Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(1,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, 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("418.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.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: | \(3.33774680449\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.1 |
$q$-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 | ||||||||
\(3\) | −3.30278 | −1.90686 | −0.953429 | − | 0.301617i | \(-0.902474\pi\) | ||||
−0.953429 | + | 0.301617i | \(0.902474\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.30278 | 0.582619 | 0.291309 | − | 0.956629i | \(-0.405909\pi\) | ||||
0.291309 | + | 0.956629i | \(0.405909\pi\) | |||||||
\(6\) | 3.30278 | 1.34835 | ||||||||
\(7\) | −2.30278 | −0.870367 | −0.435184 | − | 0.900342i | \(-0.643317\pi\) | ||||
−0.435184 | + | 0.900342i | \(0.643317\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | −1.30278 | −0.411974 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.30278 | −0.953429 | ||||||||
\(13\) | 0.302776 | 0.0839749 | 0.0419874 | − | 0.999118i | \(-0.486631\pi\) | ||||
0.0419874 | + | 0.999118i | \(0.486631\pi\) | |||||||
\(14\) | 2.30278 | 0.615443 | ||||||||
\(15\) | −4.30278 | −1.11097 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.60555 | 0.631939 | 0.315970 | − | 0.948769i | \(-0.397670\pi\) | ||||
0.315970 | + | 0.948769i | \(0.397670\pi\) | |||||||
\(18\) | −7.90833 | −1.86401 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.30278 | 0.291309 | ||||||||
\(21\) | 7.60555 | 1.65967 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −8.60555 | −1.79438 | −0.897191 | − | 0.441643i | \(-0.854396\pi\) | ||||
−0.897191 | + | 0.441643i | \(0.854396\pi\) | |||||||
\(24\) | 3.30278 | 0.674176 | ||||||||
\(25\) | −3.30278 | −0.660555 | ||||||||
\(26\) | −0.302776 | −0.0593792 | ||||||||
\(27\) | −16.2111 | −3.11983 | ||||||||
\(28\) | −2.30278 | −0.435184 | ||||||||
\(29\) | −4.69722 | −0.872253 | −0.436126 | − | 0.899885i | \(-0.643650\pi\) | ||||
−0.436126 | + | 0.899885i | \(0.643650\pi\) | |||||||
\(30\) | 4.30278 | 0.785576 | ||||||||
\(31\) | 0.302776 | 0.0543801 | 0.0271901 | − | 0.999630i | \(-0.491344\pi\) | ||||
0.0271901 | + | 0.999630i | \(0.491344\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.30278 | −0.574939 | ||||||||
\(34\) | −2.60555 | −0.446848 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 7.90833 | 1.31805 | ||||||||
\(37\) | −9.21110 | −1.51430 | −0.757148 | − | 0.653243i | \(-0.773408\pi\) | ||||
−0.757148 | + | 0.653243i | \(0.773408\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.30278 | −0.205987 | ||||||||
\(41\) | −6.90833 | −1.07890 | −0.539450 | − | 0.842018i | \(-0.681368\pi\) | ||||
−0.539450 | + | 0.842018i | \(0.681368\pi\) | |||||||
\(42\) | −7.60555 | −1.17356 | ||||||||
\(43\) | 11.9083 | 1.81600 | 0.908001 | − | 0.418967i | \(-0.137608\pi\) | ||||
0.908001 | + | 0.418967i | \(0.137608\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 10.3028 | 1.53585 | ||||||||
\(46\) | 8.60555 | 1.26882 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | −3.30278 | −0.476715 | ||||||||
\(49\) | −1.69722 | −0.242461 | ||||||||
\(50\) | 3.30278 | 0.467083 | ||||||||
\(51\) | −8.60555 | −1.20502 | ||||||||
\(52\) | 0.302776 | 0.0419874 | ||||||||
\(53\) | −3.39445 | −0.466263 | −0.233132 | − | 0.972445i | \(-0.574897\pi\) | ||||
−0.233132 | + | 0.972445i | \(0.574897\pi\) | |||||||
\(54\) | 16.2111 | 2.20605 | ||||||||
\(55\) | 1.30278 | 0.175666 | ||||||||
\(56\) | 2.30278 | 0.307721 | ||||||||
\(57\) | −3.30278 | −0.437463 | ||||||||
\(58\) | 4.69722 | 0.616776 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −4.30278 | −0.555486 | ||||||||
\(61\) | −3.21110 | −0.411140 | −0.205570 | − | 0.978642i | \(-0.565905\pi\) | ||||
−0.205570 | + | 0.978642i | \(0.565905\pi\) | |||||||
\(62\) | −0.302776 | −0.0384525 | ||||||||
\(63\) | −18.2111 | −2.29438 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.394449 | 0.0489253 | ||||||||
\(66\) | 3.30278 | 0.406544 | ||||||||
\(67\) | 11.5139 | 1.40664 | 0.703322 | − | 0.710871i | \(-0.251699\pi\) | ||||
0.703322 | + | 0.710871i | \(0.251699\pi\) | |||||||
\(68\) | 2.60555 | 0.315970 | ||||||||
\(69\) | 28.4222 | 3.42163 | ||||||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | −13.3028 | −1.57875 | −0.789375 | − | 0.613912i | \(-0.789595\pi\) | ||||
−0.789375 | + | 0.613912i | \(0.789595\pi\) | |||||||
\(72\) | −7.90833 | −0.932005 | ||||||||
\(73\) | 4.60555 | 0.539039 | 0.269520 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269520 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(74\) | 9.21110 | 1.07077 | ||||||||
\(75\) | 10.9083 | 1.25959 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −2.30278 | −0.262426 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.81665 | −0.654425 | −0.327212 | − | 0.944951i | \(-0.606109\pi\) | ||||
−0.327212 | + | 0.944951i | \(0.606109\pi\) | |||||||
\(80\) | 1.30278 | 0.145655 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 6.90833 | 0.762897 | ||||||||
\(83\) | 10.6972 | 1.17417 | 0.587086 | − | 0.809524i | \(-0.300275\pi\) | ||||
0.587086 | + | 0.809524i | \(0.300275\pi\) | |||||||
\(84\) | 7.60555 | 0.829834 | ||||||||
\(85\) | 3.39445 | 0.368180 | ||||||||
\(86\) | −11.9083 | −1.28411 | ||||||||
\(87\) | 15.5139 | 1.66326 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −2.60555 | −0.276188 | −0.138094 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138094 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(90\) | −10.3028 | −1.08601 | ||||||||
\(91\) | −0.697224 | −0.0730890 | ||||||||
\(92\) | −8.60555 | −0.897191 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 1.30278 | 0.133662 | ||||||||
\(96\) | 3.30278 | 0.337088 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 1.69722 | 0.171446 | ||||||||
\(99\) | 7.90833 | 0.794817 | ||||||||
\(100\) | −3.30278 | −0.330278 | ||||||||
\(101\) | −13.8167 | −1.37481 | −0.687404 | − | 0.726275i | \(-0.741250\pi\) | ||||
−0.687404 | + | 0.726275i | \(0.741250\pi\) | |||||||
\(102\) | 8.60555 | 0.852077 | ||||||||
\(103\) | −5.30278 | −0.522498 | −0.261249 | − | 0.965271i | \(-0.584134\pi\) | ||||
−0.261249 | + | 0.965271i | \(0.584134\pi\) | |||||||
\(104\) | −0.302776 | −0.0296896 | ||||||||
\(105\) | 9.90833 | 0.966954 | ||||||||
\(106\) | 3.39445 | 0.329698 | ||||||||
\(107\) | −11.2111 | −1.08382 | −0.541909 | − | 0.840437i | \(-0.682298\pi\) | ||||
−0.541909 | + | 0.840437i | \(0.682298\pi\) | |||||||
\(108\) | −16.2111 | −1.55991 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −1.30278 | −0.124215 | ||||||||
\(111\) | 30.4222 | 2.88755 | ||||||||
\(112\) | −2.30278 | −0.217592 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 3.30278 | 0.309333 | ||||||||
\(115\) | −11.2111 | −1.04544 | ||||||||
\(116\) | −4.69722 | −0.436126 | ||||||||
\(117\) | 2.39445 | 0.221367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | 4.30278 | 0.392788 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.21110 | 0.290720 | ||||||||
\(123\) | 22.8167 | 2.05731 | ||||||||
\(124\) | 0.302776 | 0.0271901 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | 18.2111 | 1.62237 | ||||||||
\(127\) | −12.6056 | −1.11856 | −0.559281 | − | 0.828978i | \(-0.688923\pi\) | ||||
−0.559281 | + | 0.828978i | \(0.688923\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −39.3305 | −3.46286 | ||||||||
\(130\) | −0.394449 | −0.0345954 | ||||||||
\(131\) | −6.11943 | −0.534657 | −0.267329 | − | 0.963605i | \(-0.586141\pi\) | ||||
−0.267329 | + | 0.963605i | \(0.586141\pi\) | |||||||
\(132\) | −3.30278 | −0.287470 | ||||||||
\(133\) | −2.30278 | −0.199676 | ||||||||
\(134\) | −11.5139 | −0.994648 | ||||||||
\(135\) | −21.1194 | −1.81767 | ||||||||
\(136\) | −2.60555 | −0.223424 | ||||||||
\(137\) | −21.5139 | −1.83805 | −0.919027 | − | 0.394194i | \(-0.871024\pi\) | ||||
−0.919027 | + | 0.394194i | \(0.871024\pi\) | |||||||
\(138\) | −28.4222 | −2.41946 | ||||||||
\(139\) | −2.69722 | −0.228776 | −0.114388 | − | 0.993436i | \(-0.536491\pi\) | ||||
−0.114388 | + | 0.993436i | \(0.536491\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 19.8167 | 1.66886 | ||||||||
\(142\) | 13.3028 | 1.11634 | ||||||||
\(143\) | 0.302776 | 0.0253194 | ||||||||
\(144\) | 7.90833 | 0.659027 | ||||||||
\(145\) | −6.11943 | −0.508191 | ||||||||
\(146\) | −4.60555 | −0.381158 | ||||||||
\(147\) | 5.60555 | 0.462338 | ||||||||
\(148\) | −9.21110 | −0.757148 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −10.9083 | −0.890661 | ||||||||
\(151\) | 12.4222 | 1.01090 | 0.505452 | − | 0.862855i | \(-0.331326\pi\) | ||||
0.505452 | + | 0.862855i | \(0.331326\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 20.6056 | 1.66586 | ||||||||
\(154\) | 2.30278 | 0.185563 | ||||||||
\(155\) | 0.394449 | 0.0316829 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 11.9083 | 0.950388 | 0.475194 | − | 0.879881i | \(-0.342378\pi\) | ||||
0.475194 | + | 0.879881i | \(0.342378\pi\) | |||||||
\(158\) | 5.81665 | 0.462748 | ||||||||
\(159\) | 11.2111 | 0.889098 | ||||||||
\(160\) | −1.30278 | −0.102993 | ||||||||
\(161\) | 19.8167 | 1.56177 | ||||||||
\(162\) | −29.8167 | −2.34262 | ||||||||
\(163\) | −18.6056 | −1.45730 | −0.728650 | − | 0.684887i | \(-0.759852\pi\) | ||||
−0.728650 | + | 0.684887i | \(0.759852\pi\) | |||||||
\(164\) | −6.90833 | −0.539450 | ||||||||
\(165\) | −4.30278 | −0.334971 | ||||||||
\(166\) | −10.6972 | −0.830266 | ||||||||
\(167\) | 16.4222 | 1.27079 | 0.635394 | − | 0.772188i | \(-0.280838\pi\) | ||||
0.635394 | + | 0.772188i | \(0.280838\pi\) | |||||||
\(168\) | −7.60555 | −0.586781 | ||||||||
\(169\) | −12.9083 | −0.992948 | ||||||||
\(170\) | −3.39445 | −0.260342 | ||||||||
\(171\) | 7.90833 | 0.604765 | ||||||||
\(172\) | 11.9083 | 0.908001 | ||||||||
\(173\) | 20.3305 | 1.54570 | 0.772851 | − | 0.634588i | \(-0.218830\pi\) | ||||
0.772851 | + | 0.634588i | \(0.218830\pi\) | |||||||
\(174\) | −15.5139 | −1.17610 | ||||||||
\(175\) | 7.60555 | 0.574926 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.60555 | 0.195294 | ||||||||
\(179\) | 12.1194 | 0.905849 | 0.452924 | − | 0.891549i | \(-0.350381\pi\) | ||||
0.452924 | + | 0.891549i | \(0.350381\pi\) | |||||||
\(180\) | 10.3028 | 0.767924 | ||||||||
\(181\) | 21.0278 | 1.56298 | 0.781490 | − | 0.623917i | \(-0.214460\pi\) | ||||
0.781490 | + | 0.623917i | \(0.214460\pi\) | |||||||
\(182\) | 0.697224 | 0.0516817 | ||||||||
\(183\) | 10.6056 | 0.783985 | ||||||||
\(184\) | 8.60555 | 0.634410 | ||||||||
\(185\) | −12.0000 | −0.882258 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 2.60555 | 0.190537 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 37.3305 | 2.71540 | ||||||||
\(190\) | −1.30278 | −0.0945133 | ||||||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | −3.30278 | −0.238357 | ||||||||
\(193\) | 7.72498 | 0.556056 | 0.278028 | − | 0.960573i | \(-0.410319\pi\) | ||||
0.278028 | + | 0.960573i | \(0.410319\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | −1.30278 | −0.0932937 | ||||||||
\(196\) | −1.69722 | −0.121230 | ||||||||
\(197\) | −21.6333 | −1.54131 | −0.770655 | − | 0.637253i | \(-0.780071\pi\) | ||||
−0.770655 | + | 0.637253i | \(0.780071\pi\) | |||||||
\(198\) | −7.90833 | −0.562020 | ||||||||
\(199\) | −23.8167 | −1.68832 | −0.844159 | − | 0.536093i | \(-0.819900\pi\) | ||||
−0.844159 | + | 0.536093i | \(0.819900\pi\) | |||||||
\(200\) | 3.30278 | 0.233542 | ||||||||
\(201\) | −38.0278 | −2.68227 | ||||||||
\(202\) | 13.8167 | 0.972136 | ||||||||
\(203\) | 10.8167 | 0.759180 | ||||||||
\(204\) | −8.60555 | −0.602509 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 5.30278 | 0.369462 | ||||||||
\(207\) | −68.0555 | −4.73019 | ||||||||
\(208\) | 0.302776 | 0.0209937 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | −9.90833 | −0.683740 | ||||||||
\(211\) | 17.3944 | 1.19748 | 0.598742 | − | 0.800942i | \(-0.295668\pi\) | ||||
0.598742 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(212\) | −3.39445 | −0.233132 | ||||||||
\(213\) | 43.9361 | 3.01045 | ||||||||
\(214\) | 11.2111 | 0.766375 | ||||||||
\(215\) | 15.5139 | 1.05804 | ||||||||
\(216\) | 16.2111 | 1.10303 | ||||||||
\(217\) | −0.697224 | −0.0473307 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −15.2111 | −1.02787 | ||||||||
\(220\) | 1.30278 | 0.0878331 | ||||||||
\(221\) | 0.788897 | 0.0530670 | ||||||||
\(222\) | −30.4222 | −2.04180 | ||||||||
\(223\) | −10.7889 | −0.722478 | −0.361239 | − | 0.932473i | \(-0.617646\pi\) | ||||
−0.361239 | + | 0.932473i | \(0.617646\pi\) | |||||||
\(224\) | 2.30278 | 0.153861 | ||||||||
\(225\) | −26.1194 | −1.74130 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8167 | −1.31528 | −0.657639 | − | 0.753333i | \(-0.728445\pi\) | ||||
−0.657639 | + | 0.753333i | \(0.728445\pi\) | |||||||
\(228\) | −3.30278 | −0.218732 | ||||||||
\(229\) | 1.09167 | 0.0721398 | 0.0360699 | − | 0.999349i | \(-0.488516\pi\) | ||||
0.0360699 | + | 0.999349i | \(0.488516\pi\) | |||||||
\(230\) | 11.2111 | 0.739238 | ||||||||
\(231\) | 7.60555 | 0.500409 | ||||||||
\(232\) | 4.69722 | 0.308388 | ||||||||
\(233\) | −5.21110 | −0.341391 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(234\) | −2.39445 | −0.156530 | ||||||||
\(235\) | −7.81665 | −0.509902 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.2111 | 1.24790 | ||||||||
\(238\) | 6.00000 | 0.388922 | ||||||||
\(239\) | 22.9361 | 1.48361 | 0.741806 | − | 0.670615i | \(-0.233970\pi\) | ||||
0.741806 | + | 0.670615i | \(0.233970\pi\) | |||||||
\(240\) | −4.30278 | −0.277743 | ||||||||
\(241\) | 23.9083 | 1.54007 | 0.770035 | − | 0.638001i | \(-0.220239\pi\) | ||||
0.770035 | + | 0.638001i | \(0.220239\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −49.8444 | −3.19752 | ||||||||
\(244\) | −3.21110 | −0.205570 | ||||||||
\(245\) | −2.21110 | −0.141262 | ||||||||
\(246\) | −22.8167 | −1.45474 | ||||||||
\(247\) | 0.302776 | 0.0192652 | ||||||||
\(248\) | −0.302776 | −0.0192263 | ||||||||
\(249\) | −35.3305 | −2.23898 | ||||||||
\(250\) | 10.8167 | 0.684105 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | −18.2111 | −1.14719 | ||||||||
\(253\) | −8.60555 | −0.541026 | ||||||||
\(254\) | 12.6056 | 0.790943 | ||||||||
\(255\) | −11.2111 | −0.702066 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.60555 | 0.162530 | 0.0812649 | − | 0.996693i | \(-0.474104\pi\) | ||||
0.0812649 | + | 0.996693i | \(0.474104\pi\) | |||||||
\(258\) | 39.3305 | 2.44861 | ||||||||
\(259\) | 21.2111 | 1.31799 | ||||||||
\(260\) | 0.394449 | 0.0244627 | ||||||||
\(261\) | −37.1472 | −2.29935 | ||||||||
\(262\) | 6.11943 | 0.378060 | ||||||||
\(263\) | −16.6972 | −1.02959 | −0.514797 | − | 0.857312i | \(-0.672133\pi\) | ||||
−0.514797 | + | 0.857312i | \(0.672133\pi\) | |||||||
\(264\) | 3.30278 | 0.203272 | ||||||||
\(265\) | −4.42221 | −0.271654 | ||||||||
\(266\) | 2.30278 | 0.141192 | ||||||||
\(267\) | 8.60555 | 0.526651 | ||||||||
\(268\) | 11.5139 | 0.703322 | ||||||||
\(269\) | 1.81665 | 0.110763 | 0.0553817 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553817 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(270\) | 21.1194 | 1.28529 | ||||||||
\(271\) | 11.5139 | 0.699418 | 0.349709 | − | 0.936858i | \(-0.386280\pi\) | ||||
0.349709 | + | 0.936858i | \(0.386280\pi\) | |||||||
\(272\) | 2.60555 | 0.157985 | ||||||||
\(273\) | 2.30278 | 0.139370 | ||||||||
\(274\) | 21.5139 | 1.29970 | ||||||||
\(275\) | −3.30278 | −0.199165 | ||||||||
\(276\) | 28.4222 | 1.71082 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 2.69722 | 0.161769 | ||||||||
\(279\) | 2.39445 | 0.143352 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −18.5139 | −1.10445 | −0.552223 | − | 0.833697i | \(-0.686220\pi\) | ||||
−0.552223 | + | 0.833697i | \(0.686220\pi\) | |||||||
\(282\) | −19.8167 | −1.18006 | ||||||||
\(283\) | 27.9361 | 1.66063 | 0.830314 | − | 0.557296i | \(-0.188161\pi\) | ||||
0.830314 | + | 0.557296i | \(0.188161\pi\) | |||||||
\(284\) | −13.3028 | −0.789375 | ||||||||
\(285\) | −4.30278 | −0.254874 | ||||||||
\(286\) | −0.302776 | −0.0179035 | ||||||||
\(287\) | 15.9083 | 0.939039 | ||||||||
\(288\) | −7.90833 | −0.466003 | ||||||||
\(289\) | −10.2111 | −0.600653 | ||||||||
\(290\) | 6.11943 | 0.359345 | ||||||||
\(291\) | −26.4222 | −1.54890 | ||||||||
\(292\) | 4.60555 | 0.269520 | ||||||||
\(293\) | 28.5416 | 1.66742 | 0.833710 | − | 0.552202i | \(-0.186212\pi\) | ||||
0.833710 | + | 0.552202i | \(0.186212\pi\) | |||||||
\(294\) | −5.60555 | −0.326922 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.21110 | 0.535384 | ||||||||
\(297\) | −16.2111 | −0.940664 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.60555 | −0.150683 | ||||||||
\(300\) | 10.9083 | 0.629793 | ||||||||
\(301\) | −27.4222 | −1.58059 | ||||||||
\(302\) | −12.4222 | −0.714818 | ||||||||
\(303\) | 45.6333 | 2.62157 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −4.18335 | −0.239538 | ||||||||
\(306\) | −20.6056 | −1.17794 | ||||||||
\(307\) | −23.8167 | −1.35929 | −0.679644 | − | 0.733542i | \(-0.737866\pi\) | ||||
−0.679644 | + | 0.733542i | \(0.737866\pi\) | |||||||
\(308\) | −2.30278 | −0.131213 | ||||||||
\(309\) | 17.5139 | 0.996330 | ||||||||
\(310\) | −0.394449 | −0.0224032 | ||||||||
\(311\) | 4.18335 | 0.237216 | 0.118608 | − | 0.992941i | \(-0.462157\pi\) | ||||
0.118608 | + | 0.992941i | \(0.462157\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −7.11943 | −0.402414 | −0.201207 | − | 0.979549i | \(-0.564486\pi\) | ||||
−0.201207 | + | 0.979549i | \(0.564486\pi\) | |||||||
\(314\) | −11.9083 | −0.672026 | ||||||||
\(315\) | −23.7250 | −1.33675 | ||||||||
\(316\) | −5.81665 | −0.327212 | ||||||||
\(317\) | 7.81665 | 0.439027 | 0.219514 | − | 0.975609i | \(-0.429553\pi\) | ||||
0.219514 | + | 0.975609i | \(0.429553\pi\) | |||||||
\(318\) | −11.2111 | −0.628687 | ||||||||
\(319\) | −4.69722 | −0.262994 | ||||||||
\(320\) | 1.30278 | 0.0728274 | ||||||||
\(321\) | 37.0278 | 2.06669 | ||||||||
\(322\) | −19.8167 | −1.10434 | ||||||||
\(323\) | 2.60555 | 0.144977 | ||||||||
\(324\) | 29.8167 | 1.65648 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 18.6056 | 1.03047 | ||||||||
\(327\) | −6.60555 | −0.365288 | ||||||||
\(328\) | 6.90833 | 0.381449 | ||||||||
\(329\) | 13.8167 | 0.761737 | ||||||||
\(330\) | 4.30278 | 0.236860 | ||||||||
\(331\) | −9.72498 | −0.534533 | −0.267267 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267267 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(332\) | 10.6972 | 0.587086 | ||||||||
\(333\) | −72.8444 | −3.99185 | ||||||||
\(334\) | −16.4222 | −0.898583 | ||||||||
\(335\) | 15.0000 | 0.819538 | ||||||||
\(336\) | 7.60555 | 0.414917 | ||||||||
\(337\) | −5.69722 | −0.310348 | −0.155174 | − | 0.987887i | \(-0.549594\pi\) | ||||
−0.155174 | + | 0.987887i | \(0.549594\pi\) | |||||||
\(338\) | 12.9083 | 0.702120 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.39445 | 0.184090 | ||||||||
\(341\) | 0.302776 | 0.0163962 | ||||||||
\(342\) | −7.90833 | −0.427633 | ||||||||
\(343\) | 20.0278 | 1.08140 | ||||||||
\(344\) | −11.9083 | −0.642054 | ||||||||
\(345\) | 37.0278 | 1.99351 | ||||||||
\(346\) | −20.3305 | −1.09298 | ||||||||
\(347\) | 17.2111 | 0.923940 | 0.461970 | − | 0.886895i | \(-0.347143\pi\) | ||||
0.461970 | + | 0.886895i | \(0.347143\pi\) | |||||||
\(348\) | 15.5139 | 0.831631 | ||||||||
\(349\) | 3.57779 | 0.191515 | 0.0957575 | − | 0.995405i | \(-0.469473\pi\) | ||||
0.0957575 | + | 0.995405i | \(0.469473\pi\) | |||||||
\(350\) | −7.60555 | −0.406534 | ||||||||
\(351\) | −4.90833 | −0.261987 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −0.788897 | −0.0419888 | −0.0209944 | − | 0.999780i | \(-0.506683\pi\) | ||||
−0.0209944 | + | 0.999780i | \(0.506683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.3305 | −0.919809 | ||||||||
\(356\) | −2.60555 | −0.138094 | ||||||||
\(357\) | 19.8167 | 1.04881 | ||||||||
\(358\) | −12.1194 | −0.640532 | ||||||||
\(359\) | −27.5139 | −1.45213 | −0.726063 | − | 0.687628i | \(-0.758652\pi\) | ||||
−0.726063 | + | 0.687628i | \(0.758652\pi\) | |||||||
\(360\) | −10.3028 | −0.543004 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −21.0278 | −1.10519 | ||||||||
\(363\) | −3.30278 | −0.173351 | ||||||||
\(364\) | −0.697224 | −0.0365445 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | −10.6056 | −0.554361 | ||||||||
\(367\) | 7.21110 | 0.376416 | 0.188208 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188208 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(368\) | −8.60555 | −0.448595 | ||||||||
\(369\) | −54.6333 | −2.84410 | ||||||||
\(370\) | 12.0000 | 0.623850 | ||||||||
