Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(649,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.f (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.p.649.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.438447 | 0.165717 | 0.0828587 | − | 0.996561i | \(-0.473595\pi\) | ||||
0.0828587 | + | 0.996561i | \(0.473595\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.56155i | − | 0.470826i | −0.971895 | − | 0.235413i | \(-0.924356\pi\) | ||
0.971895 | − | 0.235413i | \(-0.0756443\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 0.561553 | − | 3.56155i | 0.155747 | − | 0.987797i | ||||
\(14\) | 0.438447 | 0.117180 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.68466i | − | 1.62127i | −0.585553 | − | 0.810634i | \(-0.699123\pi\) | ||
0.585553 | − | 0.810634i | \(-0.300877\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | − | 7.68466i | − | 1.76298i | −0.472201 | − | 0.881491i | \(-0.656540\pi\) | ||
0.472201 | − | 0.881491i | \(-0.343460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.438447i | 0.0956770i | ||||||||
\(22\) | − | 1.56155i | − | 0.332924i | ||||||
\(23\) | 3.12311i | 0.651213i | 0.945505 | + | 0.325606i | \(0.105568\pi\) | ||||
−0.945505 | + | 0.325606i | \(0.894432\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.561553 | − | 3.56155i | 0.110130 | − | 0.698478i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.438447 | 0.0828587 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.56155i | − | 0.998884i | −0.866347 | − | 0.499442i | \(-0.833538\pi\) | ||
0.866347 | − | 0.499442i | \(-0.166462\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.56155 | 0.271831 | ||||||||
\(34\) | − | 6.68466i | − | 1.14641i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.56155 | 0.749915 | 0.374957 | − | 0.927042i | \(-0.377657\pi\) | ||||
0.374957 | + | 0.927042i | \(0.377657\pi\) | |||||||
\(38\) | − | 7.68466i | − | 1.24662i | ||||||
\(39\) | 3.56155 | + | 0.561553i | 0.570305 | + | 0.0899204i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.56155i | 0.712395i | 0.934411 | + | 0.356197i | \(0.115927\pi\) | ||||
−0.934411 | + | 0.356197i | \(0.884073\pi\) | |||||||
\(42\) | 0.438447i | 0.0676539i | ||||||||
\(43\) | 11.1231i | 1.69626i | 0.529790 | + | 0.848129i | \(0.322271\pi\) | ||||
−0.529790 | + | 0.848129i | \(0.677729\pi\) | |||||||
\(44\) | − | 1.56155i | − | 0.235413i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.12311i | 0.460477i | ||||||||
\(47\) | 8.12311 | 1.18488 | 0.592438 | − | 0.805616i | \(-0.298165\pi\) | ||||
0.592438 | + | 0.805616i | \(0.298165\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −6.80776 | −0.972538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.68466 | 0.936039 | ||||||||
\(52\) | 0.561553 | − | 3.56155i | 0.0778734 | − | 0.493899i | ||||
\(53\) | 5.00000i | 0.686803i | 0.939189 | + | 0.343401i | \(0.111579\pi\) | ||||
−0.939189 | + | 0.343401i | \(0.888421\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.438447 | 0.0585900 | ||||||||
\(57\) | 7.68466 | 1.01786 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | − | 9.56155i | − | 1.24481i | −0.782696 | − | 0.622404i | \(-0.786156\pi\) | ||
0.782696 | − | 0.622404i | \(-0.213844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.684658 | −0.0876615 | −0.0438308 | − | 0.999039i | \(-0.513956\pi\) | ||||
−0.0438308 | + | 0.999039i | \(0.513956\pi\) | |||||||
\(62\) | − | 5.56155i | − | 0.706318i | ||||||
\(63\) | −0.438447 | −0.0552392 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.56155 | 0.192214 | ||||||||
\(67\) | −4.12311 | −0.503718 | −0.251859 | − | 0.967764i | \(-0.581042\pi\) | ||||
−0.251859 | + | 0.967764i | \(0.581042\pi\) | |||||||
\(68\) | − | 6.68466i | − | 0.810634i | ||||||
\(69\) | −3.12311 | −0.375978 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9309i | 1.65329i | 0.562724 | + | 0.826645i | \(0.309753\pi\) | ||||
−0.562724 | + | 0.826645i | \(0.690247\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 7.12311 | 0.833696 | 0.416848 | − | 0.908976i | \(-0.363135\pi\) | ||||
0.416848 | + | 0.908976i | \(0.363135\pi\) | |||||||
\(74\) | 4.56155 | 0.530270 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.68466i | − | 0.881491i | ||||||
\(77\) | − | 0.684658i | − | 0.0780241i | ||||||
\(78\) | 3.56155 | + | 0.561553i | 0.403266 | + | 0.0635833i | ||||
\(79\) | 2.31534 | 0.260496 | 0.130248 | − | 0.991481i | \(-0.458423\pi\) | ||||
0.130248 | + | 0.991481i | \(0.458423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.56155i | 0.503739i | ||||||||
\(83\) | 14.9309 | 1.63888 | 0.819438 | − | 0.573168i | \(-0.194286\pi\) | ||||
0.819438 | + | 0.573168i | \(0.194286\pi\) | |||||||
\(84\) | 0.438447i | 0.0478385i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.1231i | 1.19944i | ||||||||
\(87\) | 1.00000i | 0.107211i | ||||||||
\(88\) | − | 1.56155i | − | 0.166462i | ||||||
\(89\) | − | 5.12311i | − | 0.543048i | −0.962432 | − | 0.271524i | \(-0.912472\pi\) | ||
0.962432 | − | 0.271524i | \(-0.0875277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.246211 | − | 1.56155i | 0.0258100 | − | 0.163695i | ||||
\(92\) | 3.12311i | 0.325606i | ||||||||
\(93\) | 5.56155 | 0.576706 | ||||||||
\(94\) | 8.12311 | 0.837834 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −13.1231 | −1.33245 | −0.666225 | − | 0.745751i | \(-0.732091\pi\) | ||||
−0.666225 | + | 0.745751i | \(0.732091\pi\) | |||||||
\(98\) | −6.80776 | −0.687688 | ||||||||
\(99\) | 1.56155i | 0.156942i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4384 | −1.23767 | −0.618836 | − | 0.785520i | \(-0.712395\pi\) | ||||
−0.618836 | + | 0.785520i | \(0.712395\pi\) | |||||||
\(102\) | 6.68466 | 0.661880 | ||||||||
\(103\) | 7.12311i | 0.701860i | 0.936402 | + | 0.350930i | \(0.114135\pi\) | ||||
−0.936402 | + | 0.350930i | \(0.885865\pi\) | |||||||
\(104\) | 0.561553 | − | 3.56155i | 0.0550648 | − | 0.349239i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000i | 0.485643i | ||||||||
\(107\) | 0.315342i | 0.0304852i | 0.999884 | + | 0.0152426i | \(0.00485206\pi\) | ||||
−0.999884 | + | 0.0152426i | \(0.995148\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 20.5616i | − | 1.96944i | −0.174146 | − | 0.984720i | \(-0.555717\pi\) | ||
0.174146 | − | 0.984720i | \(-0.444283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.56155i | 0.432963i | ||||||||
\(112\) | 0.438447 | 0.0414294 | ||||||||
\(113\) | − | 4.24621i | − | 0.399450i | −0.979852 | − | 0.199725i | \(-0.935995\pi\) | ||
0.979852 | − | 0.199725i | \(-0.0640049\pi\) | |||||||
\(114\) | 7.68466 | 0.719734 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −0.561553 | + | 3.56155i | −0.0519156 | + | 0.329266i | ||||
\(118\) | − | 9.56155i | − | 0.880212i | ||||||
\(119\) | − | 2.93087i | − | 0.268672i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.56155 | 0.778323 | ||||||||
\(122\) | −0.684658 | −0.0619861 | ||||||||
\(123\) | −4.56155 | −0.411301 | ||||||||
\(124\) | − | 5.56155i | − | 0.499442i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.438447 | −0.0390600 | ||||||||
\(127\) | − | 11.4384i | − | 1.01500i | −0.861652 | − | 0.507499i | \(-0.830570\pi\) | ||
0.861652 | − | 0.507499i | \(-0.169430\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.1231 | −0.979335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.31534 | −0.551774 | −0.275887 | − | 0.961190i | \(-0.588972\pi\) | ||||
−0.275887 | + | 0.961190i | \(0.588972\pi\) | |||||||
\(132\) | 1.56155 | 0.135916 | ||||||||
\(133\) | − | 3.36932i | − | 0.292157i | ||||||
\(134\) | −4.12311 | −0.356182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 6.68466i | − | 0.573205i | ||||||
\(137\) | 6.56155 | 0.560591 | 0.280296 | − | 0.959914i | \(-0.409567\pi\) | ||||
0.280296 | + | 0.959914i | \(0.409567\pi\) | |||||||
\(138\) | −3.12311 | −0.265856 | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.12311i | 0.684089i | ||||||||
\(142\) | 13.9309i | 1.16905i | ||||||||
\(143\) | −5.56155 | − | 0.876894i | −0.465080 | − | 0.0733296i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.12311 | 0.589512 | ||||||||
\(147\) | − | 6.80776i | − | 0.561495i | ||||||
\(148\) | 4.56155 | 0.374957 | ||||||||
\(149\) | 19.3693i | 1.58680i | 0.608703 | + | 0.793398i | \(0.291690\pi\) | ||||
−0.608703 | + | 0.793398i | \(0.708310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.31534i | 0.269799i | 0.990859 | + | 0.134899i | \(0.0430711\pi\) | ||||
−0.990859 | + | 0.134899i | \(0.956929\pi\) | |||||||
\(152\) | − | 7.68466i | − | 0.623308i | ||||||
\(153\) | 6.68466i | 0.540423i | ||||||||
\(154\) | − | 0.684658i | − | 0.0551713i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.56155 | + | 0.561553i | 0.285152 | + | 0.0449602i | ||||
\(157\) | 10.6847i | 0.852729i | 0.904552 | + | 0.426364i | \(0.140206\pi\) | ||||
−0.904552 | + | 0.426364i | \(0.859794\pi\) | |||||||
\(158\) | 2.31534 | 0.184199 | ||||||||
\(159\) | −5.00000 | −0.396526 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.36932i | 0.107917i | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 16.4924 | 1.29179 | 0.645893 | − | 0.763428i | \(-0.276485\pi\) | ||||
0.645893 | + | 0.763428i | \(0.276485\pi\) | |||||||
\(164\) | 4.56155i | 0.356197i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.9309 | 1.15886 | ||||||||
\(167\) | 13.4384 | 1.03990 | 0.519949 | − | 0.854197i | \(-0.325951\pi\) | ||||
0.519949 | + | 0.854197i | \(0.325951\pi\) | |||||||
\(168\) | 0.438447i | 0.0338269i | ||||||||
\(169\) | −12.3693 | − | 4.00000i | −0.951486 | − | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.68466i | 0.587661i | ||||||||
\(172\) | 11.1231i | 0.848129i | ||||||||
\(173\) | − | 0.123106i | − | 0.00935955i | −0.999989 | − | 0.00467977i | \(-0.998510\pi\) | ||
0.999989 | − | 0.00467977i | \(-0.00148962\pi\) | |||||||
\(174\) | 1.00000i | 0.0758098i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.56155i | − | 0.117706i | ||||||
\(177\) | 9.56155 | 0.718690 | ||||||||
\(178\) | − | 5.12311i | − | 0.383993i | ||||||
\(179\) | 19.1231 | 1.42933 | 0.714664 | − | 0.699468i | \(-0.246580\pi\) | ||||
0.714664 | + | 0.699468i | \(0.246580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.192236 | 0.0142888 | 0.00714439 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714439 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(182\) | 0.246211 | − | 1.56155i | 0.0182504 | − | 0.115750i | ||||
\(183\) | − | 0.684658i | − | 0.0506114i | ||||||
\(184\) | 3.12311i | 0.230238i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.56155 | 0.407793 | ||||||||
\(187\) | −10.4384 | −0.763335 | ||||||||
\(188\) | 8.12311 | 0.592438 | ||||||||
\(189\) | − | 0.438447i | − | 0.0318923i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4924 | −1.19335 | −0.596675 | − | 0.802483i | \(-0.703512\pi\) | ||||
−0.596675 | + | 0.802483i | \(0.703512\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −4.87689 | −0.351047 | −0.175523 | − | 0.984475i | \(-0.556162\pi\) | ||||
−0.175523 | + | 0.984475i | \(0.556162\pi\) | |||||||
\(194\) | −13.1231 | −0.942184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.80776 | −0.486269 | ||||||||
\(197\) | 12.2462 | 0.872506 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(198\) | 1.56155i | 0.110975i | ||||||||
\(199\) | 5.93087 | 0.420428 | 0.210214 | − | 0.977655i | \(-0.432584\pi\) | ||||
0.210214 | + | 0.977655i | \(0.432584\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.12311i | − | 0.290821i | ||||||
\(202\) | −12.4384 | −0.875166 | ||||||||
\(203\) | 0.438447 | 0.0307730 | ||||||||
\(204\) | 6.68466 | 0.468020 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.12311i | 0.496290i | ||||||||
\(207\) | − | 3.12311i | − | 0.217071i | ||||||
\(208\) | 0.561553 | − | 3.56155i | 0.0389367 | − | 0.246949i | ||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3693 | −1.19575 | −0.597877 | − | 0.801588i | \(-0.703989\pi\) | ||||
−0.597877 | + | 0.801588i | \(0.703989\pi\) | |||||||
\(212\) | 5.00000i | 0.343401i | ||||||||
\(213\) | −13.9309 | −0.954527 | ||||||||
\(214\) | 0.315342i | 0.0215563i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | − | 2.43845i | − | 0.165533i | ||||||
\(218\) | − | 20.5616i | − | 1.39260i | ||||||
\(219\) | 7.12311i | 0.481335i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.8078 | − | 3.75379i | −1.60148 | − | 0.252507i | ||||
\(222\) | 4.56155i | 0.306151i | ||||||||
\(223\) | 15.3693 | 1.02921 | 0.514603 | − | 0.857429i | \(-0.327939\pi\) | ||||
0.514603 | + | 0.857429i | \(0.327939\pi\) | |||||||
\(224\) | 0.438447 | 0.0292950 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 4.24621i | − | 0.282454i | ||||||
\(227\) | −3.31534 | −0.220047 | −0.110023 | − | 0.993929i | \(-0.535093\pi\) | ||||
−0.110023 | + | 0.993929i | \(0.535093\pi\) | |||||||
\(228\) | 7.68466 | 0.508929 | ||||||||
\(229\) | − | 7.19224i | − | 0.475276i | −0.971354 | − | 0.237638i | \(-0.923627\pi\) | ||
0.971354 | − | 0.237638i | \(-0.0763732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.684658 | 0.0450472 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 3.12311i | 0.204601i | 0.994754 | + | 0.102301i | \(0.0326204\pi\) | ||||
−0.994754 | + | 0.102301i | \(0.967380\pi\) | |||||||
\(234\) | −0.561553 | + | 3.56155i | −0.0367099 | + | 0.232826i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 9.56155i | − | 0.622404i | ||||||
\(237\) | 2.31534i | 0.150398i | ||||||||
\(238\) | − | 2.93087i | − | 0.189980i | ||||||
\(239\) | 6.93087i | 0.448321i | 0.974552 | + | 0.224160i | \(0.0719639\pi\) | ||||
−0.974552 | + | 0.224160i | \(0.928036\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.2462i | − | 1.30417i | −0.758145 | − | 0.652087i | \(-0.773894\pi\) | ||
0.758145 | − | 0.652087i | \(-0.226106\pi\) | |||||||
\(242\) | 8.56155 | 0.550357 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.684658 | −0.0438308 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.56155 | −0.290834 | ||||||||
\(247\) | −27.3693 | − | 4.31534i | −1.74147 | − | 0.274579i | ||||
\(248\) | − | 5.56155i | − | 0.353159i | ||||||
\(249\) | 14.9309i | 0.946205i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4384 | 0.721988 | 0.360994 | − | 0.932568i | \(-0.382437\pi\) | ||||
0.360994 | + | 0.932568i | \(0.382437\pi\) | |||||||
\(252\) | −0.438447 | −0.0276196 | ||||||||
\(253\) | 4.87689 | 0.306608 | ||||||||
\(254\) | − | 11.4384i | − | 0.717712i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8078i | 0.986061i | 0.870012 | + | 0.493031i | \(0.164111\pi\) | ||||
−0.870012 | + | 0.493031i | \(0.835889\pi\) | |||||||
\(258\) | −11.1231 | −0.692494 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −6.31534 | −0.390163 | ||||||||
\(263\) | 24.7386i | 1.52545i | 0.646723 | + | 0.762725i | \(0.276139\pi\) | ||||
−0.646723 | + | 0.762725i | \(0.723861\pi\) | |||||||
\(264\) | 1.56155 | 0.0961069 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 3.36932i | − | 0.206586i | ||||||
\(267\) | 5.12311 | 0.313529 | ||||||||
\(268\) | −4.12311 | −0.251859 | ||||||||
\(269\) | 9.49242 | 0.578763 | 0.289382 | − | 0.957214i | \(-0.406550\pi\) | ||||
0.289382 | + | 0.957214i | \(0.406550\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.19224i | − | 0.254660i | −0.991860 | − | 0.127330i | \(-0.959359\pi\) | ||
0.991860 | − | 0.127330i | \(-0.0406408\pi\) | |||||||
\(272\) | − | 6.68466i | − | 0.405317i | ||||||
\(273\) | 1.56155 | + | 0.246211i | 0.0945095 | + | 0.0149014i | ||||
\(274\) | 6.56155 | 0.396398 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.12311 | −0.187989 | ||||||||
\(277\) | 15.6155i | 0.938246i | 0.883133 | + | 0.469123i | \(0.155430\pi\) | ||||
−0.883133 | + | 0.469123i | \(0.844570\pi\) | |||||||
\(278\) | −16.4924 | −0.989150 | ||||||||
\(279\) | 5.56155i | 0.332961i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.93087i | 0.353806i | 0.984228 | + | 0.176903i | \(0.0566079\pi\) | ||||
−0.984228 | + | 0.176903i | \(0.943392\pi\) | |||||||
\(282\) | 8.12311i | 0.483724i | ||||||||
\(283\) | − | 7.36932i | − | 0.438060i | −0.975718 | − | 0.219030i | \(-0.929711\pi\) | ||
0.975718 | − | 0.219030i | \(-0.0702893\pi\) | |||||||
\(284\) | 13.9309i | 0.826645i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.56155 | − | 0.876894i | −0.328862 | − | 0.0518519i | ||||
\(287\) | 2.00000i | 0.118056i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −27.6847 | −1.62851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.1231i | − | 0.769290i | ||||||
\(292\) | 7.12311 | 0.416848 | ||||||||
\(293\) | 0.630683 | 0.0368449 | 0.0184225 | − | 0.999830i | \(-0.494136\pi\) | ||||
0.0184225 | + | 0.999830i | \(0.494136\pi\) | |||||||
\(294\) | − | 6.80776i | − | 0.397037i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.56155 | 0.265135 | ||||||||
\(297\) | −1.56155 | −0.0906105 | ||||||||
\(298\) | 19.3693i | 1.12203i | ||||||||
\(299\) | 11.1231 | + | 1.75379i | 0.643266 | + | 0.101424i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.87689i | 0.281100i | ||||||||
\(302\) | 3.31534i | 0.190776i | ||||||||
\(303\) | − | 12.4384i | − | 0.714570i | ||||||
\(304\) | − | 7.68466i | − | 0.440745i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.68466i | 0.382136i | ||||||||
\(307\) | 2.06913 | 0.118092 | 0.0590458 | − | 0.998255i | \(-0.481194\pi\) | ||||
0.0590458 | + | 0.998255i | \(0.481194\pi\) | |||||||
\(308\) | − | 0.684658i | − | 0.0390120i | ||||||
\(309\) | −7.12311 | −0.405219 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8769 | 0.843591 | 0.421796 | − | 0.906691i | \(-0.361400\pi\) | ||||
0.421796 | + | 0.906691i | \(0.361400\pi\) | |||||||
\(312\) | 3.56155 | + | 0.561553i | 0.201633 | + | 0.0317917i | ||||
\(313\) | 24.8617i | 1.40527i | 0.711551 | + | 0.702634i | \(0.247993\pi\) | ||||
−0.711551 | + | 0.702634i | \(0.752007\pi\) | |||||||
\(314\) | 10.6847i | 0.602970i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.31534 | 0.130248 | ||||||||
\(317\) | −30.0000 | −1.68497 | −0.842484 | − | 0.538721i | \(-0.818908\pi\) | ||||
−0.842484 | + | 0.538721i | \(0.818908\pi\) | |||||||
\(318\) | −5.00000 | −0.280386 | ||||||||
\(319\) | − | 1.56155i | − | 0.0874302i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.315342 | −0.0176006 | ||||||||
\(322\) | 1.36932i | 0.0763090i | ||||||||
\(323\) | −51.3693 | −2.85827 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.4924 | 0.913431 | ||||||||
\(327\) | 20.5616 | 1.13706 | ||||||||
\(328\) | 4.56155i | 0.251870i | ||||||||
\(329\) | 3.56155 | 0.196355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.4924i | − | 1.34623i | −0.739540 | − | 0.673113i | \(-0.764957\pi\) | ||
0.739540 | − | 0.673113i | \(-0.235043\pi\) | |||||||
\(332\) | 14.9309 | 0.819438 | ||||||||
\(333\) | −4.56155 | −0.249972 | ||||||||
\(334\) | 13.4384 | 0.735319 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.438447i | 0.0239193i | ||||||||
\(337\) | 10.6847i | 0.582030i | 0.956718 | + | 0.291015i | \(0.0939930\pi\) | ||||
−0.956718 | + | 0.291015i | \(0.906007\pi\) | |||||||
\(338\) | −12.3693 | − | 4.00000i | −0.672802 | − | 0.217571i | ||||
\(339\) | 4.24621 | 0.230623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.68466 | −0.470301 | ||||||||
\(342\) | 7.68466i | 0.415539i | ||||||||
\(343\) | −6.05398 | −0.326884 | ||||||||
\(344\) | 11.1231i | 0.599718i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 0.123106i | − | 0.00661820i | ||||||
\(347\) | − | 18.5616i | − | 0.996436i | −0.867052 | − | 0.498218i | \(-0.833988\pi\) | ||
0.867052 | − | 0.498218i | \(-0.166012\pi\) | |||||||
\(348\) | 1.00000i | 0.0536056i | ||||||||
\(349\) | 22.0000i | 1.17763i | 0.808267 | + | 0.588817i | \(0.200406\pi\) | ||||
−0.808267 | + | 0.588817i | \(0.799594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.56155 | − | 0.561553i | −0.190102 | − | 0.0299735i | ||||
\(352\) | − | 1.56155i | − | 0.0832310i | ||||||
\(353\) | −15.4384 | −0.821706 | −0.410853 | − | 0.911702i | \(-0.634769\pi\) | ||||
−0.410853 | + | 0.911702i | \(0.634769\pi\) | |||||||
\(354\) | 9.56155 | 0.508191 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.12311i | − | 0.271524i | ||||||
\(357\) | 2.93087 | 0.155118 | ||||||||
\(358\) | 19.1231 | 1.01069 | ||||||||
\(359\) | 3.87689i | 0.204615i | 0.994753 | + | 0.102307i | \(0.0326225\pi\) | ||||
−0.994753 | + | 0.102307i | \(0.967377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −40.0540 | −2.10810 | ||||||||
\(362\) | 0.192236 | 0.0101037 | ||||||||
\(363\) | 8.56155i | 0.449365i | ||||||||
\(364\) | 0.246211 | − | 1.56155i | 0.0129050 | − | 0.0818476i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 0.684658i | − | 0.0357877i | ||||||
\(367\) | − | 19.6847i | − | 1.02753i | −0.857931 | − | 0.513765i | \(-0.828250\pi\) | ||
0.857931 | − | 0.513765i | \(-0.171750\pi\) | |||||||
\(368\) | 3.12311i | 0.162803i | ||||||||
\(369\) | − | 4.56155i | − | 0.237465i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.19224i | 0.113815i | ||||||||
\(372\) | 5.56155 | 0.288353 | ||||||||
\(373\) | − | 32.4384i | − | 1.67960i | −0.542897 | − | 0.839800i | \(-0.682672\pi\) | ||
0.542897 | − | 0.839800i | \(-0.317328\pi\) | |||||||
\(374\) | −10.4384 | −0.539759 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.12311 | 0.418917 | ||||||||
\(377\) | 0.561553 | − | 3.56155i | 0.0289214 | − | 0.183429i | ||||
\(378\) | − | 0.438447i | − | 0.0225513i | ||||||
\(379\) | 7.31534i | 0.375764i | 0.982192 | + | 0.187882i | \(0.0601622\pi\) | ||||
−0.982192 | + | 0.187882i | \(0.939838\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4384 | 0.586009 | ||||||||
\(382\) | −16.4924 | −0.843826 | ||||||||
\(383\) | 13.9309 | 0.711834 | 0.355917 | − | 0.934518i | \(-0.384169\pi\) | ||||
0.355917 | + | 0.934518i | \(0.384169\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.87689 | −0.248227 | ||||||||
\(387\) | − | 11.1231i | − | 0.565419i | ||||||
\(388\) | −13.1231 | −0.666225 | ||||||||
\(389\) | 6.80776 | 0.345167 | 0.172584 | − | 0.984995i | \(-0.444788\pi\) | ||||
0.172584 | + | 0.984995i | \(0.444788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8769 | 1.05579 | ||||||||
\(392\) | −6.80776 | −0.343844 | ||||||||
\(393\) | − | 6.31534i | − | 0.318567i | ||||||
\(394\) | 12.2462 | 0.616955 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.56155i | 0.0784710i | ||||||||
\(397\) | −35.0540 | −1.75931 | −0.879654 | − | 0.475614i | \(-0.842226\pi\) | ||||
−0.879654 | + | 0.475614i | \(0.842226\pi\) | |||||||
\(398\) | 5.93087 | 0.297288 | ||||||||
\(399\) | 3.36932 | 0.168677 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000i | 1.09863i | 0.835616 | + | 0.549314i | \(0.185111\pi\) | ||||
−0.835616 | + | 0.549314i | \(0.814889\pi\) | |||||||
\(402\) | − | 4.12311i | − | 0.205642i | ||||||
\(403\) | −19.8078 | − | 3.12311i | −0.986695 | − | 0.155573i | ||||
\(404\) | −12.4384 | −0.618836 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.438447 | 0.0217598 | ||||||||
\(407\) | − | 7.12311i | − | 0.353079i | ||||||
\(408\) | 6.68466 | 0.330940 | ||||||||
\(409\) | 27.6155i | 1.36550i | 0.730652 | + | 0.682750i | \(0.239216\pi\) | ||||
−0.730652 | + | 0.682750i | \(0.760784\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.56155i | 0.323658i | ||||||||
\(412\) | 7.12311i | 0.350930i | ||||||||
\(413\) | − | 4.19224i | − | 0.206286i | ||||||
\(414\) | − | 3.12311i | − | 0.153492i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.561553 | − | 3.56155i | 0.0275324 | − | 0.174619i | ||||
\(417\) | − | 16.4924i | − | 0.807637i | ||||||
\(418\) | −12.0000 | −0.586939 | ||||||||
\(419\) | 5.68466 | 0.277714 | 0.138857 | − | 0.990312i | \(-0.455657\pi\) | ||||
0.138857 | + | 0.990312i | \(0.455657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.63068i | − | 0.225686i | −0.993613 | − | 0.112843i | \(-0.964004\pi\) | ||
0.993613 | − | 0.112843i | \(-0.0359957\pi\) | |||||||
\(422\) | −17.3693 | −0.845525 | ||||||||
\(423\) | −8.12311 | −0.394959 | ||||||||
\(424\) | 5.00000i | 0.242821i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.9309 | −0.674953 | ||||||||
\(427\) | −0.300187 | −0.0145270 | ||||||||
\(428\) | 0.315342i | 0.0152426i | ||||||||
\(429\) | 0.876894 | − | 5.56155i | 0.0423369 | − | 0.268514i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.17708i | − | 0.393876i | −0.980416 | − | 0.196938i | \(-0.936900\pi\) | ||
0.980416 | − | 0.196938i | \(-0.0630998\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 5.05398i | − | 0.242879i | −0.992599 | − | 0.121439i | \(-0.961249\pi\) | ||
0.992599 | − | 0.121439i | \(-0.0387510\pi\) | |||||||
\(434\) | − | 2.43845i | − | 0.117049i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 20.5616i | − | 0.984720i | ||||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | 7.12311i | 0.340355i | ||||||||
\(439\) | 27.3002 | 1.30297 | 0.651483 | − | 0.758663i | \(-0.274147\pi\) | ||||
0.651483 | + | 0.758663i | \(0.274147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.80776 | 0.324179 | ||||||||
\(442\) | −23.8078 | − | 3.75379i | −1.13242 | − | 0.178550i | ||||
\(443\) | 28.5616i | 1.35700i | 0.734600 | + | 0.678500i | \(0.237370\pi\) | ||||
−0.734600 | + | 0.678500i | \(0.762630\pi\) | |||||||
\(444\) | 4.56155i | 0.216482i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.3693 | 0.727758 | ||||||||
\(447\) | −19.3693 | −0.916137 | ||||||||
\(448\) | 0.438447 | 0.0207147 | ||||||||
\(449\) | − | 5.43845i | − | 0.256656i | −0.991732 | − | 0.128328i | \(-0.959039\pi\) | ||
0.991732 | − | 0.128328i | \(-0.0409611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.12311 | 0.335414 | ||||||||
\(452\) | − | 4.24621i | − | 0.199725i | ||||||
\(453\) | −3.31534 | −0.155768 | ||||||||
\(454\) | −3.31534 | −0.155597 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.68466 | 0.359867 | ||||||||
\(457\) | −28.7386 | −1.34434 | −0.672168 | − | 0.740398i | \(-0.734637\pi\) | ||||
−0.672168 | + | 0.740398i | \(0.734637\pi\) | |||||||
\(458\) | − | 7.19224i | − | 0.336071i | ||||||
\(459\) | −6.68466 | −0.312013 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 22.2462i | − | 1.03611i | −0.855348 | − | 0.518055i | \(-0.826656\pi\) | ||
0.855348 | − | 0.518055i | \(-0.173344\pi\) | |||||||
\(462\) | 0.684658 | 0.0318532 | ||||||||
\(463\) | −11.5616 | −0.537311 | −0.268655 | − | 0.963236i | \(-0.586579\pi\) | ||||
−0.268655 | + | 0.963236i | \(0.586579\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.12311i | 0.144675i | ||||||||
\(467\) | 40.8078i | 1.88836i | 0.329433 | + | 0.944179i | \(0.393143\pi\) | ||||
−0.329433 | + | 0.944179i | \(0.606857\pi\) | |||||||
\(468\) | −0.561553 | + | 3.56155i | −0.0259578 | + | 0.164633i | ||||
\(469\) | −1.80776 | −0.0834748 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6847 | −0.492323 | ||||||||
\(472\) | − | 9.56155i | − | 0.440106i | ||||||
\(473\) | 17.3693 | 0.798642 | ||||||||
\(474\) | 2.31534i | 0.106347i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.93087i | − | 0.134336i | ||||||
\(477\) | − | 5.00000i | − | 0.228934i | ||||||
\(478\) | 6.93087i | 0.317011i | ||||||||
\(479\) | 32.1231i | 1.46774i | 0.679289 | + | 0.733871i | \(0.262288\pi\) | ||||
−0.679289 | + | 0.733871i | \(0.737712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.56155 | − | 16.2462i | 0.116797 | − | 0.740763i | ||||
\(482\) | − | 20.2462i | − | 0.922190i | ||||||
\(483\) | −1.36932 | −0.0623061 | ||||||||
\(484\) | 8.56155 | 0.389161 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −6.68466 | −0.302911 | −0.151455 | − | 0.988464i | \(-0.548396\pi\) | ||||
−0.151455 | + | 0.988464i | \(0.548396\pi\) | |||||||
\(488\) | −0.684658 | −0.0309930 | ||||||||
\(489\) | 16.4924i | 0.745813i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.7386 | 1.74825 | 0.874125 | − | 0.485701i | \(-0.161436\pi\) | ||||
0.874125 | + | 0.485701i | \(0.161436\pi\) | |||||||
\(492\) | −4.56155 | −0.205651 | ||||||||
\(493\) | − | 6.68466i | − | 0.301062i | ||||||
\(494\) | −27.3693 | − | 4.31534i | −1.23140 | − | 0.194156i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.56155i | − | 0.249721i | ||||||
\(497\) | 6.10795i | 0.273979i | ||||||||
\(498\) | 14.9309i | 0.669068i | ||||||||
\(499\) | − | 28.1231i | − | 1.25896i | −0.777015 | − | 0.629482i | \(-0.783267\pi\) | ||
0.777015 | − | 0.629482i | \(-0.216733\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.4384i | 0.600386i | ||||||||
\(502\) | 11.4384 | 0.510523 | ||||||||
\(503\) | 8.73863i | 0.389636i | 0.980839 | + | 0.194818i | \(0.0624117\pi\) | ||||
−0.980839 | + | 0.194818i | \(0.937588\pi\) | |||||||
\(504\) | −0.438447 | −0.0195300 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.87689 | 0.216804 | ||||||||
\(507\) | 4.00000 | − | 12.3693i | 0.177646 | − | 0.549341i | ||||
\(508\) | − | 11.4384i | − | 0.507499i | ||||||
\(509\) | 22.4924i | 0.996959i | 0.866901 | + | 0.498480i | \(0.166108\pi\) | ||||
−0.866901 | + | 0.498480i | \(0.833892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.12311 | 0.138158 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.68466 | −0.339286 | ||||||||
\(514\) | 15.8078i | 0.697251i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.1231 | −0.489667 | ||||||||
\(517\) | − | 12.6847i | − | 0.557871i | ||||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | 0.123106 | 0.00540374 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2462 | −0.711759 | −0.355880 | − | 0.934532i | \(-0.615819\pi\) | ||||
−0.355880 | + | 0.934532i | \(0.615819\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | 0.630683i | 0.0275778i | 0.999905 | + | 0.0137889i | \(0.00438929\pi\) | ||||
−0.999905 | + | 0.0137889i | \(0.995611\pi\) | |||||||
\(524\) | −6.31534 | −0.275887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7386i | 1.07866i | ||||||||
\(527\) | −37.1771 | −1.61946 | ||||||||
\(528\) | 1.56155 | 0.0679579 | ||||||||
\(529\) | 13.2462 | 0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.56155i | 0.414936i | ||||||||
\(532\) | − | 3.36932i | − | 0.146078i | ||||||
\(533\) | 16.2462 | + | 2.56155i | 0.703702 | + | 0.110953i | ||||
\(534\) | 5.12311 | 0.221698 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.12311 | −0.178091 | ||||||||
\(537\) | 19.1231i | 0.825223i | ||||||||
\(538\) | 9.49242 | 0.409247 | ||||||||
\(539\) | 10.6307i | 0.457896i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2462i | 1.38637i | 0.720758 | + | 0.693186i | \(0.243794\pi\) | ||||
−0.720758 | + | 0.693186i | \(0.756206\pi\) | |||||||
\(542\) | − | 4.19224i | − | 0.180072i | ||||||
\(543\) | 0.192236i | 0.00824963i | ||||||||
\(544\) | − | 6.68466i | − | 0.286602i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.56155 | + | 0.246211i | 0.0668283 | + | 0.0105369i | ||||
\(547\) | − | 7.12311i | − | 0.304562i | −0.988337 | − | 0.152281i | \(-0.951338\pi\) | ||
0.988337 | − | 0.152281i | \(-0.0486619\pi\) | |||||||
\(548\) | 6.56155 | 0.280296 | ||||||||
\(549\) | 0.684658 | 0.0292205 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.68466i | − | 0.327377i | ||||||
\(552\) | −3.12311 | −0.132928 | ||||||||
\(553\) | 1.01515 | 0.0431688 | ||||||||
\(554\) | 15.6155i | 0.663440i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.4924 | −0.699435 | ||||||||
\(557\) | 41.8617 | 1.77374 | 0.886869 | − | 0.462020i | \(-0.152875\pi\) | ||||
0.886869 | + | 0.462020i | \(0.152875\pi\) | |||||||
\(558\) | 5.56155i | 0.235439i | ||||||||
\(559\) | 39.6155 | + | 6.24621i | 1.67556 | + | 0.264187i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 10.4384i | − | 0.440712i | ||||||
\(562\) | 5.93087i | 0.250179i | ||||||||
\(563\) | 43.3002i | 1.82489i | 0.409205 | + | 0.912443i | \(0.365806\pi\) | ||||
−0.409205 | + | 0.912443i | \(0.634194\pi\) | |||||||
\(564\) | 8.12311i | 0.342044i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 7.36932i | − | 0.309755i | ||||||
\(567\) | 0.438447 | 0.0184131 | ||||||||
\(568\) | 13.9309i | 0.584526i | ||||||||
\(569\) | 7.31534 | 0.306675 | 0.153338 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153338 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1231 | 1.13507 | 0.567533 | − | 0.823350i | \(-0.307898\pi\) | ||||
0.567533 | + | 0.823350i | \(0.307898\pi\) | |||||||
\(572\) | −5.56155 | − | 0.876894i | −0.232540 | − | 0.0366648i | ||||
\(573\) | − | 16.4924i | − | 0.688981i | ||||||
\(574\) | 2.00000i | 0.0834784i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −8.63068 | −0.359300 | −0.179650 | − | 0.983731i | \(-0.557497\pi\) | ||||
−0.179650 | + | 0.983731i | \(0.557497\pi\) | |||||||
\(578\) | −27.6847 | −1.15153 | ||||||||
\(579\) | − | 4.87689i | − | 0.202677i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.54640 | 0.271590 | ||||||||
\(582\) | − | 13.1231i | − | 0.543970i | ||||||
\(583\) | 7.80776 | 0.323365 | ||||||||
\(584\) | 7.12311 | 0.294756 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.630683 | 0.0260533 | ||||||||
\(587\) | 18.9309 | 0.781361 | 0.390680 | − | 0.920526i | \(-0.372240\pi\) | ||||
0.390680 | + | 0.920526i | \(0.372240\pi\) | |||||||
\(588\) | − | 6.80776i | − | 0.280747i | ||||||
\(589\) | −42.7386 | −1.76101 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.2462i | 0.503742i | ||||||||
\(592\) | 4.56155 | 0.187479 | ||||||||
\(593\) | −24.8078 | −1.01873 | −0.509366 | − | 0.860550i | \(-0.670120\pi\) | ||||
−0.509366 | + | 0.860550i | \(0.670120\pi\) | |||||||
\(594\) | −1.56155 | −0.0640713 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.3693i | 0.793398i | ||||||||
\(597\) | 5.93087i | 0.242734i | ||||||||
\(598\) | 11.1231 | + | 1.75379i | 0.454858 | + | 0.0717178i | ||||
\(599\) | 22.9848 | 0.939135 | 0.469568 | − | 0.882896i | \(-0.344410\pi\) | ||||
0.469568 | + | 0.882896i | \(0.344410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7386 | 0.478829 | 0.239414 | − | 0.970917i | \(-0.423045\pi\) | ||||
0.239414 | + | 0.970917i | \(0.423045\pi\) | |||||||
\(602\) | 4.87689i | 0.198767i | ||||||||
\(603\) | 4.12311 | 0.167906 | ||||||||
\(604\) | 3.31534i | 0.134899i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 12.4384i | − | 0.505277i | ||||||
\(607\) | − | 47.0540i | − | 1.90986i | −0.296828 | − | 0.954931i | \(-0.595929\pi\) | ||
0.296828 | − | 0.954931i | \(-0.404071\pi\) | |||||||
\(608\) | − | 7.68466i | − | 0.311654i | ||||||
\(609\) | 0.438447i | 0.0177668i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.56155 | − | 28.9309i | 0.184541 | − | 1.17042i | ||||
\(612\) | 6.68466i | 0.270211i | ||||||||
\(613\) | −39.3693 | −1.59011 | −0.795056 | − | 0.606536i | \(-0.792559\pi\) | ||||
−0.795056 | + | 0.606536i | \(0.792559\pi\) | |||||||
\(614\) | 2.06913 | 0.0835033 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.684658i | − | 0.0275857i | ||||||
\(617\) | −27.6847 | −1.11454 | −0.557271 | − | 0.830331i | \(-0.688152\pi\) | ||||
−0.557271 | + | 0.830331i | \(0.688152\pi\) | |||||||
\(618\) | −7.12311 | −0.286533 | ||||||||
\(619\) | − | 2.24621i | − | 0.0902829i | −0.998981 | − | 0.0451414i | \(-0.985626\pi\) | ||
0.998981 | − | 0.0451414i | \(-0.0143738\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.12311 | 0.125326 | ||||||||
\(622\) | 14.8769 | 0.596509 | ||||||||
\(623\) | − | 2.24621i | − | 0.0899926i | ||||||
\(624\) | 3.56155 | + | 0.561553i | 0.142576 | + | 0.0224801i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.8617i | 0.993675i | ||||||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | 10.6847i | 0.426364i | ||||||||
\(629\) | − | 30.4924i | − | 1.21581i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.8769i | − | 0.910715i | −0.890309 | − | 0.455357i | \(-0.849511\pi\) | ||
0.890309 | − | 0.455357i | \(-0.150489\pi\) | |||||||
\(632\) | 2.31534 | 0.0920993 | ||||||||
\(633\) | − | 17.3693i | − | 0.690368i | ||||||
\(634\) | −30.0000 | −1.19145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.00000 | −0.198263 | ||||||||
\(637\) | −3.82292 | + | 24.2462i | −0.151470 | + | 0.960670i | ||||
\(638\) | − | 1.56155i | − | 0.0618225i | ||||||
\(639\) | − | 13.9309i | − | 0.551097i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.4233 | −0.767174 | −0.383587 | − | 0.923505i | \(-0.625311\pi\) | ||||
−0.383587 | + | 0.923505i | \(0.625311\pi\) | |||||||
\(642\) | −0.315342 | −0.0124455 | ||||||||
\(643\) | 15.6847 | 0.618543 | 0.309271 | − | 0.950974i | \(-0.399915\pi\) | ||||
0.309271 | + | 0.950974i | \(0.399915\pi\) | |||||||
\(644\) | 1.36932i | 0.0539586i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −51.3693 | −2.02110 | ||||||||
\(647\) | 10.8769i | 0.427615i | 0.976876 | + | 0.213807i | \(0.0685865\pi\) | ||||
−0.976876 | + | 0.213807i | \(0.931413\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −14.9309 | −0.586088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.43845 | 0.0955703 | ||||||||
\(652\) | 16.4924 | 0.645893 | ||||||||
\(653\) | − | 46.3002i | − | 1.81187i | −0.423421 | − | 0.905933i | \(-0.639171\pi\) | ||
0.423421 | − | 0.905933i | \(-0.360829\pi\) | |||||||
\(654\) | 20.5616 | 0.804020 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.56155i | 0.178099i | ||||||||
\(657\) | −7.12311 | −0.277899 | ||||||||
\(658\) | 3.56155 | 0.138844 | ||||||||
\(659\) | 12.5616 | 0.489329 | 0.244664 | − | 0.969608i | \(-0.421322\pi\) | ||||
0.244664 | + | 0.969608i | \(0.421322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.3002i | − | 0.595108i | −0.954705 | − | 0.297554i | \(-0.903829\pi\) | ||
0.954705 | − | 0.297554i | \(-0.0961709\pi\) | |||||||
\(662\) | − | 24.4924i | − | 0.951925i | ||||||
\(663\) | 3.75379 | − | 23.8078i | 0.145785 | − | 0.924617i | ||||
\(664\) | 14.9309 | 0.579430 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.56155 | −0.176757 | ||||||||
\(667\) | 3.12311i | 0.120927i | ||||||||
\(668\) | 13.4384 | 0.519949 | ||||||||
\(669\) | 15.3693i | 0.594212i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.06913i | 0.0412733i | ||||||||
\(672\) | 0.438447i | 0.0169135i | ||||||||
\(673\) | 22.1231i | 0.852783i | 0.904539 | + | 0.426392i | \(0.140215\pi\) | ||||
−0.904539 | + | 0.426392i | \(0.859785\pi\) | |||||||
\(674\) | 10.6847i | 0.411558i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3693 | − | 4.00000i | −0.475743 | − | 0.153846i | ||||
\(677\) | 36.2462i | 1.39306i | 0.717530 | + | 0.696528i | \(0.245273\pi\) | ||||
−0.717530 | + | 0.696528i | \(0.754727\pi\) | |||||||
\(678\) | 4.24621 | 0.163075 | ||||||||
\(679\) | −5.75379 | −0.220810 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3.31534i | − | 0.127044i | ||||||
\(682\) | −8.68466 | −0.332553 | ||||||||
\(683\) | 35.6695 | 1.36486 | 0.682428 | − | 0.730953i | \(-0.260924\pi\) | ||||
0.682428 | + | 0.730953i | \(0.260924\pi\) | |||||||
\(684\) | 7.68466i | 0.293830i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.05398 | −0.231142 | ||||||||
\(687\) | 7.19224 | 0.274401 | ||||||||
\(688\) | 11.1231i | 0.424064i | ||||||||
\(689\) | 17.8078 | + | 2.80776i | 0.678422 | + | 0.106967i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.0000i | 1.33146i | 0.746191 | + | 0.665731i | \(0.231880\pi\) | ||||
−0.746191 | + | 0.665731i | \(0.768120\pi\) | |||||||
\(692\) | − | 0.123106i | − | 0.00467977i | ||||||
\(693\) | 0.684658i | 0.0260080i | ||||||||
\(694\) | − | 18.5616i | − | 0.704587i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000i | 0.0379049i | ||||||||
\(697\) | 30.4924 | 1.15498 | ||||||||
\(698\) | 22.0000i | 0.832712i | ||||||||
\(699\) | −3.12311 | −0.118127 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.6847 | 1.00787 | 0.503933 | − | 0.863743i | \(-0.331886\pi\) | ||||
0.503933 | + | 0.863743i | \(0.331886\pi\) | |||||||
\(702\) | −3.56155 | − | 0.561553i | −0.134422 | − | 0.0211944i | ||||
\(703\) | − | 35.0540i | − | 1.32209i | ||||||
\(704\) | − | 1.56155i | − | 0.0588532i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.4384 | −0.581034 | ||||||||
\(707\) | −5.45360 | −0.205104 | ||||||||
\(708\) | 9.56155 | 0.359345 | ||||||||
\(709\) | − | 6.49242i | − | 0.243828i | −0.992541 | − | 0.121914i | \(-0.961097\pi\) | ||
0.992541 | − | 0.121914i | \(-0.0389032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.31534 | −0.0868321 | ||||||||
\(712\) | − | 5.12311i | − | 0.191997i | ||||||
\(713\) | 17.3693 | 0.650486 | ||||||||
\(714\) | 2.93087 | 0.109685 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.1231 | 0.714664 | ||||||||
\(717\) | −6.93087 | −0.258838 | ||||||||
\(718\) | 3.87689i | 0.144684i | ||||||||
\(719\) | −25.3693 | −0.946116 | −0.473058 | − | 0.881031i | \(-0.656850\pi\) | ||||
−0.473058 | + | 0.881031i | \(0.656850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.12311i | 0.116311i | ||||||||
\(722\) | −40.0540 | −1.49065 | ||||||||
\(723\) | 20.2462 | 0.752965 | ||||||||
\(724\) | 0.192236 | 0.00714439 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.56155i | 0.317749i | ||||||||
\(727\) | 0.384472i | 0.0142593i | 0.999975 | + | 0.00712964i | \(0.00226945\pi\) | ||||
−0.999975 | + | 0.00712964i | \(0.997731\pi\) | |||||||
\(728\) | 0.246211 | − | 1.56155i | 0.00912520 | − | 0.0578750i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.3542 | 2.75009 | ||||||||
\(732\) | − | 0.684658i | − | 0.0253057i | ||||||
\(733\) | 39.6847 | 1.46579 | 0.732893 | − | 0.680344i | \(-0.238170\pi\) | ||||
0.732893 | + | 0.680344i | \(0.238170\pi\) | |||||||
\(734\) | − | 19.6847i | − | 0.726574i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.12311i | 0.115119i | ||||||||
\(737\) | 6.43845i | 0.237163i | ||||||||
\(738\) | − | 4.56155i | − | 0.167913i | ||||||
\(739\) | 47.4924i | 1.74704i | 0.486791 | + | 0.873519i | \(0.338167\pi\) | ||||
−0.486791 | + | 0.873519i | \(0.661833\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.31534 | − | 27.3693i | 0.158528 | − | 1.00544i | ||||
\(742\) | 2.19224i | 0.0804795i | ||||||||
\(743\) | 26.3693 | 0.967396 | 0.483698 | − | 0.875235i | \(-0.339293\pi\) | ||||
0.483698 | + | 0.875235i | \(0.339293\pi\) | |||||||
\(744\) | 5.56155 | 0.203896 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 32.4384i | − | 1.18766i | ||||||
\(747\) | −14.9309 | −0.546292 | ||||||||
\(748\) | −10.4384 | −0.381667 | ||||||||
\(749\) | 0.138261i | 0.00505193i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.8078 | −0.540343 | −0.270171 | − | 0.962812i | \(-0.587080\pi\) | ||||
−0.270171 | + | 0.962812i | \(0.587080\pi\) | |||||||
\(752\) | 8.12311 | 0.296219 | ||||||||
\(753\) | 11.4384i | 0.416840i | ||||||||
\(754\) | 0.561553 | − | 3.56155i | 0.0204505 | − | 0.129704i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 0.438447i | − | 0.0159462i | ||||||
\(757\) | 2.93087i | 0.106524i | 0.998581 | + | 0.0532621i | \(0.0169619\pi\) | ||||
−0.998581 | + | 0.0532621i | \(0.983038\pi\) | |||||||
\(758\) | 7.31534i | 0.265705i | ||||||||
\(759\) | 4.87689i | 0.177020i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.6695i | 1.54677i | 0.633938 | + | 0.773384i | \(0.281438\pi\) | ||||
−0.633938 | + | 0.773384i | \(0.718562\pi\) | |||||||
\(762\) | 11.4384 | 0.414371 | ||||||||
\(763\) | − | 9.01515i | − | 0.326371i | ||||||
\(764\) | −16.4924 | −0.596675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.9309 | 0.503343 | ||||||||
\(767\) | −34.0540 | − | 5.36932i | −1.22962 | − | 0.193875i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 2.24621i | 0.0810004i | 0.999180 | + | 0.0405002i | \(0.0128951\pi\) | ||||
−0.999180 | + | 0.0405002i | \(0.987105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8078 | −0.569303 | ||||||||
\(772\) | −4.87689 | −0.175523 | ||||||||
\(773\) | −31.2311 | −1.12330 | −0.561652 | − | 0.827374i | \(-0.689834\pi\) | ||||
−0.561652 | + | 0.827374i | \(0.689834\pi\) | |||||||
\(774\) | − | 11.1231i | − | 0.399812i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.1231 | −0.471092 | ||||||||
\(777\) | 2.00000i | 0.0717496i | ||||||||
\(778\) | 6.80776 | 0.244070 | ||||||||
\(779\) | 35.0540 | 1.25594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.7538 | 0.778412 | ||||||||
\(782\) | 20.8769 | 0.746556 | ||||||||
\(783\) | − | 1.00000i | − | 0.0357371i | ||||||
\(784\) | −6.80776 | −0.243134 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 6.31534i | − | 0.225261i | ||||||
\(787\) | 30.9309 | 1.10257 | 0.551283 | − | 0.834318i | \(-0.314138\pi\) | ||||
0.551283 | + | 0.834318i | \(0.314138\pi\) | |||||||
\(788\) | 12.2462 | 0.436253 | ||||||||
\(789\) | −24.7386 | −0.880719 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.86174i | − | 0.0661958i | ||||||
\(792\) | 1.56155i | 0.0554874i | ||||||||
\(793\) | −0.384472 | + | 2.43845i | −0.0136530 | + | 0.0865918i | ||||
\(794\) | −35.0540 | −1.24402 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.93087 | 0.210214 | ||||||||
\(797\) | 48.5464i | 1.71960i | 0.510630 | + | 0.859801i | \(0.329412\pi\) | ||||
−0.510630 | + | 0.859801i | \(0.670588\pi\) | |||||||
\(798\) | 3.36932 | 0.119273 | ||||||||
\(799\) | − | 54.3002i | − | 1.92100i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.12311i | 0.181016i | ||||||||
\(802\) | 22.0000i | 0.776847i | ||||||||
\(803\) | − | 11.1231i | − | 0.392526i | ||||||
\(804\) | − | 4.12311i | − | 0.145411i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.8078 | − | 3.12311i | −0.697699 | − | 0.110007i | ||||
\(807\) | 9.49242i | 0.334149i | ||||||||
\(808\) | −12.4384 | −0.437583 | ||||||||
\(809\) | 7.12311 | 0.250435 | 0.125218 | − | 0.992129i | \(-0.460037\pi\) | ||||
0.125218 | + | 0.992129i | \(0.460037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.1771i | − | 1.16500i | −0.812829 | − | 0.582502i | \(-0.802074\pi\) | ||
0.812829 | − | 0.582502i | \(-0.197926\pi\) | |||||||
\(812\) | 0.438447 | 0.0153865 | ||||||||
\(813\) | 4.19224 | 0.147028 | ||||||||
\(814\) | − | 7.12311i | − | 0.249665i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.68466 | 0.234010 | ||||||||
\(817\) | 85.4773 | 2.99047 | ||||||||
\(818\) | 27.6155i | 0.965554i | ||||||||
\(819\) | −0.246211 | + | 1.56155i | −0.00860332 | + | 0.0545651i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.6155i | 0.405385i | 0.979242 | + | 0.202692i | \(0.0649691\pi\) | ||||
−0.979242 | + | 0.202692i | \(0.935031\pi\) | |||||||
\(822\) | 6.56155i | 0.228860i | ||||||||
\(823\) | − | 28.8078i | − | 1.00418i | −0.864817 | − | 0.502088i | \(-0.832565\pi\) | ||
0.864817 | − | 0.502088i | \(-0.167435\pi\) | |||||||
\(824\) | 7.12311i | 0.248145i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 4.19224i | − | 0.145867i | ||||||
\(827\) | 41.3153 | 1.43668 | 0.718338 | − | 0.695695i | \(-0.244903\pi\) | ||||
0.718338 | + | 0.695695i | \(0.244903\pi\) | |||||||
\(828\) | − | 3.12311i | − | 0.108535i | ||||||
\(829\) | 21.8078 | 0.757415 | 0.378707 | − | 0.925516i | \(-0.376369\pi\) | ||||
0.378707 | + | 0.925516i | \(0.376369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.6155 | −0.541697 | ||||||||
\(832\) | 0.561553 | − | 3.56155i | 0.0194683 | − | 0.123475i | ||||
\(833\) | 45.5076i | 1.57674i | ||||||||
\(834\) | − | 16.4924i | − | 0.571086i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | −5.56155 | −0.192235 | ||||||||
\(838\) | 5.68466 | 0.196373 | ||||||||
\(839\) | − | 40.0000i | − | 1.38095i | −0.723355 | − | 0.690477i | \(-0.757401\pi\) | ||
0.723355 | − | 0.690477i | \(-0.242599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | − | 4.63068i | − | 0.159584i | ||||||
\(843\) | −5.93087 | −0.204270 | ||||||||
\(844\) | −17.3693 | −0.597877 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.12311 | −0.279278 | ||||||||
\(847\) | 3.75379 | 0.128982 | ||||||||
\(848\) | 5.00000i | 0.171701i | ||||||||
\(849\) | 7.36932 | 0.252914 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.2462i | 0.488354i | ||||||||
\(852\) | −13.9309 | −0.477264 | ||||||||
\(853\) | −28.8078 | −0.986359 | −0.493180 | − | 0.869928i | \(-0.664165\pi\) | ||||
−0.493180 | + | 0.869928i | \(0.664165\pi\) | |||||||
\(854\) | −0.300187 | −0.0102722 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.315342i | 0.0107782i | ||||||||
\(857\) | 31.6155i | 1.07997i | 0.841676 | + | 0.539983i | \(0.181569\pi\) | ||||
−0.841676 | + | 0.539983i | \(0.818431\pi\) | |||||||
\(858\) | 0.876894 | − | 5.56155i | 0.0299367 | − | 0.189868i | ||||
\(859\) | −12.7386 | −0.434637 | −0.217318 | − | 0.976101i | \(-0.569731\pi\) | ||||
−0.217318 | + | 0.976101i | \(0.569731\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | − | 8.17708i | − | 0.278512i | ||||||
\(863\) | −44.8617 | −1.52711 | −0.763556 | − | 0.645742i | \(-0.776548\pi\) | ||||
−0.763556 | + | 0.645742i | \(0.776548\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 5.05398i | − | 0.171741i | ||||||
\(867\) | − | 27.6847i | − | 0.940220i | ||||||
\(868\) | − | 2.43845i | − | 0.0827663i | ||||||
\(869\) | − | 3.61553i | − | 0.122648i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31534 | + | 14.6847i | −0.0784524 | + | 0.497571i | ||||
\(872\) | − | 20.5616i | − | 0.696302i | ||||||
\(873\) | 13.1231 | 0.444150 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.12311i | 0.240667i | ||||||||
\(877\) | 32.1771 | 1.08654 | 0.543271 | − | 0.839557i | \(-0.317185\pi\) | ||||
0.543271 | + | 0.839557i | \(0.317185\pi\) | |||||||
\(878\) | 27.3002 | 0.921337 | ||||||||
\(879\) | 0.630683i | 0.0212724i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.0388 | −1.71954 | −0.859771 | − | 0.510680i | \(-0.829394\pi\) | ||||
−0.859771 | + | 0.510680i | \(0.829394\pi\) | |||||||
\(882\) | 6.80776 | 0.229229 | ||||||||
\(883\) | − | 17.6155i | − | 0.592810i | −0.955062 | − | 0.296405i | \(-0.904212\pi\) | ||
0.955062 | − | 0.296405i | \(-0.0957878\pi\) | |||||||
\(884\) | −23.8078 | − | 3.75379i | −0.800742 | − | 0.126254i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.5616i | 0.959544i | ||||||||
\(887\) | − | 39.6155i | − | 1.33016i | −0.746772 | − | 0.665080i | \(-0.768398\pi\) | ||
0.746772 | − | 0.665080i | \(-0.231602\pi\) | |||||||
\(888\) | 4.56155i | 0.153076i | ||||||||
\(889\) | − | 5.01515i | − | 0.168203i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.56155i | − | 0.0523140i | ||||||
\(892\) | 15.3693 | 0.514603 | ||||||||
\(893\) | − | 62.4233i | − | 2.08892i | ||||||
\(894\) | −19.3693 | −0.647807 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.438447 | 0.0146475 | ||||||||
\(897\) | −1.75379 | + | 11.1231i | −0.0585573 | + | 0.371390i | ||||
\(898\) | − | 5.43845i | − | 0.181483i | ||||||
\(899\) | − | 5.56155i | − | 0.185488i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.4233 | 1.11349 | ||||||||
\(902\) | 7.12311 | 0.237173 | ||||||||
\(903\) | −4.87689 | −0.162293 | ||||||||
\(904\) | − | 4.24621i | − | 0.141227i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.31534 | −0.110145 | ||||||||
\(907\) | 14.3845i | 0.477629i | 0.971065 | + | 0.238814i | \(0.0767587\pi\) | ||||
−0.971065 | + | 0.238814i | \(0.923241\pi\) | |||||||
\(908\) | −3.31534 | −0.110023 | ||||||||
\(909\) | 12.4384 | 0.412557 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6307 | −0.749788 | −0.374894 | − | 0.927068i | \(-0.622321\pi\) | ||||
−0.374894 | + | 0.927068i | \(0.622321\pi\) | |||||||
\(912\) | 7.68466 | 0.254464 | ||||||||
\(913\) | − | 23.3153i | − | 0.771625i | ||||||
\(914\) | −28.7386 | −0.950590 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 7.19224i | − | 0.237638i | ||||||
\(917\) | −2.76894 | −0.0914386 | ||||||||
\(918\) | −6.68466 | −0.220627 | ||||||||
\(919\) | 18.5616 | 0.612289 | 0.306145 | − | 0.951985i | \(-0.400961\pi\) | ||||
0.306145 | + | 0.951985i | \(0.400961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.06913i | 0.0681802i | ||||||||
\(922\) | − | 22.2462i | − | 0.732640i | ||||||
\(923\) | 49.6155 | + | 7.82292i | 1.63312 | + | 0.257495i | ||||
\(924\) | 0.684658 | 0.0225236 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.5616 | −0.379936 | ||||||||
\(927\) | − | 7.12311i | − | 0.233953i | ||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | − | 50.4233i | − | 1.65433i | −0.561956 | − | 0.827167i | \(-0.689951\pi\) | ||
0.561956 | − | 0.827167i | \(-0.310049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.3153i | 1.71457i | ||||||||
\(932\) | 3.12311i | 0.102301i | ||||||||
\(933\) | 14.8769i | 0.487048i | ||||||||
\(934\) | 40.8078i | 1.33527i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.561553 | + | 3.56155i | −0.0183549 | + | 0.116413i | ||||
\(937\) | 11.0691i | 0.361613i | 0.983519 | + | 0.180806i | \(0.0578707\pi\) | ||||
−0.983519 | + | 0.180806i | \(0.942129\pi\) | |||||||
\(938\) | −1.80776 | −0.0590256 | ||||||||
\(939\) | −24.8617 | −0.811332 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 40.7386i | − | 1.32804i | −0.747714 | − | 0.664021i | \(-0.768849\pi\) | ||
0.747714 | − | 0.664021i | \(-0.231151\pi\) | |||||||
\(942\) | −10.6847 | −0.348125 | ||||||||
\(943\) | −14.2462 | −0.463920 | ||||||||
\(944\) | − | 9.56155i | − | 0.311202i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.3693 | 0.564725 | ||||||||
\(947\) | −16.9309 | −0.550179 | −0.275090 | − | 0.961419i | \(-0.588708\pi\) | ||||
−0.275090 | + | 0.961419i | \(0.588708\pi\) | |||||||
\(948\) | 2.31534i | 0.0751988i | ||||||||
\(949\) | 4.00000 | − | 25.3693i | 0.129845 | − | 0.823523i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 30.0000i | − | 0.972817i | ||||||
\(952\) | − | 2.93087i | − | 0.0949900i | ||||||
\(953\) | 1.80776i | 0.0585592i | 0.999571 | + | 0.0292796i | \(0.00932132\pi\) | ||||
−0.999571 | + | 0.0292796i | \(0.990679\pi\) | |||||||
\(954\) | − | 5.00000i | − | 0.161881i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.93087i | 0.224160i | ||||||||
\(957\) | 1.56155 | 0.0504778 | ||||||||
\(958\) | 32.1231i | 1.03785i | ||||||||
\(959\) | 2.87689 | 0.0928998 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0691303 | 0.00223001 | ||||||||
\(962\) | 2.56155 | − | 16.2462i | 0.0825878 | − | 0.523799i | ||||
\(963\) | − | 0.315342i | − | 0.0101617i | ||||||
\(964\) | − | 20.2462i | − | 0.652087i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.36932 | −0.0440570 | ||||||||
\(967\) | −43.6695 | −1.40432 | −0.702158 | − | 0.712021i | \(-0.747780\pi\) | ||||
−0.702158 | + | 0.712021i | \(0.747780\pi\) | |||||||
\(968\) | 8.56155 | 0.275179 | ||||||||
\(969\) | − | 51.3693i | − | 1.65022i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.93087 | 0.0619646 | 0.0309823 | − | 0.999520i | \(-0.490136\pi\) | ||||
0.0309823 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | −7.23106 | −0.231817 | ||||||||
\(974\) | −6.68466 | −0.214190 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.684658 | −0.0219154 | ||||||||
\(977\) | 31.3693 | 1.00359 | 0.501797 | − | 0.864986i | \(-0.332673\pi\) | ||||
0.501797 | + | 0.864986i | \(0.332673\pi\) | |||||||
\(978\) | 16.4924i | 0.527370i | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.5616i | 0.656480i | ||||||||
\(982\) | 38.7386 | 1.23620 | ||||||||
\(983\) | 9.06913 | 0.289260 | 0.144630 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144630 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(984\) | −4.56155 | −0.145417 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 6.68466i | − | 0.212883i | ||||||
\(987\) | 3.56155i | 0.113365i | ||||||||
\(988\) | −27.3693 | − | 4.31534i | −0.870734 | − | 0.137289i | ||||
\(989\) | −34.7386 | −1.10462 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.6847 | −0.815900 | −0.407950 | − | 0.913004i | \(-0.633756\pi\) | ||||
−0.407950 | + | 0.913004i | \(0.633756\pi\) | |||||||
\(992\) | − | 5.56155i | − | 0.176579i | ||||||
\(993\) | 24.4924 | 0.777244 | ||||||||
\(994\) | 6.10795i | 0.193732i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.9309i | 0.473103i | ||||||||
\(997\) | 53.6695i | 1.69973i | 0.527000 | + | 0.849865i | \(0.323317\pi\) | ||||
−0.527000 | + | 0.849865i | \(0.676683\pi\) | |||||||
\(998\) | − | 28.1231i | − | 0.890221i | ||||||
\(999\) | − | 4.56155i | − | 0.144321i |
(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 | 1950.2.f.p.649.3 | 4 | ||
5.2 | odd | 4 | 1950.2.b.j.1351.3 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.b.i.1351.2 | ✓ | 4 | ||
5.4 | even | 2 | 1950.2.f.k.649.2 | 4 | |||
13.12 | even | 2 | 1950.2.f.k.649.4 | 4 | |||
65.12 | odd | 4 | 1950.2.b.j.1351.2 | yes | 4 | ||
65.38 | odd | 4 | 1950.2.b.i.1351.3 | yes | 4 | ||
65.64 | even | 2 | inner | 1950.2.f.p.649.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.b.i.1351.2 | ✓ | 4 | 5.3 | odd | 4 | ||
1950.2.b.i.1351.3 | yes | 4 | 65.38 | odd | 4 | ||
1950.2.b.j.1351.2 | yes | 4 | 65.12 | odd | 4 | ||
1950.2.b.j.1351.3 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.f.k.649.2 | 4 | 5.4 | even | 2 | |||
1950.2.f.k.649.4 | 4 | 13.12 | even | 2 | |||
1950.2.f.p.649.1 | 4 | 65.64 | even | 2 | inner | ||
1950.2.f.p.649.3 | 4 | 1.1 | even | 1 | trivial |