Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.256013 | −0.181029 | −0.0905143 | − | 0.995895i | \(-0.528851\pi\) | ||||
−0.0905143 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(3\) | 0.196473 | 0.113434 | 0.0567169 | − | 0.998390i | \(-0.481937\pi\) | ||||
0.0567169 | + | 0.998390i | \(0.481937\pi\) | |||||||
\(4\) | −1.93446 | −0.967229 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.0502997 | −0.0205348 | ||||||||
\(7\) | 2.99337 | 1.13139 | 0.565695 | − | 0.824615i | \(-0.308608\pi\) | ||||
0.565695 | + | 0.824615i | \(0.308608\pi\) | |||||||
\(8\) | 1.00727 | 0.356125 | ||||||||
\(9\) | −2.96140 | −0.987133 | ||||||||
\(10\) | −0.256013 | −0.0809585 | ||||||||
\(11\) | −4.51326 | −1.36080 | −0.680400 | − | 0.732841i | \(-0.738194\pi\) | ||||
−0.680400 | + | 0.732841i | \(0.738194\pi\) | |||||||
\(12\) | −0.380069 | −0.109716 | ||||||||
\(13\) | 1.63393 | 0.453170 | 0.226585 | − | 0.973991i | \(-0.427244\pi\) | ||||
0.226585 | + | 0.973991i | \(0.427244\pi\) | |||||||
\(14\) | −0.766343 | −0.204814 | ||||||||
\(15\) | 0.196473 | 0.0507291 | ||||||||
\(16\) | 3.61104 | 0.902760 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.758157 | 0.178699 | ||||||||
\(19\) | −3.34601 | −0.767628 | −0.383814 | − | 0.923410i | \(-0.625390\pi\) | ||||
−0.383814 | + | 0.923410i | \(0.625390\pi\) | |||||||
\(20\) | −1.93446 | −0.432558 | ||||||||
\(21\) | 0.588117 | 0.128338 | ||||||||
\(22\) | 1.15545 | 0.246344 | ||||||||
\(23\) | 4.80598 | 1.00212 | 0.501058 | − | 0.865414i | \(-0.332944\pi\) | ||||
0.501058 | + | 0.865414i | \(0.332944\pi\) | |||||||
\(24\) | 0.197902 | 0.0403965 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.418307 | −0.0820367 | ||||||||
\(27\) | −1.17125 | −0.225408 | ||||||||
\(28\) | −5.79055 | −1.09431 | ||||||||
\(29\) | −5.40684 | −1.00403 | −0.502013 | − | 0.864860i | \(-0.667407\pi\) | ||||
−0.502013 | + | 0.864860i | \(0.667407\pi\) | |||||||
\(30\) | −0.0502997 | −0.00918342 | ||||||||
\(31\) | 0.0151487 | 0.00272079 | 0.00136039 | − | 0.999999i | \(-0.499567\pi\) | ||||
0.00136039 | + | 0.999999i | \(0.499567\pi\) | |||||||
\(32\) | −2.93902 | −0.519550 | ||||||||
\(33\) | −0.886734 | −0.154361 | ||||||||
\(34\) | −0.256013 | −0.0439059 | ||||||||
\(35\) | 2.99337 | 0.505973 | ||||||||
\(36\) | 5.72870 | 0.954783 | ||||||||
\(37\) | 2.16222 | 0.355467 | 0.177733 | − | 0.984079i | \(-0.443124\pi\) | ||||
0.177733 | + | 0.984079i | \(0.443124\pi\) | |||||||
\(38\) | 0.856624 | 0.138963 | ||||||||
\(39\) | 0.321023 | 0.0514047 | ||||||||
\(40\) | 1.00727 | 0.159264 | ||||||||
\(41\) | 5.25049 | 0.819989 | 0.409994 | − | 0.912088i | \(-0.365531\pi\) | ||||
0.409994 | + | 0.912088i | \(0.365531\pi\) | |||||||
\(42\) | −0.150566 | −0.0232328 | ||||||||
\(43\) | 4.32978 | 0.660285 | 0.330142 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330142 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(44\) | 8.73071 | 1.31620 | ||||||||
\(45\) | −2.96140 | −0.441459 | ||||||||
\(46\) | −1.23039 | −0.181412 | ||||||||
\(47\) | 0.863753 | 0.125991 | 0.0629957 | − | 0.998014i | \(-0.479935\pi\) | ||||
0.0629957 | + | 0.998014i | \(0.479935\pi\) | |||||||
\(48\) | 0.709472 | 0.102403 | ||||||||
\(49\) | 1.96029 | 0.280041 | ||||||||
\(50\) | −0.256013 | −0.0362057 | ||||||||
\(51\) | 0.196473 | 0.0275117 | ||||||||
\(52\) | −3.16076 | −0.438319 | ||||||||
\(53\) | −10.0463 | −1.37997 | −0.689985 | − | 0.723824i | \(-0.742383\pi\) | ||||
−0.689985 | + | 0.723824i | \(0.742383\pi\) | |||||||
\(54\) | 0.299856 | 0.0408053 | ||||||||
\(55\) | −4.51326 | −0.608568 | ||||||||
\(56\) | 3.01514 | 0.402916 | ||||||||
\(57\) | −0.657401 | −0.0870749 | ||||||||
\(58\) | 1.38422 | 0.181757 | ||||||||
\(59\) | 9.17402 | 1.19436 | 0.597178 | − | 0.802109i | \(-0.296289\pi\) | ||||
0.597178 | + | 0.802109i | \(0.296289\pi\) | |||||||
\(60\) | −0.380069 | −0.0490666 | ||||||||
\(61\) | −4.43046 | −0.567263 | −0.283631 | − | 0.958933i | \(-0.591539\pi\) | ||||
−0.283631 | + | 0.958933i | \(0.591539\pi\) | |||||||
\(62\) | −0.00387827 | −0.000492541 0 | ||||||||
\(63\) | −8.86457 | −1.11683 | ||||||||
\(64\) | −6.46965 | −0.808706 | ||||||||
\(65\) | 1.63393 | 0.202664 | ||||||||
\(66\) | 0.227015 | 0.0279437 | ||||||||
\(67\) | −12.2700 | −1.49902 | −0.749509 | − | 0.661994i | \(-0.769710\pi\) | ||||
−0.749509 | + | 0.661994i | \(0.769710\pi\) | |||||||
\(68\) | −1.93446 | −0.234587 | ||||||||
\(69\) | 0.944245 | 0.113674 | ||||||||
\(70\) | −0.766343 | −0.0915955 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −2.98294 | −0.351542 | ||||||||
\(73\) | 8.55982 | 1.00185 | 0.500926 | − | 0.865490i | \(-0.332993\pi\) | ||||
0.500926 | + | 0.865490i | \(0.332993\pi\) | |||||||
\(74\) | −0.553557 | −0.0643496 | ||||||||
\(75\) | 0.196473 | 0.0226867 | ||||||||
\(76\) | 6.47272 | 0.742472 | ||||||||
\(77\) | −13.5099 | −1.53959 | ||||||||
\(78\) | −0.0821860 | −0.00930573 | ||||||||
\(79\) | 1.73861 | 0.195609 | 0.0978045 | − | 0.995206i | \(-0.468818\pi\) | ||||
0.0978045 | + | 0.995206i | \(0.468818\pi\) | |||||||
\(80\) | 3.61104 | 0.403726 | ||||||||
\(81\) | 8.65408 | 0.961564 | ||||||||
\(82\) | −1.34419 | −0.148441 | ||||||||
\(83\) | −15.4341 | −1.69412 | −0.847059 | − | 0.531499i | \(-0.821629\pi\) | ||||
−0.847059 | + | 0.531499i | \(0.821629\pi\) | |||||||
\(84\) | −1.13769 | −0.124132 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −1.10848 | −0.119530 | ||||||||
\(87\) | −1.06230 | −0.113890 | ||||||||
\(88\) | −4.54608 | −0.484614 | ||||||||
\(89\) | 2.45612 | 0.260348 | 0.130174 | − | 0.991491i | \(-0.458446\pi\) | ||||
0.130174 | + | 0.991491i | \(0.458446\pi\) | |||||||
\(90\) | 0.758157 | 0.0799168 | ||||||||
\(91\) | 4.89096 | 0.512711 | ||||||||
\(92\) | −9.29696 | −0.969275 | ||||||||
\(93\) | 0.00297631 | 0.000308629 0 | ||||||||
\(94\) | −0.221132 | −0.0228080 | ||||||||
\(95\) | −3.34601 | −0.343294 | ||||||||
\(96\) | −0.577438 | −0.0589345 | ||||||||
\(97\) | −12.4758 | −1.26672 | −0.633361 | − | 0.773857i | \(-0.718325\pi\) | ||||
−0.633361 | + | 0.773857i | \(0.718325\pi\) | |||||||
\(98\) | −0.501859 | −0.0506955 | ||||||||
\(99\) | 13.3656 | 1.34329 | ||||||||
\(100\) | −1.93446 | −0.193446 | ||||||||
\(101\) | 6.45187 | 0.641985 | 0.320993 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320993 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(102\) | −0.0502997 | −0.00498041 | ||||||||
\(103\) | −1.85979 | −0.183250 | −0.0916251 | − | 0.995794i | \(-0.529206\pi\) | ||||
−0.0916251 | + | 0.995794i | \(0.529206\pi\) | |||||||
\(104\) | 1.64581 | 0.161385 | ||||||||
\(105\) | 0.588117 | 0.0573943 | ||||||||
\(106\) | 2.57199 | 0.249814 | ||||||||
\(107\) | −19.2296 | −1.85899 | −0.929496 | − | 0.368831i | \(-0.879758\pi\) | ||||
−0.929496 | + | 0.368831i | \(0.879758\pi\) | |||||||
\(108\) | 2.26574 | 0.218021 | ||||||||
\(109\) | −15.1606 | −1.45213 | −0.726063 | − | 0.687628i | \(-0.758652\pi\) | ||||
−0.726063 | + | 0.687628i | \(0.758652\pi\) | |||||||
\(110\) | 1.15545 | 0.110168 | ||||||||
\(111\) | 0.424818 | 0.0403219 | ||||||||
\(112\) | 10.8092 | 1.02137 | ||||||||
\(113\) | 9.00544 | 0.847161 | 0.423580 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423580 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(114\) | 0.168303 | 0.0157631 | ||||||||
