Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(0\) |
Dimension: | \(98\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08450 | −1.47397 | −0.736984 | − | 0.675911i | \(-0.763751\pi\) | ||||
−0.736984 | + | 0.675911i | \(0.763751\pi\) | |||||||
\(3\) | 0.675318 | 0.389895 | 0.194947 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194947 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(4\) | 2.34516 | 1.17258 | ||||||||
\(5\) | −1.05546 | −0.472017 | −0.236008 | − | 0.971751i | \(-0.575839\pi\) | ||||
−0.236008 | + | 0.971751i | \(0.575839\pi\) | |||||||
\(6\) | −1.40770 | −0.574692 | ||||||||
\(7\) | −4.46025 | −1.68582 | −0.842908 | − | 0.538058i | \(-0.819158\pi\) | ||||
−0.842908 | + | 0.538058i | \(0.819158\pi\) | |||||||
\(8\) | −0.719483 | −0.254376 | ||||||||
\(9\) | −2.54395 | −0.847982 | ||||||||
\(10\) | 2.20012 | 0.695738 | ||||||||
\(11\) | 3.41671 | 1.03018 | 0.515088 | − | 0.857137i | \(-0.327759\pi\) | ||||
0.515088 | + | 0.857137i | \(0.327759\pi\) | |||||||
\(12\) | 1.58373 | 0.457182 | ||||||||
\(13\) | −1.13635 | −0.315166 | −0.157583 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157583 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(14\) | 9.29741 | 2.48484 | ||||||||
\(15\) | −0.712772 | −0.184037 | ||||||||
\(16\) | −3.19055 | −0.797637 | ||||||||
\(17\) | −5.08799 | −1.23402 | −0.617010 | − | 0.786955i | \(-0.711656\pi\) | ||||
−0.617010 | + | 0.786955i | \(0.711656\pi\) | |||||||
\(18\) | 5.30287 | 1.24990 | ||||||||
\(19\) | 0.618161 | 0.141816 | 0.0709079 | − | 0.997483i | \(-0.477410\pi\) | ||||
0.0709079 | + | 0.997483i | \(0.477410\pi\) | |||||||
\(20\) | −2.47523 | −0.553477 | ||||||||
\(21\) | −3.01208 | −0.657291 | ||||||||
\(22\) | −7.12214 | −1.51845 | ||||||||
\(23\) | −7.25585 | −1.51295 | −0.756475 | − | 0.654023i | \(-0.773080\pi\) | ||||
−0.756475 | + | 0.654023i | \(0.773080\pi\) | |||||||
\(24\) | −0.485880 | −0.0991798 | ||||||||
\(25\) | −3.88600 | −0.777200 | ||||||||
\(26\) | 2.36872 | 0.464545 | ||||||||
\(27\) | −3.74392 | −0.720519 | ||||||||
\(28\) | −10.4600 | −1.97675 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.48578 | 0.271264 | ||||||||
\(31\) | 3.87154 | 0.695349 | 0.347674 | − | 0.937615i | \(-0.386971\pi\) | ||||
0.347674 | + | 0.937615i | \(0.386971\pi\) | |||||||
\(32\) | 8.08968 | 1.43007 | ||||||||
\(33\) | 2.30736 | 0.401660 | ||||||||
\(34\) | 10.6059 | 1.81890 | ||||||||
\(35\) | 4.70762 | 0.795734 | ||||||||
\(36\) | −5.96596 | −0.994326 | ||||||||
\(37\) | −0.331880 | −0.0545607 | −0.0272803 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272803 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(38\) | −1.28856 | −0.209032 | ||||||||
\(39\) | −0.767396 | −0.122882 | ||||||||
\(40\) | 0.759387 | 0.120070 | ||||||||
\(41\) | −2.73464 | −0.427079 | −0.213539 | − | 0.976934i | \(-0.568499\pi\) | ||||
−0.213539 | + | 0.976934i | \(0.568499\pi\) | |||||||
\(42\) | 6.27870 | 0.968825 | ||||||||
\(43\) | −10.7254 | −1.63561 | −0.817804 | − | 0.575496i | \(-0.804809\pi\) | ||||
−0.817804 | + | 0.575496i | \(0.804809\pi\) | |||||||
\(44\) | 8.01272 | 1.20796 | ||||||||
\(45\) | 2.68504 | 0.400262 | ||||||||
\(46\) | 15.1249 | 2.23004 | ||||||||
\(47\) | 5.64222 | 0.823002 | 0.411501 | − | 0.911409i | \(-0.365005\pi\) | ||||
0.411501 | + | 0.911409i | \(0.365005\pi\) | |||||||
\(48\) | −2.15463 | −0.310995 | ||||||||
\(49\) | 12.8938 | 1.84198 | ||||||||
\(50\) | 8.10038 | 1.14557 | ||||||||
\(51\) | −3.43601 | −0.481138 | ||||||||
\(52\) | −2.66492 | −0.369558 | ||||||||
\(53\) | −12.9130 | −1.77373 | −0.886867 | − | 0.462025i | \(-0.847123\pi\) | ||||
−0.886867 | + | 0.462025i | \(0.847123\pi\) | |||||||
\(54\) | 7.80423 | 1.06202 | ||||||||
\(55\) | −3.60620 | −0.486260 | ||||||||
\(56\) | 3.20908 | 0.428831 | ||||||||
\(57\) | 0.417455 | 0.0552932 | ||||||||
\(58\) | −2.08450 | −0.273709 | ||||||||
\(59\) | 8.45719 | 1.10103 | 0.550516 | − | 0.834825i | \(-0.314431\pi\) | ||||
0.550516 | + | 0.834825i | \(0.314431\pi\) | |||||||
\(60\) | −1.67156 | −0.215798 | ||||||||
\(61\) | 0.103400 | 0.0132390 | 0.00661951 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661951 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(62\) | −8.07024 | −1.02492 | ||||||||
\(63\) | 11.3466 | 1.42954 | ||||||||
\(64\) | −10.4819 | −1.31023 | ||||||||
\(65\) | 1.19937 | 0.148764 | ||||||||
\(66\) | −4.80971 | −0.592034 | ||||||||
\(67\) | −13.7768 | −1.68311 | −0.841553 | − | 0.540175i | \(-0.818358\pi\) | ||||
−0.841553 | + | 0.540175i | \(0.818358\pi\) | |||||||
\(68\) | −11.9321 | −1.44699 | ||||||||
\(69\) | −4.90000 | −0.589891 | ||||||||
\(70\) | −9.81306 | −1.17289 | ||||||||
\(71\) | 1.82915 | 0.217081 | 0.108540 | − | 0.994092i | \(-0.465382\pi\) | ||||
0.108540 | + | 0.994092i | \(0.465382\pi\) | |||||||
\(72\) | 1.83033 | 0.215706 | ||||||||
\(73\) | −2.52886 | −0.295980 | −0.147990 | − | 0.988989i | \(-0.547280\pi\) | ||||
−0.147990 | + | 0.988989i | \(0.547280\pi\) | |||||||
\(74\) | 0.691804 | 0.0804206 | ||||||||
\(75\) | −2.62428 | −0.303026 | ||||||||
\(76\) | 1.44968 | 0.166290 | ||||||||
\(77\) | −15.2394 | −1.73669 | ||||||||
\(78\) | 1.59964 | 0.181124 | ||||||||
\(79\) | −11.4027 | −1.28290 | −0.641450 | − | 0.767164i | \(-0.721667\pi\) | ||||
−0.641450 | + | 0.767164i | \(0.721667\pi\) | |||||||
\(80\) | 3.36750 | 0.376498 | ||||||||
\(81\) | 5.10350 | 0.567056 | ||||||||
\(82\) | 5.70037 | 0.629500 | ||||||||
\(83\) | 11.5415 | 1.26684 | 0.633420 | − | 0.773808i | \(-0.281650\pi\) | ||||
0.633420 | + | 0.773808i | \(0.281650\pi\) | |||||||
\(84\) | −7.06381 | −0.770725 | ||||||||
\(85\) | 5.37018 | 0.582478 | ||||||||
\(86\) | 22.3571 | 2.41083 | ||||||||
\(87\) | 0.675318 | 0.0724016 | ||||||||
\(88\) | −2.45826 | −0.262052 | ||||||||
\(89\) | −3.58564 | −0.380077 | −0.190039 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190039 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(90\) | −5.59697 | −0.589973 | ||||||||
\(91\) | 5.06840 | 0.531313 | ||||||||
\(92\) | −17.0161 | −1.77405 | ||||||||
\(93\) | 2.61452 | 0.271113 | ||||||||
\(94\) | −11.7612 | −1.21308 | ||||||||
\(95\) | −0.652445 | −0.0669395 | ||||||||
\(96\) | 5.46310 | 0.557576 | ||||||||
\(97\) | 9.56316 | 0.970992 | 0.485496 | − | 0.874239i | \(-0.338639\pi\) | ||||
0.485496 | + | 0.874239i | \(0.338639\pi\) | |||||||
\(98\) | −26.8772 | −2.71501 | ||||||||
\(99\) | −8.69192 | −0.873570 | ||||||||
\(100\) | −9.11328 | −0.911328 | ||||||||
\(101\) | −13.2182 | −1.31526 | −0.657629 | − | 0.753342i | \(-0.728440\pi\) | ||||
−0.657629 | + | 0.753342i | \(0.728440\pi\) | |||||||
\(102\) | 7.16238 | 0.709181 | ||||||||
\(103\) | −8.12406 | −0.800488 | −0.400244 | − | 0.916409i | \(-0.631075\pi\) | ||||
−0.400244 | + | 0.916409i | \(0.631075\pi\) | |||||||
\(104\) | 0.817584 | 0.0801707 | ||||||||
\(105\) | 3.17914 | 0.310252 | ||||||||
\(106\) | 26.9171 | 2.61442 | ||||||||
\(107\) | 1.42653 | 0.137908 | 0.0689538 | − | 0.997620i | \(-0.478034\pi\) | ||||
0.0689538 | + | 0.997620i | \(0.478034\pi\) | |||||||
\(108\) | −8.78009 | −0.844865 | ||||||||
\(109\) | −0.772312 | −0.0739741 | −0.0369870 | − | 0.999316i | \(-0.511776\pi\) | ||||
