Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.692763\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 0.692763 | 0.399967 | 0.199983 | − | 0.979799i | \(-0.435911\pi\) | ||||
0.199983 | + | 0.979799i | \(0.435911\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.58411 | −1.60286 | −0.801432 | − | 0.598086i | \(-0.795928\pi\) | ||||
−0.801432 | + | 0.598086i | \(0.795928\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.81064 | 1.44028 | 0.720142 | − | 0.693826i | \(-0.244076\pi\) | ||||
0.720142 | + | 0.693826i | \(0.244076\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52008 | −0.840027 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.20083 | −0.965087 | −0.482543 | − | 0.875872i | \(-0.660287\pi\) | ||||
−0.482543 | + | 0.875872i | \(0.660287\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.92337 | 1.08815 | 0.544073 | − | 0.839038i | \(-0.316881\pi\) | ||||
0.544073 | + | 0.839038i | \(0.316881\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.48294 | −0.641092 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.300487 | 0.0689364 | 0.0344682 | − | 0.999406i | \(-0.489026\pi\) | ||||
0.0344682 | + | 0.999406i | \(0.489026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.63987 | 0.576066 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.11886 | −0.233299 | −0.116650 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116650 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.84587 | 1.56917 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.82410 | −0.735949 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.45432 | 1.38423 | 0.692117 | − | 0.721786i | \(-0.256678\pi\) | ||||
0.692117 | + | 0.721786i | \(0.256678\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.368034 | 0.0661009 | 0.0330504 | − | 0.999454i | \(-0.489478\pi\) | ||||
0.0330504 | + | 0.999454i | \(0.489478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.21742 | −0.386002 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.6578 | −2.30858 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.36832 | −0.882547 | −0.441273 | − | 0.897373i | \(-0.645473\pi\) | ||||
−0.441273 | + | 0.897373i | \(0.645473\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.71796 | 0.435222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.470342 | 0.0734552 | 0.0367276 | − | 0.999325i | \(-0.488307\pi\) | ||||
0.0367276 | + | 0.999325i | \(0.488307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.69365 | 1.32577 | 0.662884 | − | 0.748722i | \(-0.269332\pi\) | ||||
0.662884 | + | 0.748722i | \(0.269332\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.03225 | 1.34645 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.28528 | −1.20853 | −0.604266 | − | 0.796783i | \(-0.706534\pi\) | ||||
−0.604266 | + | 0.796783i | \(0.706534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.52094 | 1.07442 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.692763 | −0.0970062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.2904 | −1.96294 | −0.981469 | − | 0.191621i | \(-0.938625\pi\) | ||||
−0.981469 | + | 0.191621i | \(0.938625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4721 | 1.54690 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.208166 | 0.0275723 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.58276 | −0.330689 | −0.165344 | − | 0.986236i | \(-0.552874\pi\) | ||||
−0.165344 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.60311 | −1.20988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.0618 | −1.74415 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.13324 | −0.749294 | −0.374647 | − | 0.927167i | \(-0.622236\pi\) | ||||
−0.374647 | + | 0.927167i | \(0.622236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.775108 | −0.0933120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.69456 | −0.675820 | −0.337910 | − | 0.941178i | \(-0.609720\pi\) | ||||
−0.337910 | + | 0.941178i | \(0.609720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.352353 | 0.0412398 | 0.0206199 | − | 0.999787i | \(-0.493436\pi\) | ||||
0.0206199 | + | 0.999787i | \(0.493436\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.43533 | 0.627617 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.1972 | −1.39000 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.179372 | 0.0201809 | 0.0100905 | − | 0.999949i | \(-0.496788\pi\) | ||||
0.0100905 | + | 0.999949i | \(0.496788\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.91104 | 0.545671 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2386 | 1.23360 | 0.616798 | − | 0.787121i | \(-0.288429\pi\) | ||||
0.616798 | + | 0.787121i | \(0.288429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.58411 | 0.388752 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.16408 | 0.553647 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.2719 | −1.72482 | −0.862409 | − | 0.506211i | \(-0.831046\pi\) | ||||
−0.862409 | + | 0.506211i | \(0.831046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.9505 | 1.56724 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.254960 | 0.0264382 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.07698 | −0.110496 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6598 | −1.38694 | −0.693472 | − | 0.720484i | \(-0.743920\pi\) | ||||
−0.693472 | + | 0.720484i | \(0.743920\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.06635 | 0.810698 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.66079 | −0.861781 | −0.430890 | − | 0.902404i | \(-0.641800\pi\) | ||||
−0.430890 | + | 0.902404i | \(0.641800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1870 | −1.39789 | −0.698943 | − | 0.715177i | \(-0.746346\pi\) | ||||
−0.698943 | + | 0.715177i | \(0.746346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.46158 | −0.923356 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.38089 | 0.810211 | 0.405105 | − | 0.914270i | \(-0.367235\pi\) | ||||
0.405105 | + | 0.914270i | \(0.367235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.81795 | −0.844606 | −0.422303 | − | 0.906455i | \(-0.638778\pi\) | ||||
−0.422303 | + | 0.906455i | \(0.638778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.71897 | −0.352989 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.435370 | 0.0409562 | 0.0204781 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204781 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.01014 | 0.373947 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.88721 | −0.914072 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.81064 | −0.349320 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.754687 | −0.0686079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.325836 | 0.0293796 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1999 | −0.912309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.07527 | −0.805300 | −0.402650 | − | 0.915354i | \(-0.631911\pi\) | ||||
−0.402650 | + | 0.915354i | \(0.631911\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.02263 | 0.530263 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0044 | 1.22357 | 0.611787 | − | 0.791023i | \(-0.290451\pi\) | ||||
0.611787 | + | 0.791023i | \(0.290451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14505 | 0.0992881 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.7060 | 1.17963 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00200 | −0.769093 | −0.384546 | − | 0.923106i | \(-0.625642\pi\) | ||||
−0.384546 | + | 0.923106i | \(0.625642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9014 | −1.09428 | −0.547141 | − | 0.837040i | \(-0.684284\pi\) | ||||
−0.547141 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.73973 | −0.483373 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.5580 | −1.05016 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.7171 | −2.21874 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.21023 | 0.429732 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.80897 | −0.312043 | −0.156022 | − | 0.987754i | \(-0.549867\pi\) | ||||
−0.156022 | + | 0.987754i | \(0.549867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1450 | 0.988348 | 0.494174 | − | 0.869363i | \(-0.335471\pi\) | ||||
0.494174 | + | 0.869363i | \(0.335471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.52008 | 0.203736 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.31908 | −0.105951 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5153 | 1.47768 | 0.738840 | − | 0.673881i | \(-0.235374\pi\) | ||||
0.738840 | + | 0.673881i | \(0.235374\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.89986 | −0.785110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.26359 | −0.336018 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.75710 | −0.529257 | −0.264629 | − | 0.964350i | \(-0.585249\pi\) | ||||
−0.264629 | + | 0.964350i | \(0.585249\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.94747 | 0.618710 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4916 | −0.811861 | −0.405930 | − | 0.913904i | \(-0.633052\pi\) | ||||
−0.405930 | + | 0.913904i | \(0.633052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.39283 | 0.184064 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.757251 | −0.0579084 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.7242 | 1.49961 | 0.749803 | − | 0.661662i | \(-0.230148\pi\) | ||||
0.749803 | + | 0.661662i | \(0.230148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29.8978 | 2.26006 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.692763 | 0.0520712 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.76708 | 0.356308 | 0.178154 | − | 0.984003i | \(-0.442987\pi\) | ||||
0.178154 | + | 0.984003i | \(0.442987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0646 | −0.971084 | −0.485542 | − | 0.874213i | \(-0.661378\pi\) | ||||
−0.485542 | + | 0.874213i | \(0.661378\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.78924 | −0.132265 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.2407 | 1.41460 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.20083 | 0.234068 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.5723 | −1.05998 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.78852 | −0.418842 | −0.209421 | − | 0.977826i | \(-0.567158\pi\) | ||||
−0.209421 | + | 0.977826i | \(0.567158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.30748 | 0.526004 | 0.263002 | − | 0.964795i | \(-0.415287\pi\) | ||||
0.263002 | + | 0.964795i | \(0.415287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.74149 | −0.697603 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.6653 | −0.973611 | −0.486805 | − | 0.873511i | \(-0.661838\pi\) | ||||
−0.486805 | + | 0.873511i | \(0.661838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1075 | 1.42538 | 0.712692 | − | 0.701477i | \(-0.247476\pi\) | ||||
0.712692 | + | 0.701477i | \(0.247476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.24888 | −0.299693 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.4057 | 1.99369 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.68576 | −0.117739 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.81963 | 0.195978 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.961808 | −0.0665296 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.34017 | −0.436475 | −0.218238 | − | 0.975896i | \(-0.570031\pi\) | ||||
−0.218238 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.94498 | −0.270305 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.1590 | −2.12503 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.40244 | 0.0952041 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.244097 | 0.0164945 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.92337 | −0.263914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.9219 | −1.66890 | −0.834448 | − | 0.551087i | \(-0.814213\pi\) | ||||
−0.834448 | + | 0.551087i | \(0.814213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.7722 | −1.31815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.19663 | −0.0794232 | −0.0397116 | − | 0.999211i | \(-0.512644\pi\) | ||||
−0.0397116 | + | 0.999211i | \(0.512644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2340 | −0.808443 | −0.404222 | − | 0.914661i | \(-0.632458\pi\) | ||||
−0.404222 | + | 0.914661i | \(0.632458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.44976 | −0.555954 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.1054 | −1.71022 | −0.855112 | − | 0.518443i | \(-0.826512\pi\) | ||||