\(115\) | 4.80598 | 0.448160 | ||||||||
\(116\) | 10.4593 | 0.971122 | ||||||||
\(117\) | −4.83871 | −0.447339 | ||||||||
\(118\) | −2.34867 | −0.216213 | ||||||||
\(119\) | 2.99337 | 0.274402 | ||||||||
\(120\) | 0.197902 | 0.0180659 | ||||||||
\(121\) | 9.36952 | 0.851775 | ||||||||
\(122\) | 1.13426 | 0.102691 | ||||||||
\(123\) | 1.03158 | 0.0930144 | ||||||||
\(124\) | −0.0293045 | −0.00263163 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.26945 | 0.202178 | ||||||||
\(127\) | 4.78000 | 0.424156 | 0.212078 | − | 0.977253i | \(-0.431977\pi\) | ||||
0.212078 | + | 0.977253i | \(0.431977\pi\) | |||||||
\(128\) | 7.53435 | 0.665949 | ||||||||
\(129\) | 0.850684 | 0.0748986 | ||||||||
\(130\) | −0.418307 | −0.0366879 | ||||||||
\(131\) | 21.1983 | 1.85210 | 0.926052 | − | 0.377397i | \(-0.123181\pi\) | ||||
0.926052 | + | 0.377397i | \(0.123181\pi\) | |||||||
\(132\) | 1.71535 | 0.149302 | ||||||||
\(133\) | −10.0159 | −0.868486 | ||||||||
\(134\) | 3.14128 | 0.271365 | ||||||||
\(135\) | −1.17125 | −0.100805 | ||||||||
\(136\) | 1.00727 | 0.0863729 | ||||||||
\(137\) | −0.387209 | −0.0330815 | −0.0165408 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165408 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(138\) | −0.241739 | −0.0205782 | ||||||||
\(139\) | −12.2334 | −1.03762 | −0.518812 | − | 0.854889i | \(-0.673625\pi\) | ||||
−0.518812 | + | 0.854889i | \(0.673625\pi\) | |||||||
\(140\) | −5.79055 | −0.489391 | ||||||||
\(141\) | 0.169704 | 0.0142917 | ||||||||
\(142\) | 0.256013 | 0.0214841 | ||||||||
\(143\) | −7.37434 | −0.616673 | ||||||||
\(144\) | −10.6937 | −0.891144 | ||||||||
\(145\) | −5.40684 | −0.449014 | ||||||||
\(146\) | −2.19143 | −0.181364 | ||||||||
\(147\) | 0.385144 | 0.0317661 | ||||||||
\(148\) | −4.18272 | −0.343818 | ||||||||
\(149\) | −2.41173 | −0.197577 | −0.0987885 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987885 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(150\) | −0.0502997 | −0.00410695 | ||||||||
\(151\) | −17.9563 | −1.46127 | −0.730633 | − | 0.682770i | \(-0.760775\pi\) | ||||
−0.730633 | + | 0.682770i | \(0.760775\pi\) | |||||||
\(152\) | −3.37035 | −0.273371 | ||||||||
\(153\) | −2.96140 | −0.239415 | ||||||||
\(154\) | 3.45871 | 0.278710 | ||||||||
\(155\) | 0.0151487 | 0.00121677 | ||||||||
\(156\) | −0.621004 | −0.0497201 | ||||||||
\(157\) | 4.14213 | 0.330578 | 0.165289 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165289 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(158\) | −0.445107 | −0.0354108 | ||||||||
\(159\) | −1.97383 | −0.156535 | ||||||||
\(160\) | −2.93902 | −0.232350 | ||||||||
\(161\) | 14.3861 | 1.13378 | ||||||||
\(162\) | −2.21556 | −0.174071 | ||||||||
\(163\) | 9.73141 | 0.762223 | 0.381111 | − | 0.924529i | \(-0.375541\pi\) | ||||
0.381111 | + | 0.924529i | \(0.375541\pi\) | |||||||
\(164\) | −10.1568 | −0.793117 | ||||||||
\(165\) | −0.886734 | −0.0690321 | ||||||||
\(166\) | 3.95134 | 0.306684 | ||||||||
\(167\) | 13.8227 | 1.06963 | 0.534815 | − | 0.844969i | \(-0.320381\pi\) | ||||
0.534815 | + | 0.844969i | \(0.320381\pi\) | |||||||
\(168\) | 0.592394 | 0.0457042 | ||||||||
\(169\) | −10.3303 | −0.794637 | ||||||||
\(170\) | −0.256013 | −0.0196353 | ||||||||
\(171\) | 9.90888 | 0.757751 | ||||||||
\(172\) | −8.37577 | −0.638647 | ||||||||
\(173\) | −15.0969 | −1.14780 | −0.573898 | − | 0.818927i | \(-0.694569\pi\) | ||||
−0.573898 | + | 0.818927i | \(0.694569\pi\) | |||||||
\(174\) | 0.271962 | 0.0206174 | ||||||||
\(175\) | 2.99337 | 0.226278 | ||||||||
\(176\) | −16.2976 | −1.22848 | ||||||||
\(177\) | 1.80245 | 0.135480 | ||||||||
\(178\) | −0.628798 | −0.0471304 | ||||||||
\(179\) | 7.12064 | 0.532221 | 0.266111 | − | 0.963942i | \(-0.414261\pi\) | ||||
0.266111 | + | 0.963942i | \(0.414261\pi\) | |||||||
\(180\) | 5.72870 | 0.426992 | ||||||||
\(181\) | −2.58241 | −0.191949 | −0.0959745 | − | 0.995384i | \(-0.530597\pi\) | ||||
−0.0959745 | + | 0.995384i | \(0.530597\pi\) | |||||||
\(182\) | −1.25215 | −0.0928155 | ||||||||
\(183\) | −0.870466 | −0.0643467 | ||||||||
\(184\) | 4.84093 | 0.356878 | ||||||||
\(185\) | 2.16222 | 0.158970 | ||||||||
\(186\) | −0.000761975 0 | −5.58707e−5 0 | ||||||||
\(187\) | −4.51326 | −0.330042 | ||||||||
\(188\) | −1.67089 | −0.121862 | ||||||||
\(189\) | −3.50600 | −0.255024 | ||||||||
\(190\) | 0.856624 | 0.0621460 | ||||||||
\(191\) | −1.16811 | −0.0845215 | −0.0422608 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422608 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(192\) | −1.27111 | −0.0917346 | ||||||||
\(193\) | 21.7456 | 1.56528 | 0.782642 | − | 0.622472i | \(-0.213872\pi\) | ||||
0.782642 | + | 0.622472i | \(0.213872\pi\) | |||||||
\(194\) | 3.19396 | 0.229313 | ||||||||
\(195\) | 0.321023 | 0.0229889 | ||||||||
\(196\) | −3.79209 | −0.270864 | ||||||||
\(197\) | −14.5883 | −1.03937 | −0.519685 | − | 0.854358i | \(-0.673951\pi\) | ||||
−0.519685 | + | 0.854358i | \(0.673951\pi\) | |||||||
\(198\) | −3.42176 | −0.243174 | ||||||||
\(199\) | −14.1428 | −1.00256 | −0.501278 | − | 0.865286i | \(-0.667137\pi\) | ||||
−0.501278 | + | 0.865286i | \(0.667137\pi\) | |||||||
\(200\) | 1.00727 | 0.0712249 | ||||||||
\(201\) | −2.41072 | −0.170039 | ||||||||
\(202\) | −1.65176 | −0.116218 | ||||||||
\(203\) | −16.1847 | −1.13594 | ||||||||
\(204\) | −0.380069 | −0.0266101 | ||||||||
\(205\) | 5.25049 | 0.366710 | ||||||||
\(206\) | 0.476130 | 0.0331735 | ||||||||
\(207\) | −14.2324 | −0.989222 | ||||||||
\(208\) | 5.90018 | 0.409104 | ||||||||
\(209\) | 15.1014 | 1.04459 | ||||||||
\(210\) | −0.150566 | −0.0103900 | ||||||||
\(211\) | −23.8139 | −1.63942 | −0.819709 | − | 0.572780i | \(-0.805865\pi\) | ||||
−0.819709 | + | 0.572780i | \(0.805865\pi\) | |||||||
\(212\) | 19.4342 | 1.33475 | ||||||||
\(213\) | −0.196473 | −0.0134621 | ||||||||
\(214\) | 4.92302 | 0.336531 | ||||||||
\(215\) | 4.32978 | 0.295288 | ||||||||
\(216\) | −1.17977 | −0.0802733 | ||||||||
\(217\) | 0.0453458 | 0.00307827 | ||||||||
\(218\) | 3.88132 | 0.262876 | ||||||||
\(219\) | 1.68177 | 0.113644 | ||||||||
\(220\) | 8.73071 | 0.588624 | ||||||||
\(221\) | 1.63393 | 0.109910 | ||||||||
\(222\) | −0.108759 | −0.00729942 | ||||||||
\(223\) | −22.9150 | −1.53450 | −0.767252 | − | 0.641345i | \(-0.778377\pi\) | ||||
−0.767252 | + | 0.641345i | \(0.778377\pi\) | |||||||
\(224\) | −8.79758 | −0.587813 | ||||||||
\(225\) | −2.96140 | −0.197427 | ||||||||
\(226\) | −2.30551 | −0.153360 | ||||||||
\(227\) | 0.447454 | 0.0296985 | 0.0148493 | − | 0.999890i | \(-0.495273\pi\) | ||||
0.0148493 | + | 0.999890i | \(0.495273\pi\) | |||||||
\(228\) | 1.27171 | 0.0842214 | ||||||||
\(229\) | −11.1238 | −0.735085 | −0.367542 | − | 0.930007i | \(-0.619801\pi\) | ||||
−0.367542 | + | 0.930007i | \(0.619801\pi\) | |||||||
\(230\) | −1.23039 | −0.0811298 | ||||||||
\(231\) | −2.65433 | −0.174642 | ||||||||
\(232\) | −5.44617 | −0.357558 | ||||||||
\(233\) | −21.3732 | −1.40020 | −0.700102 | − | 0.714043i | \(-0.746862\pi\) | ||||
−0.700102 | + | 0.714043i | \(0.746862\pi\) | |||||||
\(234\) | 1.23877 | 0.0809811 | ||||||||
\(235\) | 0.863753 | 0.0563450 | ||||||||
\(236\) | −17.7468 | −1.15522 | ||||||||
\(237\) | 0.341590 | 0.0221887 | ||||||||
\(238\) | −0.766343 | −0.0496746 | ||||||||
\(239\) | 9.88287 | 0.639270 | 0.319635 | − | 0.947541i | \(-0.396440\pi\) | ||||
0.319635 | + | 0.947541i | \(0.396440\pi\) | |||||||
\(240\) | 0.709472 | 0.0457962 | ||||||||
\(241\) | −6.69227 | −0.431087 | −0.215543 | − | 0.976494i | \(-0.569152\pi\) | ||||
−0.215543 | + | 0.976494i | \(0.569152\pi\) | |||||||
\(242\) | −2.39872 | −0.154196 | ||||||||
\(243\) | 5.21405 | 0.334482 | ||||||||
\(244\) | 8.57054 | 0.548673 | ||||||||
\(245\) | 1.96029 | 0.125238 | ||||||||
\(246\) | −0.264098 | −0.0168383 | ||||||||
\(247\) | −5.46714 | −0.347866 | ||||||||
\(248\) | 0.0152589 | 0.000968940 0 | ||||||||
\(249\) | −3.03239 | −0.192170 | ||||||||
\(250\) | −0.256013 | −0.0161917 | ||||||||
\(251\) | −18.8833 | −1.19191 | −0.595953 | − | 0.803019i | \(-0.703226\pi\) | ||||
−0.595953 | + | 0.803019i | \(0.703226\pi\) | |||||||
\(252\) | 17.1481 | 1.08023 | ||||||||
\(253\) | −21.6906 | −1.36368 | ||||||||
\(254\) | −1.22374 | −0.0767845 | ||||||||
\(255\) | 0.196473 | 0.0123036 | ||||||||
\(256\) | 11.0104 | 0.688151 | ||||||||
\(257\) | 0.360589 | 0.0224929 | 0.0112465 | − | 0.999937i | \(-0.496420\pi\) | ||||
0.0112465 | + | 0.999937i | \(0.496420\pi\) | |||||||
\(258\) | −0.217786 | −0.0135588 | ||||||||
\(259\) | 6.47233 | 0.402171 | ||||||||
\(260\) | −3.16076 | −0.196022 | ||||||||
\(261\) | 16.0118 | 0.991107 | ||||||||
\(262\) | −5.42704 | −0.335284 | ||||||||
\(263\) | −4.23386 | −0.261071 | −0.130536 | − | 0.991444i | \(-0.541670\pi\) | ||||
−0.130536 | + | 0.991444i | \(0.541670\pi\) | |||||||
\(264\) | −0.893183 | −0.0549716 | ||||||||
\(265\) | −10.0463 | −0.617141 | ||||||||
\(266\) | 2.56420 | 0.157221 | ||||||||
\(267\) | 0.482560 | 0.0295322 | ||||||||
\(268\) | 23.7358 | 1.44989 | ||||||||
\(269\) | −0.951881 | −0.0580372 | −0.0290186 | − | 0.999579i | \(-0.509238\pi\) | ||||
−0.0290186 | + | 0.999579i | \(0.509238\pi\) | |||||||
\(270\) | 0.299856 | 0.0182487 | ||||||||
\(271\) | −0.535008 | −0.0324994 | −0.0162497 | − | 0.999868i | \(-0.505173\pi\) | ||||
−0.0162497 | + | 0.999868i | \(0.505173\pi\) | |||||||
\(272\) | 3.61104 | 0.218951 | ||||||||
\(273\) | 0.960941 | 0.0581588 | ||||||||
\(274\) | 0.0991306 | 0.00598870 | ||||||||
\(275\) | −4.51326 | −0.272160 | ||||||||
\(276\) | −1.82660 | −0.109949 | ||||||||
\(277\) | −29.1825 | −1.75341 | −0.876704 | − | 0.481030i | \(-0.840263\pi\) | ||||
−0.876704 | + | 0.481030i | \(0.840263\pi\) | |||||||
\(278\) | 3.13191 | 0.187839 | ||||||||
\(279\) | −0.0448614 | −0.00268578 | ||||||||
\(280\) | 3.01514 | 0.180189 | ||||||||
\(281\) | 27.3061 | 1.62894 | 0.814471 | − | 0.580204i | \(-0.197027\pi\) | ||||
0.814471 | + | 0.580204i | \(0.197027\pi\) | |||||||
\(282\) | −0.0434465 | −0.00258720 | ||||||||
\(283\) | 25.1454 | 1.49474 | 0.747369 | − | 0.664409i | \(-0.231317\pi\) | ||||
0.747369 | + | 0.664409i | \(0.231317\pi\) | |||||||
\(284\) | 1.93446 | 0.114789 | ||||||||
\(285\) | −0.657401 | −0.0389411 | ||||||||
\(286\) | 1.88793 | 0.111636 | ||||||||
\(287\) | 15.7167 | 0.927726 | ||||||||
\(288\) | 8.70361 | 0.512865 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.38422 | 0.0812844 | ||||||||
\(291\) | −2.45115 | −0.143689 | ||||||||
\(292\) | −16.5586 | −0.969019 | ||||||||
\(293\) | 5.68827 | 0.332312 | 0.166156 | − | 0.986099i | \(-0.446864\pi\) | ||||
0.166156 | + | 0.986099i | \(0.446864\pi\) | |||||||
\(294\) | −0.0986018 | −0.00575057 | ||||||||
\(295\) | 9.17402 | 0.534132 | ||||||||
\(296\) | 2.17794 | 0.126590 | ||||||||
\(297\) | 5.28617 | 0.306735 | ||||||||
\(298\) | 0.617435 | 0.0357671 | ||||||||
\(299\) | 7.85262 | 0.454129 | ||||||||
\(300\) | −0.380069 | −0.0219433 | ||||||||
\(301\) | 12.9606 | 0.747039 | ||||||||
\(302\) | 4.59706 | 0.264531 | ||||||||
\(303\) | 1.26762 | 0.0728228 | ||||||||
\(304\) | −12.0826 | −0.692984 | ||||||||
\(305\) | −4.43046 | −0.253688 | ||||||||
\(306\) | 0.758157 | 0.0433409 | ||||||||
\(307\) | −19.3064 | −1.10187 | −0.550937 | − | 0.834547i | \(-0.685729\pi\) | ||||
−0.550937 | + | 0.834547i | \(0.685729\pi\) | |||||||
\(308\) | 26.1343 | 1.48914 | ||||||||
\(309\) | −0.365398 | −0.0207868 | ||||||||
\(310\) | −0.00387827 | −0.000220271 0 | ||||||||
\(311\) | 24.4576 | 1.38686 | 0.693432 | − | 0.720522i | \(-0.256098\pi\) | ||||
0.693432 | + | 0.720522i | \(0.256098\pi\) | |||||||
\(312\) | 0.323357 | 0.0183065 | ||||||||
\(313\) | 15.8703 | 0.897041 | 0.448520 | − | 0.893773i | \(-0.351951\pi\) | ||||
0.448520 | + | 0.893773i | \(0.351951\pi\) | |||||||
\(314\) | −1.06044 | −0.0598440 | ||||||||
\(315\) | −8.86457 | −0.499462 | ||||||||
\(316\) | −3.36327 | −0.189199 | ||||||||
\(317\) | 12.6273 | 0.709218 | 0.354609 | − | 0.935015i | \(-0.384614\pi\) | ||||
0.354609 | + | 0.935015i | \(0.384614\pi\) | |||||||
\(318\) | 0.505327 | 0.0283373 | ||||||||
\(319\) | 24.4025 | 1.36628 | ||||||||
\(320\) | −6.46965 | −0.361665 | ||||||||
\(321\) | −3.77809 | −0.210872 | ||||||||
\(322\) | −3.68303 | −0.205247 | ||||||||
\(323\) | −3.34601 | −0.186177 | ||||||||
\(324\) | −16.7409 | −0.930052 | ||||||||
\(325\) | 1.63393 | 0.0906340 | ||||||||
\(326\) | −2.49137 | −0.137984 | ||||||||
\(327\) | −2.97866 | −0.164720 | ||||||||
\(328\) | 5.28868 | 0.292018 | ||||||||
\(329\) | 2.58554 | 0.142545 | ||||||||
\(330\) | 0.227015 | 0.0124968 | ||||||||
\(331\) | 16.0187 | 0.880470 | 0.440235 | − | 0.897883i | \(-0.354895\pi\) | ||||
0.440235 | + | 0.897883i | \(0.354895\pi\) | |||||||
\(332\) | 29.8567 | 1.63860 | ||||||||
\(333\) | −6.40319 | −0.350893 | ||||||||
\(334\) | −3.53878 | −0.193634 | ||||||||
\(335\) | −12.2700 | −0.670381 | ||||||||
\(336\) | 2.12371 | 0.115858 | ||||||||
\(337\) | −26.1625 | −1.42516 | −0.712580 | − | 0.701591i | \(-0.752474\pi\) | ||||
−0.712580 | + | 0.701591i | \(0.752474\pi\) | |||||||
\(338\) | 2.64469 | 0.143852 | ||||||||
\(339\) | 1.76933 | 0.0960966 | ||||||||
\(340\) | −1.93446 | −0.104911 | ||||||||
\(341\) | −0.0683701 | −0.00370245 | ||||||||
\(342\) | −2.53680 | −0.137175 | ||||||||
\(343\) | −15.0857 | −0.814554 | ||||||||
\(344\) | 4.36127 | 0.235144 | ||||||||
\(345\) | 0.944245 | 0.0508364 | ||||||||
\(346\) | 3.86500 | 0.207784 | ||||||||
\(347\) | −1.80176 | −0.0967235 | −0.0483617 | − | 0.998830i | \(-0.515400\pi\) | ||||
−0.0483617 | + | 0.998830i | \(0.515400\pi\) | |||||||
\(348\) | 2.05497 | 0.110158 | ||||||||
\(349\) | −2.04186 | −0.109298 | −0.0546492 | − | 0.998506i | \(-0.517404\pi\) | ||||
−0.0546492 | + | 0.998506i | \(0.517404\pi\) | |||||||
\(350\) | −0.766343 | −0.0409628 | ||||||||
\(351\) | −1.91374 | −0.102148 | ||||||||
\(352\) | 13.2646 | 0.707003 | ||||||||
\(353\) | −12.9105 | −0.687155 | −0.343578 | − | 0.939124i | \(-0.611639\pi\) | ||||
−0.343578 | + | 0.939124i | \(0.611639\pi\) | |||||||
\(354\) | −0.461450 | −0.0245258 | ||||||||
\(355\) | −1.00000 | −0.0530745 | ||||||||
\(356\) | −4.75125 | −0.251816 | ||||||||
\(357\) | 0.588117 | 0.0311265 | ||||||||
\(358\) | −1.82298 | −0.0963473 | ||||||||
\(359\) | 7.21644 | 0.380869 | 0.190435 | − | 0.981700i | \(-0.439010\pi\) | ||||
0.190435 | + | 0.981700i | \(0.439010\pi\) | |||||||
\(360\) | −2.98294 | −0.157215 | ||||||||
\(361\) | −7.80419 | −0.410747 | ||||||||
\(362\) | 0.661131 | 0.0347483 | ||||||||
\(363\) | 1.84086 | 0.0966200 | ||||||||
\(364\) | −9.46134 | −0.495909 | ||||||||
\(365\) | 8.55982 | 0.448041 | ||||||||
\(366\) | 0.222851 | 0.0116486 | ||||||||
\(367\) | 12.2122 | 0.637472 | 0.318736 | − | 0.947844i | \(-0.396742\pi\) | ||||
0.318736 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(368\) | 17.3546 | 0.904670 | ||||||||
\(369\) | −15.5488 | −0.809438 | ||||||||
\(370\) | −0.553557 | −0.0287780 | ||||||||
\(371\) | −30.0724 | −1.56128 | ||||||||
\(372\) | −0.00575755 | −0.000298515 0 | ||||||||
\(373\) | −32.6907 | −1.69266 | −0.846331 | − | 0.532658i | \(-0.821193\pi\) | ||||
−0.846331 | + | 0.532658i | \(0.821193\pi\) | |||||||
\(374\) | 1.15545 | 0.0597471 | ||||||||
\(375\) | 0.196473 | 0.0101458 | ||||||||
\(376\) | 0.870035 | 0.0448686 | ||||||||
\(377\) | −8.83439 | −0.454994 | ||||||||
\(378\) | 0.897582 | 0.0461666 | ||||||||
\(379\) | −27.5902 | −1.41721 | −0.708607 | − | 0.705603i | \(-0.750676\pi\) | ||||
−0.708607 | + | 0.705603i | \(0.750676\pi\) | |||||||
\(380\) | 6.47272 | 0.332044 | ||||||||
\(381\) | 0.939141 | 0.0481136 | ||||||||
\(382\) | 0.299052 | 0.0153008 | ||||||||
\(383\) | −23.8612 | −1.21925 | −0.609625 | − | 0.792690i | \(-0.708680\pi\) | ||||
−0.609625 | + | 0.792690i | \(0.708680\pi\) | |||||||
\(384\) | 1.48030 | 0.0755411 | ||||||||
\(385\) | −13.5099 | −0.688527 | ||||||||
\(386\) | −5.56716 | −0.283361 | ||||||||
\(387\) | −12.8222 | −0.651789 | ||||||||
\(388\) | 24.1338 | 1.22521 | ||||||||
\(389\) | −11.1355 | −0.564591 | −0.282295 | − | 0.959328i | \(-0.591096\pi\) | ||||
−0.282295 | + | 0.959328i | \(0.591096\pi\) | |||||||
\(390\) | −0.0821860 | −0.00416165 | ||||||||
\(391\) | 4.80598 | 0.243049 | ||||||||
\(392\) | 1.97454 | 0.0997295 | ||||||||
\(393\) | 4.16489 | 0.210091 | ||||||||
\(394\) | 3.73479 | 0.188156 | ||||||||
\(395\) | 1.73861 | 0.0874790 | ||||||||
\(396\) | −25.8551 | −1.29927 | ||||||||
\(397\) | −26.2598 | −1.31794 | −0.658970 | − | 0.752169i | \(-0.729008\pi\) | ||||
−0.658970 | + | 0.752169i | \(0.729008\pi\) | |||||||
\(398\) | 3.62074 | 0.181491 | ||||||||
\(399\) | −1.96785 | −0.0985156 | ||||||||
\(400\) | 3.61104 | 0.180552 | ||||||||
\(401\) | −29.2301 | −1.45968 | −0.729842 | − | 0.683616i | \(-0.760406\pi\) | ||||
−0.729842 | + | 0.683616i | \(0.760406\pi\) | |||||||
\(402\) | 0.617176 | 0.0307819 | ||||||||
\(403\) | 0.0247519 | 0.00123298 | ||||||||
\(404\) | −12.4809 | −0.620947 | ||||||||
\(405\) | 8.65408 | 0.430024 | ||||||||
\(406\) | 4.14350 | 0.205638 | ||||||||
\(407\) | −9.75866 | −0.483719 | ||||||||
\(408\) | 0.197902 | 0.00979760 | ||||||||
\(409\) | 23.6621 | 1.17002 | 0.585009 | − | 0.811027i | \(-0.301091\pi\) | ||||
0.585009 | + | 0.811027i | \(0.301091\pi\) | |||||||
\(410\) | −1.34419 | −0.0663850 | ||||||||
\(411\) | −0.0760761 | −0.00375256 | ||||||||
\(412\) | 3.59768 | 0.177245 | ||||||||
\(413\) | 27.4613 | 1.35128 | ||||||||
\(414\) | 3.64369 | 0.179077 | ||||||||
\(415\) | −15.4341 | −0.757632 | ||||||||
\(416\) | −4.80214 | −0.235444 | ||||||||
\(417\) | −2.40353 | −0.117701 | ||||||||
\(418\) | −3.86617 | −0.189100 | ||||||||
\(419\) | −21.0903 | −1.03033 | −0.515164 | − | 0.857092i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857092i | \(0.672269\pi\) | |||||||
\(420\) | −1.13769 | −0.0555135 | ||||||||
\(421\) | −3.26477 | −0.159115 | −0.0795576 | − | 0.996830i | \(-0.525351\pi\) | ||||
−0.0795576 | + | 0.996830i | \(0.525351\pi\) | |||||||
\(422\) | 6.09668 | 0.296782 | ||||||||
\(423\) | −2.55792 | −0.124370 | ||||||||
\(424\) | −10.1194 | −0.491441 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 0.0502997 | 0.00243703 | ||||||||
\(427\) | −13.2620 | −0.641795 | ||||||||
\(428\) | 37.1988 | 1.79807 | ||||||||
\(429\) | −1.44886 | −0.0699516 | ||||||||
\(430\) | −1.10848 | −0.0534557 | ||||||||
\(431\) | 13.0823 | 0.630152 | 0.315076 | − | 0.949066i | \(-0.397970\pi\) | ||||
0.315076 | + | 0.949066i | \(0.397970\pi\) | |||||||
\(432\) | −4.22944 | −0.203489 | ||||||||
\(433\) | −16.3046 | −0.783547 | −0.391773 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391773 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(434\) | −0.0116091 | −0.000557255 0 | ||||||||
\(435\) | −1.06230 | −0.0509333 | ||||||||
\(436\) | 29.3276 | 1.40454 | ||||||||
\(437\) | −16.0809 | −0.769253 | ||||||||
\(438\) | −0.430556 | −0.0205728 | ||||||||
\(439\) | −5.74066 | −0.273987 | −0.136993 | − | 0.990572i | \(-0.543744\pi\) | ||||
−0.136993 | + | 0.990572i | \(0.543744\pi\) | |||||||
\(440\) | −4.54608 | −0.216726 | ||||||||
\(441\) | −5.80519 | −0.276438 | ||||||||
\(442\) | −0.418307 | −0.0198968 | ||||||||
\(443\) | −4.70047 | −0.223326 | −0.111663 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111663 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(444\) | −0.821791 | −0.0390005 | ||||||||
\(445\) | 2.45612 | 0.116431 | ||||||||
\(446\) | 5.86655 | 0.277789 | ||||||||
\(447\) | −0.473840 | −0.0224119 | ||||||||
\(448\) | −19.3661 | −0.914962 | ||||||||
\(449\) | 7.27995 | 0.343562 | 0.171781 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171781 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(450\) | 0.758157 | 0.0357399 | ||||||||
\(451\) | −23.6968 | −1.11584 | ||||||||
\(452\) | −17.4206 | −0.819398 | ||||||||
\(453\) | −3.52794 | −0.165757 | ||||||||
\(454\) | −0.114554 | −0.00537629 | ||||||||
\(455\) | 4.89096 | 0.229292 | ||||||||
\(456\) | −0.662183 | −0.0310095 | ||||||||
\(457\) | 10.6438 | 0.497895 | 0.248947 | − | 0.968517i | \(-0.419915\pi\) | ||||
0.248947 | + | 0.968517i | \(0.419915\pi\) | |||||||
\(458\) | 2.84785 | 0.133071 | ||||||||
\(459\) | −1.17125 | −0.0546694 | ||||||||
\(460\) | −9.29696 | −0.433473 | ||||||||
\(461\) | 1.28165 | 0.0596924 | 0.0298462 | − | 0.999555i | \(-0.490498\pi\) | ||||
0.0298462 | + | 0.999555i | \(0.490498\pi\) | |||||||
\(462\) | 0.679542 | 0.0316152 | ||||||||
\(463\) | −14.1688 | −0.658482 | −0.329241 | − | 0.944246i | \(-0.606793\pi\) | ||||
−0.329241 | + | 0.944246i | \(0.606793\pi\) | |||||||
\(464\) | −19.5243 | −0.906394 | ||||||||
\(465\) | 0.00297631 | 0.000138023 0 | ||||||||
\(466\) | 5.47181 | 0.253477 | ||||||||
\(467\) | 17.7602 | 0.821846 | 0.410923 | − | 0.911670i | \(-0.365206\pi\) | ||||
0.410923 | + | 0.911670i | \(0.365206\pi\) | |||||||
\(468\) | 9.36028 | 0.432679 | ||||||||
\(469\) | −36.7287 | −1.69597 | ||||||||
\(470\) | −0.221132 | −0.0102001 | ||||||||
\(471\) | 0.813816 | 0.0374987 | ||||||||
\(472\) | 9.24074 | 0.425340 | ||||||||
\(473\) | −19.5414 | −0.898515 | ||||||||
\(474\) | −0.0874515 | −0.00401678 | ||||||||
\(475\) | −3.34601 | −0.153526 | ||||||||
\(476\) | −5.79055 | −0.265410 | ||||||||
\(477\) | 29.7512 | 1.36221 | ||||||||
\(478\) | −2.53014 | −0.115726 | ||||||||
\(479\) | −23.7082 | −1.08326 | −0.541628 | − | 0.840618i | \(-0.682192\pi\) | ||||
−0.541628 | + | 0.840618i | \(0.682192\pi\) | |||||||
\(480\) | −0.577438 | −0.0263563 | ||||||||
\(481\) | 3.53291 | 0.161087 | ||||||||
\(482\) | 1.71331 | 0.0780391 | ||||||||
\(483\) | 2.82648 | 0.128609 | ||||||||
\(484\) | −18.1249 | −0.823861 | ||||||||
\(485\) | −12.4758 | −0.566495 | ||||||||
\(486\) | −1.33487 | −0.0605508 | ||||||||
\(487\) | −6.20621 | −0.281230 | −0.140615 | − | 0.990064i | \(-0.544908\pi\) | ||||
−0.140615 | + | 0.990064i | \(0.544908\pi\) | |||||||
\(488\) | −4.46269 | −0.202016 | ||||||||
\(489\) | 1.91196 | 0.0864618 | ||||||||
\(490\) | −0.501859 | −0.0226717 | ||||||||
\(491\) | −33.0432 | −1.49122 | −0.745610 | − | 0.666382i | \(-0.767842\pi\) | ||||
−0.745610 | + | 0.666382i | \(0.767842\pi\) | |||||||
\(492\) | −1.99555 | −0.0899662 | ||||||||
\(493\) | −5.40684 | −0.243512 | ||||||||
\(494\) | 1.39966 | 0.0629737 | ||||||||
\(495\) | 13.3656 | 0.600737 | ||||||||
\(496\) | 0.0547026 | 0.00245622 | ||||||||
\(497\) | −2.99337 | −0.134271 | ||||||||
\(498\) | 0.776332 | 0.0347883 | ||||||||
\(499\) | −34.6230 | −1.54994 | −0.774970 | − | 0.631998i | \(-0.782235\pi\) | ||||
−0.774970 | + | 0.631998i | \(0.782235\pi\) | |||||||
\(500\) | −1.93446 | −0.0865116 | ||||||||
\(501\) | 2.71578 | 0.121332 | ||||||||
\(502\) | 4.83438 | 0.215769 | ||||||||
\(503\) | 1.42347 | 0.0634695 | 0.0317347 | − | 0.999496i | \(-0.489897\pi\) | ||||
0.0317347 | + | 0.999496i | \(0.489897\pi\) | |||||||
\(504\) | −8.92904 | −0.397731 | ||||||||
\(505\) | 6.45187 | 0.287105 | ||||||||
\(506\) | 5.55309 | 0.246865 | ||||||||
\(507\) | −2.02962 | −0.0901386 | ||||||||
\(508\) | −9.24671 | −0.410256 | ||||||||
\(509\) | −13.7811 | −0.610837 | −0.305419 | − | 0.952218i | \(-0.598796\pi\) | ||||
−0.305419 | + | 0.952218i | \(0.598796\pi\) | |||||||
\(510\) | −0.0502997 | −0.00222731 | ||||||||
\(511\) | 25.6227 | 1.13348 | ||||||||
\(512\) | −17.8875 | −0.790524 | ||||||||
\(513\) | 3.91903 | 0.173029 | ||||||||
\(514\) | −0.0923154 | −0.00407186 | ||||||||
\(515\) | −1.85979 | −0.0819520 | ||||||||
\(516\) | −1.64561 | −0.0724440 | ||||||||
\(517\) | −3.89834 | −0.171449 | ||||||||
\(518\) | −1.65700 | −0.0728045 | ||||||||
\(519\) | −2.96613 | −0.130199 | ||||||||
\(520\) | 1.64581 | 0.0721736 | ||||||||
\(521\) | 36.2827 | 1.58958 | 0.794788 | − | 0.606888i | \(-0.207582\pi\) | ||||
0.794788 | + | 0.606888i | \(0.207582\pi\) | |||||||
\(522\) | −4.09924 | −0.179419 | ||||||||
\(523\) | 5.89721 | 0.257867 | 0.128933 | − | 0.991653i | \(-0.458845\pi\) | ||||
0.128933 | + | 0.991653i | \(0.458845\pi\) | |||||||
\(524\) | −41.0072 | −1.79141 | ||||||||
\(525\) | 0.588117 | 0.0256675 | ||||||||
\(526\) | 1.08392 | 0.0472614 | ||||||||
\(527\) | 0.0151487 | 0.000659888 0 | ||||||||
\(528\) | −3.20203 | −0.139350 | ||||||||
\(529\) | 0.0974419 | 0.00423660 | ||||||||
\(530\) | 2.57199 | 0.111720 | ||||||||
\(531\) | −27.1679 | −1.17899 | ||||||||
\(532\) | 19.3753 | 0.840025 | ||||||||
\(533\) | 8.57892 | 0.371594 | ||||||||
\(534\) | −0.123542 | −0.00534618 | ||||||||
\(535\) | −19.2296 | −0.831367 | ||||||||
\(536\) | −12.3592 | −0.533837 | ||||||||
\(537\) | 1.39901 | 0.0603718 | ||||||||
\(538\) | 0.243694 | 0.0105064 | ||||||||
\(539\) | −8.84729 | −0.381080 | ||||||||
\(540\) | 2.26574 | 0.0975019 | ||||||||
\(541\) | −24.2999 | −1.04473 | −0.522367 | − | 0.852721i | \(-0.674951\pi\) | ||||
−0.522367 | + | 0.852721i | \(0.674951\pi\) | |||||||
\(542\) | 0.136969 | 0.00588332 | ||||||||
\(543\) | −0.507374 | −0.0217735 | ||||||||
\(544\) | −2.93902 | −0.126009 | ||||||||
\(545\) | −15.1606 | −0.649411 | ||||||||
\(546\) | −0.246013 | −0.0105284 | ||||||||
\(547\) | 21.3305 | 0.912026 | 0.456013 | − | 0.889973i | \(-0.349277\pi\) | ||||
0.456013 | + | 0.889973i | \(0.349277\pi\) | |||||||
\(548\) | 0.749040 | 0.0319974 | ||||||||
\(549\) | 13.1204 | 0.559964 | ||||||||
\(550\) | 1.15545 | 0.0492687 | ||||||||
\(551\) | 18.0914 | 0.770719 | ||||||||
\(552\) | 0.951112 | 0.0404820 | ||||||||
\(553\) | 5.20431 | 0.221310 | ||||||||
\(554\) | 7.47111 | 0.317417 | ||||||||
\(555\) | 0.424818 | 0.0180325 | ||||||||
\(556\) | 23.6650 | 1.00362 | ||||||||
\(557\) | 0.501461 | 0.0212476 | 0.0106238 | − | 0.999944i | \(-0.496618\pi\) | ||||
0.0106238 | + | 0.999944i | \(0.496618\pi\) | |||||||
\(558\) | 0.0114851 | 0.000486203 0 | ||||||||
\(559\) | 7.07454 | 0.299221 | ||||||||
\(560\) | 10.8092 | 0.456772 | ||||||||
\(561\) | −0.886734 | −0.0374379 | ||||||||
\(562\) | −6.99071 | −0.294885 | ||||||||
\(563\) | −12.6810 | −0.534442 | −0.267221 | − | 0.963635i | \(-0.586105\pi\) | ||||
−0.267221 | + | 0.963635i | \(0.586105\pi\) | |||||||
\(564\) | −0.328285 | −0.0138233 | ||||||||
\(565\) | 9.00544 | 0.378862 | ||||||||
\(566\) | −6.43755 | −0.270590 | ||||||||
\(567\) | 25.9049 | 1.08790 | ||||||||
\(568\) | −1.00727 | −0.0422642 | ||||||||
\(569\) | −31.7105 | −1.32937 | −0.664686 | − | 0.747123i | \(-0.731435\pi\) | ||||
−0.664686 | + | 0.747123i | \(0.731435\pi\) | |||||||
\(570\) | 0.168303 | 0.00704945 | ||||||||
\(571\) | 40.7772 | 1.70647 | 0.853237 | − | 0.521523i | \(-0.174636\pi\) | ||||
0.853237 | + | 0.521523i | \(0.174636\pi\) | |||||||
\(572\) | 14.2653 | 0.596464 | ||||||||
\(573\) | −0.229502 | −0.00958759 | ||||||||
\(574\) | −4.02368 | −0.167945 | ||||||||
\(575\) | 4.80598 | 0.200423 | ||||||||
\(576\) | 19.1592 | 0.798301 | ||||||||
\(577\) | −22.4643 | −0.935200 | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(578\) | −0.256013 | −0.0106487 | ||||||||
\(579\) | 4.27243 | 0.177556 | ||||||||
\(580\) | 10.4593 | 0.434299 | ||||||||
\(581\) | −46.2002 | −1.91671 | ||||||||
\(582\) | 0.627527 | 0.0260118 | ||||||||
\(583\) | 45.3417 | 1.87786 | ||||||||
\(584\) | 8.62207 | 0.356784 | ||||||||
\(585\) | −4.83871 | −0.200056 | ||||||||
\(586\) | −1.45627 | −0.0601580 | ||||||||
\(587\) | −47.4882 | −1.96005 | −0.980023 | − | 0.198883i | \(-0.936269\pi\) | ||||
−0.980023 | + | 0.198883i | \(0.936269\pi\) | |||||||
\(588\) | −0.745044 | −0.0307251 | ||||||||
\(589\) | −0.0506878 | −0.00208856 | ||||||||
\(590\) | −2.34867 | −0.0966932 | ||||||||
\(591\) | −2.86620 | −0.117900 | ||||||||
\(592\) | 7.80786 | 0.320901 | ||||||||
\(593\) | 12.3754 | 0.508197 | 0.254099 | − | 0.967178i | \(-0.418221\pi\) | ||||
0.254099 | + | 0.967178i | \(0.418221\pi\) | |||||||
\(594\) | −1.35333 | −0.0555278 | ||||||||
\(595\) | 2.99337 | 0.122716 | ||||||||
\(596\) | 4.66540 | 0.191102 | ||||||||
\(597\) | −2.77868 | −0.113724 | ||||||||
\(598\) | −2.01037 | −0.0822103 | ||||||||
\(599\) | 0.219599 | 0.00897256 | 0.00448628 | − | 0.999990i | \(-0.498572\pi\) | ||||
0.00448628 | + | 0.999990i | \(0.498572\pi\) | |||||||
\(600\) | 0.197902 | 0.00807931 | ||||||||
\(601\) | 18.9651 | 0.773604 | 0.386802 | − | 0.922163i | \(-0.373580\pi\) | ||||
0.386802 | + | 0.922163i | \(0.373580\pi\) | |||||||
\(602\) | −3.31810 | −0.135235 | ||||||||
\(603\) | 36.3363 | 1.47973 | ||||||||
\(604\) | 34.7358 | 1.41338 | ||||||||
\(605\) | 9.36952 | 0.380925 | ||||||||
\(606\) | −0.324527 | −0.0131830 | ||||||||
\(607\) | 21.4753 | 0.871654 | 0.435827 | − | 0.900031i | \(-0.356456\pi\) | ||||
0.435827 | + | 0.900031i | \(0.356456\pi\) | |||||||
\(608\) | 9.83400 | 0.398821 | ||||||||
\(609\) | −3.17986 | −0.128854 | ||||||||
\(610\) | 1.13426 | 0.0459247 | ||||||||
\(611\) | 1.41131 | 0.0570955 | ||||||||
\(612\) | 5.72870 | 0.231569 | ||||||||
\(613\) | −16.1815 | −0.653563 | −0.326782 | − | 0.945100i | \(-0.605964\pi\) | ||||
−0.326782 | + | 0.945100i | \(0.605964\pi\) | |||||||