−0.0369870 | + | 0.999316i | \(0.511776\pi\) | |||||||
\(110\) | 7.51715 | 0.716732 | ||||||||
\(111\) | −0.224124 | −0.0212729 | ||||||||
\(112\) | 14.2306 | 1.34467 | ||||||||
\(113\) | −18.3009 | −1.72160 | −0.860802 | − | 0.508939i | \(-0.830038\pi\) | ||||
−0.860802 | + | 0.508939i | \(0.830038\pi\) | |||||||
\(114\) | −0.870186 | −0.0815004 | ||||||||
\(115\) | 7.65828 | 0.714138 | ||||||||
\(116\) | 2.34516 | 0.217742 | ||||||||
\(117\) | 2.89081 | 0.267255 | ||||||||
\(118\) | −17.6290 | −1.62289 | ||||||||
\(119\) | 22.6937 | 2.08033 | ||||||||
\(120\) | 0.512828 | 0.0468145 | ||||||||
\(121\) | 0.673881 | 0.0612619 | ||||||||
\(122\) | −0.215538 | −0.0195139 | ||||||||
\(123\) | −1.84675 | −0.166516 | ||||||||
\(124\) | 9.07937 | 0.815352 | ||||||||
\(125\) | 9.37884 | 0.838869 | ||||||||
\(126\) | −23.6521 | −2.10710 | ||||||||
\(127\) | 17.1679 | 1.52340 | 0.761701 | − | 0.647929i | \(-0.224365\pi\) | ||||
0.761701 | + | 0.647929i | \(0.224365\pi\) | |||||||
\(128\) | 5.67015 | 0.501175 | ||||||||
\(129\) | −7.24305 | −0.637715 | ||||||||
\(130\) | −2.50010 | −0.219273 | ||||||||
\(131\) | 4.81415 | 0.420614 | 0.210307 | − | 0.977635i | \(-0.432554\pi\) | ||||
0.210307 | + | 0.977635i | \(0.432554\pi\) | |||||||
\(132\) | 5.41113 | 0.470978 | ||||||||
\(133\) | −2.75715 | −0.239075 | ||||||||
\(134\) | 28.7178 | 2.48084 | ||||||||
\(135\) | 3.95157 | 0.340097 | ||||||||
\(136\) | 3.66073 | 0.313905 | ||||||||
\(137\) | 16.0639 | 1.37243 | 0.686216 | − | 0.727398i | \(-0.259271\pi\) | ||||
0.686216 | + | 0.727398i | \(0.259271\pi\) | |||||||
\(138\) | 10.2141 | 0.869480 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 11.0401 | 0.933061 | ||||||||
\(141\) | 3.81029 | 0.320884 | ||||||||
\(142\) | −3.81288 | −0.319970 | ||||||||
\(143\) | −3.88257 | −0.324677 | ||||||||
\(144\) | 8.11659 | 0.676382 | ||||||||
\(145\) | −1.05546 | −0.0876514 | ||||||||
\(146\) | 5.27141 | 0.436265 | ||||||||
\(147\) | 8.70743 | 0.718177 | ||||||||
\(148\) | −0.778310 | −0.0639767 | ||||||||
\(149\) | 13.6804 | 1.12074 | 0.560372 | − | 0.828241i | \(-0.310658\pi\) | ||||
0.560372 | + | 0.828241i | \(0.310658\pi\) | |||||||
\(150\) | 5.47033 | 0.446651 | ||||||||
\(151\) | 18.3090 | 1.48997 | 0.744984 | − | 0.667082i | \(-0.232457\pi\) | ||||
0.744984 | + | 0.667082i | \(0.232457\pi\) | |||||||
\(152\) | −0.444756 | −0.0360745 | ||||||||
\(153\) | 12.9436 | 1.04643 | ||||||||
\(154\) | 31.7665 | 2.55982 | ||||||||
\(155\) | −4.08626 | −0.328217 | ||||||||
\(156\) | −1.79967 | −0.144089 | ||||||||
\(157\) | 16.7761 | 1.33888 | 0.669440 | − | 0.742867i | \(-0.266534\pi\) | ||||
0.669440 | + | 0.742867i | \(0.266534\pi\) | |||||||
\(158\) | 23.7689 | 1.89095 | ||||||||
\(159\) | −8.72036 | −0.691569 | ||||||||
\(160\) | −8.53835 | −0.675016 | ||||||||
\(161\) | 32.3629 | 2.55055 | ||||||||
\(162\) | −10.6383 | −0.835821 | ||||||||
\(163\) | −5.18510 | −0.406128 | −0.203064 | − | 0.979165i | \(-0.565090\pi\) | ||||
−0.203064 | + | 0.979165i | \(0.565090\pi\) | |||||||
\(164\) | −6.41316 | −0.500784 | ||||||||
\(165\) | −2.43533 | −0.189590 | ||||||||
\(166\) | −24.0582 | −1.86728 | ||||||||
\(167\) | −25.7882 | −1.99555 | −0.997777 | − | 0.0666421i | \(-0.978771\pi\) | ||||
−0.997777 | + | 0.0666421i | \(0.978771\pi\) | |||||||
\(168\) | 2.16714 | 0.167199 | ||||||||
\(169\) | −11.7087 | −0.900670 | ||||||||
\(170\) | −11.1942 | −0.858554 | ||||||||
\(171\) | −1.57257 | −0.120257 | ||||||||
\(172\) | −25.1528 | −1.91788 | ||||||||
\(173\) | −13.2397 | −1.00660 | −0.503298 | − | 0.864113i | \(-0.667880\pi\) | ||||
−0.503298 | + | 0.864113i | \(0.667880\pi\) | |||||||
\(174\) | −1.40770 | −0.106718 | ||||||||
\(175\) | 17.3325 | 1.31022 | ||||||||
\(176\) | −10.9012 | −0.821707 | ||||||||
\(177\) | 5.71129 | 0.429287 | ||||||||
\(178\) | 7.47428 | 0.560221 | ||||||||
\(179\) | 20.1004 | 1.50237 | 0.751186 | − | 0.660091i | \(-0.229482\pi\) | ||||
0.751186 | + | 0.660091i | \(0.229482\pi\) | |||||||
\(180\) | 6.29684 | 0.469339 | ||||||||
\(181\) | 9.71878 | 0.722391 | 0.361196 | − | 0.932490i | \(-0.382369\pi\) | ||||
0.361196 | + | 0.932490i | \(0.382369\pi\) | |||||||
\(182\) | −10.5651 | −0.783137 | ||||||||
\(183\) | 0.0698278 | 0.00516182 | ||||||||
\(184\) | 5.22046 | 0.384858 | ||||||||
\(185\) | 0.350286 | 0.0257536 | ||||||||
\(186\) | −5.44997 | −0.399612 | ||||||||
\(187\) | −17.3842 | −1.27126 | ||||||||
\(188\) | 13.2319 | 0.965035 | ||||||||
\(189\) | 16.6988 | 1.21466 | ||||||||
\(190\) | 1.36002 | 0.0986666 | ||||||||
\(191\) | −23.7788 | −1.72057 | −0.860286 | − | 0.509812i | \(-0.829715\pi\) | ||||
−0.860286 | + | 0.509812i | \(0.829715\pi\) | |||||||
\(192\) | −7.07859 | −0.510854 | ||||||||
\(193\) | −0.936601 | −0.0674180 | −0.0337090 | − | 0.999432i | \(-0.510732\pi\) | ||||
−0.0337090 | + | 0.999432i | \(0.510732\pi\) | |||||||
\(194\) | −19.9344 | −1.43121 | ||||||||
\(195\) | 0.809958 | 0.0580023 | ||||||||
\(196\) | 30.2381 | 2.15986 | ||||||||
\(197\) | −8.56192 | −0.610011 | −0.305006 | − | 0.952351i | \(-0.598658\pi\) | ||||
−0.305006 | + | 0.952351i | \(0.598658\pi\) | |||||||
\(198\) | 18.1183 | 1.28761 | ||||||||
\(199\) | −0.452650 | −0.0320875 | −0.0160437 | − | 0.999871i | \(-0.505107\pi\) | ||||
−0.0160437 | + | 0.999871i | \(0.505107\pi\) | |||||||
\(200\) | 2.79591 | 0.197701 | ||||||||
\(201\) | −9.30372 | −0.656234 | ||||||||
\(202\) | 27.5533 | 1.93865 | ||||||||
\(203\) | −4.46025 | −0.313048 | ||||||||
\(204\) | −8.05799 | −0.564172 | ||||||||
\(205\) | 2.88631 | 0.201588 | ||||||||
\(206\) | 16.9346 | 1.17989 | ||||||||
\(207\) | 18.4585 | 1.28295 | ||||||||
\(208\) | 3.62558 | 0.251389 | ||||||||
\(209\) | 2.11207 | 0.146095 | ||||||||
\(210\) | −6.62693 | −0.457302 | ||||||||
\(211\) | 17.3468 | 1.19420 | 0.597100 | − | 0.802167i | \(-0.296320\pi\) | ||||
0.597100 | + | 0.802167i | \(0.296320\pi\) | |||||||
\(212\) | −30.2830 | −2.07984 | ||||||||
\(213\) | 1.23526 | 0.0846386 | ||||||||
\(214\) | −2.97360 | −0.203271 | ||||||||
\(215\) | 11.3203 | 0.772035 | ||||||||
\(216\) | 2.69369 | 0.183282 | ||||||||
\(217\) | −17.2680 | −1.17223 | ||||||||
\(218\) | 1.60989 | 0.109035 | ||||||||
\(219\) | −1.70778 | −0.115401 | ||||||||
\(220\) | −8.45712 | −0.570179 | ||||||||
\(221\) | 5.78173 | 0.388922 | ||||||||
\(222\) | 0.467188 | 0.0313556 | ||||||||
\(223\) | 5.96131 | 0.399199 | 0.199599 | − | 0.979878i | \(-0.436036\pi\) | ||||
0.199599 | + | 0.979878i | \(0.436036\pi\) | |||||||
\(224\) | −36.0820 | −2.41083 | ||||||||
\(225\) | 9.88577 | 0.659052 | ||||||||
\(226\) | 38.1483 | 2.53759 | ||||||||
\(227\) | 17.1263 | 1.13671 | 0.568356 | − | 0.822782i | \(-0.307579\pi\) | ||||
0.568356 | + | 0.822782i | \(0.307579\pi\) | |||||||
\(228\) | 0.978997 | 0.0648357 | ||||||||
\(229\) | −1.92122 | −0.126958 | −0.0634789 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634789 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(230\) | −15.9637 | −1.05262 | ||||||||
\(231\) | −10.2914 | −0.677125 | ||||||||
\(232\) | −0.719483 | −0.0472364 | ||||||||
\(233\) | −24.4304 | −1.60049 | −0.800245 | − | 0.599673i | \(-0.795297\pi\) | ||||
−0.800245 | + | 0.599673i | \(0.795297\pi\) | |||||||
\(234\) | −6.02591 | −0.393926 | ||||||||
\(235\) | −5.95514 | −0.388471 | ||||||||
\(236\) | 19.8334 | 1.29105 | ||||||||
\(237\) | −7.70042 | −0.500196 | ||||||||
\(238\) | −47.3052 | −3.06634 | ||||||||
\(239\) | 0.0183458 | 0.00118669 | 0.000593345 | − | 1.00000i | \(-0.499811\pi\) | ||||
0.000593345 | 1.00000i | \(0.499811\pi\) | ||||||||
\(240\) | 2.27413 | 0.146795 | ||||||||
\(241\) | 6.72380 | 0.433118 | 0.216559 | − | 0.976270i | \(-0.430517\pi\) | ||||
0.216559 | + | 0.976270i | \(0.430517\pi\) | |||||||
\(242\) | −1.40471 | −0.0902980 | ||||||||
\(243\) | 14.6783 | 0.941611 | ||||||||
\(244\) | 0.242489 | 0.0155238 | ||||||||
\(245\) | −13.6089 | −0.869444 | ||||||||
\(246\) | 3.84956 | 0.245439 | ||||||||
\(247\) | −0.702446 | −0.0446956 | ||||||||
\(248\) | −2.78551 | −0.176880 | ||||||||
\(249\) | 7.79416 | 0.493935 | ||||||||
\(250\) | −19.5502 | −1.23646 | ||||||||
\(251\) | −24.7796 | −1.56408 | −0.782038 | − | 0.623231i | \(-0.785820\pi\) | ||||
−0.782038 | + | 0.623231i | \(0.785820\pi\) | |||||||
\(252\) | 26.6097 | 1.67625 | ||||||||
\(253\) | −24.7911 | −1.55860 | ||||||||
\(254\) | −35.7865 | −2.24544 | ||||||||
\(255\) | 3.62658 | 0.227105 | ||||||||
\(256\) | 9.14430 | 0.571519 | ||||||||
\(257\) | 28.8583 | 1.80013 | 0.900066 | − | 0.435754i | \(-0.143518\pi\) | ||||
0.900066 | + | 0.435754i | \(0.143518\pi\) | |||||||
\(258\) | 15.0982 | 0.939971 | ||||||||
\(259\) | 1.48027 | 0.0919792 | ||||||||
\(260\) | 2.81272 | 0.174437 | ||||||||
\(261\) | −2.54395 | −0.157466 | ||||||||
\(262\) | −10.0351 | −0.619972 | ||||||||
\(263\) | −10.3087 | −0.635663 | −0.317831 | − | 0.948147i | \(-0.602955\pi\) | ||||
−0.317831 | + | 0.948147i | \(0.602955\pi\) | |||||||
\(264\) | −1.66011 | −0.102173 | ||||||||
\(265\) | 13.6292 | 0.837232 | ||||||||
\(266\) | 5.74729 | 0.352389 | ||||||||
\(267\) | −2.42145 | −0.148190 | ||||||||
\(268\) | −32.3088 | −1.97357 | ||||||||
\(269\) | −30.4910 | −1.85907 | −0.929534 | − | 0.368736i | \(-0.879791\pi\) | ||||
−0.929534 | + | 0.368736i | \(0.879791\pi\) | |||||||
\(270\) | −8.23706 | −0.501292 | ||||||||
\(271\) | 24.1764 | 1.46861 | 0.734306 | − | 0.678819i | \(-0.237508\pi\) | ||||
0.734306 | + | 0.678819i | \(0.237508\pi\) | |||||||
\(272\) | 16.2335 | 0.984300 | ||||||||
\(273\) | 3.42278 | 0.207156 | ||||||||
\(274\) | −33.4853 | −2.02292 | ||||||||
\(275\) | −13.2773 | −0.800652 | ||||||||
\(276\) | −11.4913 | −0.691694 | ||||||||
\(277\) | 9.78687 | 0.588036 | 0.294018 | − | 0.955800i | \(-0.405007\pi\) | ||||
0.294018 | + | 0.955800i | \(0.405007\pi\) | |||||||
\(278\) | 2.08450 | 0.125020 | ||||||||
\(279\) | −9.84899 | −0.589643 | ||||||||
\(280\) | −3.38706 | −0.202415 | ||||||||
\(281\) | −15.3456 | −0.915441 | −0.457721 | − | 0.889096i | \(-0.651334\pi\) | ||||
−0.457721 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(282\) | −7.94256 | −0.472973 | ||||||||
\(283\) | 29.7960 | 1.77119 | 0.885593 | − | 0.464462i | \(-0.153752\pi\) | ||||
0.885593 | + | 0.464462i | \(0.153752\pi\) | |||||||
\(284\) | 4.28965 | 0.254544 | ||||||||
\(285\) | −0.440608 | −0.0260993 | ||||||||
\(286\) | 8.09323 | 0.478563 | ||||||||
\(287\) | 12.1972 | 0.719976 | ||||||||
\(288\) | −20.5797 | −1.21267 | ||||||||
\(289\) | 8.88768 | 0.522805 | ||||||||
\(290\) | 2.20012 | 0.129195 | ||||||||
\(291\) | 6.45817 | 0.378585 | ||||||||
\(292\) | −5.93057 | −0.347060 | ||||||||
\(293\) | −3.03022 | −0.177027 | −0.0885136 | − | 0.996075i | \(-0.528212\pi\) | ||||
−0.0885136 | + | 0.996075i | \(0.528212\pi\) | |||||||
\(294\) | −18.1507 | −1.05857 | ||||||||
\(295\) | −8.92624 | −0.519706 | ||||||||
\(296\) | 0.238782 | 0.0138789 | ||||||||
\(297\) | −12.7919 | −0.742261 | ||||||||
\(298\) | −28.5169 | −1.65194 | ||||||||
\(299\) | 8.24518 | 0.476831 | ||||||||
\(300\) | −6.15436 | −0.355322 | ||||||||
\(301\) | 47.8380 | 2.75733 | ||||||||
\(302\) | −38.1653 | −2.19616 | ||||||||
\(303\) | −8.92646 | −0.512812 | ||||||||
\(304\) | −1.97227 | −0.113118 | ||||||||
\(305\) | −0.109135 | −0.00624904 | ||||||||
\(306\) | −26.9810 | −1.54240 | ||||||||
\(307\) | −6.49343 | −0.370599 | −0.185300 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185300 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(308\) | −35.7387 | −2.03640 | ||||||||
\(309\) | −5.48632 | −0.312106 | ||||||||
\(310\) | 8.51783 | 0.483780 | ||||||||
\(311\) | −12.2569 | −0.695024 | −0.347512 | − | 0.937676i | \(-0.612973\pi\) | ||||
−0.347512 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(312\) | 0.552129 | 0.0312581 | ||||||||
\(313\) | 18.9791 | 1.07276 | 0.536381 | − | 0.843976i | \(-0.319791\pi\) | ||||
0.536381 | + | 0.843976i | \(0.319791\pi\) | |||||||
\(314\) | −34.9699 | −1.97346 | ||||||||
\(315\) | −11.9759 | −0.674768 | ||||||||
\(316\) | −26.7411 | −1.50430 | ||||||||
\(317\) | −13.8489 | −0.777829 | −0.388915 | − | 0.921274i | \(-0.627150\pi\) | ||||
−0.388915 | + | 0.921274i | \(0.627150\pi\) | |||||||
\(318\) | 18.1776 | 1.01935 | ||||||||
\(319\) | 3.41671 | 0.191299 | ||||||||
\(320\) | 11.0632 | 0.618453 | ||||||||
\(321\) | 0.963360 | 0.0537695 | ||||||||
\(322\) | −67.4606 | −3.75943 | ||||||||
\(323\) | −3.14520 | −0.175003 | ||||||||
\(324\) | 11.9685 | 0.664918 | ||||||||
\(325\) | 4.41585 | 0.244947 | ||||||||
\(326\) | 10.8084 | 0.598619 | ||||||||
\(327\) | −0.521556 | −0.0288421 | ||||||||
\(328\) | 1.96753 | 0.108639 | ||||||||
\(329\) | −25.1657 | −1.38743 | ||||||||
\(330\) | 5.07646 | 0.279450 | ||||||||
\(331\) | 20.2594 | 1.11355 | 0.556777 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556777 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(332\) | 27.0666 | 1.48547 | ||||||||
\(333\) | 0.844284 | 0.0462665 | ||||||||
\(334\) | 53.7557 | 2.94138 | ||||||||
\(335\) | 14.5409 | 0.794454 | ||||||||
\(336\) | 9.61021 | 0.524280 | ||||||||
\(337\) | −7.48842 | −0.407920 | −0.203960 | − | 0.978979i | \(-0.565381\pi\) | ||||
−0.203960 | + | 0.978979i | \(0.565381\pi\) | |||||||
\(338\) | 24.4069 | 1.32756 | ||||||||
\(339\) | −12.3589 | −0.671245 | ||||||||
\(340\) | 12.5939 | 0.683002 | ||||||||
\(341\) | 13.2279 | 0.716332 | ||||||||
\(342\) | 3.27802 | 0.177255 | ||||||||
\(343\) | −26.2879 | −1.41942 | ||||||||
\(344\) | 7.71675 | 0.416059 | ||||||||
\(345\) | 5.17177 | 0.278439 | ||||||||
\(346\) | 27.5982 | 1.48369 | ||||||||
\(347\) | 34.9403 | 1.87569 | 0.937846 | − | 0.347053i | \(-0.112817\pi\) | ||||
0.937846 | + | 0.347053i | \(0.112817\pi\) | |||||||
\(348\) | 1.58373 | 0.0848966 | ||||||||
\(349\) | −13.7041 | −0.733565 | −0.366782 | − | 0.930307i | \(-0.619541\pi\) | ||||
−0.366782 | + | 0.930307i | \(0.619541\pi\) | |||||||
\(350\) | −36.1297 | −1.93122 | ||||||||
\(351\) | 4.25440 | 0.227083 | ||||||||
\(352\) | 27.6401 | 1.47322 | ||||||||
\(353\) | 29.1644 | 1.55227 | 0.776133 | − | 0.630569i | \(-0.217179\pi\) | ||||
0.776133 | + | 0.630569i | \(0.217179\pi\) | |||||||
\(354\) | −11.9052 | −0.632754 | ||||||||
\(355\) | −1.93060 | −0.102466 | ||||||||
\(356\) | −8.40889 | −0.445670 | ||||||||
\(357\) | 15.3255 | 0.811110 | ||||||||
\(358\) | −41.8993 | −2.21445 | ||||||||
\(359\) | 0.873559 | 0.0461047 | 0.0230523 | − | 0.999734i | \(-0.492662\pi\) | ||||
