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: | \(1\) |
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 | 1.12 | ||
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 | \(-0.490466\pi\) | ||||
0.0299490 | + | 0.999551i | \(0.490466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.71451 | 1.66118 | 0.830589 | − | 0.556885i | \(-0.188004\pi\) | ||||
0.830589 | + | 0.556885i | \(0.188004\pi\) | |||||||
\(6\) | 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 | \(-0.507362\pi\) | ||||
−0.0231266 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.385366 | 0.0995012 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.79993 | −1.40669 | −0.703345 | − | 0.710849i | \(-0.748311\pi\) | ||||
−0.703345 | + | 0.710849i | \(0.748311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.05905 | 0.242963 | 0.121481 | − | 0.992594i | \(-0.461236\pi\) | ||||
0.121481 | + | 0.992594i | \(0.461236\pi\) | |||||||
\(20\) | 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 | \(-0.165023\pi\) | ||||
0.868595 | + | 0.495522i | \(0.165023\pi\) | |||||||
\(32\) | 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 | \(-0.320709\pi\) | ||||
0.533945 | + | 0.845519i | \(0.320709\pi\) | |||||||
\(48\) | 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 | \(-0.281323\pi\) | ||||
0.634215 | + | 0.773157i | \(0.281323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.82191 | 0.617383 | 0.308691 | − | 0.951162i | \(-0.400109\pi\) | ||||
0.308691 | + | 0.951162i | \(0.400109\pi\) | |||||||
\(62\) | 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 | \(-0.921719\pi\) | ||||
−0.969912 | + | 0.243456i | \(0.921719\pi\) | |||||||
\(74\) | 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 | \(-0.606925\pi\) | ||||
−0.329633 | + | 0.944109i | \(0.606925\pi\) | |||||||
\(84\) | 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 | \(-0.699063\pi\) | ||||
−0.585402 | + | 0.810743i | \(0.699063\pi\) | |||||||
\(90\) | 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 | \(-0.574375\pi\) | ||||
−0.231535 | + | 0.972827i | \(0.574375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.76315 | 0.378211 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1605 | 1.60803 | 0.804015 | − | 0.594609i | \(-0.202693\pi\) | ||||
0.804015 | + | 0.594609i | \(0.202693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.212217 | 0.0209103 | 0.0104552 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104552 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(104\) | 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 | \(-0.603425\pi\) | ||||
−0.319232 | + | 0.947677i | \(0.603425\pi\) | |||||||
\(132\) | 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 | \(-0.764988\pi\) | ||||
−0.739606 | + | 0.673040i | \(0.764988\pi\) | |||||||
\(140\) | 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 | \(-0.671408\pi\) | ||||
−0.512845 | + | 0.858481i | \(0.671408\pi\) | |||||||
\(158\) | 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 | \(-0.349097\pi\) | ||||
0.456516 | + | 0.889715i | \(0.349097\pi\) | |||||||
\(168\) | 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 | \(-0.595192\pi\) | ||||
−0.294618 | + | 0.955615i | \(0.595192\pi\) | |||||||
\(174\) | 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 | \(-0.830619\pi\) | ||||
−0.861730 | + | 0.507366i | \(0.830619\pi\) | |||||||
\(182\) | 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 | \(-0.631594\pi\) | ||||
−0.401740 | + | 0.915754i | \(0.631594\pi\) | |||||||
\(200\) | 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 | \(-0.729747\pi\) | ||||
−0.660715 | + | 0.750637i | \(0.729747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.2980 | −1.75320 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.27003 | 0.217040 | 0.108520 | − | 0.994094i | \(-0.465389\pi\) | ||||
0.108520 | + | 0.994094i | \(0.465389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.1500 | −1.19938 | −0.599692 | − | 0.800231i | \(-0.704710\pi\) | ||||
−0.599692 | + | 0.800231i | \(0.704710\pi\) | |||||||
\(230\) | 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 | \(-0.471927\pi\) | ||||
0.0880802 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(242\) | 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 | \(-0.564053\pi\) | ||||
−0.199872 | + | 0.979822i | \(0.564053\pi\) | |||||||
\(252\) | 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 | \(-0.868921\pi\) | ||||
−0.916403 | + | 0.400258i | \(0.868921\pi\) | |||||||
\(258\) | 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 | \(-0.553367\pi\) | ||||
−0.166873 | + | 0.985978i | \(0.553367\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6123 | −0.644651 | −0.322326 | − | 0.946629i | \(-0.604465\pi\) | ||||
−0.322326 | + | 0.946629i | \(0.604465\pi\) | |||||||
\(272\) | 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 | \(-0.303476\pi\) | ||||
0.578917 | + | 0.815387i | \(0.303476\pi\) | |||||||
\(284\) | 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 | \(-0.495284\pi\) | ||||
0.0148146 | + | 0.999890i | \(0.495284\pi\) | |||||||
\(294\) | 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 | \(-0.313326\pi\) | ||||
0.553410 | + | 0.832909i | \(0.313326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0220167 | 0.00125249 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.2720 | 1.71657 | 0.858285 | − | 0.513174i | \(-0.171530\pi\) | ||||
0.858285 | + | 0.513174i | \(0.171530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.36212 | 0.133515 | 0.0667575 | − | 0.997769i | \(-0.478735\pi\) | ||||
0.0667575 | + | 0.997769i | \(0.478735\pi\) | |||||||
\(314\) | 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 | \(-0.476397\pi\) | ||||
0.0740832 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.103624 | 0.00553102 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.4071 | 1.40551 | 0.702754 | − | 0.711433i | \(-0.251954\pi\) | ||||
0.702754 | + | 0.711433i | \(0.251954\pi\) | |||||||
\(354\) | 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 | \(-0.657071\pi\) | ||||
−0.473671 | + | 0.880702i | \(0.657071\pi\) | |||||||
\(368\) | 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 | \(-0.814748\pi\) | ||||
−0.835372 | + | 0.549685i | \(0.814748\pi\) | |||||||
\(384\) | 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 | \(-0.637402\pi\) | ||||
−0.418381 | + | 0.908272i | \(0.637402\pi\) | |||||||
\(398\) | 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 | \(-0.681267\pi\) | ||||
−0.539183 | + | 0.842188i | \(0.681267\pi\) | |||||||
\(410\) | 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 | \(-0.287864\pi\) | ||||
0.618194 | + | 0.786025i | \(0.287864\pi\) | |||||||
\(420\) | 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 | \(-0.346985\pi\) | ||||
0.462410 | + | 0.886666i | \(0.346985\pi\) | |||||||
\(434\) | 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 | \(-0.412801\pi\) | ||||
0.270531 | + | 0.962711i | \(0.412801\pi\) | |||||||
\(440\) | 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 | \(-0.496418\pi\) | ||||
0.0112519 | + | 0.999937i | \(0.496418\pi\) | |||||||
\(462\) | 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 | \(-0.238400\pi\) | ||||
0.732400 | + | 0.680875i | \(0.238400\pi\) | |||||||
\(468\) | 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 | \(-0.514115\pi\) | ||||
−0.0443303 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(480\) | 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 | \(-0.639159\pi\) | ||||
−0.423386 | + | 0.905949i | \(0.639159\pi\) | |||||||
\(504\) | 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 | \(-0.358520\pi\) | ||||
0.429982 | + | 0.902837i | \(0.358520\pi\) | |||||||
\(510\) | 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 | \(-0.424793\pi\) | ||||
0.234078 | + | 0.972218i | \(0.424793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.7762 | 1.08339 | 0.541694 | − | 0.840576i | \(-0.317783\pi\) | ||||
0.541694 | + | 0.840576i | \(0.317783\pi\) | |||||||
\(524\) | 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 | \(-0.286026\pi\) | ||||
0.622723 | + | 0.782442i | \(0.286026\pi\) | |||||||
\(564\) | 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 | \(-0.876381\pi\) | ||||
−0.925531 | + | 0.378671i | \(0.876381\pi\) | |||||||
\(578\) | 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 | \(-0.301017\pi\) | ||||
0.585197 | + | 0.810891i | \(0.301017\pi\) | |||||||
\(588\) | 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 | \(-0.471708\pi\) | ||||
0.0887663 | + | 0.996052i | \(0.471708\pi\) | |||||||
\(594\) | 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 | \(-0.368298\pi\) | ||||
0.402050 | + | 0.915618i | \(0.368298\pi\) | |||||||
\(602\) | 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 | \(-0.402511\pi\) | ||||
0.301504 | + | 0.953465i | \(0.402511\pi\) | |||||||
\(608\) | 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 | \(-0.552131\pi\) | ||||
−0.163043 | + | 0.986619i | \(0.552131\pi\) | |||||||
\(620\) | 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 | \(-0.608754\pi\) | ||||
−0.335054 | + | 0.942199i | \(0.608754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.47815 | −0.0582022 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.6985 | 1.60002 | 0.800012 | − | 0.599985i | \(-0.204827\pi\) | ||||
0.800012 | + | 0.599985i | \(0.204827\pi\) | |||||||
\(648\) | 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 | \(-0.587734\pi\) | ||||
−0.272149 | + | 0.962255i | \(0.587734\pi\) | |||||||
\(662\) | 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 | \(-0.280733\pi\) | ||||
0.635648 | + | 0.771979i | \(0.280733\pi\) | |||||||
\(678\) | 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 | \(-0.488677\pi\) | ||||
0.0355634 | + | 0.999367i | \(0.488677\pi\) | |||||||
\(692\) | 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 | \(-0.786396\pi\) | ||||
−0.783165 | + | 0.621813i | \(0.786396\pi\) | |||||||
\(720\) | 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 | \(-0.508252\pi\) | ||||
−0.0259204 | + | 0.999664i | \(0.508252\pi\) | |||||||
\(728\) | 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 | \(-0.674014\pi\) | ||||
−0.519856 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(734\) | 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 | \(-0.446852\pi\) | ||||
0.166194 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(762\) | 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 | \(-0.597496\pi\) | ||||
−0.301526 | + | 0.953458i | \(0.597496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.04828 | −0.109781 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.9783 | −1.43792 | −0.718960 | − | 0.695052i | \(-0.755381\pi\) | ||||
−0.718960 | + | 0.695052i | \(0.755381\pi\) | |||||||
\(774\) | 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 | \(-0.630069\pi\) | ||||
−0.397346 | + | 0.917669i | \(0.630069\pi\) | |||||||
\(788\) | 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 | \(-0.683339\pi\) | ||||
−0.544654 | + | 0.838661i | \(0.683339\pi\) | |||||||
\(798\) | 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 | \(-0.540199\pi\) | ||||
−0.125953 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(812\) | 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 | \(-0.490801\pi\) | ||||
0.0288965 | + | 0.999582i | \(0.490801\pi\) | |||||||
\(830\) | 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 | \(-0.545121\pi\) | ||||
−0.141277 | + | 0.989970i | \(0.545121\pi\) | |||||||
\(840\) | 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 | \(-0.580904\pi\) | ||||
−0.251441 | + | 0.967873i | \(0.580904\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.7592 | −0.402157 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.41864 | 0.287575 | 0.143788 | − | 0.989609i | \(-0.454072\pi\) | ||||
0.143788 | + | 0.989609i | \(0.454072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.9116 | 1.46412 | 0.732062 | − | 0.681238i | \(-0.238558\pi\) | ||||
0.732062 | + | 0.681238i | \(0.238558\pi\) | |||||||
\(860\) | 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 | \(-0.727750\pi\) | ||||
−0.655993 | + | 0.754767i | \(0.727750\pi\) | |||||||
\(882\) | 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 | \(-0.542122\pi\) | ||||
−0.131945 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(888\) | 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 | \(-0.204464\pi\) | ||||
0.800696 | + | 0.599072i | \(0.204464\pi\) | |||||||
\(930\) | 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 | \(-0.520389\pi\) | ||||
−0.0640104 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.245062 | 0.00799728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.6312 | 1.68313 | 0.841564 | − | 0.540157i | \(-0.181635\pi\) | ||||
0.841564 | + | 0.540157i | \(0.181635\pi\) | |||||||
\(942\) | 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 | \(-0.521247\pi\) | ||||
−0.0666991 | + | 0.997773i | \(0.521247\pi\) | |||||||
\(972\) | 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 | \(-0.511254\pi\) | ||||
−0.0353475 | + | 0.999375i | \(0.511254\pi\) | |||||||
\(984\) | 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 | \(-0.512178\pi\) | ||||
−0.0382475 | + | 0.999268i | \(0.512178\pi\) | |||||||
\(998\) | 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.s.1.12 | ✓ | 20 | |
7.6 | odd | 2 | 8036.2.a.t.1.9 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.12 | ✓ | 20 | 1.1 | even | 1 | trivial | |
8036.2.a.t.1.9 | yes | 20 | 7.6 | odd | 2 |