Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1025,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 37x^{4} + 22x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(1.18847i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1025 |
Dual form | 2736.2.f.h.1025.8 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.42865i | − | 1.53334i | −0.642043 | − | 0.766668i | \(-0.721913\pi\) | ||
0.642043 | − | 0.766668i | \(-0.278087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.394100 | 0.148956 | 0.0744779 | − | 0.997223i | \(-0.476271\pi\) | ||||
0.0744779 | + | 0.997223i | \(0.476271\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.33407i | 0.703749i | 0.936047 | + | 0.351874i | \(0.114456\pi\) | ||||
−0.936047 | + | 0.351874i | \(0.885544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.36566i | − | 0.933466i | −0.884398 | − | 0.466733i | \(-0.845431\pi\) | ||
0.884398 | − | 0.466733i | \(-0.154569\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.494357i | − | 0.119899i | −0.998201 | − | 0.0599496i | \(-0.980906\pi\) | ||
0.998201 | − | 0.0599496i | \(-0.0190940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.300874 | − | 4.34850i | 0.0690252 | − | 0.997615i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.79116i | 0.790512i | 0.918571 | + | 0.395256i | \(0.129344\pi\) | ||||
−0.918571 | + | 0.395256i | \(0.870656\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.75561 | −1.35112 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.14971 | −0.399191 | −0.199596 | − | 0.979878i | \(-0.563963\pi\) | ||||
−0.199596 | + | 0.979878i | \(0.563963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.04509i | − | 1.26534i | −0.774423 | − | 0.632668i | \(-0.781960\pi\) | ||
0.774423 | − | 0.632668i | \(-0.218040\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.35123i | − | 0.228399i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.30877i | − | 1.20155i | −0.799416 | − | 0.600777i | \(-0.794858\pi\) | ||
0.799416 | − | 0.600777i | \(-0.205142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.81355 | −0.595576 | −0.297788 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297788 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45474 | 1.28934 | 0.644668 | − | 0.764463i | \(-0.276996\pi\) | ||||
0.644668 | + | 0.764463i | \(0.276996\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.43993i | 0.355901i | 0.984039 | + | 0.177950i | \(0.0569466\pi\) | ||||
−0.984039 | + | 0.177950i | \(0.943053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.84469 | −0.977812 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9095 | 1.49853 | 0.749266 | − | 0.662269i | \(-0.230407\pi\) | ||||
0.749266 | + | 0.662269i | \(0.230407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00270 | 1.07908 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.33616 | −0.824898 | −0.412449 | − | 0.910981i | \(-0.635327\pi\) | ||||
−0.412449 | + | 0.910981i | \(0.635327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5154 | −1.34636 | −0.673178 | − | 0.739481i | \(-0.735071\pi\) | ||||
−0.673178 | + | 0.739481i | \(0.735071\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.5397 | −1.43132 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.01758i | 0.612995i | 0.951872 | + | 0.306497i | \(0.0991571\pi\) | ||||
−0.951872 | + | 0.306497i | \(0.900843\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.759763 | −0.0901673 | −0.0450837 | − | 0.998983i | \(-0.514355\pi\) | ||||
−0.0450837 | + | 0.998983i | \(0.514355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.06479 | 0.358706 | 0.179353 | − | 0.983785i | \(-0.442599\pi\) | ||||
0.179353 | + | 0.983785i | \(0.442599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.919857i | 0.104827i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.40581i | − | 0.720710i | −0.932815 | − | 0.360355i | \(-0.882656\pi\) | ||
0.932815 | − | 0.360355i | \(-0.117344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.54018i | 0.169057i | 0.996421 | + | 0.0845285i | \(0.0269384\pi\) | ||||
−0.996421 | + | 0.0845285i | \(0.973062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.69497 | −0.183846 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2456 | −1.40403 | −0.702017 | − | 0.712160i | \(-0.747717\pi\) | ||||
−0.702017 | + | 0.712160i | \(0.747717\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.32641i | − | 0.139045i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.9095 | − | 1.03159i | −1.52968 | − | 0.105839i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.71374i | 0.174004i | 0.996208 | + | 0.0870022i | \(0.0277287\pi\) | ||||
−0.996208 | + | 0.0870022i | \(0.972271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.4769i | − | 1.34100i | −0.741910 | − | 0.670500i | \(-0.766080\pi\) | ||
0.741910 | − | 0.670500i | \(-0.233920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.577449i | − | 0.0568977i | −0.999595 | − | 0.0284489i | \(-0.990943\pi\) | ||
0.999595 | − | 0.0284489i | \(-0.00905678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.53966 | −0.728886 | −0.364443 | − | 0.931226i | \(-0.618741\pi\) | ||||
