Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.103746\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.103746 | −0.0598979 | −0.0299490 | − | 0.999551i | \(-0.509534\pi\) | ||||
−0.0299490 | + | 0.999551i | \(0.509534\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.71451 | −1.66118 | −0.830589 | − | 0.556885i | \(-0.811996\pi\) | ||||
−0.830589 | + | 0.556885i | \(0.811996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98924 | −0.996412 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.25890 | −0.379573 | −0.189786 | − | 0.981825i | \(-0.560780\pi\) | ||||
−0.189786 | + | 0.981825i | \(0.560780\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.166769 | 0.0462533 | 0.0231266 | − | 0.999733i | \(-0.492638\pi\) | ||||
0.0231266 | + | 0.999733i | \(0.492638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.385366 | 0.0995012 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.79993 | 1.40669 | 0.703345 | − | 0.710849i | \(-0.251689\pi\) | ||||
0.703345 | + | 0.710849i | \(0.251689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.05905 | −0.242963 | −0.121481 | − | 0.992594i | \(-0.538764\pi\) | ||||
−0.121481 | + | 0.992594i | \(0.538764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.98555 | −1.87362 | −0.936808 | − | 0.349844i | \(-0.886235\pi\) | ||||
−0.936808 | + | 0.349844i | \(0.886235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.79757 | 1.75951 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.621361 | 0.119581 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.21478 | −0.596970 | −0.298485 | − | 0.954414i | \(-0.596481\pi\) | ||||
−0.298485 | + | 0.954414i | \(0.596481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.67227 | −1.73719 | −0.868595 | − | 0.495522i | \(-0.834977\pi\) | ||||
−0.868595 | + | 0.495522i | \(0.834977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.130606 | 0.0227356 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70626 | 0.280507 | 0.140253 | − | 0.990116i | \(-0.455208\pi\) | ||||
0.140253 | + | 0.990116i | \(0.455208\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0173016 | −0.00277048 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83571 | −0.584940 | −0.292470 | − | 0.956275i | \(-0.594477\pi\) | ||||
−0.292470 | + | 0.956275i | \(0.594477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1035 | 1.65522 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.32109 | −1.06789 | −0.533945 | − | 0.845519i | \(-0.679291\pi\) | ||||
−0.533945 | + | 0.845519i | \(0.679291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.601721 | −0.0842579 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.82243 | 0.387690 | 0.193845 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193845 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.67619 | 0.630538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.109873 | 0.0145530 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.74300 | −1.26843 | −0.634215 | − | 0.773157i | \(-0.718677\pi\) | ||||
−0.634215 | + | 0.773157i | \(0.718677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.82191 | −0.617383 | −0.308691 | − | 0.951162i | \(-0.599891\pi\) | ||||
−0.308691 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.619464 | −0.0768350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.21471 | −0.148401 | −0.0742005 | − | 0.997243i | \(-0.523640\pi\) | ||||
−0.0742005 | + | 0.997243i | \(0.523640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.932217 | 0.112226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4015 | −1.59046 | −0.795232 | − | 0.606305i | \(-0.792651\pi\) | ||||
−0.795232 | + | 0.606305i | \(0.792651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5739 | 1.93982 | 0.969912 | − | 0.243456i | \(-0.0782811\pi\) | ||||
0.969912 | + | 0.243456i | \(0.0782811\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.912716 | −0.105391 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6084 | −1.30605 | −0.653024 | − | 0.757337i | \(-0.726500\pi\) | ||||
−0.653024 | + | 0.757337i | \(0.726500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.90325 | 0.989250 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00621 | 0.659267 | 0.329633 | − | 0.944109i | \(-0.393075\pi\) | ||||
0.329633 | + | 0.944109i | \(0.393075\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.5439 | −2.33676 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.333522 | 0.0357573 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0453 | 1.17080 | 0.585402 | − | 0.810743i | \(-0.300937\pi\) | ||||
0.585402 | + | 0.810743i | \(0.300937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00346 | 0.104054 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.93385 | 0.403605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.56071 | 0.463070 | 0.231535 | − | 0.972827i | \(-0.425625\pi\) | ||||
0.231535 | + | 0.972827i | \(0.425625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.76315 | 0.378211 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1605 | −1.60803 | −0.804015 | − | 0.594609i | \(-0.797307\pi\) | ||||
−0.804015 | + | 0.594609i | \(0.797307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.212217 | −0.0209103 | −0.0104552 | − | 0.999945i | \(-0.503328\pi\) | ||||
−0.0104552 | + | 0.999945i | \(0.503328\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6381 | 1.12510 | 0.562550 | − | 0.826763i | \(-0.309821\pi\) | ||||
0.562550 | + | 0.826763i | \(0.309821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9891 | −1.62726 | −0.813632 | − | 0.581380i | \(-0.802513\pi\) | ||||
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.177018 | −0.0168018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.66265 | −0.532697 | −0.266348 | − | 0.963877i | \(-0.585817\pi\) | ||||
−0.266348 | + | 0.963877i | \(0.585817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.3769 | 3.11241 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.498511 | −0.0460874 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.41517 | −0.855925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.103746 | 0.00935449 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14.1061 | −1.26169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.30382 | −0.736845 | −0.368423 | − | 0.929658i | \(-0.620102\pi\) | ||||
−0.368423 | + | 0.929658i | \(0.620102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.397941 | 0.0350367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30755 | 0.638464 | 0.319232 | − | 0.947677i | \(-0.396575\pi\) | ||||
0.319232 | + | 0.947677i | \(0.396575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.30805 | −0.198645 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4686 | −0.894395 | −0.447198 | − | 0.894435i | \(-0.647578\pi\) | ||||
−0.447198 | + | 0.894435i | \(0.647578\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4396 | 1.47921 | 0.739606 | − | 0.673040i | \(-0.235012\pi\) | ||||
0.739606 | + | 0.673040i | \(0.235012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.759536 | 0.0639644 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.209945 | −0.0175565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9413 | 0.991674 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2645 | −1.33244 | −0.666219 | − | 0.745756i | \(-0.732088\pi\) | ||||
−0.666219 | + | 0.745756i | \(0.732088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0691 | 0.900792 | 0.450396 | − | 0.892829i | \(-0.351283\pi\) | ||||
0.450396 | + | 0.892829i | \(0.351283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.3374 | −1.40164 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 35.9277 | 2.88578 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8519 | 1.02569 | 0.512845 | − | 0.858481i | \(-0.328592\pi\) | ||||
0.512845 | + | 0.858481i | \(0.328592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.292816 | −0.0232219 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.63928 | 0.206724 | 0.103362 | − | 0.994644i | \(-0.467040\pi\) | ||||
0.103362 | + | 0.994644i | \(0.467040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.485138 | −0.0377679 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.7990 | −0.913031 | −0.456516 | − | 0.889715i | \(-0.650903\pi\) | ||||
−0.456516 | + | 0.889715i | \(0.650903\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9722 | −0.997861 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.16575 | 0.242091 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.75018 | 0.589235 | 0.294618 | − | 0.955615i | \(-0.404808\pi\) | ||||
0.294618 | + | 0.955615i | \(0.404808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.01080 | 0.0759764 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.88020 | −0.290019 | −0.145010 | − | 0.989430i | \(-0.546321\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.1868 | 1.72346 | 0.861730 | − | 0.507366i | \(-0.169381\pi\) | ||||
0.861730 | + | 0.507366i | \(0.169381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.500255 | 0.0369799 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.33791 | −0.465972 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.30153 | −0.533941 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8532 | −1.21945 | −0.609726 | − | 0.792613i | \(-0.708720\pi\) | ||||
−0.609726 | + | 0.792613i | \(0.708720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5599 | 0.832102 | 0.416051 | − | 0.909341i | \(-0.363414\pi\) | ||||
0.416051 | + | 0.909341i | \(0.363414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0642670 | 0.00460226 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6526 | 1.04395 | 0.521977 | − | 0.852960i | \(-0.325195\pi\) | ||||
0.521977 | + | 0.852960i | \(0.325195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3345 | 0.803480 | 0.401740 | − | 0.915754i | \(-0.368406\pi\) | ||||
0.401740 | + | 0.915754i | \(0.368406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.126022 | 0.00888891 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.71451 | 0.259433 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.8599 | 1.86689 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.33324 | 0.0922220 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4952 | −1.06673 | −0.533366 | − | 0.845885i | \(-0.679073\pi\) | ||||
−0.533366 | + | 0.845885i | \(0.679073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.39035 | 0.0952655 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.2478 | 0.971690 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.71948 | −0.116191 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.967247 | 0.0650641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.7332 | 1.32143 | 0.660715 | − | 0.750637i | \(-0.270253\pi\) | ||||
0.660715 | + | 0.750637i | \(0.270253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.2980 | −1.75320 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.27003 | −0.217040 | −0.108520 | − | 0.994094i | \(-0.534611\pi\) | ||||
−0.108520 | + | 0.994094i | \(0.534611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.1500 | 1.19938 | 0.599692 | − | 0.800231i | \(-0.295290\pi\) | ||||
0.599692 | + | 0.800231i | \(0.295290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0356 | 0.788476 | 0.394238 | − | 0.919008i | \(-0.371009\pi\) | ||||
0.394238 | + | 0.919008i | \(0.371009\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.1942 | 1.77396 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.20433 | 0.0782296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.9782 | 0.968861 | 0.484431 | − | 0.874830i | \(-0.339027\pi\) | ||||
0.484431 | + | 0.874830i | \(0.339027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.73474 | −0.176160 | −0.0880802 | − | 0.996113i | \(-0.528073\pi\) | ||||
−0.0880802 | + | 0.996113i | \(0.528073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.78776 | −0.178835 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.176616 | −0.0112378 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.623121 | −0.0394887 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33313 | 0.399743 | 0.199872 | − | 0.979822i | \(-0.435947\pi\) | ||||
0.199872 | + | 0.979822i | \(0.435947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3119 | 0.711173 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.23510 | 0.139967 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3821 | 1.83281 | 0.916403 | − | 0.400258i | \(-0.131079\pi\) | ||||
0.916403 | + | 0.400258i | \(0.131079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.60974 | 0.594828 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.1326 | 0.624804 | 0.312402 | − | 0.949950i | \(-0.398866\pi\) | ||||
0.312402 | + | 0.949950i | \(0.398866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4839 | −0.644023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.14591 | −0.0701287 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.47385 | 0.333746 | 0.166873 | − | 0.985978i | \(-0.446633\pi\) | ||||
0.166873 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6123 | 0.644651 | 0.322326 | − | 0.946629i | \(-0.395535\pi\) | ||||
0.322326 | + | 0.946629i | \(0.395535\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.0753 | −0.667864 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1170 | 1.32888 | 0.664441 | − | 0.747341i | \(-0.268670\pi\) | ||||
0.664441 | + | 0.747341i | \(0.268670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.9127 | 1.73096 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.60380 | −0.513260 | −0.256630 | − | 0.966510i | \(-0.582612\pi\) | ||||
−0.256630 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.4778 | −1.15783 | −0.578917 | − | 0.815387i | \(-0.696524\pi\) | ||||
−0.578917 | + | 0.815387i | \(0.696524\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.408123 | −0.0241751 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6392 | 0.978777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.473156 | −0.0277369 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.507171 | −0.0296292 | −0.0148146 | − | 0.999890i | \(-0.504716\pi\) | ||||
−0.0148146 | + | 0.999890i | \(0.504716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.1904 | 2.10709 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.782231 | −0.0453897 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.49851 | −0.0866609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.67659 | 0.0963177 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.9110 | 1.02558 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.3930 | −1.10682 | −0.553410 | − | 0.832909i | \(-0.686674\pi\) | ||||
−0.553410 | + | 0.832909i | \(0.686674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0220167 | 0.00125249 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2720 | −1.71657 | −0.858285 | − | 0.513174i | \(-0.828470\pi\) | ||||
−0.858285 | + | 0.513174i | \(0.828470\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.36212 | −0.133515 | −0.0667575 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667575 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.7324 | 1.27678 | 0.638390 | − | 0.769713i | \(-0.279601\pi\) | ||||
0.638390 | + | 0.769713i | \(0.279601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.04709 | 0.226593 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.20741 | −0.0673911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.14242 | −0.341773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46716 | 0.0813834 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.76256 | 0.0974698 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.97931 | 0.273688 | 0.136844 | − | 0.990593i | \(-0.456304\pi\) | ||||
0.136844 | + | 0.990593i | \(0.456304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.10041 | −0.279501 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.51207 | 0.246521 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.28389 | −0.505726 | −0.252863 | − | 0.967502i | \(-0.581372\pi\) | ||||
−0.252863 | + | 0.967502i | \(0.581372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.587478 | 0.0319075 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.1764 | 0.659390 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.46273 | −0.186427 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.9523 | 1.50056 | 0.750278 | − | 0.661123i | \(-0.229920\pi\) | ||||
0.750278 | + | 0.661123i | \(0.229920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.76798 | −0.148166 | −0.0740832 | − | 0.997252i | \(-0.523603\pi\) | ||||
−0.0740832 | + | 0.997252i | \(0.523603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.103624 | 0.00553102 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.4071 | −1.40551 | −0.702754 | − | 0.711433i | \(-0.748046\pi\) | ||||
−0.702754 | + | 0.711433i | \(0.748046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.7799 | 2.64204 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9493 | −0.788994 | −0.394497 | − | 0.918897i | \(-0.629081\pi\) | ||||
−0.394497 | + | 0.918897i | \(0.629081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8784 | −0.940969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.976789 | 0.0512681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −61.5638 | −3.22239 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1485 | 0.947342 | 0.473671 | − | 0.880702i | \(-0.342929\pi\) | ||||
0.473671 | + | 0.880702i | \(0.342929\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.98924 | 0.155613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5184 | 0.699955 | 0.349977 | − | 0.936758i | \(-0.386189\pi\) | ||||
0.349977 | + | 0.936758i | \(0.386189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46346 | 0.0755726 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.536125 | −0.0276118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5253 | 1.00295 | 0.501474 | − | 0.865173i | \(-0.332791\pi\) | ||||
0.501474 | + | 0.865173i | \(0.332791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.861491 | 0.0441355 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.6971 | 1.67074 | 0.835372 | − | 0.549685i | \(-0.185252\pi\) | ||||
0.835372 | + | 0.549685i | \(0.185252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4658 | 0.582842 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6007 | −0.943092 | −0.471546 | − | 0.881841i | \(-0.656304\pi\) | ||||
−0.471546 | + | 0.881841i | \(0.656304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.1156 | −2.63560 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.758131 | −0.0382427 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.1195 | 2.16958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6724 | 0.836762 | 0.418381 | − | 0.908272i | \(-0.362598\pi\) | ||||
0.418381 | + | 0.908272i | \(0.362598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1863 | −0.908183 | −0.454091 | − | 0.890955i | \(-0.650036\pi\) | ||||
−0.454091 | + | 0.890955i | \(0.650036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.61303 | −0.0803508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −33.0712 | −1.64332 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.14801 | −0.106473 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8086 | 1.07837 | 0.539183 | − | 0.842188i | \(-0.318733\pi\) | ||||
0.539183 | + | 0.842188i | \(0.318733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.08608 | 0.0535724 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.3101 | −1.09516 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.80930 | −0.0886017 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.3082 | −1.23639 | −0.618194 | − | 0.786025i | \(-0.712136\pi\) | ||||
−0.618194 | + | 0.786025i | \(0.712136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5708 | 0.661400 | 0.330700 | − | 0.943736i | \(-0.392715\pi\) | ||||
0.330700 | + | 0.943736i | \(0.392715\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.8845 | 1.06406 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.0253 | 2.47509 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0217810 | 0.00105160 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.6571 | 1.57303 | 0.786517 | − | 0.617568i | \(-0.211882\pi\) | ||||
0.786517 | + | 0.617568i | \(0.211882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2443 | −0.924820 | −0.462410 | − | 0.886666i | \(-0.653015\pi\) | ||||
−0.462410 | + | 0.886666i | \(0.653015\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.23887 | −0.0593992 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.51615 | 0.455219 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.3365 | −0.541061 | −0.270531 | − | 0.962711i | \(-0.587199\pi\) | ||||
−0.270531 | + | 0.962711i | \(0.587199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.47862 | −0.307808 | −0.153904 | − | 0.988086i | \(-0.549185\pi\) | ||||
−0.153904 | + | 0.988086i | \(0.549185\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.0280 | −1.94491 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.68738 | 0.0798103 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.8694 | 1.17366 | 0.586830 | − | 0.809710i | \(-0.300376\pi\) | ||||
0.586830 | + | 0.809710i | \(0.300376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.25890 | 0.0592793 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.14838 | −0.0539556 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.6254 | −1.15193 | −0.575963 | − | 0.817476i | \(-0.695373\pi\) | ||||
−0.575963 | + | 0.817476i | \(0.695373\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.60385 | 0.168213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.483177 | −0.0225038 | −0.0112519 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112519 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.07820 | 0.0501081 | 0.0250541 | − | 0.999686i | \(-0.492024\pi\) | ||||
0.0250541 | + | 0.999686i | \(0.492024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.72737 | −0.172853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6546 | −1.46480 | −0.732400 | − | 0.680875i | \(-0.761600\pi\) | ||||
−0.732400 | + | 0.680875i | \(0.761600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.33333 | −0.0614367 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.82877 | 0.222027 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.31708 | −0.427497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.43690 | −0.386299 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.94043 | 0.0886605 | 0.0443303 | − | 0.999017i | \(-0.485885\pi\) | ||||
0.0443303 | + | 0.999017i | \(0.485885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.284550 | 0.0129744 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.9408 | −0.769242 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7650 | 0.940951 | 0.470476 | − | 0.882413i | \(-0.344082\pi\) | ||||
0.470476 | + | 0.882413i | \(0.344082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.273815 | −0.0123823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2595 | 1.45585 | 0.727925 | − | 0.685657i | \(-0.240485\pi\) | ||||
0.727925 | + | 0.685657i | \(0.240485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.6455 | −0.839752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.9783 | −0.628276 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.5390 | 0.919453 | 0.459726 | − | 0.888061i | \(-0.347948\pi\) | ||||
0.459726 | + | 0.888061i | \(0.347948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.22410 | 0.0546887 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9911 | 0.846772 | 0.423386 | − | 0.905949i | \(-0.360841\pi\) | ||||
0.423386 | + | 0.905949i | \(0.360841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.0283 | 2.67123 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34582 | 0.0597698 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.4017 | −0.859964 | −0.429982 | − | 0.902837i | \(-0.641480\pi\) | ||||
−0.429982 | + | 0.902837i | \(0.641480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.658053 | −0.0290537 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.788281 | 0.0347358 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.21651 | 0.405342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.804053 | −0.0352940 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.6858 | −0.468155 | −0.234078 | − | 0.972218i | \(-0.575207\pi\) | ||||
−0.234078 | + | 0.972218i | \(0.575207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7762 | −1.08339 | −0.541694 | − | 0.840576i | \(-0.682217\pi\) | ||||
−0.541694 | + | 0.840576i | \(0.682217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56.0985 | −2.44369 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 57.7400 | 2.51044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.1241 | 1.26388 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.166769 | −0.00722355 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.2299 | −1.86899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.402556 | 0.0173716 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.3160 | −1.30339 | −0.651694 | − | 0.758482i | \(-0.725941\pi\) | ||||
−0.651694 | + | 0.758482i | \(0.725941\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.40554 | −0.103232 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 63.1063 | 2.70318 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8145 | 0.505152 | 0.252576 | − | 0.967577i | \(-0.418722\pi\) | ||||
0.252576 | + | 0.967577i | \(0.418722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4138 | 0.615168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.40462 | 0.145042 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.657534 | 0.0279108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.7423 | 1.68394 | 0.841968 | − | 0.539528i | \(-0.181397\pi\) | ||||
0.841968 | + | 0.539528i | \(0.181397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.639676 | −0.0270554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.757507 | 0.0319820 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.5515 | −1.24545 | −0.622723 | − | 0.782442i | \(-0.713974\pi\) | ||||
−0.622723 | + | 0.782442i | \(0.713974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0339 | 0.884905 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.29222 | 0.347628 | 0.173814 | − | 0.984779i | \(-0.444391\pi\) | ||||
0.173814 | + | 0.984779i | \(0.444391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4987 | 0.732296 | 0.366148 | − | 0.930557i | \(-0.380676\pi\) | ||||
0.366148 | + | 0.930557i | \(0.380676\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.74845 | 0.0730426 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −79.0510 | −3.29665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.4641 | 1.85106 | 0.925531 | − | 0.378671i | \(-0.123619\pi\) | ||||
0.925531 | + | 0.378671i | \(0.123619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.19930 | −0.0498412 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.55315 | −0.147157 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.85172 | 0.0765593 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.3564 | −1.17039 | −0.585197 | − | 0.810891i | \(-0.698983\pi\) | ||||
−0.585197 | + | 0.810891i | \(0.698983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2434 | 0.422073 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.52015 | −0.0625307 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.32320 | −0.177533 | −0.0887663 | − | 0.996052i | \(-0.528292\pi\) | ||||
−0.0887663 | + | 0.996052i | \(0.528292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.17591 | −0.0481268 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.43799 | −0.385626 | −0.192813 | − | 0.981236i | \(-0.561761\pi\) | ||||
−0.192813 | + | 0.981236i | \(0.561761\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7128 | −0.804100 | −0.402050 | − | 0.915618i | \(-0.631702\pi\) | ||||
−0.402050 | + | 0.915618i | \(0.631702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.63107 | 0.147869 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.9727 | 1.42184 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8565 | −0.603008 | −0.301504 | − | 0.953465i | \(-0.597489\pi\) | ||||
−0.301504 | + | 0.953465i | \(0.597489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.22093 | −0.0493934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8325 | 0.558688 | 0.279344 | − | 0.960191i | \(-0.409883\pi\) | ||||
0.279344 | + | 0.960191i | \(0.409883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.385366 | −0.0155395 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.5481 | −0.867492 | −0.433746 | − | 0.901035i | \(-0.642808\pi\) | ||||
−0.433746 | + | 0.901035i | \(0.642808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.11291 | 0.326085 | 0.163043 | − | 0.986619i | \(-0.447869\pi\) | ||||
0.163043 | + | 0.986619i | \(0.447869\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.58327 | −0.224049 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.40943 | 0.336377 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.138319 | −0.00552391 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.89617 | 0.394586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.1578 | −1.20056 | −0.600282 | − | 0.799788i | \(-0.704945\pi\) | ||||
−0.600282 | + | 0.799788i | \(0.704945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.60757 | 0.0638951 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.8446 | 1.22403 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.0602 | 1.58476 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.1257 | −1.70336 | −0.851681 | − | 0.524060i | \(-0.824417\pi\) | ||||
−0.851681 | + | 0.524060i | \(0.824417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.9922 | 0.670107 | 0.335054 | − | 0.942199i | \(-0.391246\pi\) | ||||
0.335054 | + | 0.942199i | \(0.391246\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.47815 | −0.0582022 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.6985 | −1.60002 | −0.800012 | − | 0.599985i | \(-0.795173\pi\) | ||||
−0.800012 | + | 0.599985i | \(0.795173\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2655 | 0.481461 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0267 | −0.392377 | −0.196188 | − | 0.980566i | \(-0.562856\pi\) | ||||
−0.196188 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.1440 | −1.06060 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49.5432 | −1.93286 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.1913 | 0.864452 | 0.432226 | − | 0.901765i | \(-0.357728\pi\) | ||||
0.432226 | + | 0.901765i | \(0.357728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9938 | 0.544298 | 0.272149 | − | 0.962255i | \(-0.412266\pi\) | ||||
0.272149 | + | 0.962255i | \(0.412266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.100348 | −0.00389720 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.8866 | 1.11849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.04724 | −0.0791509 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.07030 | 0.234342 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.56955 | −0.368879 | −0.184440 | − | 0.982844i | \(-0.559047\pi\) | ||||
−0.184440 | + | 0.982844i | \(0.559047\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.46647 | 0.210405 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.0781 | −1.27130 | −0.635648 | − | 0.771979i | \(-0.719267\pi\) | ||||
−0.635648 | + | 0.771979i | \(0.719267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.339254 | 0.0130002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2408 | 0.468379 | 0.234190 | − | 0.972191i | \(-0.424756\pi\) | ||||
0.234190 | + | 0.972191i | \(0.424756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.8858 | 1.48575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.88299 | −0.0718407 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.470692 | 0.0179320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.86970 | −0.0711268 | −0.0355634 | − | 0.999367i | \(-0.511323\pi\) | ||||
−0.0355634 | + | 0.999367i | \(0.511323\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −64.7797 | −2.45723 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.79993 | −0.219688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.24865 | −0.0472281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.8538 | −1.88295 | −0.941475 | − | 0.337082i | \(-0.890560\pi\) | ||||
−0.941475 | + | 0.337082i | \(0.890560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.80701 | −0.0681528 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.82130 | −0.106256 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.14510 | 0.268340 | 0.134170 | − | 0.990958i | \(-0.457163\pi\) | ||||
0.134170 | + | 0.990958i | \(0.457163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.7003 | 1.30136 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 86.9106 | 3.25483 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.779843 | 0.0291645 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.55394 | −0.0580328 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.9999 | 1.56633 | 0.783165 | − | 0.621813i | \(-0.213604\pi\) | ||||
0.783165 | + | 0.621813i | \(0.213604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.283720 | 0.0105516 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.2823 | −1.05038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.39778 | 0.0518408 | 0.0259204 | − | 0.999664i | \(-0.491748\pi\) | ||||
0.0259204 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.4205 | −0.978538 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.2469 | −0.822830 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1491 | 1.03971 | 0.519856 | − | 0.854254i | \(-0.325986\pi\) | ||||
0.519856 | + | 0.854254i | \(0.325986\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.52920 | 0.0563289 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6496 | 0.833179 | 0.416590 | − | 0.909095i | \(-0.363225\pi\) | ||||
0.416590 | + | 0.909095i | \(0.363225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0183233 | 0.000673123 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.2233 | −0.595175 | −0.297587 | − | 0.954695i | \(-0.596182\pi\) | ||||
−0.297587 | + | 0.954695i | \(0.596182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 60.4146 | 2.21342 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.9540 | −0.656901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.6190 | −1.04432 | −0.522161 | − | 0.852847i | \(-0.674874\pi\) | ||||
−0.522161 | + | 0.852847i | \(0.674874\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.657038 | −0.0239438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.1163 | −1.49638 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.5494 | 1.47379 | 0.736897 | − | 0.676005i | \(-0.236290\pi\) | ||||
0.736897 | + | 0.676005i | \(0.236290\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.17357 | −0.0425978 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.16931 | −0.332387 | −0.166194 | − | 0.986093i | \(-0.553148\pi\) | ||||
−0.166194 | + | 0.986093i | \(0.553148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 64.3998 | 2.32838 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.62483 | −0.0586691 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7231 | 0.603052 | 0.301526 | − | 0.953458i | \(-0.402504\pi\) | ||||
0.301526 | + | 0.953458i | \(0.402504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.04828 | −0.109781 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.9783 | 1.43792 | 0.718960 | − | 0.695052i | \(-0.244619\pi\) | ||||
0.718960 | + | 0.695052i | \(0.244619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −85.0925 | −3.05661 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.05905 | 0.0379444 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8711 | 0.603697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.99754 | −0.0713863 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.7383 | −1.70385 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.2939 | 0.794693 | 0.397346 | − | 0.917669i | \(-0.369931\pi\) | ||||
0.397346 | + | 0.917669i | \(0.369931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.05122 | −0.0374245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.804144 | −0.0285560 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.08767 | 0.0385756 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.7525 | 1.08931 | 0.544654 | − | 0.838661i | \(-0.316661\pi\) | ||||
0.544654 | + | 0.838661i | \(0.316661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.4618 | −1.50219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.0171 | −1.16660 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.8648 | −0.736304 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.567891 | −0.0199907 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.2468 | −1.20405 | −0.602027 | − | 0.798476i | \(-0.705640\pi\) | ||||
−0.602027 | + | 0.798476i | \(0.705640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.17378 | 0.251905 | 0.125953 | − | 0.992036i | \(-0.459801\pi\) | ||||
0.125953 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.10099 | −0.0386133 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.80361 | −0.343406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.06221 | 0.142119 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.9117 | 1.74193 | 0.870965 | − | 0.491346i | \(-0.163495\pi\) | ||||
0.870965 | + | 0.491346i | \(0.163495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7584 | −1.00246 | −0.501228 | − | 0.865315i | \(-0.667118\pi\) | ||||
−0.501228 | + | 0.865315i | \(0.667118\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14902 | 0.0400037 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.5598 | 0.367199 | 0.183600 | − | 0.983001i | \(-0.441225\pi\) | ||||
0.183600 | + | 0.983001i | \(0.441225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.66400 | −0.0577930 | −0.0288965 | − | 0.999582i | \(-0.509199\pi\) | ||||
−0.0288965 | + | 0.999582i | \(0.509199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.29456 | −0.0795973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.8273 | 1.51671 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.00997 | −0.207735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.18432 | 0.282554 | 0.141277 | − | 0.989970i | \(-0.454879\pi\) | ||||
0.141277 | + | 0.989970i | \(0.454879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6652 | −0.643627 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.892613 | 0.0307432 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.1853 | 1.65762 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.02075 | 0.0693519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.3317 | −0.525562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6872 | 0.502882 | 0.251441 | − | 0.967873i | \(-0.419096\pi\) | ||||
0.251441 | + | 0.967873i | \(0.419096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.7592 | −0.402157 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.41864 | −0.287575 | −0.143788 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143788 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.9116 | −1.46412 | −0.732062 | − | 0.681238i | \(-0.761442\pi\) | ||||
−0.732062 | + | 0.681238i | \(0.761442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0445 | −0.648282 | −0.324141 | − | 0.946009i | \(-0.605075\pi\) | ||||
−0.324141 | + | 0.946009i | \(0.605075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.7881 | −0.978825 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.72626 | −0.0586267 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6138 | 0.495740 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.202576 | −0.00686403 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.6330 | −0.461408 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.9819 | −1.24879 | −0.624395 | − | 0.781109i | \(-0.714654\pi\) | ||||
−0.624395 | + | 0.781109i | \(0.714654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.0526171 | 0.00177473 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9419 | 1.31199 | 0.655993 | − | 0.754767i | \(-0.272250\pi\) | ||||
0.655993 | + | 0.754767i | \(0.272250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.2257 | 1.25274 | 0.626371 | − | 0.779525i | \(-0.284539\pi\) | ||||
0.626371 | + | 0.779525i | \(0.284539\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.75462 | −0.126210 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.85934 | 0.263891 | 0.131945 | − | 0.991257i | \(-0.457878\pi\) | ||||
0.131945 | + | 0.991257i | \(0.457878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2083 | −0.375492 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.75340 | 0.259458 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4130 | 0.481774 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.155465 | 0.00519081 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.0942 | 1.03705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3699 | 0.545360 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −86.1275 | −2.86298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.40729 | 0.113137 | 0.0565686 | − | 0.998399i | \(-0.481984\pi\) | ||||
0.0565686 | + | 0.998399i | \(0.481984\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.3076 | 1.60226 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.5842 | −1.34462 | −0.672308 | − | 0.740272i | \(-0.734697\pi\) | ||||
−0.672308 | + | 0.740272i | \(0.734697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.56121 | −0.250240 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.85820 | −0.0614303 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0834 | −0.695477 | −0.347738 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347738 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.01196 | 0.0662962 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.23495 | −0.0735642 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0109 | 0.493556 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.634366 | 0.0208353 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.8096 | −1.60139 | −0.800696 | − | 0.599072i | \(-0.795536\pi\) | ||||
−0.800696 | + | 0.599072i | \(0.795536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.14061 | 0.102819 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.1216 | 0.886972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.91878 | 0.128021 | 0.0640104 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640104 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.245062 | 0.00799728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.6312 | −1.68313 | −0.841564 | − | 0.540157i | \(-0.818365\pi\) | ||||
−0.841564 | + | 0.540157i | \(0.818365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.98555 | 0.292610 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.80509 | 0.188640 | 0.0943200 | − | 0.995542i | \(-0.469932\pi\) | ||||
0.0943200 | + | 0.995542i | \(0.469932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.76400 | 0.0897233 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.35840 | −0.0764765 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.18025 | −0.0706253 | −0.0353126 | − | 0.999376i | \(-0.511243\pi\) | ||||
−0.0353126 | + | 0.999376i | \(0.511243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.6012 | 2.02573 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.419870 | −0.0135725 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.5528 | 2.01783 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.7891 | −1.12106 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.9394 | −1.38227 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.1312 | 0.904638 | 0.452319 | − | 0.891856i | \(-0.350597\pi\) | ||||
0.452319 | + | 0.891856i | \(0.350597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.637253 | 0.0204715 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.15681 | 0.133398 | 0.0666991 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0666991 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.152212 | −0.00487470 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.34657 | 0.0750736 | 0.0375368 | − | 0.999295i | \(-0.488049\pi\) | ||||
0.0375368 | + | 0.999295i | \(0.488049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.9050 | −0.444405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.7846 | 1.62143 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.21649 | 0.0706950 | 0.0353475 | − | 0.999375i | \(-0.488746\pi\) | ||||
0.0353475 | + | 0.999375i | \(0.488746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.4272 | −1.73419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.4659 | 1.09595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7956 | −1.39121 | −0.695607 | − | 0.718422i | \(-0.744865\pi\) | ||||
−0.695607 | + | 0.718422i | \(0.744865\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.516585 | −0.0163933 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.1020 | −1.33472 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.41535 | 0.0764951 | 0.0382475 | − | 0.999268i | \(-0.487822\pi\) | ||||
0.0382475 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.06020 | 0.0335433 |
(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 | 8036.2.a.t.1.9 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.12 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.12 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.9 | yes | 20 | 1.1 | even | 1 | trivial |