Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4650,2,Mod(1,4650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4650, 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("4650.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4650.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: | \(37.1304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 930) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4650.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.828427 | −0.313116 | −0.156558 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156558 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.828427 | 0.180778 | ||||||||
\(22\) | −0.828427 | −0.176621 | ||||||||
\(23\) | −8.48528 | −1.76930 | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.82843 | −0.946932 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.828427 | −0.156558 | ||||||||
\(29\) | 9.65685 | 1.79323 | 0.896616 | − | 0.442808i | \(-0.146018\pi\) | ||||
0.896616 | + | 0.442808i | \(0.146018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.828427 | 0.144211 | ||||||||
\(34\) | −0.828427 | −0.142074 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.4853 | 1.72377 | 0.861885 | − | 0.507104i | \(-0.169284\pi\) | ||||
0.861885 | + | 0.507104i | \(0.169284\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82843 | 0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | 0.828427 | 0.127829 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | −0.828427 | −0.124890 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.48528 | −1.25109 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.828427 | 0.116003 | ||||||||
\(52\) | −4.82843 | −0.669582 | ||||||||
\(53\) | −0.343146 | −0.0471347 | −0.0235673 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235673 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.828427 | −0.110703 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.65685 | 1.26801 | ||||||||
\(59\) | 3.17157 | 0.412904 | 0.206452 | − | 0.978457i | \(-0.433808\pi\) | ||||
0.206452 | + | 0.978457i | \(0.433808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.828427 | 0.106069 | 0.0530346 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530346 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −0.828427 | −0.104372 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.828427 | 0.101972 | ||||||||
\(67\) | −9.17157 | −1.12049 | −0.560243 | − | 0.828328i | \(-0.689292\pi\) | ||||
−0.560243 | + | 0.828328i | \(0.689292\pi\) | |||||||
\(68\) | −0.828427 | −0.100462 | ||||||||
\(69\) | 8.48528 | 1.02151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.82843 | −0.335673 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 13.6569 | 1.59841 | 0.799207 | − | 0.601056i | \(-0.205253\pi\) | ||||
0.799207 | + | 0.601056i | \(0.205253\pi\) | |||||||
\(74\) | 10.4853 | 1.21889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.686292 | 0.0782102 | ||||||||
\(78\) | 4.82843 | 0.546712 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.65685 | 0.845558 | ||||||||
\(83\) | 1.65685 | 0.181863 | 0.0909317 | − | 0.995857i | \(-0.471016\pi\) | ||||
0.0909317 | + | 0.995857i | \(0.471016\pi\) | |||||||
\(84\) | 0.828427 | 0.0903888 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.65685 | 1.04133 | ||||||||
\(87\) | −9.65685 | −1.03532 | ||||||||
\(88\) | −0.828427 | −0.0883106 | ||||||||
\(89\) | 4.82843 | 0.511812 | 0.255906 | − | 0.966702i | \(-0.417626\pi\) | ||||
0.255906 | + | 0.966702i | \(0.417626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | −8.48528 | −0.884652 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 5.65685 | 0.583460 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 11.3137 | 1.14873 | 0.574367 | − | 0.818598i | \(-0.305248\pi\) | ||||
0.574367 | + | 0.818598i | \(0.305248\pi\) | |||||||
\(98\) | −6.31371 | −0.637781 | ||||||||
\(99\) | −0.828427 | −0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | 0.828427 | 0.0820265 | ||||||||
\(103\) | 1.51472 | 0.149250 | 0.0746248 | − | 0.997212i | \(-0.476224\pi\) | ||||
0.0746248 | + | 0.997212i | \(0.476224\pi\) | |||||||
\(104\) | −4.82843 | −0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.343146 | −0.0333293 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −11.6569 | −1.11652 | −0.558262 | − | 0.829665i | \(-0.688532\pi\) | ||||
−0.558262 | + | 0.829665i | \(0.688532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4853 | −0.995219 | ||||||||
\(112\) | −0.828427 | −0.0782790 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.65685 | 0.896616 | ||||||||
\(117\) | −4.82843 | −0.446388 | ||||||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | 0.686292 | 0.0629122 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0.828427 | 0.0750023 | ||||||||
\(123\) | −7.65685 | −0.690395 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.828427 | −0.0738022 | ||||||||
\(127\) | −16.1421 | −1.43238 | −0.716191 | − | 0.697904i | \(-0.754116\pi\) | ||||
−0.716191 | + | 0.697904i | \(0.754116\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4853 | 1.61507 | 0.807533 | − | 0.589822i | \(-0.200802\pi\) | ||||
0.807533 | + | 0.589822i | \(0.200802\pi\) | |||||||
\(132\) | 0.828427 | 0.0721053 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.17157 | −0.792303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.828427 | −0.0710370 | ||||||||
\(137\) | 6.48528 | 0.554075 | 0.277037 | − | 0.960859i | \(-0.410647\pi\) | ||||
0.277037 | + | 0.960859i | \(0.410647\pi\) | |||||||
\(138\) | 8.48528 | 0.722315 | ||||||||
\(139\) | −14.1421 | −1.19952 | −0.599760 | − | 0.800180i | \(-0.704737\pi\) | ||||
−0.599760 | + | 0.800180i | \(0.704737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.65685 | −0.476393 | ||||||||
\(142\) | −2.82843 | −0.237356 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.6569 | 1.13025 | ||||||||
\(147\) | 6.31371 | 0.520746 | ||||||||
\(148\) | 10.4853 | 0.861885 | ||||||||
\(149\) | −0.686292 | −0.0562232 | −0.0281116 | − | 0.999605i | \(-0.508949\pi\) | ||||
−0.0281116 | + | 0.999605i | \(0.508949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6569 | 1.76241 | 0.881205 | − | 0.472735i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472735i | \(0.156733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.828427 | −0.0669744 | ||||||||
\(154\) | 0.686292 | 0.0553029 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.82843 | 0.386584 | ||||||||
\(157\) | −17.3137 | −1.38178 | −0.690892 | − | 0.722958i | \(-0.742782\pi\) | ||||
−0.690892 | + | 0.722958i | \(0.742782\pi\) | |||||||
\(158\) | 11.3137 | 0.900070 | ||||||||
\(159\) | 0.343146 | 0.0272132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.02944 | 0.553997 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 14.8284 | 1.16145 | 0.580726 | − | 0.814099i | \(-0.302769\pi\) | ||||
0.580726 | + | 0.814099i | \(0.302769\pi\) | |||||||
\(164\) | 7.65685 | 0.597900 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.65685 | 0.128597 | ||||||||
\(167\) | 0.485281 | 0.0375522 | 0.0187761 | − | 0.999824i | \(-0.494023\pi\) | ||||
0.0187761 | + | 0.999824i | \(0.494023\pi\) | |||||||
\(168\) | 0.828427 | 0.0639145 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.65685 | 0.736328 | ||||||||
\(173\) | 1.31371 | 0.0998794 | 0.0499397 | − | 0.998752i | \(-0.484097\pi\) | ||||
0.0499397 | + | 0.998752i | \(0.484097\pi\) | |||||||
\(174\) | −9.65685 | −0.732084 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.828427 | −0.0624450 | ||||||||
\(177\) | −3.17157 | −0.238390 | ||||||||
\(178\) | 4.82843 | 0.361906 | ||||||||
\(179\) | −11.1716 | −0.835003 | −0.417501 | − | 0.908676i | \(-0.637094\pi\) | ||||
−0.417501 | + | 0.908676i | \(0.637094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8284 | 1.84548 | 0.922741 | − | 0.385420i | \(-0.125943\pi\) | ||||
0.922741 | + | 0.385420i | \(0.125943\pi\) | |||||||
\(182\) | 4.00000 | 0.296500 | ||||||||
\(183\) | −0.828427 | −0.0612391 | ||||||||
\(184\) | −8.48528 | −0.625543 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | 0.686292 | 0.0501866 | ||||||||
\(188\) | 5.65685 | 0.412568 | ||||||||
\(189\) | 0.828427 | 0.0602592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.485281 | −0.0351137 | −0.0175569 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175569 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −15.3137 | −1.10230 | −0.551152 | − | 0.834405i | \(-0.685812\pi\) | ||||
−0.551152 | + | 0.834405i | \(0.685812\pi\) | |||||||
\(194\) | 11.3137 | 0.812277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.31371 | −0.450979 | ||||||||
\(197\) | 26.9706 | 1.92157 | 0.960787 | − | 0.277289i | \(-0.0894360\pi\) | ||||
0.960787 | + | 0.277289i | \(0.0894360\pi\) | |||||||
\(198\) | −0.828427 | −0.0588738 | ||||||||
\(199\) | 13.6569 | 0.968109 | 0.484054 | − | 0.875038i | \(-0.339164\pi\) | ||||
0.484054 | + | 0.875038i | \(0.339164\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.17157 | 0.646913 | ||||||||
\(202\) | 11.3137 | 0.796030 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | 0.828427 | 0.0580015 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.51472 | 0.105535 | ||||||||
\(207\) | −8.48528 | −0.589768 | ||||||||
\(208\) | −4.82843 | −0.334791 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3137 | 1.60498 | 0.802491 | − | 0.596664i | \(-0.203508\pi\) | ||||
0.802491 | + | 0.596664i | \(0.203508\pi\) | |||||||
\(212\) | −0.343146 | −0.0235673 | ||||||||
\(213\) | 2.82843 | 0.193801 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.828427 | −0.0562373 | ||||||||
\(218\) | −11.6569 | −0.789502 | ||||||||
\(219\) | −13.6569 | −0.922845 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | −10.4853 | −0.703726 | ||||||||
\(223\) | 17.7990 | 1.19191 | 0.595954 | − | 0.803018i | \(-0.296774\pi\) | ||||
0.595954 | + | 0.803018i | \(0.296774\pi\) | |||||||
\(224\) | −0.828427 | −0.0553516 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −17.6569 | −1.17193 | −0.585963 | − | 0.810338i | \(-0.699284\pi\) | ||||
−0.585963 | + | 0.810338i | \(0.699284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4853 | 1.22154 | 0.610771 | − | 0.791807i | \(-0.290860\pi\) | ||||
0.610771 | + | 0.791807i | \(0.290860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.686292 | −0.0451547 | ||||||||
\(232\) | 9.65685 | 0.634004 | ||||||||
\(233\) | 6.97056 | 0.456657 | 0.228328 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228328 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(234\) | −4.82843 | −0.315644 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.17157 | 0.206452 | ||||||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 0.686292 | 0.0444857 | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0000 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(242\) | −10.3137 | −0.662990 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.828427 | 0.0530346 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.65685 | −0.488183 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −1.65685 | −0.104999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.17157 | 0.200188 | 0.100094 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100094 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(252\) | −0.828427 | −0.0521860 | ||||||||
\(253\) | 7.02944 | 0.441937 | ||||||||
\(254\) | −16.1421 | −1.01285 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.6569 | 0.976648 | 0.488324 | − | 0.872662i | \(-0.337608\pi\) | ||||
0.488324 | + | 0.872662i | \(0.337608\pi\) | |||||||
\(258\) | −9.65685 | −0.601209 | ||||||||
\(259\) | −8.68629 | −0.539740 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.65685 | 0.597744 | ||||||||
\(262\) | 18.4853 | 1.14202 | ||||||||
\(263\) | −24.4853 | −1.50983 | −0.754914 | − | 0.655824i | \(-0.772321\pi\) | ||||
−0.754914 | + | 0.655824i | \(0.772321\pi\) | |||||||
\(264\) | 0.828427 | 0.0509862 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.82843 | −0.295495 | ||||||||
\(268\) | −9.17157 | −0.560243 | ||||||||
\(269\) | −4.97056 | −0.303061 | −0.151530 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151530 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6569 | −0.829595 | −0.414797 | − | 0.909914i | \(-0.636148\pi\) | ||||
−0.414797 | + | 0.909914i | \(0.636148\pi\) | |||||||
\(272\) | −0.828427 | −0.0502308 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 6.48528 | 0.391790 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.48528 | 0.510754 | ||||||||
\(277\) | −4.14214 | −0.248877 | −0.124438 | − | 0.992227i | \(-0.539713\pi\) | ||||
−0.124438 | + | 0.992227i | \(0.539713\pi\) | |||||||
\(278\) | −14.1421 | −0.848189 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.3137 | −1.27147 | −0.635735 | − | 0.771908i | \(-0.719303\pi\) | ||||
−0.635735 | + | 0.771908i | \(0.719303\pi\) | |||||||
\(282\) | −5.65685 | −0.336861 | ||||||||
\(283\) | 14.8284 | 0.881458 | 0.440729 | − | 0.897640i | \(-0.354720\pi\) | ||||
0.440729 | + | 0.897640i | \(0.354720\pi\) | |||||||
\(284\) | −2.82843 | −0.167836 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | −6.34315 | −0.374424 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3137 | −0.663221 | ||||||||
\(292\) | 13.6569 | 0.799207 | ||||||||
\(293\) | 2.00000 | 0.116841 | 0.0584206 | − | 0.998292i | \(-0.481394\pi\) | ||||
0.0584206 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(294\) | 6.31371 | 0.368223 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.4853 | 0.609445 | ||||||||
\(297\) | 0.828427 | 0.0480702 | ||||||||
\(298\) | −0.686292 | −0.0397558 | ||||||||
\(299\) | 40.9706 | 2.36939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 21.6569 | 1.24621 | ||||||||
\(303\) | −11.3137 | −0.649956 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.828427 | −0.0473580 | ||||||||
\(307\) | 0.485281 | 0.0276965 | 0.0138482 | − | 0.999904i | \(-0.495592\pi\) | ||||
0.0138482 | + | 0.999904i | \(0.495592\pi\) | |||||||
\(308\) | 0.686292 | 0.0391051 | ||||||||
\(309\) | −1.51472 | −0.0861693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.4853 | −0.934795 | −0.467397 | − | 0.884047i | \(-0.654808\pi\) | ||||
−0.467397 | + | 0.884047i | \(0.654808\pi\) | |||||||
\(312\) | 4.82843 | 0.273356 | ||||||||
\(313\) | −0.970563 | −0.0548595 | −0.0274297 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274297 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(314\) | −17.3137 | −0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.3137 | 0.636446 | ||||||||
\(317\) | −13.3137 | −0.747772 | −0.373886 | − | 0.927475i | \(-0.621975\pi\) | ||||
−0.373886 | + | 0.927475i | \(0.621975\pi\) | |||||||
\(318\) | 0.343146 | 0.0192427 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 7.02944 | 0.391735 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.8284 | 0.821271 | ||||||||
\(327\) | 11.6569 | 0.644626 | ||||||||
\(328\) | 7.65685 | 0.422779 | ||||||||
\(329\) | −4.68629 | −0.258364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4853 | 0.686253 | 0.343127 | − | 0.939289i | \(-0.388514\pi\) | ||||
0.343127 | + | 0.939289i | \(0.388514\pi\) | |||||||
\(332\) | 1.65685 | 0.0909317 | ||||||||
\(333\) | 10.4853 | 0.574590 | ||||||||
\(334\) | 0.485281 | 0.0265534 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.828427 | 0.0451944 | ||||||||
\(337\) | 5.65685 | 0.308148 | 0.154074 | − | 0.988059i | \(-0.450761\pi\) | ||||
0.154074 | + | 0.988059i | \(0.450761\pi\) | |||||||
\(338\) | 10.3137 | 0.560992 | ||||||||
\(339\) | 14.0000 | 0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.828427 | −0.0448618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0294 | 0.595534 | ||||||||
\(344\) | 9.65685 | 0.520663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.31371 | 0.0706254 | ||||||||
\(347\) | −17.6569 | −0.947870 | −0.473935 | − | 0.880560i | \(-0.657167\pi\) | ||||
−0.473935 | + | 0.880560i | \(0.657167\pi\) | |||||||
\(348\) | −9.65685 | −0.517662 | ||||||||
\(349\) | −25.3137 | −1.35501 | −0.677506 | − | 0.735517i | \(-0.736939\pi\) | ||||
−0.677506 | + | 0.735517i | \(0.736939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.82843 | 0.257722 | ||||||||
\(352\) | −0.828427 | −0.0441553 | ||||||||
\(353\) | 23.1716 | 1.23330 | 0.616649 | − | 0.787238i | \(-0.288490\pi\) | ||||
0.616649 | + | 0.787238i | \(0.288490\pi\) | |||||||
\(354\) | −3.17157 | −0.168567 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.82843 | 0.255906 | ||||||||
\(357\) | −0.686292 | −0.0363224 | ||||||||
\(358\) | −11.1716 | −0.590436 | ||||||||
\(359\) | 10.1421 | 0.535281 | 0.267641 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267641 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 24.8284 | 1.30495 | ||||||||
\(363\) | 10.3137 | 0.541329 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.828427 | −0.0433026 | ||||||||
\(367\) | 28.1421 | 1.46901 | 0.734504 | − | 0.678605i | \(-0.237415\pi\) | ||||
0.734504 | + | 0.678605i | \(0.237415\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | 7.65685 | 0.398600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.284271 | 0.0147586 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | −0.343146 | −0.0177674 | −0.00888371 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888371 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(374\) | 0.686292 | 0.0354873 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.65685 | 0.291730 | ||||||||
\(377\) | −46.6274 | −2.40143 | ||||||||
\(378\) | 0.828427 | 0.0426097 | ||||||||
\(379\) | −9.65685 | −0.496039 | −0.248020 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248020 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1421 | 0.826987 | ||||||||
\(382\) | −0.485281 | −0.0248292 | ||||||||
\(383\) | −11.5147 | −0.588375 | −0.294187 | − | 0.955748i | \(-0.595049\pi\) | ||||
−0.294187 | + | 0.955748i | \(0.595049\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.3137 | −0.779447 | ||||||||
\(387\) | 9.65685 | 0.490885 | ||||||||
\(388\) | 11.3137 | 0.574367 | ||||||||
\(389\) | 12.6863 | 0.643221 | 0.321610 | − | 0.946872i | \(-0.395776\pi\) | ||||
0.321610 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.02944 | 0.355494 | ||||||||
\(392\) | −6.31371 | −0.318890 | ||||||||
\(393\) | −18.4853 | −0.932459 | ||||||||
\(394\) | 26.9706 | 1.35876 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.828427 | −0.0416300 | ||||||||
\(397\) | −15.6569 | −0.785795 | −0.392897 | − | 0.919582i | \(-0.628527\pi\) | ||||
−0.392897 | + | 0.919582i | \(0.628527\pi\) | |||||||
\(398\) | 13.6569 | 0.684556 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.48528 | 0.124109 | 0.0620545 | − | 0.998073i | \(-0.480235\pi\) | ||||
0.0620545 | + | 0.998073i | \(0.480235\pi\) | |||||||
\(402\) | 9.17157 | 0.457436 | ||||||||
\(403\) | −4.82843 | −0.240521 | ||||||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | −8.68629 | −0.430563 | ||||||||
\(408\) | 0.828427 | 0.0410133 | ||||||||
\(409\) | 33.3137 | 1.64726 | 0.823628 | − | 0.567130i | \(-0.191946\pi\) | ||||
0.823628 | + | 0.567130i | \(0.191946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.48528 | −0.319895 | ||||||||
\(412\) | 1.51472 | 0.0746248 | ||||||||
\(413\) | −2.62742 | −0.129287 | ||||||||
\(414\) | −8.48528 | −0.417029 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.82843 | −0.236733 | ||||||||
\(417\) | 14.1421 | 0.692543 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.79899 | −0.478712 | −0.239356 | − | 0.970932i | \(-0.576936\pi\) | ||||
−0.239356 | + | 0.970932i | \(0.576936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 23.3137 | 1.13489 | ||||||||
\(423\) | 5.65685 | 0.275046 | ||||||||
\(424\) | −0.343146 | −0.0166646 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.82843 | 0.137038 | ||||||||
\(427\) | −0.686292 | −0.0332120 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.17157 | −0.0564327 | −0.0282163 | − | 0.999602i | \(-0.508983\pi\) | ||||
−0.0282163 | + | 0.999602i | \(0.508983\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 13.6569 | 0.656307 | 0.328153 | − | 0.944624i | \(-0.393574\pi\) | ||||
0.328153 | + | 0.944624i | \(0.393574\pi\) | |||||||
\(434\) | −0.828427 | −0.0397658 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.6569 | −0.558262 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −13.6569 | −0.652550 | ||||||||
\(439\) | −0.970563 | −0.0463224 | −0.0231612 | − | 0.999732i | \(-0.507373\pi\) | ||||
−0.0231612 | + | 0.999732i | \(0.507373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.31371 | −0.300653 | ||||||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | −6.34315 | −0.301372 | −0.150686 | − | 0.988582i | \(-0.548148\pi\) | ||||
−0.150686 | + | 0.988582i | \(0.548148\pi\) | |||||||
\(444\) | −10.4853 | −0.497609 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.7990 | 0.842807 | ||||||||
\(447\) | 0.686292 | 0.0324605 | ||||||||
\(448\) | −0.828427 | −0.0391395 | ||||||||
\(449\) | −12.1421 | −0.573023 | −0.286511 | − | 0.958077i | \(-0.592496\pi\) | ||||
−0.286511 | + | 0.958077i | \(0.592496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.34315 | −0.298687 | ||||||||
\(452\) | −14.0000 | −0.658505 | ||||||||
\(453\) | −21.6569 | −1.01753 | ||||||||
\(454\) | −17.6569 | −0.828677 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3137 | 1.46479 | 0.732397 | − | 0.680878i | \(-0.238402\pi\) | ||||
0.732397 | + | 0.680878i | \(0.238402\pi\) | |||||||
\(458\) | 18.4853 | 0.863760 | ||||||||
\(459\) | 0.828427 | 0.0386677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3137 | −0.899529 | −0.449765 | − | 0.893147i | \(-0.648492\pi\) | ||||
−0.449765 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(462\) | −0.686292 | −0.0319292 | ||||||||
\(463\) | −3.17157 | −0.147395 | −0.0736977 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736977 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(464\) | 9.65685 | 0.448308 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.97056 | 0.322905 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | −4.82843 | −0.223194 | ||||||||
\(469\) | 7.59798 | 0.350842 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.3137 | 0.797774 | ||||||||
\(472\) | 3.17157 | 0.145983 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | −11.3137 | −0.519656 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.686292 | 0.0314561 | ||||||||
\(477\) | −0.343146 | −0.0157116 | ||||||||
\(478\) | 0.686292 | 0.0313902 | ||||||||
\(479\) | 21.1716 | 0.967354 | 0.483677 | − | 0.875247i | \(-0.339301\pi\) | ||||
0.483677 | + | 0.875247i | \(0.339301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50.6274 | −2.30841 | ||||||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | −7.02944 | −0.319850 | ||||||||
\(484\) | −10.3137 | −0.468805 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −20.1421 | −0.912727 | −0.456364 | − | 0.889793i | \(-0.650848\pi\) | ||||
−0.456364 | + | 0.889793i | \(0.650848\pi\) | |||||||
\(488\) | 0.828427 | 0.0375011 | ||||||||
\(489\) | −14.8284 | −0.670565 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.4558 | −1.96113 | −0.980567 | − | 0.196183i | \(-0.937145\pi\) | ||||
−0.980567 | + | 0.196183i | \(0.937145\pi\) | |||||||
\(492\) | −7.65685 | −0.345198 | ||||||||
\(493\) | −8.00000 | −0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 2.34315 | 0.105104 | ||||||||
\(498\) | −1.65685 | −0.0742454 | ||||||||
\(499\) | 18.1421 | 0.812154 | 0.406077 | − | 0.913839i | \(-0.366897\pi\) | ||||
0.406077 | + | 0.913839i | \(0.366897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.485281 | −0.0216808 | ||||||||
\(502\) | 3.17157 | 0.141554 | ||||||||
\(503\) | −12.6863 | −0.565654 | −0.282827 | − | 0.959171i | \(-0.591272\pi\) | ||||
−0.282827 | + | 0.959171i | \(0.591272\pi\) | |||||||
\(504\) | −0.828427 | −0.0369011 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.02944 | 0.312497 | ||||||||
\(507\) | −10.3137 | −0.458048 | ||||||||
\(508\) | −16.1421 | −0.716191 | ||||||||
\(509\) | 20.9706 | 0.929504 | 0.464752 | − | 0.885441i | \(-0.346144\pi\) | ||||
0.464752 | + | 0.885441i | \(0.346144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3137 | −0.500489 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.6569 | 0.690594 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.65685 | −0.425119 | ||||||||
\(517\) | −4.68629 | −0.206103 | ||||||||
\(518\) | −8.68629 | −0.381654 | ||||||||
\(519\) | −1.31371 | −0.0576654 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.2843 | 1.50202 | 0.751011 | − | 0.660290i | \(-0.229567\pi\) | ||||
0.751011 | + | 0.660290i | \(0.229567\pi\) | |||||||
\(522\) | 9.65685 | 0.422669 | ||||||||
\(523\) | −22.6274 | −0.989428 | −0.494714 | − | 0.869056i | \(-0.664727\pi\) | ||||
−0.494714 | + | 0.869056i | \(0.664727\pi\) | |||||||
\(524\) | 18.4853 | 0.807533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.4853 | −1.06761 | ||||||||
\(527\) | −0.828427 | −0.0360869 | ||||||||
\(528\) | 0.828427 | 0.0360527 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.17157 | 0.137635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.9706 | −1.60137 | ||||||||
\(534\) | −4.82843 | −0.208946 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.17157 | −0.396152 | ||||||||
\(537\) | 11.1716 | 0.482089 | ||||||||
\(538\) | −4.97056 | −0.214296 | ||||||||
\(539\) | 5.23045 | 0.225291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.2843 | 0.958076 | 0.479038 | − | 0.877794i | \(-0.340986\pi\) | ||||
0.479038 | + | 0.877794i | \(0.340986\pi\) | |||||||
\(542\) | −13.6569 | −0.586612 | ||||||||
\(543\) | −24.8284 | −1.06549 | ||||||||
\(544\) | −0.828427 | −0.0355185 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | −9.85786 | −0.421492 | −0.210746 | − | 0.977541i | \(-0.567589\pi\) | ||||
−0.210746 | + | 0.977541i | \(0.567589\pi\) | |||||||
\(548\) | 6.48528 | 0.277037 | ||||||||
\(549\) | 0.828427 | 0.0353564 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.48528 | 0.361158 | ||||||||
\(553\) | −9.37258 | −0.398563 | ||||||||
\(554\) | −4.14214 | −0.175982 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1421 | −0.599760 | ||||||||
\(557\) | −17.3137 | −0.733605 | −0.366803 | − | 0.930299i | \(-0.619548\pi\) | ||||
−0.366803 | + | 0.930299i | \(0.619548\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | −46.6274 | −1.97213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.686292 | −0.0289752 | ||||||||
\(562\) | −21.3137 | −0.899065 | ||||||||
\(563\) | −4.97056 | −0.209484 | −0.104742 | − | 0.994499i | \(-0.533402\pi\) | ||||
−0.104742 | + | 0.994499i | \(0.533402\pi\) | |||||||
\(564\) | −5.65685 | −0.238197 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.8284 | 0.623285 | ||||||||
\(567\) | −0.828427 | −0.0347907 | ||||||||
\(568\) | −2.82843 | −0.118678 | ||||||||
\(569\) | −19.1716 | −0.803714 | −0.401857 | − | 0.915702i | \(-0.631635\pi\) | ||||
−0.401857 | + | 0.915702i | \(0.631635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.1716 | −1.38819 | −0.694094 | − | 0.719885i | \(-0.744195\pi\) | ||||
−0.694094 | + | 0.719885i | \(0.744195\pi\) | |||||||
\(572\) | 4.00000 | 0.167248 | ||||||||
\(573\) | 0.485281 | 0.0202729 | ||||||||
\(574\) | −6.34315 | −0.264758 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −16.3137 | −0.678561 | ||||||||
\(579\) | 15.3137 | 0.636416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.37258 | −0.0569443 | ||||||||
\(582\) | −11.3137 | −0.468968 | ||||||||
\(583\) | 0.284271 | 0.0117733 | ||||||||
\(584\) | 13.6569 | 0.565125 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.00000 | 0.0826192 | ||||||||
\(587\) | 7.31371 | 0.301869 | 0.150935 | − | 0.988544i | \(-0.451772\pi\) | ||||
0.150935 | + | 0.988544i | \(0.451772\pi\) | |||||||
\(588\) | 6.31371 | 0.260373 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.9706 | −1.10942 | ||||||||
\(592\) | 10.4853 | 0.430942 | ||||||||
\(593\) | 26.9706 | 1.10755 | 0.553774 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553774 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.686292 | −0.0281116 | ||||||||
\(597\) | −13.6569 | −0.558938 | ||||||||
\(598\) | 40.9706 | 1.67541 | ||||||||
\(599\) | 21.4558 | 0.876662 | 0.438331 | − | 0.898814i | \(-0.355570\pi\) | ||||
0.438331 | + | 0.898814i | \(0.355570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | −9.17157 | −0.373495 | ||||||||
\(604\) | 21.6569 | 0.881205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.3137 | −0.459588 | ||||||||
\(607\) | 9.79899 | 0.397729 | 0.198864 | − | 0.980027i | \(-0.436275\pi\) | ||||
0.198864 | + | 0.980027i | \(0.436275\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.3137 | −1.10499 | ||||||||
\(612\) | −0.828427 | −0.0334872 | ||||||||
\(613\) | 49.1127 | 1.98364 | 0.991822 | − | 0.127632i | \(-0.0407376\pi\) | ||||
0.991822 | + | 0.127632i | \(0.0407376\pi\) | |||||||
\(614\) | 0.485281 | 0.0195844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.686292 | 0.0276515 | ||||||||
\(617\) | −41.5980 | −1.67467 | −0.837336 | − | 0.546689i | \(-0.815888\pi\) | ||||
−0.837336 | + | 0.546689i | \(0.815888\pi\) | |||||||
\(618\) | −1.51472 | −0.0609309 | ||||||||
\(619\) | −15.5147 | −0.623589 | −0.311795 | − | 0.950150i | \(-0.600930\pi\) | ||||
−0.311795 | + | 0.950150i | \(0.600930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.48528 | 0.340503 | ||||||||
\(622\) | −16.4853 | −0.661000 | ||||||||
\(623\) | −4.00000 | −0.160257 | ||||||||
\(624\) | 4.82843 | 0.193292 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.970563 | −0.0387915 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.3137 | −0.690892 | ||||||||
\(629\) | −8.68629 | −0.346345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6274 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(632\) | 11.3137 | 0.450035 | ||||||||
\(633\) | −23.3137 | −0.926637 | ||||||||
\(634\) | −13.3137 | −0.528755 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.343146 | 0.0136066 | ||||||||
\(637\) | 30.4853 | 1.20787 | ||||||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | −2.82843 | −0.111891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.4558 | −0.768460 | −0.384230 | − | 0.923237i | \(-0.625533\pi\) | ||||
−0.384230 | + | 0.923237i | \(0.625533\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | 8.00000 | 0.315489 | 0.157745 | − | 0.987480i | \(-0.449578\pi\) | ||||
0.157745 | + | 0.987480i | \(0.449578\pi\) | |||||||
\(644\) | 7.02944 | 0.276999 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.1421 | −0.713241 | −0.356620 | − | 0.934249i | \(-0.616071\pi\) | ||||
−0.356620 | + | 0.934249i | \(0.616071\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.62742 | −0.103135 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.828427 | 0.0324686 | ||||||||
\(652\) | 14.8284 | 0.580726 | ||||||||
\(653\) | 14.0000 | 0.547862 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(654\) | 11.6569 | 0.455819 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.65685 | 0.298950 | ||||||||
\(657\) | 13.6569 | 0.532805 | ||||||||
\(658\) | −4.68629 | −0.182691 | ||||||||
\(659\) | −11.1716 | −0.435183 | −0.217591 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217591 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6274 | 0.957896 | 0.478948 | − | 0.877843i | \(-0.341018\pi\) | ||||
0.478948 | + | 0.877843i | \(0.341018\pi\) | |||||||
\(662\) | 12.4853 | 0.485254 | ||||||||
\(663\) | −4.00000 | −0.155347 | ||||||||
\(664\) | 1.65685 | 0.0642984 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4853 | 0.406296 | ||||||||
\(667\) | −81.9411 | −3.17277 | ||||||||
\(668\) | 0.485281 | 0.0187761 | ||||||||
\(669\) | −17.7990 | −0.688149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.686292 | −0.0264940 | ||||||||
\(672\) | 0.828427 | 0.0319573 | ||||||||
\(673\) | −7.02944 | −0.270965 | −0.135482 | − | 0.990780i | \(-0.543258\pi\) | ||||
−0.135482 | + | 0.990780i | \(0.543258\pi\) | |||||||
\(674\) | 5.65685 | 0.217894 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | 38.0000 | 1.46046 | 0.730229 | − | 0.683202i | \(-0.239413\pi\) | ||||
0.730229 | + | 0.683202i | \(0.239413\pi\) | |||||||
\(678\) | 14.0000 | 0.537667 | ||||||||
\(679\) | −9.37258 | −0.359687 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6569 | 0.676612 | ||||||||
\(682\) | −0.828427 | −0.0317221 | ||||||||
\(683\) | −24.2843 | −0.929212 | −0.464606 | − | 0.885518i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885518i | \(0.653804\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.0294 | 0.421106 | ||||||||
\(687\) | −18.4853 | −0.705257 | ||||||||
\(688\) | 9.65685 | 0.368164 | ||||||||
\(689\) | 1.65685 | 0.0631211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.2843 | −1.68465 | −0.842327 | − | 0.538968i | \(-0.818815\pi\) | ||||
−0.842327 | + | 0.538968i | \(0.818815\pi\) | |||||||
\(692\) | 1.31371 | 0.0499397 | ||||||||
\(693\) | 0.686292 | 0.0260701 | ||||||||
\(694\) | −17.6569 | −0.670245 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.65685 | −0.366042 | ||||||||
\(697\) | −6.34315 | −0.240264 | ||||||||
\(698\) | −25.3137 | −0.958138 | ||||||||
\(699\) | −6.97056 | −0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 4.82843 | 0.182237 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.828427 | −0.0312225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.1716 | 0.872074 | ||||||||
\(707\) | −9.37258 | −0.352492 | ||||||||
\(708\) | −3.17157 | −0.119195 | ||||||||
\(709\) | −40.8284 | −1.53334 | −0.766672 | − | 0.642039i | \(-0.778089\pi\) | ||||
−0.766672 | + | 0.642039i | \(0.778089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3137 | 0.424297 | ||||||||
\(712\) | 4.82843 | 0.180953 | ||||||||
\(713\) | −8.48528 | −0.317776 | ||||||||
\(714\) | −0.686292 | −0.0256838 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.1716 | −0.417501 | ||||||||
\(717\) | −0.686292 | −0.0256300 | ||||||||
\(718\) | 10.1421 | 0.378501 | ||||||||
\(719\) | −35.3137 | −1.31698 | −0.658490 | − | 0.752590i | \(-0.728804\pi\) | ||||
−0.658490 | + | 0.752590i | \(0.728804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.25483 | −0.0467325 | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | −22.0000 | −0.818189 | ||||||||
\(724\) | 24.8284 | 0.922741 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.3137 | 0.382778 | ||||||||
\(727\) | 29.5147 | 1.09464 | 0.547320 | − | 0.836923i | \(-0.315648\pi\) | ||||
0.547320 | + | 0.836923i | \(0.315648\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | −0.828427 | −0.0306195 | ||||||||
\(733\) | 16.3431 | 0.603648 | 0.301824 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301824 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(734\) | 28.1421 | 1.03875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.48528 | −0.312772 | ||||||||
\(737\) | 7.59798 | 0.279875 | ||||||||
\(738\) | 7.65685 | 0.281853 | ||||||||
\(739\) | −3.51472 | −0.129291 | −0.0646455 | − | 0.997908i | \(-0.520592\pi\) | ||||
−0.0646455 | + | 0.997908i | \(0.520592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.284271 | 0.0104359 | ||||||||
\(743\) | 21.4558 | 0.787139 | 0.393569 | − | 0.919295i | \(-0.371240\pi\) | ||||
0.393569 | + | 0.919295i | \(0.371240\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.343146 | −0.0125635 | ||||||||
\(747\) | 1.65685 | 0.0606211 | ||||||||
\(748\) | 0.686292 | 0.0250933 | ||||||||
\(749\) | 3.31371 | 0.121080 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.28427 | −0.156335 | −0.0781676 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781676 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(752\) | 5.65685 | 0.206284 | ||||||||
\(753\) | −3.17157 | −0.115579 | ||||||||
\(754\) | −46.6274 | −1.69807 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.828427 | 0.0301296 | ||||||||
\(757\) | 9.51472 | 0.345818 | 0.172909 | − | 0.984938i | \(-0.444683\pi\) | ||||
0.172909 | + | 0.984938i | \(0.444683\pi\) | |||||||
\(758\) | −9.65685 | −0.350753 | ||||||||
\(759\) | −7.02944 | −0.255152 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.1127 | 1.20033 | 0.600167 | − | 0.799875i | \(-0.295101\pi\) | ||||
0.600167 | + | 0.799875i | \(0.295101\pi\) | |||||||
\(762\) | 16.1421 | 0.584768 | ||||||||
\(763\) | 9.65685 | 0.349602 | ||||||||
\(764\) | −0.485281 | −0.0175569 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.5147 | −0.416044 | ||||||||
\(767\) | −15.3137 | −0.552946 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.6569 | −0.563868 | ||||||||
\(772\) | −15.3137 | −0.551152 | ||||||||
\(773\) | 0.343146 | 0.0123421 | 0.00617105 | − | 0.999981i | \(-0.498036\pi\) | ||||
0.00617105 | + | 0.999981i | \(0.498036\pi\) | |||||||
\(774\) | 9.65685 | 0.347108 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.3137 | 0.406138 | ||||||||
\(777\) | 8.68629 | 0.311619 | ||||||||
\(778\) | 12.6863 | 0.454826 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.34315 | 0.0838443 | ||||||||
\(782\) | 7.02944 | 0.251372 | ||||||||
\(783\) | −9.65685 | −0.345108 | ||||||||
\(784\) | −6.31371 | −0.225490 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.4853 | −0.659348 | ||||||||
\(787\) | 24.9706 | 0.890104 | 0.445052 | − | 0.895505i | \(-0.353185\pi\) | ||||
0.445052 | + | 0.895505i | \(0.353185\pi\) | |||||||
\(788\) | 26.9706 | 0.960787 | ||||||||
\(789\) | 24.4853 | 0.871699 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5980 | 0.412377 | ||||||||
\(792\) | −0.828427 | −0.0294369 | ||||||||
\(793\) | −4.00000 | −0.142044 | ||||||||
\(794\) | −15.6569 | −0.555641 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6569 | 0.484054 | ||||||||
\(797\) | 1.31371 | 0.0465339 | 0.0232670 | − | 0.999729i | \(-0.492593\pi\) | ||||
0.0232670 | + | 0.999729i | \(0.492593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.68629 | −0.165789 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.82843 | 0.170604 | ||||||||
\(802\) | 2.48528 | 0.0877583 | ||||||||
\(803\) | −11.3137 | −0.399252 | ||||||||
\(804\) | 9.17157 | 0.323456 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.82843 | −0.170074 | ||||||||
\(807\) | 4.97056 | 0.174972 | ||||||||
\(808\) | 11.3137 | 0.398015 | ||||||||
\(809\) | −18.4853 | −0.649908 | −0.324954 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324954 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9706 | −0.736376 | −0.368188 | − | 0.929751i | \(-0.620022\pi\) | ||||
−0.368188 | + | 0.929751i | \(0.620022\pi\) | |||||||
\(812\) | −8.00000 | −0.280745 | ||||||||
\(813\) | 13.6569 | 0.478967 | ||||||||
\(814\) | −8.68629 | −0.304454 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.828427 | 0.0290008 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 33.3137 | 1.16479 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.6569 | 0.895430 | 0.447715 | − | 0.894176i | \(-0.352238\pi\) | ||||
0.447715 | + | 0.894176i | \(0.352238\pi\) | |||||||
\(822\) | −6.48528 | −0.226200 | ||||||||
\(823\) | 31.1716 | 1.08657 | 0.543286 | − | 0.839547i | \(-0.317180\pi\) | ||||
0.543286 | + | 0.839547i | \(0.317180\pi\) | |||||||
\(824\) | 1.51472 | 0.0527677 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.62742 | −0.0914195 | ||||||||
\(827\) | 39.3137 | 1.36707 | 0.683536 | − | 0.729917i | \(-0.260441\pi\) | ||||
0.683536 | + | 0.729917i | \(0.260441\pi\) | |||||||
\(828\) | −8.48528 | −0.294884 | ||||||||
\(829\) | 19.1716 | 0.665856 | 0.332928 | − | 0.942952i | \(-0.391963\pi\) | ||||
0.332928 | + | 0.942952i | \(0.391963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.14214 | 0.143689 | ||||||||
\(832\) | −4.82843 | −0.167396 | ||||||||
\(833\) | 5.23045 | 0.181224 | ||||||||
\(834\) | 14.1421 | 0.489702 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | −9.79899 | −0.338500 | ||||||||
\(839\) | 40.7696 | 1.40752 | 0.703761 | − | 0.710437i | \(-0.251503\pi\) | ||||
0.703761 | + | 0.710437i | \(0.251503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.2548 | 2.21568 | ||||||||
\(842\) | 14.0000 | 0.482472 | ||||||||
\(843\) | 21.3137 | 0.734083 | ||||||||
\(844\) | 23.3137 | 0.802491 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.65685 | 0.194487 | ||||||||
\(847\) | 8.54416 | 0.293581 | ||||||||
\(848\) | −0.343146 | −0.0117837 | ||||||||
\(849\) | −14.8284 | −0.508910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −88.9706 | −3.04987 | ||||||||
\(852\) | 2.82843 | 0.0969003 | ||||||||
\(853\) | −21.3137 | −0.729767 | −0.364884 | − | 0.931053i | \(-0.618891\pi\) | ||||
−0.364884 | + | 0.931053i | \(0.618891\pi\) | |||||||
\(854\) | −0.686292 | −0.0234844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | −6.68629 | −0.228399 | −0.114200 | − | 0.993458i | \(-0.536430\pi\) | ||||
−0.114200 | + | 0.993458i | \(0.536430\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | −42.4264 | −1.44757 | −0.723785 | − | 0.690025i | \(-0.757599\pi\) | ||||
−0.723785 | + | 0.690025i | \(0.757599\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.34315 | 0.216174 | ||||||||
\(862\) | −1.17157 | −0.0399039 | ||||||||
\(863\) | 3.79899 | 0.129319 | 0.0646596 | − | 0.997907i | \(-0.479404\pi\) | ||||
0.0646596 | + | 0.997907i | \(0.479404\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.6569 | 0.464079 | ||||||||
\(867\) | 16.3137 | 0.554043 | ||||||||
\(868\) | −0.828427 | −0.0281186 | ||||||||
\(869\) | −9.37258 | −0.317943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.2843 | 1.50052 | ||||||||
\(872\) | −11.6569 | −0.394751 | ||||||||
\(873\) | 11.3137 | 0.382911 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.6569 | −0.461422 | ||||||||
\(877\) | 23.6569 | 0.798835 | 0.399418 | − | 0.916769i | \(-0.369212\pi\) | ||||
0.399418 | + | 0.916769i | \(0.369212\pi\) | |||||||
\(878\) | −0.970563 | −0.0327549 | ||||||||
\(879\) | −2.00000 | −0.0674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.1421 | −1.21766 | −0.608830 | − | 0.793301i | \(-0.708361\pi\) | ||||
−0.608830 | + | 0.793301i | \(0.708361\pi\) | |||||||
\(882\) | −6.31371 | −0.212594 | ||||||||
\(883\) | −0.970563 | −0.0326620 | −0.0163310 | − | 0.999867i | \(-0.505199\pi\) | ||||
−0.0163310 | + | 0.999867i | \(0.505199\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.34315 | −0.213102 | ||||||||
\(887\) | 20.0000 | 0.671534 | 0.335767 | − | 0.941945i | \(-0.391004\pi\) | ||||
0.335767 | + | 0.941945i | \(0.391004\pi\) | |||||||
\(888\) | −10.4853 | −0.351863 | ||||||||
\(889\) | 13.3726 | 0.448502 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.828427 | −0.0277534 | ||||||||
\(892\) | 17.7990 | 0.595954 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.686292 | 0.0229530 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.828427 | −0.0276758 | ||||||||
\(897\) | −40.9706 | −1.36797 | ||||||||
\(898\) | −12.1421 | −0.405188 | ||||||||
\(899\) | 9.65685 | 0.322074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.284271 | 0.00947045 | ||||||||
\(902\) | −6.34315 | −0.211204 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.6569 | −0.719501 | ||||||||
\(907\) | −38.1421 | −1.26649 | −0.633244 | − | 0.773952i | \(-0.718277\pi\) | ||||
−0.633244 | + | 0.773952i | \(0.718277\pi\) | |||||||
\(908\) | −17.6569 | −0.585963 | ||||||||
\(909\) | 11.3137 | 0.375252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.9411 | −1.65462 | −0.827312 | − | 0.561743i | \(-0.810131\pi\) | ||||
−0.827312 | + | 0.561743i | \(0.810131\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.37258 | −0.0454259 | ||||||||
\(914\) | 31.3137 | 1.03577 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4853 | 0.610771 | ||||||||
\(917\) | −15.3137 | −0.505703 | ||||||||
\(918\) | 0.828427 | 0.0273422 | ||||||||
\(919\) | −16.9706 | −0.559807 | −0.279904 | − | 0.960028i | \(-0.590303\pi\) | ||||
−0.279904 | + | 0.960028i | \(0.590303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.485281 | −0.0159906 | ||||||||
\(922\) | −19.3137 | −0.636063 | ||||||||
\(923\) | 13.6569 | 0.449521 | ||||||||
\(924\) | −0.686292 | −0.0225773 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.17157 | −0.104224 | ||||||||
\(927\) | 1.51472 | 0.0497499 | ||||||||
\(928\) | 9.65685 | 0.317002 | ||||||||
\(929\) | −36.1421 | −1.18579 | −0.592893 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592893 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.97056 | 0.228328 | ||||||||
\(933\) | 16.4853 | 0.539704 | ||||||||
\(934\) | −36.0000 | −1.17796 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.82843 | −0.157822 | ||||||||
\(937\) | 22.6274 | 0.739205 | 0.369603 | − | 0.929190i | \(-0.379494\pi\) | ||||
0.369603 | + | 0.929190i | \(0.379494\pi\) | |||||||
\(938\) | 7.59798 | 0.248083 | ||||||||
\(939\) | 0.970563 | 0.0316731 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.0000 | −1.30396 | −0.651981 | − | 0.758235i | \(-0.726062\pi\) | ||||
−0.651981 | + | 0.758235i | \(0.726062\pi\) | |||||||
\(942\) | 17.3137 | 0.564111 | ||||||||
\(943\) | −64.9706 | −2.11573 | ||||||||
\(944\) | 3.17157 | 0.103226 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | −54.9117 | −1.78439 | −0.892195 | − | 0.451650i | \(-0.850835\pi\) | ||||
−0.892195 | + | 0.451650i | \(0.850835\pi\) | |||||||
\(948\) | −11.3137 | −0.367452 | ||||||||
\(949\) | −65.9411 | −2.14054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.3137 | 0.431727 | ||||||||
\(952\) | 0.686292 | 0.0222428 | ||||||||
\(953\) | −5.79899 | −0.187848 | −0.0939239 | − | 0.995579i | \(-0.529941\pi\) | ||||
−0.0939239 | + | 0.995579i | \(0.529941\pi\) | |||||||
\(954\) | −0.343146 | −0.0111098 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.686292 | 0.0221963 | ||||||||
\(957\) | 8.00000 | 0.258603 | ||||||||
\(958\) | 21.1716 | 0.684022 | ||||||||
\(959\) | −5.37258 | −0.173490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −50.6274 | −1.63229 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 22.0000 | 0.708572 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.02944 | −0.226168 | ||||||||
\(967\) | −7.17157 | −0.230622 | −0.115311 | − | 0.993329i | \(-0.536787\pi\) | ||||
−0.115311 | + | 0.993329i | \(0.536787\pi\) | |||||||
\(968\) | −10.3137 | −0.331495 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.45584 | −0.239269 | −0.119635 | − | 0.992818i | \(-0.538172\pi\) | ||||
−0.119635 | + | 0.992818i | \(0.538172\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 11.7157 | 0.375589 | ||||||||
\(974\) | −20.1421 | −0.645396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.828427 | 0.0265173 | ||||||||
\(977\) | 27.6569 | 0.884821 | 0.442411 | − | 0.896813i | \(-0.354123\pi\) | ||||
0.442411 | + | 0.896813i | \(0.354123\pi\) | |||||||
\(978\) | −14.8284 | −0.474161 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6569 | −0.372175 | ||||||||
\(982\) | −43.4558 | −1.38673 | ||||||||
\(983\) | −36.4853 | −1.16370 | −0.581850 | − | 0.813296i | \(-0.697671\pi\) | ||||
−0.581850 | + | 0.813296i | \(0.697671\pi\) | |||||||
\(984\) | −7.65685 | −0.244092 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.00000 | −0.254772 | ||||||||
\(987\) | 4.68629 | 0.149166 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.9411 | −2.60558 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.9411 | −1.07818 | −0.539088 | − | 0.842250i | \(-0.681231\pi\) | ||||
−0.539088 | + | 0.842250i | \(0.681231\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −12.4853 | −0.396208 | ||||||||
\(994\) | 2.34315 | 0.0743201 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.65685 | −0.0524994 | ||||||||
\(997\) | −10.2843 | −0.325706 | −0.162853 | − | 0.986650i | \(-0.552070\pi\) | ||||
−0.162853 | + | 0.986650i | \(0.552070\pi\) | |||||||
\(998\) | 18.1421 | 0.574279 | ||||||||
\(999\) | −10.4853 | −0.331740 |
(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 | 4650.2.a.cf.1.1 | 2 | ||
5.2 | odd | 4 | 930.2.d.g.559.3 | yes | 4 | ||
5.3 | odd | 4 | 930.2.d.g.559.2 | ✓ | 4 | ||
5.4 | even | 2 | 4650.2.a.cc.1.2 | 2 | |||
15.2 | even | 4 | 2790.2.d.i.559.1 | 4 | |||
15.8 | even | 4 | 2790.2.d.i.559.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.d.g.559.2 | ✓ | 4 | 5.3 | odd | 4 | ||
930.2.d.g.559.3 | yes | 4 | 5.2 | odd | 4 | ||
2790.2.d.i.559.1 | 4 | 15.2 | even | 4 | |||
2790.2.d.i.559.4 | 4 | 15.8 | even | 4 | |||
4650.2.a.cc.1.2 | 2 | 5.4 | even | 2 | |||
4650.2.a.cf.1.1 | 2 | 1.1 | even | 1 | trivial |