Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [41,2,Mod(1,41)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(41, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("41.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 41.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: | \(0.327386648287\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 41.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70928 | −1.91575 | −0.957873 | − | 0.287190i | \(-0.907279\pi\) | ||||
−0.957873 | + | 0.287190i | \(0.907279\pi\) | |||||||
\(3\) | 0.539189 | 0.311301 | 0.155650 | − | 0.987812i | \(-0.450253\pi\) | ||||
0.155650 | + | 0.987812i | \(0.450253\pi\) | |||||||
\(4\) | 5.34017 | 2.67009 | ||||||||
\(5\) | 1.70928 | 0.764411 | 0.382206 | − | 0.924077i | \(-0.375165\pi\) | ||||
0.382206 | + | 0.924077i | \(0.375165\pi\) | |||||||
\(6\) | −1.46081 | −0.596374 | ||||||||
\(7\) | 1.46081 | 0.552135 | 0.276067 | − | 0.961138i | \(-0.410969\pi\) | ||||
0.276067 | + | 0.961138i | \(0.410969\pi\) | |||||||
\(8\) | −9.04945 | −3.19946 | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | −4.63090 | −1.46442 | ||||||||
\(11\) | 3.80098 | 1.14604 | 0.573020 | − | 0.819541i | \(-0.305772\pi\) | ||||
0.573020 | + | 0.819541i | \(0.305772\pi\) | |||||||
\(12\) | 2.87936 | 0.831200 | ||||||||
\(13\) | −4.34017 | −1.20375 | −0.601874 | − | 0.798591i | \(-0.705579\pi\) | ||||
−0.601874 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(14\) | −3.95774 | −1.05775 | ||||||||
\(15\) | 0.921622 | 0.237962 | ||||||||
\(16\) | 13.8371 | 3.45928 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 7.34017 | 1.73010 | ||||||||
\(19\) | −1.80098 | −0.413174 | −0.206587 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206587 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(20\) | 9.12783 | 2.04104 | ||||||||
\(21\) | 0.787653 | 0.171880 | ||||||||
\(22\) | −10.2979 | −2.19552 | ||||||||
\(23\) | −1.26180 | −0.263102 | −0.131551 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131551 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(24\) | −4.87936 | −0.995996 | ||||||||
\(25\) | −2.07838 | −0.415676 | ||||||||
\(26\) | 11.7587 | 2.30608 | ||||||||
\(27\) | −3.07838 | −0.592434 | ||||||||
\(28\) | 7.80098 | 1.47425 | ||||||||
\(29\) | −3.07838 | −0.571640 | −0.285820 | − | 0.958283i | \(-0.592266\pi\) | ||||
−0.285820 | + | 0.958283i | \(0.592266\pi\) | |||||||
\(30\) | −2.49693 | −0.455875 | ||||||||
\(31\) | 0.581449 | 0.104431 | 0.0522157 | − | 0.998636i | \(-0.483372\pi\) | ||||
0.0522157 | + | 0.998636i | \(0.483372\pi\) | |||||||
\(32\) | −19.3896 | −3.42763 | ||||||||
\(33\) | 2.04945 | 0.356763 | ||||||||
\(34\) | 5.41855 | 0.929274 | ||||||||
\(35\) | 2.49693 | 0.422058 | ||||||||
\(36\) | −14.4680 | −2.41133 | ||||||||
\(37\) | 5.12783 | 0.843009 | 0.421505 | − | 0.906826i | \(-0.361502\pi\) | ||||
0.421505 | + | 0.906826i | \(0.361502\pi\) | |||||||
\(38\) | 4.87936 | 0.791537 | ||||||||
\(39\) | −2.34017 | −0.374728 | ||||||||
\(40\) | −15.4680 | −2.44571 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | −2.13397 | −0.329279 | ||||||||
\(43\) | 2.34017 | 0.356873 | 0.178437 | − | 0.983951i | \(-0.442896\pi\) | ||||
0.178437 | + | 0.983951i | \(0.442896\pi\) | |||||||
\(44\) | 20.2979 | 3.06003 | ||||||||
\(45\) | −4.63090 | −0.690333 | ||||||||
\(46\) | 3.41855 | 0.504038 | ||||||||
\(47\) | 12.6381 | 1.84345 | 0.921727 | − | 0.387839i | \(-0.126778\pi\) | ||||
0.921727 | + | 0.387839i | \(0.126778\pi\) | |||||||
\(48\) | 7.46081 | 1.07688 | ||||||||
\(49\) | −4.86603 | −0.695147 | ||||||||
\(50\) | 5.63090 | 0.796329 | ||||||||
\(51\) | −1.07838 | −0.151003 | ||||||||
\(52\) | −23.1773 | −3.21411 | ||||||||
\(53\) | 0.921622 | 0.126595 | 0.0632973 | − | 0.997995i | \(-0.479838\pi\) | ||||
0.0632973 | + | 0.997995i | \(0.479838\pi\) | |||||||
\(54\) | 8.34017 | 1.13495 | ||||||||
\(55\) | 6.49693 | 0.876046 | ||||||||
\(56\) | −13.2195 | −1.76653 | ||||||||
\(57\) | −0.971071 | −0.128621 | ||||||||
\(58\) | 8.34017 | 1.09512 | ||||||||
\(59\) | −5.26180 | −0.685027 | −0.342514 | − | 0.939513i | \(-0.611278\pi\) | ||||
−0.342514 | + | 0.939513i | \(0.611278\pi\) | |||||||
\(60\) | 4.92162 | 0.635379 | ||||||||
\(61\) | −7.75872 | −0.993403 | −0.496701 | − | 0.867922i | \(-0.665456\pi\) | ||||
−0.496701 | + | 0.867922i | \(0.665456\pi\) | |||||||
\(62\) | −1.57531 | −0.200064 | ||||||||
\(63\) | −3.95774 | −0.498628 | ||||||||
\(64\) | 24.8576 | 3.10720 | ||||||||
\(65\) | −7.41855 | −0.920158 | ||||||||
\(66\) | −5.55252 | −0.683468 | ||||||||
\(67\) | −3.80098 | −0.464364 | −0.232182 | − | 0.972672i | \(-0.574587\pi\) | ||||
−0.232182 | + | 0.972672i | \(0.574587\pi\) | |||||||
\(68\) | −10.6803 | −1.29518 | ||||||||
\(69\) | −0.680346 | −0.0819040 | ||||||||
\(70\) | −6.76487 | −0.808556 | ||||||||
\(71\) | −1.21953 | −0.144732 | −0.0723661 | − | 0.997378i | \(-0.523055\pi\) | ||||
−0.0723661 | + | 0.997378i | \(0.523055\pi\) | |||||||
\(72\) | 24.5174 | 2.88941 | ||||||||
\(73\) | 11.6514 | 1.36370 | 0.681848 | − | 0.731494i | \(-0.261177\pi\) | ||||
0.681848 | + | 0.731494i | \(0.261177\pi\) | |||||||
\(74\) | −13.8927 | −1.61499 | ||||||||
\(75\) | −1.12064 | −0.129400 | ||||||||
\(76\) | −9.61757 | −1.10321 | ||||||||
\(77\) | 5.55252 | 0.632768 | ||||||||
\(78\) | 6.34017 | 0.717883 | ||||||||
\(79\) | 14.8794 | 1.67406 | 0.837029 | − | 0.547158i | \(-0.184290\pi\) | ||||
0.837029 | + | 0.547158i | \(0.184290\pi\) | |||||||
\(80\) | 23.6514 | 2.64431 | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | −2.70928 | −0.299189 | ||||||||
\(83\) | −2.15676 | −0.236735 | −0.118367 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118367 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(84\) | 4.20620 | 0.458934 | ||||||||
\(85\) | −3.41855 | −0.370794 | ||||||||
\(86\) | −6.34017 | −0.683678 | ||||||||
\(87\) | −1.65983 | −0.177952 | ||||||||
\(88\) | −34.3968 | −3.66671 | ||||||||
\(89\) | −11.9421 | −1.26586 | −0.632932 | − | 0.774207i | \(-0.718149\pi\) | ||||
−0.632932 | + | 0.774207i | \(0.718149\pi\) | |||||||
\(90\) | 12.5464 | 1.32250 | ||||||||
\(91\) | −6.34017 | −0.664631 | ||||||||
\(92\) | −6.73820 | −0.702506 | ||||||||
\(93\) | 0.313511 | 0.0325096 | ||||||||
\(94\) | −34.2401 | −3.53159 | ||||||||
\(95\) | −3.07838 | −0.315835 | ||||||||
\(96\) | −10.4547 | −1.06703 | ||||||||
\(97\) | 4.15676 | 0.422055 | 0.211027 | − | 0.977480i | \(-0.432319\pi\) | ||||
0.211027 | + | 0.977480i | \(0.432319\pi\) | |||||||
\(98\) | 13.1834 | 1.33173 | ||||||||
\(99\) | −10.2979 | −1.03498 | ||||||||
\(100\) | −11.0989 | −1.10989 | ||||||||
\(101\) | 17.0205 | 1.69360 | 0.846802 | − | 0.531907i | \(-0.178525\pi\) | ||||
0.846802 | + | 0.531907i | \(0.178525\pi\) | |||||||
\(102\) | 2.92162 | 0.289284 | ||||||||
\(103\) | 16.5958 | 1.63524 | 0.817618 | − | 0.575762i | \(-0.195294\pi\) | ||||
0.817618 | + | 0.575762i | \(0.195294\pi\) | |||||||
\(104\) | 39.2762 | 3.85135 | ||||||||
\(105\) | 1.34632 | 0.131387 | ||||||||
\(106\) | −2.49693 | −0.242523 | ||||||||
\(107\) | −14.8371 | −1.43436 | −0.717178 | − | 0.696890i | \(-0.754567\pi\) | ||||
−0.717178 | + | 0.696890i | \(0.754567\pi\) | |||||||
\(108\) | −16.4391 | −1.58185 | ||||||||
\(109\) | 11.1773 | 1.07059 | 0.535294 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535294 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(110\) | −17.6020 | −1.67828 | ||||||||
\(111\) | 2.76487 | 0.262430 | ||||||||
\(112\) | 20.2134 | 1.90999 | ||||||||
\(113\) | −0.814315 | −0.0766043 | −0.0383022 | − | 0.999266i | \(-0.512195\pi\) | ||||
−0.0383022 | + | 0.999266i | \(0.512195\pi\) | |||||||
\(114\) | 2.63090 | 0.246406 | ||||||||
\(115\) | −2.15676 | −0.201118 | ||||||||
\(116\) | −16.4391 | −1.52633 | ||||||||
\(117\) | 11.7587 | 1.08709 | ||||||||
\(118\) | 14.2557 | 1.31234 | ||||||||
\(119\) | −2.92162 | −0.267825 | ||||||||
\(120\) | −8.34017 | −0.761350 | ||||||||
\(121\) | 3.44748 | 0.313407 | ||||||||
\(122\) | 21.0205 | 1.90311 | ||||||||
\(123\) | 0.539189 | 0.0486170 | ||||||||
\(124\) | 3.10504 | 0.278841 | ||||||||
\(125\) | −12.0989 | −1.08216 | ||||||||
\(126\) | 10.7226 | 0.955246 | ||||||||
\(127\) | 2.73820 | 0.242976 | 0.121488 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121488 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(128\) | −28.5669 | −2.52498 | ||||||||
\(129\) | 1.26180 | 0.111095 | ||||||||
\(130\) | 20.0989 | 1.76279 | ||||||||
\(131\) | 1.75872 | 0.153660 | 0.0768302 | − | 0.997044i | \(-0.475520\pi\) | ||||
0.0768302 | + | 0.997044i | \(0.475520\pi\) | |||||||
\(132\) | 10.9444 | 0.952588 | ||||||||
\(133\) | −2.63090 | −0.228128 | ||||||||
\(134\) | 10.2979 | 0.889604 | ||||||||
\(135\) | −5.26180 | −0.452863 | ||||||||
\(136\) | 18.0989 | 1.55197 | ||||||||
\(137\) | 10.3135 | 0.881143 | 0.440571 | − | 0.897718i | \(-0.354776\pi\) | ||||
0.440571 | + | 0.897718i | \(0.354776\pi\) | |||||||
\(138\) | 1.84324 | 0.156907 | ||||||||
\(139\) | −20.4124 | −1.73136 | −0.865679 | − | 0.500600i | \(-0.833113\pi\) | ||||
−0.865679 | + | 0.500600i | \(0.833113\pi\) | |||||||
\(140\) | 13.3340 | 1.12693 | ||||||||
\(141\) | 6.81432 | 0.573869 | ||||||||
\(142\) | 3.30406 | 0.277270 | ||||||||
\(143\) | −16.4969 | −1.37954 | ||||||||
\(144\) | −37.4885 | −3.12404 | ||||||||
\(145\) | −5.26180 | −0.436968 | ||||||||
\(146\) | −31.5669 | −2.61249 | ||||||||
\(147\) | −2.62371 | −0.216400 | ||||||||
\(148\) | 27.3835 | 2.25091 | ||||||||
\(149\) | 7.44521 | 0.609936 | 0.304968 | − | 0.952363i | \(-0.401354\pi\) | ||||
0.304968 | + | 0.952363i | \(0.401354\pi\) | |||||||
\(150\) | 3.03612 | 0.247898 | ||||||||
\(151\) | 18.2979 | 1.48906 | 0.744532 | − | 0.667587i | \(-0.232673\pi\) | ||||
0.744532 | + | 0.667587i | \(0.232673\pi\) | |||||||
\(152\) | 16.2979 | 1.32194 | ||||||||
\(153\) | 5.41855 | 0.438064 | ||||||||
\(154\) | −15.0433 | −1.21222 | ||||||||
\(155\) | 0.993857 | 0.0798285 | ||||||||
\(156\) | −12.4969 | −1.00056 | ||||||||
\(157\) | −12.6537 | −1.00987 | −0.504937 | − | 0.863156i | \(-0.668484\pi\) | ||||
−0.504937 | + | 0.863156i | \(0.668484\pi\) | |||||||
\(158\) | −40.3123 | −3.20707 | ||||||||
\(159\) | 0.496928 | 0.0394090 | ||||||||
\(160\) | −33.1422 | −2.62012 | ||||||||
\(161\) | −1.84324 | −0.145268 | ||||||||
\(162\) | −17.5236 | −1.37678 | ||||||||
\(163\) | −12.6803 | −0.993201 | −0.496601 | − | 0.867979i | \(-0.665419\pi\) | ||||
−0.496601 | + | 0.867979i | \(0.665419\pi\) | |||||||
\(164\) | 5.34017 | 0.416997 | ||||||||
\(165\) | 3.50307 | 0.272714 | ||||||||
\(166\) | 5.84324 | 0.453524 | ||||||||
\(167\) | −9.95774 | −0.770553 | −0.385277 | − | 0.922801i | \(-0.625894\pi\) | ||||
−0.385277 | + | 0.922801i | \(0.625894\pi\) | |||||||
\(168\) | −7.12783 | −0.549924 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 9.26180 | 0.710347 | ||||||||
\(171\) | 4.87936 | 0.373134 | ||||||||
\(172\) | 12.4969 | 0.952882 | ||||||||
\(173\) | −12.1568 | −0.924261 | −0.462131 | − | 0.886812i | \(-0.652915\pi\) | ||||
−0.462131 | + | 0.886812i | \(0.652915\pi\) | |||||||
\(174\) | 4.49693 | 0.340911 | ||||||||
\(175\) | −3.03612 | −0.229509 | ||||||||
\(176\) | 52.5946 | 3.96447 | ||||||||
\(177\) | −2.83710 | −0.213250 | ||||||||
\(178\) | 32.3545 | 2.42508 | ||||||||
\(179\) | 19.1350 | 1.43022 | 0.715109 | − | 0.699013i | \(-0.246377\pi\) | ||||
0.715109 | + | 0.699013i | \(0.246377\pi\) | |||||||
\(180\) | −24.7298 | −1.84325 | ||||||||
\(181\) | −15.4452 | −1.14803 | −0.574017 | − | 0.818844i | \(-0.694616\pi\) | ||||
−0.574017 | + | 0.818844i | \(0.694616\pi\) | |||||||
\(182\) | 17.1773 | 1.27326 | ||||||||
\(183\) | −4.18342 | −0.309247 | ||||||||
\(184\) | 11.4186 | 0.841787 | ||||||||
\(185\) | 8.76487 | 0.644406 | ||||||||
\(186\) | −0.849388 | −0.0622801 | ||||||||
\(187\) | −7.60197 | −0.555911 | ||||||||
\(188\) | 67.4896 | 4.92218 | ||||||||
\(189\) | −4.49693 | −0.327103 | ||||||||
\(190\) | 8.34017 | 0.605060 | ||||||||
\(191\) | −18.5536 | −1.34249 | −0.671244 | − | 0.741236i | \(-0.734240\pi\) | ||||
−0.671244 | + | 0.741236i | \(0.734240\pi\) | |||||||
\(192\) | 13.4030 | 0.967275 | ||||||||
\(193\) | −11.2618 | −0.810642 | −0.405321 | − | 0.914174i | \(-0.632840\pi\) | ||||
−0.405321 | + | 0.914174i | \(0.632840\pi\) | |||||||
\(194\) | −11.2618 | −0.808550 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | −25.9854 | −1.85610 | ||||||||
\(197\) | 8.24128 | 0.587167 | 0.293583 | − | 0.955933i | \(-0.405152\pi\) | ||||
0.293583 | + | 0.955933i | \(0.405152\pi\) | |||||||
\(198\) | 27.8999 | 1.98276 | ||||||||
\(199\) | 8.96388 | 0.635433 | 0.317716 | − | 0.948186i | \(-0.397084\pi\) | ||||
0.317716 | + | 0.948186i | \(0.397084\pi\) | |||||||
\(200\) | 18.8082 | 1.32994 | ||||||||
\(201\) | −2.04945 | −0.144557 | ||||||||
\(202\) | −46.1133 | −3.24452 | ||||||||
\(203\) | −4.49693 | −0.315623 | ||||||||
\(204\) | −5.75872 | −0.403191 | ||||||||
\(205\) | 1.70928 | 0.119381 | ||||||||
\(206\) | −44.9627 | −3.13270 | ||||||||
\(207\) | 3.41855 | 0.237606 | ||||||||
\(208\) | −60.0554 | −4.16409 | ||||||||
\(209\) | −6.84551 | −0.473514 | ||||||||
\(210\) | −3.64754 | −0.251704 | ||||||||
\(211\) | 14.4547 | 0.995100 | 0.497550 | − | 0.867435i | \(-0.334233\pi\) | ||||
0.497550 | + | 0.867435i | \(0.334233\pi\) | |||||||
\(212\) | 4.92162 | 0.338018 | ||||||||
\(213\) | −0.657560 | −0.0450552 | ||||||||
\(214\) | 40.1978 | 2.74786 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 27.8576 | 1.89547 | ||||||||
\(217\) | 0.849388 | 0.0576602 | ||||||||
\(218\) | −30.2823 | −2.05098 | ||||||||
\(219\) | 6.28231 | 0.424519 | ||||||||
\(220\) | 34.6947 | 2.33912 | ||||||||
\(221\) | 8.68035 | 0.583903 | ||||||||
\(222\) | −7.49079 | −0.502749 | ||||||||
\(223\) | 6.83710 | 0.457846 | 0.228923 | − | 0.973445i | \(-0.426480\pi\) | ||||
0.228923 | + | 0.973445i | \(0.426480\pi\) | |||||||
\(224\) | −28.3246 | −1.89252 | ||||||||
\(225\) | 5.63090 | 0.375393 | ||||||||
\(226\) | 2.20620 | 0.146754 | ||||||||
\(227\) | −5.21953 | −0.346433 | −0.173216 | − | 0.984884i | \(-0.555416\pi\) | ||||
−0.173216 | + | 0.984884i | \(0.555416\pi\) | |||||||
\(228\) | −5.18568 | −0.343430 | ||||||||
\(229\) | −17.3340 | −1.14546 | −0.572732 | − | 0.819742i | \(-0.694117\pi\) | ||||
−0.572732 | + | 0.819742i | \(0.694117\pi\) | |||||||
\(230\) | 5.84324 | 0.385292 | ||||||||
\(231\) | 2.99386 | 0.196981 | ||||||||
\(232\) | 27.8576 | 1.82894 | ||||||||
\(233\) | 21.2039 | 1.38912 | 0.694558 | − | 0.719437i | \(-0.255600\pi\) | ||||
0.694558 | + | 0.719437i | \(0.255600\pi\) | |||||||
\(234\) | −31.8576 | −2.08260 | ||||||||
\(235\) | 21.6020 | 1.40916 | ||||||||
\(236\) | −28.0989 | −1.82908 | ||||||||
\(237\) | 8.02279 | 0.521136 | ||||||||
\(238\) | 7.91548 | 0.513084 | ||||||||
\(239\) | 4.35577 | 0.281751 | 0.140876 | − | 0.990027i | \(-0.455008\pi\) | ||||
0.140876 | + | 0.990027i | \(0.455008\pi\) | |||||||
\(240\) | 12.7526 | 0.823176 | ||||||||
\(241\) | 7.39189 | 0.476153 | 0.238077 | − | 0.971246i | \(-0.423483\pi\) | ||||
0.238077 | + | 0.971246i | \(0.423483\pi\) | |||||||
\(242\) | −9.34017 | −0.600409 | ||||||||
\(243\) | 12.7226 | 0.816156 | ||||||||
\(244\) | −41.4329 | −2.65247 | ||||||||
\(245\) | −8.31739 | −0.531378 | ||||||||
\(246\) | −1.46081 | −0.0931379 | ||||||||
\(247\) | 7.81658 | 0.497357 | ||||||||
\(248\) | −5.26180 | −0.334124 | ||||||||
\(249\) | −1.16290 | −0.0736957 | ||||||||
\(250\) | 32.7792 | 2.07314 | ||||||||
\(251\) | −17.7587 | −1.12092 | −0.560460 | − | 0.828181i | \(-0.689376\pi\) | ||||
−0.560460 | + | 0.828181i | \(0.689376\pi\) | |||||||
\(252\) | −21.1350 | −1.33138 | ||||||||
\(253\) | −4.79606 | −0.301526 | ||||||||
\(254\) | −7.41855 | −0.465481 | ||||||||
\(255\) | −1.84324 | −0.115428 | ||||||||
\(256\) | 27.6803 | 1.73002 | ||||||||
\(257\) | 22.7792 | 1.42093 | 0.710465 | − | 0.703732i | \(-0.248485\pi\) | ||||
0.710465 | + | 0.703732i | \(0.248485\pi\) | |||||||
\(258\) | −3.41855 | −0.212830 | ||||||||
\(259\) | 7.49079 | 0.465455 | ||||||||
\(260\) | −39.6163 | −2.45690 | ||||||||
\(261\) | 8.34017 | 0.516244 | ||||||||
\(262\) | −4.76487 | −0.294374 | ||||||||
\(263\) | 15.4296 | 0.951431 | 0.475715 | − | 0.879599i | \(-0.342189\pi\) | ||||
0.475715 | + | 0.879599i | \(0.342189\pi\) | |||||||
\(264\) | −18.5464 | −1.14145 | ||||||||
\(265\) | 1.57531 | 0.0967703 | ||||||||
\(266\) | 7.12783 | 0.437035 | ||||||||
\(267\) | −6.43907 | −0.394065 | ||||||||
\(268\) | −20.2979 | −1.23989 | ||||||||
\(269\) | −10.2823 | −0.626924 | −0.313462 | − | 0.949601i | \(-0.601489\pi\) | ||||
−0.313462 | + | 0.949601i | \(0.601489\pi\) | |||||||
\(270\) | 14.2557 | 0.867571 | ||||||||
\(271\) | 3.41855 | 0.207662 | 0.103831 | − | 0.994595i | \(-0.466890\pi\) | ||||
0.103831 | + | 0.994595i | \(0.466890\pi\) | |||||||
\(272\) | −27.6742 | −1.67800 | ||||||||
\(273\) | −3.41855 | −0.206900 | ||||||||
\(274\) | −27.9421 | −1.68805 | ||||||||
\(275\) | −7.89988 | −0.476381 | ||||||||
\(276\) | −3.63317 | −0.218691 | ||||||||
\(277\) | 9.49466 | 0.570479 | 0.285239 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285239 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(278\) | 55.3028 | 3.31684 | ||||||||
\(279\) | −1.57531 | −0.0943111 | ||||||||
\(280\) | −22.5958 | −1.35036 | ||||||||
\(281\) | 5.31965 | 0.317344 | 0.158672 | − | 0.987331i | \(-0.449279\pi\) | ||||
0.158672 | + | 0.987331i | \(0.449279\pi\) | |||||||
\(282\) | −18.4619 | −1.09939 | ||||||||
\(283\) | −3.05172 | −0.181406 | −0.0907028 | − | 0.995878i | \(-0.528911\pi\) | ||||
−0.0907028 | + | 0.995878i | \(0.528911\pi\) | |||||||
\(284\) | −6.51253 | −0.386447 | ||||||||
\(285\) | −1.65983 | −0.0983197 | ||||||||
\(286\) | 44.6947 | 2.64285 | ||||||||
\(287\) | 1.46081 | 0.0862290 | ||||||||
\(288\) | 52.5318 | 3.09547 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 14.2557 | 0.837121 | ||||||||
\(291\) | 2.24128 | 0.131386 | ||||||||
\(292\) | 62.2206 | 3.64118 | ||||||||
\(293\) | −9.11942 | −0.532762 | −0.266381 | − | 0.963868i | \(-0.585828\pi\) | ||||
−0.266381 | + | 0.963868i | \(0.585828\pi\) | |||||||
\(294\) | 7.10835 | 0.414568 | ||||||||
\(295\) | −8.99386 | −0.523643 | ||||||||
\(296\) | −46.4040 | −2.69718 | ||||||||
\(297\) | −11.7009 | −0.678953 | ||||||||
\(298\) | −20.1711 | −1.16848 | ||||||||
\(299\) | 5.47641 | 0.316709 | ||||||||
\(300\) | −5.98440 | −0.345510 | ||||||||
\(301\) | 3.41855 | 0.197042 | ||||||||
\(302\) | −49.5741 | −2.85267 | ||||||||
\(303\) | 9.17727 | 0.527221 | ||||||||
\(304\) | −24.9204 | −1.42928 | ||||||||
\(305\) | −13.2618 | −0.759368 | ||||||||
\(306\) | −14.6803 | −0.839220 | ||||||||
\(307\) | −21.7587 | −1.24184 | −0.620918 | − | 0.783876i | \(-0.713240\pi\) | ||||
−0.620918 | + | 0.783876i | \(0.713240\pi\) | |||||||
\(308\) | 29.6514 | 1.68955 | ||||||||
\(309\) | 8.94828 | 0.509050 | ||||||||
\(310\) | −2.69263 | −0.152931 | ||||||||
\(311\) | −8.66475 | −0.491333 | −0.245666 | − | 0.969354i | \(-0.579007\pi\) | ||||
−0.245666 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(312\) | 21.1773 | 1.19893 | ||||||||
\(313\) | −30.7792 | −1.73975 | −0.869873 | − | 0.493276i | \(-0.835799\pi\) | ||||
−0.869873 | + | 0.493276i | \(0.835799\pi\) | |||||||
\(314\) | 34.2823 | 1.93466 | ||||||||
\(315\) | −6.76487 | −0.381157 | ||||||||
\(316\) | 79.4584 | 4.46988 | ||||||||
\(317\) | −0.822726 | −0.0462089 | −0.0231044 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231044 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(318\) | −1.34632 | −0.0754977 | ||||||||
\(319\) | −11.7009 | −0.655123 | ||||||||
\(320\) | 42.4885 | 2.37518 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 4.99386 | 0.278297 | ||||||||
\(323\) | 3.60197 | 0.200419 | ||||||||
\(324\) | 34.5402 | 1.91890 | ||||||||
\(325\) | 9.02052 | 0.500368 | ||||||||
\(326\) | 34.3545 | 1.90272 | ||||||||
\(327\) | 6.02666 | 0.333275 | ||||||||
\(328\) | −9.04945 | −0.499672 | ||||||||
\(329\) | 18.4619 | 1.01784 | ||||||||
\(330\) | −9.49079 | −0.522451 | ||||||||
\(331\) | 22.4235 | 1.23251 | 0.616253 | − | 0.787548i | \(-0.288650\pi\) | ||||
0.616253 | + | 0.787548i | \(0.288650\pi\) | |||||||
\(332\) | −11.5174 | −0.632102 | ||||||||
\(333\) | −13.8927 | −0.761315 | ||||||||
\(334\) | 26.9783 | 1.47618 | ||||||||
\(335\) | −6.49693 | −0.354965 | ||||||||
\(336\) | 10.8988 | 0.594580 | ||||||||
\(337\) | −26.7031 | −1.45461 | −0.727306 | − | 0.686313i | \(-0.759228\pi\) | ||||
−0.727306 | + | 0.686313i | \(0.759228\pi\) | |||||||
\(338\) | −15.8143 | −0.860185 | ||||||||
\(339\) | −0.439070 | −0.0238470 | ||||||||
\(340\) | −18.2557 | −0.990052 | ||||||||
\(341\) | 2.21008 | 0.119683 | ||||||||
\(342\) | −13.2195 | −0.714831 | ||||||||
\(343\) | −17.3340 | −0.935950 | ||||||||
\(344\) | −21.1773 | −1.14180 | ||||||||
\(345\) | −1.16290 | −0.0626084 | ||||||||
\(346\) | 32.9360 | 1.77065 | ||||||||
\(347\) | 13.4030 | 0.719508 | 0.359754 | − | 0.933047i | \(-0.382861\pi\) | ||||
0.359754 | + | 0.933047i | \(0.382861\pi\) | |||||||
\(348\) | −8.86376 | −0.475148 | ||||||||
\(349\) | −14.2907 | −0.764965 | −0.382482 | − | 0.923963i | \(-0.624931\pi\) | ||||
−0.382482 | + | 0.923963i | \(0.624931\pi\) | |||||||
\(350\) | 8.22568 | 0.439681 | ||||||||
\(351\) | 13.3607 | 0.713141 | ||||||||
\(352\) | −73.6996 | −3.92820 | ||||||||
\(353\) | −17.4947 | −0.931147 | −0.465573 | − | 0.885009i | \(-0.654152\pi\) | ||||
−0.465573 | + | 0.885009i | \(0.654152\pi\) | |||||||
\(354\) | 7.68649 | 0.408532 | ||||||||
\(355\) | −2.08452 | −0.110635 | ||||||||
\(356\) | −63.7731 | −3.37997 | ||||||||
\(357\) | −1.57531 | −0.0833740 | ||||||||
\(358\) | −51.8420 | −2.73994 | ||||||||
\(359\) | 16.1978 | 0.854887 | 0.427443 | − | 0.904042i | \(-0.359414\pi\) | ||||
0.427443 | + | 0.904042i | \(0.359414\pi\) | |||||||
\(360\) | 41.9071 | 2.20870 | ||||||||
\(361\) | −15.7565 | −0.829287 | ||||||||
\(362\) | 41.8453 | 2.19934 | ||||||||
\(363\) | 1.85884 | 0.0975640 | ||||||||
\(364\) | −33.8576 | −1.77462 | ||||||||
\(365\) | 19.9155 | 1.04242 | ||||||||
\(366\) | 11.3340 | 0.592439 | ||||||||
\(367\) | −5.97334 | −0.311806 | −0.155903 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155903 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(368\) | −17.4596 | −0.910144 | ||||||||
\(369\) | −2.70928 | −0.141039 | ||||||||
\(370\) | −23.7464 | −1.23452 | ||||||||
\(371\) | 1.34632 | 0.0698972 | ||||||||
\(372\) | 1.67420 | 0.0868034 | ||||||||
\(373\) | −13.6865 | −0.708660 | −0.354330 | − | 0.935121i | \(-0.615291\pi\) | ||||
−0.354330 | + | 0.935121i | \(0.615291\pi\) | |||||||
\(374\) | 20.5958 | 1.06498 | ||||||||
\(375\) | −6.52359 | −0.336877 | ||||||||
\(376\) | −114.368 | −5.89806 | ||||||||
\(377\) | 13.3607 | 0.688111 | ||||||||
\(378\) | 12.1834 | 0.626647 | ||||||||
\(379\) | 28.0989 | 1.44334 | 0.721672 | − | 0.692235i | \(-0.243374\pi\) | ||||
0.721672 | + | 0.692235i | \(0.243374\pi\) | |||||||
\(380\) | −16.4391 | −0.843306 | ||||||||
\(381\) | 1.47641 | 0.0756388 | ||||||||
\(382\) | 50.2667 | 2.57187 | ||||||||
\(383\) | −18.4547 | −0.942989 | −0.471495 | − | 0.881869i | \(-0.656285\pi\) | ||||
−0.471495 | + | 0.881869i | \(0.656285\pi\) | |||||||
\(384\) | −15.4030 | −0.786029 | ||||||||
\(385\) | 9.49079 | 0.483695 | ||||||||
\(386\) | 30.5113 | 1.55298 | ||||||||
\(387\) | −6.34017 | −0.322289 | ||||||||
\(388\) | 22.1978 | 1.12692 | ||||||||
\(389\) | 21.8310 | 1.10687 | 0.553437 | − | 0.832891i | \(-0.313316\pi\) | ||||
0.553437 | + | 0.832891i | \(0.313316\pi\) | |||||||
\(390\) | 10.8371 | 0.548758 | ||||||||
\(391\) | 2.52359 | 0.127623 | ||||||||
\(392\) | 44.0349 | 2.22410 | ||||||||
\(393\) | 0.948284 | 0.0478346 | ||||||||
\(394\) | −22.3279 | −1.12486 | ||||||||
\(395\) | 25.4329 | 1.27967 | ||||||||
\(396\) | −54.9926 | −2.76348 | ||||||||
\(397\) | 5.81658 | 0.291926 | 0.145963 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145963 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(398\) | −24.2856 | −1.21733 | ||||||||
\(399\) | −1.41855 | −0.0710164 | ||||||||
\(400\) | −28.7587 | −1.43794 | ||||||||
\(401\) | −25.5402 | −1.27542 | −0.637709 | − | 0.770277i | \(-0.720118\pi\) | ||||
−0.637709 | + | 0.770277i | \(0.720118\pi\) | |||||||
\(402\) | 5.55252 | 0.276935 | ||||||||
\(403\) | −2.52359 | −0.125709 | ||||||||
\(404\) | 90.8925 | 4.52207 | ||||||||
\(405\) | 11.0556 | 0.549357 | ||||||||
\(406\) | 12.1834 | 0.604653 | ||||||||
\(407\) | 19.4908 | 0.966122 | ||||||||
\(408\) | 9.75872 | 0.483129 | ||||||||
\(409\) | −9.44134 | −0.466844 | −0.233422 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233422 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(410\) | −4.63090 | −0.228704 | ||||||||
\(411\) | 5.56093 | 0.274300 | ||||||||
\(412\) | 88.6246 | 4.36622 | ||||||||
\(413\) | −7.68649 | −0.378227 | ||||||||
\(414\) | −9.26180 | −0.455192 | ||||||||
\(415\) | −3.68649 | −0.180963 | ||||||||
\(416\) | 84.1543 | 4.12600 | ||||||||
\(417\) | −11.0061 | −0.538973 | ||||||||
\(418\) | 18.5464 | 0.907133 | ||||||||
\(419\) | 33.0082 | 1.61256 | 0.806279 | − | 0.591536i | \(-0.201478\pi\) | ||||
0.806279 | + | 0.591536i | \(0.201478\pi\) | |||||||
\(420\) | 7.18956 | 0.350815 | ||||||||
\(421\) | −10.5958 | −0.516409 | −0.258204 | − | 0.966090i | \(-0.583131\pi\) | ||||
−0.258204 | + | 0.966090i | \(0.583131\pi\) | |||||||
\(422\) | −39.1617 | −1.90636 | ||||||||
\(423\) | −34.2401 | −1.66481 | ||||||||
\(424\) | −8.34017 | −0.405035 | ||||||||
\(425\) | 4.15676 | 0.201632 | ||||||||
\(426\) | 1.78151 | 0.0863144 | ||||||||
\(427\) | −11.3340 | −0.548492 | ||||||||
\(428\) | −79.2327 | −3.82986 | ||||||||
\(429\) | −8.89496 | −0.429453 | ||||||||
\(430\) | −10.8371 | −0.522611 | ||||||||
\(431\) | −10.7070 | −0.515738 | −0.257869 | − | 0.966180i | \(-0.583020\pi\) | ||||
−0.257869 | + | 0.966180i | \(0.583020\pi\) | |||||||
\(432\) | −42.5958 | −2.04939 | ||||||||
\(433\) | 25.5708 | 1.22885 | 0.614426 | − | 0.788974i | \(-0.289387\pi\) | ||||
0.614426 | + | 0.788974i | \(0.289387\pi\) | |||||||
\(434\) | −2.30122 | −0.110462 | ||||||||
\(435\) | −2.83710 | −0.136029 | ||||||||
\(436\) | 59.6886 | 2.85856 | ||||||||
\(437\) | 2.27247 | 0.108707 | ||||||||
\(438\) | −17.0205 | −0.813272 | ||||||||
\(439\) | 29.5064 | 1.40826 | 0.704131 | − | 0.710070i | \(-0.251337\pi\) | ||||
0.704131 | + | 0.710070i | \(0.251337\pi\) | |||||||
\(440\) | −58.7936 | −2.80288 | ||||||||
\(441\) | 13.1834 | 0.627782 | ||||||||
\(442\) | −23.5174 | −1.11861 | ||||||||
\(443\) | 20.3980 | 0.969140 | 0.484570 | − | 0.874753i | \(-0.338976\pi\) | ||||
0.484570 | + | 0.874753i | \(0.338976\pi\) | |||||||
\(444\) | 14.7649 | 0.700710 | ||||||||
\(445\) | −20.4124 | −0.967641 | ||||||||
\(446\) | −18.5236 | −0.877117 | ||||||||
\(447\) | 4.01438 | 0.189873 | ||||||||
\(448\) | 36.3123 | 1.71559 | ||||||||
\(449\) | 13.6020 | 0.641917 | 0.320958 | − | 0.947093i | \(-0.395995\pi\) | ||||
0.320958 | + | 0.947093i | \(0.395995\pi\) | |||||||
\(450\) | −15.2557 | −0.719158 | ||||||||
\(451\) | 3.80098 | 0.178981 | ||||||||
\(452\) | −4.34858 | −0.204540 | ||||||||
\(453\) | 9.86603 | 0.463547 | ||||||||
\(454\) | 14.1412 | 0.663677 | ||||||||
\(455\) | −10.8371 | −0.508051 | ||||||||
\(456\) | 8.78765 | 0.411520 | ||||||||
\(457\) | 8.52359 | 0.398717 | 0.199358 | − | 0.979927i | \(-0.436114\pi\) | ||||
0.199358 | + | 0.979927i | \(0.436114\pi\) | |||||||
\(458\) | 46.9627 | 2.19442 | ||||||||
\(459\) | 6.15676 | 0.287373 | ||||||||
\(460\) | −11.5174 | −0.537004 | ||||||||
\(461\) | −0.348583 | −0.0162352 | −0.00811758 | − | 0.999967i | \(-0.502584\pi\) | ||||
−0.00811758 | + | 0.999967i | \(0.502584\pi\) | |||||||
\(462\) | −8.11118 | −0.377366 | ||||||||
\(463\) | 19.2918 | 0.896565 | 0.448282 | − | 0.893892i | \(-0.352036\pi\) | ||||
0.448282 | + | 0.893892i | \(0.352036\pi\) | |||||||
\(464\) | −42.5958 | −1.97746 | ||||||||
\(465\) | 0.535877 | 0.0248507 | ||||||||
\(466\) | −57.4473 | −2.66119 | ||||||||
\(467\) | −23.4186 | −1.08368 | −0.541841 | − | 0.840481i | \(-0.682272\pi\) | ||||
−0.541841 | + | 0.840481i | \(0.682272\pi\) | |||||||
\(468\) | 62.7936 | 2.90264 | ||||||||
\(469\) | −5.55252 | −0.256392 | ||||||||
\(470\) | −58.5257 | −2.69959 | ||||||||
\(471\) | −6.82273 | −0.314375 | ||||||||
\(472\) | 47.6163 | 2.19172 | ||||||||
\(473\) | 8.89496 | 0.408991 | ||||||||
\(474\) | −21.7359 | −0.998365 | ||||||||
\(475\) | 3.74313 | 0.171746 | ||||||||
\(476\) | −15.6020 | −0.715115 | ||||||||
\(477\) | −2.49693 | −0.114327 | ||||||||
\(478\) | −11.8010 | −0.539764 | ||||||||
\(479\) | 3.98440 | 0.182052 | 0.0910260 | − | 0.995849i | \(-0.470985\pi\) | ||||
0.0910260 | + | 0.995849i | \(0.470985\pi\) | |||||||
\(480\) | −17.8699 | −0.815646 | ||||||||
\(481\) | −22.2557 | −1.01477 | ||||||||
\(482\) | −20.0267 | −0.912189 | ||||||||
\(483\) | −0.993857 | −0.0452221 | ||||||||
\(484\) | 18.4101 | 0.836825 | ||||||||
\(485\) | 7.10504 | 0.322623 | ||||||||
\(486\) | −34.4690 | −1.56355 | ||||||||
\(487\) | −36.4268 | −1.65066 | −0.825328 | − | 0.564654i | \(-0.809010\pi\) | ||||
−0.825328 | + | 0.564654i | \(0.809010\pi\) | |||||||
\(488\) | 70.2122 | 3.17836 | ||||||||
\(489\) | −6.83710 | −0.309184 | ||||||||
\(490\) | 22.5341 | 1.01799 | ||||||||
\(491\) | −11.7321 | −0.529461 | −0.264730 | − | 0.964323i | \(-0.585283\pi\) | ||||
−0.264730 | + | 0.964323i | \(0.585283\pi\) | |||||||
\(492\) | 2.87936 | 0.129812 | ||||||||
\(493\) | 6.15676 | 0.277286 | ||||||||
\(494\) | −21.1773 | −0.952811 | ||||||||
\(495\) | −17.6020 | −0.791150 | ||||||||
\(496\) | 8.04557 | 0.361257 | ||||||||
\(497\) | −1.78151 | −0.0799116 | ||||||||
\(498\) | 3.15061 | 0.141182 | ||||||||
\(499\) | 16.5392 | 0.740396 | 0.370198 | − | 0.928953i | \(-0.379290\pi\) | ||||
0.370198 | + | 0.928953i | \(0.379290\pi\) | |||||||
\(500\) | −64.6102 | −2.88946 | ||||||||
\(501\) | −5.36910 | −0.239874 | ||||||||
\(502\) | 48.1133 | 2.14740 | ||||||||
\(503\) | −31.1617 | −1.38943 | −0.694715 | − | 0.719285i | \(-0.744470\pi\) | ||||
−0.694715 | + | 0.719285i | \(0.744470\pi\) | |||||||
\(504\) | 35.8154 | 1.59534 | ||||||||
\(505\) | 29.0928 | 1.29461 | ||||||||
\(506\) | 12.9939 | 0.577647 | ||||||||
\(507\) | 3.14730 | 0.139777 | ||||||||
\(508\) | 14.6225 | 0.648768 | ||||||||
\(509\) | −16.0267 | −0.710369 | −0.355185 | − | 0.934796i | \(-0.615582\pi\) | ||||
−0.355185 | + | 0.934796i | \(0.615582\pi\) | |||||||
\(510\) | 4.99386 | 0.221132 | ||||||||
\(511\) | 17.0205 | 0.752943 | ||||||||
\(512\) | −17.8599 | −0.789303 | ||||||||
\(513\) | 5.54411 | 0.244778 | ||||||||
\(514\) | −61.7152 | −2.72214 | ||||||||
\(515\) | 28.3668 | 1.24999 | ||||||||
\(516\) | 6.73820 | 0.296633 | ||||||||
\(517\) | 48.0372 | 2.11267 | ||||||||
\(518\) | −20.2946 | −0.891694 | ||||||||
\(519\) | −6.55479 | −0.287723 | ||||||||
\(520\) | 67.1338 | 2.94401 | ||||||||
\(521\) | 2.41241 | 0.105689 | 0.0528447 | − | 0.998603i | \(-0.483171\pi\) | ||||
0.0528447 | + | 0.998603i | \(0.483171\pi\) | |||||||
\(522\) | −22.5958 | −0.988992 | ||||||||
\(523\) | −22.7214 | −0.993537 | −0.496768 | − | 0.867883i | \(-0.665480\pi\) | ||||
−0.496768 | + | 0.867883i | \(0.665480\pi\) | |||||||
\(524\) | 9.39189 | 0.410287 | ||||||||
\(525\) | −1.63704 | −0.0714463 | ||||||||
\(526\) | −41.8031 | −1.82270 | ||||||||
\(527\) | −1.16290 | −0.0506567 | ||||||||
\(528\) | 28.3584 | 1.23414 | ||||||||
\(529\) | −21.4079 | −0.930777 | ||||||||
\(530\) | −4.26794 | −0.185387 | ||||||||
\(531\) | 14.2557 | 0.618643 | ||||||||
\(532\) | −14.0494 | −0.609121 | ||||||||
\(533\) | −4.34017 | −0.187994 | ||||||||
\(534\) | 17.4452 | 0.754928 | ||||||||
\(535\) | −25.3607 | −1.09644 | ||||||||
\(536\) | 34.3968 | 1.48572 | ||||||||
\(537\) | 10.3174 | 0.445228 | ||||||||
\(538\) | 27.8576 | 1.20103 | ||||||||
\(539\) | −18.4957 | −0.796666 | ||||||||
\(540\) | −28.0989 | −1.20918 | ||||||||
\(541\) | −21.3256 | −0.916860 | −0.458430 | − | 0.888731i | \(-0.651588\pi\) | ||||
−0.458430 | + | 0.888731i | \(0.651588\pi\) | |||||||
\(542\) | −9.26180 | −0.397828 | ||||||||
\(543\) | −8.32789 | −0.357384 | ||||||||
\(544\) | 38.7792 | 1.66265 | ||||||||
\(545\) | 19.1050 | 0.818370 | ||||||||
\(546\) | 9.26180 | 0.396368 | ||||||||
\(547\) | −21.4875 | −0.918738 | −0.459369 | − | 0.888246i | \(-0.651924\pi\) | ||||
−0.459369 | + | 0.888246i | \(0.651924\pi\) | |||||||
\(548\) | 55.0759 | 2.35273 | ||||||||
\(549\) | 21.0205 | 0.897134 | ||||||||
\(550\) | 21.4030 | 0.912625 | ||||||||
\(551\) | 5.54411 | 0.236187 | ||||||||
\(552\) | 6.15676 | 0.262049 | ||||||||
\(553\) | 21.7359 | 0.924306 | ||||||||
\(554\) | −25.7237 | −1.09289 | ||||||||
\(555\) | 4.72592 | 0.200604 | ||||||||
\(556\) | −109.006 | −4.62288 | ||||||||
\(557\) | −6.08452 | −0.257809 | −0.128905 | − | 0.991657i | \(-0.541146\pi\) | ||||
−0.128905 | + | 0.991657i | \(0.541146\pi\) | |||||||
\(558\) | 4.26794 | 0.180676 | ||||||||
\(559\) | −10.1568 | −0.429585 | ||||||||
\(560\) | 34.5503 | 1.46001 | ||||||||
\(561\) | −4.09890 | −0.173056 | ||||||||
\(562\) | −14.4124 | −0.607951 | ||||||||
\(563\) | 41.4752 | 1.74797 | 0.873985 | − | 0.485952i | \(-0.161527\pi\) | ||||
0.873985 | + | 0.485952i | \(0.161527\pi\) | |||||||
\(564\) | 36.3896 | 1.53228 | ||||||||
\(565\) | −1.39189 | −0.0585572 | ||||||||
\(566\) | 8.26794 | 0.347527 | ||||||||
\(567\) | 9.44852 | 0.396801 | ||||||||
\(568\) | 11.0361 | 0.463065 | ||||||||
\(569\) | 0.447480 | 0.0187593 | 0.00937967 | − | 0.999956i | \(-0.497014\pi\) | ||||
0.00937967 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(570\) | 4.49693 | 0.188356 | ||||||||
\(571\) | −33.4440 | −1.39959 | −0.699794 | − | 0.714345i | \(-0.746725\pi\) | ||||
−0.699794 | + | 0.714345i | \(0.746725\pi\) | |||||||
\(572\) | −88.0965 | −3.68350 | ||||||||
\(573\) | −10.0039 | −0.417918 | ||||||||
\(574\) | −3.95774 | −0.165193 | ||||||||
\(575\) | 2.62249 | 0.109365 | ||||||||
\(576\) | −67.3461 | −2.80609 | ||||||||
\(577\) | 3.67420 | 0.152959 | 0.0764795 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764795 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(578\) | 35.2206 | 1.46498 | ||||||||
\(579\) | −6.07223 | −0.252353 | ||||||||
\(580\) | −28.0989 | −1.16674 | ||||||||
\(581\) | −3.15061 | −0.130709 | ||||||||
\(582\) | −6.07223 | −0.251702 | ||||||||
\(583\) | 3.50307 | 0.145082 | ||||||||
\(584\) | −105.439 | −4.36309 | ||||||||
\(585\) | 20.0989 | 0.830987 | ||||||||
\(586\) | 24.7070 | 1.02064 | ||||||||
\(587\) | −5.46081 | −0.225392 | −0.112696 | − | 0.993630i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993630i | \(0.535949\pi\) | |||||||
\(588\) | −14.0111 | −0.577807 | ||||||||
\(589\) | −1.04718 | −0.0431483 | ||||||||
\(590\) | 24.3668 | 1.00317 | ||||||||
\(591\) | 4.44360 | 0.182785 | ||||||||
\(592\) | 70.9542 | 2.91620 | ||||||||
\(593\) | −45.9299 | −1.88611 | −0.943057 | − | 0.332632i | \(-0.892063\pi\) | ||||
−0.943057 | + | 0.332632i | \(0.892063\pi\) | |||||||
\(594\) | 31.7009 | 1.30070 | ||||||||
\(595\) | −4.99386 | −0.204728 | ||||||||
\(596\) | 39.7587 | 1.62858 | ||||||||
\(597\) | 4.83323 | 0.197811 | ||||||||
\(598\) | −14.8371 | −0.606734 | ||||||||
\(599\) | 9.14608 | 0.373699 | 0.186849 | − | 0.982389i | \(-0.440172\pi\) | ||||
0.186849 | + | 0.982389i | \(0.440172\pi\) | |||||||
\(600\) | 10.1412 | 0.414011 | ||||||||
\(601\) | 27.6742 | 1.12885 | 0.564427 | − | 0.825483i | \(-0.309097\pi\) | ||||
0.564427 | + | 0.825483i | \(0.309097\pi\) | |||||||
\(602\) | −9.26180 | −0.377483 | ||||||||
\(603\) | 10.2979 | 0.419363 | ||||||||
\(604\) | 97.7140 | 3.97593 | ||||||||
\(605\) | 5.89269 | 0.239572 | ||||||||
\(606\) | −24.8638 | −1.01002 | ||||||||
\(607\) | 14.8515 | 0.602803 | 0.301401 | − | 0.953497i | \(-0.402546\pi\) | ||||
0.301401 | + | 0.953497i | \(0.402546\pi\) | |||||||
\(608\) | 34.9204 | 1.41621 | ||||||||
\(609\) | −2.42469 | −0.0982536 | ||||||||
\(610\) | 35.9299 | 1.45476 | ||||||||
\(611\) | −54.8515 | −2.21905 | ||||||||
\(612\) | 28.9360 | 1.16967 | ||||||||
\(613\) | 22.0228 | 0.889492 | 0.444746 | − | 0.895657i | \(-0.353294\pi\) | ||||
0.444746 | + | 0.895657i | \(0.353294\pi\) | |||||||
\(614\) | 58.9504 | 2.37904 | ||||||||
\(615\) | 0.921622 | 0.0371634 | ||||||||
\(616\) | −50.2472 | −2.02452 | ||||||||
\(617\) | 40.8371 | 1.64404 | 0.822020 | − | 0.569459i | \(-0.192847\pi\) | ||||
0.822020 | + | 0.569459i | \(0.192847\pi\) | |||||||
\(618\) | −24.2434 | −0.975211 | ||||||||
\(619\) | 41.4596 | 1.66640 | 0.833201 | − | 0.552971i | \(-0.186506\pi\) | ||||
0.833201 | + | 0.552971i | \(0.186506\pi\) | |||||||
\(620\) | 5.30737 | 0.213149 | ||||||||
\(621\) | 3.88428 | 0.155871 | ||||||||
\(622\) | 23.4752 | 0.941269 | ||||||||
\(623\) | −17.4452 | −0.698928 | ||||||||
\(624\) | −32.3812 | −1.29629 | ||||||||
\(625\) | −10.2885 | −0.411538 | ||||||||
\(626\) | 83.3894 | 3.33291 | ||||||||
\(627\) | −3.69102 | −0.147405 | ||||||||
\(628\) | −67.5729 | −2.69645 | ||||||||
\(629\) | −10.2557 | −0.408920 | ||||||||
\(630\) | 18.3279 | 0.730200 | ||||||||
\(631\) | 22.5236 | 0.896650 | 0.448325 | − | 0.893871i | \(-0.352021\pi\) | ||||
0.448325 | + | 0.893871i | \(0.352021\pi\) | |||||||
\(632\) | −134.650 | −5.35609 | ||||||||
\(633\) | 7.79380 | 0.309776 | ||||||||
\(634\) | 2.22899 | 0.0885245 | ||||||||
\(635\) | 4.68035 | 0.185734 | ||||||||
\(636\) | 2.65368 | 0.105225 | ||||||||
\(637\) | 21.1194 | 0.836782 | ||||||||
\(638\) | 31.7009 | 1.25505 | ||||||||
\(639\) | 3.30406 | 0.130706 | ||||||||
\(640\) | −48.8287 | −1.93012 | ||||||||
\(641\) | −3.26180 | −0.128833 | −0.0644166 | − | 0.997923i | \(-0.520519\pi\) | ||||
−0.0644166 | + | 0.997923i | \(0.520519\pi\) | |||||||
\(642\) | 21.6742 | 0.855413 | ||||||||
\(643\) | −24.6114 | −0.970580 | −0.485290 | − | 0.874353i | \(-0.661286\pi\) | ||||
−0.485290 | + | 0.874353i | \(0.661286\pi\) | |||||||
\(644\) | −9.84324 | −0.387878 | ||||||||
\(645\) | 2.15676 | 0.0849222 | ||||||||
\(646\) | −9.75872 | −0.383952 | ||||||||
\(647\) | −5.56093 | −0.218623 | −0.109311 | − | 0.994008i | \(-0.534865\pi\) | ||||
−0.109311 | + | 0.994008i | \(0.534865\pi\) | |||||||
\(648\) | −58.5318 | −2.29935 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | −24.4391 | −0.958579 | ||||||||
\(651\) | 0.457980 | 0.0179497 | ||||||||
\(652\) | −67.7152 | −2.65193 | ||||||||
\(653\) | −19.4908 | −0.762733 | −0.381367 | − | 0.924424i | \(-0.624546\pi\) | ||||
−0.381367 | + | 0.924424i | \(0.624546\pi\) | |||||||
\(654\) | −16.3279 | −0.638471 | ||||||||
\(655\) | 3.00614 | 0.117460 | ||||||||
\(656\) | 13.8371 | 0.540248 | ||||||||
\(657\) | −31.5669 | −1.23154 | ||||||||
\(658\) | −50.0183 | −1.94991 | ||||||||
\(659\) | −30.5946 | −1.19180 | −0.595898 | − | 0.803060i | \(-0.703204\pi\) | ||||
−0.595898 | + | 0.803060i | \(0.703204\pi\) | |||||||
\(660\) | 18.7070 | 0.728169 | ||||||||
\(661\) | 9.76260 | 0.379721 | 0.189861 | − | 0.981811i | \(-0.439196\pi\) | ||||
0.189861 | + | 0.981811i | \(0.439196\pi\) | |||||||
\(662\) | −60.7514 | −2.36117 | ||||||||
\(663\) | 4.68035 | 0.181770 | ||||||||
\(664\) | 19.5174 | 0.757424 | ||||||||
\(665\) | −4.49693 | −0.174383 | ||||||||
\(666\) | 37.6391 | 1.45849 | ||||||||
\(667\) | 3.88428 | 0.150400 | ||||||||
\(668\) | −53.1761 | −2.05744 | ||||||||
\(669\) | 3.68649 | 0.142528 | ||||||||
\(670\) | 17.6020 | 0.680023 | ||||||||
\(671\) | −29.4908 | −1.13848 | ||||||||
\(672\) | −15.2723 | −0.589142 | ||||||||
\(673\) | 6.94828 | 0.267837 | 0.133918 | − | 0.990992i | \(-0.457244\pi\) | ||||
0.133918 | + | 0.990992i | \(0.457244\pi\) | |||||||
\(674\) | 72.3461 | 2.78667 | ||||||||
\(675\) | 6.39803 | 0.246260 | ||||||||
\(676\) | 31.1711 | 1.19889 | ||||||||
\(677\) | −22.0060 | −0.845758 | −0.422879 | − | 0.906186i | \(-0.638980\pi\) | ||||
−0.422879 | + | 0.906186i | \(0.638980\pi\) | |||||||
\(678\) | 1.18956 | 0.0456848 | ||||||||
\(679\) | 6.07223 | 0.233031 | ||||||||
\(680\) | 30.9360 | 1.18634 | ||||||||
\(681\) | −2.81432 | −0.107845 | ||||||||
\(682\) | −5.98771 | −0.229281 | ||||||||
\(683\) | 21.2339 | 0.812493 | 0.406247 | − | 0.913764i | \(-0.366837\pi\) | ||||
0.406247 | + | 0.913764i | \(0.366837\pi\) | |||||||
\(684\) | 26.0566 | 0.996300 | ||||||||
\(685\) | 17.6286 | 0.673555 | ||||||||
\(686\) | 46.9627 | 1.79304 | ||||||||
\(687\) | −9.34632 | −0.356584 | ||||||||
\(688\) | 32.3812 | 1.23452 | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 3.15061 | 0.119942 | ||||||||
\(691\) | −8.27125 | −0.314653 | −0.157327 | − | 0.987547i | \(-0.550288\pi\) | ||||
−0.157327 | + | 0.987547i | \(0.550288\pi\) | |||||||
\(692\) | −64.9192 | −2.46786 | ||||||||
\(693\) | −15.0433 | −0.571448 | ||||||||
\(694\) | −36.3123 | −1.37840 | ||||||||
\(695\) | −34.8904 | −1.32347 | ||||||||
\(696\) | 15.0205 | 0.569351 | ||||||||
\(697\) | −2.00000 | −0.0757554 | ||||||||
\(698\) | 38.7175 | 1.46548 | ||||||||
\(699\) | 11.4329 | 0.432433 | ||||||||
\(700\) | −16.2134 | −0.612809 | ||||||||
\(701\) | −23.1857 | −0.875711 | −0.437856 | − | 0.899045i | \(-0.644262\pi\) | ||||
−0.437856 | + | 0.899045i | \(0.644262\pi\) | |||||||
\(702\) | −36.1978 | −1.36620 | ||||||||
\(703\) | −9.23513 | −0.348310 | ||||||||
\(704\) | 94.4834 | 3.56098 | ||||||||
\(705\) | 11.6475 | 0.438672 | ||||||||
\(706\) | 47.3979 | 1.78384 | ||||||||
\(707\) | 24.8638 | 0.935098 | ||||||||
\(708\) | −15.1506 | −0.569395 | ||||||||
\(709\) | 34.0144 | 1.27744 | 0.638718 | − | 0.769441i | \(-0.279465\pi\) | ||||
0.638718 | + | 0.769441i | \(0.279465\pi\) | |||||||
\(710\) | 5.64754 | 0.211948 | ||||||||
\(711\) | −40.3123 | −1.51183 | ||||||||
\(712\) | 108.070 | 4.05009 | ||||||||
\(713\) | −0.733670 | −0.0274762 | ||||||||
\(714\) | 4.26794 | 0.159724 | ||||||||
\(715\) | −28.1978 | −1.05454 | ||||||||
\(716\) | 102.184 | 3.81881 | ||||||||
\(717\) | 2.34858 | 0.0877095 | ||||||||
\(718\) | −43.8843 | −1.63775 | ||||||||
\(719\) | −29.2872 | −1.09223 | −0.546115 | − | 0.837710i | \(-0.683894\pi\) | ||||
−0.546115 | + | 0.837710i | \(0.683894\pi\) | |||||||
\(720\) | −64.0782 | −2.38805 | ||||||||
\(721\) | 24.2434 | 0.902870 | ||||||||
\(722\) | 42.6886 | 1.58870 | ||||||||
\(723\) | 3.98562 | 0.148227 | ||||||||
\(724\) | −82.4801 | −3.06535 | ||||||||
\(725\) | 6.39803 | 0.237617 | ||||||||
\(726\) | −5.03612 | −0.186908 | ||||||||
\(727\) | −26.6791 | −0.989474 | −0.494737 | − | 0.869043i | \(-0.664736\pi\) | ||||
−0.494737 | + | 0.869043i | \(0.664736\pi\) | |||||||
\(728\) | 57.3751 | 2.12646 | ||||||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | −53.9565 | −1.99702 | ||||||||
\(731\) | −4.68035 | −0.173109 | ||||||||
\(732\) | −22.3402 | −0.825717 | ||||||||
\(733\) | 38.6491 | 1.42754 | 0.713769 | − | 0.700381i | \(-0.246986\pi\) | ||||
0.713769 | + | 0.700381i | \(0.246986\pi\) | |||||||
\(734\) | 16.1834 | 0.597341 | ||||||||
\(735\) | −4.48464 | −0.165419 | ||||||||
\(736\) | 24.4657 | 0.901819 | ||||||||
\(737\) | −14.4475 | −0.532180 | ||||||||
\(738\) | 7.34017 | 0.270196 | ||||||||
\(739\) | 26.1568 | 0.962192 | 0.481096 | − | 0.876668i | \(-0.340239\pi\) | ||||
0.481096 | + | 0.876668i | \(0.340239\pi\) | |||||||
\(740\) | 46.8059 | 1.72062 | ||||||||
\(741\) | 4.21461 | 0.154828 | ||||||||
\(742\) | −3.64754 | −0.133905 | ||||||||
\(743\) | −18.5548 | −0.680709 | −0.340355 | − | 0.940297i | \(-0.610547\pi\) | ||||
−0.340355 | + | 0.940297i | \(0.610547\pi\) | |||||||
\(744\) | −2.83710 | −0.104013 | ||||||||
\(745\) | 12.7259 | 0.466242 | ||||||||
\(746\) | 37.0805 | 1.35761 | ||||||||
\(747\) | 5.84324 | 0.213793 | ||||||||
\(748\) | −40.5958 | −1.48433 | ||||||||
\(749\) | −21.6742 | −0.791958 | ||||||||
\(750\) | 17.6742 | 0.645371 | ||||||||
\(751\) | 23.0361 | 0.840600 | 0.420300 | − | 0.907385i | \(-0.361925\pi\) | ||||
0.420300 | + | 0.907385i | \(0.361925\pi\) | |||||||
\(752\) | 174.874 | 6.37702 | ||||||||
\(753\) | −9.57531 | −0.348944 | ||||||||
\(754\) | −36.1978 | −1.31825 | ||||||||
\(755\) | 31.2762 | 1.13826 | ||||||||
\(756\) | −24.0144 | −0.873394 | ||||||||
\(757\) | −37.5851 | −1.36606 | −0.683028 | − | 0.730392i | \(-0.739337\pi\) | ||||
−0.683028 | + | 0.730392i | \(0.739337\pi\) | |||||||
\(758\) | −76.1276 | −2.76508 | ||||||||
\(759\) | −2.58598 | −0.0938653 | ||||||||
\(760\) | 27.8576 | 1.01050 | ||||||||
\(761\) | 5.39576 | 0.195596 | 0.0977982 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977982 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 16.3279 | 0.591109 | ||||||||
\(764\) | −99.0792 | −3.58456 | ||||||||
\(765\) | 9.26180 | 0.334861 | ||||||||
\(766\) | 49.9988 | 1.80653 | ||||||||
\(767\) | 22.8371 | 0.824600 | ||||||||
\(768\) | 14.9249 | 0.538557 | ||||||||
\(769\) | −6.19779 | −0.223498 | −0.111749 | − | 0.993736i | \(-0.535645\pi\) | ||||
−0.111749 | + | 0.993736i | \(0.535645\pi\) | |||||||
\(770\) | −25.7132 | −0.926638 | ||||||||
\(771\) | 12.2823 | 0.442337 | ||||||||
\(772\) | −60.1399 | −2.16448 | ||||||||
\(773\) | 17.1194 | 0.615743 | 0.307871 | − | 0.951428i | \(-0.400383\pi\) | ||||
0.307871 | + | 0.951428i | \(0.400383\pi\) | |||||||
\(774\) | 17.1773 | 0.617424 | ||||||||
\(775\) | −1.20847 | −0.0434096 | ||||||||
\(776\) | −37.6163 | −1.35035 | ||||||||
\(777\) | 4.03895 | 0.144896 | ||||||||
\(778\) | −59.1461 | −2.12049 | ||||||||
\(779\) | −1.80098 | −0.0645270 | ||||||||
\(780\) | −21.3607 | −0.764835 | ||||||||
\(781\) | −4.63543 | −0.165869 | ||||||||
\(782\) | −6.83710 | −0.244494 | ||||||||
\(783\) | 9.47641 | 0.338659 | ||||||||
\(784\) | −67.3318 | −2.40471 | ||||||||
\(785\) | −21.6286 | −0.771959 | ||||||||
\(786\) | −2.56916 | −0.0916390 | ||||||||
\(787\) | 0.595825 | 0.0212389 | 0.0106194 | − | 0.999944i | \(-0.496620\pi\) | ||||
0.0106194 | + | 0.999944i | \(0.496620\pi\) | |||||||
\(788\) | 44.0098 | 1.56779 | ||||||||
\(789\) | 8.31948 | 0.296181 | ||||||||
\(790\) | −68.9048 | −2.45152 | ||||||||
\(791\) | −1.18956 | −0.0422959 | ||||||||
\(792\) | 93.1904 | 3.31138 | ||||||||
\(793\) | 33.6742 | 1.19581 | ||||||||
\(794\) | −15.7587 | −0.559256 | ||||||||
\(795\) | 0.849388 | 0.0301247 | ||||||||
\(796\) | 47.8687 | 1.69666 | ||||||||
\(797\) | 13.9155 | 0.492912 | 0.246456 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246456 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(798\) | 3.84324 | 0.136049 | ||||||||
\(799\) | −25.2762 | −0.894207 | ||||||||
\(800\) | 40.2990 | 1.42478 | ||||||||
\(801\) | 32.3545 | 1.14319 | ||||||||
\(802\) | 69.1955 | 2.44338 | ||||||||
\(803\) | 44.2868 | 1.56285 | ||||||||
\(804\) | −10.9444 | −0.385980 | ||||||||
\(805\) | −3.15061 | −0.111044 | ||||||||
\(806\) | 6.83710 | 0.240827 | ||||||||
\(807\) | −5.54411 | −0.195162 | ||||||||
\(808\) | −154.026 | −5.41863 | ||||||||
\(809\) | −36.1568 | −1.27120 | −0.635602 | − | 0.772017i | \(-0.719248\pi\) | ||||
−0.635602 | + | 0.772017i | \(0.719248\pi\) | |||||||
\(810\) | −29.9526 | −1.05243 | ||||||||
\(811\) | −8.76487 | −0.307776 | −0.153888 | − | 0.988088i | \(-0.549180\pi\) | ||||
−0.153888 | + | 0.988088i | \(0.549180\pi\) | |||||||
\(812\) | −24.0144 | −0.842739 | ||||||||
\(813\) | 1.84324 | 0.0646454 | ||||||||
\(814\) | −52.8059 | −1.85085 | ||||||||
\(815\) | −21.6742 | −0.759214 | ||||||||
\(816\) | −14.9216 | −0.522361 | ||||||||
\(817\) | −4.21461 | −0.147451 | ||||||||
\(818\) | 25.5792 | 0.894355 | ||||||||
\(819\) | 17.1773 | 0.600223 | ||||||||
\(820\) | 9.12783 | 0.318758 | ||||||||
\(821\) | −28.8599 | −1.00722 | −0.503609 | − | 0.863932i | \(-0.667995\pi\) | ||||
−0.503609 | + | 0.863932i | \(0.667995\pi\) | |||||||
\(822\) | −15.0661 | −0.525490 | ||||||||
\(823\) | 21.7165 | 0.756988 | 0.378494 | − | 0.925604i | \(-0.376442\pi\) | ||||
0.378494 | + | 0.925604i | \(0.376442\pi\) | |||||||
\(824\) | −150.183 | −5.23187 | ||||||||
\(825\) | −4.25953 | −0.148298 | ||||||||
\(826\) | 20.8248 | 0.724588 | ||||||||
\(827\) | 24.0156 | 0.835104 | 0.417552 | − | 0.908653i | \(-0.362888\pi\) | ||||
0.417552 | + | 0.908653i | \(0.362888\pi\) | |||||||
\(828\) | 18.2557 | 0.634428 | ||||||||
\(829\) | −0.187293 | −0.00650496 | −0.00325248 | − | 0.999995i | \(-0.501035\pi\) | ||||
−0.00325248 | + | 0.999995i | \(0.501035\pi\) | |||||||
\(830\) | 9.98771 | 0.346679 | ||||||||
\(831\) | 5.11942 | 0.177591 | ||||||||
\(832\) | −107.886 | −3.74029 | ||||||||
\(833\) | 9.73206 | 0.337196 | ||||||||
\(834\) | 29.8187 | 1.03254 | ||||||||
\(835\) | −17.0205 | −0.589019 | ||||||||
\(836\) | −36.5562 | −1.26432 | ||||||||
\(837\) | −1.78992 | −0.0618687 | ||||||||
\(838\) | −89.4284 | −3.08925 | ||||||||
\(839\) | −9.65860 | −0.333452 | −0.166726 | − | 0.986003i | \(-0.553320\pi\) | ||||
−0.166726 | + | 0.986003i | \(0.553320\pi\) | |||||||
\(840\) | −12.1834 | −0.420368 | ||||||||
\(841\) | −19.5236 | −0.673227 | ||||||||
\(842\) | 28.7070 | 0.989309 | ||||||||
\(843\) | 2.86830 | 0.0987894 | ||||||||
\(844\) | 77.1904 | 2.65700 | ||||||||
\(845\) | 9.97721 | 0.343227 | ||||||||
\(846\) | 92.7657 | 3.18935 | ||||||||
\(847\) | 5.03612 | 0.173043 | ||||||||
\(848\) | 12.7526 | 0.437925 | ||||||||
\(849\) | −1.64545 | −0.0564717 | ||||||||
\(850\) | −11.2618 | −0.386276 | ||||||||
\(851\) | −6.47027 | −0.221798 | ||||||||
\(852\) | −3.51148 | −0.120301 | ||||||||
\(853\) | 25.0882 | 0.859004 | 0.429502 | − | 0.903066i | \(-0.358689\pi\) | ||||
0.429502 | + | 0.903066i | \(0.358689\pi\) | |||||||
\(854\) | 30.7070 | 1.05077 | ||||||||
\(855\) | 8.34017 | 0.285228 | ||||||||
\(856\) | 134.268 | 4.58917 | ||||||||
\(857\) | 41.9604 | 1.43334 | 0.716670 | − | 0.697413i | \(-0.245665\pi\) | ||||
0.716670 | + | 0.697413i | \(0.245665\pi\) | |||||||
\(858\) | 24.0989 | 0.822723 | ||||||||
\(859\) | 14.1256 | 0.481958 | 0.240979 | − | 0.970530i | \(-0.422532\pi\) | ||||
0.240979 | + | 0.970530i | \(0.422532\pi\) | |||||||
\(860\) | 21.3607 | 0.728394 | ||||||||
\(861\) | 0.787653 | 0.0268431 | ||||||||
\(862\) | 29.0082 | 0.988024 | ||||||||
\(863\) | 38.5380 | 1.31185 | 0.655924 | − | 0.754827i | \(-0.272279\pi\) | ||||
0.655924 | + | 0.754827i | \(0.272279\pi\) | |||||||
\(864\) | 59.6886 | 2.03065 | ||||||||
\(865\) | −20.7792 | −0.706515 | ||||||||
\(866\) | −69.2783 | −2.35417 | ||||||||
\(867\) | −7.00946 | −0.238054 | ||||||||
\(868\) | 4.53588 | 0.153958 | ||||||||
\(869\) | 56.5562 | 1.91854 | ||||||||
\(870\) | 7.68649 | 0.260596 | ||||||||
\(871\) | 16.4969 | 0.558977 | ||||||||
\(872\) | −101.148 | −3.42531 | ||||||||
\(873\) | −11.2618 | −0.381154 | ||||||||
\(874\) | −6.15676 | −0.208255 | ||||||||
\(875\) | −17.6742 | −0.597497 | ||||||||
\(876\) | 33.5486 | 1.13350 | ||||||||
\(877\) | −30.7936 | −1.03983 | −0.519913 | − | 0.854219i | \(-0.674036\pi\) | ||||
−0.519913 | + | 0.854219i | \(0.674036\pi\) | |||||||
\(878\) | −79.9409 | −2.69788 | ||||||||
\(879\) | −4.91709 | −0.165849 | ||||||||
\(880\) | 89.8987 | 3.03048 | ||||||||
\(881\) | 42.8248 | 1.44280 | 0.721402 | − | 0.692516i | \(-0.243498\pi\) | ||||
0.721402 | + | 0.692516i | \(0.243498\pi\) | |||||||
\(882\) | −35.7175 | −1.20267 | ||||||||
\(883\) | 48.8503 | 1.64394 | 0.821971 | − | 0.569529i | \(-0.192875\pi\) | ||||
0.821971 | + | 0.569529i | \(0.192875\pi\) | |||||||
\(884\) | 46.3545 | 1.55907 | ||||||||
\(885\) | −4.84939 | −0.163010 | ||||||||
\(886\) | −55.2639 | −1.85663 | ||||||||
\(887\) | −30.2401 | −1.01536 | −0.507681 | − | 0.861545i | \(-0.669497\pi\) | ||||
−0.507681 | + | 0.861545i | \(0.669497\pi\) | |||||||
\(888\) | −25.0205 | −0.839634 | ||||||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 55.3028 | 1.85376 | ||||||||
\(891\) | 24.5848 | 0.823621 | ||||||||
\(892\) | 36.5113 | 1.22249 | ||||||||
\(893\) | −22.7610 | −0.761668 | ||||||||
\(894\) | −10.8760 | −0.363750 | ||||||||
\(895\) | 32.7070 | 1.09327 | ||||||||
\(896\) | −41.7308 | −1.39413 | ||||||||
\(897\) | 2.95282 | 0.0985918 | ||||||||
\(898\) | −36.8515 | −1.22975 | ||||||||
\(899\) | −1.78992 | −0.0596972 | ||||||||
\(900\) | 30.0700 | 1.00233 | ||||||||
\(901\) | −1.84324 | −0.0614074 | ||||||||
\(902\) | −10.2979 | −0.342883 | ||||||||
\(903\) | 1.84324 | 0.0613393 | ||||||||
\(904\) | 7.36910 | 0.245093 | ||||||||
\(905\) | −26.4001 | −0.877570 | ||||||||
\(906\) | −26.7298 | −0.888038 | ||||||||
\(907\) | 2.86830 | 0.0952403 | 0.0476201 | − | 0.998866i | \(-0.484836\pi\) | ||||
0.0476201 | + | 0.998866i | \(0.484836\pi\) | |||||||
\(908\) | −27.8732 | −0.925005 | ||||||||
\(909\) | −46.1133 | −1.52948 | ||||||||
\(910\) | 29.3607 | 0.973297 | ||||||||
\(911\) | 10.8227 | 0.358573 | 0.179286 | − | 0.983797i | \(-0.442621\pi\) | ||||
0.179286 | + | 0.983797i | \(0.442621\pi\) | |||||||
\(912\) | −13.4368 | −0.444937 | ||||||||
\(913\) | −8.19779 | −0.271307 | ||||||||
\(914\) | −23.0928 | −0.763840 | ||||||||
\(915\) | −7.15061 | −0.236392 | ||||||||
\(916\) | −92.5667 | −3.05849 | ||||||||
\(917\) | 2.56916 | 0.0848412 | ||||||||
\(918\) | −16.6803 | −0.550533 | ||||||||
\(919\) | 50.4235 | 1.66332 | 0.831658 | − | 0.555288i | \(-0.187392\pi\) | ||||
0.831658 | + | 0.555288i | \(0.187392\pi\) | |||||||
\(920\) | 19.5174 | 0.643471 | ||||||||
\(921\) | −11.7321 | −0.386585 | ||||||||
\(922\) | 0.944409 | 0.0311024 | ||||||||
\(923\) | 5.29299 | 0.174221 | ||||||||
\(924\) | 15.9877 | 0.525957 | ||||||||
\(925\) | −10.6576 | −0.350418 | ||||||||
\(926\) | −52.2667 | −1.71759 | ||||||||
\(927\) | −44.9627 | −1.47677 | ||||||||
\(928\) | 59.6886 | 1.95937 | ||||||||
\(929\) | −36.5692 | −1.19980 | −0.599898 | − | 0.800077i | \(-0.704792\pi\) | ||||
−0.599898 | + | 0.800077i | \(0.704792\pi\) | |||||||
\(930\) | −1.45184 | −0.0476076 | ||||||||
\(931\) | 8.76364 | 0.287217 | ||||||||
\(932\) | 113.233 | 3.70906 | ||||||||
\(933\) | −4.67194 | −0.152952 | ||||||||
\(934\) | 63.4473 | 2.07606 | ||||||||
\(935\) | −12.9939 | −0.424945 | ||||||||
\(936\) | −106.410 | −3.47812 | ||||||||
\(937\) | −10.0989 | −0.329917 | −0.164958 | − | 0.986301i | \(-0.552749\pi\) | ||||
−0.164958 | + | 0.986301i | \(0.552749\pi\) | |||||||
\(938\) | 15.0433 | 0.491181 | ||||||||
\(939\) | −16.5958 | −0.541584 | ||||||||
\(940\) | 115.358 | 3.76257 | ||||||||
\(941\) | 9.94668 | 0.324252 | 0.162126 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162126 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(942\) | 18.4846 | 0.602262 | ||||||||
\(943\) | −1.26180 | −0.0410897 | ||||||||
\(944\) | −72.8080 | −2.36970 | ||||||||
\(945\) | −7.68649 | −0.250042 | ||||||||
\(946\) | −24.0989 | −0.783523 | ||||||||
\(947\) | −9.31512 | −0.302701 | −0.151350 | − | 0.988480i | \(-0.548362\pi\) | ||||
−0.151350 | + | 0.988480i | \(0.548362\pi\) | |||||||
\(948\) | 42.8431 | 1.39148 | ||||||||
\(949\) | −50.5692 | −1.64154 | ||||||||
\(950\) | −10.1412 | −0.329023 | ||||||||
\(951\) | −0.443604 | −0.0143849 | ||||||||
\(952\) | 26.4391 | 0.856895 | ||||||||
\(953\) | 8.74417 | 0.283251 | 0.141626 | − | 0.989920i | \(-0.454767\pi\) | ||||
0.141626 | + | 0.989920i | \(0.454767\pi\) | |||||||
\(954\) | 6.76487 | 0.219021 | ||||||||
\(955\) | −31.7132 | −1.02621 | ||||||||
\(956\) | 23.2606 | 0.752301 | ||||||||
\(957\) | −6.30898 | −0.203940 | ||||||||
\(958\) | −10.7948 | −0.348765 | ||||||||
\(959\) | 15.0661 | 0.486509 | ||||||||
\(960\) | 22.9093 | 0.739396 | ||||||||
\(961\) | −30.6619 | −0.989094 | ||||||||
\(962\) | 60.2967 | 1.94404 | ||||||||
\(963\) | 40.1978 | 1.29536 | ||||||||
\(964\) | 39.4740 | 1.27137 | ||||||||
\(965\) | −19.2495 | −0.619664 | ||||||||
\(966\) | 2.69263 | 0.0866340 | ||||||||
\(967\) | 4.65037 | 0.149546 | 0.0747729 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747729 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(968\) | −31.1978 | −1.00274 | ||||||||
\(969\) | 1.94214 | 0.0623906 | ||||||||
\(970\) | −19.2495 | −0.618064 | ||||||||
\(971\) | −47.6586 | −1.52944 | −0.764719 | − | 0.644364i | \(-0.777122\pi\) | ||||
−0.764719 | + | 0.644364i | \(0.777122\pi\) | |||||||
\(972\) | 67.9409 | 2.17921 | ||||||||
\(973\) | −29.8187 | −0.955943 | ||||||||
\(974\) | 98.6902 | 3.16224 | ||||||||
\(975\) | 4.86376 | 0.155765 | ||||||||
\(976\) | −107.358 | −3.43645 | ||||||||
\(977\) | 12.2557 | 0.392093 | 0.196047 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196047 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(978\) | 18.5236 | 0.592319 | ||||||||
\(979\) | −45.3919 | −1.45073 | ||||||||
\(980\) | −44.4163 | −1.41883 | ||||||||
\(981\) | −30.2823 | −0.966840 | ||||||||
\(982\) | 31.7854 | 1.01431 | ||||||||
\(983\) | 54.9360 | 1.75219 | 0.876093 | − | 0.482142i | \(-0.160141\pi\) | ||||
0.876093 | + | 0.482142i | \(0.160141\pi\) | |||||||
\(984\) | −4.87936 | −0.155548 | ||||||||
\(985\) | 14.0866 | 0.448837 | ||||||||
\(986\) | −16.6803 | −0.531210 | ||||||||
\(987\) | 9.95443 | 0.316853 | ||||||||
\(988\) | 41.7419 | 1.32799 | ||||||||
\(989\) | −2.95282 | −0.0938942 | ||||||||
\(990\) | 47.6886 | 1.51564 | ||||||||
\(991\) | 14.4136 | 0.457864 | 0.228932 | − | 0.973442i | \(-0.426477\pi\) | ||||
0.228932 | + | 0.973442i | \(0.426477\pi\) | |||||||
\(992\) | −11.2741 | −0.357952 | ||||||||
\(993\) | 12.0905 | 0.383680 | ||||||||
\(994\) | 4.82660 | 0.153090 | ||||||||
\(995\) | 15.3217 | 0.485732 | ||||||||
\(996\) | −6.21008 | −0.196774 | ||||||||
\(997\) | −6.64915 | −0.210581 | −0.105290 | − | 0.994442i | \(-0.533577\pi\) | ||||
−0.105290 | + | 0.994442i | \(0.533577\pi\) | |||||||
\(998\) | −44.8092 | −1.41841 | ||||||||
\(999\) | −15.7854 | −0.499428 |
(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 | 41.2.a.a.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 369.2.a.f.1.3 | 3 | |||
4.3 | odd | 2 | 656.2.a.f.1.2 | 3 | |||
5.2 | odd | 4 | 1025.2.b.h.124.1 | 6 | |||
5.3 | odd | 4 | 1025.2.b.h.124.6 | 6 | |||
5.4 | even | 2 | 1025.2.a.j.1.3 | 3 | |||
7.6 | odd | 2 | 2009.2.a.g.1.1 | 3 | |||
8.3 | odd | 2 | 2624.2.a.q.1.2 | 3 | |||
8.5 | even | 2 | 2624.2.a.r.1.2 | 3 | |||
11.10 | odd | 2 | 4961.2.a.d.1.3 | 3 | |||
12.11 | even | 2 | 5904.2.a.bk.1.1 | 3 | |||
13.12 | even | 2 | 6929.2.a.b.1.3 | 3 | |||
15.14 | odd | 2 | 9225.2.a.bv.1.1 | 3 | |||
41.40 | even | 2 | 1681.2.a.d.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.2.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
369.2.a.f.1.3 | 3 | 3.2 | odd | 2 | |||
656.2.a.f.1.2 | 3 | 4.3 | odd | 2 | |||
1025.2.a.j.1.3 | 3 | 5.4 | even | 2 | |||
1025.2.b.h.124.1 | 6 | 5.2 | odd | 4 | |||
1025.2.b.h.124.6 | 6 | 5.3 | odd | 4 | |||
1681.2.a.d.1.1 | 3 | 41.40 | even | 2 | |||
2009.2.a.g.1.1 | 3 | 7.6 | odd | 2 | |||
2624.2.a.q.1.2 | 3 | 8.3 | odd | 2 | |||
2624.2.a.r.1.2 | 3 | 8.5 | even | 2 | |||
4961.2.a.d.1.3 | 3 | 11.10 | odd | 2 | |||
5904.2.a.bk.1.1 | 3 | 12.11 | even | 2 | |||
6929.2.a.b.1.3 | 3 | 13.12 | even | 2 | |||
9225.2.a.bv.1.1 | 3 | 15.14 | odd | 2 |