Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,3,Mod(53,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.s (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(10.2997539928\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.12 | ||
Character | \(\chi\) | \(=\) | 378.53 |
Dual form | 378.3.s.e.107.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 7.50889 | − | 4.33526i | 1.50178 | − | 0.867052i | 0.501781 | − | 0.864995i | \(-0.332678\pi\) |
0.999998 | − | 0.00205766i | \(-0.000654974\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.86680 | + | 5.03132i | −0.695258 | + | 0.718761i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.13099 | − | 10.6192i | 0.613099 | − | 1.06192i | ||||
\(11\) | 17.9962 | + | 10.3901i | 1.63602 | + | 0.944555i | 0.982185 | + | 0.187914i | \(0.0601728\pi\) |
0.653831 | + | 0.756640i | \(0.273161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.2723 | 1.09787 | 0.548934 | − | 0.835866i | \(-0.315034\pi\) | ||||
0.548934 | + | 0.835866i | \(0.315034\pi\) | |||||||
\(14\) | −2.40291 | + | 9.60344i | −0.171636 | + | 0.685960i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −20.8984 | − | 12.0657i | −1.22932 | − | 0.709747i | −0.262430 | − | 0.964951i | \(-0.584524\pi\) |
−0.966887 | + | 0.255204i | \(0.917857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.29128 | − | 9.16476i | −0.278488 | − | 0.482356i | 0.692521 | − | 0.721398i | \(-0.256500\pi\) |
−0.971009 | + | 0.239042i | \(0.923167\pi\) | |||||||
\(20\) | − | 17.3410i | − | 0.867052i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 29.3876 | 1.33580 | ||||||||
\(23\) | −7.83169 | + | 4.52163i | −0.340508 | + | 0.196593i | −0.660497 | − | 0.750829i | \(-0.729654\pi\) |
0.319988 | + | 0.947421i | \(0.396321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0890 | − | 43.4554i | 1.00356 | − | 1.73822i | ||||
\(26\) | 17.4799 | − | 10.0920i | 0.672304 | − | 0.388155i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.84771 | + | 13.4609i | 0.137418 | + | 0.480746i | ||||
\(29\) | − | 7.52043i | − | 0.259325i | −0.991558 | − | 0.129663i | \(-0.958611\pi\) | ||
0.991558 | − | 0.129663i | \(-0.0413894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.20366 | − | 5.54890i | 0.103344 | − | 0.178997i | −0.809716 | − | 0.586821i | \(-0.800379\pi\) |
0.913060 | + | 0.407824i | \(0.133712\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −34.1269 | −1.00373 | ||||||||
\(35\) | −14.7322 | + | 58.8786i | −0.420920 | + | 1.68224i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.11561 | − | 8.86050i | −0.138260 | − | 0.239473i | 0.788578 | − | 0.614934i | \(-0.210818\pi\) |
−0.926838 | + | 0.375462i | \(0.877484\pi\) | |||||||
\(38\) | −12.9609 | − | 7.48299i | −0.341077 | − | 0.196921i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.2620 | − | 21.2384i | −0.306549 | − | 0.530959i | ||||
\(41\) | 66.6674i | 1.62603i | 0.582240 | + | 0.813017i | \(0.302176\pi\) | ||||
−0.582240 | + | 0.813017i | \(0.697824\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.07514 | −0.164538 | −0.0822691 | − | 0.996610i | \(-0.526217\pi\) | ||||
−0.0822691 | + | 0.996610i | \(0.526217\pi\) | |||||||
\(44\) | 35.9924 | − | 20.7802i | 0.818008 | − | 0.472277i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.39455 | + | 11.0757i | −0.139012 | + | 0.240776i | ||||
\(47\) | 24.6311 | − | 14.2208i | 0.524066 | − | 0.302570i | −0.214531 | − | 0.976717i | \(-0.568822\pi\) |
0.738597 | + | 0.674148i | \(0.235489\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.62846 | − | 48.9729i | −0.0332339 | − | 0.999448i | ||||
\(50\) | − | 70.9624i | − | 1.41925i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.2723 | − | 24.7203i | 0.274467 | − | 0.475391i | ||||
\(53\) | −46.7667 | − | 27.0008i | −0.882391 | − | 0.509449i | −0.0109452 | − | 0.999940i | \(-0.503484\pi\) |
−0.871446 | + | 0.490491i | \(0.836817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 180.175 | 3.27591 | ||||||||
\(56\) | 14.2307 | + | 13.7654i | 0.254120 | + | 0.245811i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.31775 | − | 9.21061i | −0.0916853 | − | 0.158804i | ||||
\(59\) | −25.3538 | − | 14.6380i | −0.429725 | − | 0.248102i | 0.269505 | − | 0.962999i | \(-0.413140\pi\) |
−0.699229 | + | 0.714897i | \(0.746473\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.95564 | − | 15.5116i | −0.146814 | − | 0.254289i | 0.783234 | − | 0.621727i | \(-0.213568\pi\) |
−0.930048 | + | 0.367438i | \(0.880235\pi\) | |||||||
\(62\) | − | 9.06132i | − | 0.146150i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 107.169 | − | 61.8741i | 1.64875 | − | 0.951909i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.5167 | + | 82.3014i | −0.709205 | + | 1.22838i | 0.255947 | + | 0.966691i | \(0.417613\pi\) |
−0.965152 | + | 0.261688i | \(0.915721\pi\) | |||||||
\(68\) | −41.7968 | + | 24.1314i | −0.614659 | + | 0.354873i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 23.5902 | + | 82.5284i | 0.337003 | + | 1.17898i | ||||
\(71\) | 107.104i | 1.50850i | 0.656585 | + | 0.754252i | \(0.272001\pi\) | ||||
−0.656585 | + | 0.754252i | \(0.727999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58.6643 | − | 101.610i | 0.803621 | − | 1.39191i | −0.113597 | − | 0.993527i | \(-0.536237\pi\) |
0.917218 | − | 0.398386i | \(-0.130429\pi\) | |||||||
\(74\) | −12.5306 | − | 7.23457i | −0.169333 | − | 0.0977644i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.1651 | −0.278488 | ||||||||
\(77\) | −139.860 | + | 39.9781i | −1.81636 | + | 0.519196i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.7364 | + | 42.8447i | 0.313119 | + | 0.542338i | 0.979036 | − | 0.203688i | \(-0.0652928\pi\) |
−0.665917 | + | 0.746026i | \(0.731960\pi\) | |||||||
\(80\) | −30.0356 | − | 17.3410i | −0.375445 | − | 0.216763i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 47.1410 | + | 81.6505i | 0.574890 | + | 0.995738i | ||||
\(83\) | 88.9954i | 1.07223i | 0.844144 | + | 0.536117i | \(0.180109\pi\) | ||||
−0.844144 | + | 0.536117i | \(0.819891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −209.232 | −2.46155 | ||||||||
\(86\) | −8.66524 | + | 5.00288i | −0.100759 | + | 0.0581730i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 29.3876 | − | 50.9009i | 0.333951 | − | 0.578419i | ||||
\(89\) | −63.3370 | + | 36.5677i | −0.711652 | + | 0.410873i | −0.811672 | − | 0.584113i | \(-0.801443\pi\) |
0.100020 | + | 0.994985i | \(0.468109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −69.4604 | + | 71.8085i | −0.763301 | + | 0.789104i | ||||
\(92\) | 18.0865i | 0.196593i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.1112 | − | 34.8336i | 0.213949 | − | 0.370571i | ||||
\(95\) | −79.4633 | − | 45.8781i | −0.836455 | − | 0.482928i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −106.700 | −1.10000 | −0.550001 | − | 0.835164i | \(-0.685373\pi\) | ||||
−0.550001 | + | 0.835164i | \(0.685373\pi\) | |||||||
\(98\) | −36.6235 | − | 58.8279i | −0.373710 | − | 0.600284i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −50.1780 | − | 86.9108i | −0.501780 | − | 0.869108i | ||||
\(101\) | 71.1499 | + | 41.0784i | 0.704455 | + | 0.406717i | 0.809004 | − | 0.587803i | \(-0.200007\pi\) |
−0.104550 | + | 0.994520i | \(0.533340\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7585 | − | 30.7586i | −0.172412 | − | 0.298627i | 0.766850 | − | 0.641826i | \(-0.221823\pi\) |
−0.939263 | + | 0.343199i | \(0.888489\pi\) | |||||||
\(104\) | − | 40.3681i | − | 0.388155i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −76.3698 | −0.720470 | ||||||||
\(107\) | −1.32075 | + | 0.762537i | −0.0123435 | + | 0.00712651i | −0.506159 | − | 0.862440i | \(-0.668935\pi\) |
0.493816 | + | 0.869567i | \(0.335602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −100.395 | + | 173.890i | −0.921059 | + | 1.59532i | −0.123279 | + | 0.992372i | \(0.539341\pi\) |
−0.797780 | + | 0.602948i | \(0.793992\pi\) | |||||||
\(110\) | 220.669 | − | 127.403i | 2.00608 | − | 1.15821i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 27.1626 | + | 6.79645i | 0.242523 | + | 0.0606826i | ||||
\(113\) | 111.702i | 0.988512i | 0.869316 | + | 0.494256i | \(0.164559\pi\) | ||||
−0.869316 | + | 0.494256i | \(0.835441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39.2049 | + | 67.9049i | −0.340912 | + | 0.590477i | ||||
\(116\) | −13.0258 | − | 7.52043i | −0.112291 | − | 0.0648313i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −41.4025 | −0.350869 | ||||||||
\(119\) | 162.415 | − | 46.4253i | 1.36483 | − | 0.390128i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 155.408 | + | 269.175i | 1.28437 | + | 2.22459i | ||||
\(122\) | −21.9367 | − | 12.6652i | −0.179809 | − | 0.103813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.40732 | − | 11.0978i | −0.0516719 | − | 0.0894984i | ||||
\(125\) | − | 218.306i | − | 1.74645i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.661 | −0.926461 | −0.463230 | − | 0.886238i | \(-0.653310\pi\) | ||||
−0.463230 | + | 0.886238i | \(0.653310\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 87.5032 | − | 151.560i | 0.673101 | − | 1.16585i | ||||
\(131\) | 125.964 | − | 72.7252i | 0.961555 | − | 0.555154i | 0.0649037 | − | 0.997892i | \(-0.479326\pi\) |
0.896651 | + | 0.442737i | \(0.145993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 71.8625 | + | 17.9809i | 0.540319 | + | 0.135195i | ||||
\(134\) | 134.398i | 1.00297i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −34.1269 | + | 59.1096i | −0.250933 | + | 0.434629i | ||||
\(137\) | −49.0580 | − | 28.3237i | −0.358088 | − | 0.206742i | 0.310154 | − | 0.950686i | \(-0.399619\pi\) |
−0.668242 | + | 0.743944i | \(0.732953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −24.6609 | −0.177416 | −0.0887082 | − | 0.996058i | \(-0.528274\pi\) | ||||
−0.0887082 | + | 0.996058i | \(0.528274\pi\) | |||||||
\(140\) | 87.2484 | + | 84.3955i | 0.623203 | + | 0.602825i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 75.7339 | + | 131.175i | 0.533337 | + | 0.923767i | ||||
\(143\) | 256.847 | + | 148.290i | 1.79613 | + | 1.03700i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32.6030 | − | 56.4701i | −0.224849 | − | 0.389449i | ||||
\(146\) | − | 165.928i | − | 1.13649i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.4624 | −0.138260 | ||||||||
\(149\) | −93.0248 | + | 53.7079i | −0.624328 | + | 0.360456i | −0.778552 | − | 0.627580i | \(-0.784045\pi\) |
0.154224 | + | 0.988036i | \(0.450712\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.1196 | − | 52.1687i | 0.199468 | − | 0.345488i | −0.748888 | − | 0.662696i | \(-0.769412\pi\) |
0.948356 | + | 0.317208i | \(0.102745\pi\) | |||||||
\(152\) | −25.9219 | + | 14.9660i | −0.170538 | + | 0.0984604i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −143.024 | + | 147.859i | −0.928726 | + | 0.960122i | ||||
\(155\) | − | 55.5548i | − | 0.358418i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 47.3063 | − | 81.9369i | 0.301314 | − | 0.521891i | −0.675120 | − | 0.737708i | \(-0.735908\pi\) |
0.976434 | + | 0.215817i | \(0.0692415\pi\) | |||||||
\(158\) | 60.5915 | + | 34.9825i | 0.383491 | + | 0.221408i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −49.0479 | −0.306549 | ||||||||
\(161\) | 15.3655 | − | 61.4097i | 0.0954380 | − | 0.381427i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −135.827 | − | 235.260i | −0.833297 | − | 1.44331i | −0.895410 | − | 0.445243i | \(-0.853117\pi\) |
0.0621129 | − | 0.998069i | \(-0.480216\pi\) | |||||||
\(164\) | 115.471 | + | 66.6674i | 0.704093 | + | 0.406508i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62.9292 | + | 108.997i | 0.379092 | + | 0.656606i | ||||
\(167\) | − | 26.0210i | − | 0.155815i | −0.996961 | − | 0.0779073i | \(-0.975176\pi\) | ||
0.996961 | − | 0.0779073i | \(-0.0248238\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.6981 | 0.205314 | ||||||||
\(170\) | −256.256 | + | 147.949i | −1.50739 | + | 0.870289i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.07514 | + | 12.2545i | −0.0411345 | + | 0.0712471i | ||||
\(173\) | −80.0949 | + | 46.2428i | −0.462976 | + | 0.267299i | −0.713295 | − | 0.700864i | \(-0.752798\pi\) |
0.250319 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 96.5351 | + | 337.720i | 0.551629 | + | 1.92983i | ||||
\(176\) | − | 83.1208i | − | 0.472277i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −51.7145 | + | 89.5721i | −0.290531 | + | 0.503214i | ||||
\(179\) | −93.2534 | − | 53.8399i | −0.520969 | − | 0.300781i | 0.216362 | − | 0.976313i | \(-0.430581\pi\) |
−0.737331 | + | 0.675532i | \(0.763914\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 117.141 | 0.647190 | 0.323595 | − | 0.946196i | \(-0.395108\pi\) | ||||
0.323595 | + | 0.946196i | \(0.395108\pi\) | |||||||
\(182\) | −34.2950 | + | 137.063i | −0.188434 | + | 0.753093i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.7891 | + | 22.1514i | 0.0695060 | + | 0.120388i | ||||
\(185\) | −76.8252 | − | 44.3550i | −0.415271 | − | 0.239757i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −250.728 | − | 434.273i | −1.34079 | − | 2.32232i | ||||
\(188\) | − | 56.8831i | − | 0.302570i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −129.763 | −0.682963 | ||||||||
\(191\) | −126.515 | + | 73.0436i | −0.662383 | + | 0.382427i | −0.793184 | − | 0.608981i | \(-0.791578\pi\) |
0.130801 | + | 0.991409i | \(0.458245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48.2616 | − | 83.5916i | 0.250060 | − | 0.433117i | −0.713482 | − | 0.700674i | \(-0.752883\pi\) |
0.963542 | + | 0.267557i | \(0.0862162\pi\) | |||||||
\(194\) | −130.680 | + | 75.4484i | −0.673611 | + | 0.388909i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −86.4521 | − | 46.1524i | −0.441082 | − | 0.235471i | ||||
\(197\) | − | 134.797i | − | 0.684247i | −0.939655 | − | 0.342123i | \(-0.888854\pi\) | ||
0.939655 | − | 0.342123i | \(-0.111146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 133.940 | − | 231.990i | 0.673063 | − | 1.16578i | −0.303967 | − | 0.952682i | \(-0.598311\pi\) |
0.977031 | − | 0.213098i | \(-0.0683553\pi\) | |||||||
\(200\) | −122.910 | − | 70.9624i | −0.614552 | − | 0.354812i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 116.187 | 0.575185 | ||||||||
\(203\) | 37.8377 | + | 36.6005i | 0.186393 | + | 0.180298i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 289.021 | + | 500.598i | 1.40986 | + | 2.44194i | ||||
\(206\) | −43.4992 | − | 25.1143i | −0.211161 | − | 0.121914i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −28.5446 | − | 49.4406i | −0.137233 | − | 0.237695i | ||||
\(209\) | − | 219.908i | − | 1.05219i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −251.891 | −1.19380 | −0.596899 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596899 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(212\) | −93.5335 | + | 54.0016i | −0.441196 | + | 0.254724i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.07839 | + | 1.86783i | −0.00503921 | + | 0.00872816i | ||||
\(215\) | −53.1265 | + | 30.6726i | −0.247100 | + | 0.142663i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3267 | + | 43.1241i | 0.0568053 | + | 0.198728i | ||||
\(218\) | 283.961i | 1.30257i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 180.175 | − | 312.073i | 0.818978 | − | 1.41851i | ||||
\(221\) | −298.268 | − | 172.205i | −1.34963 | − | 0.779208i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 427.001 | 1.91480 | 0.957401 | − | 0.288761i | \(-0.0932434\pi\) | ||||
0.957401 | + | 0.288761i | \(0.0932434\pi\) | |||||||
\(224\) | 38.0731 | − | 10.8830i | 0.169969 | − | 0.0485846i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 78.9851 | + | 136.806i | 0.349492 | + | 0.605337i | ||||
\(227\) | 235.832 | + | 136.158i | 1.03891 | + | 0.599814i | 0.919524 | − | 0.393034i | \(-0.128575\pi\) |
0.119384 | + | 0.992848i | \(0.461908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −38.8763 | − | 67.3357i | −0.169765 | − | 0.294042i | 0.768572 | − | 0.639763i | \(-0.220968\pi\) |
−0.938337 | + | 0.345721i | \(0.887634\pi\) | |||||||
\(230\) | 110.888i | 0.482123i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.2710 | −0.0916853 | ||||||||
\(233\) | 27.7244 | − | 16.0067i | 0.118989 | − | 0.0686982i | −0.439324 | − | 0.898329i | \(-0.644782\pi\) |
0.558313 | + | 0.829630i | \(0.311449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 123.302 | − | 213.564i | 0.524687 | − | 0.908785i | ||||
\(236\) | −50.7075 | + | 29.2760i | −0.214862 | + | 0.124051i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 166.089 | − | 171.704i | 0.697853 | − | 0.721444i | ||||
\(239\) | 296.164i | 1.23918i | 0.784925 | + | 0.619590i | \(0.212701\pi\) | ||||
−0.784925 | + | 0.619590i | \(0.787299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 99.9257 | − | 173.076i | 0.414629 | − | 0.718159i | −0.580760 | − | 0.814075i | \(-0.697245\pi\) |
0.995389 | + | 0.0959157i | \(0.0305779\pi\) | |||||||
\(242\) | 380.671 | + | 219.781i | 1.57302 | + | 0.908185i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −35.8226 | −0.146814 | ||||||||
\(245\) | −224.538 | − | 360.673i | −0.916483 | − | 1.47213i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −75.5186 | − | 130.802i | −0.305743 | − | 0.529563i | ||||
\(248\) | −15.6947 | − | 9.06132i | −0.0632849 | − | 0.0365376i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −154.366 | − | 267.370i | −0.617464 | − | 1.06948i | ||||
\(251\) | 176.183i | 0.701926i | 0.936389 | + | 0.350963i | \(0.114146\pi\) | ||||
−0.936389 | + | 0.350963i | \(0.885854\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −187.921 | −0.742770 | ||||||||
\(254\) | −144.104 | + | 83.1985i | −0.567339 | + | 0.327553i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 251.692 | − | 145.315i | 0.979347 | − | 0.565426i | 0.0772739 | − | 0.997010i | \(-0.475378\pi\) |
0.902073 | + | 0.431584i | \(0.142045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 69.4767 | + | 17.3840i | 0.268250 | + | 0.0671197i | ||||
\(260\) | − | 247.496i | − | 0.951909i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 102.849 | − | 178.140i | 0.392553 | − | 0.679922i | ||||
\(263\) | 22.5084 | + | 12.9952i | 0.0855832 | + | 0.0494115i | 0.542181 | − | 0.840262i | \(-0.317599\pi\) |
−0.456598 | + | 0.889673i | \(0.650932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −468.222 | −1.76688 | ||||||||
\(266\) | 100.728 | − | 28.7924i | 0.378675 | − | 0.108242i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 95.0335 | + | 164.603i | 0.354603 | + | 0.614190i | ||||
\(269\) | 61.8759 | + | 35.7240i | 0.230022 | + | 0.132803i | 0.610582 | − | 0.791953i | \(-0.290936\pi\) |
−0.380560 | + | 0.924756i | \(0.624269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 127.939 | + | 221.596i | 0.472099 | + | 0.817699i | 0.999490 | − | 0.0319235i | \(-0.0101633\pi\) |
−0.527392 | + | 0.849622i | \(0.676830\pi\) | |||||||
\(272\) | 96.5256i | 0.354873i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −80.1114 | −0.292377 | ||||||||
\(275\) | 903.012 | − | 521.354i | 3.28368 | − | 1.89583i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 212.019 | − | 367.227i | 0.765410 | − | 1.32573i | −0.174620 | − | 0.984636i | \(-0.555870\pi\) |
0.940030 | − | 0.341093i | \(-0.110797\pi\) | |||||||
\(278\) | −30.2033 | + | 17.4379i | −0.108645 | + | 0.0627262i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 166.534 | + | 41.6689i | 0.594763 | + | 0.148818i | ||||
\(281\) | − | 195.647i | − | 0.696252i | −0.937448 | − | 0.348126i | \(-0.886818\pi\) | ||
0.937448 | − | 0.348126i | \(-0.113182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −33.3648 | + | 57.7896i | −0.117897 | + | 0.204203i | −0.918934 | − | 0.394411i | \(-0.870949\pi\) |
0.801037 | + | 0.598615i | \(0.204282\pi\) | |||||||
\(284\) | 185.509 | + | 107.104i | 0.653202 | + | 0.377126i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 419.429 | 1.46653 | ||||||||
\(287\) | −335.425 | − | 324.457i | −1.16873 | − | 1.13051i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 146.662 | + | 254.026i | 0.507481 | + | 0.878982i | ||||
\(290\) | −79.8608 | − | 46.1077i | −0.275382 | − | 0.158992i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −117.329 | − | 203.219i | −0.401811 | − | 0.695956i | ||||
\(293\) | 320.934i | 1.09534i | 0.836695 | + | 0.547669i | \(0.184485\pi\) | ||||
−0.836695 | + | 0.547669i | \(0.815515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −253.838 | −0.860469 | ||||||||
\(296\) | −25.0613 | + | 14.4691i | −0.0846665 | + | 0.0488822i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −75.9544 | + | 131.557i | −0.254881 | + | 0.441466i | ||||
\(299\) | −111.776 | + | 64.5340i | −0.373833 | + | 0.215833i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.4333 | − | 35.5973i | 0.114396 | − | 0.118264i | ||||
\(302\) | − | 85.1911i | − | 0.282090i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.1651 | + | 36.6590i | −0.0696220 | + | 0.120589i | ||||
\(305\) | −134.494 | − | 77.6501i | −0.440964 | − | 0.254590i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 142.642 | 0.464630 | 0.232315 | − | 0.972641i | \(-0.425370\pi\) | ||||
0.232315 | + | 0.972641i | \(0.425370\pi\) | |||||||
\(308\) | −70.6158 | + | 282.222i | −0.229272 | + | 0.916307i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −39.2832 | − | 68.0405i | −0.126720 | − | 0.219485i | ||||
\(311\) | −418.336 | − | 241.526i | −1.34513 | − | 0.776611i | −0.357575 | − | 0.933884i | \(-0.616396\pi\) |
−0.987555 | + | 0.157273i | \(0.949730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75.6771 | + | 131.077i | 0.241780 | + | 0.418775i | 0.961221 | − | 0.275778i | \(-0.0889355\pi\) |
−0.719442 | + | 0.694553i | \(0.755602\pi\) | |||||||
\(314\) | − | 133.802i | − | 0.426122i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 98.9456 | 0.313119 | ||||||||
\(317\) | −132.391 | + | 76.4361i | −0.417638 | + | 0.241123i | −0.694066 | − | 0.719911i | \(-0.744182\pi\) |
0.276428 | + | 0.961035i | \(0.410849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 78.1381 | − | 135.339i | 0.244947 | − | 0.424260i | ||||
\(320\) | −60.0712 | + | 34.6821i | −0.187722 | + | 0.108382i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.6044 | − | 86.0762i | −0.0764111 | − | 0.267318i | ||||
\(323\) | 255.372i | 0.790624i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 358.077 | − | 620.208i | 1.10178 | − | 1.90833i | ||||
\(326\) | −332.708 | − | 192.089i | −1.02058 | − | 0.589230i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 188.564 | 0.574890 | ||||||||
\(329\) | −48.3254 | + | 193.137i | −0.146886 | + | 0.587042i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −167.428 | − | 289.994i | −0.505825 | − | 0.876114i | −0.999977 | − | 0.00673894i | \(-0.997855\pi\) |
0.494153 | − | 0.869375i | \(-0.335478\pi\) | |||||||
\(332\) | 154.145 | + | 88.9954i | 0.464291 | + | 0.268058i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.3997 | − | 31.8691i | −0.0550888 | − | 0.0954166i | ||||
\(335\) | 823.990i | 2.45967i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6151 | −0.0344663 | −0.0172331 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172331 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(338\) | 42.4963 | − | 24.5352i | 0.125729 | − | 0.0725895i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −209.232 | + | 362.400i | −0.615388 | + | 1.06588i | ||||
\(341\) | 115.307 | − | 66.5727i | 0.338145 | − | 0.195228i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 254.324 | + | 230.148i | 0.741470 | + | 0.670986i | ||||
\(344\) | 20.0115i | 0.0581730i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −65.3972 | + | 113.271i | −0.189009 | + | 0.327374i | ||||
\(347\) | 513.432 | + | 296.430i | 1.47963 | + | 0.854265i | 0.999734 | − | 0.0230599i | \(-0.00734085\pi\) |
0.479897 | + | 0.877325i | \(0.340674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −304.583 | −0.872731 | −0.436365 | − | 0.899770i | \(-0.643734\pi\) | ||||
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(350\) | 357.035 | + | 345.360i | 1.02010 | + | 0.986743i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −58.7753 | − | 101.802i | −0.166975 | − | 0.289210i | ||||
\(353\) | −594.546 | − | 343.261i | −1.68427 | − | 0.972412i | −0.958768 | − | 0.284188i | \(-0.908276\pi\) |
−0.725499 | − | 0.688224i | \(-0.758391\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 464.323 | + | 804.231i | 1.30795 | + | 2.26544i | ||||
\(356\) | 146.271i | 0.410873i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −152.282 | −0.425369 | ||||||||
\(359\) | 418.605 | − | 241.682i | 1.16603 | − | 0.673209i | 0.213290 | − | 0.976989i | \(-0.431582\pi\) |
0.952742 | + | 0.303780i | \(0.0982488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 124.505 | − | 215.649i | 0.344889 | − | 0.597365i | ||||
\(362\) | 143.468 | − | 82.8315i | 0.396322 | − | 0.228816i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 54.9156 | + | 192.117i | 0.150867 | + | 0.527795i | ||||
\(365\) | − | 1017.30i | − | 2.78713i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 76.7208 | − | 132.884i | 0.209048 | − | 0.362082i | −0.742367 | − | 0.669994i | \(-0.766297\pi\) |
0.951415 | + | 0.307911i | \(0.0996300\pi\) | |||||||
\(368\) | 31.3268 | + | 18.0865i | 0.0851271 | + | 0.0491482i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −125.455 | −0.339068 | ||||||||
\(371\) | 363.454 | − | 103.891i | 0.979661 | − | 0.280030i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −138.261 | − | 239.475i | −0.370672 | − | 0.642023i | 0.618997 | − | 0.785393i | \(-0.287539\pi\) |
−0.989669 | + | 0.143370i | \(0.954206\pi\) | |||||||
\(374\) | −614.155 | − | 354.582i | −1.64212 | − | 0.948081i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −40.2224 | − | 69.6673i | −0.106974 | − | 0.185285i | ||||
\(377\) | − | 107.334i | − | 0.284705i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −396.161 | −1.04528 | −0.522640 | − | 0.852553i | \(-0.675053\pi\) | ||||
−0.522640 | + | 0.852553i | \(0.675053\pi\) | |||||||
\(380\) | −158.927 | + | 91.7563i | −0.418228 | + | 0.241464i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −103.299 | + | 178.920i | −0.270417 | + | 0.468376i | ||||
\(383\) | −263.830 | + | 152.322i | −0.688851 | + | 0.397708i | −0.803182 | − | 0.595734i | \(-0.796861\pi\) |
0.114330 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −876.877 | + | 906.520i | −2.27760 | + | 2.35460i | ||||
\(386\) | − | 136.505i | − | 0.353639i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −106.700 | + | 184.810i | −0.275000 | + | 0.476315i | ||||
\(389\) | 408.682 | + | 235.952i | 1.05060 | + | 0.606561i | 0.922816 | − | 0.385241i | \(-0.125882\pi\) |
0.127779 | + | 0.991803i | \(0.459215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 218.226 | 0.558124 | ||||||||
\(392\) | −138.516 | + | 4.60598i | −0.353358 | + | 0.0117500i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −95.3156 | − | 165.091i | −0.241918 | − | 0.419014i | ||||
\(395\) | 371.486 | + | 214.477i | 0.940471 | + | 0.542981i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −194.550 | − | 336.970i | −0.490050 | − | 0.848791i | 0.509885 | − | 0.860243i | \(-0.329688\pi\) |
−0.999934 | + | 0.0114517i | \(0.996355\pi\) | |||||||
\(398\) | − | 378.838i | − | 0.951856i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −200.712 | −0.501780 | ||||||||
\(401\) | 562.454 | − | 324.733i | 1.40263 | − | 0.809808i | 0.407967 | − | 0.912997i | \(-0.366238\pi\) |
0.994662 | + | 0.103189i | \(0.0329046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.7235 | − | 79.1955i | 0.113458 | − | 0.196515i | ||||
\(404\) | 142.300 | − | 82.1568i | 0.352227 | − | 0.203359i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 72.2220 | + | 18.0709i | 0.177887 | + | 0.0445096i | ||||
\(407\) | − | 212.607i | − | 0.522376i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 207.497 | − | 359.396i | 0.507328 | − | 0.878718i | −0.492636 | − | 0.870235i | \(-0.663967\pi\) |
0.999964 | − | 0.00848231i | \(-0.00270003\pi\) | |||||||
\(410\) | 707.953 | + | 408.737i | 1.72671 | + | 0.996919i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −71.0338 | −0.172412 | ||||||||
\(413\) | 197.040 | − | 56.3227i | 0.477095 | − | 0.136375i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 385.818 | + | 668.257i | 0.929683 | + | 1.61026i | ||||
\(416\) | −69.9196 | − | 40.3681i | −0.168076 | − | 0.0970387i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −155.498 | − | 269.331i | −0.372005 | − | 0.644332i | ||||
\(419\) | 45.9042i | 0.109557i | 0.998499 | + | 0.0547783i | \(0.0174452\pi\) | ||||
−0.998499 | + | 0.0547783i | \(0.982555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 315.779 | 0.750068 | 0.375034 | − | 0.927011i | \(-0.377631\pi\) | ||||
0.375034 | + | 0.927011i | \(0.377631\pi\) | |||||||
\(422\) | −308.503 | + | 178.114i | −0.731049 | + | 0.422071i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −76.3698 | + | 132.276i | −0.180117 | + | 0.311972i | ||||
\(425\) | −1048.64 | + | 605.432i | −2.46739 | + | 1.42455i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 121.629 | + | 30.4333i | 0.284846 | + | 0.0712723i | ||||
\(428\) | 3.05015i | 0.00712651i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −43.3776 | + | 75.1322i | −0.100878 | + | 0.174726i | ||||
\(431\) | 27.2604 | + | 15.7388i | 0.0632492 | + | 0.0365169i | 0.531291 | − | 0.847189i | \(-0.321707\pi\) |
−0.468042 | + | 0.883706i | \(0.655040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −318.863 | −0.736404 | −0.368202 | − | 0.929746i | \(-0.620026\pi\) | ||||
−0.368202 | + | 0.929746i | \(0.620026\pi\) | |||||||
\(434\) | 45.5904 | + | 44.0997i | 0.105047 | + | 0.101612i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 200.791 | + | 347.780i | 0.460529 | + | 0.797660i | ||||
\(437\) | 82.8793 | + | 47.8504i | 0.189655 | + | 0.109497i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −264.483 | − | 458.098i | −0.602467 | − | 1.04350i | −0.992446 | − | 0.122679i | \(-0.960851\pi\) |
0.389980 | − | 0.920823i | \(-0.372482\pi\) | |||||||
\(440\) | − | 509.613i | − | 1.15821i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −487.069 | −1.10197 | ||||||||
\(443\) | −346.977 | + | 200.327i | −0.783245 | + | 0.452206i | −0.837579 | − | 0.546316i | \(-0.816030\pi\) |
0.0543344 | + | 0.998523i | \(0.482696\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −317.061 | + | 549.165i | −0.712496 | + | 1.23408i | ||||
\(446\) | 522.967 | − | 301.935i | 1.17257 | − | 0.676985i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 38.9344 | − | 40.2506i | 0.0869072 | − | 0.0898451i | ||||
\(449\) | 410.186i | 0.913555i | 0.889581 | + | 0.456777i | \(0.150996\pi\) | ||||
−0.889581 | + | 0.456777i | \(0.849004\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −692.681 | + | 1199.76i | −1.53588 | + | 2.66022i | ||||
\(452\) | 193.473 | + | 111.702i | 0.428038 | + | 0.247128i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 385.112 | 0.848265 | ||||||||
\(455\) | −210.262 | + | 840.331i | −0.462114 | + | 1.84688i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −90.2981 | − | 156.401i | −0.197589 | − | 0.342234i | 0.750157 | − | 0.661259i | \(-0.229978\pi\) |
−0.947746 | + | 0.319026i | \(0.896644\pi\) | |||||||
\(458\) | −95.2270 | − | 54.9794i | −0.207919 | − | 0.120042i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 78.4098 | + | 135.810i | 0.170456 | + | 0.295239i | ||||
\(461\) | 277.708i | 0.602403i | 0.953560 | + | 0.301202i | \(0.0973877\pi\) | ||||
−0.953560 | + | 0.301202i | \(0.902612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −519.910 | −1.12292 | −0.561458 | − | 0.827505i | \(-0.689759\pi\) | ||||
−0.561458 | + | 0.827505i | \(0.689759\pi\) | |||||||
\(464\) | −26.0515 | + | 15.0409i | −0.0561456 | + | 0.0324157i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.6369 | − | 39.2082i | 0.0485770 | − | 0.0841378i | ||||
\(467\) | −49.5843 | + | 28.6275i | −0.106176 | + | 0.0613009i | −0.552148 | − | 0.833746i | \(-0.686192\pi\) |
0.445972 | + | 0.895047i | \(0.352858\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −182.831 | − | 639.617i | −0.389831 | − | 1.36379i | ||||
\(470\) | − | 348.749i | − | 0.742020i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −41.4025 | + | 71.7113i | −0.0877172 | + | 0.151931i | ||||
\(473\) | −127.326 | − | 73.5115i | −0.269187 | − | 0.155415i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −531.011 | −1.11792 | ||||||||
\(476\) | 82.0039 | − | 327.736i | 0.172277 | − | 0.688521i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 209.420 | + | 362.726i | 0.438117 | + | 0.758840i | ||||
\(479\) | −498.037 | − | 287.542i | −1.03974 | − | 0.600296i | −0.119982 | − | 0.992776i | \(-0.538284\pi\) |
−0.919760 | + | 0.392480i | \(0.871617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.0115 | − | 126.460i | −0.151791 | − | 0.262910i | ||||
\(482\) | − | 282.632i | − | 0.586374i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 621.634 | 1.28437 | ||||||||
\(485\) | −801.200 | + | 462.573i | −1.65196 | + | 0.953759i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −98.8020 | + | 171.130i | −0.202879 | + | 0.351397i | −0.949455 | − | 0.313904i | \(-0.898363\pi\) |
0.746576 | + | 0.665300i | \(0.231696\pi\) | |||||||
\(488\) | −43.8735 | + | 25.3304i | −0.0899047 | + | 0.0519065i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −530.036 | − | 282.959i | −1.08171 | − | 0.577468i | ||||
\(491\) | 82.1487i | 0.167309i | 0.996495 | + | 0.0836545i | \(0.0266592\pi\) | ||||
−0.996495 | + | 0.0836545i | \(0.973341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −90.7392 | + | 157.165i | −0.184055 | + | 0.318793i | ||||
\(494\) | −184.982 | − | 106.799i | −0.374457 | − | 0.216193i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.6293 | −0.0516719 | ||||||||
\(497\) | −538.874 | − | 521.253i | −1.08425 | − | 1.04880i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −93.2348 | − | 161.487i | −0.186843 | − | 0.323622i | 0.757353 | − | 0.653006i | \(-0.226492\pi\) |
−0.944196 | + | 0.329384i | \(0.893159\pi\) | |||||||
\(500\) | −378.118 | − | 218.306i | −0.756235 | − | 0.436613i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 124.580 | + | 215.780i | 0.248168 | + | 0.429840i | ||||
\(503\) | 70.5631i | 0.140285i | 0.997537 | + | 0.0701423i | \(0.0223453\pi\) | ||||
−0.997537 | + | 0.0701423i | \(0.977655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 712.343 | 1.41058 | ||||||||
\(506\) | −230.155 | + | 132.880i | −0.454852 | + | 0.262609i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −117.661 | + | 203.794i | −0.231615 | + | 0.401169i | ||||
\(509\) | 86.1465 | − | 49.7367i | 0.169247 | − | 0.0977145i | −0.412984 | − | 0.910738i | \(-0.635513\pi\) |
0.582231 | + | 0.813024i | \(0.302180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 225.723 | + | 789.673i | 0.441728 | + | 1.54535i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 205.506 | − | 355.946i | 0.399817 | − | 0.692503i | ||||
\(515\) | −266.693 | − | 153.975i | −0.517850 | − | 0.298981i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 591.021 | 1.14317 | ||||||||
\(518\) | 97.3836 | − | 27.8365i | 0.187999 | − | 0.0537384i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −175.006 | − | 303.120i | −0.336551 | − | 0.582923i | ||||
\(521\) | 323.761 | + | 186.924i | 0.621423 | + | 0.358779i | 0.777423 | − | 0.628978i | \(-0.216527\pi\) |
−0.156000 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −78.9282 | − | 136.708i | −0.150914 | − | 0.261391i | 0.780649 | − | 0.624969i | \(-0.214888\pi\) |
−0.931564 | + | 0.363578i | \(0.881555\pi\) | |||||||
\(524\) | − | 290.901i | − | 0.555154i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.7560 | 0.0698784 | ||||||||
\(527\) | −133.903 | + | 77.3088i | −0.254085 | + | 0.146696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −223.610 | + | 387.303i | −0.422703 | + | 0.732143i | ||||
\(530\) | −573.452 | + | 331.083i | −1.08199 | + | 0.624685i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 103.006 | − | 106.489i | 0.193621 | − | 0.200166i | ||||
\(533\) | 951.496i | 1.78517i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.61159 | + | 11.4516i | −0.0123581 | + | 0.0214049i | ||||
\(536\) | 232.784 | + | 134.398i | 0.434298 | + | 0.250742i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 101.043 | 0.187812 | ||||||||
\(539\) | 479.528 | − | 898.246i | 0.889662 | − | 1.66650i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 89.0870 | + | 154.303i | 0.164671 | + | 0.285218i | 0.936538 | − | 0.350565i | \(-0.114010\pi\) |
−0.771867 | + | 0.635783i | \(0.780677\pi\) | |||||||
\(542\) | 313.385 | + | 180.933i | 0.578200 | + | 0.333824i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 68.2539 | + | 118.219i | 0.125467 | + | 0.217315i | ||||
\(545\) | 1740.96i | 3.19442i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 702.119 | 1.28358 | 0.641791 | − | 0.766880i | \(-0.278192\pi\) | ||||
0.641791 | + | 0.766880i | \(0.278192\pi\) | |||||||
\(548\) | −98.1160 | + | 56.6473i | −0.179044 | + | 0.103371i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 737.306 | − | 1277.05i | 1.34056 | − | 2.32191i | ||||
\(551\) | −68.9229 | + | 39.7927i | −0.125087 | + | 0.0722190i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −335.953 | − | 84.0598i | −0.607509 | − | 0.152007i | ||||
\(554\) | − | 599.679i | − | 1.08245i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.6609 | + | 42.7139i | −0.0443541 | + | 0.0768236i | ||||
\(557\) | −657.663 | − | 379.702i | −1.18072 | − | 0.681691i | −0.224542 | − | 0.974464i | \(-0.572089\pi\) |
−0.956182 | + | 0.292773i | \(0.905422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −100.978 | −0.180641 | ||||||||
\(560\) | 233.426 | − | 66.7233i | 0.416832 | − | 0.119149i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −138.343 | − | 239.617i | −0.246162 | − | 0.426365i | ||||
\(563\) | 199.465 | + | 115.161i | 0.354290 | + | 0.204549i | 0.666573 | − | 0.745440i | \(-0.267760\pi\) |
−0.312283 | + | 0.949989i | \(0.601094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 484.257 | + | 838.757i | 0.857092 | + | 1.48453i | ||||
\(566\) | 94.3700i | 0.166731i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 302.935 | 0.533337 | ||||||||
\(569\) | 569.401 | − | 328.744i | 1.00070 | − | 0.577757i | 0.0922477 | − | 0.995736i | \(-0.470595\pi\) |
0.908457 | + | 0.417979i | \(0.137262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −202.408 | + | 350.581i | −0.354480 | + | 0.613977i | −0.987029 | − | 0.160543i | \(-0.948675\pi\) |
0.632549 | + | 0.774520i | \(0.282009\pi\) | |||||||
\(572\) | 513.693 | − | 296.581i | 0.898065 | − | 0.518498i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −640.236 | − | 160.196i | −1.11539 | − | 0.279086i | ||||
\(575\) | 453.773i | 0.789170i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −133.102 | + | 230.540i | −0.230680 | + | 0.399549i | −0.958008 | − | 0.286740i | \(-0.907428\pi\) |
0.727329 | + | 0.686289i | \(0.240762\pi\) | |||||||
\(578\) | 359.247 | + | 207.411i | 0.621534 | + | 0.358843i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −130.412 | −0.224849 | ||||||||
\(581\) | −447.765 | − | 433.123i | −0.770679 | − | 0.745479i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −561.082 | − | 971.822i | −0.962405 | − | 1.66693i | ||||
\(584\) | −287.395 | − | 165.928i | −0.492115 | − | 0.284123i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 226.935 | + | 393.062i | 0.387260 | + | 0.670755i | ||||
\(587\) | − | 1056.47i | − | 1.79979i | −0.436112 | − | 0.899893i | \(-0.643645\pi\) | ||
0.436112 | − | 0.899893i | \(-0.356355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.8058 | −0.115120 | ||||||||
\(590\) | −310.887 | + | 179.491i | −0.526927 | + | 0.304222i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.4624 | + | 35.4420i | −0.0345649 | + | 0.0598682i | ||||
\(593\) | 356.475 | − | 205.811i | 0.601138 | − | 0.347067i | −0.168351 | − | 0.985727i | \(-0.553844\pi\) |
0.769489 | + | 0.638660i | \(0.220511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1018.29 | − | 1052.71i | 1.71141 | − | 1.76927i | ||||
\(596\) | 214.832i | 0.360456i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −91.2648 | + | 158.075i | −0.152617 | + | 0.264340i | ||||
\(599\) | 162.408 | + | 93.7661i | 0.271131 | + | 0.156538i | 0.629402 | − | 0.777080i | \(-0.283300\pi\) |
−0.358270 | + | 0.933618i | \(0.616633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1046.72 | 1.74163 | 0.870813 | − | 0.491614i | \(-0.163593\pi\) | ||||
0.870813 | + | 0.491614i | \(0.163593\pi\) | |||||||
\(602\) | 17.0009 | − | 67.9457i | 0.0282407 | − | 0.112867i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −60.2392 | − | 104.337i | −0.0997338 | − | 0.172744i | ||||
\(605\) | 2333.89 | + | 1347.47i | 3.85767 | + | 2.22723i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −419.594 | − | 726.758i | −0.691259 | − | 1.19730i | −0.971426 | − | 0.237344i | \(-0.923723\pi\) |
0.280167 | − | 0.959951i | \(-0.409610\pi\) | |||||||
\(608\) | 59.8639i | 0.0984604i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −219.628 | −0.360045 | ||||||||
\(611\) | 351.542 | − | 202.963i | 0.575355 | − | 0.332181i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −560.113 | + | 970.144i | −0.913725 | + | 1.58262i | −0.104967 | + | 0.994476i | \(0.533474\pi\) |
−0.808758 | + | 0.588142i | \(0.799860\pi\) | |||||||
\(614\) | 174.699 | − | 100.863i | 0.284527 | − | 0.164272i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 113.075 | + | 395.583i | 0.183563 | + | 0.642181i | ||||
\(617\) | − | 1115.35i | − | 1.80769i | −0.427859 | − | 0.903846i | \(-0.640732\pi\) | ||
0.427859 | − | 0.903846i | \(-0.359268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 98.4595 | − | 170.537i | 0.159062 | − | 0.275504i | −0.775469 | − | 0.631386i | \(-0.782486\pi\) |
0.934531 | + | 0.355882i | \(0.115820\pi\) | |||||||
\(620\) | −96.2238 | − | 55.5548i | −0.155200 | − | 0.0896045i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −683.139 | −1.09829 | ||||||||
\(623\) | 124.265 | − | 496.637i | 0.199462 | − | 0.797170i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.190 | − | 552.854i | −0.510705 | − | 0.884566i | ||||
\(626\) | 185.370 | + | 107.024i | 0.296118 | + | 0.170964i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −94.6125 | − | 163.874i | −0.150657 | − | 0.260945i | ||||
\(629\) | 246.894i | 0.392518i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −820.657 | −1.30057 | −0.650283 | − | 0.759692i | \(-0.725350\pi\) | ||||
−0.650283 | + | 0.759692i | \(0.725350\pi\) | |||||||
\(632\) | 121.183 | − | 69.9651i | 0.191745 | − | 0.110704i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −108.097 | + | 187.229i | −0.170500 | + | 0.295314i | ||||
\(635\) | −883.500 | + | 510.089i | −1.39134 | + | 0.803290i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.2419 | − | 698.956i | −0.0364864 | − | 1.09726i | ||||
\(638\) | − | 221.008i | − | 0.346407i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −49.0479 | + | 84.9534i | −0.0766373 | + | 0.132740i | ||||
\(641\) | −329.497 | − | 190.235i | −0.514035 | − | 0.296778i | 0.220456 | − | 0.975397i | \(-0.429246\pi\) |
−0.734491 | + | 0.678619i | \(0.762579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 134.072 | 0.208510 | 0.104255 | − | 0.994551i | \(-0.466754\pi\) | ||||
0.104255 | + | 0.994551i | \(0.466754\pi\) | |||||||
\(644\) | −90.9992 | − | 88.0235i | −0.141303 | − | 0.136683i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 180.575 | + | 312.765i | 0.279528 | + | 0.484157i | ||||
\(647\) | 443.702 | + | 256.172i | 0.685784 | + | 0.395938i | 0.802031 | − | 0.597283i | \(-0.203753\pi\) |
−0.116247 | + | 0.993220i | \(0.537086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −304.181 | − | 526.856i | −0.468691 | − | 0.811797i | ||||
\(650\) | − | 1012.80i | − | 1.55815i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −543.309 | −0.833297 | ||||||||
\(653\) | 609.551 | − | 351.924i | 0.933463 | − | 0.538935i | 0.0455575 | − | 0.998962i | \(-0.485494\pi\) |
0.887905 | + | 0.460027i | \(0.152160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 630.565 | − | 1092.17i | 0.962695 | − | 1.66744i | ||||
\(656\) | 230.943 | − | 133.335i | 0.352047 | − | 0.203254i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 77.3820 | + | 270.714i | 0.117602 | + | 0.411420i | ||||
\(659\) | 664.121i | 1.00777i | 0.863771 | + | 0.503885i | \(0.168097\pi\) | ||||
−0.863771 | + | 0.503885i | \(0.831903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 507.932 | − | 879.765i | 0.768430 | − | 1.33096i | −0.169984 | − | 0.985447i | \(-0.554372\pi\) |
0.938414 | − | 0.345513i | \(-0.112295\pi\) | |||||||
\(662\) | −410.113 | − | 236.779i | −0.619506 | − | 0.357672i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 251.717 | 0.379092 | ||||||||
\(665\) | 617.560 | − | 176.526i | 0.928661 | − | 0.265452i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.0046 | + | 58.8977i | 0.0509814 | + | 0.0883024i | ||||
\(668\) | −45.0698 | − | 26.0210i | −0.0674697 | − | 0.0389536i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 582.649 | + | 1009.18i | 0.869625 | + | 1.50624i | ||||
\(671\) | − | 372.200i | − | 0.554695i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 832.049 | 1.23633 | 0.618164 | − | 0.786049i | \(-0.287877\pi\) | ||||
0.618164 | + | 0.786049i | \(0.287877\pi\) | |||||||
\(674\) | −14.2256 | + | 8.21314i | −0.0211062 | + | 0.0121857i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.6981 | − | 60.0988i | 0.0513285 | − | 0.0889036i | ||||
\(677\) | 265.283 | − | 153.161i | 0.391850 | − | 0.226235i | −0.291111 | − | 0.956689i | \(-0.594025\pi\) |
0.682962 | + | 0.730454i | \(0.260692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 519.289 | − | 536.843i | 0.764785 | − | 0.790638i | ||||
\(680\) | 591.797i | 0.870289i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 94.1480 | − | 163.069i | 0.138047 | − | 0.239104i | ||||
\(683\) | −32.8662 | − | 18.9753i | −0.0481203 | − | 0.0277823i | 0.475747 | − | 0.879582i | \(-0.342178\pi\) |
−0.523867 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −491.162 | −0.717025 | ||||||||
\(686\) | 474.222 | + | 102.039i | 0.691285 | + | 0.148744i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.1503 | + | 24.5090i | 0.0205673 | + | 0.0356236i | ||||
\(689\) | −667.468 | − | 385.363i | −0.968749 | − | 0.559308i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 149.036 | + | 258.138i | 0.215682 | + | 0.373572i | 0.953483 | − | 0.301446i | \(-0.0974692\pi\) |
−0.737801 | + | 0.675018i | \(0.764136\pi\) | |||||||
\(692\) | 184.971i | 0.267299i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 838.431 | 1.20811 | ||||||||
\(695\) | −185.176 | + | 106.911i | −0.266440 | + | 0.153829i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 804.388 | − | 1393.24i | 1.15407 | − | 1.99891i | ||||
\(698\) | −373.036 | + | 215.373i | −0.534436 | + | 0.308557i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 681.483 | + | 170.516i | 0.973547 | + | 0.243594i | ||||
\(701\) | 102.414i | 0.146097i | 0.997328 | + | 0.0730487i | \(0.0232728\pi\) | ||||
−0.997328 | + | 0.0730487i | \(0.976727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.1362 | + | 93.7667i | −0.0770074 | + | 0.133381i | ||||
\(704\) | −143.969 | − | 83.1208i | −0.204502 | − | 0.118069i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −970.890 | −1.37520 | ||||||||
\(707\) | −552.951 | + | 158.058i | −0.782110 | + | 0.223561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 219.076 | + | 379.450i | 0.308993 | + | 0.535191i | 0.978142 | − | 0.207937i | \(-0.0666748\pi\) |
−0.669150 | + | 0.743128i | \(0.733341\pi\) | |||||||
\(710\) | 1137.35 | + | 656.652i | 1.60191 | + | 0.924862i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 103.429 | + | 179.144i | 0.145265 | + | 0.251607i | ||||
\(713\) | 57.9431i | 0.0812666i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2571.51 | 3.59652 | ||||||||
\(716\) | −186.507 | + | 107.680i | −0.260484 | + | 0.150391i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 341.790 | − | 591.998i | 0.476031 | − | 0.824509i | ||||
\(719\) | −1183.93 | + | 683.542i | −1.64663 | + | 0.950685i | −0.668238 | + | 0.743948i | \(0.732951\pi\) |
−0.978397 | + | 0.206737i | \(0.933716\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 241.183 | + | 60.3472i | 0.334512 | + | 0.0836993i | ||||
\(722\) | − | 352.153i | − | 0.487746i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 117.141 | − | 202.895i | 0.161798 | − | 0.280242i | ||||
\(725\) | −326.803 | − | 188.680i | −0.450763 | − | 0.260248i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −695.754 | −0.957021 | −0.478510 | − | 0.878082i | \(-0.658823\pi\) | ||||
−0.478510 | + | 0.878082i | \(0.658823\pi\) | |||||||
\(728\) | 203.105 | + | 196.464i | 0.278991 | + | 0.269868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −719.341 | − | 1245.93i | −0.985398 | − | 1.70676i | ||||
\(731\) | 147.859 | + | 85.3665i | 0.202270 | + | 0.116780i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 570.340 | + | 987.857i | 0.778090 | + | 1.34769i | 0.933042 | + | 0.359769i | \(0.117144\pi\) |
−0.154952 | + | 0.987922i | \(0.549522\pi\) | |||||||
\(734\) | − | 216.999i | − | 0.295639i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 51.1564 | 0.0695060 | ||||||||
\(737\) | −1710.24 | + | 987.408i | −2.32054 | + | 1.33977i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 143.021 | − | 247.719i | 0.193533 | − | 0.335209i | −0.752886 | − | 0.658151i | \(-0.771339\pi\) |
0.946419 | + | 0.322942i | \(0.104672\pi\) | |||||||
\(740\) | −153.650 | + | 88.7101i | −0.207636 | + | 0.119878i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 371.677 | − | 384.241i | 0.500912 | − | 0.517845i | ||||
\(743\) | 928.085i | 1.24910i | 0.780983 | + | 0.624552i | \(0.214718\pi\) | ||||
−0.780983 | + | 0.624552i | \(0.785282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −465.676 | + | 806.574i | −0.625068 | + | 1.08265i | ||||
\(746\) | −338.668 | − | 195.530i | −0.453979 | − | 0.262105i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1002.91 | −1.34079 | ||||||||
\(749\) | 2.59127 | − | 10.3563i | 0.00345964 | − | 0.0138268i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 522.842 | + | 905.589i | 0.696194 | + | 1.20584i | 0.969776 | + | 0.243995i | \(0.0784581\pi\) |
−0.273582 | + | 0.961849i | \(0.588209\pi\) | |||||||
\(752\) | −98.5244 | − | 56.8831i | −0.131016 | − | 0.0756424i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −75.8964 | − | 131.456i | −0.100658 | − | 0.174345i | ||||
\(755\) | − | 522.306i | − | 0.691796i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −823.084 | −1.08730 | −0.543648 | − | 0.839313i | \(-0.682957\pi\) | ||||
−0.543648 | + | 0.839313i | \(0.682957\pi\) | |||||||
\(758\) | −485.197 | + | 280.128i | −0.640101 | + | 0.369562i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −129.763 | + | 224.756i | −0.170741 | + | 0.295732i | ||||
\(761\) | 661.169 | − | 381.726i | 0.868816 | − | 0.501611i | 0.00186153 | − | 0.999998i | \(-0.499407\pi\) |
0.866955 | + | 0.498387i | \(0.166074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −386.292 | − | 1351.41i | −0.506281 | − | 1.77118i | ||||
\(764\) | 292.174i | 0.382427i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −215.416 | + | 373.112i | −0.281222 | + | 0.487091i | ||||
\(767\) | −361.856 | − | 208.918i | −0.471781 | − | 0.272383i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −310.039 | −0.403172 | −0.201586 | − | 0.979471i | \(-0.564610\pi\) | ||||
−0.201586 | + | 0.979471i | \(0.564610\pi\) | |||||||
\(770\) | −432.945 | + | 1730.30i | −0.562266 | + | 2.24715i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −96.5233 | − | 167.183i | −0.125030 | − | 0.216559i | ||||
\(773\) | −348.526 | − | 201.222i | −0.450875 | − | 0.260313i | 0.257325 | − | 0.966325i | \(-0.417159\pi\) |
−0.708200 | + | 0.706012i | \(0.750492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −160.753 | − | 278.433i | −0.207423 | − | 0.359268i | ||||
\(776\) | 301.794i | 0.388909i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 667.374 | 0.857807 | ||||||||
\(779\) | 610.991 | − | 352.756i | 0.784327 | − | 0.452831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1112.82 | + | 1927.46i | −1.42487 | + | 2.46794i | ||||
\(782\) | 267.272 | − | 154.309i | 0.341780 | − | 0.197327i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −166.390 | + | 103.587i | −0.212233 | + | 0.132126i | ||||
\(785\) | − | 820.340i | − | 1.04502i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −311.572 | + | 539.658i | −0.395898 | + | 0.685715i | −0.993215 | − | 0.116290i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296233\pi\) | |||||||
\(788\) | −233.475 | − | 134.797i | −0.296288 | − | 0.171062i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 606.634 | 0.767891 | ||||||||
\(791\) | −562.008 | − | 543.631i | −0.710504 | − | 0.687270i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −127.817 | − | 221.386i | −0.161182 | − | 0.279176i | ||||
\(794\) | −476.548 | − | 275.135i | −0.600186 | − | 0.346518i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −267.879 | − | 463.980i | −0.336532 | − | 0.582890i | ||||
\(797\) | − | 221.306i | − | 0.277673i | −0.990315 | − | 0.138837i | \(-0.955664\pi\) | ||
0.990315 | − | 0.138837i | \(-0.0443363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −686.334 | −0.858991 | ||||||||
\(800\) | −245.821 | + | 141.925i | −0.307276 | + | 0.177406i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 459.242 | − | 795.430i | 0.572621 | − | 0.991808i | ||||
\(803\) | 2111.47 | − | 1219.06i | 2.62948 | − | 1.51813i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −150.849 | − | 527.732i | −0.187390 | − | 0.655568i | ||||
\(806\) | − | 129.326i | − | 0.160454i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 116.187 | − | 201.242i | 0.143796 | − | 0.249062i | ||||
\(809\) | 1114.71 | + | 643.579i | 1.37789 | + | 0.795524i | 0.991905 | − | 0.126982i | \(-0.0405290\pi\) |
0.385983 | + | 0.922506i | \(0.373862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 999.374 | 1.23227 | 0.616137 | − | 0.787639i | \(-0.288697\pi\) | ||||
0.616137 | + | 0.787639i | \(0.288697\pi\) | |||||||
\(812\) | 101.232 | − | 28.9364i | 0.124669 | − | 0.0356360i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −150.336 | − | 260.389i | −0.184688 | − | 0.319888i | ||||
\(815\) | −2039.83 | − | 1177.69i | −2.50285 | − | 1.44502i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.4365 | + | 64.8420i | 0.0458219 | + | 0.0793659i | ||||
\(818\) | − | 586.890i | − | 0.717470i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1156.08 | 1.40986 | ||||||||
\(821\) | 947.645 | − | 547.123i | 1.15426 | − | 0.666411i | 0.204336 | − | 0.978901i | \(-0.434496\pi\) |
0.949921 | + | 0.312490i | \(0.101163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −167.539 | + | 290.187i | −0.203571 | + | 0.352596i | −0.949677 | − | 0.313232i | \(-0.898588\pi\) |
0.746105 | + | 0.665828i | \(0.231922\pi\) | |||||||
\(824\) | −86.9983 | + | 50.2285i | −0.105580 | + | 0.0609569i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 201.498 | − | 208.310i | 0.243944 | − | 0.252191i | ||||
\(827\) | − | 275.340i | − | 0.332938i | −0.986047 | − | 0.166469i | \(-0.946763\pi\) | ||
0.986047 | − | 0.166469i | \(-0.0532366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −210.758 | + | 365.043i | −0.254231 | + | 0.440342i | −0.964686 | − | 0.263401i | \(-0.915156\pi\) |
0.710455 | + | 0.703742i | \(0.248489\pi\) | |||||||
\(830\) | 945.058 | + | 545.630i | 1.13862 | + | 0.657385i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −114.178 | −0.137233 | ||||||||
\(833\) | −556.860 | + | 1043.10i | −0.668500 | + | 1.25223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −112.808 | − | 195.389i | −0.135099 | − | 0.233999i | ||||
\(836\) | −380.891 | − | 219.908i | −0.455611 | − | 0.263047i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.4592 | + | 56.2210i | 0.0387341 | + | 0.0670895i | ||||
\(839\) | − | 682.819i | − | 0.813848i | −0.913462 | − | 0.406924i | \(-0.866601\pi\) | ||
0.913462 | − | 0.406924i | \(-0.133399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 784.443 | 0.932750 | ||||||||
\(842\) | 386.748 | − | 223.289i | 0.459321 | − | 0.265189i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −251.891 | + | 436.289i | −0.298449 | + | 0.516930i | ||||
\(845\) | 260.544 | − | 150.425i | 0.308336 | − | 0.178018i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2110.65 | − | 528.113i | −2.49191 | − | 0.623510i | ||||
\(848\) | 216.006i | 0.254724i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −856.210 | + | 1483.00i | −1.00731 | + | 1.74471i | ||||
\(851\) | 80.1278 | + | 46.2618i | 0.0941572 | + | 0.0543617i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 249.493 | 0.292489 | 0.146244 | − | 0.989249i | \(-0.453281\pi\) | ||||
0.146244 | + | 0.989249i | \(0.453281\pi\) | |||||||
\(854\) | 170.484 | − | 48.7319i | 0.199631 | − | 0.0570632i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.15678 | + | 3.73565i | 0.00251960 | + | 0.00436408i | ||||
\(857\) | 244.741 | + | 141.301i | 0.285578 | + | 0.164879i | 0.635946 | − | 0.771733i | \(-0.280610\pi\) |
−0.350368 | + | 0.936612i | \(0.613943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.67788 | + | 4.63823i | 0.00311744 | + | 0.00539957i | 0.867580 | − | 0.497298i | \(-0.165674\pi\) |
−0.864462 | + | 0.502697i | \(0.832341\pi\) | |||||||
\(860\) | 122.690i | 0.142663i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.5161 | 0.0516428 | ||||||||
\(863\) | −73.1639 | + | 42.2412i | −0.0847786 | + | 0.0489470i | −0.541790 | − | 0.840514i | \(-0.682253\pi\) |
0.457011 | + | 0.889461i | \(0.348920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −400.949 | + | 694.465i | −0.463525 | + | 0.802849i | ||||
\(866\) | −390.526 | + | 225.470i | −0.450953 | + | 0.260358i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 87.0198 | + | 21.7735i | 0.100253 | + | 0.0250847i | ||||
\(869\) | 1028.05i | 1.18303i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −678.172 | + | 1174.63i | −0.778613 | + | 1.34860i | ||||
\(872\) | 491.835 | + | 283.961i | 0.564031 | + | 0.325643i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 135.341 | 0.154853 | ||||||||
\(875\) | 1098.37 | + | 1062.45i | 1.25528 | + | 1.21423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −721.477 | − | 1249.63i | −0.822664 | − | 1.42490i | −0.903691 | − | 0.428185i | \(-0.859153\pi\) |
0.0810269 | − | 0.996712i | \(-0.474180\pi\) | |||||||
\(878\) | −647.848 | − | 374.035i | −0.737868 | − | 0.426008i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −360.351 | − | 624.145i | −0.409489 | − | 0.709256i | ||||
\(881\) | − | 437.949i | − | 0.497104i | −0.968619 | − | 0.248552i | \(-0.920045\pi\) | ||
0.968619 | − | 0.248552i | \(-0.0799548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 956.951 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(884\) | −596.536 | + | 344.410i | −0.674814 | + | 0.389604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −283.306 | + | 490.700i | −0.319758 | + | 0.553837i | ||||
\(887\) | 181.342 | − | 104.698i | 0.204444 | − | 0.118036i | −0.394283 | − | 0.918989i | \(-0.629007\pi\) |
0.598727 | + | 0.800953i | \(0.295674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 572.630 | − | 591.988i | 0.644129 | − | 0.665904i | ||||
\(890\) | 896.783i | 1.00762i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 427.001 | − | 739.587i | 0.478701 | − | 0.829134i | ||||
\(893\) | −260.660 | − | 150.492i | −0.291892 | − | 0.168524i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −933.640 | −1.04317 | ||||||||
\(896\) | 19.2233 | − | 76.8275i | 0.0214545 | − | 0.0857450i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 290.045 | + | 502.373i | 0.322990 | + | 0.559436i | ||||
\(899\) | −41.7301 | − | 24.0929i | −0.0464184 | − | 0.0267997i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 651.567 | + | 1128.55i | 0.723159 | + | 1.25255i | ||||
\(902\) | 1959.20i | 2.17206i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 315.941 | 0.349492 | ||||||||
\(905\) | 879.603 | − | 507.839i | 0.971937 | − | 0.561148i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 70.9229 | − | 122.842i | 0.0781951 | − | 0.135438i | −0.824276 | − | 0.566188i | \(-0.808418\pi\) |
0.902471 | + | 0.430750i | \(0.141751\pi\) | |||||||
\(908\) | 471.664 | − | 272.315i | 0.519454 | − | 0.299907i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 336.687 | + | 1177.87i | 0.369985 | + | 1.29436i | ||||
\(911\) | 200.004i | 0.219543i | 0.993957 | + | 0.109772i | \(0.0350120\pi\) | ||||
−0.993957 | + | 0.109772i | \(0.964988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −924.671 | + | 1601.58i | −1.01278 | + | 1.75419i | ||||
\(914\) | −221.184 | − | 127.701i | −0.241996 | − | 0.139716i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −155.505 | −0.169765 | ||||||||
\(917\) | −247.136 | + | 987.703i | −0.269505 | + | 1.07710i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 244.112 | + | 422.815i | 0.265628 | + | 0.460081i | 0.967728 | − | 0.251997i | \(-0.0810874\pi\) |
−0.702100 | + | 0.712078i | \(0.747754\pi\) | |||||||
\(920\) | 192.064 | + | 110.888i | 0.208765 | + | 0.120531i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 196.369 | + | 340.121i | 0.212982 | + | 0.368895i | ||||
\(923\) | 1528.62i | 1.65614i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −513.382 | −0.555008 | ||||||||
\(926\) | −636.757 | + | 367.632i | −0.687643 | + | 0.397011i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.2710 | + | 36.8424i | −0.0229213 | + | 0.0397009i | ||||
\(929\) | 1147.06 | − | 662.255i | 1.23472 | − | 0.712868i | 0.266713 | − | 0.963776i | \(-0.414062\pi\) |
0.968011 | + | 0.250908i | \(0.0807290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −440.208 | + | 274.054i | −0.472834 | + | 0.294365i | ||||
\(932\) | − | 64.0267i | − | 0.0686982i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.4854 | + | 70.1228i | −0.0433462 | + | 0.0750779i | ||||
\(935\) | −3765.37 | − | 2173.94i | −4.02714 | − | 2.32507i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1196.41 | 1.27685 | 0.638427 | − | 0.769683i | \(-0.279586\pi\) | ||||
0.638427 | + | 0.769683i | \(0.279586\pi\) | |||||||
\(938\) | −676.198 | − | 654.087i | −0.720894 | − | 0.697321i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −246.603 | − | 427.129i | −0.262344 | − | 0.454393i | ||||
\(941\) | −939.143 | − | 542.214i | −0.998027 | − | 0.576211i | −0.0903628 | − | 0.995909i | \(-0.528803\pi\) |
−0.907664 | + | 0.419698i | \(0.862136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −301.445 | − | 522.119i | −0.319666 | − | 0.553678i | ||||
\(944\) | 117.104i | 0.124051i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −207.922 | −0.219790 | ||||||||
\(947\) | 1009.73 | − | 582.965i | 1.06624 | − | 0.615592i | 0.139085 | − | 0.990280i | \(-0.455584\pi\) |
0.927151 | + | 0.374689i | \(0.122250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 837.274 | − | 1450.20i | 0.882270 | − | 1.52814i | ||||
\(950\) | −650.353 | + | 375.482i | −0.684582 | + | 0.395244i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −131.310 | − | 459.378i | −0.137931 | − | 0.482540i | ||||
\(953\) | − | 1337.53i | − | 1.40350i | −0.712425 | − | 0.701748i | \(-0.752403\pi\) | ||
0.712425 | − | 0.701748i | \(-0.247597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −633.326 | + | 1096.95i | −0.663169 | + | 1.14864i | ||||
\(956\) | 512.971 | + | 296.164i | 0.536581 | + | 0.309795i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −813.291 | −0.848946 | ||||||||
\(959\) | 381.261 | − | 108.981i | 0.397561 | − | 0.113640i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 459.973 | + | 796.697i | 0.478640 | + | 0.829029i | ||||
\(962\) | −178.841 | − | 103.254i | −0.185905 | − | 0.107332i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −199.851 | − | 346.153i | −0.207315 | − | 0.359079i | ||||
\(965\) | − | 836.907i | − | 0.867261i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1002.76 | −1.03698 | −0.518490 | − | 0.855084i | \(-0.673506\pi\) | ||||
−0.518490 | + | 0.855084i | \(0.673506\pi\) | |||||||
\(968\) | 761.343 | − | 439.561i | 0.786511 | − | 0.454092i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −654.177 | + | 1133.07i | −0.674410 | + | 1.16811i | ||||
\(971\) | −190.222 | + | 109.825i | −0.195904 | + | 0.113105i | −0.594743 | − | 0.803916i | \(-0.702746\pi\) |
0.398840 | + | 0.917021i | \(0.369413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 120.020 | − | 124.077i | 0.123350 | − | 0.127520i | ||||
\(974\) | 279.454i | 0.286914i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.8226 | + | 62.0465i | −0.0367034 | + | 0.0635722i | ||||
\(977\) | 1602.04 | + | 924.941i | 1.63976 | + | 0.946715i | 0.980915 | + | 0.194436i | \(0.0622876\pi\) |
0.658844 | + | 0.752280i | \(0.271046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1519.77 | −1.55237 | ||||||||
\(980\) | −849.242 | + | 28.2392i | −0.866573 | + | 0.0288155i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 58.0879 | + | 100.611i | 0.0591527 | + | 0.102455i | ||||
\(983\) | −274.830 | − | 158.673i | −0.279583 | − | 0.161417i | 0.353652 | − | 0.935377i | \(-0.384940\pi\) |
−0.633234 | + | 0.773960i | \(0.718273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −584.379 | − | 1012.17i | −0.593278 | − | 1.02759i | ||||
\(986\) | 256.649i | 0.260293i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −302.074 | −0.305743 | ||||||||
\(989\) | 55.4103 | − | 31.9912i | 0.0560266 | − | 0.0323470i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −807.465 | + | 1398.57i | −0.814798 | + | 1.41127i | 0.0946750 | + | 0.995508i | \(0.469819\pi\) |
−0.909473 | + | 0.415763i | \(0.863515\pi\) | |||||||
\(992\) | −31.3893 | + | 18.1226i | −0.0316425 | + | 0.0182688i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1028.57 | − | 257.361i | −1.03477 | − | 0.258914i | ||||
\(995\) | − | 2322.65i | − | 2.33433i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.16943 | + | 14.1499i | −0.00819401 | + | 0.0141924i | −0.870093 | − | 0.492887i | \(-0.835942\pi\) |
0.861899 | + | 0.507079i | \(0.169275\pi\) | |||||||
\(998\) | −228.378 | − | 131.854i | −0.228835 | − | 0.132118i | ||||
\(999\) | 0 | 0 |
(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 | 378.3.s.e.53.12 | yes | 24 | |
3.2 | odd | 2 | inner | 378.3.s.e.53.1 | ✓ | 24 | |
7.2 | even | 3 | inner | 378.3.s.e.107.1 | yes | 24 | |
21.2 | odd | 6 | inner | 378.3.s.e.107.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.3.s.e.53.1 | ✓ | 24 | 3.2 | odd | 2 | inner | |
378.3.s.e.53.12 | yes | 24 | 1.1 | even | 1 | trivial | |
378.3.s.e.107.1 | yes | 24 | 7.2 | even | 3 | inner | |
378.3.s.e.107.12 | yes | 24 | 21.2 | odd | 6 | inner |