Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.09529\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39026 | 0.983060 | 0.491530 | − | 0.870861i | \(-0.336438\pi\) | ||||
0.491530 | + | 0.870861i | \(0.336438\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0671858 | −0.0335929 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27759 | 0.482884 | 0.241442 | − | 0.970415i | \(-0.422380\pi\) | ||||
0.241442 | + | 0.970415i | \(0.422380\pi\) | |||||||
\(8\) | −2.87392 | −1.01608 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.39026 | 0.439638 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41837 | −0.393384 | −0.196692 | − | 0.980465i | \(-0.563020\pi\) | ||||
−0.196692 | + | 0.980465i | \(0.563020\pi\) | |||||||
\(14\) | 1.77618 | 0.474704 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.86111 | −0.965279 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.158146 | 0.0362811 | 0.0181406 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181406 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(20\) | −0.0671858 | −0.0150232 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00829 | 1.04430 | 0.522150 | − | 0.852853i | \(-0.325130\pi\) | ||||
0.522150 | + | 0.852853i | \(0.325130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.97189 | −0.386720 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0858360 | −0.0162215 | ||||||||
\(29\) | −6.27515 | −1.16527 | −0.582633 | − | 0.812736i | \(-0.697977\pi\) | ||||
−0.582633 | + | 0.812736i | \(0.697977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04981 | 0.547763 | 0.273881 | − | 0.961763i | \(-0.411692\pi\) | ||||
0.273881 | + | 0.961763i | \(0.411692\pi\) | |||||||
\(32\) | 0.379898 | 0.0671570 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.95128 | −1.19214 | ||||||||
\(35\) | 1.27759 | 0.215952 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.69991 | −0.772661 | −0.386330 | − | 0.922360i | \(-0.626258\pi\) | ||||
−0.386330 | + | 0.922360i | \(0.626258\pi\) | |||||||
\(38\) | 0.219863 | 0.0356665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.87392 | −0.454407 | ||||||||
\(41\) | −7.58597 | −1.18473 | −0.592365 | − | 0.805670i | \(-0.701806\pi\) | ||||
−0.592365 | + | 0.805670i | \(0.701806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.41324 | 0.825512 | 0.412756 | − | 0.910842i | \(-0.364566\pi\) | ||||
0.412756 | + | 0.910842i | \(0.364566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.96281 | 1.02661 | ||||||||
\(47\) | 8.23211 | 1.20078 | 0.600388 | − | 0.799709i | \(-0.295013\pi\) | ||||
0.600388 | + | 0.799709i | \(0.295013\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36776 | −0.766823 | ||||||||
\(50\) | 1.39026 | 0.196612 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0952940 | 0.0132149 | ||||||||
\(53\) | −9.36648 | −1.28659 | −0.643293 | − | 0.765620i | \(-0.722432\pi\) | ||||
−0.643293 | + | 0.765620i | \(0.722432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.67169 | −0.490651 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.72406 | −1.14553 | ||||||||
\(59\) | −8.09846 | −1.05433 | −0.527165 | − | 0.849763i | \(-0.676745\pi\) | ||||
−0.527165 | + | 0.849763i | \(0.676745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.2917 | −1.82987 | −0.914934 | − | 0.403603i | \(-0.867758\pi\) | ||||
−0.914934 | + | 0.403603i | \(0.867758\pi\) | |||||||
\(62\) | 4.24002 | 0.538484 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.25038 | 1.03130 | ||||||||
\(65\) | −1.41837 | −0.175927 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.38362 | −0.902053 | −0.451026 | − | 0.892511i | \(-0.648942\pi\) | ||||
−0.451026 | + | 0.892511i | \(0.648942\pi\) | |||||||
\(68\) | 0.335929 | 0.0407374 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.77618 | 0.212294 | ||||||||
\(71\) | 6.77618 | 0.804185 | 0.402092 | − | 0.915599i | \(-0.368283\pi\) | ||||
0.402092 | + | 0.915599i | \(0.368283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66107 | 1.01370 | 0.506851 | − | 0.862034i | \(-0.330810\pi\) | ||||
0.506851 | + | 0.862034i | \(0.330810\pi\) | |||||||
\(74\) | −6.53409 | −0.759572 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0106252 | −0.00121879 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.54572 | −0.286416 | −0.143208 | − | 0.989693i | \(-0.545742\pi\) | ||||
−0.143208 | + | 0.989693i | \(0.545742\pi\) | |||||||
\(80\) | −3.86111 | −0.431686 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.5464 | −1.16466 | ||||||||
\(83\) | −10.1221 | −1.11105 | −0.555524 | − | 0.831501i | \(-0.687482\pi\) | ||||
−0.555524 | + | 0.831501i | \(0.687482\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 7.52580 | 0.811527 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0447 | −1.17073 | −0.585367 | − | 0.810768i | \(-0.699050\pi\) | ||||
−0.585367 | + | 0.810768i | \(0.699050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.81209 | −0.189959 | ||||||||
\(92\) | −0.336486 | −0.0350811 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.4447 | 1.18044 | ||||||||
\(95\) | 0.158146 | 0.0162254 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.41196 | 0.651036 | 0.325518 | − | 0.945536i | \(-0.394461\pi\) | ||||
0.325518 | + | 0.945536i | \(0.394461\pi\) | |||||||
\(98\) | −7.46257 | −0.753833 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0671858 | −0.00671858 | ||||||||
\(101\) | −8.77143 | −0.872790 | −0.436395 | − | 0.899755i | \(-0.643745\pi\) | ||||
−0.436395 | + | 0.899755i | \(0.643745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5666 | 1.13969 | 0.569847 | − | 0.821751i | \(-0.307002\pi\) | ||||
0.569847 | + | 0.821751i | \(0.307002\pi\) | |||||||
\(104\) | 4.07627 | 0.399711 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.0218 | −1.26479 | ||||||||
\(107\) | −15.3467 | −1.48362 | −0.741809 | − | 0.670611i | \(-0.766032\pi\) | ||||
−0.741809 | + | 0.670611i | \(0.766032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4004 | 1.37931 | 0.689656 | − | 0.724137i | \(-0.257762\pi\) | ||||
0.689656 | + | 0.724137i | \(0.257762\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.93293 | −0.466118 | ||||||||
\(113\) | −19.3645 | −1.82166 | −0.910831 | − | 0.412780i | \(-0.864558\pi\) | ||||
−0.910831 | + | 0.412780i | \(0.864558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.00829 | 0.467026 | ||||||||
\(116\) | 0.421601 | 0.0391446 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2589 | −1.03647 | ||||||||
\(119\) | −6.38796 | −0.585583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −19.8692 | −1.79887 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.204904 | −0.0184009 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.02415 | −0.534557 | −0.267278 | − | 0.963619i | \(-0.586124\pi\) | ||||
−0.267278 | + | 0.963619i | \(0.586124\pi\) | |||||||
\(128\) | 10.7104 | 0.946671 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.97189 | −0.172946 | ||||||||
\(131\) | 18.7278 | 1.63626 | 0.818130 | − | 0.575034i | \(-0.195011\pi\) | ||||
0.818130 | + | 0.575034i | \(0.195011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.202046 | 0.0175196 | ||||||||
\(134\) | −10.2651 | −0.886772 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.3696 | 1.23218 | ||||||||
\(137\) | −3.03719 | −0.259485 | −0.129742 | − | 0.991548i | \(-0.541415\pi\) | ||||
−0.129742 | + | 0.991548i | \(0.541415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.21192 | −0.187612 | −0.0938062 | − | 0.995590i | \(-0.529903\pi\) | ||||
−0.0938062 | + | 0.995590i | \(0.529903\pi\) | |||||||
\(140\) | −0.0858360 | −0.00725446 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.42063 | 0.790562 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.27515 | −0.521122 | ||||||||
\(146\) | 12.0411 | 0.996529 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.315767 | 0.0259559 | ||||||||
\(149\) | −1.48122 | −0.121346 | −0.0606730 | − | 0.998158i | \(-0.519325\pi\) | ||||
−0.0606730 | + | 0.998158i | \(0.519325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.03395 | −0.735173 | −0.367586 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367586 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(152\) | −0.454498 | −0.0368647 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.04981 | 0.244967 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6377 | −1.40764 | −0.703820 | − | 0.710379i | \(-0.748524\pi\) | ||||
−0.703820 | + | 0.710379i | \(0.748524\pi\) | |||||||
\(158\) | −3.53921 | −0.281564 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.379898 | 0.0300335 | ||||||||
\(161\) | 6.39855 | 0.504276 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.5040 | 1.84098 | 0.920489 | − | 0.390770i | \(-0.127791\pi\) | ||||
0.920489 | + | 0.390770i | \(0.127791\pi\) | |||||||
\(164\) | 0.509669 | 0.0397985 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.0724 | −1.09223 | ||||||||
\(167\) | −0.602731 | −0.0466407 | −0.0233203 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233203 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9882 | −0.845249 | ||||||||
\(170\) | −6.95128 | −0.533139 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.363693 | −0.0277313 | ||||||||
\(173\) | −9.66389 | −0.734732 | −0.367366 | − | 0.930076i | \(-0.619740\pi\) | ||||
−0.367366 | + | 0.930076i | \(0.619740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.27759 | 0.0965768 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.3550 | −1.15090 | ||||||||
\(179\) | 1.19571 | 0.0893717 | 0.0446859 | − | 0.999001i | \(-0.485771\pi\) | ||||
0.0446859 | + | 0.999001i | \(0.485771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5741 | 1.15761 | 0.578806 | − | 0.815466i | \(-0.303519\pi\) | ||||
0.578806 | + | 0.815466i | \(0.303519\pi\) | |||||||
\(182\) | −2.51927 | −0.186741 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.3934 | −1.06110 | ||||||||
\(185\) | −4.69991 | −0.345544 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.553081 | −0.0403376 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.219863 | 0.0159506 | ||||||||
\(191\) | −18.4016 | −1.33149 | −0.665747 | − | 0.746178i | \(-0.731887\pi\) | ||||
−0.665747 | + | 0.746178i | \(0.731887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.56799 | 0.112866 | 0.0564331 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564331 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(194\) | 8.91428 | 0.640008 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.360637 | 0.0257598 | ||||||||
\(197\) | −7.97000 | −0.567839 | −0.283920 | − | 0.958848i | \(-0.591635\pi\) | ||||
−0.283920 | + | 0.958848i | \(0.591635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.53141 | 0.250335 | 0.125167 | − | 0.992136i | \(-0.460053\pi\) | ||||
0.125167 | + | 0.992136i | \(0.460053\pi\) | |||||||
\(200\) | −2.87392 | −0.203217 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1945 | −0.858005 | ||||||||
\(203\) | −8.01707 | −0.562688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.58597 | −0.529827 | ||||||||
\(206\) | 16.0806 | 1.12039 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.47647 | 0.379725 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2550 | 1.39441 | 0.697207 | − | 0.716870i | \(-0.254426\pi\) | ||||
0.697207 | + | 0.716870i | \(0.254426\pi\) | |||||||
\(212\) | 0.629295 | 0.0432201 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.3358 | −1.45849 | ||||||||
\(215\) | 5.41324 | 0.369180 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.89642 | 0.264506 | ||||||||
\(218\) | 20.0203 | 1.35595 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.09183 | 0.477048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5500 | 1.51006 | 0.755029 | − | 0.655691i | \(-0.227623\pi\) | ||||
0.755029 | + | 0.655691i | \(0.227623\pi\) | |||||||
\(224\) | 0.485354 | 0.0324291 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −26.9217 | −1.79080 | ||||||||
\(227\) | −18.8062 | −1.24821 | −0.624105 | − | 0.781341i | \(-0.714536\pi\) | ||||
−0.624105 | + | 0.781341i | \(0.714536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.8320 | −1.57486 | −0.787431 | − | 0.616403i | \(-0.788589\pi\) | ||||
−0.787431 | + | 0.616403i | \(0.788589\pi\) | |||||||
\(230\) | 6.96281 | 0.459114 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0343 | 1.18401 | ||||||||
\(233\) | 10.0918 | 0.661137 | 0.330569 | − | 0.943782i | \(-0.392759\pi\) | ||||
0.330569 | + | 0.943782i | \(0.392759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.23211 | 0.537004 | ||||||||
\(236\) | 0.544102 | 0.0354180 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.88090 | −0.575663 | ||||||||
\(239\) | −0.167227 | −0.0108170 | −0.00540850 | − | 0.999985i | \(-0.501722\pi\) | ||||
−0.00540850 | + | 0.999985i | \(0.501722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.965256 | 0.0621776 | 0.0310888 | − | 0.999517i | \(-0.490103\pi\) | ||||
0.0310888 | + | 0.999517i | \(0.490103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.960201 | 0.0614706 | ||||||||
\(245\) | −5.36776 | −0.342934 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.224308 | −0.0142724 | ||||||||
\(248\) | −8.76492 | −0.556573 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.39026 | 0.0879276 | ||||||||
\(251\) | 23.5102 | 1.48395 | 0.741975 | − | 0.670428i | \(-0.233889\pi\) | ||||
0.741975 | + | 0.670428i | \(0.233889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.37512 | −0.525502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.61062 | −0.100664 | ||||||||
\(257\) | 6.58273 | 0.410620 | 0.205310 | − | 0.978697i | \(-0.434180\pi\) | ||||
0.205310 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00457 | −0.373106 | ||||||||
\(260\) | 0.0952940 | 0.00590988 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.0365 | 1.60854 | ||||||||
\(263\) | −12.4538 | −0.767936 | −0.383968 | − | 0.923346i | \(-0.625443\pi\) | ||||
−0.383968 | + | 0.923346i | \(0.625443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.36648 | −0.575378 | ||||||||
\(266\) | 0.280895 | 0.0172228 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.496074 | 0.0303026 | ||||||||
\(269\) | −20.7729 | −1.26655 | −0.633274 | − | 0.773927i | \(-0.718290\pi\) | ||||
−0.633274 | + | 0.773927i | \(0.718290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.3903 | 0.874146 | 0.437073 | − | 0.899426i | \(-0.356015\pi\) | ||||
0.437073 | + | 0.899426i | \(0.356015\pi\) | |||||||
\(272\) | 19.3056 | 1.17057 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.22247 | −0.255089 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.4872 | −1.05070 | −0.525352 | − | 0.850885i | \(-0.676066\pi\) | ||||
−0.525352 | + | 0.850885i | \(0.676066\pi\) | |||||||
\(278\) | −3.07513 | −0.184434 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.67169 | −0.219426 | ||||||||
\(281\) | 18.8860 | 1.12664 | 0.563322 | − | 0.826238i | \(-0.309523\pi\) | ||||
0.563322 | + | 0.826238i | \(0.309523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5813 | −0.807326 | −0.403663 | − | 0.914908i | \(-0.632263\pi\) | ||||
−0.403663 | + | 0.914908i | \(0.632263\pi\) | |||||||
\(284\) | −0.455263 | −0.0270149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.69177 | −0.572087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | −8.72406 | −0.512295 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.581901 | −0.0340532 | ||||||||
\(293\) | −19.9023 | −1.16271 | −0.581353 | − | 0.813651i | \(-0.697477\pi\) | ||||
−0.581353 | + | 0.813651i | \(0.697477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.09846 | −0.471511 | ||||||||
\(296\) | 13.5072 | 0.785088 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.05927 | −0.119290 | ||||||||
\(299\) | −7.10358 | −0.410811 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.91591 | 0.398626 | ||||||||
\(302\) | −12.5595 | −0.722719 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.610619 | −0.0350214 | ||||||||
\(305\) | −14.2917 | −0.818342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9354 | −0.852410 | −0.426205 | − | 0.904627i | \(-0.640150\pi\) | ||||
−0.426205 | + | 0.904627i | \(0.640150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.24002 | 0.240817 | ||||||||
\(311\) | 4.99700 | 0.283354 | 0.141677 | − | 0.989913i | \(-0.454751\pi\) | ||||
0.141677 | + | 0.989913i | \(0.454751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.39648 | 0.531120 | 0.265560 | − | 0.964094i | \(-0.414443\pi\) | ||||
0.265560 | + | 0.964094i | \(0.414443\pi\) | |||||||
\(314\) | −24.5209 | −1.38379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.171037 | 0.00962155 | ||||||||
\(317\) | −2.15253 | −0.120898 | −0.0604492 | − | 0.998171i | \(-0.519253\pi\) | ||||
−0.0604492 | + | 0.998171i | \(0.519253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.25038 | 0.461210 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.89563 | 0.495734 | ||||||||
\(323\) | −0.790729 | −0.0439973 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.41837 | −0.0786767 | ||||||||
\(326\) | 32.6766 | 1.80979 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.8015 | 1.20378 | ||||||||
\(329\) | 10.5173 | 0.579836 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5116 | −1.07245 | −0.536227 | − | 0.844074i | \(-0.680151\pi\) | ||||
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(332\) | 0.680063 | 0.0373233 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.837950 | −0.0458506 | ||||||||
\(335\) | −7.38362 | −0.403410 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.6047 | 1.72162 | 0.860809 | − | 0.508929i | \(-0.169958\pi\) | ||||
0.860809 | + | 0.508929i | \(0.169958\pi\) | |||||||
\(338\) | −15.2765 | −0.830931 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.335929 | 0.0182183 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8009 | −0.853171 | ||||||||
\(344\) | −15.5572 | −0.838789 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.4353 | −0.722286 | ||||||||
\(347\) | −9.38313 | −0.503713 | −0.251856 | − | 0.967765i | \(-0.581041\pi\) | ||||
−0.251856 | + | 0.967765i | \(0.581041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.8131 | −1.32822 | −0.664108 | − | 0.747637i | \(-0.731188\pi\) | ||||
−0.664108 | + | 0.747637i | \(0.731188\pi\) | |||||||
\(350\) | 1.77618 | 0.0949408 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4788 | 1.03675 | 0.518375 | − | 0.855153i | \(-0.326537\pi\) | ||||
0.518375 | + | 0.855153i | \(0.326537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.77618 | 0.359642 | ||||||||
\(356\) | 0.742046 | 0.0393284 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.66235 | 0.0878578 | ||||||||
\(359\) | −29.7701 | −1.57121 | −0.785603 | − | 0.618732i | \(-0.787647\pi\) | ||||
−0.785603 | + | 0.618732i | \(0.787647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9750 | −0.998684 | ||||||||
\(362\) | 21.6520 | 1.13800 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.121747 | 0.00638126 | ||||||||
\(365\) | 8.66107 | 0.453341 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.43597 | −0.335955 | −0.167977 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167977 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(368\) | −19.3376 | −1.00804 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.53409 | −0.339691 | ||||||||
\(371\) | −11.9665 | −0.621272 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.8924 | −1.08177 | −0.540883 | − | 0.841098i | \(-0.681910\pi\) | ||||
−0.540883 | + | 0.841098i | \(0.681910\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.6584 | −1.22009 | ||||||||
\(377\) | 8.90045 | 0.458396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1991 | −0.729359 | −0.364680 | − | 0.931133i | \(-0.618822\pi\) | ||||
−0.364680 | + | 0.931133i | \(0.618822\pi\) | |||||||
\(380\) | −0.0106252 | −0.000545059 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.5830 | −1.30894 | ||||||||
\(383\) | 26.4783 | 1.35298 | 0.676489 | − | 0.736453i | \(-0.263501\pi\) | ||||
0.676489 | + | 0.736453i | \(0.263501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.17990 | 0.110954 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.430793 | −0.0218702 | ||||||||
\(389\) | 36.4965 | 1.85044 | 0.925222 | − | 0.379427i | \(-0.123879\pi\) | ||||
0.925222 | + | 0.379427i | \(0.123879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0415 | −1.26640 | ||||||||
\(392\) | 15.4265 | 0.779157 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.0804 | −0.558220 | ||||||||
\(395\) | −2.54572 | −0.128089 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.03969 | −0.403500 | −0.201750 | − | 0.979437i | \(-0.564663\pi\) | ||||
−0.201750 | + | 0.979437i | \(0.564663\pi\) | |||||||
\(398\) | 4.90956 | 0.246094 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.86111 | −0.193056 | ||||||||
\(401\) | 28.0902 | 1.40276 | 0.701379 | − | 0.712788i | \(-0.252568\pi\) | ||||
0.701379 | + | 0.712788i | \(0.252568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.32575 | −0.215481 | ||||||||
\(404\) | 0.589316 | 0.0293196 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.1458 | −0.553156 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.97950 | −0.295667 | −0.147834 | − | 0.989012i | \(-0.547230\pi\) | ||||
−0.147834 | + | 0.989012i | \(0.547230\pi\) | |||||||
\(410\) | −10.5464 | −0.520852 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.777114 | −0.0382857 | ||||||||
\(413\) | −10.3465 | −0.509119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.1221 | −0.496876 | ||||||||
\(416\) | −0.538833 | −0.0264185 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.4707 | 0.755795 | 0.377897 | − | 0.925847i | \(-0.376647\pi\) | ||||
0.377897 | + | 0.925847i | \(0.376647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5746 | 1.68506 | 0.842532 | − | 0.538647i | \(-0.181064\pi\) | ||||
0.842532 | + | 0.538647i | \(0.181064\pi\) | |||||||
\(422\) | 28.1597 | 1.37079 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.9185 | 1.30728 | ||||||||
\(425\) | −5.00000 | −0.242536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.2590 | −0.883614 | ||||||||
\(428\) | 1.03108 | 0.0498390 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.52580 | 0.362926 | ||||||||
\(431\) | −3.36052 | −0.161870 | −0.0809352 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809352 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.67779 | 0.176744 | 0.0883718 | − | 0.996088i | \(-0.471834\pi\) | ||||
0.0883718 | + | 0.996088i | \(0.471834\pi\) | |||||||
\(434\) | 5.41702 | 0.260025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.967505 | −0.0463351 | ||||||||
\(437\) | 0.792040 | 0.0378884 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.55432 | −0.0741835 | −0.0370917 | − | 0.999312i | \(-0.511809\pi\) | ||||
−0.0370917 | + | 0.999312i | \(0.511809\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.85946 | 0.468967 | ||||||||
\(443\) | −21.2059 | −1.00752 | −0.503761 | − | 0.863843i | \(-0.668051\pi\) | ||||
−0.503761 | + | 0.863843i | \(0.668051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0447 | −0.523569 | ||||||||
\(446\) | 31.3503 | 1.48448 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.5406 | 0.497997 | ||||||||
\(449\) | −15.1106 | −0.713113 | −0.356557 | − | 0.934274i | \(-0.616049\pi\) | ||||
−0.356557 | + | 0.934274i | \(0.616049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.30102 | 0.0611949 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.1454 | −1.22707 | ||||||||
\(455\) | −1.81209 | −0.0849521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.3042 | 1.93213 | 0.966064 | − | 0.258303i | \(-0.0831634\pi\) | ||||
0.966064 | + | 0.258303i | \(0.0831634\pi\) | |||||||
\(458\) | −33.1326 | −1.54818 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.336486 | −0.0156887 | ||||||||
\(461\) | 16.3158 | 0.759901 | 0.379951 | − | 0.925007i | \(-0.375941\pi\) | ||||
0.379951 | + | 0.925007i | \(0.375941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.47904 | 0.394054 | 0.197027 | − | 0.980398i | \(-0.436871\pi\) | ||||
0.197027 | + | 0.980398i | \(0.436871\pi\) | |||||||
\(464\) | 24.2291 | 1.12481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0302 | 0.649938 | ||||||||
\(467\) | 36.5669 | 1.69212 | 0.846058 | − | 0.533090i | \(-0.178969\pi\) | ||||
0.846058 | + | 0.533090i | \(0.178969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.43325 | −0.435587 | ||||||||
\(470\) | 11.4447 | 0.527907 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.2743 | 1.07129 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.158146 | 0.00725623 | ||||||||
\(476\) | 0.429180 | 0.0196714 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.232488 | −0.0106338 | ||||||||
\(479\) | 38.9513 | 1.77973 | 0.889866 | − | 0.456222i | \(-0.150798\pi\) | ||||
0.889866 | + | 0.456222i | \(0.150798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.66619 | 0.303952 | ||||||||
\(482\) | 1.34195 | 0.0611243 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.41196 | 0.291152 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.27209 | 0.374844 | 0.187422 | − | 0.982279i | \(-0.439987\pi\) | ||||
0.187422 | + | 0.982279i | \(0.439987\pi\) | |||||||
\(488\) | 41.0733 | 1.85930 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.46257 | −0.337124 | ||||||||
\(491\) | 12.1322 | 0.547518 | 0.273759 | − | 0.961798i | \(-0.411733\pi\) | ||||
0.273759 | + | 0.961798i | \(0.411733\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.3757 | 1.41309 | ||||||||
\(494\) | −0.311846 | −0.0140306 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7757 | −0.528744 | ||||||||
\(497\) | 8.65719 | 0.388328 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.3581 | −1.26948 | −0.634740 | − | 0.772725i | \(-0.718893\pi\) | ||||
−0.634740 | + | 0.772725i | \(0.718893\pi\) | |||||||
\(500\) | −0.0671858 | −0.00300464 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 32.6852 | 1.45881 | ||||||||
\(503\) | 15.2800 | 0.681300 | 0.340650 | − | 0.940190i | \(-0.389353\pi\) | ||||
0.340650 | + | 0.940190i | \(0.389353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.77143 | −0.390324 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.404737 | 0.0179573 | ||||||||
\(509\) | 22.0494 | 0.977321 | 0.488661 | − | 0.872474i | \(-0.337486\pi\) | ||||
0.488661 | + | 0.872474i | \(0.337486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0653 | 0.489500 | ||||||||
\(512\) | −23.6599 | −1.04563 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.15169 | 0.403664 | ||||||||
\(515\) | 11.5666 | 0.509687 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.34789 | −0.366785 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.07627 | 0.178756 | ||||||||
\(521\) | 23.9380 | 1.04874 | 0.524371 | − | 0.851490i | \(-0.324300\pi\) | ||||
0.524371 | + | 0.851490i | \(0.324300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3421 | −1.10813 | −0.554066 | − | 0.832473i | \(-0.686925\pi\) | ||||
−0.554066 | + | 0.832473i | \(0.686925\pi\) | |||||||
\(524\) | −1.25824 | −0.0549667 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3140 | −0.754927 | ||||||||
\(527\) | −15.2491 | −0.664260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.08298 | 0.0905642 | ||||||||
\(530\) | −13.0218 | −0.565632 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0135746 | −0.000588534 0 | ||||||||
\(533\) | 10.7597 | 0.466053 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.3467 | −0.663494 | ||||||||
\(536\) | 21.2199 | 0.916561 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.8797 | −1.24509 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.0634 | −1.50749 | −0.753747 | − | 0.657165i | \(-0.771755\pi\) | ||||
−0.753747 | + | 0.657165i | \(0.771755\pi\) | |||||||
\(542\) | 20.0062 | 0.859338 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.89949 | −0.0814399 | ||||||||
\(545\) | 14.4004 | 0.616847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.10787 | −0.0473689 | −0.0236845 | − | 0.999719i | \(-0.507540\pi\) | ||||
−0.0236845 | + | 0.999719i | \(0.507540\pi\) | |||||||
\(548\) | 0.204056 | 0.00871684 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.992388 | −0.0422771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.25239 | −0.138306 | ||||||||
\(554\) | −24.3117 | −1.03291 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.148609 | 0.00630244 | ||||||||
\(557\) | 5.41988 | 0.229648 | 0.114824 | − | 0.993386i | \(-0.463370\pi\) | ||||
0.114824 | + | 0.993386i | \(0.463370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.67795 | −0.324743 | ||||||||
\(560\) | −4.93293 | −0.208454 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.2564 | 1.10756 | ||||||||
\(563\) | −32.7448 | −1.38003 | −0.690015 | − | 0.723795i | \(-0.742396\pi\) | ||||
−0.690015 | + | 0.723795i | \(0.742396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.3645 | −0.814672 | ||||||||
\(566\) | −18.8815 | −0.793650 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.4742 | −0.817119 | ||||||||
\(569\) | 3.51736 | 0.147455 | 0.0737277 | − | 0.997278i | \(-0.476510\pi\) | ||||
0.0737277 | + | 0.997278i | \(0.476510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0252 | −1.50761 | −0.753804 | − | 0.657099i | \(-0.771783\pi\) | ||||
−0.753804 | + | 0.657099i | \(0.771783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.4740 | −0.562396 | ||||||||
\(575\) | 5.00829 | 0.208860 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5501 | 0.647357 | 0.323679 | − | 0.946167i | \(-0.395080\pi\) | ||||
0.323679 | + | 0.946167i | \(0.395080\pi\) | |||||||
\(578\) | 11.1221 | 0.462617 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.421601 | 0.0175060 | ||||||||
\(581\) | −12.9319 | −0.536507 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −24.8912 | −1.03001 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.6694 | −1.14301 | ||||||||
\(587\) | 24.2604 | 1.00133 | 0.500667 | − | 0.865640i | \(-0.333088\pi\) | ||||
0.500667 | + | 0.865640i | \(0.333088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.482315 | 0.0198735 | ||||||||
\(590\) | −11.2589 | −0.463523 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.1469 | 0.745833 | ||||||||
\(593\) | −27.4019 | −1.12526 | −0.562630 | − | 0.826709i | \(-0.690210\pi\) | ||||
−0.562630 | + | 0.826709i | \(0.690210\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.38796 | −0.261881 | ||||||||
\(596\) | 0.0995167 | 0.00407636 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.87581 | −0.403852 | ||||||||
\(599\) | −10.6773 | −0.436262 | −0.218131 | − | 0.975920i | \(-0.569996\pi\) | ||||
−0.218131 | + | 0.975920i | \(0.569996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0663 | 0.451403 | 0.225701 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225701 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(602\) | 9.61489 | 0.391874 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.606953 | 0.0246966 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.514518 | −0.0208836 | −0.0104418 | − | 0.999945i | \(-0.503324\pi\) | ||||
−0.0104418 | + | 0.999945i | \(0.503324\pi\) | |||||||
\(608\) | 0.0600792 | 0.00243653 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.8692 | −0.804479 | ||||||||
\(611\) | −11.6761 | −0.472366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0977 | 0.771348 | 0.385674 | − | 0.922635i | \(-0.373969\pi\) | ||||
0.385674 | + | 0.922635i | \(0.373969\pi\) | |||||||
\(614\) | −20.7641 | −0.837970 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.70745 | 0.189515 | 0.0947573 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947573 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.3691 | 1.50199 | 0.750996 | − | 0.660307i | \(-0.229574\pi\) | ||||
0.750996 | + | 0.660307i | \(0.229574\pi\) | |||||||
\(620\) | −0.204904 | −0.00822915 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.94711 | 0.278554 | ||||||||
\(623\) | −14.1106 | −0.565329 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.0635 | 0.522123 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.18500 | 0.0472867 | ||||||||
\(629\) | 23.4996 | 0.936989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5669 | 1.41590 | 0.707949 | − | 0.706264i | \(-0.249621\pi\) | ||||
0.707949 | + | 0.706264i | \(0.249621\pi\) | |||||||
\(632\) | 7.31621 | 0.291023 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.99257 | −0.118850 | ||||||||
\(635\) | −6.02415 | −0.239061 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.61344 | 0.301656 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.7104 | 0.423364 | ||||||||
\(641\) | −12.2098 | −0.482260 | −0.241130 | − | 0.970493i | \(-0.577518\pi\) | ||||
−0.241130 | + | 0.970493i | \(0.577518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9596 | −0.826565 | −0.413282 | − | 0.910603i | \(-0.635618\pi\) | ||||
−0.413282 | + | 0.910603i | \(0.635618\pi\) | |||||||
\(644\) | −0.429892 | −0.0169401 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.09932 | −0.0432520 | ||||||||
\(647\) | −14.8766 | −0.584859 | −0.292430 | − | 0.956287i | \(-0.594464\pi\) | ||||
−0.292430 | + | 0.956287i | \(0.594464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.97189 | −0.0773440 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.57914 | −0.0618438 | ||||||||
\(653\) | 12.1308 | 0.474713 | 0.237357 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237357 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7278 | 0.731757 | ||||||||
\(656\) | 29.2903 | 1.14359 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.6217 | 0.570014 | ||||||||
\(659\) | −7.49994 | −0.292156 | −0.146078 | − | 0.989273i | \(-0.546665\pi\) | ||||
−0.146078 | + | 0.989273i | \(0.546665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65248 | 0.375438 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(662\) | −27.1261 | −1.05429 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.0902 | 1.12892 | ||||||||
\(665\) | 0.202046 | 0.00783500 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.4278 | −1.21689 | ||||||||
\(668\) | 0.0404949 | 0.00156680 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.2651 | −0.396577 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4496 | 0.942463 | 0.471231 | − | 0.882010i | \(-0.343810\pi\) | ||||
0.471231 | + | 0.882010i | \(0.343810\pi\) | |||||||
\(674\) | 43.9386 | 1.69245 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.738254 | 0.0283944 | ||||||||
\(677\) | −46.7394 | −1.79634 | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||||
−0.898171 | + | 0.439646i | \(0.855104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.19187 | 0.314375 | ||||||||
\(680\) | 14.3696 | 0.551049 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.1941 | 1.07882 | 0.539408 | − | 0.842045i | \(-0.318648\pi\) | ||||
0.539408 | + | 0.842045i | \(0.318648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.03719 | −0.116045 | ||||||||
\(686\) | −21.9674 | −0.838718 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.9011 | −0.796849 | ||||||||
\(689\) | 13.2851 | 0.506122 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.5971 | 0.441175 | 0.220587 | − | 0.975367i | \(-0.429203\pi\) | ||||
0.220587 | + | 0.975367i | \(0.429203\pi\) | |||||||
\(692\) | 0.649276 | 0.0246818 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0450 | −0.495180 | ||||||||
\(695\) | −2.21192 | −0.0839028 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.9298 | 1.43670 | ||||||||
\(698\) | −34.4966 | −1.30572 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0858360 | −0.00324429 | ||||||||
\(701\) | 36.7019 | 1.38621 | 0.693107 | − | 0.720835i | \(-0.256241\pi\) | ||||
0.693107 | + | 0.720835i | \(0.256241\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.743272 | −0.0280330 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.0805 | 1.01919 | ||||||||
\(707\) | −11.2063 | −0.421456 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.4905 | 1.37043 | 0.685214 | − | 0.728341i | \(-0.259708\pi\) | ||||
0.685214 | + | 0.728341i | \(0.259708\pi\) | |||||||
\(710\) | 9.42063 | 0.353550 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.7415 | 1.18956 | ||||||||
\(713\) | 15.2744 | 0.572029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0803349 | −0.00300225 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.3881 | −1.54459 | ||||||||
\(719\) | 9.32888 | 0.347909 | 0.173954 | − | 0.984754i | \(-0.444346\pi\) | ||||
0.173954 | + | 0.984754i | \(0.444346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7774 | 0.550340 | ||||||||
\(722\) | −26.3801 | −0.981766 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.04636 | −0.0388875 | ||||||||
\(725\) | −6.27515 | −0.233053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.46883 | −0.314091 | −0.157046 | − | 0.987591i | \(-0.550197\pi\) | ||||
−0.157046 | + | 0.987591i | \(0.550197\pi\) | |||||||
\(728\) | 5.20780 | 0.193014 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0411 | 0.445661 | ||||||||
\(731\) | −27.0662 | −1.00108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0470 | 1.07288 | 0.536438 | − | 0.843940i | \(-0.319770\pi\) | ||||
0.536438 | + | 0.843940i | \(0.319770\pi\) | |||||||
\(734\) | −8.94765 | −0.330264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.90264 | 0.0701322 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.7551 | −0.505990 | −0.252995 | − | 0.967468i | \(-0.581416\pi\) | ||||
−0.252995 | + | 0.967468i | \(0.581416\pi\) | |||||||
\(740\) | 0.315767 | 0.0116078 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.6366 | −0.610747 | ||||||||
\(743\) | 34.9135 | 1.28085 | 0.640427 | − | 0.768019i | \(-0.278758\pi\) | ||||
0.640427 | + | 0.768019i | \(0.278758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.48122 | −0.0542676 | ||||||||
\(746\) | −29.0458 | −1.06344 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.6068 | −0.716416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0992 | 0.806412 | 0.403206 | − | 0.915109i | \(-0.367896\pi\) | ||||
0.403206 | + | 0.915109i | \(0.367896\pi\) | |||||||
\(752\) | −31.7851 | −1.15908 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.3739 | 0.450631 | ||||||||
\(755\) | −9.03395 | −0.328779 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.0300 | −1.63664 | −0.818321 | − | 0.574761i | \(-0.805095\pi\) | ||||
−0.818321 | + | 0.574761i | \(0.805095\pi\) | |||||||
\(758\) | −19.7404 | −0.717004 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.454498 | −0.0164864 | ||||||||
\(761\) | −33.6001 | −1.21800 | −0.609001 | − | 0.793169i | \(-0.708430\pi\) | ||||
−0.609001 | + | 0.793169i | \(0.708430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.3979 | 0.666048 | ||||||||
