Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.53249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.53249 | 1.46213 | 0.731066 | − | 0.682307i | \(-0.239023\pi\) | ||||
0.731066 | + | 0.682307i | \(0.239023\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.53249 | −1.03388 | ||||||||
\(7\) | −0.583820 | −0.220663 | −0.110332 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110332 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.41349 | 1.13783 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.53249 | 0.731066 | ||||||||
\(13\) | −4.55520 | −1.26338 | −0.631692 | − | 0.775219i | \(-0.717639\pi\) | ||||
−0.631692 | + | 0.775219i | \(0.717639\pi\) | |||||||
\(14\) | 0.583820 | 0.156032 | ||||||||
\(15\) | 2.53249 | 0.653885 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.04549 | 1.22371 | 0.611856 | − | 0.790969i | \(-0.290423\pi\) | ||||
0.611856 | + | 0.790969i | \(0.290423\pi\) | |||||||
\(18\) | −3.41349 | −0.804567 | ||||||||
\(19\) | −4.92944 | −1.13089 | −0.565445 | − | 0.824786i | \(-0.691296\pi\) | ||||
−0.565445 | + | 0.824786i | \(0.691296\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.47852 | −0.322639 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −0.815754 | −0.170096 | −0.0850482 | − | 0.996377i | \(-0.527104\pi\) | ||||
−0.0850482 | + | 0.996377i | \(0.527104\pi\) | |||||||
\(24\) | −2.53249 | −0.516942 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.55520 | 0.893348 | ||||||||
\(27\) | 1.04716 | 0.201526 | ||||||||
\(28\) | −0.583820 | −0.110332 | ||||||||
\(29\) | 7.94882 | 1.47606 | 0.738029 | − | 0.674769i | \(-0.235757\pi\) | ||||
0.738029 | + | 0.674769i | \(0.235757\pi\) | |||||||
\(30\) | −2.53249 | −0.462367 | ||||||||
\(31\) | −2.45826 | −0.441516 | −0.220758 | − | 0.975329i | \(-0.570853\pi\) | ||||
−0.220758 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.53249 | 0.440849 | ||||||||
\(34\) | −5.04549 | −0.865294 | ||||||||
\(35\) | −0.583820 | −0.0986836 | ||||||||
\(36\) | 3.41349 | 0.568915 | ||||||||
\(37\) | 3.39751 | 0.558547 | 0.279274 | − | 0.960212i | \(-0.409906\pi\) | ||||
0.279274 | + | 0.960212i | \(0.409906\pi\) | |||||||
\(38\) | 4.92944 | 0.799660 | ||||||||
\(39\) | −11.5360 | −1.84724 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.9373 | 1.70812 | 0.854059 | − | 0.520177i | \(-0.174134\pi\) | ||||
0.854059 | + | 0.520177i | \(0.174134\pi\) | |||||||
\(42\) | 1.47852 | 0.228140 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 3.41349 | 0.508853 | ||||||||
\(46\) | 0.815754 | 0.120276 | ||||||||
\(47\) | 7.21973 | 1.05311 | 0.526553 | − | 0.850143i | \(-0.323484\pi\) | ||||
0.526553 | + | 0.850143i | \(0.323484\pi\) | |||||||
\(48\) | 2.53249 | 0.365533 | ||||||||
\(49\) | −6.65915 | −0.951308 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 12.7776 | 1.78923 | ||||||||
\(52\) | −4.55520 | −0.631692 | ||||||||
\(53\) | 11.9243 | 1.63793 | 0.818964 | − | 0.573845i | \(-0.194549\pi\) | ||||
0.818964 | + | 0.573845i | \(0.194549\pi\) | |||||||
\(54\) | −1.04716 | −0.142500 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0.583820 | 0.0780162 | ||||||||
\(57\) | −12.4837 | −1.65351 | ||||||||
\(58\) | −7.94882 | −1.04373 | ||||||||
\(59\) | 9.88656 | 1.28712 | 0.643560 | − | 0.765395i | \(-0.277457\pi\) | ||||
0.643560 | + | 0.765395i | \(0.277457\pi\) | |||||||
\(60\) | 2.53249 | 0.326943 | ||||||||
\(61\) | −7.37908 | −0.944794 | −0.472397 | − | 0.881386i | \(-0.656611\pi\) | ||||
−0.472397 | + | 0.881386i | \(0.656611\pi\) | |||||||
\(62\) | 2.45826 | 0.312199 | ||||||||
\(63\) | −1.99286 | −0.251077 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.55520 | −0.565003 | ||||||||
\(66\) | −2.53249 | −0.311728 | ||||||||
\(67\) | 9.44673 | 1.15410 | 0.577051 | − | 0.816708i | \(-0.304203\pi\) | ||||
0.577051 | + | 0.816708i | \(0.304203\pi\) | |||||||
\(68\) | 5.04549 | 0.611856 | ||||||||
\(69\) | −2.06589 | −0.248703 | ||||||||
\(70\) | 0.583820 | 0.0697799 | ||||||||
\(71\) | 11.2834 | 1.33909 | 0.669547 | − | 0.742770i | \(-0.266488\pi\) | ||||
0.669547 | + | 0.742770i | \(0.266488\pi\) | |||||||
\(72\) | −3.41349 | −0.402284 | ||||||||
\(73\) | −1.95228 | −0.228497 | −0.114249 | − | 0.993452i | \(-0.536446\pi\) | ||||
−0.114249 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(74\) | −3.39751 | −0.394952 | ||||||||
\(75\) | 2.53249 | 0.292426 | ||||||||
\(76\) | −4.92944 | −0.565445 | ||||||||
\(77\) | −0.583820 | −0.0665325 | ||||||||
\(78\) | 11.5360 | 1.30619 | ||||||||
\(79\) | 16.0023 | 1.80040 | 0.900200 | − | 0.435476i | \(-0.143420\pi\) | ||||
0.900200 | + | 0.435476i | \(0.143420\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.58855 | −0.843173 | ||||||||
\(82\) | −10.9373 | −1.20782 | ||||||||
\(83\) | 0.0176475 | 0.00193706 | 0.000968530 | − | 1.00000i | \(-0.499692\pi\) | ||||
0.000968530 | 1.00000i | \(0.499692\pi\) | ||||||||
\(84\) | −1.47852 | −0.161319 | ||||||||
\(85\) | 5.04549 | 0.547260 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 20.1303 | 2.15819 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −4.04716 | −0.428998 | −0.214499 | − | 0.976724i | \(-0.568812\pi\) | ||||
−0.214499 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(90\) | −3.41349 | −0.359813 | ||||||||
\(91\) | 2.65942 | 0.278783 | ||||||||
\(92\) | −0.815754 | −0.0850482 | ||||||||
\(93\) | −6.22551 | −0.645555 | ||||||||
\(94\) | −7.21973 | −0.744658 | ||||||||
\(95\) | −4.92944 | −0.505750 | ||||||||
\(96\) | −2.53249 | −0.258471 | ||||||||
\(97\) | 3.09439 | 0.314188 | 0.157094 | − | 0.987584i | \(-0.449787\pi\) | ||||
0.157094 | + | 0.987584i | \(0.449787\pi\) | |||||||
\(98\) | 6.65915 | 0.672676 | ||||||||
\(99\) | 3.41349 | 0.343069 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.2277 | −1.61472 | −0.807360 | − | 0.590060i | \(-0.799104\pi\) | ||||
−0.807360 | + | 0.590060i | \(0.799104\pi\) | |||||||
\(102\) | −12.7776 | −1.26517 | ||||||||
\(103\) | 15.8775 | 1.56445 | 0.782227 | − | 0.622994i | \(-0.214084\pi\) | ||||
0.782227 | + | 0.622994i | \(0.214084\pi\) | |||||||
\(104\) | 4.55520 | 0.446674 | ||||||||
\(105\) | −1.47852 | −0.144288 | ||||||||
\(106\) | −11.9243 | −1.15819 | ||||||||
\(107\) | 1.99047 | 0.192426 | 0.0962129 | − | 0.995361i | \(-0.469327\pi\) | ||||
0.0962129 | + | 0.995361i | \(0.469327\pi\) | |||||||
\(108\) | 1.04716 | 0.100763 | ||||||||
\(109\) | 5.94794 | 0.569710 | 0.284855 | − | 0.958571i | \(-0.408055\pi\) | ||||
0.284855 | + | 0.958571i | \(0.408055\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 8.60415 | 0.816670 | ||||||||
\(112\) | −0.583820 | −0.0551658 | ||||||||
\(113\) | 1.56740 | 0.147448 | 0.0737241 | − | 0.997279i | \(-0.476512\pi\) | ||||
0.0737241 | + | 0.997279i | \(0.476512\pi\) | |||||||
\(114\) | 12.4837 | 1.16921 | ||||||||
\(115\) | −0.815754 | −0.0760694 | ||||||||
\(116\) | 7.94882 | 0.738029 | ||||||||
\(117\) | −15.5491 | −1.43752 | ||||||||
\(118\) | −9.88656 | −0.910132 | ||||||||
\(119\) | −2.94566 | −0.270028 | ||||||||
\(120\) | −2.53249 | −0.231183 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.37908 | 0.668070 | ||||||||
\(123\) | 27.6985 | 2.49749 | ||||||||
\(124\) | −2.45826 | −0.220758 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.99286 | 0.177538 | ||||||||
\(127\) | −14.2359 | −1.26323 | −0.631616 | − | 0.775281i | \(-0.717608\pi\) | ||||
−0.631616 | + | 0.775281i | \(0.717608\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.53249 | 0.222973 | ||||||||
\(130\) | 4.55520 | 0.399517 | ||||||||
\(131\) | −9.61130 | −0.839743 | −0.419871 | − | 0.907584i | \(-0.637925\pi\) | ||||
−0.419871 | + | 0.907584i | \(0.637925\pi\) | |||||||
\(132\) | 2.53249 | 0.220425 | ||||||||
\(133\) | 2.87790 | 0.249546 | ||||||||
\(134\) | −9.44673 | −0.816073 | ||||||||
\(135\) | 1.04716 | 0.0901251 | ||||||||
\(136\) | −5.04549 | −0.432647 | ||||||||
\(137\) | 14.6263 | 1.24961 | 0.624803 | − | 0.780782i | \(-0.285179\pi\) | ||||
0.624803 | + | 0.780782i | \(0.285179\pi\) | |||||||
\(138\) | 2.06589 | 0.175860 | ||||||||
\(139\) | 11.7412 | 0.995879 | 0.497939 | − | 0.867212i | \(-0.334090\pi\) | ||||
0.497939 | + | 0.867212i | \(0.334090\pi\) | |||||||
\(140\) | −0.583820 | −0.0493418 | ||||||||
\(141\) | 18.2839 | 1.53978 | ||||||||
\(142\) | −11.2834 | −0.946882 | ||||||||
\(143\) | −4.55520 | −0.380925 | ||||||||
\(144\) | 3.41349 | 0.284458 | ||||||||
\(145\) | 7.94882 | 0.660113 | ||||||||
\(146\) | 1.95228 | 0.161572 | ||||||||
\(147\) | −16.8642 | −1.39094 | ||||||||
\(148\) | 3.39751 | 0.279274 | ||||||||
\(149\) | −23.6217 | −1.93516 | −0.967581 | − | 0.252560i | \(-0.918728\pi\) | ||||
−0.967581 | + | 0.252560i | \(0.918728\pi\) | |||||||
\(150\) | −2.53249 | −0.206777 | ||||||||
\(151\) | −5.02949 | −0.409294 | −0.204647 | − | 0.978836i | \(-0.565605\pi\) | ||||
−0.204647 | + | 0.978836i | \(0.565605\pi\) | |||||||
\(152\) | 4.92944 | 0.399830 | ||||||||
\(153\) | 17.2227 | 1.39238 | ||||||||
\(154\) | 0.583820 | 0.0470456 | ||||||||
\(155\) | −2.45826 | −0.197452 | ||||||||
\(156\) | −11.5360 | −0.923618 | ||||||||
\(157\) | −14.0823 | −1.12389 | −0.561943 | − | 0.827176i | \(-0.689946\pi\) | ||||
−0.561943 | + | 0.827176i | \(0.689946\pi\) | |||||||
\(158\) | −16.0023 | −1.27308 | ||||||||
\(159\) | 30.1981 | 2.39487 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.476254 | 0.0375340 | ||||||||
\(162\) | 7.58855 | 0.596213 | ||||||||
\(163\) | 18.3786 | 1.43952 | 0.719760 | − | 0.694223i | \(-0.244252\pi\) | ||||
0.719760 | + | 0.694223i | \(0.244252\pi\) | |||||||
\(164\) | 10.9373 | 0.854059 | ||||||||
\(165\) | 2.53249 | 0.197154 | ||||||||
\(166\) | −0.0176475 | −0.00136971 | ||||||||
\(167\) | −4.93771 | −0.382091 | −0.191046 | − | 0.981581i | \(-0.561188\pi\) | ||||
−0.191046 | + | 0.981581i | \(0.561188\pi\) | |||||||
\(168\) | 1.47852 | 0.114070 | ||||||||
\(169\) | 7.74983 | 0.596141 | ||||||||
\(170\) | −5.04549 | −0.386971 | ||||||||
\(171\) | −16.8266 | −1.28676 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 4.02612 | 0.306100 | 0.153050 | − | 0.988218i | \(-0.451090\pi\) | ||||
0.153050 | + | 0.988218i | \(0.451090\pi\) | |||||||
\(174\) | −20.1303 | −1.52607 | ||||||||
\(175\) | −0.583820 | −0.0441327 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 25.0376 | 1.88194 | ||||||||
\(178\) | 4.04716 | 0.303347 | ||||||||
\(179\) | 22.7886 | 1.70330 | 0.851649 | − | 0.524112i | \(-0.175603\pi\) | ||||
0.851649 | + | 0.524112i | \(0.175603\pi\) | |||||||
\(180\) | 3.41349 | 0.254427 | ||||||||
\(181\) | 14.6773 | 1.09095 | 0.545477 | − | 0.838126i | \(-0.316348\pi\) | ||||
0.545477 | + | 0.838126i | \(0.316348\pi\) | |||||||
\(182\) | −2.65942 | −0.197129 | ||||||||
\(183\) | −18.6874 | −1.38141 | ||||||||
\(184\) | 0.815754 | 0.0601382 | ||||||||
\(185\) | 3.39751 | 0.249790 | ||||||||
\(186\) | 6.22551 | 0.456477 | ||||||||
\(187\) | 5.04549 | 0.368963 | ||||||||
\(188\) | 7.21973 | 0.526553 | ||||||||
\(189\) | −0.611352 | −0.0444693 | ||||||||
\(190\) | 4.92944 | 0.357619 | ||||||||
\(191\) | −15.6918 | −1.13542 | −0.567708 | − | 0.823230i | \(-0.692170\pi\) | ||||
−0.567708 | + | 0.823230i | \(0.692170\pi\) | |||||||
\(192\) | 2.53249 | 0.182767 | ||||||||
\(193\) | 16.6265 | 1.19680 | 0.598400 | − | 0.801197i | \(-0.295803\pi\) | ||||
0.598400 | + | 0.801197i | \(0.295803\pi\) | |||||||
\(194\) | −3.09439 | −0.222164 | ||||||||
\(195\) | −11.5360 | −0.826109 | ||||||||
\(196\) | −6.65915 | −0.475654 | ||||||||
\(197\) | −17.0689 | −1.21611 | −0.608056 | − | 0.793894i | \(-0.708050\pi\) | ||||
−0.608056 | + | 0.793894i | \(0.708050\pi\) | |||||||
\(198\) | −3.41349 | −0.242586 | ||||||||
\(199\) | 2.64964 | 0.187828 | 0.0939142 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939142 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 23.9237 | 1.68745 | ||||||||
\(202\) | 16.2277 | 1.14178 | ||||||||
\(203\) | −4.64068 | −0.325712 | ||||||||
\(204\) | 12.7776 | 0.894614 | ||||||||
\(205\) | 10.9373 | 0.763893 | ||||||||
\(206\) | −15.8775 | −1.10624 | ||||||||
\(207\) | −2.78457 | −0.193541 | ||||||||
\(208\) | −4.55520 | −0.315846 | ||||||||
\(209\) | −4.92944 | −0.340976 | ||||||||
\(210\) | 1.47852 | 0.102027 | ||||||||
\(211\) | −12.3084 | −0.847344 | −0.423672 | − | 0.905816i | \(-0.639259\pi\) | ||||
−0.423672 | + | 0.905816i | \(0.639259\pi\) | |||||||
\(212\) | 11.9243 | 0.818964 | ||||||||
\(213\) | 28.5751 | 1.95793 | ||||||||
\(214\) | −1.99047 | −0.136066 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | −1.04716 | −0.0712501 | ||||||||
\(217\) | 1.43518 | 0.0974265 | ||||||||
\(218\) | −5.94794 | −0.402846 | ||||||||
\(219\) | −4.94413 | −0.334093 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −22.9832 | −1.54602 | ||||||||
\(222\) | −8.60415 | −0.577473 | ||||||||
\(223\) | −20.1134 | −1.34690 | −0.673448 | − | 0.739235i | \(-0.735187\pi\) | ||||
−0.673448 | + | 0.739235i | \(0.735187\pi\) | |||||||
\(224\) | 0.583820 | 0.0390081 | ||||||||
\(225\) | 3.41349 | 0.227566 | ||||||||
\(226\) | −1.56740 | −0.104262 | ||||||||
\(227\) | −7.14194 | −0.474027 | −0.237014 | − | 0.971506i | \(-0.576169\pi\) | ||||
−0.237014 | + | 0.971506i | \(0.576169\pi\) | |||||||
\(228\) | −12.4837 | −0.826756 | ||||||||
\(229\) | −8.41493 | −0.556074 | −0.278037 | − | 0.960570i | \(-0.589684\pi\) | ||||
−0.278037 | + | 0.960570i | \(0.589684\pi\) | |||||||
\(230\) | 0.815754 | 0.0537892 | ||||||||
\(231\) | −1.47852 | −0.0972793 | ||||||||
\(232\) | −7.94882 | −0.521865 | ||||||||
\(233\) | −26.0543 | −1.70687 | −0.853437 | − | 0.521196i | \(-0.825486\pi\) | ||||
−0.853437 | + | 0.521196i | \(0.825486\pi\) | |||||||
\(234\) | 15.5491 | 1.01648 | ||||||||
\(235\) | 7.21973 | 0.470963 | ||||||||
\(236\) | 9.88656 | 0.643560 | ||||||||
\(237\) | 40.5256 | 2.63242 | ||||||||
\(238\) | 2.94566 | 0.190939 | ||||||||
\(239\) | 17.1905 | 1.11196 | 0.555980 | − | 0.831195i | \(-0.312343\pi\) | ||||
0.555980 | + | 0.831195i | \(0.312343\pi\) | |||||||
\(240\) | 2.53249 | 0.163471 | ||||||||
\(241\) | −26.0696 | −1.67929 | −0.839644 | − | 0.543137i | \(-0.817236\pi\) | ||||
