Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (of order \(3\), degree \(2\), 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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.8528759163648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.5 | ||
Root | \(-1.13593 + 1.30754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.2305 |
Dual form | 3456.2.i.f.1153.5 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.59327 | − | 2.75962i | 0.712532 | − | 1.23414i | −0.251372 | − | 0.967891i | \(-0.580882\pi\) |
0.963904 | − | 0.266251i | \(-0.0857850\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.607060 | − | 1.05146i | −0.229447 | − | 0.397414i | 0.728197 | − | 0.685368i | \(-0.240358\pi\) |
−0.957644 | + | 0.287954i | \(0.907025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.312284 | − | 0.540892i | −0.0941572 | − | 0.163085i | 0.815099 | − | 0.579321i | \(-0.196682\pi\) |
−0.909257 | + | 0.416236i | \(0.863349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.06440 | + | 1.84360i | −0.295212 | + | 0.511323i | −0.975034 | − | 0.222054i | \(-0.928724\pi\) |
0.679822 | + | 0.733377i | \(0.262057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83869 | 0.445947 | 0.222974 | − | 0.974824i | \(-0.428424\pi\) | ||||
0.222974 | + | 0.974824i | \(0.428424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.15403 | 1.64125 | 0.820624 | − | 0.571469i | \(-0.193626\pi\) | ||||
0.820624 | + | 0.571469i | \(0.193626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.780986 | − | 1.35271i | 0.162847 | − | 0.282059i | −0.773042 | − | 0.634355i | \(-0.781266\pi\) |
0.935889 | + | 0.352296i | \(0.114599\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.57702 | − | 4.46352i | −0.515403 | − | 0.892705i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.87551 | − | 8.44463i | −0.905360 | − | 1.56813i | −0.820434 | − | 0.571742i | \(-0.806268\pi\) |
−0.0849260 | − | 0.996387i | \(-0.527065\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.32024 | + | 5.75083i | −0.596333 | + | 1.03288i | 0.397024 | + | 0.917808i | \(0.370043\pi\) |
−0.993357 | + | 0.115071i | \(0.963290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.86884 | −0.653953 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.73511 | 1.10724 | 0.553622 | − | 0.832768i | \(-0.313245\pi\) | ||||
0.553622 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.64365 | − | 9.77508i | 0.881389 | − | 1.52661i | 0.0315923 | − | 0.999501i | \(-0.489942\pi\) |
0.849797 | − | 0.527110i | \(-0.176724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.51144 | + | 7.81404i | 0.687988 | + | 1.19163i | 0.972488 | + | 0.232954i | \(0.0748391\pi\) |
−0.284500 | + | 0.958676i | \(0.591828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.36043 | − | 2.35634i | −0.198440 | − | 0.343708i | 0.749583 | − | 0.661910i | \(-0.230254\pi\) |
−0.948023 | + | 0.318203i | \(0.896921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.76296 | − | 4.78558i | 0.394708 | − | 0.683655i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.60144 | 1.04414 | 0.522069 | − | 0.852903i | \(-0.325160\pi\) | ||||
0.522069 | + | 0.852903i | \(0.325160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99021 | −0.268360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.02547 | − | 6.97231i | 0.524071 | − | 0.907718i | −0.475536 | − | 0.879696i | \(-0.657746\pi\) |
0.999607 | − | 0.0280214i | \(-0.00892067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.79700 | − | 4.84455i | −0.358119 | − | 0.620281i | 0.629527 | − | 0.776978i | \(-0.283249\pi\) |
−0.987647 | + | 0.156698i | \(0.949915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.39176 | + | 5.87471i | 0.420697 | + | 0.728668i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.95957 | + | 6.85817i | −0.483738 | + | 0.837859i | −0.999826 | − | 0.0186768i | \(-0.994055\pi\) |
0.516087 | + | 0.856536i | \(0.327388\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.11222 | −0.962743 | −0.481371 | − | 0.876517i | \(-0.659861\pi\) | ||||
−0.481371 | + | 0.876517i | \(0.659861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.66806 | −0.663397 | −0.331698 | − | 0.943386i | \(-0.607622\pi\) | ||||
−0.331698 | + | 0.943386i | \(0.607622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.379150 | + | 0.656707i | −0.0432082 | + | 0.0748387i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.21415 | − | 5.56707i | −0.361620 | − | 0.626344i | 0.626607 | − | 0.779335i | \(-0.284443\pi\) |
−0.988228 | + | 0.152991i | \(0.951110\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.27735 | + | 5.67653i | 0.359736 | + | 0.623080i | 0.987917 | − | 0.154987i | \(-0.0495336\pi\) |
−0.628181 | + | 0.778067i | \(0.716200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.92953 | − | 5.07409i | 0.317752 | − | 0.550362i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.02926 | −0.533100 | −0.266550 | − | 0.963821i | \(-0.585884\pi\) | ||||
−0.266550 | + | 0.963821i | \(0.585884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.58463 | 0.270942 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3983 | − | 19.7424i | 1.16944 | − | 2.02553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.70138 | − | 8.14302i | −0.477353 | − | 0.826799i | 0.522311 | − | 0.852755i | \(-0.325070\pi\) |
−0.999663 | + | 0.0259565i | \(0.991737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.25154 | − | 10.8280i | −0.622052 | − | 1.07743i | −0.989103 | − | 0.147225i | \(-0.952966\pi\) |
0.367051 | − | 0.930201i | \(-0.380367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.87656 | − | 13.6426i | 0.776100 | − | 1.34425i | −0.158073 | − | 0.987427i | \(-0.550528\pi\) |
0.934174 | − | 0.356818i | \(-0.116138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.8684 | −1.34071 | −0.670353 | − | 0.742043i | \(-0.733857\pi\) | ||||
−0.670353 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1671 | −1.54853 | −0.774265 | − | 0.632862i | \(-0.781880\pi\) | ||||
−0.774265 | + | 0.632862i | \(0.781880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.10460 | + | 3.64527i | −0.197984 | + | 0.342918i | −0.947875 | − | 0.318644i | \(-0.896773\pi\) |
0.749891 | + | 0.661562i | \(0.230106\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.48864 | − | 4.31045i | −0.232067 | − | 0.401952i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.11619 | − | 1.93330i | −0.102321 | − | 0.177226i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.30496 | − | 9.18846i | 0.482269 | − | 0.835314i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.490836 | −0.0439017 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.515228 | −0.0457191 | −0.0228595 | − | 0.999739i | \(-0.507277\pi\) | ||||
−0.0228595 | + | 0.999739i | \(0.507277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3026 | + | 19.5766i | −0.987510 | + | 1.71042i | −0.357310 | + | 0.933986i | \(0.616306\pi\) |
−0.630201 | + | 0.776432i | \(0.717027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.34293 | − | 7.52217i | −0.376579 | − | 0.652255i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.62941 | − | 8.01837i | −0.395517 | − | 0.685055i | 0.597650 | − | 0.801757i | \(-0.296101\pi\) |
−0.993167 | + | 0.116702i | \(0.962768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.22132 | + | 15.9718i | −0.782142 | + | 1.35471i | 0.148550 | + | 0.988905i | \(0.452540\pi\) |
−0.930692 | + | 0.365805i | \(0.880794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.32958 | 0.111185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −31.0720 | −2.58039 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.82223 | − | 4.88824i | 0.231206 | − | 0.400460i | −0.726957 | − | 0.686683i | \(-0.759066\pi\) |
0.958163 | + | 0.286222i | \(0.0923996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.11543 | − | 5.39609i | −0.253530 | − | 0.439128i | 0.710965 | − | 0.703228i | \(-0.248258\pi\) |
−0.964495 | + | 0.264100i | \(0.914925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5801 | + | 18.3252i | 0.849812 | + | 1.47192i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.76557 | + | 13.4504i | −0.619760 | + | 1.07346i | 0.369769 | + | 0.929124i | \(0.379437\pi\) |
−0.989529 | + | 0.144332i | \(0.953897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89642 | −0.149459 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3264 | 1.20046 | 0.600228 | − | 0.799829i | \(-0.295077\pi\) | ||||
0.600228 | + | 0.799829i | \(0.295077\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.36488 | − | 7.56020i | 0.337765 | − | 0.585026i | −0.646247 | − | 0.763128i | \(-0.723662\pi\) |
0.984012 | + | 0.178102i | \(0.0569958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.23409 | + | 7.33366i | 0.325699 | + | 0.564128i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.1252 | + | 19.2695i | 0.845837 | + | 1.46503i | 0.884892 | + | 0.465795i | \(0.154232\pi\) |
−0.0390556 | + | 0.999237i | \(0.512435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12881 | + | 5.41925i | −0.236516 | + | 0.409657i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.29457 | −0.0967606 | −0.0483803 | − | 0.998829i | \(-0.515406\pi\) | ||||
−0.0483803 | + | 0.998829i | \(0.515406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.67493 | 0.496143 | 0.248072 | − | 0.968742i | \(-0.420203\pi\) | ||||
0.248072 | + | 0.968742i | \(0.420203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7308 | − | 18.5864i | 0.788947 | − | 1.36650i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.574193 | − | 0.994531i | −0.0419891 | − | 0.0727273i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.169031 | − | 0.292771i | −0.0122307 | − | 0.0211842i | 0.859845 | − | 0.510555i | \(-0.170560\pi\) |
−0.872076 | + | 0.489371i | \(0.837227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.36013 | + | 11.0161i | −0.457812 | + | 0.792954i | −0.998845 | − | 0.0480477i | \(-0.984700\pi\) |
0.541033 | + | 0.841001i | \(0.318033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.25803 | 0.517114 | 0.258557 | − | 0.965996i | \(-0.416753\pi\) | ||||
0.258557 | + | 0.965996i | \(0.416753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.112216 | −0.00795476 | −0.00397738 | − | 0.999992i | \(-0.501266\pi\) | ||||
−0.00397738 | + | 0.999992i | \(0.501266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.91945 | + | 10.2528i | −0.415464 | + | 0.719605i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.9837 | − | 31.1487i | −1.25604 | − | 2.17552i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.23409 | − | 3.86956i | −0.154535 | − | 0.267663i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.746256 | − | 1.29255i | 0.0513744 | − | 0.0889830i | −0.839195 | − | 0.543831i | \(-0.816973\pi\) |
0.890569 | + | 0.454848i | \(0.150306\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.7517 | 1.96085 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.06234 | 0.547307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.95711 | + | 3.38981i | −0.131649 | + | 0.228023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.7863 | − | 23.8786i | −0.923200 | − | 1.59903i | −0.794430 | − | 0.607355i | \(-0.792230\pi\) |
−0.128770 | − | 0.991674i | \(-0.541103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.586489 | − | 1.01583i | −0.0389267 | − | 0.0674229i | 0.845906 | − | 0.533333i | \(-0.179061\pi\) |
−0.884832 | + | 0.465910i | \(0.845727\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.81718 | + | 4.87950i | −0.186164 | + | 0.322446i | −0.943968 | − | 0.330036i | \(-0.892939\pi\) |
0.757804 | + | 0.652482i | \(0.226272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3065 | 0.937247 | 0.468623 | − | 0.883398i | \(-0.344750\pi\) | ||||