\(764\) | 1.23633 | 0.0447287 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.8116 | 1.33006 | ||||||||
\(767\) | 11.4866 | 0.414756 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6086 | 0.887408 | 0.443704 | − | 0.896173i | \(-0.353664\pi\) | ||||
0.443704 | + | 0.896173i | \(0.353664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.105346 | −0.00379150 | ||||||||
\(773\) | 23.6816 | 0.851768 | 0.425884 | − | 0.904778i | \(-0.359963\pi\) | ||||
0.425884 | + | 0.904778i | \(0.359963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.04981 | 0.109553 | ||||||||
\(776\) | −18.4275 | −0.661507 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 50.7394 | 1.81910 | ||||||||
\(779\) | −1.19969 | −0.0429833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −34.8141 | −1.24495 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.7255 | 0.740198 | ||||||||
\(785\) | −17.6377 | −0.629515 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.4210 | −0.656639 | −0.328320 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328320 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(788\) | 0.535471 | 0.0190754 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.53921 | −0.125919 | ||||||||
\(791\) | −24.7399 | −0.879651 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.2709 | 0.719840 | ||||||||
\(794\) | −11.1772 | −0.396665 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.237260 | −0.00840947 | ||||||||
\(797\) | 6.50665 | 0.230477 | 0.115239 | − | 0.993338i | \(-0.463237\pi\) | ||||
0.115239 | + | 0.993338i | \(0.463237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.1606 | −1.45616 | ||||||||
\(800\) | 0.379898 | 0.0134314 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.0526 | 1.37900 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.39855 | 0.225519 | ||||||||
\(806\) | −6.01390 | −0.211831 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.2084 | 0.886828 | ||||||||
\(809\) | −11.8505 | −0.416642 | −0.208321 | − | 0.978060i | \(-0.566800\pi\) | ||||
−0.208321 | + | 0.978060i | \(0.566800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.51391 | 0.263849 | 0.131925 | − | 0.991260i | \(-0.457884\pi\) | ||||
0.131925 | + | 0.991260i | \(0.457884\pi\) | |||||||
\(812\) | 0.538633 | 0.0189023 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.5040 | 0.823310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.856081 | 0.0299505 | ||||||||
\(818\) | −8.31305 | −0.290659 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.509669 | 0.0177984 | ||||||||
\(821\) | 37.3365 | 1.30305 | 0.651527 | − | 0.758625i | \(-0.274129\pi\) | ||||
0.651527 | + | 0.758625i | \(0.274129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.0498 | −1.50062 | −0.750311 | − | 0.661085i | \(-0.770096\pi\) | ||||
−0.750311 | + | 0.661085i | \(0.770096\pi\) | |||||||
\(824\) | −33.2416 | −1.15803 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.3843 | −0.500495 | ||||||||
\(827\) | 20.0304 | 0.696524 | 0.348262 | − | 0.937397i | \(-0.386772\pi\) | ||||
0.348262 | + | 0.937397i | \(0.386772\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.9207 | −1.66435 | −0.832177 | − | 0.554510i | \(-0.812906\pi\) | ||||
−0.832177 | + | 0.554510i | \(0.812906\pi\) | |||||||
\(830\) | −14.0724 | −0.488458 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.7021 | −0.405696 | ||||||||
\(833\) | 26.8388 | 0.929909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.602731 | −0.0208584 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.5083 | 0.742992 | ||||||||
\(839\) | −2.22093 | −0.0766750 | −0.0383375 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383375 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.3775 | 0.357843 | ||||||||
\(842\) | 48.0676 | 1.65652 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.36085 | −0.0468424 | ||||||||
\(845\) | −10.9882 | −0.378007 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 36.1651 | 1.24191 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.95128 | −0.238427 | ||||||||
\(851\) | −23.5385 | −0.806890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.37161 | −0.218160 | −0.109080 | − | 0.994033i | \(-0.534790\pi\) | ||||
−0.109080 | + | 0.994033i | \(0.534790\pi\) | |||||||
\(854\) | −25.3847 | −0.868646 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.1051 | 1.50748 | ||||||||
\(857\) | −35.9060 | −1.22653 | −0.613263 | − | 0.789878i | \(-0.710144\pi\) | ||||
−0.613263 | + | 0.789878i | \(0.710144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.4697 | 1.92672 | 0.963360 | − | 0.268212i | \(-0.0864328\pi\) | ||||
0.963360 | + | 0.268212i | \(0.0864328\pi\) | |||||||
\(860\) | −0.363693 | −0.0124018 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.67198 | −0.159128 | ||||||||
\(863\) | 31.0742 | 1.05778 | 0.528888 | − | 0.848691i | \(-0.322609\pi\) | ||||
0.528888 | + | 0.848691i | \(0.322609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.66389 | −0.328582 | ||||||||
\(866\) | 5.11308 | 0.173749 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.261784 | −0.00888552 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4727 | 0.354853 | ||||||||
\(872\) | −41.3857 | −1.40150 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.10114 | 0.0372466 | ||||||||
\(875\) | 1.27759 | 0.0431905 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8224 | 0.568053 | 0.284026 | − | 0.958816i | \(-0.408330\pi\) | ||||
0.284026 | + | 0.958816i | \(0.408330\pi\) | |||||||
\(878\) | −2.16090 | −0.0729268 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5633 | −0.894940 | −0.447470 | − | 0.894299i | \(-0.647675\pi\) | ||||
−0.447470 | + | 0.894299i | \(0.647675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.3742 | −1.82984 | −0.914919 | − | 0.403638i | \(-0.867746\pi\) | ||||
−0.914919 | + | 0.403638i | \(0.867746\pi\) | |||||||
\(884\) | −0.476470 | −0.0160254 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.4816 | −0.990455 | ||||||||
\(887\) | 41.2262 | 1.38424 | 0.692120 | − | 0.721783i | \(-0.256677\pi\) | ||||
0.692120 | + | 0.721783i | \(0.256677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.69640 | −0.258129 | ||||||||
\(890\) | −15.3550 | −0.514699 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.51504 | −0.0507273 | ||||||||
\(893\) | 1.30187 | 0.0435655 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.19571 | 0.0399682 | ||||||||
\(896\) | 13.6835 | 0.457132 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.0076 | −0.701033 | ||||||||
\(899\) | −19.1380 | −0.638289 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.8324 | 1.56021 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 55.6521 | 1.85096 | ||||||||
\(905\) | 15.5741 | 0.517699 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.4046 | 1.40802 | 0.704010 | − | 0.710190i | \(-0.251391\pi\) | ||||
0.704010 | + | 0.710190i | \(0.251391\pi\) | |||||||
\(908\) | 1.26351 | 0.0419310 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.51927 | −0.0835130 | ||||||||
\(911\) | 8.01199 | 0.265449 | 0.132725 | − | 0.991153i | \(-0.457627\pi\) | ||||
0.132725 | + | 0.991153i | \(0.457627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 57.4234 | 1.89940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.60117 | 0.0529042 | ||||||||
\(917\) | 23.9265 | 0.790123 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.2336 | 1.36017 | 0.680086 | − | 0.733132i | \(-0.261942\pi\) | ||||
0.680086 | + | 0.733132i | \(0.261942\pi\) | |||||||
\(920\) | −14.3934 | −0.474537 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.6831 | 0.747028 | ||||||||
\(923\) | −9.61110 | −0.316353 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.69991 | −0.154532 | ||||||||
\(926\) | 11.7880 | 0.387379 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.38391 | −0.0782558 | ||||||||
\(929\) | 15.1939 | 0.498495 | 0.249247 | − | 0.968440i | \(-0.419817\pi\) | ||||
0.249247 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.848889 | −0.0278212 | ||||||||
\(932\) | −0.678027 | −0.0222095 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 50.8375 | 1.66345 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.5213 | 0.833746 | 0.416873 | − | 0.908965i | \(-0.363126\pi\) | ||||
0.416873 | + | 0.908965i | \(0.363126\pi\) | |||||||
\(938\) | −13.1146 | −0.428208 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.553081 | −0.0180395 | ||||||||
\(941\) | −32.3673 | −1.05514 | −0.527572 | − | 0.849511i | \(-0.676897\pi\) | ||||
−0.527572 | + | 0.849511i | \(0.676897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.9927 | −1.23721 | ||||||||
\(944\) | 31.2691 | 1.01772 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.1516 | 1.30475 | 0.652375 | − | 0.757896i | \(-0.273773\pi\) | ||||
0.652375 | + | 0.757896i | \(0.273773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2846 | −0.398774 | ||||||||
\(950\) | 0.219863 | 0.00713331 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.3585 | 0.595001 | ||||||||
\(953\) | −35.6513 | −1.15486 | −0.577429 | − | 0.816441i | \(-0.695944\pi\) | ||||
−0.577429 | + | 0.816441i | \(0.695944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.4016 | −0.595462 | ||||||||
\(956\) | 0.0112353 | 0.000363374 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 54.1524 | 1.74958 | ||||||||
\(959\) | −3.88029 | −0.125301 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6986 | −0.699956 | ||||||||
\(962\) | 9.26772 | 0.298803 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.0648515 | −0.00208873 | ||||||||
\(965\) | 1.56799 | 0.0504753 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.0622 | −0.645156 | −0.322578 | − | 0.946543i | \(-0.604549\pi\) | ||||
−0.322578 | + | 0.946543i | \(0.604549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.91428 | 0.286220 | ||||||||
\(971\) | 41.6307 | 1.33599 | 0.667996 | − | 0.744165i | \(-0.267152\pi\) | ||||
0.667996 | + | 0.744165i | \(0.267152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.82593 | −0.0905950 | ||||||||
\(974\) | 11.5003 | 0.368494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55.1820 | 1.76633 | ||||||||
\(977\) | −19.0722 | −0.610173 | −0.305087 | − | 0.952325i | \(-0.598685\pi\) | ||||
−0.305087 | + | 0.952325i | \(0.598685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.360637 | 0.0115201 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.8668 | 0.538243 | ||||||||
\(983\) | −26.5563 | −0.847015 | −0.423507 | − | 0.905893i | \(-0.639201\pi\) | ||||
−0.423507 | + | 0.905893i | \(0.639201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.97000 | −0.253945 | ||||||||
\(986\) | 43.6203 | 1.38915 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0150703 | 0.000479452 0 | ||||||||
\(989\) | 27.1111 | 0.862082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2494 | −0.770307 | −0.385153 | − | 0.922853i | \(-0.625851\pi\) | ||||
−0.385153 | + | 0.922853i | \(0.625851\pi\) | |||||||
\(992\) | 1.15862 | 0.0367861 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0357 | 0.381750 | ||||||||
\(995\) | 3.53141 | 0.111953 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0616 | 0.508675 | 0.254338 | − | 0.967116i | \(-0.418143\pi\) | ||||
0.254338 | + | 0.967116i | \(0.418143\pi\) | |||||||
\(998\) | −39.4250 | −1.24798 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.be.1.4 | 4 | ||
3.2 | odd | 2 | 1815.2.a.x.1.1 | 4 | |||
11.5 | even | 5 | 495.2.n.d.91.1 | 8 | |||
11.9 | even | 5 | 495.2.n.d.136.1 | 8 | |||
11.10 | odd | 2 | 5445.2.a.bv.1.1 | 4 | |||
15.14 | odd | 2 | 9075.2.a.cl.1.4 | 4 | |||
33.5 | odd | 10 | 165.2.m.a.91.2 | ✓ | 8 | ||
33.20 | odd | 10 | 165.2.m.a.136.2 | yes | 8 | ||
33.32 | even | 2 | 1815.2.a.o.1.4 | 4 | |||
165.38 | even | 20 | 825.2.bx.h.124.2 | 16 | |||
165.53 | even | 20 | 825.2.bx.h.499.3 | 16 | |||
165.104 | odd | 10 | 825.2.n.k.751.1 | 8 | |||
165.119 | odd | 10 | 825.2.n.k.301.1 | 8 | |||
165.137 | even | 20 | 825.2.bx.h.124.3 | 16 | |||
165.152 | even | 20 | 825.2.bx.h.499.2 | 16 | |||
165.164 | even | 2 | 9075.2.a.dj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.91.2 | ✓ | 8 | 33.5 | odd | 10 | ||
165.2.m.a.136.2 | yes | 8 | 33.20 | odd | 10 | ||
495.2.n.d.91.1 | 8 | 11.5 | even | 5 | |||
495.2.n.d.136.1 | 8 | 11.9 | even | 5 | |||
825.2.n.k.301.1 | 8 | 165.119 | odd | 10 | |||
825.2.n.k.751.1 | 8 | 165.104 | odd | 10 | |||
825.2.bx.h.124.2 | 16 | 165.38 | even | 20 | |||
825.2.bx.h.124.3 | 16 | 165.137 | even | 20 | |||
825.2.bx.h.499.2 | 16 | 165.152 | even | 20 | |||
825.2.bx.h.499.3 | 16 | 165.53 | even | 20 | |||
1815.2.a.o.1.4 | 4 | 33.32 | even | 2 | |||
1815.2.a.x.1.1 | 4 | 3.2 | odd | 2 | |||
5445.2.a.be.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bv.1.1 | 4 | 11.10 | odd | 2 | |||
9075.2.a.cl.1.4 | 4 | 15.14 | odd | 2 | |||
9075.2.a.dj.1.1 | 4 | 165.164 | even | 2 |