Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.37108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.836038\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | 3.30104 | 1.90586 | 0.952929 | − | 0.303195i | \(-0.0980534\pi\) | ||||
0.952929 | + | 0.303195i | \(0.0980534\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.30104 | −1.47627 | −0.738135 | − | 0.674653i | \(-0.764293\pi\) | ||||
−0.738135 | + | 0.674653i | \(0.764293\pi\) | |||||||
\(6\) | −3.30104 | −1.34764 | ||||||||
\(7\) | −4.13708 | −1.56367 | −0.781834 | − | 0.623486i | \(-0.785716\pi\) | ||||
−0.781834 | + | 0.623486i | \(0.785716\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.89687 | 2.63229 | ||||||||
\(10\) | 3.30104 | 1.04388 | ||||||||
\(11\) | 0.836038 | 0.252075 | 0.126037 | − | 0.992025i | \(-0.459774\pi\) | ||||
0.126037 | + | 0.992025i | \(0.459774\pi\) | |||||||
\(12\) | 3.30104 | 0.952929 | ||||||||
\(13\) | −1.16396 | −0.322825 | −0.161413 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161413 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(14\) | 4.13708 | 1.10568 | ||||||||
\(15\) | −10.8969 | −2.81356 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.13083 | −0.274266 | −0.137133 | − | 0.990553i | \(-0.543789\pi\) | ||||
−0.137133 | + | 0.990553i | \(0.543789\pi\) | |||||||
\(18\) | −7.89687 | −1.86131 | ||||||||
\(19\) | −3.59583 | −0.824940 | −0.412470 | − | 0.910971i | \(-0.635334\pi\) | ||||
−0.412470 | + | 0.910971i | \(0.635334\pi\) | |||||||
\(20\) | −3.30104 | −0.738135 | ||||||||
\(21\) | −13.6567 | −2.98013 | ||||||||
\(22\) | −0.836038 | −0.178244 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −3.30104 | −0.673822 | ||||||||
\(25\) | 5.89687 | 1.17937 | ||||||||
\(26\) | 1.16396 | 0.228272 | ||||||||
\(27\) | 16.1648 | 3.11091 | ||||||||
\(28\) | −4.13708 | −0.781834 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 10.8969 | 1.98949 | ||||||||
\(31\) | −7.16396 | −1.28669 | −0.643343 | − | 0.765578i | \(-0.722453\pi\) | ||||
−0.643343 | + | 0.765578i | \(0.722453\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.75979 | 0.480419 | ||||||||
\(34\) | 1.13083 | 0.193935 | ||||||||
\(35\) | 13.6567 | 2.30840 | ||||||||
\(36\) | 7.89687 | 1.31615 | ||||||||
\(37\) | −2.79293 | −0.459155 | −0.229577 | − | 0.973290i | \(-0.573734\pi\) | ||||
−0.229577 | + | 0.973290i | \(0.573734\pi\) | |||||||
\(38\) | 3.59583 | 0.583321 | ||||||||
\(39\) | −3.84229 | −0.615258 | ||||||||
\(40\) | 3.30104 | 0.521940 | ||||||||
\(41\) | −7.80915 | −1.21958 | −0.609792 | − | 0.792561i | \(-0.708747\pi\) | ||||
−0.609792 | + | 0.792561i | \(0.708747\pi\) | |||||||
\(42\) | 13.6567 | 2.10727 | ||||||||
\(43\) | −6.35563 | −0.969224 | −0.484612 | − | 0.874729i | \(-0.661039\pi\) | ||||
−0.484612 | + | 0.874729i | \(0.661039\pi\) | |||||||
\(44\) | 0.836038 | 0.126037 | ||||||||
\(45\) | −26.0679 | −3.88597 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.246456 | −0.0359493 | −0.0179747 | − | 0.999838i | \(-0.505722\pi\) | ||||
−0.0179747 | + | 0.999838i | \(0.505722\pi\) | |||||||
\(48\) | 3.30104 | 0.476464 | ||||||||
\(49\) | 10.1154 | 1.44506 | ||||||||
\(50\) | −5.89687 | −0.833944 | ||||||||
\(51\) | −3.73291 | −0.522712 | ||||||||
\(52\) | −1.16396 | −0.161413 | ||||||||
\(53\) | −7.14855 | −0.981930 | −0.490965 | − | 0.871179i | \(-0.663356\pi\) | ||||
−0.490965 | + | 0.871179i | \(0.663356\pi\) | |||||||
\(54\) | −16.1648 | −2.19975 | ||||||||
\(55\) | −2.75979 | −0.372131 | ||||||||
\(56\) | 4.13708 | 0.552840 | ||||||||
\(57\) | −11.8700 | −1.57222 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −1.67208 | −0.217686 | −0.108843 | − | 0.994059i | \(-0.534715\pi\) | ||||
−0.108843 | + | 0.994059i | \(0.534715\pi\) | |||||||
\(60\) | −10.8969 | −1.40678 | ||||||||
\(61\) | −10.1371 | −1.29792 | −0.648960 | − | 0.760823i | \(-0.724796\pi\) | ||||
−0.648960 | + | 0.760823i | \(0.724796\pi\) | |||||||
\(62\) | 7.16396 | 0.909824 | ||||||||
\(63\) | −32.6700 | −4.11603 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.84229 | 0.476577 | ||||||||
\(66\) | −2.75979 | −0.339707 | ||||||||
\(67\) | −0.869172 | −0.106186 | −0.0530931 | − | 0.998590i | \(-0.516908\pi\) | ||||
−0.0530931 | + | 0.998590i | \(0.516908\pi\) | |||||||
\(68\) | −1.13083 | −0.137133 | ||||||||
\(69\) | −3.30104 | −0.397399 | ||||||||
\(70\) | −13.6567 | −1.63228 | ||||||||
\(71\) | 13.7937 | 1.63702 | 0.818508 | − | 0.574495i | \(-0.194801\pi\) | ||||
0.818508 | + | 0.574495i | \(0.194801\pi\) | |||||||
\(72\) | −7.89687 | −0.930655 | ||||||||
\(73\) | −11.8092 | −1.38216 | −0.691078 | − | 0.722780i | \(-0.742864\pi\) | ||||
−0.691078 | + | 0.722780i | \(0.742864\pi\) | |||||||
\(74\) | 2.79293 | 0.324671 | ||||||||
\(75\) | 19.4658 | 2.24772 | ||||||||
\(76\) | −3.59583 | −0.412470 | ||||||||
\(77\) | −3.45875 | −0.394162 | ||||||||
\(78\) | 3.84229 | 0.435053 | ||||||||
\(79\) | −16.4927 | −1.85557 | −0.927787 | − | 0.373110i | \(-0.878291\pi\) | ||||
−0.927787 | + | 0.373110i | \(0.878291\pi\) | |||||||
\(80\) | −3.30104 | −0.369068 | ||||||||
\(81\) | 29.6700 | 3.29667 | ||||||||
\(82\) | 7.80915 | 0.862377 | ||||||||
\(83\) | 9.19166 | 1.00892 | 0.504458 | − | 0.863436i | \(-0.331692\pi\) | ||||
0.504458 | + | 0.863436i | \(0.331692\pi\) | |||||||
\(84\) | −13.6567 | −1.49006 | ||||||||
\(85\) | 3.73291 | 0.404891 | ||||||||
\(86\) | 6.35563 | 0.685345 | ||||||||
\(87\) | −3.30104 | −0.353909 | ||||||||
\(88\) | −0.836038 | −0.0891219 | ||||||||
\(89\) | −12.3225 | −1.30618 | −0.653091 | − | 0.757280i | \(-0.726528\pi\) | ||||
−0.653091 | + | 0.757280i | \(0.726528\pi\) | |||||||
\(90\) | 26.0679 | 2.74780 | ||||||||
\(91\) | 4.81540 | 0.504792 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −23.6485 | −2.45224 | ||||||||
\(94\) | 0.246456 | 0.0254200 | ||||||||
\(95\) | 11.8700 | 1.21784 | ||||||||
\(96\) | −3.30104 | −0.336911 | ||||||||
\(97\) | 13.2042 | 1.34068 | 0.670340 | − | 0.742054i | \(-0.266148\pi\) | ||||
0.670340 | + | 0.742054i | \(0.266148\pi\) | |||||||
\(98\) | −10.1154 | −1.02181 | ||||||||
\(99\) | 6.60208 | 0.663534 | ||||||||
\(100\) | 5.89687 | 0.589687 | ||||||||
\(101\) | 8.40126 | 0.835957 | 0.417978 | − | 0.908457i | \(-0.362739\pi\) | ||||
0.417978 | + | 0.908457i | \(0.362739\pi\) | |||||||
\(102\) | 3.73291 | 0.369613 | ||||||||
\(103\) | 14.8100 | 1.45927 | 0.729635 | − | 0.683837i | \(-0.239690\pi\) | ||||
0.729635 | + | 0.683837i | \(0.239690\pi\) | |||||||
\(104\) | 1.16396 | 0.114136 | ||||||||
\(105\) | 45.0812 | 4.39948 | ||||||||
\(106\) | 7.14855 | 0.694329 | ||||||||
\(107\) | 13.1917 | 1.27529 | 0.637643 | − | 0.770332i | \(-0.279909\pi\) | ||||
0.637643 | + | 0.770332i | \(0.279909\pi\) | |||||||
\(108\) | 16.1648 | 1.55546 | ||||||||
\(109\) | 16.1010 | 1.54220 | 0.771100 | − | 0.636714i | \(-0.219707\pi\) | ||||
0.771100 | + | 0.636714i | \(0.219707\pi\) | |||||||
\(110\) | 2.75979 | 0.263136 | ||||||||
\(111\) | −9.21957 | −0.875083 | ||||||||
\(112\) | −4.13708 | −0.390917 | ||||||||
\(113\) | 2.32792 | 0.218993 | 0.109496 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109496 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(114\) | 11.8700 | 1.11173 | ||||||||
\(115\) | 3.30104 | 0.307824 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −9.19166 | −0.849770 | ||||||||
\(118\) | 1.67208 | 0.153927 | ||||||||
\(119\) | 4.67833 | 0.428861 | ||||||||
\(120\) | 10.8969 | 0.994744 | ||||||||
\(121\) | −10.3010 | −0.936458 | ||||||||
\(122\) | 10.1371 | 0.917768 | ||||||||
\(123\) | −25.7783 | −2.32435 | ||||||||
\(124\) | −7.16396 | −0.643343 | ||||||||
\(125\) | −2.96062 | −0.264805 | ||||||||
\(126\) | 32.6700 | 2.91047 | ||||||||
\(127\) | 17.7075 | 1.57129 | 0.785645 | − | 0.618678i | \(-0.212332\pi\) | ||||
0.785645 | + | 0.618678i | \(0.212332\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −20.9802 | −1.84720 | ||||||||
\(130\) | −3.84229 | −0.336991 | ||||||||
\(131\) | −14.1979 | −1.24048 | −0.620239 | − | 0.784413i | \(-0.712964\pi\) | ||||
−0.620239 | + | 0.784413i | \(0.712964\pi\) | |||||||
\(132\) | 2.75979 | 0.240209 | ||||||||
\(133\) | 14.8762 | 1.28993 | ||||||||
\(134\) | 0.869172 | 0.0750850 | ||||||||
\(135\) | −53.3606 | −4.59255 | ||||||||
\(136\) | 1.13083 | 0.0969677 | ||||||||
\(137\) | 19.8546 | 1.69629 | 0.848146 | − | 0.529763i | \(-0.177719\pi\) | ||||
0.848146 | + | 0.529763i | \(0.177719\pi\) | |||||||
\(138\) | 3.30104 | 0.281003 | ||||||||
\(139\) | −9.21957 | −0.781994 | −0.390997 | − | 0.920392i | \(-0.627870\pi\) | ||||
−0.390997 | + | 0.920392i | \(0.627870\pi\) | |||||||
\(140\) | 13.6567 | 1.15420 | ||||||||
\(141\) | −0.813562 | −0.0685143 | ||||||||
\(142\) | −13.7937 | −1.15755 | ||||||||
\(143\) | −0.973116 | −0.0813761 | ||||||||
\(144\) | 7.89687 | 0.658073 | ||||||||
\(145\) | 3.30104 | 0.274137 | ||||||||
\(146\) | 11.8092 | 0.977333 | ||||||||
\(147\) | 33.3914 | 2.75408 | ||||||||
\(148\) | −2.79293 | −0.229577 | ||||||||
\(149\) | 6.49271 | 0.531903 | 0.265952 | − | 0.963986i | \(-0.414314\pi\) | ||||
0.265952 | + | 0.963986i | \(0.414314\pi\) | |||||||
\(150\) | −19.4658 | −1.58938 | ||||||||
\(151\) | −14.3833 | −1.17050 | −0.585249 | − | 0.810853i | \(-0.699003\pi\) | ||||
−0.585249 | + | 0.810853i | \(0.699003\pi\) | |||||||
\(152\) | 3.59583 | 0.291660 | ||||||||
\(153\) | −8.93001 | −0.721948 | ||||||||
\(154\) | 3.45875 | 0.278714 | ||||||||
\(155\) | 23.6485 | 1.89950 | ||||||||
\(156\) | −3.84229 | −0.307629 | ||||||||
\(157\) | −9.79665 | −0.781858 | −0.390929 | − | 0.920421i | \(-0.627846\pi\) | ||||
−0.390929 | + | 0.920421i | \(0.627846\pi\) | |||||||
\(158\) | 16.4927 | 1.31209 | ||||||||
\(159\) | −23.5977 | −1.87142 | ||||||||
\(160\) | 3.30104 | 0.260970 | ||||||||
\(161\) | 4.13708 | 0.326047 | ||||||||
\(162\) | −29.6700 | −2.33109 | ||||||||
\(163\) | −19.8494 | −1.55472 | −0.777361 | − | 0.629055i | \(-0.783442\pi\) | ||||
−0.777361 | + | 0.629055i | \(0.783442\pi\) | |||||||
\(164\) | −7.80915 | −0.609792 | ||||||||
\(165\) | −9.11020 | −0.709228 | ||||||||
\(166\) | −9.19166 | −0.713411 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 13.6567 | 1.05363 | ||||||||
\(169\) | −11.6452 | −0.895784 | ||||||||
\(170\) | −3.73291 | −0.286301 | ||||||||
\(171\) | −28.3958 | −2.17148 | ||||||||
\(172\) | −6.35563 | −0.484612 | ||||||||
\(173\) | 18.5483 | 1.41020 | 0.705101 | − | 0.709107i | \(-0.250902\pi\) | ||||
0.705101 | + | 0.709107i | \(0.250902\pi\) | |||||||
\(174\) | 3.30104 | 0.250251 | ||||||||
\(175\) | −24.3958 | −1.84415 | ||||||||
\(176\) | 0.836038 | 0.0630187 | ||||||||
\(177\) | −5.51959 | −0.414878 | ||||||||
\(178\) | 12.3225 | 0.923610 | ||||||||
\(179\) | −3.39501 | −0.253755 | −0.126878 | − | 0.991918i | \(-0.540496\pi\) | ||||
−0.126878 | + | 0.991918i | \(0.540496\pi\) | |||||||
\(180\) | −26.0679 | −1.94299 | ||||||||
\(181\) | 22.9523 | 1.70603 | 0.853015 | − | 0.521887i | \(-0.174772\pi\) | ||||
0.853015 | + | 0.521887i | \(0.174772\pi\) | |||||||
\(182\) | −4.81540 | −0.356942 | ||||||||
\(183\) | −33.4629 | −2.47365 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 9.21957 | 0.677836 | ||||||||
\(186\) | 23.6485 | 1.73399 | ||||||||
\(187\) | −0.945415 | −0.0691356 | ||||||||
\(188\) | −0.246456 | −0.0179747 | ||||||||
\(189\) | −66.8750 | −4.86444 | ||||||||
\(190\) | −11.8700 | −0.861140 | ||||||||
\(191\) | 3.67208 | 0.265702 | 0.132851 | − | 0.991136i | \(-0.457587\pi\) | ||||
0.132851 | + | 0.991136i | \(0.457587\pi\) | |||||||
\(192\) | 3.30104 | 0.238232 | ||||||||
\(193\) | 18.7113 | 1.34687 | 0.673433 | − | 0.739249i | \(-0.264819\pi\) | ||||
0.673433 | + | 0.739249i | \(0.264819\pi\) | |||||||
\(194\) | −13.2042 | −0.948004 | ||||||||
\(195\) | 12.6836 | 0.908288 | ||||||||
\(196\) | 10.1154 | 0.722530 | ||||||||
\(197\) | 15.2042 | 1.08325 | 0.541626 | − | 0.840620i | \(-0.317809\pi\) | ||||
0.541626 | + | 0.840620i | \(0.317809\pi\) | |||||||
\(198\) | −6.60208 | −0.469190 | ||||||||
\(199\) | 6.32792 | 0.448575 | 0.224287 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224287 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(200\) | −5.89687 | −0.416972 | ||||||||
\(201\) | −2.86917 | −0.202376 | ||||||||
\(202\) | −8.40126 | −0.591111 | ||||||||
\(203\) | 4.13708 | 0.290366 | ||||||||
\(204\) | −3.73291 | −0.261356 | ||||||||
\(205\) | 25.7783 | 1.80044 | ||||||||
\(206\) | −14.8100 | −1.03186 | ||||||||
\(207\) | −7.89687 | −0.548871 | ||||||||
\(208\) | −1.16396 | −0.0807063 | ||||||||
\(209\) | −3.00625 | −0.207947 | ||||||||
\(210\) | −45.0812 | −3.11090 | ||||||||
\(211\) | −13.5627 | −0.933695 | −0.466847 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(212\) | −7.14855 | −0.490965 | ||||||||
\(213\) | 45.5337 | 3.11992 | ||||||||
\(214\) | −13.1917 | −0.901764 | ||||||||
\(215\) | 20.9802 | 1.43084 | ||||||||
\(216\) | −16.1648 | −1.09987 | ||||||||
\(217\) | 29.6379 | 2.01195 | ||||||||
\(218\) | −16.1010 | −1.09050 | ||||||||
\(219\) | −38.9825 | −2.63419 | ||||||||
\(220\) | −2.75979 | −0.186065 | ||||||||
\(221\) | 1.31624 | 0.0885400 | ||||||||
\(222\) | 9.21957 | 0.618777 | ||||||||
\(223\) | −5.20416 | −0.348497 | −0.174248 | − | 0.984702i | \(-0.555750\pi\) | ||||
−0.174248 | + | 0.984702i | \(0.555750\pi\) | |||||||
\(224\) | 4.13708 | 0.276420 | ||||||||
\(225\) | 46.5669 | 3.10446 | ||||||||
\(226\) | −2.32792 | −0.154851 | ||||||||
\(227\) | 2.62746 | 0.174391 | 0.0871955 | − | 0.996191i | \(-0.472210\pi\) | ||||
0.0871955 | + | 0.996191i | \(0.472210\pi\) | |||||||
\(228\) | −11.8700 | −0.786109 | ||||||||
\(229\) | −8.80543 | −0.581879 | −0.290940 | − | 0.956741i | \(-0.593968\pi\) | ||||
−0.290940 | + | 0.956741i | \(0.593968\pi\) | |||||||
\(230\) | −3.30104 | −0.217664 | ||||||||
\(231\) | −11.4175 | −0.751215 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −21.3590 | −1.39927 | −0.699636 | − | 0.714499i | \(-0.746655\pi\) | ||||
−0.699636 | + | 0.714499i | \(0.746655\pi\) | |||||||
\(234\) | 9.19166 | 0.600878 | ||||||||
\(235\) | 0.813562 | 0.0530709 | ||||||||
\(236\) | −1.67208 | −0.108843 | ||||||||
\(237\) | −54.4431 | −3.53646 | ||||||||
\(238\) | −4.67833 | −0.303251 | ||||||||
\(239\) | 15.6666 | 1.01339 | 0.506695 | − | 0.862125i | \(-0.330867\pi\) | ||||
0.506695 | + | 0.862125i | \(0.330867\pi\) | |||||||
\(240\) | −10.8969 | −0.703390 | ||||||||
\(241\) | −20.1369 | −1.29713 | −0.648565 | − | 0.761159i | \(-0.724631\pi\) | ||||
−0.648565 | + | 0.761159i | \(0.724631\pi\) | |||||||
\(242\) | 10.3010 | 0.662176 | ||||||||
\(243\) | 49.4475 | 3.17206 | ||||||||
\(244\) | −10.1371 | −0.648960 | ||||||||
\(245\) | −33.3914 | −2.13330 | ||||||||
\(246\) | 25.7783 | 1.64357 | ||||||||
\(247\) | 4.18541 | 0.266311 | ||||||||
\(248\) | 7.16396 | 0.454912 | ||||||||
\(249\) | 30.3421 | 1.92285 | ||||||||
\(250\) | 2.96062 | 0.187246 | ||||||||
\(251\) | −10.5436 | −0.665504 | −0.332752 | − | 0.943014i | \(-0.607977\pi\) | ||||
−0.332752 | + | 0.943014i | \(0.607977\pi\) | |||||||
\(252\) | −32.6700 | −2.05802 | ||||||||
\(253\) | −0.836038 | −0.0525612 | ||||||||
\(254\) | −17.7075 | −1.11107 | ||||||||
\(255\) | 12.3225 | 0.771664 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.54275 | 0.220991 | 0.110495 | − | 0.993877i | \(-0.464756\pi\) | ||||
0.110495 | + | 0.993877i | \(0.464756\pi\) | |||||||
\(258\) | 20.9802 | 1.30617 | ||||||||
\(259\) | 11.5546 | 0.717966 | ||||||||
\(260\) | 3.84229 | 0.238289 | ||||||||
\(261\) | −7.89687 | −0.488804 | ||||||||
\(262\) | 14.1979 | 0.877150 | ||||||||
\(263\) | 0.777728 | 0.0479568 | 0.0239784 | − | 0.999712i | \(-0.492367\pi\) | ||||
0.0239784 | + | 0.999712i | \(0.492367\pi\) | |||||||
\(264\) | −2.75979 | −0.169854 | ||||||||
\(265\) | 23.5977 | 1.44959 | ||||||||
\(266\) | −14.8762 | −0.912121 | ||||||||
\(267\) | −40.6771 | −2.48940 | ||||||||
\(268\) | −0.869172 | −0.0530931 | ||||||||
\(269\) | −25.6358 | −1.56304 | −0.781522 | − | 0.623878i | \(-0.785556\pi\) | ||||
−0.781522 | + | 0.623878i | \(0.785556\pi\) | |||||||
\(270\) | 53.3606 | 3.24742 | ||||||||
\(271\) | 10.2590 | 0.623187 | 0.311594 | − | 0.950215i | \(-0.399137\pi\) | ||||
0.311594 | + | 0.950215i | \(0.399137\pi\) | |||||||
\(272\) | −1.13083 | −0.0685665 | ||||||||
\(273\) | 15.8958 | 0.962061 | ||||||||
\(274\) | −19.8546 | −1.19946 | ||||||||
\(275\) | 4.93001 | 0.297291 | ||||||||
\(276\) | −3.30104 | −0.198699 | ||||||||
\(277\) | −7.88249 | −0.473613 | −0.236806 | − | 0.971557i | \(-0.576101\pi\) | ||||
−0.236806 | + | 0.971557i | \(0.576101\pi\) | |||||||
\(278\) | 9.21957 | 0.552953 | ||||||||
\(279\) | −56.5729 | −3.38693 | ||||||||
\(280\) | −13.6567 | −0.816142 | ||||||||
\(281\) | 11.1102 | 0.662779 | 0.331389 | − | 0.943494i | \(-0.392483\pi\) | ||||
0.331389 | + | 0.943494i | \(0.392483\pi\) | |||||||
\(282\) | 0.813562 | 0.0484469 | ||||||||
\(283\) | 11.7762 | 0.700024 | 0.350012 | − | 0.936745i | \(-0.386178\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386178\pi\) | |||||||
\(284\) | 13.7937 | 0.818508 | ||||||||
\(285\) | 39.1833 | 2.32102 | ||||||||
\(286\) | 0.973116 | 0.0575416 | ||||||||
\(287\) | 32.3071 | 1.90703 | ||||||||
\(288\) | −7.89687 | −0.465328 | ||||||||
\(289\) | −15.7212 | −0.924778 | ||||||||
\(290\) | −3.30104 | −0.193844 | ||||||||
\(291\) | 43.5875 | 2.55514 | ||||||||
\(292\) | −11.8092 | −0.691078 | ||||||||
\(293\) | −2.20335 | −0.128721 | −0.0643605 | − | 0.997927i | \(-0.520501\pi\) | ||||
−0.0643605 | + | 0.997927i | \(0.520501\pi\) | |||||||
\(294\) | −33.3914 | −1.94743 | ||||||||
\(295\) | 5.51959 | 0.321363 | ||||||||
\(296\) | 2.79293 | 0.162336 | ||||||||
\(297\) | 13.5144 | 0.784183 | ||||||||
\(298\) | −6.49271 | −0.376112 | ||||||||
\(299\) | 1.16396 | 0.0673137 | ||||||||
\(300\) | 19.4658 | 1.12386 | ||||||||
\(301\) | 26.2937 | 1.51555 | ||||||||
\(302\) | 14.3833 | 0.827668 | ||||||||
\(303\) | 27.7329 | 1.59321 | ||||||||
\(304\) | −3.59583 | −0.206235 | ||||||||
\(305\) | 33.4629 | 1.91608 | ||||||||
\(306\) | 8.93001 | 0.510495 | ||||||||
\(307\) | −21.3335 | −1.21757 | −0.608783 | − | 0.793337i | \(-0.708342\pi\) | ||||
−0.608783 | + | 0.793337i | \(0.708342\pi\) | |||||||
\(308\) | −3.45875 | −0.197081 | ||||||||
\(309\) | 48.8883 | 2.78116 | ||||||||
\(310\) | −23.6485 | −1.34315 | ||||||||
\(311\) | −10.6575 | −0.604331 | −0.302165 | − | 0.953256i | \(-0.597709\pi\) | ||||
−0.302165 | + | 0.953256i | \(0.597709\pi\) | |||||||
\(312\) | 3.84229 | 0.217527 | ||||||||
\(313\) | −13.7227 | −0.775654 | −0.387827 | − | 0.921732i | \(-0.626774\pi\) | ||||
−0.387827 | + | 0.921732i | \(0.626774\pi\) | |||||||
\(314\) | 9.79665 | 0.552857 | ||||||||
\(315\) | 107.845 | 6.07638 | ||||||||
\(316\) | −16.4927 | −0.927787 | ||||||||
\(317\) | 3.99457 | 0.224357 | 0.112179 | − | 0.993688i | \(-0.464217\pi\) | ||||
0.112179 | + | 0.993688i | \(0.464217\pi\) | |||||||
\(318\) | 23.5977 | 1.32329 | ||||||||
\(319\) | −0.836038 | −0.0468091 | ||||||||
\(320\) | −3.30104 | −0.184534 | ||||||||
\(321\) | 43.5462 | 2.43051 | ||||||||
\(322\) | −4.13708 | −0.230550 | ||||||||
\(323\) | 4.06627 | 0.226253 | ||||||||
\(324\) | 29.6700 | 1.64833 | ||||||||
\(325\) | −6.86374 | −0.380732 | ||||||||
\(326\) | 19.8494 | 1.09935 | ||||||||
\(327\) | 53.1502 | 2.93921 | ||||||||
\(328\) | 7.80915 | 0.431188 | ||||||||
\(329\) | 1.01961 | 0.0562128 | ||||||||
\(330\) | 9.11020 | 0.501500 | ||||||||
\(331\) | −1.10313 | −0.0606333 | −0.0303167 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303167 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(332\) | 9.19166 | 0.504458 | ||||||||
\(333\) | −22.0554 | −1.20863 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 2.86917 | 0.156760 | ||||||||
\(336\) | −13.6567 | −0.745032 | ||||||||
\(337\) | −7.25793 | −0.395365 | −0.197682 | − | 0.980266i | \(-0.563341\pi\) | ||||
−0.197682 | + | 0.980266i | \(0.563341\pi\) | |||||||
\(338\) | 11.6452 | 0.633415 | ||||||||
\(339\) | 7.68458 | 0.417369 | ||||||||
\(340\) | 3.73291 | 0.202446 | ||||||||
\(341\) | −5.98934 | −0.324341 | ||||||||
\(342\) | 28.3958 | 1.53547 | ||||||||
\(343\) | −12.8887 | −0.695927 | ||||||||
\(344\) | 6.35563 | 0.342672 | ||||||||
\(345\) | 10.8969 | 0.586668 | ||||||||
\(346\) | −18.5483 | −0.997164 | ||||||||
\(347\) | −13.0825 | −0.702305 | −0.351153 | − | 0.936318i | \(-0.614210\pi\) | ||||
−0.351153 | + | 0.936318i | \(0.614210\pi\) | |||||||
\(348\) | −3.30104 | −0.176954 | ||||||||
\(349\) | −16.8152 | −0.900097 | −0.450048 | − | 0.893004i | \(-0.648593\pi\) | ||||
−0.450048 | + | 0.893004i | \(0.648593\pi\) | |||||||
\(350\) | 24.3958 | 1.30401 | ||||||||
\(351\) | −18.8152 | −1.00428 | ||||||||
\(352\) | −0.836038 | −0.0445610 | ||||||||
\(353\) | −2.61206 | −0.139026 | −0.0695129 | − | 0.997581i | \(-0.522144\pi\) | ||||
−0.0695129 | + | 0.997581i | \(0.522144\pi\) | |||||||
\(354\) | 5.51959 | 0.293363 | ||||||||
\(355\) | −45.5337 | −2.41668 | ||||||||
\(356\) | −12.3225 | −0.653091 | ||||||||
\(357\) | 15.4433 | 0.817349 | ||||||||
\(358\) | 3.39501 | 0.179432 | ||||||||
\(359\) | −33.5115 | −1.76867 | −0.884334 | − | 0.466856i | \(-0.845387\pi\) | ||||
−0.884334 | + | 0.466856i | \(0.845387\pi\) | |||||||
\(360\) | 26.0679 | 1.37390 | ||||||||
\(361\) | −6.06999 | −0.319473 | ||||||||
\(362\) | −22.9523 | −1.20634 | ||||||||
\(363\) | −34.0042 | −1.78476 | ||||||||
\(364\) | 4.81540 | 0.252396 | ||||||||
\(365\) | 38.9825 | 2.04044 | ||||||||
\(366\) | 33.4629 | 1.74913 | ||||||||
\(367\) | 29.1833 | 1.52336 | 0.761679 | − | 0.647955i | \(-0.224376\pi\) | ||||
0.761679 | + | 0.647955i | \(0.224376\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −61.6679 | −3.21030 | ||||||||
\(370\) | −9.21957 | −0.479303 | ||||||||
\(371\) | 29.5741 | 1.53541 | ||||||||
\(372\) | −23.6485 | −1.22612 | ||||||||
\(373\) | −0.698959 | −0.0361907 | −0.0180954 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180954 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(374\) | 0.945415 | 0.0488862 | ||||||||
\(375\) | −9.77311 | −0.504681 | ||||||||
\(376\) | 0.246456 | 0.0127100 | ||||||||
\(377\) | 1.16396 | 0.0599471 | ||||||||
\(378\) | 66.8750 | 3.43968 | ||||||||
\(379\) | 24.5175 | 1.25938 | 0.629690 | − | 0.776847i | \(-0.283182\pi\) | ||||
0.629690 | + | 0.776847i | \(0.283182\pi\) | |||||||
\(380\) | 11.8700 | 0.608918 | ||||||||
\(381\) | 58.4533 | 2.99465 | ||||||||
\(382\) | −3.67208 | −0.187880 | ||||||||
\(383\) | −15.4504 | −0.789479 | −0.394740 | − | 0.918793i | \(-0.629165\pi\) | ||||
−0.394740 | + | 0.918793i | \(0.629165\pi\) | |||||||
\(384\) | −3.30104 | −0.168456 | ||||||||
\(385\) | 11.4175 | 0.581889 | ||||||||
\(386\) | −18.7113 | −0.952378 | ||||||||
\(387\) | −50.1896 | −2.55128 | ||||||||
\(388\) | 13.2042 | 0.670340 | ||||||||
\(389\) | −25.1608 | −1.27571 | −0.637853 | − | 0.770158i | \(-0.720177\pi\) | ||||
−0.637853 | + | 0.770158i | \(0.720177\pi\) | |||||||
\(390\) | −12.6836 | −0.642257 | ||||||||
\(391\) | 1.13083 | 0.0571884 | ||||||||
\(392\) | −10.1154 | −0.510906 | ||||||||
\(393\) | −46.8679 | −2.36417 | ||||||||
\(394\) | −15.2042 | −0.765975 | ||||||||
\(395\) | 54.4431 | 2.73933 | ||||||||
\(396\) | 6.60208 | 0.331767 | ||||||||
\(397\) | −29.8423 | −1.49774 | −0.748871 | − | 0.662716i | \(-0.769404\pi\) | ||||
−0.748871 | + | 0.662716i | \(0.769404\pi\) | |||||||
\(398\) | −6.32792 | −0.317190 | ||||||||
\(399\) | 49.1071 | 2.45843 | ||||||||
\(400\) | 5.89687 | 0.294844 | ||||||||
\(401\) | 4.55191 | 0.227311 | 0.113656 | − | 0.993520i | \(-0.463744\pi\) | ||||
0.113656 | + | 0.993520i | \(0.463744\pi\) | |||||||
\(402\) | 2.86917 | 0.143101 | ||||||||
\(403\) | 8.33858 | 0.415374 | ||||||||
\(404\) | 8.40126 | 0.417978 | ||||||||
\(405\) | −97.9418 | −4.86677 | ||||||||
\(406\) | −4.13708 | −0.205320 | ||||||||
\(407\) | −2.33499 | −0.115741 | ||||||||
\(408\) | 3.73291 | 0.184807 | ||||||||
\(409\) | −38.5329 | −1.90533 | −0.952665 | − | 0.304023i | \(-0.901670\pi\) | ||||
−0.952665 | + | 0.304023i | \(0.901670\pi\) | |||||||
\(410\) | −25.7783 | −1.27310 | ||||||||
\(411\) | 65.5408 | 3.23289 | ||||||||
\(412\) | 14.8100 | 0.729635 | ||||||||
\(413\) | 6.91751 | 0.340388 | ||||||||
\(414\) | 7.89687 | 0.388110 | ||||||||
\(415\) | −30.3421 | −1.48943 | ||||||||
\(416\) | 1.16396 | 0.0570680 | ||||||||
\(417\) | −30.4342 | −1.49037 | ||||||||
\(418\) | 3.00625 | 0.147041 | ||||||||
\(419\) | −10.2917 | −0.502781 | −0.251391 | − | 0.967886i | \(-0.580888\pi\) | ||||
−0.251391 | + | 0.967886i | \(0.580888\pi\) | |||||||
\(420\) | 45.0812 | 2.19974 | ||||||||
\(421\) | 12.9375 | 0.630533 | 0.315267 | − | 0.949003i | \(-0.397906\pi\) | ||||
0.315267 | + | 0.949003i | \(0.397906\pi\) | |||||||
\(422\) | 13.5627 | 0.660222 | ||||||||
\(423\) | −1.94623 | −0.0946291 | ||||||||
\(424\) | 7.14855 | 0.347165 | ||||||||
\(425\) | −6.66835 | −0.323463 | ||||||||
\(426\) | −45.5337 | −2.20612 | ||||||||
\(427\) | 41.9379 | 2.02952 | ||||||||
\(428\) | 13.1917 | 0.637643 | ||||||||
\(429\) | −3.21230 | −0.155091 | ||||||||
\(430\) | −20.9802 | −1.01175 | ||||||||
\(431\) | −7.61831 | −0.366961 | −0.183480 | − | 0.983023i | \(-0.558736\pi\) | ||||
−0.183480 | + | 0.983023i | \(0.558736\pi\) | |||||||
\(432\) | 16.1648 | 0.777728 | ||||||||
\(433\) | 5.75586 | 0.276609 | 0.138305 | − | 0.990390i | \(-0.455835\pi\) | ||||
0.138305 | + | 0.990390i | \(0.455835\pi\) | |||||||
\(434\) | −29.6379 | −1.42266 | ||||||||
\(435\) | 10.8969 | 0.522465 | ||||||||
\(436\) | 16.1010 | 0.771100 | ||||||||
\(437\) | 3.59583 | 0.172012 | ||||||||
\(438\) | 38.9825 | 1.86266 | ||||||||
\(439\) | −2.06084 | −0.0983583 | −0.0491792 | − | 0.998790i | \(-0.515661\pi\) | ||||
−0.0491792 | + | 0.998790i | \(0.515661\pi\) | |||||||
\(440\) | 2.75979 | 0.131568 | ||||||||
\(441\) | 79.8802 | 3.80382 | ||||||||
\(442\) | −1.31624 | −0.0626072 | ||||||||
\(443\) | −15.9254 | −0.756638 | −0.378319 | − | 0.925675i | \(-0.623498\pi\) | ||||
−0.378319 | + | 0.925675i | \(0.623498\pi\) | |||||||
\(444\) | −9.21957 | −0.437542 | ||||||||
\(445\) | 40.6771 | 1.92828 | ||||||||
\(446\) | 5.20416 | 0.246424 | ||||||||
\(447\) | 21.4327 | 1.01373 | ||||||||
\(448\) | −4.13708 | −0.195459 | ||||||||
\(449\) | 18.7821 | 0.886380 | 0.443190 | − | 0.896428i | \(-0.353847\pi\) | ||||
0.443190 | + | 0.896428i | \(0.353847\pi\) | |||||||
\(450\) | −46.5669 | −2.19518 | ||||||||
\(451\) | −6.52875 | −0.307427 | ||||||||
\(452\) | 2.32792 | 0.109496 | ||||||||
\(453\) | −47.4800 | −2.23080 | ||||||||
\(454\) | −2.62746 | −0.123313 | ||||||||
\(455\) | −15.8958 | −0.745209 | ||||||||
\(456\) | 11.8700 | 0.555863 | ||||||||
\(457\) | −37.7342 | −1.76513 | −0.882565 | − | 0.470191i | \(-0.844185\pi\) | ||||
−0.882565 | + | 0.470191i | \(0.844185\pi\) | |||||||
\(458\) | 8.80543 | 0.411451 | ||||||||
\(459\) | −18.2796 | −0.853218 | ||||||||
\(460\) | 3.30104 | 0.153912 | ||||||||
\(461\) | 0.462477 | 0.0215397 | 0.0107699 | − | 0.999942i | \(-0.496572\pi\) | ||||
0.0107699 | + | 0.999942i | \(0.496572\pi\) | |||||||
\(462\) | 11.4175 | 0.531190 | ||||||||
\(463\) | −13.3316 | −0.619574 | −0.309787 | − | 0.950806i | \(-0.600258\pi\) | ||||
−0.309787 | + | 0.950806i | \(0.600258\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 78.0648 | 3.62017 | ||||||||
\(466\) | 21.3590 | 0.989435 | ||||||||
\(467\) | 7.22770 | 0.334458 | 0.167229 | − | 0.985918i | \(-0.446518\pi\) | ||||
0.167229 | + | 0.985918i | \(0.446518\pi\) | |||||||
\(468\) | −9.19166 | −0.424885 | ||||||||
\(469\) | 3.59583 | 0.166040 | ||||||||
\(470\) | −0.813562 | −0.0375268 | ||||||||
\(471\) | −32.3392 | −1.49011 | ||||||||
\(472\) | 1.67208 | 0.0769635 | ||||||||
\(473\) | −5.31354 | −0.244317 | ||||||||
\(474\) | 54.4431 | 2.50065 | ||||||||
\(475\) | −21.2042 | −0.972914 | ||||||||
\(476\) | 4.67833 | 0.214431 | ||||||||
\(477\) | −56.4512 | −2.58472 | ||||||||
\(478\) | −15.6666 | −0.716576 | ||||||||
\(479\) | 36.4406 | 1.66501 | 0.832506 | − | 0.554016i | \(-0.186905\pi\) | ||||
0.832506 | + | 0.554016i | \(0.186905\pi\) | |||||||
\(480\) | 10.8969 | 0.497372 | ||||||||
\(481\) | 3.25086 | 0.148227 | ||||||||
\(482\) | 20.1369 | 0.917209 | ||||||||
\(483\) | 13.6567 | 0.621400 | ||||||||
\(484\) | −10.3010 | −0.468229 | ||||||||
\(485\) | −43.5875 | −1.97921 | ||||||||
\(486\) | −49.4475 | −2.24298 | ||||||||
\(487\) | 23.6717 | 1.07267 | 0.536333 | − | 0.844006i | \(-0.319809\pi\) | ||||
0.536333 | + | 0.844006i | \(0.319809\pi\) | |||||||
\(488\) | 10.1371 | 0.458884 | ||||||||
\(489\) | −65.5235 | −2.96308 | ||||||||
\(490\) | 33.3914 | 1.50847 | ||||||||
\(491\) | 10.3960 | 0.469167 | 0.234583 | − | 0.972096i | \(-0.424627\pi\) | ||||
0.234583 | + | 0.972096i | \(0.424627\pi\) | |||||||
\(492\) | −25.7783 | −1.16218 | ||||||||
\(493\) | 1.13083 | 0.0509299 | ||||||||
\(494\) | −4.18541 | −0.188311 | ||||||||
\(495\) | −21.7937 | −0.979556 | ||||||||
\(496\) | −7.16396 | −0.321671 | ||||||||
\(497\) | −57.0658 | −2.55975 | ||||||||
\(498\) | −30.3421 | −1.35966 | ||||||||
\(499\) | 38.5358 | 1.72510 | 0.862550 | − | 0.505972i | \(-0.168866\pi\) | ||||
0.862550 | + | 0.505972i | \(0.168866\pi\) | |||||||
\(500\) | −2.96062 | −0.132403 | ||||||||
\(501\) | 26.4083 | 1.17984 | ||||||||
\(502\) | 10.5436 | 0.470582 | ||||||||
\(503\) | 14.4827 | 0.645753 | 0.322877 | − | 0.946441i | \(-0.395350\pi\) | ||||
0.322877 | + | 0.946441i | \(0.395350\pi\) | |||||||
\(504\) | 32.6700 | 1.45524 | ||||||||
\(505\) | −27.7329 | −1.23410 | ||||||||
\(506\) | 0.836038 | 0.0371664 | ||||||||
\(507\) | −38.4413 | −1.70724 | ||||||||
\(508\) | 17.7075 | 0.785645 | ||||||||
\(509\) | 1.80895 | 0.0801802 | 0.0400901 | − | 0.999196i | \(-0.487236\pi\) | ||||
0.0400901 | + | 0.999196i | \(0.487236\pi\) | |||||||
\(510\) | −12.3225 | −0.545649 | ||||||||
\(511\) | 48.8554 | 2.16124 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −58.1258 | −2.56632 | ||||||||
\(514\) | −3.54275 | −0.156264 | ||||||||
\(515\) | −48.8883 | −2.15428 | ||||||||
\(516\) | −20.9802 | −0.923601 | ||||||||
\(517\) | −0.206047 | −0.00906192 | ||||||||
\(518\) | −11.5546 | −0.507678 | ||||||||
\(519\) | 61.2288 | 2.68764 | ||||||||
\(520\) | −3.84229 | −0.168495 | ||||||||
\(521\) | 29.4627 | 1.29078 | 0.645392 | − | 0.763851i | \(-0.276694\pi\) | ||||
0.645392 | + | 0.763851i | \(0.276694\pi\) | |||||||
\(522\) | 7.89687 | 0.345637 | ||||||||
\(523\) | 8.69335 | 0.380134 | 0.190067 | − | 0.981771i | \(-0.439130\pi\) | ||||
0.190067 | + | 0.981771i | \(0.439130\pi\) | |||||||
\(524\) | −14.1979 | −0.620239 | ||||||||
\(525\) | −80.5316 | −3.51469 | ||||||||
\(526\) | −0.777728 | −0.0339106 | ||||||||
\(527\) | 8.10121 | 0.352894 | ||||||||
\(528\) | 2.75979 | 0.120105 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −23.5977 | −1.02502 | ||||||||
\(531\) | −13.2042 | −0.573012 | ||||||||
\(532\) | 14.8762 | 0.644967 | ||||||||
\(533\) | 9.08956 | 0.393713 | ||||||||
\(534\) | 40.6771 | 1.76027 | ||||||||
\(535\) | −43.5462 | −1.88267 | ||||||||
\(536\) | 0.869172 | 0.0375425 | ||||||||
\(537\) | −11.2071 | −0.483621 | ||||||||
\(538\) | 25.6358 | 1.10524 | ||||||||
\(539\) | 8.45687 | 0.364263 | ||||||||
\(540\) | −53.3606 | −2.29627 | ||||||||
\(541\) | 13.6112 | 0.585193 | 0.292596 | − | 0.956236i | \(-0.405481\pi\) | ||||
0.292596 | + | 0.956236i | \(0.405481\pi\) | |||||||
\(542\) | −10.2590 | −0.440660 | ||||||||
\(543\) | 75.7664 | 3.25145 | ||||||||
\(544\) | 1.13083 | 0.0484839 | ||||||||
\(545\) | −53.1502 | −2.27670 | ||||||||
\(546\) | −15.8958 | −0.680280 | ||||||||
\(547\) | 37.2442 | 1.59245 | 0.796223 | − | 0.605004i | \(-0.206828\pi\) | ||||
0.796223 | + | 0.605004i | \(0.206828\pi\) | |||||||
\(548\) | 19.8546 | 0.848146 | ||||||||
\(549\) | −80.0512 | −3.41650 | ||||||||
\(550\) | −4.93001 | −0.210216 | ||||||||
\(551\) | 3.59583 | 0.153188 | ||||||||
\(552\) | 3.30104 | 0.140502 | ||||||||
\(553\) | 68.2316 | 2.90150 | ||||||||
\(554\) | 7.88249 | 0.334895 | ||||||||
\(555\) | 30.4342 | 1.29186 | ||||||||
\(556\) | −9.21957 | −0.390997 | ||||||||
\(557\) | −30.3750 | −1.28703 | −0.643515 | − | 0.765434i | \(-0.722525\pi\) | ||||
−0.643515 | + | 0.765434i | \(0.722525\pi\) | |||||||
\(558\) | 56.5729 | 2.39492 | ||||||||
\(559\) | 7.39771 | 0.312890 | ||||||||
\(560\) | 13.6567 | 0.577100 | ||||||||
\(561\) | −3.12085 | −0.131763 | ||||||||
\(562\) | −11.1102 | −0.468655 | ||||||||
\(563\) | −40.4131 | −1.70321 | −0.851604 | − | 0.524186i | \(-0.824370\pi\) | ||||
−0.851604 | + | 0.524186i | \(0.824370\pi\) | |||||||
\(564\) | −0.813562 | −0.0342571 | ||||||||
\(565\) | −7.68458 | −0.323293 | ||||||||
\(566\) | −11.7762 | −0.494992 | ||||||||
\(567\) | −122.747 | −5.15489 | ||||||||
\(568\) | −13.7937 | −0.578773 | ||||||||
\(569\) | −15.0088 | −0.629201 | −0.314600 | − | 0.949224i | \(-0.601870\pi\) | ||||
−0.314600 | + | 0.949224i | \(0.601870\pi\) | |||||||
\(570\) | −39.1833 | −1.64121 | ||||||||
\(571\) | −1.94460 | −0.0813789 | −0.0406894 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406894 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(572\) | −0.973116 | −0.0406880 | ||||||||
\(573\) | 12.1217 | 0.506390 | ||||||||
\(574\) | −32.3071 | −1.34847 | ||||||||
\(575\) | −5.89687 | −0.245917 | ||||||||
\(576\) | 7.89687 | 0.329036 | ||||||||
\(577\) | 3.68748 | 0.153512 | 0.0767560 | − | 0.997050i | \(-0.475544\pi\) | ||||
0.0767560 | + | 0.997050i | \(0.475544\pi\) | |||||||
\(578\) | 15.7212 | 0.653917 | ||||||||
\(579\) | 61.7666 | 2.56693 | ||||||||
\(580\) | 3.30104 | 0.137068 | ||||||||
\(581\) | −38.0266 | −1.57761 | ||||||||
\(582\) | −43.5875 | −1.80676 | ||||||||
\(583\) | −5.97646 | −0.247520 | ||||||||
\(584\) | 11.8092 | 0.488666 | ||||||||
\(585\) | 30.3421 | 1.25449 | ||||||||
\(586\) | 2.20335 | 0.0910194 | ||||||||
\(587\) | 24.7421 | 1.02121 | 0.510607 | − | 0.859814i | \(-0.329421\pi\) | ||||
0.510607 | + | 0.859814i | \(0.329421\pi\) | |||||||
\(588\) | 33.3914 | 1.37704 | ||||||||
\(589\) | 25.7604 | 1.06144 | ||||||||
\(590\) | −5.51959 | −0.227238 | ||||||||
\(591\) | 50.1896 | 2.06452 | ||||||||
\(592\) | −2.79293 | −0.114789 | ||||||||
\(593\) | 25.6614 | 1.05379 | 0.526894 | − | 0.849931i | \(-0.323356\pi\) | ||||
0.526894 | + | 0.849931i | \(0.323356\pi\) | |||||||
\(594\) | −13.5144 | −0.554501 | ||||||||
\(595\) | −15.4433 | −0.633115 | ||||||||
\(596\) | 6.49271 | 0.265952 | ||||||||
\(597\) | 20.8887 | 0.854919 | ||||||||
\(598\) | −1.16396 | −0.0475980 | ||||||||
\(599\) | −41.4094 | −1.69194 | −0.845970 | − | 0.533230i | \(-0.820978\pi\) | ||||
−0.845970 | + | 0.533230i | \(0.820978\pi\) | |||||||
\(600\) | −19.4658 | −0.794689 | ||||||||
\(601\) | 36.5405 | 1.49052 | 0.745258 | − | 0.666776i | \(-0.232326\pi\) | ||||
0.745258 | + | 0.666776i | \(0.232326\pi\) | |||||||
\(602\) | −26.2937 | −1.07165 | ||||||||
\(603\) | −6.86374 | −0.279513 | ||||||||
\(604\) | −14.3833 | −0.585249 | ||||||||
\(605\) | 34.0042 | 1.38247 | ||||||||
\(606\) | −27.7329 | −1.12657 | ||||||||
\(607\) | −33.2094 | −1.34793 | −0.673964 | − | 0.738764i | \(-0.735410\pi\) | ||||
−0.673964 | + | 0.738764i | \(0.735410\pi\) | |||||||
\(608\) | 3.59583 | 0.145830 | ||||||||
\(609\) | 13.6567 | 0.553396 | ||||||||
\(610\) | −33.4629 | −1.35487 | ||||||||
\(611\) | 0.286866 | 0.0116053 | ||||||||
\(612\) | −8.93001 | −0.360974 | ||||||||
\(613\) | 13.2860 | 0.536617 | 0.268309 | − | 0.963333i | \(-0.413535\pi\) | ||||
0.268309 | + | 0.963333i | \(0.413535\pi\) | |||||||
\(614\) | 21.3335 | 0.860950 | ||||||||
\(615\) | 85.0954 | 3.43138 | ||||||||
\(616\) | 3.45875 | 0.139357 | ||||||||
\(617\) | −7.84751 | −0.315929 | −0.157965 | − | 0.987445i | \(-0.550493\pi\) | ||||
−0.157965 | + | 0.987445i | \(0.550493\pi\) | |||||||
\(618\) | −48.8883 | −1.96658 | ||||||||
\(619\) | −24.0856 | −0.968083 | −0.484042 | − | 0.875045i | \(-0.660832\pi\) | ||||
−0.484042 | + | 0.875045i | \(0.660832\pi\) | |||||||
\(620\) | 23.6485 | 0.949748 | ||||||||
\(621\) | −16.1648 | −0.648670 | ||||||||
\(622\) | 10.6575 | 0.427326 | ||||||||
\(623\) | 50.9791 | 2.04244 | ||||||||
\(624\) | −3.84229 | −0.153815 | ||||||||
\(625\) | −19.7113 | −0.788450 | ||||||||
\(626\) | 13.7227 | 0.548471 | ||||||||
\(627\) | −9.92376 | −0.396317 | ||||||||
\(628\) | −9.79665 | −0.390929 | ||||||||
\(629\) | 3.15832 | 0.125931 | ||||||||
\(630\) | −107.845 | −4.29665 | ||||||||
\(631\) | −34.9316 | −1.39061 | −0.695303 | − | 0.718716i | \(-0.744730\pi\) | ||||
−0.695303 | + | 0.718716i | \(0.744730\pi\) | |||||||
\(632\) | 16.4927 | 0.656045 | ||||||||
\(633\) | −44.7710 | −1.77949 | ||||||||
\(634\) | −3.99457 | −0.158645 | ||||||||
\(635\) | −58.4533 | −2.31965 | ||||||||
\(636\) | −23.5977 | −0.935709 | ||||||||
\(637\) | −11.7740 | −0.466502 | ||||||||
\(638\) | 0.836038 | 0.0330990 | ||||||||
\(639\) | 108.927 | 4.30910 | ||||||||
\(640\) | 3.30104 | 0.130485 | ||||||||
\(641\) | 38.2867 | 1.51223 | 0.756116 | − | 0.654438i | \(-0.227095\pi\) | ||||
0.756116 | + | 0.654438i | \(0.227095\pi\) | |||||||
\(642\) | −43.5462 | −1.71863 | ||||||||
\(643\) | −41.1879 | −1.62429 | −0.812145 | − | 0.583455i | \(-0.801700\pi\) | ||||
−0.812145 | + | 0.583455i | \(0.801700\pi\) | |||||||
\(644\) | 4.13708 | 0.163024 | ||||||||
\(645\) | 69.2565 | 2.72697 | ||||||||
\(646\) | −4.06627 | −0.159985 | ||||||||
\(647\) | 0.170006 | 0.00668362 | 0.00334181 | − | 0.999994i | \(-0.498936\pi\) | ||||
0.00334181 | + | 0.999994i | \(0.498936\pi\) | |||||||
\(648\) | −29.6700 | −1.16555 | ||||||||
\(649\) | −1.39792 | −0.0548731 | ||||||||
\(650\) | 6.86374 | 0.269218 | ||||||||
\(651\) | 97.8359 | 3.83449 | ||||||||
\(652\) | −19.8494 | −0.777361 | ||||||||
\(653\) | −1.49664 | −0.0585679 | −0.0292840 | − | 0.999571i | \(-0.509323\pi\) | ||||
−0.0292840 | + | 0.999571i | \(0.509323\pi\) | |||||||
\(654\) | −53.1502 | −2.07834 | ||||||||
\(655\) | 46.8679 | 1.83128 | ||||||||
\(656\) | −7.80915 | −0.304896 | ||||||||
\(657\) | −93.2554 | −3.63824 | ||||||||
\(658\) | −1.01961 | −0.0397485 | ||||||||
\(659\) | 10.7290 | 0.417942 | 0.208971 | − | 0.977922i | \(-0.432989\pi\) | ||||
0.208971 | + | 0.977922i | \(0.432989\pi\) | |||||||
\(660\) | −9.11020 | −0.354614 | ||||||||
\(661\) | −37.1937 | −1.44667 | −0.723334 | − | 0.690498i | \(-0.757391\pi\) | ||||
−0.723334 | + | 0.690498i | \(0.757391\pi\) | |||||||
\(662\) | 1.10313 | 0.0428742 | ||||||||
\(663\) | 4.34497 | 0.168745 | ||||||||
\(664\) | −9.19166 | −0.356706 | ||||||||
\(665\) | −49.1071 | −1.90429 | ||||||||
\(666\) | 22.0554 | 0.854630 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | −17.1792 | −0.664185 | ||||||||
\(670\) | −2.86917 | −0.110846 | ||||||||
\(671\) | −8.47498 | −0.327173 | ||||||||
\(672\) | 13.6567 | 0.526817 | ||||||||
\(673\) | 43.2139 | 1.66577 | 0.832887 | − | 0.553443i | \(-0.186686\pi\) | ||||
0.832887 | + | 0.553443i | \(0.186686\pi\) | |||||||
\(674\) | 7.25793 | 0.279565 | ||||||||
\(675\) | 95.3217 | 3.66893 | ||||||||
\(676\) | −11.6452 | −0.447892 | ||||||||
\(677\) | −17.1658 | −0.659735 | −0.329868 | − | 0.944027i | \(-0.607004\pi\) | ||||
−0.329868 | + | 0.944027i | \(0.607004\pi\) | |||||||
\(678\) | −7.68458 | −0.295124 | ||||||||
\(679\) | −54.6267 | −2.09638 | ||||||||
\(680\) | −3.73291 | −0.143151 | ||||||||
\(681\) | 8.67337 | 0.332364 | ||||||||
\(682\) | 5.98934 | 0.229344 | ||||||||
\(683\) | 27.7092 | 1.06026 | 0.530131 | − | 0.847916i | \(-0.322143\pi\) | ||||
0.530131 | + | 0.847916i | \(0.322143\pi\) | |||||||
\(684\) | −28.3958 | −1.08574 | ||||||||
\(685\) | −65.5408 | −2.50418 | ||||||||
\(686\) | 12.8887 | 0.492094 | ||||||||
\(687\) | −29.0671 | −1.10898 | ||||||||
\(688\) | −6.35563 | −0.242306 | ||||||||
\(689\) | 8.32065 | 0.316992 | ||||||||
\(690\) | −10.8969 | −0.414837 | ||||||||
\(691\) | 13.7429 | 0.522804 | 0.261402 | − | 0.965230i | \(-0.415815\pi\) | ||||
0.261402 | + | 0.965230i | \(0.415815\pi\) | |||||||
\(692\) | 18.5483 | 0.705101 | ||||||||
\(693\) | −27.3133 | −1.03755 | ||||||||
\(694\) | 13.0825 | 0.496605 | ||||||||
\(695\) | 30.4342 | 1.15443 | ||||||||
\(696\) | 3.30104 | 0.125126 | ||||||||
\(697\) | 8.83081 | 0.334491 | ||||||||
\(698\) | 16.8152 | 0.636465 | ||||||||
\(699\) | −70.5068 | −2.66681 | ||||||||
\(700\) | −24.3958 | −0.922076 | ||||||||
\(701\) | −41.5743 | −1.57024 | −0.785120 | − | 0.619344i | \(-0.787399\pi\) | ||||
−0.785120 | + | 0.619344i | \(0.787399\pi\) | |||||||
\(702\) | 18.8152 | 0.710134 | ||||||||
\(703\) | 10.0429 | 0.378775 | ||||||||
\(704\) | 0.836038 | 0.0315094 | ||||||||
\(705\) | 2.68560 | 0.101146 | ||||||||
\(706\) | 2.61206 | 0.0983061 | ||||||||
\(707\) | −34.7567 | −1.30716 | ||||||||
\(708\) | −5.51959 | −0.207439 | ||||||||
\(709\) | 14.3910 | 0.540465 | 0.270232 | − | 0.962795i | \(-0.412899\pi\) | ||||
0.270232 | + | 0.962795i | \(0.412899\pi\) | |||||||
\(710\) | 45.5337 | 1.70885 | ||||||||
\(711\) | −130.241 | −4.88441 | ||||||||
\(712\) | 12.3225 | 0.461805 | ||||||||
\(713\) | 7.16396 | 0.268293 | ||||||||
\(714\) | −15.4433 | −0.577953 | ||||||||
\(715\) | 3.21230 | 0.120133 | ||||||||
\(716\) | −3.39501 | −0.126878 | ||||||||
\(717\) | 51.7162 | 1.93138 | ||||||||
\(718\) | 33.5115 | 1.25064 | ||||||||
\(719\) | 4.21294 | 0.157116 | 0.0785581 | − | 0.996910i | \(-0.474968\pi\) | ||||
0.0785581 | + | 0.996910i | \(0.474968\pi\) | |||||||
\(720\) | −26.0679 | −0.971493 | ||||||||
\(721\) | −61.2700 | −2.28181 | ||||||||
\(722\) | 6.06999 | 0.225902 | ||||||||
\(723\) | −66.4726 | −2.47214 | ||||||||
\(724\) | 22.9523 | 0.853015 | ||||||||
\(725\) | −5.89687 | −0.219004 | ||||||||
\(726\) | 34.0042 | 1.26201 | ||||||||
\(727\) | 8.81250 | 0.326837 | 0.163419 | − | 0.986557i | \(-0.447748\pi\) | ||||
0.163419 | + | 0.986557i | \(0.447748\pi\) | |||||||
\(728\) | −4.81540 | −0.178471 | ||||||||
\(729\) | 74.2183 | 2.74883 | ||||||||
\(730\) | −38.9825 | −1.44281 | ||||||||
\(731\) | 7.18712 | 0.265825 | ||||||||
\(732\) | −33.4629 | −1.23682 | ||||||||
\(733\) | −28.5454 | −1.05435 | −0.527174 | − | 0.849757i | \(-0.676749\pi\) | ||||
−0.527174 | + | 0.849757i | \(0.676749\pi\) | |||||||
\(734\) | −29.1833 | −1.07718 | ||||||||
\(735\) | −110.226 | −4.06576 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −0.726660 | −0.0267669 | ||||||||
\(738\) | 61.6679 | 2.27003 | ||||||||
\(739\) | 36.4306 | 1.34012 | 0.670061 | − | 0.742306i | \(-0.266268\pi\) | ||||
0.670061 | + | 0.742306i | \(0.266268\pi\) | |||||||
\(740\) | 9.21957 | 0.338918 | ||||||||
\(741\) | 13.8162 | 0.507552 | ||||||||
\(742\) | −29.5741 | −1.08570 | ||||||||
\(743\) | −34.6366 | −1.27070 | −0.635348 | − | 0.772226i | \(-0.719143\pi\) | ||||
−0.635348 | + | 0.772226i | \(0.719143\pi\) | |||||||
\(744\) | 23.6485 | 0.866997 | ||||||||
\(745\) | −21.4327 | −0.785233 | ||||||||
\(746\) | 0.698959 | 0.0255907 | ||||||||
\(747\) | 72.5854 | 2.65576 | ||||||||
\(748\) | −0.945415 | −0.0345678 | ||||||||
\(749\) | −54.5750 | −1.99413 | ||||||||
\(750\) | 9.77311 | 0.356864 | ||||||||
\(751\) | −3.25957 | −0.118943 | −0.0594717 | − | 0.998230i | \(-0.518942\pi\) | ||||
−0.0594717 | + | 0.998230i | \(0.518942\pi\) | |||||||
\(752\) | −0.246456 | −0.00898733 | ||||||||
\(753\) | −34.8047 | −1.26836 | ||||||||
\(754\) | −1.16396 | −0.0423890 | ||||||||
\(755\) | 47.4800 | 1.72797 | ||||||||
\(756\) | −66.8750 | −2.43222 | ||||||||
\(757\) | 31.9458 | 1.16109 | 0.580545 | − | 0.814228i | \(-0.302839\pi\) | ||||
0.580545 | + | 0.814228i | \(0.302839\pi\) | |||||||
\(758\) | −24.5175 | −0.890516 | ||||||||
\(759\) | −2.75979 | −0.100174 | ||||||||
\(760\) | −11.8700 | −0.430570 | ||||||||
\(761\) | −25.2695 | −0.916020 | −0.458010 | − | 0.888947i | \(-0.651438\pi\) | ||||
−0.458010 | + | 0.888947i | \(0.651438\pi\) | |||||||
\(762\) | −58.4533 | −2.11754 | ||||||||
\(763\) | −66.6113 | −2.41149 | ||||||||
\(764\) | 3.67208 | 0.132851 | ||||||||
\(765\) | 29.4783 | 1.06579 | ||||||||
\(766\) | 15.4504 | 0.558246 | ||||||||
\(767\) | 1.94623 | 0.0702744 | ||||||||
\(768\) | 3.30104 | 0.119116 | ||||||||
\(769\) | −2.08458 | −0.0751720 | −0.0375860 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375860 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(770\) | −11.4175 | −0.411458 | ||||||||
\(771\) | 11.6948 | 0.421176 | ||||||||
\(772\) | 18.7113 | 0.673433 | ||||||||
\(773\) | −53.1704 | −1.91241 | −0.956204 | − | 0.292701i | \(-0.905446\pi\) | ||||
−0.956204 | + | 0.292701i | \(0.905446\pi\) | |||||||
\(774\) | 50.1896 | 1.80403 | ||||||||
\(775\) | −42.2450 | −1.51748 | ||||||||
\(776\) | −13.2042 | −0.474002 | ||||||||
\(777\) | 38.1421 | 1.36834 | ||||||||
\(778\) | 25.1608 | 0.902060 | ||||||||
\(779\) | 28.0804 | 1.00608 | ||||||||
\(780\) | 12.6836 | 0.454144 | ||||||||
\(781\) | 11.5321 | 0.412651 | ||||||||
\(782\) | −1.13083 | −0.0404383 | ||||||||
\(783\) | −16.1648 | −0.577682 | ||||||||
\(784\) | 10.1154 | 0.361265 | ||||||||
\(785\) | 32.3392 | 1.15423 | ||||||||
\(786\) | 46.8679 | 1.67172 | ||||||||
\(787\) | 48.5679 | 1.73126 | 0.865629 | − | 0.500686i | \(-0.166919\pi\) | ||||
0.865629 | + | 0.500686i | \(0.166919\pi\) | |||||||
\(788\) | 15.2042 | 0.541626 | ||||||||
\(789\) | 2.56731 | 0.0913988 | ||||||||
\(790\) | −54.4431 | −1.93700 | ||||||||
\(791\) | −9.63081 | −0.342432 | ||||||||
\(792\) | −6.60208 | −0.234595 | ||||||||
\(793\) | 11.7992 | 0.419001 | ||||||||
\(794\) | 29.8423 | 1.05906 | ||||||||
\(795\) | 77.8969 | 2.76272 | ||||||||
\(796\) | 6.32792 | 0.224287 | ||||||||
\(797\) | −37.9692 | −1.34494 | −0.672469 | − | 0.740126i | \(-0.734766\pi\) | ||||
−0.672469 | + | 0.740126i | \(0.734766\pi\) | |||||||
\(798\) | −49.1071 | −1.73837 | ||||||||
\(799\) | 0.278700 | 0.00985968 | ||||||||
\(800\) | −5.89687 | −0.208486 | ||||||||
\(801\) | −97.3092 | −3.43825 | ||||||||
\(802\) | −4.55191 | −0.160733 | ||||||||
\(803\) | −9.87290 | −0.348407 | ||||||||
\(804\) | −2.86917 | −0.101188 | ||||||||
\(805\) | −13.6567 | −0.481334 | ||||||||
\(806\) | −8.33858 | −0.293714 | ||||||||
\(807\) | −84.6249 | −2.97894 | ||||||||
\(808\) | −8.40126 | −0.295555 | ||||||||
\(809\) | 26.9795 | 0.948549 | 0.474274 | − | 0.880377i | \(-0.342710\pi\) | ||||
0.474274 | + | 0.880377i | \(0.342710\pi\) | |||||||
\(810\) | 97.9418 | 3.44133 | ||||||||
\(811\) | 44.9333 | 1.57782 | 0.788910 | − | 0.614508i | \(-0.210646\pi\) | ||||
0.788910 | + | 0.614508i | \(0.210646\pi\) | |||||||
\(812\) | 4.13708 | 0.145183 | ||||||||
\(813\) | 33.8652 | 1.18771 | ||||||||
\(814\) | 2.33499 | 0.0818415 | ||||||||
\(815\) | 65.5235 | 2.29519 | ||||||||
\(816\) | −3.73291 | −0.130678 | ||||||||
\(817\) | 22.8538 | 0.799552 | ||||||||
\(818\) | 38.5329 | 1.34727 | ||||||||
\(819\) | 38.0266 | 1.32876 | ||||||||
\(820\) | 25.7783 | 0.900219 | ||||||||
\(821\) | 26.3960 | 0.921227 | 0.460613 | − | 0.887601i | \(-0.347629\pi\) | ||||
0.460613 | + | 0.887601i | \(0.347629\pi\) | |||||||
\(822\) | −65.5408 | −2.28600 | ||||||||
\(823\) | 32.9525 | 1.14865 | 0.574326 | − | 0.818627i | \(-0.305264\pi\) | ||||
0.574326 | + | 0.818627i | \(0.305264\pi\) | |||||||
\(824\) | −14.8100 | −0.515930 | ||||||||
\(825\) | 16.2742 | 0.566593 | ||||||||
\(826\) | −6.91751 | −0.240691 | ||||||||
\(827\) | 26.9927 | 0.938628 | 0.469314 | − | 0.883031i | \(-0.344501\pi\) | ||||
0.469314 | + | 0.883031i | \(0.344501\pi\) | |||||||
\(828\) | −7.89687 | −0.274435 | ||||||||
\(829\) | 12.5358 | 0.435387 | 0.217693 | − | 0.976017i | \(-0.430147\pi\) | ||||
0.217693 | + | 0.976017i | \(0.430147\pi\) | |||||||
\(830\) | 30.3421 | 1.05319 | ||||||||
\(831\) | −26.0204 | −0.902639 | ||||||||
\(832\) | −1.16396 | −0.0403531 | ||||||||
\(833\) | −11.4388 | −0.396331 | ||||||||
\(834\) | 30.4342 | 1.05385 | ||||||||
\(835\) | −26.4083 | −0.913898 | ||||||||
\(836\) | −3.00625 | −0.103973 | ||||||||
\(837\) | −115.804 | −4.00277 | ||||||||
\(838\) | 10.2917 | 0.355520 | ||||||||
\(839\) | −41.5089 | −1.43305 | −0.716524 | − | 0.697563i | \(-0.754268\pi\) | ||||
−0.716524 | + | 0.697563i | \(0.754268\pi\) | |||||||
\(840\) | −45.0812 | −1.55545 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −12.9375 | −0.445854 | ||||||||
\(843\) | 36.6752 | 1.26316 | ||||||||
\(844\) | −13.5627 | −0.466847 | ||||||||
\(845\) | 38.4413 | 1.32242 | ||||||||
\(846\) | 1.94623 | 0.0669129 | ||||||||
\(847\) | 42.6162 | 1.46431 | ||||||||
\(848\) | −7.14855 | −0.245482 | ||||||||
\(849\) | 38.8738 | 1.33415 | ||||||||
\(850\) | 6.66835 | 0.228723 | ||||||||
\(851\) | 2.79293 | 0.0957404 | ||||||||
\(852\) | 45.5337 | 1.55996 | ||||||||
\(853\) | −47.8387 | −1.63797 | −0.818983 | − | 0.573818i | \(-0.805462\pi\) | ||||
−0.818983 | + | 0.573818i | \(0.805462\pi\) | |||||||
\(854\) | −41.9379 | −1.43509 | ||||||||
\(855\) | 93.7358 | 3.20570 | ||||||||
\(856\) | −13.1917 | −0.450882 | ||||||||
\(857\) | −19.8593 | −0.678382 | −0.339191 | − | 0.940718i | \(-0.610153\pi\) | ||||
−0.339191 | + | 0.940718i | \(0.610153\pi\) | |||||||
\(858\) | 3.21230 | 0.109666 | ||||||||
\(859\) | −11.4561 | −0.390876 | −0.195438 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195438 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(860\) | 20.9802 | 0.715418 | ||||||||
\(861\) | 106.647 | 3.63452 | ||||||||
\(862\) | 7.61831 | 0.259481 | ||||||||
\(863\) | 21.5325 | 0.732974 | 0.366487 | − | 0.930423i | \(-0.380560\pi\) | ||||
0.366487 | + | 0.930423i | \(0.380560\pi\) | |||||||
\(864\) | −16.1648 | −0.549937 | ||||||||
\(865\) | −61.2288 | −2.08184 | ||||||||
\(866\) | −5.75586 | −0.195592 | ||||||||
\(867\) | −51.8964 | −1.76249 | ||||||||
\(868\) | 29.6379 | 1.00598 | ||||||||
\(869\) | −13.7885 | −0.467744 | ||||||||
\(870\) | −10.8969 | −0.369439 | ||||||||
\(871\) | 1.01168 | 0.0342796 | ||||||||
\(872\) | −16.1010 | −0.545250 | ||||||||
\(873\) | 104.272 | 3.52906 | ||||||||
\(874\) | −3.59583 | −0.121631 | ||||||||
\(875\) | 12.2483 | 0.414068 | ||||||||
\(876\) | −38.9825 | −1.31710 | ||||||||
\(877\) | 42.9106 | 1.44899 | 0.724494 | − | 0.689281i | \(-0.242073\pi\) | ||||
0.724494 | + | 0.689281i | \(0.242073\pi\) | |||||||
\(878\) | 2.06084 | 0.0695498 | ||||||||
\(879\) | −7.27334 | −0.245324 | ||||||||
\(880\) | −2.75979 | −0.0930327 | ||||||||
\(881\) | −55.2237 | −1.86053 | −0.930267 | − | 0.366882i | \(-0.880425\pi\) | ||||
−0.930267 | + | 0.366882i | \(0.880425\pi\) | |||||||
\(882\) | −79.8802 | −2.68971 | ||||||||
\(883\) | −12.2234 | −0.411350 | −0.205675 | − | 0.978620i | \(-0.565939\pi\) | ||||
−0.205675 | + | 0.978620i | \(0.565939\pi\) | |||||||
\(884\) | 1.31624 | 0.0442700 | ||||||||
\(885\) | 18.2204 | 0.612472 | ||||||||
\(886\) | 15.9254 | 0.535024 | ||||||||
\(887\) | −43.1248 | −1.44799 | −0.723995 | − | 0.689806i | \(-0.757696\pi\) | ||||
−0.723995 | + | 0.689806i | \(0.757696\pi\) | |||||||
\(888\) | 9.21957 | 0.309389 | ||||||||
\(889\) | −73.2574 | −2.45698 | ||||||||
\(890\) | −40.6771 | −1.36350 | ||||||||
\(891\) | 24.8052 | 0.831006 | ||||||||
\(892\) | −5.20416 | −0.174248 | ||||||||
\(893\) | 0.886215 | 0.0296560 | ||||||||
\(894\) | −21.4327 | −0.716816 | ||||||||
\(895\) | 11.2071 | 0.374611 | ||||||||
\(896\) | 4.13708 | 0.138210 | ||||||||
\(897\) | 3.84229 | 0.128290 | ||||||||
\(898\) | −18.7821 | −0.626766 | ||||||||
\(899\) | 7.16396 | 0.238932 | ||||||||
\(900\) | 46.5669 | 1.55223 | ||||||||
\(901\) | 8.08379 | 0.269310 | ||||||||
\(902\) | 6.52875 | 0.217383 | ||||||||
\(903\) | 86.7967 | 2.88841 | ||||||||
\(904\) | −2.32792 | −0.0774256 | ||||||||
\(905\) | −75.7664 | −2.51856 | ||||||||
\(906\) | 47.4800 | 1.57742 | ||||||||
\(907\) | 11.7150 | 0.388989 | 0.194495 | − | 0.980904i | \(-0.437693\pi\) | ||||
0.194495 | + | 0.980904i | \(0.437693\pi\) | |||||||
\(908\) | 2.62746 | 0.0871955 | ||||||||
\(909\) | 66.3437 | 2.20048 | ||||||||
\(910\) | 15.8958 | 0.526942 | ||||||||
\(911\) | 29.2160 | 0.967969 | 0.483984 | − | 0.875077i | \(-0.339189\pi\) | ||||
0.483984 | + | 0.875077i | \(0.339189\pi\) | |||||||
\(912\) | −11.8700 | −0.393055 | ||||||||
\(913\) | 7.68458 | 0.254322 | ||||||||
\(914\) | 37.7342 | 1.24814 | ||||||||
\(915\) | 110.462 | 3.65178 | ||||||||
\(916\) | −8.80543 | −0.290940 | ||||||||
\(917\) | 58.7379 | 1.93970 | ||||||||
\(918\) | 18.2796 | 0.603316 | ||||||||
\(919\) | 18.6117 | 0.613943 | 0.306971 | − | 0.951719i | \(-0.400684\pi\) | ||||
0.306971 | + | 0.951719i | \(0.400684\pi\) | |||||||
\(920\) | −3.30104 | −0.108832 | ||||||||
\(921\) | −70.4227 | −2.32051 | ||||||||
\(922\) | −0.462477 | −0.0152309 | ||||||||
\(923\) | −16.0554 | −0.528470 | ||||||||
\(924\) | −11.4175 | −0.375608 | ||||||||
\(925\) | −16.4695 | −0.541515 | ||||||||
\(926\) | 13.3316 | 0.438105 | ||||||||
\(927\) | 116.952 | 3.84122 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 28.0255 | 0.919486 | 0.459743 | − | 0.888052i | \(-0.347942\pi\) | ||||
0.459743 | + | 0.888052i | \(0.347942\pi\) | |||||||
\(930\) | −78.0648 | −2.55985 | ||||||||
\(931\) | −36.3734 | −1.19209 | ||||||||
\(932\) | −21.3590 | −0.699636 | ||||||||
\(933\) | −35.1808 | −1.15177 | ||||||||
\(934\) | −7.22770 | −0.236498 | ||||||||
\(935\) | 3.12085 | 0.102063 | ||||||||
\(936\) | 9.19166 | 0.300439 | ||||||||
\(937\) | 18.4158 | 0.601617 | 0.300809 | − | 0.953685i | \(-0.402743\pi\) | ||||
0.300809 | + | 0.953685i | \(0.402743\pi\) | |||||||
\(938\) | −3.59583 | −0.117408 | ||||||||
\(939\) | −45.2993 | −1.47829 | ||||||||
\(940\) | 0.813562 | 0.0265355 | ||||||||
\(941\) | −29.9006 | −0.974732 | −0.487366 | − | 0.873198i | \(-0.662042\pi\) | ||||
−0.487366 | + | 0.873198i | \(0.662042\pi\) | |||||||
\(942\) | 32.3392 | 1.05367 | ||||||||
\(943\) | 7.80915 | 0.254301 | ||||||||
\(944\) | −1.67208 | −0.0544214 | ||||||||
\(945\) | 220.757 | 7.18123 | ||||||||
\(946\) | 5.31354 | 0.172758 | ||||||||
\(947\) | 45.1527 | 1.46727 | 0.733633 | − | 0.679546i | \(-0.237823\pi\) | ||||
0.733633 | + | 0.679546i | \(0.237823\pi\) | |||||||
\(948\) | −54.4431 | −1.76823 | ||||||||
\(949\) | 13.7454 | 0.446195 | ||||||||
\(950\) | 21.2042 | 0.687954 | ||||||||
\(951\) | 13.1862 | 0.427593 | ||||||||
\(952\) | −4.67833 | −0.151625 | ||||||||
\(953\) | 17.0235 | 0.551445 | 0.275723 | − | 0.961237i | \(-0.411083\pi\) | ||||
0.275723 | + | 0.961237i | \(0.411083\pi\) | |||||||
\(954\) | 56.4512 | 1.82768 | ||||||||
\(955\) | −12.1217 | −0.392248 | ||||||||
\(956\) | 15.6666 | 0.506695 | ||||||||
\(957\) | −2.75979 | −0.0892115 | ||||||||
\(958\) | −36.4406 | −1.17734 | ||||||||
\(959\) | −82.1400 | −2.65244 | ||||||||
\(960\) | −10.8969 | −0.351695 | ||||||||
\(961\) | 20.3224 | 0.655560 | ||||||||
\(962\) | −3.25086 | −0.104812 | ||||||||
\(963\) | 104.173 | 3.35692 | ||||||||
\(964\) | −20.1369 | −0.648565 | ||||||||
\(965\) | −61.7666 | −1.98834 | ||||||||
\(966\) | −13.6567 | −0.439396 | ||||||||
\(967\) | −9.32642 | −0.299918 | −0.149959 | − | 0.988692i | \(-0.547914\pi\) | ||||
−0.149959 | + | 0.988692i | \(0.547914\pi\) | |||||||
\(968\) | 10.3010 | 0.331088 | ||||||||
\(969\) | 13.4229 | 0.431206 | ||||||||
\(970\) | 43.5875 | 1.39951 | ||||||||
\(971\) | −28.2433 | −0.906372 | −0.453186 | − | 0.891416i | \(-0.649713\pi\) | ||||
−0.453186 | + | 0.891416i | \(0.649713\pi\) | |||||||
\(972\) | 49.4475 | 1.58603 | ||||||||
\(973\) | 38.1421 | 1.22278 | ||||||||
\(974\) | −23.6717 | −0.758490 | ||||||||
\(975\) | −22.6575 | −0.725620 | ||||||||
\(976\) | −10.1371 | −0.324480 | ||||||||
\(977\) | 2.86063 | 0.0915195 | 0.0457598 | − | 0.998952i | \(-0.485429\pi\) | ||||
0.0457598 | + | 0.998952i | \(0.485429\pi\) | |||||||
\(978\) | 65.5235 | 2.09521 | ||||||||
\(979\) | −10.3021 | −0.329255 | ||||||||
\(980\) | −33.3914 | −1.06665 | ||||||||
\(981\) | 127.148 | 4.05952 | ||||||||
\(982\) | −10.3960 | −0.331751 | ||||||||
\(983\) | −4.45936 | −0.142232 | −0.0711158 | − | 0.997468i | \(-0.522656\pi\) | ||||
−0.0711158 | + | 0.997468i | \(0.522656\pi\) | |||||||
\(984\) | 25.7783 | 0.821783 | ||||||||
\(985\) | −50.1896 | −1.59917 | ||||||||
\(986\) | −1.13083 | −0.0360129 | ||||||||
\(987\) | 3.36577 | 0.107134 | ||||||||
\(988\) | 4.18541 | 0.133156 | ||||||||
\(989\) | 6.35563 | 0.202097 | ||||||||
\(990\) | 21.7937 | 0.692651 | ||||||||
\(991\) | −0.388761 | −0.0123494 | −0.00617469 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617469 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(992\) | 7.16396 | 0.227456 | ||||||||
\(993\) | −3.64147 | −0.115558 | ||||||||
\(994\) | 57.0658 | 1.81002 | ||||||||
\(995\) | −20.8887 | −0.662218 | ||||||||
\(996\) | 30.3421 | 0.961425 | ||||||||
\(997\) | −2.94289 | −0.0932022 | −0.0466011 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466011 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(998\) | −38.5358 | −1.21983 | ||||||||
\(999\) | −45.1471 | −1.42839 |
(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 | 1334.2.a.d.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.d.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |