Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x + 11 \) |
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 | 1.1 | ||
Root | \(4.03932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.03932 | −1.52672 | −0.763359 | − | 0.645974i | \(-0.776451\pi\) | ||||
−0.763359 | + | 0.645974i | \(0.776451\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.69736 | −1.71782 | −0.858909 | − | 0.512128i | \(-0.828857\pi\) | ||||
−0.858909 | + | 0.512128i | \(0.828857\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.381275 | −0.105747 | −0.0528733 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528733 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(14\) | −4.03932 | −1.07955 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.65804 | 0.887206 | 0.443603 | − | 0.896223i | \(-0.353700\pi\) | ||||
0.443603 | + | 0.896223i | \(0.353700\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.381275 | 0.0874705 | 0.0437352 | − | 0.999043i | \(-0.486074\pi\) | ||||
0.0437352 | + | 0.999043i | \(0.486074\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.03932 | 0.881451 | ||||||||
\(22\) | −5.69736 | −1.21468 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.381275 | −0.0747742 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.03932 | −0.763359 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.69736 | 0.991783 | ||||||||
\(34\) | 3.65804 | 0.627349 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.65804 | −0.601378 | −0.300689 | − | 0.953722i | \(-0.597217\pi\) | ||||
−0.300689 | + | 0.953722i | \(0.597217\pi\) | |||||||
\(38\) | 0.381275 | 0.0618510 | ||||||||
\(39\) | 0.381275 | 0.0610528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.61873 | 0.877497 | 0.438749 | − | 0.898610i | \(-0.355422\pi\) | ||||
0.438749 | + | 0.898610i | \(0.355422\pi\) | |||||||
\(42\) | 4.03932 | 0.623280 | ||||||||
\(43\) | −3.61873 | −0.551850 | −0.275925 | − | 0.961179i | \(-0.588984\pi\) | ||||
−0.275925 | + | 0.961179i | \(0.588984\pi\) | |||||||
\(44\) | −5.69736 | −0.858909 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.38127 | 0.493210 | 0.246605 | − | 0.969116i | \(-0.420685\pi\) | ||||
0.246605 | + | 0.969116i | \(0.420685\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 9.31608 | 1.33087 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.65804 | −0.512228 | ||||||||
\(52\) | −0.381275 | −0.0528733 | ||||||||
\(53\) | −9.31608 | −1.27966 | −0.639831 | − | 0.768515i | \(-0.720996\pi\) | ||||
−0.639831 | + | 0.768515i | \(0.720996\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.03932 | −0.539776 | ||||||||
\(57\) | −0.381275 | −0.0505011 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 13.3947 | 1.74384 | 0.871922 | − | 0.489645i | \(-0.162874\pi\) | ||||
0.871922 | + | 0.489645i | \(0.162874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0786 | 1.80258 | 0.901292 | − | 0.433212i | \(-0.142620\pi\) | ||||
0.901292 | + | 0.433212i | \(0.142620\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −4.03932 | −0.508906 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.69736 | 0.701297 | ||||||||
\(67\) | 2.76255 | 0.337499 | 0.168750 | − | 0.985659i | \(-0.446027\pi\) | ||||
0.168750 | + | 0.985659i | \(0.446027\pi\) | |||||||
\(68\) | 3.65804 | 0.443603 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6974 | 1.26954 | 0.634772 | − | 0.772700i | \(-0.281094\pi\) | ||||
0.634772 | + | 0.772700i | \(0.281094\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.07863 | 0.828492 | 0.414246 | − | 0.910165i | \(-0.364045\pi\) | ||||
0.414246 | + | 0.910165i | \(0.364045\pi\) | |||||||
\(74\) | −3.65804 | −0.425239 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.381275 | 0.0437352 | ||||||||
\(77\) | 23.0134 | 2.62263 | ||||||||
\(78\) | 0.381275 | 0.0431709 | ||||||||
\(79\) | 5.69736 | 0.641003 | 0.320502 | − | 0.947248i | \(-0.396149\pi\) | ||||
0.320502 | + | 0.947248i | \(0.396149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.61873 | 0.620484 | ||||||||
\(83\) | −16.1180 | −1.76918 | −0.884588 | − | 0.466374i | \(-0.845560\pi\) | ||||
−0.884588 | + | 0.466374i | \(0.845560\pi\) | |||||||
\(84\) | 4.03932 | 0.440726 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.61873 | −0.390217 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −5.69736 | −0.607341 | ||||||||
\(89\) | 5.65804 | 0.599751 | 0.299876 | − | 0.953978i | \(-0.403055\pi\) | ||||
0.299876 | + | 0.953978i | \(0.403055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.54009 | 0.161445 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 3.38127 | 0.348752 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.07863 | 0.414123 | 0.207061 | − | 0.978328i | \(-0.433610\pi\) | ||||
0.207061 | + | 0.978328i | \(0.433610\pi\) | |||||||
\(98\) | 9.31608 | 0.941067 | ||||||||
\(99\) | −5.69736 | −0.572606 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.7760 | 1.66927 | 0.834637 | − | 0.550801i | \(-0.185677\pi\) | ||||
0.834637 | + | 0.550801i | \(0.185677\pi\) | |||||||
\(102\) | −3.65804 | −0.362200 | ||||||||
\(103\) | −13.3554 | −1.31595 | −0.657973 | − | 0.753041i | \(-0.728586\pi\) | ||||
−0.657973 | + | 0.753041i | \(0.728586\pi\) | |||||||
\(104\) | −0.381275 | −0.0373871 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.31608 | −0.904858 | ||||||||
\(107\) | 6.76255 | 0.653760 | 0.326880 | − | 0.945066i | \(-0.394003\pi\) | ||||
0.326880 | + | 0.945066i | \(0.394003\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −13.0528 | −1.25023 | −0.625114 | − | 0.780534i | \(-0.714948\pi\) | ||||
−0.625114 | + | 0.780534i | \(0.714948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.65804 | 0.347206 | ||||||||
\(112\) | −4.03932 | −0.381680 | ||||||||
\(113\) | 1.65804 | 0.155976 | 0.0779878 | − | 0.996954i | \(-0.475150\pi\) | ||||
0.0779878 | + | 0.996954i | \(0.475150\pi\) | |||||||
\(114\) | −0.381275 | −0.0357097 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −0.381275 | −0.0352489 | ||||||||
\(118\) | 13.3947 | 1.23308 | ||||||||
\(119\) | −14.7760 | −1.35451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.4599 | 1.95090 | ||||||||
\(122\) | 14.0786 | 1.27462 | ||||||||
\(123\) | −5.61873 | −0.506623 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.03932 | −0.359851 | ||||||||
\(127\) | 18.6322 | 1.65334 | 0.826669 | − | 0.562689i | \(-0.190233\pi\) | ||||
0.826669 | + | 0.562689i | \(0.190233\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.61873 | 0.318611 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4734 | −1.52665 | −0.763327 | − | 0.646012i | \(-0.776435\pi\) | ||||
−0.763327 | + | 0.646012i | \(0.776435\pi\) | |||||||
\(132\) | 5.69736 | 0.495892 | ||||||||
\(133\) | −1.54009 | −0.133543 | ||||||||
\(134\) | 2.76255 | 0.238648 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.65804 | 0.313675 | ||||||||
\(137\) | 14.3420 | 1.22532 | 0.612658 | − | 0.790348i | \(-0.290100\pi\) | ||||
0.612658 | + | 0.790348i | \(0.290100\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −8.01344 | −0.679692 | −0.339846 | − | 0.940481i | \(-0.610375\pi\) | ||||
−0.339846 | + | 0.940481i | \(0.610375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.38127 | −0.284755 | ||||||||
\(142\) | 10.6974 | 0.897702 | ||||||||
\(143\) | 2.17226 | 0.181654 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.07863 | 0.585832 | ||||||||
\(147\) | −9.31608 | −0.768378 | ||||||||
\(148\) | −3.65804 | −0.300689 | ||||||||
\(149\) | 3.23745 | 0.265222 | 0.132611 | − | 0.991168i | \(-0.457664\pi\) | ||||
0.132611 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.31608 | −0.758132 | −0.379066 | − | 0.925370i | \(-0.623755\pi\) | ||||
−0.379066 | + | 0.925370i | \(0.623755\pi\) | |||||||
\(152\) | 0.381275 | 0.0309255 | ||||||||
\(153\) | 3.65804 | 0.295735 | ||||||||
\(154\) | 23.0134 | 1.85448 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.381275 | 0.0305264 | ||||||||
\(157\) | 6.84118 | 0.545986 | 0.272993 | − | 0.962016i | \(-0.411986\pi\) | ||||
0.272993 | + | 0.962016i | \(0.411986\pi\) | |||||||
\(158\) | 5.69736 | 0.453258 | ||||||||
\(159\) | 9.31608 | 0.738814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.03932 | −0.318343 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.76255 | −0.373032 | −0.186516 | − | 0.982452i | \(-0.559720\pi\) | ||||
−0.186516 | + | 0.982452i | \(0.559720\pi\) | |||||||
\(164\) | 5.61873 | 0.438749 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.1180 | −1.25100 | ||||||||
\(167\) | −14.8546 | −1.14949 | −0.574743 | − | 0.818334i | \(-0.694898\pi\) | ||||
−0.574743 | + | 0.818334i | \(0.694898\pi\) | |||||||
\(168\) | 4.03932 | 0.311640 | ||||||||
\(169\) | −12.8546 | −0.988818 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.381275 | 0.0291568 | ||||||||
\(172\) | −3.61873 | −0.275925 | ||||||||
\(173\) | −9.69736 | −0.737277 | −0.368638 | − | 0.929573i | \(-0.620176\pi\) | ||||
−0.368638 | + | 0.929573i | \(0.620176\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.69736 | −0.429455 | ||||||||
\(177\) | −13.3947 | −1.00681 | ||||||||
\(178\) | 5.65804 | 0.424088 | ||||||||
\(179\) | −5.31608 | −0.397343 | −0.198671 | − | 0.980066i | \(-0.563663\pi\) | ||||
−0.198671 | + | 0.980066i | \(0.563663\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.3688 | 1.81132 | 0.905661 | − | 0.424002i | \(-0.139375\pi\) | ||||
0.905661 | + | 0.424002i | \(0.139375\pi\) | |||||||
\(182\) | 1.54009 | 0.114159 | ||||||||
\(183\) | −14.0786 | −1.04072 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | −20.8412 | −1.52406 | ||||||||
\(188\) | 3.38127 | 0.246605 | ||||||||
\(189\) | 4.03932 | 0.293817 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4599 | 0.756853 | 0.378426 | − | 0.925631i | \(-0.376465\pi\) | ||||
0.378426 | + | 0.925631i | \(0.376465\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 14.0134 | 1.00871 | 0.504355 | − | 0.863496i | \(-0.331730\pi\) | ||||
0.504355 | + | 0.863496i | \(0.331730\pi\) | |||||||
\(194\) | 4.07863 | 0.292829 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.31608 | 0.665435 | ||||||||
\(197\) | −8.47335 | −0.603702 | −0.301851 | − | 0.953355i | \(-0.597604\pi\) | ||||
−0.301851 | + | 0.953355i | \(0.597604\pi\) | |||||||
\(198\) | −5.69736 | −0.404894 | ||||||||
\(199\) | 1.19813 | 0.0849334 | 0.0424667 | − | 0.999098i | \(-0.486478\pi\) | ||||
0.0424667 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.76255 | −0.194855 | ||||||||
\(202\) | 16.7760 | 1.18035 | ||||||||
\(203\) | 4.03932 | 0.283505 | ||||||||
\(204\) | −3.65804 | −0.256114 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.3554 | −0.930515 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −0.381275 | −0.0264367 | ||||||||
\(209\) | −2.17226 | −0.150258 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2225 | −1.11680 | −0.558400 | − | 0.829572i | \(-0.688585\pi\) | ||||
−0.558400 | + | 0.829572i | \(0.688585\pi\) | |||||||
\(212\) | −9.31608 | −0.639831 | ||||||||
\(213\) | −10.6974 | −0.732971 | ||||||||
\(214\) | 6.76255 | 0.462278 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −24.2359 | −1.64524 | ||||||||
\(218\) | −13.0528 | −0.884045 | ||||||||
\(219\) | −7.07863 | −0.478330 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.39472 | −0.0938190 | ||||||||
\(222\) | 3.65804 | 0.245512 | ||||||||
\(223\) | 13.6037 | 0.910973 | 0.455487 | − | 0.890243i | \(-0.349465\pi\) | ||||
0.455487 | + | 0.890243i | \(0.349465\pi\) | |||||||
\(224\) | −4.03932 | −0.269888 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.65804 | 0.110291 | ||||||||
\(227\) | 12.4992 | 0.829603 | 0.414801 | − | 0.909912i | \(-0.363851\pi\) | ||||
0.414801 | + | 0.909912i | \(0.363851\pi\) | |||||||
\(228\) | −0.381275 | −0.0252505 | ||||||||
\(229\) | 21.4734 | 1.41900 | 0.709500 | − | 0.704706i | \(-0.248921\pi\) | ||||
0.709500 | + | 0.704706i | \(0.248921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.0134 | −1.51417 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 11.1438 | 0.730056 | 0.365028 | − | 0.930996i | \(-0.381059\pi\) | ||||
0.365028 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(234\) | −0.381275 | −0.0249247 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.3947 | 0.871922 | ||||||||
\(237\) | −5.69736 | −0.370083 | ||||||||
\(238\) | −14.7760 | −0.957785 | ||||||||
\(239\) | 22.1707 | 1.43410 | 0.717052 | − | 0.697020i | \(-0.245491\pi\) | ||||
0.717052 | + | 0.697020i | \(0.245491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8696 | −0.893421 | −0.446710 | − | 0.894679i | \(-0.647405\pi\) | ||||
−0.446710 | + | 0.894679i | \(0.647405\pi\) | |||||||
\(242\) | 21.4599 | 1.37950 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.0786 | 0.901292 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.61873 | −0.358237 | ||||||||
\(247\) | −0.145371 | −0.00924971 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 16.1180 | 1.02143 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.73668 | 0.362096 | 0.181048 | − | 0.983474i | \(-0.442051\pi\) | ||||
0.181048 | + | 0.983474i | \(0.442051\pi\) | |||||||
\(252\) | −4.03932 | −0.254453 | ||||||||
\(253\) | −5.69736 | −0.358190 | ||||||||
\(254\) | 18.6322 | 1.16909 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6322 | 1.28700 | 0.643500 | − | 0.765446i | \(-0.277482\pi\) | ||||
0.643500 | + | 0.765446i | \(0.277482\pi\) | |||||||
\(258\) | 3.61873 | 0.225292 | ||||||||
\(259\) | 14.7760 | 0.918136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −17.4734 | −1.07951 | ||||||||
\(263\) | −19.8696 | −1.22521 | −0.612607 | − | 0.790388i | \(-0.709879\pi\) | ||||
−0.612607 | + | 0.790388i | \(0.709879\pi\) | |||||||
\(264\) | 5.69736 | 0.350648 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.54009 | −0.0944290 | ||||||||
\(267\) | −5.65804 | −0.346267 | ||||||||
\(268\) | 2.76255 | 0.168750 | ||||||||
\(269\) | −8.17226 | −0.498272 | −0.249136 | − | 0.968469i | \(-0.580147\pi\) | ||||
−0.249136 | + | 0.968469i | \(0.580147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3947 | −0.692180 | −0.346090 | − | 0.938201i | \(-0.612491\pi\) | ||||
−0.346090 | + | 0.938201i | \(0.612491\pi\) | |||||||
\(272\) | 3.65804 | 0.221801 | ||||||||
\(273\) | −1.54009 | −0.0932105 | ||||||||
\(274\) | 14.3420 | 0.866429 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 4.93481 | 0.296504 | 0.148252 | − | 0.988950i | \(-0.452635\pi\) | ||||
0.148252 | + | 0.988950i | \(0.452635\pi\) | |||||||
\(278\) | −8.01344 | −0.480614 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8955 | 0.888591 | 0.444295 | − | 0.895880i | \(-0.353454\pi\) | ||||
0.444295 | + | 0.895880i | \(0.353454\pi\) | |||||||
\(282\) | −3.38127 | −0.201352 | ||||||||
\(283\) | 14.6322 | 0.869792 | 0.434896 | − | 0.900481i | \(-0.356785\pi\) | ||||
0.434896 | + | 0.900481i | \(0.356785\pi\) | |||||||
\(284\) | 10.6974 | 0.634772 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.17226 | 0.128448 | ||||||||
\(287\) | −22.6958 | −1.33969 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.61873 | −0.212866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.07863 | −0.239094 | ||||||||
\(292\) | 7.07863 | 0.414246 | ||||||||
\(293\) | 9.39472 | 0.548845 | 0.274423 | − | 0.961609i | \(-0.411513\pi\) | ||||
0.274423 | + | 0.961609i | \(0.411513\pi\) | |||||||
\(294\) | −9.31608 | −0.543325 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.65804 | −0.212619 | ||||||||
\(297\) | 5.69736 | 0.330594 | ||||||||
\(298\) | 3.23745 | 0.187540 | ||||||||
\(299\) | −0.381275 | −0.0220497 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6172 | 0.842520 | ||||||||
\(302\) | −9.31608 | −0.536080 | ||||||||
\(303\) | −16.7760 | −0.963756 | ||||||||
\(304\) | 0.381275 | 0.0218676 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.65804 | 0.209116 | ||||||||
\(307\) | −9.22401 | −0.526442 | −0.263221 | − | 0.964736i | \(-0.584785\pi\) | ||||
−0.263221 | + | 0.964736i | \(0.584785\pi\) | |||||||
\(308\) | 23.0134 | 1.31131 | ||||||||
\(309\) | 13.3554 | 0.759762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3295 | 0.642439 | 0.321219 | − | 0.947005i | \(-0.395907\pi\) | ||||
0.321219 | + | 0.947005i | \(0.395907\pi\) | |||||||
\(312\) | 0.381275 | 0.0215854 | ||||||||
\(313\) | −15.6037 | −0.881975 | −0.440988 | − | 0.897513i | \(-0.645372\pi\) | ||||
−0.440988 | + | 0.897513i | \(0.645372\pi\) | |||||||
\(314\) | 6.84118 | 0.386070 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69736 | 0.320502 | ||||||||
\(317\) | 11.0000 | 0.617822 | 0.308911 | − | 0.951091i | \(-0.400036\pi\) | ||||
0.308911 | + | 0.951091i | \(0.400036\pi\) | |||||||
\(318\) | 9.31608 | 0.522420 | ||||||||
\(319\) | 5.69736 | 0.318991 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.76255 | −0.377449 | ||||||||
\(322\) | −4.03932 | −0.225102 | ||||||||
\(323\) | 1.39472 | 0.0776043 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.76255 | −0.263773 | ||||||||
\(327\) | 13.0528 | 0.721819 | ||||||||
\(328\) | 5.61873 | 0.310242 | ||||||||
\(329\) | −13.6580 | −0.752992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.69736 | 0.148260 | 0.0741302 | − | 0.997249i | \(-0.476382\pi\) | ||||
0.0741302 | + | 0.997249i | \(0.476382\pi\) | |||||||
\(332\) | −16.1180 | −0.884588 | ||||||||
\(333\) | −3.65804 | −0.200459 | ||||||||
\(334\) | −14.8546 | −0.812809 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.03932 | 0.220363 | ||||||||
\(337\) | 17.3161 | 0.943267 | 0.471634 | − | 0.881795i | \(-0.343664\pi\) | ||||
0.471634 | + | 0.881795i | \(0.343664\pi\) | |||||||
\(338\) | −12.8546 | −0.699200 | ||||||||
\(339\) | −1.65804 | −0.0900525 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.1842 | −1.85118 | ||||||||
\(342\) | 0.381275 | 0.0206170 | ||||||||
\(343\) | −9.35540 | −0.505144 | ||||||||
\(344\) | −3.61873 | −0.195109 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.69736 | −0.521333 | ||||||||
\(347\) | 3.47335 | 0.186459 | 0.0932297 | − | 0.995645i | \(-0.470281\pi\) | ||||
0.0932297 | + | 0.995645i | \(0.470281\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −13.1438 | −0.703573 | −0.351786 | − | 0.936080i | \(-0.614426\pi\) | ||||
−0.351786 | + | 0.936080i | \(0.614426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.381275 | 0.0203509 | ||||||||
\(352\) | −5.69736 | −0.303670 | ||||||||
\(353\) | 13.8546 | 0.737408 | 0.368704 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368704 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(354\) | −13.3947 | −0.711921 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.65804 | 0.299876 | ||||||||
\(357\) | 14.7760 | 0.782029 | ||||||||
\(358\) | −5.31608 | −0.280964 | ||||||||
\(359\) | 14.9348 | 0.788229 | 0.394115 | − | 0.919061i | \(-0.371051\pi\) | ||||
0.394115 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8546 | −0.992349 | ||||||||
\(362\) | 24.3688 | 1.28080 | ||||||||
\(363\) | −21.4599 | −1.12635 | ||||||||
\(364\) | 1.54009 | 0.0807227 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −14.0786 | −0.735902 | ||||||||
\(367\) | −28.9348 | −1.51038 | −0.755192 | − | 0.655503i | \(-0.772457\pi\) | ||||
−0.755192 | + | 0.655503i | \(0.772457\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 5.61873 | 0.292499 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.6306 | 1.95368 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | −26.4475 | −1.36940 | −0.684699 | − | 0.728826i | \(-0.740066\pi\) | ||||
−0.684699 | + | 0.728826i | \(0.740066\pi\) | |||||||
\(374\) | −20.8412 | −1.07767 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.38127 | 0.174376 | ||||||||
\(377\) | 0.381275 | 0.0196367 | ||||||||
\(378\) | 4.03932 | 0.207760 | ||||||||
\(379\) | −26.2359 | −1.34765 | −0.673824 | − | 0.738892i | \(-0.735349\pi\) | ||||
−0.673824 | + | 0.738892i | \(0.735349\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.6322 | −0.954555 | ||||||||
\(382\) | 10.4599 | 0.535176 | ||||||||
\(383\) | 29.7242 | 1.51884 | 0.759419 | − | 0.650602i | \(-0.225483\pi\) | ||||
0.759419 | + | 0.650602i | \(0.225483\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0134 | 0.713266 | ||||||||
\(387\) | −3.61873 | −0.183950 | ||||||||
\(388\) | 4.07863 | 0.207061 | ||||||||
\(389\) | 8.47490 | 0.429695 | 0.214847 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214847 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.65804 | 0.184995 | ||||||||
\(392\) | 9.31608 | 0.470533 | ||||||||
\(393\) | 17.4734 | 0.881414 | ||||||||
\(394\) | −8.47335 | −0.426881 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.69736 | −0.286303 | ||||||||
\(397\) | −21.8696 | −1.09760 | −0.548802 | − | 0.835952i | \(-0.684916\pi\) | ||||
−0.548802 | + | 0.835952i | \(0.684916\pi\) | |||||||
\(398\) | 1.19813 | 0.0600570 | ||||||||
\(399\) | 1.54009 | 0.0771010 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.71080 | −0.235246 | −0.117623 | − | 0.993058i | \(-0.537527\pi\) | ||||
−0.117623 | + | 0.993058i | \(0.537527\pi\) | |||||||
\(402\) | −2.76255 | −0.137783 | ||||||||
\(403\) | −2.28765 | −0.113956 | ||||||||
\(404\) | 16.7760 | 0.834637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.03932 | 0.200468 | ||||||||
\(407\) | 20.8412 | 1.03306 | ||||||||
\(408\) | −3.65804 | −0.181100 | ||||||||
\(409\) | 35.1055 | 1.73586 | 0.867928 | − | 0.496690i | \(-0.165451\pi\) | ||||
0.867928 | + | 0.496690i | \(0.165451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.3420 | −0.707437 | ||||||||
\(412\) | −13.3554 | −0.657973 | ||||||||
\(413\) | −54.1055 | −2.66236 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.381275 | −0.0186935 | ||||||||
\(417\) | 8.01344 | 0.392420 | ||||||||
\(418\) | −2.17226 | −0.106249 | ||||||||
\(419\) | −24.7232 | −1.20781 | −0.603904 | − | 0.797057i | \(-0.706389\pi\) | ||||
−0.603904 | + | 0.797057i | \(0.706389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.4734 | 0.851599 | 0.425800 | − | 0.904817i | \(-0.359993\pi\) | ||||
0.425800 | + | 0.904817i | \(0.359993\pi\) | |||||||
\(422\) | −16.2225 | −0.789697 | ||||||||
\(423\) | 3.38127 | 0.164403 | ||||||||
\(424\) | −9.31608 | −0.452429 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.6974 | −0.518289 | ||||||||
\(427\) | −56.8681 | −2.75204 | ||||||||
\(428\) | 6.76255 | 0.326880 | ||||||||
\(429\) | −2.17226 | −0.104878 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.84118 | 0.233192 | 0.116596 | − | 0.993179i | \(-0.462802\pi\) | ||||
0.116596 | + | 0.993179i | \(0.462802\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −16.8412 | −0.809336 | −0.404668 | − | 0.914464i | \(-0.632613\pi\) | ||||
−0.404668 | + | 0.914464i | \(0.632613\pi\) | |||||||
\(434\) | −24.2359 | −1.16336 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.0528 | −0.625114 | ||||||||
\(437\) | 0.381275 | 0.0182389 | ||||||||
\(438\) | −7.07863 | −0.338230 | ||||||||
\(439\) | −20.7108 | −0.988473 | −0.494236 | − | 0.869328i | \(-0.664552\pi\) | ||||
−0.494236 | + | 0.869328i | \(0.664552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.31608 | 0.443623 | ||||||||
\(442\) | −1.39472 | −0.0663401 | ||||||||
\(443\) | 14.8412 | 0.705126 | 0.352563 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352563 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(444\) | 3.65804 | 0.173603 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.6037 | 0.644155 | ||||||||
\(447\) | −3.23745 | −0.153126 | ||||||||
\(448\) | −4.03932 | −0.190840 | ||||||||
\(449\) | −30.1573 | −1.42321 | −0.711605 | − | 0.702580i | \(-0.752031\pi\) | ||||
−0.711605 | + | 0.702580i | \(0.752031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.0119 | −1.50738 | ||||||||
\(452\) | 1.65804 | 0.0779878 | ||||||||
\(453\) | 9.31608 | 0.437708 | ||||||||
\(454\) | 12.4992 | 0.586618 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.381275 | −0.0178548 | ||||||||
\(457\) | −12.7625 | −0.597007 | −0.298503 | − | 0.954409i | \(-0.596487\pi\) | ||||
−0.298503 | + | 0.954409i | \(0.596487\pi\) | |||||||
\(458\) | 21.4734 | 1.00338 | ||||||||
\(459\) | −3.65804 | −0.170743 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.2359 | 0.802756 | 0.401378 | − | 0.915912i | \(-0.368531\pi\) | ||||
0.401378 | + | 0.915912i | \(0.368531\pi\) | |||||||
\(462\) | −23.0134 | −1.07068 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.1438 | 0.516228 | ||||||||
\(467\) | 5.88205 | 0.272189 | 0.136094 | − | 0.990696i | \(-0.456545\pi\) | ||||
0.136094 | + | 0.990696i | \(0.456545\pi\) | |||||||
\(468\) | −0.381275 | −0.0176244 | ||||||||
\(469\) | −11.1588 | −0.515266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.84118 | −0.315225 | ||||||||
\(472\) | 13.3947 | 0.616542 | ||||||||
\(473\) | 20.6172 | 0.947979 | ||||||||
\(474\) | −5.69736 | −0.261688 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.7760 | −0.677257 | ||||||||
\(477\) | −9.31608 | −0.426554 | ||||||||
\(478\) | 22.1707 | 1.01406 | ||||||||
\(479\) | −28.4868 | −1.30160 | −0.650798 | − | 0.759251i | \(-0.725565\pi\) | ||||
−0.650798 | + | 0.759251i | \(0.725565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.39472 | 0.0635937 | ||||||||
\(482\) | −13.8696 | −0.631744 | ||||||||
\(483\) | 4.03932 | 0.183795 | ||||||||
\(484\) | 21.4599 | 0.975450 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 25.6306 | 1.16143 | 0.580717 | − | 0.814105i | \(-0.302772\pi\) | ||||
0.580717 | + | 0.814105i | \(0.302772\pi\) | |||||||
\(488\) | 14.0786 | 0.637310 | ||||||||
\(489\) | 4.76255 | 0.215370 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.9483 | 1.53206 | 0.766032 | − | 0.642803i | \(-0.222229\pi\) | ||||
0.766032 | + | 0.642803i | \(0.222229\pi\) | |||||||
\(492\) | −5.61873 | −0.253312 | ||||||||
\(493\) | −3.65804 | −0.164750 | ||||||||
\(494\) | −0.145371 | −0.00654053 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −43.2100 | −1.93823 | ||||||||
\(498\) | 16.1180 | 0.722263 | ||||||||
\(499\) | 18.0134 | 0.806393 | 0.403196 | − | 0.915114i | \(-0.367899\pi\) | ||||
0.403196 | + | 0.915114i | \(0.367899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.8546 | 0.663656 | ||||||||
\(502\) | 5.73668 | 0.256040 | ||||||||
\(503\) | −14.3813 | −0.641229 | −0.320615 | − | 0.947210i | \(-0.603889\pi\) | ||||
−0.320615 | + | 0.947210i | \(0.603889\pi\) | |||||||
\(504\) | −4.03932 | −0.179925 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.69736 | −0.253279 | ||||||||
\(507\) | 12.8546 | 0.570894 | ||||||||
\(508\) | 18.6322 | 0.826669 | ||||||||
\(509\) | 32.3797 | 1.43521 | 0.717603 | − | 0.696452i | \(-0.245239\pi\) | ||||
0.717603 | + | 0.696452i | \(0.245239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.5929 | −1.26487 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.381275 | −0.0168337 | ||||||||
\(514\) | 20.6322 | 0.910046 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.61873 | 0.159305 | ||||||||
\(517\) | −19.2643 | −0.847245 | ||||||||
\(518\) | 14.7760 | 0.649220 | ||||||||
\(519\) | 9.69736 | 0.425667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.3420 | 1.06644 | 0.533220 | − | 0.845976i | \(-0.320982\pi\) | ||||
0.533220 | + | 0.845976i | \(0.320982\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | −3.54009 | −0.154797 | −0.0773987 | − | 0.997000i | \(-0.524661\pi\) | ||||
−0.0773987 | + | 0.997000i | \(0.524661\pi\) | |||||||
\(524\) | −17.4734 | −0.763327 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.8696 | −0.866357 | ||||||||
\(527\) | 21.9483 | 0.956081 | ||||||||
\(528\) | 5.69736 | 0.247946 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3947 | 0.581281 | ||||||||
\(532\) | −1.54009 | −0.0667714 | ||||||||
\(533\) | −2.14228 | −0.0927924 | ||||||||
\(534\) | −5.65804 | −0.244847 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.76255 | 0.119324 | ||||||||
\(537\) | 5.31608 | 0.229406 | ||||||||
\(538\) | −8.17226 | −0.352331 | ||||||||
\(539\) | −53.0771 | −2.28619 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2493 | −0.999568 | −0.499784 | − | 0.866150i | \(-0.666587\pi\) | ||||
−0.499784 | + | 0.866150i | \(0.666587\pi\) | |||||||
\(542\) | −11.3947 | −0.489445 | ||||||||
\(543\) | −24.3688 | −1.04577 | ||||||||
\(544\) | 3.65804 | 0.156837 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.54009 | −0.0659098 | ||||||||
\(547\) | −32.2225 | −1.37773 | −0.688866 | − | 0.724888i | \(-0.741891\pi\) | ||||
−0.688866 | + | 0.724888i | \(0.741891\pi\) | |||||||
\(548\) | 14.3420 | 0.612658 | ||||||||
\(549\) | 14.0786 | 0.600861 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.381275 | −0.0162429 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −23.0134 | −0.978631 | ||||||||
\(554\) | 4.93481 | 0.209660 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.01344 | −0.339846 | ||||||||
\(557\) | 44.9985 | 1.90665 | 0.953323 | − | 0.301953i | \(-0.0976385\pi\) | ||||
0.953323 | + | 0.301953i | \(0.0976385\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 1.37973 | 0.0583563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.8412 | 0.879916 | ||||||||
\(562\) | 14.8955 | 0.628328 | ||||||||
\(563\) | 13.0921 | 0.551765 | 0.275883 | − | 0.961191i | \(-0.411030\pi\) | ||||
0.275883 | + | 0.961191i | \(0.411030\pi\) | |||||||
\(564\) | −3.38127 | −0.142377 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.6322 | 0.615036 | ||||||||
\(567\) | −4.03932 | −0.169635 | ||||||||
\(568\) | 10.6974 | 0.448851 | ||||||||
\(569\) | −34.0786 | −1.42865 | −0.714325 | − | 0.699814i | \(-0.753266\pi\) | ||||
−0.714325 | + | 0.699814i | \(0.753266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4734 | 0.982329 | 0.491165 | − | 0.871067i | \(-0.336571\pi\) | ||||
0.491165 | + | 0.871067i | \(0.336571\pi\) | |||||||
\(572\) | 2.17226 | 0.0908268 | ||||||||
\(573\) | −10.4599 | −0.436969 | ||||||||
\(574\) | −22.6958 | −0.947305 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −24.9348 | −1.03805 | −0.519025 | − | 0.854759i | \(-0.673705\pi\) | ||||
−0.519025 | + | 0.854759i | \(0.673705\pi\) | |||||||
\(578\) | −3.61873 | −0.150519 | ||||||||
\(579\) | −14.0134 | −0.582379 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 65.1055 | 2.70103 | ||||||||
\(582\) | −4.07863 | −0.169065 | ||||||||
\(583\) | 53.0771 | 2.19823 | ||||||||
\(584\) | 7.07863 | 0.292916 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.39472 | 0.388092 | ||||||||
\(587\) | 30.0786 | 1.24148 | 0.620739 | − | 0.784017i | \(-0.286833\pi\) | ||||
0.620739 | + | 0.784017i | \(0.286833\pi\) | |||||||
\(588\) | −9.31608 | −0.384189 | ||||||||
\(589\) | 2.28765 | 0.0942610 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.47335 | 0.348547 | ||||||||
\(592\) | −3.65804 | −0.150345 | ||||||||
\(593\) | −16.4599 | −0.675927 | −0.337964 | − | 0.941159i | \(-0.609738\pi\) | ||||
−0.337964 | + | 0.941159i | \(0.609738\pi\) | |||||||
\(594\) | 5.69736 | 0.233766 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.23745 | 0.132611 | ||||||||
\(597\) | −1.19813 | −0.0490363 | ||||||||
\(598\) | −0.381275 | −0.0155915 | ||||||||
\(599\) | −26.0269 | −1.06343 | −0.531715 | − | 0.846923i | \(-0.678452\pi\) | ||||
−0.531715 | + | 0.846923i | \(0.678452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.8546 | −1.25859 | −0.629293 | − | 0.777168i | \(-0.716656\pi\) | ||||
−0.629293 | + | 0.777168i | \(0.716656\pi\) | |||||||
\(602\) | 14.6172 | 0.595752 | ||||||||
\(603\) | 2.76255 | 0.112500 | ||||||||
\(604\) | −9.31608 | −0.379066 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.7760 | −0.681478 | ||||||||
\(607\) | −5.05020 | −0.204981 | −0.102491 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102491 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(608\) | 0.381275 | 0.0154627 | ||||||||
\(609\) | −4.03932 | −0.163681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.28920 | −0.0521553 | ||||||||
\(612\) | 3.65804 | 0.147868 | ||||||||
\(613\) | −48.5261 | −1.95995 | −0.979976 | − | 0.199117i | \(-0.936193\pi\) | ||||
−0.979976 | + | 0.199117i | \(0.936193\pi\) | |||||||
\(614\) | −9.22401 | −0.372251 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.0134 | 0.927238 | ||||||||
\(617\) | 20.7108 | 0.833786 | 0.416893 | − | 0.908956i | \(-0.363119\pi\) | ||||
0.416893 | + | 0.908956i | \(0.363119\pi\) | |||||||
\(618\) | 13.3554 | 0.537233 | ||||||||
\(619\) | 42.2359 | 1.69760 | 0.848802 | − | 0.528711i | \(-0.177324\pi\) | ||||
0.848802 | + | 0.528711i | \(0.177324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 11.3295 | 0.454273 | ||||||||
\(623\) | −22.8546 | −0.915651 | ||||||||
\(624\) | 0.381275 | 0.0152632 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.6037 | −0.623651 | ||||||||
\(627\) | 2.17226 | 0.0867517 | ||||||||
\(628\) | 6.84118 | 0.272993 | ||||||||
\(629\) | −13.3813 | −0.533546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5913 | 1.01877 | 0.509387 | − | 0.860538i | \(-0.329872\pi\) | ||||
0.509387 | + | 0.860538i | \(0.329872\pi\) | |||||||
\(632\) | 5.69736 | 0.226629 | ||||||||
\(633\) | 16.2225 | 0.644785 | ||||||||
\(634\) | 11.0000 | 0.436866 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.31608 | 0.369407 | ||||||||
\(637\) | −3.55199 | −0.140735 | ||||||||
\(638\) | 5.69736 | 0.225561 | ||||||||
\(639\) | 10.6974 | 0.423181 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.6834 | −1.44891 | −0.724453 | − | 0.689324i | \(-0.757908\pi\) | ||||
−0.724453 | + | 0.689324i | \(0.757908\pi\) | |||||||
\(642\) | −6.76255 | −0.266897 | ||||||||
\(643\) | −13.6974 | −0.540171 | −0.270086 | − | 0.962836i | \(-0.587052\pi\) | ||||
−0.270086 | + | 0.962836i | \(0.587052\pi\) | |||||||
\(644\) | −4.03932 | −0.159171 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.39472 | 0.0548745 | ||||||||
\(647\) | −24.0652 | −0.946100 | −0.473050 | − | 0.881036i | \(-0.656847\pi\) | ||||
−0.473050 | + | 0.881036i | \(0.656847\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −76.3145 | −2.99561 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.2359 | 0.949880 | ||||||||
\(652\) | −4.76255 | −0.186516 | ||||||||
\(653\) | 14.9214 | 0.583918 | 0.291959 | − | 0.956431i | \(-0.405693\pi\) | ||||
0.291959 | + | 0.956431i | \(0.405693\pi\) | |||||||
\(654\) | 13.0528 | 0.510403 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.61873 | 0.219374 | ||||||||
\(657\) | 7.07863 | 0.276164 | ||||||||
\(658\) | −13.6580 | −0.532446 | ||||||||
\(659\) | 40.8288 | 1.59046 | 0.795231 | − | 0.606306i | \(-0.207349\pi\) | ||||
0.795231 | + | 0.606306i | \(0.207349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.1045 | −1.13203 | −0.566017 | − | 0.824394i | \(-0.691516\pi\) | ||||
−0.566017 | + | 0.824394i | \(0.691516\pi\) | |||||||
\(662\) | 2.69736 | 0.104836 | ||||||||
\(663\) | 1.39472 | 0.0541664 | ||||||||
\(664\) | −16.1180 | −0.625498 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.65804 | −0.141746 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −14.8546 | −0.574743 | ||||||||
\(669\) | −13.6037 | −0.525951 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −80.2110 | −3.09651 | ||||||||
\(672\) | 4.03932 | 0.155820 | ||||||||
\(673\) | 41.9198 | 1.61589 | 0.807945 | − | 0.589258i | \(-0.200580\pi\) | ||||
0.807945 | + | 0.589258i | \(0.200580\pi\) | |||||||
\(674\) | 17.3161 | 0.666991 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8546 | −0.494409 | ||||||||
\(677\) | 24.3145 | 0.934484 | 0.467242 | − | 0.884130i | \(-0.345248\pi\) | ||||
0.467242 | + | 0.884130i | \(0.345248\pi\) | |||||||
\(678\) | −1.65804 | −0.0636767 | ||||||||
\(679\) | −16.4749 | −0.632249 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.4992 | −0.478971 | ||||||||
\(682\) | −34.1842 | −1.30898 | ||||||||
\(683\) | −44.2628 | −1.69367 | −0.846834 | − | 0.531857i | \(-0.821494\pi\) | ||||
−0.846834 | + | 0.531857i | \(0.821494\pi\) | |||||||
\(684\) | 0.381275 | 0.0145784 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.35540 | −0.357191 | ||||||||
\(687\) | −21.4734 | −0.819260 | ||||||||
\(688\) | −3.61873 | −0.137963 | ||||||||
\(689\) | 3.55199 | 0.135320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.1423 | −1.41296 | −0.706479 | − | 0.707734i | \(-0.749718\pi\) | ||||
−0.706479 | + | 0.707734i | \(0.749718\pi\) | |||||||
\(692\) | −9.69736 | −0.368638 | ||||||||
\(693\) | 23.0134 | 0.874208 | ||||||||
\(694\) | 3.47335 | 0.131847 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 20.5535 | 0.778521 | ||||||||
\(698\) | −13.1438 | −0.497501 | ||||||||
\(699\) | −11.1438 | −0.421498 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.130380 | −0.00492438 | −0.00246219 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246219 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(702\) | 0.381275 | 0.0143903 | ||||||||
\(703\) | −1.39472 | −0.0526029 | ||||||||
\(704\) | −5.69736 | −0.214727 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8546 | 0.521426 | ||||||||
\(707\) | −67.7636 | −2.54851 | ||||||||
\(708\) | −13.3947 | −0.503404 | ||||||||
\(709\) | −21.2618 | −0.798503 | −0.399251 | − | 0.916841i | \(-0.630730\pi\) | ||||
−0.399251 | + | 0.916841i | \(0.630730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.69736 | 0.213668 | ||||||||
\(712\) | 5.65804 | 0.212044 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 14.7760 | 0.552978 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.31608 | −0.198671 | ||||||||
\(717\) | −22.1707 | −0.827981 | ||||||||
\(718\) | 14.9348 | 0.557362 | ||||||||
\(719\) | −23.3026 | −0.869042 | −0.434521 | − | 0.900662i | \(-0.643082\pi\) | ||||
−0.434521 | + | 0.900662i | \(0.643082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.9467 | 2.00908 | ||||||||
\(722\) | −18.8546 | −0.701697 | ||||||||
\(723\) | 13.8696 | 0.515817 | ||||||||
\(724\) | 24.3688 | 0.905661 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.4599 | −0.796452 | ||||||||
\(727\) | −14.6053 | −0.541680 | −0.270840 | − | 0.962624i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587301\pi\) | |||||||
\(728\) | 1.54009 | 0.0570795 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.2375 | −0.489605 | ||||||||
\(732\) | −14.0786 | −0.520361 | ||||||||
\(733\) | −26.6565 | −0.984580 | −0.492290 | − | 0.870431i | \(-0.663840\pi\) | ||||
−0.492290 | + | 0.870431i | \(0.663840\pi\) | |||||||
\(734\) | −28.9348 | −1.06800 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −15.7392 | −0.579762 | ||||||||
\(738\) | 5.61873 | 0.206828 | ||||||||
\(739\) | 49.1992 | 1.80982 | 0.904910 | − | 0.425603i | \(-0.139938\pi\) | ||||
0.904910 | + | 0.425603i | \(0.139938\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.145371 | 0.00534032 | ||||||||
\(742\) | 37.6306 | 1.38146 | ||||||||
\(743\) | 17.1438 | 0.628946 | 0.314473 | − | 0.949266i | \(-0.398172\pi\) | ||||
0.314473 | + | 0.949266i | \(0.398172\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.4475 | −0.968311 | ||||||||
\(747\) | −16.1180 | −0.589725 | ||||||||
\(748\) | −20.8412 | −0.762029 | ||||||||
\(749\) | −27.3161 | −0.998108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.2752 | 1.54264 | 0.771322 | − | 0.636445i | \(-0.219596\pi\) | ||||
0.771322 | + | 0.636445i | \(0.219596\pi\) | |||||||
\(752\) | 3.38127 | 0.123302 | ||||||||
\(753\) | −5.73668 | −0.209056 | ||||||||
\(754\) | 0.381275 | 0.0138852 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.03932 | 0.146909 | ||||||||
\(757\) | 53.8939 | 1.95881 | 0.979404 | − | 0.201908i | \(-0.0647143\pi\) | ||||
0.979404 | + | 0.201908i | \(0.0647143\pi\) | |||||||
\(758\) | −26.2359 | −0.952931 | ||||||||
\(759\) | 5.69736 | 0.206801 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.6456 | −1.50965 | −0.754826 | − | 0.655925i | \(-0.772279\pi\) | ||||
−0.754826 | + | 0.655925i | \(0.772279\pi\) | |||||||
\(762\) | −18.6322 | −0.674972 | ||||||||
\(763\) | 52.7242 | 1.90875 | ||||||||
\(764\) | 10.4599 | 0.378426 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.7242 | 1.07398 | ||||||||
\(767\) | −5.10707 | −0.184406 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −12.5266 | −0.451722 | −0.225861 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225861 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.6322 | −0.743049 | ||||||||
\(772\) | 14.0134 | 0.504355 | ||||||||
\(773\) | −18.3663 | −0.660589 | −0.330295 | − | 0.943878i | \(-0.607148\pi\) | ||||
−0.330295 | + | 0.943878i | \(0.607148\pi\) | |||||||
\(774\) | −3.61873 | −0.130072 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.07863 | 0.146414 | ||||||||
\(777\) | −14.7760 | −0.530086 | ||||||||
\(778\) | 8.47490 | 0.303840 | ||||||||
\(779\) | 2.14228 | 0.0767551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.9467 | −2.18084 | ||||||||
\(782\) | 3.65804 | 0.130811 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 9.31608 | 0.332717 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4734 | 0.623254 | ||||||||
\(787\) | 32.6172 | 1.16268 | 0.581338 | − | 0.813662i | \(-0.302529\pi\) | ||||
0.581338 | + | 0.813662i | \(0.302529\pi\) | |||||||
\(788\) | −8.47335 | −0.301851 | ||||||||
\(789\) | 19.8696 | 0.707377 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.69736 | −0.238131 | ||||||||
\(792\) | −5.69736 | −0.202447 | ||||||||
\(793\) | −5.36783 | −0.190617 | ||||||||
\(794\) | −21.8696 | −0.776124 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.19813 | 0.0424667 | ||||||||
\(797\) | 21.7910 | 0.771876 | 0.385938 | − | 0.922525i | \(-0.373878\pi\) | ||||
0.385938 | + | 0.922525i | \(0.373878\pi\) | |||||||
\(798\) | 1.54009 | 0.0545186 | ||||||||
\(799\) | 12.3688 | 0.437578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.65804 | 0.199917 | ||||||||
\(802\) | −4.71080 | −0.166344 | ||||||||
\(803\) | −40.3295 | −1.42320 | ||||||||
\(804\) | −2.76255 | −0.0974276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.28765 | −0.0805790 | ||||||||
\(807\) | 8.17226 | 0.287677 | ||||||||
\(808\) | 16.7760 | 0.590177 | ||||||||
\(809\) | 8.17226 | 0.287321 | 0.143661 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143661 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.4216 | −1.03313 | −0.516566 | − | 0.856247i | \(-0.672790\pi\) | ||||
−0.516566 | + | 0.856247i | \(0.672790\pi\) | |||||||
\(812\) | 4.03932 | 0.141752 | ||||||||
\(813\) | 11.3947 | 0.399630 | ||||||||
\(814\) | 20.8412 | 0.730483 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.65804 | −0.128057 | ||||||||
\(817\) | −1.37973 | −0.0482706 | ||||||||
\(818\) | 35.1055 | 1.22744 | ||||||||
\(819\) | 1.54009 | 0.0538151 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.6974 | 1.45525 | 0.727624 | − | 0.685976i | \(-0.240625\pi\) | ||||
0.727624 | + | 0.685976i | \(0.240625\pi\) | |||||||
\(822\) | −14.3420 | −0.500233 | ||||||||
\(823\) | 26.2359 | 0.914526 | 0.457263 | − | 0.889331i | \(-0.348830\pi\) | ||||
0.457263 | + | 0.889331i | \(0.348830\pi\) | |||||||
\(824\) | −13.3554 | −0.465257 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −54.1055 | −1.88257 | ||||||||
\(827\) | 41.9358 | 1.45825 | 0.729126 | − | 0.684380i | \(-0.239927\pi\) | ||||
0.729126 | + | 0.684380i | \(0.239927\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −27.7760 | −0.964700 | −0.482350 | − | 0.875979i | \(-0.660217\pi\) | ||||
−0.482350 | + | 0.875979i | \(0.660217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.93481 | −0.171187 | ||||||||
\(832\) | −0.381275 | −0.0132183 | ||||||||
\(833\) | 34.0786 | 1.18075 | ||||||||
\(834\) | 8.01344 | 0.277483 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.17226 | −0.0751292 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −24.7232 | −0.854050 | ||||||||
\(839\) | 31.3011 | 1.08063 | 0.540317 | − | 0.841462i | \(-0.318304\pi\) | ||||
0.540317 | + | 0.841462i | \(0.318304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 17.4734 | 0.602172 | ||||||||
\(843\) | −14.8955 | −0.513028 | ||||||||
\(844\) | −16.2225 | −0.558400 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.38127 | 0.116251 | ||||||||
\(847\) | −86.6834 | −2.97848 | ||||||||
\(848\) | −9.31608 | −0.319916 | ||||||||
\(849\) | −14.6322 | −0.502175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.65804 | −0.125396 | ||||||||
\(852\) | −10.6974 | −0.366486 | ||||||||
\(853\) | 20.6172 | 0.705919 | 0.352959 | − | 0.935639i | \(-0.385175\pi\) | ||||
0.352959 | + | 0.935639i | \(0.385175\pi\) | |||||||
\(854\) | −56.8681 | −1.94599 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.76255 | 0.231139 | ||||||||
\(857\) | −0.235904 | −0.00805834 | −0.00402917 | − | 0.999992i | \(-0.501283\pi\) | ||||
−0.00402917 | + | 0.999992i | \(0.501283\pi\) | |||||||
\(858\) | −2.17226 | −0.0741597 | ||||||||
\(859\) | −23.7392 | −0.809972 | −0.404986 | − | 0.914323i | \(-0.632724\pi\) | ||||
−0.404986 | + | 0.914323i | \(0.632724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.6958 | 0.773471 | ||||||||
\(862\) | 4.84118 | 0.164891 | ||||||||
\(863\) | 20.2225 | 0.688381 | 0.344190 | − | 0.938900i | \(-0.388153\pi\) | ||||
0.344190 | + | 0.938900i | \(0.388153\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.8412 | −0.572287 | ||||||||
\(867\) | 3.61873 | 0.122898 | ||||||||
\(868\) | −24.2359 | −0.822620 | ||||||||
\(869\) | −32.4599 | −1.10113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.05329 | −0.0356894 | ||||||||
\(872\) | −13.0528 | −0.442022 | ||||||||
\(873\) | 4.07863 | 0.138041 | ||||||||
\(874\) | 0.381275 | 0.0128968 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.07863 | −0.239165 | ||||||||
\(877\) | −14.0000 | −0.472746 | −0.236373 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(878\) | −20.7108 | −0.698956 | ||||||||
\(879\) | −9.39472 | −0.316876 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0786 | 0.878612 | 0.439306 | − | 0.898338i | \(-0.355224\pi\) | ||||
0.439306 | + | 0.898338i | \(0.355224\pi\) | |||||||
\(882\) | 9.31608 | 0.313689 | ||||||||
\(883\) | −4.40971 | −0.148399 | −0.0741993 | − | 0.997243i | \(-0.523640\pi\) | ||||
−0.0741993 | + | 0.997243i | \(0.523640\pi\) | |||||||
\(884\) | −1.39472 | −0.0469095 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.8412 | 0.498599 | ||||||||
\(887\) | −22.6456 | −0.760365 | −0.380183 | − | 0.924911i | \(-0.624139\pi\) | ||||
−0.380183 | + | 0.924911i | \(0.624139\pi\) | |||||||
\(888\) | 3.65804 | 0.122756 | ||||||||
\(889\) | −75.2612 | −2.52418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.69736 | −0.190869 | ||||||||
\(892\) | 13.6037 | 0.455487 | ||||||||
\(893\) | 1.28920 | 0.0431413 | ||||||||
\(894\) | −3.23745 | −0.108277 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.03932 | −0.134944 | ||||||||
\(897\) | 0.381275 | 0.0127304 | ||||||||
\(898\) | −30.1573 | −1.00636 | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0786 | −1.13532 | ||||||||
\(902\) | −32.0119 | −1.06588 | ||||||||
\(903\) | −14.6172 | −0.486429 | ||||||||
\(904\) | 1.65804 | 0.0551457 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.31608 | 0.309506 | ||||||||
\(907\) | −16.2240 | −0.538709 | −0.269355 | − | 0.963041i | \(-0.586810\pi\) | ||||
−0.269355 | + | 0.963041i | \(0.586810\pi\) | |||||||
\(908\) | 12.4992 | 0.414801 | ||||||||
\(909\) | 16.7760 | 0.556425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.77599 | −0.0588413 | −0.0294207 | − | 0.999567i | \(-0.509366\pi\) | ||||
−0.0294207 | + | 0.999567i | \(0.509366\pi\) | |||||||
\(912\) | −0.381275 | −0.0126253 | ||||||||
\(913\) | 91.8298 | 3.03912 | ||||||||
\(914\) | −12.7625 | −0.422148 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.4734 | 0.709500 | ||||||||
\(917\) | 70.5804 | 2.33077 | ||||||||
\(918\) | −3.65804 | −0.120733 | ||||||||
\(919\) | −27.6580 | −0.912355 | −0.456177 | − | 0.889889i | \(-0.650782\pi\) | ||||
−0.456177 | + | 0.889889i | \(0.650782\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.22401 | 0.303941 | ||||||||
\(922\) | 17.2359 | 0.567634 | ||||||||
\(923\) | −4.07863 | −0.134250 | ||||||||
\(924\) | −23.0134 | −0.757087 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | −13.3554 | −0.438649 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 0.777541 | 0.0255103 | 0.0127551 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127551 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.55199 | 0.116412 | ||||||||
\(932\) | 11.1438 | 0.365028 | ||||||||
\(933\) | −11.3295 | −0.370912 | ||||||||
\(934\) | 5.88205 | 0.192466 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.381275 | −0.0124624 | ||||||||
\(937\) | −7.52510 | −0.245834 | −0.122917 | − | 0.992417i | \(-0.539225\pi\) | ||||
−0.122917 | + | 0.992417i | \(0.539225\pi\) | |||||||
\(938\) | −11.1588 | −0.364348 | ||||||||
\(939\) | 15.6037 | 0.509209 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.6322 | −1.32457 | −0.662285 | − | 0.749252i | \(-0.730413\pi\) | ||||
−0.662285 | + | 0.749252i | \(0.730413\pi\) | |||||||
\(942\) | −6.84118 | −0.222898 | ||||||||
\(943\) | 5.61873 | 0.182971 | ||||||||
\(944\) | 13.3947 | 0.435961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.6172 | 0.670322 | ||||||||
\(947\) | −23.3947 | −0.760226 | −0.380113 | − | 0.924940i | \(-0.624115\pi\) | ||||
−0.380113 | + | 0.924940i | \(0.624115\pi\) | |||||||
\(948\) | −5.69736 | −0.185042 | ||||||||
\(949\) | −2.69891 | −0.0876102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | −14.7760 | −0.478893 | ||||||||
\(953\) | 34.2902 | 1.11077 | 0.555384 | − | 0.831594i | \(-0.312571\pi\) | ||||
0.555384 | + | 0.831594i | \(0.312571\pi\) | |||||||
\(954\) | −9.31608 | −0.301619 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.1707 | 0.717052 | ||||||||
\(957\) | −5.69736 | −0.184169 | ||||||||
\(958\) | −28.4868 | −0.920367 | ||||||||
\(959\) | −57.9317 | −1.87071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 1.39472 | 0.0449676 | ||||||||
\(963\) | 6.76255 | 0.217920 | ||||||||
\(964\) | −13.8696 | −0.446710 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.03932 | 0.129963 | ||||||||
\(967\) | 5.39472 | 0.173482 | 0.0867412 | − | 0.996231i | \(-0.472355\pi\) | ||||
0.0867412 | + | 0.996231i | \(0.472355\pi\) | |||||||
\(968\) | 21.4599 | 0.689748 | ||||||||
\(969\) | −1.39472 | −0.0448049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.3807 | 1.87353 | 0.936764 | − | 0.349963i | \(-0.113806\pi\) | ||||
0.936764 | + | 0.349963i | \(0.113806\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 32.3688 | 1.03770 | ||||||||
\(974\) | 25.6306 | 0.821258 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0786 | 0.450646 | ||||||||
\(977\) | 33.4190 | 1.06917 | 0.534585 | − | 0.845115i | \(-0.320468\pi\) | ||||
0.534585 | + | 0.845115i | \(0.320468\pi\) | |||||||
\(978\) | 4.76255 | 0.152290 | ||||||||
\(979\) | −32.2359 | −1.03026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0528 | −0.416743 | ||||||||
\(982\) | 33.9483 | 1.08333 | ||||||||
\(983\) | 42.4868 | 1.35512 | 0.677559 | − | 0.735468i | \(-0.263038\pi\) | ||||
0.677559 | + | 0.735468i | \(0.263038\pi\) | |||||||
\(984\) | −5.61873 | −0.179118 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.65804 | −0.116496 | ||||||||
\(987\) | 13.6580 | 0.434740 | ||||||||
\(988\) | −0.145371 | −0.00462485 | ||||||||
\(989\) | −3.61873 | −0.115069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7625 | 0.532480 | 0.266240 | − | 0.963907i | \(-0.414219\pi\) | ||||
0.266240 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | −2.69736 | −0.0855981 | ||||||||
\(994\) | −43.2100 | −1.37054 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.1180 | 0.510717 | ||||||||
\(997\) | −15.7760 | −0.499631 | −0.249815 | − | 0.968293i | \(-0.580370\pi\) | ||||
−0.249815 | + | 0.968293i | \(0.580370\pi\) | |||||||
\(998\) | 18.0134 | 0.570206 | ||||||||
\(999\) | 3.65804 | 0.115735 |
(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 | 3450.2.a.bs.1.1 | yes | 3 | |
5.2 | odd | 4 | 3450.2.d.ba.2899.4 | 6 | |||
5.3 | odd | 4 | 3450.2.d.ba.2899.3 | 6 | |||
5.4 | even | 2 | 3450.2.a.bp.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bp.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
3450.2.a.bs.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
3450.2.d.ba.2899.3 | 6 | 5.3 | odd | 4 | |||
3450.2.d.ba.2899.4 | 6 | 5.2 | odd | 4 |