Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6011,2,Mod(1,6011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6011, 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("6011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6011.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: | \(47.9980766550\) |
Analytic rank: | \(0\) |
Dimension: | \(275\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61605 | −1.84983 | −0.924915 | − | 0.380175i | \(-0.875864\pi\) | ||||
−0.924915 | + | 0.380175i | \(0.875864\pi\) | |||||||
\(3\) | −0.908380 | −0.524454 | −0.262227 | − | 0.965006i | \(-0.584457\pi\) | ||||
−0.262227 | + | 0.965006i | \(0.584457\pi\) | |||||||
\(4\) | 4.84374 | 2.42187 | ||||||||
\(5\) | −1.38921 | −0.621274 | −0.310637 | − | 0.950529i | \(-0.600542\pi\) | ||||
−0.310637 | + | 0.950529i | \(0.600542\pi\) | |||||||
\(6\) | 2.37637 | 0.970150 | ||||||||
\(7\) | 2.01973 | 0.763387 | 0.381693 | − | 0.924289i | \(-0.375341\pi\) | ||||
0.381693 | + | 0.924289i | \(0.375341\pi\) | |||||||
\(8\) | −7.43937 | −2.63021 | ||||||||
\(9\) | −2.17484 | −0.724948 | ||||||||
\(10\) | 3.63425 | 1.14925 | ||||||||
\(11\) | −3.10444 | −0.936024 | −0.468012 | − | 0.883722i | \(-0.655030\pi\) | ||||
−0.468012 | + | 0.883722i | \(0.655030\pi\) | |||||||
\(12\) | −4.39996 | −1.27016 | ||||||||
\(13\) | 6.92822 | 1.92154 | 0.960772 | − | 0.277341i | \(-0.0894530\pi\) | ||||
0.960772 | + | 0.277341i | \(0.0894530\pi\) | |||||||
\(14\) | −5.28372 | −1.41213 | ||||||||
\(15\) | 1.26193 | 0.325829 | ||||||||
\(16\) | 9.77431 | 2.44358 | ||||||||
\(17\) | −1.38446 | −0.335782 | −0.167891 | − | 0.985806i | \(-0.553696\pi\) | ||||
−0.167891 | + | 0.985806i | \(0.553696\pi\) | |||||||
\(18\) | 5.68951 | 1.34103 | ||||||||
\(19\) | −6.85939 | −1.57365 | −0.786826 | − | 0.617175i | \(-0.788277\pi\) | ||||
−0.786826 | + | 0.617175i | \(0.788277\pi\) | |||||||
\(20\) | −6.72897 | −1.50464 | ||||||||
\(21\) | −1.83468 | −0.400361 | ||||||||
\(22\) | 8.12138 | 1.73148 | ||||||||
\(23\) | −5.18663 | −1.08149 | −0.540744 | − | 0.841187i | \(-0.681857\pi\) | ||||
−0.540744 | + | 0.841187i | \(0.681857\pi\) | |||||||
\(24\) | 6.75778 | 1.37943 | ||||||||
\(25\) | −3.07009 | −0.614019 | ||||||||
\(26\) | −18.1246 | −3.55453 | ||||||||
\(27\) | 4.70073 | 0.904656 | ||||||||
\(28\) | 9.78305 | 1.84882 | ||||||||
\(29\) | 4.77374 | 0.886461 | 0.443230 | − | 0.896408i | \(-0.353832\pi\) | ||||
0.443230 | + | 0.896408i | \(0.353832\pi\) | |||||||
\(30\) | −3.30128 | −0.602729 | ||||||||
\(31\) | 1.48072 | 0.265945 | 0.132972 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132972 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(32\) | −10.6914 | −1.88999 | ||||||||
\(33\) | 2.82001 | 0.490901 | ||||||||
\(34\) | 3.62183 | 0.621139 | ||||||||
\(35\) | −2.80583 | −0.474272 | ||||||||
\(36\) | −10.5344 | −1.75573 | ||||||||
\(37\) | 1.06338 | 0.174819 | 0.0874093 | − | 0.996172i | \(-0.472141\pi\) | ||||
0.0874093 | + | 0.996172i | \(0.472141\pi\) | |||||||
\(38\) | 17.9445 | 2.91099 | ||||||||
\(39\) | −6.29346 | −1.00776 | ||||||||
\(40\) | 10.3349 | 1.63408 | ||||||||
\(41\) | −7.51569 | −1.17375 | −0.586877 | − | 0.809676i | \(-0.699643\pi\) | ||||
−0.586877 | + | 0.809676i | \(0.699643\pi\) | |||||||
\(42\) | 4.79963 | 0.740599 | ||||||||
\(43\) | −2.10462 | −0.320952 | −0.160476 | − | 0.987040i | \(-0.551303\pi\) | ||||
−0.160476 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(44\) | −15.0371 | −2.26693 | ||||||||
\(45\) | 3.02132 | 0.450392 | ||||||||
\(46\) | 13.5685 | 2.00057 | ||||||||
\(47\) | −5.65750 | −0.825231 | −0.412616 | − | 0.910905i | \(-0.635385\pi\) | ||||
−0.412616 | + | 0.910905i | \(0.635385\pi\) | |||||||
\(48\) | −8.87880 | −1.28154 | ||||||||
\(49\) | −2.92069 | −0.417241 | ||||||||
\(50\) | 8.03153 | 1.13583 | ||||||||
\(51\) | 1.25762 | 0.176102 | ||||||||
\(52\) | 33.5585 | 4.65373 | ||||||||
\(53\) | 7.02284 | 0.964661 | 0.482331 | − | 0.875989i | \(-0.339790\pi\) | ||||
0.482331 | + | 0.875989i | \(0.339790\pi\) | |||||||
\(54\) | −12.2974 | −1.67346 | ||||||||
\(55\) | 4.31272 | 0.581527 | ||||||||
\(56\) | −15.0255 | −2.00787 | ||||||||
\(57\) | 6.23093 | 0.825307 | ||||||||
\(58\) | −12.4884 | −1.63980 | ||||||||
\(59\) | −11.3644 | −1.47952 | −0.739760 | − | 0.672871i | \(-0.765061\pi\) | ||||
−0.739760 | + | 0.672871i | \(0.765061\pi\) | |||||||
\(60\) | 6.11247 | 0.789116 | ||||||||
\(61\) | 8.72258 | 1.11681 | 0.558406 | − | 0.829568i | \(-0.311413\pi\) | ||||
0.558406 | + | 0.829568i | \(0.311413\pi\) | |||||||
\(62\) | −3.87364 | −0.491952 | ||||||||
\(63\) | −4.39260 | −0.553416 | ||||||||
\(64\) | 8.42063 | 1.05258 | ||||||||
\(65\) | −9.62476 | −1.19381 | ||||||||
\(66\) | −7.37730 | −0.908083 | ||||||||
\(67\) | −15.5722 | −1.90244 | −0.951222 | − | 0.308507i | \(-0.900171\pi\) | ||||
−0.951222 | + | 0.308507i | \(0.900171\pi\) | |||||||
\(68\) | −6.70597 | −0.813219 | ||||||||
\(69\) | 4.71143 | 0.567190 | ||||||||
\(70\) | 7.34021 | 0.877323 | ||||||||
\(71\) | 6.41118 | 0.760867 | 0.380434 | − | 0.924808i | \(-0.375775\pi\) | ||||
0.380434 | + | 0.924808i | \(0.375775\pi\) | |||||||
\(72\) | 16.1795 | 1.90677 | ||||||||
\(73\) | 8.59609 | 1.00610 | 0.503048 | − | 0.864258i | \(-0.332212\pi\) | ||||
0.503048 | + | 0.864258i | \(0.332212\pi\) | |||||||
\(74\) | −2.78186 | −0.323385 | ||||||||
\(75\) | 2.78881 | 0.322024 | ||||||||
\(76\) | −33.2251 | −3.81118 | ||||||||
\(77\) | −6.27013 | −0.714548 | ||||||||
\(78\) | 16.4640 | 1.86419 | ||||||||
\(79\) | 0.922615 | 0.103802 | 0.0519012 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0519012 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(80\) | −13.5786 | −1.51813 | ||||||||
\(81\) | 2.25449 | 0.250498 | ||||||||
\(82\) | 19.6615 | 2.17125 | ||||||||
\(83\) | 12.1081 | 1.32904 | 0.664519 | − | 0.747271i | \(-0.268636\pi\) | ||||
0.664519 | + | 0.747271i | \(0.268636\pi\) | |||||||
\(84\) | −8.88673 | −0.969622 | ||||||||
\(85\) | 1.92331 | 0.208612 | ||||||||
\(86\) | 5.50580 | 0.593706 | ||||||||
\(87\) | −4.33637 | −0.464908 | ||||||||
\(88\) | 23.0951 | 2.46194 | ||||||||
\(89\) | 0.971268 | 0.102954 | 0.0514771 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514771 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(90\) | −7.90393 | −0.833148 | ||||||||
\(91\) | 13.9931 | 1.46688 | ||||||||
\(92\) | −25.1227 | −2.61922 | ||||||||
\(93\) | −1.34506 | −0.139476 | ||||||||
\(94\) | 14.8003 | 1.52654 | ||||||||
\(95\) | 9.52914 | 0.977669 | ||||||||
\(96\) | 9.71185 | 0.991212 | ||||||||
\(97\) | 19.1610 | 1.94551 | 0.972753 | − | 0.231843i | \(-0.0744756\pi\) | ||||
0.972753 | + | 0.231843i | \(0.0744756\pi\) | |||||||
\(98\) | 7.64067 | 0.771824 | ||||||||
\(99\) | 6.75167 | 0.678569 | ||||||||
\(100\) | −14.8707 | −1.48707 | ||||||||
\(101\) | −10.3050 | −1.02538 | −0.512691 | − | 0.858573i | \(-0.671351\pi\) | ||||
−0.512691 | + | 0.858573i | \(0.671351\pi\) | |||||||
\(102\) | −3.29000 | −0.325758 | ||||||||
\(103\) | −5.12808 | −0.505285 | −0.252643 | − | 0.967560i | \(-0.581300\pi\) | ||||
−0.252643 | + | 0.967560i | \(0.581300\pi\) | |||||||
\(104\) | −51.5416 | −5.05407 | ||||||||
\(105\) | 2.54876 | 0.248734 | ||||||||
\(106\) | −18.3721 | −1.78446 | ||||||||
\(107\) | −9.64330 | −0.932253 | −0.466127 | − | 0.884718i | \(-0.654351\pi\) | ||||
−0.466127 | + | 0.884718i | \(0.654351\pi\) | |||||||
\(108\) | 22.7691 | 2.19096 | ||||||||
\(109\) | −15.6965 | −1.50345 | −0.751727 | − | 0.659475i | \(-0.770779\pi\) | ||||
−0.751727 | + | 0.659475i | \(0.770779\pi\) | |||||||
\(110\) | −11.2823 | −1.07573 | ||||||||
\(111\) | −0.965954 | −0.0916843 | ||||||||
\(112\) | 19.7415 | 1.86539 | ||||||||
\(113\) | −13.4779 | −1.26789 | −0.633947 | − | 0.773376i | \(-0.718566\pi\) | ||||
−0.633947 | + | 0.773376i | \(0.718566\pi\) | |||||||
\(114\) | −16.3005 | −1.52668 | ||||||||
\(115\) | 7.20533 | 0.671900 | ||||||||
\(116\) | 23.1227 | 2.14689 | ||||||||
\(117\) | −15.0678 | −1.39302 | ||||||||
\(118\) | 29.7299 | 2.73686 | ||||||||
\(119\) | −2.79624 | −0.256331 | ||||||||
\(120\) | −9.38798 | −0.857001 | ||||||||
\(121\) | −1.36246 | −0.123860 | ||||||||
\(122\) | −22.8187 | −2.06591 | ||||||||
\(123\) | 6.82711 | 0.615580 | ||||||||
\(124\) | 7.17221 | 0.644083 | ||||||||
\(125\) | 11.2111 | 1.00275 | ||||||||
\(126\) | 11.4913 | 1.02372 | ||||||||
\(127\) | −6.92131 | −0.614167 | −0.307083 | − | 0.951683i | \(-0.599353\pi\) | ||||
−0.307083 | + | 0.951683i | \(0.599353\pi\) | |||||||
\(128\) | −0.646031 | −0.0571016 | ||||||||
\(129\) | 1.91180 | 0.168324 | ||||||||
\(130\) | 25.1789 | 2.20834 | ||||||||
\(131\) | 10.9408 | 0.955900 | 0.477950 | − | 0.878387i | \(-0.341380\pi\) | ||||
0.477950 | + | 0.878387i | \(0.341380\pi\) | |||||||
\(132\) | 13.6594 | 1.18890 | ||||||||
\(133\) | −13.8541 | −1.20130 | ||||||||
\(134\) | 40.7377 | 3.51920 | ||||||||
\(135\) | −6.53030 | −0.562039 | ||||||||
\(136\) | 10.2995 | 0.883177 | ||||||||
\(137\) | 17.6981 | 1.51205 | 0.756025 | − | 0.654543i | \(-0.227139\pi\) | ||||
0.756025 | + | 0.654543i | \(0.227139\pi\) | |||||||
\(138\) | −12.3254 | −1.04920 | ||||||||
\(139\) | −15.6139 | −1.32436 | −0.662178 | − | 0.749347i | \(-0.730368\pi\) | ||||
−0.662178 | + | 0.749347i | \(0.730368\pi\) | |||||||
\(140\) | −13.5907 | −1.14863 | ||||||||
\(141\) | 5.13916 | 0.432796 | ||||||||
\(142\) | −16.7720 | −1.40747 | ||||||||
\(143\) | −21.5082 | −1.79861 | ||||||||
\(144\) | −21.2576 | −1.77147 | ||||||||
\(145\) | −6.63173 | −0.550735 | ||||||||
\(146\) | −22.4878 | −1.86111 | ||||||||
\(147\) | 2.65309 | 0.218824 | ||||||||
\(148\) | 5.15073 | 0.423388 | ||||||||
\(149\) | −4.49702 | −0.368410 | −0.184205 | − | 0.982888i | \(-0.558971\pi\) | ||||
−0.184205 | + | 0.982888i | \(0.558971\pi\) | |||||||
\(150\) | −7.29568 | −0.595690 | ||||||||
\(151\) | 20.0399 | 1.63082 | 0.815410 | − | 0.578883i | \(-0.196511\pi\) | ||||
0.815410 | + | 0.578883i | \(0.196511\pi\) | |||||||
\(152\) | 51.0295 | 4.13904 | ||||||||
\(153\) | 3.01099 | 0.243424 | ||||||||
\(154\) | 16.4030 | 1.32179 | ||||||||
\(155\) | −2.05703 | −0.165225 | ||||||||
\(156\) | −30.4839 | −2.44066 | ||||||||
\(157\) | 15.1413 | 1.20841 | 0.604205 | − | 0.796829i | \(-0.293491\pi\) | ||||
0.604205 | + | 0.796829i | \(0.293491\pi\) | |||||||
\(158\) | −2.41361 | −0.192017 | ||||||||
\(159\) | −6.37941 | −0.505920 | ||||||||
\(160\) | 14.8526 | 1.17420 | ||||||||
\(161\) | −10.4756 | −0.825593 | ||||||||
\(162\) | −5.89785 | −0.463379 | ||||||||
\(163\) | −11.6654 | −0.913706 | −0.456853 | − | 0.889542i | \(-0.651023\pi\) | ||||
−0.456853 | + | 0.889542i | \(0.651023\pi\) | |||||||
\(164\) | −36.4040 | −2.84268 | ||||||||
\(165\) | −3.91759 | −0.304984 | ||||||||
\(166\) | −31.6755 | −2.45849 | ||||||||
\(167\) | 17.0335 | 1.31810 | 0.659048 | − | 0.752101i | \(-0.270960\pi\) | ||||
0.659048 | + | 0.752101i | \(0.270960\pi\) | |||||||
\(168\) | 13.6489 | 1.05303 | ||||||||
\(169\) | 35.0003 | 2.69233 | ||||||||
\(170\) | −5.03149 | −0.385897 | ||||||||
\(171\) | 14.9181 | 1.14082 | ||||||||
\(172\) | −10.1942 | −0.777303 | ||||||||
\(173\) | −7.67764 | −0.583720 | −0.291860 | − | 0.956461i | \(-0.594274\pi\) | ||||
−0.291860 | + | 0.956461i | \(0.594274\pi\) | |||||||
\(174\) | 11.3442 | 0.860000 | ||||||||
\(175\) | −6.20076 | −0.468734 | ||||||||
\(176\) | −30.3438 | −2.28725 | ||||||||
\(177\) | 10.3232 | 0.775940 | ||||||||
\(178\) | −2.54089 | −0.190448 | ||||||||
\(179\) | −0.0223994 | −0.00167421 | −0.000837104 | − | 1.00000i | \(-0.500266\pi\) | ||||
−0.000837104 | 1.00000i | \(0.500266\pi\) | ||||||||
\(180\) | 14.6345 | 1.09079 | ||||||||
\(181\) | 26.4258 | 1.96421 | 0.982106 | − | 0.188327i | \(-0.0603064\pi\) | ||||
0.982106 | + | 0.188327i | \(0.0603064\pi\) | |||||||
\(182\) | −36.6068 | −2.71348 | ||||||||
\(183\) | −7.92342 | −0.585716 | ||||||||
\(184\) | 38.5853 | 2.84454 | ||||||||
\(185\) | −1.47726 | −0.108610 | ||||||||
\(186\) | 3.51874 | 0.258006 | ||||||||
\(187\) | 4.29798 | 0.314299 | ||||||||
\(188\) | −27.4034 | −1.99860 | ||||||||
\(189\) | 9.49421 | 0.690602 | ||||||||
\(190\) | −24.9287 | −1.80852 | ||||||||
\(191\) | −0.0823220 | −0.00595661 | −0.00297830 | − | 0.999996i | \(-0.500948\pi\) | ||||
−0.00297830 | + | 0.999996i | \(0.500948\pi\) | |||||||
\(192\) | −7.64913 | −0.552029 | ||||||||
\(193\) | −1.51694 | −0.109192 | −0.0545959 | − | 0.998509i | \(-0.517387\pi\) | ||||
−0.0545959 | + | 0.998509i | \(0.517387\pi\) | |||||||
\(194\) | −50.1262 | −3.59885 | ||||||||
\(195\) | 8.74295 | 0.626096 | ||||||||
\(196\) | −14.1470 | −1.01050 | ||||||||
\(197\) | −0.194024 | −0.0138236 | −0.00691181 | − | 0.999976i | \(-0.502200\pi\) | ||||
−0.00691181 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(198\) | −17.6627 | −1.25524 | ||||||||
\(199\) | 0.512178 | 0.0363073 | 0.0181537 | − | 0.999835i | \(-0.494221\pi\) | ||||
0.0181537 | + | 0.999835i | \(0.494221\pi\) | |||||||
\(200\) | 22.8396 | 1.61500 | ||||||||
\(201\) | 14.1455 | 0.997744 | ||||||||
\(202\) | 26.9583 | 1.89678 | ||||||||
\(203\) | 9.64167 | 0.676712 | ||||||||
\(204\) | 6.09158 | 0.426496 | ||||||||
\(205\) | 10.4409 | 0.729223 | ||||||||
\(206\) | 13.4153 | 0.934691 | ||||||||
\(207\) | 11.2801 | 0.784022 | ||||||||
\(208\) | 67.7186 | 4.69544 | ||||||||
\(209\) | 21.2946 | 1.47298 | ||||||||
\(210\) | −6.66770 | −0.460115 | ||||||||
\(211\) | −21.9411 | −1.51049 | −0.755245 | − | 0.655443i | \(-0.772482\pi\) | ||||
−0.755245 | + | 0.655443i | \(0.772482\pi\) | |||||||
\(212\) | 34.0168 | 2.33628 | ||||||||
\(213\) | −5.82379 | −0.399040 | ||||||||
\(214\) | 25.2274 | 1.72451 | ||||||||
\(215\) | 2.92376 | 0.199399 | ||||||||
\(216\) | −34.9704 | −2.37944 | ||||||||
\(217\) | 2.99065 | 0.203019 | ||||||||
\(218\) | 41.0629 | 2.78113 | ||||||||
\(219\) | −7.80852 | −0.527651 | ||||||||
\(220\) | 20.8897 | 1.40838 | ||||||||
\(221\) | −9.59187 | −0.645219 | ||||||||
\(222\) | 2.52699 | 0.169600 | ||||||||
\(223\) | −10.1363 | −0.678779 | −0.339389 | − | 0.940646i | \(-0.610220\pi\) | ||||
−0.339389 | + | 0.940646i | \(0.610220\pi\) | |||||||
\(224\) | −21.5937 | −1.44279 | ||||||||
\(225\) | 6.67698 | 0.445132 | ||||||||
\(226\) | 35.2589 | 2.34539 | ||||||||
\(227\) | −22.0811 | −1.46558 | −0.732788 | − | 0.680457i | \(-0.761781\pi\) | ||||
−0.732788 | + | 0.680457i | \(0.761781\pi\) | |||||||
\(228\) | 30.1810 | 1.99879 | ||||||||
\(229\) | 13.9531 | 0.922049 | 0.461024 | − | 0.887387i | \(-0.347482\pi\) | ||||
0.461024 | + | 0.887387i | \(0.347482\pi\) | |||||||
\(230\) | −18.8495 | −1.24290 | ||||||||
\(231\) | 5.69567 | 0.374747 | ||||||||
\(232\) | −35.5136 | −2.33158 | ||||||||
\(233\) | −15.8536 | −1.03860 | −0.519301 | − | 0.854591i | \(-0.673808\pi\) | ||||
−0.519301 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(234\) | 39.4182 | 2.57685 | ||||||||
\(235\) | 7.85946 | 0.512695 | ||||||||
\(236\) | −55.0462 | −3.58320 | ||||||||
\(237\) | −0.838086 | −0.0544395 | ||||||||
\(238\) | 7.31512 | 0.474169 | ||||||||
\(239\) | −15.7819 | −1.02085 | −0.510423 | − | 0.859923i | \(-0.670511\pi\) | ||||
−0.510423 | + | 0.859923i | \(0.670511\pi\) | |||||||
\(240\) | 12.3345 | 0.796190 | ||||||||
\(241\) | 7.78388 | 0.501404 | 0.250702 | − | 0.968064i | \(-0.419339\pi\) | ||||
0.250702 | + | 0.968064i | \(0.419339\pi\) | |||||||
\(242\) | 3.56427 | 0.229120 | ||||||||
\(243\) | −16.1501 | −1.03603 | ||||||||
\(244\) | 42.2499 | 2.70477 | ||||||||
\(245\) | 4.05745 | 0.259221 | ||||||||
\(246\) | −17.8601 | −1.13872 | ||||||||
\(247\) | −47.5234 | −3.02384 | ||||||||
\(248\) | −11.0156 | −0.699492 | ||||||||
\(249\) | −10.9988 | −0.697019 | ||||||||
\(250\) | −29.3287 | −1.85491 | ||||||||
\(251\) | −12.5416 | −0.791617 | −0.395808 | − | 0.918333i | \(-0.629536\pi\) | ||||
−0.395808 | + | 0.918333i | \(0.629536\pi\) | |||||||
\(252\) | −21.2766 | −1.34030 | ||||||||
\(253\) | 16.1016 | 1.01230 | ||||||||
\(254\) | 18.1065 | 1.13610 | ||||||||
\(255\) | −1.74710 | −0.109408 | ||||||||
\(256\) | −15.1512 | −0.946950 | ||||||||
\(257\) | 9.81532 | 0.612263 | 0.306132 | − | 0.951989i | \(-0.400965\pi\) | ||||
0.306132 | + | 0.951989i | \(0.400965\pi\) | |||||||
\(258\) | −5.00137 | −0.311371 | ||||||||
\(259\) | 2.14774 | 0.133454 | ||||||||
\(260\) | −46.6198 | −2.89124 | ||||||||
\(261\) | −10.3821 | −0.642638 | ||||||||
\(262\) | −28.6216 | −1.76825 | ||||||||
\(263\) | 19.3929 | 1.19582 | 0.597909 | − | 0.801564i | \(-0.295998\pi\) | ||||
0.597909 | + | 0.801564i | \(0.295998\pi\) | |||||||
\(264\) | −20.9791 | −1.29117 | ||||||||
\(265\) | −9.75621 | −0.599319 | ||||||||
\(266\) | 36.2431 | 2.22221 | ||||||||
\(267\) | −0.882281 | −0.0539947 | ||||||||
\(268\) | −75.4275 | −4.60747 | ||||||||
\(269\) | 2.77941 | 0.169463 | 0.0847317 | − | 0.996404i | \(-0.472997\pi\) | ||||
0.0847317 | + | 0.996404i | \(0.472997\pi\) | |||||||
\(270\) | 17.0836 | 1.03968 | ||||||||
\(271\) | 3.85307 | 0.234057 | 0.117029 | − | 0.993129i | \(-0.462663\pi\) | ||||
0.117029 | + | 0.993129i | \(0.462663\pi\) | |||||||
\(272\) | −13.5322 | −0.820509 | ||||||||
\(273\) | −12.7111 | −0.769311 | ||||||||
\(274\) | −46.2992 | −2.79703 | ||||||||
\(275\) | 9.53092 | 0.574736 | ||||||||
\(276\) | 22.8210 | 1.37366 | ||||||||
\(277\) | −4.99013 | −0.299828 | −0.149914 | − | 0.988699i | \(-0.547900\pi\) | ||||
−0.149914 | + | 0.988699i | \(0.547900\pi\) | |||||||
\(278\) | 40.8469 | 2.44983 | ||||||||
\(279\) | −3.22033 | −0.192796 | ||||||||
\(280\) | 20.8736 | 1.24744 | ||||||||
\(281\) | −2.00913 | −0.119855 | −0.0599275 | − | 0.998203i | \(-0.519087\pi\) | ||||
−0.0599275 | + | 0.998203i | \(0.519087\pi\) | |||||||
\(282\) | −13.4443 | −0.800598 | ||||||||
\(283\) | −9.92704 | −0.590101 | −0.295051 | − | 0.955482i | \(-0.595337\pi\) | ||||
−0.295051 | + | 0.955482i | \(0.595337\pi\) | |||||||
\(284\) | 31.0541 | 1.84272 | ||||||||
\(285\) | −8.65608 | −0.512742 | ||||||||
\(286\) | 56.2667 | 3.32712 | ||||||||
\(287\) | −15.1797 | −0.896028 | ||||||||
\(288\) | 23.2521 | 1.37014 | ||||||||
\(289\) | −15.0833 | −0.887251 | ||||||||
\(290\) | 17.3490 | 1.01877 | ||||||||
\(291\) | −17.4055 | −1.02033 | ||||||||
\(292\) | 41.6372 | 2.43663 | ||||||||
\(293\) | 9.53773 | 0.557200 | 0.278600 | − | 0.960407i | \(-0.410130\pi\) | ||||
0.278600 | + | 0.960407i | \(0.410130\pi\) | |||||||
\(294\) | −6.94064 | −0.404786 | ||||||||
\(295\) | 15.7876 | 0.919188 | ||||||||
\(296\) | −7.91088 | −0.459810 | ||||||||
\(297\) | −14.5931 | −0.846779 | ||||||||
\(298\) | 11.7644 | 0.681496 | ||||||||
\(299\) | −35.9341 | −2.07813 | ||||||||
\(300\) | 13.5083 | 0.779900 | ||||||||
\(301\) | −4.25077 | −0.245010 | ||||||||
\(302\) | −52.4254 | −3.01674 | ||||||||
\(303\) | 9.36083 | 0.537766 | ||||||||
\(304\) | −67.0458 | −3.84534 | ||||||||
\(305\) | −12.1175 | −0.693846 | ||||||||
\(306\) | −7.87692 | −0.450293 | ||||||||
\(307\) | −22.3227 | −1.27402 | −0.637011 | − | 0.770854i | \(-0.719830\pi\) | ||||
−0.637011 | + | 0.770854i | \(0.719830\pi\) | |||||||
\(308\) | −30.3709 | −1.73054 | ||||||||
\(309\) | 4.65825 | 0.264999 | ||||||||
\(310\) | 5.38130 | 0.305637 | ||||||||
\(311\) | 5.89912 | 0.334508 | 0.167254 | − | 0.985914i | \(-0.446510\pi\) | ||||
0.167254 | + | 0.985914i | \(0.446510\pi\) | |||||||
\(312\) | 46.8194 | 2.65063 | ||||||||
\(313\) | −10.8709 | −0.614460 | −0.307230 | − | 0.951635i | \(-0.599402\pi\) | ||||
−0.307230 | + | 0.951635i | \(0.599402\pi\) | |||||||
\(314\) | −39.6105 | −2.23535 | ||||||||
\(315\) | 6.10225 | 0.343823 | ||||||||
\(316\) | 4.46891 | 0.251396 | ||||||||
\(317\) | −16.6243 | −0.933714 | −0.466857 | − | 0.884333i | \(-0.654614\pi\) | ||||
−0.466857 | + | 0.884333i | \(0.654614\pi\) | |||||||
\(318\) | 16.6889 | 0.935866 | ||||||||
\(319\) | −14.8198 | −0.829748 | ||||||||
\(320\) | −11.6980 | −0.653940 | ||||||||
\(321\) | 8.75979 | 0.488924 | ||||||||
\(322\) | 27.4047 | 1.52721 | ||||||||
\(323\) | 9.49657 | 0.528403 | ||||||||
\(324\) | 10.9201 | 0.606674 | ||||||||
\(325\) | −21.2703 | −1.17986 | ||||||||
\(326\) | 30.5174 | 1.69020 | ||||||||
\(327\) | 14.2584 | 0.788492 | ||||||||
\(328\) | 55.9120 | 3.08723 | ||||||||
\(329\) | −11.4266 | −0.629970 | ||||||||
\(330\) | 10.2486 | 0.564168 | ||||||||
\(331\) | 14.9534 | 0.821914 | 0.410957 | − | 0.911655i | \(-0.365195\pi\) | ||||
0.410957 | + | 0.911655i | \(0.365195\pi\) | |||||||
\(332\) | 58.6485 | 3.21876 | ||||||||
\(333\) | −2.31269 | −0.126734 | ||||||||
\(334\) | −44.5607 | −2.43825 | ||||||||
\(335\) | 21.6330 | 1.18194 | ||||||||
\(336\) | −17.9328 | −0.978313 | ||||||||
\(337\) | −13.5200 | −0.736483 | −0.368242 | − | 0.929730i | \(-0.620040\pi\) | ||||
−0.368242 | + | 0.929730i | \(0.620040\pi\) | |||||||
\(338\) | −91.5626 | −4.98035 | ||||||||
\(339\) | 12.2431 | 0.664952 | ||||||||
\(340\) | 9.31601 | 0.505232 | ||||||||
\(341\) | −4.59680 | −0.248931 | ||||||||
\(342\) | −39.0266 | −2.11032 | ||||||||
\(343\) | −20.0371 | −1.08190 | ||||||||
\(344\) | 15.6571 | 0.844172 | ||||||||
\(345\) | −6.54518 | −0.352381 | ||||||||
\(346\) | 20.0851 | 1.07978 | ||||||||
\(347\) | 20.6212 | 1.10700 | 0.553501 | − | 0.832849i | \(-0.313292\pi\) | ||||
0.553501 | + | 0.832849i | \(0.313292\pi\) | |||||||
\(348\) | −21.0042 | −1.12595 | ||||||||
\(349\) | 3.59110 | 0.192227 | 0.0961137 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961137 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(350\) | 16.2215 | 0.867077 | ||||||||
\(351\) | 32.5677 | 1.73833 | ||||||||
\(352\) | 33.1908 | 1.76907 | ||||||||
\(353\) | −22.2986 | −1.18683 | −0.593417 | − | 0.804895i | \(-0.702221\pi\) | ||||
−0.593417 | + | 0.804895i | \(0.702221\pi\) | |||||||
\(354\) | −27.0061 | −1.43536 | ||||||||
\(355\) | −8.90648 | −0.472707 | ||||||||
\(356\) | 4.70457 | 0.249342 | ||||||||
\(357\) | 2.54005 | 0.134434 | ||||||||
\(358\) | 0.0585980 | 0.00309700 | ||||||||
\(359\) | 34.5794 | 1.82503 | 0.912517 | − | 0.409039i | \(-0.134136\pi\) | ||||
0.912517 | + | 0.409039i | \(0.134136\pi\) | |||||||
\(360\) | −22.4767 | −1.18463 | ||||||||
\(361\) | 28.0512 | 1.47638 | ||||||||
\(362\) | −69.1313 | −3.63346 | ||||||||
\(363\) | 1.23763 | 0.0649588 | ||||||||
\(364\) | 67.7791 | 3.55259 | ||||||||
\(365\) | −11.9418 | −0.625062 | ||||||||
\(366\) | 20.7281 | 1.08348 | ||||||||
\(367\) | −12.7030 | −0.663092 | −0.331546 | − | 0.943439i | \(-0.607570\pi\) | ||||
−0.331546 | + | 0.943439i | \(0.607570\pi\) | |||||||
\(368\) | −50.6958 | −2.64270 | ||||||||
\(369\) | 16.3455 | 0.850911 | ||||||||
\(370\) | 3.86459 | 0.200911 | ||||||||
\(371\) | 14.1843 | 0.736410 | ||||||||
\(372\) | −6.51509 | −0.337792 | ||||||||
\(373\) | 18.0801 | 0.936153 | 0.468076 | − | 0.883688i | \(-0.344947\pi\) | ||||
0.468076 | + | 0.883688i | \(0.344947\pi\) | |||||||
\(374\) | −11.2437 | −0.581400 | ||||||||
\(375\) | −10.1839 | −0.525895 | ||||||||
\(376\) | 42.0882 | 2.17053 | ||||||||
\(377\) | 33.0735 | 1.70337 | ||||||||
\(378\) | −24.8374 | −1.27750 | ||||||||
\(379\) | 5.37775 | 0.276237 | 0.138118 | − | 0.990416i | \(-0.455895\pi\) | ||||
0.138118 | + | 0.990416i | \(0.455895\pi\) | |||||||
\(380\) | 46.1566 | 2.36779 | ||||||||
\(381\) | 6.28718 | 0.322102 | ||||||||
\(382\) | 0.215359 | 0.0110187 | ||||||||
\(383\) | −27.7188 | −1.41636 | −0.708182 | − | 0.706030i | \(-0.750484\pi\) | ||||
−0.708182 | + | 0.706030i | \(0.750484\pi\) | |||||||
\(384\) | 0.586842 | 0.0299472 | ||||||||
\(385\) | 8.71054 | 0.443930 | ||||||||
\(386\) | 3.96840 | 0.201986 | ||||||||
\(387\) | 4.57723 | 0.232674 | ||||||||
\(388\) | 92.8109 | 4.71176 | ||||||||
\(389\) | −31.9372 | −1.61928 | −0.809641 | − | 0.586926i | \(-0.800338\pi\) | ||||
−0.809641 | + | 0.586926i | \(0.800338\pi\) | |||||||
\(390\) | −22.8720 | −1.15817 | ||||||||
\(391\) | 7.18070 | 0.363144 | ||||||||
\(392\) | 21.7281 | 1.09743 | ||||||||
\(393\) | −9.93838 | −0.501325 | ||||||||
\(394\) | 0.507576 | 0.0255713 | ||||||||
\(395\) | −1.28171 | −0.0644897 | ||||||||
\(396\) | 32.7033 | 1.64340 | ||||||||
\(397\) | −3.66376 | −0.183879 | −0.0919395 | − | 0.995765i | \(-0.529307\pi\) | ||||
−0.0919395 | + | 0.995765i | \(0.529307\pi\) | |||||||
\(398\) | −1.33988 | −0.0671623 | ||||||||
\(399\) | 12.5848 | 0.630029 | ||||||||
\(400\) | −30.0080 | −1.50040 | ||||||||
\(401\) | 25.4575 | 1.27129 | 0.635644 | − | 0.771982i | \(-0.280735\pi\) | ||||
0.635644 | + | 0.771982i | \(0.280735\pi\) | |||||||
\(402\) | −37.0053 | −1.84566 | ||||||||
\(403\) | 10.2587 | 0.511024 | ||||||||
\(404\) | −49.9145 | −2.48334 | ||||||||
\(405\) | −3.13196 | −0.155628 | ||||||||
\(406\) | −25.2231 | −1.25180 | ||||||||
\(407\) | −3.30120 | −0.163634 | ||||||||
\(408\) | −9.35589 | −0.463186 | ||||||||
\(409\) | 17.5805 | 0.869300 | 0.434650 | − | 0.900599i | \(-0.356872\pi\) | ||||
0.434650 | + | 0.900599i | \(0.356872\pi\) | |||||||
\(410\) | −27.3139 | −1.34894 | ||||||||
\(411\) | −16.0766 | −0.793000 | ||||||||
\(412\) | −24.8391 | −1.22373 | ||||||||
\(413\) | −22.9531 | −1.12945 | ||||||||
\(414\) | −29.5094 | −1.45031 | ||||||||
\(415\) | −16.8207 | −0.825697 | ||||||||
\(416\) | −74.0723 | −3.63170 | ||||||||
\(417\) | 14.1834 | 0.694563 | ||||||||
\(418\) | −55.7077 | −2.72475 | ||||||||
\(419\) | −0.920577 | −0.0449731 | −0.0224866 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224866 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(420\) | 12.3455 | 0.602401 | ||||||||
\(421\) | −14.8444 | −0.723470 | −0.361735 | − | 0.932281i | \(-0.617815\pi\) | ||||
−0.361735 | + | 0.932281i | \(0.617815\pi\) | |||||||
\(422\) | 57.3992 | 2.79415 | ||||||||
\(423\) | 12.3042 | 0.598250 | ||||||||
\(424\) | −52.2455 | −2.53727 | ||||||||
\(425\) | 4.25043 | 0.206176 | ||||||||
\(426\) | 15.2353 | 0.738155 | ||||||||
\(427\) | 17.6173 | 0.852559 | ||||||||
\(428\) | −46.7096 | −2.25779 | ||||||||
\(429\) | 19.5377 | 0.943288 | ||||||||
\(430\) | −7.64872 | −0.368854 | ||||||||
\(431\) | −14.8278 | −0.714230 | −0.357115 | − | 0.934060i | \(-0.616240\pi\) | ||||
−0.357115 | + | 0.934060i | \(0.616240\pi\) | |||||||
\(432\) | 45.9464 | 2.21060 | ||||||||
\(433\) | 3.69267 | 0.177458 | 0.0887291 | − | 0.996056i | \(-0.471719\pi\) | ||||
0.0887291 | + | 0.996056i | \(0.471719\pi\) | |||||||
\(434\) | −7.82371 | −0.375550 | ||||||||
\(435\) | 6.02413 | 0.288835 | ||||||||
\(436\) | −76.0298 | −3.64117 | ||||||||
\(437\) | 35.5771 | 1.70188 | ||||||||
\(438\) | 20.4275 | 0.976064 | ||||||||
\(439\) | 24.1807 | 1.15408 | 0.577040 | − | 0.816716i | \(-0.304208\pi\) | ||||
0.577040 | + | 0.816716i | \(0.304208\pi\) | |||||||
\(440\) | −32.0839 | −1.52954 | ||||||||
\(441\) | 6.35204 | 0.302478 | ||||||||
\(442\) | 25.0928 | 1.19354 | ||||||||
\(443\) | 26.5688 | 1.26232 | 0.631161 | − | 0.775652i | \(-0.282579\pi\) | ||||
0.631161 | + | 0.775652i | \(0.282579\pi\) | |||||||
\(444\) | −4.67883 | −0.222047 | ||||||||
\(445\) | −1.34930 | −0.0639628 | ||||||||
\(446\) | 26.5172 | 1.25562 | ||||||||
\(447\) | 4.08501 | 0.193214 | ||||||||
\(448\) | 17.0074 | 0.803524 | ||||||||
\(449\) | −6.00090 | −0.283200 | −0.141600 | − | 0.989924i | \(-0.545225\pi\) | ||||
−0.141600 | + | 0.989924i | \(0.545225\pi\) | |||||||
\(450\) | −17.4673 | −0.823418 | ||||||||
\(451\) | 23.3320 | 1.09866 | ||||||||
\(452\) | −65.2834 | −3.07067 | ||||||||
\(453\) | −18.2038 | −0.855290 | ||||||||
\(454\) | 57.7654 | 2.71107 | ||||||||
\(455\) | −19.4394 | −0.911335 | ||||||||
\(456\) | −46.3542 | −2.17074 | ||||||||
\(457\) | −29.1149 | −1.36194 | −0.680970 | − | 0.732312i | \(-0.738441\pi\) | ||||
−0.680970 | + | 0.732312i | \(0.738441\pi\) | |||||||
\(458\) | −36.5021 | −1.70563 | ||||||||
\(459\) | −6.50798 | −0.303767 | ||||||||
\(460\) | 34.9007 | 1.62725 | ||||||||
\(461\) | 10.4469 | 0.486561 | 0.243281 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243281 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(462\) | −14.9002 | −0.693218 | ||||||||
\(463\) | 14.5473 | 0.676069 | 0.338035 | − | 0.941134i | \(-0.390238\pi\) | ||||
0.338035 | + | 0.941134i | \(0.390238\pi\) | |||||||
\(464\) | 46.6600 | 2.16614 | ||||||||
\(465\) | 1.86857 | 0.0866527 | ||||||||
\(466\) | 41.4738 | 1.92124 | ||||||||
\(467\) | 36.5180 | 1.68985 | 0.844927 | − | 0.534882i | \(-0.179644\pi\) | ||||
0.844927 | + | 0.534882i | \(0.179644\pi\) | |||||||
\(468\) | −72.9845 | −3.37371 | ||||||||
\(469\) | −31.4516 | −1.45230 | ||||||||
\(470\) | −20.5608 | −0.948398 | ||||||||
\(471\) | −13.7541 | −0.633755 | ||||||||
\(472\) | 84.5441 | 3.89146 | ||||||||
\(473\) | 6.53367 | 0.300419 | ||||||||
\(474\) | 2.19248 | 0.100704 | ||||||||
\(475\) | 21.0590 | 0.966251 | ||||||||
\(476\) | −13.5443 | −0.620800 | ||||||||
\(477\) | −15.2736 | −0.699330 | ||||||||
\(478\) | 41.2863 | 1.88839 | ||||||||
\(479\) | 26.2866 | 1.20107 | 0.600533 | − | 0.799600i | \(-0.294955\pi\) | ||||
0.600533 | + | 0.799600i | \(0.294955\pi\) | |||||||
\(480\) | −13.4918 | −0.615814 | ||||||||
\(481\) | 7.36734 | 0.335922 | ||||||||
\(482\) | −20.3630 | −0.927511 | ||||||||
\(483\) | 9.51583 | 0.432985 | ||||||||
\(484\) | −6.59939 | −0.299972 | ||||||||
\(485\) | −26.6187 | −1.20869 | ||||||||
\(486\) | 42.2496 | 1.91648 | ||||||||
\(487\) | 14.6439 | 0.663576 | 0.331788 | − | 0.943354i | \(-0.392348\pi\) | ||||
0.331788 | + | 0.943354i | \(0.392348\pi\) | |||||||
\(488\) | −64.8905 | −2.93745 | ||||||||
\(489\) | 10.5966 | 0.479197 | ||||||||
\(490\) | −10.6145 | −0.479515 | ||||||||
\(491\) | 21.7624 | 0.982122 | 0.491061 | − | 0.871125i | \(-0.336609\pi\) | ||||
0.491061 | + | 0.871125i | \(0.336609\pi\) | |||||||
\(492\) | 33.0687 | 1.49085 | ||||||||
\(493\) | −6.60906 | −0.297657 | ||||||||
\(494\) | 124.324 | 5.59359 | ||||||||
\(495\) | −9.37950 | −0.421577 | ||||||||
\(496\) | 14.4730 | 0.649857 | ||||||||
\(497\) | 12.9489 | 0.580836 | ||||||||
\(498\) | 28.7734 | 1.28937 | ||||||||
\(499\) | 44.0423 | 1.97160 | 0.985802 | − | 0.167914i | \(-0.0537029\pi\) | ||||
0.985802 | + | 0.167914i | \(0.0537029\pi\) | |||||||
\(500\) | 54.3034 | 2.42852 | ||||||||
\(501\) | −15.4729 | −0.691280 | ||||||||
\(502\) | 32.8094 | 1.46436 | ||||||||
\(503\) | 7.35324 | 0.327865 | 0.163932 | − | 0.986472i | \(-0.447582\pi\) | ||||
0.163932 | + | 0.986472i | \(0.447582\pi\) | |||||||
\(504\) | 32.6782 | 1.45560 | ||||||||
\(505\) | 14.3158 | 0.637043 | ||||||||
\(506\) | −42.1226 | −1.87258 | ||||||||
\(507\) | −31.7936 | −1.41200 | ||||||||
\(508\) | −33.5250 | −1.48743 | ||||||||
\(509\) | 18.9210 | 0.838660 | 0.419330 | − | 0.907834i | \(-0.362265\pi\) | ||||
0.419330 | + | 0.907834i | \(0.362265\pi\) | |||||||
\(510\) | 4.57050 | 0.202385 | ||||||||
\(511\) | 17.3618 | 0.768041 | ||||||||
\(512\) | 40.9284 | 1.80880 | ||||||||
\(513\) | −32.2441 | −1.42361 | ||||||||
\(514\) | −25.6774 | −1.13258 | ||||||||
\(515\) | 7.12399 | 0.313920 | ||||||||
\(516\) | 9.26025 | 0.407660 | ||||||||
\(517\) | 17.5634 | 0.772436 | ||||||||
\(518\) | −5.61861 | −0.246868 | ||||||||
\(519\) | 6.97422 | 0.306134 | ||||||||
\(520\) | 71.6022 | 3.13996 | ||||||||
\(521\) | −8.65749 | −0.379292 | −0.189646 | − | 0.981853i | \(-0.560734\pi\) | ||||
−0.189646 | + | 0.981853i | \(0.560734\pi\) | |||||||
\(522\) | 27.1602 | 1.18877 | ||||||||
\(523\) | −26.2733 | −1.14885 | −0.574425 | − | 0.818557i | \(-0.694774\pi\) | ||||
−0.574425 | + | 0.818557i | \(0.694774\pi\) | |||||||
\(524\) | 52.9942 | 2.31506 | ||||||||
\(525\) | 5.63265 | 0.245829 | ||||||||
\(526\) | −50.7329 | −2.21206 | ||||||||
\(527\) | −2.05000 | −0.0892994 | ||||||||
\(528\) | 27.5637 | 1.19956 | ||||||||
\(529\) | 3.90115 | 0.169615 | ||||||||
\(530\) | 25.5228 | 1.10864 | ||||||||
\(531\) | 24.7158 | 1.07258 | ||||||||
\(532\) | −67.1057 | −2.90940 | ||||||||
\(533\) | −52.0704 | −2.25542 | ||||||||
\(534\) | 2.30810 | 0.0998810 | ||||||||
\(535\) | 13.3966 | 0.579185 | ||||||||
\(536\) | 115.847 | 5.00384 | ||||||||
\(537\) | 0.0203472 | 0.000878045 0 | ||||||||
\(538\) | −7.27108 | −0.313478 | ||||||||
\(539\) | 9.06709 | 0.390547 | ||||||||
\(540\) | −31.6311 | −1.36118 | ||||||||
\(541\) | 18.6330 | 0.801095 | 0.400548 | − | 0.916276i | \(-0.368820\pi\) | ||||
0.400548 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(542\) | −10.0798 | −0.432966 | ||||||||
\(543\) | −24.0047 | −1.03014 | ||||||||
\(544\) | 14.8018 | 0.634623 | ||||||||
\(545\) | 21.8058 | 0.934057 | ||||||||
\(546\) | 33.2529 | 1.42309 | ||||||||
\(547\) | −33.6275 | −1.43781 | −0.718905 | − | 0.695108i | \(-0.755356\pi\) | ||||
−0.718905 | + | 0.695108i | \(0.755356\pi\) | |||||||
\(548\) | 85.7249 | 3.66199 | ||||||||
\(549\) | −18.9703 | −0.809631 | ||||||||
\(550\) | −24.9334 | −1.06316 | ||||||||
\(551\) | −32.7449 | −1.39498 | ||||||||
\(552\) | −35.0501 | −1.49183 | ||||||||
\(553\) | 1.86344 | 0.0792413 | ||||||||
\(554\) | 13.0545 | 0.554631 | ||||||||
\(555\) | 1.34191 | 0.0569611 | ||||||||
\(556\) | −75.6297 | −3.20742 | ||||||||
\(557\) | −2.14991 | −0.0910944 | −0.0455472 | − | 0.998962i | \(-0.514503\pi\) | ||||
−0.0455472 | + | 0.998962i | \(0.514503\pi\) | |||||||
\(558\) | 8.42456 | 0.356640 | ||||||||
\(559\) | −14.5813 | −0.616723 | ||||||||
\(560\) | −27.4251 | −1.15892 | ||||||||
\(561\) | −3.90420 | −0.164836 | ||||||||
\(562\) | 5.25600 | 0.221711 | ||||||||
\(563\) | −13.5613 | −0.571542 | −0.285771 | − | 0.958298i | \(-0.592250\pi\) | ||||
−0.285771 | + | 0.958298i | \(0.592250\pi\) | |||||||
\(564\) | 24.8927 | 1.04817 | ||||||||
\(565\) | 18.7237 | 0.787710 | ||||||||
\(566\) | 25.9697 | 1.09159 | ||||||||
\(567\) | 4.55345 | 0.191227 | ||||||||
\(568\) | −47.6951 | −2.00124 | ||||||||
\(569\) | −11.9369 | −0.500420 | −0.250210 | − | 0.968192i | \(-0.580500\pi\) | ||||
−0.250210 | + | 0.968192i | \(0.580500\pi\) | |||||||
\(570\) | 22.6448 | 0.948485 | ||||||||
\(571\) | 27.4802 | 1.15001 | 0.575005 | − | 0.818150i | \(-0.305000\pi\) | ||||
0.575005 | + | 0.818150i | \(0.305000\pi\) | |||||||
\(572\) | −104.180 | −4.35600 | ||||||||
\(573\) | 0.0747797 | 0.00312397 | ||||||||
\(574\) | 39.7109 | 1.65750 | ||||||||
\(575\) | 15.9234 | 0.664053 | ||||||||
\(576\) | −18.3136 | −0.763065 | ||||||||
\(577\) | 17.9876 | 0.748834 | 0.374417 | − | 0.927260i | \(-0.377843\pi\) | ||||
0.374417 | + | 0.927260i | \(0.377843\pi\) | |||||||
\(578\) | 39.4586 | 1.64126 | ||||||||
\(579\) | 1.37796 | 0.0572661 | ||||||||
\(580\) | −32.1223 | −1.33381 | ||||||||
\(581\) | 24.4551 | 1.01457 | ||||||||
\(582\) | 45.5337 | 1.88743 | ||||||||
\(583\) | −21.8020 | −0.902946 | ||||||||
\(584\) | −63.9495 | −2.64625 | ||||||||
\(585\) | 20.9324 | 0.865447 | ||||||||
\(586\) | −24.9512 | −1.03073 | ||||||||
\(587\) | 25.5882 | 1.05614 | 0.528069 | − | 0.849201i | \(-0.322916\pi\) | ||||
0.528069 | + | 0.849201i | \(0.322916\pi\) | |||||||
\(588\) | 12.8509 | 0.529962 | ||||||||
\(589\) | −10.1568 | −0.418504 | ||||||||
\(590\) | −41.3011 | −1.70034 | ||||||||
\(591\) | 0.176247 | 0.00724984 | ||||||||
\(592\) | 10.3938 | 0.427183 | ||||||||
\(593\) | 22.7669 | 0.934923 | 0.467462 | − | 0.884013i | \(-0.345169\pi\) | ||||
0.467462 | + | 0.884013i | \(0.345169\pi\) | |||||||
\(594\) | 38.1764 | 1.56640 | ||||||||
\(595\) | 3.88457 | 0.159252 | ||||||||
\(596\) | −21.7824 | −0.892241 | ||||||||
\(597\) | −0.465252 | −0.0190415 | ||||||||
\(598\) | 94.0056 | 3.84418 | ||||||||
\(599\) | 9.73393 | 0.397718 | 0.198859 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198859 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(600\) | −20.7470 | −0.846993 | ||||||||
\(601\) | −0.114948 | −0.00468882 | −0.00234441 | − | 0.999997i | \(-0.500746\pi\) | ||||
−0.00234441 | + | 0.999997i | \(0.500746\pi\) | |||||||
\(602\) | 11.1202 | 0.453227 | ||||||||
\(603\) | 33.8671 | 1.37917 | ||||||||
\(604\) | 97.0678 | 3.94963 | ||||||||
\(605\) | 1.89274 | 0.0769509 | ||||||||
\(606\) | −24.4884 | −0.994774 | ||||||||
\(607\) | −18.3099 | −0.743178 | −0.371589 | − | 0.928397i | \(-0.621187\pi\) | ||||
−0.371589 | + | 0.928397i | \(0.621187\pi\) | |||||||
\(608\) | 73.3364 | 2.97418 | ||||||||
\(609\) | −8.75830 | −0.354904 | ||||||||
\(610\) | 31.7000 | 1.28350 | ||||||||
\(611\) | −39.1964 | −1.58572 | ||||||||
\(612\) | 14.5845 | 0.589542 | ||||||||
\(613\) | 2.98660 | 0.120628 | 0.0603139 | − | 0.998179i | \(-0.480790\pi\) | ||||
0.0603139 | + | 0.998179i | \(0.480790\pi\) | |||||||
\(614\) | 58.3973 | 2.35672 | ||||||||
\(615\) | −9.48430 | −0.382444 | ||||||||
\(616\) | 46.6458 | 1.87941 | ||||||||
\(617\) | 22.8282 | 0.919029 | 0.459515 | − | 0.888170i | \(-0.348023\pi\) | ||||
0.459515 | + | 0.888170i | \(0.348023\pi\) | |||||||
\(618\) | −12.1862 | −0.490202 | ||||||||
\(619\) | 10.0532 | 0.404072 | 0.202036 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202036 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(620\) | −9.96371 | −0.400152 | ||||||||
\(621\) | −24.3809 | −0.978374 | ||||||||
\(622\) | −15.4324 | −0.618783 | ||||||||
\(623\) | 1.96170 | 0.0785939 | ||||||||
\(624\) | −61.5143 | −2.46254 | ||||||||
\(625\) | −0.224068 | −0.00896272 | ||||||||
\(626\) | 28.4389 | 1.13665 | ||||||||
\(627\) | −19.3436 | −0.772507 | ||||||||
\(628\) | 73.3406 | 2.92661 | ||||||||
\(629\) | −1.47221 | −0.0587009 | ||||||||
\(630\) | −15.9638 | −0.636014 | ||||||||
\(631\) | 25.7628 | 1.02560 | 0.512800 | − | 0.858508i | \(-0.328608\pi\) | ||||
0.512800 | + | 0.858508i | \(0.328608\pi\) | |||||||
\(632\) | −6.86368 | −0.273022 | ||||||||
\(633\) | 19.9309 | 0.792182 | ||||||||
\(634\) | 43.4901 | 1.72721 | ||||||||
\(635\) | 9.61516 | 0.381566 | ||||||||
\(636\) | −30.9002 | −1.22527 | ||||||||
\(637\) | −20.2352 | −0.801747 | ||||||||
\(638\) | 38.7693 | 1.53489 | ||||||||
\(639\) | −13.9433 | −0.551589 | ||||||||
\(640\) | 0.897473 | 0.0354758 | ||||||||
\(641\) | 38.7003 | 1.52857 | 0.764285 | − | 0.644879i | \(-0.223092\pi\) | ||||
0.764285 | + | 0.644879i | \(0.223092\pi\) | |||||||
\(642\) | −22.9161 | −0.904425 | ||||||||
\(643\) | 40.8455 | 1.61079 | 0.805395 | − | 0.592738i | \(-0.201953\pi\) | ||||
0.805395 | + | 0.592738i | \(0.201953\pi\) | |||||||
\(644\) | −50.7411 | −1.99948 | ||||||||
\(645\) | −2.65589 | −0.104576 | ||||||||
\(646\) | −24.8435 | −0.977456 | ||||||||
\(647\) | 29.3855 | 1.15526 | 0.577631 | − | 0.816298i | \(-0.303977\pi\) | ||||
0.577631 | + | 0.816298i | \(0.303977\pi\) | |||||||
\(648\) | −16.7719 | −0.658864 | ||||||||
\(649\) | 35.2801 | 1.38487 | ||||||||
\(650\) | 55.6442 | 2.18255 | ||||||||
\(651\) | −2.71665 | −0.106474 | ||||||||
\(652\) | −56.5042 | −2.21288 | ||||||||
\(653\) | 22.4563 | 0.878784 | 0.439392 | − | 0.898295i | \(-0.355194\pi\) | ||||
0.439392 | + | 0.898295i | \(0.355194\pi\) | |||||||
\(654\) | −37.3008 | −1.45858 | ||||||||
\(655\) | −15.1990 | −0.593876 | ||||||||
\(656\) | −73.4608 | −2.86816 | ||||||||
\(657\) | −18.6952 | −0.729368 | ||||||||
\(658\) | 29.8927 | 1.16534 | ||||||||
\(659\) | 43.3610 | 1.68910 | 0.844552 | − | 0.535473i | \(-0.179867\pi\) | ||||
0.844552 | + | 0.535473i | \(0.179867\pi\) | |||||||
\(660\) | −18.9758 | −0.738631 | ||||||||
\(661\) | 40.6897 | 1.58265 | 0.791323 | − | 0.611398i | \(-0.209393\pi\) | ||||
0.791323 | + | 0.611398i | \(0.209393\pi\) | |||||||
\(662\) | −39.1189 | −1.52040 | ||||||||
\(663\) | 8.71307 | 0.338387 | ||||||||
\(664\) | −90.0767 | −3.49566 | ||||||||
\(665\) | 19.2463 | 0.746339 | ||||||||
\(666\) | 6.05011 | 0.234437 | ||||||||
\(667\) | −24.7596 | −0.958696 | ||||||||
\(668\) | 82.5060 | 3.19225 | ||||||||
\(669\) | 9.20764 | 0.355988 | ||||||||
\(670\) | −56.5932 | −2.18639 | ||||||||
\(671\) | −27.0787 | −1.04536 | ||||||||
\(672\) | 19.6153 | 0.756678 | ||||||||
\(673\) | 7.82055 | 0.301460 | 0.150730 | − | 0.988575i | \(-0.451838\pi\) | ||||
0.150730 | + | 0.988575i | \(0.451838\pi\) | |||||||
\(674\) | 35.3691 | 1.36237 | ||||||||
\(675\) | −14.4317 | −0.555475 | ||||||||
\(676\) | 169.532 | 6.52047 | ||||||||
\(677\) | 42.2837 | 1.62510 | 0.812548 | − | 0.582894i | \(-0.198080\pi\) | ||||
0.812548 | + | 0.582894i | \(0.198080\pi\) | |||||||
\(678\) | −32.0285 | −1.23005 | ||||||||
\(679\) | 38.7001 | 1.48517 | ||||||||
\(680\) | −14.3082 | −0.548695 | ||||||||
\(681\) | 20.0581 | 0.768627 | ||||||||
\(682\) | 12.0255 | 0.460479 | ||||||||
\(683\) | 15.0306 | 0.575131 | 0.287565 | − | 0.957761i | \(-0.407154\pi\) | ||||
0.287565 | + | 0.957761i | \(0.407154\pi\) | |||||||
\(684\) | 72.2594 | 2.76291 | ||||||||
\(685\) | −24.5864 | −0.939398 | ||||||||
\(686\) | 52.4182 | 2.00134 | ||||||||
\(687\) | −12.6748 | −0.483572 | ||||||||
\(688\) | −20.5712 | −0.784271 | ||||||||
\(689\) | 48.6558 | 1.85364 | ||||||||
\(690\) | 17.1225 | 0.651844 | ||||||||
\(691\) | 20.2573 | 0.770625 | 0.385312 | − | 0.922786i | \(-0.374094\pi\) | ||||
0.385312 | + | 0.922786i | \(0.374094\pi\) | |||||||
\(692\) | −37.1885 | −1.41369 | ||||||||
\(693\) | 13.6366 | 0.518010 | ||||||||
\(694\) | −53.9460 | −2.04776 | ||||||||
\(695\) | 21.6910 | 0.822788 | ||||||||
\(696\) | 32.2599 | 1.22281 | ||||||||
\(697\) | 10.4052 | 0.394125 | ||||||||
\(698\) | −9.39452 | −0.355588 | ||||||||
\(699\) | 14.4011 | 0.544699 | ||||||||
\(700\) | −30.0349 | −1.13521 | ||||||||
\(701\) | 10.7575 | 0.406305 | 0.203152 | − | 0.979147i | \(-0.434881\pi\) | ||||
0.203152 | + | 0.979147i | \(0.434881\pi\) | |||||||
\(702\) | −85.1988 | −3.21562 | ||||||||
\(703\) | −7.29414 | −0.275104 | ||||||||
\(704\) | −26.1413 | −0.985238 | ||||||||
\(705\) | −7.13938 | −0.268885 | ||||||||
\(706\) | 58.3343 | 2.19544 | ||||||||
\(707\) | −20.8133 | −0.782763 | ||||||||
\(708\) | 50.0029 | 1.87922 | ||||||||
\(709\) | −48.9966 | −1.84011 | −0.920053 | − | 0.391795i | \(-0.871854\pi\) | ||||
−0.920053 | + | 0.391795i | \(0.871854\pi\) | |||||||
\(710\) | 23.2998 | 0.874427 | ||||||||
\(711\) | −2.00655 | −0.0752513 | ||||||||
\(712\) | −7.22562 | −0.270792 | ||||||||
\(713\) | −7.67994 | −0.287616 | ||||||||
\(714\) | −6.64491 | −0.248680 | ||||||||
\(715\) | 29.8795 | 1.11743 | ||||||||
\(716\) | −0.108497 | −0.00405471 | ||||||||
\(717\) | 14.3360 | 0.535387 | ||||||||
\(718\) | −90.4617 | −3.37600 | ||||||||
\(719\) | −23.2652 | −0.867647 | −0.433823 | − | 0.900998i | \(-0.642836\pi\) | ||||
−0.433823 | + | 0.900998i | \(0.642836\pi\) | |||||||
\(720\) | 29.5313 | 1.10057 | ||||||||
\(721\) | −10.3573 | −0.385728 | ||||||||
\(722\) | −73.3835 | −2.73105 | ||||||||
\(723\) | −7.07073 | −0.262963 | ||||||||
\(724\) | 128.000 | 4.75706 | ||||||||
\(725\) | −14.6558 | −0.544303 | ||||||||
\(726\) | −3.23771 | −0.120163 | ||||||||
\(727\) | 22.4069 | 0.831026 | 0.415513 | − | 0.909587i | \(-0.363602\pi\) | ||||
0.415513 | + | 0.909587i | \(0.363602\pi\) | |||||||
\(728\) | −104.100 | −3.85821 | ||||||||
\(729\) | 7.90699 | 0.292852 | ||||||||
\(730\) | 31.2404 | 1.15626 | ||||||||
\(731\) | 2.91377 | 0.107770 | ||||||||
\(732\) | −38.3790 | −1.41853 | ||||||||
\(733\) | −14.6584 | −0.541419 | −0.270709 | − | 0.962661i | \(-0.587258\pi\) | ||||
−0.270709 | + | 0.962661i | \(0.587258\pi\) | |||||||
\(734\) | 33.2318 | 1.22661 | ||||||||
\(735\) | −3.68571 | −0.135949 | ||||||||
\(736\) | 55.4523 | 2.04400 | ||||||||
\(737\) | 48.3429 | 1.78073 | ||||||||
\(738\) | −42.7606 | −1.57404 | ||||||||
\(739\) | 41.5741 | 1.52933 | 0.764663 | − | 0.644430i | \(-0.222905\pi\) | ||||
0.764663 | + | 0.644430i | \(0.222905\pi\) | |||||||
\(740\) | −7.15546 | −0.263040 | ||||||||
\(741\) | 43.1693 | 1.58586 | ||||||||
\(742\) | −37.1068 | −1.36223 | ||||||||
\(743\) | 35.0828 | 1.28706 | 0.643532 | − | 0.765419i | \(-0.277468\pi\) | ||||
0.643532 | + | 0.765419i | \(0.277468\pi\) | |||||||
\(744\) | 10.0064 | 0.366851 | ||||||||
\(745\) | 6.24731 | 0.228884 | ||||||||
\(746\) | −47.2985 | −1.73172 | ||||||||
\(747\) | −26.3333 | −0.963484 | ||||||||
\(748\) | 20.8183 | 0.761192 | ||||||||
\(749\) | −19.4769 | −0.711670 | ||||||||
\(750\) | 26.6417 | 0.972816 | ||||||||
\(751\) | 2.74070 | 0.100009 | 0.0500047 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500047 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(752\) | −55.2982 | −2.01652 | ||||||||
\(753\) | 11.3925 | 0.415166 | ||||||||
\(754\) | −86.5221 | −3.15095 | ||||||||
\(755\) | −27.8396 | −1.01319 | ||||||||
\(756\) | 45.9874 | 1.67255 | ||||||||
\(757\) | −44.8032 | −1.62840 | −0.814200 | − | 0.580585i | \(-0.802824\pi\) | ||||
−0.814200 | + | 0.580585i | \(0.802824\pi\) | |||||||
\(758\) | −14.0685 | −0.510991 | ||||||||
\(759\) | −14.6264 | −0.530903 | ||||||||
\(760\) | −70.8908 | −2.57148 | ||||||||
\(761\) | 24.6446 | 0.893367 | 0.446683 | − | 0.894692i | \(-0.352605\pi\) | ||||
0.446683 | + | 0.894692i | \(0.352605\pi\) | |||||||
\(762\) | −16.4476 | −0.595834 | ||||||||
\(763\) | −31.7027 | −1.14772 | ||||||||
\(764\) | −0.398746 | −0.0144261 | ||||||||
\(765\) | −4.18290 | −0.151233 | ||||||||
\(766\) | 72.5138 | 2.62003 | ||||||||
\(767\) | −78.7352 | −2.84296 | ||||||||
\(768\) | 13.7631 | 0.496632 | ||||||||
\(769\) | 46.4915 | 1.67653 | 0.838263 | − | 0.545266i | \(-0.183571\pi\) | ||||
0.838263 | + | 0.545266i | \(0.183571\pi\) | |||||||
\(770\) | −22.7872 | −0.821195 | ||||||||
\(771\) | −8.91605 | −0.321104 | ||||||||
\(772\) | −7.34767 | −0.264448 | ||||||||
\(773\) | −13.3099 | −0.478724 | −0.239362 | − | 0.970930i | \(-0.576938\pi\) | ||||
−0.239362 | + | 0.970930i | \(0.576938\pi\) | |||||||
\(774\) | −11.9743 | −0.430406 | ||||||||
\(775\) | −4.54594 | −0.163295 | ||||||||
\(776\) | −142.546 | −5.11710 | ||||||||
\(777\) | −1.95097 | −0.0699906 | ||||||||
\(778\) | 83.5495 | 2.99539 | ||||||||
\(779\) | 51.5531 | 1.84708 | ||||||||
\(780\) | 42.3485 | 1.51632 | ||||||||
\(781\) | −19.9031 | −0.712190 | ||||||||
\(782\) | −18.7851 | −0.671754 | ||||||||
\(783\) | 22.4400 | 0.801942 | ||||||||
\(784\) | −28.5477 | −1.01956 | ||||||||
\(785\) | −21.0345 | −0.750753 | ||||||||
\(786\) | 25.9993 | 0.927366 | ||||||||
\(787\) | −6.05099 | −0.215695 | −0.107847 | − | 0.994167i | \(-0.534396\pi\) | ||||
−0.107847 | + | 0.994167i | \(0.534396\pi\) | |||||||
\(788\) | −0.939799 | −0.0334790 | ||||||||
\(789\) | −17.6161 | −0.627152 | ||||||||
\(790\) | 3.35302 | 0.119295 | ||||||||
\(791\) | −27.2217 | −0.967894 | ||||||||
\(792\) | −50.2282 | −1.78478 | ||||||||
\(793\) | 60.4320 | 2.14600 | ||||||||
\(794\) | 9.58460 | 0.340145 | ||||||||
\(795\) | 8.86235 | 0.314315 | ||||||||
\(796\) | 2.48085 | 0.0879315 | ||||||||
\(797\) | −3.69842 | −0.131005 | −0.0655023 | − | 0.997852i | \(-0.520865\pi\) | ||||
−0.0655023 | + | 0.997852i | \(0.520865\pi\) | |||||||
\(798\) | −32.9225 | −1.16545 | ||||||||
\(799\) | 7.83260 | 0.277097 | ||||||||
\(800\) | 32.8236 | 1.16049 | ||||||||
\(801\) | −2.11236 | −0.0746365 | ||||||||
\(802\) | −66.5983 | −2.35167 | ||||||||
\(803\) | −26.6860 | −0.941730 | ||||||||
\(804\) | 68.5169 | 2.41640 | ||||||||
\(805\) | 14.5528 | 0.512920 | ||||||||
\(806\) | −26.8374 | −0.945308 | ||||||||
\(807\) | −2.52476 | −0.0888757 | ||||||||
\(808\) | 76.6624 | 2.69697 | ||||||||
\(809\) | −38.3745 | −1.34917 | −0.674587 | − | 0.738195i | \(-0.735678\pi\) | ||||
−0.674587 | + | 0.738195i | \(0.735678\pi\) | |||||||
\(810\) | 8.19336 | 0.287885 | ||||||||
\(811\) | −9.85553 | −0.346075 | −0.173037 | − | 0.984915i | \(-0.555358\pi\) | ||||
−0.173037 | + | 0.984915i | \(0.555358\pi\) | |||||||
\(812\) | 46.7017 | 1.63891 | ||||||||
\(813\) | −3.50005 | −0.122752 | ||||||||
\(814\) | 8.63611 | 0.302696 | ||||||||
\(815\) | 16.2057 | 0.567662 | ||||||||
\(816\) | 12.2924 | 0.430319 | ||||||||
\(817\) | 14.4364 | 0.505066 | ||||||||
\(818\) | −45.9915 | −1.60806 | ||||||||
\(819\) | −30.4329 | −1.06341 | ||||||||
\(820\) | 50.5729 | 1.76608 | ||||||||
\(821\) | −7.13420 | −0.248985 | −0.124493 | − | 0.992221i | \(-0.539730\pi\) | ||||
−0.124493 | + | 0.992221i | \(0.539730\pi\) | |||||||
\(822\) | 42.0573 | 1.46692 | ||||||||
\(823\) | −13.5620 | −0.472742 | −0.236371 | − | 0.971663i | \(-0.575958\pi\) | ||||
−0.236371 | + | 0.971663i | \(0.575958\pi\) | |||||||
\(824\) | 38.1497 | 1.32901 | ||||||||
\(825\) | −8.65770 | −0.301422 | ||||||||
\(826\) | 60.0464 | 2.08928 | ||||||||
\(827\) | 11.0103 | 0.382867 | 0.191433 | − | 0.981506i | \(-0.438686\pi\) | ||||
0.191433 | + | 0.981506i | \(0.438686\pi\) | |||||||
\(828\) | 54.6379 | 1.89880 | ||||||||
\(829\) | 21.3151 | 0.740306 | 0.370153 | − | 0.928971i | \(-0.379305\pi\) | ||||
0.370153 | + | 0.928971i | \(0.379305\pi\) | |||||||
\(830\) | 44.0039 | 1.52740 | ||||||||
\(831\) | 4.53294 | 0.157246 | ||||||||
\(832\) | 58.3400 | 2.02258 | ||||||||
\(833\) | 4.04358 | 0.140102 | ||||||||
\(834\) | −37.1045 | −1.28482 | ||||||||
\(835\) | −23.6632 | −0.818898 | ||||||||
\(836\) | 103.145 | 3.56735 | ||||||||
\(837\) | 6.96045 | 0.240588 | ||||||||
\(838\) | 2.40828 | 0.0831926 | ||||||||
\(839\) | −29.9935 | −1.03549 | −0.517746 | − | 0.855534i | \(-0.673229\pi\) | ||||
−0.517746 | + | 0.855534i | \(0.673229\pi\) | |||||||
\(840\) | −18.9612 | −0.654223 | ||||||||
\(841\) | −6.21143 | −0.214187 | ||||||||
\(842\) | 38.8337 | 1.33830 | ||||||||
\(843\) | 1.82506 | 0.0628584 | ||||||||
\(844\) | −106.277 | −3.65821 | ||||||||
\(845\) | −48.6228 | −1.67267 | ||||||||
\(846\) | −32.1884 | −1.10666 | ||||||||
\(847\) | −2.75180 | −0.0945530 | ||||||||
\(848\) | 68.6435 | 2.35723 | ||||||||
\(849\) | 9.01753 | 0.309481 | ||||||||
\(850\) | −11.1194 | −0.381391 | ||||||||
\(851\) | −5.51536 | −0.189064 | ||||||||
\(852\) | −28.2089 | −0.966421 | ||||||||
\(853\) | 17.8596 | 0.611500 | 0.305750 | − | 0.952112i | \(-0.401093\pi\) | ||||
0.305750 | + | 0.952112i | \(0.401093\pi\) | |||||||
\(854\) | −46.0877 | −1.57709 | ||||||||
\(855\) | −20.7244 | −0.708759 | ||||||||
\(856\) | 71.7401 | 2.45203 | ||||||||
\(857\) | 48.9085 | 1.67068 | 0.835342 | − | 0.549731i | \(-0.185270\pi\) | ||||
0.835342 | + | 0.549731i | \(0.185270\pi\) | |||||||
\(858\) | −51.1116 | −1.74492 | ||||||||
\(859\) | 54.8883 | 1.87276 | 0.936382 | − | 0.350982i | \(-0.114152\pi\) | ||||
0.936382 | + | 0.350982i | \(0.114152\pi\) | |||||||
\(860\) | 14.1619 | 0.482918 | ||||||||
\(861\) | 13.7889 | 0.469925 | ||||||||
\(862\) | 38.7903 | 1.32120 | ||||||||
\(863\) | −10.9087 | −0.371336 | −0.185668 | − | 0.982613i | \(-0.559445\pi\) | ||||
−0.185668 | + | 0.982613i | \(0.559445\pi\) | |||||||
\(864\) | −50.2573 | −1.70979 | ||||||||
\(865\) | 10.6659 | 0.362650 | ||||||||
\(866\) | −9.66021 | −0.328267 | ||||||||
\(867\) | 13.7013 | 0.465322 | ||||||||
\(868\) | 14.4859 | 0.491685 | ||||||||
\(869\) | −2.86420 | −0.0971614 | ||||||||
\(870\) | −15.7595 | −0.534296 | ||||||||
\(871\) | −107.888 | −3.65563 | ||||||||
\(872\) | 116.772 | 3.95440 | ||||||||
\(873\) | −41.6722 | −1.41039 | ||||||||
\(874\) | −93.0717 | −3.14820 | ||||||||
\(875\) | 22.6433 | 0.765484 | ||||||||
\(876\) | −37.8224 | −1.27790 | ||||||||
\(877\) | −50.4513 | −1.70362 | −0.851809 | − | 0.523852i | \(-0.824494\pi\) | ||||
−0.851809 | + | 0.523852i | \(0.824494\pi\) | |||||||
\(878\) | −63.2579 | −2.13485 | ||||||||
\(879\) | −8.66389 | −0.292226 | ||||||||
\(880\) | 42.1539 | 1.42101 | ||||||||
\(881\) | −42.9642 | −1.44750 | −0.723750 | − | 0.690062i | \(-0.757583\pi\) | ||||
−0.723750 | + | 0.690062i | \(0.757583\pi\) | |||||||
\(882\) | −16.6173 | −0.559533 | ||||||||
\(883\) | 9.51782 | 0.320300 | 0.160150 | − | 0.987093i | \(-0.448802\pi\) | ||||
0.160150 | + | 0.987093i | \(0.448802\pi\) | |||||||
\(884\) | −46.4605 | −1.56264 | ||||||||
\(885\) | −14.3411 | −0.482071 | ||||||||
\(886\) | −69.5054 | −2.33508 | ||||||||
\(887\) | −15.6890 | −0.526784 | −0.263392 | − | 0.964689i | \(-0.584841\pi\) | ||||
−0.263392 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(888\) | 7.18609 | 0.241149 | ||||||||
\(889\) | −13.9792 | −0.468847 | ||||||||
\(890\) | 3.52983 | 0.118320 | ||||||||
\(891\) | −6.99891 | −0.234472 | ||||||||
\(892\) | −49.0977 | −1.64391 | ||||||||
\(893\) | 38.8070 | 1.29863 | ||||||||
\(894\) | −10.6866 | −0.357413 | ||||||||
\(895\) | 0.0311175 | 0.00104014 | ||||||||
\(896\) | −1.30481 | −0.0435906 | ||||||||
\(897\) | 32.6419 | 1.08988 | ||||||||
\(898\) | 15.6987 | 0.523871 | ||||||||
\(899\) | 7.06856 | 0.235750 | ||||||||
\(900\) | 32.3415 | 1.07805 | ||||||||
\(901\) | −9.72286 | −0.323916 | ||||||||
\(902\) | −61.0378 | −2.03234 | ||||||||
\(903\) | 3.86132 | 0.128497 | ||||||||
\(904\) | 100.267 | 3.33483 | ||||||||
\(905\) | −36.7110 | −1.22031 | ||||||||
\(906\) | 47.6222 | 1.58214 | ||||||||
\(907\) | −30.7043 | −1.01952 | −0.509759 | − | 0.860317i | \(-0.670266\pi\) | ||||
−0.509759 | + | 0.860317i | \(0.670266\pi\) | |||||||
\(908\) | −106.955 | −3.54943 | ||||||||
\(909\) | 22.4117 | 0.743349 | ||||||||
\(910\) | 50.8546 | 1.68581 | ||||||||
\(911\) | 16.3353 | 0.541211 | 0.270606 | − | 0.962690i | \(-0.412776\pi\) | ||||
0.270606 | + | 0.962690i | \(0.412776\pi\) | |||||||
\(912\) | 60.9031 | 2.01670 | ||||||||
\(913\) | −37.5889 | −1.24401 | ||||||||
\(914\) | 76.1662 | 2.51935 | ||||||||
\(915\) | 11.0073 | 0.363890 | ||||||||
\(916\) | 67.5853 | 2.23308 | ||||||||
\(917\) | 22.0974 | 0.729721 | ||||||||
\(918\) | 17.0252 | 0.561916 | ||||||||
\(919\) | −16.8723 | −0.556565 | −0.278283 | − | 0.960499i | \(-0.589765\pi\) | ||||
−0.278283 | + | 0.960499i | \(0.589765\pi\) | |||||||
\(920\) | −53.6031 | −1.76724 | ||||||||
\(921\) | 20.2775 | 0.668166 | ||||||||
\(922\) | −27.3297 | −0.900056 | ||||||||
\(923\) | 44.4181 | 1.46204 | ||||||||
\(924\) | 27.5883 | 0.907589 | ||||||||
\(925\) | −3.26468 | −0.107342 | ||||||||
\(926\) | −38.0565 | −1.25061 | ||||||||
\(927\) | 11.1528 | 0.366306 | ||||||||
\(928\) | −51.0379 | −1.67540 | ||||||||
\(929\) | 48.0874 | 1.57770 | 0.788848 | − | 0.614588i | \(-0.210678\pi\) | ||||
0.788848 | + | 0.614588i | \(0.210678\pi\) | |||||||
\(930\) | −4.88827 | −0.160293 | ||||||||
\(931\) | 20.0341 | 0.656592 | ||||||||
\(932\) | −76.7906 | −2.51536 | ||||||||
\(933\) | −5.35864 | −0.175434 | ||||||||
\(934\) | −95.5331 | −3.12594 | ||||||||
\(935\) | −5.97080 | −0.195266 | ||||||||
\(936\) | 112.095 | 3.66394 | ||||||||
\(937\) | 37.8188 | 1.23549 | 0.617743 | − | 0.786380i | \(-0.288047\pi\) | ||||
0.617743 | + | 0.786380i | \(0.288047\pi\) | |||||||
\(938\) | 82.2791 | 2.68651 | ||||||||
\(939\) | 9.87491 | 0.322256 | ||||||||
\(940\) | 38.0692 | 1.24168 | ||||||||
\(941\) | 9.47965 | 0.309028 | 0.154514 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154514 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(942\) | 35.9814 | 1.17234 | ||||||||
\(943\) | 38.9811 | 1.26940 | ||||||||
\(944\) | −111.079 | −3.61532 | ||||||||
\(945\) | −13.1895 | −0.429053 | ||||||||
\(946\) | −17.0924 | −0.555723 | ||||||||
\(947\) | 59.4509 | 1.93189 | 0.965947 | − | 0.258741i | \(-0.0833076\pi\) | ||||
0.965947 | + | 0.258741i | \(0.0833076\pi\) | |||||||
\(948\) | −4.05947 | −0.131845 | ||||||||
\(949\) | 59.5556 | 1.93326 | ||||||||
\(950\) | −55.0914 | −1.78740 | ||||||||
\(951\) | 15.1012 | 0.489690 | ||||||||
\(952\) | 20.8023 | 0.674206 | ||||||||
\(953\) | −38.3368 | −1.24185 | −0.620925 | − | 0.783870i | \(-0.713243\pi\) | ||||
−0.620925 | + | 0.783870i | \(0.713243\pi\) | |||||||
\(954\) | 39.9565 | 1.29364 | ||||||||
\(955\) | 0.114363 | 0.00370069 | ||||||||
\(956\) | −76.4434 | −2.47236 | ||||||||
\(957\) | 13.4620 | 0.435164 | ||||||||
\(958\) | −68.7672 | −2.22177 | ||||||||
\(959\) | 35.7454 | 1.15428 | ||||||||
\(960\) | 10.6263 | 0.342961 | ||||||||
\(961\) | −28.8075 | −0.929273 | ||||||||
\(962\) | −19.2733 | −0.621398 | ||||||||
\(963\) | 20.9727 | 0.675835 | ||||||||
\(964\) | 37.7031 | 1.21433 | ||||||||
\(965\) | 2.10735 | 0.0678381 | ||||||||
\(966\) | −24.8939 | −0.800949 | ||||||||
\(967\) | −43.2908 | −1.39214 | −0.696068 | − | 0.717975i | \(-0.745069\pi\) | ||||
−0.696068 | + | 0.717975i | \(0.745069\pi\) | |||||||
\(968\) | 10.1358 | 0.325778 | ||||||||
\(969\) | −8.62650 | −0.277123 | ||||||||
\(970\) | 69.6359 | 2.23588 | ||||||||
\(971\) | −5.69144 | −0.182647 | −0.0913235 | − | 0.995821i | \(-0.529110\pi\) | ||||
−0.0913235 | + | 0.995821i | \(0.529110\pi\) | |||||||
\(972\) | −78.2269 | −2.50913 | ||||||||
\(973\) | −31.5359 | −1.01100 | ||||||||
\(974\) | −38.3091 | −1.22750 | ||||||||
\(975\) | 19.3215 | 0.618784 | ||||||||
\(976\) | 85.2572 | 2.72902 | ||||||||
\(977\) | 3.27115 | 0.104654 | 0.0523268 | − | 0.998630i | \(-0.483336\pi\) | ||||
0.0523268 | + | 0.998630i | \(0.483336\pi\) | |||||||
\(978\) | −27.7214 | −0.886432 | ||||||||
\(979\) | −3.01524 | −0.0963676 | ||||||||
\(980\) | 19.6532 | 0.627799 | ||||||||
\(981\) | 34.1375 | 1.08993 | ||||||||
\(982\) | −56.9315 | −1.81676 | ||||||||
\(983\) | 53.5632 | 1.70840 | 0.854201 | − | 0.519943i | \(-0.174047\pi\) | ||||
0.854201 | + | 0.519943i | \(0.174047\pi\) | |||||||
\(984\) | −50.7894 | −1.61911 | ||||||||
\(985\) | 0.269540 | 0.00858825 | ||||||||
\(986\) | 17.2897 | 0.550615 | ||||||||
\(987\) | 10.3797 | 0.330390 | ||||||||
\(988\) | −230.191 | −7.32334 | ||||||||
\(989\) | 10.9159 | 0.347105 | ||||||||
\(990\) | 24.5373 | 0.779846 | ||||||||
\(991\) | 14.2315 | 0.452078 | 0.226039 | − | 0.974118i | \(-0.427422\pi\) | ||||
0.226039 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(992\) | −15.8309 | −0.502633 | ||||||||
\(993\) | −13.5834 | −0.431056 | ||||||||
\(994\) | −33.8749 | −1.07445 | ||||||||
\(995\) | −0.711523 | −0.0225568 | ||||||||
\(996\) | −53.2752 | −1.68809 | ||||||||
\(997\) | −33.2822 | −1.05406 | −0.527029 | − | 0.849847i | \(-0.676694\pi\) | ||||
−0.527029 | + | 0.849847i | \(0.676694\pi\) | |||||||
\(998\) | −115.217 | −3.64713 | ||||||||
\(999\) | 4.99866 | 0.158151 |
(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 | 6011.2.a.f.1.14 | ✓ | 275 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6011.2.a.f.1.14 | ✓ | 275 | 1.1 | even | 1 | trivial |