Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49199 | −1.76211 | −0.881053 | − | 0.473018i | \(-0.843165\pi\) | ||||
−0.881053 | + | 0.473018i | \(0.843165\pi\) | |||||||
\(3\) | 1.36067 | 0.785582 | 0.392791 | − | 0.919628i | \(-0.371510\pi\) | ||||
0.392791 | + | 0.919628i | \(0.371510\pi\) | |||||||
\(4\) | 4.21003 | 2.10502 | ||||||||
\(5\) | −1.81458 | −0.811503 | −0.405751 | − | 0.913983i | \(-0.632990\pi\) | ||||
−0.405751 | + | 0.913983i | \(0.632990\pi\) | |||||||
\(6\) | −3.39077 | −1.38428 | ||||||||
\(7\) | 0.512290 | 0.193627 | 0.0968136 | − | 0.995303i | \(-0.469135\pi\) | ||||
0.0968136 | + | 0.995303i | \(0.469135\pi\) | |||||||
\(8\) | −5.50738 | −1.94715 | ||||||||
\(9\) | −1.14858 | −0.382862 | ||||||||
\(10\) | 4.52191 | 1.42995 | ||||||||
\(11\) | −3.00840 | −0.907067 | −0.453534 | − | 0.891239i | \(-0.649837\pi\) | ||||
−0.453534 | + | 0.891239i | \(0.649837\pi\) | |||||||
\(12\) | 5.72845 | 1.65366 | ||||||||
\(13\) | −2.35946 | −0.654397 | −0.327198 | − | 0.944956i | \(-0.606105\pi\) | ||||
−0.327198 | + | 0.944956i | \(0.606105\pi\) | |||||||
\(14\) | −1.27662 | −0.341192 | ||||||||
\(15\) | −2.46903 | −0.637502 | ||||||||
\(16\) | 5.30430 | 1.32608 | ||||||||
\(17\) | 3.40058 | 0.824763 | 0.412381 | − | 0.911011i | \(-0.364697\pi\) | ||||
0.412381 | + | 0.911011i | \(0.364697\pi\) | |||||||
\(18\) | 2.86227 | 0.674643 | ||||||||
\(19\) | −3.31296 | −0.760046 | −0.380023 | − | 0.924977i | \(-0.624084\pi\) | ||||
−0.380023 | + | 0.924977i | \(0.624084\pi\) | |||||||
\(20\) | −7.63942 | −1.70823 | ||||||||
\(21\) | 0.697056 | 0.152110 | ||||||||
\(22\) | 7.49692 | 1.59835 | ||||||||
\(23\) | −4.63075 | −0.965578 | −0.482789 | − | 0.875737i | \(-0.660376\pi\) | ||||
−0.482789 | + | 0.875737i | \(0.660376\pi\) | |||||||
\(24\) | −7.49372 | −1.52965 | ||||||||
\(25\) | −1.70732 | −0.341463 | ||||||||
\(26\) | 5.87976 | 1.15312 | ||||||||
\(27\) | −5.64484 | −1.08635 | ||||||||
\(28\) | 2.15676 | 0.407588 | ||||||||
\(29\) | 4.84984 | 0.900593 | 0.450297 | − | 0.892879i | \(-0.351318\pi\) | ||||
0.450297 | + | 0.892879i | \(0.351318\pi\) | |||||||
\(30\) | 6.15281 | 1.12335 | ||||||||
\(31\) | −7.08465 | −1.27244 | −0.636220 | − | 0.771508i | \(-0.719503\pi\) | ||||
−0.636220 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(32\) | −2.20351 | −0.389530 | ||||||||
\(33\) | −4.09343 | −0.712575 | ||||||||
\(34\) | −8.47423 | −1.45332 | ||||||||
\(35\) | −0.929588 | −0.157129 | ||||||||
\(36\) | −4.83558 | −0.805930 | ||||||||
\(37\) | −3.49372 | −0.574364 | −0.287182 | − | 0.957876i | \(-0.592718\pi\) | ||||
−0.287182 | + | 0.957876i | \(0.592718\pi\) | |||||||
\(38\) | 8.25588 | 1.33928 | ||||||||
\(39\) | −3.21044 | −0.514082 | ||||||||
\(40\) | 9.99356 | 1.58012 | ||||||||
\(41\) | 9.86767 | 1.54107 | 0.770535 | − | 0.637397i | \(-0.219989\pi\) | ||||
0.770535 | + | 0.637397i | \(0.219989\pi\) | |||||||
\(42\) | −1.73706 | −0.268034 | ||||||||
\(43\) | 2.36986 | 0.361401 | 0.180700 | − | 0.983538i | \(-0.442164\pi\) | ||||
0.180700 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(44\) | −12.6655 | −1.90939 | ||||||||
\(45\) | 2.08419 | 0.310693 | ||||||||
\(46\) | 11.5398 | 1.70145 | ||||||||
\(47\) | 10.7109 | 1.56234 | 0.781172 | − | 0.624316i | \(-0.214622\pi\) | ||||
0.781172 | + | 0.624316i | \(0.214622\pi\) | |||||||
\(48\) | 7.21739 | 1.04174 | ||||||||
\(49\) | −6.73756 | −0.962508 | ||||||||
\(50\) | 4.25462 | 0.601694 | ||||||||
\(51\) | 4.62706 | 0.647918 | ||||||||
\(52\) | −9.93341 | −1.37752 | ||||||||
\(53\) | −6.73596 | −0.925256 | −0.462628 | − | 0.886553i | \(-0.653093\pi\) | ||||
−0.462628 | + | 0.886553i | \(0.653093\pi\) | |||||||
\(54\) | 14.0669 | 1.91426 | ||||||||
\(55\) | 5.45897 | 0.736088 | ||||||||
\(56\) | −2.82138 | −0.377022 | ||||||||
\(57\) | −4.50784 | −0.597078 | ||||||||
\(58\) | −12.0858 | −1.58694 | ||||||||
\(59\) | −3.76947 | −0.490743 | −0.245372 | − | 0.969429i | \(-0.578910\pi\) | ||||
−0.245372 | + | 0.969429i | \(0.578910\pi\) | |||||||
\(60\) | −10.3947 | −1.34195 | ||||||||
\(61\) | −5.85227 | −0.749307 | −0.374653 | − | 0.927165i | \(-0.622238\pi\) | ||||
−0.374653 | + | 0.927165i | \(0.622238\pi\) | |||||||
\(62\) | 17.6549 | 2.24217 | ||||||||
\(63\) | −0.588408 | −0.0741325 | ||||||||
\(64\) | −5.11746 | −0.639682 | ||||||||
\(65\) | 4.28142 | 0.531045 | ||||||||
\(66\) | 10.2008 | 1.25563 | ||||||||
\(67\) | −7.69235 | −0.939770 | −0.469885 | − | 0.882728i | \(-0.655705\pi\) | ||||
−0.469885 | + | 0.882728i | \(0.655705\pi\) | |||||||
\(68\) | 14.3166 | 1.73614 | ||||||||
\(69\) | −6.30091 | −0.758541 | ||||||||
\(70\) | 2.31653 | 0.276878 | ||||||||
\(71\) | 0.317430 | 0.0376720 | 0.0188360 | − | 0.999823i | \(-0.494004\pi\) | ||||
0.0188360 | + | 0.999823i | \(0.494004\pi\) | |||||||
\(72\) | 6.32570 | 0.745491 | ||||||||
\(73\) | 1.09624 | 0.128305 | 0.0641526 | − | 0.997940i | \(-0.479566\pi\) | ||||
0.0641526 | + | 0.997940i | \(0.479566\pi\) | |||||||
\(74\) | 8.70633 | 1.01209 | ||||||||
\(75\) | −2.32309 | −0.268247 | ||||||||
\(76\) | −13.9477 | −1.59991 | ||||||||
\(77\) | −1.54117 | −0.175633 | ||||||||
\(78\) | 8.00040 | 0.905867 | ||||||||
\(79\) | 10.2566 | 1.15396 | 0.576978 | − | 0.816759i | \(-0.304232\pi\) | ||||
0.576978 | + | 0.816759i | \(0.304232\pi\) | |||||||
\(80\) | −9.62505 | −1.07611 | ||||||||
\(81\) | −4.23500 | −0.470555 | ||||||||
\(82\) | −24.5902 | −2.71553 | ||||||||
\(83\) | −0.399742 | −0.0438774 | −0.0219387 | − | 0.999759i | \(-0.506984\pi\) | ||||
−0.0219387 | + | 0.999759i | \(0.506984\pi\) | |||||||
\(84\) | 2.93463 | 0.320194 | ||||||||
\(85\) | −6.17062 | −0.669297 | ||||||||
\(86\) | −5.90568 | −0.636826 | ||||||||
\(87\) | 6.59902 | 0.707489 | ||||||||
\(88\) | 16.5684 | 1.76620 | ||||||||
\(89\) | 15.2571 | 1.61725 | 0.808625 | − | 0.588324i | \(-0.200212\pi\) | ||||
0.808625 | + | 0.588324i | \(0.200212\pi\) | |||||||
\(90\) | −5.19380 | −0.547474 | ||||||||
\(91\) | −1.20873 | −0.126709 | ||||||||
\(92\) | −19.4956 | −2.03256 | ||||||||
\(93\) | −9.63985 | −0.999606 | ||||||||
\(94\) | −26.6915 | −2.75302 | ||||||||
\(95\) | 6.01162 | 0.616779 | ||||||||
\(96\) | −2.99825 | −0.306008 | ||||||||
\(97\) | 11.2814 | 1.14545 | 0.572724 | − | 0.819748i | \(-0.305887\pi\) | ||||
0.572724 | + | 0.819748i | \(0.305887\pi\) | |||||||
\(98\) | 16.7900 | 1.69604 | ||||||||
\(99\) | 3.45541 | 0.347281 | ||||||||
\(100\) | −7.18785 | −0.718785 | ||||||||
\(101\) | 6.46082 | 0.642876 | 0.321438 | − | 0.946931i | \(-0.395834\pi\) | ||||
0.321438 | + | 0.946931i | \(0.395834\pi\) | |||||||
\(102\) | −11.5306 | −1.14170 | ||||||||
\(103\) | −8.13531 | −0.801596 | −0.400798 | − | 0.916166i | \(-0.631267\pi\) | ||||
−0.400798 | + | 0.916166i | \(0.631267\pi\) | |||||||
\(104\) | 12.9945 | 1.27421 | ||||||||
\(105\) | −1.26486 | −0.123438 | ||||||||
\(106\) | 16.7860 | 1.63040 | ||||||||
\(107\) | 10.4304 | 1.00834 | 0.504171 | − | 0.863604i | \(-0.331798\pi\) | ||||
0.504171 | + | 0.863604i | \(0.331798\pi\) | |||||||
\(108\) | −23.7650 | −2.28678 | ||||||||
\(109\) | −3.74534 | −0.358739 | −0.179369 | − | 0.983782i | \(-0.557406\pi\) | ||||
−0.179369 | + | 0.983782i | \(0.557406\pi\) | |||||||
\(110\) | −13.6037 | −1.29706 | ||||||||
\(111\) | −4.75379 | −0.451210 | ||||||||
\(112\) | 2.71734 | 0.256764 | ||||||||
\(113\) | −15.2430 | −1.43394 | −0.716969 | − | 0.697105i | \(-0.754471\pi\) | ||||
−0.716969 | + | 0.697105i | \(0.754471\pi\) | |||||||
\(114\) | 11.2335 | 1.05211 | ||||||||
\(115\) | 8.40285 | 0.783569 | ||||||||
\(116\) | 20.4180 | 1.89576 | ||||||||
\(117\) | 2.71004 | 0.250543 | ||||||||
\(118\) | 9.39349 | 0.864741 | ||||||||
\(119\) | 1.74208 | 0.159697 | ||||||||
\(120\) | 13.5979 | 1.24131 | ||||||||
\(121\) | −1.94952 | −0.177229 | ||||||||
\(122\) | 14.5838 | 1.32036 | ||||||||
\(123\) | 13.4266 | 1.21064 | ||||||||
\(124\) | −29.8266 | −2.67851 | ||||||||
\(125\) | 12.1709 | 1.08860 | ||||||||
\(126\) | 1.46631 | 0.130629 | ||||||||
\(127\) | −22.0317 | −1.95500 | −0.977501 | − | 0.210932i | \(-0.932350\pi\) | ||||
−0.977501 | + | 0.210932i | \(0.932350\pi\) | |||||||
\(128\) | 17.1597 | 1.51672 | ||||||||
\(129\) | 3.22459 | 0.283910 | ||||||||
\(130\) | −10.6693 | −0.935757 | ||||||||
\(131\) | 8.36085 | 0.730491 | 0.365246 | − | 0.930911i | \(-0.380985\pi\) | ||||
0.365246 | + | 0.930911i | \(0.380985\pi\) | |||||||
\(132\) | −17.2335 | −1.49998 | ||||||||
\(133\) | −1.69720 | −0.147166 | ||||||||
\(134\) | 19.1693 | 1.65597 | ||||||||
\(135\) | 10.2430 | 0.881577 | ||||||||
\(136\) | −18.7283 | −1.60594 | ||||||||
\(137\) | −5.51957 | −0.471568 | −0.235784 | − | 0.971805i | \(-0.575766\pi\) | ||||
−0.235784 | + | 0.971805i | \(0.575766\pi\) | |||||||
\(138\) | 15.7018 | 1.33663 | ||||||||
\(139\) | 13.7119 | 1.16303 | 0.581514 | − | 0.813537i | \(-0.302461\pi\) | ||||
0.581514 | + | 0.813537i | \(0.302461\pi\) | |||||||
\(140\) | −3.91359 | −0.330759 | ||||||||
\(141\) | 14.5740 | 1.22735 | ||||||||
\(142\) | −0.791033 | −0.0663820 | ||||||||
\(143\) | 7.09821 | 0.593582 | ||||||||
\(144\) | −6.09244 | −0.507703 | ||||||||
\(145\) | −8.80040 | −0.730834 | ||||||||
\(146\) | −2.73182 | −0.226087 | ||||||||
\(147\) | −9.16758 | −0.756129 | ||||||||
\(148\) | −14.7087 | −1.20905 | ||||||||
\(149\) | −3.14875 | −0.257956 | −0.128978 | − | 0.991647i | \(-0.541170\pi\) | ||||
−0.128978 | + | 0.991647i | \(0.541170\pi\) | |||||||
\(150\) | 5.78912 | 0.472680 | ||||||||
\(151\) | 20.9607 | 1.70575 | 0.852877 | − | 0.522112i | \(-0.174856\pi\) | ||||
0.852877 | + | 0.522112i | \(0.174856\pi\) | |||||||
\(152\) | 18.2458 | 1.47993 | ||||||||
\(153\) | −3.90586 | −0.315770 | ||||||||
\(154\) | 3.84059 | 0.309484 | ||||||||
\(155\) | 12.8556 | 1.03259 | ||||||||
\(156\) | −13.5161 | −1.08215 | ||||||||
\(157\) | 6.51309 | 0.519801 | 0.259901 | − | 0.965635i | \(-0.416310\pi\) | ||||
0.259901 | + | 0.965635i | \(0.416310\pi\) | |||||||
\(158\) | −25.5594 | −2.03339 | ||||||||
\(159\) | −9.16541 | −0.726864 | ||||||||
\(160\) | 3.99844 | 0.316105 | ||||||||
\(161\) | −2.37229 | −0.186962 | ||||||||
\(162\) | 10.5536 | 0.829168 | ||||||||
\(163\) | 11.4678 | 0.898224 | 0.449112 | − | 0.893475i | \(-0.351740\pi\) | ||||
0.449112 | + | 0.893475i | \(0.351740\pi\) | |||||||
\(164\) | 41.5432 | 3.24398 | ||||||||
\(165\) | 7.42784 | 0.578257 | ||||||||
\(166\) | 0.996154 | 0.0773165 | ||||||||
\(167\) | −7.28721 | −0.563901 | −0.281951 | − | 0.959429i | \(-0.590981\pi\) | ||||
−0.281951 | + | 0.959429i | \(0.590981\pi\) | |||||||
\(168\) | −3.83895 | −0.296182 | ||||||||
\(169\) | −7.43294 | −0.571765 | ||||||||
\(170\) | 15.3771 | 1.17937 | ||||||||
\(171\) | 3.80522 | 0.290992 | ||||||||
\(172\) | 9.97719 | 0.760754 | ||||||||
\(173\) | 3.74482 | 0.284714 | 0.142357 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142357 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(174\) | −16.4447 | −1.24667 | ||||||||
\(175\) | −0.874640 | −0.0661166 | ||||||||
\(176\) | −15.9575 | −1.20284 | ||||||||
\(177\) | −5.12899 | −0.385519 | ||||||||
\(178\) | −38.0206 | −2.84977 | ||||||||
\(179\) | −7.78663 | −0.582000 | −0.291000 | − | 0.956723i | \(-0.593988\pi\) | ||||
−0.291000 | + | 0.956723i | \(0.593988\pi\) | |||||||
\(180\) | 8.77452 | 0.654014 | ||||||||
\(181\) | 21.5800 | 1.60403 | 0.802014 | − | 0.597306i | \(-0.203762\pi\) | ||||
0.802014 | + | 0.597306i | \(0.203762\pi\) | |||||||
\(182\) | 3.01214 | 0.223275 | ||||||||
\(183\) | −7.96299 | −0.588641 | ||||||||
\(184\) | 25.5033 | 1.88013 | ||||||||
\(185\) | 6.33962 | 0.466098 | ||||||||
\(186\) | 24.0224 | 1.76141 | ||||||||
\(187\) | −10.2303 | −0.748115 | ||||||||
\(188\) | 45.0932 | 3.28876 | ||||||||
\(189\) | −2.89179 | −0.210347 | ||||||||
\(190\) | −14.9809 | −1.08683 | ||||||||
\(191\) | 26.0340 | 1.88375 | 0.941876 | − | 0.335960i | \(-0.109061\pi\) | ||||
0.941876 | + | 0.335960i | \(0.109061\pi\) | |||||||
\(192\) | −6.96315 | −0.502522 | ||||||||
\(193\) | 11.0302 | 0.793971 | 0.396985 | − | 0.917825i | \(-0.370056\pi\) | ||||
0.396985 | + | 0.917825i | \(0.370056\pi\) | |||||||
\(194\) | −28.1131 | −2.01840 | ||||||||
\(195\) | 5.82559 | 0.417179 | ||||||||
\(196\) | −28.3653 | −2.02610 | ||||||||
\(197\) | 9.89003 | 0.704635 | 0.352318 | − | 0.935880i | \(-0.385394\pi\) | ||||
0.352318 | + | 0.935880i | \(0.385394\pi\) | |||||||
\(198\) | −8.61085 | −0.611946 | ||||||||
\(199\) | −10.2461 | −0.726325 | −0.363163 | − | 0.931726i | \(-0.618303\pi\) | ||||
−0.363163 | + | 0.931726i | \(0.618303\pi\) | |||||||
\(200\) | 9.40284 | 0.664882 | ||||||||
\(201\) | −10.4667 | −0.738266 | ||||||||
\(202\) | −16.1003 | −1.13281 | ||||||||
\(203\) | 2.48452 | 0.174379 | ||||||||
\(204\) | 19.4801 | 1.36388 | ||||||||
\(205\) | −17.9056 | −1.25058 | ||||||||
\(206\) | 20.2731 | 1.41250 | ||||||||
\(207\) | 5.31881 | 0.369683 | ||||||||
\(208\) | −12.5153 | −0.867779 | ||||||||
\(209\) | 9.96673 | 0.689413 | ||||||||
\(210\) | 3.15202 | 0.217510 | ||||||||
\(211\) | 22.8926 | 1.57599 | 0.787995 | − | 0.615682i | \(-0.211119\pi\) | ||||
0.787995 | + | 0.615682i | \(0.211119\pi\) | |||||||
\(212\) | −28.3586 | −1.94768 | ||||||||
\(213\) | 0.431916 | 0.0295944 | ||||||||
\(214\) | −25.9924 | −1.77680 | ||||||||
\(215\) | −4.30029 | −0.293278 | ||||||||
\(216\) | 31.0883 | 2.11529 | ||||||||
\(217\) | −3.62939 | −0.246379 | ||||||||
\(218\) | 9.33337 | 0.632135 | ||||||||
\(219\) | 1.49162 | 0.100794 | ||||||||
\(220\) | 22.9824 | 1.54948 | ||||||||
\(221\) | −8.02355 | −0.539722 | ||||||||
\(222\) | 11.8464 | 0.795079 | ||||||||
\(223\) | 25.1335 | 1.68306 | 0.841531 | − | 0.540209i | \(-0.181655\pi\) | ||||
0.841531 | + | 0.540209i | \(0.181655\pi\) | |||||||
\(224\) | −1.12884 | −0.0754236 | ||||||||
\(225\) | 1.96100 | 0.130733 | ||||||||
\(226\) | 37.9854 | 2.52675 | ||||||||
\(227\) | −5.65346 | −0.375233 | −0.187617 | − | 0.982242i | \(-0.560076\pi\) | ||||
−0.187617 | + | 0.982242i | \(0.560076\pi\) | |||||||
\(228\) | −18.9782 | −1.25686 | ||||||||
\(229\) | −6.61196 | −0.436930 | −0.218465 | − | 0.975845i | \(-0.570105\pi\) | ||||
−0.218465 | + | 0.975845i | \(0.570105\pi\) | |||||||
\(230\) | −20.9398 | −1.38073 | ||||||||
\(231\) | −2.09702 | −0.137974 | ||||||||
\(232\) | −26.7099 | −1.75359 | ||||||||
\(233\) | 8.63136 | 0.565459 | 0.282729 | − | 0.959200i | \(-0.408760\pi\) | ||||
0.282729 | + | 0.959200i | \(0.408760\pi\) | |||||||
\(234\) | −6.75341 | −0.441484 | ||||||||
\(235\) | −19.4357 | −1.26785 | ||||||||
\(236\) | −15.8696 | −1.03302 | ||||||||
\(237\) | 13.9558 | 0.906527 | ||||||||
\(238\) | −4.34126 | −0.281402 | ||||||||
\(239\) | 18.0615 | 1.16830 | 0.584151 | − | 0.811645i | \(-0.301428\pi\) | ||||
0.584151 | + | 0.811645i | \(0.301428\pi\) | |||||||
\(240\) | −13.0965 | −0.845375 | ||||||||
\(241\) | −18.8189 | −1.21223 | −0.606115 | − | 0.795377i | \(-0.707273\pi\) | ||||
−0.606115 | + | 0.795377i | \(0.707273\pi\) | |||||||
\(242\) | 4.85818 | 0.312296 | ||||||||
\(243\) | 11.1721 | 0.716691 | ||||||||
\(244\) | −24.6382 | −1.57730 | ||||||||
\(245\) | 12.2258 | 0.781078 | ||||||||
\(246\) | −33.4590 | −2.13327 | ||||||||
\(247\) | 7.81681 | 0.497372 | ||||||||
\(248\) | 39.0179 | 2.47764 | ||||||||
\(249\) | −0.543916 | −0.0344693 | ||||||||
\(250\) | −30.3299 | −1.91823 | ||||||||
\(251\) | −20.7115 | −1.30730 | −0.653650 | − | 0.756797i | \(-0.726763\pi\) | ||||
−0.653650 | + | 0.756797i | \(0.726763\pi\) | |||||||
\(252\) | −2.47722 | −0.156050 | ||||||||
\(253\) | 13.9312 | 0.875845 | ||||||||
\(254\) | 54.9030 | 3.44492 | ||||||||
\(255\) | −8.39615 | −0.525788 | ||||||||
\(256\) | −32.5269 | −2.03293 | ||||||||
\(257\) | −6.51829 | −0.406600 | −0.203300 | − | 0.979116i | \(-0.565167\pi\) | ||||
−0.203300 | + | 0.979116i | \(0.565167\pi\) | |||||||
\(258\) | −8.03567 | −0.500279 | ||||||||
\(259\) | −1.78980 | −0.111213 | ||||||||
\(260\) | 18.0249 | 1.11786 | ||||||||
\(261\) | −5.57046 | −0.344803 | ||||||||
\(262\) | −20.8352 | −1.28720 | ||||||||
\(263\) | −1.37161 | −0.0845770 | −0.0422885 | − | 0.999105i | \(-0.513465\pi\) | ||||
−0.0422885 | + | 0.999105i | \(0.513465\pi\) | |||||||
\(264\) | 22.5441 | 1.38749 | ||||||||
\(265\) | 12.2229 | 0.750848 | ||||||||
\(266\) | 4.22940 | 0.259321 | ||||||||
\(267\) | 20.7598 | 1.27048 | ||||||||
\(268\) | −32.3850 | −1.97823 | ||||||||
\(269\) | −25.6805 | −1.56577 | −0.782883 | − | 0.622170i | \(-0.786251\pi\) | ||||
−0.782883 | + | 0.622170i | \(0.786251\pi\) | |||||||
\(270\) | −25.5255 | −1.55343 | ||||||||
\(271\) | −30.7191 | −1.86605 | −0.933026 | − | 0.359810i | \(-0.882842\pi\) | ||||
−0.933026 | + | 0.359810i | \(0.882842\pi\) | |||||||
\(272\) | 18.0377 | 1.09370 | ||||||||
\(273\) | −1.64468 | −0.0995403 | ||||||||
\(274\) | 13.7547 | 0.830953 | ||||||||
\(275\) | 5.13629 | 0.309730 | ||||||||
\(276\) | −26.5270 | −1.59674 | ||||||||
\(277\) | −15.9672 | −0.959375 | −0.479687 | − | 0.877439i | \(-0.659250\pi\) | ||||
−0.479687 | + | 0.877439i | \(0.659250\pi\) | |||||||
\(278\) | −34.1699 | −2.04938 | ||||||||
\(279\) | 8.13732 | 0.487169 | ||||||||
\(280\) | 5.11960 | 0.305954 | ||||||||
\(281\) | −29.8097 | −1.77830 | −0.889149 | − | 0.457618i | \(-0.848703\pi\) | ||||
−0.889149 | + | 0.457618i | \(0.848703\pi\) | |||||||
\(282\) | −36.3182 | −2.16272 | ||||||||
\(283\) | 22.5367 | 1.33967 | 0.669834 | − | 0.742511i | \(-0.266365\pi\) | ||||
0.669834 | + | 0.742511i | \(0.266365\pi\) | |||||||
\(284\) | 1.33639 | 0.0793001 | ||||||||
\(285\) | 8.17982 | 0.484531 | ||||||||
\(286\) | −17.6887 | −1.04595 | ||||||||
\(287\) | 5.05510 | 0.298393 | ||||||||
\(288\) | 2.53092 | 0.149136 | ||||||||
\(289\) | −5.43603 | −0.319766 | ||||||||
\(290\) | 21.9305 | 1.28781 | ||||||||
\(291\) | 15.3502 | 0.899843 | ||||||||
\(292\) | 4.61521 | 0.270085 | ||||||||
\(293\) | −7.60079 | −0.444043 | −0.222021 | − | 0.975042i | \(-0.571265\pi\) | ||||
−0.222021 | + | 0.975042i | \(0.571265\pi\) | |||||||
\(294\) | 22.8455 | 1.33238 | ||||||||
\(295\) | 6.83999 | 0.398239 | ||||||||
\(296\) | 19.2413 | 1.11838 | ||||||||
\(297\) | 16.9820 | 0.985393 | ||||||||
\(298\) | 7.84667 | 0.454545 | ||||||||
\(299\) | 10.9261 | 0.631871 | ||||||||
\(300\) | −9.78028 | −0.564665 | ||||||||
\(301\) | 1.21406 | 0.0699770 | ||||||||
\(302\) | −52.2338 | −3.00572 | ||||||||
\(303\) | 8.79103 | 0.505031 | ||||||||
\(304\) | −17.5730 | −1.00788 | ||||||||
\(305\) | 10.6194 | 0.608064 | ||||||||
\(306\) | 9.73338 | 0.556420 | ||||||||
\(307\) | 25.1769 | 1.43692 | 0.718460 | − | 0.695568i | \(-0.244847\pi\) | ||||
0.718460 | + | 0.695568i | \(0.244847\pi\) | |||||||
\(308\) | −6.48839 | −0.369710 | ||||||||
\(309\) | −11.0694 | −0.629719 | ||||||||
\(310\) | −32.0361 | −1.81953 | ||||||||
\(311\) | −11.5492 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(312\) | 17.6811 | 1.00100 | ||||||||
\(313\) | −0.629683 | −0.0355918 | −0.0177959 | − | 0.999842i | \(-0.505665\pi\) | ||||
−0.0177959 | + | 0.999842i | \(0.505665\pi\) | |||||||
\(314\) | −16.2306 | −0.915945 | ||||||||
\(315\) | 1.06771 | 0.0601587 | ||||||||
\(316\) | 43.1806 | 2.42910 | ||||||||
\(317\) | 9.76090 | 0.548227 | 0.274113 | − | 0.961697i | \(-0.411616\pi\) | ||||
0.274113 | + | 0.961697i | \(0.411616\pi\) | |||||||
\(318\) | 22.8401 | 1.28081 | ||||||||
\(319\) | −14.5903 | −0.816899 | ||||||||
\(320\) | 9.28601 | 0.519104 | ||||||||
\(321\) | 14.1923 | 0.792134 | ||||||||
\(322\) | 5.91172 | 0.329447 | ||||||||
\(323\) | −11.2660 | −0.626858 | ||||||||
\(324\) | −17.8295 | −0.990526 | ||||||||
\(325\) | 4.02835 | 0.223453 | ||||||||
\(326\) | −28.5776 | −1.58277 | ||||||||
\(327\) | −5.09616 | −0.281819 | ||||||||
\(328\) | −54.3450 | −3.00070 | ||||||||
\(329\) | 5.48708 | 0.302512 | ||||||||
\(330\) | −18.5101 | −1.01895 | ||||||||
\(331\) | 35.6830 | 1.96132 | 0.980659 | − | 0.195725i | \(-0.0627060\pi\) | ||||
0.980659 | + | 0.195725i | \(0.0627060\pi\) | |||||||
\(332\) | −1.68293 | −0.0923625 | ||||||||
\(333\) | 4.01283 | 0.219902 | ||||||||
\(334\) | 18.1597 | 0.993654 | ||||||||
\(335\) | 13.9583 | 0.762626 | ||||||||
\(336\) | 3.69739 | 0.201709 | ||||||||
\(337\) | −13.6237 | −0.742131 | −0.371066 | − | 0.928607i | \(-0.621008\pi\) | ||||
−0.371066 | + | 0.928607i | \(0.621008\pi\) | |||||||
\(338\) | 18.5228 | 1.00751 | ||||||||
\(339\) | −20.7406 | −1.12648 | ||||||||
\(340\) | −25.9785 | −1.40888 | ||||||||
\(341\) | 21.3135 | 1.15419 | ||||||||
\(342\) | −9.48258 | −0.512759 | ||||||||
\(343\) | −7.03761 | −0.379995 | ||||||||
\(344\) | −13.0517 | −0.703703 | ||||||||
\(345\) | 11.4335 | 0.615558 | ||||||||
\(346\) | −9.33207 | −0.501695 | ||||||||
\(347\) | 28.1710 | 1.51230 | 0.756151 | − | 0.654398i | \(-0.227078\pi\) | ||||
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(348\) | 27.7821 | 1.48928 | ||||||||
\(349\) | 9.89154 | 0.529482 | 0.264741 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264741 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(350\) | 2.17960 | 0.116504 | ||||||||
\(351\) | 13.3188 | 0.710904 | ||||||||
\(352\) | 6.62906 | 0.353330 | ||||||||
\(353\) | 9.05771 | 0.482093 | 0.241047 | − | 0.970514i | \(-0.422509\pi\) | ||||
0.241047 | + | 0.970514i | \(0.422509\pi\) | |||||||
\(354\) | 12.7814 | 0.679325 | ||||||||
\(355\) | −0.576001 | −0.0305709 | ||||||||
\(356\) | 64.2329 | 3.40434 | ||||||||
\(357\) | 2.37040 | 0.125455 | ||||||||
\(358\) | 19.4042 | 1.02555 | ||||||||
\(359\) | −0.380069 | −0.0200593 | −0.0100296 | − | 0.999950i | \(-0.503193\pi\) | ||||
−0.0100296 | + | 0.999950i | \(0.503193\pi\) | |||||||
\(360\) | −11.4785 | −0.604968 | ||||||||
\(361\) | −8.02427 | −0.422330 | ||||||||
\(362\) | −53.7772 | −2.82646 | ||||||||
\(363\) | −2.65264 | −0.139228 | ||||||||
\(364\) | −5.08878 | −0.266725 | ||||||||
\(365\) | −1.98921 | −0.104120 | ||||||||
\(366\) | 19.8437 | 1.03725 | ||||||||
\(367\) | −20.5074 | −1.07048 | −0.535238 | − | 0.844701i | \(-0.679778\pi\) | ||||
−0.535238 | + | 0.844701i | \(0.679778\pi\) | |||||||
\(368\) | −24.5629 | −1.28043 | ||||||||
\(369\) | −11.3339 | −0.590017 | ||||||||
\(370\) | −15.7983 | −0.821314 | ||||||||
\(371\) | −3.45076 | −0.179155 | ||||||||
\(372\) | −40.5841 | −2.10419 | ||||||||
\(373\) | 28.9303 | 1.49796 | 0.748978 | − | 0.662595i | \(-0.230545\pi\) | ||||
0.748978 | + | 0.662595i | \(0.230545\pi\) | |||||||
\(374\) | 25.4939 | 1.31826 | ||||||||
\(375\) | 16.5606 | 0.855185 | ||||||||
\(376\) | −58.9890 | −3.04212 | ||||||||
\(377\) | −11.4430 | −0.589345 | ||||||||
\(378\) | 7.20633 | 0.370654 | ||||||||
\(379\) | −1.87085 | −0.0960993 | −0.0480497 | − | 0.998845i | \(-0.515301\pi\) | ||||
−0.0480497 | + | 0.998845i | \(0.515301\pi\) | |||||||
\(380\) | 25.3091 | 1.29833 | ||||||||
\(381\) | −29.9779 | −1.53581 | ||||||||
\(382\) | −64.8765 | −3.31937 | ||||||||
\(383\) | −12.8186 | −0.655002 | −0.327501 | − | 0.944851i | \(-0.606206\pi\) | ||||
−0.327501 | + | 0.944851i | \(0.606206\pi\) | |||||||
\(384\) | 23.3486 | 1.19151 | ||||||||
\(385\) | 2.79658 | 0.142527 | ||||||||
\(386\) | −27.4872 | −1.39906 | ||||||||
\(387\) | −2.72199 | −0.138366 | ||||||||
\(388\) | 47.4949 | 2.41119 | ||||||||
\(389\) | −11.9404 | −0.605405 | −0.302702 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302702 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(390\) | −14.5173 | −0.735114 | ||||||||
\(391\) | −15.7473 | −0.796373 | ||||||||
\(392\) | 37.1063 | 1.87415 | ||||||||
\(393\) | 11.3763 | 0.573860 | ||||||||
\(394\) | −24.6459 | −1.24164 | ||||||||
\(395\) | −18.6114 | −0.936439 | ||||||||
\(396\) | 14.5474 | 0.731033 | ||||||||
\(397\) | −5.56832 | −0.279466 | −0.139733 | − | 0.990189i | \(-0.544624\pi\) | ||||
−0.139733 | + | 0.990189i | \(0.544624\pi\) | |||||||
\(398\) | 25.5332 | 1.27986 | ||||||||
\(399\) | −2.30932 | −0.115611 | ||||||||
\(400\) | −9.05612 | −0.452806 | ||||||||
\(401\) | 20.2629 | 1.01188 | 0.505941 | − | 0.862568i | \(-0.331145\pi\) | ||||
0.505941 | + | 0.862568i | \(0.331145\pi\) | |||||||
\(402\) | 26.0830 | 1.30090 | ||||||||
\(403\) | 16.7160 | 0.832681 | ||||||||
\(404\) | 27.2003 | 1.35326 | ||||||||
\(405\) | 7.68472 | 0.381857 | ||||||||
\(406\) | −6.19142 | −0.307275 | ||||||||
\(407\) | 10.5105 | 0.520987 | ||||||||
\(408\) | −25.4830 | −1.26160 | ||||||||
\(409\) | −24.1456 | −1.19392 | −0.596962 | − | 0.802269i | \(-0.703626\pi\) | ||||
−0.596962 | + | 0.802269i | \(0.703626\pi\) | |||||||
\(410\) | 44.6207 | 2.20366 | ||||||||
\(411\) | −7.51029 | −0.370455 | ||||||||
\(412\) | −34.2499 | −1.68737 | ||||||||
\(413\) | −1.93106 | −0.0950213 | ||||||||
\(414\) | −13.2544 | −0.651420 | ||||||||
\(415\) | 0.725362 | 0.0356066 | ||||||||
\(416\) | 5.19911 | 0.254907 | ||||||||
\(417\) | 18.6573 | 0.913653 | ||||||||
\(418\) | −24.8370 | −1.21482 | ||||||||
\(419\) | 8.70428 | 0.425232 | 0.212616 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212616 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(420\) | −5.32510 | −0.259838 | ||||||||
\(421\) | 22.1647 | 1.08024 | 0.540122 | − | 0.841587i | \(-0.318378\pi\) | ||||
0.540122 | + | 0.841587i | \(0.318378\pi\) | |||||||
\(422\) | −57.0482 | −2.77706 | ||||||||
\(423\) | −12.3024 | −0.598162 | ||||||||
\(424\) | 37.0975 | 1.80162 | ||||||||
\(425\) | −5.80587 | −0.281626 | ||||||||
\(426\) | −1.07633 | −0.0521485 | ||||||||
\(427\) | −2.99806 | −0.145086 | ||||||||
\(428\) | 43.9122 | 2.12257 | ||||||||
\(429\) | 9.65830 | 0.466307 | ||||||||
\(430\) | 10.7163 | 0.516786 | ||||||||
\(431\) | −33.2190 | −1.60010 | −0.800052 | − | 0.599931i | \(-0.795195\pi\) | ||||
−0.800052 | + | 0.599931i | \(0.795195\pi\) | |||||||
\(432\) | −29.9419 | −1.44058 | ||||||||
\(433\) | −23.0968 | −1.10996 | −0.554980 | − | 0.831864i | \(-0.687274\pi\) | ||||
−0.554980 | + | 0.831864i | \(0.687274\pi\) | |||||||
\(434\) | 9.04442 | 0.434146 | ||||||||
\(435\) | −11.9744 | −0.574130 | ||||||||
\(436\) | −15.7680 | −0.755151 | ||||||||
\(437\) | 15.3415 | 0.733884 | ||||||||
\(438\) | −3.71710 | −0.177610 | ||||||||
\(439\) | −28.0195 | −1.33730 | −0.668650 | − | 0.743578i | \(-0.733127\pi\) | ||||
−0.668650 | + | 0.743578i | \(0.733127\pi\) | |||||||
\(440\) | −30.0647 | −1.43328 | ||||||||
\(441\) | 7.73866 | 0.368508 | ||||||||
\(442\) | 19.9946 | 0.951047 | ||||||||
\(443\) | −7.63730 | −0.362859 | −0.181430 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181430 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(444\) | −20.0136 | −0.949804 | ||||||||
\(445\) | −27.6852 | −1.31240 | ||||||||
\(446\) | −62.6325 | −2.96573 | ||||||||
\(447\) | −4.28440 | −0.202645 | ||||||||
\(448\) | −2.62162 | −0.123860 | ||||||||
\(449\) | 21.8958 | 1.03333 | 0.516664 | − | 0.856188i | \(-0.327174\pi\) | ||||
0.516664 | + | 0.856188i | \(0.327174\pi\) | |||||||
\(450\) | −4.88679 | −0.230366 | ||||||||
\(451\) | −29.6859 | −1.39786 | ||||||||
\(452\) | −64.1734 | −3.01846 | ||||||||
\(453\) | 28.5205 | 1.34001 | ||||||||
\(454\) | 14.0884 | 0.661201 | ||||||||
\(455\) | 2.19333 | 0.102825 | ||||||||
\(456\) | 24.8264 | 1.16260 | ||||||||
\(457\) | 22.8014 | 1.06661 | 0.533303 | − | 0.845924i | \(-0.320950\pi\) | ||||
0.533303 | + | 0.845924i | \(0.320950\pi\) | |||||||
\(458\) | 16.4770 | 0.769917 | ||||||||
\(459\) | −19.1958 | −0.895981 | ||||||||
\(460\) | 35.3762 | 1.64943 | ||||||||
\(461\) | 12.6269 | 0.588095 | 0.294048 | − | 0.955791i | \(-0.404998\pi\) | ||||
0.294048 | + | 0.955791i | \(0.404998\pi\) | |||||||
\(462\) | 5.22577 | 0.243125 | ||||||||
\(463\) | 32.7446 | 1.52177 | 0.760886 | − | 0.648885i | \(-0.224764\pi\) | ||||
0.760886 | + | 0.648885i | \(0.224764\pi\) | |||||||
\(464\) | 25.7250 | 1.19425 | ||||||||
\(465\) | 17.4922 | 0.811183 | ||||||||
\(466\) | −21.5093 | −0.996398 | ||||||||
\(467\) | −21.1605 | −0.979189 | −0.489595 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489595 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(468\) | 11.4094 | 0.527398 | ||||||||
\(469\) | −3.94071 | −0.181965 | ||||||||
\(470\) | 48.4337 | 2.23408 | ||||||||
\(471\) | 8.86215 | 0.408346 | ||||||||
\(472\) | 20.7599 | 0.955552 | ||||||||
\(473\) | −7.12950 | −0.327815 | ||||||||
\(474\) | −34.7778 | −1.59740 | ||||||||
\(475\) | 5.65628 | 0.259528 | ||||||||
\(476\) | 7.33423 | 0.336164 | ||||||||
\(477\) | 7.73683 | 0.354245 | ||||||||
\(478\) | −45.0092 | −2.05867 | ||||||||
\(479\) | −25.1452 | −1.14891 | −0.574457 | − | 0.818534i | \(-0.694787\pi\) | ||||
−0.574457 | + | 0.818534i | \(0.694787\pi\) | |||||||
\(480\) | 5.44055 | 0.248326 | ||||||||
\(481\) | 8.24330 | 0.375862 | ||||||||
\(482\) | 46.8965 | 2.13608 | ||||||||
\(483\) | −3.22789 | −0.146874 | ||||||||
\(484\) | −8.20752 | −0.373069 | ||||||||
\(485\) | −20.4709 | −0.929535 | ||||||||
\(486\) | −27.8408 | −1.26289 | ||||||||
\(487\) | 40.5311 | 1.83664 | 0.918321 | − | 0.395838i | \(-0.129546\pi\) | ||||
0.918321 | + | 0.395838i | \(0.129546\pi\) | |||||||
\(488\) | 32.2307 | 1.45902 | ||||||||
\(489\) | 15.6038 | 0.705628 | ||||||||
\(490\) | −30.4666 | −1.37634 | ||||||||
\(491\) | 4.51990 | 0.203980 | 0.101990 | − | 0.994785i | \(-0.467479\pi\) | ||||
0.101990 | + | 0.994785i | \(0.467479\pi\) | |||||||
\(492\) | 56.5265 | 2.54841 | ||||||||
\(493\) | 16.4923 | 0.742776 | ||||||||
\(494\) | −19.4794 | −0.876421 | ||||||||
\(495\) | −6.27009 | −0.281820 | ||||||||
\(496\) | −37.5791 | −1.68735 | ||||||||
\(497\) | 0.162616 | 0.00729433 | ||||||||
\(498\) | 1.35543 | 0.0607385 | ||||||||
\(499\) | 36.1623 | 1.61885 | 0.809423 | − | 0.587226i | \(-0.199780\pi\) | ||||
0.809423 | + | 0.587226i | \(0.199780\pi\) | |||||||
\(500\) | 51.2400 | 2.29152 | ||||||||
\(501\) | −9.91547 | −0.442991 | ||||||||
\(502\) | 51.6130 | 2.30360 | ||||||||
\(503\) | −26.9054 | −1.19965 | −0.599826 | − | 0.800131i | \(-0.704763\pi\) | ||||
−0.599826 | + | 0.800131i | \(0.704763\pi\) | |||||||
\(504\) | 3.24059 | 0.144347 | ||||||||
\(505\) | −11.7236 | −0.521695 | ||||||||
\(506\) | −34.7164 | −1.54333 | ||||||||
\(507\) | −10.1138 | −0.449168 | ||||||||
\(508\) | −92.7543 | −4.11531 | ||||||||
\(509\) | 3.48536 | 0.154486 | 0.0772429 | − | 0.997012i | \(-0.475388\pi\) | ||||
0.0772429 | + | 0.997012i | \(0.475388\pi\) | |||||||
\(510\) | 20.9232 | 0.926493 | ||||||||
\(511\) | 0.561593 | 0.0248434 | ||||||||
\(512\) | 46.7375 | 2.06553 | ||||||||
\(513\) | 18.7012 | 0.825676 | ||||||||
\(514\) | 16.2435 | 0.716472 | ||||||||
\(515\) | 14.7621 | 0.650497 | ||||||||
\(516\) | 13.5756 | 0.597634 | ||||||||
\(517\) | −32.2227 | −1.41715 | ||||||||
\(518\) | 4.46016 | 0.195968 | ||||||||
\(519\) | 5.09546 | 0.223666 | ||||||||
\(520\) | −23.5794 | −1.03403 | ||||||||
\(521\) | −11.8954 | −0.521145 | −0.260573 | − | 0.965454i | \(-0.583911\pi\) | ||||
−0.260573 | + | 0.965454i | \(0.583911\pi\) | |||||||
\(522\) | 13.8815 | 0.607578 | ||||||||
\(523\) | 21.5635 | 0.942907 | 0.471453 | − | 0.881891i | \(-0.343730\pi\) | ||||
0.471453 | + | 0.881891i | \(0.343730\pi\) | |||||||
\(524\) | 35.1995 | 1.53770 | ||||||||
\(525\) | −1.19009 | −0.0519400 | ||||||||
\(526\) | 3.41804 | 0.149034 | ||||||||
\(527\) | −24.0919 | −1.04946 | ||||||||
\(528\) | −21.7128 | −0.944929 | ||||||||
\(529\) | −1.55615 | −0.0676585 | ||||||||
\(530\) | −30.4594 | −1.32307 | ||||||||
\(531\) | 4.32956 | 0.187887 | ||||||||
\(532\) | −7.14525 | −0.309786 | ||||||||
\(533\) | −23.2824 | −1.00847 | ||||||||
\(534\) | −51.7334 | −2.23872 | ||||||||
\(535\) | −18.9267 | −0.818272 | ||||||||
\(536\) | 42.3647 | 1.82988 | ||||||||
\(537\) | −10.5950 | −0.457208 | ||||||||
\(538\) | 63.9955 | 2.75904 | ||||||||
\(539\) | 20.2693 | 0.873060 | ||||||||
\(540\) | 43.1233 | 1.85573 | ||||||||
\(541\) | 36.8686 | 1.58510 | 0.792552 | − | 0.609804i | \(-0.208752\pi\) | ||||
0.792552 | + | 0.609804i | \(0.208752\pi\) | |||||||
\(542\) | 76.5517 | 3.28818 | ||||||||
\(543\) | 29.3632 | 1.26009 | ||||||||
\(544\) | −7.49324 | −0.321270 | ||||||||
\(545\) | 6.79621 | 0.291117 | ||||||||
\(546\) | 4.09852 | 0.175401 | ||||||||
\(547\) | 6.52774 | 0.279106 | 0.139553 | − | 0.990215i | \(-0.455433\pi\) | ||||
0.139553 | + | 0.990215i | \(0.455433\pi\) | |||||||
\(548\) | −23.2376 | −0.992659 | ||||||||
\(549\) | 6.72183 | 0.286881 | ||||||||
\(550\) | −12.7996 | −0.545777 | ||||||||
\(551\) | −16.0674 | −0.684492 | ||||||||
\(552\) | 34.7015 | 1.47700 | ||||||||
\(553\) | 5.25435 | 0.223437 | ||||||||
\(554\) | 39.7901 | 1.69052 | ||||||||
\(555\) | 8.62611 | 0.366158 | ||||||||
\(556\) | 57.7275 | 2.44819 | ||||||||
\(557\) | 35.5163 | 1.50487 | 0.752437 | − | 0.658664i | \(-0.228878\pi\) | ||||
0.752437 | + | 0.658664i | \(0.228878\pi\) | |||||||
\(558\) | −20.2781 | −0.858442 | ||||||||
\(559\) | −5.59160 | −0.236499 | ||||||||
\(560\) | −4.93081 | −0.208365 | ||||||||
\(561\) | −13.9201 | −0.587706 | ||||||||
\(562\) | 74.2856 | 3.13355 | ||||||||
\(563\) | 36.6482 | 1.54454 | 0.772269 | − | 0.635296i | \(-0.219122\pi\) | ||||
0.772269 | + | 0.635296i | \(0.219122\pi\) | |||||||
\(564\) | 61.3568 | 2.58359 | ||||||||
\(565\) | 27.6595 | 1.16364 | ||||||||
\(566\) | −56.1613 | −2.36064 | ||||||||
\(567\) | −2.16955 | −0.0911124 | ||||||||
\(568\) | −1.74821 | −0.0733532 | ||||||||
\(569\) | −7.17768 | −0.300904 | −0.150452 | − | 0.988617i | \(-0.548073\pi\) | ||||
−0.150452 | + | 0.988617i | \(0.548073\pi\) | |||||||
\(570\) | −20.3840 | −0.853794 | ||||||||
\(571\) | 2.26544 | 0.0948058 | 0.0474029 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474029 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(572\) | 29.8837 | 1.24950 | ||||||||
\(573\) | 35.4236 | 1.47984 | ||||||||
\(574\) | −12.5973 | −0.525801 | ||||||||
\(575\) | 7.90616 | 0.329710 | ||||||||
\(576\) | 5.87783 | 0.244910 | ||||||||
\(577\) | −13.4283 | −0.559029 | −0.279515 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279515 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(578\) | 13.5465 | 0.563462 | ||||||||
\(579\) | 15.0084 | 0.623729 | ||||||||
\(580\) | −37.0500 | −1.53842 | ||||||||
\(581\) | −0.204784 | −0.00849586 | ||||||||
\(582\) | −38.2525 | −1.58562 | ||||||||
\(583\) | 20.2645 | 0.839270 | ||||||||
\(584\) | −6.03742 | −0.249830 | ||||||||
\(585\) | −4.91758 | −0.203317 | ||||||||
\(586\) | 18.9411 | 0.782450 | ||||||||
\(587\) | 27.4001 | 1.13092 | 0.565462 | − | 0.824774i | \(-0.308698\pi\) | ||||
0.565462 | + | 0.824774i | \(0.308698\pi\) | |||||||
\(588\) | −38.5958 | −1.59166 | ||||||||
\(589\) | 23.4712 | 0.967113 | ||||||||
\(590\) | −17.0452 | −0.701740 | ||||||||
\(591\) | 13.4570 | 0.553549 | ||||||||
\(592\) | −18.5317 | −0.761650 | ||||||||
\(593\) | −13.0818 | −0.537206 | −0.268603 | − | 0.963251i | \(-0.586562\pi\) | ||||
−0.268603 | + | 0.963251i | \(0.586562\pi\) | |||||||
\(594\) | −42.3189 | −1.73637 | ||||||||
\(595\) | −3.16114 | −0.129594 | ||||||||
\(596\) | −13.2563 | −0.543001 | ||||||||
\(597\) | −13.9415 | −0.570588 | ||||||||
\(598\) | −27.2277 | −1.11342 | ||||||||
\(599\) | 23.5557 | 0.962459 | 0.481230 | − | 0.876595i | \(-0.340190\pi\) | ||||
0.481230 | + | 0.876595i | \(0.340190\pi\) | |||||||
\(600\) | 12.7941 | 0.522319 | ||||||||
\(601\) | 14.3441 | 0.585108 | 0.292554 | − | 0.956249i | \(-0.405495\pi\) | ||||
0.292554 | + | 0.956249i | \(0.405495\pi\) | |||||||
\(602\) | −3.02542 | −0.123307 | ||||||||
\(603\) | 8.83531 | 0.359802 | ||||||||
\(604\) | 88.2450 | 3.59064 | ||||||||
\(605\) | 3.53754 | 0.143822 | ||||||||
\(606\) | −21.9072 | −0.889918 | ||||||||
\(607\) | −13.9269 | −0.565274 | −0.282637 | − | 0.959227i | \(-0.591209\pi\) | ||||
−0.282637 | + | 0.959227i | \(0.591209\pi\) | |||||||
\(608\) | 7.30016 | 0.296061 | ||||||||
\(609\) | 3.38061 | 0.136989 | ||||||||
\(610\) | −26.4634 | −1.07147 | ||||||||
\(611\) | −25.2719 | −1.02239 | ||||||||
\(612\) | −16.4438 | −0.664701 | ||||||||
\(613\) | 18.6322 | 0.752549 | 0.376275 | − | 0.926508i | \(-0.377205\pi\) | ||||
0.376275 | + | 0.926508i | \(0.377205\pi\) | |||||||
\(614\) | −62.7406 | −2.53200 | ||||||||
\(615\) | −24.3636 | −0.982435 | ||||||||
\(616\) | 8.48783 | 0.341984 | ||||||||
\(617\) | 42.3108 | 1.70337 | 0.851685 | − | 0.524054i | \(-0.175581\pi\) | ||||
0.851685 | + | 0.524054i | \(0.175581\pi\) | |||||||
\(618\) | 27.5850 | 1.10963 | ||||||||
\(619\) | −17.1210 | −0.688150 | −0.344075 | − | 0.938942i | \(-0.611808\pi\) | ||||
−0.344075 | + | 0.938942i | \(0.611808\pi\) | |||||||
\(620\) | 54.1226 | 2.17362 | ||||||||
\(621\) | 26.1399 | 1.04896 | ||||||||
\(622\) | 28.7804 | 1.15399 | ||||||||
\(623\) | 7.81606 | 0.313144 | ||||||||
\(624\) | −17.0291 | −0.681712 | ||||||||
\(625\) | −13.5485 | −0.541940 | ||||||||
\(626\) | 1.56917 | 0.0627165 | ||||||||
\(627\) | 13.5614 | 0.541590 | ||||||||
\(628\) | 27.4203 | 1.09419 | ||||||||
\(629\) | −11.8807 | −0.473714 | ||||||||
\(630\) | −2.66073 | −0.106006 | ||||||||
\(631\) | −16.8010 | −0.668839 | −0.334420 | − | 0.942424i | \(-0.608540\pi\) | ||||
−0.334420 | + | 0.942424i | \(0.608540\pi\) | |||||||
\(632\) | −56.4870 | −2.24693 | ||||||||
\(633\) | 31.1492 | 1.23807 | ||||||||
\(634\) | −24.3241 | −0.966033 | ||||||||
\(635\) | 39.9783 | 1.58649 | ||||||||
\(636\) | −38.5866 | −1.53006 | ||||||||
\(637\) | 15.8970 | 0.629863 | ||||||||
\(638\) | 36.3589 | 1.43946 | ||||||||
\(639\) | −0.364595 | −0.0144232 | ||||||||
\(640\) | −31.1376 | −1.23082 | ||||||||
\(641\) | 38.1190 | 1.50561 | 0.752805 | − | 0.658244i | \(-0.228700\pi\) | ||||
0.752805 | + | 0.658244i | \(0.228700\pi\) | |||||||
\(642\) | −35.3670 | −1.39582 | ||||||||
\(643\) | 24.9236 | 0.982891 | 0.491445 | − | 0.870908i | \(-0.336469\pi\) | ||||
0.491445 | + | 0.870908i | \(0.336469\pi\) | |||||||
\(644\) | −9.98740 | −0.393559 | ||||||||
\(645\) | −5.85127 | −0.230393 | ||||||||
\(646\) | 28.0748 | 1.10459 | ||||||||
\(647\) | 30.6660 | 1.20561 | 0.602803 | − | 0.797890i | \(-0.294050\pi\) | ||||
0.602803 | + | 0.797890i | \(0.294050\pi\) | |||||||
\(648\) | 23.3238 | 0.916244 | ||||||||
\(649\) | 11.3401 | 0.445137 | ||||||||
\(650\) | −10.0386 | −0.393747 | ||||||||
\(651\) | −4.93839 | −0.193551 | ||||||||
\(652\) | 48.2796 | 1.89078 | ||||||||
\(653\) | −41.6499 | −1.62988 | −0.814942 | − | 0.579542i | \(-0.803231\pi\) | ||||
−0.814942 | + | 0.579542i | \(0.803231\pi\) | |||||||
\(654\) | 12.6996 | 0.496594 | ||||||||
\(655\) | −15.1714 | −0.592796 | ||||||||
\(656\) | 52.3411 | 2.04358 | ||||||||
\(657\) | −1.25913 | −0.0491232 | ||||||||
\(658\) | −13.6738 | −0.533059 | ||||||||
\(659\) | −3.44756 | −0.134298 | −0.0671488 | − | 0.997743i | \(-0.521390\pi\) | ||||
−0.0671488 | + | 0.997743i | \(0.521390\pi\) | |||||||
\(660\) | 31.2715 | 1.21724 | ||||||||
\(661\) | −5.20211 | −0.202339 | −0.101169 | − | 0.994869i | \(-0.532258\pi\) | ||||
−0.101169 | + | 0.994869i | \(0.532258\pi\) | |||||||
\(662\) | −88.9219 | −3.45605 | ||||||||
\(663\) | −10.9174 | −0.423996 | ||||||||
\(664\) | 2.20153 | 0.0854360 | ||||||||
\(665\) | 3.07969 | 0.119425 | ||||||||
\(666\) | −9.99996 | −0.387490 | ||||||||
\(667\) | −22.4584 | −0.869593 | ||||||||
\(668\) | −30.6794 | −1.18702 | ||||||||
\(669\) | 34.1983 | 1.32218 | ||||||||
\(670\) | −34.7841 | −1.34383 | ||||||||
\(671\) | 17.6060 | 0.679672 | ||||||||
\(672\) | −1.53597 | −0.0592514 | ||||||||
\(673\) | 2.62727 | 0.101274 | 0.0506369 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506369 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(674\) | 33.9502 | 1.30771 | ||||||||
\(675\) | 9.63753 | 0.370949 | ||||||||
\(676\) | −31.2929 | −1.20357 | ||||||||
\(677\) | 25.1463 | 0.966452 | 0.483226 | − | 0.875496i | \(-0.339465\pi\) | ||||
0.483226 | + | 0.875496i | \(0.339465\pi\) | |||||||
\(678\) | 51.6855 | 1.98497 | ||||||||
\(679\) | 5.77932 | 0.221790 | ||||||||
\(680\) | 33.9839 | 1.30322 | ||||||||
\(681\) | −7.69248 | −0.294777 | ||||||||
\(682\) | −53.1130 | −2.03380 | ||||||||
\(683\) | −29.8515 | −1.14224 | −0.571119 | − | 0.820867i | \(-0.693490\pi\) | ||||
−0.571119 | + | 0.820867i | \(0.693490\pi\) | |||||||
\(684\) | 16.0201 | 0.612544 | ||||||||
\(685\) | 10.0157 | 0.382679 | ||||||||
\(686\) | 17.5377 | 0.669592 | ||||||||
\(687\) | −8.99667 | −0.343244 | ||||||||
\(688\) | 12.5705 | 0.479244 | ||||||||
\(689\) | 15.8933 | 0.605485 | ||||||||
\(690\) | −28.4922 | −1.08468 | ||||||||
\(691\) | −33.7003 | −1.28202 | −0.641010 | − | 0.767532i | \(-0.721484\pi\) | ||||
−0.641010 | + | 0.767532i | \(0.721484\pi\) | |||||||
\(692\) | 15.7658 | 0.599327 | ||||||||
\(693\) | 1.77017 | 0.0672431 | ||||||||
\(694\) | −70.2021 | −2.66483 | ||||||||
\(695\) | −24.8813 | −0.943800 | ||||||||
\(696\) | −36.3433 | −1.37759 | ||||||||
\(697\) | 33.5558 | 1.27102 | ||||||||
\(698\) | −24.6496 | −0.933003 | ||||||||
\(699\) | 11.7444 | 0.444214 | ||||||||
\(700\) | −3.68226 | −0.139176 | ||||||||
\(701\) | 4.91523 | 0.185646 | 0.0928228 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928228 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(702\) | −33.1903 | −1.25269 | ||||||||
\(703\) | 11.5746 | 0.436543 | ||||||||
\(704\) | 15.3954 | 0.580235 | ||||||||
\(705\) | −26.4455 | −0.995997 | ||||||||
\(706\) | −22.5718 | −0.849499 | ||||||||
\(707\) | 3.30981 | 0.124478 | ||||||||
\(708\) | −21.5932 | −0.811523 | ||||||||
\(709\) | 37.5864 | 1.41159 | 0.705793 | − | 0.708418i | \(-0.250591\pi\) | ||||
0.705793 | + | 0.708418i | \(0.250591\pi\) | |||||||
\(710\) | 1.43539 | 0.0538692 | ||||||||
\(711\) | −11.7806 | −0.441806 | ||||||||
\(712\) | −84.0267 | −3.14904 | ||||||||
\(713\) | 32.8072 | 1.22864 | ||||||||
\(714\) | −5.90701 | −0.221064 | ||||||||
\(715\) | −12.8802 | −0.481694 | ||||||||
\(716\) | −32.7819 | −1.22512 | ||||||||
\(717\) | 24.5757 | 0.917797 | ||||||||
\(718\) | 0.947130 | 0.0353466 | ||||||||
\(719\) | 29.5220 | 1.10098 | 0.550492 | − | 0.834841i | \(-0.314440\pi\) | ||||
0.550492 | + | 0.834841i | \(0.314440\pi\) | |||||||
\(720\) | 11.0552 | 0.412003 | ||||||||
\(721\) | −4.16763 | −0.155211 | ||||||||
\(722\) | 19.9964 | 0.744190 | ||||||||
\(723\) | −25.6062 | −0.952306 | ||||||||
\(724\) | 90.8524 | 3.37650 | ||||||||
\(725\) | −8.28021 | −0.307519 | ||||||||
\(726\) | 6.61037 | 0.245334 | ||||||||
\(727\) | 14.0981 | 0.522868 | 0.261434 | − | 0.965221i | \(-0.415805\pi\) | ||||
0.261434 | + | 0.965221i | \(0.415805\pi\) | |||||||
\(728\) | 6.65693 | 0.246722 | ||||||||
\(729\) | 27.9065 | 1.03357 | ||||||||
\(730\) | 4.95710 | 0.183471 | ||||||||
\(731\) | 8.05891 | 0.298070 | ||||||||
\(732\) | −33.5244 | −1.23910 | ||||||||
\(733\) | −45.4599 | −1.67910 | −0.839551 | − | 0.543282i | \(-0.817182\pi\) | ||||
−0.839551 | + | 0.543282i | \(0.817182\pi\) | |||||||
\(734\) | 51.1042 | 1.88629 | ||||||||
\(735\) | 16.6353 | 0.613601 | ||||||||
\(736\) | 10.2039 | 0.376122 | ||||||||
\(737\) | 23.1417 | 0.852435 | ||||||||
\(738\) | 28.2439 | 1.03967 | ||||||||
\(739\) | −8.32747 | −0.306331 | −0.153166 | − | 0.988201i | \(-0.548947\pi\) | ||||
−0.153166 | + | 0.988201i | \(0.548947\pi\) | |||||||
\(740\) | 26.6900 | 0.981144 | ||||||||
\(741\) | 10.6361 | 0.390726 | ||||||||
\(742\) | 8.59928 | 0.315690 | ||||||||
\(743\) | 22.1916 | 0.814130 | 0.407065 | − | 0.913399i | \(-0.366552\pi\) | ||||
0.407065 | + | 0.913399i | \(0.366552\pi\) | |||||||
\(744\) | 53.0903 | 1.94639 | ||||||||
\(745\) | 5.71365 | 0.209332 | ||||||||
\(746\) | −72.0942 | −2.63956 | ||||||||
\(747\) | 0.459137 | 0.0167990 | ||||||||
\(748\) | −43.0700 | −1.57479 | ||||||||
\(749\) | 5.34337 | 0.195242 | ||||||||
\(750\) | −41.2689 | −1.50693 | ||||||||
\(751\) | 3.98537 | 0.145428 | 0.0727141 | − | 0.997353i | \(-0.476834\pi\) | ||||
0.0727141 | + | 0.997353i | \(0.476834\pi\) | |||||||
\(752\) | 56.8138 | 2.07179 | ||||||||
\(753\) | −28.1815 | −1.02699 | ||||||||
\(754\) | 28.5159 | 1.03849 | ||||||||
\(755\) | −38.0347 | −1.38422 | ||||||||
\(756\) | −12.1745 | −0.442784 | ||||||||
\(757\) | 16.1230 | 0.586002 | 0.293001 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293001 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(758\) | 4.66216 | 0.169337 | ||||||||
\(759\) | 18.9557 | 0.688047 | ||||||||
\(760\) | −33.1083 | −1.20096 | ||||||||
\(761\) | 52.0191 | 1.88569 | 0.942845 | − | 0.333231i | \(-0.108139\pi\) | ||||
0.942845 | + | 0.333231i | \(0.108139\pi\) | |||||||
\(762\) | 74.7047 | 2.70626 | ||||||||
\(763\) | −1.91870 | −0.0694616 | ||||||||
\(764\) | 109.604 | 3.96533 | ||||||||
\(765\) | 7.08748 | 0.256248 | ||||||||
\(766\) | 31.9440 | 1.15418 | ||||||||
\(767\) | 8.89392 | 0.321141 | ||||||||
\(768\) | −44.2583 | −1.59704 | ||||||||
\(769\) | 3.18271 | 0.114771 | 0.0573857 | − | 0.998352i | \(-0.481724\pi\) | ||||
0.0573857 | + | 0.998352i | \(0.481724\pi\) | |||||||
\(770\) | −6.96905 | −0.251147 | ||||||||
\(771\) | −8.86923 | −0.319417 | ||||||||
\(772\) | 46.4375 | 1.67132 | ||||||||
\(773\) | 43.2851 | 1.55686 | 0.778428 | − | 0.627734i | \(-0.216017\pi\) | ||||
0.778428 | + | 0.627734i | \(0.216017\pi\) | |||||||
\(774\) | 6.78318 | 0.243816 | ||||||||
\(775\) | 12.0957 | 0.434492 | ||||||||
\(776\) | −62.1308 | −2.23036 | ||||||||
\(777\) | −2.43532 | −0.0873665 | ||||||||
\(778\) | 29.7555 | 1.06679 | ||||||||
\(779\) | −32.6912 | −1.17128 | ||||||||
\(780\) | 24.5259 | 0.878168 | ||||||||
\(781\) | −0.954957 | −0.0341710 | ||||||||
\(782\) | 39.2421 | 1.40329 | ||||||||
\(783\) | −27.3766 | −0.978360 | ||||||||
\(784\) | −35.7380 | −1.27636 | ||||||||
\(785\) | −11.8185 | −0.421820 | ||||||||
\(786\) | −28.3498 | −1.01120 | ||||||||
\(787\) | 42.2240 | 1.50512 | 0.752562 | − | 0.658522i | \(-0.228818\pi\) | ||||
0.752562 | + | 0.658522i | \(0.228818\pi\) | |||||||
\(788\) | 41.6373 | 1.48327 | ||||||||
\(789\) | −1.86630 | −0.0664421 | ||||||||
\(790\) | 46.3794 | 1.65010 | ||||||||
\(791\) | −7.80882 | −0.277650 | ||||||||
\(792\) | −19.0302 | −0.676210 | ||||||||
\(793\) | 13.8082 | 0.490344 | ||||||||
\(794\) | 13.8762 | 0.492448 | ||||||||
\(795\) | 16.6313 | 0.589852 | ||||||||
\(796\) | −43.1363 | −1.52893 | ||||||||
\(797\) | 22.7388 | 0.805449 | 0.402725 | − | 0.915321i | \(-0.368063\pi\) | ||||
0.402725 | + | 0.915321i | \(0.368063\pi\) | |||||||
\(798\) | 5.75481 | 0.203718 | ||||||||
\(799\) | 36.4233 | 1.28856 | ||||||||
\(800\) | 3.76210 | 0.133010 | ||||||||
\(801\) | −17.5241 | −0.619183 | ||||||||
\(802\) | −50.4951 | −1.78304 | ||||||||
\(803\) | −3.29793 | −0.116382 | ||||||||
\(804\) | −44.0652 | −1.55406 | ||||||||
\(805\) | 4.30469 | 0.151720 | ||||||||
\(806\) | −41.6561 | −1.46727 | ||||||||
\(807\) | −34.9426 | −1.23004 | ||||||||
\(808\) | −35.5822 | −1.25178 | ||||||||
\(809\) | −0.0868030 | −0.00305183 | −0.00152591 | − | 0.999999i | \(-0.500486\pi\) | ||||
−0.00152591 | + | 0.999999i | \(0.500486\pi\) | |||||||
\(810\) | −19.1503 | −0.672872 | ||||||||
\(811\) | −31.4066 | −1.10283 | −0.551417 | − | 0.834230i | \(-0.685913\pi\) | ||||
−0.551417 | + | 0.834230i | \(0.685913\pi\) | |||||||
\(812\) | 10.4599 | 0.367071 | ||||||||
\(813\) | −41.7984 | −1.46594 | ||||||||
\(814\) | −26.1921 | −0.918034 | ||||||||
\(815\) | −20.8091 | −0.728911 | ||||||||
\(816\) | 24.5433 | 0.859188 | ||||||||
\(817\) | −7.85127 | −0.274681 | ||||||||
\(818\) | 60.1708 | 2.10382 | ||||||||
\(819\) | 1.38833 | 0.0485120 | ||||||||
\(820\) | −75.3833 | −2.63250 | ||||||||
\(821\) | −6.67996 | −0.233132 | −0.116566 | − | 0.993183i | \(-0.537189\pi\) | ||||
−0.116566 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(822\) | 18.7156 | 0.652782 | ||||||||
\(823\) | 29.6088 | 1.03210 | 0.516050 | − | 0.856559i | \(-0.327402\pi\) | ||||
0.516050 | + | 0.856559i | \(0.327402\pi\) | |||||||
\(824\) | 44.8043 | 1.56083 | ||||||||
\(825\) | 6.98879 | 0.243318 | ||||||||
\(826\) | 4.81219 | 0.167437 | ||||||||
\(827\) | −43.5090 | −1.51296 | −0.756479 | − | 0.654018i | \(-0.773082\pi\) | ||||
−0.756479 | + | 0.654018i | \(0.773082\pi\) | |||||||
\(828\) | 22.3924 | 0.778188 | ||||||||
\(829\) | 27.0151 | 0.938272 | 0.469136 | − | 0.883126i | \(-0.344565\pi\) | ||||
0.469136 | + | 0.883126i | \(0.344565\pi\) | |||||||
\(830\) | −1.80760 | −0.0627426 | ||||||||
\(831\) | −21.7260 | −0.753667 | ||||||||
\(832\) | 12.0744 | 0.418606 | ||||||||
\(833\) | −22.9116 | −0.793841 | ||||||||
\(834\) | −46.4939 | −1.60995 | ||||||||
\(835\) | 13.2232 | 0.457608 | ||||||||
\(836\) | 41.9602 | 1.45122 | ||||||||
\(837\) | 39.9917 | 1.38232 | ||||||||
\(838\) | −21.6910 | −0.749303 | ||||||||
\(839\) | −17.6099 | −0.607960 | −0.303980 | − | 0.952678i | \(-0.598316\pi\) | ||||
−0.303980 | + | 0.952678i | \(0.598316\pi\) | |||||||
\(840\) | 6.96607 | 0.240352 | ||||||||
\(841\) | −5.47903 | −0.188932 | ||||||||
\(842\) | −55.2344 | −1.90350 | ||||||||
\(843\) | −40.5611 | −1.39700 | ||||||||
\(844\) | 96.3785 | 3.31748 | ||||||||
\(845\) | 13.4876 | 0.463989 | ||||||||
\(846\) | 30.6574 | 1.05402 | ||||||||
\(847\) | −0.998717 | −0.0343163 | ||||||||
\(848\) | −35.7296 | −1.22696 | ||||||||
\(849\) | 30.6650 | 1.05242 | ||||||||
\(850\) | 14.4682 | 0.496255 | ||||||||
\(851\) | 16.1785 | 0.554594 | ||||||||
\(852\) | 1.81838 | 0.0622967 | ||||||||
\(853\) | −11.5200 | −0.394438 | −0.197219 | − | 0.980359i | \(-0.563191\pi\) | ||||
−0.197219 | + | 0.980359i | \(0.563191\pi\) | |||||||
\(854\) | 7.47114 | 0.255657 | ||||||||
\(855\) | −6.90486 | −0.236141 | ||||||||
\(856\) | −57.4440 | −1.96340 | ||||||||
\(857\) | 42.6810 | 1.45795 | 0.728977 | − | 0.684538i | \(-0.239996\pi\) | ||||
0.728977 | + | 0.684538i | \(0.239996\pi\) | |||||||
\(858\) | −24.0684 | −0.821682 | ||||||||
\(859\) | 5.37251 | 0.183308 | 0.0916539 | − | 0.995791i | \(-0.470785\pi\) | ||||
0.0916539 | + | 0.995791i | \(0.470785\pi\) | |||||||
\(860\) | −18.1044 | −0.617354 | ||||||||
\(861\) | 6.87831 | 0.234412 | ||||||||
\(862\) | 82.7816 | 2.81955 | ||||||||
\(863\) | −39.3149 | −1.33830 | −0.669148 | − | 0.743129i | \(-0.733341\pi\) | ||||
−0.669148 | + | 0.743129i | \(0.733341\pi\) | |||||||
\(864\) | 12.4385 | 0.423166 | ||||||||
\(865\) | −6.79526 | −0.231046 | ||||||||
\(866\) | 57.5570 | 1.95587 | ||||||||
\(867\) | −7.39663 | −0.251203 | ||||||||
\(868\) | −15.2799 | −0.518632 | ||||||||
\(869\) | −30.8560 | −1.04672 | ||||||||
\(870\) | 29.8402 | 1.01168 | ||||||||
\(871\) | 18.1498 | 0.614982 | ||||||||
\(872\) | 20.6270 | 0.698519 | ||||||||
\(873\) | −12.9576 | −0.438548 | ||||||||
\(874\) | −38.2309 | −1.29318 | ||||||||
\(875\) | 6.23504 | 0.210783 | ||||||||
\(876\) | 6.27976 | 0.212173 | ||||||||
\(877\) | 11.6510 | 0.393426 | 0.196713 | − | 0.980461i | \(-0.436973\pi\) | ||||
0.196713 | + | 0.980461i | \(0.436973\pi\) | |||||||
\(878\) | 69.8245 | 2.35646 | ||||||||
\(879\) | −10.3421 | −0.348832 | ||||||||
\(880\) | 28.9560 | 0.976108 | ||||||||
\(881\) | −46.9121 | −1.58051 | −0.790255 | − | 0.612778i | \(-0.790052\pi\) | ||||
−0.790255 | + | 0.612778i | \(0.790052\pi\) | |||||||
\(882\) | −19.2847 | −0.649349 | ||||||||
\(883\) | −37.5313 | −1.26303 | −0.631514 | − | 0.775364i | \(-0.717566\pi\) | ||||
−0.631514 | + | 0.775364i | \(0.717566\pi\) | |||||||
\(884\) | −33.7794 | −1.13612 | ||||||||
\(885\) | 9.30695 | 0.312850 | ||||||||
\(886\) | 19.0321 | 0.639396 | ||||||||
\(887\) | −51.6675 | −1.73482 | −0.867412 | − | 0.497590i | \(-0.834218\pi\) | ||||
−0.867412 | + | 0.497590i | \(0.834218\pi\) | |||||||
\(888\) | 26.1809 | 0.878575 | ||||||||
\(889\) | −11.2866 | −0.378542 | ||||||||
\(890\) | 68.9913 | 2.31259 | ||||||||
\(891\) | 12.7406 | 0.426825 | ||||||||
\(892\) | 105.813 | 3.54287 | ||||||||
\(893\) | −35.4848 | −1.18745 | ||||||||
\(894\) | 10.6767 | 0.357083 | ||||||||
\(895\) | 14.1294 | 0.472295 | ||||||||
\(896\) | 8.79073 | 0.293678 | ||||||||
\(897\) | 14.8668 | 0.496387 | ||||||||
\(898\) | −54.5643 | −1.82083 | ||||||||
\(899\) | −34.3594 | −1.14595 | ||||||||
\(900\) | 8.25586 | 0.275195 | ||||||||
\(901\) | −22.9062 | −0.763117 | ||||||||
\(902\) | 73.9771 | 2.46317 | ||||||||
\(903\) | 1.65193 | 0.0549726 | ||||||||
\(904\) | 83.9489 | 2.79210 | ||||||||
\(905\) | −39.1585 | −1.30167 | ||||||||
\(906\) | −71.0728 | −2.36124 | ||||||||
\(907\) | 21.0701 | 0.699620 | 0.349810 | − | 0.936821i | \(-0.386246\pi\) | ||||
0.349810 | + | 0.936821i | \(0.386246\pi\) | |||||||
\(908\) | −23.8013 | −0.789872 | ||||||||
\(909\) | −7.42080 | −0.246132 | ||||||||
\(910\) | −5.46576 | −0.181188 | ||||||||
\(911\) | −11.3971 | −0.377602 | −0.188801 | − | 0.982015i | \(-0.560460\pi\) | ||||
−0.188801 | + | 0.982015i | \(0.560460\pi\) | |||||||
\(912\) | −23.9109 | −0.791770 | ||||||||
\(913\) | 1.20258 | 0.0397997 | ||||||||
\(914\) | −56.8210 | −1.87947 | ||||||||
\(915\) | 14.4495 | 0.477684 | ||||||||
\(916\) | −27.8365 | −0.919745 | ||||||||
\(917\) | 4.28318 | 0.141443 | ||||||||
\(918\) | 47.8357 | 1.57881 | ||||||||
\(919\) | 19.0341 | 0.627878 | 0.313939 | − | 0.949443i | \(-0.398351\pi\) | ||||
0.313939 | + | 0.949443i | \(0.398351\pi\) | |||||||
\(920\) | −46.2777 | −1.52573 | ||||||||
\(921\) | 34.2573 | 1.12882 | ||||||||
\(922\) | −31.4663 | −1.03629 | ||||||||
\(923\) | −0.748964 | −0.0246524 | ||||||||
\(924\) | −8.82854 | −0.290438 | ||||||||
\(925\) | 5.96489 | 0.196124 | ||||||||
\(926\) | −81.5994 | −2.68152 | ||||||||
\(927\) | 9.34409 | 0.306900 | ||||||||
\(928\) | −10.6867 | −0.350808 | ||||||||
\(929\) | 11.1706 | 0.366495 | 0.183248 | − | 0.983067i | \(-0.441339\pi\) | ||||
0.183248 | + | 0.983067i | \(0.441339\pi\) | |||||||
\(930\) | −43.5905 | −1.42939 | ||||||||
\(931\) | 22.3213 | 0.731551 | ||||||||
\(932\) | 36.3383 | 1.19030 | ||||||||
\(933\) | −15.7145 | −0.514471 | ||||||||
\(934\) | 52.7317 | 1.72543 | ||||||||
\(935\) | 18.5637 | 0.607098 | ||||||||
\(936\) | −14.9252 | −0.487847 | ||||||||
\(937\) | 11.5626 | 0.377734 | 0.188867 | − | 0.982003i | \(-0.439518\pi\) | ||||
0.188867 | + | 0.982003i | \(0.439518\pi\) | |||||||
\(938\) | 9.82022 | 0.320642 | ||||||||
\(939\) | −0.856789 | −0.0279603 | ||||||||
\(940\) | −81.8250 | −2.66884 | ||||||||
\(941\) | −27.9240 | −0.910296 | −0.455148 | − | 0.890416i | \(-0.650414\pi\) | ||||
−0.455148 | + | 0.890416i | \(0.650414\pi\) | |||||||
\(942\) | −22.0844 | −0.719549 | ||||||||
\(943\) | −45.6947 | −1.48802 | ||||||||
\(944\) | −19.9944 | −0.650762 | ||||||||
\(945\) | 5.24738 | 0.170697 | ||||||||
\(946\) | 17.7667 | 0.577644 | ||||||||
\(947\) | −17.2983 | −0.562120 | −0.281060 | − | 0.959690i | \(-0.590686\pi\) | ||||
−0.281060 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(948\) | 58.7544 | 1.90825 | ||||||||
\(949\) | −2.58654 | −0.0839626 | ||||||||
\(950\) | −14.0954 | −0.457315 | ||||||||
\(951\) | 13.2813 | 0.430677 | ||||||||
\(952\) | −9.59432 | −0.310954 | ||||||||
\(953\) | 35.6175 | 1.15376 | 0.576882 | − | 0.816827i | \(-0.304269\pi\) | ||||
0.576882 | + | 0.816827i | \(0.304269\pi\) | |||||||
\(954\) | −19.2801 | −0.624217 | ||||||||
\(955\) | −47.2406 | −1.52867 | ||||||||
\(956\) | 76.0395 | 2.45929 | ||||||||
\(957\) | −19.8525 | −0.641741 | ||||||||
\(958\) | 62.6617 | 2.02451 | ||||||||
\(959\) | −2.82762 | −0.0913085 | ||||||||
\(960\) | 12.6352 | 0.407798 | ||||||||
\(961\) | 19.1922 | 0.619104 | ||||||||
\(962\) | −20.5422 | −0.662309 | ||||||||
\(963\) | −11.9802 | −0.386055 | ||||||||
\(964\) | −79.2281 | −2.55176 | ||||||||
\(965\) | −20.0151 | −0.644309 | ||||||||
\(966\) | 8.04388 | 0.258808 | ||||||||
\(967\) | 47.5952 | 1.53056 | 0.765279 | − | 0.643699i | \(-0.222601\pi\) | ||||
0.765279 | + | 0.643699i | \(0.222601\pi\) | |||||||
\(968\) | 10.7367 | 0.345092 | ||||||||
\(969\) | −15.3293 | −0.492448 | ||||||||
\(970\) | 51.0133 | 1.63794 | ||||||||
\(971\) | 25.0675 | 0.804454 | 0.402227 | − | 0.915540i | \(-0.368236\pi\) | ||||
0.402227 | + | 0.915540i | \(0.368236\pi\) | |||||||
\(972\) | 47.0349 | 1.50865 | ||||||||
\(973\) | 7.02446 | 0.225194 | ||||||||
\(974\) | −101.003 | −3.23636 | ||||||||
\(975\) | 5.48124 | 0.175540 | ||||||||
\(976\) | −31.0422 | −0.993637 | ||||||||
\(977\) | −19.4337 | −0.621738 | −0.310869 | − | 0.950453i | \(-0.600620\pi\) | ||||
−0.310869 | + | 0.950453i | \(0.600620\pi\) | |||||||
\(978\) | −38.8846 | −1.24339 | ||||||||
\(979\) | −45.8995 | −1.46695 | ||||||||
\(980\) | 51.4710 | 1.64418 | ||||||||
\(981\) | 4.30184 | 0.137347 | ||||||||
\(982\) | −11.2635 | −0.359434 | ||||||||
\(983\) | −42.7531 | −1.36361 | −0.681805 | − | 0.731534i | \(-0.738805\pi\) | ||||
−0.681805 | + | 0.731534i | \(0.738805\pi\) | |||||||
\(984\) | −73.9455 | −2.35730 | ||||||||
\(985\) | −17.9462 | −0.571814 | ||||||||
\(986\) | −41.0987 | −1.30885 | ||||||||
\(987\) | 7.46609 | 0.237648 | ||||||||
\(988\) | 32.9090 | 1.04698 | ||||||||
\(989\) | −10.9742 | −0.348961 | ||||||||
\(990\) | 15.6250 | 0.496596 | ||||||||
\(991\) | −37.6302 | −1.19536 | −0.597681 | − | 0.801734i | \(-0.703911\pi\) | ||||
−0.597681 | + | 0.801734i | \(0.703911\pi\) | |||||||
\(992\) | 15.6111 | 0.495654 | ||||||||
\(993\) | 48.5528 | 1.54077 | ||||||||
\(994\) | −0.405238 | −0.0128534 | ||||||||
\(995\) | 18.5923 | 0.589415 | ||||||||
\(996\) | −2.28990 | −0.0725583 | ||||||||
\(997\) | −23.7150 | −0.751060 | −0.375530 | − | 0.926810i | \(-0.622539\pi\) | ||||
−0.375530 | + | 0.926810i | \(0.622539\pi\) | |||||||
\(998\) | −90.1162 | −2.85258 | ||||||||
\(999\) | 19.7215 | 0.623961 |
(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 | 5077.2.a.c.1.12 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.12 | ✓ | 216 | 1.1 | even | 1 | trivial |