Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, 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("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9841271397\) |
Analytic rank: | \(0\) |
Dimension: | \(129\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.06267 | −1.45853 | −0.729263 | − | 0.684234i | \(-0.760137\pi\) | ||||
−0.729263 | + | 0.684234i | \(0.760137\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.25459 | 1.12730 | ||||||||
\(5\) | −1.75345 | −0.784168 | −0.392084 | − | 0.919929i | \(-0.628246\pi\) | ||||
−0.392084 | + | 0.919929i | \(0.628246\pi\) | |||||||
\(6\) | −2.06267 | −0.842080 | ||||||||
\(7\) | −2.34820 | −0.887535 | −0.443767 | − | 0.896142i | \(-0.646358\pi\) | ||||
−0.443767 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(8\) | −0.525142 | −0.185666 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.61679 | 1.14373 | ||||||||
\(11\) | −5.74292 | −1.73156 | −0.865778 | − | 0.500429i | \(-0.833176\pi\) | ||||
−0.865778 | + | 0.500429i | \(0.833176\pi\) | |||||||
\(12\) | 2.25459 | 0.650845 | ||||||||
\(13\) | 5.83807 | 1.61919 | 0.809594 | − | 0.586990i | \(-0.199687\pi\) | ||||
0.809594 | + | 0.586990i | \(0.199687\pi\) | |||||||
\(14\) | 4.84355 | 1.29449 | ||||||||
\(15\) | −1.75345 | −0.452740 | ||||||||
\(16\) | −3.42599 | −0.856499 | ||||||||
\(17\) | −2.97113 | −0.720604 | −0.360302 | − | 0.932836i | \(-0.617326\pi\) | ||||
−0.360302 | + | 0.932836i | \(0.617326\pi\) | |||||||
\(18\) | −2.06267 | −0.486175 | ||||||||
\(19\) | −6.07952 | −1.39474 | −0.697369 | − | 0.716713i | \(-0.745646\pi\) | ||||
−0.697369 | + | 0.716713i | \(0.745646\pi\) | |||||||
\(20\) | −3.95332 | −0.883990 | ||||||||
\(21\) | −2.34820 | −0.512419 | ||||||||
\(22\) | 11.8457 | 2.52552 | ||||||||
\(23\) | −2.78663 | −0.581053 | −0.290527 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290527 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(24\) | −0.525142 | −0.107194 | ||||||||
\(25\) | −1.92540 | −0.385081 | ||||||||
\(26\) | −12.0420 | −2.36163 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.29423 | −1.00052 | ||||||||
\(29\) | −5.89421 | −1.09453 | −0.547264 | − | 0.836960i | \(-0.684330\pi\) | ||||
−0.547264 | + | 0.836960i | \(0.684330\pi\) | |||||||
\(30\) | 3.61679 | 0.660332 | ||||||||
\(31\) | 9.09188 | 1.63295 | 0.816475 | − | 0.577381i | \(-0.195925\pi\) | ||||
0.816475 | + | 0.577381i | \(0.195925\pi\) | |||||||
\(32\) | 8.11697 | 1.43489 | ||||||||
\(33\) | −5.74292 | −0.999714 | ||||||||
\(34\) | 6.12844 | 1.05102 | ||||||||
\(35\) | 4.11745 | 0.695976 | ||||||||
\(36\) | 2.25459 | 0.375766 | ||||||||
\(37\) | −6.61608 | −1.08768 | −0.543838 | − | 0.839190i | \(-0.683030\pi\) | ||||
−0.543838 | + | 0.839190i | \(0.683030\pi\) | |||||||
\(38\) | 12.5400 | 2.03426 | ||||||||
\(39\) | 5.83807 | 0.934839 | ||||||||
\(40\) | 0.920811 | 0.145593 | ||||||||
\(41\) | −5.29461 | −0.826880 | −0.413440 | − | 0.910531i | \(-0.635673\pi\) | ||||
−0.413440 | + | 0.910531i | \(0.635673\pi\) | |||||||
\(42\) | 4.84355 | 0.747376 | ||||||||
\(43\) | −1.19262 | −0.181873 | −0.0909367 | − | 0.995857i | \(-0.528986\pi\) | ||||
−0.0909367 | + | 0.995857i | \(0.528986\pi\) | |||||||
\(44\) | −12.9480 | −1.95198 | ||||||||
\(45\) | −1.75345 | −0.261389 | ||||||||
\(46\) | 5.74789 | 0.847481 | ||||||||
\(47\) | −2.71820 | −0.396490 | −0.198245 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198245 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(48\) | −3.42599 | −0.494500 | ||||||||
\(49\) | −1.48597 | −0.212282 | ||||||||
\(50\) | 3.97146 | 0.561650 | ||||||||
\(51\) | −2.97113 | −0.416041 | ||||||||
\(52\) | 13.1625 | 1.82531 | ||||||||
\(53\) | −4.93841 | −0.678342 | −0.339171 | − | 0.940725i | \(-0.610147\pi\) | ||||
−0.339171 | + | 0.940725i | \(0.610147\pi\) | |||||||
\(54\) | −2.06267 | −0.280693 | ||||||||
\(55\) | 10.0699 | 1.35783 | ||||||||
\(56\) | 1.23314 | 0.164785 | ||||||||
\(57\) | −6.07952 | −0.805252 | ||||||||
\(58\) | 12.1578 | 1.59640 | ||||||||
\(59\) | −8.99053 | −1.17047 | −0.585234 | − | 0.810865i | \(-0.698997\pi\) | ||||
−0.585234 | + | 0.810865i | \(0.698997\pi\) | |||||||
\(60\) | −3.95332 | −0.510372 | ||||||||
\(61\) | −3.13818 | −0.401802 | −0.200901 | − | 0.979612i | \(-0.564387\pi\) | ||||
−0.200901 | + | 0.979612i | \(0.564387\pi\) | |||||||
\(62\) | −18.7535 | −2.38170 | ||||||||
\(63\) | −2.34820 | −0.295845 | ||||||||
\(64\) | −9.89061 | −1.23633 | ||||||||
\(65\) | −10.2368 | −1.26972 | ||||||||
\(66\) | 11.8457 | 1.45811 | ||||||||
\(67\) | 10.6438 | 1.30035 | 0.650173 | − | 0.759787i | \(-0.274697\pi\) | ||||
0.650173 | + | 0.759787i | \(0.274697\pi\) | |||||||
\(68\) | −6.69868 | −0.812334 | ||||||||
\(69\) | −2.78663 | −0.335471 | ||||||||
\(70\) | −8.49293 | −1.01510 | ||||||||
\(71\) | 8.04529 | 0.954800 | 0.477400 | − | 0.878686i | \(-0.341579\pi\) | ||||
0.477400 | + | 0.878686i | \(0.341579\pi\) | |||||||
\(72\) | −0.525142 | −0.0618886 | ||||||||
\(73\) | −15.1625 | −1.77463 | −0.887317 | − | 0.461160i | \(-0.847433\pi\) | ||||
−0.887317 | + | 0.461160i | \(0.847433\pi\) | |||||||
\(74\) | 13.6468 | 1.58640 | ||||||||
\(75\) | −1.92540 | −0.222326 | ||||||||
\(76\) | −13.7068 | −1.57228 | ||||||||
\(77\) | 13.4855 | 1.53682 | ||||||||
\(78\) | −12.0420 | −1.36349 | ||||||||
\(79\) | 9.80770 | 1.10345 | 0.551726 | − | 0.834025i | \(-0.313969\pi\) | ||||
0.551726 | + | 0.834025i | \(0.313969\pi\) | |||||||
\(80\) | 6.00732 | 0.671639 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.9210 | 1.20602 | ||||||||
\(83\) | 7.39844 | 0.812084 | 0.406042 | − | 0.913854i | \(-0.366909\pi\) | ||||
0.406042 | + | 0.913854i | \(0.366909\pi\) | |||||||
\(84\) | −5.29423 | −0.577648 | ||||||||
\(85\) | 5.20973 | 0.565074 | ||||||||
\(86\) | 2.45998 | 0.265267 | ||||||||
\(87\) | −5.89421 | −0.631926 | ||||||||
\(88\) | 3.01585 | 0.321490 | ||||||||
\(89\) | −6.33713 | −0.671735 | −0.335867 | − | 0.941909i | \(-0.609029\pi\) | ||||
−0.335867 | + | 0.941909i | \(0.609029\pi\) | |||||||
\(90\) | 3.61679 | 0.381243 | ||||||||
\(91\) | −13.7089 | −1.43709 | ||||||||
\(92\) | −6.28272 | −0.655019 | ||||||||
\(93\) | 9.09188 | 0.942784 | ||||||||
\(94\) | 5.60674 | 0.578291 | ||||||||
\(95\) | 10.6602 | 1.09371 | ||||||||
\(96\) | 8.11697 | 0.828435 | ||||||||
\(97\) | 11.9290 | 1.21121 | 0.605603 | − | 0.795767i | \(-0.292932\pi\) | ||||
0.605603 | + | 0.795767i | \(0.292932\pi\) | |||||||
\(98\) | 3.06507 | 0.309618 | ||||||||
\(99\) | −5.74292 | −0.577185 | ||||||||
\(100\) | −4.34100 | −0.434100 | ||||||||
\(101\) | 6.45468 | 0.642264 | 0.321132 | − | 0.947034i | \(-0.395937\pi\) | ||||
0.321132 | + | 0.947034i | \(0.395937\pi\) | |||||||
\(102\) | 6.12844 | 0.606806 | ||||||||
\(103\) | −17.1113 | −1.68603 | −0.843013 | − | 0.537893i | \(-0.819221\pi\) | ||||
−0.843013 | + | 0.537893i | \(0.819221\pi\) | |||||||
\(104\) | −3.06581 | −0.300628 | ||||||||
\(105\) | 4.11745 | 0.401822 | ||||||||
\(106\) | 10.1863 | 0.989379 | ||||||||
\(107\) | −5.91023 | −0.571364 | −0.285682 | − | 0.958325i | \(-0.592220\pi\) | ||||
−0.285682 | + | 0.958325i | \(0.592220\pi\) | |||||||
\(108\) | 2.25459 | 0.216948 | ||||||||
\(109\) | 7.56804 | 0.724887 | 0.362443 | − | 0.932006i | \(-0.381943\pi\) | ||||
0.362443 | + | 0.932006i | \(0.381943\pi\) | |||||||
\(110\) | −20.7709 | −1.98043 | ||||||||
\(111\) | −6.61608 | −0.627970 | ||||||||
\(112\) | 8.04491 | 0.760173 | ||||||||
\(113\) | −4.78968 | −0.450575 | −0.225288 | − | 0.974292i | \(-0.572332\pi\) | ||||
−0.225288 | + | 0.974292i | \(0.572332\pi\) | |||||||
\(114\) | 12.5400 | 1.17448 | ||||||||
\(115\) | 4.88623 | 0.455643 | ||||||||
\(116\) | −13.2890 | −1.23386 | ||||||||
\(117\) | 5.83807 | 0.539729 | ||||||||
\(118\) | 18.5445 | 1.70716 | ||||||||
\(119\) | 6.97679 | 0.639561 | ||||||||
\(120\) | 0.920811 | 0.0840582 | ||||||||
\(121\) | 21.9811 | 1.99829 | ||||||||
\(122\) | 6.47301 | 0.586039 | ||||||||
\(123\) | −5.29461 | −0.477399 | ||||||||
\(124\) | 20.4985 | 1.84082 | ||||||||
\(125\) | 12.1434 | 1.08614 | ||||||||
\(126\) | 4.84355 | 0.431497 | ||||||||
\(127\) | 0.269947 | 0.0239539 | 0.0119770 | − | 0.999928i | \(-0.496188\pi\) | ||||
0.0119770 | + | 0.999928i | \(0.496188\pi\) | |||||||
\(128\) | 4.16710 | 0.368323 | ||||||||
\(129\) | −1.19262 | −0.105005 | ||||||||
\(130\) | 21.1150 | 1.85191 | ||||||||
\(131\) | −11.2691 | −0.984582 | −0.492291 | − | 0.870431i | \(-0.663840\pi\) | ||||
−0.492291 | + | 0.870431i | \(0.663840\pi\) | |||||||
\(132\) | −12.9480 | −1.12697 | ||||||||
\(133\) | 14.2759 | 1.23788 | ||||||||
\(134\) | −21.9546 | −1.89659 | ||||||||
\(135\) | −1.75345 | −0.150913 | ||||||||
\(136\) | 1.56026 | 0.133791 | ||||||||
\(137\) | −9.18249 | −0.784513 | −0.392257 | − | 0.919856i | \(-0.628305\pi\) | ||||
−0.392257 | + | 0.919856i | \(0.628305\pi\) | |||||||
\(138\) | 5.74789 | 0.489293 | ||||||||
\(139\) | −10.4519 | −0.886517 | −0.443258 | − | 0.896394i | \(-0.646178\pi\) | ||||
−0.443258 | + | 0.896394i | \(0.646178\pi\) | |||||||
\(140\) | 9.28318 | 0.784572 | ||||||||
\(141\) | −2.71820 | −0.228914 | ||||||||
\(142\) | −16.5947 | −1.39260 | ||||||||
\(143\) | −33.5275 | −2.80371 | ||||||||
\(144\) | −3.42599 | −0.285500 | ||||||||
\(145\) | 10.3352 | 0.858293 | ||||||||
\(146\) | 31.2751 | 2.58835 | ||||||||
\(147\) | −1.48597 | −0.122561 | ||||||||
\(148\) | −14.9166 | −1.22613 | ||||||||
\(149\) | 14.7891 | 1.21157 | 0.605786 | − | 0.795627i | \(-0.292859\pi\) | ||||
0.605786 | + | 0.795627i | \(0.292859\pi\) | |||||||
\(150\) | 3.97146 | 0.324269 | ||||||||
\(151\) | −7.03452 | −0.572461 | −0.286231 | − | 0.958161i | \(-0.592402\pi\) | ||||
−0.286231 | + | 0.958161i | \(0.592402\pi\) | |||||||
\(152\) | 3.19261 | 0.258955 | ||||||||
\(153\) | −2.97113 | −0.240201 | ||||||||
\(154\) | −27.8161 | −2.24149 | ||||||||
\(155\) | −15.9422 | −1.28051 | ||||||||
\(156\) | 13.1625 | 1.05384 | ||||||||
\(157\) | −22.7939 | −1.81915 | −0.909577 | − | 0.415536i | \(-0.863594\pi\) | ||||
−0.909577 | + | 0.415536i | \(0.863594\pi\) | |||||||
\(158\) | −20.2300 | −1.60941 | ||||||||
\(159\) | −4.93841 | −0.391641 | ||||||||
\(160\) | −14.2327 | −1.12520 | ||||||||
\(161\) | 6.54356 | 0.515705 | ||||||||
\(162\) | −2.06267 | −0.162058 | ||||||||
\(163\) | −18.5965 | −1.45659 | −0.728295 | − | 0.685264i | \(-0.759687\pi\) | ||||
−0.728295 | + | 0.685264i | \(0.759687\pi\) | |||||||
\(164\) | −11.9372 | −0.932139 | ||||||||
\(165\) | 10.0699 | 0.783944 | ||||||||
\(166\) | −15.2605 | −1.18445 | ||||||||
\(167\) | −11.5593 | −0.894488 | −0.447244 | − | 0.894412i | \(-0.647594\pi\) | ||||
−0.447244 | + | 0.894412i | \(0.647594\pi\) | |||||||
\(168\) | 1.23314 | 0.0951385 | ||||||||
\(169\) | 21.0830 | 1.62177 | ||||||||
\(170\) | −10.7459 | −0.824175 | ||||||||
\(171\) | −6.07952 | −0.464912 | ||||||||
\(172\) | −2.68888 | −0.205025 | ||||||||
\(173\) | −15.8244 | −1.20311 | −0.601555 | − | 0.798831i | \(-0.705452\pi\) | ||||
−0.601555 | + | 0.798831i | \(0.705452\pi\) | |||||||
\(174\) | 12.1578 | 0.921680 | ||||||||
\(175\) | 4.52123 | 0.341773 | ||||||||
\(176\) | 19.6752 | 1.48308 | ||||||||
\(177\) | −8.99053 | −0.675770 | ||||||||
\(178\) | 13.0714 | 0.979742 | ||||||||
\(179\) | −10.1264 | −0.756881 | −0.378441 | − | 0.925626i | \(-0.623540\pi\) | ||||
−0.378441 | + | 0.925626i | \(0.623540\pi\) | |||||||
\(180\) | −3.95332 | −0.294663 | ||||||||
\(181\) | 12.5748 | 0.934680 | 0.467340 | − | 0.884078i | \(-0.345212\pi\) | ||||
0.467340 | + | 0.884078i | \(0.345212\pi\) | |||||||
\(182\) | 28.2769 | 2.09603 | ||||||||
\(183\) | −3.13818 | −0.231981 | ||||||||
\(184\) | 1.46338 | 0.107882 | ||||||||
\(185\) | 11.6010 | 0.852921 | ||||||||
\(186\) | −18.7535 | −1.37507 | ||||||||
\(187\) | 17.0629 | 1.24777 | ||||||||
\(188\) | −6.12844 | −0.446962 | ||||||||
\(189\) | −2.34820 | −0.170806 | ||||||||
\(190\) | −21.9883 | −1.59520 | ||||||||
\(191\) | 14.6363 | 1.05905 | 0.529523 | − | 0.848296i | \(-0.322371\pi\) | ||||
0.529523 | + | 0.848296i | \(0.322371\pi\) | |||||||
\(192\) | −9.89061 | −0.713793 | ||||||||
\(193\) | −9.66327 | −0.695577 | −0.347789 | − | 0.937573i | \(-0.613067\pi\) | ||||
−0.347789 | + | 0.937573i | \(0.613067\pi\) | |||||||
\(194\) | −24.6055 | −1.76658 | ||||||||
\(195\) | −10.2368 | −0.733070 | ||||||||
\(196\) | −3.35026 | −0.239305 | ||||||||
\(197\) | 17.2104 | 1.22619 | 0.613097 | − | 0.790008i | \(-0.289924\pi\) | ||||
0.613097 | + | 0.790008i | \(0.289924\pi\) | |||||||
\(198\) | 11.8457 | 0.841839 | ||||||||
\(199\) | 7.80333 | 0.553164 | 0.276582 | − | 0.960990i | \(-0.410798\pi\) | ||||
0.276582 | + | 0.960990i | \(0.410798\pi\) | |||||||
\(200\) | 1.01111 | 0.0714962 | ||||||||
\(201\) | 10.6438 | 0.750755 | ||||||||
\(202\) | −13.3138 | −0.936759 | ||||||||
\(203\) | 13.8408 | 0.971431 | ||||||||
\(204\) | −6.69868 | −0.469001 | ||||||||
\(205\) | 9.28385 | 0.648412 | ||||||||
\(206\) | 35.2949 | 2.45911 | ||||||||
\(207\) | −2.78663 | −0.193684 | ||||||||
\(208\) | −20.0012 | −1.38683 | ||||||||
\(209\) | 34.9142 | 2.41507 | ||||||||
\(210\) | −8.49293 | −0.586068 | ||||||||
\(211\) | 3.59317 | 0.247364 | 0.123682 | − | 0.992322i | \(-0.460530\pi\) | ||||
0.123682 | + | 0.992322i | \(0.460530\pi\) | |||||||
\(212\) | −11.1341 | −0.764693 | ||||||||
\(213\) | 8.04529 | 0.551254 | ||||||||
\(214\) | 12.1908 | 0.833348 | ||||||||
\(215\) | 2.09121 | 0.142619 | ||||||||
\(216\) | −0.525142 | −0.0357314 | ||||||||
\(217\) | −21.3495 | −1.44930 | ||||||||
\(218\) | −15.6103 | −1.05727 | ||||||||
\(219\) | −15.1625 | −1.02459 | ||||||||
\(220\) | 22.7036 | 1.53068 | ||||||||
\(221\) | −17.3456 | −1.16679 | ||||||||
\(222\) | 13.6468 | 0.915911 | ||||||||
\(223\) | 10.5070 | 0.703600 | 0.351800 | − | 0.936075i | \(-0.385570\pi\) | ||||
0.351800 | + | 0.936075i | \(0.385570\pi\) | |||||||
\(224\) | −19.0602 | −1.27352 | ||||||||
\(225\) | −1.92540 | −0.128360 | ||||||||
\(226\) | 9.87951 | 0.657175 | ||||||||
\(227\) | 15.5628 | 1.03294 | 0.516469 | − | 0.856306i | \(-0.327246\pi\) | ||||
0.516469 | + | 0.856306i | \(0.327246\pi\) | |||||||
\(228\) | −13.7068 | −0.907758 | ||||||||
\(229\) | 23.7411 | 1.56885 | 0.784427 | − | 0.620221i | \(-0.212957\pi\) | ||||
0.784427 | + | 0.620221i | \(0.212957\pi\) | |||||||
\(230\) | −10.0787 | −0.664567 | ||||||||
\(231\) | 13.4855 | 0.887281 | ||||||||
\(232\) | 3.09530 | 0.203216 | ||||||||
\(233\) | −15.2471 | −0.998870 | −0.499435 | − | 0.866351i | \(-0.666459\pi\) | ||||
−0.499435 | + | 0.866351i | \(0.666459\pi\) | |||||||
\(234\) | −12.0420 | −0.787209 | ||||||||
\(235\) | 4.76624 | 0.310915 | ||||||||
\(236\) | −20.2700 | −1.31946 | ||||||||
\(237\) | 9.80770 | 0.637079 | ||||||||
\(238\) | −14.3908 | −0.932816 | ||||||||
\(239\) | −8.59060 | −0.555680 | −0.277840 | − | 0.960627i | \(-0.589618\pi\) | ||||
−0.277840 | + | 0.960627i | \(0.589618\pi\) | |||||||
\(240\) | 6.00732 | 0.387771 | ||||||||
\(241\) | 8.98556 | 0.578811 | 0.289405 | − | 0.957207i | \(-0.406542\pi\) | ||||
0.289405 | + | 0.957207i | \(0.406542\pi\) | |||||||
\(242\) | −45.3398 | −2.91455 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.07531 | −0.452950 | ||||||||
\(245\) | 2.60558 | 0.166465 | ||||||||
\(246\) | 10.9210 | 0.696299 | ||||||||
\(247\) | −35.4926 | −2.25834 | ||||||||
\(248\) | −4.77453 | −0.303183 | ||||||||
\(249\) | 7.39844 | 0.468857 | ||||||||
\(250\) | −25.0477 | −1.58416 | ||||||||
\(251\) | −12.8348 | −0.810127 | −0.405064 | − | 0.914288i | \(-0.632751\pi\) | ||||
−0.405064 | + | 0.914288i | \(0.632751\pi\) | |||||||
\(252\) | −5.29423 | −0.333505 | ||||||||
\(253\) | 16.0034 | 1.00613 | ||||||||
\(254\) | −0.556811 | −0.0349374 | ||||||||
\(255\) | 5.20973 | 0.326246 | ||||||||
\(256\) | 11.1859 | 0.699118 | ||||||||
\(257\) | 3.09995 | 0.193369 | 0.0966847 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966847 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(258\) | 2.45998 | 0.153152 | ||||||||
\(259\) | 15.5359 | 0.965351 | ||||||||
\(260\) | −23.0798 | −1.43135 | ||||||||
\(261\) | −5.89421 | −0.364842 | ||||||||
\(262\) | 23.2443 | 1.43604 | ||||||||
\(263\) | 3.24562 | 0.200133 | 0.100067 | − | 0.994981i | \(-0.468094\pi\) | ||||
0.100067 | + | 0.994981i | \(0.468094\pi\) | |||||||
\(264\) | 3.01585 | 0.185613 | ||||||||
\(265\) | 8.65926 | 0.531934 | ||||||||
\(266\) | −29.4464 | −1.80548 | ||||||||
\(267\) | −6.33713 | −0.387826 | ||||||||
\(268\) | 23.9974 | 1.46588 | ||||||||
\(269\) | −4.15844 | −0.253545 | −0.126772 | − | 0.991932i | \(-0.540462\pi\) | ||||
−0.126772 | + | 0.991932i | \(0.540462\pi\) | |||||||
\(270\) | 3.61679 | 0.220111 | ||||||||
\(271\) | 14.1637 | 0.860381 | 0.430190 | − | 0.902738i | \(-0.358446\pi\) | ||||
0.430190 | + | 0.902738i | \(0.358446\pi\) | |||||||
\(272\) | 10.1791 | 0.617196 | ||||||||
\(273\) | −13.7089 | −0.829702 | ||||||||
\(274\) | 18.9404 | 1.14423 | ||||||||
\(275\) | 11.0574 | 0.666789 | ||||||||
\(276\) | −6.28272 | −0.378176 | ||||||||
\(277\) | 26.6355 | 1.60037 | 0.800187 | − | 0.599750i | \(-0.204733\pi\) | ||||
0.800187 | + | 0.599750i | \(0.204733\pi\) | |||||||
\(278\) | 21.5587 | 1.29301 | ||||||||
\(279\) | 9.09188 | 0.544317 | ||||||||
\(280\) | −2.16225 | −0.129219 | ||||||||
\(281\) | −15.8670 | −0.946548 | −0.473274 | − | 0.880915i | \(-0.656928\pi\) | ||||
−0.473274 | + | 0.880915i | \(0.656928\pi\) | |||||||
\(282\) | 5.60674 | 0.333877 | ||||||||
\(283\) | 12.8776 | 0.765496 | 0.382748 | − | 0.923853i | \(-0.374978\pi\) | ||||
0.382748 | + | 0.923853i | \(0.374978\pi\) | |||||||
\(284\) | 18.1389 | 1.07634 | ||||||||
\(285\) | 10.6602 | 0.631453 | ||||||||
\(286\) | 69.1561 | 4.08929 | ||||||||
\(287\) | 12.4328 | 0.733884 | ||||||||
\(288\) | 8.11697 | 0.478297 | ||||||||
\(289\) | −8.17241 | −0.480730 | ||||||||
\(290\) | −21.3181 | −1.25184 | ||||||||
\(291\) | 11.9290 | 0.699290 | ||||||||
\(292\) | −34.1852 | −2.00054 | ||||||||
\(293\) | −2.17925 | −0.127313 | −0.0636566 | − | 0.997972i | \(-0.520276\pi\) | ||||
−0.0636566 | + | 0.997972i | \(0.520276\pi\) | |||||||
\(294\) | 3.06507 | 0.178758 | ||||||||
\(295\) | 15.7645 | 0.917843 | ||||||||
\(296\) | 3.47438 | 0.201944 | ||||||||
\(297\) | −5.74292 | −0.333238 | ||||||||
\(298\) | −30.5050 | −1.76711 | ||||||||
\(299\) | −16.2685 | −0.940834 | ||||||||
\(300\) | −4.34100 | −0.250628 | ||||||||
\(301\) | 2.80051 | 0.161419 | ||||||||
\(302\) | 14.5099 | 0.834949 | ||||||||
\(303\) | 6.45468 | 0.370811 | ||||||||
\(304\) | 20.8284 | 1.19459 | ||||||||
\(305\) | 5.50264 | 0.315080 | ||||||||
\(306\) | 6.12844 | 0.350340 | ||||||||
\(307\) | −6.21056 | −0.354456 | −0.177228 | − | 0.984170i | \(-0.556713\pi\) | ||||
−0.177228 | + | 0.984170i | \(0.556713\pi\) | |||||||
\(308\) | 30.4043 | 1.73245 | ||||||||
\(309\) | −17.1113 | −0.973428 | ||||||||
\(310\) | 32.8834 | 1.86765 | ||||||||
\(311\) | −21.1652 | −1.20017 | −0.600083 | − | 0.799938i | \(-0.704866\pi\) | ||||
−0.600083 | + | 0.799938i | \(0.704866\pi\) | |||||||
\(312\) | −3.06581 | −0.173567 | ||||||||
\(313\) | 16.1280 | 0.911610 | 0.455805 | − | 0.890080i | \(-0.349351\pi\) | ||||
0.455805 | + | 0.890080i | \(0.349351\pi\) | |||||||
\(314\) | 47.0163 | 2.65328 | ||||||||
\(315\) | 4.11745 | 0.231992 | ||||||||
\(316\) | 22.1124 | 1.24392 | ||||||||
\(317\) | −22.2477 | −1.24956 | −0.624779 | − | 0.780802i | \(-0.714811\pi\) | ||||
−0.624779 | + | 0.780802i | \(0.714811\pi\) | |||||||
\(318\) | 10.1863 | 0.571218 | ||||||||
\(319\) | 33.8500 | 1.89523 | ||||||||
\(320\) | 17.3427 | 0.969488 | ||||||||
\(321\) | −5.91023 | −0.329877 | ||||||||
\(322\) | −13.4972 | −0.752169 | ||||||||
\(323\) | 18.0630 | 1.00505 | ||||||||
\(324\) | 2.25459 | 0.125255 | ||||||||
\(325\) | −11.2406 | −0.623518 | ||||||||
\(326\) | 38.3584 | 2.12447 | ||||||||
\(327\) | 7.56804 | 0.418514 | ||||||||
\(328\) | 2.78042 | 0.153523 | ||||||||
\(329\) | 6.38287 | 0.351899 | ||||||||
\(330\) | −20.7709 | −1.14340 | ||||||||
\(331\) | −18.5760 | −1.02103 | −0.510515 | − | 0.859869i | \(-0.670545\pi\) | ||||
−0.510515 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(332\) | 16.6805 | 0.915460 | ||||||||
\(333\) | −6.61608 | −0.362559 | ||||||||
\(334\) | 23.8431 | 1.30463 | ||||||||
\(335\) | −18.6634 | −1.01969 | ||||||||
\(336\) | 8.04491 | 0.438886 | ||||||||
\(337\) | −1.96414 | −0.106994 | −0.0534968 | − | 0.998568i | \(-0.517037\pi\) | ||||
−0.0534968 | + | 0.998568i | \(0.517037\pi\) | |||||||
\(338\) | −43.4872 | −2.36539 | ||||||||
\(339\) | −4.78968 | −0.260140 | ||||||||
\(340\) | 11.7458 | 0.637007 | ||||||||
\(341\) | −52.2139 | −2.82754 | ||||||||
\(342\) | 12.5400 | 0.678087 | ||||||||
\(343\) | 19.9267 | 1.07594 | ||||||||
\(344\) | 0.626296 | 0.0337676 | ||||||||
\(345\) | 4.88623 | 0.263066 | ||||||||
\(346\) | 32.6406 | 1.75477 | ||||||||
\(347\) | 33.9997 | 1.82520 | 0.912599 | − | 0.408856i | \(-0.134072\pi\) | ||||
0.912599 | + | 0.408856i | \(0.134072\pi\) | |||||||
\(348\) | −13.2890 | −0.712368 | ||||||||
\(349\) | −30.7446 | −1.64572 | −0.822861 | − | 0.568243i | \(-0.807623\pi\) | ||||
−0.822861 | + | 0.568243i | \(0.807623\pi\) | |||||||
\(350\) | −9.32578 | −0.498484 | ||||||||
\(351\) | 5.83807 | 0.311613 | ||||||||
\(352\) | −46.6151 | −2.48459 | ||||||||
\(353\) | −6.19576 | −0.329767 | −0.164884 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164884 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(354\) | 18.5445 | 0.985627 | ||||||||
\(355\) | −14.1070 | −0.748723 | ||||||||
\(356\) | −14.2877 | −0.757244 | ||||||||
\(357\) | 6.97679 | 0.369251 | ||||||||
\(358\) | 20.8873 | 1.10393 | ||||||||
\(359\) | −0.607933 | −0.0320855 | −0.0160427 | − | 0.999871i | \(-0.505107\pi\) | ||||
−0.0160427 | + | 0.999871i | \(0.505107\pi\) | |||||||
\(360\) | 0.920811 | 0.0485310 | ||||||||
\(361\) | 17.9606 | 0.945292 | ||||||||
\(362\) | −25.9377 | −1.36325 | ||||||||
\(363\) | 21.9811 | 1.15371 | ||||||||
\(364\) | −30.9081 | −1.62002 | ||||||||
\(365\) | 26.5867 | 1.39161 | ||||||||
\(366\) | 6.47301 | 0.338350 | ||||||||
\(367\) | 31.7741 | 1.65860 | 0.829298 | − | 0.558807i | \(-0.188741\pi\) | ||||
0.829298 | + | 0.558807i | \(0.188741\pi\) | |||||||
\(368\) | 9.54699 | 0.497671 | ||||||||
\(369\) | −5.29461 | −0.275627 | ||||||||
\(370\) | −23.9290 | −1.24401 | ||||||||
\(371\) | 11.5963 | 0.602052 | ||||||||
\(372\) | 20.4985 | 1.06280 | ||||||||
\(373\) | 27.4055 | 1.41900 | 0.709501 | − | 0.704705i | \(-0.248921\pi\) | ||||
0.709501 | + | 0.704705i | \(0.248921\pi\) | |||||||
\(374\) | −35.1952 | −1.81990 | ||||||||
\(375\) | 12.1434 | 0.627081 | ||||||||
\(376\) | 1.42744 | 0.0736146 | ||||||||
\(377\) | −34.4108 | −1.77225 | ||||||||
\(378\) | 4.84355 | 0.249125 | ||||||||
\(379\) | −27.8233 | −1.42919 | −0.714593 | − | 0.699541i | \(-0.753388\pi\) | ||||
−0.714593 | + | 0.699541i | \(0.753388\pi\) | |||||||
\(380\) | 24.0343 | 1.23293 | ||||||||
\(381\) | 0.269947 | 0.0138298 | ||||||||
\(382\) | −30.1898 | −1.54465 | ||||||||
\(383\) | −3.85887 | −0.197179 | −0.0985895 | − | 0.995128i | \(-0.531433\pi\) | ||||
−0.0985895 | + | 0.995128i | \(0.531433\pi\) | |||||||
\(384\) | 4.16710 | 0.212651 | ||||||||
\(385\) | −23.6462 | −1.20512 | ||||||||
\(386\) | 19.9321 | 1.01452 | ||||||||
\(387\) | −1.19262 | −0.0606245 | ||||||||
\(388\) | 26.8950 | 1.36539 | ||||||||
\(389\) | 15.3786 | 0.779724 | 0.389862 | − | 0.920873i | \(-0.372523\pi\) | ||||
0.389862 | + | 0.920873i | \(0.372523\pi\) | |||||||
\(390\) | 21.1150 | 1.06920 | ||||||||
\(391\) | 8.27943 | 0.418709 | ||||||||
\(392\) | 0.780346 | 0.0394134 | ||||||||
\(393\) | −11.2691 | −0.568448 | ||||||||
\(394\) | −35.4994 | −1.78843 | ||||||||
\(395\) | −17.1973 | −0.865292 | ||||||||
\(396\) | −12.9480 | −0.650659 | ||||||||
\(397\) | −26.2945 | −1.31968 | −0.659842 | − | 0.751405i | \(-0.729377\pi\) | ||||
−0.659842 | + | 0.751405i | \(0.729377\pi\) | |||||||
\(398\) | −16.0957 | −0.806803 | ||||||||
\(399\) | 14.2759 | 0.714689 | ||||||||
\(400\) | 6.59642 | 0.329821 | ||||||||
\(401\) | 22.0082 | 1.09904 | 0.549518 | − | 0.835482i | \(-0.314811\pi\) | ||||
0.549518 | + | 0.835482i | \(0.314811\pi\) | |||||||
\(402\) | −21.9546 | −1.09499 | ||||||||
\(403\) | 53.0790 | 2.64405 | ||||||||
\(404\) | 14.5527 | 0.724022 | ||||||||
\(405\) | −1.75345 | −0.0871298 | ||||||||
\(406\) | −28.5489 | −1.41686 | ||||||||
\(407\) | 37.9956 | 1.88337 | ||||||||
\(408\) | 1.56026 | 0.0772445 | ||||||||
\(409\) | −12.5874 | −0.622409 | −0.311204 | − | 0.950343i | \(-0.600732\pi\) | ||||
−0.311204 | + | 0.950343i | \(0.600732\pi\) | |||||||
\(410\) | −19.1495 | −0.945726 | ||||||||
\(411\) | −9.18249 | −0.452939 | ||||||||
\(412\) | −38.5790 | −1.90065 | ||||||||
\(413\) | 21.1115 | 1.03883 | ||||||||
\(414\) | 5.74789 | 0.282494 | ||||||||
\(415\) | −12.9728 | −0.636810 | ||||||||
\(416\) | 47.3874 | 2.32336 | ||||||||
\(417\) | −10.4519 | −0.511831 | ||||||||
\(418\) | −72.0163 | −3.52243 | ||||||||
\(419\) | 20.8928 | 1.02068 | 0.510340 | − | 0.859973i | \(-0.329519\pi\) | ||||
0.510340 | + | 0.859973i | \(0.329519\pi\) | |||||||
\(420\) | 9.28318 | 0.452973 | ||||||||
\(421\) | 30.5896 | 1.49085 | 0.745424 | − | 0.666591i | \(-0.232247\pi\) | ||||
0.745424 | + | 0.666591i | \(0.232247\pi\) | |||||||
\(422\) | −7.41151 | −0.360787 | ||||||||
\(423\) | −2.71820 | −0.132163 | ||||||||
\(424\) | 2.59336 | 0.125945 | ||||||||
\(425\) | 5.72061 | 0.277491 | ||||||||
\(426\) | −16.5947 | −0.804018 | ||||||||
\(427\) | 7.36905 | 0.356614 | ||||||||
\(428\) | −13.3252 | −0.644096 | ||||||||
\(429\) | −33.5275 | −1.61873 | ||||||||
\(430\) | −4.31347 | −0.208014 | ||||||||
\(431\) | 33.6344 | 1.62011 | 0.810055 | − | 0.586354i | \(-0.199437\pi\) | ||||
0.810055 | + | 0.586354i | \(0.199437\pi\) | |||||||
\(432\) | −3.42599 | −0.164833 | ||||||||
\(433\) | −19.2716 | −0.926135 | −0.463068 | − | 0.886323i | \(-0.653251\pi\) | ||||
−0.463068 | + | 0.886323i | \(0.653251\pi\) | |||||||
\(434\) | 44.0369 | 2.11384 | ||||||||
\(435\) | 10.3352 | 0.495536 | ||||||||
\(436\) | 17.0629 | 0.817163 | ||||||||
\(437\) | 16.9414 | 0.810416 | ||||||||
\(438\) | 31.2751 | 1.49438 | ||||||||
\(439\) | −15.5932 | −0.744223 | −0.372112 | − | 0.928188i | \(-0.621366\pi\) | ||||
−0.372112 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(440\) | −5.28815 | −0.252102 | ||||||||
\(441\) | −1.48597 | −0.0707606 | ||||||||
\(442\) | 35.7782 | 1.70180 | ||||||||
\(443\) | −7.80685 | −0.370915 | −0.185457 | − | 0.982652i | \(-0.559377\pi\) | ||||
−0.185457 | + | 0.982652i | \(0.559377\pi\) | |||||||
\(444\) | −14.9166 | −0.707909 | ||||||||
\(445\) | 11.1119 | 0.526753 | ||||||||
\(446\) | −21.6724 | −1.02622 | ||||||||
\(447\) | 14.7891 | 0.699502 | ||||||||
\(448\) | 23.2251 | 1.09728 | ||||||||
\(449\) | −35.5066 | −1.67566 | −0.837831 | − | 0.545930i | \(-0.816176\pi\) | ||||
−0.837831 | + | 0.545930i | \(0.816176\pi\) | |||||||
\(450\) | 3.97146 | 0.187217 | ||||||||
\(451\) | 30.4065 | 1.43179 | ||||||||
\(452\) | −10.7988 | −0.507932 | ||||||||
\(453\) | −7.03452 | −0.330511 | ||||||||
\(454\) | −32.1009 | −1.50657 | ||||||||
\(455\) | 24.0380 | 1.12692 | ||||||||
\(456\) | 3.19261 | 0.149508 | ||||||||
\(457\) | 11.0396 | 0.516412 | 0.258206 | − | 0.966090i | \(-0.416869\pi\) | ||||
0.258206 | + | 0.966090i | \(0.416869\pi\) | |||||||
\(458\) | −48.9699 | −2.28821 | ||||||||
\(459\) | −2.97113 | −0.138680 | ||||||||
\(460\) | 11.0165 | 0.513645 | ||||||||
\(461\) | 14.8216 | 0.690311 | 0.345155 | − | 0.938546i | \(-0.387826\pi\) | ||||
0.345155 | + | 0.938546i | \(0.387826\pi\) | |||||||
\(462\) | −27.8161 | −1.29412 | ||||||||
\(463\) | −2.52769 | −0.117472 | −0.0587360 | − | 0.998274i | \(-0.518707\pi\) | ||||
−0.0587360 | + | 0.998274i | \(0.518707\pi\) | |||||||
\(464\) | 20.1935 | 0.937461 | ||||||||
\(465\) | −15.9422 | −0.739301 | ||||||||
\(466\) | 31.4497 | 1.45688 | ||||||||
\(467\) | 6.69876 | 0.309982 | 0.154991 | − | 0.987916i | \(-0.450465\pi\) | ||||
0.154991 | + | 0.987916i | \(0.450465\pi\) | |||||||
\(468\) | 13.1625 | 0.608435 | ||||||||
\(469\) | −24.9937 | −1.15410 | ||||||||
\(470\) | −9.83116 | −0.453477 | ||||||||
\(471\) | −22.7939 | −1.05029 | ||||||||
\(472\) | 4.72130 | 0.217316 | ||||||||
\(473\) | 6.84914 | 0.314924 | ||||||||
\(474\) | −20.2300 | −0.929195 | ||||||||
\(475\) | 11.7055 | 0.537086 | ||||||||
\(476\) | 15.7298 | 0.720975 | ||||||||
\(477\) | −4.93841 | −0.226114 | ||||||||
\(478\) | 17.7195 | 0.810473 | ||||||||
\(479\) | −0.230724 | −0.0105421 | −0.00527104 | − | 0.999986i | \(-0.501678\pi\) | ||||
−0.00527104 | + | 0.999986i | \(0.501678\pi\) | |||||||
\(480\) | −14.2327 | −0.649632 | ||||||||
\(481\) | −38.6251 | −1.76115 | ||||||||
\(482\) | −18.5342 | −0.844210 | ||||||||
\(483\) | 6.54356 | 0.297742 | ||||||||
\(484\) | 49.5585 | 2.25266 | ||||||||
\(485\) | −20.9169 | −0.949789 | ||||||||
\(486\) | −2.06267 | −0.0935645 | ||||||||
\(487\) | 7.98851 | 0.361994 | 0.180997 | − | 0.983484i | \(-0.442068\pi\) | ||||
0.180997 | + | 0.983484i | \(0.442068\pi\) | |||||||
\(488\) | 1.64799 | 0.0746009 | ||||||||
\(489\) | −18.5965 | −0.840963 | ||||||||
\(490\) | −5.37445 | −0.242793 | ||||||||
\(491\) | −24.1943 | −1.09187 | −0.545936 | − | 0.837827i | \(-0.683826\pi\) | ||||
−0.545936 | + | 0.837827i | \(0.683826\pi\) | |||||||
\(492\) | −11.9372 | −0.538171 | ||||||||
\(493\) | 17.5124 | 0.788720 | ||||||||
\(494\) | 73.2095 | 3.29385 | ||||||||
\(495\) | 10.0699 | 0.452610 | ||||||||
\(496\) | −31.1487 | −1.39862 | ||||||||
\(497\) | −18.8919 | −0.847418 | ||||||||
\(498\) | −15.2605 | −0.683840 | ||||||||
\(499\) | 15.1278 | 0.677214 | 0.338607 | − | 0.940928i | \(-0.390044\pi\) | ||||
0.338607 | + | 0.940928i | \(0.390044\pi\) | |||||||
\(500\) | 27.3784 | 1.22440 | ||||||||
\(501\) | −11.5593 | −0.516433 | ||||||||
\(502\) | 26.4740 | 1.18159 | ||||||||
\(503\) | 9.93484 | 0.442972 | 0.221486 | − | 0.975164i | \(-0.428909\pi\) | ||||
0.221486 | + | 0.975164i | \(0.428909\pi\) | |||||||
\(504\) | 1.23314 | 0.0549283 | ||||||||
\(505\) | −11.3180 | −0.503643 | ||||||||
\(506\) | −33.0097 | −1.46746 | ||||||||
\(507\) | 21.0830 | 0.936329 | ||||||||
\(508\) | 0.608621 | 0.0270032 | ||||||||
\(509\) | 19.4853 | 0.863670 | 0.431835 | − | 0.901953i | \(-0.357866\pi\) | ||||
0.431835 | + | 0.901953i | \(0.357866\pi\) | |||||||
\(510\) | −10.7459 | −0.475838 | ||||||||
\(511\) | 35.6045 | 1.57505 | ||||||||
\(512\) | −31.4070 | −1.38800 | ||||||||
\(513\) | −6.07952 | −0.268417 | ||||||||
\(514\) | −6.39416 | −0.282034 | ||||||||
\(515\) | 30.0039 | 1.32213 | ||||||||
\(516\) | −2.68888 | −0.118371 | ||||||||
\(517\) | 15.6104 | 0.686545 | ||||||||
\(518\) | −32.0453 | −1.40799 | ||||||||
\(519\) | −15.8244 | −0.694616 | ||||||||
\(520\) | 5.37576 | 0.235743 | ||||||||
\(521\) | 4.55599 | 0.199601 | 0.0998007 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998007 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(522\) | 12.1578 | 0.532132 | ||||||||
\(523\) | −10.0869 | −0.441071 | −0.220535 | − | 0.975379i | \(-0.570780\pi\) | ||||
−0.220535 | + | 0.975379i | \(0.570780\pi\) | |||||||
\(524\) | −25.4071 | −1.10992 | ||||||||
\(525\) | 4.52123 | 0.197322 | ||||||||
\(526\) | −6.69462 | −0.291900 | ||||||||
\(527\) | −27.0131 | −1.17671 | ||||||||
\(528\) | 19.6752 | 0.856254 | ||||||||
\(529\) | −15.2347 | −0.662377 | ||||||||
\(530\) | −17.8612 | −0.775840 | ||||||||
\(531\) | −8.99053 | −0.390156 | ||||||||
\(532\) | 32.1864 | 1.39546 | ||||||||
\(533\) | −30.9103 | −1.33887 | ||||||||
\(534\) | 13.0714 | 0.565654 | ||||||||
\(535\) | 10.3633 | 0.448045 | ||||||||
\(536\) | −5.58950 | −0.241429 | ||||||||
\(537\) | −10.1264 | −0.436986 | ||||||||
\(538\) | 8.57748 | 0.369801 | ||||||||
\(539\) | 8.53382 | 0.367578 | ||||||||
\(540\) | −3.95332 | −0.170124 | ||||||||
\(541\) | −13.3524 | −0.574066 | −0.287033 | − | 0.957921i | \(-0.592669\pi\) | ||||
−0.287033 | + | 0.957921i | \(0.592669\pi\) | |||||||
\(542\) | −29.2149 | −1.25489 | ||||||||
\(543\) | 12.5748 | 0.539638 | ||||||||
\(544\) | −24.1165 | −1.03399 | ||||||||
\(545\) | −13.2702 | −0.568433 | ||||||||
\(546\) | 28.2769 | 1.21014 | ||||||||
\(547\) | −19.6539 | −0.840340 | −0.420170 | − | 0.907445i | \(-0.638030\pi\) | ||||
−0.420170 | + | 0.907445i | \(0.638030\pi\) | |||||||
\(548\) | −20.7028 | −0.884379 | ||||||||
\(549\) | −3.13818 | −0.133934 | ||||||||
\(550\) | −22.8078 | −0.972528 | ||||||||
\(551\) | 35.8340 | 1.52658 | ||||||||
\(552\) | 1.46338 | 0.0622855 | ||||||||
\(553\) | −23.0304 | −0.979353 | ||||||||
\(554\) | −54.9402 | −2.33419 | ||||||||
\(555\) | 11.6010 | 0.492434 | ||||||||
\(556\) | −23.5647 | −0.999368 | ||||||||
\(557\) | 6.55433 | 0.277716 | 0.138858 | − | 0.990312i | \(-0.455657\pi\) | ||||
0.138858 | + | 0.990312i | \(0.455657\pi\) | |||||||
\(558\) | −18.7535 | −0.793900 | ||||||||
\(559\) | −6.96261 | −0.294487 | ||||||||
\(560\) | −14.1064 | −0.596103 | ||||||||
\(561\) | 17.0629 | 0.720398 | ||||||||
\(562\) | 32.7284 | 1.38056 | ||||||||
\(563\) | 22.2577 | 0.938051 | 0.469025 | − | 0.883185i | \(-0.344605\pi\) | ||||
0.469025 | + | 0.883185i | \(0.344605\pi\) | |||||||
\(564\) | −6.12844 | −0.258054 | ||||||||
\(565\) | 8.39848 | 0.353327 | ||||||||
\(566\) | −26.5623 | −1.11649 | ||||||||
\(567\) | −2.34820 | −0.0986150 | ||||||||
\(568\) | −4.22492 | −0.177274 | ||||||||
\(569\) | −31.1963 | −1.30782 | −0.653909 | − | 0.756573i | \(-0.726872\pi\) | ||||
−0.653909 | + | 0.756573i | \(0.726872\pi\) | |||||||
\(570\) | −21.9883 | −0.920990 | ||||||||
\(571\) | 2.54348 | 0.106441 | 0.0532206 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532206 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(572\) | −75.5910 | −3.16062 | ||||||||
\(573\) | 14.6363 | 0.611440 | ||||||||
\(574\) | −25.6447 | −1.07039 | ||||||||
\(575\) | 5.36539 | 0.223752 | ||||||||
\(576\) | −9.89061 | −0.412109 | ||||||||
\(577\) | −21.2119 | −0.883061 | −0.441530 | − | 0.897246i | \(-0.645564\pi\) | ||||
−0.441530 | + | 0.897246i | \(0.645564\pi\) | |||||||
\(578\) | 16.8570 | 0.701157 | ||||||||
\(579\) | −9.66327 | −0.401592 | ||||||||
\(580\) | 23.3017 | 0.967551 | ||||||||
\(581\) | −17.3730 | −0.720753 | ||||||||
\(582\) | −24.6055 | −1.01993 | ||||||||
\(583\) | 28.3609 | 1.17459 | ||||||||
\(584\) | 7.96245 | 0.329489 | ||||||||
\(585\) | −10.2368 | −0.423238 | ||||||||
\(586\) | 4.49507 | 0.185689 | ||||||||
\(587\) | −16.2897 | −0.672348 | −0.336174 | − | 0.941800i | \(-0.609133\pi\) | ||||
−0.336174 | + | 0.941800i | \(0.609133\pi\) | |||||||
\(588\) | −3.35026 | −0.138163 | ||||||||
\(589\) | −55.2743 | −2.27754 | ||||||||
\(590\) | −32.5168 | −1.33870 | ||||||||
\(591\) | 17.2104 | 0.707943 | ||||||||
\(592\) | 22.6667 | 0.931594 | ||||||||
\(593\) | −5.00956 | −0.205718 | −0.102859 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102859 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(594\) | 11.8457 | 0.486036 | ||||||||
\(595\) | −12.2335 | −0.501523 | ||||||||
\(596\) | 33.3435 | 1.36580 | ||||||||
\(597\) | 7.80333 | 0.319369 | ||||||||
\(598\) | 33.5566 | 1.37223 | ||||||||
\(599\) | 2.44227 | 0.0997883 | 0.0498942 | − | 0.998755i | \(-0.484112\pi\) | ||||
0.0498942 | + | 0.998755i | \(0.484112\pi\) | |||||||
\(600\) | 1.01111 | 0.0412784 | ||||||||
\(601\) | 31.6885 | 1.29260 | 0.646301 | − | 0.763082i | \(-0.276315\pi\) | ||||
0.646301 | + | 0.763082i | \(0.276315\pi\) | |||||||
\(602\) | −5.77653 | −0.235434 | ||||||||
\(603\) | 10.6438 | 0.433448 | ||||||||
\(604\) | −15.8600 | −0.645334 | ||||||||
\(605\) | −38.5429 | −1.56699 | ||||||||
\(606\) | −13.3138 | −0.540838 | ||||||||
\(607\) | 20.1771 | 0.818962 | 0.409481 | − | 0.912319i | \(-0.365710\pi\) | ||||
0.409481 | + | 0.912319i | \(0.365710\pi\) | |||||||
\(608\) | −49.3473 | −2.00130 | ||||||||
\(609\) | 13.8408 | 0.560856 | ||||||||
\(610\) | −11.3501 | −0.459553 | ||||||||
\(611\) | −15.8690 | −0.641992 | ||||||||
\(612\) | −6.69868 | −0.270778 | ||||||||
\(613\) | 10.6343 | 0.429517 | 0.214758 | − | 0.976667i | \(-0.431104\pi\) | ||||
0.214758 | + | 0.976667i | \(0.431104\pi\) | |||||||
\(614\) | 12.8103 | 0.516983 | ||||||||
\(615\) | 9.28385 | 0.374361 | ||||||||
\(616\) | −7.08180 | −0.285334 | ||||||||
\(617\) | 45.9155 | 1.84849 | 0.924244 | − | 0.381802i | \(-0.124696\pi\) | ||||
0.924244 | + | 0.381802i | \(0.124696\pi\) | |||||||
\(618\) | 35.2949 | 1.41977 | ||||||||
\(619\) | 12.6650 | 0.509051 | 0.254526 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254526 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(620\) | −35.9431 | −1.44351 | ||||||||
\(621\) | −2.78663 | −0.111824 | ||||||||
\(622\) | 43.6567 | 1.75047 | ||||||||
\(623\) | 14.8808 | 0.596188 | ||||||||
\(624\) | −20.0012 | −0.800688 | ||||||||
\(625\) | −11.6658 | −0.466632 | ||||||||
\(626\) | −33.2667 | −1.32961 | ||||||||
\(627\) | 34.9142 | 1.39434 | ||||||||
\(628\) | −51.3911 | −2.05073 | ||||||||
\(629\) | 19.6572 | 0.783784 | ||||||||
\(630\) | −8.49293 | −0.338366 | ||||||||
\(631\) | 43.5251 | 1.73271 | 0.866354 | − | 0.499430i | \(-0.166457\pi\) | ||||
0.866354 | + | 0.499430i | \(0.166457\pi\) | |||||||
\(632\) | −5.15043 | −0.204873 | ||||||||
\(633\) | 3.59317 | 0.142816 | ||||||||
\(634\) | 45.8897 | 1.82251 | ||||||||
\(635\) | −0.473340 | −0.0187839 | ||||||||
\(636\) | −11.1341 | −0.441496 | ||||||||
\(637\) | −8.67520 | −0.343724 | ||||||||
\(638\) | −69.8212 | −2.76425 | ||||||||
\(639\) | 8.04529 | 0.318267 | ||||||||
\(640\) | −7.30681 | −0.288827 | ||||||||
\(641\) | −21.4752 | −0.848221 | −0.424111 | − | 0.905610i | \(-0.639413\pi\) | ||||
−0.424111 | + | 0.905610i | \(0.639413\pi\) | |||||||
\(642\) | 12.1908 | 0.481134 | ||||||||
\(643\) | 4.46377 | 0.176034 | 0.0880169 | − | 0.996119i | \(-0.471947\pi\) | ||||
0.0880169 | + | 0.996119i | \(0.471947\pi\) | |||||||
\(644\) | 14.7531 | 0.581352 | ||||||||
\(645\) | 2.09121 | 0.0823413 | ||||||||
\(646\) | −37.2580 | −1.46590 | ||||||||
\(647\) | 17.6308 | 0.693140 | 0.346570 | − | 0.938024i | \(-0.387346\pi\) | ||||
0.346570 | + | 0.938024i | \(0.387346\pi\) | |||||||
\(648\) | −0.525142 | −0.0206295 | ||||||||
\(649\) | 51.6319 | 2.02673 | ||||||||
\(650\) | 23.1857 | 0.909417 | ||||||||
\(651\) | −21.3495 | −0.836754 | ||||||||
\(652\) | −41.9276 | −1.64201 | ||||||||
\(653\) | −3.75621 | −0.146992 | −0.0734960 | − | 0.997296i | \(-0.523416\pi\) | ||||
−0.0734960 | + | 0.997296i | \(0.523416\pi\) | |||||||
\(654\) | −15.6103 | −0.610413 | ||||||||
\(655\) | 19.7597 | 0.772077 | ||||||||
\(656\) | 18.1393 | 0.708221 | ||||||||
\(657\) | −15.1625 | −0.591545 | ||||||||
\(658\) | −13.1657 | −0.513254 | ||||||||
\(659\) | −29.9039 | −1.16489 | −0.582445 | − | 0.812870i | \(-0.697904\pi\) | ||||
−0.582445 | + | 0.812870i | \(0.697904\pi\) | |||||||
\(660\) | 22.7036 | 0.883737 | ||||||||
\(661\) | −10.4154 | −0.405111 | −0.202556 | − | 0.979271i | \(-0.564925\pi\) | ||||
−0.202556 | + | 0.979271i | \(0.564925\pi\) | |||||||
\(662\) | 38.3161 | 1.48920 | ||||||||
\(663\) | −17.3456 | −0.673648 | ||||||||
\(664\) | −3.88523 | −0.150776 | ||||||||
\(665\) | −25.0321 | −0.970704 | ||||||||
\(666\) | 13.6468 | 0.528801 | ||||||||
\(667\) | 16.4250 | 0.635978 | ||||||||
\(668\) | −26.0616 | −1.00835 | ||||||||
\(669\) | 10.5070 | 0.406224 | ||||||||
\(670\) | 38.4963 | 1.48724 | ||||||||
\(671\) | 18.0223 | 0.695743 | ||||||||
\(672\) | −19.0602 | −0.735265 | ||||||||
\(673\) | 11.0022 | 0.424103 | 0.212051 | − | 0.977259i | \(-0.431986\pi\) | ||||
0.212051 | + | 0.977259i | \(0.431986\pi\) | |||||||
\(674\) | 4.05137 | 0.156053 | ||||||||
\(675\) | −1.92540 | −0.0741088 | ||||||||
\(676\) | 47.5336 | 1.82822 | ||||||||
\(677\) | −17.7667 | −0.682831 | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||||
−0.341415 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(678\) | 9.87951 | 0.379420 | ||||||||
\(679\) | −28.0116 | −1.07499 | ||||||||
\(680\) | −2.73585 | −0.104915 | ||||||||
\(681\) | 15.5628 | 0.596368 | ||||||||
\(682\) | 107.700 | 4.12404 | ||||||||
\(683\) | 41.3786 | 1.58331 | 0.791653 | − | 0.610971i | \(-0.209221\pi\) | ||||
0.791653 | + | 0.610971i | \(0.209221\pi\) | |||||||
\(684\) | −13.7068 | −0.524094 | ||||||||
\(685\) | 16.1011 | 0.615190 | ||||||||
\(686\) | −41.1022 | −1.56929 | ||||||||
\(687\) | 23.7411 | 0.905778 | ||||||||
\(688\) | 4.08592 | 0.155774 | ||||||||
\(689\) | −28.8307 | −1.09836 | ||||||||
\(690\) | −10.0787 | −0.383688 | ||||||||
\(691\) | 22.8807 | 0.870424 | 0.435212 | − | 0.900328i | \(-0.356673\pi\) | ||||
0.435212 | + | 0.900328i | \(0.356673\pi\) | |||||||
\(692\) | −35.6777 | −1.35626 | ||||||||
\(693\) | 13.4855 | 0.512272 | ||||||||
\(694\) | −70.1300 | −2.66210 | ||||||||
\(695\) | 18.3269 | 0.695178 | ||||||||
\(696\) | 3.09530 | 0.117327 | ||||||||
\(697\) | 15.7310 | 0.595853 | ||||||||
\(698\) | 63.4159 | 2.40033 | ||||||||
\(699\) | −15.2471 | −0.576698 | ||||||||
\(700\) | 10.1935 | 0.385279 | ||||||||
\(701\) | 36.3433 | 1.37267 | 0.686333 | − | 0.727287i | \(-0.259219\pi\) | ||||
0.686333 | + | 0.727287i | \(0.259219\pi\) | |||||||
\(702\) | −12.0420 | −0.454495 | ||||||||
\(703\) | 40.2226 | 1.51702 | ||||||||
\(704\) | 56.8010 | 2.14077 | ||||||||
\(705\) | 4.76624 | 0.179507 | ||||||||
\(706\) | 12.7798 | 0.480974 | ||||||||
\(707\) | −15.1568 | −0.570032 | ||||||||
\(708\) | −20.2700 | −0.761793 | ||||||||
\(709\) | 18.4936 | 0.694542 | 0.347271 | − | 0.937765i | \(-0.387108\pi\) | ||||
0.347271 | + | 0.937765i | \(0.387108\pi\) | |||||||
\(710\) | 29.0981 | 1.09203 | ||||||||
\(711\) | 9.80770 | 0.367817 | ||||||||
\(712\) | 3.32789 | 0.124718 | ||||||||
\(713\) | −25.3357 | −0.948830 | ||||||||
\(714\) | −14.3908 | −0.538562 | ||||||||
\(715\) | 58.7890 | 2.19858 | ||||||||
\(716\) | −22.8309 | −0.853230 | ||||||||
\(717\) | −8.59060 | −0.320822 | ||||||||
\(718\) | 1.25396 | 0.0467975 | ||||||||
\(719\) | −14.1463 | −0.527567 | −0.263784 | − | 0.964582i | \(-0.584971\pi\) | ||||
−0.263784 | + | 0.964582i | \(0.584971\pi\) | |||||||
\(720\) | 6.00732 | 0.223880 | ||||||||
\(721\) | 40.1807 | 1.49641 | ||||||||
\(722\) | −37.0466 | −1.37873 | ||||||||
\(723\) | 8.98556 | 0.334177 | ||||||||
\(724\) | 28.3511 | 1.05366 | ||||||||
\(725\) | 11.3487 | 0.421481 | ||||||||
\(726\) | −45.3398 | −1.68272 | ||||||||
\(727\) | −43.1277 | −1.59952 | −0.799759 | − | 0.600321i | \(-0.795039\pi\) | ||||
−0.799759 | + | 0.600321i | \(0.795039\pi\) | |||||||
\(728\) | 7.19913 | 0.266818 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −54.8395 | −2.02970 | ||||||||
\(731\) | 3.54343 | 0.131059 | ||||||||
\(732\) | −7.07531 | −0.261511 | ||||||||
\(733\) | 28.2638 | 1.04395 | 0.521973 | − | 0.852962i | \(-0.325196\pi\) | ||||
0.521973 | + | 0.852962i | \(0.325196\pi\) | |||||||
\(734\) | −65.5394 | −2.41910 | ||||||||
\(735\) | 2.60558 | 0.0961084 | ||||||||
\(736\) | −22.6190 | −0.833748 | ||||||||
\(737\) | −61.1264 | −2.25162 | ||||||||
\(738\) | 10.9210 | 0.402008 | ||||||||
\(739\) | −11.4938 | −0.422808 | −0.211404 | − | 0.977399i | \(-0.567804\pi\) | ||||
−0.211404 | + | 0.977399i | \(0.567804\pi\) | |||||||
\(740\) | 26.1555 | 0.961495 | ||||||||
\(741\) | −35.4926 | −1.30385 | ||||||||
\(742\) | −23.9194 | −0.878109 | ||||||||
\(743\) | −45.7776 | −1.67942 | −0.839709 | − | 0.543037i | \(-0.817274\pi\) | ||||
−0.839709 | + | 0.543037i | \(0.817274\pi\) | |||||||
\(744\) | −4.77453 | −0.175043 | ||||||||
\(745\) | −25.9320 | −0.950076 | ||||||||
\(746\) | −56.5283 | −2.06965 | ||||||||
\(747\) | 7.39844 | 0.270695 | ||||||||
\(748\) | 38.4700 | 1.40660 | ||||||||
\(749\) | 13.8784 | 0.507105 | ||||||||
\(750\) | −25.0477 | −0.914613 | ||||||||
\(751\) | −8.56790 | −0.312647 | −0.156324 | − | 0.987706i | \(-0.549964\pi\) | ||||
−0.156324 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(752\) | 9.31254 | 0.339593 | ||||||||
\(753\) | −12.8348 | −0.467727 | ||||||||
\(754\) | 70.9780 | 2.58487 | ||||||||
\(755\) | 12.3347 | 0.448906 | ||||||||
\(756\) | −5.29423 | −0.192549 | ||||||||
\(757\) | 34.3507 | 1.24850 | 0.624249 | − | 0.781225i | \(-0.285405\pi\) | ||||
0.624249 | + | 0.781225i | \(0.285405\pi\) | |||||||
\(758\) | 57.3901 | 2.08450 | ||||||||
\(759\) | 16.0034 | 0.580887 | ||||||||
\(760\) | −5.59809 | −0.203064 | ||||||||
\(761\) | 17.4524 | 0.632651 | 0.316325 | − | 0.948651i | \(-0.397551\pi\) | ||||
0.316325 | + | 0.948651i | \(0.397551\pi\) | |||||||
\(762\) | −0.556811 | −0.0201711 | ||||||||
\(763\) | −17.7712 | −0.643362 | ||||||||
\(764\) | 32.9989 | 1.19386 | ||||||||
\(765\) | 5.20973 | 0.188358 | ||||||||
\(766\) | 7.95956 | 0.287591 | ||||||||
\(767\) | −52.4873 | −1.89521 | ||||||||
\(768\) | 11.1859 | 0.403636 | ||||||||
\(769\) | 27.2706 | 0.983401 | 0.491701 | − | 0.870764i | \(-0.336375\pi\) | ||||
0.491701 | + | 0.870764i | \(0.336375\pi\) | |||||||
\(770\) | 48.7742 | 1.75770 | ||||||||
\(771\) | 3.09995 | 0.111642 | ||||||||
\(772\) | −21.7867 | −0.784122 | ||||||||
\(773\) | −3.98214 | −0.143228 | −0.0716138 | − | 0.997432i | \(-0.522815\pi\) | ||||
−0.0716138 | + | 0.997432i | \(0.522815\pi\) | |||||||
\(774\) | 2.45998 | 0.0884223 | ||||||||
\(775\) | −17.5055 | −0.628817 | ||||||||
\(776\) | −6.26441 | −0.224879 | ||||||||
\(777\) | 15.5359 | 0.557346 | ||||||||
\(778\) | −31.7208 | −1.13725 | ||||||||
\(779\) | 32.1887 | 1.15328 | ||||||||
\(780\) | −23.0798 | −0.826388 | ||||||||
\(781\) | −46.2034 | −1.65329 | ||||||||
\(782\) | −17.0777 | −0.610698 | ||||||||
\(783\) | −5.89421 | −0.210642 | ||||||||
\(784\) | 5.09093 | 0.181819 | ||||||||
\(785\) | 39.9681 | 1.42652 | ||||||||
\(786\) | 23.2443 | 0.829097 | ||||||||
\(787\) | −42.5511 | −1.51678 | −0.758391 | − | 0.651800i | \(-0.774014\pi\) | ||||
−0.758391 | + | 0.651800i | \(0.774014\pi\) | |||||||
\(788\) | 38.8025 | 1.38228 | ||||||||
\(789\) | 3.24562 | 0.115547 | ||||||||
\(790\) | 35.4724 | 1.26205 | ||||||||
\(791\) | 11.2471 | 0.399901 | ||||||||
\(792\) | 3.01585 | 0.107163 | ||||||||
\(793\) | −18.3209 | −0.650593 | ||||||||
\(794\) | 54.2368 | 1.92479 | ||||||||
\(795\) | 8.65926 | 0.307112 | ||||||||
\(796\) | 17.5933 | 0.623580 | ||||||||
\(797\) | 32.9982 | 1.16886 | 0.584428 | − | 0.811445i | \(-0.301319\pi\) | ||||
0.584428 | + | 0.811445i | \(0.301319\pi\) | |||||||
\(798\) | −29.4464 | −1.04239 | ||||||||
\(799\) | 8.07611 | 0.285712 | ||||||||
\(800\) | −15.6284 | −0.552549 | ||||||||
\(801\) | −6.33713 | −0.223912 | ||||||||
\(802\) | −45.3955 | −1.60297 | ||||||||
\(803\) | 87.0769 | 3.07288 | ||||||||
\(804\) | 23.9974 | 0.846323 | ||||||||
\(805\) | −11.4738 | −0.404399 | ||||||||
\(806\) | −109.484 | −3.85642 | ||||||||
\(807\) | −4.15844 | −0.146384 | ||||||||
\(808\) | −3.38962 | −0.119246 | ||||||||
\(809\) | −14.8147 | −0.520857 | −0.260428 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260428 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(810\) | 3.61679 | 0.127081 | ||||||||
\(811\) | 29.4365 | 1.03365 | 0.516827 | − | 0.856090i | \(-0.327113\pi\) | ||||
0.516827 | + | 0.856090i | \(0.327113\pi\) | |||||||
\(812\) | 31.2053 | 1.09509 | ||||||||
\(813\) | 14.1637 | 0.496741 | ||||||||
\(814\) | −78.3723 | −2.74695 | ||||||||
\(815\) | 32.6081 | 1.14221 | ||||||||
\(816\) | 10.1791 | 0.356338 | ||||||||
\(817\) | 7.25058 | 0.253666 | ||||||||
\(818\) | 25.9637 | 0.907799 | ||||||||
\(819\) | −13.7089 | −0.479029 | ||||||||
\(820\) | 20.9313 | 0.730953 | ||||||||
\(821\) | 12.4308 | 0.433840 | 0.216920 | − | 0.976189i | \(-0.430399\pi\) | ||||
0.216920 | + | 0.976189i | \(0.430399\pi\) | |||||||
\(822\) | 18.9404 | 0.660623 | ||||||||
\(823\) | 0.940208 | 0.0327736 | 0.0163868 | − | 0.999866i | \(-0.494784\pi\) | ||||
0.0163868 | + | 0.999866i | \(0.494784\pi\) | |||||||
\(824\) | 8.98586 | 0.313037 | ||||||||
\(825\) | 11.0574 | 0.384971 | ||||||||
\(826\) | −43.5461 | −1.51516 | ||||||||
\(827\) | 10.7058 | 0.372278 | 0.186139 | − | 0.982523i | \(-0.440403\pi\) | ||||
0.186139 | + | 0.982523i | \(0.440403\pi\) | |||||||
\(828\) | −6.28272 | −0.218340 | ||||||||
\(829\) | −24.0501 | −0.835294 | −0.417647 | − | 0.908609i | \(-0.637145\pi\) | ||||
−0.417647 | + | 0.908609i | \(0.637145\pi\) | |||||||
\(830\) | 26.7586 | 0.928804 | ||||||||
\(831\) | 26.6355 | 0.923977 | ||||||||
\(832\) | −57.7420 | −2.00184 | ||||||||
\(833\) | 4.41501 | 0.152971 | ||||||||
\(834\) | 21.5587 | 0.746518 | ||||||||
\(835\) | 20.2688 | 0.701429 | ||||||||
\(836\) | 78.7173 | 2.72250 | ||||||||
\(837\) | 9.09188 | 0.314261 | ||||||||
\(838\) | −43.0949 | −1.48869 | ||||||||
\(839\) | 46.3803 | 1.60123 | 0.800613 | − | 0.599181i | \(-0.204507\pi\) | ||||
0.800613 | + | 0.599181i | \(0.204507\pi\) | |||||||
\(840\) | −2.16225 | −0.0746046 | ||||||||
\(841\) | 5.74170 | 0.197990 | ||||||||
\(842\) | −63.0962 | −2.17444 | ||||||||
\(843\) | −15.8670 | −0.546490 | ||||||||
\(844\) | 8.10114 | 0.278853 | ||||||||
\(845\) | −36.9681 | −1.27174 | ||||||||
\(846\) | 5.60674 | 0.192764 | ||||||||
\(847\) | −51.6160 | −1.77355 | ||||||||
\(848\) | 16.9190 | 0.580999 | ||||||||
\(849\) | 12.8776 | 0.441959 | ||||||||
\(850\) | −11.7997 | −0.404727 | ||||||||
\(851\) | 18.4366 | 0.631998 | ||||||||
\(852\) | 18.1389 | 0.621427 | ||||||||
\(853\) | 21.6466 | 0.741167 | 0.370583 | − | 0.928799i | \(-0.379158\pi\) | ||||
0.370583 | + | 0.928799i | \(0.379158\pi\) | |||||||
\(854\) | −15.1999 | −0.520130 | ||||||||
\(855\) | 10.6602 | 0.364569 | ||||||||
\(856\) | 3.10371 | 0.106083 | ||||||||
\(857\) | −27.5031 | −0.939487 | −0.469743 | − | 0.882803i | \(-0.655654\pi\) | ||||
−0.469743 | + | 0.882803i | \(0.655654\pi\) | |||||||
\(858\) | 69.1561 | 2.36095 | ||||||||
\(859\) | −53.8884 | −1.83865 | −0.919324 | − | 0.393500i | \(-0.871264\pi\) | ||||
−0.919324 | + | 0.393500i | \(0.871264\pi\) | |||||||
\(860\) | 4.71483 | 0.160774 | ||||||||
\(861\) | 12.4328 | 0.423708 | ||||||||
\(862\) | −69.3765 | −2.36297 | ||||||||
\(863\) | 37.5483 | 1.27816 | 0.639079 | − | 0.769141i | \(-0.279316\pi\) | ||||
0.639079 | + | 0.769141i | \(0.279316\pi\) | |||||||
\(864\) | 8.11697 | 0.276145 | ||||||||
\(865\) | 27.7474 | 0.943441 | ||||||||
\(866\) | 39.7509 | 1.35079 | ||||||||
\(867\) | −8.17241 | −0.277550 | ||||||||
\(868\) | −48.1345 | −1.63379 | ||||||||
\(869\) | −56.3248 | −1.91069 | ||||||||
\(870\) | −21.3181 | −0.722752 | ||||||||
\(871\) | 62.1391 | 2.10550 | ||||||||
\(872\) | −3.97429 | −0.134587 | ||||||||
\(873\) | 11.9290 | 0.403735 | ||||||||
\(874\) | −34.9444 | −1.18201 | ||||||||
\(875\) | −28.5150 | −0.963983 | ||||||||
\(876\) | −34.1852 | −1.15501 | ||||||||
\(877\) | 15.5272 | 0.524315 | 0.262157 | − | 0.965025i | \(-0.415566\pi\) | ||||
0.262157 | + | 0.965025i | \(0.415566\pi\) | |||||||
\(878\) | 32.1636 | 1.08547 | ||||||||
\(879\) | −2.17925 | −0.0735043 | ||||||||
\(880\) | −34.4996 | −1.16298 | ||||||||
\(881\) | −15.7766 | −0.531526 | −0.265763 | − | 0.964038i | \(-0.585624\pi\) | ||||
−0.265763 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(882\) | 3.06507 | 0.103206 | ||||||||
\(883\) | 34.1536 | 1.14936 | 0.574679 | − | 0.818379i | \(-0.305127\pi\) | ||||
0.574679 | + | 0.818379i | \(0.305127\pi\) | |||||||
\(884\) | −39.1073 | −1.31532 | ||||||||
\(885\) | 15.7645 | 0.529917 | ||||||||
\(886\) | 16.1029 | 0.540989 | ||||||||
\(887\) | 10.7691 | 0.361591 | 0.180796 | − | 0.983521i | \(-0.442133\pi\) | ||||
0.180796 | + | 0.983521i | \(0.442133\pi\) | |||||||
\(888\) | 3.47438 | 0.116593 | ||||||||
\(889\) | −0.633889 | −0.0212600 | ||||||||
\(890\) | −22.9201 | −0.768282 | ||||||||
\(891\) | −5.74292 | −0.192395 | ||||||||
\(892\) | 23.6890 | 0.793166 | ||||||||
\(893\) | 16.5254 | 0.553000 | ||||||||
\(894\) | −30.5050 | −1.02024 | ||||||||
\(895\) | 17.7561 | 0.593522 | ||||||||
\(896\) | −9.78516 | −0.326899 | ||||||||
\(897\) | −16.2685 | −0.543191 | ||||||||
\(898\) | 73.2383 | 2.44400 | ||||||||
\(899\) | −53.5894 | −1.78731 | ||||||||
\(900\) | −4.34100 | −0.144700 | ||||||||
\(901\) | 14.6726 | 0.488816 | ||||||||
\(902\) | −62.7186 | −2.08830 | ||||||||
\(903\) | 2.80051 | 0.0931953 | ||||||||
\(904\) | 2.51526 | 0.0836563 | ||||||||
\(905\) | −22.0494 | −0.732946 | ||||||||
\(906\) | 14.5099 | 0.482058 | ||||||||
\(907\) | 5.13784 | 0.170599 | 0.0852996 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0852996 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(908\) | 35.0878 | 1.16443 | ||||||||
\(909\) | 6.45468 | 0.214088 | ||||||||
\(910\) | −49.5823 | −1.64364 | ||||||||
\(911\) | −43.5976 | −1.44445 | −0.722227 | − | 0.691656i | \(-0.756881\pi\) | ||||
−0.722227 | + | 0.691656i | \(0.756881\pi\) | |||||||
\(912\) | 20.8284 | 0.689697 | ||||||||
\(913\) | −42.4886 | −1.40617 | ||||||||
\(914\) | −22.7711 | −0.753200 | ||||||||
\(915\) | 5.50264 | 0.181912 | ||||||||
\(916\) | 53.5265 | 1.76856 | ||||||||
\(917\) | 26.4619 | 0.873850 | ||||||||
\(918\) | 6.12844 | 0.202269 | ||||||||
\(919\) | −55.9314 | −1.84501 | −0.922503 | − | 0.385989i | \(-0.873860\pi\) | ||||
−0.922503 | + | 0.385989i | \(0.873860\pi\) | |||||||
\(920\) | −2.56596 | −0.0845973 | ||||||||
\(921\) | −6.21056 | −0.204645 | ||||||||
\(922\) | −30.5720 | −1.00684 | ||||||||
\(923\) | 46.9689 | 1.54600 | ||||||||
\(924\) | 30.4043 | 1.00023 | ||||||||
\(925\) | 12.7386 | 0.418843 | ||||||||
\(926\) | 5.21379 | 0.171336 | ||||||||
\(927\) | −17.1113 | −0.562009 | ||||||||
\(928\) | −47.8431 | −1.57053 | ||||||||
\(929\) | −30.7456 | −1.00873 | −0.504365 | − | 0.863491i | \(-0.668273\pi\) | ||||
−0.504365 | + | 0.863491i | \(0.668273\pi\) | |||||||
\(930\) | 32.8834 | 1.07829 | ||||||||
\(931\) | 9.03400 | 0.296077 | ||||||||
\(932\) | −34.3760 | −1.12602 | ||||||||
\(933\) | −21.1652 | −0.692916 | ||||||||
\(934\) | −13.8173 | −0.452116 | ||||||||
\(935\) | −29.9191 | −0.978458 | ||||||||
\(936\) | −3.06581 | −0.100209 | ||||||||
\(937\) | 56.9278 | 1.85975 | 0.929875 | − | 0.367876i | \(-0.119915\pi\) | ||||
0.929875 | + | 0.367876i | \(0.119915\pi\) | |||||||
\(938\) | 51.5537 | 1.68329 | ||||||||
\(939\) | 16.1280 | 0.526318 | ||||||||
\(940\) | 10.7459 | 0.350493 | ||||||||
\(941\) | 6.52231 | 0.212621 | 0.106311 | − | 0.994333i | \(-0.466096\pi\) | ||||
0.106311 | + | 0.994333i | \(0.466096\pi\) | |||||||
\(942\) | 47.0163 | 1.53187 | ||||||||
\(943\) | 14.7541 | 0.480461 | ||||||||
\(944\) | 30.8015 | 1.00250 | ||||||||
\(945\) | 4.11745 | 0.133941 | ||||||||
\(946\) | −14.1275 | −0.459325 | ||||||||
\(947\) | −14.5284 | −0.472111 | −0.236056 | − | 0.971740i | \(-0.575855\pi\) | ||||
−0.236056 | + | 0.971740i | \(0.575855\pi\) | |||||||
\(948\) | 22.1124 | 0.718177 | ||||||||
\(949\) | −88.5195 | −2.87347 | ||||||||
\(950\) | −24.1446 | −0.783354 | ||||||||
\(951\) | −22.2477 | −0.721432 | ||||||||
\(952\) | −3.66380 | −0.118745 | ||||||||
\(953\) | −4.28788 | −0.138898 | −0.0694490 | − | 0.997586i | \(-0.522124\pi\) | ||||
−0.0694490 | + | 0.997586i | \(0.522124\pi\) | |||||||
\(954\) | 10.1863 | 0.329793 | ||||||||
\(955\) | −25.6641 | −0.830470 | ||||||||
\(956\) | −19.3683 | −0.626416 | ||||||||
\(957\) | 33.8500 | 1.09421 | ||||||||
\(958\) | 0.475908 | 0.0153759 | ||||||||
\(959\) | 21.5623 | 0.696283 | ||||||||
\(960\) | 17.3427 | 0.559734 | ||||||||
\(961\) | 51.6623 | 1.66652 | ||||||||
\(962\) | 79.6707 | 2.56869 | ||||||||
\(963\) | −5.91023 | −0.190455 | ||||||||
\(964\) | 20.2588 | 0.652492 | ||||||||
\(965\) | 16.9441 | 0.545449 | ||||||||
\(966\) | −13.4972 | −0.434265 | ||||||||
\(967\) | −22.9901 | −0.739312 | −0.369656 | − | 0.929169i | \(-0.620525\pi\) | ||||
−0.369656 | + | 0.929169i | \(0.620525\pi\) | |||||||
\(968\) | −11.5432 | −0.371013 | ||||||||
\(969\) | 18.0630 | 0.580268 | ||||||||
\(970\) | 43.1447 | 1.38529 | ||||||||
\(971\) | 41.2096 | 1.32248 | 0.661240 | − | 0.750175i | \(-0.270031\pi\) | ||||
0.661240 | + | 0.750175i | \(0.270031\pi\) | |||||||
\(972\) | 2.25459 | 0.0723161 | ||||||||
\(973\) | 24.5431 | 0.786815 | ||||||||
\(974\) | −16.4776 | −0.527977 | ||||||||
\(975\) | −11.2406 | −0.359988 | ||||||||
\(976\) | 10.7514 | 0.344143 | ||||||||
\(977\) | 41.6660 | 1.33301 | 0.666507 | − | 0.745499i | \(-0.267789\pi\) | ||||
0.666507 | + | 0.745499i | \(0.267789\pi\) | |||||||
\(978\) | 38.3584 | 1.22657 | ||||||||
\(979\) | 36.3936 | 1.16315 | ||||||||
\(980\) | 5.87453 | 0.187655 | ||||||||
\(981\) | 7.56804 | 0.241629 | ||||||||
\(982\) | 49.9047 | 1.59252 | ||||||||
\(983\) | −8.68142 | −0.276894 | −0.138447 | − | 0.990370i | \(-0.544211\pi\) | ||||
−0.138447 | + | 0.990370i | \(0.544211\pi\) | |||||||
\(984\) | 2.78042 | 0.0886366 | ||||||||
\(985\) | −30.1777 | −0.961541 | ||||||||
\(986\) | −36.1223 | −1.15037 | ||||||||
\(987\) | 6.38287 | 0.203169 | ||||||||
\(988\) | −80.0215 | −2.54582 | ||||||||
\(989\) | 3.32340 | 0.105678 | ||||||||
\(990\) | −20.7709 | −0.660143 | ||||||||
\(991\) | 30.2222 | 0.960039 | 0.480020 | − | 0.877258i | \(-0.340630\pi\) | ||||
0.480020 | + | 0.877258i | \(0.340630\pi\) | |||||||
\(992\) | 73.7985 | 2.34310 | ||||||||
\(993\) | −18.5760 | −0.589492 | ||||||||
\(994\) | 38.9677 | 1.23598 | ||||||||
\(995\) | −13.6828 | −0.433773 | ||||||||
\(996\) | 16.6805 | 0.528541 | ||||||||
\(997\) | −20.2230 | −0.640468 | −0.320234 | − | 0.947338i | \(-0.603762\pi\) | ||||
−0.320234 | + | 0.947338i | \(0.603762\pi\) | |||||||
\(998\) | −31.2036 | −0.987734 | ||||||||
\(999\) | −6.61608 | −0.209323 |
(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 | 8013.2.a.d.1.20 | ✓ | 129 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.d.1.20 | ✓ | 129 | 1.1 | even | 1 | trivial |