−0.491872 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(468\) | 18.7672 | 0.867515 | ||||||||
\(469\) | 4.57853 | 0.211417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.6090 | −0.534912 | ||||||||
\(472\) | 95.2490 | 4.38419 | ||||||||
\(473\) | 17.6095 | 0.809687 | ||||||||
\(474\) | −7.16374 | −0.329042 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 46.4861 | 2.13068 | ||||||||
\(477\) | 11.0355 | 0.505281 | ||||||||
\(478\) | 63.3533 | 2.89771 | ||||||||
\(479\) | −18.2829 | −0.835367 | −0.417684 | − | 0.908593i | \(-0.637158\pi\) | ||||
−0.417684 | + | 0.908593i | \(0.637158\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.37794 | 0.199617 | ||||||||
\(482\) | −2.81437 | −0.128191 | ||||||||
\(483\) | −8.22654 | −0.374320 | ||||||||
\(484\) | 108.372 | 4.92598 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −40.4658 | −1.83556 | ||||||||
\(487\) | 12.8478 | 0.582191 | 0.291095 | − | 0.956694i | \(-0.405980\pi\) | ||||
0.291095 | + | 0.956694i | \(0.405980\pi\) | |||||||
\(488\) | −43.7432 | −1.98016 | ||||||||
\(489\) | −2.99137 | −0.135274 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.3931 | 1.37162 | 0.685812 | − | 0.727779i | \(-0.259447\pi\) | ||||
0.685812 | + | 0.727779i | \(0.259447\pi\) | |||||||
\(492\) | 7.07606 | 0.319013 | ||||||||
\(493\) | −2.42511 | −0.109221 | ||||||||
\(494\) | 21.8230 | 0.981864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −85.8482 | −3.85470 | ||||||||
\(497\) | −18.2386 | −0.818112 | ||||||||
\(498\) | −4.10467 | −0.183935 | ||||||||
\(499\) | 3.88505 | 0.173919 | 0.0869593 | − | 0.996212i | \(-0.472285\pi\) | ||||
0.0869593 | + | 0.996212i | \(0.472285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3891 | 0.508826 | ||||||||
\(502\) | −45.3260 | −2.02300 | ||||||||
\(503\) | 28.7969 | 1.28399 | 0.641994 | − | 0.766709i | \(-0.278107\pi\) | ||||
0.641994 | + | 0.766709i | \(0.278107\pi\) | |||||||
\(504\) | −74.4024 | −3.31415 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 73.6138 | 3.27253 | ||||||||
\(507\) | 7.47337 | 0.331904 | ||||||||
\(508\) | 63.8924 | 2.83477 | ||||||||
\(509\) | −10.6962 | −0.474099 | −0.237050 | − | 0.971498i | \(-0.576180\pi\) | ||||
−0.237050 | + | 0.971498i | \(0.576180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.7162 | 1.66847 | ||||||||
\(512\) | 190.895 | 8.43646 | ||||||||
\(513\) | −22.8701 | −1.00974 | ||||||||
\(514\) | 30.1951 | 1.33185 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.5308 | −0.551636 | ||||||||
\(517\) | −53.7519 | −2.36400 | ||||||||
\(518\) | −26.2100 | −1.15160 | ||||||||
\(519\) | −4.92017 | −0.215971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8613 | 0.519652 | 0.259826 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259826 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(522\) | 5.86146 | 0.256549 | ||||||||
\(523\) | −5.93707 | −0.259610 | −0.129805 | − | 0.991540i | \(-0.541435\pi\) | ||||
−0.129805 | + | 0.991540i | \(0.541435\pi\) | |||||||
\(524\) | 26.2247 | 1.14563 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −60.6961 | −2.64648 | ||||||||
\(527\) | −13.4062 | −0.583983 | ||||||||
\(528\) | −67.6676 | −2.94485 | ||||||||
\(529\) | 0.347002 | 0.0150871 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.2425 | −0.965241 | ||||||||
\(532\) | −97.6610 | −4.23414 | ||||||||
\(533\) | 2.25976 | 0.0978812 | ||||||||
\(534\) | 0.0122618 | 0.000530622 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.3058 | 0.833884 | ||||||||
\(537\) | −12.3435 | −0.532662 | ||||||||
