Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 6x^{9} + 37x^{8} - 2x^{7} - 109x^{6} + 55x^{5} + 115x^{4} - 76x^{3} - 29x^{2} + 14x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.57504\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.57504 | −1.11372 | −0.556861 | − | 0.830606i | \(-0.687994\pi\) | ||||
−0.556861 | + | 0.830606i | \(0.687994\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.480756 | 0.240378 | ||||||||
\(5\) | −0.664958 | −0.297378 | −0.148689 | − | 0.988884i | \(-0.547505\pi\) | ||||
−0.148689 | + | 0.988884i | \(0.547505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.15209 | −1.56934 | −0.784672 | − | 0.619911i | \(-0.787169\pi\) | ||||
−0.784672 | + | 0.619911i | \(0.787169\pi\) | |||||||
\(8\) | 2.39287 | 0.846008 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.04734 | 0.331197 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.20668 | 0.612023 | 0.306012 | − | 0.952028i | \(-0.401005\pi\) | ||||
0.306012 | + | 0.952028i | \(0.401005\pi\) | |||||||
\(14\) | 6.53972 | 1.74781 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.73039 | −1.18260 | ||||||||
\(17\) | 0.555008 | 0.134609 | 0.0673046 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673046 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.78925 | −1.55756 | −0.778780 | − | 0.627297i | \(-0.784161\pi\) | ||||
−0.778780 | + | 0.627297i | \(0.784161\pi\) | |||||||
\(20\) | −0.319682 | −0.0714831 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.57504 | −0.335800 | ||||||||
\(23\) | 4.88924 | 1.01948 | 0.509739 | − | 0.860329i | \(-0.329742\pi\) | ||||
0.509739 | + | 0.860329i | \(0.329742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.55783 | −0.911566 | ||||||||
\(26\) | −3.47561 | −0.681624 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.99614 | −0.377236 | ||||||||
\(29\) | −6.82104 | −1.26663 | −0.633317 | − | 0.773892i | \(-0.718307\pi\) | ||||
−0.633317 | + | 0.773892i | \(0.718307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.34874 | −0.781057 | −0.390528 | − | 0.920591i | \(-0.627708\pi\) | ||||
−0.390528 | + | 0.920591i | \(0.627708\pi\) | |||||||
\(32\) | 2.66481 | 0.471076 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.874161 | −0.149917 | ||||||||
\(35\) | 2.76097 | 0.466689 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.04417 | −0.829256 | −0.414628 | − | 0.909991i | \(-0.636088\pi\) | ||||
−0.414628 | + | 0.909991i | \(0.636088\pi\) | |||||||
\(38\) | 10.6933 | 1.73469 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.59116 | −0.251584 | ||||||||
\(41\) | 2.62576 | 0.410076 | 0.205038 | − | 0.978754i | \(-0.434268\pi\) | ||||
0.205038 | + | 0.978754i | \(0.434268\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.39322 | 1.12746 | 0.563728 | − | 0.825961i | \(-0.309367\pi\) | ||||
0.563728 | + | 0.825961i | \(0.309367\pi\) | |||||||
\(44\) | 0.480756 | 0.0724767 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.70076 | −1.13541 | ||||||||
\(47\) | −8.12666 | −1.18540 | −0.592698 | − | 0.805425i | \(-0.701937\pi\) | ||||
−0.592698 | + | 0.805425i | \(0.701937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.2399 | 1.46284 | ||||||||
\(50\) | 7.17877 | 1.01523 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.06087 | 0.147117 | ||||||||
\(53\) | 10.8520 | 1.49063 | 0.745317 | − | 0.666710i | \(-0.232298\pi\) | ||||
0.745317 | + | 0.666710i | \(0.232298\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.664958 | −0.0896629 | ||||||||
\(56\) | −9.93543 | −1.32768 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.7434 | 1.41068 | ||||||||
\(59\) | 12.5212 | 1.63012 | 0.815058 | − | 0.579380i | \(-0.196705\pi\) | ||||
0.815058 | + | 0.579380i | \(0.196705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 6.84944 | 0.869880 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.26359 | 0.657948 | ||||||||
\(65\) | −1.46735 | −0.182002 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.106558 | −0.0130181 | −0.00650905 | − | 0.999979i | \(-0.502072\pi\) | ||||
−0.00650905 | + | 0.999979i | \(0.502072\pi\) | |||||||
\(68\) | 0.266823 | 0.0323571 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.34864 | −0.519762 | ||||||||
\(71\) | −14.5818 | −1.73054 | −0.865269 | − | 0.501308i | \(-0.832852\pi\) | ||||
−0.865269 | + | 0.501308i | \(0.832852\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.84843 | 0.450425 | 0.225212 | − | 0.974310i | \(-0.427692\pi\) | ||||
0.225212 | + | 0.974310i | \(0.427692\pi\) | |||||||
\(74\) | 7.94478 | 0.923562 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.26397 | −0.374403 | ||||||||
\(77\) | −4.15209 | −0.473175 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5447 | −1.29888 | −0.649439 | − | 0.760414i | \(-0.724996\pi\) | ||||
−0.649439 | + | 0.760414i | \(0.724996\pi\) | |||||||
\(80\) | 3.14551 | 0.351678 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.13569 | −0.456710 | ||||||||
\(83\) | 11.0120 | 1.20873 | 0.604364 | − | 0.796709i | \(-0.293427\pi\) | ||||
0.604364 | + | 0.796709i | \(0.293427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.369057 | −0.0400298 | ||||||||
\(86\) | −11.6446 | −1.25567 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.39287 | 0.255081 | ||||||||
\(89\) | −13.7280 | −1.45516 | −0.727582 | − | 0.686021i | \(-0.759356\pi\) | ||||
−0.727582 | + | 0.686021i | \(0.759356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.16235 | −0.960475 | ||||||||
\(92\) | 2.35053 | 0.245060 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.7998 | 1.32020 | ||||||||
\(95\) | 4.51456 | 0.463184 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.42214 | −0.855139 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(98\) | −16.1282 | −1.62920 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.19120 | −0.219120 | ||||||||
\(101\) | −4.30166 | −0.428031 | −0.214016 | − | 0.976830i | \(-0.568654\pi\) | ||||
−0.214016 | + | 0.976830i | \(0.568654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.9878 | −1.96945 | −0.984727 | − | 0.174105i | \(-0.944297\pi\) | ||||
−0.984727 | + | 0.174105i | \(0.944297\pi\) | |||||||
\(104\) | 5.28031 | 0.517777 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.0923 | −1.66015 | ||||||||
\(107\) | 1.93095 | 0.186672 | 0.0933360 | − | 0.995635i | \(-0.470247\pi\) | ||||
0.0933360 | + | 0.995635i | \(0.470247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.72415 | −0.260927 | −0.130463 | − | 0.991453i | \(-0.541646\pi\) | ||||
−0.130463 | + | 0.991453i | \(0.541646\pi\) | |||||||
\(110\) | 1.04734 | 0.0998596 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 19.6410 | 1.85590 | ||||||||
\(113\) | −12.9048 | −1.21399 | −0.606993 | − | 0.794708i | \(-0.707624\pi\) | ||||
−0.606993 | + | 0.794708i | \(0.707624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.25114 | −0.303170 | ||||||||
\(116\) | −3.27925 | −0.304471 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.7213 | −1.81550 | ||||||||
\(119\) | −2.30445 | −0.211248 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.57504 | −0.142598 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.09068 | −0.187749 | ||||||||
\(125\) | 6.35555 | 0.568458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.247494 | −0.0219616 | −0.0109808 | − | 0.999940i | \(-0.503495\pi\) | ||||
−0.0109808 | + | 0.999940i | \(0.503495\pi\) | |||||||
\(128\) | −13.6200 | −1.20385 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.31114 | 0.202700 | ||||||||
\(131\) | −10.1462 | −0.886476 | −0.443238 | − | 0.896404i | \(-0.646170\pi\) | ||||
−0.443238 | + | 0.896404i | \(0.646170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.1896 | 2.44435 | ||||||||
\(134\) | 0.167833 | 0.0144985 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.32806 | 0.113881 | ||||||||
\(137\) | 7.01435 | 0.599276 | 0.299638 | − | 0.954053i | \(-0.403134\pi\) | ||||
0.299638 | + | 0.954053i | \(0.403134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.8476 | 1.76827 | 0.884133 | − | 0.467235i | \(-0.154750\pi\) | ||||
0.884133 | + | 0.467235i | \(0.154750\pi\) | |||||||
\(140\) | 1.32735 | 0.112182 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.9669 | 1.92734 | ||||||||
\(143\) | 2.20668 | 0.184532 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.53570 | 0.376670 | ||||||||
\(146\) | −6.06144 | −0.501648 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.42501 | −0.199335 | ||||||||
\(149\) | 7.76168 | 0.635861 | 0.317931 | − | 0.948114i | \(-0.397012\pi\) | ||||
0.317931 | + | 0.948114i | \(0.397012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.96491 | −0.485418 | −0.242709 | − | 0.970099i | \(-0.578036\pi\) | ||||
−0.242709 | + | 0.970099i | \(0.578036\pi\) | |||||||
\(152\) | −16.2458 | −1.31771 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.53972 | 0.526986 | ||||||||
\(155\) | 2.89173 | 0.232269 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.17348 | −0.572506 | −0.286253 | − | 0.958154i | \(-0.592410\pi\) | ||||
−0.286253 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(158\) | 18.1833 | 1.44659 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.77198 | −0.140088 | ||||||||
\(161\) | −20.3006 | −1.59991 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.662100 | −0.0518597 | −0.0259298 | − | 0.999664i | \(-0.508255\pi\) | ||||
−0.0259298 | + | 0.999664i | \(0.508255\pi\) | |||||||
\(164\) | 1.26235 | 0.0985731 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3444 | −1.34619 | ||||||||
\(167\) | −24.6628 | −1.90846 | −0.954232 | − | 0.299066i | \(-0.903325\pi\) | ||||
−0.954232 | + | 0.299066i | \(0.903325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.13056 | −0.625428 | ||||||||
\(170\) | 0.581280 | 0.0445821 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.55433 | 0.271015 | ||||||||
\(173\) | −18.8914 | −1.43629 | −0.718143 | − | 0.695895i | \(-0.755008\pi\) | ||||
−0.718143 | + | 0.695895i | \(0.755008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.9245 | 1.43056 | ||||||||
\(176\) | −4.73039 | −0.356566 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.6222 | 1.62065 | ||||||||
\(179\) | 9.09802 | 0.680018 | 0.340009 | − | 0.940422i | \(-0.389570\pi\) | ||||
0.340009 | + | 0.940422i | \(0.389570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4415 | 0.999096 | 0.499548 | − | 0.866286i | \(-0.333499\pi\) | ||||
0.499548 | + | 0.866286i | \(0.333499\pi\) | |||||||
\(182\) | 14.4311 | 1.06970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.6993 | 0.862486 | ||||||||
\(185\) | 3.35416 | 0.246603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.555008 | 0.0405862 | ||||||||
\(188\) | −3.90694 | −0.284943 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.11062 | −0.515859 | ||||||||
\(191\) | −4.02432 | −0.291190 | −0.145595 | − | 0.989344i | \(-0.546510\pi\) | ||||
−0.145595 | + | 0.989344i | \(0.546510\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.8101 | 1.42596 | 0.712980 | − | 0.701184i | \(-0.247345\pi\) | ||||
0.712980 | + | 0.701184i | \(0.247345\pi\) | |||||||
\(194\) | 13.2652 | 0.952387 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.92288 | 0.351634 | ||||||||
\(197\) | −0.313023 | −0.0223019 | −0.0111510 | − | 0.999938i | \(-0.503550\pi\) | ||||
−0.0111510 | + | 0.999938i | \(0.503550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.4725 | −1.73481 | −0.867405 | − | 0.497603i | \(-0.834214\pi\) | ||||
−0.867405 | + | 0.497603i | \(0.834214\pi\) | |||||||
\(200\) | −10.9063 | −0.771193 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.77529 | 0.476708 | ||||||||
\(203\) | 28.3216 | 1.98779 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.74602 | −0.121948 | ||||||||
\(206\) | 31.4816 | 2.19343 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.4385 | −0.723776 | ||||||||
\(209\) | −6.78925 | −0.469622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3430 | −1.12510 | −0.562550 | − | 0.826763i | \(-0.690180\pi\) | ||||
−0.562550 | + | 0.826763i | \(0.690180\pi\) | |||||||
\(212\) | 5.21715 | 0.358316 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.04133 | −0.207901 | ||||||||
\(215\) | −4.91618 | −0.335281 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0564 | 1.22575 | ||||||||
\(218\) | 4.29066 | 0.290600 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.319682 | −0.0215530 | ||||||||
\(221\) | 1.22473 | 0.0823840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.06727 | 0.473259 | 0.236630 | − | 0.971600i | \(-0.423957\pi\) | ||||
0.236630 | + | 0.971600i | \(0.423957\pi\) | |||||||
\(224\) | −11.0645 | −0.739280 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.3257 | 1.35204 | ||||||||
\(227\) | 28.2150 | 1.87269 | 0.936347 | − | 0.351075i | \(-0.114184\pi\) | ||||
0.936347 | + | 0.351075i | \(0.114184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.6985 | 1.83037 | 0.915184 | − | 0.403036i | \(-0.132045\pi\) | ||||
0.915184 | + | 0.403036i | \(0.132045\pi\) | |||||||
\(230\) | 5.12068 | 0.337648 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.3219 | −1.07158 | ||||||||
\(233\) | −20.8520 | −1.36606 | −0.683030 | − | 0.730391i | \(-0.739338\pi\) | ||||
−0.683030 | + | 0.730391i | \(0.739338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.40389 | 0.352511 | ||||||||
\(236\) | 6.01962 | 0.391844 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.62960 | 0.235272 | ||||||||
\(239\) | 28.1349 | 1.81989 | 0.909947 | − | 0.414725i | \(-0.136122\pi\) | ||||
0.909947 | + | 0.414725i | \(0.136122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.54194 | −0.421403 | −0.210702 | − | 0.977550i | \(-0.567575\pi\) | ||||
−0.210702 | + | 0.977550i | \(0.567575\pi\) | |||||||
\(242\) | −1.57504 | −0.101248 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.480756 | 0.0307772 | ||||||||
\(245\) | −6.80909 | −0.435017 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9817 | −0.953263 | ||||||||
\(248\) | −10.4060 | −0.660780 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0103 | −0.633105 | ||||||||
\(251\) | −9.23622 | −0.582985 | −0.291493 | − | 0.956573i | \(-0.594152\pi\) | ||||
−0.291493 | + | 0.956573i | \(0.594152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.88924 | 0.307384 | ||||||||
\(254\) | 0.389814 | 0.0244591 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.9249 | 0.682804 | ||||||||
\(257\) | 22.9183 | 1.42960 | 0.714802 | − | 0.699327i | \(-0.246517\pi\) | ||||
0.714802 | + | 0.699327i | \(0.246517\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.9439 | 1.30139 | ||||||||
\(260\) | −0.705437 | −0.0437493 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.9806 | 0.987288 | ||||||||
\(263\) | 23.9588 | 1.47736 | 0.738682 | − | 0.674054i | \(-0.235448\pi\) | ||||
0.738682 | + | 0.674054i | \(0.235448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.21611 | −0.443282 | ||||||||
\(266\) | −44.3998 | −2.72232 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0512282 | −0.00312926 | ||||||||
\(269\) | 21.8444 | 1.33188 | 0.665940 | − | 0.746005i | \(-0.268031\pi\) | ||||
0.665940 | + | 0.746005i | \(0.268031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2094 | 1.34913 | 0.674563 | − | 0.738218i | \(-0.264332\pi\) | ||||
0.674563 | + | 0.738218i | \(0.264332\pi\) | |||||||
\(272\) | −2.62540 | −0.159188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.0479 | −0.667427 | ||||||||
\(275\) | −4.55783 | −0.274848 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0104 | 1.68298 | 0.841490 | − | 0.540272i | \(-0.181679\pi\) | ||||
0.841490 | + | 0.540272i | \(0.181679\pi\) | |||||||
\(278\) | −32.8358 | −1.96936 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.60664 | 0.394822 | ||||||||
\(281\) | 22.6750 | 1.35268 | 0.676340 | − | 0.736590i | \(-0.263565\pi\) | ||||
0.676340 | + | 0.736590i | \(0.263565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1051 | −1.31401 | −0.657005 | − | 0.753886i | \(-0.728177\pi\) | ||||
−0.657005 | + | 0.753886i | \(0.728177\pi\) | |||||||
\(284\) | −7.01027 | −0.415983 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.47561 | −0.205517 | ||||||||
\(287\) | −10.9024 | −0.643550 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6920 | −0.981880 | ||||||||
\(290\) | −7.14392 | −0.419505 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.85015 | 0.108272 | ||||||||
\(293\) | 10.2956 | 0.601477 | 0.300738 | − | 0.953707i | \(-0.402767\pi\) | ||||
0.300738 | + | 0.953707i | \(0.402767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.32604 | −0.484761 | ||||||||
\(296\) | −12.0701 | −0.701558 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2250 | −0.708173 | ||||||||
\(299\) | 10.7890 | 0.623944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.6973 | −1.76936 | ||||||||
\(302\) | 9.39498 | 0.540620 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 32.1158 | 1.84196 | ||||||||
\(305\) | −0.664958 | −0.0380754 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.4405 | 1.85147 | 0.925737 | − | 0.378167i | \(-0.123445\pi\) | ||||
0.925737 | + | 0.378167i | \(0.123445\pi\) | |||||||
\(308\) | −1.99614 | −0.113741 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.55459 | −0.258683 | ||||||||
\(311\) | 4.29920 | 0.243785 | 0.121893 | − | 0.992543i | \(-0.461104\pi\) | ||||
0.121893 | + | 0.992543i | \(0.461104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.08806 | 0.344117 | 0.172059 | − | 0.985087i | \(-0.444958\pi\) | ||||
0.172059 | + | 0.985087i | \(0.444958\pi\) | |||||||
\(314\) | 11.2985 | 0.637613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.55017 | −0.312221 | ||||||||
\(317\) | 28.3357 | 1.59149 | 0.795745 | − | 0.605632i | \(-0.207080\pi\) | ||||
0.795745 | + | 0.605632i | \(0.207080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82104 | −0.381905 | ||||||||
\(320\) | −3.50006 | −0.195660 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 31.9743 | 1.78186 | ||||||||
\(323\) | −3.76809 | −0.209662 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0577 | −0.557900 | ||||||||
\(326\) | 1.04283 | 0.0577573 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.28312 | 0.346927 | ||||||||
\(329\) | 33.7427 | 1.86029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7095 | 1.19326 | 0.596630 | − | 0.802516i | \(-0.296506\pi\) | ||||
0.596630 | + | 0.802516i | \(0.296506\pi\) | |||||||
\(332\) | 5.29410 | 0.290551 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 38.8449 | 2.12550 | ||||||||
\(335\) | 0.0708564 | 0.00387130 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.98451 | −0.543891 | −0.271946 | − | 0.962313i | \(-0.587667\pi\) | ||||
−0.271946 | + | 0.962313i | \(0.587667\pi\) | |||||||
\(338\) | 12.8060 | 0.696553 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.177426 | −0.00962229 | ||||||||
\(341\) | −4.34874 | −0.235497 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4523 | −0.726355 | ||||||||
\(344\) | 17.6910 | 0.953836 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.7547 | 1.59962 | ||||||||
\(347\) | −6.67445 | −0.358303 | −0.179152 | − | 0.983821i | \(-0.557335\pi\) | ||||
−0.179152 | + | 0.983821i | \(0.557335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.9515 | −1.44268 | −0.721341 | − | 0.692580i | \(-0.756474\pi\) | ||||
−0.721341 | + | 0.692580i | \(0.756474\pi\) | |||||||
\(350\) | −29.8069 | −1.59325 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.66481 | 0.142035 | ||||||||
\(353\) | 2.87667 | 0.153110 | 0.0765548 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765548 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.69626 | 0.514624 | ||||||||
\(356\) | −6.59981 | −0.349789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.3298 | −0.757351 | ||||||||
\(359\) | −11.6302 | −0.613820 | −0.306910 | − | 0.951738i | \(-0.599295\pi\) | ||||