−0.364443 | + | 0.931226i | \(0.618741\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.29119i | 0.219457i | 0.993962 | + | 0.109728i | \(0.0349981\pi\) | ||||
−0.993962 | + | 0.109728i | \(0.965002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.2089 | −1.80702 | −0.903511 | − | 0.428566i | \(-0.859019\pi\) | ||||
−0.903511 | + | 0.428566i | \(0.859019\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9985 | 1.21212 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.194826i | − | 0.0178597i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.55212 | 0.504738 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.01937i | 0.538389i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.29119i | − | 0.203311i | −0.994820 | − | 0.101655i | \(-0.967586\pi\) | ||
0.994820 | − | 0.101655i | \(-0.0324139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3766i | 1.25609i | 0.778176 | + | 0.628046i | \(0.216145\pi\) | ||||
−0.778176 | + | 0.628046i | \(0.783855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.118574 | − | 1.71374i | 0.0102817 | − | 0.148600i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.05799i | − | 0.603005i | −0.953465 | − | 0.301502i | \(-0.902512\pi\) | ||
0.953465 | − | 0.301502i | \(-0.0974881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3574 | −0.878500 | −0.439250 | − | 0.898365i | \(-0.644756\pi\) | ||||
−0.439250 | + | 0.898365i | \(0.644756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.85569 | 0.656926 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.37060i | 0.612095i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.51058i | − | 0.287598i | −0.989607 | − | 0.143799i | \(-0.954068\pi\) | ||
0.989607 | − | 0.143799i | \(-0.0459319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.9489i | 1.62342i | 0.584063 | + | 0.811709i | \(0.301462\pi\) | ||||
−0.584063 | + | 0.811709i | \(0.698538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.1551 | −1.94019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.24024 | 0.577834 | 0.288917 | − | 0.957354i | \(-0.406705\pi\) | ||||
0.288917 | + | 0.957354i | \(0.406705\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49410i | 0.117751i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.9971 | −1.87960 | −0.939799 | − | 0.341728i | \(-0.888988\pi\) | ||||
−0.939799 | + | 0.341728i | \(0.888988\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.6356 | −1.44206 | −0.721032 | − | 0.692901i | \(-0.756332\pi\) | ||||
−0.721032 | + | 0.692901i | \(0.756332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.67233 | 0.128640 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48587 | 0.645169 | 0.322585 | − | 0.946541i | \(-0.395448\pi\) | ||||
0.322585 | + | 0.946541i | \(0.395448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.66239 | −0.201257 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0959 | 1.42730 | 0.713648 | − | 0.700504i | \(-0.247042\pi\) | ||||
0.713648 | + | 0.700504i | \(0.247042\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.0058i | − | 1.18970i | −0.803837 | − | 0.594850i | \(-0.797211\pi\) | ||
0.803837 | − | 0.594850i | \(-0.202789\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.0592 | −1.84239 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.15386 | 0.0843788 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.6335i | 1.34827i | 0.738607 | + | 0.674137i | \(0.235484\pi\) | ||||
−0.738607 | + | 0.674137i | \(0.764516\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.33628i | − | 0.672040i | −0.941855 | − | 0.336020i | \(-0.890919\pi\) | ||
0.941855 | − | 0.336020i | \(-0.109081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.7062i | 1.11902i | 0.828822 | + | 0.559512i | \(0.189011\pi\) | ||||
−0.828822 | + | 0.559512i | \(0.810989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.45474 | 0.315788 | 0.157894 | − | 0.987456i | \(-0.449530\pi\) | ||||
0.157894 | + | 0.987456i | \(0.449530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.847201 | −0.0594619 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.0753i | 0.913219i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.1497 | + | 0.702261i | 0.702070 | + | 0.0485764i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 25.8391i | − | 1.77884i | −0.457095 | − | 0.889418i | \(-0.651110\pi\) | ||
0.457095 | − | 0.889418i | \(-0.348890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 28.9883i | − | 1.97699i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.77647i | − | 0.188479i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.66384 | −0.111922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.3538i | − | 1.69782i | −0.528541 | − | 0.848908i | \(-0.677261\pi\) | ||
0.528541 | − | 0.848908i | \(-0.322739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.81895 | 0.651707 | 0.325853 | − | 0.945420i | \(-0.394348\pi\) | ||||
0.325853 | + | 0.945420i | \(0.394348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3912 | 1.08316 | 0.541580 | − | 0.840649i | \(-0.317826\pi\) | ||||
0.541580 | + | 0.840649i | \(0.317826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.27083i | 0.214279i | 0.994244 | + | 0.107139i | \(0.0341691\pi\) | ||||
−0.994244 | + | 0.107139i | \(0.965831\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.36566 | 0.545716 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.17125i | − | 0.593239i | −0.954996 | − | 0.296620i | \(-0.904141\pi\) | ||
0.954996 | − | 0.296620i | \(-0.0958593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.77147i | − | 0.629436i | −0.949185 | − | 0.314718i | \(-0.898090\pi\) | ||
0.949185 | − | 0.314718i | \(-0.101910\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.4680i | 1.49932i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6356 | − | 1.01264i | −0.931240 | − | 0.0644327i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25.0093i | − | 1.57858i | −0.614023 | − | 0.789288i | \(-0.710450\pi\) | ||
0.614023 | − | 0.789288i | \(-0.289550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.84884 | −0.556322 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8220 | −0.675060 | −0.337530 | − | 0.941315i | \(-0.609591\pi\) | ||||
−0.337530 | + | 0.941315i | \(0.609591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.88039i | − | 0.178978i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.0929i | − | 0.684018i | −0.939697 | − | 0.342009i | \(-0.888893\pi\) | ||
0.939697 | − | 0.342009i | \(-0.111107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 37.4047i | − | 2.29775i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.4124 | 1.73233 | 0.866167 | − | 0.499754i | \(-0.166576\pi\) | ||||
0.866167 | + | 0.499754i | \(0.166576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.81895 | −0.596459 | −0.298229 | − | 0.954494i | \(-0.596396\pi\) | ||||
−0.298229 | + | 0.954494i | \(0.596396\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 15.7681i | − | 0.950851i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8883 | −0.654213 | −0.327107 | − | 0.944987i | \(-0.606074\pi\) | ||||
−0.327107 | + | 0.944987i | \(0.606074\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7060 | 0.817630 | 0.408815 | − | 0.912617i | \(-0.365942\pi\) | ||||
0.408815 | + | 0.912617i | \(0.365942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.78241 | −0.224841 | −0.112421 | − | 0.993661i | \(-0.535860\pi\) | ||||
−0.112421 | + | 0.993661i | \(0.535860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.50292 | −0.0887145 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7556 | 0.985624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5366 | 0.615553 | 0.307777 | − | 0.951459i | \(-0.400415\pi\) | ||||
0.307777 | + | 0.951459i | \(0.400415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.7245i | 1.26485i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.7598 | 0.737916 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33201 | 0.192054 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.0535i | 2.06442i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.70875i | − | 0.497035i | −0.968627 | − | 0.248517i | \(-0.920057\pi\) | ||
0.968627 | − | 0.248517i | \(-0.0799433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7888i | 1.34894i | 0.738303 | + | 0.674469i | \(0.235628\pi\) | ||||
−0.738303 | + | 0.674469i | \(0.764372\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2994 | 1.14739 | 0.573696 | − | 0.819069i | \(-0.305509\pi\) | ||||
0.573696 | + | 0.819069i | \(0.305509\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9095 | −0.837400 | −0.418700 | − | 0.908125i | \(-0.637514\pi\) | ||||
−0.418700 | + | 0.908125i | \(0.637514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.01758i | − | 0.280930i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.14971 | − | 0.148739i | −0.119613 | − | 0.00827607i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.7371i | 1.26123i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.961577i | 0.0530135i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.40087i | 0.131964i | 0.997821 | + | 0.0659820i | \(0.0210180\pi\) | ||||
−0.997821 | + | 0.0659820i | \(0.978982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2035 | 0.939927 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.13719i | − | 0.116420i | −0.998304 | − | 0.0582101i | \(-0.981461\pi\) | ||
0.998304 | − | 0.0582101i | \(-0.0185393\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4437 | 0.890478 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.45619 | −0.294607 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 15.2796i | − | 0.820251i | −0.912029 | − | 0.410126i | \(-0.865485\pi\) | ||
0.912029 | − | 0.410126i | \(-0.134515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7712 | 1.16539 | 0.582693 | − | 0.812692i | \(-0.301999\pi\) | ||||
0.582693 | + | 0.812692i | \(0.301999\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.2131i | − | 1.44841i | −0.689587 | − | 0.724203i | \(-0.742208\pi\) | ||
0.689587 | − | 0.724203i | \(-0.257792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.60496i | 0.138257i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.19435i | 0.274147i | 0.990561 | + | 0.137074i | \(0.0437697\pi\) | ||||
−0.990561 | + | 0.137074i | \(0.956230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8189 | − | 2.61670i | −0.990471 | − | 0.137721i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.5081i | − | 0.550018i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4913 | −1.59163 | −0.795816 | − | 0.605539i | \(-0.792958\pi\) | ||||
−0.795816 | + | 0.605539i | \(0.792958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.29942 | 0.223215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3538i | 1.31277i | 0.754426 | + | 0.656385i | \(0.227915\pi\) | ||||
−0.754426 | + | 0.656385i | \(0.772085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.23520i | 0.372632i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7019i | 1.21748i | 0.793368 | + | 0.608742i | \(0.208326\pi\) | ||||
−0.793368 | + | 0.608742i | \(0.791674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.816636 | −0.0417282 | −0.0208641 | − | 0.999782i | \(-0.506642\pi\) | ||||
−0.0208641 | + | 0.999782i | \(0.506642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.15386 | 0.160736 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 22.3547i | − | 1.13343i | −0.823915 | − | 0.566713i | \(-0.808215\pi\) | ||
0.823915 | − | 0.566713i | \(-0.191785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.87419 | 0.0947817 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.9633 | −1.10509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.5731 | 1.63480 | 0.817399 | − | 0.576072i | \(-0.195415\pi\) | ||||
0.817399 | + | 0.576072i | \(0.195415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.81355 | −0.390190 | −0.195095 | − | 0.980784i | \(-0.562502\pi\) | ||||
−0.195095 | + | 0.980784i | \(0.562502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7114 | −1.18115 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.0592 | 0.845592 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.3145i | − | 1.15283i | −0.817157 | − | 0.576415i | \(-0.804451\pi\) | ||
0.817157 | − | 0.576415i | \(-0.195549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.49708 | −0.122873 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.28074 | 0.259221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.56950i | 0.320941i | 0.987041 | + | 0.160471i | \(0.0513012\pi\) | ||||
−0.987041 | + | 0.160471i | \(0.948699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.1763i | 1.76312i | 0.472069 | + | 0.881561i | \(0.343507\pi\) | ||||
−0.472069 | + | 0.881561i | \(0.656493\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.33968i | 0.161998i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.14411 | −0.200547 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2426 | 0.975049 | 0.487525 | − | 0.873109i | \(-0.337900\pi\) | ||||
0.487525 | + | 0.873109i | \(0.337900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.3068i | − | 1.26423i | −0.774876 | − | 0.632113i | \(-0.782188\pi\) | ||
0.774876 | − | 0.632113i | \(-0.217812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4859 | + | 1.14066i | 0.788626 | + | 0.0545653i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8743i | 1.18719i | 0.804766 | + | 0.593593i | \(0.202291\pi\) | ||||
−0.804766 | + | 0.593593i | \(0.797709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.1011i | 1.71521i | 0.514305 | + | 0.857607i | \(0.328050\pi\) | ||||
−0.514305 | + | 0.857607i | \(0.671950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.4146i | 2.15286i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.42669 | −0.350487 | −0.175244 | − | 0.984525i | \(-0.556071\pi\) | ||||
−0.175244 | + | 0.984525i | \(0.556071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.90109i | − | 0.419136i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.54778 | −0.213203 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7542 | 1.06439 | 0.532197 | − | 0.846620i | \(-0.321366\pi\) | ||||
0.532197 | + | 0.846620i | \(0.321366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.4771i | − | 0.813990i | −0.913430 | − | 0.406995i | \(-0.866577\pi\) | ||
0.913430 | − | 0.406995i | \(-0.133423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1832 | 1.44920 | 0.724602 | − | 0.689167i | \(-0.242024\pi\) | ||||
0.724602 | + | 0.689167i | \(0.242024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.5579i | − | 0.766206i | −0.923706 | − | 0.383103i | \(-0.874855\pi\) | ||
0.923706 | − | 0.383103i | \(-0.125145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.97743i | 0.0913091i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.7340i | 0.907368i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.03259 | + | 29.3768i | −0.0932615 | + | 1.34790i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 8.37355i | − | 0.382597i | −0.981532 | − | 0.191299i | \(-0.938730\pi\) | ||
0.981532 | − | 0.191299i | \(-0.0612699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.5988 | −1.12161 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.87582 | 0.266807 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 21.4107i | − | 0.970211i | −0.874456 | − | 0.485106i | \(-0.838781\pi\) | ||
0.874456 | − | 0.485106i | \(-0.161219\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.9693i | 1.44275i | 0.692543 | + | 0.721377i | \(0.256490\pi\) | ||||
−0.692543 | + | 0.721377i | \(0.743510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06272i | 0.0478627i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.299423 | −0.0134309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7220 | 0.569513 | 0.284757 | − | 0.958600i | \(-0.408087\pi\) | ||||
0.284757 | + | 0.958600i | \(0.408087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 18.3089i | − | 0.816353i | −0.912903 | − | 0.408177i | \(-0.866165\pi\) | ||
0.912903 | − | 0.408177i | \(-0.133835\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.2074 | −2.05620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.0255 | 1.59680 | 0.798402 | − | 0.602125i | \(-0.205679\pi\) | ||||
0.798402 | + | 0.602125i | \(0.205679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.20783 | 0.0534314 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.97987 | −0.0872434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.69497 | −0.250465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0928 | −0.967905 | −0.483952 | − | 0.875094i | \(-0.660799\pi\) | ||||
−0.483952 | + | 0.875094i | \(0.660799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9362i | 0.828024i | 0.910271 | + | 0.414012i | \(0.135873\pi\) | ||||
−0.910271 | + | 0.414012i | \(0.864127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.48279 | −0.151713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.62710 | 0.375091 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.8351i | 0.555950i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.8508i | 1.11763i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.9760i | − | 0.688134i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.7542 | −0.462357 | −0.231179 | − | 0.972911i | \(-0.574258\pi\) | ||||
−0.231179 | + | 0.972911i | \(0.574258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.85569 | 0.336501 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.2675i | 1.50793i | 0.656914 | + | 0.753965i | \(0.271861\pi\) | ||||
−0.656914 | + | 0.753965i | \(0.728139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.646792 | + | 9.34803i | −0.0275543 | + | 0.398239i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.52453i | − | 0.107354i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.9202i | 0.759304i | 0.925129 | + | 0.379652i | \(0.123956\pi\) | ||||
−0.925129 | + | 0.379652i | \(0.876044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.4558i | − | 1.20355i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.2627 | 1.94974 | 0.974870 | − | 0.222775i | \(-0.0715117\pi\) | ||||
0.974870 | + | 0.222775i | \(0.0715117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 65.8605i | 2.77077i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.6692 | 1.15995 | 0.579977 | − | 0.814633i | \(-0.303061\pi\) | ||||
0.579977 | + | 0.814633i | \(0.303061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.4913 | 1.44341 | 0.721707 | − | 0.692198i | \(-0.243358\pi\) | ||||
0.721707 | + | 0.692198i | \(0.243358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 25.6116i | − | 1.06808i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63974 | 0.234785 | 0.117393 | − | 0.993086i | \(-0.462546\pi\) | ||||
0.117393 | + | 0.993086i | \(0.462546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.606986i | 0.0251820i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.4635i | 1.05459i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.24286i | 0.340219i | 0.985425 | + | 0.170110i | \(0.0544122\pi\) | ||||
−0.985425 | + | 0.170110i | \(0.945588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.6356 | − | 2.11968i | −1.26232 | − | 0.0873401i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 0.815152i | − | 0.0334743i | −0.999860 | − | 0.0167371i | \(-0.994672\pi\) | ||
0.999860 | − | 0.0167371i | \(-0.00532785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.667989 | −0.0273849 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.74316 | 0.357236 | 0.178618 | − | 0.983919i | \(-0.442837\pi\) | ||||
0.178618 | + | 0.983919i | \(0.442837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2225i | 0.702520i | 0.936278 | + | 0.351260i | \(0.114247\pi\) | ||||
−0.936278 | + | 0.351260i | \(0.885753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 19.0362i | − | 0.773933i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.09294i | − | 0.287894i | −0.989585 | − | 0.143947i | \(-0.954021\pi\) | ||
0.989585 | − | 0.143947i | \(-0.0459794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.21199 | 0.332221 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.47632 | 0.301966 | 0.150983 | − | 0.988536i | \(-0.451756\pi\) | ||||
0.150983 | + | 0.988536i | \(0.451756\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.3550i | − | 1.02075i | −0.859951 | − | 0.510376i | \(-0.829506\pi\) | ||
0.859951 | − | 0.510376i | \(-0.170494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.4659 | −1.74704 | −0.873522 | − | 0.486785i | \(-0.838169\pi\) | ||||
−0.873522 | + | 0.486785i | \(0.838169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.22010 | −0.209139 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.1398 | −0.525591 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.61314 | −0.144065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0889 | 1.75515 | 0.877575 | − | 0.479439i | \(-0.159160\pi\) | ||||
0.877575 | + | 0.479439i | \(0.159160\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.85569 | −0.311744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.0369i | 0.912755i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.46574 | 0.255381 | 0.127691 | − | 0.991814i | \(-0.459244\pi\) | ||||
0.127691 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0536 | 1.61900 | 0.809498 | − | 0.587123i | \(-0.199740\pi\) | ||||
0.809498 | + | 0.587123i | \(0.199740\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.4192i | 1.35316i | 0.736370 | + | 0.676579i | \(0.236538\pi\) | ||||
−0.736370 | + | 0.676579i | \(0.763462\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.7891i | − | 0.580521i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.50663i | − | 0.372023i | −0.982548 | − | 0.186012i | \(-0.940444\pi\) | ||
0.982548 | − | 0.186012i | \(-0.0595562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.2924 | 1.92601 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.8306 | 0.499809 | 0.249904 | − | 0.968270i | \(-0.419601\pi\) | ||||
0.249904 | + | 0.968270i | \(0.419601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.6870i | − | 1.31027i | −0.755512 | − | 0.655135i | \(-0.772612\pi\) | ||
0.755512 | − | 0.655135i | \(-0.227388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.87582 | − | 0.406550i | −0.227855 | − | 0.0157653i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.14990i | − | 0.315565i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 24.5436i | − | 0.947496i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.92824i | − | 0.112875i | −0.998406 | − | 0.0564377i | \(-0.982026\pi\) | ||
0.998406 | − | 0.0564377i | \(-0.0179742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.0905 | −0.656842 | −0.328421 | − | 0.944531i | \(-0.606517\pi\) | ||||
−0.328421 | + | 0.944531i | \(0.606517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.675386i | 0.0259190i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.0793 | −1.34227 | −0.671136 | − | 0.741334i | \(-0.734194\pi\) | ||||
−0.671136 | + | 0.741334i | \(0.734194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.1993 | −0.924609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 36.7176i | − | 1.39883i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1612 | 0.728925 | 0.364462 | − | 0.931218i | \(-0.381253\pi\) | ||||
0.364462 | + | 0.931218i | \(0.381253\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.5117i | 1.34704i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.88525i | 0.0714091i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.2828i | 0.577223i | 0.957446 | + | 0.288612i | \(0.0931936\pi\) | ||||
−0.957446 | + | 0.288612i | \(0.906806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7822 | − | 2.19902i | −1.19869 | − | 0.0829376i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5.31124i | − | 0.199750i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.5648 | −0.622102 | −0.311051 | − | 0.950393i | \(-0.600681\pi\) | ||||
−0.311051 | + | 0.950393i | \(0.600681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.7091 | 1.00026 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 26.9344i | − | 1.00729i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 22.4545i | − | 0.837410i | −0.908122 | − | 0.418705i | \(-0.862484\pi\) | ||
0.908122 | − | 0.418705i | \(-0.137516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.227573i | − | 0.00847524i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.5226 | 0.539356 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0365 | −0.965642 | −0.482821 | − | 0.875719i | \(-0.660388\pi\) | ||||
−0.482821 | + | 0.875719i | \(0.660388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.17966i | − | 0.154590i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.89243 | −0.143770 | −0.0718851 | − | 0.997413i | \(-0.522901\pi\) | ||||
−0.0718851 | + | 0.997413i | \(0.522901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.7114 | −0.431394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.5916 | 1.19890 | 0.599451 | − | 0.800412i | \(-0.295386\pi\) | ||||
0.599451 | + | 0.800412i | \(0.295386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.0449 | 1.83597 | 0.917985 | − | 0.396616i | \(-0.129816\pi\) | ||||
0.917985 | + | 0.396616i | \(0.129816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0365 | −0.440985 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.97138 | −0.108572 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.60677i | 0.204594i | 0.994754 | + | 0.102297i | \(0.0326192\pi\) | ||||
−0.994754 | + | 0.102297i | \(0.967381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.3977 | 2.48925 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.28113 | 0.155600 | 0.0778001 | − | 0.996969i | \(-0.475210\pi\) | ||||
0.0778001 | + | 0.996969i | \(0.475210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29.5451i | − | 1.07101i | −0.844532 | − | 0.535504i | \(-0.820122\pi\) | ||
0.844532 | − | 0.535504i | \(-0.179878\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.902959i | 0.0326893i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.3254i | 0.770015i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0326 | 0.542089 | 0.271044 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271044 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.8445 | 1.79278 | 0.896391 | − | 0.443265i | \(-0.146180\pi\) | ||||
0.896391 | + | 0.443265i | \(0.146180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.5939i | 1.70962i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.14740 | + | 16.5832i | −0.0411098 | + | 0.594156i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.77334i | − | 0.0634551i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 24.8242i | − | 0.886014i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.0557i | − | 1.35654i | −0.734812 | − | 0.678270i | \(-0.762730\pi\) | ||
0.734812 | − | 0.678270i | \(-0.237270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.57022 | −0.269166 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.3912i | 1.25678i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.9118 | 1.55544 | 0.777718 | − | 0.628614i | \(-0.216377\pi\) | ||||
0.777718 | + | 0.628614i | \(0.216377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.20620 | 0.0426722 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.15343i | 0.252439i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.12273 | 0.180552 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.5045i | 1.45922i | 0.683863 | + | 0.729610i | \(0.260298\pi\) | ||||
−0.683863 | + | 0.729610i | \(0.739702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.1578i | − | 1.05898i | −0.848315 | − | 0.529491i | \(-0.822383\pi\) | ||
0.848315 | − | 0.529491i | \(-0.177617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 82.2775i | 2.88206i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.54381 | − | 36.7654i | 0.0889967 | − | 1.28626i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 49.1525i | − | 1.71543i | −0.514123 | − | 0.857716i | \(-0.671883\pi\) | ||
0.514123 | − | 0.857716i | \(-0.328117\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.37415 | −0.257047 | −0.128523 | − | 0.991706i | \(-0.541024\pi\) | ||||
−0.128523 | + | 0.991706i | \(0.541024\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.9149 | −1.14456 | −0.572281 | − | 0.820057i | \(-0.693941\pi\) | ||||
−0.572281 | + | 0.820057i | \(0.693941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7824i | 0.443950i | 0.975052 | + | 0.221975i | \(0.0712504\pi\) | ||||
−0.975052 | + | 0.221975i | \(0.928750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.38372i | 0.117239i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.8948i | 2.21117i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.5872 | 1.15956 | 0.579779 | − | 0.814773i | \(-0.303139\pi\) | ||||
0.579779 | + | 0.814773i | \(0.303139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3787 | −0.840646 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.73381i | − | 0.197249i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.18809 | 0.0751836 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.7087 | 0.949843 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1125 | −0.722879 | −0.361440 | − | 0.932395i | \(-0.617715\pi\) | ||||
−0.361440 | + | 0.932395i | \(0.617715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.3984 | −0.696797 | −0.348399 | − | 0.937346i | \(-0.613274\pi\) | ||||
−0.348399 | + | 0.937346i | \(0.613274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.3208 | −1.27337 | −0.636685 | − | 0.771124i | \(-0.719695\pi\) | ||||
−0.636685 | + | 0.771124i | \(0.719695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.6948 | −0.534256 | −0.267128 | − | 0.963661i | \(-0.586075\pi\) | ||||
−0.267128 | + | 0.963661i | \(0.586075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 29.0951i | − | 0.989262i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9516 | 0.507199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.8875 | 0.572210 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.37223i | 0.0801961i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 49.4556i | − | 1.67000i | −0.550251 | − | 0.834999i | \(-0.685468\pi\) | ||
0.550251 | − | 0.834999i | \(-0.314532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.1709i | − | 0.443738i | −0.975077 | − | 0.221869i | \(-0.928784\pi\) | ||
0.975077 | − | 0.221869i | \(-0.0712157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.9728 | −0.503875 | −0.251938 | − | 0.967743i | \(-0.581068\pi\) | ||||
−0.251938 | + | 0.967743i | \(0.581068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.77637 | 0.294682 | 0.147341 | − | 0.989086i | \(-0.452929\pi\) | ||||
0.147341 | + | 0.989086i | \(0.452929\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.902959i | − | 0.0302843i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6101 | + | 0.734112i | 0.355052 | + | 0.0245661i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 65.4732i | − | 2.18853i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.1449i | 0.505111i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.39317i | − | 0.179673i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.8781 | −1.82421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42.5145i | − | 1.41167i | −0.708376 | − | 0.705835i | \(-0.750572\pi\) | ||
0.708376 | − | 0.705835i | \(-0.249428\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.3470 | −1.80060 | −0.900298 | − | 0.435275i | \(-0.856651\pi\) | ||||
−0.900298 | + | 0.435275i | \(0.856651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.59490 | −0.118974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.66583i | 0.187102i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5081 | −0.874423 | −0.437211 | − | 0.899359i | \(-0.644034\pi\) | ||||
−0.437211 | + | 0.899359i | \(0.644034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.55711i | 0.0841682i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.3752i | 1.62345i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2074i | 0.531747i | 0.964008 | + | 0.265873i | \(0.0856603\pi\) | ||||
−0.964008 | + | 0.265873i | \(0.914340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.05939 | + | 29.7641i | −0.0674937 | + | 0.975480i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.95619i | − | 0.129381i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2969 | 0.826414 | 0.413207 | − | 0.910637i | \(-0.364409\pi\) | ||||
0.413207 | + | 0.910637i | \(0.364409\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.3923 | 1.77314 | 0.886569 | − | 0.462597i | \(-0.153082\pi\) | ||||
0.886569 | + | 0.462597i | \(0.153082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.4578i | − | 0.470810i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 31.9734i | − | 1.03900i | −0.854472 | − | 0.519498i | \(-0.826119\pi\) | ||
0.854472 | − | 0.519498i | \(-0.173881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 10.3150i | − | 0.334840i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.6387 | −0.765732 | −0.382866 | − | 0.923804i | \(-0.625063\pi\) | ||||
−0.382866 | + | 0.923804i | \(0.625063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.8877 | 2.06736 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.78155i | − | 0.0898210i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6333 | −0.601073 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0108 | −1.03046 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.41838 | −0.302875 | −0.151437 | − | 0.988467i | \(-0.548390\pi\) | ||||
−0.151437 | + | 0.988467i | \(0.548390\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.7292 | 0.793598 | 0.396799 | − | 0.917906i | \(-0.370121\pi\) | ||||
0.396799 | + | 0.917906i | \(0.370121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.08183 | −0.130858 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3899 | −0.556354 | −0.278177 | − | 0.960530i | \(-0.589730\pi\) | ||||
−0.278177 | + | 0.960530i | \(0.589730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.9163i | − | 0.988088i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.8306 | 0.919553 | 0.459777 | − | 0.888035i | \(-0.347930\pi\) | ||||
0.459777 | + | 0.888035i | \(0.347930\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.8512 | 1.71584 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0533i | 1.01923i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4684i | 0.936095i | 0.883703 | + | 0.468048i | \(0.155042\pi\) | ||||
−0.883703 | + | 0.468048i | \(0.844958\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.2737i | − | 0.484209i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9307 | 0.852903 | 0.426451 | − | 0.904510i | \(-0.359763\pi\) | ||||
0.426451 | + | 0.904510i | \(0.359763\pi\) | |||||||
\(998\) | 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 | 2736.2.f.h.1025.1 | 8 | ||
3.2 | odd | 2 | 2736.2.f.g.1025.8 | 8 | |||
4.3 | odd | 2 | 1368.2.f.d.1025.1 | yes | 8 | ||
12.11 | even | 2 | 1368.2.f.c.1025.8 | yes | 8 | ||
19.18 | odd | 2 | 2736.2.f.g.1025.1 | 8 | |||
57.56 | even | 2 | inner | 2736.2.f.h.1025.8 | 8 | ||
76.75 | even | 2 | 1368.2.f.c.1025.1 | ✓ | 8 | ||
228.227 | odd | 2 | 1368.2.f.d.1025.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.f.c.1025.1 | ✓ | 8 | 76.75 | even | 2 | ||
1368.2.f.c.1025.8 | yes | 8 | 12.11 | even | 2 | ||
1368.2.f.d.1025.1 | yes | 8 | 4.3 | odd | 2 | ||
1368.2.f.d.1025.8 | yes | 8 | 228.227 | odd | 2 | ||
2736.2.f.g.1025.1 | 8 | 19.18 | odd | 2 | |||
2736.2.f.g.1025.8 | 8 | 3.2 | odd | 2 | |||
2736.2.f.h.1025.1 | 8 | 1.1 | even | 1 | trivial | ||
2736.2.f.h.1025.8 | 8 | 57.56 | even | 2 | inner |