Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | 0.685916 | 0.396014 | 0.198007 | − | 0.980201i | \(-0.436553\pi\) | ||||
0.198007 | + | 0.980201i | \(0.436553\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.44966 | 0.648306 | 0.324153 | − | 0.946005i | \(-0.394921\pi\) | ||||
0.324153 | + | 0.946005i | \(0.394921\pi\) | |||||||
\(6\) | −0.685916 | −0.280024 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.52952 | −0.843173 | ||||||||
\(10\) | −1.44966 | −0.458421 | ||||||||
\(11\) | −0.0308170 | −0.00929169 | −0.00464584 | − | 0.999989i | \(-0.501479\pi\) | ||||
−0.00464584 | + | 0.999989i | \(0.501479\pi\) | |||||||
\(12\) | 0.685916 | 0.198007 | ||||||||
\(13\) | 6.22014 | 1.72516 | 0.862579 | − | 0.505923i | \(-0.168848\pi\) | ||||
0.862579 | + | 0.505923i | \(0.168848\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.994342 | 0.256738 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.48560 | −1.33045 | −0.665226 | − | 0.746642i | \(-0.731665\pi\) | ||||
−0.665226 | + | 0.746642i | \(0.731665\pi\) | |||||||
\(18\) | 2.52952 | 0.596213 | ||||||||
\(19\) | 1.99267 | 0.457150 | 0.228575 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228575 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(20\) | 1.44966 | 0.324153 | ||||||||
\(21\) | −0.685916 | −0.149679 | ||||||||
\(22\) | 0.0308170 | 0.00657021 | ||||||||
\(23\) | 8.11388 | 1.69186 | 0.845931 | − | 0.533292i | \(-0.179045\pi\) | ||||
0.845931 | + | 0.533292i | \(0.179045\pi\) | |||||||
\(24\) | −0.685916 | −0.140012 | ||||||||
\(25\) | −2.89850 | −0.579699 | ||||||||
\(26\) | −6.22014 | −1.21987 | ||||||||
\(27\) | −3.79278 | −0.729922 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.29482 | 0.426138 | 0.213069 | − | 0.977037i | \(-0.431654\pi\) | ||||
0.213069 | + | 0.977037i | \(0.431654\pi\) | |||||||
\(30\) | −0.994342 | −0.181541 | ||||||||
\(31\) | 3.66210 | 0.657733 | 0.328867 | − | 0.944376i | \(-0.393333\pi\) | ||||
0.328867 | + | 0.944376i | \(0.393333\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.0211379 | −0.00367963 | ||||||||
\(34\) | 5.48560 | 0.940772 | ||||||||
\(35\) | −1.44966 | −0.245037 | ||||||||
\(36\) | −2.52952 | −0.421587 | ||||||||
\(37\) | 6.75121 | 1.10989 | 0.554946 | − | 0.831886i | \(-0.312739\pi\) | ||||
0.554946 | + | 0.831886i | \(0.312739\pi\) | |||||||
\(38\) | −1.99267 | −0.323254 | ||||||||
\(39\) | 4.26649 | 0.683186 | ||||||||
\(40\) | −1.44966 | −0.229211 | ||||||||
\(41\) | 5.26102 | 0.821633 | 0.410817 | − | 0.911718i | \(-0.365244\pi\) | ||||
0.410817 | + | 0.911718i | \(0.365244\pi\) | |||||||
\(42\) | 0.685916 | 0.105839 | ||||||||
\(43\) | −5.40770 | −0.824667 | −0.412333 | − | 0.911033i | \(-0.635286\pi\) | ||||
−0.412333 | + | 0.911033i | \(0.635286\pi\) | |||||||
\(44\) | −0.0308170 | −0.00464584 | ||||||||
\(45\) | −3.66693 | −0.546634 | ||||||||
\(46\) | −8.11388 | −1.19633 | ||||||||
\(47\) | −3.31714 | −0.483855 | −0.241927 | − | 0.970294i | \(-0.577780\pi\) | ||||
−0.241927 | + | 0.970294i | \(0.577780\pi\) | |||||||
\(48\) | 0.685916 | 0.0990034 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.89850 | 0.409909 | ||||||||
\(51\) | −3.76266 | −0.526877 | ||||||||
\(52\) | 6.22014 | 0.862579 | ||||||||
\(53\) | −2.40729 | −0.330666 | −0.165333 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165333 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(54\) | 3.79278 | 0.516133 | ||||||||
\(55\) | −0.0446741 | −0.00602386 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.36680 | 0.181037 | ||||||||
\(58\) | −2.29482 | −0.301325 | ||||||||
\(59\) | 4.54061 | 0.591137 | 0.295568 | − | 0.955322i | \(-0.404491\pi\) | ||||
0.295568 | + | 0.955322i | \(0.404491\pi\) | |||||||
\(60\) | 0.994342 | 0.128369 | ||||||||
\(61\) | −6.20443 | −0.794396 | −0.397198 | − | 0.917733i | \(-0.630017\pi\) | ||||
−0.397198 | + | 0.917733i | \(0.630017\pi\) | |||||||
\(62\) | −3.66210 | −0.465088 | ||||||||
\(63\) | 2.52952 | 0.318690 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.01707 | 1.11843 | ||||||||
\(66\) | 0.0211379 | 0.00260189 | ||||||||
\(67\) | −0.636232 | −0.0777281 | −0.0388640 | − | 0.999245i | \(-0.512374\pi\) | ||||
−0.0388640 | + | 0.999245i | \(0.512374\pi\) | |||||||
\(68\) | −5.48560 | −0.665226 | ||||||||
\(69\) | 5.56544 | 0.670000 | ||||||||
\(70\) | 1.44966 | 0.173267 | ||||||||
\(71\) | 1.56907 | 0.186214 | 0.0931072 | − | 0.995656i | \(-0.470320\pi\) | ||||
0.0931072 | + | 0.995656i | \(0.470320\pi\) | |||||||
\(72\) | 2.52952 | 0.298107 | ||||||||
\(73\) | −8.94194 | −1.04658 | −0.523288 | − | 0.852156i | \(-0.675295\pi\) | ||||
−0.523288 | + | 0.852156i | \(0.675295\pi\) | |||||||
\(74\) | −6.75121 | −0.784812 | ||||||||
\(75\) | −1.98812 | −0.229569 | ||||||||
\(76\) | 1.99267 | 0.228575 | ||||||||
\(77\) | 0.0308170 | 0.00351193 | ||||||||
\(78\) | −4.26649 | −0.483085 | ||||||||
\(79\) | −7.94777 | −0.894194 | −0.447097 | − | 0.894486i | \(-0.647542\pi\) | ||||
−0.447097 | + | 0.894486i | \(0.647542\pi\) | |||||||
\(80\) | 1.44966 | 0.162076 | ||||||||
\(81\) | 4.98703 | 0.554114 | ||||||||
\(82\) | −5.26102 | −0.580982 | ||||||||
\(83\) | −3.11054 | −0.341426 | −0.170713 | − | 0.985321i | \(-0.554607\pi\) | ||||
−0.170713 | + | 0.985321i | \(0.554607\pi\) | |||||||
\(84\) | −0.685916 | −0.0748395 | ||||||||
\(85\) | −7.95223 | −0.862540 | ||||||||
\(86\) | 5.40770 | 0.583127 | ||||||||
\(87\) | 1.57405 | 0.168756 | ||||||||
\(88\) | 0.0308170 | 0.00328511 | ||||||||
\(89\) | 9.22104 | 0.977428 | 0.488714 | − | 0.872444i | \(-0.337466\pi\) | ||||
0.488714 | + | 0.872444i | \(0.337466\pi\) | |||||||
\(90\) | 3.66693 | 0.386529 | ||||||||
\(91\) | −6.22014 | −0.652048 | ||||||||
\(92\) | 8.11388 | 0.845931 | ||||||||
\(93\) | 2.51190 | 0.260471 | ||||||||
\(94\) | 3.31714 | 0.342137 | ||||||||
\(95\) | 2.88868 | 0.296373 | ||||||||
\(96\) | −0.685916 | −0.0700060 | ||||||||
\(97\) | 18.0193 | 1.82958 | 0.914792 | − | 0.403926i | \(-0.132355\pi\) | ||||
0.914792 | + | 0.403926i | \(0.132355\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.0779523 | 0.00783450 | ||||||||
\(100\) | −2.89850 | −0.289850 | ||||||||
\(101\) | 6.47759 | 0.644545 | 0.322272 | − | 0.946647i | \(-0.395553\pi\) | ||||
0.322272 | + | 0.946647i | \(0.395553\pi\) | |||||||
\(102\) | 3.76266 | 0.372559 | ||||||||
\(103\) | 13.5189 | 1.33206 | 0.666028 | − | 0.745927i | \(-0.267993\pi\) | ||||
0.666028 | + | 0.745927i | \(0.267993\pi\) | |||||||
\(104\) | −6.22014 | −0.609935 | ||||||||
\(105\) | −0.994342 | −0.0970378 | ||||||||
\(106\) | 2.40729 | 0.233816 | ||||||||
\(107\) | 0.845463 | 0.0817340 | 0.0408670 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408670 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(108\) | −3.79278 | −0.364961 | ||||||||
\(109\) | −17.5845 | −1.68429 | −0.842145 | − | 0.539251i | \(-0.818707\pi\) | ||||
−0.842145 | + | 0.539251i | \(0.818707\pi\) | |||||||
\(110\) | 0.0446741 | 0.00425951 | ||||||||
\(111\) | 4.63076 | 0.439532 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 13.1439 | 1.23647 | 0.618235 | − | 0.785993i | \(-0.287848\pi\) | ||||
0.618235 | + | 0.785993i | \(0.287848\pi\) | |||||||
\(114\) | −1.36680 | −0.128013 | ||||||||
\(115\) | 11.7623 | 1.09684 | ||||||||
\(116\) | 2.29482 | 0.213069 | ||||||||
\(117\) | −15.7340 | −1.45461 | ||||||||
\(118\) | −4.54061 | −0.417997 | ||||||||
\(119\) | 5.48560 | 0.502864 | ||||||||
\(120\) | −0.994342 | −0.0907706 | ||||||||
\(121\) | −10.9991 | −0.999914 | ||||||||
\(122\) | 6.20443 | 0.561723 | ||||||||
\(123\) | 3.60862 | 0.325378 | ||||||||
\(124\) | 3.66210 | 0.328867 | ||||||||
\(125\) | −11.4501 | −1.02413 | ||||||||
\(126\) | −2.52952 | −0.225348 | ||||||||
\(127\) | 1.40559 | 0.124726 | 0.0623629 | − | 0.998054i | \(-0.480136\pi\) | ||||
0.0623629 | + | 0.998054i | \(0.480136\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.70923 | −0.326579 | ||||||||
\(130\) | −9.01707 | −0.790849 | ||||||||
\(131\) | 13.9716 | 1.22071 | 0.610353 | − | 0.792129i | \(-0.291027\pi\) | ||||
0.610353 | + | 0.792129i | \(0.291027\pi\) | |||||||
\(132\) | −0.0211379 | −0.00183982 | ||||||||
\(133\) | −1.99267 | −0.172786 | ||||||||
\(134\) | 0.636232 | 0.0549621 | ||||||||
\(135\) | −5.49823 | −0.473213 | ||||||||
\(136\) | 5.48560 | 0.470386 | ||||||||
\(137\) | 2.12475 | 0.181529 | 0.0907646 | − | 0.995872i | \(-0.471069\pi\) | ||||
0.0907646 | + | 0.995872i | \(0.471069\pi\) | |||||||
\(138\) | −5.56544 | −0.473762 | ||||||||
\(139\) | −12.8453 | −1.08952 | −0.544760 | − | 0.838592i | \(-0.683379\pi\) | ||||
−0.544760 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(140\) | −1.44966 | −0.122518 | ||||||||
\(141\) | −2.27528 | −0.191613 | ||||||||
\(142\) | −1.56907 | −0.131673 | ||||||||
\(143\) | −0.191686 | −0.0160296 | ||||||||
\(144\) | −2.52952 | −0.210793 | ||||||||
\(145\) | 3.32670 | 0.276268 | ||||||||
\(146\) | 8.94194 | 0.740041 | ||||||||
\(147\) | 0.685916 | 0.0565734 | ||||||||
\(148\) | 6.75121 | 0.554946 | ||||||||
\(149\) | 19.0524 | 1.56084 | 0.780418 | − | 0.625259i | \(-0.215007\pi\) | ||||
0.780418 | + | 0.625259i | \(0.215007\pi\) | |||||||
\(150\) | 1.98812 | 0.162330 | ||||||||
\(151\) | −14.7131 | −1.19733 | −0.598667 | − | 0.800998i | \(-0.704303\pi\) | ||||
−0.598667 | + | 0.800998i | \(0.704303\pi\) | |||||||
\(152\) | −1.99267 | −0.161627 | ||||||||
\(153\) | 13.8759 | 1.12180 | ||||||||
\(154\) | −0.0308170 | −0.00248331 | ||||||||
\(155\) | 5.30879 | 0.426412 | ||||||||
\(156\) | 4.26649 | 0.341593 | ||||||||
\(157\) | −5.26211 | −0.419962 | −0.209981 | − | 0.977705i | \(-0.567340\pi\) | ||||
−0.209981 | + | 0.977705i | \(0.567340\pi\) | |||||||
\(158\) | 7.94777 | 0.632290 | ||||||||
\(159\) | −1.65120 | −0.130948 | ||||||||
\(160\) | −1.44966 | −0.114605 | ||||||||
\(161\) | −8.11388 | −0.639464 | ||||||||
\(162\) | −4.98703 | −0.391818 | ||||||||
\(163\) | 11.7413 | 0.919649 | 0.459824 | − | 0.888010i | \(-0.347912\pi\) | ||||
0.459824 | + | 0.888010i | \(0.347912\pi\) | |||||||
\(164\) | 5.26102 | 0.410817 | ||||||||
\(165\) | −0.0306427 | −0.00238553 | ||||||||
\(166\) | 3.11054 | 0.241425 | ||||||||
\(167\) | −9.95291 | −0.770180 | −0.385090 | − | 0.922879i | \(-0.625830\pi\) | ||||
−0.385090 | + | 0.922879i | \(0.625830\pi\) | |||||||
\(168\) | 0.685916 | 0.0529195 | ||||||||
\(169\) | 25.6902 | 1.97617 | ||||||||
\(170\) | 7.95223 | 0.609908 | ||||||||
\(171\) | −5.04049 | −0.385456 | ||||||||
\(172\) | −5.40770 | −0.412333 | ||||||||
\(173\) | 15.1987 | 1.15553 | 0.577767 | − | 0.816202i | \(-0.303924\pi\) | ||||
0.577767 | + | 0.816202i | \(0.303924\pi\) | |||||||
\(174\) | −1.57405 | −0.119329 | ||||||||
\(175\) | 2.89850 | 0.219106 | ||||||||
\(176\) | −0.0308170 | −0.00232292 | ||||||||
\(177\) | 3.11447 | 0.234098 | ||||||||
\(178\) | −9.22104 | −0.691146 | ||||||||
\(179\) | 23.3175 | 1.74284 | 0.871418 | − | 0.490542i | \(-0.163201\pi\) | ||||
0.871418 | + | 0.490542i | \(0.163201\pi\) | |||||||
\(180\) | −3.66693 | −0.273317 | ||||||||
\(181\) | 10.4772 | 0.778768 | 0.389384 | − | 0.921076i | \(-0.372688\pi\) | ||||
0.389384 | + | 0.921076i | \(0.372688\pi\) | |||||||
\(182\) | 6.22014 | 0.461068 | ||||||||
\(183\) | −4.25572 | −0.314592 | ||||||||
\(184\) | −8.11388 | −0.598164 | ||||||||
\(185\) | 9.78693 | 0.719549 | ||||||||
\(186\) | −2.51190 | −0.184181 | ||||||||
\(187\) | 0.169050 | 0.0123622 | ||||||||
\(188\) | −3.31714 | −0.241927 | ||||||||
\(189\) | 3.79278 | 0.275884 | ||||||||
\(190\) | −2.88868 | −0.209567 | ||||||||
\(191\) | 10.2549 | 0.742020 | 0.371010 | − | 0.928629i | \(-0.379012\pi\) | ||||
0.371010 | + | 0.928629i | \(0.379012\pi\) | |||||||
\(192\) | 0.685916 | 0.0495017 | ||||||||
\(193\) | 9.26826 | 0.667144 | 0.333572 | − | 0.942725i | \(-0.391746\pi\) | ||||
0.333572 | + | 0.942725i | \(0.391746\pi\) | |||||||
\(194\) | −18.0193 | −1.29371 | ||||||||
\(195\) | 6.18495 | 0.442913 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.5984 | 0.755108 | 0.377554 | − | 0.925988i | \(-0.376765\pi\) | ||||
0.377554 | + | 0.925988i | \(0.376765\pi\) | |||||||
\(198\) | −0.0779523 | −0.00553983 | ||||||||
\(199\) | 19.5234 | 1.38397 | 0.691987 | − | 0.721910i | \(-0.256735\pi\) | ||||
0.691987 | + | 0.721910i | \(0.256735\pi\) | |||||||
\(200\) | 2.89850 | 0.204955 | ||||||||
\(201\) | −0.436401 | −0.0307814 | ||||||||
\(202\) | −6.47759 | −0.455762 | ||||||||
\(203\) | −2.29482 | −0.161065 | ||||||||
\(204\) | −3.76266 | −0.263439 | ||||||||
\(205\) | 7.62667 | 0.532670 | ||||||||
\(206\) | −13.5189 | −0.941906 | ||||||||
\(207\) | −20.5242 | −1.42653 | ||||||||
\(208\) | 6.22014 | 0.431289 | ||||||||
\(209\) | −0.0614081 | −0.00424769 | ||||||||
\(210\) | 0.994342 | 0.0686161 | ||||||||
\(211\) | 21.5412 | 1.48296 | 0.741478 | − | 0.670977i | \(-0.234125\pi\) | ||||
0.741478 | + | 0.670977i | \(0.234125\pi\) | |||||||
\(212\) | −2.40729 | −0.165333 | ||||||||
\(213\) | 1.07625 | 0.0737434 | ||||||||
\(214\) | −0.845463 | −0.0577947 | ||||||||
\(215\) | −7.83931 | −0.534636 | ||||||||
\(216\) | 3.79278 | 0.258066 | ||||||||
\(217\) | −3.66210 | −0.248600 | ||||||||
\(218\) | 17.5845 | 1.19097 | ||||||||
\(219\) | −6.13342 | −0.414458 | ||||||||
\(220\) | −0.0446741 | −0.00301193 | ||||||||
\(221\) | −34.1212 | −2.29524 | ||||||||
\(222\) | −4.63076 | −0.310796 | ||||||||
\(223\) | −16.5991 | −1.11156 | −0.555779 | − | 0.831330i | \(-0.687580\pi\) | ||||
−0.555779 | + | 0.831330i | \(0.687580\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 7.33181 | 0.488787 | ||||||||
\(226\) | −13.1439 | −0.874317 | ||||||||
\(227\) | 2.51733 | 0.167081 | 0.0835404 | − | 0.996504i | \(-0.473377\pi\) | ||||
0.0835404 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(228\) | 1.36680 | 0.0905187 | ||||||||
\(229\) | 9.48297 | 0.626652 | 0.313326 | − | 0.949646i | \(-0.398557\pi\) | ||||
0.313326 | + | 0.949646i | \(0.398557\pi\) | |||||||
\(230\) | −11.7623 | −0.775586 | ||||||||
\(231\) | 0.0211379 | 0.00139077 | ||||||||
\(232\) | −2.29482 | −0.150662 | ||||||||
\(233\) | 6.67919 | 0.437568 | 0.218784 | − | 0.975773i | \(-0.429791\pi\) | ||||
0.218784 | + | 0.975773i | \(0.429791\pi\) | |||||||
\(234\) | 15.7340 | 1.02856 | ||||||||
\(235\) | −4.80871 | −0.313686 | ||||||||
\(236\) | 4.54061 | 0.295568 | ||||||||
\(237\) | −5.45150 | −0.354113 | ||||||||
