Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(1,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, 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("950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.91223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.25561 | 1.30228 | 0.651138 | − | 0.758959i | \(-0.274292\pi\) | ||||
0.651138 | + | 0.758959i | \(0.274292\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.25561 | 0.920848 | ||||||||
\(7\) | 4.22547 | 1.59708 | 0.798539 | − | 0.601943i | \(-0.205607\pi\) | ||||
0.798539 | + | 0.601943i | \(0.205607\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.08777 | 0.695924 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.13770 | −1.54907 | −0.774537 | − | 0.632528i | \(-0.782017\pi\) | ||||
−0.774537 | + | 0.632528i | \(0.782017\pi\) | |||||||
\(12\) | 2.25561 | 0.651138 | ||||||||
\(13\) | 3.16784 | 0.878600 | 0.439300 | − | 0.898340i | \(-0.355226\pi\) | ||||
0.439300 | + | 0.898340i | \(0.355226\pi\) | |||||||
\(14\) | 4.22547 | 1.12930 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.48108 | −1.57189 | −0.785946 | − | 0.618295i | \(-0.787824\pi\) | ||||
−0.785946 | + | 0.618295i | \(0.787824\pi\) | |||||||
\(18\) | 2.08777 | 0.492092 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.53101 | 2.07984 | ||||||||
\(22\) | −5.13770 | −1.09536 | ||||||||
\(23\) | 7.56885 | 1.57821 | 0.789107 | − | 0.614256i | \(-0.210544\pi\) | ||||
0.789107 | + | 0.614256i | \(0.210544\pi\) | |||||||
\(24\) | 2.25561 | 0.460424 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.16784 | 0.621264 | ||||||||
\(27\) | −2.05763 | −0.395991 | ||||||||
\(28\) | 4.22547 | 0.798539 | ||||||||
\(29\) | 0.832162 | 0.154529 | 0.0772643 | − | 0.997011i | \(-0.475381\pi\) | ||||
0.0772643 | + | 0.997011i | \(0.475381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.51122 | −0.810239 | −0.405119 | − | 0.914264i | \(-0.632770\pi\) | ||||
−0.405119 | + | 0.914264i | \(0.632770\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −11.5886 | −2.01732 | ||||||||
\(34\) | −6.48108 | −1.11150 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.08777 | 0.347962 | ||||||||
\(37\) | 0.137699 | 0.0226376 | 0.0113188 | − | 0.999936i | \(-0.496397\pi\) | ||||
0.0113188 | + | 0.999936i | \(0.496397\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 7.14540 | 1.14418 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6489 | −1.81926 | −0.909628 | − | 0.415425i | \(-0.863633\pi\) | ||||
−0.909628 | + | 0.415425i | \(0.863633\pi\) | |||||||
\(42\) | 9.53101 | 1.47067 | ||||||||
\(43\) | −2.51122 | −0.382957 | −0.191479 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191479 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(44\) | −5.13770 | −0.774537 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.56885 | 1.11597 | ||||||||
\(47\) | −5.96216 | −0.869670 | −0.434835 | − | 0.900510i | \(-0.643193\pi\) | ||||
−0.434835 | + | 0.900510i | \(0.643193\pi\) | |||||||
\(48\) | 2.25561 | 0.325569 | ||||||||
\(49\) | 10.8546 | 1.55066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.6188 | −2.04704 | ||||||||
\(52\) | 3.16784 | 0.439300 | ||||||||
\(53\) | 0.225470 | 0.0309707 | 0.0154853 | − | 0.999880i | \(-0.495071\pi\) | ||||
0.0154853 | + | 0.999880i | \(0.495071\pi\) | |||||||
\(54\) | −2.05763 | −0.280008 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.22547 | 0.564652 | ||||||||
\(57\) | −2.25561 | −0.298763 | ||||||||
\(58\) | 0.832162 | 0.109268 | ||||||||
\(59\) | 5.39331 | 0.702149 | 0.351074 | − | 0.936348i | \(-0.385816\pi\) | ||||
0.351074 | + | 0.936348i | \(0.385816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4509 | 1.85025 | 0.925127 | − | 0.379659i | \(-0.123959\pi\) | ||||
0.925127 | + | 0.379659i | \(0.123959\pi\) | |||||||
\(62\) | −4.51122 | −0.572925 | ||||||||
\(63\) | 8.82181 | 1.11144 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.5886 | −1.42646 | ||||||||
\(67\) | −4.11021 | −0.502142 | −0.251071 | − | 0.967969i | \(-0.580783\pi\) | ||||
−0.251071 | + | 0.967969i | \(0.580783\pi\) | |||||||
\(68\) | −6.48108 | −0.785946 | ||||||||
\(69\) | 17.0724 | 2.05527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.82446 | 0.453880 | 0.226940 | − | 0.973909i | \(-0.427128\pi\) | ||||
0.226940 | + | 0.973909i | \(0.427128\pi\) | |||||||
\(72\) | 2.08777 | 0.246046 | ||||||||
\(73\) | 4.70655 | 0.550860 | 0.275430 | − | 0.961321i | \(-0.411180\pi\) | ||||
0.275430 | + | 0.961321i | \(0.411180\pi\) | |||||||
\(74\) | 0.137699 | 0.0160072 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −21.7092 | −2.47399 | ||||||||
\(78\) | 7.14540 | 0.809058 | ||||||||
\(79\) | 10.6265 | 1.19557 | 0.597786 | − | 0.801655i | \(-0.296047\pi\) | ||||
0.597786 | + | 0.801655i | \(0.296047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9045 | −1.21161 | ||||||||
\(82\) | −11.6489 | −1.28641 | ||||||||
\(83\) | −12.0999 | −1.32813 | −0.664066 | − | 0.747674i | \(-0.731171\pi\) | ||||
−0.664066 | + | 0.747674i | \(0.731171\pi\) | |||||||
\(84\) | 9.53101 | 1.03992 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.51122 | −0.270792 | ||||||||
\(87\) | 1.87703 | 0.201239 | ||||||||
\(88\) | −5.13770 | −0.547681 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3856 | 1.40319 | ||||||||
\(92\) | 7.56885 | 0.789107 | ||||||||
\(93\) | −10.1755 | −1.05515 | ||||||||
\(94\) | −5.96216 | −0.614950 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.25561 | 0.230212 | ||||||||
\(97\) | 3.93972 | 0.400018 | 0.200009 | − | 0.979794i | \(-0.435903\pi\) | ||||
0.200009 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(98\) | 10.8546 | 1.09648 | ||||||||
\(99\) | −10.7263 | −1.07804 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.19798 | 0.318211 | 0.159105 | − | 0.987262i | \(-0.449139\pi\) | ||||
0.159105 | + | 0.987262i | \(0.449139\pi\) | |||||||
\(102\) | −14.6188 | −1.44747 | ||||||||
\(103\) | −10.6868 | −1.05300 | −0.526499 | − | 0.850176i | \(-0.676496\pi\) | ||||
−0.526499 | + | 0.850176i | \(0.676496\pi\) | |||||||
\(104\) | 3.16784 | 0.310632 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.225470 | 0.0218996 | ||||||||
\(107\) | 10.8168 | 1.04570 | 0.522848 | − | 0.852426i | \(-0.324870\pi\) | ||||
0.522848 | + | 0.852426i | \(0.324870\pi\) | |||||||
\(108\) | −2.05763 | −0.197996 | ||||||||
\(109\) | 9.24791 | 0.885789 | 0.442894 | − | 0.896574i | \(-0.353952\pi\) | ||||
0.442894 | + | 0.896574i | \(0.353952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.310596 | 0.0294804 | ||||||||
\(112\) | 4.22547 | 0.399269 | ||||||||
\(113\) | 17.6489 | 1.66027 | 0.830135 | − | 0.557562i | \(-0.188263\pi\) | ||||
0.830135 | + | 0.557562i | \(0.188263\pi\) | |||||||
\(114\) | −2.25561 | −0.211257 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.832162 | 0.0772643 | ||||||||
\(117\) | 6.61372 | 0.611439 | ||||||||
\(118\) | 5.39331 | 0.496494 | ||||||||
\(119\) | −27.3856 | −2.51043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3960 | 1.39963 | ||||||||
\(122\) | 14.4509 | 1.30833 | ||||||||
\(123\) | −26.2754 | −2.36917 | ||||||||
\(124\) | −4.51122 | −0.405119 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.82181 | 0.785910 | ||||||||
\(127\) | −12.7866 | −1.13463 | −0.567314 | − | 0.823501i | \(-0.692018\pi\) | ||||
−0.567314 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.66432 | −0.498716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.11526 | −0.184811 | −0.0924057 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924057 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(132\) | −11.5886 | −1.00866 | ||||||||
\(133\) | −4.22547 | −0.366395 | ||||||||
\(134\) | −4.11021 | −0.355068 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.48108 | −0.555748 | ||||||||
\(137\) | −5.36317 | −0.458206 | −0.229103 | − | 0.973402i | \(-0.573579\pi\) | ||||
−0.229103 | + | 0.973402i | \(0.573579\pi\) | |||||||
\(138\) | 17.0724 | 1.45330 | ||||||||
\(139\) | −10.1601 | −0.861771 | −0.430886 | − | 0.902407i | \(-0.641799\pi\) | ||||
−0.430886 | + | 0.902407i | \(0.641799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.4483 | −1.13255 | ||||||||
\(142\) | 3.82446 | 0.320941 | ||||||||
\(143\) | −16.2754 | −1.36102 | ||||||||
\(144\) | 2.08777 | 0.173981 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.70655 | 0.389517 | ||||||||
\(147\) | 24.4837 | 2.01938 | ||||||||
\(148\) | 0.137699 | 0.0113188 | ||||||||
\(149\) | −5.93972 | −0.486601 | −0.243301 | − | 0.969951i | \(-0.578230\pi\) | ||||
−0.243301 | + | 0.969951i | \(0.578230\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2978 | −1.24492 | −0.622460 | − | 0.782652i | \(-0.713867\pi\) | ||||
−0.622460 | + | 0.782652i | \(0.713867\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −13.5310 | −1.09392 | ||||||||
\(154\) | −21.7092 | −1.74938 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.14540 | 0.572090 | ||||||||
\(157\) | −12.7866 | −1.02048 | −0.510242 | − | 0.860031i | \(-0.670444\pi\) | ||||
−0.510242 | + | 0.860031i | \(0.670444\pi\) | |||||||
\(158\) | 10.6265 | 0.845397 | ||||||||
\(159\) | 0.508572 | 0.0403324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.9819 | 2.52053 | ||||||||
\(162\) | −10.9045 | −0.856740 | ||||||||
\(163\) | −11.4734 | −0.898664 | −0.449332 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449332 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(164\) | −11.6489 | −0.909628 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0999 | −0.939131 | ||||||||
\(167\) | 19.4131 | 1.50223 | 0.751115 | − | 0.660171i | \(-0.229516\pi\) | ||||
0.751115 | + | 0.660171i | \(0.229516\pi\) | |||||||
\(168\) | 9.53101 | 0.735333 | ||||||||
\(169\) | −2.96480 | −0.228062 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.08777 | −0.159656 | ||||||||
\(172\) | −2.51122 | −0.191479 | ||||||||
\(173\) | 9.78662 | 0.744063 | 0.372031 | − | 0.928220i | \(-0.378661\pi\) | ||||
0.372031 | + | 0.928220i | \(0.378661\pi\) | |||||||
\(174\) | 1.87703 | 0.142297 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.13770 | −0.387269 | ||||||||
\(177\) | 12.1652 | 0.914392 | ||||||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | −6.82446 | −0.510084 | −0.255042 | − | 0.966930i | \(-0.582089\pi\) | ||||
−0.255042 | + | 0.966930i | \(0.582089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.137699 | −0.0102351 | −0.00511755 | − | 0.999987i | \(-0.501629\pi\) | ||||
−0.00511755 | + | 0.999987i | \(0.501629\pi\) | |||||||
\(182\) | 13.3856 | 0.992207 | ||||||||
\(183\) | 32.5957 | 2.40954 | ||||||||
\(184\) | 7.56885 | 0.557983 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.1755 | −0.746107 | ||||||||
\(187\) | 33.2978 | 2.43498 | ||||||||
\(188\) | −5.96216 | −0.434835 | ||||||||
\(189\) | −8.69446 | −0.632429 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3779 | 1.40214 | 0.701068 | − | 0.713095i | \(-0.252707\pi\) | ||||
0.701068 | + | 0.713095i | \(0.252707\pi\) | |||||||
\(192\) | 2.25561 | 0.162785 | ||||||||
\(193\) | −5.42851 | −0.390752 | −0.195376 | − | 0.980728i | \(-0.562593\pi\) | ||||
−0.195376 | + | 0.980728i | \(0.562593\pi\) | |||||||
\(194\) | 3.93972 | 0.282856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.8546 | 0.775328 | ||||||||
\(197\) | −15.6489 | −1.11494 | −0.557470 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557470 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(198\) | −10.7263 | −0.762288 | ||||||||
\(199\) | 18.0499 | 1.27953 | 0.639763 | − | 0.768572i | \(-0.279033\pi\) | ||||
0.639763 | + | 0.768572i | \(0.279033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.27102 | −0.653927 | ||||||||
\(202\) | 3.19798 | 0.225009 | ||||||||
\(203\) | 3.51628 | 0.246794 | ||||||||
\(204\) | −14.6188 | −1.02352 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.6868 | −0.744582 | ||||||||
\(207\) | 15.8020 | 1.09832 | ||||||||
\(208\) | 3.16784 | 0.219650 | ||||||||
\(209\) | 5.13770 | 0.355382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50857 | −0.516911 | −0.258456 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258456 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(212\) | 0.225470 | 0.0154853 | ||||||||
\(213\) | 8.62648 | 0.591077 | ||||||||
\(214\) | 10.8168 | 0.739418 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.05763 | −0.140004 | ||||||||
\(217\) | −19.0620 | −1.29401 | ||||||||
\(218\) | 9.24791 | 0.626347 | ||||||||
\(219\) | 10.6161 | 0.717372 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.5310 | −1.38106 | ||||||||
\(222\) | 0.310596 | 0.0208458 | ||||||||
\(223\) | 27.8091 | 1.86223 | 0.931116 | − | 0.364723i | \(-0.118836\pi\) | ||||
0.931116 | + | 0.364723i | \(0.118836\pi\) | |||||||
\(224\) | 4.22547 | 0.282326 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.6489 | 1.17399 | ||||||||
\(227\) | 8.91223 | 0.591525 | 0.295763 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295763 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(228\) | −2.25561 | −0.149381 | ||||||||
\(229\) | −13.6489 | −0.901946 | −0.450973 | − | 0.892538i | \(-0.648923\pi\) | ||||
−0.450973 | + | 0.892538i | \(0.648923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −48.9674 | −3.22182 | ||||||||
\(232\) | 0.832162 | 0.0546341 | ||||||||
\(233\) | 23.2754 | 1.52482 | 0.762411 | − | 0.647093i | \(-0.224015\pi\) | ||||
0.762411 | + | 0.647093i | \(0.224015\pi\) | |||||||
\(234\) | 6.61372 | 0.432352 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.39331 | 0.351074 | ||||||||
\(237\) | 23.9692 | 1.55697 | ||||||||
\(238\) | −27.3856 | −1.77515 | ||||||||
\(239\) | 3.72898 | 0.241208 | 0.120604 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120604 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.48878 | −0.0959009 | −0.0479505 | − | 0.998850i | \(-0.515269\pi\) | ||||
−0.0479505 | + | 0.998850i | \(0.515269\pi\) | |||||||
\(242\) | 15.3960 | 0.989689 | ||||||||
\(243\) | −18.4234 | −1.18186 | ||||||||
\(244\) | 14.4509 | 0.925127 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.2754 | −1.67526 | ||||||||
\(247\) | −3.16784 | −0.201565 | ||||||||
\(248\) | −4.51122 | −0.286463 | ||||||||
\(249\) | −27.2925 | −1.72959 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.78662 | −0.554606 | −0.277303 | − | 0.960782i | \(-0.589441\pi\) | ||||
−0.277303 | + | 0.960782i | \(0.589441\pi\) | |||||||
\(252\) | 8.82181 | 0.555722 | ||||||||
\(253\) | −38.8865 | −2.44477 | ||||||||
\(254\) | −12.7866 | −0.802304 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.74175 | 0.171025 | 0.0855127 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855127 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(258\) | −5.66432 | −0.352645 | ||||||||
\(259\) | 0.581844 | 0.0361540 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.73736 | 0.107540 | ||||||||
\(262\) | −2.11526 | −0.130681 | ||||||||
\(263\) | 2.74704 | 0.169390 | 0.0846948 | − | 0.996407i | \(-0.473008\pi\) | ||||
0.0846948 | + | 0.996407i | \(0.473008\pi\) | |||||||
\(264\) | −11.5886 | −0.713231 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.22547 | −0.259080 | ||||||||
\(267\) | −22.5561 | −1.38041 | ||||||||
\(268\) | −4.11021 | −0.251071 | ||||||||
\(269\) | −9.74175 | −0.593965 | −0.296982 | − | 0.954883i | \(-0.595980\pi\) | ||||
−0.296982 | + | 0.954883i | \(0.595980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.3555 | 1.60098 | 0.800490 | − | 0.599346i | \(-0.204573\pi\) | ||||
0.800490 | + | 0.599346i | \(0.204573\pi\) | |||||||
\(272\) | −6.48108 | −0.392973 | ||||||||
\(273\) | 30.1927 | 1.82734 | ||||||||
\(274\) | −5.36317 | −0.324001 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.0724 | 1.02764 | ||||||||
\(277\) | −0.962158 | −0.0578104 | −0.0289052 | − | 0.999582i | \(-0.509202\pi\) | ||||
−0.0289052 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(278\) | −10.1601 | −0.609364 | ||||||||
\(279\) | −9.41839 | −0.563864 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6714 | −0.875219 | −0.437610 | − | 0.899165i | \(-0.644175\pi\) | ||||
−0.437610 | + | 0.899165i | \(0.644175\pi\) | |||||||
\(282\) | −13.4483 | −0.800834 | ||||||||
\(283\) | −26.1601 | −1.55506 | −0.777529 | − | 0.628847i | \(-0.783527\pi\) | ||||
−0.777529 | + | 0.628847i | \(0.783527\pi\) | |||||||
\(284\) | 3.82446 | 0.226940 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.2754 | −0.962384 | ||||||||
\(287\) | −49.2221 | −2.90549 | ||||||||
\(288\) | 2.08777 | 0.123023 | ||||||||
\(289\) | 25.0044 | 1.47085 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.88647 | 0.520934 | ||||||||
\(292\) | 4.70655 | 0.275430 | ||||||||
\(293\) | −22.4657 | −1.31246 | −0.656229 | − | 0.754562i | \(-0.727850\pi\) | ||||
−0.656229 | + | 0.754562i | \(0.727850\pi\) | |||||||
\(294\) | 24.4837 | 1.42792 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.137699 | 0.00800360 | ||||||||
\(297\) | 10.5715 | 0.613420 | ||||||||
\(298\) | −5.93972 | −0.344079 | ||||||||
\(299\) | 23.9769 | 1.38662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6111 | −0.611612 | ||||||||
\(302\) | −15.2978 | −0.880291 | ||||||||
\(303\) | 7.21338 | 0.414398 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.5310 | −0.773516 | ||||||||
\(307\) | 17.2204 | 0.982821 | 0.491410 | − | 0.870928i | \(-0.336482\pi\) | ||||
0.491410 | + | 0.870928i | \(0.336482\pi\) | |||||||
\(308\) | −21.7092 | −1.23700 | ||||||||
\(309\) | −24.1051 | −1.37129 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.87439 | −0.446516 | −0.223258 | − | 0.974759i | \(-0.571669\pi\) | ||||
−0.223258 | + | 0.974759i | \(0.571669\pi\) | |||||||
\(312\) | 7.14540 | 0.404529 | ||||||||
\(313\) | −25.1678 | −1.42257 | −0.711285 | − | 0.702904i | \(-0.751887\pi\) | ||||
−0.711285 | + | 0.702904i | \(0.751887\pi\) | |||||||
\(314\) | −12.7866 | −0.721590 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6265 | 0.597786 | ||||||||
\(317\) | −23.9045 | −1.34261 | −0.671306 | − | 0.741180i | \(-0.734266\pi\) | ||||
−0.671306 | + | 0.741180i | \(0.734266\pi\) | |||||||
\(318\) | 0.508572 | 0.0285193 | ||||||||
\(319\) | −4.27540 | −0.239376 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.3984 | 1.36178 | ||||||||
\(322\) | 31.9819 | 1.78228 | ||||||||
\(323\) | 6.48108 | 0.360617 | ||||||||
\(324\) | −10.9045 | −0.605807 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.4734 | −0.635451 | ||||||||
\(327\) | 20.8597 | 1.15354 | ||||||||
\(328\) | −11.6489 | −0.643204 | ||||||||
\(329\) | −25.1929 | −1.38893 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.7565 | 1.69053 | 0.845264 | − | 0.534348i | \(-0.179443\pi\) | ||||
0.845264 | + | 0.534348i | \(0.179443\pi\) | |||||||
\(332\) | −12.0999 | −0.664066 | ||||||||
\(333\) | 0.287484 | 0.0157540 | ||||||||
\(334\) | 19.4131 | 1.06224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.53101 | 0.519959 | ||||||||
\(337\) | 13.4734 | 0.733942 | 0.366971 | − | 0.930232i | \(-0.380395\pi\) | ||||
0.366971 | + | 0.930232i | \(0.380395\pi\) | |||||||
\(338\) | −2.96480 | −0.161264 | ||||||||
\(339\) | 39.8091 | 2.16213 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.1773 | 1.25512 | ||||||||
\(342\) | −2.08777 | −0.112894 | ||||||||
\(343\) | 16.2875 | 0.879441 | ||||||||
\(344\) | −2.51122 | −0.135396 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.78662 | 0.526132 | ||||||||
\(347\) | 28.9468 | 1.55394 | 0.776971 | − | 0.629536i | \(-0.216755\pi\) | ||||
0.776971 | + | 0.629536i | \(0.216755\pi\) | |||||||
\(348\) | 1.87703 | 0.100619 | ||||||||
\(349\) | 27.9243 | 1.49475 | 0.747377 | − | 0.664400i | \(-0.231313\pi\) | ||||
0.747377 | + | 0.664400i | \(0.231313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.51825 | −0.347918 | ||||||||
\(352\) | −5.13770 | −0.273840 | ||||||||
\(353\) | 28.3099 | 1.50678 | 0.753392 | − | 0.657571i | \(-0.228416\pi\) | ||||
0.753392 | + | 0.657571i | \(0.228416\pi\) | |||||||
\(354\) | 12.1652 | 0.646573 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | −61.7712 | −3.26928 | ||||||||
\(358\) | −6.82446 | −0.360684 | ||||||||
\(359\) | 2.60163 | 0.137309 | 0.0686545 | − | 0.997640i | \(-0.478129\pi\) | ||||
0.0686545 | + | 0.997640i | \(0.478129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −0.137699 | −0.00723731 | ||||||||
\(363\) | 34.7272 | 1.82271 | ||||||||
\(364\) | 13.3856 | 0.701596 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 32.5957 | 1.70380 | ||||||||
\(367\) | 11.6489 | 0.608069 | 0.304034 | − | 0.952661i | \(-0.401666\pi\) | ||||
0.304034 | + | 0.952661i | \(0.401666\pi\) | |||||||
\(368\) | 7.56885 | 0.394554 | ||||||||
\(369\) | −24.3203 | −1.26606 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.952717 | 0.0494626 | ||||||||
\(372\) | −10.1755 | −0.527577 | ||||||||
\(373\) | −12.8064 | −0.663091 | −0.331545 | − | 0.943439i | \(-0.607570\pi\) | ||||
−0.331545 | + | 0.943439i | \(0.607570\pi\) | |||||||
\(374\) | 33.2978 | 1.72179 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.96216 | −0.307475 | ||||||||
\(377\) | 2.63615 | 0.135769 | ||||||||
\(378\) | −8.69446 | −0.447195 | ||||||||
\(379\) | −20.9122 | −1.07419 | −0.537095 | − | 0.843522i | \(-0.680478\pi\) | ||||
−0.537095 | + | 0.843522i | \(0.680478\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.8416 | −1.47760 | ||||||||
\(382\) | 19.3779 | 0.991460 | ||||||||
\(383\) | 10.3511 | 0.528916 | 0.264458 | − | 0.964397i | \(-0.414807\pi\) | ||||
0.264458 | + | 0.964397i | \(0.414807\pi\) | |||||||
\(384\) | 2.25561 | 0.115106 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.42851 | −0.276304 | ||||||||
\(387\) | −5.24285 | −0.266509 | ||||||||
\(388\) | 3.93972 | 0.200009 | ||||||||
\(389\) | 6.56620 | 0.332920 | 0.166460 | − | 0.986048i | \(-0.446766\pi\) | ||||
0.166460 | + | 0.986048i | \(0.446766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49.0543 | −2.48078 | ||||||||
\(392\) | 10.8546 | 0.548240 | ||||||||
\(393\) | −4.77121 | −0.240676 | ||||||||
\(394\) | −15.6489 | −0.788381 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.7263 | −0.539019 | ||||||||
\(397\) | 23.5284 | 1.18085 | 0.590427 | − | 0.807091i | \(-0.298959\pi\) | ||||
0.590427 | + | 0.807091i | \(0.298959\pi\) | |||||||
\(398\) | 18.0499 | 0.904761 | ||||||||
\(399\) | −9.53101 | −0.477147 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.22041 | 0.310633 | 0.155316 | − | 0.987865i | \(-0.450360\pi\) | ||||
0.155316 | + | 0.987865i | \(0.450360\pi\) | |||||||
\(402\) | −9.27102 | −0.462396 | ||||||||
\(403\) | −14.2908 | −0.711876 | ||||||||
\(404\) | 3.19798 | 0.159105 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.51628 | 0.174510 | ||||||||
\(407\) | −0.707457 | −0.0350674 | ||||||||
\(408\) | −14.6188 | −0.723737 | ||||||||
\(409\) | −34.4905 | −1.70545 | −0.852723 | − | 0.522363i | \(-0.825051\pi\) | ||||
−0.852723 | + | 0.522363i | \(0.825051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0972 | −0.596711 | ||||||||
\(412\) | −10.6868 | −0.526499 | ||||||||
\(413\) | 22.7893 | 1.12139 | ||||||||
\(414\) | 15.8020 | 0.776627 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.16784 | 0.155316 | ||||||||
\(417\) | −22.9173 | −1.12226 | ||||||||
\(418\) | 5.13770 | 0.251293 | ||||||||
\(419\) | −10.6265 | −0.519138 | −0.259569 | − | 0.965725i | \(-0.583580\pi\) | ||||
−0.259569 | + | 0.965725i | \(0.583580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.98021 | −0.0965095 | −0.0482548 | − | 0.998835i | \(-0.515366\pi\) | ||||
−0.0482548 | + | 0.998835i | \(0.515366\pi\) | |||||||
\(422\) | −7.50857 | −0.365512 | ||||||||
\(423\) | −12.4476 | −0.605224 | ||||||||
\(424\) | 0.225470 | 0.0109498 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.62648 | 0.417954 | ||||||||
\(427\) | 61.0620 | 2.95500 | ||||||||
\(428\) | 10.8168 | 0.522848 | ||||||||
\(429\) | −36.7109 | −1.77242 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0774 | 0.726254 | 0.363127 | − | 0.931740i | \(-0.381709\pi\) | ||||
0.363127 | + | 0.931740i | \(0.381709\pi\) | |||||||
\(432\) | −2.05763 | −0.0989979 | ||||||||
\(433\) | 13.5337 | 0.650386 | 0.325193 | − | 0.945648i | \(-0.394571\pi\) | ||||
0.325193 | + | 0.945648i | \(0.394571\pi\) | |||||||
\(434\) | −19.0620 | −0.915006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.24791 | 0.442894 | ||||||||
\(437\) | −7.56885 | −0.362067 | ||||||||
\(438\) | 10.6161 | 0.507258 | ||||||||
\(439\) | 39.1773 | 1.86983 | 0.934915 | − | 0.354872i | \(-0.115476\pi\) | ||||
0.934915 | + | 0.354872i | \(0.115476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.6619 | 1.07914 | ||||||||
\(442\) | −20.5310 | −0.976560 | ||||||||
\(443\) | 19.3132 | 0.917600 | 0.458800 | − | 0.888540i | \(-0.348279\pi\) | ||||
0.458800 | + | 0.888540i | \(0.348279\pi\) | |||||||
\(444\) | 0.310596 | 0.0147402 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.8091 | 1.31680 | ||||||||
\(447\) | −13.3977 | −0.633689 | ||||||||
\(448\) | 4.22547 | 0.199635 | ||||||||
\(449\) | 41.4131 | 1.95440 | 0.977202 | − | 0.212310i | \(-0.0680985\pi\) | ||||
0.977202 | + | 0.212310i | \(0.0680985\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 59.8486 | 2.81816 | ||||||||
\(452\) | 17.6489 | 0.830135 | ||||||||
\(453\) | −34.5059 | −1.62123 | ||||||||
\(454\) | 8.91223 | 0.418272 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.25561 | −0.105629 | ||||||||
\(457\) | −37.8392 | −1.77004 | −0.885021 | − | 0.465551i | \(-0.845856\pi\) | ||||
−0.885021 | + | 0.465551i | \(0.845856\pi\) | |||||||
\(458\) | −13.6489 | −0.637772 | ||||||||
\(459\) | 13.3357 | 0.622456 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.58864 | 0.0739903 | 0.0369952 | − | 0.999315i | \(-0.488221\pi\) | ||||
0.0369952 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(462\) | −48.9674 | −2.27817 | ||||||||
\(463\) | 40.3581 | 1.87560 | 0.937800 | − | 0.347175i | \(-0.112859\pi\) | ||||
0.937800 | + | 0.347175i | \(0.112859\pi\) | |||||||
\(464\) | 0.832162 | 0.0386322 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.2754 | 1.07821 | ||||||||
\(467\) | −39.5130 | −1.82844 | −0.914221 | − | 0.405217i | \(-0.867196\pi\) | ||||
−0.914221 | + | 0.405217i | \(0.867196\pi\) | |||||||
\(468\) | 6.61372 | 0.305719 | ||||||||
\(469\) | −17.3676 | −0.801959 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.8416 | −1.32895 | ||||||||
\(472\) | 5.39331 | 0.248247 | ||||||||
\(473\) | 12.9019 | 0.593229 | ||||||||
\(474\) | 23.9692 | 1.10094 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −27.3856 | −1.25522 | ||||||||
\(477\) | 0.470730 | 0.0215532 | ||||||||
\(478\) | 3.72898 | 0.170560 | ||||||||
\(479\) | 7.61107 | 0.347759 | 0.173879 | − | 0.984767i | \(-0.444370\pi\) | ||||
0.173879 | + | 0.984767i | \(0.444370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.436209 | 0.0198894 | ||||||||
\(482\) | −1.48878 | −0.0678122 | ||||||||
\(483\) | 72.1388 | 3.28243 | ||||||||
\(484\) | 15.3960 | 0.699816 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.4234 | −0.835705 | ||||||||
\(487\) | −20.3907 | −0.923989 | −0.461995 | − | 0.886883i | \(-0.652866\pi\) | ||||
−0.461995 | + | 0.886883i | \(0.652866\pi\) | |||||||
\(488\) | 14.4509 | 0.654163 | ||||||||
\(489\) | −25.8794 | −1.17031 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.0224 | 1.12925 | 0.564623 | − | 0.825349i | \(-0.309021\pi\) | ||||
0.564623 | + | 0.825349i | \(0.309021\pi\) | |||||||
\(492\) | −26.2754 | −1.18459 | ||||||||
\(493\) | −5.39331 | −0.242902 | ||||||||
\(494\) | −3.16784 | −0.142528 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.51122 | −0.202560 | ||||||||
\(497\) | 16.1601 | 0.724881 | ||||||||
\(498\) | −27.2925 | −1.22301 | ||||||||
\(499\) | 22.6111 | 1.01221 | 0.506105 | − | 0.862472i | \(-0.331085\pi\) | ||||
0.506105 | + | 0.862472i | \(0.331085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.7884 | 1.95632 | ||||||||
\(502\) | −8.78662 | −0.392166 | ||||||||
\(503\) | 11.5035 | 0.512916 | 0.256458 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256458 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(504\) | 8.82181 | 0.392955 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.8865 | −1.72871 | ||||||||
\(507\) | −6.68744 | −0.296999 | ||||||||
\(508\) | −12.7866 | −0.567314 | ||||||||
\(509\) | 9.11526 | 0.404027 | 0.202013 | − | 0.979383i | \(-0.435252\pi\) | ||||
0.202013 | + | 0.979383i | \(0.435252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8874 | 0.879766 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.05763 | 0.0908467 | ||||||||
\(514\) | 2.74175 | 0.120933 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.66432 | −0.249358 | ||||||||
\(517\) | 30.6318 | 1.34718 | ||||||||
\(518\) | 0.581844 | 0.0255648 | ||||||||
\(519\) | 22.0748 | 0.968975 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.4888 | 0.678576 | 0.339288 | − | 0.940683i | \(-0.389814\pi\) | ||||
0.339288 | + | 0.940683i | \(0.389814\pi\) | |||||||
\(522\) | 1.73736 | 0.0760423 | ||||||||
\(523\) | 4.34073 | 0.189807 | 0.0949035 | − | 0.995486i | \(-0.469746\pi\) | ||||
0.0949035 | + | 0.995486i | \(0.469746\pi\) | |||||||
\(524\) | −2.11526 | −0.0924057 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.74704 | 0.119776 | ||||||||
\(527\) | 29.2376 | 1.27361 | ||||||||
\(528\) | −11.5886 | −0.504331 | ||||||||
\(529\) | 34.2875 | 1.49076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2600 | 0.488642 | ||||||||
\(532\) | −4.22547 | −0.183197 | ||||||||
\(533\) | −36.9019 | −1.59840 | ||||||||
\(534\) | −22.5561 | −0.976097 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.11021 | −0.177534 | ||||||||
\(537\) | −15.3933 | −0.664270 | ||||||||
\(538\) | −9.74175 | −0.419996 | ||||||||
\(539\) | −55.7677 | −2.40208 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5491 | 0.840480 | 0.420240 | − | 0.907413i | \(-0.361946\pi\) | ||||
0.420240 | + | 0.907413i | \(0.361946\pi\) | |||||||
\(542\) | 26.3555 | 1.13206 | ||||||||
\(543\) | −0.310596 | −0.0133289 | ||||||||
\(544\) | −6.48108 | −0.277874 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.1927 | 1.29213 | ||||||||
\(547\) | −41.8038 | −1.78740 | −0.893700 | − | 0.448665i | \(-0.851900\pi\) | ||||
−0.893700 | + | 0.448665i | \(0.851900\pi\) | |||||||
\(548\) | −5.36317 | −0.229103 | ||||||||
\(549\) | 30.1703 | 1.28763 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.832162 | −0.0354513 | ||||||||
\(552\) | 17.0724 | 0.726648 | ||||||||
\(553\) | 44.9019 | 1.90942 | ||||||||
\(554\) | −0.962158 | −0.0408782 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.1601 | −0.430886 | ||||||||
\(557\) | −9.76418 | −0.413722 | −0.206861 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206861 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(558\) | −9.41839 | −0.398712 | ||||||||
\(559\) | −7.95513 | −0.336466 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 75.1069 | 3.17102 | ||||||||
\(562\) | −14.6714 | −0.618874 | ||||||||
\(563\) | 11.4509 | 0.482600 | 0.241300 | − | 0.970451i | \(-0.422426\pi\) | ||||
0.241300 | + | 0.970451i | \(0.422426\pi\) | |||||||
\(564\) | −13.4483 | −0.566275 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.1601 | −1.09959 | ||||||||
\(567\) | −46.0767 | −1.93504 | ||||||||
\(568\) | 3.82446 | 0.160471 | ||||||||
\(569\) | −13.4338 | −0.563174 | −0.281587 | − | 0.959536i | \(-0.590861\pi\) | ||||
−0.281587 | + | 0.959536i | \(0.590861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.6335 | 1.57491 | 0.787457 | − | 0.616370i | \(-0.211397\pi\) | ||||
0.787457 | + | 0.616370i | \(0.211397\pi\) | |||||||
\(572\) | −16.2754 | −0.680509 | ||||||||
\(573\) | 43.7090 | 1.82597 | ||||||||
\(574\) | −49.2221 | −2.05449 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.08777 | 0.0869905 | ||||||||
\(577\) | 1.56885 | 0.0653121 | 0.0326560 | − | 0.999467i | \(-0.489603\pi\) | ||||
0.0326560 | + | 0.999467i | \(0.489603\pi\) | |||||||
\(578\) | 25.0044 | 1.04005 | ||||||||
\(579\) | −12.2446 | −0.508868 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −51.1276 | −2.12113 | ||||||||
\(582\) | 8.88647 | 0.368356 | ||||||||
\(583\) | −1.15840 | −0.0479759 | ||||||||
\(584\) | 4.70655 | 0.194758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.4657 | −0.928048 | ||||||||
\(587\) | 25.8693 | 1.06774 | 0.533871 | − | 0.845566i | \(-0.320737\pi\) | ||||
0.533871 | + | 0.845566i | \(0.320737\pi\) | |||||||
\(588\) | 24.4837 | 1.00969 | ||||||||
\(589\) | 4.51122 | 0.185881 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.2978 | −1.45196 | ||||||||
\(592\) | 0.137699 | 0.00565940 | ||||||||
\(593\) | −28.9243 | −1.18778 | −0.593890 | − | 0.804547i | \(-0.702408\pi\) | ||||
−0.593890 | + | 0.804547i | \(0.702408\pi\) | |||||||
\(594\) | 10.5715 | 0.433754 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.93972 | −0.243301 | ||||||||
\(597\) | 40.7136 | 1.66630 | ||||||||
\(598\) | 23.9769 | 0.980488 | ||||||||
\(599\) | 41.3581 | 1.68985 | 0.844923 | − | 0.534887i | \(-0.179646\pi\) | ||||
0.844923 | + | 0.534887i | \(0.179646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.68147 | 0.109379 | 0.0546897 | − | 0.998503i | \(-0.482583\pi\) | ||||
0.0546897 | + | 0.998503i | \(0.482583\pi\) | |||||||
\(602\) | −10.6111 | −0.432475 | ||||||||
\(603\) | −8.58117 | −0.349452 | ||||||||
\(604\) | −15.2978 | −0.622460 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.21338 | 0.293024 | ||||||||
\(607\) | 3.31324 | 0.134480 | 0.0672401 | − | 0.997737i | \(-0.478581\pi\) | ||||
0.0672401 | + | 0.997737i | \(0.478581\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 7.93134 | 0.321394 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8871 | −0.764092 | ||||||||
\(612\) | −13.5310 | −0.546959 | ||||||||
\(613\) | −10.0603 | −0.406331 | −0.203165 | − | 0.979144i | \(-0.565123\pi\) | ||||
−0.203165 | + | 0.979144i | \(0.565123\pi\) | |||||||
\(614\) | 17.2204 | 0.694959 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.7092 | −0.874688 | ||||||||
\(617\) | −27.6265 | −1.11220 | −0.556100 | − | 0.831115i | \(-0.687703\pi\) | ||||
−0.556100 | + | 0.831115i | \(0.687703\pi\) | |||||||
\(618\) | −24.1051 | −0.969651 | ||||||||
\(619\) | 16.6714 | 0.670078 | 0.335039 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335039 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.5739 | −0.624959 | ||||||||
\(622\) | −7.87439 | −0.315734 | ||||||||
\(623\) | −42.2547 | −1.69290 | ||||||||
\(624\) | 7.14540 | 0.286045 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.1678 | −1.00591 | ||||||||
\(627\) | 11.5886 | 0.462806 | ||||||||
\(628\) | −12.7866 | −0.510242 | ||||||||
\(629\) | −0.892439 | −0.0355839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.709194 | −0.0282326 | −0.0141163 | − | 0.999900i | \(-0.504494\pi\) | ||||
−0.0141163 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(632\) | 10.6265 | 0.422699 | ||||||||
\(633\) | −16.9364 | −0.673162 | ||||||||
\(634\) | −23.9045 | −0.949370 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.508572 | 0.0201662 | ||||||||
\(637\) | 34.3856 | 1.36241 | ||||||||
\(638\) | −4.27540 | −0.169265 | ||||||||
\(639\) | 7.98459 | 0.315866 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.43553 | −0.0961978 | −0.0480989 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480989 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(642\) | 24.3984 | 0.962927 | ||||||||
\(643\) | 7.70390 | 0.303812 | 0.151906 | − | 0.988395i | \(-0.451459\pi\) | ||||
0.151906 | + | 0.988395i | \(0.451459\pi\) | |||||||
\(644\) | 31.9819 | 1.26027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.48108 | 0.254995 | ||||||||
\(647\) | −10.0499 | −0.395103 | −0.197552 | − | 0.980292i | \(-0.563299\pi\) | ||||
−0.197552 | + | 0.980292i | \(0.563299\pi\) | |||||||
\(648\) | −10.9045 | −0.428370 | ||||||||
\(649\) | −27.7092 | −1.08768 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.9964 | −1.68516 | ||||||||
\(652\) | −11.4734 | −0.449332 | ||||||||
\(653\) | −7.09283 | −0.277564 | −0.138782 | − | 0.990323i | \(-0.544319\pi\) | ||||
−0.138782 | + | 0.990323i | \(0.544319\pi\) | |||||||
\(654\) | 20.8597 | 0.815677 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.6489 | −0.454814 | ||||||||
\(657\) | 9.82620 | 0.383356 | ||||||||
\(658\) | −25.1929 | −0.982122 | ||||||||
\(659\) | −1.16346 | −0.0453218 | −0.0226609 | − | 0.999743i | \(-0.507214\pi\) | ||||
−0.0226609 | + | 0.999743i | \(0.507214\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79432 | 0.0697909 | 0.0348955 | − | 0.999391i | \(-0.488890\pi\) | ||||
0.0348955 | + | 0.999391i | \(0.488890\pi\) | |||||||
\(662\) | 30.7565 | 1.19538 | ||||||||
\(663\) | −46.3099 | −1.79853 | ||||||||
\(664\) | −12.0999 | −0.469566 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.287484 | 0.0111398 | ||||||||
\(667\) | 6.29851 | 0.243879 | ||||||||
\(668\) | 19.4131 | 0.751115 | ||||||||
\(669\) | 62.7263 | 2.42514 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −74.2446 | −2.86618 | ||||||||
\(672\) | 9.53101 | 0.367667 | ||||||||
\(673\) | −25.2824 | −0.974566 | −0.487283 | − | 0.873244i | \(-0.662012\pi\) | ||||
−0.487283 | + | 0.873244i | \(0.662012\pi\) | |||||||
\(674\) | 13.4734 | 0.518975 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.96480 | −0.114031 | ||||||||
\(677\) | −4.89682 | −0.188200 | −0.0941001 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0941001 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(678\) | 39.8091 | 1.52886 | ||||||||
\(679\) | 16.6472 | 0.638860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.1025 | 0.770330 | ||||||||
\(682\) | 23.1773 | 0.887504 | ||||||||
\(683\) | 10.1980 | 0.390215 | 0.195107 | − | 0.980782i | \(-0.437494\pi\) | ||||
0.195107 | + | 0.980782i | \(0.437494\pi\) | |||||||
\(684\) | −2.08777 | −0.0798279 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.2875 | 0.621859 | ||||||||
\(687\) | −30.7866 | −1.17458 | ||||||||
\(688\) | −2.51122 | −0.0957393 | ||||||||
\(689\) | 0.714253 | 0.0272109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.9846 | −1.52109 | −0.760543 | − | 0.649288i | \(-0.775067\pi\) | ||||
−0.760543 | + | 0.649288i | \(0.775067\pi\) | |||||||
\(692\) | 9.78662 | 0.372031 | ||||||||
\(693\) | −45.3238 | −1.72171 | ||||||||
\(694\) | 28.9468 | 1.09880 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.87703 | 0.0711487 | ||||||||
\(697\) | 75.4975 | 2.85967 | ||||||||
\(698\) | 27.9243 | 1.05695 | ||||||||
\(699\) | 52.5002 | 1.98574 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.91729 | 0.185723 | 0.0928617 | − | 0.995679i | \(-0.470399\pi\) | ||||
0.0928617 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(702\) | −6.51825 | −0.246015 | ||||||||
\(703\) | −0.137699 | −0.00519342 | ||||||||
\(704\) | −5.13770 | −0.193634 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.3099 | 1.06546 | ||||||||
\(707\) | 13.5130 | 0.508207 | ||||||||
\(708\) | 12.1652 | 0.457196 | ||||||||
\(709\) | −36.8865 | −1.38530 | −0.692650 | − | 0.721274i | \(-0.743557\pi\) | ||||
−0.692650 | + | 0.721274i | \(0.743557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.1857 | 0.832027 | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | −34.1447 | −1.27873 | ||||||||
\(714\) | −61.7712 | −2.31173 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.82446 | −0.255042 | ||||||||
\(717\) | 8.41113 | 0.314119 | ||||||||
\(718\) | 2.60163 | 0.0970921 | ||||||||
\(719\) | −23.8891 | −0.890914 | −0.445457 | − | 0.895303i | \(-0.646959\pi\) | ||||
−0.445457 | + | 0.895303i | \(0.646959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.1566 | −1.68172 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −3.35811 | −0.124889 | ||||||||
\(724\) | −0.137699 | −0.00511755 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 34.7272 | 1.28885 | ||||||||
\(727\) | 19.6894 | 0.730240 | 0.365120 | − | 0.930961i | \(-0.381028\pi\) | ||||
0.365120 | + | 0.930961i | \(0.381028\pi\) | |||||||
\(728\) | 13.3856 | 0.496104 | ||||||||
\(729\) | −8.84251 | −0.327500 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.2754 | 0.601967 | ||||||||
\(732\) | 32.5957 | 1.20477 | ||||||||
\(733\) | 1.76418 | 0.0651615 | 0.0325808 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325808 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(734\) | 11.6489 | 0.429969 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.56885 | 0.278991 | ||||||||
\(737\) | 21.1170 | 0.777855 | ||||||||
\(738\) | −24.3203 | −0.895241 | ||||||||
\(739\) | 28.1755 | 1.03645 | 0.518227 | − | 0.855243i | \(-0.326592\pi\) | ||||
0.518227 | + | 0.855243i | \(0.326592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.14540 | −0.262493 | ||||||||
\(742\) | 0.952717 | 0.0349753 | ||||||||
\(743\) | −5.42851 | −0.199153 | −0.0995763 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995763 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(744\) | −10.1755 | −0.373053 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.8064 | −0.468876 | ||||||||
\(747\) | −25.2617 | −0.924278 | ||||||||
\(748\) | 33.2978 | 1.21749 | ||||||||
\(749\) | 45.7059 | 1.67006 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8640 | 0.943792 | 0.471896 | − | 0.881654i | \(-0.343570\pi\) | ||||
0.471896 | + | 0.881654i | \(0.343570\pi\) | |||||||
\(752\) | −5.96216 | −0.217418 | ||||||||
\(753\) | −19.8192 | −0.722251 | ||||||||
\(754\) | 2.63615 | 0.0960031 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.69446 | −0.316215 | ||||||||
\(757\) | −3.76947 | −0.137004 | −0.0685019 | − | 0.997651i | \(-0.521822\pi\) | ||||
−0.0685019 | + | 0.997651i | \(0.521822\pi\) | |||||||
\(758\) | −20.9122 | −0.759566 | ||||||||
\(759\) | −87.7127 | −3.18377 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3605 | 0.665568 | 0.332784 | − | 0.943003i | \(-0.392012\pi\) | ||||
0.332784 | + | 0.943003i | \(0.392012\pi\) | |||||||
\(762\) | −28.8416 | −1.04482 | ||||||||
\(763\) | 39.0767 | 1.41467 | ||||||||
\(764\) | 19.3779 | 0.701068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.3511 | 0.374000 | ||||||||
\(767\) | 17.0851 | 0.616908 | ||||||||
\(768\) | 2.25561 | 0.0813923 | ||||||||
\(769\) | −38.1300 | −1.37500 | −0.687501 | − | 0.726183i | \(-0.741292\pi\) | ||||
−0.687501 | + | 0.726183i | \(0.741292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.18431 | 0.222722 | ||||||||
\(772\) | −5.42851 | −0.195376 | ||||||||
\(773\) | −29.1575 | −1.04872 | −0.524361 | − | 0.851496i | \(-0.675696\pi\) | ||||
−0.524361 | + | 0.851496i | \(0.675696\pi\) | |||||||
\(774\) | −5.24285 | −0.188450 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.93972 | 0.141428 | ||||||||
\(777\) | 1.31241 | 0.0470825 | ||||||||
\(778\) | 6.56620 | 0.235410 | ||||||||
\(779\) | 11.6489 | 0.417366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6489 | −0.703094 | ||||||||
\(782\) | −49.0543 | −1.75418 | ||||||||
\(783\) | −1.71228 | −0.0611920 | ||||||||
\(784\) | 10.8546 | 0.387664 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.77121 | −0.170183 | ||||||||
\(787\) | −47.0165 | −1.67596 | −0.837978 | − | 0.545704i | \(-0.816262\pi\) | ||||
−0.837978 | + | 0.545704i | \(0.816262\pi\) | |||||||
\(788\) | −15.6489 | −0.557470 | ||||||||
\(789\) | 6.19624 | 0.220592 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 74.5750 | 2.65158 | ||||||||
\(792\) | −10.7263 | −0.381144 | ||||||||
\(793\) | 45.7782 | 1.62563 | ||||||||
\(794\) | 23.5284 | 0.834990 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0499 | 0.639763 | ||||||||
\(797\) | −42.6359 | −1.51024 | −0.755121 | − | 0.655586i | \(-0.772422\pi\) | ||||
−0.755121 | + | 0.655586i | \(0.772422\pi\) | |||||||
\(798\) | −9.53101 | −0.337394 | ||||||||
\(799\) | 38.6412 | 1.36703 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8777 | −0.737678 | ||||||||
\(802\) | 6.22041 | 0.219650 | ||||||||
\(803\) | −24.1808 | −0.853323 | ||||||||
\(804\) | −9.27102 | −0.326964 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.2908 | −0.503372 | ||||||||
\(807\) | −21.9736 | −0.773506 | ||||||||
\(808\) | 3.19798 | 0.112504 | ||||||||
\(809\) | 49.4630 | 1.73903 | 0.869514 | − | 0.493909i | \(-0.164432\pi\) | ||||
0.869514 | + | 0.493909i | \(0.164432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.7816 | −0.589280 | −0.294640 | − | 0.955608i | \(-0.595200\pi\) | ||||
−0.294640 | + | 0.955608i | \(0.595200\pi\) | |||||||
\(812\) | 3.51628 | 0.123397 | ||||||||
\(813\) | 59.4476 | 2.08492 | ||||||||
\(814\) | −0.707457 | −0.0247964 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.6188 | −0.511760 | ||||||||
\(817\) | 2.51122 | 0.0878564 | ||||||||
\(818\) | −34.4905 | −1.20593 | ||||||||
\(819\) | 27.9461 | 0.976515 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5337 | 0.402527 | 0.201264 | − | 0.979537i | \(-0.435495\pi\) | ||||
0.201264 | + | 0.979537i | \(0.435495\pi\) | |||||||
\(822\) | −12.0972 | −0.421939 | ||||||||
\(823\) | 32.6309 | 1.13744 | 0.568720 | − | 0.822531i | \(-0.307439\pi\) | ||||
0.568720 | + | 0.822531i | \(0.307439\pi\) | |||||||
\(824\) | −10.6868 | −0.372291 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.7893 | 0.792940 | ||||||||
\(827\) | 6.64650 | 0.231122 | 0.115561 | − | 0.993300i | \(-0.463133\pi\) | ||||
0.115561 | + | 0.993300i | \(0.463133\pi\) | |||||||
\(828\) | 15.8020 | 0.549158 | ||||||||
\(829\) | −30.9217 | −1.07395 | −0.536977 | − | 0.843597i | \(-0.680434\pi\) | ||||
−0.536977 | + | 0.843597i | \(0.680434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.17025 | −0.0752852 | ||||||||
\(832\) | 3.16784 | 0.109825 | ||||||||
\(833\) | −70.3495 | −2.43747 | ||||||||
\(834\) | −22.9173 | −0.793561 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.13770 | 0.177691 | ||||||||
\(837\) | 9.28243 | 0.320848 | ||||||||
\(838\) | −10.6265 | −0.367086 | ||||||||
\(839\) | −48.7109 | −1.68169 | −0.840844 | − | 0.541277i | \(-0.817941\pi\) | ||||
−0.840844 | + | 0.541277i | \(0.817941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3075 | −0.976121 | ||||||||
\(842\) | −1.98021 | −0.0682426 | ||||||||
\(843\) | −33.0928 | −1.13978 | ||||||||
\(844\) | −7.50857 | −0.258456 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.4476 | −0.427958 | ||||||||
\(847\) | 65.0551 | 2.23532 | ||||||||
\(848\) | 0.225470 | 0.00774267 | ||||||||
\(849\) | −59.0070 | −2.02512 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.04222 | 0.0357270 | ||||||||
\(852\) | 8.62648 | 0.295538 | ||||||||
\(853\) | 46.1447 | 1.57997 | 0.789983 | − | 0.613129i | \(-0.210089\pi\) | ||||
0.789983 | + | 0.613129i | \(0.210089\pi\) | |||||||
\(854\) | 61.0620 | 2.08950 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.8168 | 0.369709 | ||||||||
\(857\) | −8.40607 | −0.287146 | −0.143573 | − | 0.989640i | \(-0.545859\pi\) | ||||
−0.143573 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(858\) | −36.7109 | −1.25329 | ||||||||
\(859\) | −8.49581 | −0.289873 | −0.144937 | − | 0.989441i | \(-0.546298\pi\) | ||||
−0.144937 | + | 0.989441i | \(0.546298\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −111.026 | −3.78375 | ||||||||
\(862\) | 15.0774 | 0.513539 | ||||||||
\(863\) | 3.37352 | 0.114836 | 0.0574179 | − | 0.998350i | \(-0.481713\pi\) | ||||
0.0574179 | + | 0.998350i | \(0.481713\pi\) | |||||||
\(864\) | −2.05763 | −0.0700021 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.5337 | 0.459892 | ||||||||
\(867\) | 56.4001 | 1.91545 | ||||||||
\(868\) | −19.0620 | −0.647007 | ||||||||
\(869\) | −54.5957 | −1.85203 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0205 | −0.441182 | ||||||||
\(872\) | 9.24791 | 0.313174 | ||||||||
\(873\) | 8.22524 | 0.278382 | ||||||||
\(874\) | −7.56885 | −0.256020 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6161 | 0.358686 | ||||||||
\(877\) | −13.2780 | −0.448368 | −0.224184 | − | 0.974547i | \(-0.571972\pi\) | ||||
−0.224184 | + | 0.974547i | \(0.571972\pi\) | |||||||
\(878\) | 39.1773 | 1.32217 | ||||||||
\(879\) | −50.6738 | −1.70918 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.6489 | −0.897825 | −0.448912 | − | 0.893576i | \(-0.648188\pi\) | ||||
−0.448912 | + | 0.893576i | \(0.648188\pi\) | |||||||
\(882\) | 22.6619 | 0.763066 | ||||||||
\(883\) | −47.7884 | −1.60821 | −0.804103 | − | 0.594490i | \(-0.797354\pi\) | ||||
−0.804103 | + | 0.594490i | \(0.797354\pi\) | |||||||
\(884\) | −20.5310 | −0.690532 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.3132 | 0.648841 | ||||||||
\(887\) | −36.3304 | −1.21985 | −0.609927 | − | 0.792457i | \(-0.708801\pi\) | ||||
−0.609927 | + | 0.792457i | \(0.708801\pi\) | |||||||
\(888\) | 0.310596 | 0.0104229 | ||||||||
\(889\) | −54.0295 | −1.81209 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 56.0242 | 1.87688 | ||||||||
\(892\) | 27.8091 | 0.931116 | ||||||||
\(893\) | 5.96216 | 0.199516 | ||||||||
\(894\) | −13.3977 | −0.448086 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.22547 | 0.141163 | ||||||||
\(897\) | 54.0825 | 1.80576 | ||||||||
\(898\) | 41.4131 | 1.38197 | ||||||||
\(899\) | −3.75406 | −0.125205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.46129 | −0.0486826 | ||||||||
\(902\) | 59.8486 | 1.99274 | ||||||||
\(903\) | −23.9344 | −0.796488 | ||||||||
\(904\) | 17.6489 | 0.586994 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −34.5059 | −1.14638 | ||||||||
\(907\) | −39.3873 | −1.30784 | −0.653918 | − | 0.756566i | \(-0.726876\pi\) | ||||
−0.653918 | + | 0.756566i | \(0.726876\pi\) | |||||||
\(908\) | 8.91223 | 0.295763 | ||||||||
\(909\) | 6.67664 | 0.221450 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5561 | −0.681054 | −0.340527 | − | 0.940235i | \(-0.610605\pi\) | ||||
−0.340527 | + | 0.940235i | \(0.610605\pi\) | |||||||
\(912\) | −2.25561 | −0.0746907 | ||||||||
\(913\) | 62.1654 | 2.05738 | ||||||||
\(914\) | −37.8392 | −1.25161 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.6489 | −0.450973 | ||||||||
\(917\) | −8.93799 | −0.295158 | ||||||||
\(918\) | 13.3357 | 0.440143 | ||||||||
\(919\) | 12.4054 | 0.409216 | 0.204608 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204608 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.8425 | 1.27990 | ||||||||
\(922\) | 1.58864 | 0.0523190 | ||||||||
\(923\) | 12.1153 | 0.398779 | ||||||||
\(924\) | −48.9674 | −1.61091 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 40.3581 | 1.32625 | ||||||||
\(927\) | −22.3115 | −0.732806 | ||||||||
\(928\) | 0.832162 | 0.0273171 | ||||||||
\(929\) | −31.3330 | −1.02800 | −0.514002 | − | 0.857789i | \(-0.671838\pi\) | ||||
−0.514002 | + | 0.857789i | \(0.671838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.8546 | −0.355745 | ||||||||
\(932\) | 23.2754 | 0.762411 | ||||||||
\(933\) | −17.7615 | −0.581487 | ||||||||
\(934\) | −39.5130 | −1.29290 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.61372 | 0.216176 | ||||||||
\(937\) | 7.27299 | 0.237598 | 0.118799 | − | 0.992918i | \(-0.462096\pi\) | ||||
0.118799 | + | 0.992918i | \(0.462096\pi\) | |||||||
\(938\) | −17.3676 | −0.567071 | ||||||||
\(939\) | −56.7688 | −1.85258 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.72128 | 0.219107 | 0.109554 | − | 0.993981i | \(-0.465058\pi\) | ||||
0.109554 | + | 0.993981i | \(0.465058\pi\) | |||||||
\(942\) | −28.8416 | −0.939710 | ||||||||
\(943\) | −88.1689 | −2.87117 | ||||||||
\(944\) | 5.39331 | 0.175537 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.9019 | 0.419476 | ||||||||
\(947\) | 10.0757 | 0.327416 | 0.163708 | − | 0.986509i | \(-0.447655\pi\) | ||||
0.163708 | + | 0.986509i | \(0.447655\pi\) | |||||||
\(948\) | 23.9692 | 0.778483 | ||||||||
\(949\) | 14.9096 | 0.483986 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.9193 | −1.74845 | ||||||||
\(952\) | −27.3856 | −0.887573 | ||||||||
\(953\) | −8.14473 | −0.263834 | −0.131917 | − | 0.991261i | \(-0.542113\pi\) | ||||
−0.131917 | + | 0.991261i | \(0.542113\pi\) | |||||||
\(954\) | 0.470730 | 0.0152404 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.72898 | 0.120604 | ||||||||
\(957\) | −9.64363 | −0.311734 | ||||||||
\(958\) | 7.61107 | 0.245903 | ||||||||
\(959\) | −22.6619 | −0.731791 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.6489 | −0.343513 | ||||||||
\(962\) | 0.436209 | 0.0140639 | ||||||||
\(963\) | 22.5829 | 0.727724 | ||||||||
\(964\) | −1.48878 | −0.0479505 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 72.1388 | 2.32103 | ||||||||
\(967\) | 47.1773 | 1.51712 | 0.758560 | − | 0.651604i | \(-0.225903\pi\) | ||||
0.758560 | + | 0.651604i | \(0.225903\pi\) | |||||||
\(968\) | 15.3960 | 0.494845 | ||||||||
\(969\) | 14.6188 | 0.469623 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.230528 | 0.00739801 | 0.00369901 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369901 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(972\) | −18.4234 | −0.590932 | ||||||||
\(973\) | −42.9313 | −1.37632 | ||||||||
\(974\) | −20.3907 | −0.653359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.4509 | 0.462563 | ||||||||
\(977\) | −5.80905 | −0.185848 | −0.0929240 | − | 0.995673i | \(-0.529621\pi\) | ||||
−0.0929240 | + | 0.995673i | \(0.529621\pi\) | |||||||
\(978\) | −25.8794 | −0.827533 | ||||||||
\(979\) | 51.3770 | 1.64202 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.3075 | 0.616441 | ||||||||
\(982\) | 25.0224 | 0.798498 | ||||||||
\(983\) | −22.3511 | −0.712889 | −0.356444 | − | 0.934317i | \(-0.616011\pi\) | ||||
−0.356444 | + | 0.934317i | \(0.616011\pi\) | |||||||
\(984\) | −26.2754 | −0.837629 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.39331 | −0.171758 | ||||||||
\(987\) | −56.8254 | −1.80877 | ||||||||
\(988\) | −3.16784 | −0.100782 | ||||||||
\(989\) | −19.0070 | −0.604388 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.9415 | −1.10995 | −0.554976 | − | 0.831866i | \(-0.687273\pi\) | ||||
−0.554976 | + | 0.831866i | \(0.687273\pi\) | |||||||
\(992\) | −4.51122 | −0.143231 | ||||||||
\(993\) | 69.3746 | 2.20154 | ||||||||
\(994\) | 16.1601 | 0.512568 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −27.2925 | −0.864797 | ||||||||
\(997\) | −9.35282 | −0.296207 | −0.148103 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148103 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(998\) | 22.6111 | 0.715741 | ||||||||
\(999\) | −0.283334 | −0.00896430 |
(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 | 950.2.a.m.1.2 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cj.1.3 | 3 | |||
4.3 | odd | 2 | 7600.2.a.bm.1.2 | 3 | |||
5.2 | odd | 4 | 950.2.b.g.799.5 | 6 | |||
5.3 | odd | 4 | 950.2.b.g.799.2 | 6 | |||
5.4 | even | 2 | 950.2.a.k.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.co.1.1 | 3 | |||
20.19 | odd | 2 | 7600.2.a.cb.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.k.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
950.2.a.m.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
950.2.b.g.799.2 | 6 | 5.3 | odd | 4 | |||
950.2.b.g.799.5 | 6 | 5.2 | odd | 4 | |||
7600.2.a.bm.1.2 | 3 | 4.3 | odd | 2 | |||
7600.2.a.cb.1.2 | 3 | 20.19 | odd | 2 | |||
8550.2.a.cj.1.3 | 3 | 3.2 | odd | 2 | |||
8550.2.a.co.1.1 | 3 | 15.14 | odd | 2 |