Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11348.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.723742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.03967 | −1.44227 | −0.721133 | − | 0.692796i | \(-0.756379\pi\) | ||||
−0.721133 | + | 0.692796i | \(0.756379\pi\) | |||||||
\(3\) | 2.19994 | 1.27014 | 0.635068 | − | 0.772456i | \(-0.280972\pi\) | ||||
0.635068 | + | 0.772456i | \(0.280972\pi\) | |||||||
\(4\) | 2.16027 | 1.08013 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −4.48716 | −1.83187 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.326891 | −0.115573 | ||||||||
\(9\) | 1.83973 | 0.613245 | ||||||||
\(10\) | 2.03967 | 0.645001 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.75246 | 1.37192 | ||||||||
\(13\) | 5.64742 | 1.56631 | 0.783157 | − | 0.621824i | \(-0.213608\pi\) | ||||
0.783157 | + | 0.621824i | \(0.213608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.19994 | −0.568022 | ||||||||
\(16\) | −3.65378 | −0.913445 | ||||||||
\(17\) | 4.19994 | 1.01863 | 0.509317 | − | 0.860579i | \(-0.329898\pi\) | ||||
0.509317 | + | 0.860579i | \(0.329898\pi\) | |||||||
\(18\) | −3.75246 | −0.884462 | ||||||||
\(19\) | −7.52683 | −1.72677 | −0.863387 | − | 0.504543i | \(-0.831661\pi\) | ||||
−0.863387 | + | 0.504543i | \(0.831661\pi\) | |||||||
\(20\) | −2.16027 | −0.483050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.03967 | 0.434860 | ||||||||
\(23\) | 7.79213 | 1.62477 | 0.812386 | − | 0.583121i | \(-0.198169\pi\) | ||||
0.812386 | + | 0.583121i | \(0.198169\pi\) | |||||||
\(24\) | −0.719140 | −0.146794 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.5189 | −2.25904 | ||||||||
\(27\) | −2.55252 | −0.491232 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.894968 | 0.166191 | 0.0830957 | − | 0.996542i | \(-0.473519\pi\) | ||||
0.0830957 | + | 0.996542i | \(0.473519\pi\) | |||||||
\(30\) | 4.48716 | 0.819239 | ||||||||
\(31\) | 5.11902 | 0.919403 | 0.459702 | − | 0.888073i | \(-0.347956\pi\) | ||||
0.459702 | + | 0.888073i | \(0.347956\pi\) | |||||||
\(32\) | 8.10630 | 1.43301 | ||||||||
\(33\) | −2.19994 | −0.382960 | ||||||||
\(34\) | −8.56650 | −1.46914 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.97431 | 0.662386 | ||||||||
\(37\) | 0.287218 | 0.0472183 | 0.0236092 | − | 0.999721i | \(-0.492484\pi\) | ||||
0.0236092 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(38\) | 15.3523 | 2.49047 | ||||||||
\(39\) | 12.4240 | 1.98943 | ||||||||
\(40\) | 0.326891 | 0.0516860 | ||||||||
\(41\) | −5.43955 | −0.849515 | −0.424758 | − | 0.905307i | \(-0.639641\pi\) | ||||
−0.424758 | + | 0.905307i | \(0.639641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.68710 | 0.409778 | 0.204889 | − | 0.978785i | \(-0.434317\pi\) | ||||
0.204889 | + | 0.978785i | \(0.434317\pi\) | |||||||
\(44\) | −2.16027 | −0.325672 | ||||||||
\(45\) | −1.83973 | −0.274251 | ||||||||
\(46\) | −15.8934 | −2.34335 | ||||||||
\(47\) | −7.00636 | −1.02198 | −0.510991 | − | 0.859586i | \(-0.670722\pi\) | ||||
−0.510991 | + | 0.859586i | \(0.670722\pi\) | |||||||
\(48\) | −8.03810 | −1.16020 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.03967 | −0.288453 | ||||||||
\(51\) | 9.23961 | 1.29380 | ||||||||
\(52\) | 12.1999 | 1.69183 | ||||||||
\(53\) | 13.6614 | 1.87654 | 0.938270 | − | 0.345905i | \(-0.112428\pi\) | ||||
0.938270 | + | 0.345905i | \(0.112428\pi\) | |||||||
\(54\) | 5.20630 | 0.708487 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5586 | −2.19324 | ||||||||
\(58\) | −1.82544 | −0.239692 | ||||||||
\(59\) | −12.5446 | −1.63317 | −0.816583 | − | 0.577228i | \(-0.804134\pi\) | ||||
−0.816583 | + | 0.577228i | \(0.804134\pi\) | |||||||
\(60\) | −4.75246 | −0.613539 | ||||||||
\(61\) | 6.48716 | 0.830595 | 0.415298 | − | 0.909686i | \(-0.363677\pi\) | ||||
0.415298 | + | 0.909686i | \(0.363677\pi\) | |||||||
\(62\) | −10.4411 | −1.32602 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.22664 | −1.15333 | ||||||||
\(65\) | −5.64742 | −0.700477 | ||||||||
\(66\) | 4.48716 | 0.552331 | ||||||||
\(67\) | −11.5509 | −1.41117 | −0.705586 | − | 0.708624i | \(-0.749316\pi\) | ||||
−0.705586 | + | 0.708624i | \(0.749316\pi\) | |||||||
\(68\) | 9.07299 | 1.10026 | ||||||||
\(69\) | 17.1422 | 2.06368 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −0.601392 | −0.0708748 | ||||||||
\(73\) | 2.69503 | 0.315429 | 0.157715 | − | 0.987485i | \(-0.449587\pi\) | ||||
0.157715 | + | 0.987485i | \(0.449587\pi\) | |||||||
\(74\) | −0.585831 | −0.0681014 | ||||||||
\(75\) | 2.19994 | 0.254027 | ||||||||
\(76\) | −16.2600 | −1.86515 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −25.3409 | −2.86929 | ||||||||
\(79\) | 12.1346 | 1.36525 | 0.682624 | − | 0.730770i | \(-0.260839\pi\) | ||||
0.682624 | + | 0.730770i | \(0.260839\pi\) | |||||||
\(80\) | 3.65378 | 0.408505 | ||||||||
\(81\) | −11.1346 | −1.23718 | ||||||||
\(82\) | 11.0949 | 1.22523 | ||||||||
\(83\) | 3.12695 | 0.343228 | 0.171614 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171614 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.19994 | −0.455547 | ||||||||
\(86\) | −5.48080 | −0.591010 | ||||||||
\(87\) | 1.96888 | 0.211086 | ||||||||
\(88\) | 0.326891 | 0.0348467 | ||||||||
\(89\) | 3.44748 | 0.365433 | 0.182716 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182716 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(90\) | 3.75246 | 0.395544 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.8331 | 1.75497 | ||||||||
\(93\) | 11.2615 | 1.16777 | ||||||||
\(94\) | 14.2907 | 1.47397 | ||||||||
\(95\) | 7.52683 | 0.772237 | ||||||||
\(96\) | 17.8334 | 1.82011 | ||||||||
\(97\) | −2.34245 | −0.237840 | −0.118920 | − | 0.992904i | \(-0.537943\pi\) | ||||
−0.118920 | + | 0.992904i | \(0.537943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.83973 | −0.184900 | ||||||||
\(100\) | 2.16027 | 0.216027 | ||||||||
\(101\) | 19.2777 | 1.91820 | 0.959102 | − | 0.283061i | \(-0.0913498\pi\) | ||||
0.959102 | + | 0.283061i | \(0.0913498\pi\) | |||||||
\(102\) | −18.8458 | −1.86601 | ||||||||
\(103\) | −14.7585 | −1.45420 | −0.727100 | − | 0.686532i | \(-0.759132\pi\) | ||||
−0.727100 | + | 0.686532i | \(0.759132\pi\) | |||||||
\(104\) | −1.84609 | −0.181024 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.8648 | −2.70647 | ||||||||
\(107\) | 6.47923 | 0.626370 | 0.313185 | − | 0.949692i | \(-0.398604\pi\) | ||||
0.313185 | + | 0.949692i | \(0.398604\pi\) | |||||||
\(108\) | −5.51411 | −0.530596 | ||||||||
\(109\) | 2.39988 | 0.229867 | 0.114933 | − | 0.993373i | \(-0.463335\pi\) | ||||
0.114933 | + | 0.993373i | \(0.463335\pi\) | |||||||
\(110\) | −2.03967 | −0.194475 | ||||||||
\(111\) | 0.631862 | 0.0599737 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3999 | 1.35463 | 0.677313 | − | 0.735695i | \(-0.263144\pi\) | ||||
0.677313 | + | 0.735695i | \(0.263144\pi\) | |||||||
\(114\) | 33.7741 | 3.16323 | ||||||||
\(115\) | −7.79213 | −0.726620 | ||||||||
\(116\) | 1.93337 | 0.179509 | ||||||||
\(117\) | 10.3898 | 0.960533 | ||||||||
\(118\) | 25.5868 | 2.35546 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.719140 | 0.0656482 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.2317 | −1.19794 | ||||||||
\(123\) | −11.9667 | −1.07900 | ||||||||
\(124\) | 11.0584 | 0.993078 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.07935 | 0.539455 | 0.269727 | − | 0.962937i | \(-0.413066\pi\) | ||||
0.269727 | + | 0.962937i | \(0.413066\pi\) | |||||||
\(128\) | 2.60673 | 0.230405 | ||||||||
\(129\) | 5.91145 | 0.520474 | ||||||||
\(130\) | 11.5189 | 1.01027 | ||||||||
\(131\) | 13.9486 | 1.21870 | 0.609349 | − | 0.792902i | \(-0.291431\pi\) | ||||
0.609349 | + | 0.792902i | \(0.291431\pi\) | |||||||
\(132\) | −4.75246 | −0.413648 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 23.5601 | 2.03529 | ||||||||
\(135\) | 2.55252 | 0.219686 | ||||||||
\(136\) | −1.37292 | −0.117727 | ||||||||
\(137\) | 13.0870 | 1.11810 | 0.559048 | − | 0.829135i | \(-0.311167\pi\) | ||||
0.559048 | + | 0.829135i | \(0.311167\pi\) | |||||||
\(138\) | −34.9645 | −2.97638 | ||||||||
\(139\) | 0.863845 | 0.0732704 | 0.0366352 | − | 0.999329i | \(-0.488336\pi\) | ||||
0.0366352 | + | 0.999329i | \(0.488336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.4136 | −1.29806 | ||||||||
\(142\) | −16.3174 | −1.36932 | ||||||||
\(143\) | −5.64742 | −0.472261 | ||||||||
\(144\) | −6.72199 | −0.560165 | ||||||||
\(145\) | −0.894968 | −0.0743231 | ||||||||
\(146\) | −5.49698 | −0.454933 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.620467 | 0.0510021 | ||||||||
\(149\) | 7.43828 | 0.609368 | 0.304684 | − | 0.952454i | \(-0.401449\pi\) | ||||
0.304684 | + | 0.952454i | \(0.401449\pi\) | |||||||
\(150\) | −4.48716 | −0.366375 | ||||||||
\(151\) | −4.37577 | −0.356095 | −0.178047 | − | 0.984022i | \(-0.556978\pi\) | ||||
−0.178047 | + | 0.984022i | \(0.556978\pi\) | |||||||
\(152\) | 2.46045 | 0.199569 | ||||||||
\(153\) | 7.72677 | 0.624672 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.11902 | −0.411170 | ||||||||
\(156\) | 26.8391 | 2.14885 | ||||||||
\(157\) | −13.7522 | −1.09754 | −0.548771 | − | 0.835973i | \(-0.684904\pi\) | ||||
−0.548771 | + | 0.835973i | \(0.684904\pi\) | |||||||
\(158\) | −24.7506 | −1.96905 | ||||||||
\(159\) | 30.0543 | 2.38346 | ||||||||
\(160\) | −8.10630 | −0.640860 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 22.7109 | 1.78434 | ||||||||
\(163\) | −9.07172 | −0.710552 | −0.355276 | − | 0.934762i | \(-0.615613\pi\) | ||||
−0.355276 | + | 0.934762i | \(0.615613\pi\) | |||||||
\(164\) | −11.7509 | −0.917590 | ||||||||
\(165\) | 2.19994 | 0.171265 | ||||||||
\(166\) | −6.37796 | −0.495026 | ||||||||
\(167\) | 8.90102 | 0.688782 | 0.344391 | − | 0.938826i | \(-0.388085\pi\) | ||||
0.344391 | + | 0.938826i | \(0.388085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.8934 | 1.45334 | ||||||||
\(170\) | 8.56650 | 0.657021 | ||||||||
\(171\) | −13.8474 | −1.05893 | ||||||||
\(172\) | 5.80484 | 0.442615 | ||||||||
\(173\) | 10.9204 | 0.830259 | 0.415129 | − | 0.909762i | \(-0.363736\pi\) | ||||
0.415129 | + | 0.909762i | \(0.363736\pi\) | |||||||
\(174\) | −4.01586 | −0.304442 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.65378 | 0.275414 | ||||||||
\(177\) | −27.5973 | −2.07434 | ||||||||
\(178\) | −7.03174 | −0.527051 | ||||||||
\(179\) | −11.1203 | −0.831170 | −0.415585 | − | 0.909554i | \(-0.636423\pi\) | ||||
−0.415585 | + | 0.909554i | \(0.636423\pi\) | |||||||
\(180\) | −3.97431 | −0.296228 | ||||||||
\(181\) | −14.1679 | −1.05309 | −0.526546 | − | 0.850147i | \(-0.676513\pi\) | ||||
−0.526546 | + | 0.850147i | \(0.676513\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2714 | 1.05497 | ||||||||
\(184\) | −2.54718 | −0.187780 | ||||||||
\(185\) | −0.287218 | −0.0211167 | ||||||||
\(186\) | −22.9698 | −1.68423 | ||||||||
\(187\) | −4.19994 | −0.307130 | ||||||||
\(188\) | −15.1356 | −1.10388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.3523 | −1.11377 | ||||||||
\(191\) | −8.55857 | −0.619276 | −0.309638 | − | 0.950854i | \(-0.600208\pi\) | ||||
−0.309638 | + | 0.950854i | \(0.600208\pi\) | |||||||
\(192\) | −20.2981 | −1.46489 | ||||||||
\(193\) | 4.97651 | 0.358217 | 0.179108 | − | 0.983829i | \(-0.442679\pi\) | ||||
0.179108 | + | 0.983829i | \(0.442679\pi\) | |||||||
\(194\) | 4.77784 | 0.343029 | ||||||||
\(195\) | −12.4240 | −0.889700 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.07172 | 0.218851 | 0.109425 | − | 0.993995i | \(-0.465099\pi\) | ||||
0.109425 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(198\) | 3.75246 | 0.266675 | ||||||||
\(199\) | −12.3126 | −0.872817 | −0.436409 | − | 0.899749i | \(-0.643750\pi\) | ||||
−0.436409 | + | 0.899749i | \(0.643750\pi\) | |||||||
\(200\) | −0.326891 | −0.0231147 | ||||||||
\(201\) | −25.4114 | −1.79238 | ||||||||
\(202\) | −39.3202 | −2.76656 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 19.9600 | 1.39748 | ||||||||
\(205\) | 5.43955 | 0.379915 | ||||||||
\(206\) | 30.1025 | 2.09734 | ||||||||
\(207\) | 14.3354 | 0.996382 | ||||||||
\(208\) | −20.6345 | −1.43074 | ||||||||
\(209\) | 7.52683 | 0.520642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.87910 | −0.198206 | −0.0991028 | − | 0.995077i | \(-0.531597\pi\) | ||||
−0.0991028 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(212\) | 29.5123 | 2.02691 | ||||||||
\(213\) | 17.5995 | 1.20590 | ||||||||
\(214\) | −13.2155 | −0.903393 | ||||||||
\(215\) | −2.68710 | −0.183258 | ||||||||
\(216\) | 0.834394 | 0.0567733 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.89497 | −0.331529 | ||||||||
\(219\) | 5.92890 | 0.400638 | ||||||||
\(220\) | 2.16027 | 0.145645 | ||||||||
\(221\) | 23.7188 | 1.59550 | ||||||||
\(222\) | −1.28879 | −0.0864980 | ||||||||
\(223\) | 11.6408 | 0.779523 | 0.389762 | − | 0.920916i | \(-0.372557\pi\) | ||||
0.389762 | + | 0.920916i | \(0.372557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.83973 | 0.122649 | ||||||||
\(226\) | −29.3710 | −1.95373 | ||||||||
\(227\) | 13.2637 | 0.880344 | 0.440172 | − | 0.897913i | \(-0.354917\pi\) | ||||
0.440172 | + | 0.897913i | \(0.354917\pi\) | |||||||
\(228\) | −35.7709 | −2.36899 | ||||||||
\(229\) | 25.6789 | 1.69691 | 0.848453 | − | 0.529270i | \(-0.177534\pi\) | ||||
0.848453 | + | 0.529270i | \(0.177534\pi\) | |||||||
\(230\) | 15.8934 | 1.04798 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.292557 | −0.0192073 | ||||||||
\(233\) | 5.10284 | 0.334298 | 0.167149 | − | 0.985932i | \(-0.446544\pi\) | ||||
0.167149 | + | 0.985932i | \(0.446544\pi\) | |||||||
\(234\) | −21.1917 | −1.38535 | ||||||||
\(235\) | 7.00636 | 0.457044 | ||||||||
\(236\) | −27.0996 | −1.76404 | ||||||||
\(237\) | 26.6953 | 1.73405 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4481 | −0.805201 | −0.402600 | − | 0.915376i | \(-0.631894\pi\) | ||||
−0.402600 | + | 0.915376i | \(0.631894\pi\) | |||||||
\(240\) | 8.03810 | 0.518857 | ||||||||
\(241\) | 3.77595 | 0.243230 | 0.121615 | − | 0.992577i | \(-0.461193\pi\) | ||||
0.121615 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(242\) | −2.03967 | −0.131115 | ||||||||
\(243\) | −16.8379 | −1.08015 | ||||||||
\(244\) | 14.0140 | 0.897154 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 24.4081 | 1.55621 | ||||||||
\(247\) | −42.5072 | −2.70467 | ||||||||
\(248\) | −1.67336 | −0.106259 | ||||||||
\(249\) | 6.87910 | 0.435946 | ||||||||
\(250\) | 2.03967 | 0.129000 | ||||||||
\(251\) | −2.97304 | −0.187657 | −0.0938284 | − | 0.995588i | \(-0.529911\pi\) | ||||
−0.0938284 | + | 0.995588i | \(0.529911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.79213 | −0.489887 | ||||||||
\(254\) | −12.3999 | −0.778038 | ||||||||
\(255\) | −9.23961 | −0.578607 | ||||||||
\(256\) | 13.1364 | 0.821025 | ||||||||
\(257\) | 14.6319 | 0.912710 | 0.456355 | − | 0.889798i | \(-0.349155\pi\) | ||||
0.456355 | + | 0.889798i | \(0.349155\pi\) | |||||||
\(258\) | −12.0574 | −0.750663 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.1999 | −0.756608 | ||||||||
\(261\) | 1.64650 | 0.101916 | ||||||||
\(262\) | −28.4506 | −1.75769 | ||||||||
\(263\) | 10.7204 | 0.661049 | 0.330524 | − | 0.943797i | \(-0.392774\pi\) | ||||
0.330524 | + | 0.943797i | \(0.392774\pi\) | |||||||
\(264\) | 0.719140 | 0.0442600 | ||||||||
\(265\) | −13.6614 | −0.839214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.58426 | 0.464149 | ||||||||
\(268\) | −24.9531 | −1.52425 | ||||||||
\(269\) | −1.59346 | −0.0971550 | −0.0485775 | − | 0.998819i | \(-0.515469\pi\) | ||||
−0.0485775 | + | 0.998819i | \(0.515469\pi\) | |||||||
\(270\) | −5.20630 | −0.316845 | ||||||||
\(271\) | −19.9175 | −1.20990 | −0.604951 | − | 0.796263i | \(-0.706807\pi\) | ||||
−0.604951 | + | 0.796263i | \(0.706807\pi\) | |||||||
\(272\) | −15.3457 | −0.930467 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.6932 | −1.61259 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 37.0317 | 2.22905 | ||||||||
\(277\) | −1.40811 | −0.0846054 | −0.0423027 | − | 0.999105i | \(-0.513469\pi\) | ||||
−0.0423027 | + | 0.999105i | \(0.513469\pi\) | |||||||
\(278\) | −1.76196 | −0.105675 | ||||||||
\(279\) | 9.41763 | 0.563819 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4256 | 0.800902 | 0.400451 | − | 0.916318i | \(-0.368853\pi\) | ||||
0.400451 | + | 0.916318i | \(0.368853\pi\) | |||||||
\(282\) | 31.4386 | 1.87214 | ||||||||
\(283\) | −16.0921 | −0.956574 | −0.478287 | − | 0.878204i | \(-0.658742\pi\) | ||||
−0.478287 | + | 0.878204i | \(0.658742\pi\) | |||||||
\(284\) | 17.2821 | 1.02551 | ||||||||
\(285\) | 16.5586 | 0.980845 | ||||||||
\(286\) | 11.5189 | 0.681127 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.9134 | 0.878783 | ||||||||
\(289\) | 0.639491 | 0.0376171 | ||||||||
\(290\) | 1.82544 | 0.107194 | ||||||||
\(291\) | −5.15325 | −0.302089 | ||||||||
\(292\) | 5.82198 | 0.340706 | ||||||||
\(293\) | −11.4282 | −0.667640 | −0.333820 | − | 0.942637i | \(-0.608338\pi\) | ||||
−0.333820 | + | 0.942637i | \(0.608338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.5446 | 0.730374 | ||||||||
\(296\) | −0.0938889 | −0.00545718 | ||||||||
\(297\) | 2.55252 | 0.148112 | ||||||||
\(298\) | −15.1717 | −0.878871 | ||||||||
\(299\) | 44.0055 | 2.54490 | ||||||||
\(300\) | 4.75246 | 0.274383 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.92514 | 0.513584 | ||||||||
\(303\) | 42.4098 | 2.43638 | ||||||||
\(304\) | 27.5014 | 1.57731 | ||||||||
\(305\) | −6.48716 | −0.371454 | ||||||||
\(306\) | −15.7601 | −0.900944 | ||||||||
\(307\) | 16.7906 | 0.958288 | 0.479144 | − | 0.877736i | \(-0.340947\pi\) | ||||
0.479144 | + | 0.877736i | \(0.340947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.4678 | −1.84703 | ||||||||
\(310\) | 10.4411 | 0.593016 | ||||||||
\(311\) | −27.3663 | −1.55180 | −0.775899 | − | 0.630857i | \(-0.782703\pi\) | ||||
−0.775899 | + | 0.630857i | \(0.782703\pi\) | |||||||
\(312\) | −4.06129 | −0.229925 | ||||||||
\(313\) | 14.2692 | 0.806541 | 0.403270 | − | 0.915081i | \(-0.367873\pi\) | ||||
0.403270 | + | 0.915081i | \(0.367873\pi\) | |||||||
\(314\) | 28.0499 | 1.58295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.2139 | 1.47465 | ||||||||
\(317\) | 9.47379 | 0.532101 | 0.266050 | − | 0.963959i | \(-0.414281\pi\) | ||||
0.266050 | + | 0.963959i | \(0.414281\pi\) | |||||||
\(318\) | −61.3009 | −3.43758 | ||||||||
\(319\) | −0.894968 | −0.0501086 | ||||||||
\(320\) | 9.22664 | 0.515785 | ||||||||
\(321\) | 14.2539 | 0.795575 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.6122 | −1.75895 | ||||||||
\(324\) | −24.0537 | −1.33631 | ||||||||
\(325\) | 5.64742 | 0.313263 | ||||||||
\(326\) | 18.5033 | 1.02481 | ||||||||
\(327\) | 5.27959 | 0.291962 | ||||||||
\(328\) | 1.77814 | 0.0981814 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.48716 | −0.247010 | ||||||||
\(331\) | 6.12319 | 0.336561 | 0.168280 | − | 0.985739i | \(-0.446179\pi\) | ||||
0.168280 | + | 0.985739i | \(0.446179\pi\) | |||||||
\(332\) | 6.75505 | 0.370731 | ||||||||
\(333\) | 0.528404 | 0.0289564 | ||||||||
\(334\) | −18.1552 | −0.993407 | ||||||||
\(335\) | 11.5509 | 0.631095 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2457 | 0.721538 | 0.360769 | − | 0.932655i | \(-0.382514\pi\) | ||||
0.360769 | + | 0.932655i | \(0.382514\pi\) | |||||||
\(338\) | −38.5363 | −2.09610 | ||||||||
\(339\) | 31.6789 | 1.72056 | ||||||||
\(340\) | −9.07299 | −0.492052 | ||||||||
\(341\) | −5.11902 | −0.277210 | ||||||||
\(342\) | 28.2441 | 1.52727 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.878388 | −0.0473595 | ||||||||
\(345\) | −17.1422 | −0.922906 | ||||||||
\(346\) | −22.2739 | −1.19745 | ||||||||
\(347\) | 21.0997 | 1.13269 | 0.566345 | − | 0.824168i | \(-0.308357\pi\) | ||||
0.566345 | + | 0.824168i | \(0.308357\pi\) | |||||||
\(348\) | 4.25330 | 0.228001 | ||||||||
\(349\) | 16.1666 | 0.865380 | 0.432690 | − | 0.901543i | \(-0.357565\pi\) | ||||
0.432690 | + | 0.901543i | \(0.357565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.4151 | −0.769423 | ||||||||
\(352\) | −8.10630 | −0.432067 | ||||||||
\(353\) | 17.7429 | 0.944362 | 0.472181 | − | 0.881502i | \(-0.343467\pi\) | ||||
0.472181 | + | 0.881502i | \(0.343467\pi\) | |||||||
\(354\) | 56.2895 | 2.99175 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 7.44748 | 0.394716 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.6818 | 1.19877 | ||||||||
\(359\) | 36.5186 | 1.92738 | 0.963689 | − | 0.267028i | \(-0.0860415\pi\) | ||||
0.963689 | + | 0.267028i | \(0.0860415\pi\) | |||||||
\(360\) | 0.601392 | 0.0316962 | ||||||||
\(361\) | 37.6532 | 1.98175 | ||||||||
\(362\) | 28.8979 | 1.51884 | ||||||||
\(363\) | 2.19994 | 0.115467 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.69503 | −0.141064 | ||||||||
\(366\) | −29.1089 | −1.52155 | ||||||||
\(367\) | 35.2114 | 1.83802 | 0.919011 | − | 0.394232i | \(-0.128989\pi\) | ||||
0.919011 | + | 0.394232i | \(0.128989\pi\) | |||||||
\(368\) | −28.4707 | −1.48414 | ||||||||
\(369\) | −10.0073 | −0.520961 | ||||||||
\(370\) | 0.585831 | 0.0304559 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 24.3279 | 1.26134 | ||||||||
\(373\) | −33.8385 | −1.75209 | −0.876046 | − | 0.482228i | \(-0.839828\pi\) | ||||
−0.876046 | + | 0.482228i | \(0.839828\pi\) | |||||||
\(374\) | 8.56650 | 0.442963 | ||||||||
\(375\) | −2.19994 | −0.113604 | ||||||||
\(376\) | 2.29032 | 0.118114 | ||||||||
\(377\) | 5.05427 | 0.260308 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2735 | 1.24685 | 0.623424 | − | 0.781884i | \(-0.285741\pi\) | ||||
0.623424 | + | 0.781884i | \(0.285741\pi\) | |||||||
\(380\) | 16.2600 | 0.834118 | ||||||||
\(381\) | 13.3742 | 0.685181 | ||||||||
\(382\) | 17.4567 | 0.893162 | ||||||||
\(383\) | 4.16443 | 0.212793 | 0.106396 | − | 0.994324i | \(-0.466069\pi\) | ||||
0.106396 | + | 0.994324i | \(0.466069\pi\) | |||||||
\(384\) | 5.73465 | 0.292645 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.1504 | −0.516644 | ||||||||
\(387\) | 4.94354 | 0.251294 | ||||||||
\(388\) | −5.06032 | −0.256899 | ||||||||
\(389\) | −24.4634 | −1.24034 | −0.620171 | − | 0.784467i | \(-0.712937\pi\) | ||||
−0.620171 | + | 0.784467i | \(0.712937\pi\) | |||||||
\(390\) | 25.3409 | 1.28319 | ||||||||
\(391\) | 32.7265 | 1.65505 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.6861 | 1.54791 | ||||||||
\(394\) | −6.26530 | −0.315641 | ||||||||
\(395\) | −12.1346 | −0.610557 | ||||||||
\(396\) | −3.97431 | −0.199717 | ||||||||
\(397\) | 0.683233 | 0.0342905 | 0.0171452 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171452 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(398\) | 25.1137 | 1.25884 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.65378 | −0.182689 | ||||||||
\(401\) | 6.75592 | 0.337374 | 0.168687 | − | 0.985670i | \(-0.446047\pi\) | ||||
0.168687 | + | 0.985670i | \(0.446047\pi\) | |||||||
\(402\) | 51.8309 | 2.58509 | ||||||||
\(403\) | 28.9093 | 1.44007 | ||||||||
\(404\) | 41.6450 | 2.07192 | ||||||||
\(405\) | 11.1346 | 0.553282 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.287218 | −0.0142369 | ||||||||
\(408\) | −3.02035 | −0.149529 | ||||||||
\(409\) | −28.7093 | −1.41959 | −0.709793 | − | 0.704411i | \(-0.751211\pi\) | ||||
−0.709793 | + | 0.704411i | \(0.751211\pi\) | |||||||
\(410\) | −11.0949 | −0.547938 | ||||||||
\(411\) | 28.7906 | 1.42013 | ||||||||
\(412\) | −31.8823 | −1.57073 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −29.2396 | −1.43705 | ||||||||
\(415\) | −3.12695 | −0.153496 | ||||||||
\(416\) | 45.7797 | 2.24454 | ||||||||
\(417\) | 1.90041 | 0.0930633 | ||||||||
\(418\) | −15.3523 | −0.750904 | ||||||||
\(419\) | −22.1508 | −1.08214 | −0.541068 | − | 0.840979i | \(-0.681980\pi\) | ||||
−0.541068 | + | 0.840979i | \(0.681980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7572 | 0.719224 | 0.359612 | − | 0.933102i | \(-0.382909\pi\) | ||||
0.359612 | + | 0.933102i | \(0.382909\pi\) | |||||||
\(422\) | 5.87243 | 0.285865 | ||||||||
\(423\) | −12.8898 | −0.626725 | ||||||||
\(424\) | −4.46579 | −0.216878 | ||||||||
\(425\) | 4.19994 | 0.203727 | ||||||||
\(426\) | −35.8973 | −1.73923 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.9969 | 0.676563 | ||||||||
\(429\) | −12.4240 | −0.599836 | ||||||||
\(430\) | 5.48080 | 0.264308 | ||||||||
\(431\) | 20.5985 | 0.992197 | 0.496099 | − | 0.868266i | \(-0.334765\pi\) | ||||
0.496099 | + | 0.868266i | \(0.334765\pi\) | |||||||
\(432\) | 9.32634 | 0.448714 | ||||||||
\(433\) | −33.2631 | −1.59852 | −0.799262 | − | 0.600983i | \(-0.794776\pi\) | ||||
−0.799262 | + | 0.600983i | \(0.794776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.96888 | −0.0944004 | ||||||||
\(436\) | 5.18438 | 0.248287 | ||||||||
\(437\) | −58.6500 | −2.80561 | ||||||||
\(438\) | −12.0930 | −0.577827 | ||||||||
\(439\) | −8.02798 | −0.383154 | −0.191577 | − | 0.981478i | \(-0.561360\pi\) | ||||
−0.191577 | + | 0.981478i | \(0.561360\pi\) | |||||||
\(440\) | −0.326891 | −0.0155839 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.3787 | −2.30114 | ||||||||
\(443\) | −33.4837 | −1.59086 | −0.795429 | − | 0.606046i | \(-0.792755\pi\) | ||||
−0.795429 | + | 0.606046i | \(0.792755\pi\) | |||||||
\(444\) | 1.36499 | 0.0647796 | ||||||||
\(445\) | −3.44748 | −0.163426 | ||||||||
\(446\) | −23.7434 | −1.12428 | ||||||||
\(447\) | 16.3638 | 0.773980 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.22979 | 0.388388 | 0.194194 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194194 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(450\) | −3.75246 | −0.176892 | ||||||||
\(451\) | 5.43955 | 0.256139 | ||||||||
\(452\) | 31.1076 | 1.46318 | ||||||||
\(453\) | −9.62642 | −0.452289 | ||||||||
\(454\) | −27.0537 | −1.26969 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.41285 | 0.253480 | ||||||||
\(457\) | −20.6046 | −0.963843 | −0.481921 | − | 0.876214i | \(-0.660061\pi\) | ||||
−0.481921 | + | 0.876214i | \(0.660061\pi\) | |||||||
\(458\) | −52.3765 | −2.44739 | ||||||||
\(459\) | −10.7204 | −0.500386 | ||||||||
\(460\) | −16.8331 | −0.784846 | ||||||||
\(461\) | −29.4517 | −1.37170 | −0.685850 | − | 0.727743i | \(-0.740570\pi\) | ||||
−0.685850 | + | 0.727743i | \(0.740570\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4173 | 1.13477 | 0.567385 | − | 0.823453i | \(-0.307955\pi\) | ||||
0.567385 | + | 0.823453i | \(0.307955\pi\) | |||||||
\(464\) | −3.27002 | −0.151807 | ||||||||
\(465\) | −11.2615 | −0.522241 | ||||||||
\(466\) | −10.4081 | −0.482147 | ||||||||
\(467\) | −30.5612 | −1.41420 | −0.707101 | − | 0.707113i | \(-0.749997\pi\) | ||||
−0.707101 | + | 0.707113i | \(0.749997\pi\) | |||||||
\(468\) | 22.4446 | 1.03750 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14.2907 | −0.659180 | ||||||||
\(471\) | −30.2539 | −1.39403 | ||||||||
\(472\) | 4.10071 | 0.188751 | ||||||||
\(473\) | −2.68710 | −0.123553 | ||||||||
\(474\) | −54.4498 | −2.50096 | ||||||||
\(475\) | −7.52683 | −0.345355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.1334 | 1.15078 | ||||||||
\(478\) | 25.3901 | 1.16131 | ||||||||
\(479\) | −30.9524 | −1.41425 | −0.707126 | − | 0.707088i | \(-0.750008\pi\) | ||||
−0.707126 | + | 0.707088i | \(0.750008\pi\) | |||||||
\(480\) | −17.8334 | −0.813978 | ||||||||
\(481\) | 1.62204 | 0.0739587 | ||||||||
\(482\) | −7.70170 | −0.350803 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.16027 | 0.0981939 | ||||||||
\(485\) | 2.34245 | 0.106365 | ||||||||
\(486\) | 34.3437 | 1.55786 | ||||||||
\(487\) | 0.477034 | 0.0216165 | 0.0108082 | − | 0.999942i | \(-0.496560\pi\) | ||||
0.0108082 | + | 0.999942i | \(0.496560\pi\) | |||||||
\(488\) | −2.12059 | −0.0959947 | ||||||||
\(489\) | −19.9572 | −0.902497 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2964 | 0.825706 | 0.412853 | − | 0.910798i | \(-0.364532\pi\) | ||||
0.412853 | + | 0.910798i | \(0.364532\pi\) | |||||||
\(492\) | −25.8512 | −1.16546 | ||||||||
\(493\) | 3.75881 | 0.169288 | ||||||||
\(494\) | 86.7008 | 3.90085 | ||||||||
\(495\) | 1.83973 | 0.0826899 | ||||||||
\(496\) | −18.7038 | −0.839825 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.0311 | −0.628750 | ||||||||
\(499\) | −20.3840 | −0.912514 | −0.456257 | − | 0.889848i | \(-0.650810\pi\) | ||||
−0.456257 | + | 0.889848i | \(0.650810\pi\) | |||||||
\(500\) | −2.16027 | −0.0966100 | ||||||||
\(501\) | 19.5817 | 0.874846 | ||||||||
\(502\) | 6.06404 | 0.270651 | ||||||||
\(503\) | 19.4005 | 0.865025 | 0.432513 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432513 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.2777 | −0.857847 | ||||||||
\(506\) | 15.8934 | 0.706548 | ||||||||
\(507\) | 41.5643 | 1.84594 | ||||||||
\(508\) | 13.1330 | 0.582683 | ||||||||
\(509\) | 5.13616 | 0.227656 | 0.113828 | − | 0.993500i | \(-0.463689\pi\) | ||||
0.113828 | + | 0.993500i | \(0.463689\pi\) | |||||||
\(510\) | 18.8458 | 0.834506 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.0074 | −1.41454 | ||||||||
\(513\) | 19.2124 | 0.848246 | ||||||||
\(514\) | −29.8442 | −1.31637 | ||||||||
\(515\) | 14.7585 | 0.650338 | ||||||||
\(516\) | 12.7703 | 0.562181 | ||||||||
\(517\) | 7.00636 | 0.308139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.0241 | 1.05454 | ||||||||
\(520\) | 1.84609 | 0.0809565 | ||||||||
\(521\) | 33.0445 | 1.44770 | 0.723852 | − | 0.689955i | \(-0.242370\pi\) | ||||
0.723852 | + | 0.689955i | \(0.242370\pi\) | |||||||
\(522\) | −3.35833 | −0.146990 | ||||||||
\(523\) | −6.23138 | −0.272479 | −0.136240 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136240 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(524\) | 30.1328 | 1.31636 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.8661 | −0.953409 | ||||||||
\(527\) | 21.4996 | 0.936536 | ||||||||
\(528\) | 8.03810 | 0.349813 | ||||||||
\(529\) | 37.7173 | 1.63988 | ||||||||
\(530\) | 27.8648 | 1.21037 | ||||||||
\(531\) | −23.0787 | −1.00153 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.7195 | −1.33061 | ||||||||
\(534\) | −15.4694 | −0.669427 | ||||||||
\(535\) | −6.47923 | −0.280121 | ||||||||
\(536\) | 3.77590 | 0.163094 | ||||||||
\(537\) | −24.4640 | −1.05570 | ||||||||
\(538\) | 3.25014 | 0.140123 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.51411 | 0.237290 | ||||||||
\(541\) | −5.03780 | −0.216592 | −0.108296 | − | 0.994119i | \(-0.534539\pi\) | ||||
−0.108296 | + | 0.994119i | \(0.534539\pi\) | |||||||
\(542\) | 40.6252 | 1.74500 | ||||||||
\(543\) | −31.1685 | −1.33757 | ||||||||
\(544\) | 34.0460 | 1.45971 | ||||||||
\(545\) | −2.39988 | −0.102800 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7686 | 0.631461 | 0.315731 | − | 0.948849i | \(-0.397750\pi\) | ||||
0.315731 | + | 0.948849i | \(0.397750\pi\) | |||||||
\(548\) | 28.2714 | 1.20769 | ||||||||
\(549\) | 11.9346 | 0.509358 | ||||||||
\(550\) | 2.03967 | 0.0869720 | ||||||||
\(551\) | −6.73628 | −0.286975 | ||||||||
\(552\) | −5.60363 | −0.238507 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.87209 | 0.122023 | ||||||||
\(555\) | −0.631862 | −0.0268210 | ||||||||
\(556\) | 1.86614 | 0.0791418 | ||||||||
\(557\) | −14.6357 | −0.620136 | −0.310068 | − | 0.950714i | \(-0.600352\pi\) | ||||
−0.310068 | + | 0.950714i | \(0.600352\pi\) | |||||||
\(558\) | −19.2089 | −0.813177 | ||||||||
\(559\) | 15.1752 | 0.641841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.23961 | −0.390097 | ||||||||
\(562\) | −27.3838 | −1.15511 | ||||||||
\(563\) | −3.22822 | −0.136053 | −0.0680266 | − | 0.997684i | \(-0.521670\pi\) | ||||
−0.0680266 | + | 0.997684i | \(0.521670\pi\) | |||||||
\(564\) | −33.2974 | −1.40207 | ||||||||
\(565\) | −14.3999 | −0.605807 | ||||||||
\(566\) | 32.8225 | 1.37963 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.61513 | −0.109728 | ||||||||
\(569\) | −3.34622 | −0.140281 | −0.0701404 | − | 0.997537i | \(-0.522345\pi\) | ||||
−0.0701404 | + | 0.997537i | \(0.522345\pi\) | |||||||
\(570\) | −33.7741 | −1.41464 | ||||||||
\(571\) | −0.351656 | −0.0147164 | −0.00735818 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735818 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(572\) | −12.1999 | −0.510105 | ||||||||
\(573\) | −18.8283 | −0.786565 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.79213 | 0.324954 | ||||||||
\(576\) | −16.9746 | −0.707274 | ||||||||
\(577\) | 3.49571 | 0.145528 | 0.0727641 | − | 0.997349i | \(-0.476818\pi\) | ||||
0.0727641 | + | 0.997349i | \(0.476818\pi\) | |||||||
\(578\) | −1.30435 | −0.0542540 | ||||||||
\(579\) | 10.9480 | 0.454984 | ||||||||
\(580\) | −1.93337 | −0.0802788 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.5110 | 0.435693 | ||||||||
\(583\) | −13.6614 | −0.565798 | ||||||||
\(584\) | −0.880981 | −0.0364552 | ||||||||
\(585\) | −10.3898 | −0.429564 | ||||||||
\(586\) | 23.3097 | 0.962915 | ||||||||
\(587\) | 14.6480 | 0.604589 | 0.302295 | − | 0.953215i | \(-0.402247\pi\) | ||||
0.302295 | + | 0.953215i | \(0.402247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.5300 | −1.58760 | ||||||||
\(590\) | −25.5868 | −1.05339 | ||||||||
\(591\) | 6.75759 | 0.277970 | ||||||||
\(592\) | −1.04943 | −0.0431314 | ||||||||
\(593\) | −19.9959 | −0.821135 | −0.410567 | − | 0.911830i | \(-0.634669\pi\) | ||||
−0.410567 | + | 0.911830i | \(0.634669\pi\) | |||||||
\(594\) | −5.20630 | −0.213617 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0687 | 0.658198 | ||||||||
\(597\) | −27.0870 | −1.10860 | ||||||||
\(598\) | −89.7567 | −3.67043 | ||||||||
\(599\) | −34.6500 | −1.41576 | −0.707881 | − | 0.706332i | \(-0.750349\pi\) | ||||
−0.707881 | + | 0.706332i | \(0.750349\pi\) | |||||||
\(600\) | −0.719140 | −0.0293588 | ||||||||
\(601\) | −1.21423 | −0.0495295 | −0.0247647 | − | 0.999693i | \(-0.507884\pi\) | ||||
−0.0247647 | + | 0.999693i | \(0.507884\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.2507 | −0.865394 | ||||||||
\(604\) | −9.45282 | −0.384630 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −86.5021 | −3.51391 | ||||||||
\(607\) | −25.8474 | −1.04911 | −0.524556 | − | 0.851376i | \(-0.675769\pi\) | ||||
−0.524556 | + | 0.851376i | \(0.675769\pi\) | |||||||
\(608\) | −61.0148 | −2.47448 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.2317 | 0.535735 | ||||||||
\(611\) | −39.5679 | −1.60074 | ||||||||
\(612\) | 16.6919 | 0.674729 | ||||||||
\(613\) | −34.1095 | −1.37767 | −0.688835 | − | 0.724918i | \(-0.741878\pi\) | ||||
−0.688835 | + | 0.724918i | \(0.741878\pi\) | |||||||
\(614\) | −34.2472 | −1.38211 | ||||||||
\(615\) | 11.9667 | 0.482543 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.76644 | −0.111373 | −0.0556864 | − | 0.998448i | \(-0.517735\pi\) | ||||
−0.0556864 | + | 0.998448i | \(0.517735\pi\) | |||||||
\(618\) | 66.2238 | 2.66391 | ||||||||
\(619\) | 17.9121 | 0.719949 | 0.359974 | − | 0.932962i | \(-0.382785\pi\) | ||||
0.359974 | + | 0.932962i | \(0.382785\pi\) | |||||||
\(620\) | −11.0584 | −0.444118 | ||||||||
\(621\) | −19.8895 | −0.798139 | ||||||||
\(622\) | 55.8182 | 2.23811 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −45.3946 | −1.81724 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.1044 | −1.16325 | ||||||||
\(627\) | 16.5586 | 0.661286 | ||||||||
\(628\) | −29.7083 | −1.18549 | ||||||||
\(629\) | 1.20630 | 0.0480982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6335 | 0.423314 | 0.211657 | − | 0.977344i | \(-0.432114\pi\) | ||||
0.211657 | + | 0.977344i | \(0.432114\pi\) | |||||||
\(632\) | −3.96669 | −0.157786 | ||||||||
\(633\) | −6.33385 | −0.251748 | ||||||||
\(634\) | −19.3234 | −0.767431 | ||||||||
\(635\) | −6.07935 | −0.241251 | ||||||||
\(636\) | 64.9252 | 2.57445 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.82544 | 0.0722700 | ||||||||
\(639\) | 14.7179 | 0.582230 | ||||||||
\(640\) | −2.60673 | −0.103040 | ||||||||
\(641\) | 17.5601 | 0.693584 | 0.346792 | − | 0.937942i | \(-0.387271\pi\) | ||||
0.346792 | + | 0.937942i | \(0.387271\pi\) | |||||||
\(642\) | −29.0733 | −1.14743 | ||||||||
\(643\) | −30.0626 | −1.18555 | −0.592776 | − | 0.805367i | \(-0.701968\pi\) | ||||
−0.592776 | + | 0.805367i | \(0.701968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.91145 | −0.232763 | ||||||||
\(646\) | 64.4786 | 2.53688 | ||||||||
\(647\) | −3.47287 | −0.136532 | −0.0682662 | − | 0.997667i | \(-0.521747\pi\) | ||||
−0.0682662 | + | 0.997667i | \(0.521747\pi\) | |||||||
\(648\) | 3.63979 | 0.142985 | ||||||||
\(649\) | 12.5446 | 0.492418 | ||||||||
\(650\) | −11.5189 | −0.451808 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.5973 | −0.767490 | ||||||||
\(653\) | −14.6024 | −0.571437 | −0.285718 | − | 0.958314i | \(-0.592232\pi\) | ||||
−0.285718 | + | 0.958314i | \(0.592232\pi\) | |||||||
\(654\) | −10.7686 | −0.421087 | ||||||||
\(655\) | −13.9486 | −0.545018 | ||||||||
\(656\) | 19.8749 | 0.775986 | ||||||||
\(657\) | 4.95814 | 0.193435 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1876 | 1.44862 | 0.724312 | − | 0.689472i | \(-0.242157\pi\) | ||||
0.724312 | + | 0.689472i | \(0.242157\pi\) | |||||||
\(660\) | 4.75246 | 0.184989 | ||||||||
\(661\) | −34.7703 | −1.35241 | −0.676204 | − | 0.736714i | \(-0.736376\pi\) | ||||
−0.676204 | + | 0.736714i | \(0.736376\pi\) | |||||||
\(662\) | −12.4893 | −0.485410 | ||||||||
\(663\) | 52.1800 | 2.02650 | ||||||||
\(664\) | −1.02217 | −0.0396680 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.07777 | −0.0417628 | ||||||||
\(667\) | 6.97371 | 0.270023 | ||||||||
\(668\) | 19.2286 | 0.743976 | ||||||||
\(669\) | 25.6090 | 0.990100 | ||||||||
\(670\) | −23.5601 | −0.910208 | ||||||||
\(671\) | −6.48716 | −0.250434 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8299 | −0.957123 | −0.478562 | − | 0.878054i | \(-0.658842\pi\) | ||||
−0.478562 | + | 0.878054i | \(0.658842\pi\) | |||||||
\(674\) | −27.0168 | −1.04065 | ||||||||
\(675\) | −2.55252 | −0.0982464 | ||||||||
\(676\) | 40.8148 | 1.56980 | ||||||||
\(677\) | −45.4850 | −1.74813 | −0.874065 | − | 0.485809i | \(-0.838525\pi\) | ||||
−0.874065 | + | 0.485809i | \(0.838525\pi\) | |||||||
\(678\) | −64.6145 | −2.48151 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.37292 | 0.0526492 | ||||||||
\(681\) | 29.1794 | 1.11816 | ||||||||
\(682\) | 10.4411 | 0.399811 | ||||||||
\(683\) | −40.3945 | −1.54565 | −0.772827 | − | 0.634617i | \(-0.781158\pi\) | ||||
−0.772827 | + | 0.634617i | \(0.781158\pi\) | |||||||
\(684\) | −29.9140 | −1.14379 | ||||||||
\(685\) | −13.0870 | −0.500028 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 56.4919 | 2.15530 | ||||||||
\(688\) | −9.81807 | −0.374310 | ||||||||
\(689\) | 77.1518 | 2.93925 | ||||||||
\(690\) | 34.9645 | 1.33108 | ||||||||
\(691\) | 17.6360 | 0.670906 | 0.335453 | − | 0.942057i | \(-0.391111\pi\) | ||||
0.335453 | + | 0.942057i | \(0.391111\pi\) | |||||||
\(692\) | 23.5909 | 0.896790 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.0365 | −1.63364 | ||||||||
\(695\) | −0.863845 | −0.0327675 | ||||||||
\(696\) | −0.643608 | −0.0243959 | ||||||||
\(697\) | −22.8458 | −0.865346 | ||||||||
\(698\) | −32.9746 | −1.24811 | ||||||||
\(699\) | 11.2259 | 0.424604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.01815 | −0.265072 | −0.132536 | − | 0.991178i | \(-0.542312\pi\) | ||||
−0.132536 | + | 0.991178i | \(0.542312\pi\) | |||||||
\(702\) | 29.4022 | 1.10971 | ||||||||
\(703\) | −2.16184 | −0.0815354 | ||||||||
\(704\) | 9.22664 | 0.347742 | ||||||||
\(705\) | 15.4136 | 0.580508 | ||||||||
\(706\) | −36.1898 | −1.36202 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −59.6176 | −2.24057 | ||||||||
\(709\) | −39.0733 | −1.46743 | −0.733714 | − | 0.679458i | \(-0.762215\pi\) | ||||
−0.733714 | + | 0.679458i | \(0.762215\pi\) | |||||||
\(710\) | 16.3174 | 0.612381 | ||||||||
\(711\) | 22.3244 | 0.837230 | ||||||||
\(712\) | −1.12695 | −0.0422343 | ||||||||
\(713\) | 39.8881 | 1.49382 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.64742 | 0.211202 | ||||||||
\(716\) | −24.0228 | −0.897774 | ||||||||
\(717\) | −27.3851 | −1.02271 | ||||||||
\(718\) | −74.4860 | −2.77979 | ||||||||
\(719\) | 6.82355 | 0.254476 | 0.127238 | − | 0.991872i | \(-0.459389\pi\) | ||||
0.127238 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(720\) | 6.72199 | 0.250514 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −76.8002 | −2.85821 | ||||||||
\(723\) | 8.30686 | 0.308935 | ||||||||
\(724\) | −30.6064 | −1.13748 | ||||||||
\(725\) | 0.894968 | 0.0332383 | ||||||||
\(726\) | −4.48716 | −0.166534 | ||||||||
\(727\) | 25.3574 | 0.940454 | 0.470227 | − | 0.882545i | \(-0.344172\pi\) | ||||
0.470227 | + | 0.882545i | \(0.344172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.63852 | −0.134760 | ||||||||
\(730\) | 5.49698 | 0.203452 | ||||||||
\(731\) | 11.2856 | 0.417415 | ||||||||
\(732\) | 30.8299 | 1.13951 | ||||||||
\(733\) | −47.8560 | −1.76760 | −0.883801 | − | 0.467863i | \(-0.845024\pi\) | ||||
−0.883801 | + | 0.467863i | \(0.845024\pi\) | |||||||
\(734\) | −71.8198 | −2.65092 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 63.1654 | 2.32831 | ||||||||
\(737\) | 11.5509 | 0.425484 | ||||||||
\(738\) | 20.4117 | 0.751364 | ||||||||
\(739\) | 7.35893 | 0.270703 | 0.135351 | − | 0.990798i | \(-0.456784\pi\) | ||||
0.135351 | + | 0.990798i | \(0.456784\pi\) | |||||||
\(740\) | −0.620467 | −0.0228088 | ||||||||
\(741\) | −93.5133 | −3.43530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4792 | 1.26492 | 0.632460 | − | 0.774593i | \(-0.282045\pi\) | ||||
0.632460 | + | 0.774593i | \(0.282045\pi\) | |||||||
\(744\) | −3.68129 | −0.134963 | ||||||||
\(745\) | −7.43828 | −0.272518 | ||||||||
\(746\) | 69.0195 | 2.52698 | ||||||||
\(747\) | 5.75276 | 0.210482 | ||||||||
\(748\) | −9.07299 | −0.331741 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.48716 | 0.163848 | ||||||||
\(751\) | −50.3606 | −1.83769 | −0.918843 | − | 0.394624i | \(-0.870875\pi\) | ||||
−0.918843 | + | 0.394624i | \(0.870875\pi\) | |||||||
\(752\) | 25.5997 | 0.933525 | ||||||||
\(753\) | −6.54052 | −0.238350 | ||||||||
\(754\) | −10.3091 | −0.375433 | ||||||||
\(755\) | 4.37577 | 0.159250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6154 | −0.567551 | −0.283775 | − | 0.958891i | \(-0.591587\pi\) | ||||
−0.283775 | + | 0.958891i | \(0.591587\pi\) | |||||||
\(758\) | −49.5101 | −1.79829 | ||||||||
\(759\) | −17.1422 | −0.622223 | ||||||||
\(760\) | −2.46045 | −0.0892500 | ||||||||
\(761\) | −25.3155 | −0.917686 | −0.458843 | − | 0.888517i | \(-0.651736\pi\) | ||||
−0.458843 | + | 0.888517i | \(0.651736\pi\) | |||||||
\(762\) | −27.2790 | −0.988213 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.4888 | −0.668901 | ||||||||
\(765\) | −7.72677 | −0.279362 | ||||||||
\(766\) | −8.49408 | −0.306904 | ||||||||
\(767\) | −70.8446 | −2.55805 | ||||||||
\(768\) | 28.8993 | 1.04281 | ||||||||
\(769\) | −40.0616 | −1.44466 | −0.722329 | − | 0.691549i | \(-0.756928\pi\) | ||||
−0.722329 | + | 0.691549i | \(0.756928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.1892 | 1.15927 | ||||||||
\(772\) | 10.7506 | 0.386922 | ||||||||
\(773\) | −15.5185 | −0.558162 | −0.279081 | − | 0.960268i | \(-0.590030\pi\) | ||||
−0.279081 | + | 0.960268i | \(0.590030\pi\) | |||||||
\(774\) | −10.0832 | −0.362434 | ||||||||
\(775\) | 5.11902 | 0.183881 | ||||||||
\(776\) | 0.765727 | 0.0274880 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 49.8973 | 1.78890 | ||||||||
\(779\) | 40.9426 | 1.46692 | ||||||||
\(780\) | −26.8391 | −0.960995 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | −66.7513 | −2.38702 | ||||||||
\(783\) | −2.28442 | −0.0816386 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7522 | 0.490835 | ||||||||
\(786\) | −62.5897 | −2.23250 | ||||||||
\(787\) | 14.7204 | 0.524726 | 0.262363 | − | 0.964969i | \(-0.415498\pi\) | ||||
0.262363 | + | 0.964969i | \(0.415498\pi\) | |||||||
\(788\) | 6.63573 | 0.236388 | ||||||||
\(789\) | 23.5843 | 0.839622 | ||||||||
\(790\) | 24.7506 | 0.880586 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.601392 | 0.0213695 | ||||||||
\(793\) | 36.6357 | 1.30097 | ||||||||
\(794\) | −1.39357 | −0.0494560 | ||||||||
\(795\) | −30.0543 | −1.06592 | ||||||||
\(796\) | −26.5985 | −0.942759 | ||||||||
\(797\) | 8.03778 | 0.284713 | 0.142356 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142356 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.4263 | −1.04103 | ||||||||
\(800\) | 8.10630 | 0.286601 | ||||||||
\(801\) | 6.34245 | 0.224100 | ||||||||
\(802\) | −13.7799 | −0.486584 | ||||||||
\(803\) | −2.69503 | −0.0951055 | ||||||||
\(804\) | −54.8953 | −1.93601 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −58.9655 | −2.07697 | ||||||||
\(807\) | −3.50552 | −0.123400 | ||||||||
\(808\) | −6.30171 | −0.221693 | ||||||||
\(809\) | −15.5513 | −0.546754 | −0.273377 | − | 0.961907i | \(-0.588141\pi\) | ||||
−0.273377 | + | 0.961907i | \(0.588141\pi\) | |||||||
\(810\) | −22.7109 | −0.797980 | ||||||||
\(811\) | 40.8052 | 1.43286 | 0.716432 | − | 0.697657i | \(-0.245774\pi\) | ||||
0.716432 | + | 0.697657i | \(0.245774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.8173 | −1.53674 | ||||||||
\(814\) | 0.585831 | 0.0205334 | ||||||||
\(815\) | 9.07172 | 0.317768 | ||||||||
\(816\) | −33.7595 | −1.18182 | ||||||||
\(817\) | −20.2253 | −0.707594 | ||||||||
\(818\) | 58.5577 | 2.04742 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.7509 | 0.410359 | ||||||||
\(821\) | −26.6734 | −0.930909 | −0.465454 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465454 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(822\) | −58.7233 | −2.04821 | ||||||||
\(823\) | −0.430651 | −0.0150116 | −0.00750578 | − | 0.999972i | \(-0.502389\pi\) | ||||
−0.00750578 | + | 0.999972i | \(0.502389\pi\) | |||||||
\(824\) | 4.82442 | 0.168067 | ||||||||
\(825\) | −2.19994 | −0.0765921 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.1302 | −1.70842 | −0.854212 | − | 0.519924i | \(-0.825960\pi\) | ||||
−0.854212 | + | 0.519924i | \(0.825960\pi\) | |||||||
\(828\) | 30.9684 | 1.07623 | ||||||||
\(829\) | −19.4408 | −0.675208 | −0.337604 | − | 0.941288i | \(-0.609616\pi\) | ||||
−0.337604 | + | 0.941288i | \(0.609616\pi\) | |||||||
\(830\) | 6.37796 | 0.221382 | ||||||||
\(831\) | −3.09777 | −0.107460 | ||||||||
\(832\) | −52.1068 | −1.80648 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.87621 | −0.134222 | ||||||||
\(835\) | −8.90102 | −0.308033 | ||||||||
\(836\) | 16.2600 | 0.562362 | ||||||||
\(837\) | −13.0664 | −0.451640 | ||||||||
\(838\) | 45.1803 | 1.56073 | ||||||||
\(839\) | −50.8077 | −1.75408 | −0.877038 | − | 0.480421i | \(-0.840484\pi\) | ||||
−0.877038 | + | 0.480421i | \(0.840484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1990 | −0.972380 | ||||||||
\(842\) | −30.0999 | −1.03731 | ||||||||
\(843\) | 29.5354 | 1.01725 | ||||||||
\(844\) | −6.21963 | −0.214089 | ||||||||
\(845\) | −18.8934 | −0.649953 | ||||||||
\(846\) | 26.2910 | 0.903905 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −49.9158 | −1.71412 | ||||||||
\(849\) | −35.4016 | −1.21498 | ||||||||
\(850\) | −8.56650 | −0.293829 | ||||||||
\(851\) | 2.23804 | 0.0767190 | ||||||||
\(852\) | 38.0196 | 1.30253 | ||||||||
\(853\) | 19.7547 | 0.676390 | 0.338195 | − | 0.941076i | \(-0.390184\pi\) | ||||
0.338195 | + | 0.941076i | \(0.390184\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.8474 | 0.473570 | ||||||||
\(856\) | −2.11800 | −0.0723918 | ||||||||
\(857\) | −9.86100 | −0.336845 | −0.168423 | − | 0.985715i | \(-0.553867\pi\) | ||||
−0.168423 | + | 0.985715i | \(0.553867\pi\) | |||||||
\(858\) | 25.3409 | 0.865123 | ||||||||
\(859\) | 4.47795 | 0.152786 | 0.0763929 | − | 0.997078i | \(-0.475660\pi\) | ||||
0.0763929 | + | 0.997078i | \(0.475660\pi\) | |||||||
\(860\) | −5.80484 | −0.197944 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.0143 | −1.43101 | ||||||||
\(863\) | 55.5123 | 1.88966 | 0.944830 | − | 0.327561i | \(-0.106227\pi\) | ||||
0.944830 | + | 0.327561i | \(0.106227\pi\) | |||||||
\(864\) | −20.6915 | −0.703938 | ||||||||
\(865\) | −10.9204 | −0.371303 | ||||||||
\(866\) | 67.8459 | 2.30550 | ||||||||
\(867\) | 1.40684 | 0.0477789 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.1346 | −0.411637 | ||||||||
\(870\) | 4.01586 | 0.136151 | ||||||||
\(871\) | −65.2331 | −2.21034 | ||||||||
\(872\) | −0.784499 | −0.0265665 | ||||||||
\(873\) | −4.30949 | −0.145854 | ||||||||
\(874\) | 119.627 | 4.04644 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.8080 | 0.432742 | ||||||||
\(877\) | 10.7024 | 0.361393 | 0.180696 | − | 0.983539i | \(-0.442165\pi\) | ||||
0.180696 | + | 0.983539i | \(0.442165\pi\) | |||||||
\(878\) | 16.3744 | 0.552611 | ||||||||
\(879\) | −25.1413 | −0.847993 | ||||||||
\(880\) | −3.65378 | −0.123169 | ||||||||
\(881\) | 3.64045 | 0.122650 | 0.0613249 | − | 0.998118i | \(-0.480467\pi\) | ||||
0.0613249 | + | 0.998118i | \(0.480467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.1889 | −1.41977 | −0.709884 | − | 0.704319i | \(-0.751253\pi\) | ||||
−0.709884 | + | 0.704319i | \(0.751253\pi\) | |||||||
\(884\) | 51.2390 | 1.72335 | ||||||||
\(885\) | 27.5973 | 0.927674 | ||||||||
\(886\) | 68.2958 | 2.29444 | ||||||||
\(887\) | −29.6820 | −0.996624 | −0.498312 | − | 0.866998i | \(-0.666047\pi\) | ||||
−0.498312 | + | 0.866998i | \(0.666047\pi\) | |||||||
\(888\) | −0.206550 | −0.00693136 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.03174 | 0.235704 | ||||||||
\(891\) | 11.1346 | 0.373023 | ||||||||
\(892\) | 25.1471 | 0.841989 | ||||||||
\(893\) | 52.7357 | 1.76473 | ||||||||
\(894\) | −33.3767 | −1.11629 | ||||||||
\(895\) | 11.1203 | 0.371710 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 96.8093 | 3.23237 | ||||||||
\(898\) | −16.7861 | −0.560159 | ||||||||
\(899\) | 4.58136 | 0.152797 | ||||||||
\(900\) | 3.97431 | 0.132477 | ||||||||
\(901\) | 57.3771 | 1.91151 | ||||||||
\(902\) | −11.0949 | −0.369420 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.70719 | −0.156559 | ||||||||
\(905\) | 14.1679 | 0.470957 | ||||||||
\(906\) | 19.6348 | 0.652321 | ||||||||
\(907\) | −20.3971 | −0.677274 | −0.338637 | − | 0.940917i | \(-0.609966\pi\) | ||||
−0.338637 | + | 0.940917i | \(0.609966\pi\) | |||||||
\(908\) | 28.6532 | 0.950889 | ||||||||
\(909\) | 35.4659 | 1.17633 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.3589 | −0.376338 | −0.188169 | − | 0.982137i | \(-0.560255\pi\) | ||||
−0.188169 | + | 0.982137i | \(0.560255\pi\) | |||||||
\(912\) | 60.5014 | 2.00340 | ||||||||
\(913\) | −3.12695 | −0.103487 | ||||||||
\(914\) | 42.0267 | 1.39012 | ||||||||
\(915\) | −14.2714 | −0.471796 | ||||||||
\(916\) | 55.4732 | 1.83289 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 21.8661 | 0.721690 | ||||||||
\(919\) | 45.1197 | 1.48836 | 0.744181 | − | 0.667979i | \(-0.232840\pi\) | ||||
0.744181 | + | 0.667979i | \(0.232840\pi\) | |||||||
\(920\) | 2.54718 | 0.0839779 | ||||||||
\(921\) | 36.9382 | 1.21716 | ||||||||
\(922\) | 60.0718 | 1.97836 | ||||||||
\(923\) | 45.1794 | 1.48710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.287218 | 0.00944367 | ||||||||
\(926\) | −49.8034 | −1.63664 | ||||||||
\(927\) | −27.1517 | −0.891780 | ||||||||
\(928\) | 7.25489 | 0.238153 | ||||||||
\(929\) | −5.06286 | −0.166107 | −0.0830536 | − | 0.996545i | \(-0.526467\pi\) | ||||
−0.0830536 | + | 0.996545i | \(0.526467\pi\) | |||||||
\(930\) | 22.9698 | 0.753211 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.0235 | 0.361087 | ||||||||
\(933\) | −60.2041 | −1.97099 | ||||||||
\(934\) | 62.3348 | 2.03966 | ||||||||
\(935\) | 4.19994 | 0.137353 | ||||||||
\(936\) | −3.39632 | −0.111012 | ||||||||
\(937\) | 9.96481 | 0.325536 | 0.162768 | − | 0.986664i | \(-0.447958\pi\) | ||||
0.162768 | + | 0.986664i | \(0.447958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.3913 | 1.02442 | ||||||||
\(940\) | 15.1356 | 0.493669 | ||||||||
\(941\) | 41.6118 | 1.35651 | 0.678253 | − | 0.734828i | \(-0.262737\pi\) | ||||
0.678253 | + | 0.734828i | \(0.262737\pi\) | |||||||
\(942\) | 61.7081 | 2.01056 | ||||||||
\(943\) | −42.3857 | −1.38027 | ||||||||
\(944\) | 45.8352 | 1.49181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.48080 | 0.178196 | ||||||||
\(947\) | 33.9477 | 1.10315 | 0.551576 | − | 0.834125i | \(-0.314027\pi\) | ||||
0.551576 | + | 0.834125i | \(0.314027\pi\) | |||||||
\(948\) | 57.6691 | 1.87300 | ||||||||
\(949\) | 15.2200 | 0.494061 | ||||||||
\(950\) | 15.3523 | 0.498094 | ||||||||
\(951\) | 20.8418 | 0.675840 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.2835 | −1.69363 | −0.846814 | − | 0.531889i | \(-0.821482\pi\) | ||||
−0.846814 | + | 0.531889i | \(0.821482\pi\) | |||||||
\(954\) | −51.2638 | −1.65973 | ||||||||
\(955\) | 8.55857 | 0.276949 | ||||||||
\(956\) | −26.8912 | −0.869724 | ||||||||
\(957\) | −1.96888 | −0.0636447 | ||||||||
\(958\) | 63.1328 | 2.03973 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 20.2981 | 0.655117 | ||||||||
\(961\) | −4.79564 | −0.154698 | ||||||||
\(962\) | −3.30843 | −0.106668 | ||||||||
\(963\) | 11.9200 | 0.384118 | ||||||||
\(964\) | 8.15706 | 0.262721 | ||||||||
\(965\) | −4.97651 | −0.160199 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.2044 | −0.746202 | −0.373101 | − | 0.927791i | \(-0.621706\pi\) | ||||
−0.373101 | + | 0.927791i | \(0.621706\pi\) | |||||||
\(968\) | −0.326891 | −0.0105067 | ||||||||
\(969\) | −69.5450 | −2.23411 | ||||||||
\(970\) | −4.77784 | −0.153407 | ||||||||
\(971\) | −4.23011 | −0.135751 | −0.0678753 | − | 0.997694i | \(-0.521622\pi\) | ||||
−0.0678753 | + | 0.997694i | \(0.521622\pi\) | |||||||
\(972\) | −36.3743 | −1.16670 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.972993 | −0.0311767 | ||||||||
\(975\) | 12.4240 | 0.397886 | ||||||||
\(976\) | −23.7027 | −0.758704 | ||||||||
\(977\) | −42.1067 | −1.34711 | −0.673557 | − | 0.739136i | \(-0.735234\pi\) | ||||
−0.673557 | + | 0.739136i | \(0.735234\pi\) | |||||||
\(978\) | 40.7062 | 1.30164 | ||||||||
\(979\) | −3.44748 | −0.110182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.41514 | 0.140965 | ||||||||
\(982\) | −37.3187 | −1.19089 | ||||||||
\(983\) | −32.9417 | −1.05068 | −0.525338 | − | 0.850894i | \(-0.676061\pi\) | ||||
−0.525338 | + | 0.850894i | \(0.676061\pi\) | |||||||
\(984\) | 3.91180 | 0.124704 | ||||||||
\(985\) | −3.07172 | −0.0978730 | ||||||||
\(986\) | −7.66675 | −0.244159 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −91.8269 | −2.92140 | ||||||||
\(989\) | 20.9382 | 0.665796 | ||||||||
\(990\) | −3.75246 | −0.119261 | ||||||||
\(991\) | −34.5738 | −1.09827 | −0.549137 | − | 0.835732i | \(-0.685043\pi\) | ||||
−0.549137 | + | 0.835732i | \(0.685043\pi\) | |||||||
\(992\) | 41.4963 | 1.31751 | ||||||||
\(993\) | 13.4706 | 0.427478 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.3126 | 0.390336 | ||||||||
\(996\) | 14.8607 | 0.470879 | ||||||||
\(997\) | −17.3050 | −0.548054 | −0.274027 | − | 0.961722i | \(-0.588356\pi\) | ||||
−0.274027 | + | 0.961722i | \(0.588356\pi\) | |||||||
\(998\) | 41.5767 | 1.31609 | ||||||||
\(999\) | −0.733128 | −0.0231951 |
(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 | 2695.2.a.l.1.1 | 4 | ||
7.6 | odd | 2 | 385.2.a.h.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 3465.2.a.bk.1.4 | 4 | |||
28.27 | even | 2 | 6160.2.a.br.1.4 | 4 | |||
35.13 | even | 4 | 1925.2.b.p.1849.7 | 8 | |||
35.27 | even | 4 | 1925.2.b.p.1849.2 | 8 | |||
35.34 | odd | 2 | 1925.2.a.x.1.4 | 4 | |||
77.76 | even | 2 | 4235.2.a.r.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.a.h.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
1925.2.a.x.1.4 | 4 | 35.34 | odd | 2 | |||
1925.2.b.p.1849.2 | 8 | 35.27 | even | 4 | |||
1925.2.b.p.1849.7 | 8 | 35.13 | even | 4 | |||
2695.2.a.l.1.1 | 4 | 1.1 | even | 1 | trivial | ||
3465.2.a.bk.1.4 | 4 | 21.20 | even | 2 | |||
4235.2.a.r.1.4 | 4 | 77.76 | even | 2 | |||
6160.2.a.br.1.4 | 4 | 28.27 | even | 2 |