Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22360 | −0.865215 | −0.432607 | − | 0.901582i | \(-0.642406\pi\) | ||||
−0.432607 | + | 0.901582i | \(0.642406\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.502806 | −0.251403 | ||||||||
\(5\) | 1.43997 | 0.643975 | 0.321987 | − | 0.946744i | \(-0.395649\pi\) | ||||
0.321987 | + | 0.946744i | \(0.395649\pi\) | |||||||
\(6\) | −1.22360 | −0.499532 | ||||||||
\(7\) | −1.77841 | −0.672174 | −0.336087 | − | 0.941831i | \(-0.609104\pi\) | ||||
−0.336087 | + | 0.941831i | \(0.609104\pi\) | |||||||
\(8\) | 3.06243 | 1.08273 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.76195 | −0.557177 | ||||||||
\(11\) | −4.03409 | −1.21632 | −0.608161 | − | 0.793814i | \(-0.708093\pi\) | ||||
−0.608161 | + | 0.793814i | \(0.708093\pi\) | |||||||
\(12\) | −0.502806 | −0.145148 | ||||||||
\(13\) | 1.49492 | 0.414617 | 0.207309 | − | 0.978276i | \(-0.433530\pi\) | ||||
0.207309 | + | 0.978276i | \(0.433530\pi\) | |||||||
\(14\) | 2.17605 | 0.581575 | ||||||||
\(15\) | 1.43997 | 0.371799 | ||||||||
\(16\) | −2.74157 | −0.685393 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.22360 | −0.288405 | ||||||||
\(19\) | 0.978337 | 0.224446 | 0.112223 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112223 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(20\) | −0.724027 | −0.161897 | ||||||||
\(21\) | −1.77841 | −0.388080 | ||||||||
\(22\) | 4.93610 | 1.05238 | ||||||||
\(23\) | 2.98194 | 0.621777 | 0.310889 | − | 0.950446i | \(-0.399373\pi\) | ||||
0.310889 | + | 0.950446i | \(0.399373\pi\) | |||||||
\(24\) | 3.06243 | 0.625116 | ||||||||
\(25\) | −2.92648 | −0.585296 | ||||||||
\(26\) | −1.82919 | −0.358733 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.894194 | 0.168987 | ||||||||
\(29\) | 3.44515 | 0.639748 | 0.319874 | − | 0.947460i | \(-0.396359\pi\) | ||||
0.319874 | + | 0.947460i | \(0.396359\pi\) | |||||||
\(30\) | −1.76195 | −0.321686 | ||||||||
\(31\) | 5.60765 | 1.00716 | 0.503582 | − | 0.863947i | \(-0.332015\pi\) | ||||
0.503582 | + | 0.863947i | \(0.332015\pi\) | |||||||
\(32\) | −2.77028 | −0.489720 | ||||||||
\(33\) | −4.03409 | −0.702244 | ||||||||
\(34\) | −1.22360 | −0.209845 | ||||||||
\(35\) | −2.56085 | −0.432863 | ||||||||
\(36\) | −0.502806 | −0.0838011 | ||||||||
\(37\) | 0.00295062 | 0.000485079 0 | 0.000242539 | − | 1.00000i | \(-0.499923\pi\) | ||||
0.000242539 | 1.00000i | \(0.499923\pi\) | ||||||||
\(38\) | −1.19709 | −0.194194 | ||||||||
\(39\) | 1.49492 | 0.239379 | ||||||||
\(40\) | 4.40981 | 0.697253 | ||||||||
\(41\) | 8.32343 | 1.29990 | 0.649951 | − | 0.759976i | \(-0.274789\pi\) | ||||
0.649951 | + | 0.759976i | \(0.274789\pi\) | |||||||
\(42\) | 2.17605 | 0.335773 | ||||||||
\(43\) | 2.89385 | 0.441307 | 0.220654 | − | 0.975352i | \(-0.429181\pi\) | ||||
0.220654 | + | 0.975352i | \(0.429181\pi\) | |||||||
\(44\) | 2.02836 | 0.305787 | ||||||||
\(45\) | 1.43997 | 0.214658 | ||||||||
\(46\) | −3.64870 | −0.537971 | ||||||||
\(47\) | −6.47494 | −0.944467 | −0.472234 | − | 0.881473i | \(-0.656552\pi\) | ||||
−0.472234 | + | 0.881473i | \(0.656552\pi\) | |||||||
\(48\) | −2.74157 | −0.395712 | ||||||||
\(49\) | −3.83727 | −0.548182 | ||||||||
\(50\) | 3.58084 | 0.506407 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.751657 | −0.104236 | ||||||||
\(53\) | −3.00170 | −0.412315 | −0.206158 | − | 0.978519i | \(-0.566096\pi\) | ||||
−0.206158 | + | 0.978519i | \(0.566096\pi\) | |||||||
\(54\) | −1.22360 | −0.166511 | ||||||||
\(55\) | −5.80897 | −0.783281 | ||||||||
\(56\) | −5.44624 | −0.727785 | ||||||||
\(57\) | 0.978337 | 0.129584 | ||||||||
\(58\) | −4.21548 | −0.553519 | ||||||||
\(59\) | −4.07376 | −0.530359 | −0.265179 | − | 0.964199i | \(-0.585431\pi\) | ||||
−0.265179 | + | 0.964199i | \(0.585431\pi\) | |||||||
\(60\) | −0.724027 | −0.0934715 | ||||||||
\(61\) | −3.04725 | −0.390160 | −0.195080 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195080 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(62\) | −6.86151 | −0.871413 | ||||||||
\(63\) | −1.77841 | −0.224058 | ||||||||
\(64\) | 8.87285 | 1.10911 | ||||||||
\(65\) | 2.15265 | 0.267003 | ||||||||
\(66\) | 4.93610 | 0.607592 | ||||||||
\(67\) | 10.5594 | 1.29003 | 0.645016 | − | 0.764169i | \(-0.276851\pi\) | ||||
0.645016 | + | 0.764169i | \(0.276851\pi\) | |||||||
\(68\) | −0.502806 | −0.0609742 | ||||||||
\(69\) | 2.98194 | 0.358983 | ||||||||
\(70\) | 3.13346 | 0.374520 | ||||||||
\(71\) | −12.5257 | −1.48653 | −0.743263 | − | 0.668999i | \(-0.766723\pi\) | ||||
−0.743263 | + | 0.668999i | \(0.766723\pi\) | |||||||
\(72\) | 3.06243 | 0.360911 | ||||||||
\(73\) | 4.54543 | 0.532002 | 0.266001 | − | 0.963973i | \(-0.414298\pi\) | ||||
0.266001 | + | 0.963973i | \(0.414298\pi\) | |||||||
\(74\) | −0.00361037 | −0.000419697 0 | ||||||||
\(75\) | −2.92648 | −0.337921 | ||||||||
\(76\) | −0.491914 | −0.0564264 | ||||||||
\(77\) | 7.17424 | 0.817581 | ||||||||
\(78\) | −1.82919 | −0.207115 | ||||||||
\(79\) | −8.54162 | −0.961007 | −0.480504 | − | 0.876993i | \(-0.659546\pi\) | ||||
−0.480504 | + | 0.876993i | \(0.659546\pi\) | |||||||
\(80\) | −3.94779 | −0.441376 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.1845 | −1.12469 | ||||||||
\(83\) | 2.65805 | 0.291759 | 0.145879 | − | 0.989302i | \(-0.453399\pi\) | ||||
0.145879 | + | 0.989302i | \(0.453399\pi\) | |||||||
\(84\) | 0.894194 | 0.0975646 | ||||||||
\(85\) | 1.43997 | 0.156187 | ||||||||
\(86\) | −3.54091 | −0.381826 | ||||||||
\(87\) | 3.44515 | 0.369359 | ||||||||
\(88\) | −12.3541 | −1.31695 | ||||||||
\(89\) | −2.75226 | −0.291739 | −0.145869 | − | 0.989304i | \(-0.546598\pi\) | ||||
−0.145869 | + | 0.989304i | \(0.546598\pi\) | |||||||
\(90\) | −1.76195 | −0.185726 | ||||||||
\(91\) | −2.65858 | −0.278695 | ||||||||
\(92\) | −1.49934 | −0.156317 | ||||||||
\(93\) | 5.60765 | 0.581486 | ||||||||
\(94\) | 7.92273 | 0.817167 | ||||||||
\(95\) | 1.40878 | 0.144538 | ||||||||
\(96\) | −2.77028 | −0.282740 | ||||||||
\(97\) | 3.36257 | 0.341418 | 0.170709 | − | 0.985322i | \(-0.445394\pi\) | ||||
0.170709 | + | 0.985322i | \(0.445394\pi\) | |||||||
\(98\) | 4.69528 | 0.474295 | ||||||||
\(99\) | −4.03409 | −0.405441 | ||||||||
\(100\) | 1.47145 | 0.147145 | ||||||||
\(101\) | 12.8388 | 1.27751 | 0.638753 | − | 0.769411i | \(-0.279450\pi\) | ||||
0.638753 | + | 0.769411i | \(0.279450\pi\) | |||||||
\(102\) | −1.22360 | −0.121154 | ||||||||
\(103\) | −14.0201 | −1.38144 | −0.690718 | − | 0.723124i | \(-0.742706\pi\) | ||||
−0.690718 | + | 0.723124i | \(0.742706\pi\) | |||||||
\(104\) | 4.57810 | 0.448920 | ||||||||
\(105\) | −2.56085 | −0.249914 | ||||||||
\(106\) | 3.67287 | 0.356741 | ||||||||
\(107\) | 9.83296 | 0.950588 | 0.475294 | − | 0.879827i | \(-0.342342\pi\) | ||||
0.475294 | + | 0.879827i | \(0.342342\pi\) | |||||||
\(108\) | −0.502806 | −0.0483826 | ||||||||
\(109\) | 13.9552 | 1.33666 | 0.668331 | − | 0.743864i | \(-0.267009\pi\) | ||||
0.668331 | + | 0.743864i | \(0.267009\pi\) | |||||||
\(110\) | 7.10785 | 0.677706 | ||||||||
\(111\) | 0.00295062 | 0.000280060 0 | ||||||||
\(112\) | 4.87563 | 0.460704 | ||||||||
\(113\) | 4.18898 | 0.394066 | 0.197033 | − | 0.980397i | \(-0.436869\pi\) | ||||
0.197033 | + | 0.980397i | \(0.436869\pi\) | |||||||
\(114\) | −1.19709 | −0.112118 | ||||||||
\(115\) | 4.29391 | 0.400409 | ||||||||
\(116\) | −1.73224 | −0.160835 | ||||||||
\(117\) | 1.49492 | 0.138206 | ||||||||
\(118\) | 4.98465 | 0.458874 | ||||||||
\(119\) | −1.77841 | −0.163026 | ||||||||
\(120\) | 4.40981 | 0.402559 | ||||||||
\(121\) | 5.27384 | 0.479440 | ||||||||
\(122\) | 3.72861 | 0.337572 | ||||||||
\(123\) | 8.32343 | 0.750499 | ||||||||
\(124\) | −2.81956 | −0.253204 | ||||||||
\(125\) | −11.4139 | −1.02089 | ||||||||
\(126\) | 2.17605 | 0.193858 | ||||||||
\(127\) | −4.75965 | −0.422350 | −0.211175 | − | 0.977448i | \(-0.567729\pi\) | ||||
−0.211175 | + | 0.977448i | \(0.567729\pi\) | |||||||
\(128\) | −5.31626 | −0.469895 | ||||||||
\(129\) | 2.89385 | 0.254789 | ||||||||
\(130\) | −2.63398 | −0.231015 | ||||||||
\(131\) | −1.09758 | −0.0958956 | −0.0479478 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479478 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(132\) | 2.02836 | 0.176546 | ||||||||
\(133\) | −1.73988 | −0.150867 | ||||||||
\(134\) | −12.9204 | −1.11616 | ||||||||
\(135\) | 1.43997 | 0.123933 | ||||||||
\(136\) | 3.06243 | 0.262601 | ||||||||
\(137\) | −11.5071 | −0.983119 | −0.491560 | − | 0.870844i | \(-0.663573\pi\) | ||||
−0.491560 | + | 0.870844i | \(0.663573\pi\) | |||||||
\(138\) | −3.64870 | −0.310598 | ||||||||
\(139\) | 18.1838 | 1.54233 | 0.771164 | − | 0.636637i | \(-0.219675\pi\) | ||||
0.771164 | + | 0.636637i | \(0.219675\pi\) | |||||||
\(140\) | 1.28761 | 0.108823 | ||||||||
\(141\) | −6.47494 | −0.545288 | ||||||||
\(142\) | 15.3264 | 1.28616 | ||||||||
\(143\) | −6.03065 | −0.504308 | ||||||||
\(144\) | −2.74157 | −0.228464 | ||||||||
\(145\) | 4.96091 | 0.411981 | ||||||||
\(146\) | −5.56178 | −0.460296 | ||||||||
\(147\) | −3.83727 | −0.316493 | ||||||||
\(148\) | −0.00148359 | −0.000121950 0 | ||||||||
\(149\) | 7.04423 | 0.577086 | 0.288543 | − | 0.957467i | \(-0.406829\pi\) | ||||
0.288543 | + | 0.957467i | \(0.406829\pi\) | |||||||
\(150\) | 3.58084 | 0.292374 | ||||||||
\(151\) | 6.11906 | 0.497962 | 0.248981 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248981 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(152\) | 2.99609 | 0.243015 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −8.77839 | −0.707383 | ||||||||
\(155\) | 8.07486 | 0.648588 | ||||||||
\(156\) | −0.751657 | −0.0601807 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 10.4515 | 0.831478 | ||||||||
\(159\) | −3.00170 | −0.238050 | ||||||||
\(160\) | −3.98912 | −0.315368 | ||||||||
\(161\) | −5.30310 | −0.417943 | ||||||||
\(162\) | −1.22360 | −0.0961350 | ||||||||
\(163\) | 19.5803 | 1.53365 | 0.766823 | − | 0.641859i | \(-0.221837\pi\) | ||||
0.766823 | + | 0.641859i | \(0.221837\pi\) | |||||||
\(164\) | −4.18508 | −0.326800 | ||||||||
\(165\) | −5.80897 | −0.452228 | ||||||||
\(166\) | −3.25238 | −0.252434 | ||||||||
\(167\) | −21.2436 | −1.64388 | −0.821940 | − | 0.569574i | \(-0.807108\pi\) | ||||
−0.821940 | + | 0.569574i | \(0.807108\pi\) | |||||||
\(168\) | −5.44624 | −0.420187 | ||||||||
\(169\) | −10.7652 | −0.828093 | ||||||||
\(170\) | −1.76195 | −0.135135 | ||||||||
\(171\) | 0.978337 | 0.0748153 | ||||||||
\(172\) | −1.45504 | −0.110946 | ||||||||
\(173\) | 22.3508 | 1.69930 | 0.849650 | − | 0.527347i | \(-0.176813\pi\) | ||||
0.849650 | + | 0.527347i | \(0.176813\pi\) | |||||||
\(174\) | −4.21548 | −0.319574 | ||||||||
\(175\) | 5.20447 | 0.393421 | ||||||||
\(176\) | 11.0597 | 0.833659 | ||||||||
\(177\) | −4.07376 | −0.306203 | ||||||||
\(178\) | 3.36766 | 0.252417 | ||||||||
\(179\) | 6.82845 | 0.510383 | 0.255191 | − | 0.966891i | \(-0.417862\pi\) | ||||
0.255191 | + | 0.966891i | \(0.417862\pi\) | |||||||
\(180\) | −0.724027 | −0.0539658 | ||||||||
\(181\) | 0.0495339 | 0.00368183 | 0.00184091 | − | 0.999998i | \(-0.499414\pi\) | ||||
0.00184091 | + | 0.999998i | \(0.499414\pi\) | |||||||
\(182\) | 3.25304 | 0.241131 | ||||||||
\(183\) | −3.04725 | −0.225259 | ||||||||
\(184\) | 9.13198 | 0.673218 | ||||||||
\(185\) | 0.00424881 | 0.000312378 0 | ||||||||
\(186\) | −6.86151 | −0.503111 | ||||||||
\(187\) | −4.03409 | −0.295002 | ||||||||
\(188\) | 3.25564 | 0.237442 | ||||||||
\(189\) | −1.77841 | −0.129360 | ||||||||
\(190\) | −1.72378 | −0.125056 | ||||||||
\(191\) | −13.2905 | −0.961664 | −0.480832 | − | 0.876813i | \(-0.659665\pi\) | ||||
−0.480832 | + | 0.876813i | \(0.659665\pi\) | |||||||
\(192\) | 8.87285 | 0.640343 | ||||||||
\(193\) | 10.7795 | 0.775928 | 0.387964 | − | 0.921675i | \(-0.373179\pi\) | ||||
0.387964 | + | 0.921675i | \(0.373179\pi\) | |||||||
\(194\) | −4.11444 | −0.295400 | ||||||||
\(195\) | 2.15265 | 0.154154 | ||||||||
\(196\) | 1.92941 | 0.137815 | ||||||||
\(197\) | 21.7139 | 1.54705 | 0.773525 | − | 0.633766i | \(-0.218492\pi\) | ||||
0.773525 | + | 0.633766i | \(0.218492\pi\) | |||||||
\(198\) | 4.93610 | 0.350793 | ||||||||
\(199\) | 4.44333 | 0.314979 | 0.157490 | − | 0.987521i | \(-0.449660\pi\) | ||||
0.157490 | + | 0.987521i | \(0.449660\pi\) | |||||||
\(200\) | −8.96215 | −0.633719 | ||||||||
\(201\) | 10.5594 | 0.744800 | ||||||||
\(202\) | −15.7095 | −1.10532 | ||||||||
\(203\) | −6.12687 | −0.430022 | ||||||||
\(204\) | −0.502806 | −0.0352035 | ||||||||
\(205\) | 11.9855 | 0.837104 | ||||||||
\(206\) | 17.1549 | 1.19524 | ||||||||
\(207\) | 2.98194 | 0.207259 | ||||||||
\(208\) | −4.09844 | −0.284176 | ||||||||
\(209\) | −3.94670 | −0.272999 | ||||||||
\(210\) | 3.13346 | 0.216229 | ||||||||
\(211\) | −2.12234 | −0.146108 | −0.0730539 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730539 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(212\) | 1.50927 | 0.103657 | ||||||||
\(213\) | −12.5257 | −0.858246 | ||||||||
\(214\) | −12.0316 | −0.822463 | ||||||||
\(215\) | 4.16705 | 0.284191 | ||||||||
\(216\) | 3.06243 | 0.208372 | ||||||||
\(217\) | −9.97268 | −0.676990 | ||||||||
\(218\) | −17.0755 | −1.15650 | ||||||||
\(219\) | 4.54543 | 0.307152 | ||||||||
\(220\) | 2.92079 | 0.196919 | ||||||||
\(221\) | 1.49492 | 0.100559 | ||||||||
\(222\) | −0.00361037 | −0.000242312 0 | ||||||||
\(223\) | −19.9671 | −1.33710 | −0.668549 | − | 0.743668i | \(-0.733084\pi\) | ||||
−0.668549 | + | 0.743668i | \(0.733084\pi\) | |||||||
\(224\) | 4.92668 | 0.329177 | ||||||||
\(225\) | −2.92648 | −0.195099 | ||||||||
\(226\) | −5.12563 | −0.340952 | ||||||||
\(227\) | 25.6205 | 1.70049 | 0.850246 | − | 0.526386i | \(-0.176453\pi\) | ||||
0.850246 | + | 0.526386i | \(0.176453\pi\) | |||||||
\(228\) | −0.491914 | −0.0325778 | ||||||||
\(229\) | 28.3808 | 1.87545 | 0.937727 | − | 0.347372i | \(-0.112926\pi\) | ||||
0.937727 | + | 0.347372i | \(0.112926\pi\) | |||||||
\(230\) | −5.25402 | −0.346440 | ||||||||
\(231\) | 7.17424 | 0.472030 | ||||||||
\(232\) | 10.5505 | 0.692676 | ||||||||
\(233\) | −3.26740 | −0.214054 | −0.107027 | − | 0.994256i | \(-0.534133\pi\) | ||||
−0.107027 | + | 0.994256i | \(0.534133\pi\) | |||||||
\(234\) | −1.82919 | −0.119578 | ||||||||
\(235\) | −9.32373 | −0.608213 | ||||||||
\(236\) | 2.04831 | 0.133334 | ||||||||
\(237\) | −8.54162 | −0.554838 | ||||||||
\(238\) | 2.17605 | 0.141053 | ||||||||
\(239\) | 22.1109 | 1.43024 | 0.715118 | − | 0.699003i | \(-0.246373\pi\) | ||||
0.715118 | + | 0.699003i | \(0.246373\pi\) | |||||||
\(240\) | −3.94779 | −0.254829 | ||||||||
\(241\) | −23.4687 | −1.51175 | −0.755875 | − | 0.654716i | \(-0.772788\pi\) | ||||
−0.755875 | + | 0.654716i | \(0.772788\pi\) | |||||||
\(242\) | −6.45307 | −0.414819 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.53217 | 0.0980875 | ||||||||
\(245\) | −5.52556 | −0.353015 | ||||||||
\(246\) | −10.1845 | −0.649343 | ||||||||
\(247\) | 1.46254 | 0.0930592 | ||||||||
\(248\) | 17.1730 | 1.09049 | ||||||||
\(249\) | 2.65805 | 0.168447 | ||||||||
\(250\) | 13.9660 | 0.883290 | ||||||||
\(251\) | 17.9834 | 1.13510 | 0.567551 | − | 0.823338i | \(-0.307891\pi\) | ||||
0.567551 | + | 0.823338i | \(0.307891\pi\) | |||||||
\(252\) | 0.894194 | 0.0563289 | ||||||||
\(253\) | −12.0294 | −0.756282 | ||||||||
\(254\) | 5.82390 | 0.365424 | ||||||||
\(255\) | 1.43997 | 0.0901745 | ||||||||
\(256\) | −11.2407 | −0.702546 | ||||||||
\(257\) | 26.0376 | 1.62418 | 0.812091 | − | 0.583530i | \(-0.198329\pi\) | ||||
0.812091 | + | 0.583530i | \(0.198329\pi\) | |||||||
\(258\) | −3.54091 | −0.220447 | ||||||||
\(259\) | −0.00524740 | −0.000326057 0 | ||||||||
\(260\) | −1.08237 | −0.0671254 | ||||||||
\(261\) | 3.44515 | 0.213249 | ||||||||
\(262\) | 1.34299 | 0.0829703 | ||||||||
\(263\) | −28.6152 | −1.76449 | −0.882243 | − | 0.470794i | \(-0.843968\pi\) | ||||
−0.882243 | + | 0.470794i | \(0.843968\pi\) | |||||||
\(264\) | −12.3541 | −0.760343 | ||||||||
\(265\) | −4.32236 | −0.265521 | ||||||||
\(266\) | 2.12892 | 0.130532 | ||||||||
\(267\) | −2.75226 | −0.168435 | ||||||||
\(268\) | −5.30932 | −0.324318 | ||||||||
\(269\) | 4.81904 | 0.293822 | 0.146911 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146911 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(270\) | −1.76195 | −0.107229 | ||||||||
\(271\) | 8.14633 | 0.494854 | 0.247427 | − | 0.968907i | \(-0.420415\pi\) | ||||
0.247427 | + | 0.968907i | \(0.420415\pi\) | |||||||
\(272\) | −2.74157 | −0.166232 | ||||||||
\(273\) | −2.65858 | −0.160905 | ||||||||
\(274\) | 14.0801 | 0.850610 | ||||||||
\(275\) | 11.8057 | 0.711909 | ||||||||
\(276\) | −1.49934 | −0.0902495 | ||||||||
\(277\) | −27.2492 | −1.63725 | −0.818624 | − | 0.574330i | \(-0.805263\pi\) | ||||
−0.818624 | + | 0.574330i | \(0.805263\pi\) | |||||||
\(278\) | −22.2496 | −1.33444 | ||||||||
\(279\) | 5.60765 | 0.335721 | ||||||||
\(280\) | −7.84244 | −0.468675 | ||||||||
\(281\) | −2.90218 | −0.173130 | −0.0865648 | − | 0.996246i | \(-0.527589\pi\) | ||||
−0.0865648 | + | 0.996246i | \(0.527589\pi\) | |||||||
\(282\) | 7.92273 | 0.471792 | ||||||||
\(283\) | 17.8270 | 1.05971 | 0.529854 | − | 0.848089i | \(-0.322247\pi\) | ||||
0.529854 | + | 0.848089i | \(0.322247\pi\) | |||||||
\(284\) | 6.29800 | 0.373717 | ||||||||
\(285\) | 1.40878 | 0.0834488 | ||||||||
\(286\) | 7.37909 | 0.436335 | ||||||||
\(287\) | −14.8024 | −0.873761 | ||||||||
\(288\) | −2.77028 | −0.163240 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.07017 | −0.356452 | ||||||||
\(291\) | 3.36257 | 0.197118 | ||||||||
\(292\) | −2.28547 | −0.133747 | ||||||||
\(293\) | −6.35919 | −0.371508 | −0.185754 | − | 0.982596i | \(-0.559473\pi\) | ||||
−0.185754 | + | 0.982596i | \(0.559473\pi\) | |||||||
\(294\) | 4.69528 | 0.273834 | ||||||||
\(295\) | −5.86610 | −0.341538 | ||||||||
\(296\) | 0.00903606 | 0.000525210 0 | ||||||||
\(297\) | −4.03409 | −0.234081 | ||||||||
\(298\) | −8.61932 | −0.499304 | ||||||||
\(299\) | 4.45777 | 0.257800 | ||||||||
\(300\) | 1.47145 | 0.0849544 | ||||||||
\(301\) | −5.14643 | −0.296635 | ||||||||
\(302\) | −7.48727 | −0.430844 | ||||||||
\(303\) | 12.8388 | 0.737569 | ||||||||
\(304\) | −2.68218 | −0.153834 | ||||||||
\(305\) | −4.38795 | −0.251253 | ||||||||
\(306\) | −1.22360 | −0.0699485 | ||||||||
\(307\) | −6.77718 | −0.386794 | −0.193397 | − | 0.981121i | \(-0.561951\pi\) | ||||
−0.193397 | + | 0.981121i | \(0.561951\pi\) | |||||||
\(308\) | −3.60725 | −0.205542 | ||||||||
\(309\) | −14.0201 | −0.797573 | ||||||||
\(310\) | −9.88039 | −0.561168 | ||||||||
\(311\) | −19.3852 | −1.09923 | −0.549617 | − | 0.835416i | \(-0.685226\pi\) | ||||
−0.549617 | + | 0.835416i | \(0.685226\pi\) | |||||||
\(312\) | 4.57810 | 0.259184 | ||||||||
\(313\) | 16.6914 | 0.943455 | 0.471727 | − | 0.881744i | \(-0.343631\pi\) | ||||
0.471727 | + | 0.881744i | \(0.343631\pi\) | |||||||
\(314\) | −1.22360 | −0.0690517 | ||||||||
\(315\) | −2.56085 | −0.144288 | ||||||||
\(316\) | 4.29478 | 0.241600 | ||||||||
\(317\) | 27.3880 | 1.53826 | 0.769131 | − | 0.639091i | \(-0.220689\pi\) | ||||
0.769131 | + | 0.639091i | \(0.220689\pi\) | |||||||
\(318\) | 3.67287 | 0.205965 | ||||||||
\(319\) | −13.8980 | −0.778140 | ||||||||
\(320\) | 12.7767 | 0.714237 | ||||||||
\(321\) | 9.83296 | 0.548822 | ||||||||
\(322\) | 6.48886 | 0.361610 | ||||||||
\(323\) | 0.978337 | 0.0544361 | ||||||||
\(324\) | −0.502806 | −0.0279337 | ||||||||
\(325\) | −4.37487 | −0.242674 | ||||||||
\(326\) | −23.9584 | −1.32693 | ||||||||
\(327\) | 13.9552 | 0.771722 | ||||||||
\(328\) | 25.4899 | 1.40745 | ||||||||
\(329\) | 11.5151 | 0.634847 | ||||||||
\(330\) | 7.10785 | 0.391274 | ||||||||
\(331\) | 23.1358 | 1.27166 | 0.635830 | − | 0.771829i | \(-0.280658\pi\) | ||||
0.635830 | + | 0.771829i | \(0.280658\pi\) | |||||||
\(332\) | −1.33648 | −0.0733490 | ||||||||
\(333\) | 0.00295062 | 0.000161693 0 | ||||||||
\(334\) | 25.9937 | 1.42231 | ||||||||
\(335\) | 15.2052 | 0.830748 | ||||||||
\(336\) | 4.87563 | 0.265987 | ||||||||
\(337\) | 10.7292 | 0.584459 | 0.292230 | − | 0.956348i | \(-0.405603\pi\) | ||||
0.292230 | + | 0.956348i | \(0.405603\pi\) | |||||||
\(338\) | 13.1723 | 0.716478 | ||||||||
\(339\) | 4.18898 | 0.227514 | ||||||||
\(340\) | −0.724027 | −0.0392659 | ||||||||
\(341\) | −22.6217 | −1.22504 | ||||||||
\(342\) | −1.19709 | −0.0647313 | ||||||||
\(343\) | 19.2731 | 1.04065 | ||||||||
\(344\) | 8.86220 | 0.477818 | ||||||||
\(345\) | 4.29391 | 0.231176 | ||||||||
\(346\) | −27.3484 | −1.47026 | ||||||||
\(347\) | 4.65783 | 0.250046 | 0.125023 | − | 0.992154i | \(-0.460100\pi\) | ||||
0.125023 | + | 0.992154i | \(0.460100\pi\) | |||||||
\(348\) | −1.73224 | −0.0928579 | ||||||||
\(349\) | −24.5007 | −1.31149 | −0.655746 | − | 0.754982i | \(-0.727646\pi\) | ||||
−0.655746 | + | 0.754982i | \(0.727646\pi\) | |||||||
\(350\) | −6.36819 | −0.340394 | ||||||||
\(351\) | 1.49492 | 0.0797931 | ||||||||
\(352\) | 11.1755 | 0.595658 | ||||||||
\(353\) | −18.7132 | −0.996003 | −0.498001 | − | 0.867176i | \(-0.665933\pi\) | ||||
−0.498001 | + | 0.867176i | \(0.665933\pi\) | |||||||
\(354\) | 4.98465 | 0.264931 | ||||||||
\(355\) | −18.0366 | −0.957285 | ||||||||
\(356\) | 1.38385 | 0.0733440 | ||||||||
\(357\) | −1.77841 | −0.0941232 | ||||||||
\(358\) | −8.35529 | −0.441591 | ||||||||
\(359\) | 29.6667 | 1.56575 | 0.782875 | − | 0.622180i | \(-0.213753\pi\) | ||||
0.782875 | + | 0.622180i | \(0.213753\pi\) | |||||||
\(360\) | 4.40981 | 0.232418 | ||||||||
\(361\) | −18.0429 | −0.949624 | ||||||||
\(362\) | −0.0606096 | −0.00318557 | ||||||||
\(363\) | 5.27384 | 0.276805 | ||||||||
\(364\) | 1.33675 | 0.0700648 | ||||||||
\(365\) | 6.54529 | 0.342596 | ||||||||
\(366\) | 3.72861 | 0.194897 | ||||||||
\(367\) | 22.8390 | 1.19219 | 0.596094 | − | 0.802915i | \(-0.296719\pi\) | ||||
0.596094 | + | 0.802915i | \(0.296719\pi\) | |||||||
\(368\) | −8.17520 | −0.426162 | ||||||||
\(369\) | 8.32343 | 0.433301 | ||||||||
\(370\) | −0.00519883 | −0.000270274 0 | ||||||||
\(371\) | 5.33824 | 0.277148 | ||||||||
\(372\) | −2.81956 | −0.146188 | ||||||||
\(373\) | 30.3342 | 1.57065 | 0.785324 | − | 0.619085i | \(-0.212497\pi\) | ||||
0.785324 | + | 0.619085i | \(0.212497\pi\) | |||||||
\(374\) | 4.93610 | 0.255240 | ||||||||
\(375\) | −11.4139 | −0.589412 | ||||||||
\(376\) | −19.8291 | −1.02261 | ||||||||
\(377\) | 5.15023 | 0.265250 | ||||||||
\(378\) | 2.17605 | 0.111924 | ||||||||
\(379\) | −36.9670 | −1.89887 | −0.949434 | − | 0.313966i | \(-0.898342\pi\) | ||||
−0.949434 | + | 0.313966i | \(0.898342\pi\) | |||||||
\(380\) | −0.708343 | −0.0363372 | ||||||||
\(381\) | −4.75965 | −0.243844 | ||||||||
\(382\) | 16.2622 | 0.832046 | ||||||||
\(383\) | −22.4314 | −1.14619 | −0.573096 | − | 0.819488i | \(-0.694258\pi\) | ||||
−0.573096 | + | 0.819488i | \(0.694258\pi\) | |||||||
\(384\) | −5.31626 | −0.271294 | ||||||||
\(385\) | 10.3307 | 0.526501 | ||||||||
\(386\) | −13.1898 | −0.671344 | ||||||||
\(387\) | 2.89385 | 0.147102 | ||||||||
\(388\) | −1.69072 | −0.0858335 | ||||||||
\(389\) | 27.9731 | 1.41829 | 0.709147 | − | 0.705061i | \(-0.249080\pi\) | ||||
0.709147 | + | 0.705061i | \(0.249080\pi\) | |||||||
\(390\) | −2.63398 | −0.133377 | ||||||||
\(391\) | 2.98194 | 0.150803 | ||||||||
\(392\) | −11.7514 | −0.593534 | ||||||||
\(393\) | −1.09758 | −0.0553653 | ||||||||
\(394\) | −26.5691 | −1.33853 | ||||||||
\(395\) | −12.2997 | −0.618865 | ||||||||
\(396\) | 2.02836 | 0.101929 | ||||||||
\(397\) | −12.2729 | −0.615957 | −0.307978 | − | 0.951393i | \(-0.599652\pi\) | ||||
−0.307978 | + | 0.951393i | \(0.599652\pi\) | |||||||
\(398\) | −5.43685 | −0.272525 | ||||||||
\(399\) | −1.73988 | −0.0871030 | ||||||||
\(400\) | 8.02316 | 0.401158 | ||||||||
\(401\) | 1.26743 | 0.0632922 | 0.0316461 | − | 0.999499i | \(-0.489925\pi\) | ||||
0.0316461 | + | 0.999499i | \(0.489925\pi\) | |||||||
\(402\) | −12.9204 | −0.644412 | ||||||||
\(403\) | 8.38301 | 0.417588 | ||||||||
\(404\) | −6.45542 | −0.321169 | ||||||||
\(405\) | 1.43997 | 0.0715528 | ||||||||
\(406\) | 7.49683 | 0.372061 | ||||||||
\(407\) | −0.0119030 | −0.000590012 0 | ||||||||
\(408\) | 3.06243 | 0.151613 | ||||||||
\(409\) | −17.3814 | −0.859455 | −0.429727 | − | 0.902959i | \(-0.641390\pi\) | ||||
−0.429727 | + | 0.902959i | \(0.641390\pi\) | |||||||
\(410\) | −14.6655 | −0.724275 | ||||||||
\(411\) | −11.5071 | −0.567604 | ||||||||
\(412\) | 7.04937 | 0.347298 | ||||||||
\(413\) | 7.24480 | 0.356494 | ||||||||
\(414\) | −3.64870 | −0.179324 | ||||||||
\(415\) | 3.82751 | 0.187885 | ||||||||
\(416\) | −4.14135 | −0.203046 | ||||||||
\(417\) | 18.1838 | 0.890463 | ||||||||
\(418\) | 4.82917 | 0.236202 | ||||||||
\(419\) | 19.2565 | 0.940743 | 0.470372 | − | 0.882468i | \(-0.344120\pi\) | ||||
0.470372 | + | 0.882468i | \(0.344120\pi\) | |||||||
\(420\) | 1.28761 | 0.0628291 | ||||||||
\(421\) | 37.5063 | 1.82794 | 0.913972 | − | 0.405777i | \(-0.132999\pi\) | ||||
0.913972 | + | 0.405777i | \(0.132999\pi\) | |||||||
\(422\) | 2.59689 | 0.126415 | ||||||||
\(423\) | −6.47494 | −0.314822 | ||||||||
\(424\) | −9.19249 | −0.446427 | ||||||||
\(425\) | −2.92648 | −0.141955 | ||||||||
\(426\) | 15.3264 | 0.742567 | ||||||||
\(427\) | 5.41924 | 0.262255 | ||||||||
\(428\) | −4.94407 | −0.238981 | ||||||||
\(429\) | −6.03065 | −0.291163 | ||||||||
\(430\) | −5.09880 | −0.245886 | ||||||||
\(431\) | 9.74557 | 0.469428 | 0.234714 | − | 0.972065i | \(-0.424585\pi\) | ||||
0.234714 | + | 0.972065i | \(0.424585\pi\) | |||||||
\(432\) | −2.74157 | −0.131904 | ||||||||
\(433\) | −34.3295 | −1.64977 | −0.824884 | − | 0.565302i | \(-0.808760\pi\) | ||||
−0.824884 | + | 0.565302i | \(0.808760\pi\) | |||||||
\(434\) | 12.2026 | 0.585741 | ||||||||
\(435\) | 4.96091 | 0.237858 | ||||||||
\(436\) | −7.01674 | −0.336041 | ||||||||
\(437\) | 2.91734 | 0.139555 | ||||||||
\(438\) | −5.56178 | −0.265752 | ||||||||
\(439\) | 6.96917 | 0.332621 | 0.166310 | − | 0.986073i | \(-0.446815\pi\) | ||||
0.166310 | + | 0.986073i | \(0.446815\pi\) | |||||||
\(440\) | −17.7896 | −0.848084 | ||||||||
\(441\) | −3.83727 | −0.182727 | ||||||||
\(442\) | −1.82919 | −0.0870055 | ||||||||
\(443\) | −6.65599 | −0.316235 | −0.158118 | − | 0.987420i | \(-0.550543\pi\) | ||||
−0.158118 | + | 0.987420i | \(0.550543\pi\) | |||||||
\(444\) | −0.00148359 | −7.04080e−5 0 | ||||||||
\(445\) | −3.96317 | −0.187872 | ||||||||
\(446\) | 24.4318 | 1.15688 | ||||||||
\(447\) | 7.04423 | 0.333181 | ||||||||
\(448\) | −15.7795 | −0.745513 | ||||||||
\(449\) | 36.8460 | 1.73887 | 0.869435 | − | 0.494048i | \(-0.164483\pi\) | ||||
0.869435 | + | 0.494048i | \(0.164483\pi\) | |||||||
\(450\) | 3.58084 | 0.168802 | ||||||||
\(451\) | −33.5774 | −1.58110 | ||||||||
\(452\) | −2.10625 | −0.0990695 | ||||||||
\(453\) | 6.11906 | 0.287499 | ||||||||
\(454\) | −31.3492 | −1.47129 | ||||||||
\(455\) | −3.82828 | −0.179473 | ||||||||
\(456\) | 2.99609 | 0.140305 | ||||||||
\(457\) | 0.0138535 | 0.000648040 0 | 0.000324020 | − | 1.00000i | \(-0.499897\pi\) | ||||
0.000324020 | 1.00000i | \(0.499897\pi\) | ||||||||
\(458\) | −34.7267 | −1.62267 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −2.15900 | −0.100664 | ||||||||
\(461\) | 26.3681 | 1.22809 | 0.614043 | − | 0.789273i | \(-0.289542\pi\) | ||||
0.614043 | + | 0.789273i | \(0.289542\pi\) | |||||||
\(462\) | −8.77839 | −0.408408 | ||||||||
\(463\) | −1.86513 | −0.0866799 | −0.0433399 | − | 0.999060i | \(-0.513800\pi\) | ||||
−0.0433399 | + | 0.999060i | \(0.513800\pi\) | |||||||
\(464\) | −9.44512 | −0.438479 | ||||||||
\(465\) | 8.07486 | 0.374463 | ||||||||
\(466\) | 3.99798 | 0.185203 | ||||||||
\(467\) | −30.2276 | −1.39876 | −0.699382 | − | 0.714748i | \(-0.746541\pi\) | ||||
−0.699382 | + | 0.714748i | \(0.746541\pi\) | |||||||
\(468\) | −0.751657 | −0.0347454 | ||||||||
\(469\) | −18.7788 | −0.867126 | ||||||||
\(470\) | 11.4085 | 0.526235 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −12.4756 | −0.574237 | ||||||||
\(473\) | −11.6740 | −0.536772 | ||||||||
\(474\) | 10.4515 | 0.480054 | ||||||||
\(475\) | −2.86309 | −0.131367 | ||||||||
\(476\) | 0.894194 | 0.0409853 | ||||||||
\(477\) | −3.00170 | −0.137438 | ||||||||
\(478\) | −27.0549 | −1.23746 | ||||||||
\(479\) | −21.5174 | −0.983154 | −0.491577 | − | 0.870834i | \(-0.663579\pi\) | ||||
−0.491577 | + | 0.870834i | \(0.663579\pi\) | |||||||
\(480\) | −3.98912 | −0.182078 | ||||||||
\(481\) | 0.00441095 | 0.000201122 0 | ||||||||
\(482\) | 28.7162 | 1.30799 | ||||||||
\(483\) | −5.30310 | −0.241299 | ||||||||
\(484\) | −2.65172 | −0.120533 | ||||||||
\(485\) | 4.84201 | 0.219864 | ||||||||
\(486\) | −1.22360 | −0.0555036 | ||||||||
\(487\) | 18.2971 | 0.829123 | 0.414561 | − | 0.910021i | \(-0.363935\pi\) | ||||
0.414561 | + | 0.910021i | \(0.363935\pi\) | |||||||
\(488\) | −9.33198 | −0.422439 | ||||||||
\(489\) | 19.5803 | 0.885451 | ||||||||
\(490\) | 6.76107 | 0.305434 | ||||||||
\(491\) | −7.88733 | −0.355950 | −0.177975 | − | 0.984035i | \(-0.556955\pi\) | ||||
−0.177975 | + | 0.984035i | \(0.556955\pi\) | |||||||
\(492\) | −4.18508 | −0.188678 | ||||||||
\(493\) | 3.44515 | 0.155162 | ||||||||
\(494\) | −1.78956 | −0.0805162 | ||||||||
\(495\) | −5.80897 | −0.261094 | ||||||||
\(496\) | −15.3738 | −0.690303 | ||||||||
\(497\) | 22.2758 | 0.999204 | ||||||||
\(498\) | −3.25238 | −0.145743 | ||||||||
\(499\) | −0.669836 | −0.0299860 | −0.0149930 | − | 0.999888i | \(-0.504773\pi\) | ||||
−0.0149930 | + | 0.999888i | \(0.504773\pi\) | |||||||
\(500\) | 5.73899 | 0.256655 | ||||||||
\(501\) | −21.2436 | −0.949094 | ||||||||
\(502\) | −22.0045 | −0.982108 | ||||||||
\(503\) | 36.3297 | 1.61986 | 0.809931 | − | 0.586526i | \(-0.199505\pi\) | ||||
0.809931 | + | 0.586526i | \(0.199505\pi\) | |||||||
\(504\) | −5.44624 | −0.242595 | ||||||||
\(505\) | 18.4875 | 0.822682 | ||||||||
\(506\) | 14.7192 | 0.654346 | ||||||||
\(507\) | −10.7652 | −0.478099 | ||||||||
\(508\) | 2.39318 | 0.106180 | ||||||||
\(509\) | 27.2873 | 1.20949 | 0.604744 | − | 0.796420i | \(-0.293276\pi\) | ||||
0.604744 | + | 0.796420i | \(0.293276\pi\) | |||||||
\(510\) | −1.76195 | −0.0780203 | ||||||||
\(511\) | −8.08362 | −0.357598 | ||||||||
\(512\) | 24.3867 | 1.07775 | ||||||||
\(513\) | 0.978337 | 0.0431946 | ||||||||
\(514\) | −31.8596 | −1.40527 | ||||||||
\(515\) | −20.1885 | −0.889610 | ||||||||
\(516\) | −1.45504 | −0.0640547 | ||||||||
\(517\) | 26.1205 | 1.14878 | ||||||||
\(518\) | 0.00642071 | 0.000282110 0 | ||||||||
\(519\) | 22.3508 | 0.981091 | ||||||||
\(520\) | 6.59233 | 0.289093 | ||||||||
\(521\) | 8.24738 | 0.361324 | 0.180662 | − | 0.983545i | \(-0.442176\pi\) | ||||
0.180662 | + | 0.983545i | \(0.442176\pi\) | |||||||
\(522\) | −4.21548 | −0.184506 | ||||||||
\(523\) | 6.24833 | 0.273220 | 0.136610 | − | 0.990625i | \(-0.456379\pi\) | ||||
0.136610 | + | 0.990625i | \(0.456379\pi\) | |||||||
\(524\) | 0.551868 | 0.0241085 | ||||||||
\(525\) | 5.20447 | 0.227142 | ||||||||
\(526\) | 35.0135 | 1.52666 | ||||||||
\(527\) | 5.60765 | 0.244273 | ||||||||
\(528\) | 11.0597 | 0.481313 | ||||||||
\(529\) | −14.1080 | −0.613393 | ||||||||
\(530\) | 5.28883 | 0.229732 | ||||||||
\(531\) | −4.07376 | −0.176786 | ||||||||
\(532\) | 0.874823 | 0.0379284 | ||||||||
\(533\) | 12.4429 | 0.538962 | ||||||||
\(534\) | 3.36766 | 0.145733 | ||||||||
\(535\) | 14.1592 | 0.612155 | ||||||||
\(536\) | 32.3373 | 1.39676 | ||||||||
\(537\) | 6.82845 | 0.294670 | ||||||||
\(538\) | −5.89657 | −0.254219 | ||||||||
\(539\) | 15.4799 | 0.666766 | ||||||||
\(540\) | −0.724027 | −0.0311572 | ||||||||
\(541\) | −9.55644 | −0.410863 | −0.205432 | − | 0.978671i | \(-0.565860\pi\) | ||||
−0.205432 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(542\) | −9.96784 | −0.428155 | ||||||||
\(543\) | 0.0495339 | 0.00212570 | ||||||||
\(544\) | −2.77028 | −0.118775 | ||||||||
\(545\) | 20.0950 | 0.860777 | ||||||||
\(546\) | 3.25304 | 0.139217 | ||||||||
\(547\) | 13.6758 | 0.584736 | 0.292368 | − | 0.956306i | \(-0.405557\pi\) | ||||
0.292368 | + | 0.956306i | \(0.405557\pi\) | |||||||
\(548\) | 5.78585 | 0.247159 | ||||||||
\(549\) | −3.04725 | −0.130053 | ||||||||
\(550\) | −14.4454 | −0.615954 | ||||||||
\(551\) | 3.37052 | 0.143589 | ||||||||
\(552\) | 9.13198 | 0.388683 | ||||||||
\(553\) | 15.1905 | 0.645964 | ||||||||
\(554\) | 33.3421 | 1.41657 | ||||||||
\(555\) | 0.00424881 | 0.000180352 0 | ||||||||
\(556\) | −9.14292 | −0.387746 | ||||||||
\(557\) | 30.1391 | 1.27703 | 0.638517 | − | 0.769608i | \(-0.279548\pi\) | ||||
0.638517 | + | 0.769608i | \(0.279548\pi\) | |||||||
\(558\) | −6.86151 | −0.290471 | ||||||||
\(559\) | 4.32608 | 0.182974 | ||||||||
\(560\) | 7.02077 | 0.296682 | ||||||||
\(561\) | −4.03409 | −0.170319 | ||||||||
\(562\) | 3.55110 | 0.149794 | ||||||||
\(563\) | 17.6923 | 0.745643 | 0.372821 | − | 0.927903i | \(-0.378390\pi\) | ||||
0.372821 | + | 0.927903i | \(0.378390\pi\) | |||||||
\(564\) | 3.25564 | 0.137087 | ||||||||
\(565\) | 6.03201 | 0.253769 | ||||||||
\(566\) | −21.8131 | −0.916875 | ||||||||
\(567\) | −1.77841 | −0.0746860 | ||||||||
\(568\) | −38.3591 | −1.60951 | ||||||||
\(569\) | −10.5912 | −0.444008 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(570\) | −1.72378 | −0.0722011 | ||||||||
\(571\) | 35.4429 | 1.48324 | 0.741619 | − | 0.670821i | \(-0.234058\pi\) | ||||
0.741619 | + | 0.670821i | \(0.234058\pi\) | |||||||
\(572\) | 3.03225 | 0.126785 | ||||||||
\(573\) | −13.2905 | −0.555217 | ||||||||
\(574\) | 18.1122 | 0.755991 | ||||||||
\(575\) | −8.72659 | −0.363924 | ||||||||
\(576\) | 8.87285 | 0.369702 | ||||||||
\(577\) | −45.9966 | −1.91486 | −0.957432 | − | 0.288658i | \(-0.906791\pi\) | ||||
−0.957432 | + | 0.288658i | \(0.906791\pi\) | |||||||
\(578\) | −1.22360 | −0.0508950 | ||||||||
\(579\) | 10.7795 | 0.447982 | ||||||||
\(580\) | −2.49438 | −0.103573 | ||||||||
\(581\) | −4.72709 | −0.196113 | ||||||||
\(582\) | −4.11444 | −0.170549 | ||||||||
\(583\) | 12.1091 | 0.501508 | ||||||||
\(584\) | 13.9201 | 0.576016 | ||||||||
\(585\) | 2.15265 | 0.0890010 | ||||||||
\(586\) | 7.78110 | 0.321434 | ||||||||
\(587\) | 39.0590 | 1.61214 | 0.806070 | − | 0.591821i | \(-0.201591\pi\) | ||||
0.806070 | + | 0.591821i | \(0.201591\pi\) | |||||||
\(588\) | 1.92941 | 0.0795673 | ||||||||
\(589\) | 5.48617 | 0.226054 | ||||||||
\(590\) | 7.17776 | 0.295504 | ||||||||
\(591\) | 21.7139 | 0.893190 | ||||||||
\(592\) | −0.00808933 | −0.000332470 0 | ||||||||
\(593\) | 24.6123 | 1.01071 | 0.505353 | − | 0.862913i | \(-0.331362\pi\) | ||||
0.505353 | + | 0.862913i | \(0.331362\pi\) | |||||||
\(594\) | 4.93610 | 0.202531 | ||||||||
\(595\) | −2.56085 | −0.104985 | ||||||||
\(596\) | −3.54189 | −0.145081 | ||||||||
\(597\) | 4.44333 | 0.181853 | ||||||||
\(598\) | −5.45452 | −0.223052 | ||||||||
\(599\) | 40.9930 | 1.67493 | 0.837465 | − | 0.546492i | \(-0.184037\pi\) | ||||
0.837465 | + | 0.546492i | \(0.184037\pi\) | |||||||
\(600\) | −8.96215 | −0.365878 | ||||||||
\(601\) | 18.9194 | 0.771739 | 0.385869 | − | 0.922553i | \(-0.373902\pi\) | ||||
0.385869 | + | 0.922553i | \(0.373902\pi\) | |||||||
\(602\) | 6.29717 | 0.256653 | ||||||||
\(603\) | 10.5594 | 0.430011 | ||||||||
\(604\) | −3.07670 | −0.125189 | ||||||||
\(605\) | 7.59419 | 0.308748 | ||||||||
\(606\) | −15.7095 | −0.638156 | ||||||||
\(607\) | −14.0761 | −0.571330 | −0.285665 | − | 0.958330i | \(-0.592214\pi\) | ||||
−0.285665 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(608\) | −2.71026 | −0.109916 | ||||||||
\(609\) | −6.12687 | −0.248273 | ||||||||
\(610\) | 5.36909 | 0.217388 | ||||||||
\(611\) | −9.67954 | −0.391592 | ||||||||
\(612\) | −0.502806 | −0.0203247 | ||||||||
\(613\) | −41.7383 | −1.68579 | −0.842897 | − | 0.538074i | \(-0.819152\pi\) | ||||
−0.842897 | + | 0.538074i | \(0.819152\pi\) | |||||||
\(614\) | 8.29254 | 0.334660 | ||||||||
\(615\) | 11.9855 | 0.483302 | ||||||||
\(616\) | 21.9706 | 0.885221 | ||||||||
\(617\) | 42.2403 | 1.70053 | 0.850266 | − | 0.526354i | \(-0.176441\pi\) | ||||
0.850266 | + | 0.526354i | \(0.176441\pi\) | |||||||
\(618\) | 17.1549 | 0.690072 | ||||||||
\(619\) | 0.835762 | 0.0335921 | 0.0167960 | − | 0.999859i | \(-0.494653\pi\) | ||||
0.0167960 | + | 0.999859i | \(0.494653\pi\) | |||||||
\(620\) | −4.06009 | −0.163057 | ||||||||
\(621\) | 2.98194 | 0.119661 | ||||||||
\(622\) | 23.7197 | 0.951074 | ||||||||
\(623\) | 4.89463 | 0.196099 | ||||||||
\(624\) | −4.09844 | −0.164069 | ||||||||
\(625\) | −1.80330 | −0.0721318 | ||||||||
\(626\) | −20.4236 | −0.816291 | ||||||||
\(627\) | −3.94670 | −0.157616 | ||||||||
\(628\) | −0.502806 | −0.0200642 | ||||||||
\(629\) | 0.00295062 | 0.000117649 0 | ||||||||
\(630\) | 3.13346 | 0.124840 | ||||||||
\(631\) | −31.9472 | −1.27180 | −0.635898 | − | 0.771773i | \(-0.719370\pi\) | ||||
−0.635898 | + | 0.771773i | \(0.719370\pi\) | |||||||
\(632\) | −26.1581 | −1.04051 | ||||||||
\(633\) | −2.12234 | −0.0843553 | ||||||||
\(634\) | −33.5119 | −1.33093 | ||||||||
\(635\) | −6.85376 | −0.271983 | ||||||||
\(636\) | 1.50927 | 0.0598466 | ||||||||
\(637\) | −5.73643 | −0.227286 | ||||||||
\(638\) | 17.0056 | 0.673258 | ||||||||
\(639\) | −12.5257 | −0.495509 | ||||||||
\(640\) | −7.65526 | −0.302601 | ||||||||
\(641\) | −14.6474 | −0.578536 | −0.289268 | − | 0.957248i | \(-0.593412\pi\) | ||||
−0.289268 | + | 0.957248i | \(0.593412\pi\) | |||||||
\(642\) | −12.0316 | −0.474849 | ||||||||
\(643\) | −28.1866 | −1.11157 | −0.555786 | − | 0.831325i | \(-0.687583\pi\) | ||||
−0.555786 | + | 0.831325i | \(0.687583\pi\) | |||||||
\(644\) | 2.66643 | 0.105072 | ||||||||
\(645\) | 4.16705 | 0.164078 | ||||||||
\(646\) | −1.19709 | −0.0470990 | ||||||||
\(647\) | 33.0682 | 1.30005 | 0.650023 | − | 0.759915i | \(-0.274759\pi\) | ||||
0.650023 | + | 0.759915i | \(0.274759\pi\) | |||||||
\(648\) | 3.06243 | 0.120304 | ||||||||
\(649\) | 16.4339 | 0.645087 | ||||||||
\(650\) | 5.35308 | 0.209965 | ||||||||
\(651\) | −9.97268 | −0.390860 | ||||||||
\(652\) | −9.84509 | −0.385563 | ||||||||
\(653\) | 10.5888 | 0.414373 | 0.207187 | − | 0.978301i | \(-0.433569\pi\) | ||||
0.207187 | + | 0.978301i | \(0.433569\pi\) | |||||||
\(654\) | −17.0755 | −0.667705 | ||||||||
\(655\) | −1.58048 | −0.0617544 | ||||||||
\(656\) | −22.8193 | −0.890944 | ||||||||
\(657\) | 4.54543 | 0.177334 | ||||||||
\(658\) | −14.0898 | −0.549279 | ||||||||
\(659\) | −35.0849 | −1.36671 | −0.683357 | − | 0.730085i | \(-0.739481\pi\) | ||||
−0.683357 | + | 0.730085i | \(0.739481\pi\) | |||||||
\(660\) | 2.92079 | 0.113691 | ||||||||
\(661\) | 39.3829 | 1.53182 | 0.765909 | − | 0.642949i | \(-0.222289\pi\) | ||||
0.765909 | + | 0.642949i | \(0.222289\pi\) | |||||||
\(662\) | −28.3090 | −1.10026 | ||||||||
\(663\) | 1.49492 | 0.0580580 | ||||||||
\(664\) | 8.14008 | 0.315896 | ||||||||
\(665\) | −2.50538 | −0.0971544 | ||||||||
\(666\) | −0.00361037 | −0.000139899 0 | ||||||||
\(667\) | 10.2732 | 0.397781 | ||||||||
\(668\) | 10.6814 | 0.413277 | ||||||||
\(669\) | −19.9671 | −0.771974 | ||||||||
\(670\) | −18.6051 | −0.718776 | ||||||||
\(671\) | 12.2929 | 0.474560 | ||||||||
\(672\) | 4.92668 | 0.190051 | ||||||||
\(673\) | −31.4479 | −1.21223 | −0.606114 | − | 0.795378i | \(-0.707273\pi\) | ||||
−0.606114 | + | 0.795378i | \(0.707273\pi\) | |||||||
\(674\) | −13.1283 | −0.505683 | ||||||||
\(675\) | −2.92648 | −0.112640 | ||||||||
\(676\) | 5.41281 | 0.208185 | ||||||||
\(677\) | −24.8759 | −0.956059 | −0.478030 | − | 0.878344i | \(-0.658649\pi\) | ||||
−0.478030 | + | 0.878344i | \(0.658649\pi\) | |||||||
\(678\) | −5.12563 | −0.196849 | ||||||||
\(679\) | −5.98002 | −0.229492 | ||||||||
\(680\) | 4.40981 | 0.169109 | ||||||||
\(681\) | 25.6205 | 0.981779 | ||||||||
\(682\) | 27.6799 | 1.05992 | ||||||||
\(683\) | −43.0324 | −1.64659 | −0.823294 | − | 0.567616i | \(-0.807866\pi\) | ||||
−0.823294 | + | 0.567616i | \(0.807866\pi\) | |||||||
\(684\) | −0.491914 | −0.0188088 | ||||||||
\(685\) | −16.5699 | −0.633104 | ||||||||
\(686\) | −23.5825 | −0.900384 | ||||||||
\(687\) | 28.3808 | 1.08279 | ||||||||
\(688\) | −7.93369 | −0.302469 | ||||||||
\(689\) | −4.48731 | −0.170953 | ||||||||
\(690\) | −5.25402 | −0.200017 | ||||||||
\(691\) | 9.68382 | 0.368390 | 0.184195 | − | 0.982890i | \(-0.441032\pi\) | ||||
0.184195 | + | 0.982890i | \(0.441032\pi\) | |||||||
\(692\) | −11.2381 | −0.427209 | ||||||||
\(693\) | 7.17424 | 0.272527 | ||||||||
\(694\) | −5.69932 | −0.216343 | ||||||||
\(695\) | 26.1841 | 0.993220 | ||||||||
\(696\) | 10.5505 | 0.399917 | ||||||||
\(697\) | 8.32343 | 0.315273 | ||||||||
\(698\) | 29.9790 | 1.13472 | ||||||||
\(699\) | −3.26740 | −0.123584 | ||||||||
\(700\) | −2.61684 | −0.0989073 | ||||||||
\(701\) | −5.20454 | −0.196573 | −0.0982864 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982864 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(702\) | −1.82919 | −0.0690382 | ||||||||
\(703\) | 0.00288670 | 0.000108874 0 | ||||||||
\(704\) | −35.7938 | −1.34903 | ||||||||
\(705\) | −9.32373 | −0.351152 | ||||||||
\(706\) | 22.8974 | 0.861756 | ||||||||
\(707\) | −22.8326 | −0.858707 | ||||||||
\(708\) | 2.04831 | 0.0769804 | ||||||||
\(709\) | 50.1566 | 1.88367 | 0.941835 | − | 0.336076i | \(-0.109100\pi\) | ||||
0.941835 | + | 0.336076i | \(0.109100\pi\) | |||||||
\(710\) | 22.0696 | 0.828258 | ||||||||
\(711\) | −8.54162 | −0.320336 | ||||||||
\(712\) | −8.42860 | −0.315875 | ||||||||
\(713\) | 16.7217 | 0.626232 | ||||||||
\(714\) | 2.17605 | 0.0814368 | ||||||||
\(715\) | −8.68396 | −0.324762 | ||||||||
\(716\) | −3.43339 | −0.128312 | ||||||||
\(717\) | 22.1109 | 0.825747 | ||||||||
\(718\) | −36.3001 | −1.35471 | ||||||||
\(719\) | −4.83288 | −0.180236 | −0.0901180 | − | 0.995931i | \(-0.528724\pi\) | ||||
−0.0901180 | + | 0.995931i | \(0.528724\pi\) | |||||||
\(720\) | −3.94779 | −0.147125 | ||||||||
\(721\) | 24.9333 | 0.928566 | ||||||||
\(722\) | 22.0772 | 0.821629 | ||||||||
\(723\) | −23.4687 | −0.872810 | ||||||||
\(724\) | −0.0249060 | −0.000925623 0 | ||||||||
\(725\) | −10.0822 | −0.374442 | ||||||||
\(726\) | −6.45307 | −0.239496 | ||||||||
\(727\) | 27.0232 | 1.00224 | 0.501118 | − | 0.865379i | \(-0.332922\pi\) | ||||
0.501118 | + | 0.865379i | \(0.332922\pi\) | |||||||
\(728\) | −8.14172 | −0.301752 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.00881 | −0.296419 | ||||||||
\(731\) | 2.89385 | 0.107033 | ||||||||
\(732\) | 1.53217 | 0.0566308 | ||||||||
\(733\) | −42.9678 | −1.58705 | −0.793526 | − | 0.608537i | \(-0.791757\pi\) | ||||
−0.793526 | + | 0.608537i | \(0.791757\pi\) | |||||||
\(734\) | −27.9458 | −1.03150 | ||||||||
\(735\) | −5.52556 | −0.203813 | ||||||||
\(736\) | −8.26079 | −0.304497 | ||||||||
\(737\) | −42.5974 | −1.56910 | ||||||||
\(738\) | −10.1845 | −0.374898 | ||||||||
\(739\) | 16.8426 | 0.619566 | 0.309783 | − | 0.950807i | \(-0.399744\pi\) | ||||
0.309783 | + | 0.950807i | \(0.399744\pi\) | |||||||
\(740\) | −0.00213633 | −7.85329e−5 0 | ||||||||
\(741\) | 1.46254 | 0.0537277 | ||||||||
\(742\) | −6.53186 | −0.239792 | ||||||||
\(743\) | −26.9717 | −0.989496 | −0.494748 | − | 0.869037i | \(-0.664740\pi\) | ||||
−0.494748 | + | 0.869037i | \(0.664740\pi\) | |||||||
\(744\) | 17.1730 | 0.629594 | ||||||||
\(745\) | 10.1435 | 0.371629 | ||||||||
\(746\) | −37.1169 | −1.35895 | ||||||||
\(747\) | 2.65805 | 0.0972528 | ||||||||
\(748\) | 2.02836 | 0.0741643 | ||||||||
\(749\) | −17.4870 | −0.638961 | ||||||||
\(750\) | 13.9660 | 0.509968 | ||||||||
\(751\) | −7.93966 | −0.289722 | −0.144861 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144861 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(752\) | 17.7515 | 0.647331 | ||||||||
\(753\) | 17.9834 | 0.655352 | ||||||||
\(754\) | −6.30182 | −0.229499 | ||||||||
\(755\) | 8.81127 | 0.320675 | ||||||||
\(756\) | 0.894194 | 0.0325215 | ||||||||
\(757\) | −11.5997 | −0.421600 | −0.210800 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210800 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(758\) | 45.2328 | 1.64293 | ||||||||
\(759\) | −12.0294 | −0.436639 | ||||||||
\(760\) | 4.31428 | 0.156496 | ||||||||
\(761\) | 19.0430 | 0.690309 | 0.345154 | − | 0.938546i | \(-0.387827\pi\) | ||||
0.345154 | + | 0.938546i | \(0.387827\pi\) | |||||||
\(762\) | 5.82390 | 0.210978 | ||||||||
\(763\) | −24.8179 | −0.898470 | ||||||||
\(764\) | 6.68253 | 0.241765 | ||||||||
\(765\) | 1.43997 | 0.0520623 | ||||||||
\(766\) | 27.4471 | 0.991703 | ||||||||
\(767\) | −6.08997 | −0.219896 | ||||||||
\(768\) | −11.2407 | −0.405615 | ||||||||
\(769\) | 18.8111 | 0.678345 | 0.339173 | − | 0.940724i | \(-0.389853\pi\) | ||||
0.339173 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(770\) | −12.6406 | −0.455537 | ||||||||
\(771\) | 26.0376 | 0.937722 | ||||||||
\(772\) | −5.42002 | −0.195071 | ||||||||
\(773\) | 43.1808 | 1.55310 | 0.776552 | − | 0.630053i | \(-0.216967\pi\) | ||||
0.776552 | + | 0.630053i | \(0.216967\pi\) | |||||||
\(774\) | −3.54091 | −0.127275 | ||||||||
\(775\) | −16.4107 | −0.589489 | ||||||||
\(776\) | 10.2976 | 0.369664 | ||||||||
\(777\) | −0.00524740 | −0.000188249 0 | ||||||||
\(778\) | −34.2279 | −1.22713 | ||||||||
\(779\) | 8.14312 | 0.291758 | ||||||||
\(780\) | −1.08237 | −0.0387549 | ||||||||
\(781\) | 50.5297 | 1.80810 | ||||||||
\(782\) | −3.64870 | −0.130477 | ||||||||
\(783\) | 3.44515 | 0.123120 | ||||||||
\(784\) | 10.5202 | 0.375720 | ||||||||
\(785\) | 1.43997 | 0.0513948 | ||||||||
\(786\) | 1.34299 | 0.0479029 | ||||||||
\(787\) | −16.7278 | −0.596282 | −0.298141 | − | 0.954522i | \(-0.596367\pi\) | ||||
−0.298141 | + | 0.954522i | \(0.596367\pi\) | |||||||
\(788\) | −10.9179 | −0.388933 | ||||||||
\(789\) | −28.6152 | −1.01873 | ||||||||
\(790\) | 15.0499 | 0.535451 | ||||||||
\(791\) | −7.44971 | −0.264881 | ||||||||
\(792\) | −12.3541 | −0.438984 | ||||||||
\(793\) | −4.55540 | −0.161767 | ||||||||
\(794\) | 15.0170 | 0.532935 | ||||||||
\(795\) | −4.32236 | −0.153298 | ||||||||
\(796\) | −2.23413 | −0.0791868 | ||||||||
\(797\) | 40.8113 | 1.44561 | 0.722805 | − | 0.691052i | \(-0.242853\pi\) | ||||
0.722805 | + | 0.691052i | \(0.242853\pi\) | |||||||
\(798\) | 2.12892 | 0.0753628 | ||||||||
\(799\) | −6.47494 | −0.229067 | ||||||||
\(800\) | 8.10716 | 0.286632 | ||||||||
\(801\) | −2.75226 | −0.0972462 | ||||||||
\(802\) | −1.55082 | −0.0547614 | ||||||||
\(803\) | −18.3366 | −0.647086 | ||||||||
\(804\) | −5.30932 | −0.187245 | ||||||||
\(805\) | −7.63631 | −0.269145 | ||||||||
\(806\) | −10.2574 | −0.361303 | ||||||||
\(807\) | 4.81904 | 0.169638 | ||||||||
\(808\) | 39.3179 | 1.38320 | ||||||||
\(809\) | 41.2829 | 1.45143 | 0.725714 | − | 0.687996i | \(-0.241509\pi\) | ||||
0.725714 | + | 0.687996i | \(0.241509\pi\) | |||||||
\(810\) | −1.76195 | −0.0619085 | ||||||||
\(811\) | −22.2285 | −0.780548 | −0.390274 | − | 0.920699i | \(-0.627620\pi\) | ||||
−0.390274 | + | 0.920699i | \(0.627620\pi\) | |||||||
\(812\) | 3.08063 | 0.108109 | ||||||||
\(813\) | 8.14633 | 0.285704 | ||||||||
\(814\) | 0.0145645 | 0.000510487 0 | ||||||||
\(815\) | 28.1950 | 0.987629 | ||||||||
\(816\) | −2.74157 | −0.0959742 | ||||||||
\(817\) | 2.83116 | 0.0990496 | ||||||||
\(818\) | 21.2679 | 0.743613 | ||||||||
\(819\) | −2.65858 | −0.0928983 | ||||||||
\(820\) | −6.02639 | −0.210451 | ||||||||
\(821\) | 53.4128 | 1.86412 | 0.932060 | − | 0.362303i | \(-0.118009\pi\) | ||||
0.932060 | + | 0.362303i | \(0.118009\pi\) | |||||||
\(822\) | 14.0801 | 0.491100 | ||||||||
\(823\) | −46.8531 | −1.63320 | −0.816598 | − | 0.577206i | \(-0.804143\pi\) | ||||
−0.816598 | + | 0.577206i | \(0.804143\pi\) | |||||||
\(824\) | −42.9354 | −1.49573 | ||||||||
\(825\) | 11.8057 | 0.411021 | ||||||||
\(826\) | −8.86473 | −0.308444 | ||||||||
\(827\) | −41.2175 | −1.43327 | −0.716637 | − | 0.697446i | \(-0.754320\pi\) | ||||
−0.716637 | + | 0.697446i | \(0.754320\pi\) | |||||||
\(828\) | −1.49934 | −0.0521056 | ||||||||
\(829\) | 43.5296 | 1.51185 | 0.755924 | − | 0.654660i | \(-0.227188\pi\) | ||||
0.755924 | + | 0.654660i | \(0.227188\pi\) | |||||||
\(830\) | −4.68334 | −0.162561 | ||||||||
\(831\) | −27.2492 | −0.945265 | ||||||||
\(832\) | 13.2642 | 0.459855 | ||||||||
\(833\) | −3.83727 | −0.132954 | ||||||||
\(834\) | −22.2496 | −0.770442 | ||||||||
\(835\) | −30.5902 | −1.05862 | ||||||||
\(836\) | 1.98442 | 0.0686327 | ||||||||
\(837\) | 5.60765 | 0.193829 | ||||||||
\(838\) | −23.5623 | −0.813945 | ||||||||
\(839\) | −5.90659 | −0.203918 | −0.101959 | − | 0.994789i | \(-0.532511\pi\) | ||||
−0.101959 | + | 0.994789i | \(0.532511\pi\) | |||||||
\(840\) | −7.84244 | −0.270590 | ||||||||
\(841\) | −17.1310 | −0.590723 | ||||||||
\(842\) | −45.8926 | −1.58156 | ||||||||
\(843\) | −2.90218 | −0.0999564 | ||||||||
\(844\) | 1.06712 | 0.0367320 | ||||||||
\(845\) | −15.5016 | −0.533271 | ||||||||
\(846\) | 7.92273 | 0.272389 | ||||||||
\(847\) | −9.37904 | −0.322267 | ||||||||
\(848\) | 8.22937 | 0.282598 | ||||||||
\(849\) | 17.8270 | 0.611822 | ||||||||
\(850\) | 3.58084 | 0.122822 | ||||||||
\(851\) | 0.00879856 | 0.000301611 0 | ||||||||
\(852\) | 6.29800 | 0.215766 | ||||||||
\(853\) | −33.8417 | −1.15872 | −0.579359 | − | 0.815073i | \(-0.696697\pi\) | ||||
−0.579359 | + | 0.815073i | \(0.696697\pi\) | |||||||
\(854\) | −6.63097 | −0.226907 | ||||||||
\(855\) | 1.40878 | 0.0481792 | ||||||||
\(856\) | 30.1127 | 1.02923 | ||||||||
\(857\) | 30.6365 | 1.04652 | 0.523261 | − | 0.852172i | \(-0.324715\pi\) | ||||
0.523261 | + | 0.852172i | \(0.324715\pi\) | |||||||
\(858\) | 7.37909 | 0.251918 | ||||||||
\(859\) | 20.2674 | 0.691514 | 0.345757 | − | 0.938324i | \(-0.387622\pi\) | ||||
0.345757 | + | 0.938324i | \(0.387622\pi\) | |||||||
\(860\) | −2.09522 | −0.0714465 | ||||||||
\(861\) | −14.8024 | −0.504466 | ||||||||
\(862\) | −11.9247 | −0.406156 | ||||||||
\(863\) | 2.70101 | 0.0919434 | 0.0459717 | − | 0.998943i | \(-0.485362\pi\) | ||||
0.0459717 | + | 0.998943i | \(0.485362\pi\) | |||||||
\(864\) | −2.77028 | −0.0942467 | ||||||||
\(865\) | 32.1845 | 1.09431 | ||||||||
\(866\) | 42.0055 | 1.42740 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 5.01433 | 0.170197 | ||||||||
\(869\) | 34.4576 | 1.16889 | ||||||||
\(870\) | −6.07017 | −0.205798 | ||||||||
\(871\) | 15.7855 | 0.534870 | ||||||||
\(872\) | 42.7367 | 1.44725 | ||||||||
\(873\) | 3.36257 | 0.113806 | ||||||||
\(874\) | −3.56965 | −0.120745 | ||||||||
\(875\) | 20.2986 | 0.686217 | ||||||||
\(876\) | −2.28547 | −0.0772189 | ||||||||
\(877\) | 6.05186 | 0.204357 | 0.102178 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102178 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(878\) | −8.52747 | −0.287788 | ||||||||
\(879\) | −6.35919 | −0.214490 | ||||||||
\(880\) | 15.9257 | 0.536856 | ||||||||
\(881\) | 26.6644 | 0.898348 | 0.449174 | − | 0.893444i | \(-0.351718\pi\) | ||||
0.449174 | + | 0.893444i | \(0.351718\pi\) | |||||||
\(882\) | 4.69528 | 0.158098 | ||||||||
\(883\) | −25.8013 | −0.868283 | −0.434142 | − | 0.900845i | \(-0.642948\pi\) | ||||
−0.434142 | + | 0.900845i | \(0.642948\pi\) | |||||||
\(884\) | −0.751657 | −0.0252810 | ||||||||
\(885\) | −5.86610 | −0.197187 | ||||||||
\(886\) | 8.14426 | 0.273612 | ||||||||
\(887\) | −6.48143 | −0.217625 | −0.108813 | − | 0.994062i | \(-0.534705\pi\) | ||||
−0.108813 | + | 0.994062i | \(0.534705\pi\) | |||||||
\(888\) | 0.00903606 | 0.000303230 0 | ||||||||
\(889\) | 8.46459 | 0.283893 | ||||||||
\(890\) | 4.84933 | 0.162550 | ||||||||
\(891\) | −4.03409 | −0.135147 | ||||||||
\(892\) | 10.0396 | 0.336151 | ||||||||
\(893\) | −6.33468 | −0.211982 | ||||||||
\(894\) | −8.61932 | −0.288273 | ||||||||
\(895\) | 9.83278 | 0.328674 | ||||||||
\(896\) | 9.45446 | 0.315851 | ||||||||
\(897\) | 4.45777 | 0.148841 | ||||||||
\(898\) | −45.0847 | −1.50450 | ||||||||
\(899\) | 19.3192 | 0.644331 | ||||||||
\(900\) | 1.47145 | 0.0490485 | ||||||||
\(901\) | −3.00170 | −0.100001 | ||||||||
\(902\) | 41.0853 | 1.36799 | ||||||||
\(903\) | −5.14643 | −0.171263 | ||||||||
\(904\) | 12.8285 | 0.426668 | ||||||||
\(905\) | 0.0713274 | 0.00237100 | ||||||||
\(906\) | −7.48727 | −0.248748 | ||||||||
\(907\) | −42.7587 | −1.41978 | −0.709890 | − | 0.704312i | \(-0.751255\pi\) | ||||
−0.709890 | + | 0.704312i | \(0.751255\pi\) | |||||||
\(908\) | −12.8821 | −0.427509 | ||||||||
\(909\) | 12.8388 | 0.425836 | ||||||||
\(910\) | 4.68428 | 0.155282 | ||||||||
\(911\) | 23.1259 | 0.766197 | 0.383098 | − | 0.923708i | \(-0.374857\pi\) | ||||
0.383098 | + | 0.923708i | \(0.374857\pi\) | |||||||
\(912\) | −2.68218 | −0.0888159 | ||||||||
\(913\) | −10.7228 | −0.354872 | ||||||||
\(914\) | −0.0169511 | −0.000560694 0 | ||||||||
\(915\) | −4.38795 | −0.145061 | ||||||||
\(916\) | −14.2700 | −0.471495 | ||||||||
\(917\) | 1.95193 | 0.0644585 | ||||||||
\(918\) | −1.22360 | −0.0403848 | ||||||||
\(919\) | 19.6361 | 0.647734 | 0.323867 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323867 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(920\) | 13.1498 | 0.433536 | ||||||||
\(921\) | −6.77718 | −0.223316 | ||||||||
\(922\) | −32.2640 | −1.06256 | ||||||||
\(923\) | −18.7250 | −0.616339 | ||||||||
\(924\) | −3.60725 | −0.118670 | ||||||||
\(925\) | −0.00863493 | −0.000283915 0 | ||||||||
\(926\) | 2.28217 | 0.0749967 | ||||||||
\(927\) | −14.0201 | −0.460479 | ||||||||
\(928\) | −9.54401 | −0.313297 | ||||||||
\(929\) | 45.2482 | 1.48455 | 0.742273 | − | 0.670097i | \(-0.233748\pi\) | ||||
0.742273 | + | 0.670097i | \(0.233748\pi\) | |||||||
\(930\) | −9.88039 | −0.323991 | ||||||||
\(931\) | −3.75415 | −0.123037 | ||||||||
\(932\) | 1.64287 | 0.0538139 | ||||||||
\(933\) | −19.3852 | −0.634644 | ||||||||
\(934\) | 36.9864 | 1.21023 | ||||||||
\(935\) | −5.80897 | −0.189974 | ||||||||
\(936\) | 4.57810 | 0.149640 | ||||||||
\(937\) | 18.4117 | 0.601485 | 0.300743 | − | 0.953705i | \(-0.402766\pi\) | ||||
0.300743 | + | 0.953705i | \(0.402766\pi\) | |||||||
\(938\) | 22.9778 | 0.750251 | ||||||||
\(939\) | 16.6914 | 0.544704 | ||||||||
\(940\) | 4.68803 | 0.152907 | ||||||||
\(941\) | −35.6431 | −1.16193 | −0.580966 | − | 0.813928i | \(-0.697325\pi\) | ||||
−0.580966 | + | 0.813928i | \(0.697325\pi\) | |||||||
\(942\) | −1.22360 | −0.0398670 | ||||||||
\(943\) | 24.8200 | 0.808249 | ||||||||
\(944\) | 11.1685 | 0.363504 | ||||||||
\(945\) | −2.56085 | −0.0833046 | ||||||||
\(946\) | 14.2843 | 0.464423 | ||||||||
\(947\) | 48.0440 | 1.56122 | 0.780611 | − | 0.625018i | \(-0.214908\pi\) | ||||
0.780611 | + | 0.625018i | \(0.214908\pi\) | |||||||
\(948\) | 4.29478 | 0.139488 | ||||||||
\(949\) | 6.79507 | 0.220577 | ||||||||
\(950\) | 3.50327 | 0.113661 | ||||||||
\(951\) | 27.3880 | 0.888116 | ||||||||
\(952\) | −5.44624 | −0.176514 | ||||||||
\(953\) | 35.2943 | 1.14329 | 0.571647 | − | 0.820500i | \(-0.306305\pi\) | ||||
0.571647 | + | 0.820500i | \(0.306305\pi\) | |||||||
\(954\) | 3.67287 | 0.118914 | ||||||||
\(955\) | −19.1379 | −0.619287 | ||||||||
\(956\) | −11.1175 | −0.359566 | ||||||||
\(957\) | −13.8980 | −0.449259 | ||||||||
\(958\) | 26.3286 | 0.850640 | ||||||||
\(959\) | 20.4643 | 0.660828 | ||||||||
\(960\) | 12.7767 | 0.412365 | ||||||||
\(961\) | 0.445750 | 0.0143790 | ||||||||
\(962\) | −0.00539723 | −0.000174014 0 | ||||||||
\(963\) | 9.83296 | 0.316863 | ||||||||
\(964\) | 11.8002 | 0.380059 | ||||||||
\(965\) | 15.5222 | 0.499678 | ||||||||
\(966\) | 6.48886 | 0.208776 | ||||||||
\(967\) | 20.8179 | 0.669459 | 0.334729 | − | 0.942314i | \(-0.391355\pi\) | ||||
0.334729 | + | 0.942314i | \(0.391355\pi\) | |||||||
\(968\) | 16.1508 | 0.519106 | ||||||||
\(969\) | 0.978337 | 0.0314287 | ||||||||
\(970\) | −5.92468 | −0.190230 | ||||||||
\(971\) | 0.0226047 | 0.000725421 0 | 0.000362710 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000362710 | 1.00000i | \(0.499885\pi\) | ||||||||
\(972\) | −0.502806 | −0.0161275 | ||||||||
\(973\) | −32.3381 | −1.03671 | ||||||||
\(974\) | −22.3884 | −0.717370 | ||||||||
\(975\) | −4.37487 | −0.140108 | ||||||||
\(976\) | 8.35425 | 0.267413 | ||||||||
\(977\) | 11.1634 | 0.357148 | 0.178574 | − | 0.983926i | \(-0.442852\pi\) | ||||
0.178574 | + | 0.983926i | \(0.442852\pi\) | |||||||
\(978\) | −23.9584 | −0.766105 | ||||||||
\(979\) | 11.1028 | 0.354848 | ||||||||
\(980\) | 2.77829 | 0.0887492 | ||||||||
\(981\) | 13.9552 | 0.445554 | ||||||||
\(982\) | 9.65092 | 0.307973 | ||||||||
\(983\) | −33.9837 | −1.08391 | −0.541956 | − | 0.840407i | \(-0.682316\pi\) | ||||
−0.541956 | + | 0.840407i | \(0.682316\pi\) | |||||||
\(984\) | 25.4899 | 0.812589 | ||||||||
\(985\) | 31.2674 | 0.996261 | ||||||||
\(986\) | −4.21548 | −0.134248 | ||||||||
\(987\) | 11.5151 | 0.366529 | ||||||||
\(988\) | −0.735374 | −0.0233954 | ||||||||
\(989\) | 8.62927 | 0.274395 | ||||||||
\(990\) | 7.10785 | 0.225902 | ||||||||
\(991\) | −55.6265 | −1.76703 | −0.883517 | − | 0.468400i | \(-0.844831\pi\) | ||||
−0.883517 | + | 0.468400i | \(0.844831\pi\) | |||||||
\(992\) | −15.5347 | −0.493229 | ||||||||
\(993\) | 23.1358 | 0.734194 | ||||||||
\(994\) | −27.2566 | −0.864527 | ||||||||
\(995\) | 6.39826 | 0.202839 | ||||||||
\(996\) | −1.33648 | −0.0423481 | ||||||||
\(997\) | −19.7876 | −0.626680 | −0.313340 | − | 0.949641i | \(-0.601448\pi\) | ||||
−0.313340 | + | 0.949641i | \(0.601448\pi\) | |||||||
\(998\) | 0.819610 | 0.0259443 | ||||||||
\(999\) | 0.00295062 | 9.33534e−5 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8007.2.a.i.1.18 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.i.1.18 | ✓ | 63 | 1.1 | even | 1 | trivial |