Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92684 | −1.36248 | −0.681241 | − | 0.732059i | \(-0.738560\pi\) | ||||
−0.681241 | + | 0.732059i | \(0.738560\pi\) | |||||||
\(3\) | −1.97893 | −1.14253 | −0.571267 | − | 0.820764i | \(-0.693548\pi\) | ||||
−0.571267 | + | 0.820764i | \(0.693548\pi\) | |||||||
\(4\) | 1.71272 | 0.856359 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.81308 | 1.55668 | ||||||||
\(7\) | −3.74943 | −1.41715 | −0.708575 | − | 0.705635i | \(-0.750662\pi\) | ||||
−0.708575 | + | 0.705635i | \(0.750662\pi\) | |||||||
\(8\) | 0.553547 | 0.195709 | ||||||||
\(9\) | 0.916158 | 0.305386 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.698136 | 0.210496 | 0.105248 | − | 0.994446i | \(-0.466436\pi\) | ||||
0.105248 | + | 0.994446i | \(0.466436\pi\) | |||||||
\(12\) | −3.38935 | −0.978420 | ||||||||
\(13\) | −4.67579 | −1.29683 | −0.648415 | − | 0.761287i | \(-0.724568\pi\) | ||||
−0.648415 | + | 0.761287i | \(0.724568\pi\) | |||||||
\(14\) | 7.22455 | 1.93084 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.49203 | −1.12301 | ||||||||
\(17\) | −5.65460 | −1.37144 | −0.685721 | − | 0.727865i | \(-0.740513\pi\) | ||||
−0.685721 | + | 0.727865i | \(0.740513\pi\) | |||||||
\(18\) | −1.76529 | −0.416083 | ||||||||
\(19\) | 0.797009 | 0.182846 | 0.0914232 | − | 0.995812i | \(-0.470858\pi\) | ||||
0.0914232 | + | 0.995812i | \(0.470858\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.41985 | 1.61914 | ||||||||
\(22\) | −1.34520 | −0.286797 | ||||||||
\(23\) | 2.87362 | 0.599191 | 0.299595 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299595 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(24\) | −1.09543 | −0.223604 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.00950 | 1.76691 | ||||||||
\(27\) | 4.12377 | 0.793621 | ||||||||
\(28\) | −6.42171 | −1.21359 | ||||||||
\(29\) | 0.568476 | 0.105563 | 0.0527816 | − | 0.998606i | \(-0.483191\pi\) | ||||
0.0527816 | + | 0.998606i | \(0.483191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.19964 | −0.933884 | −0.466942 | − | 0.884288i | \(-0.654644\pi\) | ||||
−0.466942 | + | 0.884288i | \(0.654644\pi\) | |||||||
\(32\) | 7.54834 | 1.33437 | ||||||||
\(33\) | −1.38156 | −0.240499 | ||||||||
\(34\) | 10.8955 | 1.86856 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.56912 | 0.261520 | ||||||||
\(37\) | −5.93333 | −0.975433 | −0.487717 | − | 0.873002i | \(-0.662170\pi\) | ||||
−0.487717 | + | 0.873002i | \(0.662170\pi\) | |||||||
\(38\) | −1.53571 | −0.249125 | ||||||||
\(39\) | 9.25304 | 1.48167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54335 | 0.709553 | 0.354776 | − | 0.934951i | \(-0.384557\pi\) | ||||
0.354776 | + | 0.934951i | \(0.384557\pi\) | |||||||
\(42\) | −14.2969 | −2.20606 | ||||||||
\(43\) | 7.00846 | 1.06878 | 0.534390 | − | 0.845238i | \(-0.320541\pi\) | ||||
0.534390 | + | 0.845238i | \(0.320541\pi\) | |||||||
\(44\) | 1.19571 | 0.180260 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.53700 | −0.816387 | ||||||||
\(47\) | 3.53934 | 0.516266 | 0.258133 | − | 0.966109i | \(-0.416893\pi\) | ||||
0.258133 | + | 0.966109i | \(0.416893\pi\) | |||||||
\(48\) | 8.88941 | 1.28308 | ||||||||
\(49\) | 7.05822 | 1.00832 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.1900 | 1.56692 | ||||||||
\(52\) | −8.00830 | −1.11055 | ||||||||
\(53\) | −3.89119 | −0.534496 | −0.267248 | − | 0.963628i | \(-0.586114\pi\) | ||||
−0.267248 | + | 0.963628i | \(0.586114\pi\) | |||||||
\(54\) | −7.94586 | −1.08129 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.07549 | −0.277349 | ||||||||
\(57\) | −1.57722 | −0.208908 | ||||||||
\(58\) | −1.09536 | −0.143828 | ||||||||
\(59\) | 13.8320 | 1.80078 | 0.900389 | − | 0.435086i | \(-0.143282\pi\) | ||||
0.900389 | + | 0.435086i | \(0.143282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.157951 | 0.0202236 | 0.0101118 | − | 0.999949i | \(-0.496781\pi\) | ||||
0.0101118 | + | 0.999949i | \(0.496781\pi\) | |||||||
\(62\) | 10.0189 | 1.27240 | ||||||||
\(63\) | −3.43507 | −0.432778 | ||||||||
\(64\) | −5.56039 | −0.695049 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.66205 | 0.327676 | ||||||||
\(67\) | −12.2343 | −1.49466 | −0.747328 | − | 0.664455i | \(-0.768664\pi\) | ||||
−0.747328 | + | 0.664455i | \(0.768664\pi\) | |||||||
\(68\) | −9.68473 | −1.17445 | ||||||||
\(69\) | −5.68668 | −0.684596 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.17528 | −0.732871 | −0.366435 | − | 0.930444i | \(-0.619422\pi\) | ||||
−0.366435 | + | 0.930444i | \(0.619422\pi\) | |||||||
\(72\) | 0.507137 | 0.0597667 | ||||||||
\(73\) | 4.72201 | 0.552670 | 0.276335 | − | 0.961061i | \(-0.410880\pi\) | ||||
0.276335 | + | 0.961061i | \(0.410880\pi\) | |||||||
\(74\) | 11.4326 | 1.32901 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.36505 | 0.156582 | ||||||||
\(77\) | −2.61761 | −0.298305 | ||||||||
\(78\) | −17.8291 | −2.01875 | ||||||||
\(79\) | −4.93666 | −0.555417 | −0.277709 | − | 0.960665i | \(-0.589575\pi\) | ||||
−0.277709 | + | 0.960665i | \(0.589575\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9091 | −1.21213 | ||||||||
\(82\) | −8.75432 | −0.966753 | ||||||||
\(83\) | 1.99090 | 0.218530 | 0.109265 | − | 0.994013i | \(-0.465150\pi\) | ||||
0.109265 | + | 0.994013i | \(0.465150\pi\) | |||||||
\(84\) | 12.7081 | 1.38657 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −13.5042 | −1.45619 | ||||||||
\(87\) | −1.12497 | −0.120610 | ||||||||
\(88\) | 0.386452 | 0.0411959 | ||||||||
\(89\) | 6.08236 | 0.644729 | 0.322365 | − | 0.946616i | \(-0.395522\pi\) | ||||
0.322365 | + | 0.946616i | \(0.395522\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5315 | 1.83780 | ||||||||
\(92\) | 4.92170 | 0.513122 | ||||||||
\(93\) | 10.2897 | 1.06699 | ||||||||
\(94\) | −6.81975 | −0.703403 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.9376 | −1.52457 | ||||||||
\(97\) | 7.70151 | 0.781970 | 0.390985 | − | 0.920397i | \(-0.372135\pi\) | ||||
0.390985 | + | 0.920397i | \(0.372135\pi\) | |||||||
\(98\) | −13.6001 | −1.37381 | ||||||||
\(99\) | 0.639603 | 0.0642825 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.53866 | 0.551118 | 0.275559 | − | 0.961284i | \(-0.411137\pi\) | ||||
0.275559 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(102\) | −21.5614 | −2.13490 | ||||||||
\(103\) | −1.88041 | −0.185283 | −0.0926414 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926414 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(104\) | −2.58827 | −0.253801 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.49770 | 0.728241 | ||||||||
\(107\) | 7.94967 | 0.768524 | 0.384262 | − | 0.923224i | \(-0.374456\pi\) | ||||
0.384262 | + | 0.923224i | \(0.374456\pi\) | |||||||
\(108\) | 7.06286 | 0.679624 | ||||||||
\(109\) | −5.51071 | −0.527831 | −0.263915 | − | 0.964546i | \(-0.585014\pi\) | ||||
−0.263915 | + | 0.964546i | \(0.585014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.7416 | 1.11447 | ||||||||
\(112\) | 16.8426 | 1.59147 | ||||||||
\(113\) | 6.23225 | 0.586280 | 0.293140 | − | 0.956069i | \(-0.405300\pi\) | ||||
0.293140 | + | 0.956069i | \(0.405300\pi\) | |||||||
\(114\) | 3.03906 | 0.284634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.973638 | 0.0904001 | ||||||||
\(117\) | −4.28376 | −0.396034 | ||||||||
\(118\) | −26.6521 | −2.45353 | ||||||||
\(119\) | 21.2015 | 1.94354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5126 | −0.955691 | ||||||||
\(122\) | −0.304347 | −0.0275543 | ||||||||
\(123\) | −8.99097 | −0.810689 | ||||||||
\(124\) | −8.90552 | −0.799740 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.61883 | 0.589653 | ||||||||
\(127\) | 13.6028 | 1.20705 | 0.603527 | − | 0.797342i | \(-0.293761\pi\) | ||||
0.603527 | + | 0.797342i | \(0.293761\pi\) | |||||||
\(128\) | −4.38269 | −0.387379 | ||||||||
\(129\) | −13.8692 | −1.22112 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.84906 | −0.336294 | −0.168147 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168147 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(132\) | −2.36623 | −0.205953 | ||||||||
\(133\) | −2.98833 | −0.259121 | ||||||||
\(134\) | 23.5735 | 2.03644 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.13009 | −0.268403 | ||||||||
\(137\) | 16.0210 | 1.36877 | 0.684383 | − | 0.729123i | \(-0.260072\pi\) | ||||
0.684383 | + | 0.729123i | \(0.260072\pi\) | |||||||
\(138\) | 10.9573 | 0.932750 | ||||||||
\(139\) | −2.73566 | −0.232035 | −0.116018 | − | 0.993247i | \(-0.537013\pi\) | ||||
−0.116018 | + | 0.993247i | \(0.537013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.00410 | −0.589852 | ||||||||
\(142\) | 11.8988 | 0.998523 | ||||||||
\(143\) | −3.26434 | −0.272977 | ||||||||
\(144\) | −4.11541 | −0.342951 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.09857 | −0.753003 | ||||||||
\(147\) | −13.9677 | −1.15204 | ||||||||
\(148\) | −10.1621 | −0.835321 | ||||||||
\(149\) | 6.77335 | 0.554895 | 0.277447 | − | 0.960741i | \(-0.410512\pi\) | ||||
0.277447 | + | 0.960741i | \(0.410512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.34546 | 0.353628 | 0.176814 | − | 0.984244i | \(-0.443421\pi\) | ||||
0.176814 | + | 0.984244i | \(0.443421\pi\) | |||||||
\(152\) | 0.441182 | 0.0357846 | ||||||||
\(153\) | −5.18050 | −0.418819 | ||||||||
\(154\) | 5.04372 | 0.406435 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 15.8479 | 1.26884 | ||||||||
\(157\) | −7.53813 | −0.601608 | −0.300804 | − | 0.953686i | \(-0.597255\pi\) | ||||
−0.300804 | + | 0.953686i | \(0.597255\pi\) | |||||||
\(158\) | 9.51215 | 0.756746 | ||||||||
\(159\) | 7.70039 | 0.610680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7744 | −0.849144 | ||||||||
\(162\) | 21.0202 | 1.65150 | ||||||||
\(163\) | −8.72339 | −0.683269 | −0.341634 | − | 0.939833i | \(-0.610980\pi\) | ||||
−0.341634 | + | 0.939833i | \(0.610980\pi\) | |||||||
\(164\) | 7.78148 | 0.607632 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.83615 | −0.297743 | ||||||||
\(167\) | −7.02667 | −0.543740 | −0.271870 | − | 0.962334i | \(-0.587642\pi\) | ||||
−0.271870 | + | 0.962334i | \(0.587642\pi\) | |||||||
\(168\) | 4.10724 | 0.316880 | ||||||||
\(169\) | 8.86297 | 0.681767 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.730186 | 0.0558387 | ||||||||
\(172\) | 12.0035 | 0.915259 | ||||||||
\(173\) | 17.0132 | 1.29349 | 0.646744 | − | 0.762707i | \(-0.276130\pi\) | ||||
0.646744 | + | 0.762707i | \(0.276130\pi\) | |||||||
\(174\) | 2.16764 | 0.164329 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.13605 | −0.236389 | ||||||||
\(177\) | −27.3726 | −2.05745 | ||||||||
\(178\) | −11.7197 | −0.878432 | ||||||||
\(179\) | 12.9003 | 0.964213 | 0.482107 | − | 0.876113i | \(-0.339872\pi\) | ||||
0.482107 | + | 0.876113i | \(0.339872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2274 | 1.05752 | 0.528758 | − | 0.848772i | \(-0.322658\pi\) | ||||
0.528758 | + | 0.848772i | \(0.322658\pi\) | |||||||
\(182\) | −33.7805 | −2.50397 | ||||||||
\(183\) | −0.312574 | −0.0231061 | ||||||||
\(184\) | 1.59068 | 0.117267 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −19.8267 | −1.45376 | ||||||||
\(187\) | −3.94768 | −0.288683 | ||||||||
\(188\) | 6.06189 | 0.442109 | ||||||||
\(189\) | −15.4618 | −1.12468 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3875 | −0.968688 | −0.484344 | − | 0.874878i | \(-0.660942\pi\) | ||||
−0.484344 | + | 0.874878i | \(0.660942\pi\) | |||||||
\(192\) | 11.0036 | 0.794117 | ||||||||
\(193\) | 16.9893 | 1.22292 | 0.611460 | − | 0.791276i | \(-0.290583\pi\) | ||||
0.611460 | + | 0.791276i | \(0.290583\pi\) | |||||||
\(194\) | −14.8396 | −1.06542 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0887 | 0.863481 | ||||||||
\(197\) | −0.531396 | −0.0378604 | −0.0189302 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189302 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(198\) | −1.23241 | −0.0875838 | ||||||||
\(199\) | 16.3966 | 1.16232 | 0.581161 | − | 0.813789i | \(-0.302599\pi\) | ||||
0.581161 | + | 0.813789i | \(0.302599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.2108 | 1.70770 | ||||||||
\(202\) | −10.6721 | −0.750888 | ||||||||
\(203\) | −2.13146 | −0.149599 | ||||||||
\(204\) | 19.1654 | 1.34185 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.62326 | 0.252445 | ||||||||
\(207\) | 2.63269 | 0.182984 | ||||||||
\(208\) | 21.0038 | 1.45635 | ||||||||
\(209\) | 0.556421 | 0.0384884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.17014 | 0.149399 | 0.0746993 | − | 0.997206i | \(-0.476200\pi\) | ||||
0.0746993 | + | 0.997206i | \(0.476200\pi\) | |||||||
\(212\) | −6.66451 | −0.457720 | ||||||||
\(213\) | 12.2204 | 0.837330 | ||||||||
\(214\) | −15.3178 | −1.04710 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.28270 | 0.155318 | ||||||||
\(217\) | 19.4957 | 1.32345 | ||||||||
\(218\) | 10.6183 | 0.719160 | ||||||||
\(219\) | −9.34452 | −0.631444 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.4397 | 1.77853 | ||||||||
\(222\) | −22.6243 | −1.51844 | ||||||||
\(223\) | −2.53114 | −0.169498 | −0.0847488 | − | 0.996402i | \(-0.527009\pi\) | ||||
−0.0847488 | + | 0.996402i | \(0.527009\pi\) | |||||||
\(224\) | −28.3020 | −1.89100 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0086 | −0.798797 | ||||||||
\(227\) | −27.2508 | −1.80870 | −0.904351 | − | 0.426790i | \(-0.859644\pi\) | ||||
−0.904351 | + | 0.426790i | \(0.859644\pi\) | |||||||
\(228\) | −2.70134 | −0.178901 | ||||||||
\(229\) | 10.1576 | 0.671235 | 0.335618 | − | 0.941998i | \(-0.391055\pi\) | ||||
0.335618 | + | 0.941998i | \(0.391055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.18007 | 0.340823 | ||||||||
\(232\) | 0.314678 | 0.0206596 | ||||||||