\(238\) | −5.48560 | −0.355578 | ||||||||
\(239\) | −8.65865 | −0.560082 | −0.280041 | − | 0.959988i | \(-0.590348\pi\) | ||||
−0.280041 | + | 0.959988i | \(0.590348\pi\) | |||||||
\(240\) | 0.994342 | 0.0641845 | ||||||||
\(241\) | 30.2892 | 1.95110 | 0.975549 | − | 0.219781i | \(-0.0705342\pi\) | ||||
0.975549 | + | 0.219781i | \(0.0705342\pi\) | |||||||
\(242\) | 10.9991 | 0.707046 | ||||||||
\(243\) | 14.7990 | 0.949359 | ||||||||
\(244\) | −6.20443 | −0.397198 | ||||||||
\(245\) | 1.44966 | 0.0926151 | ||||||||
\(246\) | −3.60862 | −0.230077 | ||||||||
\(247\) | 12.3947 | 0.788655 | ||||||||
\(248\) | −3.66210 | −0.232544 | ||||||||
\(249\) | −2.13357 | −0.135209 | ||||||||
\(250\) | 11.4501 | 0.724168 | ||||||||
\(251\) | −27.4516 | −1.73273 | −0.866363 | − | 0.499414i | \(-0.833549\pi\) | ||||
−0.866363 | + | 0.499414i | \(0.833549\pi\) | |||||||
\(252\) | 2.52952 | 0.159345 | ||||||||
\(253\) | −0.250046 | −0.0157203 | ||||||||
\(254\) | −1.40559 | −0.0881944 | ||||||||
\(255\) | −5.45456 | −0.341578 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.6464 | −1.10075 | −0.550377 | − | 0.834916i | \(-0.685516\pi\) | ||||
−0.550377 | + | 0.834916i | \(0.685516\pi\) | |||||||
\(258\) | 3.70923 | 0.230926 | ||||||||
\(259\) | −6.75121 | −0.419500 | ||||||||
\(260\) | 9.01707 | 0.559215 | ||||||||
\(261\) | −5.80480 | −0.359308 | ||||||||
\(262\) | −13.9716 | −0.863170 | ||||||||
\(263\) | 31.6063 | 1.94893 | 0.974465 | − | 0.224540i | \(-0.0720878\pi\) | ||||
0.974465 | + | 0.224540i | \(0.0720878\pi\) | |||||||
\(264\) | 0.0211379 | 0.00130095 | ||||||||
\(265\) | −3.48974 | −0.214373 | ||||||||
\(266\) | 1.99267 | 0.122178 | ||||||||
\(267\) | 6.32486 | 0.387075 | ||||||||
\(268\) | −0.636232 | −0.0388640 | ||||||||
\(269\) | 8.76947 | 0.534684 | 0.267342 | − | 0.963602i | \(-0.413855\pi\) | ||||
0.267342 | + | 0.963602i | \(0.413855\pi\) | |||||||
\(270\) | 5.49823 | 0.334612 | ||||||||
\(271\) | 3.46805 | 0.210669 | 0.105334 | − | 0.994437i | \(-0.466409\pi\) | ||||
0.105334 | + | 0.994437i | \(0.466409\pi\) | |||||||
\(272\) | −5.48560 | −0.332613 | ||||||||
\(273\) | −4.26649 | −0.258220 | ||||||||
\(274\) | −2.12475 | −0.128361 | ||||||||
\(275\) | 0.0893231 | 0.00538639 | ||||||||
\(276\) | 5.56544 | 0.335000 | ||||||||
\(277\) | −7.15105 | −0.429665 | −0.214832 | − | 0.976651i | \(-0.568921\pi\) | ||||
−0.214832 | + | 0.976651i | \(0.568921\pi\) | |||||||
\(278\) | 12.8453 | 0.770407 | ||||||||
\(279\) | −9.26337 | −0.554583 | ||||||||
\(280\) | 1.44966 | 0.0866335 | ||||||||
\(281\) | −1.72925 | −0.103158 | −0.0515792 | − | 0.998669i | \(-0.516425\pi\) | ||||
−0.0515792 | + | 0.998669i | \(0.516425\pi\) | |||||||
\(282\) | 2.27528 | 0.135491 | ||||||||
\(283\) | −6.18264 | −0.367520 | −0.183760 | − | 0.982971i | \(-0.558827\pi\) | ||||
−0.183760 | + | 0.982971i | \(0.558827\pi\) | |||||||
\(284\) | 1.56907 | 0.0931072 | ||||||||
\(285\) | 1.98139 | 0.117368 | ||||||||
\(286\) | 0.191686 | 0.0113347 | ||||||||
\(287\) | −5.26102 | −0.310548 | ||||||||
\(288\) | 2.52952 | 0.149053 | ||||||||
\(289\) | 13.0918 | 0.770105 | ||||||||
\(290\) | −3.32670 | −0.195351 | ||||||||
\(291\) | 12.3597 | 0.724540 | ||||||||
\(292\) | −8.94194 | −0.523288 | ||||||||
\(293\) | −12.7021 | −0.742063 | −0.371032 | − | 0.928620i | \(-0.620996\pi\) | ||||
−0.371032 | + | 0.928620i | \(0.620996\pi\) | |||||||
\(294\) | −0.685916 | −0.0400034 | ||||||||
\(295\) | 6.58232 | 0.383237 | ||||||||
\(296\) | −6.75121 | −0.392406 | ||||||||
\(297\) | 0.116882 | 0.00678220 | ||||||||
\(298\) | −19.0524 | −1.10368 | ||||||||
\(299\) | 50.4695 | 2.91873 | ||||||||
\(300\) | −1.98812 | −0.114784 | ||||||||
\(301\) | 5.40770 | 0.311695 | ||||||||
\(302\) | 14.7131 | 0.846643 | ||||||||
\(303\) | 4.44308 | 0.255249 | ||||||||
\(304\) | 1.99267 | 0.114287 | ||||||||
\(305\) | −8.99429 | −0.515011 | ||||||||
\(306\) | −13.8759 | −0.793234 | ||||||||
\(307\) | 11.3220 | 0.646181 | 0.323090 | − | 0.946368i | \(-0.395278\pi\) | ||||
0.323090 | + | 0.946368i | \(0.395278\pi\) | |||||||
\(308\) | 0.0308170 | 0.00175596 | ||||||||
\(309\) | 9.27282 | 0.527512 | ||||||||
\(310\) | −5.30879 | −0.301519 | ||||||||
\(311\) | −27.8624 | −1.57993 | −0.789966 | − | 0.613150i | \(-0.789902\pi\) | ||||
−0.789966 | + | 0.613150i | \(0.789902\pi\) | |||||||
\(312\) | −4.26649 | −0.241543 | ||||||||
\(313\) | −2.64490 | −0.149499 | −0.0747494 | − | 0.997202i | \(-0.523816\pi\) | ||||
−0.0747494 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(314\) | 5.26211 | 0.296958 | ||||||||
\(315\) | 3.66693 | 0.206608 | ||||||||
\(316\) | −7.94777 | −0.447097 | ||||||||
\(317\) | 21.6517 | 1.21608 | 0.608042 | − | 0.793905i | \(-0.291955\pi\) | ||||
0.608042 | + | 0.793905i | \(0.291955\pi\) | |||||||
\(318\) | 1.65120 | 0.0925945 | ||||||||
\(319\) | −0.0707196 | −0.00395954 | ||||||||
\(320\) | 1.44966 | 0.0810382 | ||||||||
\(321\) | 0.579917 | 0.0323678 | ||||||||
\(322\) | 8.11388 | 0.452169 | ||||||||
\(323\) | −10.9310 | −0.608216 | ||||||||
\(324\) | 4.98703 | 0.277057 | ||||||||
\(325\) | −18.0291 | −1.00007 | ||||||||
\(326\) | −11.7413 | −0.650290 | ||||||||
\(327\) | −12.0615 | −0.667002 | ||||||||
\(328\) | −5.26102 | −0.290491 | ||||||||
\(329\) | 3.31714 | 0.182880 | ||||||||
\(330\) | 0.0306427 | 0.00168682 | ||||||||
\(331\) | 8.21795 | 0.451699 | 0.225850 | − | 0.974162i | \(-0.427484\pi\) | ||||
0.225850 | + | 0.974162i | \(0.427484\pi\) | |||||||
\(332\) | −3.11054 | −0.170713 | ||||||||
\(333\) | −17.0773 | −0.935831 | ||||||||
\(334\) | 9.95291 | 0.544599 | ||||||||
\(335\) | −0.922317 | −0.0503916 | ||||||||
\(336\) | −0.685916 | −0.0374198 | ||||||||
\(337\) | 0.122451 | 0.00667033 | 0.00333517 | − | 0.999994i | \(-0.498938\pi\) | ||||
0.00333517 | + | 0.999994i | \(0.498938\pi\) | |||||||
\(338\) | −25.6902 | −1.39736 | ||||||||
\(339\) | 9.01558 | 0.489659 | ||||||||
\(340\) | −7.95223 | −0.431270 | ||||||||
\(341\) | −0.112855 | −0.00611145 | ||||||||
\(342\) | 5.04049 | 0.272559 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.40770 | 0.291564 | ||||||||
\(345\) | 8.06798 | 0.434365 | ||||||||
\(346\) | −15.1987 | −0.817086 | ||||||||
\(347\) | 15.9204 | 0.854650 | 0.427325 | − | 0.904098i | \(-0.359456\pi\) | ||||
0.427325 | + | 0.904098i | \(0.359456\pi\) | |||||||
\(348\) | 1.57405 | 0.0843782 | ||||||||
\(349\) | −15.4343 | −0.826180 | −0.413090 | − | 0.910690i | \(-0.635551\pi\) | ||||
−0.413090 | + | 0.910690i | \(0.635551\pi\) | |||||||
\(350\) | −2.89850 | −0.154931 | ||||||||
\(351\) | −23.5917 | −1.25923 | ||||||||
\(352\) | 0.0308170 | 0.00164255 | ||||||||
\(353\) | −12.2792 | −0.653555 | −0.326777 | − | 0.945101i | \(-0.605963\pi\) | ||||
−0.326777 | + | 0.945101i | \(0.605963\pi\) | |||||||
\(354\) | −3.11447 | −0.165532 | ||||||||
\(355\) | 2.27461 | 0.120724 | ||||||||
\(356\) | 9.22104 | 0.488714 | ||||||||
\(357\) | 3.76266 | 0.199141 | ||||||||
\(358\) | −23.3175 | −1.23237 | ||||||||
\(359\) | 8.69460 | 0.458883 | 0.229442 | − | 0.973322i | \(-0.426310\pi\) | ||||
0.229442 | + | 0.973322i | \(0.426310\pi\) | |||||||
\(360\) | 3.66693 | 0.193264 | ||||||||
\(361\) | −15.0293 | −0.791014 | ||||||||
\(362\) | −10.4772 | −0.550672 | ||||||||
\(363\) | −7.54442 | −0.395979 | ||||||||
\(364\) | −6.22014 | −0.326024 | ||||||||
\(365\) | −12.9627 | −0.678501 | ||||||||
\(366\) | 4.25572 | 0.222450 | ||||||||
\(367\) | 19.3936 | 1.01234 | 0.506169 | − | 0.862434i | \(-0.331061\pi\) | ||||
0.506169 | + | 0.862434i | \(0.331061\pi\) | |||||||
\(368\) | 8.11388 | 0.422965 | ||||||||
\(369\) | −13.3079 | −0.692779 | ||||||||
\(370\) | −9.78693 | −0.508798 | ||||||||
\(371\) | 2.40729 | 0.124980 | ||||||||
\(372\) | 2.51190 | 0.130236 | ||||||||
\(373\) | −10.3958 | −0.538276 | −0.269138 | − | 0.963102i | \(-0.586739\pi\) | ||||
−0.269138 | + | 0.963102i | \(0.586739\pi\) | |||||||
\(374\) | −0.169050 | −0.00874136 | ||||||||
\(375\) | −7.85381 | −0.405569 | ||||||||
\(376\) | 3.31714 | 0.171068 | ||||||||
\(377\) | 14.2741 | 0.735155 | ||||||||
\(378\) | −3.79278 | −0.195080 | ||||||||
\(379\) | 12.1040 | 0.621740 | 0.310870 | − | 0.950452i | \(-0.399380\pi\) | ||||
0.310870 | + | 0.950452i | \(0.399380\pi\) | |||||||
\(380\) | 2.88868 | 0.148186 | ||||||||
\(381\) | 0.964115 | 0.0493931 | ||||||||
\(382\) | −10.2549 | −0.524687 | ||||||||
\(383\) | −24.9672 | −1.27577 | −0.637883 | − | 0.770134i | \(-0.720190\pi\) | ||||
−0.637883 | + | 0.770134i | \(0.720190\pi\) | |||||||
\(384\) | −0.685916 | −0.0350030 | ||||||||
\(385\) | 0.0446741 | 0.00227680 | ||||||||
\(386\) | −9.26826 | −0.471742 | ||||||||
\(387\) | 13.6789 | 0.695337 | ||||||||
\(388\) | 18.0193 | 0.914792 | ||||||||
\(389\) | −7.59387 | −0.385025 | −0.192512 | − | 0.981295i | \(-0.561664\pi\) | ||||
−0.192512 | + | 0.981295i | \(0.561664\pi\) | |||||||
\(390\) | −6.18495 | −0.313187 | ||||||||
\(391\) | −44.5095 | −2.25094 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 9.58336 | 0.483416 | ||||||||
\(394\) | −10.5984 | −0.533942 | ||||||||
\(395\) | −11.5215 | −0.579711 | ||||||||
\(396\) | 0.0779523 | 0.00391725 | ||||||||
\(397\) | −27.8996 | −1.40024 | −0.700120 | − | 0.714025i | \(-0.746870\pi\) | ||||
−0.700120 | + | 0.714025i | \(0.746870\pi\) | |||||||
\(398\) | −19.5234 | −0.978618 | ||||||||
\(399\) | −1.36680 | −0.0684257 | ||||||||
\(400\) | −2.89850 | −0.144925 | ||||||||
\(401\) | −29.8254 | −1.48941 | −0.744704 | − | 0.667395i | \(-0.767409\pi\) | ||||
−0.744704 | + | 0.667395i | \(0.767409\pi\) | |||||||
\(402\) | 0.436401 | 0.0217657 | ||||||||
\(403\) | 22.7788 | 1.13469 | ||||||||
\(404\) | 6.47759 | 0.322272 | ||||||||
\(405\) | 7.22948 | 0.359236 | ||||||||
\(406\) | 2.29482 | 0.113890 | ||||||||
\(407\) | −0.208052 | −0.0103128 | ||||||||
\(408\) | 3.76266 | 0.186279 | ||||||||
\(409\) | −20.0637 | −0.992085 | −0.496043 | − | 0.868298i | \(-0.665214\pi\) | ||||
−0.496043 | + | 0.868298i | \(0.665214\pi\) | |||||||
\(410\) | −7.62667 | −0.376654 | ||||||||
\(411\) | 1.45740 | 0.0718880 | ||||||||
\(412\) | 13.5189 | 0.666028 | ||||||||
\(413\) | −4.54061 | −0.223429 | ||||||||
\(414\) | 20.5242 | 1.00871 | ||||||||
\(415\) | −4.50921 | −0.221348 | ||||||||
\(416\) | −6.22014 | −0.304968 | ||||||||
\(417\) | −8.81076 | −0.431465 | ||||||||
\(418\) | 0.0614081 | 0.00300357 | ||||||||
\(419\) | 35.1960 | 1.71944 | 0.859718 | − | 0.510769i | \(-0.170639\pi\) | ||||
0.859718 | + | 0.510769i | \(0.170639\pi\) | |||||||
\(420\) | −0.994342 | −0.0485189 | ||||||||
\(421\) | −22.9700 | −1.11949 | −0.559746 | − | 0.828664i | \(-0.689101\pi\) | ||||
−0.559746 | + | 0.828664i | \(0.689101\pi\) | |||||||
\(422\) | −21.5412 | −1.04861 | ||||||||
\(423\) | 8.39077 | 0.407973 | ||||||||
\(424\) | 2.40729 | 0.116908 | ||||||||
\(425\) | 15.9000 | 0.771263 | ||||||||
\(426\) | −1.07625 | −0.0521445 | ||||||||
\(427\) | 6.20443 | 0.300253 | ||||||||
\(428\) | 0.845463 | 0.0408670 | ||||||||
\(429\) | −0.131481 | −0.00634795 | ||||||||
\(430\) | 7.83931 | 0.378045 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −3.79278 | −0.182480 | ||||||||
\(433\) | −30.5862 | −1.46988 | −0.734941 | − | 0.678131i | \(-0.762790\pi\) | ||||
−0.734941 | + | 0.678131i | \(0.762790\pi\) | |||||||
\(434\) | 3.66210 | 0.175787 | ||||||||
\(435\) | 2.28184 | 0.109406 | ||||||||
\(436\) | −17.5845 | −0.842145 | ||||||||
\(437\) | 16.1683 | 0.773434 | ||||||||
\(438\) | 6.13342 | 0.293066 | ||||||||
\(439\) | 21.7019 | 1.03578 | 0.517888 | − | 0.855448i | \(-0.326718\pi\) | ||||
0.517888 | + | 0.855448i | \(0.326718\pi\) | |||||||
\(440\) | 0.0446741 | 0.00212975 | ||||||||
\(441\) | −2.52952 | −0.120453 | ||||||||
\(442\) | 34.1212 | 1.62298 | ||||||||
\(443\) | 18.8299 | 0.894634 | 0.447317 | − | 0.894375i | \(-0.352380\pi\) | ||||
0.447317 | + | 0.894375i | \(0.352380\pi\) | |||||||
\(444\) | 4.63076 | 0.219766 | ||||||||
\(445\) | 13.3673 | 0.633672 | ||||||||
\(446\) | 16.5991 | 0.785990 | ||||||||
\(447\) | 13.0684 | 0.618112 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 14.2002 | 0.670150 | 0.335075 | − | 0.942192i | \(-0.391238\pi\) | ||||
0.335075 | + | 0.942192i | \(0.391238\pi\) | |||||||
\(450\) | −7.33181 | −0.345625 | ||||||||
\(451\) | −0.162129 | −0.00763436 | ||||||||
\(452\) | 13.1439 | 0.618235 | ||||||||
\(453\) | −10.0919 | −0.474161 | ||||||||
\(454\) | −2.51733 | −0.118144 | ||||||||
\(455\) | −9.01707 | −0.422727 | ||||||||
\(456\) | −1.36680 | −0.0640064 | ||||||||
\(457\) | −6.48130 | −0.303182 | −0.151591 | − | 0.988443i | \(-0.548440\pi\) | ||||
−0.151591 | + | 0.988443i | \(0.548440\pi\) | |||||||
\(458\) | −9.48297 | −0.443110 | ||||||||
\(459\) | 20.8057 | 0.971126 | ||||||||
\(460\) | 11.7623 | 0.548422 | ||||||||
\(461\) | −36.2829 | −1.68986 | −0.844931 | − | 0.534875i | \(-0.820359\pi\) | ||||
−0.844931 | + | 0.534875i | \(0.820359\pi\) | |||||||
\(462\) | −0.0211379 | −0.000983424 0 | ||||||||
\(463\) | 21.2718 | 0.988584 | 0.494292 | − | 0.869296i | \(-0.335427\pi\) | ||||
0.494292 | + | 0.869296i | \(0.335427\pi\) | |||||||
\(464\) | 2.29482 | 0.106534 | ||||||||
\(465\) | 3.64138 | 0.168865 | ||||||||
\(466\) | −6.67919 | −0.309407 | ||||||||
\(467\) | 31.3240 | 1.44950 | 0.724750 | − | 0.689012i | \(-0.241955\pi\) | ||||
0.724750 | + | 0.689012i | \(0.241955\pi\) | |||||||
\(468\) | −15.7340 | −0.727303 | ||||||||
\(469\) | 0.636232 | 0.0293785 | ||||||||
\(470\) | 4.80871 | 0.221809 | ||||||||
\(471\) | −3.60937 | −0.166311 | ||||||||
\(472\) | −4.54061 | −0.208998 | ||||||||
\(473\) | 0.166649 | 0.00766254 | ||||||||
\(474\) | 5.45150 | 0.250396 | ||||||||
\(475\) | −5.77574 | −0.265009 | ||||||||
\(476\) | 5.48560 | 0.251432 | ||||||||
\(477\) | 6.08928 | 0.278809 | ||||||||
\(478\) | 8.65865 | 0.396038 | ||||||||
\(479\) | 13.2576 | 0.605756 | 0.302878 | − | 0.953029i | \(-0.402053\pi\) | ||||
0.302878 | + | 0.953029i | \(0.402053\pi\) | |||||||
\(480\) | −0.994342 | −0.0453853 | ||||||||
\(481\) | 41.9935 | 1.91474 | ||||||||
\(482\) | −30.2892 | −1.37964 | ||||||||
\(483\) | −5.56544 | −0.253236 | ||||||||
\(484\) | −10.9991 | −0.499957 | ||||||||
\(485\) | 26.1218 | 1.18613 | ||||||||
\(486\) | −14.7990 | −0.671298 | ||||||||
\(487\) | −7.13345 | −0.323247 | −0.161624 | − | 0.986852i | \(-0.551673\pi\) | ||||
−0.161624 | + | 0.986852i | \(0.551673\pi\) | |||||||
\(488\) | 6.20443 | 0.280861 | ||||||||
\(489\) | 8.05354 | 0.364193 | ||||||||
\(490\) | −1.44966 | −0.0654888 | ||||||||
\(491\) | 2.55846 | 0.115462 | 0.0577309 | − | 0.998332i | \(-0.481613\pi\) | ||||
0.0577309 | + | 0.998332i | \(0.481613\pi\) | |||||||
\(492\) | 3.60862 | 0.162689 | ||||||||
\(493\) | −12.5885 | −0.566956 | ||||||||
\(494\) | −12.3947 | −0.557663 | ||||||||
\(495\) | 0.113004 | 0.00507915 | ||||||||
\(496\) | 3.66210 | 0.164433 | ||||||||
\(497\) | −1.56907 | −0.0703824 | ||||||||
\(498\) | 2.13357 | 0.0956074 | ||||||||
\(499\) | 25.5539 | 1.14395 | 0.571974 | − | 0.820272i | \(-0.306178\pi\) | ||||
0.571974 | + | 0.820272i | \(0.306178\pi\) | |||||||
\(500\) | −11.4501 | −0.512064 | ||||||||
\(501\) | −6.82686 | −0.305002 | ||||||||
\(502\) | 27.4516 | 1.22522 | ||||||||
\(503\) | −19.9164 | −0.888029 | −0.444014 | − | 0.896020i | \(-0.646446\pi\) | ||||
−0.444014 | + | 0.896020i | \(0.646446\pi\) | |||||||
\(504\) | −2.52952 | −0.112674 | ||||||||
\(505\) | 9.39028 | 0.417862 | ||||||||
\(506\) | 0.250046 | 0.0111159 | ||||||||
\(507\) | 17.6213 | 0.782590 | ||||||||
\(508\) | 1.40559 | 0.0623629 | ||||||||
\(509\) | −25.4468 | −1.12791 | −0.563955 | − | 0.825806i | \(-0.690721\pi\) | ||||
−0.563955 | + | 0.825806i | \(0.690721\pi\) | |||||||
\(510\) | 5.45456 | 0.241532 | ||||||||
\(511\) | 8.94194 | 0.395568 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.55776 | −0.333683 | ||||||||
\(514\) | 17.6464 | 0.778351 | ||||||||
\(515\) | 19.5977 | 0.863580 | ||||||||
\(516\) | −3.70923 | −0.163290 | ||||||||
\(517\) | 0.102224 | 0.00449583 | ||||||||
\(518\) | 6.75121 | 0.296631 | ||||||||
\(519\) | 10.4250 | 0.457607 | ||||||||
\(520\) | −9.01707 | −0.395425 | ||||||||
\(521\) | −12.9030 | −0.565292 | −0.282646 | − | 0.959224i | \(-0.591212\pi\) | ||||
−0.282646 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(522\) | 5.80480 | 0.254069 | ||||||||
\(523\) | 2.69005 | 0.117628 | 0.0588138 | − | 0.998269i | \(-0.481268\pi\) | ||||
0.0588138 | + | 0.998269i | \(0.481268\pi\) | |||||||
\(524\) | 13.9716 | 0.610353 | ||||||||
\(525\) | 1.98812 | 0.0867689 | ||||||||
\(526\) | −31.6063 | −1.37810 | ||||||||
\(527\) | −20.0888 | −0.875083 | ||||||||
\(528\) | −0.0211379 | −0.000919909 0 | ||||||||
\(529\) | 42.8351 | 1.86240 | ||||||||
\(530\) | 3.48974 | 0.151585 | ||||||||
\(531\) | −11.4856 | −0.498431 | ||||||||
\(532\) | −1.99267 | −0.0863931 | ||||||||
\(533\) | 32.7243 | 1.41745 | ||||||||
\(534\) | −6.32486 | −0.273703 | ||||||||
\(535\) | 1.22563 | 0.0529887 | ||||||||
\(536\) | 0.636232 | 0.0274810 | ||||||||
\(537\) | 15.9939 | 0.690187 | ||||||||
\(538\) | −8.76947 | −0.378079 | ||||||||
\(539\) | −0.0308170 | −0.00132738 | ||||||||
\(540\) | −5.49823 | −0.236606 | ||||||||
\(541\) | 39.4037 | 1.69410 | 0.847049 | − | 0.531514i | \(-0.178377\pi\) | ||||
0.847049 | + | 0.531514i | \(0.178377\pi\) | |||||||
\(542\) | −3.46805 | −0.148965 | ||||||||
\(543\) | 7.18651 | 0.308403 | ||||||||
\(544\) | 5.48560 | 0.235193 | ||||||||
\(545\) | −25.4915 | −1.09194 | ||||||||
\(546\) | 4.26649 | 0.182589 | ||||||||
\(547\) | −22.0756 | −0.943886 | −0.471943 | − | 0.881629i | \(-0.656447\pi\) | ||||
−0.471943 | + | 0.881629i | \(0.656447\pi\) | |||||||
\(548\) | 2.12475 | 0.0907646 | ||||||||
\(549\) | 15.6942 | 0.669813 | ||||||||
\(550\) | −0.0893231 | −0.00380875 | ||||||||
\(551\) | 4.57282 | 0.194809 | ||||||||
\(552\) | −5.56544 | −0.236881 | ||||||||
\(553\) | 7.94777 | 0.337973 | ||||||||
\(554\) | 7.15105 | 0.303819 | ||||||||
\(555\) | 6.71301 | 0.284951 | ||||||||
\(556\) | −12.8453 | −0.544760 | ||||||||
\(557\) | 41.5496 | 1.76051 | 0.880257 | − | 0.474498i | \(-0.157370\pi\) | ||||
0.880257 | + | 0.474498i | \(0.157370\pi\) | |||||||
\(558\) | 9.26337 | 0.392150 | ||||||||
\(559\) | −33.6367 | −1.42268 | ||||||||
\(560\) | −1.44966 | −0.0612591 | ||||||||
\(561\) | 0.115954 | 0.00489558 | ||||||||
\(562\) | 1.72925 | 0.0729439 | ||||||||
\(563\) | −0.0444233 | −0.00187222 | −0.000936109 | − | 1.00000i | \(-0.500298\pi\) | ||||
−0.000936109 | 1.00000i | \(0.500298\pi\) | ||||||||
\(564\) | −2.27528 | −0.0958065 | ||||||||
\(565\) | 19.0541 | 0.801611 | ||||||||
\(566\) | 6.18264 | 0.259876 | ||||||||
\(567\) | −4.98703 | −0.209436 | ||||||||
\(568\) | −1.56907 | −0.0658367 | ||||||||
\(569\) | 5.30329 | 0.222325 | 0.111163 | − | 0.993802i | \(-0.464543\pi\) | ||||
0.111163 | + | 0.993802i | \(0.464543\pi\) | |||||||
\(570\) | −1.98139 | −0.0829915 | ||||||||
\(571\) | 4.51455 | 0.188928 | 0.0944641 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944641 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(572\) | −0.191686 | −0.00801481 | ||||||||
\(573\) | 7.03401 | 0.293850 | ||||||||
\(574\) | 5.26102 | 0.219591 | ||||||||
\(575\) | −23.5181 | −0.980771 | ||||||||
\(576\) | −2.52952 | −0.105397 | ||||||||
\(577\) | −44.9834 | −1.87268 | −0.936341 | − | 0.351092i | \(-0.885810\pi\) | ||||
−0.936341 | + | 0.351092i | \(0.885810\pi\) | |||||||
\(578\) | −13.0918 | −0.544546 | ||||||||
\(579\) | 6.35725 | 0.264198 | ||||||||
\(580\) | 3.32670 | 0.138134 | ||||||||
\(581\) | 3.11054 | 0.129047 | ||||||||
\(582\) | −12.3597 | −0.512327 | ||||||||
\(583\) | 0.0741855 | 0.00307245 | ||||||||
\(584\) | 8.94194 | 0.370020 | ||||||||
\(585\) | −22.8089 | −0.943030 | ||||||||
\(586\) | 12.7021 | 0.524718 | ||||||||
\(587\) | 25.7132 | 1.06130 | 0.530649 | − | 0.847592i | \(-0.321948\pi\) | ||||
0.530649 | + | 0.847592i | \(0.321948\pi\) | |||||||
\(588\) | 0.685916 | 0.0282867 | ||||||||
\(589\) | 7.29736 | 0.300683 | ||||||||
\(590\) | −6.58232 | −0.270990 | ||||||||
\(591\) | 7.26964 | 0.299033 | ||||||||
\(592\) | 6.75121 | 0.277473 | ||||||||
\(593\) | 16.9784 | 0.697220 | 0.348610 | − | 0.937268i | \(-0.386654\pi\) | ||||
0.348610 | + | 0.937268i | \(0.386654\pi\) | |||||||
\(594\) | −0.116882 | −0.00479574 | ||||||||
\(595\) | 7.95223 | 0.326010 | ||||||||
\(596\) | 19.0524 | 0.780418 | ||||||||
\(597\) | 13.3914 | 0.548073 | ||||||||
\(598\) | −50.4695 | −2.06385 | ||||||||
\(599\) | 4.67359 | 0.190958 | 0.0954789 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954789 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(600\) | 1.98812 | 0.0811649 | ||||||||
\(601\) | −28.1126 | −1.14674 | −0.573368 | − | 0.819298i | \(-0.694363\pi\) | ||||
−0.573368 | + | 0.819298i | \(0.694363\pi\) | |||||||
\(602\) | −5.40770 | −0.220401 | ||||||||
\(603\) | 1.60936 | 0.0655383 | ||||||||
\(604\) | −14.7131 | −0.598667 | ||||||||
\(605\) | −15.9448 | −0.648250 | ||||||||
\(606\) | −4.44308 | −0.180488 | ||||||||
\(607\) | 16.3675 | 0.664335 | 0.332168 | − | 0.943220i | \(-0.392220\pi\) | ||||
0.332168 | + | 0.943220i | \(0.392220\pi\) | |||||||
\(608\) | −1.99267 | −0.0808134 | ||||||||
\(609\) | −1.57405 | −0.0637839 | ||||||||
\(610\) | 8.99429 | 0.364168 | ||||||||
\(611\) | −20.6331 | −0.834725 | ||||||||
\(612\) | 13.8759 | 0.560901 | ||||||||
\(613\) | 24.0957 | 0.973218 | 0.486609 | − | 0.873620i | \(-0.338234\pi\) | ||||
0.486609 | + | 0.873620i | \(0.338234\pi\) | |||||||
\(614\) | −11.3220 | −0.456919 | ||||||||
\(615\) | 5.23125 | 0.210944 | ||||||||
\(616\) | −0.0308170 | −0.00124165 | ||||||||
\(617\) | 20.1151 | 0.809802 | 0.404901 | − | 0.914361i | \(-0.367306\pi\) | ||||
0.404901 | + | 0.914361i | \(0.367306\pi\) | |||||||
\(618\) | −9.27282 | −0.373008 | ||||||||
\(619\) | 15.6598 | 0.629419 | 0.314709 | − | 0.949188i | \(-0.398093\pi\) | ||||
0.314709 | + | 0.949188i | \(0.398093\pi\) | |||||||
\(620\) | 5.30879 | 0.213206 | ||||||||
\(621\) | −30.7742 | −1.23493 | ||||||||
\(622\) | 27.8624 | 1.11718 | ||||||||
\(623\) | −9.22104 | −0.369433 | ||||||||
\(624\) | 4.26649 | 0.170796 | ||||||||
\(625\) | −2.10623 | −0.0842490 | ||||||||
\(626\) | 2.64490 | 0.105712 | ||||||||
\(627\) | −0.0421208 | −0.00168214 | ||||||||
\(628\) | −5.26211 | −0.209981 | ||||||||
\(629\) | −37.0344 | −1.47666 | ||||||||
\(630\) | −3.66693 | −0.146094 | ||||||||
\(631\) | −6.11162 | −0.243300 | −0.121650 | − | 0.992573i | \(-0.538818\pi\) | ||||
−0.121650 | + | 0.992573i | \(0.538818\pi\) | |||||||
\(632\) | 7.94777 | 0.316145 | ||||||||
\(633\) | 14.7754 | 0.587271 | ||||||||
\(634\) | −21.6517 | −0.859901 | ||||||||
\(635\) | 2.03762 | 0.0808604 | ||||||||
\(636\) | −1.65120 | −0.0654742 | ||||||||
\(637\) | 6.22014 | 0.246451 | ||||||||
\(638\) | 0.0707196 | 0.00279982 | ||||||||
\(639\) | −3.96899 | −0.157011 | ||||||||
\(640\) | −1.44966 | −0.0573027 | ||||||||
\(641\) | 12.6500 | 0.499645 | 0.249823 | − | 0.968292i | \(-0.419628\pi\) | ||||
0.249823 | + | 0.968292i | \(0.419628\pi\) | |||||||
\(642\) | −0.579917 | −0.0228875 | ||||||||
\(643\) | 31.2782 | 1.23349 | 0.616747 | − | 0.787162i | \(-0.288450\pi\) | ||||
0.616747 | + | 0.787162i | \(0.288450\pi\) | |||||||
\(644\) | −8.11388 | −0.319732 | ||||||||
\(645\) | −5.37710 | −0.211723 | ||||||||
\(646\) | 10.9310 | 0.430074 | ||||||||
\(647\) | 29.2020 | 1.14805 | 0.574024 | − | 0.818839i | \(-0.305382\pi\) | ||||
0.574024 | + | 0.818839i | \(0.305382\pi\) | |||||||
\(648\) | −4.98703 | −0.195909 | ||||||||
\(649\) | −0.139928 | −0.00549266 | ||||||||
\(650\) | 18.0291 | 0.707158 | ||||||||
\(651\) | −2.51190 | −0.0984489 | ||||||||
\(652\) | 11.7413 | 0.459824 | ||||||||
\(653\) | −8.40767 | −0.329018 | −0.164509 | − | 0.986376i | \(-0.552604\pi\) | ||||
−0.164509 | + | 0.986376i | \(0.552604\pi\) | |||||||
\(654\) | 12.0615 | 0.471641 | ||||||||
\(655\) | 20.2541 | 0.791391 | ||||||||
\(656\) | 5.26102 | 0.205408 | ||||||||
\(657\) | 22.6188 | 0.882444 | ||||||||
\(658\) | −3.31714 | −0.129316 | ||||||||
\(659\) | 6.67436 | 0.259996 | 0.129998 | − | 0.991514i | \(-0.458503\pi\) | ||||
0.129998 | + | 0.991514i | \(0.458503\pi\) | |||||||
\(660\) | −0.0306427 | −0.00119276 | ||||||||
\(661\) | −10.8115 | −0.420520 | −0.210260 | − | 0.977646i | \(-0.567431\pi\) | ||||
−0.210260 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(662\) | −8.21795 | −0.319400 | ||||||||
\(663\) | −23.4043 | −0.908947 | ||||||||
\(664\) | 3.11054 | 0.120712 | ||||||||
\(665\) | −2.88868 | −0.112018 | ||||||||
\(666\) | 17.0773 | 0.661732 | ||||||||
\(667\) | 18.6199 | 0.720966 | ||||||||
\(668\) | −9.95291 | −0.385090 | ||||||||
\(669\) | −11.3856 | −0.440192 | ||||||||
\(670\) | 0.922317 | 0.0356322 | ||||||||
\(671\) | 0.191202 | 0.00738128 | ||||||||
\(672\) | 0.685916 | 0.0264598 | ||||||||
\(673\) | −21.6068 | −0.832880 | −0.416440 | − | 0.909163i | \(-0.636722\pi\) | ||||
−0.416440 | + | 0.909163i | \(0.636722\pi\) | |||||||
\(674\) | −0.122451 | −0.00471664 | ||||||||
\(675\) | 10.9934 | 0.423135 | ||||||||
\(676\) | 25.6902 | 0.988084 | ||||||||
\(677\) | 29.8146 | 1.14587 | 0.572934 | − | 0.819602i | \(-0.305805\pi\) | ||||
0.572934 | + | 0.819602i | \(0.305805\pi\) | |||||||
\(678\) | −9.01558 | −0.346241 | ||||||||
\(679\) | −18.0193 | −0.691518 | ||||||||
\(680\) | 7.95223 | 0.304954 | ||||||||
\(681\) | 1.72667 | 0.0661663 | ||||||||
\(682\) | 0.112855 | 0.00432145 | ||||||||
\(683\) | −3.13287 | −0.119876 | −0.0599380 | − | 0.998202i | \(-0.519090\pi\) | ||||
−0.0599380 | + | 0.998202i | \(0.519090\pi\) | |||||||
\(684\) | −5.04049 | −0.192728 | ||||||||
\(685\) | 3.08015 | 0.117686 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 6.50452 | 0.248163 | ||||||||
\(688\) | −5.40770 | −0.206167 | ||||||||
\(689\) | −14.9737 | −0.570451 | ||||||||
\(690\) | −8.06798 | −0.307143 | ||||||||
\(691\) | 17.5682 | 0.668324 | 0.334162 | − | 0.942516i | \(-0.391547\pi\) | ||||
0.334162 | + | 0.942516i | \(0.391547\pi\) | |||||||
\(692\) | 15.1987 | 0.577767 | ||||||||
\(693\) | −0.0779523 | −0.00296116 | ||||||||
\(694\) | −15.9204 | −0.604329 | ||||||||
\(695\) | −18.6212 | −0.706342 | ||||||||
\(696\) | −1.57405 | −0.0596644 | ||||||||
\(697\) | −28.8598 | −1.09314 | ||||||||
\(698\) | 15.4343 | 0.584198 | ||||||||
\(699\) | 4.58136 | 0.173283 | ||||||||
\(700\) | 2.89850 | 0.109553 | ||||||||
\(701\) | 16.6710 | 0.629654 | 0.314827 | − | 0.949149i | \(-0.398053\pi\) | ||||
0.314827 | + | 0.949149i | \(0.398053\pi\) | |||||||
\(702\) | 23.5917 | 0.890410 | ||||||||
\(703\) | 13.4529 | 0.507386 | ||||||||
\(704\) | −0.0308170 | −0.00116146 | ||||||||
\(705\) | −3.29837 | −0.124224 | ||||||||
\(706\) | 12.2792 | 0.462133 | ||||||||
\(707\) | −6.47759 | −0.243615 | ||||||||
\(708\) | 3.11447 | 0.117049 | ||||||||
\(709\) | −3.03723 | −0.114065 | −0.0570327 | − | 0.998372i | \(-0.518164\pi\) | ||||
−0.0570327 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(710\) | −2.27461 | −0.0853647 | ||||||||
\(711\) | 20.1040 | 0.753960 | ||||||||
\(712\) | −9.22104 | −0.345573 | ||||||||
\(713\) | 29.7139 | 1.11279 | ||||||||
\(714\) | −3.76266 | −0.140814 | ||||||||
\(715\) | −0.277879 | −0.0103921 | ||||||||
\(716\) | 23.3175 | 0.871418 | ||||||||
\(717\) | −5.93911 | −0.221800 | ||||||||
\(718\) | −8.69460 | −0.324480 | ||||||||
\(719\) | 38.2013 | 1.42467 | 0.712333 | − | 0.701841i | \(-0.247638\pi\) | ||||
0.712333 | + | 0.701841i | \(0.247638\pi\) | |||||||
\(720\) | −3.66693 | −0.136659 | ||||||||
\(721\) | −13.5189 | −0.503470 | ||||||||
\(722\) | 15.0293 | 0.559332 | ||||||||
\(723\) | 20.7758 | 0.772662 | ||||||||
\(724\) | 10.4772 | 0.389384 | ||||||||
\(725\) | −6.65153 | −0.247032 | ||||||||
\(726\) | 7.54442 | 0.280000 | ||||||||
\(727\) | −11.0846 | −0.411104 | −0.205552 | − | 0.978646i | \(-0.565899\pi\) | ||||
−0.205552 | + | 0.978646i | \(0.565899\pi\) | |||||||
\(728\) | 6.22014 | 0.230534 | ||||||||
\(729\) | −4.81019 | −0.178155 | ||||||||
\(730\) | 12.9627 | 0.479773 | ||||||||
\(731\) | 29.6645 | 1.09718 | ||||||||
\(732\) | −4.25572 | −0.157296 | ||||||||
\(733\) | −4.23493 | −0.156421 | −0.0782103 | − | 0.996937i | \(-0.524921\pi\) | ||||
−0.0782103 | + | 0.996937i | \(0.524921\pi\) | |||||||
\(734\) | −19.3936 | −0.715831 | ||||||||
\(735\) | 0.994342 | 0.0366769 | ||||||||
\(736\) | −8.11388 | −0.299082 | ||||||||
\(737\) | 0.0196068 | 0.000722225 0 | ||||||||
\(738\) | 13.3079 | 0.489869 | ||||||||
\(739\) | −31.7481 | −1.16787 | −0.583937 | − | 0.811799i | \(-0.698489\pi\) | ||||
−0.583937 | + | 0.811799i | \(0.698489\pi\) | |||||||
\(740\) | 9.78693 | 0.359775 | ||||||||
\(741\) | 8.50171 | 0.312318 | ||||||||
\(742\) | −2.40729 | −0.0883743 | ||||||||
\(743\) | −28.5024 | −1.04565 | −0.522826 | − | 0.852439i | \(-0.675122\pi\) | ||||
−0.522826 | + | 0.852439i | \(0.675122\pi\) | |||||||
\(744\) | −2.51190 | −0.0920905 | ||||||||
\(745\) | 27.6195 | 1.01190 | ||||||||
\(746\) | 10.3958 | 0.380618 | ||||||||
\(747\) | 7.86817 | 0.287881 | ||||||||
\(748\) | 0.169050 | 0.00618108 | ||||||||
\(749\) | −0.845463 | −0.0308926 | ||||||||
\(750\) | 7.85381 | 0.286780 | ||||||||
\(751\) | −48.3090 | −1.76282 | −0.881411 | − | 0.472351i | \(-0.843406\pi\) | ||||
−0.881411 | + | 0.472351i | \(0.843406\pi\) | |||||||
\(752\) | −3.31714 | −0.120964 | ||||||||
\(753\) | −18.8295 | −0.686183 | ||||||||
\(754\) | −14.2741 | −0.519833 | ||||||||
\(755\) | −21.3289 | −0.776239 | ||||||||
\(756\) | 3.79278 | 0.137942 | ||||||||
\(757\) | −12.3826 | −0.450053 | −0.225027 | − | 0.974353i | \(-0.572247\pi\) | ||||
−0.225027 | + | 0.974353i | \(0.572247\pi\) | |||||||
\(758\) | −12.1040 | −0.439637 | ||||||||
\(759\) | −0.171510 | −0.00622543 | ||||||||
\(760\) | −2.88868 | −0.104784 | ||||||||
\(761\) | −5.64665 | −0.204691 | −0.102345 | − | 0.994749i | \(-0.532635\pi\) | ||||
−0.102345 | + | 0.994749i | \(0.532635\pi\) | |||||||
\(762\) | −0.964115 | −0.0349262 | ||||||||
\(763\) | 17.5845 | 0.636602 | ||||||||
\(764\) | 10.2549 | 0.371010 | ||||||||
\(765\) | 20.1153 | 0.727271 | ||||||||
\(766\) | 24.9672 | 0.902102 | ||||||||
\(767\) | 28.2432 | 1.01980 | ||||||||
\(768\) | 0.685916 | 0.0247509 | ||||||||
\(769\) | 14.5728 | 0.525510 | 0.262755 | − | 0.964863i | \(-0.415369\pi\) | ||||
0.262755 | + | 0.964863i | \(0.415369\pi\) | |||||||
\(770\) | −0.0446741 | −0.00160994 | ||||||||
\(771\) | −12.1040 | −0.435914 | ||||||||
\(772\) | 9.26826 | 0.333572 | ||||||||
\(773\) | 4.71945 | 0.169747 | 0.0848734 | − | 0.996392i | \(-0.472951\pi\) | ||||
0.0848734 | + | 0.996392i | \(0.472951\pi\) | |||||||
\(774\) | −13.6789 | −0.491677 | ||||||||
\(775\) | −10.6146 | −0.381288 | ||||||||
\(776\) | −18.0193 | −0.646855 | ||||||||
\(777\) | −4.63076 | −0.166128 | ||||||||
\(778\) | 7.59387 | 0.272253 | ||||||||
\(779\) | 10.4835 | 0.375609 | ||||||||
\(780\) | 6.18495 | 0.221457 | ||||||||
\(781\) | −0.0483541 | −0.00173025 | ||||||||
\(782\) | 44.5095 | 1.59166 | ||||||||
\(783\) | −8.70376 | −0.311047 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.62825 | −0.272264 | ||||||||
\(786\) | −9.58336 | −0.341827 | ||||||||
\(787\) | −27.2083 | −0.969871 | −0.484935 | − | 0.874550i | \(-0.661157\pi\) | ||||
−0.484935 | + | 0.874550i | \(0.661157\pi\) | |||||||
\(788\) | 10.5984 | 0.377554 | ||||||||
\(789\) | 21.6793 | 0.771803 | ||||||||
\(790\) | 11.5215 | 0.409918 | ||||||||
\(791\) | −13.1439 | −0.467342 | ||||||||
\(792\) | −0.0779523 | −0.00276991 | ||||||||
\(793\) | −38.5924 | −1.37046 | ||||||||
\(794\) | 27.8996 | 0.990119 | ||||||||
\(795\) | −2.39367 | −0.0848946 | ||||||||
\(796\) | 19.5234 | 0.691987 | ||||||||
\(797\) | 32.0017 | 1.13356 | 0.566779 | − | 0.823870i | \(-0.308189\pi\) | ||||
0.566779 | + | 0.823870i | \(0.308189\pi\) | |||||||
\(798\) | 1.36680 | 0.0483843 | ||||||||
\(799\) | 18.1965 | 0.643746 | ||||||||
\(800\) | 2.89850 | 0.102477 | ||||||||
\(801\) | −23.3248 | −0.824141 | ||||||||
\(802\) | 29.8254 | 1.05317 | ||||||||
\(803\) | 0.275564 | 0.00972445 | ||||||||
\(804\) | −0.436401 | −0.0153907 | ||||||||
\(805\) | −11.7623 | −0.414568 | ||||||||
\(806\) | −22.7788 | −0.802350 | ||||||||
\(807\) | 6.01512 | 0.211742 | ||||||||
\(808\) | −6.47759 | −0.227881 | ||||||||
\(809\) | −19.2720 | −0.677568 | −0.338784 | − | 0.940864i | \(-0.610016\pi\) | ||||
−0.338784 | + | 0.940864i | \(0.610016\pi\) | |||||||
\(810\) | −7.22948 | −0.254018 | ||||||||
\(811\) | 32.7314 | 1.14935 | 0.574677 | − | 0.818380i | \(-0.305128\pi\) | ||||
0.574677 | + | 0.818380i | \(0.305128\pi\) | |||||||
\(812\) | −2.29482 | −0.0805325 | ||||||||
\(813\) | 2.37879 | 0.0834278 | ||||||||
\(814\) | 0.208052 | 0.00729223 | ||||||||
\(815\) | 17.0208 | 0.596214 | ||||||||
\(816\) | −3.76266 | −0.131719 | ||||||||
\(817\) | −10.7758 | −0.376996 | ||||||||
\(818\) | 20.0637 | 0.701510 | ||||||||
\(819\) | 15.7340 | 0.549790 | ||||||||
\(820\) | 7.62667 | 0.266335 | ||||||||
\(821\) | 18.9537 | 0.661488 | 0.330744 | − | 0.943721i | \(-0.392700\pi\) | ||||
0.330744 | + | 0.943721i | \(0.392700\pi\) | |||||||
\(822\) | −1.45740 | −0.0508325 | ||||||||
\(823\) | 14.1095 | 0.491827 | 0.245914 | − | 0.969292i | \(-0.420912\pi\) | ||||
0.245914 | + | 0.969292i | \(0.420912\pi\) | |||||||
\(824\) | −13.5189 | −0.470953 | ||||||||
\(825\) | 0.0612681 | 0.00213308 | ||||||||
\(826\) | 4.54061 | 0.157988 | ||||||||
\(827\) | −50.3314 | −1.75020 | −0.875098 | − | 0.483946i | \(-0.839203\pi\) | ||||
−0.875098 | + | 0.483946i | \(0.839203\pi\) | |||||||
\(828\) | −20.5242 | −0.713266 | ||||||||
\(829\) | 31.8882 | 1.10752 | 0.553762 | − | 0.832675i | \(-0.313192\pi\) | ||||
0.553762 | + | 0.832675i | \(0.313192\pi\) | |||||||
\(830\) | 4.50921 | 0.156517 | ||||||||
\(831\) | −4.90502 | −0.170153 | ||||||||
\(832\) | 6.22014 | 0.215645 | ||||||||
\(833\) | −5.48560 | −0.190065 | ||||||||
\(834\) | 8.81076 | 0.305092 | ||||||||
\(835\) | −14.4283 | −0.499312 | ||||||||
\(836\) | −0.0614081 | −0.00212385 | ||||||||
\(837\) | −13.8896 | −0.480094 | ||||||||
\(838\) | −35.1960 | −1.21582 | ||||||||
\(839\) | 27.8915 | 0.962921 | 0.481460 | − | 0.876468i | \(-0.340107\pi\) | ||||
0.481460 | + | 0.876468i | \(0.340107\pi\) | |||||||
\(840\) | 0.994342 | 0.0343081 | ||||||||
\(841\) | −23.7338 | −0.818407 | ||||||||
\(842\) | 22.9700 | 0.791600 | ||||||||
\(843\) | −1.18612 | −0.0408521 | ||||||||
\(844\) | 21.5412 | 0.741478 | ||||||||
\(845\) | 37.2419 | 1.28116 | ||||||||
\(846\) | −8.39077 | −0.288481 | ||||||||
\(847\) | 10.9991 | 0.377932 | ||||||||
\(848\) | −2.40729 | −0.0826666 | ||||||||
\(849\) | −4.24077 | −0.145543 | ||||||||
\(850\) | −15.9000 | −0.545365 | ||||||||
\(851\) | 54.7785 | 1.87778 | ||||||||
\(852\) | 1.07625 | 0.0368717 | ||||||||
\(853\) | −1.47676 | −0.0505634 | −0.0252817 | − | 0.999680i | \(-0.508048\pi\) | ||||
−0.0252817 | + | 0.999680i | \(0.508048\pi\) | |||||||
\(854\) | −6.20443 | −0.212311 | ||||||||
\(855\) | −7.30698 | −0.249894 | ||||||||
\(856\) | −0.845463 | −0.0288973 | ||||||||
\(857\) | 51.1010 | 1.74558 | 0.872788 | − | 0.488100i | \(-0.162310\pi\) | ||||
0.872788 | + | 0.488100i | \(0.162310\pi\) | |||||||
\(858\) | 0.131481 | 0.00448868 | ||||||||
\(859\) | 36.8114 | 1.25599 | 0.627994 | − | 0.778218i | \(-0.283876\pi\) | ||||
0.627994 | + | 0.778218i | \(0.283876\pi\) | |||||||
\(860\) | −7.83931 | −0.267318 | ||||||||
\(861\) | −3.60862 | −0.122981 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −10.8980 | −0.370971 | −0.185486 | − | 0.982647i | \(-0.559386\pi\) | ||||
−0.185486 | + | 0.982647i | \(0.559386\pi\) | |||||||
\(864\) | 3.79278 | 0.129033 | ||||||||
\(865\) | 22.0328 | 0.749139 | ||||||||
\(866\) | 30.5862 | 1.03936 | ||||||||
\(867\) | 8.97986 | 0.304972 | ||||||||
\(868\) | −3.66210 | −0.124300 | ||||||||
\(869\) | 0.244927 | 0.00830857 | ||||||||
\(870\) | −2.28184 | −0.0773615 | ||||||||
\(871\) | −3.95745 | −0.134093 | ||||||||
\(872\) | 17.5845 | 0.595486 | ||||||||
\(873\) | −45.5802 | −1.54266 | ||||||||
\(874\) | −16.1683 | −0.546900 | ||||||||
\(875\) | 11.4501 | 0.387084 | ||||||||
\(876\) | −6.13342 | −0.207229 | ||||||||
\(877\) | −21.8750 | −0.738666 | −0.369333 | − | 0.929297i | \(-0.620414\pi\) | ||||
−0.369333 | + | 0.929297i | \(0.620414\pi\) | |||||||
\(878\) | −21.7019 | −0.732405 | ||||||||
\(879\) | −8.71255 | −0.293867 | ||||||||
\(880\) | −0.0446741 | −0.00150596 | ||||||||
\(881\) | −39.1598 | −1.31933 | −0.659663 | − | 0.751561i | \(-0.729301\pi\) | ||||
−0.659663 | + | 0.751561i | \(0.729301\pi\) | |||||||
\(882\) | 2.52952 | 0.0851734 | ||||||||
\(883\) | 24.2995 | 0.817742 | 0.408871 | − | 0.912592i | \(-0.365923\pi\) | ||||
0.408871 | + | 0.912592i | \(0.365923\pi\) | |||||||
\(884\) | −34.1212 | −1.14762 | ||||||||
\(885\) | 4.51491 | 0.151767 | ||||||||
\(886\) | −18.8299 | −0.632602 | ||||||||
\(887\) | 36.8751 | 1.23814 | 0.619072 | − | 0.785334i | \(-0.287509\pi\) | ||||
0.619072 | + | 0.785334i | \(0.287509\pi\) | |||||||
\(888\) | −4.63076 | −0.155398 | ||||||||
\(889\) | −1.40559 | −0.0471419 | ||||||||
\(890\) | −13.3673 | −0.448074 | ||||||||
\(891\) | −0.153685 | −0.00514866 | ||||||||
\(892\) | −16.5991 | −0.555779 | ||||||||
\(893\) | −6.60996 | −0.221194 | ||||||||
\(894\) | −13.0684 | −0.437071 | ||||||||
\(895\) | 33.8024 | 1.12989 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 34.6178 | 1.15586 | ||||||||
\(898\) | −14.2002 | −0.473867 | ||||||||
\(899\) | 8.40388 | 0.280285 | ||||||||
\(900\) | 7.33181 | 0.244394 | ||||||||
\(901\) | 13.2054 | 0.439936 | ||||||||
\(902\) | 0.162129 | 0.00539831 | ||||||||
\(903\) | 3.70923 | 0.123435 | ||||||||
\(904\) | −13.1439 | −0.437158 | ||||||||
\(905\) | 15.1884 | 0.504880 | ||||||||
\(906\) | 10.0919 | 0.335282 | ||||||||
\(907\) | 10.8381 | 0.359874 | 0.179937 | − | 0.983678i | \(-0.442411\pi\) | ||||
0.179937 | + | 0.983678i | \(0.442411\pi\) | |||||||
\(908\) | 2.51733 | 0.0835404 | ||||||||
\(909\) | −16.3852 | −0.543463 | ||||||||
\(910\) | 9.01707 | 0.298913 | ||||||||
\(911\) | −27.6501 | −0.916087 | −0.458044 | − | 0.888930i | \(-0.651450\pi\) | ||||
−0.458044 | + | 0.888930i | \(0.651450\pi\) | |||||||
\(912\) | 1.36680 | 0.0452594 | ||||||||
\(913\) | 0.0958576 | 0.00317242 | ||||||||
\(914\) | 6.48130 | 0.214382 | ||||||||
\(915\) | −6.16932 | −0.203952 | ||||||||
\(916\) | 9.48297 | 0.313326 | ||||||||
\(917\) | −13.9716 | −0.461384 | ||||||||
\(918\) | −20.8057 | −0.686690 | ||||||||
\(919\) | 20.4983 | 0.676177 | 0.338088 | − | 0.941114i | \(-0.390220\pi\) | ||||
0.338088 | + | 0.941114i | \(0.390220\pi\) | |||||||
\(920\) | −11.7623 | −0.387793 | ||||||||
\(921\) | 7.76594 | 0.255896 | ||||||||
\(922\) | 36.2829 | 1.19491 | ||||||||
\(923\) | 9.75984 | 0.321249 | ||||||||
\(924\) | 0.0211379 | 0.000695386 0 | ||||||||
\(925\) | −19.5684 | −0.643404 | ||||||||
\(926\) | −21.2718 | −0.699035 | ||||||||
\(927\) | −34.1963 | −1.12315 | ||||||||
\(928\) | −2.29482 | −0.0753312 | ||||||||
\(929\) | 12.9612 | 0.425243 | 0.212621 | − | 0.977135i | \(-0.431800\pi\) | ||||
0.212621 | + | 0.977135i | \(0.431800\pi\) | |||||||
\(930\) | −3.64138 | −0.119406 | ||||||||
\(931\) | 1.99267 | 0.0653071 | ||||||||
\(932\) | 6.67919 | 0.218784 | ||||||||
\(933\) | −19.1113 | −0.625675 | ||||||||
\(934\) | −31.3240 | −1.02495 | ||||||||
\(935\) | 0.245064 | 0.00801445 | ||||||||
\(936\) | 15.7340 | 0.514281 | ||||||||
\(937\) | −33.4423 | −1.09251 | −0.546256 | − | 0.837618i | \(-0.683947\pi\) | ||||
−0.546256 | + | 0.837618i | \(0.683947\pi\) | |||||||
\(938\) | −0.636232 | −0.0207737 | ||||||||
\(939\) | −1.81418 | −0.0592035 | ||||||||
\(940\) | −4.80871 | −0.156843 | ||||||||
\(941\) | −11.1379 | −0.363084 | −0.181542 | − | 0.983383i | \(-0.558109\pi\) | ||||
−0.181542 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(942\) | 3.60937 | 0.117600 | ||||||||
\(943\) | 42.6873 | 1.39009 | ||||||||
\(944\) | 4.54061 | 0.147784 | ||||||||
\(945\) | 5.49823 | 0.178858 | ||||||||
\(946\) | −0.166649 | −0.00541824 | ||||||||
\(947\) | −34.2659 | −1.11349 | −0.556745 | − | 0.830683i | \(-0.687950\pi\) | ||||
−0.556745 | + | 0.830683i | \(0.687950\pi\) | |||||||
\(948\) | −5.45150 | −0.177056 | ||||||||
\(949\) | −55.6202 | −1.80551 | ||||||||
\(950\) | 5.77574 | 0.187390 | ||||||||
\(951\) | 14.8513 | 0.481585 | ||||||||
\(952\) | −5.48560 | −0.177789 | ||||||||
\(953\) | 37.6925 | 1.22098 | 0.610490 | − | 0.792024i | \(-0.290973\pi\) | ||||
0.610490 | + | 0.792024i | \(0.290973\pi\) | |||||||
\(954\) | −6.08928 | −0.197148 | ||||||||
\(955\) | 14.8661 | 0.481056 | ||||||||
\(956\) | −8.65865 | −0.280041 | ||||||||
\(957\) | −0.0485077 | −0.00156803 | ||||||||
\(958\) | −13.2576 | −0.428334 | ||||||||
\(959\) | −2.12475 | −0.0686116 | ||||||||
\(960\) | 0.994342 | 0.0320922 | ||||||||
\(961\) | −17.5890 | −0.567387 | ||||||||
\(962\) | −41.9935 | −1.35392 | ||||||||
\(963\) | −2.13862 | −0.0689159 | ||||||||
\(964\) | 30.2892 | 0.975549 | ||||||||
\(965\) | 13.4358 | 0.432513 | ||||||||
\(966\) | 5.56544 | 0.179065 | ||||||||
\(967\) | −24.3424 | −0.782798 | −0.391399 | − | 0.920221i | \(-0.628009\pi\) | ||||
−0.391399 | + | 0.920221i | \(0.628009\pi\) | |||||||
\(968\) | 10.9991 | 0.353523 | ||||||||
\(969\) | −7.49773 | −0.240862 | ||||||||
\(970\) | −26.1218 | −0.838720 | ||||||||
\(971\) | −44.0029 | −1.41212 | −0.706061 | − | 0.708151i | \(-0.749529\pi\) | ||||
−0.706061 | + | 0.708151i | \(0.749529\pi\) | |||||||
\(972\) | 14.7990 | 0.474679 | ||||||||
\(973\) | 12.8453 | 0.411800 | ||||||||
\(974\) | 7.13345 | 0.228570 | ||||||||
\(975\) | −12.3664 | −0.396042 | ||||||||
\(976\) | −6.20443 | −0.198599 | ||||||||
\(977\) | −7.29605 | −0.233421 | −0.116711 | − | 0.993166i | \(-0.537235\pi\) | ||||
−0.116711 | + | 0.993166i | \(0.537235\pi\) | |||||||
\(978\) | −8.05354 | −0.257524 | ||||||||
\(979\) | −0.284165 | −0.00908196 | ||||||||
\(980\) | 1.44966 | 0.0463076 | ||||||||
\(981\) | 44.4803 | 1.42015 | ||||||||
\(982\) | −2.55846 | −0.0816438 | ||||||||
\(983\) | −33.3403 | −1.06339 | −0.531695 | − | 0.846936i | \(-0.678445\pi\) | ||||
−0.531695 | + | 0.846936i | \(0.678445\pi\) | |||||||
\(984\) | −3.60862 | −0.115038 | ||||||||
\(985\) | 15.3641 | 0.489541 | ||||||||
\(986\) | 12.5885 | 0.400898 | ||||||||
\(987\) | 2.27528 | 0.0724229 | ||||||||
\(988\) | 12.3947 | 0.394327 | ||||||||
\(989\) | −43.8775 | −1.39522 | ||||||||
\(990\) | −0.113004 | −0.00359150 | ||||||||
\(991\) | 18.3156 | 0.581815 | 0.290907 | − | 0.956751i | \(-0.406043\pi\) | ||||
0.290907 | + | 0.956751i | \(0.406043\pi\) | |||||||
\(992\) | −3.66210 | −0.116272 | ||||||||
\(993\) | 5.63682 | 0.178879 | ||||||||
\(994\) | 1.56907 | 0.0497679 | ||||||||
\(995\) | 28.3022 | 0.897239 | ||||||||
\(996\) | −2.13357 | −0.0676046 | ||||||||
\(997\) | −42.8296 | −1.35643 | −0.678214 | − | 0.734864i | \(-0.737246\pi\) | ||||
−0.678214 | + | 0.734864i | \(0.737246\pi\) | |||||||
\(998\) | −25.5539 | −0.808894 | ||||||||
\(999\) | −25.6059 | −0.810134 |
(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 | 6034.2.a.n.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.14 | ✓ | 24 | 1.1 | even | 1 | trivial |