Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-1.87592\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.87592 | 1.32648 | 0.663238 | − | 0.748409i | \(-0.269182\pi\) | ||||
0.663238 | + | 0.748409i | \(0.269182\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.51907 | 0.759536 | ||||||||
\(5\) | −1.33107 | −0.595271 | −0.297636 | − | 0.954680i | \(-0.596198\pi\) | ||||
−0.297636 | + | 0.954680i | \(0.596198\pi\) | |||||||
\(6\) | 1.87592 | 0.765841 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.902182 | −0.318969 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.49697 | −0.789612 | ||||||||
\(11\) | 1.19223 | 0.359471 | 0.179736 | − | 0.983715i | \(-0.442476\pi\) | ||||
0.179736 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(12\) | 1.51907 | 0.438518 | ||||||||
\(13\) | 0.956777 | 0.265362 | 0.132681 | − | 0.991159i | \(-0.457641\pi\) | ||||
0.132681 | + | 0.991159i | \(0.457641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.33107 | −0.343680 | ||||||||
\(16\) | −4.73056 | −1.18264 | ||||||||
\(17\) | 3.26275 | 0.791333 | 0.395666 | − | 0.918394i | \(-0.370514\pi\) | ||||
0.395666 | + | 0.918394i | \(0.370514\pi\) | |||||||
\(18\) | 1.87592 | 0.442158 | ||||||||
\(19\) | −6.16735 | −1.41489 | −0.707444 | − | 0.706769i | \(-0.750152\pi\) | ||||
−0.707444 | + | 0.706769i | \(0.750152\pi\) | |||||||
\(20\) | −2.02199 | −0.452130 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.23653 | 0.476830 | ||||||||
\(23\) | −6.99354 | −1.45825 | −0.729127 | − | 0.684378i | \(-0.760074\pi\) | ||||
−0.729127 | + | 0.684378i | \(0.760074\pi\) | |||||||
\(24\) | −0.902182 | −0.184157 | ||||||||
\(25\) | −3.22826 | −0.645652 | ||||||||
\(26\) | 1.79484 | 0.351996 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.28683 | −0.424653 | −0.212327 | − | 0.977199i | \(-0.568104\pi\) | ||||
−0.212327 | + | 0.977199i | \(0.568104\pi\) | |||||||
\(30\) | −2.49697 | −0.455883 | ||||||||
\(31\) | −1.84740 | −0.331804 | −0.165902 | − | 0.986142i | \(-0.553053\pi\) | ||||
−0.165902 | + | 0.986142i | \(0.553053\pi\) | |||||||
\(32\) | −7.06979 | −1.24977 | ||||||||
\(33\) | 1.19223 | 0.207541 | ||||||||
\(34\) | 6.12065 | 1.04968 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.51907 | 0.253179 | ||||||||
\(37\) | −6.15612 | −1.01206 | −0.506030 | − | 0.862516i | \(-0.668888\pi\) | ||||
−0.506030 | + | 0.862516i | \(0.668888\pi\) | |||||||
\(38\) | −11.5695 | −1.87681 | ||||||||
\(39\) | 0.956777 | 0.153207 | ||||||||
\(40\) | 1.20086 | 0.189873 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.98160 | −0.912186 | −0.456093 | − | 0.889932i | \(-0.650752\pi\) | ||||
−0.456093 | + | 0.889932i | \(0.650752\pi\) | |||||||
\(44\) | 1.81108 | 0.273031 | ||||||||
\(45\) | −1.33107 | −0.198424 | ||||||||
\(46\) | −13.1193 | −1.93434 | ||||||||
\(47\) | 6.24381 | 0.910754 | 0.455377 | − | 0.890299i | \(-0.349505\pi\) | ||||
0.455377 | + | 0.890299i | \(0.349505\pi\) | |||||||
\(48\) | −4.73056 | −0.682798 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.05596 | −0.856442 | ||||||||
\(51\) | 3.26275 | 0.456876 | ||||||||
\(52\) | 1.45341 | 0.201552 | ||||||||
\(53\) | 11.8675 | 1.63012 | 0.815060 | − | 0.579377i | \(-0.196704\pi\) | ||||
0.815060 | + | 0.579377i | \(0.196704\pi\) | |||||||
\(54\) | 1.87592 | 0.255280 | ||||||||
\(55\) | −1.58694 | −0.213983 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.16735 | −0.816886 | ||||||||
\(58\) | −4.28990 | −0.563292 | ||||||||
\(59\) | −4.26878 | −0.555748 | −0.277874 | − | 0.960618i | \(-0.589630\pi\) | ||||
−0.277874 | + | 0.960618i | \(0.589630\pi\) | |||||||
\(60\) | −2.02199 | −0.261037 | ||||||||
\(61\) | 4.85206 | 0.621242 | 0.310621 | − | 0.950534i | \(-0.399463\pi\) | ||||
0.310621 | + | 0.950534i | \(0.399463\pi\) | |||||||
\(62\) | −3.46558 | −0.440129 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.80123 | −0.475153 | ||||||||
\(65\) | −1.27353 | −0.157962 | ||||||||
\(66\) | 2.23653 | 0.275298 | ||||||||
\(67\) | 3.76060 | 0.459430 | 0.229715 | − | 0.973258i | \(-0.426221\pi\) | ||||
0.229715 | + | 0.973258i | \(0.426221\pi\) | |||||||
\(68\) | 4.95635 | 0.601046 | ||||||||
\(69\) | −6.99354 | −0.841923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3437 | −1.34625 | −0.673124 | − | 0.739530i | \(-0.735048\pi\) | ||||
−0.673124 | + | 0.739530i | \(0.735048\pi\) | |||||||
\(72\) | −0.902182 | −0.106323 | ||||||||
\(73\) | −6.06858 | −0.710273 | −0.355137 | − | 0.934814i | \(-0.615566\pi\) | ||||
−0.355137 | + | 0.934814i | \(0.615566\pi\) | |||||||
\(74\) | −11.5484 | −1.34247 | ||||||||
\(75\) | −3.22826 | −0.372768 | ||||||||
\(76\) | −9.36866 | −1.07466 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.79484 | 0.203225 | ||||||||
\(79\) | −14.1656 | −1.59376 | −0.796878 | − | 0.604140i | \(-0.793517\pi\) | ||||
−0.796878 | + | 0.604140i | \(0.793517\pi\) | |||||||
\(80\) | 6.29670 | 0.703992 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.87592 | 0.207161 | ||||||||
\(83\) | 2.10474 | 0.231025 | 0.115512 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115512 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.34294 | −0.471058 | ||||||||
\(86\) | −11.2210 | −1.20999 | ||||||||
\(87\) | −2.28683 | −0.245174 | ||||||||
\(88\) | −1.07561 | −0.114660 | ||||||||
\(89\) | −9.71613 | −1.02991 | −0.514954 | − | 0.857218i | \(-0.672191\pi\) | ||||
−0.514954 | + | 0.857218i | \(0.672191\pi\) | |||||||
\(90\) | −2.49697 | −0.263204 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.6237 | −1.10760 | ||||||||
\(93\) | −1.84740 | −0.191567 | ||||||||
\(94\) | 11.7129 | 1.20809 | ||||||||
\(95\) | 8.20916 | 0.842242 | ||||||||
\(96\) | −7.06979 | −0.721558 | ||||||||
\(97\) | 0.622368 | 0.0631919 | 0.0315960 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315960 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.19223 | 0.119824 | ||||||||
\(100\) | −4.90396 | −0.490396 | ||||||||
\(101\) | −7.06334 | −0.702829 | −0.351415 | − | 0.936220i | \(-0.614299\pi\) | ||||
−0.351415 | + | 0.936220i | \(0.614299\pi\) | |||||||
\(102\) | 6.12065 | 0.606035 | ||||||||
\(103\) | 17.8241 | 1.75626 | 0.878132 | − | 0.478418i | \(-0.158790\pi\) | ||||
0.878132 | + | 0.478418i | \(0.158790\pi\) | |||||||
\(104\) | −0.863187 | −0.0846425 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.2624 | 2.16231 | ||||||||
\(107\) | 10.7720 | 1.04137 | 0.520684 | − | 0.853749i | \(-0.325677\pi\) | ||||
0.520684 | + | 0.853749i | \(0.325677\pi\) | |||||||
\(108\) | 1.51907 | 0.146173 | ||||||||
\(109\) | −9.04356 | −0.866216 | −0.433108 | − | 0.901342i | \(-0.642583\pi\) | ||||
−0.433108 | + | 0.901342i | \(0.642583\pi\) | |||||||
\(110\) | −2.97697 | −0.283843 | ||||||||
\(111\) | −6.15612 | −0.584313 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.09784 | −0.479565 | −0.239782 | − | 0.970827i | \(-0.577076\pi\) | ||||
−0.239782 | + | 0.970827i | \(0.577076\pi\) | |||||||
\(114\) | −11.5695 | −1.08358 | ||||||||
\(115\) | 9.30887 | 0.868057 | ||||||||
\(116\) | −3.47386 | −0.322540 | ||||||||
\(117\) | 0.956777 | 0.0884541 | ||||||||
\(118\) | −8.00789 | −0.737186 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.20086 | 0.109623 | ||||||||
\(121\) | −9.57858 | −0.870780 | ||||||||
\(122\) | 9.10207 | 0.824062 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −2.80634 | −0.252017 | ||||||||
\(125\) | 10.9524 | 0.979609 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.16734 | 0.813470 | 0.406735 | − | 0.913546i | \(-0.366667\pi\) | ||||
0.406735 | + | 0.913546i | \(0.366667\pi\) | |||||||
\(128\) | 7.00879 | 0.619495 | ||||||||
\(129\) | −5.98160 | −0.526651 | ||||||||
\(130\) | −2.38905 | −0.209533 | ||||||||
\(131\) | 4.49020 | 0.392311 | 0.196155 | − | 0.980573i | \(-0.437154\pi\) | ||||
0.196155 | + | 0.980573i | \(0.437154\pi\) | |||||||
\(132\) | 1.81108 | 0.157635 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.05457 | 0.609422 | ||||||||
\(135\) | −1.33107 | −0.114560 | ||||||||
\(136\) | −2.94359 | −0.252411 | ||||||||
\(137\) | −7.16553 | −0.612192 | −0.306096 | − | 0.952001i | \(-0.599023\pi\) | ||||
−0.306096 | + | 0.952001i | \(0.599023\pi\) | |||||||
\(138\) | −13.1193 | −1.11679 | ||||||||
\(139\) | −10.8857 | −0.923310 | −0.461655 | − | 0.887060i | \(-0.652744\pi\) | ||||
−0.461655 | + | 0.887060i | \(0.652744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.24381 | 0.525824 | ||||||||
\(142\) | −21.2798 | −1.78576 | ||||||||
\(143\) | 1.14070 | 0.0953901 | ||||||||
\(144\) | −4.73056 | −0.394214 | ||||||||
\(145\) | 3.04392 | 0.252784 | ||||||||
\(146\) | −11.3842 | −0.942160 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.35160 | −0.768696 | ||||||||
\(149\) | −10.1880 | −0.834633 | −0.417317 | − | 0.908761i | \(-0.637029\pi\) | ||||
−0.417317 | + | 0.908761i | \(0.637029\pi\) | |||||||
\(150\) | −6.05596 | −0.494467 | ||||||||
\(151\) | −17.1572 | −1.39623 | −0.698116 | − | 0.715985i | \(-0.745978\pi\) | ||||
−0.698116 | + | 0.715985i | \(0.745978\pi\) | |||||||
\(152\) | 5.56408 | 0.451306 | ||||||||
\(153\) | 3.26275 | 0.263778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.45902 | 0.197513 | ||||||||
\(156\) | 1.45341 | 0.116366 | ||||||||
\(157\) | 17.1453 | 1.36834 | 0.684172 | − | 0.729320i | \(-0.260164\pi\) | ||||
0.684172 | + | 0.729320i | \(0.260164\pi\) | |||||||
\(158\) | −26.5735 | −2.11408 | ||||||||
\(159\) | 11.8675 | 0.941150 | ||||||||
\(160\) | 9.41036 | 0.743955 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.87592 | 0.147386 | ||||||||
\(163\) | 9.69691 | 0.759520 | 0.379760 | − | 0.925085i | \(-0.376007\pi\) | ||||
0.379760 | + | 0.925085i | \(0.376007\pi\) | |||||||
\(164\) | 1.51907 | 0.118620 | ||||||||
\(165\) | −1.58694 | −0.123543 | ||||||||
\(166\) | 3.94832 | 0.306449 | ||||||||
\(167\) | 1.78167 | 0.137869 | 0.0689347 | − | 0.997621i | \(-0.478040\pi\) | ||||
0.0689347 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0846 | −0.929583 | ||||||||
\(170\) | −8.14700 | −0.624846 | ||||||||
\(171\) | −6.16735 | −0.471629 | ||||||||
\(172\) | −9.08649 | −0.692838 | ||||||||
\(173\) | −7.95559 | −0.604853 | −0.302426 | − | 0.953173i | \(-0.597797\pi\) | ||||
−0.302426 | + | 0.953173i | \(0.597797\pi\) | |||||||
\(174\) | −4.28990 | −0.325217 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.63993 | −0.425125 | ||||||||
\(177\) | −4.26878 | −0.320861 | ||||||||
\(178\) | −18.2267 | −1.36615 | ||||||||
\(179\) | 6.55130 | 0.489667 | 0.244833 | − | 0.969565i | \(-0.421267\pi\) | ||||
0.244833 | + | 0.969565i | \(0.421267\pi\) | |||||||
\(180\) | −2.02199 | −0.150710 | ||||||||
\(181\) | −16.4764 | −1.22468 | −0.612341 | − | 0.790593i | \(-0.709772\pi\) | ||||
−0.612341 | + | 0.790593i | \(0.709772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85206 | 0.358674 | ||||||||
\(184\) | 6.30945 | 0.465139 | ||||||||
\(185\) | 8.19421 | 0.602450 | ||||||||
\(186\) | −3.46558 | −0.254109 | ||||||||
\(187\) | 3.88995 | 0.284461 | ||||||||
\(188\) | 9.48480 | 0.691750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.3997 | 1.11721 | ||||||||
\(191\) | −22.5981 | −1.63514 | −0.817570 | − | 0.575829i | \(-0.804679\pi\) | ||||
−0.817570 | + | 0.575829i | \(0.804679\pi\) | |||||||
\(192\) | −3.80123 | −0.274330 | ||||||||
\(193\) | −2.60607 | −0.187589 | −0.0937943 | − | 0.995592i | \(-0.529900\pi\) | ||||
−0.0937943 | + | 0.995592i | \(0.529900\pi\) | |||||||
\(194\) | 1.16751 | 0.0838225 | ||||||||
\(195\) | −1.27353 | −0.0911997 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.3863 | −1.16747 | −0.583737 | − | 0.811942i | \(-0.698410\pi\) | ||||
−0.583737 | + | 0.811942i | \(0.698410\pi\) | |||||||
\(198\) | 2.23653 | 0.158943 | ||||||||
\(199\) | −8.52046 | −0.604000 | −0.302000 | − | 0.953308i | \(-0.597654\pi\) | ||||
−0.302000 | + | 0.953308i | \(0.597654\pi\) | |||||||
\(200\) | 2.91248 | 0.205943 | ||||||||
\(201\) | 3.76060 | 0.265252 | ||||||||
\(202\) | −13.2503 | −0.932285 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.95635 | 0.347014 | ||||||||
\(205\) | −1.33107 | −0.0929657 | ||||||||
\(206\) | 33.4366 | 2.32964 | ||||||||
\(207\) | −6.99354 | −0.486085 | ||||||||
\(208\) | −4.52610 | −0.313828 | ||||||||
\(209\) | −7.35291 | −0.508612 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0347 | 1.58577 | 0.792886 | − | 0.609369i | \(-0.208577\pi\) | ||||
0.792886 | + | 0.609369i | \(0.208577\pi\) | |||||||
\(212\) | 18.0275 | 1.23813 | ||||||||
\(213\) | −11.3437 | −0.777256 | ||||||||
\(214\) | 20.2074 | 1.38135 | ||||||||
\(215\) | 7.96191 | 0.542998 | ||||||||
\(216\) | −0.902182 | −0.0613857 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.9650 | −1.14901 | ||||||||
\(219\) | −6.06858 | −0.410076 | ||||||||
\(220\) | −2.41067 | −0.162528 | ||||||||
\(221\) | 3.12172 | 0.209990 | ||||||||
\(222\) | −11.5484 | −0.775077 | ||||||||
\(223\) | 9.56418 | 0.640465 | 0.320232 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320232 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.22826 | −0.215217 | ||||||||
\(226\) | −9.56314 | −0.636131 | ||||||||
\(227\) | 24.7536 | 1.64296 | 0.821478 | − | 0.570241i | \(-0.193150\pi\) | ||||
0.821478 | + | 0.570241i | \(0.193150\pi\) | |||||||
\(228\) | −9.36866 | −0.620454 | ||||||||
\(229\) | 3.35230 | 0.221526 | 0.110763 | − | 0.993847i | \(-0.464671\pi\) | ||||
0.110763 | + | 0.993847i | \(0.464671\pi\) | |||||||
\(230\) | 17.4627 | 1.15146 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.06314 | 0.135451 | ||||||||
\(233\) | −1.02338 | −0.0670440 | −0.0335220 | − | 0.999438i | \(-0.510672\pi\) | ||||
−0.0335220 | + | 0.999438i | \(0.510672\pi\) | |||||||
\(234\) | 1.79484 | 0.117332 | ||||||||
\(235\) | −8.31093 | −0.542145 | ||||||||
\(236\) | −6.48459 | −0.422111 | ||||||||
\(237\) | −14.1656 | −0.920155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.4140 | −1.70858 | −0.854290 | − | 0.519796i | \(-0.826008\pi\) | ||||
−0.854290 | + | 0.519796i | \(0.826008\pi\) | |||||||
\(240\) | 6.29670 | 0.406450 | ||||||||
\(241\) | 22.1097 | 1.42421 | 0.712105 | − | 0.702073i | \(-0.247742\pi\) | ||||
0.712105 | + | 0.702073i | \(0.247742\pi\) | |||||||
\(242\) | −17.9686 | −1.15507 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.37062 | 0.471856 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.87592 | 0.119604 | ||||||||
\(247\) | −5.90078 | −0.375458 | ||||||||
\(248\) | 1.66669 | 0.105835 | ||||||||
\(249\) | 2.10474 | 0.133382 | ||||||||
\(250\) | 20.5457 | 1.29943 | ||||||||
\(251\) | −19.7611 | −1.24731 | −0.623656 | − | 0.781699i | \(-0.714353\pi\) | ||||
−0.623656 | + | 0.781699i | \(0.714353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.33792 | −0.524200 | ||||||||
\(254\) | 17.1972 | 1.07905 | ||||||||
\(255\) | −4.34294 | −0.271965 | ||||||||
\(256\) | 20.7504 | 1.29690 | ||||||||
\(257\) | −17.4492 | −1.08845 | −0.544224 | − | 0.838940i | \(-0.683176\pi\) | ||||
−0.544224 | + | 0.838940i | \(0.683176\pi\) | |||||||
\(258\) | −11.2210 | −0.698589 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.93459 | −0.119978 | ||||||||
\(261\) | −2.28683 | −0.141551 | ||||||||
\(262\) | 8.42325 | 0.520390 | ||||||||
\(263\) | 21.4392 | 1.32200 | 0.660998 | − | 0.750387i | \(-0.270133\pi\) | ||||
0.660998 | + | 0.750387i | \(0.270133\pi\) | |||||||
\(264\) | −1.07561 | −0.0661992 | ||||||||
\(265\) | −15.7964 | −0.970363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.71613 | −0.594618 | ||||||||
\(268\) | 5.71262 | 0.348954 | ||||||||
\(269\) | 2.02049 | 0.123192 | 0.0615959 | − | 0.998101i | \(-0.480381\pi\) | ||||
0.0615959 | + | 0.998101i | \(0.480381\pi\) | |||||||
\(270\) | −2.49697 | −0.151961 | ||||||||
\(271\) | 11.0931 | 0.673861 | 0.336930 | − | 0.941530i | \(-0.390611\pi\) | ||||
0.336930 | + | 0.941530i | \(0.390611\pi\) | |||||||
\(272\) | −15.4346 | −0.935863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.4420 | −0.812058 | ||||||||
\(275\) | −3.84883 | −0.232093 | ||||||||
\(276\) | −10.6237 | −0.639471 | ||||||||
\(277\) | 13.9305 | 0.837002 | 0.418501 | − | 0.908216i | \(-0.362556\pi\) | ||||
0.418501 | + | 0.908216i | \(0.362556\pi\) | |||||||
\(278\) | −20.4206 | −1.22475 | ||||||||
\(279\) | −1.84740 | −0.110601 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.20264 | −0.0717434 | −0.0358717 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358717 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(282\) | 11.7129 | 0.697492 | ||||||||
\(283\) | −5.10533 | −0.303480 | −0.151740 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151740 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(284\) | −17.2319 | −1.02252 | ||||||||
\(285\) | 8.20916 | 0.486269 | ||||||||
\(286\) | 2.13986 | 0.126533 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.06979 | −0.416591 | ||||||||
\(289\) | −6.35447 | −0.373792 | ||||||||
\(290\) | 5.71015 | 0.335311 | ||||||||
\(291\) | 0.622368 | 0.0364839 | ||||||||
\(292\) | −9.21860 | −0.539478 | ||||||||
\(293\) | −28.2532 | −1.65057 | −0.825286 | − | 0.564715i | \(-0.808986\pi\) | ||||
−0.825286 | + | 0.564715i | \(0.808986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.68203 | 0.330821 | ||||||||
\(296\) | 5.55394 | 0.322816 | ||||||||
\(297\) | 1.19223 | 0.0691803 | ||||||||
\(298\) | −19.1119 | −1.10712 | ||||||||
\(299\) | −6.69126 | −0.386966 | ||||||||
\(300\) | −4.90396 | −0.283130 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −32.1855 | −1.85207 | ||||||||
\(303\) | −7.06334 | −0.405779 | ||||||||
\(304\) | 29.1751 | 1.67330 | ||||||||
\(305\) | −6.45841 | −0.369808 | ||||||||
\(306\) | 6.12065 | 0.349894 | ||||||||
\(307\) | 1.22364 | 0.0698370 | 0.0349185 | − | 0.999390i | \(-0.488883\pi\) | ||||
0.0349185 | + | 0.999390i | \(0.488883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8241 | 1.01398 | ||||||||
\(310\) | 4.61292 | 0.261996 | ||||||||
\(311\) | −7.70437 | −0.436875 | −0.218437 | − | 0.975851i | \(-0.570096\pi\) | ||||
−0.218437 | + | 0.975851i | \(0.570096\pi\) | |||||||
\(312\) | −0.863187 | −0.0488683 | ||||||||
\(313\) | 2.06116 | 0.116504 | 0.0582518 | − | 0.998302i | \(-0.481447\pi\) | ||||
0.0582518 | + | 0.998302i | \(0.481447\pi\) | |||||||
\(314\) | 32.1632 | 1.81508 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.5186 | −1.21051 | ||||||||
\(317\) | −10.8641 | −0.610187 | −0.305093 | − | 0.952322i | \(-0.598688\pi\) | ||||
−0.305093 | + | 0.952322i | \(0.598688\pi\) | |||||||
\(318\) | 22.2624 | 1.24841 | ||||||||
\(319\) | −2.72643 | −0.152651 | ||||||||
\(320\) | 5.05969 | 0.282845 | ||||||||
\(321\) | 10.7720 | 0.601234 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.1225 | −1.11965 | ||||||||
\(324\) | 1.51907 | 0.0843929 | ||||||||
\(325\) | −3.08873 | −0.171332 | ||||||||
\(326\) | 18.1906 | 1.00748 | ||||||||
\(327\) | −9.04356 | −0.500110 | ||||||||
\(328\) | −0.902182 | −0.0498147 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.97697 | −0.163877 | ||||||||
\(331\) | 28.8910 | 1.58799 | 0.793997 | − | 0.607921i | \(-0.207996\pi\) | ||||
0.793997 | + | 0.607921i | \(0.207996\pi\) | |||||||
\(332\) | 3.19725 | 0.175472 | ||||||||
\(333\) | −6.15612 | −0.337353 | ||||||||
\(334\) | 3.34226 | 0.182880 | ||||||||
\(335\) | −5.00560 | −0.273485 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3472 | 1.10838 | 0.554192 | − | 0.832389i | \(-0.313027\pi\) | ||||
0.554192 | + | 0.832389i | \(0.313027\pi\) | |||||||
\(338\) | −22.6697 | −1.23307 | ||||||||
\(339\) | −5.09784 | −0.276877 | ||||||||
\(340\) | −6.59723 | −0.357785 | ||||||||
\(341\) | −2.20253 | −0.119274 | ||||||||
\(342\) | −11.5695 | −0.625605 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.39649 | 0.290959 | ||||||||
\(345\) | 9.30887 | 0.501173 | ||||||||
\(346\) | −14.9241 | −0.802322 | ||||||||
\(347\) | 8.70651 | 0.467390 | 0.233695 | − | 0.972310i | \(-0.424918\pi\) | ||||
0.233695 | + | 0.972310i | \(0.424918\pi\) | |||||||
\(348\) | −3.47386 | −0.186218 | ||||||||
\(349\) | 0.668717 | 0.0357956 | 0.0178978 | − | 0.999840i | \(-0.494303\pi\) | ||||
0.0178978 | + | 0.999840i | \(0.494303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.956777 | 0.0510690 | ||||||||
\(352\) | −8.42883 | −0.449258 | ||||||||
\(353\) | −11.0813 | −0.589798 | −0.294899 | − | 0.955528i | \(-0.595286\pi\) | ||||
−0.294899 | + | 0.955528i | \(0.595286\pi\) | |||||||
\(354\) | −8.00789 | −0.425615 | ||||||||
\(355\) | 15.0992 | 0.801382 | ||||||||
\(356\) | −14.7595 | −0.782252 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.2897 | 0.649531 | ||||||||
\(359\) | −9.64446 | −0.509015 | −0.254507 | − | 0.967071i | \(-0.581913\pi\) | ||||
−0.254507 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(360\) | 1.20086 | 0.0632911 | ||||||||
\(361\) | 19.0363 | 1.00191 | ||||||||
\(362\) | −30.9084 | −1.62451 | ||||||||
\(363\) | −9.57858 | −0.502745 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.07768 | 0.422805 | ||||||||
\(366\) | 9.10207 | 0.475773 | ||||||||
\(367\) | 35.5344 | 1.85488 | 0.927440 | − | 0.373971i | \(-0.122004\pi\) | ||||
0.927440 | + | 0.373971i | \(0.122004\pi\) | |||||||
\(368\) | 33.0834 | 1.72459 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 15.3717 | 0.799135 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.80634 | −0.145502 | ||||||||
\(373\) | 0.914929 | 0.0473732 | 0.0236866 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236866 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(374\) | 7.29723 | 0.377331 | ||||||||
\(375\) | 10.9524 | 0.565578 | ||||||||
\(376\) | −5.63305 | −0.290503 | ||||||||
\(377\) | −2.18799 | −0.112687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.54979 | −0.0796071 | −0.0398036 | − | 0.999208i | \(-0.512673\pi\) | ||||
−0.0398036 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(380\) | 12.4703 | 0.639713 | ||||||||
\(381\) | 9.16734 | 0.469657 | ||||||||
\(382\) | −42.3922 | −2.16897 | ||||||||
\(383\) | 38.3803 | 1.96114 | 0.980570 | − | 0.196167i | \(-0.0628496\pi\) | ||||
0.980570 | + | 0.196167i | \(0.0628496\pi\) | |||||||
\(384\) | 7.00879 | 0.357666 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.88877 | −0.248832 | ||||||||
\(387\) | −5.98160 | −0.304062 | ||||||||
\(388\) | 0.945422 | 0.0479965 | ||||||||
\(389\) | 4.21777 | 0.213849 | 0.106925 | − | 0.994267i | \(-0.465900\pi\) | ||||
0.106925 | + | 0.994267i | \(0.465900\pi\) | |||||||
\(390\) | −2.38905 | −0.120974 | ||||||||
\(391\) | −22.8182 | −1.15396 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.49020 | 0.226501 | ||||||||
\(394\) | −30.7394 | −1.54863 | ||||||||
\(395\) | 18.8554 | 0.948717 | ||||||||
\(396\) | 1.81108 | 0.0910104 | ||||||||
\(397\) | 29.8860 | 1.49993 | 0.749967 | − | 0.661475i | \(-0.230069\pi\) | ||||
0.749967 | + | 0.661475i | \(0.230069\pi\) | |||||||
\(398\) | −15.9837 | −0.801190 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.2715 | 0.763575 | ||||||||
\(401\) | 17.2699 | 0.862417 | 0.431209 | − | 0.902252i | \(-0.358087\pi\) | ||||
0.431209 | + | 0.902252i | \(0.358087\pi\) | |||||||
\(402\) | 7.05457 | 0.351850 | ||||||||
\(403\) | −1.76755 | −0.0880481 | ||||||||
\(404\) | −10.7297 | −0.533824 | ||||||||
\(405\) | −1.33107 | −0.0661412 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.33952 | −0.363807 | ||||||||
\(408\) | −2.94359 | −0.145730 | ||||||||
\(409\) | 0.572746 | 0.0283205 | 0.0141602 | − | 0.999900i | \(-0.495493\pi\) | ||||
0.0141602 | + | 0.999900i | \(0.495493\pi\) | |||||||
\(410\) | −2.49697 | −0.123317 | ||||||||
\(411\) | −7.16553 | −0.353450 | ||||||||
\(412\) | 27.0761 | 1.33395 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.1193 | −0.644779 | ||||||||
\(415\) | −2.80155 | −0.137522 | ||||||||
\(416\) | −6.76421 | −0.331643 | ||||||||
\(417\) | −10.8857 | −0.533073 | ||||||||
\(418\) | −13.7935 | −0.674661 | ||||||||
\(419\) | −9.37586 | −0.458041 | −0.229020 | − | 0.973422i | \(-0.573552\pi\) | ||||
−0.229020 | + | 0.973422i | \(0.573552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.621048 | 0.0302680 | 0.0151340 | − | 0.999885i | \(-0.495183\pi\) | ||||
0.0151340 | + | 0.999885i | \(0.495183\pi\) | |||||||
\(422\) | 43.2112 | 2.10349 | ||||||||
\(423\) | 6.24381 | 0.303585 | ||||||||
\(424\) | −10.7066 | −0.519958 | ||||||||
\(425\) | −10.5330 | −0.510926 | ||||||||
\(426\) | −21.2798 | −1.03101 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.3634 | 0.790957 | ||||||||
\(429\) | 1.14070 | 0.0550735 | ||||||||
\(430\) | 14.9359 | 0.720273 | ||||||||
\(431\) | 39.2853 | 1.89231 | 0.946154 | − | 0.323718i | \(-0.104933\pi\) | ||||
0.946154 | + | 0.323718i | \(0.104933\pi\) | |||||||
\(432\) | −4.73056 | −0.227599 | ||||||||
\(433\) | 6.54587 | 0.314575 | 0.157287 | − | 0.987553i | \(-0.449725\pi\) | ||||
0.157287 | + | 0.987553i | \(0.449725\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.04392 | 0.145945 | ||||||||
\(436\) | −13.7378 | −0.657922 | ||||||||
\(437\) | 43.1317 | 2.06327 | ||||||||
\(438\) | −11.3842 | −0.543956 | ||||||||
\(439\) | −11.9986 | −0.572664 | −0.286332 | − | 0.958130i | \(-0.592436\pi\) | ||||
−0.286332 | + | 0.958130i | \(0.592436\pi\) | |||||||
\(440\) | 1.43171 | 0.0682540 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.85610 | 0.278546 | ||||||||
\(443\) | −4.85767 | −0.230795 | −0.115397 | − | 0.993319i | \(-0.536814\pi\) | ||||
−0.115397 | + | 0.993319i | \(0.536814\pi\) | |||||||
\(444\) | −9.35160 | −0.443807 | ||||||||
\(445\) | 12.9328 | 0.613074 | ||||||||
\(446\) | 17.9416 | 0.849561 | ||||||||
\(447\) | −10.1880 | −0.481876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.35529 | 0.394311 | 0.197155 | − | 0.980372i | \(-0.436830\pi\) | ||||
0.197155 | + | 0.980372i | \(0.436830\pi\) | |||||||
\(450\) | −6.05596 | −0.285481 | ||||||||
\(451\) | 1.19223 | 0.0561400 | ||||||||
\(452\) | −7.74399 | −0.364247 | ||||||||
\(453\) | −17.1572 | −0.806114 | ||||||||
\(454\) | 46.4358 | 2.17934 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.56408 | 0.260562 | ||||||||
\(457\) | −38.9673 | −1.82281 | −0.911407 | − | 0.411506i | \(-0.865003\pi\) | ||||
−0.911407 | + | 0.411506i | \(0.865003\pi\) | |||||||
\(458\) | 6.28864 | 0.293849 | ||||||||
\(459\) | 3.26275 | 0.152292 | ||||||||
\(460\) | 14.1408 | 0.659320 | ||||||||
\(461\) | 23.6532 | 1.10164 | 0.550819 | − | 0.834625i | \(-0.314315\pi\) | ||||
0.550819 | + | 0.834625i | \(0.314315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.86553 | −0.0866985 | −0.0433492 | − | 0.999060i | \(-0.513803\pi\) | ||||
−0.0433492 | + | 0.999060i | \(0.513803\pi\) | |||||||
\(464\) | 10.8180 | 0.502213 | ||||||||
\(465\) | 2.45902 | 0.114034 | ||||||||
\(466\) | −1.91978 | −0.0889322 | ||||||||
\(467\) | 5.20134 | 0.240689 | 0.120345 | − | 0.992732i | \(-0.461600\pi\) | ||||
0.120345 | + | 0.992732i | \(0.461600\pi\) | |||||||
\(468\) | 1.45341 | 0.0671841 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.5906 | −0.719142 | ||||||||
\(471\) | 17.1453 | 0.790014 | ||||||||
\(472\) | 3.85122 | 0.177267 | ||||||||
\(473\) | −7.13145 | −0.327905 | ||||||||
\(474\) | −26.5735 | −1.22056 | ||||||||
\(475\) | 19.9098 | 0.913526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.8675 | 0.543373 | ||||||||
\(478\) | −49.5506 | −2.26639 | ||||||||
\(479\) | −2.97785 | −0.136062 | −0.0680308 | − | 0.997683i | \(-0.521672\pi\) | ||||
−0.0680308 | + | 0.997683i | \(0.521672\pi\) | |||||||
\(480\) | 9.41036 | 0.429522 | ||||||||
\(481\) | −5.89004 | −0.268563 | ||||||||
\(482\) | 41.4760 | 1.88918 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.5506 | −0.661389 | ||||||||
\(485\) | −0.828414 | −0.0376163 | ||||||||
\(486\) | 1.87592 | 0.0850934 | ||||||||
\(487\) | 41.2011 | 1.86700 | 0.933500 | − | 0.358578i | \(-0.116738\pi\) | ||||
0.933500 | + | 0.358578i | \(0.116738\pi\) | |||||||
\(488\) | −4.37744 | −0.198157 | ||||||||
\(489\) | 9.69691 | 0.438509 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.81187 | −0.442803 | −0.221402 | − | 0.975183i | \(-0.571063\pi\) | ||||
−0.221402 | + | 0.975183i | \(0.571063\pi\) | |||||||
\(492\) | 1.51907 | 0.0684851 | ||||||||
\(493\) | −7.46135 | −0.336042 | ||||||||
\(494\) | −11.0694 | −0.498036 | ||||||||
\(495\) | −1.58694 | −0.0713276 | ||||||||
\(496\) | 8.73926 | 0.392404 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.94832 | 0.176928 | ||||||||
\(499\) | 15.2282 | 0.681708 | 0.340854 | − | 0.940116i | \(-0.389284\pi\) | ||||
0.340854 | + | 0.940116i | \(0.389284\pi\) | |||||||
\(500\) | 16.6374 | 0.744048 | ||||||||
\(501\) | 1.78167 | 0.0795989 | ||||||||
\(502\) | −37.0703 | −1.65453 | ||||||||
\(503\) | −7.15496 | −0.319024 | −0.159512 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159512 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.40178 | 0.418374 | ||||||||
\(506\) | −15.6413 | −0.695339 | ||||||||
\(507\) | −12.0846 | −0.536695 | ||||||||
\(508\) | 13.9258 | 0.617860 | ||||||||
\(509\) | −2.75329 | −0.122037 | −0.0610187 | − | 0.998137i | \(-0.519435\pi\) | ||||
−0.0610187 | + | 0.998137i | \(0.519435\pi\) | |||||||
\(510\) | −8.14700 | −0.360755 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.9084 | 1.10081 | ||||||||
\(513\) | −6.16735 | −0.272295 | ||||||||
\(514\) | −32.7332 | −1.44380 | ||||||||
\(515\) | −23.7251 | −1.04545 | ||||||||
\(516\) | −9.08649 | −0.400010 | ||||||||
\(517\) | 7.44407 | 0.327390 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.95559 | −0.349212 | ||||||||
\(520\) | 1.14896 | 0.0503852 | ||||||||
\(521\) | −21.3386 | −0.934861 | −0.467431 | − | 0.884030i | \(-0.654820\pi\) | ||||
−0.467431 | + | 0.884030i | \(0.654820\pi\) | |||||||
\(522\) | −4.28990 | −0.187764 | ||||||||
\(523\) | −5.54381 | −0.242414 | −0.121207 | − | 0.992627i | \(-0.538676\pi\) | ||||
−0.121207 | + | 0.992627i | \(0.538676\pi\) | |||||||
\(524\) | 6.82094 | 0.297974 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.2182 | 1.75360 | ||||||||
\(527\) | −6.02761 | −0.262567 | ||||||||
\(528\) | −5.63993 | −0.245446 | ||||||||
\(529\) | 25.9096 | 1.12651 | ||||||||
\(530\) | −29.6327 | −1.28716 | ||||||||
\(531\) | −4.26878 | −0.185249 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.956777 | 0.0414426 | ||||||||
\(534\) | −18.2267 | −0.788745 | ||||||||
\(535\) | −14.3382 | −0.619896 | ||||||||
\(536\) | −3.39274 | −0.146544 | ||||||||
\(537\) | 6.55130 | 0.282709 | ||||||||
\(538\) | 3.79028 | 0.163411 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.02199 | −0.0870124 | ||||||||
\(541\) | 9.42177 | 0.405073 | 0.202537 | − | 0.979275i | \(-0.435081\pi\) | ||||
0.202537 | + | 0.979275i | \(0.435081\pi\) | |||||||
\(542\) | 20.8098 | 0.893859 | ||||||||
\(543\) | −16.4764 | −0.707071 | ||||||||
\(544\) | −23.0670 | −0.988987 | ||||||||
\(545\) | 12.0376 | 0.515633 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.9252 | 1.06573 | 0.532863 | − | 0.846202i | \(-0.321116\pi\) | ||||
0.532863 | + | 0.846202i | \(0.321116\pi\) | |||||||
\(548\) | −10.8850 | −0.464982 | ||||||||
\(549\) | 4.85206 | 0.207081 | ||||||||
\(550\) | −7.22010 | −0.307866 | ||||||||
\(551\) | 14.1037 | 0.600837 | ||||||||
\(552\) | 6.30945 | 0.268548 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.1325 | 1.11026 | ||||||||
\(555\) | 8.19421 | 0.347825 | ||||||||
\(556\) | −16.5361 | −0.701287 | ||||||||
\(557\) | 7.44490 | 0.315451 | 0.157725 | − | 0.987483i | \(-0.449584\pi\) | ||||
0.157725 | + | 0.987483i | \(0.449584\pi\) | |||||||
\(558\) | −3.46558 | −0.146710 | ||||||||
\(559\) | −5.72306 | −0.242060 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.88995 | 0.164234 | ||||||||
\(562\) | −2.25605 | −0.0951658 | ||||||||
\(563\) | 33.3241 | 1.40444 | 0.702222 | − | 0.711958i | \(-0.252191\pi\) | ||||
0.702222 | + | 0.711958i | \(0.252191\pi\) | |||||||
\(564\) | 9.48480 | 0.399382 | ||||||||
\(565\) | 6.78557 | 0.285471 | ||||||||
\(566\) | −9.57719 | −0.402559 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2341 | 0.429412 | ||||||||
\(569\) | 33.6371 | 1.41014 | 0.705071 | − | 0.709137i | \(-0.250915\pi\) | ||||
0.705071 | + | 0.709137i | \(0.250915\pi\) | |||||||
\(570\) | 15.3997 | 0.645023 | ||||||||
\(571\) | 16.5003 | 0.690518 | 0.345259 | − | 0.938507i | \(-0.387791\pi\) | ||||
0.345259 | + | 0.938507i | \(0.387791\pi\) | |||||||
\(572\) | 1.73280 | 0.0724522 | ||||||||
\(573\) | −22.5981 | −0.944049 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.5770 | 0.941525 | ||||||||
\(576\) | −3.80123 | −0.158384 | ||||||||
\(577\) | 16.8768 | 0.702592 | 0.351296 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(578\) | −11.9205 | −0.495826 | ||||||||
\(579\) | −2.60607 | −0.108304 | ||||||||
\(580\) | 4.62393 | 0.191998 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.16751 | 0.0483949 | ||||||||
\(583\) | 14.1487 | 0.585981 | ||||||||
\(584\) | 5.47496 | 0.226555 | ||||||||
\(585\) | −1.27353 | −0.0526542 | ||||||||
\(586\) | −53.0008 | −2.18944 | ||||||||
\(587\) | −25.8123 | −1.06539 | −0.532694 | − | 0.846308i | \(-0.678820\pi\) | ||||
−0.532694 | + | 0.846308i | \(0.678820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3936 | 0.469465 | ||||||||
\(590\) | 10.6590 | 0.438826 | ||||||||
\(591\) | −16.3863 | −0.674042 | ||||||||
\(592\) | 29.1219 | 1.19690 | ||||||||
\(593\) | 17.2786 | 0.709547 | 0.354774 | − | 0.934952i | \(-0.384558\pi\) | ||||
0.354774 | + | 0.934952i | \(0.384558\pi\) | |||||||
\(594\) | 2.23653 | 0.0917659 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.4763 | −0.633934 | ||||||||
\(597\) | −8.52046 | −0.348719 | ||||||||
\(598\) | −12.5523 | −0.513300 | ||||||||
\(599\) | 25.0317 | 1.02277 | 0.511384 | − | 0.859352i | \(-0.329133\pi\) | ||||
0.511384 | + | 0.859352i | \(0.329133\pi\) | |||||||
\(600\) | 2.91248 | 0.118901 | ||||||||
\(601\) | 31.0336 | 1.26589 | 0.632944 | − | 0.774198i | \(-0.281846\pi\) | ||||
0.632944 | + | 0.774198i | \(0.281846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.76060 | 0.153143 | ||||||||
\(604\) | −26.0630 | −1.06049 | ||||||||
\(605\) | 12.7497 | 0.518350 | ||||||||
\(606\) | −13.2503 | −0.538255 | ||||||||
\(607\) | −8.46352 | −0.343524 | −0.171762 | − | 0.985138i | \(-0.554946\pi\) | ||||
−0.171762 | + | 0.985138i | \(0.554946\pi\) | |||||||
\(608\) | 43.6019 | 1.76829 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1155 | −0.490540 | ||||||||
\(611\) | 5.97394 | 0.241680 | ||||||||
\(612\) | 4.95635 | 0.200349 | ||||||||
\(613\) | −40.4704 | −1.63458 | −0.817291 | − | 0.576225i | \(-0.804525\pi\) | ||||
−0.817291 | + | 0.576225i | \(0.804525\pi\) | |||||||
\(614\) | 2.29546 | 0.0926370 | ||||||||
\(615\) | −1.33107 | −0.0536738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.0283 | −1.28941 | −0.644706 | − | 0.764430i | \(-0.723020\pi\) | ||||
−0.644706 | + | 0.764430i | \(0.723020\pi\) | |||||||
\(618\) | 33.4366 | 1.34502 | ||||||||
\(619\) | −40.1469 | −1.61364 | −0.806819 | − | 0.590798i | \(-0.798813\pi\) | ||||
−0.806819 | + | 0.590798i | \(0.798813\pi\) | |||||||
\(620\) | 3.73542 | 0.150018 | ||||||||
\(621\) | −6.99354 | −0.280641 | ||||||||
\(622\) | −14.4528 | −0.579504 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.52610 | −0.181189 | ||||||||
\(625\) | 1.56298 | 0.0625194 | ||||||||
\(626\) | 3.86657 | 0.154539 | ||||||||
\(627\) | −7.35291 | −0.293647 | ||||||||
\(628\) | 26.0450 | 1.03931 | ||||||||
\(629\) | −20.0859 | −0.800877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.26664 | 0.329090 | 0.164545 | − | 0.986370i | \(-0.447384\pi\) | ||||
0.164545 | + | 0.986370i | \(0.447384\pi\) | |||||||
\(632\) | 12.7800 | 0.508359 | ||||||||
\(633\) | 23.0347 | 0.915546 | ||||||||
\(634\) | −20.3801 | −0.809398 | ||||||||
\(635\) | −12.2023 | −0.484235 | ||||||||
\(636\) | 18.0275 | 0.714837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.11456 | −0.202487 | ||||||||
\(639\) | −11.3437 | −0.448749 | ||||||||
\(640\) | −9.32916 | −0.368768 | ||||||||
\(641\) | −10.8409 | −0.428189 | −0.214094 | − | 0.976813i | \(-0.568680\pi\) | ||||
−0.214094 | + | 0.976813i | \(0.568680\pi\) | |||||||
\(642\) | 20.2074 | 0.797522 | ||||||||
\(643\) | −27.7902 | −1.09594 | −0.547969 | − | 0.836499i | \(-0.684599\pi\) | ||||
−0.547969 | + | 0.836499i | \(0.684599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.96191 | 0.313500 | ||||||||
\(646\) | −37.7482 | −1.48518 | ||||||||
\(647\) | −34.1540 | −1.34273 | −0.671366 | − | 0.741126i | \(-0.734292\pi\) | ||||
−0.671366 | + | 0.741126i | \(0.734292\pi\) | |||||||
\(648\) | −0.902182 | −0.0354411 | ||||||||
\(649\) | −5.08938 | −0.199775 | ||||||||
\(650\) | −5.79420 | −0.227267 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.7303 | 0.576883 | ||||||||
\(653\) | −0.920987 | −0.0360410 | −0.0180205 | − | 0.999838i | \(-0.505736\pi\) | ||||
−0.0180205 | + | 0.999838i | \(0.505736\pi\) | |||||||
\(654\) | −16.9650 | −0.663383 | ||||||||
\(655\) | −5.97675 | −0.233531 | ||||||||
\(656\) | −4.73056 | −0.184698 | ||||||||
\(657\) | −6.06858 | −0.236758 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.06675 | 0.197372 | 0.0986862 | − | 0.995119i | \(-0.468536\pi\) | ||||
0.0986862 | + | 0.995119i | \(0.468536\pi\) | |||||||
\(660\) | −2.41067 | −0.0938354 | ||||||||
\(661\) | −22.6196 | −0.879801 | −0.439901 | − | 0.898046i | \(-0.644986\pi\) | ||||
−0.439901 | + | 0.898046i | \(0.644986\pi\) | |||||||
\(662\) | 54.1972 | 2.10644 | ||||||||
\(663\) | 3.12172 | 0.121238 | ||||||||
\(664\) | −1.89886 | −0.0736899 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.5484 | −0.447491 | ||||||||
\(667\) | 15.9930 | 0.619253 | ||||||||
\(668\) | 2.70648 | 0.104717 | ||||||||
\(669\) | 9.56418 | 0.369773 | ||||||||
\(670\) | −9.39011 | −0.362772 | ||||||||
\(671\) | 5.78477 | 0.223319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7602 | 0.530418 | 0.265209 | − | 0.964191i | \(-0.414559\pi\) | ||||
0.265209 | + | 0.964191i | \(0.414559\pi\) | |||||||
\(674\) | 38.1697 | 1.47024 | ||||||||
\(675\) | −3.22826 | −0.124256 | ||||||||
\(676\) | −18.3573 | −0.706052 | ||||||||
\(677\) | 0.583084 | 0.0224097 | 0.0112049 | − | 0.999937i | \(-0.496433\pi\) | ||||
0.0112049 | + | 0.999937i | \(0.496433\pi\) | |||||||
\(678\) | −9.56314 | −0.367270 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.91812 | 0.150253 | ||||||||
\(681\) | 24.7536 | 0.948561 | ||||||||
\(682\) | −4.13177 | −0.158214 | ||||||||
\(683\) | 27.6868 | 1.05941 | 0.529704 | − | 0.848183i | \(-0.322303\pi\) | ||||
0.529704 | + | 0.848183i | \(0.322303\pi\) | |||||||
\(684\) | −9.36866 | −0.358220 | ||||||||
\(685\) | 9.53780 | 0.364420 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.35230 | 0.127898 | ||||||||
\(688\) | 28.2964 | 1.07879 | ||||||||
\(689\) | 11.3545 | 0.432572 | ||||||||
\(690\) | 17.4627 | 0.664793 | ||||||||
\(691\) | −14.8271 | −0.564049 | −0.282025 | − | 0.959407i | \(-0.591006\pi\) | ||||
−0.282025 | + | 0.959407i | \(0.591006\pi\) | |||||||
\(692\) | −12.0851 | −0.459407 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3327 | 0.619981 | ||||||||
\(695\) | 14.4895 | 0.549620 | ||||||||
\(696\) | 2.06314 | 0.0782029 | ||||||||
\(697\) | 3.26275 | 0.123585 | ||||||||
\(698\) | 1.25446 | 0.0474820 | ||||||||
\(699\) | −1.02338 | −0.0387079 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.79286 | 0.105485 | 0.0527424 | − | 0.998608i | \(-0.483204\pi\) | ||||
0.0527424 | + | 0.998608i | \(0.483204\pi\) | |||||||
\(702\) | 1.79484 | 0.0677417 | ||||||||
\(703\) | 37.9670 | 1.43195 | ||||||||
\(704\) | −4.53194 | −0.170804 | ||||||||
\(705\) | −8.31093 | −0.313008 | ||||||||
\(706\) | −20.7876 | −0.782353 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.48459 | −0.243706 | ||||||||
\(709\) | −42.6863 | −1.60312 | −0.801558 | − | 0.597917i | \(-0.795995\pi\) | ||||
−0.801558 | + | 0.597917i | \(0.795995\pi\) | |||||||
\(710\) | 28.3249 | 1.06301 | ||||||||
\(711\) | −14.1656 | −0.531252 | ||||||||
\(712\) | 8.76572 | 0.328509 | ||||||||
\(713\) | 12.9199 | 0.483854 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.51835 | −0.0567830 | ||||||||
\(716\) | 9.95189 | 0.371920 | ||||||||
\(717\) | −26.4140 | −0.986449 | ||||||||
\(718\) | −18.0922 | −0.675196 | ||||||||
\(719\) | −44.1357 | −1.64598 | −0.822992 | − | 0.568053i | \(-0.807697\pi\) | ||||
−0.822992 | + | 0.568053i | \(0.807697\pi\) | |||||||
\(720\) | 6.29670 | 0.234664 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 35.7105 | 1.32901 | ||||||||
\(723\) | 22.1097 | 0.822268 | ||||||||
\(724\) | −25.0289 | −0.930191 | ||||||||
\(725\) | 7.38248 | 0.274178 | ||||||||
\(726\) | −17.9686 | −0.666879 | ||||||||
\(727\) | 13.6510 | 0.506288 | 0.253144 | − | 0.967429i | \(-0.418535\pi\) | ||||
0.253144 | + | 0.967429i | \(0.418535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.1531 | 0.560840 | ||||||||
\(731\) | −19.5165 | −0.721843 | ||||||||
\(732\) | 7.37062 | 0.272426 | ||||||||
\(733\) | −15.2128 | −0.561896 | −0.280948 | − | 0.959723i | \(-0.590649\pi\) | ||||
−0.280948 | + | 0.959723i | \(0.590649\pi\) | |||||||
\(734\) | 66.6597 | 2.46045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 49.4429 | 1.82249 | ||||||||
\(737\) | 4.48350 | 0.165152 | ||||||||
\(738\) | 1.87592 | 0.0690535 | ||||||||
\(739\) | 12.6595 | 0.465689 | 0.232844 | − | 0.972514i | \(-0.425197\pi\) | ||||
0.232844 | + | 0.972514i | \(0.425197\pi\) | |||||||
\(740\) | 12.4476 | 0.457583 | ||||||||
\(741\) | −5.90078 | −0.216771 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.8862 | −1.20648 | −0.603238 | − | 0.797561i | \(-0.706123\pi\) | ||||
−0.603238 | + | 0.797561i | \(0.706123\pi\) | |||||||
\(744\) | 1.66669 | 0.0611040 | ||||||||
\(745\) | 13.5609 | 0.496833 | ||||||||
\(746\) | 1.71633 | 0.0628394 | ||||||||
\(747\) | 2.10474 | 0.0770083 | ||||||||
\(748\) | 5.90912 | 0.216059 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 20.5457 | 0.750225 | ||||||||
\(751\) | 5.59396 | 0.204127 | 0.102063 | − | 0.994778i | \(-0.467456\pi\) | ||||
0.102063 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(752\) | −29.5368 | −1.07709 | ||||||||
\(753\) | −19.7611 | −0.720136 | ||||||||
\(754\) | −4.10448 | −0.149476 | ||||||||
\(755\) | 22.8373 | 0.831136 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.2675 | −1.79066 | −0.895329 | − | 0.445406i | \(-0.853059\pi\) | ||||
−0.895329 | + | 0.445406i | \(0.853059\pi\) | |||||||
\(758\) | −2.90727 | −0.105597 | ||||||||
\(759\) | −8.33792 | −0.302647 | ||||||||
\(760\) | −7.40616 | −0.268649 | ||||||||
\(761\) | −37.0827 | −1.34425 | −0.672123 | − | 0.740439i | \(-0.734618\pi\) | ||||
−0.672123 | + | 0.740439i | \(0.734618\pi\) | |||||||
\(762\) | 17.1972 | 0.622988 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −34.3281 | −1.24195 | ||||||||
\(765\) | −4.34294 | −0.157019 | ||||||||
\(766\) | 71.9983 | 2.60140 | ||||||||
\(767\) | −4.08427 | −0.147475 | ||||||||
\(768\) | 20.7504 | 0.748765 | ||||||||
\(769\) | 46.4807 | 1.67614 | 0.838069 | − | 0.545564i | \(-0.183684\pi\) | ||||
0.838069 | + | 0.545564i | \(0.183684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.4492 | −0.628416 | ||||||||
\(772\) | −3.95880 | −0.142480 | ||||||||
\(773\) | 53.4446 | 1.92227 | 0.961134 | − | 0.276081i | \(-0.0890360\pi\) | ||||
0.961134 | + | 0.276081i | \(0.0890360\pi\) | |||||||
\(774\) | −11.2210 | −0.403331 | ||||||||
\(775\) | 5.96390 | 0.214230 | ||||||||
\(776\) | −0.561489 | −0.0201563 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.91219 | 0.283666 | ||||||||
\(779\) | −6.16735 | −0.220968 | ||||||||
\(780\) | −1.93459 | −0.0692694 | ||||||||
\(781\) | −13.5243 | −0.483937 | ||||||||
\(782\) | −42.8050 | −1.53071 | ||||||||
\(783\) | −2.28683 | −0.0817246 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.8216 | −0.814536 | ||||||||
\(786\) | 8.42325 | 0.300447 | ||||||||
\(787\) | 19.7132 | 0.702700 | 0.351350 | − | 0.936244i | \(-0.385723\pi\) | ||||
0.351350 | + | 0.936244i | \(0.385723\pi\) | |||||||
\(788\) | −24.8920 | −0.886739 | ||||||||
\(789\) | 21.4392 | 0.763255 | ||||||||
\(790\) | 35.3711 | 1.25845 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.07561 | −0.0382201 | ||||||||
\(793\) | 4.64234 | 0.164854 | ||||||||
\(794\) | 56.0637 | 1.98962 | ||||||||
\(795\) | −15.7964 | −0.560239 | ||||||||
\(796\) | −12.9432 | −0.458759 | ||||||||
\(797\) | −42.7009 | −1.51254 | −0.756271 | − | 0.654259i | \(-0.772981\pi\) | ||||
−0.756271 | + | 0.654259i | \(0.772981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.3720 | 0.720709 | ||||||||
\(800\) | 22.8231 | 0.806920 | ||||||||
\(801\) | −9.71613 | −0.343303 | ||||||||
\(802\) | 32.3969 | 1.14397 | ||||||||
\(803\) | −7.23515 | −0.255323 | ||||||||
\(804\) | 5.71262 | 0.201468 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.31579 | −0.116794 | ||||||||
\(807\) | 2.02049 | 0.0711248 | ||||||||
\(808\) | 6.37242 | 0.224181 | ||||||||
\(809\) | −6.30079 | −0.221524 | −0.110762 | − | 0.993847i | \(-0.535329\pi\) | ||||
−0.110762 | + | 0.993847i | \(0.535329\pi\) | |||||||
\(810\) | −2.49697 | −0.0877347 | ||||||||
\(811\) | −21.0846 | −0.740379 | −0.370189 | − | 0.928956i | \(-0.620707\pi\) | ||||
−0.370189 | + | 0.928956i | \(0.620707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0931 | 0.389054 | ||||||||
\(814\) | −13.7683 | −0.482580 | ||||||||
\(815\) | −12.9072 | −0.452121 | ||||||||
\(816\) | −15.4346 | −0.540321 | ||||||||
\(817\) | 36.8907 | 1.29064 | ||||||||
\(818\) | 1.07443 | 0.0375664 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.02199 | −0.0706108 | ||||||||
\(821\) | −4.52453 | −0.157907 | −0.0789537 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789537 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(822\) | −13.4420 | −0.468842 | ||||||||
\(823\) | −40.2931 | −1.40453 | −0.702264 | − | 0.711916i | \(-0.747827\pi\) | ||||
−0.702264 | + | 0.711916i | \(0.747827\pi\) | |||||||
\(824\) | −16.0806 | −0.560195 | ||||||||
\(825\) | −3.84883 | −0.133999 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1628 | −0.388169 | −0.194085 | − | 0.980985i | \(-0.562174\pi\) | ||||
−0.194085 | + | 0.980985i | \(0.562174\pi\) | |||||||
\(828\) | −10.6237 | −0.369199 | ||||||||
\(829\) | −38.5413 | −1.33859 | −0.669297 | − | 0.742995i | \(-0.733404\pi\) | ||||
−0.669297 | + | 0.742995i | \(0.733404\pi\) | |||||||
\(830\) | −5.25547 | −0.182420 | ||||||||
\(831\) | 13.9305 | 0.483243 | ||||||||
\(832\) | −3.63693 | −0.126088 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.4206 | −0.707108 | ||||||||
\(835\) | −2.37151 | −0.0820697 | ||||||||
\(836\) | −11.1696 | −0.386309 | ||||||||
\(837\) | −1.84740 | −0.0638556 | ||||||||
\(838\) | −17.5883 | −0.607579 | ||||||||
\(839\) | 0.657012 | 0.0226826 | 0.0113413 | − | 0.999936i | \(-0.496390\pi\) | ||||
0.0113413 | + | 0.999936i | \(0.496390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7704 | −0.819670 | ||||||||
\(842\) | 1.16504 | 0.0401498 | ||||||||
\(843\) | −1.20264 | −0.0414211 | ||||||||
\(844\) | 34.9913 | 1.20445 | ||||||||
\(845\) | 16.0854 | 0.553354 | ||||||||
\(846\) | 11.7129 | 0.402697 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −56.1397 | −1.92785 | ||||||||
\(849\) | −5.10533 | −0.175214 | ||||||||
\(850\) | −19.7591 | −0.677730 | ||||||||
\(851\) | 43.0531 | 1.47584 | ||||||||
\(852\) | −17.2319 | −0.590354 | ||||||||
\(853\) | −2.29577 | −0.0786058 | −0.0393029 | − | 0.999227i | \(-0.512514\pi\) | ||||
−0.0393029 | + | 0.999227i | \(0.512514\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.20916 | 0.280747 | ||||||||
\(856\) | −9.71830 | −0.332165 | ||||||||
\(857\) | −18.9064 | −0.645830 | −0.322915 | − | 0.946428i | \(-0.604663\pi\) | ||||
−0.322915 | + | 0.946428i | \(0.604663\pi\) | |||||||
\(858\) | 2.13986 | 0.0730536 | ||||||||
\(859\) | −33.0093 | −1.12626 | −0.563131 | − | 0.826368i | \(-0.690403\pi\) | ||||
−0.563131 | + | 0.826368i | \(0.690403\pi\) | |||||||
\(860\) | 12.0947 | 0.412426 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 73.6961 | 2.51010 | ||||||||
\(863\) | −32.3940 | −1.10271 | −0.551353 | − | 0.834272i | \(-0.685888\pi\) | ||||
−0.551353 | + | 0.834272i | \(0.685888\pi\) | |||||||
\(864\) | −7.06979 | −0.240519 | ||||||||
\(865\) | 10.5894 | 0.360051 | ||||||||
\(866\) | 12.2795 | 0.417275 | ||||||||
\(867\) | −6.35447 | −0.215809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.8887 | −0.572909 | ||||||||
\(870\) | 5.71015 | 0.193592 | ||||||||
\(871\) | 3.59805 | 0.121915 | ||||||||
\(872\) | 8.15893 | 0.276296 | ||||||||
\(873\) | 0.622368 | 0.0210640 | ||||||||
\(874\) | 80.9115 | 2.73687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.21860 | −0.311468 | ||||||||
\(877\) | 2.48394 | 0.0838768 | 0.0419384 | − | 0.999120i | \(-0.486647\pi\) | ||||
0.0419384 | + | 0.999120i | \(0.486647\pi\) | |||||||
\(878\) | −22.5085 | −0.759625 | ||||||||
\(879\) | −28.2532 | −0.952958 | ||||||||
\(880\) | 7.50712 | 0.253065 | ||||||||
\(881\) | −4.62881 | −0.155949 | −0.0779744 | − | 0.996955i | \(-0.524845\pi\) | ||||
−0.0779744 | + | 0.996955i | \(0.524845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8165 | 0.464962 | 0.232481 | − | 0.972601i | \(-0.425316\pi\) | ||||
0.232481 | + | 0.972601i | \(0.425316\pi\) | |||||||
\(884\) | 4.74212 | 0.159495 | ||||||||
\(885\) | 5.68203 | 0.190999 | ||||||||
\(886\) | −9.11260 | −0.306144 | ||||||||
\(887\) | 13.3709 | 0.448950 | 0.224475 | − | 0.974480i | \(-0.427933\pi\) | ||||
0.224475 | + | 0.974480i | \(0.427933\pi\) | |||||||
\(888\) | 5.55394 | 0.186378 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.2609 | 0.813228 | ||||||||
\(891\) | 1.19223 | 0.0399412 | ||||||||
\(892\) | 14.5287 | 0.486456 | ||||||||
\(893\) | −38.5078 | −1.28861 | ||||||||
\(894\) | −19.1119 | −0.639196 | ||||||||
\(895\) | −8.72021 | −0.291485 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.69126 | −0.223415 | ||||||||
\(898\) | 15.6739 | 0.523043 | ||||||||
\(899\) | 4.22470 | 0.140901 | ||||||||
\(900\) | −4.90396 | −0.163465 | ||||||||
\(901\) | 38.7205 | 1.28997 | ||||||||
\(902\) | 2.23653 | 0.0744683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.59918 | 0.152966 | ||||||||
\(905\) | 21.9312 | 0.729018 | ||||||||
\(906\) | −32.1855 | −1.06929 | ||||||||
\(907\) | 35.7979 | 1.18865 | 0.594325 | − | 0.804225i | \(-0.297419\pi\) | ||||
0.594325 | + | 0.804225i | \(0.297419\pi\) | |||||||
\(908\) | 37.6025 | 1.24788 | ||||||||
\(909\) | −7.06334 | −0.234276 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.9779 | 1.42392 | 0.711960 | − | 0.702220i | \(-0.247808\pi\) | ||||
0.711960 | + | 0.702220i | \(0.247808\pi\) | |||||||
\(912\) | 29.1751 | 0.966083 | ||||||||
\(913\) | 2.50933 | 0.0830468 | ||||||||
\(914\) | −73.0995 | −2.41792 | ||||||||
\(915\) | −6.45841 | −0.213508 | ||||||||
\(916\) | 5.09238 | 0.168257 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.12065 | 0.202012 | ||||||||
\(919\) | 13.4263 | 0.442893 | 0.221447 | − | 0.975173i | \(-0.428922\pi\) | ||||
0.221447 | + | 0.975173i | \(0.428922\pi\) | |||||||
\(920\) | −8.39829 | −0.276884 | ||||||||
\(921\) | 1.22364 | 0.0403204 | ||||||||
\(922\) | 44.3715 | 1.46130 | ||||||||
\(923\) | −10.8534 | −0.357243 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.8736 | 0.653439 | ||||||||
\(926\) | −3.49958 | −0.115003 | ||||||||
\(927\) | 17.8241 | 0.585421 | ||||||||
\(928\) | 16.1674 | 0.530721 | ||||||||
\(929\) | 32.5053 | 1.06646 | 0.533232 | − | 0.845969i | \(-0.320977\pi\) | ||||
0.533232 | + | 0.845969i | \(0.320977\pi\) | |||||||
\(930\) | 4.61292 | 0.151264 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.55459 | −0.0509223 | ||||||||
\(933\) | −7.70437 | −0.252230 | ||||||||
\(934\) | 9.75729 | 0.319268 | ||||||||
\(935\) | −5.17778 | −0.169332 | ||||||||
\(936\) | −0.863187 | −0.0282142 | ||||||||
\(937\) | 10.0847 | 0.329454 | 0.164727 | − | 0.986339i | \(-0.447326\pi\) | ||||
0.164727 | + | 0.986339i | \(0.447326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.06116 | 0.0672634 | ||||||||
\(940\) | −12.6249 | −0.411779 | ||||||||
\(941\) | −45.9898 | −1.49923 | −0.749613 | − | 0.661876i | \(-0.769760\pi\) | ||||
−0.749613 | + | 0.661876i | \(0.769760\pi\) | |||||||
\(942\) | 32.1632 | 1.04793 | ||||||||
\(943\) | −6.99354 | −0.227741 | ||||||||
\(944\) | 20.1938 | 0.657251 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.3780 | −0.434957 | ||||||||
\(947\) | 2.76566 | 0.0898719 | 0.0449359 | − | 0.998990i | \(-0.485692\pi\) | ||||
0.0449359 | + | 0.998990i | \(0.485692\pi\) | |||||||
\(948\) | −21.5186 | −0.698891 | ||||||||
\(949\) | −5.80628 | −0.188480 | ||||||||
\(950\) | 37.3492 | 1.21177 | ||||||||
\(951\) | −10.8641 | −0.352292 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.52118 | 0.308421 | 0.154211 | − | 0.988038i | \(-0.450717\pi\) | ||||
0.154211 | + | 0.988038i | \(0.450717\pi\) | |||||||
\(954\) | 22.2624 | 0.720771 | ||||||||
\(955\) | 30.0796 | 0.973352 | ||||||||
\(956\) | −40.1248 | −1.29773 | ||||||||
\(957\) | −2.72643 | −0.0881329 | ||||||||
\(958\) | −5.58621 | −0.180482 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.05969 | 0.163301 | ||||||||
\(961\) | −27.5871 | −0.889906 | ||||||||
\(962\) | −11.0492 | −0.356242 | ||||||||
\(963\) | 10.7720 | 0.347123 | ||||||||
\(964\) | 33.5862 | 1.08174 | ||||||||
\(965\) | 3.46885 | 0.111666 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.5417 | −0.403314 | −0.201657 | − | 0.979456i | \(-0.564633\pi\) | ||||
−0.201657 | + | 0.979456i | \(0.564633\pi\) | |||||||
\(968\) | 8.64163 | 0.277752 | ||||||||
\(969\) | −20.1225 | −0.646429 | ||||||||
\(970\) | −1.55404 | −0.0498971 | ||||||||
\(971\) | 1.59591 | 0.0512153 | 0.0256076 | − | 0.999672i | \(-0.491848\pi\) | ||||
0.0256076 | + | 0.999672i | \(0.491848\pi\) | |||||||
\(972\) | 1.51907 | 0.0487243 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 77.2899 | 2.47653 | ||||||||
\(975\) | −3.08873 | −0.0989184 | ||||||||
\(976\) | −22.9530 | −0.734707 | ||||||||
\(977\) | 3.70916 | 0.118667 | 0.0593333 | − | 0.998238i | \(-0.481103\pi\) | ||||
0.0593333 | + | 0.998238i | \(0.481103\pi\) | |||||||
\(978\) | 18.1906 | 0.581672 | ||||||||
\(979\) | −11.5839 | −0.370222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.04356 | −0.288739 | ||||||||
\(982\) | −18.4063 | −0.587368 | ||||||||
\(983\) | 14.2656 | 0.455001 | 0.227501 | − | 0.973778i | \(-0.426945\pi\) | ||||
0.227501 | + | 0.973778i | \(0.426945\pi\) | |||||||
\(984\) | −0.902182 | −0.0287605 | ||||||||
\(985\) | 21.8112 | 0.694964 | ||||||||
\(986\) | −13.9969 | −0.445752 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.96372 | −0.285174 | ||||||||
\(989\) | 41.8326 | 1.33020 | ||||||||
\(990\) | −2.97697 | −0.0946143 | ||||||||
\(991\) | 57.4385 | 1.82459 | 0.912297 | − | 0.409530i | \(-0.134307\pi\) | ||||
0.912297 | + | 0.409530i | \(0.134307\pi\) | |||||||
\(992\) | 13.0608 | 0.414680 | ||||||||
\(993\) | 28.8910 | 0.916829 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3413 | 0.359543 | ||||||||
\(996\) | 3.19725 | 0.101309 | ||||||||
\(997\) | −28.4978 | −0.902534 | −0.451267 | − | 0.892389i | \(-0.649028\pi\) | ||||
−0.451267 | + | 0.892389i | \(0.649028\pi\) | |||||||
\(998\) | 28.5669 | 0.904268 | ||||||||
\(999\) | −6.15612 | −0.194771 |
(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 | 6027.2.a.bm.1.14 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.14 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.14 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.14 | yes | 16 | 1.1 | even | 1 | trivial |