Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.8569169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 44x^{2} - 9x - 41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.18325\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.93408 | −1.75937 | −0.879686 | − | 0.475555i | \(-0.842247\pi\) | ||||
−0.879686 | + | 0.475555i | \(0.842247\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.93408 | −1.24406 | ||||||||
\(11\) | −4.81154 | −1.45073 | −0.725366 | − | 0.688363i | \(-0.758330\pi\) | ||||
−0.725366 | + | 0.688363i | \(0.758330\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 3.93408 | 1.01577 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.61347 | −0.876396 | −0.438198 | − | 0.898878i | \(-0.644383\pi\) | ||||
−0.438198 | + | 0.898878i | \(0.644383\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 7.71258 | 1.76939 | 0.884693 | − | 0.466174i | \(-0.154368\pi\) | ||||
0.884693 | + | 0.466174i | \(0.154368\pi\) | |||||||
\(20\) | −3.93408 | −0.879686 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −4.81154 | −1.02582 | ||||||||
\(23\) | −3.86172 | −0.805224 | −0.402612 | − | 0.915371i | \(-0.631898\pi\) | ||||
−0.402612 | + | 0.915371i | \(0.631898\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 10.4770 | 2.09539 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.45147 | −0.826618 | −0.413309 | − | 0.910591i | \(-0.635627\pi\) | ||||
−0.413309 | + | 0.910591i | \(0.635627\pi\) | |||||||
\(30\) | 3.93408 | 0.718261 | ||||||||
\(31\) | −1.01880 | −0.182981 | −0.0914906 | − | 0.995806i | \(-0.529163\pi\) | ||||
−0.0914906 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.81154 | 0.837581 | ||||||||
\(34\) | −3.61347 | −0.619706 | ||||||||
\(35\) | −3.93408 | −0.664980 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.30140 | −1.20034 | −0.600172 | − | 0.799871i | \(-0.704901\pi\) | ||||
−0.600172 | + | 0.799871i | \(0.704901\pi\) | |||||||
\(38\) | 7.71258 | 1.25114 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.93408 | −0.622032 | ||||||||
\(41\) | −7.28601 | −1.13788 | −0.568942 | − | 0.822378i | \(-0.692647\pi\) | ||||
−0.568942 | + | 0.822378i | \(0.692647\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −4.73996 | −0.722838 | −0.361419 | − | 0.932404i | \(-0.617708\pi\) | ||||
−0.361419 | + | 0.932404i | \(0.617708\pi\) | |||||||
\(44\) | −4.81154 | −0.725366 | ||||||||
\(45\) | −3.93408 | −0.586457 | ||||||||
\(46\) | −3.86172 | −0.569380 | ||||||||
\(47\) | 10.4986 | 1.53138 | 0.765691 | − | 0.643208i | \(-0.222397\pi\) | ||||
0.765691 | + | 0.643208i | \(0.222397\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.4770 | 1.48166 | ||||||||
\(51\) | 3.61347 | 0.505988 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5944 | −1.45525 | −0.727626 | − | 0.685975i | \(-0.759376\pi\) | ||||
−0.727626 | + | 0.685975i | \(0.759376\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 18.9289 | 2.55238 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −7.71258 | −1.02156 | ||||||||
\(58\) | −4.45147 | −0.584507 | ||||||||
\(59\) | 3.70984 | 0.482980 | 0.241490 | − | 0.970403i | \(-0.422364\pi\) | ||||
0.241490 | + | 0.970403i | \(0.422364\pi\) | |||||||
\(60\) | 3.93408 | 0.507887 | ||||||||
\(61\) | −11.8947 | −1.52296 | −0.761482 | − | 0.648186i | \(-0.775528\pi\) | ||||
−0.761482 | + | 0.648186i | \(0.775528\pi\) | |||||||
\(62\) | −1.01880 | −0.129387 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.81154 | 0.592259 | ||||||||
\(67\) | 3.12611 | 0.381915 | 0.190957 | − | 0.981598i | \(-0.438841\pi\) | ||||
0.190957 | + | 0.981598i | \(0.438841\pi\) | |||||||
\(68\) | −3.61347 | −0.438198 | ||||||||
\(69\) | 3.86172 | 0.464896 | ||||||||
\(70\) | −3.93408 | −0.470212 | ||||||||
\(71\) | 8.73053 | 1.03612 | 0.518061 | − | 0.855343i | \(-0.326654\pi\) | ||||
0.518061 | + | 0.855343i | \(0.326654\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.7564 | 1.84414 | 0.922072 | − | 0.387019i | \(-0.126495\pi\) | ||||
0.922072 | + | 0.387019i | \(0.126495\pi\) | |||||||
\(74\) | −7.30140 | −0.848771 | ||||||||
\(75\) | −10.4770 | −1.20977 | ||||||||
\(76\) | 7.71258 | 0.884693 | ||||||||
\(77\) | −4.81154 | −0.548325 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.731774 | −0.0823310 | −0.0411655 | − | 0.999152i | \(-0.513107\pi\) | ||||
−0.0411655 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(80\) | −3.93408 | −0.439843 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.28601 | −0.804605 | ||||||||
\(83\) | 0.380858 | 0.0418046 | 0.0209023 | − | 0.999782i | \(-0.493346\pi\) | ||||
0.0209023 | + | 0.999782i | \(0.493346\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 14.2157 | 1.54191 | ||||||||
\(86\) | −4.73996 | −0.511123 | ||||||||
\(87\) | 4.45147 | 0.477248 | ||||||||
\(88\) | −4.81154 | −0.512912 | ||||||||
\(89\) | −0.469836 | −0.0498025 | −0.0249013 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249013 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(90\) | −3.93408 | −0.414688 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.86172 | −0.402612 | ||||||||
\(93\) | 1.01880 | 0.105644 | ||||||||
\(94\) | 10.4986 | 1.08285 | ||||||||
\(95\) | −30.3419 | −3.11301 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.3667 | −1.15411 | −0.577057 | − | 0.816704i | \(-0.695799\pi\) | ||||
−0.577057 | + | 0.816704i | \(0.695799\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −4.81154 | −0.483578 | ||||||||
\(100\) | 10.4770 | 1.04770 | ||||||||
\(101\) | 2.43888 | 0.242678 | 0.121339 | − | 0.992611i | \(-0.461281\pi\) | ||||
0.121339 | + | 0.992611i | \(0.461281\pi\) | |||||||
\(102\) | 3.61347 | 0.357787 | ||||||||
\(103\) | 18.5174 | 1.82457 | 0.912287 | − | 0.409551i | \(-0.134315\pi\) | ||||
0.912287 | + | 0.409551i | \(0.134315\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.93408 | 0.383926 | ||||||||
\(106\) | −10.5944 | −1.02902 | ||||||||
\(107\) | −18.9523 | −1.83219 | −0.916095 | − | 0.400961i | \(-0.868676\pi\) | ||||
−0.916095 | + | 0.400961i | \(0.868676\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 13.0695 | 1.25184 | 0.625918 | − | 0.779889i | \(-0.284725\pi\) | ||||
0.625918 | + | 0.779889i | \(0.284725\pi\) | |||||||
\(110\) | 18.9289 | 1.80480 | ||||||||
\(111\) | 7.30140 | 0.693018 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 0.383319 | 0.0360596 | 0.0180298 | − | 0.999837i | \(-0.494261\pi\) | ||||
0.0180298 | + | 0.999837i | \(0.494261\pi\) | |||||||
\(114\) | −7.71258 | −0.722349 | ||||||||
\(115\) | 15.1923 | 1.41669 | ||||||||
\(116\) | −4.45147 | −0.413309 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.70984 | 0.341519 | ||||||||
\(119\) | −3.61347 | −0.331247 | ||||||||
\(120\) | 3.93408 | 0.359130 | ||||||||
\(121\) | 12.1509 | 1.10463 | ||||||||
\(122\) | −11.8947 | −1.07690 | ||||||||
\(123\) | 7.28601 | 0.656957 | ||||||||
\(124\) | −1.01880 | −0.0914906 | ||||||||
\(125\) | −21.5467 | −1.92720 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −8.48244 | −0.752695 | −0.376347 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376347 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.73996 | 0.417330 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1450 | 0.886372 | 0.443186 | − | 0.896430i | \(-0.353848\pi\) | ||||
0.443186 | + | 0.896430i | \(0.353848\pi\) | |||||||
\(132\) | 4.81154 | 0.418791 | ||||||||
\(133\) | 7.71258 | 0.668765 | ||||||||
\(134\) | 3.12611 | 0.270055 | ||||||||
\(135\) | 3.93408 | 0.338591 | ||||||||
\(136\) | −3.61347 | −0.309853 | ||||||||
\(137\) | 1.73976 | 0.148638 | 0.0743189 | − | 0.997235i | \(-0.476322\pi\) | ||||
0.0743189 | + | 0.997235i | \(0.476322\pi\) | |||||||
\(138\) | 3.86172 | 0.328731 | ||||||||
\(139\) | −6.78513 | −0.575507 | −0.287754 | − | 0.957704i | \(-0.592908\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592908\pi\) | |||||||
\(140\) | −3.93408 | −0.332490 | ||||||||
\(141\) | −10.4986 | −0.884144 | ||||||||
\(142\) | 8.73053 | 0.732649 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 17.5124 | 1.45433 | ||||||||
\(146\) | 15.7564 | 1.30401 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −7.30140 | −0.600172 | ||||||||
\(149\) | 19.2424 | 1.57640 | 0.788199 | − | 0.615420i | \(-0.211014\pi\) | ||||
0.788199 | + | 0.615420i | \(0.211014\pi\) | |||||||
\(150\) | −10.4770 | −0.855440 | ||||||||
\(151\) | −6.95569 | −0.566046 | −0.283023 | − | 0.959113i | \(-0.591337\pi\) | ||||
−0.283023 | + | 0.959113i | \(0.591337\pi\) | |||||||
\(152\) | 7.71258 | 0.625572 | ||||||||
\(153\) | −3.61347 | −0.292132 | ||||||||
\(154\) | −4.81154 | −0.387725 | ||||||||
\(155\) | 4.00802 | 0.321932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.09347 | 0.0872686 | 0.0436343 | − | 0.999048i | \(-0.486106\pi\) | ||||
0.0436343 | + | 0.999048i | \(0.486106\pi\) | |||||||
\(158\) | −0.731774 | −0.0582168 | ||||||||
\(159\) | 10.5944 | 0.840190 | ||||||||
\(160\) | −3.93408 | −0.311016 | ||||||||
\(161\) | −3.86172 | −0.304346 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 17.2244 | 1.34912 | 0.674558 | − | 0.738222i | \(-0.264334\pi\) | ||||
0.674558 | + | 0.738222i | \(0.264334\pi\) | |||||||
\(164\) | −7.28601 | −0.568942 | ||||||||
\(165\) | −18.9289 | −1.47362 | ||||||||
\(166\) | 0.380858 | 0.0295603 | ||||||||
\(167\) | 21.5911 | 1.67077 | 0.835384 | − | 0.549667i | \(-0.185245\pi\) | ||||
0.835384 | + | 0.549667i | \(0.185245\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 14.2157 | 1.09029 | ||||||||
\(171\) | 7.71258 | 0.589795 | ||||||||
\(172\) | −4.73996 | −0.361419 | ||||||||
\(173\) | 23.4276 | 1.78117 | 0.890584 | − | 0.454819i | \(-0.150296\pi\) | ||||
0.890584 | + | 0.454819i | \(0.150296\pi\) | |||||||
\(174\) | 4.45147 | 0.337465 | ||||||||
\(175\) | 10.4770 | 0.791983 | ||||||||
\(176\) | −4.81154 | −0.362683 | ||||||||
\(177\) | −3.70984 | −0.278849 | ||||||||
\(178\) | −0.469836 | −0.0352157 | ||||||||
\(179\) | 3.15190 | 0.235584 | 0.117792 | − | 0.993038i | \(-0.462418\pi\) | ||||
0.117792 | + | 0.993038i | \(0.462418\pi\) | |||||||
\(180\) | −3.93408 | −0.293229 | ||||||||
\(181\) | 1.49375 | 0.111029 | 0.0555147 | − | 0.998458i | \(-0.482320\pi\) | ||||
0.0555147 | + | 0.998458i | \(0.482320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8947 | 0.879284 | ||||||||
\(184\) | −3.86172 | −0.284690 | ||||||||
\(185\) | 28.7243 | 2.11185 | ||||||||
\(186\) | 1.01880 | 0.0747017 | ||||||||
\(187\) | 17.3864 | 1.27142 | ||||||||
\(188\) | 10.4986 | 0.765691 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −30.3419 | −2.20123 | ||||||||
\(191\) | 3.19802 | 0.231401 | 0.115700 | − | 0.993284i | \(-0.463089\pi\) | ||||
0.115700 | + | 0.993284i | \(0.463089\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 3.88466 | 0.279624 | 0.139812 | − | 0.990178i | \(-0.455350\pi\) | ||||
0.139812 | + | 0.990178i | \(0.455350\pi\) | |||||||
\(194\) | −11.3667 | −0.816082 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.9583 | 0.851994 | 0.425997 | − | 0.904725i | \(-0.359923\pi\) | ||||
0.425997 | + | 0.904725i | \(0.359923\pi\) | |||||||
\(198\) | −4.81154 | −0.341941 | ||||||||
\(199\) | 25.6975 | 1.82165 | 0.910823 | − | 0.412797i | \(-0.135448\pi\) | ||||
0.910823 | + | 0.412797i | \(0.135448\pi\) | |||||||
\(200\) | 10.4770 | 0.740832 | ||||||||
\(201\) | −3.12611 | −0.220499 | ||||||||
\(202\) | 2.43888 | 0.171599 | ||||||||
\(203\) | −4.45147 | −0.312432 | ||||||||
\(204\) | 3.61347 | 0.252994 | ||||||||
\(205\) | 28.6637 | 2.00196 | ||||||||
\(206\) | 18.5174 | 1.29017 | ||||||||
\(207\) | −3.86172 | −0.268408 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.1093 | −2.56691 | ||||||||
\(210\) | 3.93408 | 0.271477 | ||||||||
\(211\) | −18.5638 | −1.27799 | −0.638993 | − | 0.769212i | \(-0.720649\pi\) | ||||
−0.638993 | + | 0.769212i | \(0.720649\pi\) | |||||||
\(212\) | −10.5944 | −0.727626 | ||||||||
\(213\) | −8.73053 | −0.598206 | ||||||||
\(214\) | −18.9523 | −1.29555 | ||||||||
\(215\) | 18.6474 | 1.27174 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.01880 | −0.0691604 | ||||||||
\(218\) | 13.0695 | 0.885181 | ||||||||
\(219\) | −15.7564 | −1.06472 | ||||||||
\(220\) | 18.9289 | 1.27619 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.30140 | 0.490038 | ||||||||
\(223\) | 18.0768 | 1.21051 | 0.605255 | − | 0.796032i | \(-0.293071\pi\) | ||||
0.605255 | + | 0.796032i | \(0.293071\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 10.4770 | 0.698463 | ||||||||
\(226\) | 0.383319 | 0.0254980 | ||||||||
\(227\) | 4.25355 | 0.282318 | 0.141159 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141159 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(228\) | −7.71258 | −0.510778 | ||||||||
\(229\) | −16.2898 | −1.07646 | −0.538229 | − | 0.842799i | \(-0.680906\pi\) | ||||
−0.538229 | + | 0.842799i | \(0.680906\pi\) | |||||||
\(230\) | 15.1923 | 1.00175 | ||||||||
\(231\) | 4.81154 | 0.316576 | ||||||||
\(232\) | −4.45147 | −0.292254 | ||||||||
\(233\) | 10.5462 | 0.690905 | 0.345452 | − | 0.938436i | \(-0.387725\pi\) | ||||
0.345452 | + | 0.938436i | \(0.387725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.3024 | −2.69427 | ||||||||
\(236\) | 3.70984 | 0.241490 | ||||||||
\(237\) | 0.731774 | 0.0475338 | ||||||||
\(238\) | −3.61347 | −0.234227 | ||||||||
\(239\) | −15.8572 | −1.02571 | −0.512857 | − | 0.858474i | \(-0.671413\pi\) | ||||
−0.512857 | + | 0.858474i | \(0.671413\pi\) | |||||||
\(240\) | 3.93408 | 0.253944 | ||||||||
\(241\) | −15.5235 | −0.999957 | −0.499979 | − | 0.866038i | \(-0.666659\pi\) | ||||
−0.499979 | + | 0.866038i | \(0.666659\pi\) | |||||||
\(242\) | 12.1509 | 0.781088 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.8947 | −0.761482 | ||||||||
\(245\) | −3.93408 | −0.251339 | ||||||||
\(246\) | 7.28601 | 0.464539 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.01880 | −0.0646936 | ||||||||
\(249\) | −0.380858 | −0.0241359 | ||||||||
\(250\) | −21.5467 | −1.36274 | ||||||||
\(251\) | 7.93745 | 0.501007 | 0.250504 | − | 0.968116i | \(-0.419404\pi\) | ||||
0.250504 | + | 0.968116i | \(0.419404\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 18.5808 | 1.16817 | ||||||||
\(254\) | −8.48244 | −0.532236 | ||||||||
\(255\) | −14.2157 | −0.890221 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.3365 | 0.956665 | 0.478332 | − | 0.878179i | \(-0.341241\pi\) | ||||
0.478332 | + | 0.878179i | \(0.341241\pi\) | |||||||
\(258\) | 4.73996 | 0.295097 | ||||||||
\(259\) | −7.30140 | −0.453687 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.45147 | −0.275539 | ||||||||
\(262\) | 10.1450 | 0.626760 | ||||||||
\(263\) | 14.6702 | 0.904604 | 0.452302 | − | 0.891865i | \(-0.350603\pi\) | ||||
0.452302 | + | 0.891865i | \(0.350603\pi\) | |||||||
\(264\) | 4.81154 | 0.296130 | ||||||||
\(265\) | 41.6791 | 2.56033 | ||||||||
\(266\) | 7.71258 | 0.472888 | ||||||||
\(267\) | 0.469836 | 0.0287535 | ||||||||
\(268\) | 3.12611 | 0.190957 | ||||||||
\(269\) | 13.0947 | 0.798395 | 0.399198 | − | 0.916865i | \(-0.369289\pi\) | ||||
0.399198 | + | 0.916865i | \(0.369289\pi\) | |||||||
\(270\) | 3.93408 | 0.239420 | ||||||||
\(271\) | −10.8665 | −0.660092 | −0.330046 | − | 0.943965i | \(-0.607064\pi\) | ||||
−0.330046 | + | 0.943965i | \(0.607064\pi\) | |||||||
\(272\) | −3.61347 | −0.219099 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.73976 | 0.105103 | ||||||||
\(275\) | −50.4102 | −3.03985 | ||||||||
\(276\) | 3.86172 | 0.232448 | ||||||||
\(277\) | 22.9560 | 1.37929 | 0.689645 | − | 0.724147i | \(-0.257766\pi\) | ||||
0.689645 | + | 0.724147i | \(0.257766\pi\) | |||||||
\(278\) | −6.78513 | −0.406945 | ||||||||
\(279\) | −1.01880 | −0.0609937 | ||||||||
\(280\) | −3.93408 | −0.235106 | ||||||||
\(281\) | −9.42525 | −0.562263 | −0.281132 | − | 0.959669i | \(-0.590710\pi\) | ||||
−0.281132 | + | 0.959669i | \(0.590710\pi\) | |||||||
\(282\) | −10.4986 | −0.625184 | ||||||||
\(283\) | −19.1238 | −1.13679 | −0.568396 | − | 0.822755i | \(-0.692436\pi\) | ||||
−0.568396 | + | 0.822755i | \(0.692436\pi\) | |||||||
\(284\) | 8.73053 | 0.518061 | ||||||||
\(285\) | 30.3419 | 1.79730 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.28601 | −0.430079 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.94280 | −0.231930 | ||||||||
\(290\) | 17.5124 | 1.02837 | ||||||||
\(291\) | 11.3667 | 0.666328 | ||||||||
\(292\) | 15.7564 | 0.922072 | ||||||||
\(293\) | −19.6143 | −1.14588 | −0.572940 | − | 0.819597i | \(-0.694197\pi\) | ||||
−0.572940 | + | 0.819597i | \(0.694197\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −14.5948 | −0.849742 | ||||||||
\(296\) | −7.30140 | −0.424385 | ||||||||
\(297\) | 4.81154 | 0.279194 | ||||||||
\(298\) | 19.2424 | 1.11468 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.4770 | −0.604887 | ||||||||
\(301\) | −4.73996 | −0.273207 | ||||||||
\(302\) | −6.95569 | −0.400255 | ||||||||
\(303\) | −2.43888 | −0.140110 | ||||||||
\(304\) | 7.71258 | 0.442347 | ||||||||
\(305\) | 46.7948 | 2.67946 | ||||||||
\(306\) | −3.61347 | −0.206569 | ||||||||
\(307\) | 6.84964 | 0.390930 | 0.195465 | − | 0.980711i | \(-0.437378\pi\) | ||||
0.195465 | + | 0.980711i | \(0.437378\pi\) | |||||||
\(308\) | −4.81154 | −0.274163 | ||||||||
\(309\) | −18.5174 | −1.05342 | ||||||||
\(310\) | 4.00802 | 0.227640 | ||||||||
\(311\) | 11.1603 | 0.632843 | 0.316422 | − | 0.948619i | \(-0.397519\pi\) | ||||
0.316422 | + | 0.948619i | \(0.397519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7636 | 0.777966 | 0.388983 | − | 0.921245i | \(-0.372826\pi\) | ||||
0.388983 | + | 0.921245i | \(0.372826\pi\) | |||||||
\(314\) | 1.09347 | 0.0617082 | ||||||||
\(315\) | −3.93408 | −0.221660 | ||||||||
\(316\) | −0.731774 | −0.0411655 | ||||||||
\(317\) | 1.05913 | 0.0594867 | 0.0297434 | − | 0.999558i | \(-0.490531\pi\) | ||||
0.0297434 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(318\) | 10.5944 | 0.594104 | ||||||||
\(319\) | 21.4184 | 1.19920 | ||||||||
\(320\) | −3.93408 | −0.219922 | ||||||||
\(321\) | 18.9523 | 1.05782 | ||||||||
\(322\) | −3.86172 | −0.215205 | ||||||||
\(323\) | −27.8692 | −1.55068 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.2244 | 0.953969 | ||||||||
\(327\) | −13.0695 | −0.722747 | ||||||||
\(328\) | −7.28601 | −0.402302 | ||||||||
\(329\) | 10.4986 | 0.578808 | ||||||||
\(330\) | −18.9289 | −1.04200 | ||||||||
\(331\) | −2.59428 | −0.142594 | −0.0712972 | − | 0.997455i | \(-0.522714\pi\) | ||||
−0.0712972 | + | 0.997455i | \(0.522714\pi\) | |||||||
\(332\) | 0.380858 | 0.0209023 | ||||||||
\(333\) | −7.30140 | −0.400114 | ||||||||
\(334\) | 21.5911 | 1.18141 | ||||||||
\(335\) | −12.2983 | −0.671930 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −18.0032 | −0.980696 | −0.490348 | − | 0.871527i | \(-0.663130\pi\) | ||||
−0.490348 | + | 0.871527i | \(0.663130\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.383319 | −0.0208190 | ||||||||
\(340\) | 14.2157 | 0.770954 | ||||||||
\(341\) | 4.90197 | 0.265457 | ||||||||
\(342\) | 7.71258 | 0.417048 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.73996 | −0.255562 | ||||||||
\(345\) | −15.1923 | −0.817926 | ||||||||
\(346\) | 23.4276 | 1.25948 | ||||||||
\(347\) | 32.2122 | 1.72924 | 0.864621 | − | 0.502424i | \(-0.167558\pi\) | ||||
0.864621 | + | 0.502424i | \(0.167558\pi\) | |||||||
\(348\) | 4.45147 | 0.238624 | ||||||||
\(349\) | 26.9689 | 1.44361 | 0.721807 | − | 0.692095i | \(-0.243312\pi\) | ||||
0.721807 | + | 0.692095i | \(0.243312\pi\) | |||||||
\(350\) | 10.4770 | 0.560017 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.81154 | −0.256456 | ||||||||
\(353\) | −15.0234 | −0.799614 | −0.399807 | − | 0.916599i | \(-0.630923\pi\) | ||||
−0.399807 | + | 0.916599i | \(0.630923\pi\) | |||||||
\(354\) | −3.70984 | −0.197176 | ||||||||
\(355\) | −34.3465 | −1.82293 | ||||||||
\(356\) | −0.469836 | −0.0249013 | ||||||||
\(357\) | 3.61347 | 0.191245 | ||||||||
\(358\) | 3.15190 | 0.166583 | ||||||||
\(359\) | −0.187328 | −0.00988678 | −0.00494339 | − | 0.999988i | \(-0.501574\pi\) | ||||
−0.00494339 | + | 0.999988i | \(0.501574\pi\) | |||||||
\(360\) | −3.93408 | −0.207344 | ||||||||
\(361\) | 40.4838 | 2.13073 | ||||||||
\(362\) | 1.49375 | 0.0785097 | ||||||||
\(363\) | −12.1509 | −0.637756 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −61.9867 | −3.24453 | ||||||||
\(366\) | 11.8947 | 0.621748 | ||||||||
\(367\) | −15.6194 | −0.815323 | −0.407662 | − | 0.913133i | \(-0.633656\pi\) | ||||
−0.407662 | + | 0.913133i | \(0.633656\pi\) | |||||||
\(368\) | −3.86172 | −0.201306 | ||||||||
\(369\) | −7.28601 | −0.379294 | ||||||||
\(370\) | 28.7243 | 1.49330 | ||||||||
\(371\) | −10.5944 | −0.550033 | ||||||||
\(372\) | 1.01880 | 0.0528221 | ||||||||
\(373\) | −35.0244 | −1.81350 | −0.906748 | − | 0.421673i | \(-0.861443\pi\) | ||||
−0.906748 | + | 0.421673i | \(0.861443\pi\) | |||||||
\(374\) | 17.3864 | 0.899027 | ||||||||
\(375\) | 21.5467 | 1.11267 | ||||||||
\(376\) | 10.4986 | 0.541426 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 7.86687 | 0.404094 | 0.202047 | − | 0.979376i | \(-0.435241\pi\) | ||||
0.202047 | + | 0.979376i | \(0.435241\pi\) | |||||||
\(380\) | −30.3419 | −1.55650 | ||||||||
\(381\) | 8.48244 | 0.434569 | ||||||||
\(382\) | 3.19802 | 0.163625 | ||||||||
\(383\) | 25.0867 | 1.28187 | 0.640935 | − | 0.767595i | \(-0.278547\pi\) | ||||
0.640935 | + | 0.767595i | \(0.278547\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 18.9289 | 0.964709 | ||||||||
\(386\) | 3.88466 | 0.197724 | ||||||||
\(387\) | −4.73996 | −0.240946 | ||||||||
\(388\) | −11.3667 | −0.577057 | ||||||||
\(389\) | −10.1352 | −0.513877 | −0.256939 | − | 0.966428i | \(-0.582714\pi\) | ||||
−0.256939 | + | 0.966428i | \(0.582714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9542 | 0.705696 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −10.1450 | −0.511747 | ||||||||
\(394\) | 11.9583 | 0.602451 | ||||||||
\(395\) | 2.87885 | 0.144851 | ||||||||
\(396\) | −4.81154 | −0.241789 | ||||||||
\(397\) | −12.0921 | −0.606884 | −0.303442 | − | 0.952850i | \(-0.598136\pi\) | ||||
−0.303442 | + | 0.952850i | \(0.598136\pi\) | |||||||
\(398\) | 25.6975 | 1.28810 | ||||||||
\(399\) | −7.71258 | −0.386112 | ||||||||
\(400\) | 10.4770 | 0.523848 | ||||||||
\(401\) | 0.593140 | 0.0296200 | 0.0148100 | − | 0.999890i | \(-0.495286\pi\) | ||||
0.0148100 | + | 0.999890i | \(0.495286\pi\) | |||||||
\(402\) | −3.12611 | −0.155916 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.43888 | 0.121339 | ||||||||
\(405\) | −3.93408 | −0.195486 | ||||||||
\(406\) | −4.45147 | −0.220923 | ||||||||
\(407\) | 35.1310 | 1.74138 | ||||||||
\(408\) | 3.61347 | 0.178894 | ||||||||
\(409\) | 12.2539 | 0.605918 | 0.302959 | − | 0.953004i | \(-0.402025\pi\) | ||||
0.302959 | + | 0.953004i | \(0.402025\pi\) | |||||||
\(410\) | 28.6637 | 1.41560 | ||||||||
\(411\) | −1.73976 | −0.0858161 | ||||||||
\(412\) | 18.5174 | 0.912287 | ||||||||
\(413\) | 3.70984 | 0.182549 | ||||||||
\(414\) | −3.86172 | −0.189793 | ||||||||
\(415\) | −1.49832 | −0.0735499 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.78513 | 0.332269 | ||||||||
\(418\) | −37.1093 | −1.81508 | ||||||||
\(419\) | 15.8430 | 0.773980 | 0.386990 | − | 0.922084i | \(-0.373515\pi\) | ||||
0.386990 | + | 0.922084i | \(0.373515\pi\) | |||||||
\(420\) | 3.93408 | 0.191963 | ||||||||
\(421\) | −29.5123 | −1.43834 | −0.719170 | − | 0.694834i | \(-0.755478\pi\) | ||||
−0.719170 | + | 0.694834i | \(0.755478\pi\) | |||||||
\(422\) | −18.5638 | −0.903673 | ||||||||
\(423\) | 10.4986 | 0.510461 | ||||||||
\(424\) | −10.5944 | −0.514509 | ||||||||
\(425\) | −37.8582 | −1.83639 | ||||||||
\(426\) | −8.73053 | −0.422995 | ||||||||
\(427\) | −11.8947 | −0.575627 | ||||||||
\(428\) | −18.9523 | −0.916095 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.6474 | 0.899256 | ||||||||
\(431\) | 25.2998 | 1.21865 | 0.609324 | − | 0.792921i | \(-0.291441\pi\) | ||||
0.609324 | + | 0.792921i | \(0.291441\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.5267 | −0.890334 | −0.445167 | − | 0.895448i | \(-0.646856\pi\) | ||||
−0.445167 | + | 0.895448i | \(0.646856\pi\) | |||||||
\(434\) | −1.01880 | −0.0489038 | ||||||||
\(435\) | −17.5124 | −0.839657 | ||||||||
\(436\) | 13.0695 | 0.625918 | ||||||||
\(437\) | −29.7838 | −1.42475 | ||||||||
\(438\) | −15.7564 | −0.752868 | ||||||||
\(439\) | 9.04946 | 0.431907 | 0.215954 | − | 0.976404i | \(-0.430714\pi\) | ||||
0.215954 | + | 0.976404i | \(0.430714\pi\) | |||||||
\(440\) | 18.9289 | 0.902402 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.9039 | 0.945662 | 0.472831 | − | 0.881153i | \(-0.343232\pi\) | ||||
0.472831 | + | 0.881153i | \(0.343232\pi\) | |||||||
\(444\) | 7.30140 | 0.346509 | ||||||||
\(445\) | 1.84837 | 0.0876212 | ||||||||
\(446\) | 18.0768 | 0.855960 | ||||||||
\(447\) | −19.2424 | −0.910134 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 2.84944 | 0.134474 | 0.0672368 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672368 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(450\) | 10.4770 | 0.493888 | ||||||||
\(451\) | 35.0569 | 1.65076 | ||||||||
\(452\) | 0.383319 | 0.0180298 | ||||||||
\(453\) | 6.95569 | 0.326807 | ||||||||
\(454\) | 4.25355 | 0.199629 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.71258 | −0.361174 | ||||||||
\(457\) | −22.6889 | −1.06134 | −0.530671 | − | 0.847578i | \(-0.678060\pi\) | ||||
−0.530671 | + | 0.847578i | \(0.678060\pi\) | |||||||
\(458\) | −16.2898 | −0.761170 | ||||||||
\(459\) | 3.61347 | 0.168663 | ||||||||
\(460\) | 15.1923 | 0.708345 | ||||||||
\(461\) | −9.94245 | −0.463066 | −0.231533 | − | 0.972827i | \(-0.574374\pi\) | ||||
−0.231533 | + | 0.972827i | \(0.574374\pi\) | |||||||
\(462\) | 4.81154 | 0.223853 | ||||||||
\(463\) | 22.5357 | 1.04732 | 0.523662 | − | 0.851926i | \(-0.324565\pi\) | ||||
0.523662 | + | 0.851926i | \(0.324565\pi\) | |||||||
\(464\) | −4.45147 | −0.206654 | ||||||||
\(465\) | −4.00802 | −0.185868 | ||||||||
\(466\) | 10.5462 | 0.488543 | ||||||||
\(467\) | −21.7935 | −1.00849 | −0.504243 | − | 0.863562i | \(-0.668228\pi\) | ||||
−0.504243 | + | 0.863562i | \(0.668228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.12611 | 0.144350 | ||||||||
\(470\) | −41.3024 | −1.90514 | ||||||||
\(471\) | −1.09347 | −0.0503846 | ||||||||
\(472\) | 3.70984 | 0.170759 | ||||||||
\(473\) | 22.8065 | 1.04864 | ||||||||
\(474\) | 0.731774 | 0.0336115 | ||||||||
\(475\) | 80.8043 | 3.70755 | ||||||||
\(476\) | −3.61347 | −0.165623 | ||||||||
\(477\) | −10.5944 | −0.485084 | ||||||||
\(478\) | −15.8572 | −0.725290 | ||||||||
\(479\) | −37.7401 | −1.72439 | −0.862195 | − | 0.506577i | \(-0.830911\pi\) | ||||
−0.862195 | + | 0.506577i | \(0.830911\pi\) | |||||||
\(480\) | 3.93408 | 0.179565 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −15.5235 | −0.707076 | ||||||||
\(483\) | 3.86172 | 0.175714 | ||||||||
\(484\) | 12.1509 | 0.552313 | ||||||||
\(485\) | 44.7175 | 2.03052 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 2.57450 | 0.116662 | 0.0583308 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583308 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(488\) | −11.8947 | −0.538449 | ||||||||
\(489\) | −17.2244 | −0.778912 | ||||||||
\(490\) | −3.93408 | −0.177723 | ||||||||
\(491\) | −12.5532 | −0.566519 | −0.283259 | − | 0.959043i | \(-0.591416\pi\) | ||||
−0.283259 | + | 0.959043i | \(0.591416\pi\) | |||||||
\(492\) | 7.28601 | 0.328479 | ||||||||
\(493\) | 16.0853 | 0.724445 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.9289 | 0.850793 | ||||||||
\(496\) | −1.01880 | −0.0457453 | ||||||||
\(497\) | 8.73053 | 0.391618 | ||||||||
\(498\) | −0.380858 | −0.0170667 | ||||||||
\(499\) | 3.79738 | 0.169994 | 0.0849970 | − | 0.996381i | \(-0.472912\pi\) | ||||
0.0849970 | + | 0.996381i | \(0.472912\pi\) | |||||||
\(500\) | −21.5467 | −0.963600 | ||||||||
\(501\) | −21.5911 | −0.964619 | ||||||||
\(502\) | 7.93745 | 0.354266 | ||||||||
\(503\) | 34.5483 | 1.54043 | 0.770216 | − | 0.637784i | \(-0.220149\pi\) | ||||
0.770216 | + | 0.637784i | \(0.220149\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −9.59475 | −0.426961 | ||||||||
\(506\) | 18.5808 | 0.826018 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.48244 | −0.376347 | ||||||||
\(509\) | 34.6920 | 1.53770 | 0.768849 | − | 0.639431i | \(-0.220830\pi\) | ||||
0.768849 | + | 0.639431i | \(0.220830\pi\) | |||||||
\(510\) | −14.2157 | −0.629481 | ||||||||
\(511\) | 15.7564 | 0.697021 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.71258 | −0.340519 | ||||||||
\(514\) | 15.3365 | 0.676464 | ||||||||
\(515\) | −72.8489 | −3.21011 | ||||||||
\(516\) | 4.73996 | 0.208665 | ||||||||
\(517\) | −50.5146 | −2.22163 | ||||||||
\(518\) | −7.30140 | −0.320805 | ||||||||
\(519\) | −23.4276 | −1.02836 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5590 | −0.462599 | −0.231300 | − | 0.972883i | \(-0.574298\pi\) | ||||
−0.231300 | + | 0.972883i | \(0.574298\pi\) | |||||||
\(522\) | −4.45147 | −0.194836 | ||||||||
\(523\) | −22.6374 | −0.989864 | −0.494932 | − | 0.868932i | \(-0.664807\pi\) | ||||
−0.494932 | + | 0.868932i | \(0.664807\pi\) | |||||||
\(524\) | 10.1450 | 0.443186 | ||||||||
\(525\) | −10.4770 | −0.457252 | ||||||||
\(526\) | 14.6702 | 0.639652 | ||||||||
\(527\) | 3.68139 | 0.160364 | ||||||||
\(528\) | 4.81154 | 0.209395 | ||||||||
\(529\) | −8.08712 | −0.351614 | ||||||||
\(530\) | 41.6791 | 1.81043 | ||||||||
\(531\) | 3.70984 | 0.160993 | ||||||||
\(532\) | 7.71258 | 0.334383 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.469836 | 0.0203318 | ||||||||
\(535\) | 74.5599 | 3.22350 | ||||||||
\(536\) | 3.12611 | 0.135027 | ||||||||
\(537\) | −3.15190 | −0.136014 | ||||||||
\(538\) | 13.0947 | 0.564551 | ||||||||
\(539\) | −4.81154 | −0.207248 | ||||||||
\(540\) | 3.93408 | 0.169296 | ||||||||
\(541\) | −1.92266 | −0.0826618 | −0.0413309 | − | 0.999146i | \(-0.513160\pi\) | ||||
−0.0413309 | + | 0.999146i | \(0.513160\pi\) | |||||||
\(542\) | −10.8665 | −0.466755 | ||||||||
\(543\) | −1.49375 | −0.0641029 | ||||||||
\(544\) | −3.61347 | −0.154926 | ||||||||
\(545\) | −51.4166 | −2.20244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.5913 | −1.00869 | −0.504346 | − | 0.863502i | \(-0.668266\pi\) | ||||
−0.504346 | + | 0.863502i | \(0.668266\pi\) | |||||||
\(548\) | 1.73976 | 0.0743189 | ||||||||
\(549\) | −11.8947 | −0.507655 | ||||||||
\(550\) | −50.4102 | −2.14950 | ||||||||
\(551\) | −34.3323 | −1.46261 | ||||||||
\(552\) | 3.86172 | 0.164366 | ||||||||
\(553\) | −0.731774 | −0.0311182 | ||||||||
\(554\) | 22.9560 | 0.975306 | ||||||||
\(555\) | −28.7243 | −1.21928 | ||||||||
\(556\) | −6.78513 | −0.287754 | ||||||||
\(557\) | 37.2227 | 1.57718 | 0.788589 | − | 0.614921i | \(-0.210812\pi\) | ||||
0.788589 | + | 0.614921i | \(0.210812\pi\) | |||||||
\(558\) | −1.01880 | −0.0431291 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.93408 | −0.166245 | ||||||||
\(561\) | −17.3864 | −0.734053 | ||||||||
\(562\) | −9.42525 | −0.397580 | ||||||||
\(563\) | 35.3321 | 1.48907 | 0.744535 | − | 0.667583i | \(-0.232671\pi\) | ||||
0.744535 | + | 0.667583i | \(0.232671\pi\) | |||||||
\(564\) | −10.4986 | −0.442072 | ||||||||
\(565\) | −1.50801 | −0.0634423 | ||||||||
\(566\) | −19.1238 | −0.803833 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 8.73053 | 0.366325 | ||||||||
\(569\) | −42.5755 | −1.78486 | −0.892430 | − | 0.451186i | \(-0.851001\pi\) | ||||
−0.892430 | + | 0.451186i | \(0.851001\pi\) | |||||||
\(570\) | 30.3419 | 1.27088 | ||||||||
\(571\) | 31.7267 | 1.32772 | 0.663861 | − | 0.747856i | \(-0.268917\pi\) | ||||
0.663861 | + | 0.747856i | \(0.268917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.19802 | −0.133599 | ||||||||
\(574\) | −7.28601 | −0.304112 | ||||||||
\(575\) | −40.4591 | −1.68726 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 30.9593 | 1.28885 | 0.644427 | − | 0.764666i | \(-0.277096\pi\) | ||||
0.644427 | + | 0.764666i | \(0.277096\pi\) | |||||||
\(578\) | −3.94280 | −0.163999 | ||||||||
\(579\) | −3.88466 | −0.161441 | ||||||||
\(580\) | 17.5124 | 0.727164 | ||||||||
\(581\) | 0.380858 | 0.0158007 | ||||||||
\(582\) | 11.3667 | 0.471165 | ||||||||
\(583\) | 50.9753 | 2.11118 | ||||||||
\(584\) | 15.7564 | 0.652003 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.6143 | −0.810259 | ||||||||
\(587\) | 1.79841 | 0.0742282 | 0.0371141 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371141 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −7.85754 | −0.323764 | ||||||||
\(590\) | −14.5948 | −0.600858 | ||||||||
\(591\) | −11.9583 | −0.491899 | ||||||||
\(592\) | −7.30140 | −0.300086 | ||||||||
\(593\) | 28.6678 | 1.17725 | 0.588624 | − | 0.808407i | \(-0.299670\pi\) | ||||
0.588624 | + | 0.808407i | \(0.299670\pi\) | |||||||
\(594\) | 4.81154 | 0.197420 | ||||||||
\(595\) | 14.2157 | 0.582786 | ||||||||
\(596\) | 19.2424 | 0.788199 | ||||||||
\(597\) | −25.6975 | −1.05173 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.13836 | 0.291665 | 0.145833 | − | 0.989309i | \(-0.453414\pi\) | ||||
0.145833 | + | 0.989309i | \(0.453414\pi\) | |||||||
\(600\) | −10.4770 | −0.427720 | ||||||||
\(601\) | 26.6183 | 1.08579 | 0.542893 | − | 0.839802i | \(-0.317329\pi\) | ||||
0.542893 | + | 0.839802i | \(0.317329\pi\) | |||||||
\(602\) | −4.73996 | −0.193186 | ||||||||
\(603\) | 3.12611 | 0.127305 | ||||||||
\(604\) | −6.95569 | −0.283023 | ||||||||
\(605\) | −47.8025 | −1.94345 | ||||||||
\(606\) | −2.43888 | −0.0990728 | ||||||||
\(607\) | −45.6948 | −1.85470 | −0.927348 | − | 0.374200i | \(-0.877917\pi\) | ||||
−0.927348 | + | 0.374200i | \(0.877917\pi\) | |||||||
\(608\) | 7.71258 | 0.312786 | ||||||||
\(609\) | 4.45147 | 0.180383 | ||||||||
\(610\) | 46.7948 | 1.89467 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.61347 | −0.146066 | ||||||||
\(613\) | 11.7581 | 0.474904 | 0.237452 | − | 0.971399i | \(-0.423688\pi\) | ||||
0.237452 | + | 0.971399i | \(0.423688\pi\) | |||||||
\(614\) | 6.84964 | 0.276429 | ||||||||
\(615\) | −28.6637 | −1.15583 | ||||||||
\(616\) | −4.81154 | −0.193862 | ||||||||
\(617\) | −45.6887 | −1.83936 | −0.919678 | − | 0.392672i | \(-0.871551\pi\) | ||||
−0.919678 | + | 0.392672i | \(0.871551\pi\) | |||||||
\(618\) | −18.5174 | −0.744879 | ||||||||
\(619\) | −22.5395 | −0.905937 | −0.452969 | − | 0.891526i | \(-0.649635\pi\) | ||||
−0.452969 | + | 0.891526i | \(0.649635\pi\) | |||||||
\(620\) | 4.00802 | 0.160966 | ||||||||
\(621\) | 3.86172 | 0.154965 | ||||||||
\(622\) | 11.1603 | 0.447488 | ||||||||
\(623\) | −0.469836 | −0.0188236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.3818 | 1.29527 | ||||||||
\(626\) | 13.7636 | 0.550105 | ||||||||
\(627\) | 37.1093 | 1.48200 | ||||||||
\(628\) | 1.09347 | 0.0436343 | ||||||||
\(629\) | 26.3834 | 1.05198 | ||||||||
\(630\) | −3.93408 | −0.156737 | ||||||||
\(631\) | 12.7494 | 0.507544 | 0.253772 | − | 0.967264i | \(-0.418329\pi\) | ||||
0.253772 | + | 0.967264i | \(0.418329\pi\) | |||||||
\(632\) | −0.731774 | −0.0291084 | ||||||||
\(633\) | 18.5638 | 0.737846 | ||||||||
\(634\) | 1.05913 | 0.0420635 | ||||||||
\(635\) | 33.3706 | 1.32427 | ||||||||
\(636\) | 10.5944 | 0.420095 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.4184 | 0.847964 | ||||||||
\(639\) | 8.73053 | 0.345374 | ||||||||
\(640\) | −3.93408 | −0.155508 | ||||||||
\(641\) | 9.79264 | 0.386786 | 0.193393 | − | 0.981121i | \(-0.438051\pi\) | ||||
0.193393 | + | 0.981121i | \(0.438051\pi\) | |||||||
\(642\) | 18.9523 | 0.747989 | ||||||||
\(643\) | −31.5951 | −1.24599 | −0.622995 | − | 0.782226i | \(-0.714084\pi\) | ||||
−0.622995 | + | 0.782226i | \(0.714084\pi\) | |||||||
\(644\) | −3.86172 | −0.152173 | ||||||||
\(645\) | −18.6474 | −0.734240 | ||||||||
\(646\) | −27.8692 | −1.09650 | ||||||||
\(647\) | 6.07753 | 0.238932 | 0.119466 | − | 0.992838i | \(-0.461882\pi\) | ||||
0.119466 | + | 0.992838i | \(0.461882\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −17.8500 | −0.700675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.01880 | 0.0399298 | ||||||||
\(652\) | 17.2244 | 0.674558 | ||||||||
\(653\) | 10.6316 | 0.416048 | 0.208024 | − | 0.978124i | \(-0.433297\pi\) | ||||
0.208024 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(654\) | −13.0695 | −0.511060 | ||||||||
\(655\) | −39.9112 | −1.55946 | ||||||||
\(656\) | −7.28601 | −0.284471 | ||||||||
\(657\) | 15.7564 | 0.614714 | ||||||||
\(658\) | 10.4986 | 0.409279 | ||||||||
\(659\) | −34.0689 | −1.32714 | −0.663568 | − | 0.748116i | \(-0.730959\pi\) | ||||
−0.663568 | + | 0.748116i | \(0.730959\pi\) | |||||||
\(660\) | −18.9289 | −0.736808 | ||||||||
\(661\) | −10.8620 | −0.422484 | −0.211242 | − | 0.977434i | \(-0.567751\pi\) | ||||
−0.211242 | + | 0.977434i | \(0.567751\pi\) | |||||||
\(662\) | −2.59428 | −0.100829 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.380858 | 0.0147802 | ||||||||
\(665\) | −30.3419 | −1.17661 | ||||||||
\(666\) | −7.30140 | −0.282924 | ||||||||
\(667\) | 17.1903 | 0.665613 | ||||||||
\(668\) | 21.5911 | 0.835384 | ||||||||
\(669\) | −18.0768 | −0.698888 | ||||||||
\(670\) | −12.2983 | −0.475127 | ||||||||
\(671\) | 57.2320 | 2.20942 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 44.8669 | 1.72949 | 0.864747 | − | 0.502208i | \(-0.167479\pi\) | ||||
0.864747 | + | 0.502208i | \(0.167479\pi\) | |||||||
\(674\) | −18.0032 | −0.693457 | ||||||||
\(675\) | −10.4770 | −0.403258 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.6948 | 1.52560 | 0.762798 | − | 0.646637i | \(-0.223825\pi\) | ||||
0.762798 | + | 0.646637i | \(0.223825\pi\) | |||||||
\(678\) | −0.383319 | −0.0147213 | ||||||||
\(679\) | −11.3667 | −0.436214 | ||||||||
\(680\) | 14.2157 | 0.545147 | ||||||||
\(681\) | −4.25355 | −0.162996 | ||||||||
\(682\) | 4.90197 | 0.187706 | ||||||||
\(683\) | 36.7583 | 1.40652 | 0.703258 | − | 0.710935i | \(-0.251728\pi\) | ||||
0.703258 | + | 0.710935i | \(0.251728\pi\) | |||||||
\(684\) | 7.71258 | 0.294898 | ||||||||
\(685\) | −6.84435 | −0.261509 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 16.2898 | 0.621493 | ||||||||
\(688\) | −4.73996 | −0.180709 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −15.1923 | −0.578361 | ||||||||
\(691\) | 20.0634 | 0.763250 | 0.381625 | − | 0.924317i | \(-0.375365\pi\) | ||||
0.381625 | + | 0.924317i | \(0.375365\pi\) | |||||||
\(692\) | 23.4276 | 0.890584 | ||||||||
\(693\) | −4.81154 | −0.182775 | ||||||||
\(694\) | 32.2122 | 1.22276 | ||||||||
\(695\) | 26.6932 | 1.01253 | ||||||||
\(696\) | 4.45147 | 0.168733 | ||||||||
\(697\) | 26.3278 | 0.997237 | ||||||||
\(698\) | 26.9689 | 1.02079 | ||||||||
\(699\) | −10.5462 | −0.398894 | ||||||||
\(700\) | 10.4770 | 0.395992 | ||||||||
\(701\) | 38.1795 | 1.44202 | 0.721010 | − | 0.692925i | \(-0.243678\pi\) | ||||
0.721010 | + | 0.692925i | \(0.243678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.3126 | −2.12387 | ||||||||
\(704\) | −4.81154 | −0.181342 | ||||||||
\(705\) | 41.3024 | 1.55554 | ||||||||
\(706\) | −15.0234 | −0.565412 | ||||||||
\(707\) | 2.43888 | 0.0917236 | ||||||||
\(708\) | −3.70984 | −0.139424 | ||||||||
\(709\) | 28.4246 | 1.06751 | 0.533753 | − | 0.845640i | \(-0.320781\pi\) | ||||
0.533753 | + | 0.845640i | \(0.320781\pi\) | |||||||
\(710\) | −34.3465 | −1.28900 | ||||||||
\(711\) | −0.731774 | −0.0274437 | ||||||||
\(712\) | −0.469836 | −0.0176079 | ||||||||
\(713\) | 3.93431 | 0.147341 | ||||||||
\(714\) | 3.61347 | 0.135231 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.15190 | 0.117792 | ||||||||
\(717\) | 15.8572 | 0.592196 | ||||||||
\(718\) | −0.187328 | −0.00699101 | ||||||||
\(719\) | −2.84829 | −0.106223 | −0.0531116 | − | 0.998589i | \(-0.516914\pi\) | ||||
−0.0531116 | + | 0.998589i | \(0.516914\pi\) | |||||||
\(720\) | −3.93408 | −0.146614 | ||||||||
\(721\) | 18.5174 | 0.689624 | ||||||||
\(722\) | 40.4838 | 1.50665 | ||||||||
\(723\) | 15.5235 | 0.577325 | ||||||||
\(724\) | 1.49375 | 0.0555147 | ||||||||
\(725\) | −46.6379 | −1.73209 | ||||||||
\(726\) | −12.1509 | −0.450962 | ||||||||
\(727\) | −21.5949 | −0.800912 | −0.400456 | − | 0.916316i | \(-0.631148\pi\) | ||||
−0.400456 | + | 0.916316i | \(0.631148\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −61.9867 | −2.29423 | ||||||||
\(731\) | 17.1277 | 0.633492 | ||||||||
\(732\) | 11.8947 | 0.439642 | ||||||||
\(733\) | −25.3980 | −0.938097 | −0.469048 | − | 0.883173i | \(-0.655403\pi\) | ||||
−0.469048 | + | 0.883173i | \(0.655403\pi\) | |||||||
\(734\) | −15.6194 | −0.576521 | ||||||||
\(735\) | 3.93408 | 0.145111 | ||||||||
\(736\) | −3.86172 | −0.142345 | ||||||||
\(737\) | −15.0414 | −0.554057 | ||||||||
\(738\) | −7.28601 | −0.268202 | ||||||||
\(739\) | 23.4637 | 0.863125 | 0.431563 | − | 0.902083i | \(-0.357962\pi\) | ||||
0.431563 | + | 0.902083i | \(0.357962\pi\) | |||||||
\(740\) | 28.7243 | 1.05593 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.5944 | −0.388932 | ||||||||
\(743\) | 12.2641 | 0.449928 | 0.224964 | − | 0.974367i | \(-0.427774\pi\) | ||||
0.224964 | + | 0.974367i | \(0.427774\pi\) | |||||||
\(744\) | 1.01880 | 0.0373509 | ||||||||
\(745\) | −75.7010 | −2.77347 | ||||||||
\(746\) | −35.0244 | −1.28234 | ||||||||
\(747\) | 0.380858 | 0.0139349 | ||||||||
\(748\) | 17.3864 | 0.635708 | ||||||||
\(749\) | −18.9523 | −0.692503 | ||||||||
\(750\) | 21.5467 | 0.786776 | ||||||||
\(751\) | 15.1978 | 0.554574 | 0.277287 | − | 0.960787i | \(-0.410565\pi\) | ||||
0.277287 | + | 0.960787i | \(0.410565\pi\) | |||||||
\(752\) | 10.4986 | 0.382846 | ||||||||
\(753\) | −7.93745 | −0.289257 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.3642 | 0.995886 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 1.47834 | 0.0537311 | 0.0268655 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268655 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(758\) | 7.86687 | 0.285738 | ||||||||
\(759\) | −18.5808 | −0.674441 | ||||||||
\(760\) | −30.3419 | −1.10061 | ||||||||
\(761\) | −7.59688 | −0.275387 | −0.137693 | − | 0.990475i | \(-0.543969\pi\) | ||||
−0.137693 | + | 0.990475i | \(0.543969\pi\) | |||||||
\(762\) | 8.48244 | 0.307286 | ||||||||
\(763\) | 13.0695 | 0.473149 | ||||||||
\(764\) | 3.19802 | 0.115700 | ||||||||
\(765\) | 14.2157 | 0.513969 | ||||||||
\(766\) | 25.0867 | 0.906419 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 10.2870 | 0.370958 | 0.185479 | − | 0.982648i | \(-0.440616\pi\) | ||||
0.185479 | + | 0.982648i | \(0.440616\pi\) | |||||||
\(770\) | 18.9289 | 0.682152 | ||||||||
\(771\) | −15.3365 | −0.552331 | ||||||||
\(772\) | 3.88466 | 0.139812 | ||||||||
\(773\) | 11.5082 | 0.413922 | 0.206961 | − | 0.978349i | \(-0.433643\pi\) | ||||
0.206961 | + | 0.978349i | \(0.433643\pi\) | |||||||
\(774\) | −4.73996 | −0.170374 | ||||||||
\(775\) | −10.6739 | −0.383417 | ||||||||
\(776\) | −11.3667 | −0.408041 | ||||||||
\(777\) | 7.30140 | 0.261936 | ||||||||
\(778\) | −10.1352 | −0.363366 | ||||||||
\(779\) | −56.1939 | −2.01335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.0072 | −1.50314 | ||||||||
\(782\) | 13.9542 | 0.499002 | ||||||||
\(783\) | 4.45147 | 0.159083 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.30181 | −0.153538 | ||||||||
\(786\) | −10.1450 | −0.361860 | ||||||||
\(787\) | 17.9919 | 0.641341 | 0.320670 | − | 0.947191i | \(-0.396092\pi\) | ||||
0.320670 | + | 0.947191i | \(0.396092\pi\) | |||||||
\(788\) | 11.9583 | 0.425997 | ||||||||
\(789\) | −14.6702 | −0.522274 | ||||||||
\(790\) | 2.87885 | 0.102425 | ||||||||
\(791\) | 0.383319 | 0.0136293 | ||||||||
\(792\) | −4.81154 | −0.170971 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.0921 | −0.429132 | ||||||||
\(795\) | −41.6791 | −1.47821 | ||||||||
\(796\) | 25.6975 | 0.910823 | ||||||||
\(797\) | −33.6262 | −1.19110 | −0.595551 | − | 0.803318i | \(-0.703066\pi\) | ||||
−0.595551 | + | 0.803318i | \(0.703066\pi\) | |||||||
\(798\) | −7.71258 | −0.273022 | ||||||||
\(799\) | −37.9365 | −1.34210 | ||||||||
\(800\) | 10.4770 | 0.370416 | ||||||||
\(801\) | −0.469836 | −0.0166008 | ||||||||
\(802\) | 0.593140 | 0.0209445 | ||||||||
\(803\) | −75.8123 | −2.67536 | ||||||||
\(804\) | −3.12611 | −0.110249 | ||||||||
\(805\) | 15.1923 | 0.535458 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0947 | −0.460954 | ||||||||
\(808\) | 2.43888 | 0.0857996 | ||||||||
\(809\) | −39.5694 | −1.39119 | −0.695594 | − | 0.718435i | \(-0.744859\pi\) | ||||
−0.695594 | + | 0.718435i | \(0.744859\pi\) | |||||||
\(810\) | −3.93408 | −0.138229 | ||||||||
\(811\) | −13.7186 | −0.481725 | −0.240863 | − | 0.970559i | \(-0.577430\pi\) | ||||
−0.240863 | + | 0.970559i | \(0.577430\pi\) | |||||||
\(812\) | −4.45147 | −0.156216 | ||||||||
\(813\) | 10.8665 | 0.381104 | ||||||||
\(814\) | 35.1310 | 1.23134 | ||||||||
\(815\) | −67.7619 | −2.37360 | ||||||||
\(816\) | 3.61347 | 0.126497 | ||||||||
\(817\) | −36.5573 | −1.27898 | ||||||||
\(818\) | 12.2539 | 0.428449 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.6637 | 1.00098 | ||||||||
\(821\) | −5.77385 | −0.201509 | −0.100754 | − | 0.994911i | \(-0.532126\pi\) | ||||
−0.100754 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(822\) | −1.73976 | −0.0606811 | ||||||||
\(823\) | −12.6373 | −0.440507 | −0.220253 | − | 0.975443i | \(-0.570688\pi\) | ||||
−0.220253 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(824\) | 18.5174 | 0.645084 | ||||||||
\(825\) | 50.4102 | 1.75506 | ||||||||
\(826\) | 3.70984 | 0.129082 | ||||||||
\(827\) | −1.59504 | −0.0554649 | −0.0277325 | − | 0.999615i | \(-0.508829\pi\) | ||||
−0.0277325 | + | 0.999615i | \(0.508829\pi\) | |||||||
\(828\) | −3.86172 | −0.134204 | ||||||||
\(829\) | 22.1618 | 0.769713 | 0.384856 | − | 0.922976i | \(-0.374251\pi\) | ||||
0.384856 | + | 0.922976i | \(0.374251\pi\) | |||||||
\(830\) | −1.49832 | −0.0520076 | ||||||||
\(831\) | −22.9560 | −0.796334 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.61347 | −0.125199 | ||||||||
\(834\) | 6.78513 | 0.234950 | ||||||||
\(835\) | −84.9410 | −2.93950 | ||||||||
\(836\) | −37.1093 | −1.28345 | ||||||||
\(837\) | 1.01880 | 0.0352147 | ||||||||
\(838\) | 15.8430 | 0.547286 | ||||||||
\(839\) | 4.11002 | 0.141894 | 0.0709468 | − | 0.997480i | \(-0.477398\pi\) | ||||
0.0709468 | + | 0.997480i | \(0.477398\pi\) | |||||||
\(840\) | 3.93408 | 0.135739 | ||||||||
\(841\) | −9.18439 | −0.316703 | ||||||||
\(842\) | −29.5123 | −1.01706 | ||||||||
\(843\) | 9.42525 | 0.324623 | ||||||||
\(844\) | −18.5638 | −0.638993 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.4986 | 0.360950 | ||||||||
\(847\) | 12.1509 | 0.417509 | ||||||||
\(848\) | −10.5944 | −0.363813 | ||||||||
\(849\) | 19.1238 | 0.656327 | ||||||||
\(850\) | −37.8582 | −1.29853 | ||||||||
\(851\) | 28.1960 | 0.966546 | ||||||||
\(852\) | −8.73053 | −0.299103 | ||||||||
\(853\) | 26.3560 | 0.902412 | 0.451206 | − | 0.892420i | \(-0.350994\pi\) | ||||
0.451206 | + | 0.892420i | \(0.350994\pi\) | |||||||
\(854\) | −11.8947 | −0.407029 | ||||||||
\(855\) | −30.3419 | −1.03767 | ||||||||
\(856\) | −18.9523 | −0.647777 | ||||||||
\(857\) | 6.47039 | 0.221024 | 0.110512 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110512 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.4673 | −1.24425 | −0.622125 | − | 0.782918i | \(-0.713730\pi\) | ||||
−0.622125 | + | 0.782918i | \(0.713730\pi\) | |||||||
\(860\) | 18.6474 | 0.635870 | ||||||||
\(861\) | 7.28601 | 0.248306 | ||||||||
\(862\) | 25.2998 | 0.861714 | ||||||||
\(863\) | 50.9368 | 1.73391 | 0.866954 | − | 0.498389i | \(-0.166075\pi\) | ||||
0.866954 | + | 0.498389i | \(0.166075\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −92.1660 | −3.13374 | ||||||||
\(866\) | −18.5267 | −0.629561 | ||||||||
\(867\) | 3.94280 | 0.133905 | ||||||||
\(868\) | −1.01880 | −0.0345802 | ||||||||
\(869\) | 3.52096 | 0.119440 | ||||||||
\(870\) | −17.5124 | −0.593727 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 13.0695 | 0.442591 | ||||||||
\(873\) | −11.3667 | −0.384705 | ||||||||
\(874\) | −29.7838 | −1.00745 | ||||||||
\(875\) | −21.5467 | −0.728413 | ||||||||
\(876\) | −15.7564 | −0.532358 | ||||||||
\(877\) | −33.5197 | −1.13188 | −0.565940 | − | 0.824446i | \(-0.691487\pi\) | ||||
−0.565940 | + | 0.824446i | \(0.691487\pi\) | |||||||
\(878\) | 9.04946 | 0.305404 | ||||||||
\(879\) | 19.6143 | 0.661574 | ||||||||
\(880\) | 18.9289 | 0.638095 | ||||||||
\(881\) | −21.3685 | −0.719924 | −0.359962 | − | 0.932967i | \(-0.617210\pi\) | ||||
−0.359962 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −27.9621 | −0.941000 | −0.470500 | − | 0.882400i | \(-0.655926\pi\) | ||||
−0.470500 | + | 0.882400i | \(0.655926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.5948 | 0.490599 | ||||||||
\(886\) | 19.9039 | 0.668684 | ||||||||
\(887\) | −25.2726 | −0.848572 | −0.424286 | − | 0.905528i | \(-0.639475\pi\) | ||||
−0.424286 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(888\) | 7.30140 | 0.245019 | ||||||||
\(889\) | −8.48244 | −0.284492 | ||||||||
\(890\) | 1.84837 | 0.0619576 | ||||||||
\(891\) | −4.81154 | −0.161193 | ||||||||
\(892\) | 18.0768 | 0.605255 | ||||||||
\(893\) | 80.9715 | 2.70961 | ||||||||
\(894\) | −19.2424 | −0.643562 | ||||||||
\(895\) | −12.3998 | −0.414479 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.84944 | 0.0950871 | ||||||||
\(899\) | 4.53514 | 0.151255 | ||||||||
\(900\) | 10.4770 | 0.349232 | ||||||||
\(901\) | 38.2825 | 1.27538 | ||||||||
\(902\) | 35.0569 | 1.16727 | ||||||||
\(903\) | 4.73996 | 0.157736 | ||||||||
\(904\) | 0.383319 | 0.0127490 | ||||||||
\(905\) | −5.87652 | −0.195342 | ||||||||
\(906\) | 6.95569 | 0.231087 | ||||||||
\(907\) | −45.8740 | −1.52322 | −0.761611 | − | 0.648034i | \(-0.775591\pi\) | ||||
−0.761611 | + | 0.648034i | \(0.775591\pi\) | |||||||
\(908\) | 4.25355 | 0.141159 | ||||||||
\(909\) | 2.43888 | 0.0808926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5865 | 0.781454 | 0.390727 | − | 0.920507i | \(-0.372224\pi\) | ||||
0.390727 | + | 0.920507i | \(0.372224\pi\) | |||||||
\(912\) | −7.71258 | −0.255389 | ||||||||
\(913\) | −1.83251 | −0.0606473 | ||||||||
\(914\) | −22.6889 | −0.750482 | ||||||||
\(915\) | −46.7948 | −1.54699 | ||||||||
\(916\) | −16.2898 | −0.538229 | ||||||||
\(917\) | 10.1450 | 0.335017 | ||||||||
\(918\) | 3.61347 | 0.119262 | ||||||||
\(919\) | −17.3816 | −0.573365 | −0.286682 | − | 0.958026i | \(-0.592552\pi\) | ||||
−0.286682 | + | 0.958026i | \(0.592552\pi\) | |||||||
\(920\) | 15.1923 | 0.500875 | ||||||||
\(921\) | −6.84964 | −0.225703 | ||||||||
\(922\) | −9.94245 | −0.327437 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.81154 | 0.158288 | ||||||||
\(925\) | −76.4964 | −2.51519 | ||||||||
\(926\) | 22.5357 | 0.740570 | ||||||||
\(927\) | 18.5174 | 0.608191 | ||||||||
\(928\) | −4.45147 | −0.146127 | ||||||||
\(929\) | 28.1143 | 0.922401 | 0.461200 | − | 0.887296i | \(-0.347419\pi\) | ||||
0.461200 | + | 0.887296i | \(0.347419\pi\) | |||||||
\(930\) | −4.00802 | −0.131428 | ||||||||
\(931\) | 7.71258 | 0.252769 | ||||||||
\(932\) | 10.5462 | 0.345452 | ||||||||
\(933\) | −11.1603 | −0.365372 | ||||||||
\(934\) | −21.7935 | −0.713107 | ||||||||
\(935\) | −68.3993 | −2.23690 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.39725 | −0.143652 | −0.0718260 | − | 0.997417i | \(-0.522883\pi\) | ||||
−0.0718260 | + | 0.997417i | \(0.522883\pi\) | |||||||
\(938\) | 3.12611 | 0.102071 | ||||||||
\(939\) | −13.7636 | −0.449159 | ||||||||
\(940\) | −41.3024 | −1.34714 | ||||||||
\(941\) | 22.4304 | 0.731209 | 0.365604 | − | 0.930770i | \(-0.380862\pi\) | ||||
0.365604 | + | 0.930770i | \(0.380862\pi\) | |||||||
\(942\) | −1.09347 | −0.0356273 | ||||||||
\(943\) | 28.1365 | 0.916251 | ||||||||
\(944\) | 3.70984 | 0.120745 | ||||||||
\(945\) | 3.93408 | 0.127975 | ||||||||
\(946\) | 22.8065 | 0.741503 | ||||||||
\(947\) | −57.2579 | −1.86063 | −0.930316 | − | 0.366759i | \(-0.880467\pi\) | ||||
−0.930316 | + | 0.366759i | \(0.880467\pi\) | |||||||
\(948\) | 0.731774 | 0.0237669 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 80.8043 | 2.62164 | ||||||||
\(951\) | −1.05913 | −0.0343447 | ||||||||
\(952\) | −3.61347 | −0.117113 | ||||||||
\(953\) | −12.2786 | −0.397744 | −0.198872 | − | 0.980025i | \(-0.563728\pi\) | ||||
−0.198872 | + | 0.980025i | \(0.563728\pi\) | |||||||
\(954\) | −10.5944 | −0.343006 | ||||||||
\(955\) | −12.5813 | −0.407120 | ||||||||
\(956\) | −15.8572 | −0.512857 | ||||||||
\(957\) | −21.4184 | −0.692359 | ||||||||
\(958\) | −37.7401 | −1.21933 | ||||||||
\(959\) | 1.73976 | 0.0561798 | ||||||||
\(960\) | 3.93408 | 0.126972 | ||||||||
\(961\) | −29.9621 | −0.966518 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.9523 | −0.610730 | ||||||||
\(964\) | −15.5235 | −0.499979 | ||||||||
\(965\) | −15.2825 | −0.491962 | ||||||||
\(966\) | 3.86172 | 0.124249 | ||||||||
\(967\) | −11.7694 | −0.378477 | −0.189238 | − | 0.981931i | \(-0.560602\pi\) | ||||
−0.189238 | + | 0.981931i | \(0.560602\pi\) | |||||||
\(968\) | 12.1509 | 0.390544 | ||||||||
\(969\) | 27.8692 | 0.895287 | ||||||||
\(970\) | 44.7175 | 1.43579 | ||||||||
\(971\) | −37.3432 | −1.19840 | −0.599200 | − | 0.800600i | \(-0.704514\pi\) | ||||
−0.599200 | + | 0.800600i | \(0.704514\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.78513 | −0.217521 | ||||||||
\(974\) | 2.57450 | 0.0824922 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.8947 | −0.380741 | ||||||||
\(977\) | 47.1492 | 1.50844 | 0.754218 | − | 0.656625i | \(-0.228016\pi\) | ||||
0.754218 | + | 0.656625i | \(0.228016\pi\) | |||||||
\(978\) | −17.2244 | −0.550774 | ||||||||
\(979\) | 2.26063 | 0.0722502 | ||||||||
\(980\) | −3.93408 | −0.125669 | ||||||||
\(981\) | 13.0695 | 0.417278 | ||||||||
\(982\) | −12.5532 | −0.400589 | ||||||||
\(983\) | −24.3817 | −0.777654 | −0.388827 | − | 0.921311i | \(-0.627120\pi\) | ||||
−0.388827 | + | 0.921311i | \(0.627120\pi\) | |||||||
\(984\) | 7.28601 | 0.232269 | ||||||||
\(985\) | −47.0449 | −1.49897 | ||||||||
\(986\) | 16.0853 | 0.512260 | ||||||||
\(987\) | −10.4986 | −0.334175 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.3044 | 0.582046 | ||||||||
\(990\) | 18.9289 | 0.601602 | ||||||||
\(991\) | −28.4168 | −0.902688 | −0.451344 | − | 0.892350i | \(-0.649055\pi\) | ||||
−0.451344 | + | 0.892350i | \(0.649055\pi\) | |||||||
\(992\) | −1.01880 | −0.0323468 | ||||||||
\(993\) | 2.59428 | 0.0823269 | ||||||||
\(994\) | 8.73053 | 0.276915 | ||||||||
\(995\) | −101.096 | −3.20495 | ||||||||
\(996\) | −0.380858 | −0.0120680 | ||||||||
\(997\) | −9.94278 | −0.314891 | −0.157445 | − | 0.987528i | \(-0.550326\pi\) | ||||
−0.157445 | + | 0.987528i | \(0.550326\pi\) | |||||||
\(998\) | 3.79738 | 0.120204 | ||||||||
\(999\) | 7.30140 | 0.231006 |
(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 | 7098.2.a.cs.1.1 | yes | 6 | |
13.12 | even | 2 | 7098.2.a.cp.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cp.1.6 | ✓ | 6 | 13.12 | even | 2 | ||
7098.2.a.cs.1.1 | yes | 6 | 1.1 | even | 1 | trivial |