\(233\) | 28.0714 | 1.83902 | 0.919508 | − | 0.393070i | \(-0.128587\pi\) | ||||
0.919508 | + | 0.393070i | \(0.128587\pi\) | |||||||
\(234\) | 8.25412 | 0.539589 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 23.6904 | 1.54211 | ||||||||
\(237\) | 9.76929 | 0.634584 | ||||||||
\(238\) | −40.8519 | −2.64804 | ||||||||
\(239\) | 22.7913 | 1.47425 | 0.737123 | − | 0.675758i | \(-0.236184\pi\) | ||||
0.737123 | + | 0.675758i | \(0.236184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 20.2561 | 1.30211 | ||||||||
\(243\) | 9.21706 | 0.591275 | ||||||||
\(244\) | 0.270526 | 0.0173186 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.3242 | 1.10455 | ||||||||
\(247\) | −3.72664 | −0.237121 | ||||||||
\(248\) | −2.87825 | −0.182769 | ||||||||
\(249\) | −3.93986 | −0.249678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.86874 | 0.117954 | 0.0589770 | − | 0.998259i | \(-0.481216\pi\) | ||||
0.0589770 | + | 0.998259i | \(0.481216\pi\) | |||||||
\(252\) | −5.88330 | −0.370613 | ||||||||
\(253\) | 2.00618 | 0.126127 | ||||||||
\(254\) | −26.2105 | −1.64459 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.5655 | 1.22285 | ||||||||
\(257\) | −0.966573 | −0.0602932 | −0.0301466 | − | 0.999545i | \(-0.509597\pi\) | ||||
−0.0301466 | + | 0.999545i | \(0.509597\pi\) | |||||||
\(258\) | 26.7238 | 1.66375 | ||||||||
\(259\) | 22.2466 | 1.38234 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.520814 | 0.0322375 | ||||||||
\(262\) | 7.41653 | 0.458195 | ||||||||
\(263\) | −4.57283 | −0.281973 | −0.140986 | − | 0.990012i | \(-0.545027\pi\) | ||||
−0.140986 | + | 0.990012i | \(0.545027\pi\) | |||||||
\(264\) | −0.764760 | −0.0470677 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.75803 | 0.353048 | ||||||||
\(267\) | −12.0366 | −0.736626 | ||||||||
\(268\) | −20.9539 | −1.27996 | ||||||||
\(269\) | 8.18085 | 0.498795 | 0.249398 | − | 0.968401i | \(-0.419767\pi\) | ||||
0.249398 | + | 0.968401i | \(0.419767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.88291 | −0.539598 | −0.269799 | − | 0.962917i | \(-0.586957\pi\) | ||||
−0.269799 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(272\) | 25.4006 | 1.54014 | ||||||||
\(273\) | −34.6936 | −2.09975 | ||||||||
\(274\) | −30.8699 | −1.86492 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.73968 | −0.586260 | ||||||||
\(277\) | −4.57055 | −0.274618 | −0.137309 | − | 0.990528i | \(-0.543845\pi\) | ||||
−0.137309 | + | 0.990528i | \(0.543845\pi\) | |||||||
\(278\) | 5.27118 | 0.316144 | ||||||||
\(279\) | −4.76370 | −0.285195 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0161 | −0.836128 | −0.418064 | − | 0.908418i | \(-0.637291\pi\) | ||||
−0.418064 | + | 0.908418i | \(0.637291\pi\) | |||||||
\(282\) | 13.4958 | 0.803663 | ||||||||
\(283\) | −18.3301 | −1.08961 | −0.544804 | − | 0.838563i | \(-0.683396\pi\) | ||||
−0.544804 | + | 0.838563i | \(0.683396\pi\) | |||||||
\(284\) | −10.5765 | −0.627600 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.28986 | 0.371927 | ||||||||
\(287\) | −17.0350 | −1.00554 | ||||||||
\(288\) | 6.91547 | 0.407498 | ||||||||
\(289\) | 14.9745 | 0.880851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.2407 | −0.893427 | ||||||||
\(292\) | 8.08747 | 0.473284 | ||||||||
\(293\) | 7.61523 | 0.444886 | 0.222443 | − | 0.974946i | \(-0.428597\pi\) | ||||
0.222443 | + | 0.974946i | \(0.428597\pi\) | |||||||
\(294\) | 26.9135 | 1.56963 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.28438 | −0.190901 | ||||||||
\(297\) | 2.87896 | 0.167054 | ||||||||
\(298\) | −13.0512 | −0.756034 | ||||||||
\(299\) | −13.4364 | −0.777048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.2777 | −1.51462 | ||||||||
\(302\) | −8.37300 | −0.481812 | ||||||||
\(303\) | −10.9606 | −0.629671 | ||||||||
\(304\) | −3.58019 | −0.205338 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.98201 | 0.570634 | ||||||||
\(307\) | 24.7729 | 1.41386 | 0.706932 | − | 0.707281i | \(-0.250079\pi\) | ||||
0.706932 | + | 0.707281i | \(0.250079\pi\) | |||||||
\(308\) | −4.48323 | −0.255456 | ||||||||
\(309\) | 3.72121 | 0.211692 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.1846 | −1.25797 | −0.628986 | − | 0.777416i | \(-0.716530\pi\) | ||||
−0.628986 | + | 0.777416i | \(0.716530\pi\) | |||||||
\(312\) | 5.12200 | 0.289976 | ||||||||
\(313\) | 30.5525 | 1.72693 | 0.863465 | − | 0.504409i | \(-0.168290\pi\) | ||||
0.863465 | + | 0.504409i | \(0.168290\pi\) | |||||||
\(314\) | 14.5248 | 0.819681 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.45510 | −0.475637 | ||||||||
\(317\) | −8.49126 | −0.476916 | −0.238458 | − | 0.971153i | \(-0.576642\pi\) | ||||
−0.238458 | + | 0.971153i | \(0.576642\pi\) | |||||||
\(318\) | −14.8374 | −0.832041 | ||||||||
\(319\) | 0.396873 | 0.0222206 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.7318 | −0.878065 | ||||||||
\(322\) | 20.7606 | 1.15694 | ||||||||
\(323\) | −4.50676 | −0.250763 | ||||||||
\(324\) | −18.6843 | −1.03801 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.8086 | 0.930942 | ||||||||
\(327\) | 10.9053 | 0.603065 | ||||||||
\(328\) | 2.51496 | 0.138866 | ||||||||
\(329\) | −13.2705 | −0.731626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.76018 | −0.371573 | −0.185787 | − | 0.982590i | \(-0.559483\pi\) | ||||
−0.185787 | + | 0.982590i | \(0.559483\pi\) | |||||||
\(332\) | 3.40986 | 0.187140 | ||||||||
\(333\) | −5.43587 | −0.297884 | ||||||||
\(334\) | 13.5393 | 0.740836 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −33.3302 | −1.81831 | ||||||||
\(337\) | 1.43313 | 0.0780674 | 0.0390337 | − | 0.999238i | \(-0.487572\pi\) | ||||
0.0390337 | + | 0.999238i | \(0.487572\pi\) | |||||||
\(338\) | −17.0775 | −0.928895 | ||||||||
\(339\) | −12.3332 | −0.669846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.63006 | −0.196579 | ||||||||
\(342\) | −1.40695 | −0.0760793 | ||||||||
\(343\) | −0.218274 | −0.0117857 | ||||||||
\(344\) | 3.87951 | 0.209169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32.7817 | −1.76236 | ||||||||
\(347\) | 16.3681 | 0.878686 | 0.439343 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439343 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(348\) | −1.92676 | −0.103285 | ||||||||
\(349\) | −27.5620 | −1.47536 | −0.737680 | − | 0.675151i | \(-0.764079\pi\) | ||||
−0.737680 | + | 0.675151i | \(0.764079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.2819 | −1.02919 | ||||||||
\(352\) | 5.26977 | 0.280880 | ||||||||
\(353\) | 8.42308 | 0.448315 | 0.224158 | − | 0.974553i | \(-0.428037\pi\) | ||||
0.224158 | + | 0.974553i | \(0.428037\pi\) | |||||||
\(354\) | 52.7427 | 2.80324 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.4174 | 0.552120 | ||||||||
\(357\) | −41.9563 | −2.22056 | ||||||||
\(358\) | −24.8568 | −1.31372 | ||||||||
\(359\) | −28.2768 | −1.49239 | −0.746196 | − | 0.665726i | \(-0.768122\pi\) | ||||
−0.746196 | + | 0.665726i | \(0.768122\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3648 | −0.966567 | ||||||||
\(362\) | −27.4140 | −1.44085 | ||||||||
\(363\) | 20.8037 | 1.09191 | ||||||||
\(364\) | 30.0266 | 1.57382 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.602281 | 0.0314817 | ||||||||
\(367\) | −31.5019 | −1.64439 | −0.822194 | − | 0.569208i | \(-0.807250\pi\) | ||||
−0.822194 | + | 0.569208i | \(0.807250\pi\) | |||||||
\(368\) | −12.9084 | −0.672896 | ||||||||
\(369\) | 4.16243 | 0.216687 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.5897 | 0.757461 | ||||||||
\(372\) | 17.6234 | 0.913730 | ||||||||
\(373\) | 11.5758 | 0.599374 | 0.299687 | − | 0.954038i | \(-0.403118\pi\) | ||||
0.299687 | + | 0.954038i | \(0.403118\pi\) | |||||||
\(374\) | 7.60655 | 0.393325 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.95919 | 0.101038 | ||||||||
\(377\) | −2.65807 | −0.136898 | ||||||||
\(378\) | 29.7924 | 1.53236 | ||||||||
\(379\) | 29.1806 | 1.49891 | 0.749454 | − | 0.662056i | \(-0.230316\pi\) | ||||
0.749454 | + | 0.662056i | \(0.230316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.9190 | −1.37910 | ||||||||
\(382\) | 25.7957 | 1.31982 | ||||||||
\(383\) | −31.1678 | −1.59260 | −0.796301 | − | 0.604901i | \(-0.793213\pi\) | ||||
−0.796301 | + | 0.604901i | \(0.793213\pi\) | |||||||
\(384\) | 8.67304 | 0.442594 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.7358 | −1.66621 | ||||||||
\(387\) | 6.42085 | 0.326390 | ||||||||
\(388\) | 13.1905 | 0.669647 | ||||||||
\(389\) | −16.3224 | −0.827579 | −0.413789 | − | 0.910373i | \(-0.635795\pi\) | ||||
−0.413789 | + | 0.910373i | \(0.635795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2491 | −0.821755 | ||||||||
\(392\) | 3.90706 | 0.197336 | ||||||||
\(393\) | 7.61701 | 0.384227 | ||||||||
\(394\) | 1.02392 | 0.0515842 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.09546 | 0.0550489 | ||||||||
\(397\) | 21.0372 | 1.05583 | 0.527913 | − | 0.849298i | \(-0.322975\pi\) | ||||
0.527913 | + | 0.849298i | \(0.322975\pi\) | |||||||
\(398\) | −31.5936 | −1.58364 | ||||||||
\(399\) | 5.91369 | 0.296055 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8430 | −0.791163 | −0.395582 | − | 0.918431i | \(-0.629457\pi\) | ||||
−0.395582 | + | 0.918431i | \(0.629457\pi\) | |||||||
\(402\) | −46.6503 | −2.32671 | ||||||||
\(403\) | 24.3124 | 1.21109 | ||||||||
\(404\) | 9.48617 | 0.471954 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.10698 | 0.203826 | ||||||||
\(407\) | −4.14227 | −0.205325 | ||||||||
\(408\) | 6.19422 | 0.306660 | ||||||||
\(409\) | 29.4016 | 1.45381 | 0.726907 | − | 0.686735i | \(-0.240957\pi\) | ||||
0.726907 | + | 0.686735i | \(0.240957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.7044 | −1.56386 | ||||||||
\(412\) | −3.22062 | −0.158669 | ||||||||
\(413\) | −51.8622 | −2.55197 | ||||||||
\(414\) | −5.07277 | −0.249313 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −35.2944 | −1.73045 | ||||||||
\(417\) | 5.41367 | 0.265109 | ||||||||
\(418\) | −1.07213 | −0.0524398 | ||||||||
\(419\) | 29.5763 | 1.44490 | 0.722448 | − | 0.691425i | \(-0.243017\pi\) | ||||
0.722448 | + | 0.691425i | \(0.243017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.95390 | −0.436386 | −0.218193 | − | 0.975906i | \(-0.570016\pi\) | ||||
−0.218193 | + | 0.975906i | \(0.570016\pi\) | |||||||
\(422\) | −4.18151 | −0.203553 | ||||||||
\(423\) | 3.24259 | 0.157660 | ||||||||
\(424\) | −2.15396 | −0.104605 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −23.5468 | −1.14085 | ||||||||
\(427\) | −0.592227 | −0.0286599 | ||||||||
\(428\) | 13.6155 | 0.658132 | ||||||||
\(429\) | 6.45989 | 0.311886 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0344 | −0.579679 | −0.289839 | − | 0.957075i | \(-0.593602\pi\) | ||||
−0.289839 | + | 0.957075i | \(0.593602\pi\) | |||||||
\(432\) | −18.5241 | −0.891243 | ||||||||
\(433\) | −18.1591 | −0.872670 | −0.436335 | − | 0.899784i | \(-0.643724\pi\) | ||||
−0.436335 | + | 0.899784i | \(0.643724\pi\) | |||||||
\(434\) | −37.5651 | −1.80318 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.43830 | −0.452012 | ||||||||
\(437\) | 2.29030 | 0.109560 | ||||||||
\(438\) | 18.0054 | 0.860332 | ||||||||
\(439\) | −8.59787 | −0.410354 | −0.205177 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205177 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.46644 | 0.307926 | ||||||||
\(442\) | −50.9451 | −2.42321 | ||||||||
\(443\) | 26.4202 | 1.25526 | 0.627631 | − | 0.778511i | \(-0.284025\pi\) | ||||
0.627631 | + | 0.778511i | \(0.284025\pi\) | |||||||
\(444\) | 20.1101 | 0.954383 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.87711 | 0.230938 | ||||||||
\(447\) | −13.4040 | −0.633987 | ||||||||
\(448\) | 20.8483 | 0.984989 | ||||||||
\(449\) | 11.9923 | 0.565950 | 0.282975 | − | 0.959127i | \(-0.408679\pi\) | ||||
0.282975 | + | 0.959127i | \(0.408679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17188 | 0.149358 | ||||||||
\(452\) | 10.6741 | 0.502066 | ||||||||
\(453\) | −8.59935 | −0.404033 | ||||||||
\(454\) | 52.5080 | 2.46432 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.873068 | −0.0408852 | ||||||||
\(457\) | 30.4011 | 1.42211 | 0.711053 | − | 0.703139i | \(-0.248219\pi\) | ||||
0.711053 | + | 0.703139i | \(0.248219\pi\) | |||||||
\(458\) | −19.5722 | −0.914547 | ||||||||
\(459\) | −23.3183 | −1.08840 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58678 | −0.120478 | −0.0602391 | − | 0.998184i | \(-0.519186\pi\) | ||||
−0.0602391 | + | 0.998184i | \(0.519186\pi\) | |||||||
\(462\) | −9.98117 | −0.464366 | ||||||||
\(463\) | 39.3392 | 1.82825 | 0.914124 | − | 0.405434i | \(-0.132880\pi\) | ||||
0.914124 | + | 0.405434i | \(0.132880\pi\) | |||||||
\(464\) | −2.55361 | −0.118548 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −54.0891 | −2.50563 | ||||||||
\(467\) | −22.5514 | −1.04355 | −0.521777 | − | 0.853082i | \(-0.674731\pi\) | ||||
−0.521777 | + | 0.853082i | \(0.674731\pi\) | |||||||
\(468\) | −7.33687 | −0.339147 | ||||||||
\(469\) | 45.8716 | 2.11815 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.9174 | 0.687359 | ||||||||
\(472\) | 7.65669 | 0.352428 | ||||||||
\(473\) | 4.89286 | 0.224974 | ||||||||
\(474\) | −18.8239 | −0.864609 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 36.3122 | 1.66437 | ||||||||
\(477\) | −3.56494 | −0.163228 | ||||||||
\(478\) | −43.9152 | −2.00864 | ||||||||
\(479\) | −36.0343 | −1.64645 | −0.823224 | − | 0.567716i | \(-0.807827\pi\) | ||||
−0.823224 | + | 0.567716i | \(0.807827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7430 | 1.26497 | ||||||||
\(482\) | 1.92684 | 0.0877652 | ||||||||
\(483\) | 21.3218 | 0.970176 | ||||||||
\(484\) | −18.0051 | −0.818415 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17.7598 | −0.805602 | ||||||||
\(487\) | 31.1634 | 1.41215 | 0.706075 | − | 0.708137i | \(-0.250464\pi\) | ||||
0.706075 | + | 0.708137i | \(0.250464\pi\) | |||||||
\(488\) | 0.0874335 | 0.00395793 | ||||||||
\(489\) | 17.2630 | 0.780659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.1073 | −0.907431 | −0.453715 | − | 0.891147i | \(-0.649902\pi\) | ||||
−0.453715 | + | 0.891147i | \(0.649902\pi\) | |||||||
\(492\) | −15.3990 | −0.694240 | ||||||||
\(493\) | −3.21450 | −0.144774 | ||||||||
\(494\) | 7.18065 | 0.323073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.3570 | 1.04876 | ||||||||
\(497\) | 23.1538 | 1.03859 | ||||||||
\(498\) | 7.59148 | 0.340182 | ||||||||
\(499\) | −32.3094 | −1.44637 | −0.723184 | − | 0.690656i | \(-0.757322\pi\) | ||||
−0.723184 | + | 0.690656i | \(0.757322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9053 | 0.621242 | ||||||||
\(502\) | −3.60077 | −0.160710 | ||||||||
\(503\) | −8.53483 | −0.380549 | −0.190275 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190275 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(504\) | −1.90147 | −0.0846984 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.86558 | −0.171846 | ||||||||
\(507\) | −17.5392 | −0.778942 | ||||||||
\(508\) | 23.2978 | 1.03367 | ||||||||
\(509\) | −22.6149 | −1.00239 | −0.501193 | − | 0.865335i | \(-0.667105\pi\) | ||||
−0.501193 | + | 0.865335i | \(0.667105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7048 | −0.783216 | ||||||||
\(512\) | −28.9343 | −1.27873 | ||||||||
\(513\) | 3.28668 | 0.145111 | ||||||||
\(514\) | 1.86243 | 0.0821484 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −23.7541 | −1.04572 | ||||||||
\(517\) | 2.47094 | 0.108672 | ||||||||
\(518\) | −42.8657 | −1.88341 | ||||||||
\(519\) | −33.6679 | −1.47786 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.6994 | 0.468747 | 0.234374 | − | 0.972147i | \(-0.424696\pi\) | ||||
0.234374 | + | 0.972147i | \(0.424696\pi\) | |||||||
\(522\) | −1.00353 | −0.0439231 | ||||||||
\(523\) | −39.2992 | −1.71843 | −0.859217 | − | 0.511611i | \(-0.829049\pi\) | ||||
−0.859217 | + | 0.511611i | \(0.829049\pi\) | |||||||
\(524\) | −6.59235 | −0.287988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.81111 | 0.384183 | ||||||||
\(527\) | 29.4019 | 1.28077 | ||||||||
\(528\) | 6.20602 | 0.270082 | ||||||||
\(529\) | −14.7423 | −0.640971 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6723 | 0.549932 | ||||||||
\(532\) | −5.11816 | −0.221900 | ||||||||
\(533\) | −21.2437 | −0.920169 | ||||||||
\(534\) | 23.1925 | 1.00364 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.77226 | −0.292517 | ||||||||
\(537\) | −25.5288 | −1.10165 | ||||||||
\(538\) | −15.7632 | −0.679600 | ||||||||
\(539\) | 4.92760 | 0.212247 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.2776 | −1.08677 | −0.543385 | − | 0.839483i | \(-0.682858\pi\) | ||||
−0.543385 | + | 0.839483i | \(0.682858\pi\) | |||||||
\(542\) | 17.1160 | 0.735193 | ||||||||
\(543\) | −28.1551 | −1.20825 | ||||||||
\(544\) | −42.6828 | −1.83001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 66.8491 | 2.86088 | ||||||||
\(547\) | −36.4817 | −1.55984 | −0.779922 | − | 0.625876i | \(-0.784741\pi\) | ||||
−0.779922 | + | 0.625876i | \(0.784741\pi\) | |||||||
\(548\) | 27.4394 | 1.17215 | ||||||||
\(549\) | 0.144708 | 0.00617600 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.453080 | 0.0193019 | ||||||||
\(552\) | −3.14785 | −0.133981 | ||||||||
\(553\) | 18.5096 | 0.787110 | ||||||||
\(554\) | 8.80673 | 0.374162 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.68541 | −0.198706 | ||||||||
\(557\) | −40.8140 | −1.72935 | −0.864673 | − | 0.502336i | \(-0.832474\pi\) | ||||
−0.864673 | + | 0.502336i | \(0.832474\pi\) | |||||||
\(558\) | 9.17889 | 0.388573 | ||||||||
\(559\) | −32.7700 | −1.38602 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.81218 | 0.329830 | ||||||||
\(562\) | 27.0067 | 1.13921 | ||||||||
\(563\) | 2.45066 | 0.103283 | 0.0516415 | − | 0.998666i | \(-0.483555\pi\) | ||||
0.0516415 | + | 0.998666i | \(0.483555\pi\) | |||||||
\(564\) | −11.9960 | −0.505125 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 35.3191 | 1.48457 | ||||||||
\(567\) | 40.9030 | 1.71776 | ||||||||
\(568\) | −3.41831 | −0.143429 | ||||||||
\(569\) | −4.85975 | −0.203731 | −0.101866 | − | 0.994798i | \(-0.532481\pi\) | ||||
−0.101866 | + | 0.994798i | \(0.532481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2845 | 0.639638 | 0.319819 | − | 0.947479i | \(-0.396378\pi\) | ||||
0.319819 | + | 0.947479i | \(0.396378\pi\) | |||||||
\(572\) | −5.59088 | −0.233767 | ||||||||
\(573\) | 26.4930 | 1.10676 | ||||||||
\(574\) | 32.8237 | 1.37004 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.09419 | −0.212258 | ||||||||
\(577\) | 17.1153 | 0.712518 | 0.356259 | − | 0.934387i | \(-0.384052\pi\) | ||||
0.356259 | + | 0.934387i | \(0.384052\pi\) | |||||||
\(578\) | −28.8534 | −1.20014 | ||||||||
\(579\) | −33.6207 | −1.39723 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.46475 | −0.309690 | ||||||||
\(582\) | 29.3665 | 1.21728 | ||||||||
\(583\) | −2.71658 | −0.112509 | ||||||||
\(584\) | 2.61386 | 0.108162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6733 | −0.606150 | ||||||||
\(587\) | −12.3850 | −0.511184 | −0.255592 | − | 0.966785i | \(-0.582270\pi\) | ||||
−0.255592 | + | 0.966785i | \(0.582270\pi\) | |||||||
\(588\) | −23.9227 | −0.986557 | ||||||||
\(589\) | −4.14416 | −0.170757 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.05160 | 0.0432568 | ||||||||
\(592\) | 26.6527 | 1.09542 | ||||||||
\(593\) | −3.37993 | −0.138797 | −0.0693985 | − | 0.997589i | \(-0.522108\pi\) | ||||
−0.0693985 | + | 0.997589i | \(0.522108\pi\) | |||||||
\(594\) | −5.54729 | −0.227608 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.6008 | 0.475189 | ||||||||
\(597\) | −32.4476 | −1.32799 | ||||||||
\(598\) | 25.8898 | 1.05871 | ||||||||
\(599\) | 40.3761 | 1.64972 | 0.824861 | − | 0.565336i | \(-0.191253\pi\) | ||||
0.824861 | + | 0.565336i | \(0.191253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.52198 | −0.184455 | −0.0922276 | − | 0.995738i | \(-0.529399\pi\) | ||||
−0.0922276 | + | 0.995738i | \(0.529399\pi\) | |||||||
\(602\) | 50.6330 | 2.06365 | ||||||||
\(603\) | −11.2085 | −0.456447 | ||||||||
\(604\) | 7.44254 | 0.302833 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 21.1194 | 0.857916 | ||||||||
\(607\) | −16.9609 | −0.688423 | −0.344211 | − | 0.938892i | \(-0.611854\pi\) | ||||
−0.344211 | + | 0.938892i | \(0.611854\pi\) | |||||||
\(608\) | 6.01610 | 0.243985 | ||||||||
\(609\) | 4.21801 | 0.170922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.5492 | −0.669509 | ||||||||
\(612\) | −8.87274 | −0.358659 | ||||||||
\(613\) | 33.3874 | 1.34850 | 0.674252 | − | 0.738502i | \(-0.264466\pi\) | ||||
0.674252 | + | 0.738502i | \(0.264466\pi\) | |||||||
\(614\) | −47.7335 | −1.92637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44897 | −0.0583808 | ||||||||
\(617\) | 11.7930 | 0.474768 | 0.237384 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237384 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(618\) | −7.17017 | −0.288427 | ||||||||
\(619\) | −37.6940 | −1.51505 | −0.757525 | − | 0.652806i | \(-0.773592\pi\) | ||||
−0.757525 | + | 0.652806i | \(0.773592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8501 | 0.475530 | ||||||||
\(622\) | 42.7462 | 1.71397 | ||||||||
\(623\) | −22.8054 | −0.913679 | ||||||||
\(624\) | −41.5650 | −1.66393 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −58.8698 | −2.35291 | ||||||||
\(627\) | −1.10112 | −0.0439744 | ||||||||
\(628\) | −12.9107 | −0.515193 | ||||||||
\(629\) | 33.5506 | 1.33775 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.35466 | −0.332594 | −0.166297 | − | 0.986076i | \(-0.553181\pi\) | ||||
−0.166297 | + | 0.986076i | \(0.553181\pi\) | |||||||
\(632\) | −2.73267 | −0.108700 | ||||||||
\(633\) | −4.29455 | −0.170693 | ||||||||
\(634\) | 16.3613 | 0.649790 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.1886 | 0.522961 | ||||||||
\(637\) | −33.0027 | −1.30761 | ||||||||
\(638\) | −0.764712 | −0.0302752 | ||||||||
\(639\) | −5.65753 | −0.223808 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.9207 | 0.589331 | 0.294665 | − | 0.955601i | \(-0.404792\pi\) | ||||
0.294665 | + | 0.955601i | \(0.404792\pi\) | |||||||
\(642\) | 30.3128 | 1.19635 | ||||||||
\(643\) | 21.2101 | 0.836445 | 0.418223 | − | 0.908345i | \(-0.362653\pi\) | ||||
0.418223 | + | 0.908345i | \(0.362653\pi\) | |||||||
\(644\) | −18.4535 | −0.727172 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.68382 | 0.341660 | ||||||||
\(647\) | −48.0405 | −1.88867 | −0.944334 | − | 0.328988i | \(-0.893292\pi\) | ||||
−0.944334 | + | 0.328988i | \(0.893292\pi\) | |||||||
\(648\) | −6.03872 | −0.237223 | ||||||||
\(649\) | 9.65665 | 0.379057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.5806 | −1.51209 | ||||||||
\(652\) | −14.9407 | −0.585123 | ||||||||
\(653\) | −10.2639 | −0.401656 | −0.200828 | − | 0.979627i | \(-0.564363\pi\) | ||||
−0.200828 | + | 0.979627i | \(0.564363\pi\) | |||||||
\(654\) | −21.0128 | −0.821665 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20.4089 | −0.796834 | ||||||||
\(657\) | 4.32611 | 0.168778 | ||||||||
\(658\) | 25.5701 | 0.996828 | ||||||||
\(659\) | −7.09124 | −0.276235 | −0.138118 | − | 0.990416i | \(-0.544105\pi\) | ||||
−0.138118 | + | 0.990416i | \(0.544105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.59563 | −0.217645 | −0.108822 | − | 0.994061i | \(-0.534708\pi\) | ||||
−0.108822 | + | 0.994061i | \(0.534708\pi\) | |||||||
\(662\) | 13.0258 | 0.506262 | ||||||||
\(663\) | −52.3222 | −2.03203 | ||||||||
\(664\) | 1.10206 | 0.0427682 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4741 | 0.405861 | ||||||||
\(667\) | 1.63358 | 0.0632525 | ||||||||
\(668\) | −12.0347 | −0.465636 | ||||||||
\(669\) | 5.00895 | 0.193657 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.110271 | 0.00425698 | ||||||||
\(672\) | 56.0076 | 2.16054 | ||||||||
\(673\) | −41.0740 | −1.58329 | −0.791644 | − | 0.610983i | \(-0.790774\pi\) | ||||
−0.791644 | + | 0.610983i | \(0.790774\pi\) | |||||||
\(674\) | −2.76141 | −0.106366 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.1798 | 0.583837 | ||||||||
\(677\) | −6.53408 | −0.251125 | −0.125562 | − | 0.992086i | \(-0.540074\pi\) | ||||
−0.125562 | + | 0.992086i | \(0.540074\pi\) | |||||||
\(678\) | 23.7641 | 0.912653 | ||||||||
\(679\) | −28.8762 | −1.10817 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.9275 | 2.06650 | ||||||||
\(682\) | 6.99455 | 0.267835 | ||||||||
\(683\) | −46.7203 | −1.78770 | −0.893851 | − | 0.448363i | \(-0.852007\pi\) | ||||
−0.893851 | + | 0.448363i | \(0.852007\pi\) | |||||||
\(684\) | 1.25060 | 0.0478180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.420580 | 0.0160578 | ||||||||
\(687\) | −20.1012 | −0.766910 | ||||||||
\(688\) | −31.4822 | −1.20025 | ||||||||
\(689\) | 18.1944 | 0.693150 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.6615 | 1.35663 | 0.678314 | − | 0.734772i | \(-0.262711\pi\) | ||||
0.678314 | + | 0.734772i | \(0.262711\pi\) | |||||||
\(692\) | 29.1388 | 1.10769 | ||||||||
\(693\) | −2.39815 | −0.0910980 | ||||||||
\(694\) | −31.5388 | −1.19719 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.622726 | −0.0236044 | ||||||||
\(697\) | −25.6908 | −0.973110 | ||||||||
\(698\) | 53.1076 | 2.01015 | ||||||||
\(699\) | −55.5512 | −2.10114 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.66032 | −0.289326 | −0.144663 | − | 0.989481i | \(-0.546210\pi\) | ||||
−0.144663 | + | 0.989481i | \(0.546210\pi\) | |||||||
\(702\) | 37.1531 | 1.40225 | ||||||||
\(703\) | −4.72892 | −0.178354 | ||||||||
\(704\) | −3.88191 | −0.146305 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.2299 | −0.610822 | ||||||||
\(707\) | −20.7668 | −0.781017 | ||||||||
\(708\) | −46.8816 | −1.76192 | ||||||||
\(709\) | −43.2173 | −1.62306 | −0.811530 | − | 0.584310i | \(-0.801365\pi\) | ||||
−0.811530 | + | 0.584310i | \(0.801365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.52276 | −0.169617 | ||||||||
\(712\) | 3.36688 | 0.126179 | ||||||||
\(713\) | −14.9418 | −0.559574 | ||||||||
\(714\) | 80.8431 | 3.02548 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.0946 | 0.825712 | ||||||||
\(717\) | −45.1024 | −1.68438 | ||||||||
\(718\) | 54.4849 | 2.03336 | ||||||||
\(719\) | −39.7493 | −1.48240 | −0.741199 | − | 0.671286i | \(-0.765742\pi\) | ||||
−0.741199 | + | 0.671286i | \(0.765742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.05048 | 0.262574 | ||||||||
\(722\) | 35.3860 | 1.31693 | ||||||||
\(723\) | 1.97893 | 0.0735971 | ||||||||
\(724\) | 24.3676 | 0.905614 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −40.0854 | −1.48771 | ||||||||
\(727\) | 27.2563 | 1.01088 | 0.505440 | − | 0.862862i | \(-0.331330\pi\) | ||||
0.505440 | + | 0.862862i | \(0.331330\pi\) | |||||||
\(728\) | 9.70453 | 0.359674 | ||||||||
\(729\) | 14.4875 | 0.536573 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.6300 | −1.46577 | ||||||||
\(732\) | −0.535351 | −0.0197871 | ||||||||
\(733\) | 5.66884 | 0.209383 | 0.104692 | − | 0.994505i | \(-0.466614\pi\) | ||||
0.104692 | + | 0.994505i | \(0.466614\pi\) | |||||||
\(734\) | 60.6992 | 2.24045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.6910 | 0.799542 | ||||||||
\(737\) | −8.54120 | −0.314619 | ||||||||
\(738\) | −8.02034 | −0.295233 | ||||||||
\(739\) | −2.42742 | −0.0892940 | −0.0446470 | − | 0.999003i | \(-0.514216\pi\) | ||||
−0.0446470 | + | 0.999003i | \(0.514216\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.37476 | 0.270919 | ||||||||
\(742\) | −28.1121 | −1.03203 | ||||||||
\(743\) | −5.88156 | −0.215774 | −0.107887 | − | 0.994163i | \(-0.534408\pi\) | ||||
−0.107887 | + | 0.994163i | \(0.534408\pi\) | |||||||
\(744\) | 5.69585 | 0.208820 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.3048 | −0.816637 | ||||||||
\(747\) | 1.82398 | 0.0667360 | ||||||||
\(748\) | −6.76126 | −0.247216 | ||||||||
\(749\) | −29.8067 | −1.08911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7495 | 0.720670 | 0.360335 | − | 0.932823i | \(-0.382662\pi\) | ||||
0.360335 | + | 0.932823i | \(0.382662\pi\) | |||||||
\(752\) | −15.8988 | −0.579771 | ||||||||
\(753\) | −3.69811 | −0.134767 | ||||||||
\(754\) | 5.12168 | 0.186521 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −26.4817 | −0.963130 | ||||||||
\(757\) | −13.2891 | −0.482999 | −0.241499 | − | 0.970401i | \(-0.577639\pi\) | ||||
−0.241499 | + | 0.970401i | \(0.577639\pi\) | |||||||
\(758\) | −56.2264 | −2.04224 | ||||||||
\(759\) | −3.97008 | −0.144105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.5946 | 1.47155 | 0.735777 | − | 0.677224i | \(-0.236817\pi\) | ||||
0.735777 | + | 0.677224i | \(0.236817\pi\) | |||||||
\(762\) | 51.8686 | 1.87900 | ||||||||
\(763\) | 20.6620 | 0.748016 | ||||||||
\(764\) | −22.9291 | −0.829544 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 60.0555 | 2.16989 | ||||||||
\(767\) | −64.6756 | −2.33530 | ||||||||
\(768\) | −38.7188 | −1.39714 | ||||||||
\(769\) | −2.05159 | −0.0739823 | −0.0369911 | − | 0.999316i | \(-0.511777\pi\) | ||||
−0.0369911 | + | 0.999316i | \(0.511777\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.91278 | 0.0688871 | ||||||||
\(772\) | 29.0979 | 1.04726 | ||||||||
\(773\) | 12.2422 | 0.440320 | 0.220160 | − | 0.975464i | \(-0.429342\pi\) | ||||
0.220160 | + | 0.975464i | \(0.429342\pi\) | |||||||
\(774\) | −12.3720 | −0.444701 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.26315 | 0.153038 | ||||||||
\(777\) | −44.0244 | −1.57937 | ||||||||
\(778\) | 31.4507 | 1.12756 | ||||||||
\(779\) | 3.62109 | 0.129739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.31118 | −0.154266 | ||||||||
\(782\) | 31.3095 | 1.11963 | ||||||||
\(783\) | 2.34427 | 0.0837772 | ||||||||
\(784\) | −31.7057 | −1.13235 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.6768 | −0.523503 | ||||||||
\(787\) | −37.5149 | −1.33726 | −0.668632 | − | 0.743594i | \(-0.733120\pi\) | ||||
−0.668632 | + | 0.743594i | \(0.733120\pi\) | |||||||
\(788\) | −0.910132 | −0.0324221 | ||||||||
\(789\) | 9.04930 | 0.322164 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.3674 | −0.830848 | ||||||||
\(792\) | 0.354051 | 0.0125806 | ||||||||
\(793\) | −0.738546 | −0.0262265 | ||||||||
\(794\) | −40.5353 | −1.43855 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.0827 | 0.995365 | ||||||||
\(797\) | −13.6762 | −0.484435 | −0.242217 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242217 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(798\) | −11.3947 | −0.403369 | ||||||||
\(799\) | −20.0135 | −0.708028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.57241 | 0.196891 | ||||||||
\(802\) | 30.5270 | 1.07795 | ||||||||
\(803\) | 3.29661 | 0.116335 | ||||||||
\(804\) | 41.4662 | 1.46240 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −46.8462 | −1.65009 | ||||||||
\(807\) | −16.1893 | −0.569891 | ||||||||
\(808\) | 3.06591 | 0.107858 | ||||||||
\(809\) | −45.6843 | −1.60617 | −0.803087 | − | 0.595862i | \(-0.796810\pi\) | ||||
−0.803087 | + | 0.595862i | \(0.796810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.9423 | −0.875841 | −0.437921 | − | 0.899014i | \(-0.644285\pi\) | ||||
−0.437921 | + | 0.899014i | \(0.644285\pi\) | |||||||
\(812\) | −3.65059 | −0.128111 | ||||||||
\(813\) | 17.5786 | 0.616510 | ||||||||
\(814\) | 7.98150 | 0.279752 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −50.2661 | −1.75966 | ||||||||
\(817\) | 5.58580 | 0.195422 | ||||||||
\(818\) | −56.6522 | −1.98080 | ||||||||
\(819\) | 16.0616 | 0.561239 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.06732 | 0.176851 | 0.0884254 | − | 0.996083i | \(-0.471817\pi\) | ||||
0.0884254 | + | 0.996083i | \(0.471817\pi\) | |||||||
\(822\) | 61.0893 | 2.13073 | ||||||||
\(823\) | −0.229410 | −0.00799674 | −0.00399837 | − | 0.999992i | \(-0.501273\pi\) | ||||
−0.00399837 | + | 0.999992i | \(0.501273\pi\) | |||||||
\(824\) | −1.04090 | −0.0362614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 99.9303 | 3.47702 | ||||||||
\(827\) | −9.37695 | −0.326069 | −0.163034 | − | 0.986620i | \(-0.552128\pi\) | ||||
−0.163034 | + | 0.986620i | \(0.552128\pi\) | |||||||
\(828\) | 4.50905 | 0.156700 | ||||||||
\(829\) | −28.6245 | −0.994169 | −0.497085 | − | 0.867702i | \(-0.665596\pi\) | ||||
−0.497085 | + | 0.867702i | \(0.665596\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.04479 | 0.313760 | ||||||||
\(832\) | 25.9992 | 0.901360 | ||||||||
\(833\) | −39.9114 | −1.38285 | ||||||||
\(834\) | −10.4313 | −0.361206 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.952992 | 0.0329599 | ||||||||
\(837\) | −21.4422 | −0.741150 | ||||||||
\(838\) | −56.9888 | −1.96865 | ||||||||
\(839\) | −6.86107 | −0.236870 | −0.118435 | − | 0.992962i | \(-0.537788\pi\) | ||||
−0.118435 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6768 | −0.988856 | ||||||||
\(842\) | 17.2527 | 0.594569 | ||||||||
\(843\) | 27.7368 | 0.955305 | ||||||||
\(844\) | 3.71684 | 0.127939 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.24796 | −0.214809 | ||||||||
\(847\) | 39.4163 | 1.35436 | ||||||||
\(848\) | 17.4794 | 0.600243 | ||||||||
\(849\) | 36.2739 | 1.24492 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.0501 | −0.584471 | ||||||||
\(852\) | 20.9301 | 0.717055 | ||||||||
\(853\) | −10.5083 | −0.359796 | −0.179898 | − | 0.983685i | \(-0.557577\pi\) | ||||
−0.179898 | + | 0.983685i | \(0.557577\pi\) | |||||||
\(854\) | 1.14113 | 0.0390486 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.40052 | 0.150407 | ||||||||
\(857\) | −11.2247 | −0.383427 | −0.191713 | − | 0.981451i | \(-0.561404\pi\) | ||||
−0.191713 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(858\) | −12.4472 | −0.424940 | ||||||||
\(859\) | −32.3311 | −1.10312 | −0.551561 | − | 0.834135i | \(-0.685968\pi\) | ||||
−0.551561 | + | 0.834135i | \(0.685968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.7110 | 1.14887 | ||||||||
\(862\) | 23.1885 | 0.789802 | ||||||||
\(863\) | 10.6333 | 0.361960 | 0.180980 | − | 0.983487i | \(-0.442073\pi\) | ||||
0.180980 | + | 0.983487i | \(0.442073\pi\) | |||||||
\(864\) | 31.1277 | 1.05898 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.9897 | 1.18900 | ||||||||
\(867\) | −29.6334 | −1.00640 | ||||||||
\(868\) | 33.3906 | 1.13335 | ||||||||
\(869\) | −3.44646 | −0.116913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.2049 | 1.93831 | ||||||||
\(872\) | −3.05044 | −0.103301 | ||||||||
\(873\) | 7.05580 | 0.238803 | ||||||||
\(874\) | −4.41304 | −0.149273 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.0045 | −0.540743 | ||||||||
\(877\) | 45.2033 | 1.52641 | 0.763203 | − | 0.646158i | \(-0.223625\pi\) | ||||
0.763203 | + | 0.646158i | \(0.223625\pi\) | |||||||
\(878\) | 16.5667 | 0.559100 | ||||||||
\(879\) | −15.0700 | −0.508298 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.7627 | 1.74393 | 0.871965 | − | 0.489568i | \(-0.162846\pi\) | ||||
0.871965 | + | 0.489568i | \(0.162846\pi\) | |||||||
\(882\) | −12.4598 | −0.419543 | ||||||||
\(883\) | 42.7753 | 1.43950 | 0.719752 | − | 0.694231i | \(-0.244255\pi\) | ||||
0.719752 | + | 0.694231i | \(0.244255\pi\) | |||||||
\(884\) | 45.2837 | 1.52306 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50.9076 | −1.71027 | ||||||||
\(887\) | −22.6388 | −0.760135 | −0.380068 | − | 0.924959i | \(-0.624099\pi\) | ||||
−0.380068 | + | 0.924959i | \(0.624099\pi\) | |||||||
\(888\) | 6.49955 | 0.218111 | ||||||||
\(889\) | −51.0028 | −1.71058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.61606 | −0.255148 | ||||||||
\(892\) | −4.33513 | −0.145151 | ||||||||
\(893\) | 2.82088 | 0.0943973 | ||||||||
\(894\) | 25.8273 | 0.863796 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.4326 | 0.548975 | ||||||||
\(897\) | 26.5897 | 0.887805 | ||||||||
\(898\) | −23.1072 | −0.771097 | ||||||||
\(899\) | −2.95587 | −0.0985838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.0031 | 0.733030 | ||||||||
\(902\) | −6.11171 | −0.203498 | ||||||||
\(903\) | 52.0017 | 1.73051 | ||||||||
\(904\) | 3.44984 | 0.114740 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.5696 | 0.550487 | ||||||||
\(907\) | 45.7335 | 1.51856 | 0.759279 | − | 0.650766i | \(-0.225552\pi\) | ||||
0.759279 | + | 0.650766i | \(0.225552\pi\) | |||||||
\(908\) | −46.6730 | −1.54890 | ||||||||
\(909\) | 5.07429 | 0.168304 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.4550 | −1.17468 | −0.587339 | − | 0.809341i | \(-0.699824\pi\) | ||||
−0.587339 | + | 0.809341i | \(0.699824\pi\) | |||||||
\(912\) | 7.08494 | 0.234606 | ||||||||
\(913\) | 1.38992 | 0.0459997 | ||||||||
\(914\) | −58.5782 | −1.93759 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.3972 | 0.574818 | ||||||||
\(917\) | 14.4318 | 0.476579 | ||||||||
\(918\) | 44.9306 | 1.48293 | ||||||||
\(919\) | 15.2959 | 0.504566 | 0.252283 | − | 0.967653i | \(-0.418819\pi\) | ||||
0.252283 | + | 0.967653i | \(0.418819\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.0238 | −1.61539 | ||||||||
\(922\) | 4.98431 | 0.164149 | ||||||||
\(923\) | 28.8743 | 0.950408 | ||||||||
\(924\) | 8.87199 | 0.291867 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −75.8004 | −2.49096 | ||||||||
\(927\) | −1.72276 | −0.0565828 | ||||||||
\(928\) | 4.29105 | 0.140861 | ||||||||
\(929\) | −16.9767 | −0.556988 | −0.278494 | − | 0.960438i | \(-0.589835\pi\) | ||||
−0.278494 | + | 0.960438i | \(0.589835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.62546 | 0.184367 | ||||||||
\(932\) | 48.0783 | 1.57486 | ||||||||
\(933\) | 43.9017 | 1.43728 | ||||||||
\(934\) | 43.4529 | 1.42182 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.37126 | −0.0775072 | ||||||||
\(937\) | 1.77519 | 0.0579928 | 0.0289964 | − | 0.999580i | \(-0.490769\pi\) | ||||
0.0289964 | + | 0.999580i | \(0.490769\pi\) | |||||||
\(938\) | −88.3873 | −2.88595 | ||||||||
\(939\) | −60.4612 | −1.97308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5581 | 1.74594 | 0.872972 | − | 0.487771i | \(-0.162190\pi\) | ||||
0.872972 | + | 0.487771i | \(0.162190\pi\) | |||||||
\(942\) | −28.7435 | −0.936514 | ||||||||
\(943\) | 13.0559 | 0.425157 | ||||||||
\(944\) | −62.1340 | −2.02229 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.42776 | −0.306523 | ||||||||
\(947\) | −34.8652 | −1.13297 | −0.566483 | − | 0.824074i | \(-0.691696\pi\) | ||||
−0.566483 | + | 0.824074i | \(0.691696\pi\) | |||||||
\(948\) | 16.7320 | 0.543431 | ||||||||
\(949\) | −22.0791 | −0.716718 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.8036 | 0.544894 | ||||||||
\(952\) | 11.7360 | 0.380367 | ||||||||
\(953\) | −26.4851 | −0.857935 | −0.428968 | − | 0.903320i | \(-0.641123\pi\) | ||||
−0.428968 | + | 0.903320i | \(0.641123\pi\) | |||||||
\(954\) | 6.86908 | 0.222395 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 39.0351 | 1.26248 | ||||||||
\(957\) | −0.785384 | −0.0253879 | ||||||||
\(958\) | 69.4324 | 2.24326 | ||||||||
\(959\) | −60.0696 | −1.93975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.96370 | −0.127861 | ||||||||
\(962\) | −53.4563 | −1.72350 | ||||||||
\(963\) | 7.28316 | 0.234696 | ||||||||
\(964\) | −1.71272 | −0.0551629 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −41.0838 | −1.32185 | ||||||||
\(967\) | 49.3662 | 1.58751 | 0.793755 | − | 0.608238i | \(-0.208123\pi\) | ||||
0.793755 | + | 0.608238i | \(0.208123\pi\) | |||||||
\(968\) | −5.81923 | −0.187037 | ||||||||
\(969\) | 8.91856 | 0.286506 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.1030 | 1.22278 | 0.611392 | − | 0.791328i | \(-0.290610\pi\) | ||||
0.611392 | + | 0.791328i | \(0.290610\pi\) | |||||||
\(972\) | 15.7862 | 0.506343 | ||||||||
\(973\) | 10.2571 | 0.328829 | ||||||||
\(974\) | −60.0470 | −1.92403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.709522 | −0.0227112 | ||||||||
\(977\) | 24.5264 | 0.784669 | 0.392334 | − | 0.919823i | \(-0.371668\pi\) | ||||
0.392334 | + | 0.919823i | \(0.371668\pi\) | |||||||
\(978\) | −33.2630 | −1.06363 | ||||||||
\(979\) | 4.24632 | 0.135713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.04868 | −0.161192 | ||||||||
\(982\) | 38.7436 | 1.23636 | ||||||||
\(983\) | −5.40368 | −0.172351 | −0.0861753 | − | 0.996280i | \(-0.527465\pi\) | ||||
−0.0861753 | + | 0.996280i | \(0.527465\pi\) | |||||||
\(984\) | −4.97693 | −0.158659 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.19383 | 0.197252 | ||||||||
\(987\) | 26.2614 | 0.835909 | ||||||||
\(988\) | −6.38269 | −0.203060 | ||||||||
\(989\) | 20.1396 | 0.640403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.7855 | 0.946167 | 0.473084 | − | 0.881018i | \(-0.343141\pi\) | ||||
0.473084 | + | 0.881018i | \(0.343141\pi\) | |||||||
\(992\) | −39.2487 | −1.24615 | ||||||||
\(993\) | 13.3779 | 0.424536 | ||||||||
\(994\) | −44.6136 | −1.41506 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.74786 | −0.213814 | ||||||||
\(997\) | 30.6856 | 0.971822 | 0.485911 | − | 0.874008i | \(-0.338488\pi\) | ||||
0.485911 | + | 0.874008i | \(0.338488\pi\) | |||||||
\(998\) | 62.2551 | 1.97065 | ||||||||
\(999\) | −24.4677 | −0.774124 |
(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 | 6025.2.a.l.1.10 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.31 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.10 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.31 | yes | 40 | 5.4 | even | 2 |