Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.7 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.b.1609.19 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.131247 | + | 2.23221i | −0.0586956 | + | 0.998276i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.13753i | − | 1.94180i | −0.239478 | − | 0.970902i | \(-0.576976\pi\) | ||
0.239478 | − | 0.970902i | \(-0.423024\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.58948 | −0.479245 | −0.239623 | − | 0.970866i | \(-0.577024\pi\) | ||||
−0.239623 | + | 0.970866i | \(0.577024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.13766i | 0.592880i | 0.955051 | + | 0.296440i | \(0.0957995\pi\) | ||||
−0.955051 | + | 0.296440i | \(0.904200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23221 | + | 0.131247i | 0.576355 | + | 0.0338879i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.84639i | 1.90303i | 0.307605 | + | 0.951514i | \(0.400472\pi\) | ||||
−0.307605 | + | 0.951514i | \(0.599528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19030 | 0.502488 | 0.251244 | − | 0.967924i | \(-0.419160\pi\) | ||||
0.251244 | + | 0.967924i | \(0.419160\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.13753 | −1.12110 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.33309i | − | 1.11203i | −0.831173 | − | 0.556013i | \(-0.812330\pi\) | ||
0.831173 | − | 0.556013i | \(-0.187670\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96555 | − | 0.585944i | −0.993110 | − | 0.117189i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.166293 | 0.0308799 | 0.0154399 | − | 0.999881i | \(-0.495085\pi\) | ||||
0.0154399 | + | 0.999881i | \(0.495085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.09364 | −0.196423 | −0.0982116 | − | 0.995166i | \(-0.531312\pi\) | ||||
−0.0982116 | + | 0.995166i | \(0.531312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.58948i | 0.276692i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.4681 | + | 0.674287i | 1.93846 | + | 0.113975i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.96897i | − | 0.488095i | −0.969763 | − | 0.244048i | \(-0.921525\pi\) | ||
0.969763 | − | 0.244048i | \(-0.0784753\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.13766 | 0.342300 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9924 | −1.71672 | −0.858362 | − | 0.513045i | \(-0.828517\pi\) | ||||
−0.858362 | + | 0.513045i | \(0.828517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.88353i | 0.592233i | 0.955152 | + | 0.296117i | \(0.0956917\pi\) | ||||
−0.955152 | + | 0.296117i | \(0.904308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.131247 | − | 2.23221i | 0.0195652 | − | 0.332759i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.39193i | 0.932358i | 0.884690 | + | 0.466179i | \(0.154370\pi\) | ||||
−0.884690 | + | 0.466179i | \(0.845630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.3942 | −2.77060 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.84639 | 1.09871 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5030i | 1.58006i | 0.613070 | + | 0.790029i | \(0.289934\pi\) | ||||
−0.613070 | + | 0.790029i | \(0.710066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.208615 | − | 3.54805i | 0.0281296 | − | 0.478419i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.19030i | − | 0.290112i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.22807 | −0.941014 | −0.470507 | − | 0.882396i | \(-0.655929\pi\) | ||||
−0.470507 | + | 0.882396i | \(0.655929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.90971 | 1.26881 | 0.634404 | − | 0.773002i | \(-0.281246\pi\) | ||||
0.634404 | + | 0.773002i | \(0.281246\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.13753i | 0.647268i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.77171 | − | 0.280562i | −0.591858 | − | 0.0347995i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.33309 | −0.642029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2863 | 1.33944 | 0.669719 | − | 0.742615i | \(-0.266415\pi\) | ||||
0.669719 | + | 0.742615i | \(0.266415\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.60168i | − | 0.772668i | −0.922359 | − | 0.386334i | \(-0.873741\pi\) | ||
0.922359 | − | 0.386334i | \(-0.126259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.585944 | + | 4.96555i | −0.0676590 | + | 0.573372i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.16599i | 0.930600i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.35082 | −0.827032 | −0.413516 | − | 0.910497i | \(-0.635699\pi\) | ||||
−0.413516 | + | 0.910497i | \(0.635699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.97928i | 0.875839i | 0.899014 | + | 0.437920i | \(0.144285\pi\) | ||||
−0.899014 | + | 0.437920i | \(0.855715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.5148 | − | 1.02982i | −1.89975 | − | 0.111699i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.166293i | − | 0.0178285i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6997 | 1.13416 | 0.567082 | − | 0.823661i | \(-0.308072\pi\) | ||||
0.567082 | + | 0.823661i | \(0.308072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9823 | 1.15126 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.09364i | 0.113405i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.287471 | + | 4.88921i | −0.0294939 | + | 0.501622i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.21273i | − | 0.123134i | −0.998103 | − | 0.0615670i | \(-0.980390\pi\) | ||
0.998103 | − | 0.0615670i | \(-0.0196098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.58948 | 0.159748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.301193 | 0.0299698 | 0.0149849 | − | 0.999888i | \(-0.495230\pi\) | ||||
0.0149849 | + | 0.999888i | \(0.495230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.803026i | 0.0791245i | 0.999217 | + | 0.0395623i | \(0.0125963\pi\) | ||||
−0.999217 | + | 0.0395623i | \(0.987404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.674287 | − | 11.4681i | 0.0658037 | − | 1.11917i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4533i | 1.39725i | 0.715489 | + | 0.698624i | \(0.246204\pi\) | ||||
−0.715489 | + | 0.698624i | \(0.753796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.720132 | −0.0689761 | −0.0344881 | − | 0.999405i | \(-0.510980\pi\) | ||||
−0.0344881 | + | 0.999405i | \(0.510980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.96897 | −0.281802 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.73412i | 0.633493i | 0.948510 | + | 0.316746i | \(0.102590\pi\) | ||||
−0.948510 | + | 0.316746i | \(0.897410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.9046 | + | 0.699954i | 1.11011 | + | 0.0652711i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.13766i | − | 0.197627i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40.3110 | 3.69531 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.47356 | −0.770324 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9924i | 0.991151i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.95967 | − | 11.0073i | 0.175278 | − | 0.984519i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.46495i | 0.307465i | 0.988113 | + | 0.153732i | \(0.0491293\pi\) | ||||
−0.988113 | + | 0.153732i | \(0.950871\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.88353 | 0.341926 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8300 | −1.20834 | −0.604168 | − | 0.796857i | \(-0.706494\pi\) | ||||
−0.604168 | + | 0.796857i | \(0.706494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.2527i | − | 0.975733i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.23221 | − | 0.131247i | −0.192118 | − | 0.0112960i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.75541i | 0.748025i | 0.927424 | + | 0.374013i | \(0.122018\pi\) | ||||
−0.927424 | + | 0.374013i | \(0.877982\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.79685 | 0.576501 | 0.288251 | − | 0.957555i | \(-0.406926\pi\) | ||||
0.288251 | + | 0.957555i | \(0.406926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.39193 | 0.538297 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.39776i | − | 0.284135i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0218256 | + | 0.371202i | −0.00181251 | + | 0.0308266i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.3942i | 1.59961i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2220 | 1.16511 | 0.582554 | − | 0.812792i | \(-0.302053\pi\) | ||||
0.582554 | + | 0.812792i | \(0.302053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.96765 | 0.567019 | 0.283510 | − | 0.958969i | \(-0.408501\pi\) | ||||
0.283510 | + | 0.958969i | \(0.408501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.84639i | − | 0.634343i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.143537 | − | 2.44123i | 0.0115292 | − | 0.196085i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.5394i | 1.87865i | 0.343027 | + | 0.939325i | \(0.388548\pi\) | ||||
−0.343027 | + | 0.939325i | \(0.611452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5030 | 0.912247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.3989 | −2.15934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.48265i | − | 0.586086i | −0.956099 | − | 0.293043i | \(-0.905332\pi\) | ||
0.956099 | − | 0.293043i | \(-0.0946679\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.54805 | − | 0.208615i | −0.276215 | − | 0.0162406i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.48930i | 0.734304i | 0.930161 | + | 0.367152i | \(0.119667\pi\) | ||||
−0.930161 | + | 0.367152i | \(0.880333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.43041 | 0.648493 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.19030 | −0.167496 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.0437i | 1.59992i | 0.600051 | + | 0.799962i | \(0.295147\pi\) | ||||
−0.600051 | + | 0.799962i | \(0.704853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.01031 | + | 25.5106i | −0.227558 | + | 1.92842i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.22807i | 0.543295i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.55392 | 0.415120 | 0.207560 | − | 0.978222i | \(-0.433448\pi\) | ||||
0.207560 | + | 0.978222i | \(0.433448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.126497 | −0.00940243 | −0.00470121 | − | 0.999989i | \(-0.501496\pi\) | ||||
−0.00470121 | + | 0.999989i | \(0.501496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.90971i | − | 0.732547i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.62737 | + | 0.389669i | 0.487254 | + | 0.0286491i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.4717i | − | 0.912018i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.13753 | 0.373700 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8499 | −0.929784 | −0.464892 | − | 0.885367i | \(-0.653907\pi\) | ||||
−0.464892 | + | 0.885367i | \(0.653907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9422i | 1.65141i | 0.564100 | + | 0.825707i | \(0.309223\pi\) | ||||
−0.564100 | + | 0.825707i | \(0.690777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.280562 | + | 4.77171i | −0.0200915 | + | 0.341709i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.57232i | 0.539505i | 0.962930 | + | 0.269753i | \(0.0869419\pi\) | ||||
−0.962930 | + | 0.269753i | \(0.913058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8138 | −1.12101 | −0.560505 | − | 0.828151i | \(-0.689393\pi\) | ||||
−0.560505 | + | 0.828151i | \(0.689393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.854336i | − | 0.0599627i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.44272 | − | 24.5374i | 0.100764 | − | 1.71376i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.33309i | 0.370676i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.48143 | −0.240815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8626 | −1.22971 | −0.614855 | − | 0.788640i | \(-0.710786\pi\) | ||||
−0.614855 | + | 0.788640i | \(0.710786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 11.2863i | − | 0.773325i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.66888 | − | 0.509704i | −0.591212 | − | 0.0347615i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.61860i | 0.381415i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.60168 | −0.446100 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.7729 | −1.12827 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.23944i | 0.283894i | 0.989874 | + | 0.141947i | \(0.0453362\pi\) | ||||
−0.989874 | + | 0.141947i | \(0.954664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.96555 | + | 0.585944i | 0.331037 | + | 0.0390629i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.50951i | − | 0.631168i | −0.948898 | − | 0.315584i | \(-0.897800\pi\) | ||
0.948898 | − | 0.315584i | \(-0.102200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1809 | 0.738857 | 0.369429 | − | 0.929259i | \(-0.379553\pi\) | ||||
0.369429 | + | 0.929259i | \(0.379553\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.16599 | 0.537282 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.05644i | − | 0.0692096i | −0.999401 | − | 0.0346048i | \(-0.988983\pi\) | ||
0.999401 | − | 0.0346048i | \(-0.0110173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2681 | − | 0.838923i | −0.930751 | − | 0.0547253i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.35082i | 0.477487i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.35097 | −0.410810 | −0.205405 | − | 0.978677i | \(-0.565851\pi\) | ||||
−0.205405 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.56297 | −0.358342 | −0.179171 | − | 0.983818i | \(-0.557342\pi\) | ||||
−0.179171 | + | 0.983818i | \(0.557342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.54544 | − | 43.2920i | 0.162622 | − | 2.76582i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.68211i | 0.297915i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.97928 | 0.505666 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.13053 | 0.386955 | 0.193478 | − | 0.981105i | \(-0.438023\pi\) | ||||
0.193478 | + | 0.981105i | \(0.438023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.47683i | 0.532934i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.02982 | + | 17.5148i | −0.0644897 | + | 1.09682i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.0238i | − | 1.31143i | −0.755010 | − | 0.655713i | \(-0.772368\pi\) | ||
0.755010 | − | 0.655713i | \(-0.227632\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.2532 | −0.947785 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.166293 | −0.0102933 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.2397i | − | 1.67967i | −0.542841 | − | 0.839836i | \(-0.682651\pi\) | ||
0.542841 | − | 0.839836i | \(-0.317349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.6771 | − | 1.50974i | −1.57733 | − | 0.0927424i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.6997i | − | 0.654810i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.61800 | −0.403507 | −0.201753 | − | 0.979436i | \(-0.564664\pi\) | ||||
−0.201753 | + | 0.979436i | \(0.564664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5286 | 0.700310 | 0.350155 | − | 0.936692i | \(-0.386129\pi\) | ||||
0.350155 | + | 0.936692i | \(0.386129\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.9823i | − | 0.664679i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.89263 | + | 0.931345i | 0.475943 | + | 0.0561622i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.2244i | 1.63576i | 0.575391 | + | 0.817879i | \(0.304850\pi\) | ||||
−0.575391 | + | 0.817879i | \(0.695150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.09364 | 0.0654744 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.9886 | −0.834489 | −0.417244 | − | 0.908794i | \(-0.637004\pi\) | ||||
−0.417244 | + | 0.908794i | \(0.637004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.1526i | − | 1.25739i | −0.777651 | − | 0.628696i | \(-0.783589\pi\) | ||
0.777651 | − | 0.628696i | \(-0.216411\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.88921 | + | 0.287471i | 0.289612 | + | 0.0170283i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 56.4737i | 3.33354i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −44.5658 | −2.62152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.21273 | −0.0710914 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.54350i | 0.207013i | 0.994629 | + | 0.103507i | \(0.0330063\pi\) | ||||
−0.994629 | + | 0.103507i | \(0.966994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.948665 | − | 16.1346i | 0.0552334 | − | 0.939392i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.58948i | − | 0.0922308i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.4003 | 0.659299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.9518 | 1.15000 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 0.301193i | − | 0.0173031i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.30062 | + | 22.1206i | −0.0744735 | + | 1.26662i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.211948i | − | 0.0120965i | −0.999982 | − | 0.00604825i | \(-0.998075\pi\) | ||
0.999982 | − | 0.00604825i | \(-0.00192523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.803026 | 0.0456826 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.73795 | −0.495483 | −0.247742 | − | 0.968826i | \(-0.579688\pi\) | ||||
−0.247742 | + | 0.968826i | \(0.579688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6370i | 1.33604i | 0.744144 | + | 0.668020i | \(0.232858\pi\) | ||||
−0.744144 | + | 0.668020i | \(0.767142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.4681 | − | 0.674287i | −0.646152 | − | 0.0379918i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.0553i | − | 1.01409i | −0.861921 | − | 0.507043i | \(-0.830738\pi\) | ||
0.861921 | − | 0.507043i | \(-0.169262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.264319 | −0.0147990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4533 | 0.806702 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.1859i | 0.956249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.25255 | − | 10.6147i | 0.0694789 | − | 0.588795i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.720132i | 0.0398234i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.8387 | 1.81046 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9544 | −1.04183 | −0.520913 | − | 0.853610i | \(-0.674408\pi\) | ||||
−0.520913 | + | 0.853610i | \(0.674408\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.96897i | 0.162698i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.23221 | − | 0.131247i | −0.121959 | − | 0.00717081i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1789i | 0.772375i | 0.922420 | + | 0.386187i | \(0.126208\pi\) | ||||
−0.922420 | + | 0.386187i | \(0.873792\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.73412 | 0.365747 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.73831 | 0.0941350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 63.6756i | 3.43816i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.699954 | − | 11.9046i | 0.0376843 | − | 0.640922i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.86111i | − | 0.422006i | −0.977485 | − | 0.211003i | \(-0.932327\pi\) | ||
0.977485 | − | 0.211003i | \(-0.0676730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9328 | 0.745808 | 0.372904 | − | 0.927870i | \(-0.378362\pi\) | ||||
0.372904 | + | 0.927870i | \(0.378362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.13766 | −0.114100 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1430i | 0.859206i | 0.903018 | + | 0.429603i | \(0.141346\pi\) | ||||
−0.903018 | + | 0.429603i | \(0.858654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.48130 | + | 25.1934i | −0.0786191 | + | 1.33713i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 40.3110i | − | 2.13349i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.11711 | −0.111737 | −0.0558684 | − | 0.998438i | \(-0.517793\pi\) | ||||
−0.0558684 | + | 0.998438i | \(0.517793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2026 | −0.747506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.47356i | 0.444747i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7363 | + | 0.866453i | 0.771336 | + | 0.0453522i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.8434i | 1.61001i | 0.593267 | + | 0.805006i | \(0.297838\pi\) | ||||
−0.593267 | + | 0.805006i | \(0.702162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9924 | 0.572241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 59.0970 | 3.06816 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.51060i | − | 0.129994i | −0.997885 | − | 0.0649969i | \(-0.979296\pi\) | ||
0.997885 | − | 0.0649969i | \(-0.0207038\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.0073 | − | 1.95967i | −0.568412 | − | 0.101197i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.355478i | 0.0183081i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7842 | 1.11898 | 0.559489 | − | 0.828838i | \(-0.310997\pi\) | ||||
0.559489 | + | 0.828838i | \(0.310997\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.46495 | 0.177515 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.84768i | 0.349900i | 0.984577 | + | 0.174950i | \(0.0559764\pi\) | ||||
−0.984577 | + | 0.174950i | \(0.944024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.2282 | − | 1.07176i | −0.928996 | − | 0.0546222i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3.88353i | − | 0.197411i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.1047 | 1.07005 | 0.535025 | − | 0.844836i | \(-0.320302\pi\) | ||||
0.535025 | + | 0.844836i | \(0.320302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.8455 | 2.11622 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.8300i | 0.697633i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.964776 | − | 16.4086i | 0.0485431 | − | 0.825606i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.8970i | − | 1.04879i | −0.851475 | − | 0.524395i | \(-0.824292\pi\) | ||
0.851475 | − | 0.524395i | \(-0.175708\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.2527 | −0.563340 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.02781 | −0.101264 | −0.0506319 | − | 0.998717i | \(-0.516124\pi\) | ||||
−0.0506319 | + | 0.998717i | \(0.516124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.33783i | − | 0.116456i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.131247 | + | 2.23221i | −0.00652173 | + | 0.110920i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.71911i | 0.233917i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2065 | 1.39472 | 0.697362 | − | 0.716720i | \(-0.254357\pi\) | ||||
0.697362 | + | 0.716720i | \(0.254357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.75541 | 0.431873 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.1344i | 1.82726i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.8114 | − | 1.04726i | −0.874329 | − | 0.0514079i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.79685i | − | 0.332843i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.1725 | 1.42517 | 0.712584 | − | 0.701587i | \(-0.247525\pi\) | ||||
0.712584 | + | 0.701587i | \(0.247525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4645 | −1.72843 | −0.864216 | − | 0.503121i | \(-0.832185\pi\) | ||||
−0.864216 | + | 0.503121i | \(0.832185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.39193i | − | 0.310786i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.59754 | − | 38.9616i | 0.223014 | − | 1.88992i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 50.9114i | − | 2.46378i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.39776 | −0.164046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7109 | −1.33479 | −0.667394 | − | 0.744704i | \(-0.732590\pi\) | ||||
−0.667394 | + | 0.744704i | \(0.732590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00944i | 0.336852i | 0.985714 | + | 0.168426i | \(0.0538684\pi\) | ||||
−0.985714 | + | 0.168426i | \(0.946132\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.371202 | + | 0.0218256i | 0.0177978 | + | 0.00104646i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11.6811i | − | 0.558780i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.31691 | 0.349217 | 0.174608 | − | 0.984638i | \(-0.444134\pi\) | ||||
0.174608 | + | 0.984638i | \(0.444134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3942 | 0.923534 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.4169i | − | 0.732480i | −0.930520 | − | 0.366240i | \(-0.880645\pi\) | ||
0.930520 | − | 0.366240i | \(-0.119355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.40430 | + | 23.8840i | −0.0665704 | + | 1.13221i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.2220i | − | 0.672676i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8020 | 0.604165 | 0.302082 | − | 0.953282i | \(-0.402318\pi\) | ||||
0.302082 | + | 0.953282i | \(0.402318\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4722 | 0.822732 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.96765i | − | 0.327369i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.44140 | + | 24.5148i | −0.0675737 | + | 1.14927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3179i | 0.950431i | 0.879869 | + | 0.475215i | \(0.157630\pi\) | ||||
−0.879869 | + | 0.475215i | \(0.842370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.84639 | −0.366238 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.656940 | 0.0305967 | 0.0152984 | − | 0.999883i | \(-0.495130\pi\) | ||||
0.0152984 | + | 0.999883i | \(0.495130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.92569i | − | 0.461286i | −0.973038 | − | 0.230643i | \(-0.925917\pi\) | ||
0.973038 | − | 0.230643i | \(-0.0740829\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.44123 | − | 0.143537i | −0.113210 | − | 0.00665638i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.7341i | − | 0.496713i | −0.968669 | − | 0.248357i | \(-0.920110\pi\) | ||
0.968669 | − | 0.248357i | \(-0.0798905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.13753 | 0.237229 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.5394 | 1.08464 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.17279i | − | 0.283825i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8760 | − | 1.28339i | −0.499026 | − | 0.0588860i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.5030i | − | 0.526686i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.2098 | −0.832027 | −0.416013 | − | 0.909358i | \(-0.636573\pi\) | ||||
−0.416013 | + | 0.909358i | \(0.636573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.34664 | 0.289382 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.3989i | 1.24669i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.70707 | + | 0.159168i | 0.122922 | + | 0.00722742i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.8666i | 1.35338i | 0.736267 | + | 0.676692i | \(0.236587\pi\) | ||||
−0.736267 | + | 0.676692i | \(0.763413\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.48265 | −0.338377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9497 | −1.30648 | −0.653242 | − | 0.757150i | \(-0.726591\pi\) | ||||
−0.653242 | + | 0.757150i | \(0.726591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30480i | 0.0587653i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.208615 | + | 3.54805i | −0.00937653 | + | 0.159473i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 57.9837i | − | 2.60092i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9517 | 0.758863 | 0.379432 | − | 0.925220i | \(-0.376120\pi\) | ||||
0.379432 | + | 0.925220i | \(0.376120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.48930 | 0.423951 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 29.1064i | − | 1.29779i | −0.760877 | − | 0.648896i | \(-0.775231\pi\) | ||
0.760877 | − | 0.648896i | \(-0.224769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0395308 | + | 0.672327i | −0.00175910 | + | 0.0299181i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 8.43041i | − | 0.374408i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.75308 | 0.255001 | 0.127500 | − | 0.991839i | \(-0.459305\pi\) | ||||
0.127500 | + | 0.991839i | \(0.459305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.9163 | −1.50037 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.19030i | 0.0967039i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.79253 | − | 0.105395i | −0.0789881 | − | 0.00464426i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.1598i | − | 0.446828i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0437 | 0.923716 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.12822 | −0.0494281 | −0.0247140 | − | 0.999695i | \(-0.507868\pi\) | ||||
−0.0247140 | + | 0.999695i | \(0.507868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.52130i | − | 0.241429i | −0.992687 | − | 0.120715i | \(-0.961481\pi\) | ||
0.992687 | − | 0.120715i | \(-0.0385186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.5106 | + | 3.01031i | 1.11338 | + | 0.131380i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.58111i | − | 0.373799i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.44188 | −0.236604 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.22807 | 0.313671 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 23.4980i | − | 1.01781i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.2627 | − | 1.89695i | −1.39484 | − | 0.0820124i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.55392i | − | 0.239669i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.8266 | 1.32780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7228 | −1.49285 | −0.746424 | − | 0.665471i | \(-0.768231\pi\) | ||||
−0.746424 | + | 0.665471i | \(0.768231\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.126497i | 0.00542850i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0945154 | − | 1.60749i | 0.00404860 | − | 0.0688572i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.9636i | − | 1.62321i | −0.584209 | − | 0.811603i | \(-0.698595\pi\) | ||
0.584209 | − | 0.811603i | \(-0.301405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.90971 | −0.422936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.364231 | 0.0155168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.7651i | 1.60593i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.389669 | − | 6.62737i | 0.0165405 | − | 0.281316i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.1346i | − | 0.683647i | −0.939764 | − | 0.341823i | \(-0.888956\pi\) | ||
0.939764 | − | 0.341823i | \(-0.111044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.30168 | −0.351124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4717 | −0.526554 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 0.748928i | − | 0.0315635i | −0.999875 | − | 0.0157818i | \(-0.994976\pi\) | ||
0.999875 | − | 0.0157818i | \(-0.00502370\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0320 | − | 0.883836i | −0.632401 | − | 0.0371833i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.13753i | − | 0.215756i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.2395 | 0.680797 | 0.340399 | − | 0.940281i | \(-0.389438\pi\) | ||||
0.340399 | + | 0.940281i | \(0.389438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9827 | −1.54768 | −0.773839 | − | 0.633382i | \(-0.781666\pi\) | ||||
−0.773839 | + | 0.633382i | \(0.781666\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8499i | 0.536811i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.12489 | + | 26.4817i | −0.130317 | + | 1.10436i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.4555i | − | 1.55929i | −0.626219 | − | 0.779647i | \(-0.715398\pi\) | ||
0.626219 | − | 0.779647i | \(-0.284602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.9422 | 0.953444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.9938 | 1.70071 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.2837i | − | 0.757235i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.77171 | + | 0.280562i | 0.197286 | + | 0.0115998i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.3877i | 1.62570i | 0.582471 | + | 0.812852i | \(0.302086\pi\) | ||||
−0.582471 | + | 0.812852i | \(0.697914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.39539 | −0.0987004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.57232 | 0.311483 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.4835i | − | 0.553699i | −0.960913 | − | 0.276849i | \(-0.910710\pi\) | ||
0.960913 | − | 0.276849i | \(-0.0892903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.29072 | + | 89.9828i | −0.216898 | + | 3.68894i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.8138i | 0.647215i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.3879 | −1.24161 | −0.620807 | − | 0.783963i | \(-0.713195\pi\) | ||||
−0.620807 | + | 0.783963i | \(0.713195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5247 | 0.592473 | 0.296237 | − | 0.955115i | \(-0.404268\pi\) | ||||
0.296237 | + | 0.955115i | \(0.404268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.11213 | − | 18.9148i | 0.0452146 | − | 0.768996i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.1735i | − | 1.54941i | −0.632321 | − | 0.774707i | \(-0.717898\pi\) | ||
0.632321 | − | 0.774707i | \(-0.282102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.854336 | −0.0346195 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.6638 | −0.552777 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0977i | 0.892517i | 0.894904 | + | 0.446258i | \(0.147244\pi\) | ||||
−0.894904 | + | 0.446258i | \(0.852756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.5374 | − | 1.44272i | −0.989442 | − | 0.0581762i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.6287i | 1.07203i | 0.844208 | + | 0.536016i | \(0.180071\pi\) | ||||
−0.844208 | + | 0.536016i | \(0.819929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3643 | 1.34102 | 0.670512 | − | 0.741899i | \(-0.266075\pi\) | ||||
0.670512 | + | 0.741899i | \(0.266075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.33309 | 0.214010 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 54.9699i | − | 2.20232i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3133 | + | 5.81907i | 0.972534 | + | 0.232763i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.48143i | 0.139035i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.2957 | 0.928859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.1516 | −0.762412 | −0.381206 | − | 0.924490i | \(-0.624491\pi\) | ||||
−0.381206 | + | 0.924490i | \(0.624491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8626i | 0.709974i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.73451 | − | 0.454766i | −0.306935 | − | 0.0180468i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 41.4582i | − | 1.64263i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.2863 | −0.446479 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.5893 | 1.52419 | 0.762094 | − | 0.647467i | \(-0.224172\pi\) | ||||
0.762094 | + | 0.647467i | \(0.224172\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.9692i | 1.33961i | 0.742535 | + | 0.669807i | \(0.233623\pi\) | ||||
−0.742535 | + | 0.669807i | \(0.766377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.509704 | + | 8.66888i | −0.0200696 | + | 0.341337i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 41.6986i | − | 1.63934i | −0.572835 | − | 0.819670i | \(-0.694157\pi\) | ||
0.572835 | − | 0.819670i | \(-0.305843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4888 | 0.450977 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.61860 | 0.220210 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 46.2684i | − | 1.81062i | −0.424750 | − | 0.905311i | \(-0.639638\pi\) | ||
0.424750 | − | 0.905311i | \(-0.360362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.81515 | − | 30.8716i | 0.0709240 | − | 1.20625i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.60168i | 0.257556i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.6714 | −0.532561 | −0.266280 | − | 0.963896i | \(-0.585795\pi\) | ||||
−0.266280 | + | 0.963896i | \(0.585795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.9138 | −1.24130 | −0.620652 | − | 0.784086i | \(-0.713132\pi\) | ||||
−0.620652 | + | 0.784086i | \(0.713132\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.7729i | 0.651406i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.1184 | + | 1.47689i | 0.974051 | + | 0.0572713i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.886857i | − | 0.0343393i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.23944 | 0.163906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7513 | −0.608071 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0200i | − | 1.38847i | −0.719750 | − | 0.694234i | \(-0.755743\pi\) | ||
0.719750 | − | 0.694234i | \(-0.244257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.585944 | − | 4.96555i | 0.0225530 | − | 0.191124i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 39.4383i | − | 1.51574i | −0.652408 | − | 0.757868i | \(-0.726241\pi\) | ||
0.652408 | − | 0.757868i | \(-0.273759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.23043 | −0.239102 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.50951 | −0.364405 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.89018i | 0.0723258i | 0.999346 | + | 0.0361629i | \(0.0115135\pi\) | ||||
−0.999346 | + | 0.0361629i | \(0.988486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5439 | − | 1.14912i | −0.746736 | − | 0.0439058i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 11.1809i | − | 0.426579i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.5895 | −0.936785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.5705 | 1.61946 | 0.809730 | − | 0.586803i | \(-0.199614\pi\) | ||||
0.809730 | + | 0.586803i | \(0.199614\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 8.16599i | − | 0.310200i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.892068 | + | 15.1720i | −0.0338381 | + | 0.575507i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 86.2506i | − | 3.26697i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.05644 | −0.0399582 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6231 | −1.15662 | −0.578309 | − | 0.815818i | \(-0.696287\pi\) | ||||
−0.578309 | + | 0.815818i | \(0.696287\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.50292i | − | 0.245262i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.838923 | + | 14.2681i | −0.0315957 | + | 0.537369i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.54739i | − | 0.0581955i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00019 | 0.338009 | 0.169005 | − | 0.985615i | \(-0.445945\pi\) | ||||
0.169005 | + | 0.985615i | \(0.445945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.35082 | 0.275677 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.83248i | 0.218428i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.58453 | + | 0.445947i | 0.283645 | + | 0.0166775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.35097i | 0.237181i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.6949 | −1.44308 | −0.721538 | − | 0.692374i | \(-0.756565\pi\) | ||||
−0.721538 | + | 0.692374i | \(0.756565\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.12557 | 0.153644 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.56297i | 0.206889i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.825737 | − | 0.0974386i | −0.0306671 | − | 0.00361878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.7793i | 1.17863i | 0.807903 | + | 0.589315i | \(0.200602\pi\) | ||||
−0.807903 | + | 0.589315i | \(0.799398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.4717 | −1.12704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.0764341i | 0.00282316i | 0.999999 | + | 0.00141158i | \(0.000449320\pi\) | ||||
−0.999999 | + | 0.00141158i | \(0.999551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −43.2920 | − | 2.54544i | −1.59685 | − | 0.0938899i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.58948i | − | 0.0585492i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.44098 | −0.163364 | −0.0816820 | − | 0.996658i | \(-0.526029\pi\) | ||||
−0.0816820 | + | 0.996658i | \(0.526029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.68211 | 0.172002 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.5586i | 1.81813i | 0.416656 | + | 0.909064i | \(0.363202\pi\) | ||||
−0.416656 | + | 0.909064i | \(0.636798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.86660 | + | 31.7464i | −0.0683868 | + | 1.16310i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.97928i | − | 0.291946i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 74.2540 | 2.71318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4764 | −0.966139 | −0.483069 | − | 0.875582i | \(-0.660478\pi\) | ||||
−0.483069 | + | 0.875582i | \(0.660478\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 6.13053i | − | 0.223409i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.914486 | + | 15.5533i | −0.0332815 | + | 0.566042i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.41467i | − | 0.305836i | −0.988239 | − | 0.152918i | \(-0.951133\pi\) | ||
0.988239 | − | 0.152918i | \(-0.0488671\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.47683 | 0.307689 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.9896 | −1.26837 | −0.634186 | − | 0.773180i | \(-0.718665\pi\) | ||||
−0.634186 | + | 0.773180i | \(0.718665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.69970i | 0.133938i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.5148 | + | 1.02982i | 0.633249 | + | 0.0372331i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.4511i | − | 0.557909i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.6147 | 0.743386 | 0.371693 | − | 0.928356i | \(-0.378777\pi\) | ||||
0.371693 | + | 0.928356i | \(0.378777\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0238 | −0.757152 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.23263i | 0.152237i | 0.997099 | + | 0.0761185i | \(0.0242527\pi\) | ||||
−0.997099 | + | 0.0761185i | \(0.975747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.43052 | + | 0.640811i | 0.195070 | + | 0.0230186i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.2532i | 0.547204i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0766 | −0.862633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.9393 | −0.641919 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.166293i | 0.00594284i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52.5450 | − | 3.08949i | −1.87541 | − | 0.110269i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.1107i | − | 0.574283i | −0.957888 | − | 0.287142i | \(-0.907295\pi\) | ||
0.957888 | − | 0.287142i | \(-0.0927051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.2397 | −0.969759 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.5967 | 1.23012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.1836i | 0.752251i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.50974 | + | 25.6771i | −0.0535449 | + | 0.910674i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9384i | 1.27300i | 0.771276 | + | 0.636501i | \(0.219619\pi\) | ||||
−0.771276 | + | 0.636501i | \(0.780381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.1535 | −1.77430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6997 | −0.378055 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4932i | 0.370297i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.59604 | − | 61.1602i | 0.126744 | − | 2.15561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.61800i | 0.232965i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.60283 | −0.0915106 | −0.0457553 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457553 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1447 | 0.426458 | 0.213229 | − | 0.977002i | \(-0.431602\pi\) | ||||
0.213229 | + | 0.977002i | \(0.431602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.5286i | − | 0.404324i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7029 | + | 0.982078i | 0.585076 | + | 0.0344007i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.50609i | 0.297590i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.9823 | −0.383752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.4149 | −0.956786 | −0.478393 | − | 0.878146i | \(-0.658781\pi\) | ||||
−0.478393 | + | 0.878146i | \(0.658781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.8864i | − | 1.21606i | −0.793913 | − | 0.608031i | \(-0.791959\pi\) | ||
0.793913 | − | 0.608031i | \(-0.208041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.931345 | − | 7.89263i | 0.0324253 | − | 0.274786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.7690i | 1.31336i | 0.754171 | + | 0.656678i | \(0.228039\pi\) | ||||
−0.754171 | + | 0.656678i | \(0.771961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.2440 | −1.25881 | −0.629404 | − | 0.777079i | \(-0.716701\pi\) | ||||
−0.629404 | + | 0.777079i | \(0.716701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.2244 | 0.944405 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 152.174i | − | 5.27253i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1821 | − | 1.24545i | −0.733038 | − | 0.0431004i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.09364i | − | 0.0378017i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.2110 | −0.870380 | −0.435190 | − | 0.900339i | \(-0.643319\pi\) | ||||
−0.435190 | + | 0.900339i | \(0.643319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9723 | −0.999046 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.9886i | 0.481792i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.10647 | + | 18.8185i | −0.0380637 | + | 0.647375i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.5332i | 1.49582i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.1526 | −0.725955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8338 | −0.542775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 41.3678i | − | 1.41641i | −0.706009 | − | 0.708203i | \(-0.749506\pi\) | ||
0.706009 | − | 0.708203i | \(-0.250494\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.287471 | − | 4.88921i | 0.00983129 | − | 0.167207i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40.5195i | − | 1.38412i | −0.721841 | − | 0.692059i | \(-0.756704\pi\) | ||
0.721841 | − | 0.692059i | \(-0.243296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.7240 | −0.911810 | −0.455905 | − | 0.890028i | \(-0.650684\pi\) | ||||
−0.455905 | + | 0.890028i | \(0.650684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.4737 | 1.92462 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.0616i | 1.15947i | 0.814805 | + | 0.579735i | \(0.196844\pi\) | ||||
−0.814805 | + | 0.579735i | \(0.803156\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.9740 | − | 2.76193i | −1.59717 | − | 0.0939085i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.5658i | 1.51353i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6840 | 0.396351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.13766 | −0.0724319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.21273i | 0.0410447i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −56.5501 | − | 10.0678i | −1.91174 | − | 0.340355i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 29.2015i | − | 0.986065i | −0.870011 | − | 0.493033i | \(-0.835888\pi\) | ||
0.870011 | − | 0.493033i | \(-0.164112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.54350 | 0.119519 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.2971 | 1.72824 | 0.864121 | − | 0.503284i | \(-0.167875\pi\) | ||||
0.864121 | + | 0.503284i | \(0.167875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.5324i | − | 0.859234i | −0.903011 | − | 0.429617i | \(-0.858649\pi\) | ||
0.903011 | − | 0.429617i | \(-0.141351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.1346 | − | 0.948665i | −0.542358 | − | 0.0318890i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.53683i | − | 0.219485i | −0.993960 | − | 0.109743i | \(-0.964997\pi\) | ||
0.993960 | − | 0.109743i | \(-0.0350027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.8013 | 0.597036 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.58948 | −0.0532495 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.0002i | 0.468499i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.728937 | + | 12.3975i | −0.0243657 | + | 0.414404i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 11.4003i | − | 0.380646i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.181865 | −0.00606553 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −90.2569 | −3.00689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 19.9518i | − | 0.663953i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0166024 | − | 0.282368i | 0.000551881 | − | 0.00938622i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 28.2281i | − | 0.937299i | −0.883384 | − | 0.468650i | \(-0.844741\pi\) | ||
0.883384 | − | 0.468650i | \(-0.155259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.301193 | −0.00998994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2819 | 1.16894 | 0.584470 | − | 0.811415i | \(-0.301302\pi\) | ||||
0.584470 | + | 0.811415i | \(0.301302\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.6829i | − | 0.419742i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.1206 | + | 1.30062i | 0.731284 | + | 0.0429973i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 71.0522i | 2.34635i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.62615 | −0.251563 | −0.125782 | − | 0.992058i | \(-0.540144\pi\) | ||||
−0.125782 | + | 0.992058i | \(0.540144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.211948 | −0.00698392 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.1263i | 0.794126i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.73965 | + | 14.7426i | −0.0571993 | + | 0.484732i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.803026i | − | 0.0263748i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.8223 | 1.53619 | 0.768095 | − | 0.640336i | \(-0.221205\pi\) | ||||
0.768095 | + | 0.640336i | \(0.221205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.4790 | −1.39219 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.73795i | 0.286068i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.8394 | + | 1.63687i | 0.910445 | + | 0.0535314i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.9956i | − | 1.92730i | −0.267161 | − | 0.963652i | \(-0.586086\pi\) | ||
0.267161 | − | 0.963652i | \(-0.413914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.6370 | 0.771363 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.4639 | −0.667104 | −0.333552 | − | 0.942732i | \(-0.608247\pi\) | ||||
−0.333552 | + | 0.942732i | \(0.608247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.6235i | 1.90904i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.674287 | + | 11.4681i | −0.0219346 | + | 0.373056i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 55.8815i | − | 1.81590i | −0.419075 | − | 0.907952i | \(-0.637645\pi\) | ||
0.419075 | − | 0.907952i | \(-0.362355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.1121 | 0.458099 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0553 | −0.585483 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.68604i | 0.184189i | 0.995750 | + | 0.0920945i | \(0.0293562\pi\) | ||||
−0.995750 | + | 0.0920945i | \(0.970644\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.68651 | − | 28.6837i | 0.0545743 | − | 0.928181i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.264319i | 0.00854423i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.9812 | 1.45252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8040 | −0.961418 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 14.4533i | − | 0.465750i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51.2118 | − | 3.01110i | −1.64857 | − | 0.0969307i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.84847i | − | 0.123759i | −0.998084 | − | 0.0618793i | \(-0.980291\pi\) | ||
0.998084 | − | 0.0618793i | \(-0.0197094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1859 | 0.552091 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.5115 | −1.30008 | −0.650039 | − | 0.759901i | \(-0.725247\pi\) | ||||
−0.650039 | + | 0.759901i | \(0.725247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 34.9190i | − | 1.11945i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.6147 | − | 1.25255i | −0.339941 | − | 0.0401137i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.9866i | 1.27928i | 0.768673 | + | 0.639642i | \(0.220917\pi\) | ||||
−0.768673 | + | 0.639642i | \(0.779083\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.0069 | −0.543543 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.720132 | 0.0229920 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 12.6615i | − | 0.403840i | −0.979402 | − | 0.201920i | \(-0.935282\pi\) | ||
0.979402 | − | 0.201920i | \(-0.0647181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.9030 | − | 0.993847i | −0.538575 | − | 0.0316666i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 32.8387i | − | 1.04527i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.7113 | 0.658580 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.35522 | −0.0430501 | −0.0215250 | − | 0.999768i | \(-0.506852\pi\) | ||||
−0.0215250 | + | 0.999768i | \(0.506852\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9544i | 0.601498i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.07552 | − | 35.2997i | 0.0657983 | − | 1.11908i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.85396i | 0.280408i | 0.990123 | + | 0.140204i | \(0.0447758\pi\) | ||||
−0.990123 | + | 0.140204i | \(0.955224\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.96897 | 0.0939340 |
(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 | 4020.2.g.b.1609.7 | ✓ | 24 | |
5.4 | even | 2 | inner | 4020.2.g.b.1609.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.b.1609.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4020.2.g.b.1609.19 | yes | 24 | 5.4 | even | 2 | inner |