Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76060 | −1.95204 | −0.976019 | − | 0.217686i | \(-0.930149\pi\) | ||||
−0.976019 | + | 0.217686i | \(0.930149\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.62090 | 2.81045 | ||||||||
\(5\) | −0.677149 | −0.302830 | −0.151415 | − | 0.988470i | \(-0.548383\pi\) | ||||
−0.151415 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(6\) | −2.76060 | −1.12701 | ||||||||
\(7\) | 3.14387 | 1.18827 | 0.594135 | − | 0.804366i | \(-0.297495\pi\) | ||||
0.594135 | + | 0.804366i | \(0.297495\pi\) | |||||||
\(8\) | −9.99585 | −3.53407 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.86934 | 0.591136 | ||||||||
\(11\) | −2.07367 | −0.625235 | −0.312617 | − | 0.949879i | \(-0.601206\pi\) | ||||
−0.312617 | + | 0.949879i | \(0.601206\pi\) | |||||||
\(12\) | 5.62090 | 1.62261 | ||||||||
\(13\) | 5.11851 | 1.41962 | 0.709809 | − | 0.704394i | \(-0.248781\pi\) | ||||
0.709809 | + | 0.704394i | \(0.248781\pi\) | |||||||
\(14\) | −8.67895 | −2.31955 | ||||||||
\(15\) | −0.677149 | −0.174839 | ||||||||
\(16\) | 16.3527 | 4.08818 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.76060 | −0.650679 | ||||||||
\(19\) | 1.32055 | 0.302955 | 0.151477 | − | 0.988461i | \(-0.451597\pi\) | ||||
0.151477 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(20\) | −3.80619 | −0.851090 | ||||||||
\(21\) | 3.14387 | 0.686048 | ||||||||
\(22\) | 5.72457 | 1.22048 | ||||||||
\(23\) | 1.26188 | 0.263120 | 0.131560 | − | 0.991308i | \(-0.458001\pi\) | ||||
0.131560 | + | 0.991308i | \(0.458001\pi\) | |||||||
\(24\) | −9.99585 | −2.04040 | ||||||||
\(25\) | −4.54147 | −0.908294 | ||||||||
\(26\) | −14.1301 | −2.77115 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 17.6714 | 3.33957 | ||||||||
\(29\) | 2.79382 | 0.518800 | 0.259400 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259400 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(30\) | 1.86934 | 0.341293 | ||||||||
\(31\) | −1.04665 | −0.187983 | −0.0939916 | − | 0.995573i | \(-0.529963\pi\) | ||||
−0.0939916 | + | 0.995573i | \(0.529963\pi\) | |||||||
\(32\) | −25.1516 | −4.44622 | ||||||||
\(33\) | −2.07367 | −0.360979 | ||||||||
\(34\) | 2.76060 | 0.473439 | ||||||||
\(35\) | −2.12887 | −0.359844 | ||||||||
\(36\) | 5.62090 | 0.936817 | ||||||||
\(37\) | 1.14118 | 0.187608 | 0.0938042 | − | 0.995591i | \(-0.470097\pi\) | ||||
0.0938042 | + | 0.995591i | \(0.470097\pi\) | |||||||
\(38\) | −3.64550 | −0.591379 | ||||||||
\(39\) | 5.11851 | 0.819617 | ||||||||
\(40\) | 6.76869 | 1.07022 | ||||||||
\(41\) | −8.84359 | −1.38114 | −0.690569 | − | 0.723267i | \(-0.742640\pi\) | ||||
−0.690569 | + | 0.723267i | \(0.742640\pi\) | |||||||
\(42\) | −8.67895 | −1.33919 | ||||||||
\(43\) | −12.3593 | −1.88477 | −0.942385 | − | 0.334529i | \(-0.891423\pi\) | ||||
−0.942385 | + | 0.334529i | \(0.891423\pi\) | |||||||
\(44\) | −11.6559 | −1.75719 | ||||||||
\(45\) | −0.677149 | −0.100943 | ||||||||
\(46\) | −3.48354 | −0.513620 | ||||||||
\(47\) | 2.89101 | 0.421698 | 0.210849 | − | 0.977519i | \(-0.432377\pi\) | ||||
0.210849 | + | 0.977519i | \(0.432377\pi\) | |||||||
\(48\) | 16.3527 | 2.36031 | ||||||||
\(49\) | 2.88389 | 0.411984 | ||||||||
\(50\) | 12.5372 | 1.77302 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 28.7706 | 3.98977 | ||||||||
\(53\) | −6.36246 | −0.873952 | −0.436976 | − | 0.899473i | \(-0.643950\pi\) | ||||
−0.436976 | + | 0.899473i | \(0.643950\pi\) | |||||||
\(54\) | −2.76060 | −0.375670 | ||||||||
\(55\) | 1.40418 | 0.189340 | ||||||||
\(56\) | −31.4256 | −4.19942 | ||||||||
\(57\) | 1.32055 | 0.174911 | ||||||||
\(58\) | −7.71262 | −1.01272 | ||||||||
\(59\) | −4.43671 | −0.577610 | −0.288805 | − | 0.957388i | \(-0.593258\pi\) | ||||
−0.288805 | + | 0.957388i | \(0.593258\pi\) | |||||||
\(60\) | −3.80619 | −0.491377 | ||||||||
\(61\) | −14.2855 | −1.82908 | −0.914538 | − | 0.404499i | \(-0.867446\pi\) | ||||
−0.914538 | + | 0.404499i | \(0.867446\pi\) | |||||||
\(62\) | 2.88937 | 0.366950 | ||||||||
\(63\) | 3.14387 | 0.396090 | ||||||||
\(64\) | 36.7280 | 4.59100 | ||||||||
\(65\) | −3.46599 | −0.429904 | ||||||||
\(66\) | 5.72457 | 0.704645 | ||||||||
\(67\) | −6.45138 | −0.788161 | −0.394081 | − | 0.919076i | \(-0.628937\pi\) | ||||
−0.394081 | + | 0.919076i | \(0.628937\pi\) | |||||||
\(68\) | −5.62090 | −0.681634 | ||||||||
\(69\) | 1.26188 | 0.151912 | ||||||||
\(70\) | 5.87694 | 0.702429 | ||||||||
\(71\) | −13.7214 | −1.62843 | −0.814217 | − | 0.580561i | \(-0.802833\pi\) | ||||
−0.814217 | + | 0.580561i | \(0.802833\pi\) | |||||||
\(72\) | −9.99585 | −1.17802 | ||||||||
\(73\) | −0.815601 | −0.0954589 | −0.0477294 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477294 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(74\) | −3.15033 | −0.366219 | ||||||||
\(75\) | −4.54147 | −0.524404 | ||||||||
\(76\) | 7.42268 | 0.851439 | ||||||||
\(77\) | −6.51934 | −0.742947 | ||||||||
\(78\) | −14.1301 | −1.59992 | ||||||||
\(79\) | −5.63591 | −0.634090 | −0.317045 | − | 0.948411i | \(-0.602691\pi\) | ||||
−0.317045 | + | 0.948411i | \(0.602691\pi\) | |||||||
\(80\) | −11.0732 | −1.23803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 24.4136 | 2.69603 | ||||||||
\(83\) | 3.91819 | 0.430078 | 0.215039 | − | 0.976605i | \(-0.431012\pi\) | ||||
0.215039 | + | 0.976605i | \(0.431012\pi\) | |||||||
\(84\) | 17.6714 | 1.92810 | ||||||||
\(85\) | 0.677149 | 0.0734471 | ||||||||
\(86\) | 34.1190 | 3.67914 | ||||||||
\(87\) | 2.79382 | 0.299529 | ||||||||
\(88\) | 20.7281 | 2.20962 | ||||||||
\(89\) | 6.79853 | 0.720643 | 0.360322 | − | 0.932828i | \(-0.382667\pi\) | ||||
0.360322 | + | 0.932828i | \(0.382667\pi\) | |||||||
\(90\) | 1.86934 | 0.197045 | ||||||||
\(91\) | 16.0919 | 1.68689 | ||||||||
\(92\) | 7.09289 | 0.739485 | ||||||||
\(93\) | −1.04665 | −0.108532 | ||||||||
\(94\) | −7.98092 | −0.823169 | ||||||||
\(95\) | −0.894209 | −0.0917439 | ||||||||
\(96\) | −25.1516 | −2.56703 | ||||||||
\(97\) | −10.8745 | −1.10414 | −0.552070 | − | 0.833797i | \(-0.686162\pi\) | ||||
−0.552070 | + | 0.833797i | \(0.686162\pi\) | |||||||
\(98\) | −7.96125 | −0.804208 | ||||||||
\(99\) | −2.07367 | −0.208412 | ||||||||
\(100\) | −25.5272 | −2.55272 | ||||||||
\(101\) | −0.683072 | −0.0679682 | −0.0339841 | − | 0.999422i | \(-0.510820\pi\) | ||||
−0.0339841 | + | 0.999422i | \(0.510820\pi\) | |||||||
\(102\) | 2.76060 | 0.273340 | ||||||||
\(103\) | −10.4174 | −1.02646 | −0.513229 | − | 0.858252i | \(-0.671551\pi\) | ||||
−0.513229 | + | 0.858252i | \(0.671551\pi\) | |||||||
\(104\) | −51.1639 | −5.01703 | ||||||||
\(105\) | −2.12887 | −0.207756 | ||||||||
\(106\) | 17.5642 | 1.70599 | ||||||||
\(107\) | −4.74721 | −0.458930 | −0.229465 | − | 0.973317i | \(-0.573698\pi\) | ||||
−0.229465 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(108\) | 5.62090 | 0.540872 | ||||||||
\(109\) | −5.05330 | −0.484018 | −0.242009 | − | 0.970274i | \(-0.577806\pi\) | ||||
−0.242009 | + | 0.970274i | \(0.577806\pi\) | |||||||
\(110\) | −3.87639 | −0.369599 | ||||||||
\(111\) | 1.14118 | 0.108316 | ||||||||
\(112\) | 51.4108 | 4.85786 | ||||||||
\(113\) | 1.01792 | 0.0957581 | 0.0478790 | − | 0.998853i | \(-0.484754\pi\) | ||||
0.0478790 | + | 0.998853i | \(0.484754\pi\) | |||||||
\(114\) | −3.64550 | −0.341433 | ||||||||
\(115\) | −0.854480 | −0.0796806 | ||||||||
\(116\) | 15.7038 | 1.45806 | ||||||||
\(117\) | 5.11851 | 0.473206 | ||||||||
\(118\) | 12.2480 | 1.12752 | ||||||||
\(119\) | −3.14387 | −0.288198 | ||||||||
\(120\) | 6.76869 | 0.617894 | ||||||||
\(121\) | −6.69990 | −0.609081 | ||||||||
\(122\) | 39.4367 | 3.57043 | ||||||||
\(123\) | −8.84359 | −0.797400 | ||||||||
\(124\) | −5.88310 | −0.528318 | ||||||||
\(125\) | 6.46100 | 0.577889 | ||||||||
\(126\) | −8.67895 | −0.773182 | ||||||||
\(127\) | 3.11216 | 0.276160 | 0.138080 | − | 0.990421i | \(-0.455907\pi\) | ||||
0.138080 | + | 0.990421i | \(0.455907\pi\) | |||||||
\(128\) | −51.0881 | −4.51559 | ||||||||
\(129\) | −12.3593 | −1.08817 | ||||||||
\(130\) | 9.56822 | 0.839188 | ||||||||
\(131\) | 4.19643 | 0.366644 | 0.183322 | − | 0.983053i | \(-0.441315\pi\) | ||||
0.183322 | + | 0.983053i | \(0.441315\pi\) | |||||||
\(132\) | −11.6559 | −1.01452 | ||||||||
\(133\) | 4.15163 | 0.359992 | ||||||||
\(134\) | 17.8097 | 1.53852 | ||||||||
\(135\) | −0.677149 | −0.0582797 | ||||||||
\(136\) | 9.99585 | 0.857137 | ||||||||
\(137\) | 13.4645 | 1.15035 | 0.575174 | − | 0.818031i | \(-0.304934\pi\) | ||||
0.575174 | + | 0.818031i | \(0.304934\pi\) | |||||||
\(138\) | −3.48354 | −0.296538 | ||||||||
\(139\) | −4.51887 | −0.383285 | −0.191643 | − | 0.981465i | \(-0.561381\pi\) | ||||
−0.191643 | + | 0.981465i | \(0.561381\pi\) | |||||||
\(140\) | −11.9661 | −1.01132 | ||||||||
\(141\) | 2.89101 | 0.243467 | ||||||||
\(142\) | 37.8793 | 3.17876 | ||||||||
\(143\) | −10.6141 | −0.887595 | ||||||||
\(144\) | 16.3527 | 1.36273 | ||||||||
\(145\) | −1.89183 | −0.157108 | ||||||||
\(146\) | 2.25155 | 0.186339 | ||||||||
\(147\) | 2.88389 | 0.237859 | ||||||||
\(148\) | 6.41444 | 0.527264 | ||||||||
\(149\) | −6.44984 | −0.528391 | −0.264196 | − | 0.964469i | \(-0.585106\pi\) | ||||
−0.264196 | + | 0.964469i | \(0.585106\pi\) | |||||||
\(150\) | 12.5372 | 1.02366 | ||||||||
\(151\) | 18.8081 | 1.53058 | 0.765291 | − | 0.643684i | \(-0.222595\pi\) | ||||
0.765291 | + | 0.643684i | \(0.222595\pi\) | |||||||
\(152\) | −13.2000 | −1.07066 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 17.9973 | 1.45026 | ||||||||
\(155\) | 0.708736 | 0.0569270 | ||||||||
\(156\) | 28.7706 | 2.30349 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 15.5585 | 1.23777 | ||||||||
\(159\) | −6.36246 | −0.504576 | ||||||||
\(160\) | 17.0314 | 1.34645 | ||||||||
\(161\) | 3.96717 | 0.312657 | ||||||||
\(162\) | −2.76060 | −0.216893 | ||||||||
\(163\) | −24.8104 | −1.94330 | −0.971651 | − | 0.236418i | \(-0.924026\pi\) | ||||
−0.971651 | + | 0.236418i | \(0.924026\pi\) | |||||||
\(164\) | −49.7090 | −3.88162 | ||||||||
\(165\) | 1.40418 | 0.109316 | ||||||||
\(166\) | −10.8166 | −0.839528 | ||||||||
\(167\) | 7.58853 | 0.587218 | 0.293609 | − | 0.955926i | \(-0.405144\pi\) | ||||
0.293609 | + | 0.955926i | \(0.405144\pi\) | |||||||
\(168\) | −31.4256 | −2.42454 | ||||||||
\(169\) | 13.1991 | 1.01532 | ||||||||
\(170\) | −1.86934 | −0.143372 | ||||||||
\(171\) | 1.32055 | 0.100985 | ||||||||
\(172\) | −69.4702 | −5.29706 | ||||||||
\(173\) | −0.321536 | −0.0244459 | −0.0122230 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122230 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(174\) | −7.71262 | −0.584692 | ||||||||
\(175\) | −14.2778 | −1.07930 | ||||||||
\(176\) | −33.9102 | −2.55607 | ||||||||
\(177\) | −4.43671 | −0.333483 | ||||||||
\(178\) | −18.7680 | −1.40672 | ||||||||
\(179\) | 19.2910 | 1.44188 | 0.720940 | − | 0.692998i | \(-0.243710\pi\) | ||||
0.720940 | + | 0.692998i | \(0.243710\pi\) | |||||||
\(180\) | −3.80619 | −0.283697 | ||||||||
\(181\) | −10.4593 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(182\) | −44.4233 | −3.29287 | ||||||||
\(183\) | −14.2855 | −1.05602 | ||||||||
\(184\) | −12.6135 | −0.929883 | ||||||||
\(185\) | −0.772747 | −0.0568135 | ||||||||
\(186\) | 2.88937 | 0.211859 | ||||||||
\(187\) | 2.07367 | 0.151642 | ||||||||
\(188\) | 16.2501 | 1.18516 | ||||||||
\(189\) | 3.14387 | 0.228683 | ||||||||
\(190\) | 2.46855 | 0.179087 | ||||||||
\(191\) | −17.6034 | −1.27374 | −0.636869 | − | 0.770972i | \(-0.719771\pi\) | ||||
−0.636869 | + | 0.770972i | \(0.719771\pi\) | |||||||
\(192\) | 36.7280 | 2.65062 | ||||||||
\(193\) | 1.13470 | 0.0816773 | 0.0408386 | − | 0.999166i | \(-0.486997\pi\) | ||||
0.0408386 | + | 0.999166i | \(0.486997\pi\) | |||||||
\(194\) | 30.0202 | 2.15532 | ||||||||
\(195\) | −3.46599 | −0.248205 | ||||||||
\(196\) | 16.2100 | 1.15786 | ||||||||
\(197\) | −15.6748 | −1.11678 | −0.558392 | − | 0.829577i | \(-0.688581\pi\) | ||||
−0.558392 | + | 0.829577i | \(0.688581\pi\) | |||||||
\(198\) | 5.72457 | 0.406827 | ||||||||
\(199\) | −2.91334 | −0.206521 | −0.103261 | − | 0.994654i | \(-0.532928\pi\) | ||||
−0.103261 | + | 0.994654i | \(0.532928\pi\) | |||||||
\(200\) | 45.3959 | 3.20997 | ||||||||
\(201\) | −6.45138 | −0.455045 | ||||||||
\(202\) | 1.88569 | 0.132676 | ||||||||
\(203\) | 8.78340 | 0.616474 | ||||||||
\(204\) | −5.62090 | −0.393542 | ||||||||
\(205\) | 5.98843 | 0.418250 | ||||||||
\(206\) | 28.7583 | 2.00368 | ||||||||
\(207\) | 1.26188 | 0.0877066 | ||||||||
\(208\) | 83.7016 | 5.80366 | ||||||||
\(209\) | −2.73838 | −0.189418 | ||||||||
\(210\) | 5.87694 | 0.405548 | ||||||||
\(211\) | 1.99437 | 0.137298 | 0.0686490 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686490 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(212\) | −35.7628 | −2.45620 | ||||||||
\(213\) | −13.7214 | −0.940176 | ||||||||
\(214\) | 13.1051 | 0.895849 | ||||||||
\(215\) | 8.36907 | 0.570766 | ||||||||
\(216\) | −9.99585 | −0.680132 | ||||||||
\(217\) | −3.29051 | −0.223375 | ||||||||
\(218\) | 13.9501 | 0.944822 | ||||||||
\(219\) | −0.815601 | −0.0551132 | ||||||||
\(220\) | 7.89278 | 0.532131 | ||||||||
\(221\) | −5.11851 | −0.344308 | ||||||||
\(222\) | −3.15033 | −0.211436 | ||||||||
\(223\) | −2.95748 | −0.198047 | −0.0990237 | − | 0.995085i | \(-0.531572\pi\) | ||||
−0.0990237 | + | 0.995085i | \(0.531572\pi\) | |||||||
\(224\) | −79.0733 | −5.28331 | ||||||||
\(225\) | −4.54147 | −0.302765 | ||||||||
\(226\) | −2.81007 | −0.186923 | ||||||||
\(227\) | −12.6127 | −0.837132 | −0.418566 | − | 0.908186i | \(-0.637467\pi\) | ||||
−0.418566 | + | 0.908186i | \(0.637467\pi\) | |||||||
\(228\) | 7.42268 | 0.491579 | ||||||||
\(229\) | 8.41701 | 0.556212 | 0.278106 | − | 0.960550i | \(-0.410293\pi\) | ||||
0.278106 | + | 0.960550i | \(0.410293\pi\) | |||||||
\(230\) | 2.35887 | 0.155540 | ||||||||
\(231\) | −6.51934 | −0.428941 | ||||||||
\(232\) | −27.9266 | −1.83347 | ||||||||
\(233\) | 6.72680 | 0.440688 | 0.220344 | − | 0.975422i | \(-0.429282\pi\) | ||||
0.220344 | + | 0.975422i | \(0.429282\pi\) | |||||||
\(234\) | −14.1301 | −0.923716 | ||||||||
\(235\) | −1.95765 | −0.127703 | ||||||||
\(236\) | −24.9383 | −1.62334 | ||||||||
\(237\) | −5.63591 | −0.366092 | ||||||||
\(238\) | 8.67895 | 0.562573 | ||||||||
\(239\) | 13.6784 | 0.884782 | 0.442391 | − | 0.896822i | \(-0.354130\pi\) | ||||
0.442391 | + | 0.896822i | \(0.354130\pi\) | |||||||
\(240\) | −11.0732 | −0.714775 | ||||||||
\(241\) | −8.88981 | −0.572643 | −0.286322 | − | 0.958134i | \(-0.592433\pi\) | ||||
−0.286322 | + | 0.958134i | \(0.592433\pi\) | |||||||
\(242\) | 18.4957 | 1.18895 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −80.2977 | −5.14053 | ||||||||
\(245\) | −1.95282 | −0.124761 | ||||||||
\(246\) | 24.4136 | 1.55655 | ||||||||
\(247\) | 6.75924 | 0.430080 | ||||||||
\(248\) | 10.4621 | 0.664346 | ||||||||
\(249\) | 3.91819 | 0.248305 | ||||||||
\(250\) | −17.8362 | −1.12806 | ||||||||
\(251\) | 2.89315 | 0.182614 | 0.0913070 | − | 0.995823i | \(-0.470896\pi\) | ||||
0.0913070 | + | 0.995823i | \(0.470896\pi\) | |||||||
\(252\) | 17.6714 | 1.11319 | ||||||||
\(253\) | −2.61672 | −0.164512 | ||||||||
\(254\) | −8.59144 | −0.539075 | ||||||||
\(255\) | 0.677149 | 0.0424047 | ||||||||
\(256\) | 67.5777 | 4.22361 | ||||||||
\(257\) | 5.42647 | 0.338494 | 0.169247 | − | 0.985574i | \(-0.445866\pi\) | ||||
0.169247 | + | 0.985574i | \(0.445866\pi\) | |||||||
\(258\) | 34.1190 | 2.12415 | ||||||||
\(259\) | 3.58771 | 0.222929 | ||||||||
\(260\) | −19.4820 | −1.20822 | ||||||||
\(261\) | 2.79382 | 0.172933 | ||||||||
\(262\) | −11.5847 | −0.715702 | ||||||||
\(263\) | −19.4244 | −1.19776 | −0.598881 | − | 0.800838i | \(-0.704388\pi\) | ||||
−0.598881 | + | 0.800838i | \(0.704388\pi\) | |||||||
\(264\) | 20.7281 | 1.27573 | ||||||||
\(265\) | 4.30834 | 0.264659 | ||||||||
\(266\) | −11.4610 | −0.702717 | ||||||||
\(267\) | 6.79853 | 0.416063 | ||||||||
\(268\) | −36.2626 | −2.21509 | ||||||||
\(269\) | −13.0613 | −0.796359 | −0.398179 | − | 0.917308i | \(-0.630358\pi\) | ||||
−0.398179 | + | 0.917308i | \(0.630358\pi\) | |||||||
\(270\) | 1.86934 | 0.113764 | ||||||||
\(271\) | −22.4597 | −1.36433 | −0.682164 | − | 0.731199i | \(-0.738961\pi\) | ||||
−0.682164 | + | 0.731199i | \(0.738961\pi\) | |||||||
\(272\) | −16.3527 | −0.991530 | ||||||||
\(273\) | 16.0919 | 0.973926 | ||||||||
\(274\) | −37.1700 | −2.24552 | ||||||||
\(275\) | 9.41750 | 0.567897 | ||||||||
\(276\) | 7.09289 | 0.426942 | ||||||||
\(277\) | 18.1823 | 1.09247 | 0.546233 | − | 0.837633i | \(-0.316061\pi\) | ||||
0.546233 | + | 0.837633i | \(0.316061\pi\) | |||||||
\(278\) | 12.4748 | 0.748187 | ||||||||
\(279\) | −1.04665 | −0.0626611 | ||||||||
\(280\) | 21.2798 | 1.27171 | ||||||||
\(281\) | −12.2995 | −0.733726 | −0.366863 | − | 0.930275i | \(-0.619568\pi\) | ||||
−0.366863 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(282\) | −7.98092 | −0.475257 | ||||||||
\(283\) | 13.4204 | 0.797758 | 0.398879 | − | 0.917004i | \(-0.369399\pi\) | ||||
0.398879 | + | 0.917004i | \(0.369399\pi\) | |||||||
\(284\) | −77.1268 | −4.57663 | ||||||||
\(285\) | −0.894209 | −0.0529683 | ||||||||
\(286\) | 29.3012 | 1.73262 | ||||||||
\(287\) | −27.8031 | −1.64116 | ||||||||
\(288\) | −25.1516 | −1.48207 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.22260 | 0.306681 | ||||||||
\(291\) | −10.8745 | −0.637476 | ||||||||
\(292\) | −4.58441 | −0.268283 | ||||||||
\(293\) | 21.0032 | 1.22702 | 0.613509 | − | 0.789688i | \(-0.289757\pi\) | ||||
0.613509 | + | 0.789688i | \(0.289757\pi\) | |||||||
\(294\) | −7.96125 | −0.464310 | ||||||||
\(295\) | 3.00431 | 0.174918 | ||||||||
\(296\) | −11.4070 | −0.663021 | ||||||||
\(297\) | −2.07367 | −0.120326 | ||||||||
\(298\) | 17.8054 | 1.03144 | ||||||||
\(299\) | 6.45893 | 0.373530 | ||||||||
\(300\) | −25.5272 | −1.47381 | ||||||||
\(301\) | −38.8559 | −2.23962 | ||||||||
\(302\) | −51.9216 | −2.98775 | ||||||||
\(303\) | −0.683072 | −0.0392414 | ||||||||
\(304\) | 21.5946 | 1.23853 | ||||||||
\(305\) | 9.67345 | 0.553900 | ||||||||
\(306\) | 2.76060 | 0.157813 | ||||||||
\(307\) | −2.31157 | −0.131928 | −0.0659642 | − | 0.997822i | \(-0.521012\pi\) | ||||
−0.0659642 | + | 0.997822i | \(0.521012\pi\) | |||||||
\(308\) | −36.6445 | −2.08802 | ||||||||
\(309\) | −10.4174 | −0.592626 | ||||||||
\(310\) | −1.95653 | −0.111124 | ||||||||
\(311\) | 2.29825 | 0.130322 | 0.0651609 | − | 0.997875i | \(-0.479244\pi\) | ||||
0.0651609 | + | 0.997875i | \(0.479244\pi\) | |||||||
\(312\) | −51.1639 | −2.89658 | ||||||||
\(313\) | 7.60296 | 0.429745 | 0.214872 | − | 0.976642i | \(-0.431066\pi\) | ||||
0.214872 | + | 0.976642i | \(0.431066\pi\) | |||||||
\(314\) | −2.76060 | −0.155790 | ||||||||
\(315\) | −2.12887 | −0.119948 | ||||||||
\(316\) | −31.6789 | −1.78208 | ||||||||
\(317\) | −0.421117 | −0.0236523 | −0.0118262 | − | 0.999930i | \(-0.503764\pi\) | ||||
−0.0118262 | + | 0.999930i | \(0.503764\pi\) | |||||||
\(318\) | 17.5642 | 0.984952 | ||||||||
\(319\) | −5.79346 | −0.324372 | ||||||||
\(320\) | −24.8704 | −1.39030 | ||||||||
\(321\) | −4.74721 | −0.264963 | ||||||||
\(322\) | −10.9518 | −0.610318 | ||||||||
\(323\) | −1.32055 | −0.0734773 | ||||||||
\(324\) | 5.62090 | 0.312272 | ||||||||
\(325\) | −23.2455 | −1.28943 | ||||||||
\(326\) | 68.4916 | 3.79340 | ||||||||
\(327\) | −5.05330 | −0.279448 | ||||||||
\(328\) | 88.3993 | 4.88103 | ||||||||
\(329\) | 9.08895 | 0.501090 | ||||||||
\(330\) | −3.87639 | −0.213388 | ||||||||
\(331\) | −6.39080 | −0.351270 | −0.175635 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175635 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(332\) | 22.0238 | 1.20871 | ||||||||
\(333\) | 1.14118 | 0.0625361 | ||||||||
\(334\) | −20.9489 | −1.14627 | ||||||||
\(335\) | 4.36854 | 0.238679 | ||||||||
\(336\) | 51.4108 | 2.80469 | ||||||||
\(337\) | −22.7087 | −1.23702 | −0.618510 | − | 0.785777i | \(-0.712263\pi\) | ||||
−0.618510 | + | 0.785777i | \(0.712263\pi\) | |||||||
\(338\) | −36.4375 | −1.98194 | ||||||||
\(339\) | 1.01792 | 0.0552859 | ||||||||
\(340\) | 3.80619 | 0.206420 | ||||||||
\(341\) | 2.17040 | 0.117534 | ||||||||
\(342\) | −3.64550 | −0.197126 | ||||||||
\(343\) | −12.9405 | −0.698721 | ||||||||
\(344\) | 123.541 | 6.66091 | ||||||||
\(345\) | −0.854480 | −0.0460036 | ||||||||
\(346\) | 0.887631 | 0.0477194 | ||||||||
\(347\) | 21.7522 | 1.16772 | 0.583861 | − | 0.811854i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811854i | \(0.301541\pi\) | |||||||
\(348\) | 15.7038 | 0.841812 | ||||||||
\(349\) | 12.0038 | 0.642551 | 0.321275 | − | 0.946986i | \(-0.395888\pi\) | ||||
0.321275 | + | 0.946986i | \(0.395888\pi\) | |||||||
\(350\) | 39.4152 | 2.10683 | ||||||||
\(351\) | 5.11851 | 0.273206 | ||||||||
\(352\) | 52.1561 | 2.77993 | ||||||||
\(353\) | −1.00882 | −0.0536939 | −0.0268470 | − | 0.999640i | \(-0.508547\pi\) | ||||
−0.0268470 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(354\) | 12.2480 | 0.650972 | ||||||||
\(355\) | 9.29145 | 0.493139 | ||||||||
\(356\) | 38.2139 | 2.02533 | ||||||||
\(357\) | −3.14387 | −0.166391 | ||||||||
\(358\) | −53.2548 | −2.81460 | ||||||||
\(359\) | 26.7983 | 1.41436 | 0.707180 | − | 0.707033i | \(-0.249967\pi\) | ||||
0.707180 | + | 0.707033i | \(0.249967\pi\) | |||||||
\(360\) | 6.76869 | 0.356741 | ||||||||
\(361\) | −17.2562 | −0.908218 | ||||||||
\(362\) | 28.8740 | 1.51758 | ||||||||
\(363\) | −6.69990 | −0.351653 | ||||||||
\(364\) | 90.4510 | 4.74092 | ||||||||
\(365\) | 0.552284 | 0.0289078 | ||||||||
\(366\) | 39.4367 | 2.06139 | ||||||||
\(367\) | 26.8416 | 1.40112 | 0.700560 | − | 0.713594i | \(-0.252934\pi\) | ||||
0.700560 | + | 0.713594i | \(0.252934\pi\) | |||||||
\(368\) | 20.6352 | 1.07568 | ||||||||
\(369\) | −8.84359 | −0.460379 | ||||||||
\(370\) | 2.13324 | 0.110902 | ||||||||
\(371\) | −20.0027 | −1.03849 | ||||||||
\(372\) | −5.88310 | −0.305024 | ||||||||
\(373\) | −0.452858 | −0.0234481 | −0.0117241 | − | 0.999931i | \(-0.503732\pi\) | ||||
−0.0117241 | + | 0.999931i | \(0.503732\pi\) | |||||||
\(374\) | −5.72457 | −0.296010 | ||||||||
\(375\) | 6.46100 | 0.333645 | ||||||||
\(376\) | −28.8981 | −1.49031 | ||||||||
\(377\) | 14.3002 | 0.736498 | ||||||||
\(378\) | −8.67895 | −0.446397 | ||||||||
\(379\) | 25.2634 | 1.29770 | 0.648848 | − | 0.760918i | \(-0.275251\pi\) | ||||
0.648848 | + | 0.760918i | \(0.275251\pi\) | |||||||
\(380\) | −5.02626 | −0.257842 | ||||||||
\(381\) | 3.11216 | 0.159441 | ||||||||
\(382\) | 48.5959 | 2.48638 | ||||||||
\(383\) | 21.4661 | 1.09687 | 0.548434 | − | 0.836194i | \(-0.315224\pi\) | ||||
0.548434 | + | 0.836194i | \(0.315224\pi\) | |||||||
\(384\) | −51.0881 | −2.60708 | ||||||||
\(385\) | 4.41456 | 0.224987 | ||||||||
\(386\) | −3.13244 | −0.159437 | ||||||||
\(387\) | −12.3593 | −0.628257 | ||||||||
\(388\) | −61.1246 | −3.10313 | ||||||||
\(389\) | 2.06444 | 0.104671 | 0.0523356 | − | 0.998630i | \(-0.483333\pi\) | ||||
0.0523356 | + | 0.998630i | \(0.483333\pi\) | |||||||
\(390\) | 9.56822 | 0.484505 | ||||||||
\(391\) | −1.26188 | −0.0638159 | ||||||||
\(392\) | −28.8269 | −1.45598 | ||||||||
\(393\) | 4.19643 | 0.211682 | ||||||||
\(394\) | 43.2718 | 2.18000 | ||||||||
\(395\) | 3.81636 | 0.192022 | ||||||||
\(396\) | −11.6559 | −0.585731 | ||||||||
\(397\) | −12.0212 | −0.603326 | −0.301663 | − | 0.953415i | \(-0.597542\pi\) | ||||
−0.301663 | + | 0.953415i | \(0.597542\pi\) | |||||||
\(398\) | 8.04257 | 0.403138 | ||||||||
\(399\) | 4.15163 | 0.207841 | ||||||||
\(400\) | −74.2654 | −3.71327 | ||||||||
\(401\) | −32.9380 | −1.64484 | −0.822422 | − | 0.568878i | \(-0.807378\pi\) | ||||
−0.822422 | + | 0.568878i | \(0.807378\pi\) | |||||||
\(402\) | 17.8097 | 0.888265 | ||||||||
\(403\) | −5.35727 | −0.266865 | ||||||||
\(404\) | −3.83948 | −0.191021 | ||||||||
\(405\) | −0.677149 | −0.0336478 | ||||||||
\(406\) | −24.2474 | −1.20338 | ||||||||
\(407\) | −2.36642 | −0.117299 | ||||||||
\(408\) | 9.99585 | 0.494869 | ||||||||
\(409\) | 17.8596 | 0.883100 | 0.441550 | − | 0.897237i | \(-0.354429\pi\) | ||||
0.441550 | + | 0.897237i | \(0.354429\pi\) | |||||||
\(410\) | −16.5317 | −0.816440 | ||||||||
\(411\) | 13.4645 | 0.664154 | ||||||||
\(412\) | −58.5552 | −2.88481 | ||||||||
\(413\) | −13.9484 | −0.686356 | ||||||||
\(414\) | −3.48354 | −0.171207 | ||||||||
\(415\) | −2.65320 | −0.130241 | ||||||||
\(416\) | −128.739 | −6.31194 | ||||||||
\(417\) | −4.51887 | −0.221290 | ||||||||
\(418\) | 7.55957 | 0.369751 | ||||||||
\(419\) | −8.79922 | −0.429870 | −0.214935 | − | 0.976628i | \(-0.568954\pi\) | ||||
−0.214935 | + | 0.976628i | \(0.568954\pi\) | |||||||
\(420\) | −11.9661 | −0.583888 | ||||||||
\(421\) | 36.8792 | 1.79738 | 0.898691 | − | 0.438583i | \(-0.144519\pi\) | ||||
0.898691 | + | 0.438583i | \(0.144519\pi\) | |||||||
\(422\) | −5.50565 | −0.268011 | ||||||||
\(423\) | 2.89101 | 0.140566 | ||||||||
\(424\) | 63.5983 | 3.08860 | ||||||||
\(425\) | 4.54147 | 0.220294 | ||||||||
\(426\) | 37.8793 | 1.83526 | ||||||||
\(427\) | −44.9118 | −2.17344 | ||||||||
\(428\) | −26.6836 | −1.28980 | ||||||||
\(429\) | −10.6141 | −0.512453 | ||||||||
\(430\) | −23.1036 | −1.11416 | ||||||||
\(431\) | −10.5544 | −0.508388 | −0.254194 | − | 0.967153i | \(-0.581810\pi\) | ||||
−0.254194 | + | 0.967153i | \(0.581810\pi\) | |||||||
\(432\) | 16.3527 | 0.786771 | ||||||||
\(433\) | 12.1603 | 0.584385 | 0.292193 | − | 0.956359i | \(-0.405615\pi\) | ||||
0.292193 | + | 0.956359i | \(0.405615\pi\) | |||||||
\(434\) | 9.08379 | 0.436036 | ||||||||
\(435\) | −1.89183 | −0.0907065 | ||||||||
\(436\) | −28.4041 | −1.36031 | ||||||||
\(437\) | 1.66637 | 0.0797133 | ||||||||
\(438\) | 2.25155 | 0.107583 | ||||||||
\(439\) | 39.3094 | 1.87614 | 0.938068 | − | 0.346453i | \(-0.112614\pi\) | ||||
0.938068 | + | 0.346453i | \(0.112614\pi\) | |||||||
\(440\) | −14.0360 | −0.669141 | ||||||||
\(441\) | 2.88389 | 0.137328 | ||||||||
\(442\) | 14.1301 | 0.672102 | ||||||||
\(443\) | 7.46622 | 0.354731 | 0.177365 | − | 0.984145i | \(-0.443243\pi\) | ||||
0.177365 | + | 0.984145i | \(0.443243\pi\) | |||||||
\(444\) | 6.41444 | 0.304416 | ||||||||
\(445\) | −4.60362 | −0.218233 | ||||||||
\(446\) | 8.16441 | 0.386596 | ||||||||
\(447\) | −6.44984 | −0.305067 | ||||||||
\(448\) | 115.468 | 5.45535 | ||||||||
\(449\) | 36.1899 | 1.70791 | 0.853954 | − | 0.520348i | \(-0.174198\pi\) | ||||
0.853954 | + | 0.520348i | \(0.174198\pi\) | |||||||
\(450\) | 12.5372 | 0.591008 | ||||||||
\(451\) | 18.3387 | 0.863535 | ||||||||
\(452\) | 5.72164 | 0.269123 | ||||||||
\(453\) | 18.8081 | 0.883682 | ||||||||
\(454\) | 34.8185 | 1.63411 | ||||||||
\(455\) | −10.8966 | −0.510841 | ||||||||
\(456\) | −13.2000 | −0.618147 | ||||||||
\(457\) | 4.00965 | 0.187563 | 0.0937817 | − | 0.995593i | \(-0.470104\pi\) | ||||
0.0937817 | + | 0.995593i | \(0.470104\pi\) | |||||||
\(458\) | −23.2360 | −1.08575 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −4.80295 | −0.223938 | ||||||||
\(461\) | −14.0063 | −0.652340 | −0.326170 | − | 0.945311i | \(-0.605758\pi\) | ||||
−0.326170 | + | 0.945311i | \(0.605758\pi\) | |||||||
\(462\) | 17.9973 | 0.837309 | ||||||||
\(463\) | −40.8451 | −1.89823 | −0.949117 | − | 0.314924i | \(-0.898021\pi\) | ||||
−0.949117 | + | 0.314924i | \(0.898021\pi\) | |||||||
\(464\) | 45.6866 | 2.12095 | ||||||||
\(465\) | 0.708736 | 0.0328668 | ||||||||
\(466\) | −18.5700 | −0.860239 | ||||||||
\(467\) | 19.8667 | 0.919322 | 0.459661 | − | 0.888095i | \(-0.347971\pi\) | ||||
0.459661 | + | 0.888095i | \(0.347971\pi\) | |||||||
\(468\) | 28.7706 | 1.32992 | ||||||||
\(469\) | −20.2823 | −0.936548 | ||||||||
\(470\) | 5.40428 | 0.249281 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 44.3487 | 2.04131 | ||||||||
\(473\) | 25.6290 | 1.17842 | ||||||||
\(474\) | 15.5585 | 0.714625 | ||||||||
\(475\) | −5.99723 | −0.275172 | ||||||||
\(476\) | −17.6714 | −0.809965 | ||||||||
\(477\) | −6.36246 | −0.291317 | ||||||||
\(478\) | −37.7606 | −1.72713 | ||||||||
\(479\) | −20.1498 | −0.920669 | −0.460334 | − | 0.887746i | \(-0.652270\pi\) | ||||
−0.460334 | + | 0.887746i | \(0.652270\pi\) | |||||||
\(480\) | 17.0314 | 0.777373 | ||||||||
\(481\) | 5.84112 | 0.266332 | ||||||||
\(482\) | 24.5412 | 1.11782 | ||||||||
\(483\) | 3.96717 | 0.180513 | ||||||||
\(484\) | −37.6595 | −1.71179 | ||||||||
\(485\) | 7.36368 | 0.334367 | ||||||||
\(486\) | −2.76060 | −0.125223 | ||||||||
\(487\) | 17.5488 | 0.795211 | 0.397606 | − | 0.917556i | \(-0.369841\pi\) | ||||
0.397606 | + | 0.917556i | \(0.369841\pi\) | |||||||
\(488\) | 142.796 | 6.46408 | ||||||||
\(489\) | −24.8104 | −1.12197 | ||||||||
\(490\) | 5.39096 | 0.243539 | ||||||||
\(491\) | 18.4100 | 0.830833 | 0.415416 | − | 0.909631i | \(-0.363636\pi\) | ||||
0.415416 | + | 0.909631i | \(0.363636\pi\) | |||||||
\(492\) | −49.7090 | −2.24105 | ||||||||
\(493\) | −2.79382 | −0.125827 | ||||||||
\(494\) | −18.6595 | −0.839533 | ||||||||
\(495\) | 1.40418 | 0.0631134 | ||||||||
\(496\) | −17.1155 | −0.768510 | ||||||||
\(497\) | −43.1383 | −1.93502 | ||||||||
\(498\) | −10.8166 | −0.484702 | ||||||||
\(499\) | 37.7091 | 1.68809 | 0.844045 | − | 0.536273i | \(-0.180168\pi\) | ||||
0.844045 | + | 0.536273i | \(0.180168\pi\) | |||||||
\(500\) | 36.3166 | 1.62413 | ||||||||
\(501\) | 7.58853 | 0.339030 | ||||||||
\(502\) | −7.98682 | −0.356469 | ||||||||
\(503\) | −22.1498 | −0.987613 | −0.493806 | − | 0.869572i | \(-0.664395\pi\) | ||||
−0.493806 | + | 0.869572i | \(0.664395\pi\) | |||||||
\(504\) | −31.4256 | −1.39981 | ||||||||
\(505\) | 0.462541 | 0.0205828 | ||||||||
\(506\) | 7.22370 | 0.321133 | ||||||||
\(507\) | 13.1991 | 0.586194 | ||||||||
\(508\) | 17.4932 | 0.776134 | ||||||||
\(509\) | 27.7313 | 1.22917 | 0.614585 | − | 0.788851i | \(-0.289323\pi\) | ||||
0.614585 | + | 0.788851i | \(0.289323\pi\) | |||||||
\(510\) | −1.86934 | −0.0827756 | ||||||||
\(511\) | −2.56414 | −0.113431 | ||||||||
\(512\) | −84.3786 | −3.72904 | ||||||||
\(513\) | 1.32055 | 0.0583037 | ||||||||
\(514\) | −14.9803 | −0.660753 | ||||||||
\(515\) | 7.05414 | 0.310842 | ||||||||
\(516\) | −69.4702 | −3.05826 | ||||||||
\(517\) | −5.99500 | −0.263660 | ||||||||
\(518\) | −9.90421 | −0.435166 | ||||||||
\(519\) | −0.321536 | −0.0141139 | ||||||||
\(520\) | 34.6456 | 1.51931 | ||||||||
\(521\) | 21.2034 | 0.928938 | 0.464469 | − | 0.885589i | \(-0.346245\pi\) | ||||
0.464469 | + | 0.885589i | \(0.346245\pi\) | |||||||
\(522\) | −7.71262 | −0.337572 | ||||||||
\(523\) | −27.4540 | −1.20048 | −0.600240 | − | 0.799820i | \(-0.704928\pi\) | ||||
−0.600240 | + | 0.799820i | \(0.704928\pi\) | |||||||
\(524\) | 23.5877 | 1.03043 | ||||||||
\(525\) | −14.2778 | −0.623133 | ||||||||
\(526\) | 53.6231 | 2.33808 | ||||||||
\(527\) | 1.04665 | 0.0455926 | ||||||||
\(528\) | −33.9102 | −1.47575 | ||||||||
\(529\) | −21.4077 | −0.930768 | ||||||||
\(530\) | −11.8936 | −0.516624 | ||||||||
\(531\) | −4.43671 | −0.192537 | ||||||||
\(532\) | 23.3359 | 1.01174 | ||||||||
\(533\) | −45.2660 | −1.96069 | ||||||||
\(534\) | −18.7680 | −0.812172 | ||||||||
\(535\) | 3.21457 | 0.138978 | ||||||||
\(536\) | 64.4870 | 2.78541 | ||||||||
\(537\) | 19.2910 | 0.832470 | ||||||||
\(538\) | 36.0569 | 1.55452 | ||||||||
\(539\) | −5.98023 | −0.257587 | ||||||||
\(540\) | −3.80619 | −0.163792 | ||||||||
\(541\) | 18.8676 | 0.811182 | 0.405591 | − | 0.914055i | \(-0.367066\pi\) | ||||
0.405591 | + | 0.914055i | \(0.367066\pi\) | |||||||
\(542\) | 62.0021 | 2.66322 | ||||||||
\(543\) | −10.4593 | −0.448853 | ||||||||
\(544\) | 25.1516 | 1.07837 | ||||||||
\(545\) | 3.42184 | 0.146575 | ||||||||
\(546\) | −44.4233 | −1.90114 | ||||||||
\(547\) | 24.8923 | 1.06432 | 0.532159 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532159 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(548\) | 75.6825 | 3.23300 | ||||||||
\(549\) | −14.2855 | −0.609692 | ||||||||
\(550\) | −25.9979 | −1.10856 | ||||||||
\(551\) | 3.68938 | 0.157173 | ||||||||
\(552\) | −12.6135 | −0.536868 | ||||||||
\(553\) | −17.7186 | −0.753470 | ||||||||
\(554\) | −50.1939 | −2.13254 | ||||||||
\(555\) | −0.772747 | −0.0328013 | ||||||||
\(556\) | −25.4001 | −1.07720 | ||||||||
\(557\) | −24.7797 | −1.04995 | −0.524974 | − | 0.851118i | \(-0.675925\pi\) | ||||
−0.524974 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(558\) | 2.88937 | 0.122317 | ||||||||
\(559\) | −63.2610 | −2.67566 | ||||||||
\(560\) | −34.8128 | −1.47111 | ||||||||
\(561\) | 2.07367 | 0.0875504 | ||||||||
\(562\) | 33.9539 | 1.43226 | ||||||||
\(563\) | −42.4418 | −1.78871 | −0.894354 | − | 0.447360i | \(-0.852364\pi\) | ||||
−0.894354 | + | 0.447360i | \(0.852364\pi\) | |||||||
\(564\) | 16.2501 | 0.684253 | ||||||||
\(565\) | −0.689285 | −0.0289984 | ||||||||
\(566\) | −37.0482 | −1.55725 | ||||||||
\(567\) | 3.14387 | 0.132030 | ||||||||
\(568\) | 137.157 | 5.75499 | ||||||||
\(569\) | −18.6400 | −0.781431 | −0.390715 | − | 0.920512i | \(-0.627772\pi\) | ||||
−0.390715 | + | 0.920512i | \(0.627772\pi\) | |||||||
\(570\) | 2.46855 | 0.103396 | ||||||||
\(571\) | 20.0120 | 0.837474 | 0.418737 | − | 0.908108i | \(-0.362473\pi\) | ||||
0.418737 | + | 0.908108i | \(0.362473\pi\) | |||||||
\(572\) | −59.6608 | −2.49454 | ||||||||
\(573\) | −17.6034 | −0.735393 | ||||||||
\(574\) | 76.7531 | 3.20361 | ||||||||
\(575\) | −5.73078 | −0.238990 | ||||||||
\(576\) | 36.7280 | 1.53033 | ||||||||
\(577\) | −16.1352 | −0.671718 | −0.335859 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335859 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(578\) | −2.76060 | −0.114826 | ||||||||
\(579\) | 1.13470 | 0.0471564 | ||||||||
\(580\) | −10.6338 | −0.441545 | ||||||||
\(581\) | 12.3183 | 0.511048 | ||||||||
\(582\) | 30.0202 | 1.24438 | ||||||||
\(583\) | 13.1936 | 0.546425 | ||||||||
\(584\) | 8.15263 | 0.337358 | ||||||||
\(585\) | −3.46599 | −0.143301 | ||||||||
\(586\) | −57.9813 | −2.39519 | ||||||||
\(587\) | 23.8858 | 0.985871 | 0.492935 | − | 0.870066i | \(-0.335924\pi\) | ||||
0.492935 | + | 0.870066i | \(0.335924\pi\) | |||||||
\(588\) | 16.2100 | 0.668491 | ||||||||
\(589\) | −1.38215 | −0.0569504 | ||||||||
\(590\) | −8.29370 | −0.341446 | ||||||||
\(591\) | −15.6748 | −0.644776 | ||||||||
\(592\) | 18.6614 | 0.766977 | ||||||||
\(593\) | −9.10968 | −0.374090 | −0.187045 | − | 0.982351i | \(-0.559891\pi\) | ||||
−0.187045 | + | 0.982351i | \(0.559891\pi\) | |||||||
\(594\) | 5.72457 | 0.234882 | ||||||||
\(595\) | 2.12887 | 0.0872750 | ||||||||
\(596\) | −36.2539 | −1.48502 | ||||||||
\(597\) | −2.91334 | −0.119235 | ||||||||
\(598\) | −17.8305 | −0.729144 | ||||||||
\(599\) | −19.0805 | −0.779606 | −0.389803 | − | 0.920898i | \(-0.627457\pi\) | ||||
−0.389803 | + | 0.920898i | \(0.627457\pi\) | |||||||
\(600\) | 45.3959 | 1.85328 | ||||||||
\(601\) | 3.40864 | 0.139041 | 0.0695207 | − | 0.997581i | \(-0.477853\pi\) | ||||
0.0695207 | + | 0.997581i | \(0.477853\pi\) | |||||||
\(602\) | 107.265 | 4.37181 | ||||||||
\(603\) | −6.45138 | −0.262720 | ||||||||
\(604\) | 105.719 | 4.30163 | ||||||||
\(605\) | 4.53683 | 0.184448 | ||||||||
\(606\) | 1.88569 | 0.0766008 | ||||||||
\(607\) | 8.80303 | 0.357304 | 0.178652 | − | 0.983912i | \(-0.442826\pi\) | ||||
0.178652 | + | 0.983912i | \(0.442826\pi\) | |||||||
\(608\) | −33.2139 | −1.34700 | ||||||||
\(609\) | 8.78340 | 0.355921 | ||||||||
\(610\) | −26.7045 | −1.08123 | ||||||||
\(611\) | 14.7977 | 0.598650 | ||||||||
\(612\) | −5.62090 | −0.227211 | ||||||||
\(613\) | 23.2586 | 0.939405 | 0.469703 | − | 0.882825i | \(-0.344361\pi\) | ||||
0.469703 | + | 0.882825i | \(0.344361\pi\) | |||||||
\(614\) | 6.38132 | 0.257529 | ||||||||
\(615\) | 5.98843 | 0.241477 | ||||||||
\(616\) | 65.1663 | 2.62563 | ||||||||
\(617\) | 2.03154 | 0.0817866 | 0.0408933 | − | 0.999164i | \(-0.486980\pi\) | ||||
0.0408933 | + | 0.999164i | \(0.486980\pi\) | |||||||
\(618\) | 28.7583 | 1.15683 | ||||||||
\(619\) | 31.1951 | 1.25384 | 0.626919 | − | 0.779084i | \(-0.284316\pi\) | ||||
0.626919 | + | 0.779084i | \(0.284316\pi\) | |||||||
\(620\) | 3.98373 | 0.159991 | ||||||||
\(621\) | 1.26188 | 0.0506374 | ||||||||
\(622\) | −6.34455 | −0.254393 | ||||||||
\(623\) | 21.3737 | 0.856318 | ||||||||
\(624\) | 83.7016 | 3.35075 | ||||||||
\(625\) | 18.3323 | 0.733291 | ||||||||
\(626\) | −20.9887 | −0.838878 | ||||||||
\(627\) | −2.73838 | −0.109360 | ||||||||
\(628\) | 5.62090 | 0.224298 | ||||||||
\(629\) | −1.14118 | −0.0455017 | ||||||||
\(630\) | 5.87694 | 0.234143 | ||||||||
\(631\) | 20.2642 | 0.806705 | 0.403352 | − | 0.915045i | \(-0.367845\pi\) | ||||
0.403352 | + | 0.915045i | \(0.367845\pi\) | |||||||
\(632\) | 56.3358 | 2.24092 | ||||||||
\(633\) | 1.99437 | 0.0792691 | ||||||||
\(634\) | 1.16254 | 0.0461702 | ||||||||
\(635\) | −2.10740 | −0.0836296 | ||||||||
\(636\) | −35.7628 | −1.41809 | ||||||||
\(637\) | 14.7612 | 0.584860 | ||||||||
\(638\) | 15.9934 | 0.633186 | ||||||||
\(639\) | −13.7214 | −0.542811 | ||||||||
\(640\) | 34.5943 | 1.36746 | ||||||||
\(641\) | 47.7941 | 1.88775 | 0.943876 | − | 0.330299i | \(-0.107150\pi\) | ||||
0.943876 | + | 0.330299i | \(0.107150\pi\) | |||||||
\(642\) | 13.1051 | 0.517219 | ||||||||
\(643\) | −29.9901 | −1.18269 | −0.591346 | − | 0.806418i | \(-0.701403\pi\) | ||||
−0.591346 | + | 0.806418i | \(0.701403\pi\) | |||||||
\(644\) | 22.2991 | 0.878707 | ||||||||
\(645\) | 8.36907 | 0.329532 | ||||||||
\(646\) | 3.64550 | 0.143430 | ||||||||
\(647\) | −41.6952 | −1.63921 | −0.819604 | − | 0.572930i | \(-0.805807\pi\) | ||||
−0.819604 | + | 0.572930i | \(0.805807\pi\) | |||||||
\(648\) | −9.99585 | −0.392674 | ||||||||
\(649\) | 9.20026 | 0.361142 | ||||||||
\(650\) | 64.1716 | 2.51702 | ||||||||
\(651\) | −3.29051 | −0.128965 | ||||||||
\(652\) | −139.457 | −5.46156 | ||||||||
\(653\) | 19.4940 | 0.762858 | 0.381429 | − | 0.924398i | \(-0.375432\pi\) | ||||
0.381429 | + | 0.924398i | \(0.375432\pi\) | |||||||
\(654\) | 13.9501 | 0.545493 | ||||||||
\(655\) | −2.84161 | −0.111031 | ||||||||
\(656\) | −144.617 | −5.64634 | ||||||||
\(657\) | −0.815601 | −0.0318196 | ||||||||
\(658\) | −25.0909 | −0.978147 | ||||||||
\(659\) | 13.5672 | 0.528504 | 0.264252 | − | 0.964454i | \(-0.414875\pi\) | ||||
0.264252 | + | 0.964454i | \(0.414875\pi\) | |||||||
\(660\) | 7.89278 | 0.307226 | ||||||||
\(661\) | 5.59687 | 0.217693 | 0.108847 | − | 0.994059i | \(-0.465284\pi\) | ||||
0.108847 | + | 0.994059i | \(0.465284\pi\) | |||||||
\(662\) | 17.6424 | 0.685692 | ||||||||
\(663\) | −5.11851 | −0.198786 | ||||||||
\(664\) | −39.1657 | −1.51992 | ||||||||
\(665\) | −2.81127 | −0.109016 | ||||||||
\(666\) | −3.15033 | −0.122073 | ||||||||
\(667\) | 3.52546 | 0.136506 | ||||||||
\(668\) | 42.6544 | 1.65035 | ||||||||
\(669\) | −2.95748 | −0.114343 | ||||||||
\(670\) | −12.0598 | −0.465911 | ||||||||
\(671\) | 29.6235 | 1.14360 | ||||||||
\(672\) | −79.0733 | −3.05032 | ||||||||
\(673\) | 19.1066 | 0.736504 | 0.368252 | − | 0.929726i | \(-0.379956\pi\) | ||||
0.368252 | + | 0.929726i | \(0.379956\pi\) | |||||||
\(674\) | 62.6895 | 2.41471 | ||||||||
\(675\) | −4.54147 | −0.174801 | ||||||||
\(676\) | 74.1910 | 2.85350 | ||||||||
\(677\) | −45.8575 | −1.76245 | −0.881223 | − | 0.472701i | \(-0.843279\pi\) | ||||
−0.881223 | + | 0.472701i | \(0.843279\pi\) | |||||||
\(678\) | −2.81007 | −0.107920 | ||||||||
\(679\) | −34.1880 | −1.31202 | ||||||||
\(680\) | −6.76869 | −0.259567 | ||||||||
\(681\) | −12.6127 | −0.483318 | ||||||||
\(682\) | −5.99160 | −0.229430 | ||||||||
\(683\) | −19.8726 | −0.760402 | −0.380201 | − | 0.924904i | \(-0.624145\pi\) | ||||
−0.380201 | + | 0.924904i | \(0.624145\pi\) | |||||||
\(684\) | 7.42268 | 0.283813 | ||||||||
\(685\) | −9.11746 | −0.348360 | ||||||||
\(686\) | 35.7235 | 1.36393 | ||||||||
\(687\) | 8.41701 | 0.321129 | ||||||||
\(688\) | −202.108 | −7.70529 | ||||||||
\(689\) | −32.5663 | −1.24068 | ||||||||
\(690\) | 2.35887 | 0.0898008 | ||||||||
\(691\) | 21.1493 | 0.804557 | 0.402278 | − | 0.915517i | \(-0.368218\pi\) | ||||
0.402278 | + | 0.915517i | \(0.368218\pi\) | |||||||
\(692\) | −1.80732 | −0.0687041 | ||||||||
\(693\) | −6.51934 | −0.247649 | ||||||||
\(694\) | −60.0492 | −2.27944 | ||||||||
\(695\) | 3.05995 | 0.116070 | ||||||||
\(696\) | −27.9266 | −1.05856 | ||||||||
\(697\) | 8.84359 | 0.334975 | ||||||||
\(698\) | −33.1378 | −1.25428 | ||||||||
\(699\) | 6.72680 | 0.254431 | ||||||||
\(700\) | −80.2539 | −3.03331 | ||||||||
\(701\) | −43.5604 | −1.64525 | −0.822626 | − | 0.568583i | \(-0.807492\pi\) | ||||
−0.822626 | + | 0.568583i | \(0.807492\pi\) | |||||||
\(702\) | −14.1301 | −0.533308 | ||||||||
\(703\) | 1.50698 | 0.0568368 | ||||||||
\(704\) | −76.1618 | −2.87046 | ||||||||
\(705\) | −1.95765 | −0.0737292 | ||||||||
\(706\) | 2.78494 | 0.104813 | ||||||||
\(707\) | −2.14748 | −0.0807645 | ||||||||
\(708\) | −24.9383 | −0.937238 | ||||||||
\(709\) | −16.9167 | −0.635322 | −0.317661 | − | 0.948204i | \(-0.602897\pi\) | ||||
−0.317661 | + | 0.948204i | \(0.602897\pi\) | |||||||
\(710\) | −25.6500 | −0.962626 | ||||||||
\(711\) | −5.63591 | −0.211363 | ||||||||
\(712\) | −67.9572 | −2.54680 | ||||||||
\(713\) | −1.32074 | −0.0494621 | ||||||||
\(714\) | 8.67895 | 0.324801 | ||||||||
\(715\) | 7.18732 | 0.268791 | ||||||||
\(716\) | 108.433 | 4.05233 | ||||||||
\(717\) | 13.6784 | 0.510829 | ||||||||
\(718\) | −73.9794 | −2.76089 | ||||||||
\(719\) | −28.2602 | −1.05393 | −0.526964 | − | 0.849888i | \(-0.676670\pi\) | ||||
−0.526964 | + | 0.849888i | \(0.676670\pi\) | |||||||
\(720\) | −11.0732 | −0.412675 | ||||||||
\(721\) | −32.7509 | −1.21971 | ||||||||
\(722\) | 47.6373 | 1.77288 | ||||||||
\(723\) | −8.88981 | −0.330616 | ||||||||
\(724\) | −58.7909 | −2.18495 | ||||||||
\(725\) | −12.6881 | −0.471223 | ||||||||
\(726\) | 18.4957 | 0.686441 | ||||||||
\(727\) | 36.1396 | 1.34034 | 0.670171 | − | 0.742206i | \(-0.266221\pi\) | ||||
0.670171 | + | 0.742206i | \(0.266221\pi\) | |||||||
\(728\) | −160.852 | −5.96158 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.52463 | −0.0564292 | ||||||||
\(731\) | 12.3593 | 0.457124 | ||||||||
\(732\) | −80.2977 | −2.96789 | ||||||||
\(733\) | −5.29296 | −0.195500 | −0.0977500 | − | 0.995211i | \(-0.531165\pi\) | ||||
−0.0977500 | + | 0.995211i | \(0.531165\pi\) | |||||||
\(734\) | −74.0988 | −2.73504 | ||||||||
\(735\) | −1.95282 | −0.0720309 | ||||||||
\(736\) | −31.7383 | −1.16989 | ||||||||
\(737\) | 13.3780 | 0.492786 | ||||||||
\(738\) | 24.4136 | 0.898677 | ||||||||
\(739\) | 13.0956 | 0.481730 | 0.240865 | − | 0.970559i | \(-0.422569\pi\) | ||||
0.240865 | + | 0.970559i | \(0.422569\pi\) | |||||||
\(740\) | −4.34354 | −0.159672 | ||||||||
\(741\) | 6.75924 | 0.248307 | ||||||||
\(742\) | 55.2195 | 2.02717 | ||||||||
\(743\) | 5.27872 | 0.193658 | 0.0968288 | − | 0.995301i | \(-0.469130\pi\) | ||||
0.0968288 | + | 0.995301i | \(0.469130\pi\) | |||||||
\(744\) | 10.4621 | 0.383560 | ||||||||
\(745\) | 4.36750 | 0.160013 | ||||||||
\(746\) | 1.25016 | 0.0457716 | ||||||||
\(747\) | 3.91819 | 0.143359 | ||||||||
\(748\) | 11.6559 | 0.426182 | ||||||||
\(749\) | −14.9246 | −0.545333 | ||||||||
\(750\) | −17.8362 | −0.651287 | ||||||||
\(751\) | 8.96559 | 0.327159 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(752\) | 47.2760 | 1.72398 | ||||||||
\(753\) | 2.89315 | 0.105432 | ||||||||
\(754\) | −39.4771 | −1.43767 | ||||||||
\(755\) | −12.7359 | −0.463507 | ||||||||
\(756\) | 17.6714 | 0.642701 | ||||||||
\(757\) | −10.0218 | −0.364249 | −0.182125 | − | 0.983275i | \(-0.558297\pi\) | ||||
−0.182125 | + | 0.983275i | \(0.558297\pi\) | |||||||
\(758\) | −69.7422 | −2.53315 | ||||||||
\(759\) | −2.61672 | −0.0949808 | ||||||||
\(760\) | 8.93838 | 0.324229 | ||||||||
\(761\) | 52.6570 | 1.90881 | 0.954407 | − | 0.298510i | \(-0.0964895\pi\) | ||||
0.954407 | + | 0.298510i | \(0.0964895\pi\) | |||||||
\(762\) | −8.59144 | −0.311235 | ||||||||
\(763\) | −15.8869 | −0.575144 | ||||||||
\(764\) | −98.9470 | −3.57978 | ||||||||
\(765\) | 0.677149 | 0.0244824 | ||||||||
\(766\) | −59.2594 | −2.14113 | ||||||||
\(767\) | −22.7093 | −0.819986 | ||||||||
\(768\) | 67.5777 | 2.43850 | ||||||||
\(769\) | 46.5962 | 1.68030 | 0.840150 | − | 0.542353i | \(-0.182467\pi\) | ||||
0.840150 | + | 0.542353i | \(0.182467\pi\) | |||||||
\(770\) | −12.1868 | −0.439183 | ||||||||
\(771\) | 5.42647 | 0.195430 | ||||||||
\(772\) | 6.37802 | 0.229550 | ||||||||
\(773\) | −20.4378 | −0.735097 | −0.367548 | − | 0.930004i | \(-0.619803\pi\) | ||||
−0.367548 | + | 0.930004i | \(0.619803\pi\) | |||||||
\(774\) | 34.1190 | 1.22638 | ||||||||
\(775\) | 4.75331 | 0.170744 | ||||||||
\(776\) | 108.700 | 3.90211 | ||||||||
\(777\) | 3.58771 | 0.128708 | ||||||||
\(778\) | −5.69909 | −0.204322 | ||||||||
\(779\) | −11.6784 | −0.418422 | ||||||||
\(780\) | −19.4820 | −0.697568 | ||||||||
\(781\) | 28.4537 | 1.01815 | ||||||||
\(782\) | 3.48354 | 0.124571 | ||||||||
\(783\) | 2.79382 | 0.0998431 | ||||||||
\(784\) | 47.1594 | 1.68427 | ||||||||
\(785\) | −0.677149 | −0.0241685 | ||||||||
\(786\) | −11.5847 | −0.413211 | ||||||||
\(787\) | 42.8208 | 1.52640 | 0.763199 | − | 0.646163i | \(-0.223628\pi\) | ||||
0.763199 | + | 0.646163i | \(0.223628\pi\) | |||||||
\(788\) | −88.1066 | −3.13867 | ||||||||
\(789\) | −19.4244 | −0.691528 | ||||||||
\(790\) | −10.5354 | −0.374834 | ||||||||
\(791\) | 3.20021 | 0.113786 | ||||||||
\(792\) | 20.7281 | 0.736541 | ||||||||
\(793\) | −73.1207 | −2.59659 | ||||||||
\(794\) | 33.1856 | 1.17771 | ||||||||
\(795\) | 4.30834 | 0.152801 | ||||||||
\(796\) | −16.3756 | −0.580418 | ||||||||
\(797\) | 11.1258 | 0.394095 | 0.197048 | − | 0.980394i | \(-0.436865\pi\) | ||||
0.197048 | + | 0.980394i | \(0.436865\pi\) | |||||||
\(798\) | −11.4610 | −0.405714 | ||||||||
\(799\) | −2.89101 | −0.102277 | ||||||||
\(800\) | 114.225 | 4.03847 | ||||||||
\(801\) | 6.79853 | 0.240214 | ||||||||
\(802\) | 90.9285 | 3.21080 | ||||||||
\(803\) | 1.69129 | 0.0596842 | ||||||||
\(804\) | −36.2626 | −1.27888 | ||||||||
\(805\) | −2.68637 | −0.0946820 | ||||||||
\(806\) | 14.7893 | 0.520930 | ||||||||
\(807\) | −13.0613 | −0.459778 | ||||||||
\(808\) | 6.82788 | 0.240204 | ||||||||
\(809\) | −18.4187 | −0.647566 | −0.323783 | − | 0.946131i | \(-0.604955\pi\) | ||||
−0.323783 | + | 0.946131i | \(0.604955\pi\) | |||||||
\(810\) | 1.86934 | 0.0656818 | ||||||||
\(811\) | 28.6276 | 1.00525 | 0.502626 | − | 0.864504i | \(-0.332367\pi\) | ||||
0.502626 | + | 0.864504i | \(0.332367\pi\) | |||||||
\(812\) | 49.3706 | 1.73257 | ||||||||
\(813\) | −22.4597 | −0.787695 | ||||||||
\(814\) | 6.53274 | 0.228973 | ||||||||
\(815\) | 16.8004 | 0.588491 | ||||||||
\(816\) | −16.3527 | −0.572460 | ||||||||
\(817\) | −16.3210 | −0.571000 | ||||||||
\(818\) | −49.3031 | −1.72384 | ||||||||
\(819\) | 16.0919 | 0.562296 | ||||||||
\(820\) | 33.6604 | 1.17547 | ||||||||
\(821\) | 48.7037 | 1.69977 | 0.849885 | − | 0.526968i | \(-0.176671\pi\) | ||||
0.849885 | + | 0.526968i | \(0.176671\pi\) | |||||||
\(822\) | −37.1700 | −1.29645 | ||||||||
\(823\) | −50.6702 | −1.76625 | −0.883126 | − | 0.469136i | \(-0.844565\pi\) | ||||
−0.883126 | + | 0.469136i | \(0.844565\pi\) | |||||||
\(824\) | 104.131 | 3.62757 | ||||||||
\(825\) | 9.41750 | 0.327875 | ||||||||
\(826\) | 38.5059 | 1.33979 | ||||||||
\(827\) | −20.2177 | −0.703038 | −0.351519 | − | 0.936181i | \(-0.614335\pi\) | ||||
−0.351519 | + | 0.936181i | \(0.614335\pi\) | |||||||
\(828\) | 7.09289 | 0.246495 | ||||||||
\(829\) | −1.11565 | −0.0387481 | −0.0193740 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193740 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(830\) | 7.32443 | 0.254235 | ||||||||
\(831\) | 18.1823 | 0.630736 | ||||||||
\(832\) | 187.993 | 6.51748 | ||||||||
\(833\) | −2.88389 | −0.0999208 | ||||||||
\(834\) | 12.4748 | 0.431966 | ||||||||
\(835\) | −5.13857 | −0.177827 | ||||||||
\(836\) | −15.3922 | −0.532349 | ||||||||
\(837\) | −1.04665 | −0.0361774 | ||||||||
\(838\) | 24.2911 | 0.839122 | ||||||||
\(839\) | −46.7403 | −1.61366 | −0.806828 | − | 0.590787i | \(-0.798817\pi\) | ||||
−0.806828 | + | 0.590787i | \(0.798817\pi\) | |||||||
\(840\) | 21.2798 | 0.734224 | ||||||||
\(841\) | −21.1946 | −0.730847 | ||||||||
\(842\) | −101.809 | −3.50856 | ||||||||
\(843\) | −12.2995 | −0.423617 | ||||||||
\(844\) | 11.2102 | 0.385869 | ||||||||
\(845\) | −8.93778 | −0.307469 | ||||||||
\(846\) | −7.98092 | −0.274390 | ||||||||
\(847\) | −21.0636 | −0.723753 | ||||||||
\(848\) | −104.044 | −3.57287 | ||||||||
\(849\) | 13.4204 | 0.460586 | ||||||||
\(850\) | −12.5372 | −0.430021 | ||||||||
\(851\) | 1.44003 | 0.0493634 | ||||||||
\(852\) | −77.1268 | −2.64232 | ||||||||
\(853\) | −33.0862 | −1.13285 | −0.566424 | − | 0.824114i | \(-0.691674\pi\) | ||||
−0.566424 | + | 0.824114i | \(0.691674\pi\) | |||||||
\(854\) | 123.984 | 4.24263 | ||||||||
\(855\) | −0.894209 | −0.0305813 | ||||||||
\(856\) | 47.4524 | 1.62189 | ||||||||
\(857\) | 37.8379 | 1.29252 | 0.646259 | − | 0.763118i | \(-0.276333\pi\) | ||||
0.646259 | + | 0.763118i | \(0.276333\pi\) | |||||||
\(858\) | 29.3012 | 1.00033 | ||||||||
\(859\) | −39.3519 | −1.34267 | −0.671335 | − | 0.741154i | \(-0.734279\pi\) | ||||
−0.671335 | + | 0.741154i | \(0.734279\pi\) | |||||||
\(860\) | 47.0417 | 1.60411 | ||||||||
\(861\) | −27.8031 | −0.947526 | ||||||||
\(862\) | 29.1365 | 0.992393 | ||||||||
\(863\) | 28.8886 | 0.983379 | 0.491690 | − | 0.870771i | \(-0.336379\pi\) | ||||
0.491690 | + | 0.870771i | \(0.336379\pi\) | |||||||
\(864\) | −25.1516 | −0.855675 | ||||||||
\(865\) | 0.217728 | 0.00740297 | ||||||||
\(866\) | −33.5696 | −1.14074 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −18.4957 | −0.627784 | ||||||||
\(869\) | 11.6870 | 0.396455 | ||||||||
\(870\) | 5.22260 | 0.177063 | ||||||||
\(871\) | −33.0214 | −1.11889 | ||||||||
\(872\) | 50.5121 | 1.71055 | ||||||||
\(873\) | −10.8745 | −0.368047 | ||||||||
\(874\) | −4.60018 | −0.155603 | ||||||||
\(875\) | 20.3125 | 0.686688 | ||||||||
\(876\) | −4.58441 | −0.154893 | ||||||||
\(877\) | −24.2504 | −0.818876 | −0.409438 | − | 0.912338i | \(-0.634275\pi\) | ||||
−0.409438 | + | 0.912338i | \(0.634275\pi\) | |||||||
\(878\) | −108.517 | −3.66229 | ||||||||
\(879\) | 21.0032 | 0.708419 | ||||||||
\(880\) | 22.9622 | 0.774057 | ||||||||
\(881\) | −33.3623 | −1.12400 | −0.562002 | − | 0.827136i | \(-0.689969\pi\) | ||||
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(882\) | −7.96125 | −0.268069 | ||||||||
\(883\) | 25.2569 | 0.849962 | 0.424981 | − | 0.905202i | \(-0.360281\pi\) | ||||
0.424981 | + | 0.905202i | \(0.360281\pi\) | |||||||
\(884\) | −28.7706 | −0.967661 | ||||||||
\(885\) | 3.00431 | 0.100989 | ||||||||
\(886\) | −20.6112 | −0.692448 | ||||||||
\(887\) | −12.6760 | −0.425619 | −0.212809 | − | 0.977094i | \(-0.568261\pi\) | ||||
−0.212809 | + | 0.977094i | \(0.568261\pi\) | |||||||
\(888\) | −11.4070 | −0.382795 | ||||||||
\(889\) | 9.78423 | 0.328152 | ||||||||
\(890\) | 12.7087 | 0.425998 | ||||||||
\(891\) | −2.07367 | −0.0694705 | ||||||||
\(892\) | −16.6237 | −0.556602 | ||||||||
\(893\) | 3.81772 | 0.127755 | ||||||||
\(894\) | 17.8054 | 0.595502 | ||||||||
\(895\) | −13.0629 | −0.436645 | ||||||||
\(896\) | −160.614 | −5.36574 | ||||||||
\(897\) | 6.45893 | 0.215657 | ||||||||
\(898\) | −99.9059 | −3.33390 | ||||||||
\(899\) | −2.92414 | −0.0975257 | ||||||||
\(900\) | −25.5272 | −0.850905 | ||||||||
\(901\) | 6.36246 | 0.211964 | ||||||||
\(902\) | −50.6257 | −1.68565 | ||||||||
\(903\) | −38.8559 | −1.29304 | ||||||||
\(904\) | −10.1750 | −0.338416 | ||||||||
\(905\) | 7.08253 | 0.235431 | ||||||||
\(906\) | −51.9216 | −1.72498 | ||||||||
\(907\) | −44.8810 | −1.49025 | −0.745124 | − | 0.666925i | \(-0.767610\pi\) | ||||
−0.745124 | + | 0.666925i | \(0.767610\pi\) | |||||||
\(908\) | −70.8946 | −2.35272 | ||||||||
\(909\) | −0.683072 | −0.0226561 | ||||||||
\(910\) | 30.0812 | 0.997181 | ||||||||
\(911\) | −47.8158 | −1.58421 | −0.792104 | − | 0.610386i | \(-0.791014\pi\) | ||||
−0.792104 | + | 0.610386i | \(0.791014\pi\) | |||||||
\(912\) | 21.5946 | 0.715068 | ||||||||
\(913\) | −8.12504 | −0.268900 | ||||||||
\(914\) | −11.0690 | −0.366131 | ||||||||
\(915\) | 9.67345 | 0.319794 | ||||||||
\(916\) | 47.3112 | 1.56321 | ||||||||
\(917\) | 13.1930 | 0.435671 | ||||||||
\(918\) | 2.76060 | 0.0911133 | ||||||||
\(919\) | −16.5303 | −0.545285 | −0.272642 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272642 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(920\) | 8.54125 | 0.281597 | ||||||||
\(921\) | −2.31157 | −0.0761689 | ||||||||
\(922\) | 38.6659 | 1.27339 | ||||||||
\(923\) | −70.2332 | −2.31175 | ||||||||
\(924\) | −36.6445 | −1.20552 | ||||||||
\(925\) | −5.18262 | −0.170403 | ||||||||
\(926\) | 112.757 | 3.70542 | ||||||||
\(927\) | −10.4174 | −0.342152 | ||||||||
\(928\) | −70.2692 | −2.30670 | ||||||||
\(929\) | −34.1173 | −1.11935 | −0.559676 | − | 0.828712i | \(-0.689074\pi\) | ||||
−0.559676 | + | 0.828712i | \(0.689074\pi\) | |||||||
\(930\) | −1.95653 | −0.0641573 | ||||||||
\(931\) | 3.80831 | 0.124812 | ||||||||
\(932\) | 37.8107 | 1.23853 | ||||||||
\(933\) | 2.29825 | 0.0752414 | ||||||||
\(934\) | −54.8440 | −1.79455 | ||||||||
\(935\) | −1.40418 | −0.0459217 | ||||||||
\(936\) | −51.1639 | −1.67234 | ||||||||
\(937\) | −38.1875 | −1.24753 | −0.623766 | − | 0.781611i | \(-0.714398\pi\) | ||||
−0.623766 | + | 0.781611i | \(0.714398\pi\) | |||||||
\(938\) | 55.9912 | 1.82818 | ||||||||
\(939\) | 7.60296 | 0.248113 | ||||||||
\(940\) | −11.0037 | −0.358902 | ||||||||
\(941\) | −3.24152 | −0.105671 | −0.0528353 | − | 0.998603i | \(-0.516826\pi\) | ||||
−0.0528353 | + | 0.998603i | \(0.516826\pi\) | |||||||
\(942\) | −2.76060 | −0.0899451 | ||||||||
\(943\) | −11.1595 | −0.363404 | ||||||||
\(944\) | −72.5523 | −2.36138 | ||||||||
\(945\) | −2.12887 | −0.0692520 | ||||||||
\(946\) | −70.7515 | −2.30033 | ||||||||
\(947\) | −19.4148 | −0.630898 | −0.315449 | − | 0.948943i | \(-0.602155\pi\) | ||||
−0.315449 | + | 0.948943i | \(0.602155\pi\) | |||||||
\(948\) | −31.6789 | −1.02888 | ||||||||
\(949\) | −4.17466 | −0.135515 | ||||||||
\(950\) | 16.5559 | 0.537146 | ||||||||
\(951\) | −0.421117 | −0.0136557 | ||||||||
\(952\) | 31.4256 | 1.01851 | ||||||||
\(953\) | 22.8141 | 0.739023 | 0.369511 | − | 0.929226i | \(-0.379525\pi\) | ||||
0.369511 | + | 0.929226i | \(0.379525\pi\) | |||||||
\(954\) | 17.5642 | 0.568662 | ||||||||
\(955\) | 11.9201 | 0.385726 | ||||||||
\(956\) | 76.8850 | 2.48664 | ||||||||
\(957\) | −5.79346 | −0.187276 | ||||||||
\(958\) | 55.6256 | 1.79718 | ||||||||
\(959\) | 42.3305 | 1.36692 | ||||||||
\(960\) | −24.8704 | −0.802687 | ||||||||
\(961\) | −29.9045 | −0.964662 | ||||||||
\(962\) | −16.1250 | −0.519891 | ||||||||
\(963\) | −4.74721 | −0.152977 | ||||||||
\(964\) | −49.9688 | −1.60939 | ||||||||
\(965\) | −0.768359 | −0.0247344 | ||||||||
\(966\) | −10.9518 | −0.352367 | ||||||||
\(967\) | 2.41482 | 0.0776553 | 0.0388277 | − | 0.999246i | \(-0.487638\pi\) | ||||
0.0388277 | + | 0.999246i | \(0.487638\pi\) | |||||||
\(968\) | 66.9712 | 2.15254 | ||||||||
\(969\) | −1.32055 | −0.0424221 | ||||||||
\(970\) | −20.3282 | −0.652698 | ||||||||
\(971\) | −36.1202 | −1.15915 | −0.579576 | − | 0.814918i | \(-0.696782\pi\) | ||||
−0.579576 | + | 0.814918i | \(0.696782\pi\) | |||||||
\(972\) | 5.62090 | 0.180291 | ||||||||
\(973\) | −14.2067 | −0.455446 | ||||||||
\(974\) | −48.4451 | −1.55228 | ||||||||
\(975\) | −23.2455 | −0.744453 | ||||||||
\(976\) | −233.608 | −7.47760 | ||||||||
\(977\) | −23.1685 | −0.741226 | −0.370613 | − | 0.928787i | \(-0.620852\pi\) | ||||
−0.370613 | + | 0.928787i | \(0.620852\pi\) | |||||||
\(978\) | 68.4916 | 2.19012 | ||||||||
\(979\) | −14.0979 | −0.450571 | ||||||||
\(980\) | −10.9766 | −0.350635 | ||||||||
\(981\) | −5.05330 | −0.161339 | ||||||||
\(982\) | −50.8227 | −1.62182 | ||||||||
\(983\) | −37.6772 | −1.20171 | −0.600857 | − | 0.799356i | \(-0.705174\pi\) | ||||
−0.600857 | + | 0.799356i | \(0.705174\pi\) | |||||||
\(984\) | 88.3993 | 2.81807 | ||||||||
\(985\) | 10.6142 | 0.338196 | ||||||||
\(986\) | 7.71262 | 0.245620 | ||||||||
\(987\) | 9.08895 | 0.289305 | ||||||||
\(988\) | 37.9930 | 1.20872 | ||||||||
\(989\) | −15.5959 | −0.495920 | ||||||||
\(990\) | −3.87639 | −0.123200 | ||||||||
\(991\) | −13.8694 | −0.440575 | −0.220287 | − | 0.975435i | \(-0.570700\pi\) | ||||
−0.220287 | + | 0.975435i | \(0.570700\pi\) | |||||||
\(992\) | 26.3248 | 0.835815 | ||||||||
\(993\) | −6.39080 | −0.202806 | ||||||||
\(994\) | 119.087 | 3.77723 | ||||||||
\(995\) | 1.97277 | 0.0625409 | ||||||||
\(996\) | 22.0238 | 0.697850 | ||||||||
\(997\) | 4.02316 | 0.127415 | 0.0637074 | − | 0.997969i | \(-0.479708\pi\) | ||||
0.0637074 | + | 0.997969i | \(0.479708\pi\) | |||||||
\(998\) | −104.100 | −3.29521 | ||||||||
\(999\) | 1.14118 | 0.0361052 |
(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 | 8007.2.a.e.1.2 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.2 | ✓ | 46 | 1.1 | even | 1 | trivial |