\(614\) | 4.94269 | 0.199471 | ||||||||
\(615\) | 1.03158 | 0.0415973 | ||||||||
\(616\) | −13.6081 | −0.548287 | ||||||||
\(617\) | −29.6298 | −1.19285 | −0.596425 | − | 0.802669i | \(-0.703413\pi\) | ||||
−0.596425 | + | 0.802669i | \(0.703413\pi\) | |||||||
\(618\) | 0.0935467 | 0.00376300 | ||||||||
\(619\) | −4.83528 | −0.194346 | −0.0971732 | − | 0.995267i | \(-0.530980\pi\) | ||||
−0.0971732 | + | 0.995267i | \(0.530980\pi\) | |||||||
\(620\) | −0.0293045 | −0.00117690 | ||||||||
\(621\) | −5.62902 | −0.225885 | ||||||||
\(622\) | −6.26147 | −0.251062 | ||||||||
\(623\) | 7.35207 | 0.294555 | ||||||||
\(624\) | 1.15923 | 0.0464061 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.06300 | −0.162390 | ||||||||
\(627\) | 2.96702 | 0.118492 | ||||||||
\(628\) | −8.01277 | −0.319744 | ||||||||
\(629\) | 2.16222 | 0.0862133 | ||||||||
\(630\) | 2.26945 | 0.0904169 | ||||||||
\(631\) | 24.5189 | 0.976081 | 0.488040 | − | 0.872821i | \(-0.337712\pi\) | ||||
0.488040 | + | 0.872821i | \(0.337712\pi\) | |||||||
\(632\) | 1.75125 | 0.0696612 | ||||||||
\(633\) | −4.67879 | −0.185965 | ||||||||
\(634\) | −3.23275 | −0.128389 | ||||||||
\(635\) | 4.78000 | 0.189689 | ||||||||
\(636\) | 3.81830 | 0.151405 | ||||||||
\(637\) | 3.20297 | 0.126906 | ||||||||
\(638\) | −6.24736 | −0.247335 | ||||||||
\(639\) | 2.96140 | 0.117151 | ||||||||
\(640\) | 7.53435 | 0.297821 | ||||||||
\(641\) | −42.7514 | −1.68858 | −0.844290 | − | 0.535887i | \(-0.819977\pi\) | ||||
−0.844290 | + | 0.535887i | \(0.819977\pi\) | |||||||
\(642\) | 0.967241 | 0.0381740 | ||||||||
\(643\) | 12.4530 | 0.491098 | 0.245549 | − | 0.969384i | \(-0.421032\pi\) | ||||
0.245549 | + | 0.969384i | \(0.421032\pi\) | |||||||
\(644\) | −27.8293 | −1.09663 | ||||||||
\(645\) | 0.850684 | 0.0334957 | ||||||||
\(646\) | 0.856624 | 0.0337034 | ||||||||
\(647\) | −0.200365 | −0.00787716 | −0.00393858 | − | 0.999992i | \(-0.501254\pi\) | ||||
−0.00393858 | + | 0.999992i | \(0.501254\pi\) | |||||||
\(648\) | 8.71701 | 0.342437 | ||||||||
\(649\) | −41.4047 | −1.62528 | ||||||||
\(650\) | −0.418307 | −0.0164073 | ||||||||
\(651\) | 0.00890922 | 0.000349180 0 | ||||||||
\(652\) | −18.8250 | −0.737244 | ||||||||
\(653\) | 17.6841 | 0.692031 | 0.346015 | − | 0.938229i | \(-0.387534\pi\) | ||||
0.346015 | + | 0.938229i | \(0.387534\pi\) | |||||||
\(654\) | 0.762575 | 0.0298191 | ||||||||
\(655\) | 21.1983 | 0.828286 | ||||||||
\(656\) | 18.9597 | 0.740253 | ||||||||
\(657\) | −25.3490 | −0.988960 | ||||||||
\(658\) | −0.661931 | −0.0258048 | ||||||||
\(659\) | 34.3116 | 1.33659 | 0.668296 | − | 0.743896i | \(-0.267024\pi\) | ||||
0.668296 | + | 0.743896i | \(0.267024\pi\) | |||||||
\(660\) | 1.71535 | 0.0667699 | ||||||||
\(661\) | −6.07210 | −0.236177 | −0.118089 | − | 0.993003i | \(-0.537677\pi\) | ||||
−0.118089 | + | 0.993003i | \(0.537677\pi\) | |||||||
\(662\) | −4.10101 | −0.159390 | ||||||||
\(663\) | 0.321023 | 0.0124675 | ||||||||
\(664\) | −15.5464 | −0.603317 | ||||||||
\(665\) | −10.0159 | −0.388399 | ||||||||
\(666\) | 1.63930 | 0.0635216 | ||||||||
\(667\) | −25.9852 | −1.00615 | ||||||||
\(668\) | −26.7394 | −1.03458 | ||||||||
\(669\) | −4.50219 | −0.174065 | ||||||||
\(670\) | 3.14128 | 0.121358 | ||||||||
\(671\) | 19.9958 | 0.771931 | ||||||||
\(672\) | −1.72849 | −0.0666778 | ||||||||
\(673\) | 31.7403 | 1.22350 | 0.611748 | − | 0.791052i | \(-0.290467\pi\) | ||||
0.611748 | + | 0.791052i | \(0.290467\pi\) | |||||||
\(674\) | 6.69793 | 0.257995 | ||||||||
\(675\) | −1.17125 | −0.0450816 | ||||||||
\(676\) | 19.9835 | 0.768596 | ||||||||
\(677\) | 23.1595 | 0.890093 | 0.445047 | − | 0.895507i | \(-0.353187\pi\) | ||||
0.445047 | + | 0.895507i | \(0.353187\pi\) | |||||||
\(678\) | −0.452971 | −0.0173962 | ||||||||
\(679\) | −37.3446 | −1.43315 | ||||||||
\(680\) | 1.00727 | 0.0386271 | ||||||||
\(681\) | 0.0879126 | 0.00336882 | ||||||||
\(682\) | 0.0175036 | 0.000670249 0 | ||||||||
\(683\) | −0.336970 | −0.0128938 | −0.00644690 | − | 0.999979i | \(-0.502052\pi\) | ||||
−0.00644690 | + | 0.999979i | \(0.502052\pi\) | |||||||
\(684\) | −19.1683 | −0.732919 | ||||||||
\(685\) | −0.387209 | −0.0147945 | ||||||||
\(686\) | 3.86215 | 0.147458 | ||||||||
\(687\) | −2.18554 | −0.0833834 | ||||||||
\(688\) | 15.6350 | 0.596079 | ||||||||
\(689\) | −16.4150 | −0.625361 | ||||||||
\(690\) | −0.241739 | −0.00920285 | ||||||||
\(691\) | −20.5156 | −0.780449 | −0.390225 | − | 0.920720i | \(-0.627603\pi\) | ||||
−0.390225 | + | 0.920720i | \(0.627603\pi\) | |||||||
\(692\) | 29.2043 | 1.11018 | ||||||||
\(693\) | 40.0081 | 1.51978 | ||||||||
\(694\) | 0.461274 | 0.0175097 | ||||||||
\(695\) | −12.2334 | −0.464039 | ||||||||
\(696\) | −1.07002 | −0.0405592 | ||||||||
\(697\) | 5.25049 | 0.198876 | ||||||||
\(698\) | 0.522744 | 0.0197861 | ||||||||
\(699\) | −4.19925 | −0.158830 | ||||||||
\(700\) | −5.79055 | −0.218862 | ||||||||
\(701\) | 5.77880 | 0.218262 | 0.109131 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109131 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(702\) | 0.489943 | 0.0184917 | ||||||||
\(703\) | −7.23482 | −0.272866 | ||||||||
\(704\) | 29.1992 | 1.10049 | ||||||||
\(705\) | 0.169704 | 0.00639143 | ||||||||
\(706\) | 3.30525 | 0.124395 | ||||||||
\(707\) | 19.3129 | 0.726335 | ||||||||
\(708\) | −3.48676 | −0.131040 | ||||||||
\(709\) | 30.9761 | 1.16333 | 0.581666 | − | 0.813428i | \(-0.302401\pi\) | ||||
0.581666 | + | 0.813428i | \(0.302401\pi\) | |||||||
\(710\) | 0.256013 | 0.00960800 | ||||||||
\(711\) | −5.14872 | −0.193092 | ||||||||
\(712\) | 2.47398 | 0.0927163 | ||||||||
\(713\) | 0.0728044 | 0.00272655 | ||||||||
\(714\) | −0.150566 | −0.00563478 | ||||||||
\(715\) | −7.37434 | −0.275785 | ||||||||
\(716\) | −13.7746 | −0.514780 | ||||||||
\(717\) | 1.94172 | 0.0725147 | ||||||||
\(718\) | −1.84750 | −0.0689482 | ||||||||
\(719\) | 32.1646 | 1.19954 | 0.599768 | − | 0.800174i | \(-0.295259\pi\) | ||||
0.599768 | + | 0.800174i | \(0.295259\pi\) | |||||||
\(720\) | −10.6937 | −0.398532 | ||||||||
\(721\) | −5.56704 | −0.207327 | ||||||||
\(722\) | 1.99797 | 0.0743569 | ||||||||
\(723\) | −1.31485 | −0.0488998 | ||||||||
\(724\) | 4.99556 | 0.185659 | ||||||||
\(725\) | −5.40684 | −0.200805 | ||||||||
\(726\) | −0.471284 | −0.0174910 | ||||||||
\(727\) | −29.7656 | −1.10394 | −0.551972 | − | 0.833863i | \(-0.686124\pi\) | ||||
−0.551972 | + | 0.833863i | \(0.686124\pi\) | |||||||
\(728\) | 4.92653 | 0.182589 | ||||||||
\(729\) | −24.9378 | −0.923622 | ||||||||
\(730\) | −2.19143 | −0.0811083 | ||||||||
\(731\) | 4.32978 | 0.160143 | ||||||||
\(732\) | 1.68388 | 0.0622380 | ||||||||
\(733\) | 27.9754 | 1.03329 | 0.516647 | − | 0.856198i | \(-0.327180\pi\) | ||||
0.516647 | + | 0.856198i | \(0.327180\pi\) | |||||||
\(734\) | −3.12649 | −0.115401 | ||||||||
\(735\) | 0.385144 | 0.0142062 | ||||||||
\(736\) | −14.1249 | −0.520649 | ||||||||
\(737\) | 55.3777 | 2.03986 | ||||||||
\(738\) | 3.98070 | 0.146531 | ||||||||
\(739\) | 33.5438 | 1.23393 | 0.616964 | − | 0.786992i | \(-0.288363\pi\) | ||||
0.616964 | + | 0.786992i | \(0.288363\pi\) | |||||||
\(740\) | −4.18272 | −0.153760 | ||||||||
\(741\) | −1.07415 | −0.0394597 | ||||||||
\(742\) | 7.69894 | 0.282637 | ||||||||
\(743\) | −49.9137 | −1.83116 | −0.915579 | − | 0.402138i | \(-0.868267\pi\) | ||||
−0.915579 | + | 0.402138i | \(0.868267\pi\) | |||||||
\(744\) | 0.00299796 | 0.000109911 0 | ||||||||
\(745\) | −2.41173 | −0.0883591 | ||||||||
\(746\) | 8.36925 | 0.306420 | ||||||||
\(747\) | 45.7067 | 1.67232 | ||||||||
\(748\) | 8.73071 | 0.319226 | ||||||||
\(749\) | −57.5613 | −2.10324 | ||||||||
\(750\) | −0.0502997 | −0.00183668 | ||||||||
\(751\) | 49.1635 | 1.79400 | 0.897000 | − | 0.442030i | \(-0.145741\pi\) | ||||
0.897000 | + | 0.442030i | \(0.145741\pi\) | |||||||
\(752\) | 3.11905 | 0.113740 | ||||||||
\(753\) | −3.71007 | −0.135202 | ||||||||
\(754\) | 2.26172 | 0.0823670 | ||||||||
\(755\) | −17.9563 | −0.653498 | ||||||||
\(756\) | 6.78221 | 0.246666 | ||||||||
\(757\) | 13.9284 | 0.506237 | 0.253119 | − | 0.967435i | \(-0.418544\pi\) | ||||
0.253119 | + | 0.967435i | \(0.418544\pi\) | |||||||
\(758\) | 7.06346 | 0.256556 | ||||||||
\(759\) | −4.26162 | −0.154687 | ||||||||
\(760\) | −3.37035 | −0.122255 | ||||||||
\(761\) | 29.4978 | 1.06930 | 0.534648 | − | 0.845075i | \(-0.320444\pi\) | ||||
0.534648 | + | 0.845075i | \(0.320444\pi\) | |||||||
\(762\) | −0.240432 | −0.00870995 | ||||||||
\(763\) | −45.3815 | −1.64292 | ||||||||
\(764\) | 2.25966 | 0.0817517 | ||||||||
\(765\) | −2.96140 | −0.107070 | ||||||||
\(766\) | 6.10878 | 0.220719 | ||||||||
\(767\) | 14.9897 | 0.541246 | ||||||||
\(768\) | 2.16325 | 0.0780595 | ||||||||
\(769\) | −40.4548 | −1.45884 | −0.729419 | − | 0.684067i | \(-0.760209\pi\) | ||||
−0.729419 | + | 0.684067i | \(0.760209\pi\) | |||||||
\(770\) | 3.45871 | 0.124643 | ||||||||
\(771\) | 0.0708459 | 0.00255145 | ||||||||
\(772\) | −42.0660 | −1.51399 | ||||||||
\(773\) | −15.0094 | −0.539852 | −0.269926 | − | 0.962881i | \(-0.586999\pi\) | ||||
−0.269926 | + | 0.962881i | \(0.586999\pi\) | |||||||
\(774\) | 3.28265 | 0.117992 | ||||||||
\(775\) | 0.0151487 | 0.000544158 0 | ||||||||
\(776\) | −12.5665 | −0.451111 | ||||||||
\(777\) | 1.27164 | 0.0456198 | ||||||||
\(778\) | 2.85083 | 0.102207 | ||||||||
\(779\) | −17.5682 | −0.629447 | ||||||||
\(780\) | −0.621004 | −0.0222355 | ||||||||
\(781\) | 4.51326 | 0.161497 | ||||||||
\(782\) | −1.23039 | −0.0439988 | ||||||||
\(783\) | 6.33278 | 0.226315 | ||||||||
\(784\) | 7.07868 | 0.252810 | ||||||||
\(785\) | 4.14213 | 0.147839 | ||||||||
\(786\) | −1.06627 | −0.0380325 | ||||||||
\(787\) | 52.3683 | 1.86673 | 0.933363 | − | 0.358933i | \(-0.116859\pi\) | ||||
0.933363 | + | 0.358933i | \(0.116859\pi\) | |||||||
\(788\) | 28.2204 | 1.00531 | ||||||||
\(789\) | −0.831840 | −0.0296143 | ||||||||
\(790\) | −0.445107 | −0.0158362 | ||||||||
\(791\) | 26.9567 | 0.958468 | ||||||||
\(792\) | 13.4628 | 0.478379 | ||||||||
\(793\) | −7.23906 | −0.257066 | ||||||||
\(794\) | 6.72285 | 0.238585 | ||||||||
\(795\) | −1.97383 | −0.0700046 | ||||||||
\(796\) | 27.3586 | 0.969701 | ||||||||
\(797\) | 16.3220 | 0.578155 | 0.289077 | − | 0.957306i | \(-0.406652\pi\) | ||||
0.289077 | + | 0.957306i | \(0.406652\pi\) | |||||||
\(798\) | 0.503795 | 0.0178341 | ||||||||
\(799\) | 0.863753 | 0.0305574 | ||||||||
\(800\) | −2.93902 | −0.103910 | ||||||||
\(801\) | −7.27354 | −0.256998 | ||||||||
\(802\) | 7.48330 | 0.264244 | ||||||||
\(803\) | −38.6327 | −1.36332 | ||||||||
\(804\) | 4.66344 | 0.164467 | ||||||||
\(805\) | 14.3861 | 0.507043 | ||||||||
\(806\) | −0.00633681 | −0.000223205 0 | ||||||||
\(807\) | −0.187019 | −0.00658338 | ||||||||
\(808\) | 6.49879 | 0.228627 | ||||||||
\(809\) | −30.6249 | −1.07671 | −0.538357 | − | 0.842717i | \(-0.680955\pi\) | ||||
−0.538357 | + | 0.842717i | \(0.680955\pi\) | |||||||
\(810\) | −2.21556 | −0.0778467 | ||||||||
\(811\) | −20.8972 | −0.733799 | −0.366899 | − | 0.930261i | \(-0.619581\pi\) | ||||
−0.366899 | + | 0.930261i | \(0.619581\pi\) | |||||||
\(812\) | 31.3086 | 1.09872 | ||||||||
\(813\) | −0.105115 | −0.00368653 | ||||||||
\(814\) | 2.49835 | 0.0875669 | ||||||||
\(815\) | 9.73141 | 0.340876 | ||||||||
\(816\) | 0.709472 | 0.0248365 | ||||||||
\(817\) | −14.4875 | −0.506853 | ||||||||
\(818\) | −6.05782 | −0.211807 | ||||||||
\(819\) | −14.4841 | −0.506114 | ||||||||
\(820\) | −10.1568 | −0.354693 | ||||||||
\(821\) | 27.1289 | 0.946806 | 0.473403 | − | 0.880846i | \(-0.343025\pi\) | ||||
0.473403 | + | 0.880846i | \(0.343025\pi\) | |||||||
\(822\) | 0.0194765 | 0.000679321 0 | ||||||||
\(823\) | −4.36324 | −0.152093 | −0.0760464 | − | 0.997104i | \(-0.524230\pi\) | ||||
−0.0760464 | + | 0.997104i | \(0.524230\pi\) | |||||||
\(824\) | −1.87331 | −0.0652599 | ||||||||
\(825\) | −0.886734 | −0.0308721 | ||||||||
\(826\) | −7.03045 | −0.244621 | ||||||||
\(827\) | −22.1533 | −0.770347 | −0.385173 | − | 0.922844i | \(-0.625858\pi\) | ||||
−0.385173 | + | 0.922844i | \(0.625858\pi\) | |||||||
\(828\) | 27.5320 | 0.956803 | ||||||||
\(829\) | −11.5838 | −0.402321 | −0.201161 | − | 0.979558i | \(-0.564471\pi\) | ||||
−0.201161 | + | 0.979558i | \(0.564471\pi\) | |||||||
\(830\) | 3.95134 | 0.137153 | ||||||||
\(831\) | −5.73358 | −0.198896 | ||||||||
\(832\) | −10.5709 | −0.366481 | ||||||||
\(833\) | 1.96029 | 0.0679199 | ||||||||
\(834\) | 0.615336 | 0.0213073 | ||||||||
\(835\) | 13.8227 | 0.478353 | ||||||||
\(836\) | −29.2131 | −1.01036 | ||||||||
\(837\) | −0.0177430 | −0.000613287 0 | ||||||||
\(838\) | 5.39939 | 0.186519 | ||||||||
\(839\) | 8.64816 | 0.298567 | 0.149284 | − | 0.988794i | \(-0.452303\pi\) | ||||
0.149284 | + | 0.988794i | \(0.452303\pi\) | |||||||
\(840\) | 0.592394 | 0.0204395 | ||||||||
\(841\) | 0.233954 | 0.00806737 | ||||||||
\(842\) | 0.835825 | 0.0288044 | ||||||||
\(843\) | 5.36490 | 0.184777 | ||||||||
\(844\) | 46.0670 | 1.58569 | ||||||||
\(845\) | −10.3303 | −0.355372 | ||||||||
\(846\) | 0.654860 | 0.0225146 | ||||||||
\(847\) | 28.0465 | 0.963689 | ||||||||
\(848\) | −36.2777 | −1.24578 | ||||||||
\(849\) | 4.94039 | 0.169554 | ||||||||
\(850\) | −0.256013 | −0.00878118 | ||||||||
\(851\) | 10.3916 | 0.356219 | ||||||||
\(852\) | 0.380069 | 0.0130209 | ||||||||
\(853\) | 47.4429 | 1.62441 | 0.812207 | − | 0.583369i | \(-0.198266\pi\) | ||||
0.812207 | + | 0.583369i | \(0.198266\pi\) | |||||||
\(854\) | 3.39526 | 0.116183 | ||||||||
\(855\) | 9.90888 | 0.338877 | ||||||||
\(856\) | −19.3694 | −0.662033 | ||||||||
\(857\) | 4.89427 | 0.167185 | 0.0835925 | − | 0.996500i | \(-0.473361\pi\) | ||||
0.0835925 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(858\) | 0.370927 | 0.0126632 | ||||||||
\(859\) | 23.4313 | 0.799466 | 0.399733 | − | 0.916632i | \(-0.369103\pi\) | ||||
0.399733 | + | 0.916632i | \(0.369103\pi\) | |||||||
\(860\) | −8.37577 | −0.285611 | ||||||||
\(861\) | 3.08790 | 0.105235 | ||||||||
\(862\) | −3.34924 | −0.114076 | ||||||||
\(863\) | 33.3022 | 1.13362 | 0.566810 | − | 0.823849i | \(-0.308178\pi\) | ||||
0.566810 | + | 0.823849i | \(0.308178\pi\) | |||||||
\(864\) | 3.44234 | 0.117111 | ||||||||
\(865\) | −15.0969 | −0.513310 | ||||||||
\(866\) | 4.17418 | 0.141844 | ||||||||
\(867\) | 0.196473 | 0.00667257 | ||||||||
\(868\) | −0.0877195 | −0.00297739 | ||||||||
\(869\) | −7.84680 | −0.266185 | ||||||||
\(870\) | 0.271962 | 0.00922039 | ||||||||
\(871\) | −20.0483 | −0.679310 | ||||||||
\(872\) | −15.2709 | −0.517138 | ||||||||
\(873\) | 36.9457 | 1.25042 | ||||||||
\(874\) | 4.11692 | 0.139257 | ||||||||
\(875\) | 2.99337 | 0.101195 | ||||||||
\(876\) | −3.25332 | −0.109919 | ||||||||
\(877\) | −26.6764 | −0.900799 | −0.450399 | − | 0.892827i | \(-0.648718\pi\) | ||||
−0.450399 | + | 0.892827i | \(0.648718\pi\) | |||||||
\(878\) | 1.46968 | 0.0495994 | ||||||||
\(879\) | 1.11759 | 0.0376954 | ||||||||
\(880\) | −16.2976 | −0.549391 | ||||||||
\(881\) | 51.4538 | 1.73352 | 0.866762 | − | 0.498722i | \(-0.166197\pi\) | ||||
0.866762 | + | 0.498722i | \(0.166197\pi\) | |||||||
\(882\) | 1.48621 | 0.0500431 | ||||||||
\(883\) | 1.61861 | 0.0544706 | 0.0272353 | − | 0.999629i | \(-0.491330\pi\) | ||||
0.0272353 | + | 0.999629i | \(0.491330\pi\) | |||||||
\(884\) | −3.16076 | −0.106308 | ||||||||
\(885\) | 1.80245 | 0.0605886 | ||||||||
\(886\) | 1.20338 | 0.0404284 | ||||||||
\(887\) | 11.9868 | 0.402479 | 0.201239 | − | 0.979542i | \(-0.435503\pi\) | ||||
0.201239 | + | 0.979542i | \(0.435503\pi\) | |||||||
\(888\) | 0.427907 | 0.0143596 | ||||||||
\(889\) | 14.3083 | 0.479886 | ||||||||
\(890\) | −0.628798 | −0.0210774 | ||||||||
\(891\) | −39.0581 | −1.30850 | ||||||||
\(892\) | 44.3282 | 1.48422 | ||||||||
\(893\) | −2.89013 | −0.0967145 | ||||||||
\(894\) | 0.121309 | 0.00405719 | ||||||||
\(895\) | 7.12064 | 0.238017 | ||||||||
\(896\) | 22.5531 | 0.753447 | ||||||||
\(897\) | 1.54283 | 0.0515135 | ||||||||
\(898\) | −1.86376 | −0.0621946 | ||||||||
\(899\) | −0.0819067 | −0.00273174 | ||||||||
\(900\) | 5.72870 | 0.190957 | ||||||||
\(901\) | −10.0463 | −0.334692 | ||||||||
\(902\) | 6.06670 | 0.201999 | ||||||||
\(903\) | 2.54642 | 0.0847394 | ||||||||
\(904\) | 9.07093 | 0.301695 | ||||||||
\(905\) | −2.58241 | −0.0858422 | ||||||||
\(906\) | 0.903198 | 0.0300067 | ||||||||
\(907\) | −29.9710 | −0.995172 | −0.497586 | − | 0.867415i | \(-0.665780\pi\) | ||||
−0.497586 | + | 0.867415i | \(0.665780\pi\) | |||||||
\(908\) | −0.865580 | −0.0287253 | ||||||||
\(909\) | −19.1066 | −0.633725 | ||||||||
\(910\) | −1.25215 | −0.0415083 | ||||||||
\(911\) | 16.4482 | 0.544954 | 0.272477 | − | 0.962162i | \(-0.412157\pi\) | ||||
0.272477 | + | 0.962162i | \(0.412157\pi\) | |||||||
\(912\) | −2.37390 | −0.0786078 | ||||||||
\(913\) | 69.6583 | 2.30535 | ||||||||
\(914\) | −2.72495 | −0.0901332 | ||||||||
\(915\) | −0.870466 | −0.0287767 | ||||||||
\(916\) | 21.5186 | 0.710995 | ||||||||
\(917\) | 63.4544 | 2.09545 | ||||||||
\(918\) | 0.299856 | 0.00989673 | ||||||||
\(919\) | −21.2572 | −0.701212 | −0.350606 | − | 0.936523i | \(-0.614024\pi\) | ||||
−0.350606 | + | 0.936523i | \(0.614024\pi\) | |||||||
\(920\) | 4.84093 | 0.159601 | ||||||||
\(921\) | −3.79318 | −0.124990 | ||||||||
\(922\) | −0.328119 | −0.0108060 | ||||||||
\(923\) | −1.63393 | −0.0537814 | ||||||||
\(924\) | 5.13468 | 0.168919 | ||||||||
\(925\) | 2.16222 | 0.0710933 | ||||||||
\(926\) | 3.62741 | 0.119204 | ||||||||
\(927\) | 5.50757 | 0.180892 | ||||||||
\(928\) | 15.8908 | 0.521642 | ||||||||
\(929\) | 51.5700 | 1.69196 | 0.845979 | − | 0.533216i | \(-0.179017\pi\) | ||||
0.845979 | + | 0.533216i | \(0.179017\pi\) | |||||||
\(930\) | −0.000761975 0 | −2.49862e−5 0 | ||||||||
\(931\) | −6.55915 | −0.214967 | ||||||||
\(932\) | 41.3455 | 1.35432 | ||||||||
\(933\) | 4.80526 | 0.157317 | ||||||||
\(934\) | −4.54686 | −0.148778 | ||||||||
\(935\) | −4.51326 | −0.147599 | ||||||||
\(936\) | −4.87390 | −0.159308 | ||||||||
\(937\) | −13.0092 | −0.424990 | −0.212495 | − | 0.977162i | \(-0.568159\pi\) | ||||
−0.212495 | + | 0.977162i | \(0.568159\pi\) | |||||||
\(938\) | 9.40302 | 0.307019 | ||||||||
\(939\) | 3.11808 | 0.101755 | ||||||||
\(940\) | −1.67089 | −0.0544985 | ||||||||
\(941\) | 3.94223 | 0.128513 | 0.0642566 | − | 0.997933i | \(-0.479532\pi\) | ||||
0.0642566 | + | 0.997933i | \(0.479532\pi\) | |||||||
\(942\) | −0.208348 | −0.00678833 | ||||||||
\(943\) | 25.2338 | 0.821724 | ||||||||
\(944\) | 33.1277 | 1.07822 | ||||||||
\(945\) | −3.50600 | −0.114050 | ||||||||
\(946\) | 5.00286 | 0.162657 | ||||||||
\(947\) | 29.5663 | 0.960775 | 0.480387 | − | 0.877056i | \(-0.340496\pi\) | ||||
0.480387 | + | 0.877056i | \(0.340496\pi\) | |||||||
\(948\) | −0.660791 | −0.0214615 | ||||||||
\(949\) | 13.9861 | 0.454009 | ||||||||
\(950\) | 0.856624 | 0.0277925 | ||||||||
\(951\) | 2.48092 | 0.0804493 | ||||||||
\(952\) | 3.01514 | 0.0977214 | ||||||||
\(953\) | 11.7629 | 0.381039 | 0.190519 | − | 0.981683i | \(-0.438983\pi\) | ||||
0.190519 | + | 0.981683i | \(0.438983\pi\) | |||||||
\(954\) | −7.61670 | −0.246600 | ||||||||
\(955\) | −1.16811 | −0.0377992 | ||||||||
\(956\) | −19.1180 | −0.618320 | ||||||||
\(957\) | 4.79443 | 0.154982 | ||||||||
\(958\) | 6.06961 | 0.196100 | ||||||||
\(959\) | −1.15906 | −0.0374281 | ||||||||
\(960\) | −1.27111 | −0.0410249 | ||||||||
\(961\) | −30.9998 | −0.999993 | ||||||||
\(962\) | −0.904471 | −0.0291613 | ||||||||
\(963\) | 56.9464 | 1.83507 | ||||||||
\(964\) | 12.9459 | 0.416960 | ||||||||
\(965\) | 21.7456 | 0.700016 | ||||||||
\(966\) | −0.723616 | −0.0232820 | ||||||||
\(967\) | −0.308221 | −0.00991173 | −0.00495587 | − | 0.999988i | \(-0.501578\pi\) | ||||
−0.00495587 | + | 0.999988i | \(0.501578\pi\) | |||||||
\(968\) | 9.43767 | 0.303338 | ||||||||
\(969\) | −0.657401 | −0.0211188 | ||||||||
\(970\) | 3.19396 | 0.102552 | ||||||||
\(971\) | −15.2376 | −0.488999 | −0.244500 | − | 0.969649i | \(-0.578624\pi\) | ||||
−0.244500 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(972\) | −10.0864 | −0.323520 | ||||||||
\(973\) | −36.6191 | −1.17396 | ||||||||
\(974\) | 1.58887 | 0.0509108 | ||||||||
\(975\) | 0.321023 | 0.0102809 | ||||||||
\(976\) | −15.9986 | −0.512102 | ||||||||
\(977\) | 50.7456 | 1.62350 | 0.811748 | − | 0.584008i | \(-0.198516\pi\) | ||||
0.811748 | + | 0.584008i | \(0.198516\pi\) | |||||||
\(978\) | −0.489487 | −0.0156521 | ||||||||
\(979\) | −11.0851 | −0.354281 | ||||||||
\(980\) | −3.79209 | −0.121134 | ||||||||
\(981\) | 44.8967 | 1.43344 | ||||||||
\(982\) | 8.45950 | 0.269954 | ||||||||
\(983\) | 8.65035 | 0.275903 | 0.137952 | − | 0.990439i | \(-0.455948\pi\) | ||||
0.137952 | + | 0.990439i | \(0.455948\pi\) | |||||||
\(984\) | 1.03908 | 0.0331247 | ||||||||
\(985\) | −14.5883 | −0.464821 | ||||||||
\(986\) | 1.38422 | 0.0440826 | ||||||||
\(987\) | 0.507988 | 0.0161694 | ||||||||
\(988\) | 10.5760 | 0.336466 | ||||||||
\(989\) | 20.8088 | 0.661682 | ||||||||
\(990\) | −3.42176 | −0.108751 | ||||||||
\(991\) | 37.3022 | 1.18494 | 0.592472 | − | 0.805591i | \(-0.298152\pi\) | ||||
0.592472 | + | 0.805591i | \(0.298152\pi\) | |||||||
\(992\) | −0.0445224 | −0.00141359 | ||||||||
\(993\) | 3.14725 | 0.0998750 | ||||||||
\(994\) | 0.766343 | 0.0243069 | ||||||||
\(995\) | −14.1428 | −0.448357 | ||||||||
\(996\) | 5.86603 | 0.185872 | ||||||||
\(997\) | 16.4849 | 0.522082 | 0.261041 | − | 0.965328i | \(-0.415934\pi\) | ||||
0.261041 | + | 0.965328i | \(0.415934\pi\) | |||||||
\(998\) | 8.86395 | 0.280584 | ||||||||
\(999\) | −2.53251 | −0.0801250 |
(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 | 6035.2.a.a.1.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6035.2.a.a.1.17 | ✓ | 36 | 1.1 | even | 1 | trivial |