\(371\) | 7.81665 | 0.405820 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | 17.9083 | 0.927258 | 0.463629 | − | 0.886029i | \(-0.346547\pi\) | ||||
0.463629 | + | 0.886029i | \(0.346547\pi\) | |||||||
\(374\) | −2.60555 | −0.134730 | ||||||||
\(375\) | 35.7250 | 1.84483 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −1.42221 | −0.0732473 | ||||||||
\(378\) | −37.3305 | −1.92008 | ||||||||
\(379\) | −31.5139 | −1.61876 | −0.809380 | − | 0.587286i | \(-0.800196\pi\) | ||||
−0.809380 | + | 0.587286i | \(0.800196\pi\) | |||||||
\(380\) | 1.30278 | 0.0668310 | ||||||||
\(381\) | 41.6333 | 2.13294 | ||||||||
\(382\) | 6.00000 | 0.306987 | ||||||||
\(383\) | 21.5139 | 1.09931 | 0.549654 | − | 0.835392i | \(-0.314760\pi\) | ||||
0.549654 | + | 0.835392i | \(0.314760\pi\) | |||||||
\(384\) | 3.30278 | 0.168544 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | −7.72498 | −0.393191 | ||||||||
\(387\) | 94.1749 | 4.78718 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | −19.5416 | −0.990800 | −0.495400 | − | 0.868665i | \(-0.664979\pi\) | ||||
−0.495400 | + | 0.868665i | \(0.664979\pi\) | |||||||
\(390\) | 1.30278 | 0.0659686 | ||||||||
\(391\) | −22.4222 | −1.13394 | ||||||||
\(392\) | 1.69722 | 0.0857228 | ||||||||
\(393\) | 20.2111 | 1.01952 | ||||||||
\(394\) | 21.6333 | 1.08987 | ||||||||
\(395\) | −7.57779 | −0.381280 | ||||||||
\(396\) | 7.90833 | 0.397408 | ||||||||
\(397\) | 35.7527 | 1.79438 | 0.897189 | − | 0.441646i | \(-0.145605\pi\) | ||||
0.897189 | + | 0.441646i | \(0.145605\pi\) | |||||||
\(398\) | 23.8167 | 1.19382 | ||||||||
\(399\) | 7.60555 | 0.380754 | ||||||||
\(400\) | −3.30278 | −0.165139 | ||||||||
\(401\) | 15.3944 | 0.768762 | 0.384381 | − | 0.923175i | \(-0.374415\pi\) | ||||
0.384381 | + | 0.923175i | \(0.374415\pi\) | |||||||
\(402\) | 38.0278 | 1.89665 | ||||||||
\(403\) | 0.0916731 | 0.00456656 | ||||||||
\(404\) | −13.8167 | −0.687404 | ||||||||
\(405\) | 38.8444 | 1.93019 | ||||||||
\(406\) | −10.8167 | −0.536822 | ||||||||
\(407\) | −9.21110 | −0.456577 | ||||||||
\(408\) | 8.60555 | 0.426038 | ||||||||
\(409\) | −38.1472 | −1.88626 | −0.943128 | − | 0.332428i | \(-0.892132\pi\) | ||||
−0.943128 | + | 0.332428i | \(0.892132\pi\) | |||||||
\(410\) | 9.00000 | 0.444478 | ||||||||
\(411\) | 71.0555 | 3.50491 | ||||||||
\(412\) | −5.30278 | −0.261249 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 68.0555 | 3.34475 | ||||||||
\(415\) | 13.9361 | 0.684095 | ||||||||
\(416\) | −0.302776 | −0.0148448 | ||||||||
\(417\) | 8.90833 | 0.436243 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | 23.2111 | 1.13394 | 0.566968 | − | 0.823740i | \(-0.308116\pi\) | ||||
0.566968 | + | 0.823740i | \(0.308116\pi\) | |||||||
\(420\) | 9.90833 | 0.483477 | ||||||||
\(421\) | 20.2389 | 0.986382 | 0.493191 | − | 0.869921i | \(-0.335830\pi\) | ||||
0.493191 | + | 0.869921i | \(0.335830\pi\) | |||||||
\(422\) | −17.3944 | −0.846749 | ||||||||
\(423\) | −47.4500 | −2.30710 | ||||||||
\(424\) | 3.39445 | 0.164849 | ||||||||
\(425\) | −8.60555 | −0.417431 | ||||||||
\(426\) | −43.9361 | −2.12871 | ||||||||
\(427\) | 7.39445 | 0.357842 | ||||||||
\(428\) | −11.2111 | −0.541909 | ||||||||
\(429\) | −1.00000 | −0.0482805 | ||||||||
\(430\) | −15.5139 | −0.748146 | ||||||||
\(431\) | 17.2111 | 0.829030 | 0.414515 | − | 0.910043i | \(-0.363951\pi\) | ||||
0.414515 | + | 0.910043i | \(0.363951\pi\) | |||||||
\(432\) | −16.2111 | −0.779957 | ||||||||
\(433\) | 26.2389 | 1.26096 | 0.630480 | − | 0.776206i | \(-0.282858\pi\) | ||||
0.630480 | + | 0.776206i | \(0.282858\pi\) | |||||||
\(434\) | 0.697224 | 0.0334678 | ||||||||
\(435\) | 20.2111 | 0.969048 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −8.60555 | −0.411659 | ||||||||
\(438\) | 15.2111 | 0.726815 | ||||||||
\(439\) | −10.7889 | −0.514926 | −0.257463 | − | 0.966288i | \(-0.582887\pi\) | ||||
−0.257463 | + | 0.966288i | \(0.582887\pi\) | |||||||
\(440\) | −1.30278 | −0.0621074 | ||||||||
\(441\) | −13.4222 | −0.639153 | ||||||||
\(442\) | −0.788897 | −0.0375240 | ||||||||
\(443\) | −3.63331 | −0.172624 | −0.0863118 | − | 0.996268i | \(-0.527508\pi\) | ||||
−0.0863118 | + | 0.996268i | \(0.527508\pi\) | |||||||
\(444\) | 30.4222 | 1.44377 | ||||||||
\(445\) | −3.39445 | −0.160912 | ||||||||
\(446\) | 10.7889 | 0.510869 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.30278 | −0.108796 | ||||||||
\(449\) | −10.1833 | −0.480582 | −0.240291 | − | 0.970701i | \(-0.577243\pi\) | ||||
−0.240291 | + | 0.970701i | \(0.577243\pi\) | |||||||
\(450\) | 26.1194 | 1.23128 | ||||||||
\(451\) | −6.90833 | −0.325300 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.0278 | −1.92765 | ||||||||
\(454\) | 19.8167 | 0.930042 | ||||||||
\(455\) | −0.908327 | −0.0425830 | ||||||||
\(456\) | 3.30278 | 0.154667 | ||||||||
\(457\) | 0.183346 | 0.00857657 | 0.00428829 | − | 0.999991i | \(-0.498635\pi\) | ||||
0.00428829 | + | 0.999991i | \(0.498635\pi\) | |||||||
\(458\) | −1.09167 | −0.0510105 | ||||||||
\(459\) | −42.2389 | −1.97154 | ||||||||
\(460\) | −11.2111 | −0.522720 | ||||||||
\(461\) | −22.4222 | −1.04431 | −0.522153 | − | 0.852852i | \(-0.674871\pi\) | ||||
−0.522153 | + | 0.852852i | \(0.674871\pi\) | |||||||
\(462\) | −7.60555 | −0.353842 | ||||||||
\(463\) | 13.2111 | 0.613972 | 0.306986 | − | 0.951714i | \(-0.400680\pi\) | ||||
0.306986 | + | 0.951714i | \(0.400680\pi\) | |||||||
\(464\) | −4.69722 | −0.218063 | ||||||||
\(465\) | −1.30278 | −0.0604148 | ||||||||
\(466\) | 5.21110 | 0.241400 | ||||||||
\(467\) | −15.3944 | −0.712370 | −0.356185 | − | 0.934415i | \(-0.615923\pi\) | ||||
−0.356185 | + | 0.934415i | \(0.615923\pi\) | |||||||
\(468\) | 2.39445 | 0.110683 | ||||||||
\(469\) | −26.5139 | −1.22430 | ||||||||
\(470\) | 7.81665 | 0.360555 | ||||||||
\(471\) | −39.3305 | −1.81226 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.9083 | 0.547545 | ||||||||
\(474\) | −19.2111 | −0.882395 | ||||||||
\(475\) | −3.30278 | −0.151542 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | −26.8444 | −1.22912 | ||||||||
\(478\) | −22.9361 | −1.04907 | ||||||||
\(479\) | 3.27502 | 0.149639 | 0.0748197 | − | 0.997197i | \(-0.476162\pi\) | ||||
0.0748197 | + | 0.997197i | \(0.476162\pi\) | |||||||
\(480\) | 4.30278 | 0.196394 | ||||||||
\(481\) | −2.78890 | −0.127163 | ||||||||
\(482\) | −23.9083 | −1.08899 | ||||||||
\(483\) | −65.4500 | −2.97808 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.4222 | 0.473248 | ||||||||
\(486\) | 49.8444 | 2.26099 | ||||||||
\(487\) | 10.3305 | 0.468121 | 0.234061 | − | 0.972222i | \(-0.424799\pi\) | ||||
0.234061 | + | 0.972222i | \(0.424799\pi\) | |||||||
\(488\) | 3.21110 | 0.145360 | ||||||||
\(489\) | 61.4500 | 2.77886 | ||||||||
\(490\) | 2.21110 | 0.0998874 | ||||||||
\(491\) | 31.9361 | 1.44126 | 0.720628 | − | 0.693322i | \(-0.243854\pi\) | ||||
0.720628 | + | 0.693322i | \(0.243854\pi\) | |||||||
\(492\) | 22.8167 | 1.02865 | ||||||||
\(493\) | −12.2389 | −0.551210 | ||||||||
\(494\) | −0.302776 | −0.0136225 | ||||||||
\(495\) | 10.3028 | 0.463075 | ||||||||
\(496\) | 0.302776 | 0.0135950 | ||||||||
\(497\) | 30.6333 | 1.37409 | ||||||||
\(498\) | 35.3305 | 1.58320 | ||||||||
\(499\) | −34.0000 | −1.52205 | −0.761025 | − | 0.648723i | \(-0.775303\pi\) | ||||
−0.761025 | + | 0.648723i | \(0.775303\pi\) | |||||||
\(500\) | −10.8167 | −0.483735 | ||||||||
\(501\) | −54.2389 | −2.42321 | ||||||||
\(502\) | −24.0000 | −1.07117 | ||||||||
\(503\) | −3.11943 | −0.139088 | −0.0695442 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695442 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(504\) | 18.2111 | 0.811187 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 8.60555 | 0.382563 | ||||||||
\(507\) | 42.6333 | 1.89341 | ||||||||
\(508\) | −12.6056 | −0.559281 | ||||||||
\(509\) | 10.4222 | 0.461956 | 0.230978 | − | 0.972959i | \(-0.425807\pi\) | ||||
0.230978 | + | 0.972959i | \(0.425807\pi\) | |||||||
\(510\) | 11.2111 | 0.496436 | ||||||||
\(511\) | −10.6056 | −0.469162 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.2111 | −0.715738 | ||||||||
\(514\) | −2.60555 | −0.114926 | ||||||||
\(515\) | −6.90833 | −0.304417 | ||||||||
\(516\) | −39.3305 | −1.73143 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | −21.2111 | −0.931962 | ||||||||
\(519\) | −67.1472 | −2.94743 | ||||||||
\(520\) | −0.394449 | −0.0172977 | ||||||||
\(521\) | 7.57779 | 0.331989 | 0.165995 | − | 0.986127i | \(-0.446917\pi\) | ||||
0.165995 | + | 0.986127i | \(0.446917\pi\) | |||||||
\(522\) | 37.1472 | 1.62589 | ||||||||
\(523\) | −17.0278 | −0.744572 | −0.372286 | − | 0.928118i | \(-0.621426\pi\) | ||||
−0.372286 | + | 0.928118i | \(0.621426\pi\) | |||||||
\(524\) | −6.11943 | −0.267329 | ||||||||
\(525\) | −25.1194 | −1.09630 | ||||||||
\(526\) | 16.6972 | 0.728034 | ||||||||
\(527\) | 0.788897 | 0.0343649 | ||||||||
\(528\) | −3.30278 | −0.143735 | ||||||||
\(529\) | 51.0555 | 2.21980 | ||||||||
\(530\) | 4.42221 | 0.192088 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.30278 | −0.0998380 | ||||||||
\(533\) | −2.09167 | −0.0906004 | ||||||||
\(534\) | −8.60555 | −0.372399 | ||||||||
\(535\) | −14.6056 | −0.631453 | ||||||||
\(536\) | −11.5139 | −0.497324 | ||||||||
\(537\) | −40.0278 | −1.72733 | ||||||||
\(538\) | −1.81665 | −0.0783215 | ||||||||
\(539\) | −1.69722 | −0.0731046 | ||||||||
\(540\) | −21.1194 | −0.908836 | ||||||||
\(541\) | −17.8167 | −0.765998 | −0.382999 | − | 0.923749i | \(-0.625109\pi\) | ||||
−0.382999 | + | 0.923749i | \(0.625109\pi\) | |||||||
\(542\) | −11.5139 | −0.494563 | ||||||||
\(543\) | −69.4500 | −2.98038 | ||||||||
\(544\) | −2.60555 | −0.111712 | ||||||||
\(545\) | 2.60555 | 0.111610 | ||||||||
\(546\) | −2.30278 | −0.0985497 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | −21.5139 | −0.919027 | ||||||||
\(549\) | −25.3944 | −1.08381 | ||||||||
\(550\) | 3.30278 | 0.140831 | ||||||||
\(551\) | −4.69722 | −0.200108 | ||||||||
\(552\) | −28.4222 | −1.20973 | ||||||||
\(553\) | 13.3944 | 0.569590 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 39.6333 | 1.68234 | ||||||||
\(556\) | −2.69722 | −0.114388 | ||||||||
\(557\) | 15.6333 | 0.662405 | 0.331202 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331202 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(558\) | −2.39445 | −0.101365 | ||||||||
\(559\) | 3.60555 | 0.152499 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −8.60555 | −0.363327 | ||||||||
\(562\) | 18.5139 | 0.780961 | ||||||||
\(563\) | −21.6333 | −0.911735 | −0.455868 | − | 0.890048i | \(-0.650671\pi\) | ||||
−0.455868 | + | 0.890048i | \(0.650671\pi\) | |||||||
\(564\) | 19.8167 | 0.834432 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.9361 | −1.17424 | ||||||||
\(567\) | −68.6611 | −2.88349 | ||||||||
\(568\) | 13.3028 | 0.558172 | ||||||||
\(569\) | 44.7250 | 1.87497 | 0.937484 | − | 0.348027i | \(-0.113148\pi\) | ||||
0.937484 | + | 0.348027i | \(0.113148\pi\) | |||||||
\(570\) | 4.30278 | 0.180223 | ||||||||
\(571\) | 39.9361 | 1.67127 | 0.835637 | − | 0.549283i | \(-0.185099\pi\) | ||||
0.835637 | + | 0.549283i | \(0.185099\pi\) | |||||||
\(572\) | 0.302776 | 0.0126597 | ||||||||
\(573\) | 19.8167 | 0.827853 | ||||||||
\(574\) | −15.9083 | −0.664001 | ||||||||
\(575\) | 28.4222 | 1.18529 | ||||||||
\(576\) | 7.90833 | 0.329514 | ||||||||
\(577\) | −28.9083 | −1.20347 | −0.601735 | − | 0.798696i | \(-0.705524\pi\) | ||||
−0.601735 | + | 0.798696i | \(0.705524\pi\) | |||||||
\(578\) | 10.2111 | 0.424726 | ||||||||
\(579\) | −25.5139 | −1.06032 | ||||||||
\(580\) | −6.11943 | −0.254095 | ||||||||
\(581\) | −24.6333 | −1.02196 | ||||||||
\(582\) | 26.4222 | 1.09524 | ||||||||
\(583\) | −3.39445 | −0.140584 | ||||||||
\(584\) | −4.60555 | −0.190579 | ||||||||
\(585\) | 3.11943 | 0.128973 | ||||||||
\(586\) | −28.5416 | −1.17904 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 5.60555 | 0.231169 | ||||||||
\(589\) | 0.302776 | 0.0124757 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 71.4500 | 2.93906 | ||||||||
\(592\) | −9.21110 | −0.378574 | ||||||||
\(593\) | −42.0000 | −1.72473 | −0.862367 | − | 0.506284i | \(-0.831019\pi\) | ||||
−0.862367 | + | 0.506284i | \(0.831019\pi\) | |||||||
\(594\) | 16.2111 | 0.665150 | ||||||||
\(595\) | −7.81665 | −0.320452 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 78.6611 | 3.21938 | ||||||||
\(598\) | 2.60555 | 0.106549 | ||||||||
\(599\) | −45.1194 | −1.84353 | −0.921765 | − | 0.387749i | \(-0.873253\pi\) | ||||
−0.921765 | + | 0.387749i | \(0.873253\pi\) | |||||||
\(600\) | −10.9083 | −0.445331 | ||||||||
\(601\) | 14.9083 | 0.608123 | 0.304062 | − | 0.952652i | \(-0.401657\pi\) | ||||
0.304062 | + | 0.952652i | \(0.401657\pi\) | |||||||
\(602\) | 27.4222 | 1.11765 | ||||||||
\(603\) | 91.0555 | 3.70807 | ||||||||
\(604\) | 12.4222 | 0.505452 | ||||||||
\(605\) | 1.30278 | 0.0529654 | ||||||||
\(606\) | −45.6333 | −1.85373 | ||||||||
\(607\) | −17.8167 | −0.723156 | −0.361578 | − | 0.932342i | \(-0.617762\pi\) | ||||
−0.361578 | + | 0.932342i | \(0.617762\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −35.7250 | −1.44765 | ||||||||
\(610\) | 4.18335 | 0.169379 | ||||||||
\(611\) | −1.81665 | −0.0734939 | ||||||||
\(612\) | 20.6056 | 0.832930 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 23.8167 | 0.961162 | ||||||||
\(615\) | 29.7250 | 1.19863 | ||||||||
\(616\) | 2.30278 | 0.0927815 | ||||||||
\(617\) | 12.9083 | 0.519670 | 0.259835 | − | 0.965653i | \(-0.416332\pi\) | ||||
0.259835 | + | 0.965653i | \(0.416332\pi\) | |||||||
\(618\) | −17.5139 | −0.704512 | ||||||||
\(619\) | 22.8444 | 0.918194 | 0.459097 | − | 0.888386i | \(-0.348173\pi\) | ||||
0.459097 | + | 0.888386i | \(0.348173\pi\) | |||||||
\(620\) | 0.394449 | 0.0158414 | ||||||||
\(621\) | 139.505 | 5.59816 | ||||||||
\(622\) | −4.18335 | −0.167737 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 2.42221 | 0.0968882 | ||||||||
\(626\) | 7.11943 | 0.284550 | ||||||||
\(627\) | −3.30278 | −0.131900 | ||||||||
\(628\) | 11.9083 | 0.475194 | ||||||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 23.7250 | 0.945226 | ||||||||
\(631\) | −8.97224 | −0.357179 | −0.178590 | − | 0.983924i | \(-0.557153\pi\) | ||||
−0.178590 | + | 0.983924i | \(0.557153\pi\) | |||||||
\(632\) | 5.81665 | 0.231374 | ||||||||
\(633\) | −57.4500 | −2.28343 | ||||||||
\(634\) | −7.81665 | −0.310439 | ||||||||
\(635\) | −16.4222 | −0.651695 | ||||||||
\(636\) | 11.2111 | 0.444549 | ||||||||
\(637\) | −0.513878 | −0.0203606 | ||||||||
\(638\) | 4.69722 | 0.185965 | ||||||||
\(639\) | −105.203 | −4.16175 | ||||||||
\(640\) | −1.30278 | −0.0514967 | ||||||||
\(641\) | −30.2389 | −1.19436 | −0.597182 | − | 0.802106i | \(-0.703713\pi\) | ||||
−0.597182 | + | 0.802106i | \(0.703713\pi\) | |||||||
\(642\) | −37.0278 | −1.46137 | ||||||||
\(643\) | −2.42221 | −0.0955224 | −0.0477612 | − | 0.998859i | \(-0.515209\pi\) | ||||
−0.0477612 | + | 0.998859i | \(0.515209\pi\) | |||||||
\(644\) | 19.8167 | 0.780886 | ||||||||
\(645\) | −51.2389 | −2.01753 | ||||||||
\(646\) | −2.60555 | −0.102514 | ||||||||
\(647\) | 4.18335 | 0.164464 | 0.0822322 | − | 0.996613i | \(-0.473795\pi\) | ||||
0.0822322 | + | 0.996613i | \(0.473795\pi\) | |||||||
\(648\) | −29.8167 | −1.17131 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | 2.30278 | 0.0902529 | ||||||||
\(652\) | −18.6056 | −0.728650 | ||||||||
\(653\) | −17.3305 | −0.678196 | −0.339098 | − | 0.940751i | \(-0.610122\pi\) | ||||
−0.339098 | + | 0.940751i | \(0.610122\pi\) | |||||||
\(654\) | 6.60555 | 0.258297 | ||||||||
\(655\) | −7.97224 | −0.311501 | ||||||||
\(656\) | −6.90833 | −0.269725 | ||||||||
\(657\) | 36.4222 | 1.42097 | ||||||||
\(658\) | −13.8167 | −0.538629 | ||||||||
\(659\) | −7.02776 | −0.273763 | −0.136881 | − | 0.990587i | \(-0.543708\pi\) | ||||
−0.136881 | + | 0.990587i | \(0.543708\pi\) | |||||||
\(660\) | −4.30278 | −0.167485 | ||||||||
\(661\) | −19.6333 | −0.763647 | −0.381824 | − | 0.924235i | \(-0.624704\pi\) | ||||
−0.381824 | + | 0.924235i | \(0.624704\pi\) | |||||||
\(662\) | 9.72498 | 0.377972 | ||||||||
\(663\) | −2.60555 | −0.101191 | ||||||||
\(664\) | −10.6972 | −0.415133 | ||||||||
\(665\) | −3.00000 | −0.116335 | ||||||||
\(666\) | 72.8444 | 2.82266 | ||||||||
\(667\) | 40.4222 | 1.56515 | ||||||||
\(668\) | 16.4222 | 0.635394 | ||||||||
\(669\) | 35.6333 | 1.37766 | ||||||||
\(670\) | −15.0000 | −0.579501 | ||||||||
\(671\) | −3.21110 | −0.123963 | ||||||||
\(672\) | −7.60555 | −0.293391 | ||||||||
\(673\) | −2.30278 | −0.0887655 | −0.0443827 | − | 0.999015i | \(-0.514132\pi\) | ||||
−0.0443827 | + | 0.999015i | \(0.514132\pi\) | |||||||
\(674\) | 5.69722 | 0.219449 | ||||||||
\(675\) | 53.5416 | 2.06082 | ||||||||
\(676\) | −12.9083 | −0.496474 | ||||||||
\(677\) | −4.69722 | −0.180529 | −0.0902645 | − | 0.995918i | \(-0.528771\pi\) | ||||
−0.0902645 | + | 0.995918i | \(0.528771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.4222 | −0.706979 | ||||||||
\(680\) | −3.39445 | −0.130171 | ||||||||
\(681\) | 65.4500 | 2.50805 | ||||||||
\(682\) | −0.302776 | −0.0115939 | ||||||||
\(683\) | −46.4222 | −1.77630 | −0.888148 | − | 0.459557i | \(-0.848008\pi\) | ||||
−0.888148 | + | 0.459557i | \(0.848008\pi\) | |||||||
\(684\) | 7.90833 | 0.302382 | ||||||||
\(685\) | −28.0278 | −1.07089 | ||||||||
\(686\) | −20.0278 | −0.764663 | ||||||||
\(687\) | −3.60555 | −0.137560 | ||||||||
\(688\) | 11.9083 | 0.454001 | ||||||||
\(689\) | −1.02776 | −0.0391544 | ||||||||
\(690\) | −37.0278 | −1.40962 | ||||||||
\(691\) | 3.57779 | 0.136106 | 0.0680529 | − | 0.997682i | \(-0.478321\pi\) | ||||
0.0680529 | + | 0.997682i | \(0.478321\pi\) | |||||||
\(692\) | 20.3305 | 0.772851 | ||||||||
\(693\) | −18.2111 | −0.691783 | ||||||||
\(694\) | −17.2111 | −0.653325 | ||||||||
\(695\) | −3.51388 | −0.133289 | ||||||||
\(696\) | −15.5139 | −0.588052 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | −3.57779 | −0.135422 | ||||||||
\(699\) | 17.2111 | 0.650984 | ||||||||
\(700\) | 7.60555 | 0.287463 | ||||||||
\(701\) | 15.6333 | 0.590462 | 0.295231 | − | 0.955426i | \(-0.404603\pi\) | ||||
0.295231 | + | 0.955426i | \(0.404603\pi\) | |||||||
\(702\) | 4.90833 | 0.185253 | ||||||||
\(703\) | −9.21110 | −0.347403 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 25.8167 | 0.972311 | ||||||||
\(706\) | 0.788897 | 0.0296905 | ||||||||
\(707\) | 31.8167 | 1.19659 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.3028 | 0.687375 | 0.343688 | − | 0.939084i | \(-0.388324\pi\) | ||||
0.343688 | + | 0.939084i | \(0.388324\pi\) | |||||||
\(710\) | 17.3305 | 0.650403 | ||||||||
\(711\) | −46.0000 | −1.72513 | ||||||||
\(712\) | 2.60555 | 0.0976472 | ||||||||
\(713\) | −2.60555 | −0.0975787 | ||||||||
\(714\) | −19.8167 | −0.741620 | ||||||||
\(715\) | 0.394449 | 0.0147515 | ||||||||
\(716\) | 12.1194 | 0.452924 | ||||||||
\(717\) | −75.7527 | −2.82904 | ||||||||
\(718\) | 27.5139 | 1.02681 | ||||||||
\(719\) | −4.18335 | −0.156012 | −0.0780062 | − | 0.996953i | \(-0.524855\pi\) | ||||
−0.0780062 | + | 0.996953i | \(0.524855\pi\) | |||||||
\(720\) | 10.3028 | 0.383962 | ||||||||
\(721\) | 12.2111 | 0.454765 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −78.9638 | −2.93670 | ||||||||
\(724\) | 21.0278 | 0.781490 | ||||||||
\(725\) | 15.5139 | 0.576171 | ||||||||
\(726\) | 3.30278 | 0.122578 | ||||||||
\(727\) | −43.6333 | −1.61827 | −0.809135 | − | 0.587623i | \(-0.800064\pi\) | ||||
−0.809135 | + | 0.587623i | \(0.800064\pi\) | |||||||
\(728\) | 0.697224 | 0.0258409 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 31.0278 | 1.14760 | ||||||||
\(732\) | 10.6056 | 0.391992 | ||||||||
\(733\) | 7.21110 | 0.266348 | 0.133174 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133174 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(734\) | −7.21110 | −0.266167 | ||||||||
\(735\) | 7.30278 | 0.269367 | ||||||||
\(736\) | 8.60555 | 0.317205 | ||||||||
\(737\) | 11.5139 | 0.424119 | ||||||||
\(738\) | 54.6333 | 2.01108 | ||||||||
\(739\) | 35.3583 | 1.30068 | 0.650338 | − | 0.759645i | \(-0.274627\pi\) | ||||
0.650338 | + | 0.759645i | \(0.274627\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | −1.00000 | −0.0367359 | ||||||||
\(742\) | −7.81665 | −0.286958 | ||||||||
\(743\) | 45.6333 | 1.67412 | 0.837062 | − | 0.547108i | \(-0.184271\pi\) | ||||
0.837062 | + | 0.547108i | \(0.184271\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.9083 | −0.655670 | ||||||||
\(747\) | 84.5971 | 3.09525 | ||||||||
\(748\) | 2.60555 | 0.0952684 | ||||||||
\(749\) | 25.8167 | 0.943320 | ||||||||
\(750\) | −35.7250 | −1.30449 | ||||||||
\(751\) | 16.8444 | 0.614661 | 0.307331 | − | 0.951603i | \(-0.400564\pi\) | ||||
0.307331 | + | 0.951603i | \(0.400564\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | −79.2666 | −2.88864 | ||||||||
\(754\) | 1.42221 | 0.0517937 | ||||||||
\(755\) | 16.1833 | 0.588972 | ||||||||
\(756\) | 37.3305 | 1.35770 | ||||||||
\(757\) | −23.5416 | −0.855635 | −0.427818 | − | 0.903865i | \(-0.640717\pi\) | ||||
−0.427818 | + | 0.903865i | \(0.640717\pi\) | |||||||
\(758\) | 31.5139 | 1.14464 | ||||||||
\(759\) | 28.4222 | 1.03166 | ||||||||
\(760\) | −1.30278 | −0.0472566 | ||||||||
\(761\) | −30.2389 | −1.09616 | −0.548079 | − | 0.836427i | \(-0.684641\pi\) | ||||
−0.548079 | + | 0.836427i | \(0.684641\pi\) | |||||||
\(762\) | −41.6333 | −1.50822 | ||||||||
\(763\) | −4.60555 | −0.166732 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 26.8444 | 0.970562 | ||||||||
\(766\) | −21.5139 | −0.777328 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.30278 | −0.119179 | ||||||||
\(769\) | 5.63331 | 0.203142 | 0.101571 | − | 0.994828i | \(-0.467613\pi\) | ||||
0.101571 | + | 0.994828i | \(0.467613\pi\) | |||||||
\(770\) | 3.00000 | 0.108112 | ||||||||
\(771\) | −8.60555 | −0.309921 | ||||||||
\(772\) | 7.72498 | 0.278028 | ||||||||
\(773\) | 19.5778 | 0.704164 | 0.352082 | − | 0.935969i | \(-0.385474\pi\) | ||||
0.352082 | + | 0.935969i | \(0.385474\pi\) | |||||||
\(774\) | −94.1749 | −3.38505 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | −70.0555 | −2.51323 | ||||||||
\(778\) | 19.5416 | 0.700602 | ||||||||
\(779\) | −6.90833 | −0.247516 | ||||||||
\(780\) | −1.30278 | −0.0466469 | ||||||||
\(781\) | −13.3028 | −0.476011 | ||||||||
\(782\) | 22.4222 | 0.801816 | ||||||||
\(783\) | 76.1472 | 2.72128 | ||||||||
\(784\) | −1.69722 | −0.0606152 | ||||||||
\(785\) | 15.5139 | 0.553714 | ||||||||
\(786\) | −20.2111 | −0.720906 | ||||||||
\(787\) | 21.0278 | 0.749559 | 0.374779 | − | 0.927114i | \(-0.377718\pi\) | ||||
0.374779 | + | 0.927114i | \(0.377718\pi\) | |||||||
\(788\) | −21.6333 | −0.770655 | ||||||||
\(789\) | 55.1472 | 1.96329 | ||||||||
\(790\) | 7.57779 | 0.269606 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.90833 | −0.281010 | ||||||||
\(793\) | −0.972244 | −0.0345254 | ||||||||
\(794\) | −35.7527 | −1.26882 | ||||||||
\(795\) | 14.6056 | 0.518006 | ||||||||
\(796\) | −23.8167 | −0.844159 | ||||||||
\(797\) | 9.39445 | 0.332768 | 0.166384 | − | 0.986061i | \(-0.446791\pi\) | ||||
0.166384 | + | 0.986061i | \(0.446791\pi\) | |||||||
\(798\) | −7.60555 | −0.269234 | ||||||||
\(799\) | −15.6333 | −0.553067 | ||||||||
\(800\) | 3.30278 | 0.116771 | ||||||||
\(801\) | −20.6056 | −0.728061 | ||||||||
\(802\) | −15.3944 | −0.543597 | ||||||||
\(803\) | 4.60555 | 0.162526 | ||||||||
\(804\) | −38.0278 | −1.34114 | ||||||||
\(805\) | 25.8167 | 0.909917 | ||||||||
\(806\) | −0.0916731 | −0.00322905 | ||||||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | 13.8167 | 0.486068 | ||||||||
\(809\) | 18.7889 | 0.660582 | 0.330291 | − | 0.943879i | \(-0.392853\pi\) | ||||
0.330291 | + | 0.943879i | \(0.392853\pi\) | |||||||
\(810\) | −38.8444 | −1.36485 | ||||||||
\(811\) | −13.6333 | −0.478730 | −0.239365 | − | 0.970930i | \(-0.576939\pi\) | ||||
−0.239365 | + | 0.970930i | \(0.576939\pi\) | |||||||
\(812\) | 10.8167 | 0.379590 | ||||||||
\(813\) | −38.0278 | −1.33369 | ||||||||
\(814\) | 9.21110 | 0.322849 | ||||||||
\(815\) | −24.2389 | −0.849050 | ||||||||
\(816\) | −8.60555 | −0.301255 | ||||||||
\(817\) | 11.9083 | 0.416620 | ||||||||
\(818\) | 38.1472 | 1.33379 | ||||||||
\(819\) | −5.51388 | −0.192670 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −27.3944 | −0.956073 | −0.478036 | − | 0.878340i | \(-0.658651\pi\) | ||||
−0.478036 | + | 0.878340i | \(0.658651\pi\) | |||||||
\(822\) | −71.0555 | −2.47835 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 5.30278 | 0.184731 | ||||||||
\(825\) | 10.9083 | 0.379779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.0555 | −1.74060 | −0.870300 | − | 0.492521i | \(-0.836075\pi\) | ||||
−0.870300 | + | 0.492521i | \(0.836075\pi\) | |||||||
\(828\) | −68.0555 | −2.36509 | ||||||||
\(829\) | −56.4222 | −1.95962 | −0.979812 | − | 0.199921i | \(-0.935932\pi\) | ||||
−0.979812 | + | 0.199921i | \(0.935932\pi\) | |||||||
\(830\) | −13.9361 | −0.483729 | ||||||||
\(831\) | 33.0278 | 1.14572 | ||||||||
\(832\) | 0.302776 | 0.0104969 | ||||||||
\(833\) | −4.42221 | −0.153220 | ||||||||
\(834\) | −8.90833 | −0.308470 | ||||||||
\(835\) | 21.3944 | 0.740385 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | −4.90833 | −0.169657 | ||||||||
\(838\) | −23.2111 | −0.801814 | ||||||||
\(839\) | 45.1194 | 1.55770 | 0.778848 | − | 0.627213i | \(-0.215804\pi\) | ||||
0.778848 | + | 0.627213i | \(0.215804\pi\) | |||||||
\(840\) | −9.90833 | −0.341870 | ||||||||
\(841\) | −6.93608 | −0.239175 | ||||||||
\(842\) | −20.2389 | −0.697477 | ||||||||
\(843\) | 61.1472 | 2.10602 | ||||||||
\(844\) | 17.3944 | 0.598742 | ||||||||
\(845\) | −16.8167 | −0.578510 | ||||||||
\(846\) | 47.4500 | 1.63136 | ||||||||
\(847\) | −2.30278 | −0.0791243 | ||||||||
\(848\) | −3.39445 | −0.116566 | ||||||||
\(849\) | −92.2666 | −3.16658 | ||||||||
\(850\) | 8.60555 | 0.295168 | ||||||||
\(851\) | 79.2666 | 2.71722 | ||||||||
\(852\) | 43.9361 | 1.50523 | ||||||||
\(853\) | −17.5778 | −0.601852 | −0.300926 | − | 0.953647i | \(-0.597296\pi\) | ||||
−0.300926 | + | 0.953647i | \(0.597296\pi\) | |||||||
\(854\) | −7.39445 | −0.253033 | ||||||||
\(855\) | 10.3028 | 0.352347 | ||||||||
\(856\) | 11.2111 | 0.383188 | ||||||||
\(857\) | 10.5416 | 0.360095 | 0.180048 | − | 0.983658i | \(-0.442375\pi\) | ||||
0.180048 | + | 0.983658i | \(0.442375\pi\) | |||||||
\(858\) | 1.00000 | 0.0341394 | ||||||||
\(859\) | −48.8444 | −1.66655 | −0.833275 | − | 0.552859i | \(-0.813537\pi\) | ||||
−0.833275 | + | 0.552859i | \(0.813537\pi\) | |||||||
\(860\) | 15.5139 | 0.529019 | ||||||||
\(861\) | −52.5416 | −1.79061 | ||||||||
\(862\) | −17.2111 | −0.586212 | ||||||||
\(863\) | 14.7250 | 0.501244 | 0.250622 | − | 0.968085i | \(-0.419365\pi\) | ||||
0.250622 | + | 0.968085i | \(0.419365\pi\) | |||||||
\(864\) | 16.2111 | 0.551513 | ||||||||
\(865\) | 26.4861 | 0.900555 | ||||||||
\(866\) | −26.2389 | −0.891633 | ||||||||
\(867\) | 33.7250 | 1.14536 | ||||||||
\(868\) | −0.697224 | −0.0236653 | ||||||||
\(869\) | −5.81665 | −0.197316 | ||||||||
\(870\) | −20.2111 | −0.685221 | ||||||||
\(871\) | 3.48612 | 0.118123 | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 63.2666 | 2.14125 | ||||||||
\(874\) | 8.60555 | 0.291087 | ||||||||
\(875\) | 24.9083 | 0.842055 | ||||||||
\(876\) | −15.2111 | −0.513936 | ||||||||
\(877\) | −42.5694 | −1.43747 | −0.718733 | − | 0.695286i | \(-0.755278\pi\) | ||||
−0.718733 | + | 0.695286i | \(0.755278\pi\) | |||||||
\(878\) | 10.7889 | 0.364108 | ||||||||
\(879\) | −94.2666 | −3.17953 | ||||||||
\(880\) | 1.30278 | 0.0439166 | ||||||||
\(881\) | −23.0917 | −0.777978 | −0.388989 | − | 0.921242i | \(-0.627176\pi\) | ||||
−0.388989 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(882\) | 13.4222 | 0.451949 | ||||||||
\(883\) | −2.97224 | −0.100024 | −0.0500120 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500120 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(884\) | 0.788897 | 0.0265335 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.63331 | 0.122063 | ||||||||
\(887\) | −32.8444 | −1.10281 | −0.551404 | − | 0.834239i | \(-0.685908\pi\) | ||||
−0.551404 | + | 0.834239i | \(0.685908\pi\) | |||||||
\(888\) | −30.4222 | −1.02090 | ||||||||
\(889\) | 29.0278 | 0.973560 | ||||||||
\(890\) | 3.39445 | 0.113782 | ||||||||
\(891\) | 29.8167 | 0.998895 | ||||||||
\(892\) | −10.7889 | −0.361239 | ||||||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7889 | 0.527765 | ||||||||
\(896\) | 2.30278 | 0.0769303 | ||||||||
\(897\) | 8.60555 | 0.287331 | ||||||||
\(898\) | 10.1833 | 0.339823 | ||||||||
\(899\) | −1.42221 | −0.0474332 | ||||||||
\(900\) | −26.1194 | −0.870648 | ||||||||
\(901\) | −8.84441 | −0.294650 | ||||||||
\(902\) | 6.90833 | 0.230022 | ||||||||
\(903\) | 90.5694 | 3.01396 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.3944 | 0.910622 | ||||||||
\(906\) | 41.0278 | 1.36306 | ||||||||
\(907\) | 52.8444 | 1.75467 | 0.877335 | − | 0.479879i | \(-0.159319\pi\) | ||||
0.877335 | + | 0.479879i | \(0.159319\pi\) | |||||||
\(908\) | −19.8167 | −0.657639 | ||||||||
\(909\) | −109.267 | −3.62414 | ||||||||
\(910\) | 0.908327 | 0.0301107 | ||||||||
\(911\) | −15.6333 | −0.517955 | −0.258977 | − | 0.965883i | \(-0.583385\pi\) | ||||
−0.258977 | + | 0.965883i | \(0.583385\pi\) | |||||||
\(912\) | −3.30278 | −0.109366 | ||||||||
\(913\) | 10.6972 | 0.354026 | ||||||||
\(914\) | −0.183346 | −0.00606455 | ||||||||
\(915\) | 13.8167 | 0.456764 | ||||||||
\(916\) | 1.09167 | 0.0360699 | ||||||||
\(917\) | 14.0917 | 0.465348 | ||||||||
\(918\) | 42.2389 | 1.39409 | ||||||||
\(919\) | −19.1194 | −0.630692 | −0.315346 | − | 0.948977i | \(-0.602121\pi\) | ||||
−0.315346 | + | 0.948977i | \(0.602121\pi\) | |||||||
\(920\) | 11.2111 | 0.369619 | ||||||||
\(921\) | 78.6611 | 2.59197 | ||||||||
\(922\) | 22.4222 | 0.738436 | ||||||||
\(923\) | −4.02776 | −0.132575 | ||||||||
\(924\) | 7.60555 | 0.250204 | ||||||||
\(925\) | 30.4222 | 1.00028 | ||||||||
\(926\) | −13.2111 | −0.434144 | ||||||||
\(927\) | −41.9361 | −1.37736 | ||||||||
\(928\) | 4.69722 | 0.154194 | ||||||||
\(929\) | 9.51388 | 0.312140 | 0.156070 | − | 0.987746i | \(-0.450117\pi\) | ||||
0.156070 | + | 0.987746i | \(0.450117\pi\) | |||||||
\(930\) | 1.30278 | 0.0427197 | ||||||||
\(931\) | −1.69722 | −0.0556243 | ||||||||
\(932\) | −5.21110 | −0.170695 | ||||||||
\(933\) | −13.8167 | −0.452337 | ||||||||
\(934\) | 15.3944 | 0.503722 | ||||||||
\(935\) | 3.39445 | 0.111010 | ||||||||
\(936\) | −2.39445 | −0.0782650 | ||||||||
\(937\) | 58.8444 | 1.92236 | 0.961182 | − | 0.275917i | \(-0.0889814\pi\) | ||||
0.961182 | + | 0.275917i | \(0.0889814\pi\) | |||||||
\(938\) | 26.5139 | 0.865709 | ||||||||
\(939\) | 23.5139 | 0.767346 | ||||||||
\(940\) | −7.81665 | −0.254951 | ||||||||
\(941\) | −14.3667 | −0.468341 | −0.234170 | − | 0.972196i | \(-0.575237\pi\) | ||||
−0.234170 | + | 0.972196i | \(0.575237\pi\) | |||||||
\(942\) | 39.3305 | 1.28146 | ||||||||
\(943\) | 59.4500 | 1.93596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.6333 | 1.58204 | ||||||||
\(946\) | −11.9083 | −0.387173 | ||||||||
\(947\) | 4.18335 | 0.135940 | 0.0679702 | − | 0.997687i | \(-0.478348\pi\) | ||||
0.0679702 | + | 0.997687i | \(0.478348\pi\) | |||||||
\(948\) | 19.2111 | 0.623948 | ||||||||
\(949\) | 1.39445 | 0.0452657 | ||||||||
\(950\) | 3.30278 | 0.107156 | ||||||||
\(951\) | −25.8167 | −0.837162 | ||||||||
\(952\) | 6.00000 | 0.194461 | ||||||||
\(953\) | 21.6333 | 0.700772 | 0.350386 | − | 0.936605i | \(-0.386050\pi\) | ||||
0.350386 | + | 0.936605i | \(0.386050\pi\) | |||||||
\(954\) | 26.8444 | 0.869120 | ||||||||
\(955\) | −7.81665 | −0.252941 | ||||||||
\(956\) | 22.9361 | 0.741806 | ||||||||
\(957\) | 15.5139 | 0.501492 | ||||||||
\(958\) | −3.27502 | −0.105811 | ||||||||
\(959\) | 49.5416 | 1.59978 | ||||||||
\(960\) | −4.30278 | −0.138871 | ||||||||
\(961\) | −30.9083 | −0.997043 | ||||||||
\(962\) | 2.78890 | 0.0899177 | ||||||||
\(963\) | −88.6611 | −2.85706 | ||||||||
\(964\) | 23.9083 | 0.770035 | ||||||||
\(965\) | 10.0639 | 0.323969 | ||||||||
\(966\) | 65.4500 | 2.10582 | ||||||||
\(967\) | −19.6333 | −0.631365 | −0.315682 | − | 0.948865i | \(-0.602233\pi\) | ||||
−0.315682 | + | 0.948865i | \(0.602233\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −8.60555 | −0.276450 | ||||||||
\(970\) | −10.4222 | −0.334637 | ||||||||
\(971\) | 22.9361 | 0.736054 | 0.368027 | − | 0.929815i | \(-0.380033\pi\) | ||||
0.368027 | + | 0.929815i | \(0.380033\pi\) | |||||||
\(972\) | −49.8444 | −1.59876 | ||||||||
\(973\) | 6.21110 | 0.199119 | ||||||||
\(974\) | −10.3305 | −0.331012 | ||||||||
\(975\) | 3.30278 | 0.105773 | ||||||||
\(976\) | −3.21110 | −0.102785 | ||||||||
\(977\) | −15.6333 | −0.500154 | −0.250077 | − | 0.968226i | \(-0.580456\pi\) | ||||
−0.250077 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(978\) | −61.4500 | −1.96495 | ||||||||
\(979\) | −2.60555 | −0.0832738 | ||||||||
\(980\) | −2.21110 | −0.0706311 | ||||||||
\(981\) | 15.8167 | 0.504987 | ||||||||
\(982\) | −31.9361 | −1.01912 | ||||||||
\(983\) | 19.6972 | 0.628244 | 0.314122 | − | 0.949383i | \(-0.398290\pi\) | ||||
0.314122 | + | 0.949383i | \(0.398290\pi\) | |||||||
\(984\) | −22.8167 | −0.727368 | ||||||||
\(985\) | −28.1833 | −0.897996 | ||||||||
\(986\) | 12.2389 | 0.389765 | ||||||||
\(987\) | −45.6333 | −1.45252 | ||||||||
\(988\) | 0.302776 | 0.00963258 | ||||||||
\(989\) | −102.478 | −3.25860 | ||||||||
\(990\) | −10.3028 | −0.327444 | ||||||||
\(991\) | −15.0917 | −0.479403 | −0.239701 | − | 0.970847i | \(-0.577050\pi\) | ||||
−0.239701 | + | 0.970847i | \(0.577050\pi\) | |||||||
\(992\) | −0.302776 | −0.00961314 | ||||||||
\(993\) | 32.1194 | 1.01928 | ||||||||
\(994\) | −30.6333 | −0.971630 | ||||||||
\(995\) | −31.0278 | −0.983646 | ||||||||
\(996\) | −35.3305 | −1.11949 | ||||||||
\(997\) | 21.8167 | 0.690940 | 0.345470 | − | 0.938430i | \(-0.387719\pi\) | ||||
0.345470 | + | 0.938430i | \(0.387719\pi\) | |||||||
\(998\) | 34.0000 | 1.07625 | ||||||||
\(999\) | 149.322 | 4.72434 |
(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 | 418.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 3762.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 3344.2.a.o.1.2 | 2 | |||
11.10 | odd | 2 | 4598.2.a.bc.1.1 | 2 | |||
19.18 | odd | 2 | 7942.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3344.2.a.o.1.2 | 2 | 4.3 | odd | 2 | |||
3762.2.a.bb.1.1 | 2 | 3.2 | odd | 2 | |||
4598.2.a.bc.1.1 | 2 | 11.10 | odd | 2 | |||
7942.2.a.bb.1.2 | 2 | 19.18 | odd | 2 |