0.0230523 | + | 0.999734i | \(0.492662\pi\) | |||||||
\(360\) | −1.93184 | −0.101817 | ||||||||
\(361\) | −18.6179 | −0.979888 | ||||||||
\(362\) | −20.2588 | −1.06478 | ||||||||
\(363\) | 0.455084 | 0.0238857 | ||||||||
\(364\) | 11.8862 | 0.623006 | ||||||||
\(365\) | 2.66911 | 0.139708 | ||||||||
\(366\) | −0.145556 | −0.00760835 | ||||||||
\(367\) | 10.9683 | 0.572541 | 0.286270 | − | 0.958149i | \(-0.407584\pi\) | ||||
0.286270 | + | 0.958149i | \(0.407584\pi\) | |||||||
\(368\) | 23.1502 | 1.20679 | ||||||||
\(369\) | 6.95677 | 0.362155 | ||||||||
\(370\) | −0.730173 | −0.0379599 | ||||||||
\(371\) | 57.5951 | 2.99019 | ||||||||
\(372\) | 6.13146 | 0.317901 | ||||||||
\(373\) | 16.9007 | 0.875087 | 0.437544 | − | 0.899197i | \(-0.355849\pi\) | ||||
0.437544 | + | 0.899197i | \(0.355849\pi\) | |||||||
\(374\) | 36.2374 | 1.87379 | ||||||||
\(375\) | 6.33369 | 0.327070 | ||||||||
\(376\) | −4.05948 | −0.209352 | ||||||||
\(377\) | −1.13635 | −0.0585249 | ||||||||
\(378\) | −34.8088 | −1.79037 | ||||||||
\(379\) | −7.36209 | −0.378165 | −0.189083 | − | 0.981961i | \(-0.560551\pi\) | ||||
−0.189083 | + | 0.981961i | \(0.560551\pi\) | |||||||
\(380\) | −1.53009 | −0.0784918 | ||||||||
\(381\) | 11.5938 | 0.593966 | ||||||||
\(382\) | 49.5670 | 2.53607 | ||||||||
\(383\) | 18.4873 | 0.944654 | 0.472327 | − | 0.881423i | \(-0.343414\pi\) | ||||
0.472327 | + | 0.881423i | \(0.343414\pi\) | |||||||
\(384\) | 3.82915 | 0.195406 | ||||||||
\(385\) | 16.0846 | 0.819746 | ||||||||
\(386\) | 1.95235 | 0.0993720 | ||||||||
\(387\) | 27.2848 | 1.38697 | ||||||||
\(388\) | 22.4271 | 1.13856 | ||||||||
\(389\) | 7.53765 | 0.382174 | 0.191087 | − | 0.981573i | \(-0.438799\pi\) | ||||
0.191087 | + | 0.981573i | \(0.438799\pi\) | |||||||
\(390\) | −1.68836 | −0.0854934 | ||||||||
\(391\) | 36.9177 | 1.86701 | ||||||||
\(392\) | −9.27689 | −0.468554 | ||||||||
\(393\) | 3.25108 | 0.163995 | ||||||||
\(394\) | 17.8474 | 0.899137 | ||||||||
\(395\) | 12.0351 | 0.605551 | ||||||||
\(396\) | −20.3839 | −1.02433 | ||||||||
\(397\) | −0.585866 | −0.0294038 | −0.0147019 | − | 0.999892i | \(-0.504680\pi\) | ||||
−0.0147019 | + | 0.999892i | \(0.504680\pi\) | |||||||
\(398\) | 0.943550 | 0.0472959 | ||||||||
\(399\) | −1.86195 | −0.0932142 | ||||||||
\(400\) | 12.3985 | 0.619924 | ||||||||
\(401\) | −8.79080 | −0.438992 | −0.219496 | − | 0.975613i | \(-0.570441\pi\) | ||||
−0.219496 | + | 0.975613i | \(0.570441\pi\) | |||||||
\(402\) | 19.3936 | 0.967267 | ||||||||
\(403\) | −4.39942 | −0.219151 | ||||||||
\(404\) | −30.9987 | −1.54224 | ||||||||
\(405\) | −5.38655 | −0.267660 | ||||||||
\(406\) | 9.29741 | 0.461423 | ||||||||
\(407\) | −1.13393 | −0.0562071 | ||||||||
\(408\) | 2.47215 | 0.122390 | ||||||||
\(409\) | 23.5170 | 1.16284 | 0.581421 | − | 0.813603i | \(-0.302497\pi\) | ||||
0.581421 | + | 0.813603i | \(0.302497\pi\) | |||||||
\(410\) | −6.01652 | −0.297135 | ||||||||
\(411\) | 10.8482 | 0.535104 | ||||||||
\(412\) | −19.0522 | −0.938635 | ||||||||
\(413\) | −37.7212 | −1.85614 | ||||||||
\(414\) | −38.4768 | −1.89103 | ||||||||
\(415\) | −12.1816 | −0.597970 | ||||||||
\(416\) | −9.19270 | −0.450709 | ||||||||
\(417\) | −0.675318 | −0.0330704 | ||||||||
\(418\) | −4.40263 | −0.215339 | ||||||||
\(419\) | 20.1236 | 0.983100 | 0.491550 | − | 0.870849i | \(-0.336430\pi\) | ||||
0.491550 | + | 0.870849i | \(0.336430\pi\) | |||||||
\(420\) | 7.45559 | 0.363795 | ||||||||
\(421\) | 6.37619 | 0.310756 | 0.155378 | − | 0.987855i | \(-0.450340\pi\) | ||||
0.155378 | + | 0.987855i | \(0.450340\pi\) | |||||||
\(422\) | −36.1594 | −1.76021 | ||||||||
\(423\) | −14.3535 | −0.697891 | ||||||||
\(424\) | 9.29067 | 0.451195 | ||||||||
\(425\) | 19.7719 | 0.959080 | ||||||||
\(426\) | −2.57490 | −0.124754 | ||||||||
\(427\) | −0.461190 | −0.0223185 | ||||||||
\(428\) | 3.34543 | 0.161708 | ||||||||
\(429\) | −2.62197 | −0.126590 | ||||||||
\(430\) | −23.5971 | −1.13795 | ||||||||
\(431\) | −0.0942294 | −0.00453887 | −0.00226944 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226944 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(432\) | 11.9452 | 0.574713 | ||||||||
\(433\) | 11.3307 | 0.544519 | 0.272260 | − | 0.962224i | \(-0.412229\pi\) | ||||
0.272260 | + | 0.962224i | \(0.412229\pi\) | |||||||
\(434\) | 35.9953 | 1.72783 | ||||||||
\(435\) | −0.712772 | −0.0341748 | ||||||||
\(436\) | −1.81119 | −0.0867404 | ||||||||
\(437\) | −4.48528 | −0.214560 | ||||||||
\(438\) | 3.55988 | 0.170098 | ||||||||
\(439\) | 13.7418 | 0.655860 | 0.327930 | − | 0.944702i | \(-0.393649\pi\) | ||||
0.327930 | + | 0.944702i | \(0.393649\pi\) | |||||||
\(440\) | 2.59460 | 0.123693 | ||||||||
\(441\) | −32.8012 | −1.56196 | ||||||||
\(442\) | −12.0521 | −0.573258 | ||||||||
\(443\) | −8.26354 | −0.392613 | −0.196306 | − | 0.980543i | \(-0.562895\pi\) | ||||
−0.196306 | + | 0.980543i | \(0.562895\pi\) | |||||||
\(444\) | −0.525606 | −0.0249442 | ||||||||
\(445\) | 3.78451 | 0.179403 | ||||||||
\(446\) | −12.4264 | −0.588406 | ||||||||
\(447\) | 9.23864 | 0.436973 | ||||||||
\(448\) | 46.7518 | 2.20881 | ||||||||
\(449\) | −26.3231 | −1.24226 | −0.621132 | − | 0.783706i | \(-0.713327\pi\) | ||||
−0.621132 | + | 0.783706i | \(0.713327\pi\) | |||||||
\(450\) | −20.6069 | −0.971420 | ||||||||
\(451\) | −9.34346 | −0.439966 | ||||||||
\(452\) | −42.9185 | −2.01872 | ||||||||
\(453\) | 12.3644 | 0.580931 | ||||||||
\(454\) | −35.6999 | −1.67548 | ||||||||
\(455\) | −5.34950 | −0.250789 | ||||||||
\(456\) | −0.300352 | −0.0140653 | ||||||||
\(457\) | 20.5645 | 0.961968 | 0.480984 | − | 0.876729i | \(-0.340280\pi\) | ||||
0.480984 | + | 0.876729i | \(0.340280\pi\) | |||||||
\(458\) | 4.00479 | 0.187132 | ||||||||
\(459\) | 19.0491 | 0.889134 | ||||||||
\(460\) | 17.9599 | 0.837383 | ||||||||
\(461\) | 18.5076 | 0.861987 | 0.430994 | − | 0.902355i | \(-0.358163\pi\) | ||||
0.430994 | + | 0.902355i | \(0.358163\pi\) | |||||||
\(462\) | 21.4525 | 0.998060 | ||||||||
\(463\) | −8.50393 | −0.395211 | −0.197606 | − | 0.980282i | \(-0.563317\pi\) | ||||
−0.197606 | + | 0.980282i | \(0.563317\pi\) | |||||||
\(464\) | −3.19055 | −0.148118 | ||||||||
\(465\) | −2.75952 | −0.127970 | ||||||||
\(466\) | 50.9253 | 2.35907 | ||||||||
\(467\) | 3.71225 | 0.171782 | 0.0858911 | − | 0.996305i | \(-0.472626\pi\) | ||||
0.0858911 | + | 0.996305i | \(0.472626\pi\) | |||||||
\(468\) | 6.77941 | 0.313378 | ||||||||
\(469\) | 61.4480 | 2.83741 | ||||||||
\(470\) | 12.4135 | 0.572593 | ||||||||
\(471\) | 11.3292 | 0.522022 | ||||||||
\(472\) | −6.08481 | −0.280076 | ||||||||
\(473\) | −36.6455 | −1.68496 | ||||||||
\(474\) | 16.0516 | 0.737273 | ||||||||
\(475\) | −2.40217 | −0.110219 | ||||||||
\(476\) | 53.2204 | 2.43935 | ||||||||
\(477\) | 32.8499 | 1.50409 | ||||||||
\(478\) | −0.0382419 | −0.00174914 | ||||||||
\(479\) | −22.3175 | −1.01971 | −0.509856 | − | 0.860260i | \(-0.670301\pi\) | ||||
−0.509856 | + | 0.860260i | \(0.670301\pi\) | |||||||
\(480\) | −5.76610 | −0.263185 | ||||||||
\(481\) | 0.377131 | 0.0171957 | ||||||||
\(482\) | −14.0158 | −0.638402 | ||||||||
\(483\) | 21.8552 | 0.994448 | ||||||||
\(484\) | 1.58036 | 0.0718344 | ||||||||
\(485\) | −10.0936 | −0.458325 | ||||||||
\(486\) | −30.5969 | −1.38790 | ||||||||
\(487\) | −8.58459 | −0.389005 | −0.194502 | − | 0.980902i | \(-0.562309\pi\) | ||||
−0.194502 | + | 0.980902i | \(0.562309\pi\) | |||||||
\(488\) | −0.0743946 | −0.00336768 | ||||||||
\(489\) | −3.50159 | −0.158347 | ||||||||
\(490\) | 28.3679 | 1.28153 | ||||||||
\(491\) | 11.7907 | 0.532109 | 0.266054 | − | 0.963958i | \(-0.414280\pi\) | ||||
0.266054 | + | 0.963958i | \(0.414280\pi\) | |||||||
\(492\) | −4.33092 | −0.195253 | ||||||||
\(493\) | −5.08799 | −0.229152 | ||||||||
\(494\) | 1.46425 | 0.0658798 | ||||||||
\(495\) | 9.17399 | 0.412340 | ||||||||
\(496\) | −12.3523 | −0.554636 | ||||||||
\(497\) | −8.15848 | −0.365958 | ||||||||
\(498\) | −16.2470 | −0.728043 | ||||||||
\(499\) | −27.6417 | −1.23741 | −0.618706 | − | 0.785623i | \(-0.712343\pi\) | ||||
−0.618706 | + | 0.785623i | \(0.712343\pi\) | |||||||
\(500\) | 21.9949 | 0.983640 | ||||||||
\(501\) | −17.4153 | −0.778056 | ||||||||
\(502\) | 51.6532 | 2.30540 | ||||||||
\(503\) | 5.36667 | 0.239288 | 0.119644 | − | 0.992817i | \(-0.461825\pi\) | ||||
0.119644 | + | 0.992817i | \(0.461825\pi\) | |||||||
\(504\) | −8.16372 | −0.363641 | ||||||||
\(505\) | 13.9513 | 0.620824 | ||||||||
\(506\) | 51.6772 | 2.29733 | ||||||||
\(507\) | −7.90710 | −0.351167 | ||||||||
\(508\) | 40.2613 | 1.78631 | ||||||||
\(509\) | 2.61691 | 0.115993 | 0.0579964 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579964 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(510\) | −7.55962 | −0.334746 | ||||||||
\(511\) | 11.2793 | 0.498968 | ||||||||
\(512\) | −30.4016 | −1.34357 | ||||||||
\(513\) | −2.31435 | −0.102181 | ||||||||
\(514\) | −60.1553 | −2.65334 | ||||||||
\(515\) | 8.57464 | 0.377844 | ||||||||
\(516\) | −16.9861 | −0.747771 | ||||||||
\(517\) | 19.2778 | 0.847836 | ||||||||
\(518\) | −3.08562 | −0.135574 | ||||||||
\(519\) | −8.94100 | −0.392466 | ||||||||
\(520\) | −0.862929 | −0.0378419 | ||||||||
\(521\) | −40.4559 | −1.77241 | −0.886203 | − | 0.463298i | \(-0.846666\pi\) | ||||
−0.886203 | + | 0.463298i | \(0.846666\pi\) | |||||||
\(522\) | 5.30287 | 0.232100 | ||||||||
\(523\) | 15.2392 | 0.666365 | 0.333182 | − | 0.942862i | \(-0.391878\pi\) | ||||
0.333182 | + | 0.942862i | \(0.391878\pi\) | |||||||
\(524\) | 11.2899 | 0.493203 | ||||||||
\(525\) | 11.7050 | 0.510846 | ||||||||
\(526\) | 21.4886 | 0.936946 | ||||||||
\(527\) | −19.6984 | −0.858074 | ||||||||
\(528\) | −7.36175 | −0.320379 | ||||||||
\(529\) | 29.6474 | 1.28902 | ||||||||
\(530\) | −28.4100 | −1.23405 | ||||||||
\(531\) | −21.5146 | −0.933656 | ||||||||
\(532\) | −6.46596 | −0.280335 | ||||||||
\(533\) | 3.10750 | 0.134601 | ||||||||
\(534\) | 5.04751 | 0.218427 | ||||||||
\(535\) | −1.50565 | −0.0650948 | ||||||||
\(536\) | 9.91219 | 0.428141 | ||||||||
\(537\) | 13.5741 | 0.585767 | ||||||||
\(538\) | 63.5586 | 2.74021 | ||||||||
\(539\) | 44.0544 | 1.89756 | ||||||||
\(540\) | 9.26706 | 0.398791 | ||||||||
\(541\) | 14.2505 | 0.612679 | 0.306339 | − | 0.951922i | \(-0.400896\pi\) | ||||
0.306339 | + | 0.951922i | \(0.400896\pi\) | |||||||
\(542\) | −50.3958 | −2.16469 | ||||||||
\(543\) | 6.56326 | 0.281657 | ||||||||
\(544\) | −41.1603 | −1.76473 | ||||||||
\(545\) | 0.815146 | 0.0349170 | ||||||||
\(546\) | −7.13480 | −0.305341 | ||||||||
\(547\) | −38.2495 | −1.63543 | −0.817716 | − | 0.575621i | \(-0.804760\pi\) | ||||
−0.817716 | + | 0.575621i | \(0.804760\pi\) | |||||||
\(548\) | 37.6724 | 1.60928 | ||||||||
\(549\) | −0.263044 | −0.0112264 | ||||||||
\(550\) | 27.6766 | 1.18014 | ||||||||
\(551\) | 0.618161 | 0.0263345 | ||||||||
\(552\) | 3.52547 | 0.150054 | ||||||||
\(553\) | 50.8588 | 2.16273 | ||||||||
\(554\) | −20.4008 | −0.866746 | ||||||||
\(555\) | 0.236554 | 0.0100412 | ||||||||
\(556\) | −2.34516 | −0.0994569 | ||||||||
\(557\) | −11.0649 | −0.468835 | −0.234418 | − | 0.972136i | \(-0.575318\pi\) | ||||
−0.234418 | + | 0.972136i | \(0.575318\pi\) | |||||||
\(558\) | 20.5303 | 0.869115 | ||||||||
\(559\) | 12.1878 | 0.515489 | ||||||||
\(560\) | −15.0199 | −0.634707 | ||||||||
\(561\) | −11.7398 | −0.495656 | ||||||||
\(562\) | 31.9880 | 1.34933 | ||||||||
\(563\) | −35.9931 | −1.51693 | −0.758463 | − | 0.651716i | \(-0.774050\pi\) | ||||
−0.758463 | + | 0.651716i | \(0.774050\pi\) | |||||||
\(564\) | 8.93573 | 0.376262 | ||||||||
\(565\) | 19.3159 | 0.812627 | ||||||||
\(566\) | −62.1098 | −2.61067 | ||||||||
\(567\) | −22.7629 | −0.955952 | ||||||||
\(568\) | −1.31605 | −0.0552200 | ||||||||
\(569\) | 32.8236 | 1.37604 | 0.688018 | − | 0.725693i | \(-0.258481\pi\) | ||||
0.688018 | + | 0.725693i | \(0.258481\pi\) | |||||||
\(570\) | 0.918449 | 0.0384696 | ||||||||
\(571\) | 27.7249 | 1.16025 | 0.580125 | − | 0.814527i | \(-0.303004\pi\) | ||||
0.580125 | + | 0.814527i | \(0.303004\pi\) | |||||||
\(572\) | −9.10524 | −0.380709 | ||||||||
\(573\) | −16.0582 | −0.670842 | ||||||||
\(574\) | −25.4251 | −1.06122 | ||||||||
\(575\) | 28.1962 | 1.17586 | ||||||||
\(576\) | 26.6653 | 1.11106 | ||||||||
\(577\) | 8.10036 | 0.337223 | 0.168611 | − | 0.985683i | \(-0.446072\pi\) | ||||
0.168611 | + | 0.985683i | \(0.446072\pi\) | |||||||
\(578\) | −18.5264 | −0.770597 | ||||||||
\(579\) | −0.632503 | −0.0262859 | ||||||||
\(580\) | −2.47523 | −0.102778 | ||||||||
\(581\) | −51.4778 | −2.13566 | ||||||||
\(582\) | −13.4621 | −0.558021 | ||||||||
\(583\) | −44.1198 | −1.82726 | ||||||||
\(584\) | 1.81947 | 0.0752902 | ||||||||
\(585\) | −3.05114 | −0.126149 | ||||||||
\(586\) | 6.31650 | 0.260932 | ||||||||
\(587\) | −8.07451 | −0.333270 | −0.166635 | − | 0.986019i | \(-0.553290\pi\) | ||||
−0.166635 | + | 0.986019i | \(0.553290\pi\) | |||||||
\(588\) | 20.4203 | 0.842119 | ||||||||
\(589\) | 2.39323 | 0.0986115 | ||||||||
\(590\) | 18.6068 | 0.766029 | ||||||||
\(591\) | −5.78201 | −0.237840 | ||||||||
\(592\) | 1.05888 | 0.0435196 | ||||||||
\(593\) | 26.5293 | 1.08943 | 0.544713 | − | 0.838622i | \(-0.316639\pi\) | ||||
0.544713 | + | 0.838622i | \(0.316639\pi\) | |||||||
\(594\) | 26.6647 | 1.09407 | ||||||||
\(595\) | −23.9524 | −0.981951 | ||||||||
\(596\) | 32.0828 | 1.31416 | ||||||||
\(597\) | −0.305682 | −0.0125107 | ||||||||
\(598\) | −17.1871 | −0.702833 | ||||||||
\(599\) | −10.1086 | −0.413026 | −0.206513 | − | 0.978444i | \(-0.566212\pi\) | ||||
−0.206513 | + | 0.978444i | \(0.566212\pi\) | |||||||
\(600\) | 1.88813 | 0.0770825 | ||||||||
\(601\) | 7.44814 | 0.303816 | 0.151908 | − | 0.988395i | \(-0.451458\pi\) | ||||
0.151908 | + | 0.988395i | \(0.451458\pi\) | |||||||
\(602\) | −99.7185 | −4.06422 | ||||||||
\(603\) | 35.0475 | 1.42724 | ||||||||
\(604\) | 42.9376 | 1.74711 | ||||||||
\(605\) | −0.711256 | −0.0289167 | ||||||||
\(606\) | 18.6073 | 0.755868 | ||||||||
\(607\) | 28.7249 | 1.16591 | 0.582954 | − | 0.812505i | \(-0.301897\pi\) | ||||
0.582954 | + | 0.812505i | \(0.301897\pi\) | |||||||
\(608\) | 5.00072 | 0.202806 | ||||||||
\(609\) | −3.01208 | −0.122056 | ||||||||
\(610\) | 0.227492 | 0.00921088 | ||||||||
\(611\) | −6.41152 | −0.259382 | ||||||||
\(612\) | 30.3547 | 1.22702 | ||||||||
\(613\) | 8.55372 | 0.345482 | 0.172741 | − | 0.984967i | \(-0.444738\pi\) | ||||
0.172741 | + | 0.984967i | \(0.444738\pi\) | |||||||
\(614\) | 13.5356 | 0.546251 | ||||||||
\(615\) | 1.94917 | 0.0785983 | ||||||||
\(616\) | 10.9645 | 0.441771 | ||||||||
\(617\) | 16.6510 | 0.670344 | 0.335172 | − | 0.942157i | \(-0.391206\pi\) | ||||
0.335172 | + | 0.942157i | \(0.391206\pi\) | |||||||
\(618\) | 11.4363 | 0.460034 | ||||||||
\(619\) | 2.74701 | 0.110412 | 0.0552058 | − | 0.998475i | \(-0.482419\pi\) | ||||
0.0552058 | + | 0.998475i | \(0.482419\pi\) | |||||||
\(620\) | −9.58293 | −0.384860 | ||||||||
\(621\) | 27.1654 | 1.09011 | ||||||||
\(622\) | 25.5495 | 1.02444 | ||||||||
\(623\) | 15.9928 | 0.640740 | ||||||||
\(624\) | 2.44842 | 0.0980151 | ||||||||
\(625\) | 9.53099 | 0.381240 | ||||||||
\(626\) | −39.5620 | −1.58122 | ||||||||
\(627\) | 1.42632 | 0.0569617 | ||||||||
\(628\) | 39.3426 | 1.56994 | ||||||||
\(629\) | 1.68860 | 0.0673289 | ||||||||
\(630\) | 24.9639 | 0.994586 | ||||||||
\(631\) | −48.8148 | −1.94329 | −0.971644 | − | 0.236449i | \(-0.924017\pi\) | ||||
−0.971644 | + | 0.236449i | \(0.924017\pi\) | |||||||
\(632\) | 8.20403 | 0.326339 | ||||||||
\(633\) | 11.7146 | 0.465612 | ||||||||
\(634\) | 28.8680 | 1.14649 | ||||||||
\(635\) | −18.1200 | −0.719071 | ||||||||
\(636\) | −20.4506 | −0.810920 | ||||||||
\(637\) | −14.6519 | −0.580529 | ||||||||
\(638\) | −7.12214 | −0.281968 | ||||||||
\(639\) | −4.65327 | −0.184080 | ||||||||
\(640\) | −5.98463 | −0.236563 | ||||||||
\(641\) | 20.4597 | 0.808109 | 0.404055 | − | 0.914735i | \(-0.367601\pi\) | ||||
0.404055 | + | 0.914735i | \(0.367601\pi\) | |||||||
\(642\) | −2.00813 | −0.0792545 | ||||||||
\(643\) | 42.4320 | 1.67335 | 0.836677 | − | 0.547697i | \(-0.184495\pi\) | ||||
0.836677 | + | 0.547697i | \(0.184495\pi\) | |||||||
\(644\) | 75.8961 | 2.99073 | ||||||||
\(645\) | 7.64477 | 0.301012 | ||||||||
\(646\) | 6.55618 | 0.257949 | ||||||||
\(647\) | −42.3907 | −1.66655 | −0.833276 | − | 0.552858i | \(-0.813537\pi\) | ||||
−0.833276 | + | 0.552858i | \(0.813537\pi\) | |||||||
\(648\) | −3.67188 | −0.144245 | ||||||||
\(649\) | 28.8957 | 1.13426 | ||||||||
\(650\) | −9.20486 | −0.361044 | ||||||||
\(651\) | −11.6614 | −0.457046 | ||||||||
\(652\) | −12.1599 | −0.476217 | ||||||||
\(653\) | 0.0404139 | 0.00158152 | 0.000790758 | − | 1.00000i | \(-0.499748\pi\) | ||||
0.000790758 | 1.00000i | \(0.499748\pi\) | ||||||||
\(654\) | 1.08719 | 0.0425123 | ||||||||
\(655\) | −5.08115 | −0.198537 | ||||||||
\(656\) | 8.72500 | 0.340654 | ||||||||
\(657\) | 6.43328 | 0.250986 | ||||||||
\(658\) | 52.4580 | 2.04503 | ||||||||
\(659\) | 5.10664 | 0.198927 | 0.0994633 | − | 0.995041i | \(-0.468287\pi\) | ||||
0.0994633 | + | 0.995041i | \(0.468287\pi\) | |||||||
\(660\) | −5.71124 | −0.222310 | ||||||||
\(661\) | 30.2222 | 1.17551 | 0.587754 | − | 0.809039i | \(-0.300012\pi\) | ||||
0.587754 | + | 0.809039i | \(0.300012\pi\) | |||||||
\(662\) | −42.2307 | −1.64134 | ||||||||
\(663\) | 3.90451 | 0.151638 | ||||||||
\(664\) | −8.30390 | −0.322254 | ||||||||
\(665\) | 2.91007 | 0.112848 | ||||||||
\(666\) | −1.75991 | −0.0681952 | ||||||||
\(667\) | −7.25585 | −0.280948 | ||||||||
\(668\) | −60.4775 | −2.33994 | ||||||||
\(669\) | 4.02578 | 0.155646 | ||||||||
\(670\) | −30.3106 | −1.17100 | ||||||||
\(671\) | 0.353287 | 0.0136385 | ||||||||
\(672\) | −24.3668 | −0.939970 | ||||||||
\(673\) | −34.8039 | −1.34159 | −0.670796 | − | 0.741642i | \(-0.734047\pi\) | ||||
−0.670796 | + | 0.741642i | \(0.734047\pi\) | |||||||
\(674\) | 15.6096 | 0.601261 | ||||||||
\(675\) | 14.5489 | 0.559987 | ||||||||
\(676\) | −27.4588 | −1.05611 | ||||||||
\(677\) | −38.5040 | −1.47983 | −0.739914 | − | 0.672702i | \(-0.765134\pi\) | ||||
−0.739914 | + | 0.672702i | \(0.765134\pi\) | |||||||
\(678\) | 25.7622 | 0.989393 | ||||||||
\(679\) | −42.6541 | −1.63691 | ||||||||
\(680\) | −3.86376 | −0.148168 | ||||||||
\(681\) | 11.5657 | 0.443198 | ||||||||
\(682\) | −27.5736 | −1.05585 | ||||||||
\(683\) | 41.7040 | 1.59576 | 0.797880 | − | 0.602817i | \(-0.205955\pi\) | ||||
0.797880 | + | 0.602817i | \(0.205955\pi\) | |||||||
\(684\) | −3.68792 | −0.141011 | ||||||||
\(685\) | −16.9548 | −0.647811 | ||||||||
\(686\) | 54.7973 | 2.09217 | ||||||||
\(687\) | −1.29743 | −0.0495002 | ||||||||
\(688\) | 34.2199 | 1.30462 | ||||||||
\(689\) | 14.6736 | 0.559021 | ||||||||
\(690\) | −10.7806 | −0.410409 | ||||||||
\(691\) | −16.5973 | −0.631393 | −0.315696 | − | 0.948860i | \(-0.602238\pi\) | ||||
−0.315696 | + | 0.948860i | \(0.602238\pi\) | |||||||
\(692\) | −31.0492 | −1.18031 | ||||||||
\(693\) | 38.7681 | 1.47268 | ||||||||
\(694\) | −72.8331 | −2.76471 | ||||||||
\(695\) | 1.05546 | 0.0400360 | ||||||||
\(696\) | −0.485880 | −0.0184172 | ||||||||
\(697\) | 13.9138 | 0.527024 | ||||||||
\(698\) | 28.5663 | 1.08125 | ||||||||
\(699\) | −16.4983 | −0.624023 | ||||||||
\(700\) | 40.6475 | 1.53633 | ||||||||
\(701\) | 14.7383 | 0.556659 | 0.278330 | − | 0.960486i | \(-0.410219\pi\) | ||||
0.278330 | + | 0.960486i | \(0.410219\pi\) | |||||||
\(702\) | −8.86832 | −0.334713 | ||||||||
\(703\) | −0.205155 | −0.00773756 | ||||||||
\(704\) | −35.8135 | −1.34977 | ||||||||
\(705\) | −4.02161 | −0.151463 | ||||||||
\(706\) | −60.7934 | −2.28799 | ||||||||
\(707\) | 58.9564 | 2.21728 | ||||||||
\(708\) | 13.3939 | 0.503373 | ||||||||
\(709\) | 6.19457 | 0.232642 | 0.116321 | − | 0.993212i | \(-0.462890\pi\) | ||||
0.116321 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(710\) | 4.02435 | 0.151031 | ||||||||
\(711\) | 29.0078 | 1.08788 | ||||||||
\(712\) | 2.57981 | 0.0966824 | ||||||||
\(713\) | −28.0913 | −1.05203 | ||||||||
\(714\) | −31.9460 | −1.19555 | ||||||||
\(715\) | 4.09790 | 0.153253 | ||||||||
\(716\) | 47.1385 | 1.76165 | ||||||||
\(717\) | 0.0123892 | 0.000462684 0 | ||||||||
\(718\) | −1.82094 | −0.0679568 | ||||||||
\(719\) | −32.4660 | −1.21078 | −0.605388 | − | 0.795930i | \(-0.706982\pi\) | ||||
−0.605388 | + | 0.795930i | \(0.706982\pi\) | |||||||
\(720\) | −8.56675 | −0.319264 | ||||||||
\(721\) | 36.2354 | 1.34948 | ||||||||
\(722\) | 38.8090 | 1.44432 | ||||||||
\(723\) | 4.54070 | 0.168870 | ||||||||
\(724\) | 22.7921 | 0.847061 | ||||||||
\(725\) | −3.88600 | −0.144322 | ||||||||
\(726\) | −0.948624 | −0.0352067 | ||||||||
\(727\) | 28.3178 | 1.05025 | 0.525125 | − | 0.851025i | \(-0.324019\pi\) | ||||
0.525125 | + | 0.851025i | \(0.324019\pi\) | |||||||
\(728\) | −3.64663 | −0.135153 | ||||||||
\(729\) | −5.39802 | −0.199927 | ||||||||
\(730\) | −5.56378 | −0.205925 | ||||||||
\(731\) | 54.5708 | 2.01837 | ||||||||
\(732\) | 0.163757 | 0.00605264 | ||||||||
\(733\) | 19.1050 | 0.705659 | 0.352829 | − | 0.935688i | \(-0.385220\pi\) | ||||
0.352829 | + | 0.935688i | \(0.385220\pi\) | |||||||
\(734\) | −22.8635 | −0.843906 | ||||||||
\(735\) | −9.19036 | −0.338992 | ||||||||
\(736\) | −58.6975 | −2.16362 | ||||||||
\(737\) | −47.0713 | −1.73389 | ||||||||
\(738\) | −14.5014 | −0.533805 | ||||||||
\(739\) | −44.5396 | −1.63842 | −0.819208 | − | 0.573497i | \(-0.805586\pi\) | ||||
−0.819208 | + | 0.573497i | \(0.805586\pi\) | |||||||
\(740\) | 0.821477 | 0.0301981 | ||||||||
\(741\) | −0.474374 | −0.0174266 | ||||||||
\(742\) | −120.057 | −4.40744 | ||||||||
