Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.43045\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43045 | −1.71859 | −0.859295 | − | 0.511481i | \(-0.829097\pi\) | ||||
−0.859295 | + | 0.511481i | \(0.829097\pi\) | |||||||
\(3\) | 1.43421 | 0.828039 | 0.414020 | − | 0.910268i | \(-0.364124\pi\) | ||||
0.414020 | + | 0.910268i | \(0.364124\pi\) | |||||||
\(4\) | 3.90710 | 1.95355 | ||||||||
\(5\) | 1.25863 | 0.562877 | 0.281438 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281438 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(6\) | −3.48577 | −1.42306 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.63512 | −1.63876 | ||||||||
\(9\) | −0.943053 | −0.314351 | ||||||||
\(10\) | −3.05904 | −0.967354 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.60359 | 1.61762 | ||||||||
\(13\) | −3.17831 | −0.881504 | −0.440752 | − | 0.897629i | \(-0.645288\pi\) | ||||
−0.440752 | + | 0.897629i | \(0.645288\pi\) | |||||||
\(14\) | −2.43045 | −0.649566 | ||||||||
\(15\) | 1.80514 | 0.466084 | ||||||||
\(16\) | 3.45123 | 0.862807 | ||||||||
\(17\) | 5.92418 | 1.43682 | 0.718412 | − | 0.695617i | \(-0.244869\pi\) | ||||
0.718412 | + | 0.695617i | \(0.244869\pi\) | |||||||
\(18\) | 2.29204 | 0.540240 | ||||||||
\(19\) | 2.86222 | 0.656638 | 0.328319 | − | 0.944567i | \(-0.393518\pi\) | ||||
0.328319 | + | 0.944567i | \(0.393518\pi\) | |||||||
\(20\) | 4.91760 | 1.09961 | ||||||||
\(21\) | 1.43421 | 0.312969 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.76343 | 1.41027 | 0.705136 | − | 0.709072i | \(-0.250886\pi\) | ||||
0.705136 | + | 0.709072i | \(0.250886\pi\) | |||||||
\(24\) | −6.64771 | −1.35696 | ||||||||
\(25\) | −3.41585 | −0.683170 | ||||||||
\(26\) | 7.72473 | 1.51494 | ||||||||
\(27\) | −5.65515 | −1.08833 | ||||||||
\(28\) | 3.90710 | 0.738372 | ||||||||
\(29\) | 4.49549 | 0.834792 | 0.417396 | − | 0.908725i | \(-0.362943\pi\) | ||||
0.417396 | + | 0.908725i | \(0.362943\pi\) | |||||||
\(30\) | −4.38730 | −0.801008 | ||||||||
\(31\) | 9.72751 | 1.74711 | 0.873556 | − | 0.486723i | \(-0.161808\pi\) | ||||
0.873556 | + | 0.486723i | \(0.161808\pi\) | |||||||
\(32\) | 0.882184 | 0.155950 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.3984 | −2.46931 | ||||||||
\(35\) | 1.25863 | 0.212747 | ||||||||
\(36\) | −3.68460 | −0.614100 | ||||||||
\(37\) | −5.45495 | −0.896789 | −0.448394 | − | 0.893836i | \(-0.648004\pi\) | ||||
−0.448394 | + | 0.893836i | \(0.648004\pi\) | |||||||
\(38\) | −6.95648 | −1.12849 | ||||||||
\(39\) | −4.55835 | −0.729920 | ||||||||
\(40\) | −5.83390 | −0.922421 | ||||||||
\(41\) | −0.314484 | −0.0491142 | −0.0245571 | − | 0.999698i | \(-0.507818\pi\) | ||||
−0.0245571 | + | 0.999698i | \(0.507818\pi\) | |||||||
\(42\) | −3.48577 | −0.537866 | ||||||||
\(43\) | −0.132562 | −0.0202155 | −0.0101078 | − | 0.999949i | \(-0.503217\pi\) | ||||
−0.0101078 | + | 0.999949i | \(0.503217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.18696 | −0.176941 | ||||||||
\(46\) | −16.4382 | −2.42368 | ||||||||
\(47\) | 9.37505 | 1.36749 | 0.683746 | − | 0.729720i | \(-0.260350\pi\) | ||||
0.683746 | + | 0.729720i | \(0.260350\pi\) | |||||||
\(48\) | 4.94977 | 0.714438 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.30206 | 1.17409 | ||||||||
\(51\) | 8.49650 | 1.18975 | ||||||||
\(52\) | −12.4180 | −1.72206 | ||||||||
\(53\) | 4.35192 | 0.597783 | 0.298891 | − | 0.954287i | \(-0.403383\pi\) | ||||
0.298891 | + | 0.954287i | \(0.403383\pi\) | |||||||
\(54\) | 13.7446 | 1.87040 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.63512 | −0.619393 | ||||||||
\(57\) | 4.10501 | 0.543722 | ||||||||
\(58\) | −10.9261 | −1.43466 | ||||||||
\(59\) | −6.94685 | −0.904403 | −0.452202 | − | 0.891916i | \(-0.649361\pi\) | ||||
−0.452202 | + | 0.891916i | \(0.649361\pi\) | |||||||
\(60\) | 7.05285 | 0.910519 | ||||||||
\(61\) | −2.45215 | −0.313966 | −0.156983 | − | 0.987601i | \(-0.550177\pi\) | ||||
−0.156983 | + | 0.987601i | \(0.550177\pi\) | |||||||
\(62\) | −23.6423 | −3.00257 | ||||||||
\(63\) | −0.943053 | −0.118813 | ||||||||
\(64\) | −9.04656 | −1.13082 | ||||||||
\(65\) | −4.00032 | −0.496179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.41987 | −1.15082 | −0.575410 | − | 0.817865i | \(-0.695158\pi\) | ||||
−0.575410 | + | 0.817865i | \(0.695158\pi\) | |||||||
\(68\) | 23.1464 | 2.80691 | ||||||||
\(69\) | 9.70015 | 1.16776 | ||||||||
\(70\) | −3.05904 | −0.365626 | ||||||||
\(71\) | −0.116610 | −0.0138391 | −0.00691954 | − | 0.999976i | \(-0.502203\pi\) | ||||
−0.00691954 | + | 0.999976i | \(0.502203\pi\) | |||||||
\(72\) | 4.37116 | 0.515146 | ||||||||
\(73\) | 0.615032 | 0.0719840 | 0.0359920 | − | 0.999352i | \(-0.488541\pi\) | ||||
0.0359920 | + | 0.999352i | \(0.488541\pi\) | |||||||
\(74\) | 13.2580 | 1.54121 | ||||||||
\(75\) | −4.89903 | −0.565691 | ||||||||
\(76\) | 11.1830 | 1.28277 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.0789 | 1.25443 | ||||||||
\(79\) | 8.52928 | 0.959619 | 0.479810 | − | 0.877373i | \(-0.340706\pi\) | ||||
0.479810 | + | 0.877373i | \(0.340706\pi\) | |||||||
\(80\) | 4.34382 | 0.485654 | ||||||||
\(81\) | −5.28149 | −0.586833 | ||||||||
\(82\) | 0.764339 | 0.0844072 | ||||||||
\(83\) | 0.950532 | 0.104334 | 0.0521672 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521672 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(84\) | 5.60359 | 0.611401 | ||||||||
\(85\) | 7.45636 | 0.808756 | ||||||||
\(86\) | 0.322186 | 0.0347422 | ||||||||
\(87\) | 6.44746 | 0.691241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0552 | 1.06585 | 0.532923 | − | 0.846164i | \(-0.321094\pi\) | ||||
0.532923 | + | 0.846164i | \(0.321094\pi\) | |||||||
\(90\) | 2.88484 | 0.304089 | ||||||||
\(91\) | −3.17831 | −0.333177 | ||||||||
\(92\) | 26.4254 | 2.75504 | ||||||||
\(93\) | 13.9513 | 1.44668 | ||||||||
\(94\) | −22.7856 | −2.35016 | ||||||||
\(95\) | 3.60248 | 0.369606 | ||||||||
\(96\) | 1.26523 | 0.129132 | ||||||||
\(97\) | 17.5770 | 1.78467 | 0.892337 | − | 0.451369i | \(-0.149064\pi\) | ||||
0.892337 | + | 0.451369i | \(0.149064\pi\) | |||||||
\(98\) | −2.43045 | −0.245513 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3461 | −1.33461 | ||||||||
\(101\) | −12.4761 | −1.24142 | −0.620711 | − | 0.784039i | \(-0.713156\pi\) | ||||
−0.620711 | + | 0.784039i | \(0.713156\pi\) | |||||||
\(102\) | −20.6503 | −2.04469 | ||||||||
\(103\) | 8.21802 | 0.809746 | 0.404873 | − | 0.914373i | \(-0.367316\pi\) | ||||
0.404873 | + | 0.914373i | \(0.367316\pi\) | |||||||
\(104\) | 14.7318 | 1.44457 | ||||||||
\(105\) | 1.80514 | 0.176163 | ||||||||
\(106\) | −10.5771 | −1.02734 | ||||||||
\(107\) | 12.1885 | 1.17831 | 0.589154 | − | 0.808020i | \(-0.299461\pi\) | ||||
0.589154 | + | 0.808020i | \(0.299461\pi\) | |||||||
\(108\) | −22.0952 | −2.12612 | ||||||||
\(109\) | 0.886088 | 0.0848718 | 0.0424359 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424359 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.82353 | −0.742577 | ||||||||
\(112\) | 3.45123 | 0.326110 | ||||||||
\(113\) | 4.54502 | 0.427559 | 0.213780 | − | 0.976882i | \(-0.431423\pi\) | ||||
0.213780 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(114\) | −9.97703 | −0.934435 | ||||||||
\(115\) | 8.51266 | 0.793810 | ||||||||
\(116\) | 17.5643 | 1.63081 | ||||||||
\(117\) | 2.99731 | 0.277102 | ||||||||
\(118\) | 16.8840 | 1.55430 | ||||||||
\(119\) | 5.92418 | 0.543069 | ||||||||
\(120\) | −8.36702 | −0.763801 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.95984 | 0.539579 | ||||||||
\(123\) | −0.451035 | −0.0406685 | ||||||||
\(124\) | 38.0064 | 3.41307 | ||||||||
\(125\) | −10.5924 | −0.947417 | ||||||||
\(126\) | 2.29204 | 0.204192 | ||||||||
\(127\) | −8.02779 | −0.712351 | −0.356175 | − | 0.934419i | \(-0.615919\pi\) | ||||
−0.356175 | + | 0.934419i | \(0.615919\pi\) | |||||||
\(128\) | 20.2229 | 1.78747 | ||||||||
\(129\) | −0.190121 | −0.0167392 | ||||||||
\(130\) | 9.72259 | 0.852727 | ||||||||
\(131\) | 0.101461 | 0.00886466 | 0.00443233 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443233 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.86222 | 0.248186 | ||||||||
\(134\) | 22.8945 | 1.97779 | ||||||||
\(135\) | −7.11775 | −0.612598 | ||||||||
\(136\) | −27.4593 | −2.35461 | ||||||||
\(137\) | −4.56409 | −0.389937 | −0.194968 | − | 0.980810i | \(-0.562460\pi\) | ||||
−0.194968 | + | 0.980810i | \(0.562460\pi\) | |||||||
\(138\) | −23.5758 | −2.00690 | ||||||||
\(139\) | −3.82533 | −0.324460 | −0.162230 | − | 0.986753i | \(-0.551869\pi\) | ||||
−0.162230 | + | 0.986753i | \(0.551869\pi\) | |||||||
\(140\) | 4.91760 | 0.415613 | ||||||||
\(141\) | 13.4458 | 1.13234 | ||||||||
\(142\) | 0.283415 | 0.0237837 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.25469 | −0.271224 | ||||||||
\(145\) | 5.65817 | 0.469885 | ||||||||
\(146\) | −1.49480 | −0.123711 | ||||||||
\(147\) | 1.43421 | 0.118291 | ||||||||
\(148\) | −21.3130 | −1.75192 | ||||||||
\(149\) | −4.87223 | −0.399149 | −0.199574 | − | 0.979883i | \(-0.563956\pi\) | ||||
−0.199574 | + | 0.979883i | \(0.563956\pi\) | |||||||
\(150\) | 11.9069 | 0.972191 | ||||||||
\(151\) | −16.9739 | −1.38131 | −0.690657 | − | 0.723183i | \(-0.742678\pi\) | ||||
−0.690657 | + | 0.723183i | \(0.742678\pi\) | |||||||
\(152\) | −13.2667 | −1.07607 | ||||||||
\(153\) | −5.58681 | −0.451667 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2434 | 0.983410 | ||||||||
\(156\) | −17.8099 | −1.42594 | ||||||||
\(157\) | 2.24483 | 0.179157 | 0.0895785 | − | 0.995980i | \(-0.471448\pi\) | ||||
0.0895785 | + | 0.995980i | \(0.471448\pi\) | |||||||
\(158\) | −20.7300 | −1.64919 | ||||||||
\(159\) | 6.24156 | 0.494988 | ||||||||
\(160\) | 1.11034 | 0.0877804 | ||||||||
\(161\) | 6.76343 | 0.533033 | ||||||||
\(162\) | 12.8364 | 1.00852 | ||||||||
\(163\) | −15.8372 | −1.24047 | −0.620235 | − | 0.784416i | \(-0.712963\pi\) | ||||
−0.620235 | + | 0.784416i | \(0.712963\pi\) | |||||||
\(164\) | −1.22872 | −0.0959470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31022 | −0.179308 | ||||||||
\(167\) | 20.7416 | 1.60503 | 0.802515 | − | 0.596632i | \(-0.203495\pi\) | ||||
0.802515 | + | 0.596632i | \(0.203495\pi\) | |||||||
\(168\) | −6.64771 | −0.512882 | ||||||||
\(169\) | −2.89835 | −0.222950 | ||||||||
\(170\) | −18.1223 | −1.38992 | ||||||||
\(171\) | −2.69922 | −0.206415 | ||||||||
\(172\) | −0.517933 | −0.0394920 | ||||||||
\(173\) | −21.5554 | −1.63883 | −0.819414 | − | 0.573202i | \(-0.805701\pi\) | ||||
−0.819414 | + | 0.573202i | \(0.805701\pi\) | |||||||
\(174\) | −15.6703 | −1.18796 | ||||||||
\(175\) | −3.41585 | −0.258214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.96322 | −0.748881 | ||||||||
\(178\) | −24.4386 | −1.83175 | ||||||||
\(179\) | 4.78161 | 0.357394 | 0.178697 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178697 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(180\) | −4.63755 | −0.345663 | ||||||||
\(181\) | −7.85284 | −0.583697 | −0.291849 | − | 0.956465i | \(-0.594270\pi\) | ||||
−0.291849 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(182\) | 7.72473 | 0.572595 | ||||||||
\(183\) | −3.51689 | −0.259976 | ||||||||
\(184\) | −31.3493 | −2.31110 | ||||||||
\(185\) | −6.86578 | −0.504782 | ||||||||
\(186\) | −33.9079 | −2.48625 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 36.6293 | 2.67146 | ||||||||
\(189\) | −5.65515 | −0.411352 | ||||||||
\(190\) | −8.75565 | −0.635201 | ||||||||
\(191\) | −8.83029 | −0.638937 | −0.319469 | − | 0.947597i | \(-0.603504\pi\) | ||||
−0.319469 | + | 0.947597i | \(0.603504\pi\) | |||||||
\(192\) | −12.9746 | −0.936364 | ||||||||
\(193\) | 25.6023 | 1.84289 | 0.921446 | − | 0.388507i | \(-0.127009\pi\) | ||||
0.921446 | + | 0.388507i | \(0.127009\pi\) | |||||||
\(194\) | −42.7201 | −3.06712 | ||||||||
\(195\) | −5.73728 | −0.410855 | ||||||||
\(196\) | 3.90710 | 0.279079 | ||||||||
\(197\) | −11.1977 | −0.797802 | −0.398901 | − | 0.916994i | \(-0.630608\pi\) | ||||
−0.398901 | + | 0.916994i | \(0.630608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2503 | −0.868400 | −0.434200 | − | 0.900817i | \(-0.642969\pi\) | ||||
−0.434200 | + | 0.900817i | \(0.642969\pi\) | |||||||
\(200\) | 15.8328 | 1.11955 | ||||||||
\(201\) | −13.5100 | −0.952924 | ||||||||
\(202\) | 30.3227 | 2.13350 | ||||||||
\(203\) | 4.49549 | 0.315522 | ||||||||
\(204\) | 33.1967 | 2.32423 | ||||||||
\(205\) | −0.395820 | −0.0276453 | ||||||||
\(206\) | −19.9735 | −1.39162 | ||||||||
\(207\) | −6.37827 | −0.443320 | ||||||||
\(208\) | −10.9691 | −0.760568 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.38730 | −0.302752 | ||||||||
\(211\) | −14.2636 | −0.981946 | −0.490973 | − | 0.871175i | \(-0.663359\pi\) | ||||
−0.490973 | + | 0.871175i | \(0.663359\pi\) | |||||||
\(212\) | 17.0034 | 1.16780 | ||||||||
\(213\) | −0.167243 | −0.0114593 | ||||||||
\(214\) | −29.6236 | −2.02503 | ||||||||
\(215\) | −0.166847 | −0.0113788 | ||||||||
\(216\) | 26.2123 | 1.78352 | ||||||||
\(217\) | 9.72751 | 0.660347 | ||||||||
\(218\) | −2.15359 | −0.145860 | ||||||||
\(219\) | 0.882082 | 0.0596056 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.8289 | −1.26657 | ||||||||
\(222\) | 19.0147 | 1.27618 | ||||||||
\(223\) | −2.96400 | −0.198484 | −0.0992421 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992421 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(224\) | 0.882184 | 0.0589434 | ||||||||
\(225\) | 3.22132 | 0.214755 | ||||||||
\(226\) | −11.0465 | −0.734799 | ||||||||
\(227\) | 8.25605 | 0.547974 | 0.273987 | − | 0.961733i | \(-0.411658\pi\) | ||||
0.273987 | + | 0.961733i | \(0.411658\pi\) | |||||||
\(228\) | 16.0387 | 1.06219 | ||||||||
\(229\) | 13.1081 | 0.866208 | 0.433104 | − | 0.901344i | \(-0.357418\pi\) | ||||
0.433104 | + | 0.901344i | \(0.357418\pi\) | |||||||
\(230\) | −20.6896 | −1.36423 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8371 | −1.36802 | ||||||||
\(233\) | −12.8277 | −0.840369 | −0.420185 | − | 0.907439i | \(-0.638035\pi\) | ||||
−0.420185 | + | 0.907439i | \(0.638035\pi\) | |||||||
\(234\) | −7.28483 | −0.476224 | ||||||||
\(235\) | 11.7997 | 0.769730 | ||||||||
\(236\) | −27.1420 | −1.76680 | ||||||||
\(237\) | 12.2328 | 0.794603 | ||||||||
\(238\) | −14.3984 | −0.933312 | ||||||||
\(239\) | −4.98109 | −0.322200 | −0.161100 | − | 0.986938i | \(-0.551504\pi\) | ||||
−0.161100 | + | 0.986938i | \(0.551504\pi\) | |||||||
\(240\) | 6.22994 | 0.402141 | ||||||||
\(241\) | −2.62686 | −0.169211 | −0.0846053 | − | 0.996415i | \(-0.526963\pi\) | ||||
−0.0846053 | + | 0.996415i | \(0.526963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.39070 | 0.602414 | ||||||||
\(244\) | −9.58081 | −0.613349 | ||||||||
\(245\) | 1.25863 | 0.0804110 | ||||||||
\(246\) | 1.09622 | 0.0698924 | ||||||||
\(247\) | −9.09701 | −0.578829 | ||||||||
\(248\) | −45.0881 | −2.86310 | ||||||||
\(249\) | 1.36326 | 0.0863930 | ||||||||
\(250\) | 25.7444 | 1.62822 | ||||||||
\(251\) | −26.2229 | −1.65518 | −0.827588 | − | 0.561337i | \(-0.810287\pi\) | ||||
−0.827588 | + | 0.561337i | \(0.810287\pi\) | |||||||
\(252\) | −3.68460 | −0.232108 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.5112 | 1.22424 | ||||||||
\(255\) | 10.6940 | 0.669681 | ||||||||
\(256\) | −31.0576 | −1.94110 | ||||||||
\(257\) | 29.9518 | 1.86834 | 0.934170 | − | 0.356827i | \(-0.116141\pi\) | ||||
0.934170 | + | 0.356827i | \(0.116141\pi\) | |||||||
\(258\) | 0.462081 | 0.0287679 | ||||||||
\(259\) | −5.45495 | −0.338954 | ||||||||
\(260\) | −15.6296 | −0.969309 | ||||||||
\(261\) | −4.23949 | −0.262418 | ||||||||
\(262\) | −0.246595 | −0.0152347 | ||||||||
\(263\) | 3.33709 | 0.205774 | 0.102887 | − | 0.994693i | \(-0.467192\pi\) | ||||
0.102887 | + | 0.994693i | \(0.467192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.47747 | 0.336478 | ||||||||
\(266\) | −6.95648 | −0.426529 | ||||||||
\(267\) | 14.4212 | 0.882562 | ||||||||
\(268\) | −36.8044 | −2.24818 | ||||||||
\(269\) | −1.73581 | −0.105834 | −0.0529172 | − | 0.998599i | \(-0.516852\pi\) | ||||
−0.0529172 | + | 0.998599i | \(0.516852\pi\) | |||||||
\(270\) | 17.2994 | 1.05280 | ||||||||
\(271\) | −2.47596 | −0.150404 | −0.0752019 | − | 0.997168i | \(-0.523960\pi\) | ||||
−0.0752019 | + | 0.997168i | \(0.523960\pi\) | |||||||
\(272\) | 20.4457 | 1.23970 | ||||||||
\(273\) | −4.55835 | −0.275884 | ||||||||
\(274\) | 11.0928 | 0.670141 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 37.8995 | 2.28128 | ||||||||
\(277\) | 5.15571 | 0.309776 | 0.154888 | − | 0.987932i | \(-0.450498\pi\) | ||||
0.154888 | + | 0.987932i | \(0.450498\pi\) | |||||||
\(278\) | 9.29728 | 0.557614 | ||||||||
\(279\) | −9.17356 | −0.549206 | ||||||||
\(280\) | −5.83390 | −0.348642 | ||||||||
\(281\) | −22.5705 | −1.34644 | −0.673222 | − | 0.739441i | \(-0.735090\pi\) | ||||
−0.673222 | + | 0.739441i | \(0.735090\pi\) | |||||||
\(282\) | −32.6793 | −1.94602 | ||||||||
\(283\) | −8.48757 | −0.504534 | −0.252267 | − | 0.967658i | \(-0.581176\pi\) | ||||
−0.252267 | + | 0.967658i | \(0.581176\pi\) | |||||||
\(284\) | −0.455608 | −0.0270353 | ||||||||
\(285\) | 5.16669 | 0.306049 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.314484 | −0.0185634 | ||||||||
\(288\) | −0.831946 | −0.0490229 | ||||||||
\(289\) | 18.0959 | 1.06447 | ||||||||
\(290\) | −13.7519 | −0.807540 | ||||||||
\(291\) | 25.2090 | 1.47778 | ||||||||
\(292\) | 2.40299 | 0.140624 | ||||||||
\(293\) | 24.6261 | 1.43867 | 0.719336 | − | 0.694662i | \(-0.244446\pi\) | ||||
0.719336 | + | 0.694662i | \(0.244446\pi\) | |||||||
\(294\) | −3.48577 | −0.203294 | ||||||||
\(295\) | −8.74353 | −0.509068 | ||||||||
\(296\) | 25.2843 | 1.46962 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.8417 | 0.685973 | ||||||||
\(299\) | −21.4963 | −1.24316 | ||||||||
\(300\) | −19.1410 | −1.10511 | ||||||||
\(301\) | −0.132562 | −0.00764075 | ||||||||
\(302\) | 41.2542 | 2.37391 | ||||||||
\(303\) | −17.8934 | −1.02795 | ||||||||
\(304\) | 9.87817 | 0.566552 | ||||||||
\(305\) | −3.08636 | −0.176724 | ||||||||
\(306\) | 13.5785 | 0.776230 | ||||||||
\(307\) | 4.59391 | 0.262188 | 0.131094 | − | 0.991370i | \(-0.458151\pi\) | ||||
0.131094 | + | 0.991370i | \(0.458151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7863 | 0.670502 | ||||||||
\(310\) | −29.7569 | −1.69008 | ||||||||
\(311\) | −2.21073 | −0.125359 | −0.0626796 | − | 0.998034i | \(-0.519965\pi\) | ||||
−0.0626796 | + | 0.998034i | \(0.519965\pi\) | |||||||
\(312\) | 21.1285 | 1.19616 | ||||||||
\(313\) | −9.69928 | −0.548236 | −0.274118 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274118 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(314\) | −5.45595 | −0.307897 | ||||||||
\(315\) | −1.18696 | −0.0668774 | ||||||||
\(316\) | 33.3248 | 1.87466 | ||||||||
\(317\) | 6.45539 | 0.362571 | 0.181286 | − | 0.983431i | \(-0.441974\pi\) | ||||
0.181286 | + | 0.983431i | \(0.441974\pi\) | |||||||
\(318\) | −15.1698 | −0.850680 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.3863 | −0.636513 | ||||||||
\(321\) | 17.4809 | 0.975686 | ||||||||
\(322\) | −16.4382 | −0.916065 | ||||||||
\(323\) | 16.9563 | 0.943474 | ||||||||
\(324\) | −20.6353 | −1.14641 | ||||||||
\(325\) | 10.8566 | 0.602217 | ||||||||
\(326\) | 38.4917 | 2.13186 | ||||||||
\(327\) | 1.27083 | 0.0702772 | ||||||||
\(328\) | 1.45767 | 0.0804864 | ||||||||
\(329\) | 9.37505 | 0.516863 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.62076 | 0.199015 | 0.0995075 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995075 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(332\) | 3.71382 | 0.203823 | ||||||||
\(333\) | 5.14431 | 0.281906 | ||||||||
\(334\) | −50.4114 | −2.75839 | ||||||||
\(335\) | −11.8561 | −0.647770 | ||||||||
\(336\) | 4.94977 | 0.270032 | ||||||||
\(337\) | −6.40510 | −0.348908 | −0.174454 | − | 0.984665i | \(-0.555816\pi\) | ||||
−0.174454 | + | 0.984665i | \(0.555816\pi\) | |||||||
\(338\) | 7.04430 | 0.383159 | ||||||||
\(339\) | 6.51849 | 0.354036 | ||||||||
\(340\) | 29.1327 | 1.57994 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.56033 | 0.354742 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.614440 | 0.0331284 | ||||||||
\(345\) | 12.2089 | 0.657306 | ||||||||
\(346\) | 52.3894 | 2.81647 | ||||||||
\(347\) | −17.4600 | −0.937302 | −0.468651 | − | 0.883383i | \(-0.655260\pi\) | ||||
−0.468651 | + | 0.883383i | \(0.655260\pi\) | |||||||
\(348\) | 25.1909 | 1.35037 | ||||||||
\(349\) | −21.6249 | −1.15755 | −0.578777 | − | 0.815486i | \(-0.696470\pi\) | ||||
−0.578777 | + | 0.815486i | \(0.696470\pi\) | |||||||
\(350\) | 8.30206 | 0.443764 | ||||||||
\(351\) | 17.9738 | 0.959371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40150 | 0.234268 | 0.117134 | − | 0.993116i | \(-0.462629\pi\) | ||||
0.117134 | + | 0.993116i | \(0.462629\pi\) | |||||||
\(354\) | 24.2151 | 1.28702 | ||||||||
\(355\) | −0.146769 | −0.00778970 | ||||||||
\(356\) | 39.2865 | 2.08218 | ||||||||
\(357\) | 8.49650 | 0.449682 | ||||||||
\(358\) | −11.6215 | −0.614214 | ||||||||
\(359\) | −10.6817 | −0.563760 | −0.281880 | − | 0.959450i | \(-0.590958\pi\) | ||||
−0.281880 | + | 0.959450i | \(0.590958\pi\) | |||||||
\(360\) | 5.50167 | 0.289964 | ||||||||
\(361\) | −10.8077 | −0.568827 | ||||||||
\(362\) | 19.0860 | 1.00314 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.4180 | −0.650879 | ||||||||
\(365\) | 0.774098 | 0.0405181 | ||||||||
\(366\) | 8.54765 | 0.446793 | ||||||||
\(367\) | 10.2167 | 0.533309 | 0.266655 | − | 0.963792i | \(-0.414082\pi\) | ||||
0.266655 | + | 0.963792i | \(0.414082\pi\) | |||||||
\(368\) | 23.3421 | 1.21679 | ||||||||
\(369\) | 0.296575 | 0.0154391 | ||||||||
\(370\) | 16.6869 | 0.867513 | ||||||||
\(371\) | 4.35192 | 0.225941 | ||||||||
\(372\) | 54.5090 | 2.82616 | ||||||||
\(373\) | −27.8851 | −1.44383 | −0.721917 | − | 0.691980i | \(-0.756739\pi\) | ||||
−0.721917 | + | 0.691980i | \(0.756739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.1918 | −0.784499 | ||||||||
\(376\) | −43.4544 | −2.24099 | ||||||||
\(377\) | −14.2881 | −0.735873 | ||||||||
\(378\) | 13.7446 | 0.706945 | ||||||||
\(379\) | 1.14803 | 0.0589703 | 0.0294852 | − | 0.999565i | \(-0.490613\pi\) | ||||
0.0294852 | + | 0.999565i | \(0.490613\pi\) | |||||||
\(380\) | 14.0752 | 0.722044 | ||||||||
\(381\) | −11.5135 | −0.589855 | ||||||||
\(382\) | 21.4616 | 1.09807 | ||||||||
\(383\) | −19.9516 | −1.01948 | −0.509740 | − | 0.860328i | \(-0.670258\pi\) | ||||
−0.509740 | + | 0.860328i | \(0.670258\pi\) | |||||||
\(384\) | 29.0038 | 1.48009 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −62.2251 | −3.16717 | ||||||||
\(387\) | 0.125013 | 0.00635476 | ||||||||
\(388\) | 68.6751 | 3.48645 | ||||||||
\(389\) | 2.60000 | 0.131825 | 0.0659127 | − | 0.997825i | \(-0.479004\pi\) | ||||
0.0659127 | + | 0.997825i | \(0.479004\pi\) | |||||||
\(390\) | 13.9442 | 0.706092 | ||||||||
\(391\) | 40.0678 | 2.02631 | ||||||||
\(392\) | −4.63512 | −0.234109 | ||||||||
\(393\) | 0.145516 | 0.00734029 | ||||||||
\(394\) | 27.2154 | 1.37109 | ||||||||
\(395\) | 10.7352 | 0.540148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.77237 | 0.440272 | 0.220136 | − | 0.975469i | \(-0.429350\pi\) | ||||
0.220136 | + | 0.975469i | \(0.429350\pi\) | |||||||
\(398\) | 29.7737 | 1.49242 | ||||||||
\(399\) | 4.10501 | 0.205508 | ||||||||
\(400\) | −11.7889 | −0.589444 | ||||||||
\(401\) | 28.3535 | 1.41591 | 0.707953 | − | 0.706260i | \(-0.249619\pi\) | ||||
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(402\) | 32.8355 | 1.63769 | ||||||||
\(403\) | −30.9170 | −1.54009 | ||||||||
\(404\) | −48.7455 | −2.42518 | ||||||||
\(405\) | −6.64745 | −0.330315 | ||||||||
\(406\) | −10.9261 | −0.542252 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −39.3822 | −1.94971 | ||||||||
\(409\) | 19.9055 | 0.984264 | 0.492132 | − | 0.870521i | \(-0.336218\pi\) | ||||
0.492132 | + | 0.870521i | \(0.336218\pi\) | |||||||
\(410\) | 0.962021 | 0.0475108 | ||||||||
\(411\) | −6.54585 | −0.322883 | ||||||||
\(412\) | 32.1086 | 1.58188 | ||||||||
\(413\) | −6.94685 | −0.341832 | ||||||||
\(414\) | 15.5021 | 0.761886 | ||||||||
\(415\) | 1.19637 | 0.0587275 | ||||||||
\(416\) | −2.80385 | −0.137470 | ||||||||
\(417\) | −5.48631 | −0.268666 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.8957 | −1.50935 | −0.754676 | − | 0.656097i | \(-0.772206\pi\) | ||||
−0.754676 | + | 0.656097i | \(0.772206\pi\) | |||||||
\(420\) | 7.05285 | 0.344144 | ||||||||
\(421\) | −24.1931 | −1.17910 | −0.589551 | − | 0.807732i | \(-0.700695\pi\) | ||||
−0.589551 | + | 0.807732i | \(0.700695\pi\) | |||||||
\(422\) | 34.6670 | 1.68756 | ||||||||
\(423\) | −8.84117 | −0.429872 | ||||||||
\(424\) | −20.1717 | −0.979623 | ||||||||
\(425\) | −20.2361 | −0.981595 | ||||||||
\(426\) | 0.406476 | 0.0196938 | ||||||||
\(427\) | −2.45215 | −0.118668 | ||||||||
\(428\) | 47.6218 | 2.30188 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.405513 | 0.0195556 | ||||||||
\(431\) | 19.4001 | 0.934468 | 0.467234 | − | 0.884134i | \(-0.345251\pi\) | ||||
0.467234 | + | 0.884134i | \(0.345251\pi\) | |||||||
\(432\) | −19.5172 | −0.939022 | ||||||||
\(433\) | −21.3877 | −1.02783 | −0.513914 | − | 0.857842i | \(-0.671805\pi\) | ||||
−0.513914 | + | 0.857842i | \(0.671805\pi\) | |||||||
\(434\) | −23.6423 | −1.13486 | ||||||||
\(435\) | 8.11498 | 0.389083 | ||||||||
\(436\) | 3.46203 | 0.165801 | ||||||||
\(437\) | 19.3584 | 0.926038 | ||||||||
\(438\) | −2.14386 | −0.102438 | ||||||||
\(439\) | −31.7315 | −1.51446 | −0.757232 | − | 0.653146i | \(-0.773449\pi\) | ||||
−0.757232 | + | 0.653146i | \(0.773449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.943053 | −0.0449073 | ||||||||
\(442\) | 45.7627 | 2.17671 | ||||||||
\(443\) | −1.66610 | −0.0791590 | −0.0395795 | − | 0.999216i | \(-0.512602\pi\) | ||||
−0.0395795 | + | 0.999216i | \(0.512602\pi\) | |||||||
\(444\) | −30.5673 | −1.45066 | ||||||||
\(445\) | 12.6557 | 0.599940 | ||||||||
\(446\) | 7.20386 | 0.341113 | ||||||||
\(447\) | −6.98779 | −0.330511 | ||||||||
\(448\) | −9.04656 | −0.427410 | ||||||||
\(449\) | −17.1858 | −0.811047 | −0.405524 | − | 0.914085i | \(-0.632911\pi\) | ||||
−0.405524 | + | 0.914085i | \(0.632911\pi\) | |||||||
\(450\) | −7.82927 | −0.369076 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 17.7578 | 0.835258 | ||||||||
\(453\) | −24.3440 | −1.14378 | ||||||||
\(454\) | −20.0659 | −0.941742 | ||||||||
\(455\) | −4.00032 | −0.187538 | ||||||||
\(456\) | −19.0272 | −0.891030 | ||||||||
\(457\) | 10.2206 | 0.478101 | 0.239051 | − | 0.971007i | \(-0.423164\pi\) | ||||
0.239051 | + | 0.971007i | \(0.423164\pi\) | |||||||
\(458\) | −31.8586 | −1.48866 | ||||||||
\(459\) | −33.5021 | −1.56375 | ||||||||
\(460\) | 33.2598 | 1.55075 | ||||||||
\(461\) | −22.1160 | −1.03004 | −0.515022 | − | 0.857177i | \(-0.672216\pi\) | ||||
−0.515022 | + | 0.857177i | \(0.672216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3717 | −1.41149 | −0.705747 | − | 0.708464i | \(-0.749389\pi\) | ||||
−0.705747 | + | 0.708464i | \(0.749389\pi\) | |||||||
\(464\) | 15.5150 | 0.720265 | ||||||||
\(465\) | 17.5595 | 0.814302 | ||||||||
\(466\) | 31.1771 | 1.44425 | ||||||||
\(467\) | 25.1909 | 1.16570 | 0.582848 | − | 0.812581i | \(-0.301938\pi\) | ||||
0.582848 | + | 0.812581i | \(0.301938\pi\) | |||||||
\(468\) | 11.7108 | 0.541332 | ||||||||
\(469\) | −9.41987 | −0.434969 | ||||||||
\(470\) | −28.6787 | −1.32285 | ||||||||
\(471\) | 3.21955 | 0.148349 | ||||||||
\(472\) | 32.1995 | 1.48210 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −29.7311 | −1.36560 | ||||||||
\(475\) | −9.77690 | −0.448595 | ||||||||
\(476\) | 23.1464 | 1.06091 | ||||||||
\(477\) | −4.10409 | −0.187913 | ||||||||
\(478\) | 12.1063 | 0.553729 | ||||||||
\(479\) | −21.2040 | −0.968835 | −0.484417 | − | 0.874837i | \(-0.660968\pi\) | ||||
−0.484417 | + | 0.874837i | \(0.660968\pi\) | |||||||
\(480\) | 1.59246 | 0.0726856 | ||||||||
\(481\) | 17.3375 | 0.790523 | ||||||||
\(482\) | 6.38445 | 0.290804 | ||||||||
\(483\) | 9.70015 | 0.441372 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.1230 | 1.00455 | ||||||||
\(486\) | −22.8237 | −1.03530 | ||||||||
\(487\) | −16.8198 | −0.762176 | −0.381088 | − | 0.924539i | \(-0.624451\pi\) | ||||
−0.381088 | + | 0.924539i | \(0.624451\pi\) | |||||||
\(488\) | 11.3660 | 0.514515 | ||||||||
\(489\) | −22.7139 | −1.02716 | ||||||||
\(490\) | −3.05904 | −0.138193 | ||||||||
\(491\) | 4.83804 | 0.218338 | 0.109169 | − | 0.994023i | \(-0.465181\pi\) | ||||
0.109169 | + | 0.994023i | \(0.465181\pi\) | |||||||
\(492\) | −1.76224 | −0.0794479 | ||||||||
\(493\) | 26.6321 | 1.19945 | ||||||||
\(494\) | 22.1099 | 0.994770 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.5719 | 1.50742 | ||||||||
\(497\) | −0.116610 | −0.00523068 | ||||||||
\(498\) | −3.31334 | −0.148474 | ||||||||
\(499\) | 30.5836 | 1.36911 | 0.684554 | − | 0.728962i | \(-0.259997\pi\) | ||||
0.684554 | + | 0.728962i | \(0.259997\pi\) | |||||||
\(500\) | −41.3858 | −1.85083 | ||||||||
\(501\) | 29.7477 | 1.32903 | ||||||||
\(502\) | 63.7335 | 2.84457 | ||||||||
\(503\) | −28.2407 | −1.25919 | −0.629594 | − | 0.776924i | \(-0.716779\pi\) | ||||
−0.629594 | + | 0.776924i | \(0.716779\pi\) | |||||||
\(504\) | 4.37116 | 0.194707 | ||||||||
\(505\) | −15.7029 | −0.698768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.15683 | −0.184611 | ||||||||
\(508\) | −31.3654 | −1.39161 | ||||||||
\(509\) | −4.20065 | −0.186190 | −0.0930952 | − | 0.995657i | \(-0.529676\pi\) | ||||
−0.0930952 | + | 0.995657i | \(0.529676\pi\) | |||||||
\(510\) | −25.9912 | −1.15091 | ||||||||
\(511\) | 0.615032 | 0.0272074 | ||||||||
\(512\) | 35.0383 | 1.54849 | ||||||||
\(513\) | −16.1863 | −0.714641 | ||||||||
\(514\) | −72.7964 | −3.21091 | ||||||||
\(515\) | 10.3435 | 0.455787 | ||||||||
\(516\) | −0.742823 | −0.0327009 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.2580 | 0.582523 | ||||||||
\(519\) | −30.9149 | −1.35701 | ||||||||
\(520\) | 18.5419 | 0.813118 | ||||||||
\(521\) | −20.6470 | −0.904560 | −0.452280 | − | 0.891876i | \(-0.649389\pi\) | ||||
−0.452280 | + | 0.891876i | \(0.649389\pi\) | |||||||
\(522\) | 10.3039 | 0.450988 | ||||||||
\(523\) | −22.6341 | −0.989719 | −0.494859 | − | 0.868973i | \(-0.664780\pi\) | ||||
−0.494859 | + | 0.868973i | \(0.664780\pi\) | |||||||
\(524\) | 0.396417 | 0.0173176 | ||||||||
\(525\) | −4.89903 | −0.213811 | ||||||||
\(526\) | −8.11063 | −0.353640 | ||||||||
\(527\) | 57.6275 | 2.51030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7440 | 0.988869 | ||||||||
\(530\) | −13.3127 | −0.578268 | ||||||||
\(531\) | 6.55125 | 0.284300 | ||||||||
\(532\) | 11.1830 | 0.484843 | ||||||||
\(533\) | 0.999529 | 0.0432944 | ||||||||
\(534\) | −35.0500 | −1.51676 | ||||||||
\(535\) | 15.3409 | 0.663243 | ||||||||
\(536\) | 43.6622 | 1.88592 | ||||||||
\(537\) | 6.85781 | 0.295936 | ||||||||
\(538\) | 4.21881 | 0.181886 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.8098 | −1.19674 | ||||||||
\(541\) | 42.7163 | 1.83652 | 0.918258 | − | 0.395982i | \(-0.129596\pi\) | ||||
0.918258 | + | 0.395982i | \(0.129596\pi\) | |||||||
\(542\) | 6.01770 | 0.258482 | ||||||||
\(543\) | −11.2626 | −0.483324 | ||||||||
\(544\) | 5.22622 | 0.224072 | ||||||||
\(545\) | 1.11526 | 0.0477724 | ||||||||
\(546\) | 11.0789 | 0.474131 | ||||||||
\(547\) | 44.4827 | 1.90194 | 0.950972 | − | 0.309278i | \(-0.100087\pi\) | ||||
0.950972 | + | 0.309278i | \(0.100087\pi\) | |||||||
\(548\) | −17.8324 | −0.761761 | ||||||||
\(549\) | 2.31251 | 0.0986955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.8671 | 0.548156 | ||||||||
\(552\) | −44.9613 | −1.91368 | ||||||||
\(553\) | 8.52928 | 0.362702 | ||||||||
\(554\) | −12.5307 | −0.532379 | ||||||||
\(555\) | −9.84694 | −0.417979 | ||||||||
\(556\) | −14.9459 | −0.633849 | ||||||||
\(557\) | −24.9911 | −1.05891 | −0.529454 | − | 0.848339i | \(-0.677603\pi\) | ||||
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(558\) | 22.2959 | 0.943860 | ||||||||
\(559\) | 0.421323 | 0.0178201 | ||||||||
\(560\) | 4.34382 | 0.183560 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 54.8565 | 2.31398 | ||||||||
\(563\) | 9.01005 | 0.379729 | 0.189864 | − | 0.981810i | \(-0.439195\pi\) | ||||
0.189864 | + | 0.981810i | \(0.439195\pi\) | |||||||
\(564\) | 52.5339 | 2.21208 | ||||||||
\(565\) | 5.72050 | 0.240663 | ||||||||
\(566\) | 20.6286 | 0.867086 | ||||||||
\(567\) | −5.28149 | −0.221802 | ||||||||
\(568\) | 0.540502 | 0.0226789 | ||||||||
\(569\) | 29.1738 | 1.22303 | 0.611516 | − | 0.791232i | \(-0.290560\pi\) | ||||
0.611516 | + | 0.791232i | \(0.290560\pi\) | |||||||
\(570\) | −12.5574 | −0.525972 | ||||||||
\(571\) | 1.78994 | 0.0749067 | 0.0374533 | − | 0.999298i | \(-0.488075\pi\) | ||||
0.0374533 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6645 | −0.529065 | ||||||||
\(574\) | 0.764339 | 0.0319029 | ||||||||
\(575\) | −23.1028 | −0.963455 | ||||||||
\(576\) | 8.53138 | 0.355474 | ||||||||
\(577\) | −21.5850 | −0.898594 | −0.449297 | − | 0.893382i | \(-0.648325\pi\) | ||||
−0.449297 | + | 0.893382i | \(0.648325\pi\) | |||||||
\(578\) | −43.9813 | −1.82938 | ||||||||
\(579\) | 36.7189 | 1.52599 | ||||||||
\(580\) | 22.1070 | 0.917944 | ||||||||
\(581\) | 0.950532 | 0.0394347 | ||||||||
\(582\) | −61.2694 | −2.53970 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.85074 | −0.117965 | ||||||||
\(585\) | 3.77251 | 0.155974 | ||||||||
\(586\) | −59.8526 | −2.47249 | ||||||||
\(587\) | 5.52355 | 0.227981 | 0.113991 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113991 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(588\) | 5.60359 | 0.231088 | ||||||||
\(589\) | 27.8423 | 1.14722 | ||||||||
\(590\) | 21.2507 | 0.874879 | ||||||||
\(591\) | −16.0598 | −0.660611 | ||||||||
\(592\) | −18.8263 | −0.773756 | ||||||||
\(593\) | −40.7867 | −1.67491 | −0.837454 | − | 0.546508i | \(-0.815957\pi\) | ||||
−0.837454 | + | 0.546508i | \(0.815957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.45636 | 0.305681 | ||||||||
\(596\) | −19.0363 | −0.779757 | ||||||||
\(597\) | −17.5694 | −0.719069 | ||||||||
\(598\) | 52.2457 | 2.13648 | ||||||||
\(599\) | −26.5149 | −1.08337 | −0.541685 | − | 0.840582i | \(-0.682213\pi\) | ||||
−0.541685 | + | 0.840582i | \(0.682213\pi\) | |||||||
\(600\) | 22.7076 | 0.927033 | ||||||||
\(601\) | −37.7699 | −1.54067 | −0.770333 | − | 0.637641i | \(-0.779910\pi\) | ||||
−0.770333 | + | 0.637641i | \(0.779910\pi\) | |||||||
\(602\) | 0.322186 | 0.0131313 | ||||||||
\(603\) | 8.88343 | 0.361761 | ||||||||
\(604\) | −66.3186 | −2.69847 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 43.4890 | 1.76662 | ||||||||
\(607\) | −27.7244 | −1.12530 | −0.562649 | − | 0.826696i | \(-0.690218\pi\) | ||||
−0.562649 | + | 0.826696i | \(0.690218\pi\) | |||||||
\(608\) | 2.52500 | 0.102402 | ||||||||
\(609\) | 6.44746 | 0.261264 | ||||||||
\(610\) | 7.50125 | 0.303717 | ||||||||
\(611\) | −29.7968 | −1.20545 | ||||||||
\(612\) | −21.8282 | −0.882354 | ||||||||
\(613\) | 36.2264 | 1.46317 | 0.731586 | − | 0.681749i | \(-0.238780\pi\) | ||||
0.731586 | + | 0.681749i | \(0.238780\pi\) | |||||||
\(614\) | −11.1653 | −0.450594 | ||||||||
\(615\) | −0.567687 | −0.0228914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1920 | 1.65833 | 0.829163 | − | 0.559007i | \(-0.188817\pi\) | ||||
0.829163 | + | 0.559007i | \(0.188817\pi\) | |||||||
\(618\) | −28.6461 | −1.15232 | ||||||||
\(619\) | −35.7395 | −1.43649 | −0.718247 | − | 0.695789i | \(-0.755055\pi\) | ||||
−0.718247 | + | 0.695789i | \(0.755055\pi\) | |||||||
\(620\) | 47.8360 | 1.92114 | ||||||||
\(621\) | −38.2482 | −1.53485 | ||||||||
\(622\) | 5.37308 | 0.215441 | ||||||||
\(623\) | 10.0552 | 0.402852 | ||||||||
\(624\) | −15.7319 | −0.629780 | ||||||||
\(625\) | 3.74725 | 0.149890 | ||||||||
\(626\) | 23.5736 | 0.942192 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.77077 | 0.349992 | ||||||||
\(629\) | −32.3161 | −1.28853 | ||||||||
\(630\) | 2.88484 | 0.114935 | ||||||||
\(631\) | 2.76508 | 0.110076 | 0.0550380 | − | 0.998484i | \(-0.482472\pi\) | ||||
0.0550380 | + | 0.998484i | \(0.482472\pi\) | |||||||
\(632\) | −39.5342 | −1.57259 | ||||||||
\(633\) | −20.4569 | −0.813090 | ||||||||
\(634\) | −15.6895 | −0.623111 | ||||||||
\(635\) | −10.1040 | −0.400966 | ||||||||
\(636\) | 24.3864 | 0.966983 | ||||||||
\(637\) | −3.17831 | −0.125929 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.109970 | 0.00435033 | ||||||||
\(640\) | 25.4531 | 1.00612 | ||||||||
\(641\) | 38.4864 | 1.52012 | 0.760061 | − | 0.649851i | \(-0.225169\pi\) | ||||
0.760061 | + | 0.649851i | \(0.225169\pi\) | |||||||
\(642\) | −42.4864 | −1.67680 | ||||||||
\(643\) | −26.3781 | −1.04025 | −0.520126 | − | 0.854089i | \(-0.674115\pi\) | ||||
−0.520126 | + | 0.854089i | \(0.674115\pi\) | |||||||
\(644\) | 26.4254 | 1.04131 | ||||||||
\(645\) | −0.239293 | −0.00942213 | ||||||||
\(646\) | −41.2115 | −1.62144 | ||||||||
\(647\) | −27.3211 | −1.07410 | −0.537051 | − | 0.843549i | \(-0.680462\pi\) | ||||
−0.537051 | + | 0.843549i | \(0.680462\pi\) | |||||||
\(648\) | 24.4803 | 0.961678 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −26.3865 | −1.03496 | ||||||||
\(651\) | 13.9513 | 0.546793 | ||||||||
\(652\) | −61.8777 | −2.42332 | ||||||||
\(653\) | −8.46165 | −0.331130 | −0.165565 | − | 0.986199i | \(-0.552945\pi\) | ||||
−0.165565 | + | 0.986199i | \(0.552945\pi\) | |||||||
\(654\) | −3.08870 | −0.120778 | ||||||||
\(655\) | 0.127702 | 0.00498971 | ||||||||
\(656\) | −1.08536 | −0.0423761 | ||||||||
\(657\) | −0.580007 | −0.0226282 | ||||||||
\(658\) | −22.7856 | −0.888276 | ||||||||
\(659\) | −5.29247 | −0.206165 | −0.103083 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103083 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.2700 | −0.749517 | −0.374759 | − | 0.927122i | \(-0.622274\pi\) | ||||
−0.374759 | + | 0.927122i | \(0.622274\pi\) | |||||||
\(662\) | −8.80008 | −0.342025 | ||||||||
\(663\) | −27.0045 | −1.04877 | ||||||||
\(664\) | −4.40583 | −0.170979 | ||||||||
\(665\) | 3.60248 | 0.139698 | ||||||||
\(666\) | −12.5030 | −0.484481 | ||||||||
\(667\) | 30.4050 | 1.17728 | ||||||||
\(668\) | 81.0393 | 3.13551 | ||||||||
\(669\) | −4.25099 | −0.164353 | ||||||||
\(670\) | 28.8158 | 1.11325 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.26523 | 0.0488074 | ||||||||
\(673\) | −18.9922 | −0.732096 | −0.366048 | − | 0.930596i | \(-0.619289\pi\) | ||||
−0.366048 | + | 0.930596i | \(0.619289\pi\) | |||||||
\(674\) | 15.5673 | 0.599629 | ||||||||
\(675\) | 19.3171 | 0.743517 | ||||||||
\(676\) | −11.3241 | −0.435544 | ||||||||
\(677\) | 32.4219 | 1.24607 | 0.623037 | − | 0.782192i | \(-0.285899\pi\) | ||||
0.623037 | + | 0.782192i | \(0.285899\pi\) | |||||||
\(678\) | −15.8429 | −0.608442 | ||||||||
\(679\) | 17.5770 | 0.674544 | ||||||||
\(680\) | −34.5611 | −1.32536 | ||||||||
\(681\) | 11.8409 | 0.453744 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1260 | 0.578779 | 0.289389 | − | 0.957211i | \(-0.406548\pi\) | ||||
0.289389 | + | 0.957211i | \(0.406548\pi\) | |||||||
\(684\) | −10.5461 | −0.403241 | ||||||||
\(685\) | −5.74451 | −0.219486 | ||||||||
\(686\) | −2.43045 | −0.0927951 | ||||||||
\(687\) | 18.7997 | 0.717255 | ||||||||
\(688\) | −0.457502 | −0.0174421 | ||||||||
\(689\) | −13.8318 | −0.526948 | ||||||||
\(690\) | −29.6732 | −1.12964 | ||||||||
\(691\) | −31.4108 | −1.19492 | −0.597461 | − | 0.801898i | \(-0.703824\pi\) | ||||
−0.597461 | + | 0.801898i | \(0.703824\pi\) | |||||||
\(692\) | −84.2192 | −3.20153 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.4357 | 1.61084 | ||||||||
\(695\) | −4.81468 | −0.182631 | ||||||||
\(696\) | −29.8847 | −1.13278 | ||||||||
\(697\) | −1.86306 | −0.0705685 | ||||||||
\(698\) | 52.5583 | 1.98936 | ||||||||
\(699\) | −18.3975 | −0.695859 | ||||||||
\(700\) | −13.3461 | −0.504434 | ||||||||
\(701\) | −16.0647 | −0.606755 | −0.303377 | − | 0.952870i | \(-0.598114\pi\) | ||||
−0.303377 | + | 0.952870i | \(0.598114\pi\) | |||||||
\(702\) | −43.6845 | −1.64877 | ||||||||
\(703\) | −15.6133 | −0.588865 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.9232 | 0.637366 | ||||||||
\(706\) | −10.6976 | −0.402611 | ||||||||
\(707\) | −12.4761 | −0.469214 | ||||||||
\(708\) | −38.9273 | −1.46298 | ||||||||
\(709\) | 39.6978 | 1.49088 | 0.745441 | − | 0.666572i | \(-0.232239\pi\) | ||||
0.745441 | + | 0.666572i | \(0.232239\pi\) | |||||||
\(710\) | 0.356716 | 0.0133873 | ||||||||
\(711\) | −8.04356 | −0.301657 | ||||||||
\(712\) | −46.6069 | −1.74667 | ||||||||
\(713\) | 65.7913 | 2.46391 | ||||||||
\(714\) | −20.6503 | −0.772819 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.6822 | 0.698187 | ||||||||
\(717\) | −7.14391 | −0.266794 | ||||||||
\(718\) | 25.9614 | 0.968873 | ||||||||
\(719\) | −9.86241 | −0.367806 | −0.183903 | − | 0.982944i | \(-0.558873\pi\) | ||||
−0.183903 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(720\) | −4.09645 | −0.152666 | ||||||||
\(721\) | 8.21802 | 0.306055 | ||||||||
\(722\) | 26.2676 | 0.977580 | ||||||||
\(723\) | −3.76745 | −0.140113 | ||||||||
\(724\) | −30.6818 | −1.14028 | ||||||||
\(725\) | −15.3559 | −0.570305 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.5764 | −1.17111 | −0.585553 | − | 0.810634i | \(-0.699122\pi\) | ||||
−0.585553 | + | 0.810634i | \(0.699122\pi\) | |||||||
\(728\) | 14.7318 | 0.545998 | ||||||||
\(729\) | 29.3127 | 1.08565 | ||||||||
\(730\) | −1.88141 | −0.0696340 | ||||||||
\(731\) | −0.785321 | −0.0290462 | ||||||||
\(732\) | −13.7409 | −0.507877 | ||||||||
\(733\) | 41.2926 | 1.52518 | 0.762588 | − | 0.646885i | \(-0.223928\pi\) | ||||
0.762588 | + | 0.646885i | \(0.223928\pi\) | |||||||
\(734\) | −24.8313 | −0.916540 | ||||||||
\(735\) | 1.80514 | 0.0665835 | ||||||||
\(736\) | 5.96659 | 0.219931 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.720812 | −0.0265335 | ||||||||
\(739\) | 35.4095 | 1.30256 | 0.651281 | − | 0.758837i | \(-0.274232\pi\) | ||||
0.651281 | + | 0.758837i | \(0.274232\pi\) | |||||||
\(740\) | −26.8253 | −0.986116 | ||||||||
\(741\) | −13.0470 | −0.479293 | ||||||||
\(742\) | −10.5771 | −0.388299 | ||||||||
\(743\) | −4.02408 | −0.147629 | −0.0738146 | − | 0.997272i | \(-0.523517\pi\) | ||||
−0.0738146 | + | 0.997272i | \(0.523517\pi\) | |||||||
\(744\) | −64.6657 | −2.37076 | ||||||||
\(745\) | −6.13235 | −0.224672 | ||||||||
\(746\) | 67.7733 | 2.48136 | ||||||||
\(747\) | −0.896402 | −0.0327976 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1885 | 0.445359 | ||||||||
\(750\) | 36.9228 | 1.34823 | ||||||||
\(751\) | 24.4190 | 0.891062 | 0.445531 | − | 0.895267i | \(-0.353015\pi\) | ||||
0.445531 | + | 0.895267i | \(0.353015\pi\) | |||||||
\(752\) | 32.3554 | 1.17988 | ||||||||
\(753\) | −37.6091 | −1.37055 | ||||||||
\(754\) | 34.7265 | 1.26466 | ||||||||
\(755\) | −21.3638 | −0.777510 | ||||||||
\(756\) | −22.0952 | −0.803596 | ||||||||
\(757\) | −1.31723 | −0.0478755 | −0.0239377 | − | 0.999713i | \(-0.507620\pi\) | ||||
−0.0239377 | + | 0.999713i | \(0.507620\pi\) | |||||||
\(758\) | −2.79023 | −0.101346 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.6979 | −0.605696 | ||||||||
\(761\) | −7.24404 | −0.262596 | −0.131298 | − | 0.991343i | \(-0.541915\pi\) | ||||
−0.131298 | + | 0.991343i | \(0.541915\pi\) | |||||||
\(762\) | 27.9830 | 1.01372 | ||||||||
\(763\) | 0.886088 | 0.0320785 | ||||||||
\(764\) | −34.5008 | −1.24820 | ||||||||
\(765\) | −7.03174 | −0.254233 | ||||||||
\(766\) | 48.4915 | 1.75207 | ||||||||
\(767\) | 22.0792 | 0.797235 | ||||||||
\(768\) | −44.5430 | −1.60731 | ||||||||
\(769\) | 44.3139 | 1.59800 | 0.798999 | − | 0.601332i | \(-0.205363\pi\) | ||||
0.798999 | + | 0.601332i | \(0.205363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.9570 | 1.54706 | ||||||||
\(772\) | 100.031 | 3.60018 | ||||||||
\(773\) | 19.0559 | 0.685395 | 0.342697 | − | 0.939446i | \(-0.388659\pi\) | ||||
0.342697 | + | 0.939446i | \(0.388659\pi\) | |||||||
\(774\) | −0.303838 | −0.0109212 | ||||||||
\(775\) | −33.2277 | −1.19357 | ||||||||
\(776\) | −81.4714 | −2.92465 | ||||||||
\(777\) | −7.82353 | −0.280668 | ||||||||
\(778\) | −6.31918 | −0.226554 | ||||||||
\(779\) | −0.900123 | −0.0322502 | ||||||||
\(780\) | −22.4161 | −0.802626 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −97.3828 | −3.48240 | ||||||||
\(783\) | −25.4227 | −0.908533 | ||||||||
\(784\) | 3.45123 | 0.123258 | ||||||||
\(785\) | 2.82541 | 0.100843 | ||||||||
\(786\) | −0.353669 | −0.0126149 | ||||||||
\(787\) | 31.4600 | 1.12143 | 0.560714 | − | 0.828009i | \(-0.310527\pi\) | ||||
0.560714 | + | 0.828009i | \(0.310527\pi\) | |||||||
\(788\) | −43.7505 | −1.55855 | ||||||||
\(789\) | 4.78607 | 0.170389 | ||||||||
\(790\) | −26.0914 | −0.928292 | ||||||||
\(791\) | 4.54502 | 0.161602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.79370 | 0.276763 | ||||||||
\(794\) | −21.3208 | −0.756648 | ||||||||
\(795\) | 7.85582 | 0.278617 | ||||||||
\(796\) | −47.8631 | −1.69646 | ||||||||
\(797\) | −12.5453 | −0.444376 | −0.222188 | − | 0.975004i | \(-0.571320\pi\) | ||||
−0.222188 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(798\) | −9.97703 | −0.353183 | ||||||||
\(799\) | 55.5395 | 1.96485 | ||||||||
\(800\) | −3.01340 | −0.106540 | ||||||||
\(801\) | −9.48255 | −0.335049 | ||||||||
\(802\) | −68.9118 | −2.43336 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −52.7850 | −1.86159 | ||||||||
\(805\) | 8.51266 | 0.300032 | ||||||||
\(806\) | 75.1424 | 2.64678 | ||||||||
\(807\) | −2.48951 | −0.0876350 | ||||||||
\(808\) | 57.8284 | 2.03440 | ||||||||
\(809\) | −5.38024 | −0.189159 | −0.0945796 | − | 0.995517i | \(-0.530151\pi\) | ||||
−0.0945796 | + | 0.995517i | \(0.530151\pi\) | |||||||
\(810\) | 16.1563 | 0.567675 | ||||||||
\(811\) | 13.6999 | 0.481070 | 0.240535 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240535 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(812\) | 17.5643 | 0.616387 | ||||||||
\(813\) | −3.55103 | −0.124540 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.9333 | −0.698231 | ||||||||
\(816\) | 29.3234 | 1.02652 | ||||||||
\(817\) | −0.379421 | −0.0132743 | ||||||||
\(818\) | −48.3794 | −1.69155 | ||||||||
\(819\) | 2.99731 | 0.104735 | ||||||||
\(820\) | −1.54651 | −0.0540064 | ||||||||
\(821\) | −9.23116 | −0.322170 | −0.161085 | − | 0.986941i | \(-0.551499\pi\) | ||||
−0.161085 | + | 0.986941i | \(0.551499\pi\) | |||||||
\(822\) | 15.9094 | 0.554903 | ||||||||
\(823\) | −12.4427 | −0.433724 | −0.216862 | − | 0.976202i | \(-0.569582\pi\) | ||||
−0.216862 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(824\) | −38.0915 | −1.32698 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.8840 | 0.587469 | ||||||||
\(827\) | −4.48387 | −0.155919 | −0.0779597 | − | 0.996957i | \(-0.524841\pi\) | ||||
−0.0779597 | + | 0.996957i | \(0.524841\pi\) | |||||||
\(828\) | −24.9205 | −0.866048 | ||||||||
\(829\) | −36.8776 | −1.28081 | −0.640405 | − | 0.768037i | \(-0.721234\pi\) | ||||
−0.640405 | + | 0.768037i | \(0.721234\pi\) | |||||||
\(830\) | −2.90772 | −0.100928 | ||||||||
\(831\) | 7.39435 | 0.256507 | ||||||||
\(832\) | 28.7528 | 0.996823 | ||||||||
\(833\) | 5.92418 | 0.205261 | ||||||||
\(834\) | 13.3342 | 0.461726 | ||||||||
\(835\) | 26.1060 | 0.903435 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −55.0105 | −1.90144 | ||||||||
\(838\) | 75.0905 | 2.59396 | ||||||||
\(839\) | 9.16407 | 0.316379 | 0.158189 | − | 0.987409i | \(-0.449434\pi\) | ||||
0.158189 | + | 0.987409i | \(0.449434\pi\) | |||||||
\(840\) | −8.36702 | −0.288689 | ||||||||
\(841\) | −8.79054 | −0.303122 | ||||||||
\(842\) | 58.8003 | 2.02639 | ||||||||
\(843\) | −32.3708 | −1.11491 | ||||||||
\(844\) | −55.7293 | −1.91828 | ||||||||
\(845\) | −3.64795 | −0.125493 | ||||||||
\(846\) | 21.4880 | 0.738774 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.0195 | 0.515771 | ||||||||
\(849\) | −12.1729 | −0.417774 | ||||||||
\(850\) | 49.1829 | 1.68696 | ||||||||
\(851\) | −36.8942 | −1.26472 | ||||||||
\(852\) | −0.653435 | −0.0223863 | ||||||||
\(853\) | 6.52049 | 0.223257 | 0.111629 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111629 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(854\) | 5.95984 | 0.203942 | ||||||||
\(855\) | −3.39732 | −0.116186 | ||||||||
\(856\) | −56.4952 | −1.93097 | ||||||||
\(857\) | 48.0736 | 1.64216 | 0.821082 | − | 0.570810i | \(-0.193371\pi\) | ||||
0.821082 | + | 0.570810i | \(0.193371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.316298 | −0.0107920 | −0.00539598 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539598 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(860\) | −0.651887 | −0.0222291 | ||||||||
\(861\) | −0.451035 | −0.0153712 | ||||||||
\(862\) | −47.1509 | −1.60597 | ||||||||
\(863\) | 3.62693 | 0.123462 | 0.0617311 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617311 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(864\) | −4.98888 | −0.169725 | ||||||||
\(865\) | −27.1303 | −0.922458 | ||||||||
\(866\) | 51.9818 | 1.76641 | ||||||||
\(867\) | 25.9533 | 0.881420 | ||||||||
\(868\) | 38.0064 | 1.29002 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −19.7231 | −0.668675 | ||||||||
\(871\) | 29.9393 | 1.01445 | ||||||||
\(872\) | −4.10712 | −0.139085 | ||||||||
\(873\) | −16.5760 | −0.561014 | ||||||||
\(874\) | −47.0497 | −1.59148 | ||||||||
\(875\) | −10.5924 | −0.358090 | ||||||||
\(876\) | 3.44638 | 0.116442 | ||||||||
\(877\) | 26.7076 | 0.901852 | 0.450926 | − | 0.892561i | \(-0.351094\pi\) | ||||
0.450926 | + | 0.892561i | \(0.351094\pi\) | |||||||
\(878\) | 77.1220 | 2.60274 | ||||||||
\(879\) | 35.3189 | 1.19128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.91937 | 0.0983560 | 0.0491780 | − | 0.998790i | \(-0.484340\pi\) | ||||
0.0491780 | + | 0.998790i | \(0.484340\pi\) | |||||||
\(882\) | 2.29204 | 0.0771772 | ||||||||
\(883\) | −45.1574 | −1.51967 | −0.759834 | − | 0.650117i | \(-0.774720\pi\) | ||||
−0.759834 | + | 0.650117i | \(0.774720\pi\) | |||||||
\(884\) | −73.5663 | −2.47430 | ||||||||
\(885\) | −12.5400 | −0.421528 | ||||||||
\(886\) | 4.04939 | 0.136042 | ||||||||
\(887\) | −24.0249 | −0.806676 | −0.403338 | − | 0.915051i | \(-0.632150\pi\) | ||||
−0.403338 | + | 0.915051i | \(0.632150\pi\) | |||||||
\(888\) | 36.2630 | 1.21691 | ||||||||
\(889\) | −8.02779 | −0.269243 | ||||||||
\(890\) | −30.7592 | −1.03105 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.5806 | −0.387749 | ||||||||
\(893\) | 26.8334 | 0.897947 | ||||||||
\(894\) | 16.9835 | 0.568013 | ||||||||
\(895\) | 6.01828 | 0.201169 | ||||||||
\(896\) | 20.2229 | 0.675599 | ||||||||
\(897\) | −30.8301 | −1.02939 | ||||||||
\(898\) | 41.7692 | 1.39386 | ||||||||
\(899\) | 43.7300 | 1.45848 | ||||||||
\(900\) | 12.5860 | 0.419534 | ||||||||
\(901\) | 25.7816 | 0.858909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.190121 | −0.00632684 | ||||||||
\(904\) | −21.0667 | −0.700667 | ||||||||
\(905\) | −9.88384 | −0.328550 | ||||||||
\(906\) | 59.1670 | 1.96569 | ||||||||
\(907\) | −16.0270 | −0.532166 | −0.266083 | − | 0.963950i | \(-0.585730\pi\) | ||||
−0.266083 | + | 0.963950i | \(0.585730\pi\) | |||||||
\(908\) | 32.2572 | 1.07049 | ||||||||
\(909\) | 11.7657 | 0.390242 | ||||||||
\(910\) | 9.72259 | 0.322301 | ||||||||
\(911\) | −16.4043 | −0.543500 | −0.271750 | − | 0.962368i | \(-0.587602\pi\) | ||||
−0.271750 | + | 0.962368i | \(0.587602\pi\) | |||||||
\(912\) | 14.1673 | 0.469127 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.8408 | −0.821660 | ||||||||
\(915\) | −4.42647 | −0.146335 | ||||||||
\(916\) | 51.2147 | 1.69218 | ||||||||
\(917\) | 0.101461 | 0.00335053 | ||||||||
\(918\) | 81.4253 | 2.68744 | ||||||||
\(919\) | 32.3201 | 1.06614 | 0.533071 | − | 0.846070i | \(-0.321038\pi\) | ||||
0.533071 | + | 0.846070i | \(0.321038\pi\) | |||||||
\(920\) | −39.4572 | −1.30086 | ||||||||
\(921\) | 6.58861 | 0.217102 | ||||||||
\(922\) | 53.7518 | 1.77022 | ||||||||
\(923\) | 0.370623 | 0.0121992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6333 | 0.612659 | ||||||||
\(926\) | 73.8171 | 2.42578 | ||||||||
\(927\) | −7.75003 | −0.254544 | ||||||||
\(928\) | 3.96585 | 0.130185 | ||||||||
\(929\) | −8.19531 | −0.268879 | −0.134440 | − | 0.990922i | \(-0.542923\pi\) | ||||
−0.134440 | + | 0.990922i | \(0.542923\pi\) | |||||||
\(930\) | −42.6775 | −1.39945 | ||||||||
\(931\) | 2.86222 | 0.0938054 | ||||||||
\(932\) | −50.1190 | −1.64170 | ||||||||
\(933\) | −3.17065 | −0.103802 | ||||||||
\(934\) | −61.2253 | −2.00335 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.8929 | −0.454103 | ||||||||
\(937\) | 34.1374 | 1.11522 | 0.557610 | − | 0.830103i | \(-0.311718\pi\) | ||||
0.557610 | + | 0.830103i | \(0.311718\pi\) | |||||||
\(938\) | 22.8945 | 0.747533 | ||||||||
\(939\) | −13.9108 | −0.453961 | ||||||||
\(940\) | 46.1027 | 1.50371 | ||||||||
\(941\) | 0.979371 | 0.0319266 | 0.0159633 | − | 0.999873i | \(-0.494919\pi\) | ||||
0.0159633 | + | 0.999873i | \(0.494919\pi\) | |||||||
\(942\) | −7.82496 | −0.254951 | ||||||||
\(943\) | −2.12699 | −0.0692644 | ||||||||
\(944\) | −23.9752 | −0.780326 | ||||||||
\(945\) | −7.11775 | −0.231540 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.935599 | 0.0304029 | 0.0152014 | − | 0.999884i | \(-0.495161\pi\) | ||||
0.0152014 | + | 0.999884i | \(0.495161\pi\) | |||||||
\(948\) | 47.7946 | 1.55230 | ||||||||
\(949\) | −1.95476 | −0.0634542 | ||||||||
\(950\) | 23.7623 | 0.770950 | ||||||||
\(951\) | 9.25837 | 0.300223 | ||||||||
\(952\) | −27.4593 | −0.889960 | ||||||||
\(953\) | 16.7321 | 0.542004 | 0.271002 | − | 0.962579i | \(-0.412645\pi\) | ||||
0.271002 | + | 0.962579i | \(0.412645\pi\) | |||||||
\(954\) | 9.97480 | 0.322946 | ||||||||
\(955\) | −11.1141 | −0.359643 | ||||||||
\(956\) | −19.4616 | −0.629434 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 51.5353 | 1.66503 | ||||||||
\(959\) | −4.56409 | −0.147382 | ||||||||
\(960\) | −16.3303 | −0.527058 | ||||||||
\(961\) | 63.6245 | 2.05240 | ||||||||
\(962\) | −42.1380 | −1.35859 | ||||||||
\(963\) | −11.4944 | −0.370402 | ||||||||
\(964\) | −10.2634 | −0.330561 | ||||||||
\(965\) | 32.2238 | 1.03732 | ||||||||
\(966\) | −23.5758 | −0.758538 | ||||||||
\(967\) | 36.4439 | 1.17196 | 0.585978 | − | 0.810327i | \(-0.300710\pi\) | ||||
0.585978 | + | 0.810327i | \(0.300710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.3188 | 0.781233 | ||||||||
\(970\) | −53.7688 | −1.72641 | ||||||||
\(971\) | −33.2417 | −1.06678 | −0.533389 | − | 0.845870i | \(-0.679082\pi\) | ||||
−0.533389 | + | 0.845870i | \(0.679082\pi\) | |||||||
\(972\) | 36.6904 | 1.17685 | ||||||||
\(973\) | −3.82533 | −0.122634 | ||||||||
\(974\) | 40.8796 | 1.30987 | ||||||||
\(975\) | 15.5706 | 0.498659 | ||||||||
\(976\) | −8.46294 | −0.270892 | ||||||||
\(977\) | 22.5666 | 0.721970 | 0.360985 | − | 0.932572i | \(-0.382441\pi\) | ||||
0.360985 | + | 0.932572i | \(0.382441\pi\) | |||||||
\(978\) | 55.2050 | 1.76526 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.91760 | 0.157087 | ||||||||
\(981\) | −0.835628 | −0.0266795 | ||||||||
\(982\) | −11.7586 | −0.375233 | ||||||||
\(983\) | −15.1048 | −0.481767 | −0.240884 | − | 0.970554i | \(-0.577437\pi\) | ||||
−0.240884 | + | 0.970554i | \(0.577437\pi\) | |||||||
\(984\) | 2.09060 | 0.0666459 | ||||||||
\(985\) | −14.0938 | −0.449064 | ||||||||
\(986\) | −64.7281 | −2.06136 | ||||||||
\(987\) | 13.4458 | 0.427983 | ||||||||
\(988\) | −35.5429 | −1.13077 | ||||||||
\(989\) | −0.896574 | −0.0285094 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.1534 | −1.75201 | −0.876003 | − | 0.482305i | \(-0.839800\pi\) | ||||
−0.876003 | + | 0.482305i | \(0.839800\pi\) | |||||||
\(992\) | 8.58145 | 0.272461 | ||||||||
\(993\) | 5.19292 | 0.164792 | ||||||||
\(994\) | 0.283415 | 0.00898939 | ||||||||
\(995\) | −15.4186 | −0.488802 | ||||||||
\(996\) | 5.32639 | 0.168773 | ||||||||
\(997\) | 49.7048 | 1.57417 | 0.787083 | − | 0.616847i | \(-0.211590\pi\) | ||||
0.787083 | + | 0.616847i | \(0.211590\pi\) | |||||||
\(998\) | −74.3319 | −2.35293 | ||||||||
\(999\) | 30.8486 | 0.976006 |
(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 | 847.2.a.p.1.1 | 8 | ||
3.2 | odd | 2 | 7623.2.a.ct.1.8 | 8 | |||
7.6 | odd | 2 | 5929.2.a.bt.1.1 | 8 | |||
11.2 | odd | 10 | 847.2.f.v.323.1 | 16 | |||
11.3 | even | 5 | 77.2.f.b.64.1 | ✓ | 16 | ||
11.4 | even | 5 | 77.2.f.b.71.1 | yes | 16 | ||
11.5 | even | 5 | 847.2.f.w.729.4 | 16 | |||
11.6 | odd | 10 | 847.2.f.v.729.1 | 16 | |||
11.7 | odd | 10 | 847.2.f.x.148.4 | 16 | |||
11.8 | odd | 10 | 847.2.f.x.372.4 | 16 | |||
11.9 | even | 5 | 847.2.f.w.323.4 | 16 | |||
11.10 | odd | 2 | 847.2.a.o.1.8 | 8 | |||
33.14 | odd | 10 | 693.2.m.i.64.4 | 16 | |||
33.26 | odd | 10 | 693.2.m.i.379.4 | 16 | |||
33.32 | even | 2 | 7623.2.a.cw.1.1 | 8 | |||
77.3 | odd | 30 | 539.2.q.f.471.1 | 32 | |||
77.4 | even | 15 | 539.2.q.g.324.4 | 32 | |||
77.25 | even | 15 | 539.2.q.g.471.1 | 32 | |||
77.26 | odd | 30 | 539.2.q.f.214.1 | 32 | |||
77.37 | even | 15 | 539.2.q.g.214.1 | 32 | |||
77.47 | odd | 30 | 539.2.q.f.361.4 | 32 | |||
77.48 | odd | 10 | 539.2.f.e.148.1 | 16 | |||
77.58 | even | 15 | 539.2.q.g.361.4 | 32 | |||
77.59 | odd | 30 | 539.2.q.f.324.4 | 32 | |||
77.69 | odd | 10 | 539.2.f.e.295.1 | 16 | |||
77.76 | even | 2 | 5929.2.a.bs.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.1 | ✓ | 16 | 11.3 | even | 5 | ||
77.2.f.b.71.1 | yes | 16 | 11.4 | even | 5 | ||
539.2.f.e.148.1 | 16 | 77.48 | odd | 10 | |||
539.2.f.e.295.1 | 16 | 77.69 | odd | 10 | |||
539.2.q.f.214.1 | 32 | 77.26 | odd | 30 | |||
539.2.q.f.324.4 | 32 | 77.59 | odd | 30 | |||
539.2.q.f.361.4 | 32 | 77.47 | odd | 30 | |||
539.2.q.f.471.1 | 32 | 77.3 | odd | 30 | |||
539.2.q.g.214.1 | 32 | 77.37 | even | 15 | |||
539.2.q.g.324.4 | 32 | 77.4 | even | 15 | |||
539.2.q.g.361.4 | 32 | 77.58 | even | 15 | |||
539.2.q.g.471.1 | 32 | 77.25 | even | 15 | |||
693.2.m.i.64.4 | 16 | 33.14 | odd | 10 | |||
693.2.m.i.379.4 | 16 | 33.26 | odd | 10 | |||
847.2.a.o.1.8 | 8 | 11.10 | odd | 2 | |||
847.2.a.p.1.1 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.v.323.1 | 16 | 11.2 | odd | 10 | |||
847.2.f.v.729.1 | 16 | 11.6 | odd | 10 | |||
847.2.f.w.323.4 | 16 | 11.9 | even | 5 | |||
847.2.f.w.729.4 | 16 | 11.5 | even | 5 | |||
847.2.f.x.148.4 | 16 | 11.7 | odd | 10 | |||
847.2.f.x.372.4 | 16 | 11.8 | odd | 10 | |||
5929.2.a.bs.1.8 | 8 | 77.76 | even | 2 | |||
5929.2.a.bt.1.1 | 8 | 7.6 | odd | 2 | |||
7623.2.a.ct.1.8 | 8 | 3.2 | odd | 2 | |||
7623.2.a.cw.1.1 | 8 | 33.32 | even | 2 |