Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (of order \(2\), degree \(1\), 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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.17 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.18 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.984102 | −0.492051 | −0.246025 | − | 0.969263i | \(-0.579125\pi\) | ||||
−0.246025 | + | 0.969263i | \(0.579125\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −3.03154 | −0.757886 | ||||||||
\(5\) | − | 2.95865i | − | 0.591731i | −0.955230 | − | 0.295865i | \(-0.904392\pi\) | ||
0.955230 | − | 0.295865i | \(-0.0956079\pi\) | |||||||
\(6\) | −1.70451 | −0.284086 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 6.91976 | 0.864969 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 2.91162i | 0.291162i | ||||||||
\(11\) | 1.64161i | 0.149237i | 0.997212 | + | 0.0746185i | \(0.0237739\pi\) | ||||
−0.997212 | + | 0.0746185i | \(0.976226\pi\) | |||||||
\(12\) | −5.25079 | −0.437566 | ||||||||
\(13\) | −20.6451 | −1.58808 | −0.794041 | − | 0.607864i | \(-0.792027\pi\) | ||||
−0.794041 | + | 0.607864i | \(0.792027\pi\) | |||||||
\(14\) | − | 2.60369i | − | 0.185978i | ||||||
\(15\) | − | 5.12454i | − | 0.341636i | ||||||
\(16\) | 5.31643 | 0.332277 | ||||||||
\(17\) | 1.80914i | 0.106420i | 0.998583 | + | 0.0532100i | \(0.0169453\pi\) | ||||
−0.998583 | + | 0.0532100i | \(0.983055\pi\) | |||||||
\(18\) | −2.95231 | −0.164017 | ||||||||
\(19\) | − | 30.5833i | − | 1.60965i | −0.593513 | − | 0.804825i | \(-0.702259\pi\) | ||
0.593513 | − | 0.804825i | \(-0.297741\pi\) | |||||||
\(20\) | 8.96928i | 0.448464i | ||||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | − | 1.61551i | − | 0.0734322i | ||||||
\(23\) | −4.61202 | + | 22.5328i | −0.200523 | + | 0.979689i | ||||
\(24\) | 11.9854 | 0.499390 | ||||||||
\(25\) | 16.2464 | 0.649855 | ||||||||
\(26\) | 20.3169 | 0.781417 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 8.02071i | − | 0.286454i | ||||||
\(29\) | −23.0792 | −0.795835 | −0.397918 | − | 0.917421i | \(-0.630267\pi\) | ||||
−0.397918 | + | 0.917421i | \(0.630267\pi\) | |||||||
\(30\) | 5.04307i | 0.168102i | ||||||||
\(31\) | −46.3849 | −1.49629 | −0.748144 | − | 0.663537i | \(-0.769055\pi\) | ||||
−0.748144 | + | 0.663537i | \(0.769055\pi\) | |||||||
\(32\) | −32.9109 | −1.02847 | ||||||||
\(33\) | 2.84335i | 0.0861620i | ||||||||
\(34\) | − | 1.78038i | − | 0.0523641i | ||||||
\(35\) | 7.82786 | 0.223653 | ||||||||
\(36\) | −9.09463 | −0.252629 | ||||||||
\(37\) | 61.7024i | 1.66763i | 0.552042 | + | 0.833816i | \(0.313849\pi\) | ||||
−0.552042 | + | 0.833816i | \(0.686151\pi\) | |||||||
\(38\) | 30.0971i | 0.792029i | ||||||||
\(39\) | −35.7583 | −0.916880 | ||||||||
\(40\) | − | 20.4732i | − | 0.511829i | ||||||
\(41\) | −46.0087 | −1.12216 | −0.561082 | − | 0.827760i | \(-0.689615\pi\) | ||||
−0.561082 | + | 0.827760i | \(0.689615\pi\) | |||||||
\(42\) | − | 4.50972i | − | 0.107374i | ||||||
\(43\) | 47.1312i | 1.09608i | 0.836454 | + | 0.548038i | \(0.184625\pi\) | ||||
−0.836454 | + | 0.548038i | \(0.815375\pi\) | |||||||
\(44\) | − | 4.97660i | − | 0.113105i | ||||||
\(45\) | − | 8.87596i | − | 0.197244i | ||||||
\(46\) | 4.53870 | − | 22.1746i | 0.0986674 | − | 0.482057i | ||||
\(47\) | −77.1309 | −1.64108 | −0.820541 | − | 0.571587i | \(-0.806328\pi\) | ||||
−0.820541 | + | 0.571587i | \(0.806328\pi\) | |||||||
\(48\) | 9.20832 | 0.191840 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | −15.9881 | −0.319762 | ||||||||
\(51\) | 3.13352i | 0.0614417i | ||||||||
\(52\) | 62.5864 | 1.20359 | ||||||||
\(53\) | − | 75.2969i | − | 1.42070i | −0.703851 | − | 0.710348i | \(-0.748538\pi\) | ||
0.703851 | − | 0.710348i | \(-0.251462\pi\) | |||||||
\(54\) | −5.11354 | −0.0946953 | ||||||||
\(55\) | 4.85694 | 0.0883081 | ||||||||
\(56\) | 18.3080i | 0.326928i | ||||||||
\(57\) | − | 52.9719i | − | 0.929331i | ||||||
\(58\) | 22.7123 | 0.391592 | ||||||||
\(59\) | −59.3394 | −1.00575 | −0.502876 | − | 0.864359i | \(-0.667725\pi\) | ||||
−0.502876 | + | 0.864359i | \(0.667725\pi\) | |||||||
\(60\) | 15.5353i | 0.258921i | ||||||||
\(61\) | − | 13.6900i | − | 0.224426i | −0.993684 | − | 0.112213i | \(-0.964206\pi\) | ||
0.993684 | − | 0.112213i | \(-0.0357939\pi\) | |||||||
\(62\) | 45.6475 | 0.736250 | ||||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | 11.1220 | 0.173781 | ||||||||
\(65\) | 61.0816i | 0.939717i | ||||||||
\(66\) | − | 2.79814i | − | 0.0423961i | ||||||
\(67\) | − | 24.4518i | − | 0.364953i | −0.983210 | − | 0.182476i | \(-0.941589\pi\) | ||
0.983210 | − | 0.182476i | \(-0.0584113\pi\) | |||||||
\(68\) | − | 5.48449i | − | 0.0806543i | ||||||
\(69\) | −7.98826 | + | 39.0280i | −0.115772 | + | 0.565624i | ||||
\(70\) | −7.70341 | −0.110049 | ||||||||
\(71\) | −24.4667 | −0.344601 | −0.172301 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172301 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(72\) | 20.7593 | 0.288323 | ||||||||
\(73\) | −5.03409 | −0.0689602 | −0.0344801 | − | 0.999405i | \(-0.510978\pi\) | ||||
−0.0344801 | + | 0.999405i | \(0.510978\pi\) | |||||||
\(74\) | − | 60.7214i | − | 0.820560i | ||||||
\(75\) | 28.1395 | 0.375194 | ||||||||
\(76\) | 92.7147i | 1.21993i | ||||||||
\(77\) | −4.34328 | −0.0564063 | ||||||||
\(78\) | 35.1898 | 0.451152 | ||||||||
\(79\) | − | 120.358i | − | 1.52352i | −0.647862 | − | 0.761758i | \(-0.724337\pi\) | ||
0.647862 | − | 0.761758i | \(-0.275663\pi\) | |||||||
\(80\) | − | 15.7295i | − | 0.196618i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 45.2773 | 0.552162 | ||||||||
\(83\) | 84.7183i | 1.02070i | 0.859966 | + | 0.510351i | \(0.170485\pi\) | ||||
−0.859966 | + | 0.510351i | \(0.829515\pi\) | |||||||
\(84\) | − | 13.8923i | − | 0.165384i | ||||||
\(85\) | 5.35262 | 0.0629720 | ||||||||
\(86\) | − | 46.3819i | − | 0.539325i | ||||||
\(87\) | −39.9744 | −0.459476 | ||||||||
\(88\) | 11.3595i | 0.129085i | ||||||||
\(89\) | 62.8049i | 0.705673i | 0.935685 | + | 0.352837i | \(0.114783\pi\) | ||||
−0.935685 | + | 0.352837i | \(0.885217\pi\) | |||||||
\(90\) | 8.73485i | 0.0970539i | ||||||||
\(91\) | − | 54.6217i | − | 0.600239i | ||||||
\(92\) | 13.9815 | − | 68.3093i | 0.151973 | − | 0.742492i | ||||
\(93\) | −80.3410 | −0.863882 | ||||||||
\(94\) | 75.9047 | 0.807496 | ||||||||
\(95\) | −90.4855 | −0.952479 | ||||||||
\(96\) | −57.0034 | −0.593785 | ||||||||
\(97\) | − | 49.7308i | − | 0.512689i | −0.966586 | − | 0.256344i | \(-0.917482\pi\) | ||
0.966586 | − | 0.256344i | \(-0.0825181\pi\) | |||||||
\(98\) | 6.88871 | 0.0702930 | ||||||||
\(99\) | 4.92482i | 0.0497456i | ||||||||
\(100\) | −49.2516 | −0.492516 | ||||||||
\(101\) | −94.1838 | −0.932513 | −0.466257 | − | 0.884650i | \(-0.654398\pi\) | ||||
−0.466257 | + | 0.884650i | \(0.654398\pi\) | |||||||
\(102\) | − | 3.08371i | − | 0.0302324i | ||||||
\(103\) | 124.143i | 1.20527i | 0.798015 | + | 0.602637i | \(0.205883\pi\) | ||||
−0.798015 | + | 0.602637i | \(0.794117\pi\) | |||||||
\(104\) | −142.859 | −1.37364 | ||||||||
\(105\) | 13.5582 | 0.129126 | ||||||||
\(106\) | 74.0998i | 0.699055i | ||||||||
\(107\) | 209.537i | 1.95829i | 0.203156 | + | 0.979146i | \(0.434880\pi\) | ||||
−0.203156 | + | 0.979146i | \(0.565120\pi\) | |||||||
\(108\) | −15.7524 | −0.145855 | ||||||||
\(109\) | − | 98.4084i | − | 0.902829i | −0.892314 | − | 0.451415i | \(-0.850920\pi\) | ||
0.892314 | − | 0.451415i | \(-0.149080\pi\) | |||||||
\(110\) | −4.77973 | −0.0434521 | ||||||||
\(111\) | 106.872i | 0.962808i | ||||||||
\(112\) | 14.0659i | 0.125589i | ||||||||
\(113\) | − | 163.527i | − | 1.44714i | −0.690251 | − | 0.723570i | \(-0.742500\pi\) | ||
0.690251 | − | 0.723570i | \(-0.257500\pi\) | |||||||
\(114\) | 52.1297i | 0.457278i | ||||||||
\(115\) | 66.6669 | + | 13.6454i | 0.579712 | + | 0.118655i | ||||
\(116\) | 69.9657 | 0.603152 | ||||||||
\(117\) | −61.9352 | −0.529361 | ||||||||
\(118\) | 58.3960 | 0.494881 | ||||||||
\(119\) | −4.78654 | −0.0402230 | ||||||||
\(120\) | − | 35.4605i | − | 0.295505i | ||||||
\(121\) | 118.305 | 0.977728 | ||||||||
\(122\) | 13.4723i | 0.110429i | ||||||||
\(123\) | −79.6894 | −0.647882 | ||||||||
\(124\) | 140.618 | 1.13402 | ||||||||
\(125\) | − | 122.034i | − | 0.976270i | ||||||
\(126\) | − | 7.81107i | − | 0.0619926i | ||||||
\(127\) | 132.335 | 1.04201 | 0.521003 | − | 0.853555i | \(-0.325558\pi\) | ||||
0.521003 | + | 0.853555i | \(0.325558\pi\) | |||||||
\(128\) | 120.699 | 0.942957 | ||||||||
\(129\) | 81.6337i | 0.632819i | ||||||||
\(130\) | − | 60.1105i | − | 0.462389i | ||||||
\(131\) | 112.519 | 0.858923 | 0.429462 | − | 0.903085i | \(-0.358703\pi\) | ||||
0.429462 | + | 0.903085i | \(0.358703\pi\) | |||||||
\(132\) | − | 8.61972i | − | 0.0653009i | ||||||
\(133\) | 80.9159 | 0.608390 | ||||||||
\(134\) | 24.0631i | 0.179575i | ||||||||
\(135\) | − | 15.3736i | − | 0.113879i | ||||||
\(136\) | 12.5188i | 0.0920501i | ||||||||
\(137\) | − | 88.6187i | − | 0.646851i | −0.946254 | − | 0.323426i | \(-0.895165\pi\) | ||
0.946254 | − | 0.323426i | \(-0.104835\pi\) | |||||||
\(138\) | 7.86126 | − | 38.4076i | 0.0569656 | − | 0.278316i | ||||
\(139\) | 158.393 | 1.13952 | 0.569760 | − | 0.821811i | \(-0.307036\pi\) | ||||
0.569760 | + | 0.821811i | \(0.307036\pi\) | |||||||
\(140\) | −23.7305 | −0.169504 | ||||||||
\(141\) | −133.595 | −0.947480 | ||||||||
\(142\) | 24.0777 | 0.169561 | ||||||||
\(143\) | − | 33.8911i | − | 0.237001i | ||||||
\(144\) | 15.9493 | 0.110759 | ||||||||
\(145\) | 68.2834i | 0.470920i | ||||||||
\(146\) | 4.95406 | 0.0339319 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | − | 187.053i | − | 1.26387i | ||||||
\(149\) | 241.254i | 1.61915i | 0.587015 | + | 0.809576i | \(0.300303\pi\) | ||||
−0.587015 | + | 0.809576i | \(0.699697\pi\) | |||||||
\(150\) | −27.6922 | −0.184615 | ||||||||
\(151\) | −39.1314 | −0.259148 | −0.129574 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129574 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(152\) | − | 211.629i | − | 1.39230i | ||||||
\(153\) | 5.42742i | 0.0354734i | ||||||||
\(154\) | 4.27423 | 0.0277548 | ||||||||
\(155\) | 137.237i | 0.885399i | ||||||||
\(156\) | 108.403 | 0.694890 | ||||||||
\(157\) | − | 33.6563i | − | 0.214371i | −0.994239 | − | 0.107186i | \(-0.965816\pi\) | ||
0.994239 | − | 0.107186i | \(-0.0341839\pi\) | |||||||
\(158\) | 118.444i | 0.749647i | ||||||||
\(159\) | − | 130.418i | − | 0.820239i | ||||||
\(160\) | 97.3720i | 0.608575i | ||||||||
\(161\) | −59.6163 | − | 12.2023i | −0.370288 | − | 0.0757905i | ||||
\(162\) | −8.85692 | −0.0546723 | ||||||||
\(163\) | 24.0778 | 0.147717 | 0.0738583 | − | 0.997269i | \(-0.476469\pi\) | ||||
0.0738583 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(164\) | 139.477 | 0.850472 | ||||||||
\(165\) | 8.41247 | 0.0509847 | ||||||||
\(166\) | − | 83.3715i | − | 0.502238i | ||||||
\(167\) | −118.883 | −0.711876 | −0.355938 | − | 0.934510i | \(-0.615839\pi\) | ||||
−0.355938 | + | 0.934510i | \(0.615839\pi\) | |||||||
\(168\) | 31.7103i | 0.188752i | ||||||||
\(169\) | 257.219 | 1.52201 | ||||||||
\(170\) | −5.26752 | −0.0309854 | ||||||||
\(171\) | − | 91.7500i | − | 0.536550i | ||||||
\(172\) | − | 142.880i | − | 0.830700i | ||||||
\(173\) | −74.7281 | −0.431955 | −0.215977 | − | 0.976398i | \(-0.569294\pi\) | ||||
−0.215977 | + | 0.976398i | \(0.569294\pi\) | |||||||
\(174\) | 39.3389 | 0.226085 | ||||||||
\(175\) | 42.9839i | 0.245622i | ||||||||
\(176\) | 8.72748i | 0.0495880i | ||||||||
\(177\) | −102.779 | −0.580671 | ||||||||
\(178\) | − | 61.8065i | − | 0.347227i | ||||||
\(179\) | 277.617 | 1.55093 | 0.775466 | − | 0.631390i | \(-0.217515\pi\) | ||||
0.775466 | + | 0.631390i | \(0.217515\pi\) | |||||||
\(180\) | 26.9079i | 0.149488i | ||||||||
\(181\) | − | 53.3247i | − | 0.294611i | −0.989091 | − | 0.147306i | \(-0.952940\pi\) | ||
0.989091 | − | 0.147306i | \(-0.0470601\pi\) | |||||||
\(182\) | 53.7533i | 0.295348i | ||||||||
\(183\) | − | 23.7117i | − | 0.129572i | ||||||
\(184\) | −31.9141 | + | 155.922i | −0.173446 | + | 0.847401i | ||||
\(185\) | 182.556 | 0.986789 | ||||||||
\(186\) | 79.0638 | 0.425074 | ||||||||
\(187\) | −2.96990 | −0.0158818 | ||||||||
\(188\) | 233.826 | 1.24375 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 89.0469 | 0.468668 | ||||||||
\(191\) | − | 262.168i | − | 1.37261i | −0.727316 | − | 0.686303i | \(-0.759232\pi\) | ||
0.727316 | − | 0.686303i | \(-0.240768\pi\) | |||||||
\(192\) | 19.2639 | 0.100333 | ||||||||
\(193\) | 64.1974 | 0.332629 | 0.166314 | − | 0.986073i | \(-0.446813\pi\) | ||||
0.166314 | + | 0.986073i | \(0.446813\pi\) | |||||||
\(194\) | 48.9402i | 0.252269i | ||||||||
\(195\) | 105.796i | 0.542546i | ||||||||
\(196\) | 21.2208 | 0.108269 | ||||||||
\(197\) | −328.623 | −1.66814 | −0.834068 | − | 0.551662i | \(-0.813994\pi\) | ||||
−0.834068 | + | 0.551662i | \(0.813994\pi\) | |||||||
\(198\) | − | 4.84652i | − | 0.0244774i | ||||||
\(199\) | − | 354.709i | − | 1.78246i | −0.453556 | − | 0.891228i | \(-0.649845\pi\) | ||
0.453556 | − | 0.891228i | \(-0.350155\pi\) | |||||||
\(200\) | 112.421 | 0.562105 | ||||||||
\(201\) | − | 42.3518i | − | 0.210706i | ||||||
\(202\) | 92.6865 | 0.458844 | ||||||||
\(203\) | − | 61.0619i | − | 0.300797i | ||||||
\(204\) | − | 9.49941i | − | 0.0465658i | ||||||
\(205\) | 136.124i | 0.664019i | ||||||||
\(206\) | − | 122.170i | − | 0.593056i | ||||||
\(207\) | −13.8361 | + | 67.5985i | −0.0668409 | + | 0.326563i | ||||
\(208\) | −109.758 | −0.527683 | ||||||||
\(209\) | 50.2058 | 0.240219 | ||||||||
\(210\) | −13.3427 | −0.0635367 | ||||||||
\(211\) | −285.944 | −1.35519 | −0.677593 | − | 0.735437i | \(-0.736977\pi\) | ||||
−0.677593 | + | 0.735437i | \(0.736977\pi\) | |||||||
\(212\) | 228.266i | 1.07673i | ||||||||
\(213\) | −42.3775 | −0.198955 | ||||||||
\(214\) | − | 206.206i | − | 0.963580i | ||||||
\(215\) | 139.445 | 0.648581 | ||||||||
\(216\) | 35.9561 | 0.166463 | ||||||||
\(217\) | − | 122.723i | − | 0.565544i | ||||||
\(218\) | 96.8439i | 0.444238i | ||||||||
\(219\) | −8.71931 | −0.0398142 | ||||||||
\(220\) | −14.7240 | −0.0669274 | ||||||||
\(221\) | − | 37.3498i | − | 0.169004i | ||||||
\(222\) | − | 105.173i | − | 0.473751i | ||||||
\(223\) | 396.446 | 1.77779 | 0.888893 | − | 0.458115i | \(-0.151475\pi\) | ||||
0.888893 | + | 0.458115i | \(0.151475\pi\) | |||||||
\(224\) | − | 87.0741i | − | 0.388724i | ||||||
\(225\) | 48.7391 | 0.216618 | ||||||||
\(226\) | 160.927i | 0.712067i | ||||||||
\(227\) | 168.217i | 0.741042i | 0.928824 | + | 0.370521i | \(0.120821\pi\) | ||||
−0.928824 | + | 0.370521i | \(0.879179\pi\) | |||||||
\(228\) | 160.587i | 0.704327i | ||||||||
\(229\) | 182.998i | 0.799118i | 0.916708 | + | 0.399559i | \(0.130837\pi\) | ||||
−0.916708 | + | 0.399559i | \(0.869163\pi\) | |||||||
\(230\) | −65.6070 | − | 13.4284i | −0.285248 | − | 0.0583845i | ||||
\(231\) | −7.52278 | −0.0325662 | ||||||||
\(232\) | −159.703 | −0.688373 | ||||||||
\(233\) | 146.908 | 0.630505 | 0.315253 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315253 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(234\) | 60.9506 | 0.260472 | ||||||||
\(235\) | 228.203i | 0.971079i | ||||||||
\(236\) | 179.890 | 0.762245 | ||||||||
\(237\) | − | 208.466i | − | 0.879602i | ||||||
\(238\) | 4.71044 | 0.0197918 | ||||||||
\(239\) | 279.831 | 1.17084 | 0.585421 | − | 0.810729i | \(-0.300929\pi\) | ||||
0.585421 | + | 0.810729i | \(0.300929\pi\) | |||||||
\(240\) | − | 27.2442i | − | 0.113518i | ||||||
\(241\) | − | 274.634i | − | 1.13956i | −0.821797 | − | 0.569780i | \(-0.807028\pi\) | ||
0.821797 | − | 0.569780i | \(-0.192972\pi\) | |||||||
\(242\) | −116.424 | −0.481092 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 41.5018i | 0.170089i | ||||||||
\(245\) | 20.7106i | 0.0845329i | ||||||||
\(246\) | 78.4225 | 0.318791 | ||||||||
\(247\) | 631.395i | 2.55626i | ||||||||
\(248\) | −320.972 | −1.29424 | ||||||||
\(249\) | 146.736i | 0.589303i | ||||||||
\(250\) | 120.094i | 0.480374i | ||||||||
\(251\) | 176.637i | 0.703731i | 0.936051 | + | 0.351866i | \(0.114453\pi\) | ||||
−0.936051 | + | 0.351866i | \(0.885547\pi\) | |||||||
\(252\) | − | 24.0621i | − | 0.0954846i | ||||||
\(253\) | −36.9901 | − | 7.57113i | −0.146206 | − | 0.0299254i | ||||
\(254\) | −130.231 | −0.512720 | ||||||||
\(255\) | 9.27101 | 0.0363569 | ||||||||
\(256\) | −163.268 | −0.637764 | ||||||||
\(257\) | −322.584 | −1.25519 | −0.627595 | − | 0.778540i | \(-0.715961\pi\) | ||||
−0.627595 | + | 0.778540i | \(0.715961\pi\) | |||||||
\(258\) | − | 80.3359i | − | 0.311379i | ||||||
\(259\) | −163.249 | −0.630306 | ||||||||
\(260\) | − | 185.171i | − | 0.712198i | ||||||
\(261\) | −69.2377 | −0.265278 | ||||||||
\(262\) | −110.730 | −0.422634 | ||||||||
\(263\) | − | 177.102i | − | 0.673393i | −0.941613 | − | 0.336696i | \(-0.890690\pi\) | ||
0.941613 | − | 0.336696i | \(-0.109310\pi\) | |||||||
\(264\) | 19.6753i | 0.0745275i | ||||||||
\(265\) | −222.777 | −0.840669 | ||||||||
\(266\) | −79.6295 | −0.299359 | ||||||||
\(267\) | 108.781i | 0.407421i | ||||||||
\(268\) | 74.1268i | 0.276593i | ||||||||
\(269\) | −55.4512 | −0.206138 | −0.103069 | − | 0.994674i | \(-0.532866\pi\) | ||||
−0.103069 | + | 0.994674i | \(0.532866\pi\) | |||||||
\(270\) | 15.1292i | 0.0560341i | ||||||||
\(271\) | −180.846 | −0.667327 | −0.333663 | − | 0.942692i | \(-0.608285\pi\) | ||||
−0.333663 | + | 0.942692i | \(0.608285\pi\) | |||||||
\(272\) | 9.61817i | 0.0353609i | ||||||||
\(273\) | − | 94.6076i | − | 0.346548i | ||||||
\(274\) | 87.2098i | 0.318284i | ||||||||
\(275\) | 26.6701i | 0.0969824i | ||||||||
\(276\) | 24.2167 | − | 118.315i | 0.0877418 | − | 0.428678i | ||||
\(277\) | −152.629 | −0.551007 | −0.275503 | − | 0.961300i | \(-0.588845\pi\) | ||||
−0.275503 | + | 0.961300i | \(0.588845\pi\) | |||||||
\(278\) | −155.875 | −0.560702 | ||||||||
\(279\) | −139.155 | −0.498763 | ||||||||
\(280\) | 54.1669 | 0.193453 | ||||||||
\(281\) | − | 211.984i | − | 0.754391i | −0.926134 | − | 0.377196i | \(-0.876888\pi\) | ||
0.926134 | − | 0.377196i | \(-0.123112\pi\) | |||||||
\(282\) | 131.471 | 0.466208 | ||||||||
\(283\) | − | 496.918i | − | 1.75589i | −0.478757 | − | 0.877947i | \(-0.658913\pi\) | ||
0.478757 | − | 0.877947i | \(-0.341087\pi\) | |||||||
\(284\) | 74.1718 | 0.261168 | ||||||||
\(285\) | −156.725 | −0.549914 | ||||||||
\(286\) | 33.3523i | 0.116616i | ||||||||
\(287\) | − | 121.728i | − | 0.424138i | ||||||
\(288\) | −98.7328 | −0.342822 | ||||||||
\(289\) | 285.727 | 0.988675 | ||||||||
\(290\) | − | 67.1978i | − | 0.231717i | ||||||
\(291\) | − | 86.1363i | − | 0.296001i | ||||||
\(292\) | 15.2611 | 0.0522640 | ||||||||
\(293\) | 584.701i | 1.99557i | 0.0665528 | + | 0.997783i | \(0.478800\pi\) | ||||
−0.0665528 | + | 0.997783i | \(0.521200\pi\) | |||||||
\(294\) | 11.9316 | 0.0405837 | ||||||||
\(295\) | 175.565i | 0.595134i | ||||||||
\(296\) | 426.965i | 1.44245i | ||||||||
\(297\) | 8.53004i | 0.0287207i | ||||||||
\(298\) | − | 237.418i | − | 0.796706i | ||||||
\(299\) | 95.2155 | − | 465.192i | 0.318447 | − | 1.55583i | ||||
\(300\) | −85.3063 | −0.284354 | ||||||||
\(301\) | −124.698 | −0.414278 | ||||||||
\(302\) | 38.5093 | 0.127514 | ||||||||
\(303\) | −163.131 | −0.538387 | ||||||||
\(304\) | − | 162.594i | − | 0.534849i | ||||||
\(305\) | −40.5039 | −0.132800 | ||||||||
\(306\) | − | 5.34114i | − | 0.0174547i | ||||||
\(307\) | −536.733 | −1.74832 | −0.874158 | − | 0.485641i | \(-0.838586\pi\) | ||||
−0.874158 | + | 0.485641i | \(0.838586\pi\) | |||||||
\(308\) | 13.1668 | 0.0427495 | ||||||||
\(309\) | 215.022i | 0.695866i | ||||||||
\(310\) | − | 135.055i | − | 0.435662i | ||||||
\(311\) | −171.080 | −0.550096 | −0.275048 | − | 0.961431i | \(-0.588694\pi\) | ||||
−0.275048 | + | 0.961431i | \(0.588694\pi\) | |||||||
\(312\) | −247.439 | −0.793073 | ||||||||
\(313\) | 132.047i | 0.421875i | 0.977500 | + | 0.210937i | \(0.0676516\pi\) | ||||
−0.977500 | + | 0.210937i | \(0.932348\pi\) | |||||||
\(314\) | 33.1212i | 0.105482i | ||||||||
\(315\) | 23.4836 | 0.0745510 | ||||||||
\(316\) | 364.870i | 1.15465i | ||||||||
\(317\) | 41.3975 | 0.130591 | 0.0652957 | − | 0.997866i | \(-0.479201\pi\) | ||||
0.0652957 | + | 0.997866i | \(0.479201\pi\) | |||||||
\(318\) | 128.345i | 0.403599i | ||||||||
\(319\) | − | 37.8870i | − | 0.118768i | ||||||
\(320\) | − | 32.9061i | − | 0.102832i | ||||||
\(321\) | 362.929i | 1.13062i | ||||||||
\(322\) | 58.6685 | + | 12.0083i | 0.182200 | + | 0.0372928i | ||||
\(323\) | 55.3296 | 0.171299 | ||||||||
\(324\) | −27.2839 | −0.0842095 | ||||||||
\(325\) | −335.408 | −1.03202 | ||||||||
\(326\) | −23.6950 | −0.0726841 | ||||||||
\(327\) | − | 170.448i | − | 0.521249i | ||||||
\(328\) | −318.369 | −0.970637 | ||||||||
\(329\) | − | 204.069i | − | 0.620271i | ||||||
\(330\) | −8.27873 | −0.0250871 | ||||||||
\(331\) | −529.880 | −1.60085 | −0.800423 | − | 0.599436i | \(-0.795392\pi\) | ||||
−0.800423 | + | 0.599436i | \(0.795392\pi\) | |||||||
\(332\) | − | 256.827i | − | 0.773576i | ||||||
\(333\) | 185.107i | 0.555877i | ||||||||
\(334\) | 116.993 | 0.350279 | ||||||||
\(335\) | −72.3445 | −0.215954 | ||||||||
\(336\) | 24.3629i | 0.0725087i | ||||||||
\(337\) | − | 107.305i | − | 0.318412i | −0.987245 | − | 0.159206i | \(-0.949107\pi\) | ||
0.987245 | − | 0.159206i | \(-0.0508933\pi\) | |||||||
\(338\) | −253.130 | −0.748904 | ||||||||
\(339\) | − | 283.237i | − | 0.835507i | ||||||
\(340\) | −16.2267 | −0.0477256 | ||||||||
\(341\) | − | 76.1458i | − | 0.223301i | ||||||
\(342\) | 90.2914i | 0.264010i | ||||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | 326.137i | 0.948072i | ||||||||
\(345\) | 115.470 | + | 23.6345i | 0.334697 | + | 0.0685057i | ||||
\(346\) | 73.5401 | 0.212544 | ||||||||
\(347\) | −205.554 | −0.592373 | −0.296187 | − | 0.955130i | \(-0.595715\pi\) | ||||
−0.296187 | + | 0.955130i | \(0.595715\pi\) | |||||||
\(348\) | 121.184 | 0.348230 | ||||||||
\(349\) | 257.695 | 0.738382 | 0.369191 | − | 0.929354i | \(-0.379635\pi\) | ||||
0.369191 | + | 0.929354i | \(0.379635\pi\) | |||||||
\(350\) | − | 42.3005i | − | 0.120859i | ||||||
\(351\) | −107.275 | −0.305627 | ||||||||
\(352\) | − | 54.0268i | − | 0.153485i | ||||||
\(353\) | −219.135 | −0.620779 | −0.310390 | − | 0.950609i | \(-0.600460\pi\) | ||||
−0.310390 | + | 0.950609i | \(0.600460\pi\) | |||||||
\(354\) | 101.145 | 0.285720 | ||||||||
\(355\) | 72.3884i | 0.203911i | ||||||||
\(356\) | − | 190.396i | − | 0.534820i | ||||||
\(357\) | −8.29053 | −0.0232228 | ||||||||
\(358\) | −273.203 | −0.763137 | ||||||||
\(359\) | 188.537i | 0.525173i | 0.964908 | + | 0.262587i | \(0.0845756\pi\) | ||||
−0.964908 | + | 0.262587i | \(0.915424\pi\) | |||||||
\(360\) | − | 61.4195i | − | 0.170610i | ||||||
\(361\) | −574.340 | −1.59097 | ||||||||
\(362\) | 52.4769i | 0.144964i | ||||||||
\(363\) | 204.910 | 0.564492 | ||||||||
\(364\) | 165.588i | 0.454912i | ||||||||
\(365\) | 14.8941i | 0.0408059i | ||||||||
\(366\) | 23.3348i | 0.0637562i | ||||||||
\(367\) | − | 262.250i | − | 0.714577i | −0.933994 | − | 0.357288i | \(-0.883701\pi\) | ||
0.933994 | − | 0.357288i | \(-0.116299\pi\) | |||||||
\(368\) | −24.5195 | + | 119.794i | −0.0666290 | + | 0.325528i | ||||
\(369\) | −138.026 | −0.374055 | ||||||||
\(370\) | −179.654 | −0.485550 | ||||||||
\(371\) | 199.217 | 0.536973 | ||||||||
\(372\) | 243.557 | 0.654724 | ||||||||
\(373\) | − | 65.3990i | − | 0.175333i | −0.996150 | − | 0.0876663i | \(-0.972059\pi\) | ||
0.996150 | − | 0.0876663i | \(-0.0279409\pi\) | |||||||
\(374\) | 2.92268 | 0.00781466 | ||||||||
\(375\) | − | 211.369i | − | 0.563649i | ||||||
\(376\) | −533.727 | −1.41949 | ||||||||
\(377\) | 476.472 | 1.26385 | ||||||||
\(378\) | − | 13.5292i | − | 0.0357914i | ||||||
\(379\) | 296.488i | 0.782291i | 0.920329 | + | 0.391145i | \(0.127921\pi\) | ||||
−0.920329 | + | 0.391145i | \(0.872079\pi\) | |||||||
\(380\) | 274.311 | 0.721870 | ||||||||
\(381\) | 229.210 | 0.601602 | ||||||||
\(382\) | 258.000i | 0.675392i | ||||||||
\(383\) | − | 479.187i | − | 1.25114i | −0.780168 | − | 0.625570i | \(-0.784866\pi\) | ||
0.780168 | − | 0.625570i | \(-0.215134\pi\) | |||||||
\(384\) | 209.056 | 0.544417 | ||||||||
\(385\) | 12.8503i | 0.0333773i | ||||||||
\(386\) | −63.1767 | −0.163670 | ||||||||
\(387\) | 141.394i | 0.365358i | ||||||||
\(388\) | 150.761i | 0.388560i | ||||||||
\(389\) | 101.204i | 0.260164i | 0.991503 | + | 0.130082i | \(0.0415241\pi\) | ||||
−0.991503 | + | 0.130082i | \(0.958476\pi\) | |||||||
\(390\) | − | 104.114i | − | 0.266960i | ||||||
\(391\) | −40.7651 | − | 8.34380i | −0.104259 | − | 0.0213396i | ||||
\(392\) | −48.4383 | −0.123567 | ||||||||
\(393\) | 194.889 | 0.495900 | ||||||||
\(394\) | 323.398 | 0.820808 | ||||||||
\(395\) | −356.097 | −0.901510 | ||||||||
\(396\) | − | 14.9298i | − | 0.0377015i | ||||||
\(397\) | 376.793 | 0.949102 | 0.474551 | − | 0.880228i | \(-0.342611\pi\) | ||||
0.474551 | + | 0.880228i | \(0.342611\pi\) | |||||||
\(398\) | 349.069i | 0.877059i | ||||||||
\(399\) | 140.150 | 0.351254 | ||||||||
\(400\) | 86.3727 | 0.215932 | ||||||||
\(401\) | 5.99307i | 0.0149453i | 0.999972 | + | 0.00747265i | \(0.00237864\pi\) | ||||
−0.999972 | + | 0.00747265i | \(0.997621\pi\) | |||||||
\(402\) | 41.6785i | 0.103678i | ||||||||
\(403\) | 957.620 | 2.37623 | ||||||||
\(404\) | 285.522 | 0.706738 | ||||||||
\(405\) | − | 26.6279i | − | 0.0657478i | ||||||
\(406\) | 60.0911i | 0.148008i | ||||||||
\(407\) | −101.291 | −0.248872 | ||||||||
\(408\) | 21.6832i | 0.0531452i | ||||||||
\(409\) | −392.937 | −0.960726 | −0.480363 | − | 0.877070i | \(-0.659495\pi\) | ||||
−0.480363 | + | 0.877070i | \(0.659495\pi\) | |||||||
\(410\) | − | 133.960i | − | 0.326731i | ||||||
\(411\) | − | 153.492i | − | 0.373460i | ||||||
\(412\) | − | 376.346i | − | 0.913460i | ||||||
\(413\) | − | 156.997i | − | 0.380139i | ||||||
\(414\) | 13.6161 | − | 66.5239i | 0.0328891 | − | 0.160686i | ||||
\(415\) | 250.652 | 0.603981 | ||||||||
\(416\) | 679.448 | 1.63329 | ||||||||
\(417\) | 274.345 | 0.657902 | ||||||||
\(418\) | −49.4076 | −0.118200 | ||||||||
\(419\) | − | 337.328i | − | 0.805080i | −0.915402 | − | 0.402540i | \(-0.868127\pi\) | ||
0.915402 | − | 0.402540i | \(-0.131873\pi\) | |||||||
\(420\) | −41.1024 | −0.0978629 | ||||||||
\(421\) | 715.484i | 1.69949i | 0.527197 | + | 0.849743i | \(0.323243\pi\) | ||||
−0.527197 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(422\) | 281.398 | 0.666821 | ||||||||
\(423\) | −231.393 | −0.547028 | ||||||||
\(424\) | − | 521.036i | − | 1.22886i | ||||||
\(425\) | 29.3920i | 0.0691576i | ||||||||
\(426\) | 41.7038 | 0.0978962 | ||||||||
\(427\) | 36.2203 | 0.0848250 | ||||||||
\(428\) | − | 635.221i | − | 1.48416i | ||||||
\(429\) | − | 58.7011i | − | 0.136832i | ||||||
\(430\) | −137.228 | −0.319135 | ||||||||
\(431\) | 795.766i | 1.84632i | 0.384410 | + | 0.923162i | \(0.374405\pi\) | ||||
−0.384410 | + | 0.923162i | \(0.625595\pi\) | |||||||
\(432\) | 27.6250 | 0.0639467 | ||||||||
\(433\) | 217.649i | 0.502654i | 0.967902 | + | 0.251327i | \(0.0808669\pi\) | ||||
−0.967902 | + | 0.251327i | \(0.919133\pi\) | |||||||
\(434\) | 120.772i | 0.278276i | ||||||||
\(435\) | 118.270i | 0.271886i | ||||||||
\(436\) | 298.329i | 0.684241i | ||||||||
\(437\) | 689.130 | + | 141.051i | 1.57696 | + | 0.322771i | ||||
\(438\) | 8.58069 | 0.0195906 | ||||||||
\(439\) | 431.228 | 0.982297 | 0.491148 | − | 0.871076i | \(-0.336577\pi\) | ||||
0.491148 | + | 0.871076i | \(0.336577\pi\) | |||||||
\(440\) | 33.6089 | 0.0763838 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 36.7561i | 0.0831585i | ||||||||
\(443\) | −239.193 | −0.539940 | −0.269970 | − | 0.962869i | \(-0.587014\pi\) | ||||
−0.269970 | + | 0.962869i | \(0.587014\pi\) | |||||||
\(444\) | − | 323.986i | − | 0.729698i | ||||||
\(445\) | 185.818 | 0.417569 | ||||||||
\(446\) | −390.143 | −0.874761 | ||||||||
\(447\) | 417.864i | 0.934818i | ||||||||
\(448\) | 29.4260i | 0.0656831i | ||||||||
\(449\) | −97.7033 | −0.217602 | −0.108801 | − | 0.994064i | \(-0.534701\pi\) | ||||
−0.108801 | + | 0.994064i | \(0.534701\pi\) | |||||||
\(450\) | −47.9643 | −0.106587 | ||||||||
\(451\) | − | 75.5282i | − | 0.167468i | ||||||
\(452\) | 495.739i | 1.09677i | ||||||||
\(453\) | −67.7776 | −0.149619 | ||||||||
\(454\) | − | 165.542i | − | 0.364630i | ||||||
\(455\) | −161.607 | −0.355180 | ||||||||
\(456\) | − | 366.553i | − | 0.803843i | ||||||
\(457\) | 196.469i | 0.429911i | 0.976624 | + | 0.214956i | \(0.0689607\pi\) | ||||
−0.976624 | + | 0.214956i | \(0.931039\pi\) | |||||||
\(458\) | − | 180.089i | − | 0.393207i | ||||||
\(459\) | 9.40057i | 0.0204806i | ||||||||
\(460\) | −202.104 | − | 41.3665i | −0.439355 | − | 0.0899273i | ||||
\(461\) | −217.422 | −0.471632 | −0.235816 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235816 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(462\) | 7.40319 | 0.0160242 | ||||||||
\(463\) | 838.394 | 1.81079 | 0.905393 | − | 0.424574i | \(-0.139576\pi\) | ||||
0.905393 | + | 0.424574i | \(0.139576\pi\) | |||||||
\(464\) | −122.699 | −0.264438 | ||||||||
\(465\) | 237.701i | 0.511185i | ||||||||
\(466\) | −144.572 | −0.310241 | ||||||||
\(467\) | − | 392.675i | − | 0.840845i | −0.907328 | − | 0.420423i | \(-0.861882\pi\) | ||
0.907328 | − | 0.420423i | \(-0.138118\pi\) | |||||||
\(468\) | 187.759 | 0.401195 | ||||||||
\(469\) | 64.6935 | 0.137939 | ||||||||
\(470\) | − | 224.576i | − | 0.477820i | ||||||
\(471\) | − | 58.2944i | − | 0.123767i | ||||||
\(472\) | −410.614 | −0.869945 | ||||||||
\(473\) | −77.3709 | −0.163575 | ||||||||
\(474\) | 205.151i | 0.432809i | ||||||||
\(475\) | − | 496.868i | − | 1.04604i | ||||||
\(476\) | 14.5106 | 0.0304844 | ||||||||
\(477\) | − | 225.891i | − | 0.473565i | ||||||
\(478\) | −275.383 | −0.576114 | ||||||||
\(479\) | 285.575i | 0.596190i | 0.954536 | + | 0.298095i | \(0.0963512\pi\) | ||||
−0.954536 | + | 0.298095i | \(0.903649\pi\) | |||||||
\(480\) | 168.653i | 0.351361i | ||||||||
\(481\) | − | 1273.85i | − | 2.64834i | ||||||
\(482\) | 270.268i | 0.560721i | ||||||||
\(483\) | −103.258 | − | 21.1349i | −0.213786 | − | 0.0437576i | ||||
\(484\) | −358.647 | −0.741006 | ||||||||
\(485\) | −147.136 | −0.303374 | ||||||||
\(486\) | −15.3406 | −0.0315651 | ||||||||
\(487\) | 199.314 | 0.409269 | 0.204635 | − | 0.978838i | \(-0.434399\pi\) | ||||
0.204635 | + | 0.978838i | \(0.434399\pi\) | |||||||
\(488\) | − | 94.7313i | − | 0.194122i | ||||||
\(489\) | 41.7040 | 0.0852842 | ||||||||
\(490\) | − | 20.3813i | − | 0.0415945i | ||||||
\(491\) | −178.193 | −0.362918 | −0.181459 | − | 0.983398i | \(-0.558082\pi\) | ||||
−0.181459 | + | 0.983398i | \(0.558082\pi\) | |||||||
\(492\) | 241.582 | 0.491020 | ||||||||
\(493\) | − | 41.7536i | − | 0.0846928i | ||||||
\(494\) | − | 621.357i | − | 1.25781i | ||||||
\(495\) | 14.5708 | 0.0294360 | ||||||||
\(496\) | −246.602 | −0.497182 | ||||||||
\(497\) | − | 64.7327i | − | 0.130247i | ||||||
\(498\) | − | 144.404i | − | 0.289967i | ||||||
\(499\) | 623.881 | 1.25026 | 0.625131 | − | 0.780520i | \(-0.285046\pi\) | ||||
0.625131 | + | 0.780520i | \(0.285046\pi\) | |||||||
\(500\) | 369.950i | 0.739901i | ||||||||
\(501\) | −205.912 | −0.411002 | ||||||||
\(502\) | − | 173.828i | − | 0.346272i | ||||||
\(503\) | 259.558i | 0.516021i | 0.966142 | + | 0.258010i | \(0.0830669\pi\) | ||||
−0.966142 | + | 0.258010i | \(0.916933\pi\) | |||||||
\(504\) | 54.9239i | 0.108976i | ||||||||
\(505\) | 278.657i | 0.551796i | ||||||||
\(506\) | 36.4020 | + | 7.45076i | 0.0719407 | + | 0.0147248i | ||||
\(507\) | 445.516 | 0.878730 | ||||||||
\(508\) | −401.178 | −0.789721 | ||||||||
\(509\) | −590.340 | −1.15980 | −0.579902 | − | 0.814686i | \(-0.696909\pi\) | ||||
−0.579902 | + | 0.814686i | \(0.696909\pi\) | |||||||
\(510\) | −9.12362 | −0.0178894 | ||||||||
\(511\) | − | 13.3190i | − | 0.0260645i | ||||||
\(512\) | −322.122 | −0.629145 | ||||||||
\(513\) | − | 158.916i | − | 0.309777i | ||||||
\(514\) | 317.456 | 0.617618 | ||||||||
\(515\) | 367.297 | 0.713198 | ||||||||
\(516\) | − | 247.476i | − | 0.479605i | ||||||
\(517\) | − | 126.619i | − | 0.244910i | ||||||
\(518\) | 160.654 | 0.310143 | ||||||||
\(519\) | −129.433 | −0.249389 | ||||||||
\(520\) | 422.670i | 0.812826i | ||||||||
\(521\) | 597.731i | 1.14728i | 0.819109 | + | 0.573638i | \(0.194468\pi\) | ||||
−0.819109 | + | 0.573638i | \(0.805532\pi\) | |||||||
\(522\) | 68.1369 | 0.130531 | ||||||||
\(523\) | 976.357i | 1.86684i | 0.358786 | + | 0.933420i | \(0.383191\pi\) | ||||
−0.358786 | + | 0.933420i | \(0.616809\pi\) | |||||||
\(524\) | −341.106 | −0.650966 | ||||||||
\(525\) | 74.4502i | 0.141810i | ||||||||
\(526\) | 174.287i | 0.331344i | ||||||||
\(527\) | − | 83.9169i | − | 0.159235i | ||||||
\(528\) | 15.1164i | 0.0286296i | ||||||||
\(529\) | −486.458 | − | 207.844i | −0.919581 | − | 0.392900i | ||||
\(530\) | 219.236 | 0.413652 | ||||||||
\(531\) | −178.018 | −0.335251 | ||||||||
\(532\) | −245.300 | −0.461090 | ||||||||
\(533\) | 949.853 | 1.78209 | ||||||||
\(534\) | − | 107.052i | − | 0.200472i | ||||||
\(535\) | 619.948 | 1.15878 | ||||||||
\(536\) | − | 169.201i | − | 0.315673i | ||||||
\(537\) | 480.846 | 0.895431 | ||||||||
\(538\) | 54.5696 | 0.101430 | ||||||||
\(539\) | − | 11.4912i | − | 0.0213196i | ||||||
\(540\) | 46.6058i | 0.0863070i | ||||||||
\(541\) | −978.363 | −1.80843 | −0.904217 | − | 0.427074i | \(-0.859545\pi\) | ||||
−0.904217 | + | 0.427074i | \(0.859545\pi\) | |||||||
\(542\) | 177.970 | 0.328359 | ||||||||
\(543\) | − | 92.3610i | − | 0.170094i | ||||||
\(544\) | − | 59.5405i | − | 0.109449i | ||||||
\(545\) | −291.156 | −0.534232 | ||||||||
\(546\) | 93.1035i | 0.170519i | ||||||||
\(547\) | 682.278 | 1.24731 | 0.623654 | − | 0.781700i | \(-0.285647\pi\) | ||||
0.623654 | + | 0.781700i | \(0.285647\pi\) | |||||||
\(548\) | 268.651i | 0.490240i | ||||||||
\(549\) | − | 41.0699i | − | 0.0748086i | ||||||
\(550\) | − | 26.2461i | − | 0.0477203i | ||||||
\(551\) | 705.840i | 1.28102i | ||||||||
\(552\) | −55.2768 | + | 270.064i | −0.100139 | + | 0.489247i | ||||
\(553\) | 318.437 | 0.575835 | ||||||||
\(554\) | 150.202 | 0.271123 | ||||||||
\(555\) | 316.196 | 0.569723 | ||||||||
\(556\) | −480.176 | −0.863626 | ||||||||
\(557\) | − | 896.298i | − | 1.60915i | −0.593850 | − | 0.804576i | \(-0.702393\pi\) | ||
0.593850 | − | 0.804576i | \(-0.297607\pi\) | |||||||
\(558\) | 136.942 | 0.245417 | ||||||||
\(559\) | − | 973.028i | − | 1.74066i | ||||||
\(560\) | 41.6163 | 0.0743147 | ||||||||
\(561\) | −5.14401 | −0.00916936 | ||||||||
\(562\) | 208.614i | 0.371199i | ||||||||
\(563\) | − | 311.938i | − | 0.554064i | −0.960861 | − | 0.277032i | \(-0.910649\pi\) | ||
0.960861 | − | 0.277032i | \(-0.0893508\pi\) | |||||||
\(564\) | 404.998 | 0.718081 | ||||||||
\(565\) | −483.819 | −0.856317 | ||||||||
\(566\) | 489.018i | 0.863990i | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | −169.303 | −0.298069 | ||||||||
\(569\) | − | 685.321i | − | 1.20443i | −0.798334 | − | 0.602216i | \(-0.794285\pi\) | ||
0.798334 | − | 0.602216i | \(-0.205715\pi\) | |||||||
\(570\) | 154.234 | 0.270586 | ||||||||
\(571\) | − | 284.733i | − | 0.498656i | −0.968419 | − | 0.249328i | \(-0.919790\pi\) | ||
0.968419 | − | 0.249328i | \(-0.0802097\pi\) | |||||||
\(572\) | 102.742i | 0.179619i | ||||||||
\(573\) | − | 454.088i | − | 0.792475i | ||||||
\(574\) | 119.792i | 0.208698i | ||||||||
\(575\) | −74.9286 | + | 366.077i | −0.130311 | + | 0.636656i | ||||
\(576\) | 33.3660 | 0.0579271 | ||||||||
\(577\) | −427.106 | −0.740219 | −0.370109 | − | 0.928988i | \(-0.620680\pi\) | ||||
−0.370109 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(578\) | −281.185 | −0.486478 | ||||||||
\(579\) | 111.193 | 0.192043 | ||||||||
\(580\) | − | 207.004i | − | 0.356904i | ||||||
\(581\) | −224.144 | −0.385789 | ||||||||
\(582\) | 84.7669i | 0.145648i | ||||||||
\(583\) | 123.608 | 0.212020 | ||||||||
\(584\) | −34.8347 | −0.0596485 | ||||||||
\(585\) | 183.245i | 0.313239i | ||||||||
\(586\) | − | 575.405i | − | 0.981920i | ||||||
\(587\) | 936.975 | 1.59621 | 0.798105 | − | 0.602519i | \(-0.205836\pi\) | ||||
0.798105 | + | 0.602519i | \(0.205836\pi\) | |||||||
\(588\) | 36.7555 | 0.0625094 | ||||||||
\(589\) | 1418.61i | 2.40850i | ||||||||
\(590\) | − | 172.773i | − | 0.292836i | ||||||
\(591\) | −569.191 | −0.963099 | ||||||||
\(592\) | 328.036i | 0.554115i | ||||||||
\(593\) | 967.284 | 1.63117 | 0.815585 | − | 0.578637i | \(-0.196415\pi\) | ||||
0.815585 | + | 0.578637i | \(0.196415\pi\) | |||||||
\(594\) | − | 8.39443i | − | 0.0141320i | ||||||
\(595\) | 14.1617i | 0.0238012i | ||||||||
\(596\) | − | 731.371i | − | 1.22713i | ||||||
\(597\) | − | 614.373i | − | 1.02910i | ||||||
\(598\) | −93.7018 | + | 457.797i | −0.156692 | + | 0.765546i | ||||
\(599\) | −695.902 | −1.16177 | −0.580887 | − | 0.813985i | \(-0.697294\pi\) | ||||
−0.580887 | + | 0.813985i | \(0.697294\pi\) | |||||||
\(600\) | 194.719 | 0.324531 | ||||||||
\(601\) | −482.402 | −0.802665 | −0.401333 | − | 0.915932i | \(-0.631453\pi\) | ||||
−0.401333 | + | 0.915932i | \(0.631453\pi\) | |||||||
\(602\) | 122.715 | 0.203846 | ||||||||
\(603\) | − | 73.3555i | − | 0.121651i | ||||||
\(604\) | 118.629 | 0.196405 | ||||||||
\(605\) | − | 350.024i | − | 0.578552i | ||||||
\(606\) | 160.538 | 0.264914 | ||||||||
\(607\) | −534.976 | −0.881344 | −0.440672 | − | 0.897668i | \(-0.645260\pi\) | ||||
−0.440672 | + | 0.897668i | \(0.645260\pi\) | |||||||
\(608\) | 1006.53i | 1.65547i | ||||||||
\(609\) | − | 105.762i | − | 0.173666i | ||||||
\(610\) | 39.8600 | 0.0653442 | ||||||||
\(611\) | 1592.37 | 2.60617 | ||||||||
\(612\) | − | 16.4535i | − | 0.0268848i | ||||||
\(613\) | − | 7.13100i | − | 0.0116329i | −0.999983 | − | 0.00581647i | \(-0.998149\pi\) | ||
0.999983 | − | 0.00581647i | \(-0.00185145\pi\) | |||||||
\(614\) | 528.200 | 0.860261 | ||||||||
\(615\) | 235.773i | 0.383371i | ||||||||
\(616\) | −30.0544 | −0.0487897 | ||||||||
\(617\) | 675.408i | 1.09466i | 0.836916 | + | 0.547332i | \(0.184357\pi\) | ||||
−0.836916 | + | 0.547332i | \(0.815643\pi\) | |||||||
\(618\) | − | 211.604i | − | 0.342401i | ||||||
\(619\) | − | 201.503i | − | 0.325529i | −0.986665 | − | 0.162765i | \(-0.947959\pi\) | ||
0.986665 | − | 0.162765i | \(-0.0520411\pi\) | |||||||
\(620\) | − | 416.039i | − | 0.671031i | ||||||
\(621\) | −23.9648 | + | 117.084i | −0.0385906 | + | 0.188541i | ||||
\(622\) | 168.360 | 0.270675 | ||||||||
\(623\) | −166.166 | −0.266719 | ||||||||
\(624\) | −190.106 | −0.304658 | ||||||||
\(625\) | 45.1040 | 0.0721665 | ||||||||
\(626\) | − | 129.947i | − | 0.207584i | ||||||
\(627\) | 86.9590 | 0.138691 | ||||||||
\(628\) | 102.031i | 0.162469i | ||||||||
\(629\) | −111.628 | −0.177470 | ||||||||
\(630\) | −23.1102 | −0.0366829 | ||||||||
\(631\) | 804.427i | 1.27485i | 0.770514 | + | 0.637423i | \(0.219999\pi\) | ||||
−0.770514 | + | 0.637423i | \(0.780001\pi\) | |||||||
\(632\) | − | 832.846i | − | 1.31779i | ||||||
\(633\) | −495.270 | −0.782418 | ||||||||
\(634\) | −40.7394 | −0.0642577 | ||||||||
\(635\) | − | 391.532i | − | 0.616587i | ||||||
\(636\) | 395.368i | 0.621648i | ||||||||
\(637\) | 144.515 | 0.226869 | ||||||||
\(638\) | 37.2847i | 0.0584399i | ||||||||
\(639\) | −73.4000 | −0.114867 | ||||||||
\(640\) | − | 357.105i | − | 0.557977i | ||||||
\(641\) | 184.130i | 0.287255i | 0.989632 | + | 0.143627i | \(0.0458767\pi\) | ||||
−0.989632 | + | 0.143627i | \(0.954123\pi\) | |||||||
\(642\) | − | 357.159i | − | 0.556323i | ||||||
\(643\) | − | 778.840i | − | 1.21126i | −0.795747 | − | 0.605630i | \(-0.792921\pi\) | ||
0.795747 | − | 0.605630i | \(-0.207079\pi\) | |||||||
\(644\) | 180.729 | + | 36.9917i | 0.280636 | + | 0.0574405i | ||||
\(645\) | 241.526 | 0.374459 | ||||||||
\(646\) | −54.4499 | −0.0842878 | ||||||||
\(647\) | 143.648 | 0.222022 | 0.111011 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111011 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(648\) | 62.2778 | 0.0961077 | ||||||||
\(649\) | − | 97.4119i | − | 0.150095i | ||||||
\(650\) | 330.075 | 0.507808 | ||||||||
\(651\) | − | 212.562i | − | 0.326517i | ||||||
\(652\) | −72.9929 | −0.111952 | ||||||||
\(653\) | −533.097 | −0.816382 | −0.408191 | − | 0.912897i | \(-0.633840\pi\) | ||||
−0.408191 | + | 0.912897i | \(0.633840\pi\) | |||||||
\(654\) | 167.739i | 0.256481i | ||||||||
\(655\) | − | 332.904i | − | 0.508251i | ||||||
\(656\) | −244.602 | −0.372869 | ||||||||
\(657\) | −15.1023 | −0.0229867 | ||||||||
\(658\) | 200.825i | 0.305205i | ||||||||
\(659\) | 129.534i | 0.196562i | 0.995159 | + | 0.0982809i | \(0.0313344\pi\) | ||||
−0.995159 | + | 0.0982809i | \(0.968666\pi\) | |||||||
\(660\) | −25.5028 | −0.0386406 | ||||||||
\(661\) | 613.199i | 0.927684i | 0.885918 | + | 0.463842i | \(0.153530\pi\) | ||||
−0.885918 | + | 0.463842i | \(0.846470\pi\) | |||||||
\(662\) | 521.456 | 0.787697 | ||||||||
\(663\) | − | 64.6918i | − | 0.0975744i | ||||||
\(664\) | 586.230i | 0.882877i | ||||||||
\(665\) | − | 239.402i | − | 0.360003i | ||||||
\(666\) | − | 182.164i | − | 0.273520i | ||||||
\(667\) | 106.442 | − | 520.041i | 0.159583 | − | 0.779671i | ||||
\(668\) | 360.400 | 0.539520 | ||||||||
\(669\) | 686.665 | 1.02641 | ||||||||
\(670\) | 71.1944 | 0.106260 | ||||||||
\(671\) | 22.4736 | 0.0334926 | ||||||||
\(672\) | − | 150.817i | − | 0.224430i | ||||||
\(673\) | −1086.59 | −1.61455 | −0.807275 | − | 0.590175i | \(-0.799059\pi\) | ||||
−0.807275 | + | 0.590175i | \(0.799059\pi\) | |||||||
\(674\) | 105.599i | 0.156675i | ||||||||
\(675\) | 84.4186 | 0.125065 | ||||||||
\(676\) | −779.770 | −1.15351 | ||||||||
\(677\) | 591.555i | 0.873788i | 0.899513 | + | 0.436894i | \(0.143922\pi\) | ||||
−0.899513 | + | 0.436894i | \(0.856078\pi\) | |||||||
\(678\) | 278.734i | 0.411112i | ||||||||
\(679\) | 131.575 | 0.193778 | ||||||||
\(680\) | 37.0388 | 0.0544689 | ||||||||
\(681\) | 291.360i | 0.427841i | ||||||||
\(682\) | 74.9352i | 0.109876i | ||||||||
\(683\) | −213.493 | −0.312581 | −0.156290 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156290 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(684\) | 278.144i | 0.406643i | ||||||||
\(685\) | −262.192 | −0.382762 | ||||||||
\(686\) | 18.2258i | 0.0265683i | ||||||||
\(687\) | 316.962i | 0.461371i | ||||||||
\(688\) | 250.570i | 0.364200i | ||||||||
\(689\) | 1554.51i | 2.25618i | ||||||||
\(690\) | −113.635 | − | 23.2587i | −0.164688 | − | 0.0337083i | ||||
\(691\) | 1199.99 | 1.73660 | 0.868298 | − | 0.496044i | \(-0.165214\pi\) | ||||
0.868298 | + | 0.496044i | \(0.165214\pi\) | |||||||
\(692\) | 226.542 | 0.327372 | ||||||||
\(693\) | −13.0298 | −0.0188021 | ||||||||
\(694\) | 202.286 | 0.291478 | ||||||||
\(695\) | − | 468.630i | − | 0.674288i | ||||||
\(696\) | −276.613 | −0.397432 | ||||||||
\(697\) | − | 83.2363i | − | 0.119421i | ||||||
\(698\) | −253.598 | −0.363321 | ||||||||
\(699\) | 254.452 | 0.364022 | ||||||||
\(700\) | − | 130.307i | − | 0.186154i | ||||||
\(701\) | − | 974.622i | − | 1.39033i | −0.718850 | − | 0.695165i | \(-0.755331\pi\) | ||
0.718850 | − | 0.695165i | \(-0.244669\pi\) | |||||||
\(702\) | 105.569 | 0.150384 | ||||||||
\(703\) | 1887.06 | 2.68430 | ||||||||
\(704\) | 18.2579i | 0.0259346i | ||||||||
\(705\) | 395.260i | 0.560653i | ||||||||
\(706\) | 215.651 | 0.305455 | ||||||||
\(707\) | − | 249.187i | − | 0.352457i | ||||||
\(708\) | 311.578 | 0.440083 | ||||||||
\(709\) | 688.631i | 0.971271i | 0.874162 | + | 0.485635i | \(0.161412\pi\) | ||||
−0.874162 | + | 0.485635i | \(0.838588\pi\) | |||||||
\(710\) | − | 71.2376i | − | 0.100335i | ||||||
\(711\) | − | 361.073i | − | 0.507838i | ||||||
\(712\) | 434.595i | 0.610386i | ||||||||
\(713\) | 213.928 | − | 1045.18i | 0.300040 | − | 1.46590i | ||||
\(714\) | 8.15872 | 0.0114268 | ||||||||
\(715\) | −100.272 | −0.140240 | ||||||||
\(716\) | −841.607 | −1.17543 | ||||||||
\(717\) | 484.682 | 0.675986 | ||||||||
\(718\) | − | 185.540i | − | 0.258412i | ||||||
\(719\) | 57.7261 | 0.0802866 | 0.0401433 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401433 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(720\) | − | 47.1884i | − | 0.0655394i | ||||||
\(721\) | −328.452 | −0.455551 | ||||||||
\(722\) | 565.210 | 0.782839 | ||||||||
\(723\) | − | 475.680i | − | 0.657925i | ||||||
\(724\) | 161.656i | 0.223282i | ||||||||
\(725\) | −374.954 | −0.517178 | ||||||||
\(726\) | −201.653 | −0.277759 | ||||||||
\(727\) | − | 734.127i | − | 1.00980i | −0.863177 | − | 0.504902i | \(-0.831529\pi\) | ||
0.863177 | − | 0.504902i | \(-0.168471\pi\) | |||||||
\(728\) | − | 377.969i | − | 0.519188i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 14.6574i | − | 0.0200786i | ||||||
\(731\) | −85.2671 | −0.116644 | ||||||||
\(732\) | 71.8832i | 0.0982010i | ||||||||
\(733\) | − | 692.573i | − | 0.944847i | −0.881372 | − | 0.472423i | \(-0.843379\pi\) | ||
0.881372 | − | 0.472423i | \(-0.156621\pi\) | |||||||
\(734\) | 258.080i | 0.351608i | ||||||||
\(735\) | 35.8718i | 0.0488051i | ||||||||
\(736\) | 151.786 | − | 741.577i | 0.206231 | − | 1.00758i | ||||
\(737\) | 40.1403 | 0.0544645 | ||||||||
\(738\) | 135.832 | 0.184054 | ||||||||
\(739\) | 639.157 | 0.864895 | 0.432447 | − | 0.901659i | \(-0.357650\pi\) | ||||
0.432447 | + | 0.901659i | \(0.357650\pi\) | |||||||
\(740\) | −553.426 | −0.747873 | ||||||||
\(741\) | 1093.61i | 1.47585i | ||||||||
\(742\) | −196.050 | −0.264218 | ||||||||
\(743\) | − | 745.887i | − | 1.00389i | −0.864901 | − | 0.501943i | \(-0.832619\pi\) | ||
0.864901 | − | 0.501943i | \(-0.167381\pi\) | |||||||
\(744\) | −555.940 | −0.747232 | ||||||||
\(745\) | 713.786 | 0.958102 | ||||||||
\(746\) | 64.3593i | 0.0862725i | ||||||||
\(747\) | 254.155i | 0.340234i | ||||||||
\(748\) | 9.00337 | 0.0120366 | ||||||||
\(749\) | −554.384 | −0.740165 | ||||||||
\(750\) | 208.008i | 0.277344i | ||||||||
\(751\) | 1.32171i | 0.00175993i | 1.00000 | 0.000879967i | \(0.000280102\pi\) | |||||
−1.00000 | 0.000879967i | \(0.999720\pi\) | ||||||||
\(752\) | −410.061 | −0.545294 | ||||||||
\(753\) | 305.943i | 0.406299i | ||||||||
\(754\) | −468.897 | −0.621880 | ||||||||
\(755\) | 115.776i | 0.153346i | ||||||||
\(756\) | − | 41.6768i | − | 0.0551281i | ||||||
\(757\) | − | 464.771i | − | 0.613964i | −0.951715 | − | 0.306982i | \(-0.900681\pi\) | ||
0.951715 | − | 0.306982i | \(-0.0993192\pi\) | |||||||
\(758\) | − | 291.775i | − | 0.384927i | ||||||
\(759\) | −64.0687 | − | 13.1136i | −0.0844120 | − | 0.0172774i | ||||
\(760\) | −626.137 | −0.823865 | ||||||||
\(761\) | −1046.21 | −1.37479 | −0.687394 | − | 0.726285i | \(-0.741245\pi\) | ||||
−0.687394 | + | 0.726285i | \(0.741245\pi\) | |||||||
\(762\) | −225.566 | −0.296019 | ||||||||
\(763\) | 260.364 | 0.341237 | ||||||||
\(764\) | 794.773i | 1.04028i | ||||||||
\(765\) | 16.0579 | 0.0209907 | ||||||||
\(766\) | 471.569i | 0.615625i | ||||||||
\(767\) | 1225.07 | 1.59722 | ||||||||
\(768\) | −282.788 | −0.368213 | ||||||||
\(769\) | − | 1061.61i | − | 1.38051i | −0.723566 | − | 0.690255i | \(-0.757498\pi\) | ||
0.723566 | − | 0.690255i | \(-0.242502\pi\) | |||||||
\(770\) | − | 12.6460i | − | 0.0164233i | ||||||
\(771\) | −558.732 | −0.724685 | ||||||||
\(772\) | −194.617 | −0.252095 | ||||||||
\(773\) | 384.077i | 0.496866i | 0.968649 | + | 0.248433i | \(0.0799155\pi\) | ||||
−0.968649 | + | 0.248433i | \(0.920084\pi\) | |||||||
\(774\) | − | 139.146i | − | 0.179775i | ||||||
\(775\) | −753.587 | −0.972370 | ||||||||
\(776\) | − | 344.125i | − | 0.443460i | ||||||
\(777\) | −282.756 | −0.363907 | ||||||||
\(778\) | − | 99.5950i | − | 0.128014i | ||||||
\(779\) | 1407.10i | 1.80629i | ||||||||
\(780\) | − | 320.726i | − | 0.411188i | ||||||
\(781\) | − | 40.1646i | − | 0.0514272i | ||||||
\(782\) | 40.1170 | + | 8.21115i | 0.0513005 | + | 0.0105002i | ||||
\(783\) | −119.923 | −0.153159 | ||||||||
\(784\) | −37.2150 | −0.0474681 | ||||||||
\(785\) | −99.5773 | −0.126850 | ||||||||
\(786\) | −191.790 | −0.244008 | ||||||||
\(787\) | − | 493.710i | − | 0.627332i | −0.949533 | − | 0.313666i | \(-0.898443\pi\) | ||
0.949533 | − | 0.313666i | \(-0.101557\pi\) | |||||||
\(788\) | 996.234 | 1.26426 | ||||||||
\(789\) | − | 306.750i | − | 0.388783i | ||||||
\(790\) | 350.435 | 0.443589 | ||||||||
\(791\) | 432.651 | 0.546968 | ||||||||
\(792\) | 34.0785i | 0.0430285i | ||||||||
\(793\) | 282.631i | 0.356407i | ||||||||
\(794\) | −370.803 | −0.467006 | ||||||||
\(795\) | −385.862 | −0.485361 | ||||||||
\(796\) | 1075.31i | 1.35090i | ||||||||
\(797\) | − | 57.2706i | − | 0.0718577i | −0.999354 | − | 0.0359288i | \(-0.988561\pi\) | ||
0.999354 | − | 0.0359288i | \(-0.0114390\pi\) | |||||||
\(798\) | −137.922 | −0.172835 | ||||||||
\(799\) | − | 139.541i | − | 0.174644i | ||||||
\(800\) | −534.683 | −0.668354 | ||||||||
\(801\) | 188.415i | 0.235224i | ||||||||
\(802\) | − | 5.89779i | − | 0.00735385i | ||||||
\(803\) | − | 8.26400i | − | 0.0102914i | ||||||
\(804\) | 128.391i | 0.159691i | ||||||||
\(805\) | −36.1023 | + | 176.384i | −0.0448475 | + | 0.219111i | ||||
\(806\) | −942.396 | −1.16923 | ||||||||
\(807\) | −96.0442 | −0.119014 | ||||||||
\(808\) | −651.729 | −0.806595 | ||||||||
\(809\) | −557.511 | −0.689136 | −0.344568 | − | 0.938761i | \(-0.611975\pi\) | ||||
−0.344568 | + | 0.938761i | \(0.611975\pi\) | |||||||
\(810\) | 26.2045i | 0.0323513i | ||||||||
\(811\) | 181.946 | 0.224348 | 0.112174 | − | 0.993689i | \(-0.464219\pi\) | ||||
0.112174 | + | 0.993689i | \(0.464219\pi\) | |||||||
\(812\) | 185.112i | 0.227970i | ||||||||
\(813\) | −313.234 | −0.385281 | ||||||||
\(814\) | 99.6807 | 0.122458 | ||||||||
\(815\) | − | 71.2379i | − | 0.0874084i | ||||||
\(816\) | 16.6592i | 0.0204156i | ||||||||
\(817\) | 1441.43 | 1.76430 | ||||||||
\(818\) | 386.690 | 0.472726 | ||||||||
\(819\) | − | 163.865i | − | 0.200080i | ||||||
\(820\) | − | 412.665i | − | 0.503250i | ||||||
\(821\) | −1108.28 | −1.34992 | −0.674959 | − | 0.737855i | \(-0.735839\pi\) | ||||
−0.674959 | + | 0.737855i | \(0.735839\pi\) | |||||||
\(822\) | 151.052i | 0.183761i | ||||||||
\(823\) | 639.531 | 0.777073 | 0.388537 | − | 0.921433i | \(-0.372981\pi\) | ||||
0.388537 | + | 0.921433i | \(0.372981\pi\) | |||||||
\(824\) | 859.041i | 1.04253i | ||||||||
\(825\) | 46.1941i | 0.0559928i | ||||||||
\(826\) | 154.501i | 0.187048i | ||||||||
\(827\) | 1328.39i | 1.60628i | 0.595791 | + | 0.803140i | \(0.296839\pi\) | ||||
−0.595791 | + | 0.803140i | \(0.703161\pi\) | |||||||
\(828\) | 41.9446 | − | 204.928i | 0.0506578 | − | 0.247497i | ||||
\(829\) | −585.865 | −0.706712 | −0.353356 | − | 0.935489i | \(-0.614960\pi\) | ||||
−0.353356 | + | 0.935489i | \(0.614960\pi\) | |||||||
\(830\) | −246.667 | −0.297189 | ||||||||
\(831\) | −264.361 | −0.318124 | ||||||||
\(832\) | −229.614 | −0.275979 | ||||||||
\(833\) | − | 12.6640i | − | 0.0152029i | ||||||
\(834\) | −269.984 | −0.323721 | ||||||||
\(835\) | 351.734i | 0.421239i | ||||||||
\(836\) | −152.201 | −0.182059 | ||||||||
\(837\) | −241.023 | −0.287961 | ||||||||
\(838\) | 331.966i | 0.396140i | ||||||||
\(839\) | − | 1423.22i | − | 1.69633i | −0.529734 | − | 0.848164i | \(-0.677708\pi\) | ||
0.529734 | − | 0.848164i | \(-0.322292\pi\) | |||||||
\(840\) | 93.8198 | 0.111690 | ||||||||
\(841\) | −308.349 | −0.366646 | ||||||||
\(842\) | − | 704.109i | − | 0.836234i | ||||||
\(843\) | − | 367.167i | − | 0.435548i | ||||||
\(844\) | 866.853 | 1.02708 | ||||||||
\(845\) | − | 761.021i | − | 0.900617i | ||||||
\(846\) | 227.714 | 0.269165 | ||||||||
\(847\) | 313.006i | 0.369547i | ||||||||
\(848\) | − | 400.310i | − | 0.472064i | ||||||
\(849\) | − | 860.688i | − | 1.01377i | ||||||
\(850\) | − | 28.9247i | − | 0.0340291i | ||||||
\(851\) | −1390.33 | − | 284.573i | −1.63376 | − | 0.334398i | ||||
\(852\) | 128.469 | 0.150786 | ||||||||
\(853\) | −178.396 | −0.209140 | −0.104570 | − | 0.994518i | \(-0.533347\pi\) | ||||
−0.104570 | + | 0.994518i | \(0.533347\pi\) | |||||||
\(854\) | −35.6444 | −0.0417382 | ||||||||
\(855\) | −271.456 | −0.317493 | ||||||||
\(856\) | 1449.95i | 1.69386i | ||||||||
\(857\) | −15.2764 | −0.0178254 | −0.00891271 | − | 0.999960i | \(-0.502837\pi\) | ||||
−0.00891271 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(858\) | 57.7678i | 0.0673285i | ||||||||
\(859\) | −460.564 | −0.536163 | −0.268081 | − | 0.963396i | \(-0.586390\pi\) | ||||
−0.268081 | + | 0.963396i | \(0.586390\pi\) | |||||||
\(860\) | −422.733 | −0.491551 | ||||||||
\(861\) | − | 210.838i | − | 0.244876i | ||||||
\(862\) | − | 783.115i | − | 0.908486i | ||||||
\(863\) | 472.358 | 0.547345 | 0.273672 | − | 0.961823i | \(-0.411762\pi\) | ||||
0.273672 | + | 0.961823i | \(0.411762\pi\) | |||||||
\(864\) | −171.010 | −0.197928 | ||||||||
\(865\) | 221.095i | 0.255601i | ||||||||
\(866\) | − | 214.189i | − | 0.247331i | ||||||
\(867\) | 494.894 | 0.570812 | ||||||||
\(868\) | 372.040i | 0.428617i | ||||||||
\(869\) | 197.580 | 0.227365 | ||||||||
\(870\) | − | 116.390i | − | 0.133782i | ||||||
\(871\) | 504.810i | 0.579575i | ||||||||
\(872\) | − | 680.962i | − | 0.780920i | ||||||
\(873\) | − | 149.192i | − | 0.170896i | ||||||
\(874\) | −678.174 | − | 138.809i | −0.775943 | − | 0.158820i | ||||
\(875\) | 322.871 | 0.368995 | ||||||||
\(876\) | 26.4330 | 0.0301746 | ||||||||
\(877\) | −561.186 | −0.639893 | −0.319947 | − | 0.947436i | \(-0.603665\pi\) | ||||
−0.319947 | + | 0.947436i | \(0.603665\pi\) | |||||||
\(878\) | −424.372 | −0.483340 | ||||||||
\(879\) | 1012.73i | 1.15214i | ||||||||
\(880\) | 25.8216 | 0.0293427 | ||||||||
\(881\) | 219.031i | 0.248617i | 0.992244 | + | 0.124308i | \(0.0396712\pi\) | ||||
−0.992244 | + | 0.124308i | \(0.960329\pi\) | |||||||
\(882\) | 20.6661 | 0.0234310 | ||||||||
\(883\) | 335.195 | 0.379609 | 0.189805 | − | 0.981822i | \(-0.439215\pi\) | ||||
0.189805 | + | 0.981822i | \(0.439215\pi\) | |||||||
\(884\) | 113.228i | 0.128086i | ||||||||
\(885\) | 304.087i | 0.343601i | ||||||||
\(886\) | 235.391 | 0.265678 | ||||||||
\(887\) | −911.215 | −1.02730 | −0.513650 | − | 0.858000i | \(-0.671707\pi\) | ||||
−0.513650 | + | 0.858000i | \(0.671707\pi\) | |||||||
\(888\) | 739.526i | 0.832799i | ||||||||
\(889\) | 350.125i | 0.393841i | ||||||||
\(890\) | −182.864 | −0.205465 | ||||||||
\(891\) | 14.7745i | 0.0165819i | ||||||||
\(892\) | −1201.84 | −1.34736 | ||||||||
\(893\) | 2358.92i | 2.64157i | ||||||||
\(894\) | − | 411.220i | − | 0.459978i | ||||||
\(895\) | − | 821.371i | − | 0.917733i | ||||||
\(896\) | 319.338i | 0.356404i | ||||||||
\(897\) | 164.918 | − | 805.737i | 0.183855 | − | 0.898257i | ||||
\(898\) | 96.1500 | 0.107071 | ||||||||
\(899\) | 1070.53 | 1.19080 | ||||||||
\(900\) | −147.755 | −0.164172 | ||||||||
\(901\) | 136.223 | 0.151191 | ||||||||
\(902\) | 74.3274i | 0.0824029i | ||||||||
\(903\) | −215.982 | −0.239183 | ||||||||
\(904\) | − | 1131.57i | − | 1.25173i | ||||||
\(905\) | −157.769 | −0.174331 | ||||||||
\(906\) | 66.7001 | 0.0736204 | ||||||||
\(907\) | 727.272i | 0.801843i | 0.916112 | + | 0.400922i | \(0.131310\pi\) | ||||
−0.916112 | + | 0.400922i | \(0.868690\pi\) | |||||||
\(908\) | − | 509.956i | − | 0.561625i | ||||||
\(909\) | −282.551 | −0.310838 | ||||||||
\(910\) | 159.037 | 0.174766 | ||||||||
\(911\) | − | 160.214i | − | 0.175866i | −0.996126 | − | 0.0879329i | \(-0.971974\pi\) | ||
0.996126 | − | 0.0879329i | \(-0.0280261\pi\) | |||||||
\(912\) | − | 281.621i | − | 0.308795i | ||||||
\(913\) | −139.074 | −0.152327 | ||||||||
\(914\) | − | 193.346i | − | 0.211538i | ||||||
\(915\) | −70.1548 | −0.0766719 | ||||||||
\(916\) | − | 554.766i | − | 0.605640i | ||||||
\(917\) | 297.697i | 0.324642i | ||||||||
\(918\) | − | 9.25112i | − | 0.0100775i | ||||||
\(919\) | − | 885.855i | − | 0.963933i | −0.876190 | − | 0.481967i | \(-0.839923\pi\) | ||
0.876190 | − | 0.481967i | \(-0.160077\pi\) | |||||||
\(920\) | 461.318 | + | 94.4226i | 0.501433 | + | 0.102633i | ||||
\(921\) | −929.649 | −1.00939 | ||||||||
\(922\) | 213.966 | 0.232067 | ||||||||
\(923\) | 505.116 | 0.547255 | ||||||||
\(924\) | 22.8056 | 0.0246814 | ||||||||
\(925\) | 1002.44i | 1.08372i | ||||||||
\(926\) | −825.065 | −0.890999 | ||||||||
\(927\) | 372.430i | 0.401758i | ||||||||
\(928\) | 759.559 | 0.818490 | ||||||||
\(929\) | 152.772 | 0.164448 | 0.0822241 | − | 0.996614i | \(-0.473798\pi\) | ||||
0.0822241 | + | 0.996614i | \(0.473798\pi\) | |||||||
\(930\) | − | 233.922i | − | 0.251529i | ||||||
\(931\) | 214.083i | 0.229950i | ||||||||
\(932\) | −445.357 | −0.477851 | ||||||||
\(933\) | −296.319 | −0.317598 | ||||||||
\(934\) | 386.432i | 0.413739i | ||||||||
\(935\) | 8.78689i | 0.00939775i | ||||||||
\(936\) | −428.577 | −0.457881 | ||||||||
\(937\) | 584.541i | 0.623843i | 0.950108 | + | 0.311921i | \(0.100973\pi\) | ||||
−0.950108 | + | 0.311921i | \(0.899027\pi\) | |||||||
\(938\) | −63.6650 | −0.0678731 | ||||||||
\(939\) | 228.712i | 0.243569i | ||||||||
\(940\) | − | 691.809i | − | 0.735967i | ||||||
\(941\) | − | 591.924i | − | 0.629037i | −0.949251 | − | 0.314518i | \(-0.898157\pi\) | ||
0.949251 | − | 0.314518i | \(-0.101843\pi\) | |||||||
\(942\) | 57.3676i | 0.0608998i | ||||||||
\(943\) | 212.193 | − | 1036.71i | 0.225019 | − | 1.09937i | ||||
\(944\) | −315.474 | −0.334188 | ||||||||
\(945\) | 40.6747 | 0.0430421 | ||||||||
\(946\) | 76.1409 | 0.0804872 | ||||||||
\(947\) | 1307.91 | 1.38111 | 0.690553 | − | 0.723281i | \(-0.257367\pi\) | ||||
0.690553 | + | 0.723281i | \(0.257367\pi\) | |||||||
\(948\) | 631.973i | 0.666638i | ||||||||
\(949\) | 103.929 | 0.109514 | ||||||||
\(950\) | 488.969i | 0.514704i | ||||||||
\(951\) | 71.7026 | 0.0753970 | ||||||||
\(952\) | −33.1217 | −0.0347917 | ||||||||
\(953\) | − | 1276.91i | − | 1.33989i | −0.742412 | − | 0.669943i | \(-0.766318\pi\) | ||
0.742412 | − | 0.669943i | \(-0.233682\pi\) | |||||||
\(954\) | 222.299i | 0.233018i | ||||||||
\(955\) | −775.663 | −0.812213 | ||||||||
\(956\) | −848.321 | −0.887365 | ||||||||
\(957\) | − | 65.6222i | − | 0.0685708i | ||||||
\(958\) | − | 281.035i | − | 0.293356i | ||||||
\(959\) | 234.463 | 0.244487 | ||||||||
\(960\) | − | 56.9951i | − | 0.0593699i | ||||||
\(961\) | 1190.56 | 1.23888 | ||||||||
\(962\) | 1253.60i | 1.30312i | ||||||||
\(963\) | 628.612i | 0.652764i | ||||||||
\(964\) | 832.564i | 0.863656i | ||||||||
\(965\) | − | 189.938i | − | 0.196827i | ||||||
\(966\) | 101.617 | + | 20.7989i | 0.105193 | + | 0.0215310i | ||||
\(967\) | 223.374 | 0.230997 | 0.115498 | − | 0.993308i | \(-0.463154\pi\) | ||||
0.115498 | + | 0.993308i | \(0.463154\pi\) | |||||||
\(968\) | 818.643 | 0.845705 | ||||||||
\(969\) | 95.8336 | 0.0988995 | ||||||||
\(970\) | 144.797 | 0.149275 | ||||||||
\(971\) | 1668.29i | 1.71811i | 0.511879 | + | 0.859057i | \(0.328950\pi\) | ||||
−0.511879 | + | 0.859057i | \(0.671050\pi\) | |||||||
\(972\) | −47.2571 | −0.0486184 | ||||||||
\(973\) | 419.069i | 0.430698i | ||||||||
\(974\) | −196.145 | −0.201381 | ||||||||
\(975\) | −580.943 | −0.595839 | ||||||||
\(976\) | − | 72.7818i | − | 0.0745715i | ||||||
\(977\) | 494.183i | 0.505817i | 0.967490 | + | 0.252909i | \(0.0813872\pi\) | ||||
−0.967490 | + | 0.252909i | \(0.918613\pi\) | |||||||
\(978\) | −41.0410 | −0.0419642 | ||||||||
\(979\) | −103.101 | −0.105313 | ||||||||
\(980\) | − | 62.7850i | − | 0.0640663i | ||||||
\(981\) | − | 295.225i | − | 0.300943i | ||||||
\(982\) | 175.360 | 0.178574 | ||||||||
\(983\) | 1237.71i | 1.25912i | 0.776953 | + | 0.629559i | \(0.216764\pi\) | ||||
−0.776953 | + | 0.629559i | \(0.783236\pi\) | |||||||
\(984\) | −551.431 | −0.560398 | ||||||||
\(985\) | 972.280i | 0.987087i | ||||||||
\(986\) | 41.0898i | 0.0416732i | ||||||||
\(987\) | − | 353.458i | − | 0.358114i | ||||||
\(988\) | − | 1914.10i | − | 1.93735i | ||||||
\(989\) | −1062.00 | − | 217.370i | −1.07381 | − | 0.219788i | ||||
\(990\) | −14.3392 | −0.0144840 | ||||||||
\(991\) | 643.200 | 0.649042 | 0.324521 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324521 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(992\) | 1526.57 | 1.53888 | ||||||||
\(993\) | −917.779 | −0.924248 | ||||||||
\(994\) | 63.7036i | 0.0640881i | ||||||||
\(995\) | −1049.46 | −1.05473 | ||||||||
\(996\) | − | 444.838i | − | 0.446624i | ||||||
\(997\) | 210.864 | 0.211499 | 0.105749 | − | 0.994393i | \(-0.466276\pi\) | ||||
0.105749 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(998\) | −613.962 | −0.615193 | ||||||||
\(999\) | 320.615i | 0.320936i |
(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 | 483.3.f.a.22.17 | ✓ | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.17 | ✓ | 48 | 1.1 | even | 1 | trivial | |
483.3.f.a.22.18 | yes | 48 | 23.22 | odd | 2 | inner |