−0.306910 | + | 0.951738i | \(0.599295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.0939 | 1.42599 | ||||||||
\(362\) | −21.1709 | −1.11272 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.40485 | −0.230877 | ||||||||
\(365\) | −2.55904 | −0.133946 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.7261 | −1.23849 | −0.619245 | − | 0.785198i | \(-0.712561\pi\) | ||||
−0.619245 | + | 0.785198i | \(0.712561\pi\) | |||||||
\(368\) | −23.1280 | −1.20563 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.28294 | −0.274647 | ||||||||
\(371\) | −45.0585 | −2.33932 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6466 | 1.06904 | 0.534521 | − | 0.845155i | \(-0.320492\pi\) | ||||
0.534521 | + | 0.845155i | \(0.320492\pi\) | |||||||
\(374\) | −0.874161 | −0.0452018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.4461 | −1.00285 | ||||||||
\(377\) | −15.0519 | −0.775210 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3322 | −1.40396 | −0.701980 | − | 0.712196i | \(-0.747701\pi\) | ||||
−0.701980 | + | 0.712196i | \(0.747701\pi\) | |||||||
\(380\) | 2.17040 | 0.111339 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.33848 | 0.324305 | ||||||||
\(383\) | 13.2603 | 0.677570 | 0.338785 | − | 0.940864i | \(-0.389984\pi\) | ||||
0.338785 | + | 0.940864i | \(0.389984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76097 | 0.140712 | ||||||||
\(386\) | −31.2017 | −1.58812 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.04899 | −0.205556 | ||||||||
\(389\) | −21.9449 | −1.11265 | −0.556326 | − | 0.830964i | \(-0.687789\pi\) | ||||
−0.556326 | + | 0.830964i | \(0.687789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.71357 | 0.137231 | ||||||||
\(392\) | 24.5027 | 1.23757 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.493024 | 0.0248382 | ||||||||
\(395\) | 7.67672 | 0.386258 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9744 | −0.550791 | −0.275395 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275395 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(398\) | 38.5452 | 1.93210 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5603 | 1.07801 | ||||||||
\(401\) | 14.1612 | 0.707177 | 0.353589 | − | 0.935401i | \(-0.384961\pi\) | ||||
0.353589 | + | 0.935401i | \(0.384961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.59628 | −0.478025 | ||||||||
\(404\) | −2.06805 | −0.102889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −44.6077 | −2.21384 | ||||||||
\(407\) | −5.04417 | −0.250030 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1898 | 0.998323 | 0.499162 | − | 0.866509i | \(-0.333641\pi\) | ||||
0.499162 | + | 0.866509i | \(0.333641\pi\) | |||||||
\(410\) | 2.75006 | 0.135816 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.60924 | −0.473413 | ||||||||
\(413\) | −51.9890 | −2.55821 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.32253 | −0.359449 | ||||||||
\(416\) | 5.88038 | 0.288309 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.6933 | 0.523029 | ||||||||
\(419\) | −6.66184 | −0.325452 | −0.162726 | − | 0.986671i | \(-0.552029\pi\) | ||||
−0.162726 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0791 | 1.66092 | 0.830458 | − | 0.557082i | \(-0.188079\pi\) | ||||
0.830458 | + | 0.557082i | \(0.188079\pi\) | |||||||
\(422\) | 25.7409 | 1.25305 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.9674 | 1.26109 | ||||||||
\(425\) | −2.52963 | −0.122705 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.15209 | −0.200934 | ||||||||
\(428\) | 0.928315 | 0.0448718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.74318 | 0.373409 | ||||||||
\(431\) | 3.49979 | 0.168579 | 0.0842894 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842894 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.96208 | 0.286519 | 0.143260 | − | 0.989685i | \(-0.454242\pi\) | ||||
0.143260 | + | 0.989685i | \(0.454242\pi\) | |||||||
\(434\) | −28.4395 | −1.36514 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.30965 | −0.0627210 | ||||||||
\(437\) | −33.1943 | −1.58790 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7745 | 1.70742 | 0.853711 | − | 0.520746i | \(-0.174346\pi\) | ||||
0.853711 | + | 0.520746i | \(0.174346\pi\) | |||||||
\(440\) | −1.59116 | −0.0758555 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.92899 | −0.0917529 | ||||||||
\(443\) | 12.4530 | 0.591659 | 0.295829 | − | 0.955241i | \(-0.404404\pi\) | ||||
0.295829 | + | 0.955241i | \(0.404404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.12854 | 0.432734 | ||||||||
\(446\) | −11.1312 | −0.527079 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.8549 | −1.03255 | ||||||||
\(449\) | 21.5415 | 1.01661 | 0.508304 | − | 0.861178i | \(-0.330273\pi\) | ||||
0.508304 | + | 0.861178i | \(0.330273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.62576 | 0.123642 | ||||||||
\(452\) | −6.20408 | −0.291815 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −44.4398 | −2.08566 | ||||||||
\(455\) | 6.09257 | 0.285624 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.2977 | 0.668820 | 0.334410 | − | 0.942428i | \(-0.391463\pi\) | ||||
0.334410 | + | 0.942428i | \(0.391463\pi\) | |||||||
\(458\) | −43.6263 | −2.03852 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.56300 | −0.0728754 | ||||||||
\(461\) | 16.7508 | 0.780162 | 0.390081 | − | 0.920781i | \(-0.372447\pi\) | ||||
0.390081 | + | 0.920781i | \(0.372447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95141 | −0.230111 | −0.115056 | − | 0.993359i | \(-0.536705\pi\) | ||||
−0.115056 | + | 0.993359i | \(0.536705\pi\) | |||||||
\(464\) | 32.2661 | 1.49792 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.8427 | 1.52141 | ||||||||
\(467\) | 13.6976 | 0.633851 | 0.316926 | − | 0.948450i | \(-0.397349\pi\) | ||||
0.316926 | + | 0.948450i | \(0.397349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.442438 | 0.0204299 | ||||||||
\(470\) | −8.51135 | −0.392599 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.9615 | 1.37909 | ||||||||
\(473\) | 7.39322 | 0.339940 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.9442 | 1.41982 | ||||||||
\(476\) | −1.10788 | −0.0507794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −44.3136 | −2.02686 | ||||||||
\(479\) | 0.678782 | 0.0310143 | 0.0155072 | − | 0.999880i | \(-0.495064\pi\) | ||||
0.0155072 | + | 0.999880i | \(0.495064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1309 | −0.507524 | ||||||||
\(482\) | 10.3038 | 0.469327 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.480756 | 0.0218525 | ||||||||
\(485\) | 5.60037 | 0.254300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.9423 | −1.58339 | −0.791693 | − | 0.610919i | \(-0.790800\pi\) | ||||
−0.791693 | + | 0.610919i | \(0.790800\pi\) | |||||||
\(488\) | 2.39287 | 0.108320 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.7246 | 0.484488 | ||||||||
\(491\) | 3.04634 | 0.137479 | 0.0687397 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687397 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.78573 | −0.170501 | ||||||||
\(494\) | 23.5968 | 1.06167 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.5712 | 0.923675 | ||||||||
\(497\) | 60.5449 | 2.71581 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.9286 | −0.757828 | −0.378914 | − | 0.925432i | \(-0.623702\pi\) | ||||
−0.378914 | + | 0.925432i | \(0.623702\pi\) | |||||||
\(500\) | 3.05547 | 0.136645 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.5474 | 0.649284 | ||||||||
\(503\) | −31.0454 | −1.38425 | −0.692124 | − | 0.721779i | \(-0.743325\pi\) | ||||
−0.692124 | + | 0.721779i | \(0.743325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.86042 | 0.127287 | ||||||||
\(506\) | −7.70076 | −0.342340 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.118984 | −0.00527908 | ||||||||
\(509\) | 0.726829 | 0.0322161 | 0.0161081 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161081 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9790 | −0.706871 | ||||||||
\(512\) | 10.0329 | 0.443394 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.0973 | −1.59218 | ||||||||
\(515\) | 13.2910 | 0.585673 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.12666 | −0.357410 | ||||||||
\(518\) | −32.9875 | −1.44939 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.51118 | −0.153975 | ||||||||
\(521\) | 33.5607 | 1.47032 | 0.735161 | − | 0.677893i | \(-0.237107\pi\) | ||||
0.735161 | + | 0.677893i | \(0.237107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.242645 | 0.0106101 | 0.00530507 | − | 0.999986i | \(-0.498311\pi\) | ||||
0.00530507 | + | 0.999986i | \(0.498311\pi\) | |||||||
\(524\) | −4.87783 | −0.213089 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37.7362 | −1.64537 | ||||||||
\(527\) | −2.41359 | −0.105137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.904686 | 0.0393342 | ||||||||
\(530\) | 11.3657 | 0.493693 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.5523 | 0.587567 | ||||||||
\(533\) | 5.79422 | 0.250976 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28400 | −0.0555122 | ||||||||
\(536\) | −0.254979 | −0.0110134 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.4059 | −1.48334 | ||||||||
\(539\) | 10.2399 | 0.441063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9828 | −1.03110 | −0.515551 | − | 0.856859i | \(-0.672413\pi\) | ||||
−0.515551 | + | 0.856859i | \(0.672413\pi\) | |||||||
\(542\) | −34.9807 | −1.50255 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.47899 | 0.0634112 | ||||||||
\(545\) | 1.81145 | 0.0775939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.8037 | −1.44534 | −0.722671 | − | 0.691192i | \(-0.757086\pi\) | ||||
−0.722671 | + | 0.691192i | \(0.757086\pi\) | |||||||
\(548\) | 3.37219 | 0.144053 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.17877 | 0.306104 | ||||||||
\(551\) | 46.3097 | 1.97286 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.9346 | 2.03839 | ||||||||
\(554\) | −44.1175 | −1.87437 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.0226 | 0.425052 | ||||||||
\(557\) | −3.91424 | −0.165852 | −0.0829258 | − | 0.996556i | \(-0.526426\pi\) | ||||
−0.0829258 | + | 0.996556i | \(0.526426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3145 | 0.690029 | ||||||||
\(560\) | −13.0604 | −0.551904 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.7141 | −1.50651 | ||||||||
\(563\) | 9.83958 | 0.414689 | 0.207344 | − | 0.978268i | \(-0.433518\pi\) | ||||
0.207344 | + | 0.978268i | \(0.433518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.58117 | 0.361013 | ||||||||
\(566\) | 34.8164 | 1.46344 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −34.8923 | −1.46405 | ||||||||
\(569\) | 7.46080 | 0.312773 | 0.156387 | − | 0.987696i | \(-0.450015\pi\) | ||||
0.156387 | + | 0.987696i | \(0.450015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1776 | 1.34659 | 0.673295 | − | 0.739374i | \(-0.264879\pi\) | ||||
0.673295 | + | 0.739374i | \(0.264879\pi\) | |||||||
\(572\) | 1.06087 | 0.0443574 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.1718 | 0.716736 | ||||||||
\(575\) | −22.2843 | −0.929321 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.2854 | −1.51058 | −0.755291 | − | 0.655389i | \(-0.772505\pi\) | ||||
−0.755291 | + | 0.655389i | \(0.772505\pi\) | |||||||
\(578\) | 26.2905 | 1.09354 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.18056 | 0.0905430 | ||||||||
\(581\) | −45.7230 | −1.89691 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8520 | 0.449443 | ||||||||
\(584\) | 9.20880 | 0.381063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2160 | −0.669878 | ||||||||
\(587\) | 32.1672 | 1.32768 | 0.663841 | − | 0.747874i | \(-0.268925\pi\) | ||||
0.663841 | + | 0.747874i | \(0.268925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.5247 | 1.21654 | ||||||||
\(590\) | 13.1139 | 0.539889 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.8609 | 0.980676 | ||||||||
\(593\) | 31.5275 | 1.29468 | 0.647340 | − | 0.762201i | \(-0.275881\pi\) | ||||
0.647340 | + | 0.762201i | \(0.275881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.53236 | 0.0628206 | ||||||||
\(596\) | 3.73147 | 0.152847 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.9931 | −0.694900 | ||||||||
\(599\) | 9.91924 | 0.405289 | 0.202645 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202645 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.16233 | −0.251367 | −0.125683 | − | 0.992070i | \(-0.540112\pi\) | ||||
−0.125683 | + | 0.992070i | \(0.540112\pi\) | |||||||
\(602\) | 48.3496 | 1.97058 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.86766 | −0.116684 | ||||||||
\(605\) | −0.664958 | −0.0270344 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.6484 | −0.594560 | −0.297280 | − | 0.954790i | \(-0.596079\pi\) | ||||
−0.297280 | + | 0.954790i | \(0.596079\pi\) | |||||||
\(608\) | −18.0920 | −0.733729 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.04734 | 0.0424054 | ||||||||
\(611\) | −17.9330 | −0.725490 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1981 | 0.936962 | 0.468481 | − | 0.883474i | \(-0.344801\pi\) | ||||
0.468481 | + | 0.883474i | \(0.344801\pi\) | |||||||
