Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.333070 | −0.235516 | −0.117758 | − | 0.993042i | \(-0.537571\pi\) | ||||
−0.117758 | + | 0.993042i | \(0.537571\pi\) | |||||||
\(3\) | −1.03111 | −0.595311 | −0.297656 | − | 0.954673i | \(-0.596205\pi\) | ||||
−0.297656 | + | 0.954673i | \(0.596205\pi\) | |||||||
\(4\) | −1.88906 | −0.944532 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.343432 | 0.140205 | ||||||||
\(7\) | 2.91492 | 1.10173 | 0.550867 | − | 0.834593i | \(-0.314297\pi\) | ||||
0.550867 | + | 0.834593i | \(0.314297\pi\) | |||||||
\(8\) | 1.29533 | 0.457969 | ||||||||
\(9\) | −1.93681 | −0.645604 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.85066 | −1.76404 | −0.882020 | − | 0.471213i | \(-0.843816\pi\) | ||||
−0.882020 | + | 0.471213i | \(0.843816\pi\) | |||||||
\(12\) | 1.94783 | 0.562291 | ||||||||
\(13\) | 5.25897 | 1.45858 | 0.729288 | − | 0.684207i | \(-0.239852\pi\) | ||||
0.729288 | + | 0.684207i | \(0.239852\pi\) | |||||||
\(14\) | −0.970871 | −0.259476 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.34669 | 0.836673 | ||||||||
\(17\) | 1.44402 | 0.350226 | 0.175113 | − | 0.984548i | \(-0.443971\pi\) | ||||
0.175113 | + | 0.984548i | \(0.443971\pi\) | |||||||
\(18\) | 0.645094 | 0.152050 | ||||||||
\(19\) | −4.06597 | −0.932798 | −0.466399 | − | 0.884574i | \(-0.654449\pi\) | ||||
−0.466399 | + | 0.884574i | \(0.654449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00560 | −0.655875 | ||||||||
\(22\) | 1.94868 | 0.415460 | ||||||||
\(23\) | 1.01807 | 0.212283 | 0.106141 | − | 0.994351i | \(-0.466150\pi\) | ||||
0.106141 | + | 0.994351i | \(0.466150\pi\) | |||||||
\(24\) | −1.33563 | −0.272634 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.75160 | −0.343518 | ||||||||
\(27\) | 5.09040 | 0.979647 | ||||||||
\(28\) | −5.50646 | −1.04062 | ||||||||
\(29\) | −7.18385 | −1.33401 | −0.667004 | − | 0.745055i | \(-0.732423\pi\) | ||||
−0.667004 | + | 0.745055i | \(0.732423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.93668 | 1.24587 | 0.622933 | − | 0.782276i | \(-0.285941\pi\) | ||||
0.622933 | + | 0.782276i | \(0.285941\pi\) | |||||||
\(32\) | −3.70534 | −0.655019 | ||||||||
\(33\) | 6.03267 | 1.05015 | ||||||||
\(34\) | −0.480959 | −0.0824838 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.65876 | 0.609794 | ||||||||
\(37\) | −5.29003 | −0.869675 | −0.434838 | − | 0.900509i | \(-0.643194\pi\) | ||||
−0.434838 | + | 0.900509i | \(0.643194\pi\) | |||||||
\(38\) | 1.35425 | 0.219689 | ||||||||
\(39\) | −5.42257 | −0.868306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.45798 | −0.696220 | −0.348110 | − | 0.937454i | \(-0.613176\pi\) | ||||
−0.348110 | + | 0.937454i | \(0.613176\pi\) | |||||||
\(42\) | 1.00107 | 0.154469 | ||||||||
\(43\) | 3.29679 | 0.502756 | 0.251378 | − | 0.967889i | \(-0.419116\pi\) | ||||
0.251378 | + | 0.967889i | \(0.419116\pi\) | |||||||
\(44\) | 11.0523 | 1.66619 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.339090 | −0.0499960 | ||||||||
\(47\) | 1.96909 | 0.287221 | 0.143611 | − | 0.989634i | \(-0.454129\pi\) | ||||
0.143611 | + | 0.989634i | \(0.454129\pi\) | |||||||
\(48\) | −3.45081 | −0.498081 | ||||||||
\(49\) | 1.49673 | 0.213819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.48894 | −0.208493 | ||||||||
\(52\) | −9.93453 | −1.37767 | ||||||||
\(53\) | 0.430807 | 0.0591759 | 0.0295879 | − | 0.999562i | \(-0.490580\pi\) | ||||
0.0295879 | + | 0.999562i | \(0.490580\pi\) | |||||||
\(54\) | −1.69546 | −0.230723 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.77578 | 0.504560 | ||||||||
\(57\) | 4.19246 | 0.555305 | ||||||||
\(58\) | 2.39272 | 0.314180 | ||||||||
\(59\) | 8.44640 | 1.09963 | 0.549814 | − | 0.835287i | \(-0.314699\pi\) | ||||
0.549814 | + | 0.835287i | \(0.314699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.27665 | 0.419532 | 0.209766 | − | 0.977752i | \(-0.432730\pi\) | ||||
0.209766 | + | 0.977752i | \(0.432730\pi\) | |||||||
\(62\) | −2.31040 | −0.293421 | ||||||||
\(63\) | −5.64565 | −0.711285 | ||||||||
\(64\) | −5.45925 | −0.682406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00930 | −0.247328 | ||||||||
\(67\) | 13.7065 | 1.67451 | 0.837256 | − | 0.546812i | \(-0.184159\pi\) | ||||
0.837256 | + | 0.546812i | \(0.184159\pi\) | |||||||
\(68\) | −2.72784 | −0.330800 | ||||||||
\(69\) | −1.04974 | −0.126374 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.02073 | 0.477173 | 0.238586 | − | 0.971121i | \(-0.423316\pi\) | ||||
0.238586 | + | 0.971121i | \(0.423316\pi\) | |||||||
\(72\) | −2.50881 | −0.295666 | ||||||||
\(73\) | −3.64203 | −0.426267 | −0.213134 | − | 0.977023i | \(-0.568367\pi\) | ||||
−0.213134 | + | 0.977023i | \(0.568367\pi\) | |||||||
\(74\) | 1.76195 | 0.204822 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.68088 | 0.881058 | ||||||||
\(77\) | −17.0542 | −1.94350 | ||||||||
\(78\) | 1.80610 | 0.204500 | ||||||||
\(79\) | −8.06707 | −0.907616 | −0.453808 | − | 0.891100i | \(-0.649935\pi\) | ||||
−0.453808 | + | 0.891100i | \(0.649935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.561685 | 0.0624094 | ||||||||
\(82\) | 1.48482 | 0.163971 | ||||||||
\(83\) | −9.94154 | −1.09123 | −0.545613 | − | 0.838037i | \(-0.683703\pi\) | ||||
−0.545613 | + | 0.838037i | \(0.683703\pi\) | |||||||
\(84\) | 5.67777 | 0.619495 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.09806 | −0.118407 | ||||||||
\(87\) | 7.40733 | 0.794150 | ||||||||
\(88\) | −7.57853 | −0.807874 | ||||||||
\(89\) | −7.05272 | −0.747586 | −0.373793 | − | 0.927512i | \(-0.621943\pi\) | ||||
−0.373793 | + | 0.927512i | \(0.621943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.3294 | 1.60696 | ||||||||
\(92\) | −1.92321 | −0.200508 | ||||||||
\(93\) | −7.15248 | −0.741678 | ||||||||
\(94\) | −0.655845 | −0.0676453 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.82062 | 0.389940 | ||||||||
\(97\) | −3.07235 | −0.311950 | −0.155975 | − | 0.987761i | \(-0.549852\pi\) | ||||
−0.155975 | + | 0.987761i | \(0.549852\pi\) | |||||||
\(98\) | −0.498517 | −0.0503578 | ||||||||
\(99\) | 11.3316 | 1.13887 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.95908 | 0.791958 | 0.395979 | − | 0.918260i | \(-0.370405\pi\) | ||||
0.395979 | + | 0.918260i | \(0.370405\pi\) | |||||||
\(102\) | 0.495921 | 0.0491035 | ||||||||
\(103\) | 6.26170 | 0.616983 | 0.308492 | − | 0.951227i | \(-0.400176\pi\) | ||||
0.308492 | + | 0.951227i | \(0.400176\pi\) | |||||||
\(104\) | 6.81210 | 0.667981 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.143489 | −0.0139369 | ||||||||
\(107\) | −4.96053 | −0.479553 | −0.239776 | − | 0.970828i | \(-0.577074\pi\) | ||||
−0.239776 | + | 0.970828i | \(0.577074\pi\) | |||||||
\(108\) | −9.61608 | −0.925308 | ||||||||
\(109\) | −11.4289 | −1.09469 | −0.547344 | − | 0.836907i | \(-0.684361\pi\) | ||||
−0.547344 | + | 0.836907i | \(0.684361\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.45460 | 0.517727 | ||||||||
\(112\) | 9.75533 | 0.921792 | ||||||||
\(113\) | 14.5891 | 1.37242 | 0.686212 | − | 0.727402i | \(-0.259272\pi\) | ||||
0.686212 | + | 0.727402i | \(0.259272\pi\) | |||||||
\(114\) | −1.39638 | −0.130783 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.5708 | 1.26001 | ||||||||
\(117\) | −10.1856 | −0.941662 | ||||||||
\(118\) | −2.81324 | −0.258980 | ||||||||
\(119\) | 4.20919 | 0.385856 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.2302 | 2.11183 | ||||||||
\(122\) | −1.09135 | −0.0988065 | ||||||||
\(123\) | 4.59667 | 0.414467 | ||||||||
\(124\) | −13.1038 | −1.17676 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.88040 | 0.167519 | ||||||||
\(127\) | 10.6738 | 0.947146 | 0.473573 | − | 0.880754i | \(-0.342964\pi\) | ||||
0.473573 | + | 0.880754i | \(0.342964\pi\) | |||||||
\(128\) | 9.22900 | 0.815736 | ||||||||
\(129\) | −3.39935 | −0.299296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.69054 | 0.497185 | 0.248592 | − | 0.968608i | \(-0.420032\pi\) | ||||
0.248592 | + | 0.968608i | \(0.420032\pi\) | |||||||
\(132\) | −11.3961 | −0.991903 | ||||||||
\(133\) | −11.8520 | −1.02770 | ||||||||
\(134\) | −4.56521 | −0.394374 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.87048 | 0.160392 | ||||||||
\(137\) | −2.39550 | −0.204661 | −0.102331 | − | 0.994750i | \(-0.532630\pi\) | ||||
−0.102331 | + | 0.994750i | \(0.532630\pi\) | |||||||
\(138\) | 0.349638 | 0.0297632 | ||||||||
\(139\) | 15.8916 | 1.34791 | 0.673956 | − | 0.738772i | \(-0.264594\pi\) | ||||
0.673956 | + | 0.738772i | \(0.264594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.03035 | −0.170986 | ||||||||
\(142\) | −1.33918 | −0.112382 | ||||||||
\(143\) | −30.7684 | −2.57298 | ||||||||
\(144\) | −6.48192 | −0.540160 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.21305 | 0.100393 | ||||||||
\(147\) | −1.54330 | −0.127289 | ||||||||
\(148\) | 9.99320 | 0.821436 | ||||||||
\(149\) | −23.4096 | −1.91779 | −0.958893 | − | 0.283767i | \(-0.908416\pi\) | ||||
−0.958893 | + | 0.283767i | \(0.908416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0186 | −1.79185 | −0.895925 | − | 0.444206i | \(-0.853486\pi\) | ||||
−0.895925 | + | 0.444206i | \(0.853486\pi\) | |||||||
\(152\) | −5.26678 | −0.427192 | ||||||||
\(153\) | −2.79679 | −0.226107 | ||||||||
\(154\) | 5.68023 | 0.457726 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.2436 | 0.820143 | ||||||||
\(157\) | 15.2432 | 1.21654 | 0.608271 | − | 0.793729i | \(-0.291863\pi\) | ||||
0.608271 | + | 0.793729i | \(0.291863\pi\) | |||||||
\(158\) | 2.68690 | 0.213758 | ||||||||
\(159\) | −0.444209 | −0.0352281 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.96760 | 0.233879 | ||||||||
\(162\) | −0.187080 | −0.0146984 | ||||||||
\(163\) | 1.04988 | 0.0822332 | 0.0411166 | − | 0.999154i | \(-0.486908\pi\) | ||||
0.0411166 | + | 0.999154i | \(0.486908\pi\) | |||||||
\(164\) | 8.42141 | 0.657602 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.31123 | 0.257001 | ||||||||
\(167\) | −10.7693 | −0.833353 | −0.416676 | − | 0.909055i | \(-0.636805\pi\) | ||||
−0.416676 | + | 0.909055i | \(0.636805\pi\) | |||||||
\(168\) | −3.89324 | −0.300370 | ||||||||
\(169\) | 14.6567 | 1.12744 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.87503 | 0.602219 | ||||||||
\(172\) | −6.22785 | −0.474869 | ||||||||
\(173\) | −15.6941 | −1.19320 | −0.596598 | − | 0.802540i | \(-0.703481\pi\) | ||||
−0.596598 | + | 0.802540i | \(0.703481\pi\) | |||||||
\(174\) | −2.46716 | −0.187035 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.5803 | −1.47592 | ||||||||
\(177\) | −8.70916 | −0.654621 | ||||||||
\(178\) | 2.34905 | 0.176069 | ||||||||
\(179\) | 3.10495 | 0.232075 | 0.116038 | − | 0.993245i | \(-0.462981\pi\) | ||||
0.116038 | + | 0.993245i | \(0.462981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2216 | 1.50306 | 0.751528 | − | 0.659701i | \(-0.229317\pi\) | ||||
0.751528 | + | 0.659701i | \(0.229317\pi\) | |||||||
\(182\) | −5.10578 | −0.378465 | ||||||||
\(183\) | −3.37858 | −0.249752 | ||||||||
\(184\) | 1.31874 | 0.0972189 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.38228 | 0.174677 | ||||||||
\(187\) | −8.44845 | −0.617812 | ||||||||
\(188\) | −3.71974 | −0.271290 | ||||||||
\(189\) | 14.8381 | 1.07931 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.2015 | −1.60644 | −0.803221 | − | 0.595681i | \(-0.796882\pi\) | ||||
−0.803221 | + | 0.595681i | \(0.796882\pi\) | |||||||
\(192\) | 5.62908 | 0.406244 | ||||||||
\(193\) | −2.27894 | −0.164041 | −0.0820207 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820207 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(194\) | 1.02331 | 0.0734692 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.82743 | −0.201959 | ||||||||
\(197\) | 3.93329 | 0.280236 | 0.140118 | − | 0.990135i | \(-0.455252\pi\) | ||||
0.140118 | + | 0.990135i | \(0.455252\pi\) | |||||||
\(198\) | −3.77423 | −0.268222 | ||||||||
\(199\) | −23.7466 | −1.68335 | −0.841677 | − | 0.539981i | \(-0.818431\pi\) | ||||
−0.841677 | + | 0.539981i | \(0.818431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.1329 | −0.996855 | ||||||||
\(202\) | −2.65093 | −0.186519 | ||||||||
\(203\) | −20.9403 | −1.46972 | ||||||||
\(204\) | 2.81270 | 0.196929 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.08558 | −0.145309 | ||||||||
\(207\) | −1.97182 | −0.137051 | ||||||||
\(208\) | 17.6001 | 1.22035 | ||||||||
\(209\) | 23.7886 | 1.64549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.51792 | 0.448712 | 0.224356 | − | 0.974507i | \(-0.427972\pi\) | ||||
0.224356 | + | 0.974507i | \(0.427972\pi\) | |||||||
\(212\) | −0.813822 | −0.0558935 | ||||||||
\(213\) | −4.14581 | −0.284066 | ||||||||
\(214\) | 1.65220 | 0.112942 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.59374 | 0.448647 | ||||||||
\(217\) | 20.2198 | 1.37261 | ||||||||
\(218\) | 3.80662 | 0.257817 | ||||||||
\(219\) | 3.75533 | 0.253762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.59404 | 0.510831 | ||||||||
\(222\) | −1.81676 | −0.121933 | ||||||||
\(223\) | −16.5368 | −1.10739 | −0.553693 | − | 0.832721i | \(-0.686782\pi\) | ||||
−0.553693 | + | 0.832721i | \(0.686782\pi\) | |||||||
\(224\) | −10.8008 | −0.721657 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.85918 | −0.323228 | ||||||||
\(227\) | 18.2508 | 1.21135 | 0.605674 | − | 0.795713i | \(-0.292904\pi\) | ||||
0.605674 | + | 0.795713i | \(0.292904\pi\) | |||||||
\(228\) | −7.91983 | −0.524504 | ||||||||
\(229\) | 11.8502 | 0.783086 | 0.391543 | − | 0.920160i | \(-0.371941\pi\) | ||||
0.391543 | + | 0.920160i | \(0.371941\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.5847 | 1.15699 | ||||||||
\(232\) | −9.30546 | −0.610933 | ||||||||
\(233\) | 4.45651 | 0.291955 | 0.145978 | − | 0.989288i | \(-0.453367\pi\) | ||||
0.145978 | + | 0.989288i | \(0.453367\pi\) | |||||||
\(234\) | 3.39253 | 0.221777 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.9558 | −1.03863 | ||||||||
\(237\) | 8.31803 | 0.540314 | ||||||||
\(238\) | −1.40196 | −0.0908753 | ||||||||
\(239\) | −17.5740 | −1.13676 | −0.568382 | − | 0.822765i | \(-0.692431\pi\) | ||||
−0.568382 | + | 0.822765i | \(0.692431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −7.73727 | −0.497371 | ||||||||
\(243\) | −15.8503 | −1.01680 | ||||||||
\(244\) | −6.18980 | −0.396261 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.53101 | −0.0976137 | ||||||||
\(247\) | −21.3828 | −1.36056 | ||||||||
\(248\) | 8.98530 | 0.570567 | ||||||||
\(249\) | 10.2508 | 0.649619 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0655 | −1.07717 | −0.538583 | − | 0.842572i | \(-0.681040\pi\) | ||||
−0.538583 | + | 0.842572i | \(0.681040\pi\) | |||||||
\(252\) | 10.6650 | 0.671831 | ||||||||
\(253\) | −5.95639 | −0.374475 | ||||||||
\(254\) | −3.55512 | −0.223068 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.84459 | 0.490287 | ||||||||
\(257\) | 7.84310 | 0.489239 | 0.244620 | − | 0.969619i | \(-0.421337\pi\) | ||||
0.244620 | + | 0.969619i | \(0.421337\pi\) | |||||||
\(258\) | 1.13222 | 0.0704891 | ||||||||
\(259\) | −15.4200 | −0.958151 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.9138 | 0.861241 | ||||||||
\(262\) | −1.89535 | −0.117095 | ||||||||
\(263\) | −30.1496 | −1.85911 | −0.929553 | − | 0.368688i | \(-0.879807\pi\) | ||||
−0.929553 | + | 0.368688i | \(0.879807\pi\) | |||||||
\(264\) | 7.81430 | 0.480937 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.94753 | 0.242039 | ||||||||
\(267\) | 7.27212 | 0.445047 | ||||||||
\(268\) | −25.8924 | −1.58163 | ||||||||
\(269\) | 2.40509 | 0.146641 | 0.0733204 | − | 0.997308i | \(-0.476640\pi\) | ||||
0.0733204 | + | 0.997308i | \(0.476640\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9386 | −1.87938 | −0.939692 | − | 0.342022i | \(-0.888888\pi\) | ||||
−0.939692 | + | 0.342022i | \(0.888888\pi\) | |||||||
\(272\) | 4.83269 | 0.293025 | ||||||||
\(273\) | −15.8063 | −0.956643 | ||||||||
\(274\) | 0.797869 | 0.0482010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.98304 | 0.119365 | ||||||||
\(277\) | 19.3911 | 1.16510 | 0.582550 | − | 0.812795i | \(-0.302055\pi\) | ||||
0.582550 | + | 0.812795i | \(0.302055\pi\) | |||||||
\(278\) | −5.29303 | −0.317455 | ||||||||
\(279\) | −13.4351 | −0.804336 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.2129 | −1.56373 | −0.781864 | − | 0.623448i | \(-0.785731\pi\) | ||||
−0.781864 | + | 0.623448i | \(0.785731\pi\) | |||||||
\(282\) | 0.676248 | 0.0402700 | ||||||||
\(283\) | 20.3156 | 1.20764 | 0.603819 | − | 0.797121i | \(-0.293645\pi\) | ||||
0.603819 | + | 0.797121i | \(0.293645\pi\) | |||||||
\(284\) | −7.59542 | −0.450705 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2480 | 0.605979 | ||||||||
\(287\) | −12.9946 | −0.767049 | ||||||||
\(288\) | 7.17656 | 0.422883 | ||||||||
\(289\) | −14.9148 | −0.877342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.16793 | 0.185707 | ||||||||
\(292\) | 6.88003 | 0.402623 | ||||||||
\(293\) | −0.889038 | −0.0519382 | −0.0259691 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259691 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(294\) | 0.514026 | 0.0299786 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.85233 | −0.398284 | ||||||||
\(297\) | −29.7822 | −1.72814 | ||||||||
\(298\) | 7.79702 | 0.451669 | ||||||||
\(299\) | 5.35401 | 0.309631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.60986 | 0.553903 | ||||||||
\(302\) | 7.33374 | 0.422009 | ||||||||
\(303\) | −8.20669 | −0.471462 | ||||||||
\(304\) | −13.6076 | −0.780447 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.931528 | 0.0532519 | ||||||||
\(307\) | −29.1697 | −1.66480 | −0.832401 | − | 0.554173i | \(-0.813035\pi\) | ||||
−0.832401 | + | 0.554173i | \(0.813035\pi\) | |||||||
\(308\) | 32.2164 | 1.83570 | ||||||||
\(309\) | −6.45650 | −0.367297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.909742 | 0.0515867 | 0.0257934 | − | 0.999667i | \(-0.491789\pi\) | ||||
0.0257934 | + | 0.999667i | \(0.491789\pi\) | |||||||
\(312\) | −7.02402 | −0.397657 | ||||||||
\(313\) | 23.8202 | 1.34640 | 0.673198 | − | 0.739463i | \(-0.264920\pi\) | ||||
0.673198 | + | 0.739463i | \(0.264920\pi\) | |||||||
\(314\) | −5.07706 | −0.286515 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.2392 | 0.857272 | ||||||||
\(317\) | 3.49764 | 0.196447 | 0.0982236 | − | 0.995164i | \(-0.468684\pi\) | ||||
0.0982236 | + | 0.995164i | \(0.468684\pi\) | |||||||
\(318\) | 0.147953 | 0.00829678 | ||||||||
\(319\) | 42.0302 | 2.35324 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.11485 | 0.285483 | ||||||||
\(322\) | −0.988417 | −0.0550823 | ||||||||
\(323\) | −5.87134 | −0.326690 | ||||||||
\(324\) | −1.06106 | −0.0589477 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.349685 | −0.0193672 | ||||||||
\(327\) | 11.7844 | 0.651681 | ||||||||
\(328\) | −5.77456 | −0.318847 | ||||||||
\(329\) | 5.73973 | 0.316442 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41133 | −0.132539 | −0.0662693 | − | 0.997802i | \(-0.521110\pi\) | ||||
−0.0662693 | + | 0.997802i | \(0.521110\pi\) | |||||||
\(332\) | 18.7802 | 1.03070 | ||||||||
\(333\) | 10.2458 | 0.561466 | ||||||||
\(334\) | 3.58693 | 0.196268 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.0588 | −0.548753 | ||||||||
\(337\) | −18.3801 | −1.00123 | −0.500615 | − | 0.865670i | \(-0.666893\pi\) | ||||
−0.500615 | + | 0.865670i | \(0.666893\pi\) | |||||||
\(338\) | −4.88172 | −0.265530 | ||||||||
\(339\) | −15.0429 | −0.817019 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.5842 | −2.19775 | ||||||||
\(342\) | −2.62294 | −0.141832 | ||||||||
\(343\) | −16.0416 | −0.866163 | ||||||||
\(344\) | 4.27043 | 0.230246 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.22722 | 0.281017 | ||||||||
\(347\) | −22.1659 | −1.18993 | −0.594963 | − | 0.803753i | \(-0.702833\pi\) | ||||
−0.594963 | + | 0.803753i | \(0.702833\pi\) | |||||||
\(348\) | −13.9929 | −0.750100 | ||||||||
\(349\) | −8.81153 | −0.471670 | −0.235835 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235835 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.7702 | 1.42889 | ||||||||
\(352\) | 21.6787 | 1.15548 | ||||||||
\(353\) | 20.1876 | 1.07448 | 0.537238 | − | 0.843431i | \(-0.319468\pi\) | ||||
0.537238 | + | 0.843431i | \(0.319468\pi\) | |||||||
\(354\) | 2.90076 | 0.154174 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.3230 | 0.706119 | ||||||||
\(357\) | −4.34014 | −0.229704 | ||||||||
\(358\) | −1.03417 | −0.0546574 | ||||||||
\(359\) | 21.3173 | 1.12508 | 0.562541 | − | 0.826769i | \(-0.309824\pi\) | ||||
0.562541 | + | 0.826769i | \(0.309824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46787 | −0.129888 | ||||||||
\(362\) | −6.73519 | −0.353994 | ||||||||
\(363\) | −23.9529 | −1.25720 | ||||||||
\(364\) | −28.9583 | −1.51783 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.12530 | 0.0588206 | ||||||||
\(367\) | 9.10147 | 0.475093 | 0.237546 | − | 0.971376i | \(-0.423657\pi\) | ||||
0.237546 | + | 0.971376i | \(0.423657\pi\) | |||||||
\(368\) | 3.40718 | 0.177611 | ||||||||
\(369\) | 8.63427 | 0.449482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.25577 | 0.0651961 | ||||||||
\(372\) | 13.5115 | 0.700538 | ||||||||
\(373\) | −6.33715 | −0.328125 | −0.164063 | − | 0.986450i | \(-0.552460\pi\) | ||||
−0.164063 | + | 0.986450i | \(0.552460\pi\) | |||||||
\(374\) | 2.81393 | 0.145505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.55062 | 0.131538 | ||||||||
\(377\) | −37.7796 | −1.94575 | ||||||||
\(378\) | −4.94212 | −0.254195 | ||||||||
\(379\) | −20.7733 | −1.06705 | −0.533526 | − | 0.845784i | \(-0.679133\pi\) | ||||
−0.533526 | + | 0.845784i | \(0.679133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0059 | −0.563847 | ||||||||
\(382\) | 7.39464 | 0.378343 | ||||||||
\(383\) | 7.29626 | 0.372822 | 0.186411 | − | 0.982472i | \(-0.440314\pi\) | ||||
0.186411 | + | 0.982472i | \(0.440314\pi\) | |||||||
\(384\) | −9.51611 | −0.485617 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.759045 | 0.0386344 | ||||||||
\(387\) | −6.38527 | −0.324581 | ||||||||
\(388\) | 5.80387 | 0.294647 | ||||||||
\(389\) | −0.402390 | −0.0204020 | −0.0102010 | − | 0.999948i | \(-0.503247\pi\) | ||||
−0.0102010 | + | 0.999948i | \(0.503247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.47012 | 0.0743469 | ||||||||
\(392\) | 1.93876 | 0.0979224 | ||||||||
\(393\) | −5.86757 | −0.295980 | ||||||||
\(394\) | −1.31006 | −0.0660000 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.4062 | −1.07570 | ||||||||
\(397\) | −32.2805 | −1.62011 | −0.810057 | − | 0.586351i | \(-0.800564\pi\) | ||||
−0.810057 | + | 0.586351i | \(0.800564\pi\) | |||||||
\(398\) | 7.90929 | 0.396457 | ||||||||
\(399\) | 12.2207 | 0.611799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.2445 | −1.26065 | −0.630324 | − | 0.776332i | \(-0.717078\pi\) | ||||
−0.630324 | + | 0.776332i | \(0.717078\pi\) | |||||||
\(402\) | 4.70723 | 0.234775 | ||||||||
\(403\) | 36.4798 | 1.81719 | ||||||||
\(404\) | −15.0352 | −0.748030 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.97459 | 0.346143 | ||||||||
\(407\) | 30.9501 | 1.53414 | ||||||||
\(408\) | −1.92867 | −0.0954834 | ||||||||
\(409\) | 15.2153 | 0.752348 | 0.376174 | − | 0.926549i | \(-0.377239\pi\) | ||||
0.376174 | + | 0.926549i | \(0.377239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47002 | 0.121837 | ||||||||
\(412\) | −11.8287 | −0.582761 | ||||||||
\(413\) | 24.6205 | 1.21150 | ||||||||
\(414\) | 0.656753 | 0.0322777 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.4863 | −0.955394 | ||||||||
\(417\) | −16.3860 | −0.802427 | ||||||||
\(418\) | −7.92327 | −0.387540 | ||||||||
\(419\) | −24.2883 | −1.18656 | −0.593280 | − | 0.804996i | \(-0.702167\pi\) | ||||
−0.593280 | + | 0.804996i | \(0.702167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.24005 | 0.0604366 | 0.0302183 | − | 0.999543i | \(-0.490380\pi\) | ||||
0.0302183 | + | 0.999543i | \(0.490380\pi\) | |||||||
\(422\) | −2.17092 | −0.105679 | ||||||||
\(423\) | −3.81376 | −0.185431 | ||||||||
\(424\) | 0.558037 | 0.0271007 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.38085 | 0.0669022 | ||||||||
\(427\) | 9.55115 | 0.462213 | ||||||||
\(428\) | 9.37076 | 0.452953 | ||||||||
\(429\) | 31.7256 | 1.53173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7031 | −1.23807 | −0.619036 | − | 0.785362i | \(-0.712477\pi\) | ||||
−0.619036 | + | 0.785362i | \(0.712477\pi\) | |||||||
\(432\) | 17.0360 | 0.819644 | ||||||||
\(433\) | −21.4579 | −1.03120 | −0.515601 | − | 0.856829i | \(-0.672431\pi\) | ||||
−0.515601 | + | 0.856829i | \(0.672431\pi\) | |||||||
\(434\) | −6.73462 | −0.323272 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.5899 | 1.03397 | ||||||||
\(437\) | −4.13946 | −0.198017 | ||||||||
\(438\) | −1.25079 | −0.0597649 | ||||||||
\(439\) | −17.7057 | −0.845048 | −0.422524 | − | 0.906352i | \(-0.638856\pi\) | ||||
−0.422524 | + | 0.906352i | \(0.638856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.89889 | −0.138043 | ||||||||
\(442\) | −2.52935 | −0.120309 | ||||||||
\(443\) | −14.5582 | −0.691682 | −0.345841 | − | 0.938293i | \(-0.612406\pi\) | ||||
−0.345841 | + | 0.938293i | \(0.612406\pi\) | |||||||
\(444\) | −10.3041 | −0.489010 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.50791 | 0.260807 | ||||||||
\(447\) | 24.1378 | 1.14168 | ||||||||
\(448\) | −15.9132 | −0.751830 | ||||||||
\(449\) | 16.8552 | 0.795446 | 0.397723 | − | 0.917505i | \(-0.369800\pi\) | ||||
0.397723 | + | 0.917505i | \(0.369800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0821 | 1.22816 | ||||||||
\(452\) | −27.5597 | −1.29630 | ||||||||
\(453\) | 22.7036 | 1.06671 | ||||||||
\(454\) | −6.07879 | −0.285292 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.43063 | 0.254312 | ||||||||
\(457\) | −21.9145 | −1.02512 | −0.512558 | − | 0.858653i | \(-0.671302\pi\) | ||||
−0.512558 | + | 0.858653i | \(0.671302\pi\) | |||||||
\(458\) | −3.94696 | −0.184429 | ||||||||
\(459\) | 7.35062 | 0.343098 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.72445 | 0.313189 | 0.156594 | − | 0.987663i | \(-0.449948\pi\) | ||||
0.156594 | + | 0.987663i | \(0.449948\pi\) | |||||||
\(462\) | −5.85694 | −0.272490 | ||||||||
\(463\) | −26.5995 | −1.23618 | −0.618092 | − | 0.786106i | \(-0.712094\pi\) | ||||
−0.618092 | + | 0.786106i | \(0.712094\pi\) | |||||||
\(464\) | −24.0421 | −1.11613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.48433 | −0.0687602 | ||||||||
\(467\) | −7.75161 | −0.358702 | −0.179351 | − | 0.983785i | \(-0.557400\pi\) | ||||
−0.179351 | + | 0.983785i | \(0.557400\pi\) | |||||||
\(468\) | 19.2413 | 0.889431 | ||||||||
\(469\) | 39.9532 | 1.84487 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.7174 | −0.724221 | ||||||||
\(472\) | 10.9409 | 0.503595 | ||||||||
\(473\) | −19.2884 | −0.886881 | ||||||||
\(474\) | −2.77049 | −0.127253 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.95143 | −0.364453 | ||||||||
\(477\) | −0.834393 | −0.0382042 | ||||||||
\(478\) | 5.85336 | 0.267726 | ||||||||
\(479\) | −40.0472 | −1.82980 | −0.914901 | − | 0.403679i | \(-0.867731\pi\) | ||||
−0.914901 | + | 0.403679i | \(0.867731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8201 | −1.26849 | ||||||||
\(482\) | −0.333070 | −0.0151709 | ||||||||
\(483\) | −3.05992 | −0.139231 | ||||||||
\(484\) | −43.8833 | −1.99470 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.27927 | 0.239473 | ||||||||
\(487\) | −10.4935 | −0.475504 | −0.237752 | − | 0.971326i | \(-0.576411\pi\) | ||||
−0.237752 | + | 0.971326i | \(0.576411\pi\) | |||||||
\(488\) | 4.24434 | 0.192132 | ||||||||
\(489\) | −1.08255 | −0.0489544 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.0414 | 1.31062 | 0.655311 | − | 0.755359i | \(-0.272538\pi\) | ||||
0.655311 | + | 0.755359i | \(0.272538\pi\) | |||||||
\(492\) | −8.68340 | −0.391478 | ||||||||
\(493\) | −10.3736 | −0.467204 | ||||||||
\(494\) | 7.12197 | 0.320433 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.2150 | 1.04238 | ||||||||
\(497\) | 11.7201 | 0.525718 | ||||||||
\(498\) | −3.41424 | −0.152996 | ||||||||
\(499\) | −9.82170 | −0.439679 | −0.219840 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219840 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1043 | 0.496104 | ||||||||
\(502\) | 5.68402 | 0.253690 | ||||||||
\(503\) | −32.6913 | −1.45763 | −0.728817 | − | 0.684709i | \(-0.759929\pi\) | ||||
−0.728817 | + | 0.684709i | \(0.759929\pi\) | |||||||
\(504\) | −7.31298 | −0.325746 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.98390 | 0.0881949 | ||||||||
\(507\) | −15.1127 | −0.671179 | ||||||||
\(508\) | −20.1635 | −0.894610 | ||||||||
\(509\) | −16.3559 | −0.724962 | −0.362481 | − | 0.931991i | \(-0.618070\pi\) | ||||
−0.362481 | + | 0.931991i | \(0.618070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6162 | −0.469633 | ||||||||
\(512\) | −21.0708 | −0.931206 | ||||||||
\(513\) | −20.6974 | −0.913813 | ||||||||
\(514\) | −2.61230 | −0.115224 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.42159 | 0.282695 | ||||||||
\(517\) | −11.5205 | −0.506670 | ||||||||
\(518\) | 5.13593 | 0.225660 | ||||||||
\(519\) | 16.1823 | 0.710324 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8661 | −0.476052 | −0.238026 | − | 0.971259i | \(-0.576500\pi\) | ||||
−0.238026 | + | 0.971259i | \(0.576500\pi\) | |||||||
\(522\) | −4.63426 | −0.202836 | ||||||||
\(523\) | −30.9516 | −1.35342 | −0.676710 | − | 0.736250i | \(-0.736595\pi\) | ||||
−0.676710 | + | 0.736250i | \(0.736595\pi\) | |||||||
\(524\) | −10.7498 | −0.469607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0419 | 0.437849 | ||||||||
\(527\) | 10.0167 | 0.436334 | ||||||||
\(528\) | 20.1895 | 0.878635 | ||||||||
\(529\) | −21.9635 | −0.954936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.3591 | −0.709924 | ||||||||
\(532\) | 22.3891 | 0.970692 | ||||||||
\(533\) | −23.4444 | −1.01549 | ||||||||
\(534\) | −2.42213 | −0.104816 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17.7544 | 0.766873 | ||||||||
\(537\) | −3.20155 | −0.138157 | ||||||||
\(538\) | −0.801063 | −0.0345363 | ||||||||
\(539\) | −8.75687 | −0.377185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3353 | 1.34721 | 0.673606 | − | 0.739091i | \(-0.264745\pi\) | ||||
0.673606 | + | 0.739091i | \(0.264745\pi\) | |||||||
\(542\) | 10.3047 | 0.442625 | ||||||||
\(543\) | −20.8506 | −0.894786 | ||||||||
\(544\) | −5.35058 | −0.229404 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.26462 | 0.225305 | ||||||||
\(547\) | 37.6463 | 1.60964 | 0.804821 | − | 0.593518i | \(-0.202261\pi\) | ||||
0.804821 | + | 0.593518i | \(0.202261\pi\) | |||||||
\(548\) | 4.52525 | 0.193309 | ||||||||
\(549\) | −6.34626 | −0.270852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.2093 | 1.24436 | ||||||||
\(552\) | −1.35977 | −0.0578755 | ||||||||
\(553\) | −23.5148 | −0.999952 | ||||||||
\(554\) | −6.45860 | −0.274400 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.0203 | −1.27315 | ||||||||
\(557\) | 23.6732 | 1.00307 | 0.501534 | − | 0.865138i | \(-0.332769\pi\) | ||||
0.501534 | + | 0.865138i | \(0.332769\pi\) | |||||||
\(558\) | 4.47482 | 0.189434 | ||||||||
\(559\) | 17.3377 | 0.733307 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.71128 | 0.367791 | ||||||||
\(562\) | 8.73072 | 0.368283 | ||||||||
\(563\) | −17.4383 | −0.734935 | −0.367468 | − | 0.930036i | \(-0.619775\pi\) | ||||
−0.367468 | + | 0.930036i | \(0.619775\pi\) | |||||||
\(564\) | 3.83546 | 0.161502 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.76652 | −0.284418 | ||||||||
\(567\) | 1.63726 | 0.0687586 | ||||||||
\(568\) | 5.20817 | 0.218530 | ||||||||
\(569\) | −1.59178 | −0.0667309 | −0.0333654 | − | 0.999443i | \(-0.510623\pi\) | ||||
−0.0333654 | + | 0.999443i | \(0.510623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.95835 | 0.374895 | 0.187448 | − | 0.982275i | \(-0.439978\pi\) | ||||
0.187448 | + | 0.982275i | \(0.439978\pi\) | |||||||
\(572\) | 58.1235 | 2.43027 | ||||||||
\(573\) | 22.8921 | 0.956333 | ||||||||
\(574\) | 4.32812 | 0.180652 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.5735 | 0.440564 | ||||||||
\(577\) | −35.6551 | −1.48434 | −0.742171 | − | 0.670211i | \(-0.766204\pi\) | ||||
−0.742171 | + | 0.670211i | \(0.766204\pi\) | |||||||
\(578\) | 4.96768 | 0.206628 | ||||||||
\(579\) | 2.34983 | 0.0976557 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.9788 | −1.20224 | ||||||||
\(582\) | −1.05514 | −0.0437371 | ||||||||
\(583\) | −2.52050 | −0.104389 | ||||||||
\(584\) | −4.71763 | −0.195217 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.296112 | 0.0122323 | ||||||||
\(587\) | −44.6462 | −1.84275 | −0.921374 | − | 0.388678i | \(-0.872932\pi\) | ||||
−0.921374 | + | 0.388678i | \(0.872932\pi\) | |||||||
\(588\) | 2.91539 | 0.120228 | ||||||||
\(589\) | −28.2044 | −1.16214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.05566 | −0.166827 | ||||||||
\(592\) | −17.7041 | −0.727634 | ||||||||
\(593\) | −15.0888 | −0.619622 | −0.309811 | − | 0.950798i | \(-0.600266\pi\) | ||||
−0.309811 | + | 0.950798i | \(0.600266\pi\) | |||||||
\(594\) | 9.91954 | 0.407004 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.2222 | 1.81141 | ||||||||
\(597\) | 24.4854 | 1.00212 | ||||||||
\(598\) | −1.78326 | −0.0729230 | ||||||||
\(599\) | 5.24328 | 0.214234 | 0.107117 | − | 0.994246i | \(-0.465838\pi\) | ||||
0.107117 | + | 0.994246i | \(0.465838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.89463 | −0.281238 | −0.140619 | − | 0.990064i | \(-0.544909\pi\) | ||||
−0.140619 | + | 0.990064i | \(0.544909\pi\) | |||||||
\(602\) | −3.20076 | −0.130453 | ||||||||
\(603\) | −26.5469 | −1.08107 | ||||||||
\(604\) | 41.5946 | 1.69246 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.73340 | 0.111037 | ||||||||
\(607\) | −34.0874 | −1.38356 | −0.691782 | − | 0.722106i | \(-0.743174\pi\) | ||||
−0.691782 | + | 0.722106i | \(0.743174\pi\) | |||||||
\(608\) | 15.0658 | 0.611000 | ||||||||
\(609\) | 21.5918 | 0.874942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3554 | 0.418934 | ||||||||
\(612\) | 5.28332 | 0.213566 | ||||||||
\(613\) | 46.7467 | 1.88808 | 0.944040 | − | 0.329831i | \(-0.106992\pi\) | ||||
0.944040 | + | 0.329831i | \(0.106992\pi\) | |||||||
\(614\) | 9.71555 | 0.392088 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.0908 | −0.890063 | ||||||||
\(617\) | −3.53207 | −0.142196 | −0.0710979 | − | 0.997469i | \(-0.522650\pi\) | ||||
−0.0710979 | + | 0.997469i | \(0.522650\pi\) | |||||||
\(618\) | 2.15046 | 0.0865044 | ||||||||
\(619\) | −5.50908 | −0.221428 | −0.110714 | − | 0.993852i | \(-0.535314\pi\) | ||||
−0.110714 | + | 0.993852i | \(0.535314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.18239 | 0.207962 | ||||||||
\(622\) | −0.303008 | −0.0121495 | ||||||||
\(623\) | −20.5581 | −0.823642 | ||||||||
\(624\) | −18.1477 | −0.726489 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.93378 | −0.317098 | ||||||||
\(627\) | −24.5287 | −0.979580 | ||||||||
\(628\) | −28.7954 | −1.14906 | ||||||||
\(629\) | −7.63889 | −0.304583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.40113 | 0.334444 | 0.167222 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167222 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(632\) | −10.4495 | −0.415660 | ||||||||
\(633\) | −6.72068 | −0.267123 | ||||||||
\(634\) | −1.16496 | −0.0462664 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.839140 | 0.0332741 | ||||||||
\(637\) | 7.87127 | 0.311871 | ||||||||
\(638\) | −13.9990 | −0.554226 | ||||||||
\(639\) | −7.78740 | −0.308065 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.6572 | 1.13189 | 0.565945 | − | 0.824443i | \(-0.308511\pi\) | ||||
0.565945 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(642\) | −1.70360 | −0.0672359 | ||||||||
\(643\) | −12.2879 | −0.484588 | −0.242294 | − | 0.970203i | \(-0.577900\pi\) | ||||
−0.242294 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(644\) | −5.60598 | −0.220907 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.95557 | 0.0769407 | ||||||||
\(647\) | −28.5820 | −1.12367 | −0.561837 | − | 0.827248i | \(-0.689905\pi\) | ||||
−0.561837 | + | 0.827248i | \(0.689905\pi\) | |||||||
\(648\) | 0.727568 | 0.0285816 | ||||||||
\(649\) | −49.4170 | −1.93979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.8489 | −0.817132 | ||||||||
\(652\) | −1.98330 | −0.0776719 | ||||||||
\(653\) | 37.3291 | 1.46080 | 0.730400 | − | 0.683019i | \(-0.239334\pi\) | ||||
0.730400 | + | 0.683019i | \(0.239334\pi\) | |||||||
\(654\) | −3.92504 | −0.153481 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.9195 | −0.582508 | ||||||||
\(657\) | 7.05393 | 0.275200 | ||||||||
\(658\) | −1.91173 | −0.0745271 | ||||||||
\(659\) | 26.9165 | 1.04852 | 0.524258 | − | 0.851559i | \(-0.324343\pi\) | ||||
0.524258 | + | 0.851559i | \(0.324343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.47194 | 0.212834 | 0.106417 | − | 0.994322i | \(-0.466062\pi\) | ||||
0.106417 | + | 0.994322i | \(0.466062\pi\) | |||||||
\(662\) | 0.803141 | 0.0312150 | ||||||||
\(663\) | −7.83029 | −0.304103 | ||||||||
\(664\) | −12.8776 | −0.499747 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.41257 | −0.132234 | ||||||||
\(667\) | −7.31368 | −0.283187 | ||||||||
\(668\) | 20.3439 | 0.787128 | ||||||||
\(669\) | 17.0512 | 0.659239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.1705 | −0.740071 | ||||||||
\(672\) | 11.1368 | 0.429610 | ||||||||
\(673\) | 23.1664 | 0.892997 | 0.446499 | − | 0.894784i | \(-0.352671\pi\) | ||||
0.446499 | + | 0.894784i | \(0.352671\pi\) | |||||||
\(674\) | 6.12187 | 0.235806 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.6875 | −1.06490 | ||||||||
\(677\) | 25.7492 | 0.989620 | 0.494810 | − | 0.869001i | \(-0.335238\pi\) | ||||
0.494810 | + | 0.869001i | \(0.335238\pi\) | |||||||
\(678\) | 5.01035 | 0.192421 | ||||||||
\(679\) | −8.95565 | −0.343686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.8186 | −0.721129 | ||||||||
\(682\) | 13.5174 | 0.517607 | ||||||||
\(683\) | 16.8086 | 0.643163 | 0.321581 | − | 0.946882i | \(-0.395786\pi\) | ||||
0.321581 | + | 0.946882i | \(0.395786\pi\) | |||||||
\(684\) | −14.8764 | −0.568815 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.34296 | 0.203995 | ||||||||
\(687\) | −12.2189 | −0.466180 | ||||||||
\(688\) | 11.0333 | 0.420642 | ||||||||
\(689\) | 2.26560 | 0.0863125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0705 | −1.02981 | −0.514905 | − | 0.857247i | \(-0.672173\pi\) | ||||
−0.514905 | + | 0.857247i | \(0.672173\pi\) | |||||||
\(692\) | 29.6471 | 1.12701 | ||||||||
\(693\) | 33.0307 | 1.25473 | ||||||||
\(694\) | 7.38278 | 0.280247 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.59495 | 0.363695 | ||||||||
\(697\) | −6.43740 | −0.243834 | ||||||||
\(698\) | 2.93486 | 0.111086 | ||||||||
\(699\) | −4.59515 | −0.173804 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.70437 | −0.215451 | −0.107726 | − | 0.994181i | \(-0.534357\pi\) | ||||
−0.107726 | + | 0.994181i | \(0.534357\pi\) | |||||||
\(702\) | −8.91636 | −0.336526 | ||||||||
\(703\) | 21.5091 | 0.811231 | ||||||||
\(704\) | 31.9402 | 1.20379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.72387 | −0.253056 | ||||||||
\(707\) | 23.2001 | 0.872528 | ||||||||
\(708\) | 16.4522 | 0.618310 | ||||||||
\(709\) | −47.1794 | −1.77186 | −0.885929 | − | 0.463821i | \(-0.846478\pi\) | ||||
−0.885929 | + | 0.463821i | \(0.846478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6244 | 0.585961 | ||||||||
\(712\) | −9.13560 | −0.342371 | ||||||||
\(713\) | 7.06205 | 0.264476 | ||||||||
\(714\) | 1.44557 | 0.0540991 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.86545 | −0.219202 | ||||||||
\(717\) | 18.1207 | 0.676729 | ||||||||
\(718\) | −7.10014 | −0.264975 | ||||||||
\(719\) | 8.68947 | 0.324063 | 0.162031 | − | 0.986786i | \(-0.448195\pi\) | ||||
0.162031 | + | 0.986786i | \(0.448195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.2523 | 0.679752 | ||||||||
\(722\) | 0.821973 | 0.0305907 | ||||||||
\(723\) | −1.03111 | −0.0383474 | ||||||||
\(724\) | −38.1998 | −1.41968 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.97798 | 0.296091 | ||||||||
\(727\) | −28.3067 | −1.04984 | −0.524919 | − | 0.851152i | \(-0.675905\pi\) | ||||
−0.524919 | + | 0.851152i | \(0.675905\pi\) | |||||||
\(728\) | 19.8567 | 0.735938 | ||||||||
\(729\) | 14.6584 | 0.542903 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.76062 | 0.176078 | ||||||||
\(732\) | 6.38236 | 0.235899 | ||||||||
\(733\) | 35.7145 | 1.31914 | 0.659572 | − | 0.751641i | \(-0.270737\pi\) | ||||
0.659572 | + | 0.751641i | \(0.270737\pi\) | |||||||
\(734\) | −3.03143 | −0.111892 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.77231 | −0.139049 | ||||||||
\(737\) | −80.1918 | −2.95390 | ||||||||
\(738\) | −2.87582 | −0.105860 | ||||||||
\(739\) | 23.3411 | 0.858617 | 0.429309 | − | 0.903158i | \(-0.358757\pi\) | ||||
0.429309 | + | 0.903158i | \(0.358757\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.0480 | 0.809954 | ||||||||
\(742\) | −0.418258 | −0.0153547 | ||||||||
\(743\) | 48.4819 | 1.77863 | 0.889313 | − | 0.457298i | \(-0.151183\pi\) | ||||
0.889313 | + | 0.457298i | \(0.151183\pi\) | |||||||
\(744\) | −9.26483 | −0.339665 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.11072 | 0.0772788 | ||||||||
\(747\) | 19.2549 | 0.704500 | ||||||||
\(748\) | 15.9597 | 0.583543 | ||||||||
\(749\) | −14.4595 | −0.528340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.2145 | −0.993071 | −0.496535 | − | 0.868016i | \(-0.665395\pi\) | ||||
−0.496535 | + | 0.868016i | \(0.665395\pi\) | |||||||
\(752\) | 6.58994 | 0.240311 | ||||||||
\(753\) | 17.5964 | 0.641250 | ||||||||
\(754\) | 12.5833 | 0.458255 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −28.0301 | −1.01944 | ||||||||
\(757\) | 34.2995 | 1.24664 | 0.623318 | − | 0.781968i | \(-0.285784\pi\) | ||||
0.623318 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(758\) | 6.91896 | 0.251308 | ||||||||
\(759\) | 6.14169 | 0.222929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.8695 | −1.33652 | −0.668260 | − | 0.743928i | \(-0.732961\pi\) | ||||
−0.668260 | + | 0.743928i | \(0.732961\pi\) | |||||||
\(762\) | 3.66572 | 0.132795 | ||||||||
\(763\) | −33.3142 | −1.20606 | ||||||||
\(764\) | 41.9400 | 1.51734 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.43017 | −0.0878055 | ||||||||
\(767\) | 44.4193 | 1.60389 | ||||||||
\(768\) | −8.08863 | −0.291873 | ||||||||
\(769\) | 38.5560 | 1.39036 | 0.695182 | − | 0.718834i | \(-0.255324\pi\) | ||||
0.695182 | + | 0.718834i | \(0.255324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.08710 | −0.291250 | ||||||||
\(772\) | 4.30506 | 0.154942 | ||||||||
\(773\) | −31.5788 | −1.13581 | −0.567905 | − | 0.823094i | \(-0.692246\pi\) | ||||
−0.567905 | + | 0.823094i | \(0.692246\pi\) | |||||||
\(774\) | 2.12674 | 0.0764441 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.97971 | −0.142863 | ||||||||
\(777\) | 15.8997 | 0.570398 | ||||||||
\(778\) | 0.134024 | 0.00480499 | ||||||||
\(779\) | 18.1260 | 0.649432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.5239 | −0.841752 | ||||||||
\(782\) | −0.489651 | −0.0175099 | ||||||||
\(783\) | −36.5686 | −1.30686 | ||||||||
\(784\) | 5.00911 | 0.178897 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.95431 | 0.0697080 | ||||||||
\(787\) | 9.97778 | 0.355669 | 0.177835 | − | 0.984060i | \(-0.443091\pi\) | ||||
0.177835 | + | 0.984060i | \(0.443091\pi\) | |||||||
\(788\) | −7.43024 | −0.264691 | ||||||||
\(789\) | 31.0876 | 1.10675 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.5259 | 1.51205 | ||||||||
\(792\) | 14.6782 | 0.521567 | ||||||||
\(793\) | 17.2318 | 0.611919 | ||||||||
\(794\) | 10.7517 | 0.381563 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 44.8589 | 1.58998 | ||||||||
\(797\) | 34.8558 | 1.23466 | 0.617329 | − | 0.786705i | \(-0.288215\pi\) | ||||
0.617329 | + | 0.786705i | \(0.288215\pi\) | |||||||
\(798\) | −4.07034 | −0.144088 | ||||||||
\(799\) | 2.84340 | 0.100592 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6598 | 0.482645 | ||||||||
\(802\) | 8.40817 | 0.296903 | ||||||||
\(803\) | 21.3083 | 0.751952 | ||||||||
\(804\) | 26.6979 | 0.941562 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.1503 | −0.427977 | ||||||||
\(807\) | −2.47991 | −0.0872970 | ||||||||
\(808\) | 10.3096 | 0.362692 | ||||||||
\(809\) | 51.0838 | 1.79601 | 0.898006 | − | 0.439984i | \(-0.145016\pi\) | ||||
0.898006 | + | 0.439984i | \(0.145016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.5274 | −0.685699 | −0.342849 | − | 0.939390i | \(-0.611392\pi\) | ||||
−0.342849 | + | 0.939390i | \(0.611392\pi\) | |||||||
\(812\) | 39.5576 | 1.38820 | ||||||||
\(813\) | 31.9011 | 1.11882 | ||||||||
\(814\) | −10.3086 | −0.361315 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.98303 | −0.174441 | ||||||||
\(817\) | −13.4047 | −0.468970 | ||||||||
\(818\) | −5.06776 | −0.177190 | ||||||||
\(819\) | −29.6903 | −1.03746 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.3733 | −0.885536 | −0.442768 | − | 0.896636i | \(-0.646003\pi\) | ||||
−0.442768 | + | 0.896636i | \(0.646003\pi\) | |||||||
\(822\) | −0.822690 | −0.0286946 | ||||||||
\(823\) | 22.3168 | 0.777913 | 0.388957 | − | 0.921256i | \(-0.372836\pi\) | ||||
0.388957 | + | 0.921256i | \(0.372836\pi\) | |||||||
\(824\) | 8.11097 | 0.282559 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.20036 | −0.285327 | ||||||||
\(827\) | 4.78461 | 0.166377 | 0.0831887 | − | 0.996534i | \(-0.473490\pi\) | ||||
0.0831887 | + | 0.996534i | \(0.473490\pi\) | |||||||
\(828\) | 3.72489 | 0.129449 | ||||||||
\(829\) | 7.61397 | 0.264444 | 0.132222 | − | 0.991220i | \(-0.457789\pi\) | ||||
0.132222 | + | 0.991220i | \(0.457789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.9944 | −0.693597 | ||||||||
\(832\) | −28.7100 | −0.995340 | ||||||||
\(833\) | 2.16131 | 0.0748850 | ||||||||
\(834\) | 5.45769 | 0.188984 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −44.9382 | −1.55422 | ||||||||
\(837\) | 35.3105 | 1.22051 | ||||||||
\(838\) | 8.08969 | 0.279454 | ||||||||
\(839\) | 33.0206 | 1.14000 | 0.569999 | − | 0.821646i | \(-0.306944\pi\) | ||||
0.569999 | + | 0.821646i | \(0.306944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.6077 | 0.779575 | ||||||||
\(842\) | −0.413025 | −0.0142338 | ||||||||
\(843\) | 27.0283 | 0.930906 | ||||||||
\(844\) | −12.3128 | −0.423823 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.27025 | 0.0436721 | ||||||||
\(847\) | 67.7140 | 2.32668 | ||||||||
\(848\) | 1.44178 | 0.0495109 | ||||||||
\(849\) | −20.9476 | −0.718921 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.38563 | −0.184617 | ||||||||
\(852\) | 7.83171 | 0.268310 | ||||||||
\(853\) | −26.1191 | −0.894301 | −0.447151 | − | 0.894459i | \(-0.647561\pi\) | ||||
−0.447151 | + | 0.894459i | \(0.647561\pi\) | |||||||
\(854\) | −3.18120 | −0.108859 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.42553 | −0.219620 | ||||||||
\(857\) | −12.0143 | −0.410400 | −0.205200 | − | 0.978720i | \(-0.565785\pi\) | ||||
−0.205200 | + | 0.978720i | \(0.565785\pi\) | |||||||
\(858\) | −10.5668 | −0.360746 | ||||||||
\(859\) | −16.9150 | −0.577132 | −0.288566 | − | 0.957460i | \(-0.593179\pi\) | ||||
−0.288566 | + | 0.957460i | \(0.593179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.3989 | 0.456633 | ||||||||
\(862\) | 8.56092 | 0.291586 | ||||||||
\(863\) | −15.6125 | −0.531456 | −0.265728 | − | 0.964048i | \(-0.585612\pi\) | ||||
−0.265728 | + | 0.964048i | \(0.585612\pi\) | |||||||
\(864\) | −18.8617 | −0.641687 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.14699 | 0.242865 | ||||||||
\(867\) | 15.3788 | 0.522292 | ||||||||
\(868\) | −38.1966 | −1.29648 | ||||||||
\(869\) | 47.1976 | 1.60107 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.0818 | 2.44240 | ||||||||
\(872\) | −14.8042 | −0.501333 | ||||||||
\(873\) | 5.95057 | 0.201396 | ||||||||
\(874\) | 1.37873 | 0.0466362 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.09406 | −0.239686 | ||||||||
\(877\) | −10.0352 | −0.338863 | −0.169432 | − | 0.985542i | \(-0.554193\pi\) | ||||
−0.169432 | + | 0.985542i | \(0.554193\pi\) | |||||||
\(878\) | 5.89724 | 0.199022 | ||||||||
\(879\) | 0.916696 | 0.0309194 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.4908 | −1.02726 | −0.513630 | − | 0.858012i | \(-0.671700\pi\) | ||||
−0.513630 | + | 0.858012i | \(0.671700\pi\) | |||||||
\(882\) | 0.965534 | 0.0325112 | ||||||||
\(883\) | 45.8663 | 1.54352 | 0.771762 | − | 0.635912i | \(-0.219376\pi\) | ||||
0.771762 | + | 0.635912i | \(0.219376\pi\) | |||||||
\(884\) | −14.3456 | −0.482496 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.84890 | 0.162902 | ||||||||
\(887\) | −19.4561 | −0.653272 | −0.326636 | − | 0.945150i | \(-0.605915\pi\) | ||||
−0.326636 | + | 0.945150i | \(0.605915\pi\) | |||||||
\(888\) | 7.06551 | 0.237103 | ||||||||
\(889\) | 31.1132 | 1.04350 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.28622 | −0.110093 | ||||||||
\(892\) | 31.2391 | 1.04596 | ||||||||
\(893\) | −8.00627 | −0.267920 | ||||||||
\(894\) | −8.03959 | −0.268884 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 26.9018 | 0.898725 | ||||||||
\(897\) | −5.52057 | −0.184327 | ||||||||
\(898\) | −5.61396 | −0.187340 | ||||||||
\(899\) | −49.8321 | −1.66199 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.622093 | 0.0207249 | ||||||||
\(902\) | −8.68717 | −0.289251 | ||||||||
\(903\) | −9.90882 | −0.329745 | ||||||||
\(904\) | 18.8977 | 0.628527 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.56189 | −0.251227 | ||||||||
\(907\) | 18.5957 | 0.617460 | 0.308730 | − | 0.951150i | \(-0.400096\pi\) | ||||
0.308730 | + | 0.951150i | \(0.400096\pi\) | |||||||
\(908\) | −34.4769 | −1.14416 | ||||||||
\(909\) | −15.4153 | −0.511292 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 60.0890 | 1.99084 | 0.995419 | − | 0.0956059i | \(-0.0304788\pi\) | ||||
0.995419 | + | 0.0956059i | \(0.0304788\pi\) | |||||||
\(912\) | 14.0309 | 0.464609 | ||||||||
\(913\) | 58.1645 | 1.92496 | ||||||||
\(914\) | 7.29905 | 0.241431 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.3859 | −0.739650 | ||||||||
\(917\) | 16.5874 | 0.547765 | ||||||||
\(918\) | −2.44827 | −0.0808050 | ||||||||
\(919\) | 54.4741 | 1.79693 | 0.898467 | − | 0.439040i | \(-0.144682\pi\) | ||||
0.898467 | + | 0.439040i | \(0.144682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0772 | 0.991076 | ||||||||
\(922\) | −2.23971 | −0.0737610 | ||||||||
\(923\) | 21.1449 | 0.695992 | ||||||||
\(924\) | −33.2187 | −1.09281 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.85950 | 0.291141 | ||||||||
\(927\) | −12.1277 | −0.398327 | ||||||||
\(928\) | 26.6186 | 0.873799 | ||||||||
\(929\) | 16.3989 | 0.538030 | 0.269015 | − | 0.963136i | \(-0.413302\pi\) | ||||
0.269015 | + | 0.963136i | \(0.413302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.08568 | −0.199450 | ||||||||
\(932\) | −8.41863 | −0.275761 | ||||||||
\(933\) | −0.938043 | −0.0307102 | ||||||||
\(934\) | 2.58183 | 0.0844800 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.1938 | −0.431252 | ||||||||
\(937\) | 37.0074 | 1.20898 | 0.604490 | − | 0.796613i | \(-0.293377\pi\) | ||||
0.604490 | + | 0.796613i | \(0.293377\pi\) | |||||||
\(938\) | −13.3072 | −0.434496 | ||||||||
\(939\) | −24.5612 | −0.801524 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6164 | −0.704674 | −0.352337 | − | 0.935873i | \(-0.614613\pi\) | ||||
−0.352337 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(942\) | 5.23501 | 0.170566 | ||||||||
\(943\) | −4.53855 | −0.147795 | ||||||||
\(944\) | 28.2675 | 0.920029 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.42438 | 0.208875 | ||||||||
\(947\) | −42.1072 | −1.36830 | −0.684151 | − | 0.729341i | \(-0.739827\pi\) | ||||
−0.684151 | + | 0.729341i | \(0.739827\pi\) | |||||||
\(948\) | −15.7133 | −0.510344 | ||||||||
\(949\) | −19.1533 | −0.621743 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.60645 | −0.116947 | ||||||||
\(952\) | 5.45229 | 0.176710 | ||||||||
\(953\) | 46.7030 | 1.51286 | 0.756429 | − | 0.654075i | \(-0.226942\pi\) | ||||
0.756429 | + | 0.654075i | \(0.226942\pi\) | |||||||
\(954\) | 0.277911 | 0.00899770 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33.1983 | 1.07371 | ||||||||
\(957\) | −43.3378 | −1.40091 | ||||||||
\(958\) | 13.3385 | 0.430948 | ||||||||
\(959\) | −6.98268 | −0.225482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1176 | 0.552180 | ||||||||
\(962\) | 9.26603 | 0.298749 | ||||||||
\(963\) | 9.60762 | 0.309601 | ||||||||
\(964\) | −1.88906 | −0.0608427 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.01917 | 0.0327911 | ||||||||
\(967\) | 6.24268 | 0.200751 | 0.100376 | − | 0.994950i | \(-0.467996\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(968\) | 30.0908 | 0.967154 | ||||||||
\(969\) | 6.05399 | 0.194482 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.7115 | 0.985579 | 0.492789 | − | 0.870149i | \(-0.335977\pi\) | ||||
0.492789 | + | 0.870149i | \(0.335977\pi\) | |||||||
\(972\) | 29.9423 | 0.960400 | ||||||||
\(973\) | 46.3228 | 1.48504 | ||||||||
\(974\) | 3.49506 | 0.111989 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9659 | 0.351011 | ||||||||
\(977\) | 0.0525151 | 0.00168011 | 0.000840054 | − | 1.00000i | \(-0.499733\pi\) | ||||
0.000840054 | 1.00000i | \(0.499733\pi\) | ||||||||
\(978\) | 0.360563 | 0.0115295 | ||||||||
\(979\) | 41.2630 | 1.31877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.1356 | 0.706736 | ||||||||
\(982\) | −9.67283 | −0.308672 | ||||||||
\(983\) | 4.00915 | 0.127872 | 0.0639360 | − | 0.997954i | \(-0.479635\pi\) | ||||
0.0639360 | + | 0.997954i | \(0.479635\pi\) | |||||||
\(984\) | 5.95420 | 0.189813 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.45514 | 0.110034 | ||||||||
\(987\) | −5.91829 | −0.188381 | ||||||||
\(988\) | 40.3935 | 1.28509 | ||||||||
\(989\) | 3.35637 | 0.106726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5335 | −0.684035 | −0.342017 | − | 0.939694i | \(-0.611110\pi\) | ||||
−0.342017 | + | 0.939694i | \(0.611110\pi\) | |||||||
\(992\) | −25.7028 | −0.816065 | ||||||||
\(993\) | 2.48634 | 0.0789017 | ||||||||
\(994\) | −3.90361 | −0.123815 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.3645 | −0.613586 | ||||||||
\(997\) | −29.3420 | −0.929271 | −0.464635 | − | 0.885502i | \(-0.653815\pi\) | ||||
−0.464635 | + | 0.885502i | \(0.653815\pi\) | |||||||
\(998\) | 3.27131 | 0.103552 | ||||||||
\(999\) | −26.9283 | −0.851975 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6025.2.a.m.1.20 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.n.1.21 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.20 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.n.1.21 | yes | 40 | 5.4 | even | 2 |