\(538\) | 8.23639 | 0.355096 | ||||||||
\(539\) | −0.823106 | −0.0354537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.2259 | −0.869580 | −0.434790 | − | 0.900532i | \(-0.643177\pi\) | ||||
−0.434790 | + | 0.900532i | \(0.643177\pi\) | |||||||
\(542\) | −4.93385 | −0.211927 | ||||||||
\(543\) | −15.2579 | −0.654778 | ||||||||
\(544\) | 96.0235 | 4.11698 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.89450 | 0.252261 | ||||||||
\(547\) | 43.0374 | 1.84014 | 0.920072 | − | 0.391749i | \(-0.128130\pi\) | ||||
0.920072 | + | 0.391749i | \(0.128130\pi\) | |||||||
\(548\) | 31.0811 | 1.32772 | ||||||||
\(549\) | 10.2149 | 0.435961 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.09483 | 0.217047 | ||||||||
\(552\) | −34.6880 | −1.47642 | ||||||||
\(553\) | 10.2381 | 0.435367 | ||||||||
\(554\) | 26.9983 | 1.14705 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.5147 | 1.54857 | ||||||||
\(557\) | −27.1432 | −1.15009 | −0.575047 | − | 0.818121i | \(-0.695016\pi\) | ||||
−0.575047 | + | 0.818121i | \(0.695016\pi\) | |||||||
\(558\) | 32.4026 | 1.37171 | ||||||||
\(559\) | −4.00174 | −0.169256 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.5671 | −0.446143 | ||||||||
\(562\) | −5.68042 | −0.239614 | ||||||||
\(563\) | 6.85771 | 0.289018 | 0.144509 | − | 0.989503i | \(-0.453840\pi\) | ||||
0.144509 | + | 0.989503i | \(0.453840\pi\) | |||||||
\(564\) | 38.2493 | 1.61059 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.39785 | −0.142822 | ||||||||
\(567\) | 14.0513 | 0.590099 | ||||||||
\(568\) | −76.9047 | −3.22685 | ||||||||
\(569\) | 34.1608 | 1.43210 | 0.716048 | − | 0.698051i | \(-0.245949\pi\) | ||||
0.716048 | + | 0.698051i | \(0.245949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6990 | 0.573284 | 0.286642 | − | 0.958038i | \(-0.407461\pi\) | ||||
0.286642 | + | 0.958038i | \(0.407461\pi\) | |||||||
\(572\) | −39.4274 | −1.64854 | ||||||||
\(573\) | −0.949801 | −0.0396785 | ||||||||
\(574\) | −13.5288 | −0.564682 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −133.075 | −5.54480 | ||||||||
\(577\) | 10.4072 | 0.433259 | 0.216629 | − | 0.976254i | \(-0.430494\pi\) | ||||
0.216629 | + | 0.976254i | \(0.430494\pi\) | |||||||
\(578\) | −22.5091 | −0.936257 | ||||||||
\(579\) | 0.326007 | 0.0135484 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.86619 | 0.243371 | ||||||||
\(582\) | 20.9890 | 0.870022 | ||||||||
\(583\) | −23.1841 | −0.960188 | ||||||||
\(584\) | 159.034 | 6.58087 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.6403 | −1.34836 | ||||||||
\(587\) | −38.7926 | −1.60114 | −0.800572 | − | 0.599237i | \(-0.795471\pi\) | ||||
−0.800572 | + | 0.599237i | \(0.795471\pi\) | |||||||
\(588\) | 0.585714 | 0.0241544 | ||||||||
\(589\) | 28.1646 | 1.16050 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.20350 | −0.0906400 | ||||||||
\(592\) | −68.3758 | −2.81023 | ||||||||
\(593\) | 40.6345 | 1.66866 | 0.834328 | − | 0.551268i | \(-0.185856\pi\) | ||||
0.834328 | + | 0.551268i | \(0.185856\pi\) | |||||||
\(594\) | 55.2768 | 2.26804 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 62.3001 | 2.55191 | ||||||||
\(597\) | 5.28046 | 0.216115 | ||||||||
\(598\) | −16.7286 | −0.684085 | ||||||||
\(599\) | −10.5304 | −0.430261 | −0.215131 | − | 0.976585i | \(-0.569018\pi\) | ||||
−0.215131 | + | 0.976585i | \(0.569018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2969 | 0.583184 | 0.291592 | − | 0.956543i | \(-0.405815\pi\) | ||||
0.291592 | + | 0.956543i | \(0.405815\pi\) | |||||||
\(602\) | 23.9578 | 0.976446 | ||||||||
