Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 10x^{6} + 9x^{5} + 28x^{4} - 22x^{3} - 16x^{2} + 7x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.651939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.651939 | −0.460991 | −0.230495 | − | 0.973073i | \(-0.574035\pi\) | ||||
−0.230495 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(3\) | −2.38619 | −1.37767 | −0.688833 | − | 0.724920i | \(-0.741877\pi\) | ||||
−0.688833 | + | 0.724920i | \(0.741877\pi\) | |||||||
\(4\) | −1.57498 | −0.787488 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.55565 | 0.635092 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.33067 | 0.824015 | ||||||||
\(9\) | 2.69390 | 0.897966 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.86336 | 0.863335 | 0.431667 | − | 0.902033i | \(-0.357925\pi\) | ||||
0.431667 | + | 0.902033i | \(0.357925\pi\) | |||||||
\(12\) | 3.75819 | 1.08490 | ||||||||
\(13\) | 0.353935 | 0.0981638 | 0.0490819 | − | 0.998795i | \(-0.484370\pi\) | ||||
0.0490819 | + | 0.998795i | \(0.484370\pi\) | |||||||
\(14\) | −0.651939 | −0.174238 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.63050 | 0.407624 | ||||||||
\(17\) | −4.74269 | −1.15027 | −0.575136 | − | 0.818058i | \(-0.695051\pi\) | ||||
−0.575136 | + | 0.818058i | \(0.695051\pi\) | |||||||
\(18\) | −1.75626 | −0.413954 | ||||||||
\(19\) | −4.16177 | −0.954776 | −0.477388 | − | 0.878693i | \(-0.658416\pi\) | ||||
−0.477388 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.38619 | −0.520709 | ||||||||
\(22\) | −1.86674 | −0.397989 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −5.56141 | −1.13522 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.230744 | −0.0452526 | ||||||||
\(27\) | 0.730420 | 0.140569 | ||||||||
\(28\) | −1.57498 | −0.297642 | ||||||||
\(29\) | −1.30729 | −0.242758 | −0.121379 | − | 0.992606i | \(-0.538732\pi\) | ||||
−0.121379 | + | 0.992606i | \(0.538732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.275454 | −0.0494730 | −0.0247365 | − | 0.999694i | \(-0.507875\pi\) | ||||
−0.0247365 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(32\) | −5.72432 | −1.01193 | ||||||||
\(33\) | −6.83251 | −1.18939 | ||||||||
\(34\) | 3.09195 | 0.530265 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.24282 | −0.707137 | ||||||||
\(37\) | −7.76097 | −1.27590 | −0.637948 | − | 0.770080i | \(-0.720216\pi\) | ||||
−0.637948 | + | 0.770080i | \(0.720216\pi\) | |||||||
\(38\) | 2.71322 | 0.440143 | ||||||||
\(39\) | −0.844555 | −0.135237 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8109 | 1.84455 | 0.922275 | − | 0.386534i | \(-0.126328\pi\) | ||||
0.922275 | + | 0.386534i | \(0.126328\pi\) | |||||||
\(42\) | 1.55565 | 0.240042 | ||||||||
\(43\) | 2.76959 | 0.422359 | 0.211180 | − | 0.977447i | \(-0.432270\pi\) | ||||
0.211180 | + | 0.977447i | \(0.432270\pi\) | |||||||
\(44\) | −4.50972 | −0.679866 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.651939 | 0.0961232 | ||||||||
\(47\) | −3.46539 | −0.505480 | −0.252740 | − | 0.967534i | \(-0.581332\pi\) | ||||
−0.252740 | + | 0.967534i | \(0.581332\pi\) | |||||||
\(48\) | −3.89067 | −0.561570 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3170 | 1.58469 | ||||||||
\(52\) | −0.557439 | −0.0773028 | ||||||||
\(53\) | −8.57275 | −1.17756 | −0.588779 | − | 0.808294i | \(-0.700391\pi\) | ||||
−0.588779 | + | 0.808294i | \(0.700391\pi\) | |||||||
\(54\) | −0.476189 | −0.0648012 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.33067 | 0.311448 | ||||||||
\(57\) | 9.93077 | 1.31536 | ||||||||
\(58\) | 0.852276 | 0.111909 | ||||||||
\(59\) | 11.7387 | 1.52825 | 0.764126 | − | 0.645067i | \(-0.223171\pi\) | ||||
0.764126 | + | 0.645067i | \(0.223171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.35523 | 1.06978 | 0.534889 | − | 0.844922i | \(-0.320353\pi\) | ||||
0.534889 | + | 0.844922i | \(0.320353\pi\) | |||||||
\(62\) | 0.179579 | 0.0228066 | ||||||||
\(63\) | 2.69390 | 0.339399 | ||||||||
\(64\) | 0.470914 | 0.0588642 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.45438 | 0.548297 | ||||||||
\(67\) | 1.62871 | 0.198978 | 0.0994892 | − | 0.995039i | \(-0.468279\pi\) | ||||
0.0994892 | + | 0.995039i | \(0.468279\pi\) | |||||||
\(68\) | 7.46962 | 0.905825 | ||||||||
\(69\) | 2.38619 | 0.287263 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.755603 | 0.0896736 | 0.0448368 | − | 0.998994i | \(-0.485723\pi\) | ||||
0.0448368 | + | 0.998994i | \(0.485723\pi\) | |||||||
\(72\) | 6.27858 | 0.739937 | ||||||||
\(73\) | 6.60981 | 0.773619 | 0.386810 | − | 0.922160i | \(-0.373577\pi\) | ||||
0.386810 | + | 0.922160i | \(0.373577\pi\) | |||||||
\(74\) | 5.05968 | 0.588176 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.55469 | 0.751874 | ||||||||
\(77\) | 2.86336 | 0.326310 | ||||||||
\(78\) | 0.550599 | 0.0623430 | ||||||||
\(79\) | 3.73268 | 0.419959 | 0.209980 | − | 0.977706i | \(-0.432660\pi\) | ||||
0.209980 | + | 0.977706i | \(0.432660\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.82461 | −1.09162 | ||||||||
\(82\) | −7.69998 | −0.850321 | ||||||||
\(83\) | −3.36397 | −0.369244 | −0.184622 | − | 0.982810i | \(-0.559106\pi\) | ||||
−0.184622 | + | 0.982810i | \(0.559106\pi\) | |||||||
\(84\) | 3.75819 | 0.410052 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.80561 | −0.194704 | ||||||||
\(87\) | 3.11945 | 0.334440 | ||||||||
\(88\) | 6.67353 | 0.711401 | ||||||||
\(89\) | −13.3680 | −1.41701 | −0.708503 | − | 0.705708i | \(-0.750629\pi\) | ||||
−0.708503 | + | 0.705708i | \(0.750629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.353935 | 0.0371024 | ||||||||
\(92\) | 1.57498 | 0.164203 | ||||||||
\(93\) | 0.657285 | 0.0681573 | ||||||||
\(94\) | 2.25923 | 0.233021 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 13.6593 | 1.39410 | ||||||||
\(97\) | 15.4998 | 1.57377 | 0.786885 | − | 0.617099i | \(-0.211692\pi\) | ||||
0.786885 | + | 0.617099i | \(0.211692\pi\) | |||||||
\(98\) | −0.651939 | −0.0658558 | ||||||||
\(99\) | 7.71359 | 0.775245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2876 | 1.42167 | 0.710834 | − | 0.703360i | \(-0.248318\pi\) | ||||
0.710834 | + | 0.703360i | \(0.248318\pi\) | |||||||
\(102\) | −7.37797 | −0.730528 | ||||||||
\(103\) | −7.26200 | −0.715546 | −0.357773 | − | 0.933809i | \(-0.616464\pi\) | ||||
−0.357773 | + | 0.933809i | \(0.616464\pi\) | |||||||
\(104\) | 0.824904 | 0.0808885 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.58891 | 0.542843 | ||||||||
\(107\) | −12.7892 | −1.23637 | −0.618187 | − | 0.786031i | \(-0.712133\pi\) | ||||
−0.618187 | + | 0.786031i | \(0.712133\pi\) | |||||||
\(108\) | −1.15039 | −0.110697 | ||||||||
\(109\) | −1.39334 | −0.133458 | −0.0667288 | − | 0.997771i | \(-0.521256\pi\) | ||||
−0.0667288 | + | 0.997771i | \(0.521256\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.5191 | 1.75776 | ||||||||
\(112\) | 1.63050 | 0.154068 | ||||||||
\(113\) | 9.96960 | 0.937861 | 0.468930 | − | 0.883235i | \(-0.344639\pi\) | ||||
0.468930 | + | 0.883235i | \(0.344639\pi\) | |||||||
\(114\) | −6.47426 | −0.606370 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.05896 | 0.191169 | ||||||||
\(117\) | 0.953464 | 0.0881478 | ||||||||
\(118\) | −7.65294 | −0.704510 | ||||||||
\(119\) | −4.74269 | −0.434762 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.80118 | −0.254653 | ||||||||
\(122\) | −5.44710 | −0.493158 | ||||||||
\(123\) | −28.1830 | −2.54118 | ||||||||
\(124\) | 0.433833 | 0.0389594 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.75626 | −0.156460 | ||||||||
\(127\) | 4.28578 | 0.380301 | 0.190151 | − | 0.981755i | \(-0.439102\pi\) | ||||
0.190151 | + | 0.981755i | \(0.439102\pi\) | |||||||
\(128\) | 11.1416 | 0.984790 | ||||||||
\(129\) | −6.60877 | −0.581870 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.89892 | 0.864872 | 0.432436 | − | 0.901665i | \(-0.357654\pi\) | ||||
0.432436 | + | 0.901665i | \(0.357654\pi\) | |||||||
\(132\) | 10.7610 | 0.936628 | ||||||||
\(133\) | −4.16177 | −0.360871 | ||||||||
\(134\) | −1.06182 | −0.0917272 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.0536 | −0.947841 | ||||||||
\(137\) | −7.58744 | −0.648239 | −0.324119 | − | 0.946016i | \(-0.605068\pi\) | ||||
−0.324119 | + | 0.946016i | \(0.605068\pi\) | |||||||
\(138\) | −1.55565 | −0.132426 | ||||||||
\(139\) | 8.54023 | 0.724373 | 0.362186 | − | 0.932106i | \(-0.382030\pi\) | ||||
0.362186 | + | 0.932106i | \(0.382030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.26908 | 0.696382 | ||||||||
\(142\) | −0.492607 | −0.0413387 | ||||||||
\(143\) | 1.01344 | 0.0847483 | ||||||||
\(144\) | 4.39239 | 0.366033 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.30919 | −0.356631 | ||||||||
\(147\) | −2.38619 | −0.196810 | ||||||||
\(148\) | 12.2233 | 1.00475 | ||||||||
\(149\) | −0.273337 | −0.0223927 | −0.0111963 | − | 0.999937i | \(-0.503564\pi\) | ||||
−0.0111963 | + | 0.999937i | \(0.503564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9419 | −0.971815 | −0.485908 | − | 0.874010i | \(-0.661511\pi\) | ||||
−0.485908 | + | 0.874010i | \(0.661511\pi\) | |||||||
\(152\) | −9.69970 | −0.786750 | ||||||||
\(153\) | −12.7763 | −1.03290 | ||||||||
\(154\) | −1.86674 | −0.150426 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.33015 | 0.106498 | ||||||||
\(157\) | 13.2610 | 1.05834 | 0.529172 | − | 0.848514i | \(-0.322503\pi\) | ||||
0.529172 | + | 0.848514i | \(0.322503\pi\) | |||||||
\(158\) | −2.43348 | −0.193597 | ||||||||
\(159\) | 20.4562 | 1.62228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 6.40505 | 0.503228 | ||||||||
\(163\) | −19.3954 | −1.51916 | −0.759581 | − | 0.650413i | \(-0.774596\pi\) | ||||
−0.759581 | + | 0.650413i | \(0.774596\pi\) | |||||||
\(164\) | −18.6019 | −1.45256 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.19310 | 0.170218 | ||||||||
\(167\) | 0.682953 | 0.0528485 | 0.0264243 | − | 0.999651i | \(-0.491588\pi\) | ||||
0.0264243 | + | 0.999651i | \(0.491588\pi\) | |||||||
\(168\) | −5.56141 | −0.429072 | ||||||||
\(169\) | −12.8747 | −0.990364 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2114 | −0.857356 | ||||||||
\(172\) | −4.36204 | −0.332603 | ||||||||
\(173\) | −12.2636 | −0.932385 | −0.466192 | − | 0.884683i | \(-0.654375\pi\) | ||||
−0.466192 | + | 0.884683i | \(0.654375\pi\) | |||||||
\(174\) | −2.03369 | −0.154174 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.66870 | 0.351916 | ||||||||
\(177\) | −28.0108 | −2.10542 | ||||||||
\(178\) | 8.71513 | 0.653227 | ||||||||
\(179\) | 20.1013 | 1.50244 | 0.751219 | − | 0.660053i | \(-0.229466\pi\) | ||||
0.751219 | + | 0.660053i | \(0.229466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.54773 | −0.709677 | −0.354839 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(182\) | −0.230744 | −0.0171039 | ||||||||
\(183\) | −19.9372 | −1.47380 | ||||||||
\(184\) | −2.33067 | −0.171819 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.428510 | −0.0314199 | ||||||||
\(187\) | −13.5800 | −0.993070 | ||||||||
\(188\) | 5.45791 | 0.398059 | ||||||||
\(189\) | 0.730420 | 0.0531302 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6207 | −0.985558 | −0.492779 | − | 0.870154i | \(-0.664019\pi\) | ||||
−0.492779 | + | 0.870154i | \(0.664019\pi\) | |||||||
\(192\) | −1.12369 | −0.0810952 | ||||||||
\(193\) | −9.08238 | −0.653764 | −0.326882 | − | 0.945065i | \(-0.605998\pi\) | ||||
−0.326882 | + | 0.945065i | \(0.605998\pi\) | |||||||
\(194\) | −10.1050 | −0.725494 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.57498 | −0.112498 | ||||||||
\(197\) | −17.9479 | −1.27874 | −0.639368 | − | 0.768901i | \(-0.720804\pi\) | ||||
−0.639368 | + | 0.768901i | \(0.720804\pi\) | |||||||
\(198\) | −5.02879 | −0.357381 | ||||||||
\(199\) | −0.102119 | −0.00723901 | −0.00361950 | − | 0.999993i | \(-0.501152\pi\) | ||||
−0.00361950 | + | 0.999993i | \(0.501152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.88641 | −0.274126 | ||||||||
\(202\) | −9.31463 | −0.655375 | ||||||||
\(203\) | −1.30729 | −0.0917540 | ||||||||
\(204\) | −17.8239 | −1.24792 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.73438 | 0.329860 | ||||||||
\(207\) | −2.69390 | −0.187239 | ||||||||
\(208\) | 0.577090 | 0.0400140 | ||||||||
\(209\) | −11.9166 | −0.824291 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9081 | −0.888627 | −0.444314 | − | 0.895871i | \(-0.646552\pi\) | ||||
−0.444314 | + | 0.895871i | \(0.646552\pi\) | |||||||
\(212\) | 13.5019 | 0.927312 | ||||||||
\(213\) | −1.80301 | −0.123540 | ||||||||
\(214\) | 8.33775 | 0.569957 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.70237 | 0.115831 | ||||||||
\(217\) | −0.275454 | −0.0186990 | ||||||||
\(218\) | 0.908372 | 0.0615227 | ||||||||
\(219\) | −15.7722 | −1.06579 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.67860 | −0.112915 | ||||||||
\(222\) | −12.0734 | −0.810310 | ||||||||
\(223\) | −7.22195 | −0.483618 | −0.241809 | − | 0.970324i | \(-0.577741\pi\) | ||||
−0.241809 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(224\) | −5.72432 | −0.382472 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.49957 | −0.432345 | ||||||||
\(227\) | 5.30284 | 0.351962 | 0.175981 | − | 0.984394i | \(-0.443690\pi\) | ||||
0.175981 | + | 0.984394i | \(0.443690\pi\) | |||||||
\(228\) | −15.6407 | −1.03583 | ||||||||
\(229\) | 18.4259 | 1.21762 | 0.608809 | − | 0.793317i | \(-0.291648\pi\) | ||||
0.608809 | + | 0.793317i | \(0.291648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.83251 | −0.449546 | ||||||||
\(232\) | −3.04687 | −0.200037 | ||||||||
\(233\) | 6.04063 | 0.395735 | 0.197867 | − | 0.980229i | \(-0.436598\pi\) | ||||
0.197867 | + | 0.980229i | \(0.436598\pi\) | |||||||
\(234\) | −0.621600 | −0.0406353 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.4882 | −1.20348 | ||||||||
\(237\) | −8.90688 | −0.578564 | ||||||||
\(238\) | 3.09195 | 0.200421 | ||||||||
\(239\) | 0.955399 | 0.0617996 | 0.0308998 | − | 0.999522i | \(-0.490163\pi\) | ||||
0.0308998 | + | 0.999522i | \(0.490163\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.976650 | 0.0629116 | 0.0314558 | − | 0.999505i | \(-0.489986\pi\) | ||||
0.0314558 | + | 0.999505i | \(0.489986\pi\) | |||||||
\(242\) | 1.82620 | 0.117393 | ||||||||
\(243\) | 21.2521 | 1.36332 | ||||||||
\(244\) | −13.1593 | −0.842437 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.3736 | 1.17146 | ||||||||
\(247\) | −1.47300 | −0.0937245 | ||||||||
\(248\) | −0.641992 | −0.0407665 | ||||||||
\(249\) | 8.02707 | 0.508695 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.62574 | 0.544452 | 0.272226 | − | 0.962233i | \(-0.412240\pi\) | ||||
0.272226 | + | 0.962233i | \(0.412240\pi\) | |||||||
\(252\) | −4.24282 | −0.267273 | ||||||||
\(253\) | −2.86336 | −0.180018 | ||||||||
\(254\) | −2.79407 | −0.175315 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.20549 | −0.512843 | ||||||||
\(257\) | 22.9498 | 1.43157 | 0.715785 | − | 0.698320i | \(-0.246069\pi\) | ||||
0.715785 | + | 0.698320i | \(0.246069\pi\) | |||||||
\(258\) | 4.30852 | 0.268237 | ||||||||
\(259\) | −7.76097 | −0.482243 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.52171 | −0.217989 | ||||||||
\(262\) | −6.45349 | −0.398698 | ||||||||
\(263\) | −29.6718 | −1.82964 | −0.914822 | − | 0.403858i | \(-0.867669\pi\) | ||||
−0.914822 | + | 0.403858i | \(0.867669\pi\) | |||||||
\(264\) | −15.9243 | −0.980074 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.71322 | 0.166358 | ||||||||
\(267\) | 31.8986 | 1.95216 | ||||||||
\(268\) | −2.56518 | −0.156693 | ||||||||
\(269\) | −25.9055 | −1.57949 | −0.789743 | − | 0.613438i | \(-0.789786\pi\) | ||||
−0.789743 | + | 0.613438i | \(0.789786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4377 | −1.30225 | −0.651124 | − | 0.758971i | \(-0.725702\pi\) | ||||
−0.651124 | + | 0.758971i | \(0.725702\pi\) | |||||||
\(272\) | −7.73295 | −0.468879 | ||||||||
\(273\) | −0.844555 | −0.0511148 | ||||||||
\(274\) | 4.94655 | 0.298832 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.75819 | −0.226216 | ||||||||
\(277\) | 5.47056 | 0.328694 | 0.164347 | − | 0.986403i | \(-0.447448\pi\) | ||||
0.164347 | + | 0.986403i | \(0.447448\pi\) | |||||||
\(278\) | −5.56771 | −0.333929 | ||||||||
\(279\) | −0.742045 | −0.0444251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7416 | 0.939065 | 0.469532 | − | 0.882915i | \(-0.344423\pi\) | ||||
0.469532 | + | 0.882915i | \(0.344423\pi\) | |||||||
\(282\) | −5.39094 | −0.321026 | ||||||||
\(283\) | −17.4821 | −1.03920 | −0.519602 | − | 0.854408i | \(-0.673920\pi\) | ||||
−0.519602 | + | 0.854408i | \(0.673920\pi\) | |||||||
\(284\) | −1.19006 | −0.0706169 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.660703 | −0.0390682 | ||||||||
\(287\) | 11.8109 | 0.697175 | ||||||||
\(288\) | −15.4207 | −0.908675 | ||||||||
\(289\) | 5.49313 | 0.323125 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −36.9856 | −2.16813 | ||||||||
\(292\) | −10.4103 | −0.609216 | ||||||||
\(293\) | −22.5324 | −1.31636 | −0.658178 | − | 0.752862i | \(-0.728673\pi\) | ||||
−0.658178 | + | 0.752862i | \(0.728673\pi\) | |||||||
\(294\) | 1.55565 | 0.0907274 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.0882 | −1.05136 | ||||||||
\(297\) | 2.09145 | 0.121358 | ||||||||
\(298\) | 0.178199 | 0.0103228 | ||||||||
\(299\) | −0.353935 | −0.0204686 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.76959 | 0.159637 | ||||||||
\(302\) | 7.78537 | 0.447998 | ||||||||
\(303\) | −34.0929 | −1.95858 | ||||||||
\(304\) | −6.78576 | −0.389190 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.32939 | 0.476159 | ||||||||
\(307\) | 14.8992 | 0.850344 | 0.425172 | − | 0.905112i | \(-0.360214\pi\) | ||||
0.425172 | + | 0.905112i | \(0.360214\pi\) | |||||||
\(308\) | −4.50972 | −0.256965 | ||||||||
\(309\) | 17.3285 | 0.985785 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.4177 | −1.04437 | −0.522187 | − | 0.852831i | \(-0.674884\pi\) | ||||
−0.522187 | + | 0.852831i | \(0.674884\pi\) | |||||||
\(312\) | −1.96838 | −0.111437 | ||||||||
\(313\) | 25.7564 | 1.45584 | 0.727919 | − | 0.685664i | \(-0.240488\pi\) | ||||
0.727919 | + | 0.685664i | \(0.240488\pi\) | |||||||
\(314\) | −8.64538 | −0.487887 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.87888 | −0.330713 | ||||||||
\(317\) | −16.0330 | −0.900505 | −0.450252 | − | 0.892901i | \(-0.648666\pi\) | ||||
−0.450252 | + | 0.892901i | \(0.648666\pi\) | |||||||
\(318\) | −13.3362 | −0.747857 | ||||||||
\(319\) | −3.74325 | −0.209582 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.5173 | 1.70331 | ||||||||
\(322\) | 0.651939 | 0.0363312 | ||||||||
\(323\) | 19.7380 | 1.09825 | ||||||||
\(324\) | 15.4735 | 0.859640 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.6446 | 0.700319 | ||||||||
\(327\) | 3.32477 | 0.183860 | ||||||||
\(328\) | 27.5272 | 1.51994 | ||||||||
\(329\) | −3.46539 | −0.191053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5035 | −1.01705 | −0.508523 | − | 0.861048i | \(-0.669808\pi\) | ||||
−0.508523 | + | 0.861048i | \(0.669808\pi\) | |||||||
\(332\) | 5.29817 | 0.290775 | ||||||||
\(333\) | −20.9072 | −1.14571 | ||||||||
\(334\) | −0.445244 | −0.0243627 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.89067 | −0.212254 | ||||||||
\(337\) | 13.0653 | 0.711712 | 0.355856 | − | 0.934541i | \(-0.384189\pi\) | ||||
0.355856 | + | 0.934541i | \(0.384189\pi\) | |||||||
\(338\) | 8.39354 | 0.456549 | ||||||||
\(339\) | −23.7893 | −1.29206 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.788724 | −0.0427118 | ||||||||
\(342\) | 7.30914 | 0.395233 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.45500 | 0.348030 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.99512 | 0.429821 | ||||||||
\(347\) | −7.28070 | −0.390849 | −0.195424 | − | 0.980719i | \(-0.562608\pi\) | ||||
−0.195424 | + | 0.980719i | \(0.562608\pi\) | |||||||
\(348\) | −4.91306 | −0.263367 | ||||||||
\(349\) | −15.7564 | −0.843420 | −0.421710 | − | 0.906731i | \(-0.638570\pi\) | ||||
−0.421710 | + | 0.906731i | \(0.638570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.258521 | 0.0137988 | ||||||||
\(352\) | −16.3908 | −0.873631 | ||||||||
\(353\) | 13.4427 | 0.715482 | 0.357741 | − | 0.933821i | \(-0.383547\pi\) | ||||
0.357741 | + | 0.933821i | \(0.383547\pi\) | |||||||
\(354\) | 18.2613 | 0.970580 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21.0543 | 1.11587 | ||||||||
\(357\) | 11.3170 | 0.598957 | ||||||||
\(358\) | −13.1048 | −0.692610 | ||||||||
\(359\) | 2.96947 | 0.156722 | 0.0783612 | − | 0.996925i | \(-0.475031\pi\) | ||||
0.0783612 | + | 0.996925i | \(0.475031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.67966 | −0.0884033 | ||||||||
\(362\) | 6.22454 | 0.327155 | ||||||||
\(363\) | 6.68414 | 0.350827 | ||||||||
\(364\) | −0.557439 | −0.0292177 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.9978 | 0.679407 | ||||||||
\(367\) | −8.64514 | −0.451273 | −0.225636 | − | 0.974212i | \(-0.572446\pi\) | ||||
−0.225636 | + | 0.974212i | \(0.572446\pi\) | |||||||
\(368\) | −1.63050 | −0.0849955 | ||||||||
\(369\) | 31.8173 | 1.65634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.57275 | −0.445075 | ||||||||
\(372\) | −1.03521 | −0.0536730 | ||||||||
\(373\) | 31.8219 | 1.64767 | 0.823837 | − | 0.566827i | \(-0.191829\pi\) | ||||
0.823837 | + | 0.566827i | \(0.191829\pi\) | |||||||
\(374\) | 8.85335 | 0.457796 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.07668 | −0.416523 | ||||||||
\(377\) | −0.462697 | −0.0238301 | ||||||||
\(378\) | −0.476189 | −0.0244925 | ||||||||
\(379\) | 26.2130 | 1.34647 | 0.673234 | − | 0.739429i | \(-0.264904\pi\) | ||||
0.673234 | + | 0.739429i | \(0.264904\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.2267 | −0.523928 | ||||||||
\(382\) | 8.87986 | 0.454333 | ||||||||
\(383\) | −16.8240 | −0.859664 | −0.429832 | − | 0.902909i | \(-0.641427\pi\) | ||||
−0.429832 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(384\) | −26.5860 | −1.35671 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.92116 | 0.301379 | ||||||||
\(387\) | 7.46100 | 0.379264 | ||||||||
\(388\) | −24.4119 | −1.23933 | ||||||||
\(389\) | 9.88794 | 0.501338 | 0.250669 | − | 0.968073i | \(-0.419349\pi\) | ||||
0.250669 | + | 0.968073i | \(0.419349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.74269 | 0.239848 | ||||||||
\(392\) | 2.33067 | 0.117716 | ||||||||
\(393\) | −23.6207 | −1.19151 | ||||||||
\(394\) | 11.7010 | 0.589486 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.1487 | −0.610496 | ||||||||
\(397\) | −12.6857 | −0.636675 | −0.318338 | − | 0.947977i | \(-0.603125\pi\) | ||||
−0.318338 | + | 0.947977i | \(0.603125\pi\) | |||||||
\(398\) | 0.0665752 | 0.00333712 | ||||||||
\(399\) | 9.93077 | 0.497160 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3580 | 1.51601 | 0.758003 | − | 0.652251i | \(-0.226175\pi\) | ||||
0.758003 | + | 0.652251i | \(0.226175\pi\) | |||||||
\(402\) | 2.53370 | 0.126370 | ||||||||
\(403\) | −0.0974928 | −0.00485646 | ||||||||
\(404\) | −22.5026 | −1.11955 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.852276 | 0.0422978 | ||||||||
\(407\) | −22.2224 | −1.10152 | ||||||||
\(408\) | 26.3761 | 1.30581 | ||||||||
\(409\) | −34.5070 | −1.70626 | −0.853130 | − | 0.521699i | \(-0.825298\pi\) | ||||
−0.853130 | + | 0.521699i | \(0.825298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.1051 | 0.893057 | ||||||||
\(412\) | 11.4375 | 0.563484 | ||||||||
\(413\) | 11.7387 | 0.577625 | ||||||||
\(414\) | 1.75626 | 0.0863153 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.02604 | −0.0993346 | ||||||||
\(417\) | −20.3786 | −0.997944 | ||||||||
\(418\) | 7.76893 | 0.379991 | ||||||||
\(419\) | −17.9612 | −0.877463 | −0.438731 | − | 0.898618i | \(-0.644572\pi\) | ||||
−0.438731 | + | 0.898618i | \(0.644572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.18195 | 0.252553 | 0.126277 | − | 0.991995i | \(-0.459697\pi\) | ||||
0.126277 | + | 0.991995i | \(0.459697\pi\) | |||||||
\(422\) | 8.41527 | 0.409649 | ||||||||
\(423\) | −9.33541 | −0.453903 | ||||||||
\(424\) | −19.9802 | −0.970325 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.17545 | 0.0569509 | ||||||||
\(427\) | 8.35523 | 0.404338 | ||||||||
\(428\) | 20.1426 | 0.973629 | ||||||||
\(429\) | −2.41826 | −0.116755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.8620 | −1.48657 | −0.743286 | − | 0.668974i | \(-0.766734\pi\) | ||||
−0.743286 | + | 0.668974i | \(0.766734\pi\) | |||||||
\(432\) | 1.19095 | 0.0572995 | ||||||||
\(433\) | −36.7775 | −1.76742 | −0.883708 | − | 0.468040i | \(-0.844960\pi\) | ||||
−0.883708 | + | 0.468040i | \(0.844960\pi\) | |||||||
\(434\) | 0.179579 | 0.00862008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.19447 | 0.105096 | ||||||||
\(437\) | 4.16177 | 0.199085 | ||||||||
\(438\) | 10.2825 | 0.491319 | ||||||||
\(439\) | −17.3533 | −0.828228 | −0.414114 | − | 0.910225i | \(-0.635909\pi\) | ||||
−0.414114 | + | 0.910225i | \(0.635909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.69390 | 0.128281 | ||||||||
\(442\) | 1.09435 | 0.0520528 | ||||||||
\(443\) | 20.4177 | 0.970074 | 0.485037 | − | 0.874494i | \(-0.338806\pi\) | ||||
0.485037 | + | 0.874494i | \(0.338806\pi\) | |||||||
\(444\) | −29.1672 | −1.38421 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.70827 | 0.222943 | ||||||||
\(447\) | 0.652234 | 0.0308496 | ||||||||
\(448\) | 0.470914 | 0.0222486 | ||||||||
\(449\) | −25.7809 | −1.21667 | −0.608337 | − | 0.793679i | \(-0.708163\pi\) | ||||
−0.608337 | + | 0.793679i | \(0.708163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.8188 | 1.59246 | ||||||||
\(452\) | −15.7019 | −0.738554 | ||||||||
\(453\) | 28.4955 | 1.33884 | ||||||||
\(454\) | −3.45713 | −0.162251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 23.1453 | 1.08388 | ||||||||
\(457\) | 24.5564 | 1.14870 | 0.574350 | − | 0.818610i | \(-0.305255\pi\) | ||||
0.574350 | + | 0.818610i | \(0.305255\pi\) | |||||||
\(458\) | −12.0126 | −0.561310 | ||||||||
\(459\) | −3.46416 | −0.161693 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9461 | −0.602961 | −0.301480 | − | 0.953472i | \(-0.597481\pi\) | ||||
−0.301480 | + | 0.953472i | \(0.597481\pi\) | |||||||
\(462\) | 4.45438 | 0.207237 | ||||||||
\(463\) | 15.7702 | 0.732902 | 0.366451 | − | 0.930437i | \(-0.380573\pi\) | ||||
0.366451 | + | 0.930437i | \(0.380573\pi\) | |||||||
\(464\) | −2.13154 | −0.0989542 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.93812 | −0.182430 | ||||||||
\(467\) | 0.0437045 | 0.00202240 | 0.00101120 | − | 0.999999i | \(-0.499678\pi\) | ||||
0.00101120 | + | 0.999999i | \(0.499678\pi\) | |||||||
\(468\) | −1.50168 | −0.0694153 | ||||||||
\(469\) | 1.62871 | 0.0752068 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.6433 | −1.45805 | ||||||||
\(472\) | 27.3591 | 1.25930 | ||||||||
\(473\) | 7.93034 | 0.364637 | ||||||||
\(474\) | 5.80674 | 0.266713 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.46962 | 0.342370 | ||||||||
\(477\) | −23.0941 | −1.05741 | ||||||||
\(478\) | −0.622862 | −0.0284890 | ||||||||
\(479\) | −31.0038 | −1.41660 | −0.708299 | − | 0.705913i | \(-0.750537\pi\) | ||||
−0.708299 | + | 0.705913i | \(0.750537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.74688 | −0.125247 | ||||||||
\(482\) | −0.636717 | −0.0290017 | ||||||||
\(483\) | 2.38619 | 0.108575 | ||||||||
\(484\) | 4.41179 | 0.200536 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.8551 | −0.628480 | ||||||||
\(487\) | −30.1026 | −1.36408 | −0.682038 | − | 0.731316i | \(-0.738906\pi\) | ||||
−0.682038 | + | 0.731316i | \(0.738906\pi\) | |||||||
\(488\) | 19.4733 | 0.881513 | ||||||||
\(489\) | 46.2810 | 2.09290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4179 | −0.740930 | −0.370465 | − | 0.928847i | \(-0.620802\pi\) | ||||
−0.370465 | + | 0.928847i | \(0.620802\pi\) | |||||||
\(492\) | 44.3875 | 2.00114 | ||||||||
\(493\) | 6.20009 | 0.279238 | ||||||||
\(494\) | 0.960304 | 0.0432061 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.449127 | −0.0201664 | ||||||||
\(497\) | 0.755603 | 0.0338934 | ||||||||
\(498\) | −5.23316 | −0.234504 | ||||||||
\(499\) | −30.1437 | −1.34942 | −0.674709 | − | 0.738084i | \(-0.735731\pi\) | ||||
−0.674709 | + | 0.738084i | \(0.735731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.62966 | −0.0728077 | ||||||||
\(502\) | −5.62346 | −0.250987 | ||||||||
\(503\) | −5.01211 | −0.223479 | −0.111740 | − | 0.993738i | \(-0.535642\pi\) | ||||
−0.111740 | + | 0.993738i | \(0.535642\pi\) | |||||||
\(504\) | 6.27858 | 0.279670 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.86674 | 0.0829865 | ||||||||
\(507\) | 30.7215 | 1.36439 | ||||||||
\(508\) | −6.74999 | −0.299482 | ||||||||
\(509\) | −1.78352 | −0.0790530 | −0.0395265 | − | 0.999219i | \(-0.512585\pi\) | ||||
−0.0395265 | + | 0.999219i | \(0.512585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.60981 | 0.292401 | ||||||||
\(512\) | −16.9338 | −0.748374 | ||||||||
\(513\) | −3.03984 | −0.134212 | ||||||||
\(514\) | −14.9619 | −0.659941 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.4087 | 0.458216 | ||||||||
\(517\) | −9.92266 | −0.436398 | ||||||||
\(518\) | 5.05968 | 0.222310 | ||||||||
\(519\) | 29.2633 | 1.28452 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.95951 | −0.261091 | −0.130545 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130545 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(522\) | 2.29594 | 0.100491 | ||||||||
\(523\) | 18.1146 | 0.792095 | 0.396047 | − | 0.918230i | \(-0.370382\pi\) | ||||
0.396047 | + | 0.918230i | \(0.370382\pi\) | |||||||
\(524\) | −15.5905 | −0.681076 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.3442 | 0.843449 | ||||||||
\(527\) | 1.30639 | 0.0569074 | ||||||||
\(528\) | −11.1404 | −0.484823 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.6229 | 1.37232 | ||||||||
\(532\) | 6.55469 | 0.284182 | ||||||||
\(533\) | 4.18028 | 0.181068 | ||||||||
\(534\) | −20.7959 | −0.899929 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.79598 | 0.163961 | ||||||||
\(537\) | −47.9654 | −2.06986 | ||||||||
\(538\) | 16.8888 | 0.728128 | ||||||||
\(539\) | 2.86336 | 0.123334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.5317 | −1.22667 | −0.613337 | − | 0.789821i | \(-0.710173\pi\) | ||||
−0.613337 | + | 0.789821i | \(0.710173\pi\) | |||||||
\(542\) | 13.9761 | 0.600325 | ||||||||
\(543\) | 22.7827 | 0.977698 | ||||||||
\(544\) | 27.1487 | 1.16399 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.550599 | 0.0235634 | ||||||||
\(547\) | −22.7052 | −0.970806 | −0.485403 | − | 0.874291i | \(-0.661327\pi\) | ||||
−0.485403 | + | 0.874291i | \(0.661327\pi\) | |||||||
\(548\) | 11.9500 | 0.510480 | ||||||||
\(549\) | 22.5081 | 0.960623 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.44066 | 0.231780 | ||||||||
\(552\) | 5.56141 | 0.236709 | ||||||||
\(553\) | 3.73268 | 0.158730 | ||||||||
\(554\) | −3.56647 | −0.151525 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.4506 | −0.570434 | ||||||||
\(557\) | 7.53910 | 0.319442 | 0.159721 | − | 0.987162i | \(-0.448941\pi\) | ||||
0.159721 | + | 0.987162i | \(0.448941\pi\) | |||||||
\(558\) | 0.483768 | 0.0204795 | ||||||||
\(559\) | 0.980256 | 0.0414604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.4045 | 1.36812 | ||||||||
\(562\) | −10.2626 | −0.432900 | ||||||||
\(563\) | 20.9082 | 0.881175 | 0.440587 | − | 0.897710i | \(-0.354770\pi\) | ||||
0.440587 | + | 0.897710i | \(0.354770\pi\) | |||||||
\(564\) | −13.0236 | −0.548392 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.3973 | 0.479064 | ||||||||
\(567\) | −9.82461 | −0.412595 | ||||||||
\(568\) | 1.76106 | 0.0738924 | ||||||||
\(569\) | 23.3003 | 0.976799 | 0.488399 | − | 0.872620i | \(-0.337581\pi\) | ||||
0.488399 | + | 0.872620i | \(0.337581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.3434 | −1.81387 | −0.906933 | − | 0.421275i | \(-0.861583\pi\) | ||||
−0.906933 | + | 0.421275i | \(0.861583\pi\) | |||||||
\(572\) | −1.59615 | −0.0667382 | ||||||||
\(573\) | 32.5015 | 1.35777 | ||||||||
\(574\) | −7.69998 | −0.321391 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.26859 | 0.0528580 | ||||||||
\(577\) | −21.0757 | −0.877393 | −0.438697 | − | 0.898635i | \(-0.644560\pi\) | ||||
−0.438697 | + | 0.898635i | \(0.644560\pi\) | |||||||
\(578\) | −3.58119 | −0.148958 | ||||||||
\(579\) | 21.6723 | 0.900669 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.36397 | −0.139561 | ||||||||
\(582\) | 24.1123 | 0.999489 | ||||||||
\(583\) | −24.5469 | −1.01663 | ||||||||
\(584\) | 15.4053 | 0.637474 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.6898 | 0.606828 | ||||||||
\(587\) | −4.31958 | −0.178288 | −0.0891442 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891442 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(588\) | 3.75819 | 0.154985 | ||||||||
\(589\) | 1.14638 | 0.0472356 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.8271 | 1.76167 | ||||||||
\(592\) | −12.6542 | −0.520086 | ||||||||
\(593\) | 36.5048 | 1.49907 | 0.749536 | − | 0.661963i | \(-0.230277\pi\) | ||||
0.749536 | + | 0.661963i | \(0.230277\pi\) | |||||||
\(594\) | −1.36350 | −0.0559451 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.430499 | 0.0176339 | ||||||||
\(597\) | 0.243675 | 0.00997294 | ||||||||
\(598\) | 0.230744 | 0.00943582 | ||||||||
\(599\) | 5.43768 | 0.222178 | 0.111089 | − | 0.993810i | \(-0.464566\pi\) | ||||
0.111089 | + | 0.993810i | \(0.464566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1151 | −0.902093 | −0.451046 | − | 0.892500i | \(-0.648949\pi\) | ||||
−0.451046 | + | 0.892500i | \(0.648949\pi\) | |||||||
\(602\) | −1.80561 | −0.0735911 | ||||||||
\(603\) | 4.38757 | 0.178676 | ||||||||
\(604\) | 18.8081 | 0.765292 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.2265 | 0.902889 | ||||||||
\(607\) | −27.0386 | −1.09746 | −0.548731 | − | 0.835999i | \(-0.684889\pi\) | ||||
−0.548731 | + | 0.835999i | \(0.684889\pi\) | |||||||
\(608\) | 23.8233 | 0.966163 | ||||||||
\(609\) | 3.11945 | 0.126406 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.22652 | −0.0496198 | ||||||||
\(612\) | 20.1224 | 0.813400 | ||||||||
\(613\) | 39.7891 | 1.60707 | 0.803534 | − | 0.595259i | \(-0.202950\pi\) | ||||
0.803534 | + | 0.595259i | \(0.202950\pi\) | |||||||
\(614\) | −9.71340 | −0.392001 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.67353 | 0.268884 | ||||||||
\(617\) | 24.0782 | 0.969350 | 0.484675 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484675 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(618\) | −11.2971 | −0.454437 | ||||||||
\(619\) | 14.5254 | 0.583824 | 0.291912 | − | 0.956445i | \(-0.405709\pi\) | ||||
0.291912 | + | 0.956445i | \(0.405709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.730420 | −0.0293107 | ||||||||
\(622\) | 12.0072 | 0.481447 | ||||||||
\(623\) | −13.3680 | −0.535578 | ||||||||
\(624\) | −1.37704 | −0.0551259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.7916 | −0.671127 | ||||||||
\(627\) | 28.4354 | 1.13560 | ||||||||
\(628\) | −20.8858 | −0.833433 | ||||||||
\(629\) | 36.8079 | 1.46763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6182 | 1.01984 | 0.509922 | − | 0.860221i | \(-0.329674\pi\) | ||||
0.509922 | + | 0.860221i | \(0.329674\pi\) | |||||||
\(632\) | 8.69963 | 0.346053 | ||||||||
\(633\) | 30.8011 | 1.22423 | ||||||||
\(634\) | 10.4526 | 0.415124 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −32.2180 | −1.27753 | ||||||||
\(637\) | 0.353935 | 0.0140234 | ||||||||
\(638\) | 2.44037 | 0.0966152 | ||||||||
\(639\) | 2.03552 | 0.0805238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.316131 | 0.0124864 | 0.00624322 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624322 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(642\) | −19.8954 | −0.785211 | ||||||||
\(643\) | −4.13925 | −0.163236 | −0.0816180 | − | 0.996664i | \(-0.526009\pi\) | ||||
−0.0816180 | + | 0.996664i | \(0.526009\pi\) | |||||||
\(644\) | 1.57498 | 0.0620627 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8680 | −0.506284 | ||||||||
\(647\) | −9.73220 | −0.382612 | −0.191306 | − | 0.981530i | \(-0.561272\pi\) | ||||
−0.191306 | + | 0.981530i | \(0.561272\pi\) | |||||||
\(648\) | −22.8979 | −0.899514 | ||||||||
\(649\) | 33.6122 | 1.31939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.657285 | 0.0257610 | ||||||||
\(652\) | 30.5472 | 1.19632 | ||||||||
\(653\) | −24.6537 | −0.964775 | −0.482388 | − | 0.875958i | \(-0.660230\pi\) | ||||
−0.482388 | + | 0.875958i | \(0.660230\pi\) | |||||||
\(654\) | −2.16755 | −0.0847578 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.2576 | 0.751884 | ||||||||
\(657\) | 17.8061 | 0.694684 | ||||||||
\(658\) | 2.25923 | 0.0880738 | ||||||||
\(659\) | −6.51299 | −0.253710 | −0.126855 | − | 0.991921i | \(-0.540488\pi\) | ||||
−0.126855 | + | 0.991921i | \(0.540488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.1145 | −1.05463 | −0.527317 | − | 0.849669i | \(-0.676802\pi\) | ||||
−0.527317 | + | 0.849669i | \(0.676802\pi\) | |||||||
\(662\) | 12.0632 | 0.468849 | ||||||||
\(663\) | 4.00547 | 0.155559 | ||||||||
\(664\) | −7.84029 | −0.304262 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.6303 | 0.528162 | ||||||||
\(667\) | 1.30729 | 0.0506186 | ||||||||
\(668\) | −1.07563 | −0.0416176 | ||||||||
\(669\) | 17.2329 | 0.666264 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.9240 | 0.923576 | ||||||||
\(672\) | 13.6593 | 0.526919 | ||||||||
\(673\) | 18.6626 | 0.719392 | 0.359696 | − | 0.933070i | \(-0.382880\pi\) | ||||
0.359696 | + | 0.933070i | \(0.382880\pi\) | |||||||
\(674\) | −8.51778 | −0.328093 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.2774 | 0.779899 | ||||||||
\(677\) | −8.11307 | −0.311811 | −0.155905 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155905 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(678\) | 15.5092 | 0.595627 | ||||||||
\(679\) | 15.4998 | 0.594830 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.6536 | −0.484886 | ||||||||
\(682\) | 0.514200 | 0.0196897 | ||||||||
\(683\) | −25.2742 | −0.967090 | −0.483545 | − | 0.875320i | \(-0.660651\pi\) | ||||
−0.483545 | + | 0.875320i | \(0.660651\pi\) | |||||||
\(684\) | 17.6576 | 0.675157 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.651939 | −0.0248912 | ||||||||
\(687\) | −43.9677 | −1.67747 | ||||||||
\(688\) | 4.51582 | 0.172164 | ||||||||
\(689\) | −3.03419 | −0.115594 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.02172 | −0.305161 | −0.152580 | − | 0.988291i | \(-0.548758\pi\) | ||||
−0.152580 | + | 0.988291i | \(0.548758\pi\) | |||||||
\(692\) | 19.3149 | 0.734241 | ||||||||
\(693\) | 7.71359 | 0.293015 | ||||||||
\(694\) | 4.74658 | 0.180178 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.27040 | 0.275584 | ||||||||
\(697\) | −56.0154 | −2.12173 | ||||||||
\(698\) | 10.2722 | 0.388809 | ||||||||
\(699\) | −14.4141 | −0.545191 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6848 | 0.479098 | 0.239549 | − | 0.970884i | \(-0.423000\pi\) | ||||
0.239549 | + | 0.970884i | \(0.423000\pi\) | |||||||
\(702\) | −0.168540 | −0.00636113 | ||||||||
\(703\) | 32.2994 | 1.21819 | ||||||||
\(704\) | 1.34839 | 0.0508195 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.76382 | −0.329831 | ||||||||
\(707\) | 14.2876 | 0.537340 | ||||||||
\(708\) | 44.1163 | 1.65799 | ||||||||
\(709\) | 37.3305 | 1.40198 | 0.700989 | − | 0.713172i | \(-0.252742\pi\) | ||||
0.700989 | + | 0.713172i | \(0.252742\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0555 | 0.377109 | ||||||||
\(712\) | −31.1564 | −1.16763 | ||||||||
\(713\) | 0.275454 | 0.0103158 | ||||||||
\(714\) | −7.37797 | −0.276114 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −31.6590 | −1.18315 | ||||||||
\(717\) | −2.27976 | −0.0851392 | ||||||||
\(718\) | −1.93591 | −0.0722476 | ||||||||
\(719\) | 47.5659 | 1.77391 | 0.886954 | − | 0.461859i | \(-0.152817\pi\) | ||||
0.886954 | + | 0.461859i | \(0.152817\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.26200 | −0.270451 | ||||||||
\(722\) | 1.09504 | 0.0407531 | ||||||||
\(723\) | −2.33047 | −0.0866712 | ||||||||
\(724\) | 15.0374 | 0.558862 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.35766 | −0.161728 | ||||||||
\(727\) | −42.7962 | −1.58722 | −0.793611 | − | 0.608425i | \(-0.791802\pi\) | ||||
−0.793611 | + | 0.608425i | \(0.791802\pi\) | |||||||
\(728\) | 0.824904 | 0.0305730 | ||||||||
\(729\) | −21.2377 | −0.786582 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1353 | −0.485828 | ||||||||
\(732\) | 31.4005 | 1.16060 | ||||||||
\(733\) | −39.5165 | −1.45957 | −0.729787 | − | 0.683674i | \(-0.760381\pi\) | ||||
−0.729787 | + | 0.683674i | \(0.760381\pi\) | |||||||
\(734\) | 5.63611 | 0.208033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.72432 | 0.211001 | ||||||||
\(737\) | 4.66358 | 0.171785 | ||||||||
\(738\) | −20.7430 | −0.763559 | ||||||||
\(739\) | −36.9529 | −1.35933 | −0.679667 | − | 0.733520i | \(-0.737876\pi\) | ||||
−0.679667 | + | 0.733520i | \(0.737876\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.51485 | 0.129121 | ||||||||
\(742\) | 5.58891 | 0.205175 | ||||||||
\(743\) | −18.7266 | −0.687011 | −0.343506 | − | 0.939151i | \(-0.611614\pi\) | ||||
−0.343506 | + | 0.939151i | \(0.611614\pi\) | |||||||
\(744\) | 1.53191 | 0.0561627 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.7459 | −0.759562 | ||||||||
\(747\) | −9.06219 | −0.331568 | ||||||||
\(748\) | 21.3882 | 0.782030 | ||||||||
\(749\) | −12.7892 | −0.467305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.0833 | −1.49915 | −0.749575 | − | 0.661919i | \(-0.769742\pi\) | ||||
−0.749575 | + | 0.661919i | \(0.769742\pi\) | |||||||
\(752\) | −5.65031 | −0.206046 | ||||||||
\(753\) | −20.5827 | −0.750074 | ||||||||
\(754\) | 0.301650 | 0.0109855 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.15039 | −0.0418394 | ||||||||
\(757\) | 6.31603 | 0.229560 | 0.114780 | − | 0.993391i | \(-0.463384\pi\) | ||||
0.114780 | + | 0.993391i | \(0.463384\pi\) | |||||||
\(758\) | −17.0893 | −0.620710 | ||||||||
\(759\) | 6.83251 | 0.248005 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9208 | 1.26588 | 0.632939 | − | 0.774202i | \(-0.281849\pi\) | ||||
0.632939 | + | 0.774202i | \(0.281849\pi\) | |||||||
\(762\) | 6.66717 | 0.241526 | ||||||||
\(763\) | −1.39334 | −0.0504423 | ||||||||
\(764\) | 21.4522 | 0.776115 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.9682 | 0.396297 | ||||||||
\(767\) | 4.15474 | 0.150019 | ||||||||
\(768\) | 19.5799 | 0.706527 | ||||||||
\(769\) | −14.5251 | −0.523789 | −0.261894 | − | 0.965097i | \(-0.584347\pi\) | ||||
−0.261894 | + | 0.965097i | \(0.584347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −54.7626 | −1.97223 | ||||||||
\(772\) | 14.3045 | 0.514831 | ||||||||
\(773\) | 26.1385 | 0.940137 | 0.470069 | − | 0.882630i | \(-0.344229\pi\) | ||||
0.470069 | + | 0.882630i | \(0.344229\pi\) | |||||||
\(774\) | −4.86412 | −0.174837 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.1250 | 1.29681 | ||||||||
\(777\) | 18.5191 | 0.664370 | ||||||||
\(778\) | −6.44633 | −0.231112 | ||||||||
\(779\) | −49.1542 | −1.76113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.16356 | 0.0774184 | ||||||||
\(782\) | −3.09195 | −0.110568 | ||||||||
\(783\) | −0.954873 | −0.0341244 | ||||||||
\(784\) | 1.63050 | 0.0582320 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.3992 | 0.549273 | ||||||||
\(787\) | −4.06084 | −0.144753 | −0.0723767 | − | 0.997377i | \(-0.523058\pi\) | ||||
−0.0723767 | + | 0.997377i | \(0.523058\pi\) | |||||||
\(788\) | 28.2675 | 1.00699 | ||||||||
\(789\) | 70.8026 | 2.52064 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.96960 | 0.354478 | ||||||||
\(792\) | 17.9778 | 0.638814 | ||||||||
\(793\) | 2.95721 | 0.105013 | ||||||||
\(794\) | 8.27028 | 0.293501 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.160835 | 0.00570063 | ||||||||
\(797\) | −11.5894 | −0.410518 | −0.205259 | − | 0.978708i | \(-0.565804\pi\) | ||||
−0.205259 | + | 0.978708i | \(0.565804\pi\) | |||||||
\(798\) | −6.47426 | −0.229186 | ||||||||
\(799\) | 16.4353 | 0.581439 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.0120 | −1.27242 | ||||||||
\(802\) | −19.7916 | −0.698864 | ||||||||
\(803\) | 18.9262 | 0.667893 | ||||||||
\(804\) | 6.12099 | 0.215871 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0635594 | 0.00223878 | ||||||||
\(807\) | 61.8154 | 2.17601 | ||||||||
\(808\) | 33.2996 | 1.17148 | ||||||||
\(809\) | −43.5663 | −1.53171 | −0.765855 | − | 0.643014i | \(-0.777684\pi\) | ||||
−0.765855 | + | 0.643014i | \(0.777684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2940 | −0.607274 | −0.303637 | − | 0.952788i | \(-0.598201\pi\) | ||||
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(812\) | 2.05896 | 0.0722552 | ||||||||
\(813\) | 51.1544 | 1.79406 | ||||||||
\(814\) | 14.4877 | 0.507793 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.4523 | 0.645959 | ||||||||
\(817\) | −11.5264 | −0.403258 | ||||||||
\(818\) | 22.4964 | 0.786570 | ||||||||
\(819\) | 0.953464 | 0.0333167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.83003 | 0.238370 | 0.119185 | − | 0.992872i | \(-0.461972\pi\) | ||||
0.119185 | + | 0.992872i | \(0.461972\pi\) | |||||||
\(822\) | −11.8034 | −0.411691 | ||||||||
\(823\) | −36.1463 | −1.25998 | −0.629990 | − | 0.776604i | \(-0.716941\pi\) | ||||
−0.629990 | + | 0.776604i | \(0.716941\pi\) | |||||||
\(824\) | −16.9253 | −0.589621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.65294 | −0.266280 | ||||||||
\(827\) | 2.07579 | 0.0721824 | 0.0360912 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360912 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(828\) | 4.24282 | 0.147448 | ||||||||
\(829\) | 14.9828 | 0.520375 | 0.260188 | − | 0.965558i | \(-0.416216\pi\) | ||||
0.260188 | + | 0.965558i | \(0.416216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0538 | −0.452831 | ||||||||
\(832\) | 0.166673 | 0.00577834 | ||||||||
\(833\) | −4.74269 | −0.164325 | ||||||||
\(834\) | 13.2856 | 0.460043 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.7684 | 0.649119 | ||||||||
\(837\) | −0.201197 | −0.00695439 | ||||||||
\(838\) | 11.7096 | 0.404502 | ||||||||
\(839\) | −11.1509 | −0.384970 | −0.192485 | − | 0.981300i | \(-0.561655\pi\) | ||||
−0.192485 | + | 0.981300i | \(0.561655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2910 | −0.941068 | ||||||||
\(842\) | −3.37832 | −0.116425 | ||||||||
\(843\) | −37.5624 | −1.29372 | ||||||||
\(844\) | 20.3299 | 0.699783 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.08612 | 0.209245 | ||||||||
\(847\) | −2.80118 | −0.0962497 | ||||||||
\(848\) | −13.9778 | −0.480001 | ||||||||
\(849\) | 41.7157 | 1.43168 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.76097 | 0.266043 | ||||||||
\(852\) | 2.83970 | 0.0972865 | ||||||||
\(853\) | −49.4279 | −1.69238 | −0.846189 | − | 0.532883i | \(-0.821109\pi\) | ||||
−0.846189 | + | 0.532883i | \(0.821109\pi\) | |||||||
\(854\) | −5.44710 | −0.186396 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.8072 | −1.01879 | ||||||||
\(857\) | 40.5065 | 1.38368 | 0.691838 | − | 0.722053i | \(-0.256801\pi\) | ||||
0.691838 | + | 0.722053i | \(0.256801\pi\) | |||||||
\(858\) | 1.57656 | 0.0538229 | ||||||||
\(859\) | 39.8116 | 1.35836 | 0.679178 | − | 0.733974i | \(-0.262336\pi\) | ||||
0.679178 | + | 0.733974i | \(0.262336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.1830 | −0.960474 | ||||||||
\(862\) | 20.1202 | 0.685296 | ||||||||
\(863\) | −16.9478 | −0.576911 | −0.288455 | − | 0.957493i | \(-0.593142\pi\) | ||||
−0.288455 | + | 0.957493i | \(0.593142\pi\) | |||||||
\(864\) | −4.18116 | −0.142246 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.9767 | 0.814762 | ||||||||
\(867\) | −13.1077 | −0.445159 | ||||||||
\(868\) | 0.433833 | 0.0147253 | ||||||||
\(869\) | 10.6880 | 0.362566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.576457 | 0.0195325 | ||||||||
\(872\) | −3.24741 | −0.109971 | ||||||||
\(873\) | 41.7550 | 1.41319 | ||||||||
\(874\) | −2.71322 | −0.0917761 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.8409 | 0.839296 | ||||||||
\(877\) | −28.8892 | −0.975519 | −0.487759 | − | 0.872978i | \(-0.662186\pi\) | ||||
−0.487759 | + | 0.872978i | \(0.662186\pi\) | |||||||
\(878\) | 11.3133 | 0.381805 | ||||||||
\(879\) | 53.7666 | 1.81350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.86183 | 0.298563 | 0.149281 | − | 0.988795i | \(-0.452304\pi\) | ||||
0.149281 | + | 0.988795i | \(0.452304\pi\) | |||||||
\(882\) | −1.75626 | −0.0591363 | ||||||||
\(883\) | 51.1548 | 1.72149 | 0.860747 | − | 0.509032i | \(-0.169997\pi\) | ||||
0.860747 | + | 0.509032i | \(0.169997\pi\) | |||||||
\(884\) | 2.64376 | 0.0889193 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.3111 | −0.447195 | ||||||||
\(887\) | 0.577892 | 0.0194037 | 0.00970186 | − | 0.999953i | \(-0.496912\pi\) | ||||
0.00970186 | + | 0.999953i | \(0.496912\pi\) | |||||||
\(888\) | 43.1619 | 1.44842 | ||||||||
\(889\) | 4.28578 | 0.143740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.1314 | −0.942437 | ||||||||
\(892\) | 11.3744 | 0.380843 | ||||||||
\(893\) | 14.4222 | 0.482620 | ||||||||
\(894\) | −0.425217 | −0.0142214 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.1416 | 0.372216 | ||||||||
\(897\) | 0.844555 | 0.0281989 | ||||||||
\(898\) | 16.8076 | 0.560876 | ||||||||
\(899\) | 0.360099 | 0.0120100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.6579 | 1.35451 | ||||||||
\(902\) | −22.0478 | −0.734111 | ||||||||
\(903\) | −6.60877 | −0.219926 | ||||||||
\(904\) | 23.2358 | 0.772812 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.5774 | −0.617192 | ||||||||
\(907\) | −19.1910 | −0.637228 | −0.318614 | − | 0.947885i | \(-0.603217\pi\) | ||||
−0.318614 | + | 0.947885i | \(0.603217\pi\) | |||||||
\(908\) | −8.35185 | −0.277166 | ||||||||
\(909\) | 38.4893 | 1.27661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0336 | 0.597481 | 0.298740 | − | 0.954334i | \(-0.403434\pi\) | ||||
0.298740 | + | 0.954334i | \(0.403434\pi\) | |||||||
\(912\) | 16.1921 | 0.536174 | ||||||||
\(913\) | −9.63225 | −0.318781 | ||||||||
\(914\) | −16.0093 | −0.529540 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.0203 | −0.958859 | ||||||||
\(917\) | 9.89892 | 0.326891 | ||||||||
\(918\) | 2.25842 | 0.0745390 | ||||||||
\(919\) | −32.7118 | −1.07906 | −0.539531 | − | 0.841966i | \(-0.681399\pi\) | ||||
−0.539531 | + | 0.841966i | \(0.681399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.5524 | −1.17149 | ||||||||
\(922\) | 8.44008 | 0.277959 | ||||||||
\(923\) | 0.267434 | 0.00880271 | ||||||||
\(924\) | 10.7610 | 0.354012 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.2812 | −0.337861 | ||||||||
\(927\) | −19.5631 | −0.642536 | ||||||||
\(928\) | 7.48337 | 0.245654 | ||||||||
\(929\) | −21.5139 | −0.705850 | −0.352925 | − | 0.935652i | \(-0.614813\pi\) | ||||
−0.352925 | + | 0.935652i | \(0.614813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.16177 | −0.136397 | ||||||||
\(932\) | −9.51384 | −0.311636 | ||||||||
\(933\) | 43.9482 | 1.43880 | ||||||||
\(934\) | −0.0284927 | −0.000932309 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.22221 | 0.0726351 | ||||||||
\(937\) | −15.2891 | −0.499473 | −0.249736 | − | 0.968314i | \(-0.580344\pi\) | ||||
−0.249736 | + | 0.968314i | \(0.580344\pi\) | |||||||
\(938\) | −1.06182 | −0.0346696 | ||||||||
\(939\) | −61.4596 | −2.00566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.7826 | 0.579695 | 0.289847 | − | 0.957073i | \(-0.406395\pi\) | ||||
0.289847 | + | 0.957073i | \(0.406395\pi\) | |||||||
\(942\) | 20.6295 | 0.672146 | ||||||||
\(943\) | −11.8109 | −0.384615 | ||||||||
\(944\) | 19.1400 | 0.622953 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.17010 | −0.168094 | ||||||||
\(947\) | −15.5324 | −0.504737 | −0.252368 | − | 0.967631i | \(-0.581209\pi\) | ||||
−0.252368 | + | 0.967631i | \(0.581209\pi\) | |||||||
\(948\) | 14.0281 | 0.455612 | ||||||||
\(949\) | 2.33944 | 0.0759415 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.2578 | 1.24060 | ||||||||
\(952\) | −11.0536 | −0.358250 | ||||||||
\(953\) | −46.1468 | −1.49484 | −0.747420 | − | 0.664352i | \(-0.768708\pi\) | ||||
−0.747420 | + | 0.664352i | \(0.768708\pi\) | |||||||
\(954\) | 15.0560 | 0.487455 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.50473 | −0.0486664 | ||||||||
\(957\) | 8.93210 | 0.288734 | ||||||||
\(958\) | 20.2126 | 0.653038 | ||||||||
\(959\) | −7.58744 | −0.245011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9241 | −0.997552 | ||||||||
\(962\) | 1.79080 | 0.0577376 | ||||||||
\(963\) | −34.4527 | −1.11022 | ||||||||
\(964\) | −1.53820 | −0.0495421 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.55565 | −0.0500522 | ||||||||
\(967\) | −42.1181 | −1.35443 | −0.677213 | − | 0.735787i | \(-0.736813\pi\) | ||||
−0.677213 | + | 0.735787i | \(0.736813\pi\) | |||||||
\(968\) | −6.52862 | −0.209838 | ||||||||
\(969\) | −47.0986 | −1.51302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.5447 | −0.980227 | −0.490113 | − | 0.871659i | \(-0.663045\pi\) | ||||
−0.490113 | + | 0.871659i | \(0.663045\pi\) | |||||||
\(972\) | −33.4716 | −1.07360 | ||||||||
\(973\) | 8.54023 | 0.273787 | ||||||||
\(974\) | 19.6250 | 0.628827 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.6232 | 0.436067 | ||||||||
\(977\) | −12.7366 | −0.407479 | −0.203740 | − | 0.979025i | \(-0.565310\pi\) | ||||
−0.203740 | + | 0.979025i | \(0.565310\pi\) | |||||||
\(978\) | −30.1724 | −0.964807 | ||||||||
\(979\) | −38.2774 | −1.22335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.75351 | −0.119840 | ||||||||
\(982\) | 10.7035 | 0.341562 | ||||||||
\(983\) | 37.3247 | 1.19047 | 0.595237 | − | 0.803551i | \(-0.297058\pi\) | ||||
0.595237 | + | 0.803551i | \(0.297058\pi\) | |||||||
\(984\) | −65.6852 | −2.09397 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.04208 | −0.128726 | ||||||||
\(987\) | 8.26908 | 0.263208 | ||||||||
\(988\) | 2.31993 | 0.0738069 | ||||||||
\(989\) | −2.76959 | −0.0880680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6356 | −0.687277 | −0.343638 | − | 0.939102i | \(-0.611659\pi\) | ||||
−0.343638 | + | 0.939102i | \(0.611659\pi\) | |||||||
\(992\) | 1.57679 | 0.0500630 | ||||||||
\(993\) | 44.1529 | 1.40115 | ||||||||
\(994\) | −0.492607 | −0.0156246 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.6424 | −0.400591 | ||||||||
\(997\) | 30.2771 | 0.958885 | 0.479443 | − | 0.877573i | \(-0.340839\pi\) | ||||
0.479443 | + | 0.877573i | \(0.340839\pi\) | |||||||
\(998\) | 19.6519 | 0.622069 | ||||||||
\(999\) | −5.66877 | −0.179352 |
(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 | 4025.2.a.u.1.4 | ✓ | 8 | |
5.4 | even | 2 | 4025.2.a.v.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.u.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4025.2.a.v.1.5 | yes | 8 | 5.4 | even | 2 |