−0.839644 | + | 0.543137i | \(0.817236\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −22.3594 | −1.43436 | ||||||||
\(244\) | −7.37908 | −0.472397 | ||||||||
\(245\) | −6.65915 | −0.425438 | ||||||||
\(246\) | −27.6985 | −1.76599 | ||||||||
\(247\) | 22.4546 | 1.42875 | ||||||||
\(248\) | 2.45826 | 0.156100 | ||||||||
\(249\) | 0.0446920 | 0.00283224 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −19.8815 | −1.25491 | −0.627454 | − | 0.778654i | \(-0.715903\pi\) | ||||
−0.627454 | + | 0.778654i | \(0.715903\pi\) | |||||||
\(252\) | −1.99286 | −0.125539 | ||||||||
\(253\) | −0.815754 | −0.0512860 | ||||||||
\(254\) | 14.2359 | 0.893240 | ||||||||
\(255\) | 12.7776 | 0.800167 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.58725 | 0.598036 | 0.299018 | − | 0.954247i | \(-0.403341\pi\) | ||||
0.299018 | + | 0.954247i | \(0.403341\pi\) | |||||||
\(258\) | −2.53249 | −0.157666 | ||||||||
\(259\) | −1.98353 | −0.123251 | ||||||||
\(260\) | −4.55520 | −0.282501 | ||||||||
\(261\) | 27.1332 | 1.67950 | ||||||||
\(262\) | 9.61130 | 0.593788 | ||||||||
\(263\) | −1.68571 | −0.103946 | −0.0519728 | − | 0.998649i | \(-0.516551\pi\) | ||||
−0.0519728 | + | 0.998649i | \(0.516551\pi\) | |||||||
\(264\) | −2.53249 | −0.155864 | ||||||||
\(265\) | 11.9243 | 0.732504 | ||||||||
\(266\) | −2.87790 | −0.176456 | ||||||||
\(267\) | −10.2494 | −0.627252 | ||||||||
\(268\) | 9.44673 | 0.577051 | ||||||||
\(269\) | 1.64644 | 0.100385 | 0.0501927 | − | 0.998740i | \(-0.484016\pi\) | ||||
0.0501927 | + | 0.998740i | \(0.484016\pi\) | |||||||
\(270\) | −1.04716 | −0.0637281 | ||||||||
\(271\) | −2.11722 | −0.128612 | −0.0643060 | − | 0.997930i | \(-0.520483\pi\) | ||||
−0.0643060 | + | 0.997930i | \(0.520483\pi\) | |||||||
\(272\) | 5.04549 | 0.305928 | ||||||||
\(273\) | 6.73494 | 0.407617 | ||||||||
\(274\) | −14.6263 | −0.883605 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −2.06589 | −0.124352 | ||||||||
\(277\) | 11.7728 | 0.707357 | 0.353678 | − | 0.935367i | \(-0.384931\pi\) | ||||
0.353678 | + | 0.935367i | \(0.384931\pi\) | |||||||
\(278\) | −11.7412 | −0.704193 | ||||||||
\(279\) | −8.39125 | −0.502371 | ||||||||
\(280\) | 0.583820 | 0.0348899 | ||||||||
\(281\) | 6.18333 | 0.368867 | 0.184433 | − | 0.982845i | \(-0.440955\pi\) | ||||
0.184433 | + | 0.982845i | \(0.440955\pi\) | |||||||
\(282\) | −18.2839 | −1.08879 | ||||||||
\(283\) | −29.0060 | −1.72422 | −0.862112 | − | 0.506717i | \(-0.830859\pi\) | ||||
−0.862112 | + | 0.506717i | \(0.830859\pi\) | |||||||
\(284\) | 11.2834 | 0.669547 | ||||||||
\(285\) | −12.4837 | −0.739473 | ||||||||
\(286\) | 4.55520 | 0.269355 | ||||||||
\(287\) | −6.38541 | −0.376919 | ||||||||
\(288\) | −3.41349 | −0.201142 | ||||||||
\(289\) | 8.45697 | 0.497469 | ||||||||
\(290\) | −7.94882 | −0.466771 | ||||||||
\(291\) | 7.83651 | 0.459384 | ||||||||
\(292\) | −1.95228 | −0.114249 | ||||||||
\(293\) | 31.7771 | 1.85644 | 0.928220 | − | 0.372033i | \(-0.121339\pi\) | ||||
0.928220 | + | 0.372033i | \(0.121339\pi\) | |||||||
\(294\) | 16.8642 | 0.983541 | ||||||||
\(295\) | 9.88656 | 0.575618 | ||||||||
\(296\) | −3.39751 | −0.197476 | ||||||||
\(297\) | 1.04716 | 0.0607623 | ||||||||
\(298\) | 23.6217 | 1.36837 | ||||||||
\(299\) | 3.71592 | 0.214897 | ||||||||
\(300\) | 2.53249 | 0.146213 | ||||||||
\(301\) | −0.583820 | −0.0336508 | ||||||||
\(302\) | 5.02949 | 0.289415 | ||||||||
\(303\) | −41.0965 | −2.36093 | ||||||||
\(304\) | −4.92944 | −0.282723 | ||||||||
\(305\) | −7.37908 | −0.422525 | ||||||||
\(306\) | −17.2227 | −0.984558 | ||||||||
\(307\) | 29.9260 | 1.70797 | 0.853984 | − | 0.520299i | \(-0.174180\pi\) | ||||
0.853984 | + | 0.520299i | \(0.174180\pi\) | |||||||
\(308\) | −0.583820 | −0.0332662 | ||||||||
\(309\) | 40.2095 | 2.28744 | ||||||||
\(310\) | 2.45826 | 0.139620 | ||||||||
\(311\) | −33.8063 | −1.91698 | −0.958490 | − | 0.285127i | \(-0.907964\pi\) | ||||
−0.958490 | + | 0.285127i | \(0.907964\pi\) | |||||||
\(312\) | 11.5360 | 0.653096 | ||||||||
\(313\) | −10.0501 | −0.568065 | −0.284032 | − | 0.958815i | \(-0.591672\pi\) | ||||
−0.284032 | + | 0.958815i | \(0.591672\pi\) | |||||||
\(314\) | 14.0823 | 0.794708 | ||||||||
\(315\) | −1.99286 | −0.112285 | ||||||||
\(316\) | 16.0023 | 0.900200 | ||||||||
\(317\) | −5.78777 | −0.325074 | −0.162537 | − | 0.986702i | \(-0.551968\pi\) | ||||
−0.162537 | + | 0.986702i | \(0.551968\pi\) | |||||||
\(318\) | −30.1981 | −1.69343 | ||||||||
\(319\) | 7.94882 | 0.445048 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 5.04083 | 0.281352 | ||||||||
\(322\) | −0.476254 | −0.0265406 | ||||||||
\(323\) | −24.8714 | −1.38388 | ||||||||
\(324\) | −7.58855 | −0.421586 | ||||||||
\(325\) | −4.55520 | −0.252677 | ||||||||
\(326\) | −18.3786 | −1.01789 | ||||||||
\(327\) | 15.0631 | 0.832991 | ||||||||
\(328\) | −10.9373 | −0.603911 | ||||||||
\(329\) | −4.21502 | −0.232382 | ||||||||
\(330\) | −2.53249 | −0.139409 | ||||||||
\(331\) | −2.60786 | −0.143341 | −0.0716704 | − | 0.997428i | \(-0.522833\pi\) | ||||
−0.0716704 | + | 0.997428i | \(0.522833\pi\) | |||||||
\(332\) | 0.0176475 | 0.000968530 0 | ||||||||
\(333\) | 11.5974 | 0.635532 | ||||||||
\(334\) | 4.93771 | 0.270179 | ||||||||
\(335\) | 9.44673 | 0.516130 | ||||||||
\(336\) | −1.47852 | −0.0806597 | ||||||||
\(337\) | −3.61378 | −0.196855 | −0.0984277 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984277 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(338\) | −7.74983 | −0.421535 | ||||||||
\(339\) | 3.96941 | 0.215589 | ||||||||
\(340\) | 5.04549 | 0.273630 | ||||||||
\(341\) | −2.45826 | −0.133122 | ||||||||
\(342\) | 16.8266 | 0.909878 | ||||||||
\(343\) | 7.97449 | 0.430582 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | −2.06589 | −0.111224 | ||||||||
\(346\) | −4.02612 | −0.216445 | ||||||||
\(347\) | −16.2439 | −0.872016 | −0.436008 | − | 0.899943i | \(-0.643608\pi\) | ||||
−0.436008 | + | 0.899943i | \(0.643608\pi\) | |||||||
\(348\) | 20.1303 | 1.07910 | ||||||||
\(349\) | −36.5970 | −1.95899 | −0.979495 | − | 0.201468i | \(-0.935429\pi\) | ||||
−0.979495 | + | 0.201468i | \(0.935429\pi\) | |||||||
\(350\) | 0.583820 | 0.0312065 | ||||||||
\(351\) | −4.77002 | −0.254605 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −3.60517 | −0.191884 | −0.0959419 | − | 0.995387i | \(-0.530586\pi\) | ||||
−0.0959419 | + | 0.995387i | \(0.530586\pi\) | |||||||
\(354\) | −25.0376 | −1.33073 | ||||||||
\(355\) | 11.2834 | 0.598861 | ||||||||
\(356\) | −4.04716 | −0.214499 | ||||||||
\(357\) | −7.45984 | −0.394817 | ||||||||
\(358\) | −22.7886 | −1.20441 | ||||||||
\(359\) | −0.996118 | −0.0525731 | −0.0262865 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262865 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(360\) | −3.41349 | −0.179907 | ||||||||
\(361\) | 5.29936 | 0.278913 | ||||||||
\(362\) | −14.6773 | −0.771421 | ||||||||
\(363\) | 2.53249 | 0.132921 | ||||||||
\(364\) | 2.65942 | 0.139391 | ||||||||
\(365\) | −1.95228 | −0.102187 | ||||||||
\(366\) | 18.6874 | 0.976807 | ||||||||
