Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58708 | −1.12224 | −0.561118 | − | 0.827736i | \(-0.689628\pi\) | ||||
−0.561118 | + | 0.827736i | \(0.689628\pi\) | |||||||
\(3\) | 1.81144 | 1.04583 | 0.522917 | − | 0.852383i | \(-0.324844\pi\) | ||||
0.522917 | + | 0.852383i | \(0.324844\pi\) | |||||||
\(4\) | 0.518823 | 0.259411 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.87490 | −1.17367 | ||||||||
\(7\) | 0.0644914 | 0.0243755 | 0.0121877 | − | 0.999926i | \(-0.496120\pi\) | ||||
0.0121877 | + | 0.999926i | \(0.496120\pi\) | |||||||
\(8\) | 2.35075 | 0.831114 | ||||||||
\(9\) | 0.281309 | 0.0937698 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.11471 | −0.939120 | −0.469560 | − | 0.882901i | \(-0.655587\pi\) | ||||
−0.469560 | + | 0.882901i | \(0.655587\pi\) | |||||||
\(12\) | 0.939816 | 0.271301 | ||||||||
\(13\) | 1.08890 | 0.302006 | 0.151003 | − | 0.988533i | \(-0.451750\pi\) | ||||
0.151003 | + | 0.988533i | \(0.451750\pi\) | |||||||
\(14\) | −0.102353 | −0.0273550 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.76847 | −1.19212 | ||||||||
\(17\) | 7.86988 | 1.90873 | 0.954363 | − | 0.298650i | \(-0.0965363\pi\) | ||||
0.954363 | + | 0.298650i | \(0.0965363\pi\) | |||||||
\(18\) | −0.446460 | −0.105232 | ||||||||
\(19\) | −4.43016 | −1.01635 | −0.508174 | − | 0.861254i | \(-0.669679\pi\) | ||||
−0.508174 | + | 0.861254i | \(0.669679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.116822 | 0.0254927 | ||||||||
\(22\) | 4.94329 | 1.05391 | ||||||||
\(23\) | 1.31833 | 0.274892 | 0.137446 | − | 0.990509i | \(-0.456111\pi\) | ||||
0.137446 | + | 0.990509i | \(0.456111\pi\) | |||||||
\(24\) | 4.25823 | 0.869208 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.72817 | −0.338922 | ||||||||
\(27\) | −4.92474 | −0.947767 | ||||||||
\(28\) | 0.0334596 | 0.00632327 | ||||||||
\(29\) | 9.34210 | 1.73478 | 0.867392 | − | 0.497625i | \(-0.165794\pi\) | ||||
0.867392 | + | 0.497625i | \(0.165794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.65119 | −1.37419 | −0.687097 | − | 0.726565i | \(-0.741115\pi\) | ||||
−0.687097 | + | 0.726565i | \(0.741115\pi\) | |||||||
\(32\) | 2.86645 | 0.506721 | ||||||||
\(33\) | −5.64210 | −0.982164 | ||||||||
\(34\) | −12.4901 | −2.14204 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.145950 | 0.0243250 | ||||||||
\(37\) | −5.72218 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(38\) | 7.03101 | 1.14058 | ||||||||
\(39\) | 1.97247 | 0.315848 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.40082 | −0.999640 | −0.499820 | − | 0.866129i | \(-0.666600\pi\) | ||||
−0.499820 | + | 0.866129i | \(0.666600\pi\) | |||||||
\(42\) | −0.185406 | −0.0286088 | ||||||||
\(43\) | −7.30399 | −1.11385 | −0.556924 | − | 0.830563i | \(-0.688019\pi\) | ||||
−0.556924 | + | 0.830563i | \(0.688019\pi\) | |||||||
\(44\) | −1.61598 | −0.243618 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.09230 | −0.308493 | ||||||||
\(47\) | 5.56242 | 0.811362 | 0.405681 | − | 0.914015i | \(-0.367034\pi\) | ||||
0.405681 | + | 0.914015i | \(0.367034\pi\) | |||||||
\(48\) | −8.63779 | −1.24676 | ||||||||
\(49\) | −6.99584 | −0.999406 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.2558 | 1.99621 | ||||||||
\(52\) | 0.564945 | 0.0783438 | ||||||||
\(53\) | −2.24472 | −0.308336 | −0.154168 | − | 0.988045i | \(-0.549270\pi\) | ||||
−0.154168 | + | 0.988045i | \(0.549270\pi\) | |||||||
\(54\) | 7.81596 | 1.06362 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.151603 | 0.0202588 | ||||||||
\(57\) | −8.02496 | −1.06293 | ||||||||
\(58\) | −14.8267 | −1.94684 | ||||||||
\(59\) | 8.40941 | 1.09481 | 0.547406 | − | 0.836867i | \(-0.315615\pi\) | ||||
0.547406 | + | 0.836867i | \(0.315615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.891498 | −0.114145 | −0.0570723 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570723 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(62\) | 12.1431 | 1.54217 | ||||||||
\(63\) | 0.0181420 | 0.00228568 | ||||||||
\(64\) | 4.98766 | 0.623457 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.95447 | 1.10222 | ||||||||
\(67\) | −0.205157 | −0.0250639 | −0.0125319 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125319 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(68\) | 4.08307 | 0.495145 | ||||||||
\(69\) | 2.38808 | 0.287491 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.18178 | 0.258930 | 0.129465 | − | 0.991584i | \(-0.458674\pi\) | ||||
0.129465 | + | 0.991584i | \(0.458674\pi\) | |||||||
\(72\) | 0.661287 | 0.0779334 | ||||||||
\(73\) | −1.46593 | −0.171574 | −0.0857872 | − | 0.996313i | \(-0.527341\pi\) | ||||
−0.0857872 | + | 0.996313i | \(0.527341\pi\) | |||||||
\(74\) | 9.08156 | 1.05571 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.29847 | −0.263652 | ||||||||
\(77\) | −0.200872 | −0.0228915 | ||||||||
\(78\) | −3.13047 | −0.354456 | ||||||||
\(79\) | 6.60582 | 0.743213 | 0.371607 | − | 0.928390i | \(-0.378807\pi\) | ||||
0.371607 | + | 0.928390i | \(0.378807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.76479 | −1.08498 | ||||||||
\(82\) | 10.1586 | 1.12183 | ||||||||
\(83\) | −11.9378 | −1.31035 | −0.655174 | − | 0.755478i | \(-0.727405\pi\) | ||||
−0.655174 | + | 0.755478i | \(0.727405\pi\) | |||||||
\(84\) | 0.0606101 | 0.00661310 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.5920 | 1.25000 | ||||||||
\(87\) | 16.9226 | 1.81430 | ||||||||
\(88\) | −7.32189 | −0.780516 | ||||||||
\(89\) | −3.41007 | −0.361467 | −0.180734 | − | 0.983532i | \(-0.557847\pi\) | ||||
−0.180734 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0702246 | 0.00736154 | ||||||||
\(92\) | 0.683982 | 0.0713100 | ||||||||
\(93\) | −13.8597 | −1.43718 | ||||||||
\(94\) | −8.82800 | −0.910539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.19239 | 0.529946 | ||||||||
\(97\) | 8.77669 | 0.891137 | 0.445569 | − | 0.895248i | \(-0.353001\pi\) | ||||
0.445569 | + | 0.895248i | \(0.353001\pi\) | |||||||
\(98\) | 11.1030 | 1.12157 | ||||||||
\(99\) | −0.876197 | −0.0880611 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.01796 | −0.200794 | −0.100397 | − | 0.994947i | \(-0.532011\pi\) | ||||
−0.100397 | + | 0.994947i | \(0.532011\pi\) | |||||||
\(102\) | −22.6251 | −2.24022 | ||||||||
\(103\) | 6.47931 | 0.638426 | 0.319213 | − | 0.947683i | \(-0.396582\pi\) | ||||
0.319213 | + | 0.947683i | \(0.396582\pi\) | |||||||
\(104\) | 2.55972 | 0.251002 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.56255 | 0.346025 | ||||||||
\(107\) | 7.26553 | 0.702385 | 0.351193 | − | 0.936303i | \(-0.385776\pi\) | ||||
0.351193 | + | 0.936303i | \(0.385776\pi\) | |||||||
\(108\) | −2.55507 | −0.245862 | ||||||||
\(109\) | −1.82410 | −0.174717 | −0.0873586 | − | 0.996177i | \(-0.527843\pi\) | ||||
−0.0873586 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3654 | −0.983838 | ||||||||
\(112\) | −0.307525 | −0.0290584 | ||||||||
\(113\) | −3.62469 | −0.340983 | −0.170491 | − | 0.985359i | \(-0.554535\pi\) | ||||
−0.170491 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(114\) | 12.7363 | 1.19286 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.84689 | 0.450023 | ||||||||
\(117\) | 0.306317 | 0.0283190 | ||||||||
\(118\) | −13.3464 | −1.22864 | ||||||||
\(119\) | 0.507540 | 0.0465261 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29859 | −0.118053 | ||||||||
\(122\) | 1.41488 | 0.128097 | ||||||||
\(123\) | −11.5947 | −1.04546 | ||||||||
\(124\) | −3.96961 | −0.356482 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0287929 | −0.00256507 | ||||||||
\(127\) | −18.0032 | −1.59753 | −0.798764 | − | 0.601645i | \(-0.794512\pi\) | ||||
−0.798764 | + | 0.601645i | \(0.794512\pi\) | |||||||
\(128\) | −13.6487 | −1.20639 | ||||||||
\(129\) | −13.2307 | −1.16490 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.2832 | −1.77216 | −0.886078 | − | 0.463537i | \(-0.846580\pi\) | ||||
−0.886078 | + | 0.463537i | \(0.846580\pi\) | |||||||
\(132\) | −2.92725 | −0.254785 | ||||||||
\(133\) | −0.285707 | −0.0247740 | ||||||||
\(134\) | 0.325600 | 0.0281276 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.5001 | 1.58637 | ||||||||
\(137\) | −5.76429 | −0.492477 | −0.246238 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246238 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(138\) | −3.79007 | −0.322633 | ||||||||
\(139\) | 13.2382 | 1.12285 | 0.561426 | − | 0.827527i | \(-0.310253\pi\) | ||||
0.561426 | + | 0.827527i | \(0.310253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0760 | 0.848550 | ||||||||
\(142\) | −3.46266 | −0.290580 | ||||||||
\(143\) | −3.39160 | −0.283620 | ||||||||
\(144\) | −1.34141 | −0.111785 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.32655 | 0.192547 | ||||||||
\(147\) | −12.6725 | −1.04521 | ||||||||
\(148\) | −2.96880 | −0.244034 | ||||||||
\(149\) | 11.0016 | 0.901286 | 0.450643 | − | 0.892704i | \(-0.351195\pi\) | ||||
0.450643 | + | 0.892704i | \(0.351195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.93660 | −0.238977 | −0.119488 | − | 0.992836i | \(-0.538125\pi\) | ||||
−0.119488 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(152\) | −10.4142 | −0.844701 | ||||||||
\(153\) | 2.21387 | 0.178981 | ||||||||
\(154\) | 0.318800 | 0.0256896 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.02336 | 0.0819346 | ||||||||
\(157\) | 15.5005 | 1.23707 | 0.618537 | − | 0.785755i | \(-0.287726\pi\) | ||||
0.618537 | + | 0.785755i | \(0.287726\pi\) | |||||||
\(158\) | −10.4840 | −0.834060 | ||||||||
\(159\) | −4.06617 | −0.322468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0850212 | 0.00670061 | ||||||||
\(162\) | 15.4975 | 1.21760 | ||||||||
\(163\) | −7.71386 | −0.604196 | −0.302098 | − | 0.953277i | \(-0.597687\pi\) | ||||
−0.302098 | + | 0.953277i | \(0.597687\pi\) | |||||||
\(164\) | −3.32089 | −0.259318 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.9463 | 1.47052 | ||||||||
\(167\) | −10.1357 | −0.784320 | −0.392160 | − | 0.919897i | \(-0.628272\pi\) | ||||
−0.392160 | + | 0.919897i | \(0.628272\pi\) | |||||||
\(168\) | 0.274620 | 0.0211874 | ||||||||
\(169\) | −11.8143 | −0.908792 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.24624 | −0.0953027 | ||||||||
\(172\) | −3.78948 | −0.288945 | ||||||||
\(173\) | −6.25726 | −0.475731 | −0.237865 | − | 0.971298i | \(-0.576448\pi\) | ||||
−0.237865 | + | 0.971298i | \(0.576448\pi\) | |||||||
\(174\) | −26.8576 | −2.03607 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.8524 | 1.11954 | ||||||||
\(177\) | 15.2331 | 1.14499 | ||||||||
\(178\) | 5.41206 | 0.405651 | ||||||||
\(179\) | −20.4876 | −1.53131 | −0.765657 | − | 0.643250i | \(-0.777586\pi\) | ||||
−0.765657 | + | 0.643250i | \(0.777586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.38386 | −0.474509 | −0.237254 | − | 0.971448i | \(-0.576247\pi\) | ||||
−0.237254 | + | 0.971448i | \(0.576247\pi\) | |||||||
\(182\) | −0.111452 | −0.00826138 | ||||||||
\(183\) | −1.61489 | −0.119376 | ||||||||
\(184\) | 3.09907 | 0.228466 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 21.9964 | 1.61285 | ||||||||
\(187\) | −24.5124 | −1.79252 | ||||||||
\(188\) | 2.88591 | 0.210477 | ||||||||
\(189\) | −0.317604 | −0.0231023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.46713 | 0.685018 | 0.342509 | − | 0.939515i | \(-0.388723\pi\) | ||||
0.342509 | + | 0.939515i | \(0.388723\pi\) | |||||||
\(192\) | 9.03483 | 0.652033 | ||||||||
\(193\) | −2.15639 | −0.155220 | −0.0776102 | − | 0.996984i | \(-0.524729\pi\) | ||||
−0.0776102 | + | 0.996984i | \(0.524729\pi\) | |||||||
\(194\) | −13.9293 | −1.00007 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.62960 | −0.259257 | ||||||||
\(197\) | −4.35613 | −0.310362 | −0.155181 | − | 0.987886i | \(-0.549596\pi\) | ||||
−0.155181 | + | 0.987886i | \(0.549596\pi\) | |||||||
\(198\) | 1.39059 | 0.0988253 | ||||||||
\(199\) | −10.1846 | −0.721967 | −0.360983 | − | 0.932572i | \(-0.617559\pi\) | ||||
−0.360983 | + | 0.932572i | \(0.617559\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.371629 | −0.0262127 | ||||||||
\(202\) | 3.20266 | 0.225339 | ||||||||
\(203\) | 0.602485 | 0.0422862 | ||||||||
\(204\) | 7.39623 | 0.517840 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.2832 | −0.716463 | ||||||||
\(207\) | 0.370860 | 0.0257765 | ||||||||
\(208\) | −5.19238 | −0.360027 | ||||||||
\(209\) | 13.7987 | 0.954473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5472 | 1.27684 | 0.638421 | − | 0.769687i | \(-0.279588\pi\) | ||||
0.638421 | + | 0.769687i | \(0.279588\pi\) | |||||||
\(212\) | −1.16461 | −0.0799858 | ||||||||
\(213\) | 3.95216 | 0.270797 | ||||||||
\(214\) | −11.5310 | −0.788241 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.5768 | −0.787703 | ||||||||
\(217\) | −0.493436 | −0.0334966 | ||||||||
\(218\) | 2.89499 | 0.196074 | ||||||||
\(219\) | −2.65545 | −0.179439 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56949 | 0.576447 | ||||||||
\(222\) | 16.4507 | 1.10410 | ||||||||
\(223\) | 7.24666 | 0.485272 | 0.242636 | − | 0.970117i | \(-0.421988\pi\) | ||||
0.242636 | + | 0.970117i | \(0.421988\pi\) | |||||||
\(224\) | 0.184861 | 0.0123516 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.75268 | 0.382663 | ||||||||
\(227\) | −18.8256 | −1.24950 | −0.624748 | − | 0.780826i | \(-0.714798\pi\) | ||||
−0.624748 | + | 0.780826i | \(0.714798\pi\) | |||||||
\(228\) | −4.16353 | −0.275737 | ||||||||
\(229\) | 24.4964 | 1.61877 | 0.809385 | − | 0.587279i | \(-0.199801\pi\) | ||||
0.809385 | + | 0.587279i | \(0.199801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.363867 | −0.0239407 | ||||||||
\(232\) | 21.9609 | 1.44180 | ||||||||
\(233\) | 9.08981 | 0.595493 | 0.297747 | − | 0.954645i | \(-0.403765\pi\) | ||||
0.297747 | + | 0.954645i | \(0.403765\pi\) | |||||||
\(234\) | −0.486150 | −0.0317806 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.36299 | 0.284007 | ||||||||
\(237\) | 11.9660 | 0.777278 | ||||||||
\(238\) | −0.805506 | −0.0522132 | ||||||||
\(239\) | −5.63343 | −0.364396 | −0.182198 | − | 0.983262i | \(-0.558321\pi\) | ||||
−0.182198 | + | 0.983262i | \(0.558321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 2.06096 | 0.132484 | ||||||||
\(243\) | −2.91410 | −0.186940 | ||||||||
\(244\) | −0.462529 | −0.0296104 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.4017 | 1.17325 | ||||||||
\(247\) | −4.82399 | −0.306943 | ||||||||
\(248\) | −17.9860 | −1.14211 | ||||||||
\(249\) | −21.6247 | −1.37041 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3485 | −0.905668 | −0.452834 | − | 0.891595i | \(-0.649587\pi\) | ||||
−0.452834 | + | 0.891595i | \(0.649587\pi\) | |||||||
\(252\) | 0.00941251 | 0.000592932 0 | ||||||||
\(253\) | −4.10623 | −0.258156 | ||||||||
\(254\) | 28.5725 | 1.79280 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.6863 | 0.730392 | ||||||||
\(257\) | 12.6265 | 0.787620 | 0.393810 | − | 0.919192i | \(-0.371157\pi\) | ||||
0.393810 | + | 0.919192i | \(0.371157\pi\) | |||||||
\(258\) | 20.9982 | 1.30729 | ||||||||
\(259\) | −0.369032 | −0.0229305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.62802 | 0.162670 | ||||||||
\(262\) | 32.1911 | 1.98877 | ||||||||
\(263\) | −16.9720 | −1.04654 | −0.523268 | − | 0.852168i | \(-0.675287\pi\) | ||||
−0.523268 | + | 0.852168i | \(0.675287\pi\) | |||||||
\(264\) | −13.2632 | −0.816291 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.453440 | 0.0278022 | ||||||||
\(267\) | −6.17714 | −0.378035 | ||||||||
\(268\) | −0.106440 | −0.00650185 | ||||||||
\(269\) | −22.2900 | −1.35905 | −0.679523 | − | 0.733654i | \(-0.737813\pi\) | ||||
−0.679523 | + | 0.733654i | \(0.737813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.3970 | −1.84649 | −0.923243 | − | 0.384216i | \(-0.874472\pi\) | ||||
−0.923243 | + | 0.384216i | \(0.874472\pi\) | |||||||
\(272\) | −37.5273 | −2.27542 | ||||||||
\(273\) | 0.127208 | 0.00769895 | ||||||||
\(274\) | 9.14840 | 0.552675 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.23899 | 0.0745785 | ||||||||
\(277\) | −3.61385 | −0.217135 | −0.108568 | − | 0.994089i | \(-0.534626\pi\) | ||||
−0.108568 | + | 0.994089i | \(0.534626\pi\) | |||||||
\(278\) | −21.0101 | −1.26010 | ||||||||
\(279\) | −2.15235 | −0.128858 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.01500 | −0.537790 | −0.268895 | − | 0.963170i | \(-0.586658\pi\) | ||||
−0.268895 | + | 0.963170i | \(0.586658\pi\) | |||||||
\(282\) | −15.9914 | −0.952273 | ||||||||
\(283\) | 1.66251 | 0.0988261 | 0.0494131 | − | 0.998778i | \(-0.484265\pi\) | ||||
0.0494131 | + | 0.998778i | \(0.484265\pi\) | |||||||
\(284\) | 1.13196 | 0.0671693 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.38274 | 0.318288 | ||||||||
\(287\) | −0.412798 | −0.0243667 | ||||||||
\(288\) | 0.806359 | 0.0475151 | ||||||||
\(289\) | 44.9350 | 2.64323 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8984 | 0.931982 | ||||||||
\(292\) | −0.760560 | −0.0445084 | ||||||||
\(293\) | −30.2574 | −1.76766 | −0.883828 | − | 0.467812i | \(-0.845043\pi\) | ||||
−0.883828 | + | 0.467812i | \(0.845043\pi\) | |||||||
\(294\) | 20.1123 | 1.17297 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.4514 | −0.781847 | ||||||||
\(297\) | 15.3391 | 0.890067 | ||||||||
\(298\) | −17.4604 | −1.01145 | ||||||||
\(299\) | 1.43553 | 0.0830189 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.471045 | −0.0271506 | ||||||||
\(302\) | 4.66061 | 0.268188 | ||||||||
\(303\) | −3.65541 | −0.209998 | ||||||||
\(304\) | 21.1251 | 1.21161 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.51359 | −0.200859 | ||||||||
\(307\) | −29.0908 | −1.66030 | −0.830151 | − | 0.557539i | \(-0.811746\pi\) | ||||
−0.830151 | + | 0.557539i | \(0.811746\pi\) | |||||||
\(308\) | −0.104217 | −0.00593831 | ||||||||
\(309\) | 11.7369 | 0.667687 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.202626 | 0.0114899 | 0.00574494 | − | 0.999983i | \(-0.498171\pi\) | ||||
0.00574494 | + | 0.999983i | \(0.498171\pi\) | |||||||
\(312\) | 4.63678 | 0.262506 | ||||||||
\(313\) | 15.3145 | 0.865627 | 0.432814 | − | 0.901483i | \(-0.357521\pi\) | ||||
0.432814 | + | 0.901483i | \(0.357521\pi\) | |||||||
\(314\) | −24.6005 | −1.38829 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.42725 | 0.192798 | ||||||||
\(317\) | 13.4881 | 0.757569 | 0.378785 | − | 0.925485i | \(-0.376342\pi\) | ||||
0.378785 | + | 0.925485i | \(0.376342\pi\) | |||||||
\(318\) | 6.45333 | 0.361885 | ||||||||
\(319\) | −29.0979 | −1.62917 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1611 | 0.734579 | ||||||||
\(322\) | −0.134935 | −0.00751966 | ||||||||
\(323\) | −34.8648 | −1.93993 | ||||||||
\(324\) | −5.06620 | −0.281455 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.2425 | 0.678050 | ||||||||
\(327\) | −3.30425 | −0.182725 | ||||||||
\(328\) | −15.0467 | −0.830815 | ||||||||
\(329\) | 0.358728 | 0.0197773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.3538 | 1.77832 | 0.889162 | − | 0.457593i | \(-0.151288\pi\) | ||||
0.889162 | + | 0.457593i | \(0.151288\pi\) | |||||||
\(332\) | −6.19362 | −0.339919 | ||||||||
\(333\) | −1.60970 | −0.0882112 | ||||||||
\(334\) | 16.0861 | 0.880192 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.557063 | −0.0303903 | ||||||||
\(337\) | −14.8297 | −0.807827 | −0.403913 | − | 0.914797i | \(-0.632350\pi\) | ||||
−0.403913 | + | 0.914797i | \(0.632350\pi\) | |||||||
\(338\) | 18.7502 | 1.01988 | ||||||||
\(339\) | −6.56591 | −0.356611 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.8312 | 1.29053 | ||||||||
\(342\) | 1.97789 | 0.106952 | ||||||||
\(343\) | −0.902612 | −0.0487365 | ||||||||
\(344\) | −17.1698 | −0.925736 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.93077 | 0.533882 | ||||||||
\(347\) | −25.0660 | −1.34561 | −0.672806 | − | 0.739819i | \(-0.734911\pi\) | ||||
−0.672806 | + | 0.739819i | \(0.734911\pi\) | |||||||
\(348\) | 8.77985 | 0.470649 | ||||||||
\(349\) | 19.2180 | 1.02872 | 0.514358 | − | 0.857576i | \(-0.328030\pi\) | ||||
0.514358 | + | 0.857576i | \(0.328030\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.36254 | −0.286231 | ||||||||
\(352\) | −8.92815 | −0.475872 | ||||||||
\(353\) | −22.6187 | −1.20387 | −0.601936 | − | 0.798544i | \(-0.705604\pi\) | ||||
−0.601936 | + | 0.798544i | \(0.705604\pi\) | |||||||
\(354\) | −24.1762 | −1.28495 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.76922 | −0.0937687 | ||||||||
\(357\) | 0.919377 | 0.0486586 | ||||||||
\(358\) | 32.5154 | 1.71849 | ||||||||
\(359\) | 9.49426 | 0.501088 | 0.250544 | − | 0.968105i | \(-0.419391\pi\) | ||||
0.250544 | + | 0.968105i | \(0.419391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.626297 | 0.0329630 | ||||||||
\(362\) | 10.1317 | 0.532510 | ||||||||
\(363\) | −2.35231 | −0.123464 | ||||||||
\(364\) | 0.0364341 | 0.00190967 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.56296 | 0.133968 | ||||||||
\(367\) | −29.1574 | −1.52201 | −0.761003 | − | 0.648749i | \(-0.775293\pi\) | ||||
−0.761003 | + | 0.648749i | \(0.775293\pi\) | |||||||
\(368\) | −6.28643 | −0.327703 | ||||||||
\(369\) | −1.80061 | −0.0937360 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.144765 | −0.00751583 | ||||||||
\(372\) | −7.19071 | −0.372821 | ||||||||
\(373\) | 35.1988 | 1.82252 | 0.911262 | − | 0.411828i | \(-0.135110\pi\) | ||||
0.911262 | + | 0.411828i | \(0.135110\pi\) | |||||||
\(374\) | 38.9031 | 2.01163 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.0758 | 0.674334 | ||||||||
\(377\) | 10.1726 | 0.523915 | ||||||||
\(378\) | 0.504062 | 0.0259262 | ||||||||
\(379\) | −31.9147 | −1.63935 | −0.819673 | − | 0.572832i | \(-0.805845\pi\) | ||||
−0.819673 | + | 0.572832i | \(0.805845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.6117 | −1.67075 | ||||||||
\(382\) | −15.0251 | −0.768751 | ||||||||
\(383\) | −20.2534 | −1.03490 | −0.517451 | − | 0.855713i | \(-0.673119\pi\) | ||||
−0.517451 | + | 0.855713i | \(0.673119\pi\) | |||||||
\(384\) | −24.7238 | −1.26168 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.42237 | 0.174194 | ||||||||
\(387\) | −2.05468 | −0.104445 | ||||||||
\(388\) | 4.55354 | 0.231171 | ||||||||
\(389\) | 27.5404 | 1.39635 | 0.698176 | − | 0.715926i | \(-0.253995\pi\) | ||||
0.698176 | + | 0.715926i | \(0.253995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3751 | 0.524692 | ||||||||
\(392\) | −16.4454 | −0.830621 | ||||||||
\(393\) | −36.7418 | −1.85338 | ||||||||
\(394\) | 6.91353 | 0.348299 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.454591 | −0.0228441 | ||||||||
\(397\) | 4.77657 | 0.239729 | 0.119865 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119865 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(398\) | 16.1638 | 0.810217 | ||||||||
\(399\) | −0.517541 | −0.0259095 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.02237 | −0.100992 | −0.0504962 | − | 0.998724i | \(-0.516080\pi\) | ||||
−0.0504962 | + | 0.998724i | \(0.516080\pi\) | |||||||
\(402\) | 0.589804 | 0.0294168 | ||||||||
\(403\) | −8.33137 | −0.415015 | ||||||||
\(404\) | −1.04696 | −0.0520884 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.956192 | −0.0474550 | ||||||||
\(407\) | 17.8229 | 0.883450 | ||||||||
\(408\) | 33.5118 | 1.65908 | ||||||||
\(409\) | −31.4714 | −1.55616 | −0.778082 | − | 0.628163i | \(-0.783807\pi\) | ||||
−0.778082 | + | 0.628163i | \(0.783807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4417 | −0.515049 | ||||||||
\(412\) | 3.36161 | 0.165615 | ||||||||
\(413\) | 0.542335 | 0.0266866 | ||||||||
\(414\) | −0.588584 | −0.0289273 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.12127 | 0.153033 | ||||||||
\(417\) | 23.9802 | 1.17432 | ||||||||
\(418\) | −21.8996 | −1.07114 | ||||||||
\(419\) | −18.3424 | −0.896084 | −0.448042 | − | 0.894012i | \(-0.647879\pi\) | ||||
−0.448042 | + | 0.894012i | \(0.647879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.7191 | −1.35095 | −0.675474 | − | 0.737384i | \(-0.736061\pi\) | ||||
−0.675474 | + | 0.737384i | \(0.736061\pi\) | |||||||
\(422\) | −29.4359 | −1.43292 | ||||||||
\(423\) | 1.56476 | 0.0760812 | ||||||||
\(424\) | −5.27676 | −0.256262 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.27239 | −0.303898 | ||||||||
\(427\) | −0.0574940 | −0.00278233 | ||||||||
\(428\) | 3.76952 | 0.182207 | ||||||||
\(429\) | −6.14368 | −0.296619 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.86749 | 0.282627 | 0.141314 | − | 0.989965i | \(-0.454867\pi\) | ||||
0.141314 | + | 0.989965i | \(0.454867\pi\) | |||||||
\(432\) | 23.4835 | 1.12985 | ||||||||
\(433\) | −15.0366 | −0.722611 | −0.361306 | − | 0.932447i | \(-0.617669\pi\) | ||||
−0.361306 | + | 0.932447i | \(0.617669\pi\) | |||||||
\(434\) | 0.783123 | 0.0375911 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.946385 | −0.0453236 | ||||||||
\(437\) | −5.84043 | −0.279385 | ||||||||
\(438\) | 4.21441 | 0.201372 | ||||||||
\(439\) | 20.8095 | 0.993185 | 0.496593 | − | 0.867984i | \(-0.334584\pi\) | ||||
0.496593 | + | 0.867984i | \(0.334584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.96800 | −0.0937141 | ||||||||
\(442\) | −13.6005 | −0.646908 | ||||||||
\(443\) | 10.0002 | 0.475124 | 0.237562 | − | 0.971372i | \(-0.423652\pi\) | ||||
0.237562 | + | 0.971372i | \(0.423652\pi\) | |||||||
\(444\) | −5.37780 | −0.255219 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.5010 | −0.544589 | ||||||||
\(447\) | 19.9287 | 0.942596 | ||||||||
\(448\) | 0.321661 | 0.0151971 | ||||||||
\(449\) | −2.65024 | −0.125072 | −0.0625362 | − | 0.998043i | \(-0.519919\pi\) | ||||
−0.0625362 | + | 0.998043i | \(0.519919\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9367 | 0.938782 | ||||||||
\(452\) | −1.88057 | −0.0884548 | ||||||||
\(453\) | −5.31946 | −0.249930 | ||||||||
\(454\) | 29.8777 | 1.40223 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.8646 | −0.883418 | ||||||||
\(457\) | 5.43669 | 0.254318 | 0.127159 | − | 0.991882i | \(-0.459414\pi\) | ||||
0.127159 | + | 0.991882i | \(0.459414\pi\) | |||||||
\(458\) | −38.8778 | −1.81664 | ||||||||
\(459\) | −38.7571 | −1.80903 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0079 | 0.745564 | 0.372782 | − | 0.927919i | \(-0.378404\pi\) | ||||
0.372782 | + | 0.927919i | \(0.378404\pi\) | |||||||
\(462\) | 0.577487 | 0.0268671 | ||||||||
\(463\) | 1.33278 | 0.0619394 | 0.0309697 | − | 0.999520i | \(-0.490140\pi\) | ||||
0.0309697 | + | 0.999520i | \(0.490140\pi\) | |||||||
\(464\) | −44.5475 | −2.06807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.4263 | −0.668284 | ||||||||
\(467\) | −7.86721 | −0.364051 | −0.182026 | − | 0.983294i | \(-0.558265\pi\) | ||||
−0.182026 | + | 0.983294i | \(0.558265\pi\) | |||||||
\(468\) | 0.158924 | 0.00734628 | ||||||||
\(469\) | −0.0132308 | −0.000610944 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.0782 | 1.29378 | ||||||||
\(472\) | 19.7684 | 0.909914 | ||||||||
\(473\) | 22.7498 | 1.04604 | ||||||||
\(474\) | −18.9911 | −0.872288 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.263323 | 0.0120694 | ||||||||
\(477\) | −0.631460 | −0.0289126 | ||||||||
\(478\) | 8.94070 | 0.408938 | ||||||||
\(479\) | 7.30904 | 0.333958 | 0.166979 | − | 0.985960i | \(-0.446599\pi\) | ||||
0.166979 | + | 0.985960i | \(0.446599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.23087 | −0.284103 | ||||||||
\(482\) | −1.58708 | −0.0722895 | ||||||||
\(483\) | 0.154011 | 0.00700773 | ||||||||
\(484\) | −0.673736 | −0.0306244 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.62491 | 0.209790 | ||||||||
\(487\) | 24.3739 | 1.10449 | 0.552243 | − | 0.833683i | \(-0.313772\pi\) | ||||