\(603\) | −4.50828 | −0.183591 | ||||||||
\(604\) | −122.710 | −4.99299 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.9297 | 1.13457 | ||||||||
\(607\) | 23.0505 | 0.935591 | 0.467795 | − | 0.883837i | \(-0.345048\pi\) | ||||
0.467795 | + | 0.883837i | \(0.345048\pi\) | |||||||
\(608\) | −201.733 | −8.18134 | ||||||||
\(609\) | 1.37614 | 0.0557639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.2150 | 0.494167 | ||||||||
\(612\) | −45.7728 | −1.85025 | ||||||||
\(613\) | −20.9443 | −0.845932 | −0.422966 | − | 0.906146i | \(-0.639011\pi\) | ||||
−0.422966 | + | 0.906146i | \(0.639011\pi\) | |||||||
\(614\) | −82.0058 | −3.30948 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 156.309 | 6.29788 | ||||||||
\(617\) | −34.0970 | −1.37269 | −0.686346 | − | 0.727275i | \(-0.740786\pi\) | ||||
−0.686346 | + | 0.727275i | \(0.740786\pi\) | |||||||
\(618\) | 19.4563 | 0.782646 | ||||||||
\(619\) | 5.94768 | 0.239058 | 0.119529 | − | 0.992831i | \(-0.461862\pi\) | ||||
0.119529 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.5313 | 0.703508 | ||||||||
\(622\) | 19.6493 | 0.787867 | ||||||||
\(623\) | −0.0175240 | −0.000702084 0 | ||||||||
\(624\) | 15.3774 | 0.615587 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −47.4292 | −1.89565 | ||||||||
\(627\) | 22.2000 | 0.886584 | ||||||||
\(628\) | 105.644 | 4.21564 | ||||||||
\(629\) | −10.6777 | −0.425747 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1383 | 1.23960 | 0.619798 | − | 0.784761i | \(-0.287215\pi\) | ||||
0.619798 | + | 0.784761i | \(0.287215\pi\) | |||||||
\(632\) | 43.1698 | 1.71720 | ||||||||
\(633\) | 12.6180 | 0.501520 | ||||||||
\(634\) | −30.5442 | −1.21306 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.4976 | 0.654172 | ||||||||
\(637\) | 0.187050 | 0.00741118 | ||||||||
\(638\) | −12.3141 | −0.487521 | ||||||||
\(639\) | 17.9587 | 0.710436 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.4089 | −1.63555 | −0.817776 | − | 0.575536i | \(-0.804793\pi\) | ||||
−0.817776 | + | 0.575536i | \(0.804793\pi\) | |||||||
\(642\) | 22.1784 | 0.875312 | ||||||||
\(643\) | −38.2661 | −1.50907 | −0.754534 | − | 0.656261i | \(-0.772137\pi\) | ||||
−0.754534 | + | 0.656261i | \(0.772137\pi\) | |||||||
\(644\) | 74.8630 | 2.95001 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −53.2258 | −2.09414 | ||||||||
\(647\) | 38.1859 | 1.50124 | 0.750622 | − | 0.660732i | \(-0.229754\pi\) | ||||
0.750622 | + | 0.660732i | \(0.229754\pi\) | |||||||
\(648\) | 59.2486 | 2.32750 | ||||||||
\(649\) | 46.7284 | 1.83425 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.60740 | 0.298157 | ||||||||
\(652\) | 27.2220 | 1.06609 | ||||||||
\(653\) | −0.323660 | −0.0126658 | −0.00633290 | − | 0.999980i | \(-0.502016\pi\) | ||||
−0.00633290 | + | 0.999980i | \(0.502016\pi\) | |||||||
\(654\) | −27.9854 | −1.09432 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −35.2935 | −1.37798 | ||||||||
\(657\) | −37.1375 | −1.44887 | ||||||||
\(658\) | −73.1294 | −2.85088 | ||||||||
\(659\) | −23.9845 | −0.934303 | −0.467151 | − | 0.884177i | \(-0.654720\pi\) | ||||
−0.467151 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3973 | 0.482198 | 0.241099 | − | 0.970501i | \(-0.422492\pi\) | ||||
0.241099 | + | 0.970501i | \(0.422492\pi\) | |||||||
\(662\) | −36.7388 | −1.42789 | ||||||||
\(663\) | 2.40136 | 0.0932609 | ||||||||
\(664\) | 24.7354 | 0.959918 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.8079 | 1.00003 | ||||||||
\(667\) | −3.90549 | −0.151221 | ||||||||
\(668\) | −103.643 | −4.01005 | ||||||||
\(669\) | −6.55844 | −0.253564 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.4601 | −0.828458 | ||||||||
\(672\) | −54.4889 | −2.10196 | ||||||||
\(673\) | −30.2704 | −1.16684 | −0.583418 | − | 0.812172i | \(-0.698285\pi\) | ||||
−0.583418 | + | 0.812172i | \(0.698285\pi\) | |||||||
\(674\) | 60.2340 | 2.32013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −68.0090 | −2.61573 | ||||||||
\(677\) | −10.3794 | −0.398912 | −0.199456 | − | 0.979907i | \(-0.563917\pi\) | ||||
−0.199456 | + | 0.979907i | \(0.563917\pi\) | |||||||
\(678\) | 37.0194 | 1.42172 | ||||||||
\(679\) | −29.9964 | −1.15116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8872 | 0.455517 | ||||||||
\(682\) | −68.0736 | −2.60667 | ||||||||
\(683\) | −42.6642 | −1.63250 | −0.816251 | − | 0.577697i | \(-0.803951\pi\) | ||||
−0.816251 | + | 0.577697i | \(0.803951\pi\) | |||||||
\(684\) | 96.1625 | 3.67687 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −52.6735 | −2.01108 | ||||||||
\(687\) | −5.51454 | −0.210393 | ||||||||
\(688\) | 62.5002 | 2.38280 | ||||||||
\(689\) | 5.26856 | 0.200716 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.7595 | −1.70273 | −0.851366 | − | 0.524573i | \(-0.824225\pi\) | ||||
−0.851366 | + | 0.524573i | \(0.824225\pi\) | |||||||
\(692\) | 44.7744 | 1.70207 | ||||||||
\(693\) | −36.5012 | −1.38657 | ||||||||
\(694\) | −45.0897 | −1.71158 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.80261 | 0.219948 | ||||||||
\(697\) | −5.51150 | −0.208763 | ||||||||
\(698\) | −8.51471 | −0.322286 | ||||||||
\(699\) | 4.45551 | 0.168523 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4117 | 0.544323 | 0.272162 | − | 0.962252i | \(-0.412261\pi\) | ||||
0.272162 | + | 0.962252i | \(0.412261\pi\) | |||||||
\(702\) | −12.5616 | −0.474106 | ||||||||
\(703\) | 22.4324 | 0.846054 | ||||||||
\(704\) | 279.573 | 10.5368 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −49.6302 | −1.86786 | ||||||||
\(707\) | −39.9157 | −1.50118 | ||||||||
\(708\) | −33.2515 | −1.24967 | ||||||||
\(709\) | −14.0009 | −0.525817 | −0.262908 | − | 0.964821i | \(-0.584682\pi\) | ||||
−0.262908 | + | 0.964821i | \(0.584682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0810 | −0.378066 | ||||||||
\(712\) | −0.0738916 | −0.00276921 | ||||||||
\(713\) | −21.5899 | −0.808547 | ||||||||
\(714\) | −14.3765 | −0.538028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 112.328 | 4.19790 | ||||||||
\(717\) | −14.6457 | −0.546953 | ||||||||
\(718\) | 80.5590 | 3.00643 | ||||||||
\(719\) | 2.38506 | 0.0889476 | 0.0444738 | − | 0.999011i | \(-0.485839\pi\) | ||||
0.0444738 | + | 0.999011i | \(0.485839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.8059 | −1.03555 | ||||||||
\(722\) | 58.3472 | 2.17146 | ||||||||
\(723\) | 0.650611 | 0.0241965 | ||||||||
\(724\) | 138.849 | 5.16029 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −33.5155 | −1.24388 | ||||||||
\(727\) | −18.9362 | −0.702303 | −0.351151 | − | 0.936319i | \(-0.614210\pi\) | ||||
−0.351151 | + | 0.936319i | \(0.614210\pi\) | |||||||
\(728\) | −35.5211 | −1.31650 | ||||||||
\(729\) | −6.75392 | −0.250145 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.76014 | 0.360992 | ||||||||
\(732\) | 15.2708 | 0.564425 | ||||||||
\(733\) | −9.15528 | −0.338158 | −0.169079 | − | 0.985602i | \(-0.554079\pi\) | ||||
−0.169079 | + | 0.985602i | \(0.554079\pi\) | |||||||
\(734\) | 10.9933 | 0.405768 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 154.640 | 5.70011 | ||||||||
\(737\) | 9.47128 | 0.348879 | ||||||||
\(738\) | 13.3212 | 0.490362 | ||||||||
\(739\) | 27.9642 | 1.02868 | 0.514341 | − | 0.857586i | \(-0.328037\pi\) | ||||
0.514341 | + | 0.857586i | \(0.328037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.04493 | −0.185330 | ||||||||
\(742\) | −31.5420 | −1.15794 | ||||||||
\(743\) | −26.4697 | −0.971081 | −0.485540 | − | 0.874214i | \(-0.661377\pi\) | ||||
−0.485540 | + | 0.874214i | \(0.661377\pi\) | |||||||
\(744\) | 32.0773 | 1.17601 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.3289 | −0.744295 | ||||||||
\(747\) | −5.77618 | −0.211339 | ||||||||
\(748\) | 96.1624 | 3.51605 | ||||||||
\(749\) | −31.6963 | −1.15816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.79196 | 0.138370 | 0.0691852 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691852 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(752\) | −190.778 | −6.95694 | ||||||||
\(753\) | 10.4782 | 0.381848 | ||||||||
\(754\) | 2.79837 | 0.101911 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 56.2148 | 2.04451 | ||||||||
\(757\) | −45.5341 | −1.65496 | −0.827482 | − | 0.561492i | \(-0.810228\pi\) | ||||
−0.827482 | + | 0.561492i | \(0.810228\pi\) | |||||||
\(758\) | −27.1359 | −0.985619 | ||||||||
\(759\) | −17.0177 | −0.617702 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.64478 | −0.240873 | −0.120436 | − | 0.992721i | \(-0.538429\pi\) | ||||
−0.120436 | + | 0.992721i | \(0.538429\pi\) | |||||||
\(762\) | −19.7597 | −0.715819 | ||||||||
\(763\) | 39.9954 | 1.44793 | ||||||||
\(764\) | 8.64336 | 0.312706 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 90.6644 | 3.27584 | ||||||||
\(767\) | −10.6190 | −0.383429 | ||||||||
\(768\) | −81.7381 | −2.94947 | ||||||||
\(769\) | 15.0592 | 0.543049 | 0.271525 | − | 0.962431i | \(-0.412472\pi\) | ||||
0.271525 | + | 0.962431i | \(0.412472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.98035 | −0.251391 | ||||||||
\(772\) | −2.96672 | −0.106775 | ||||||||
\(773\) | −7.96647 | −0.286534 | −0.143267 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143267 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(774\) | −23.5902 | −0.847931 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −126.483 | −4.54047 | ||||||||
\(777\) | 6.05909 | 0.217369 | ||||||||
\(778\) | −80.9923 | −2.90371 | ||||||||
\(779\) | 11.5789 | 0.414858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.7289 | −1.35004 | ||||||||
\(782\) | 40.8007 | 1.45903 | ||||||||
\(783\) | −2.93264 | −0.104804 | ||||||||
\(784\) | −2.92139 | −0.104335 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.11039 | −0.289288 | ||||||||
\(787\) | −20.7723 | −0.740451 | −0.370226 | − | 0.928942i | \(-0.620720\pi\) | ||||
−0.370226 | + | 0.928942i | \(0.620720\pi\) | |||||||
\(788\) | 20.0523 | 0.714332 | ||||||||
\(789\) | 14.0314 | 0.499531 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −52.9063 | −1.88113 | ||||||||
\(792\) | −153.911 | −5.46899 | ||||||||
\(793\) | 4.87678 | 0.173179 | ||||||||
\(794\) | −46.2732 | −1.64217 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −48.0531 | −1.70320 | ||||||||
\(797\) | 2.33880 | 0.0828444 | 0.0414222 | − | 0.999142i | \(-0.486811\pi\) | ||||
0.0414222 | + | 0.999142i | \(0.486811\pi\) | |||||||
\(798\) | 30.2032 | 1.06918 | ||||||||
\(799\) | −29.7922 | −1.05397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0172551 | 0.000609679 0 | ||||||||
\(802\) | 106.858 | 3.77327 | ||||||||
\(803\) | 78.0209 | 2.75330 | ||||||||
\(804\) | −6.73967 | −0.237690 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.4696 | 0.544894 | ||||||||
\(807\) | −1.90404 | −0.0670256 | ||||||||
\(808\) | −168.308 | −5.92106 | ||||||||
\(809\) | −50.5106 | −1.77586 | −0.887928 | − | 0.459982i | \(-0.847856\pi\) | ||||
−0.887928 | + | 0.459982i | \(0.847856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6544 | −0.725274 | −0.362637 | − | 0.931930i | \(-0.618124\pi\) | ||||
−0.362637 | + | 0.931930i | \(0.618124\pi\) | |||||||
\(812\) | −12.5231 | −0.439475 | ||||||||
\(813\) | 1.14058 | 0.0400019 | ||||||||
\(814\) | −54.2188 | −1.90037 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −37.5050 | −1.31294 | ||||||||
\(817\) | −20.5048 | −0.717371 | ||||||||
\(818\) | 14.5303 | 0.508040 | ||||||||
\(819\) | 8.29486 | 0.289846 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.30646 | 0.324798 | 0.162399 | − | 0.986725i | \(-0.448077\pi\) | ||||
0.162399 | + | 0.986725i | \(0.448077\pi\) | |||||||
\(822\) | −9.61230 | −0.335267 | ||||||||
\(823\) | 19.6925 | 0.686436 | 0.343218 | − | 0.939256i | \(-0.388483\pi\) | ||||
0.343218 | + | 0.939256i | \(0.388483\pi\) | |||||||
\(824\) | −117.246 | −4.08447 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 63.5740 | 2.21202 | ||||||||
\(827\) | 13.4233 | 0.466774 | 0.233387 | − | 0.972384i | \(-0.425019\pi\) | ||||
0.233387 | + | 0.972384i | \(0.425019\pi\) | |||||||
\(828\) | −73.7143 | −2.56175 | ||||||||
\(829\) | 40.6611 | 1.41222 | 0.706109 | − | 0.708103i | \(-0.250449\pi\) | ||||
0.706109 | + | 0.708103i | \(0.250449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.24132 | −0.216509 | ||||||||
\(832\) | −63.5325 | −2.20259 | ||||||||
\(833\) | −0.456209 | −0.0158067 | ||||||||
\(834\) | −11.2927 | −0.391035 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −202.024 | −6.98716 | ||||||||
\(837\) | −16.2119 | −0.560365 | ||||||||
\(838\) | −80.9515 | −2.79642 | ||||||||
\(839\) | −31.2319 | −1.07824 | −0.539122 | − | 0.842228i | \(-0.681244\pi\) | ||||
−0.539122 | + | 0.842228i | \(0.681244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3467 | −0.977472 | ||||||||
\(842\) | 57.1884 | 1.97084 | ||||||||
\(843\) | 1.31317 | 0.0452280 | ||||||||
\(844\) | −114.826 | −3.95247 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 72.0073 | 2.47566 | ||||||||
\(847\) | 47.8987 | 1.64582 | ||||||||
\(848\) | −82.2856 | −2.82570 | ||||||||
\(849\) | 0.785497 | 0.0269582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1958 | −0.589463 | ||||||||
\(852\) | 26.8475 | 0.919780 | ||||||||
\(853\) | −15.6453 | −0.535684 | −0.267842 | − | 0.963463i | \(-0.586310\pi\) | ||||
−0.267842 | + | 0.963463i | \(0.586310\pi\) | |||||||
\(854\) | −29.1965 | −0.999082 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −133.650 | −4.56808 | ||||||||
\(857\) | −11.5099 | −0.393172 | −0.196586 | − | 0.980487i | \(-0.562986\pi\) | ||||
−0.196586 | + | 0.980487i | \(0.562986\pi\) | |||||||
\(858\) | 12.1935 | 0.416280 | ||||||||
\(859\) | 18.9398 | 0.646218 | 0.323109 | − | 0.946362i | \(-0.395272\pi\) | ||||
0.323109 | + | 0.946362i | \(0.395272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.12752 | 0.106586 | ||||||||
\(862\) | −33.4163 | −1.13816 | ||||||||
\(863\) | 5.57862 | 0.189899 | 0.0949493 | − | 0.995482i | \(-0.469731\pi\) | ||||
0.0949493 | + | 0.995482i | \(0.469731\pi\) | |||||||
\(864\) | 116.120 | 3.95047 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 78.1910 | 2.65704 | ||||||||
\(867\) | 5.20354 | 0.176722 | ||||||||
\(868\) | −69.2287 | −2.34978 | ||||||||
\(869\) | 21.1787 | 0.718440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.15233 | −0.0729291 | ||||||||
\(872\) | 168.644 | 5.71102 | ||||||||
\(873\) | 29.5362 | 0.999648 | ||||||||
\(874\) | −85.7169 | −2.89942 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −55.5189 | −1.87581 | ||||||||
\(877\) | 38.6574 | 1.30537 | 0.652684 | − | 0.757631i | \(-0.273643\pi\) | ||||
0.652684 | + | 0.757631i | \(0.273643\pi\) | |||||||
\(878\) | 55.9707 | 1.88892 | ||||||||
\(879\) | 7.54562 | 0.254507 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3265 | 0.550055 | 0.275028 | − | 0.961436i | \(-0.411313\pi\) | ||||
0.275028 | + | 0.961436i | \(0.411313\pi\) | |||||||
\(882\) | 1.10265 | 0.0371283 | ||||||||
\(883\) | −31.6712 | −1.06582 | −0.532911 | − | 0.846171i | \(-0.678902\pi\) | ||||
−0.532911 | + | 0.846171i | \(0.678902\pi\) | |||||||
\(884\) | −21.8528 | −0.734988 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.6221 | −1.19675 | ||||||||
\(887\) | −19.9371 | −0.669423 | −0.334711 | − | 0.942321i | \(-0.608639\pi\) | ||||
−0.334711 | + | 0.942321i | \(0.608639\pi\) | |||||||
\(888\) | 25.5487 | 0.857360 | ||||||||
\(889\) | 28.2396 | 0.947125 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.0669 | 0.973778 | ||||||||
\(892\) | 59.6830 | 1.99833 | ||||||||
\(893\) | 62.5894 | 2.09447 | ||||||||
\(894\) | −19.2673 | −0.644394 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 212.858 | 7.11109 | ||||||||
\(897\) | 3.86724 | 0.129123 | ||||||||
\(898\) | −47.2838 | −1.57788 | ||||||||
\(899\) | 3.61156 | 0.120452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8499 | −0.428091 | ||||||||
\(902\) | −27.9861 | −0.931836 | ||||||||
\(903\) | −5.53843 | −0.184307 | ||||||||
\(904\) | −223.085 | −7.41968 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 37.9499 | 1.26080 | ||||||||
\(907\) | 4.26367 | 0.141573 | 0.0707865 | − | 0.997491i | \(-0.477449\pi\) | ||||
0.0707865 | + | 0.997491i | \(0.477449\pi\) | |||||||
\(908\) | −108.175 | −3.58992 | ||||||||
\(909\) | 39.3032 | 1.30361 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.46818 | 0.114906 | 0.0574530 | − | 0.998348i | \(-0.481702\pi\) | ||||
0.0574530 | + | 0.998348i | \(0.481702\pi\) | |||||||
\(912\) | 78.7930 | 2.60910 | ||||||||
\(913\) | 12.1350 | 0.401609 | ||||||||
\(914\) | −70.9996 | −2.34846 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50.1833 | 1.65810 | ||||||||
\(917\) | 11.5910 | 0.382767 | ||||||||
\(918\) | 30.6374 | 1.01118 | ||||||||
\(919\) | −2.81869 | −0.0929800 | −0.0464900 | − | 0.998919i | \(-0.514804\pi\) | ||||
−0.0464900 | + | 0.998919i | \(0.514804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.9577 | 0.624676 | ||||||||
\(922\) | 15.3080 | 0.504143 | ||||||||
\(923\) | 8.57383 | 0.282211 | ||||||||
\(924\) | −54.5677 | −1.79515 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.0855 | −0.725773 | ||||||||
\(927\) | 27.3793 | 0.899254 | ||||||||
\(928\) | −25.8682 | −0.849166 | ||||||||
\(929\) | 43.0563 | 1.41263 | 0.706316 | − | 0.707897i | \(-0.250356\pi\) | ||||
0.706316 | + | 0.707897i | \(0.250356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.958435 | 0.0314114 | ||||||||
\(932\) | −40.5459 | −1.32813 | ||||||||
\(933\) | −4.54243 | −0.148712 | ||||||||
\(934\) | −59.8304 | −1.95771 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 34.9761 | 1.14323 | ||||||||
\(937\) | 19.1635 | 0.626044 | 0.313022 | − | 0.949746i | \(-0.398659\pi\) | ||||
0.313022 | + | 0.949746i | \(0.398659\pi\) | |||||||
\(938\) | 12.8857 | 0.420732 | ||||||||
\(939\) | 10.9644 | 0.357810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.7480 | 1.19795 | 0.598975 | − | 0.800767i | \(-0.295575\pi\) | ||||
0.598975 | + | 0.800767i | \(0.295575\pi\) | |||||||
\(942\) | −32.6719 | −1.06451 | ||||||||
\(943\) | −8.87594 | −0.289040 | ||||||||
\(944\) | 165.850 | 5.39795 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.5597 | 1.61133 | ||||||||
\(947\) | −6.22386 | −0.202248 | −0.101124 | − | 0.994874i | \(-0.532244\pi\) | ||||
−0.101124 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(948\) | −15.0706 | −0.489470 | ||||||||
\(949\) | −17.7301 | −0.575544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.06104 | 0.228970 | ||||||||
\(952\) | 86.6350 | 2.80786 | ||||||||
\(953\) | −52.3602 | −1.69611 | −0.848056 | − | 0.529906i | \(-0.822227\pi\) | ||||
−0.848056 | + | 0.529906i | \(0.822227\pi\) | |||||||
\(954\) | 31.0580 | 1.00554 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 133.278 | 4.31053 | ||||||||
\(957\) | 2.84672 | 0.0920213 | ||||||||
\(958\) | −51.4548 | −1.66243 | ||||||||
\(959\) | 13.7374 | 0.443604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0350 | −0.355968 | ||||||||
\(962\) | 12.3211 | 0.397250 | ||||||||
\(963\) | 31.2099 | 1.00573 | ||||||||
\(964\) | −5.92068 | −0.190692 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.1525 | −0.744920 | ||||||||
\(967\) | −23.5339 | −0.756800 | −0.378400 | − | 0.925642i | \(-0.623526\pi\) | ||||
−0.378400 | + | 0.925642i | \(0.623526\pi\) | |||||||
\(968\) | 201.970 | 6.49155 | ||||||||
\(969\) | 12.3045 | 0.395276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.8945 | 1.44073 | 0.720366 | − | 0.693594i | \(-0.243974\pi\) | ||||
0.720366 | + | 0.693594i | \(0.243974\pi\) | |||||||
\(972\) | −85.1291 | −2.73052 | ||||||||
\(973\) | 16.1390 | 0.517393 | ||||||||
\(974\) | 36.1585 | 1.15859 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −76.1667 | −2.43804 | ||||||||
\(977\) | 54.7799 | 1.75257 | 0.876283 | − | 0.481798i | \(-0.160016\pi\) | ||||
0.876283 | + | 0.481798i | \(0.160016\pi\) | |||||||
\(978\) | −8.41881 | −0.269204 | ||||||||
\(979\) | −0.0362507 | −0.00115858 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.3817 | −1.25736 | ||||||||
\(982\) | 85.5375 | 2.72961 | ||||||||
\(983\) | 34.4464 | 1.09867 | 0.549335 | − | 0.835602i | \(-0.314881\pi\) | ||||
0.549335 | + | 0.835602i | \(0.314881\pi\) | |||||||
\(984\) | 13.1875 | 0.420402 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.82516 | −0.217357 | ||||||||
\(987\) | 16.9057 | 0.538113 | ||||||||
\(988\) | 45.9097 | 1.46058 | ||||||||
\(989\) | 15.7181 | 0.499807 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.9650 | −1.23776 | −0.618882 | − | 0.785484i | \(-0.712414\pi\) | ||||
−0.618882 | + | 0.785484i | \(0.712414\pi\) | |||||||
\(992\) | −143.002 | −4.54031 | ||||||||
\(993\) | 8.49307 | 0.269519 | ||||||||
\(994\) | −51.3301 | −1.62809 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.63513 | −0.273614 | ||||||||
\(997\) | 13.8322 | 0.438070 | 0.219035 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219035 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(998\) | 10.9340 | 0.346108 | ||||||||
\(999\) | −12.9123 | −0.408528 |
(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 | 6025.2.a.q.1.66 | 66 | ||
5.2 | odd | 4 | 1205.2.b.d.724.66 | yes | 66 | ||
5.3 | odd | 4 | 1205.2.b.d.724.1 | ✓ | 66 | ||
5.4 | even | 2 | inner | 6025.2.a.q.1.1 | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.d.724.1 | ✓ | 66 | 5.3 | odd | 4 | ||
1205.2.b.d.724.66 | yes | 66 | 5.2 | odd | 4 | ||
6025.2.a.q.1.1 | 66 | 5.4 | even | 2 | inner | ||
6025.2.a.q.1.66 | 66 | 1.1 | even | 1 | trivial |