Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1925,2,Mod(1,1925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, 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("1925.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1925 = 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1925.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: | \(15.3712023891\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.71503\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1925.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71503 | −1.91982 | −0.959908 | − | 0.280316i | \(-0.909561\pi\) | ||||
−0.959908 | + | 0.280316i | \(0.909561\pi\) | |||||||
\(3\) | 0.525975 | 0.303672 | 0.151836 | − | 0.988406i | \(-0.451481\pi\) | ||||
0.151836 | + | 0.988406i | \(0.451481\pi\) | |||||||
\(4\) | 5.37138 | 2.68569 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.42804 | −0.582994 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −9.15341 | −3.23622 | ||||||||
\(9\) | −2.72335 | −0.907783 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.82522 | 0.815570 | ||||||||
\(13\) | 5.27345 | 1.46259 | 0.731296 | − | 0.682061i | \(-0.238916\pi\) | ||||
0.731296 | + | 0.682061i | \(0.238916\pi\) | |||||||
\(14\) | 2.71503 | 0.725622 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1090 | 3.52725 | ||||||||
\(17\) | −5.04671 | −1.22401 | −0.612004 | − | 0.790855i | \(-0.709636\pi\) | ||||
−0.612004 | + | 0.790855i | \(0.709636\pi\) | |||||||
\(18\) | 7.39398 | 1.74278 | ||||||||
\(19\) | 6.37138 | 1.46170 | 0.730848 | − | 0.682540i | \(-0.239125\pi\) | ||||
0.730848 | + | 0.682540i | \(0.239125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.525975 | −0.114777 | ||||||||
\(22\) | −2.71503 | −0.578846 | ||||||||
\(23\) | −7.72930 | −1.61167 | −0.805835 | − | 0.592140i | \(-0.798283\pi\) | ||||
−0.805835 | + | 0.592140i | \(0.798283\pi\) | |||||||
\(24\) | −4.81447 | −0.982749 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.3176 | −2.80791 | ||||||||
\(27\) | −3.01034 | −0.579340 | ||||||||
\(28\) | −5.37138 | −1.01510 | ||||||||
\(29\) | 7.19109 | 1.33535 | 0.667676 | − | 0.744452i | \(-0.267289\pi\) | ||||
0.667676 | + | 0.744452i | \(0.267289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.15734 | −1.28550 | −0.642748 | − | 0.766078i | \(-0.722206\pi\) | ||||
−0.642748 | + | 0.766078i | \(0.722206\pi\) | |||||||
\(32\) | −19.9995 | −3.53545 | ||||||||
\(33\) | 0.525975 | 0.0915606 | ||||||||
\(34\) | 13.7020 | 2.34987 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −14.6282 | −2.43803 | ||||||||
\(37\) | −3.65636 | −0.601101 | −0.300551 | − | 0.953766i | \(-0.597170\pi\) | ||||
−0.300551 | + | 0.953766i | \(0.597170\pi\) | |||||||
\(38\) | −17.2985 | −2.80619 | ||||||||
\(39\) | 2.77370 | 0.444148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14263 | 0.646970 | 0.323485 | − | 0.946233i | \(-0.395145\pi\) | ||||
0.323485 | + | 0.946233i | \(0.395145\pi\) | |||||||
\(42\) | 1.42804 | 0.220351 | ||||||||
\(43\) | 10.2054 | 1.55630 | 0.778151 | − | 0.628077i | \(-0.216158\pi\) | ||||
0.778151 | + | 0.628077i | \(0.216158\pi\) | |||||||
\(44\) | 5.37138 | 0.809767 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.9853 | 3.09411 | ||||||||
\(47\) | 11.4487 | 1.66997 | 0.834984 | − | 0.550275i | \(-0.185477\pi\) | ||||
0.834984 | + | 0.550275i | \(0.185477\pi\) | |||||||
\(48\) | 7.42099 | 1.07113 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.65445 | −0.371697 | ||||||||
\(52\) | 28.3257 | 3.92807 | ||||||||
\(53\) | 0.365435 | 0.0501964 | 0.0250982 | − | 0.999685i | \(-0.492010\pi\) | ||||
0.0250982 | + | 0.999685i | \(0.492010\pi\) | |||||||
\(54\) | 8.17316 | 1.11223 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.15341 | 1.22318 | ||||||||
\(57\) | 3.35119 | 0.443876 | ||||||||
\(58\) | −19.5240 | −2.56363 | ||||||||
\(59\) | −2.10828 | −0.274474 | −0.137237 | − | 0.990538i | \(-0.543822\pi\) | ||||
−0.137237 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3378 | −1.45165 | −0.725826 | − | 0.687879i | \(-0.758542\pi\) | ||||
−0.725826 | + | 0.687879i | \(0.758542\pi\) | |||||||
\(62\) | 19.4324 | 2.46792 | ||||||||
\(63\) | 2.72335 | 0.343110 | ||||||||
\(64\) | 26.0813 | 3.26017 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.42804 | −0.175779 | ||||||||
\(67\) | 4.94537 | 0.604173 | 0.302086 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302086 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(68\) | −27.1078 | −3.28731 | ||||||||
\(69\) | −4.06542 | −0.489419 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.72737 | 0.205001 | 0.102500 | − | 0.994733i | \(-0.467316\pi\) | ||||
0.102500 | + | 0.994733i | \(0.467316\pi\) | |||||||
\(72\) | 24.9279 | 2.93779 | ||||||||
\(73\) | 11.9342 | 1.39679 | 0.698397 | − | 0.715710i | \(-0.253897\pi\) | ||||
0.698397 | + | 0.715710i | \(0.253897\pi\) | |||||||
\(74\) | 9.92711 | 1.15400 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.2232 | 3.92567 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −7.53069 | −0.852682 | ||||||||
\(79\) | −5.40955 | −0.608622 | −0.304311 | − | 0.952573i | \(-0.598426\pi\) | ||||
−0.304311 | + | 0.952573i | \(0.598426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.58668 | 0.731854 | ||||||||
\(82\) | −11.2474 | −1.24206 | ||||||||
\(83\) | 2.04363 | 0.224318 | 0.112159 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112159 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(84\) | −2.82522 | −0.308256 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −27.7079 | −2.98781 | ||||||||
\(87\) | 3.78234 | 0.405509 | ||||||||
\(88\) | −9.15341 | −0.975757 | ||||||||
\(89\) | −1.29607 | −0.137383 | −0.0686916 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686916 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.27345 | −0.552808 | ||||||||
\(92\) | −41.5170 | −4.32845 | ||||||||
\(93\) | −3.76458 | −0.390369 | ||||||||
\(94\) | −31.0836 | −3.20603 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.5193 | −1.07362 | ||||||||
\(97\) | 1.05710 | 0.107332 | 0.0536661 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536661 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(98\) | −2.71503 | −0.274259 | ||||||||
\(99\) | −2.72335 | −0.273707 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.85373 | −0.681972 | −0.340986 | − | 0.940068i | \(-0.610761\pi\) | ||||
−0.340986 | + | 0.940068i | \(0.610761\pi\) | |||||||
\(102\) | 7.20690 | 0.713589 | ||||||||
\(103\) | −0.393263 | −0.0387494 | −0.0193747 | − | 0.999812i | \(-0.506168\pi\) | ||||
−0.0193747 | + | 0.999812i | \(0.506168\pi\) | |||||||
\(104\) | −48.2700 | −4.73327 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.992168 | −0.0963678 | ||||||||
\(107\) | 9.74434 | 0.942021 | 0.471011 | − | 0.882128i | \(-0.343889\pi\) | ||||
0.471011 | + | 0.882128i | \(0.343889\pi\) | |||||||
\(108\) | −16.1697 | −1.55593 | ||||||||
\(109\) | −0.103367 | −0.00990075 | −0.00495038 | − | 0.999988i | \(-0.501576\pi\) | ||||
−0.00495038 | + | 0.999988i | \(0.501576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.92315 | −0.182538 | ||||||||
\(112\) | −14.1090 | −1.33318 | ||||||||
\(113\) | 10.6373 | 1.00068 | 0.500338 | − | 0.865830i | \(-0.333209\pi\) | ||||
0.500338 | + | 0.865830i | \(0.333209\pi\) | |||||||
\(114\) | −9.09858 | −0.852160 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 38.6261 | 3.58634 | ||||||||
\(117\) | −14.3614 | −1.32772 | ||||||||
\(118\) | 5.72404 | 0.526940 | ||||||||
\(119\) | 5.04671 | 0.462631 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 30.7824 | 2.78690 | ||||||||
\(123\) | 2.17892 | 0.196467 | ||||||||
\(124\) | −38.4448 | −3.45245 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.39398 | −0.658708 | ||||||||
\(127\) | 17.3047 | 1.53554 | 0.767772 | − | 0.640723i | \(-0.221365\pi\) | ||||
0.767772 | + | 0.640723i | \(0.221365\pi\) | |||||||
\(128\) | −30.8125 | −2.72347 | ||||||||
\(129\) | 5.36777 | 0.472606 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.21188 | −0.367994 | −0.183997 | − | 0.982927i | \(-0.558904\pi\) | ||||
−0.183997 | + | 0.982927i | \(0.558904\pi\) | |||||||
\(132\) | 2.82522 | 0.245903 | ||||||||
\(133\) | −6.37138 | −0.552469 | ||||||||
\(134\) | −13.4268 | −1.15990 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 46.1946 | 3.96116 | ||||||||
\(137\) | −10.0108 | −0.855280 | −0.427640 | − | 0.903949i | \(-0.640655\pi\) | ||||
−0.427640 | + | 0.903949i | \(0.640655\pi\) | |||||||
\(138\) | 11.0377 | 0.939595 | ||||||||
\(139\) | 16.5921 | 1.40732 | 0.703662 | − | 0.710535i | \(-0.251547\pi\) | ||||
0.703662 | + | 0.710535i | \(0.251547\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.02174 | 0.507122 | ||||||||
\(142\) | −4.68985 | −0.393564 | ||||||||
\(143\) | 5.27345 | 0.440988 | ||||||||
\(144\) | −38.4238 | −3.20198 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −32.4018 | −2.68159 | ||||||||
\(147\) | 0.525975 | 0.0433817 | ||||||||
\(148\) | −19.6397 | −1.61437 | ||||||||
\(149\) | 16.3802 | 1.34192 | 0.670959 | − | 0.741495i | \(-0.265883\pi\) | ||||
0.670959 | + | 0.741495i | \(0.265883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.72876 | −0.140685 | −0.0703424 | − | 0.997523i | \(-0.522409\pi\) | ||||
−0.0703424 | + | 0.997523i | \(0.522409\pi\) | |||||||
\(152\) | −58.3199 | −4.73037 | ||||||||
\(153\) | 13.7440 | 1.11113 | ||||||||
\(154\) | 2.71503 | 0.218783 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.8986 | 1.19284 | ||||||||
\(157\) | 11.2513 | 0.897954 | 0.448977 | − | 0.893543i | \(-0.351789\pi\) | ||||
0.448977 | + | 0.893543i | \(0.351789\pi\) | |||||||
\(158\) | 14.6871 | 1.16844 | ||||||||
\(159\) | 0.192210 | 0.0152432 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.72930 | 0.609154 | ||||||||
\(162\) | −17.8830 | −1.40502 | ||||||||
\(163\) | −6.30843 | −0.494114 | −0.247057 | − | 0.969001i | \(-0.579464\pi\) | ||||
−0.247057 | + | 0.969001i | \(0.579464\pi\) | |||||||
\(164\) | 22.2517 | 1.73756 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.54852 | −0.430648 | ||||||||
\(167\) | −11.8399 | −0.916201 | −0.458100 | − | 0.888900i | \(-0.651470\pi\) | ||||
−0.458100 | + | 0.888900i | \(0.651470\pi\) | |||||||
\(168\) | 4.81447 | 0.371444 | ||||||||
\(169\) | 14.8093 | 1.13917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.3515 | −1.32690 | ||||||||
\(172\) | 54.8169 | 4.17975 | ||||||||
\(173\) | −10.5394 | −0.801295 | −0.400647 | − | 0.916232i | \(-0.631215\pi\) | ||||
−0.400647 | + | 0.916232i | \(0.631215\pi\) | |||||||
\(174\) | −10.2692 | −0.778502 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.1090 | 1.06351 | ||||||||
\(177\) | −1.10890 | −0.0833502 | ||||||||
\(178\) | 3.51887 | 0.263750 | ||||||||
\(179\) | 11.0794 | 0.828110 | 0.414055 | − | 0.910252i | \(-0.364112\pi\) | ||||
0.414055 | + | 0.910252i | \(0.364112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70122 | 0.498098 | 0.249049 | − | 0.968491i | \(-0.419882\pi\) | ||||
0.249049 | + | 0.968491i | \(0.419882\pi\) | |||||||
\(182\) | 14.3176 | 1.06129 | ||||||||
\(183\) | −5.96338 | −0.440826 | ||||||||
\(184\) | 70.7494 | 5.21572 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.2210 | 0.749437 | ||||||||
\(187\) | −5.04671 | −0.369052 | ||||||||
\(188\) | 61.4955 | 4.48502 | ||||||||
\(189\) | 3.01034 | 0.218970 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.1680 | 1.53167 | 0.765833 | − | 0.643040i | \(-0.222327\pi\) | ||||
0.765833 | + | 0.643040i | \(0.222327\pi\) | |||||||
\(192\) | 13.7181 | 0.990022 | ||||||||
\(193\) | −10.7288 | −0.772275 | −0.386138 | − | 0.922441i | \(-0.626191\pi\) | ||||
−0.386138 | + | 0.922441i | \(0.626191\pi\) | |||||||
\(194\) | −2.87006 | −0.206058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.37138 | 0.383670 | ||||||||
\(197\) | 16.1526 | 1.15082 | 0.575412 | − | 0.817864i | \(-0.304842\pi\) | ||||
0.575412 | + | 0.817864i | \(0.304842\pi\) | |||||||
\(198\) | 7.39398 | 0.525467 | ||||||||
\(199\) | −12.6432 | −0.896254 | −0.448127 | − | 0.893970i | \(-0.647909\pi\) | ||||
−0.448127 | + | 0.893970i | \(0.647909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.60114 | 0.183470 | ||||||||
\(202\) | 18.6081 | 1.30926 | ||||||||
\(203\) | −7.19109 | −0.504716 | ||||||||
\(204\) | −14.2581 | −0.998263 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.06772 | 0.0743917 | ||||||||
\(207\) | 21.0496 | 1.46305 | ||||||||
\(208\) | 74.4031 | 5.15893 | ||||||||
\(209\) | 6.37138 | 0.440718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.48920 | −0.584420 | −0.292210 | − | 0.956354i | \(-0.594391\pi\) | ||||
−0.292210 | + | 0.956354i | \(0.594391\pi\) | |||||||
\(212\) | 1.96289 | 0.134812 | ||||||||
\(213\) | 0.908552 | 0.0622530 | ||||||||
\(214\) | −26.4562 | −1.80851 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 27.5549 | 1.87487 | ||||||||
\(217\) | 7.15734 | 0.485872 | ||||||||
\(218\) | 0.280644 | 0.0190076 | ||||||||
\(219\) | 6.27711 | 0.424167 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.6136 | −1.79022 | ||||||||
\(222\) | 5.22142 | 0.350439 | ||||||||
\(223\) | 7.53215 | 0.504390 | 0.252195 | − | 0.967676i | \(-0.418848\pi\) | ||||
0.252195 | + | 0.967676i | \(0.418848\pi\) | |||||||
\(224\) | 19.9995 | 1.33628 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −28.8807 | −1.92111 | ||||||||
\(227\) | −17.6460 | −1.17120 | −0.585602 | − | 0.810599i | \(-0.699142\pi\) | ||||
−0.585602 | + | 0.810599i | \(0.699142\pi\) | |||||||
\(228\) | 18.0005 | 1.19211 | ||||||||
\(229\) | 13.2705 | 0.876939 | 0.438469 | − | 0.898746i | \(-0.355521\pi\) | ||||
0.438469 | + | 0.898746i | \(0.355521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.525975 | −0.0346066 | ||||||||
\(232\) | −65.8230 | −4.32149 | ||||||||
\(233\) | 10.3195 | 0.676051 | 0.338025 | − | 0.941137i | \(-0.390241\pi\) | ||||
0.338025 | + | 0.941137i | \(0.390241\pi\) | |||||||
\(234\) | 38.9917 | 2.54897 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.3244 | −0.737154 | ||||||||
\(237\) | −2.84529 | −0.184822 | ||||||||
\(238\) | −13.7020 | −0.888167 | ||||||||
\(239\) | −2.77046 | −0.179206 | −0.0896032 | − | 0.995978i | \(-0.528560\pi\) | ||||
−0.0896032 | + | 0.995978i | \(0.528560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9346 | 1.21968 | 0.609841 | − | 0.792524i | \(-0.291233\pi\) | ||||
0.609841 | + | 0.792524i | \(0.291233\pi\) | |||||||
\(242\) | −2.71503 | −0.174529 | ||||||||
\(243\) | 12.4955 | 0.801584 | ||||||||
\(244\) | −60.8995 | −3.89869 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.91583 | −0.377180 | ||||||||
\(247\) | 33.5992 | 2.13786 | ||||||||
\(248\) | 65.5140 | 4.16015 | ||||||||
\(249\) | 1.07490 | 0.0681190 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.48777 | 0.535743 | 0.267872 | − | 0.963455i | \(-0.413680\pi\) | ||||
0.267872 | + | 0.963455i | \(0.413680\pi\) | |||||||
\(252\) | 14.6282 | 0.921487 | ||||||||
\(253\) | −7.72930 | −0.485937 | ||||||||
\(254\) | −46.9828 | −2.94796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 31.4942 | 1.96839 | ||||||||
\(257\) | 1.10707 | 0.0690573 | 0.0345286 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345286 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(258\) | −14.5736 | −0.907316 | ||||||||
\(259\) | 3.65636 | 0.227195 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.5839 | −1.21221 | ||||||||
\(262\) | 11.4354 | 0.706481 | ||||||||
\(263\) | 26.3914 | 1.62737 | 0.813683 | − | 0.581309i | \(-0.197459\pi\) | ||||
0.813683 | + | 0.581309i | \(0.197459\pi\) | |||||||
\(264\) | −4.81447 | −0.296310 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.2985 | 1.06064 | ||||||||
\(267\) | −0.681701 | −0.0417194 | ||||||||
\(268\) | 26.5635 | 1.62262 | ||||||||
\(269\) | 6.04003 | 0.368267 | 0.184134 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184134 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.27547 | 0.259716 | 0.129858 | − | 0.991533i | \(-0.458548\pi\) | ||||
0.129858 | + | 0.991533i | \(0.458548\pi\) | |||||||
\(272\) | −71.2041 | −4.31738 | ||||||||
\(273\) | −2.77370 | −0.167872 | ||||||||
\(274\) | 27.1796 | 1.64198 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −21.8369 | −1.31443 | ||||||||
\(277\) | 9.61128 | 0.577486 | 0.288743 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288743 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(278\) | −45.0480 | −2.70180 | ||||||||
\(279\) | 19.4919 | 1.16695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4966 | −0.745483 | −0.372741 | − | 0.927935i | \(-0.621582\pi\) | ||||
−0.372741 | + | 0.927935i | \(0.621582\pi\) | |||||||
\(282\) | −16.3492 | −0.973581 | ||||||||
\(283\) | 12.6457 | 0.751711 | 0.375856 | − | 0.926678i | \(-0.377349\pi\) | ||||
0.375856 | + | 0.926678i | \(0.377349\pi\) | |||||||
\(284\) | 9.27835 | 0.550569 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.3176 | −0.846615 | ||||||||
\(287\) | −4.14263 | −0.244532 | ||||||||
\(288\) | 54.4658 | 3.20943 | ||||||||
\(289\) | 8.46931 | 0.498195 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.556009 | 0.0325938 | ||||||||
\(292\) | 64.1033 | 3.75136 | ||||||||
\(293\) | 20.3335 | 1.18790 | 0.593948 | − | 0.804503i | \(-0.297568\pi\) | ||||
0.593948 | + | 0.804503i | \(0.297568\pi\) | |||||||
\(294\) | −1.42804 | −0.0832849 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 33.4681 | 1.94529 | ||||||||
\(297\) | −3.01034 | −0.174678 | ||||||||
\(298\) | −44.4727 | −2.57623 | ||||||||
\(299\) | −40.7601 | −2.35722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.2054 | −0.588227 | ||||||||
\(302\) | 4.69365 | 0.270089 | ||||||||
\(303\) | −3.60489 | −0.207096 | ||||||||
\(304\) | 89.8939 | 5.15577 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −37.3153 | −2.13317 | ||||||||
\(307\) | −27.0342 | −1.54292 | −0.771462 | − | 0.636276i | \(-0.780474\pi\) | ||||
−0.771462 | + | 0.636276i | \(0.780474\pi\) | |||||||
\(308\) | −5.37138 | −0.306063 | ||||||||
\(309\) | −0.206847 | −0.0117671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.0710 | 1.64847 | 0.824234 | − | 0.566250i | \(-0.191606\pi\) | ||||
0.824234 | + | 0.566250i | \(0.191606\pi\) | |||||||
\(312\) | −25.3888 | −1.43736 | ||||||||
\(313\) | 18.0949 | 1.02279 | 0.511393 | − | 0.859347i | \(-0.329130\pi\) | ||||
0.511393 | + | 0.859347i | \(0.329130\pi\) | |||||||
\(314\) | −30.5477 | −1.72391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.0568 | −1.63457 | ||||||||
\(317\) | 0.617596 | 0.0346876 | 0.0173438 | − | 0.999850i | \(-0.494479\pi\) | ||||
0.0173438 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(318\) | −0.521856 | −0.0292642 | ||||||||
\(319\) | 7.19109 | 0.402624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.12528 | 0.286065 | ||||||||
\(322\) | −20.9853 | −1.16946 | ||||||||
\(323\) | −32.1546 | −1.78913 | ||||||||
\(324\) | 35.3796 | 1.96553 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.1276 | 0.948609 | ||||||||
\(327\) | −0.0543684 | −0.00300658 | ||||||||
\(328\) | −37.9192 | −2.09374 | ||||||||
\(329\) | −11.4487 | −0.631188 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1826 | 1.21927 | 0.609634 | − | 0.792683i | \(-0.291317\pi\) | ||||
0.609634 | + | 0.792683i | \(0.291317\pi\) | |||||||
\(332\) | 10.9771 | 0.602448 | ||||||||
\(333\) | 9.95754 | 0.545670 | ||||||||
\(334\) | 32.1457 | 1.75894 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.42099 | −0.404848 | ||||||||
\(337\) | 2.50380 | 0.136391 | 0.0681953 | − | 0.997672i | \(-0.478276\pi\) | ||||
0.0681953 | + | 0.997672i | \(0.478276\pi\) | |||||||
\(338\) | −40.2076 | −2.18700 | ||||||||
\(339\) | 5.59497 | 0.303877 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.15734 | −0.387592 | ||||||||
\(342\) | 47.1099 | 2.54741 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −93.4138 | −5.03654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.6148 | 1.53834 | ||||||||
\(347\) | −20.9259 | −1.12336 | −0.561681 | − | 0.827354i | \(-0.689845\pi\) | ||||
−0.561681 | + | 0.827354i | \(0.689845\pi\) | |||||||
\(348\) | 20.3164 | 1.08907 | ||||||||
\(349\) | −16.2685 | −0.870830 | −0.435415 | − | 0.900230i | \(-0.643398\pi\) | ||||
−0.435415 | + | 0.900230i | \(0.643398\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.8749 | −0.847338 | ||||||||
\(352\) | −19.9995 | −1.06598 | ||||||||
\(353\) | 19.2778 | 1.02605 | 0.513027 | − | 0.858372i | \(-0.328524\pi\) | ||||
0.513027 | + | 0.858372i | \(0.328524\pi\) | |||||||
\(354\) | 3.01070 | 0.160017 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.96169 | −0.368969 | ||||||||
\(357\) | 2.65445 | 0.140488 | ||||||||
\(358\) | −30.0808 | −1.58982 | ||||||||
\(359\) | −13.5857 | −0.717026 | −0.358513 | − | 0.933525i | \(-0.616716\pi\) | ||||
−0.358513 | + | 0.933525i | \(0.616716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.5945 | 1.13655 | ||||||||
\(362\) | −18.1940 | −0.956256 | ||||||||
\(363\) | 0.525975 | 0.0276065 | ||||||||
\(364\) | −28.3257 | −1.48467 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.1908 | 0.846304 | ||||||||
\(367\) | −6.40691 | −0.334438 | −0.167219 | − | 0.985920i | \(-0.553479\pi\) | ||||
−0.167219 | + | 0.985920i | \(0.553479\pi\) | |||||||
\(368\) | −109.053 | −5.68477 | ||||||||
\(369\) | −11.2818 | −0.587309 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.365435 | −0.0189725 | ||||||||
\(372\) | −20.2210 | −1.04841 | ||||||||
\(373\) | 14.7026 | 0.761274 | 0.380637 | − | 0.924725i | \(-0.375705\pi\) | ||||
0.380637 | + | 0.924725i | \(0.375705\pi\) | |||||||
\(374\) | 13.7020 | 0.708512 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −104.795 | −5.40438 | ||||||||
\(377\) | 37.9218 | 1.95307 | ||||||||
\(378\) | −8.17316 | −0.420382 | ||||||||
\(379\) | −3.65587 | −0.187790 | −0.0938948 | − | 0.995582i | \(-0.529932\pi\) | ||||
−0.0938948 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.10185 | 0.466302 | ||||||||
\(382\) | −57.4719 | −2.94052 | ||||||||
\(383\) | 23.4296 | 1.19720 | 0.598598 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598598 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(384\) | −16.2066 | −0.827041 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.1290 | 1.48263 | ||||||||
\(387\) | −27.7928 | −1.41279 | ||||||||
\(388\) | 5.67809 | 0.288261 | ||||||||
\(389\) | 0.508487 | 0.0257813 | 0.0128907 | − | 0.999917i | \(-0.495897\pi\) | ||||
0.0128907 | + | 0.999917i | \(0.495897\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.0076 | 1.97270 | ||||||||
\(392\) | −9.15341 | −0.462317 | ||||||||
\(393\) | −2.21535 | −0.111749 | ||||||||
\(394\) | −43.8548 | −2.20937 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.6282 | −0.735093 | ||||||||
\(397\) | −12.0457 | −0.604556 | −0.302278 | − | 0.953220i | \(-0.597747\pi\) | ||||
−0.302278 | + | 0.953220i | \(0.597747\pi\) | |||||||
\(398\) | 34.3267 | 1.72064 | ||||||||
\(399\) | −3.35119 | −0.167769 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.9084 | −1.89305 | −0.946527 | − | 0.322623i | \(-0.895435\pi\) | ||||
−0.946527 | + | 0.322623i | \(0.895435\pi\) | |||||||
\(402\) | −7.06217 | −0.352229 | ||||||||
\(403\) | −37.7438 | −1.88016 | ||||||||
\(404\) | −36.8140 | −1.83157 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.5240 | 0.968961 | ||||||||
\(407\) | −3.65636 | −0.181239 | ||||||||
\(408\) | 24.2972 | 1.20289 | ||||||||
\(409\) | 38.3939 | 1.89846 | 0.949228 | − | 0.314590i | \(-0.101867\pi\) | ||||
0.949228 | + | 0.314590i | \(0.101867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.26543 | −0.259725 | ||||||||
\(412\) | −2.11237 | −0.104069 | ||||||||
\(413\) | 2.10828 | 0.103742 | ||||||||
\(414\) | −57.1502 | −2.80878 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −105.467 | −5.17092 | ||||||||
\(417\) | 8.72704 | 0.427365 | ||||||||
\(418\) | −17.2985 | −0.846097 | ||||||||
\(419\) | 18.8624 | 0.921491 | 0.460745 | − | 0.887532i | \(-0.347582\pi\) | ||||
0.460745 | + | 0.887532i | \(0.347582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0677 | −1.46541 | −0.732706 | − | 0.680545i | \(-0.761743\pi\) | ||||
−0.732706 | + | 0.680545i | \(0.761743\pi\) | |||||||
\(422\) | 23.0484 | 1.12198 | ||||||||
\(423\) | −31.1789 | −1.51597 | ||||||||
\(424\) | −3.34498 | −0.162447 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.46675 | −0.119514 | ||||||||
\(427\) | 11.3378 | 0.548673 | ||||||||
\(428\) | 52.3406 | 2.52998 | ||||||||
\(429\) | 2.77370 | 0.133916 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.4992 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(432\) | −42.4729 | −2.04348 | ||||||||
\(433\) | −16.0344 | −0.770564 | −0.385282 | − | 0.922799i | \(-0.625896\pi\) | ||||
−0.385282 | + | 0.922799i | \(0.625896\pi\) | |||||||
\(434\) | −19.4324 | −0.932784 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.555223 | −0.0265904 | ||||||||
\(437\) | −49.2463 | −2.35577 | ||||||||
\(438\) | −17.0425 | −0.814323 | ||||||||
\(439\) | 41.6376 | 1.98726 | 0.993628 | − | 0.112707i | \(-0.0359523\pi\) | ||||
0.993628 | + | 0.112707i | \(0.0359523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.72335 | −0.129683 | ||||||||
\(442\) | 72.2566 | 3.43690 | ||||||||
\(443\) | 11.3656 | 0.539997 | 0.269998 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269998 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(444\) | −10.3300 | −0.490240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.4500 | −0.968336 | ||||||||
\(447\) | 8.61558 | 0.407503 | ||||||||
\(448\) | −26.0813 | −1.23223 | ||||||||
\(449\) | −4.10578 | −0.193764 | −0.0968820 | − | 0.995296i | \(-0.530887\pi\) | ||||
−0.0968820 | + | 0.995296i | \(0.530887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.14263 | 0.195069 | ||||||||
\(452\) | 57.1372 | 2.68751 | ||||||||
\(453\) | −0.909288 | −0.0427221 | ||||||||
\(454\) | 47.9093 | 2.24849 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.6748 | −1.43648 | ||||||||
\(457\) | 15.3963 | 0.720207 | 0.360104 | − | 0.932912i | \(-0.382741\pi\) | ||||
0.360104 | + | 0.932912i | \(0.382741\pi\) | |||||||
\(458\) | −36.0298 | −1.68356 | ||||||||
\(459\) | 15.1923 | 0.709117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.5380 | −0.909977 | −0.454989 | − | 0.890497i | \(-0.650357\pi\) | ||||
−0.454989 | + | 0.890497i | \(0.650357\pi\) | |||||||
\(462\) | 1.42804 | 0.0664384 | ||||||||
\(463\) | 4.84367 | 0.225104 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(464\) | 101.459 | 4.71012 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.0177 | −1.29789 | ||||||||
\(467\) | 22.0487 | 1.02029 | 0.510147 | − | 0.860087i | \(-0.329591\pi\) | ||||
0.510147 | + | 0.860087i | \(0.329591\pi\) | |||||||
\(468\) | −77.1408 | −3.56584 | ||||||||
\(469\) | −4.94537 | −0.228356 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.91792 | 0.272683 | ||||||||
\(472\) | 19.2979 | 0.888259 | ||||||||
\(473\) | 10.2054 | 0.469243 | ||||||||
\(474\) | 7.72505 | 0.354823 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 27.1078 | 1.24249 | ||||||||
\(477\) | −0.995208 | −0.0455675 | ||||||||
\(478\) | 7.52189 | 0.344043 | ||||||||
\(479\) | −5.66221 | −0.258713 | −0.129356 | − | 0.991598i | \(-0.541291\pi\) | ||||
−0.129356 | + | 0.991598i | \(0.541291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.2816 | −0.879165 | ||||||||
\(482\) | −51.4079 | −2.34156 | ||||||||
\(483\) | 4.06542 | 0.184983 | ||||||||
\(484\) | 5.37138 | 0.244154 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −33.9255 | −1.53889 | ||||||||
\(487\) | −41.5337 | −1.88207 | −0.941035 | − | 0.338310i | \(-0.890145\pi\) | ||||
−0.941035 | + | 0.338310i | \(0.890145\pi\) | |||||||
\(488\) | 103.779 | 4.69786 | ||||||||
\(489\) | −3.31808 | −0.150049 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.02259 | 0.362054 | 0.181027 | − | 0.983478i | \(-0.442058\pi\) | ||||
0.181027 | + | 0.983478i | \(0.442058\pi\) | |||||||
\(492\) | 11.7038 | 0.527649 | ||||||||
\(493\) | −36.2914 | −1.63448 | ||||||||
\(494\) | −91.2227 | −4.10430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −100.983 | −4.53427 | ||||||||
\(497\) | −1.72737 | −0.0774830 | ||||||||
\(498\) | −2.91838 | −0.130776 | ||||||||
\(499\) | −11.6103 | −0.519748 | −0.259874 | − | 0.965643i | \(-0.583681\pi\) | ||||
−0.259874 | + | 0.965643i | \(0.583681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.22751 | −0.278225 | ||||||||
\(502\) | −23.0445 | −1.02853 | ||||||||
\(503\) | −0.173084 | −0.00771742 | −0.00385871 | − | 0.999993i | \(-0.501228\pi\) | ||||
−0.00385871 | + | 0.999993i | \(0.501228\pi\) | |||||||
\(504\) | −24.9279 | −1.11038 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.9853 | 0.932909 | ||||||||
\(507\) | 7.78930 | 0.345935 | ||||||||
\(508\) | 92.9503 | 4.12400 | ||||||||
\(509\) | −31.9779 | −1.41740 | −0.708698 | − | 0.705512i | \(-0.750717\pi\) | ||||
−0.708698 | + | 0.705512i | \(0.750717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9342 | −0.527939 | ||||||||
\(512\) | −23.8827 | −1.05548 | ||||||||
\(513\) | −19.1800 | −0.846819 | ||||||||
\(514\) | −3.00573 | −0.132577 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 28.8323 | 1.26927 | ||||||||
\(517\) | 11.4487 | 0.503514 | ||||||||
\(518\) | −9.92711 | −0.436172 | ||||||||
\(519\) | −5.54346 | −0.243331 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2941 | −0.582425 | −0.291212 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291212 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(522\) | 53.1707 | 2.32722 | ||||||||
\(523\) | 24.9187 | 1.08962 | 0.544810 | − | 0.838559i | \(-0.316602\pi\) | ||||
0.544810 | + | 0.838559i | \(0.316602\pi\) | |||||||
\(524\) | −22.6236 | −0.988319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −71.6535 | −3.12424 | ||||||||
\(527\) | 36.1210 | 1.57346 | ||||||||
\(528\) | 7.42099 | 0.322957 | ||||||||
\(529\) | 36.7421 | 1.59748 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.74158 | 0.249163 | ||||||||
\(532\) | −34.2232 | −1.48376 | ||||||||
\(533\) | 21.8459 | 0.946253 | ||||||||
\(534\) | 1.85084 | 0.0800936 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −45.2670 | −1.95523 | ||||||||
\(537\) | 5.82747 | 0.251474 | ||||||||
\(538\) | −16.3989 | −0.707005 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.59578 | −0.326568 | −0.163284 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163284 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(542\) | −11.6080 | −0.498607 | ||||||||
\(543\) | 3.52468 | 0.151258 | ||||||||
\(544\) | 100.932 | 4.32742 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.53069 | 0.322284 | ||||||||
\(547\) | −5.60892 | −0.239820 | −0.119910 | − | 0.992785i | \(-0.538261\pi\) | ||||
−0.119910 | + | 0.992785i | \(0.538261\pi\) | |||||||
\(548\) | −53.7718 | −2.29702 | ||||||||
\(549\) | 30.8767 | 1.31778 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.8172 | 1.95188 | ||||||||
\(552\) | 37.2125 | 1.58387 | ||||||||
\(553\) | 5.40955 | 0.230038 | ||||||||
\(554\) | −26.0949 | −1.10867 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 89.1226 | 3.77964 | ||||||||
\(557\) | −3.14063 | −0.133073 | −0.0665364 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665364 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(558\) | −52.9212 | −2.24033 | ||||||||
\(559\) | 53.8174 | 2.27623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.65445 | −0.112071 | ||||||||
\(562\) | 33.9286 | 1.43119 | ||||||||
\(563\) | −34.9166 | −1.47156 | −0.735779 | − | 0.677222i | \(-0.763184\pi\) | ||||
−0.735779 | + | 0.677222i | \(0.763184\pi\) | |||||||
\(564\) | 32.3451 | 1.36197 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −34.3336 | −1.44315 | ||||||||
\(567\) | −6.58668 | −0.276615 | ||||||||
\(568\) | −15.8113 | −0.663427 | ||||||||
\(569\) | −16.9318 | −0.709817 | −0.354909 | − | 0.934901i | \(-0.615488\pi\) | ||||
−0.354909 | + | 0.934901i | \(0.615488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.06027 | 0.0862195 | 0.0431098 | − | 0.999070i | \(-0.486273\pi\) | ||||
0.0431098 | + | 0.999070i | \(0.486273\pi\) | |||||||
\(572\) | 28.3257 | 1.18436 | ||||||||
\(573\) | 11.1339 | 0.465124 | ||||||||
\(574\) | 11.2474 | 0.469456 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −71.0286 | −2.95953 | ||||||||
\(577\) | −35.4282 | −1.47489 | −0.737447 | − | 0.675405i | \(-0.763969\pi\) | ||||
−0.737447 | + | 0.675405i | \(0.763969\pi\) | |||||||
\(578\) | −22.9944 | −0.956442 | ||||||||
\(579\) | −5.64308 | −0.234518 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.04363 | −0.0847841 | ||||||||
\(582\) | −1.50958 | −0.0625741 | ||||||||
\(583\) | 0.365435 | 0.0151348 | ||||||||
\(584\) | −109.239 | −4.52033 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −55.2061 | −2.28054 | ||||||||
\(587\) | −29.5569 | −1.21995 | −0.609973 | − | 0.792423i | \(-0.708820\pi\) | ||||
−0.609973 | + | 0.792423i | \(0.708820\pi\) | |||||||
\(588\) | 2.82522 | 0.116510 | ||||||||
\(589\) | −45.6022 | −1.87900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.49586 | 0.349473 | ||||||||
\(592\) | −51.5875 | −2.12023 | ||||||||
\(593\) | −38.8831 | −1.59674 | −0.798369 | − | 0.602169i | \(-0.794303\pi\) | ||||
−0.798369 | + | 0.602169i | \(0.794303\pi\) | |||||||
\(594\) | 8.17316 | 0.335349 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 87.9843 | 3.60398 | ||||||||
\(597\) | −6.65002 | −0.272167 | ||||||||
\(598\) | 110.665 | 4.52542 | ||||||||
\(599\) | −7.75954 | −0.317046 | −0.158523 | − | 0.987355i | \(-0.550673\pi\) | ||||
−0.158523 | + | 0.987355i | \(0.550673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.3951 | −0.587187 | −0.293594 | − | 0.955930i | \(-0.594851\pi\) | ||||
−0.293594 | + | 0.955930i | \(0.594851\pi\) | |||||||
\(602\) | 27.7079 | 1.12929 | ||||||||
\(603\) | −13.4680 | −0.548458 | ||||||||
\(604\) | −9.28586 | −0.377836 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.78739 | 0.397586 | ||||||||
\(607\) | 30.9908 | 1.25788 | 0.628939 | − | 0.777454i | \(-0.283489\pi\) | ||||
0.628939 | + | 0.777454i | \(0.283489\pi\) | |||||||
\(608\) | −127.425 | −5.16776 | ||||||||
\(609\) | −3.78234 | −0.153268 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.3742 | 2.44248 | ||||||||
\(612\) | 73.8241 | 2.98416 | ||||||||
\(613\) | −46.1777 | −1.86510 | −0.932551 | − | 0.361039i | \(-0.882422\pi\) | ||||
−0.932551 | + | 0.361039i | \(0.882422\pi\) | |||||||
\(614\) | 73.3987 | 2.96213 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.15341 | 0.368801 | ||||||||
\(617\) | −23.1545 | −0.932167 | −0.466083 | − | 0.884741i | \(-0.654335\pi\) | ||||
−0.466083 | + | 0.884741i | \(0.654335\pi\) | |||||||
\(618\) | 0.561595 | 0.0225907 | ||||||||
\(619\) | 7.98316 | 0.320870 | 0.160435 | − | 0.987046i | \(-0.448710\pi\) | ||||
0.160435 | + | 0.987046i | \(0.448710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.2678 | 0.933706 | ||||||||
\(622\) | −78.9287 | −3.16475 | ||||||||
\(623\) | 1.29607 | 0.0519259 | ||||||||
\(624\) | 39.1342 | 1.56662 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −49.1283 | −1.96356 | ||||||||
\(627\) | 3.35119 | 0.133834 | ||||||||
\(628\) | 60.4352 | 2.41163 | ||||||||
\(629\) | 18.4526 | 0.735752 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.41825 | 0.136078 | 0.0680392 | − | 0.997683i | \(-0.478326\pi\) | ||||
0.0680392 | + | 0.997683i | \(0.478326\pi\) | |||||||
\(632\) | 49.5159 | 1.96963 | ||||||||
\(633\) | −4.46511 | −0.177472 | ||||||||
\(634\) | −1.67679 | −0.0665939 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.03243 | 0.0409387 | ||||||||
\(637\) | 5.27345 | 0.208942 | ||||||||
\(638\) | −19.5240 | −0.772963 | ||||||||
\(639\) | −4.70422 | −0.186096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.6627 | −0.421151 | −0.210575 | − | 0.977578i | \(-0.567534\pi\) | ||||
−0.210575 | + | 0.977578i | \(0.567534\pi\) | |||||||
\(642\) | −13.9153 | −0.549193 | ||||||||
\(643\) | −7.99093 | −0.315131 | −0.157566 | − | 0.987508i | \(-0.550365\pi\) | ||||
−0.157566 | + | 0.987508i | \(0.550365\pi\) | |||||||
\(644\) | 41.5170 | 1.63600 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 87.3006 | 3.43479 | ||||||||
\(647\) | 1.37419 | 0.0540251 | 0.0270126 | − | 0.999635i | \(-0.491401\pi\) | ||||
0.0270126 | + | 0.999635i | \(0.491401\pi\) | |||||||
\(648\) | −60.2906 | −2.36844 | ||||||||
\(649\) | −2.10828 | −0.0827571 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.76458 | 0.147546 | ||||||||
\(652\) | −33.8850 | −1.32704 | ||||||||
\(653\) | 7.97082 | 0.311922 | 0.155961 | − | 0.987763i | \(-0.450153\pi\) | ||||
0.155961 | + | 0.987763i | \(0.450153\pi\) | |||||||
\(654\) | 0.147612 | 0.00577208 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 58.4484 | 2.28203 | ||||||||
\(657\) | −32.5011 | −1.26799 | ||||||||
\(658\) | 31.0836 | 1.21177 | ||||||||
\(659\) | 10.1116 | 0.393891 | 0.196946 | − | 0.980414i | \(-0.436898\pi\) | ||||
0.196946 | + | 0.980414i | \(0.436898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4985 | 0.525033 | 0.262516 | − | 0.964928i | \(-0.415448\pi\) | ||||
0.262516 | + | 0.964928i | \(0.415448\pi\) | |||||||
\(662\) | −60.2265 | −2.34077 | ||||||||
\(663\) | −13.9981 | −0.543641 | ||||||||
\(664\) | −18.7062 | −0.725941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.0350 | −1.04759 | ||||||||
\(667\) | −55.5821 | −2.15215 | ||||||||
\(668\) | −63.5968 | −2.46063 | ||||||||
\(669\) | 3.96172 | 0.153169 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.3378 | −0.437689 | ||||||||
\(672\) | 10.5193 | 0.405790 | ||||||||
\(673\) | 22.8185 | 0.879588 | 0.439794 | − | 0.898099i | \(-0.355051\pi\) | ||||
0.439794 | + | 0.898099i | \(0.355051\pi\) | |||||||
\(674\) | −6.79789 | −0.261845 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 79.5462 | 3.05947 | ||||||||
\(677\) | −32.1403 | −1.23525 | −0.617627 | − | 0.786471i | \(-0.711906\pi\) | ||||
−0.617627 | + | 0.786471i | \(0.711906\pi\) | |||||||
\(678\) | −15.1905 | −0.583388 | ||||||||
\(679\) | −1.05710 | −0.0405678 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.28134 | −0.355662 | ||||||||
\(682\) | 19.4324 | 0.744104 | ||||||||
\(683\) | 16.6797 | 0.638233 | 0.319116 | − | 0.947716i | \(-0.396614\pi\) | ||||
0.319116 | + | 0.947716i | \(0.396614\pi\) | |||||||
\(684\) | −93.2016 | −3.56365 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.71503 | 0.103660 | ||||||||
\(687\) | 6.97995 | 0.266302 | ||||||||
\(688\) | 143.987 | 5.48947 | ||||||||
\(689\) | 1.92710 | 0.0734168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.41565 | −0.320146 | −0.160073 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160073 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(692\) | −56.6111 | −2.15203 | ||||||||
\(693\) | 2.72335 | 0.103452 | ||||||||
\(694\) | 56.8144 | 2.15665 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34.6213 | −1.31232 | ||||||||
\(697\) | −20.9067 | −0.791896 | ||||||||
\(698\) | 44.1693 | 1.67183 | ||||||||
\(699\) | 5.42778 | 0.205298 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.3923 | 1.60113 | 0.800567 | − | 0.599244i | \(-0.204532\pi\) | ||||
0.800567 | + | 0.599244i | \(0.204532\pi\) | |||||||
\(702\) | 43.1008 | 1.62673 | ||||||||
\(703\) | −23.2960 | −0.878627 | ||||||||
\(704\) | 26.0813 | 0.982978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.3398 | −1.96984 | ||||||||
\(707\) | 6.85373 | 0.257761 | ||||||||
\(708\) | −5.95634 | −0.223853 | ||||||||
\(709\) | −40.9740 | −1.53881 | −0.769405 | − | 0.638761i | \(-0.779447\pi\) | ||||
−0.769405 | + | 0.638761i | \(0.779447\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7321 | 0.552497 | ||||||||
\(712\) | 11.8635 | 0.444602 | ||||||||
\(713\) | 55.3212 | 2.07180 | ||||||||
\(714\) | −7.20690 | −0.269711 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 59.5115 | 2.22405 | ||||||||
\(717\) | −1.45720 | −0.0544199 | ||||||||
\(718\) | 36.8856 | 1.37656 | ||||||||
\(719\) | −43.0602 | −1.60587 | −0.802937 | − | 0.596063i | \(-0.796731\pi\) | ||||
−0.802937 | + | 0.596063i | \(0.796731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.393263 | 0.0146459 | ||||||||
\(722\) | −58.6298 | −2.18198 | ||||||||
\(723\) | 9.95911 | 0.370383 | ||||||||
\(724\) | 35.9948 | 1.33774 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.42804 | −0.0529995 | ||||||||
\(727\) | −32.1941 | −1.19401 | −0.597006 | − | 0.802237i | \(-0.703643\pi\) | ||||
−0.597006 | + | 0.802237i | \(0.703643\pi\) | |||||||
\(728\) | 48.2700 | 1.78901 | ||||||||
\(729\) | −13.1878 | −0.488435 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.5035 | −1.90493 | ||||||||
\(732\) | −32.0316 | −1.18392 | ||||||||
\(733\) | −12.8367 | −0.474134 | −0.237067 | − | 0.971493i | \(-0.576186\pi\) | ||||
−0.237067 | + | 0.971493i | \(0.576186\pi\) | |||||||
\(734\) | 17.3949 | 0.642059 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 154.582 | 5.69799 | ||||||||
\(737\) | 4.94537 | 0.182165 | ||||||||
\(738\) | 30.6305 | 1.12752 | ||||||||
\(739\) | 21.8387 | 0.803351 | 0.401676 | − | 0.915782i | \(-0.368428\pi\) | ||||
0.401676 | + | 0.915782i | \(0.368428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.6723 | 0.649209 | ||||||||
\(742\) | 0.992168 | 0.0364236 | ||||||||
\(743\) | 28.0653 | 1.02962 | 0.514809 | − | 0.857305i | \(-0.327863\pi\) | ||||
0.514809 | + | 0.857305i | \(0.327863\pi\) | |||||||
\(744\) | 34.4588 | 1.26332 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −39.9181 | −1.46151 | ||||||||
\(747\) | −5.56552 | −0.203632 | ||||||||
\(748\) | −27.1078 | −0.991161 | ||||||||
\(749\) | −9.74434 | −0.356051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.7954 | −1.34268 | −0.671342 | − | 0.741148i | \(-0.734282\pi\) | ||||
−0.671342 | + | 0.741148i | \(0.734282\pi\) | |||||||
\(752\) | 161.530 | 5.89039 | ||||||||
\(753\) | 4.46436 | 0.162690 | ||||||||
\(754\) | −102.959 | −3.74954 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 16.1697 | 0.588086 | ||||||||
\(757\) | −35.2014 | −1.27942 | −0.639709 | − | 0.768617i | \(-0.720945\pi\) | ||||
−0.639709 | + | 0.768617i | \(0.720945\pi\) | |||||||
\(758\) | 9.92581 | 0.360522 | ||||||||
\(759\) | −4.06542 | −0.147565 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6132 | 1.10973 | 0.554865 | − | 0.831941i | \(-0.312770\pi\) | ||||
0.554865 | + | 0.831941i | \(0.312770\pi\) | |||||||
\(762\) | −24.7118 | −0.895214 | ||||||||
\(763\) | 0.103367 | 0.00374213 | ||||||||
\(764\) | 113.702 | 4.11358 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −63.6120 | −2.29840 | ||||||||
\(767\) | −11.1179 | −0.401444 | ||||||||
\(768\) | 16.5652 | 0.597745 | ||||||||
\(769\) | −47.6690 | −1.71899 | −0.859493 | − | 0.511147i | \(-0.829221\pi\) | ||||
−0.859493 | + | 0.511147i | \(0.829221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.582293 | 0.0209708 | ||||||||
\(772\) | −57.6284 | −2.07409 | ||||||||
\(773\) | 1.89344 | 0.0681024 | 0.0340512 | − | 0.999420i | \(-0.489159\pi\) | ||||
0.0340512 | + | 0.999420i | \(0.489159\pi\) | |||||||
\(774\) | 75.4582 | 2.71229 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.67607 | −0.347351 | ||||||||
\(777\) | 1.92315 | 0.0689927 | ||||||||
\(778\) | −1.38056 | −0.0494954 | ||||||||
\(779\) | 26.3943 | 0.945673 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.72737 | 0.0618100 | ||||||||
\(782\) | −105.907 | −3.78721 | ||||||||
\(783\) | −21.6476 | −0.773623 | ||||||||
\(784\) | 14.1090 | 0.503893 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.01473 | 0.214538 | ||||||||
\(787\) | 26.8097 | 0.955663 | 0.477831 | − | 0.878452i | \(-0.341423\pi\) | ||||
0.477831 | + | 0.878452i | \(0.341423\pi\) | |||||||
\(788\) | 86.7618 | 3.09076 | ||||||||
\(789\) | 13.8812 | 0.494185 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6373 | −0.378220 | ||||||||
\(792\) | 24.9279 | 0.885776 | ||||||||
\(793\) | −59.7891 | −2.12317 | ||||||||
\(794\) | 32.7044 | 1.16064 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67.9116 | −2.40706 | ||||||||
\(797\) | −40.9793 | −1.45156 | −0.725781 | − | 0.687926i | \(-0.758522\pi\) | ||||
−0.725781 | + | 0.687926i | \(0.758522\pi\) | |||||||
\(798\) | 9.09858 | 0.322086 | ||||||||
\(799\) | −57.7784 | −2.04405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.52965 | 0.124714 | ||||||||
\(802\) | 102.922 | 3.63432 | ||||||||
\(803\) | 11.9342 | 0.421149 | ||||||||
\(804\) | 13.9717 | 0.492745 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 102.476 | 3.60955 | ||||||||
\(807\) | 3.17691 | 0.111832 | ||||||||
\(808\) | 62.7350 | 2.20701 | ||||||||
\(809\) | 40.8891 | 1.43758 | 0.718792 | − | 0.695225i | \(-0.244695\pi\) | ||||
0.718792 | + | 0.695225i | \(0.244695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.6998 | 1.00778 | 0.503892 | − | 0.863766i | \(-0.331901\pi\) | ||||
0.503892 | + | 0.863766i | \(0.331901\pi\) | |||||||
\(812\) | −38.6261 | −1.35551 | ||||||||
\(813\) | 2.24879 | 0.0788685 | ||||||||
\(814\) | 9.92711 | 0.347945 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −37.4516 | −1.31107 | ||||||||
\(817\) | 65.0223 | 2.27484 | ||||||||
\(818\) | −104.241 | −3.64468 | ||||||||
\(819\) | 14.3614 | 0.501829 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.3816 | −0.501922 | −0.250961 | − | 0.967997i | \(-0.580747\pi\) | ||||
−0.250961 | + | 0.967997i | \(0.580747\pi\) | |||||||
\(822\) | 14.2958 | 0.498623 | ||||||||
\(823\) | −11.5388 | −0.402217 | −0.201109 | − | 0.979569i | \(-0.564454\pi\) | ||||
−0.201109 | + | 0.979569i | \(0.564454\pi\) | |||||||
\(824\) | 3.59970 | 0.125401 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.72404 | −0.199165 | ||||||||
\(827\) | −3.11653 | −0.108372 | −0.0541861 | − | 0.998531i | \(-0.517256\pi\) | ||||
−0.0541861 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(828\) | 113.065 | 3.92930 | ||||||||
\(829\) | −19.0261 | −0.660804 | −0.330402 | − | 0.943840i | \(-0.607184\pi\) | ||||
−0.330402 | + | 0.943840i | \(0.607184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.05530 | 0.175366 | ||||||||
\(832\) | 137.539 | 4.76829 | ||||||||
\(833\) | −5.04671 | −0.174858 | ||||||||
\(834\) | −23.6942 | −0.820462 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 34.2232 | 1.18363 | ||||||||
\(837\) | 21.5460 | 0.744740 | ||||||||
\(838\) | −51.2121 | −1.76909 | ||||||||
\(839\) | 6.17238 | 0.213094 | 0.106547 | − | 0.994308i | \(-0.466021\pi\) | ||||
0.106547 | + | 0.994308i | \(0.466021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7118 | 0.783164 | ||||||||
\(842\) | 81.6348 | 2.81332 | ||||||||
\(843\) | −6.57289 | −0.226382 | ||||||||
\(844\) | −45.5987 | −1.56957 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 84.6516 | 2.91038 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 5.15593 | 0.177055 | ||||||||
\(849\) | 6.65135 | 0.228274 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2611 | 0.968777 | ||||||||
\(852\) | 4.88018 | 0.167192 | ||||||||
\(853\) | 37.9832 | 1.30052 | 0.650261 | − | 0.759711i | \(-0.274660\pi\) | ||||
0.650261 | + | 0.759711i | \(0.274660\pi\) | |||||||
\(854\) | −30.7824 | −1.05335 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −89.1940 | −3.04859 | ||||||||
\(857\) | 32.8604 | 1.12249 | 0.561245 | − | 0.827650i | \(-0.310323\pi\) | ||||
0.561245 | + | 0.827650i | \(0.310323\pi\) | |||||||
\(858\) | −7.53069 | −0.257093 | ||||||||
\(859\) | 19.3742 | 0.661038 | 0.330519 | − | 0.943799i | \(-0.392776\pi\) | ||||
0.330519 | + | 0.943799i | \(0.392776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.17892 | −0.0742574 | ||||||||
\(862\) | −61.0861 | −2.08060 | ||||||||
\(863\) | −21.7480 | −0.740309 | −0.370154 | − | 0.928970i | \(-0.620695\pi\) | ||||
−0.370154 | + | 0.928970i | \(0.620695\pi\) | |||||||
\(864\) | 60.2054 | 2.04823 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43.5338 | 1.47934 | ||||||||
\(867\) | 4.45465 | 0.151288 | ||||||||
\(868\) | 38.4448 | 1.30490 | ||||||||
\(869\) | −5.40955 | −0.183507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.0791 | 0.883658 | ||||||||
\(872\) | 0.946159 | 0.0320410 | ||||||||
\(873\) | −2.87885 | −0.0974344 | ||||||||
\(874\) | 133.705 | 4.52265 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.7167 | 1.13918 | ||||||||
\(877\) | −23.8741 | −0.806170 | −0.403085 | − | 0.915163i | \(-0.632062\pi\) | ||||
−0.403085 | + | 0.915163i | \(0.632062\pi\) | |||||||
\(878\) | −113.047 | −3.81517 | ||||||||
\(879\) | 10.6949 | 0.360731 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.2243 | −0.950901 | −0.475451 | − | 0.879742i | \(-0.657715\pi\) | ||||
−0.475451 | + | 0.879742i | \(0.657715\pi\) | |||||||
\(882\) | 7.39398 | 0.248968 | ||||||||
\(883\) | −1.43110 | −0.0481603 | −0.0240801 | − | 0.999710i | \(-0.507666\pi\) | ||||
−0.0240801 | + | 0.999710i | \(0.507666\pi\) | |||||||
\(884\) | −142.952 | −4.80799 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.8580 | −1.03669 | ||||||||
\(887\) | −11.8013 | −0.396249 | −0.198124 | − | 0.980177i | \(-0.563485\pi\) | ||||
−0.198124 | + | 0.980177i | \(0.563485\pi\) | |||||||
\(888\) | 17.6034 | 0.590732 | ||||||||
\(889\) | −17.3047 | −0.580381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.58668 | 0.220662 | ||||||||
\(892\) | 40.4581 | 1.35464 | ||||||||
\(893\) | 72.9442 | 2.44098 | ||||||||
\(894\) | −23.3915 | −0.782330 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 30.8125 | 1.02937 | ||||||||
\(897\) | −21.4388 | −0.715820 | ||||||||
\(898\) | 11.1473 | 0.371991 | ||||||||
\(899\) | −51.4691 | −1.71659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.84425 | −0.0614408 | ||||||||
\(902\) | −11.2474 | −0.374496 | ||||||||
\(903\) | −5.36777 | −0.178628 | ||||||||
\(904\) | −97.3678 | −3.23840 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.46874 | 0.0820185 | ||||||||
\(907\) | −6.23945 | −0.207177 | −0.103589 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103589 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(908\) | −94.7832 | −3.14549 | ||||||||
\(909\) | 18.6651 | 0.619082 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7801 | 0.622212 | 0.311106 | − | 0.950375i | \(-0.399301\pi\) | ||||
0.311106 | + | 0.950375i | \(0.399301\pi\) | |||||||
\(912\) | 47.2820 | 1.56566 | ||||||||
\(913\) | 2.04363 | 0.0676343 | ||||||||
\(914\) | −41.8013 | −1.38267 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 71.2809 | 2.35519 | ||||||||
\(917\) | 4.21188 | 0.139089 | ||||||||
\(918\) | −41.2476 | −1.36137 | ||||||||
\(919\) | −13.6006 | −0.448641 | −0.224321 | − | 0.974515i | \(-0.572016\pi\) | ||||
−0.224321 | + | 0.974515i | \(0.572016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.2193 | −0.468543 | ||||||||
\(922\) | 53.0464 | 1.74699 | ||||||||
\(923\) | 9.10918 | 0.299832 | ||||||||
\(924\) | −2.82522 | −0.0929428 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.1507 | −0.432159 | ||||||||
\(927\) | 1.07099 | 0.0351760 | ||||||||
\(928\) | −143.819 | −4.72107 | ||||||||
\(929\) | −9.66398 | −0.317065 | −0.158533 | − | 0.987354i | \(-0.550676\pi\) | ||||
−0.158533 | + | 0.987354i | \(0.550676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.37138 | 0.208814 | ||||||||
\(932\) | 55.4298 | 1.81566 | ||||||||
\(933\) | 15.2907 | 0.500593 | ||||||||
\(934\) | −59.8630 | −1.95878 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 131.456 | 4.29678 | ||||||||
\(937\) | −24.4712 | −0.799440 | −0.399720 | − | 0.916637i | \(-0.630893\pi\) | ||||
−0.399720 | + | 0.916637i | \(0.630893\pi\) | |||||||
\(938\) | 13.4268 | 0.438401 | ||||||||
\(939\) | 9.51749 | 0.310592 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.5314 | 1.84287 | 0.921435 | − | 0.388532i | \(-0.127018\pi\) | ||||
0.921435 | + | 0.388532i | \(0.127018\pi\) | |||||||
\(942\) | −16.0673 | −0.523502 | ||||||||
\(943\) | −32.0196 | −1.04270 | ||||||||
\(944\) | −29.7457 | −0.968140 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7079 | −0.900860 | ||||||||
\(947\) | 19.3925 | 0.630171 | 0.315085 | − | 0.949063i | \(-0.397967\pi\) | ||||
0.315085 | + | 0.949063i | \(0.397967\pi\) | |||||||
\(948\) | −15.2832 | −0.496374 | ||||||||
\(949\) | 62.9345 | 2.04294 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.324840 | 0.0105337 | ||||||||
\(952\) | −46.1946 | −1.49718 | ||||||||
\(953\) | 55.8965 | 1.81067 | 0.905333 | − | 0.424702i | \(-0.139621\pi\) | ||||
0.905333 | + | 0.424702i | \(0.139621\pi\) | |||||||
\(954\) | 2.70202 | 0.0874811 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.8812 | −0.481293 | ||||||||
\(957\) | 3.78234 | 0.122266 | ||||||||
\(958\) | 15.3731 | 0.496681 | ||||||||
\(959\) | 10.0108 | 0.323265 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2275 | 0.652500 | ||||||||
\(962\) | 52.3501 | 1.68784 | ||||||||
\(963\) | −26.5373 | −0.855151 | ||||||||
\(964\) | 101.705 | 3.27569 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.0377 | −0.355133 | ||||||||
\(967\) | 48.7740 | 1.56847 | 0.784233 | − | 0.620466i | \(-0.213057\pi\) | ||||
0.784233 | + | 0.620466i | \(0.213057\pi\) | |||||||
\(968\) | −9.15341 | −0.294202 | ||||||||
\(969\) | −16.9125 | −0.543308 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.6694 | 0.791677 | 0.395839 | − | 0.918320i | \(-0.370454\pi\) | ||||
0.395839 | + | 0.918320i | \(0.370454\pi\) | |||||||
\(972\) | 67.1179 | 2.15281 | ||||||||
\(973\) | −16.5921 | −0.531918 | ||||||||
\(974\) | 112.765 | 3.61323 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −159.965 | −5.12034 | ||||||||
\(977\) | −22.3101 | −0.713762 | −0.356881 | − | 0.934150i | \(-0.616160\pi\) | ||||
−0.356881 | + | 0.934150i | \(0.616160\pi\) | |||||||
\(978\) | 9.00868 | 0.288066 | ||||||||
\(979\) | −1.29607 | −0.0414226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.281504 | 0.00898774 | ||||||||
\(982\) | −21.7816 | −0.695078 | ||||||||
\(983\) | 57.4546 | 1.83252 | 0.916259 | − | 0.400587i | \(-0.131194\pi\) | ||||
0.916259 | + | 0.400587i | \(0.131194\pi\) | |||||||
\(984\) | −19.9446 | −0.635809 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 98.5321 | 3.13790 | ||||||||
\(987\) | −6.02174 | −0.191674 | ||||||||
\(988\) | 180.474 | 5.74164 | ||||||||
\(989\) | −78.8803 | −2.50825 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.4406 | −1.09404 | −0.547021 | − | 0.837119i | \(-0.684238\pi\) | ||||
−0.547021 | + | 0.837119i | \(0.684238\pi\) | |||||||
\(992\) | 143.144 | 4.54481 | ||||||||
\(993\) | 11.6675 | 0.370257 | ||||||||
\(994\) | 4.68985 | 0.148753 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.77370 | 0.182947 | ||||||||
\(997\) | −25.7609 | −0.815856 | −0.407928 | − | 0.913014i | \(-0.633749\pi\) | ||||
−0.407928 | + | 0.913014i | \(0.633749\pi\) | |||||||
\(998\) | 31.5223 | 0.997819 | ||||||||
\(999\) | 11.0069 | 0.348242 |
(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 | 1925.2.a.bb.1.1 | ✓ | 7 | |
5.2 | odd | 4 | 1925.2.b.r.1849.1 | 14 | |||
5.3 | odd | 4 | 1925.2.b.r.1849.14 | 14 | |||
5.4 | even | 2 | 1925.2.a.bd.1.7 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1925.2.a.bb.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1925.2.a.bd.1.7 | yes | 7 | 5.4 | even | 2 | ||
1925.2.b.r.1849.1 | 14 | 5.2 | odd | 4 | |||
1925.2.b.r.1849.14 | 14 | 5.3 | odd | 4 |