Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 28x^{5} + 90x^{4} + 143x^{3} - 418x^{2} - 256x + 160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.15736\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.15736 | 1.19337 | 0.596686 | − | 0.802475i | \(-0.296484\pi\) | ||||
0.596686 | + | 0.802475i | \(0.296484\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.84615 | −1.46117 | −0.730584 | − | 0.682823i | \(-0.760752\pi\) | ||||
−0.730584 | + | 0.682823i | \(0.760752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.88967 | 1.91085 | 0.955425 | − | 0.295233i | \(-0.0953973\pi\) | ||||
0.955425 | + | 0.295233i | \(0.0953973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52837 | 1.34083 | 0.670414 | − | 0.741988i | \(-0.266117\pi\) | ||||
0.670414 | + | 0.741988i | \(0.266117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.73402 | 1.31547 | 0.657737 | − | 0.753247i | \(-0.271514\pi\) | ||||
0.657737 | + | 0.753247i | \(0.271514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.15736 | −0.688993 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.53661 | 0.945948 | 0.472974 | − | 0.881076i | \(-0.343180\pi\) | ||||
0.472974 | + | 0.881076i | \(0.343180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.37924 | −0.627510 | −0.313755 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313755 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.57845 | −1.18152 | −0.590762 | − | 0.806846i | \(-0.701173\pi\) | ||||
−0.590762 | + | 0.806846i | \(0.701173\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.84615 | 0.843606 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.15736 | −0.533692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.221881 | −0.0364771 | −0.0182385 | − | 0.999834i | \(-0.505806\pi\) | ||||
−0.0182385 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.88967 | −1.10323 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.95590 | −0.617808 | −0.308904 | − | 0.951093i | \(-0.599962\pi\) | ||||
−0.308904 | + | 0.951093i | \(0.599962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.21536 | −0.185341 | −0.0926704 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926704 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.99348 | −0.436644 | −0.218322 | − | 0.975877i | \(-0.570058\pi\) | ||||
−0.218322 | + | 0.975877i | \(0.570058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.96894 | 0.424135 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.52837 | −0.774127 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.21887 | 0.991588 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.84615 | 0.653454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.73402 | −0.759490 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.3745 | −1.61103 | −0.805513 | − | 0.592579i | \(-0.798110\pi\) | ||||
−0.805513 | + | 0.592579i | \(0.798110\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2189 | 1.43643 | 0.718215 | − | 0.695822i | \(-0.244960\pi\) | ||||
0.718215 | + | 0.695822i | \(0.244960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.15736 | 0.397790 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.88967 | −0.854558 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.53661 | −0.546143 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.85861 | −0.813968 | −0.406984 | − | 0.913435i | \(-0.633419\pi\) | ||||
−0.406984 | + | 0.913435i | \(0.633419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.91478 | 0.458190 | 0.229095 | − | 0.973404i | \(-0.426423\pi\) | ||||
0.229095 | + | 0.973404i | \(0.426423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.3010 | −1.74372 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.83791 | 0.881834 | 0.440917 | − | 0.897548i | \(-0.354653\pi\) | ||||
0.440917 | + | 0.897548i | \(0.354653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7490 | 1.39938 | 0.699690 | − | 0.714447i | \(-0.253321\pi\) | ||||
0.699690 | + | 0.714447i | \(0.253321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.52837 | −0.599636 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.37924 | 0.362293 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.96242 | 0.314016 | 0.157008 | − | 0.987597i | \(-0.449815\pi\) | ||||
0.157008 | + | 0.987597i | \(0.449815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.7532 | 2.28035 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.57845 | 0.682154 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.73402 | −0.588298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.48656 | 0.557076 | 0.278538 | − | 0.960425i | \(-0.410150\pi\) | ||||
0.278538 | + | 0.960425i | \(0.410150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.84615 | −0.487056 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.57769 | −0.355994 | −0.177997 | − | 0.984031i | \(-0.556962\pi\) | ||||
−0.177997 | + | 0.984031i | \(0.556962\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.784639 | 0.0773128 | 0.0386564 | − | 0.999253i | \(-0.487692\pi\) | ||||
0.0386564 | + | 0.999253i | \(0.487692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.15736 | 0.308127 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.08465 | 0.491551 | 0.245776 | − | 0.969327i | \(-0.420957\pi\) | ||||
0.245776 | + | 0.969327i | \(0.420957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.79230 | −0.171671 | −0.0858356 | − | 0.996309i | \(-0.527356\pi\) | ||||
−0.0858356 | + | 0.996309i | \(0.527356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.221881 | 0.0210600 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.45562 | −0.513222 | −0.256611 | − | 0.966515i | \(-0.582606\pi\) | ||||
−0.256611 | + | 0.966515i | \(0.582606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.53661 | −0.423041 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.88967 | 0.636950 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.4551 | 1.60010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4851 | 1.13501 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.95590 | 0.356692 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1240 | 1.16457 | 0.582284 | − | 0.812985i | \(-0.302159\pi\) | ||||
0.582284 | + | 0.812985i | \(0.302159\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.21536 | 0.107007 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.58250 | 0.400375 | 0.200187 | − | 0.979758i | \(-0.435845\pi\) | ||||
0.200187 | + | 0.979758i | \(0.435845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.1044 | 1.56985 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8684 | 1.01399 | 0.506993 | − | 0.861950i | \(-0.330757\pi\) | ||||
0.506993 | + | 0.861950i | \(0.330757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5254 | −0.892750 | −0.446375 | − | 0.894846i | \(-0.647285\pi\) | ||||
−0.446375 | + | 0.894846i | \(0.647285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.99348 | 0.252096 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.3883 | −2.79207 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.37924 | 0.280631 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.96894 | −0.244874 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.73059 | 0.305622 | 0.152811 | − | 0.988255i | \(-0.451167\pi\) | ||||
0.152811 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.21837 | 0.180529 | 0.0902643 | − | 0.995918i | \(-0.471229\pi\) | ||||
0.0902643 | + | 0.995918i | \(0.471229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.52837 | 0.446942 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.57845 | 0.528394 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.0531 | −1.76003 | −0.880016 | − | 0.474945i | \(-0.842468\pi\) | ||||
−0.880016 | + | 0.474945i | \(0.842468\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.21887 | −0.572494 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.3237 | 1.12887 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.5802 | −0.985355 | −0.492677 | − | 0.870212i | \(-0.663982\pi\) | ||||
−0.492677 | + | 0.870212i | \(0.663982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.84615 | −0.377272 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.2328 | 0.869218 | 0.434609 | − | 0.900619i | \(-0.356887\pi\) | ||||
0.434609 | + | 0.900619i | \(0.356887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.4675 | 2.65135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.73402 | 0.438492 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.79138 | −0.440310 | −0.220155 | − | 0.975465i | \(-0.570656\pi\) | ||||
−0.220155 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.15736 | 0.238674 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.3745 | 0.930126 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.461711 | −0.0345099 | −0.0172549 | − | 0.999851i | \(-0.505493\pi\) | ||||
−0.0172549 | + | 0.999851i | \(0.505493\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9076 | −1.77704 | −0.888520 | − | 0.458838i | \(-0.848266\pi\) | ||||
−0.888520 | + | 0.458838i | \(0.848266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.2189 | −0.829323 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.221881 | 0.0163130 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.7913 | −1.95917 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.15736 | −0.229664 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9649 | 0.865749 | 0.432875 | − | 0.901454i | \(-0.357499\pi\) | ||||
0.432875 | + | 0.901454i | \(0.357499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.67742 | 0.264707 | 0.132353 | − | 0.991203i | \(-0.457747\pi\) | ||||
0.132353 | + | 0.991203i | \(0.457747\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.88967 | 0.493379 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9063 | 1.27577 | 0.637886 | − | 0.770131i | \(-0.279809\pi\) | ||||
0.637886 | + | 0.770131i | \(0.279809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8328 | −0.909697 | −0.454848 | − | 0.890569i | \(-0.650307\pi\) | ||||
−0.454848 | + | 0.890569i | \(0.650307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6695 | −0.748852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.95590 | 0.276292 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.53661 | 0.315316 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.7879 | −1.92213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.45959 | 0.375854 | 0.187927 | − | 0.982183i | \(-0.439823\pi\) | ||||
0.187927 | + | 0.982183i | \(0.439823\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.85861 | 0.469944 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.21536 | 0.0828869 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.7706 | −1.41000 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.91478 | −0.264536 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.0887 | 2.56212 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2071 | 1.68799 | 0.843994 | − | 0.536352i | \(-0.180198\pi\) | ||||
0.843994 | + | 0.536352i | \(0.180198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.46282 | −0.628069 | −0.314035 | − | 0.949412i | \(-0.601681\pi\) | ||||
−0.314035 | + | 0.949412i | \(0.601681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.16836 | 0.0772077 | 0.0386038 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386038 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.3010 | 1.00673 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.95443 | 0.521112 | 0.260556 | − | 0.965459i | \(-0.416094\pi\) | ||||
0.260556 | + | 0.965459i | \(0.416094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.99348 | 0.195273 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.83791 | −0.509127 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.6435 | 1.40000 | 0.700001 | − | 0.714142i | \(-0.253183\pi\) | ||||
0.700001 | + | 0.714142i | \(0.253183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.3117 | 1.63047 | 0.815235 | − | 0.579130i | \(-0.196607\pi\) | ||||
0.815235 | + | 0.579130i | \(0.196607\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.96894 | −0.189679 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 39.5055 | 2.51368 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.7490 | −0.807932 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4411 | 0.974634 | 0.487317 | − | 0.873225i | \(-0.337976\pi\) | ||||
0.487317 | + | 0.873225i | \(0.337976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9851 | −1.38219 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.52837 | 0.346200 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.95691 | 0.621095 | 0.310547 | − | 0.950558i | \(-0.399488\pi\) | ||||
0.310547 | + | 0.950558i | \(0.399488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.700560 | −0.0435307 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.37924 | −0.209170 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4957 | −0.832179 | −0.416089 | − | 0.909324i | \(-0.636600\pi\) | ||||
−0.416089 | + | 0.909324i | \(0.636600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.21887 | −0.443452 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.96242 | −0.181297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.4578 | −1.36928 | −0.684639 | − | 0.728882i | \(-0.740040\pi\) | ||||
−0.684639 | + | 0.728882i | \(0.740040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8705 | −1.02481 | −0.512406 | − | 0.858743i | \(-0.671246\pi\) | ||||
−0.512406 | + | 0.858743i | \(0.671246\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.7532 | −1.31656 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.84615 | −0.292234 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6173 | 1.71945 | 0.859723 | − | 0.510761i | \(-0.170636\pi\) | ||||
0.859723 | + | 0.510761i | \(0.170636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.57845 | −0.393842 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2629 | 0.671888 | 0.335944 | − | 0.941882i | \(-0.390945\pi\) | ||||
0.335944 | + | 0.941882i | \(0.390945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.1828 | −1.79418 | −0.897090 | − | 0.441847i | \(-0.854323\pi\) | ||||
−0.897090 | + | 0.441847i | \(0.854323\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.73402 | 0.339654 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4902 | −0.737274 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5629 | 0.797818 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.48656 | −0.321628 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1216 | 0.591313 | 0.295657 | − | 0.955294i | \(-0.404462\pi\) | ||||
0.295657 | + | 0.955294i | \(0.404462\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.3745 | 0.720472 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.84615 | 0.281202 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.2557 | 1.80757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.83734 | −0.221180 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.57769 | 0.205533 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.2189 | −0.642391 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.50547 | 0.371287 | 0.185643 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185643 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.784639 | −0.0446365 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.5371 | 1.56149 | 0.780743 | − | 0.624852i | \(-0.214841\pi\) | ||||
0.780743 | + | 0.624852i | \(0.214841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4107 | 0.644971 | 0.322485 | − | 0.946574i | \(-0.395482\pi\) | ||||
0.322485 | + | 0.946574i | \(0.395482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.15736 | −0.177897 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.7200 | −1.16375 | −0.581875 | − | 0.813278i | \(-0.697681\pi\) | ||||
−0.581875 | + | 0.813278i | \(0.697681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3763 | 0.916897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.08465 | −0.283797 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.6998 | 1.76382 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.88967 | 0.382170 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.79230 | 0.0991144 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.45150 | −0.521078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3874 | 0.735837 | 0.367919 | − | 0.929858i | \(-0.380071\pi\) | ||||
0.367919 | + | 0.929858i | \(0.380071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.221881 | −0.0121590 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | 0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1569 | 1.09802 | 0.549009 | − | 0.835816i | \(-0.315005\pi\) | ||||
0.549009 | + | 0.835816i | \(0.315005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.45562 | 0.296309 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.8801 | 1.72641 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.7275 | −0.687221 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.53661 | 0.244243 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.95526 | 0.373378 | 0.186689 | − | 0.982419i | \(-0.440224\pi\) | ||||
0.186689 | + | 0.982419i | \(0.440224\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.149016 | 0.00797664 | 0.00398832 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00398832 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.88967 | −0.367743 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8624 | 1.58941 | 0.794707 | − | 0.606993i | \(-0.207624\pi\) | ||||
0.794707 | + | 0.606993i | \(0.207624\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.85861 | 0.364017 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.4551 | −0.923821 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.7189 | 0.565722 | 0.282861 | − | 0.959161i | \(-0.408716\pi\) | ||||
0.282861 | + | 0.959161i | \(0.408716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8790 | 0.730474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.4851 | −0.655299 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.91478 | −0.204909 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.0871262 | −0.00454795 | −0.00227398 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227398 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.95590 | −0.205936 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.7926 | 1.18333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.2747 | −0.635561 | −0.317780 | − | 0.948164i | \(-0.602937\pi\) | ||||
−0.317780 | + | 0.948164i | \(0.602937\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.2819 | −1.19908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4419 | 0.947299 | 0.473649 | − | 0.880714i | \(-0.342936\pi\) | ||||
0.473649 | + | 0.880714i | \(0.342936\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1240 | −0.672364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0990 | −1.53799 | −0.768993 | − | 0.639257i | \(-0.779242\pi\) | ||||
−0.768993 | + | 0.639257i | \(0.779242\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.3010 | 0.779813 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.21536 | −0.0617803 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.74599 | 0.240631 | 0.120316 | − | 0.992736i | \(-0.461609\pi\) | ||||
0.120316 | + | 0.992736i | \(0.461609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.0801 | 1.26835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.58250 | −0.231157 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.83791 | −0.394368 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2317 | −0.764455 | −0.382227 | − | 0.924068i | \(-0.624843\pi\) | ||||
−0.382227 | + | 0.924068i | \(0.624843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.1044 | −0.906353 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.5296 | 1.52458 | 0.762288 | − | 0.647239i | \(-0.224076\pi\) | ||||
0.762288 | + | 0.647239i | \(0.224076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.3234 | −2.25772 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.07527 | 0.0532991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.2610 | 1.10074 | 0.550369 | − | 0.834922i | \(-0.314487\pi\) | ||||
0.550369 | + | 0.834922i | \(0.314487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8684 | −0.585425 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −39.0709 | −1.92255 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.7490 | −0.625822 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5254 | 0.515429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.2422 | −1.77055 | −0.885274 | − | 0.465069i | \(-0.846029\pi\) | ||||
−0.885274 | + | 0.465069i | \(0.846029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00730 | −0.0490929 | −0.0245464 | − | 0.999699i | \(-0.507814\pi\) | ||||
−0.0245464 | + | 0.999699i | \(0.507814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.99348 | −0.145548 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.52837 | 0.268165 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.4220 | 1.71419 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.3883 | 1.61200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.9295 | −1.39348 | −0.696742 | − | 0.717321i | \(-0.745368\pi\) | ||||
−0.696742 | + | 0.717321i | \(0.745368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0203 | 0.962113 | 0.481056 | − | 0.876690i | \(-0.340253\pi\) | ||||
0.481056 | + | 0.876690i | \(0.340253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.37924 | −0.162022 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.0130 | 1.24437 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6347 | 0.698475 | 0.349238 | − | 0.937034i | \(-0.386441\pi\) | ||||
0.349238 | + | 0.937034i | \(0.386441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.96894 | 0.141378 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0508 | 0.620060 | 0.310030 | − | 0.950727i | \(-0.399661\pi\) | ||||
0.310030 | + | 0.950727i | \(0.399661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.96242 | −0.140432 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.73059 | −0.176451 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.14737 | 0.195726 | 0.0978632 | − | 0.995200i | \(-0.468799\pi\) | ||||
0.0978632 | + | 0.995200i | \(0.468799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1709 | 0.902722 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.21837 | −0.104228 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.7532 | −1.01981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.8504 | −1.48990 | −0.744950 | − | 0.667121i | \(-0.767526\pi\) | ||||
−0.744950 | + | 0.667121i | \(0.767526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.52837 | −0.258042 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.5357 | −1.37561 | −0.687807 | − | 0.725894i | \(-0.741426\pi\) | ||||
−0.687807 | + | 0.725894i | \(0.741426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.2328 | −1.91625 | −0.958126 | − | 0.286346i | \(-0.907559\pi\) | ||||
−0.958126 | + | 0.286346i | \(0.907559\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.57845 | −0.305068 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.0990 | 1.34654 | 0.673272 | − | 0.739395i | \(-0.264889\pi\) | ||||
0.673272 | + | 0.739395i | \(0.264889\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.15736 | −0.145793 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.0531 | 1.01615 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.88982 | 0.270814 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.73402 | 0.263095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.21887 | 0.330529 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.0991 | −0.507129 | −0.253564 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253564 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.52869 | −0.0697022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.3237 | −0.651752 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.48656 | −0.249132 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.44172 | 0.427845 | 0.213923 | − | 0.976851i | \(-0.431376\pi\) | ||||
0.213923 | + | 0.976851i | \(0.431376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5802 | 0.568895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.9696 | −1.53302 | −0.766512 | − | 0.642230i | \(-0.778010\pi\) | ||||
−0.766512 | + | 0.642230i | \(0.778010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.6817 | −0.841383 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.84615 | 0.217818 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.6551 | −0.971365 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.2275 | −1.44270 | −0.721351 | − | 0.692570i | \(-0.756478\pi\) | ||||
−0.721351 | + | 0.692570i | \(0.756478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2328 | −0.501843 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.6427 | −1.05417 | −0.527087 | − | 0.849811i | \(-0.676716\pi\) | ||||
−0.527087 | + | 0.849811i | \(0.676716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.57769 | 0.159205 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.4675 | −1.53076 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.9633 | −0.884859 | −0.442429 | − | 0.896803i | \(-0.645883\pi\) | ||||
−0.442429 | + | 0.896803i | \(0.645883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.3604 | 0.546791 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.73402 | −0.253163 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.784639 | −0.0345753 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.5068 | 0.638010 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.79138 | 0.254213 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.5165 | 1.29314 | 0.646571 | − | 0.762854i | \(-0.276202\pi\) | ||||
0.646571 | + | 0.762854i | \(0.276202\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.6977 | 1.03623 | 0.518113 | − | 0.855312i | \(-0.326635\pi\) | ||||
0.518113 | + | 0.855312i | \(0.326635\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.15736 | −0.137799 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.3681 | −1.58422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.41919 | −0.105182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.3745 | −0.537008 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.2549 | −1.18054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.08465 | −0.219828 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.461711 | 0.0199243 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.3879 | −0.619732 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3066 | 0.916041 | 0.458020 | − | 0.888942i | \(-0.348559\pi\) | ||||
0.458020 | + | 0.888942i | \(0.348559\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.9076 | 1.02597 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.79230 | 0.0767737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.5676 | −1.00768 | −0.503839 | − | 0.863798i | \(-0.668079\pi\) | ||||
−0.503839 | + | 0.863798i | \(0.668079\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.2189 | 0.478810 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3767 | −0.825474 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.7471 | 1.05236 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.221881 | −0.00941834 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4238 | −0.568783 | −0.284392 | − | 0.958708i | \(-0.591792\pi\) | ||||
−0.284392 | + | 0.958708i | \(0.591792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.37344 | −0.354159 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.7913 | 1.13113 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.5293 | −0.696628 | −0.348314 | − | 0.937378i | \(-0.613246\pi\) | ||||
−0.348314 | + | 0.937378i | \(0.613246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.45562 | 0.229520 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.15736 | 0.132597 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.97352 | 0.376190 | 0.188095 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188095 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.2167 | −1.30638 | −0.653189 | − | 0.757194i | \(-0.726569\pi\) | ||||
−0.653189 | + | 0.757194i | \(0.726569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.9649 | −0.499841 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.53661 | 0.189190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5281 | −0.812965 | −0.406482 | − | 0.913659i | \(-0.633245\pi\) | ||||
−0.406482 | + | 0.913659i | \(0.633245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.67742 | −0.152828 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.2531 | 1.66998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.9837 | −1.44888 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.88967 | −0.284853 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.3779 | −1.54275 | −0.771375 | − | 0.636381i | \(-0.780431\pi\) | ||||
−0.771375 | + | 0.636381i | \(0.780431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.7210 | −1.55427 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.9063 | −0.736568 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.7885 | −0.771550 | −0.385775 | − | 0.922593i | \(-0.626066\pi\) | ||||
−0.385775 | + | 0.922593i | \(0.626066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.4551 | −0.715589 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8328 | 0.525214 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7557 | −0.807197 | −0.403599 | − | 0.914936i | \(-0.632241\pi\) | ||||
−0.403599 | + | 0.914936i | \(0.632241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.2216 | 1.68146 | 0.840732 | − | 0.541452i | \(-0.182125\pi\) | ||||
0.840732 | + | 0.541452i | \(0.182125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4851 | −0.507593 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.8922 | 1.90330 | 0.951648 | − | 0.307190i | \(-0.0993886\pi\) | ||||
0.951648 | + | 0.307190i | \(0.0993886\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6695 | 0.432350 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.6241 | −0.834361 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.19718 | −0.129133 | −0.0645664 | − | 0.997913i | \(-0.520566\pi\) | ||||
−0.0645664 | + | 0.997913i | \(0.520566\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.95590 | −0.159517 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.8138 | −1.84440 | −0.922198 | − | 0.386718i | \(-0.873609\pi\) | ||||
−0.922198 | + | 0.386718i | \(0.873609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.0330 | 1.76984 | 0.884918 | − | 0.465747i | \(-0.154214\pi\) | ||||
0.884918 | + | 0.465747i | \(0.154214\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.53661 | −0.182048 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.35345 | 0.374738 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.7879 | 1.10974 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.22664 | −0.0489095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.4041 | −1.48903 | −0.744516 | − | 0.667604i | \(-0.767320\pi\) | ||||
−0.744516 | + | 0.667604i | \(0.767320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.45959 | −0.216999 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.1240 | −0.520811 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.4550 | 0.810458 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.85861 | −0.271323 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9524 | 0.432593 | 0.216297 | − | 0.976328i | \(-0.430602\pi\) | ||||
0.216297 | + | 0.976328i | \(0.430602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.5462 | −1.59899 | −0.799493 | − | 0.600675i | \(-0.794899\pi\) | ||||
−0.799493 | + | 0.600675i | \(0.794899\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.21536 | −0.0478548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6696 | −0.458781 | −0.229390 | − | 0.973334i | \(-0.573673\pi\) | ||||
−0.229390 | + | 0.973334i | \(0.573673\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 59.9687 | 2.35398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.7706 | 0.814063 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.3282 | 0.482441 | 0.241221 | − | 0.970470i | \(-0.422452\pi\) | ||||
0.241221 | + | 0.970470i | \(0.422452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.58250 | −0.179053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.91478 | 0.152730 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.47250 | −0.368996 | −0.184498 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184498 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.8017 | −0.770198 | −0.385099 | − | 0.922875i | \(-0.625833\pi\) | ||||
−0.385099 | + | 0.922875i | \(0.625833\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −38.0887 | −1.47924 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.1044 | −0.702058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3303 | −0.593592 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.2071 | −0.974561 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −54.3683 | −2.09886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.90899 | 0.381964 | 0.190982 | − | 0.981594i | \(-0.438833\pi\) | ||||
0.190982 | + | 0.981594i | \(0.438833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.3704 | 1.70529 | 0.852647 | − | 0.522487i | \(-0.174996\pi\) | ||||
0.852647 | + | 0.522487i | \(0.174996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3231 | 0.664799 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.46282 | 0.362616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.09371 | −0.233169 | −0.116585 | − | 0.993181i | \(-0.537195\pi\) | ||||
−0.116585 | + | 0.993181i | \(0.537195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.8684 | −0.453468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.16836 | −0.0445759 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.7356 | 1.89478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.18330 | −0.0830566 | −0.0415283 | − | 0.999137i | \(-0.513223\pi\) | ||||
−0.0415283 | + | 0.999137i | \(0.513223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.3010 | −0.581239 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5254 | 0.399250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.8697 | −0.828374 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.95443 | −0.300864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.7026 | 0.933006 | 0.466503 | − | 0.884520i | \(-0.345514\pi\) | ||||
0.466503 | + | 0.884520i | \(0.345514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.27227 | −0.0479847 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.99348 | −0.112741 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.2961 | −0.424833 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0093 | −0.526130 | −0.263065 | − | 0.964778i | \(-0.584733\pi\) | ||||
−0.263065 | + | 0.964778i | \(0.584733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.83791 | 0.293945 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.8439 | −1.11766 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.3883 | 1.24865 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.6435 | −0.808291 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.3733 | −0.946263 | −0.473131 | − | 0.880992i | \(-0.656876\pi\) | ||||
−0.473131 | + | 0.880992i | \(0.656876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47739 | 0.0922628 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.3117 | −0.941353 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.37924 | −0.125502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7313 | 1.47355 | 0.736776 | − | 0.676137i | \(-0.236347\pi\) | ||||
0.736776 | + | 0.676137i | \(0.236347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.71897 | −0.248510 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.65713 | 0.0981432 | 0.0490716 | − | 0.998795i | \(-0.484374\pi\) | ||||
0.0490716 | + | 0.998795i | \(0.484374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.96894 | 0.109511 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.84615 | 0.178510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.5553 | −1.05042 | −0.525212 | − | 0.850971i | \(-0.676014\pi\) | ||||
−0.525212 | + | 0.850971i | \(0.676014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.5055 | −1.45127 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.3117 | 1.25877 | 0.629387 | − | 0.777092i | \(-0.283306\pi\) | ||||
0.629387 | + | 0.777092i | \(0.283306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.73059 | −0.136678 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7490 | 0.466460 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0541 | 0.586603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.6656 | −1.77583 | −0.887917 | − | 0.460003i | \(-0.847848\pi\) | ||||
−0.887917 | + | 0.460003i | \(0.847848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4411 | −0.562705 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.21837 | −0.0807348 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.7595 | 1.37239 | 0.686197 | − | 0.727416i | \(-0.259279\pi\) | ||||
0.686197 | + | 0.727416i | \(0.259279\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.9851 | 0.798007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.6281 | 1.90777 | 0.953883 | − | 0.300178i | \(-0.0970460\pi\) | ||||
0.953883 | + | 0.300178i | \(0.0970460\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.65894 | −0.204867 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.52837 | −0.199879 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −85.2563 | −3.07843 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.4558 | −0.845838 | −0.422919 | − | 0.906168i | \(-0.638995\pi\) | ||||
−0.422919 | + | 0.906168i | \(0.638995\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.95691 | −0.358589 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.6368 | 1.35370 | 0.676851 | − | 0.736120i | \(-0.263344\pi\) | ||||
0.676851 | + | 0.736120i | \(0.263344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.57845 | −0.236305 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.700560 | 0.0251325 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6832 | −0.812711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.2378 | 1.18934 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.37924 | 0.120764 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.0531 | 0.787110 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.6751 | 0.736989 | 0.368494 | − | 0.929630i | \(-0.379873\pi\) | ||||
0.368494 | + | 0.929630i | \(0.379873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4957 | 0.480459 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.2254 | −0.612464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 77.2943 | 2.74480 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.21887 | 0.256027 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.3374 | 1.53509 | 0.767546 | − | 0.640994i | \(-0.221478\pi\) | ||||
0.767546 | + | 0.640994i | \(0.221478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.5491 | −0.585464 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.96242 | 0.104672 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.9716 | −0.669493 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.3237 | −0.504845 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.4578 | 0.790553 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.2355 | 0.887234 | 0.443617 | − | 0.896217i | \(-0.353695\pi\) | ||||
0.443617 | + | 0.896217i | \(0.353695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.7789 | −0.870104 | −0.435052 | − | 0.900405i | \(-0.643270\pi\) | ||||
−0.435052 | + | 0.900405i | \(0.643270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.8705 | 0.591676 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5802 | 0.440664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.96891 | −0.243811 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.7532 | 0.760118 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.2166 | 1.40357 | 0.701785 | − | 0.712389i | \(-0.252387\pi\) | ||||
0.701785 | + | 0.712389i | \(0.252387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.9065 | −0.693897 | −0.346949 | − | 0.937884i | \(-0.612782\pi\) | ||||
−0.346949 | + | 0.937884i | \(0.612782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.84615 | 0.168721 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.8464 | −1.24650 | −0.623250 | − | 0.782023i | \(-0.714188\pi\) | ||||
−0.623250 | + | 0.782023i | \(0.714188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2844 | −0.773970 | −0.386985 | − | 0.922086i | \(-0.626484\pi\) | ||||
−0.386985 | + | 0.922086i | \(0.626484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.6173 | −0.992723 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.4134 | 0.568691 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2328 | −0.388726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.57845 | 0.227385 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.05570 | −0.278114 | −0.139057 | − | 0.990284i | \(-0.544407\pi\) | ||||
−0.139057 | + | 0.990284i | \(0.544407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5807 | −0.606231 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.2629 | −0.387914 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.4675 | −1.18572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.4201 | 1.35449 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.1828 | 1.03587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.00659 | −0.0345054 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.6279 | −0.945960 | −0.472980 | − | 0.881073i | \(-0.656822\pi\) | ||||
−0.472980 | + | 0.881073i | \(0.656822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.73402 | −0.196099 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.8455 | 0.575430 | 0.287715 | − | 0.957716i | \(-0.407104\pi\) | ||||
0.287715 | + | 0.957716i | \(0.407104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.6982 | 1.69568 | 0.847840 | − | 0.530253i | \(-0.177903\pi\) | ||||
0.847840 | + | 0.530253i | \(0.177903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.4902 | 0.425666 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.5659 | 1.07452 | 0.537258 | − | 0.843418i | \(-0.319460\pi\) | ||||
0.537258 | + | 0.843418i | \(0.319460\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.79138 | 0.196913 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.5629 | −0.460620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.9837 | −1.28851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.88967 | −0.233448 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.48656 | 0.185692 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.15736 | −0.106738 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.27991 | −0.0769871 | −0.0384935 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384935 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.1216 | −0.341395 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.2139 | −0.647331 | −0.323666 | − | 0.946172i | \(-0.604915\pi\) | ||||
−0.323666 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.8453 | 1.44186 | 0.720929 | − | 0.693009i | \(-0.243715\pi\) | ||||
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.3745 | −0.415965 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9128 | 0.567875 | 0.283938 | − | 0.958843i | \(-0.408359\pi\) | ||||
0.283938 | + | 0.958843i | \(0.408359\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.4373 | 1.38976 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.84615 | −0.162352 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.1647 | −0.574394 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.461711 | 0.0154333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.2557 | −1.04360 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.2302 | 0.741419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.9086 | 1.32955 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.83734 | 0.127699 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9076 | 0.794716 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.7377 | 0.954221 | 0.477110 | − | 0.878843i | \(-0.341684\pi\) | ||||
0.477110 | + | 0.878843i | \(0.341684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.57769 | −0.118665 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.6087 | −1.31230 | −0.656148 | − | 0.754632i | \(-0.727815\pi\) | ||||
−0.656148 | + | 0.754632i | \(0.727815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61.7833 | −2.04473 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.2189 | 0.370884 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.4686 | 0.477796 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0473 | −0.529350 | −0.264675 | − | 0.964338i | \(-0.585265\pi\) | ||||
−0.264675 | + | 0.964338i | \(0.585265\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.50547 | −0.214363 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47.2536 | −1.55537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.221881 | −0.00729542 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.784639 | 0.0257709 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.1604 | −0.563016 | −0.281508 | − | 0.959559i | \(-0.590835\pi\) | ||||
−0.281508 | + | 0.959559i | \(0.590835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0240 | 0.557938 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.5371 | −0.901524 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.7913 | 0.876169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.3225 | −0.631239 | −0.315619 | − | 0.948886i | \(-0.602212\pi\) | ||||
−0.315619 | + | 0.948886i | \(0.602212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.4107 | −0.372374 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.07888 | −0.165567 | −0.0827834 | − | 0.996568i | \(-0.526381\pi\) | ||||
−0.0827834 | + | 0.996568i | \(0.526381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.9464 | −0.584415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.15736 | 0.102709 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.4433 | 1.15175 | 0.575876 | − | 0.817537i | \(-0.304661\pi\) | ||||
0.575876 | + | 0.817537i | \(0.304661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.9715 | 0.875533 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.7200 | 0.671891 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.4982 | −0.955539 | −0.477770 | − | 0.878485i | \(-0.658555\pi\) | ||||
−0.477770 | + | 0.878485i | \(0.658555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9649 | −0.387175 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.3763 | −0.529371 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.4728 | 1.21006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2760 | 0.396001 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.08465 | 0.163850 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.67742 | −0.118380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.1741 | 1.61349 | 0.806745 | − | 0.590900i | \(-0.201227\pi\) | ||||
0.806745 | + | 0.590900i | \(0.201227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.6998 | −1.01834 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.6964 | −0.953002 | −0.476501 | − | 0.879174i | \(-0.658095\pi\) | ||||
−0.476501 | + | 0.879174i | \(0.658095\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.2324 | −1.06538 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.88967 | −0.220646 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.5776 | −1.20221 | −0.601106 | − | 0.799169i | \(-0.705273\pi\) | ||||
−0.601106 | + | 0.799169i | \(0.705273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3563 | −0.458830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.79230 | −0.0572237 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.7906 | 1.04586 | 0.522928 | − | 0.852377i | \(-0.324840\pi\) | ||||
0.522928 | + | 0.852377i | \(0.324840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9063 | −0.570543 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.45150 | 0.300845 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.51362 | −0.175323 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.5492 | 1.31986 | 0.659928 | − | 0.751329i | \(-0.270587\pi\) | ||||
0.659928 | + | 0.751329i | \(0.270587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.3874 | −0.424836 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8328 | 0.406829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.2867 | −1.02253 | −0.511265 | − | 0.859423i | \(-0.670823\pi\) | ||||
−0.511265 | + | 0.859423i | \(0.670823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.221881 | 0.00702002 |
(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 | 4020.2.a.h.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.h.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial |