Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, 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("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.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: | \(32.0439663311\) |
Analytic rank: | \(1\) |
Dimension: | \(157\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60727 | −1.84362 | −0.921811 | − | 0.387641i | \(-0.873290\pi\) | ||||
−0.921811 | + | 0.387641i | \(0.873290\pi\) | |||||||
\(3\) | 1.83175 | 1.05756 | 0.528781 | − | 0.848758i | \(-0.322649\pi\) | ||||
0.528781 | + | 0.848758i | \(0.322649\pi\) | |||||||
\(4\) | 4.79788 | 2.39894 | ||||||||
\(5\) | −1.15472 | −0.516405 | −0.258202 | − | 0.966091i | \(-0.583130\pi\) | ||||
−0.258202 | + | 0.966091i | \(0.583130\pi\) | |||||||
\(6\) | −4.77588 | −1.94974 | ||||||||
\(7\) | −1.01890 | −0.385107 | −0.192554 | − | 0.981286i | \(-0.561677\pi\) | ||||
−0.192554 | + | 0.981286i | \(0.561677\pi\) | |||||||
\(8\) | −7.29484 | −2.57911 | ||||||||
\(9\) | 0.355310 | 0.118437 | ||||||||
\(10\) | 3.01066 | 0.952055 | ||||||||
\(11\) | −0.0753550 | −0.0227204 | −0.0113602 | − | 0.999935i | \(-0.503616\pi\) | ||||
−0.0113602 | + | 0.999935i | \(0.503616\pi\) | |||||||
\(12\) | 8.78852 | 2.53703 | ||||||||
\(13\) | −0.480633 | −0.133304 | −0.0666518 | − | 0.997776i | \(-0.521232\pi\) | ||||
−0.0666518 | + | 0.997776i | \(0.521232\pi\) | |||||||
\(14\) | 2.65654 | 0.709991 | ||||||||
\(15\) | −2.11515 | −0.546130 | ||||||||
\(16\) | 9.42388 | 2.35597 | ||||||||
\(17\) | 4.79189 | 1.16220 | 0.581102 | − | 0.813831i | \(-0.302622\pi\) | ||||
0.581102 | + | 0.813831i | \(0.302622\pi\) | |||||||
\(18\) | −0.926390 | −0.218352 | ||||||||
\(19\) | 5.38687 | 1.23583 | 0.617917 | − | 0.786243i | \(-0.287977\pi\) | ||||
0.617917 | + | 0.786243i | \(0.287977\pi\) | |||||||
\(20\) | −5.54019 | −1.23882 | ||||||||
\(21\) | −1.86637 | −0.407274 | ||||||||
\(22\) | 0.196471 | 0.0418878 | ||||||||
\(23\) | −3.84351 | −0.801428 | −0.400714 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400714 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(24\) | −13.3623 | −2.72757 | ||||||||
\(25\) | −3.66663 | −0.733326 | ||||||||
\(26\) | 1.25314 | 0.245761 | ||||||||
\(27\) | −4.84441 | −0.932308 | ||||||||
\(28\) | −4.88855 | −0.923848 | ||||||||
\(29\) | 6.34587 | 1.17840 | 0.589199 | − | 0.807988i | \(-0.299443\pi\) | ||||
0.589199 | + | 0.807988i | \(0.299443\pi\) | |||||||
\(30\) | 5.51478 | 1.00686 | ||||||||
\(31\) | −3.87811 | −0.696529 | −0.348265 | − | 0.937396i | \(-0.613229\pi\) | ||||
−0.348265 | + | 0.937396i | \(0.613229\pi\) | |||||||
\(32\) | −9.98096 | −1.76440 | ||||||||
\(33\) | −0.138032 | −0.0240282 | ||||||||
\(34\) | −12.4938 | −2.14266 | ||||||||
\(35\) | 1.17654 | 0.198871 | ||||||||
\(36\) | 1.70473 | 0.284122 | ||||||||
\(37\) | −8.07254 | −1.32712 | −0.663559 | − | 0.748124i | \(-0.730955\pi\) | ||||
−0.663559 | + | 0.748124i | \(0.730955\pi\) | |||||||
\(38\) | −14.0451 | −2.27841 | ||||||||
\(39\) | −0.880400 | −0.140977 | ||||||||
\(40\) | 8.42346 | 1.33187 | ||||||||
\(41\) | 6.27018 | 0.979237 | 0.489619 | − | 0.871937i | \(-0.337136\pi\) | ||||
0.489619 | + | 0.871937i | \(0.337136\pi\) | |||||||
\(42\) | 4.86613 | 0.750860 | ||||||||
\(43\) | −8.53557 | −1.30166 | −0.650831 | − | 0.759222i | \(-0.725580\pi\) | ||||
−0.650831 | + | 0.759222i | \(0.725580\pi\) | |||||||
\(44\) | −0.361544 | −0.0545048 | ||||||||
\(45\) | −0.410282 | −0.0611612 | ||||||||
\(46\) | 10.0211 | 1.47753 | ||||||||
\(47\) | −1.62043 | −0.236363 | −0.118182 | − | 0.992992i | \(-0.537707\pi\) | ||||
−0.118182 | + | 0.992992i | \(0.537707\pi\) | |||||||
\(48\) | 17.2622 | 2.49158 | ||||||||
\(49\) | −5.96185 | −0.851693 | ||||||||
\(50\) | 9.55991 | 1.35198 | ||||||||
\(51\) | 8.77755 | 1.22910 | ||||||||
\(52\) | −2.30602 | −0.319787 | ||||||||
\(53\) | 3.70097 | 0.508368 | 0.254184 | − | 0.967156i | \(-0.418193\pi\) | ||||
0.254184 | + | 0.967156i | \(0.418193\pi\) | |||||||
\(54\) | 12.6307 | 1.71882 | ||||||||
\(55\) | 0.0870136 | 0.0117329 | ||||||||
\(56\) | 7.43269 | 0.993235 | ||||||||
\(57\) | 9.86741 | 1.30697 | ||||||||
\(58\) | −16.5454 | −2.17252 | ||||||||
\(59\) | 5.72151 | 0.744878 | 0.372439 | − | 0.928057i | \(-0.378522\pi\) | ||||
0.372439 | + | 0.928057i | \(0.378522\pi\) | |||||||
\(60\) | −10.1482 | −1.31013 | ||||||||
\(61\) | 1.57985 | 0.202279 | 0.101139 | − | 0.994872i | \(-0.467751\pi\) | ||||
0.101139 | + | 0.994872i | \(0.467751\pi\) | |||||||
\(62\) | 10.1113 | 1.28414 | ||||||||
\(63\) | −0.362024 | −0.0456108 | ||||||||
\(64\) | 7.17535 | 0.896919 | ||||||||
\(65\) | 0.554995 | 0.0688386 | ||||||||
\(66\) | 0.359886 | 0.0442989 | ||||||||
\(67\) | −12.0493 | −1.47206 | −0.736030 | − | 0.676949i | \(-0.763302\pi\) | ||||
−0.736030 | + | 0.676949i | \(0.763302\pi\) | |||||||
\(68\) | 22.9909 | 2.78806 | ||||||||
\(69\) | −7.04036 | −0.847560 | ||||||||
\(70\) | −3.06755 | −0.366643 | ||||||||
\(71\) | 15.2328 | 1.80780 | 0.903899 | − | 0.427745i | \(-0.140692\pi\) | ||||
0.903899 | + | 0.427745i | \(0.140692\pi\) | |||||||
\(72\) | −2.59193 | −0.305461 | ||||||||
\(73\) | 7.02673 | 0.822416 | 0.411208 | − | 0.911541i | \(-0.365107\pi\) | ||||
0.411208 | + | 0.911541i | \(0.365107\pi\) | |||||||
\(74\) | 21.0473 | 2.44670 | ||||||||
\(75\) | −6.71635 | −0.775538 | ||||||||
\(76\) | 25.8456 | 2.96469 | ||||||||
\(77\) | 0.0767790 | 0.00874978 | ||||||||
\(78\) | 2.29544 | 0.259908 | ||||||||
\(79\) | −2.19477 | −0.246931 | −0.123466 | − | 0.992349i | \(-0.539401\pi\) | ||||
−0.123466 | + | 0.992349i | \(0.539401\pi\) | |||||||
\(80\) | −10.8819 | −1.21663 | ||||||||
\(81\) | −9.93968 | −1.10441 | ||||||||
\(82\) | −16.3481 | −1.80534 | ||||||||
\(83\) | −8.97436 | −0.985064 | −0.492532 | − | 0.870294i | \(-0.663929\pi\) | ||||
−0.492532 | + | 0.870294i | \(0.663929\pi\) | |||||||
\(84\) | −8.95460 | −0.977026 | ||||||||
\(85\) | −5.53327 | −0.600168 | ||||||||
\(86\) | 22.2546 | 2.39977 | ||||||||
\(87\) | 11.6240 | 1.24623 | ||||||||
\(88\) | 0.549702 | 0.0585985 | ||||||||
\(89\) | 1.48870 | 0.157802 | 0.0789008 | − | 0.996882i | \(-0.474859\pi\) | ||||
0.0789008 | + | 0.996882i | \(0.474859\pi\) | |||||||
\(90\) | 1.06972 | 0.112758 | ||||||||
\(91\) | 0.489716 | 0.0513362 | ||||||||
\(92\) | −18.4407 | −1.92258 | ||||||||
\(93\) | −7.10373 | −0.736623 | ||||||||
\(94\) | 4.22489 | 0.435764 | ||||||||
\(95\) | −6.22031 | −0.638190 | ||||||||
\(96\) | −18.2826 | −1.86596 | ||||||||
\(97\) | −3.54976 | −0.360423 | −0.180212 | − | 0.983628i | \(-0.557678\pi\) | ||||
−0.180212 | + | 0.983628i | \(0.557678\pi\) | |||||||
\(98\) | 15.5442 | 1.57020 | ||||||||
\(99\) | −0.0267744 | −0.00269093 | ||||||||
\(100\) | −17.5920 | −1.75920 | ||||||||
\(101\) | 3.74777 | 0.372918 | 0.186459 | − | 0.982463i | \(-0.440299\pi\) | ||||
0.186459 | + | 0.982463i | \(0.440299\pi\) | |||||||
\(102\) | −22.8855 | −2.26600 | ||||||||
\(103\) | 2.17975 | 0.214777 | 0.107389 | − | 0.994217i | \(-0.465751\pi\) | ||||
0.107389 | + | 0.994217i | \(0.465751\pi\) | |||||||
\(104\) | 3.50614 | 0.343805 | ||||||||
\(105\) | 2.15512 | 0.210318 | ||||||||
\(106\) | −9.64945 | −0.937237 | ||||||||
\(107\) | −13.5794 | −1.31277 | −0.656387 | − | 0.754424i | \(-0.727916\pi\) | ||||
−0.656387 | + | 0.754424i | \(0.727916\pi\) | |||||||
\(108\) | −23.2429 | −2.23655 | ||||||||
\(109\) | 4.68781 | 0.449010 | 0.224505 | − | 0.974473i | \(-0.427923\pi\) | ||||
0.224505 | + | 0.974473i | \(0.427923\pi\) | |||||||
\(110\) | −0.226868 | −0.0216310 | ||||||||
\(111\) | −14.7869 | −1.40351 | ||||||||
\(112\) | −9.60196 | −0.907300 | ||||||||
\(113\) | 11.0750 | 1.04185 | 0.520924 | − | 0.853603i | \(-0.325588\pi\) | ||||
0.520924 | + | 0.853603i | \(0.325588\pi\) | |||||||
\(114\) | −25.7270 | −2.40956 | ||||||||
\(115\) | 4.43817 | 0.413861 | ||||||||
\(116\) | 30.4467 | 2.82691 | ||||||||
\(117\) | −0.170774 | −0.0157880 | ||||||||
\(118\) | −14.9176 | −1.37327 | ||||||||
\(119\) | −4.88245 | −0.447573 | ||||||||
\(120\) | 15.4297 | 1.40853 | ||||||||
\(121\) | −10.9943 | −0.999484 | ||||||||
\(122\) | −4.11910 | −0.372925 | ||||||||
\(123\) | 11.4854 | 1.03560 | ||||||||
\(124\) | −18.6067 | −1.67093 | ||||||||
\(125\) | 10.0075 | 0.895098 | ||||||||
\(126\) | 0.943896 | 0.0840890 | ||||||||
\(127\) | 0.427077 | 0.0378970 | 0.0189485 | − | 0.999820i | \(-0.493968\pi\) | ||||
0.0189485 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(128\) | 1.25382 | 0.110823 | ||||||||
\(129\) | −15.6350 | −1.37659 | ||||||||
\(130\) | −1.44702 | −0.126912 | ||||||||
\(131\) | −15.9941 | −1.39741 | −0.698704 | − | 0.715411i | \(-0.746240\pi\) | ||||
−0.698704 | + | 0.715411i | \(0.746240\pi\) | |||||||
\(132\) | −0.662259 | −0.0576422 | ||||||||
\(133\) | −5.48867 | −0.475928 | ||||||||
\(134\) | 31.4159 | 2.71392 | ||||||||
\(135\) | 5.59392 | 0.481448 | ||||||||
\(136\) | −34.9561 | −2.99746 | ||||||||
\(137\) | 15.3692 | 1.31308 | 0.656539 | − | 0.754292i | \(-0.272020\pi\) | ||||
0.656539 | + | 0.754292i | \(0.272020\pi\) | |||||||
\(138\) | 18.3561 | 1.56258 | ||||||||
\(139\) | −18.0680 | −1.53250 | −0.766252 | − | 0.642540i | \(-0.777881\pi\) | ||||
−0.766252 | + | 0.642540i | \(0.777881\pi\) | |||||||
\(140\) | 5.64488 | 0.477080 | ||||||||
\(141\) | −2.96821 | −0.249969 | ||||||||
\(142\) | −39.7160 | −3.33290 | ||||||||
\(143\) | 0.0362181 | 0.00302871 | ||||||||
\(144\) | 3.34840 | 0.279033 | ||||||||
\(145\) | −7.32767 | −0.608530 | ||||||||
\(146\) | −18.3206 | −1.51622 | ||||||||
\(147\) | −10.9206 | −0.900717 | ||||||||
\(148\) | −38.7311 | −3.18367 | ||||||||
\(149\) | −21.2328 | −1.73946 | −0.869731 | − | 0.493526i | \(-0.835708\pi\) | ||||
−0.869731 | + | 0.493526i | \(0.835708\pi\) | |||||||
\(150\) | 17.5114 | 1.42980 | ||||||||
\(151\) | 5.55500 | 0.452060 | 0.226030 | − | 0.974120i | \(-0.427425\pi\) | ||||
0.226030 | + | 0.974120i | \(0.427425\pi\) | |||||||
\(152\) | −39.2964 | −3.18736 | ||||||||
\(153\) | 1.70261 | 0.137648 | ||||||||
\(154\) | −0.200184 | −0.0161313 | ||||||||
\(155\) | 4.47812 | 0.359691 | ||||||||
\(156\) | −4.22405 | −0.338195 | ||||||||
\(157\) | 0.915628 | 0.0730751 | 0.0365375 | − | 0.999332i | \(-0.488367\pi\) | ||||
0.0365375 | + | 0.999332i | \(0.488367\pi\) | |||||||
\(158\) | 5.72238 | 0.455248 | ||||||||
\(159\) | 6.77926 | 0.537630 | ||||||||
\(160\) | 11.5252 | 0.911145 | ||||||||
\(161\) | 3.91615 | 0.308636 | ||||||||
\(162\) | 25.9155 | 2.03611 | ||||||||
\(163\) | 11.4408 | 0.896115 | 0.448057 | − | 0.894005i | \(-0.352116\pi\) | ||||
0.448057 | + | 0.894005i | \(0.352116\pi\) | |||||||
\(164\) | 30.0835 | 2.34913 | ||||||||
\(165\) | 0.159387 | 0.0124083 | ||||||||
\(166\) | 23.3986 | 1.81609 | ||||||||
\(167\) | −13.1313 | −1.01613 | −0.508066 | − | 0.861318i | \(-0.669639\pi\) | ||||
−0.508066 | + | 0.861318i | \(0.669639\pi\) | |||||||
\(168\) | 13.6148 | 1.05041 | ||||||||
\(169\) | −12.7690 | −0.982230 | ||||||||
\(170\) | 14.4268 | 1.10648 | ||||||||
\(171\) | 1.91401 | 0.146368 | ||||||||
\(172\) | −40.9526 | −3.12261 | ||||||||
\(173\) | −23.9185 | −1.81849 | −0.909245 | − | 0.416262i | \(-0.863340\pi\) | ||||
−0.909245 | + | 0.416262i | \(0.863340\pi\) | |||||||
\(174\) | −30.3071 | −2.29757 | ||||||||
\(175\) | 3.73592 | 0.282409 | ||||||||
\(176\) | −0.710136 | −0.0535285 | ||||||||
\(177\) | 10.4804 | 0.787754 | ||||||||
\(178\) | −3.88144 | −0.290926 | ||||||||
\(179\) | −19.3904 | −1.44930 | −0.724652 | − | 0.689115i | \(-0.758000\pi\) | ||||
−0.724652 | + | 0.689115i | \(0.758000\pi\) | |||||||
\(180\) | −1.96848 | −0.146722 | ||||||||
\(181\) | 11.0732 | 0.823065 | 0.411533 | − | 0.911395i | \(-0.364994\pi\) | ||||
0.411533 | + | 0.911395i | \(0.364994\pi\) | |||||||
\(182\) | −1.27682 | −0.0946444 | ||||||||
\(183\) | 2.89389 | 0.213922 | ||||||||
\(184\) | 28.0378 | 2.06697 | ||||||||
\(185\) | 9.32149 | 0.685330 | ||||||||
\(186\) | 18.5214 | 1.35805 | ||||||||
\(187\) | −0.361093 | −0.0264057 | ||||||||
\(188\) | −7.77460 | −0.567021 | ||||||||
\(189\) | 4.93596 | 0.359038 | ||||||||
\(190\) | 16.2181 | 1.17658 | ||||||||
\(191\) | −16.6181 | −1.20244 | −0.601221 | − | 0.799083i | \(-0.705319\pi\) | ||||
−0.601221 | + | 0.799083i | \(0.705319\pi\) | |||||||
\(192\) | 13.1435 | 0.948547 | ||||||||
\(193\) | −13.5168 | −0.972962 | −0.486481 | − | 0.873691i | \(-0.661720\pi\) | ||||
−0.486481 | + | 0.873691i | \(0.661720\pi\) | |||||||
\(194\) | 9.25519 | 0.664484 | ||||||||
\(195\) | 1.01661 | 0.0728011 | ||||||||
\(196\) | −28.6042 | −2.04316 | ||||||||
\(197\) | 3.04756 | 0.217130 | 0.108565 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108565 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(198\) | 0.0698081 | 0.00496105 | ||||||||
\(199\) | 24.0733 | 1.70651 | 0.853255 | − | 0.521493i | \(-0.174625\pi\) | ||||
0.853255 | + | 0.521493i | \(0.174625\pi\) | |||||||
\(200\) | 26.7475 | 1.89133 | ||||||||
\(201\) | −22.0714 | −1.55679 | ||||||||
\(202\) | −9.77148 | −0.687519 | ||||||||
\(203\) | −6.46579 | −0.453809 | ||||||||
\(204\) | 42.1136 | 2.94854 | ||||||||
\(205\) | −7.24027 | −0.505683 | ||||||||
\(206\) | −5.68321 | −0.395968 | ||||||||
\(207\) | −1.36564 | −0.0949184 | ||||||||
\(208\) | −4.52943 | −0.314059 | ||||||||
\(209\) | −0.405928 | −0.0280786 | ||||||||
\(210\) | −5.61899 | −0.387747 | ||||||||
\(211\) | −7.44328 | −0.512416 | −0.256208 | − | 0.966622i | \(-0.582473\pi\) | ||||
−0.256208 | + | 0.966622i | \(0.582473\pi\) | |||||||
\(212\) | 17.7568 | 1.21954 | ||||||||
\(213\) | 27.9027 | 1.91186 | ||||||||
\(214\) | 35.4053 | 2.42026 | ||||||||
\(215\) | 9.85616 | 0.672185 | ||||||||
\(216\) | 35.3392 | 2.40453 | ||||||||
\(217\) | 3.95140 | 0.268238 | ||||||||
\(218\) | −12.2224 | −0.827805 | ||||||||
\(219\) | 12.8712 | 0.869756 | ||||||||
\(220\) | 0.417481 | 0.0281465 | ||||||||
\(221\) | −2.30314 | −0.154926 | ||||||||
\(222\) | 38.5535 | 2.58754 | ||||||||
\(223\) | 4.37262 | 0.292812 | 0.146406 | − | 0.989225i | \(-0.453229\pi\) | ||||
0.146406 | + | 0.989225i | \(0.453229\pi\) | |||||||
\(224\) | 10.1696 | 0.679483 | ||||||||
\(225\) | −1.30279 | −0.0868527 | ||||||||
\(226\) | −28.8755 | −1.92077 | ||||||||
\(227\) | −14.3997 | −0.955743 | −0.477872 | − | 0.878430i | \(-0.658592\pi\) | ||||
−0.477872 | + | 0.878430i | \(0.658592\pi\) | |||||||
\(228\) | 47.3426 | 3.13534 | ||||||||
\(229\) | −2.94469 | −0.194590 | −0.0972951 | − | 0.995256i | \(-0.531019\pi\) | ||||
−0.0972951 | + | 0.995256i | \(0.531019\pi\) | |||||||
\(230\) | −11.5715 | −0.763003 | ||||||||
\(231\) | 0.140640 | 0.00925343 | ||||||||
\(232\) | −46.2921 | −3.03922 | ||||||||
\(233\) | −4.55987 | −0.298727 | −0.149363 | − | 0.988782i | \(-0.547722\pi\) | ||||
−0.149363 | + | 0.988782i | \(0.547722\pi\) | |||||||
\(234\) | 0.445254 | 0.0291071 | ||||||||
\(235\) | 1.87113 | 0.122059 | ||||||||
\(236\) | 27.4511 | 1.78692 | ||||||||
\(237\) | −4.02028 | −0.261145 | ||||||||
\(238\) | 12.7299 | 0.825155 | ||||||||
\(239\) | −18.4957 | −1.19639 | −0.598194 | − | 0.801351i | \(-0.704115\pi\) | ||||
−0.598194 | + | 0.801351i | \(0.704115\pi\) | |||||||
\(240\) | −19.9329 | −1.28667 | ||||||||
\(241\) | 5.05414 | 0.325566 | 0.162783 | − | 0.986662i | \(-0.447953\pi\) | ||||
0.162783 | + | 0.986662i | \(0.447953\pi\) | |||||||
\(242\) | 28.6652 | 1.84267 | ||||||||
\(243\) | −3.67378 | −0.235673 | ||||||||
\(244\) | 7.57992 | 0.485254 | ||||||||
\(245\) | 6.88424 | 0.439818 | ||||||||
\(246\) | −29.9456 | −1.90926 | ||||||||
\(247\) | −2.58911 | −0.164741 | ||||||||
\(248\) | 28.2902 | 1.79643 | ||||||||
\(249\) | −16.4388 | −1.04177 | ||||||||
\(250\) | −26.0923 | −1.65022 | ||||||||
\(251\) | −22.5966 | −1.42629 | −0.713143 | − | 0.701018i | \(-0.752729\pi\) | ||||
−0.713143 | + | 0.701018i | \(0.752729\pi\) | |||||||
\(252\) | −1.73695 | −0.109417 | ||||||||
\(253\) | 0.289628 | 0.0182088 | ||||||||
\(254\) | −1.11351 | −0.0698677 | ||||||||
\(255\) | −10.1356 | −0.634714 | ||||||||
\(256\) | −17.6198 | −1.10123 | ||||||||
\(257\) | −1.82103 | −0.113593 | −0.0567964 | − | 0.998386i | \(-0.518089\pi\) | ||||
−0.0567964 | + | 0.998386i | \(0.518089\pi\) | |||||||
\(258\) | 40.7648 | 2.53791 | ||||||||
\(259\) | 8.22509 | 0.511082 | ||||||||
\(260\) | 2.66280 | 0.165140 | ||||||||
\(261\) | 2.25475 | 0.139565 | ||||||||
\(262\) | 41.7009 | 2.57629 | ||||||||
\(263\) | 23.2240 | 1.43206 | 0.716028 | − | 0.698071i | \(-0.245958\pi\) | ||||
0.716028 | + | 0.698071i | \(0.245958\pi\) | |||||||
\(264\) | 1.00692 | 0.0619715 | ||||||||
\(265\) | −4.27357 | −0.262523 | ||||||||
\(266\) | 14.3105 | 0.877431 | ||||||||
\(267\) | 2.72692 | 0.166885 | ||||||||
\(268\) | −57.8112 | −3.53138 | ||||||||
\(269\) | 15.9970 | 0.975352 | 0.487676 | − | 0.873025i | \(-0.337845\pi\) | ||||
0.487676 | + | 0.873025i | \(0.337845\pi\) | |||||||
\(270\) | −14.5849 | −0.887608 | ||||||||
\(271\) | −4.35694 | −0.264665 | −0.132333 | − | 0.991205i | \(-0.542247\pi\) | ||||
−0.132333 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(272\) | 45.1582 | 2.73812 | ||||||||
\(273\) | 0.897037 | 0.0542911 | ||||||||
\(274\) | −40.0717 | −2.42082 | ||||||||
\(275\) | 0.276299 | 0.0166615 | ||||||||
\(276\) | −33.7788 | −2.03324 | ||||||||
\(277\) | 1.09551 | 0.0658230 | 0.0329115 | − | 0.999458i | \(-0.489522\pi\) | ||||
0.0329115 | + | 0.999458i | \(0.489522\pi\) | |||||||
\(278\) | 47.1081 | 2.82536 | ||||||||
\(279\) | −1.37793 | −0.0824946 | ||||||||
\(280\) | −8.58264 | −0.512911 | ||||||||
\(281\) | 21.1359 | 1.26086 | 0.630430 | − | 0.776246i | \(-0.282879\pi\) | ||||
0.630430 | + | 0.776246i | \(0.282879\pi\) | |||||||
\(282\) | 7.73895 | 0.460848 | ||||||||
\(283\) | 4.55851 | 0.270975 | 0.135488 | − | 0.990779i | \(-0.456740\pi\) | ||||
0.135488 | + | 0.990779i | \(0.456740\pi\) | |||||||
\(284\) | 73.0850 | 4.33680 | ||||||||
\(285\) | −11.3941 | −0.674926 | ||||||||
\(286\) | −0.0944305 | −0.00558379 | ||||||||
\(287\) | −6.38867 | −0.377111 | ||||||||
\(288\) | −3.54633 | −0.208970 | ||||||||
\(289\) | 5.96223 | 0.350719 | ||||||||
\(290\) | 19.1053 | 1.12190 | ||||||||
\(291\) | −6.50227 | −0.381170 | ||||||||
\(292\) | 33.7134 | 1.97293 | ||||||||
\(293\) | −13.6257 | −0.796023 | −0.398012 | − | 0.917380i | \(-0.630300\pi\) | ||||
−0.398012 | + | 0.917380i | \(0.630300\pi\) | |||||||
\(294\) | 28.4730 | 1.66058 | ||||||||
\(295\) | −6.60672 | −0.384658 | ||||||||
\(296\) | 58.8879 | 3.42279 | ||||||||
\(297\) | 0.365051 | 0.0211824 | ||||||||
\(298\) | 55.3598 | 3.20691 | ||||||||
\(299\) | 1.84732 | 0.106833 | ||||||||
\(300\) | −32.2242 | −1.86047 | ||||||||
\(301\) | 8.69687 | 0.501280 | ||||||||
\(302\) | −14.4834 | −0.833426 | ||||||||
\(303\) | 6.86499 | 0.394383 | ||||||||
\(304\) | 50.7652 | 2.91159 | ||||||||
\(305\) | −1.82428 | −0.104458 | ||||||||
\(306\) | −4.43916 | −0.253770 | ||||||||
\(307\) | 32.1118 | 1.83271 | 0.916357 | − | 0.400362i | \(-0.131116\pi\) | ||||
0.916357 | + | 0.400362i | \(0.131116\pi\) | |||||||
\(308\) | 0.368376 | 0.0209902 | ||||||||
\(309\) | 3.99276 | 0.227140 | ||||||||
\(310\) | −11.6757 | −0.663134 | ||||||||
\(311\) | −3.36747 | −0.190952 | −0.0954759 | − | 0.995432i | \(-0.530437\pi\) | ||||
−0.0954759 | + | 0.995432i | \(0.530437\pi\) | |||||||
\(312\) | 6.42237 | 0.363595 | ||||||||
\(313\) | −24.2343 | −1.36980 | −0.684901 | − | 0.728636i | \(-0.740155\pi\) | ||||
−0.684901 | + | 0.728636i | \(0.740155\pi\) | |||||||
\(314\) | −2.38729 | −0.134723 | ||||||||
\(315\) | 0.418035 | 0.0235536 | ||||||||
\(316\) | −10.5303 | −0.592374 | ||||||||
\(317\) | 7.33522 | 0.411987 | 0.205993 | − | 0.978553i | \(-0.433957\pi\) | ||||
0.205993 | + | 0.978553i | \(0.433957\pi\) | |||||||
\(318\) | −17.6754 | −0.991186 | ||||||||
\(319\) | −0.478193 | −0.0267737 | ||||||||
\(320\) | −8.28549 | −0.463173 | ||||||||
\(321\) | −24.8741 | −1.38834 | ||||||||
\(322\) | −10.2105 | −0.569007 | ||||||||
\(323\) | 25.8133 | 1.43629 | ||||||||
\(324\) | −47.6894 | −2.64941 | ||||||||
\(325\) | 1.76230 | 0.0977550 | ||||||||
\(326\) | −29.8294 | −1.65210 | ||||||||
\(327\) | 8.58689 | 0.474856 | ||||||||
\(328\) | −45.7399 | −2.52556 | ||||||||
\(329\) | 1.65105 | 0.0910252 | ||||||||
\(330\) | −0.415566 | −0.0228762 | ||||||||
\(331\) | −5.15352 | −0.283263 | −0.141632 | − | 0.989919i | \(-0.545235\pi\) | ||||
−0.141632 | + | 0.989919i | \(0.545235\pi\) | |||||||
\(332\) | −43.0579 | −2.36311 | ||||||||
\(333\) | −2.86825 | −0.157179 | ||||||||
\(334\) | 34.2369 | 1.87336 | ||||||||
\(335\) | 13.9136 | 0.760179 | ||||||||
\(336\) | −17.5884 | −0.959526 | ||||||||
\(337\) | −17.3320 | −0.944135 | −0.472067 | − | 0.881563i | \(-0.656492\pi\) | ||||
−0.472067 | + | 0.881563i | \(0.656492\pi\) | |||||||
\(338\) | 33.2923 | 1.81086 | ||||||||
\(339\) | 20.2866 | 1.10182 | ||||||||
\(340\) | −26.5480 | −1.43977 | ||||||||
\(341\) | 0.292235 | 0.0158254 | ||||||||
\(342\) | −4.99035 | −0.269847 | ||||||||
\(343\) | 13.2068 | 0.713100 | ||||||||
\(344\) | 62.2656 | 3.35714 | ||||||||
\(345\) | 8.12961 | 0.437684 | ||||||||
\(346\) | 62.3621 | 3.35261 | ||||||||
\(347\) | −30.4509 | −1.63469 | −0.817345 | − | 0.576149i | \(-0.804555\pi\) | ||||
−0.817345 | + | 0.576149i | \(0.804555\pi\) | |||||||
\(348\) | 55.7708 | 2.98963 | ||||||||
\(349\) | 13.8507 | 0.741409 | 0.370705 | − | 0.928751i | \(-0.379116\pi\) | ||||
0.370705 | + | 0.928751i | \(0.379116\pi\) | |||||||
\(350\) | −9.74057 | −0.520655 | ||||||||
\(351\) | 2.32838 | 0.124280 | ||||||||
\(352\) | 0.752115 | 0.0400879 | ||||||||
\(353\) | 4.87813 | 0.259637 | 0.129818 | − | 0.991538i | \(-0.458561\pi\) | ||||
0.129818 | + | 0.991538i | \(0.458561\pi\) | |||||||
\(354\) | −27.3252 | −1.45232 | ||||||||
\(355\) | −17.5895 | −0.933556 | ||||||||
