Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28892 | −1.61851 | −0.809254 | − | 0.587459i | \(-0.800128\pi\) | ||||
−0.809254 | + | 0.587459i | \(0.800128\pi\) | |||||||
\(3\) | −1.23476 | −0.712887 | −0.356443 | − | 0.934317i | \(-0.616011\pi\) | ||||
−0.356443 | + | 0.934317i | \(0.616011\pi\) | |||||||
\(4\) | 3.23914 | 1.61957 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.82625 | 1.15381 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.83628 | −1.00278 | ||||||||
\(9\) | −1.47538 | −0.491792 | ||||||||
\(10\) | 2.28892 | 0.723819 | ||||||||
\(11\) | −4.24991 | −1.28139 | −0.640697 | − | 0.767793i | \(-0.721355\pi\) | ||||
−0.640697 | + | 0.767793i | \(0.721355\pi\) | |||||||
\(12\) | −3.99954 | −1.15457 | ||||||||
\(13\) | −5.17662 | −1.43574 | −0.717868 | − | 0.696179i | \(-0.754882\pi\) | ||||
−0.717868 | + | 0.696179i | \(0.754882\pi\) | |||||||
\(14\) | 2.28892 | 0.611739 | ||||||||
\(15\) | 1.23476 | 0.318813 | ||||||||
\(16\) | 0.0137336 | 0.00343339 | ||||||||
\(17\) | 5.50025 | 1.33401 | 0.667004 | − | 0.745054i | \(-0.267576\pi\) | ||||
0.667004 | + | 0.745054i | \(0.267576\pi\) | |||||||
\(18\) | 3.37702 | 0.795970 | ||||||||
\(19\) | 2.06636 | 0.474057 | 0.237028 | − | 0.971503i | \(-0.423827\pi\) | ||||
0.237028 | + | 0.971503i | \(0.423827\pi\) | |||||||
\(20\) | −3.23914 | −0.724293 | ||||||||
\(21\) | 1.23476 | 0.269446 | ||||||||
\(22\) | 9.72768 | 2.07395 | ||||||||
\(23\) | −3.42535 | −0.714234 | −0.357117 | − | 0.934060i | \(-0.616240\pi\) | ||||
−0.357117 | + | 0.934060i | \(0.616240\pi\) | |||||||
\(24\) | 3.50211 | 0.714866 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 11.8489 | 2.32375 | ||||||||
\(27\) | 5.52600 | 1.06348 | ||||||||
\(28\) | −3.23914 | −0.612139 | ||||||||
\(29\) | 10.7573 | 1.99758 | 0.998790 | − | 0.0491731i | \(-0.0156586\pi\) | ||||
0.998790 | + | 0.0491731i | \(0.0156586\pi\) | |||||||
\(30\) | −2.82625 | −0.516001 | ||||||||
\(31\) | −2.23815 | −0.401983 | −0.200992 | − | 0.979593i | \(-0.564416\pi\) | ||||
−0.200992 | + | 0.979593i | \(0.564416\pi\) | |||||||
\(32\) | 5.64113 | 0.997219 | ||||||||
\(33\) | 5.24760 | 0.913490 | ||||||||
\(34\) | −12.5896 | −2.15910 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −4.77895 | −0.796492 | ||||||||
\(37\) | 7.31231 | 1.20214 | 0.601068 | − | 0.799198i | \(-0.294742\pi\) | ||||
0.601068 | + | 0.799198i | \(0.294742\pi\) | |||||||
\(38\) | −4.72974 | −0.767264 | ||||||||
\(39\) | 6.39187 | 1.02352 | ||||||||
\(40\) | 2.83628 | 0.448455 | ||||||||
\(41\) | −9.61223 | −1.50118 | −0.750589 | − | 0.660769i | \(-0.770230\pi\) | ||||
−0.750589 | + | 0.660769i | \(0.770230\pi\) | |||||||
\(42\) | −2.82625 | −0.436100 | ||||||||
\(43\) | −7.31457 | −1.11546 | −0.557731 | − | 0.830022i | \(-0.688328\pi\) | ||||
−0.557731 | + | 0.830022i | \(0.688328\pi\) | |||||||
\(44\) | −13.7660 | −2.07531 | ||||||||
\(45\) | 1.47538 | 0.219936 | ||||||||
\(46\) | 7.84033 | 1.15599 | ||||||||
\(47\) | 12.8166 | 1.86949 | 0.934745 | − | 0.355320i | \(-0.115628\pi\) | ||||
0.934745 | + | 0.355320i | \(0.115628\pi\) | |||||||
\(48\) | −0.0169576 | −0.00244762 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.28892 | −0.323702 | ||||||||
\(51\) | −6.79147 | −0.950996 | ||||||||
\(52\) | −16.7678 | −2.32527 | ||||||||
\(53\) | −3.37750 | −0.463935 | −0.231968 | − | 0.972723i | \(-0.574516\pi\) | ||||
−0.231968 | + | 0.972723i | \(0.574516\pi\) | |||||||
\(54\) | −12.6485 | −1.72125 | ||||||||
\(55\) | 4.24991 | 0.573057 | ||||||||
\(56\) | 2.83628 | 0.379014 | ||||||||
\(57\) | −2.55146 | −0.337949 | ||||||||
\(58\) | −24.6226 | −3.23310 | ||||||||
\(59\) | −12.1196 | −1.57784 | −0.788920 | − | 0.614495i | \(-0.789360\pi\) | ||||
−0.788920 | + | 0.614495i | \(0.789360\pi\) | |||||||
\(60\) | 3.99954 | 0.516339 | ||||||||
\(61\) | −0.787009 | −0.100766 | −0.0503831 | − | 0.998730i | \(-0.516044\pi\) | ||||
−0.0503831 | + | 0.998730i | \(0.516044\pi\) | |||||||
\(62\) | 5.12293 | 0.650613 | ||||||||
\(63\) | 1.47538 | 0.185880 | ||||||||
\(64\) | −12.9395 | −1.61744 | ||||||||
\(65\) | 5.17662 | 0.642081 | ||||||||
\(66\) | −12.0113 | −1.47849 | ||||||||
\(67\) | −10.2824 | −1.25620 | −0.628099 | − | 0.778133i | \(-0.716167\pi\) | ||||
−0.628099 | + | 0.778133i | \(0.716167\pi\) | |||||||
\(68\) | 17.8161 | 2.16052 | ||||||||
\(69\) | 4.22947 | 0.509168 | ||||||||
\(70\) | −2.28892 | −0.273578 | ||||||||
\(71\) | −3.37445 | −0.400473 | −0.200237 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200237 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(72\) | 4.18458 | 0.493158 | ||||||||
\(73\) | −9.34915 | −1.09424 | −0.547118 | − | 0.837056i | \(-0.684275\pi\) | ||||
−0.547118 | + | 0.837056i | \(0.684275\pi\) | |||||||
\(74\) | −16.7373 | −1.94567 | ||||||||
\(75\) | −1.23476 | −0.142577 | ||||||||
\(76\) | 6.69324 | 0.767767 | ||||||||
\(77\) | 4.24991 | 0.484322 | ||||||||
\(78\) | −14.6304 | −1.65657 | ||||||||
\(79\) | −5.57508 | −0.627245 | −0.313623 | − | 0.949548i | \(-0.601543\pi\) | ||||
−0.313623 | + | 0.949548i | \(0.601543\pi\) | |||||||
\(80\) | −0.0137336 | −0.00153546 | ||||||||
\(81\) | −2.39713 | −0.266348 | ||||||||
\(82\) | 22.0016 | 2.42967 | ||||||||
\(83\) | −7.49068 | −0.822208 | −0.411104 | − | 0.911588i | \(-0.634857\pi\) | ||||
−0.411104 | + | 0.911588i | \(0.634857\pi\) | |||||||
\(84\) | 3.99954 | 0.436386 | ||||||||
\(85\) | −5.50025 | −0.596586 | ||||||||
\(86\) | 16.7424 | 1.80538 | ||||||||
\(87\) | −13.2826 | −1.42405 | ||||||||
\(88\) | 12.0539 | 1.28495 | ||||||||
\(89\) | −4.70327 | −0.498546 | −0.249273 | − | 0.968433i | \(-0.580192\pi\) | ||||
−0.249273 | + | 0.968433i | \(0.580192\pi\) | |||||||
\(90\) | −3.37702 | −0.355969 | ||||||||
\(91\) | 5.17662 | 0.542657 | ||||||||
\(92\) | −11.0952 | −1.15675 | ||||||||
\(93\) | 2.76357 | 0.286568 | ||||||||
\(94\) | −29.3361 | −3.02578 | ||||||||
\(95\) | −2.06636 | −0.212005 | ||||||||
\(96\) | −6.96541 | −0.710905 | ||||||||
\(97\) | 8.93925 | 0.907643 | 0.453821 | − | 0.891093i | \(-0.350060\pi\) | ||||
0.453821 | + | 0.891093i | \(0.350060\pi\) | |||||||
\(98\) | −2.28892 | −0.231215 | ||||||||
\(99\) | 6.27022 | 0.630180 | ||||||||
\(100\) | 3.23914 | 0.323914 | ||||||||
\(101\) | −19.9434 | −1.98445 | −0.992223 | − | 0.124472i | \(-0.960276\pi\) | ||||
−0.992223 | + | 0.124472i | \(0.960276\pi\) | |||||||
\(102\) | 15.5451 | 1.53920 | ||||||||
\(103\) | −6.89669 | −0.679551 | −0.339776 | − | 0.940507i | \(-0.610351\pi\) | ||||
−0.339776 | + | 0.940507i | \(0.610351\pi\) | |||||||
\(104\) | 14.6824 | 1.43972 | ||||||||
\(105\) | −1.23476 | −0.120500 | ||||||||
\(106\) | 7.73082 | 0.750883 | ||||||||
\(107\) | −10.9224 | −1.05591 | −0.527953 | − | 0.849274i | \(-0.677040\pi\) | ||||
−0.527953 | + | 0.849274i | \(0.677040\pi\) | |||||||
\(108\) | 17.8995 | 1.72238 | ||||||||
\(109\) | −2.35087 | −0.225172 | −0.112586 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112586 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(110\) | −9.72768 | −0.927498 | ||||||||
\(111\) | −9.02892 | −0.856987 | ||||||||
\(112\) | −0.0137336 | −0.00129770 | ||||||||
\(113\) | −3.12664 | −0.294130 | −0.147065 | − | 0.989127i | \(-0.546983\pi\) | ||||
−0.147065 | + | 0.989127i | \(0.546983\pi\) | |||||||
\(114\) | 5.84007 | 0.546973 | ||||||||
\(115\) | 3.42535 | 0.319415 | ||||||||
\(116\) | 34.8444 | 3.23522 | ||||||||
\(117\) | 7.63747 | 0.706085 | ||||||||
\(118\) | 27.7408 | 2.55375 | ||||||||
\(119\) | −5.50025 | −0.504208 | ||||||||
\(120\) | −3.50211 | −0.319698 | ||||||||
\(121\) | 7.06170 | 0.641973 | ||||||||
\(122\) | 1.80140 | 0.163091 | ||||||||
\(123\) | 11.8688 | 1.07017 | ||||||||
\(124\) | −7.24967 | −0.651039 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.37702 | −0.300848 | ||||||||
\(127\) | 10.0699 | 0.893560 | 0.446780 | − | 0.894644i | \(-0.352571\pi\) | ||||
0.446780 | + | 0.894644i | \(0.352571\pi\) | |||||||
\(128\) | 18.3352 | 1.62062 | ||||||||
\(129\) | 9.03171 | 0.795198 | ||||||||
\(130\) | −11.8489 | −1.03921 | ||||||||
\(131\) | −19.7491 | −1.72548 | −0.862742 | − | 0.505645i | \(-0.831255\pi\) | ||||
−0.862742 | + | 0.505645i | \(0.831255\pi\) | |||||||
\(132\) | 16.9977 | 1.47946 | ||||||||
\(133\) | −2.06636 | −0.179177 | ||||||||
\(134\) | 23.5356 | 2.03317 | ||||||||
\(135\) | −5.52600 | −0.475602 | ||||||||
\(136\) | −15.6003 | −1.33771 | ||||||||
\(137\) | −4.91543 | −0.419953 | −0.209977 | − | 0.977706i | \(-0.567339\pi\) | ||||
−0.209977 | + | 0.977706i | \(0.567339\pi\) | |||||||
\(138\) | −9.68090 | −0.824093 | ||||||||
\(139\) | 3.50610 | 0.297384 | 0.148692 | − | 0.988884i | \(-0.452494\pi\) | ||||
0.148692 | + | 0.988884i | \(0.452494\pi\) | |||||||
\(140\) | 3.23914 | 0.273757 | ||||||||
\(141\) | −15.8253 | −1.33273 | ||||||||
\(142\) | 7.72382 | 0.648169 | ||||||||
\(143\) | 22.0002 | 1.83975 | ||||||||
\(144\) | −0.0202622 | −0.00168851 | ||||||||
\(145\) | −10.7573 | −0.893345 | ||||||||
\(146\) | 21.3994 | 1.77103 | ||||||||
\(147\) | −1.23476 | −0.101841 | ||||||||
\(148\) | 23.6856 | 1.94694 | ||||||||
\(149\) | −12.9909 | −1.06425 | −0.532127 | − | 0.846665i | \(-0.678607\pi\) | ||||
−0.532127 | + | 0.846665i | \(0.678607\pi\) | |||||||
\(150\) | 2.82625 | 0.230763 | ||||||||
\(151\) | −9.83820 | −0.800621 | −0.400310 | − | 0.916380i | \(-0.631098\pi\) | ||||
−0.400310 | + | 0.916380i | \(0.631098\pi\) | |||||||
\(152\) | −5.86079 | −0.475373 | ||||||||
\(153\) | −8.11495 | −0.656055 | ||||||||
\(154\) | −9.72768 | −0.783879 | ||||||||
\(155\) | 2.23815 | 0.179772 | ||||||||
\(156\) | 20.7041 | 1.65766 | ||||||||
\(157\) | 11.6402 | 0.928991 | 0.464496 | − | 0.885575i | \(-0.346236\pi\) | ||||
0.464496 | + | 0.885575i | \(0.346236\pi\) | |||||||
\(158\) | 12.7609 | 1.01520 | ||||||||
\(159\) | 4.17039 | 0.330733 | ||||||||
\(160\) | −5.64113 | −0.445970 | ||||||||
\(161\) | 3.42535 | 0.269955 | ||||||||
\(162\) | 5.48683 | 0.431086 | ||||||||
\(163\) | 12.7824 | 1.00120 | 0.500598 | − | 0.865680i | \(-0.333113\pi\) | ||||
0.500598 | + | 0.865680i | \(0.333113\pi\) | |||||||
\(164\) | −31.1353 | −2.43126 | ||||||||
\(165\) | −5.24760 | −0.408525 | ||||||||
\(166\) | 17.1455 | 1.33075 | ||||||||
\(167\) | −7.41059 | −0.573449 | −0.286724 | − | 0.958013i | \(-0.592566\pi\) | ||||
−0.286724 | + | 0.958013i | \(0.592566\pi\) | |||||||
\(168\) | −3.50211 | −0.270194 | ||||||||
\(169\) | 13.7974 | 1.06134 | ||||||||
\(170\) | 12.5896 | 0.965580 | ||||||||
\(171\) | −3.04867 | −0.233137 | ||||||||
\(172\) | −23.6929 | −1.80657 | ||||||||
\(173\) | 8.94627 | 0.680172 | 0.340086 | − | 0.940394i | \(-0.389544\pi\) | ||||
0.340086 | + | 0.940394i | \(0.389544\pi\) | |||||||
\(174\) | 30.4029 | 2.30483 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −0.0583663 | −0.00439953 | ||||||||
\(177\) | 14.9648 | 1.12482 | ||||||||
\(178\) | 10.7654 | 0.806900 | ||||||||
\(179\) | −16.4716 | −1.23114 | −0.615571 | − | 0.788081i | \(-0.711075\pi\) | ||||
−0.615571 | + | 0.788081i | \(0.711075\pi\) | |||||||
\(180\) | 4.77895 | 0.356202 | ||||||||
\(181\) | 16.8450 | 1.25208 | 0.626038 | − | 0.779792i | \(-0.284675\pi\) | ||||
0.626038 | + | 0.779792i | \(0.284675\pi\) | |||||||
\(182\) | −11.8489 | −0.878296 | ||||||||
\(183\) | 0.971764 | 0.0718349 | ||||||||
\(184\) | 9.71524 | 0.716217 | ||||||||
\(185\) | −7.31231 | −0.537612 | ||||||||
\(186\) | −6.32557 | −0.463813 | ||||||||
\(187\) | −23.3756 | −1.70939 | ||||||||
\(188\) | 41.5146 | 3.02777 | ||||||||
\(189\) | −5.52600 | −0.401957 | ||||||||
\(190\) | 4.72974 | 0.343131 | ||||||||
\(191\) | −20.2823 | −1.46757 | −0.733787 | − | 0.679380i | \(-0.762249\pi\) | ||||
−0.733787 | + | 0.679380i | \(0.762249\pi\) | |||||||
\(192\) | 15.9772 | 1.15305 | ||||||||
\(193\) | −6.35064 | −0.457129 | −0.228565 | − | 0.973529i | \(-0.573403\pi\) | ||||
−0.228565 | + | 0.973529i | \(0.573403\pi\) | |||||||
\(194\) | −20.4612 | −1.46903 | ||||||||
\(195\) | −6.39187 | −0.457731 | ||||||||
\(196\) | 3.23914 | 0.231367 | ||||||||
\(197\) | 3.71252 | 0.264506 | 0.132253 | − | 0.991216i | \(-0.457779\pi\) | ||||
0.132253 | + | 0.991216i | \(0.457779\pi\) | |||||||
\(198\) | −14.3520 | −1.01995 | ||||||||
\(199\) | 13.2835 | 0.941646 | 0.470823 | − | 0.882228i | \(-0.343957\pi\) | ||||
0.470823 | + | 0.882228i | \(0.343957\pi\) | |||||||
\(200\) | −2.83628 | −0.200555 | ||||||||
\(201\) | 12.6963 | 0.895527 | ||||||||
\(202\) | 45.6489 | 3.21184 | ||||||||
\(203\) | −10.7573 | −0.755014 | ||||||||
\(204\) | −21.9985 | −1.54020 | ||||||||
\(205\) | 9.61223 | 0.671347 | ||||||||
\(206\) | 15.7860 | 1.09986 | ||||||||
\(207\) | 5.05368 | 0.351255 | ||||||||
\(208\) | −0.0710934 | −0.00492944 | ||||||||
\(209\) | −8.78186 | −0.607454 | ||||||||
\(210\) | 2.82625 | 0.195030 | ||||||||
\(211\) | 14.1290 | 0.972677 | 0.486339 | − | 0.873770i | \(-0.338332\pi\) | ||||
0.486339 | + | 0.873770i | \(0.338332\pi\) | |||||||
\(212\) | −10.9402 | −0.751375 | ||||||||
\(213\) | 4.16662 | 0.285492 | ||||||||
\(214\) | 25.0004 | 1.70899 | ||||||||
\(215\) | 7.31457 | 0.498849 | ||||||||
\(216\) | −15.6733 | −1.06643 | ||||||||
\(217\) | 2.23815 | 0.151935 | ||||||||
\(218\) | 5.38094 | 0.364443 | ||||||||
\(219\) | 11.5439 | 0.780066 | ||||||||
\(220\) | 13.7660 | 0.928105 | ||||||||
\(221\) | −28.4727 | −1.91528 | ||||||||
\(222\) | 20.6664 | 1.38704 | ||||||||
\(223\) | 25.0249 | 1.67579 | 0.837895 | − | 0.545832i | \(-0.183786\pi\) | ||||
0.837895 | + | 0.545832i | \(0.183786\pi\) | |||||||
\(224\) | −5.64113 | −0.376914 | ||||||||
\(225\) | −1.47538 | −0.0983585 | ||||||||
\(226\) | 7.15663 | 0.476052 | ||||||||
\(227\) | −14.9275 | −0.990774 | −0.495387 | − | 0.868672i | \(-0.664974\pi\) | ||||
−0.495387 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(228\) | −8.26452 | −0.547331 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −7.84033 | −0.516976 | ||||||||
\(231\) | −5.24760 | −0.345267 | ||||||||
\(232\) | −30.5107 | −2.00313 | ||||||||
\(233\) | −20.9874 | −1.37493 | −0.687465 | − | 0.726217i | \(-0.741277\pi\) | ||||
−0.687465 | + | 0.726217i | \(0.741277\pi\) | |||||||
\(234\) | −17.4815 | −1.14280 | ||||||||
\(235\) | −12.8166 | −0.836061 | ||||||||
\(236\) | −39.2571 | −2.55542 | ||||||||
\(237\) | 6.88386 | 0.447155 | ||||||||
\(238\) | 12.5896 | 0.816064 | ||||||||
\(239\) | 2.12440 | 0.137416 | 0.0687081 | − | 0.997637i | \(-0.478112\pi\) | ||||
0.0687081 | + | 0.997637i | \(0.478112\pi\) | |||||||
\(240\) | 0.0169576 | 0.00109461 | ||||||||
\(241\) | 20.3646 | 1.31180 | 0.655899 | − | 0.754849i | \(-0.272290\pi\) | ||||
0.655899 | + | 0.754849i | \(0.272290\pi\) | |||||||
\(242\) | −16.1636 | −1.03904 | ||||||||
\(243\) | −13.6181 | −0.873603 | ||||||||
\(244\) | −2.54923 | −0.163198 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −27.1666 | −1.73208 | ||||||||
\(247\) | −10.6968 | −0.680620 | ||||||||
\(248\) | 6.34801 | 0.403099 | ||||||||
\(249\) | 9.24916 | 0.586141 | ||||||||
\(250\) | 2.28892 | 0.144764 | ||||||||
\(251\) | −6.12192 | −0.386412 | −0.193206 | − | 0.981158i | \(-0.561889\pi\) | ||||
−0.193206 | + | 0.981158i | \(0.561889\pi\) | |||||||
\(252\) | 4.77895 | 0.301046 | ||||||||
\(253\) | 14.5574 | 0.915216 | ||||||||
\(254\) | −23.0492 | −1.44623 | ||||||||
\(255\) | 6.79147 | 0.425299 | ||||||||
\(256\) | −16.0888 | −1.00555 | ||||||||
\(257\) | −8.88979 | −0.554530 | −0.277265 | − | 0.960793i | \(-0.589428\pi\) | ||||
−0.277265 | + | 0.960793i | \(0.589428\pi\) | |||||||
\(258\) | −20.6728 | −1.28703 | ||||||||
\(259\) | −7.31231 | −0.454365 | ||||||||
\(260\) | 16.7678 | 1.03989 | ||||||||
\(261\) | −15.8711 | −0.982395 | ||||||||
\(262\) | 45.2040 | 2.79271 | ||||||||
\(263\) | 23.1737 | 1.42895 | 0.714474 | − | 0.699662i | \(-0.246666\pi\) | ||||
0.714474 | + | 0.699662i | \(0.246666\pi\) | |||||||
\(264\) | −14.8837 | −0.916026 | ||||||||
\(265\) | 3.37750 | 0.207478 | ||||||||
\(266\) | 4.72974 | 0.289999 | ||||||||
\(267\) | 5.80739 | 0.355406 | ||||||||
\(268\) | −33.3062 | −2.03450 | ||||||||
\(269\) | −27.0061 | −1.64659 | −0.823296 | − | 0.567613i | \(-0.807867\pi\) | ||||
−0.823296 | + | 0.567613i | \(0.807867\pi\) | |||||||
\(270\) | 12.6485 | 0.769766 | ||||||||
\(271\) | −4.32393 | −0.262660 | −0.131330 | − | 0.991339i | \(-0.541925\pi\) | ||||
−0.131330 | + | 0.991339i | \(0.541925\pi\) | |||||||
\(272\) | 0.0755380 | 0.00458017 | ||||||||
\(273\) | −6.39187 | −0.386853 | ||||||||
\(274\) | 11.2510 | 0.679698 | ||||||||
\(275\) | −4.24991 | −0.256279 | ||||||||
\(276\) | 13.6998 | 0.824633 | ||||||||
\(277\) | −2.14336 | −0.128782 | −0.0643909 | − | 0.997925i | \(-0.520510\pi\) | ||||
−0.0643909 | + | 0.997925i | \(0.520510\pi\) | |||||||
\(278\) | −8.02517 | −0.481318 | ||||||||
\(279\) | 3.30211 | 0.197692 | ||||||||
\(280\) | −2.83628 | −0.169500 | ||||||||
\(281\) | −12.0655 | −0.719770 | −0.359885 | − | 0.932997i | \(-0.617184\pi\) | ||||
−0.359885 | + | 0.932997i | \(0.617184\pi\) | |||||||
\(282\) | 36.2229 | 2.15704 | ||||||||
\(283\) | −28.3417 | −1.68474 | −0.842371 | − | 0.538898i | \(-0.818841\pi\) | ||||
−0.842371 | + | 0.538898i | \(0.818841\pi\) | |||||||
\(284\) | −10.9303 | −0.648594 | ||||||||
\(285\) | 2.55146 | 0.151135 | ||||||||
\(286\) | −50.3565 | −2.97764 | ||||||||
\(287\) | 9.61223 | 0.567392 | ||||||||
\(288\) | −8.32279 | −0.490425 | ||||||||
\(289\) | 13.2528 | 0.779577 | ||||||||
\(290\) | 24.6226 | 1.44589 | ||||||||
\(291\) | −11.0378 | −0.647047 | ||||||||
\(292\) | −30.2832 | −1.77219 | ||||||||
\(293\) | 13.6939 | 0.800009 | 0.400004 | − | 0.916513i | \(-0.369009\pi\) | ||||
0.400004 | + | 0.916513i | \(0.369009\pi\) | |||||||
\(294\) | 2.82625 | 0.164830 | ||||||||
\(295\) | 12.1196 | 0.705632 | ||||||||
\(296\) | −20.7398 | −1.20547 | ||||||||
\(297\) | −23.4850 | −1.36274 | ||||||||
\(298\) | 29.7350 | 1.72250 | ||||||||
\(299\) | 17.7317 | 1.02545 | ||||||||
\(300\) | −3.99954 | −0.230914 | ||||||||
\(301\) | 7.31457 | 0.421605 | ||||||||
\(302\) | 22.5188 | 1.29581 | ||||||||
\(303\) | 24.6253 | 1.41469 | ||||||||
\(304\) | 0.0283785 | 0.00162762 | ||||||||
\(305\) | 0.787009 | 0.0450640 | ||||||||
\(306\) | 18.5744 | 1.06183 | ||||||||
\(307\) | −16.6186 | −0.948473 | −0.474237 | − | 0.880397i | \(-0.657276\pi\) | ||||
−0.474237 | + | 0.880397i | \(0.657276\pi\) | |||||||
\(308\) | 13.7660 | 0.784392 | ||||||||
\(309\) | 8.51573 | 0.484443 | ||||||||
\(310\) | −5.12293 | −0.290963 | ||||||||
\(311\) | −8.06307 | −0.457215 | −0.228607 | − | 0.973519i | \(-0.573417\pi\) | ||||
−0.228607 | + | 0.973519i | \(0.573417\pi\) | |||||||
\(312\) | −18.1291 | −1.02636 | ||||||||
\(313\) | 28.0551 | 1.58577 | 0.792883 | − | 0.609374i | \(-0.208579\pi\) | ||||
0.792883 | + | 0.609374i | \(0.208579\pi\) | |||||||
\(314\) | −26.6435 | −1.50358 | ||||||||
\(315\) | −1.47538 | −0.0831281 | ||||||||
\(316\) | −18.0584 | −1.01587 | ||||||||
\(317\) | 29.3418 | 1.64800 | 0.823999 | − | 0.566591i | \(-0.191738\pi\) | ||||
0.823999 | + | 0.566591i | \(0.191738\pi\) | |||||||
\(318\) | −9.54567 | −0.535295 | ||||||||
\(319\) | −45.7175 | −2.55969 | ||||||||
\(320\) | 12.9395 | 0.723342 | ||||||||
\(321\) | 13.4865 | 0.752741 | ||||||||
\(322\) | −7.84033 | −0.436925 | ||||||||
\(323\) | 11.3655 | 0.632395 | ||||||||
\(324\) | −7.76463 | −0.431368 | ||||||||
\(325\) | −5.17662 | −0.287147 | ||||||||
\(326\) | −29.2579 | −1.62044 | ||||||||
\(327\) | 2.90275 | 0.160522 | ||||||||
\(328\) | 27.2630 | 1.50535 | ||||||||
\(329\) | −12.8166 | −0.706601 | ||||||||
\(330\) | 12.0113 | 0.661201 | ||||||||
\(331\) | −24.2101 | −1.33071 | −0.665354 | − | 0.746528i | \(-0.731719\pi\) | ||||
−0.665354 | + | 0.746528i | \(0.731719\pi\) | |||||||
\(332\) | −24.2633 | −1.33162 | ||||||||
\(333\) | −10.7884 | −0.591202 | ||||||||
\(334\) | 16.9622 | 0.928131 | ||||||||
\(335\) | 10.2824 | 0.561789 | ||||||||
\(336\) | 0.0169576 | 0.000925112 0 | ||||||||
\(337\) | 8.57543 | 0.467134 | 0.233567 | − | 0.972341i | \(-0.424960\pi\) | ||||
0.233567 | + | 0.972341i | \(0.424960\pi\) | |||||||
\(338\) | −31.5811 | −1.71779 | ||||||||
\(339\) | 3.86064 | 0.209681 | ||||||||
\(340\) | −17.8161 | −0.966212 | ||||||||
\(341\) | 9.51192 | 0.515099 | ||||||||
\(342\) | 6.97815 | 0.377335 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 20.7462 | 1.11856 | ||||||||
\(345\) | −4.22947 | −0.227707 | ||||||||
\(346\) | −20.4773 | −1.10086 | ||||||||
\(347\) | 30.5449 | 1.63973 | 0.819867 | − | 0.572554i | \(-0.194047\pi\) | ||||
0.819867 | + | 0.572554i | \(0.194047\pi\) | |||||||
\(348\) | −43.0243 | −2.30634 | ||||||||
\(349\) | 1.50682 | 0.0806585 | 0.0403292 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403292 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(350\) | 2.28892 | 0.122348 | ||||||||
\(351\) | −28.6060 | −1.52688 | ||||||||
\(352\) | −23.9743 | −1.27783 | ||||||||
\(353\) | 4.33349 | 0.230648 | 0.115324 | − | 0.993328i | \(-0.463209\pi\) | ||||
0.115324 | + | 0.993328i | \(0.463209\pi\) | |||||||
\(354\) | −34.2531 | −1.82053 | ||||||||
\(355\) | 3.37445 | 0.179097 | ||||||||
\(356\) | −15.2345 | −0.807429 | ||||||||
\(357\) | 6.79147 | 0.359443 | ||||||||
\(358\) | 37.7020 | 1.99261 | ||||||||
\(359\) | 32.0004 | 1.68892 | 0.844459 | − | 0.535619i | \(-0.179922\pi\) | ||||
0.844459 | + | 0.535619i | \(0.179922\pi\) | |||||||
\(360\) | −4.18458 | −0.220547 | ||||||||
\(361\) | −14.7301 | −0.775270 | ||||||||
\(362\) | −38.5567 | −2.02650 | ||||||||
\(363\) | −8.71948 | −0.457654 | ||||||||
\(364\) | 16.7678 | 0.878871 | ||||||||
\(365\) | 9.34915 | 0.489357 | ||||||||
\(366\) | −2.22429 | −0.116265 | ||||||||
\(367\) | −13.0534 | −0.681380 | −0.340690 | − | 0.940176i | \(-0.610661\pi\) | ||||
−0.340690 | + | 0.940176i | \(0.610661\pi\) | |||||||
\(368\) | −0.0470422 | −0.00245224 | ||||||||
\(369\) | 14.1817 | 0.738268 | ||||||||
\(370\) | 16.7373 | 0.870129 | ||||||||
\(371\) | 3.37750 | 0.175351 | ||||||||
\(372\) | 8.95157 | 0.464117 | ||||||||
\(373\) | −25.1430 | −1.30186 | −0.650928 | − | 0.759139i | \(-0.725620\pi\) | ||||
−0.650928 | + | 0.759139i | \(0.725620\pi\) | |||||||
\(374\) | 53.5047 | 2.76666 | ||||||||
\(375\) | 1.23476 | 0.0637625 | ||||||||
\(376\) | −36.3514 | −1.87468 | ||||||||
\(377\) | −55.6865 | −2.86800 | ||||||||
\(378\) | 12.6485 | 0.650571 | ||||||||
\(379\) | 1.88304 | 0.0967254 | 0.0483627 | − | 0.998830i | \(-0.484600\pi\) | ||||
0.0483627 | + | 0.998830i | \(0.484600\pi\) | |||||||
\(380\) | −6.69324 | −0.343356 | ||||||||
\(381\) | −12.4339 | −0.637007 | ||||||||
\(382\) | 46.4244 | 2.37528 | ||||||||
\(383\) | 33.1675 | 1.69478 | 0.847389 | − | 0.530972i | \(-0.178173\pi\) | ||||
0.847389 | + | 0.530972i | \(0.178173\pi\) | |||||||
\(384\) | −22.6396 | −1.15532 | ||||||||
\(385\) | −4.24991 | −0.216595 | ||||||||
\(386\) | 14.5361 | 0.739867 | ||||||||
\(387\) | 10.7917 | 0.548575 | ||||||||
\(388\) | 28.9554 | 1.46999 | ||||||||
\(389\) | −15.2910 | −0.775285 | −0.387643 | − | 0.921810i | \(-0.626711\pi\) | ||||
−0.387643 | + | 0.921810i | \(0.626711\pi\) | |||||||
\(390\) | 14.6304 | 0.740841 | ||||||||
\(391\) | −18.8403 | −0.952794 | ||||||||
\(392\) | −2.83628 | −0.143254 | ||||||||
\(393\) | 24.3853 | 1.23007 | ||||||||
\(394\) | −8.49766 | −0.428106 | ||||||||
\(395\) | 5.57508 | 0.280513 | ||||||||
\(396\) | 20.3101 | 1.02062 | ||||||||
\(397\) | 23.2690 | 1.16784 | 0.583918 | − | 0.811813i | \(-0.301519\pi\) | ||||
0.583918 | + | 0.811813i | \(0.301519\pi\) | |||||||
\(398\) | −30.4049 | −1.52406 | ||||||||
\(399\) | 2.55146 | 0.127733 | ||||||||
\(400\) | 0.0137336 | 0.000686678 0 | ||||||||
\(401\) | 19.5247 | 0.975018 | 0.487509 | − | 0.873118i | \(-0.337906\pi\) | ||||
0.487509 | + | 0.873118i | \(0.337906\pi\) | |||||||
\(402\) | −29.0607 | −1.44942 | ||||||||
\(403\) | 11.5860 | 0.577142 | ||||||||
\(404\) | −64.5995 | −3.21395 | ||||||||
\(405\) | 2.39713 | 0.119114 | ||||||||
\(406\) | 24.6226 | 1.22200 | ||||||||
\(407\) | −31.0766 | −1.54041 | ||||||||
\(408\) | 19.2625 | 0.953637 | ||||||||
\(409\) | 13.2205 | 0.653712 | 0.326856 | − | 0.945074i | \(-0.394011\pi\) | ||||
0.326856 | + | 0.945074i | \(0.394011\pi\) | |||||||
\(410\) | −22.0016 | −1.08658 | ||||||||
\(411\) | 6.06935 | 0.299379 | ||||||||
\(412\) | −22.3393 | −1.10058 | ||||||||
\(413\) | 12.1196 | 0.596368 | ||||||||
\(414\) | −11.5674 | −0.568509 | ||||||||
\(415\) | 7.49068 | 0.367703 | ||||||||
\(416\) | −29.2020 | −1.43174 | ||||||||
\(417\) | −4.32918 | −0.212001 | ||||||||
\(418\) | 20.1009 | 0.983169 | ||||||||
\(419\) | −21.9974 | −1.07464 | −0.537321 | − | 0.843378i | \(-0.680564\pi\) | ||||
−0.537321 | + | 0.843378i | \(0.680564\pi\) | |||||||
\(420\) | −3.99954 | −0.195158 | ||||||||
\(421\) | −7.43644 | −0.362430 | −0.181215 | − | 0.983444i | \(-0.558003\pi\) | ||||
−0.181215 | + | 0.983444i | \(0.558003\pi\) | |||||||
\(422\) | −32.3400 | −1.57429 | ||||||||
\(423\) | −18.9093 | −0.919401 | ||||||||
\(424\) | 9.57954 | 0.465224 | ||||||||
\(425\) | 5.50025 | 0.266802 | ||||||||
\(426\) | −9.53704 | −0.462071 | ||||||||
\(427\) | 0.787009 | 0.0380860 | ||||||||
\(428\) | −35.3791 | −1.71011 | ||||||||
\(429\) | −27.1648 | −1.31153 | ||||||||
\(430\) | −16.7424 | −0.807392 | ||||||||
\(431\) | 25.4620 | 1.22646 | 0.613230 | − | 0.789904i | \(-0.289870\pi\) | ||||
0.613230 | + | 0.789904i | \(0.289870\pi\) | |||||||
\(432\) | 0.0758916 | 0.00365134 | ||||||||
\(433\) | −30.3596 | −1.45899 | −0.729494 | − | 0.683987i | \(-0.760245\pi\) | ||||
−0.729494 | + | 0.683987i | \(0.760245\pi\) | |||||||
\(434\) | −5.12293 | −0.245909 | ||||||||
\(435\) | 13.2826 | 0.636854 | ||||||||
\(436\) | −7.61478 | −0.364682 | ||||||||
\(437\) | −7.07802 | −0.338587 | ||||||||
\(438\) | −26.4231 | −1.26254 | ||||||||
\(439\) | −23.8409 | −1.13786 | −0.568932 | − | 0.822385i | \(-0.692643\pi\) | ||||
−0.568932 | + | 0.822385i | \(0.692643\pi\) | |||||||
\(440\) | −12.0539 | −0.574648 | ||||||||
\(441\) | −1.47538 | −0.0702561 | ||||||||
\(442\) | 65.1717 | 3.09990 | ||||||||
\(443\) | −33.5119 | −1.59220 | −0.796100 | − | 0.605165i | \(-0.793107\pi\) | ||||
−0.796100 | + | 0.605165i | \(0.793107\pi\) | |||||||
\(444\) | −29.2459 | −1.38795 | ||||||||
\(445\) | 4.70327 | 0.222956 | ||||||||
\(446\) | −57.2798 | −2.71228 | ||||||||
\(447\) | 16.0406 | 0.758693 | ||||||||
\(448\) | 12.9395 | 0.611335 | ||||||||
\(449\) | 27.9818 | 1.32054 | 0.660270 | − | 0.751028i | \(-0.270442\pi\) | ||||
0.660270 | + | 0.751028i | \(0.270442\pi\) | |||||||
\(450\) | 3.37702 | 0.159194 | ||||||||
\(451\) | 40.8511 | 1.92360 | ||||||||
\(452\) | −10.1276 | −0.476364 | ||||||||
\(453\) | 12.1478 | 0.570752 | ||||||||
\(454\) | 34.1678 | 1.60358 | ||||||||
\(455\) | −5.17662 | −0.242684 | ||||||||
\(456\) | 7.23665 | 0.338887 | ||||||||
\(457\) | 13.7035 | 0.641024 | 0.320512 | − | 0.947244i | \(-0.396145\pi\) | ||||
0.320512 | + | 0.947244i | \(0.396145\pi\) | |||||||
\(458\) | −2.28892 | −0.106954 | ||||||||
\(459\) | 30.3944 | 1.41869 | ||||||||
\(460\) | 11.0952 | 0.517315 | ||||||||
\(461\) | −2.60658 | −0.121401 | −0.0607003 | − | 0.998156i | \(-0.519333\pi\) | ||||
−0.0607003 | + | 0.998156i | \(0.519333\pi\) | |||||||
\(462\) | 12.0113 | 0.558817 | ||||||||
\(463\) | −3.79212 | −0.176235 | −0.0881174 | − | 0.996110i | \(-0.528085\pi\) | ||||
−0.0881174 | + | 0.996110i | \(0.528085\pi\) | |||||||
\(464\) | 0.147736 | 0.00685847 | ||||||||
\(465\) | −2.76357 | −0.128157 | ||||||||
\(466\) | 48.0384 | 2.22534 | ||||||||
\(467\) | 5.97820 | 0.276638 | 0.138319 | − | 0.990388i | \(-0.455830\pi\) | ||||
0.138319 | + | 0.990388i | \(0.455830\pi\) | |||||||
\(468\) | 24.7388 | 1.14355 | ||||||||
\(469\) | 10.2824 | 0.474798 | ||||||||
\(470\) | 29.3361 | 1.35317 | ||||||||
\(471\) | −14.3728 | −0.662266 | ||||||||
\(472\) | 34.3747 | 1.58222 | ||||||||
\(473\) | 31.0862 | 1.42935 | ||||||||
\(474\) | −15.7566 | −0.723724 | ||||||||
\(475\) | 2.06636 | 0.0948113 | ||||||||
\(476\) | −17.8161 | −0.816599 | ||||||||
\(477\) | 4.98309 | 0.228160 | ||||||||
\(478\) | −4.86258 | −0.222409 | ||||||||
\(479\) | 8.01970 | 0.366429 | 0.183215 | − | 0.983073i | \(-0.441350\pi\) | ||||
0.183215 | + | 0.983073i | \(0.441350\pi\) | |||||||
\(480\) | 6.96541 | 0.317926 | ||||||||
\(481\) | −37.8531 | −1.72595 | ||||||||
\(482\) | −46.6128 | −2.12316 | ||||||||
\(483\) | −4.22947 | −0.192447 | ||||||||
\(484\) | 22.8738 | 1.03972 | ||||||||
\(485\) | −8.93925 | −0.405910 | ||||||||
\(486\) | 31.1708 | 1.41393 | ||||||||
\(487\) | −28.5490 | −1.29368 | −0.646839 | − | 0.762627i | \(-0.723909\pi\) | ||||
−0.646839 | + | 0.762627i | \(0.723909\pi\) | |||||||
\(488\) | 2.23218 | 0.101046 | ||||||||
\(489\) | −15.7832 | −0.713739 | ||||||||
\(490\) | 2.28892 | 0.103403 | ||||||||
\(491\) | −10.0342 | −0.452837 | −0.226418 | − | 0.974030i | \(-0.572702\pi\) | ||||
−0.226418 | + | 0.974030i | \(0.572702\pi\) | |||||||
\(492\) | 38.4445 | 1.73321 | ||||||||
\(493\) | 59.1679 | 2.66479 | ||||||||
\(494\) | 24.4841 | 1.10159 | ||||||||
\(495\) | −6.27022 | −0.281825 | ||||||||
\(496\) | −0.0307377 | −0.00138016 | ||||||||
\(497\) | 3.37445 | 0.151365 | ||||||||
\(498\) | −21.1705 | −0.948675 | ||||||||
\(499\) | 27.5309 | 1.23245 | 0.616226 | − | 0.787570i | \(-0.288661\pi\) | ||||
0.616226 | + | 0.787570i | \(0.288661\pi\) | |||||||
\(500\) | −3.23914 | −0.144859 | ||||||||
\(501\) | 9.15027 | 0.408804 | ||||||||
\(502\) | 14.0126 | 0.625412 | ||||||||
\(503\) | 26.5894 | 1.18556 | 0.592781 | − | 0.805364i | \(-0.298030\pi\) | ||||
0.592781 | + | 0.805364i | \(0.298030\pi\) | |||||||
\(504\) | −4.18458 | −0.186396 | ||||||||
\(505\) | 19.9434 | 0.887471 | ||||||||
\(506\) | −33.3207 | −1.48128 | ||||||||
\(507\) | −17.0365 | −0.756615 | ||||||||
\(508\) | 32.6178 | 1.44718 | ||||||||
\(509\) | 0.673363 | 0.0298463 | 0.0149231 | − | 0.999889i | \(-0.495250\pi\) | ||||
0.0149231 | + | 0.999889i | \(0.495250\pi\) | |||||||
\(510\) | −15.5451 | −0.688349 | ||||||||
\(511\) | 9.34915 | 0.413582 | ||||||||
\(512\) | 0.155377 | 0.00686676 | ||||||||
\(513\) | 11.4187 | 0.504149 | ||||||||
\(514\) | 20.3480 | 0.897511 | ||||||||
\(515\) | 6.89669 | 0.303905 | ||||||||
\(516\) | 29.2549 | 1.28788 | ||||||||
\(517\) | −54.4692 | −2.39555 | ||||||||
\(518\) | 16.7373 | 0.735393 | ||||||||
\(519\) | −11.0465 | −0.484886 | ||||||||
\(520\) | −14.6824 | −0.643864 | ||||||||
\(521\) | −24.3699 | −1.06767 | −0.533833 | − | 0.845590i | \(-0.679249\pi\) | ||||
−0.533833 | + | 0.845590i | \(0.679249\pi\) | |||||||
\(522\) | 36.3276 | 1.59001 | ||||||||
\(523\) | −6.08298 | −0.265990 | −0.132995 | − | 0.991117i | \(-0.542459\pi\) | ||||
−0.132995 | + | 0.991117i | \(0.542459\pi\) | |||||||
\(524\) | −63.9699 | −2.79454 | ||||||||
\(525\) | 1.23476 | 0.0538892 | ||||||||
\(526\) | −53.0426 | −2.31277 | ||||||||
\(527\) | −12.3104 | −0.536249 | ||||||||
\(528\) | 0.0720682 | 0.00313636 | ||||||||
\(529\) | −11.2670 | −0.489869 | ||||||||
\(530\) | −7.73082 | −0.335805 | ||||||||
\(531\) | 17.8810 | 0.775970 | ||||||||
\(532\) | −6.69324 | −0.290189 | ||||||||
\(533\) | 49.7589 | 2.15530 | ||||||||
\(534\) | −13.2926 | −0.575228 | ||||||||
\(535\) | 10.9224 | 0.472215 | ||||||||
\(536\) | 29.1638 | 1.25969 | ||||||||
\(537\) | 20.3384 | 0.877665 | ||||||||
\(538\) | 61.8147 | 2.66502 | ||||||||
\(539\) | −4.24991 | −0.183056 | ||||||||
\(540\) | −17.8995 | −0.770270 | ||||||||
\(541\) | 15.1637 | 0.651938 | 0.325969 | − | 0.945380i | \(-0.394309\pi\) | ||||
0.325969 | + | 0.945380i | \(0.394309\pi\) | |||||||
\(542\) | 9.89711 | 0.425117 | ||||||||
\(543\) | −20.7994 | −0.892589 | ||||||||
\(544\) | 31.0276 | 1.33030 | ||||||||
\(545\) | 2.35087 | 0.100700 | ||||||||
\(546\) | 14.6304 | 0.626125 | ||||||||
\(547\) | 26.8278 | 1.14707 | 0.573537 | − | 0.819180i | \(-0.305571\pi\) | ||||
0.573537 | + | 0.819180i | \(0.305571\pi\) | |||||||
\(548\) | −15.9217 | −0.680143 | ||||||||
\(549\) | 1.16114 | 0.0495561 | ||||||||
\(550\) | 9.72768 | 0.414790 | ||||||||
\(551\) | 22.2285 | 0.946966 | ||||||||
\(552\) | −11.9960 | −0.510582 | ||||||||
\(553\) | 5.57508 | 0.237076 | ||||||||
\(554\) | 4.90596 | 0.208434 | ||||||||
\(555\) | 9.02892 | 0.383256 | ||||||||
\(556\) | 11.3567 | 0.481633 | ||||||||
\(557\) | 16.6723 | 0.706429 | 0.353214 | − | 0.935542i | \(-0.385089\pi\) | ||||
0.353214 | + | 0.935542i | \(0.385089\pi\) | |||||||
\(558\) | −7.55826 | −0.319967 | ||||||||
\(559\) | 37.8648 | 1.60151 | ||||||||
\(560\) | 0.0137336 | 0.000580348 0 | ||||||||
\(561\) | 28.8631 | 1.21860 | ||||||||
\(562\) | 27.6170 | 1.16495 | ||||||||
\(563\) | −6.38946 | −0.269284 | −0.134642 | − | 0.990894i | \(-0.542988\pi\) | ||||
−0.134642 | + | 0.990894i | \(0.542988\pi\) | |||||||
\(564\) | −51.2605 | −2.15845 | ||||||||
\(565\) | 3.12664 | 0.131539 | ||||||||
\(566\) | 64.8719 | 2.72677 | ||||||||
\(567\) | 2.39713 | 0.100670 | ||||||||
\(568\) | 9.57087 | 0.401585 | ||||||||
\(569\) | −13.6707 | −0.573106 | −0.286553 | − | 0.958064i | \(-0.592510\pi\) | ||||
−0.286553 | + | 0.958064i | \(0.592510\pi\) | |||||||
\(570\) | −5.84007 | −0.244614 | ||||||||
\(571\) | 42.9758 | 1.79848 | 0.899240 | − | 0.437456i | \(-0.144120\pi\) | ||||
0.899240 | + | 0.437456i | \(0.144120\pi\) | |||||||
\(572\) | 71.2615 | 2.97959 | ||||||||
\(573\) | 25.0437 | 1.04621 | ||||||||
\(574\) | −22.0016 | −0.918329 | ||||||||
\(575\) | −3.42535 | −0.142847 | ||||||||
\(576\) | 19.0907 | 0.795445 | ||||||||
\(577\) | −29.2570 | −1.21798 | −0.608992 | − | 0.793177i | \(-0.708426\pi\) | ||||
−0.608992 | + | 0.793177i | \(0.708426\pi\) | |||||||
\(578\) | −30.3346 | −1.26175 | ||||||||
\(579\) | 7.84150 | 0.325881 | ||||||||
\(580\) | −34.8444 | −1.44683 | ||||||||
\(581\) | 7.49068 | 0.310766 | ||||||||
\(582\) | 25.2646 | 1.04725 | ||||||||
\(583\) | 14.3541 | 0.594485 | ||||||||
\(584\) | 26.5168 | 1.09727 | ||||||||
\(585\) | −7.63747 | −0.315771 | ||||||||
\(586\) | −31.3443 | −1.29482 | ||||||||
\(587\) | −40.0257 | −1.65204 | −0.826020 | − | 0.563641i | \(-0.809400\pi\) | ||||
−0.826020 | + | 0.563641i | \(0.809400\pi\) | |||||||
\(588\) | −3.99954 | −0.164938 | ||||||||
\(589\) | −4.62483 | −0.190563 | ||||||||
\(590\) | −27.7408 | −1.14207 | ||||||||
\(591\) | −4.58406 | −0.188563 | ||||||||
\(592\) | 0.100424 | 0.00412740 | ||||||||
\(593\) | −41.4179 | −1.70083 | −0.850414 | − | 0.526114i | \(-0.823649\pi\) | ||||
−0.850414 | + | 0.526114i | \(0.823649\pi\) | |||||||
\(594\) | 53.7551 | 2.20560 | ||||||||
\(595\) | 5.50025 | 0.225488 | ||||||||
\(596\) | −42.0792 | −1.72363 | ||||||||
\(597\) | −16.4019 | −0.671287 | ||||||||
\(598\) | −40.5864 | −1.65970 | ||||||||
\(599\) | −38.2839 | −1.56424 | −0.782118 | − | 0.623130i | \(-0.785861\pi\) | ||||
−0.782118 | + | 0.623130i | \(0.785861\pi\) | |||||||
\(600\) | 3.50211 | 0.142973 | ||||||||
\(601\) | 4.09602 | 0.167080 | 0.0835401 | − | 0.996504i | \(-0.473377\pi\) | ||||
0.0835401 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(602\) | −16.7424 | −0.682371 | ||||||||
\(603\) | 15.1705 | 0.617789 | ||||||||
\(604\) | −31.8673 | −1.29666 | ||||||||
\(605\) | −7.06170 | −0.287099 | ||||||||
\(606\) | −56.3652 | −2.28968 | ||||||||
\(607\) | 25.4079 | 1.03128 | 0.515638 | − | 0.856807i | \(-0.327555\pi\) | ||||
0.515638 | + | 0.856807i | \(0.327555\pi\) | |||||||
\(608\) | 11.6566 | 0.472738 | ||||||||
\(609\) | 13.2826 | 0.538240 | ||||||||
\(610\) | −1.80140 | −0.0729365 | ||||||||
\(611\) | −66.3466 | −2.68410 | ||||||||
\(612\) | −26.2854 | −1.06253 | ||||||||
\(613\) | −16.6802 | −0.673708 | −0.336854 | − | 0.941557i | \(-0.609363\pi\) | ||||
−0.336854 | + | 0.941557i | \(0.609363\pi\) | |||||||
\(614\) | 38.0386 | 1.53511 | ||||||||
\(615\) | −11.8688 | −0.478595 | ||||||||
