Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (of order \(2\), degree \(1\), not 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.16516096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} + 9x^{4} + 13x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.5 | ||
Root | \(2.68667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.h.609.2 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 2.31446i | 1.33625i | 0.744047 | + | 0.668127i | \(0.232904\pi\) | ||||
−0.744047 | + | 0.668127i | \(0.767096\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.94827 | − | 1.09737i | 0.871295 | − | 0.490760i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.45033i | − | 0.548172i | −0.961705 | − | 0.274086i | \(-0.911625\pi\) | ||
0.961705 | − | 0.274086i | \(-0.0883754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.35673 | −0.785575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.89655 | 1.17485 | 0.587427 | − | 0.809277i | \(-0.300141\pi\) | ||||
0.587427 | + | 0.809277i | \(0.300141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.05888i | − | 0.848380i | −0.905573 | − | 0.424190i | \(-0.860559\pi\) | ||
0.905573 | − | 0.424190i | \(-0.139441\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.53982 | + | 4.50920i | 0.655780 | + | 1.16427i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.92301i | 0.951469i | 0.879589 | + | 0.475735i | \(0.157818\pi\) | ||||
−0.879589 | + | 0.475735i | \(0.842182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.35673 | 0.732498 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.37334i | − | 1.12042i | −0.828351 | − | 0.560209i | \(-0.810721\pi\) | ||
0.828351 | − | 0.560209i | \(-0.189279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.59155 | − | 4.27596i | 0.518310 | − | 0.855193i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.48883i | 0.286526i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.43637 | 1.51522 | 0.757609 | − | 0.652709i | \(-0.226368\pi\) | ||||
0.757609 | + | 0.652709i | \(0.226368\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.01841i | 1.56990i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.59155 | − | 2.82564i | −0.269021 | − | 0.477620i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.95953i | − | 0.979741i | −0.871795 | − | 0.489871i | \(-0.837044\pi\) | ||
0.871795 | − | 0.489871i | \(-0.162956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.07965 | 1.13365 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4364 | 1.62989 | 0.814944 | − | 0.579540i | \(-0.196768\pi\) | ||||
0.814944 | + | 0.579540i | \(0.196768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.45033i | − | 0.221173i | −0.993867 | − | 0.110586i | \(-0.964727\pi\) | ||
0.993867 | − | 0.110586i | \(-0.0352729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.59155 | + | 2.58620i | −0.684468 | + | 0.385529i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.90686i | − | 0.715739i | −0.933772 | − | 0.357869i | \(-0.883503\pi\) | ||
0.933772 | − | 0.357869i | \(-0.116497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89655 | 0.699507 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.07965 | −1.27140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.23127i | 0.581209i | 0.956843 | + | 0.290605i | \(0.0938564\pi\) | ||||
−0.956843 | + | 0.290605i | \(0.906144\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.59155 | − | 4.27596i | 1.02364 | − | 0.576571i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.31446i | − | 0.306558i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.35673 | 0.437008 | 0.218504 | − | 0.975836i | \(-0.429882\pi\) | ||||
0.218504 | + | 0.975836i | \(0.429882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3329 | 1.32300 | 0.661498 | − | 0.749947i | \(-0.269921\pi\) | ||||
0.661498 | + | 0.749947i | \(0.269921\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.41802i | 0.430631i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.35673 | − | 5.95953i | −0.416351 | − | 0.739189i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.84404i | 1.20264i | 0.799008 | + | 0.601320i | \(0.205358\pi\) | ||||
−0.799008 | + | 0.601320i | \(0.794642\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.4364 | 1.49716 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.64327 | −1.02577 | −0.512884 | − | 0.858458i | \(-0.671423\pi\) | ||||
−0.512884 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.43418i | 0.284899i | 0.989802 | + | 0.142449i | \(0.0454978\pi\) | ||||
−0.989802 | + | 0.142449i | \(0.954502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.89655 | + | 5.99804i | 1.14276 | + | 0.692594i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.65127i | − | 0.644022i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4364 | −1.39920 | −0.699601 | − | 0.714534i | \(-0.746639\pi\) | ||||
−0.699601 | + | 0.714534i | \(0.746639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.5160 | −1.16845 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6635i | 1.39000i | 0.719011 | + | 0.694999i | \(0.244595\pi\) | ||||
−0.719011 | + | 0.694999i | \(0.755405\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.30500 | + | 7.64310i | 0.466943 | + | 0.829011i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 13.8868i | − | 1.48882i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3662 | −1.31081 | −0.655407 | − | 0.755276i | \(-0.727503\pi\) | ||||
−0.655407 | + | 0.755276i | \(0.727503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.43637 | −0.465058 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.5256i | 2.02472i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.94827 | + | 1.09737i | −0.199889 | + | 0.112588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.05888i | 0.310582i | 0.987869 | + | 0.155291i | \(0.0496315\pi\) | ||||
−0.987869 | + | 0.155291i | \(0.950369\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.18310 | −0.922936 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.35673 | 0.334007 | 0.167003 | − | 0.985956i | \(-0.446591\pi\) | ||||
0.167003 | + | 0.985956i | \(0.446591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0611i | 1.28695i | 0.765466 | + | 0.643476i | \(0.222508\pi\) | ||||
−0.765466 | + | 0.643476i | \(0.777492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.53982 | − | 3.68358i | 0.638221 | − | 0.359480i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.77099i | 0.557903i | 0.960305 | + | 0.278951i | \(0.0899868\pi\) | ||||
−0.960305 | + | 0.278951i | \(0.910013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.64327 | −0.636310 | −0.318155 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318155 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.7931 | 1.30918 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.41606i | 0.885789i | 0.896574 | + | 0.442894i | \(0.146048\pi\) | ||||
−0.896574 | + | 0.442894i | \(0.853952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.89655 | − | 10.4687i | −0.549856 | − | 0.976215i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.20893i | 0.666466i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.68965 | 0.521569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.18310 | 0.380282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.1546i | 2.17794i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.356726 | − | 11.1746i | 0.0319065 | − | 0.999491i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.0934i | − | 0.984383i | −0.870487 | − | 0.492192i | \(-0.836196\pi\) | ||
0.870487 | − | 0.492192i | \(-0.163804\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.35673 | 0.295543 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.61000 | −0.402778 | −0.201389 | − | 0.979511i | \(-0.564545\pi\) | ||||
−0.201389 | + | 0.979511i | \(0.564545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.45033i | 0.125759i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.63380 | + | 2.90066i | 0.140615 | + | 0.249649i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 13.1808i | − | 1.12612i | −0.826417 | − | 0.563058i | \(-0.809625\pi\) | ||
0.826417 | − | 0.563058i | \(-0.190375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.18310 | 0.100349 | 0.0501745 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501745 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3567 | 0.956409 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.9191i | − | 0.996722i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6896 | + | 6.58423i | −0.970772 | + | 0.546791i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.3329i | 0.934719i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.46018 | −0.447315 | −0.223658 | − | 0.974668i | \(-0.571800\pi\) | ||||
−0.223658 | + | 0.974668i | \(0.571800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.07965 | 0.413376 | 0.206688 | − | 0.978407i | \(-0.433732\pi\) | ||||
0.206688 | + | 0.978407i | \(0.433732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 9.24546i | − | 0.747451i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.4364 | − | 9.25784i | 1.32020 | − | 0.743608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.11775i | 0.488250i | 0.969744 | + | 0.244125i | \(0.0785007\pi\) | ||||
−0.969744 | + | 0.244125i | \(0.921499\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.79310 | −0.776643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.79310 | −0.614182 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.4365i | − | 1.28740i | −0.765277 | − | 0.643701i | \(-0.777398\pi\) | ||
0.765277 | − | 0.643701i | \(-0.222602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.89655 | + | 17.5703i | 0.770445 | + | 1.36785i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.80329i | 0.294308i | 0.989114 | + | 0.147154i | \(0.0470112\pi\) | ||||
−0.989114 | + | 0.147154i | \(0.952989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.64327 | 0.280252 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.35673 | 0.180223 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.3838i | 0.865491i | 0.901516 | + | 0.432746i | \(0.142455\pi\) | ||||
−0.901516 | + | 0.432746i | \(0.857545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.20155 | − | 3.75860i | −0.468793 | − | 0.284123i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.76901i | 0.583954i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0702 | 0.752680 | 0.376340 | − | 0.926482i | \(-0.377182\pi\) | ||||
0.376340 | + | 0.926482i | \(0.377182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.573097 | 0.0425980 | 0.0212990 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212990 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.9151i | 1.76786i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.53982 | − | 11.6108i | −0.480817 | − | 0.853643i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2862i | 1.11784i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.15930 | 0.157066 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.18310 | 0.230321 | 0.115160 | − | 0.993347i | \(-0.463262\pi\) | ||||
0.115160 | + | 0.993347i | \(0.463262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.05888i | − | 0.220183i | −0.993921 | − | 0.110091i | \(-0.964886\pi\) | ||
0.993921 | − | 0.110091i | \(-0.0351143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.7931 | − | 7.76901i | 0.987744 | − | 0.556350i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4933i | 1.53134i | 0.643235 | + | 0.765669i | \(0.277592\pi\) | ||||
−0.643235 | + | 0.765669i | \(0.722408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.81690 | −0.341461 | −0.170731 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170731 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.7836 | −1.60703 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.70197i | 0.610758i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.3329 | − | 11.4526i | 1.42011 | − | 0.799883i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6635i | 0.880173i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.89655 | −0.269530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5066 | −0.723301 | −0.361650 | − | 0.932314i | \(-0.617787\pi\) | ||||
−0.361650 | + | 0.932314i | \(0.617787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 20.0045i | − | 1.37069i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.59155 | − | 2.82564i | −0.108543 | − | 0.192707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.2355i | − | 0.830600i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.63380 | −0.380697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.8947i | − | 1.13136i | −0.824626 | − | 0.565678i | \(-0.808615\pi\) | ||
0.824626 | − | 0.565678i | \(-0.191385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.10757 | + | 10.0773i | −0.407171 | + | 0.671818i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 17.1342i | − | 1.13724i | −0.822602 | − | 0.568618i | \(-0.807478\pi\) | ||
0.822602 | − | 0.568618i | \(-0.192522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.0464 | −1.65511 | −0.827555 | − | 0.561384i | \(-0.810269\pi\) | ||||
−0.827555 | + | 0.561384i | \(0.810269\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.0796 | 0.860578 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.2986i | − | 1.26429i | −0.774849 | − | 0.632147i | \(-0.782174\pi\) | ||
0.774849 | − | 0.632147i | \(-0.217826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.38465 | − | 9.55991i | −0.351256 | − | 0.623620i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 28.7835i | − | 1.86969i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.7693 | 1.21408 | 0.607042 | − | 0.794669i | \(-0.292356\pi\) | ||||
0.607042 | + | 0.794669i | \(0.292356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4364 | −0.929929 | −0.464964 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464964 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 19.8724i | − | 1.27482i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.53982 | − | 5.37334i | 0.609477 | − | 0.343290i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.05888i | 0.194632i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.3091 | −1.85739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9762 | 0.692811 | 0.346406 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346406 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 20.9375i | − | 1.31633i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.6896 | + | 9.96375i | −1.10777 | + | 0.623954i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.6392i | − | 1.10030i | −0.835066 | − | 0.550150i | \(-0.814570\pi\) | ||
0.835066 | − | 0.550150i | \(-0.185430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.64327 | −0.537067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.1404 | 0.875266 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.68976i | − | 0.104195i | −0.998642 | − | 0.0520975i | \(-0.983409\pi\) | ||
0.998642 | − | 0.0520975i | \(-0.0165907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.64327 | + | 8.24367i | 0.285234 | + | 0.506405i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 28.6211i | − | 1.75158i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.1022 | 1.65245 | 0.826226 | − | 0.563339i | \(-0.190484\pi\) | ||||
0.826226 | + | 0.563339i | \(0.190484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.9524 | −1.45500 | −0.727502 | − | 0.686105i | \(-0.759319\pi\) | ||||
−0.727502 | + | 0.686105i | \(0.759319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.2678i | − | 0.621436i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0981 | − | 16.6615i | 0.608938 | − | 1.00473i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.23549i | 0.494822i | 0.968911 | + | 0.247411i | \(0.0795799\pi\) | ||||
−0.968911 | + | 0.247411i | \(0.920420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.8822 | −1.19032 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4364 | −0.622582 | −0.311291 | − | 0.950315i | \(-0.600761\pi\) | ||||
−0.311291 | + | 0.950315i | \(0.600761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.4687i | − | 0.622302i | −0.950361 | − | 0.311151i | \(-0.899286\pi\) | ||
0.950361 | − | 0.311151i | \(-0.100714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.53982 | − | 4.50920i | −0.150446 | − | 0.267102i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 15.1362i | − | 0.893459i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.61000 | 0.0947059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.07965 | −0.415016 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4668i | 0.961999i | 0.876721 | + | 0.481000i | \(0.159726\pi\) | ||||
−0.876721 | + | 0.481000i | \(0.840274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.53982 | − | 3.68358i | 0.380763 | − | 0.214466i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.80131i | 0.336626i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.4364 | −0.950540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10345 | −0.121241 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.76901i | 0.446318i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.1314 | − | 11.3391i | 1.15272 | − | 0.649273i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.87634i | − | 0.449526i | −0.974413 | − | 0.224763i | \(-0.927839\pi\) | ||
0.974413 | − | 0.224763i | \(-0.0721609\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.2295 | −1.71969 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.89655 | −0.220953 | −0.110477 | − | 0.993879i | \(-0.535238\pi\) | ||||
−0.110477 | + | 0.993879i | \(0.535238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.76901i | − | 0.439130i | −0.975598 | − | 0.219565i | \(-0.929536\pi\) | ||
0.975598 | − | 0.219565i | \(-0.0704638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.75084 | + | 6.65925i | 0.211336 | + | 0.375206i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0510i | 1.07001i | 0.844849 | + | 0.535005i | \(0.179690\pi\) | ||||
−0.844849 | + | 0.535005i | \(0.820310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3793 | −1.30899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3567 | −0.745500 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.92301i | − | 0.218282i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0796 | − | 7.92723i | −0.725528 | − | 0.439724i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 15.3756i | − | 0.850272i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.11655 | −0.392348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0450i | 0.769660i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8026 | + | 19.1789i | 0.590207 | + | 1.04785i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.89249i | − | 0.375458i | −0.982221 | − | 0.187729i | \(-0.939887\pi\) | ||
0.982221 | − | 0.187729i | \(-0.0601127\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7931 | −1.18364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.8727 | 1.78016 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.2539i | − | 0.931623i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.2295 | − | 13.6473i | 1.30447 | − | 0.734747i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.5503i | 1.64002i | 0.572346 | + | 0.820012i | \(0.306033\pi\) | ||||
−0.572346 | + | 0.820012i | \(0.693967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7693 | −0.897640 | −0.448820 | − | 0.893622i | \(-0.648156\pi\) | ||||
−0.448820 | + | 0.893622i | \(0.648156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.55416 | 0.243083 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.0999i | − | 1.54883i | −0.632676 | − | 0.774417i | \(-0.718044\pi\) | ||
0.632676 | − | 0.774417i | \(-0.281956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.8395 | + | 9.48489i | −0.893746 | + | 0.503406i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.1685i | 0.696949i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.6896 | −0.616956 | −0.308478 | − | 0.951231i | \(-0.599820\pi\) | ||||
−0.308478 | + | 0.951231i | \(0.599820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.68161i | 0.508153i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.67120 | + | 4.74244i | 0.139817 | + | 0.248231i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.20095i | 0.219288i | 0.993971 | + | 0.109644i | \(0.0349710\pi\) | ||||
−0.993971 | + | 0.109644i | \(0.965029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.5957 | −1.28040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.13672 | 0.318603 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9456i | 0.877412i | 0.898631 | + | 0.438706i | \(0.144563\pi\) | ||||
−0.898631 | + | 0.438706i | \(0.855437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.8633 | + | 0.825627i | 1.33557 | + | 0.0426352i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.3533i | 0.945241i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3662 | 0.532476 | 0.266238 | − | 0.963907i | \(-0.414219\pi\) | ||||
0.266238 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.6753 | 1.31539 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.5907i | 1.05214i | 0.850442 | + | 0.526068i | \(0.176334\pi\) | ||||
−0.850442 | + | 0.526068i | \(0.823666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.20155 | − | 11.0102i | −0.316060 | − | 0.561133i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.41802i | 0.173748i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.10345 | −0.410861 | −0.205431 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205431 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0796 | 1.06604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.6697i | − | 0.538213i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.2295 | + | 13.6473i | −1.21912 | + | 0.686672i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.46891i | 0.174100i | 0.996204 | + | 0.0870499i | \(0.0277440\pi\) | ||||
−0.996204 | + | 0.0870499i | \(0.972256\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.35673 | −0.168046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9524 | −0.796625 | −0.398312 | − | 0.917250i | \(-0.630404\pi\) | ||||
−0.398312 | + | 0.917250i | \(0.630404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 25.8058i | − | 1.28548i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.4881 | + | 11.5400i | −1.01806 | + | 0.573427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 23.2216i | − | 1.15105i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.92982 | 0.194317 | 0.0971586 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971586 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.5066 | 1.50478 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.86835i | − | 0.239556i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8965 | + | 24.6719i | 0.682155 | + | 1.21110i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.73823i | 0.134092i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.2996 | −1.67565 | −0.837824 | − | 0.545941i | \(-0.816172\pi\) | ||||
−0.837824 | + | 0.545941i | \(0.816172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0891 | −1.27151 | −0.635753 | − | 0.771893i | \(-0.719310\pi\) | ||||
−0.635753 | + | 0.771893i | \(0.719310\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5641i | 0.562267i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.7746 | + | 10.1667i | 0.813690 | + | 0.493156i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.9861i | − | 0.725229i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.5862 | 1.33187 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2996 | −0.496117 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.2319i | 1.74119i | 0.491999 | + | 0.870596i | \(0.336266\pi\) | ||||
−0.491999 | + | 0.870596i | \(0.663734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.2389 | − | 27.0552i | −0.730651 | − | 1.29720i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.37334i | 0.257042i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0891 | −1.14971 | −0.574855 | − | 0.818255i | \(-0.694942\pi\) | ||||
−0.574855 | + | 0.818255i | \(0.694942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.5398 | −0.549515 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.52337i | − | 0.262423i | −0.991354 | − | 0.131212i | \(-0.958113\pi\) | ||
0.991354 | − | 0.131212i | \(-0.0418868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0927 | + | 13.5703i | −1.14211 | + | 0.643295i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 12.6374i | − | 0.597727i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.92982 | −0.374231 | −0.187116 | − | 0.982338i | \(-0.559914\pi\) | ||||
−0.187116 | + | 0.982338i | \(0.559914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.6658 | 1.91488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.7566i | 0.552375i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.64327 | + | 4.86835i | −0.405203 | + | 0.228232i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.6534i | − | 1.05968i | −0.848098 | − | 0.529840i | \(-0.822252\pi\) | ||
0.848098 | − | 0.529840i | \(-0.177748\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.84070 | −0.272621 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3900 | 0.623634 | 0.311817 | − | 0.950142i | \(-0.399062\pi\) | ||||
0.311817 | + | 0.950142i | \(0.399062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.9029i | − | 0.785546i | −0.919635 | − | 0.392773i | \(-0.871516\pi\) | ||
0.919635 | − | 0.392773i | \(-0.128484\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.4269 | + | 38.0413i | 0.993649 | + | 1.76412i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.2501i | 1.02961i | 0.857306 | + | 0.514807i | \(0.172136\pi\) | ||||
−0.857306 | + | 0.514807i | \(0.827864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2771 | 0.659254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1593 | −0.652426 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.65127i | − | 0.259846i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.59155 | + | 4.27596i | −0.118908 | + | 0.196195i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.97194i | − | 0.456584i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.366196 | 0.0167319 | 0.00836597 | − | 0.999965i | \(-0.497337\pi\) | ||||
0.00836597 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2295 | −0.831192 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 18.0368i | − | 0.820704i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.35673 | + | 5.95953i | 0.152421 | + | 0.270608i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8461i | 1.21651i | 0.793740 | + | 0.608257i | \(0.208131\pi\) | ||||
−0.793740 | + | 0.608257i | \(0.791869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 38.0415 | 1.72030 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7266 | 1.07076 | 0.535382 | − | 0.844610i | \(-0.320168\pi\) | ||||
0.535382 | + | 0.844610i | \(0.320168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 23.5381i | − | 1.06010i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.8912 | + | 10.0773i | −0.804150 | + | 0.452940i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.5356i | 0.562298i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.81690 | 0.305166 | 0.152583 | − | 0.988291i | \(-0.451241\pi\) | ||||
0.152583 | + | 0.988291i | \(0.451241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.80257 | −0.393270 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.4102i | − | 1.04381i | −0.853004 | − | 0.521904i | \(-0.825222\pi\) | ||
0.853004 | − | 0.521904i | \(-0.174778\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.53982 | − | 3.68358i | 0.291018 | − | 0.163917i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.43221i | 0.374488i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9204 | −0.749981 | −0.374991 | − | 0.927029i | \(-0.622354\pi\) | ||||
−0.374991 | + | 0.927029i | \(0.622354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.53035 | 0.156174 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.48883i | − | 0.0657336i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.3329 | + | 25.4467i | 0.631584 | + | 1.12131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.1198i | − | 0.840888i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.3473 | −1.15652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.49345 | −0.153051 | −0.0765254 | − | 0.997068i | \(-0.524383\pi\) | ||||
−0.0765254 | + | 0.997068i | \(0.524383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.9271i | − | 0.652714i | −0.945247 | − | 0.326357i | \(-0.894179\pi\) | ||
0.945247 | − | 0.326357i | \(-0.105821\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.69912 | − | 14.3532i | 0.379661 | − | 0.626427i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.0960i | 1.44168i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.87275 | −0.255337 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.91088 | −0.343303 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 31.9236i | − | 1.38276i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.33292 | + | 11.2435i | 0.273796 | + | 0.486098i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.3070i | 1.00577i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0796 | 0.821819 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.6991 | −0.545978 | −0.272989 | − | 0.962017i | \(-0.588012\pi\) | ||||
−0.272989 | + | 0.962017i | \(0.588012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.32641i | 0.0569217i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9429 | + | 7.29014i | −0.554414 | + | 0.312275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.8162i | 1.36036i | 0.733043 | + | 0.680182i | \(0.238099\pi\) | ||||
−0.733043 | + | 0.680182i | \(0.761901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.3519 | −1.03931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0368i | 0.767003i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.8727 | − | 15.1362i | 1.14068 | − | 0.642494i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9.64731i | − | 0.408770i | −0.978891 | − | 0.204385i | \(-0.934481\pi\) | ||
0.978891 | − | 0.204385i | \(-0.0655194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.43637 | −0.187639 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.3793 | −1.49372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.28216i | − | 0.180471i | −0.995920 | − | 0.0902357i | \(-0.971238\pi\) | ||
0.995920 | − | 0.0902357i | \(-0.0287620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3329 | + | 18.3451i | 0.434709 | + | 0.771783i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.2517i | 0.640510i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.2295 | −1.77035 | −0.885176 | − | 0.465257i | \(-0.845962\pi\) | ||||
−0.885176 | + | 0.465257i | \(0.845962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2200 | 0.804332 | 0.402166 | − | 0.915567i | \(-0.368257\pi\) | ||||
0.402166 | + | 0.915567i | \(0.368257\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.36715i | 0.307767i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9762 | − | 13.9253i | −0.958174 | − | 0.580724i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 40.7919i | − | 1.69819i | −0.528239 | − | 0.849096i | \(-0.677148\pi\) | ||
0.528239 | − | 0.849096i | \(-0.322852\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.07965 | 0.294220 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.3662 | 0.761958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.4873i | 0.682836i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.91088 | + | 14.0450i | 0.327075 | + | 0.580689i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.8851i | 1.31604i | 0.753001 | + | 0.658019i | \(0.228605\pi\) | ||||
−0.753001 | + | 0.658019i | \(0.771395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.43637 | −0.347615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.7455 | −2.04626 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.8973i | 1.59732i | 0.601783 | + | 0.798660i | \(0.294457\pi\) | ||||
−0.601783 | + | 0.798660i | \(0.705543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0850 | − | 6.24366i | 0.454441 | − | 0.255965i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 11.1485i | − | 0.456279i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.1629 | 1.15071 | 0.575353 | − | 0.817905i | \(-0.304865\pi\) | ||||
0.575353 | + | 0.817905i | \(0.304865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.56363 | −0.226945 | −0.113473 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 23.1997i | − | 0.944764i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.14982 | − | 4.59042i | 0.331337 | − | 0.186627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.9986i | − | 1.37996i | −0.723828 | − | 0.689980i | \(-0.757619\pi\) | ||
0.723828 | − | 0.689980i | \(-0.242381\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.1404 | −0.816128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0095 | −0.607218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 17.5703i | − | 0.709659i | −0.934931 | − | 0.354830i | \(-0.884539\pi\) | ||
0.934931 | − | 0.354830i | \(-0.115461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.5066 | + | 47.0597i | 1.06885 | + | 1.89763i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.0791i | − | 0.526544i | −0.964722 | − | 0.263272i | \(-0.915198\pi\) | ||
0.964722 | − | 0.263272i | \(-0.0848016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.9393 | −0.761234 | −0.380617 | − | 0.924733i | \(-0.624288\pi\) | ||||
−0.380617 | + | 0.924733i | \(0.624288\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.9350i | 0.718552i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.5677 | − | 22.1627i | −0.462710 | − | 0.886510i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 9.01841i | − | 0.360161i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.3793 | 0.932194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6896 | −1.26154 | −0.630772 | − | 0.775968i | \(-0.717262\pi\) | ||||
−0.630772 | + | 0.775968i | \(0.717262\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 24.3170i | − | 0.966514i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.1736 | − | 21.6131i | −0.483096 | − | 0.857688i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 14.9779i | − | 0.593448i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.3698 | 0.805818 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.9750 | 1.89490 | 0.947449 | − | 0.319908i | \(-0.103652\pi\) | ||||
0.947449 | + | 0.319908i | \(0.103652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.200927i | − | 0.00792378i | −0.999992 | − | 0.00396189i | \(-0.998739\pi\) | ||
0.999992 | − | 0.00396189i | \(-0.00126111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.53982 | − | 3.68358i | 0.257505 | − | 0.145041i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.58798i | − | 0.0624299i | −0.999513 | − | 0.0312150i | \(-0.990062\pi\) | ||
0.999513 | − | 0.0312150i | \(-0.00993765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0796 | 0.513421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.3186 | 1.10989 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.5624i | 1.31340i | 0.754152 | + | 0.656700i | \(0.228048\pi\) | ||||
−0.754152 | + | 0.656700i | \(0.771952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.98155 | + | 5.05889i | −0.350938 | + | 0.197667i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.73669i | − | 0.223809i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3567 | 0.598213 | 0.299107 | − | 0.954220i | \(-0.403311\pi\) | ||||
0.299107 | + | 0.954220i | \(0.403311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8026 | 0.497962 | 0.248981 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248981 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.7735i | 1.07863i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.59155 | + | 2.82564i | 0.0617176 | + | 0.109573i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.2400i | 1.24834i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.1022 | 1.51178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.2627 | 1.55433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 7.82545i | − | 0.301649i | −0.988561 | − | 0.150824i | \(-0.951807\pi\) | ||
0.988561 | − | 0.150824i | \(-0.0481928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.36620 | + | 3.85838i | 0.245035 | + | 0.148509i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6516i | 0.832137i | 0.909333 | + | 0.416069i | \(0.136592\pi\) | ||||
−0.909333 | + | 0.416069i | \(0.863408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.43637 | 0.170252 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.6564 | 1.51964 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.38751i | 0.244411i | 0.992505 | + | 0.122206i | \(0.0389967\pi\) | ||||
−0.992505 | + | 0.122206i | \(0.961003\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4643 | − | 25.6799i | −0.552652 | − | 0.981179i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 57.9688i | − | 2.21165i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9429 | 0.493086 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.4958 | −1.69270 | −0.846351 | − | 0.532626i | \(-0.821205\pi\) | ||||
−0.846351 | + | 0.532626i | \(0.821205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.3185i | 0.505928i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.30500 | − | 1.29830i | 0.0874336 | − | 0.0492473i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.9420i | 1.55079i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.6658 | 1.68942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5160 | 0.661571 | 0.330785 | − | 0.943706i | \(-0.392686\pi\) | ||||
0.330785 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.95953i | 0.224768i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.1260 | − | 12.4626i | 0.833314 | − | 0.469367i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.86835i | − | 0.183093i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4269 | −0.429146 | −0.214573 | − | 0.976708i | \(-0.568836\pi\) | ||||
−0.214573 | + | 0.976708i | \(0.568836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.3091 | 1.09918 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 45.3315i | − | 1.69768i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0796 | − | 23.2216i | −0.489151 | − | 0.868439i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.4408i | 1.62233i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.8965 | 0.592841 | 0.296421 | − | 0.955057i | \(-0.404207\pi\) | ||||
0.296421 | + | 0.955057i | \(0.404207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9429 | 0.705471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 33.4124i | − | 1.24262i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5493 | + | 25.6558i | −0.577486 | + | 0.952832i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.9905i | − | 1.55734i | −0.627434 | − | 0.778670i | \(-0.715895\pi\) | ||
0.627434 | − | 0.778670i | \(-0.284105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.4458 | 0.535031 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.68965 | 0.210439 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.632884i | 0.0233761i | 0.999932 | + | 0.0116881i | \(0.00372051\pi\) | ||||
−0.999932 | + | 0.0116881i | \(0.996279\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.4364 | + | 22.0795i | 0.458723 | + | 0.814416i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.3578i | 1.41293i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.5493 | −1.08699 | −0.543494 | − | 0.839413i | \(-0.682899\pi\) | ||||
−0.543494 | + | 0.839413i | \(0.682899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.07965 | −0.260077 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.3374i | − | 1.14966i | −0.818274 | − | 0.574829i | \(-0.805069\pi\) | ||
0.818274 | − | 0.574829i | \(-0.194931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6379 | + | 5.99184i | −0.389743 | + | 0.219524i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 29.8443i | − | 1.09195i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.36983 | 0.305827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0131 | −0.912741 | −0.456371 | − | 0.889790i | \(-0.650851\pi\) | ||||
−0.456371 | + | 0.889790i | \(0.650851\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.4040i | 0.925772i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.89655 | − | 5.57426i | 0.360172 | − | 0.202868i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.0900i | − | 1.16633i | −0.812354 | − | 0.583165i | \(-0.801814\pi\) | ||
0.812354 | − | 0.583165i | \(-0.198186\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 48.4589 | 1.75895 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.4922 | −1.46784 | −0.733921 | − | 0.679235i | \(-0.762312\pi\) | ||||
−0.733921 | + | 0.679235i | \(0.762312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.63492i | 0.348808i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.1457 | − | 18.0127i | −0.366819 | − | 0.651250i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.2678i | − | 0.370749i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.09398 | −0.111572 | −0.0557859 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557859 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.8251 | 1.47028 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.96350i | 0.0706220i | 0.999376 | + | 0.0353110i | \(0.0112422\pi\) | ||||
−0.999376 | + | 0.0353110i | \(0.988758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.8633 | − | 36.0736i | 0.785352 | − | 1.29580i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 20.0045i | − | 0.717658i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.4364 | −0.373922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.6789 | −1.20513 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.93300i | − | 0.319239i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.71345 | + | 11.9191i | 0.239613 | + | 0.425410i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.107331i | 0.00382595i | 0.999998 | + | 0.00191297i | \(0.000608919\pi\) | ||||
−0.999998 | + | 0.00191297i | \(0.999391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.91088 | 0.139231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6564 | 0.485565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 31.6071i | − | 1.12240i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.0796 | + | 10.7467i | −0.676685 | + | 0.381145i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.32068i | − | 0.294734i | −0.989082 | − | 0.147367i | \(-0.952920\pi\) | ||
0.989082 | − | 0.147367i | \(-0.0470798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.2496 | 0.681003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.1437 | 1.02974 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.48489i | 0.334714i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.1831 | + | 8.55193i | −0.535134 | + | 0.301416i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 62.7270i | 2.20810i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.6231 | 0.971177 | 0.485588 | − | 0.874188i | \(-0.338605\pi\) | ||||
0.485588 | + | 0.874188i | \(0.338605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0095 | −0.807972 | −0.403986 | − | 0.914765i | \(-0.632376\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632376\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 55.4369i | − | 1.94426i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0369 | − | 32.0227i | −0.631805 | − | 1.12171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.45033i | 0.0507405i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4553 | 0.365338 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1355 | 1.08664 | 0.543318 | − | 0.839527i | \(-0.317168\pi\) | ||||
0.543318 | + | 0.839527i | \(0.317168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4201i | 0.711800i | 0.934524 | + | 0.355900i | \(0.115826\pi\) | ||||
−0.934524 | + | 0.355900i | \(0.884174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.5624 | + | 23.3716i | 1.34257 | + | 0.813696i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.902638i | 0.0313878i | 0.999877 | + | 0.0156939i | \(0.00499573\pi\) | ||||
−0.999877 | + | 0.0156939i | \(0.995004\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4971 | 0.468773 | 0.234386 | − | 0.972143i | \(-0.424692\pi\) | ||||
0.234386 | + | 0.972143i | \(0.424692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0607 | −0.661209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.2092i | 0.665560i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17363 | + | 7.40986i | 0.144434 | + | 0.256429i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.5603i | 0.434149i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.1022 | 1.14282 | 0.571408 | − | 0.820666i | \(-0.306397\pi\) | ||||
0.571408 | + | 0.820666i | \(0.306397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 24.1546i | − | 0.831928i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.09810 | − | 3.99803i | 0.244182 | − | 0.137536i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.06686i | − | 0.208460i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.2295 | 0.831553 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.0226 | −1.09772 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.9097i | − | 1.74312i | −0.490293 | − | 0.871558i | \(-0.663110\pi\) | ||
0.490293 | − | 0.871558i | \(-0.336890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.59155 | − | 2.58620i | 0.157028 | − | 0.0884463i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.2333i | 0.725317i | 0.931922 | + | 0.362659i | \(0.118131\pi\) | ||||
−0.931922 | + | 0.362659i | \(0.881869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4827 | 1.00594 | 0.502969 | − | 0.864304i | \(-0.332241\pi\) | ||||
0.502969 | + | 0.864304i | \(0.332241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.0320 | 1.19389 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.7755i | 0.877408i | 0.898632 | + | 0.438704i | \(0.144562\pi\) | ||||
−0.898632 | + | 0.438704i | \(0.855438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4922 | + | 22.1787i | 0.424748 | + | 0.754098i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.72628i | 0.126551i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.4589 | −1.64386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.1117 | 1.02030 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.20893i | − | 0.243985i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.2069 | − | 0.517369i | −0.547893 | − | 0.0174903i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.2687i | 1.83252i | 0.400581 | + | 0.916261i | \(0.368808\pi\) | ||||
−0.400581 | + | 0.916261i | \(0.631192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −38.1117 | −1.28548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.4922 | −0.959927 | −0.479964 | − | 0.877288i | \(-0.659350\pi\) | ||||
−0.479964 | + | 0.877288i | \(0.659350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.5264i | 1.36382i | 0.731435 | + | 0.681911i | \(0.238851\pi\) | ||||
−0.731435 | + | 0.681911i | \(0.761149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.52549 | + | 15.1362i | 0.286581 | + | 0.508797i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.4705i | 0.385142i | 0.981283 | + | 0.192571i | \(0.0616826\pi\) | ||||
−0.981283 | + | 0.192571i | \(0.938317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0891 | −0.539612 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.9762 | −1.37275 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.90686i | 0.164202i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.6195 | − | 11.0507i | 0.655807 | − | 0.369385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 38.0413i | − | 1.27016i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −50.6182 | −1.68821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5993 | −0.553003 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.86835i | − | 0.162009i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.11655 | − | 0.628901i | 0.0371154 | − | 0.0209054i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1000i | 1.59714i | 0.601905 | + | 0.798568i | \(0.294409\pi\) | ||||
−0.601905 | + | 0.798568i | \(0.705591\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.91088 | −0.262387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8062 | 0.424288 | 0.212144 | − | 0.977238i | \(-0.431955\pi\) | ||||
0.212144 | + | 0.977238i | \(0.431955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.3439i | 1.63304i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.2438 | + | 46.5933i | 0.867593 | + | 1.54033i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.68601i | 0.220792i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.7135 | −1.27704 | −0.638519 | − | 0.769606i | \(-0.720453\pi\) | ||||
−0.638519 | + | 0.769606i | \(0.720453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2295 | 0.600682 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.4387i | 0.870241i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.4827 | − | 15.4444i | −0.837868 | − | 0.507809i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 30.7815i | − | 1.01100i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.0189 | 1.18174 | 0.590872 | − | 0.806766i | \(-0.298784\pi\) | ||||
0.590872 | + | 0.806766i | \(0.298784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.89655 | −0.160478 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 9.01841i | − | 0.295249i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.7746 | + | 29.7817i | 0.548590 | + | 0.973966i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.2421i | 1.47799i | 0.673709 | + | 0.738997i | \(0.264700\pi\) | ||||
−0.673709 | + | 0.738997i | \(0.735300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.9811 | 0.586790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7455 | −0.382892 | −0.191446 | − | 0.981503i | \(-0.561318\pi\) | ||||
−0.191446 | + | 0.981503i | \(0.561318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 56.0781i | − | 1.82616i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.20690 | − | 2.36955i | 0.136850 | − | 0.0770815i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 13.7752i | − | 0.447635i | −0.974631 | − | 0.223817i | \(-0.928148\pi\) | ||
0.974631 | − | 0.223817i | \(-0.0718519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.44584 | 0.241702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.0927 | −1.42981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.01421i | 0.291999i | 0.989285 | + | 0.145999i | \(0.0466398\pi\) | ||||
−0.989285 | + | 0.145999i | \(0.953360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.20155 | − | 3.49304i | 0.200677 | − | 0.113032i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 54.1105i | − | 1.74914i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.1166 | −0.617306 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.1724 | 1.29588 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 13.6006i | − | 0.438274i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.35673 | − | 5.95953i | −0.108057 | − | 0.191844i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3232i | 0.975129i | 0.873087 | + | 0.487564i | \(0.162115\pi\) | ||||
−0.873087 | + | 0.487564i | \(0.837885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.07965 | 0.291680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5636 | 1.01292 | 0.506462 | − | 0.862262i | \(-0.330953\pi\) | ||||
0.506462 | + | 0.862262i | \(0.330953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.71588i | − | 0.0550086i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.3473 | − | 30.2723i | 0.587582 | − | 0.969490i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 43.1285i | − | 1.37980i | −0.723903 | − | 0.689902i | \(-0.757654\pi\) | ||
0.723903 | − | 0.689902i | \(-0.242346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.1855 | −1.54002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6564 | 0.499870 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 7.81570i | − | 0.249282i | −0.992202 | − | 0.124641i | \(-0.960222\pi\) | ||
0.992202 | − | 0.124641i | \(-0.0397779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.5862 | + | 41.8749i | 0.751519 | + | 1.33425i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 16.4710i | − | 0.524277i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.79310 | −0.247806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5197 | 0.747126 | 0.373563 | − | 0.927605i | \(-0.378136\pi\) | ||||
0.373563 | + | 0.927605i | \(0.378136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18.5157i | − | 0.587577i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.38465 | + | 5.28593i | −0.297513 | + | 0.167575i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.6395i | 1.06537i | 0.846313 | + | 0.532686i | \(0.178817\pi\) | ||||
−0.846313 | + | 0.532686i | \(0.821183\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.87275 | 0.280721 |
(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 | 1520.2.d.h.609.5 | 6 | ||
4.3 | odd | 2 | 95.2.b.b.39.5 | yes | 6 | ||
5.2 | odd | 4 | 7600.2.a.ck.1.5 | 6 | |||
5.3 | odd | 4 | 7600.2.a.ck.1.2 | 6 | |||
5.4 | even | 2 | inner | 1520.2.d.h.609.2 | 6 | ||
12.11 | even | 2 | 855.2.c.d.514.2 | 6 | |||
20.3 | even | 4 | 475.2.a.j.1.5 | 6 | |||
20.7 | even | 4 | 475.2.a.j.1.2 | 6 | |||
20.19 | odd | 2 | 95.2.b.b.39.2 | ✓ | 6 | ||
60.23 | odd | 4 | 4275.2.a.br.1.2 | 6 | |||
60.47 | odd | 4 | 4275.2.a.br.1.5 | 6 | |||
60.59 | even | 2 | 855.2.c.d.514.5 | 6 | |||
76.75 | even | 2 | 1805.2.b.e.1084.2 | 6 | |||
380.227 | odd | 4 | 9025.2.a.bx.1.5 | 6 | |||
380.303 | odd | 4 | 9025.2.a.bx.1.2 | 6 | |||
380.379 | even | 2 | 1805.2.b.e.1084.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.2 | ✓ | 6 | 20.19 | odd | 2 | ||
95.2.b.b.39.5 | yes | 6 | 4.3 | odd | 2 | ||
475.2.a.j.1.2 | 6 | 20.7 | even | 4 | |||
475.2.a.j.1.5 | 6 | 20.3 | even | 4 | |||
855.2.c.d.514.2 | 6 | 12.11 | even | 2 | |||
855.2.c.d.514.5 | 6 | 60.59 | even | 2 | |||
1520.2.d.h.609.2 | 6 | 5.4 | even | 2 | inner | ||
1520.2.d.h.609.5 | 6 | 1.1 | even | 1 | trivial | ||
1805.2.b.e.1084.2 | 6 | 76.75 | even | 2 | |||
1805.2.b.e.1084.5 | 6 | 380.379 | even | 2 | |||
4275.2.a.br.1.2 | 6 | 60.23 | odd | 4 | |||
4275.2.a.br.1.5 | 6 | 60.47 | odd | 4 | |||
7600.2.a.ck.1.2 | 6 | 5.3 | odd | 4 | |||
7600.2.a.ck.1.5 | 6 | 5.2 | odd | 4 | |||
9025.2.a.bx.1.2 | 6 | 380.303 | odd | 4 | |||
9025.2.a.bx.1.5 | 6 | 380.227 | odd | 4 |