Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(0\) |
Dimension: | \(130\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17988 | −1.54140 | −0.770702 | − | 0.637195i | \(-0.780094\pi\) | ||||
−0.770702 | + | 0.637195i | \(0.780094\pi\) | |||||||
\(3\) | −0.326610 | −0.188569 | −0.0942843 | − | 0.995545i | \(-0.530056\pi\) | ||||
−0.0942843 | + | 0.995545i | \(0.530056\pi\) | |||||||
\(4\) | 2.75186 | 1.37593 | ||||||||
\(5\) | 0.291618 | 0.130416 | 0.0652078 | − | 0.997872i | \(-0.479229\pi\) | ||||
0.0652078 | + | 0.997872i | \(0.479229\pi\) | |||||||
\(6\) | 0.711970 | 0.290661 | ||||||||
\(7\) | 2.70764 | 1.02339 | 0.511696 | − | 0.859167i | \(-0.329017\pi\) | ||||
0.511696 | + | 0.859167i | \(0.329017\pi\) | |||||||
\(8\) | −1.63895 | −0.579458 | ||||||||
\(9\) | −2.89333 | −0.964442 | ||||||||
\(10\) | −0.635691 | −0.201023 | ||||||||
\(11\) | 0.168835 | 0.0509058 | 0.0254529 | − | 0.999676i | \(-0.491897\pi\) | ||||
0.0254529 | + | 0.999676i | \(0.491897\pi\) | |||||||
\(12\) | −0.898785 | −0.259457 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −5.90232 | −1.57746 | ||||||||
\(15\) | −0.0952456 | −0.0245923 | ||||||||
\(16\) | −1.93100 | −0.482749 | ||||||||
\(17\) | 3.50001 | 0.848878 | 0.424439 | − | 0.905457i | \(-0.360471\pi\) | ||||
0.424439 | + | 0.905457i | \(0.360471\pi\) | |||||||
\(18\) | 6.30709 | 1.48660 | ||||||||
\(19\) | 7.68699 | 1.76352 | 0.881758 | − | 0.471702i | \(-0.156360\pi\) | ||||
0.881758 | + | 0.471702i | \(0.156360\pi\) | |||||||
\(20\) | 0.802492 | 0.179443 | ||||||||
\(21\) | −0.884343 | −0.192980 | ||||||||
\(22\) | −0.368040 | −0.0784664 | ||||||||
\(23\) | 2.84517 | 0.593259 | 0.296630 | − | 0.954993i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954993i | \(0.404137\pi\) | |||||||
\(24\) | 0.535299 | 0.109268 | ||||||||
\(25\) | −4.91496 | −0.982992 | ||||||||
\(26\) | −2.17988 | −0.427509 | ||||||||
\(27\) | 1.92482 | 0.370432 | ||||||||
\(28\) | 7.45104 | 1.40811 | ||||||||
\(29\) | 6.95406 | 1.29134 | 0.645668 | − | 0.763618i | \(-0.276579\pi\) | ||||
0.645668 | + | 0.763618i | \(0.276579\pi\) | |||||||
\(30\) | 0.207623 | 0.0379067 | ||||||||
\(31\) | 9.68368 | 1.73924 | 0.869620 | − | 0.493722i | \(-0.164364\pi\) | ||||
0.869620 | + | 0.493722i | \(0.164364\pi\) | |||||||
\(32\) | 7.48724 | 1.32357 | ||||||||
\(33\) | −0.0551434 | −0.00959923 | ||||||||
\(34\) | −7.62959 | −1.30846 | ||||||||
\(35\) | 0.789597 | 0.133466 | ||||||||
\(36\) | −7.96202 | −1.32700 | ||||||||
\(37\) | 1.54939 | 0.254718 | 0.127359 | − | 0.991857i | \(-0.459350\pi\) | ||||
0.127359 | + | 0.991857i | \(0.459350\pi\) | |||||||
\(38\) | −16.7567 | −2.71829 | ||||||||
\(39\) | −0.326610 | −0.0522995 | ||||||||
\(40\) | −0.477949 | −0.0755704 | ||||||||
\(41\) | −5.82149 | −0.909165 | −0.454582 | − | 0.890705i | \(-0.650211\pi\) | ||||
−0.454582 | + | 0.890705i | \(0.650211\pi\) | |||||||
\(42\) | 1.92776 | 0.297460 | ||||||||
\(43\) | −8.32800 | −1.27001 | −0.635004 | − | 0.772509i | \(-0.719002\pi\) | ||||
−0.635004 | + | 0.772509i | \(0.719002\pi\) | |||||||
\(44\) | 0.464611 | 0.0700427 | ||||||||
\(45\) | −0.843747 | −0.125778 | ||||||||
\(46\) | −6.20212 | −0.914452 | ||||||||
\(47\) | 8.82116 | 1.28670 | 0.643349 | − | 0.765573i | \(-0.277544\pi\) | ||||
0.643349 | + | 0.765573i | \(0.277544\pi\) | |||||||
\(48\) | 0.630684 | 0.0910314 | ||||||||
\(49\) | 0.331312 | 0.0473302 | ||||||||
\(50\) | 10.7140 | 1.51519 | ||||||||
\(51\) | −1.14314 | −0.160072 | ||||||||
\(52\) | 2.75186 | 0.381614 | ||||||||
\(53\) | 6.74630 | 0.926676 | 0.463338 | − | 0.886182i | \(-0.346652\pi\) | ||||
0.463338 | + | 0.886182i | \(0.346652\pi\) | |||||||
\(54\) | −4.19587 | −0.570986 | ||||||||
\(55\) | 0.0492355 | 0.00663891 | ||||||||
\(56\) | −4.43770 | −0.593012 | ||||||||
\(57\) | −2.51065 | −0.332544 | ||||||||
\(58\) | −15.1590 | −1.99047 | ||||||||
\(59\) | −6.51027 | −0.847565 | −0.423782 | − | 0.905764i | \(-0.639298\pi\) | ||||
−0.423782 | + | 0.905764i | \(0.639298\pi\) | |||||||
\(60\) | −0.262102 | −0.0338372 | ||||||||
\(61\) | −5.01113 | −0.641609 | −0.320804 | − | 0.947145i | \(-0.603953\pi\) | ||||
−0.320804 | + | 0.947145i | \(0.603953\pi\) | |||||||
\(62\) | −21.1092 | −2.68087 | ||||||||
\(63\) | −7.83408 | −0.987002 | ||||||||
\(64\) | −12.4593 | −1.55741 | ||||||||
\(65\) | 0.291618 | 0.0361708 | ||||||||
\(66\) | 0.120206 | 0.0147963 | ||||||||
\(67\) | 12.2773 | 1.49991 | 0.749956 | − | 0.661488i | \(-0.230075\pi\) | ||||
0.749956 | + | 0.661488i | \(0.230075\pi\) | |||||||
\(68\) | 9.63154 | 1.16800 | ||||||||
\(69\) | −0.929262 | −0.111870 | ||||||||
\(70\) | −1.72122 | −0.205726 | ||||||||
\(71\) | 13.8169 | 1.63976 | 0.819880 | − | 0.572535i | \(-0.194040\pi\) | ||||
0.819880 | + | 0.572535i | \(0.194040\pi\) | |||||||
\(72\) | 4.74203 | 0.558853 | ||||||||
\(73\) | −9.79307 | −1.14619 | −0.573096 | − | 0.819488i | \(-0.694258\pi\) | ||||
−0.573096 | + | 0.819488i | \(0.694258\pi\) | |||||||
\(74\) | −3.37747 | −0.392623 | ||||||||
\(75\) | 1.60528 | 0.185361 | ||||||||
\(76\) | 21.1535 | 2.42647 | ||||||||
\(77\) | 0.457145 | 0.0520965 | ||||||||
\(78\) | 0.711970 | 0.0806147 | ||||||||
\(79\) | −9.92858 | −1.11705 | −0.558527 | − | 0.829487i | \(-0.688633\pi\) | ||||
−0.558527 | + | 0.829487i | \(0.688633\pi\) | |||||||
\(80\) | −0.563114 | −0.0629581 | ||||||||
\(81\) | 8.05131 | 0.894590 | ||||||||
\(82\) | 12.6901 | 1.40139 | ||||||||
\(83\) | −3.56820 | −0.391661 | −0.195831 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195831 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(84\) | −2.43359 | −0.265526 | ||||||||
\(85\) | 1.02067 | 0.110707 | ||||||||
\(86\) | 18.1540 | 1.95760 | ||||||||
\(87\) | −2.27127 | −0.243505 | ||||||||
\(88\) | −0.276713 | −0.0294978 | ||||||||
\(89\) | −1.79988 | −0.190787 | −0.0953935 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953935 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(90\) | 1.83926 | 0.193875 | ||||||||
\(91\) | 2.70764 | 0.283838 | ||||||||
\(92\) | 7.82950 | 0.816282 | ||||||||
\(93\) | −3.16279 | −0.327966 | ||||||||
\(94\) | −19.2290 | −1.98332 | ||||||||
\(95\) | 2.24167 | 0.229990 | ||||||||
\(96\) | −2.44541 | −0.249584 | ||||||||
\(97\) | 11.7153 | 1.18951 | 0.594756 | − | 0.803906i | \(-0.297249\pi\) | ||||
0.594756 | + | 0.803906i | \(0.297249\pi\) | |||||||
\(98\) | −0.722218 | −0.0729551 | ||||||||
\(99\) | −0.488496 | −0.0490957 | ||||||||
\(100\) | −13.5253 | −1.35253 | ||||||||
\(101\) | 3.02445 | 0.300944 | 0.150472 | − | 0.988614i | \(-0.451921\pi\) | ||||
0.150472 | + | 0.988614i | \(0.451921\pi\) | |||||||
\(102\) | 2.49190 | 0.246735 | ||||||||
\(103\) | −2.91522 | −0.287245 | −0.143623 | − | 0.989633i | \(-0.545875\pi\) | ||||
−0.143623 | + | 0.989633i | \(0.545875\pi\) | |||||||
\(104\) | −1.63895 | −0.160713 | ||||||||
\(105\) | −0.257891 | −0.0251675 | ||||||||
\(106\) | −14.7061 | −1.42838 | ||||||||
\(107\) | 8.25646 | 0.798182 | 0.399091 | − | 0.916911i | \(-0.369326\pi\) | ||||
0.399091 | + | 0.916911i | \(0.369326\pi\) | |||||||
\(108\) | 5.29683 | 0.509688 | ||||||||
\(109\) | 0.264215 | 0.0253072 | 0.0126536 | − | 0.999920i | \(-0.495972\pi\) | ||||
0.0126536 | + | 0.999920i | \(0.495972\pi\) | |||||||