0.468623 | + | 0.883398i | \(0.344750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.67016 | −0.565579 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.43313 | − | 4.21431i | 0.157386 | − | 0.272601i | −0.776539 | − | 0.630069i | \(-0.783027\pi\) |
0.933925 | + | 0.357468i | \(0.116360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.68209 | + | 4.64552i | 0.172769 | + | 0.299244i | 0.939387 | − | 0.342859i | \(-0.111395\pi\) |
−0.766618 | + | 0.642103i | \(0.778062\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.80427 | − | 15.2494i | −0.562484 | − | 0.974251i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.61478 | + | 13.1892i | −0.484517 | + | 0.839208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7664 | 0.932047 | 0.466023 | − | 0.884772i | \(-0.345686\pi\) | ||||
0.466023 | + | 0.884772i | \(0.345686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.975557 | −0.0613328 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.19564 | − | 7.26707i | 0.261717 | − | 0.453307i | −0.704981 | − | 0.709226i | \(-0.749045\pi\) |
0.966698 | + | 0.255919i | \(0.0823780\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.08861 | − | 7.08169i | −0.254054 | − | 0.440035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.85651 | − | 8.41172i | −0.299465 | − | 0.518689i | 0.676549 | − | 0.736398i | \(-0.263475\pi\) |
−0.976014 | + | 0.217709i | \(0.930142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1111 | − | 20.9771i | 0.743981 | − | 1.28861i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.519050 | 0.0316471 | 0.0158235 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158235 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9533 | 1.02984 | 0.514920 | − | 0.857238i | \(-0.327821\pi\) | ||||
0.514920 | + | 0.857238i | \(0.327821\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.60952 | + | 2.78777i | −0.0970579 | + | 0.168109i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3626 | − | 19.6805i | −0.682710 | − | 1.18249i | −0.974151 | − | 0.225899i | \(-0.927468\pi\) |
0.291441 | − | 0.956589i | \(-0.405865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.83592 | − | 10.1081i | −0.348142 | − | 0.602999i | 0.637778 | − | 0.770220i | \(-0.279854\pi\) |
−0.985919 | + | 0.167221i | \(0.946521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0284 | − | 22.5658i | 0.774456 | − | 1.34140i | −0.160644 | − | 0.987012i | \(-0.551357\pi\) |
0.935100 | − | 0.354385i | \(-0.115310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.7041 | −0.808929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6192 | −0.801131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6664 | − | 25.4030i | 0.856823 | − | 1.48406i | −0.0181212 | − | 0.999836i | \(-0.505768\pi\) |
0.874944 | − | 0.484224i | \(-0.160898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.8273 | − | 22.2175i | −0.746835 | − | 1.29356i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.66257 | + | 2.87965i | 0.0961488 | + | 0.166535i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.47742 | − | 9.48718i | 0.315713 | − | 0.546832i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.8255 | −1.02069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2190 | 0.640305 | 0.320152 | − | 0.947366i | \(-0.396266\pi\) | ||||
0.320152 | + | 0.947366i | \(0.396266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1358 | + | 29.6801i | −0.971682 | + | 1.68300i | −0.281206 | + | 0.959648i | \(0.590734\pi\) |
−0.690476 | + | 0.723355i | \(0.742599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8824 | + | 18.8489i | 0.615109 | + | 1.06540i | 0.990365 | + | 0.138479i | \(0.0442214\pi\) |
−0.375256 | + | 0.926921i | \(0.622445\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.30124 | + | 5.71791i | 0.185416 | + | 0.321150i | 0.943717 | − | 0.330755i | \(-0.107303\pi\) |
−0.758301 | + | 0.651905i | \(0.773970\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.04509 | + | 5.27425i | −0.170492 | + | 0.295301i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1540 | 0.731910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9719 | 0.608614 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.65173 | + | 2.86088i | −0.0910629 | + | 0.157725i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.88444 | + | 10.1921i | 0.323438 | + | 0.560211i | 0.981195 | − | 0.193019i | \(-0.0618280\pi\) |
−0.657757 | + | 0.753230i | \(0.728495\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.6173 | + | 21.8538i | 0.689358 | + | 1.19400i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.15221 | − | 10.6559i | 0.335132 | − | 0.580466i | −0.648378 | − | 0.761319i | \(-0.724552\pi\) |
0.983510 | + | 0.180853i | \(0.0578857\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.14743 | 0.224596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2080 | −0.821153 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.05467 | − | 5.29084i | 0.163983 | − | 0.284027i | −0.772310 | − | 0.635245i | \(-0.780899\pi\) |
0.936294 | + | 0.351218i | \(0.114232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5970 | + | 20.0866i | 0.620772 | + | 1.07521i | 0.989342 | + | 0.145609i | \(0.0465141\pi\) |
−0.368570 | + | 0.929600i | \(0.620153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.54985 | − | 9.61263i | −0.295389 | − | 0.511629i | 0.679686 | − | 0.733503i | \(-0.262116\pi\) |
−0.975075 | + | 0.221874i | \(0.928783\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9249 | + | 22.3867i | −0.685985 | + | 1.18816i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.34365 | −0.123693 | −0.0618466 | − | 0.998086i | \(-0.519699\pi\) | ||||