\(614\) | −51.0951 | −2.06203 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.93543 | −0.400310 | ||||||||
\(617\) | 0.149954 | 0.00603693 | 0.00301847 | − | 0.999995i | \(-0.499039\pi\) | ||||
0.00301847 | + | 0.999995i | \(0.499039\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.4179 | 1.10202 | 0.551009 | − | 0.834499i | \(-0.314243\pi\) | ||||
0.551009 | + | 0.834499i | \(0.314243\pi\) | |||||||
\(620\) | 1.39021 | 0.0558324 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.77141 | −0.271509 | ||||||||
\(623\) | 56.9999 | 2.28365 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5630 | 0.742519 | ||||||||
\(626\) | −9.58894 | −0.383251 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.44869 | −0.137618 | ||||||||
\(629\) | −2.79955 | −0.111626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.66672 | 0.185779 | 0.0928896 | − | 0.995676i | \(-0.470390\pi\) | ||||
0.0928896 | + | 0.995676i | \(0.470390\pi\) | |||||||
\(632\) | −27.6249 | −1.09886 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −44.6298 | −1.77248 | ||||||||
\(635\) | 0.164573 | 0.00653089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5962 | 0.895292 | ||||||||
\(638\) | 10.7434 | 0.425336 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.05672 | 0.357998 | ||||||||
\(641\) | −15.1800 | −0.599575 | −0.299788 | − | 0.954006i | \(-0.596916\pi\) | ||||
−0.299788 | + | 0.954006i | \(0.596916\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.8497 | −1.05885 | −0.529425 | − | 0.848357i | \(-0.677592\pi\) | ||||
−0.529425 | + | 0.848357i | \(0.677592\pi\) | |||||||
\(644\) | −9.75963 | −0.384583 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.93489 | 0.233505 | ||||||||
\(647\) | −26.4109 | −1.03832 | −0.519159 | − | 0.854678i | \(-0.673755\pi\) | ||||
−0.519159 | + | 0.854678i | \(0.673755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.5212 | 0.491498 | ||||||||
\(650\) | 15.8413 | 0.621345 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.318308 | −0.0124659 | ||||||||
\(653\) | −3.27170 | −0.128032 | −0.0640158 | − | 0.997949i | \(-0.520391\pi\) | ||||
−0.0640158 | + | 0.997949i | \(0.520391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.74678 | 0.263618 | ||||||||
\(656\) | −12.4209 | −0.484954 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −53.1461 | −2.07185 | ||||||||
\(659\) | −21.3103 | −0.830133 | −0.415067 | − | 0.909791i | \(-0.636242\pi\) | ||||
−0.415067 | + | 0.909791i | \(0.636242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.1532 | 1.25061 | 0.625306 | − | 0.780379i | \(-0.284974\pi\) | ||||
0.625306 | + | 0.780379i | \(0.284974\pi\) | |||||||
\(662\) | −34.1933 | −1.32896 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.3504 | 1.02259 | ||||||||
\(665\) | −18.7449 | −0.726896 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.3497 | −1.29131 | ||||||||
\(668\) | −11.8568 | −0.458753 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.111602 | −0.00431155 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.45786 | −0.326027 | −0.163013 | − | 0.986624i | \(-0.552121\pi\) | ||||
−0.163013 | + | 0.986624i | \(0.552121\pi\) | |||||||
\(674\) | 15.7260 | 0.605744 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.90881 | −0.150339 | ||||||||
\(677\) | −7.96311 | −0.306047 | −0.153024 | − | 0.988223i | \(-0.548901\pi\) | ||||
−0.153024 | + | 0.988223i | \(0.548901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.9695 | 1.34201 | ||||||||
\(680\) | −0.883106 | −0.0338656 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.84944 | 0.262279 | ||||||||
\(683\) | −17.0017 | −0.650550 | −0.325275 | − | 0.945619i | \(-0.605457\pi\) | ||||
−0.325275 | + | 0.945619i | \(0.605457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.66424 | −0.178212 | ||||||||
\(686\) | 21.1879 | 0.808958 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −34.9728 | −1.33332 | ||||||||
\(689\) | 23.9469 | 0.912303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2525 | −0.656317 | −0.328158 | − | 0.944623i | \(-0.606428\pi\) | ||||
−0.328158 | + | 0.944623i | \(0.606428\pi\) | |||||||
\(692\) | −9.08215 | −0.345251 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.5125 | 0.399050 | ||||||||
\(695\) | −13.8627 | −0.525844 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.45732 | 0.0552000 | ||||||||
\(698\) | 42.4498 | 1.60675 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.09808 | 0.343875 | ||||||||
\(701\) | 51.6390 | 1.95038 | 0.975188 | − | 0.221377i | \(-0.0710551\pi\) | ||||
0.975188 | + | 0.221377i | \(0.0710551\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.2461 | 1.29162 | ||||||||
\(704\) | 5.26359 | 0.198379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.53087 | −0.170522 | ||||||||
\(707\) | 17.8609 | 0.671728 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.0695 | 1.35462 | 0.677310 | − | 0.735698i | \(-0.263146\pi\) | ||||
0.677310 | + | 0.735698i | \(0.263146\pi\) | |||||||
\(710\) | −15.2720 | −0.573149 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32.8493 | −1.23108 | ||||||||
\(713\) | −21.2620 | −0.796269 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46735 | −0.0548758 | ||||||||
\(716\) | 4.37392 | 0.163461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3181 | 0.683626 | ||||||||
\(719\) | −7.32908 | −0.273329 | −0.136664 | − | 0.990617i | \(-0.543638\pi\) | ||||
−0.136664 | + | 0.990617i | \(0.543638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 82.9911 | 3.09075 | ||||||||
\(722\) | −42.6740 | −1.58816 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.46206 | 0.240161 | ||||||||
\(725\) | 31.0891 | 1.15462 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.5709 | −1.09672 | −0.548361 | − | 0.836242i | \(-0.684748\pi\) | ||||
−0.548361 | + | 0.836242i | \(0.684748\pi\) | |||||||
\(728\) | −21.9243 | −0.812570 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.03060 | 0.149179 | ||||||||
\(731\) | 4.10330 | 0.151766 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.3129 | 1.78448 | 0.892239 | − | 0.451563i | \(-0.149134\pi\) | ||||
0.892239 | + | 0.451563i | \(0.149134\pi\) | |||||||
\(734\) | 37.3695 | 1.37933 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.0289 | 0.480251 | ||||||||
\(737\) | −0.106558 | −0.00392510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.3822 | 0.896915 | 0.448457 | − | 0.893804i | \(-0.351974\pi\) | ||||
0.448457 | + | 0.893804i | \(0.351974\pi\) | |||||||
\(740\) | 1.61253 | 0.0592778 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 70.9689 | 2.60535 | ||||||||
\(743\) | 26.4089 | 0.968849 | 0.484424 | − | 0.874833i | \(-0.339029\pi\) | ||||
0.484424 | + | 0.874833i | \(0.339029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.16119 | −0.189091 | ||||||||
\(746\) | −32.5193 | −1.19062 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.266823 | 0.00975603 | ||||||||
\(749\) | −8.01748 | −0.292952 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0998497 | −0.00364357 | −0.00182178 | − | 0.999998i | \(-0.500580\pi\) | ||||
−0.00182178 | + | 0.999998i | \(0.500580\pi\) | |||||||
\(752\) | 38.4423 | 1.40184 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 23.7073 | 0.863369 | ||||||||
\(755\) | 3.96641 | 0.144353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.11193 | 0.222142 | 0.111071 | − | 0.993812i | \(-0.464572\pi\) | ||||
0.111071 | + | 0.993812i | \(0.464572\pi\) | |||||||
\(758\) | 43.0493 | 1.56362 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.8028 | 0.391858 | ||||||||
\(761\) | 45.5077 | 1.64965 | 0.824827 | − | 0.565385i | \(-0.191273\pi\) | ||||
0.824827 | + | 0.565385i | \(0.191273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3109 | 0.409484 | ||||||||
\(764\) | −1.93472 | −0.0699956 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.8855 | −0.754625 | ||||||||
\(767\) | 27.6302 | 0.997668 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.4644 | −0.449478 | −0.224739 | − | 0.974419i | \(-0.572153\pi\) | ||||
−0.224739 | + | 0.974419i | \(0.572153\pi\) | |||||||
\(770\) | −4.34864 | −0.156714 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.52381 | 0.342769 | ||||||||
\(773\) | 21.9139 | 0.788190 | 0.394095 | − | 0.919070i | \(-0.371058\pi\) | ||||
0.394095 | + | 0.919070i | \(0.371058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.8208 | 0.711985 | ||||||||
\(776\) | −20.1531 | −0.723454 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.5642 | 1.23919 | ||||||||
\(779\) | −17.8270 | −0.638717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.5818 | −0.521777 | ||||||||
\(782\) | −4.27398 | −0.152837 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −48.4386 | −1.72995 | ||||||||
\(785\) | 4.77006 | 0.170251 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.5182 | −0.624456 | −0.312228 | − | 0.950007i | \(-0.601075\pi\) | ||||
−0.312228 | + | 0.950007i | \(0.601075\pi\) | |||||||
\(788\) | −0.150487 | −0.00536089 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.0912 | −0.430184 | ||||||||
\(791\) | 53.5821 | 1.90516 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.20668 | 0.0783615 | ||||||||
\(794\) | 17.2852 | 0.613428 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.7653 | −0.417010 | ||||||||
\(797\) | −40.6397 | −1.43953 | −0.719766 | − | 0.694217i | \(-0.755751\pi\) | ||||
−0.719766 | + | 0.694217i | \(0.755751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.51036 | −0.159565 | ||||||||
\(800\) | −12.1457 | −0.429417 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.3045 | −0.787600 | ||||||||
\(803\) | 3.84843 | 0.135808 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4990 | 0.475778 | ||||||||
\(806\) | 15.1145 | 0.532387 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.2933 | −0.362118 | ||||||||
\(809\) | −7.30213 | −0.256729 | −0.128365 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128365 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.58750 | 0.196204 | 0.0981019 | − | 0.995176i | \(-0.468723\pi\) | ||||
0.0981019 | + | 0.995176i | \(0.468723\pi\) | |||||||
\(812\) | 13.6158 | 0.477820 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.94478 | 0.278464 | ||||||||
\(815\) | 0.440268 | 0.0154219 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50.1944 | −1.75608 | ||||||||
\(818\) | −31.7998 | −1.11186 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.839410 | −0.0293135 | ||||||||
\(821\) | 48.2701 | 1.68464 | 0.842318 | − | 0.538980i | \(-0.181190\pi\) | ||||
0.842318 | + | 0.538980i | \(0.181190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.9312 | −1.11305 | −0.556526 | − | 0.830830i | \(-0.687866\pi\) | ||||
−0.556526 | + | 0.830830i | \(0.687866\pi\) | |||||||
\(824\) | −47.8282 | −1.66617 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 81.8848 | 2.84914 | ||||||||
\(827\) | 45.8879 | 1.59568 | 0.797839 | − | 0.602871i | \(-0.205977\pi\) | ||||
0.797839 | + | 0.602871i | \(0.205977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.3612 | −0.672441 | −0.336221 | − | 0.941783i | \(-0.609149\pi\) | ||||
−0.336221 | + | 0.941783i | \(0.609149\pi\) | |||||||
\(830\) | 11.5333 | 0.400327 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.6151 | 0.402680 | ||||||||
\(833\) | 5.68322 | 0.196912 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3997 | 0.567536 | ||||||||
\(836\) | −3.26397 | −0.112887 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.4927 | 0.362463 | ||||||||
\(839\) | 1.48442 | 0.0512479 | 0.0256239 | − | 0.999672i | \(-0.491843\pi\) | ||||
0.0256239 | + | 0.999672i | \(0.491843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.5265 | 0.604363 | ||||||||
\(842\) | −53.6760 | −1.84980 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.85700 | −0.270449 | ||||||||
\(845\) | 5.40648 | 0.185989 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.15209 | −0.142668 | ||||||||
\(848\) | −51.3341 | −1.76282 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.98428 | 0.136660 | ||||||||
\(851\) | −24.6622 | −0.845408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.91635 | −0.0656146 | −0.0328073 | − | 0.999462i | \(-0.510445\pi\) | ||||
−0.0328073 | + | 0.999462i | \(0.510445\pi\) | |||||||
\(854\) | 6.53972 | 0.223785 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.62052 | 0.157926 | ||||||||
\(857\) | 37.2576 | 1.27270 | 0.636348 | − | 0.771402i | \(-0.280444\pi\) | ||||
0.636348 | + | 0.771402i | \(0.280444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6063 | −0.566600 | −0.283300 | − | 0.959031i | \(-0.591429\pi\) | ||||
−0.283300 | + | 0.959031i | \(0.591429\pi\) | |||||||
\(860\) | −2.36348 | −0.0805940 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.51231 | −0.187750 | ||||||||
\(863\) | 8.66162 | 0.294845 | 0.147422 | − | 0.989074i | \(-0.452902\pi\) | ||||
0.147422 | + | 0.989074i | \(0.452902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.5620 | 0.427120 | ||||||||
\(866\) | −9.39052 | −0.319103 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.68070 | 0.294642 | ||||||||
\(869\) | −11.5447 | −0.391626 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.235139 | −0.00796738 | ||||||||
\(872\) | −6.51856 | −0.220746 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 52.2824 | 1.76848 | ||||||||
\(875\) | −26.3889 | −0.892106 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.4656 | −0.792378 | −0.396189 | − | 0.918169i | \(-0.629667\pi\) | ||||
−0.396189 | + | 0.918169i | \(0.629667\pi\) | |||||||
\(878\) | −56.3463 | −1.90160 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.14551 | 0.106035 | ||||||||
\(881\) | 5.76381 | 0.194188 | 0.0970938 | − | 0.995275i | \(-0.469045\pi\) | ||||
0.0970938 | + | 0.995275i | \(0.469045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0682 | 0.978224 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(884\) | 0.588794 | 0.0198033 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.6139 | −0.658943 | ||||||||
\(887\) | −35.6351 | −1.19651 | −0.598255 | − | 0.801306i | \(-0.704139\pi\) | ||||
−0.598255 | + | 0.801306i | \(0.704139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.02762 | 0.0344653 | ||||||||
\(890\) | −14.3778 | −0.481946 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.39763 | 0.113761 | ||||||||
\(893\) | 55.1739 | 1.84633 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.04980 | −0.202222 | ||||||||
\(896\) | 56.5515 | 1.88925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.9288 | −1.13222 | ||||||||
\(899\) | 29.6629 | 0.989313 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.02294 | 0.200653 | ||||||||
\(902\) | −4.13569 | −0.137703 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.8796 | −1.02704 | ||||||||
\(905\) | −8.93801 | −0.297109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.48853 | 0.182244 | 0.0911218 | − | 0.995840i | \(-0.470955\pi\) | ||||
0.0911218 | + | 0.995840i | \(0.470955\pi\) | |||||||
\(908\) | 13.5645 | 0.450154 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.59606 | −0.318106 | ||||||||
\(911\) | −12.8974 | −0.427310 | −0.213655 | − | 0.976909i | \(-0.568537\pi\) | ||||
−0.213655 | + | 0.976909i | \(0.568537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.0120 | 0.364445 | ||||||||
\(914\) | −22.5195 | −0.744880 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.3162 | 0.439980 | ||||||||
\(917\) | 42.1279 | 1.39119 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0449 | 1.61784 | 0.808921 | − | 0.587918i | \(-0.200052\pi\) | ||||
0.808921 | + | 0.587918i | \(0.200052\pi\) | |||||||
\(920\) | −7.77956 | −0.256485 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.3832 | −0.868884 | ||||||||
\(923\) | −32.1773 | −1.05913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.9905 | 0.755922 | ||||||||
\(926\) | 7.79867 | 0.256280 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.1768 | −0.596681 | ||||||||
\(929\) | 28.3566 | 0.930351 | 0.465176 | − | 0.885218i | \(-0.345991\pi\) | ||||
0.465176 | + | 0.885218i | \(0.345991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −69.5211 | −2.27846 | ||||||||
\(932\) | −10.0247 | −0.328370 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.5743 | −0.705934 | ||||||||
\(935\) | −0.369057 | −0.0120695 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.87929 | 0.322742 | 0.161371 | − | 0.986894i | \(-0.448408\pi\) | ||||
0.161371 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(938\) | −0.696858 | −0.0227532 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.59795 | 0.0847358 | ||||||||
\(941\) | 22.6523 | 0.738444 | 0.369222 | − | 0.929341i | \(-0.379624\pi\) | ||||
0.369222 | + | 0.929341i | \(0.379624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8380 | 0.418063 | ||||||||
\(944\) | −59.2299 | −1.92777 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.6446 | −0.378599 | ||||||||
\(947\) | 31.5071 | 1.02384 | 0.511922 | − | 0.859032i | \(-0.328934\pi\) | ||||
0.511922 | + | 0.859032i | \(0.328934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.49226 | 0.275670 | ||||||||
\(950\) | −48.7385 | −1.58128 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.51424 | −0.178718 | ||||||||
\(953\) | −39.0222 | −1.26405 | −0.632027 | − | 0.774946i | \(-0.717777\pi\) | ||||
−0.632027 | + | 0.774946i | \(0.717777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.67601 | 0.0865935 | ||||||||
\(956\) | 13.5260 | 0.437462 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.06911 | −0.0345414 | ||||||||
\(959\) | −29.1242 | −0.940470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0885 | −0.389951 | ||||||||
\(962\) | 17.5316 | 0.565241 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.14508 | −0.101296 | ||||||||
\(965\) | −13.1729 | −0.424049 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1623 | 0.712693 | 0.356346 | − | 0.934354i | \(-0.384022\pi\) | ||||
0.356346 | + | 0.934354i | \(0.384022\pi\) | |||||||
\(968\) | 2.39287 | 0.0769098 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.82081 | −0.283219 | ||||||||
\(971\) | −37.9123 | −1.21666 | −0.608331 | − | 0.793683i | \(-0.708161\pi\) | ||||
−0.608331 | + | 0.793683i | \(0.708161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −86.5610 | −2.77502 | ||||||||
\(974\) | 55.0356 | 1.76345 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.73039 | −0.151416 | ||||||||
\(977\) | 3.54195 | 0.113317 | 0.0566584 | − | 0.998394i | \(-0.481955\pi\) | ||||
0.0566584 | + | 0.998394i | \(0.481955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.7280 | −0.438749 | ||||||||
\(980\) | −3.27351 | −0.104568 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.79811 | −0.153114 | ||||||||
\(983\) | −47.1388 | −1.50349 | −0.751747 | − | 0.659452i | \(-0.770789\pi\) | ||||
−0.751747 | + | 0.659452i | \(0.770789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.208147 | 0.00663211 | ||||||||
\(986\) | 5.96268 | 0.189890 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.20254 | −0.229143 | ||||||||
\(989\) | 36.1472 | 1.14941 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.7061 | 1.16601 | 0.583004 | − | 0.812469i | \(-0.301877\pi\) | ||||
0.583004 | + | 0.812469i | \(0.301877\pi\) | |||||||
\(992\) | −11.5886 | −0.367937 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −95.3607 | −3.02466 | ||||||||
\(995\) | 16.2732 | 0.515895 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5336 | −0.903670 | −0.451835 | − | 0.892102i | \(-0.649230\pi\) | ||||
−0.451835 | + | 0.892102i | \(0.649230\pi\) | |||||||
\(998\) | 26.6632 | 0.844010 | ||||||||
\(999\) | 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 | 6039.2.a.d.1.2 | 11 | ||
3.2 | odd | 2 | 2013.2.a.a.1.10 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.a.1.10 | ✓ | 11 | 3.2 | odd | 2 | ||
6039.2.a.d.1.2 | 11 | 1.1 | even | 1 | trivial |