\(743\) | −50.2070 | −1.84192 | −0.920959 | − | 0.389661i | \(-0.872592\pi\) | ||||
−0.920959 | + | 0.389661i | \(0.872592\pi\) | |||||||
\(744\) | −1.88110 | −0.0689646 | ||||||||
\(745\) | −14.4392 | −0.529011 | ||||||||
\(746\) | −35.2297 | −1.28985 | ||||||||
\(747\) | −29.3609 | −1.07426 | ||||||||
\(748\) | −40.7686 | −1.49065 | ||||||||
\(749\) | −6.36267 | −0.232487 | ||||||||
\(750\) | −13.2026 | −0.482091 | ||||||||
\(751\) | 2.22914 | 0.0813424 | 0.0406712 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406712 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(752\) | −18.0018 | −0.656457 | ||||||||
\(753\) | −16.7341 | −0.609825 | ||||||||
\(754\) | 2.36872 | 0.0862638 | ||||||||
\(755\) | −19.3245 | −0.703291 | ||||||||
\(756\) | 39.1614 | 1.42429 | ||||||||
\(757\) | 3.59224 | 0.130562 | 0.0652811 | − | 0.997867i | \(-0.479206\pi\) | ||||
0.0652811 | + | 0.997867i | \(0.479206\pi\) | |||||||
\(758\) | 15.3463 | 0.557403 | ||||||||
\(759\) | −16.7419 | −0.607691 | ||||||||
\(760\) | 0.469423 | 0.0170278 | ||||||||
\(761\) | −6.68938 | −0.242490 | −0.121245 | − | 0.992623i | \(-0.538689\pi\) | ||||
−0.121245 | + | 0.992623i | \(0.538689\pi\) | |||||||
\(762\) | −24.1672 | −0.875487 | ||||||||
\(763\) | 3.44470 | 0.124707 | ||||||||
\(764\) | −55.7650 | −2.01751 | ||||||||
\(765\) | −13.6615 | −0.493931 | ||||||||
\(766\) | −38.5368 | −1.39239 | ||||||||
\(767\) | −9.61032 | −0.347008 | ||||||||
\(768\) | 6.17530 | 0.222832 | ||||||||
\(769\) | −45.0135 | −1.62323 | −0.811615 | − | 0.584193i | \(-0.801411\pi\) | ||||
−0.811615 | + | 0.584193i | \(0.801411\pi\) | |||||||
\(770\) | −33.5284 | −1.20828 | ||||||||
\(771\) | 19.4885 | 0.701862 | ||||||||
\(772\) | −2.19648 | −0.0790530 | ||||||||
\(773\) | 30.0578 | 1.08110 | 0.540551 | − | 0.841311i | \(-0.318216\pi\) | ||||
0.540551 | + | 0.841311i | \(0.318216\pi\) | |||||||
\(774\) | −56.8754 | −2.04434 | ||||||||
\(775\) | −15.0448 | −0.540425 | ||||||||
\(776\) | −6.88053 | −0.246997 | ||||||||
\(777\) | 0.999649 | 0.0358622 | ||||||||
\(778\) | −15.7123 | −0.563312 | ||||||||
\(779\) | −1.69045 | −0.0605665 | ||||||||
\(780\) | 1.89948 | 0.0680122 | ||||||||
\(781\) | 6.24968 | 0.223631 | ||||||||
\(782\) | −76.9552 | −2.75191 | ||||||||
\(783\) | −3.74392 | −0.133797 | ||||||||
\(784\) | −41.1384 | −1.46923 | ||||||||
\(785\) | −17.7065 | −0.631974 | ||||||||
\(786\) | −6.77689 | −0.241724 | ||||||||
\(787\) | 18.0745 | 0.644288 | 0.322144 | − | 0.946691i | \(-0.395597\pi\) | ||||
0.322144 | + | 0.946691i | \(0.395597\pi\) | |||||||
\(788\) | −20.0791 | −0.715287 | ||||||||
\(789\) | −6.96166 | −0.247842 | ||||||||
\(790\) | −25.0872 | −0.892562 | ||||||||
\(791\) | 81.6266 | 2.90231 | ||||||||
\(792\) | 6.25369 | 0.222215 | ||||||||
\(793\) | −0.117498 | −0.00417249 | ||||||||
\(794\) | 1.22124 | 0.0433402 | ||||||||
\(795\) | 9.20401 | 0.326432 | ||||||||
\(796\) | −1.06153 | −0.0376251 | ||||||||
\(797\) | 36.3251 | 1.28670 | 0.643351 | − | 0.765572i | \(-0.277544\pi\) | ||||
0.643351 | + | 0.765572i | \(0.277544\pi\) | |||||||
\(798\) | 3.88125 | 0.137395 | ||||||||
\(799\) | −28.7076 | −1.01560 | ||||||||
\(800\) | −31.4365 | −1.11145 | ||||||||
\(801\) | 9.12167 | 0.322298 | ||||||||
\(802\) | 18.3245 | 0.647059 | ||||||||
\(803\) | −8.64036 | −0.304912 | ||||||||
\(804\) | −21.8187 | −0.769486 | ||||||||
\(805\) | −34.1578 | −1.20390 | ||||||||
\(806\) | 9.17061 | 0.323021 | ||||||||
\(807\) | −20.5911 | −0.724841 | ||||||||
\(808\) | 9.51026 | 0.334570 | ||||||||
\(809\) | −9.35333 | −0.328846 | −0.164423 | − | 0.986390i | \(-0.552576\pi\) | ||||
−0.164423 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(810\) | 11.2283 | 0.394522 | ||||||||
\(811\) | −46.2580 | −1.62434 | −0.812169 | − | 0.583422i | \(-0.801714\pi\) | ||||
−0.812169 | + | 0.583422i | \(0.801714\pi\) | |||||||
\(812\) | −10.4600 | −0.367074 | ||||||||
\(813\) | 16.3267 | 0.572604 | ||||||||
\(814\) | 2.36369 | 0.0828474 | ||||||||
\(815\) | 5.47267 | 0.191699 | ||||||||
\(816\) | 10.9628 | 0.383774 | ||||||||
\(817\) | −6.63002 | −0.231955 | ||||||||
\(818\) | −49.0213 | −1.71399 | ||||||||
\(819\) | −12.8937 | −0.450544 | ||||||||
\(820\) | 6.76885 | 0.236378 | ||||||||
\(821\) | −16.6686 | −0.581738 | −0.290869 | − | 0.956763i | \(-0.593944\pi\) | ||||
−0.290869 | + | 0.956763i | \(0.593944\pi\) | |||||||
\(822\) | −22.6132 | −0.788726 | ||||||||
\(823\) | −8.49071 | −0.295968 | −0.147984 | − | 0.988990i | \(-0.547278\pi\) | ||||
−0.147984 | + | 0.988990i | \(0.547278\pi\) | |||||||
\(824\) | 5.84513 | 0.203625 | ||||||||
\(825\) | −8.96641 | −0.312170 | ||||||||
\(826\) | 78.6300 | 2.73589 | ||||||||
\(827\) | 1.72886 | 0.0601185 | 0.0300592 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300592 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(828\) | 43.2881 | 1.50436 | ||||||||
\(829\) | 41.8634 | 1.45398 | 0.726988 | − | 0.686650i | \(-0.240920\pi\) | ||||
0.726988 | + | 0.686650i | \(0.240920\pi\) | |||||||
\(830\) | 25.3926 | 0.881389 | ||||||||
\(831\) | 6.60925 | 0.229272 | ||||||||
\(832\) | 11.9111 | 0.412942 | ||||||||
\(833\) | −65.6037 | −2.27303 | ||||||||
\(834\) | 1.40770 | 0.0487447 | ||||||||
\(835\) | 27.2185 | 0.941935 | ||||||||
\(836\) | 4.95315 | 0.171308 | ||||||||
\(837\) | −14.4947 | −0.501012 | ||||||||
\(838\) | −41.9476 | −1.44906 | ||||||||
\(839\) | 41.0285 | 1.41646 | 0.708231 | − | 0.705981i | \(-0.249493\pi\) | ||||
0.708231 | + | 0.705981i | \(0.249493\pi\) | |||||||
\(840\) | −2.28734 | −0.0789207 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −13.2912 | −0.458045 | ||||||||
\(843\) | −10.3631 | −0.356926 | ||||||||
\(844\) | 40.6809 | 1.40029 | ||||||||
\(845\) | 12.3581 | 0.425132 | ||||||||
\(846\) | 29.9199 | 1.02867 | ||||||||
\(847\) | −3.00568 | −0.103276 | ||||||||
\(848\) | 41.1995 | 1.41480 | ||||||||
\(849\) | 20.1217 | 0.690576 | ||||||||
\(850\) | −41.2147 | −1.41365 | ||||||||
\(851\) | 2.40807 | 0.0825475 | ||||||||
\(852\) | 2.89688 | 0.0992454 | ||||||||
\(853\) | −3.44729 | −0.118033 | −0.0590164 | − | 0.998257i | \(-0.518796\pi\) | ||||
−0.0590164 | + | 0.998257i | \(0.518796\pi\) | |||||||
\(854\) | 0.961352 | 0.0328968 | ||||||||
\(855\) | 1.65979 | 0.0567635 | ||||||||
\(856\) | −1.02636 | −0.0350804 | ||||||||
\(857\) | −49.9311 | −1.70562 | −0.852808 | − | 0.522225i | \(-0.825102\pi\) | ||||
−0.852808 | + | 0.522225i | \(0.825102\pi\) | |||||||
\(858\) | 5.46550 | 0.186589 | ||||||||
\(859\) | 47.2252 | 1.61130 | 0.805651 | − | 0.592391i | \(-0.201816\pi\) | ||||
0.805651 | + | 0.592391i | \(0.201816\pi\) | |||||||
\(860\) | 26.5478 | 0.905272 | ||||||||
\(861\) | 8.23696 | 0.280715 | ||||||||
\(862\) | 0.196422 | 0.00669015 | ||||||||
\(863\) | −46.2033 | −1.57278 | −0.786389 | − | 0.617732i | \(-0.788052\pi\) | ||||
−0.786389 | + | 0.617732i | \(0.788052\pi\) | |||||||
\(864\) | −30.2872 | −1.03039 | ||||||||
\(865\) | 13.9740 | 0.475130 | ||||||||
\(866\) | −23.6189 | −0.802603 | ||||||||
\(867\) | 6.00201 | 0.203839 | ||||||||
\(868\) | −40.4963 | −1.37453 | ||||||||
\(869\) | −38.9596 | −1.32161 | ||||||||
\(870\) | 1.48578 | 0.0503725 | ||||||||
\(871\) | 15.6553 | 0.530458 | ||||||||
\(872\) | 0.555666 | 0.0188172 | ||||||||
\(873\) | −24.3282 | −0.823384 | ||||||||
\(874\) | 9.34959 | 0.316255 | ||||||||
\(875\) | −41.8319 | −1.41418 | ||||||||
\(876\) | −4.00502 | −0.135317 | ||||||||
\(877\) | 26.6466 | 0.899792 | 0.449896 | − | 0.893081i | \(-0.351461\pi\) | ||||
0.449896 | + | 0.893081i | \(0.351461\pi\) | |||||||
\(878\) | −28.6448 | −0.966716 | ||||||||
\(879\) | −2.04636 | −0.0690220 | ||||||||
\(880\) | 11.5058 | 0.387860 | ||||||||
\(881\) | 27.7842 | 0.936074 | 0.468037 | − | 0.883709i | \(-0.344961\pi\) | ||||
0.468037 | + | 0.883709i | \(0.344961\pi\) | |||||||
\(882\) | 68.3743 | 2.30228 | ||||||||
\(883\) | −53.8452 | −1.81203 | −0.906017 | − | 0.423241i | \(-0.860892\pi\) | ||||
−0.906017 | + | 0.423241i | \(0.860892\pi\) | |||||||
\(884\) | 13.5591 | 0.456041 | ||||||||
\(885\) | −6.02805 | −0.202631 | ||||||||
\(886\) | 17.2254 | 0.578698 | ||||||||
\(887\) | 0.536307 | 0.0180074 | 0.00900372 | − | 0.999959i | \(-0.497134\pi\) | ||||
0.00900372 | + | 0.999959i | \(0.497134\pi\) | |||||||
\(888\) | 0.161254 | 0.00541131 | ||||||||
\(889\) | −76.5729 | −2.56817 | ||||||||
\(890\) | −7.88882 | −0.264434 | ||||||||
\(891\) | 17.4372 | 0.584167 | ||||||||
\(892\) | 13.9802 | 0.468092 | ||||||||
\(893\) | 3.48780 | 0.116715 | ||||||||
\(894\) | −19.2580 | −0.644083 | ||||||||
\(895\) | −21.2152 | −0.709145 | ||||||||
\(896\) | −25.2903 | −0.844889 | ||||||||
\(897\) | 5.56811 | 0.185914 | ||||||||
\(898\) | 54.8706 | 1.83106 | ||||||||
\(899\) | 3.87154 | 0.129123 | ||||||||
\(900\) | 23.1837 | 0.772790 | ||||||||
\(901\) | 65.7011 | 2.18882 | ||||||||
\(902\) | 19.4765 | 0.648496 | ||||||||
\(903\) | 32.3058 | 1.07507 | ||||||||
\(904\) | 13.1672 | 0.437935 | ||||||||
\(905\) | −10.2578 | −0.340981 | ||||||||
\(906\) | −25.7737 | −0.856273 | ||||||||
\(907\) | 37.8000 | 1.25513 | 0.627564 | − | 0.778565i | \(-0.284052\pi\) | ||||
0.627564 | + | 0.778565i | \(0.284052\pi\) | |||||||
\(908\) | 40.1639 | 1.33289 | ||||||||
\(909\) | 33.6263 | 1.11531 | ||||||||
\(910\) | 11.1511 | 0.369654 | ||||||||
\(911\) | 0.641496 | 0.0212537 | 0.0106269 | − | 0.999944i | \(-0.496617\pi\) | ||||
0.0106269 | + | 0.999944i | \(0.496617\pi\) | |||||||
\(912\) | −1.33191 | −0.0441040 | ||||||||
\(913\) | 39.4338 | 1.30507 | ||||||||
\(914\) | −42.8668 | −1.41791 | ||||||||
\(915\) | −0.0737006 | −0.00243647 | ||||||||
\(916\) | −4.50557 | −0.148868 | ||||||||
\(917\) | −21.4723 | −0.709078 | ||||||||
\(918\) | −39.7079 | −1.31055 | ||||||||
\(919\) | −30.5688 | −1.00837 | −0.504185 | − | 0.863596i | \(-0.668207\pi\) | ||||
−0.504185 | + | 0.863596i | \(0.668207\pi\) | |||||||
\(920\) | −5.51000 | −0.181659 | ||||||||
\(921\) | −4.38513 | −0.144495 | ||||||||
\(922\) | −38.5793 | −1.27054 | ||||||||
\(923\) | −2.07856 | −0.0684165 | ||||||||
\(924\) | −24.1350 | −0.793983 | ||||||||
\(925\) | 1.28968 | 0.0424045 | ||||||||
\(926\) | 17.7265 | 0.582529 | ||||||||
\(927\) | 20.6672 | 0.678799 | ||||||||
\(928\) | 8.08968 | 0.265557 | ||||||||
\(929\) | −57.4583 | −1.88515 | −0.942573 | − | 0.334001i | \(-0.891601\pi\) | ||||
−0.942573 | + | 0.334001i | \(0.891601\pi\) | |||||||
\(930\) | 5.75224 | 0.188623 | ||||||||
\(931\) | 7.97046 | 0.261221 | ||||||||
\(932\) | −57.2932 | −1.87670 | ||||||||
\(933\) | −8.27729 | −0.270986 | ||||||||
\(934\) | −7.73819 | −0.253201 | ||||||||
\(935\) | 18.3483 | 0.600055 | ||||||||
\(936\) | −2.07989 | −0.0679833 | ||||||||
\(937\) | −28.1473 | −0.919532 | −0.459766 | − | 0.888040i | \(-0.652067\pi\) | ||||
−0.459766 | + | 0.888040i | \(0.652067\pi\) | |||||||
\(938\) | −128.089 | −4.18224 | ||||||||
\(939\) | 12.8169 | 0.418265 | ||||||||
\(940\) | −13.9658 | −0.455513 | ||||||||
\(941\) | 49.8996 | 1.62668 | 0.813340 | − | 0.581789i | \(-0.197647\pi\) | ||||
0.813340 | + | 0.581789i | \(0.197647\pi\) | |||||||
\(942\) | −23.6158 | −0.769443 | ||||||||
\(943\) | 19.8421 | 0.646149 | ||||||||
\(944\) | −26.9831 | −0.878225 | ||||||||
\(945\) | −17.6250 | −0.573341 | ||||||||
\(946\) | 76.3878 | 2.48358 | ||||||||
\(947\) | −32.9118 | −1.06949 | −0.534744 | − | 0.845014i | \(-0.679592\pi\) | ||||
−0.534744 | + | 0.845014i | \(0.679592\pi\) | |||||||
\(948\) | −18.0587 | −0.586520 | ||||||||
\(949\) | 2.87366 | 0.0932831 | ||||||||
\(950\) | 5.00734 | 0.162460 | ||||||||
\(951\) | −9.35238 | −0.303272 | ||||||||
\(952\) | −16.3278 | −0.529186 | ||||||||
\(953\) | 40.8707 | 1.32393 | 0.661966 | − | 0.749534i | \(-0.269722\pi\) | ||||
0.661966 | + | 0.749534i | \(0.269722\pi\) | |||||||
\(954\) | −68.4758 | −2.21699 | ||||||||
\(955\) | 25.0976 | 0.812139 | ||||||||
\(956\) | 0.0430238 | 0.00139149 | ||||||||
\(957\) | 2.30736 | 0.0745864 | ||||||||
\(958\) | 46.5209 | 1.50302 | ||||||||
\(959\) | −71.6490 | −2.31367 | ||||||||
\(960\) | 7.47119 | 0.241132 | ||||||||
\(961\) | −16.0112 | −0.516490 | ||||||||
\(962\) | −0.786131 | −0.0253459 | ||||||||
\(963\) | −3.62901 | −0.116943 | ||||||||
\(964\) | 15.7684 | 0.507865 | ||||||||
\(965\) | 0.988547 | 0.0318225 | ||||||||
\(966\) | −45.5573 | −1.46578 | ||||||||
\(967\) | −38.3688 | −1.23386 | −0.616928 | − | 0.787019i | \(-0.711623\pi\) | ||||
−0.616928 | + | 0.787019i | \(0.711623\pi\) | |||||||
\(968\) | −0.484846 | −0.0155835 | ||||||||
\(969\) | −2.12401 | −0.0682329 | ||||||||
\(970\) | 21.0401 | 0.675555 | ||||||||
\(971\) | −11.6950 | −0.375309 | −0.187655 | − | 0.982235i | \(-0.560089\pi\) | ||||
−0.187655 | + | 0.982235i | \(0.560089\pi\) | |||||||
\(972\) | 34.4228 | 1.10411 | ||||||||
\(973\) | 4.46025 | 0.142989 | ||||||||
\(974\) | 17.8946 | 0.573380 | ||||||||
\(975\) | 2.98210 | 0.0955037 | ||||||||
\(976\) | −0.329903 | −0.0105599 | ||||||||
\(977\) | 3.95004 | 0.126373 | 0.0631865 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631865 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(978\) | 7.29907 | 0.233399 | ||||||||
\(979\) | −12.2511 | −0.391546 | ||||||||
\(980\) | −31.9151 | −1.01949 | ||||||||
\(981\) | 1.96472 | 0.0627287 | ||||||||
\(982\) | −24.5779 | −0.784311 | ||||||||
\(983\) | −14.0025 | −0.446611 | −0.223305 | − | 0.974749i | \(-0.571685\pi\) | ||||
−0.223305 | + | 0.974749i | \(0.571685\pi\) | |||||||
\(984\) | 1.32871 | 0.0423576 | ||||||||
\(985\) | 9.03678 | 0.287936 | ||||||||
\(986\) | 10.6059 | 0.337762 | ||||||||
\(987\) | −16.9948 | −0.540951 | ||||||||
\(988\) | −1.64735 | −0.0524091 | ||||||||
\(989\) | 77.8219 | 2.47459 | ||||||||
\(990\) | −19.1232 | −0.607776 | ||||||||
\(991\) | 22.8076 | 0.724506 | 0.362253 | − | 0.932080i | \(-0.382008\pi\) | ||||
0.362253 | + | 0.932080i | \(0.382008\pi\) | |||||||
\(992\) | 31.3195 | 0.994396 | ||||||||
\(993\) | 13.6815 | 0.434169 | ||||||||
\(994\) | 17.0064 | 0.539410 | ||||||||
\(995\) | 0.477754 | 0.0151458 | ||||||||
\(996\) | 18.2785 | 0.579177 | ||||||||
\(997\) | 5.71050 | 0.180853 | 0.0904266 | − | 0.995903i | \(-0.471177\pi\) | ||||
0.0904266 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(998\) | 57.6192 | 1.82390 | ||||||||
\(999\) | 1.24253 | 0.0393120 |
(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 | 4031.2.a.d.1.14 | ✓ | 98 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.d.1.14 | ✓ | 98 | 1.1 | even | 1 | trivial |