−0.0618466 | + | 0.998086i | \(0.519699\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.1802 | 1.69369 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.03075 | + | 15.6417i | −0.472691 | + | 0.818725i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2442 | − | 17.7435i | −0.534745 | − | 0.926206i | −0.999176 | − | 0.0405961i | \(-0.987074\pi\) |
0.464431 | − | 0.885610i | \(-0.346259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.61453 | − | 7.99259i | −0.239574 | − | 0.414955i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.91408 | − | 6.77939i | 0.202663 | − | 0.351023i | −0.746722 | − | 0.665136i | \(-0.768374\pi\) |
0.949386 | + | 0.314113i | \(0.101707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7580 | 1.06909 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6174 | 1.21314 | 0.606571 | − | 0.795029i | \(-0.292545\pi\) | ||||
0.606571 | + | 0.795029i | \(0.292545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.08388 | + | 14.0017i | −0.413067 | + | 0.715453i | −0.995223 | − | 0.0976240i | \(-0.968876\pi\) |
0.582157 | + | 0.813077i | \(0.302209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.20818 | + | 2.09262i | 0.0615744 | + | 0.106650i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.466974 | − | 0.808822i | −0.0236765 | − | 0.0410089i | 0.853944 | − | 0.520364i | \(-0.174204\pi\) |
−0.877621 | + | 0.479355i | \(0.840871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43599 | − | 2.48721i | 0.0726211 | − | 0.125783i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.4840 | −1.03066 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5828 | 0.982833 | 0.491417 | − | 0.870925i | \(-0.336479\pi\) | ||||
0.491417 | + | 0.870925i | \(0.336479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.55347 | + | 14.8150i | −0.427140 | + | 0.739828i | −0.996618 | − | 0.0821788i | \(-0.973812\pi\) |
0.569478 | + | 0.822007i | \(0.307145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.06815 | − | 12.2424i | −0.352090 | − | 0.609837i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.10327 | − | 3.64296i | −0.104255 | − | 0.180575i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.41720 | − | 12.8470i | 0.366757 | − | 0.635242i | −0.622300 | − | 0.782779i | \(-0.713801\pi\) |
0.989056 | + | 0.147538i | \(0.0471348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.77479 | −0.480986 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.8868 | 1.02529 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.76913 | − | 11.7245i | 0.330694 | − | 0.572778i | −0.651954 | − | 0.758258i | \(-0.726051\pi\) |
0.982648 | + | 0.185480i | \(0.0593840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7346 | + | 18.5928i | 0.523171 | + | 0.906158i | 0.999636 | + | 0.0269650i | \(0.00858426\pi\) |
−0.476466 | + | 0.879193i | \(0.658082\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.73833 | − | 8.20703i | −0.229843 | − | 0.398099i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.39589 | + | 5.88186i | −0.164339 | + | 0.284643i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.628294 | −0.0302638 | −0.0151319 | − | 0.999886i | \(-0.504817\pi\) | ||||
−0.0151319 | + | 0.999886i | \(0.504817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9996 | −0.672777 | −0.336389 | − | 0.941723i | \(-0.609206\pi\) | ||||
−0.336389 | + | 0.941723i | \(0.609206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.58720 | − | 9.67731i | 0.267272 | − | 0.462929i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6162 | + | 30.5121i | 0.840774 | + | 1.45626i | 0.889241 | + | 0.457438i | \(0.151233\pi\) |
−0.0484677 | + | 0.998825i | \(0.515434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.5936 | − | 20.0806i | −0.550827 | − | 0.954060i | −0.998215 | − | 0.0597201i | \(-0.980979\pi\) |
0.447388 | − | 0.894340i | \(-0.352354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.01296 | + | 13.8789i | −0.379851 | + | 0.657921i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.37349 | 0.112012 | 0.0560061 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560061 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.04968 | −0.331956 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.11801 | − | 7.13260i | 0.193055 | − | 0.334381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.87416 | − | 4.97818i | −0.134447 | − | 0.232870i | 0.790939 | − | 0.611895i | \(-0.209593\pi\) |
−0.925386 | + | 0.379026i | \(0.876259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0780 | + | 17.4555i | 0.469378 | + | 0.812986i | 0.999387 | − | 0.0350058i | \(-0.0111450\pi\) |
−0.530009 | + | 0.847992i | \(0.677812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8516 | + | 23.9918i | −0.643741 | + | 1.11499i | 0.340850 | + | 0.940118i | \(0.389285\pi\) |
−0.984591 | + | 0.174874i | \(0.944048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.7764 | 1.70181 | 0.850904 | − | 0.525322i | \(-0.176055\pi\) | ||||
0.850904 | + | 0.525322i | \(0.176055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.61478 | 0.443969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.81770 | − | 4.88040i | 0.129558 | − | 0.224401i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.4361 | − | 31.9322i | −0.845905 | − | 1.46515i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.76037 | − | 4.78109i | −0.126124 | − | 0.218454i | 0.796048 | − | 0.605234i | \(-0.206920\pi\) |
−0.922172 | + | 0.386780i | \(0.873587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.16887 | + | 12.4169i | −0.326872 | + | 0.566160i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.9623 | −1.36052 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.2903 | 1.01007 | 0.505035 | − | 0.863099i | \(-0.331480\pi\) | ||||
0.505035 | + | 0.863099i | \(0.331480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.207080 | + | 0.358672i | −0.00934537 | + | 0.0161867i | −0.870660 | − | 0.491885i | \(-0.836308\pi\) |
