Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.a (trivial) |
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: | yes |
Analytic conductor: | \(16.0020205651\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.69402\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.69402 | −0.757591 | −0.378795 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378795 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.12928 | −1.56072 | −0.780360 | − | 0.625330i | \(-0.784964\pi\) | ||||
−0.780360 | + | 0.625330i | \(0.784964\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48865 | 0.750358 | 0.375179 | − | 0.926952i | \(-0.377581\pi\) | ||||
0.375179 | + | 0.926952i | \(0.377581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.35347 | 0.375386 | 0.187693 | − | 0.982228i | \(-0.439899\pi\) | ||||
0.187693 | + | 0.982228i | \(0.439899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.69402 | −0.437395 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.89205 | −1.91410 | −0.957052 | − | 0.289918i | \(-0.906372\pi\) | ||||
−0.957052 | + | 0.289918i | \(0.906372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.08686 | 1.16701 | 0.583503 | − | 0.812111i | \(-0.301682\pi\) | ||||
0.583503 | + | 0.812111i | \(0.301682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.12928 | −0.901083 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.55829 | 1.36750 | 0.683749 | − | 0.729717i | \(-0.260348\pi\) | ||||
0.683749 | + | 0.729717i | \(0.260348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.13028 | −0.426056 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.41203 | 1.37638 | 0.688189 | − | 0.725531i | \(-0.258406\pi\) | ||||
0.688189 | + | 0.725531i | \(0.258406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.69564 | 0.843361 | 0.421681 | − | 0.906744i | \(-0.361440\pi\) | ||||
0.421681 | + | 0.906744i | \(0.361440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.48865 | 0.433219 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.99510 | 1.18239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0133728 | −0.00219847 | −0.00109924 | − | 0.999999i | \(-0.500350\pi\) | ||||
−0.00109924 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.35347 | 0.216729 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.02270 | −0.159719 | −0.0798593 | − | 0.996806i | \(-0.525447\pi\) | ||||
−0.0798593 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.67968 | −1.32364 | −0.661819 | − | 0.749663i | \(-0.730215\pi\) | ||||
−0.661819 | + | 0.749663i | \(0.730215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.69402 | −0.252530 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.31896 | 0.775850 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.0509 | 1.43585 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.89205 | −1.10511 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1374 | 1.66720 | 0.833601 | − | 0.552367i | \(-0.186275\pi\) | ||||
0.833601 | + | 0.552367i | \(0.186275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.21584 | −0.568464 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.08686 | 0.673772 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0660655 | −0.00860099 | −0.00430050 | − | 0.999991i | \(-0.501369\pi\) | ||||
−0.00430050 | + | 0.999991i | \(0.501369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3680 | 1.32749 | 0.663746 | − | 0.747958i | \(-0.268966\pi\) | ||||
0.663746 | + | 0.747958i | \(0.268966\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.12928 | −0.520240 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.29282 | −0.284389 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.10634 | 0.746008 | 0.373004 | − | 0.927830i | \(-0.378328\pi\) | ||||
0.373004 | + | 0.927830i | \(0.378328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.55829 | 0.789526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.95916 | −1.18193 | −0.590967 | − | 0.806696i | \(-0.701254\pi\) | ||||
−0.590967 | + | 0.806696i | \(0.701254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.76173 | −0.440277 | −0.220139 | − | 0.975469i | \(-0.570651\pi\) | ||||
−0.220139 | + | 0.975469i | \(0.570651\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.13028 | −0.245984 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.2764 | −1.17110 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4241 | 1.28531 | 0.642655 | − | 0.766155i | \(-0.277833\pi\) | ||||
0.642655 | + | 0.766155i | \(0.277833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4077 | 1.14240 | 0.571199 | − | 0.820811i | \(-0.306478\pi\) | ||||
0.571199 | + | 0.820811i | \(0.306478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3693 | 1.45011 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.41203 | 0.794653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.46475 | 0.685262 | 0.342631 | − | 0.939470i | \(-0.388682\pi\) | ||||
0.342631 | + | 0.939470i | \(0.388682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.58886 | −0.585872 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.69564 | 0.486915 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.61727 | −0.884114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.7791 | 1.90673 | 0.953364 | − | 0.301822i | \(-0.0975947\pi\) | ||||
0.953364 | + | 0.301822i | \(0.0975947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.48865 | 0.250119 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0599 | 1.39901 | 0.699507 | − | 0.714625i | \(-0.253403\pi\) | ||||
0.699507 | + | 0.714625i | \(0.253403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8777 | −1.76154 | −0.880770 | − | 0.473545i | \(-0.842974\pi\) | ||||
−0.880770 | + | 0.473545i | \(0.842974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.99510 | 0.682652 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1294 | 1.26926 | 0.634632 | − | 0.772815i | \(-0.281152\pi\) | ||||
0.634632 | + | 0.772815i | \(0.281152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.71046 | 0.834311 | 0.417155 | − | 0.908835i | \(-0.363027\pi\) | ||||
0.417155 | + | 0.908835i | \(0.363027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0133728 | −0.00126929 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25013 | −0.305747 | −0.152873 | − | 0.988246i | \(-0.548853\pi\) | ||||
−0.152873 | + | 0.988246i | \(0.548853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.1099 | −1.03600 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.35347 | 0.125129 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.5885 | 2.98738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.80660 | −0.436963 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.02270 | −0.0922136 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0789 | 1.08037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6967 | −1.48159 | −0.740797 | − | 0.671729i | \(-0.765552\pi\) | ||||
−0.740797 | + | 0.671729i | \(0.765552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.67968 | −0.764203 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.32465 | −0.814699 | −0.407349 | − | 0.913272i | \(-0.633547\pi\) | ||||
−0.407349 | + | 0.913272i | \(0.633547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.0051 | −1.82137 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.69402 | −0.145798 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.0786 | −1.88630 | −0.943150 | − | 0.332367i | \(-0.892153\pi\) | ||||
−0.943150 | + | 0.332367i | \(0.892153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.95579 | 0.165888 | 0.0829441 | − | 0.996554i | \(-0.473568\pi\) | ||||
0.0829441 | + | 0.996554i | \(0.473568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.31896 | 0.447937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.36832 | 0.281673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.5562 | −1.04273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0509 | 0.828988 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.90601 | −0.156146 | −0.0780730 | − | 0.996948i | \(-0.524877\pi\) | ||||
−0.0780730 | + | 0.996948i | \(0.524877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.47280 | −0.526749 | −0.263374 | − | 0.964694i | \(-0.584835\pi\) | ||||
−0.263374 | + | 0.964694i | \(0.584835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.89205 | −0.638034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.95452 | −0.638923 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.438526 | 0.0349982 | 0.0174991 | − | 0.999847i | \(-0.494430\pi\) | ||||
0.0174991 | + | 0.999847i | \(0.494430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.1374 | 0.962560 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.0810 | −2.13428 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2469 | −0.959252 | −0.479626 | − | 0.877473i | \(-0.659228\pi\) | ||||
−0.479626 | + | 0.877473i | \(0.659228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.21584 | −0.328203 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1681 | −0.859086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.08686 | 0.389002 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.71361 | 0.662483 | 0.331242 | − | 0.943546i | \(-0.392532\pi\) | ||||
0.331242 | + | 0.943546i | \(0.392532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.79652 | 0.664955 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0660655 | −0.00496579 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.3884 | 1.59864 | 0.799322 | − | 0.600903i | \(-0.205192\pi\) | ||||
0.799322 | + | 0.600903i | \(0.205192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.85644 | −0.137988 | −0.0689942 | − | 0.997617i | \(-0.521979\pi\) | ||||
−0.0689942 | + | 0.997617i | \(0.521979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3680 | 0.766428 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0226538 | 0.00166554 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.6406 | −1.43626 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.12928 | −0.300361 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4811 | 0.830746 | 0.415373 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415373 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.0096 | −1.80023 | −0.900115 | − | 0.435653i | \(-0.856518\pi\) | ||||
−0.900115 | + | 0.435653i | \(0.856518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.29282 | −0.164192 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.2259 | 1.79727 | 0.898634 | − | 0.438699i | \(-0.144561\pi\) | ||||
0.898634 | + | 0.438699i | \(0.144561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.2035 | −1.78663 | −0.893315 | − | 0.449431i | \(-0.851627\pi\) | ||||
−0.893315 | + | 0.449431i | \(0.851627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.10634 | 0.430708 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.6063 | −2.14814 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.73248 | 0.121001 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.55829 | 0.455833 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6594 | 0.875672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.16157 | −0.355337 | −0.177669 | − | 0.984090i | \(-0.556855\pi\) | ||||
−0.177669 | + | 0.984090i | \(0.556855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.95916 | −0.682390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.7036 | 1.00278 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.3896 | −1.31625 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.76173 | −0.254194 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.6817 | −0.718527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.36856 | 0.158610 | 0.0793052 | − | 0.996850i | \(-0.474730\pi\) | ||||
0.0793052 | + | 0.996850i | \(0.474730\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13028 | −0.142019 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.662698 | −0.0439848 | −0.0219924 | − | 0.999758i | \(-0.507001\pi\) | ||||
−0.0219924 | + | 0.999758i | \(0.507001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.4020 | 1.87686 | 0.938428 | − | 0.345475i | \(-0.112282\pi\) | ||||
0.938428 | + | 0.345475i | \(0.112282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.2764 | −0.676134 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.11158 | 0.0728218 | 0.0364109 | − | 0.999337i | \(-0.488407\pi\) | ||||
0.0364109 | + | 0.999337i | \(0.488407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.01045 | −0.587777 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.4241 | 0.742074 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.03519 | −0.325700 | −0.162850 | − | 0.986651i | \(-0.552069\pi\) | ||||
−0.162850 | + | 0.986651i | \(0.552069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9384 | 1.02668 | 0.513341 | − | 0.858185i | \(-0.328408\pi\) | ||||
0.513341 | + | 0.858185i | \(0.328408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.0266 | −1.08779 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.88493 | 0.438078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4077 | 0.659564 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4875 | 0.788205 | 0.394102 | − | 0.919067i | \(-0.371056\pi\) | ||||
0.394102 | + | 0.919067i | \(0.371056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.3213 | 1.02611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.3693 | 0.837220 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.4024 | 0.836016 | 0.418008 | − | 0.908443i | \(-0.362728\pi\) | ||||
0.418008 | + | 0.908443i | \(0.362728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0552200 | 0.00343120 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.41203 | 0.458793 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2710 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.5611 | −1.26306 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.46475 | 0.395636 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.0795 | 1.28524 | 0.642619 | − | 0.766186i | \(-0.277848\pi\) | ||||
0.642619 | + | 0.766186i | \(0.277848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.7180 | −1.38002 | −0.690011 | − | 0.723799i | \(-0.742394\pi\) | ||||
−0.690011 | + | 0.723799i | \(0.742394\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.58886 | −0.338253 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.30153 | −0.319694 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.7334 | −1.54617 | −0.773084 | − | 0.634303i | \(-0.781287\pi\) | ||||
−0.773084 | + | 0.634303i | \(0.781287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.69564 | 0.281120 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0242 | −1.19454 | −0.597271 | − | 0.802039i | \(-0.703748\pi\) | ||||
−0.597271 | + | 0.802039i | \(0.703748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.01267 | −0.416860 | −0.208430 | − | 0.978037i | \(-0.566835\pi\) | ||||
−0.208430 | + | 0.978037i | \(0.566835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.61727 | −0.510443 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.22301 | 0.249276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.2844 | 2.66379 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.7791 | 1.10085 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.63359 | 0.153856 | 0.0769279 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769279 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.111917 | 0.00651603 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.48865 | 0.144406 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.87647 | 0.513339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.8408 | 2.06583 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.0599 | 0.807722 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.5637 | −1.00570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3105 | 0.702597 | 0.351299 | − | 0.936263i | \(-0.385740\pi\) | ||||
0.351299 | + | 0.936263i | \(0.385740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.8777 | −1.01703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.9999 | 1.36091 | 0.680453 | − | 0.732791i | \(-0.261783\pi\) | ||||
0.680453 | + | 0.732791i | \(0.261783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.38113 | 0.191113 | 0.0955564 | − | 0.995424i | \(-0.469537\pi\) | ||||
0.0955564 | + | 0.995424i | \(0.469537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.99510 | 0.394129 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.85532 | −0.441199 | −0.220599 | − | 0.975365i | \(-0.570801\pi\) | ||||
−0.220599 | + | 0.975365i | \(0.570801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4460 | 1.03278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1294 | 0.732810 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −40.1458 | −2.23377 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.88327 | −0.159935 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.71046 | 0.481689 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.9635 | −1.21089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.1080 | −1.32510 | −0.662548 | − | 0.749019i | \(-0.730525\pi\) | ||||
−0.662548 | + | 0.749019i | \(0.730525\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0133728 | −0.000732825 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3443 | −0.565169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7093 | 0.692321 | 0.346161 | − | 0.938175i | \(-0.387485\pi\) | ||||
0.346161 | + | 0.938175i | \(0.387485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.25013 | −0.176523 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6858 | 0.632822 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5982 | −0.680240 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1099 | −0.598138 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.7727 | −1.16882 | −0.584410 | − | 0.811459i | \(-0.698674\pi\) | ||||
−0.584410 | + | 0.811459i | \(0.698674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.7390 | −1.91307 | −0.956533 | − | 0.291625i | \(-0.905804\pi\) | ||||
−0.956533 | + | 0.291625i | \(0.905804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.35347 | 0.0722430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.84039 | −0.204403 | −0.102202 | − | 0.994764i | \(-0.532589\pi\) | ||||
−0.102202 | + | 0.994764i | \(0.532589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.8711 | 0.895423 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.5885 | 1.72477 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.9436 | −1.05258 | −0.526292 | − | 0.850304i | \(-0.676418\pi\) | ||||
−0.526292 | + | 0.850304i | \(0.676418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.87619 | 0.361905 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.80660 | −0.252281 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.37246 | 0.333550 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6497 | −0.608108 | −0.304054 | − | 0.952655i | \(-0.598340\pi\) | ||||
−0.304054 | + | 0.952655i | \(0.598340\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.02270 | −0.0532395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.1188 | −2.60204 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0130 | −0.725568 | −0.362784 | − | 0.931873i | \(-0.618174\pi\) | ||||
−0.362784 | + | 0.931873i | \(0.618174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0789 | 0.623750 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0320 | 0.516673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.20637 | 0.164700 | 0.0823502 | − | 0.996603i | \(-0.473757\pi\) | ||||
0.0823502 | + | 0.996603i | \(0.473757\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.6967 | −0.855398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.38840 | −0.0709437 | −0.0354719 | − | 0.999371i | \(-0.511293\pi\) | ||||
−0.0354719 | + | 0.999371i | \(0.511293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.4084 | 0.887214 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.67968 | −0.441213 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6756 | −0.946891 | −0.473446 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473446 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.7584 | −2.61753 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.32465 | −0.470367 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.3527 | −0.973740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.4874 | 1.88144 | 0.940719 | − | 0.339187i | \(-0.110152\pi\) | ||||
0.940719 | + | 0.339187i | \(0.110152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.0051 | −1.05157 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6036 | 0.879084 | 0.439542 | − | 0.898222i | \(-0.355141\pi\) | ||||
0.439542 | + | 0.898222i | \(0.355141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.35541 | 0.316586 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.69402 | −0.0841768 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0332803 | −0.00164964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.15357 | 0.304275 | 0.152137 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152137 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.0786 | −1.08906 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.272803 | 0.0134237 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6310 | −0.865471 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.95579 | 0.0957756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.1239 | −0.983118 | −0.491559 | − | 0.870844i | \(-0.663573\pi\) | ||||
−0.491559 | + | 0.870844i | \(0.663573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2139 | 0.887691 | 0.443846 | − | 0.896103i | \(-0.353614\pi\) | ||||
0.443846 | + | 0.896103i | \(0.353614\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.31896 | 0.258617 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.8123 | 0.815515 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.8125 | −2.07184 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.36832 | 0.162624 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.4864 | 0.986795 | 0.493398 | − | 0.869804i | \(-0.335755\pi\) | ||||
0.493398 | + | 0.869804i | \(0.335755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.7693 | 0.998111 | 0.499055 | − | 0.866570i | \(-0.333680\pi\) | ||||
0.499055 | + | 0.866570i | \(0.333680\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.5562 | −0.602022 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.3612 | 1.59588 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5543 | 0.599186 | 0.299593 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299593 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.0509 | 0.478617 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.828246 | 0.0393511 | 0.0196756 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196756 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9514 | −0.519148 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.90601 | −0.0901510 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6090 | 0.878213 | 0.439107 | − | 0.898435i | \(-0.355295\pi\) | ||||
0.439107 | + | 0.898435i | \(0.355295\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.54514 | −0.119846 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.47280 | −0.304119 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.46768 | 0.443851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.2882 | −1.18293 | −0.591466 | − | 0.806330i | \(-0.701451\pi\) | ||||
−0.591466 | + | 0.806330i | \(0.701451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.89205 | −0.368369 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.4877 | 1.46653 | 0.733263 | − | 0.679945i | \(-0.237996\pi\) | ||||
0.733263 | + | 0.679945i | \(0.237996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3225 | 0.805044 | 0.402522 | − | 0.915410i | \(-0.368134\pi\) | ||||
0.402522 | + | 0.915410i | \(0.368134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.95452 | −0.368882 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.6138 | −1.18527 | −0.592633 | − | 0.805473i | \(-0.701911\pi\) | ||||
−0.592633 | + | 0.805473i | \(0.701911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.2148 | −1.16431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.438526 | 0.0202062 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.6007 | −0.993202 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8364 | −0.497210 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.1374 | 0.555734 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1003 | 0.872717 | 0.436359 | − | 0.899773i | \(-0.356268\pi\) | ||||
0.436359 | + | 0.899773i | \(0.356268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0180997 | −0.000825276 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −27.0810 | −1.23223 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.8123 | −1.44452 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.8243 | 0.717068 | 0.358534 | − | 0.933517i | \(-0.383277\pi\) | ||||
0.358534 | + | 0.933517i | \(0.383277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2469 | −0.553825 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8932 | −0.672121 | −0.336061 | − | 0.941840i | \(-0.609095\pi\) | ||||
−0.336061 | + | 0.941840i | \(0.609095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −58.4961 | −2.63453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.21584 | −0.189488 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.1241 | 1.84467 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.95799 | −0.266716 | −0.133358 | − | 0.991068i | \(-0.542576\pi\) | ||||
−0.133358 | + | 0.991068i | \(0.542576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.4302 | −1.40140 | −0.700701 | − | 0.713455i | \(-0.747129\pi\) | ||||
−0.700701 | + | 0.713455i | \(0.747129\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.8179 | −1.05988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.1681 | −0.495993 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.98258 | −0.220849 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5332 | 0.687150 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.08686 | 0.224591 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.2852 | 1.33453 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2371 | 0.582165 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.71361 | 0.382485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.7533 | 1.47876 | 0.739379 | − | 0.673289i | \(-0.235119\pi\) | ||||
0.739379 | + | 0.673289i | \(0.235119\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.7117 | 1.91138 | 0.955690 | − | 0.294376i | \(-0.0951118\pi\) | ||||
0.955690 | + | 0.294376i | \(0.0951118\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.79652 | 0.383912 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.0582 | −1.61428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0112 | 0.870053 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0660655 | −0.00286700 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.38419 | −0.0599561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.2415 | −0.961583 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.3884 | 0.922977 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.0133 | 1.07740 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6423 | −1.05946 | −0.529728 | − | 0.848168i | \(-0.677706\pi\) | ||||
−0.529728 | + | 0.848168i | \(0.677706\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.85644 | −0.0796676 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.7557 | −0.632066 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1292 | −0.732390 | −0.366195 | − | 0.930538i | \(-0.619340\pi\) | ||||
−0.366195 | + | 0.930538i | \(0.619340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.3680 | 0.442497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.7040 | 1.60624 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −47.1733 | −2.00601 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0226538 | 0.000961602 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.33857 | 0.183831 | 0.0919155 | − | 0.995767i | \(-0.470701\pi\) | ||||
0.0919155 | + | 0.995767i | \(0.470701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7477 | −0.496875 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6406 | −0.829226 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.824504 | −0.0347487 | −0.0173744 | − | 0.999849i | \(-0.505531\pi\) | ||||
−0.0173744 | + | 0.999849i | \(0.505531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.50580 | 0.231631 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.12928 | −0.173413 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.12359 | 0.382481 | 0.191240 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191240 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.28710 | −0.263107 | −0.131553 | − | 0.991309i | \(-0.541997\pi\) | ||||
−0.131553 | + | 0.991309i | \(0.541997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.4811 | 0.479632 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9710 | −0.582631 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.0704 | 0.669020 | 0.334510 | − | 0.942392i | \(-0.391429\pi\) | ||||
0.334510 | + | 0.942392i | \(0.391429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.0096 | −1.03936 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.9765 | −1.78296 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.2058 | 1.25100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.29282 | −0.0947962 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.45147 | −0.348829 | −0.174415 | − | 0.984672i | \(-0.555803\pi\) | ||||
−0.174415 | + | 0.984672i | \(0.555803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.8861 | 0.984208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.2259 | 1.03765 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.4745 | 1.29250 | 0.646250 | − | 0.763125i | \(-0.276336\pi\) | ||||
0.646250 | + | 0.763125i | \(0.276336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.2057 | −2.26321 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.2035 | −1.03151 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.26080 | −0.174091 | −0.0870457 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870457 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.6592 | −1.37299 | −0.686493 | − | 0.727136i | \(-0.740851\pi\) | ||||
−0.686493 | + | 0.727136i | \(0.740851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.10634 | 0.248669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.14250 | 0.331040 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.0428 | −1.70647 | −0.853233 | − | 0.521530i | \(-0.825361\pi\) | ||||
−0.853233 | + | 0.521530i | \(0.825361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.6063 | −1.24023 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.19907 | 0.291243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.1736 | 1.62260 | 0.811298 | − | 0.584632i | \(-0.198761\pi\) | ||||
0.811298 | + | 0.584632i | \(0.198761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.73248 | 0.0698602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.71175 | −0.109171 | −0.0545855 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545855 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.3649 | −0.778340 | −0.389170 | − | 0.921166i | \(-0.627238\pi\) | ||||
−0.389170 | + | 0.921166i | \(0.627238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.55829 | 0.263175 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.6948 | −1.06950 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.81051 | −0.392420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.6594 | 0.505570 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.105539 | 0.00420811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.9758 | 1.27294 | 0.636469 | − | 0.771302i | \(-0.280394\pi\) | ||||
0.636469 | + | 0.771302i | \(0.280394\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.16157 | −0.205154 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2846 | 1.12244 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6037 | 0.538997 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.95916 | −0.393978 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.4659 | −1.32182 | −0.660912 | − | 0.750464i | \(-0.729830\pi\) | ||||
−0.660912 | + | 0.750464i | \(0.729830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.3135 | −0.682777 | −0.341388 | − | 0.939922i | \(-0.610897\pi\) | ||||
−0.341388 | + | 0.939922i | \(0.610897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.7036 | 0.578953 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6129 | 1.00695 | 0.503473 | − | 0.864011i | \(-0.332055\pi\) | ||||
0.503473 | + | 0.864011i | \(0.332055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.164414 | −0.00645382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.3896 | −0.759938 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.35684 | 0.366161 | 0.183081 | − | 0.983098i | \(-0.441393\pi\) | ||||
0.183081 | + | 0.983098i | \(0.441393\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.7962 | 0.617208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.76173 | −0.146759 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.42266 | 0.0554188 | 0.0277094 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277094 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.25492 | 0.165497 | 0.0827485 | − | 0.996570i | \(-0.473630\pi\) | ||||
0.0827485 | + | 0.996570i | \(0.473630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.6817 | −0.414842 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.5831 | 1.37985 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.6103 | 1.88220 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.36856 | 0.0915738 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.8025 | 0.996093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.0475 | −1.46663 | −0.733313 | − | 0.679892i | \(-0.762027\pi\) | ||||
−0.733313 | + | 0.679892i | \(0.762027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.13028 | −0.0819945 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.7193 | −1.48810 | −0.744052 | − | 0.668122i | \(-0.767098\pi\) | ||||
−0.744052 | + | 0.668122i | \(0.767098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −77.5442 | −2.97587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.662698 | −0.0253946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.56755 | −0.327828 | −0.163914 | − | 0.986475i | \(-0.552412\pi\) | ||||
−0.163914 | + | 0.986475i | \(0.552412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.4017 | 1.42904 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.4020 | 1.08360 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4277 | 0.625844 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.7047 | 1.20610 | 0.603051 | − | 0.797702i | \(-0.293951\pi\) | ||||
0.603051 | + | 0.797702i | \(0.293951\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.2764 | −0.390366 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.31316 | −0.125675 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.07118 | 0.305718 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.11158 | 0.0420437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.0946 | −1.62766 | −0.813830 | − | 0.581103i | \(-0.802621\pi\) | ||||
−0.813830 | + | 0.581103i | \(0.802621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0680256 | −0.00256563 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.01045 | −0.339353 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −58.0574 | −2.18347 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8750 | −0.896643 | −0.448321 | − | 0.893872i | \(-0.647978\pi\) | ||||
−0.448321 | + | 0.893872i | \(0.647978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4241 | 0.428437 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.7954 | 1.15330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.70603 | −0.213393 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.03519 | −0.188043 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.9206 | −0.407269 | −0.203635 | − | 0.979047i | \(-0.565275\pi\) | ||||
−0.203635 | + | 0.979047i | \(0.565275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 73.8219 | 2.74927 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.9384 | 0.592755 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.7897 | −0.586415 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2704 | −0.566348 | −0.283174 | − | 0.959069i | \(-0.591387\pi\) | ||||
−0.283174 | + | 0.959069i | \(0.591387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.5005 | 2.53358 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4949 | 0.793931 | 0.396966 | − | 0.917834i | \(-0.370063\pi\) | ||||
0.396966 | + | 0.917834i | \(0.370063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.0266 | −0.628034 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.1966 | 0.559773 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.6120 | 0.905368 | 0.452684 | − | 0.891671i | \(-0.350467\pi\) | ||||
0.452684 | + | 0.891671i | \(0.350467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.88493 | 0.252924 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.9574 | −1.09903 | −0.549514 | − | 0.835484i | \(-0.685187\pi\) | ||||
−0.549514 | + | 0.835484i | \(0.685187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.22882 | 0.118295 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.4077 | 0.380799 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.2148 | −1.98097 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.9459 | 1.23870 | 0.619351 | − | 0.785114i | \(-0.287396\pi\) | ||||
0.619351 | + | 0.785114i | \(0.287396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.4875 | 0.455070 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9651 | 0.399060 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.7652 | 0.500303 | 0.250152 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250152 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.3213 | 0.592427 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.19742 | 0.333406 | 0.166703 | − | 0.986007i | \(-0.446688\pi\) | ||||
0.166703 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.9679 | −1.30213 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.3693 | 0.483369 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0894178 | −0.00322869 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.3873 | 0.843368 | 0.421684 | − | 0.906743i | \(-0.361439\pi\) | ||||
0.421684 | + | 0.906743i | \(0.361439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.4024 | 0.482674 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.59137 | 0.0932050 | 0.0466025 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466025 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0030 | −0.359319 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0552200 | 0.00198101 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.20233 | −0.186393 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7849 | −0.886873 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.41203 | 0.264884 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.742874 | −0.0265143 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.99368 | 0.284944 | 0.142472 | − | 0.989799i | \(-0.454495\pi\) | ||||
0.142472 | + | 0.989799i | \(0.454495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.2710 | 0.365657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4207 | 0.477185 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0329 | 0.498321 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.5611 | −0.729227 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.4523 | 0.547348 | 0.273674 | − | 0.961823i | \(-0.411761\pi\) | ||||
0.273674 | + | 0.961823i | \(0.411761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.9775 | −1.48506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.46475 | 0.228421 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.36165 | −0.330365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.8759 | 1.61691 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.0795 | 0.742032 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.25639 | −0.290279 | −0.145140 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145140 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.6623 | −0.936240 | −0.468120 | − | 0.883665i | \(-0.655068\pi\) | ||||
−0.468120 | + | 0.883665i | \(0.655068\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.7180 | −0.796756 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.7466 | 0.726721 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.1523 | −1.54470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.58886 | −0.195291 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.60659 | −0.265472 | −0.132736 | − | 0.991151i | \(-0.542376\pi\) | ||||
−0.132736 | + | 0.991151i | \(0.542376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.8995 | 1.18166 | 0.590832 | − | 0.806795i | \(-0.298800\pi\) | ||||
0.590832 | + | 0.806795i | \(0.298800\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.30153 | −0.184576 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.3492 | 0.777157 | 0.388578 | − | 0.921416i | \(-0.372966\pi\) | ||||
0.388578 | + | 0.921416i | \(0.372966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8694 | 0.551166 | 0.275583 | − | 0.961277i | \(-0.411129\pi\) | ||||
0.275583 | + | 0.961277i | \(0.411129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.7334 | −0.892681 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −79.3226 | −2.74836 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.69402 | −0.0586241 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.69564 | 0.162305 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.54100 | 0.260344 | 0.130172 | − | 0.991491i | \(-0.458447\pi\) | ||||
0.130172 | + | 0.991491i | \(0.458447\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9382 | 0.894419 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.0242 | −0.689669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.9191 | 0.650835 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.8478 | 0.681978 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.01267 | −0.240674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0877027 | −0.00300641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.5679 | 1.35478 | 0.677389 | − | 0.735625i | \(-0.263111\pi\) | ||||
0.677389 | + | 0.735625i | \(0.263111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.61727 | −0.294705 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.3571 | 0.797864 | 0.398932 | − | 0.916981i | \(-0.369381\pi\) | ||||
0.398932 | + | 0.916981i | \(0.369381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.6810 | −1.49038 | −0.745189 | − | 0.666854i | \(-0.767641\pi\) | ||||
−0.745189 | + | 0.666854i | \(0.767641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.22301 | 0.143920 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.6590 | −1.41809 | −0.709044 | − | 0.705165i | \(-0.750873\pi\) | ||||
−0.709044 | + | 0.705165i | \(0.750873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.7611 | −0.501891 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.2844 | 1.53794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.4306 | 0.964443 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.26476 | 0.280041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.7791 | 0.635576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.8770 | −1.68615 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.4805 | −1.50200 | −0.751000 | − | 0.660302i | \(-0.770428\pi\) | ||||
−0.751000 | + | 0.660302i | \(0.770428\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.63359 | 0.0888287 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.85366 | −0.163524 | −0.0817619 | − | 0.996652i | \(-0.526055\pi\) | ||||
−0.0817619 | + | 0.996652i | \(0.526055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.3649 | 1.05551 | 0.527757 | − | 0.849395i | \(-0.323033\pi\) | ||||
0.527757 | + | 0.849395i | \(0.323033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.111917 | 0.00376203 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4960 | −0.486727 | −0.243364 | − | 0.969935i | \(-0.578251\pi\) | ||||
−0.243364 | + | 0.969935i | \(0.578251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.9454 | 2.31235 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.48865 | 0.0833731 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.0568 | 0.905423 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.2325 | −1.21112 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.87647 | 0.296377 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.8042 | 1.16078 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −95.7891 | −3.19120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35.8408 | 1.19271 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.14486 | 0.104539 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.11429 | 0.103408 | 0.0517042 | − | 0.998662i | \(-0.483535\pi\) | ||||
0.0517042 | + | 0.998662i | \(0.483535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.0599 | 0.466338 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.8426 | −1.88328 | −0.941640 | − | 0.336620i | \(-0.890716\pi\) | ||||
−0.941640 | + | 0.336620i | \(0.890716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9013 | 0.857207 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.5637 | −0.580639 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.5041 | 1.27152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0944 | 1.15766 | 0.578829 | − | 0.815449i | \(-0.303510\pi\) | ||||
0.578829 | + | 0.815449i | \(0.303510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3105 | 0.405645 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.4794 | −0.443681 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0284878 | 0.000936673 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8777 | −0.587180 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.1328 | −0.365255 | −0.182627 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182627 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.1278 | 1.67565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.9999 | 0.785720 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.2716 | 1.08810 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.43915 | 0.0470149 | 0.0235075 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235075 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.38113 | 0.110339 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.6688 | −0.901976 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.70715 | −0.218415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.99510 | 0.227551 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.1562 | 0.719979 | 0.359989 | − | 0.932956i | \(-0.382780\pi\) | ||||
0.359989 | + | 0.932956i | \(0.382780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.09140 | −0.165274 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.85532 | −0.254726 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.1214 | 0.587010 | 0.293505 | − | 0.955957i | \(-0.405178\pi\) | ||||
0.293505 | + | 0.955957i | \(0.405178\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.4493 | −0.629366 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.4460 | 0.596274 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 91.1686 | 2.94399 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.95101 | −0.288742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.1294 | 0.423088 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42.3669 | 1.36384 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.2636 | 1.29479 | 0.647395 | − | 0.762155i | \(-0.275858\pi\) | ||||
0.647395 | + | 0.762155i | \(0.275858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.1458 | −1.28967 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.8192 | 0.539752 | 0.269876 | − | 0.962895i | \(-0.413017\pi\) | ||||
0.269876 | + | 0.962895i | \(0.413017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.07601 | −0.258905 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.88327 | −0.0923387 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1817 | 0.581685 | 0.290842 | − | 0.956771i | \(-0.406064\pi\) | ||||
0.290842 | + | 0.956771i | \(0.406064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0885 | 0.514192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.71046 | 0.278104 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.6117 | 1.23152 | 0.615761 | − | 0.787933i | \(-0.288849\pi\) | ||||
0.615761 | + | 0.787933i | \(0.288849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.7332 | −1.36159 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.9635 | −0.699105 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.9239 | −1.81007 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.98885 | 0.222008 | 0.111004 | − | 0.993820i | \(-0.464593\pi\) | ||||
0.111004 | + | 0.993820i | \(0.464593\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.1080 | −0.765045 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.6954 | 1.35353 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.03760 | −0.159542 | −0.0797712 | − | 0.996813i | \(-0.525419\pi\) | ||||
−0.0797712 | + | 0.996813i | \(0.525419\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0133728 | −0.000423097 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 | 2004.2.a.d.1.2 | ✓ | 9 | |
3.2 | odd | 2 | 6012.2.a.h.1.8 | 9 | |||
4.3 | odd | 2 | 8016.2.a.bb.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.d.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial | |
6012.2.a.h.1.8 | 9 | 3.2 | odd | 2 | |||
8016.2.a.bb.1.2 | 9 | 4.3 | odd | 2 |