Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36790 | −1.67436 | −0.837181 | − | 0.546926i | \(-0.815798\pi\) | ||||
−0.837181 | + | 0.546926i | \(0.815798\pi\) | |||||||
\(3\) | −2.62074 | −1.51309 | −0.756543 | − | 0.653943i | \(-0.773113\pi\) | ||||
−0.756543 | + | 0.653943i | \(0.773113\pi\) | |||||||
\(4\) | 3.60697 | 1.80349 | ||||||||
\(5\) | 3.23023 | 1.44460 | 0.722301 | − | 0.691578i | \(-0.243084\pi\) | ||||
0.722301 | + | 0.691578i | \(0.243084\pi\) | |||||||
\(6\) | 6.20567 | 2.53345 | ||||||||
\(7\) | 1.16162 | 0.439052 | 0.219526 | − | 0.975607i | \(-0.429549\pi\) | ||||
0.219526 | + | 0.975607i | \(0.429549\pi\) | |||||||
\(8\) | −3.80516 | −1.34533 | ||||||||
\(9\) | 3.86830 | 1.28943 | ||||||||
\(10\) | −7.64888 | −2.41879 | ||||||||
\(11\) | −5.95997 | −1.79700 | −0.898499 | − | 0.438976i | \(-0.855341\pi\) | ||||
−0.898499 | + | 0.438976i | \(0.855341\pi\) | |||||||
\(12\) | −9.45295 | −2.72883 | ||||||||
\(13\) | −4.69577 | −1.30237 | −0.651186 | − | 0.758918i | \(-0.725728\pi\) | ||||
−0.651186 | + | 0.758918i | \(0.725728\pi\) | |||||||
\(14\) | −2.75061 | −0.735131 | ||||||||
\(15\) | −8.46560 | −2.18581 | ||||||||
\(16\) | 1.79630 | 0.449075 | ||||||||
\(17\) | 0.273086 | 0.0662330 | 0.0331165 | − | 0.999451i | \(-0.489457\pi\) | ||||
0.0331165 | + | 0.999451i | \(0.489457\pi\) | |||||||
\(18\) | −9.15976 | −2.15898 | ||||||||
\(19\) | 8.27742 | 1.89897 | 0.949485 | − | 0.313813i | \(-0.101606\pi\) | ||||
0.949485 | + | 0.313813i | \(0.101606\pi\) | |||||||
\(20\) | 11.6513 | 2.60532 | ||||||||
\(21\) | −3.04431 | −0.664323 | ||||||||
\(22\) | 14.1126 | 3.00882 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 9.97234 | 2.03559 | ||||||||
\(25\) | 5.43438 | 1.08688 | ||||||||
\(26\) | 11.1191 | 2.18064 | ||||||||
\(27\) | −2.27558 | −0.437936 | ||||||||
\(28\) | 4.18994 | 0.791823 | ||||||||
\(29\) | −8.08895 | −1.50208 | −0.751040 | − | 0.660257i | \(-0.770448\pi\) | ||||
−0.751040 | + | 0.660257i | \(0.770448\pi\) | |||||||
\(30\) | 20.0457 | 3.65983 | ||||||||
\(31\) | 0.403546 | 0.0724790 | 0.0362395 | − | 0.999343i | \(-0.488462\pi\) | ||||
0.0362395 | + | 0.999343i | \(0.488462\pi\) | |||||||
\(32\) | 3.35684 | 0.593411 | ||||||||
\(33\) | 15.6195 | 2.71901 | ||||||||
\(34\) | −0.646641 | −0.110898 | ||||||||
\(35\) | 3.75230 | 0.634255 | ||||||||
\(36\) | 13.9528 | 2.32547 | ||||||||
\(37\) | 4.87945 | 0.802176 | 0.401088 | − | 0.916040i | \(-0.368632\pi\) | ||||
0.401088 | + | 0.916040i | \(0.368632\pi\) | |||||||
\(38\) | −19.6001 | −3.17956 | ||||||||
\(39\) | 12.3064 | 1.97060 | ||||||||
\(40\) | −12.2915 | −1.94346 | ||||||||
\(41\) | 7.36311 | 1.14993 | 0.574963 | − | 0.818180i | \(-0.305017\pi\) | ||||
0.574963 | + | 0.818180i | \(0.305017\pi\) | |||||||
\(42\) | 7.20864 | 1.11232 | ||||||||
\(43\) | −1.48896 | −0.227064 | −0.113532 | − | 0.993534i | \(-0.536216\pi\) | ||||
−0.113532 | + | 0.993534i | \(0.536216\pi\) | |||||||
\(44\) | −21.4974 | −3.24086 | ||||||||
\(45\) | 12.4955 | 1.86272 | ||||||||
\(46\) | −2.36790 | −0.349128 | ||||||||
\(47\) | −2.84372 | −0.414799 | −0.207399 | − | 0.978256i | \(-0.566500\pi\) | ||||
−0.207399 | + | 0.978256i | \(0.566500\pi\) | |||||||
\(48\) | −4.70764 | −0.679490 | ||||||||
\(49\) | −5.65064 | −0.807234 | ||||||||
\(50\) | −12.8681 | −1.81982 | ||||||||
\(51\) | −0.715688 | −0.100216 | ||||||||
\(52\) | −16.9375 | −2.34881 | ||||||||
\(53\) | −9.11543 | −1.25210 | −0.626050 | − | 0.779783i | \(-0.715330\pi\) | ||||
−0.626050 | + | 0.779783i | \(0.715330\pi\) | |||||||
\(54\) | 5.38836 | 0.733263 | ||||||||
\(55\) | −19.2521 | −2.59595 | ||||||||
\(56\) | −4.42015 | −0.590667 | ||||||||
\(57\) | −21.6930 | −2.87331 | ||||||||
\(58\) | 19.1539 | 2.51503 | ||||||||
\(59\) | 7.08591 | 0.922507 | 0.461254 | − | 0.887268i | \(-0.347400\pi\) | ||||
0.461254 | + | 0.887268i | \(0.347400\pi\) | |||||||
\(60\) | −30.5352 | −3.94208 | ||||||||
\(61\) | 3.67954 | 0.471116 | 0.235558 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235558 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(62\) | −0.955558 | −0.121356 | ||||||||
\(63\) | 4.49350 | 0.566127 | ||||||||
\(64\) | −11.5413 | −1.44266 | ||||||||
\(65\) | −15.1684 | −1.88141 | ||||||||
\(66\) | −36.9856 | −4.55261 | ||||||||
\(67\) | 5.34809 | 0.653374 | 0.326687 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326687 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(68\) | 0.985013 | 0.119450 | ||||||||
\(69\) | −2.62074 | −0.315500 | ||||||||
\(70\) | −8.88510 | −1.06197 | ||||||||
\(71\) | 1.23645 | 0.146740 | 0.0733701 | − | 0.997305i | \(-0.476625\pi\) | ||||
0.0733701 | + | 0.997305i | \(0.476625\pi\) | |||||||
\(72\) | −14.7195 | −1.73471 | ||||||||
\(73\) | −14.3861 | −1.68377 | −0.841884 | − | 0.539658i | \(-0.818553\pi\) | ||||
−0.841884 | + | 0.539658i | \(0.818553\pi\) | |||||||
\(74\) | −11.5541 | −1.34313 | ||||||||
\(75\) | −14.2421 | −1.64454 | ||||||||
\(76\) | 29.8564 | 3.42476 | ||||||||
\(77\) | −6.92323 | −0.788975 | ||||||||
\(78\) | −29.1404 | −3.29950 | ||||||||
\(79\) | 12.2858 | 1.38226 | 0.691128 | − | 0.722732i | \(-0.257114\pi\) | ||||
0.691128 | + | 0.722732i | \(0.257114\pi\) | |||||||
\(80\) | 5.80247 | 0.648735 | ||||||||
\(81\) | −5.64117 | −0.626797 | ||||||||
\(82\) | −17.4352 | −1.92539 | ||||||||
\(83\) | 4.40796 | 0.483836 | 0.241918 | − | 0.970297i | \(-0.422223\pi\) | ||||
0.241918 | + | 0.970297i | \(0.422223\pi\) | |||||||
\(84\) | −10.9807 | −1.19810 | ||||||||
\(85\) | 0.882130 | 0.0956804 | ||||||||
\(86\) | 3.52571 | 0.380187 | ||||||||
\(87\) | 21.1991 | 2.27278 | ||||||||
\(88\) | 22.6786 | 2.41755 | ||||||||
\(89\) | 4.11367 | 0.436048 | 0.218024 | − | 0.975943i | \(-0.430039\pi\) | ||||
0.218024 | + | 0.975943i | \(0.430039\pi\) | |||||||
\(90\) | −29.5881 | −3.11886 | ||||||||
\(91\) | −5.45471 | −0.571809 | ||||||||
\(92\) | 3.60697 | 0.376053 | ||||||||
\(93\) | −1.05759 | −0.109667 | ||||||||
\(94\) | 6.73365 | 0.694523 | ||||||||
\(95\) | 26.7380 | 2.74326 | ||||||||
\(96\) | −8.79742 | −0.897883 | ||||||||
\(97\) | 1.62836 | 0.165335 | 0.0826673 | − | 0.996577i | \(-0.473656\pi\) | ||||
0.0826673 | + | 0.996577i | \(0.473656\pi\) | |||||||
\(98\) | 13.3802 | 1.35160 | ||||||||
\(99\) | −23.0549 | −2.31711 | ||||||||
\(100\) | 19.6017 | 1.96017 | ||||||||
\(101\) | 0.409125 | 0.0407095 | 0.0203547 | − | 0.999793i | \(-0.493520\pi\) | ||||
0.0203547 | + | 0.999793i | \(0.493520\pi\) | |||||||
\(102\) | 1.69468 | 0.167798 | ||||||||
\(103\) | 15.9314 | 1.56977 | 0.784886 | − | 0.619640i | \(-0.212721\pi\) | ||||
0.784886 | + | 0.619640i | \(0.212721\pi\) | |||||||
\(104\) | 17.8681 | 1.75211 | ||||||||
\(105\) | −9.83383 | −0.959683 | ||||||||
\(106\) | 21.5845 | 2.09647 | ||||||||
\(107\) | −9.82848 | −0.950155 | −0.475078 | − | 0.879944i | \(-0.657580\pi\) | ||||
−0.475078 | + | 0.879944i | \(0.657580\pi\) | |||||||
\(108\) | −8.20796 | −0.789812 | ||||||||
\(109\) | −1.25265 | −0.119982 | −0.0599909 | − | 0.998199i | \(-0.519107\pi\) | ||||
−0.0599909 | + | 0.998199i | \(0.519107\pi\) | |||||||
\(110\) | 45.5870 | 4.34655 | ||||||||
\(111\) | −12.7878 | −1.21376 | ||||||||
\(112\) | 2.08662 | 0.197167 | ||||||||
\(113\) | −9.36258 | −0.880757 | −0.440379 | − | 0.897812i | \(-0.645156\pi\) | ||||
−0.440379 | + | 0.897812i | \(0.645156\pi\) | |||||||
\(114\) | 51.3669 | 4.81095 | ||||||||
\(115\) | 3.23023 | 0.301220 | ||||||||
\(116\) | −29.1766 | −2.70898 | ||||||||
\(117\) | −18.1646 | −1.67932 | ||||||||
\(118\) | −16.7788 | −1.54461 | ||||||||
\(119\) | 0.317222 | 0.0290797 | ||||||||
\(120\) | 32.2129 | 2.94063 | ||||||||
\(121\) | 24.5212 | 2.22920 | ||||||||
\(122\) | −8.71279 | −0.788819 | ||||||||
\(123\) | −19.2968 | −1.73994 | ||||||||
\(124\) | 1.45558 | 0.130715 | ||||||||
\(125\) | 1.40316 | 0.125503 | ||||||||
\(126\) | −10.6402 | −0.947902 | ||||||||
\(127\) | −15.4924 | −1.37472 | −0.687362 | − | 0.726315i | \(-0.741231\pi\) | ||||
−0.687362 | + | 0.726315i | \(0.741231\pi\) | |||||||
\(128\) | 20.6150 | 1.82212 | ||||||||
\(129\) | 3.90217 | 0.343567 | ||||||||
\(130\) | 35.9174 | 3.15016 | ||||||||
\(131\) | −9.82582 | −0.858486 | −0.429243 | − | 0.903189i | \(-0.641220\pi\) | ||||
−0.429243 | + | 0.903189i | \(0.641220\pi\) | |||||||
\(132\) | 56.3392 | 4.90370 | ||||||||
\(133\) | 9.61523 | 0.833746 | ||||||||
\(134\) | −12.6638 | −1.09398 | ||||||||
\(135\) | −7.35066 | −0.632644 | ||||||||
\(136\) | −1.03913 | −0.0891050 | ||||||||
\(137\) | −19.1051 | −1.63226 | −0.816129 | − | 0.577870i | \(-0.803884\pi\) | ||||
−0.816129 | + | 0.577870i | \(0.803884\pi\) | |||||||
\(138\) | 6.20567 | 0.528262 | ||||||||
\(139\) | −8.54556 | −0.724825 | −0.362413 | − | 0.932018i | \(-0.618047\pi\) | ||||
−0.362413 | + | 0.932018i | \(0.618047\pi\) | |||||||
\(140\) | 13.5345 | 1.14387 | ||||||||
\(141\) | 7.45266 | 0.627627 | ||||||||
\(142\) | −2.92781 | −0.245696 | ||||||||
\(143\) | 27.9866 | 2.34036 | ||||||||
\(144\) | 6.94863 | 0.579052 | ||||||||
\(145\) | −26.1292 | −2.16991 | ||||||||
\(146\) | 34.0650 | 2.81924 | ||||||||
\(147\) | 14.8089 | 1.22141 | ||||||||
\(148\) | 17.6000 | 1.44671 | ||||||||
\(149\) | 11.5712 | 0.947952 | 0.473976 | − | 0.880538i | \(-0.342818\pi\) | ||||
0.473976 | + | 0.880538i | \(0.342818\pi\) | |||||||
\(150\) | 33.7240 | 2.75355 | ||||||||
\(151\) | 11.8956 | 0.968054 | 0.484027 | − | 0.875053i | \(-0.339174\pi\) | ||||
0.484027 | + | 0.875053i | \(0.339174\pi\) | |||||||
\(152\) | −31.4969 | −2.55473 | ||||||||
\(153\) | 1.05638 | 0.0854030 | ||||||||
\(154\) | 16.3935 | 1.32103 | ||||||||
\(155\) | 1.30355 | 0.104703 | ||||||||
\(156\) | 44.3889 | 3.55395 | ||||||||
\(157\) | −24.7242 | −1.97321 | −0.986604 | − | 0.163131i | \(-0.947841\pi\) | ||||
−0.986604 | + | 0.163131i | \(0.947841\pi\) | |||||||
\(158\) | −29.0915 | −2.31440 | ||||||||
\(159\) | 23.8892 | 1.89454 | ||||||||
\(160\) | 10.8434 | 0.857243 | ||||||||
\(161\) | 1.16162 | 0.0915486 | ||||||||
\(162\) | 13.3578 | 1.04948 | ||||||||
\(163\) | −1.11031 | −0.0869662 | −0.0434831 | − | 0.999054i | \(-0.513845\pi\) | ||||
−0.0434831 | + | 0.999054i | \(0.513845\pi\) | |||||||
\(164\) | 26.5585 | 2.07387 | ||||||||
\(165\) | 50.4547 | 3.92789 | ||||||||
\(166\) | −10.4376 | −0.810117 | ||||||||
\(167\) | −0.423596 | −0.0327788 | −0.0163894 | − | 0.999866i | \(-0.505217\pi\) | ||||
−0.0163894 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(168\) | 11.5841 | 0.893731 | ||||||||
\(169\) | 9.05025 | 0.696173 | ||||||||
\(170\) | −2.08880 | −0.160204 | ||||||||
\(171\) | 32.0195 | 2.44859 | ||||||||
\(172\) | −5.37062 | −0.409506 | ||||||||
\(173\) | −1.60089 | −0.121713 | −0.0608565 | − | 0.998147i | \(-0.519383\pi\) | ||||
−0.0608565 | + | 0.998147i | \(0.519383\pi\) | |||||||
\(174\) | −50.1974 | −3.80545 | ||||||||
\(175\) | 6.31270 | 0.477195 | ||||||||
\(176\) | −10.7059 | −0.806987 | ||||||||
\(177\) | −18.5704 | −1.39583 | ||||||||
\(178\) | −9.74077 | −0.730101 | ||||||||
\(179\) | 11.1500 | 0.833388 | 0.416694 | − | 0.909047i | \(-0.363189\pi\) | ||||
0.416694 | + | 0.909047i | \(0.363189\pi\) | |||||||
\(180\) | 45.0709 | 3.35938 | ||||||||
\(181\) | −2.23764 | −0.166323 | −0.0831613 | − | 0.996536i | \(-0.526502\pi\) | ||||
−0.0831613 | + | 0.996536i | \(0.526502\pi\) | |||||||
\(182\) | 12.9162 | 0.957414 | ||||||||
\(183\) | −9.64312 | −0.712840 | ||||||||
\(184\) | −3.80515 | −0.280520 | ||||||||
\(185\) | 15.7617 | 1.15883 | ||||||||
\(186\) | 2.50427 | 0.183622 | ||||||||
\(187\) | −1.62758 | −0.119021 | ||||||||
\(188\) | −10.2572 | −0.748084 | ||||||||
\(189\) | −2.64337 | −0.192277 | ||||||||
\(190\) | −63.3129 | −4.59320 | ||||||||
\(191\) | 10.0081 | 0.724158 | 0.362079 | − | 0.932147i | \(-0.382067\pi\) | ||||
0.362079 | + | 0.932147i | \(0.382067\pi\) | |||||||
\(192\) | 30.2467 | 2.18287 | ||||||||
\(193\) | 16.8540 | 1.21318 | 0.606589 | − | 0.795016i | \(-0.292537\pi\) | ||||
0.606589 | + | 0.795016i | \(0.292537\pi\) | |||||||
\(194\) | −3.85580 | −0.276830 | ||||||||
\(195\) | 39.7525 | 2.84674 | ||||||||
\(196\) | −20.3817 | −1.45583 | ||||||||
\(197\) | −11.3691 | −0.810012 | −0.405006 | − | 0.914314i | \(-0.632731\pi\) | ||||
−0.405006 | + | 0.914314i | \(0.632731\pi\) | |||||||
\(198\) | 54.5918 | 3.87967 | ||||||||
\(199\) | 8.71490 | 0.617783 | 0.308892 | − | 0.951097i | \(-0.400042\pi\) | ||||
0.308892 | + | 0.951097i | \(0.400042\pi\) | |||||||
\(200\) | −20.6787 | −1.46220 | ||||||||
\(201\) | −14.0160 | −0.988611 | ||||||||
\(202\) | −0.968770 | −0.0681624 | ||||||||
\(203\) | −9.39630 | −0.659491 | ||||||||
\(204\) | −2.58147 | −0.180739 | ||||||||
\(205\) | 23.7846 | 1.66119 | ||||||||
\(206\) | −37.7242 | −2.62837 | ||||||||
\(207\) | 3.86830 | 0.268865 | ||||||||
\(208\) | −8.43502 | −0.584863 | ||||||||
\(209\) | −49.3331 | −3.41244 | ||||||||
\(210\) | 23.2856 | 1.60686 | ||||||||
\(211\) | 13.4361 | 0.924982 | 0.462491 | − | 0.886624i | \(-0.346956\pi\) | ||||
0.462491 | + | 0.886624i | \(0.346956\pi\) | |||||||
\(212\) | −32.8791 | −2.25815 | ||||||||
\(213\) | −3.24043 | −0.222031 | ||||||||
\(214\) | 23.2729 | 1.59090 | ||||||||
\(215\) | −4.80967 | −0.328017 | ||||||||
\(216\) | 8.65895 | 0.589167 | ||||||||
\(217\) | 0.468768 | 0.0318220 | ||||||||
\(218\) | 2.96615 | 0.200893 | ||||||||
\(219\) | 37.7023 | 2.54769 | ||||||||
\(220\) | −69.4416 | −4.68175 | ||||||||
\(221\) | −1.28235 | −0.0862601 | ||||||||
\(222\) | 30.2802 | 2.03228 | ||||||||
\(223\) | −22.3198 | −1.49464 | −0.747321 | − | 0.664463i | \(-0.768660\pi\) | ||||
−0.747321 | + | 0.664463i | \(0.768660\pi\) | |||||||
\(224\) | 3.89938 | 0.260538 | ||||||||
\(225\) | 21.0218 | 1.40145 | ||||||||
\(226\) | 22.1697 | 1.47471 | ||||||||
\(227\) | −22.2610 | −1.47752 | −0.738758 | − | 0.673971i | \(-0.764587\pi\) | ||||
−0.738758 | + | 0.673971i | \(0.764587\pi\) | |||||||
\(228\) | −78.2460 | −5.18197 | ||||||||
\(229\) | 5.15383 | 0.340574 | 0.170287 | − | 0.985394i | \(-0.445530\pi\) | ||||
0.170287 | + | 0.985394i | \(0.445530\pi\) | |||||||
\(230\) | −7.64887 | −0.504352 | ||||||||
\(231\) | 18.1440 | 1.19379 | ||||||||
\(232\) | 30.7797 | 2.02079 | ||||||||
\(233\) | 0.303341 | 0.0198725 | 0.00993627 | − | 0.999951i | \(-0.496837\pi\) | ||||
0.00993627 | + | 0.999951i | \(0.496837\pi\) | |||||||
