Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.72061\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.72061 | 1.57074 | 0.785372 | − | 0.619024i | \(-0.212471\pi\) | ||||
0.785372 | + | 0.619024i | \(0.212471\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.72061 | 1.11068 | ||||||||
\(7\) | 1.91272 | 0.722939 | 0.361469 | − | 0.932384i | \(-0.382275\pi\) | ||||
0.361469 | + | 0.932384i | \(0.382275\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.40172 | 1.46724 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.72061 | 0.785372 | ||||||||
\(13\) | 1.20875 | 0.335246 | 0.167623 | − | 0.985851i | \(-0.446391\pi\) | ||||
0.167623 | + | 0.985851i | \(0.446391\pi\) | |||||||
\(14\) | 1.91272 | 0.511195 | ||||||||
\(15\) | 2.72061 | 0.702458 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.77479 | −0.915521 | −0.457760 | − | 0.889076i | \(-0.651348\pi\) | ||||
−0.457760 | + | 0.889076i | \(0.651348\pi\) | |||||||
\(18\) | 4.40172 | 1.03749 | ||||||||
\(19\) | 5.93546 | 1.36169 | 0.680844 | − | 0.732428i | \(-0.261613\pi\) | ||||
0.680844 | + | 0.732428i | \(0.261613\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 5.20376 | 1.13555 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 0.791254 | 0.164988 | 0.0824939 | − | 0.996592i | \(-0.473711\pi\) | ||||
0.0824939 | + | 0.996592i | \(0.473711\pi\) | |||||||
\(24\) | 2.72061 | 0.555342 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.20875 | 0.237055 | ||||||||
\(27\) | 3.81352 | 0.733913 | ||||||||
\(28\) | 1.91272 | 0.361469 | ||||||||
\(29\) | 0.597002 | 0.110860 | 0.0554302 | − | 0.998463i | \(-0.482347\pi\) | ||||
0.0554302 | + | 0.998463i | \(0.482347\pi\) | |||||||
\(30\) | 2.72061 | 0.496713 | ||||||||
\(31\) | 7.15695 | 1.28543 | 0.642713 | − | 0.766107i | \(-0.277809\pi\) | ||||
0.642713 | + | 0.766107i | \(0.277809\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.72061 | −0.473597 | ||||||||
\(34\) | −3.77479 | −0.647371 | ||||||||
\(35\) | 1.91272 | 0.323308 | ||||||||
\(36\) | 4.40172 | 0.733619 | ||||||||
\(37\) | 1.12735 | 0.185335 | 0.0926676 | − | 0.995697i | \(-0.470461\pi\) | ||||
0.0926676 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(38\) | 5.93546 | 0.962859 | ||||||||
\(39\) | 3.28853 | 0.526586 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.3674 | −1.61912 | −0.809558 | − | 0.587039i | \(-0.800293\pi\) | ||||
−0.809558 | + | 0.587039i | \(0.800293\pi\) | |||||||
\(42\) | 5.20376 | 0.802957 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 4.40172 | 0.656169 | ||||||||
\(46\) | 0.791254 | 0.116664 | ||||||||
\(47\) | −12.0994 | −1.76488 | −0.882439 | − | 0.470426i | \(-0.844100\pi\) | ||||
−0.882439 | + | 0.470426i | \(0.844100\pi\) | |||||||
\(48\) | 2.72061 | 0.392686 | ||||||||
\(49\) | −3.34151 | −0.477359 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −10.2697 | −1.43805 | ||||||||
\(52\) | 1.20875 | 0.167623 | ||||||||
\(53\) | −11.3466 | −1.55857 | −0.779287 | − | 0.626667i | \(-0.784419\pi\) | ||||
−0.779287 | + | 0.626667i | \(0.784419\pi\) | |||||||
\(54\) | 3.81352 | 0.518955 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.91272 | 0.255598 | ||||||||
\(57\) | 16.1481 | 2.13887 | ||||||||
\(58\) | 0.597002 | 0.0783902 | ||||||||
\(59\) | −4.42095 | −0.575558 | −0.287779 | − | 0.957697i | \(-0.592917\pi\) | ||||
−0.287779 | + | 0.957697i | \(0.592917\pi\) | |||||||
\(60\) | 2.72061 | 0.351229 | ||||||||
\(61\) | −2.65531 | −0.339977 | −0.169989 | − | 0.985446i | \(-0.554373\pi\) | ||||
−0.169989 | + | 0.985446i | \(0.554373\pi\) | |||||||
\(62\) | 7.15695 | 0.908933 | ||||||||
\(63\) | 8.41924 | 1.06072 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.20875 | 0.149926 | ||||||||
\(66\) | −2.72061 | −0.334884 | ||||||||
\(67\) | 15.5544 | 1.90027 | 0.950134 | − | 0.311841i | \(-0.100946\pi\) | ||||
0.950134 | + | 0.311841i | \(0.100946\pi\) | |||||||
\(68\) | −3.77479 | −0.457760 | ||||||||
\(69\) | 2.15269 | 0.259154 | ||||||||
\(70\) | 1.91272 | 0.228613 | ||||||||
\(71\) | −4.84257 | −0.574708 | −0.287354 | − | 0.957825i | \(-0.592776\pi\) | ||||
−0.287354 | + | 0.957825i | \(0.592776\pi\) | |||||||
\(72\) | 4.40172 | 0.518747 | ||||||||
\(73\) | −2.10242 | −0.246069 | −0.123035 | − | 0.992402i | \(-0.539263\pi\) | ||||
−0.123035 | + | 0.992402i | \(0.539263\pi\) | |||||||
\(74\) | 1.12735 | 0.131052 | ||||||||
\(75\) | 2.72061 | 0.314149 | ||||||||
\(76\) | 5.93546 | 0.680844 | ||||||||
\(77\) | −1.91272 | −0.217974 | ||||||||
\(78\) | 3.28853 | 0.372352 | ||||||||
\(79\) | −0.235281 | −0.0264711 | −0.0132356 | − | 0.999912i | \(-0.504213\pi\) | ||||
−0.0132356 | + | 0.999912i | \(0.504213\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.83004 | −0.314449 | ||||||||
\(82\) | −10.3674 | −1.14489 | ||||||||
\(83\) | 10.7230 | 1.17700 | 0.588499 | − | 0.808498i | \(-0.299719\pi\) | ||||
0.588499 | + | 0.808498i | \(0.299719\pi\) | |||||||
\(84\) | 5.20376 | 0.567776 | ||||||||
\(85\) | −3.77479 | −0.409433 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 1.62421 | 0.174133 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −1.84824 | −0.195913 | −0.0979566 | − | 0.995191i | \(-0.531231\pi\) | ||||
−0.0979566 | + | 0.995191i | \(0.531231\pi\) | |||||||
\(90\) | 4.40172 | 0.463982 | ||||||||
\(91\) | 2.31199 | 0.242362 | ||||||||
\(92\) | 0.791254 | 0.0824939 | ||||||||
\(93\) | 19.4713 | 2.01908 | ||||||||
\(94\) | −12.0994 | −1.24796 | ||||||||
\(95\) | 5.93546 | 0.608966 | ||||||||
\(96\) | 2.72061 | 0.277671 | ||||||||
\(97\) | −0.701016 | −0.0711774 | −0.0355887 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355887 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(98\) | −3.34151 | −0.337544 | ||||||||
\(99\) | −4.40172 | −0.442389 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −3.90878 | −0.388938 | −0.194469 | − | 0.980909i | \(-0.562298\pi\) | ||||
−0.194469 | + | 0.980909i | \(0.562298\pi\) | |||||||
\(102\) | −10.2697 | −1.01685 | ||||||||
\(103\) | 6.85994 | 0.675930 | 0.337965 | − | 0.941159i | \(-0.390261\pi\) | ||||
0.337965 | + | 0.941159i | \(0.390261\pi\) | |||||||
\(104\) | 1.20875 | 0.118527 | ||||||||
\(105\) | 5.20376 | 0.507835 | ||||||||
\(106\) | −11.3466 | −1.10208 | ||||||||
\(107\) | 11.6856 | 1.12969 | 0.564844 | − | 0.825198i | \(-0.308936\pi\) | ||||
0.564844 | + | 0.825198i | \(0.308936\pi\) | |||||||
\(108\) | 3.81352 | 0.366957 | ||||||||
\(109\) | 15.9177 | 1.52464 | 0.762321 | − | 0.647200i | \(-0.224060\pi\) | ||||
0.762321 | + | 0.647200i | \(0.224060\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 3.06708 | 0.291114 | ||||||||
\(112\) | 1.91272 | 0.180735 | ||||||||
\(113\) | 2.03490 | 0.191427 | 0.0957137 | − | 0.995409i | \(-0.469487\pi\) | ||||
0.0957137 | + | 0.995409i | \(0.469487\pi\) | |||||||
\(114\) | 16.1481 | 1.51241 | ||||||||
\(115\) | 0.791254 | 0.0737848 | ||||||||
\(116\) | 0.597002 | 0.0554302 | ||||||||
\(117\) | 5.32056 | 0.491886 | ||||||||
\(118\) | −4.42095 | −0.406981 | ||||||||
\(119\) | −7.22010 | −0.661866 | ||||||||
\(120\) | 2.72061 | 0.248357 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.65531 | −0.240400 | ||||||||
\(123\) | −28.2057 | −2.54322 | ||||||||
\(124\) | 7.15695 | 0.642713 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 8.41924 | 0.750045 | ||||||||
\(127\) | 8.31619 | 0.737942 | 0.368971 | − | 0.929441i | \(-0.379710\pi\) | ||||
0.368971 | + | 0.929441i | \(0.379710\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.72061 | 0.239536 | ||||||||
\(130\) | 1.20875 | 0.106014 | ||||||||
\(131\) | −8.39059 | −0.733090 | −0.366545 | − | 0.930400i | \(-0.619459\pi\) | ||||
−0.366545 | + | 0.930400i | \(0.619459\pi\) | |||||||
\(132\) | −2.72061 | −0.236799 | ||||||||
\(133\) | 11.3529 | 0.984418 | ||||||||
\(134\) | 15.5544 | 1.34369 | ||||||||
\(135\) | 3.81352 | 0.328216 | ||||||||
\(136\) | −3.77479 | −0.323686 | ||||||||
\(137\) | −15.8708 | −1.35593 | −0.677967 | − | 0.735092i | \(-0.737139\pi\) | ||||
−0.677967 | + | 0.735092i | \(0.737139\pi\) | |||||||
\(138\) | 2.15269 | 0.183249 | ||||||||
\(139\) | 9.81204 | 0.832246 | 0.416123 | − | 0.909308i | \(-0.363389\pi\) | ||||
0.416123 | + | 0.909308i | \(0.363389\pi\) | |||||||
\(140\) | 1.91272 | 0.161654 | ||||||||
\(141\) | −32.9177 | −2.77217 | ||||||||
\(142\) | −4.84257 | −0.406380 | ||||||||
\(143\) | −1.20875 | −0.101080 | ||||||||
\(144\) | 4.40172 | 0.366810 | ||||||||
\(145\) | 0.597002 | 0.0495783 | ||||||||
\(146\) | −2.10242 | −0.173997 | ||||||||
\(147\) | −9.09096 | −0.749809 | ||||||||
\(148\) | 1.12735 | 0.0926676 | ||||||||
\(149\) | −3.06332 | −0.250957 | −0.125478 | − | 0.992096i | \(-0.540047\pi\) | ||||
−0.125478 | + | 0.992096i | \(0.540047\pi\) | |||||||
\(150\) | 2.72061 | 0.222137 | ||||||||
\(151\) | −3.50114 | −0.284919 | −0.142460 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142460 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(152\) | 5.93546 | 0.481430 | ||||||||
\(153\) | −16.6156 | −1.34329 | ||||||||
\(154\) | −1.91272 | −0.154131 | ||||||||
\(155\) | 7.15695 | 0.574860 | ||||||||
\(156\) | 3.28853 | 0.263293 | ||||||||
\(157\) | −6.52120 | −0.520448 | −0.260224 | − | 0.965548i | \(-0.583796\pi\) | ||||
−0.260224 | + | 0.965548i | \(0.583796\pi\) | |||||||
\(158\) | −0.235281 | −0.0187179 | ||||||||
\(159\) | −30.8696 | −2.44812 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.51345 | 0.119276 | ||||||||
\(162\) | −2.83004 | −0.222349 | ||||||||
\(163\) | −0.0708121 | −0.00554643 | −0.00277321 | − | 0.999996i | \(-0.500883\pi\) | ||||
−0.00277321 | + | 0.999996i | \(0.500883\pi\) | |||||||
\(164\) | −10.3674 | −0.809558 | ||||||||
\(165\) | −2.72061 | −0.211799 | ||||||||
\(166\) | 10.7230 | 0.832263 | ||||||||
\(167\) | −9.52120 | −0.736773 | −0.368386 | − | 0.929673i | \(-0.620090\pi\) | ||||
−0.368386 | + | 0.929673i | \(0.620090\pi\) | |||||||
\(168\) | 5.20376 | 0.401478 | ||||||||
\(169\) | −11.5389 | −0.887610 | ||||||||
\(170\) | −3.77479 | −0.289513 | ||||||||
\(171\) | 26.1262 | 1.99792 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −10.1851 | −0.774359 | −0.387180 | − | 0.922004i | \(-0.626551\pi\) | ||||
−0.387180 | + | 0.922004i | \(0.626551\pi\) | |||||||
\(174\) | 1.62421 | 0.123131 | ||||||||
\(175\) | 1.91272 | 0.144588 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −12.0277 | −0.904055 | ||||||||
\(178\) | −1.84824 | −0.138532 | ||||||||
\(179\) | 16.5986 | 1.24063 | 0.620317 | − | 0.784351i | \(-0.287004\pi\) | ||||
0.620317 | + | 0.784351i | \(0.287004\pi\) | |||||||
\(180\) | 4.40172 | 0.328085 | ||||||||
\(181\) | 12.9709 | 0.964119 | 0.482060 | − | 0.876138i | \(-0.339889\pi\) | ||||
0.482060 | + | 0.876138i | \(0.339889\pi\) | |||||||
\(182\) | 2.31199 | 0.171376 | ||||||||
\(183\) | −7.22405 | −0.534017 | ||||||||
\(184\) | 0.791254 | 0.0583320 | ||||||||
\(185\) | 1.12735 | 0.0828844 | ||||||||
\(186\) | 19.4713 | 1.42770 | ||||||||
\(187\) | 3.77479 | 0.276040 | ||||||||
\(188\) | −12.0994 | −0.882439 | ||||||||
\(189\) | 7.29419 | 0.530574 | ||||||||
\(190\) | 5.93546 | 0.430604 | ||||||||
\(191\) | −4.33138 | −0.313408 | −0.156704 | − | 0.987646i | \(-0.550087\pi\) | ||||
−0.156704 | + | 0.987646i | \(0.550087\pi\) | |||||||
\(192\) | 2.72061 | 0.196343 | ||||||||
\(193\) | 1.94220 | 0.139802 | 0.0699012 | − | 0.997554i | \(-0.477732\pi\) | ||||
0.0699012 | + | 0.997554i | \(0.477732\pi\) | |||||||
\(194\) | −0.701016 | −0.0503300 | ||||||||
\(195\) | 3.28853 | 0.235496 | ||||||||
\(196\) | −3.34151 | −0.238680 | ||||||||
\(197\) | 7.27531 | 0.518344 | 0.259172 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259172 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(198\) | −4.40172 | −0.312816 | ||||||||
\(199\) | −12.3540 | −0.875749 | −0.437875 | − | 0.899036i | \(-0.644269\pi\) | ||||
−0.437875 | + | 0.899036i | \(0.644269\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 42.3174 | 2.98484 | ||||||||
\(202\) | −3.90878 | −0.275021 | ||||||||
\(203\) | 1.14190 | 0.0801453 | ||||||||
\(204\) | −10.2697 | −0.719025 | ||||||||
\(205\) | −10.3674 | −0.724091 | ||||||||
\(206\) | 6.85994 | 0.477955 | ||||||||
\(207\) | 3.48288 | 0.242077 | ||||||||
\(208\) | 1.20875 | 0.0838114 | ||||||||
\(209\) | −5.93546 | −0.410565 | ||||||||
\(210\) | 5.20376 | 0.359093 | ||||||||
\(211\) | −5.49748 | −0.378462 | −0.189231 | − | 0.981933i | \(-0.560599\pi\) | ||||
−0.189231 | + | 0.981933i | \(0.560599\pi\) | |||||||
\(212\) | −11.3466 | −0.779287 | ||||||||
\(213\) | −13.1747 | −0.902719 | ||||||||
\(214\) | 11.6856 | 0.798810 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 3.81352 | 0.259477 | ||||||||
\(217\) | 13.6892 | 0.929285 | ||||||||
\(218\) | 15.9177 | 1.07808 | ||||||||
\(219\) | −5.71986 | −0.386512 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −4.56276 | −0.306925 | ||||||||
\(222\) | 3.06708 | 0.205849 | ||||||||
\(223\) | −19.9298 | −1.33460 | −0.667298 | − | 0.744791i | \(-0.732549\pi\) | ||||
−0.667298 | + | 0.744791i | \(0.732549\pi\) | |||||||
\(224\) | 1.91272 | 0.127799 | ||||||||
\(225\) | 4.40172 | 0.293448 | ||||||||
\(226\) | 2.03490 | 0.135360 | ||||||||
\(227\) | 7.77896 | 0.516307 | 0.258154 | − | 0.966104i | \(-0.416886\pi\) | ||||
0.258154 | + | 0.966104i | \(0.416886\pi\) | |||||||
\(228\) | 16.1481 | 1.06943 | ||||||||
\(229\) | −8.96590 | −0.592483 | −0.296242 | − | 0.955113i | \(-0.595733\pi\) | ||||
−0.296242 | + | 0.955113i | \(0.595733\pi\) | |||||||
\(230\) | 0.791254 | 0.0521738 | ||||||||
\(231\) | −5.20376 | −0.342382 | ||||||||
\(232\) | 0.597002 | 0.0391951 | ||||||||
\(233\) | 16.7903 | 1.09997 | 0.549984 | − | 0.835175i | \(-0.314634\pi\) | ||||
0.549984 | + | 0.835175i | \(0.314634\pi\) | |||||||
\(234\) | 5.32056 | 0.347816 | ||||||||
\(235\) | −12.0994 | −0.789278 | ||||||||
\(236\) | −4.42095 | −0.287779 | ||||||||
\(237\) | −0.640107 | −0.0415794 | ||||||||
\(238\) | −7.22010 | −0.468010 | ||||||||
\(239\) | −8.02935 | −0.519375 | −0.259688 | − | 0.965693i | \(-0.583620\pi\) | ||||
−0.259688 | + | 0.965693i | \(0.583620\pi\) | |||||||
\(240\) | 2.72061 | 0.175615 | ||||||||
\(241\) | −1.12866 | −0.0727034 | −0.0363517 | − | 0.999339i | \(-0.511574\pi\) | ||||
−0.0363517 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −19.1400 | −1.22783 | ||||||||
\(244\) | −2.65531 | −0.169989 | ||||||||
\(245\) | −3.34151 | −0.213482 | ||||||||
\(246\) | −28.2057 | −1.79833 | ||||||||
\(247\) | 7.17447 | 0.456500 | ||||||||
\(248\) | 7.15695 | 0.454467 | ||||||||
\(249\) | 29.1730 | 1.84876 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −7.67613 | −0.484513 | −0.242256 | − | 0.970212i | \(-0.577888\pi\) | ||||
−0.242256 | + | 0.970212i | \(0.577888\pi\) | |||||||
\(252\) | 8.41924 | 0.530362 | ||||||||
\(253\) | −0.791254 | −0.0497457 | ||||||||
\(254\) | 8.31619 | 0.521804 | ||||||||
\(255\) | −10.2697 | −0.643115 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.37594 | −0.584855 | −0.292428 | − | 0.956288i | \(-0.594463\pi\) | ||||
−0.292428 | + | 0.956288i | \(0.594463\pi\) | |||||||
\(258\) | 2.72061 | 0.169378 | ||||||||
\(259\) | 2.15630 | 0.133986 | ||||||||
\(260\) | 1.20875 | 0.0749632 | ||||||||
\(261\) | 2.62783 | 0.162659 | ||||||||
\(262\) | −8.39059 | −0.518373 | ||||||||
\(263\) | 19.6649 | 1.21259 | 0.606296 | − | 0.795239i | \(-0.292655\pi\) | ||||
0.606296 | + | 0.795239i | \(0.292655\pi\) | |||||||
\(264\) | −2.72061 | −0.167442 | ||||||||
\(265\) | −11.3466 | −0.697016 | ||||||||
\(266\) | 11.3529 | 0.696089 | ||||||||
\(267\) | −5.02834 | −0.307730 | ||||||||
\(268\) | 15.5544 | 0.950134 | ||||||||
\(269\) | 2.38473 | 0.145400 | 0.0726999 | − | 0.997354i | \(-0.476838\pi\) | ||||
0.0726999 | + | 0.997354i | \(0.476838\pi\) | |||||||
\(270\) | 3.81352 | 0.232084 | ||||||||
\(271\) | −4.10433 | −0.249320 | −0.124660 | − | 0.992199i | \(-0.539784\pi\) | ||||
−0.124660 | + | 0.992199i | \(0.539784\pi\) | |||||||
\(272\) | −3.77479 | −0.228880 | ||||||||
\(273\) | 6.29002 | 0.380689 | ||||||||
\(274\) | −15.8708 | −0.958791 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 2.15269 | 0.129577 | ||||||||
\(277\) | −27.0052 | −1.62258 | −0.811291 | − | 0.584642i | \(-0.801235\pi\) | ||||
−0.811291 | + | 0.584642i | \(0.801235\pi\) | |||||||
\(278\) | 9.81204 | 0.588487 | ||||||||
\(279\) | 31.5029 | 1.88603 | ||||||||
\(280\) | 1.91272 | 0.114307 | ||||||||
\(281\) | −1.83659 | −0.109562 | −0.0547808 | − | 0.998498i | \(-0.517446\pi\) | ||||
−0.0547808 | + | 0.998498i | \(0.517446\pi\) | |||||||
\(282\) | −32.9177 | −1.96022 | ||||||||
\(283\) | −2.44280 | −0.145209 | −0.0726046 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726046 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(284\) | −4.84257 | −0.287354 | ||||||||
\(285\) | 16.1481 | 0.956530 | ||||||||
\(286\) | −1.20875 | −0.0714746 | ||||||||
\(287\) | −19.8299 | −1.17052 | ||||||||
\(288\) | 4.40172 | 0.259374 | ||||||||
\(289\) | −2.75097 | −0.161822 | ||||||||
\(290\) | 0.597002 | 0.0350571 | ||||||||
\(291\) | −1.90719 | −0.111801 | ||||||||
\(292\) | −2.10242 | −0.123035 | ||||||||
\(293\) | −7.62521 | −0.445469 | −0.222735 | − | 0.974879i | \(-0.571498\pi\) | ||||
−0.222735 | + | 0.974879i | \(0.571498\pi\) | |||||||
\(294\) | −9.09096 | −0.530195 | ||||||||
\(295\) | −4.42095 | −0.257397 | ||||||||
\(296\) | 1.12735 | 0.0655259 | ||||||||
\(297\) | −3.81352 | −0.221283 | ||||||||
\(298\) | −3.06332 | −0.177453 | ||||||||
\(299\) | 0.956425 | 0.0553115 | ||||||||
\(300\) | 2.72061 | 0.157074 | ||||||||
\(301\) | 1.91272 | 0.110247 | ||||||||
\(302\) | −3.50114 | −0.201468 | ||||||||
\(303\) | −10.6343 | −0.610923 | ||||||||
\(304\) | 5.93546 | 0.340422 | ||||||||
\(305\) | −2.65531 | −0.152042 | ||||||||
\(306\) | −16.6156 | −0.949848 | ||||||||
\(307\) | −10.9760 | −0.626434 | −0.313217 | − | 0.949682i | \(-0.601407\pi\) | ||||
−0.313217 | + | 0.949682i | \(0.601407\pi\) | |||||||
\(308\) | −1.91272 | −0.108987 | ||||||||
\(309\) | 18.6632 | 1.06171 | ||||||||
\(310\) | 7.15695 | 0.406487 | ||||||||
\(311\) | 8.53162 | 0.483784 | 0.241892 | − | 0.970303i | \(-0.422232\pi\) | ||||
0.241892 | + | 0.970303i | \(0.422232\pi\) | |||||||
\(312\) | 3.28853 | 0.186176 | ||||||||
\(313\) | −10.9279 | −0.617682 | −0.308841 | − | 0.951114i | \(-0.599941\pi\) | ||||
−0.308841 | + | 0.951114i | \(0.599941\pi\) | |||||||
\(314\) | −6.52120 | −0.368013 | ||||||||
\(315\) | 8.41924 | 0.474370 | ||||||||
\(316\) | −0.235281 | −0.0132356 | ||||||||
\(317\) | 5.05291 | 0.283800 | 0.141900 | − | 0.989881i | \(-0.454679\pi\) | ||||
0.141900 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(318\) | −30.8696 | −1.73108 | ||||||||
\(319\) | −0.597002 | −0.0334257 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 31.7919 | 1.77445 | ||||||||
\(322\) | 1.51345 | 0.0843410 | ||||||||
\(323\) | −22.4051 | −1.24665 | ||||||||
\(324\) | −2.83004 | −0.157224 | ||||||||
\(325\) | 1.20875 | 0.0670492 | ||||||||
\(326\) | −0.0708121 | −0.00392192 | ||||||||
\(327\) | 43.3059 | 2.39482 | ||||||||
\(328\) | −10.3674 | −0.572444 | ||||||||
\(329\) | −23.1427 | −1.27590 | ||||||||
\(330\) | −2.72061 | −0.149765 | ||||||||
\(331\) | 31.7736 | 1.74644 | 0.873218 | − | 0.487329i | \(-0.162029\pi\) | ||||
0.873218 | + | 0.487329i | \(0.162029\pi\) | |||||||
\(332\) | 10.7230 | 0.588499 | ||||||||
\(333\) | 4.96227 | 0.271931 | ||||||||
\(334\) | −9.52120 | −0.520977 | ||||||||
\(335\) | 15.5544 | 0.849826 | ||||||||
\(336\) | 5.20376 | 0.283888 | ||||||||
\(337\) | 16.5299 | 0.900441 | 0.450221 | − | 0.892917i | \(-0.351345\pi\) | ||||
0.450221 | + | 0.892917i | \(0.351345\pi\) | |||||||
\(338\) | −11.5389 | −0.627635 | ||||||||
\(339\) | 5.53617 | 0.300683 | ||||||||
\(340\) | −3.77479 | −0.204717 | ||||||||
\(341\) | −7.15695 | −0.387571 | ||||||||
\(342\) | 26.1262 | 1.41274 | ||||||||
\(343\) | −19.7804 | −1.06804 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 2.15269 | 0.115897 | ||||||||
\(346\) | −10.1851 | −0.547555 | ||||||||
\(347\) | 2.73720 | 0.146941 | 0.0734703 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734703 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(348\) | 1.62421 | 0.0870667 | ||||||||
\(349\) | 14.0391 | 0.751498 | 0.375749 | − | 0.926722i | \(-0.377386\pi\) | ||||
0.375749 | + | 0.926722i | \(0.377386\pi\) | |||||||
\(350\) | 1.91272 | 0.102239 | ||||||||
\(351\) | 4.60958 | 0.246041 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −31.8160 | −1.69340 | −0.846698 | − | 0.532074i | \(-0.821413\pi\) | ||||
−0.846698 | + | 0.532074i | \(0.821413\pi\) | |||||||
\(354\) | −12.0277 | −0.639263 | ||||||||
\(355\) | −4.84257 | −0.257017 | ||||||||
\(356\) | −1.84824 | −0.0979566 | ||||||||
\(357\) | −19.6431 | −1.03962 | ||||||||
\(358\) | 16.5986 | 0.877261 | ||||||||
\(359\) | −3.43246 | −0.181158 | −0.0905792 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905792 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(360\) | 4.40172 | 0.231991 | ||||||||
\(361\) | 16.2297 | 0.854197 | ||||||||
\(362\) | 12.9709 | 0.681735 | ||||||||
\(363\) | 2.72061 | 0.142795 | ||||||||
\(364\) | 2.31199 | 0.121181 | ||||||||
\(365\) | −2.10242 | −0.110046 | ||||||||
\(366\) | −7.22405 | −0.377607 | ||||||||
\(367\) | 30.7599 | 1.60566 | 0.802828 | − | 0.596211i | \(-0.203328\pi\) | ||||
0.802828 | + | 0.596211i | \(0.203328\pi\) | |||||||
\(368\) | 0.791254 | 0.0412470 | ||||||||
\(369\) | −45.6344 | −2.37563 | ||||||||
\(370\) | 1.12735 | 0.0586081 | ||||||||
\(371\) | −21.7028 | −1.12675 | ||||||||
\(372\) | 19.4713 | 1.00954 | ||||||||
\(373\) | 26.0052 | 1.34650 | 0.673250 | − | 0.739415i | \(-0.264898\pi\) | ||||
0.673250 | + | 0.739415i | \(0.264898\pi\) | |||||||
\(374\) | 3.77479 | 0.195190 | ||||||||
\(375\) | 2.72061 | 0.140492 | ||||||||
\(376\) | −12.0994 | −0.623979 | ||||||||
\(377\) | 0.721623 | 0.0371655 | ||||||||
\(378\) | 7.29419 | 0.375173 | ||||||||
\(379\) | −18.6814 | −0.959601 | −0.479800 | − | 0.877378i | \(-0.659291\pi\) | ||||
−0.479800 | + | 0.877378i | \(0.659291\pi\) | |||||||
\(380\) | 5.93546 | 0.304483 | ||||||||
\(381\) | 22.6251 | 1.15912 | ||||||||
\(382\) | −4.33138 | −0.221613 | ||||||||
\(383\) | 17.2652 | 0.882212 | 0.441106 | − | 0.897455i | \(-0.354586\pi\) | ||||
0.441106 | + | 0.897455i | \(0.354586\pi\) | |||||||
\(384\) | 2.72061 | 0.138836 | ||||||||
\(385\) | −1.91272 | −0.0974811 | ||||||||
\(386\) | 1.94220 | 0.0988552 | ||||||||
\(387\) | 4.40172 | 0.223752 | ||||||||
\(388\) | −0.701016 | −0.0355887 | ||||||||
\(389\) | 11.3509 | 0.575513 | 0.287757 | − | 0.957704i | \(-0.407091\pi\) | ||||
0.287757 | + | 0.957704i | \(0.407091\pi\) | |||||||
\(390\) | 3.28853 | 0.166521 | ||||||||
\(391\) | −2.98682 | −0.151050 | ||||||||
\(392\) | −3.34151 | −0.168772 | ||||||||
\(393\) | −22.8275 | −1.15150 | ||||||||
\(394\) | 7.27531 | 0.366525 | ||||||||
\(395\) | −0.235281 | −0.0118383 | ||||||||
\(396\) | −4.40172 | −0.221195 | ||||||||
\(397\) | 33.4940 | 1.68101 | 0.840507 | − | 0.541801i | \(-0.182257\pi\) | ||||
0.840507 | + | 0.541801i | \(0.182257\pi\) | |||||||
\(398\) | −12.3540 | −0.619248 | ||||||||
\(399\) | 30.8867 | 1.54627 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −10.6671 | −0.532691 | −0.266345 | − | 0.963878i | \(-0.585816\pi\) | ||||
−0.266345 | + | 0.963878i | \(0.585816\pi\) | |||||||
\(402\) | 42.3174 | 2.11060 | ||||||||
\(403\) | 8.65093 | 0.430934 | ||||||||
\(404\) | −3.90878 | −0.194469 | ||||||||
\(405\) | −2.83004 | −0.140626 | ||||||||
\(406\) | 1.14190 | 0.0566713 | ||||||||
\(407\) | −1.12735 | −0.0558806 | ||||||||
\(408\) | −10.2697 | −0.508427 | ||||||||
\(409\) | −5.64176 | −0.278967 | −0.139483 | − | 0.990224i | \(-0.544544\pi\) | ||||
−0.139483 | + | 0.990224i | \(0.544544\pi\) | |||||||
\(410\) | −10.3674 | −0.512010 | ||||||||
\(411\) | −43.1783 | −2.12983 | ||||||||
\(412\) | 6.85994 | 0.337965 | ||||||||
\(413\) | −8.45602 | −0.416093 | ||||||||
\(414\) | 3.48288 | 0.171174 | ||||||||
\(415\) | 10.7230 | 0.526369 | ||||||||
\(416\) | 1.20875 | 0.0592636 | ||||||||
\(417\) | 26.6947 | 1.30725 | ||||||||
\(418\) | −5.93546 | −0.290313 | ||||||||
\(419\) | −12.2933 | −0.600566 | −0.300283 | − | 0.953850i | \(-0.597081\pi\) | ||||
−0.300283 | + | 0.953850i | \(0.597081\pi\) | |||||||
\(420\) | 5.20376 | 0.253917 | ||||||||
\(421\) | 9.99247 | 0.487003 | 0.243502 | − | 0.969900i | \(-0.421704\pi\) | ||||
0.243502 | + | 0.969900i | \(0.421704\pi\) | |||||||
\(422\) | −5.49748 | −0.267613 | ||||||||
\(423\) | −53.2581 | −2.58950 | ||||||||
\(424\) | −11.3466 | −0.551039 | ||||||||
\(425\) | −3.77479 | −0.183104 | ||||||||
\(426\) | −13.1747 | −0.638319 | ||||||||
\(427\) | −5.07885 | −0.245783 | ||||||||
\(428\) | 11.6856 | 0.564844 | ||||||||
\(429\) | −3.28853 | −0.158772 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | −20.3287 | −0.979200 | −0.489600 | − | 0.871947i | \(-0.662857\pi\) | ||||
−0.489600 | + | 0.871947i | \(0.662857\pi\) | |||||||
\(432\) | 3.81352 | 0.183478 | ||||||||
\(433\) | −33.7115 | −1.62007 | −0.810035 | − | 0.586381i | \(-0.800552\pi\) | ||||
−0.810035 | + | 0.586381i | \(0.800552\pi\) | |||||||
\(434\) | 13.6892 | 0.657103 | ||||||||
\(435\) | 1.62421 | 0.0778748 | ||||||||
\(436\) | 15.9177 | 0.762321 | ||||||||
\(437\) | 4.69646 | 0.224662 | ||||||||
\(438\) | −5.71986 | −0.273305 | ||||||||
\(439\) | −8.79633 | −0.419826 | −0.209913 | − | 0.977720i | \(-0.567318\pi\) | ||||
−0.209913 | + | 0.977720i | \(0.567318\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −14.7084 | −0.700400 | ||||||||
\(442\) | −4.56276 | −0.217028 | ||||||||
\(443\) | −20.3959 | −0.969040 | −0.484520 | − | 0.874780i | \(-0.661006\pi\) | ||||
−0.484520 | + | 0.874780i | \(0.661006\pi\) | |||||||
\(444\) | 3.06708 | 0.145557 | ||||||||
\(445\) | −1.84824 | −0.0876150 | ||||||||
\(446\) | −19.9298 | −0.943702 | ||||||||
\(447\) | −8.33409 | −0.394189 | ||||||||
\(448\) | 1.91272 | 0.0903674 | ||||||||
\(449\) | 23.4319 | 1.10582 | 0.552910 | − | 0.833241i | \(-0.313517\pi\) | ||||
0.552910 | + | 0.833241i | \(0.313517\pi\) | |||||||
\(450\) | 4.40172 | 0.207499 | ||||||||
\(451\) | 10.3674 | 0.488182 | ||||||||
\(452\) | 2.03490 | 0.0957137 | ||||||||
\(453\) | −9.52525 | −0.447535 | ||||||||
\(454\) | 7.77896 | 0.365084 | ||||||||
\(455\) | 2.31199 | 0.108388 | ||||||||
\(456\) | 16.1481 | 0.756203 | ||||||||
\(457\) | −19.0784 | −0.892450 | −0.446225 | − | 0.894921i | \(-0.647232\pi\) | ||||
−0.446225 | + | 0.894921i | \(0.647232\pi\) | |||||||
\(458\) | −8.96590 | −0.418949 | ||||||||
\(459\) | −14.3953 | −0.671913 | ||||||||
\(460\) | 0.791254 | 0.0368924 | ||||||||
\(461\) | 34.5032 | 1.60698 | 0.803488 | − | 0.595321i | \(-0.202975\pi\) | ||||
0.803488 | + | 0.595321i | \(0.202975\pi\) | |||||||
\(462\) | −5.20376 | −0.242101 | ||||||||
\(463\) | −32.9370 | −1.53071 | −0.765356 | − | 0.643607i | \(-0.777437\pi\) | ||||
−0.765356 | + | 0.643607i | \(0.777437\pi\) | |||||||
\(464\) | 0.597002 | 0.0277151 | ||||||||
\(465\) | 19.4713 | 0.902958 | ||||||||
\(466\) | 16.7903 | 0.777794 | ||||||||
\(467\) | 36.3551 | 1.68231 | 0.841156 | − | 0.540792i | \(-0.181875\pi\) | ||||
0.841156 | + | 0.540792i | \(0.181875\pi\) | |||||||
\(468\) | 5.32056 | 0.245943 | ||||||||
\(469\) | 29.7511 | 1.37378 | ||||||||
\(470\) | −12.0994 | −0.558104 | ||||||||
\(471\) | −17.7416 | −0.817492 | ||||||||
\(472\) | −4.42095 | −0.203490 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −0.640107 | −0.0294011 | ||||||||
\(475\) | 5.93546 | 0.272338 | ||||||||
\(476\) | −7.22010 | −0.330933 | ||||||||
\(477\) | −49.9445 | −2.28680 | ||||||||
\(478\) | −8.02935 | −0.367254 | ||||||||
\(479\) | 8.98706 | 0.410629 | 0.205315 | − | 0.978696i | \(-0.434178\pi\) | ||||
0.205315 | + | 0.978696i | \(0.434178\pi\) | |||||||
\(480\) | 2.72061 | 0.124178 | ||||||||
\(481\) | 1.36268 | 0.0621328 | ||||||||
\(482\) | −1.12866 | −0.0514090 | ||||||||
\(483\) | 4.11749 | 0.187352 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −0.701016 | −0.0318315 | ||||||||
\(486\) | −19.1400 | −0.868208 | ||||||||
\(487\) | −6.66801 | −0.302156 | −0.151078 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(488\) | −2.65531 | −0.120200 | ||||||||
\(489\) | −0.192652 | −0.00871202 | ||||||||
\(490\) | −3.34151 | −0.150954 | ||||||||
\(491\) | 27.9655 | 1.26206 | 0.631032 | − | 0.775757i | \(-0.282632\pi\) | ||||
0.631032 | + | 0.775757i | \(0.282632\pi\) | |||||||
\(492\) | −28.2057 | −1.27161 | ||||||||
\(493\) | −2.25356 | −0.101495 | ||||||||
\(494\) | 7.17447 | 0.322795 | ||||||||
\(495\) | −4.40172 | −0.197842 | ||||||||
\(496\) | 7.15695 | 0.321357 | ||||||||
\(497\) | −9.26247 | −0.415479 | ||||||||
\(498\) | 29.1730 | 1.30727 | ||||||||
\(499\) | −27.9426 | −1.25088 | −0.625442 | − | 0.780271i | \(-0.715081\pi\) | ||||
−0.625442 | + | 0.780271i | \(0.715081\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −25.9035 | −1.15728 | ||||||||
\(502\) | −7.67613 | −0.342602 | ||||||||
\(503\) | −9.30955 | −0.415092 | −0.207546 | − | 0.978225i | \(-0.566548\pi\) | ||||
−0.207546 | + | 0.978225i | \(0.566548\pi\) | |||||||
\(504\) | 8.41924 | 0.375023 | ||||||||
\(505\) | −3.90878 | −0.173938 | ||||||||
\(506\) | −0.791254 | −0.0351755 | ||||||||
\(507\) | −31.3929 | −1.39421 | ||||||||
\(508\) | 8.31619 | 0.368971 | ||||||||
\(509\) | −2.82087 | −0.125033 | −0.0625165 | − | 0.998044i | \(-0.519913\pi\) | ||||
−0.0625165 | + | 0.998044i | \(0.519913\pi\) | |||||||
\(510\) | −10.2697 | −0.454751 | ||||||||
\(511\) | −4.02133 | −0.177893 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 22.6350 | 0.999361 | ||||||||
\(514\) | −9.37594 | −0.413555 | ||||||||
\(515\) | 6.85994 | 0.302285 | ||||||||
\(516\) | 2.72061 | 0.119768 | ||||||||
\(517\) | 12.0994 | 0.532131 | ||||||||
\(518\) | 2.15630 | 0.0947424 | ||||||||
\(519\) | −27.7097 | −1.21632 | ||||||||
\(520\) | 1.20875 | 0.0530070 | ||||||||
\(521\) | −17.0892 | −0.748692 | −0.374346 | − | 0.927289i | \(-0.622133\pi\) | ||||
−0.374346 | + | 0.927289i | \(0.622133\pi\) | |||||||
\(522\) | 2.62783 | 0.115017 | ||||||||
\(523\) | −0.934960 | −0.0408830 | −0.0204415 | − | 0.999791i | \(-0.506507\pi\) | ||||
−0.0204415 | + | 0.999791i | \(0.506507\pi\) | |||||||
\(524\) | −8.39059 | −0.366545 | ||||||||
\(525\) | 5.20376 | 0.227111 | ||||||||
\(526\) | 19.6649 | 0.857431 | ||||||||
\(527\) | −27.0160 | −1.17683 | ||||||||
\(528\) | −2.72061 | −0.118399 | ||||||||
\(529\) | −22.3739 | −0.972779 | ||||||||
\(530\) | −11.3466 | −0.492864 | ||||||||
\(531\) | −19.4597 | −0.844481 | ||||||||
\(532\) | 11.3529 | 0.492209 | ||||||||
\(533\) | −12.5316 | −0.542802 | ||||||||
\(534\) | −5.02834 | −0.217598 | ||||||||
\(535\) | 11.6856 | 0.505212 | ||||||||
\(536\) | 15.5544 | 0.671846 | ||||||||
\(537\) | 45.1582 | 1.94872 | ||||||||
\(538\) | 2.38473 | 0.102813 | ||||||||
\(539\) | 3.34151 | 0.143929 | ||||||||
\(540\) | 3.81352 | 0.164108 | ||||||||
\(541\) | −23.5381 | −1.01198 | −0.505991 | − | 0.862539i | \(-0.668873\pi\) | ||||
−0.505991 | + | 0.862539i | \(0.668873\pi\) | |||||||
\(542\) | −4.10433 | −0.176296 | ||||||||
\(543\) | 35.2887 | 1.51438 | ||||||||
\(544\) | −3.77479 | −0.161843 | ||||||||
\(545\) | 15.9177 | 0.681840 | ||||||||
\(546\) | 6.29002 | 0.269188 | ||||||||
\(547\) | 21.2179 | 0.907211 | 0.453606 | − | 0.891203i | \(-0.350138\pi\) | ||||
0.453606 | + | 0.891203i | \(0.350138\pi\) | |||||||
\(548\) | −15.8708 | −0.677967 | ||||||||
\(549\) | −11.6879 | −0.498828 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 3.54348 | 0.150957 | ||||||||
\(552\) | 2.15269 | 0.0916247 | ||||||||
\(553\) | −0.450025 | −0.0191370 | ||||||||
\(554\) | −27.0052 | −1.14734 | ||||||||
\(555\) | 3.06708 | 0.130190 | ||||||||
\(556\) | 9.81204 | 0.416123 | ||||||||
\(557\) | 22.9932 | 0.974254 | 0.487127 | − | 0.873331i | \(-0.338045\pi\) | ||||
0.487127 | + | 0.873331i | \(0.338045\pi\) | |||||||
\(558\) | 31.5029 | 1.33362 | ||||||||
\(559\) | 1.20875 | 0.0511245 | ||||||||
\(560\) | 1.91272 | 0.0808270 | ||||||||
\(561\) | 10.2697 | 0.433588 | ||||||||
\(562\) | −1.83659 | −0.0774718 | ||||||||
\(563\) | 3.75876 | 0.158413 | 0.0792065 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792065 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(564\) | −32.9177 | −1.38609 | ||||||||
\(565\) | 2.03490 | 0.0856089 | ||||||||
\(566\) | −2.44280 | −0.102678 | ||||||||
\(567\) | −5.41306 | −0.227327 | ||||||||
\(568\) | −4.84257 | −0.203190 | ||||||||
\(569\) | −32.0681 | −1.34436 | −0.672182 | − | 0.740386i | \(-0.734643\pi\) | ||||
−0.672182 | + | 0.740386i | \(0.734643\pi\) | |||||||
\(570\) | 16.1481 | 0.676369 | ||||||||
\(571\) | 29.5503 | 1.23664 | 0.618320 | − | 0.785927i | \(-0.287814\pi\) | ||||
0.618320 | + | 0.785927i | \(0.287814\pi\) | |||||||
\(572\) | −1.20875 | −0.0505402 | ||||||||
\(573\) | −11.7840 | −0.492284 | ||||||||
\(574\) | −19.8299 | −0.827684 | ||||||||
\(575\) | 0.791254 | 0.0329976 | ||||||||
\(576\) | 4.40172 | 0.183405 | ||||||||
\(577\) | −30.9087 | −1.28675 | −0.643373 | − | 0.765553i | \(-0.722466\pi\) | ||||
−0.643373 | + | 0.765553i | \(0.722466\pi\) | |||||||
\(578\) | −2.75097 | −0.114425 | ||||||||
\(579\) | 5.28396 | 0.219594 | ||||||||
\(580\) | 0.597002 | 0.0247891 | ||||||||
\(581\) | 20.5100 | 0.850897 | ||||||||
\(582\) | −1.90719 | −0.0790556 | ||||||||
\(583\) | 11.3466 | 0.469928 | ||||||||
\(584\) | −2.10242 | −0.0869987 | ||||||||
\(585\) | 5.32056 | 0.219978 | ||||||||
\(586\) | −7.62521 | −0.314994 | ||||||||
\(587\) | 25.2434 | 1.04191 | 0.520953 | − | 0.853586i | \(-0.325577\pi\) | ||||
0.520953 | + | 0.853586i | \(0.325577\pi\) | |||||||
\(588\) | −9.09096 | −0.374905 | ||||||||
\(589\) | 42.4798 | 1.75035 | ||||||||
\(590\) | −4.42095 | −0.182007 | ||||||||
\(591\) | 19.7933 | 0.814186 | ||||||||
\(592\) | 1.12735 | 0.0463338 | ||||||||
\(593\) | −3.53476 | −0.145155 | −0.0725776 | − | 0.997363i | \(-0.523122\pi\) | ||||
−0.0725776 | + | 0.997363i | \(0.523122\pi\) | |||||||
\(594\) | −3.81352 | −0.156471 | ||||||||
\(595\) | −7.22010 | −0.295995 | ||||||||
\(596\) | −3.06332 | −0.125478 | ||||||||
\(597\) | −33.6103 | −1.37558 | ||||||||
\(598\) | 0.956425 | 0.0391111 | ||||||||
\(599\) | 12.1990 | 0.498436 | 0.249218 | − | 0.968447i | \(-0.419826\pi\) | ||||
0.249218 | + | 0.968447i | \(0.419826\pi\) | |||||||
\(600\) | 2.72061 | 0.111068 | ||||||||
\(601\) | 26.4493 | 1.07889 | 0.539445 | − | 0.842021i | \(-0.318634\pi\) | ||||
0.539445 | + | 0.842021i | \(0.318634\pi\) | |||||||
\(602\) | 1.91272 | 0.0779565 | ||||||||
\(603\) | 68.4659 | 2.78815 | ||||||||
\(604\) | −3.50114 | −0.142460 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −10.6343 | −0.431987 | ||||||||
\(607\) | −9.77084 | −0.396586 | −0.198293 | − | 0.980143i | \(-0.563540\pi\) | ||||
−0.198293 | + | 0.980143i | \(0.563540\pi\) | |||||||
\(608\) | 5.93546 | 0.240715 | ||||||||
\(609\) | 3.10665 | 0.125888 | ||||||||
\(610\) | −2.65531 | −0.107510 | ||||||||
\(611\) | −14.6251 | −0.591668 | ||||||||
\(612\) | −16.6156 | −0.671644 | ||||||||
\(613\) | −29.1266 | −1.17641 | −0.588205 | − | 0.808712i | \(-0.700165\pi\) | ||||
−0.588205 | + | 0.808712i | \(0.700165\pi\) | |||||||
\(614\) | −10.9760 | −0.442956 | ||||||||
\(615\) | −28.2057 | −1.13736 | ||||||||
\(616\) | −1.91272 | −0.0770656 | ||||||||
\(617\) | 30.5532 | 1.23003 | 0.615013 | − | 0.788517i | \(-0.289151\pi\) | ||||
0.615013 | + | 0.788517i | \(0.289151\pi\) | |||||||
\(618\) | 18.6632 | 0.750745 | ||||||||
\(619\) | 18.4567 | 0.741836 | 0.370918 | − | 0.928666i | \(-0.379043\pi\) | ||||
0.370918 | + | 0.928666i | \(0.379043\pi\) | |||||||
\(620\) | 7.15695 | 0.287430 | ||||||||
\(621\) | 3.01747 | 0.121087 | ||||||||
\(622\) | 8.53162 | 0.342087 | ||||||||
\(623\) | −3.53516 | −0.141633 | ||||||||
\(624\) | 3.28853 | 0.131646 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.9279 | −0.436767 | ||||||||
\(627\) | −16.1481 | −0.644892 | ||||||||
\(628\) | −6.52120 | −0.260224 | ||||||||
\(629\) | −4.25551 | −0.169678 | ||||||||
\(630\) | 8.41924 | 0.335430 | ||||||||
\(631\) | −27.1736 | −1.08176 | −0.540882 | − | 0.841098i | \(-0.681910\pi\) | ||||
−0.540882 | + | 0.841098i | \(0.681910\pi\) | |||||||
\(632\) | −0.235281 | −0.00935896 | ||||||||
\(633\) | −14.9565 | −0.594467 | ||||||||
\(634\) | 5.05291 | 0.200677 | ||||||||
\(635\) | 8.31619 | 0.330018 | ||||||||
\(636\) | −30.8696 | −1.22406 | ||||||||
\(637\) | −4.03904 | −0.160033 | ||||||||
\(638\) | −0.597002 | −0.0236355 | ||||||||
\(639\) | −21.3156 | −0.843233 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −18.7156 | −0.739222 | −0.369611 | − | 0.929187i | \(-0.620509\pi\) | ||||
−0.369611 | + | 0.929187i | \(0.620509\pi\) | |||||||
\(642\) | 31.7919 | 1.25473 | ||||||||
\(643\) | −22.4437 | −0.885094 | −0.442547 | − | 0.896745i | \(-0.645925\pi\) | ||||
−0.442547 | + | 0.896745i | \(0.645925\pi\) | |||||||
\(644\) | 1.51345 | 0.0596381 | ||||||||
\(645\) | 2.72061 | 0.107124 | ||||||||
\(646\) | −22.4051 | −0.881518 | ||||||||
\(647\) | 6.70090 | 0.263440 | 0.131720 | − | 0.991287i | \(-0.457950\pi\) | ||||
0.131720 | + | 0.991287i | \(0.457950\pi\) | |||||||
\(648\) | −2.83004 | −0.111174 | ||||||||
\(649\) | 4.42095 | 0.173537 | ||||||||
\(650\) | 1.20875 | 0.0474109 | ||||||||
\(651\) | 37.2430 | 1.45967 | ||||||||
\(652\) | −0.0708121 | −0.00277321 | ||||||||
\(653\) | −23.8883 | −0.934822 | −0.467411 | − | 0.884040i | \(-0.654813\pi\) | ||||
−0.467411 | + | 0.884040i | \(0.654813\pi\) | |||||||
\(654\) | 43.3059 | 1.69339 | ||||||||
\(655\) | −8.39059 | −0.327848 | ||||||||
\(656\) | −10.3674 | −0.404779 | ||||||||
\(657\) | −9.25425 | −0.361043 | ||||||||
\(658\) | −23.1427 | −0.902197 | ||||||||
\(659\) | 6.89215 | 0.268480 | 0.134240 | − | 0.990949i | \(-0.457141\pi\) | ||||
0.134240 | + | 0.990949i | \(0.457141\pi\) | |||||||
\(660\) | −2.72061 | −0.105900 | ||||||||
\(661\) | −34.7551 | −1.35182 | −0.675908 | − | 0.736986i | \(-0.736248\pi\) | ||||
−0.675908 | + | 0.736986i | \(0.736248\pi\) | |||||||
\(662\) | 31.7736 | 1.23492 | ||||||||
\(663\) | −12.4135 | −0.482100 | ||||||||
\(664\) | 10.7230 | 0.416131 | ||||||||
\(665\) | 11.3529 | 0.440245 | ||||||||
\(666\) | 4.96227 | 0.192284 | ||||||||
\(667\) | 0.472380 | 0.0182906 | ||||||||
\(668\) | −9.52120 | −0.368386 | ||||||||
\(669\) | −54.2211 | −2.09631 | ||||||||
\(670\) | 15.5544 | 0.600918 | ||||||||
\(671\) | 2.65531 | 0.102507 | ||||||||
\(672\) | 5.20376 | 0.200739 | ||||||||
\(673\) | −26.8790 | −1.03611 | −0.518055 | − | 0.855347i | \(-0.673344\pi\) | ||||
−0.518055 | + | 0.855347i | \(0.673344\pi\) | |||||||
\(674\) | 16.5299 | 0.636708 | ||||||||
\(675\) | 3.81352 | 0.146783 | ||||||||
\(676\) | −11.5389 | −0.443805 | ||||||||
\(677\) | −13.6546 | −0.524787 | −0.262394 | − | 0.964961i | \(-0.584512\pi\) | ||||
−0.262394 | + | 0.964961i | \(0.584512\pi\) | |||||||
\(678\) | 5.53617 | 0.212615 | ||||||||
\(679\) | −1.34084 | −0.0514569 | ||||||||
\(680\) | −3.77479 | −0.144757 | ||||||||
\(681\) | 21.1635 | 0.810987 | ||||||||
\(682\) | −7.15695 | −0.274054 | ||||||||
\(683\) | 19.7840 | 0.757014 | 0.378507 | − | 0.925598i | \(-0.376438\pi\) | ||||
0.378507 | + | 0.925598i | \(0.376438\pi\) | |||||||
\(684\) | 26.1262 | 0.998961 | ||||||||
\(685\) | −15.8708 | −0.606393 | ||||||||
\(686\) | −19.7804 | −0.755219 | ||||||||
\(687\) | −24.3927 | −0.930640 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −13.7151 | −0.522505 | ||||||||
\(690\) | 2.15269 | 0.0819516 | ||||||||
\(691\) | −24.6686 | −0.938437 | −0.469218 | − | 0.883082i | \(-0.655464\pi\) | ||||
−0.469218 | + | 0.883082i | \(0.655464\pi\) | |||||||
\(692\) | −10.1851 | −0.387180 | ||||||||
\(693\) | −8.41924 | −0.319820 | ||||||||
\(694\) | 2.73720 | 0.103903 | ||||||||
\(695\) | 9.81204 | 0.372192 | ||||||||
\(696\) | 1.62421 | 0.0615655 | ||||||||
\(697\) | 39.1348 | 1.48234 | ||||||||
\(698\) | 14.0391 | 0.531389 | ||||||||
\(699\) | 45.6798 | 1.72777 | ||||||||
\(700\) | 1.91272 | 0.0722939 | ||||||||
\(701\) | −0.950137 | −0.0358862 | −0.0179431 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179431 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(702\) | 4.60958 | 0.173977 | ||||||||
\(703\) | 6.69134 | 0.252369 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −32.9177 | −1.23975 | ||||||||
\(706\) | −31.8160 | −1.19741 | ||||||||
\(707\) | −7.47639 | −0.281179 | ||||||||
\(708\) | −12.0277 | −0.452027 | ||||||||
\(709\) | −9.66206 | −0.362866 | −0.181433 | − | 0.983403i | \(-0.558074\pi\) | ||||
−0.181433 | + | 0.983403i | \(0.558074\pi\) | |||||||
\(710\) | −4.84257 | −0.181739 | ||||||||
\(711\) | −1.03564 | −0.0388395 | ||||||||
\(712\) | −1.84824 | −0.0692658 | ||||||||
\(713\) | 5.66297 | 0.212080 | ||||||||
\(714\) | −19.6431 | −0.735124 | ||||||||
\(715\) | −1.20875 | −0.0452045 | ||||||||
\(716\) | 16.5986 | 0.620317 | ||||||||
\(717\) | −21.8447 | −0.815806 | ||||||||
\(718\) | −3.43246 | −0.128098 | ||||||||
\(719\) | 30.0475 | 1.12058 | 0.560290 | − | 0.828296i | \(-0.310690\pi\) | ||||
0.560290 | + | 0.828296i | \(0.310690\pi\) | |||||||
\(720\) | 4.40172 | 0.164042 | ||||||||
\(721\) | 13.1211 | 0.488656 | ||||||||
\(722\) | 16.2297 | 0.604008 | ||||||||
\(723\) | −3.07064 | −0.114198 | ||||||||
\(724\) | 12.9709 | 0.482060 | ||||||||
\(725\) | 0.597002 | 0.0221721 | ||||||||
\(726\) | 2.72061 | 0.100971 | ||||||||
\(727\) | 36.8592 | 1.36703 | 0.683515 | − | 0.729936i | \(-0.260450\pi\) | ||||
0.683515 | + | 0.729936i | \(0.260450\pi\) | |||||||
\(728\) | 2.31199 | 0.0856880 | ||||||||
\(729\) | −43.5824 | −1.61416 | ||||||||
\(730\) | −2.10242 | −0.0778140 | ||||||||
\(731\) | −3.77479 | −0.139616 | ||||||||
\(732\) | −7.22405 | −0.267009 | ||||||||
\(733\) | −25.6801 | −0.948517 | −0.474259 | − | 0.880386i | \(-0.657284\pi\) | ||||
−0.474259 | + | 0.880386i | \(0.657284\pi\) | |||||||
\(734\) | 30.7599 | 1.13537 | ||||||||
\(735\) | −9.09096 | −0.335325 | ||||||||
\(736\) | 0.791254 | 0.0291660 | ||||||||
\(737\) | −15.5544 | −0.572953 | ||||||||
\(738\) | −45.6344 | −1.67982 | ||||||||
\(739\) | −40.8543 | −1.50285 | −0.751424 | − | 0.659820i | \(-0.770633\pi\) | ||||
−0.751424 | + | 0.659820i | \(0.770633\pi\) | |||||||
\(740\) | 1.12735 | 0.0414422 | ||||||||
\(741\) | 19.5189 | 0.717046 | ||||||||
\(742\) | −21.7028 | −0.796735 | ||||||||
\(743\) | 48.6927 | 1.78636 | 0.893180 | − | 0.449699i | \(-0.148469\pi\) | ||||
0.893180 | + | 0.449699i | \(0.148469\pi\) | |||||||
\(744\) | 19.4713 | 0.713851 | ||||||||
\(745\) | −3.06332 | −0.112231 | ||||||||
\(746\) | 26.0052 | 0.952119 | ||||||||
\(747\) | 47.1994 | 1.72694 | ||||||||
\(748\) | 3.77479 | 0.138020 | ||||||||
\(749\) | 22.3512 | 0.816695 | ||||||||
\(750\) | 2.72061 | 0.0993426 | ||||||||
\(751\) | 28.7921 | 1.05064 | 0.525319 | − | 0.850906i | \(-0.323946\pi\) | ||||
0.525319 | + | 0.850906i | \(0.323946\pi\) | |||||||
\(752\) | −12.0994 | −0.441220 | ||||||||
\(753\) | −20.8837 | −0.761046 | ||||||||
\(754\) | 0.721623 | 0.0262800 | ||||||||
\(755\) | −3.50114 | −0.127420 | ||||||||
\(756\) | 7.29419 | 0.265287 | ||||||||
\(757\) | 2.21937 | 0.0806642 | 0.0403321 | − | 0.999186i | \(-0.487158\pi\) | ||||
0.0403321 | + | 0.999186i | \(0.487158\pi\) | |||||||
\(758\) | −18.6814 | −0.678540 | ||||||||
\(759\) | −2.15269 | −0.0781378 | ||||||||
\(760\) | 5.93546 | 0.215302 | ||||||||
\(761\) | 2.96812 | 0.107594 | 0.0537972 | − | 0.998552i | \(-0.482868\pi\) | ||||
0.0537972 | + | 0.998552i | \(0.482868\pi\) | |||||||
\(762\) | 22.6251 | 0.819621 | ||||||||
\(763\) | 30.4461 | 1.10222 | ||||||||
\(764\) | −4.33138 | −0.156704 | ||||||||
\(765\) | −16.6156 | −0.600737 | ||||||||
\(766\) | 17.2652 | 0.623818 | ||||||||
\(767\) | −5.34380 | −0.192953 | ||||||||
\(768\) | 2.72061 | 0.0981715 | ||||||||
\(769\) | −19.5103 | −0.703561 | −0.351781 | − | 0.936082i | \(-0.614424\pi\) | ||||
−0.351781 | + | 0.936082i | \(0.614424\pi\) | |||||||
\(770\) | −1.91272 | −0.0689295 | ||||||||
\(771\) | −25.5083 | −0.918658 | ||||||||
\(772\) | 1.94220 | 0.0699012 | ||||||||
\(773\) | −34.3646 | −1.23601 | −0.618005 | − | 0.786174i | \(-0.712059\pi\) | ||||
−0.618005 | + | 0.786174i | \(0.712059\pi\) | |||||||
\(774\) | 4.40172 | 0.158216 | ||||||||
\(775\) | 7.15695 | 0.257085 | ||||||||
\(776\) | −0.701016 | −0.0251650 | ||||||||
\(777\) | 5.86645 | 0.210458 | ||||||||
\(778\) | 11.3509 | 0.406949 | ||||||||
\(779\) | −61.5354 | −2.20473 | ||||||||
\(780\) | 3.28853 | 0.117748 | ||||||||
\(781\) | 4.84257 | 0.173281 | ||||||||
\(782\) | −2.98682 | −0.106808 | ||||||||
\(783\) | 2.27668 | 0.0813619 | ||||||||
\(784\) | −3.34151 | −0.119340 | ||||||||
\(785\) | −6.52120 | −0.232752 | ||||||||
\(786\) | −22.8275 | −0.814231 | ||||||||
\(787\) | 19.7549 | 0.704186 | 0.352093 | − | 0.935965i | \(-0.385470\pi\) | ||||
0.352093 | + | 0.935965i | \(0.385470\pi\) | |||||||
\(788\) | 7.27531 | 0.259172 | ||||||||
\(789\) | 53.5006 | 1.90467 | ||||||||
\(790\) | −0.235281 | −0.00837091 | ||||||||
\(791\) | 3.89219 | 0.138390 | ||||||||
\(792\) | −4.40172 | −0.156408 | ||||||||
\(793\) | −3.20959 | −0.113976 | ||||||||
\(794\) | 33.4940 | 1.18866 | ||||||||
\(795\) | −30.8696 | −1.09483 | ||||||||
\(796\) | −12.3540 | −0.437875 | ||||||||
\(797\) | −30.6839 | −1.08688 | −0.543440 | − | 0.839448i | \(-0.682878\pi\) | ||||
−0.543440 | + | 0.839448i | \(0.682878\pi\) | |||||||
\(798\) | 30.8867 | 1.09338 | ||||||||
\(799\) | 45.6727 | 1.61578 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −8.13543 | −0.287451 | ||||||||
\(802\) | −10.6671 | −0.376669 | ||||||||
\(803\) | 2.10242 | 0.0741927 | ||||||||
\(804\) | 42.3174 | 1.49242 | ||||||||
\(805\) | 1.51345 | 0.0533419 | ||||||||
\(806\) | 8.65093 | 0.304716 | ||||||||
\(807\) | 6.48793 | 0.228386 | ||||||||
\(808\) | −3.90878 | −0.137510 | ||||||||
\(809\) | 31.2009 | 1.09697 | 0.548483 | − | 0.836162i | \(-0.315205\pi\) | ||||
0.548483 | + | 0.836162i | \(0.315205\pi\) | |||||||
\(810\) | −2.83004 | −0.0994374 | ||||||||
\(811\) | 30.9511 | 1.08684 | 0.543420 | − | 0.839461i | \(-0.317129\pi\) | ||||
0.543420 | + | 0.839461i | \(0.317129\pi\) | |||||||
\(812\) | 1.14190 | 0.0400727 | ||||||||
\(813\) | −11.1663 | −0.391619 | ||||||||
\(814\) | −1.12735 | −0.0395136 | ||||||||
\(815\) | −0.0708121 | −0.00248044 | ||||||||
\(816\) | −10.2697 | −0.359512 | ||||||||
\(817\) | 5.93546 | 0.207656 | ||||||||
\(818\) | −5.64176 | −0.197259 | ||||||||
\(819\) | 10.1767 | 0.355603 | ||||||||
\(820\) | −10.3674 | −0.362045 | ||||||||
\(821\) | 49.2147 | 1.71761 | 0.858803 | − | 0.512306i | \(-0.171209\pi\) | ||||
0.858803 | + | 0.512306i | \(0.171209\pi\) | |||||||
\(822\) | −43.1783 | −1.50602 | ||||||||
\(823\) | 6.63026 | 0.231116 | 0.115558 | − | 0.993301i | \(-0.463134\pi\) | ||||
0.115558 | + | 0.993301i | \(0.463134\pi\) | |||||||
\(824\) | 6.85994 | 0.238977 | ||||||||
\(825\) | −2.72061 | −0.0947195 | ||||||||
\(826\) | −8.45602 | −0.294222 | ||||||||
\(827\) | −11.4359 | −0.397667 | −0.198833 | − | 0.980033i | \(-0.563715\pi\) | ||||
−0.198833 | + | 0.980033i | \(0.563715\pi\) | |||||||
\(828\) | 3.48288 | 0.121038 | ||||||||
\(829\) | 32.8379 | 1.14051 | 0.570254 | − | 0.821468i | \(-0.306845\pi\) | ||||
0.570254 | + | 0.821468i | \(0.306845\pi\) | |||||||
\(830\) | 10.7230 | 0.372199 | ||||||||
\(831\) | −73.4705 | −2.54866 | ||||||||
\(832\) | 1.20875 | 0.0419057 | ||||||||
\(833\) | 12.6135 | 0.437032 | ||||||||
\(834\) | 26.6947 | 0.924363 | ||||||||
\(835\) | −9.52120 | −0.329495 | ||||||||
\(836\) | −5.93546 | −0.205282 | ||||||||
\(837\) | 27.2932 | 0.943391 | ||||||||
\(838\) | −12.2933 | −0.424664 | ||||||||
\(839\) | 17.6411 | 0.609039 | 0.304520 | − | 0.952506i | \(-0.401504\pi\) | ||||
0.304520 | + | 0.952506i | \(0.401504\pi\) | |||||||
\(840\) | 5.20376 | 0.179547 | ||||||||
\(841\) | −28.6436 | −0.987710 | ||||||||
\(842\) | 9.99247 | 0.344363 | ||||||||
\(843\) | −4.99664 | −0.172093 | ||||||||
\(844\) | −5.49748 | −0.189231 | ||||||||
\(845\) | −11.5389 | −0.396951 | ||||||||
\(846\) | −53.2581 | −1.83105 | ||||||||
\(847\) | 1.91272 | 0.0657217 | ||||||||
\(848\) | −11.3466 | −0.389644 | ||||||||
\(849\) | −6.64590 | −0.228087 | ||||||||
\(850\) | −3.77479 | −0.129474 | ||||||||
\(851\) | 0.892020 | 0.0305781 | ||||||||
\(852\) | −13.1747 | −0.451359 | ||||||||
\(853\) | 30.5864 | 1.04726 | 0.523629 | − | 0.851946i | \(-0.324578\pi\) | ||||
0.523629 | + | 0.851946i | \(0.324578\pi\) | |||||||
\(854\) | −5.07885 | −0.173795 | ||||||||
\(855\) | 26.1262 | 0.893498 | ||||||||
\(856\) | 11.6856 | 0.399405 | ||||||||
\(857\) | 48.9983 | 1.67375 | 0.836875 | − | 0.547394i | \(-0.184380\pi\) | ||||
0.836875 | + | 0.547394i | \(0.184380\pi\) | |||||||
\(858\) | −3.28853 | −0.112268 | ||||||||
\(859\) | −36.0523 | −1.23009 | −0.615044 | − | 0.788493i | \(-0.710862\pi\) | ||||
−0.615044 | + | 0.788493i | \(0.710862\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | −53.9494 | −1.83859 | ||||||||
\(862\) | −20.3287 | −0.692399 | ||||||||
\(863\) | 40.1399 | 1.36638 | 0.683190 | − | 0.730241i | \(-0.260592\pi\) | ||||
0.683190 | + | 0.730241i | \(0.260592\pi\) | |||||||
\(864\) | 3.81352 | 0.129739 | ||||||||
\(865\) | −10.1851 | −0.346304 | ||||||||
\(866\) | −33.7115 | −1.14556 | ||||||||
\(867\) | −7.48430 | −0.254180 | ||||||||
\(868\) | 13.6892 | 0.464642 | ||||||||
\(869\) | 0.235281 | 0.00798135 | ||||||||
\(870\) | 1.62421 | 0.0550658 | ||||||||
\(871\) | 18.8013 | 0.637057 | ||||||||
\(872\) | 15.9177 | 0.539042 | ||||||||
\(873\) | −3.08567 | −0.104434 | ||||||||
\(874\) | 4.69646 | 0.158860 | ||||||||
\(875\) | 1.91272 | 0.0646616 | ||||||||
\(876\) | −5.71986 | −0.193256 | ||||||||
\(877\) | 58.5488 | 1.97705 | 0.988526 | − | 0.151049i | \(-0.0482652\pi\) | ||||
0.988526 | + | 0.151049i | \(0.0482652\pi\) | |||||||
\(878\) | −8.79633 | −0.296862 | ||||||||
\(879\) | −20.7452 | −0.699719 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 49.4346 | 1.66550 | 0.832748 | − | 0.553653i | \(-0.186766\pi\) | ||||
0.832748 | + | 0.553653i | \(0.186766\pi\) | |||||||
\(882\) | −14.7084 | −0.495258 | ||||||||
\(883\) | −46.3441 | −1.55960 | −0.779801 | − | 0.626028i | \(-0.784680\pi\) | ||||
−0.779801 | + | 0.626028i | \(0.784680\pi\) | |||||||
\(884\) | −4.56276 | −0.153462 | ||||||||
\(885\) | −12.0277 | −0.404306 | ||||||||
\(886\) | −20.3959 | −0.685215 | ||||||||
\(887\) | 25.9287 | 0.870602 | 0.435301 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435301 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(888\) | 3.06708 | 0.102924 | ||||||||
\(889\) | 15.9065 | 0.533487 | ||||||||
\(890\) | −1.84824 | −0.0619532 | ||||||||
\(891\) | 2.83004 | 0.0948099 | ||||||||
\(892\) | −19.9298 | −0.667298 | ||||||||
\(893\) | −71.8156 | −2.40322 | ||||||||
\(894\) | −8.33409 | −0.278734 | ||||||||
\(895\) | 16.5986 | 0.554829 | ||||||||
\(896\) | 1.91272 | 0.0638994 | ||||||||
\(897\) | 2.60206 | 0.0868802 | ||||||||
\(898\) | 23.4319 | 0.781933 | ||||||||
\(899\) | 4.27271 | 0.142503 | ||||||||
\(900\) | 4.40172 | 0.146724 | ||||||||
\(901\) | 42.8310 | 1.42691 | ||||||||
\(902\) | 10.3674 | 0.345197 | ||||||||
\(903\) | 5.20376 | 0.173170 | ||||||||
\(904\) | 2.03490 | 0.0676798 | ||||||||
\(905\) | 12.9709 | 0.431167 | ||||||||
\(906\) | −9.52525 | −0.316455 | ||||||||
\(907\) | −50.9527 | −1.69186 | −0.845929 | − | 0.533296i | \(-0.820953\pi\) | ||||
−0.845929 | + | 0.533296i | \(0.820953\pi\) | |||||||
\(908\) | 7.77896 | 0.258154 | ||||||||
\(909\) | −17.2053 | −0.570665 | ||||||||
\(910\) | 2.31199 | 0.0766417 | ||||||||
\(911\) | −25.6757 | −0.850674 | −0.425337 | − | 0.905035i | \(-0.639844\pi\) | ||||
−0.425337 | + | 0.905035i | \(0.639844\pi\) | |||||||
\(912\) | 16.1481 | 0.534716 | ||||||||
\(913\) | −10.7230 | −0.354878 | ||||||||
\(914\) | −19.0784 | −0.631058 | ||||||||
\(915\) | −7.22405 | −0.238820 | ||||||||
\(916\) | −8.96590 | −0.296242 | ||||||||
\(917\) | −16.0488 | −0.529979 | ||||||||
\(918\) | −14.3953 | −0.475114 | ||||||||
\(919\) | 43.9593 | 1.45008 | 0.725042 | − | 0.688704i | \(-0.241820\pi\) | ||||
0.725042 | + | 0.688704i | \(0.241820\pi\) | |||||||
\(920\) | 0.791254 | 0.0260869 | ||||||||
\(921\) | −29.8615 | −0.983969 | ||||||||
\(922\) | 34.5032 | 1.13630 | ||||||||
\(923\) | −5.85344 | −0.192668 | ||||||||
\(924\) | −5.20376 | −0.171191 | ||||||||
\(925\) | 1.12735 | 0.0370670 | ||||||||
\(926\) | −32.9370 | −1.08238 | ||||||||
\(927\) | 30.1955 | 0.991751 | ||||||||
\(928\) | 0.597002 | 0.0195975 | ||||||||
\(929\) | −6.10050 | −0.200151 | −0.100075 | − | 0.994980i | \(-0.531908\pi\) | ||||
−0.100075 | + | 0.994980i | \(0.531908\pi\) | |||||||
\(930\) | 19.4713 | 0.638488 | ||||||||
\(931\) | −19.8334 | −0.650015 | ||||||||
\(932\) | 16.7903 | 0.549984 | ||||||||
\(933\) | 23.2112 | 0.759901 | ||||||||
\(934\) | 36.3551 | 1.18957 | ||||||||
\(935\) | 3.77479 | 0.123449 | ||||||||
\(936\) | 5.32056 | 0.173908 | ||||||||
\(937\) | 8.15730 | 0.266487 | 0.133244 | − | 0.991083i | \(-0.457461\pi\) | ||||
0.133244 | + | 0.991083i | \(0.457461\pi\) | |||||||
\(938\) | 29.7511 | 0.971408 | ||||||||
\(939\) | −29.7306 | −0.970220 | ||||||||
\(940\) | −12.0994 | −0.394639 | ||||||||
\(941\) | −0.279419 | −0.00910880 | −0.00455440 | − | 0.999990i | \(-0.501450\pi\) | ||||
−0.00455440 | + | 0.999990i | \(0.501450\pi\) | |||||||
\(942\) | −17.7416 | −0.578054 | ||||||||
\(943\) | −8.20325 | −0.267135 | ||||||||
\(944\) | −4.42095 | −0.143890 | ||||||||
\(945\) | 7.29419 | 0.237280 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 43.0750 | 1.39975 | 0.699875 | − | 0.714265i | \(-0.253239\pi\) | ||||
0.699875 | + | 0.714265i | \(0.253239\pi\) | |||||||
\(948\) | −0.640107 | −0.0207897 | ||||||||
\(949\) | −2.54129 | −0.0824937 | ||||||||
\(950\) | 5.93546 | 0.192572 | ||||||||
\(951\) | 13.7470 | 0.445777 | ||||||||
\(952\) | −7.22010 | −0.234005 | ||||||||
\(953\) | 35.2696 | 1.14249 | 0.571247 | − | 0.820778i | \(-0.306460\pi\) | ||||
0.571247 | + | 0.820778i | \(0.306460\pi\) | |||||||
\(954\) | −49.9445 | −1.61701 | ||||||||
\(955\) | −4.33138 | −0.140160 | ||||||||
\(956\) | −8.02935 | −0.259688 | ||||||||
\(957\) | −1.62421 | −0.0525032 | ||||||||
\(958\) | 8.98706 | 0.290359 | ||||||||
\(959\) | −30.3564 | −0.980258 | ||||||||
\(960\) | 2.72061 | 0.0878073 | ||||||||
\(961\) | 20.2219 | 0.652320 | ||||||||
\(962\) | 1.36268 | 0.0439345 | ||||||||
\(963\) | 51.4366 | 1.65752 | ||||||||
\(964\) | −1.12866 | −0.0363517 | ||||||||
\(965\) | 1.94220 | 0.0625215 | ||||||||
\(966\) | 4.11749 | 0.132478 | ||||||||
\(967\) | −50.2807 | −1.61692 | −0.808459 | − | 0.588553i | \(-0.799698\pi\) | ||||
−0.808459 | + | 0.588553i | \(0.799698\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −60.9556 | −1.95818 | ||||||||
\(970\) | −0.701016 | −0.0225083 | ||||||||
\(971\) | 38.1828 | 1.22535 | 0.612673 | − | 0.790337i | \(-0.290094\pi\) | ||||
0.612673 | + | 0.790337i | \(0.290094\pi\) | |||||||
\(972\) | −19.1400 | −0.613916 | ||||||||
\(973\) | 18.7676 | 0.601663 | ||||||||
\(974\) | −6.66801 | −0.213657 | ||||||||
\(975\) | 3.28853 | 0.105317 | ||||||||
\(976\) | −2.65531 | −0.0849943 | ||||||||
\(977\) | −14.4882 | −0.463520 | −0.231760 | − | 0.972773i | \(-0.574448\pi\) | ||||
−0.231760 | + | 0.972773i | \(0.574448\pi\) | |||||||
\(978\) | −0.192652 | −0.00616033 | ||||||||
\(979\) | 1.84824 | 0.0590700 | ||||||||
\(980\) | −3.34151 | −0.106741 | ||||||||
\(981\) | 70.0653 | 2.23701 | ||||||||
\(982\) | 27.9655 | 0.892413 | ||||||||
\(983\) | −42.9493 | −1.36987 | −0.684935 | − | 0.728604i | \(-0.740170\pi\) | ||||
−0.684935 | + | 0.728604i | \(0.740170\pi\) | |||||||
\(984\) | −28.2057 | −0.899164 | ||||||||
\(985\) | 7.27531 | 0.231811 | ||||||||
\(986\) | −2.25356 | −0.0717678 | ||||||||
\(987\) | −62.9623 | −2.00411 | ||||||||
\(988\) | 7.17447 | 0.228250 | ||||||||
\(989\) | 0.791254 | 0.0251604 | ||||||||
\(990\) | −4.40172 | −0.139896 | ||||||||
\(991\) | 23.1905 | 0.736669 | 0.368334 | − | 0.929693i | \(-0.379928\pi\) | ||||
0.368334 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(992\) | 7.15695 | 0.227233 | ||||||||
\(993\) | 86.4436 | 2.74321 | ||||||||
\(994\) | −9.26247 | −0.293788 | ||||||||
\(995\) | −12.3540 | −0.391647 | ||||||||
\(996\) | 29.1730 | 0.924381 | ||||||||
\(997\) | −33.9549 | −1.07536 | −0.537681 | − | 0.843149i | \(-0.680699\pi\) | ||||
−0.537681 | + | 0.843149i | \(0.680699\pi\) | |||||||
\(998\) | −27.9426 | −0.884508 | ||||||||
\(999\) | 4.29918 | 0.136020 |
(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 | 4730.2.a.be.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.be.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial |