Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4507648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.20475\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.656184 | 0.463992 | 0.231996 | − | 0.972717i | \(-0.425474\pi\) | ||||
0.231996 | + | 0.972717i | \(0.425474\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.56942 | −0.784711 | ||||||||
\(5\) | −1.35996 | −0.608194 | −0.304097 | − | 0.952641i | \(-0.598355\pi\) | ||||
−0.304097 | + | 0.952641i | \(0.598355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.34220 | −0.828092 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.892385 | −0.282197 | ||||||||
\(11\) | 1.90551 | 0.574534 | 0.287267 | − | 0.957851i | \(-0.407253\pi\) | ||||
0.287267 | + | 0.957851i | \(0.407253\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.60193 | 0.400483 | ||||||||
\(17\) | 3.56633 | 0.864963 | 0.432482 | − | 0.901643i | \(-0.357638\pi\) | ||||
0.432482 | + | 0.901643i | \(0.357638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.985255 | −0.226033 | −0.113016 | − | 0.993593i | \(-0.536051\pi\) | ||||
−0.113016 | + | 0.993593i | \(0.536051\pi\) | |||||||
\(20\) | 2.13436 | 0.477256 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.25037 | 0.266579 | ||||||||
\(23\) | −1.69605 | −0.353651 | −0.176826 | − | 0.984242i | \(-0.556583\pi\) | ||||
−0.176826 | + | 0.984242i | \(0.556583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.15050 | −0.630100 | ||||||||
\(26\) | −0.656184 | −0.128688 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.54835 | −1.21600 | −0.607999 | − | 0.793938i | \(-0.708028\pi\) | ||||
−0.607999 | + | 0.793938i | \(0.708028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.69550 | −1.38215 | −0.691077 | − | 0.722781i | \(-0.742863\pi\) | ||||
−0.691077 | + | 0.722781i | \(0.742863\pi\) | |||||||
\(32\) | 5.73556 | 1.01391 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.34017 | 0.401336 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.02005 | −0.332095 | −0.166047 | − | 0.986118i | \(-0.553100\pi\) | ||||
−0.166047 | + | 0.986118i | \(0.553100\pi\) | |||||||
\(38\) | −0.646508 | −0.104877 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.18530 | 0.503640 | ||||||||
\(41\) | 9.88779 | 1.54421 | 0.772107 | − | 0.635493i | \(-0.219203\pi\) | ||||
0.772107 | + | 0.635493i | \(0.219203\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.16639 | −0.482869 | −0.241435 | − | 0.970417i | \(-0.577618\pi\) | ||||
−0.241435 | + | 0.970417i | \(0.577618\pi\) | |||||||
\(44\) | −2.99055 | −0.450843 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.11292 | −0.164091 | ||||||||
\(47\) | 7.76416 | 1.13252 | 0.566260 | − | 0.824227i | \(-0.308390\pi\) | ||||
0.566260 | + | 0.824227i | \(0.308390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.06731 | −0.292362 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.56942 | 0.217640 | ||||||||
\(53\) | −0.354194 | −0.0486522 | −0.0243261 | − | 0.999704i | \(-0.507744\pi\) | ||||
−0.0243261 | + | 0.999704i | \(0.507744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.59143 | −0.349428 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.29692 | −0.564214 | ||||||||
\(59\) | 2.16385 | 0.281709 | 0.140854 | − | 0.990030i | \(-0.455015\pi\) | ||||
0.140854 | + | 0.990030i | \(0.455015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2002 | −1.56207 | −0.781037 | − | 0.624484i | \(-0.785309\pi\) | ||||
−0.781037 | + | 0.624484i | \(0.785309\pi\) | |||||||
\(62\) | −5.04967 | −0.641308 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.559715 | 0.0699644 | ||||||||
\(65\) | 1.35996 | 0.168683 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3134 | 1.38215 | 0.691076 | − | 0.722782i | \(-0.257137\pi\) | ||||
0.691076 | + | 0.722782i | \(0.257137\pi\) | |||||||
\(68\) | −5.59709 | −0.678746 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.05268 | 1.07436 | 0.537178 | − | 0.843469i | \(-0.319490\pi\) | ||||
0.537178 | + | 0.843469i | \(0.319490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.13619 | 0.835228 | 0.417614 | − | 0.908625i | \(-0.362866\pi\) | ||||
0.417614 | + | 0.908625i | \(0.362866\pi\) | |||||||
\(74\) | −1.32553 | −0.154089 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.54628 | 0.177371 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.39629 | −0.607130 | −0.303565 | − | 0.952811i | \(-0.598177\pi\) | ||||
−0.303565 | + | 0.952811i | \(0.598177\pi\) | |||||||
\(80\) | −2.17857 | −0.243571 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.48821 | 0.716503 | ||||||||
\(83\) | −2.03494 | −0.223364 | −0.111682 | − | 0.993744i | \(-0.535624\pi\) | ||||
−0.111682 | + | 0.993744i | \(0.535624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.85008 | −0.526065 | ||||||||
\(86\) | −2.07773 | −0.224048 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.46309 | −0.475767 | ||||||||
\(89\) | −6.89864 | −0.731254 | −0.365627 | − | 0.930761i | \(-0.619145\pi\) | ||||
−0.365627 | + | 0.930761i | \(0.619145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.66182 | 0.277514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.09472 | 0.525480 | ||||||||
\(95\) | 1.33991 | 0.137472 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6223 | 1.48467 | 0.742334 | − | 0.670030i | \(-0.233719\pi\) | ||||
0.742334 | + | 0.670030i | \(0.233719\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.94447 | 0.494447 | ||||||||
\(101\) | 2.81368 | 0.279972 | 0.139986 | − | 0.990153i | \(-0.455294\pi\) | ||||
0.139986 | + | 0.990153i | \(0.455294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.04988 | −0.596112 | −0.298056 | − | 0.954548i | \(-0.596338\pi\) | ||||
−0.298056 | + | 0.954548i | \(0.596338\pi\) | |||||||
\(104\) | 2.34220 | 0.229671 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.232416 | −0.0225743 | ||||||||
\(107\) | −17.3204 | −1.67442 | −0.837211 | − | 0.546880i | \(-0.815815\pi\) | ||||
−0.837211 | + | 0.546880i | \(0.815815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5762 | 1.01302 | 0.506509 | − | 0.862234i | \(-0.330936\pi\) | ||||
0.506509 | + | 0.862234i | \(0.330936\pi\) | |||||||
\(110\) | −1.70045 | −0.162132 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.34665 | 0.220755 | 0.110377 | − | 0.993890i | \(-0.464794\pi\) | ||||
0.110377 | + | 0.993890i | \(0.464794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.30657 | 0.215089 | ||||||||
\(116\) | 10.2771 | 0.954208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.41988 | 0.130711 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.36902 | −0.669911 | ||||||||
\(122\) | −8.00557 | −0.724790 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0775 | 1.08459 | ||||||||
\(125\) | 11.0844 | 0.991417 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1639 | −1.61179 | −0.805894 | − | 0.592060i | \(-0.798315\pi\) | ||||
−0.805894 | + | 0.592060i | \(0.798315\pi\) | |||||||
\(128\) | −11.1038 | −0.981450 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.892385 | 0.0782674 | ||||||||
\(131\) | 10.1014 | 0.882560 | 0.441280 | − | 0.897369i | \(-0.354524\pi\) | ||||
0.441280 | + | 0.897369i | \(0.354524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.42367 | 0.641308 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.35306 | −0.716269 | ||||||||
\(137\) | −6.55601 | −0.560118 | −0.280059 | − | 0.959983i | \(-0.590354\pi\) | ||||
−0.280059 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8243 | 1.17256 | 0.586281 | − | 0.810108i | \(-0.300591\pi\) | ||||
0.586281 | + | 0.810108i | \(0.300591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.94023 | 0.498493 | ||||||||
\(143\) | −1.90551 | −0.159347 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.90551 | 0.739563 | ||||||||
\(146\) | 4.68265 | 0.387539 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.17032 | 0.260598 | ||||||||
\(149\) | −8.09389 | −0.663078 | −0.331539 | − | 0.943442i | \(-0.607568\pi\) | ||||
−0.331539 | + | 0.943442i | \(0.607568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0365 | 0.979520 | 0.489760 | − | 0.871857i | \(-0.337084\pi\) | ||||
0.489760 | + | 0.871857i | \(0.337084\pi\) | |||||||
\(152\) | 2.30766 | 0.187176 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.4656 | 0.840617 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3935 | 1.46796 | 0.733982 | − | 0.679169i | \(-0.237660\pi\) | ||||
0.733982 | + | 0.679169i | \(0.237660\pi\) | |||||||
\(158\) | −3.54096 | −0.281704 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.80014 | −0.616655 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.51286 | 0.196823 | 0.0984114 | − | 0.995146i | \(-0.468624\pi\) | ||||
0.0984114 | + | 0.995146i | \(0.468624\pi\) | |||||||
\(164\) | −15.5181 | −1.21176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.33530 | −0.103639 | ||||||||
\(167\) | 17.9095 | 1.38588 | 0.692941 | − | 0.720995i | \(-0.256315\pi\) | ||||
0.692941 | + | 0.720995i | \(0.256315\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.18254 | −0.244090 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.96940 | 0.378913 | ||||||||
\(173\) | 6.51981 | 0.495692 | 0.247846 | − | 0.968799i | \(-0.420277\pi\) | ||||
0.247846 | + | 0.968799i | \(0.420277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.05250 | 0.230091 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.52678 | −0.339296 | ||||||||
\(179\) | 26.6014 | 1.98828 | 0.994141 | − | 0.108091i | \(-0.0344738\pi\) | ||||
0.994141 | + | 0.108091i | \(0.0344738\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6402 | 1.83149 | 0.915746 | − | 0.401758i | \(-0.131601\pi\) | ||||
0.915746 | + | 0.401758i | \(0.131601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.97249 | 0.292856 | ||||||||
\(185\) | 2.74720 | 0.201978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.79569 | 0.496950 | ||||||||
\(188\) | −12.1853 | −0.888701 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.879227 | 0.0637858 | ||||||||
\(191\) | −3.02099 | −0.218591 | −0.109295 | − | 0.994009i | \(-0.534859\pi\) | ||||
−0.109295 | + | 0.994009i | \(0.534859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2522 | 1.52977 | 0.764884 | − | 0.644168i | \(-0.222796\pi\) | ||||
0.764884 | + | 0.644168i | \(0.222796\pi\) | |||||||
\(194\) | 9.59491 | 0.688874 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.72191 | 0.193928 | 0.0969639 | − | 0.995288i | \(-0.469087\pi\) | ||||
0.0969639 | + | 0.995288i | \(0.469087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6670 | 1.53593 | 0.767967 | − | 0.640490i | \(-0.221269\pi\) | ||||
0.767967 | + | 0.640490i | \(0.221269\pi\) | |||||||
\(200\) | 7.37910 | 0.521781 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.84629 | 0.129905 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4470 | −0.939181 | ||||||||
\(206\) | −3.96983 | −0.276591 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.60193 | −0.111074 | ||||||||
\(209\) | −1.87741 | −0.129864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3885 | 1.26592 | 0.632959 | − | 0.774186i | \(-0.281840\pi\) | ||||
0.632959 | + | 0.774186i | \(0.281840\pi\) | |||||||
\(212\) | 0.555879 | 0.0381780 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.3653 | −0.776918 | ||||||||
\(215\) | 4.30617 | 0.293678 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.93995 | 0.470033 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.06704 | 0.274200 | ||||||||
\(221\) | −3.56633 | −0.239898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.2216 | −1.48807 | −0.744035 | − | 0.668141i | \(-0.767090\pi\) | ||||
−0.744035 | + | 0.668141i | \(0.767090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.53984 | 0.102428 | ||||||||
\(227\) | 26.7374 | 1.77463 | 0.887313 | − | 0.461167i | \(-0.152569\pi\) | ||||
0.887313 | + | 0.461167i | \(0.152569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7008 | 1.10362 | 0.551809 | − | 0.833970i | \(-0.313938\pi\) | ||||
0.551809 | + | 0.833970i | \(0.313938\pi\) | |||||||
\(230\) | 1.51353 | 0.0997994 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.3375 | 1.00696 | ||||||||
\(233\) | 13.8776 | 0.909149 | 0.454575 | − | 0.890709i | \(-0.349791\pi\) | ||||
0.454575 | + | 0.890709i | \(0.349791\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5590 | −0.688791 | ||||||||
\(236\) | −3.39599 | −0.221060 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.465845 | −0.0301330 | −0.0150665 | − | 0.999886i | \(-0.504796\pi\) | ||||