\(356\) | 7.14259 | 0.378556 | ||||||||
\(357\) | −8.94342 | −0.473336 | ||||||||
\(358\) | 50.5560 | 2.67197 | ||||||||
\(359\) | −35.6623 | −1.88218 | −0.941091 | − | 0.338153i | \(-0.890198\pi\) | ||||
−0.941091 | + | 0.338153i | \(0.890198\pi\) | |||||||
\(360\) | 2.99294 | 0.157742 | ||||||||
\(361\) | 10.0184 | 0.527285 | ||||||||
\(362\) | −28.8709 | −1.51742 | ||||||||
\(363\) | −20.1389 | −1.05702 | ||||||||
\(364\) | 2.34960 | 0.123152 | ||||||||
\(365\) | −8.11388 | −0.424700 | ||||||||
\(366\) | −7.54516 | −0.394392 | ||||||||
\(367\) | −33.5515 | −1.75137 | −0.875687 | − | 0.482878i | \(-0.839591\pi\) | ||||
−0.875687 | + | 0.482878i | \(0.839591\pi\) | |||||||
\(368\) | −36.2208 | −1.88814 | ||||||||
\(369\) | 2.22786 | 0.115978 | ||||||||
\(370\) | −24.3037 | −1.26349 | ||||||||
\(371\) | −3.77091 | −0.195776 | ||||||||
\(372\) | −34.0828 | −1.76711 | ||||||||
\(373\) | −18.9687 | −0.982160 | −0.491080 | − | 0.871114i | \(-0.663398\pi\) | ||||
−0.491080 | + | 0.871114i | \(0.663398\pi\) | |||||||
\(374\) | 0.941469 | 0.0486822 | ||||||||
\(375\) | 18.3312 | 0.946621 | ||||||||
\(376\) | 11.8207 | 0.609608 | ||||||||
\(377\) | −3.05003 | −0.157085 | ||||||||
\(378\) | −12.8694 | −0.661930 | ||||||||
\(379\) | −33.7463 | −1.73343 | −0.866715 | − | 0.498804i | \(-0.833773\pi\) | ||||
−0.866715 | + | 0.498804i | \(0.833773\pi\) | |||||||
\(380\) | −29.8443 | −1.53098 | ||||||||
\(381\) | 0.782299 | 0.0400784 | ||||||||
\(382\) | 43.3279 | 2.21685 | ||||||||
\(383\) | 26.4576 | 1.35192 | 0.675960 | − | 0.736938i | \(-0.263729\pi\) | ||||
0.675960 | + | 0.736938i | \(0.263729\pi\) | |||||||
\(384\) | 2.29669 | 0.117202 | ||||||||
\(385\) | −0.0886579 | −0.00451843 | ||||||||
\(386\) | 35.2421 | 1.79377 | ||||||||
\(387\) | −3.03277 | −0.154165 | ||||||||
\(388\) | −17.0313 | −0.864634 | ||||||||
\(389\) | 4.33977 | 0.220035 | 0.110018 | − | 0.993930i | \(-0.464909\pi\) | ||||
0.110018 | + | 0.993930i | \(0.464909\pi\) | |||||||
\(390\) | −2.65058 | −0.134218 | ||||||||
\(391\) | −18.4177 | −0.931423 | ||||||||
\(392\) | 43.4907 | 2.19661 | ||||||||
\(393\) | −29.2971 | −1.47785 | ||||||||
\(394\) | −7.94584 | −0.400305 | ||||||||
\(395\) | 2.53434 | 0.127517 | ||||||||
\(396\) | −0.128460 | −0.00645537 | ||||||||
\(397\) | −28.0190 | −1.40623 | −0.703117 | − | 0.711074i | \(-0.748209\pi\) | ||||
−0.703117 | + | 0.711074i | \(0.748209\pi\) | |||||||
\(398\) | −62.7657 | −3.14616 | ||||||||
\(399\) | −10.0539 | −0.503323 | ||||||||
\(400\) | −34.5539 | −1.72769 | ||||||||
\(401\) | −31.0130 | −1.54872 | −0.774358 | − | 0.632747i | \(-0.781927\pi\) | ||||
−0.774358 | + | 0.632747i | \(0.781927\pi\) | |||||||
\(402\) | 57.5461 | 2.87014 | ||||||||
\(403\) | 1.86395 | 0.0928499 | ||||||||
\(404\) | 17.9814 | 0.894606 | ||||||||
\(405\) | 11.4775 | 0.570322 | ||||||||
\(406\) | 16.8581 | 0.836653 | ||||||||
\(407\) | 0.608307 | 0.0301526 | ||||||||
\(408\) | −64.0308 | −3.17000 | ||||||||
\(409\) | 9.95578 | 0.492282 | 0.246141 | − | 0.969234i | \(-0.420837\pi\) | ||||
0.246141 | + | 0.969234i | \(0.420837\pi\) | |||||||
\(410\) | 18.8774 | 0.932287 | ||||||||
\(411\) | 28.1525 | 1.38866 | ||||||||
\(412\) | 10.4582 | 0.515237 | ||||||||
\(413\) | −5.82964 | −0.286858 | ||||||||
\(414\) | 3.56059 | 0.174994 | ||||||||
\(415\) | 10.3628 | 0.508692 | ||||||||
\(416\) | 4.79718 | 0.235201 | ||||||||
\(417\) | −33.0960 | −1.62072 | ||||||||
\(418\) | 1.05837 | 0.0517663 | ||||||||
\(419\) | −4.83309 | −0.236112 | −0.118056 | − | 0.993007i | \(-0.537666\pi\) | ||||
−0.118056 | + | 0.993007i | \(0.537666\pi\) | |||||||
\(420\) | 10.3400 | 0.504541 | ||||||||
\(421\) | 17.1174 | 0.834252 | 0.417126 | − | 0.908849i | \(-0.363037\pi\) | ||||
0.417126 | + | 0.908849i | \(0.363037\pi\) | |||||||
\(422\) | 19.4067 | 0.944701 | ||||||||
\(423\) | −0.575753 | −0.0279941 | ||||||||
\(424\) | −26.9980 | −1.31114 | ||||||||
\(425\) | −17.5701 | −0.852275 | ||||||||
\(426\) | −72.7499 | −3.52474 | ||||||||
\(427\) | −1.60970 | −0.0778990 | ||||||||
\(428\) | −65.1525 | −3.14926 | ||||||||
\(429\) | 0.0663425 | 0.00320305 | ||||||||
\(430\) | −25.6977 | −1.23925 | ||||||||
\(431\) | −11.6025 | −0.558874 | −0.279437 | − | 0.960164i | \(-0.590148\pi\) | ||||
−0.279437 | + | 0.960164i | \(0.590148\pi\) | |||||||
\(432\) | −45.6532 | −2.19649 | ||||||||
\(433\) | −24.1896 | −1.16248 | −0.581240 | − | 0.813732i | \(-0.697432\pi\) | ||||
−0.581240 | + | 0.813732i | \(0.697432\pi\) | |||||||
\(434\) | −10.3024 | −0.494530 | ||||||||
\(435\) | −13.4225 | −0.643558 | ||||||||
\(436\) | 22.4915 | 1.07715 | ||||||||
\(437\) | −20.7045 | −0.990432 | ||||||||
\(438\) | −33.5588 | −1.60350 | ||||||||
\(439\) | 4.11750 | 0.196517 | 0.0982587 | − | 0.995161i | \(-0.468673\pi\) | ||||
0.0982587 | + | 0.995161i | \(0.468673\pi\) | |||||||
\(440\) | −0.634750 | −0.0302605 | ||||||||
\(441\) | −2.11830 | −0.100872 | ||||||||
\(442\) | 6.00492 | 0.285625 | ||||||||
\(443\) | −26.1064 | −1.24035 | −0.620175 | − | 0.784463i | \(-0.712939\pi\) | ||||
−0.620175 | + | 0.784463i | \(0.712939\pi\) | |||||||
\(444\) | −70.9457 | −3.36693 | ||||||||
\(445\) | −1.71902 | −0.0814895 | ||||||||
\(446\) | −11.4006 | −0.539835 | ||||||||
\(447\) | −38.8933 | −1.83959 | ||||||||
\(448\) | −7.31094 | −0.345410 | ||||||||
\(449\) | −4.22039 | −0.199172 | −0.0995862 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995862 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(450\) | 3.39673 | 0.160123 | ||||||||
\(451\) | −0.472489 | −0.0222487 | ||||||||
\(452\) | 53.1365 | 2.49933 | ||||||||
\(453\) | 10.1754 | 0.478081 | ||||||||
\(454\) | 37.5440 | 1.76203 | ||||||||
\(455\) | −0.565482 | −0.0265102 | ||||||||
\(456\) | −71.9811 | −3.37083 | ||||||||
\(457\) | −3.22372 | −0.150799 | −0.0753996 | − | 0.997153i | \(-0.524023\pi\) | ||||
−0.0753996 | + | 0.997153i | \(0.524023\pi\) | |||||||
\(458\) | 7.67760 | 0.358751 | ||||||||
\(459\) | −23.2139 | −1.08353 | ||||||||
\(460\) | 21.2938 | 0.992828 | ||||||||
\(461\) | 1.00504 | 0.0468093 | 0.0234046 | − | 0.999726i | \(-0.492549\pi\) | ||||
0.0234046 | + | 0.999726i | \(0.492549\pi\) | |||||||
\(462\) | −0.366687 | −0.0170598 | ||||||||
\(463\) | −3.22289 | −0.149781 | −0.0748903 | − | 0.997192i | \(-0.523861\pi\) | ||||
−0.0748903 | + | 0.997192i | \(0.523861\pi\) | |||||||
\(464\) | 59.8027 | 2.77627 | ||||||||
\(465\) | 8.20279 | 0.380395 | ||||||||
\(466\) | 11.8888 | 0.550739 | ||||||||
\(467\) | −17.3202 | −0.801483 | −0.400741 | − | 0.916191i | \(-0.631247\pi\) | ||||
−0.400741 | + | 0.916191i | \(0.631247\pi\) | |||||||
\(468\) | −0.819351 | −0.0378745 | ||||||||
\(469\) | 12.2770 | 0.566901 | ||||||||
\(470\) | −4.87855 | −0.225031 | ||||||||
\(471\) | 1.67720 | 0.0772814 | ||||||||
\(472\) | −41.7375 | −1.92112 | ||||||||
\(473\) | 0.643198 | 0.0295743 | ||||||||
\(474\) | 10.4820 | 0.481453 | ||||||||
\(475\) | −19.7517 | −0.906269 | ||||||||
\(476\) | −23.4254 | −1.07370 | ||||||||
\(477\) | 1.31499 | 0.0602093 | ||||||||
\(478\) | 48.2234 | 2.20569 | ||||||||
\(479\) | 38.1310 | 1.74225 | 0.871125 | − | 0.491061i | \(-0.163391\pi\) | ||||
0.871125 | + | 0.491061i | \(0.163391\pi\) | |||||||
\(480\) | 21.1112 | 0.963592 | ||||||||
\(481\) | 3.87993 | 0.176910 | ||||||||
\(482\) | −13.1775 | −0.600220 | ||||||||
\(483\) | 7.17340 | 0.326401 | ||||||||
\(484\) | −52.7494 | −2.39770 | ||||||||
\(485\) | 4.09896 | 0.186124 | ||||||||
\(486\) | 9.57856 | 0.434492 | ||||||||
\(487\) | −1.75904 | −0.0797098 | −0.0398549 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398549 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(488\) | −11.5247 | −0.521700 | ||||||||
\(489\) | 20.9567 | 0.947697 | ||||||||
\(490\) | −17.9491 | −0.810858 | ||||||||
\(491\) | −6.66025 | −0.300573 | −0.150286 | − | 0.988642i | \(-0.548020\pi\) | ||||
−0.150286 | + | 0.988642i | \(0.548020\pi\) | |||||||
\(492\) | 55.1056 | 2.48435 | ||||||||
\(493\) | 30.4087 | 1.36954 | ||||||||
\(494\) | 6.75052 | 0.303720 | ||||||||
\(495\) | 0.0309168 | 0.00138961 | ||||||||
\(496\) | −36.5469 | −1.64100 | ||||||||
\(497\) | −15.5206 | −0.696196 | ||||||||
\(498\) | 42.8604 | 1.92062 | ||||||||
\(499\) | 35.2943 | 1.57999 | 0.789994 | − | 0.613115i | \(-0.210084\pi\) | ||||
0.789994 | + | 0.613115i | \(0.210084\pi\) | |||||||
\(500\) | 48.0148 | 2.14728 | ||||||||
\(501\) | −24.0533 | −1.07462 | ||||||||
\(502\) | 58.9156 | 2.62953 | ||||||||
\(503\) | 19.5774 | 0.872913 | 0.436456 | − | 0.899725i | \(-0.356233\pi\) | ||||
0.436456 | + | 0.899725i | \(0.356233\pi\) | |||||||
\(504\) | 2.64091 | 0.117635 | ||||||||
\(505\) | −4.32762 | −0.192576 | ||||||||
\(506\) | −0.755140 | −0.0335701 | ||||||||
\(507\) | −23.3896 | −1.03877 | ||||||||
\(508\) | 2.04906 | 0.0909125 | ||||||||
\(509\) | 21.8081 | 0.966627 | 0.483313 | − | 0.875447i | \(-0.339433\pi\) | ||||
0.483313 | + | 0.875447i | \(0.339433\pi\) | |||||||
\(510\) | 26.4262 | 1.17017 | ||||||||
\(511\) | −7.15952 | −0.316718 | ||||||||
\(512\) | 43.4319 | 1.91944 | ||||||||
\(513\) | −26.0962 | −1.15218 | ||||||||
\(514\) | 4.74793 | 0.209422 | ||||||||
\(515\) | −2.51699 | −0.110912 | ||||||||
\(516\) | −75.0150 | −3.30235 | ||||||||
\(517\) | 0.122107 | 0.00537027 | ||||||||
\(518\) | −21.4451 | −0.942242 | ||||||||
\(519\) | −43.8127 | −1.92317 | ||||||||
\(520\) | −4.04859 | −0.177543 | ||||||||
\(521\) | −32.4806 | −1.42300 | −0.711500 | − | 0.702686i | \(-0.751984\pi\) | ||||
−0.711500 | + | 0.702686i | \(0.751984\pi\) | |||||||
\(522\) | −5.87875 | −0.257306 | ||||||||
\(523\) | −1.86675 | −0.0816274 | −0.0408137 | − | 0.999167i | \(-0.512995\pi\) | ||||
−0.0408137 | + | 0.999167i | \(0.512995\pi\) | |||||||
\(524\) | −76.7376 | −3.35230 | ||||||||
\(525\) | 6.84327 | 0.298665 | ||||||||
\(526\) | −60.5515 | −2.64017 | ||||||||
\(527\) | −18.5835 | −0.809510 | ||||||||
\(528\) | −1.30079 | −0.0566097 | ||||||||
\(529\) | −8.22740 | −0.357713 | ||||||||
\(530\) | 11.1424 | 0.483994 | ||||||||
\(531\) | 2.03291 | 0.0882208 | ||||||||
\(532\) | −26.3340 | −1.14172 | ||||||||
\(533\) | −3.01365 | −0.130536 | ||||||||
\(534\) | −7.10983 | −0.307672 | ||||||||
\(535\) | 15.6804 | 0.677922 | ||||||||
\(536\) | 87.8979 | 3.79661 | ||||||||
\(537\) | −35.5183 | −1.53273 | ||||||||
\(538\) | −41.7085 | −1.79818 | ||||||||
\(539\) | 0.449255 | 0.0193508 | ||||||||
\(540\) | 26.8389 | 1.15496 | ||||||||
\(541\) | −20.1723 | −0.867275 | −0.433637 | − | 0.901088i | \(-0.642770\pi\) | ||||
−0.433637 | + | 0.901088i | \(0.642770\pi\) | |||||||
\(542\) | 11.3597 | 0.487942 | ||||||||
\(543\) | 20.2834 | 0.870442 | ||||||||
\(544\) | −47.8277 | −2.05060 | ||||||||
\(545\) | −5.41309 | −0.231871 | ||||||||
\(546\) | −2.33882 | −0.100092 | ||||||||
\(547\) | 25.5123 | 1.09083 | 0.545414 | − | 0.838167i | \(-0.316373\pi\) | ||||
0.545414 | + | 0.838167i | \(0.316373\pi\) | |||||||
\(548\) | 73.7395 | 3.14999 | ||||||||
\(549\) | 0.561335 | 0.0239572 | ||||||||
\(550\) | −0.720387 | −0.0307174 | ||||||||
\(551\) | 34.1844 | 1.45630 | ||||||||
\(552\) | 51.3583 | 2.18595 | ||||||||
\(553\) | 2.23625 | 0.0950950 | ||||||||
\(554\) | −2.85630 | −0.121353 | ||||||||
\(555\) | 17.0747 | 0.724779 | ||||||||
\(556\) | −86.6879 | −3.67638 | ||||||||
\(557\) | 5.41060 | 0.229255 | 0.114627 | − | 0.993409i | \(-0.463433\pi\) | ||||
0.114627 | + | 0.993409i | \(0.463433\pi\) | |||||||
\(558\) | 3.59264 | 0.152089 | ||||||||
\(559\) | 4.10248 | 0.173516 | ||||||||
\(560\) | 11.0875 | 0.468534 | ||||||||
\(561\) | −0.661432 | −0.0279257 | ||||||||
\(562\) | −55.1070 | −2.32455 | ||||||||
\(563\) | 26.5761 | 1.12005 | 0.560024 | − | 0.828476i | \(-0.310792\pi\) | ||||
0.560024 | + | 0.828476i | \(0.310792\pi\) | |||||||
\(564\) | −14.2411 | −0.599660 | ||||||||
\(565\) | −12.7885 | −0.538015 | ||||||||
\(566\) | −11.8853 | −0.499576 | ||||||||
\(567\) | 10.1275 | 0.425316 | ||||||||
\(568\) | −111.121 | −4.66252 | ||||||||
\(569\) | 36.9142 | 1.54753 | 0.773763 | − | 0.633475i | \(-0.218372\pi\) | ||||
0.773763 | + | 0.633475i | \(0.218372\pi\) | |||||||
\(570\) | 29.7074 | 1.24431 | ||||||||
\(571\) | 4.26468 | 0.178471 | 0.0892356 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892356 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(572\) | 0.173770 | 0.00726569 | ||||||||
\(573\) | −30.4402 | −1.27166 | ||||||||
\(574\) | 16.6570 | 0.695250 | ||||||||
\(575\) | 14.0927 | 0.587708 | ||||||||
\(576\) | 2.54947 | 0.106228 | ||||||||
\(577\) | −34.2167 | −1.42446 | −0.712229 | − | 0.701947i | \(-0.752314\pi\) | ||||
−0.712229 | + | 0.701947i | \(0.752314\pi\) | |||||||
\(578\) | −15.5452 | −0.646594 | ||||||||
\(579\) | −24.7594 | −1.02897 | ||||||||
\(580\) | −35.1573 | −1.45983 | ||||||||
\(581\) | 9.14395 | 0.379355 | ||||||||
\(582\) | 16.9532 | 0.702733 | ||||||||
\(583\) | −0.278887 | −0.0115503 | ||||||||
\(584\) | −51.2588 | −2.12111 | ||||||||
\(585\) | 0.197195 | 0.00815301 | ||||||||
\(586\) | 35.5260 | 1.46757 | ||||||||
\(587\) | 40.7025 | 1.67997 | 0.839986 | − | 0.542609i | \(-0.182563\pi\) | ||||
0.839986 | + | 0.542609i | \(0.182563\pi\) | |||||||
\(588\) | −52.3958 | −2.16077 | ||||||||
\(589\) | −20.8909 | −0.860795 | ||||||||
\(590\) | 17.2255 | 0.709164 | ||||||||
\(591\) | 5.58238 | 0.229628 | ||||||||
\(592\) | −76.0747 | −3.12665 | ||||||||
\(593\) | −15.2334 | −0.625562 | −0.312781 | − | 0.949825i | \(-0.601261\pi\) | ||||
−0.312781 | + | 0.949825i | \(0.601261\pi\) | |||||||
\(594\) | −0.951787 | −0.0390523 | ||||||||
\(595\) | 5.63784 | 0.231129 | ||||||||
\(596\) | −101.873 | −4.17286 | ||||||||
\(597\) | 44.0963 | 1.80474 | ||||||||
\(598\) | −4.81647 | −0.196960 | ||||||||
\(599\) | 41.3147 | 1.68807 | 0.844037 | − | 0.536285i | \(-0.180173\pi\) | ||||
0.844037 | + | 0.536285i | \(0.180173\pi\) | |||||||
\(600\) | 48.9947 | 2.00020 | ||||||||
\(601\) | 10.0865 | 0.411437 | 0.205719 | − | 0.978611i | \(-0.434047\pi\) | ||||
0.205719 | + | 0.978611i | \(0.434047\pi\) | |||||||
\(602\) | −22.6751 | −0.924170 | ||||||||
\(603\) | −4.28125 | −0.174346 | ||||||||
\(604\) | 26.6522 | 1.08446 | ||||||||
\(605\) | 12.6953 | 0.516138 | ||||||||
\(606\) | −17.8989 | −0.727093 | ||||||||
\(607\) | −23.8802 | −0.969266 | −0.484633 | − | 0.874717i | \(-0.661047\pi\) | ||||
−0.484633 | + | 0.874717i | \(0.661047\pi\) | |||||||
\(608\) | −53.7662 | −2.18051 | ||||||||
\(609\) | −11.8437 | −0.479931 | ||||||||
\(610\) | 4.75639 | 0.192580 | ||||||||
\(611\) | 0.778830 | 0.0315081 | ||||||||
\(612\) | 8.16890 | 0.330208 | ||||||||
\(613\) | −29.8943 | −1.20742 | −0.603709 | − | 0.797204i | \(-0.706311\pi\) | ||||
−0.603709 | + | 0.797204i | \(0.706311\pi\) | |||||||
\(614\) | −83.7241 | −3.37883 | ||||||||
\(615\) | −13.2624 | −0.534791 | ||||||||
\(616\) | −0.560090 | −0.0225667 | ||||||||
\(617\) | −38.0974 | −1.53374 | −0.766872 | − | 0.641800i | \(-0.778188\pi\) | ||||
−0.766872 | + | 0.641800i | \(0.778188\pi\) | |||||||
\(618\) | −10.4102 | −0.418760 | ||||||||
\(619\) | 44.4171 | 1.78527 | 0.892637 | − | 0.450776i | \(-0.148853\pi\) | ||||
0.892637 | + | 0.450776i | \(0.148853\pi\) | |||||||
\(620\) | 21.4855 | 0.862877 | ||||||||
\(621\) | 18.6196 | 0.747178 | ||||||||
\(622\) | 8.77992 | 0.352043 | ||||||||
\(623\) | −1.51683 | −0.0607705 | ||||||||
\(624\) | −8.29678 | −0.332137 | ||||||||
\(625\) | 6.77734 | 0.271094 | ||||||||
\(626\) | 63.1854 | 2.52540 | ||||||||
\(627\) | −0.743559 | −0.0296949 | ||||||||
\(628\) | 4.39307 | 0.175303 | ||||||||
\(629\) | −38.6828 | −1.54238 | ||||||||
\(630\) | −1.08993 | −0.0434239 | ||||||||
\(631\) | −41.4048 | −1.64830 | −0.824150 | − | 0.566371i | \(-0.808347\pi\) | ||||
−0.824150 | + | 0.566371i | \(0.808347\pi\) | |||||||
\(632\) | 16.0105 | 0.636864 | ||||||||
\(633\) | −13.6342 | −0.541912 | ||||||||
\(634\) | −19.1249 | −0.759548 | ||||||||
\(635\) | −0.493153 | −0.0195702 | ||||||||
\(636\) | 32.5261 | 1.28974 | ||||||||
\(637\) | 2.86546 | 0.113534 | ||||||||
\(638\) | 1.24678 | 0.0493605 | ||||||||
\(639\) | 5.41236 | 0.214110 | ||||||||
\(640\) | −1.44781 | −0.0572297 | ||||||||
\(641\) | −4.95359 | −0.195655 | −0.0978275 | − | 0.995203i | \(-0.531189\pi\) | ||||
−0.0978275 | + | 0.995203i | \(0.531189\pi\) | |||||||
\(642\) | 64.8537 | 2.55957 | ||||||||
\(643\) | −13.4679 | −0.531121 | −0.265560 | − | 0.964094i | \(-0.585557\pi\) | ||||
−0.265560 | + | 0.964094i | \(0.585557\pi\) | |||||||
\(644\) | 18.7892 | 0.740398 | ||||||||
\(645\) | 18.0540 | 0.710877 | ||||||||
\(646\) | −67.3024 | −2.64798 | ||||||||
\(647\) | −28.2537 | −1.11077 | −0.555383 | − | 0.831594i | \(-0.687428\pi\) | ||||
−0.555383 | + | 0.831594i | \(0.687428\pi\) | |||||||
\(648\) | 72.5084 | 2.84840 | ||||||||
\(649\) | −0.431145 | −0.0169239 | ||||||||
\(650\) | −4.59481 | −0.180223 | ||||||||
\(651\) | 7.23798 | 0.283679 | ||||||||
\(652\) | 54.8917 | 2.14972 | ||||||||
\(653\) | 21.8515 | 0.855116 | 0.427558 | − | 0.903988i | \(-0.359374\pi\) | ||||
0.427558 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(654\) | −22.3884 | −0.875455 | ||||||||
\(655\) | 18.4686 | 0.721628 | ||||||||
\(656\) | 59.0894 | 2.30705 | ||||||||
\(657\) | 2.49667 | 0.0974042 | ||||||||
\(658\) | −4.30473 | −0.167816 | ||||||||
\(659\) | −48.2531 | −1.87967 | −0.939836 | − | 0.341625i | \(-0.889023\pi\) | ||||
−0.939836 | + | 0.341625i | \(0.889023\pi\) | |||||||
\(660\) | 0.764721 | 0.0297667 | ||||||||
\(661\) | 21.2733 | 0.827437 | 0.413719 | − | 0.910405i | \(-0.364230\pi\) | ||||
0.413719 | + | 0.910405i | \(0.364230\pi\) | |||||||
\(662\) | 13.4366 | 0.522230 | ||||||||
\(663\) | −4.21878 | −0.163844 | ||||||||
\(664\) | 65.4665 | 2.54059 | ||||||||
\(665\) | 6.33786 | 0.245772 | ||||||||
\(666\) | 7.47832 | 0.289779 | ||||||||
\(667\) | −24.3904 | −0.944401 | ||||||||
\(668\) | −63.0024 | −2.43764 | ||||||||
\(669\) | 8.00954 | 0.309667 | ||||||||
\(670\) | −36.2765 | −1.40148 | ||||||||
\(671\) | −0.119049 | −0.00459585 | ||||||||
\(672\) | 18.6281 | 0.718596 | ||||||||
\(673\) | 16.5835 | 0.639246 | 0.319623 | − | 0.947545i | \(-0.396444\pi\) | ||||
0.319623 | + | 0.947545i | \(0.396444\pi\) | |||||||
\(674\) | 45.1893 | 1.74063 | ||||||||
\(675\) | 17.7627 | 0.683686 | ||||||||
\(676\) | −61.2641 | −2.35631 | ||||||||
\(677\) | 26.1285 | 1.00420 | 0.502100 | − | 0.864809i | \(-0.332561\pi\) | ||||
0.502100 | + | 0.864809i | \(0.332561\pi\) | |||||||
\(678\) | −52.8928 | −2.03134 | ||||||||
\(679\) | 3.61684 | 0.138802 | ||||||||
\(680\) | 40.3643 | 1.54790 | ||||||||
\(681\) | −26.3767 | −1.01076 | ||||||||
\(682\) | −0.761937 | −0.0291761 | ||||||||
\(683\) | −38.9697 | −1.49113 | −0.745566 | − | 0.666432i | \(-0.767821\pi\) | ||||
−0.745566 | + | 0.666432i | \(0.767821\pi\) | |||||||
\(684\) | 9.18318 | 0.351128 | ||||||||
\(685\) | −17.7470 | −0.678080 | ||||||||
\(686\) | −34.4337 | −1.31469 | ||||||||
\(687\) | −5.39393 | −0.205791 | ||||||||
\(688\) | −80.4382 | −3.06668 | ||||||||
\(689\) | −1.77881 | −0.0677672 | ||||||||
\(690\) | −21.1961 | −0.806923 | ||||||||
\(691\) | −20.2103 | −0.768835 | −0.384418 | − | 0.923159i | \(-0.625598\pi\) | ||||
−0.384418 | + | 0.923159i | \(0.625598\pi\) | |||||||
\(692\) | −114.758 | −4.36245 | ||||||||
\(693\) | 0.0272803 | 0.00103629 | ||||||||
\(694\) | 79.3938 | 3.01375 | ||||||||
\(695\) | 20.8634 | 0.791392 | ||||||||
\(696\) | −84.7955 | −3.21417 | ||||||||
\(697\) | 30.0460 | 1.13807 | ||||||||
\(698\) | −36.1125 | −1.36688 | ||||||||
\(699\) | −8.35254 | −0.315922 | ||||||||
\(700\) | 17.9245 | 0.677482 | ||||||||
\(701\) | 26.2971 | 0.993228 | 0.496614 | − | 0.867971i | \(-0.334576\pi\) | ||||
0.496614 | + | 0.867971i | \(0.334576\pi\) | |||||||
\(702\) | −6.07074 | −0.229125 | ||||||||
\(703\) | −43.4858 | −1.64010 | ||||||||
\(704\) | −0.540698 | −0.0203783 | ||||||||
\(705\) | 3.42744 | 0.129085 | ||||||||
\(706\) | −12.7186 | −0.478672 | ||||||||
\(707\) | −3.81860 | −0.143613 | ||||||||
\(708\) | 50.2836 | 1.88977 | ||||||||
\(709\) | 12.7455 | 0.478667 | 0.239333 | − | 0.970937i | \(-0.423071\pi\) | ||||
0.239333 | + | 0.970937i | \(0.423071\pi\) | |||||||
\(710\) | 45.8607 | 1.72112 | ||||||||
\(711\) | −0.779825 | −0.0292457 | ||||||||
\(712\) | −10.8598 | −0.406988 | ||||||||
\(713\) | 14.9056 | 0.558218 | ||||||||
\(714\) | 23.3180 | 0.872653 | ||||||||
\(715\) | −0.0418216 | −0.00156404 | ||||||||
\(716\) | −93.0327 | −3.47679 | ||||||||
\(717\) | −33.8795 | −1.26525 | ||||||||
\(718\) | 92.9813 | 3.47003 | ||||||||
\(719\) | 36.3325 | 1.35498 | 0.677488 | − | 0.735534i | \(-0.263069\pi\) | ||||
0.677488 | + | 0.735534i | \(0.263069\pi\) | |||||||
\(720\) | −3.86645 | −0.144094 | ||||||||
\(721\) | −2.22094 | −0.0827122 | ||||||||
\(722\) | −26.1208 | −0.972114 | ||||||||
\(723\) | 9.25792 | 0.344306 | ||||||||
\(724\) | 53.1279 | 1.97448 | ||||||||
\(725\) | −23.2680 | −0.864150 | ||||||||
\(726\) | 52.5075 | 1.94874 | ||||||||
\(727\) | −7.22985 | −0.268140 | −0.134070 | − | 0.990972i | \(-0.542805\pi\) | ||||
−0.134070 | + | 0.990972i | \(0.542805\pi\) | |||||||
\(728\) | −3.57239 | −0.132402 | ||||||||
\(729\) | 23.0896 | 0.855170 | ||||||||
\(730\) | 21.1551 | 0.782985 | ||||||||
\(731\) | −40.9016 | −1.51280 | ||||||||
\(732\) | 13.8845 | 0.513186 | ||||||||
\(733\) | 2.47865 | 0.0915510 | 0.0457755 | − | 0.998952i | \(-0.485424\pi\) | ||||
0.0457755 | + | 0.998952i | \(0.485424\pi\) | |||||||
\(734\) | 87.4780 | 3.22887 | ||||||||
\(735\) | 12.6102 | 0.465135 | ||||||||
\(736\) | 38.3620 | 1.41404 | ||||||||
\(737\) | 0.907977 | 0.0334458 | ||||||||
\(738\) | −5.80863 | −0.213819 | ||||||||
\(739\) | 30.8999 | 1.13667 | 0.568335 | − | 0.822797i | \(-0.307588\pi\) | ||||
0.568335 | + | 0.822797i | \(0.307588\pi\) | |||||||
\(740\) | 44.7234 | 1.64406 | ||||||||
\(741\) | −4.74260 | −0.174224 | ||||||||
\(742\) | 9.83180 | 0.360937 | ||||||||
\(743\) | −21.4036 | −0.785223 | −0.392612 | − | 0.919704i | \(-0.628428\pi\) | ||||
−0.392612 | + | 0.919704i | \(0.628428\pi\) | |||||||
\(744\) | 51.8206 | 1.89983 | ||||||||
\(745\) | 24.5179 | 0.898266 | ||||||||
\(746\) | 49.4565 | 1.81073 | ||||||||
\(747\) | −3.18868 | −0.116668 | ||||||||
\(748\) | −1.73248 | −0.0633458 | ||||||||
\(749\) | 13.8361 | 0.505558 | ||||||||
\(750\) | −47.7946 | −1.74521 | ||||||||
\(751\) | 15.9269 | 0.581182 | 0.290591 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290591 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(752\) | −15.2707 | −0.556865 | ||||||||
\(753\) | −41.3914 | −1.50839 | ||||||||
\(754\) | 7.95227 | 0.289605 | ||||||||
\(755\) | −6.41445 | −0.233446 | ||||||||
\(756\) | 23.6821 | 0.861311 | ||||||||
\(757\) | 12.7141 | 0.462102 | 0.231051 | − | 0.972942i | \(-0.425784\pi\) | ||||
0.231051 | + | 0.972942i | \(0.425784\pi\) | |||||||
\(758\) | 87.9858 | 3.19579 | ||||||||
\(759\) | 0.530526 | 0.0192569 | ||||||||
\(760\) | 45.3761 | 1.64597 | ||||||||
\(761\) | −12.7971 | −0.463893 | −0.231946 | − | 0.972729i | \(-0.574509\pi\) | ||||
−0.231946 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(762\) | −2.03967 | −0.0738894 | ||||||||
\(763\) | −4.77639 | −0.172917 | ||||||||
\(764\) | −79.7315 | −2.88459 | ||||||||
\(765\) | −1.96603 | −0.0710818 | ||||||||
\(766\) | −68.9822 | −2.49243 | ||||||||
\(767\) | −2.74995 | −0.0992949 | ||||||||
\(768\) | −32.2750 | −1.16462 | ||||||||
\(769\) | −17.5407 | −0.632534 | −0.316267 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(770\) | 0.231156 | 0.00833027 | ||||||||
\(771\) | −3.33567 | −0.120131 | ||||||||
\(772\) | −64.8521 | −2.33408 | ||||||||
\(773\) | 45.6066 | 1.64036 | 0.820178 | − | 0.572109i | \(-0.193874\pi\) | ||||
0.820178 | + | 0.572109i | \(0.193874\pi\) | |||||||
\(774\) | 7.90727 | 0.284221 | ||||||||
\(775\) | 14.2196 | 0.510783 | ||||||||
\(776\) | 25.8949 | 0.929573 | ||||||||
\(777\) | 15.0663 | 0.540501 | ||||||||
\(778\) | −11.3150 | −0.405662 | ||||||||
\(779\) | 33.7767 | 1.21017 | ||||||||
\(780\) | 4.87758 | 0.174645 | ||||||||
\(781\) | −1.14787 | −0.0410739 | ||||||||
\(782\) | 48.0200 | 1.71719 | ||||||||
\(783\) | −30.7420 | −1.09863 | ||||||||
\(784\) | −56.1837 | −2.00656 | ||||||||
\(785\) | −1.05729 | −0.0377363 | ||||||||
\(786\) | 76.3857 | 2.72459 | ||||||||
\(787\) | −51.0311 | −1.81906 | −0.909531 | − | 0.415635i | \(-0.863559\pi\) | ||||
−0.909531 | + | 0.415635i | \(0.863559\pi\) | |||||||
\(788\) | 14.6218 | 0.520882 | ||||||||
\(789\) | 42.5407 | 1.51449 | ||||||||
\(790\) | −6.60772 | −0.235092 | ||||||||
\(791\) | −11.2843 | −0.401223 | ||||||||
\(792\) | 0.195315 | 0.00694020 | ||||||||
\(793\) | −0.759327 | −0.0269645 | ||||||||
\(794\) | 73.0533 | 2.59256 | ||||||||
\(795\) | −7.82812 | −0.277635 | ||||||||
\(796\) | 115.501 | 4.09382 | ||||||||
\(797\) | −17.9409 | −0.635500 | −0.317750 | − | 0.948175i | \(-0.602927\pi\) | ||||
−0.317750 | + | 0.948175i | \(0.602927\pi\) | |||||||
\(798\) | 26.2132 | 0.927938 | ||||||||
\(799\) | −7.76490 | −0.274702 | ||||||||
\(800\) | 36.5965 | 1.29388 | ||||||||
\(801\) | 0.528949 | 0.0186895 | ||||||||
\(802\) | 80.8595 | 2.85525 | ||||||||
\(803\) | −0.529499 | −0.0186856 | ||||||||
\(804\) | −105.896 | −3.73465 | ||||||||
\(805\) | −4.52204 | −0.159381 | ||||||||
\(806\) | −4.85982 | −0.171180 | ||||||||
\(807\) | 29.3025 | 1.03150 | ||||||||
\(808\) | −27.3394 | −0.961797 | ||||||||
\(809\) | 12.6932 | 0.446269 | 0.223134 | − | 0.974788i | \(-0.428371\pi\) | ||||
0.223134 | + | 0.974788i | \(0.428371\pi\) | |||||||
\(810\) | −29.9250 | −1.05146 | ||||||||
\(811\) | 24.6581 | 0.865862 | 0.432931 | − | 0.901427i | \(-0.357479\pi\) | ||||
0.432931 | + | 0.901427i | \(0.357479\pi\) | |||||||
\(812\) | −31.0221 | −1.08866 | ||||||||
\(813\) | −7.98082 | −0.279900 | ||||||||
\(814\) | −1.58602 | −0.0555900 | ||||||||
\(815\) | −13.2109 | −0.462758 | ||||||||
\(816\) | 82.7186 | 2.89573 | ||||||||
\(817\) | −45.9801 | −1.60864 | ||||||||
\(818\) | −25.9574 | −0.907581 | ||||||||
\(819\) | 0.174001 | 0.00608008 | ||||||||
\(820\) | −34.7380 | −1.21310 | ||||||||
\(821\) | −36.4455 | −1.27196 | −0.635978 | − | 0.771707i | \(-0.719403\pi\) | ||||
−0.635978 | + | 0.771707i | \(0.719403\pi\) | |||||||
\(822\) | −73.4013 | −2.56017 | ||||||||
\(823\) | 4.72736 | 0.164786 | 0.0823928 | − | 0.996600i | \(-0.473744\pi\) | ||||
0.0823928 | + | 0.996600i | \(0.473744\pi\) | |||||||
\(824\) | −15.9009 | −0.553935 | ||||||||
\(825\) | 0.506111 | 0.0176205 | ||||||||
\(826\) | 15.1995 | 0.528857 | ||||||||
\(827\) | 47.7679 | 1.66105 | 0.830527 | − | 0.556979i | \(-0.188040\pi\) | ||||
0.830527 | + | 0.556979i | \(0.188040\pi\) | |||||||
\(828\) | −6.55217 | −0.227704 | ||||||||
\(829\) | −8.47959 | −0.294508 | −0.147254 | − | 0.989099i | \(-0.547043\pi\) | ||||
−0.147254 | + | 0.989099i | \(0.547043\pi\) | |||||||
\(830\) | −27.0188 | −0.937835 | ||||||||
\(831\) | 2.00671 | 0.0696118 | ||||||||
\(832\) | −3.44871 | −0.119562 | ||||||||
\(833\) | −28.5685 | −0.989841 | ||||||||
\(834\) | 86.2903 | 2.98799 | ||||||||
\(835\) | 15.1629 | 0.524735 | ||||||||
\(836\) | −1.94759 | −0.0673589 | ||||||||
\(837\) | 18.7872 | 0.649380 | ||||||||
\(838\) | 12.6012 | 0.435300 | ||||||||
\(839\) | 55.8042 | 1.92658 | 0.963288 | − | 0.268470i | \(-0.0865180\pi\) | ||||
0.963288 | + | 0.268470i | \(0.0865180\pi\) | |||||||
\(840\) | −15.7213 | −0.542435 | ||||||||
\(841\) | 11.2700 | 0.388622 | ||||||||
\(842\) | −44.6298 | −1.53804 | ||||||||
\(843\) | 38.7156 | 1.33344 | ||||||||
\(844\) | −35.7119 | −1.22926 | ||||||||
\(845\) | 14.7446 | 0.507228 | ||||||||
\(846\) | 1.50115 | 0.0516104 | ||||||||
\(847\) | 11.2021 | 0.384908 | ||||||||
\(848\) | 34.8775 | 1.19770 | ||||||||
\(849\) | 8.35005 | 0.286573 | ||||||||
\(850\) | 45.8101 | 1.57127 | ||||||||
\(851\) | 31.0269 | 1.06359 | ||||||||
\(852\) | 133.874 | 4.58643 | ||||||||
\(853\) | 17.1626 | 0.587637 | 0.293819 | − | 0.955861i | \(-0.405074\pi\) | ||||
0.293819 | + | 0.955861i | \(0.405074\pi\) | |||||||
\(854\) | 4.19694 | 0.143616 | ||||||||
\(855\) | −2.21014 | −0.0755851 | ||||||||
\(856\) | 99.0598 | 3.38579 | ||||||||
\(857\) | −18.8202 | −0.642887 | −0.321444 | − | 0.946929i | \(-0.604168\pi\) | ||||
−0.321444 | + | 0.946929i | \(0.604168\pi\) | |||||||
\(858\) | −0.172973 | −0.00590521 | ||||||||
\(859\) | −11.5195 | −0.393041 | −0.196521 | − | 0.980500i | \(-0.562964\pi\) | ||||
−0.196521 | + | 0.980500i | \(0.562964\pi\) | |||||||
\(860\) | 47.2887 | 1.61253 | ||||||||
\(861\) | −11.7024 | −0.398818 | ||||||||
\(862\) | 30.2509 | 1.03035 | ||||||||
\(863\) | −42.0945 | −1.43291 | −0.716456 | − | 0.697632i | \(-0.754237\pi\) | ||||
−0.716456 | + | 0.697632i | \(0.754237\pi\) | |||||||
\(864\) | 48.3519 | 1.64497 | ||||||||
\(865\) | 27.6191 | 0.939077 | ||||||||
\(866\) | 63.0690 | 2.14317 | ||||||||
\(867\) | 10.9213 | 0.370907 | ||||||||
\(868\) | 18.9583 | 0.643488 | ||||||||
\(869\) | 0.165387 | 0.00561038 | ||||||||
\(870\) | 34.9961 | 1.18648 | ||||||||
\(871\) | 5.79131 | 0.196231 | ||||||||
\(872\) | −34.1968 | −1.15805 | ||||||||
\(873\) | −1.26126 | −0.0426873 | ||||||||
\(874\) | 53.9824 | 1.82598 | ||||||||
\(875\) | −10.1966 | −0.344708 | ||||||||
\(876\) | 61.7545 | 2.08649 | ||||||||
\(877\) | 0.647423 | 0.0218619 | 0.0109310 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109310 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(878\) | −10.7354 | −0.362304 | ||||||||
\(879\) | −24.9589 | −0.841844 | ||||||||
\(880\) | 0.820006 | 0.0276424 | ||||||||
\(881\) | 44.3105 | 1.49286 | 0.746429 | − | 0.665465i | \(-0.231767\pi\) | ||||
0.746429 | + | 0.665465i | \(0.231767\pi\) | |||||||
\(882\) | 5.52300 | 0.185969 | ||||||||
\(883\) | 19.5057 | 0.656419 | 0.328209 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328209 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(884\) | −11.0502 | −0.371658 | ||||||||
\(885\) | −12.1019 | −0.406800 | ||||||||
\(886\) | 68.0665 | 2.28674 | ||||||||
\(887\) | 34.3705 | 1.15405 | 0.577024 | − | 0.816727i | \(-0.304214\pi\) | ||||
0.577024 | + | 0.816727i | \(0.304214\pi\) | |||||||
\(888\) | 107.868 | 3.61981 | ||||||||
\(889\) | −0.435148 | −0.0145944 | ||||||||
\(890\) | 4.48196 | 0.150236 | ||||||||
\(891\) | 0.749005 | 0.0250926 | ||||||||
\(892\) | 20.9793 | 0.702438 | ||||||||
\(893\) | −8.72903 | −0.292106 | ||||||||
\(894\) | 101.405 | 3.39150 | ||||||||
\(895\) | 22.3904 | 0.748428 | ||||||||
\(896\) | −1.27752 | −0.0426788 | ||||||||
\(897\) | 3.38383 | 0.112983 | ||||||||
\(898\) | 11.0037 | 0.367198 | ||||||||
\(899\) | −24.6100 | −0.820789 | ||||||||
\(900\) | −6.25063 | −0.208354 | ||||||||
\(901\) | 17.7347 | 0.590827 | ||||||||
\(902\) | 1.23191 | 0.0410181 | ||||||||
\(903\) | 15.9305 | 0.530134 | ||||||||
\(904\) | −80.7903 | −2.68704 | ||||||||
\(905\) | −12.7864 | −0.425035 | ||||||||
\(906\) | −26.5300 | −0.881400 | ||||||||
\(907\) | 11.2174 | 0.372467 | 0.186233 | − | 0.982506i | \(-0.440372\pi\) | ||||
0.186233 | + | 0.982506i | \(0.440372\pi\) | |||||||
\(908\) | −69.0881 | −2.29277 | ||||||||
\(909\) | 1.33162 | 0.0441671 | ||||||||
\(910\) | 1.47437 | 0.0488748 | ||||||||
\(911\) | 26.0372 | 0.862651 | 0.431326 | − | 0.902196i | \(-0.358046\pi\) | ||||
0.431326 | + | 0.902196i | \(0.358046\pi\) | |||||||
\(912\) | 92.9893 | 3.07918 | ||||||||
\(913\) | 0.676263 | 0.0223810 | ||||||||
\(914\) | 8.40512 | 0.278017 | ||||||||
\(915\) | −3.34162 | −0.110470 | ||||||||
\(916\) | −14.1282 | −0.466810 | ||||||||
\(917\) | 16.2963 | 0.538152 | ||||||||
\(918\) | 60.5250 | 1.99762 | ||||||||
\(919\) | −9.37181 | −0.309147 | −0.154574 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154574 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(920\) | −32.3757 | −1.06740 | ||||||||
\(921\) | 58.8207 | 1.93821 | ||||||||
\(922\) | −2.62041 | −0.0862986 | ||||||||
\(923\) | −7.32138 | −0.240986 | ||||||||
\(924\) | 0.674774 | 0.0221984 | ||||||||
\(925\) | 29.5990 | 0.973210 | ||||||||
\(926\) | 8.40296 | 0.276139 | ||||||||
\(927\) | 0.774487 | 0.0254375 | ||||||||
\(928\) | −63.3379 | −2.07917 | ||||||||
\(929\) | 47.2204 | 1.54925 | 0.774626 | − | 0.632419i | \(-0.217938\pi\) | ||||
0.774626 | + | 0.632419i | \(0.217938\pi\) | |||||||
\(930\) | −21.3869 | −0.701305 | ||||||||
\(931\) | −32.1157 | −1.05255 | ||||||||
\(932\) | −21.8777 | −0.716627 | ||||||||
\(933\) | −6.16837 | −0.201943 | ||||||||
\(934\) | 45.1585 | 1.47763 | ||||||||
\(935\) | 0.416960 | 0.0136360 | ||||||||
\(936\) | 1.24577 | 0.0407191 | ||||||||
\(937\) | 26.0269 | 0.850261 | 0.425131 | − | 0.905132i | \(-0.360228\pi\) | ||||
0.425131 | + | 0.905132i | \(0.360228\pi\) | |||||||
\(938\) | −32.0096 | −1.04515 | ||||||||
\(939\) | −44.3912 | −1.44865 | ||||||||
\(940\) | 8.97746 | 0.292812 | ||||||||
\(941\) | 53.0192 | 1.72838 | 0.864189 | − | 0.503168i | \(-0.167832\pi\) | ||||
0.864189 | + | 0.503168i | \(0.167832\pi\) | |||||||
\(942\) | −4.37293 | −0.142478 | ||||||||
\(943\) | −24.0995 | −0.784788 | ||||||||
\(944\) | 53.9189 | 1.75491 | ||||||||
\(945\) | −5.69963 | −0.185409 | ||||||||
\(946\) | −1.67699 | −0.0545238 | ||||||||
\(947\) | 9.26704 | 0.301138 | 0.150569 | − | 0.988599i | \(-0.451889\pi\) | ||||
0.150569 | + | 0.988599i | \(0.451889\pi\) | |||||||
\(948\) | −19.2888 | −0.626472 | ||||||||
\(949\) | −3.37728 | −0.109631 | ||||||||
\(950\) | 51.4980 | 1.67082 | ||||||||
\(951\) | 13.4363 | 0.435701 | ||||||||
\(952\) | 35.6166 | 1.15434 | ||||||||
\(953\) | −28.0583 | −0.908899 | −0.454449 | − | 0.890773i | \(-0.650164\pi\) | ||||
−0.454449 | + | 0.890773i | \(0.650164\pi\) | |||||||
\(954\) | −3.42854 | −0.111003 | ||||||||
\(955\) | 19.1892 | 0.620947 | ||||||||
\(956\) | −88.7401 | −2.87006 | ||||||||
\(957\) | −0.875930 | −0.0283148 | ||||||||
\(958\) | −99.4180 | −3.21205 | ||||||||
\(959\) | −15.6596 | −0.505676 | ||||||||
\(960\) | −15.1770 | −0.489834 | ||||||||
\(961\) | −15.9602 | −0.514847 | ||||||||
\(962\) | −10.1160 | −0.326154 | ||||||||
\(963\) | −4.82491 | −0.155480 | ||||||||
\(964\) | 24.2491 | 0.781012 | ||||||||
\(965\) | 15.6081 | 0.502442 | ||||||||
\(966\) | −18.7030 | −0.601760 | ||||||||
\(967\) | −51.8873 | −1.66858 | −0.834292 | − | 0.551323i | \(-0.814123\pi\) | ||||
−0.834292 | + | 0.551323i | \(0.814123\pi\) | |||||||
\(968\) | 80.2018 | 2.57778 | ||||||||
\(969\) | 47.2836 | 1.51897 | ||||||||
\(970\) | −10.6871 | −0.343143 | ||||||||
\(971\) | 45.6433 | 1.46476 | 0.732382 | − | 0.680894i | \(-0.238409\pi\) | ||||
0.732382 | + | 0.680894i | \(0.238409\pi\) | |||||||
\(972\) | −17.6264 | −0.565366 | ||||||||
\(973\) | 18.4094 | 0.590178 | ||||||||
\(974\) | 4.58631 | 0.146955 | ||||||||
\(975\) | 3.22810 | 0.103382 | ||||||||
\(976\) | 14.8883 | 0.476563 | ||||||||
\(977\) | −12.7401 | −0.407593 | −0.203797 | − | 0.979013i | \(-0.565328\pi\) | ||||
−0.203797 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(978\) | −54.6400 | −1.74719 | ||||||||
\(979\) | −0.112181 | −0.00358531 | ||||||||
\(980\) | 33.0297 | 1.05510 | ||||||||
\(981\) | 1.66562 | 0.0531793 | ||||||||
\(982\) | 17.3651 | 0.554143 | ||||||||
\(983\) | 39.2025 | 1.25037 | 0.625184 | − | 0.780478i | \(-0.285024\pi\) | ||||
0.625184 | + | 0.780478i | \(0.285024\pi\) | |||||||
\(984\) | −83.7841 | −2.67094 | ||||||||
\(985\) | −3.51907 | −0.112127 | ||||||||
\(986\) | −79.2839 | −2.52491 | ||||||||
\(987\) | 3.02431 | 0.0962647 | ||||||||
\(988\) | −12.4222 | −0.395204 | ||||||||
\(989\) | 32.8066 | 1.04319 | ||||||||
\(990\) | −0.0806085 | −0.00256191 | ||||||||
\(991\) | −49.8832 | −1.58459 | −0.792296 | − | 0.610137i | \(-0.791115\pi\) | ||||
−0.792296 | + | 0.610137i | \(0.791115\pi\) | |||||||
\(992\) | 38.7073 | 1.22896 | ||||||||
\(993\) | −9.43996 | −0.299568 | ||||||||
\(994\) | 40.4666 | 1.28352 | ||||||||
\(995\) | −27.7978 | −0.881250 | ||||||||
\(996\) | −78.8713 | −2.49913 | ||||||||
\(997\) | 22.8494 | 0.723649 | 0.361825 | − | 0.932246i | \(-0.382154\pi\) | ||||
0.361825 | + | 0.932246i | \(0.382154\pi\) | |||||||
\(998\) | −92.0218 | −2.91290 | ||||||||
\(999\) | 39.1067 | 1.23728 |
(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 | 4013.2.a.b.1.8 | ✓ | 157 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.b.1.8 | ✓ | 157 | 1.1 | even | 1 | trivial |