\(234\) | 43.0121 | 2.81179 | ||||||||
\(235\) | −9.18586 | −0.599220 | ||||||||
\(236\) | 25.5587 | 1.66373 | ||||||||
\(237\) | −32.1978 | −2.09147 | ||||||||
\(238\) | −0.751152 | −0.0486900 | ||||||||
\(239\) | 6.94556 | 0.449271 | 0.224636 | − | 0.974443i | \(-0.427881\pi\) | ||||
0.224636 | + | 0.974443i | \(0.427881\pi\) | |||||||
\(240\) | −15.2068 | −0.981593 | ||||||||
\(241\) | −13.1719 | −0.848477 | −0.424238 | − | 0.905551i | \(-0.639458\pi\) | ||||
−0.424238 | + | 0.905551i | \(0.639458\pi\) | |||||||
\(242\) | −58.0639 | −3.73249 | ||||||||
\(243\) | 21.6108 | 1.38633 | ||||||||
\(244\) | 13.2720 | 0.849652 | ||||||||
\(245\) | −18.2529 | −1.16613 | ||||||||
\(246\) | 45.6931 | 2.91328 | ||||||||
\(247\) | −38.8688 | −2.47317 | ||||||||
\(248\) | −1.53555 | −0.0975078 | ||||||||
\(249\) | −11.5521 | −0.732086 | ||||||||
\(250\) | −3.32255 | −0.210137 | ||||||||
\(251\) | 10.1886 | 0.643099 | 0.321550 | − | 0.946893i | \(-0.395796\pi\) | ||||
0.321550 | + | 0.946893i | \(0.395796\pi\) | |||||||
\(252\) | 16.2079 | 1.02100 | ||||||||
\(253\) | −5.95996 | −0.374700 | ||||||||
\(254\) | 36.6844 | 2.30179 | ||||||||
\(255\) | −2.31184 | −0.144773 | ||||||||
\(256\) | −25.7317 | −1.60823 | ||||||||
\(257\) | −5.09460 | −0.317792 | −0.158896 | − | 0.987295i | \(-0.550794\pi\) | ||||
−0.158896 | + | 0.987295i | \(0.550794\pi\) | |||||||
\(258\) | −9.23997 | −0.575256 | ||||||||
\(259\) | 5.66807 | 0.352197 | ||||||||
\(260\) | −54.7120 | −3.39310 | ||||||||
\(261\) | −31.2905 | −1.93683 | ||||||||
\(262\) | 23.2666 | 1.43742 | ||||||||
\(263\) | 8.99407 | 0.554598 | 0.277299 | − | 0.960784i | \(-0.410561\pi\) | ||||
0.277299 | + | 0.960784i | \(0.410561\pi\) | |||||||
\(264\) | −59.4348 | −3.65796 | ||||||||
\(265\) | −29.4449 | −1.80879 | ||||||||
\(266\) | −22.7679 | −1.39599 | ||||||||
\(267\) | −10.7809 | −0.659778 | ||||||||
\(268\) | 19.2904 | 1.17835 | ||||||||
\(269\) | −18.9194 | −1.15353 | −0.576767 | − | 0.816908i | \(-0.695686\pi\) | ||||
−0.576767 | + | 0.816908i | \(0.695686\pi\) | |||||||
\(270\) | 17.4057 | 1.05927 | ||||||||
\(271\) | −10.3231 | −0.627084 | −0.313542 | − | 0.949574i | \(-0.601516\pi\) | ||||
−0.313542 | + | 0.949574i | \(0.601516\pi\) | |||||||
\(272\) | 0.490544 | 0.0297436 | ||||||||
\(273\) | 14.2954 | 0.865196 | ||||||||
\(274\) | 45.2390 | 2.73299 | ||||||||
\(275\) | −32.3887 | −1.95311 | ||||||||
\(276\) | −9.45295 | −0.569000 | ||||||||
\(277\) | 23.3823 | 1.40491 | 0.702454 | − | 0.711730i | \(-0.252088\pi\) | ||||
0.702454 | + | 0.711730i | \(0.252088\pi\) | |||||||
\(278\) | 20.2351 | 1.21362 | ||||||||
\(279\) | 1.56104 | 0.0934567 | ||||||||
\(280\) | −14.2781 | −0.853280 | ||||||||
\(281\) | −9.32947 | −0.556550 | −0.278275 | − | 0.960501i | \(-0.589763\pi\) | ||||
−0.278275 | + | 0.960501i | \(0.589763\pi\) | |||||||
\(282\) | −17.6472 | −1.05087 | ||||||||
\(283\) | 9.07449 | 0.539422 | 0.269711 | − | 0.962941i | \(-0.413072\pi\) | ||||
0.269711 | + | 0.962941i | \(0.413072\pi\) | |||||||
\(284\) | 4.45986 | 0.264644 | ||||||||
\(285\) | −70.0733 | −4.15079 | ||||||||
\(286\) | −66.2697 | −3.91861 | ||||||||
\(287\) | 8.55315 | 0.504877 | ||||||||
\(288\) | 12.9853 | 0.765164 | ||||||||
\(289\) | −16.9254 | −0.995613 | ||||||||
\(290\) | 61.8714 | 3.63321 | ||||||||
\(291\) | −4.26751 | −0.250166 | ||||||||
\(292\) | −51.8903 | −3.03665 | ||||||||
\(293\) | −0.732174 | −0.0427740 | −0.0213870 | − | 0.999771i | \(-0.506808\pi\) | ||||
−0.0213870 | + | 0.999771i | \(0.506808\pi\) | |||||||
\(294\) | −35.0660 | −2.04509 | ||||||||
\(295\) | 22.8891 | 1.33266 | ||||||||
\(296\) | −18.5670 | −1.07919 | ||||||||
\(297\) | 13.5624 | 0.786970 | ||||||||
\(298\) | −27.3996 | −1.58721 | ||||||||
\(299\) | −4.69577 | −0.271563 | ||||||||
\(300\) | −51.3710 | −2.96590 | ||||||||
\(301\) | −1.72960 | −0.0996927 | ||||||||
\(302\) | −28.1677 | −1.62087 | ||||||||
\(303\) | −1.07221 | −0.0615970 | ||||||||
\(304\) | 14.8687 | 0.852780 | ||||||||
\(305\) | 11.8857 | 0.680576 | ||||||||
\(306\) | −2.50140 | −0.142996 | ||||||||
\(307\) | −8.27546 | −0.472306 | −0.236153 | − | 0.971716i | \(-0.575887\pi\) | ||||
−0.236153 | + | 0.971716i | \(0.575887\pi\) | |||||||
\(308\) | −24.9719 | −1.42290 | ||||||||
\(309\) | −41.7522 | −2.37520 | ||||||||
\(310\) | −3.08667 | −0.175311 | ||||||||
\(311\) | −13.1401 | −0.745106 | −0.372553 | − | 0.928011i | \(-0.621518\pi\) | ||||
−0.372553 | + | 0.928011i | \(0.621518\pi\) | |||||||
\(312\) | −46.8278 | −2.65110 | ||||||||
\(313\) | 12.0949 | 0.683644 | 0.341822 | − | 0.939765i | \(-0.388956\pi\) | ||||
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(314\) | 58.5446 | 3.30386 | ||||||||
\(315\) | 14.5150 | 0.817829 | ||||||||
\(316\) | 44.3144 | 2.49288 | ||||||||
\(317\) | −8.29138 | −0.465690 | −0.232845 | − | 0.972514i | \(-0.574803\pi\) | ||||
−0.232845 | + | 0.972514i | \(0.574803\pi\) | |||||||
\(318\) | −56.5674 | −3.17214 | ||||||||
\(319\) | 48.2099 | 2.69923 | ||||||||
\(320\) | −37.2810 | −2.08407 | ||||||||
\(321\) | 25.7579 | 1.43767 | ||||||||
\(322\) | −2.75061 | −0.153285 | ||||||||
\(323\) | 2.26045 | 0.125775 | ||||||||
\(324\) | −20.3475 | −1.13042 | ||||||||
\(325\) | −25.5186 | −1.41552 | ||||||||
\(326\) | 2.62911 | 0.145613 | ||||||||
\(327\) | 3.28286 | 0.181543 | ||||||||
\(328\) | −28.0178 | −1.54702 | ||||||||
\(329\) | −3.30332 | −0.182118 | ||||||||
\(330\) | −119.472 | −6.57671 | ||||||||
\(331\) | −4.88230 | −0.268356 | −0.134178 | − | 0.990957i | \(-0.542839\pi\) | ||||
−0.134178 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(332\) | 15.8994 | 0.872592 | ||||||||
\(333\) | 18.8751 | 1.03435 | ||||||||
\(334\) | 1.00303 | 0.0548836 | ||||||||
\(335\) | 17.2756 | 0.943865 | ||||||||
\(336\) | −5.46850 | −0.298331 | ||||||||
\(337\) | 16.9669 | 0.924244 | 0.462122 | − | 0.886816i | \(-0.347088\pi\) | ||||
0.462122 | + | 0.886816i | \(0.347088\pi\) | |||||||
\(338\) | −21.4301 | −1.16565 | ||||||||
\(339\) | 24.5369 | 1.33266 | ||||||||
\(340\) | 3.18182 | 0.172558 | ||||||||
\(341\) | −2.40512 | −0.130245 | ||||||||
\(342\) | −75.8191 | −4.09983 | ||||||||
\(343\) | −14.6953 | −0.793469 | ||||||||
\(344\) | 5.66571 | 0.305475 | ||||||||
\(345\) | −8.46560 | −0.455773 | ||||||||
\(346\) | 3.79074 | 0.203792 | ||||||||
\(347\) | −32.7364 | −1.75738 | −0.878690 | − | 0.477392i | \(-0.841582\pi\) | ||||
−0.878690 | + | 0.477392i | \(0.841582\pi\) | |||||||
\(348\) | 76.4644 | 4.09892 | ||||||||
\(349\) | −19.7796 | −1.05878 | −0.529389 | − | 0.848379i | \(-0.677579\pi\) | ||||
−0.529389 | + | 0.848379i | \(0.677579\pi\) | |||||||
\(350\) | −14.9479 | −0.798997 | ||||||||
\(351\) | 10.6856 | 0.570356 | ||||||||
\(352\) | −20.0067 | −1.06636 | ||||||||
\(353\) | −20.9130 | −1.11309 | −0.556543 | − | 0.830819i | \(-0.687873\pi\) | ||||
−0.556543 | + | 0.830819i | \(0.687873\pi\) | |||||||
\(354\) | 43.9728 | 2.33713 | ||||||||
\(355\) | 3.99403 | 0.211981 | ||||||||
\(356\) | 14.8379 | 0.786406 | ||||||||
\(357\) | −0.831358 | −0.0440002 | ||||||||
\(358\) | −26.4021 | −1.39539 | ||||||||
\(359\) | 1.15416 | 0.0609142 | 0.0304571 | − | 0.999536i | \(-0.490304\pi\) | ||||
0.0304571 | + | 0.999536i | \(0.490304\pi\) | |||||||
\(360\) | −47.5473 | −2.50596 | ||||||||
\(361\) | 49.5156 | 2.60609 | ||||||||
\(362\) | 5.29852 | 0.278484 | ||||||||
\(363\) | −64.2638 | −3.37297 | ||||||||
\(364\) | −19.6750 | −1.03125 | ||||||||
\(365\) | −46.4705 | −2.43238 | ||||||||
\(366\) | 22.8340 | 1.19355 | ||||||||
\(367\) | −13.3643 | −0.697610 | −0.348805 | − | 0.937195i | \(-0.613412\pi\) | ||||
−0.348805 | + | 0.937195i | \(0.613412\pi\) | |||||||
\(368\) | 1.79630 | 0.0936387 | ||||||||
\(369\) | 28.4827 | 1.48275 | ||||||||
\(370\) | −37.3223 | −1.94029 | ||||||||
\(371\) | −10.5887 | −0.549737 | ||||||||
\(372\) | −3.81470 | −0.197783 | ||||||||
\(373\) | 6.30895 | 0.326665 | 0.163332 | − | 0.986571i | \(-0.447776\pi\) | ||||
0.163332 | + | 0.986571i | \(0.447776\pi\) | |||||||
\(374\) | 3.85396 | 0.199283 | ||||||||
\(375\) | −3.67732 | −0.189896 | ||||||||
\(376\) | 10.8208 | 0.558040 | ||||||||
\(377\) | 37.9838 | 1.95627 | ||||||||
\(378\) | 6.25924 | 0.321941 | ||||||||
\(379\) | −5.67432 | −0.291470 | −0.145735 | − | 0.989324i | \(-0.546555\pi\) | ||||
−0.145735 | + | 0.989324i | \(0.546555\pi\) | |||||||
\(380\) | 96.4431 | 4.94742 | ||||||||
\(381\) | 40.6015 | 2.08008 | ||||||||
\(382\) | −23.6981 | −1.21250 | ||||||||
\(383\) | −34.4123 | −1.75839 | −0.879193 | − | 0.476466i | \(-0.841917\pi\) | ||||
−0.879193 | + | 0.476466i | \(0.841917\pi\) | |||||||
\(384\) | −54.0265 | −2.75703 | ||||||||
\(385\) | −22.3636 | −1.13975 | ||||||||
\(386\) | −39.9087 | −2.03130 | ||||||||
\(387\) | −5.75973 | −0.292783 | ||||||||
\(388\) | 5.87344 | 0.298179 | ||||||||
\(389\) | 24.7281 | 1.25376 | 0.626881 | − | 0.779115i | \(-0.284331\pi\) | ||||
0.626881 | + | 0.779115i | \(0.284331\pi\) | |||||||
\(390\) | −94.1302 | −4.76647 | ||||||||
\(391\) | 0.273086 | 0.0138105 | ||||||||
\(392\) | 21.5015 | 1.08599 | ||||||||
\(393\) | 25.7509 | 1.29896 | ||||||||
\(394\) | 26.9209 | 1.35625 | ||||||||
\(395\) | 39.6858 | 1.99681 | ||||||||
\(396\) | −83.1584 | −4.17887 | ||||||||
\(397\) | 0.200175 | 0.0100465 | 0.00502325 | − | 0.999987i | \(-0.498401\pi\) | ||||
0.00502325 | + | 0.999987i | \(0.498401\pi\) | |||||||
\(398\) | −20.6361 | −1.03439 | ||||||||
\(399\) | −25.1990 | −1.26153 | ||||||||
\(400\) | 9.76179 | 0.488090 | ||||||||
\(401\) | 20.6837 | 1.03290 | 0.516448 | − | 0.856319i | \(-0.327254\pi\) | ||||
0.516448 | + | 0.856319i | \(0.327254\pi\) | |||||||
\(402\) | 33.1885 | 1.65529 | ||||||||
\(403\) | −1.89496 | −0.0943946 | ||||||||
\(404\) | 1.47570 | 0.0734190 | ||||||||
\(405\) | −18.2223 | −0.905472 | ||||||||
\(406\) | 22.2495 | 1.10423 | ||||||||
\(407\) | −29.0813 | −1.44151 | ||||||||
\(408\) | 2.72330 | 0.134824 | ||||||||
\(409\) | 20.0039 | 0.989130 | 0.494565 | − | 0.869141i | \(-0.335327\pi\) | ||||
0.494565 | + | 0.869141i | \(0.335327\pi\) | |||||||
\(410\) | −56.3195 | −2.78142 | ||||||||
\(411\) | 50.0696 | 2.46975 | ||||||||
\(412\) | 57.4643 | 2.83106 | ||||||||
\(413\) | 8.23115 | 0.405028 | ||||||||
\(414\) | −9.15975 | −0.450177 | ||||||||
\(415\) | 14.2387 | 0.698951 | ||||||||
\(416\) | −15.7630 | −0.772842 | ||||||||
\(417\) | 22.3957 | 1.09672 | ||||||||
\(418\) | 116.816 | 5.71366 | ||||||||
\(419\) | 23.3874 | 1.14255 | 0.571274 | − | 0.820759i | \(-0.306449\pi\) | ||||
0.571274 | + | 0.820759i | \(0.306449\pi\) | |||||||
\(420\) | −35.4703 | −1.73078 | ||||||||
\(421\) | −29.1388 | −1.42014 | −0.710070 | − | 0.704131i | \(-0.751337\pi\) | ||||
−0.710070 | + | 0.704131i | \(0.751337\pi\) | |||||||
\(422\) | −31.8155 | −1.54875 | ||||||||
\(423\) | −11.0003 | −0.534855 | ||||||||
\(424\) | 34.6856 | 1.68448 | ||||||||
\(425\) | 1.48405 | 0.0719872 | ||||||||
\(426\) | 7.67303 | 0.371759 | ||||||||
\(427\) | 4.27423 | 0.206844 | ||||||||
\(428\) | −35.4511 | −1.71359 | ||||||||
\(429\) | −73.3458 | −3.54117 | ||||||||
\(430\) | 11.3888 | 0.549219 | ||||||||
\(431\) | −26.1859 | −1.26133 | −0.630665 | − | 0.776055i | \(-0.717218\pi\) | ||||
−0.630665 | + | 0.776055i | \(0.717218\pi\) | |||||||
\(432\) | −4.08763 | −0.196666 | ||||||||
\(433\) | 15.5373 | 0.746675 | 0.373337 | − | 0.927696i | \(-0.378213\pi\) | ||||
0.373337 | + | 0.927696i | \(0.378213\pi\) | |||||||
\(434\) | −1.11000 | −0.0532816 | ||||||||
\(435\) | 68.4778 | 3.28326 | ||||||||
\(436\) | −4.51826 | −0.216385 | ||||||||
\(437\) | 8.27741 | 0.395962 | ||||||||
\(438\) | −89.2755 | −4.26575 | ||||||||
\(439\) | 18.6711 | 0.891122 | 0.445561 | − | 0.895252i | \(-0.353004\pi\) | ||||
0.445561 | + | 0.895252i | \(0.353004\pi\) | |||||||
\(440\) | 73.2571 | 3.49239 | ||||||||
\(441\) | −21.8583 | −1.04087 | ||||||||
\(442\) | 3.03648 | 0.144431 | ||||||||
\(443\) | 37.3852 | 1.77622 | 0.888112 | − | 0.459627i | \(-0.152017\pi\) | ||||
0.888112 | + | 0.459627i | \(0.152017\pi\) | |||||||
\(444\) | −46.1251 | −2.18900 | ||||||||
\(445\) | 13.2881 | 0.629916 | ||||||||
\(446\) | 52.8511 | 2.50257 | ||||||||
\(447\) | −30.3252 | −1.43433 | ||||||||
\(448\) | −13.4066 | −0.633402 | ||||||||
\(449\) | 23.9745 | 1.13143 | 0.565714 | − | 0.824602i | \(-0.308601\pi\) | ||||
0.565714 | + | 0.824602i | \(0.308601\pi\) | |||||||
\(450\) | −49.7776 | −2.34654 | ||||||||
\(451\) | −43.8839 | −2.06641 | ||||||||
\(452\) | −33.7705 | −1.58843 | ||||||||
\(453\) | −31.1754 | −1.46475 | ||||||||
\(454\) | 52.7120 | 2.47390 | ||||||||
\(455\) | −17.6200 | −0.826036 | ||||||||
\(456\) | 82.5452 | 3.86553 | ||||||||
\(457\) | 29.2875 | 1.37001 | 0.685006 | − | 0.728537i | \(-0.259800\pi\) | ||||
0.685006 | + | 0.728537i | \(0.259800\pi\) | |||||||
\(458\) | −12.2038 | −0.570245 | ||||||||
\(459\) | −0.621429 | −0.0290058 | ||||||||
\(460\) | 11.6513 | 0.543247 | ||||||||
\(461\) | −23.4979 | −1.09440 | −0.547202 | − | 0.837000i | \(-0.684307\pi\) | ||||
−0.547202 | + | 0.837000i | \(0.684307\pi\) | |||||||
\(462\) | −42.9633 | −1.99883 | ||||||||
\(463\) | −0.980451 | −0.0455654 | −0.0227827 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227827 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(464\) | −14.5302 | −0.674547 | ||||||||
\(465\) | −3.41626 | −0.158425 | ||||||||
\(466\) | −0.718283 | −0.0332738 | ||||||||
\(467\) | −16.5640 | −0.766492 | −0.383246 | − | 0.923646i | \(-0.625194\pi\) | ||||
−0.383246 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(468\) | −65.5193 | −3.02863 | ||||||||
\(469\) | 6.21246 | 0.286865 | ||||||||
\(470\) | 21.7512 | 1.00331 | ||||||||
\(471\) | 64.7959 | 2.98564 | ||||||||
\(472\) | −26.9630 | −1.24107 | ||||||||
\(473\) | 8.87413 | 0.408033 | ||||||||
\(474\) | 76.2414 | 3.50188 | ||||||||
\(475\) | 44.9827 | 2.06395 | ||||||||
\(476\) | 1.14421 | 0.0524449 | ||||||||
\(477\) | −35.2612 | −1.61450 | ||||||||
\(478\) | −16.4464 | −0.752242 | ||||||||
\(479\) | −7.45352 | −0.340560 | −0.170280 | − | 0.985396i | \(-0.554467\pi\) | ||||
−0.170280 | + | 0.985396i | \(0.554467\pi\) | |||||||
\(480\) | −28.4177 | −1.29708 | ||||||||
\(481\) | −22.9128 | −1.04473 | ||||||||
\(482\) | 31.1898 | 1.42066 | ||||||||
\(483\) | −3.04431 | −0.138521 | ||||||||
\(484\) | 88.4473 | 4.02033 | ||||||||
\(485\) | 5.25997 | 0.238843 | ||||||||
\(486\) | −51.1723 | −2.32122 | ||||||||
\(487\) | 30.8128 | 1.39626 | 0.698130 | − | 0.715971i | \(-0.254016\pi\) | ||||
0.698130 | + | 0.715971i | \(0.254016\pi\) | |||||||
\(488\) | −14.0012 | −0.633805 | ||||||||
\(489\) | 2.90984 | 0.131587 | ||||||||
\(490\) | 43.2210 | 1.95253 | ||||||||
\(491\) | −19.7841 | −0.892843 | −0.446421 | − | 0.894823i | \(-0.647302\pi\) | ||||
−0.446421 | + | 0.894823i | \(0.647302\pi\) | |||||||
\(492\) | −69.6031 | −3.13795 | ||||||||
\(493\) | −2.20898 | −0.0994873 | ||||||||
\(494\) | 92.0377 | 4.14097 | ||||||||
\(495\) | −74.4727 | −3.34730 | ||||||||
\(496\) | 0.724890 | 0.0325485 | ||||||||
\(497\) | 1.43629 | 0.0644265 | ||||||||
\(498\) | 27.3543 | 1.22578 | ||||||||
\(499\) | −34.9866 | −1.56622 | −0.783108 | − | 0.621885i | \(-0.786367\pi\) | ||||
−0.783108 | + | 0.621885i | \(0.786367\pi\) | |||||||
\(500\) | 5.06116 | 0.226342 | ||||||||
\(501\) | 1.11014 | 0.0495972 | ||||||||
\(502\) | −24.1256 | −1.07678 | ||||||||
\(503\) | −14.9569 | −0.666896 | −0.333448 | − | 0.942769i | \(-0.608212\pi\) | ||||
−0.333448 | + | 0.942769i | \(0.608212\pi\) | |||||||
\(504\) | −17.0985 | −0.761626 | ||||||||
\(505\) | 1.32157 | 0.0588090 | ||||||||
\(506\) | 14.1126 | 0.627383 | ||||||||
\(507\) | −23.7184 | −1.05337 | ||||||||
\(508\) | −55.8805 | −2.47930 | ||||||||
\(509\) | −35.2583 | −1.56280 | −0.781399 | − | 0.624031i | \(-0.785494\pi\) | ||||
−0.781399 | + | 0.624031i | \(0.785494\pi\) | |||||||
\(510\) | 5.47421 | 0.242402 | ||||||||
\(511\) | −16.7112 | −0.739261 | ||||||||
\(512\) | 19.7003 | 0.870639 | ||||||||
\(513\) | −18.8359 | −0.831627 | ||||||||
\(514\) | 12.0635 | 0.532099 | ||||||||
\(515\) | 51.4622 | 2.26770 | ||||||||
\(516\) | 14.0750 | 0.619619 | ||||||||
\(517\) | 16.9485 | 0.745393 | ||||||||
\(518\) | −13.4214 | −0.589704 | ||||||||
\(519\) | 4.19551 | 0.184162 | ||||||||
\(520\) | 57.7182 | 2.53111 | ||||||||
\(521\) | −25.2947 | −1.10818 | −0.554091 | − | 0.832456i | \(-0.686934\pi\) | ||||
−0.554091 | + | 0.832456i | \(0.686934\pi\) | |||||||
\(522\) | 74.0928 | 3.24295 | ||||||||
\(523\) | −7.08519 | −0.309814 | −0.154907 | − | 0.987929i | \(-0.549508\pi\) | ||||
−0.154907 | + | 0.987929i | \(0.549508\pi\) | |||||||
\(524\) | −35.4414 | −1.54827 | ||||||||
\(525\) | −16.5440 | −0.722038 | ||||||||
\(526\) | −21.2971 | −0.928598 | ||||||||
\(527\) | 0.110203 | 0.00480050 | ||||||||
\(528\) | 28.0574 | 1.22104 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 69.7228 | 3.02857 | ||||||||
\(531\) | 27.4104 | 1.18951 | ||||||||
\(532\) | 34.6818 | 1.50365 | ||||||||
\(533\) | −34.5755 | −1.49763 | ||||||||
\(534\) | 25.5281 | 1.10471 | ||||||||
\(535\) | −31.7483 | −1.37260 | ||||||||
\(536\) | −20.3503 | −0.879000 | ||||||||
\(537\) | −29.2212 | −1.26099 | ||||||||
\(538\) | 44.7993 | 1.93143 | ||||||||
\(539\) | 33.6776 | 1.45060 | ||||||||
\(540\) | −26.5136 | −1.14096 | ||||||||
\(541\) | 42.4556 | 1.82531 | 0.912655 | − | 0.408731i | \(-0.134029\pi\) | ||||
0.912655 | + | 0.408731i | \(0.134029\pi\) | |||||||
\(542\) | 24.4441 | 1.04996 | ||||||||
\(543\) | 5.86428 | 0.251660 | ||||||||
\(544\) | 0.916706 | 0.0393034 | ||||||||
\(545\) | −4.04633 | −0.173326 | ||||||||
\(546\) | −33.8501 | −1.44865 | ||||||||
\(547\) | −26.1683 | −1.11887 | −0.559437 | − | 0.828873i | \(-0.688983\pi\) | ||||
−0.559437 | + | 0.828873i | \(0.688983\pi\) | |||||||
\(548\) | −68.9115 | −2.94375 | ||||||||
\(549\) | 14.2335 | 0.607473 | ||||||||
\(550\) | 76.6935 | 3.27022 | ||||||||
\(551\) | −66.9556 | −2.85240 | ||||||||
\(552\) | 9.97233 | 0.424451 | ||||||||
\(553\) | 14.2714 | 0.606882 | ||||||||
\(554\) | −55.3671 | −2.35232 | ||||||||
\(555\) | −41.3075 | −1.75340 | ||||||||
\(556\) | −30.8236 | −1.30721 | ||||||||
\(557\) | −32.1710 | −1.36313 | −0.681565 | − | 0.731757i | \(-0.738700\pi\) | ||||
−0.681565 | + | 0.731757i | \(0.738700\pi\) | |||||||
\(558\) | −3.69638 | −0.156480 | ||||||||
\(559\) | 6.99180 | 0.295721 | ||||||||
\(560\) | 6.74027 | 0.284828 | ||||||||
\(561\) | 4.26548 | 0.180089 | ||||||||
\(562\) | 22.0913 | 0.931865 | ||||||||
\(563\) | 1.40481 | 0.0592055 | 0.0296027 | − | 0.999562i | \(-0.490576\pi\) | ||||
0.0296027 | + | 0.999562i | \(0.490576\pi\) | |||||||
\(564\) | 26.8815 | 1.13192 | ||||||||
\(565\) | −30.2433 | −1.27234 | ||||||||
\(566\) | −21.4875 | −0.903188 | ||||||||
\(567\) | −6.55291 | −0.275196 | ||||||||
\(568\) | −4.70490 | −0.197413 | ||||||||
\(569\) | −18.5474 | −0.777546 | −0.388773 | − | 0.921334i | \(-0.627101\pi\) | ||||
−0.388773 | + | 0.921334i | \(0.627101\pi\) | |||||||
\(570\) | 165.927 | 6.94992 | ||||||||
\(571\) | −20.3961 | −0.853551 | −0.426775 | − | 0.904358i | \(-0.640350\pi\) | ||||
−0.426775 | + | 0.904358i | \(0.640350\pi\) | |||||||
\(572\) | 100.947 | 4.22080 | ||||||||
\(573\) | −26.2286 | −1.09571 | ||||||||
\(574\) | −20.2530 | −0.845346 | ||||||||
\(575\) | 5.43438 | 0.226629 | ||||||||
\(576\) | −44.6451 | −1.86021 | ||||||||
\(577\) | −22.7231 | −0.945974 | −0.472987 | − | 0.881069i | \(-0.656824\pi\) | ||||
−0.472987 | + | 0.881069i | \(0.656824\pi\) | |||||||
\(578\) | 40.0778 | 1.66702 | ||||||||
\(579\) | −44.1700 | −1.83564 | ||||||||
\(580\) | −94.2472 | −3.91340 | ||||||||
\(581\) | 5.12038 | 0.212429 | ||||||||
\(582\) | 10.1051 | 0.418868 | ||||||||
\(583\) | 54.3277 | 2.25002 | ||||||||
\(584\) | 54.7414 | 2.26522 | ||||||||
\(585\) | −58.6759 | −2.42595 | ||||||||
\(586\) | 1.73372 | 0.0716192 | ||||||||
\(587\) | −45.5761 | −1.88113 | −0.940564 | − | 0.339615i | \(-0.889703\pi\) | ||||
−0.940564 | + | 0.339615i | \(0.889703\pi\) | |||||||
\(588\) | 53.4152 | 2.20280 | ||||||||
\(589\) | 3.34032 | 0.137635 | ||||||||
\(590\) | −54.1993 | −2.23135 | ||||||||
\(591\) | 29.7954 | 1.22562 | ||||||||
\(592\) | 8.76495 | 0.360237 | ||||||||
\(593\) | −22.0569 | −0.905767 | −0.452884 | − | 0.891570i | \(-0.649605\pi\) | ||||
−0.452884 | + | 0.891570i | \(0.649605\pi\) | |||||||
\(594\) | −32.1145 | −1.31767 | ||||||||
\(595\) | 1.02470 | 0.0420086 | ||||||||
\(596\) | 41.7371 | 1.70962 | ||||||||
\(597\) | −22.8395 | −0.934760 | ||||||||
\(598\) | 11.1191 | 0.454695 | ||||||||
\(599\) | −6.86560 | −0.280521 | −0.140260 | − | 0.990115i | \(-0.544794\pi\) | ||||
−0.140260 | + | 0.990115i | \(0.544794\pi\) | |||||||
\(600\) | 54.1935 | 2.21244 | ||||||||
\(601\) | 42.3508 | 1.72752 | 0.863762 | − | 0.503900i | \(-0.168102\pi\) | ||||
0.863762 | + | 0.503900i | \(0.168102\pi\) | |||||||
\(602\) | 4.09554 | 0.166922 | ||||||||
\(603\) | 20.6880 | 0.842481 | ||||||||
\(604\) | 42.9073 | 1.74587 | ||||||||
\(605\) | 79.2091 | 3.22031 | ||||||||
\(606\) | 2.53890 | 0.103136 | ||||||||
\(607\) | 36.4480 | 1.47938 | 0.739689 | − | 0.672949i | \(-0.234972\pi\) | ||||
0.739689 | + | 0.672949i | \(0.234972\pi\) | |||||||
\(608\) | 27.7860 | 1.12687 | ||||||||
\(609\) | 24.6253 | 0.997867 | ||||||||
\(610\) | −28.1443 | −1.13953 | ||||||||
\(611\) | 13.3534 | 0.540223 | ||||||||
\(612\) | 3.81032 | 0.154023 | ||||||||
\(613\) | −33.1476 | −1.33882 | −0.669409 | − | 0.742895i | \(-0.733452\pi\) | ||||
−0.669409 | + | 0.742895i | \(0.733452\pi\) | |||||||
\(614\) | 19.5955 | 0.790810 | ||||||||
\(615\) | −62.3332 | −2.51352 | ||||||||
\(616\) | 26.3439 | 1.06143 | ||||||||
\(617\) | −15.7496 | −0.634057 | −0.317028 | − | 0.948416i | \(-0.602685\pi\) | ||||
−0.317028 | + | 0.948416i | \(0.602685\pi\) | |||||||
\(618\) | 98.8653 | 3.97695 | ||||||||
\(619\) | 23.6842 | 0.951946 | 0.475973 | − | 0.879460i | \(-0.342096\pi\) | ||||
0.475973 | + | 0.879460i | \(0.342096\pi\) | |||||||
\(620\) | 4.70185 | 0.188831 | ||||||||
\(621\) | −2.27558 | −0.0913160 | ||||||||
\(622\) | 31.1145 | 1.24758 | ||||||||
\(623\) | 4.77852 | 0.191447 | ||||||||
\(624\) | 22.1060 | 0.884949 | ||||||||
\(625\) | −22.6394 | −0.905576 | ||||||||
\(626\) | −28.6396 | −1.14467 | ||||||||
\(627\) | 129.289 | 5.16332 | ||||||||
\(628\) | −89.1796 | −3.55865 | ||||||||
\(629\) | 1.33251 | 0.0531305 | ||||||||
\(630\) | −34.3702 | −1.36934 | ||||||||
\(631\) | −21.7893 | −0.867418 | −0.433709 | − | 0.901053i | \(-0.642795\pi\) | ||||
−0.433709 | + | 0.901053i | \(0.642795\pi\) | |||||||
\(632\) | −46.7492 | −1.85959 | ||||||||
\(633\) | −35.2127 | −1.39958 | ||||||||
\(634\) | 19.6332 | 0.779733 | ||||||||
\(635\) | −50.0439 | −1.98593 | ||||||||
\(636\) | 86.1677 | 3.41677 | ||||||||
\(637\) | 26.5341 | 1.05132 | ||||||||
\(638\) | −114.156 | −4.51949 | ||||||||
\(639\) | 4.78297 | 0.189211 | ||||||||
\(640\) | 66.5911 | 2.63224 | ||||||||
\(641\) | −31.9045 | −1.26015 | −0.630075 | − | 0.776534i | \(-0.716976\pi\) | ||||
−0.630075 | + | 0.776534i | \(0.716976\pi\) | |||||||
\(642\) | −60.9923 | −2.40717 | ||||||||
\(643\) | 7.18518 | 0.283356 | 0.141678 | − | 0.989913i | \(-0.454750\pi\) | ||||
0.141678 | + | 0.989913i | \(0.454750\pi\) | |||||||
\(644\) | 4.18993 | 0.165107 | ||||||||
\(645\) | 12.6049 | 0.496318 | ||||||||
\(646\) | −5.35252 | −0.210592 | ||||||||
\(647\) | −1.64595 | −0.0647088 | −0.0323544 | − | 0.999476i | \(-0.510301\pi\) | ||||
−0.0323544 | + | 0.999476i | \(0.510301\pi\) | |||||||
\(648\) | 21.4655 | 0.843246 | ||||||||
\(649\) | −42.2318 | −1.65774 | ||||||||
\(650\) | 60.4256 | 2.37009 | ||||||||
\(651\) | −1.22852 | −0.0481495 | ||||||||
\(652\) | −4.00486 | −0.156842 | ||||||||
\(653\) | −6.79202 | −0.265792 | −0.132896 | − | 0.991130i | \(-0.542428\pi\) | ||||
−0.132896 | + | 0.991130i | \(0.542428\pi\) | |||||||
\(654\) | −7.77351 | −0.303968 | ||||||||
\(655\) | −31.7396 | −1.24017 | ||||||||
\(656\) | 13.2264 | 0.516403 | ||||||||
\(657\) | −55.6498 | −2.17111 | ||||||||
\(658\) | 7.82196 | 0.304932 | ||||||||
\(659\) | −31.3243 | −1.22022 | −0.610111 | − | 0.792316i | \(-0.708875\pi\) | ||||
−0.610111 | + | 0.792316i | \(0.708875\pi\) | |||||||
\(660\) | 181.989 | 7.08390 | ||||||||
\(661\) | −35.3664 | −1.37559 | −0.687796 | − | 0.725904i | \(-0.741422\pi\) | ||||
−0.687796 | + | 0.725904i | \(0.741422\pi\) | |||||||
\(662\) | 11.5608 | 0.449324 | ||||||||
\(663\) | 3.36071 | 0.130519 | ||||||||
\(664\) | −16.7730 | −0.650917 | ||||||||
\(665\) | 31.0594 | 1.20443 | ||||||||
\(666\) | −44.6945 | −1.73188 | ||||||||
\(667\) | −8.08895 | −0.313205 | ||||||||
\(668\) | −1.52790 | −0.0591162 | ||||||||
\(669\) | 58.4944 | 2.26152 | ||||||||
\(670\) | −40.9069 | −1.58037 | ||||||||
\(671\) | −21.9299 | −0.846595 | ||||||||
\(672\) | −10.2193 | −0.394217 | ||||||||
\(673\) | −2.89140 | −0.111455 | −0.0557276 | − | 0.998446i | \(-0.517748\pi\) | ||||
−0.0557276 | + | 0.998446i | \(0.517748\pi\) | |||||||
\(674\) | −40.1759 | −1.54752 | ||||||||
\(675\) | −12.3664 | −0.475983 | ||||||||
\(676\) | 32.6440 | 1.25554 | ||||||||
\(677\) | 44.9906 | 1.72913 | 0.864565 | − | 0.502522i | \(-0.167594\pi\) | ||||
0.864565 | + | 0.502522i | \(0.167594\pi\) | |||||||
\(678\) | −58.1011 | −2.23136 | ||||||||
\(679\) | 1.89154 | 0.0725905 | ||||||||
\(680\) | −3.35664 | −0.128721 | ||||||||
\(681\) | 58.3404 | 2.23561 | ||||||||
\(682\) | 5.69509 | 0.218076 | ||||||||
\(683\) | −15.4299 | −0.590409 | −0.295204 | − | 0.955434i | \(-0.595388\pi\) | ||||
−0.295204 | + | 0.955434i | \(0.595388\pi\) | |||||||
\(684\) | 115.493 | 4.41600 | ||||||||
\(685\) | −61.7138 | −2.35796 | ||||||||
\(686\) | 34.7969 | 1.32855 | ||||||||
\(687\) | −13.5069 | −0.515319 | ||||||||
\(688\) | −2.67461 | −0.101969 | ||||||||
\(689\) | 42.8040 | 1.63070 | ||||||||
\(690\) | 20.0457 | 0.763128 | ||||||||
\(691\) | −40.4436 | −1.53855 | −0.769274 | − | 0.638920i | \(-0.779382\pi\) | ||||
−0.769274 | + | 0.638920i | \(0.779382\pi\) | |||||||
\(692\) | −5.77435 | −0.219508 | ||||||||
\(693\) | −26.7811 | −1.01733 | ||||||||
\(694\) | 77.5166 | 2.94249 | ||||||||
\(695\) | −27.6041 | −1.04708 | ||||||||
\(696\) | −80.6657 | −3.05763 | ||||||||
\(697\) | 2.01076 | 0.0761630 | ||||||||
\(698\) | 46.8362 | 1.77278 | ||||||||
\(699\) | −0.794980 | −0.0300689 | ||||||||
\(700\) | 22.7697 | 0.860615 | ||||||||
\(701\) | −46.0718 | −1.74011 | −0.870055 | − | 0.492955i | \(-0.835917\pi\) | ||||
−0.870055 | + | 0.492955i | \(0.835917\pi\) | |||||||
\(702\) | −25.3025 | −0.954982 | ||||||||
\(703\) | 40.3892 | 1.52331 | ||||||||
\(704\) | 68.7856 | 2.59246 | ||||||||
\(705\) | 24.0738 | 0.906671 | ||||||||
\(706\) | 49.5200 | 1.86371 | ||||||||
\(707\) | 0.475249 | 0.0178736 | ||||||||
\(708\) | −66.9828 | −2.51737 | ||||||||
\(709\) | −52.1758 | −1.95950 | −0.979752 | − | 0.200214i | \(-0.935836\pi\) | ||||
−0.979752 | + | 0.200214i | \(0.935836\pi\) | |||||||
\(710\) | −9.45748 | −0.354933 | ||||||||
\(711\) | 47.5250 | 1.78233 | ||||||||
\(712\) | −15.6531 | −0.586626 | ||||||||
\(713\) | 0.403546 | 0.0151129 | ||||||||
\(714\) | 1.96858 | 0.0736722 | ||||||||
\(715\) | 90.4032 | 3.38089 | ||||||||
\(716\) | 40.2176 | 1.50300 | ||||||||
\(717\) | −18.2025 | −0.679786 | ||||||||
\(718\) | −2.73294 | −0.101992 | ||||||||
\(719\) | −34.8949 | −1.30136 | −0.650680 | − | 0.759352i | \(-0.725516\pi\) | ||||
−0.650680 | + | 0.759352i | \(0.725516\pi\) | |||||||
\(720\) | 22.4457 | 0.836500 | ||||||||
\(721\) | 18.5063 | 0.689211 | ||||||||
\(722\) | −117.248 | −4.36353 | ||||||||
\(723\) | 34.5202 | 1.28382 | ||||||||
\(724\) | −8.07111 | −0.299960 | ||||||||
\(725\) | −43.9585 | −1.63258 | ||||||||
\(726\) | 152.170 | 5.64758 | ||||||||
\(727\) | 43.8113 | 1.62487 | 0.812436 | − | 0.583051i | \(-0.198141\pi\) | ||||
0.812436 | + | 0.583051i | \(0.198141\pi\) | |||||||
\(728\) | 20.7560 | 0.769269 | ||||||||
\(729\) | −39.7129 | −1.47085 | ||||||||
\(730\) | 110.038 | 4.07268 | ||||||||
\(731\) | −0.406613 | −0.0150391 | ||||||||
\(732\) | −34.7825 | −1.28560 | ||||||||
\(733\) | −40.3876 | −1.49175 | −0.745874 | − | 0.666087i | \(-0.767968\pi\) | ||||
−0.745874 | + | 0.666087i | \(0.767968\pi\) | |||||||
\(734\) | 31.6454 | 1.16805 | ||||||||
\(735\) | 47.8360 | 1.76446 | ||||||||
\(736\) | 3.35684 | 0.123735 | ||||||||
\(737\) | −31.8745 | −1.17411 | ||||||||
\(738\) | −67.4443 | −2.48266 | ||||||||
\(739\) | 11.0165 | 0.405250 | 0.202625 | − | 0.979256i | \(-0.435053\pi\) | ||||
0.202625 | + | 0.979256i | \(0.435053\pi\) | |||||||
\(740\) | 56.8521 | 2.08993 | ||||||||
\(741\) | 101.865 | 3.74211 | ||||||||
\(742\) | 25.0730 | 0.920458 | ||||||||
\(743\) | −33.8313 | −1.24115 | −0.620575 | − | 0.784147i | \(-0.713101\pi\) | ||||
−0.620575 | + | 0.784147i | \(0.713101\pi\) | |||||||
\(744\) | 4.02430 | 0.147538 | ||||||||
\(745\) | 37.3777 | 1.36941 | ||||||||
\(746\) | −14.9390 | −0.546955 | ||||||||
\(747\) | 17.0513 | 0.623874 | ||||||||
\(748\) | −5.87064 | −0.214652 | ||||||||
\(749\) | −11.4170 | −0.417167 | ||||||||
\(750\) | 8.70755 | 0.317955 | ||||||||
\(751\) | 11.6347 | 0.424558 | 0.212279 | − | 0.977209i | \(-0.431912\pi\) | ||||
0.212279 | + | 0.977209i | \(0.431912\pi\) | |||||||
\(752\) | −5.10817 | −0.186276 | ||||||||
\(753\) | −26.7017 | −0.973065 | ||||||||
\(754\) | −89.9421 | −3.27550 | ||||||||
\(755\) | 38.4257 | 1.39845 | ||||||||
\(756\) | −9.53455 | −0.346768 | ||||||||
\(757\) | 19.0459 | 0.692236 | 0.346118 | − | 0.938191i | \(-0.387500\pi\) | ||||
0.346118 | + | 0.938191i | \(0.387500\pi\) | |||||||
\(758\) | 13.4363 | 0.488027 | ||||||||
\(759\) | 15.6195 | 0.566953 | ||||||||
\(760\) | −101.742 | −3.69057 | ||||||||
\(761\) | 32.4268 | 1.17547 | 0.587736 | − | 0.809053i | \(-0.300019\pi\) | ||||
0.587736 | + | 0.809053i | \(0.300019\pi\) | |||||||
\(762\) | −96.1405 | −3.48280 | ||||||||
\(763\) | −1.45510 | −0.0526782 | ||||||||
\(764\) | 36.0988 | 1.30601 | ||||||||
\(765\) | 3.41234 | 0.123373 | ||||||||
\(766\) | 81.4850 | 2.94417 | ||||||||
\(767\) | −33.2738 | −1.20145 | ||||||||
\(768\) | 67.4362 | 2.43340 | ||||||||
\(769\) | 32.9396 | 1.18783 | 0.593917 | − | 0.804526i | \(-0.297581\pi\) | ||||
0.593917 | + | 0.804526i | \(0.297581\pi\) | |||||||
\(770\) | 52.9549 | 1.90836 | ||||||||
\(771\) | 13.3516 | 0.480847 | ||||||||
\(772\) | 60.7919 | 2.18795 | ||||||||
\(773\) | 17.1105 | 0.615424 | 0.307712 | − | 0.951480i | \(-0.400437\pi\) | ||||
0.307712 | + | 0.951480i | \(0.400437\pi\) | |||||||
\(774\) | 13.6385 | 0.490225 | ||||||||
\(775\) | 2.19302 | 0.0787757 | ||||||||
\(776\) | −6.19615 | −0.222429 | ||||||||
\(777\) | −14.8546 | −0.532904 | ||||||||
\(778\) | −58.5537 | −2.09925 | ||||||||
\(779\) | 60.9476 | 2.18367 | ||||||||
\(780\) | 143.386 | 5.13405 | ||||||||
\(781\) | −7.36923 | −0.263692 | ||||||||
\(782\) | −0.646641 | −0.0231238 | ||||||||
\(783\) | 18.4071 | 0.657815 | ||||||||
\(784\) | −10.1502 | −0.362509 | ||||||||
\(785\) | −79.8650 | −2.85050 | ||||||||
\(786\) | −60.9758 | −2.17493 | ||||||||
\(787\) | −12.5717 | −0.448134 | −0.224067 | − | 0.974574i | \(-0.571933\pi\) | ||||
−0.224067 | + | 0.974574i | \(0.571933\pi\) | |||||||
\(788\) | −41.0079 | −1.46085 | ||||||||
\(789\) | −23.5711 | −0.839155 | ||||||||
\(790\) | −93.9723 | −3.34338 | ||||||||
\(791\) | −10.8758 | −0.386698 | ||||||||
\(792\) | 87.7275 | 3.11726 | ||||||||
\(793\) | −17.2783 | −0.613569 | ||||||||
\(794\) | −0.473995 | −0.0168215 | ||||||||
\(795\) | 77.1676 | 2.73685 | ||||||||
\(796\) | 31.4344 | 1.11416 | ||||||||
\(797\) | −27.2521 | −0.965319 | −0.482660 | − | 0.875808i | \(-0.660329\pi\) | ||||
−0.482660 | + | 0.875808i | \(0.660329\pi\) | |||||||
\(798\) | 59.6689 | 2.11226 | ||||||||
\(799\) | −0.776579 | −0.0274734 | ||||||||
\(800\) | 18.2424 | 0.644965 | ||||||||
\(801\) | 15.9129 | 0.562254 | ||||||||
\(802\) | −48.9771 | −1.72944 | ||||||||
\(803\) | 85.7408 | 3.02573 | ||||||||
\(804\) | −50.5552 | −1.78295 | ||||||||
\(805\) | 3.75230 | 0.132251 | ||||||||
\(806\) | 4.48708 | 0.158051 | ||||||||
\(807\) | 49.5828 | 1.74540 | ||||||||
\(808\) | −1.55679 | −0.0547675 | ||||||||
\(809\) | −47.4499 | −1.66825 | −0.834124 | − | 0.551577i | \(-0.814026\pi\) | ||||
−0.834124 | + | 0.551577i | \(0.814026\pi\) | |||||||
\(810\) | 43.1486 | 1.51609 | ||||||||
\(811\) | 26.7380 | 0.938897 | 0.469449 | − | 0.882960i | \(-0.344453\pi\) | ||||
0.469449 | + | 0.882960i | \(0.344453\pi\) | |||||||
\(812\) | −33.8922 | −1.18938 | ||||||||
\(813\) | 27.0542 | 0.948832 | ||||||||
\(814\) | 68.8618 | 2.41361 | ||||||||
\(815\) | −3.58656 | −0.125632 | ||||||||
\(816\) | −1.28559 | −0.0450047 | ||||||||
\(817\) | −12.3247 | −0.431187 | ||||||||
\(818\) | −47.3674 | −1.65616 | ||||||||
\(819\) | −21.1004 | −0.737309 | ||||||||
\(820\) | 85.7902 | 2.99592 | ||||||||
\(821\) | −18.1586 | −0.633739 | −0.316870 | − | 0.948469i | \(-0.602632\pi\) | ||||
−0.316870 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(822\) | −118.560 | −4.13525 | ||||||||
\(823\) | 31.4304 | 1.09560 | 0.547798 | − | 0.836611i | \(-0.315466\pi\) | ||||
0.547798 | + | 0.836611i | \(0.315466\pi\) | |||||||
\(824\) | −60.6216 | −2.11185 | ||||||||
\(825\) | 84.8826 | 2.95523 | ||||||||
\(826\) | −19.4906 | −0.678164 | ||||||||
\(827\) | 34.4447 | 1.19776 | 0.598879 | − | 0.800839i | \(-0.295613\pi\) | ||||
0.598879 | + | 0.800839i | \(0.295613\pi\) | |||||||
\(828\) | 13.9528 | 0.484894 | ||||||||
\(829\) | 7.54813 | 0.262157 | 0.131079 | − | 0.991372i | \(-0.458156\pi\) | ||||
0.131079 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(830\) | −33.7159 | −1.17030 | ||||||||
\(831\) | −61.2791 | −2.12575 | ||||||||
\(832\) | 54.1952 | 1.87888 | ||||||||
\(833\) | −1.54311 | −0.0534655 | ||||||||
\(834\) | −53.0309 | −1.83631 | ||||||||
\(835\) | −1.36831 | −0.0473524 | ||||||||
\(836\) | −177.943 | −6.15429 | ||||||||
\(837\) | −0.918302 | −0.0317412 | ||||||||
\(838\) | −55.3791 | −1.91304 | ||||||||
\(839\) | −30.6368 | −1.05770 | −0.528849 | − | 0.848716i | \(-0.677376\pi\) | ||||
−0.528849 | + | 0.848716i | \(0.677376\pi\) | |||||||
\(840\) | 37.4192 | 1.29109 | ||||||||
\(841\) | 36.4311 | 1.25624 | ||||||||
\(842\) | 68.9980 | 2.37783 | ||||||||
\(843\) | 24.4502 | 0.842108 | ||||||||
\(844\) | 48.4638 | 1.66819 | ||||||||
\(845\) | 29.2344 | 1.00569 | ||||||||
\(846\) | 26.0478 | 0.895541 | ||||||||
\(847\) | 28.4843 | 0.978734 | ||||||||
\(848\) | −16.3741 | −0.562288 | ||||||||
\(849\) | −23.7819 | −0.816193 | ||||||||
\(850\) | −3.51410 | −0.120533 | ||||||||
\(851\) | 4.87944 | 0.167265 | ||||||||
\(852\) | −11.6881 | −0.400429 | ||||||||
\(853\) | −26.6251 | −0.911625 | −0.455813 | − | 0.890076i | \(-0.650651\pi\) | ||||
−0.455813 | + | 0.890076i | \(0.650651\pi\) | |||||||
\(854\) | −10.1210 | −0.346332 | ||||||||
\(855\) | 103.430 | 3.53724 | ||||||||
\(856\) | 37.3989 | 1.27827 | ||||||||
\(857\) | 2.67059 | 0.0912255 | 0.0456128 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456128 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(858\) | 173.676 | 5.92919 | ||||||||
\(859\) | −55.1713 | −1.88242 | −0.941210 | − | 0.337823i | \(-0.890310\pi\) | ||||
−0.941210 | + | 0.337823i | \(0.890310\pi\) | |||||||
\(860\) | −17.3483 | −0.591574 | ||||||||
\(861\) | −22.4156 | −0.763922 | ||||||||
\(862\) | 62.0057 | 2.11192 | ||||||||
\(863\) | 33.3886 | 1.13656 | 0.568281 | − | 0.822835i | \(-0.307609\pi\) | ||||
0.568281 | + | 0.822835i | \(0.307609\pi\) | |||||||
\(864\) | −7.63877 | −0.259876 | ||||||||
\(865\) | −5.17123 | −0.175827 | ||||||||
\(866\) | −36.7908 | −1.25020 | ||||||||
\(867\) | 44.3572 | 1.50645 | ||||||||
\(868\) | 1.69083 | 0.0573906 | ||||||||
\(869\) | −73.2227 | −2.48391 | ||||||||
\(870\) | −162.149 | −5.49737 | ||||||||
\(871\) | −25.1134 | −0.850935 | ||||||||
\(872\) | 4.76651 | 0.161414 | ||||||||
\(873\) | 6.29897 | 0.213188 | ||||||||
\(874\) | −19.6001 | −0.662984 | ||||||||
\(875\) | 1.62994 | 0.0551021 | ||||||||
\(876\) | 135.991 | 4.59472 | ||||||||
\(877\) | −31.1685 | −1.05249 | −0.526243 | − | 0.850334i | \(-0.676400\pi\) | ||||
−0.526243 | + | 0.850334i | \(0.676400\pi\) | |||||||
\(878\) | −44.2113 | −1.49206 | ||||||||
\(879\) | 1.91884 | 0.0647208 | ||||||||
\(880\) | −34.5825 | −1.16578 | ||||||||
\(881\) | 0.0372684 | 0.00125560 | 0.000627802 | − | 1.00000i | \(-0.499800\pi\) | ||||
0.000627802 | 1.00000i | \(0.499800\pi\) | ||||||||
\(882\) | 51.7584 | 1.74280 | ||||||||
\(883\) | −32.3896 | −1.09000 | −0.544998 | − | 0.838437i | \(-0.683470\pi\) | ||||
−0.544998 | + | 0.838437i | \(0.683470\pi\) | |||||||
\(884\) | −4.62539 | −0.155569 | ||||||||
\(885\) | −59.9865 | −2.01643 | ||||||||
\(886\) | −88.5246 | −2.97404 | ||||||||
\(887\) | −56.6582 | −1.90240 | −0.951198 | − | 0.308581i | \(-0.900146\pi\) | ||||
−0.951198 | + | 0.308581i | \(0.900146\pi\) | |||||||
\(888\) | 48.6595 | 1.63290 | ||||||||
\(889\) | −17.9963 | −0.603575 | ||||||||
\(890\) | −31.4649 | −1.05471 | ||||||||
\(891\) | 33.6212 | 1.12635 | ||||||||
\(892\) | −80.5068 | −2.69557 | ||||||||
\(893\) | −23.5386 | −0.787691 | ||||||||
\(894\) | 71.8073 | 2.40159 | ||||||||
\(895\) | 36.0170 | 1.20391 | ||||||||
\(896\) | 23.9468 | 0.800006 | ||||||||
\(897\) | 12.3064 | 0.410899 | ||||||||
\(898\) | −56.7694 | −1.89442 | ||||||||
\(899\) | −3.26426 | −0.108869 | ||||||||
\(900\) | 75.8251 | 2.52750 | ||||||||
\(901\) | −2.48930 | −0.0829304 | ||||||||
\(902\) | 103.913 | 3.45992 | ||||||||
\(903\) | 4.53285 | 0.150844 | ||||||||
\(904\) | 35.6261 | 1.18490 | ||||||||
\(905\) | −7.22809 | −0.240270 | ||||||||
\(906\) | 73.8204 | 2.45252 | ||||||||
\(907\) | −10.4365 | −0.346538 | −0.173269 | − | 0.984875i | \(-0.555433\pi\) | ||||
−0.173269 | + | 0.984875i | \(0.555433\pi\) | |||||||
\(908\) | −80.2949 | −2.66468 | ||||||||
\(909\) | 1.58262 | 0.0524921 | ||||||||
\(910\) | 41.7224 | 1.38308 | ||||||||
\(911\) | 38.8754 | 1.28800 | 0.643999 | − | 0.765026i | \(-0.277274\pi\) | ||||
0.643999 | + | 0.765026i | \(0.277274\pi\) | |||||||
\(912\) | −38.9671 | −1.29033 | ||||||||
\(913\) | −26.2713 | −0.869452 | ||||||||
\(914\) | −69.3500 | −2.29390 | ||||||||
\(915\) | −31.1495 | −1.02977 | ||||||||
\(916\) | 18.5897 | 0.614221 | ||||||||
\(917\) | −11.4139 | −0.376920 | ||||||||
\(918\) | 1.47149 | 0.0485663 | ||||||||
\(919\) | 18.5725 | 0.612649 | 0.306325 | − | 0.951927i | \(-0.400901\pi\) | ||||
0.306325 | + | 0.951927i | \(0.400901\pi\) | |||||||
\(920\) | −12.2915 | −0.405240 | ||||||||
\(921\) | 21.6879 | 0.714639 | ||||||||
\(922\) | 55.6407 | 1.83243 | ||||||||
\(923\) | −5.80610 | −0.191110 | ||||||||
\(924\) | 65.4449 | 2.15298 | ||||||||
\(925\) | 26.5168 | 0.871866 | ||||||||
\(926\) | 2.32161 | 0.0762930 | ||||||||
\(927\) | 61.6276 | 2.02412 | ||||||||
\(928\) | −27.1533 | −0.891351 | ||||||||
\(929\) | 2.69095 | 0.0882872 | 0.0441436 | − | 0.999025i | \(-0.485944\pi\) | ||||
0.0441436 | + | 0.999025i | \(0.485944\pi\) | |||||||
\(930\) | 8.08938 | 0.265261 | ||||||||
\(931\) | −46.7727 | −1.53291 | ||||||||
\(932\) | 1.09414 | 0.0358399 | ||||||||
\(933\) | 34.4368 | 1.12741 | ||||||||
\(934\) | 39.2220 | 1.28338 | ||||||||
\(935\) | −5.25746 | −0.171937 | ||||||||
\(936\) | 69.1192 | 2.25923 | ||||||||
\(937\) | 49.5245 | 1.61790 | 0.808948 | − | 0.587881i | \(-0.200038\pi\) | ||||
0.808948 | + | 0.587881i | \(0.200038\pi\) | |||||||
\(938\) | −14.7105 | −0.480315 | ||||||||
\(939\) | −31.6976 | −1.03441 | ||||||||
\(940\) | −33.1331 | −1.08068 | ||||||||
\(941\) | 12.4547 | 0.406010 | 0.203005 | − | 0.979178i | \(-0.434929\pi\) | ||||
0.203005 | + | 0.979178i | \(0.434929\pi\) | |||||||
\(942\) | −153.430 | −4.99903 | ||||||||
\(943\) | 7.36311 | 0.239776 | ||||||||
\(944\) | 12.7284 | 0.414275 | ||||||||
\(945\) | −8.53868 | −0.277763 | ||||||||
\(946\) | −21.0131 | −0.683195 | ||||||||
\(947\) | −34.1295 | −1.10906 | −0.554530 | − | 0.832164i | \(-0.687102\pi\) | ||||
−0.554530 | + | 0.832164i | \(0.687102\pi\) | |||||||
\(948\) | −116.137 | −3.77194 | ||||||||
\(949\) | 67.5539 | 2.19289 | ||||||||
\(950\) | −106.515 | −3.45579 | ||||||||
\(951\) | 21.7296 | 0.704630 | ||||||||
\(952\) | −1.20708 | −0.0391217 | ||||||||
\(953\) | −7.39659 | −0.239599 | −0.119800 | − | 0.992798i | \(-0.538225\pi\) | ||||
−0.119800 | + | 0.992798i | \(0.538225\pi\) | |||||||
\(954\) | 83.4951 | 2.70326 | ||||||||
\(955\) | 32.3283 | 1.04612 | ||||||||
\(956\) | 25.0524 | 0.810254 | ||||||||
\(957\) | −126.346 | −4.08418 | ||||||||
\(958\) | 17.6492 | 0.570221 | ||||||||
\(959\) | −22.1929 | −0.716646 | ||||||||
\(960\) | 97.7039 | 3.15338 | ||||||||
\(961\) | −30.8372 | −0.994747 | ||||||||
\(962\) | 54.2552 | 1.74926 | ||||||||
\(963\) | −38.0195 | −1.22516 | ||||||||
\(964\) | −47.5107 | −1.53022 | ||||||||
\(965\) | 54.4423 | 1.75256 | ||||||||
\(966\) | 7.20864 | 0.231934 | ||||||||
\(967\) | −14.9572 | −0.480991 | −0.240495 | − | 0.970650i | \(-0.577310\pi\) | ||||
−0.240495 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(968\) | −93.3070 | −2.99900 | ||||||||
\(969\) | −5.92405 | −0.190308 | ||||||||
\(970\) | −12.4551 | −0.399909 | ||||||||
\(971\) | 54.4507 | 1.74741 | 0.873703 | − | 0.486459i | \(-0.161712\pi\) | ||||
0.873703 | + | 0.486459i | \(0.161712\pi\) | |||||||
\(972\) | 77.9496 | 2.50023 | ||||||||
\(973\) | −9.92671 | −0.318236 | ||||||||
\(974\) | −72.9617 | −2.33784 | ||||||||
\(975\) | 66.8777 | 2.14180 | ||||||||
\(976\) | 6.60956 | 0.211567 | ||||||||
\(977\) | −18.4733 | −0.591012 | −0.295506 | − | 0.955341i | \(-0.595488\pi\) | ||||
−0.295506 | + | 0.955341i | \(0.595488\pi\) | |||||||
\(978\) | −6.89022 | −0.220325 | ||||||||
\(979\) | −24.5173 | −0.783577 | ||||||||
\(980\) | −65.8375 | −2.10310 | ||||||||
\(981\) | −4.84561 | −0.154708 | ||||||||
\(982\) | 46.8468 | 1.49494 | ||||||||
\(983\) | 10.9429 | 0.349025 | 0.174513 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174513 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(984\) | 73.4275 | 2.34078 | ||||||||
\(985\) | −36.7247 | −1.17015 | ||||||||
\(986\) | 5.23065 | 0.166578 | ||||||||
\(987\) | 8.65717 | 0.275561 | ||||||||
\(988\) | −140.199 | −4.46032 | ||||||||
\(989\) | −1.48896 | −0.0473460 | ||||||||
\(990\) | 176.344 | 5.60459 | ||||||||
\(991\) | 7.24628 | 0.230186 | 0.115093 | − | 0.993355i | \(-0.463283\pi\) | ||||
0.115093 | + | 0.993355i | \(0.463283\pi\) | |||||||
\(992\) | 1.35464 | 0.0430098 | ||||||||
\(993\) | 12.7953 | 0.406046 | ||||||||
\(994\) | −3.40100 | −0.107873 | ||||||||
\(995\) | 28.1511 | 0.892451 | ||||||||
\(996\) | −41.6682 | −1.32031 | ||||||||
\(997\) | −11.4549 | −0.362781 | −0.181390 | − | 0.983411i | \(-0.558060\pi\) | ||||
−0.181390 | + | 0.983411i | \(0.558060\pi\) | |||||||
\(998\) | 82.8450 | 2.62241 | ||||||||
\(999\) | −11.1036 | −0.351302 |
(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 | 4003.2.a.b.1.19 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.19 | ✓ | 152 | 1.1 | even | 1 | trivial |