−0.0150665 | + | 0.999886i | \(0.504796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.69314 | −0.366727 | −0.183364 | − | 0.983045i | \(-0.558699\pi\) | ||||
−0.183364 | + | 0.983045i | \(0.558699\pi\) | |||||||
\(242\) | −4.83543 | −0.310833 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.1473 | 1.22578 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.985255 | 0.0626902 | ||||||||
\(248\) | 18.0244 | 1.14455 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.27339 | 0.460010 | ||||||||
\(251\) | 17.9066 | 1.13025 | 0.565126 | − | 0.825005i | \(-0.308828\pi\) | ||||
0.565126 | + | 0.825005i | \(0.308828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.23185 | −0.203185 | ||||||||
\(254\) | −11.9189 | −0.747857 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.40559 | −0.525350 | ||||||||
\(257\) | 25.9756 | 1.62031 | 0.810156 | − | 0.586214i | \(-0.199382\pi\) | ||||
0.810156 | + | 0.586214i | \(0.199382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.13436 | −0.132367 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.62835 | 0.409501 | ||||||||
\(263\) | −27.8402 | −1.71670 | −0.858349 | − | 0.513067i | \(-0.828509\pi\) | ||||
−0.858349 | + | 0.513067i | \(0.828509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.481690 | 0.0295900 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.7555 | −1.08459 | ||||||||
\(269\) | 5.90486 | 0.360025 | 0.180013 | − | 0.983664i | \(-0.442386\pi\) | ||||
0.180013 | + | 0.983664i | \(0.442386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.34932 | 0.264203 | 0.132101 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132101 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(272\) | 5.71303 | 0.346403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.30195 | −0.259890 | ||||||||
\(275\) | −6.00332 | −0.362014 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08051 | 0.0649217 | 0.0324609 | − | 0.999473i | \(-0.489666\pi\) | ||||
0.0324609 | + | 0.999473i | \(0.489666\pi\) | |||||||
\(278\) | 9.07129 | 0.544060 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4912 | −0.864473 | −0.432236 | − | 0.901760i | \(-0.642275\pi\) | ||||
−0.432236 | + | 0.901760i | \(0.642275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.4979 | −1.45625 | −0.728123 | − | 0.685446i | \(-0.759607\pi\) | ||||
−0.728123 | + | 0.685446i | \(0.759607\pi\) | |||||||
\(284\) | −14.2075 | −0.843059 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.25037 | −0.0739357 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.28126 | −0.251839 | ||||||||
\(290\) | 5.84365 | 0.343151 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1997 | −0.655413 | ||||||||
\(293\) | 1.16105 | 0.0678296 | 0.0339148 | − | 0.999425i | \(-0.489203\pi\) | ||||
0.0339148 | + | 0.999425i | \(0.489203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.94275 | −0.171334 | ||||||||
\(296\) | 4.73136 | 0.275005 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.31108 | −0.307663 | ||||||||
\(299\) | 1.69605 | 0.0980852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.89818 | 0.454489 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.57831 | −0.0905224 | ||||||||
\(305\) | 16.5918 | 0.950044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.3731 | −1.44812 | −0.724060 | − | 0.689737i | \(-0.757726\pi\) | ||||
−0.724060 | + | 0.689737i | \(0.757726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.86736 | 0.390040 | ||||||||
\(311\) | 24.4645 | 1.38726 | 0.693628 | − | 0.720333i | \(-0.256011\pi\) | ||||
0.693628 | + | 0.720333i | \(0.256011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.61665 | −0.373995 | −0.186997 | − | 0.982360i | \(-0.559876\pi\) | ||||
−0.186997 | + | 0.982360i | \(0.559876\pi\) | |||||||
\(314\) | 12.0695 | 0.681124 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.46906 | 0.476422 | ||||||||
\(317\) | −8.19803 | −0.460447 | −0.230224 | − | 0.973138i | \(-0.573946\pi\) | ||||
−0.230224 | + | 0.973138i | \(0.573946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.4780 | −0.698632 | ||||||||
\(320\) | −0.761192 | −0.0425519 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.51375 | −0.195510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.15050 | 0.174758 | ||||||||
\(326\) | 1.64890 | 0.0913242 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −23.1592 | −1.27875 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.724715 | −0.0398339 | −0.0199170 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199170 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(332\) | 3.19369 | 0.175276 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.7519 | 0.643038 | ||||||||
\(335\) | −15.3858 | −0.840616 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.58299 | −0.467545 | −0.233773 | − | 0.972291i | \(-0.575107\pi\) | ||||
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(338\) | 0.656184 | 0.0356917 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.61183 | 0.412809 | ||||||||
\(341\) | −14.6639 | −0.794094 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.41630 | 0.399860 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.27820 | 0.229997 | ||||||||
\(347\) | 25.9250 | 1.39173 | 0.695864 | − | 0.718173i | \(-0.255021\pi\) | ||||
0.695864 | + | 0.718173i | \(0.255021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1403 | −0.917501 | −0.458750 | − | 0.888565i | \(-0.651703\pi\) | ||||
−0.458750 | + | 0.888565i | \(0.651703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9292 | 0.582527 | ||||||||
\(353\) | −18.9101 | −1.00648 | −0.503242 | − | 0.864146i | \(-0.667860\pi\) | ||||
−0.503242 | + | 0.864146i | \(0.667860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3113 | −0.653417 | ||||||||
\(356\) | 10.8269 | 0.573823 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4554 | 0.922547 | ||||||||
\(359\) | −14.1049 | −0.744431 | −0.372215 | − | 0.928146i | \(-0.621402\pi\) | ||||
−0.372215 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0293 | −0.948909 | ||||||||
\(362\) | 16.1685 | 0.849798 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.70495 | −0.507980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.360258 | −0.0188053 | −0.00940266 | − | 0.999956i | \(-0.502993\pi\) | ||||
−0.00940266 | + | 0.999956i | \(0.502993\pi\) | |||||||
\(368\) | −2.71696 | −0.141631 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.80267 | 0.0937162 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.1680 | −1.30315 | −0.651575 | − | 0.758584i | \(-0.725892\pi\) | ||||
−0.651575 | + | 0.758584i | \(0.725892\pi\) | |||||||
\(374\) | 4.45923 | 0.230581 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.1852 | −0.937830 | ||||||||
\(377\) | 6.54835 | 0.337257 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8947 | 1.63832 | 0.819161 | − | 0.573564i | \(-0.194440\pi\) | ||||
0.819161 | + | 0.573564i | \(0.194440\pi\) | |||||||
\(380\) | −2.10288 | −0.107876 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.98232 | −0.101424 | ||||||||
\(383\) | 32.8172 | 1.67688 | 0.838440 | − | 0.544994i | \(-0.183468\pi\) | ||||
0.838440 | + | 0.544994i | \(0.183468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.9454 | 0.709800 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.9486 | −1.16504 | ||||||||
\(389\) | 25.3087 | 1.28320 | 0.641600 | − | 0.767040i | \(-0.278271\pi\) | ||||
0.641600 | + | 0.767040i | \(0.278271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.04869 | −0.305895 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.78607 | 0.0899810 | ||||||||
\(395\) | 7.33875 | 0.369253 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.29395 | 0.265696 | 0.132848 | − | 0.991136i | \(-0.457588\pi\) | ||||
0.132848 | + | 0.991136i | \(0.457588\pi\) | |||||||
\(398\) | 14.2175 | 0.712661 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.04689 | −0.252345 | ||||||||
\(401\) | 24.6335 | 1.23014 | 0.615070 | − | 0.788473i | \(-0.289128\pi\) | ||||
0.615070 | + | 0.788473i | \(0.289128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.69550 | 0.383340 | ||||||||
\(404\) | −4.41586 | −0.219697 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.84924 | −0.190800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2223 | −0.505458 | −0.252729 | − | 0.967537i | \(-0.581328\pi\) | ||||
−0.252729 | + | 0.967537i | \(0.581328\pi\) | |||||||
\(410\) | −8.82372 | −0.435773 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.49481 | 0.467776 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.76745 | 0.135849 | ||||||||
\(416\) | −5.73556 | −0.281209 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.23193 | −0.0602556 | ||||||||
\(419\) | 30.6503 | 1.49736 | 0.748682 | − | 0.662929i | \(-0.230687\pi\) | ||||
0.748682 | + | 0.662929i | \(0.230687\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.9764 | 1.26601 | 0.633007 | − | 0.774146i | \(-0.281820\pi\) | ||||
0.633007 | + | 0.774146i | \(0.281820\pi\) | |||||||
\(422\) | 12.0662 | 0.587376 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.829592 | 0.0402885 | ||||||||
\(425\) | −11.2357 | −0.545014 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 27.1830 | 1.31394 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.82564 | 0.136264 | ||||||||
\(431\) | −14.8818 | −0.716829 | −0.358415 | − | 0.933563i | \(-0.616683\pi\) | ||||
−0.358415 | + | 0.933563i | \(0.616683\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.0871 | 1.92647 | 0.963233 | − | 0.268669i | \(-0.0865837\pi\) | ||||
0.963233 | + | 0.268669i | \(0.0865837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.5986 | −0.794927 | ||||||||
\(437\) | 1.67104 | 0.0799368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00243 | 0.143298 | 0.0716491 | − | 0.997430i | \(-0.477174\pi\) | ||||
0.0716491 | + | 0.997430i | \(0.477174\pi\) | |||||||
\(440\) | 6.06963 | 0.289358 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.34017 | −0.111311 | ||||||||
\(443\) | −1.43566 | −0.0682101 | −0.0341051 | − | 0.999418i | \(-0.510858\pi\) | ||||
−0.0341051 | + | 0.999418i | \(0.510858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.38189 | 0.444744 | ||||||||
\(446\) | −14.5815 | −0.690453 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.6313 | −0.926460 | −0.463230 | − | 0.886238i | \(-0.653310\pi\) | ||||
−0.463230 | + | 0.886238i | \(0.653310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.8413 | 0.887203 | ||||||||
\(452\) | −3.68289 | −0.173229 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.5447 | 0.823413 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.6421 | 0.497815 | 0.248907 | − | 0.968527i | \(-0.419929\pi\) | ||||
0.248907 | + | 0.968527i | \(0.419929\pi\) | |||||||
\(458\) | 10.9588 | 0.512070 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.61998 | −0.168782 | ||||||||
\(461\) | −38.5930 | −1.79745 | −0.898727 | − | 0.438509i | \(-0.855507\pi\) | ||||
−0.898727 | + | 0.438509i | \(0.855507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.9993 | −1.30124 | −0.650618 | − | 0.759405i | \(-0.725490\pi\) | ||||
−0.650618 | + | 0.759405i | \(0.725490\pi\) | |||||||
\(464\) | −10.4900 | −0.486987 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.10623 | 0.421838 | ||||||||
\(467\) | −25.8199 | −1.19480 | −0.597401 | − | 0.801943i | \(-0.703800\pi\) | ||||
−0.597401 | + | 0.801943i | \(0.703800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.92862 | −0.319594 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.06816 | −0.233281 | ||||||||
\(473\) | −6.03359 | −0.277425 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.10405 | 0.142423 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.305680 | −0.0139815 | ||||||||
\(479\) | −39.4071 | −1.80055 | −0.900277 | − | 0.435317i | \(-0.856636\pi\) | ||||
−0.900277 | + | 0.435317i | \(0.856636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.02005 | 0.0921065 | ||||||||
\(482\) | −3.73575 | −0.170159 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5651 | 0.525687 | ||||||||
\(485\) | −19.8858 | −0.902966 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.0959 | −1.54503 | −0.772517 | − | 0.634994i | \(-0.781003\pi\) | ||||
−0.772517 | + | 0.634994i | \(0.781003\pi\) | |||||||
\(488\) | 28.5753 | 1.29354 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.70414 | 0.437942 | 0.218971 | − | 0.975731i | \(-0.429730\pi\) | ||||
0.218971 | + | 0.975731i | \(0.429730\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3536 | −1.05179 | ||||||||
\(494\) | 0.646508 | 0.0290878 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.3277 | −0.553529 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0463 | 0.807862 | 0.403931 | − | 0.914789i | \(-0.367644\pi\) | ||||
0.403931 | + | 0.914789i | \(0.367644\pi\) | |||||||
\(500\) | −17.3961 | −0.777976 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.7500 | 0.524428 | ||||||||
\(503\) | 16.4922 | 0.735352 | 0.367676 | − | 0.929954i | \(-0.380154\pi\) | ||||
0.367676 | + | 0.929954i | \(0.380154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.82650 | −0.170277 | ||||||||
\(506\) | −2.12069 | −0.0942761 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.5069 | 1.26479 | ||||||||
\(509\) | −19.1977 | −0.850921 | −0.425460 | − | 0.904977i | \(-0.639888\pi\) | ||||
−0.425460 | + | 0.904977i | \(0.639888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.6921 | 0.737692 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0448 | 0.751812 | ||||||||
\(515\) | 8.22760 | 0.362552 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7947 | 0.650670 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.18530 | −0.139685 | ||||||||
\(521\) | −8.76034 | −0.383797 | −0.191899 | − | 0.981415i | \(-0.561465\pi\) | ||||
−0.191899 | + | 0.981415i | \(0.561465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7406 | 0.513381 | 0.256690 | − | 0.966494i | \(-0.417368\pi\) | ||||
0.256690 | + | 0.966494i | \(0.417368\pi\) | |||||||
\(524\) | −15.8533 | −0.692555 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.2683 | −0.796534 | ||||||||
\(527\) | −27.4447 | −1.19551 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1234 | −0.874931 | ||||||||
\(530\) | 0.316077 | 0.0137295 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.88779 | −0.428288 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.5550 | 1.01837 | ||||||||
\(536\) | −26.4982 | −1.14455 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.87467 | 0.167049 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4587 | 0.707614 | 0.353807 | − | 0.935318i | \(-0.384887\pi\) | ||||
0.353807 | + | 0.935318i | \(0.384887\pi\) | |||||||
\(542\) | 2.85396 | 0.122588 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.4549 | 0.876997 | ||||||||
\(545\) | −14.3833 | −0.616112 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.19375 | −0.350339 | −0.175170 | − | 0.984538i | \(-0.556047\pi\) | ||||
−0.175170 | + | 0.984538i | \(0.556047\pi\) | |||||||
\(548\) | 10.2891 | 0.439531 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.93928 | −0.167972 | ||||||||
\(551\) | 6.45179 | 0.274856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.709015 | 0.0301232 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.6962 | −0.920123 | ||||||||
\(557\) | 13.8144 | 0.585335 | 0.292667 | − | 0.956214i | \(-0.405457\pi\) | ||||
0.292667 | + | 0.956214i | \(0.405457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.16639 | 0.133924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.50889 | −0.401108 | ||||||||
\(563\) | 9.75559 | 0.411149 | 0.205575 | − | 0.978641i | \(-0.434094\pi\) | ||||
0.205575 | + | 0.978641i | \(0.434094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.19136 | −0.134262 | ||||||||
\(566\) | −16.0751 | −0.675687 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.2032 | −0.889666 | ||||||||
\(569\) | 1.43264 | 0.0600593 | 0.0300296 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300296 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2872 | 0.681598 | 0.340799 | − | 0.940136i | \(-0.389303\pi\) | ||||
0.340799 | + | 0.940136i | \(0.389303\pi\) | |||||||
\(572\) | 2.99055 | 0.125041 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.34342 | 0.222836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.81846 | 0.200595 | 0.100297 | − | 0.994957i | \(-0.468021\pi\) | ||||
0.100297 | + | 0.994957i | \(0.468021\pi\) | |||||||
\(578\) | −2.80929 | −0.116851 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.9765 | −0.580343 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.674920 | −0.0279523 | ||||||||
\(584\) | −16.7144 | −0.691645 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.761866 | 0.0314724 | ||||||||
\(587\) | 36.6215 | 1.51153 | 0.755765 | − | 0.654843i | \(-0.227265\pi\) | ||||
0.755765 | + | 0.654843i | \(0.227265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.58203 | 0.312412 | ||||||||
\(590\) | −1.93099 | −0.0794974 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.23599 | −0.132998 | ||||||||
\(593\) | −18.7081 | −0.768251 | −0.384125 | − | 0.923281i | \(-0.625497\pi\) | ||||
−0.384125 | + | 0.923281i | \(0.625497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.7027 | 0.520325 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.11292 | 0.0455108 | ||||||||
\(599\) | 25.4194 | 1.03861 | 0.519305 | − | 0.854589i | \(-0.326191\pi\) | ||||
0.519305 | + | 0.854589i | \(0.326191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7790 | −0.725219 | −0.362609 | − | 0.931941i | \(-0.618114\pi\) | ||||
−0.362609 | + | 0.931941i | \(0.618114\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.8904 | −0.768640 | ||||||||
\(605\) | 10.0216 | 0.407436 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.0047 | −1.05550 | −0.527750 | − | 0.849400i | \(-0.676964\pi\) | ||||
−0.527750 | + | 0.849400i | \(0.676964\pi\) | |||||||
\(608\) | −5.65098 | −0.229178 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.8873 | 0.440813 | ||||||||
\(611\) | −7.76416 | −0.314104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.8230 | 1.08337 | 0.541685 | − | 0.840582i | \(-0.317787\pi\) | ||||
0.541685 | + | 0.840582i | \(0.317787\pi\) | |||||||
\(614\) | −16.6494 | −0.671916 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.6491 | 0.750784 | 0.375392 | − | 0.926866i | \(-0.377508\pi\) | ||||
0.375392 | + | 0.926866i | \(0.377508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0685 | −0.525269 | −0.262634 | − | 0.964895i | \(-0.584591\pi\) | ||||
−0.262634 | + | 0.964895i | \(0.584591\pi\) | |||||||
\(620\) | −16.4249 | −0.659642 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.0532 | 0.643676 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.678175 | 0.0271270 | ||||||||
\(626\) | −4.34174 | −0.173531 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.8672 | −1.15193 | ||||||||
\(629\) | −7.20418 | −0.287250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.1745 | −1.95761 | −0.978804 | − | 0.204801i | \(-0.934345\pi\) | ||||
−0.978804 | + | 0.204801i | \(0.934345\pi\) | |||||||
\(632\) | 12.6392 | 0.502760 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.37941 | −0.213644 | ||||||||
\(635\) | 24.7023 | 0.980279 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.18784 | −0.324160 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.1008 | 0.596912 | ||||||||
\(641\) | −4.37503 | −0.172803 | −0.0864016 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864016 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.34651 | 0.210846 | 0.105423 | − | 0.994427i | \(-0.466380\pi\) | ||||
0.105423 | + | 0.994427i | \(0.466380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.30566 | −0.0907151 | ||||||||
\(647\) | −29.7346 | −1.16899 | −0.584493 | − | 0.811398i | \(-0.698707\pi\) | ||||
−0.584493 | + | 0.811398i | \(0.698707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.12324 | 0.161851 | ||||||||
\(650\) | 2.06731 | 0.0810865 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.94375 | −0.154449 | ||||||||
\(653\) | 2.54262 | 0.0995005 | 0.0497503 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497503 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.7375 | −0.536768 | ||||||||
\(656\) | 15.8396 | 0.618432 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.87019 | −0.0728523 | −0.0364261 | − | 0.999336i | \(-0.511597\pi\) | ||||
−0.0364261 | + | 0.999336i | \(0.511597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0763 | 0.469714 | 0.234857 | − | 0.972030i | \(-0.424538\pi\) | ||||
0.234857 | + | 0.972030i | \(0.424538\pi\) | |||||||
\(662\) | −0.475546 | −0.0184826 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.76624 | 0.184966 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1063 | 0.430040 | ||||||||
\(668\) | −28.1076 | −1.08752 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0959 | −0.390039 | ||||||||
\(671\) | −23.2476 | −0.897464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.81691 | −0.301320 | −0.150660 | − | 0.988586i | \(-0.548140\pi\) | ||||
−0.150660 | + | 0.988586i | \(0.548140\pi\) | |||||||
\(674\) | −5.63202 | −0.216937 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.56942 | −0.0603624 | ||||||||
\(677\) | 6.25628 | 0.240448 | 0.120224 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120224 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.3598 | 0.435630 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.62220 | −0.368453 | ||||||||
\(683\) | −22.3656 | −0.855795 | −0.427898 | − | 0.903827i | \(-0.640746\pi\) | ||||
−0.427898 | + | 0.903827i | \(0.640746\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.91593 | 0.340660 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.07234 | −0.193381 | ||||||||
\(689\) | 0.354194 | 0.0134937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.80771 | 0.144852 | 0.0724260 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724260 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(692\) | −10.2323 | −0.388975 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.0116 | 0.645751 | ||||||||
\(695\) | −18.8005 | −0.713145 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.2632 | 1.33569 | ||||||||
\(698\) | −11.2472 | −0.425713 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.14218 | 0.307526 | 0.153763 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153763 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.99027 | 0.0750643 | ||||||||
\(704\) | 1.06654 | 0.0401969 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.4085 | −0.467001 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0319 | −0.902536 | −0.451268 | − | 0.892388i | \(-0.649028\pi\) | ||||
−0.451268 | + | 0.892388i | \(0.649028\pi\) | |||||||
\(710\) | −8.07848 | −0.303180 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.1580 | 0.605546 | ||||||||
\(713\) | 13.0520 | 0.488800 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.59143 | 0.0969138 | ||||||||
\(716\) | −41.7488 | −1.56023 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.25544 | −0.345410 | ||||||||
\(719\) | −32.6960 | −1.21936 | −0.609678 | − | 0.792649i | \(-0.708701\pi\) | ||||
−0.609678 | + | 0.792649i | \(0.708701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.8305 | −0.440286 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.6709 | −1.43719 | ||||||||
\(725\) | 20.6306 | 0.766201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7712 | 0.584921 | 0.292460 | − | 0.956278i | \(-0.405526\pi\) | ||||
0.292460 | + | 0.956278i | \(0.405526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.36823 | −0.235699 | ||||||||
\(731\) | −11.2924 | −0.417664 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5094 | −0.868340 | −0.434170 | − | 0.900831i | \(-0.642958\pi\) | ||||
−0.434170 | + | 0.900831i | \(0.642958\pi\) | |||||||
\(734\) | −0.236396 | −0.00872552 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.72781 | −0.358572 | ||||||||
\(737\) | 21.5578 | 0.794093 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.5267 | −0.828658 | −0.414329 | − | 0.910127i | \(-0.635984\pi\) | ||||
−0.414329 | + | 0.910127i | \(0.635984\pi\) | |||||||
\(740\) | −4.31151 | −0.158494 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9795 | 0.512857 | 0.256429 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256429 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.0074 | 0.403280 | ||||||||
\(746\) | −16.5149 | −0.604652 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.6653 | −0.389963 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.54591 | 0.0929017 | 0.0464509 | − | 0.998921i | \(-0.485209\pi\) | ||||
0.0464509 | + | 0.998921i | \(0.485209\pi\) | |||||||
\(752\) | 12.4377 | 0.453555 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.29692 | 0.156485 | ||||||||
\(755\) | −16.3692 | −0.595738 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6921 | 0.715721 | 0.357861 | − | 0.933775i | \(-0.383506\pi\) | ||||
0.357861 | + | 0.933775i | \(0.383506\pi\) | |||||||
\(758\) | 20.9288 | 0.760168 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.13833 | −0.113839 | ||||||||
\(761\) | −39.0905 | −1.41703 | −0.708515 | − | 0.705696i | \(-0.750635\pi\) | ||||
−0.708515 | + | 0.705696i | \(0.750635\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.74120 | 0.171531 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5341 | 0.778059 | ||||||||
\(767\) | −2.16385 | −0.0781320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7389 | 0.783926 | 0.391963 | − | 0.919981i | \(-0.371796\pi\) | ||||
0.391963 | + | 0.919981i | \(0.371796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −33.3537 | −1.20043 | ||||||||
\(773\) | 4.12806 | 0.148476 | 0.0742381 | − | 0.997241i | \(-0.476348\pi\) | ||||
0.0742381 | + | 0.997241i | \(0.476348\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.2447 | 0.870895 | ||||||||
\(776\) | −34.2483 | −1.22944 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.6071 | 0.595395 | ||||||||
\(779\) | −9.74199 | −0.349043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2500 | 0.617254 | ||||||||
\(782\) | −3.96905 | −0.141933 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.0145 | −0.892807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.7863 | −1.38258 | −0.691291 | − | 0.722576i | \(-0.742958\pi\) | ||||
−0.691291 | + | 0.722576i | \(0.742958\pi\) | |||||||
\(788\) | −4.27182 | −0.152177 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.81557 | 0.171330 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2002 | 0.433242 | ||||||||
\(794\) | 3.47381 | 0.123281 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.0047 | −1.20526 | ||||||||
\(797\) | 19.9651 | 0.707201 | 0.353601 | − | 0.935397i | \(-0.384957\pi\) | ||||
0.353601 | + | 0.935397i | \(0.384957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.6896 | 0.979587 | ||||||||
\(800\) | −18.0699 | −0.638867 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.1641 | 0.570775 | ||||||||
\(803\) | 13.5981 | 0.479866 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.04967 | 0.177867 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.59020 | −0.231842 | ||||||||
\(809\) | 30.2441 | 1.06332 | 0.531662 | − | 0.846956i | \(-0.321568\pi\) | ||||
0.531662 | + | 0.846956i | \(0.321568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.4099 | −0.822034 | −0.411017 | − | 0.911628i | \(-0.634826\pi\) | ||||
−0.411017 | + | 0.911628i | \(0.634826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.52581 | −0.0885295 | ||||||||
\(815\) | −3.41740 | −0.119706 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.11970 | 0.109144 | ||||||||
\(818\) | −6.70768 | −0.234528 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.1041 | 0.736986 | ||||||||
\(821\) | 46.5536 | 1.62473 | 0.812366 | − | 0.583147i | \(-0.198179\pi\) | ||||
0.812366 | + | 0.583147i | \(0.198179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.68031 | −0.198003 | −0.0990017 | − | 0.995087i | \(-0.531565\pi\) | ||||
−0.0990017 | + | 0.995087i | \(0.531565\pi\) | |||||||
\(824\) | 14.1700 | 0.493636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.3198 | −1.68024 | −0.840122 | − | 0.542398i | \(-0.817517\pi\) | ||||
−0.840122 | + | 0.542398i | \(0.817517\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.8545 | 0.411722 | 0.205861 | − | 0.978581i | \(-0.434000\pi\) | ||||
0.205861 | + | 0.978581i | \(0.434000\pi\) | |||||||
\(830\) | 1.81595 | 0.0630327 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.559715 | −0.0194046 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.3563 | −0.842884 | ||||||||
\(836\) | 2.94646 | 0.101905 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.1122 | 0.694765 | ||||||||
\(839\) | −2.69386 | −0.0930025 | −0.0465013 | − | 0.998918i | \(-0.514807\pi\) | ||||
−0.0465013 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8809 | 0.478652 | ||||||||
\(842\) | 17.0453 | 0.587420 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.8593 | −0.993380 | ||||||||
\(845\) | −1.35996 | −0.0467841 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.567394 | −0.0194844 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.37271 | −0.252882 | ||||||||
\(851\) | 3.42612 | 0.117446 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.48965 | 0.0852440 | 0.0426220 | − | 0.999091i | \(-0.486429\pi\) | ||||
0.0426220 | + | 0.999091i | \(0.486429\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40.5677 | 1.38658 | ||||||||
\(857\) | 46.2110 | 1.57854 | 0.789270 | − | 0.614047i | \(-0.210459\pi\) | ||||
0.789270 | + | 0.614047i | \(0.210459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9170 | 0.372482 | 0.186241 | − | 0.982504i | \(-0.440369\pi\) | ||||
0.186241 | + | 0.982504i | \(0.440369\pi\) | |||||||
\(860\) | −6.75820 | −0.230453 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.76517 | −0.332603 | ||||||||
\(863\) | 29.2330 | 0.995104 | 0.497552 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497552 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.86670 | −0.301477 | ||||||||
\(866\) | 26.3045 | 0.893865 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2827 | −0.348817 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3134 | −0.383340 | ||||||||
\(872\) | −24.7716 | −0.838873 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.09651 | 0.0370901 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.38110 | −0.249242 | −0.124621 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124621 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(878\) | 1.97015 | 0.0664892 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.15129 | −0.139940 | ||||||||
\(881\) | 16.4854 | 0.555407 | 0.277703 | − | 0.960667i | \(-0.410427\pi\) | ||||
0.277703 | + | 0.960667i | \(0.410427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.4427 | 0.418732 | 0.209366 | − | 0.977837i | \(-0.432860\pi\) | ||||
0.209366 | + | 0.977837i | \(0.432860\pi\) | |||||||
\(884\) | 5.59709 | 0.188250 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.942055 | −0.0316490 | ||||||||
\(887\) | −8.11331 | −0.272418 | −0.136209 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136209 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.15624 | 0.206358 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 34.8751 | 1.16771 | ||||||||
\(893\) | −7.64968 | −0.255987 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.1769 | −1.20926 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8818 | −0.429870 | ||||||||
\(899\) | 50.3929 | 1.68070 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26317 | −0.0420824 | ||||||||
\(902\) | 12.3634 | 0.411655 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.49633 | −0.182805 | ||||||||
\(905\) | −33.5098 | −1.11390 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.4796 | −0.613605 | −0.306803 | − | 0.951773i | \(-0.599259\pi\) | ||||
−0.306803 | + | 0.951773i | \(0.599259\pi\) | |||||||
\(908\) | −41.9623 | −1.39257 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8660 | −0.525663 | −0.262831 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262831 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.87761 | −0.128330 | ||||||||
\(914\) | 6.98315 | 0.230982 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.2106 | −0.866022 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4568 | 1.43351 | 0.716753 | − | 0.697327i | \(-0.245627\pi\) | ||||
0.716753 | + | 0.697327i | \(0.245627\pi\) | |||||||
\(920\) | −5.40244 | −0.178113 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.3241 | −0.834004 | ||||||||
\(923\) | −9.05268 | −0.297973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.36418 | 0.209253 | ||||||||
\(926\) | −18.3727 | −0.603763 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37.5585 | −1.23292 | ||||||||
\(929\) | −25.6312 | −0.840931 | −0.420465 | − | 0.907309i | \(-0.638133\pi\) | ||||
−0.420465 | + | 0.907309i | \(0.638133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.7798 | −0.713420 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.9426 | −0.554379 | ||||||||
\(935\) | −9.24189 | −0.302242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9639 | −0.782867 | −0.391433 | − | 0.920206i | \(-0.628021\pi\) | ||||
−0.391433 | + | 0.920206i | \(0.628021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.5715 | 0.540502 | ||||||||
\(941\) | −42.2934 | −1.37872 | −0.689362 | − | 0.724417i | \(-0.742109\pi\) | ||||
−0.689362 | + | 0.724417i | \(0.742109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7702 | −0.546113 | ||||||||
\(944\) | 3.46634 | 0.112820 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.95914 | −0.128723 | ||||||||
\(947\) | 49.5957 | 1.61165 | 0.805823 | − | 0.592157i | \(-0.201723\pi\) | ||||
0.805823 | + | 0.592157i | \(0.201723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.13619 | −0.231650 | ||||||||
\(950\) | 2.03683 | 0.0660833 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.7156 | −0.606259 | −0.303129 | − | 0.952949i | \(-0.598031\pi\) | ||||
−0.303129 | + | 0.952949i | \(0.598031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.10843 | 0.132946 | ||||||||
\(956\) | 0.731107 | 0.0236457 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.8583 | −0.835443 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2208 | 0.910348 | ||||||||
\(962\) | 1.32553 | 0.0427367 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.93494 | 0.287775 | ||||||||
\(965\) | −28.9022 | −0.930395 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.3284 | −1.10393 | −0.551964 | − | 0.833868i | \(-0.686121\pi\) | ||||
−0.551964 | + | 0.833868i | \(0.686121\pi\) | |||||||
\(968\) | 17.2597 | 0.554748 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.0487 | −0.418969 | ||||||||
\(971\) | 56.7118 | 1.81997 | 0.909984 | − | 0.414642i | \(-0.136093\pi\) | ||||
0.909984 | + | 0.414642i | \(0.136093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.3732 | −0.716884 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.5439 | −0.625585 | ||||||||
\(977\) | 39.8809 | 1.27590 | 0.637951 | − | 0.770077i | \(-0.279782\pi\) | ||||
0.637951 | + | 0.770077i | \(0.279782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.1454 | −0.420130 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.36770 | 0.203201 | ||||||||
\(983\) | 41.2678 | 1.31624 | 0.658120 | − | 0.752913i | \(-0.271352\pi\) | ||||
0.658120 | + | 0.752913i | \(0.271352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.70169 | −0.117946 | ||||||||
\(986\) | −15.3243 | −0.488024 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.54628 | −0.0491937 | ||||||||
\(989\) | 5.37036 | 0.170767 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1784 | −0.831583 | −0.415792 | − | 0.909460i | \(-0.636495\pi\) | ||||
−0.415792 | + | 0.909460i | \(0.636495\pi\) | |||||||
\(992\) | −44.1380 | −1.40138 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.4663 | −0.934145 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.62009 | −0.273001 | −0.136501 | − | 0.990640i | \(-0.543586\pi\) | ||||
−0.136501 | + | 0.990640i | \(0.543586\pi\) | |||||||
\(998\) | 11.8417 | 0.374842 | ||||||||
\(999\) | 0 | 0 |
(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 | 5733.2.a.bu.1.4 | 6 | ||
3.2 | odd | 2 | 637.2.a.m.1.3 | ✓ | 6 | ||
7.6 | odd | 2 | 5733.2.a.br.1.4 | 6 | |||
21.2 | odd | 6 | 637.2.e.o.508.4 | 12 | |||
21.5 | even | 6 | 637.2.e.n.508.4 | 12 | |||
21.11 | odd | 6 | 637.2.e.o.79.4 | 12 | |||
21.17 | even | 6 | 637.2.e.n.79.4 | 12 | |||
21.20 | even | 2 | 637.2.a.n.1.3 | yes | 6 | ||
39.38 | odd | 2 | 8281.2.a.cc.1.4 | 6 | |||
273.272 | even | 2 | 8281.2.a.cd.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.m.1.3 | ✓ | 6 | 3.2 | odd | 2 | ||
637.2.a.n.1.3 | yes | 6 | 21.20 | even | 2 | ||
637.2.e.n.79.4 | 12 | 21.17 | even | 6 | |||
637.2.e.n.508.4 | 12 | 21.5 | even | 6 | |||
637.2.e.o.79.4 | 12 | 21.11 | odd | 6 | |||
637.2.e.o.508.4 | 12 | 21.2 | odd | 6 | |||
5733.2.a.br.1.4 | 6 | 7.6 | odd | 2 | |||
5733.2.a.bu.1.4 | 6 | 1.1 | even | 1 | trivial | ||
8281.2.a.cc.1.4 | 6 | 39.38 | odd | 2 | |||
8281.2.a.cd.1.4 | 6 | 273.272 | even | 2 |