Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("768.383");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.2.f.b.383.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23607i | 0.467190i | 0.972334 | + | 0.233595i | \(0.0750489\pi\) | ||||
−0.972334 | + | 0.233595i | \(0.924951\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607i | 1.57873i | 0.613922 | + | 0.789367i | \(0.289591\pi\) | ||||
−0.613922 | + | 0.789367i | \(0.710409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.47214i | − | 1.24035i | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||
0.784465 | − | 0.620174i | \(-0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.23607 | + | 2.00000i | 1.35195 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.47214i | − | 0.599581i | −0.954005 | − | 0.299791i | \(-0.903083\pi\) | ||
0.954005 | − | 0.299791i | \(-0.0969168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.763932 | 0.175258 | 0.0876290 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876290 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.763932 | − | 2.00000i | 0.166704 | − | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.76393 | 0.884640 | 0.442320 | − | 0.896857i | \(-0.354156\pi\) | ||||
0.442320 | + | 0.896857i | \(0.354156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.23607i | − | 0.940426i | −0.882553 | − | 0.470213i | \(-0.844177\pi\) | ||
0.882553 | − | 0.470213i | \(-0.155823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607 | − | 8.47214i | 0.563327 | − | 1.47481i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.00000i | − | 0.676123i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.47214i | − | 1.39281i | −0.717649 | − | 0.696405i | \(-0.754782\pi\) | ||
0.717649 | − | 0.696405i | \(-0.245218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.76393 | + | 7.23607i | −0.442583 | + | 1.15870i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.47214i | − | 1.01078i | −0.862892 | − | 0.505389i | \(-0.831349\pi\) | ||
0.862892 | − | 0.505389i | \(-0.168651\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.23607 | 1.10349 | 0.551745 | − | 0.834013i | \(-0.313962\pi\) | ||||
0.551745 | + | 0.834013i | \(0.313962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.23607 | − | 6.47214i | −1.07869 | − | 0.964809i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.47214 | 0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.52786 | + | 4.00000i | −0.213944 | + | 0.560112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.23607 | −0.444508 | −0.222254 | − | 0.974989i | \(-0.571341\pi\) | ||||
−0.222254 | + | 0.974989i | \(0.571341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 16.9443i | − | 2.28477i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.23607 | − | 0.472136i | −0.163721 | − | 0.0625359i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.23607i | − | 0.160922i | −0.996758 | − | 0.0804612i | \(-0.974361\pi\) | ||
0.996758 | − | 0.0804612i | \(-0.0256393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.472136i | 0.0604508i | 0.999543 | + | 0.0302254i | \(0.00962251\pi\) | ||||
−0.999543 | + | 0.0302254i | \(0.990377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.47214 | + | 2.76393i | −0.311460 | + | 0.348223i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721i | 1.79505i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.70820 | 1.18605 | 0.593023 | − | 0.805186i | \(-0.297934\pi\) | ||||
0.593023 | + | 0.805186i | \(0.297934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | + | 1.52786i | 0.481543 | + | 0.183933i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4164 | 1.82959 | 0.914796 | − | 0.403917i | \(-0.132352\pi\) | ||||
0.914796 | + | 0.403917i | \(0.132352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.85410 | − | 3.38197i | −1.02238 | − | 0.390516i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.291796i | − | 0.0328296i | −0.999865 | − | 0.0164148i | \(-0.994775\pi\) | ||
0.999865 | − | 0.0164148i | \(-0.00522523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.76393i | − | 0.303381i | −0.988428 | − | 0.151690i | \(-0.951528\pi\) | ||
0.988428 | − | 0.151690i | \(-0.0484717\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000i | 0.867722i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.70820 | − | 2.94427i | −0.826406 | − | 0.315659i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.00000i | − | 0.423999i | −0.977270 | − | 0.212000i | \(-0.932002\pi\) | ||
0.977270 | − | 0.212000i | \(-0.0679975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.52786 | 0.579478 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.23607 | + | 8.47214i | −0.335565 | + | 0.878520i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47214 | −0.253636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.472136 | 0.0479381 | 0.0239691 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239691 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4721 | + | 11.7082i | −1.05249 | + | 1.17672i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.70820 | 0.169973 | 0.0849863 | − | 0.996382i | \(-0.472915\pi\) | ||||
0.0849863 | + | 0.996382i | \(0.472915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1803i | 1.39723i | 0.715498 | + | 0.698615i | \(0.246200\pi\) | ||||
−0.715498 | + | 0.698615i | \(0.753800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.47214 | + | 6.47214i | −0.241256 | + | 0.631616i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.1803i | − | 1.37087i | −0.728136 | − | 0.685433i | \(-0.759613\pi\) | ||
0.728136 | − | 0.685433i | \(-0.240387\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.47214i | 0.811483i | 0.913988 | + | 0.405742i | \(0.132987\pi\) | ||||
−0.913988 | + | 0.405742i | \(0.867013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.23607 | + | 13.7082i | −0.496986 | + | 1.30113i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.00000i | − | 0.752577i | −0.926503 | − | 0.376288i | \(-0.877200\pi\) | ||
0.926503 | − | 0.376288i | \(-0.122800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.94427 | − | 10.0000i | 0.826898 | − | 0.924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.05573 | 0.280118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.4164 | −1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | + | 10.4721i | −0.360668 | + | 0.944241i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.2361i | − | 1.17451i | −0.809402 | − | 0.587256i | \(-0.800208\pi\) | ||
0.809402 | − | 0.587256i | \(-0.199792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7082 | − | 4.47214i | −1.03085 | − | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.76393i | 0.590967i | 0.955348 | + | 0.295484i | \(0.0954808\pi\) | ||||
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.944272i | 0.0818788i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.70820 | + | 14.9443i | 0.663417 | + | 1.28620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.52786i | − | 0.130534i | −0.997868 | − | 0.0652671i | \(-0.979210\pi\) | ||
0.997868 | − | 0.0652671i | \(-0.0207899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.70820 | −0.823439 | −0.411720 | − | 0.911311i | \(-0.635072\pi\) | ||||
−0.411720 | + | 0.911311i | \(0.635072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | + | 4.94427i | 1.09010 | + | 0.416383i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.4164 | −1.28026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.85410 | − | 3.38197i | −0.730274 | − | 0.278940i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.70820 | 0.795327 | 0.397664 | − | 0.917531i | \(-0.369821\pi\) | ||||
0.397664 | + | 0.917531i | \(0.369821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.7082i | − | 1.60383i | −0.597438 | − | 0.801915i | \(-0.703814\pi\) | ||
0.597438 | − | 0.801915i | \(-0.296186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.94427 | − | 5.52786i | 0.399721 | − | 0.446901i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9443i | 1.36100i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.47214i | − | 0.356915i | −0.983948 | − | 0.178458i | \(-0.942889\pi\) | ||
0.983948 | − | 0.178458i | \(-0.0571108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.23607 | + | 2.00000i | 0.415247 | + | 0.158610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.05573i | − | 0.240825i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.18034 | −0.327429 | −0.163715 | − | 0.986508i | \(-0.552348\pi\) | ||||
−0.163715 | + | 0.986508i | \(0.552348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.4721 | + | 27.4164i | −0.815255 | + | 2.13436i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5279 | −1.04682 | −0.523409 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523409 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70820 | + | 1.52786i | 0.130630 | + | 0.116839i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.6525 | 1.72224 | 0.861118 | − | 0.508405i | \(-0.169765\pi\) | ||||
0.861118 | + | 0.508405i | \(0.169765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.76393i | 0.511305i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.763932 | + | 2.00000i | −0.0574206 | + | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.18034i | − | 0.461940i | −0.972961 | − | 0.230970i | \(-0.925810\pi\) | ||
0.972961 | − | 0.230970i | \(-0.0741900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4721i | 1.52168i | 0.648938 | + | 0.760841i | \(0.275213\pi\) | ||||
−0.648938 | + | 0.760841i | \(0.724787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.291796 | − | 0.763932i | 0.0215702 | − | 0.0564715i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.4164i | 2.01569i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9443 | 0.946579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.70820 | − | 2.94427i | 0.415211 | − | 0.214164i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9443 | −0.936615 | −0.468307 | − | 0.883566i | \(-0.655136\pi\) | ||||
−0.468307 | + | 0.883566i | \(0.655136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8885 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.94427 | − | 23.4164i | 0.640513 | − | 1.67688i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.76393 | 0.339416 | 0.169708 | − | 0.985494i | \(-0.445718\pi\) | ||||
0.169708 | + | 0.985494i | \(0.445718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.18034i | 0.438113i | 0.975712 | + | 0.219056i | \(0.0702979\pi\) | ||||
−0.975712 | + | 0.219056i | \(0.929702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.7082 | − | 6.00000i | −1.10797 | − | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.88854i | 0.413295i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.9443i | 1.46281i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.52786 | − | 4.94427i | −0.384213 | − | 0.343651i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000i | 0.276686i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2361 | −0.773523 | −0.386761 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386761 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.9443 | − | 9.52786i | −1.70915 | − | 0.652838i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.4164 | −1.59699 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.47214 | 0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.23607 | − | 1.23607i | −0.218673 | − | 0.0835257i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.0557 | −0.743689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.1803i | − | 0.681726i | −0.940113 | − | 0.340863i | \(-0.889281\pi\) | ||
0.940113 | − | 0.340863i | \(-0.110719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2361 | + | 10.9443i | 0.815738 | + | 0.729618i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.18034i | 0.144714i | 0.997379 | + | 0.0723571i | \(0.0230521\pi\) | ||||
−0.997379 | + | 0.0723571i | \(0.976948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.5279i | − | 0.761783i | −0.924620 | − | 0.380891i | \(-0.875617\pi\) | ||
0.924620 | − | 0.380891i | \(-0.124383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.4721 | + | 4.00000i | 0.689016 | + | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.9443i | 1.63415i | 0.576529 | + | 0.817077i | \(0.304407\pi\) | ||||
−0.576529 | + | 0.817077i | \(0.695593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8885 | 1.68878 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.180340 | + | 0.472136i | −0.0117143 | + | 0.0306685i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.7082 | −1.13134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.41641i | − | 0.217381i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.70820 | + | 4.47214i | −0.108253 | + | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.7082i | − | 1.49645i | −0.663446 | − | 0.748224i | \(-0.730907\pi\) | ||
0.663446 | − | 0.748224i | \(-0.269093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.9443i | − | 0.813799i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.94427 | − | 12.9443i | 0.309622 | − | 0.810602i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 20.9443i | − | 1.30647i | −0.757156 | − | 0.653234i | \(-0.773412\pi\) | ||
0.757156 | − | 0.653234i | \(-0.226588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4721 | 0.650707 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.6525 | + | 9.52786i | 0.659372 | + | 0.589760i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4721 | −0.645740 | −0.322870 | − | 0.946443i | \(-0.604648\pi\) | ||||
−0.322870 | + | 0.946443i | \(0.604648\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4721 | 0.643298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.47214 | + | 6.47214i | −0.151292 | + | 0.396088i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.1803 | −0.986533 | −0.493266 | − | 0.869878i | \(-0.664197\pi\) | ||||
−0.493266 | + | 0.869878i | \(0.664197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.291796i | − | 0.0177253i | −0.999961 | − | 0.00886267i | \(-0.997179\pi\) | ||
0.999961 | − | 0.00886267i | \(-0.00282111\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.94427 | − | 3.41641i | −0.541332 | − | 0.206770i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.6525i | 1.72781i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.52786i | 0.452306i | 0.974092 | + | 0.226153i | \(0.0726149\pi\) | ||||
−0.974092 | + | 0.226153i | \(0.927385\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.4721 | − | 11.7082i | 0.626950 | − | 0.700952i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.9443i | − | 1.48805i | −0.668151 | − | 0.744025i | \(-0.732914\pi\) | ||
0.668151 | − | 0.744025i | \(-0.267086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.7639 | −1.23429 | −0.617144 | − | 0.786850i | \(-0.711710\pi\) | ||||
−0.617144 | + | 0.786850i | \(0.711710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | + | 1.52786i | 0.236940 | + | 0.0905029i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.763932 | − | 0.291796i | −0.0447825 | − | 0.0171054i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7639 | 1.21304 | 0.606521 | − | 0.795068i | \(-0.292565\pi\) | ||||
0.606521 | + | 0.795068i | \(0.292565\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000i | 0.232889i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.1803 | − | 12.4721i | 1.40309 | − | 0.723707i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0557i | 0.639369i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.94427i | 0.515539i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.76393 | − | 1.05573i | −0.158784 | − | 0.0606500i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.52786i | − | 0.0874852i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.5967 | 1.57503 | 0.787515 | − | 0.616296i | \(-0.211367\pi\) | ||||
0.787515 | + | 0.616296i | \(0.211367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.76393 | − | 22.9443i | 0.498563 | − | 1.30525i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.52786 | −0.313456 | −0.156728 | − | 0.987642i | \(-0.550095\pi\) | ||||
−0.156728 | + | 0.987642i | \(0.550095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.472136 | 0.0266867 | 0.0133434 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133434 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.00000 | − | 8.94427i | 0.450749 | − | 0.503953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1246 | −0.737152 | −0.368576 | − | 0.929598i | \(-0.620155\pi\) | ||||
−0.368576 | + | 0.929598i | \(0.620155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9443i | 1.39661i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.76393 | + | 22.9443i | −0.489155 | + | 1.28062i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.88854i | − | 0.105081i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 24.4721i | − | 1.35747i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.23607 | − | 13.7082i | 0.289555 | − | 0.758065i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.88854i | − | 0.545173i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5410 | −1.78862 | −0.894308 | − | 0.447452i | \(-0.852332\pi\) | ||||
−0.894308 | + | 0.447452i | \(0.852332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.9443 | − | 18.9443i | 0.928540 | − | 1.03814i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.4164 | −1.71646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3607 | 1.21806 | 0.609032 | − | 0.793146i | \(-0.291558\pi\) | ||||
0.609032 | + | 0.793146i | \(0.291558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.94427 | + | 12.9443i | −0.268536 | + | 0.703036i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.4164 | 1.48468 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164i | 0.832408i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.9443 | − | 4.94427i | −0.696896 | − | 0.266191i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 23.7082i | − | 1.27272i | −0.771391 | − | 0.636362i | \(-0.780439\pi\) | ||
0.771391 | − | 0.636362i | \(-0.219561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.4721i | − | 1.52408i | −0.647531 | − | 0.762039i | \(-0.724198\pi\) | ||
0.647531 | − | 0.762039i | \(-0.275802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6525 | + | 10.6525i | −1.10235 | + | 0.568587i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.88854i | − | 0.526314i | −0.964753 | − | 0.263157i | \(-0.915236\pi\) | ||
0.964753 | − | 0.263157i | \(-0.0847637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −49.8885 | −2.64781 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.94427 | − | 1.88854i | −0.261679 | − | 0.0999523i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.4164 | 1.65809 | 0.829047 | − | 0.559178i | \(-0.188883\pi\) | ||||
0.829047 | + | 0.559178i | \(0.188883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4164 | −0.969285 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.5623 | + | 10.1459i | 1.39416 | + | 0.532522i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.47214 | −0.338767 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.23607i | − | 0.273321i | −0.990618 | − | 0.136660i | \(-0.956363\pi\) | ||
0.990618 | − | 0.136660i | \(-0.0436369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.9443 | − | 14.4721i | 0.673852 | − | 0.753389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.00000i | − | 0.207670i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58359i | 0.133773i | 0.997761 | + | 0.0668867i | \(0.0213066\pi\) | ||||
−0.997761 | + | 0.0668867i | \(0.978693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.47214 | + | 0.944272i | 0.127661 | + | 0.0487620i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 21.3050i | − | 1.09726i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.6525 | −0.547181 | −0.273590 | − | 0.961846i | \(-0.588211\pi\) | ||||
−0.273590 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.18034 | + | 21.4164i | −0.419092 | + | 1.09720i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9443 | 1.47898 | 0.739492 | − | 0.673166i | \(-0.235066\pi\) | ||||
0.739492 | + | 0.673166i | \(0.235066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.9443 | 1.06742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.1803 | + | 14.4721i | 0.822493 | + | 0.735660i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.1803 | −1.63161 | −0.815804 | − | 0.578328i | \(-0.803705\pi\) | ||||
−0.815804 | + | 0.578328i | \(0.803705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.11146i | 0.309070i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.18034 | − | 10.9443i | 0.210870 | − | 0.552065i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.944272i | 0.0475115i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.4164i | − | 0.874104i | −0.899436 | − | 0.437052i | \(-0.856022\pi\) | ||
0.899436 | − | 0.437052i | \(-0.143978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.583592 | − | 1.52786i | 0.0292161 | − | 0.0764889i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.3607i | 1.41626i | 0.706080 | + | 0.708132i | \(0.250462\pi\) | ||||
−0.706080 | + | 0.708132i | \(0.749538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.4164 | −1.16645 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.23607 | − | 28.9443i | −0.160802 | − | 1.43825i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.3607 | 2.19888 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8885 | 1.57679 | 0.788394 | − | 0.615171i | \(-0.210913\pi\) | ||||
0.788394 | + | 0.615171i | \(0.210913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.944272 | + | 2.47214i | −0.0465775 | + | 0.121941i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.52786 | 0.0751813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.94427i | 0.439057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7082 | + | 6.00000i | 0.769234 | + | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1803i | 0.497342i | 0.968588 | + | 0.248671i | \(0.0799938\pi\) | ||||
−0.968588 | + | 0.248671i | \(0.920006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.4164i | − | 1.04377i | −0.853015 | − | 0.521886i | \(-0.825229\pi\) | ||
0.853015 | − | 0.521886i | \(-0.174771\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.8885 | − | 16.0000i | −0.869771 | − | 0.777947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 13.5279i | − | 0.656198i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.583592 | −0.0282420 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.8885 | − | 14.4721i | −1.82928 | − | 0.698721i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4721 | 0.791600 | 0.395800 | − | 0.918337i | \(-0.370467\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.9443 | + | 9.52786i | 1.19599 | + | 0.456826i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.88854 | −0.0903413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.1803i | 1.05861i | 0.848432 | + | 0.529305i | \(0.177547\pi\) | ||||
−0.848432 | + | 0.529305i | \(0.822453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2361 | + | 10.9443i | 0.582670 | + | 0.521156i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2918i | 0.774047i | 0.922070 | + | 0.387023i | \(0.126497\pi\) | ||||
−0.922070 | + | 0.387023i | \(0.873503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9443i | 0.613617i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.7082 | − | 6.00000i | −0.742973 | − | 0.283790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.583592i | 0.0275414i | 0.999905 | + | 0.0137707i | \(0.00438349\pi\) | ||||
−0.999905 | + | 0.0137707i | \(0.995617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.8885 | 1.59575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.1803 | + | 31.8885i | −0.572282 | + | 1.49825i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.8885 | −0.838628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.4164 | + | 5.88854i | −0.532872 | + | 0.274854i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.18034 | −0.380996 | −0.190498 | − | 0.981688i | \(-0.561010\pi\) | ||||
−0.190498 | + | 0.981688i | \(0.561010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.7639i | 1.61562i | 0.589445 | + | 0.807808i | \(0.299346\pi\) | ||||
−0.589445 | + | 0.807808i | \(0.700654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.4721 | − | 27.4164i | 0.485634 | − | 1.27141i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.7639i | − | 0.498095i | −0.968491 | − | 0.249048i | \(-0.919882\pi\) | ||
0.968491 | − | 0.249048i | \(-0.0801176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000i | 0.554109i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.76393 | + | 7.23607i | −0.127355 | + | 0.333420i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.8885i | 1.74212i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.18034 | 0.191807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.23607 | − | 6.47214i | −0.331317 | − | 0.296339i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.11146 | −0.279240 | −0.139620 | − | 0.990205i | \(-0.544588\pi\) | ||||
−0.139620 | + | 0.990205i | \(0.544588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.8885 | −1.72757 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.88854 | + | 4.94427i | −0.0859317 | + | 0.224972i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.52786 | −0.0693767 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.6525i | − | 1.47962i | −0.672813 | − | 0.739812i | \(-0.734914\pi\) | ||
0.672813 | − | 0.739812i | \(-0.265086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.76393 | + | 2.58359i | 0.305876 | + | 0.116834i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.0689i | − | 1.44725i | −0.690194 | − | 0.723624i | \(-0.742475\pi\) | ||
0.690194 | − | 0.723624i | \(-0.257525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.7771i | − | 0.530413i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.8885 | − | 37.8885i | 1.52318 | − | 1.70296i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.0557i | 0.854766i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.2361 | −1.21925 | −0.609627 | − | 0.792688i | \(-0.708681\pi\) | ||||
−0.609627 | + | 0.792688i | \(0.708681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.8885 | + | 8.36068i | 0.977908 | + | 0.373528i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5279 | −0.959880 | −0.479940 | − | 0.877301i | \(-0.659342\pi\) | ||||
−0.479940 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.52786 | −0.245987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3262 | + | 4.32624i | 0.503016 | + | 0.192135i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7082 | 1.13950 | 0.569748 | − | 0.821819i | \(-0.307041\pi\) | ||||
0.569748 | + | 0.821819i | \(0.307041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.47214i | 0.109361i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.81966 | − | 3.52786i | −0.0803400 | − | 0.155759i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 45.8885i | − | 2.02209i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 41.8885i | − | 1.84226i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.6525 | − | 14.0000i | −1.60887 | − | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.3607i | 1.06726i | 0.845718 | + | 0.533630i | \(0.179173\pi\) | ||||
−0.845718 | + | 0.533630i | \(0.820827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8197 | −0.516838 | −0.258419 | − | 0.966033i | \(-0.583201\pi\) | ||||
−0.258419 | + | 0.966033i | \(0.583201\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.18034 | − | 10.9443i | 0.182445 | − | 0.477647i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9443 | −0.563861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.47214 | − | 2.76393i | 0.107282 | − | 0.119944i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.9443 | −1.25372 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.8885i | 1.98393i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.81966 | + | 10.0000i | −0.164831 | + | 0.431532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6525i | 1.23415i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3607i | 1.13333i | 0.823947 | + | 0.566667i | \(0.191767\pi\) | ||||
−0.823947 | + | 0.566667i | \(0.808233\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6525 | − | 33.1246i | 0.542970 | − | 1.42151i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 27.4164i | − | 1.17439i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.23607 | −0.309392 | −0.154696 | − | 0.987962i | \(-0.549440\pi\) | ||||
−0.154696 | + | 0.987962i | \(0.549440\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.944272 | + | 1.05573i | −0.0403005 | + | 0.0450574i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.63932 | 0.155040 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.360680 | 0.0153377 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9443 | − | 44.3607i | 0.719244 | − | 1.88301i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6525 | 0.620845 | 0.310423 | − | 0.950599i | \(-0.399529\pi\) | ||||
0.310423 | + | 0.950599i | \(0.399529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 32.3607i | − | 1.36871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.9443 | − | 8.00000i | −0.884268 | − | 0.337760i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.5410i | − | 1.28715i | −0.765383 | − | 0.643575i | \(-0.777450\pi\) | ||
0.765383 | − | 0.643575i | \(-0.222550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.8885i | 1.08914i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.0557 | + | 1.23607i | −0.464297 | + | 0.0519100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 46.4721i | − | 1.94821i | −0.226089 | − | 0.974107i | \(-0.572594\pi\) | ||
0.226089 | − | 0.974107i | \(-0.427406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.12461 | 0.214458 | 0.107229 | − | 0.994234i | \(-0.465802\pi\) | ||||
0.107229 | + | 0.994234i | \(0.465802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.9443 | + | 8.00000i | 0.874960 | + | 0.334205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5279 | −0.564151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4721 | 1.18531 | 0.592655 | − | 0.805456i | \(-0.298080\pi\) | ||||
0.592655 | + | 0.805456i | \(0.298080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.2361 | + | 7.34752i | 0.799424 | + | 0.305353i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.41641 | 0.141736 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.9443i | − | 0.701760i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.9443 | + | 32.3607i | −1.19670 | + | 1.33795i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5967i | 0.891393i | 0.895184 | + | 0.445697i | \(0.147044\pi\) | ||||
−0.895184 | + | 0.445697i | \(0.852956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.00000i | − | 0.164817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.70820 | − | 2.94427i | −0.317073 | − | 0.121111i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.9443i | − | 1.18860i | −0.804244 | − | 0.594299i | \(-0.797429\pi\) | ||
0.804244 | − | 0.594299i | \(-0.202571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.88854 | −0.405391 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.81966 | − | 10.0000i | 0.156328 | − | 0.409273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.41641 | 0.303026 | 0.151513 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151513 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.7771 | −1.37780 | −0.688898 | − | 0.724858i | \(-0.741905\pi\) | ||||
−0.688898 | + | 0.724858i | \(0.741905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.7082 | + | 19.4164i | 0.884026 | + | 0.790697i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 53.1246 | 2.15982 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7639i | 1.41102i | 0.708698 | + | 0.705512i | \(0.249283\pi\) | ||||
−0.708698 | + | 0.705512i | \(0.750717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.63932 | − | 9.52786i | 0.147473 | − | 0.386089i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7771i | 1.44739i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3050i | 0.779720i | 0.920874 | + | 0.389860i | \(0.127477\pi\) | ||||
−0.920874 | + | 0.389860i | \(0.872523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.9443 | − | 33.8885i | 0.521963 | − | 1.36652i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 21.8885i | − | 0.881200i | −0.897704 | − | 0.440600i | \(-0.854766\pi\) | ||
0.897704 | − | 0.440600i | \(-0.145234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.1246 | 1.17062 | 0.585308 | − | 0.810811i | \(-0.300973\pi\) | ||||
0.585308 | + | 0.810811i | \(0.300973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.88854 | + | 11.4164i | 0.236299 | + | 0.458125i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.94427 | 0.198088 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.47214 | − | 6.47214i | 0.0987276 | − | 0.258472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.9443 | −0.835103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.1246i | 0.761339i | 0.924711 | + | 0.380669i | \(0.124306\pi\) | ||||
−0.924711 | + | 0.380669i | \(0.875694\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1803 | + | 6.94427i | 0.722604 | + | 0.276010i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.8328i | 1.69977i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 24.4721i | − | 0.969621i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.4721 | + | 30.8328i | 1.36370 | + | 1.21973i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.3050i | 0.999485i | 0.866174 | + | 0.499743i | \(0.166572\pi\) | ||||
−0.866174 | + | 0.499743i | \(0.833428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.3475 | −0.526375 | −0.263187 | − | 0.964745i | \(-0.584774\pi\) | ||||
−0.263187 | + | 0.964745i | \(0.584774\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.8885 | + | 14.4721i | 1.49186 | + | 0.569840i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.3050 | −1.30935 | −0.654676 | − | 0.755909i | \(-0.727195\pi\) | ||||
−0.654676 | + | 0.755909i | \(0.727195\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.47214 | 0.254054 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4721 | − | 4.00000i | −0.410435 | − | 0.156772i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.2918 | −0.559281 | −0.279641 | − | 0.960105i | \(-0.590215\pi\) | ||||
−0.279641 | + | 0.960105i | \(0.590215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21.8885i | − | 0.855256i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.47214 | + | 4.00000i | 0.174475 | + | 0.156055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 28.2918i | − | 1.10209i | −0.834475 | − | 0.551046i | \(-0.814229\pi\) | ||
0.834475 | − | 0.551046i | \(-0.185771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 51.3050i | 1.99553i | 0.0668107 | + | 0.997766i | \(0.478718\pi\) | ||||
−0.0668107 | + | 0.997766i | \(0.521282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.8885 | + | 6.83282i | 0.694733 | + | 0.265365i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.05573i | − | 0.118496i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.7771 | −0.456011 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.29180 | + | 16.4721i | −0.243255 | + | 0.636850i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.47214 | −0.0954358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4164 | −0.979731 | −0.489865 | − | 0.871798i | \(-0.662954\pi\) | ||||
−0.489865 | + | 0.871798i | \(0.662954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.0344 | − | 25.2705i | −0.501696 | − | 0.972662i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2918 | −0.549278 | −0.274639 | − | 0.961547i | \(-0.588558\pi\) | ||||
−0.274639 | + | 0.961547i | \(0.588558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.583592i | 0.0223962i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.34752 | − | 3.52786i | 0.0516372 | − | 0.135188i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.2361i | 0.506464i | 0.967406 | + | 0.253232i | \(0.0814936\pi\) | ||||
−0.967406 | + | 0.253232i | \(0.918506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.94427i | 0.188911i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.12461 | + | 18.6525i | −0.271821 | + | 0.711636i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4721i | 0.551344i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.7082 | 1.13015 | 0.565077 | − | 0.825038i | \(-0.308847\pi\) | ||||
0.565077 | + | 0.825038i | \(0.308847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4721 | − | 12.9443i | −0.549751 | − | 0.491712i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.4164 | 1.19169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.4164 | − | 40.3607i | 0.583102 | − | 1.52658i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2918 | −0.539794 | −0.269897 | − | 0.962889i | \(-0.586990\pi\) | ||||
−0.269897 | + | 0.962889i | \(0.586990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.47214i | − | 0.244101i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.8885 | − | 16.0000i | −1.57761 | − | 0.602595i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.11146i | 0.0794095i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.52786i | 0.282715i | 0.989959 | + | 0.141357i | \(0.0451467\pi\) | ||||
−0.989959 | + | 0.141357i | \(0.954853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.583592 | − | 0.652476i | 0.0218864 | − | 0.0244698i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9443i | 0.484767i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −75.7771 | −2.83390 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.9443 | − | 4.94427i | −0.483413 | − | 0.184647i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.8328 | −1.14987 | −0.574935 | − | 0.818199i | \(-0.694973\pi\) | ||||
−0.574935 | + | 0.818199i | \(0.694973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5279 | −0.652772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.23607 | + | 1.23607i | 0.120351 | + | 0.0459699i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.0689 | 0.968174 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1803i | 0.525920i | 0.964807 | + | 0.262960i | \(0.0846987\pi\) | ||||
−0.964807 | + | 0.262960i | \(0.915301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 17.8885i | − | 0.661632i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4164i | 1.08652i | 0.839565 | + | 0.543260i | \(0.182810\pi\) | ||||
−0.839565 | + | 0.543260i | \(0.817190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.6525 | + | 10.9443i | 1.05686 | + | 0.403686i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.8328i | 1.87245i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1246 | −0.482797 | −0.241398 | − | 0.970426i | \(-0.577606\pi\) | ||||
−0.241398 | + | 0.970426i | \(0.577606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.11146 | + | 5.52786i | −0.0775663 | + | 0.203071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.41641 | −0.272082 | −0.136041 | − | 0.990703i | \(-0.543438\pi\) | ||||
−0.136041 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.4164 | −1.15101 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.52786 | − | 6.18034i | 0.202254 | − | 0.226127i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5279 | 0.640454 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.5967i | 0.642114i | 0.947060 | + | 0.321057i | \(0.104038\pi\) | ||||
−0.947060 | + | 0.321057i | \(0.895962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6525 | + | 38.3607i | −0.533966 | + | 1.39794i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.7771i | 2.32109i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.41641i | − | 0.196863i | −0.995144 | − | 0.0984313i | \(-0.968618\pi\) | ||
0.995144 | − | 0.0984313i | \(-0.0313825\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | + | 20.9443i | −0.290382 | + | 0.760229i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.2492i | 1.53153i | 0.643119 | + | 0.765767i | \(0.277640\pi\) | ||||
−0.643119 | + | 0.765767i | \(0.722360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4721 | −0.379117 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0000 | + | 17.8885i | −0.578481 | + | 0.646762i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.52786 | −0.199600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.7771 | 1.79501 | 0.897504 | − | 0.441007i | \(-0.145378\pi\) | ||||
0.897504 | + | 0.441007i | \(0.145378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.9443 | + | 33.8885i | −0.466177 | + | 1.22047i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.81966 | 0.281254 | 0.140627 | − | 0.990063i | \(-0.455088\pi\) | ||||
0.140627 | + | 0.990063i | \(0.455088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 28.6525i | − | 1.02923i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.9443 | − | 6.47214i | −0.607872 | − | 0.232187i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.94427i | − | 0.177147i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.7214i | 2.88844i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.3475 | − | 22.0000i | −0.405527 | − | 0.786216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4721i | 0.516533i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1803 | −1.00452 | −0.502260 | − | 0.864716i | \(-0.667498\pi\) | ||||
−0.502260 | + | 0.864716i | \(0.667498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.9443 | + | 6.47214i | 0.603232 | + | 0.230414i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.88854 | 0.351596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.11146 | 0.0749800 |