\(367\) | −1.64638 | −0.0859402 | −0.0429701 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429701 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(368\) | −0.815754 | −0.0425241 | ||||||||
\(369\) | 37.3343 | 1.94355 | ||||||||
\(370\) | −3.39751 | −0.176628 | ||||||||
\(371\) | −6.96164 | −0.361431 | ||||||||
\(372\) | −6.22551 | −0.322778 | ||||||||
\(373\) | −14.5695 | −0.754381 | −0.377190 | − | 0.926136i | \(-0.623110\pi\) | ||||
−0.377190 | + | 0.926136i | \(0.623110\pi\) | |||||||
\(374\) | −5.04549 | −0.260896 | ||||||||
\(375\) | 2.53249 | 0.130777 | ||||||||
\(376\) | −7.21973 | −0.372329 | ||||||||
\(377\) | −36.2084 | −1.86483 | ||||||||
\(378\) | 0.611352 | 0.0314446 | ||||||||
\(379\) | 17.4192 | 0.894765 | 0.447383 | − | 0.894343i | \(-0.352356\pi\) | ||||
0.447383 | + | 0.894343i | \(0.352356\pi\) | |||||||
\(380\) | −4.92944 | −0.252875 | ||||||||
\(381\) | −36.0523 | −1.84701 | ||||||||
\(382\) | 15.6918 | 0.802861 | ||||||||
\(383\) | −30.5126 | −1.55912 | −0.779559 | − | 0.626328i | \(-0.784557\pi\) | ||||
−0.779559 | + | 0.626328i | \(0.784557\pi\) | |||||||
\(384\) | −2.53249 | −0.129235 | ||||||||
\(385\) | −0.583820 | −0.0297542 | ||||||||
\(386\) | −16.6265 | −0.846266 | ||||||||
\(387\) | 3.41349 | 0.173517 | ||||||||
\(388\) | 3.09439 | 0.157094 | ||||||||
\(389\) | 16.1307 | 0.817858 | 0.408929 | − | 0.912566i | \(-0.365902\pi\) | ||||
0.408929 | + | 0.912566i | \(0.365902\pi\) | |||||||
\(390\) | 11.5360 | 0.584147 | ||||||||
\(391\) | −4.11588 | −0.208149 | ||||||||
\(392\) | 6.65915 | 0.336338 | ||||||||
\(393\) | −24.3405 | −1.22782 | ||||||||
\(394\) | 17.0689 | 0.859920 | ||||||||
\(395\) | 16.0023 | 0.805163 | ||||||||
\(396\) | 3.41349 | 0.171534 | ||||||||
\(397\) | −20.6024 | −1.03401 | −0.517003 | − | 0.855983i | \(-0.672952\pi\) | ||||
−0.517003 | + | 0.855983i | \(0.672952\pi\) | |||||||
\(398\) | −2.64964 | −0.132815 | ||||||||
\(399\) | 7.28826 | 0.364869 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.69504 | 0.384272 | 0.192136 | − | 0.981368i | \(-0.438459\pi\) | ||||
0.192136 | + | 0.981368i | \(0.438459\pi\) | |||||||
\(402\) | −23.9237 | −1.19321 | ||||||||
\(403\) | 11.1979 | 0.557805 | ||||||||
\(404\) | −16.2277 | −0.807360 | ||||||||
\(405\) | −7.58855 | −0.377078 | ||||||||
\(406\) | 4.64068 | 0.230313 | ||||||||
\(407\) | 3.39751 | 0.168408 | ||||||||
\(408\) | −12.7776 | −0.632587 | ||||||||
\(409\) | −35.5918 | −1.75990 | −0.879950 | − | 0.475066i | \(-0.842424\pi\) | ||||
−0.879950 | + | 0.475066i | \(0.842424\pi\) | |||||||
\(410\) | −10.9373 | −0.540154 | ||||||||
\(411\) | 37.0408 | 1.82709 | ||||||||
\(412\) | 15.8775 | 0.782227 | ||||||||
\(413\) | −5.77197 | −0.284020 | ||||||||
\(414\) | 2.78457 | 0.136854 | ||||||||
\(415\) | 0.0176475 | 0.000866280 0 | ||||||||
\(416\) | 4.55520 | 0.223337 | ||||||||
\(417\) | 29.7345 | 1.45611 | ||||||||
\(418\) | 4.92944 | 0.241107 | ||||||||
\(419\) | 23.2886 | 1.13772 | 0.568861 | − | 0.822434i | \(-0.307384\pi\) | ||||
0.568861 | + | 0.822434i | \(0.307384\pi\) | |||||||
\(420\) | −1.47852 | −0.0721442 | ||||||||
\(421\) | −27.6647 | −1.34830 | −0.674148 | − | 0.738596i | \(-0.735489\pi\) | ||||
−0.674148 | + | 0.738596i | \(0.735489\pi\) | |||||||
\(422\) | 12.3084 | 0.599163 | ||||||||
\(423\) | 24.6445 | 1.19825 | ||||||||
\(424\) | −11.9243 | −0.579095 | ||||||||
\(425\) | 5.04549 | 0.244742 | ||||||||
\(426\) | −28.5751 | −1.38447 | ||||||||
\(427\) | 4.30805 | 0.208481 | ||||||||
\(428\) | 1.99047 | 0.0962129 | ||||||||
\(429\) | −11.5360 | −0.556962 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | −31.7418 | −1.52895 | −0.764473 | − | 0.644656i | \(-0.777001\pi\) | ||||
−0.764473 | + | 0.644656i | \(0.777001\pi\) | |||||||
\(432\) | 1.04716 | 0.0503815 | ||||||||
\(433\) | −3.14451 | −0.151116 | −0.0755579 | − | 0.997141i | \(-0.524074\pi\) | ||||
−0.0755579 | + | 0.997141i | \(0.524074\pi\) | |||||||
\(434\) | −1.43518 | −0.0688909 | ||||||||
\(435\) | 20.1303 | 0.965173 | ||||||||
\(436\) | 5.94794 | 0.284855 | ||||||||
\(437\) | 4.02121 | 0.192360 | ||||||||
\(438\) | 4.94413 | 0.236240 | ||||||||
\(439\) | −1.21375 | −0.0579292 | −0.0289646 | − | 0.999580i | \(-0.509221\pi\) | ||||
−0.0289646 | + | 0.999580i | \(0.509221\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −22.7310 | −1.08243 | ||||||||
\(442\) | 22.9832 | 1.09320 | ||||||||
\(443\) | 14.3917 | 0.683771 | 0.341886 | − | 0.939742i | \(-0.388934\pi\) | ||||
0.341886 | + | 0.939742i | \(0.388934\pi\) | |||||||
\(444\) | 8.60415 | 0.408335 | ||||||||
\(445\) | −4.04716 | −0.191854 | ||||||||
\(446\) | 20.1134 | 0.952399 | ||||||||
\(447\) | −59.8216 | −2.82946 | ||||||||
\(448\) | −0.583820 | −0.0275829 | ||||||||
\(449\) | 37.0597 | 1.74896 | 0.874478 | − | 0.485065i | \(-0.161204\pi\) | ||||
0.874478 | + | 0.485065i | \(0.161204\pi\) | |||||||
\(450\) | −3.41349 | −0.160913 | ||||||||
\(451\) | 10.9373 | 0.515017 | ||||||||
\(452\) | 1.56740 | 0.0737241 | ||||||||
\(453\) | −12.7371 | −0.598442 | ||||||||
\(454\) | 7.14194 | 0.335188 | ||||||||
\(455\) | 2.65942 | 0.124675 | ||||||||
\(456\) | 12.4837 | 0.584605 | ||||||||
\(457\) | 26.5804 | 1.24338 | 0.621690 | − | 0.783263i | \(-0.286446\pi\) | ||||
0.621690 | + | 0.783263i | \(0.286446\pi\) | |||||||
\(458\) | 8.41493 | 0.393204 | ||||||||
\(459\) | 5.28343 | 0.246609 | ||||||||
\(460\) | −0.815754 | −0.0380347 | ||||||||
\(461\) | 20.9312 | 0.974865 | 0.487433 | − | 0.873161i | \(-0.337933\pi\) | ||||
0.487433 | + | 0.873161i | \(0.337933\pi\) | |||||||
\(462\) | 1.47852 | 0.0687868 | ||||||||
\(463\) | −15.7816 | −0.733434 | −0.366717 | − | 0.930333i | \(-0.619518\pi\) | ||||
−0.366717 | + | 0.930333i | \(0.619518\pi\) | |||||||
\(464\) | 7.94882 | 0.369015 | ||||||||
\(465\) | −6.22551 | −0.288701 | ||||||||
\(466\) | 26.0543 | 1.20694 | ||||||||
\(467\) | −14.4659 | −0.669400 | −0.334700 | − | 0.942325i | \(-0.608635\pi\) | ||||
−0.334700 | + | 0.942325i | \(0.608635\pi\) | |||||||
\(468\) | −15.5491 | −0.718759 | ||||||||
\(469\) | −5.51519 | −0.254668 | ||||||||
\(470\) | −7.21973 | −0.333021 | ||||||||
\(471\) | −35.6631 | −1.64327 | ||||||||
\(472\) | −9.88656 | −0.455066 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −40.5256 | −1.86140 | ||||||||
\(475\) | −4.92944 | −0.226178 | ||||||||
\(476\) | −2.94566 | −0.135014 | ||||||||
\(477\) | 40.7035 | 1.86368 | ||||||||
\(478\) | −17.1905 | −0.786275 | ||||||||
\(479\) | 0.630533 | 0.0288098 | 0.0144049 | − | 0.999896i | \(-0.495415\pi\) | ||||
0.0144049 | + | 0.999896i | \(0.495415\pi\) | |||||||
\(480\) | −2.53249 | −0.115592 | ||||||||
\(481\) | −15.4763 | −0.705660 | ||||||||
\(482\) | 26.0696 | 1.18744 | ||||||||
\(483\) | 1.20611 | 0.0548797 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.09439 | 0.140509 | ||||||||
\(486\) | 22.3594 | 1.01424 | ||||||||
\(487\) | −26.5453 | −1.20288 | −0.601442 | − | 0.798916i | \(-0.705407\pi\) | ||||
−0.601442 | + | 0.798916i | \(0.705407\pi\) | |||||||
\(488\) | 7.37908 | 0.334035 | ||||||||
\(489\) | 46.5435 | 2.10477 | ||||||||
\(490\) | 6.65915 | 0.300830 | ||||||||
\(491\) | 11.5756 | 0.522401 | 0.261200 | − | 0.965285i | \(-0.415882\pi\) | ||||
0.261200 | + | 0.965285i | \(0.415882\pi\) | |||||||
\(492\) | 27.6985 | 1.24875 | ||||||||
\(493\) | 40.1057 | 1.80627 | ||||||||
\(494\) | −22.4546 | −1.01028 | ||||||||
\(495\) | 3.41349 | 0.153425 | ||||||||
\(496\) | −2.45826 | −0.110379 | ||||||||
\(497\) | −6.58748 | −0.295489 | ||||||||
\(498\) | −0.0446920 | −0.00200269 | ||||||||
\(499\) | 38.0328 | 1.70258 | 0.851291 | − | 0.524693i | \(-0.175820\pi\) | ||||
0.851291 | + | 0.524693i | \(0.175820\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.5047 | −0.558668 | ||||||||
\(502\) | 19.8815 | 0.887354 | ||||||||
\(503\) | 14.6478 | 0.653112 | 0.326556 | − | 0.945178i | \(-0.394112\pi\) | ||||
0.326556 | + | 0.945178i | \(0.394112\pi\) | |||||||
\(504\) | 1.99286 | 0.0887692 | ||||||||
\(505\) | −16.2277 | −0.722124 | ||||||||
\(506\) | 0.815754 | 0.0362647 | ||||||||
\(507\) | 19.6264 | 0.871637 | ||||||||
\(508\) | −14.2359 | −0.631616 | ||||||||
\(509\) | 22.6830 | 1.00541 | 0.502703 | − | 0.864459i | \(-0.332339\pi\) | ||||
0.502703 | + | 0.864459i | \(0.332339\pi\) | |||||||
\(510\) | −12.7776 | −0.565803 | ||||||||
\(511\) | 1.13978 | 0.0504210 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.16190 | −0.227904 | ||||||||
\(514\) | −9.58725 | −0.422876 | ||||||||
\(515\) | 15.8775 | 0.699645 | ||||||||
\(516\) | 2.53249 | 0.111487 | ||||||||
\(517\) | 7.21973 | 0.317523 | ||||||||
\(518\) | 1.98353 | 0.0871515 | ||||||||
\(519\) | 10.1961 | 0.447559 | ||||||||
\(520\) | 4.55520 | 0.199759 | ||||||||
\(521\) | 6.33354 | 0.277478 | 0.138739 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138739 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(522\) | −27.1332 | −1.18759 | ||||||||
\(523\) | 35.8448 | 1.56738 | 0.783691 | − | 0.621151i | \(-0.213335\pi\) | ||||
0.783691 | + | 0.621151i | \(0.213335\pi\) | |||||||
\(524\) | −9.61130 | −0.419871 | ||||||||
\(525\) | −1.47852 | −0.0645278 | ||||||||
\(526\) | 1.68571 | 0.0735007 | ||||||||
\(527\) | −12.4031 | −0.540289 | ||||||||
\(528\) | 2.53249 | 0.110212 | ||||||||
\(529\) | −22.3345 | −0.971067 | ||||||||
\(530\) | −11.9243 | −0.517958 | ||||||||
\(531\) | 33.7477 | 1.46452 | ||||||||
\(532\) | 2.87790 | 0.124773 | ||||||||
\(533\) | −49.8215 | −2.15801 | ||||||||
\(534\) | 10.2494 | 0.443534 | ||||||||
\(535\) | 1.99047 | 0.0860554 | ||||||||
\(536\) | −9.44673 | −0.408037 | ||||||||
\(537\) | 57.7118 | 2.49045 | ||||||||
\(538\) | −1.64644 | −0.0709832 | ||||||||
\(539\) | −6.65915 | −0.286830 | ||||||||
\(540\) | 1.04716 | 0.0450625 | ||||||||
\(541\) | −33.6136 | −1.44516 | −0.722580 | − | 0.691287i | \(-0.757044\pi\) | ||||
−0.722580 | + | 0.691287i | \(0.757044\pi\) | |||||||
\(542\) | 2.11722 | 0.0909424 | ||||||||
\(543\) | 37.1700 | 1.59512 | ||||||||
\(544\) | −5.04549 | −0.216324 | ||||||||
\(545\) | 5.94794 | 0.254782 | ||||||||
\(546\) | −6.73494 | −0.288229 | ||||||||
\(547\) | −8.36898 | −0.357832 | −0.178916 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178916 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(548\) | 14.6263 | 0.624803 | ||||||||
\(549\) | −25.1884 | −1.07502 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −39.1832 | −1.66926 | ||||||||
\(552\) | 2.06589 | 0.0879299 | ||||||||
\(553\) | −9.34247 | −0.397282 | ||||||||
\(554\) | −11.7728 | −0.500177 | ||||||||
\(555\) | 8.60415 | 0.365226 | ||||||||
\(556\) | 11.7412 | 0.497939 | ||||||||
\(557\) | 4.53983 | 0.192359 | 0.0961793 | − | 0.995364i | \(-0.469338\pi\) | ||||
0.0961793 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(558\) | 8.39125 | 0.355230 | ||||||||
\(559\) | −4.55520 | −0.192664 | ||||||||
\(560\) | −0.583820 | −0.0246709 | ||||||||
\(561\) | 12.7776 | 0.539472 | ||||||||
\(562\) | −6.18333 | −0.260828 | ||||||||
\(563\) | 17.1652 | 0.723427 | 0.361714 | − | 0.932289i | \(-0.382192\pi\) | ||||
0.361714 | + | 0.932289i | \(0.382192\pi\) | |||||||
\(564\) | 18.2839 | 0.769889 | ||||||||
\(565\) | 1.56740 | 0.0659408 | ||||||||
\(566\) | 29.0060 | 1.21921 | ||||||||
\(567\) | 4.43035 | 0.186057 | ||||||||
\(568\) | −11.2834 | −0.473441 | ||||||||
\(569\) | −40.6384 | −1.70365 | −0.851824 | − | 0.523828i | \(-0.824504\pi\) | ||||
−0.851824 | + | 0.523828i | \(0.824504\pi\) | |||||||
\(570\) | 12.4837 | 0.522886 | ||||||||
\(571\) | 34.0159 | 1.42352 | 0.711761 | − | 0.702422i | \(-0.247898\pi\) | ||||
0.711761 | + | 0.702422i | \(0.247898\pi\) | |||||||
\(572\) | −4.55520 | −0.190462 | ||||||||
\(573\) | −39.7392 | −1.66013 | ||||||||
\(574\) | 6.38541 | 0.266522 | ||||||||
\(575\) | −0.815754 | −0.0340193 | ||||||||
\(576\) | 3.41349 | 0.142229 | ||||||||
\(577\) | 0.948124 | 0.0394709 | 0.0197355 | − | 0.999805i | \(-0.493718\pi\) | ||||
0.0197355 | + | 0.999805i | \(0.493718\pi\) | |||||||
\(578\) | −8.45697 | −0.351764 | ||||||||
\(579\) | 42.1064 | 1.74988 | ||||||||
\(580\) | 7.94882 | 0.330057 | ||||||||
\(581\) | −0.0103029 | −0.000427438 0 | ||||||||
\(582\) | −7.83651 | −0.324834 | ||||||||
\(583\) | 11.9243 | 0.493854 | ||||||||
\(584\) | 1.95228 | 0.0807860 | ||||||||
\(585\) | −15.5491 | −0.642877 | ||||||||
\(586\) | −31.7771 | −1.31270 | ||||||||
\(587\) | 9.62369 | 0.397212 | 0.198606 | − | 0.980079i | \(-0.436359\pi\) | ||||
0.198606 | + | 0.980079i | \(0.436359\pi\) | |||||||
\(588\) | −16.8642 | −0.695469 | ||||||||
\(589\) | 12.1178 | 0.499307 | ||||||||
\(590\) | −9.88656 | −0.407023 | ||||||||
\(591\) | −43.2269 | −1.77812 | ||||||||
\(592\) | 3.39751 | 0.139637 | ||||||||
\(593\) | 17.5234 | 0.719599 | 0.359800 | − | 0.933030i | \(-0.382845\pi\) | ||||
0.359800 | + | 0.933030i | \(0.382845\pi\) | |||||||
\(594\) | −1.04716 | −0.0429654 | ||||||||
\(595\) | −2.94566 | −0.120760 | ||||||||
\(596\) | −23.6217 | −0.967581 | ||||||||
\(597\) | 6.71019 | 0.274630 | ||||||||
\(598\) | −3.71592 | −0.151955 | ||||||||
\(599\) | 1.17796 | 0.0481300 | 0.0240650 | − | 0.999710i | \(-0.492339\pi\) | ||||
0.0240650 | + | 0.999710i | \(0.492339\pi\) | |||||||
\(600\) | −2.53249 | −0.103388 | ||||||||
\(601\) | 4.94523 | 0.201720 | 0.100860 | − | 0.994901i | \(-0.467841\pi\) | ||||
0.100860 | + | 0.994901i | \(0.467841\pi\) | |||||||
\(602\) | 0.583820 | 0.0237947 | ||||||||
\(603\) | 32.2463 | 1.31317 | ||||||||
\(604\) | −5.02949 | −0.204647 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 41.0965 | 1.66943 | ||||||||
\(607\) | 47.2175 | 1.91650 | 0.958250 | − | 0.285932i | \(-0.0923031\pi\) | ||||
0.958250 | + | 0.285932i | \(0.0923031\pi\) | |||||||
\(608\) | 4.92944 | 0.199915 | ||||||||
\(609\) | −11.7525 | −0.476234 | ||||||||
\(610\) | 7.37908 | 0.298770 | ||||||||
\(611\) | −32.8873 | −1.33048 | ||||||||
\(612\) | 17.2227 | 0.696188 | ||||||||
\(613\) | −11.0345 | −0.445679 | −0.222839 | − | 0.974855i | \(-0.571533\pi\) | ||||
−0.222839 | + | 0.974855i | \(0.571533\pi\) | |||||||
\(614\) | −29.9260 | −1.20772 | ||||||||
\(615\) | 27.6985 | 1.11691 | ||||||||
\(616\) | 0.583820 | 0.0235228 | ||||||||
\(617\) | 18.0283 | 0.725791 | 0.362895 | − | 0.931830i | \(-0.381788\pi\) | ||||
0.362895 | + | 0.931830i | \(0.381788\pi\) | |||||||
\(618\) | −40.2095 | −1.61746 | ||||||||
\(619\) | 15.4212 | 0.619830 | 0.309915 | − | 0.950764i | \(-0.399699\pi\) | ||||
0.309915 | + | 0.950764i | \(0.399699\pi\) | |||||||
\(620\) | −2.45826 | −0.0987261 | ||||||||
\(621\) | −0.854224 | −0.0342788 | ||||||||
\(622\) | 33.8063 | 1.35551 | ||||||||
\(623\) | 2.36281 | 0.0946641 | ||||||||
\(624\) | −11.5360 | −0.461809 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0501 | 0.401682 | ||||||||
\(627\) | −12.4837 | −0.498552 | ||||||||
\(628\) | −14.0823 | −0.561943 | ||||||||
\(629\) | 17.1421 | 0.683500 | ||||||||
\(630\) | 1.99286 | 0.0793976 | ||||||||
\(631\) | −19.0201 | −0.757180 | −0.378590 | − | 0.925564i | \(-0.623591\pi\) | ||||
−0.378590 | + | 0.925564i | \(0.623591\pi\) | |||||||
\(632\) | −16.0023 | −0.636538 | ||||||||
\(633\) | −31.1708 | −1.23893 | ||||||||
\(634\) | 5.78777 | 0.229862 | ||||||||
\(635\) | −14.2359 | −0.564935 | ||||||||
\(636\) | 30.1981 | 1.19743 | ||||||||
\(637\) | 30.3338 | 1.20187 | ||||||||
\(638\) | −7.94882 | −0.314697 | ||||||||
\(639\) | 38.5158 | 1.52366 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −18.1488 | −0.716836 | −0.358418 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358418 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(642\) | −5.04083 | −0.198946 | ||||||||
\(643\) | 23.5214 | 0.927593 | 0.463796 | − | 0.885942i | \(-0.346487\pi\) | ||||
0.463796 | + | 0.885942i | \(0.346487\pi\) | |||||||
\(644\) | 0.476254 | 0.0187670 | ||||||||
\(645\) | 2.53249 | 0.0997166 | ||||||||
\(646\) | 24.8714 | 0.978553 | ||||||||
\(647\) | −8.30021 | −0.326315 | −0.163157 | − | 0.986600i | \(-0.552168\pi\) | ||||
−0.163157 | + | 0.986600i | \(0.552168\pi\) | |||||||
\(648\) | 7.58855 | 0.298107 | ||||||||
\(649\) | 9.88656 | 0.388081 | ||||||||
\(650\) | 4.55520 | 0.178670 | ||||||||
\(651\) | 3.63458 | 0.142450 | ||||||||
\(652\) | 18.3786 | 0.719760 | ||||||||
\(653\) | −35.7957 | −1.40079 | −0.700396 | − | 0.713754i | \(-0.746993\pi\) | ||||
−0.700396 | + | 0.713754i | \(0.746993\pi\) | |||||||
\(654\) | −15.0631 | −0.589013 | ||||||||
\(655\) | −9.61130 | −0.375544 | ||||||||
\(656\) | 10.9373 | 0.427029 | ||||||||
\(657\) | −6.66410 | −0.259991 | ||||||||
\(658\) | 4.21502 | 0.164319 | ||||||||
\(659\) | 8.74484 | 0.340651 | 0.170325 | − | 0.985388i | \(-0.445518\pi\) | ||||
0.170325 | + | 0.985388i | \(0.445518\pi\) | |||||||
\(660\) | 2.53249 | 0.0985769 | ||||||||
\(661\) | −24.4400 | −0.950607 | −0.475304 | − | 0.879822i | \(-0.657662\pi\) | ||||
−0.475304 | + | 0.879822i | \(0.657662\pi\) | |||||||
\(662\) | 2.60786 | 0.101357 | ||||||||
\(663\) | −58.2047 | −2.26048 | ||||||||
\(664\) | −0.0176475 | −0.000684854 0 | ||||||||
\(665\) | 2.87790 | 0.111600 | ||||||||
\(666\) | −11.5974 | −0.449389 | ||||||||
\(667\) | −6.48428 | −0.251072 | ||||||||
\(668\) | −4.93771 | −0.191046 | ||||||||
\(669\) | −50.9370 | −1.96934 | ||||||||
\(670\) | −9.44673 | −0.364959 | ||||||||
\(671\) | −7.37908 | −0.284866 | ||||||||
\(672\) | 1.47852 | 0.0570350 | ||||||||
\(673\) | 33.8166 | 1.30354 | 0.651768 | − | 0.758419i | \(-0.274028\pi\) | ||||
0.651768 | + | 0.758419i | \(0.274028\pi\) | |||||||
\(674\) | 3.61378 | 0.139198 | ||||||||
\(675\) | 1.04716 | 0.0403052 | ||||||||
\(676\) | 7.74983 | 0.298070 | ||||||||
\(677\) | −27.9108 | −1.07270 | −0.536349 | − | 0.843996i | \(-0.680197\pi\) | ||||
−0.536349 | + | 0.843996i | \(0.680197\pi\) | |||||||
\(678\) | −3.96941 | −0.152444 | ||||||||
\(679\) | −1.80657 | −0.0693297 | ||||||||
\(680\) | −5.04549 | −0.193486 | ||||||||
\(681\) | −18.0869 | −0.693090 | ||||||||
\(682\) | 2.45826 | 0.0941316 | ||||||||
\(683\) | 51.8370 | 1.98349 | 0.991745 | − | 0.128228i | \(-0.0409289\pi\) | ||||
0.991745 | + | 0.128228i | \(0.0409289\pi\) | |||||||
\(684\) | −16.8266 | −0.643381 | ||||||||
\(685\) | 14.6263 | 0.558841 | ||||||||
\(686\) | −7.97449 | −0.304467 | ||||||||
\(687\) | −21.3107 | −0.813054 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −54.3175 | −2.06933 | ||||||||
\(690\) | 2.06589 | 0.0786469 | ||||||||
\(691\) | 15.0849 | 0.573856 | 0.286928 | − | 0.957952i | \(-0.407366\pi\) | ||||
0.286928 | + | 0.957952i | \(0.407366\pi\) | |||||||
\(692\) | 4.02612 | 0.153050 | ||||||||
\(693\) | −1.99286 | −0.0757027 | ||||||||
\(694\) | 16.2439 | 0.616608 | ||||||||
\(695\) | 11.7412 | 0.445371 | ||||||||
\(696\) | −20.1303 | −0.763036 | ||||||||
\(697\) | 55.1840 | 2.09024 | ||||||||
\(698\) | 36.5970 | 1.38522 | ||||||||
\(699\) | −65.9822 | −2.49568 | ||||||||
\(700\) | −0.583820 | −0.0220663 | ||||||||
\(701\) | 19.8774 | 0.750760 | 0.375380 | − | 0.926871i | \(-0.377512\pi\) | ||||
0.375380 | + | 0.926871i | \(0.377512\pi\) | |||||||
\(702\) | 4.77002 | 0.180033 | ||||||||
\(703\) | −16.7478 | −0.631656 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 18.2839 | 0.688610 | ||||||||
\(706\) | 3.60517 | 0.135682 | ||||||||
\(707\) | 9.47407 | 0.356309 | ||||||||
\(708\) | 25.0376 | 0.940970 | ||||||||
\(709\) | 35.4530 | 1.33147 | 0.665734 | − | 0.746190i | \(-0.268119\pi\) | ||||
0.665734 | + | 0.746190i | \(0.268119\pi\) | |||||||
\(710\) | −11.2834 | −0.423458 | ||||||||
\(711\) | 54.6237 | 2.04855 | ||||||||
\(712\) | 4.04716 | 0.151674 | ||||||||
\(713\) | 2.00533 | 0.0751004 | ||||||||
\(714\) | 7.45984 | 0.279178 | ||||||||
\(715\) | −4.55520 | −0.170355 | ||||||||
\(716\) | 22.7886 | 0.851649 | ||||||||
\(717\) | 43.5347 | 1.62583 | ||||||||
\(718\) | 0.996118 | 0.0371748 | ||||||||
\(719\) | −17.9118 | −0.667998 | −0.333999 | − | 0.942573i | \(-0.608398\pi\) | ||||
−0.333999 | + | 0.942573i | \(0.608398\pi\) | |||||||
\(720\) | 3.41349 | 0.127213 | ||||||||
\(721\) | −9.26959 | −0.345217 | ||||||||
\(722\) | −5.29936 | −0.197222 | ||||||||
\(723\) | −66.0208 | −2.45534 | ||||||||
\(724\) | 14.6773 | 0.545477 | ||||||||
\(725\) | 7.94882 | 0.295212 | ||||||||
\(726\) | −2.53249 | −0.0939894 | ||||||||
\(727\) | −41.4357 | −1.53677 | −0.768383 | − | 0.639991i | \(-0.778938\pi\) | ||||
−0.768383 | + | 0.639991i | \(0.778938\pi\) | |||||||
\(728\) | −2.65942 | −0.0985645 | ||||||||
\(729\) | −33.8592 | −1.25404 | ||||||||
\(730\) | 1.95228 | 0.0722572 | ||||||||
\(731\) | 5.04549 | 0.186614 | ||||||||
\(732\) | −18.6874 | −0.690707 | ||||||||
\(733\) | 31.1540 | 1.15070 | 0.575349 | − | 0.817908i | \(-0.304866\pi\) | ||||
0.575349 | + | 0.817908i | \(0.304866\pi\) | |||||||
\(734\) | 1.64638 | 0.0607689 | ||||||||
\(735\) | −16.8642 | −0.622046 | ||||||||
\(736\) | 0.815754 | 0.0300691 | ||||||||
\(737\) | 9.44673 | 0.347975 | ||||||||
\(738\) | −37.3343 | −1.37430 | ||||||||
\(739\) | 50.0623 | 1.84157 | 0.920786 | − | 0.390068i | \(-0.127549\pi\) | ||||
0.920786 | + | 0.390068i | \(0.127549\pi\) | |||||||
\(740\) | 3.39751 | 0.124895 | ||||||||
\(741\) | 56.8659 | 2.08902 | ||||||||
\(742\) | 6.96164 | 0.255570 | ||||||||
\(743\) | 43.2272 | 1.58585 | 0.792926 | − | 0.609318i | \(-0.208557\pi\) | ||||
0.792926 | + | 0.609318i | \(0.208557\pi\) | |||||||
\(744\) | 6.22551 | 0.228238 | ||||||||
\(745\) | −23.6217 | −0.865431 | ||||||||
\(746\) | 14.5695 | 0.533428 | ||||||||
\(747\) | 0.0602394 | 0.00220405 | ||||||||
\(748\) | 5.04549 | 0.184481 | ||||||||
\(749\) | −1.16207 | −0.0424613 | ||||||||
\(750\) | −2.53249 | −0.0924733 | ||||||||
\(751\) | −29.8808 | −1.09037 | −0.545183 | − | 0.838317i | \(-0.683540\pi\) | ||||
−0.545183 | + | 0.838317i | \(0.683540\pi\) | |||||||
\(752\) | 7.21973 | 0.263276 | ||||||||
\(753\) | −50.3496 | −1.83484 | ||||||||
\(754\) | 36.2084 | 1.31863 | ||||||||
\(755\) | −5.02949 | −0.183042 | ||||||||
\(756\) | −0.611352 | −0.0222347 | ||||||||
\(757\) | 28.0307 | 1.01879 | 0.509397 | − | 0.860532i | \(-0.329869\pi\) | ||||
0.509397 | + | 0.860532i | \(0.329869\pi\) | |||||||
\(758\) | −17.4192 | −0.632695 | ||||||||
\(759\) | −2.06589 | −0.0749869 | ||||||||
\(760\) | 4.92944 | 0.178809 | ||||||||
\(761\) | 10.4620 | 0.379247 | 0.189624 | − | 0.981857i | \(-0.439273\pi\) | ||||
0.189624 | + | 0.981857i | \(0.439273\pi\) | |||||||
\(762\) | 36.0523 | 1.30604 | ||||||||
\(763\) | −3.47253 | −0.125714 | ||||||||
\(764\) | −15.6918 | −0.567708 | ||||||||
\(765\) | 17.2227 | 0.622689 | ||||||||
\(766\) | 30.5126 | 1.10246 | ||||||||
\(767\) | −45.0352 | −1.62613 | ||||||||
\(768\) | 2.53249 | 0.0913833 | ||||||||
\(769\) | 16.1772 | 0.583366 | 0.291683 | − | 0.956515i | \(-0.405785\pi\) | ||||
0.291683 | + | 0.956515i | \(0.405785\pi\) | |||||||
\(770\) | 0.583820 | 0.0210394 | ||||||||
\(771\) | 24.2796 | 0.874408 | ||||||||
\(772\) | 16.6265 | 0.598400 | ||||||||
\(773\) | −29.7787 | −1.07106 | −0.535532 | − | 0.844515i | \(-0.679889\pi\) | ||||
−0.535532 | + | 0.844515i | \(0.679889\pi\) | |||||||
\(774\) | −3.41349 | −0.122695 | ||||||||
\(775\) | −2.45826 | −0.0883033 | ||||||||
\(776\) | −3.09439 | −0.111082 | ||||||||
\(777\) | −5.02327 | −0.180209 | ||||||||
\(778\) | −16.1307 | −0.578313 | ||||||||
\(779\) | −53.9147 | −1.93169 | ||||||||
\(780\) | −11.5360 | −0.413054 | ||||||||
\(781\) | 11.2834 | 0.403752 | ||||||||
\(782\) | 4.11588 | 0.147184 | ||||||||
\(783\) | 8.32367 | 0.297464 | ||||||||
\(784\) | −6.65915 | −0.237827 | ||||||||
\(785\) | −14.0823 | −0.502617 | ||||||||
\(786\) | 24.3405 | 0.868196 | ||||||||
\(787\) | 9.30091 | 0.331542 | 0.165771 | − | 0.986164i | \(-0.446989\pi\) | ||||
0.165771 | + | 0.986164i | \(0.446989\pi\) | |||||||
\(788\) | −17.0689 | −0.608056 | ||||||||
\(789\) | −4.26905 | −0.151982 | ||||||||
\(790\) | −16.0023 | −0.569337 | ||||||||
\(791\) | −0.915077 | −0.0325364 | ||||||||
\(792\) | −3.41349 | −0.121293 | ||||||||
\(793\) | 33.6132 | 1.19364 | ||||||||
\(794\) | 20.6024 | 0.731153 | ||||||||
\(795\) | 30.1981 | 1.07102 | ||||||||
\(796\) | 2.64964 | 0.0939142 | ||||||||
\(797\) | 29.8483 | 1.05728 | 0.528641 | − | 0.848845i | \(-0.322702\pi\) | ||||
0.528641 | + | 0.848845i | \(0.322702\pi\) | |||||||
\(798\) | −7.28826 | −0.258001 | ||||||||
\(799\) | 36.4271 | 1.28870 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −13.8149 | −0.488127 | ||||||||
\(802\) | −7.69504 | −0.271721 | ||||||||
\(803\) | −1.95228 | −0.0688946 | ||||||||
\(804\) | 23.9237 | 0.843725 | ||||||||
\(805\) | 0.476254 | 0.0167857 | ||||||||
\(806\) | −11.1979 | −0.394428 | ||||||||
\(807\) | 4.16960 | 0.146777 | ||||||||
\(808\) | 16.2277 | 0.570890 | ||||||||
\(809\) | −25.3798 | −0.892305 | −0.446153 | − | 0.894957i | \(-0.647206\pi\) | ||||
−0.446153 | + | 0.894957i | \(0.647206\pi\) | |||||||
\(810\) | 7.58855 | 0.266635 | ||||||||
\(811\) | 25.9330 | 0.910632 | 0.455316 | − | 0.890330i | \(-0.349526\pi\) | ||||
0.455316 | + | 0.890330i | \(0.349526\pi\) | |||||||
\(812\) | −4.64068 | −0.162856 | ||||||||
\(813\) | −5.36184 | −0.188048 | ||||||||
\(814\) | −3.39751 | −0.119083 | ||||||||
\(815\) | 18.3786 | 0.643773 | ||||||||
\(816\) | 12.7776 | 0.447307 | ||||||||
\(817\) | −4.92944 | −0.172459 | ||||||||
\(818\) | 35.5918 | 1.24444 | ||||||||
\(819\) | 9.07789 | 0.317207 | ||||||||
\(820\) | 10.9373 | 0.381947 | ||||||||
\(821\) | 10.6854 | 0.372924 | 0.186462 | − | 0.982462i | \(-0.440298\pi\) | ||||
0.186462 | + | 0.982462i | \(0.440298\pi\) | |||||||
\(822\) | −37.0408 | −1.29195 | ||||||||
\(823\) | −39.8524 | −1.38917 | −0.694583 | − | 0.719413i | \(-0.744411\pi\) | ||||
−0.694583 | + | 0.719413i | \(0.744411\pi\) | |||||||
\(824\) | −15.8775 | −0.553118 | ||||||||
\(825\) | 2.53249 | 0.0881699 | ||||||||
\(826\) | 5.77197 | 0.200833 | ||||||||
\(827\) | 34.0616 | 1.18444 | 0.592218 | − | 0.805778i | \(-0.298252\pi\) | ||||
0.592218 | + | 0.805778i | \(0.298252\pi\) | |||||||
\(828\) | −2.78457 | −0.0967704 | ||||||||
\(829\) | −39.6901 | −1.37849 | −0.689247 | − | 0.724526i | \(-0.742058\pi\) | ||||
−0.689247 | + | 0.724526i | \(0.742058\pi\) | |||||||
\(830\) | −0.0176475 | −0.000612552 0 | ||||||||
\(831\) | 29.8144 | 1.03425 | ||||||||
\(832\) | −4.55520 | −0.157923 | ||||||||
\(833\) | −33.5987 | −1.16413 | ||||||||
\(834\) | −29.7345 | −1.02962 | ||||||||
\(835\) | −4.93771 | −0.170876 | ||||||||
\(836\) | −4.92944 | −0.170488 | ||||||||
\(837\) | −2.57419 | −0.0889770 | ||||||||
\(838\) | −23.2886 | −0.804490 | ||||||||
\(839\) | −24.2538 | −0.837333 | −0.418667 | − | 0.908140i | \(-0.637502\pi\) | ||||
−0.418667 | + | 0.908140i | \(0.637502\pi\) | |||||||
\(840\) | 1.47852 | 0.0510137 | ||||||||
\(841\) | 34.1837 | 1.17875 | ||||||||
\(842\) | 27.6647 | 0.953390 | ||||||||
\(843\) | 15.6592 | 0.539332 | ||||||||
\(844\) | −12.3084 | −0.423672 | ||||||||
\(845\) | 7.74983 | 0.266602 | ||||||||
\(846\) | −24.6445 | −0.847294 | ||||||||
\(847\) | −0.583820 | −0.0200603 | ||||||||
\(848\) | 11.9243 | 0.409482 | ||||||||
\(849\) | −73.4572 | −2.52104 | ||||||||
\(850\) | −5.04549 | −0.173059 | ||||||||
\(851\) | −2.77153 | −0.0950069 | ||||||||
\(852\) | 28.5751 | 0.978966 | ||||||||
\(853\) | 42.6761 | 1.46120 | 0.730600 | − | 0.682805i | \(-0.239240\pi\) | ||||
0.730600 | + | 0.682805i | \(0.239240\pi\) | |||||||
\(854\) | −4.30805 | −0.147419 | ||||||||
\(855\) | −16.8266 | −0.575457 | ||||||||
\(856\) | −1.99047 | −0.0680328 | ||||||||
\(857\) | 40.1740 | 1.37232 | 0.686160 | − | 0.727451i | \(-0.259295\pi\) | ||||
0.686160 | + | 0.727451i | \(0.259295\pi\) | |||||||
\(858\) | 11.5360 | 0.393832 | ||||||||
\(859\) | −54.1225 | −1.84663 | −0.923317 | − | 0.384038i | \(-0.874533\pi\) | ||||
−0.923317 | + | 0.384038i | \(0.874533\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | −16.1710 | −0.551105 | ||||||||
\(862\) | 31.7418 | 1.08113 | ||||||||
\(863\) | −12.4671 | −0.424385 | −0.212192 | − | 0.977228i | \(-0.568060\pi\) | ||||
−0.212192 | + | 0.977228i | \(0.568060\pi\) | |||||||
\(864\) | −1.04716 | −0.0356251 | ||||||||
\(865\) | 4.02612 | 0.136892 | ||||||||
\(866\) | 3.14451 | 0.106855 | ||||||||
\(867\) | 21.4172 | 0.727365 | ||||||||
\(868\) | 1.43518 | 0.0487132 | ||||||||
\(869\) | 16.0023 | 0.542841 | ||||||||
\(870\) | −20.1303 | −0.682480 | ||||||||
\(871\) | −43.0317 | −1.45807 | ||||||||
\(872\) | −5.94794 | −0.201423 | ||||||||
\(873\) | 10.5627 | 0.357492 | ||||||||
\(874\) | −4.02121 | −0.136019 | ||||||||
\(875\) | −0.583820 | −0.0197367 | ||||||||
\(876\) | −4.94413 | −0.167047 | ||||||||
\(877\) | 13.5911 | 0.458940 | 0.229470 | − | 0.973316i | \(-0.426301\pi\) | ||||
0.229470 | + | 0.973316i | \(0.426301\pi\) | |||||||
\(878\) | 1.21375 | 0.0409621 | ||||||||
\(879\) | 80.4751 | 2.71436 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −43.5037 | −1.46568 | −0.732839 | − | 0.680402i | \(-0.761805\pi\) | ||||
−0.732839 | + | 0.680402i | \(0.761805\pi\) | |||||||
\(882\) | 22.7310 | 0.765391 | ||||||||
\(883\) | −33.3274 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(884\) | −22.9832 | −0.773009 | ||||||||
\(885\) | 25.0376 | 0.841629 | ||||||||
\(886\) | −14.3917 | −0.483499 | ||||||||
\(887\) | 6.15054 | 0.206515 | 0.103257 | − | 0.994655i | \(-0.467073\pi\) | ||||
0.103257 | + | 0.994655i | \(0.467073\pi\) | |||||||
\(888\) | −8.60415 | −0.288736 | ||||||||
\(889\) | 8.31121 | 0.278749 | ||||||||
\(890\) | 4.04716 | 0.135661 | ||||||||
\(891\) | −7.58855 | −0.254226 | ||||||||
\(892\) | −20.1134 | −0.673448 | ||||||||
\(893\) | −35.5892 | −1.19095 | ||||||||
\(894\) | 59.8216 | 2.00073 | ||||||||
\(895\) | 22.7886 | 0.761738 | ||||||||
\(896\) | 0.583820 | 0.0195041 | ||||||||
\(897\) | 9.41052 | 0.314208 | ||||||||
\(898\) | −37.0597 | −1.23670 | ||||||||
\(899\) | −19.5403 | −0.651704 | ||||||||
\(900\) | 3.41349 | 0.113783 | ||||||||
\(901\) | 60.1639 | 2.00435 | ||||||||
\(902\) | −10.9373 | −0.364172 | ||||||||
\(903\) | −1.47852 | −0.0492020 | ||||||||
\(904\) | −1.56740 | −0.0521308 | ||||||||
\(905\) | 14.6773 | 0.487890 | ||||||||
\(906\) | 12.7371 | 0.423163 | ||||||||
\(907\) | 0.695483 | 0.0230931 | 0.0115466 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115466 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(908\) | −7.14194 | −0.237014 | ||||||||
\(909\) | −55.3932 | −1.83728 | ||||||||
\(910\) | −2.65942 | −0.0881588 | ||||||||
\(911\) | 3.77664 | 0.125126 | 0.0625629 | − | 0.998041i | \(-0.480073\pi\) | ||||
0.0625629 | + | 0.998041i | \(0.480073\pi\) | |||||||
\(912\) | −12.4837 | −0.413378 | ||||||||
\(913\) | 0.0176475 | 0.000584046 0 | ||||||||
\(914\) | −26.5804 | −0.879202 | ||||||||
\(915\) | −18.6874 | −0.617787 | ||||||||
\(916\) | −8.41493 | −0.278037 | ||||||||
\(917\) | 5.61127 | 0.185300 | ||||||||
\(918\) | −5.28343 | −0.174379 | ||||||||
\(919\) | 53.9165 | 1.77854 | 0.889271 | − | 0.457381i | \(-0.151212\pi\) | ||||
0.889271 | + | 0.457381i | \(0.151212\pi\) | |||||||
\(920\) | 0.815754 | 0.0268946 | ||||||||
\(921\) | 75.7873 | 2.49728 | ||||||||
\(922\) | −20.9312 | −0.689334 | ||||||||
\(923\) | −51.3981 | −1.69179 | ||||||||
\(924\) | −1.47852 | −0.0486396 | ||||||||
\(925\) | 3.39751 | 0.111709 | ||||||||
\(926\) | 15.7816 | 0.518616 | ||||||||
\(927\) | 54.1976 | 1.78008 | ||||||||
\(928\) | −7.94882 | −0.260933 | ||||||||
\(929\) | 3.14341 | 0.103132 | 0.0515659 | − | 0.998670i | \(-0.483579\pi\) | ||||
0.0515659 | + | 0.998670i | \(0.483579\pi\) | |||||||
\(930\) | 6.22551 | 0.204143 | ||||||||
\(931\) | 32.8259 | 1.07582 | ||||||||
\(932\) | −26.0543 | −0.853437 | ||||||||
\(933\) | −85.6140 | −2.80288 | ||||||||
\(934\) | 14.4659 | 0.473337 | ||||||||
\(935\) | 5.04549 | 0.165005 | ||||||||
\(936\) | 15.5491 | 0.508239 | ||||||||
\(937\) | −6.42862 | −0.210014 | −0.105007 | − | 0.994471i | \(-0.533486\pi\) | ||||
−0.105007 | + | 0.994471i | \(0.533486\pi\) | |||||||
\(938\) | 5.51519 | 0.180077 | ||||||||
\(939\) | −25.4517 | −0.830586 | ||||||||
\(940\) | 7.21973 | 0.235481 | ||||||||
\(941\) | −17.2433 | −0.562115 | −0.281058 | − | 0.959691i | \(-0.590685\pi\) | ||||
−0.281058 | + | 0.959691i | \(0.590685\pi\) | |||||||
\(942\) | 35.6631 | 1.16197 | ||||||||
\(943\) | −8.92214 | −0.290545 | ||||||||
\(944\) | 9.88656 | 0.321780 | ||||||||
\(945\) | −0.611352 | −0.0198873 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 1.87122 | 0.0608066 | 0.0304033 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304033 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(948\) | 40.5256 | 1.31621 | ||||||||
\(949\) | 8.89304 | 0.288680 | ||||||||
\(950\) | 4.92944 | 0.159932 | ||||||||
\(951\) | −14.6575 | −0.475301 | ||||||||
\(952\) | 2.94566 | 0.0954694 | ||||||||
\(953\) | 51.3865 | 1.66457 | 0.832285 | − | 0.554347i | \(-0.187032\pi\) | ||||
0.832285 | + | 0.554347i | \(0.187032\pi\) | |||||||
\(954\) | −40.7035 | −1.31782 | ||||||||
\(955\) | −15.6918 | −0.507774 | ||||||||
\(956\) | 17.1905 | 0.555980 | ||||||||
\(957\) | 20.1303 | 0.650719 | ||||||||
\(958\) | −0.630533 | −0.0203716 | ||||||||
\(959\) | −8.53911 | −0.275742 | ||||||||
\(960\) | 2.53249 | 0.0817357 | ||||||||
\(961\) | −24.9570 | −0.805063 | ||||||||
\(962\) | 15.4763 | 0.498977 | ||||||||
\(963\) | 6.79444 | 0.218948 | ||||||||
\(964\) | −26.0696 | −0.839644 | ||||||||
\(965\) | 16.6265 | 0.535226 | ||||||||
\(966\) | −1.20611 | −0.0388058 | ||||||||
\(967\) | 16.4900 | 0.530284 | 0.265142 | − | 0.964209i | \(-0.414581\pi\) | ||||
0.265142 | + | 0.964209i | \(0.414581\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −62.9866 | −2.02342 | ||||||||
\(970\) | −3.09439 | −0.0993549 | ||||||||
\(971\) | −34.4893 | −1.10681 | −0.553407 | − | 0.832911i | \(-0.686673\pi\) | ||||
−0.553407 | + | 0.832911i | \(0.686673\pi\) | |||||||
\(972\) | −22.3594 | −0.717178 | ||||||||
\(973\) | −6.85477 | −0.219754 | ||||||||
\(974\) | 26.5453 | 0.850568 | ||||||||
\(975\) | −11.5360 | −0.369447 | ||||||||
\(976\) | −7.37908 | −0.236198 | ||||||||
\(977\) | 32.0527 | 1.02546 | 0.512729 | − | 0.858551i | \(-0.328635\pi\) | ||||
0.512729 | + | 0.858551i | \(0.328635\pi\) | |||||||
\(978\) | −46.5435 | −1.48830 | ||||||||
\(979\) | −4.04716 | −0.129348 | ||||||||
\(980\) | −6.65915 | −0.212719 | ||||||||
\(981\) | 20.3033 | 0.648233 | ||||||||
\(982\) | −11.5756 | −0.369393 | ||||||||
\(983\) | 33.0705 | 1.05478 | 0.527392 | − | 0.849622i | \(-0.323170\pi\) | ||||
0.527392 | + | 0.849622i | \(0.323170\pi\) | |||||||
\(984\) | −27.6985 | −0.882997 | ||||||||
\(985\) | −17.0689 | −0.543861 | ||||||||
\(986\) | −40.1057 | −1.27723 | ||||||||
\(987\) | −10.6745 | −0.339773 | ||||||||
\(988\) | 22.4546 | 0.714375 | ||||||||
\(989\) | −0.815754 | −0.0259395 | ||||||||
\(990\) | −3.41349 | −0.108488 | ||||||||
\(991\) | 17.7451 | 0.563693 | 0.281846 | − | 0.959460i | \(-0.409053\pi\) | ||||
0.281846 | + | 0.959460i | \(0.409053\pi\) | |||||||
\(992\) | 2.45826 | 0.0780498 | ||||||||
\(993\) | −6.60436 | −0.209583 | ||||||||
\(994\) | 6.58748 | 0.208942 | ||||||||
\(995\) | 2.64964 | 0.0839994 | ||||||||
\(996\) | 0.0446920 | 0.00141612 | ||||||||
\(997\) | −17.4927 | −0.553998 | −0.276999 | − | 0.960870i | \(-0.589340\pi\) | ||||
−0.276999 | + | 0.960870i | \(0.589340\pi\) | |||||||
\(998\) | −38.0328 | −1.20391 | ||||||||
\(999\) | 3.55773 | 0.112562 |
(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 | 4730.2.a.z.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.z.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |