Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.58 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.769245 | −0.543938 | −0.271969 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271969 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(3\) | −2.98873 | −1.72554 | −0.862772 | − | 0.505593i | \(-0.831274\pi\) | ||||
−0.862772 | + | 0.505593i | \(0.831274\pi\) | |||||||
\(4\) | −1.40826 | −0.704131 | ||||||||
\(5\) | −1.88149 | −0.841428 | −0.420714 | − | 0.907193i | \(-0.638220\pi\) | ||||
−0.420714 | + | 0.907193i | \(0.638220\pi\) | |||||||
\(6\) | 2.29906 | 0.938589 | ||||||||
\(7\) | 1.15926 | 0.438159 | 0.219080 | − | 0.975707i | \(-0.429695\pi\) | ||||
0.219080 | + | 0.975707i | \(0.429695\pi\) | |||||||
\(8\) | 2.62179 | 0.926942 | ||||||||
\(9\) | 5.93250 | 1.97750 | ||||||||
\(10\) | 1.44733 | 0.457685 | ||||||||
\(11\) | −1.23417 | −0.372116 | −0.186058 | − | 0.982539i | \(-0.559571\pi\) | ||||
−0.186058 | + | 0.982539i | \(0.559571\pi\) | |||||||
\(12\) | 4.20892 | 1.21501 | ||||||||
\(13\) | −1.79142 | −0.496849 | −0.248425 | − | 0.968651i | \(-0.579913\pi\) | ||||
−0.248425 | + | 0.968651i | \(0.579913\pi\) | |||||||
\(14\) | −0.891755 | −0.238332 | ||||||||
\(15\) | 5.62327 | 1.45192 | ||||||||
\(16\) | 0.799730 | 0.199933 | ||||||||
\(17\) | −2.20700 | −0.535276 | −0.267638 | − | 0.963520i | \(-0.586243\pi\) | ||||
−0.267638 | + | 0.963520i | \(0.586243\pi\) | |||||||
\(18\) | −4.56355 | −1.07564 | ||||||||
\(19\) | −5.66298 | −1.29918 | −0.649589 | − | 0.760286i | \(-0.725059\pi\) | ||||
−0.649589 | + | 0.760286i | \(0.725059\pi\) | |||||||
\(20\) | 2.64963 | 0.592476 | ||||||||
\(21\) | −3.46472 | −0.756063 | ||||||||
\(22\) | 0.949379 | 0.202408 | ||||||||
\(23\) | −3.44247 | −0.717804 | −0.358902 | − | 0.933375i | \(-0.616849\pi\) | ||||
−0.358902 | + | 0.933375i | \(0.616849\pi\) | |||||||
\(24\) | −7.83581 | −1.59948 | ||||||||
\(25\) | −1.45999 | −0.291998 | ||||||||
\(26\) | 1.37804 | 0.270255 | ||||||||
\(27\) | −8.76446 | −1.68672 | ||||||||
\(28\) | −1.63254 | −0.308522 | ||||||||
\(29\) | 8.45248 | 1.56959 | 0.784793 | − | 0.619757i | \(-0.212769\pi\) | ||||
0.784793 | + | 0.619757i | \(0.212769\pi\) | |||||||
\(30\) | −4.32567 | −0.789755 | ||||||||
\(31\) | −4.76215 | −0.855308 | −0.427654 | − | 0.903943i | \(-0.640660\pi\) | ||||
−0.427654 | + | 0.903943i | \(0.640660\pi\) | |||||||
\(32\) | −5.85876 | −1.03569 | ||||||||
\(33\) | 3.68860 | 0.642103 | ||||||||
\(34\) | 1.69772 | 0.291157 | ||||||||
\(35\) | −2.18114 | −0.368680 | ||||||||
\(36\) | −8.35453 | −1.39242 | ||||||||
\(37\) | 6.89479 | 1.13350 | 0.566748 | − | 0.823891i | \(-0.308201\pi\) | ||||
0.566748 | + | 0.823891i | \(0.308201\pi\) | |||||||
\(38\) | 4.35622 | 0.706672 | ||||||||
\(39\) | 5.35405 | 0.857335 | ||||||||
\(40\) | −4.93287 | −0.779955 | ||||||||
\(41\) | 6.86584 | 1.07226 | 0.536132 | − | 0.844134i | \(-0.319885\pi\) | ||||
0.536132 | + | 0.844134i | \(0.319885\pi\) | |||||||
\(42\) | 2.66521 | 0.411252 | ||||||||
\(43\) | 7.89845 | 1.20450 | 0.602251 | − | 0.798307i | \(-0.294271\pi\) | ||||
0.602251 | + | 0.798307i | \(0.294271\pi\) | |||||||
\(44\) | 1.73804 | 0.262019 | ||||||||
\(45\) | −11.1620 | −1.66393 | ||||||||
\(46\) | 2.64810 | 0.390441 | ||||||||
\(47\) | −8.34671 | −1.21749 | −0.608747 | − | 0.793365i | \(-0.708327\pi\) | ||||
−0.608747 | + | 0.793365i | \(0.708327\pi\) | |||||||
\(48\) | −2.39018 | −0.344992 | ||||||||
\(49\) | −5.65611 | −0.808016 | ||||||||
\(50\) | 1.12309 | 0.158829 | ||||||||
\(51\) | 6.59612 | 0.923641 | ||||||||
\(52\) | 2.52278 | 0.349847 | ||||||||
\(53\) | 7.02234 | 0.964592 | 0.482296 | − | 0.876008i | \(-0.339803\pi\) | ||||
0.482296 | + | 0.876008i | \(0.339803\pi\) | |||||||
\(54\) | 6.74201 | 0.917472 | ||||||||
\(55\) | 2.32208 | 0.313109 | ||||||||
\(56\) | 3.03934 | 0.406148 | ||||||||
\(57\) | 16.9251 | 2.24179 | ||||||||
\(58\) | −6.50203 | −0.853758 | ||||||||
\(59\) | −12.6414 | −1.64578 | −0.822888 | − | 0.568204i | \(-0.807639\pi\) | ||||
−0.822888 | + | 0.568204i | \(0.807639\pi\) | |||||||
\(60\) | −7.91904 | −1.02234 | ||||||||
\(61\) | 1.75090 | 0.224179 | 0.112090 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112090 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(62\) | 3.66326 | 0.465235 | ||||||||
\(63\) | 6.87732 | 0.866461 | ||||||||
\(64\) | 2.90736 | 0.363420 | ||||||||
\(65\) | 3.37053 | 0.418063 | ||||||||
\(66\) | −2.83744 | −0.349264 | ||||||||
\(67\) | 7.30899 | 0.892935 | 0.446468 | − | 0.894800i | \(-0.352682\pi\) | ||||
0.446468 | + | 0.894800i | \(0.352682\pi\) | |||||||
\(68\) | 3.10803 | 0.376904 | ||||||||
\(69\) | 10.2886 | 1.23860 | ||||||||
\(70\) | 1.67783 | 0.200539 | ||||||||
\(71\) | −1.18255 | −0.140343 | −0.0701714 | − | 0.997535i | \(-0.522355\pi\) | ||||
−0.0701714 | + | 0.997535i | \(0.522355\pi\) | |||||||
\(72\) | 15.5538 | 1.83303 | ||||||||
\(73\) | 1.03781 | 0.121466 | 0.0607330 | − | 0.998154i | \(-0.480656\pi\) | ||||
0.0607330 | + | 0.998154i | \(0.480656\pi\) | |||||||
\(74\) | −5.30378 | −0.616551 | ||||||||
\(75\) | 4.36352 | 0.503856 | ||||||||
\(76\) | 7.97497 | 0.914792 | ||||||||
\(77\) | −1.43073 | −0.163046 | ||||||||
\(78\) | −4.11858 | −0.466337 | ||||||||
\(79\) | 15.9912 | 1.79915 | 0.899575 | − | 0.436766i | \(-0.143876\pi\) | ||||
0.899575 | + | 0.436766i | \(0.143876\pi\) | |||||||
\(80\) | −1.50469 | −0.168229 | ||||||||
\(81\) | 8.39709 | 0.933010 | ||||||||
\(82\) | −5.28151 | −0.583245 | ||||||||
\(83\) | 1.65913 | 0.182113 | 0.0910565 | − | 0.995846i | \(-0.470976\pi\) | ||||
0.0910565 | + | 0.995846i | \(0.470976\pi\) | |||||||
\(84\) | 4.87923 | 0.532368 | ||||||||
\(85\) | 4.15245 | 0.450396 | ||||||||
\(86\) | −6.07584 | −0.655175 | ||||||||
\(87\) | −25.2622 | −2.70839 | ||||||||
\(88\) | −3.23573 | −0.344930 | ||||||||
\(89\) | 12.1183 | 1.28454 | 0.642269 | − | 0.766479i | \(-0.277993\pi\) | ||||
0.642269 | + | 0.766479i | \(0.277993\pi\) | |||||||
\(90\) | 8.58627 | 0.905073 | ||||||||
\(91\) | −2.07672 | −0.217699 | ||||||||
\(92\) | 4.84790 | 0.505428 | ||||||||
\(93\) | 14.2328 | 1.47587 | ||||||||
\(94\) | 6.42066 | 0.662241 | ||||||||
\(95\) | 10.6549 | 1.09316 | ||||||||
\(96\) | 17.5103 | 1.78713 | ||||||||
\(97\) | −4.20548 | −0.427002 | −0.213501 | − | 0.976943i | \(-0.568487\pi\) | ||||
−0.213501 | + | 0.976943i | \(0.568487\pi\) | |||||||
\(98\) | 4.35093 | 0.439511 | ||||||||
\(99\) | −7.32172 | −0.735861 | ||||||||
\(100\) | 2.05605 | 0.205605 | ||||||||
\(101\) | 11.8276 | 1.17689 | 0.588447 | − | 0.808536i | \(-0.299739\pi\) | ||||
0.588447 | + | 0.808536i | \(0.299739\pi\) | |||||||
\(102\) | −5.07403 | −0.502404 | ||||||||
\(103\) | 10.5426 | 1.03880 | 0.519398 | − | 0.854533i | \(-0.326156\pi\) | ||||
0.519398 | + | 0.854533i | \(0.326156\pi\) | |||||||
\(104\) | −4.69671 | −0.460550 | ||||||||
\(105\) | 6.51883 | 0.636173 | ||||||||
\(106\) | −5.40189 | −0.524678 | ||||||||
\(107\) | 10.7514 | 1.03938 | 0.519688 | − | 0.854356i | \(-0.326048\pi\) | ||||
0.519688 | + | 0.854356i | \(0.326048\pi\) | |||||||
\(108\) | 12.3427 | 1.18767 | ||||||||
\(109\) | 10.3332 | 0.989736 | 0.494868 | − | 0.868968i | \(-0.335216\pi\) | ||||
0.494868 | + | 0.868968i | \(0.335216\pi\) | |||||||
\(110\) | −1.78625 | −0.170312 | ||||||||
\(111\) | −20.6067 | −1.95590 | ||||||||
\(112\) | 0.927096 | 0.0876023 | ||||||||
\(113\) | −7.11858 | −0.669660 | −0.334830 | − | 0.942279i | \(-0.608679\pi\) | ||||
−0.334830 | + | 0.942279i | \(0.608679\pi\) | |||||||
\(114\) | −13.0196 | −1.21939 | ||||||||
\(115\) | 6.47697 | 0.603980 | ||||||||
\(116\) | −11.9033 | −1.10520 | ||||||||
\(117\) | −10.6276 | −0.982520 | ||||||||
\(118\) | 9.72436 | 0.895200 | ||||||||
\(119\) | −2.55849 | −0.234536 | ||||||||
\(120\) | 14.7430 | 1.34585 | ||||||||
\(121\) | −9.47682 | −0.861529 | ||||||||
\(122\) | −1.34687 | −0.121940 | ||||||||
\(123\) | −20.5201 | −1.85024 | ||||||||
\(124\) | 6.70636 | 0.602249 | ||||||||
\(125\) | 12.1544 | 1.08712 | ||||||||
\(126\) | −5.29034 | −0.471301 | ||||||||
\(127\) | 8.35066 | 0.741001 | 0.370501 | − | 0.928832i | \(-0.379186\pi\) | ||||
0.370501 | + | 0.928832i | \(0.379186\pi\) | |||||||
\(128\) | 9.48105 | 0.838015 | ||||||||
\(129\) | −23.6063 | −2.07842 | ||||||||
\(130\) | −2.59276 | −0.227400 | ||||||||
\(131\) | 7.34443 | 0.641686 | 0.320843 | − | 0.947132i | \(-0.396034\pi\) | ||||
0.320843 | + | 0.947132i | \(0.396034\pi\) | |||||||
\(132\) | −5.19452 | −0.452125 | ||||||||
\(133\) | −6.56488 | −0.569247 | ||||||||
\(134\) | −5.62240 | −0.485701 | ||||||||
\(135\) | 16.4903 | 1.41926 | ||||||||
\(136\) | −5.78628 | −0.496169 | ||||||||
\(137\) | −5.73568 | −0.490032 | −0.245016 | − | 0.969519i | \(-0.578793\pi\) | ||||
−0.245016 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(138\) | −7.91445 | −0.673722 | ||||||||
\(139\) | −15.2992 | −1.29766 | −0.648832 | − | 0.760932i | \(-0.724742\pi\) | ||||
−0.648832 | + | 0.760932i | \(0.724742\pi\) | |||||||
\(140\) | 3.07162 | 0.259599 | ||||||||
\(141\) | 24.9461 | 2.10084 | ||||||||
\(142\) | 0.909670 | 0.0763378 | ||||||||
\(143\) | 2.21091 | 0.184886 | ||||||||
\(144\) | 4.74440 | 0.395367 | ||||||||
\(145\) | −15.9033 | −1.32069 | ||||||||
\(146\) | −0.798326 | −0.0660699 | ||||||||
\(147\) | 16.9046 | 1.39427 | ||||||||
\(148\) | −9.70967 | −0.798130 | ||||||||
\(149\) | 0.636582 | 0.0521508 | 0.0260754 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260754 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(150\) | −3.35661 | −0.274066 | ||||||||
\(151\) | 6.86672 | 0.558806 | 0.279403 | − | 0.960174i | \(-0.409863\pi\) | ||||
0.279403 | + | 0.960174i | \(0.409863\pi\) | |||||||
\(152\) | −14.8471 | −1.20426 | ||||||||
\(153\) | −13.0930 | −1.05851 | ||||||||
\(154\) | 1.10058 | 0.0886871 | ||||||||
\(155\) | 8.95995 | 0.719680 | ||||||||
\(156\) | −7.53992 | −0.603676 | ||||||||
\(157\) | −13.9086 | −1.11003 | −0.555014 | − | 0.831841i | \(-0.687287\pi\) | ||||
−0.555014 | + | 0.831841i | \(0.687287\pi\) | |||||||
\(158\) | −12.3011 | −0.978626 | ||||||||
\(159\) | −20.9879 | −1.66445 | ||||||||
\(160\) | 11.0232 | 0.871461 | ||||||||
\(161\) | −3.99072 | −0.314512 | ||||||||
\(162\) | −6.45942 | −0.507500 | ||||||||
\(163\) | −5.88216 | −0.460726 | −0.230363 | − | 0.973105i | \(-0.573991\pi\) | ||||
−0.230363 | + | 0.973105i | \(0.573991\pi\) | |||||||
\(164\) | −9.66891 | −0.755015 | ||||||||
\(165\) | −6.94007 | −0.540284 | ||||||||
\(166\) | −1.27627 | −0.0990581 | ||||||||
\(167\) | 1.75646 | 0.135919 | 0.0679597 | − | 0.997688i | \(-0.478351\pi\) | ||||
0.0679597 | + | 0.997688i | \(0.478351\pi\) | |||||||
\(168\) | −9.08375 | −0.700827 | ||||||||
\(169\) | −9.79083 | −0.753141 | ||||||||
\(170\) | −3.19425 | −0.244988 | ||||||||
\(171\) | −33.5957 | −2.56913 | ||||||||
\(172\) | −11.1231 | −0.848128 | ||||||||
\(173\) | 5.40460 | 0.410904 | 0.205452 | − | 0.978667i | \(-0.434134\pi\) | ||||
0.205452 | + | 0.978667i | \(0.434134\pi\) | |||||||
\(174\) | 19.4328 | 1.47320 | ||||||||
\(175\) | −1.69251 | −0.127942 | ||||||||
\(176\) | −0.987003 | −0.0743982 | ||||||||
\(177\) | 37.7819 | 2.83986 | ||||||||
\(178\) | −9.32194 | −0.698709 | ||||||||
\(179\) | −17.8483 | −1.33405 | −0.667024 | − | 0.745036i | \(-0.732432\pi\) | ||||
−0.667024 | + | 0.745036i | \(0.732432\pi\) | |||||||
\(180\) | 15.7190 | 1.17162 | ||||||||
\(181\) | 7.39098 | 0.549368 | 0.274684 | − | 0.961535i | \(-0.411427\pi\) | ||||
0.274684 | + | 0.961535i | \(0.411427\pi\) | |||||||
\(182\) | 1.59750 | 0.118415 | ||||||||
\(183\) | −5.23296 | −0.386831 | ||||||||
\(184\) | −9.02541 | −0.665362 | ||||||||
\(185\) | −12.9725 | −0.953756 | ||||||||
\(186\) | −10.9485 | −0.802783 | ||||||||
\(187\) | 2.72381 | 0.199185 | ||||||||
\(188\) | 11.7544 | 0.857275 | ||||||||
\(189\) | −10.1603 | −0.739053 | ||||||||
\(190\) | −8.19619 | −0.594614 | ||||||||
\(191\) | −25.3418 | −1.83367 | −0.916835 | − | 0.399265i | \(-0.869265\pi\) | ||||
−0.916835 | + | 0.399265i | \(0.869265\pi\) | |||||||
\(192\) | −8.68932 | −0.627097 | ||||||||
\(193\) | −3.08605 | −0.222139 | −0.111069 | − | 0.993813i | \(-0.535428\pi\) | ||||
−0.111069 | + | 0.993813i | \(0.535428\pi\) | |||||||
\(194\) | 3.23504 | 0.232263 | ||||||||
\(195\) | −10.0736 | −0.721386 | ||||||||
\(196\) | 7.96530 | 0.568950 | ||||||||
\(197\) | 11.6044 | 0.826783 | 0.413391 | − | 0.910553i | \(-0.364344\pi\) | ||||
0.413391 | + | 0.910553i | \(0.364344\pi\) | |||||||
\(198\) | 5.63219 | 0.400263 | ||||||||
\(199\) | 14.8121 | 1.05000 | 0.525000 | − | 0.851102i | \(-0.324065\pi\) | ||||
0.525000 | + | 0.851102i | \(0.324065\pi\) | |||||||
\(200\) | −3.82779 | −0.270665 | ||||||||
\(201\) | −21.8446 | −1.54080 | ||||||||
\(202\) | −9.09835 | −0.640158 | ||||||||
\(203\) | 9.79863 | 0.687729 | ||||||||
\(204\) | −9.28907 | −0.650365 | ||||||||
\(205\) | −12.9180 | −0.902233 | ||||||||
\(206\) | −8.10985 | −0.565040 | ||||||||
\(207\) | −20.4224 | −1.41946 | ||||||||
\(208\) | −1.43265 | −0.0993363 | ||||||||
\(209\) | 6.98909 | 0.483445 | ||||||||
\(210\) | −5.01458 | −0.346039 | ||||||||
\(211\) | 11.1856 | 0.770046 | 0.385023 | − | 0.922907i | \(-0.374193\pi\) | ||||
0.385023 | + | 0.922907i | \(0.374193\pi\) | |||||||
\(212\) | −9.88930 | −0.679200 | ||||||||
\(213\) | 3.53432 | 0.242168 | ||||||||
\(214\) | −8.27044 | −0.565356 | ||||||||
\(215\) | −14.8609 | −1.01350 | ||||||||
\(216\) | −22.9786 | −1.56349 | ||||||||
\(217\) | −5.52058 | −0.374761 | ||||||||
\(218\) | −7.94872 | −0.538355 | ||||||||
\(219\) | −3.10172 | −0.209595 | ||||||||
\(220\) | −3.27010 | −0.220470 | ||||||||
\(221\) | 3.95365 | 0.265951 | ||||||||
\(222\) | 15.8516 | 1.06389 | ||||||||
\(223\) | −1.30279 | −0.0872410 | −0.0436205 | − | 0.999048i | \(-0.513889\pi\) | ||||
−0.0436205 | + | 0.999048i | \(0.513889\pi\) | |||||||
\(224\) | −6.79183 | −0.453799 | ||||||||
\(225\) | −8.66140 | −0.577427 | ||||||||
\(226\) | 5.47593 | 0.364254 | ||||||||
\(227\) | 2.22961 | 0.147984 | 0.0739922 | − | 0.997259i | \(-0.476426\pi\) | ||||
0.0739922 | + | 0.997259i | \(0.476426\pi\) | |||||||
\(228\) | −23.8350 | −1.57851 | ||||||||
\(229\) | −22.5889 | −1.49272 | −0.746359 | − | 0.665544i | \(-0.768200\pi\) | ||||
−0.746359 | + | 0.665544i | \(0.768200\pi\) | |||||||
\(230\) | −4.98237 | −0.328528 | ||||||||
\(231\) | 4.27605 | 0.281343 | ||||||||
\(232\) | 22.1606 | 1.45492 | ||||||||
\(233\) | 13.5988 | 0.890884 | 0.445442 | − | 0.895311i | \(-0.353047\pi\) | ||||
0.445442 | + | 0.895311i | \(0.353047\pi\) | |||||||
\(234\) | 8.17521 | 0.534430 | ||||||||
\(235\) | 15.7043 | 1.02443 | ||||||||
\(236\) | 17.8025 | 1.15884 | ||||||||
\(237\) | −47.7934 | −3.10451 | ||||||||
\(238\) | 1.96810 | 0.127573 | ||||||||
\(239\) | 1.21432 | 0.0785477 | 0.0392738 | − | 0.999228i | \(-0.487496\pi\) | ||||
0.0392738 | + | 0.999228i | \(0.487496\pi\) | |||||||
\(240\) | 4.49710 | 0.290286 | ||||||||
\(241\) | −23.4075 | −1.50781 | −0.753906 | − | 0.656983i | \(-0.771832\pi\) | ||||
−0.753906 | + | 0.656983i | \(0.771832\pi\) | |||||||
\(242\) | 7.28999 | 0.468619 | ||||||||
\(243\) | 1.19675 | 0.0767713 | ||||||||
\(244\) | −2.46572 | −0.157852 | ||||||||
\(245\) | 10.6419 | 0.679888 | ||||||||
\(246\) | 15.7850 | 1.00641 | ||||||||
\(247\) | 10.1448 | 0.645495 | ||||||||
\(248\) | −12.4854 | −0.792821 | ||||||||
\(249\) | −4.95868 | −0.314244 | ||||||||
\(250\) | −9.34972 | −0.591328 | ||||||||
\(251\) | 16.8290 | 1.06224 | 0.531118 | − | 0.847298i | \(-0.321772\pi\) | ||||
0.531118 | + | 0.847298i | \(0.321772\pi\) | |||||||
\(252\) | −9.68507 | −0.610102 | ||||||||
\(253\) | 4.24859 | 0.267106 | ||||||||
\(254\) | −6.42370 | −0.403059 | ||||||||
\(255\) | −12.4105 | −0.777178 | ||||||||
\(256\) | −13.1080 | −0.819248 | ||||||||
\(257\) | 2.49984 | 0.155936 | 0.0779679 | − | 0.996956i | \(-0.475157\pi\) | ||||
0.0779679 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(258\) | 18.1590 | 1.13053 | ||||||||
\(259\) | 7.99286 | 0.496652 | ||||||||
\(260\) | −4.74659 | −0.294371 | ||||||||
\(261\) | 50.1444 | 3.10386 | ||||||||
\(262\) | −5.64966 | −0.349037 | ||||||||
\(263\) | 11.6908 | 0.720888 | 0.360444 | − | 0.932781i | \(-0.382625\pi\) | ||||
0.360444 | + | 0.932781i | \(0.382625\pi\) | |||||||
\(264\) | 9.67073 | 0.595192 | ||||||||
\(265\) | −13.2125 | −0.811635 | ||||||||
\(266\) | 5.04999 | 0.309635 | ||||||||
\(267\) | −36.2183 | −2.21653 | ||||||||
\(268\) | −10.2930 | −0.628744 | ||||||||
\(269\) | 12.9245 | 0.788019 | 0.394009 | − | 0.919106i | \(-0.371088\pi\) | ||||
0.394009 | + | 0.919106i | \(0.371088\pi\) | |||||||
\(270\) | −12.6850 | −0.771987 | ||||||||
\(271\) | −25.1070 | −1.52514 | −0.762570 | − | 0.646906i | \(-0.776062\pi\) | ||||
−0.762570 | + | 0.646906i | \(0.776062\pi\) | |||||||
\(272\) | −1.76500 | −0.107019 | ||||||||
\(273\) | 6.20675 | 0.375649 | ||||||||
\(274\) | 4.41214 | 0.266547 | ||||||||
\(275\) | 1.80188 | 0.108657 | ||||||||
\(276\) | −14.4891 | −0.872138 | ||||||||
\(277\) | 1.61680 | 0.0971440 | 0.0485720 | − | 0.998820i | \(-0.484533\pi\) | ||||
0.0485720 | + | 0.998820i | \(0.484533\pi\) | |||||||
\(278\) | 11.7688 | 0.705849 | ||||||||
\(279\) | −28.2515 | −1.69137 | ||||||||
\(280\) | −5.71848 | −0.341745 | ||||||||
\(281\) | −0.240678 | −0.0143576 | −0.00717882 | − | 0.999974i | \(-0.502285\pi\) | ||||
−0.00717882 | + | 0.999974i | \(0.502285\pi\) | |||||||
\(282\) | −19.1896 | −1.14273 | ||||||||
\(283\) | −16.5928 | −0.986337 | −0.493169 | − | 0.869934i | \(-0.664161\pi\) | ||||
−0.493169 | + | 0.869934i | \(0.664161\pi\) | |||||||
\(284\) | 1.66534 | 0.0988198 | ||||||||
\(285\) | −31.8445 | −1.88630 | ||||||||
\(286\) | −1.70073 | −0.100566 | ||||||||
\(287\) | 7.95930 | 0.469823 | ||||||||
\(288\) | −34.7571 | −2.04808 | ||||||||
\(289\) | −12.1292 | −0.713480 | ||||||||
\(290\) | 12.2335 | 0.718376 | ||||||||
\(291\) | 12.5690 | 0.736811 | ||||||||
\(292\) | −1.46150 | −0.0855280 | ||||||||
\(293\) | −25.4600 | −1.48739 | −0.743695 | − | 0.668520i | \(-0.766928\pi\) | ||||
−0.743695 | + | 0.668520i | \(0.766928\pi\) | |||||||
\(294\) | −13.0038 | −0.758395 | ||||||||
\(295\) | 23.7848 | 1.38480 | ||||||||
\(296\) | 18.0767 | 1.05068 | ||||||||
\(297\) | 10.8168 | 0.627657 | ||||||||
\(298\) | −0.489687 | −0.0283668 | ||||||||
\(299\) | 6.16688 | 0.356640 | ||||||||
\(300\) | −6.14498 | −0.354781 | ||||||||
\(301\) | 9.15636 | 0.527764 | ||||||||
\(302\) | −5.28219 | −0.303956 | ||||||||
\(303\) | −35.3496 | −2.03078 | ||||||||
\(304\) | −4.52886 | −0.259748 | ||||||||
\(305\) | −3.29430 | −0.188631 | ||||||||
\(306\) | 10.0717 | 0.575763 | ||||||||
\(307\) | −24.3963 | −1.39237 | −0.696186 | − | 0.717861i | \(-0.745121\pi\) | ||||
−0.696186 | + | 0.717861i | \(0.745121\pi\) | |||||||
\(308\) | 2.01484 | 0.114806 | ||||||||
\(309\) | −31.5090 | −1.79249 | ||||||||
\(310\) | −6.89239 | −0.391462 | ||||||||
\(311\) | 11.9703 | 0.678774 | 0.339387 | − | 0.940647i | \(-0.389780\pi\) | ||||
0.339387 | + | 0.940647i | \(0.389780\pi\) | |||||||
\(312\) | 14.0372 | 0.794700 | ||||||||
\(313\) | −15.2036 | −0.859361 | −0.429680 | − | 0.902981i | \(-0.641374\pi\) | ||||
−0.429680 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(314\) | 10.6991 | 0.603786 | ||||||||
\(315\) | −12.9396 | −0.729065 | ||||||||
\(316\) | −22.5198 | −1.26684 | ||||||||
\(317\) | 17.0036 | 0.955016 | 0.477508 | − | 0.878627i | \(-0.341540\pi\) | ||||
0.477508 | + | 0.878627i | \(0.341540\pi\) | |||||||
\(318\) | 16.1448 | 0.905356 | ||||||||
\(319\) | −10.4318 | −0.584069 | ||||||||
\(320\) | −5.47017 | −0.305792 | ||||||||
\(321\) | −32.1330 | −1.79349 | ||||||||
\(322\) | 3.06984 | 0.171075 | ||||||||
\(323\) | 12.4982 | 0.695418 | ||||||||
\(324\) | −11.8253 | −0.656962 | ||||||||
\(325\) | 2.61545 | 0.145079 | ||||||||
\(326\) | 4.52482 | 0.250607 | ||||||||
\(327\) | −30.8830 | −1.70783 | ||||||||
\(328\) | 18.0008 | 0.993926 | ||||||||
\(329\) | −9.67602 | −0.533456 | ||||||||
\(330\) | 5.33861 | 0.293881 | ||||||||
\(331\) | 15.1664 | 0.833618 | 0.416809 | − | 0.908994i | \(-0.363148\pi\) | ||||
0.416809 | + | 0.908994i | \(0.363148\pi\) | |||||||
\(332\) | −2.33649 | −0.128231 | ||||||||
\(333\) | 40.9033 | 2.24149 | ||||||||
\(334\) | −1.35115 | −0.0739317 | ||||||||
\(335\) | −13.7518 | −0.751341 | ||||||||
\(336\) | −2.77084 | −0.151162 | ||||||||
\(337\) | 8.01882 | 0.436813 | 0.218407 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218407 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(338\) | 7.53154 | 0.409662 | ||||||||
\(339\) | 21.2755 | 1.15553 | ||||||||
\(340\) | −5.84774 | −0.317138 | ||||||||
\(341\) | 5.87731 | 0.318274 | ||||||||
\(342\) | 25.8433 | 1.39744 | ||||||||
\(343\) | −14.6717 | −0.792199 | ||||||||
\(344\) | 20.7081 | 1.11650 | ||||||||
\(345\) | −19.3579 | −1.04219 | ||||||||
\(346\) | −4.15746 | −0.223506 | ||||||||
\(347\) | −20.4071 | −1.09551 | −0.547755 | − | 0.836638i | \(-0.684518\pi\) | ||||
−0.547755 | + | 0.836638i | \(0.684518\pi\) | |||||||
\(348\) | 35.5758 | 1.90706 | ||||||||
\(349\) | 3.38606 | 0.181252 | 0.0906258 | − | 0.995885i | \(-0.471113\pi\) | ||||
0.0906258 | + | 0.995885i | \(0.471113\pi\) | |||||||
\(350\) | 1.30195 | 0.0695924 | ||||||||
\(351\) | 15.7008 | 0.838046 | ||||||||
\(352\) | 7.23071 | 0.385398 | ||||||||
\(353\) | 34.9227 | 1.85875 | 0.929373 | − | 0.369141i | \(-0.120348\pi\) | ||||
0.929373 | + | 0.369141i | \(0.120348\pi\) | |||||||
\(354\) | −29.0635 | −1.54471 | ||||||||
\(355\) | 2.22496 | 0.118088 | ||||||||
\(356\) | −17.0658 | −0.904483 | ||||||||
\(357\) | 7.64662 | 0.404702 | ||||||||
\(358\) | 13.7297 | 0.725639 | ||||||||
\(359\) | −32.1291 | −1.69571 | −0.847855 | − | 0.530228i | \(-0.822106\pi\) | ||||
−0.847855 | + | 0.530228i | \(0.822106\pi\) | |||||||
\(360\) | −29.2643 | −1.54236 | ||||||||
\(361\) | 13.0694 | 0.687862 | ||||||||
\(362\) | −5.68547 | −0.298822 | ||||||||
\(363\) | 28.3237 | 1.48661 | ||||||||
\(364\) | 2.92456 | 0.153289 | ||||||||
\(365\) | −1.95262 | −0.102205 | ||||||||
\(366\) | 4.02542 | 0.210412 | ||||||||
\(367\) | 7.04206 | 0.367593 | 0.183796 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183796 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(368\) | −2.75304 | −0.143512 | ||||||||
\(369\) | 40.7316 | 2.12040 | ||||||||
\(370\) | 9.97901 | 0.518784 | ||||||||
\(371\) | 8.14072 | 0.422645 | ||||||||
\(372\) | −20.0435 | −1.03921 | ||||||||
\(373\) | 4.61216 | 0.238809 | 0.119404 | − | 0.992846i | \(-0.461902\pi\) | ||||
0.119404 | + | 0.992846i | \(0.461902\pi\) | |||||||
\(374\) | −2.09528 | −0.108344 | ||||||||
\(375\) | −36.3263 | −1.87588 | ||||||||
\(376\) | −21.8833 | −1.12855 | ||||||||
\(377\) | −15.1419 | −0.779848 | ||||||||
\(378\) | 7.81575 | 0.401999 | ||||||||
\(379\) | 4.16167 | 0.213771 | 0.106885 | − | 0.994271i | \(-0.465912\pi\) | ||||
0.106885 | + | 0.994271i | \(0.465912\pi\) | |||||||
\(380\) | −15.0048 | −0.769732 | ||||||||
\(381\) | −24.9579 | −1.27863 | ||||||||
\(382\) | 19.4941 | 0.997403 | ||||||||
\(383\) | 13.6658 | 0.698291 | 0.349145 | − | 0.937069i | \(-0.386472\pi\) | ||||
0.349145 | + | 0.937069i | \(0.386472\pi\) | |||||||
\(384\) | −28.3363 | −1.44603 | ||||||||
\(385\) | 2.69190 | 0.137192 | ||||||||
\(386\) | 2.37392 | 0.120830 | ||||||||
\(387\) | 46.8576 | 2.38190 | ||||||||
\(388\) | 5.92242 | 0.300665 | ||||||||
\(389\) | −11.8251 | −0.599554 | −0.299777 | − | 0.954009i | \(-0.596912\pi\) | ||||
−0.299777 | + | 0.954009i | \(0.596912\pi\) | |||||||
\(390\) | 7.74907 | 0.392389 | ||||||||
\(391\) | 7.59751 | 0.384223 | ||||||||
\(392\) | −14.8291 | −0.748984 | ||||||||
\(393\) | −21.9505 | −1.10726 | ||||||||
\(394\) | −8.92666 | −0.449718 | ||||||||
\(395\) | −30.0873 | −1.51386 | ||||||||
\(396\) | 10.3109 | 0.518143 | ||||||||
\(397\) | 11.6358 | 0.583985 | 0.291992 | − | 0.956421i | \(-0.405682\pi\) | ||||
0.291992 | + | 0.956421i | \(0.405682\pi\) | |||||||
\(398\) | −11.3941 | −0.571135 | ||||||||
\(399\) | 19.6206 | 0.982260 | ||||||||
\(400\) | −1.16760 | −0.0583799 | ||||||||
\(401\) | 19.9344 | 0.995475 | 0.497738 | − | 0.867328i | \(-0.334164\pi\) | ||||
0.497738 | + | 0.867328i | \(0.334164\pi\) | |||||||
\(402\) | 16.8038 | 0.838099 | ||||||||
\(403\) | 8.53099 | 0.424959 | ||||||||
\(404\) | −16.6564 | −0.828689 | ||||||||
\(405\) | −15.7991 | −0.785061 | ||||||||
\(406\) | −7.53755 | −0.374082 | ||||||||
\(407\) | −8.50934 | −0.421792 | ||||||||
\(408\) | 17.2936 | 0.856162 | ||||||||
\(409\) | −10.5743 | −0.522867 | −0.261434 | − | 0.965221i | \(-0.584195\pi\) | ||||
−0.261434 | + | 0.965221i | \(0.584195\pi\) | |||||||
\(410\) | 9.93711 | 0.490759 | ||||||||
\(411\) | 17.1424 | 0.845572 | ||||||||
\(412\) | −14.8468 | −0.731448 | ||||||||
\(413\) | −14.6547 | −0.721112 | ||||||||
\(414\) | 15.7098 | 0.772097 | ||||||||
\(415\) | −3.12163 | −0.153235 | ||||||||
\(416\) | 10.4955 | 0.514583 | ||||||||
\(417\) | 45.7253 | 2.23918 | ||||||||
\(418\) | −5.37632 | −0.262964 | ||||||||
\(419\) | −15.6866 | −0.766341 | −0.383171 | − | 0.923678i | \(-0.625168\pi\) | ||||
−0.383171 | + | 0.923678i | \(0.625168\pi\) | |||||||
\(420\) | −9.18023 | −0.447949 | ||||||||
\(421\) | 22.5092 | 1.09703 | 0.548516 | − | 0.836140i | \(-0.315193\pi\) | ||||
0.548516 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(422\) | −8.60444 | −0.418857 | ||||||||
\(423\) | −49.5169 | −2.40759 | ||||||||
\(424\) | 18.4111 | 0.894121 | ||||||||
\(425\) | 3.22220 | 0.156299 | ||||||||
\(426\) | −2.71876 | −0.131724 | ||||||||
\(427\) | 2.02975 | 0.0982263 | ||||||||
\(428\) | −15.1408 | −0.731857 | ||||||||
\(429\) | −6.60781 | −0.319028 | ||||||||
\(430\) | 11.4316 | 0.551283 | ||||||||
\(431\) | 30.4291 | 1.46572 | 0.732860 | − | 0.680380i | \(-0.238185\pi\) | ||||
0.732860 | + | 0.680380i | \(0.238185\pi\) | |||||||
\(432\) | −7.00920 | −0.337230 | ||||||||
\(433\) | −8.64527 | −0.415465 | −0.207733 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207733 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(434\) | 4.24667 | 0.203847 | ||||||||
\(435\) | 47.5306 | 2.27892 | ||||||||
\(436\) | −14.5518 | −0.696904 | ||||||||
\(437\) | 19.4946 | 0.932554 | ||||||||
\(438\) | 2.38598 | 0.114007 | ||||||||
\(439\) | −21.9272 | −1.04653 | −0.523264 | − | 0.852171i | \(-0.675286\pi\) | ||||
−0.523264 | + | 0.852171i | \(0.675286\pi\) | |||||||
\(440\) | 6.08800 | 0.290234 | ||||||||
\(441\) | −33.5549 | −1.59785 | ||||||||
\(442\) | −3.04132 | −0.144661 | ||||||||
\(443\) | −26.9727 | −1.28151 | −0.640757 | − | 0.767744i | \(-0.721379\pi\) | ||||
−0.640757 | + | 0.767744i | \(0.721379\pi\) | |||||||
\(444\) | 29.0196 | 1.37721 | ||||||||
\(445\) | −22.8005 | −1.08085 | ||||||||
\(446\) | 1.00216 | 0.0474537 | ||||||||
\(447\) | −1.90257 | −0.0899885 | ||||||||
\(448\) | 3.37039 | 0.159236 | ||||||||
\(449\) | 31.0658 | 1.46608 | 0.733042 | − | 0.680184i | \(-0.238100\pi\) | ||||
0.733042 | + | 0.680184i | \(0.238100\pi\) | |||||||
\(450\) | 6.66274 | 0.314084 | ||||||||
\(451\) | −8.47361 | −0.399007 | ||||||||
\(452\) | 10.0248 | 0.471529 | ||||||||
\(453\) | −20.5228 | −0.964244 | ||||||||
\(454\) | −1.71512 | −0.0804944 | ||||||||
\(455\) | 3.90733 | 0.183178 | ||||||||
\(456\) | 44.3741 | 2.07801 | ||||||||
\(457\) | 12.8893 | 0.602935 | 0.301467 | − | 0.953477i | \(-0.402524\pi\) | ||||
0.301467 | + | 0.953477i | \(0.402524\pi\) | |||||||
\(458\) | 17.3764 | 0.811946 | ||||||||
\(459\) | 19.3431 | 0.902861 | ||||||||
\(460\) | −9.12127 | −0.425282 | ||||||||
\(461\) | 30.0423 | 1.39921 | 0.699604 | − | 0.714531i | \(-0.253360\pi\) | ||||
0.699604 | + | 0.714531i | \(0.253360\pi\) | |||||||
\(462\) | −3.28933 | −0.153033 | ||||||||
\(463\) | −4.78800 | −0.222517 | −0.111259 | − | 0.993791i | \(-0.535488\pi\) | ||||
−0.111259 | + | 0.993791i | \(0.535488\pi\) | |||||||
\(464\) | 6.75971 | 0.313811 | ||||||||
\(465\) | −26.7789 | −1.24184 | ||||||||
\(466\) | −10.4608 | −0.484586 | ||||||||
\(467\) | 18.8014 | 0.870025 | 0.435013 | − | 0.900424i | \(-0.356744\pi\) | ||||
0.435013 | + | 0.900424i | \(0.356744\pi\) | |||||||
\(468\) | 14.9664 | 0.691823 | ||||||||
\(469\) | 8.47302 | 0.391248 | ||||||||
\(470\) | −12.0804 | −0.557228 | ||||||||
\(471\) | 41.5691 | 1.91540 | ||||||||
\(472\) | −33.1432 | −1.52554 | ||||||||
\(473\) | −9.74803 | −0.448215 | ||||||||
\(474\) | 36.7648 | 1.68866 | ||||||||
\(475\) | 8.26791 | 0.379358 | ||||||||
\(476\) | 3.60302 | 0.165144 | ||||||||
\(477\) | 41.6600 | 1.90748 | ||||||||
\(478\) | −0.934107 | −0.0427251 | ||||||||
\(479\) | −27.6614 | −1.26388 | −0.631941 | − | 0.775017i | \(-0.717741\pi\) | ||||
−0.631941 | + | 0.775017i | \(0.717741\pi\) | |||||||
\(480\) | −32.9454 | −1.50374 | ||||||||
\(481\) | −12.3514 | −0.563176 | ||||||||
\(482\) | 18.0061 | 0.820156 | ||||||||
\(483\) | 11.9272 | 0.542705 | ||||||||
\(484\) | 13.3459 | 0.606630 | ||||||||
\(485\) | 7.91258 | 0.359292 | ||||||||
\(486\) | −0.920590 | −0.0417588 | ||||||||
\(487\) | −2.99237 | −0.135597 | −0.0677986 | − | 0.997699i | \(-0.521598\pi\) | ||||
−0.0677986 | + | 0.997699i | \(0.521598\pi\) | |||||||
\(488\) | 4.59048 | 0.207801 | ||||||||
\(489\) | 17.5802 | 0.795004 | ||||||||
\(490\) | −8.18625 | −0.369817 | ||||||||
\(491\) | 11.9556 | 0.539549 | 0.269774 | − | 0.962924i | \(-0.413051\pi\) | ||||
0.269774 | + | 0.962924i | \(0.413051\pi\) | |||||||
\(492\) | 28.8977 | 1.30281 | ||||||||
\(493\) | −18.6546 | −0.840161 | ||||||||
\(494\) | −7.80380 | −0.351109 | ||||||||
\(495\) | 13.7758 | 0.619174 | ||||||||
\(496\) | −3.80844 | −0.171004 | ||||||||
\(497\) | −1.37088 | −0.0614925 | ||||||||
\(498\) | 3.81444 | 0.170929 | ||||||||
\(499\) | −44.4358 | −1.98922 | −0.994610 | − | 0.103684i | \(-0.966937\pi\) | ||||
−0.994610 | + | 0.103684i | \(0.966937\pi\) | |||||||
\(500\) | −17.1166 | −0.765478 | ||||||||
\(501\) | −5.24960 | −0.234535 | ||||||||
\(502\) | −12.9456 | −0.577790 | ||||||||
\(503\) | 31.1841 | 1.39043 | 0.695215 | − | 0.718801i | \(-0.255309\pi\) | ||||
0.695215 | + | 0.718801i | \(0.255309\pi\) | |||||||
\(504\) | 18.0309 | 0.803159 | ||||||||
\(505\) | −22.2536 | −0.990273 | ||||||||
\(506\) | −3.26820 | −0.145289 | ||||||||
\(507\) | 29.2621 | 1.29958 | ||||||||
\(508\) | −11.7599 | −0.521762 | ||||||||
\(509\) | 28.6058 | 1.26793 | 0.633966 | − | 0.773361i | \(-0.281426\pi\) | ||||
0.633966 | + | 0.773361i | \(0.281426\pi\) | |||||||
\(510\) | 9.54674 | 0.422737 | ||||||||
\(511\) | 1.20309 | 0.0532214 | ||||||||
\(512\) | −8.87887 | −0.392394 | ||||||||
\(513\) | 49.6330 | 2.19135 | ||||||||
\(514\) | −1.92299 | −0.0848194 | ||||||||
\(515\) | −19.8358 | −0.874072 | ||||||||
\(516\) | 33.2439 | 1.46348 | ||||||||
\(517\) | 10.3013 | 0.453049 | ||||||||
\(518\) | −6.14846 | −0.270148 | ||||||||
\(519\) | −16.1529 | −0.709033 | ||||||||
\(520\) | 8.83682 | 0.387520 | ||||||||
\(521\) | −45.2656 | −1.98312 | −0.991560 | − | 0.129646i | \(-0.958616\pi\) | ||||
−0.991560 | + | 0.129646i | \(0.958616\pi\) | |||||||
\(522\) | −38.5733 | −1.68831 | ||||||||
\(523\) | 37.1552 | 1.62468 | 0.812341 | − | 0.583182i | \(-0.198193\pi\) | ||||
0.812341 | + | 0.583182i | \(0.198193\pi\) | |||||||
\(524\) | −10.3429 | −0.451831 | ||||||||
\(525\) | 5.05846 | 0.220769 | ||||||||
\(526\) | −8.99312 | −0.392119 | ||||||||
\(527\) | 10.5101 | 0.457825 | ||||||||
\(528\) | 2.94989 | 0.128377 | ||||||||
\(529\) | −11.1494 | −0.484758 | ||||||||
\(530\) | 10.1636 | 0.441479 | ||||||||
\(531\) | −74.9954 | −3.25452 | ||||||||
\(532\) | 9.24507 | 0.400825 | ||||||||
\(533\) | −12.2996 | −0.532753 | ||||||||
\(534\) | 27.8608 | 1.20565 | ||||||||
\(535\) | −20.2286 | −0.874560 | ||||||||
\(536\) | 19.1626 | 0.827699 | ||||||||
\(537\) | 53.3439 | 2.30196 | ||||||||
\(538\) | −9.94208 | −0.428633 | ||||||||
\(539\) | 6.98061 | 0.300676 | ||||||||
\(540\) | −23.2226 | −0.999342 | ||||||||
\(541\) | −0.284165 | −0.0122172 | −0.00610861 | − | 0.999981i | \(-0.501944\pi\) | ||||
−0.00610861 | + | 0.999981i | \(0.501944\pi\) | |||||||
\(542\) | 19.3134 | 0.829581 | ||||||||
\(543\) | −22.0897 | −0.947958 | ||||||||
\(544\) | 12.9303 | 0.554381 | ||||||||
\(545\) | −19.4417 | −0.832792 | ||||||||
\(546\) | −4.77451 | −0.204330 | ||||||||
\(547\) | 30.9706 | 1.32421 | 0.662104 | − | 0.749412i | \(-0.269664\pi\) | ||||
0.662104 | + | 0.749412i | \(0.269664\pi\) | |||||||
\(548\) | 8.07735 | 0.345047 | ||||||||
\(549\) | 10.3872 | 0.443315 | ||||||||
\(550\) | −1.38608 | −0.0591028 | ||||||||
\(551\) | −47.8663 | −2.03917 | ||||||||
\(552\) | 26.9745 | 1.14811 | ||||||||
\(553\) | 18.5380 | 0.788315 | ||||||||
\(554\) | −1.24371 | −0.0528403 | ||||||||
\(555\) | 38.7712 | 1.64575 | ||||||||
\(556\) | 21.5453 | 0.913726 | ||||||||
\(557\) | −16.3774 | −0.693931 | −0.346965 | − | 0.937878i | \(-0.612788\pi\) | ||||
−0.346965 | + | 0.937878i | \(0.612788\pi\) | |||||||
\(558\) | 21.7323 | 0.920002 | ||||||||
\(559\) | −14.1494 | −0.598456 | ||||||||
\(560\) | −1.74432 | −0.0737111 | ||||||||
\(561\) | −8.14073 | −0.343702 | ||||||||
\(562\) | 0.185140 | 0.00780966 | ||||||||
\(563\) | −13.7536 | −0.579644 | −0.289822 | − | 0.957081i | \(-0.593596\pi\) | ||||
−0.289822 | + | 0.957081i | \(0.593596\pi\) | |||||||
\(564\) | −35.1306 | −1.47927 | ||||||||
\(565\) | 13.3936 | 0.563471 | ||||||||
\(566\) | 12.7639 | 0.536506 | ||||||||
\(567\) | 9.73442 | 0.408807 | ||||||||
\(568\) | −3.10039 | −0.130090 | ||||||||
\(569\) | −22.1204 | −0.927333 | −0.463667 | − | 0.886010i | \(-0.653467\pi\) | ||||
−0.463667 | + | 0.886010i | \(0.653467\pi\) | |||||||
\(570\) | 24.4962 | 1.02603 | ||||||||
\(571\) | −38.0461 | −1.59218 | −0.796089 | − | 0.605179i | \(-0.793102\pi\) | ||||
−0.796089 | + | 0.605179i | \(0.793102\pi\) | |||||||
\(572\) | −3.11354 | −0.130184 | ||||||||
\(573\) | 75.7399 | 3.16408 | ||||||||
\(574\) | −6.12265 | −0.255554 | ||||||||
\(575\) | 5.02597 | 0.209597 | ||||||||
\(576\) | 17.2479 | 0.718664 | ||||||||
\(577\) | 5.66941 | 0.236020 | 0.118010 | − | 0.993012i | \(-0.462348\pi\) | ||||
0.118010 | + | 0.993012i | \(0.462348\pi\) | |||||||
\(578\) | 9.33029 | 0.388089 | ||||||||
\(579\) | 9.22336 | 0.383310 | ||||||||
\(580\) | 22.3960 | 0.929943 | ||||||||
\(581\) | 1.92336 | 0.0797945 | ||||||||
\(582\) | −9.66867 | −0.400779 | ||||||||
\(583\) | −8.66676 | −0.358941 | ||||||||
\(584\) | 2.72090 | 0.112592 | ||||||||
\(585\) | 19.9957 | 0.826720 | ||||||||
\(586\) | 19.5850 | 0.809047 | ||||||||
\(587\) | −29.2969 | −1.20921 | −0.604606 | − | 0.796524i | \(-0.706670\pi\) | ||||
−0.604606 | + | 0.796524i | \(0.706670\pi\) | |||||||
\(588\) | −23.8061 | −0.981748 | ||||||||
\(589\) | 26.9680 | 1.11120 | ||||||||
\(590\) | −18.2963 | −0.753247 | ||||||||
\(591\) | −34.6826 | −1.42665 | ||||||||
\(592\) | 5.51397 | 0.226623 | ||||||||
\(593\) | −10.4679 | −0.429867 | −0.214933 | − | 0.976629i | \(-0.568953\pi\) | ||||
−0.214933 | + | 0.976629i | \(0.568953\pi\) | |||||||
\(594\) | −8.32079 | −0.341406 | ||||||||
\(595\) | 4.81377 | 0.197345 | ||||||||
\(596\) | −0.896475 | −0.0367210 | ||||||||
\(597\) | −44.2693 | −1.81182 | ||||||||
\(598\) | −4.74384 | −0.193990 | ||||||||
\(599\) | −43.1571 | −1.76335 | −0.881676 | − | 0.471855i | \(-0.843584\pi\) | ||||
−0.881676 | + | 0.471855i | \(0.843584\pi\) | |||||||
\(600\) | 11.4402 | 0.467045 | ||||||||
\(601\) | −30.5145 | −1.24471 | −0.622356 | − | 0.782734i | \(-0.713824\pi\) | ||||
−0.622356 | + | 0.782734i | \(0.713824\pi\) | |||||||
\(602\) | −7.04348 | −0.287071 | ||||||||
\(603\) | 43.3606 | 1.76578 | ||||||||
\(604\) | −9.67015 | −0.393473 | ||||||||
\(605\) | 17.8306 | 0.724915 | ||||||||
\(606\) | 27.1925 | 1.10462 | ||||||||
\(607\) | −16.6646 | −0.676396 | −0.338198 | − | 0.941075i | \(-0.609817\pi\) | ||||
−0.338198 | + | 0.941075i | \(0.609817\pi\) | |||||||
\(608\) | 33.1781 | 1.34555 | ||||||||
\(609\) | −29.2855 | −1.18671 | ||||||||
\(610\) | 2.53412 | 0.102604 | ||||||||
\(611\) | 14.9524 | 0.604910 | ||||||||
\(612\) | 18.4384 | 0.745329 | ||||||||
\(613\) | 19.5027 | 0.787705 | 0.393853 | − | 0.919174i | \(-0.371142\pi\) | ||||
0.393853 | + | 0.919174i | \(0.371142\pi\) | |||||||
\(614\) | 18.7667 | 0.757364 | ||||||||
\(615\) | 38.6085 | 1.55684 | ||||||||
\(616\) | −3.75106 | −0.151134 | ||||||||
\(617\) | −14.0955 | −0.567464 | −0.283732 | − | 0.958904i | \(-0.591573\pi\) | ||||
−0.283732 | + | 0.958904i | \(0.591573\pi\) | |||||||
\(618\) | 24.2382 | 0.975002 | ||||||||
\(619\) | −19.3521 | −0.777829 | −0.388914 | − | 0.921274i | \(-0.627150\pi\) | ||||
−0.388914 | + | 0.921274i | \(0.627150\pi\) | |||||||
\(620\) | −12.6180 | −0.506750 | ||||||||
\(621\) | 30.1714 | 1.21073 | ||||||||
\(622\) | −9.20810 | −0.369211 | ||||||||
\(623\) | 14.0483 | 0.562832 | ||||||||
\(624\) | 4.28180 | 0.171409 | ||||||||
\(625\) | −15.5685 | −0.622739 | ||||||||
\(626\) | 11.6953 | 0.467439 | ||||||||
\(627\) | −20.8885 | −0.834206 | ||||||||
\(628\) | 19.5870 | 0.781605 | ||||||||
\(629\) | −15.2168 | −0.606733 | ||||||||
\(630\) | 9.95373 | 0.396566 | ||||||||
\(631\) | 31.8185 | 1.26667 | 0.633337 | − | 0.773876i | \(-0.281685\pi\) | ||||
0.633337 | + | 0.773876i | \(0.281685\pi\) | |||||||
\(632\) | 41.9255 | 1.66771 | ||||||||
\(633\) | −33.4306 | −1.32875 | ||||||||
\(634\) | −13.0799 | −0.519469 | ||||||||
\(635\) | −15.7117 | −0.623500 | ||||||||
\(636\) | 29.5564 | 1.17199 | ||||||||
\(637\) | 10.1324 | 0.401462 | ||||||||
\(638\) | 8.02461 | 0.317697 | ||||||||
\(639\) | −7.01548 | −0.277528 | ||||||||
\(640\) | −17.8385 | −0.705129 | ||||||||
\(641\) | 22.6910 | 0.896239 | 0.448120 | − | 0.893974i | \(-0.352094\pi\) | ||||
0.448120 | + | 0.893974i | \(0.352094\pi\) | |||||||
\(642\) | 24.7181 | 0.975546 | ||||||||
\(643\) | 7.91528 | 0.312148 | 0.156074 | − | 0.987745i | \(-0.450116\pi\) | ||||
0.156074 | + | 0.987745i | \(0.450116\pi\) | |||||||
\(644\) | 5.61998 | 0.221458 | ||||||||
\(645\) | 44.4151 | 1.74884 | ||||||||
\(646\) | −9.61417 | −0.378264 | ||||||||
\(647\) | 34.1361 | 1.34203 | 0.671015 | − | 0.741444i | \(-0.265859\pi\) | ||||
0.671015 | + | 0.741444i | \(0.265859\pi\) | |||||||
\(648\) | 22.0154 | 0.864846 | ||||||||
\(649\) | 15.6017 | 0.612420 | ||||||||
\(650\) | −2.01192 | −0.0789140 | ||||||||
\(651\) | 16.4995 | 0.646667 | ||||||||
\(652\) | 8.28363 | 0.324412 | ||||||||
\(653\) | −9.96921 | −0.390125 | −0.195063 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195063 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(654\) | 23.7566 | 0.928955 | ||||||||
\(655\) | −13.8185 | −0.539933 | ||||||||
\(656\) | 5.49082 | 0.214380 | ||||||||
\(657\) | 6.15678 | 0.240199 | ||||||||
\(658\) | 7.44322 | 0.290167 | ||||||||
\(659\) | −6.67772 | −0.260127 | −0.130063 | − | 0.991506i | \(-0.541518\pi\) | ||||
−0.130063 | + | 0.991506i | \(0.541518\pi\) | |||||||
\(660\) | 9.77344 | 0.380431 | ||||||||
\(661\) | 2.68068 | 0.104267 | 0.0521333 | − | 0.998640i | \(-0.483398\pi\) | ||||
0.0521333 | + | 0.998640i | \(0.483398\pi\) | |||||||
\(662\) | −11.6666 | −0.453437 | ||||||||
\(663\) | −11.8164 | −0.458910 | ||||||||
\(664\) | 4.34988 | 0.168808 | ||||||||
\(665\) | 12.3518 | 0.478981 | ||||||||
\(666\) | −31.4647 | −1.21923 | ||||||||
\(667\) | −29.0974 | −1.12666 | ||||||||
\(668\) | −2.47356 | −0.0957051 | ||||||||
\(669\) | 3.89368 | 0.150538 | ||||||||
\(670\) | 10.5785 | 0.408683 | ||||||||
\(671\) | −2.16090 | −0.0834208 | ||||||||
\(672\) | 20.2990 | 0.783049 | ||||||||
\(673\) | −12.2858 | −0.473582 | −0.236791 | − | 0.971561i | \(-0.576096\pi\) | ||||
−0.236791 | + | 0.971561i | \(0.576096\pi\) | |||||||
\(674\) | −6.16844 | −0.237599 | ||||||||
\(675\) | 12.7960 | 0.492520 | ||||||||
\(676\) | 13.7881 | 0.530310 | ||||||||
\(677\) | −23.8413 | −0.916297 | −0.458149 | − | 0.888876i | \(-0.651487\pi\) | ||||
−0.458149 | + | 0.888876i | \(0.651487\pi\) | |||||||
\(678\) | −16.3661 | −0.628535 | ||||||||
\(679\) | −4.87525 | −0.187095 | ||||||||
\(680\) | 10.8868 | 0.417491 | ||||||||
\(681\) | −6.66370 | −0.255354 | ||||||||
\(682\) | −4.52109 | −0.173121 | ||||||||
\(683\) | 36.8014 | 1.40817 | 0.704083 | − | 0.710118i | \(-0.251358\pi\) | ||||
0.704083 | + | 0.710118i | \(0.251358\pi\) | |||||||
\(684\) | 47.3115 | 1.80900 | ||||||||
\(685\) | 10.7916 | 0.412327 | ||||||||
\(686\) | 11.2862 | 0.430907 | ||||||||
\(687\) | 67.5122 | 2.57575 | ||||||||
\(688\) | 6.31663 | 0.240819 | ||||||||
\(689\) | −12.5799 | −0.479257 | ||||||||
\(690\) | 14.8910 | 0.566889 | ||||||||
\(691\) | 21.2987 | 0.810239 | 0.405120 | − | 0.914264i | \(-0.367230\pi\) | ||||
0.405120 | + | 0.914264i | \(0.367230\pi\) | |||||||
\(692\) | −7.61109 | −0.289330 | ||||||||
\(693\) | −8.48778 | −0.322424 | ||||||||
\(694\) | 15.6981 | 0.595890 | ||||||||
\(695\) | 28.7854 | 1.09189 | ||||||||
\(696\) | −66.2321 | −2.51052 | ||||||||
\(697\) | −15.1529 | −0.573957 | ||||||||
\(698\) | −2.60471 | −0.0985896 | ||||||||
\(699\) | −40.6430 | −1.53726 | ||||||||
\(700\) | 2.38350 | 0.0900878 | ||||||||
\(701\) | −18.5541 | −0.700779 | −0.350389 | − | 0.936604i | \(-0.613951\pi\) | ||||
−0.350389 | + | 0.936604i | \(0.613951\pi\) | |||||||
\(702\) | −12.0777 | −0.455845 | ||||||||
\(703\) | −39.0451 | −1.47261 | ||||||||
\(704\) | −3.58818 | −0.135235 | ||||||||
\(705\) | −46.9358 | −1.76770 | ||||||||
\(706\) | −26.8641 | −1.01104 | ||||||||
\(707\) | 13.7113 | 0.515667 | ||||||||
\(708\) | −53.2068 | −1.99963 | ||||||||
\(709\) | −27.7909 | −1.04371 | −0.521854 | − | 0.853035i | \(-0.674759\pi\) | ||||
−0.521854 | + | 0.853035i | \(0.674759\pi\) | |||||||
\(710\) | −1.71154 | −0.0642328 | ||||||||
\(711\) | 94.8679 | 3.55782 | ||||||||
\(712\) | 31.7716 | 1.19069 | ||||||||
\(713\) | 16.3935 | 0.613943 | ||||||||
\(714\) | −5.88212 | −0.220133 | ||||||||
\(715\) | −4.15981 | −0.155568 | ||||||||
\(716\) | 25.1352 | 0.939345 | ||||||||
\(717\) | −3.62927 | −0.135537 | ||||||||
\(718\) | 24.7151 | 0.922361 | ||||||||
\(719\) | −23.3909 | −0.872334 | −0.436167 | − | 0.899866i | \(-0.643664\pi\) | ||||
−0.436167 | + | 0.899866i | \(0.643664\pi\) | |||||||
\(720\) | −8.92655 | −0.332673 | ||||||||
\(721\) | 12.2216 | 0.455158 | ||||||||
\(722\) | −10.0536 | −0.374155 | ||||||||
\(723\) | 69.9588 | 2.60179 | ||||||||
\(724\) | −10.4084 | −0.386827 | ||||||||
\(725\) | −12.3405 | −0.458317 | ||||||||
\(726\) | −21.7878 | −0.808622 | ||||||||
\(727\) | −25.4118 | −0.942471 | −0.471236 | − | 0.882007i | \(-0.656192\pi\) | ||||
−0.471236 | + | 0.882007i | \(0.656192\pi\) | |||||||
\(728\) | −5.44471 | −0.201794 | ||||||||
\(729\) | −28.7680 | −1.06548 | ||||||||
\(730\) | 1.50204 | 0.0555931 | ||||||||
\(731\) | −17.4319 | −0.644741 | ||||||||
\(732\) | 7.36938 | 0.272380 | ||||||||
\(733\) | −16.6366 | −0.614486 | −0.307243 | − | 0.951631i | \(-0.599406\pi\) | ||||
−0.307243 | + | 0.951631i | \(0.599406\pi\) | |||||||
\(734\) | −5.41707 | −0.199948 | ||||||||
\(735\) | −31.8058 | −1.17318 | ||||||||
\(736\) | 20.1686 | 0.743424 | ||||||||
\(737\) | −9.02054 | −0.332276 | ||||||||
\(738\) | −31.3326 | −1.15337 | ||||||||
\(739\) | −47.4815 | −1.74664 | −0.873318 | − | 0.487150i | \(-0.838037\pi\) | ||||
−0.873318 | + | 0.487150i | \(0.838037\pi\) | |||||||
\(740\) | 18.2687 | 0.671569 | ||||||||
\(741\) | −30.3199 | −1.11383 | ||||||||
\(742\) | −6.26220 | −0.229893 | ||||||||
\(743\) | −39.6440 | −1.45440 | −0.727198 | − | 0.686427i | \(-0.759178\pi\) | ||||
−0.727198 | + | 0.686427i | \(0.759178\pi\) | |||||||
\(744\) | 37.3153 | 1.36805 | ||||||||
\(745\) | −1.19772 | −0.0438812 | ||||||||
\(746\) | −3.54788 | −0.129897 | ||||||||
\(747\) | 9.84278 | 0.360129 | ||||||||
\(748\) | −3.83584 | −0.140252 | ||||||||
\(749\) | 12.4637 | 0.455412 | ||||||||
\(750\) | 27.9438 | 1.02036 | ||||||||
\(751\) | −20.6767 | −0.754505 | −0.377252 | − | 0.926111i | \(-0.623131\pi\) | ||||
−0.377252 | + | 0.926111i | \(0.623131\pi\) | |||||||
\(752\) | −6.67512 | −0.243416 | ||||||||
\(753\) | −50.2972 | −1.83293 | ||||||||
\(754\) | 11.6478 | 0.424189 | ||||||||
\(755\) | −12.9197 | −0.470195 | ||||||||
\(756\) | 14.3084 | 0.520390 | ||||||||
\(757\) | −29.4407 | −1.07004 | −0.535020 | − | 0.844839i | \(-0.679696\pi\) | ||||
−0.535020 | + | 0.844839i | \(0.679696\pi\) | |||||||
\(758\) | −3.20134 | −0.116278 | ||||||||
\(759\) | −12.6979 | −0.460904 | ||||||||
\(760\) | 27.9348 | 1.01330 | ||||||||
\(761\) | −13.5406 | −0.490846 | −0.245423 | − | 0.969416i | \(-0.578927\pi\) | ||||
−0.245423 | + | 0.969416i | \(0.578927\pi\) | |||||||
\(762\) | 19.1987 | 0.695496 | ||||||||
\(763\) | 11.9788 | 0.433662 | ||||||||
\(764\) | 35.6880 | 1.29115 | ||||||||
\(765\) | 24.6344 | 0.890659 | ||||||||
\(766\) | −10.5124 | −0.379827 | ||||||||
\(767\) | 22.6461 | 0.817702 | ||||||||
\(768\) | 39.1762 | 1.41365 | ||||||||
\(769\) | −47.8047 | −1.72388 | −0.861941 | − | 0.507009i | \(-0.830751\pi\) | ||||
−0.861941 | + | 0.507009i | \(0.830751\pi\) | |||||||
\(770\) | −2.07073 | −0.0746238 | ||||||||
\(771\) | −7.47134 | −0.269074 | ||||||||
\(772\) | 4.34597 | 0.156415 | ||||||||
\(773\) | 22.6571 | 0.814921 | 0.407460 | − | 0.913223i | \(-0.366414\pi\) | ||||
0.407460 | + | 0.913223i | \(0.366414\pi\) | |||||||
\(774\) | −36.0449 | −1.29561 | ||||||||
\(775\) | 6.95270 | 0.249748 | ||||||||
\(776\) | −11.0259 | −0.395806 | ||||||||
\(777\) | −23.8885 | −0.856995 | ||||||||
\(778\) | 9.09636 | 0.326120 | ||||||||
\(779\) | −38.8811 | −1.39306 | ||||||||
\(780\) | 14.1863 | 0.507951 | ||||||||
\(781\) | 1.45947 | 0.0522239 | ||||||||
\(782\) | −5.84435 | −0.208993 | ||||||||
\(783\) | −74.0815 | −2.64746 | ||||||||
\(784\) | −4.52336 | −0.161549 | ||||||||
\(785\) | 26.1689 | 0.934009 | ||||||||
\(786\) | 16.8853 | 0.602279 | ||||||||
\(787\) | 20.8385 | 0.742813 | 0.371406 | − | 0.928470i | \(-0.378876\pi\) | ||||
0.371406 | + | 0.928470i | \(0.378876\pi\) | |||||||
\(788\) | −16.3421 | −0.582164 | ||||||||
\(789\) | −34.9408 | −1.24392 | ||||||||
\(790\) | 23.1445 | 0.823444 | ||||||||
\(791\) | −8.25230 | −0.293418 | ||||||||
\(792\) | −19.1960 | −0.682100 | ||||||||
\(793\) | −3.13658 | −0.111383 | ||||||||
\(794\) | −8.95078 | −0.317651 | ||||||||
\(795\) | 39.4885 | 1.40051 | ||||||||
\(796\) | −20.8593 | −0.739338 | ||||||||
\(797\) | 2.32140 | 0.0822281 | 0.0411140 | − | 0.999154i | \(-0.486909\pi\) | ||||
0.0411140 | + | 0.999154i | \(0.486909\pi\) | |||||||
\(798\) | −15.0931 | −0.534289 | ||||||||
\(799\) | 18.4212 | 0.651694 | ||||||||
\(800\) | 8.55374 | 0.302420 | ||||||||
\(801\) | 71.8919 | 2.54017 | ||||||||
\(802\) | −15.3344 | −0.541477 | ||||||||
\(803\) | −1.28083 | −0.0451994 | ||||||||
\(804\) | 30.7629 | 1.08492 | ||||||||
\(805\) | 7.50850 | 0.264640 | ||||||||
\(806\) | −6.56242 | −0.231151 | ||||||||
\(807\) | −38.6277 | −1.35976 | ||||||||
\(808\) | 31.0096 | 1.09091 | ||||||||
\(809\) | −45.2074 | −1.58941 | −0.794704 | − | 0.606997i | \(-0.792374\pi\) | ||||
−0.794704 | + | 0.606997i | \(0.792374\pi\) | |||||||
\(810\) | 12.1533 | 0.427025 | ||||||||
\(811\) | −45.4734 | −1.59679 | −0.798394 | − | 0.602135i | \(-0.794317\pi\) | ||||
−0.798394 | + | 0.602135i | \(0.794317\pi\) | |||||||
\(812\) | −13.7991 | −0.484252 | ||||||||
\(813\) | 75.0379 | 2.63169 | ||||||||
\(814\) | 6.54576 | 0.229429 | ||||||||
\(815\) | 11.0672 | 0.387668 | ||||||||
\(816\) | 5.27511 | 0.184666 | ||||||||
\(817\) | −44.7288 | −1.56486 | ||||||||
\(818\) | 8.13425 | 0.284407 | ||||||||
\(819\) | −12.3201 | −0.430500 | ||||||||
\(820\) | 18.1920 | 0.635291 | ||||||||
\(821\) | 2.35462 | 0.0821767 | 0.0410883 | − | 0.999156i | \(-0.486917\pi\) | ||||
0.0410883 | + | 0.999156i | \(0.486917\pi\) | |||||||
\(822\) | −13.1867 | −0.459939 | ||||||||
\(823\) | −39.0138 | −1.35994 | −0.679968 | − | 0.733242i | \(-0.738006\pi\) | ||||
−0.679968 | + | 0.733242i | \(0.738006\pi\) | |||||||
\(824\) | 27.6405 | 0.962903 | ||||||||
\(825\) | −5.38532 | −0.187493 | ||||||||
\(826\) | 11.2731 | 0.392240 | ||||||||
\(827\) | −18.8571 | −0.655727 | −0.327863 | − | 0.944725i | \(-0.606329\pi\) | ||||
−0.327863 | + | 0.944725i | \(0.606329\pi\) | |||||||
\(828\) | 28.7602 | 0.999485 | ||||||||
\(829\) | 44.9946 | 1.56273 | 0.781364 | − | 0.624076i | \(-0.214524\pi\) | ||||
0.781364 | + | 0.624076i | \(0.214524\pi\) | |||||||
\(830\) | 2.40130 | 0.0833503 | ||||||||
\(831\) | −4.83217 | −0.167626 | ||||||||
\(832\) | −5.20829 | −0.180565 | ||||||||
\(833\) | 12.4830 | 0.432511 | ||||||||
\(834\) | −35.1739 | −1.21797 | ||||||||
\(835\) | −3.30477 | −0.114366 | ||||||||
\(836\) | −9.84247 | −0.340409 | ||||||||
\(837\) | 41.7377 | 1.44267 | ||||||||
\(838\) | 12.0668 | 0.416842 | ||||||||
\(839\) | 9.28809 | 0.320660 | 0.160330 | − | 0.987063i | \(-0.448744\pi\) | ||||
0.160330 | + | 0.987063i | \(0.448744\pi\) | |||||||
\(840\) | 17.0910 | 0.589695 | ||||||||
\(841\) | 42.4445 | 1.46360 | ||||||||
\(842\) | −17.3151 | −0.596718 | ||||||||
\(843\) | 0.719321 | 0.0247747 | ||||||||
\(844\) | −15.7522 | −0.542214 | ||||||||
\(845\) | 18.4214 | 0.633714 | ||||||||
\(846\) | 38.0906 | 1.30958 | ||||||||
\(847\) | −10.9861 | −0.377487 | ||||||||
\(848\) | 5.61597 | 0.192853 | ||||||||
\(849\) | 49.5913 | 1.70197 | ||||||||
\(850\) | −2.47866 | −0.0850172 | ||||||||
\(851\) | −23.7351 | −0.813627 | ||||||||
\(852\) | −4.97725 | −0.170518 | ||||||||
\(853\) | 19.6823 | 0.673909 | 0.336954 | − | 0.941521i | \(-0.390603\pi\) | ||||
0.336954 | + | 0.941521i | \(0.390603\pi\) | |||||||
\(854\) | −1.56137 | −0.0534290 | ||||||||
\(855\) | 63.2100 | 2.16174 | ||||||||
\(856\) | 28.1878 | 0.963441 | ||||||||
\(857\) | 12.8317 | 0.438322 | 0.219161 | − | 0.975689i | \(-0.429668\pi\) | ||||
0.219161 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(858\) | 5.08303 | 0.173532 | ||||||||
\(859\) | −17.6648 | −0.602715 | −0.301357 | − | 0.953511i | \(-0.597440\pi\) | ||||
−0.301357 | + | 0.953511i | \(0.597440\pi\) | |||||||
\(860\) | 20.9280 | 0.713639 | ||||||||
\(861\) | −23.7882 | −0.810699 | ||||||||
\(862\) | −23.4074 | −0.797261 | ||||||||
\(863\) | −49.7153 | −1.69233 | −0.846164 | − | 0.532923i | \(-0.821093\pi\) | ||||
−0.846164 | + | 0.532923i | \(0.821093\pi\) | |||||||
\(864\) | 51.3489 | 1.74693 | ||||||||
\(865\) | −10.1687 | −0.345746 | ||||||||
\(866\) | 6.65033 | 0.225987 | ||||||||
\(867\) | 36.2508 | 1.23114 | ||||||||
\(868\) | 7.77442 | 0.263881 | ||||||||
\(869\) | −19.7359 | −0.669493 | ||||||||
\(870\) | −36.5626 | −1.23959 | ||||||||
\(871\) | −13.0934 | −0.443654 | ||||||||
\(872\) | 27.0913 | 0.917428 | ||||||||
\(873\) | −24.9490 | −0.844397 | ||||||||
\(874\) | −14.9961 | −0.507252 | ||||||||
\(875\) | 14.0901 | 0.476334 | ||||||||
\(876\) | 4.36804 | 0.147582 | ||||||||
\(877\) | −4.70793 | −0.158976 | −0.0794878 | − | 0.996836i | \(-0.525328\pi\) | ||||
−0.0794878 | + | 0.996836i | \(0.525328\pi\) | |||||||
\(878\) | 16.8674 | 0.569246 | ||||||||
\(879\) | 76.0931 | 2.56655 | ||||||||
\(880\) | 1.85704 | 0.0626007 | ||||||||
\(881\) | 15.4886 | 0.521824 | 0.260912 | − | 0.965363i | \(-0.415977\pi\) | ||||
0.260912 | + | 0.965363i | \(0.415977\pi\) | |||||||
\(882\) | 25.8119 | 0.869133 | ||||||||
\(883\) | −39.8260 | −1.34025 | −0.670125 | − | 0.742248i | \(-0.733760\pi\) | ||||
−0.670125 | + | 0.742248i | \(0.733760\pi\) | |||||||
\(884\) | −5.56778 | −0.187265 | ||||||||
\(885\) | −71.0862 | −2.38954 | ||||||||
\(886\) | 20.7486 | 0.697064 | ||||||||
\(887\) | 3.09616 | 0.103959 | 0.0519795 | − | 0.998648i | \(-0.483447\pi\) | ||||
0.0519795 | + | 0.998648i | \(0.483447\pi\) | |||||||
\(888\) | −54.0263 | −1.81300 | ||||||||
\(889\) | 9.68059 | 0.324677 | ||||||||
\(890\) | 17.5391 | 0.587913 | ||||||||
\(891\) | −10.3634 | −0.347188 | ||||||||
\(892\) | 1.83467 | 0.0614292 | ||||||||
\(893\) | 47.2673 | 1.58174 | ||||||||
\(894\) | 1.46354 | 0.0489482 | ||||||||
\(895\) | 33.5815 | 1.12251 | ||||||||
\(896\) | 10.9910 | 0.367184 | ||||||||
\(897\) | −18.4311 | −0.615398 | ||||||||
\(898\) | −23.8972 | −0.797459 | ||||||||
\(899\) | −40.2520 | −1.34248 | ||||||||
\(900\) | 12.1975 | 0.406584 | ||||||||
\(901\) | −15.4983 | −0.516323 | ||||||||
\(902\) | 6.51828 | 0.217035 | ||||||||
\(903\) | −27.3659 | −0.910680 | ||||||||
\(904\) | −18.6634 | −0.620736 | ||||||||
\(905\) | −13.9061 | −0.462253 | ||||||||
\(906\) | 15.7870 | 0.524489 | ||||||||
\(907\) | −52.5988 | −1.74652 | −0.873258 | − | 0.487259i | \(-0.837997\pi\) | ||||
−0.873258 | + | 0.487259i | \(0.837997\pi\) | |||||||
\(908\) | −3.13988 | −0.104201 | ||||||||
\(909\) | 70.1676 | 2.32731 | ||||||||
\(910\) | −3.00569 | −0.0996376 | ||||||||
\(911\) | −48.7874 | −1.61640 | −0.808199 | − | 0.588910i | \(-0.799557\pi\) | ||||
−0.808199 | + | 0.588910i | \(0.799557\pi\) | |||||||
\(912\) | 13.5355 | 0.448206 | ||||||||
\(913\) | −2.04765 | −0.0677672 | ||||||||
\(914\) | −9.91500 | −0.327959 | ||||||||
\(915\) | 9.84576 | 0.325491 | ||||||||
\(916\) | 31.8111 | 1.05107 | ||||||||
\(917\) | 8.51411 | 0.281161 | ||||||||
\(918\) | −14.8796 | −0.491100 | ||||||||
\(919\) | 12.5481 | 0.413924 | 0.206962 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206962 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(920\) | 16.9812 | 0.559855 | ||||||||
\(921\) | 72.9141 | 2.40260 | ||||||||
\(922\) | −23.1098 | −0.761082 | ||||||||
\(923\) | 2.11844 | 0.0697292 | ||||||||
\(924\) | −6.02180 | −0.198103 | ||||||||
\(925\) | −10.0663 | −0.330979 | ||||||||
\(926\) | 3.68314 | 0.121036 | ||||||||
\(927\) | 62.5441 | 2.05422 | ||||||||
\(928\) | −49.5211 | −1.62561 | ||||||||
\(929\) | 28.2201 | 0.925873 | 0.462936 | − | 0.886391i | \(-0.346796\pi\) | ||||
0.462936 | + | 0.886391i | \(0.346796\pi\) | |||||||
\(930\) | 20.5995 | 0.675484 | ||||||||
\(931\) | 32.0305 | 1.04976 | ||||||||
\(932\) | −19.1506 | −0.627299 | ||||||||
\(933\) | −35.7760 | −1.17125 | ||||||||
\(934\) | −14.4629 | −0.473240 | ||||||||
\(935\) | −5.12483 | −0.167600 | ||||||||
\(936\) | −27.8632 | −0.910739 | ||||||||
\(937\) | −15.5735 | −0.508763 | −0.254381 | − | 0.967104i | \(-0.581872\pi\) | ||||
−0.254381 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(938\) | −6.51783 | −0.212815 | ||||||||
\(939\) | 45.4396 | 1.48286 | ||||||||
\(940\) | −22.1157 | −0.721336 | ||||||||
\(941\) | 49.8449 | 1.62490 | 0.812449 | − | 0.583032i | \(-0.198134\pi\) | ||||
0.812449 | + | 0.583032i | \(0.198134\pi\) | |||||||
\(942\) | −31.9768 | −1.04186 | ||||||||
\(943\) | −23.6354 | −0.769675 | ||||||||
\(944\) | −10.1097 | −0.329044 | ||||||||
\(945\) | 19.1165 | 0.621860 | ||||||||
\(946\) | 7.49862 | 0.243801 | ||||||||
\(947\) | 16.8703 | 0.548211 | 0.274106 | − | 0.961700i | \(-0.411618\pi\) | ||||
0.274106 | + | 0.961700i | \(0.411618\pi\) | |||||||
\(948\) | 67.3056 | 2.18599 | ||||||||
\(949\) | −1.85914 | −0.0603502 | ||||||||
\(950\) | −6.36004 | −0.206347 | ||||||||
\(951\) | −50.8191 | −1.64792 | ||||||||
\(952\) | −6.70781 | −0.217401 | ||||||||
\(953\) | 40.3392 | 1.30671 | 0.653357 | − | 0.757050i | \(-0.273360\pi\) | ||||
0.653357 | + | 0.757050i | \(0.273360\pi\) | |||||||
\(954\) | −32.0468 | −1.03755 | ||||||||
\(955\) | 47.6804 | 1.54290 | ||||||||
\(956\) | −1.71008 | −0.0553079 | ||||||||
\(957\) | 31.1778 | 1.00784 | ||||||||
\(958\) | 21.2784 | 0.687473 | ||||||||
\(959\) | −6.64915 | −0.214712 | ||||||||
\(960\) | 16.3489 | 0.527658 | ||||||||
\(961\) | −8.32190 | −0.268448 | ||||||||
\(962\) | 9.50126 | 0.306333 | ||||||||
\(963\) | 63.7826 | 2.05537 | ||||||||
\(964\) | 32.9640 | 1.06170 | ||||||||
\(965\) | 5.80637 | 0.186914 | ||||||||
\(966\) | −9.17491 | −0.295198 | ||||||||
\(967\) | 52.6815 | 1.69412 | 0.847062 | − | 0.531494i | \(-0.178369\pi\) | ||||
0.847062 | + | 0.531494i | \(0.178369\pi\) | |||||||
\(968\) | −24.8462 | −0.798588 | ||||||||
\(969\) | −37.3537 | −1.19997 | ||||||||
\(970\) | −6.08671 | −0.195432 | ||||||||
\(971\) | 57.6289 | 1.84940 | 0.924700 | − | 0.380697i | \(-0.124316\pi\) | ||||
0.924700 | + | 0.380697i | \(0.124316\pi\) | |||||||
\(972\) | −1.68533 | −0.0540571 | ||||||||
\(973\) | −17.7358 | −0.568584 | ||||||||
\(974\) | 2.30186 | 0.0737565 | ||||||||
\(975\) | −7.81687 | −0.250340 | ||||||||
\(976\) | 1.40024 | 0.0448207 | ||||||||
\(977\) | 7.22940 | 0.231289 | 0.115644 | − | 0.993291i | \(-0.463107\pi\) | ||||
0.115644 | + | 0.993291i | \(0.463107\pi\) | |||||||
\(978\) | −13.5235 | −0.432433 | ||||||||
\(979\) | −14.9560 | −0.477997 | ||||||||
\(980\) | −14.9866 | −0.478730 | ||||||||
\(981\) | 61.3015 | 1.95720 | ||||||||
\(982\) | −9.19678 | −0.293481 | ||||||||
\(983\) | −0.0912068 | −0.00290904 | −0.00145452 | − | 0.999999i | \(-0.500463\pi\) | ||||
−0.00145452 | + | 0.999999i | \(0.500463\pi\) | |||||||
\(984\) | −53.7994 | −1.71506 | ||||||||
\(985\) | −21.8337 | −0.695678 | ||||||||
\(986\) | 14.3500 | 0.456996 | ||||||||
\(987\) | 28.9190 | 0.920502 | ||||||||
\(988\) | −14.2865 | −0.454514 | ||||||||
\(989\) | −27.1901 | −0.864596 | ||||||||
\(990\) | −10.5969 | −0.336792 | ||||||||
\(991\) | −31.7069 | −1.00720 | −0.503602 | − | 0.863936i | \(-0.667992\pi\) | ||||
−0.503602 | + | 0.863936i | \(0.667992\pi\) | |||||||
\(992\) | 27.9003 | 0.885836 | ||||||||
\(993\) | −45.3281 | −1.43844 | ||||||||
\(994\) | 1.05454 | 0.0334481 | ||||||||
\(995\) | −27.8688 | −0.883500 | ||||||||
\(996\) | 6.98313 | 0.221269 | ||||||||
\(997\) | 11.0006 | 0.348392 | 0.174196 | − | 0.984711i | \(-0.444267\pi\) | ||||
0.174196 | + | 0.984711i | \(0.444267\pi\) | |||||||
\(998\) | 34.1820 | 1.08201 | ||||||||
\(999\) | −60.4291 | −1.91189 |
(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 | 4001.2.a.a.1.58 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.a.1.58 | ✓ | 149 | 1.1 | even | 1 | trivial |