−0.855112 | + | 0.518443i | \(0.826512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.6954 | 1.93711 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.124262 | 0.00807169 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8474 | −1.67193 | −0.835964 | − | 0.548784i | \(-0.815091\pi\) | ||||
−0.835964 | + | 0.548784i | \(0.815091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0375 | −0.968650 | −0.484325 | − | 0.874888i | \(-0.660935\pi\) | ||||
−0.484325 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8745 | 0.954200 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.9559 | −1.72215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.17892 | 0.0750130 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.78568 | 0.493397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.8418 | −1.31552 | −0.657762 | − | 0.753226i | \(-0.728497\pi\) | ||||
−0.657762 | + | 0.753226i | \(0.728497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.58130 | 0.225154 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.48294 | 0.155488 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.4010 | −0.835934 | −0.417967 | − | 0.908462i | \(-0.637257\pi\) | ||||
−0.417967 | + | 0.908462i | \(0.637257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.4567 | −1.27112 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.7855 | −1.16279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.41728 | −0.519032 | −0.259516 | − | 0.965739i | \(-0.583563\pi\) | ||||
−0.259516 | + | 0.965739i | \(0.583563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51.2184 | 3.14632 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.2726 | −0.689870 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.89470 | −0.298435 | −0.149218 | − | 0.988804i | \(-0.547676\pi\) | ||||
−0.149218 | + | 0.988804i | \(0.547676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9323 | 0.907072 | 0.453536 | − | 0.891238i | \(-0.350162\pi\) | ||||
0.453536 | + | 0.891238i | \(0.350162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3572 | 0.626844 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.1133 | −1.51439 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.76980 | 0.406758 | 0.203379 | − | 0.979100i | \(-0.434808\pi\) | ||||
0.203379 | + | 0.979100i | \(0.434808\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.927476 | −0.0555265 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2942 | 0.733411 | 0.366705 | − | 0.930337i | \(-0.380486\pi\) | ||||
0.366705 | + | 0.930337i | \(0.380486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.09484 | 0.183969 | 0.0919846 | − | 0.995760i | \(-0.470679\pi\) | ||||
0.0919846 | + | 0.995760i | \(0.470679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.746091 | −0.0441946 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.79230 | 0.105796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.46300 | −0.554731 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.8018 | 1.09841 | 0.549207 | − | 0.835686i | \(-0.314930\pi\) | ||||
0.549207 | + | 0.835686i | \(0.314930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.58411 | −0.208675 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.2403 | 0.710255 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.38972 | −0.253864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.1283 | 1.90948 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.99987 | −0.344684 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.25692 | 0.530049 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.82586 | −0.161280 | −0.0806402 | − | 0.996743i | \(-0.525696\pi\) | ||||
−0.0806402 | + | 0.996743i | \(0.525696\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.82822 | −0.559108 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.9631 | 1.30212 | 0.651058 | − | 0.759028i | \(-0.274325\pi\) | ||||
0.651058 | + | 0.759028i | \(0.274325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5078 | −0.989599 | −0.494799 | − | 0.869007i | \(-0.664758\pi\) | ||||
−0.494799 | + | 0.869007i | \(0.664758\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 34.4186 | 1.93927 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.53591 | −0.254762 | −0.127381 | − | 0.991854i | \(-0.540657\pi\) | ||||
−0.127381 | + | 0.991854i | \(0.540657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.8600 | −1.33591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.80596 | 0.324057 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.300487 | −0.0167195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.7823 | 1.70749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.10874 | −0.337814 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.5722 | −1.74063 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.8706 | −1.97163 | −0.985813 | − | 0.167849i | \(-0.946318\pi\) | ||||
−0.985813 | + | 0.167849i | \(0.946318\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.5286 | 0.741363 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.9822 | 1.20102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6893 | 1.12702 | 0.563509 | − | 0.826110i | \(-0.309451\pi\) | ||||
0.563509 | + | 0.826110i | \(0.309451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.301608 | 0.0163811 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17801 | −0.0637931 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.98513 | 0.107187 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.77807 | 0.149566 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.48174 | 0.401641 | 0.200820 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200820 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7804 | 0.737647 | 0.368823 | − | 0.929500i | \(-0.379761\pi\) | ||||
0.368823 | + | 0.929500i | \(0.379761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0034 | −0.800821 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.9004 | −1.91079 | −0.955394 | − | 0.295336i | \(-0.904569\pi\) | ||||
−0.955394 | + | 0.295336i | \(0.904569\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.4099 | 1.08325 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.63987 | −0.139717 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4040 | 1.28800 | 0.643998 | − | 0.765027i | \(-0.277275\pi\) | ||||
0.643998 | + | 0.765027i | \(0.277275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9097 | −0.995248 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.522819 | −0.0274409 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.26287 | −0.0661018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6956 | 1.13250 | 0.566251 | − | 0.824233i | \(-0.308393\pi\) | ||||
0.566251 | + | 0.824233i | \(0.308393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.18530 | −0.0617043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54.4555 | −2.82719 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.9830 | 0.775789 | 0.387894 | − | 0.921704i | \(-0.373203\pi\) | ||||
0.387894 | + | 0.921704i | \(0.373203\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.06613 | −0.364893 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.2461 | 1.50625 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1479 | 0.572631 | 0.286315 | − | 0.958135i | \(-0.407570\pi\) | ||||
0.286315 | + | 0.958135i | \(0.407570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.28701 | −0.322093 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.15935 | −0.161435 | −0.0807177 | − | 0.996737i | \(-0.525721\pi\) | ||||
−0.0807177 | + | 0.996737i | \(0.525721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43.7161 | 2.22798 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.9087 | −1.11368 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.2268 | 0.670627 | 0.335313 | − | 0.942107i | \(-0.391158\pi\) | ||||
0.335313 | + | 0.942107i | \(0.391158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.11886 | 0.0565834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.70175 | 0.489389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.642889 | −0.0323473 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7146 | 0.989446 | 0.494723 | − | 0.869051i | \(-0.335270\pi\) | ||||
0.494723 | + | 0.869051i | \(0.335270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.793245 | 0.0397119 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.86494 | 0.392756 | 0.196378 | − | 0.980528i | \(-0.437082\pi\) | ||||
0.196378 | + | 0.980528i | \(0.437082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.44393 | 0.0719275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.6017 | −0.874637 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.1831 | 0.851734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.23480 | 0.0610570 | 0.0305285 | − | 0.999534i | \(-0.490281\pi\) | ||||
0.0305285 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.23625 | −0.307611 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.81064 | 0.187509 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −40.2804 | −1.97729 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.93761 | −0.437676 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.6080 | −1.15333 | −0.576664 | − | 0.816982i | \(-0.695646\pi\) | ||||
−0.576664 | + | 0.816982i | \(0.695646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6336 | −0.664463 | −0.332231 | − | 0.943198i | \(-0.607801\pi\) | ||||
−0.332231 | + | 0.943198i | \(0.607801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.8796 | 1.01520 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.84587 | −0.380581 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.84197 | −0.476286 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.69974 | −0.420027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.74132 | 0.469223 | 0.234611 | − | 0.972089i | \(-0.424618\pi\) | ||||
0.234611 | + | 0.972089i | \(0.424618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3878 | 1.26812 | 0.634060 | − | 0.773284i | \(-0.281387\pi\) | ||||
0.634060 | + | 0.773284i | \(0.281387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.5086 | −0.887421 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.336204 | −0.0160828 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7372 | 1.22837 | 0.614184 | − | 0.789163i | \(-0.289485\pi\) | ||||
0.614184 | + | 0.789163i | \(0.289485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.9534 | −0.902542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.988469 | −0.0469636 | −0.0234818 | − | 0.999724i | \(-0.507475\pi\) | ||||
−0.0234818 | + | 0.999724i | \(0.507475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 58.3204 | 2.76465 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.63871 | −0.124807 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.09037 | 0.0986507 | 0.0493253 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493253 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50549 | −0.0708906 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.41362 | 0.395306 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −53.5844 | −2.51208 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9053 | 0.510129 | 0.255065 | − | 0.966924i | \(-0.417903\pi\) | ||||
0.255065 | + | 0.966924i | \(0.417903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.82410 | 0.178494 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5249 | −0.629917 | −0.314959 | − | 0.949105i | \(-0.601991\pi\) | ||||
−0.314959 | + | 0.949105i | \(0.601991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0581 | −1.21102 | −0.605510 | − | 0.795837i | \(-0.707031\pi\) | ||||
−0.605510 | + | 0.795837i | \(0.707031\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.913807 | −0.0423768 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.03898 | 0.186902 | 0.0934509 | − | 0.995624i | \(-0.470210\pi\) | ||||
0.0934509 | + | 0.995624i | \(0.470210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.3715 | −1.07920 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8267 | 0.591022 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.8269 | −1.27948 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.35758 | 0.108173 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.0130 | 1.64892 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.89988 | −0.132499 | −0.0662494 | − | 0.997803i | \(-0.521103\pi\) | ||||
−0.0662494 | + | 0.997803i | \(0.521103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.0619 | −0.960341 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.95365 | −0.134396 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.9583 | 2.22308 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2211 | 0.780362 | 0.390181 | − | 0.920738i | \(-0.372412\pi\) | ||||
0.390181 | + | 0.920738i | \(0.372412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.68107 | −0.211685 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3473 | 1.64033 | 0.820165 | − | 0.572127i | \(-0.193881\pi\) | ||||
0.820165 | + | 0.572127i | \(0.193881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.45432 | −0.335726 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.9107 | −1.29944 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.6999 | −0.973373 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.02762 | −0.404132 | −0.202066 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202066 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.26816 | −0.324717 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.88686 | 0.351658 | 0.175829 | − | 0.984421i | \(-0.443739\pi\) | ||||
0.175829 | + | 0.984421i | \(0.443739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.0413 | 1.38132 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.65766 | 0.0736194 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.5727 | 1.70970 | 0.854852 | − | 0.518873i | \(-0.173648\pi\) | ||||
0.854852 | + | 0.518873i | \(0.173648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.34269 | 0.0593971 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.14909 | −0.0507337 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.8478 | 2.24062 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.5198 | 1.16634 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6642 | 0.599792 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7094 | −1.30159 | −0.650797 | − | 0.759252i | \(-0.725565\pi\) | ||||
−0.650797 | + | 0.759252i | \(0.725565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4939 | −1.24595 | −0.622975 | − | 0.782242i | \(-0.714076\pi\) | ||||
−0.622975 | + | 0.782242i | \(0.714076\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.7120 | 0.903948 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.368034 | −0.0160318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7481 | −0.945571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.52008 | −0.109362 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.84533 | 0.0799300 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.0381 | −1.29866 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.30246 | 0.142511 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0733 | −1.03691 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.5547 | −1.87256 | −0.936282 | − | 0.351250i | \(-0.885757\pi\) | ||||
−0.936282 | + | 0.351250i | \(0.885757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.05067 | −0.388401 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.6045 | 1.35379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.7898 | 0.846149 | 0.423075 | − | 0.906095i | \(-0.360951\pi\) | ||||
0.423075 | + | 0.906095i | \(0.360951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.50877 | 0.277788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.23993 | 0.0954241 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.683521 | 0.0290663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.3292 | 0.565794 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.6368 | 1.67947 | 0.839734 | − | 0.542999i | \(-0.182711\pi\) | ||||
0.839734 | + | 0.542999i | \(0.182711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.1084 | 1.44263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.21742 | 0.0936193 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4248 | 0.481496 | 0.240748 | − | 0.970588i | \(-0.422607\pi\) | ||||
0.240748 | + | 0.970588i | \(0.422607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.56042 | −0.0656472 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.7142 | 0.785922 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.1045 | 1.89088 | 0.945440 | − | 0.325797i | \(-0.105633\pi\) | ||||
0.945440 | + | 0.325797i | \(0.105633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.36082 | 0.0987974 | 0.0493987 | − | 0.998779i | \(-0.484269\pi\) | ||||
0.0493987 | + | 0.998779i | \(0.484269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.01007 | −0.167523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.77847 | −0.366088 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.880750 | −0.0366661 | −0.0183330 | − | 0.999832i | \(-0.505836\pi\) | ||||
−0.0183330 | + | 0.999832i | \(0.505836\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.06235 | 0.210384 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.8262 | 1.77673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.7412 | 1.89440 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.4369 | 1.46513 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.6217 | −0.933699 | −0.466849 | − | 0.884337i | \(-0.654611\pi\) | ||||
−0.466849 | + | 0.884337i | \(0.654611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.110589 | 0.00455676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.46679 | −0.389412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.7829 | 0.935580 | 0.467790 | − | 0.883840i | \(-0.345050\pi\) | ||||
0.467790 | + | 0.883840i | \(0.345050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6578 | 0.559913 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9297 | 0.570106 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.6684 | −1.82510 | −0.912550 | − | 0.408966i | \(-0.865890\pi\) | ||||
−0.912550 | + | 0.408966i | \(0.865890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7217 | −0.845257 | −0.422628 | − | 0.906303i | \(-0.638892\pi\) | ||||
−0.422628 | + | 0.906303i | \(0.638892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.4562 | 0.629427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.70488 | 0.109969 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.9290 | −1.41772 | −0.708862 | − | 0.705347i | \(-0.750791\pi\) | ||||
−0.708862 | + | 0.705347i | \(0.750791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.6784 | 0.797410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.5062 | −1.31506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.34421 | −0.0946819 | −0.0473410 | − | 0.998879i | \(-0.515075\pi\) | ||||
−0.0473410 | + | 0.998879i | \(0.515075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.16783 | −0.0470915 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.1366 | 1.81713 | 0.908566 | − | 0.417741i | \(-0.137178\pi\) | ||||
0.908566 | + | 0.417741i | \(0.137178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.4049 | 1.54362 | 0.771811 | − | 0.635852i | \(-0.219351\pi\) | ||||
0.771811 | + | 0.635852i | \(0.219351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.27866 | 0.171697 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −62.0063 | −2.48423 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.67166 | −0.106866 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.666304 | −0.0266096 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.36832 | 0.214049 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.61255 | 0.263241 | 0.131621 | − | 0.991300i | \(-0.457982\pi\) | ||||
0.131621 | + | 0.991300i | \(0.457982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.39223 | −0.174575 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.5268 | 1.29079 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.5074 | 1.16913 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.3507 | 0.567707 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.06934 | −0.0422365 | −0.0211182 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211182 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6006 | 1.60113 | 0.800566 | − | 0.599245i | \(-0.204532\pi\) | ||||
0.800566 | + | 0.599245i | \(0.204532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.5858 | −0.849940 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.55716 | 0.0612183 | 0.0306091 | − | 0.999531i | \(-0.490255\pi\) | ||||
0.0306091 | + | 0.999531i | \(0.490255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.20083 | −0.125644 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.971561 | 0.0380785 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1250 | −0.513620 | −0.256810 | − | 0.966462i | \(-0.582671\pi\) | ||||
−0.256810 | + | 0.966462i | \(0.582671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.1935 | −1.96122 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.887958 | −0.0346425 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.17999 | −0.318647 | −0.159324 | − | 0.987226i | \(-0.550931\pi\) | ||||
−0.159324 | + | 0.987226i | \(0.550931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7286 | −0.572878 | −0.286439 | − | 0.958099i | \(-0.592472\pi\) | ||||
−0.286439 | + | 0.958099i | \(0.592472\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.71796 | −0.105557 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.10398 | −0.159145 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.34038 | −0.322941 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2650 | −0.667503 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.26699 | 0.319143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5275 | 0.521445 | 0.260723 | − | 0.965414i | \(-0.416039\pi\) | ||||
0.260723 | + | 0.965414i | \(0.416039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.0034 | −1.15483 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.7809 | 0.990839 | 0.495420 | − | 0.868654i | \(-0.335014\pi\) | ||||
0.495420 | + | 0.868654i | \(0.335014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.0525 | −1.99759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.828981 | −0.0317666 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.9326 | −0.954020 | −0.477010 | − | 0.878898i | \(-0.658279\pi\) | ||||
−0.477010 | + | 0.878898i | \(0.658279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.2642 | 1.23275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.47524 | −0.323350 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −56.0665 | −2.13596 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3247 | −0.621022 | −0.310511 | − | 0.950570i | \(-0.600500\pi\) | ||||
−0.310511 | + | 0.950570i | \(0.600500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.7379 | 1.16764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.2401 | 1.75399 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.470342 | −0.0178155 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0849 | −0.684033 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.69946 | −0.215266 | −0.107633 | − | 0.994191i | \(-0.534327\pi\) | ||||
−0.107633 | + | 0.994191i | \(0.534327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.61311 | −0.0608396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.5719 | 0.774781 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.0031 | −1.24121 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3714 | 0.464619 | 0.232309 | − | 0.972642i | \(-0.425372\pi\) | ||||
0.232309 | + | 0.972642i | \(0.425372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.452032 | −0.0169525 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.411781 | −0.0154213 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.0094 | 1.68326 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.9061 | −0.668716 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −52.0627 | −1.94161 | −0.970805 | − | 0.239869i | \(-0.922895\pi\) | ||||
−0.970805 | + | 0.239869i | \(0.922895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.0615 | −2.01336 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4174 | −0.387428 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 58.4857 | 2.17210 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.8084 | −1.25389 | −0.626943 | − | 0.779065i | \(-0.715694\pi\) | ||||
−0.626943 | + | 0.779065i | \(0.715694\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.42863 | −0.164023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.69365 | −0.321546 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.37380 | 0.272358 | 0.136179 | − | 0.990684i | \(-0.456518\pi\) | ||||
0.136179 | + | 0.990684i | \(0.456518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.6741 | −0.688803 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.6314 | 0.723134 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.110613 | 0.00406896 | 0.00203448 | − | 0.999998i | \(-0.499352\pi\) | ||||
0.00203448 | + | 0.999998i | \(0.499352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.816713 | 0.0300027 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.2344 | 0.815702 | 0.407851 | − | 0.913049i | \(-0.366278\pi\) | ||||
0.407851 | + | 0.913049i | \(0.366278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6518 | 0.500163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.3222 | −1.03625 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.9365 | 1.16693 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.1473 | 1.02711 | 0.513554 | − | 0.858057i | \(-0.328328\pi\) | ||||
0.513554 | + | 0.858057i | \(0.328328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.4384 | −0.526165 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.5291 | −1.58419 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2648 | 0.409426 | 0.204713 | − | 0.978822i | \(-0.434374\pi\) | ||||
0.204713 | + | 0.978822i | \(0.434374\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.48099 | 0.0900542 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5576 | −0.853962 | −0.426981 | − | 0.904261i | \(-0.640423\pi\) | ||||
−0.426981 | + | 0.904261i | \(0.640423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.6020 | −1.21647 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.03225 | −0.326562 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.92337 | 0.141665 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5349 | −0.452021 | −0.226011 | − | 0.974125i | \(-0.572568\pi\) | ||||
−0.226011 | + | 0.974125i | \(0.572568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.28374 | −0.334346 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 54.3872 | 1.95617 | 0.978085 | − | 0.208205i | \(-0.0667620\pi\) | ||||
0.978085 | + | 0.208205i | \(0.0667620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.88755 | 0.103724 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.1717 | −0.508405 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.141332 | 0.00506374 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.2273 | 0.652225 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.5061 | −1.01873 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −66.3608 | −2.36852 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.50206 | −0.338712 | −0.169356 | − | 0.985555i | \(-0.554169\pi\) | ||||
−0.169356 | + | 0.985555i | \(0.554169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.83118 | −0.207595 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.65904 | 0.0589886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.1331 | −0.359838 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.4822 | 1.25842 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6128 | 1.50942 | 0.754711 | − | 0.656058i | \(-0.227777\pi\) | ||||
0.754711 | + | 0.656058i | \(0.227777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.28528 | 0.293112 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.0065 | 1.44889 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.12782 | −0.0398000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2812 | 0.538591 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.39087 | −0.119364 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.8115 | −0.802011 | −0.401006 | − | 0.916076i | \(-0.631339\pi\) | ||||
−0.401006 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.69462 | −0.0946209 | −0.0473105 | − | 0.998880i | \(-0.515065\pi\) | ||||
−0.0473105 | + | 0.998880i | \(0.515065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3445 | 0.362799 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.2182 | 0.848327 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.61233 | 0.0913938 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.6765 | −1.31652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.74454 | 0.200486 | 0.100243 | − | 0.994963i | \(-0.468038\pi\) | ||||
0.100243 | + | 0.994963i | \(0.468038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8613 | 0.622605 | 0.311302 | − | 0.950311i | \(-0.399235\pi\) | ||||
0.311302 | + | 0.950311i | \(0.399235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.3976 | −0.605705 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.3309 | 1.12425 | 0.562127 | − | 0.827051i | \(-0.309983\pi\) | ||||
0.562127 | + | 0.827051i | \(0.309983\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.458180 | 0.0159132 | 0.00795662 | − | 0.999968i | \(-0.497467\pi\) | ||||
0.00795662 | + | 0.999968i | \(0.497467\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.68986 | 0.162689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.52094 | −0.260585 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.6029 | 1.30130 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.40740 | −0.0486469 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.6189 | −0.504701 | −0.252350 | − | 0.967636i | \(-0.581204\pi\) | ||||
−0.252350 | + | 0.967636i | \(0.581204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.5670 | 0.916102 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.51697 | 0.293340 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.57617 | −0.295029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.87584 | −0.0988149 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.14399 | 0.0735816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00643 | 0.205898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5233 | −0.394549 | −0.197274 | − | 0.980348i | \(-0.563209\pi\) | ||||
−0.197274 | + | 0.980348i | \(0.563209\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.71407 | 0.0928194 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.2779 | 1.68330 | 0.841651 | − | 0.540022i | \(-0.181584\pi\) | ||||
0.841651 | + | 0.540022i | \(0.181584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3279 | 0.488863 | 0.244431 | − | 0.969667i | \(-0.421399\pi\) | ||||
0.244431 | + | 0.969667i | \(0.421399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.24164 | 0.0423150 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8495 | −0.539524 | −0.269762 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269762 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −70.6939 | −2.40366 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.692763 | 0.0235275 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.574139 | −0.0194763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0630 | −0.815342 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34.4238 | 1.16507 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.8682 | −1.31399 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.8841 | −1.71823 | −0.859116 | − | 0.511780i | \(-0.828986\pi\) | ||||
−0.859116 | + | 0.511780i | \(0.828986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0252 | 0.439329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7076 | −1.33778 | −0.668892 | − | 0.743359i | \(-0.733231\pi\) | ||||
−0.668892 | + | 0.743359i | \(0.733231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0582 | −0.641358 | −0.320679 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320679 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.48294 | −0.0834631 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.3854 | 0.919512 | 0.459756 | − | 0.888045i | \(-0.347937\pi\) | ||||
0.459756 | + | 0.888045i | \(0.347937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.5826 | −1.15986 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.7194 | −0.526620 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.48962 | −0.0833119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.0858 | −0.571114 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.04103 | −0.101537 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.74345 | 0.0914991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2904 | 0.476082 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.9501 | 0.763730 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.8250 | 1.55652 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9406 | 0.595709 | 0.297855 | − | 0.954611i | \(-0.403729\pi\) | ||||
0.297855 | + | 0.954611i | \(0.403729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.8259 | 0.723919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3761 | 1.03954 | 0.519769 | − | 0.854307i | \(-0.326018\pi\) | ||||
0.519769 | + | 0.854307i | \(0.326018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.9728 | −1.19053 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.41285 | 0.212002 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 53.3658 | 1.76229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9055 | −0.557660 | −0.278830 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278830 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.95765 | −0.0645068 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.3419 | −0.735391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.1192 | −1.38487 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35.7524 | 1.17426 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.8038 | 0.715358 | 0.357679 | − | 0.933845i | \(-0.383568\pi\) | ||||
0.357679 | + | 0.933845i | \(0.383568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.25995 | 0.0740667 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.9080 | 0.520803 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.4721 | −0.375179 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.3037 | −1.12065 | −0.560326 | − | 0.828272i | \(-0.689324\pi\) | ||||
−0.560326 | + | 0.828272i | \(0.689324\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1287 | −0.395807 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7394 | 0.415293 | 0.207647 | − | 0.978204i | \(-0.433420\pi\) | ||||
0.207647 | + | 0.978204i | \(0.433420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.526250 | −0.0171370 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 52.2287 | 1.69900 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.6263 | −1.45016 | −0.725081 | − | 0.688664i | \(-0.758197\pi\) | ||||
−0.725081 | + | 0.688664i | \(0.758197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.38241 | 0.0448750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.14231 | −0.101896 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.3491 | 0.497206 | 0.248603 | − | 0.968605i | \(-0.420028\pi\) | ||||
0.248603 | + | 0.968605i | \(0.420028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7467 | 0.671348 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5293 | −0.534317 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.3033 | −1.10771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8646 | −0.995631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.1205 | −0.680599 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.1908 | −0.843113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.432866 | −0.0139200 | −0.00696002 | − | 0.999976i | \(-0.502215\pi\) | ||||
−0.00696002 | + | 0.999976i | \(0.502215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.208166 | −0.00668726 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.1896 | −1.00092 | −0.500462 | − | 0.865759i | \(-0.666836\pi\) | ||||
−0.500462 | + | 0.865759i | \(0.666836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.1625 | −1.57608 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.3248 | 0.682940 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.5044 | −0.496029 | −0.248015 | − | 0.968756i | \(-0.579778\pi\) | ||||
−0.248015 | + | 0.968756i | \(0.579778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52.0836 | 1.66460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.2219 | 0.709492 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.89845 | −0.220026 | −0.110013 | − | 0.993930i | \(-0.535089\pi\) | ||||
−0.110013 | + | 0.993930i | \(0.535089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.9779 | 1.56057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.8720 | −0.696194 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.72702 | −0.309301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.14244 | −0.0362907 | −0.0181453 | − | 0.999835i | \(-0.505776\pi\) | ||||
−0.0181453 | + | 0.999835i | \(0.505776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.8498 | −0.788584 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.0676 | −2.28470 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05148 | −0.0649710 | −0.0324855 | − | 0.999472i | \(-0.510342\pi\) | ||||
−0.0324855 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.5290 | 0.649510 |
(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 | 4012.2.a.g.1.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial |