Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | −0.920246 | −0.531304 | −0.265652 | − | 0.964069i | \(-0.585587\pi\) | ||||
−0.265652 | + | 0.964069i | \(0.585587\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.96551 | 1.32622 | 0.663109 | − | 0.748523i | \(-0.269237\pi\) | ||||
0.663109 | + | 0.748523i | \(0.269237\pi\) | |||||||
\(6\) | 0.920246 | 0.375689 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.15315 | −0.717716 | ||||||||
\(10\) | −2.96551 | −0.937778 | ||||||||
\(11\) | −3.73387 | −1.12580 | −0.562902 | − | 0.826523i | \(-0.690315\pi\) | ||||
−0.562902 | + | 0.826523i | \(0.690315\pi\) | |||||||
\(12\) | −0.920246 | −0.265652 | ||||||||
\(13\) | −4.18929 | −1.16190 | −0.580950 | − | 0.813939i | \(-0.697319\pi\) | ||||
−0.580950 | + | 0.813939i | \(0.697319\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.72900 | −0.704625 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.64502 | 1.36912 | 0.684559 | − | 0.728958i | \(-0.259995\pi\) | ||||
0.684559 | + | 0.728958i | \(0.259995\pi\) | |||||||
\(18\) | 2.15315 | 0.507502 | ||||||||
\(19\) | 1.59892 | 0.366817 | 0.183408 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183408 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(20\) | 2.96551 | 0.663109 | ||||||||
\(21\) | 0.920246 | 0.200814 | ||||||||
\(22\) | 3.73387 | 0.796064 | ||||||||
\(23\) | 4.99189 | 1.04088 | 0.520441 | − | 0.853898i | \(-0.325768\pi\) | ||||
0.520441 | + | 0.853898i | \(0.325768\pi\) | |||||||
\(24\) | 0.920246 | 0.187844 | ||||||||
\(25\) | 3.79427 | 0.758854 | ||||||||
\(26\) | 4.18929 | 0.821588 | ||||||||
\(27\) | 4.74216 | 0.912630 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.281679 | −0.0523066 | −0.0261533 | − | 0.999658i | \(-0.508326\pi\) | ||||
−0.0261533 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(30\) | 2.72900 | 0.498245 | ||||||||
\(31\) | −0.595843 | −0.107017 | −0.0535083 | − | 0.998567i | \(-0.517040\pi\) | ||||
−0.0535083 | + | 0.998567i | \(0.517040\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.43608 | 0.598145 | ||||||||
\(34\) | −5.64502 | −0.968112 | ||||||||
\(35\) | −2.96551 | −0.501263 | ||||||||
\(36\) | −2.15315 | −0.358858 | ||||||||
\(37\) | −1.75109 | −0.287878 | −0.143939 | − | 0.989587i | \(-0.545977\pi\) | ||||
−0.143939 | + | 0.989587i | \(0.545977\pi\) | |||||||
\(38\) | −1.59892 | −0.259379 | ||||||||
\(39\) | 3.85518 | 0.617323 | ||||||||
\(40\) | −2.96551 | −0.468889 | ||||||||
\(41\) | 1.43359 | 0.223889 | 0.111945 | − | 0.993714i | \(-0.464292\pi\) | ||||
0.111945 | + | 0.993714i | \(0.464292\pi\) | |||||||
\(42\) | −0.920246 | −0.141997 | ||||||||
\(43\) | 7.07586 | 1.07906 | 0.539529 | − | 0.841967i | \(-0.318602\pi\) | ||||
0.539529 | + | 0.841967i | \(0.318602\pi\) | |||||||
\(44\) | −3.73387 | −0.562902 | ||||||||
\(45\) | −6.38519 | −0.951848 | ||||||||
\(46\) | −4.99189 | −0.736014 | ||||||||
\(47\) | −8.92805 | −1.30229 | −0.651145 | − | 0.758953i | \(-0.725711\pi\) | ||||
−0.651145 | + | 0.758953i | \(0.725711\pi\) | |||||||
\(48\) | −0.920246 | −0.132826 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.79427 | −0.536591 | ||||||||
\(51\) | −5.19480 | −0.727418 | ||||||||
\(52\) | −4.18929 | −0.580950 | ||||||||
\(53\) | −10.7665 | −1.47889 | −0.739447 | − | 0.673214i | \(-0.764913\pi\) | ||||
−0.739447 | + | 0.673214i | \(0.764913\pi\) | |||||||
\(54\) | −4.74216 | −0.645327 | ||||||||
\(55\) | −11.0729 | −1.49306 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −1.47140 | −0.194891 | ||||||||
\(58\) | 0.281679 | 0.0369863 | ||||||||
\(59\) | 2.59695 | 0.338094 | 0.169047 | − | 0.985608i | \(-0.445931\pi\) | ||||
0.169047 | + | 0.985608i | \(0.445931\pi\) | |||||||
\(60\) | −2.72900 | −0.352313 | ||||||||
\(61\) | −11.3867 | −1.45792 | −0.728960 | − | 0.684556i | \(-0.759996\pi\) | ||||
−0.728960 | + | 0.684556i | \(0.759996\pi\) | |||||||
\(62\) | 0.595843 | 0.0756721 | ||||||||
\(63\) | 2.15315 | 0.271271 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.4234 | −1.54093 | ||||||||
\(66\) | −3.43608 | −0.422952 | ||||||||
\(67\) | −0.827398 | −0.101083 | −0.0505414 | − | 0.998722i | \(-0.516095\pi\) | ||||
−0.0505414 | + | 0.998722i | \(0.516095\pi\) | |||||||
\(68\) | 5.64502 | 0.684559 | ||||||||
\(69\) | −4.59377 | −0.553025 | ||||||||
\(70\) | 2.96551 | 0.354447 | ||||||||
\(71\) | −8.62062 | −1.02308 | −0.511540 | − | 0.859260i | \(-0.670925\pi\) | ||||
−0.511540 | + | 0.859260i | \(0.670925\pi\) | |||||||
\(72\) | 2.15315 | 0.253751 | ||||||||
\(73\) | 0.950530 | 0.111251 | 0.0556256 | − | 0.998452i | \(-0.482285\pi\) | ||||
0.0556256 | + | 0.998452i | \(0.482285\pi\) | |||||||
\(74\) | 1.75109 | 0.203561 | ||||||||
\(75\) | −3.49166 | −0.403182 | ||||||||
\(76\) | 1.59892 | 0.183408 | ||||||||
\(77\) | 3.73387 | 0.425514 | ||||||||
\(78\) | −3.85518 | −0.436513 | ||||||||
\(79\) | 13.6713 | 1.53814 | 0.769070 | − | 0.639165i | \(-0.220720\pi\) | ||||
0.769070 | + | 0.639165i | \(0.220720\pi\) | |||||||
\(80\) | 2.96551 | 0.331555 | ||||||||
\(81\) | 2.09549 | 0.232832 | ||||||||
\(82\) | −1.43359 | −0.158314 | ||||||||
\(83\) | 10.7904 | 1.18440 | 0.592199 | − | 0.805792i | \(-0.298260\pi\) | ||||
0.592199 | + | 0.805792i | \(0.298260\pi\) | |||||||
\(84\) | 0.920246 | 0.100407 | ||||||||
\(85\) | 16.7404 | 1.81575 | ||||||||
\(86\) | −7.07586 | −0.763009 | ||||||||
\(87\) | 0.259214 | 0.0277907 | ||||||||
\(88\) | 3.73387 | 0.398032 | ||||||||
\(89\) | −5.53491 | −0.586699 | −0.293350 | − | 0.956005i | \(-0.594770\pi\) | ||||
−0.293350 | + | 0.956005i | \(0.594770\pi\) | |||||||
\(90\) | 6.38519 | 0.673058 | ||||||||
\(91\) | 4.18929 | 0.439157 | ||||||||
\(92\) | 4.99189 | 0.520441 | ||||||||
\(93\) | 0.548322 | 0.0568583 | ||||||||
\(94\) | 8.92805 | 0.920858 | ||||||||
\(95\) | 4.74161 | 0.486479 | ||||||||
\(96\) | 0.920246 | 0.0939222 | ||||||||
\(97\) | 4.82510 | 0.489914 | 0.244957 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244957 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 8.03958 | 0.808008 | ||||||||
\(100\) | 3.79427 | 0.379427 | ||||||||
\(101\) | 11.0551 | 1.10002 | 0.550010 | − | 0.835158i | \(-0.314624\pi\) | ||||
0.550010 | + | 0.835158i | \(0.314624\pi\) | |||||||
\(102\) | 5.19480 | 0.514362 | ||||||||
\(103\) | 14.8392 | 1.46215 | 0.731075 | − | 0.682297i | \(-0.239019\pi\) | ||||
0.731075 | + | 0.682297i | \(0.239019\pi\) | |||||||
\(104\) | 4.18929 | 0.410794 | ||||||||
\(105\) | 2.72900 | 0.266323 | ||||||||
\(106\) | 10.7665 | 1.04574 | ||||||||
\(107\) | −5.78284 | −0.559048 | −0.279524 | − | 0.960139i | \(-0.590177\pi\) | ||||
−0.279524 | + | 0.960139i | \(0.590177\pi\) | |||||||
\(108\) | 4.74216 | 0.456315 | ||||||||
\(109\) | −1.51331 | −0.144949 | −0.0724744 | − | 0.997370i | \(-0.523090\pi\) | ||||
−0.0724744 | + | 0.997370i | \(0.523090\pi\) | |||||||
\(110\) | 11.0729 | 1.05575 | ||||||||
\(111\) | 1.61144 | 0.152951 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.08038 | 0.289777 | 0.144889 | − | 0.989448i | \(-0.453718\pi\) | ||||
0.144889 | + | 0.989448i | \(0.453718\pi\) | |||||||
\(114\) | 1.47140 | 0.137809 | ||||||||
\(115\) | 14.8035 | 1.38044 | ||||||||
\(116\) | −0.281679 | −0.0261533 | ||||||||
\(117\) | 9.02016 | 0.833914 | ||||||||
\(118\) | −2.59695 | −0.239069 | ||||||||
\(119\) | −5.64502 | −0.517478 | ||||||||
\(120\) | 2.72900 | 0.249123 | ||||||||
\(121\) | 2.94181 | 0.267437 | ||||||||
\(122\) | 11.3867 | 1.03091 | ||||||||
\(123\) | −1.31926 | −0.118953 | ||||||||
\(124\) | −0.595843 | −0.0535083 | ||||||||
\(125\) | −3.57561 | −0.319812 | ||||||||
\(126\) | −2.15315 | −0.191818 | ||||||||
\(127\) | −0.225215 | −0.0199846 | −0.00999231 | − | 0.999950i | \(-0.503181\pi\) | ||||
−0.00999231 | + | 0.999950i | \(0.503181\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.51153 | −0.573308 | ||||||||
\(130\) | 12.4234 | 1.08960 | ||||||||
\(131\) | −12.8742 | −1.12483 | −0.562413 | − | 0.826857i | \(-0.690127\pi\) | ||||
−0.562413 | + | 0.826857i | \(0.690127\pi\) | |||||||
\(132\) | 3.43608 | 0.299072 | ||||||||
\(133\) | −1.59892 | −0.138644 | ||||||||
\(134\) | 0.827398 | 0.0714763 | ||||||||
\(135\) | 14.0629 | 1.21035 | ||||||||
\(136\) | −5.64502 | −0.484056 | ||||||||
\(137\) | −11.8084 | −1.00886 | −0.504429 | − | 0.863453i | \(-0.668297\pi\) | ||||
−0.504429 | + | 0.863453i | \(0.668297\pi\) | |||||||
\(138\) | 4.59377 | 0.391048 | ||||||||
\(139\) | −3.68604 | −0.312646 | −0.156323 | − | 0.987706i | \(-0.549964\pi\) | ||||
−0.156323 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(140\) | −2.96551 | −0.250632 | ||||||||
\(141\) | 8.21601 | 0.691912 | ||||||||
\(142\) | 8.62062 | 0.723426 | ||||||||
\(143\) | 15.6423 | 1.30807 | ||||||||
\(144\) | −2.15315 | −0.179429 | ||||||||
\(145\) | −0.835324 | −0.0693699 | ||||||||
\(146\) | −0.950530 | −0.0786664 | ||||||||
\(147\) | −0.920246 | −0.0759006 | ||||||||
\(148\) | −1.75109 | −0.143939 | ||||||||
\(149\) | 3.42446 | 0.280543 | 0.140271 | − | 0.990113i | \(-0.455202\pi\) | ||||
0.140271 | + | 0.990113i | \(0.455202\pi\) | |||||||
\(150\) | 3.49166 | 0.285093 | ||||||||
\(151\) | 21.8871 | 1.78115 | 0.890575 | − | 0.454837i | \(-0.150303\pi\) | ||||
0.890575 | + | 0.454837i | \(0.150303\pi\) | |||||||
\(152\) | −1.59892 | −0.129689 | ||||||||
\(153\) | −12.1546 | −0.982637 | ||||||||
\(154\) | −3.73387 | −0.300884 | ||||||||
\(155\) | −1.76698 | −0.141927 | ||||||||
\(156\) | 3.85518 | 0.308661 | ||||||||
\(157\) | 2.80024 | 0.223484 | 0.111742 | − | 0.993737i | \(-0.464357\pi\) | ||||
0.111742 | + | 0.993737i | \(0.464357\pi\) | |||||||
\(158\) | −13.6713 | −1.08763 | ||||||||
\(159\) | 9.90784 | 0.785743 | ||||||||
\(160\) | −2.96551 | −0.234444 | ||||||||
\(161\) | −4.99189 | −0.393416 | ||||||||
\(162\) | −2.09549 | −0.164637 | ||||||||
\(163\) | 5.01493 | 0.392800 | 0.196400 | − | 0.980524i | \(-0.437075\pi\) | ||||
0.196400 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(164\) | 1.43359 | 0.111945 | ||||||||
\(165\) | 10.1897 | 0.793271 | ||||||||
\(166\) | −10.7904 | −0.837495 | ||||||||
\(167\) | 4.31481 | 0.333890 | 0.166945 | − | 0.985966i | \(-0.446610\pi\) | ||||
0.166945 | + | 0.985966i | \(0.446610\pi\) | |||||||
\(168\) | −0.920246 | −0.0709985 | ||||||||
\(169\) | 4.55016 | 0.350012 | ||||||||
\(170\) | −16.7404 | −1.28393 | ||||||||
\(171\) | −3.44270 | −0.263270 | ||||||||
\(172\) | 7.07586 | 0.539529 | ||||||||
\(173\) | 9.90231 | 0.752858 | 0.376429 | − | 0.926445i | \(-0.377152\pi\) | ||||
0.376429 | + | 0.926445i | \(0.377152\pi\) | |||||||
\(174\) | −0.259214 | −0.0196510 | ||||||||
\(175\) | −3.79427 | −0.286820 | ||||||||
\(176\) | −3.73387 | −0.281451 | ||||||||
\(177\) | −2.38983 | −0.179631 | ||||||||
\(178\) | 5.53491 | 0.414859 | ||||||||
\(179\) | 17.3323 | 1.29548 | 0.647740 | − | 0.761861i | \(-0.275714\pi\) | ||||
0.647740 | + | 0.761861i | \(0.275714\pi\) | |||||||
\(180\) | −6.38519 | −0.475924 | ||||||||
\(181\) | 0.496174 | 0.0368803 | 0.0184402 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184402 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(182\) | −4.18929 | −0.310531 | ||||||||
\(183\) | 10.4786 | 0.774599 | ||||||||
\(184\) | −4.99189 | −0.368007 | ||||||||
\(185\) | −5.19290 | −0.381789 | ||||||||
\(186\) | −0.548322 | −0.0402049 | ||||||||
\(187\) | −21.0778 | −1.54136 | ||||||||
\(188\) | −8.92805 | −0.651145 | ||||||||
\(189\) | −4.74216 | −0.344942 | ||||||||
\(190\) | −4.74161 | −0.343993 | ||||||||
\(191\) | 12.9619 | 0.937890 | 0.468945 | − | 0.883227i | \(-0.344634\pi\) | ||||
0.468945 | + | 0.883227i | \(0.344634\pi\) | |||||||
\(192\) | −0.920246 | −0.0664130 | ||||||||
\(193\) | 16.1898 | 1.16537 | 0.582685 | − | 0.812698i | \(-0.302002\pi\) | ||||
0.582685 | + | 0.812698i | \(0.302002\pi\) | |||||||
\(194\) | −4.82510 | −0.346422 | ||||||||
\(195\) | 11.4326 | 0.818704 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.3336 | 1.37746 | 0.688731 | − | 0.725017i | \(-0.258168\pi\) | ||||
0.688731 | + | 0.725017i | \(0.258168\pi\) | |||||||
\(198\) | −8.03958 | −0.571348 | ||||||||
\(199\) | −4.28872 | −0.304019 | −0.152010 | − | 0.988379i | \(-0.548574\pi\) | ||||
−0.152010 | + | 0.988379i | \(0.548574\pi\) | |||||||
\(200\) | −3.79427 | −0.268295 | ||||||||
\(201\) | 0.761410 | 0.0537057 | ||||||||
\(202\) | −11.0551 | −0.777832 | ||||||||
\(203\) | 0.281679 | 0.0197700 | ||||||||
\(204\) | −5.19480 | −0.363709 | ||||||||
\(205\) | 4.25133 | 0.296926 | ||||||||
\(206\) | −14.8392 | −1.03390 | ||||||||
\(207\) | −10.7483 | −0.747057 | ||||||||
\(208\) | −4.18929 | −0.290475 | ||||||||
\(209\) | −5.97015 | −0.412964 | ||||||||
\(210\) | −2.72900 | −0.188319 | ||||||||
\(211\) | 13.5601 | 0.933518 | 0.466759 | − | 0.884384i | \(-0.345421\pi\) | ||||
0.466759 | + | 0.884384i | \(0.345421\pi\) | |||||||
\(212\) | −10.7665 | −0.739447 | ||||||||
\(213\) | 7.93309 | 0.543566 | ||||||||
\(214\) | 5.78284 | 0.395307 | ||||||||
\(215\) | 20.9835 | 1.43107 | ||||||||
\(216\) | −4.74216 | −0.322663 | ||||||||
\(217\) | 0.595843 | 0.0404484 | ||||||||
\(218\) | 1.51331 | 0.102494 | ||||||||
\(219\) | −0.874721 | −0.0591082 | ||||||||
\(220\) | −11.0729 | −0.746531 | ||||||||
\(221\) | −23.6486 | −1.59078 | ||||||||
\(222\) | −1.61144 | −0.108153 | ||||||||
\(223\) | 12.1396 | 0.812926 | 0.406463 | − | 0.913667i | \(-0.366762\pi\) | ||||
0.406463 | + | 0.913667i | \(0.366762\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −8.16963 | −0.544642 | ||||||||
\(226\) | −3.08038 | −0.204904 | ||||||||
\(227\) | 13.9190 | 0.923840 | 0.461920 | − | 0.886922i | \(-0.347161\pi\) | ||||
0.461920 | + | 0.886922i | \(0.347161\pi\) | |||||||
\(228\) | −1.47140 | −0.0974456 | ||||||||
\(229\) | −12.5004 | −0.826048 | −0.413024 | − | 0.910720i | \(-0.635527\pi\) | ||||
−0.413024 | + | 0.910720i | \(0.635527\pi\) | |||||||
\(230\) | −14.8035 | −0.976116 | ||||||||
\(231\) | −3.43608 | −0.226078 | ||||||||
\(232\) | 0.281679 | 0.0184932 | ||||||||
\(233\) | −0.392089 | −0.0256866 | −0.0128433 | − | 0.999918i | \(-0.504088\pi\) | ||||
−0.0128433 | + | 0.999918i | \(0.504088\pi\) | |||||||
\(234\) | −9.02016 | −0.589666 | ||||||||
\(235\) | −26.4763 | −1.72712 | ||||||||
\(236\) | 2.59695 | 0.169047 | ||||||||
\(237\) | −12.5809 | −0.817220 | ||||||||
\(238\) | 5.64502 | 0.365912 | ||||||||
\(239\) | 17.1919 | 1.11205 | 0.556026 | − | 0.831165i | \(-0.312325\pi\) | ||||
0.556026 | + | 0.831165i | \(0.312325\pi\) | |||||||
\(240\) | −2.72900 | −0.176156 | ||||||||
\(241\) | −5.92629 | −0.381746 | −0.190873 | − | 0.981615i | \(-0.561132\pi\) | ||||
−0.190873 | + | 0.981615i | \(0.561132\pi\) | |||||||
\(242\) | −2.94181 | −0.189106 | ||||||||
\(243\) | −16.1549 | −1.03633 | ||||||||
\(244\) | −11.3867 | −0.728960 | ||||||||
\(245\) | 2.96551 | 0.189460 | ||||||||
\(246\) | 1.31926 | 0.0841127 | ||||||||
\(247\) | −6.69833 | −0.426204 | ||||||||
\(248\) | 0.595843 | 0.0378361 | ||||||||
\(249\) | −9.92980 | −0.629275 | ||||||||
\(250\) | 3.57561 | 0.226141 | ||||||||
\(251\) | 26.0565 | 1.64467 | 0.822336 | − | 0.569002i | \(-0.192670\pi\) | ||||
0.822336 | + | 0.569002i | \(0.192670\pi\) | |||||||
\(252\) | 2.15315 | 0.135636 | ||||||||
\(253\) | −18.6391 | −1.17183 | ||||||||
\(254\) | 0.225215 | 0.0141313 | ||||||||
\(255\) | −15.4053 | −0.964715 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.88491 | −0.491847 | −0.245923 | − | 0.969289i | \(-0.579091\pi\) | ||||
−0.245923 | + | 0.969289i | \(0.579091\pi\) | |||||||
\(258\) | 6.51153 | 0.405390 | ||||||||
\(259\) | 1.75109 | 0.108808 | ||||||||
\(260\) | −12.4234 | −0.770467 | ||||||||
\(261\) | 0.606497 | 0.0375412 | ||||||||
\(262\) | 12.8742 | 0.795371 | ||||||||
\(263\) | 3.97875 | 0.245340 | 0.122670 | − | 0.992447i | \(-0.460854\pi\) | ||||
0.122670 | + | 0.992447i | \(0.460854\pi\) | |||||||
\(264\) | −3.43608 | −0.211476 | ||||||||
\(265\) | −31.9283 | −1.96134 | ||||||||
\(266\) | 1.59892 | 0.0980359 | ||||||||
\(267\) | 5.09348 | 0.311716 | ||||||||
\(268\) | −0.827398 | −0.0505414 | ||||||||
\(269\) | −7.78372 | −0.474582 | −0.237291 | − | 0.971439i | \(-0.576259\pi\) | ||||
−0.237291 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(270\) | −14.0629 | −0.855844 | ||||||||
\(271\) | 13.3878 | 0.813254 | 0.406627 | − | 0.913594i | \(-0.366705\pi\) | ||||
0.406627 | + | 0.913594i | \(0.366705\pi\) | |||||||
\(272\) | 5.64502 | 0.342279 | ||||||||
\(273\) | −3.85518 | −0.233326 | ||||||||
\(274\) | 11.8084 | 0.713371 | ||||||||
\(275\) | −14.1673 | −0.854322 | ||||||||
\(276\) | −4.59377 | −0.276512 | ||||||||
\(277\) | 15.3841 | 0.924344 | 0.462172 | − | 0.886790i | \(-0.347070\pi\) | ||||
0.462172 | + | 0.886790i | \(0.347070\pi\) | |||||||
\(278\) | 3.68604 | 0.221074 | ||||||||
\(279\) | 1.28294 | 0.0768075 | ||||||||
\(280\) | 2.96551 | 0.177223 | ||||||||
\(281\) | 23.8750 | 1.42427 | 0.712133 | − | 0.702045i | \(-0.247729\pi\) | ||||
0.712133 | + | 0.702045i | \(0.247729\pi\) | |||||||
\(282\) | −8.21601 | −0.489256 | ||||||||
\(283\) | −25.3162 | −1.50489 | −0.752445 | − | 0.658656i | \(-0.771125\pi\) | ||||
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(284\) | −8.62062 | −0.511540 | ||||||||
\(285\) | −4.36345 | −0.258468 | ||||||||
\(286\) | −15.6423 | −0.924947 | ||||||||
\(287\) | −1.43359 | −0.0846222 | ||||||||
\(288\) | 2.15315 | 0.126875 | ||||||||
\(289\) | 14.8662 | 0.874483 | ||||||||
\(290\) | 0.835324 | 0.0490519 | ||||||||
\(291\) | −4.44027 | −0.260293 | ||||||||
\(292\) | 0.950530 | 0.0556256 | ||||||||
\(293\) | −9.72297 | −0.568022 | −0.284011 | − | 0.958821i | \(-0.591665\pi\) | ||||
−0.284011 | + | 0.958821i | \(0.591665\pi\) | |||||||
\(294\) | 0.920246 | 0.0536698 | ||||||||
\(295\) | 7.70129 | 0.448387 | ||||||||
\(296\) | 1.75109 | 0.101780 | ||||||||
\(297\) | −17.7066 | −1.02744 | ||||||||
\(298\) | −3.42446 | −0.198374 | ||||||||
\(299\) | −20.9125 | −1.20940 | ||||||||
\(300\) | −3.49166 | −0.201591 | ||||||||
\(301\) | −7.07586 | −0.407846 | ||||||||
\(302\) | −21.8871 | −1.25946 | ||||||||
\(303\) | −10.1734 | −0.584446 | ||||||||
\(304\) | 1.59892 | 0.0917042 | ||||||||
\(305\) | −33.7675 | −1.93352 | ||||||||
\(306\) | 12.1546 | 0.694829 | ||||||||
\(307\) | −16.3176 | −0.931295 | −0.465648 | − | 0.884970i | \(-0.654179\pi\) | ||||
−0.465648 | + | 0.884970i | \(0.654179\pi\) | |||||||
\(308\) | 3.73387 | 0.212757 | ||||||||
\(309\) | −13.6557 | −0.776846 | ||||||||
\(310\) | 1.76698 | 0.100358 | ||||||||
\(311\) | 30.4396 | 1.72607 | 0.863035 | − | 0.505144i | \(-0.168561\pi\) | ||||
0.863035 | + | 0.505144i | \(0.168561\pi\) | |||||||
\(312\) | −3.85518 | −0.218256 | ||||||||
\(313\) | 3.79828 | 0.214691 | 0.107346 | − | 0.994222i | \(-0.465765\pi\) | ||||
0.107346 | + | 0.994222i | \(0.465765\pi\) | |||||||
\(314\) | −2.80024 | −0.158027 | ||||||||
\(315\) | 6.38519 | 0.359765 | ||||||||
\(316\) | 13.6713 | 0.769070 | ||||||||
\(317\) | 31.4929 | 1.76882 | 0.884408 | − | 0.466715i | \(-0.154563\pi\) | ||||
0.884408 | + | 0.466715i | \(0.154563\pi\) | |||||||
\(318\) | −9.90784 | −0.555604 | ||||||||
\(319\) | 1.05176 | 0.0588870 | ||||||||
\(320\) | 2.96551 | 0.165777 | ||||||||
\(321\) | 5.32164 | 0.297025 | ||||||||
\(322\) | 4.99189 | 0.278187 | ||||||||
\(323\) | 9.02591 | 0.502215 | ||||||||
\(324\) | 2.09549 | 0.116416 | ||||||||
\(325\) | −15.8953 | −0.881713 | ||||||||
\(326\) | −5.01493 | −0.277751 | ||||||||
\(327\) | 1.39262 | 0.0770119 | ||||||||
\(328\) | −1.43359 | −0.0791568 | ||||||||
\(329\) | 8.92805 | 0.492220 | ||||||||
\(330\) | −10.1897 | −0.560927 | ||||||||
\(331\) | 17.6665 | 0.971041 | 0.485520 | − | 0.874225i | \(-0.338630\pi\) | ||||
0.485520 | + | 0.874225i | \(0.338630\pi\) | |||||||
\(332\) | 10.7904 | 0.592199 | ||||||||
\(333\) | 3.77037 | 0.206615 | ||||||||
\(334\) | −4.31481 | −0.236096 | ||||||||
\(335\) | −2.45366 | −0.134058 | ||||||||
\(336\) | 0.920246 | 0.0502035 | ||||||||
\(337\) | 34.6562 | 1.88785 | 0.943923 | − | 0.330166i | \(-0.107105\pi\) | ||||
0.943923 | + | 0.330166i | \(0.107105\pi\) | |||||||
\(338\) | −4.55016 | −0.247496 | ||||||||
\(339\) | −2.83470 | −0.153960 | ||||||||
\(340\) | 16.7404 | 0.907874 | ||||||||
\(341\) | 2.22480 | 0.120480 | ||||||||
\(342\) | 3.44270 | 0.186160 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −7.07586 | −0.381505 | ||||||||
\(345\) | −13.6229 | −0.733431 | ||||||||
\(346\) | −9.90231 | −0.532351 | ||||||||
\(347\) | −33.2148 | −1.78306 | −0.891532 | − | 0.452959i | \(-0.850369\pi\) | ||||
−0.891532 | + | 0.452959i | \(0.850369\pi\) | |||||||
\(348\) | 0.259214 | 0.0138953 | ||||||||
\(349\) | 7.55703 | 0.404518 | 0.202259 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202259 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(350\) | 3.79427 | 0.202812 | ||||||||
\(351\) | −19.8663 | −1.06038 | ||||||||
\(352\) | 3.73387 | 0.199016 | ||||||||
\(353\) | −15.2892 | −0.813760 | −0.406880 | − | 0.913482i | \(-0.633383\pi\) | ||||
−0.406880 | + | 0.913482i | \(0.633383\pi\) | |||||||
\(354\) | 2.38983 | 0.127018 | ||||||||
\(355\) | −25.5646 | −1.35683 | ||||||||
\(356\) | −5.53491 | −0.293350 | ||||||||
\(357\) | 5.19480 | 0.274938 | ||||||||
\(358\) | −17.3323 | −0.916043 | ||||||||
\(359\) | 6.70872 | 0.354073 | 0.177036 | − | 0.984204i | \(-0.443349\pi\) | ||||
0.177036 | + | 0.984204i | \(0.443349\pi\) | |||||||
\(360\) | 6.38519 | 0.336529 | ||||||||
\(361\) | −16.4435 | −0.865446 | ||||||||
\(362\) | −0.496174 | −0.0260783 | ||||||||
\(363\) | −2.70718 | −0.142090 | ||||||||
\(364\) | 4.18929 | 0.219579 | ||||||||
\(365\) | 2.81881 | 0.147543 | ||||||||
\(366\) | −10.4786 | −0.547724 | ||||||||
\(367\) | 14.1782 | 0.740094 | 0.370047 | − | 0.929013i | \(-0.379342\pi\) | ||||
0.370047 | + | 0.929013i | \(0.379342\pi\) | |||||||
\(368\) | 4.99189 | 0.260220 | ||||||||
\(369\) | −3.08673 | −0.160689 | ||||||||
\(370\) | 5.19290 | 0.269966 | ||||||||
\(371\) | 10.7665 | 0.558970 | ||||||||
\(372\) | 0.548322 | 0.0284292 | ||||||||
\(373\) | −9.62992 | −0.498618 | −0.249309 | − | 0.968424i | \(-0.580204\pi\) | ||||
−0.249309 | + | 0.968424i | \(0.580204\pi\) | |||||||
\(374\) | 21.0778 | 1.08991 | ||||||||
\(375\) | 3.29044 | 0.169917 | ||||||||
\(376\) | 8.92805 | 0.460429 | ||||||||
\(377\) | 1.18004 | 0.0607750 | ||||||||
\(378\) | 4.74216 | 0.243911 | ||||||||
\(379\) | 0.704386 | 0.0361819 | 0.0180909 | − | 0.999836i | \(-0.494241\pi\) | ||||
0.0180909 | + | 0.999836i | \(0.494241\pi\) | |||||||
\(380\) | 4.74161 | 0.243239 | ||||||||
\(381\) | 0.207253 | 0.0106179 | ||||||||
\(382\) | −12.9619 | −0.663188 | ||||||||
\(383\) | 11.5952 | 0.592489 | 0.296245 | − | 0.955112i | \(-0.404266\pi\) | ||||
0.296245 | + | 0.955112i | \(0.404266\pi\) | |||||||
\(384\) | 0.920246 | 0.0469611 | ||||||||
\(385\) | 11.0729 | 0.564325 | ||||||||
\(386\) | −16.1898 | −0.824040 | ||||||||
\(387\) | −15.2354 | −0.774457 | ||||||||
\(388\) | 4.82510 | 0.244957 | ||||||||
\(389\) | −4.89619 | −0.248247 | −0.124123 | − | 0.992267i | \(-0.539612\pi\) | ||||
−0.124123 | + | 0.992267i | \(0.539612\pi\) | |||||||
\(390\) | −11.4326 | −0.578911 | ||||||||
\(391\) | 28.1793 | 1.42509 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 11.8474 | 0.597624 | ||||||||
\(394\) | −19.3336 | −0.974013 | ||||||||
\(395\) | 40.5424 | 2.03991 | ||||||||
\(396\) | 8.03958 | 0.404004 | ||||||||
\(397\) | 23.3345 | 1.17112 | 0.585562 | − | 0.810627i | \(-0.300874\pi\) | ||||
0.585562 | + | 0.810627i | \(0.300874\pi\) | |||||||
\(398\) | 4.28872 | 0.214974 | ||||||||
\(399\) | 1.47140 | 0.0736620 | ||||||||
\(400\) | 3.79427 | 0.189714 | ||||||||
\(401\) | 24.8657 | 1.24173 | 0.620866 | − | 0.783917i | \(-0.286781\pi\) | ||||
0.620866 | + | 0.783917i | \(0.286781\pi\) | |||||||
\(402\) | −0.761410 | −0.0379757 | ||||||||
\(403\) | 2.49616 | 0.124343 | ||||||||
\(404\) | 11.0551 | 0.550010 | ||||||||
\(405\) | 6.21419 | 0.308786 | ||||||||
\(406\) | −0.281679 | −0.0139795 | ||||||||
\(407\) | 6.53837 | 0.324095 | ||||||||
\(408\) | 5.19480 | 0.257181 | ||||||||
\(409\) | 0.240956 | 0.0119145 | 0.00595726 | − | 0.999982i | \(-0.498104\pi\) | ||||
0.00595726 | + | 0.999982i | \(0.498104\pi\) | |||||||
\(410\) | −4.25133 | −0.209958 | ||||||||
\(411\) | 10.8666 | 0.536011 | ||||||||
\(412\) | 14.8392 | 0.731075 | ||||||||
\(413\) | −2.59695 | −0.127788 | ||||||||
\(414\) | 10.7483 | 0.528249 | ||||||||
\(415\) | 31.9990 | 1.57077 | ||||||||
\(416\) | 4.18929 | 0.205397 | ||||||||
\(417\) | 3.39207 | 0.166110 | ||||||||
\(418\) | 5.97015 | 0.292010 | ||||||||
\(419\) | 6.22872 | 0.304293 | 0.152146 | − | 0.988358i | \(-0.451381\pi\) | ||||
0.152146 | + | 0.988358i | \(0.451381\pi\) | |||||||
\(420\) | 2.72900 | 0.133162 | ||||||||
\(421\) | 2.28185 | 0.111210 | 0.0556052 | − | 0.998453i | \(-0.482291\pi\) | ||||
0.0556052 | + | 0.998453i | \(0.482291\pi\) | |||||||
\(422\) | −13.5601 | −0.660097 | ||||||||
\(423\) | 19.2234 | 0.934674 | ||||||||
\(424\) | 10.7665 | 0.522868 | ||||||||
\(425\) | 21.4187 | 1.03896 | ||||||||
\(426\) | −7.93309 | −0.384360 | ||||||||
\(427\) | 11.3867 | 0.551042 | ||||||||
\(428\) | −5.78284 | −0.279524 | ||||||||
\(429\) | −14.3947 | −0.694985 | ||||||||
\(430\) | −20.9835 | −1.01192 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 4.74216 | 0.228157 | ||||||||
\(433\) | −7.69716 | −0.369902 | −0.184951 | − | 0.982748i | \(-0.559213\pi\) | ||||
−0.184951 | + | 0.982748i | \(0.559213\pi\) | |||||||
\(434\) | −0.595843 | −0.0286014 | ||||||||
\(435\) | 0.768704 | 0.0368565 | ||||||||
\(436\) | −1.51331 | −0.0724744 | ||||||||
\(437\) | 7.98162 | 0.381813 | ||||||||
\(438\) | 0.874721 | 0.0417958 | ||||||||
\(439\) | 15.6183 | 0.745420 | 0.372710 | − | 0.927948i | \(-0.378429\pi\) | ||||
0.372710 | + | 0.927948i | \(0.378429\pi\) | |||||||
\(440\) | 11.0729 | 0.527877 | ||||||||
\(441\) | −2.15315 | −0.102531 | ||||||||
\(442\) | 23.6486 | 1.12485 | ||||||||
\(443\) | 21.4825 | 1.02067 | 0.510333 | − | 0.859977i | \(-0.329522\pi\) | ||||
0.510333 | + | 0.859977i | \(0.329522\pi\) | |||||||
\(444\) | 1.61144 | 0.0764755 | ||||||||
\(445\) | −16.4139 | −0.778091 | ||||||||
\(446\) | −12.1396 | −0.574825 | ||||||||
\(447\) | −3.15135 | −0.149054 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 5.15008 | 0.243047 | 0.121524 | − | 0.992589i | \(-0.461222\pi\) | ||||
0.121524 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(450\) | 8.16963 | 0.385120 | ||||||||
\(451\) | −5.35285 | −0.252056 | ||||||||
\(452\) | 3.08038 | 0.144889 | ||||||||
\(453\) | −20.1415 | −0.946332 | ||||||||
\(454\) | −13.9190 | −0.653253 | ||||||||
\(455\) | 12.4234 | 0.582418 | ||||||||
\(456\) | 1.47140 | 0.0689045 | ||||||||
\(457\) | −24.1714 | −1.13069 | −0.565346 | − | 0.824854i | \(-0.691257\pi\) | ||||
−0.565346 | + | 0.824854i | \(0.691257\pi\) | |||||||
\(458\) | 12.5004 | 0.584104 | ||||||||
\(459\) | 26.7696 | 1.24950 | ||||||||
\(460\) | 14.8035 | 0.690218 | ||||||||
\(461\) | −19.9699 | −0.930090 | −0.465045 | − | 0.885287i | \(-0.653962\pi\) | ||||
−0.465045 | + | 0.885287i | \(0.653962\pi\) | |||||||
\(462\) | 3.43608 | 0.159861 | ||||||||
\(463\) | 24.5172 | 1.13941 | 0.569706 | − | 0.821849i | \(-0.307057\pi\) | ||||
0.569706 | + | 0.821849i | \(0.307057\pi\) | |||||||
\(464\) | −0.281679 | −0.0130766 | ||||||||
\(465\) | 1.62606 | 0.0754065 | ||||||||
\(466\) | 0.392089 | 0.0181632 | ||||||||
\(467\) | 4.73023 | 0.218889 | 0.109444 | − | 0.993993i | \(-0.465093\pi\) | ||||
0.109444 | + | 0.993993i | \(0.465093\pi\) | |||||||
\(468\) | 9.02016 | 0.416957 | ||||||||
\(469\) | 0.827398 | 0.0382057 | ||||||||
\(470\) | 26.4763 | 1.22126 | ||||||||
\(471\) | −2.57691 | −0.118738 | ||||||||
\(472\) | −2.59695 | −0.119534 | ||||||||
\(473\) | −26.4203 | −1.21481 | ||||||||
\(474\) | 12.5809 | 0.577862 | ||||||||
\(475\) | 6.06672 | 0.278360 | ||||||||
\(476\) | −5.64502 | −0.258739 | ||||||||
\(477\) | 23.1819 | 1.06143 | ||||||||
\(478\) | −17.1919 | −0.786340 | ||||||||
\(479\) | −15.6484 | −0.714993 | −0.357497 | − | 0.933914i | \(-0.616370\pi\) | ||||
−0.357497 | + | 0.933914i | \(0.616370\pi\) | |||||||
\(480\) | 2.72900 | 0.124561 | ||||||||
\(481\) | 7.33585 | 0.334486 | ||||||||
\(482\) | 5.92629 | 0.269935 | ||||||||
\(483\) | 4.59377 | 0.209024 | ||||||||
\(484\) | 2.94181 | 0.133718 | ||||||||
\(485\) | 14.3089 | 0.649733 | ||||||||
\(486\) | 16.1549 | 0.732799 | ||||||||
\(487\) | −35.3945 | −1.60388 | −0.801939 | − | 0.597406i | \(-0.796198\pi\) | ||||
−0.801939 | + | 0.597406i | \(0.796198\pi\) | |||||||
\(488\) | 11.3867 | 0.515453 | ||||||||
\(489\) | −4.61497 | −0.208696 | ||||||||
\(490\) | −2.96551 | −0.133968 | ||||||||
\(491\) | 12.5717 | 0.567354 | 0.283677 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283677 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(492\) | −1.31926 | −0.0594767 | ||||||||
\(493\) | −1.59009 | −0.0716138 | ||||||||
\(494\) | 6.69833 | 0.301372 | ||||||||
\(495\) | 23.8415 | 1.07159 | ||||||||
\(496\) | −0.595843 | −0.0267541 | ||||||||
\(497\) | 8.62062 | 0.386688 | ||||||||
\(498\) | 9.92980 | 0.444965 | ||||||||
\(499\) | −23.1265 | −1.03529 | −0.517643 | − | 0.855597i | \(-0.673190\pi\) | ||||
−0.517643 | + | 0.855597i | \(0.673190\pi\) | |||||||
\(500\) | −3.57561 | −0.159906 | ||||||||
\(501\) | −3.97069 | −0.177397 | ||||||||
\(502\) | −26.0565 | −1.16296 | ||||||||
\(503\) | −9.56311 | −0.426398 | −0.213199 | − | 0.977009i | \(-0.568388\pi\) | ||||
−0.213199 | + | 0.977009i | \(0.568388\pi\) | |||||||
\(504\) | −2.15315 | −0.0959088 | ||||||||
\(505\) | 32.7840 | 1.45887 | ||||||||
\(506\) | 18.6391 | 0.828609 | ||||||||
\(507\) | −4.18726 | −0.185963 | ||||||||
\(508\) | −0.225215 | −0.00999231 | ||||||||
\(509\) | −7.03707 | −0.311912 | −0.155956 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155956 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(510\) | 15.4053 | 0.682156 | ||||||||
\(511\) | −0.950530 | −0.0420490 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.58232 | 0.334768 | ||||||||
\(514\) | 7.88491 | 0.347788 | ||||||||
\(515\) | 44.0059 | 1.93913 | ||||||||
\(516\) | −6.51153 | −0.286654 | ||||||||
\(517\) | 33.3362 | 1.46613 | ||||||||
\(518\) | −1.75109 | −0.0769387 | ||||||||
\(519\) | −9.11256 | −0.399997 | ||||||||
\(520\) | 12.4234 | 0.544802 | ||||||||
\(521\) | 28.7774 | 1.26076 | 0.630380 | − | 0.776286i | \(-0.282899\pi\) | ||||
0.630380 | + | 0.776286i | \(0.282899\pi\) | |||||||
\(522\) | −0.606497 | −0.0265457 | ||||||||
\(523\) | −9.00158 | −0.393612 | −0.196806 | − | 0.980442i | \(-0.563057\pi\) | ||||
−0.196806 | + | 0.980442i | \(0.563057\pi\) | |||||||
\(524\) | −12.8742 | −0.562413 | ||||||||
\(525\) | 3.49166 | 0.152389 | ||||||||
\(526\) | −3.97875 | −0.173482 | ||||||||
\(527\) | −3.36354 | −0.146518 | ||||||||
\(528\) | 3.43608 | 0.149536 | ||||||||
\(529\) | 1.91900 | 0.0834346 | ||||||||
\(530\) | 31.9283 | 1.38687 | ||||||||
\(531\) | −5.59162 | −0.242656 | ||||||||
\(532\) | −1.59892 | −0.0693218 | ||||||||
\(533\) | −6.00573 | −0.260137 | ||||||||
\(534\) | −5.09348 | −0.220416 | ||||||||
\(535\) | −17.1491 | −0.741420 | ||||||||
\(536\) | 0.827398 | 0.0357382 | ||||||||
\(537\) | −15.9500 | −0.688294 | ||||||||
\(538\) | 7.78372 | 0.335580 | ||||||||
\(539\) | −3.73387 | −0.160829 | ||||||||
\(540\) | 14.0629 | 0.605173 | ||||||||
\(541\) | 0.811603 | 0.0348935 | 0.0174468 | − | 0.999848i | \(-0.494446\pi\) | ||||
0.0174468 | + | 0.999848i | \(0.494446\pi\) | |||||||
\(542\) | −13.3878 | −0.575057 | ||||||||
\(543\) | −0.456602 | −0.0195947 | ||||||||
\(544\) | −5.64502 | −0.242028 | ||||||||
\(545\) | −4.48774 | −0.192234 | ||||||||
\(546\) | 3.85518 | 0.164986 | ||||||||
\(547\) | 4.85868 | 0.207742 | 0.103871 | − | 0.994591i | \(-0.466877\pi\) | ||||
0.103871 | + | 0.994591i | \(0.466877\pi\) | |||||||
\(548\) | −11.8084 | −0.504429 | ||||||||
\(549\) | 24.5173 | 1.04637 | ||||||||
\(550\) | 14.1673 | 0.604097 | ||||||||
\(551\) | −0.450382 | −0.0191869 | ||||||||
\(552\) | 4.59377 | 0.195524 | ||||||||
\(553\) | −13.6713 | −0.581362 | ||||||||
\(554\) | −15.3841 | −0.653610 | ||||||||
\(555\) | 4.77874 | 0.202846 | ||||||||
\(556\) | −3.68604 | −0.156323 | ||||||||
\(557\) | −42.9449 | −1.81964 | −0.909818 | − | 0.415008i | \(-0.863779\pi\) | ||||
−0.909818 | + | 0.415008i | \(0.863779\pi\) | |||||||
\(558\) | −1.28294 | −0.0543111 | ||||||||
\(559\) | −29.6428 | −1.25376 | ||||||||
\(560\) | −2.96551 | −0.125316 | ||||||||
\(561\) | 19.3967 | 0.818931 | ||||||||
\(562\) | −23.8750 | −1.00711 | ||||||||
\(563\) | −17.0067 | −0.716747 | −0.358374 | − | 0.933578i | \(-0.616669\pi\) | ||||
−0.358374 | + | 0.933578i | \(0.616669\pi\) | |||||||
\(564\) | 8.21601 | 0.345956 | ||||||||
\(565\) | 9.13490 | 0.384308 | ||||||||
\(566\) | 25.3162 | 1.06412 | ||||||||
\(567\) | −2.09549 | −0.0880021 | ||||||||
\(568\) | 8.62062 | 0.361713 | ||||||||
\(569\) | 33.9507 | 1.42329 | 0.711644 | − | 0.702540i | \(-0.247951\pi\) | ||||
0.711644 | + | 0.702540i | \(0.247951\pi\) | |||||||
\(570\) | 4.36345 | 0.182765 | ||||||||
\(571\) | −11.3356 | −0.474378 | −0.237189 | − | 0.971464i | \(-0.576226\pi\) | ||||
−0.237189 | + | 0.971464i | \(0.576226\pi\) | |||||||
\(572\) | 15.6423 | 0.654037 | ||||||||
\(573\) | −11.9281 | −0.498305 | ||||||||
\(574\) | 1.43359 | 0.0598369 | ||||||||
\(575\) | 18.9406 | 0.789877 | ||||||||
\(576\) | −2.15315 | −0.0897145 | ||||||||
\(577\) | 25.9991 | 1.08236 | 0.541179 | − | 0.840908i | \(-0.317978\pi\) | ||||
0.541179 | + | 0.840908i | \(0.317978\pi\) | |||||||
\(578\) | −14.8662 | −0.618353 | ||||||||
\(579\) | −14.8986 | −0.619166 | ||||||||
\(580\) | −0.835324 | −0.0346850 | ||||||||
\(581\) | −10.7904 | −0.447660 | ||||||||
\(582\) | 4.44027 | 0.184055 | ||||||||
\(583\) | 40.2008 | 1.66495 | ||||||||
\(584\) | −0.950530 | −0.0393332 | ||||||||
\(585\) | 26.7494 | 1.10595 | ||||||||
\(586\) | 9.72297 | 0.401652 | ||||||||
\(587\) | 32.4335 | 1.33867 | 0.669336 | − | 0.742960i | \(-0.266579\pi\) | ||||
0.669336 | + | 0.742960i | \(0.266579\pi\) | |||||||
\(588\) | −0.920246 | −0.0379503 | ||||||||
\(589\) | −0.952703 | −0.0392554 | ||||||||
\(590\) | −7.70129 | −0.317057 | ||||||||
\(591\) | −17.7917 | −0.731852 | ||||||||
\(592\) | −1.75109 | −0.0719696 | ||||||||
\(593\) | 8.70949 | 0.357656 | 0.178828 | − | 0.983880i | \(-0.442769\pi\) | ||||
0.178828 | + | 0.983880i | \(0.442769\pi\) | |||||||
\(594\) | 17.7066 | 0.726512 | ||||||||
\(595\) | −16.7404 | −0.686288 | ||||||||
\(596\) | 3.42446 | 0.140271 | ||||||||
\(597\) | 3.94668 | 0.161527 | ||||||||
\(598\) | 20.9125 | 0.855175 | ||||||||
\(599\) | −30.4873 | −1.24568 | −0.622838 | − | 0.782351i | \(-0.714021\pi\) | ||||
−0.622838 | + | 0.782351i | \(0.714021\pi\) | |||||||
\(600\) | 3.49166 | 0.142547 | ||||||||
\(601\) | −33.5614 | −1.36900 | −0.684499 | − | 0.729014i | \(-0.739979\pi\) | ||||
−0.684499 | + | 0.729014i | \(0.739979\pi\) | |||||||
\(602\) | 7.07586 | 0.288390 | ||||||||
\(603\) | 1.78151 | 0.0725487 | ||||||||
\(604\) | 21.8871 | 0.890575 | ||||||||
\(605\) | 8.72397 | 0.354680 | ||||||||
\(606\) | 10.1734 | 0.413265 | ||||||||
\(607\) | 23.0581 | 0.935898 | 0.467949 | − | 0.883756i | \(-0.344993\pi\) | ||||
0.467949 | + | 0.883756i | \(0.344993\pi\) | |||||||
\(608\) | −1.59892 | −0.0648446 | ||||||||
\(609\) | −0.259214 | −0.0105039 | ||||||||
\(610\) | 33.7675 | 1.36721 | ||||||||
\(611\) | 37.4022 | 1.51313 | ||||||||
\(612\) | −12.1546 | −0.491319 | ||||||||
\(613\) | 5.78694 | 0.233732 | 0.116866 | − | 0.993148i | \(-0.462715\pi\) | ||||
0.116866 | + | 0.993148i | \(0.462715\pi\) | |||||||
\(614\) | 16.3176 | 0.658525 | ||||||||
\(615\) | −3.91227 | −0.157758 | ||||||||
\(616\) | −3.73387 | −0.150442 | ||||||||
\(617\) | 7.82002 | 0.314822 | 0.157411 | − | 0.987533i | \(-0.449685\pi\) | ||||
0.157411 | + | 0.987533i | \(0.449685\pi\) | |||||||
\(618\) | 13.6557 | 0.549313 | ||||||||
\(619\) | −38.0806 | −1.53059 | −0.765294 | − | 0.643681i | \(-0.777407\pi\) | ||||
−0.765294 | + | 0.643681i | \(0.777407\pi\) | |||||||
\(620\) | −1.76698 | −0.0709636 | ||||||||
\(621\) | 23.6724 | 0.949939 | ||||||||
\(622\) | −30.4396 | −1.22052 | ||||||||
\(623\) | 5.53491 | 0.221752 | ||||||||
\(624\) | 3.85518 | 0.154331 | ||||||||
\(625\) | −29.5749 | −1.18299 | ||||||||
\(626\) | −3.79828 | −0.151810 | ||||||||
\(627\) | 5.49401 | 0.219410 | ||||||||
\(628\) | 2.80024 | 0.111742 | ||||||||
\(629\) | −9.88496 | −0.394139 | ||||||||
\(630\) | −6.38519 | −0.254392 | ||||||||
\(631\) | 42.7598 | 1.70224 | 0.851121 | − | 0.524969i | \(-0.175923\pi\) | ||||
0.851121 | + | 0.524969i | \(0.175923\pi\) | |||||||
\(632\) | −13.6713 | −0.543815 | ||||||||
\(633\) | −12.4787 | −0.495982 | ||||||||
\(634\) | −31.4929 | −1.25074 | ||||||||
\(635\) | −0.667879 | −0.0265040 | ||||||||
\(636\) | 9.90784 | 0.392872 | ||||||||
\(637\) | −4.18929 | −0.165986 | ||||||||
\(638\) | −1.05176 | −0.0416394 | ||||||||
\(639\) | 18.5615 | 0.734280 | ||||||||
\(640\) | −2.96551 | −0.117222 | ||||||||
\(641\) | −8.44630 | −0.333609 | −0.166804 | − | 0.985990i | \(-0.553345\pi\) | ||||
−0.166804 | + | 0.985990i | \(0.553345\pi\) | |||||||
\(642\) | −5.32164 | −0.210028 | ||||||||
\(643\) | 20.1993 | 0.796584 | 0.398292 | − | 0.917259i | \(-0.369603\pi\) | ||||
0.398292 | + | 0.917259i | \(0.369603\pi\) | |||||||
\(644\) | −4.99189 | −0.196708 | ||||||||
\(645\) | −19.3100 | −0.760332 | ||||||||
\(646\) | −9.02591 | −0.355120 | ||||||||
\(647\) | 18.1854 | 0.714943 | 0.357471 | − | 0.933924i | \(-0.383639\pi\) | ||||
0.357471 | + | 0.933924i | \(0.383639\pi\) | |||||||
\(648\) | −2.09549 | −0.0823185 | ||||||||
\(649\) | −9.69668 | −0.380628 | ||||||||
\(650\) | 15.8953 | 0.623465 | ||||||||
\(651\) | −0.548322 | −0.0214904 | ||||||||
\(652\) | 5.01493 | 0.196400 | ||||||||
\(653\) | −19.3459 | −0.757063 | −0.378531 | − | 0.925588i | \(-0.623571\pi\) | ||||
−0.378531 | + | 0.925588i | \(0.623571\pi\) | |||||||
\(654\) | −1.39262 | −0.0544556 | ||||||||
\(655\) | −38.1787 | −1.49176 | ||||||||
\(656\) | 1.43359 | 0.0559723 | ||||||||
\(657\) | −2.04663 | −0.0798467 | ||||||||
\(658\) | −8.92805 | −0.348052 | ||||||||
\(659\) | 28.1137 | 1.09515 | 0.547576 | − | 0.836756i | \(-0.315551\pi\) | ||||
0.547576 | + | 0.836756i | \(0.315551\pi\) | |||||||
\(660\) | 10.1897 | 0.396635 | ||||||||
\(661\) | 33.8790 | 1.31774 | 0.658870 | − | 0.752256i | \(-0.271035\pi\) | ||||
0.658870 | + | 0.752256i | \(0.271035\pi\) | |||||||
\(662\) | −17.6665 | −0.686630 | ||||||||
\(663\) | 21.7625 | 0.845187 | ||||||||
\(664\) | −10.7904 | −0.418748 | ||||||||
\(665\) | −4.74161 | −0.183872 | ||||||||
\(666\) | −3.77037 | −0.146099 | ||||||||
\(667\) | −1.40611 | −0.0544449 | ||||||||
\(668\) | 4.31481 | 0.166945 | ||||||||
\(669\) | −11.1714 | −0.431911 | ||||||||
\(670\) | 2.45366 | 0.0947932 | ||||||||
\(671\) | 42.5166 | 1.64133 | ||||||||
\(672\) | −0.920246 | −0.0354993 | ||||||||
\(673\) | −43.9445 | −1.69394 | −0.846969 | − | 0.531643i | \(-0.821575\pi\) | ||||
−0.846969 | + | 0.531643i | \(0.821575\pi\) | |||||||
\(674\) | −34.6562 | −1.33491 | ||||||||
\(675\) | 17.9931 | 0.692553 | ||||||||
\(676\) | 4.55016 | 0.175006 | ||||||||
\(677\) | −29.0469 | −1.11636 | −0.558182 | − | 0.829718i | \(-0.688501\pi\) | ||||
−0.558182 | + | 0.829718i | \(0.688501\pi\) | |||||||
\(678\) | 2.83470 | 0.108866 | ||||||||
\(679\) | −4.82510 | −0.185170 | ||||||||
\(680\) | −16.7404 | −0.641964 | ||||||||
\(681\) | −12.8089 | −0.490840 | ||||||||
\(682\) | −2.22480 | −0.0851920 | ||||||||
\(683\) | −4.86375 | −0.186106 | −0.0930531 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930531 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(684\) | −3.44270 | −0.131635 | ||||||||
\(685\) | −35.0179 | −1.33797 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 11.5034 | 0.438883 | ||||||||
\(688\) | 7.07586 | 0.269765 | ||||||||
\(689\) | 45.1041 | 1.71833 | ||||||||
\(690\) | 13.6229 | 0.518614 | ||||||||
\(691\) | 22.6241 | 0.860660 | 0.430330 | − | 0.902672i | \(-0.358397\pi\) | ||||
0.430330 | + | 0.902672i | \(0.358397\pi\) | |||||||
\(692\) | 9.90231 | 0.376429 | ||||||||
\(693\) | −8.03958 | −0.305398 | ||||||||
\(694\) | 33.2148 | 1.26082 | ||||||||
\(695\) | −10.9310 | −0.414637 | ||||||||
\(696\) | −0.259214 | −0.00982550 | ||||||||
\(697\) | 8.09265 | 0.306531 | ||||||||
\(698\) | −7.55703 | −0.286038 | ||||||||
\(699\) | 0.360819 | 0.0136474 | ||||||||
\(700\) | −3.79427 | −0.143410 | ||||||||
\(701\) | −21.4443 | −0.809939 | −0.404969 | − | 0.914330i | \(-0.632718\pi\) | ||||
−0.404969 | + | 0.914330i | \(0.632718\pi\) | |||||||
\(702\) | 19.8663 | 0.749805 | ||||||||
\(703\) | −2.79986 | −0.105599 | ||||||||
\(704\) | −3.73387 | −0.140726 | ||||||||
\(705\) | 24.3647 | 0.917627 | ||||||||
\(706\) | 15.2892 | 0.575415 | ||||||||
\(707\) | −11.0551 | −0.415769 | ||||||||
\(708\) | −2.38983 | −0.0898154 | ||||||||
\(709\) | 36.4867 | 1.37029 | 0.685143 | − | 0.728408i | \(-0.259740\pi\) | ||||
0.685143 | + | 0.728408i | \(0.259740\pi\) | |||||||
\(710\) | 25.5646 | 0.959421 | ||||||||
\(711\) | −29.4363 | −1.10395 | ||||||||
\(712\) | 5.53491 | 0.207430 | ||||||||
\(713\) | −2.97438 | −0.111392 | ||||||||
\(714\) | −5.19480 | −0.194411 | ||||||||
\(715\) | 46.3874 | 1.73479 | ||||||||
\(716\) | 17.3323 | 0.647740 | ||||||||
\(717\) | −15.8208 | −0.590838 | ||||||||
\(718\) | −6.70872 | −0.250367 | ||||||||
\(719\) | 20.5648 | 0.766938 | 0.383469 | − | 0.923554i | \(-0.374729\pi\) | ||||
0.383469 | + | 0.923554i | \(0.374729\pi\) | |||||||
\(720\) | −6.38519 | −0.237962 | ||||||||
\(721\) | −14.8392 | −0.552641 | ||||||||
\(722\) | 16.4435 | 0.611962 | ||||||||
\(723\) | 5.45365 | 0.202823 | ||||||||
\(724\) | 0.496174 | 0.0184402 | ||||||||
\(725\) | −1.06877 | −0.0396931 | ||||||||
\(726\) | 2.70718 | 0.100473 | ||||||||
\(727\) | 3.06023 | 0.113497 | 0.0567487 | − | 0.998388i | \(-0.481927\pi\) | ||||
0.0567487 | + | 0.998388i | \(0.481927\pi\) | |||||||
\(728\) | −4.18929 | −0.155265 | ||||||||
\(729\) | 8.57998 | 0.317777 | ||||||||
\(730\) | −2.81881 | −0.104329 | ||||||||
\(731\) | 39.9433 | 1.47736 | ||||||||
\(732\) | 10.4786 | 0.387300 | ||||||||
\(733\) | 2.35676 | 0.0870491 | 0.0435245 | − | 0.999052i | \(-0.486141\pi\) | ||||
0.0435245 | + | 0.999052i | \(0.486141\pi\) | |||||||
\(734\) | −14.1782 | −0.523326 | ||||||||
\(735\) | −2.72900 | −0.100661 | ||||||||
\(736\) | −4.99189 | −0.184004 | ||||||||
\(737\) | 3.08940 | 0.113799 | ||||||||
\(738\) | 3.08673 | 0.113624 | ||||||||
\(739\) | −34.2481 | −1.25984 | −0.629918 | − | 0.776661i | \(-0.716912\pi\) | ||||
−0.629918 | + | 0.776661i | \(0.716912\pi\) | |||||||
\(740\) | −5.19290 | −0.190895 | ||||||||
\(741\) | 6.16411 | 0.226444 | ||||||||
\(742\) | −10.7665 | −0.395251 | ||||||||
\(743\) | −26.3559 | −0.966903 | −0.483452 | − | 0.875371i | \(-0.660617\pi\) | ||||
−0.483452 | + | 0.875371i | \(0.660617\pi\) | |||||||
\(744\) | −0.548322 | −0.0201025 | ||||||||
\(745\) | 10.1553 | 0.372061 | ||||||||
\(746\) | 9.62992 | 0.352576 | ||||||||
\(747\) | −23.2333 | −0.850061 | ||||||||
\(748\) | −21.0778 | −0.770680 | ||||||||
\(749\) | 5.78284 | 0.211300 | ||||||||
\(750\) | −3.29044 | −0.120150 | ||||||||
\(751\) | 10.4102 | 0.379874 | 0.189937 | − | 0.981796i | \(-0.439172\pi\) | ||||
0.189937 | + | 0.981796i | \(0.439172\pi\) | |||||||
\(752\) | −8.92805 | −0.325573 | ||||||||
\(753\) | −23.9784 | −0.873821 | ||||||||
\(754\) | −1.18004 | −0.0429744 | ||||||||
\(755\) | 64.9066 | 2.36219 | ||||||||
\(756\) | −4.74216 | −0.172471 | ||||||||
\(757\) | −11.1410 | −0.404928 | −0.202464 | − | 0.979290i | \(-0.564895\pi\) | ||||
−0.202464 | + | 0.979290i | \(0.564895\pi\) | |||||||
\(758\) | −0.704386 | −0.0255844 | ||||||||
\(759\) | 17.1525 | 0.622598 | ||||||||
\(760\) | −4.74161 | −0.171996 | ||||||||
\(761\) | 27.5200 | 0.997598 | 0.498799 | − | 0.866718i | \(-0.333775\pi\) | ||||
0.498799 | + | 0.866718i | \(0.333775\pi\) | |||||||
\(762\) | −0.207253 | −0.00750800 | ||||||||
\(763\) | 1.51331 | 0.0547855 | ||||||||
\(764\) | 12.9619 | 0.468945 | ||||||||
\(765\) | −36.0445 | −1.30319 | ||||||||
\(766\) | −11.5952 | −0.418953 | ||||||||
\(767\) | −10.8794 | −0.392832 | ||||||||
\(768\) | −0.920246 | −0.0332065 | ||||||||
\(769\) | 1.61368 | 0.0581907 | 0.0290953 | − | 0.999577i | \(-0.490737\pi\) | ||||
0.0290953 | + | 0.999577i | \(0.490737\pi\) | |||||||
\(770\) | −11.0729 | −0.399038 | ||||||||
\(771\) | 7.25605 | 0.261320 | ||||||||
\(772\) | 16.1898 | 0.582685 | ||||||||
\(773\) | 23.5910 | 0.848510 | 0.424255 | − | 0.905543i | \(-0.360536\pi\) | ||||
0.424255 | + | 0.905543i | \(0.360536\pi\) | |||||||
\(774\) | 15.2354 | 0.547624 | ||||||||
\(775\) | −2.26079 | −0.0812099 | ||||||||
\(776\) | −4.82510 | −0.173211 | ||||||||
\(777\) | −1.61144 | −0.0578100 | ||||||||
\(778\) | 4.89619 | 0.175537 | ||||||||
\(779\) | 2.29219 | 0.0821263 | ||||||||
\(780\) | 11.4326 | 0.409352 | ||||||||
\(781\) | 32.1883 | 1.15179 | ||||||||
\(782\) | −28.1793 | −1.00769 | ||||||||
\(783\) | −1.33577 | −0.0477365 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 8.30416 | 0.296388 | ||||||||
\(786\) | −11.8474 | −0.422584 | ||||||||
\(787\) | −11.4838 | −0.409353 | −0.204676 | − | 0.978830i | \(-0.565614\pi\) | ||||
−0.204676 | + | 0.978830i | \(0.565614\pi\) | |||||||
\(788\) | 19.3336 | 0.688731 | ||||||||
\(789\) | −3.66143 | −0.130350 | ||||||||
\(790\) | −40.5424 | −1.44243 | ||||||||
\(791\) | −3.08038 | −0.109526 | ||||||||
\(792\) | −8.03958 | −0.285674 | ||||||||
\(793\) | 47.7023 | 1.69396 | ||||||||
\(794\) | −23.3345 | −0.828110 | ||||||||
\(795\) | 29.3818 | 1.04207 | ||||||||
\(796\) | −4.28872 | −0.152010 | ||||||||
\(797\) | −13.7209 | −0.486019 | −0.243009 | − | 0.970024i | \(-0.578135\pi\) | ||||
−0.243009 | + | 0.970024i | \(0.578135\pi\) | |||||||
\(798\) | −1.47140 | −0.0520869 | ||||||||
\(799\) | −50.3990 | −1.78299 | ||||||||
\(800\) | −3.79427 | −0.134148 | ||||||||
\(801\) | 11.9175 | 0.421083 | ||||||||
\(802\) | −24.8657 | −0.878037 | ||||||||
\(803\) | −3.54916 | −0.125247 | ||||||||
\(804\) | 0.761410 | 0.0268528 | ||||||||
\(805\) | −14.8035 | −0.521756 | ||||||||
\(806\) | −2.49616 | −0.0879234 | ||||||||
\(807\) | 7.16293 | 0.252147 | ||||||||
\(808\) | −11.0551 | −0.388916 | ||||||||
\(809\) | −13.7223 | −0.482450 | −0.241225 | − | 0.970469i | \(-0.577549\pi\) | ||||
−0.241225 | + | 0.970469i | \(0.577549\pi\) | |||||||
\(810\) | −6.21419 | −0.218344 | ||||||||
\(811\) | 11.5696 | 0.406265 | 0.203132 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203132 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(812\) | 0.281679 | 0.00988501 | ||||||||
\(813\) | −12.3201 | −0.432085 | ||||||||
\(814\) | −6.53837 | −0.229170 | ||||||||
\(815\) | 14.8719 | 0.520938 | ||||||||
\(816\) | −5.19480 | −0.181854 | ||||||||
\(817\) | 11.3137 | 0.395817 | ||||||||
\(818\) | −0.240956 | −0.00842484 | ||||||||
\(819\) | −9.02016 | −0.315190 | ||||||||
\(820\) | 4.25133 | 0.148463 | ||||||||
\(821\) | 13.9858 | 0.488107 | 0.244054 | − | 0.969762i | \(-0.421523\pi\) | ||||
0.244054 | + | 0.969762i | \(0.421523\pi\) | |||||||
\(822\) | −10.8666 | −0.379017 | ||||||||
\(823\) | −19.1504 | −0.667542 | −0.333771 | − | 0.942654i | \(-0.608321\pi\) | ||||
−0.333771 | + | 0.942654i | \(0.608321\pi\) | |||||||
\(824\) | −14.8392 | −0.516948 | ||||||||
\(825\) | 13.0374 | 0.453905 | ||||||||
\(826\) | 2.59695 | 0.0903595 | ||||||||
\(827\) | 49.3630 | 1.71652 | 0.858259 | − | 0.513216i | \(-0.171546\pi\) | ||||
0.858259 | + | 0.513216i | \(0.171546\pi\) | |||||||
\(828\) | −10.7483 | −0.373529 | ||||||||
\(829\) | −2.76014 | −0.0958635 | −0.0479318 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479318 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(830\) | −31.9990 | −1.11070 | ||||||||
\(831\) | −14.1572 | −0.491108 | ||||||||
\(832\) | −4.18929 | −0.145238 | ||||||||
\(833\) | 5.64502 | 0.195588 | ||||||||
\(834\) | −3.39207 | −0.117458 | ||||||||
\(835\) | 12.7956 | 0.442811 | ||||||||
\(836\) | −5.97015 | −0.206482 | ||||||||
\(837\) | −2.82558 | −0.0976665 | ||||||||
\(838\) | −6.22872 | −0.215168 | ||||||||
\(839\) | 11.1669 | 0.385524 | 0.192762 | − | 0.981246i | \(-0.438255\pi\) | ||||
0.192762 | + | 0.981246i | \(0.438255\pi\) | |||||||
\(840\) | −2.72900 | −0.0941595 | ||||||||
\(841\) | −28.9207 | −0.997264 | ||||||||
\(842\) | −2.28185 | −0.0786376 | ||||||||
\(843\) | −21.9709 | −0.756718 | ||||||||
\(844\) | 13.5601 | 0.466759 | ||||||||
\(845\) | 13.4936 | 0.464192 | ||||||||
\(846\) | −19.2234 | −0.660915 | ||||||||
\(847\) | −2.94181 | −0.101082 | ||||||||
\(848\) | −10.7665 | −0.369724 | ||||||||
\(849\) | 23.2971 | 0.799554 | ||||||||
\(850\) | −21.4187 | −0.734656 | ||||||||
\(851\) | −8.74128 | −0.299647 | ||||||||
\(852\) | 7.93309 | 0.271783 | ||||||||
\(853\) | −52.3890 | −1.79376 | −0.896882 | − | 0.442270i | \(-0.854173\pi\) | ||||
−0.896882 | + | 0.442270i | \(0.854173\pi\) | |||||||
\(854\) | −11.3867 | −0.389646 | ||||||||
\(855\) | −10.2094 | −0.349154 | ||||||||
\(856\) | 5.78284 | 0.197653 | ||||||||
\(857\) | −0.850670 | −0.0290583 | −0.0145292 | − | 0.999894i | \(-0.504625\pi\) | ||||
−0.0145292 | + | 0.999894i | \(0.504625\pi\) | |||||||
\(858\) | 14.3947 | 0.491428 | ||||||||
\(859\) | −1.82823 | −0.0623785 | −0.0311892 | − | 0.999513i | \(-0.509929\pi\) | ||||
−0.0311892 | + | 0.999513i | \(0.509929\pi\) | |||||||
\(860\) | 20.9835 | 0.715533 | ||||||||
\(861\) | 1.31926 | 0.0449601 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 17.4958 | 0.595563 | 0.297782 | − | 0.954634i | \(-0.403753\pi\) | ||||
0.297782 | + | 0.954634i | \(0.403753\pi\) | |||||||
\(864\) | −4.74216 | −0.161332 | ||||||||
\(865\) | 29.3654 | 0.998455 | ||||||||
\(866\) | 7.69716 | 0.261560 | ||||||||
\(867\) | −13.6806 | −0.464616 | ||||||||
\(868\) | 0.595843 | 0.0202242 | ||||||||
\(869\) | −51.0468 | −1.73165 | ||||||||
\(870\) | −0.768704 | −0.0260615 | ||||||||
\(871\) | 3.46621 | 0.117448 | ||||||||
\(872\) | 1.51331 | 0.0512471 | ||||||||
\(873\) | −10.3891 | −0.351619 | ||||||||
\(874\) | −7.98162 | −0.269982 | ||||||||
\(875\) | 3.57561 | 0.120878 | ||||||||
\(876\) | −0.874721 | −0.0295541 | ||||||||
\(877\) | −15.9725 | −0.539354 | −0.269677 | − | 0.962951i | \(-0.586917\pi\) | ||||
−0.269677 | + | 0.962951i | \(0.586917\pi\) | |||||||
\(878\) | −15.6183 | −0.527091 | ||||||||
\(879\) | 8.94752 | 0.301792 | ||||||||
\(880\) | −11.0729 | −0.373266 | ||||||||
\(881\) | −7.31983 | −0.246611 | −0.123306 | − | 0.992369i | \(-0.539350\pi\) | ||||
−0.123306 | + | 0.992369i | \(0.539350\pi\) | |||||||
\(882\) | 2.15315 | 0.0725002 | ||||||||
\(883\) | −41.2582 | −1.38845 | −0.694224 | − | 0.719759i | \(-0.744252\pi\) | ||||
−0.694224 | + | 0.719759i | \(0.744252\pi\) | |||||||
\(884\) | −23.6486 | −0.795389 | ||||||||
\(885\) | −7.08708 | −0.238230 | ||||||||
\(886\) | −21.4825 | −0.721720 | ||||||||
\(887\) | −38.7293 | −1.30040 | −0.650202 | − | 0.759762i | \(-0.725316\pi\) | ||||
−0.650202 | + | 0.759762i | \(0.725316\pi\) | |||||||
\(888\) | −1.61144 | −0.0540763 | ||||||||
\(889\) | 0.225215 | 0.00755348 | ||||||||
\(890\) | 16.4139 | 0.550194 | ||||||||
\(891\) | −7.82428 | −0.262123 | ||||||||
\(892\) | 12.1396 | 0.406463 | ||||||||
\(893\) | −14.2752 | −0.477702 | ||||||||
\(894\) | 3.15135 | 0.105397 | ||||||||
\(895\) | 51.3993 | 1.71809 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 19.2446 | 0.642560 | ||||||||
\(898\) | −5.15008 | −0.171860 | ||||||||
\(899\) | 0.167837 | 0.00559767 | ||||||||
\(900\) | −8.16963 | −0.272321 | ||||||||
\(901\) | −60.7772 | −2.02478 | ||||||||
\(902\) | 5.35285 | 0.178230 | ||||||||
\(903\) | 6.51153 | 0.216690 | ||||||||
\(904\) | −3.08038 | −0.102452 | ||||||||
\(905\) | 1.47141 | 0.0489113 | ||||||||
\(906\) | 20.1415 | 0.669158 | ||||||||
\(907\) | 3.54657 | 0.117762 | 0.0588810 | − | 0.998265i | \(-0.481247\pi\) | ||||
0.0588810 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(908\) | 13.9190 | 0.461920 | ||||||||
\(909\) | −23.8032 | −0.789502 | ||||||||
\(910\) | −12.4234 | −0.411832 | ||||||||
\(911\) | −13.1576 | −0.435932 | −0.217966 | − | 0.975956i | \(-0.569942\pi\) | ||||
−0.217966 | + | 0.975956i | \(0.569942\pi\) | |||||||
\(912\) | −1.47140 | −0.0487228 | ||||||||
\(913\) | −40.2899 | −1.33340 | ||||||||
\(914\) | 24.1714 | 0.799520 | ||||||||
\(915\) | 31.0744 | 1.02729 | ||||||||
\(916\) | −12.5004 | −0.413024 | ||||||||
\(917\) | 12.8742 | 0.425144 | ||||||||
\(918\) | −26.7696 | −0.883528 | ||||||||
\(919\) | −24.0443 | −0.793147 | −0.396573 | − | 0.918003i | \(-0.629801\pi\) | ||||
−0.396573 | + | 0.918003i | \(0.629801\pi\) | |||||||
\(920\) | −14.8035 | −0.488058 | ||||||||
\(921\) | 15.0162 | 0.494801 | ||||||||
\(922\) | 19.9699 | 0.657673 | ||||||||
\(923\) | 36.1143 | 1.18872 | ||||||||
\(924\) | −3.43608 | −0.113039 | ||||||||
\(925\) | −6.64413 | −0.218458 | ||||||||
\(926\) | −24.5172 | −0.805686 | ||||||||
\(927\) | −31.9510 | −1.04941 | ||||||||
\(928\) | 0.281679 | 0.00924658 | ||||||||
\(929\) | −9.38922 | −0.308050 | −0.154025 | − | 0.988067i | \(-0.549224\pi\) | ||||
−0.154025 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(930\) | −1.62606 | −0.0533205 | ||||||||
\(931\) | 1.59892 | 0.0524024 | ||||||||
\(932\) | −0.392089 | −0.0128433 | ||||||||
\(933\) | −28.0119 | −0.917068 | ||||||||
\(934\) | −4.73023 | −0.154778 | ||||||||
\(935\) | −62.5064 | −2.04418 | ||||||||
\(936\) | −9.02016 | −0.294833 | ||||||||
\(937\) | −22.4978 | −0.734970 | −0.367485 | − | 0.930030i | \(-0.619781\pi\) | ||||
−0.367485 | + | 0.930030i | \(0.619781\pi\) | |||||||
\(938\) | −0.827398 | −0.0270155 | ||||||||
\(939\) | −3.49535 | −0.114066 | ||||||||
\(940\) | −26.4763 | −0.863561 | ||||||||
\(941\) | 30.5767 | 0.996773 | 0.498386 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498386 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(942\) | 2.57691 | 0.0839603 | ||||||||
\(943\) | 7.15633 | 0.233042 | ||||||||
\(944\) | 2.59695 | 0.0845235 | ||||||||
\(945\) | −14.0629 | −0.457468 | ||||||||
\(946\) | 26.4203 | 0.859000 | ||||||||
\(947\) | −20.0129 | −0.650331 | −0.325166 | − | 0.945657i | \(-0.605420\pi\) | ||||
−0.325166 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(948\) | −12.5809 | −0.408610 | ||||||||
\(949\) | −3.98205 | −0.129263 | ||||||||
\(950\) | −6.06672 | −0.196831 | ||||||||
\(951\) | −28.9812 | −0.939779 | ||||||||
\(952\) | 5.64502 | 0.182956 | ||||||||
\(953\) | 22.3561 | 0.724184 | 0.362092 | − | 0.932142i | \(-0.382063\pi\) | ||||
0.362092 | + | 0.932142i | \(0.382063\pi\) | |||||||
\(954\) | −23.1819 | −0.750542 | ||||||||
\(955\) | 38.4387 | 1.24385 | ||||||||
\(956\) | 17.1919 | 0.556026 | ||||||||
\(957\) | −0.967874 | −0.0312869 | ||||||||
\(958\) | 15.6484 | 0.505577 | ||||||||
\(959\) | 11.8084 | 0.381313 | ||||||||
\(960\) | −2.72900 | −0.0880782 | ||||||||
\(961\) | −30.6450 | −0.988547 | ||||||||
\(962\) | −7.33585 | −0.236517 | ||||||||
\(963\) | 12.4513 | 0.401238 | ||||||||
\(964\) | −5.92629 | −0.190873 | ||||||||
\(965\) | 48.0111 | 1.54553 | ||||||||
\(966\) | −4.59377 | −0.147802 | ||||||||
\(967\) | −7.43118 | −0.238971 | −0.119485 | − | 0.992836i | \(-0.538124\pi\) | ||||
−0.119485 | + | 0.992836i | \(0.538124\pi\) | |||||||
\(968\) | −2.94181 | −0.0945532 | ||||||||
\(969\) | −8.30606 | −0.266829 | ||||||||
\(970\) | −14.3089 | −0.459431 | ||||||||
\(971\) | 14.4503 | 0.463731 | 0.231866 | − | 0.972748i | \(-0.425517\pi\) | ||||
0.231866 | + | 0.972748i | \(0.425517\pi\) | |||||||
\(972\) | −16.1549 | −0.518167 | ||||||||
\(973\) | 3.68604 | 0.118169 | ||||||||
\(974\) | 35.3945 | 1.13411 | ||||||||
\(975\) | 14.6276 | 0.468458 | ||||||||
\(976\) | −11.3867 | −0.364480 | ||||||||
\(977\) | 28.9904 | 0.927486 | 0.463743 | − | 0.885970i | \(-0.346506\pi\) | ||||
0.463743 | + | 0.885970i | \(0.346506\pi\) | |||||||
\(978\) | 4.61497 | 0.147571 | ||||||||
\(979\) | 20.6667 | 0.660509 | ||||||||
\(980\) | 2.96551 | 0.0947299 | ||||||||
\(981\) | 3.25838 | 0.104032 | ||||||||
\(982\) | −12.5717 | −0.401180 | ||||||||
\(983\) | 6.71003 | 0.214017 | 0.107008 | − | 0.994258i | \(-0.465873\pi\) | ||||
0.107008 | + | 0.994258i | \(0.465873\pi\) | |||||||
\(984\) | 1.31926 | 0.0420564 | ||||||||
\(985\) | 57.3341 | 1.82682 | ||||||||
\(986\) | 1.59009 | 0.0506386 | ||||||||
\(987\) | −8.21601 | −0.261518 | ||||||||
\(988\) | −6.69833 | −0.213102 | ||||||||
\(989\) | 35.3219 | 1.12317 | ||||||||
\(990\) | −23.8415 | −0.757732 | ||||||||
\(991\) | −39.6410 | −1.25924 | −0.629619 | − | 0.776904i | \(-0.716789\pi\) | ||||
−0.629619 | + | 0.776904i | \(0.716789\pi\) | |||||||
\(992\) | 0.595843 | 0.0189180 | ||||||||
\(993\) | −16.2576 | −0.515918 | ||||||||
\(994\) | −8.62062 | −0.273430 | ||||||||
\(995\) | −12.7183 | −0.403196 | ||||||||
\(996\) | −9.92980 | −0.314638 | ||||||||
\(997\) | −11.2595 | −0.356592 | −0.178296 | − | 0.983977i | \(-0.557058\pi\) | ||||
−0.178296 | + | 0.983977i | \(0.557058\pi\) | |||||||
\(998\) | 23.1265 | 0.732057 | ||||||||
\(999\) | −8.30398 | −0.262726 |
(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 | 6034.2.a.n.1.8 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.8 | ✓ | 24 | 1.1 | even | 1 | trivial |