Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.38498000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 5x^{3} + 38x^{2} - x - 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.752765\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −0.247235 | −0.142741 | −0.0713705 | − | 0.997450i | \(-0.522737\pi\) | ||||
−0.0713705 | + | 0.997450i | \(0.522737\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.247235 | −0.100933 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.93888 | −0.979625 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.247235 | −0.0713705 | ||||||||
\(13\) | 2.83439 | 0.786119 | 0.393060 | − | 0.919513i | \(-0.371417\pi\) | ||||
0.393060 | + | 0.919513i | \(0.371417\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.247235 | 0.0638357 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.76549 | −1.39834 | −0.699168 | − | 0.714957i | \(-0.746446\pi\) | ||||
−0.699168 | + | 0.714957i | \(0.746446\pi\) | |||||||
\(18\) | −2.93888 | −0.692699 | ||||||||
\(19\) | 3.66941 | 0.841821 | 0.420910 | − | 0.907102i | \(-0.361711\pi\) | ||||
0.420910 | + | 0.907102i | \(0.361711\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.247235 | −0.0539510 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.17432 | −1.49595 | −0.747974 | − | 0.663728i | \(-0.768973\pi\) | ||||
−0.747974 | + | 0.663728i | \(0.768973\pi\) | |||||||
\(24\) | −0.247235 | −0.0504666 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.83439 | 0.555870 | ||||||||
\(27\) | 1.46830 | 0.282574 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 1.41528 | 0.262810 | 0.131405 | − | 0.991329i | \(-0.458051\pi\) | ||||
0.131405 | + | 0.991329i | \(0.458051\pi\) | |||||||
\(30\) | 0.247235 | 0.0451387 | ||||||||
\(31\) | −0.356435 | −0.0640176 | −0.0320088 | − | 0.999488i | \(-0.510190\pi\) | ||||
−0.0320088 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.76549 | −0.988773 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.93888 | −0.489813 | ||||||||
\(37\) | 2.94752 | 0.484570 | 0.242285 | − | 0.970205i | \(-0.422103\pi\) | ||||
0.242285 | + | 0.970205i | \(0.422103\pi\) | |||||||
\(38\) | 3.66941 | 0.595257 | ||||||||
\(39\) | −0.700760 | −0.112211 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.22578 | 0.347608 | 0.173804 | − | 0.984780i | \(-0.444394\pi\) | ||||
0.173804 | + | 0.984780i | \(0.444394\pi\) | |||||||
\(42\) | −0.247235 | −0.0381491 | ||||||||
\(43\) | 9.64018 | 1.47011 | 0.735057 | − | 0.678006i | \(-0.237156\pi\) | ||||
0.735057 | + | 0.678006i | \(0.237156\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.93888 | 0.438102 | ||||||||
\(46\) | −7.17432 | −1.05780 | ||||||||
\(47\) | 3.13615 | 0.457455 | 0.228727 | − | 0.973491i | \(-0.426544\pi\) | ||||
0.228727 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(48\) | −0.247235 | −0.0356852 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.42543 | 0.199600 | ||||||||
\(52\) | 2.83439 | 0.393060 | ||||||||
\(53\) | 0.874146 | 0.120073 | 0.0600366 | − | 0.998196i | \(-0.480878\pi\) | ||||
0.0600366 | + | 0.998196i | \(0.480878\pi\) | |||||||
\(54\) | 1.46830 | 0.199810 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −0.907206 | −0.120162 | ||||||||
\(58\) | 1.41528 | 0.185835 | ||||||||
\(59\) | −10.4962 | −1.36649 | −0.683243 | − | 0.730191i | \(-0.739431\pi\) | ||||
−0.683243 | + | 0.730191i | \(0.739431\pi\) | |||||||
\(60\) | 0.247235 | 0.0319179 | ||||||||
\(61\) | −9.20135 | −1.17811 | −0.589056 | − | 0.808092i | \(-0.700500\pi\) | ||||
−0.589056 | + | 0.808092i | \(0.700500\pi\) | |||||||
\(62\) | −0.356435 | −0.0452673 | ||||||||
\(63\) | −2.93888 | −0.370263 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.83439 | −0.351563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5466 | −1.65498 | −0.827492 | − | 0.561478i | \(-0.810233\pi\) | ||||
−0.827492 | + | 0.561478i | \(0.810233\pi\) | |||||||
\(68\) | −5.76549 | −0.699168 | ||||||||
\(69\) | 1.77374 | 0.213533 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −12.5139 | −1.48512 | −0.742561 | − | 0.669779i | \(-0.766389\pi\) | ||||
−0.742561 | + | 0.669779i | \(0.766389\pi\) | |||||||
\(72\) | −2.93888 | −0.346350 | ||||||||
\(73\) | −7.19836 | −0.842504 | −0.421252 | − | 0.906944i | \(-0.638409\pi\) | ||||
−0.421252 | + | 0.906944i | \(0.638409\pi\) | |||||||
\(74\) | 2.94752 | 0.342643 | ||||||||
\(75\) | −0.247235 | −0.0285482 | ||||||||
\(76\) | 3.66941 | 0.420910 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.700760 | −0.0793455 | ||||||||
\(79\) | 6.14508 | 0.691376 | 0.345688 | − | 0.938350i | \(-0.387646\pi\) | ||||
0.345688 | + | 0.938350i | \(0.387646\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.45361 | 0.939290 | ||||||||
\(82\) | 2.22578 | 0.245796 | ||||||||
\(83\) | 3.08217 | 0.338312 | 0.169156 | − | 0.985589i | \(-0.445896\pi\) | ||||
0.169156 | + | 0.985589i | \(0.445896\pi\) | |||||||
\(84\) | −0.247235 | −0.0269755 | ||||||||
\(85\) | 5.76549 | 0.625355 | ||||||||
\(86\) | 9.64018 | 1.03953 | ||||||||
\(87\) | −0.349905 | −0.0375138 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.75443 | −0.609968 | −0.304984 | − | 0.952357i | \(-0.598651\pi\) | ||||
−0.304984 | + | 0.952357i | \(0.598651\pi\) | |||||||
\(90\) | 2.93888 | 0.309785 | ||||||||
\(91\) | 2.83439 | 0.297125 | ||||||||
\(92\) | −7.17432 | −0.747974 | ||||||||
\(93\) | 0.0881230 | 0.00913793 | ||||||||
\(94\) | 3.13615 | 0.323469 | ||||||||
\(95\) | −3.66941 | −0.376474 | ||||||||
\(96\) | −0.247235 | −0.0252333 | ||||||||
\(97\) | 12.5278 | 1.27200 | 0.636001 | − | 0.771689i | \(-0.280588\pi\) | ||||
0.636001 | + | 0.771689i | \(0.280588\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.90123 | −0.587195 | −0.293597 | − | 0.955929i | \(-0.594852\pi\) | ||||
−0.293597 | + | 0.955929i | \(0.594852\pi\) | |||||||
\(102\) | 1.42543 | 0.141138 | ||||||||
\(103\) | −11.9671 | −1.17915 | −0.589576 | − | 0.807713i | \(-0.700705\pi\) | ||||
−0.589576 | + | 0.807713i | \(0.700705\pi\) | |||||||
\(104\) | 2.83439 | 0.277935 | ||||||||
\(105\) | 0.247235 | 0.0241276 | ||||||||
\(106\) | 0.874146 | 0.0849046 | ||||||||
\(107\) | −6.28895 | −0.607976 | −0.303988 | − | 0.952676i | \(-0.598318\pi\) | ||||
−0.303988 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(108\) | 1.46830 | 0.141287 | ||||||||
\(109\) | −3.42125 | −0.327696 | −0.163848 | − | 0.986486i | \(-0.552391\pi\) | ||||
−0.163848 | + | 0.986486i | \(0.552391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.728730 | −0.0691680 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −16.8223 | −1.58251 | −0.791253 | − | 0.611489i | \(-0.790571\pi\) | ||||
−0.791253 | + | 0.611489i | \(0.790571\pi\) | |||||||
\(114\) | −0.907206 | −0.0849676 | ||||||||
\(115\) | 7.17432 | 0.669008 | ||||||||
\(116\) | 1.41528 | 0.131405 | ||||||||
\(117\) | −8.32993 | −0.770102 | ||||||||
\(118\) | −10.4962 | −0.966251 | ||||||||
\(119\) | −5.76549 | −0.528521 | ||||||||
\(120\) | 0.247235 | 0.0225693 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.20135 | −0.833051 | ||||||||
\(123\) | −0.550290 | −0.0496180 | ||||||||
\(124\) | −0.356435 | −0.0320088 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.93888 | −0.261816 | ||||||||
\(127\) | 0.175760 | 0.0155961 | 0.00779807 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779807 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.38339 | −0.209845 | ||||||||
\(130\) | −2.83439 | −0.248593 | ||||||||
\(131\) | −11.4391 | −0.999438 | −0.499719 | − | 0.866187i | \(-0.666563\pi\) | ||||
−0.499719 | + | 0.866187i | \(0.666563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.66941 | 0.318178 | ||||||||
\(134\) | −13.5466 | −1.17025 | ||||||||
\(135\) | −1.46830 | −0.126371 | ||||||||
\(136\) | −5.76549 | −0.494387 | ||||||||
\(137\) | −9.95341 | −0.850377 | −0.425189 | − | 0.905105i | \(-0.639792\pi\) | ||||
−0.425189 | + | 0.905105i | \(0.639792\pi\) | |||||||
\(138\) | 1.77374 | 0.150991 | ||||||||
\(139\) | −0.627224 | −0.0532005 | −0.0266002 | − | 0.999646i | \(-0.508468\pi\) | ||||
−0.0266002 | + | 0.999646i | \(0.508468\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −0.775365 | −0.0652975 | ||||||||
\(142\) | −12.5139 | −1.05014 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.93888 | −0.244906 | ||||||||
\(145\) | −1.41528 | −0.117532 | ||||||||
\(146\) | −7.19836 | −0.595740 | ||||||||
\(147\) | −0.247235 | −0.0203916 | ||||||||
\(148\) | 2.94752 | 0.242285 | ||||||||
\(149\) | −15.0315 | −1.23143 | −0.615713 | − | 0.787970i | \(-0.711132\pi\) | ||||
−0.615713 | + | 0.787970i | \(0.711132\pi\) | |||||||
\(150\) | −0.247235 | −0.0201866 | ||||||||
\(151\) | 0.516467 | 0.0420295 | 0.0210148 | − | 0.999779i | \(-0.493310\pi\) | ||||
0.0210148 | + | 0.999779i | \(0.493310\pi\) | |||||||
\(152\) | 3.66941 | 0.297629 | ||||||||
\(153\) | 16.9441 | 1.36985 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.356435 | 0.0286295 | ||||||||
\(156\) | −0.700760 | −0.0561057 | ||||||||
\(157\) | −22.7782 | −1.81790 | −0.908949 | − | 0.416907i | \(-0.863114\pi\) | ||||
−0.908949 | + | 0.416907i | \(0.863114\pi\) | |||||||
\(158\) | 6.14508 | 0.488876 | ||||||||
\(159\) | −0.216119 | −0.0171394 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −7.17432 | −0.565415 | ||||||||
\(162\) | 8.45361 | 0.664178 | ||||||||
\(163\) | 3.72353 | 0.291649 | 0.145825 | − | 0.989310i | \(-0.453416\pi\) | ||||
0.145825 | + | 0.989310i | \(0.453416\pi\) | |||||||
\(164\) | 2.22578 | 0.173804 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.08217 | 0.239223 | ||||||||
\(167\) | 15.5825 | 1.20581 | 0.602906 | − | 0.797812i | \(-0.294009\pi\) | ||||
0.602906 | + | 0.797812i | \(0.294009\pi\) | |||||||
\(168\) | −0.247235 | −0.0190746 | ||||||||
\(169\) | −4.96622 | −0.382017 | ||||||||
\(170\) | 5.76549 | 0.442193 | ||||||||
\(171\) | −10.7839 | −0.824669 | ||||||||
\(172\) | 9.64018 | 0.735057 | ||||||||
\(173\) | 5.89952 | 0.448532 | 0.224266 | − | 0.974528i | \(-0.428002\pi\) | ||||
0.224266 | + | 0.974528i | \(0.428002\pi\) | |||||||
\(174\) | −0.349905 | −0.0265263 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.59502 | 0.195053 | ||||||||
\(178\) | −5.75443 | −0.431313 | ||||||||
\(179\) | 16.3323 | 1.22073 | 0.610367 | − | 0.792119i | \(-0.291022\pi\) | ||||
0.610367 | + | 0.792119i | \(0.291022\pi\) | |||||||
\(180\) | 2.93888 | 0.219051 | ||||||||
\(181\) | −3.48610 | −0.259120 | −0.129560 | − | 0.991572i | \(-0.541356\pi\) | ||||
−0.129560 | + | 0.991572i | \(0.541356\pi\) | |||||||
\(182\) | 2.83439 | 0.210099 | ||||||||
\(183\) | 2.27489 | 0.168165 | ||||||||
\(184\) | −7.17432 | −0.528898 | ||||||||
\(185\) | −2.94752 | −0.216706 | ||||||||
\(186\) | 0.0881230 | 0.00646149 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.13615 | 0.228727 | ||||||||
\(189\) | 1.46830 | 0.106803 | ||||||||
\(190\) | −3.66941 | −0.266207 | ||||||||
\(191\) | 25.9703 | 1.87914 | 0.939572 | − | 0.342352i | \(-0.111223\pi\) | ||||
0.939572 | + | 0.342352i | \(0.111223\pi\) | |||||||
\(192\) | −0.247235 | −0.0178426 | ||||||||
\(193\) | −0.677502 | −0.0487677 | −0.0243838 | − | 0.999703i | \(-0.507762\pi\) | ||||
−0.0243838 | + | 0.999703i | \(0.507762\pi\) | |||||||
\(194\) | 12.5278 | 0.899441 | ||||||||
\(195\) | 0.700760 | 0.0501825 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.80812 | 0.413811 | 0.206906 | − | 0.978361i | \(-0.433661\pi\) | ||||
0.206906 | + | 0.978361i | \(0.433661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.9475 | 0.776046 | 0.388023 | − | 0.921650i | \(-0.373158\pi\) | ||||
0.388023 | + | 0.921650i | \(0.373158\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 3.34919 | 0.236234 | ||||||||
\(202\) | −5.90123 | −0.415209 | ||||||||
\(203\) | 1.41528 | 0.0993329 | ||||||||
\(204\) | 1.42543 | 0.0998000 | ||||||||
\(205\) | −2.22578 | −0.155455 | ||||||||
\(206\) | −11.9671 | −0.833787 | ||||||||
\(207\) | 21.0844 | 1.46547 | ||||||||
\(208\) | 2.83439 | 0.196530 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.247235 | 0.0170608 | ||||||||
\(211\) | −6.42786 | −0.442512 | −0.221256 | − | 0.975216i | \(-0.571016\pi\) | ||||
−0.221256 | + | 0.975216i | \(0.571016\pi\) | |||||||
\(212\) | 0.874146 | 0.0600366 | ||||||||
\(213\) | 3.09386 | 0.211988 | ||||||||
\(214\) | −6.28895 | −0.429904 | ||||||||
\(215\) | −9.64018 | −0.657455 | ||||||||
\(216\) | 1.46830 | 0.0999049 | ||||||||
\(217\) | −0.356435 | −0.0241964 | ||||||||
\(218\) | −3.42125 | −0.231716 | ||||||||
\(219\) | 1.77968 | 0.120260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3417 | −1.09926 | ||||||||
\(222\) | −0.728730 | −0.0489091 | ||||||||
\(223\) | 23.2048 | 1.55391 | 0.776955 | − | 0.629557i | \(-0.216763\pi\) | ||||
0.776955 | + | 0.629557i | \(0.216763\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.93888 | −0.195925 | ||||||||
\(226\) | −16.8223 | −1.11900 | ||||||||
\(227\) | −25.5715 | −1.69724 | −0.848621 | − | 0.529001i | \(-0.822567\pi\) | ||||
−0.848621 | + | 0.529001i | \(0.822567\pi\) | |||||||
\(228\) | −0.907206 | −0.0600812 | ||||||||
\(229\) | 4.02501 | 0.265980 | 0.132990 | − | 0.991117i | \(-0.457542\pi\) | ||||
0.132990 | + | 0.991117i | \(0.457542\pi\) | |||||||
\(230\) | 7.17432 | 0.473060 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.41528 | 0.0929174 | ||||||||
\(233\) | −3.67721 | −0.240902 | −0.120451 | − | 0.992719i | \(-0.538434\pi\) | ||||
−0.120451 | + | 0.992719i | \(0.538434\pi\) | |||||||
\(234\) | −8.32993 | −0.544544 | ||||||||
\(235\) | −3.13615 | −0.204580 | ||||||||
\(236\) | −10.4962 | −0.683243 | ||||||||
\(237\) | −1.51928 | −0.0986877 | ||||||||
\(238\) | −5.76549 | −0.373721 | ||||||||
\(239\) | −1.09444 | −0.0707931 | −0.0353966 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353966 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(240\) | 0.247235 | 0.0159589 | ||||||||
\(241\) | 6.24902 | 0.402535 | 0.201267 | − | 0.979536i | \(-0.435494\pi\) | ||||
0.201267 | + | 0.979536i | \(0.435494\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.49491 | −0.416649 | ||||||||
\(244\) | −9.20135 | −0.589056 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −0.550290 | −0.0350852 | ||||||||
\(247\) | 10.4006 | 0.661772 | ||||||||
\(248\) | −0.356435 | −0.0226336 | ||||||||
\(249\) | −0.762019 | −0.0482910 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −19.2916 | −1.21767 | −0.608836 | − | 0.793296i | \(-0.708363\pi\) | ||||
−0.608836 | + | 0.793296i | \(0.708363\pi\) | |||||||
\(252\) | −2.93888 | −0.185132 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.175760 | 0.0110281 | ||||||||
\(255\) | −1.42543 | −0.0892638 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.2663 | 1.57607 | 0.788035 | − | 0.615630i | \(-0.211099\pi\) | ||||
0.788035 | + | 0.615630i | \(0.211099\pi\) | |||||||
\(258\) | −2.38339 | −0.148383 | ||||||||
\(259\) | 2.94752 | 0.183150 | ||||||||
\(260\) | −2.83439 | −0.175782 | ||||||||
\(261\) | −4.15932 | −0.257455 | ||||||||
\(262\) | −11.4391 | −0.706710 | ||||||||
\(263\) | 2.99352 | 0.184589 | 0.0922943 | − | 0.995732i | \(-0.470580\pi\) | ||||
0.0922943 | + | 0.995732i | \(0.470580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.874146 | −0.0536984 | ||||||||
\(266\) | 3.66941 | 0.224986 | ||||||||
\(267\) | 1.42269 | 0.0870675 | ||||||||
\(268\) | −13.5466 | −0.827492 | ||||||||
\(269\) | −22.5013 | −1.37193 | −0.685964 | − | 0.727635i | \(-0.740619\pi\) | ||||
−0.685964 | + | 0.727635i | \(0.740619\pi\) | |||||||
\(270\) | −1.46830 | −0.0893576 | ||||||||
\(271\) | −13.6286 | −0.827881 | −0.413940 | − | 0.910304i | \(-0.635848\pi\) | ||||
−0.413940 | + | 0.910304i | \(0.635848\pi\) | |||||||
\(272\) | −5.76549 | −0.349584 | ||||||||
\(273\) | −0.700760 | −0.0424119 | ||||||||
\(274\) | −9.95341 | −0.601307 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.77374 | 0.106767 | ||||||||
\(277\) | −23.5465 | −1.41477 | −0.707387 | − | 0.706827i | \(-0.750126\pi\) | ||||
−0.707387 | + | 0.706827i | \(0.750126\pi\) | |||||||
\(278\) | −0.627224 | −0.0376184 | ||||||||
\(279\) | 1.04752 | 0.0627132 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −19.1837 | −1.14440 | −0.572201 | − | 0.820113i | \(-0.693910\pi\) | ||||
−0.572201 | + | 0.820113i | \(0.693910\pi\) | |||||||
\(282\) | −0.775365 | −0.0461723 | ||||||||
\(283\) | 17.2722 | 1.02673 | 0.513363 | − | 0.858172i | \(-0.328399\pi\) | ||||
0.513363 | + | 0.858172i | \(0.328399\pi\) | |||||||
\(284\) | −12.5139 | −0.742561 | ||||||||
\(285\) | 0.907206 | 0.0537382 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.22578 | 0.131384 | ||||||||
\(288\) | −2.93888 | −0.173175 | ||||||||
\(289\) | 16.2409 | 0.955345 | ||||||||
\(290\) | −1.41528 | −0.0831079 | ||||||||
\(291\) | −3.09730 | −0.181567 | ||||||||
\(292\) | −7.19836 | −0.421252 | ||||||||
\(293\) | −32.9318 | −1.92389 | −0.961947 | − | 0.273235i | \(-0.911906\pi\) | ||||
−0.961947 | + | 0.273235i | \(0.911906\pi\) | |||||||
\(294\) | −0.247235 | −0.0144190 | ||||||||
\(295\) | 10.4962 | 0.611111 | ||||||||
\(296\) | 2.94752 | 0.171321 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.0315 | −0.870750 | ||||||||
\(299\) | −20.3348 | −1.17599 | ||||||||
\(300\) | −0.247235 | −0.0142741 | ||||||||
\(301\) | 9.64018 | 0.555651 | ||||||||
\(302\) | 0.516467 | 0.0297194 | ||||||||
\(303\) | 1.45899 | 0.0838168 | ||||||||
\(304\) | 3.66941 | 0.210455 | ||||||||
\(305\) | 9.20135 | 0.526868 | ||||||||
\(306\) | 16.9441 | 0.968627 | ||||||||
\(307\) | −7.97195 | −0.454983 | −0.227492 | − | 0.973780i | \(-0.573052\pi\) | ||||
−0.227492 | + | 0.973780i | \(0.573052\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.95868 | 0.168313 | ||||||||
\(310\) | 0.356435 | 0.0202441 | ||||||||
\(311\) | −4.00836 | −0.227293 | −0.113647 | − | 0.993521i | \(-0.536253\pi\) | ||||
−0.113647 | + | 0.993521i | \(0.536253\pi\) | |||||||
\(312\) | −0.700760 | −0.0396727 | ||||||||
\(313\) | 5.27260 | 0.298025 | 0.149013 | − | 0.988835i | \(-0.452390\pi\) | ||||
0.149013 | + | 0.988835i | \(0.452390\pi\) | |||||||
\(314\) | −22.7782 | −1.28545 | ||||||||
\(315\) | 2.93888 | 0.165587 | ||||||||
\(316\) | 6.14508 | 0.345688 | ||||||||
\(317\) | −4.65978 | −0.261720 | −0.130860 | − | 0.991401i | \(-0.541774\pi\) | ||||
−0.130860 | + | 0.991401i | \(0.541774\pi\) | |||||||
\(318\) | −0.216119 | −0.0121194 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 1.55485 | 0.0867831 | ||||||||
\(322\) | −7.17432 | −0.399809 | ||||||||
\(323\) | −21.1560 | −1.17715 | ||||||||
\(324\) | 8.45361 | 0.469645 | ||||||||
\(325\) | 2.83439 | 0.157224 | ||||||||
\(326\) | 3.72353 | 0.206227 | ||||||||
\(327\) | 0.845851 | 0.0467757 | ||||||||
\(328\) | 2.22578 | 0.122898 | ||||||||
\(329\) | 3.13615 | 0.172902 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.0199 | −1.37522 | −0.687608 | − | 0.726082i | \(-0.741339\pi\) | ||||
−0.687608 | + | 0.726082i | \(0.741339\pi\) | |||||||
\(332\) | 3.08217 | 0.169156 | ||||||||
\(333\) | −8.66240 | −0.474697 | ||||||||
\(334\) | 15.5825 | 0.852638 | ||||||||
\(335\) | 13.5466 | 0.740131 | ||||||||
\(336\) | −0.247235 | −0.0134878 | ||||||||
\(337\) | 15.9367 | 0.868130 | 0.434065 | − | 0.900882i | \(-0.357079\pi\) | ||||
0.434065 | + | 0.900882i | \(0.357079\pi\) | |||||||
\(338\) | −4.96622 | −0.270127 | ||||||||
\(339\) | 4.15905 | 0.225889 | ||||||||
\(340\) | 5.76549 | 0.312678 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.7839 | −0.583129 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.64018 | 0.519764 | ||||||||
\(345\) | −1.77374 | −0.0954949 | ||||||||
\(346\) | 5.89952 | 0.317160 | ||||||||
\(347\) | −12.4275 | −0.667142 | −0.333571 | − | 0.942725i | \(-0.608254\pi\) | ||||
−0.333571 | + | 0.942725i | \(0.608254\pi\) | |||||||
\(348\) | −0.349905 | −0.0187569 | ||||||||
\(349\) | −16.2129 | −0.867854 | −0.433927 | − | 0.900948i | \(-0.642872\pi\) | ||||
−0.433927 | + | 0.900948i | \(0.642872\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 4.16173 | 0.222137 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.8320 | −1.16200 | −0.580999 | − | 0.813904i | \(-0.697338\pi\) | ||||
−0.580999 | + | 0.813904i | \(0.697338\pi\) | |||||||
\(354\) | 2.59502 | 0.137924 | ||||||||
\(355\) | 12.5139 | 0.664166 | ||||||||
\(356\) | −5.75443 | −0.304984 | ||||||||
\(357\) | 1.42543 | 0.0754417 | ||||||||
\(358\) | 16.3323 | 0.863189 | ||||||||
\(359\) | −18.2106 | −0.961116 | −0.480558 | − | 0.876963i | \(-0.659566\pi\) | ||||
−0.480558 | + | 0.876963i | \(0.659566\pi\) | |||||||
\(360\) | 2.93888 | 0.154892 | ||||||||
\(361\) | −5.53541 | −0.291338 | ||||||||
\(362\) | −3.48610 | −0.183226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.83439 | 0.148563 | ||||||||
\(365\) | 7.19836 | 0.376779 | ||||||||
\(366\) | 2.27489 | 0.118911 | ||||||||
\(367\) | −5.27857 | −0.275539 | −0.137770 | − | 0.990464i | \(-0.543993\pi\) | ||||
−0.137770 | + | 0.990464i | \(0.543993\pi\) | |||||||
\(368\) | −7.17432 | −0.373987 | ||||||||
\(369\) | −6.54129 | −0.340526 | ||||||||
\(370\) | −2.94752 | −0.153234 | ||||||||
\(371\) | 0.874146 | 0.0453834 | ||||||||
\(372\) | 0.0881230 | 0.00456897 | ||||||||
\(373\) | 18.5799 | 0.962031 | 0.481016 | − | 0.876712i | \(-0.340268\pi\) | ||||
0.481016 | + | 0.876712i | \(0.340268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.247235 | 0.0127671 | ||||||||
\(376\) | 3.13615 | 0.161735 | ||||||||
\(377\) | 4.01145 | 0.206600 | ||||||||
\(378\) | 1.46830 | 0.0755210 | ||||||||
\(379\) | 22.8406 | 1.17324 | 0.586621 | − | 0.809862i | \(-0.300458\pi\) | ||||
0.586621 | + | 0.809862i | \(0.300458\pi\) | |||||||
\(380\) | −3.66941 | −0.188237 | ||||||||
\(381\) | −0.0434539 | −0.00222621 | ||||||||
\(382\) | 25.9703 | 1.32876 | ||||||||
\(383\) | −22.4735 | −1.14834 | −0.574171 | − | 0.818736i | \(-0.694675\pi\) | ||||
−0.574171 | + | 0.818736i | \(0.694675\pi\) | |||||||
\(384\) | −0.247235 | −0.0126166 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.677502 | −0.0344840 | ||||||||
\(387\) | −28.3313 | −1.44016 | ||||||||
\(388\) | 12.5278 | 0.636001 | ||||||||
\(389\) | 36.2498 | 1.83794 | 0.918968 | − | 0.394333i | \(-0.129024\pi\) | ||||
0.918968 | + | 0.394333i | \(0.129024\pi\) | |||||||
\(390\) | 0.700760 | 0.0354844 | ||||||||
\(391\) | 41.3634 | 2.09184 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 2.82814 | 0.142661 | ||||||||
\(394\) | 5.80812 | 0.292609 | ||||||||
\(395\) | −6.14508 | −0.309193 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.02992 | −0.403010 | −0.201505 | − | 0.979487i | \(-0.564583\pi\) | ||||
−0.201505 | + | 0.979487i | \(0.564583\pi\) | |||||||
\(398\) | 10.9475 | 0.548748 | ||||||||
\(399\) | −0.907206 | −0.0454171 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.672421 | 0.0335791 | 0.0167896 | − | 0.999859i | \(-0.494655\pi\) | ||||
0.0167896 | + | 0.999859i | \(0.494655\pi\) | |||||||
\(402\) | 3.34919 | 0.167043 | ||||||||
\(403\) | −1.01028 | −0.0503254 | ||||||||
\(404\) | −5.90123 | −0.293597 | ||||||||
\(405\) | −8.45361 | −0.420063 | ||||||||
\(406\) | 1.41528 | 0.0702390 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.42543 | 0.0705692 | ||||||||
\(409\) | −21.7385 | −1.07490 | −0.537450 | − | 0.843296i | \(-0.680612\pi\) | ||||
−0.537450 | + | 0.843296i | \(0.680612\pi\) | |||||||
\(410\) | −2.22578 | −0.109923 | ||||||||
\(411\) | 2.46083 | 0.121384 | ||||||||
\(412\) | −11.9671 | −0.589576 | ||||||||
\(413\) | −10.4962 | −0.516483 | ||||||||
\(414\) | 21.0844 | 1.03624 | ||||||||
\(415\) | −3.08217 | −0.151298 | ||||||||
\(416\) | 2.83439 | 0.138968 | ||||||||
\(417\) | 0.155072 | 0.00759389 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.38003 | −0.360538 | −0.180269 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180269 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(420\) | 0.247235 | 0.0120638 | ||||||||
\(421\) | 29.4497 | 1.43529 | 0.717646 | − | 0.696408i | \(-0.245220\pi\) | ||||
0.717646 | + | 0.696408i | \(0.245220\pi\) | |||||||
\(422\) | −6.42786 | −0.312903 | ||||||||
\(423\) | −9.21676 | −0.448134 | ||||||||
\(424\) | 0.874146 | 0.0424523 | ||||||||
\(425\) | −5.76549 | −0.279667 | ||||||||
\(426\) | 3.09386 | 0.149898 | ||||||||
\(427\) | −9.20135 | −0.445285 | ||||||||
\(428\) | −6.28895 | −0.303988 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.64018 | −0.464891 | ||||||||
\(431\) | −19.6701 | −0.947477 | −0.473739 | − | 0.880665i | \(-0.657096\pi\) | ||||
−0.473739 | + | 0.880665i | \(0.657096\pi\) | |||||||
\(432\) | 1.46830 | 0.0706434 | ||||||||
\(433\) | −17.0504 | −0.819390 | −0.409695 | − | 0.912222i | \(-0.634365\pi\) | ||||
−0.409695 | + | 0.912222i | \(0.634365\pi\) | |||||||
\(434\) | −0.356435 | −0.0171094 | ||||||||
\(435\) | 0.349905 | 0.0167767 | ||||||||
\(436\) | −3.42125 | −0.163848 | ||||||||
\(437\) | −26.3255 | −1.25932 | ||||||||
\(438\) | 1.77968 | 0.0850365 | ||||||||
\(439\) | 29.9589 | 1.42986 | 0.714929 | − | 0.699197i | \(-0.246459\pi\) | ||||
0.714929 | + | 0.699197i | \(0.246459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.93888 | −0.139946 | ||||||||
\(442\) | −16.3417 | −0.777293 | ||||||||
\(443\) | 41.2954 | 1.96201 | 0.981003 | − | 0.193994i | \(-0.0621442\pi\) | ||||
0.981003 | + | 0.193994i | \(0.0621442\pi\) | |||||||
\(444\) | −0.728730 | −0.0345840 | ||||||||
\(445\) | 5.75443 | 0.272786 | ||||||||
\(446\) | 23.2048 | 1.09878 | ||||||||
\(447\) | 3.71630 | 0.175775 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 33.9263 | 1.60108 | 0.800541 | − | 0.599278i | \(-0.204546\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204546\pi\) | |||||||
\(450\) | −2.93888 | −0.138540 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −16.8223 | −0.791253 | ||||||||
\(453\) | −0.127689 | −0.00599934 | ||||||||
\(454\) | −25.5715 | −1.20013 | ||||||||
\(455\) | −2.83439 | −0.132878 | ||||||||
\(456\) | −0.907206 | −0.0424838 | ||||||||
\(457\) | 19.9928 | 0.935225 | 0.467613 | − | 0.883934i | \(-0.345114\pi\) | ||||
0.467613 | + | 0.883934i | \(0.345114\pi\) | |||||||
\(458\) | 4.02501 | 0.188076 | ||||||||
\(459\) | −8.46544 | −0.395133 | ||||||||
\(460\) | 7.17432 | 0.334504 | ||||||||
\(461\) | −17.4739 | −0.813840 | −0.406920 | − | 0.913464i | \(-0.633397\pi\) | ||||
−0.406920 | + | 0.913464i | \(0.633397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.7730 | −1.94135 | −0.970677 | − | 0.240386i | \(-0.922726\pi\) | ||||
−0.970677 | + | 0.240386i | \(0.922726\pi\) | |||||||
\(464\) | 1.41528 | 0.0657026 | ||||||||
\(465\) | −0.0881230 | −0.00408661 | ||||||||
\(466\) | −3.67721 | −0.170343 | ||||||||
\(467\) | −13.7476 | −0.636164 | −0.318082 | − | 0.948063i | \(-0.603039\pi\) | ||||
−0.318082 | + | 0.948063i | \(0.603039\pi\) | |||||||
\(468\) | −8.32993 | −0.385051 | ||||||||
\(469\) | −13.5466 | −0.625525 | ||||||||
\(470\) | −3.13615 | −0.144660 | ||||||||
\(471\) | 5.63156 | 0.259489 | ||||||||
\(472\) | −10.4962 | −0.483125 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.51928 | −0.0697827 | ||||||||
\(475\) | 3.66941 | 0.168364 | ||||||||
\(476\) | −5.76549 | −0.264261 | ||||||||
\(477\) | −2.56901 | −0.117627 | ||||||||
\(478\) | −1.09444 | −0.0500583 | ||||||||
\(479\) | −20.6636 | −0.944145 | −0.472072 | − | 0.881560i | \(-0.656494\pi\) | ||||
−0.472072 | + | 0.881560i | \(0.656494\pi\) | |||||||
\(480\) | 0.247235 | 0.0112847 | ||||||||
\(481\) | 8.35444 | 0.380930 | ||||||||
\(482\) | 6.24902 | 0.284635 | ||||||||
\(483\) | 1.77374 | 0.0807079 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.5278 | −0.568856 | ||||||||
\(486\) | −6.49491 | −0.294615 | ||||||||
\(487\) | −22.1049 | −1.00167 | −0.500835 | − | 0.865543i | \(-0.666974\pi\) | ||||
−0.500835 | + | 0.865543i | \(0.666974\pi\) | |||||||
\(488\) | −9.20135 | −0.416526 | ||||||||
\(489\) | −0.920586 | −0.0416303 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 10.6974 | 0.482768 | 0.241384 | − | 0.970430i | \(-0.422399\pi\) | ||||
0.241384 | + | 0.970430i | \(0.422399\pi\) | |||||||
\(492\) | −0.550290 | −0.0248090 | ||||||||
\(493\) | −8.15976 | −0.367497 | ||||||||
\(494\) | 10.4006 | 0.467943 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.356435 | −0.0160044 | ||||||||
\(497\) | −12.5139 | −0.561323 | ||||||||
\(498\) | −0.762019 | −0.0341469 | ||||||||
\(499\) | 1.85809 | 0.0831794 | 0.0415897 | − | 0.999135i | \(-0.486758\pi\) | ||||
0.0415897 | + | 0.999135i | \(0.486758\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −3.85254 | −0.172119 | ||||||||
\(502\) | −19.2916 | −0.861024 | ||||||||
\(503\) | −13.5487 | −0.604108 | −0.302054 | − | 0.953291i | \(-0.597672\pi\) | ||||
−0.302054 | + | 0.953291i | \(0.597672\pi\) | |||||||
\(504\) | −2.93888 | −0.130908 | ||||||||
\(505\) | 5.90123 | 0.262601 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.22782 | 0.0545295 | ||||||||
\(508\) | 0.175760 | 0.00779807 | ||||||||
\(509\) | −6.36772 | −0.282244 | −0.141122 | − | 0.989992i | \(-0.545071\pi\) | ||||
−0.141122 | + | 0.989992i | \(0.545071\pi\) | |||||||
\(510\) | −1.42543 | −0.0631190 | ||||||||
\(511\) | −7.19836 | −0.318437 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.38778 | 0.237876 | ||||||||
\(514\) | 25.2663 | 1.11445 | ||||||||
\(515\) | 11.9671 | 0.527333 | ||||||||
\(516\) | −2.38339 | −0.104923 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.94752 | 0.129507 | ||||||||
\(519\) | −1.45857 | −0.0640240 | ||||||||
\(520\) | −2.83439 | −0.124296 | ||||||||
\(521\) | −24.1693 | −1.05888 | −0.529439 | − | 0.848348i | \(-0.677598\pi\) | ||||
−0.529439 | + | 0.848348i | \(0.677598\pi\) | |||||||
\(522\) | −4.15932 | −0.182048 | ||||||||
\(523\) | −30.5849 | −1.33738 | −0.668692 | − | 0.743540i | \(-0.733145\pi\) | ||||
−0.668692 | + | 0.743540i | \(0.733145\pi\) | |||||||
\(524\) | −11.4391 | −0.499719 | ||||||||
\(525\) | −0.247235 | −0.0107902 | ||||||||
\(526\) | 2.99352 | 0.130524 | ||||||||
\(527\) | 2.05502 | 0.0895181 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.4708 | 1.23786 | ||||||||
\(530\) | −0.874146 | −0.0379705 | ||||||||
\(531\) | 30.8469 | 1.33864 | ||||||||
\(532\) | 3.66941 | 0.159089 | ||||||||
\(533\) | 6.30873 | 0.273261 | ||||||||
\(534\) | 1.42269 | 0.0615660 | ||||||||
\(535\) | 6.28895 | 0.271895 | ||||||||
\(536\) | −13.5466 | −0.585125 | ||||||||
\(537\) | −4.03791 | −0.174249 | ||||||||
\(538\) | −22.5013 | −0.970100 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.46830 | −0.0631854 | ||||||||
\(541\) | 22.1914 | 0.954082 | 0.477041 | − | 0.878881i | \(-0.341709\pi\) | ||||
0.477041 | + | 0.878881i | \(0.341709\pi\) | |||||||
\(542\) | −13.6286 | −0.585400 | ||||||||
\(543\) | 0.861886 | 0.0369871 | ||||||||
\(544\) | −5.76549 | −0.247193 | ||||||||
\(545\) | 3.42125 | 0.146550 | ||||||||
\(546\) | −0.700760 | −0.0299898 | ||||||||
\(547\) | 17.1879 | 0.734903 | 0.367452 | − | 0.930043i | \(-0.380230\pi\) | ||||
0.367452 | + | 0.930043i | \(0.380230\pi\) | |||||||
\(548\) | −9.95341 | −0.425189 | ||||||||
\(549\) | 27.0416 | 1.15411 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.19323 | 0.221239 | ||||||||
\(552\) | 1.77374 | 0.0754954 | ||||||||
\(553\) | 6.14508 | 0.261315 | ||||||||
\(554\) | −23.5465 | −1.00040 | ||||||||
\(555\) | 0.728730 | 0.0309329 | ||||||||
\(556\) | −0.627224 | −0.0266002 | ||||||||
\(557\) | −6.02990 | −0.255495 | −0.127747 | − | 0.991807i | \(-0.540775\pi\) | ||||
−0.127747 | + | 0.991807i | \(0.540775\pi\) | |||||||
\(558\) | 1.04752 | 0.0443449 | ||||||||
\(559\) | 27.3240 | 1.15568 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.1837 | −0.809215 | ||||||||
\(563\) | 27.1986 | 1.14628 | 0.573142 | − | 0.819456i | \(-0.305724\pi\) | ||||
0.573142 | + | 0.819456i | \(0.305724\pi\) | |||||||
\(564\) | −0.775365 | −0.0326488 | ||||||||
\(565\) | 16.8223 | 0.707718 | ||||||||
\(566\) | 17.2722 | 0.726005 | ||||||||
\(567\) | 8.45361 | 0.355018 | ||||||||
\(568\) | −12.5139 | −0.525070 | ||||||||
\(569\) | 31.8782 | 1.33641 | 0.668203 | − | 0.743979i | \(-0.267064\pi\) | ||||
0.668203 | + | 0.743979i | \(0.267064\pi\) | |||||||
\(570\) | 0.907206 | 0.0379987 | ||||||||
\(571\) | −26.4539 | −1.10706 | −0.553531 | − | 0.832829i | \(-0.686720\pi\) | ||||
−0.553531 | + | 0.832829i | \(0.686720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.42075 | −0.268231 | ||||||||
\(574\) | 2.22578 | 0.0929022 | ||||||||
\(575\) | −7.17432 | −0.299190 | ||||||||
\(576\) | −2.93888 | −0.122453 | ||||||||
\(577\) | −30.0526 | −1.25111 | −0.625554 | − | 0.780181i | \(-0.715127\pi\) | ||||
−0.625554 | + | 0.780181i | \(0.715127\pi\) | |||||||
\(578\) | 16.2409 | 0.675531 | ||||||||
\(579\) | 0.167502 | 0.00696115 | ||||||||
\(580\) | −1.41528 | −0.0587661 | ||||||||
\(581\) | 3.08217 | 0.127870 | ||||||||
\(582\) | −3.09730 | −0.128387 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.19836 | −0.297870 | ||||||||
\(585\) | 8.32993 | 0.344400 | ||||||||
\(586\) | −32.9318 | −1.36040 | ||||||||
\(587\) | 26.7574 | 1.10440 | 0.552198 | − | 0.833713i | \(-0.313789\pi\) | ||||
0.552198 | + | 0.833713i | \(0.313789\pi\) | |||||||
\(588\) | −0.247235 | −0.0101958 | ||||||||
\(589\) | −1.30791 | −0.0538913 | ||||||||
\(590\) | 10.4962 | 0.432121 | ||||||||
\(591\) | −1.43597 | −0.0590679 | ||||||||
\(592\) | 2.94752 | 0.121142 | ||||||||
\(593\) | −3.33504 | −0.136954 | −0.0684768 | − | 0.997653i | \(-0.521814\pi\) | ||||
−0.0684768 | + | 0.997653i | \(0.521814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.76549 | 0.236362 | ||||||||
\(596\) | −15.0315 | −0.615713 | ||||||||
\(597\) | −2.70660 | −0.110774 | ||||||||
\(598\) | −20.3348 | −0.831553 | ||||||||
\(599\) | −3.33155 | −0.136123 | −0.0680617 | − | 0.997681i | \(-0.521681\pi\) | ||||
−0.0680617 | + | 0.997681i | \(0.521681\pi\) | |||||||
\(600\) | −0.247235 | −0.0100933 | ||||||||
\(601\) | −41.5433 | −1.69459 | −0.847293 | − | 0.531126i | \(-0.821769\pi\) | ||||
−0.847293 | + | 0.531126i | \(0.821769\pi\) | |||||||
\(602\) | 9.64018 | 0.392904 | ||||||||
\(603\) | 39.8118 | 1.62126 | ||||||||
\(604\) | 0.516467 | 0.0210148 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.45899 | 0.0592674 | ||||||||
\(607\) | 20.9676 | 0.851049 | 0.425525 | − | 0.904947i | \(-0.360090\pi\) | ||||
0.425525 | + | 0.904947i | \(0.360090\pi\) | |||||||
\(608\) | 3.66941 | 0.148814 | ||||||||
\(609\) | −0.349905 | −0.0141789 | ||||||||
\(610\) | 9.20135 | 0.372552 | ||||||||
\(611\) | 8.88908 | 0.359614 | ||||||||
\(612\) | 16.9441 | 0.684923 | ||||||||
\(613\) | −2.77191 | −0.111956 | −0.0559782 | − | 0.998432i | \(-0.517828\pi\) | ||||
−0.0559782 | + | 0.998432i | \(0.517828\pi\) | |||||||
\(614\) | −7.97195 | −0.321722 | ||||||||
\(615\) | 0.550290 | 0.0221898 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.3567 | 1.94677 | 0.973384 | − | 0.229180i | \(-0.0736043\pi\) | ||||
0.973384 | + | 0.229180i | \(0.0736043\pi\) | |||||||
\(618\) | 2.95868 | 0.119016 | ||||||||
\(619\) | 46.8795 | 1.88425 | 0.942123 | − | 0.335268i | \(-0.108827\pi\) | ||||
0.942123 | + | 0.335268i | \(0.108827\pi\) | |||||||
\(620\) | 0.356435 | 0.0143148 | ||||||||
\(621\) | −10.5340 | −0.422716 | ||||||||
\(622\) | −4.00836 | −0.160721 | ||||||||
\(623\) | −5.75443 | −0.230546 | ||||||||
\(624\) | −0.700760 | −0.0280529 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.27260 | 0.210736 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.7782 | −0.908949 | ||||||||
\(629\) | −16.9939 | −0.677592 | ||||||||
\(630\) | 2.93888 | 0.117088 | ||||||||
\(631\) | −21.5815 | −0.859145 | −0.429573 | − | 0.903032i | \(-0.641336\pi\) | ||||
−0.429573 | + | 0.903032i | \(0.641336\pi\) | |||||||
\(632\) | 6.14508 | 0.244438 | ||||||||
\(633\) | 1.58919 | 0.0631647 | ||||||||
\(634\) | −4.65978 | −0.185064 | ||||||||
\(635\) | −0.175760 | −0.00697481 | ||||||||
\(636\) | −0.216119 | −0.00856969 | ||||||||
\(637\) | 2.83439 | 0.112303 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.7766 | 1.45486 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 22.9849 | 0.907850 | 0.453925 | − | 0.891040i | \(-0.350023\pi\) | ||||
0.453925 | + | 0.891040i | \(0.350023\pi\) | |||||||
\(642\) | 1.55485 | 0.0613649 | ||||||||
\(643\) | −32.9082 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(644\) | −7.17432 | −0.282708 | ||||||||
\(645\) | 2.38339 | 0.0938457 | ||||||||
\(646\) | −21.1560 | −0.832370 | ||||||||
\(647\) | 19.9201 | 0.783140 | 0.391570 | − | 0.920148i | \(-0.371932\pi\) | ||||
0.391570 | + | 0.920148i | \(0.371932\pi\) | |||||||
\(648\) | 8.45361 | 0.332089 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.83439 | 0.111174 | ||||||||
\(651\) | 0.0881230 | 0.00345381 | ||||||||
\(652\) | 3.72353 | 0.145825 | ||||||||
\(653\) | 34.0859 | 1.33389 | 0.666943 | − | 0.745109i | \(-0.267602\pi\) | ||||
0.666943 | + | 0.745109i | \(0.267602\pi\) | |||||||
\(654\) | 0.845851 | 0.0330754 | ||||||||
\(655\) | 11.4391 | 0.446962 | ||||||||
\(656\) | 2.22578 | 0.0869021 | ||||||||
\(657\) | 21.1551 | 0.825338 | ||||||||
\(658\) | 3.13615 | 0.122260 | ||||||||
\(659\) | 7.54952 | 0.294088 | 0.147044 | − | 0.989130i | \(-0.453024\pi\) | ||||
0.147044 | + | 0.989130i | \(0.453024\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.0094 | 1.59508 | 0.797541 | − | 0.603265i | \(-0.206134\pi\) | ||||
0.797541 | + | 0.603265i | \(0.206134\pi\) | |||||||
\(662\) | −25.0199 | −0.972424 | ||||||||
\(663\) | 4.04022 | 0.156909 | ||||||||
\(664\) | 3.08217 | 0.119611 | ||||||||
\(665\) | −3.66941 | −0.142294 | ||||||||
\(666\) | −8.66240 | −0.335661 | ||||||||
\(667\) | −10.1536 | −0.393150 | ||||||||
\(668\) | 15.5825 | 0.602906 | ||||||||
\(669\) | −5.73703 | −0.221807 | ||||||||
\(670\) | 13.5466 | 0.523352 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.247235 | −0.00953728 | ||||||||
\(673\) | 48.3741 | 1.86469 | 0.932343 | − | 0.361576i | \(-0.117761\pi\) | ||||
0.932343 | + | 0.361576i | \(0.117761\pi\) | |||||||
\(674\) | 15.9367 | 0.613860 | ||||||||
\(675\) | 1.46830 | 0.0565147 | ||||||||
\(676\) | −4.96622 | −0.191008 | ||||||||
\(677\) | 5.38363 | 0.206910 | 0.103455 | − | 0.994634i | \(-0.467010\pi\) | ||||
0.103455 | + | 0.994634i | \(0.467010\pi\) | |||||||
\(678\) | 4.15905 | 0.159727 | ||||||||
\(679\) | 12.5278 | 0.480771 | ||||||||
\(680\) | 5.76549 | 0.221096 | ||||||||
\(681\) | 6.32217 | 0.242266 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.5734 | 0.481106 | 0.240553 | − | 0.970636i | \(-0.422671\pi\) | ||||
0.240553 | + | 0.970636i | \(0.422671\pi\) | |||||||
\(684\) | −10.7839 | −0.412334 | ||||||||
\(685\) | 9.95341 | 0.380300 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −0.995121 | −0.0379662 | ||||||||
\(688\) | 9.64018 | 0.367528 | ||||||||
\(689\) | 2.47767 | 0.0943919 | ||||||||
\(690\) | −1.77374 | −0.0675251 | ||||||||
\(691\) | −26.0427 | −0.990712 | −0.495356 | − | 0.868690i | \(-0.664962\pi\) | ||||
−0.495356 | + | 0.868690i | \(0.664962\pi\) | |||||||
\(692\) | 5.89952 | 0.224266 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.4275 | −0.471741 | ||||||||
\(695\) | 0.627224 | 0.0237920 | ||||||||
\(696\) | −0.349905 | −0.0132631 | ||||||||
\(697\) | −12.8327 | −0.486073 | ||||||||
\(698\) | −16.2129 | −0.613666 | ||||||||
\(699\) | 0.909134 | 0.0343866 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −46.1549 | −1.74325 | −0.871624 | − | 0.490176i | \(-0.836933\pi\) | ||||
−0.871624 | + | 0.490176i | \(0.836933\pi\) | |||||||
\(702\) | 4.16173 | 0.157074 | ||||||||
\(703\) | 10.8157 | 0.407921 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.775365 | 0.0292019 | ||||||||
\(706\) | −21.8320 | −0.821656 | ||||||||
\(707\) | −5.90123 | −0.221939 | ||||||||
\(708\) | 2.59502 | 0.0975267 | ||||||||
\(709\) | 44.5132 | 1.67173 | 0.835865 | − | 0.548935i | \(-0.184967\pi\) | ||||
0.835865 | + | 0.548935i | \(0.184967\pi\) | |||||||
\(710\) | 12.5139 | 0.469637 | ||||||||
\(711\) | −18.0596 | −0.677289 | ||||||||
\(712\) | −5.75443 | −0.215656 | ||||||||
\(713\) | 2.55718 | 0.0957670 | ||||||||
\(714\) | 1.42543 | 0.0533453 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.3323 | 0.610367 | ||||||||
\(717\) | 0.270582 | 0.0101051 | ||||||||
\(718\) | −18.2106 | −0.679612 | ||||||||
\(719\) | 24.2008 | 0.902536 | 0.451268 | − | 0.892389i | \(-0.350972\pi\) | ||||
0.451268 | + | 0.892389i | \(0.350972\pi\) | |||||||
\(720\) | 2.93888 | 0.109525 | ||||||||
\(721\) | −11.9671 | −0.445678 | ||||||||
\(722\) | −5.53541 | −0.206007 | ||||||||
\(723\) | −1.54498 | −0.0574582 | ||||||||
\(724\) | −3.48610 | −0.129560 | ||||||||
\(725\) | 1.41528 | 0.0525620 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.25083 | −0.194742 | −0.0973712 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973712 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(728\) | 2.83439 | 0.105050 | ||||||||
\(729\) | −23.7551 | −0.879817 | ||||||||
\(730\) | 7.19836 | 0.266423 | ||||||||
\(731\) | −55.5803 | −2.05571 | ||||||||
\(732\) | 2.27489 | 0.0840825 | ||||||||
\(733\) | −47.6047 | −1.75832 | −0.879160 | − | 0.476526i | \(-0.841896\pi\) | ||||
−0.879160 | + | 0.476526i | \(0.841896\pi\) | |||||||
\(734\) | −5.27857 | −0.194836 | ||||||||
\(735\) | 0.247235 | 0.00911939 | ||||||||
\(736\) | −7.17432 | −0.264449 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.54129 | −0.240788 | ||||||||
\(739\) | 27.2113 | 1.00098 | 0.500491 | − | 0.865742i | \(-0.333153\pi\) | ||||
0.500491 | + | 0.865742i | \(0.333153\pi\) | |||||||
\(740\) | −2.94752 | −0.108353 | ||||||||
\(741\) | −2.57138 | −0.0944619 | ||||||||
\(742\) | 0.874146 | 0.0320909 | ||||||||
\(743\) | −5.29833 | −0.194377 | −0.0971885 | − | 0.995266i | \(-0.530985\pi\) | ||||
−0.0971885 | + | 0.995266i | \(0.530985\pi\) | |||||||
\(744\) | 0.0881230 | 0.00323075 | ||||||||
\(745\) | 15.0315 | 0.550710 | ||||||||
\(746\) | 18.5799 | 0.680259 | ||||||||
\(747\) | −9.05811 | −0.331419 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.28895 | −0.229793 | ||||||||
\(750\) | 0.247235 | 0.00902773 | ||||||||
\(751\) | −20.0625 | −0.732089 | −0.366045 | − | 0.930597i | \(-0.619288\pi\) | ||||
−0.366045 | + | 0.930597i | \(0.619288\pi\) | |||||||
\(752\) | 3.13615 | 0.114364 | ||||||||
\(753\) | 4.76954 | 0.173812 | ||||||||
\(754\) | 4.01145 | 0.146088 | ||||||||
\(755\) | −0.516467 | −0.0187962 | ||||||||
\(756\) | 1.46830 | 0.0534014 | ||||||||
\(757\) | −4.36865 | −0.158781 | −0.0793907 | − | 0.996844i | \(-0.525297\pi\) | ||||
−0.0793907 | + | 0.996844i | \(0.525297\pi\) | |||||||
\(758\) | 22.8406 | 0.829607 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.66941 | −0.133104 | ||||||||
\(761\) | 2.16435 | 0.0784576 | 0.0392288 | − | 0.999230i | \(-0.487510\pi\) | ||||
0.0392288 | + | 0.999230i | \(0.487510\pi\) | |||||||
\(762\) | −0.0434539 | −0.00157417 | ||||||||
\(763\) | −3.42125 | −0.123857 | ||||||||
\(764\) | 25.9703 | 0.939572 | ||||||||
\(765\) | −16.9441 | −0.612613 | ||||||||
\(766\) | −22.4735 | −0.812000 | ||||||||
\(767\) | −29.7503 | −1.07422 | ||||||||
\(768\) | −0.247235 | −0.00892131 | ||||||||
\(769\) | −32.7883 | −1.18237 | −0.591187 | − | 0.806534i | \(-0.701341\pi\) | ||||
−0.591187 | + | 0.806534i | \(0.701341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.24671 | −0.224970 | ||||||||
\(772\) | −0.677502 | −0.0243838 | ||||||||
\(773\) | −7.29845 | −0.262507 | −0.131253 | − | 0.991349i | \(-0.541900\pi\) | ||||
−0.131253 | + | 0.991349i | \(0.541900\pi\) | |||||||
\(774\) | −28.3313 | −1.01835 | ||||||||
\(775\) | −0.356435 | −0.0128035 | ||||||||
\(776\) | 12.5278 | 0.449720 | ||||||||
\(777\) | −0.728730 | −0.0261430 | ||||||||
\(778\) | 36.2498 | 1.29962 | ||||||||
\(779\) | 8.16730 | 0.292624 | ||||||||
\(780\) | 0.700760 | 0.0250912 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 41.3634 | 1.47915 | ||||||||
\(783\) | 2.07804 | 0.0742632 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 22.7782 | 0.812989 | ||||||||
\(786\) | 2.82814 | 0.100876 | ||||||||
\(787\) | −0.836360 | −0.0298130 | −0.0149065 | − | 0.999889i | \(-0.504745\pi\) | ||||
−0.0149065 | + | 0.999889i | \(0.504745\pi\) | |||||||
\(788\) | 5.80812 | 0.206906 | ||||||||
\(789\) | −0.740103 | −0.0263484 | ||||||||
\(790\) | −6.14508 | −0.218632 | ||||||||
\(791\) | −16.8223 | −0.598131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.0802 | −0.926137 | ||||||||
\(794\) | −8.02992 | −0.284971 | ||||||||
\(795\) | 0.216119 | 0.00766496 | ||||||||
\(796\) | 10.9475 | 0.388023 | ||||||||
\(797\) | −2.03251 | −0.0719952 | −0.0359976 | − | 0.999352i | \(-0.511461\pi\) | ||||
−0.0359976 | + | 0.999352i | \(0.511461\pi\) | |||||||
\(798\) | −0.907206 | −0.0321147 | ||||||||
\(799\) | −18.0814 | −0.639676 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 16.9115 | 0.597540 | ||||||||
\(802\) | 0.672421 | 0.0237440 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.34919 | 0.118117 | ||||||||
\(805\) | 7.17432 | 0.252861 | ||||||||
\(806\) | −1.01028 | −0.0355855 | ||||||||
\(807\) | 5.56310 | 0.195830 | ||||||||
\(808\) | −5.90123 | −0.207605 | ||||||||
\(809\) | −42.1998 | −1.48367 | −0.741833 | − | 0.670585i | \(-0.766043\pi\) | ||||
−0.741833 | + | 0.670585i | \(0.766043\pi\) | |||||||
\(810\) | −8.45361 | −0.297030 | ||||||||
\(811\) | −3.03390 | −0.106535 | −0.0532673 | − | 0.998580i | \(-0.516964\pi\) | ||||
−0.0532673 | + | 0.998580i | \(0.516964\pi\) | |||||||
\(812\) | 1.41528 | 0.0496665 | ||||||||
\(813\) | 3.36947 | 0.118173 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.72353 | −0.130430 | ||||||||
\(816\) | 1.42543 | 0.0499000 | ||||||||
\(817\) | 35.3738 | 1.23757 | ||||||||
\(818\) | −21.7385 | −0.760069 | ||||||||
\(819\) | −8.32993 | −0.291071 | ||||||||
\(820\) | −2.22578 | −0.0777276 | ||||||||
\(821\) | 34.5900 | 1.20720 | 0.603599 | − | 0.797288i | \(-0.293733\pi\) | ||||
0.603599 | + | 0.797288i | \(0.293733\pi\) | |||||||
\(822\) | 2.46083 | 0.0858312 | ||||||||
\(823\) | 50.7373 | 1.76859 | 0.884295 | − | 0.466928i | \(-0.154639\pi\) | ||||
0.884295 | + | 0.466928i | \(0.154639\pi\) | |||||||
\(824\) | −11.9671 | −0.416894 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.4962 | −0.365209 | ||||||||
\(827\) | −12.9190 | −0.449239 | −0.224619 | − | 0.974447i | \(-0.572114\pi\) | ||||
−0.224619 | + | 0.974447i | \(0.572114\pi\) | |||||||
\(828\) | 21.0844 | 0.732734 | ||||||||
\(829\) | 12.8251 | 0.445434 | 0.222717 | − | 0.974883i | \(-0.428507\pi\) | ||||
0.222717 | + | 0.974883i | \(0.428507\pi\) | |||||||
\(830\) | −3.08217 | −0.106984 | ||||||||
\(831\) | 5.82151 | 0.201946 | ||||||||
\(832\) | 2.83439 | 0.0982649 | ||||||||
\(833\) | −5.76549 | −0.199762 | ||||||||
\(834\) | 0.155072 | 0.00536969 | ||||||||
\(835\) | −15.5825 | −0.539255 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.523352 | −0.0180897 | ||||||||
\(838\) | −7.38003 | −0.254939 | ||||||||
\(839\) | −8.02823 | −0.277165 | −0.138583 | − | 0.990351i | \(-0.544255\pi\) | ||||
−0.138583 | + | 0.990351i | \(0.544255\pi\) | |||||||
\(840\) | 0.247235 | 0.00853041 | ||||||||
\(841\) | −26.9970 | −0.930931 | ||||||||
\(842\) | 29.4497 | 1.01490 | ||||||||
\(843\) | 4.74287 | 0.163353 | ||||||||
\(844\) | −6.42786 | −0.221256 | ||||||||
\(845\) | 4.96622 | 0.170843 | ||||||||
\(846\) | −9.21676 | −0.316879 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.874146 | 0.0300183 | ||||||||
\(849\) | −4.27029 | −0.146556 | ||||||||
\(850\) | −5.76549 | −0.197755 | ||||||||
\(851\) | −21.1465 | −0.724891 | ||||||||
\(852\) | 3.09386 | 0.105994 | ||||||||
\(853\) | −30.1638 | −1.03279 | −0.516395 | − | 0.856351i | \(-0.672726\pi\) | ||||
−0.516395 | + | 0.856351i | \(0.672726\pi\) | |||||||
\(854\) | −9.20135 | −0.314864 | ||||||||
\(855\) | 10.7839 | 0.368803 | ||||||||
\(856\) | −6.28895 | −0.214952 | ||||||||
\(857\) | 32.8279 | 1.12138 | 0.560689 | − | 0.828026i | \(-0.310536\pi\) | ||||
0.560689 | + | 0.828026i | \(0.310536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7882 | 1.39168 | 0.695838 | − | 0.718199i | \(-0.255033\pi\) | ||||
0.695838 | + | 0.718199i | \(0.255033\pi\) | |||||||
\(860\) | −9.64018 | −0.328727 | ||||||||
\(861\) | −0.550290 | −0.0187538 | ||||||||
\(862\) | −19.6701 | −0.669968 | ||||||||
\(863\) | 42.0371 | 1.43096 | 0.715479 | − | 0.698634i | \(-0.246208\pi\) | ||||
0.715479 | + | 0.698634i | \(0.246208\pi\) | |||||||
\(864\) | 1.46830 | 0.0499524 | ||||||||
\(865\) | −5.89952 | −0.200590 | ||||||||
\(866\) | −17.0504 | −0.579397 | ||||||||
\(867\) | −4.01530 | −0.136367 | ||||||||
\(868\) | −0.356435 | −0.0120982 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.349905 | 0.0118629 | ||||||||
\(871\) | −38.3964 | −1.30101 | ||||||||
\(872\) | −3.42125 | −0.115858 | ||||||||
\(873\) | −36.8175 | −1.24608 | ||||||||
\(874\) | −26.3255 | −0.890474 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 1.77968 | 0.0601299 | ||||||||
\(877\) | −2.16379 | −0.0730659 | −0.0365330 | − | 0.999332i | \(-0.511631\pi\) | ||||
−0.0365330 | + | 0.999332i | \(0.511631\pi\) | |||||||
\(878\) | 29.9589 | 1.01106 | ||||||||
\(879\) | 8.14187 | 0.274619 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.74157 | 0.328202 | 0.164101 | − | 0.986444i | \(-0.447528\pi\) | ||||
0.164101 | + | 0.986444i | \(0.447528\pi\) | |||||||
\(882\) | −2.93888 | −0.0989571 | ||||||||
\(883\) | 25.2808 | 0.850768 | 0.425384 | − | 0.905013i | \(-0.360139\pi\) | ||||
0.425384 | + | 0.905013i | \(0.360139\pi\) | |||||||
\(884\) | −16.3417 | −0.549629 | ||||||||
\(885\) | −2.59502 | −0.0872306 | ||||||||
\(886\) | 41.2954 | 1.38735 | ||||||||
\(887\) | −45.8358 | −1.53901 | −0.769507 | − | 0.638638i | \(-0.779498\pi\) | ||||
−0.769507 | + | 0.638638i | \(0.779498\pi\) | |||||||
\(888\) | −0.728730 | −0.0244546 | ||||||||
\(889\) | 0.175760 | 0.00589479 | ||||||||
\(890\) | 5.75443 | 0.192889 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.2048 | 0.776955 | ||||||||
\(893\) | 11.5078 | 0.385095 | ||||||||
\(894\) | 3.71630 | 0.124292 | ||||||||
\(895\) | −16.3323 | −0.545929 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 5.02747 | 0.167862 | ||||||||
\(898\) | 33.9263 | 1.13214 | ||||||||
\(899\) | −0.504454 | −0.0168245 | ||||||||
\(900\) | −2.93888 | −0.0979625 | ||||||||
\(901\) | −5.03988 | −0.167903 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.38339 | −0.0793141 | ||||||||
\(904\) | −16.8223 | −0.559500 | ||||||||
\(905\) | 3.48610 | 0.115882 | ||||||||
\(906\) | −0.127689 | −0.00424217 | ||||||||
\(907\) | −15.1299 | −0.502381 | −0.251190 | − | 0.967938i | \(-0.580822\pi\) | ||||
−0.251190 | + | 0.967938i | \(0.580822\pi\) | |||||||
\(908\) | −25.5715 | −0.848621 | ||||||||
\(909\) | 17.3430 | 0.575231 | ||||||||
\(910\) | −2.83439 | −0.0939592 | ||||||||
\(911\) | 14.7067 | 0.487255 | 0.243627 | − | 0.969869i | \(-0.421663\pi\) | ||||
0.243627 | + | 0.969869i | \(0.421663\pi\) | |||||||
\(912\) | −0.907206 | −0.0300406 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.9928 | 0.661304 | ||||||||
\(915\) | −2.27489 | −0.0752056 | ||||||||
\(916\) | 4.02501 | 0.132990 | ||||||||
\(917\) | −11.4391 | −0.377752 | ||||||||
\(918\) | −8.46544 | −0.279401 | ||||||||
\(919\) | 1.78904 | 0.0590151 | 0.0295075 | − | 0.999565i | \(-0.490606\pi\) | ||||
0.0295075 | + | 0.999565i | \(0.490606\pi\) | |||||||
\(920\) | 7.17432 | 0.236530 | ||||||||
\(921\) | 1.97094 | 0.0649448 | ||||||||
\(922\) | −17.4739 | −0.575472 | ||||||||
\(923\) | −35.4692 | −1.16748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.94752 | 0.0969140 | ||||||||
\(926\) | −41.7730 | −1.37275 | ||||||||
\(927\) | 35.1698 | 1.15513 | ||||||||
\(928\) | 1.41528 | 0.0464587 | ||||||||
\(929\) | 50.8053 | 1.66687 | 0.833433 | − | 0.552620i | \(-0.186372\pi\) | ||||
0.833433 | + | 0.552620i | \(0.186372\pi\) | |||||||
\(930\) | −0.0881230 | −0.00288967 | ||||||||
\(931\) | 3.66941 | 0.120260 | ||||||||
\(932\) | −3.67721 | −0.120451 | ||||||||
\(933\) | 0.991006 | 0.0324441 | ||||||||
\(934\) | −13.7476 | −0.449836 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.32993 | −0.272272 | ||||||||
\(937\) | 56.0500 | 1.83107 | 0.915537 | − | 0.402233i | \(-0.131766\pi\) | ||||
0.915537 | + | 0.402233i | \(0.131766\pi\) | |||||||
\(938\) | −13.5466 | −0.442313 | ||||||||
\(939\) | −1.30357 | −0.0425404 | ||||||||
\(940\) | −3.13615 | −0.102290 | ||||||||
\(941\) | 31.8530 | 1.03838 | 0.519188 | − | 0.854660i | \(-0.326234\pi\) | ||||
0.519188 | + | 0.854660i | \(0.326234\pi\) | |||||||
\(942\) | 5.63156 | 0.183486 | ||||||||
\(943\) | −15.9684 | −0.520004 | ||||||||
\(944\) | −10.4962 | −0.341621 | ||||||||
\(945\) | −1.46830 | −0.0477637 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7087 | 0.542959 | 0.271479 | − | 0.962444i | \(-0.412487\pi\) | ||||
0.271479 | + | 0.962444i | \(0.412487\pi\) | |||||||
\(948\) | −1.51928 | −0.0493438 | ||||||||
\(949\) | −20.4030 | −0.662308 | ||||||||
\(950\) | 3.66941 | 0.119051 | ||||||||
\(951\) | 1.15206 | 0.0373581 | ||||||||
\(952\) | −5.76549 | −0.186861 | ||||||||
\(953\) | 2.96987 | 0.0962036 | 0.0481018 | − | 0.998842i | \(-0.484683\pi\) | ||||
0.0481018 | + | 0.998842i | \(0.484683\pi\) | |||||||
\(954\) | −2.56901 | −0.0831747 | ||||||||
\(955\) | −25.9703 | −0.840379 | ||||||||
\(956\) | −1.09444 | −0.0353966 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.6636 | −0.667611 | ||||||||
\(959\) | −9.95341 | −0.321412 | ||||||||
\(960\) | 0.247235 | 0.00797946 | ||||||||
\(961\) | −30.8730 | −0.995902 | ||||||||
\(962\) | 8.35444 | 0.269358 | ||||||||
\(963\) | 18.4824 | 0.595588 | ||||||||
\(964\) | 6.24902 | 0.201267 | ||||||||
\(965\) | 0.677502 | 0.0218096 | ||||||||
\(966\) | 1.77374 | 0.0570691 | ||||||||
\(967\) | −20.4576 | −0.657873 | −0.328936 | − | 0.944352i | \(-0.606690\pi\) | ||||
−0.328936 | + | 0.944352i | \(0.606690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.23049 | 0.168027 | ||||||||
\(970\) | −12.5278 | −0.402242 | ||||||||
\(971\) | −60.0213 | −1.92618 | −0.963088 | − | 0.269187i | \(-0.913245\pi\) | ||||
−0.963088 | + | 0.269187i | \(0.913245\pi\) | |||||||
\(972\) | −6.49491 | −0.208324 | ||||||||
\(973\) | −0.627224 | −0.0201079 | ||||||||
\(974\) | −22.1049 | −0.708287 | ||||||||
\(975\) | −0.700760 | −0.0224423 | ||||||||
\(976\) | −9.20135 | −0.294528 | ||||||||
\(977\) | 16.7790 | 0.536808 | 0.268404 | − | 0.963306i | \(-0.413504\pi\) | ||||
0.268404 | + | 0.963306i | \(0.413504\pi\) | |||||||
\(978\) | −0.920586 | −0.0294371 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 10.0546 | 0.321019 | ||||||||
\(982\) | 10.6974 | 0.341369 | ||||||||
\(983\) | 48.6058 | 1.55028 | 0.775141 | − | 0.631788i | \(-0.217679\pi\) | ||||
0.775141 | + | 0.631788i | \(0.217679\pi\) | |||||||
\(984\) | −0.550290 | −0.0175426 | ||||||||
\(985\) | −5.80812 | −0.185062 | ||||||||
\(986\) | −8.15976 | −0.259860 | ||||||||
\(987\) | −0.775365 | −0.0246802 | ||||||||
\(988\) | 10.4006 | 0.330886 | ||||||||
\(989\) | −69.1617 | −2.19921 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.7217 | 1.77006 | 0.885028 | − | 0.465537i | \(-0.154139\pi\) | ||||
0.885028 | + | 0.465537i | \(0.154139\pi\) | |||||||
\(992\) | −0.356435 | −0.0113168 | ||||||||
\(993\) | 6.18578 | 0.196300 | ||||||||
\(994\) | −12.5139 | −0.396915 | ||||||||
\(995\) | −10.9475 | −0.347058 | ||||||||
\(996\) | −0.762019 | −0.0241455 | ||||||||
\(997\) | 38.8069 | 1.22903 | 0.614513 | − | 0.788907i | \(-0.289353\pi\) | ||||
0.614513 | + | 0.788907i | \(0.289353\pi\) | |||||||
\(998\) | 1.85809 | 0.0588167 | ||||||||
\(999\) | 4.32784 | 0.136927 |
(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 | 8470.2.a.da.1.4 | 6 | ||
11.3 | even | 5 | 770.2.n.h.141.2 | yes | 12 | ||
11.4 | even | 5 | 770.2.n.h.71.2 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.cu.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.h.71.2 | ✓ | 12 | 11.4 | even | 5 | ||
770.2.n.h.141.2 | yes | 12 | 11.3 | even | 5 | ||
8470.2.a.cu.1.4 | 6 | 11.10 | odd | 2 | |||
8470.2.a.da.1.4 | 6 | 1.1 | even | 1 | trivial |