0.861315 | + | 0.508071i | \(0.169641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.96454 | − | 15.5270i | −0.403743 | − | 0.699303i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.92460 | + | 8.52966i | 0.220899 | + | 0.382607i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7069 | + | 18.5448i | −0.479305 | + | 0.830181i | −0.999718 | − | 0.0237336i | \(-0.992445\pi\) |
0.520413 | + | 0.853915i | \(0.325778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.8397 | 0.929198 | 0.464599 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464599 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.8416 | −1.77293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.79067 | − | 3.10154i | 0.0793703 | − | 0.137473i | −0.823608 | − | 0.567159i | \(-0.808042\pi\) |
0.902978 | + | 0.429686i | \(0.141376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.44085 | + | 5.95973i | 0.152214 | + | 0.263643i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.0990 | − | 43.4727i | −1.10599 | − | 1.91564i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.849684 | + | 1.47170i | −0.0373691 | + | 0.0647251i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.33816 | 0.277680 | 0.138840 | − | 0.990315i | \(-0.455663\pi\) | ||||
0.138840 | + | 0.990315i | \(0.455663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9934 | 0.917978 | 0.458989 | − | 0.888442i | \(-0.348212\pi\) | ||||
0.458989 | + | 0.888442i | \(0.348212\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.10489 | + | 10.5740i | −0.265933 | + | 0.460610i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2801 | + | 17.8057i | 0.446962 | + | 0.774161i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0142 | + | 20.8093i | 0.520394 | + | 0.901349i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.0960 | + | 38.2715i | −0.955295 | + | 1.65462i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.45131 | −0.148658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.88956 | 0.0812384 | 0.0406192 | − | 0.999175i | \(-0.487067\pi\) | ||||
0.0406192 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.7586 | + | 44.6152i | −1.10338 | + | 1.91110i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.95041 | + | 10.3064i | 0.254421 | + | 0.440671i | 0.964738 | − | 0.263211i | \(-0.0847817\pi\) |
−0.710317 | + | 0.703882i | \(0.751448\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.8796 | − | 60.4132i | −1.48592 | − | 2.57369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.90236 | + | 6.75909i | −0.165945 | + | 0.287426i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.55236 | −0.277632 | −0.138816 | − | 0.990318i | \(-0.544330\pi\) | ||||
−0.138816 | + | 0.990318i | \(0.544330\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.2080 | −0.812410 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.42079 | + | 2.46088i | −0.0598791 | + | 0.103714i | −0.894411 | − | 0.447246i | \(-0.852405\pi\) |
0.834532 | + | 0.550960i | \(0.185738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.70638 | + | 11.6158i | 0.282140 | + | 0.488680i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.59442 | + | 11.4219i | 0.276453 | + | 0.478830i | 0.970501 | − | 0.241099i | \(-0.0775078\pi\) |
−0.694048 | + | 0.719929i | \(0.744174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.97548 | + | 17.2780i | −0.417461 | + | 0.723064i | −0.995683 | − | 0.0928157i | \(-0.970413\pi\) |
0.578222 | + | 0.815879i | \(0.303747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.05045 | −0.335727 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.34556 | 0.0560164 | 0.0280082 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280082 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.97909 | − | 6.89199i | 0.165081 | − | 0.285928i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.37381 | − | 4.11155i | −0.0983131 | − | 0.170283i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2237 | + | 17.7079i | 0.421976 | + | 0.730884i | 0.996133 | − | 0.0878615i | \(-0.0280033\pi\) |
−0.574157 | + | 0.818745i | \(0.694670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.7531 | + | 41.1416i | −0.978730 | + | 1.69521i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0810 | 1.02995 | 0.514976 | − | 0.857204i | \(-0.327801\pi\) | ||||
0.514976 | + | 0.857204i | \(0.327801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.11359 | −0.291629 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.37676 | − | 4.11668i | 0.0971119 | − | 0.168203i | −0.813376 | − | 0.581738i | \(-0.802373\pi\) |
0.910488 | + | 0.413535i | \(0.135706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.9340 | + | 34.5267i | 0.813124 | + | 1.40837i | 0.910667 | + | 0.413141i | \(0.135568\pi\) |
−0.0975429 | + | 0.995231i | \(0.531098\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.9045 | − | 29.2794i | −0.687264 | − | 1.19038i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0643 | − | 36.4844i | 0.854973 | − | 1.48086i | −0.0216961 | − | 0.999765i | \(-0.506907\pi\) |
0.876670 | − | 0.481093i | \(-0.159760\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.79221 | 0.234328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.0554 | 1.49665 | 0.748327 | − | 0.663330i | \(-0.230857\pi\) | ||||
0.748327 | + | 0.663330i | \(0.230857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0793 | + | 20.9220i | −0.486295 | + | 0.842288i | −0.999876 | − | 0.0157534i | \(-0.994985\pi\) |
0.513581 | + | 0.858041i | \(0.328319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2530 | − | 42.0074i | −0.974810 | − | 1.68842i | −0.680562 | − | 0.732691i | \(-0.738264\pi\) |
−0.294248 | − | 0.955729i | \(-0.595069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.05306 | + | 5.28805i | 0.122318 | + | 0.211861i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1031 | − | 20.9631i | 0.484122 | − | 0.838524i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.3838 | 0.493773 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.3164 | 1.52535 | 0.762677 | − | 0.646780i | \(-0.223885\pi\) | ||||
0.762677 | + | 0.646780i | \(0.223885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.820897 | + | 1.42184i | −0.0325763 | + | 0.0564238i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.88180 | + | 10.1876i | 0.233045 | + | 0.403647i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.3651 | + | 23.1491i | 0.527890 | + | 0.914333i | 0.999471 | + | 0.0325101i | \(0.0103501\pi\) |
−0.471581 | + | 0.881823i | \(0.656317\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.35536 | − | 12.7399i | 0.290067 | − | 0.502411i | −0.683758 | − | 0.729709i | \(-0.739656\pi\) |
0.973825 | + | 0.227298i | \(0.0729890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.36931 | 0.289717 | 0.144859 | − | 0.989452i | \(-0.453727\pi\) | ||||
0.144859 | + | 0.989452i | \(0.453727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.02835 | −0.197380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.2260 | + | 21.1760i | −0.478440 | + | 0.828683i | −0.999694 | − | 0.0247186i | \(-0.992131\pi\) |
0.521254 | + | 0.853401i | \(0.325464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0161 | + | 62.3817i | 1.40727 | + | 2.43746i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.95593 | − | 6.85187i | −0.154101 | − | 0.266911i | 0.778630 | − | 0.627483i | \(-0.215915\pi\) |
−0.932731 | + | 0.360572i | \(0.882581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7468 | + | 25.5423i | −0.573585 | + | 0.993479i | 0.422609 | + | 0.906312i | \(0.361114\pi\) |
−0.996194 | + | 0.0871663i | \(0.972219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.6778 | −1.07330 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2308 | −0.589740 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.74692 | + | 3.02575i | −0.0674390 | + | 0.116808i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.26908 | − | 16.0545i | −0.357297 | − | 0.618856i | 0.630211 | − | 0.776424i | \(-0.282968\pi\) |
−0.987508 | + | 0.157567i | \(0.949635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4799 | + | 21.6158i | 0.479642 | + | 0.830764i | 0.999727 | − | 0.0233505i | \(-0.00743337\pi\) |
−0.520086 | + | 0.854114i | \(0.674100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.70803 | + | 9.88661i | −0.219054 | + | 0.379413i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.8166 | −0.911315 | −0.455658 | − | 0.890155i | \(-0.650596\pi\) | ||||
−0.455658 | + | 0.890155i | \(0.650596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.5036 | −1.12727 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.09100 | + | 14.0140i | −0.308242 | + | 0.533891i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.926507 | − | 1.60476i | −0.0352460 | − | 0.0610479i | 0.847864 | − | 0.530213i | \(-0.177888\pi\) |
−0.883110 | + | 0.469165i | \(0.844555\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.3841 | + | 50.8947i | 1.11460 | + | 1.93055i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.3769 | − | 17.9733i | 0.393053 | − | 0.680788i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9501 | −0.980122 | −0.490061 | − | 0.871688i | \(-0.663026\pi\) | ||||
−0.490061 | + | 0.871688i | \(0.663026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.1832 | 1.81726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.59012 | + | 13.1465i | −0.285456 | + | 0.494424i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.18041 | + | 3.77658i | 0.0818869 | + | 0.141832i | 0.904060 | − | 0.427405i | \(-0.140572\pi\) |
−0.822174 | + | 0.569237i | \(0.807239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.18612 | + | 8.98263i | 0.194222 | + | 0.336402i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.11839 | − | 3.66915i | 0.0792232 | − | 0.137219i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.3650 | −1.13242 | −0.566212 | − | 0.824260i | \(-0.691592\pi\) | ||||
−0.566212 | + | 0.824260i | \(0.691592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1262 | −0.712296 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.1286 | + | 43.5239i | −0.933251 | + | 1.61644i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.47800 | − | 11.2202i | −0.240256 | − | 0.416135i | 0.720531 | − | 0.693422i | \(-0.243898\pi\) |
−0.960787 | + | 0.277287i | \(0.910565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.29512 | + | 14.3676i | 0.306806 | + | 0.531404i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6357 | + | 18.4216i | −0.392838 | + | 0.680416i | −0.992823 | − | 0.119596i | \(-0.961840\pi\) |
0.599985 | + | 0.800012i | \(0.295173\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.94604 | 0.182190 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.4687 | −0.421883 | −0.210942 | − | 0.977499i | \(-0.567653\pi\) | ||||
−0.210942 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0094 | + | 31.1932i | −0.660701 | + | 1.14437i | 0.319731 | + | 0.947508i | \(0.396407\pi\) |
−0.980432 | + | 0.196859i | \(0.936926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.99314 | − | 15.5766i | −0.329483 | − | 0.570682i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.41893 | + | 14.5820i | 0.307621 | + | 0.532815i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.34620 | − | 7.52783i | 0.158595 | − | 0.274695i | −0.775767 | − | 0.631019i | \(-0.782637\pi\) |
0.934362 | + | 0.356325i | \(0.115970\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8549 | −0.722594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7265 | 0.971390 | 0.485695 | − | 0.874128i | \(-0.338567\pi\) | ||||
0.485695 | + | 0.874128i | \(0.338567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0267 | + | 20.8309i | −0.435969 | + | 0.755121i | −0.997374 | − | 0.0724203i | \(-0.976928\pi\) |
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.81441 | + | 16.9991i | 0.355305 | + | 0.615407i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.56944 | + | 14.8427i | 0.309424 | + | 0.535939i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00296 | + | 1.73717i | −0.0361675 | + | 0.0626439i | −0.883543 | − | 0.468351i | \(-0.844848\pi\) |
0.847375 | + | 0.530995i | \(0.178182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.0297 | −1.08009 | −0.540046 | − | 0.841635i | \(-0.681593\pi\) | ||||
−0.540046 | + | 0.841635i | \(0.681593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.2253 | 1.22941 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.3748 | − | 69.9313i | 1.44658 | − | 2.50555i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53332 | + | 4.38783i | 0.0906491 | + | 0.157009i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.7453 | + | 42.8601i | 0.883198 | + | 1.52974i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.04245 | + | 3.53763i | −0.0728054 | + | 0.126103i | −0.900130 | − | 0.435622i | \(-0.856529\pi\) |
0.827324 | + | 0.561724i | \(0.189862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.11047 | 0.181707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9085 | 0.422885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.31103 | + | 14.3951i | −0.294392 | + | 0.509901i | −0.974843 | − | 0.222892i | \(-0.928450\pi\) |
0.680451 | + | 0.732793i | \(0.261784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.50141 | − | 4.33258i | −0.0884937 | − | 0.153276i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.77005 | + | 3.06581i | 0.0624635 | + | 0.108190i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.02151 | + | 5.23341i | −0.106494 | + | 0.184453i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.2163 | −1.69519 | −0.847597 | − | 0.530641i | \(-0.821951\pi\) | ||||
−0.847597 | + | 0.530641i | \(0.821951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.91987 | 0.242990 | 0.121495 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121495 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.4191 | − | 42.2951i | 0.855363 | − | 1.48153i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.2750 | + | 55.9019i | 1.12916 | + | 1.95576i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.53494 | − | 13.0509i | −0.262971 | − | 0.455479i | 0.704059 | − | 0.710142i | \(-0.251369\pi\) |
−0.967030 | + | 0.254662i | \(0.918036\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.6790 | + | 39.2812i | −0.790541 | + | 1.36926i | 0.135091 | + | 0.990833i | \(0.456867\pi\) |
−0.925632 | + | 0.378424i | \(0.876466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.3507 | −0.394702 | −0.197351 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197351 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.8614 | 1.03713 | 0.518566 | − | 0.855038i | \(-0.326466\pi\) | ||||
0.518566 | + | 0.855038i | \(0.326466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.08021 | − | 8.79919i | 0.176019 | − | 0.304874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9089 | − | 24.0909i | −0.481336 | − | 0.833699i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0215 | − | 22.5539i | −0.449551 | − | 0.778646i | 0.548805 | − | 0.835950i | \(-0.315083\pi\) |
−0.998357 | + | 0.0573042i | \(0.981749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.0412 | + | 57.2291i | −1.13935 | + | 1.97342i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.9842 | 0.928284 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8817 | −0.442621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.26002 | − | 9.11063i | 0.180311 | − | 0.312308i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.04718 | + | 1.81377i | 0.0358547 | + | 0.0621021i | 0.883396 | − | 0.468627i | \(-0.155251\pi\) |
−0.847541 | + | 0.530730i | \(0.821918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.47263 | − | 9.47887i | −0.186941 | − | 0.323792i | 0.757288 | − | 0.653082i | \(-0.226524\pi\) |
−0.944229 | + | 0.329290i | \(0.893191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4294 | + | 23.2603i | −0.458204 | + | 0.793633i | −0.998866 | − | 0.0476073i | \(-0.984840\pi\) |
0.540662 | + | 0.841240i | \(0.318174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.4778 | −1.68424 | −0.842121 | − | 0.539288i | \(-0.818693\pi\) | ||||
−0.842121 | + | 0.539288i | \(0.818693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 70.9021 | 2.41074 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.00746 | + | 3.47701i | −0.0680983 | + | 0.117950i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.42916 | − | 14.5997i | −0.285611 | − | 0.494693i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.297967 | + | 0.516093i | 0.0100731 | + | 0.0174471i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3449 | − | 19.6499i | 0.383090 | − | 0.663531i | −0.608412 | − | 0.793621i | \(-0.708193\pi\) |
0.991502 | + | 0.130090i | \(0.0415267\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.8224 | −0.364616 | −0.182308 | − | 0.983241i | \(-0.558357\pi\) | ||||
−0.182308 | + | 0.983241i | \(0.558357\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7591 | −1.10243 | −0.551215 | − | 0.834363i | \(-0.685836\pi\) | ||||
−0.551215 | + | 0.834363i | \(0.685836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.6048 | + | 28.7604i | −0.557535 | + | 0.965679i | 0.440166 | + | 0.897916i | \(0.354919\pi\) |
−0.997701 | + | 0.0677629i | \(0.978414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.312774 | + | 0.541741i | 0.0104901 | + | 0.0181694i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.73260 | − | 16.8574i | −0.325689 | − | 0.564110i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.06260 | + | 3.57252i | −0.0689450 | + | 0.119416i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.7515 | 2.15958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9767 | 0.465630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6350 | − | 18.4203i | 0.353518 | − | 0.612311i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2085 | − | 17.6816i | −0.338966 | − | 0.587107i | 0.645272 | − | 0.763953i | \(-0.276744\pi\) |
−0.984239 | + | 0.176846i | \(0.943411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.7162 | + | 51.4700i | 0.984541 | + | 1.70528i | 0.643957 | + | 0.765062i | \(0.277292\pi\) |
0.340585 | + | 0.940214i | \(0.389375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.04693 | − | 3.54538i | 0.0677434 | − | 0.117335i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.4454 | 0.906325 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2045 | −0.765447 | −0.382724 | − | 0.923863i | \(-0.625014\pi\) | ||||
−0.382724 | + | 0.923863i | \(0.625014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.63467 | − | 14.9557i | 0.284214 | − | 0.492272i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.3565 | − | 30.0623i | −0.570678 | − | 0.988443i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.370924 | + | 0.642460i | 0.0121696 | + | 0.0210784i | 0.872046 | − | 0.489424i | \(-0.162793\pi\) |
−0.859876 | + | 0.510502i | \(0.829460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.7663 | − | 34.2362i | 0.647814 | − | 1.12205i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.65938 | −0.119674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.43708 | 0.0796161 | 0.0398080 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398080 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.25473 | − | 9.10146i | 0.171299 | − | 0.296699i | −0.767575 | − | 0.640959i | \(-0.778537\pi\) |
0.938874 | + | 0.344260i | \(0.111870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.81521 | − | 15.2684i | −0.287063 | − | 0.497207i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.4659 | − | 45.8403i | −0.860026 | − | 1.48961i | −0.871902 | − | 0.489680i | \(-0.837114\pi\) |
0.0118761 | − | 0.999929i | \(-0.496220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.03311 | − | 10.4496i | 0.195843 | − | 0.339210i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.5979 | 0.472873 | 0.236437 | − | 0.971647i | \(-0.424020\pi\) | ||||
0.236437 | + | 0.971647i | \(0.424020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.07725 | −0.0348590 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.62065 | + | 9.73526i | −0.181500 | + | 0.314368i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.54800 | − | 11.3415i | −0.211226 | − | 0.365854i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.2668 | + | 35.1031i | 0.652411 | + | 1.13001i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.3029 | − | 47.2900i | 0.878003 | − | 1.52075i | 0.0244732 | − | 0.999700i | \(-0.492209\pi\) |
0.853529 | − | 0.521045i | \(-0.174458\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5365 | 1.33297 | 0.666485 | − | 0.745519i | \(-0.267798\pi\) | ||||
0.666485 | + | 0.745519i | \(0.267798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.3916 | 0.717841 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.4039 | − | 52.6611i | 0.972707 | − | 1.68478i | 0.285404 | − | 0.958407i | \(-0.407872\pi\) |
0.687303 | − | 0.726371i | \(-0.258794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.57056 | + | 2.72028i | 0.0501952 | + | 0.0869406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.9506 | + | 25.8952i | 0.476851 | + | 0.825929i | 0.999648 | − | 0.0265275i | \(-0.00844494\pi\) |
−0.522797 | + | 0.852457i | \(0.675112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5640 | − | 20.0294i | 0.368460 | − | 0.638191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.0935 | 0.448146 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.3402 | −1.78971 | −0.894853 | − | 0.446361i | \(-0.852720\pi\) | ||||
−0.894853 | + | 0.446361i | \(0.852720\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.178790 | + | 0.309673i | −0.00566802 | + | 0.00981730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.26572 | − | 9.12049i | −0.166767 | − | 0.288849i | 0.770514 | − | 0.637423i | \(-0.219999\pi\) |
−0.937281 | + | 0.348574i | \(0.886666\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3456.2.i.f.2305.5 | 10 | ||
3.2 | odd | 2 | 1152.2.i.g.769.3 | yes | 10 | ||
4.3 | odd | 2 | 3456.2.i.g.2305.5 | 10 | |||
8.3 | odd | 2 | 3456.2.i.h.2305.1 | 10 | |||
8.5 | even | 2 | 3456.2.i.e.2305.1 | 10 | |||
9.2 | odd | 6 | 1152.2.i.g.385.3 | yes | 10 | ||
9.7 | even | 3 | inner | 3456.2.i.f.1153.5 | 10 | ||
12.11 | even | 2 | 1152.2.i.f.769.3 | yes | 10 | ||
24.5 | odd | 2 | 1152.2.i.e.769.3 | yes | 10 | ||
24.11 | even | 2 | 1152.2.i.h.769.3 | yes | 10 | ||
36.7 | odd | 6 | 3456.2.i.g.1153.5 | 10 | |||
36.11 | even | 6 | 1152.2.i.f.385.3 | yes | 10 | ||
72.11 | even | 6 | 1152.2.i.h.385.3 | yes | 10 | ||
72.29 | odd | 6 | 1152.2.i.e.385.3 | ✓ | 10 | ||
72.43 | odd | 6 | 3456.2.i.h.1153.1 | 10 | |||
72.61 | even | 6 | 3456.2.i.e.1153.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.e.385.3 | ✓ | 10 | 72.29 | odd | 6 | ||
1152.2.i.e.769.3 | yes | 10 | 24.5 | odd | 2 | ||
1152.2.i.f.385.3 | yes | 10 | 36.11 | even | 6 | ||
1152.2.i.f.769.3 | yes | 10 | 12.11 | even | 2 | ||
1152.2.i.g.385.3 | yes | 10 | 9.2 | odd | 6 | ||
1152.2.i.g.769.3 | yes | 10 | 3.2 | odd | 2 | ||
1152.2.i.h.385.3 | yes | 10 | 72.11 | even | 6 | ||
1152.2.i.h.769.3 | yes | 10 | 24.11 | even | 2 | ||
3456.2.i.e.1153.1 | 10 | 72.61 | even | 6 | |||
3456.2.i.e.2305.1 | 10 | 8.5 | even | 2 | |||
3456.2.i.f.1153.5 | 10 | 9.7 | even | 3 | inner | ||
3456.2.i.f.2305.5 | 10 | 1.1 | even | 1 | trivial | ||
3456.2.i.g.1153.5 | 10 | 36.7 | odd | 6 | |||
3456.2.i.g.2305.5 | 10 | 4.3 | odd | 2 | |||
3456.2.i.h.1153.1 | 10 | 72.43 | odd | 6 | |||
3456.2.i.h.2305.1 | 10 | 8.3 | odd | 2 |