\(616\) | −12.0539 | −0.485666 | ||||||||
\(617\) | 19.7477 | 0.795011 | 0.397505 | − | 0.917600i | \(-0.369876\pi\) | ||||
0.397505 | + | 0.917600i | \(0.369876\pi\) | |||||||
\(618\) | −19.4918 | −0.784075 | ||||||||
\(619\) | 30.1313 | 1.21108 | 0.605540 | − | 0.795815i | \(-0.292957\pi\) | ||||
0.605540 | + | 0.795815i | \(0.292957\pi\) | |||||||
\(620\) | 7.24967 | 0.291154 | ||||||||
\(621\) | −18.9285 | −0.759573 | ||||||||
\(622\) | 18.4557 | 0.740006 | ||||||||
\(623\) | 4.70327 | 0.188432 | ||||||||
\(624\) | 0.0877830 | 0.00351413 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −64.2157 | −2.56658 | ||||||||
\(627\) | 10.8435 | 0.433046 | ||||||||
\(628\) | 37.7043 | 1.50457 | ||||||||
\(629\) | 40.2196 | 1.60366 | ||||||||
\(630\) | 3.37702 | 0.134544 | ||||||||
\(631\) | −6.00301 | −0.238976 | −0.119488 | − | 0.992836i | \(-0.538125\pi\) | ||||
−0.119488 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(632\) | 15.8125 | 0.628987 | ||||||||
\(633\) | −17.4458 | −0.693409 | ||||||||
\(634\) | −67.1609 | −2.66730 | ||||||||
\(635\) | −10.0699 | −0.399612 | ||||||||
\(636\) | 13.5085 | 0.535645 | ||||||||
\(637\) | −5.17662 | −0.205105 | ||||||||
\(638\) | 104.644 | 4.14288 | ||||||||
\(639\) | 4.97858 | 0.196950 | ||||||||
\(640\) | −18.3352 | −0.724764 | ||||||||
\(641\) | −10.4335 | −0.412100 | −0.206050 | − | 0.978541i | \(-0.566061\pi\) | ||||
−0.206050 | + | 0.978541i | \(0.566061\pi\) | |||||||
\(642\) | −30.8694 | −1.21832 | ||||||||
\(643\) | 42.9244 | 1.69277 | 0.846386 | − | 0.532570i | \(-0.178774\pi\) | ||||
0.846386 | + | 0.532570i | \(0.178774\pi\) | |||||||
\(644\) | 11.0952 | 0.437211 | ||||||||
\(645\) | −9.03171 | −0.355623 | ||||||||
\(646\) | −26.0148 | −1.02354 | ||||||||
\(647\) | 12.1895 | 0.479218 | 0.239609 | − | 0.970869i | \(-0.422981\pi\) | ||||
0.239609 | + | 0.970869i | \(0.422981\pi\) | |||||||
\(648\) | 6.79893 | 0.267087 | ||||||||
\(649\) | 51.5073 | 2.02184 | ||||||||
\(650\) | 11.8489 | 0.464750 | ||||||||
\(651\) | −2.76357 | −0.108313 | ||||||||
\(652\) | 41.4040 | 1.62151 | ||||||||
\(653\) | 14.8871 | 0.582578 | 0.291289 | − | 0.956635i | \(-0.405916\pi\) | ||||
0.291289 | + | 0.956635i | \(0.405916\pi\) | |||||||
\(654\) | −6.64414 | −0.259807 | ||||||||
\(655\) | 19.7491 | 0.771660 | ||||||||
\(656\) | −0.132010 | −0.00515413 | ||||||||
\(657\) | 13.7935 | 0.538137 | ||||||||
\(658\) | 29.3361 | 1.14364 | ||||||||
\(659\) | 15.5012 | 0.603840 | 0.301920 | − | 0.953333i | \(-0.402372\pi\) | ||||
0.301920 | + | 0.953333i | \(0.402372\pi\) | |||||||
\(660\) | −16.9977 | −0.661634 | ||||||||
\(661\) | 27.9806 | 1.08832 | 0.544159 | − | 0.838982i | \(-0.316849\pi\) | ||||
0.544159 | + | 0.838982i | \(0.316849\pi\) | |||||||
\(662\) | 55.4149 | 2.15376 | ||||||||
\(663\) | 35.1569 | 1.36538 | ||||||||
\(664\) | 21.2457 | 0.824491 | ||||||||
\(665\) | 2.06636 | 0.0801302 | ||||||||
\(666\) | 24.6938 | 0.956865 | ||||||||
\(667\) | −36.8475 | −1.42674 | ||||||||
\(668\) | −24.0039 | −0.928739 | ||||||||
\(669\) | −30.8996 | −1.19465 | ||||||||
\(670\) | −23.5356 | −0.909260 | ||||||||
\(671\) | 3.34472 | 0.129121 | ||||||||
\(672\) | 6.96541 | 0.268697 | ||||||||
\(673\) | −11.0603 | −0.426344 | −0.213172 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213172 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(674\) | −19.6284 | −0.756059 | ||||||||
\(675\) | 5.52600 | 0.212696 | ||||||||
\(676\) | 44.6917 | 1.71891 | ||||||||
\(677\) | −13.0447 | −0.501347 | −0.250673 | − | 0.968072i | \(-0.580652\pi\) | ||||
−0.250673 | + | 0.968072i | \(0.580652\pi\) | |||||||
\(678\) | −8.83669 | −0.339371 | ||||||||
\(679\) | −8.93925 | −0.343057 | ||||||||
\(680\) | 15.6003 | 0.598243 | ||||||||
\(681\) | 18.4318 | 0.706310 | ||||||||
\(682\) | −21.7720 | −0.833692 | ||||||||
\(683\) | −35.3192 | −1.35145 | −0.675726 | − | 0.737153i | \(-0.736170\pi\) | ||||
−0.675726 | + | 0.737153i | \(0.736170\pi\) | |||||||
\(684\) | −9.87505 | −0.377582 | ||||||||
\(685\) | 4.91543 | 0.187809 | ||||||||
\(686\) | 2.28892 | 0.0873912 | ||||||||
\(687\) | −1.23476 | −0.0471089 | ||||||||
\(688\) | −0.100455 | −0.00382981 | ||||||||
\(689\) | 17.4840 | 0.666089 | ||||||||
\(690\) | 9.68090 | 0.368545 | ||||||||
\(691\) | 34.4836 | 1.31182 | 0.655910 | − | 0.754839i | \(-0.272285\pi\) | ||||
0.655910 | + | 0.754839i | \(0.272285\pi\) | |||||||
\(692\) | 28.9782 | 1.10159 | ||||||||
\(693\) | −6.27022 | −0.238186 | ||||||||
\(694\) | −69.9146 | −2.65392 | ||||||||
\(695\) | −3.50610 | −0.132994 | ||||||||
\(696\) | 37.6733 | 1.42800 | ||||||||
\(697\) | −52.8697 | −2.00258 | ||||||||
\(698\) | −3.44899 | −0.130546 | ||||||||
\(699\) | 25.9143 | 0.980170 | ||||||||
\(700\) | −3.23914 | −0.122428 | ||||||||
\(701\) | 42.9267 | 1.62132 | 0.810660 | − | 0.585518i | \(-0.199109\pi\) | ||||
0.810660 | + | 0.585518i | \(0.199109\pi\) | |||||||
\(702\) | 65.4768 | 2.47126 | ||||||||
\(703\) | 15.1099 | 0.569881 | ||||||||
\(704\) | 54.9918 | 2.07258 | ||||||||
\(705\) | 15.8253 | 0.596017 | ||||||||
\(706\) | −9.91899 | −0.373306 | ||||||||
\(707\) | 19.9434 | 0.750050 | ||||||||
\(708\) | 48.4730 | 1.82173 | ||||||||
\(709\) | −3.85826 | −0.144900 | −0.0724499 | − | 0.997372i | \(-0.523082\pi\) | ||||
−0.0724499 | + | 0.997372i | \(0.523082\pi\) | |||||||
\(710\) | −7.72382 | −0.289870 | ||||||||
\(711\) | 8.22534 | 0.308474 | ||||||||
\(712\) | 13.3398 | 0.499930 | ||||||||
\(713\) | 7.66643 | 0.287110 | ||||||||
\(714\) | −15.5451 | −0.581761 | ||||||||
\(715\) | −22.0002 | −0.822759 | ||||||||
\(716\) | −53.3537 | −1.99392 | ||||||||
\(717\) | −2.62312 | −0.0979622 | ||||||||
\(718\) | −73.2463 | −2.73353 | ||||||||
\(719\) | −24.5534 | −0.915688 | −0.457844 | − | 0.889033i | \(-0.651378\pi\) | ||||
−0.457844 | + | 0.889033i | \(0.651378\pi\) | |||||||
\(720\) | 0.0202622 | 0.000755127 0 | ||||||||
\(721\) | 6.89669 | 0.256846 | ||||||||
\(722\) | 33.7160 | 1.25478 | ||||||||
\(723\) | −25.1453 | −0.935163 | ||||||||
\(724\) | 54.5632 | 2.02782 | ||||||||
\(725\) | 10.7573 | 0.399516 | ||||||||
\(726\) | 19.9582 | 0.740717 | ||||||||
\(727\) | −5.40848 | −0.200590 | −0.100295 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100295 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(728\) | −14.6824 | −0.544164 | ||||||||
\(729\) | 24.0065 | 0.889128 | ||||||||
\(730\) | −21.3994 | −0.792028 | ||||||||
\(731\) | −40.2320 | −1.48803 | ||||||||
\(732\) | 3.14768 | 0.116342 | ||||||||
\(733\) | 14.3497 | 0.530018 | 0.265009 | − | 0.964246i | \(-0.414625\pi\) | ||||
0.265009 | + | 0.964246i | \(0.414625\pi\) | |||||||
\(734\) | 29.8780 | 1.10282 | ||||||||
\(735\) | 1.23476 | 0.0455447 | ||||||||
\(736\) | −19.3228 | −0.712248 | ||||||||
\(737\) | 43.6993 | 1.60969 | ||||||||
\(738\) | −32.4606 | −1.19489 | ||||||||
\(739\) | 0.357320 | 0.0131442 | 0.00657212 | − | 0.999978i | \(-0.497908\pi\) | ||||
0.00657212 | + | 0.999978i | \(0.497908\pi\) | |||||||
\(740\) | −23.6856 | −0.870699 | ||||||||
\(741\) | 13.2079 | 0.485205 | ||||||||
\(742\) | −7.73082 | −0.283807 | ||||||||
\(743\) | 17.4493 | 0.640153 | 0.320076 | − | 0.947392i | \(-0.396291\pi\) | ||||
0.320076 | + | 0.947392i | \(0.396291\pi\) | |||||||
\(744\) | −7.83825 | −0.287364 | ||||||||
\(745\) | 12.9909 | 0.475949 | ||||||||
\(746\) | 57.5503 | 2.10706 | ||||||||
\(747\) | 11.0516 | 0.404356 | ||||||||
\(748\) | −75.7167 | −2.76848 | ||||||||
\(749\) | 10.9224 | 0.399095 | ||||||||
\(750\) | −2.82625 | −0.103200 | ||||||||
\(751\) | −34.7459 | −1.26790 | −0.633949 | − | 0.773375i | \(-0.718567\pi\) | ||||
−0.633949 | + | 0.773375i | \(0.718567\pi\) | |||||||
\(752\) | 0.176017 | 0.00641868 | ||||||||
\(753\) | 7.55908 | 0.275468 | ||||||||
\(754\) | 127.462 | 4.64188 | ||||||||
\(755\) | 9.83820 | 0.358049 | ||||||||
\(756\) | −17.8995 | −0.650997 | ||||||||
\(757\) | 11.6872 | 0.424777 | 0.212389 | − | 0.977185i | \(-0.431876\pi\) | ||||
0.212389 | + | 0.977185i | \(0.431876\pi\) | |||||||
\(758\) | −4.31013 | −0.156551 | ||||||||
\(759\) | −17.9748 | −0.652446 | ||||||||
\(760\) | 5.86079 | 0.212593 | ||||||||
\(761\) | −18.1052 | −0.656311 | −0.328156 | − | 0.944624i | \(-0.606427\pi\) | ||||
−0.328156 | + | 0.944624i | \(0.606427\pi\) | |||||||
\(762\) | 28.4601 | 1.03100 | ||||||||
\(763\) | 2.35087 | 0.0851071 | ||||||||
\(764\) | −65.6971 | −2.37684 | ||||||||
\(765\) | 8.11495 | 0.293397 | ||||||||
\(766\) | −75.9176 | −2.74301 | ||||||||
\(767\) | 62.7387 | 2.26536 | ||||||||
\(768\) | 19.8657 | 0.716842 | ||||||||
\(769\) | −40.6786 | −1.46691 | −0.733455 | − | 0.679738i | \(-0.762093\pi\) | ||||
−0.733455 | + | 0.679738i | \(0.762093\pi\) | |||||||
\(770\) | 9.72768 | 0.350561 | ||||||||
\(771\) | 10.9767 | 0.395317 | ||||||||
\(772\) | −20.5706 | −0.740352 | ||||||||
\(773\) | 46.0140 | 1.65501 | 0.827505 | − | 0.561459i | \(-0.189760\pi\) | ||||
0.827505 | + | 0.561459i | \(0.189760\pi\) | |||||||
\(774\) | −24.7014 | −0.887874 | ||||||||
\(775\) | −2.23815 | −0.0803966 | ||||||||
\(776\) | −25.3542 | −0.910163 | ||||||||
\(777\) | 9.02892 | 0.323911 | ||||||||
\(778\) | 34.9998 | 1.25481 | ||||||||
\(779\) | −19.8624 | −0.711643 | ||||||||
\(780\) | −20.7041 | −0.741327 | ||||||||
\(781\) | 14.3411 | 0.513164 | ||||||||
\(782\) | 43.1238 | 1.54210 | ||||||||
\(783\) | 59.4448 | 2.12439 | ||||||||
\(784\) | 0.0137336 | 0.000490484 0 | ||||||||
\(785\) | −11.6402 | −0.415458 | ||||||||
\(786\) | −55.8159 | −1.99089 | ||||||||
\(787\) | 21.5149 | 0.766923 | 0.383462 | − | 0.923557i | \(-0.374732\pi\) | ||||
0.383462 | + | 0.923557i | \(0.374732\pi\) | |||||||
\(788\) | 12.0254 | 0.428386 | ||||||||
\(789\) | −28.6138 | −1.01868 | ||||||||
\(790\) | −12.7609 | −0.454012 | ||||||||
\(791\) | 3.12664 | 0.111171 | ||||||||
\(792\) | −17.7841 | −0.631930 | ||||||||
\(793\) | 4.07405 | 0.144674 | ||||||||
\(794\) | −53.2607 | −1.89015 | ||||||||
\(795\) | −4.17039 | −0.147909 | ||||||||
\(796\) | 43.0272 | 1.52506 | ||||||||
\(797\) | −13.6599 | −0.483859 | −0.241929 | − | 0.970294i | \(-0.577780\pi\) | ||||
−0.241929 | + | 0.970294i | \(0.577780\pi\) | |||||||
\(798\) | −5.84007 | −0.206736 | ||||||||
\(799\) | 70.4944 | 2.49391 | ||||||||
\(800\) | 5.64113 | 0.199444 | ||||||||
\(801\) | 6.93910 | 0.245181 | ||||||||
\(802\) | −44.6904 | −1.57807 | ||||||||
\(803\) | 39.7330 | 1.40215 | ||||||||
\(804\) | 41.1250 | 1.45037 | ||||||||
\(805\) | −3.42535 | −0.120728 | ||||||||
\(806\) | −26.5195 | −0.934109 | ||||||||
\(807\) | 33.3460 | 1.17383 | ||||||||
\(808\) | 56.5652 | 1.98996 | ||||||||
\(809\) | 22.5169 | 0.791651 | 0.395825 | − | 0.918326i | \(-0.370459\pi\) | ||||
0.395825 | + | 0.918326i | \(0.370459\pi\) | |||||||
\(810\) | −5.48683 | −0.192787 | ||||||||
\(811\) | −9.89975 | −0.347627 | −0.173814 | − | 0.984779i | \(-0.555609\pi\) | ||||
−0.173814 | + | 0.984779i | \(0.555609\pi\) | |||||||
\(812\) | −34.8444 | −1.22280 | ||||||||
\(813\) | 5.33900 | 0.187247 | ||||||||
\(814\) | 71.1318 | 2.49317 | ||||||||
\(815\) | −12.7824 | −0.447748 | ||||||||
\(816\) | −0.0932710 | −0.00326514 | ||||||||
\(817\) | −15.1146 | −0.528792 | ||||||||
\(818\) | −30.2606 | −1.05804 | ||||||||
\(819\) | −7.63747 | −0.266875 | ||||||||
\(820\) | 31.1353 | 1.08729 | ||||||||
\(821\) | −29.0409 | −1.01353 | −0.506767 | − | 0.862083i | \(-0.669160\pi\) | ||||
−0.506767 | + | 0.862083i | \(0.669160\pi\) | |||||||
\(822\) | −13.8922 | −0.484547 | ||||||||
\(823\) | −49.8840 | −1.73885 | −0.869423 | − | 0.494069i | \(-0.835509\pi\) | ||||
−0.869423 | + | 0.494069i | \(0.835509\pi\) | |||||||
\(824\) | 19.5610 | 0.681438 | ||||||||
\(825\) | 5.24760 | 0.182698 | ||||||||
\(826\) | −27.7408 | −0.965226 | ||||||||
\(827\) | 1.91499 | 0.0665907 | 0.0332954 | − | 0.999446i | \(-0.489400\pi\) | ||||
0.0332954 | + | 0.999446i | \(0.489400\pi\) | |||||||
\(828\) | 16.3696 | 0.568882 | ||||||||
\(829\) | −9.93682 | −0.345120 | −0.172560 | − | 0.984999i | \(-0.555204\pi\) | ||||
−0.172560 | + | 0.984999i | \(0.555204\pi\) | |||||||
\(830\) | −17.1455 | −0.595130 | ||||||||
\(831\) | 2.64652 | 0.0918068 | ||||||||
\(832\) | 66.9831 | 2.32222 | ||||||||
\(833\) | 5.50025 | 0.190573 | ||||||||
\(834\) | 9.90913 | 0.343125 | ||||||||
\(835\) | 7.41059 | 0.256454 | ||||||||
\(836\) | −28.4456 | −0.983813 | ||||||||
\(837\) | −12.3680 | −0.427501 | ||||||||
\(838\) | 50.3501 | 1.73932 | ||||||||
\(839\) | −49.2984 | −1.70197 | −0.850986 | − | 0.525189i | \(-0.823995\pi\) | ||||
−0.850986 | + | 0.525189i | \(0.823995\pi\) | |||||||
\(840\) | 3.50211 | 0.120834 | ||||||||
\(841\) | 86.7195 | 2.99033 | ||||||||
\(842\) | 17.0214 | 0.586596 | ||||||||
\(843\) | 14.8980 | 0.513115 | ||||||||
\(844\) | 45.7656 | 1.57532 | ||||||||
\(845\) | −13.7974 | −0.474646 | ||||||||
\(846\) | 43.2818 | 1.48806 | ||||||||
\(847\) | −7.06170 | −0.242643 | ||||||||
\(848\) | −0.0463851 | −0.00159287 | ||||||||
\(849\) | 34.9951 | 1.20103 | ||||||||
\(850\) | −12.5896 | −0.431820 | ||||||||
\(851\) | −25.0472 | −0.858607 | ||||||||
\(852\) | 13.4962 | 0.462374 | ||||||||
\(853\) | −10.8776 | −0.372441 | −0.186220 | − | 0.982508i | \(-0.559624\pi\) | ||||
−0.186220 | + | 0.982508i | \(0.559624\pi\) | |||||||
\(854\) | −1.80140 | −0.0616426 | ||||||||
\(855\) | 3.04867 | 0.104262 | ||||||||
\(856\) | 30.9789 | 1.05884 | ||||||||
\(857\) | −50.3237 | −1.71903 | −0.859513 | − | 0.511115i | \(-0.829233\pi\) | ||||
−0.859513 | + | 0.511115i | \(0.829233\pi\) | |||||||
\(858\) | 62.1780 | 2.12272 | ||||||||
\(859\) | −50.2860 | −1.71574 | −0.857868 | − | 0.513870i | \(-0.828211\pi\) | ||||
−0.857868 | + | 0.513870i | \(0.828211\pi\) | |||||||
\(860\) | 23.6929 | 0.807921 | ||||||||
\(861\) | −11.8688 | −0.404486 | ||||||||
\(862\) | −58.2804 | −1.98504 | ||||||||
\(863\) | −34.0057 | −1.15757 | −0.578784 | − | 0.815481i | \(-0.696472\pi\) | ||||
−0.578784 | + | 0.815481i | \(0.696472\pi\) | |||||||
\(864\) | 31.1729 | 1.06052 | ||||||||
\(865\) | −8.94627 | −0.304182 | ||||||||
\(866\) | 69.4905 | 2.36138 | ||||||||
\(867\) | −16.3640 | −0.555750 | ||||||||
\(868\) | 7.24967 | 0.246070 | ||||||||
\(869\) | 23.6936 | 0.803749 | ||||||||
\(870\) | −30.4029 | −1.03075 | ||||||||
\(871\) | 53.2282 | 1.80357 | ||||||||
\(872\) | 6.66772 | 0.225797 | ||||||||
\(873\) | −13.1888 | −0.446372 | ||||||||
\(874\) | 16.2010 | 0.548007 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 37.3923 | 1.26337 | ||||||||
\(877\) | 0.837955 | 0.0282957 | 0.0141479 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141479 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(878\) | 54.5698 | 1.84164 | ||||||||
\(879\) | −16.9087 | −0.570316 | ||||||||
\(880\) | 0.0583663 | 0.00196753 | ||||||||
\(881\) | 39.6615 | 1.33623 | 0.668114 | − | 0.744059i | \(-0.267102\pi\) | ||||
0.668114 | + | 0.744059i | \(0.267102\pi\) | |||||||
\(882\) | 3.37702 | 0.113710 | ||||||||
\(883\) | −6.93084 | −0.233241 | −0.116621 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116621 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(884\) | −92.2271 | −3.10193 | ||||||||
\(885\) | −14.9648 | −0.503036 | ||||||||
\(886\) | 76.7060 | 2.57699 | ||||||||
\(887\) | 41.7929 | 1.40327 | 0.701634 | − | 0.712537i | \(-0.252454\pi\) | ||||
0.701634 | + | 0.712537i | \(0.252454\pi\) | |||||||
\(888\) | 25.6085 | 0.859367 | ||||||||
\(889\) | −10.0699 | −0.337734 | ||||||||
\(890\) | −10.7654 | −0.360857 | ||||||||
\(891\) | 10.1876 | 0.341297 | ||||||||
\(892\) | 81.0590 | 2.71406 | ||||||||
\(893\) | 26.4837 | 0.886244 | ||||||||
\(894\) | −36.7155 | −1.22795 | ||||||||
\(895\) | 16.4716 | 0.550584 | ||||||||
\(896\) | −18.3352 | −0.612538 | ||||||||
\(897\) | −21.8944 | −0.731031 | ||||||||
\(898\) | −64.0479 | −2.13731 | ||||||||
\(899\) | −24.0764 | −0.802994 | ||||||||
\(900\) | −4.77895 | −0.159298 | ||||||||
\(901\) | −18.5771 | −0.618894 | ||||||||
\(902\) | −93.5047 | −3.11337 | ||||||||
\(903\) | −9.03171 | −0.300556 | ||||||||
\(904\) | 8.86804 | 0.294947 | ||||||||
\(905\) | −16.8450 | −0.559946 | ||||||||
\(906\) | −27.8052 | −0.923767 | ||||||||
\(907\) | 52.2909 | 1.73629 | 0.868146 | − | 0.496309i | \(-0.165312\pi\) | ||||
0.868146 | + | 0.496309i | \(0.165312\pi\) | |||||||
\(908\) | −48.3523 | −1.60463 | ||||||||
\(909\) | 29.4241 | 0.975936 | ||||||||
\(910\) | 11.8489 | 0.392786 | ||||||||
\(911\) | 24.0791 | 0.797775 | 0.398887 | − | 0.917000i | \(-0.369396\pi\) | ||||
0.398887 | + | 0.917000i | \(0.369396\pi\) | |||||||
\(912\) | −0.0350406 | −0.00116031 | ||||||||
\(913\) | 31.8347 | 1.05357 | ||||||||
\(914\) | −31.3662 | −1.03750 | ||||||||
\(915\) | −0.971764 | −0.0321255 | ||||||||
\(916\) | 3.23914 | 0.107024 | ||||||||
\(917\) | 19.7491 | 0.652172 | ||||||||
\(918\) | −69.5702 | −2.29616 | ||||||||
\(919\) | 2.37397 | 0.0783101 | 0.0391550 | − | 0.999233i | \(-0.487533\pi\) | ||||
0.0391550 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(920\) | −9.71524 | −0.320302 | ||||||||
\(921\) | 20.5199 | 0.676154 | ||||||||
\(922\) | 5.96625 | 0.196488 | ||||||||
\(923\) | 17.4682 | 0.574974 | ||||||||
\(924\) | −16.9977 | −0.559183 | ||||||||
\(925\) | 7.31231 | 0.240427 | ||||||||
\(926\) | 8.67984 | 0.285237 | ||||||||
\(927\) | 10.1752 | 0.334198 | ||||||||
\(928\) | 60.6833 | 1.99203 | ||||||||
\(929\) | −11.6053 | −0.380758 | −0.190379 | − | 0.981711i | \(-0.560972\pi\) | ||||
−0.190379 | + | 0.981711i | \(0.560972\pi\) | |||||||
\(930\) | 6.32557 | 0.207424 | ||||||||
\(931\) | 2.06636 | 0.0677224 | ||||||||
\(932\) | −67.9811 | −2.22679 | ||||||||
\(933\) | 9.95592 | 0.325942 | ||||||||
\(934\) | −13.6836 | −0.447741 | ||||||||
\(935\) | 23.3756 | 0.764463 | ||||||||
\(936\) | −21.6620 | −0.708045 | ||||||||
\(937\) | −3.52771 | −0.115245 | −0.0576226 | − | 0.998338i | \(-0.518352\pi\) | ||||
−0.0576226 | + | 0.998338i | \(0.518352\pi\) | |||||||
\(938\) | −23.5356 | −0.768465 | ||||||||
\(939\) | −34.6412 | −1.13047 | ||||||||
\(940\) | −41.5146 | −1.35406 | ||||||||
\(941\) | 21.9597 | 0.715865 | 0.357932 | − | 0.933748i | \(-0.383482\pi\) | ||||
0.357932 | + | 0.933748i | \(0.383482\pi\) | |||||||
\(942\) | 32.8982 | 1.07188 | ||||||||
\(943\) | 32.9252 | 1.07219 | ||||||||
\(944\) | −0.166445 | −0.00541734 | ||||||||
\(945\) | 5.52600 | 0.179761 | ||||||||
\(946\) | −71.1538 | −2.31341 | ||||||||
\(947\) | −14.2735 | −0.463826 | −0.231913 | − | 0.972737i | \(-0.574498\pi\) | ||||
−0.231913 | + | 0.972737i | \(0.574498\pi\) | |||||||
\(948\) | 22.2978 | 0.724198 | ||||||||
\(949\) | 48.3970 | 1.57103 | ||||||||
\(950\) | −4.72974 | −0.153453 | ||||||||
\(951\) | −36.2299 | −1.17484 | ||||||||
\(952\) | 15.6003 | 0.505607 | ||||||||
\(953\) | 45.6186 | 1.47773 | 0.738866 | − | 0.673852i | \(-0.235362\pi\) | ||||
0.738866 | + | 0.673852i | \(0.235362\pi\) | |||||||
\(954\) | −11.4059 | −0.369279 | ||||||||
\(955\) | 20.2823 | 0.656319 | ||||||||
\(956\) | 6.88123 | 0.222555 | ||||||||
\(957\) | 56.4500 | 1.82477 | ||||||||
\(958\) | −18.3564 | −0.593069 | ||||||||
\(959\) | 4.91543 | 0.158727 | ||||||||
\(960\) | −15.9772 | −0.515661 | ||||||||
\(961\) | −25.9907 | −0.838410 | ||||||||
\(962\) | 86.6425 | 2.79347 | ||||||||
\(963\) | 16.1146 | 0.519286 | ||||||||
\(964\) | 65.9637 | 2.12455 | ||||||||
\(965\) | 6.35064 | 0.204434 | ||||||||
\(966\) | 9.68090 | 0.311478 | ||||||||
\(967\) | −16.1597 | −0.519660 | −0.259830 | − | 0.965654i | \(-0.583667\pi\) | ||||
−0.259830 | + | 0.965654i | \(0.583667\pi\) | |||||||
\(968\) | −20.0290 | −0.643756 | ||||||||
\(969\) | −14.0337 | −0.450826 | ||||||||
\(970\) | 20.4612 | 0.656969 | ||||||||
\(971\) | 39.6113 | 1.27119 | 0.635593 | − | 0.772024i | \(-0.280756\pi\) | ||||
0.635593 | + | 0.772024i | \(0.280756\pi\) | |||||||
\(972\) | −44.1110 | −1.41486 | ||||||||
\(973\) | −3.50610 | −0.112400 | ||||||||
\(974\) | 65.3462 | 2.09383 | ||||||||
\(975\) | 6.39187 | 0.204704 | ||||||||
\(976\) | −0.0108084 | −0.000345969 0 | ||||||||
\(977\) | −10.8739 | −0.347888 | −0.173944 | − | 0.984756i | \(-0.555651\pi\) | ||||
−0.173944 | + | 0.984756i | \(0.555651\pi\) | |||||||
\(978\) | 36.1263 | 1.15519 | ||||||||
\(979\) | 19.9885 | 0.638834 | ||||||||
\(980\) | −3.23914 | −0.103470 | ||||||||
\(981\) | 3.46842 | 0.110738 | ||||||||
\(982\) | 22.9674 | 0.732920 | ||||||||
\(983\) | −18.7160 | −0.596947 | −0.298473 | − | 0.954418i | \(-0.596477\pi\) | ||||
−0.298473 | + | 0.954418i | \(0.596477\pi\) | |||||||
\(984\) | −33.6631 | −1.07314 | ||||||||
\(985\) | −3.71252 | −0.118291 | ||||||||
\(986\) | −135.430 | −4.31298 | ||||||||
\(987\) | 15.8253 | 0.503726 | ||||||||
\(988\) | −34.6484 | −1.10231 | ||||||||
\(989\) | 25.0549 | 0.796701 | ||||||||
\(990\) | 14.3520 | 0.456136 | ||||||||
\(991\) | 44.1775 | 1.40335 | 0.701673 | − | 0.712499i | \(-0.252437\pi\) | ||||
0.701673 | + | 0.712499i | \(0.252437\pi\) | |||||||
\(992\) | −12.6257 | −0.400865 | ||||||||
\(993\) | 29.8936 | 0.948644 | ||||||||
\(994\) | −7.72382 | −0.244985 | ||||||||
\(995\) | −13.2835 | −0.421117 | ||||||||
\(996\) | 29.9593 | 0.949296 | ||||||||
\(997\) | 20.2237 | 0.640492 | 0.320246 | − | 0.947334i | \(-0.396234\pi\) | ||||
0.320246 | + | 0.947334i | \(0.396234\pi\) | |||||||
\(998\) | −63.0159 | −1.99473 | ||||||||
\(999\) | 40.4078 | 1.27845 |
(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 | 8015.2.a.l.1.7 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.7 | ✓ | 62 | 1.1 | even | 1 | trivial |