\(110\) | −0.107327 | −0.0102332 | ||||||||
\(111\) | −0.506046 | −0.0480317 | ||||||||
\(112\) | −5.22845 | −0.494042 | ||||||||
\(113\) | −4.96955 | −0.467496 | −0.233748 | − | 0.972297i | \(-0.575099\pi\) | ||||
−0.233748 | + | 0.972297i | \(0.575099\pi\) | |||||||
\(114\) | 5.47290 | 0.512584 | ||||||||
\(115\) | 0.829704 | 0.0773703 | ||||||||
\(116\) | 19.1366 | 1.77679 | ||||||||
\(117\) | −2.89333 | −0.267488 | ||||||||
\(118\) | 14.1916 | 1.30644 | ||||||||
\(119\) | 9.47677 | 0.868734 | ||||||||
\(120\) | 0.156103 | 0.0142502 | ||||||||
\(121\) | −10.9715 | −0.997409 | ||||||||
\(122\) | 10.9236 | 0.988979 | ||||||||
\(123\) | 1.90136 | 0.171440 | ||||||||
\(124\) | 26.6481 | 2.39307 | ||||||||
\(125\) | −2.89138 | −0.258613 | ||||||||
\(126\) | 17.0773 | 1.52137 | ||||||||
\(127\) | 15.1998 | 1.34876 | 0.674380 | − | 0.738384i | \(-0.264411\pi\) | ||||
0.674380 | + | 0.738384i | \(0.264411\pi\) | |||||||
\(128\) | 12.1852 | 1.07703 | ||||||||
\(129\) | 2.72001 | 0.239484 | ||||||||
\(130\) | −0.635691 | −0.0557538 | ||||||||
\(131\) | 6.70859 | 0.586132 | 0.293066 | − | 0.956092i | \(-0.405324\pi\) | ||||
0.293066 | + | 0.956092i | \(0.405324\pi\) | |||||||
\(132\) | −0.151747 | −0.0132079 | ||||||||
\(133\) | 20.8136 | 1.80477 | ||||||||
\(134\) | −26.7630 | −2.31197 | ||||||||
\(135\) | 0.561313 | 0.0483101 | ||||||||
\(136\) | −5.73636 | −0.491889 | ||||||||
\(137\) | −7.93872 | −0.678250 | −0.339125 | − | 0.940741i | \(-0.610131\pi\) | ||||
−0.339125 | + | 0.940741i | \(0.610131\pi\) | |||||||
\(138\) | 2.02568 | 0.172437 | ||||||||
\(139\) | −12.6949 | −1.07677 | −0.538385 | − | 0.842699i | \(-0.680965\pi\) | ||||
−0.538385 | + | 0.842699i | \(0.680965\pi\) | |||||||
\(140\) | 2.17286 | 0.183640 | ||||||||
\(141\) | −2.88108 | −0.242631 | ||||||||
\(142\) | −30.1190 | −2.52753 | ||||||||
\(143\) | 0.168835 | 0.0141187 | ||||||||
\(144\) | 5.58700 | 0.465584 | ||||||||
\(145\) | 2.02793 | 0.168410 | ||||||||
\(146\) | 21.3477 | 1.76675 | ||||||||
\(147\) | −0.108210 | −0.00892500 | ||||||||
\(148\) | 4.26369 | 0.350473 | ||||||||
\(149\) | 9.32642 | 0.764050 | 0.382025 | − | 0.924152i | \(-0.375227\pi\) | ||||
0.382025 | + | 0.924152i | \(0.375227\pi\) | |||||||
\(150\) | −3.49930 | −0.285717 | ||||||||
\(151\) | 17.3475 | 1.41172 | 0.705860 | − | 0.708352i | \(-0.250561\pi\) | ||||
0.705860 | + | 0.708352i | \(0.250561\pi\) | |||||||
\(152\) | −12.5986 | −1.02188 | ||||||||
\(153\) | −10.1267 | −0.818693 | ||||||||
\(154\) | −0.996520 | −0.0803019 | ||||||||
\(155\) | 2.82394 | 0.226824 | ||||||||
\(156\) | −0.898785 | −0.0719604 | ||||||||
\(157\) | −14.1294 | −1.12764 | −0.563822 | − | 0.825896i | \(-0.690670\pi\) | ||||
−0.563822 | + | 0.825896i | \(0.690670\pi\) | |||||||
\(158\) | 21.6431 | 1.72183 | ||||||||
\(159\) | −2.20341 | −0.174742 | ||||||||
\(160\) | 2.18342 | 0.172614 | ||||||||
\(161\) | 7.70370 | 0.607136 | ||||||||
\(162\) | −17.5509 | −1.37893 | ||||||||
\(163\) | 1.65487 | 0.129619 | 0.0648097 | − | 0.997898i | \(-0.479356\pi\) | ||||
0.0648097 | + | 0.997898i | \(0.479356\pi\) | |||||||
\(164\) | −16.0199 | −1.25095 | ||||||||
\(165\) | −0.0160808 | −0.00125189 | ||||||||
\(166\) | 7.77824 | 0.603709 | ||||||||
\(167\) | 16.7139 | 1.29336 | 0.646679 | − | 0.762762i | \(-0.276157\pi\) | ||||
0.646679 | + | 0.762762i | \(0.276157\pi\) | |||||||
\(168\) | 1.44940 | 0.111823 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.22493 | −0.170644 | ||||||||
\(171\) | −22.2410 | −1.70081 | ||||||||
\(172\) | −22.9175 | −1.74744 | ||||||||
\(173\) | −5.82151 | −0.442601 | −0.221301 | − | 0.975206i | \(-0.571030\pi\) | ||||
−0.221301 | + | 0.975206i | \(0.571030\pi\) | |||||||
\(174\) | 4.95108 | 0.375340 | ||||||||
\(175\) | −13.3079 | −1.00599 | ||||||||
\(176\) | −0.326021 | −0.0245747 | ||||||||
\(177\) | 2.12632 | 0.159824 | ||||||||
\(178\) | 3.92352 | 0.294080 | ||||||||
\(179\) | 14.9430 | 1.11689 | 0.558446 | − | 0.829541i | \(-0.311398\pi\) | ||||
0.558446 | + | 0.829541i | \(0.311398\pi\) | |||||||
\(180\) | −2.32187 | −0.173062 | ||||||||
\(181\) | −24.7113 | −1.83678 | −0.918389 | − | 0.395679i | \(-0.870509\pi\) | ||||
−0.918389 | + | 0.395679i | \(0.870509\pi\) | |||||||
\(182\) | −5.90232 | −0.437509 | ||||||||
\(183\) | 1.63669 | 0.120987 | ||||||||
\(184\) | −4.66310 | −0.343769 | ||||||||
\(185\) | 0.451829 | 0.0332192 | ||||||||
\(186\) | 6.89449 | 0.505528 | ||||||||
\(187\) | 0.590926 | 0.0432128 | ||||||||
\(188\) | 24.2746 | 1.77041 | ||||||||
\(189\) | 5.21172 | 0.379097 | ||||||||
\(190\) | −4.88655 | −0.354508 | ||||||||
\(191\) | −20.0819 | −1.45307 | −0.726537 | − | 0.687127i | \(-0.758871\pi\) | ||||
−0.726537 | + | 0.687127i | \(0.758871\pi\) | |||||||
\(192\) | 4.06932 | 0.293678 | ||||||||
\(193\) | 6.05552 | 0.435886 | 0.217943 | − | 0.975962i | \(-0.430065\pi\) | ||||
0.217943 | + | 0.975962i | \(0.430065\pi\) | |||||||
\(194\) | −25.5380 | −1.83352 | ||||||||
\(195\) | −0.0952456 | −0.00682068 | ||||||||
\(196\) | 0.911722 | 0.0651230 | ||||||||
\(197\) | −16.1404 | −1.14996 | −0.574979 | − | 0.818168i | \(-0.694990\pi\) | ||||
−0.574979 | + | 0.818168i | \(0.694990\pi\) | |||||||
\(198\) | 1.06486 | 0.0756763 | ||||||||
\(199\) | −23.6286 | −1.67498 | −0.837492 | − | 0.546450i | \(-0.815979\pi\) | ||||
−0.837492 | + | 0.546450i | \(0.815979\pi\) | |||||||
\(200\) | 8.05539 | 0.569602 | ||||||||
\(201\) | −4.00990 | −0.282836 | ||||||||
\(202\) | −6.59291 | −0.463876 | ||||||||
\(203\) | 18.8291 | 1.32154 | ||||||||
\(204\) | −3.14576 | −0.220247 | ||||||||
\(205\) | −1.69765 | −0.118569 | ||||||||
\(206\) | 6.35482 | 0.442761 | ||||||||
\(207\) | −8.23201 | −0.572164 | ||||||||
\(208\) | −1.93100 | −0.133891 | ||||||||
\(209\) | 1.29784 | 0.0897731 | ||||||||
\(210\) | 0.562169 | 0.0387934 | ||||||||
\(211\) | 6.46260 | 0.444904 | 0.222452 | − | 0.974944i | \(-0.428594\pi\) | ||||
0.222452 | + | 0.974944i | \(0.428594\pi\) | |||||||
\(212\) | 18.5649 | 1.27504 | ||||||||
\(213\) | −4.51273 | −0.309207 | ||||||||
\(214\) | −17.9980 | −1.23032 | ||||||||
\(215\) | −2.42860 | −0.165629 | ||||||||
\(216\) | −3.15469 | −0.214650 | ||||||||
\(217\) | 26.2199 | 1.77992 | ||||||||
\(218\) | −0.575955 | −0.0390086 | ||||||||
\(219\) | 3.19852 | 0.216136 | ||||||||
\(220\) | 0.135489 | 0.00913467 | ||||||||
\(221\) | 3.50001 | 0.235436 | ||||||||
\(222\) | 1.10312 | 0.0740363 | ||||||||
\(223\) | −4.57954 | −0.306669 | −0.153334 | − | 0.988174i | \(-0.549001\pi\) | ||||
−0.153334 | + | 0.988174i | \(0.549001\pi\) | |||||||
\(224\) | 20.2728 | 1.35453 | ||||||||
\(225\) | 14.2206 | 0.948038 | ||||||||
\(226\) | 10.8330 | 0.720601 | ||||||||
\(227\) | 6.17014 | 0.409527 | 0.204763 | − | 0.978812i | \(-0.434358\pi\) | ||||
0.204763 | + | 0.978812i | \(0.434358\pi\) | |||||||
\(228\) | −6.90895 | −0.457556 | ||||||||
\(229\) | −26.7394 | −1.76699 | −0.883494 | − | 0.468443i | \(-0.844815\pi\) | ||||
−0.883494 | + | 0.468443i | \(0.844815\pi\) | |||||||
\(230\) | −1.80865 | −0.119259 | ||||||||
\(231\) | −0.149308 | −0.00982377 | ||||||||
\(232\) | −11.3974 | −0.748275 | ||||||||
\(233\) | 8.40915 | 0.550902 | 0.275451 | − | 0.961315i | \(-0.411173\pi\) | ||||
0.275451 | + | 0.961315i | \(0.411173\pi\) | |||||||
\(234\) | 6.30709 | 0.412307 | ||||||||
\(235\) | 2.57241 | 0.167806 | ||||||||
\(236\) | −17.9153 | −1.16619 | ||||||||
\(237\) | 3.24278 | 0.210641 | ||||||||
\(238\) | −20.6582 | −1.33907 | ||||||||
\(239\) | −0.882942 | −0.0571127 | −0.0285564 | − | 0.999592i | \(-0.509091\pi\) | ||||
−0.0285564 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(240\) | 0.183919 | 0.0118719 | ||||||||
\(241\) | 5.97100 | 0.384626 | 0.192313 | − | 0.981334i | \(-0.438401\pi\) | ||||
0.192313 | + | 0.981334i | \(0.438401\pi\) | |||||||
\(242\) | 23.9165 | 1.53741 | ||||||||
\(243\) | −8.40411 | −0.539124 | ||||||||
\(244\) | −13.7899 | −0.882808 | ||||||||
\(245\) | 0.0966165 | 0.00617260 | ||||||||
\(246\) | −4.14473 | −0.264258 | ||||||||
\(247\) | 7.68699 | 0.489111 | ||||||||
\(248\) | −15.8711 | −1.00782 | ||||||||
\(249\) | 1.16541 | 0.0738550 | ||||||||
\(250\) | 6.30285 | 0.398628 | ||||||||
\(251\) | 20.7812 | 1.31169 | 0.655847 | − | 0.754893i | \(-0.272311\pi\) | ||||
0.655847 | + | 0.754893i | \(0.272311\pi\) | |||||||
\(252\) | −21.5583 | −1.35804 | ||||||||
\(253\) | 0.480365 | 0.0302003 | ||||||||
\(254\) | −33.1336 | −2.07899 | ||||||||
\(255\) | −0.333361 | −0.0208759 | ||||||||
\(256\) | −1.64359 | −0.102724 | ||||||||
\(257\) | 2.29089 | 0.142902 | 0.0714508 | − | 0.997444i | \(-0.477237\pi\) | ||||
0.0714508 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(258\) | −5.92929 | −0.369141 | ||||||||
\(259\) | 4.19518 | 0.260676 | ||||||||
\(260\) | 0.802492 | 0.0497684 | ||||||||
\(261\) | −20.1203 | −1.24542 | ||||||||
\(262\) | −14.6239 | −0.903467 | ||||||||
\(263\) | −16.5263 | −1.01906 | −0.509528 | − | 0.860454i | \(-0.670180\pi\) | ||||
−0.509528 | + | 0.860454i | \(0.670180\pi\) | |||||||
\(264\) | 0.0903775 | 0.00556235 | ||||||||
\(265\) | 1.96734 | 0.120853 | ||||||||
\(266\) | −45.3710 | −2.78188 | ||||||||
\(267\) | 0.587860 | 0.0359764 | ||||||||
\(268\) | 33.7854 | 2.06377 | ||||||||
\(269\) | 3.92007 | 0.239011 | 0.119505 | − | 0.992834i | \(-0.461869\pi\) | ||||
0.119505 | + | 0.992834i | \(0.461869\pi\) | |||||||
\(270\) | −1.22359 | −0.0744655 | ||||||||
\(271\) | 10.6132 | 0.644709 | 0.322354 | − | 0.946619i | \(-0.395526\pi\) | ||||
0.322354 | + | 0.946619i | \(0.395526\pi\) | |||||||
\(272\) | −6.75852 | −0.409795 | ||||||||
\(273\) | −0.884343 | −0.0535229 | ||||||||
\(274\) | 17.3054 | 1.04546 | ||||||||
\(275\) | −0.829819 | −0.0500400 | ||||||||
\(276\) | −2.55720 | −0.153925 | ||||||||
\(277\) | −25.7909 | −1.54962 | −0.774812 | − | 0.632192i | \(-0.782156\pi\) | ||||
−0.774812 | + | 0.632192i | \(0.782156\pi\) | |||||||
\(278\) | 27.6734 | 1.65974 | ||||||||
\(279\) | −28.0180 | −1.67740 | ||||||||
\(280\) | −1.29411 | −0.0773381 | ||||||||
\(281\) | −14.8298 | −0.884670 | −0.442335 | − | 0.896850i | \(-0.645850\pi\) | ||||
−0.442335 | + | 0.896850i | \(0.645850\pi\) | |||||||
\(282\) | 6.28040 | 0.373993 | ||||||||
\(283\) | 27.2717 | 1.62113 | 0.810566 | − | 0.585647i | \(-0.199160\pi\) | ||||
0.810566 | + | 0.585647i | \(0.199160\pi\) | |||||||
\(284\) | 38.0220 | 2.25619 | ||||||||
\(285\) | −0.732151 | −0.0433689 | ||||||||
\(286\) | −0.368040 | −0.0217627 | ||||||||
\(287\) | −15.7625 | −0.930431 | ||||||||
\(288\) | −21.6630 | −1.27651 | ||||||||
\(289\) | −4.74991 | −0.279406 | ||||||||
\(290\) | −4.42063 | −0.259589 | ||||||||
\(291\) | −3.82635 | −0.224305 | ||||||||
\(292\) | −26.9491 | −1.57708 | ||||||||
\(293\) | 10.9628 | 0.640453 | 0.320226 | − | 0.947341i | \(-0.396241\pi\) | ||||
0.320226 | + | 0.947341i | \(0.396241\pi\) | |||||||
\(294\) | 0.235884 | 0.0137570 | ||||||||
\(295\) | −1.89851 | −0.110536 | ||||||||
\(296\) | −2.53937 | −0.147598 | ||||||||
\(297\) | 0.324978 | 0.0188571 | ||||||||
\(298\) | −20.3304 | −1.17771 | ||||||||
\(299\) | 2.84517 | 0.164540 | ||||||||
\(300\) | 4.41749 | 0.255044 | ||||||||
\(301\) | −22.5492 | −1.29972 | ||||||||
\(302\) | −37.8154 | −2.17603 | ||||||||
\(303\) | −0.987815 | −0.0567485 | ||||||||
\(304\) | −14.8436 | −0.851336 | ||||||||
\(305\) | −1.46134 | −0.0836758 | ||||||||
\(306\) | 22.0749 | 1.26194 | ||||||||
\(307\) | −9.37561 | −0.535094 | −0.267547 | − | 0.963545i | \(-0.586213\pi\) | ||||
−0.267547 | + | 0.963545i | \(0.586213\pi\) | |||||||
\(308\) | 1.25800 | 0.0716811 | ||||||||
\(309\) | 0.952142 | 0.0541654 | ||||||||
\(310\) | −6.15583 | −0.349628 | ||||||||
\(311\) | 7.81013 | 0.442872 | 0.221436 | − | 0.975175i | \(-0.428926\pi\) | ||||
0.221436 | + | 0.975175i | \(0.428926\pi\) | |||||||
\(312\) | 0.535299 | 0.0303054 | ||||||||
\(313\) | −8.35024 | −0.471984 | −0.235992 | − | 0.971755i | \(-0.575834\pi\) | ||||
−0.235992 | + | 0.971755i | \(0.575834\pi\) | |||||||
\(314\) | 30.8002 | 1.73816 | ||||||||
\(315\) | −2.28456 | −0.128720 | ||||||||
\(316\) | −27.3220 | −1.53699 | ||||||||
\(317\) | −6.37453 | −0.358029 | −0.179015 | − | 0.983846i | \(-0.557291\pi\) | ||||
−0.179015 | + | 0.983846i | \(0.557291\pi\) | |||||||
\(318\) | 4.80316 | 0.269348 | ||||||||
\(319\) | 1.17409 | 0.0657365 | ||||||||
\(320\) | −3.63335 | −0.203110 | ||||||||
\(321\) | −2.69664 | −0.150512 | ||||||||
\(322\) | −16.7931 | −0.935843 | ||||||||
\(323\) | 26.9046 | 1.49701 | ||||||||
\(324\) | 22.1561 | 1.23089 | ||||||||
\(325\) | −4.91496 | −0.272633 | ||||||||
\(326\) | −3.60741 | −0.199796 | ||||||||
\(327\) | −0.0862953 | −0.00477214 | ||||||||
\(328\) | 9.54116 | 0.526823 | ||||||||
\(329\) | 23.8845 | 1.31680 | ||||||||
\(330\) | 0.0350542 | 0.00192967 | ||||||||
\(331\) | 7.09181 | 0.389801 | 0.194900 | − | 0.980823i | \(-0.437562\pi\) | ||||
0.194900 | + | 0.980823i | \(0.437562\pi\) | |||||||
\(332\) | −9.81919 | −0.538898 | ||||||||
\(333\) | −4.48288 | −0.245660 | ||||||||
\(334\) | −36.4342 | −1.99359 | ||||||||
\(335\) | 3.58029 | 0.195612 | ||||||||
\(336\) | 1.70766 | 0.0931607 | ||||||||
\(337\) | −2.86334 | −0.155976 | −0.0779881 | − | 0.996954i | \(-0.524850\pi\) | ||||
−0.0779881 | + | 0.996954i | \(0.524850\pi\) | |||||||
\(338\) | −2.17988 | −0.118570 | ||||||||
\(339\) | 1.62311 | 0.0881551 | ||||||||
\(340\) | 2.80873 | 0.152325 | ||||||||
\(341\) | 1.63495 | 0.0885374 | ||||||||
\(342\) | 48.4825 | 2.62163 | ||||||||
\(343\) | −18.0564 | −0.974954 | ||||||||
\(344\) | 13.6492 | 0.735916 | ||||||||
\(345\) | −0.270990 | −0.0145896 | ||||||||
\(346\) | 12.6902 | 0.682228 | ||||||||
\(347\) | 7.35668 | 0.394927 | 0.197464 | − | 0.980310i | \(-0.436730\pi\) | ||||
0.197464 | + | 0.980310i | \(0.436730\pi\) | |||||||
\(348\) | −6.25020 | −0.335046 | ||||||||
\(349\) | −8.48941 | −0.454427 | −0.227214 | − | 0.973845i | \(-0.572962\pi\) | ||||
−0.227214 | + | 0.973845i | \(0.572962\pi\) | |||||||
\(350\) | 29.0096 | 1.55063 | ||||||||
\(351\) | 1.92482 | 0.102739 | ||||||||
\(352\) | 1.26411 | 0.0673774 | ||||||||
\(353\) | 16.4328 | 0.874630 | 0.437315 | − | 0.899309i | \(-0.355930\pi\) | ||||
0.437315 | + | 0.899309i | \(0.355930\pi\) | |||||||
\(354\) | −4.63511 | −0.246354 | ||||||||
\(355\) | 4.02925 | 0.213850 | ||||||||
\(356\) | −4.95302 | −0.262509 | ||||||||
\(357\) | −3.09521 | −0.163816 | ||||||||
\(358\) | −32.5739 | −1.72158 | ||||||||
\(359\) | 29.6992 | 1.56746 | 0.783732 | − | 0.621099i | \(-0.213314\pi\) | ||||
0.783732 | + | 0.621099i | \(0.213314\pi\) | |||||||
\(360\) | 1.38286 | 0.0728832 | ||||||||
\(361\) | 40.0898 | 2.10999 | ||||||||
\(362\) | 53.8676 | 2.83122 | ||||||||
\(363\) | 3.58340 | 0.188080 | ||||||||
\(364\) | 7.45104 | 0.390540 | ||||||||
\(365\) | −2.85584 | −0.149481 | ||||||||
\(366\) | −3.56777 | −0.186490 | ||||||||
\(367\) | −0.00321504 | −0.000167824 0 | −8.39118e−5 | − | 1.00000i | \(-0.500027\pi\) | ||||
−8.39118e−5 | 1.00000i | \(0.500027\pi\) | ||||||||
\(368\) | −5.49402 | −0.286395 | ||||||||
\(369\) | 16.8435 | 0.876836 | ||||||||
\(370\) | −0.984932 | −0.0512042 | ||||||||
\(371\) | 18.2666 | 0.948352 | ||||||||
\(372\) | −8.70354 | −0.451258 | ||||||||
\(373\) | 21.2449 | 1.10002 | 0.550009 | − | 0.835159i | \(-0.314624\pi\) | ||||
0.550009 | + | 0.835159i | \(0.314624\pi\) | |||||||
\(374\) | −1.28815 | −0.0666084 | ||||||||
\(375\) | 0.944356 | 0.0487663 | ||||||||
\(376\) | −14.4575 | −0.745588 | ||||||||
\(377\) | 6.95406 | 0.358152 | ||||||||
\(378\) | −11.3609 | −0.584342 | ||||||||
\(379\) | 11.6409 | 0.597953 | 0.298976 | − | 0.954261i | \(-0.403355\pi\) | ||||
0.298976 | + | 0.954261i | \(0.403355\pi\) | |||||||
\(380\) | 6.16874 | 0.316450 | ||||||||
\(381\) | −4.96440 | −0.254334 | ||||||||
\(382\) | 43.7760 | 2.23978 | ||||||||
\(383\) | −26.3183 | −1.34480 | −0.672401 | − | 0.740187i | \(-0.734737\pi\) | ||||
−0.672401 | + | 0.740187i | \(0.734737\pi\) | |||||||
\(384\) | −3.97980 | −0.203093 | ||||||||
\(385\) | 0.133312 | 0.00679420 | ||||||||
\(386\) | −13.2003 | −0.671876 | ||||||||
\(387\) | 24.0956 | 1.22485 | ||||||||
\(388\) | 32.2389 | 1.63668 | ||||||||
\(389\) | 24.3850 | 1.23637 | 0.618185 | − | 0.786032i | \(-0.287868\pi\) | ||||
0.618185 | + | 0.786032i | \(0.287868\pi\) | |||||||
\(390\) | 0.207623 | 0.0105134 | ||||||||
\(391\) | 9.95814 | 0.503605 | ||||||||
\(392\) | −0.543005 | −0.0274259 | ||||||||
\(393\) | −2.19109 | −0.110526 | ||||||||
\(394\) | 35.1841 | 1.77255 | ||||||||
\(395\) | −2.89536 | −0.145681 | ||||||||
\(396\) | −1.34427 | −0.0675521 | ||||||||
\(397\) | −4.07064 | −0.204300 | −0.102150 | − | 0.994769i | \(-0.532572\pi\) | ||||
−0.102150 | + | 0.994769i | \(0.532572\pi\) | |||||||
\(398\) | 51.5073 | 2.58183 | ||||||||
\(399\) | −6.79793 | −0.340322 | ||||||||
\(400\) | 9.49077 | 0.474539 | ||||||||
\(401\) | −37.3461 | −1.86498 | −0.932489 | − | 0.361199i | \(-0.882367\pi\) | ||||
−0.932489 | + | 0.361199i | \(0.882367\pi\) | |||||||
\(402\) | 8.74107 | 0.435965 | ||||||||
\(403\) | 9.68368 | 0.482378 | ||||||||
\(404\) | 8.32284 | 0.414077 | ||||||||
\(405\) | 2.34791 | 0.116669 | ||||||||
\(406\) | −41.0450 | −2.03703 | ||||||||
\(407\) | 0.261591 | 0.0129666 | ||||||||
\(408\) | 1.87356 | 0.0927548 | ||||||||
\(409\) | 20.1606 | 0.996876 | 0.498438 | − | 0.866925i | \(-0.333907\pi\) | ||||
0.498438 | + | 0.866925i | \(0.333907\pi\) | |||||||
\(410\) | 3.70067 | 0.182763 | ||||||||
\(411\) | 2.59287 | 0.127897 | ||||||||
\(412\) | −8.02227 | −0.395229 | ||||||||
\(413\) | −17.6275 | −0.867390 | ||||||||
\(414\) | 17.9447 | 0.881936 | ||||||||
\(415\) | −1.04055 | −0.0510788 | ||||||||
\(416\) | 7.48724 | 0.367092 | ||||||||
\(417\) | 4.14630 | 0.203045 | ||||||||
\(418\) | −2.82912 | −0.138377 | ||||||||
\(419\) | −30.9154 | −1.51032 | −0.755158 | − | 0.655543i | \(-0.772440\pi\) | ||||
−0.755158 | + | 0.655543i | \(0.772440\pi\) | |||||||
\(420\) | −0.709678 | −0.0346287 | ||||||||
\(421\) | −33.2467 | −1.62034 | −0.810172 | − | 0.586193i | \(-0.800626\pi\) | ||||
−0.810172 | + | 0.586193i | \(0.800626\pi\) | |||||||
\(422\) | −14.0877 | −0.685777 | ||||||||
\(423\) | −25.5225 | −1.24095 | ||||||||
\(424\) | −11.0569 | −0.536970 | ||||||||
\(425\) | −17.2024 | −0.834440 | ||||||||
\(426\) | 9.83719 | 0.476614 | ||||||||
\(427\) | −13.5683 | −0.656617 | ||||||||
\(428\) | 22.7206 | 1.09824 | ||||||||
\(429\) | −0.0551434 | −0.00266235 | ||||||||
\(430\) | 5.29404 | 0.255301 | ||||||||
\(431\) | −17.3805 | −0.837187 | −0.418594 | − | 0.908174i | \(-0.637477\pi\) | ||||
−0.418594 | + | 0.908174i | \(0.637477\pi\) | |||||||
\(432\) | −3.71683 | −0.178826 | ||||||||
\(433\) | 26.6625 | 1.28132 | 0.640658 | − | 0.767826i | \(-0.278662\pi\) | ||||
0.640658 | + | 0.767826i | \(0.278662\pi\) | |||||||
\(434\) | −57.1561 | −2.74358 | ||||||||
\(435\) | −0.662343 | −0.0317569 | ||||||||
\(436\) | 0.727081 | 0.0348209 | ||||||||
\(437\) | 21.8708 | 1.04622 | ||||||||
\(438\) | −6.97237 | −0.333153 | ||||||||
\(439\) | 32.1940 | 1.53654 | 0.768269 | − | 0.640127i | \(-0.221118\pi\) | ||||
0.768269 | + | 0.640127i | \(0.221118\pi\) | |||||||
\(440\) | −0.0806947 | −0.00384697 | ||||||||
\(441\) | −0.958593 | −0.0456473 | ||||||||
\(442\) | −7.62959 | −0.362903 | ||||||||
\(443\) | −14.4085 | −0.684570 | −0.342285 | − | 0.939596i | \(-0.611201\pi\) | ||||
−0.342285 | + | 0.939596i | \(0.611201\pi\) | |||||||
\(444\) | −1.39257 | −0.0660882 | ||||||||
\(445\) | −0.524878 | −0.0248816 | ||||||||
\(446\) | 9.98283 | 0.472701 | ||||||||
\(447\) | −3.04611 | −0.144076 | ||||||||
\(448\) | −33.7352 | −1.59384 | ||||||||
\(449\) | 1.36637 | 0.0644830 | 0.0322415 | − | 0.999480i | \(-0.489735\pi\) | ||||
0.0322415 | + | 0.999480i | \(0.489735\pi\) | |||||||
\(450\) | −30.9991 | −1.46131 | ||||||||
\(451\) | −0.982874 | −0.0462817 | ||||||||
\(452\) | −13.6755 | −0.643241 | ||||||||
\(453\) | −5.66587 | −0.266206 | ||||||||
\(454\) | −13.4501 | −0.631246 | ||||||||
\(455\) | 0.789597 | 0.0370169 | ||||||||
\(456\) | 4.11484 | 0.192695 | ||||||||
\(457\) | −22.6456 | −1.05932 | −0.529658 | − | 0.848211i | \(-0.677680\pi\) | ||||
−0.529658 | + | 0.848211i | \(0.677680\pi\) | |||||||
\(458\) | 58.2885 | 2.72364 | ||||||||
\(459\) | 6.73690 | 0.314452 | ||||||||
\(460\) | 2.28323 | 0.106456 | ||||||||
\(461\) | −36.8876 | −1.71802 | −0.859012 | − | 0.511955i | \(-0.828922\pi\) | ||||
−0.859012 | + | 0.511955i | \(0.828922\pi\) | |||||||
\(462\) | 0.325474 | 0.0151424 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −13.4283 | −0.623392 | ||||||||
\(465\) | −0.922327 | −0.0427719 | ||||||||
\(466\) | −18.3309 | −0.849163 | ||||||||
\(467\) | 31.4527 | 1.45546 | 0.727729 | − | 0.685864i | \(-0.240576\pi\) | ||||
0.727729 | + | 0.685864i | \(0.240576\pi\) | |||||||
\(468\) | −7.96202 | −0.368044 | ||||||||
\(469\) | 33.2425 | 1.53500 | ||||||||
\(470\) | −5.60754 | −0.258656 | ||||||||
\(471\) | 4.61479 | 0.212638 | ||||||||
\(472\) | 10.6700 | 0.491128 | ||||||||
\(473\) | −1.40606 | −0.0646508 | ||||||||
\(474\) | −7.06885 | −0.324683 | ||||||||
\(475\) | −37.7812 | −1.73352 | ||||||||
\(476\) | 26.0787 | 1.19532 | ||||||||
\(477\) | −19.5193 | −0.893725 | ||||||||
\(478\) | 1.92470 | 0.0880338 | ||||||||
\(479\) | 14.2575 | 0.651443 | 0.325722 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325722 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(480\) | −0.713127 | −0.0325496 | ||||||||
\(481\) | 1.54939 | 0.0706459 | ||||||||
\(482\) | −13.0160 | −0.592864 | ||||||||
\(483\) | −2.51611 | −0.114487 | ||||||||
\(484\) | −30.1920 | −1.37236 | ||||||||
\(485\) | 3.41640 | 0.155131 | ||||||||
\(486\) | 18.3199 | 0.831008 | ||||||||
\(487\) | 14.2083 | 0.643842 | 0.321921 | − | 0.946767i | \(-0.395672\pi\) | ||||
0.321921 | + | 0.946767i | \(0.395672\pi\) | |||||||
\(488\) | 8.21301 | 0.371785 | ||||||||
\(489\) | −0.540498 | −0.0244421 | ||||||||
\(490\) | −0.210612 | −0.00951448 | ||||||||
\(491\) | 22.3791 | 1.00995 | 0.504977 | − | 0.863133i | \(-0.331501\pi\) | ||||
0.504977 | + | 0.863133i | \(0.331501\pi\) | |||||||
\(492\) | 5.23227 | 0.235889 | ||||||||
\(493\) | 24.3393 | 1.09619 | ||||||||
\(494\) | −16.7567 | −0.753918 | ||||||||
\(495\) | −0.142454 | −0.00640284 | ||||||||
\(496\) | −18.6992 | −0.839617 | ||||||||
\(497\) | 37.4111 | 1.67812 | ||||||||
\(498\) | −2.54045 | −0.113840 | ||||||||
\(499\) | 38.0238 | 1.70218 | 0.851090 | − | 0.525020i | \(-0.175942\pi\) | ||||
0.851090 | + | 0.525020i | \(0.175942\pi\) | |||||||
\(500\) | −7.95667 | −0.355833 | ||||||||
\(501\) | −5.45892 | −0.243887 | ||||||||
\(502\) | −45.3003 | −2.02185 | ||||||||
\(503\) | 17.2494 | 0.769112 | 0.384556 | − | 0.923102i | \(-0.374354\pi\) | ||||
0.384556 | + | 0.923102i | \(0.374354\pi\) | |||||||
\(504\) | 12.8397 | 0.571926 | ||||||||
\(505\) | 0.881983 | 0.0392477 | ||||||||
\(506\) | −1.04714 | −0.0465509 | ||||||||
\(507\) | −0.326610 | −0.0145053 | ||||||||
\(508\) | 41.8276 | 1.85580 | ||||||||
\(509\) | 24.5379 | 1.08763 | 0.543813 | − | 0.839207i | \(-0.316980\pi\) | ||||
0.543813 | + | 0.839207i | \(0.316980\pi\) | |||||||
\(510\) | 0.726685 | 0.0321781 | ||||||||
\(511\) | −26.5161 | −1.17300 | ||||||||
\(512\) | −20.7875 | −0.918686 | ||||||||
\(513\) | 14.7961 | 0.653263 | ||||||||
\(514\) | −4.99384 | −0.220269 | ||||||||
\(515\) | −0.850132 | −0.0374613 | ||||||||
\(516\) | 7.48508 | 0.329512 | ||||||||
\(517\) | 1.48932 | 0.0655004 | ||||||||
\(518\) | −9.14497 | −0.401807 | ||||||||
\(519\) | 1.90137 | 0.0834607 | ||||||||
\(520\) | −0.477949 | −0.0209594 | ||||||||
\(521\) | 2.83634 | 0.124262 | 0.0621312 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621312 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(522\) | 43.8599 | 1.91969 | ||||||||
\(523\) | 3.53266 | 0.154472 | 0.0772362 | − | 0.997013i | \(-0.475390\pi\) | ||||
0.0772362 | + | 0.997013i | \(0.475390\pi\) | |||||||
\(524\) | 18.4611 | 0.806476 | ||||||||
\(525\) | 4.34651 | 0.189697 | ||||||||
\(526\) | 36.0253 | 1.57078 | ||||||||
\(527\) | 33.8930 | 1.47640 | ||||||||
\(528\) | 0.106482 | 0.00463402 | ||||||||
\(529\) | −14.9050 | −0.648044 | ||||||||
\(530\) | −4.28857 | −0.186283 | ||||||||
\(531\) | 18.8363 | 0.817427 | ||||||||
\(532\) | 57.2760 | 2.48323 | ||||||||
\(533\) | −5.82149 | −0.252157 | ||||||||
\(534\) | −1.28146 | −0.0554543 | ||||||||
\(535\) | 2.40773 | 0.104095 | ||||||||
\(536\) | −20.1219 | −0.869136 | ||||||||
\(537\) | −4.88054 | −0.210611 | ||||||||
\(538\) | −8.54527 | −0.368413 | ||||||||
\(539\) | 0.0559371 | 0.00240938 | ||||||||
\(540\) | 1.54465 | 0.0664713 | ||||||||
\(541\) | −24.5108 | −1.05380 | −0.526901 | − | 0.849927i | \(-0.676646\pi\) | ||||
−0.526901 | + | 0.849927i | \(0.676646\pi\) | |||||||
\(542\) | −23.1355 | −0.993757 | ||||||||
\(543\) | 8.07097 | 0.346359 | ||||||||
\(544\) | 26.2054 | 1.12355 | ||||||||
\(545\) | 0.0770498 | 0.00330045 | ||||||||
\(546\) | 1.92776 | 0.0825004 | ||||||||
\(547\) | 5.45482 | 0.233231 | 0.116616 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116616 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(548\) | −21.8462 | −0.933224 | ||||||||
\(549\) | 14.4988 | 0.618795 | ||||||||
\(550\) | 1.80890 | 0.0771318 | ||||||||
\(551\) | 53.4557 | 2.27729 | ||||||||
\(552\) | 1.52302 | 0.0648240 | ||||||||
\(553\) | −26.8830 | −1.14318 | ||||||||
\(554\) | 56.2209 | 2.38860 | ||||||||
\(555\) | −0.147572 | −0.00626409 | ||||||||
\(556\) | −34.9346 | −1.48156 | ||||||||
\(557\) | 21.5938 | 0.914958 | 0.457479 | − | 0.889220i | \(-0.348752\pi\) | ||||
0.457479 | + | 0.889220i | \(0.348752\pi\) | |||||||
\(558\) | 61.0758 | 2.58555 | ||||||||
\(559\) | −8.32800 | −0.352237 | ||||||||
\(560\) | −1.52471 | −0.0644308 | ||||||||
\(561\) | −0.193003 | −0.00814858 | ||||||||
\(562\) | 32.3271 | 1.36363 | ||||||||
\(563\) | −16.2200 | −0.683590 | −0.341795 | − | 0.939775i | \(-0.611035\pi\) | ||||
−0.341795 | + | 0.939775i | \(0.611035\pi\) | |||||||
\(564\) | −7.92833 | −0.333843 | ||||||||
\(565\) | −1.44921 | −0.0609688 | ||||||||
\(566\) | −59.4488 | −2.49882 | ||||||||
\(567\) | 21.8000 | 0.915516 | ||||||||
\(568\) | −22.6452 | −0.950172 | ||||||||
\(569\) | 29.0467 | 1.21770 | 0.608850 | − | 0.793286i | \(-0.291631\pi\) | ||||
0.608850 | + | 0.793286i | \(0.291631\pi\) | |||||||
\(570\) | 1.59600 | 0.0668490 | ||||||||
\(571\) | −3.69878 | −0.154789 | −0.0773946 | − | 0.997001i | \(-0.524660\pi\) | ||||
−0.0773946 | + | 0.997001i | \(0.524660\pi\) | |||||||
\(572\) | 0.464611 | 0.0194264 | ||||||||
\(573\) | 6.55895 | 0.274004 | ||||||||
\(574\) | 34.3603 | 1.43417 | ||||||||
\(575\) | −13.9839 | −0.583169 | ||||||||
\(576\) | 36.0487 | 1.50203 | ||||||||
\(577\) | 8.32690 | 0.346654 | 0.173327 | − | 0.984864i | \(-0.444548\pi\) | ||||
0.173327 | + | 0.984864i | \(0.444548\pi\) | |||||||
\(578\) | 10.3542 | 0.430678 | ||||||||
\(579\) | −1.97779 | −0.0821943 | ||||||||
\(580\) | 5.58057 | 0.231721 | ||||||||
\(581\) | −9.66141 | −0.400823 | ||||||||
\(582\) | 8.34096 | 0.345744 | ||||||||
\(583\) | 1.13901 | 0.0471732 | ||||||||
\(584\) | 16.0504 | 0.664170 | ||||||||
\(585\) | −0.843747 | −0.0348846 | ||||||||
\(586\) | −23.8975 | −0.987197 | ||||||||
\(587\) | 4.51395 | 0.186310 | 0.0931552 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931552 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(588\) | −0.297778 | −0.0122802 | ||||||||
\(589\) | 74.4383 | 3.06718 | ||||||||
\(590\) | 4.13852 | 0.170380 | ||||||||
\(591\) | 5.27163 | 0.216846 | ||||||||
\(592\) | −2.99186 | −0.122965 | ||||||||
\(593\) | 28.6319 | 1.17577 | 0.587886 | − | 0.808944i | \(-0.299960\pi\) | ||||
0.587886 | + | 0.808944i | \(0.299960\pi\) | |||||||
\(594\) | −0.708411 | −0.0290665 | ||||||||
\(595\) | 2.76360 | 0.113297 | ||||||||
\(596\) | 25.6650 | 1.05128 | ||||||||
\(597\) | 7.71733 | 0.315849 | ||||||||
\(598\) | −6.20212 | −0.253623 | ||||||||
\(599\) | 16.1038 | 0.657985 | 0.328992 | − | 0.944333i | \(-0.393291\pi\) | ||||
0.328992 | + | 0.944333i | \(0.393291\pi\) | |||||||
\(600\) | −2.63097 | −0.107409 | ||||||||
\(601\) | 34.4758 | 1.40630 | 0.703149 | − | 0.711042i | \(-0.251776\pi\) | ||||
0.703149 | + | 0.711042i | \(0.251776\pi\) | |||||||
\(602\) | 49.1545 | 2.00339 | ||||||||
\(603\) | −35.5222 | −1.44658 | ||||||||
\(604\) | 47.7378 | 1.94243 | ||||||||
\(605\) | −3.19949 | −0.130078 | ||||||||
\(606\) | 2.15331 | 0.0874724 | ||||||||
\(607\) | −11.3308 | −0.459905 | −0.229952 | − | 0.973202i | \(-0.573857\pi\) | ||||
−0.229952 | + | 0.973202i | \(0.573857\pi\) | |||||||
\(608\) | 57.5543 | 2.33414 | ||||||||
\(609\) | −6.14977 | −0.249201 | ||||||||
\(610\) | 3.18553 | 0.128978 | ||||||||
\(611\) | 8.82116 | 0.356866 | ||||||||
\(612\) | −27.8672 | −1.12646 | ||||||||
\(613\) | −25.2170 | −1.01851 | −0.509253 | − | 0.860617i | \(-0.670078\pi\) | ||||
−0.509253 | + | 0.860617i | \(0.670078\pi\) | |||||||
\(614\) | 20.4377 | 0.824797 | ||||||||
\(615\) | 0.554471 | 0.0223584 | ||||||||
\(616\) | −0.749240 | −0.0301878 | ||||||||
\(617\) | 7.10053 | 0.285857 | 0.142928 | − | 0.989733i | \(-0.454348\pi\) | ||||
0.142928 | + | 0.989733i | \(0.454348\pi\) | |||||||
\(618\) | −2.07555 | −0.0834909 | ||||||||
\(619\) | −14.5074 | −0.583103 | −0.291551 | − | 0.956555i | \(-0.594171\pi\) | ||||
−0.291551 | + | 0.956555i | \(0.594171\pi\) | |||||||
\(620\) | 7.77107 | 0.312094 | ||||||||
\(621\) | 5.47645 | 0.219762 | ||||||||
\(622\) | −17.0251 | −0.682644 | ||||||||
\(623\) | −4.87343 | −0.195250 | ||||||||
\(624\) | 0.630684 | 0.0252476 | ||||||||
\(625\) | 23.7316 | 0.949265 | ||||||||
\(626\) | 18.2025 | 0.727518 | ||||||||
\(627\) | −0.423886 | −0.0169284 | ||||||||
\(628\) | −38.8820 | −1.55156 | ||||||||
\(629\) | 5.42287 | 0.216224 | ||||||||
\(630\) | 4.98006 | 0.198410 | ||||||||
\(631\) | 47.3458 | 1.88481 | 0.942403 | − | 0.334479i | \(-0.108560\pi\) | ||||
0.942403 | + | 0.334479i | \(0.108560\pi\) | |||||||
\(632\) | 16.2725 | 0.647285 | ||||||||
\(633\) | −2.11075 | −0.0838949 | ||||||||
\(634\) | 13.8957 | 0.551868 | ||||||||
\(635\) | 4.43253 | 0.175900 | ||||||||
\(636\) | −6.06348 | −0.240432 | ||||||||
\(637\) | 0.331312 | 0.0131270 | ||||||||
\(638\) | −2.55937 | −0.101326 | ||||||||
\(639\) | −39.9767 | −1.58145 | ||||||||
\(640\) | 3.55341 | 0.140461 | ||||||||
\(641\) | 5.32982 | 0.210515 | 0.105258 | − | 0.994445i | \(-0.466433\pi\) | ||||
0.105258 | + | 0.994445i | \(0.466433\pi\) | |||||||
\(642\) | 5.87835 | 0.232000 | ||||||||
\(643\) | −17.5454 | −0.691921 | −0.345961 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345961 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(644\) | 21.1995 | 0.835376 | ||||||||
\(645\) | 0.793205 | 0.0312324 | ||||||||
\(646\) | −58.6486 | −2.30750 | ||||||||
\(647\) | −29.4645 | −1.15837 | −0.579185 | − | 0.815196i | \(-0.696629\pi\) | ||||
−0.579185 | + | 0.815196i | \(0.696629\pi\) | |||||||
\(648\) | −13.1957 | −0.518377 | ||||||||
\(649\) | −1.09916 | −0.0431459 | ||||||||
\(650\) | 10.7140 | 0.420238 | ||||||||
\(651\) | −8.56369 | −0.335638 | ||||||||
\(652\) | 4.55396 | 0.178347 | ||||||||
\(653\) | −11.0939 | −0.434136 | −0.217068 | − | 0.976156i | \(-0.569649\pi\) | ||||
−0.217068 | + | 0.976156i | \(0.569649\pi\) | |||||||
\(654\) | 0.188113 | 0.00735580 | ||||||||
\(655\) | 1.95635 | 0.0764408 | ||||||||
\(656\) | 11.2413 | 0.438899 | ||||||||
\(657\) | 28.3346 | 1.10544 | ||||||||
\(658\) | −52.0653 | −2.02972 | ||||||||
\(659\) | 33.4967 | 1.30485 | 0.652423 | − | 0.757855i | \(-0.273753\pi\) | ||||
0.652423 | + | 0.757855i | \(0.273753\pi\) | |||||||
\(660\) | −0.0442521 | −0.00172251 | ||||||||
\(661\) | 27.6118 | 1.07397 | 0.536987 | − | 0.843591i | \(-0.319562\pi\) | ||||
0.536987 | + | 0.843591i | \(0.319562\pi\) | |||||||
\(662\) | −15.4593 | −0.600841 | ||||||||
\(663\) | −1.14314 | −0.0443959 | ||||||||
\(664\) | 5.84812 | 0.226951 | ||||||||
\(665\) | 6.06962 | 0.235370 | ||||||||
\(666\) | 9.77212 | 0.378662 | ||||||||
\(667\) | 19.7855 | 0.766097 | ||||||||
\(668\) | 45.9942 | 1.77957 | ||||||||
\(669\) | 1.49573 | 0.0578281 | ||||||||
\(670\) | −7.80458 | −0.301517 | ||||||||
\(671\) | −0.846055 | −0.0326616 | ||||||||
\(672\) | −6.62129 | −0.255422 | ||||||||
\(673\) | −20.3307 | −0.783691 | −0.391845 | − | 0.920031i | \(-0.628163\pi\) | ||||
−0.391845 | + | 0.920031i | \(0.628163\pi\) | |||||||
\(674\) | 6.24173 | 0.240423 | ||||||||
\(675\) | −9.46042 | −0.364132 | ||||||||
\(676\) | 2.75186 | 0.105841 | ||||||||
\(677\) | 3.46907 | 0.133327 | 0.0666635 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666635 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(678\) | −3.53817 | −0.135883 | ||||||||
\(679\) | 31.7209 | 1.21734 | ||||||||
\(680\) | −1.67283 | −0.0641500 | ||||||||
\(681\) | −2.01523 | −0.0772238 | ||||||||
\(682\) | −3.56398 | −0.136472 | ||||||||
\(683\) | 5.65848 | 0.216516 | 0.108258 | − | 0.994123i | \(-0.465473\pi\) | ||||
0.108258 | + | 0.994123i | \(0.465473\pi\) | |||||||
\(684\) | −61.2039 | −2.34019 | ||||||||
\(685\) | −2.31507 | −0.0884545 | ||||||||
\(686\) | 39.3607 | 1.50280 | ||||||||
\(687\) | 8.73336 | 0.333198 | ||||||||
\(688\) | 16.0813 | 0.613096 | ||||||||
\(689\) | 6.74630 | 0.257014 | ||||||||
\(690\) | 0.590724 | 0.0224885 | ||||||||
\(691\) | 2.11003 | 0.0802695 | 0.0401347 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401347 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(692\) | −16.0200 | −0.608988 | ||||||||
\(693\) | −1.32267 | −0.0502441 | ||||||||
\(694\) | −16.0366 | −0.608743 | ||||||||
\(695\) | −3.70207 | −0.140428 | ||||||||
\(696\) | 3.72250 | 0.141101 | ||||||||
\(697\) | −20.3753 | −0.771770 | ||||||||
\(698\) | 18.5058 | 0.700457 | ||||||||
\(699\) | −2.74652 | −0.103883 | ||||||||
\(700\) | −36.6215 | −1.38416 | ||||||||
\(701\) | 20.5301 | 0.775413 | 0.387706 | − | 0.921783i | \(-0.373267\pi\) | ||||
0.387706 | + | 0.921783i | \(0.373267\pi\) | |||||||
\(702\) | −4.19587 | −0.158363 | ||||||||
\(703\) | 11.9101 | 0.449198 | ||||||||
\(704\) | −2.10356 | −0.0792810 | ||||||||
\(705\) | −0.840177 | −0.0316429 | ||||||||
\(706\) | −35.8214 | −1.34816 | ||||||||
\(707\) | 8.18911 | 0.307983 | ||||||||
\(708\) | 5.85133 | 0.219906 | ||||||||
\(709\) | 16.0353 | 0.602220 | 0.301110 | − | 0.953589i | \(-0.402643\pi\) | ||||
0.301110 | + | 0.953589i | \(0.402643\pi\) | |||||||
\(710\) | −8.78326 | −0.329630 | ||||||||
\(711\) | 28.7266 | 1.07733 | ||||||||
\(712\) | 2.94992 | 0.110553 | ||||||||
\(713\) | 27.5517 | 1.03182 | ||||||||
\(714\) | 6.74718 | 0.252507 | ||||||||
\(715\) | 0.0492355 | 0.00184130 | ||||||||
\(716\) | 41.1210 | 1.53676 | ||||||||
\(717\) | 0.288378 | 0.0107697 | ||||||||
\(718\) | −64.7406 | −2.41610 | ||||||||
\(719\) | −9.11783 | −0.340038 | −0.170019 | − | 0.985441i | \(-0.554383\pi\) | ||||
−0.170019 | + | 0.985441i | \(0.554383\pi\) | |||||||
\(720\) | 1.62927 | 0.0607194 | ||||||||
\(721\) | −7.89337 | −0.293964 | ||||||||
\(722\) | −87.3907 | −3.25235 | ||||||||
\(723\) | −1.95019 | −0.0725283 | ||||||||
\(724\) | −68.0020 | −2.52728 | ||||||||
\(725\) | −34.1789 | −1.26937 | ||||||||
\(726\) | −7.81137 | −0.289907 | ||||||||
\(727\) | −20.4399 | −0.758076 | −0.379038 | − | 0.925381i | \(-0.623745\pi\) | ||||
−0.379038 | + | 0.925381i | \(0.623745\pi\) | |||||||
\(728\) | −4.43770 | −0.164472 | ||||||||
\(729\) | −21.4091 | −0.792928 | ||||||||
\(730\) | 6.22537 | 0.230411 | ||||||||
\(731\) | −29.1481 | −1.07808 | ||||||||
\(732\) | 4.50393 | 0.166470 | ||||||||
\(733\) | 38.4202 | 1.41908 | 0.709542 | − | 0.704663i | \(-0.248902\pi\) | ||||
0.709542 | + | 0.704663i | \(0.248902\pi\) | |||||||
\(734\) | 0.00700838 | 0.000258684 0 | ||||||||
\(735\) | −0.0315560 | −0.00116396 | ||||||||
\(736\) | 21.3025 | 0.785220 | ||||||||
\(737\) | 2.07284 | 0.0763542 | ||||||||
\(738\) | −36.7167 | −1.35156 | ||||||||
\(739\) | 4.92646 | 0.181223 | 0.0906114 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906114 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(740\) | 1.24337 | 0.0457072 | ||||||||
\(741\) | −2.51065 | −0.0922310 | ||||||||
\(742\) | −39.8188 | −1.46179 | ||||||||
\(743\) | −7.15125 | −0.262354 | −0.131177 | − | 0.991359i | \(-0.541876\pi\) | ||||
−0.131177 | + | 0.991359i | \(0.541876\pi\) | |||||||
\(744\) | 5.18367 | 0.190042 | ||||||||
\(745\) | 2.71975 | 0.0996441 | ||||||||
\(746\) | −46.3112 | −1.69557 | ||||||||
\(747\) | 10.3240 | 0.377735 | ||||||||
\(748\) | 1.62614 | 0.0594577 | ||||||||
\(749\) | 22.3555 | 0.816852 | ||||||||
\(750\) | −2.05858 | −0.0751686 | ||||||||
\(751\) | −36.4619 | −1.33051 | −0.665256 | − | 0.746615i | \(-0.731678\pi\) | ||||
−0.665256 | + | 0.746615i | \(0.731678\pi\) | |||||||
\(752\) | −17.0336 | −0.621153 | ||||||||
\(753\) | −6.78734 | −0.247344 | ||||||||
\(754\) | −15.1590 | −0.552057 | ||||||||
\(755\) | 5.05885 | 0.184110 | ||||||||
\(756\) | 14.3419 | 0.521610 | ||||||||
\(757\) | −9.10343 | −0.330870 | −0.165435 | − | 0.986221i | \(-0.552903\pi\) | ||||
−0.165435 | + | 0.986221i | \(0.552903\pi\) | |||||||
\(758\) | −25.3757 | −0.921687 | ||||||||
\(759\) | −0.156892 | −0.00569483 | ||||||||
\(760\) | −3.67399 | −0.133270 | ||||||||
\(761\) | 18.3635 | 0.665676 | 0.332838 | − | 0.942984i | \(-0.391994\pi\) | ||||
0.332838 | + | 0.942984i | \(0.391994\pi\) | |||||||
\(762\) | 10.8218 | 0.392032 | ||||||||
\(763\) | 0.715398 | 0.0258992 | ||||||||
\(764\) | −55.2625 | −1.99933 | ||||||||
\(765\) | −2.95312 | −0.106770 | ||||||||
\(766\) | 57.3706 | 2.07289 | ||||||||
\(767\) | −6.51027 | −0.235072 | ||||||||
\(768\) | 0.536814 | 0.0193706 | ||||||||
\(769\) | 40.4451 | 1.45849 | 0.729245 | − | 0.684253i | \(-0.239872\pi\) | ||||
0.729245 | + | 0.684253i | \(0.239872\pi\) | |||||||
\(770\) | −0.290603 | −0.0104726 | ||||||||
\(771\) | −0.748227 | −0.0269467 | ||||||||
\(772\) | 16.6639 | 0.599747 | ||||||||
\(773\) | −34.4022 | −1.23736 | −0.618681 | − | 0.785642i | \(-0.712333\pi\) | ||||
−0.618681 | + | 0.785642i | \(0.712333\pi\) | |||||||
\(774\) | −52.5254 | −1.88799 | ||||||||
\(775\) | −47.5949 | −1.70966 | ||||||||
\(776\) | −19.2009 | −0.689272 | ||||||||
\(777\) | −1.37019 | −0.0491553 | ||||||||
\(778\) | −53.1564 | −1.90575 | ||||||||
\(779\) | −44.7497 | −1.60333 | ||||||||
\(780\) | −0.262102 | −0.00938476 | ||||||||
\(781\) | 2.33278 | 0.0834733 | ||||||||
\(782\) | −21.7075 | −0.776258 | ||||||||
\(783\) | 13.3853 | 0.478352 | ||||||||
\(784\) | −0.639762 | −0.0228486 | ||||||||
\(785\) | −4.12038 | −0.147063 | ||||||||
\(786\) | 4.77631 | 0.170365 | ||||||||
\(787\) | −41.4548 | −1.47771 | −0.738853 | − | 0.673867i | \(-0.764632\pi\) | ||||
−0.738853 | + | 0.673867i | \(0.764632\pi\) | |||||||
\(788\) | −44.4161 | −1.58226 | ||||||||
\(789\) | 5.39767 | 0.192162 | ||||||||
\(790\) | 6.31152 | 0.224554 | ||||||||
\(791\) | −13.4558 | −0.478431 | ||||||||
\(792\) | 0.800622 | 0.0284489 | ||||||||
\(793\) | −5.01113 | −0.177950 | ||||||||
\(794\) | 8.87349 | 0.314908 | ||||||||
\(795\) | −0.642555 | −0.0227891 | ||||||||
\(796\) | −65.0224 | −2.30466 | ||||||||
\(797\) | 10.1920 | 0.361020 | 0.180510 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180510 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(798\) | 14.8187 | 0.524575 | ||||||||
\(799\) | 30.8742 | 1.09225 | ||||||||
\(800\) | −36.7995 | −1.30106 | ||||||||
\(801\) | 5.20764 | 0.184003 | ||||||||
\(802\) | 81.4099 | 2.87468 | ||||||||
\(803\) | −1.65342 | −0.0583478 | ||||||||
\(804\) | −11.0347 | −0.389162 | ||||||||
\(805\) | 2.24654 | 0.0791801 | ||||||||
\(806\) | −21.1092 | −0.743540 | ||||||||
\(807\) | −1.28034 | −0.0450700 | ||||||||
\(808\) | −4.95693 | −0.174384 | ||||||||
\(809\) | 4.35354 | 0.153062 | 0.0765311 | − | 0.997067i | \(-0.475616\pi\) | ||||
0.0765311 | + | 0.997067i | \(0.475616\pi\) | |||||||
\(810\) | −5.11815 | −0.179833 | ||||||||
\(811\) | −6.85412 | −0.240681 | −0.120340 | − | 0.992733i | \(-0.538399\pi\) | ||||
−0.120340 | + | 0.992733i | \(0.538399\pi\) | |||||||
\(812\) | 51.8149 | 1.81835 | ||||||||
\(813\) | −3.46640 | −0.121572 | ||||||||
\(814\) | −0.570236 | −0.0199868 | ||||||||
\(815\) | 0.482590 | 0.0169044 | ||||||||
\(816\) | 2.20740 | 0.0772745 | ||||||||
\(817\) | −64.0172 | −2.23968 | ||||||||
\(818\) | −43.9475 | −1.53659 | ||||||||
\(819\) | −7.83408 | −0.273745 | ||||||||
\(820\) | −4.67170 | −0.163143 | ||||||||
\(821\) | −6.23411 | −0.217572 | −0.108786 | − | 0.994065i | \(-0.534696\pi\) | ||||
−0.108786 | + | 0.994065i | \(0.534696\pi\) | |||||||
\(822\) | −5.65213 | −0.197141 | ||||||||
\(823\) | 34.2162 | 1.19270 | 0.596351 | − | 0.802724i | \(-0.296617\pi\) | ||||
0.596351 | + | 0.802724i | \(0.296617\pi\) | |||||||
\(824\) | 4.77791 | 0.166447 | ||||||||
\(825\) | 0.271027 | 0.00943597 | ||||||||
\(826\) | 38.4257 | 1.33700 | ||||||||
\(827\) | −17.0563 | −0.593104 | −0.296552 | − | 0.955017i | \(-0.595837\pi\) | ||||
−0.296552 | + | 0.955017i | \(0.595837\pi\) | |||||||
\(828\) | −22.6533 | −0.787257 | ||||||||
\(829\) | 14.2766 | 0.495846 | 0.247923 | − | 0.968780i | \(-0.420252\pi\) | ||||
0.247923 | + | 0.968780i | \(0.420252\pi\) | |||||||
\(830\) | 2.26828 | 0.0787330 | ||||||||
\(831\) | 8.42357 | 0.292210 | ||||||||
\(832\) | −12.4593 | −0.431947 | ||||||||
\(833\) | 1.15960 | 0.0401776 | ||||||||
\(834\) | −9.03841 | −0.312974 | ||||||||
\(835\) | 4.87407 | 0.168674 | ||||||||
\(836\) | 3.57146 | 0.123521 | ||||||||
\(837\) | 18.6393 | 0.644270 | ||||||||
\(838\) | 67.3917 | 2.32801 | ||||||||
\(839\) | 22.2095 | 0.766758 | 0.383379 | − | 0.923591i | \(-0.374760\pi\) | ||||
0.383379 | + | 0.923591i | \(0.374760\pi\) | |||||||
\(840\) | 0.422671 | 0.0145835 | ||||||||
\(841\) | 19.3589 | 0.667548 | ||||||||
\(842\) | 72.4736 | 2.49760 | ||||||||
\(843\) | 4.84356 | 0.166821 | ||||||||
\(844\) | 17.7842 | 0.612156 | ||||||||
\(845\) | 0.291618 | 0.0100320 | ||||||||
\(846\) | 55.6359 | 1.91280 | ||||||||
\(847\) | −29.7069 | −1.02074 | ||||||||
\(848\) | −13.0271 | −0.447352 | ||||||||
\(849\) | −8.90721 | −0.305695 | ||||||||
\(850\) | 37.4991 | 1.28621 | ||||||||
\(851\) | 4.40827 | 0.151114 | ||||||||
\(852\) | −12.4184 | −0.425447 | ||||||||
\(853\) | 3.50891 | 0.120143 | 0.0600715 | − | 0.998194i | \(-0.480867\pi\) | ||||
0.0600715 | + | 0.998194i | \(0.480867\pi\) | |||||||
\(854\) | 29.5773 | 1.01211 | ||||||||
\(855\) | −6.48587 | −0.221812 | ||||||||
\(856\) | −13.5320 | −0.462513 | ||||||||
\(857\) | 17.6296 | 0.602215 | 0.301107 | − | 0.953590i | \(-0.402644\pi\) | ||||
0.301107 | + | 0.953590i | \(0.402644\pi\) | |||||||
\(858\) | 0.120206 | 0.00410376 | ||||||||
\(859\) | 22.6444 | 0.772616 | 0.386308 | − | 0.922370i | \(-0.373750\pi\) | ||||
0.386308 | + | 0.922370i | \(0.373750\pi\) | |||||||
\(860\) | −6.68315 | −0.227894 | ||||||||
\(861\) | 5.14820 | 0.175450 | ||||||||
\(862\) | 37.8872 | 1.29044 | ||||||||
\(863\) | 17.4816 | 0.595082 | 0.297541 | − | 0.954709i | \(-0.403834\pi\) | ||||
0.297541 | + | 0.954709i | \(0.403834\pi\) | |||||||
\(864\) | 14.4116 | 0.490293 | ||||||||
\(865\) | −1.69766 | −0.0577222 | ||||||||
\(866\) | −58.1209 | −1.97503 | ||||||||
\(867\) | 1.55137 | 0.0526873 | ||||||||
\(868\) | 72.1534 | 2.44905 | ||||||||
\(869\) | −1.67630 | −0.0568645 | ||||||||
\(870\) | 1.44382 | 0.0489503 | ||||||||
\(871\) | 12.2773 | 0.416001 | ||||||||
\(872\) | −0.433036 | −0.0146644 | ||||||||
\(873\) | −33.8963 | −1.14721 | ||||||||
\(874\) | −47.6756 | −1.61265 | ||||||||
\(875\) | −7.82882 | −0.264663 | ||||||||
\(876\) | 8.80187 | 0.297388 | ||||||||
\(877\) | 10.0910 | 0.340748 | 0.170374 | − | 0.985379i | \(-0.445502\pi\) | ||||
0.170374 | + | 0.985379i | \(0.445502\pi\) | |||||||
\(878\) | −70.1790 | −2.36843 | ||||||||
\(879\) | −3.58056 | −0.120769 | ||||||||
\(880\) | −0.0950736 | −0.00320493 | ||||||||
\(881\) | 54.2913 | 1.82912 | 0.914561 | − | 0.404448i | \(-0.132536\pi\) | ||||
0.914561 | + | 0.404448i | \(0.132536\pi\) | |||||||
\(882\) | 2.08961 | 0.0703609 | ||||||||
\(883\) | −3.54795 | −0.119398 | −0.0596989 | − | 0.998216i | \(-0.519014\pi\) | ||||
−0.0596989 | + | 0.998216i | \(0.519014\pi\) | |||||||
\(884\) | 9.63154 | 0.323944 | ||||||||
\(885\) | 0.620074 | 0.0208436 | ||||||||
\(886\) | 31.4088 | 1.05520 | ||||||||
\(887\) | 40.1171 | 1.34700 | 0.673500 | − | 0.739187i | \(-0.264790\pi\) | ||||
0.673500 | + | 0.739187i | \(0.264790\pi\) | |||||||
\(888\) | 0.829386 | 0.0278324 | ||||||||
\(889\) | 41.1555 | 1.38031 | ||||||||
\(890\) | 1.14417 | 0.0383526 | ||||||||
\(891\) | 1.35935 | 0.0455398 | ||||||||
\(892\) | −12.6022 | −0.421954 | ||||||||
\(893\) | 67.8082 | 2.26911 | ||||||||
\(894\) | 6.64013 | 0.222079 | ||||||||
\(895\) | 4.35765 | 0.145660 | ||||||||
\(896\) | 32.9930 | 1.10222 | ||||||||
\(897\) | −0.929262 | −0.0310272 | ||||||||
\(898\) | −2.97852 | −0.0993945 | ||||||||
\(899\) | 67.3408 | 2.24594 | ||||||||
\(900\) | 39.1330 | 1.30443 | ||||||||
\(901\) | 23.6121 | 0.786635 | ||||||||
\(902\) | 2.14254 | 0.0713389 | ||||||||
\(903\) | 7.36481 | 0.245086 | ||||||||
\(904\) | 8.14487 | 0.270894 | ||||||||
\(905\) | −7.20627 | −0.239545 | ||||||||
\(906\) | 12.3509 | 0.410331 | ||||||||
\(907\) | −12.9984 | −0.431605 | −0.215802 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215802 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(908\) | 16.9793 | 0.563479 | ||||||||
\(909\) | −8.75071 | −0.290243 | ||||||||
\(910\) | −1.72122 | −0.0570580 | ||||||||
\(911\) | 8.63660 | 0.286143 | 0.143072 | − | 0.989712i | \(-0.454302\pi\) | ||||
0.143072 | + | 0.989712i | \(0.454302\pi\) | |||||||
\(912\) | 4.84806 | 0.160535 | ||||||||
\(913\) | −0.602439 | −0.0199378 | ||||||||
\(914\) | 49.3646 | 1.63283 | ||||||||
\(915\) | 0.477287 | 0.0157786 | ||||||||
\(916\) | −73.5829 | −2.43125 | ||||||||
\(917\) | 18.1644 | 0.599843 | ||||||||
\(918\) | −14.6856 | −0.484697 | ||||||||
\(919\) | −44.9298 | −1.48210 | −0.741048 | − | 0.671452i | \(-0.765671\pi\) | ||||
−0.741048 | + | 0.671452i | \(0.765671\pi\) | |||||||
\(920\) | −1.35985 | −0.0448328 | ||||||||
\(921\) | 3.06217 | 0.100902 | ||||||||
\(922\) | 80.4103 | 2.64817 | ||||||||
\(923\) | 13.8169 | 0.454788 | ||||||||
\(924\) | −0.410875 | −0.0135168 | ||||||||
\(925\) | −7.61517 | −0.250385 | ||||||||
\(926\) | 2.17988 | 0.0716352 | ||||||||
\(927\) | 8.43468 | 0.277031 | ||||||||
\(928\) | 52.0667 | 1.70917 | ||||||||
\(929\) | −51.6750 | −1.69540 | −0.847700 | − | 0.530476i | \(-0.822013\pi\) | ||||
−0.847700 | + | 0.530476i | \(0.822013\pi\) | |||||||
\(930\) | 2.01056 | 0.0659288 | ||||||||
\(931\) | 2.54679 | 0.0834676 | ||||||||
\(932\) | 23.1408 | 0.758002 | ||||||||
\(933\) | −2.55087 | −0.0835117 | ||||||||
\(934\) | −68.5630 | −2.24345 | ||||||||
\(935\) | 0.172325 | 0.00563562 | ||||||||
\(936\) | 4.74203 | 0.154998 | ||||||||
\(937\) | −6.39325 | −0.208858 | −0.104429 | − | 0.994532i | \(-0.533302\pi\) | ||||
−0.104429 | + | 0.994532i | \(0.533302\pi\) | |||||||
\(938\) | −72.4645 | −2.36605 | ||||||||
\(939\) | 2.72728 | 0.0890013 | ||||||||
\(940\) | 7.07891 | 0.230889 | ||||||||
\(941\) | 44.3523 | 1.44584 | 0.722921 | − | 0.690931i | \(-0.242799\pi\) | ||||
0.722921 | + | 0.690931i | \(0.242799\pi\) | |||||||
\(942\) | −10.0597 | −0.327762 | ||||||||
\(943\) | −16.5631 | −0.539370 | ||||||||
\(944\) | 12.5713 | 0.409161 | ||||||||
\(945\) | 1.51983 | 0.0494402 | ||||||||
\(946\) | 3.06504 | 0.0996530 | ||||||||
\(947\) | 37.1363 | 1.20677 | 0.603384 | − | 0.797450i | \(-0.293818\pi\) | ||||
0.603384 | + | 0.797450i | \(0.293818\pi\) | |||||||
\(948\) | 8.92366 | 0.289827 | ||||||||
\(949\) | −9.79307 | −0.317897 | ||||||||
\(950\) | 82.3584 | 2.67206 | ||||||||
\(951\) | 2.08199 | 0.0675130 | ||||||||
\(952\) | −15.5320 | −0.503395 | ||||||||
\(953\) | −58.4326 | −1.89282 | −0.946409 | − | 0.322970i | \(-0.895319\pi\) | ||||
−0.946409 | + | 0.322970i | \(0.895319\pi\) | |||||||
\(954\) | 42.5495 | 1.37759 | ||||||||
\(955\) | −5.85624 | −0.189504 | ||||||||
\(956\) | −2.42973 | −0.0785830 | ||||||||
\(957\) | −0.383470 | −0.0123958 | ||||||||
\(958\) | −31.0796 | −1.00414 | ||||||||
\(959\) | −21.4952 | −0.694116 | ||||||||
\(960\) | 1.18669 | 0.0383002 | ||||||||
\(961\) | 62.7736 | 2.02496 | ||||||||
\(962\) | −3.37747 | −0.108894 | ||||||||
\(963\) | −23.8886 | −0.769800 | ||||||||
\(964\) | 16.4313 | 0.529217 | ||||||||
\(965\) | 1.76590 | 0.0568463 | ||||||||
\(966\) | 5.48480 | 0.176471 | ||||||||
\(967\) | −19.8739 | −0.639102 | −0.319551 | − | 0.947569i | \(-0.603532\pi\) | ||||
−0.319551 | + | 0.947569i | \(0.603532\pi\) | |||||||
\(968\) | 17.9818 | 0.577956 | ||||||||
\(969\) | −8.78731 | −0.282289 | ||||||||
\(970\) | −7.44734 | −0.239120 | ||||||||
\(971\) | 47.5671 | 1.52650 | 0.763250 | − | 0.646103i | \(-0.223602\pi\) | ||||
0.763250 | + | 0.646103i | \(0.223602\pi\) | |||||||
\(972\) | −23.1269 | −0.741796 | ||||||||
\(973\) | −34.3733 | −1.10196 | ||||||||
\(974\) | −30.9724 | −0.992421 | ||||||||
\(975\) | 1.60528 | 0.0514100 | ||||||||
\(976\) | 9.67647 | 0.309736 | ||||||||
\(977\) | −0.345350 | −0.0110487 | −0.00552436 | − | 0.999985i | \(-0.501758\pi\) | ||||
−0.00552436 | + | 0.999985i | \(0.501758\pi\) | |||||||
\(978\) | 1.17822 | 0.0376752 | ||||||||
\(979\) | −0.303884 | −0.00971216 | ||||||||
\(980\) | 0.265875 | 0.00849306 | ||||||||
\(981\) | −0.764459 | −0.0244073 | ||||||||
\(982\) | −48.7836 | −1.55675 | ||||||||
\(983\) | 50.1414 | 1.59926 | 0.799632 | − | 0.600491i | \(-0.205028\pi\) | ||||
0.799632 | + | 0.600491i | \(0.205028\pi\) | |||||||
\(984\) | −3.11624 | −0.0993422 | ||||||||
\(985\) | −4.70684 | −0.149973 | ||||||||
\(986\) | −53.0566 | −1.68967 | ||||||||
\(987\) | −7.80094 | −0.248307 | ||||||||
\(988\) | 21.1535 | 0.672982 | ||||||||
\(989\) | −23.6946 | −0.753444 | ||||||||
\(990\) | 0.310533 | 0.00986937 | ||||||||
\(991\) | 26.1433 | 0.830469 | 0.415234 | − | 0.909714i | \(-0.363700\pi\) | ||||
0.415234 | + | 0.909714i | \(0.363700\pi\) | |||||||
\(992\) | 72.5040 | 2.30201 | ||||||||
\(993\) | −2.31626 | −0.0735042 | ||||||||
\(994\) | −81.5515 | −2.58666 | ||||||||
\(995\) | −6.89052 | −0.218444 | ||||||||
\(996\) | 3.20705 | 0.101619 | ||||||||
\(997\) | −36.1390 | −1.14453 | −0.572267 | − | 0.820067i | \(-0.693936\pi\) | ||||
−0.572267 | + | 0.820067i | \(0.693936\pi\) | |||||||
\(998\) | −82.8872 | −2.62375 | ||||||||
\(999\) | 2.98229 | 0.0943556 |
(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 | 6019.2.a.e.1.19 | ✓ | 130 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.e.1.19 | ✓ | 130 | 1.1 | even | 1 | trivial |