0.552243 | + | 0.833683i | \(0.313772\pi\) | |||||||
\(488\) | −2.09569 | −0.0948672 | ||||||||
\(489\) | −13.9732 | −0.631890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6542 | 0.706465 | 0.353232 | − | 0.935536i | \(-0.385083\pi\) | ||||
0.353232 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(492\) | −6.01559 | −0.271204 | ||||||||
\(493\) | 73.5212 | 3.31123 | ||||||||
\(494\) | 7.65606 | 0.344462 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.4845 | 1.63820 | ||||||||
\(497\) | 0.140706 | 0.00631153 | ||||||||
\(498\) | 34.3201 | 1.53792 | ||||||||
\(499\) | −28.7368 | −1.28644 | −0.643218 | − | 0.765683i | \(-0.722401\pi\) | ||||
−0.643218 | + | 0.765683i | \(0.722401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3601 | −0.820269 | ||||||||
\(502\) | 22.7722 | 1.01637 | ||||||||
\(503\) | −0.207761 | −0.00926360 | −0.00463180 | − | 0.999989i | \(-0.501474\pi\) | ||||
−0.00463180 | + | 0.999989i | \(0.501474\pi\) | |||||||
\(504\) | 0.0426473 | 0.00189966 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.51691 | 0.289712 | ||||||||
\(507\) | −21.4009 | −0.950446 | ||||||||
\(508\) | −9.34048 | −0.414417 | ||||||||
\(509\) | 9.52541 | 0.422206 | 0.211103 | − | 0.977464i | \(-0.432294\pi\) | ||||
0.211103 | + | 0.977464i | \(0.432294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0945401 | −0.00418221 | ||||||||
\(512\) | 8.75036 | 0.386715 | ||||||||
\(513\) | 21.8174 | 0.963261 | ||||||||
\(514\) | −20.0393 | −0.883894 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.86441 | −0.302189 | ||||||||
\(517\) | −17.3253 | −0.761966 | ||||||||
\(518\) | 0.585683 | 0.0257334 | ||||||||
\(519\) | −11.3346 | −0.497536 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.1721 | 1.49711 | 0.748553 | − | 0.663075i | \(-0.230749\pi\) | ||||
0.748553 | + | 0.663075i | \(0.230749\pi\) | |||||||
\(522\) | −4.17088 | −0.182554 | ||||||||
\(523\) | 19.9061 | 0.870432 | 0.435216 | − | 0.900326i | \(-0.356672\pi\) | ||||
0.435216 | + | 0.900326i | \(0.356672\pi\) | |||||||
\(524\) | −10.5234 | −0.459717 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.9359 | 1.17446 | ||||||||
\(527\) | −60.2139 | −2.62296 | ||||||||
\(528\) | 26.9042 | 1.17085 | ||||||||
\(529\) | −21.2620 | −0.924435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.36565 | 0.102660 | ||||||||
\(532\) | −0.148231 | −0.00642665 | ||||||||
\(533\) | −6.96984 | −0.301897 | ||||||||
\(534\) | 9.80362 | 0.424244 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.482271 | −0.0208309 | ||||||||
\(537\) | −37.1120 | −1.60150 | ||||||||
\(538\) | 35.3760 | 1.52517 | ||||||||
\(539\) | 21.7900 | 0.938562 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.8350 | −0.637808 | −0.318904 | − | 0.947787i | \(-0.603315\pi\) | ||||
−0.318904 | + | 0.947787i | \(0.603315\pi\) | |||||||
\(542\) | 48.2425 | 2.07219 | ||||||||
\(543\) | −11.5640 | −0.496258 | ||||||||
\(544\) | 22.5586 | 0.967191 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.201889 | −0.00864003 | ||||||||
\(547\) | −26.9418 | −1.15195 | −0.575974 | − | 0.817468i | \(-0.695377\pi\) | ||||
−0.575974 | + | 0.817468i | \(0.695377\pi\) | |||||||
\(548\) | −2.99065 | −0.127754 | ||||||||
\(549\) | −0.250787 | −0.0107033 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.3870 | −1.76314 | ||||||||
\(552\) | 5.61377 | 0.238938 | ||||||||
\(553\) | 0.426019 | 0.0181162 | ||||||||
\(554\) | 5.73546 | 0.243677 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.86829 | 0.291280 | ||||||||
\(557\) | −35.8208 | −1.51777 | −0.758887 | − | 0.651222i | \(-0.774257\pi\) | ||||
−0.758887 | + | 0.651222i | \(0.774257\pi\) | |||||||
\(558\) | 3.41596 | 0.144609 | ||||||||
\(559\) | −7.95331 | −0.336389 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.4027 | −1.87468 | ||||||||
\(562\) | 14.3075 | 0.603526 | ||||||||
\(563\) | 39.5803 | 1.66811 | 0.834055 | − | 0.551682i | \(-0.186014\pi\) | ||||
0.834055 | + | 0.551682i | \(0.186014\pi\) | |||||||
\(564\) | 5.22765 | 0.220124 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.63854 | −0.110906 | ||||||||
\(567\) | −0.629745 | −0.0264468 | ||||||||
\(568\) | 5.12881 | 0.215200 | ||||||||
\(569\) | 7.96023 | 0.333710 | 0.166855 | − | 0.985981i | \(-0.446639\pi\) | ||||
0.166855 | + | 0.985981i | \(0.446639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.11420 | 0.130325 | 0.0651625 | − | 0.997875i | \(-0.479243\pi\) | ||||
0.0651625 | + | 0.997875i | \(0.479243\pi\) | |||||||
\(572\) | −1.75964 | −0.0735742 | ||||||||
\(573\) | 17.1491 | 0.716415 | ||||||||
\(574\) | 0.655143 | 0.0273452 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.40307 | 0.0584614 | ||||||||
\(577\) | −1.43705 | −0.0598250 | −0.0299125 | − | 0.999553i | \(-0.509523\pi\) | ||||
−0.0299125 | + | 0.999553i | \(0.509523\pi\) | |||||||
\(578\) | −71.3154 | −2.96633 | ||||||||
\(579\) | −3.90617 | −0.162335 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.769888 | −0.0319403 | ||||||||
\(582\) | −25.2321 | −1.04590 | ||||||||
\(583\) | 6.99164 | 0.289564 | ||||||||
\(584\) | −3.44604 | −0.142598 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.0209 | 1.98373 | ||||||||
\(587\) | −13.8048 | −0.569783 | −0.284892 | − | 0.958560i | \(-0.591958\pi\) | ||||
−0.284892 | + | 0.958560i | \(0.591958\pi\) | |||||||
\(588\) | −6.57480 | −0.271140 | ||||||||
\(589\) | 33.8960 | 1.39666 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.89087 | −0.324587 | ||||||||
\(592\) | 27.2860 | 1.12145 | ||||||||
\(593\) | 6.55202 | 0.269059 | 0.134530 | − | 0.990910i | \(-0.457048\pi\) | ||||
0.134530 | + | 0.990910i | \(0.457048\pi\) | |||||||
\(594\) | −24.3444 | −0.998864 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.70788 | 0.233804 | ||||||||
\(597\) | −18.4488 | −0.755058 | ||||||||
\(598\) | −2.27830 | −0.0931667 | ||||||||
\(599\) | −0.304293 | −0.0124331 | −0.00621653 | − | 0.999981i | \(-0.501979\pi\) | ||||
−0.00621653 | + | 0.999981i | \(0.501979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.74779 | −0.234457 | −0.117229 | − | 0.993105i | \(-0.537401\pi\) | ||||
−0.117229 | + | 0.993105i | \(0.537401\pi\) | |||||||
\(602\) | 0.747586 | 0.0304693 | ||||||||
\(603\) | −0.0577125 | −0.00235023 | ||||||||
\(604\) | −1.52357 | −0.0619933 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.80143 | 0.235667 | ||||||||
\(607\) | 8.27242 | 0.335767 | 0.167884 | − | 0.985807i | \(-0.446307\pi\) | ||||
0.167884 | + | 0.985807i | \(0.446307\pi\) | |||||||
\(608\) | −12.6988 | −0.515005 | ||||||||
\(609\) | 1.09137 | 0.0442243 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.05690 | 0.245036 | ||||||||
\(612\) | 1.14861 | 0.0464297 | ||||||||
\(613\) | −7.23604 | −0.292261 | −0.146130 | − | 0.989265i | \(-0.546682\pi\) | ||||
−0.146130 | + | 0.989265i | \(0.546682\pi\) | |||||||
\(614\) | 46.1695 | 1.86325 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.472199 | −0.0190255 | ||||||||
\(617\) | 38.1701 | 1.53667 | 0.768335 | − | 0.640048i | \(-0.221086\pi\) | ||||
0.768335 | + | 0.640048i | \(0.221086\pi\) | |||||||
\(618\) | −18.6274 | −0.749302 | ||||||||
\(619\) | 19.8009 | 0.795865 | 0.397932 | − | 0.917415i | \(-0.369728\pi\) | ||||
0.397932 | + | 0.917415i | \(0.369728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.49245 | −0.260533 | ||||||||
\(622\) | −0.321584 | −0.0128943 | ||||||||
\(623\) | −0.219921 | −0.00881093 | ||||||||
\(624\) | −9.40567 | −0.376528 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24.3054 | −0.971437 | ||||||||
\(627\) | 24.9954 | 0.998221 | ||||||||
\(628\) | 8.04201 | 0.320911 | ||||||||
\(629\) | −45.0329 | −1.79558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.7838 | −1.38472 | −0.692362 | − | 0.721551i | \(-0.743430\pi\) | ||||
−0.692362 | + | 0.721551i | \(0.743430\pi\) | |||||||
\(632\) | 15.5286 | 0.617695 | ||||||||
\(633\) | 33.5971 | 1.33537 | ||||||||
\(634\) | −21.4067 | −0.850171 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.10962 | −0.0836519 | ||||||||
\(637\) | −7.61776 | −0.301827 | ||||||||
\(638\) | 46.1807 | 1.82831 | ||||||||
\(639\) | 0.613755 | 0.0242798 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.1011 | −1.78139 | −0.890694 | − | 0.454603i | \(-0.849781\pi\) | ||||
−0.890694 | + | 0.454603i | \(0.849781\pi\) | |||||||
\(642\) | −20.8876 | −0.824370 | ||||||||
\(643\) | 22.6840 | 0.894569 | 0.447285 | − | 0.894392i | \(-0.352391\pi\) | ||||
0.447285 | + | 0.894392i | \(0.352391\pi\) | |||||||
\(644\) | 0.0441109 | 0.00173821 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 55.3332 | 2.17706 | ||||||||
\(647\) | 5.70435 | 0.224261 | 0.112131 | − | 0.993693i | \(-0.464233\pi\) | ||||
0.112131 | + | 0.993693i | \(0.464233\pi\) | |||||||
\(648\) | −22.9546 | −0.901740 | ||||||||
\(649\) | −26.1929 | −1.02816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.893830 | −0.0350319 | ||||||||
\(652\) | −4.00213 | −0.156735 | ||||||||
\(653\) | −9.26570 | −0.362595 | −0.181297 | − | 0.983428i | \(-0.558030\pi\) | ||||
−0.181297 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(654\) | 5.24410 | 0.205061 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.5221 | 1.19169 | ||||||||
\(657\) | −0.412381 | −0.0160885 | ||||||||
\(658\) | −0.569330 | −0.0221948 | ||||||||
\(659\) | 33.4266 | 1.30212 | 0.651058 | − | 0.759028i | \(-0.274325\pi\) | ||||
0.651058 | + | 0.759028i | \(0.274325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9425 | −1.51469 | −0.757345 | − | 0.653015i | \(-0.773504\pi\) | ||||
−0.757345 | + | 0.653015i | \(0.773504\pi\) | |||||||
\(662\) | −51.3480 | −1.99570 | ||||||||
\(663\) | 15.5231 | 0.602868 | ||||||||
\(664\) | −28.0628 | −1.08905 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.55473 | 0.0989937 | ||||||||
\(667\) | 12.3160 | 0.476878 | ||||||||
\(668\) | −5.25861 | −0.203462 | ||||||||
\(669\) | 13.1269 | 0.507514 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.77676 | 0.107195 | ||||||||
\(672\) | 0.334865 | 0.0129177 | ||||||||
\(673\) | −27.0760 | −1.04370 | −0.521851 | − | 0.853037i | \(-0.674758\pi\) | ||||
−0.521851 | + | 0.853037i | \(0.674758\pi\) | |||||||
\(674\) | 23.5360 | 0.906572 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.12953 | −0.235751 | ||||||||
\(677\) | −40.1184 | −1.54187 | −0.770937 | − | 0.636911i | \(-0.780212\pi\) | ||||
−0.770937 | + | 0.636911i | \(0.780212\pi\) | |||||||
\(678\) | 10.4206 | 0.400202 | ||||||||
\(679\) | 0.566021 | 0.0217219 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.1014 | −1.30677 | ||||||||
\(682\) | −37.8221 | −1.44828 | ||||||||
\(683\) | 9.16420 | 0.350658 | 0.175329 | − | 0.984510i | \(-0.443901\pi\) | ||||
0.175329 | + | 0.984510i | \(0.443901\pi\) | |||||||
\(684\) | −0.646580 | −0.0247226 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.43252 | 0.0546938 | ||||||||
\(687\) | 44.3738 | 1.69297 | ||||||||
\(688\) | 34.8289 | 1.32784 | ||||||||
\(689\) | −2.44427 | −0.0931192 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.48079 | −0.132415 | −0.0662077 | − | 0.997806i | \(-0.521090\pi\) | ||||
−0.0662077 | + | 0.997806i | \(0.521090\pi\) | |||||||
\(692\) | −3.24641 | −0.123410 | ||||||||
\(693\) | −0.0565072 | −0.00214653 | ||||||||
\(694\) | 39.7817 | 1.51009 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 39.7808 | 1.50789 | ||||||||
\(697\) | −50.3736 | −1.90804 | ||||||||
\(698\) | −30.5005 | −1.15446 | ||||||||
\(699\) | 16.4656 | 0.622788 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.3573 | −0.580036 | −0.290018 | − | 0.957021i | \(-0.593661\pi\) | ||||
−0.290018 | + | 0.957021i | \(0.593661\pi\) | |||||||
\(702\) | 8.51078 | 0.321219 | ||||||||
\(703\) | 25.3502 | 0.956100 | ||||||||
\(704\) | −15.5351 | −0.585501 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.8977 | 1.35103 | ||||||||
\(707\) | −0.130141 | −0.00489446 | ||||||||
\(708\) | 7.90329 | 0.297024 | ||||||||
\(709\) | −46.4365 | −1.74396 | −0.871979 | − | 0.489543i | \(-0.837164\pi\) | ||||
−0.871979 | + | 0.489543i | \(0.837164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.85828 | 0.0696909 | ||||||||
\(712\) | −8.01622 | −0.300421 | ||||||||
\(713\) | −10.0868 | −0.377755 | ||||||||
\(714\) | −1.45912 | −0.0546064 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.6294 | −0.397240 | ||||||||
\(717\) | −10.2046 | −0.381098 | ||||||||
\(718\) | −15.0682 | −0.562338 | ||||||||
\(719\) | 31.5267 | 1.17575 | 0.587875 | − | 0.808952i | \(-0.299965\pi\) | ||||
0.587875 | + | 0.808952i | \(0.299965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.417860 | 0.0155619 | ||||||||
\(722\) | −0.993984 | −0.0369923 | ||||||||
\(723\) | 1.81144 | 0.0673681 | ||||||||
\(724\) | −3.31209 | −0.123093 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.73330 | 0.138556 | ||||||||
\(727\) | −3.11621 | −0.115574 | −0.0577870 | − | 0.998329i | \(-0.518404\pi\) | ||||
−0.0577870 | + | 0.998329i | \(0.518404\pi\) | |||||||
\(728\) | 0.165080 | 0.00611828 | ||||||||
\(729\) | 24.0157 | 0.889469 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −57.4815 | −2.12603 | ||||||||
\(732\) | −0.837843 | −0.0309676 | ||||||||
\(733\) | −12.7951 | −0.472599 | −0.236299 | − | 0.971680i | \(-0.575935\pi\) | ||||
−0.236299 | + | 0.971680i | \(0.575935\pi\) | |||||||
\(734\) | 46.2752 | 1.70805 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.77893 | 0.139293 | ||||||||
\(737\) | 0.639003 | 0.0235380 | ||||||||
\(738\) | 2.85771 | 0.105194 | ||||||||
\(739\) | −30.5478 | −1.12372 | −0.561860 | − | 0.827232i | \(-0.689914\pi\) | ||||
−0.561860 | + | 0.827232i | \(0.689914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.73836 | −0.321012 | ||||||||
\(742\) | 0.229754 | 0.00843452 | ||||||||
\(743\) | 2.28803 | 0.0839397 | 0.0419699 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419699 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(744\) | −32.5806 | −1.19446 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −55.8633 | −2.04530 | ||||||||
\(747\) | −3.35823 | −0.122871 | ||||||||
\(748\) | −12.7176 | −0.465001 | ||||||||
\(749\) | 0.468564 | 0.0171210 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.3570 | −1.47265 | −0.736323 | − | 0.676630i | \(-0.763440\pi\) | ||||
−0.736323 | + | 0.676630i | \(0.763440\pi\) | |||||||
\(752\) | −26.5242 | −0.967238 | ||||||||
\(753\) | −25.9914 | −0.947179 | ||||||||
\(754\) | −16.1447 | −0.587956 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.164780 | −0.00599299 | ||||||||
\(757\) | −2.91012 | −0.105770 | −0.0528851 | − | 0.998601i | \(-0.516842\pi\) | ||||
−0.0528851 | + | 0.998601i | \(0.516842\pi\) | |||||||
\(758\) | 50.6511 | 1.83973 | ||||||||
\(759\) | −7.43818 | −0.269989 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.6866 | −1.36614 | −0.683069 | − | 0.730354i | \(-0.739355\pi\) | ||||
−0.683069 | + | 0.730354i | \(0.739355\pi\) | |||||||
\(762\) | 51.7574 | 1.87497 | ||||||||
\(763\) | −0.117639 | −0.00425881 | ||||||||
\(764\) | 4.91176 | 0.177701 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.1438 | 1.16140 | ||||||||
\(767\) | 9.15699 | 0.330640 | ||||||||
\(768\) | 21.1690 | 0.763869 | ||||||||
\(769\) | 5.83460 | 0.210401 | 0.105201 | − | 0.994451i | \(-0.466452\pi\) | ||||
0.105201 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.8721 | 0.823720 | ||||||||
\(772\) | −1.11878 | −0.0402659 | ||||||||
\(773\) | 15.0568 | 0.541554 | 0.270777 | − | 0.962642i | \(-0.412719\pi\) | ||||
0.270777 | + | 0.962642i | \(0.412719\pi\) | |||||||
\(774\) | 3.26094 | 0.117212 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.6318 | 0.740637 | ||||||||
\(777\) | −0.668478 | −0.0239815 | ||||||||
\(778\) | −43.7087 | −1.56703 | ||||||||
\(779\) | 28.3566 | 1.01598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.79561 | −0.243166 | ||||||||
\(782\) | −16.4661 | −0.588828 | ||||||||
\(783\) | −46.0074 | −1.64417 | ||||||||
\(784\) | 33.3594 | 1.19141 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 58.3122 | 2.07993 | ||||||||
\(787\) | −8.82663 | −0.314635 | −0.157318 | − | 0.987548i | \(-0.550285\pi\) | ||||
−0.157318 | + | 0.987548i | \(0.550285\pi\) | |||||||
\(788\) | −2.26006 | −0.0805114 | ||||||||
\(789\) | −30.7437 | −1.09450 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.233762 | −0.00831161 | ||||||||
\(792\) | −2.05972 | −0.0731889 | ||||||||
\(793\) | −0.970750 | −0.0344723 | ||||||||
\(794\) | −7.58079 | −0.269032 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.28400 | −0.187286 | ||||||||
\(797\) | 17.7244 | 0.627831 | 0.313916 | − | 0.949451i | \(-0.398359\pi\) | ||||
0.313916 | + | 0.949451i | \(0.398359\pi\) | |||||||
\(798\) | 0.821379 | 0.0290765 | ||||||||
\(799\) | 43.7755 | 1.54867 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.959286 | −0.0338947 | ||||||||
\(802\) | 3.20966 | 0.113337 | ||||||||
\(803\) | 4.56596 | 0.161129 | ||||||||
\(804\) | −0.192809 | −0.00679986 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.2225 | 0.465744 | ||||||||
\(807\) | −40.3770 | −1.42134 | ||||||||
\(808\) | −4.74371 | −0.166883 | ||||||||
\(809\) | −23.8068 | −0.837003 | −0.418502 | − | 0.908216i | \(-0.637445\pi\) | ||||
−0.418502 | + | 0.908216i | \(0.637445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4561 | −1.42061 | −0.710303 | − | 0.703896i | \(-0.751442\pi\) | ||||
−0.710303 | + | 0.703896i | \(0.751442\pi\) | |||||||
\(812\) | 0.312583 | 0.0109695 | ||||||||
\(813\) | −55.0623 | −1.93112 | ||||||||
\(814\) | −28.2864 | −0.991438 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −67.9783 | −2.37972 | ||||||||
\(817\) | 32.3578 | 1.13206 | ||||||||
\(818\) | 49.9477 | 1.74638 | ||||||||
\(819\) | 0.0197548 | 0.000690290 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.14174 | 0.109647 | 0.0548237 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548237 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(822\) | 16.5718 | 0.578006 | ||||||||
\(823\) | −8.01920 | −0.279532 | −0.139766 | − | 0.990185i | \(-0.544635\pi\) | ||||
−0.139766 | + | 0.990185i | \(0.544635\pi\) | |||||||
\(824\) | 15.2312 | 0.530605 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.860729 | −0.0299486 | ||||||||
\(827\) | −8.81985 | −0.306696 | −0.153348 | − | 0.988172i | \(-0.549006\pi\) | ||||
−0.153348 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(828\) | 0.192410 | 0.00668672 | ||||||||
\(829\) | 32.1961 | 1.11822 | 0.559109 | − | 0.829094i | \(-0.311143\pi\) | ||||
0.559109 | + | 0.829094i | \(0.311143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.54626 | −0.227087 | ||||||||
\(832\) | 5.43105 | 0.188288 | ||||||||
\(833\) | −55.0564 | −1.90759 | ||||||||
\(834\) | −38.0585 | −1.31786 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.15906 | 0.247601 | ||||||||
\(837\) | 37.6801 | 1.30242 | ||||||||
\(838\) | 29.1108 | 1.00562 | ||||||||
\(839\) | −28.0117 | −0.967070 | −0.483535 | − | 0.875325i | \(-0.660647\pi\) | ||||
−0.483535 | + | 0.875325i | \(0.660647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.2748 | 2.00948 | ||||||||
\(842\) | 43.9925 | 1.51608 | ||||||||
\(843\) | −16.3301 | −0.562439 | ||||||||
\(844\) | 9.62272 | 0.331228 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.48340 | −0.0853810 | ||||||||
\(847\) | −0.0837477 | −0.00287761 | ||||||||
\(848\) | 10.7039 | 0.367572 | ||||||||
\(849\) | 3.01154 | 0.103356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.54374 | −0.258596 | ||||||||
\(852\) | 2.05047 | 0.0702480 | ||||||||
\(853\) | 55.6683 | 1.90605 | 0.953023 | − | 0.302898i | \(-0.0979541\pi\) | ||||
0.953023 | + | 0.302898i | \(0.0979541\pi\) | |||||||
\(854\) | 0.0912475 | 0.00312243 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.0794 | 0.583762 | ||||||||
\(857\) | 8.05803 | 0.275257 | 0.137629 | − | 0.990484i | \(-0.456052\pi\) | ||||
0.137629 | + | 0.990484i | \(0.456052\pi\) | |||||||
\(858\) | 9.75051 | 0.332877 | ||||||||
\(859\) | 24.6779 | 0.841999 | 0.421000 | − | 0.907061i | \(-0.361679\pi\) | ||||
0.421000 | + | 0.907061i | \(0.361679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.747758 | −0.0254835 | ||||||||
\(862\) | −9.31218 | −0.317174 | ||||||||
\(863\) | 4.35714 | 0.148319 | 0.0741594 | − | 0.997246i | \(-0.476373\pi\) | ||||
0.0741594 | + | 0.997246i | \(0.476373\pi\) | |||||||
\(864\) | −14.1165 | −0.480253 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.8642 | 0.810940 | ||||||||
\(867\) | 81.3969 | 2.76438 | ||||||||
\(868\) | −0.256006 | −0.00868941 | ||||||||
\(869\) | −20.5752 | −0.697966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.223395 | −0.00756944 | ||||||||
\(872\) | −4.28800 | −0.145210 | ||||||||
\(873\) | 2.46896 | 0.0835618 | ||||||||
\(874\) | 9.26922 | 0.313536 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.37771 | −0.0465484 | ||||||||
\(877\) | −33.5278 | −1.13215 | −0.566076 | − | 0.824353i | \(-0.691539\pi\) | ||||
−0.566076 | + | 0.824353i | \(0.691539\pi\) | |||||||
\(878\) | −33.0264 | −1.11459 | ||||||||
\(879\) | −54.8094 | −1.84868 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.62147 | 0.0883196 | 0.0441598 | − | 0.999024i | \(-0.485939\pi\) | ||||
0.0441598 | + | 0.999024i | \(0.485939\pi\) | |||||||
\(882\) | 3.12337 | 0.105169 | ||||||||
\(883\) | −18.5159 | −0.623109 | −0.311554 | − | 0.950228i | \(-0.600850\pi\) | ||||
−0.311554 | + | 0.950228i | \(0.600850\pi\) | |||||||
\(884\) | 4.44605 | 0.149537 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.8711 | −0.533201 | ||||||||
\(887\) | 38.9847 | 1.30898 | 0.654489 | − | 0.756072i | \(-0.272884\pi\) | ||||
0.654489 | + | 0.756072i | \(0.272884\pi\) | |||||||
\(888\) | −24.3664 | −0.817682 | ||||||||
\(889\) | −1.16105 | −0.0389405 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.4145 | 1.01892 | ||||||||
\(892\) | 3.75973 | 0.125885 | ||||||||
\(893\) | −24.6424 | −0.824626 | ||||||||
\(894\) | −31.6285 | −1.05781 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.880224 | −0.0294062 | ||||||||
\(897\) | 2.60038 | 0.0868240 | ||||||||
\(898\) | 4.20614 | 0.140361 | ||||||||
\(899\) | −71.4782 | −2.38393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6657 | −0.588528 | ||||||||
\(902\) | −31.6411 | −1.05353 | ||||||||
\(903\) | −0.853269 | −0.0283950 | ||||||||
\(904\) | −8.52074 | −0.283396 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.44241 | 0.280480 | ||||||||
\(907\) | −24.5838 | −0.816292 | −0.408146 | − | 0.912917i | \(-0.633825\pi\) | ||||
−0.408146 | + | 0.912917i | \(0.633825\pi\) | |||||||
\(908\) | −9.76714 | −0.324134 | ||||||||
\(909\) | −0.567671 | −0.0188285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.85950 | −0.0616080 | −0.0308040 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308040 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(912\) | 38.2668 | 1.26714 | ||||||||
\(913\) | 37.1829 | 1.23057 | ||||||||
\(914\) | −8.62847 | −0.285404 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.7093 | 0.419927 | ||||||||
\(917\) | −1.30810 | −0.0431971 | ||||||||
\(918\) | 61.5106 | 2.03015 | ||||||||
\(919\) | −52.9084 | −1.74529 | −0.872644 | − | 0.488357i | \(-0.837597\pi\) | ||||
−0.872644 | + | 0.488357i | \(0.837597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.6963 | −1.73640 | ||||||||
\(922\) | −25.4059 | −0.836698 | ||||||||
\(923\) | 2.37574 | 0.0781983 | ||||||||
\(924\) | −0.188783 | −0.00621049 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.11522 | −0.0695106 | ||||||||
\(927\) | 1.82269 | 0.0598650 | ||||||||
\(928\) | 26.7786 | 0.879052 | ||||||||
\(929\) | 44.0809 | 1.44625 | 0.723124 | − | 0.690718i | \(-0.242705\pi\) | ||||
0.723124 | + | 0.690718i | \(0.242705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.9927 | 1.01574 | ||||||||
\(932\) | 4.71600 | 0.154478 | ||||||||
\(933\) | 0.367045 | 0.0120165 | ||||||||
\(934\) | 12.4859 | 0.408551 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.720074 | 0.0235364 | ||||||||
\(937\) | −52.8193 | −1.72553 | −0.862765 | − | 0.505604i | \(-0.831270\pi\) | ||||
−0.862765 | + | 0.505604i | \(0.831270\pi\) | |||||||
\(938\) | 0.0209984 | 0.000685622 0 | ||||||||
\(939\) | 27.7413 | 0.905303 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3015 | 0.401017 | 0.200508 | − | 0.979692i | \(-0.435741\pi\) | ||||
0.200508 | + | 0.979692i | \(0.435741\pi\) | |||||||
\(942\) | −44.5624 | −1.45192 | ||||||||
\(943\) | −8.43841 | −0.274793 | ||||||||
\(944\) | −40.1000 | −1.30514 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.1058 | −1.17390 | ||||||||
\(947\) | 7.11954 | 0.231354 | 0.115677 | − | 0.993287i | \(-0.463096\pi\) | ||||
0.115677 | + | 0.993287i | \(0.463096\pi\) | |||||||
\(948\) | 6.20826 | 0.201635 | ||||||||
\(949\) | −1.59625 | −0.0518165 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.4329 | 0.792292 | ||||||||
\(952\) | 1.19310 | 0.0386685 | ||||||||
\(953\) | −11.3501 | −0.367665 | −0.183832 | − | 0.982958i | \(-0.558850\pi\) | ||||
−0.183832 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(954\) | 1.00218 | 0.0324467 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.92275 | −0.0945285 | ||||||||
\(957\) | −52.7091 | −1.70384 | ||||||||
\(958\) | −11.6000 | −0.374780 | ||||||||
\(959\) | −0.371748 | −0.0120044 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.5408 | 0.888412 | ||||||||
\(962\) | 9.88889 | 0.318831 | ||||||||
\(963\) | 2.04386 | 0.0658625 | ||||||||
\(964\) | 0.518823 | 0.0167102 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.244427 | −0.00786432 | ||||||||
\(967\) | 51.3389 | 1.65095 | 0.825473 | − | 0.564441i | \(-0.190908\pi\) | ||||
0.825473 | + | 0.564441i | \(0.190908\pi\) | |||||||
\(968\) | −3.05265 | −0.0981158 | ||||||||
\(969\) | −63.1554 | −2.02884 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3139 | 1.45419 | 0.727097 | − | 0.686535i | \(-0.240869\pi\) | ||||
0.727097 | + | 0.686535i | \(0.240869\pi\) | |||||||
\(972\) | −1.51190 | −0.0484943 | ||||||||
\(973\) | 0.853752 | 0.0273700 | ||||||||
\(974\) | −38.6833 | −1.23949 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.25108 | 0.136074 | ||||||||
\(977\) | 49.5972 | 1.58675 | 0.793377 | − | 0.608730i | \(-0.208321\pi\) | ||||
0.793377 | + | 0.608730i | \(0.208321\pi\) | |||||||
\(978\) | 22.1766 | 0.709129 | ||||||||
\(979\) | 10.6214 | 0.339461 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.513137 | −0.0163832 | ||||||||
\(982\) | −24.8445 | −0.792819 | ||||||||
\(983\) | −43.7321 | −1.39484 | −0.697418 | − | 0.716665i | \(-0.745668\pi\) | ||||
−0.697418 | + | 0.716665i | \(0.745668\pi\) | |||||||
\(984\) | −27.2562 | −0.868895 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −116.684 | −3.71597 | ||||||||
\(987\) | 0.649814 | 0.0206838 | ||||||||
\(988\) | −2.50280 | −0.0796246 | ||||||||
\(989\) | −9.62910 | −0.306188 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7710 | 1.45396 | 0.726981 | − | 0.686657i | \(-0.240923\pi\) | ||||
0.726981 | + | 0.686657i | \(0.240923\pi\) | |||||||
\(992\) | −21.9317 | −0.696334 | ||||||||
\(993\) | 58.6068 | 1.85983 | ||||||||
\(994\) | −0.223312 | −0.00708302 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.2194 | −0.355499 | ||||||||
\(997\) | 38.4455 | 1.21758 | 0.608790 | − | 0.793331i | \(-0.291655\pi\) | ||||
0.608790 | + | 0.793331i | \(0.291655\pi\) | |||||||
\(998\) | 45.6076 | 1.44368 | ||||||||
\(999\) | 28.1803 | 0.891584 |
(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 | 6025.2.a.m.1.12 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.n.1.29 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.12 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.n.1.29 | yes | 40 | 5.4 | even | 2 |