Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29335 | −1.62164 | −0.810820 | − | 0.585296i | \(-0.800978\pi\) | ||||
−0.810820 | + | 0.585296i | \(0.800978\pi\) | |||||||
\(3\) | 2.59523 | 1.49836 | 0.749180 | − | 0.662367i | \(-0.230448\pi\) | ||||
0.749180 | + | 0.662367i | \(0.230448\pi\) | |||||||
\(4\) | 3.25943 | 1.62972 | ||||||||
\(5\) | 0.281199 | 0.125756 | 0.0628779 | − | 0.998021i | \(-0.479972\pi\) | ||||
0.0628779 | + | 0.998021i | \(0.479972\pi\) | |||||||
\(6\) | −5.95177 | −2.42980 | ||||||||
\(7\) | −4.71795 | −1.78322 | −0.891609 | − | 0.452806i | \(-0.850423\pi\) | ||||
−0.891609 | + | 0.452806i | \(0.850423\pi\) | |||||||
\(8\) | −2.88831 | −1.02117 | ||||||||
\(9\) | 3.73524 | 1.24508 | ||||||||
\(10\) | −0.644885 | −0.203931 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 8.45899 | 2.44190 | ||||||||
\(13\) | 1.91363 | 0.530746 | 0.265373 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265373 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(14\) | 10.8199 | 2.89174 | ||||||||
\(15\) | 0.729776 | 0.188427 | ||||||||
\(16\) | 0.105032 | 0.0262580 | ||||||||
\(17\) | −3.77647 | −0.915929 | −0.457964 | − | 0.888971i | \(-0.651421\pi\) | ||||
−0.457964 | + | 0.888971i | \(0.651421\pi\) | |||||||
\(18\) | −8.56619 | −2.01907 | ||||||||
\(19\) | 7.73570 | 1.77469 | 0.887346 | − | 0.461104i | \(-0.152547\pi\) | ||||
0.887346 | + | 0.461104i | \(0.152547\pi\) | |||||||
\(20\) | 0.916548 | 0.204946 | ||||||||
\(21\) | −12.2442 | −2.67190 | ||||||||
\(22\) | 2.29335 | 0.488943 | ||||||||
\(23\) | 9.13416 | 1.90460 | 0.952302 | − | 0.305157i | \(-0.0987090\pi\) | ||||
0.952302 | + | 0.305157i | \(0.0987090\pi\) | |||||||
\(24\) | −7.49584 | −1.53008 | ||||||||
\(25\) | −4.92093 | −0.984185 | ||||||||
\(26\) | −4.38862 | −0.860679 | ||||||||
\(27\) | 1.90812 | 0.367217 | ||||||||
\(28\) | −15.3778 | −2.90614 | ||||||||
\(29\) | −2.69092 | −0.499691 | −0.249845 | − | 0.968286i | \(-0.580380\pi\) | ||||
−0.249845 | + | 0.968286i | \(0.580380\pi\) | |||||||
\(30\) | −1.67363 | −0.305561 | ||||||||
\(31\) | −2.71223 | −0.487130 | −0.243565 | − | 0.969885i | \(-0.578317\pi\) | ||||
−0.243565 | + | 0.969885i | \(0.578317\pi\) | |||||||
\(32\) | 5.53575 | 0.978591 | ||||||||
\(33\) | −2.59523 | −0.451772 | ||||||||
\(34\) | 8.66075 | 1.48531 | ||||||||
\(35\) | −1.32668 | −0.224250 | ||||||||
\(36\) | 12.1748 | 2.02913 | ||||||||
\(37\) | 11.2479 | 1.84915 | 0.924575 | − | 0.380999i | \(-0.124420\pi\) | ||||
0.924575 | + | 0.380999i | \(0.124420\pi\) | |||||||
\(38\) | −17.7406 | −2.87791 | ||||||||
\(39\) | 4.96632 | 0.795248 | ||||||||
\(40\) | −0.812189 | −0.128418 | ||||||||
\(41\) | 7.75370 | 1.21092 | 0.605462 | − | 0.795874i | \(-0.292988\pi\) | ||||
0.605462 | + | 0.795874i | \(0.292988\pi\) | |||||||
\(42\) | 28.0802 | 4.33286 | ||||||||
\(43\) | 0.287443 | 0.0438346 | 0.0219173 | − | 0.999760i | \(-0.493023\pi\) | ||||
0.0219173 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(44\) | −3.25943 | −0.491378 | ||||||||
\(45\) | 1.05034 | 0.156576 | ||||||||
\(46\) | −20.9478 | −3.08858 | ||||||||
\(47\) | 7.01709 | 1.02355 | 0.511774 | − | 0.859120i | \(-0.328989\pi\) | ||||
0.511774 | + | 0.859120i | \(0.328989\pi\) | |||||||
\(48\) | 0.272583 | 0.0393440 | ||||||||
\(49\) | 15.2591 | 2.17987 | ||||||||
\(50\) | 11.2854 | 1.59599 | ||||||||
\(51\) | −9.80082 | −1.37239 | ||||||||
\(52\) | 6.23735 | 0.864965 | ||||||||
\(53\) | 6.07298 | 0.834187 | 0.417094 | − | 0.908864i | \(-0.363049\pi\) | ||||
0.417094 | + | 0.908864i | \(0.363049\pi\) | |||||||
\(54\) | −4.37597 | −0.595494 | ||||||||
\(55\) | −0.281199 | −0.0379168 | ||||||||
\(56\) | 13.6269 | 1.82097 | ||||||||
\(57\) | 20.0760 | 2.65913 | ||||||||
\(58\) | 6.17120 | 0.810319 | ||||||||
\(59\) | 1.04516 | 0.136069 | 0.0680343 | − | 0.997683i | \(-0.478327\pi\) | ||||
0.0680343 | + | 0.997683i | \(0.478327\pi\) | |||||||
\(60\) | 2.37866 | 0.307083 | ||||||||
\(61\) | 1.72594 | 0.220984 | 0.110492 | − | 0.993877i | \(-0.464757\pi\) | ||||
0.110492 | + | 0.993877i | \(0.464757\pi\) | |||||||
\(62\) | 6.22007 | 0.789950 | ||||||||
\(63\) | −17.6227 | −2.22025 | ||||||||
\(64\) | −12.9054 | −1.61318 | ||||||||
\(65\) | 0.538110 | 0.0667444 | ||||||||
\(66\) | 5.95177 | 0.732612 | ||||||||
\(67\) | 3.00535 | 0.367161 | 0.183581 | − | 0.983005i | \(-0.441231\pi\) | ||||
0.183581 | + | 0.983005i | \(0.441231\pi\) | |||||||
\(68\) | −12.3091 | −1.49270 | ||||||||
\(69\) | 23.7053 | 2.85378 | ||||||||
\(70\) | 3.04254 | 0.363653 | ||||||||
\(71\) | 9.41019 | 1.11678 | 0.558392 | − | 0.829577i | \(-0.311418\pi\) | ||||
0.558392 | + | 0.829577i | \(0.311418\pi\) | |||||||
\(72\) | −10.7885 | −1.27144 | ||||||||
\(73\) | 1.80168 | 0.210871 | 0.105435 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105435 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(74\) | −25.7954 | −2.99866 | ||||||||
\(75\) | −12.7710 | −1.47466 | ||||||||
\(76\) | 25.2140 | 2.89224 | ||||||||
\(77\) | 4.71795 | 0.537661 | ||||||||
\(78\) | −11.3895 | −1.28961 | ||||||||
\(79\) | 3.95095 | 0.444516 | 0.222258 | − | 0.974988i | \(-0.428657\pi\) | ||||
0.222258 | + | 0.974988i | \(0.428657\pi\) | |||||||
\(80\) | 0.0295349 | 0.00330210 | ||||||||
\(81\) | −6.25371 | −0.694856 | ||||||||
\(82\) | −17.7819 | −1.96368 | ||||||||
\(83\) | −7.21069 | −0.791476 | −0.395738 | − | 0.918363i | \(-0.629511\pi\) | ||||
−0.395738 | + | 0.918363i | \(0.629511\pi\) | |||||||
\(84\) | −39.9091 | −4.35444 | ||||||||
\(85\) | −1.06194 | −0.115183 | ||||||||
\(86\) | −0.659205 | −0.0710840 | ||||||||
\(87\) | −6.98356 | −0.748716 | ||||||||
\(88\) | 2.88831 | 0.307895 | ||||||||
\(89\) | 13.1047 | 1.38910 | 0.694550 | − | 0.719444i | \(-0.255604\pi\) | ||||
0.694550 | + | 0.719444i | \(0.255604\pi\) | |||||||
\(90\) | −2.40880 | −0.253910 | ||||||||
\(91\) | −9.02842 | −0.946436 | ||||||||
\(92\) | 29.7722 | 3.10396 | ||||||||
\(93\) | −7.03886 | −0.729896 | ||||||||
\(94\) | −16.0926 | −1.65983 | ||||||||
\(95\) | 2.17527 | 0.223178 | ||||||||
\(96\) | 14.3666 | 1.46628 | ||||||||
\(97\) | −17.8476 | −1.81215 | −0.906074 | − | 0.423120i | \(-0.860935\pi\) | ||||
−0.906074 | + | 0.423120i | \(0.860935\pi\) | |||||||
\(98\) | −34.9943 | −3.53496 | ||||||||
\(99\) | −3.73524 | −0.375406 | ||||||||
\(100\) | −16.0394 | −1.60394 | ||||||||
\(101\) | 8.23021 | 0.818937 | 0.409468 | − | 0.912324i | \(-0.365714\pi\) | ||||
0.409468 | + | 0.912324i | \(0.365714\pi\) | |||||||
\(102\) | 22.4767 | 2.22552 | ||||||||
\(103\) | −16.5081 | −1.62660 | −0.813298 | − | 0.581847i | \(-0.802330\pi\) | ||||
−0.813298 | + | 0.581847i | \(0.802330\pi\) | |||||||
\(104\) | −5.52716 | −0.541983 | ||||||||
\(105\) | −3.44305 | −0.336007 | ||||||||
\(106\) | −13.9274 | −1.35275 | ||||||||
\(107\) | −12.2154 | −1.18091 | −0.590456 | − | 0.807070i | \(-0.701052\pi\) | ||||
−0.590456 | + | 0.807070i | \(0.701052\pi\) | |||||||
\(108\) | 6.21938 | 0.598460 | ||||||||
\(109\) | −1.64547 | −0.157608 | −0.0788038 | − | 0.996890i | \(-0.525110\pi\) | ||||
−0.0788038 | + | 0.996890i | \(0.525110\pi\) | |||||||
\(110\) | 0.644885 | 0.0614874 | ||||||||
\(111\) | 29.1911 | 2.77069 | ||||||||
\(112\) | −0.495537 | −0.0468238 | ||||||||
\(113\) | 6.81133 | 0.640756 | 0.320378 | − | 0.947290i | \(-0.396190\pi\) | ||||
0.320378 | + | 0.947290i | \(0.396190\pi\) | |||||||
\(114\) | −46.0411 | −4.31214 | ||||||||
\(115\) | 2.56851 | 0.239515 | ||||||||
\(116\) | −8.77086 | −0.814354 | ||||||||
\(117\) | 7.14787 | 0.660821 | ||||||||
\(118\) | −2.39692 | −0.220654 | ||||||||
\(119\) | 17.8172 | 1.63330 | ||||||||
\(120\) | −2.10782 | −0.192417 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.95818 | −0.358357 | ||||||||
\(123\) | 20.1227 | 1.81440 | ||||||||
\(124\) | −8.84031 | −0.793884 | ||||||||
\(125\) | −2.78975 | −0.249523 | ||||||||
\(126\) | 40.4149 | 3.60044 | ||||||||
\(127\) | −4.54374 | −0.403192 | −0.201596 | − | 0.979469i | \(-0.564613\pi\) | ||||
−0.201596 | + | 0.979469i | \(0.564613\pi\) | |||||||
\(128\) | 18.5251 | 1.63741 | ||||||||
\(129\) | 0.745981 | 0.0656800 | ||||||||
\(130\) | −1.23407 | −0.108235 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −8.45899 | −0.736260 | ||||||||
\(133\) | −36.4967 | −3.16466 | ||||||||
\(134\) | −6.89229 | −0.595403 | ||||||||
\(135\) | 0.536560 | 0.0461797 | ||||||||
\(136\) | 10.9076 | 0.935321 | ||||||||
\(137\) | 11.3341 | 0.968340 | 0.484170 | − | 0.874974i | \(-0.339122\pi\) | ||||
0.484170 | + | 0.874974i | \(0.339122\pi\) | |||||||
\(138\) | −54.3644 | −4.62780 | ||||||||
\(139\) | 3.87976 | 0.329077 | 0.164538 | − | 0.986371i | \(-0.447387\pi\) | ||||
0.164538 | + | 0.986371i | \(0.447387\pi\) | |||||||
\(140\) | −4.32423 | −0.365464 | ||||||||
\(141\) | 18.2110 | 1.53364 | ||||||||
\(142\) | −21.5808 | −1.81102 | ||||||||
\(143\) | −1.91363 | −0.160026 | ||||||||
\(144\) | 0.392320 | 0.0326933 | ||||||||
\(145\) | −0.756682 | −0.0628390 | ||||||||
\(146\) | −4.13188 | −0.341956 | ||||||||
\(147\) | 39.6009 | 3.26622 | ||||||||
\(148\) | 36.6619 | 3.01359 | ||||||||
\(149\) | 18.7850 | 1.53893 | 0.769463 | − | 0.638692i | \(-0.220524\pi\) | ||||
0.769463 | + | 0.638692i | \(0.220524\pi\) | |||||||
\(150\) | 29.2882 | 2.39137 | ||||||||
\(151\) | 0.153103 | 0.0124594 | 0.00622968 | − | 0.999981i | \(-0.498017\pi\) | ||||
0.00622968 | + | 0.999981i | \(0.498017\pi\) | |||||||
\(152\) | −22.3431 | −1.81227 | ||||||||
\(153\) | −14.1060 | −1.14040 | ||||||||
\(154\) | −10.8199 | −0.871892 | ||||||||
\(155\) | −0.762674 | −0.0612594 | ||||||||
\(156\) | 16.1874 | 1.29603 | ||||||||
\(157\) | −21.6506 | −1.72790 | −0.863951 | − | 0.503575i | \(-0.832018\pi\) | ||||
−0.863951 | + | 0.503575i | \(0.832018\pi\) | |||||||
\(158\) | −9.06088 | −0.720845 | ||||||||
\(159\) | 15.7608 | 1.24991 | ||||||||
\(160\) | 1.55664 | 0.123064 | ||||||||
\(161\) | −43.0945 | −3.39632 | ||||||||
\(162\) | 14.3419 | 1.12681 | ||||||||
\(163\) | 7.12788 | 0.558299 | 0.279150 | − | 0.960248i | \(-0.409947\pi\) | ||||
0.279150 | + | 0.960248i | \(0.409947\pi\) | |||||||
\(164\) | 25.2727 | 1.97346 | ||||||||
\(165\) | −0.729776 | −0.0568130 | ||||||||
\(166\) | 16.5366 | 1.28349 | ||||||||
\(167\) | 12.1770 | 0.942283 | 0.471142 | − | 0.882058i | \(-0.343842\pi\) | ||||
0.471142 | + | 0.882058i | \(0.343842\pi\) | |||||||
\(168\) | 35.3650 | 2.72847 | ||||||||
\(169\) | −9.33802 | −0.718309 | ||||||||
\(170\) | 2.43539 | 0.186786 | ||||||||
\(171\) | 28.8947 | 2.20963 | ||||||||
\(172\) | 0.936900 | 0.0714380 | ||||||||
\(173\) | −0.905373 | −0.0688343 | −0.0344171 | − | 0.999408i | \(-0.510957\pi\) | ||||
−0.0344171 | + | 0.999408i | \(0.510957\pi\) | |||||||
\(174\) | 16.0157 | 1.21415 | ||||||||
\(175\) | 23.2167 | 1.75502 | ||||||||
\(176\) | −0.105032 | −0.00791710 | ||||||||
\(177\) | 2.71244 | 0.203880 | ||||||||
\(178\) | −30.0537 | −2.25262 | ||||||||
\(179\) | 10.2399 | 0.765367 | 0.382684 | − | 0.923879i | \(-0.375000\pi\) | ||||
0.382684 | + | 0.923879i | \(0.375000\pi\) | |||||||
\(180\) | 3.42352 | 0.255174 | ||||||||
\(181\) | 16.6370 | 1.23662 | 0.618308 | − | 0.785936i | \(-0.287818\pi\) | ||||
0.618308 | + | 0.785936i | \(0.287818\pi\) | |||||||
\(182\) | 20.7053 | 1.53478 | ||||||||
\(183\) | 4.47922 | 0.331114 | ||||||||
\(184\) | −26.3823 | −1.94493 | ||||||||
\(185\) | 3.16291 | 0.232541 | ||||||||
\(186\) | 16.1425 | 1.18363 | ||||||||
\(187\) | 3.77647 | 0.276163 | ||||||||
\(188\) | 22.8717 | 1.66809 | ||||||||
\(189\) | −9.00241 | −0.654829 | ||||||||
\(190\) | −4.98864 | −0.361914 | ||||||||
\(191\) | 3.34395 | 0.241960 | 0.120980 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120980 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(192\) | −33.4927 | −2.41712 | ||||||||
\(193\) | 23.3847 | 1.68327 | 0.841633 | − | 0.540049i | \(-0.181594\pi\) | ||||
0.841633 | + | 0.540049i | \(0.181594\pi\) | |||||||
\(194\) | 40.9307 | 2.93865 | ||||||||
\(195\) | 1.39652 | 0.100007 | ||||||||
\(196\) | 49.7359 | 3.55257 | ||||||||
\(197\) | −22.4252 | −1.59773 | −0.798864 | − | 0.601511i | \(-0.794566\pi\) | ||||
−0.798864 | + | 0.601511i | \(0.794566\pi\) | |||||||
\(198\) | 8.56619 | 0.608773 | ||||||||
\(199\) | −9.54885 | −0.676900 | −0.338450 | − | 0.940984i | \(-0.609903\pi\) | ||||
−0.338450 | + | 0.940984i | \(0.609903\pi\) | |||||||
\(200\) | 14.2132 | 1.00502 | ||||||||
\(201\) | 7.79957 | 0.550140 | ||||||||
\(202\) | −18.8747 | −1.32802 | ||||||||
\(203\) | 12.6956 | 0.891058 | ||||||||
\(204\) | −31.9451 | −2.23661 | ||||||||
\(205\) | 2.18033 | 0.152281 | ||||||||
\(206\) | 37.8589 | 2.63775 | ||||||||
\(207\) | 34.1183 | 2.37138 | ||||||||
\(208\) | 0.200993 | 0.0139363 | ||||||||
\(209\) | −7.73570 | −0.535090 | ||||||||
\(210\) | 7.89610 | 0.544883 | ||||||||
\(211\) | −3.55835 | −0.244967 | −0.122483 | − | 0.992471i | \(-0.539086\pi\) | ||||
−0.122483 | + | 0.992471i | \(0.539086\pi\) | |||||||
\(212\) | 19.7945 | 1.35949 | ||||||||
\(213\) | 24.4216 | 1.67334 | ||||||||
\(214\) | 28.0142 | 1.91501 | ||||||||
\(215\) | 0.0808285 | 0.00551246 | ||||||||
\(216\) | −5.51124 | −0.374992 | ||||||||
\(217\) | 12.7962 | 0.868659 | ||||||||
\(218\) | 3.77363 | 0.255583 | ||||||||
\(219\) | 4.67578 | 0.315960 | ||||||||
\(220\) | −0.916548 | −0.0617936 | ||||||||
\(221\) | −7.22677 | −0.486125 | ||||||||
\(222\) | −66.9452 | −4.49306 | ||||||||
\(223\) | −15.4303 | −1.03329 | −0.516644 | − | 0.856201i | \(-0.672819\pi\) | ||||
−0.516644 | + | 0.856201i | \(0.672819\pi\) | |||||||
\(224\) | −26.1174 | −1.74504 | ||||||||
\(225\) | −18.3808 | −1.22539 | ||||||||
\(226\) | −15.6207 | −1.03908 | ||||||||
\(227\) | 3.65157 | 0.242363 | 0.121182 | − | 0.992630i | \(-0.461332\pi\) | ||||
0.121182 | + | 0.992630i | \(0.461332\pi\) | |||||||
\(228\) | 65.4362 | 4.33362 | ||||||||
\(229\) | −26.7903 | −1.77035 | −0.885176 | − | 0.465256i | \(-0.845962\pi\) | ||||
−0.885176 | + | 0.465256i | \(0.845962\pi\) | |||||||
\(230\) | −5.89049 | −0.388407 | ||||||||
\(231\) | 12.2442 | 0.805609 | ||||||||
\(232\) | 7.77221 | 0.510271 | ||||||||
\(233\) | −21.8606 | −1.43213 | −0.716067 | − | 0.698031i | \(-0.754060\pi\) | ||||
−0.716067 | + | 0.698031i | \(0.754060\pi\) | |||||||
\(234\) | −16.3925 | −1.07161 | ||||||||
\(235\) | 1.97320 | 0.128717 | ||||||||
\(236\) | 3.40663 | 0.221753 | ||||||||
\(237\) | 10.2536 | 0.666045 | ||||||||
\(238\) | −40.8610 | −2.64863 | ||||||||
\(239\) | 20.1220 | 1.30159 | 0.650794 | − | 0.759255i | \(-0.274436\pi\) | ||||
0.650794 | + | 0.759255i | \(0.274436\pi\) | |||||||
\(240\) | 0.0766499 | 0.00494773 | ||||||||
\(241\) | 2.77843 | 0.178974 | 0.0894872 | − | 0.995988i | \(-0.471477\pi\) | ||||
0.0894872 | + | 0.995988i | \(0.471477\pi\) | |||||||
\(242\) | −2.29335 | −0.147422 | ||||||||
\(243\) | −21.9542 | −1.40836 | ||||||||
\(244\) | 5.62559 | 0.360142 | ||||||||
\(245\) | 4.29083 | 0.274131 | ||||||||
\(246\) | −46.1482 | −2.94230 | ||||||||
\(247\) | 14.8033 | 0.941910 | ||||||||
\(248\) | 7.83375 | 0.497444 | ||||||||
\(249\) | −18.7134 | −1.18592 | ||||||||
\(250\) | 6.39786 | 0.404636 | ||||||||
\(251\) | −5.90539 | −0.372745 | −0.186372 | − | 0.982479i | \(-0.559673\pi\) | ||||
−0.186372 | + | 0.982479i | \(0.559673\pi\) | |||||||
\(252\) | −57.4399 | −3.61838 | ||||||||
\(253\) | −9.13416 | −0.574260 | ||||||||
\(254\) | 10.4204 | 0.653832 | ||||||||
\(255\) | −2.75598 | −0.172586 | ||||||||
\(256\) | −16.6737 | −1.04210 | ||||||||
\(257\) | −27.9676 | −1.74457 | −0.872287 | − | 0.488994i | \(-0.837364\pi\) | ||||
−0.872287 | + | 0.488994i | \(0.837364\pi\) | |||||||
\(258\) | −1.71079 | −0.106509 | ||||||||
\(259\) | −53.0673 | −3.29744 | ||||||||
\(260\) | 1.75393 | 0.108774 | ||||||||
\(261\) | −10.0512 | −0.622155 | ||||||||
\(262\) | −2.29335 | −0.141683 | ||||||||
\(263\) | 12.2507 | 0.755413 | 0.377707 | − | 0.925925i | \(-0.376713\pi\) | ||||
0.377707 | + | 0.925925i | \(0.376713\pi\) | |||||||
\(264\) | 7.49584 | 0.461337 | ||||||||
\(265\) | 1.70771 | 0.104904 | ||||||||
\(266\) | 83.6995 | 5.13194 | ||||||||
\(267\) | 34.0099 | 2.08137 | ||||||||
\(268\) | 9.79572 | 0.598369 | ||||||||
\(269\) | 19.8139 | 1.20808 | 0.604038 | − | 0.796956i | \(-0.293558\pi\) | ||||
0.604038 | + | 0.796956i | \(0.293558\pi\) | |||||||
\(270\) | −1.23052 | −0.0748869 | ||||||||
\(271\) | 10.3760 | 0.630296 | 0.315148 | − | 0.949043i | \(-0.397946\pi\) | ||||
0.315148 | + | 0.949043i | \(0.397946\pi\) | |||||||
\(272\) | −0.396651 | −0.0240505 | ||||||||
\(273\) | −23.4309 | −1.41810 | ||||||||
\(274\) | −25.9931 | −1.57030 | ||||||||
\(275\) | 4.92093 | 0.296743 | ||||||||
\(276\) | 77.2657 | 4.65085 | ||||||||
\(277\) | 7.68149 | 0.461536 | 0.230768 | − | 0.973009i | \(-0.425876\pi\) | ||||
0.230768 | + | 0.973009i | \(0.425876\pi\) | |||||||
\(278\) | −8.89762 | −0.533644 | ||||||||
\(279\) | −10.1308 | −0.606516 | ||||||||
\(280\) | 3.83187 | 0.228998 | ||||||||
\(281\) | −11.0934 | −0.661777 | −0.330888 | − | 0.943670i | \(-0.607348\pi\) | ||||
−0.330888 | + | 0.943670i | \(0.607348\pi\) | |||||||
\(282\) | −41.7641 | −2.48702 | ||||||||
\(283\) | −9.93802 | −0.590754 | −0.295377 | − | 0.955381i | \(-0.595445\pi\) | ||||
−0.295377 | + | 0.955381i | \(0.595445\pi\) | |||||||
\(284\) | 30.6719 | 1.82004 | ||||||||
\(285\) | 5.64533 | 0.334401 | ||||||||
\(286\) | 4.38862 | 0.259504 | ||||||||
\(287\) | −36.5816 | −2.15934 | ||||||||
\(288\) | 20.6773 | 1.21842 | ||||||||
\(289\) | −2.73827 | −0.161075 | ||||||||
\(290\) | 1.73533 | 0.101902 | ||||||||
\(291\) | −46.3187 | −2.71525 | ||||||||
\(292\) | 5.87245 | 0.343659 | ||||||||
\(293\) | 18.7157 | 1.09338 | 0.546690 | − | 0.837335i | \(-0.315887\pi\) | ||||
0.546690 | + | 0.837335i | \(0.315887\pi\) | |||||||
\(294\) | −90.8185 | −5.29664 | ||||||||
\(295\) | 0.293898 | 0.0171114 | ||||||||
\(296\) | −32.4876 | −1.88830 | ||||||||
\(297\) | −1.90812 | −0.110720 | ||||||||
\(298\) | −43.0804 | −2.49558 | ||||||||
\(299\) | 17.4794 | 1.01086 | ||||||||
\(300\) | −41.6261 | −2.40328 | ||||||||
\(301\) | −1.35614 | −0.0781667 | ||||||||
\(302\) | −0.351119 | −0.0202046 | ||||||||
\(303\) | 21.3593 | 1.22706 | ||||||||
\(304\) | 0.812497 | 0.0465999 | ||||||||
\(305\) | 0.485332 | 0.0277901 | ||||||||
\(306\) | 32.3500 | 1.84932 | ||||||||
\(307\) | 30.9048 | 1.76383 | 0.881916 | − | 0.471406i | \(-0.156253\pi\) | ||||
0.881916 | + | 0.471406i | \(0.156253\pi\) | |||||||
\(308\) | 15.3778 | 0.876234 | ||||||||
\(309\) | −42.8425 | −2.43722 | ||||||||
\(310\) | 1.74907 | 0.0993408 | ||||||||
\(311\) | 17.3892 | 0.986053 | 0.493027 | − | 0.870014i | \(-0.335890\pi\) | ||||
0.493027 | + | 0.870014i | \(0.335890\pi\) | |||||||
\(312\) | −14.3443 | −0.812085 | ||||||||
\(313\) | −23.6434 | −1.33640 | −0.668202 | − | 0.743980i | \(-0.732936\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(314\) | 49.6522 | 2.80204 | ||||||||
\(315\) | −4.95547 | −0.279209 | ||||||||
\(316\) | 12.8778 | 0.724435 | ||||||||
\(317\) | 4.42026 | 0.248267 | 0.124133 | − | 0.992266i | \(-0.460385\pi\) | ||||
0.124133 | + | 0.992266i | \(0.460385\pi\) | |||||||
\(318\) | −36.1449 | −2.02691 | ||||||||
\(319\) | 2.69092 | 0.150662 | ||||||||
\(320\) | −3.62899 | −0.202867 | ||||||||
\(321\) | −31.7019 | −1.76943 | ||||||||
\(322\) | 98.8306 | 5.50762 | ||||||||
\(323\) | −29.2137 | −1.62549 | ||||||||
\(324\) | −20.3835 | −1.13242 | ||||||||
\(325\) | −9.41684 | −0.522352 | ||||||||
\(326\) | −16.3467 | −0.905360 | ||||||||
\(327\) | −4.27038 | −0.236153 | ||||||||
\(328\) | −22.3951 | −1.23656 | ||||||||
\(329\) | −33.1063 | −1.82521 | ||||||||
\(330\) | 1.67363 | 0.0921302 | ||||||||
\(331\) | 0.709655 | 0.0390062 | 0.0195031 | − | 0.999810i | \(-0.493792\pi\) | ||||
0.0195031 | + | 0.999810i | \(0.493792\pi\) | |||||||
\(332\) | −23.5027 | −1.28988 | ||||||||
\(333\) | 42.0138 | 2.30234 | ||||||||
\(334\) | −27.9260 | −1.52804 | ||||||||
\(335\) | 0.845099 | 0.0461727 | ||||||||
\(336\) | −1.28603 | −0.0701589 | ||||||||
\(337\) | −1.45977 | −0.0795189 | −0.0397595 | − | 0.999209i | \(-0.512659\pi\) | ||||
−0.0397595 | + | 0.999209i | \(0.512659\pi\) | |||||||
\(338\) | 21.4153 | 1.16484 | ||||||||
\(339\) | 17.6770 | 0.960082 | ||||||||
\(340\) | −3.46131 | −0.187716 | ||||||||
\(341\) | 2.71223 | 0.146875 | ||||||||
\(342\) | −66.2655 | −3.58323 | ||||||||
\(343\) | −38.9659 | −2.10396 | ||||||||
\(344\) | −0.830224 | −0.0447627 | ||||||||
\(345\) | 6.66589 | 0.358880 | ||||||||
\(346\) | 2.07633 | 0.111624 | ||||||||
\(347\) | −0.293106 | −0.0157347 | −0.00786737 | − | 0.999969i | \(-0.502504\pi\) | ||||
−0.00786737 | + | 0.999969i | \(0.502504\pi\) | |||||||
\(348\) | −22.7624 | −1.22020 | ||||||||
\(349\) | 30.8214 | 1.64983 | 0.824916 | − | 0.565256i | \(-0.191223\pi\) | ||||
0.824916 | + | 0.565256i | \(0.191223\pi\) | |||||||
\(350\) | −53.2439 | −2.84601 | ||||||||
\(351\) | 3.65143 | 0.194899 | ||||||||
\(352\) | −5.53575 | −0.295056 | ||||||||
\(353\) | −28.8749 | −1.53686 | −0.768428 | − | 0.639937i | \(-0.778961\pi\) | ||||
−0.768428 | + | 0.639937i | \(0.778961\pi\) | |||||||
\(354\) | −6.22056 | −0.330619 | ||||||||
\(355\) | 2.64613 | 0.140442 | ||||||||
\(356\) | 42.7140 | 2.26384 | ||||||||
\(357\) | 46.2398 | 2.44727 | ||||||||
\(358\) | −23.4837 | −1.24115 | ||||||||
\(359\) | 29.4641 | 1.55505 | 0.777527 | − | 0.628849i | \(-0.216474\pi\) | ||||
0.777527 | + | 0.628849i | \(0.216474\pi\) | |||||||
\(360\) | −3.03372 | −0.159891 | ||||||||
\(361\) | 40.8411 | 2.14953 | ||||||||
\(362\) | −38.1543 | −2.00535 | ||||||||
\(363\) | 2.59523 | 0.136214 | ||||||||
\(364\) | −29.4275 | −1.54242 | ||||||||
\(365\) | 0.506630 | 0.0265182 | ||||||||
\(366\) | −10.2724 | −0.536947 | ||||||||
\(367\) | 20.9596 | 1.09408 | 0.547041 | − | 0.837106i | \(-0.315754\pi\) | ||||
0.547041 | + | 0.837106i | \(0.315754\pi\) | |||||||
\(368\) | 0.959380 | 0.0500112 | ||||||||
\(369\) | 28.9619 | 1.50770 | ||||||||
\(370\) | −7.25364 | −0.377099 | ||||||||
\(371\) | −28.6520 | −1.48754 | ||||||||
\(372\) | −22.9427 | −1.18952 | ||||||||
\(373\) | 10.0616 | 0.520968 | 0.260484 | − | 0.965478i | \(-0.416118\pi\) | ||||
0.260484 | + | 0.965478i | \(0.416118\pi\) | |||||||
\(374\) | −8.66075 | −0.447837 | ||||||||
\(375\) | −7.24006 | −0.373875 | ||||||||
\(376\) | −20.2675 | −1.04522 | ||||||||
\(377\) | −5.14942 | −0.265209 | ||||||||
\(378\) | 20.6456 | 1.06190 | ||||||||
\(379\) | −37.1517 | −1.90836 | −0.954178 | − | 0.299238i | \(-0.903268\pi\) | ||||
−0.954178 | + | 0.299238i | \(0.903268\pi\) | |||||||
\(380\) | 7.09014 | 0.363716 | ||||||||
\(381\) | −11.7921 | −0.604126 | ||||||||
\(382\) | −7.66883 | −0.392371 | ||||||||
\(383\) | −23.4540 | −1.19844 | −0.599222 | − | 0.800583i | \(-0.704524\pi\) | ||||
−0.599222 | + | 0.800583i | \(0.704524\pi\) | |||||||
\(384\) | 48.0771 | 2.45342 | ||||||||
\(385\) | 1.32668 | 0.0676139 | ||||||||
\(386\) | −53.6292 | −2.72965 | ||||||||
\(387\) | 1.07367 | 0.0545776 | ||||||||
\(388\) | −58.1730 | −2.95329 | ||||||||
\(389\) | 0.189350 | 0.00960045 | 0.00480023 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00480023 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(390\) | −3.20271 | −0.162175 | ||||||||
\(391\) | −34.4949 | −1.74448 | ||||||||
\(392\) | −44.0730 | −2.22602 | ||||||||
\(393\) | 2.59523 | 0.130912 | ||||||||
\(394\) | 51.4287 | 2.59094 | ||||||||
\(395\) | 1.11100 | 0.0559005 | ||||||||
\(396\) | −12.1748 | −0.611805 | ||||||||
\(397\) | −12.0872 | −0.606638 | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||||
−0.303319 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(398\) | 21.8988 | 1.09769 | ||||||||
\(399\) | −94.7174 | −4.74180 | ||||||||
\(400\) | −0.516856 | −0.0258428 | ||||||||
\(401\) | −11.7293 | −0.585735 | −0.292868 | − | 0.956153i | \(-0.594609\pi\) | ||||
−0.292868 | + | 0.956153i | \(0.594609\pi\) | |||||||
\(402\) | −17.8871 | −0.892128 | ||||||||
\(403\) | −5.19020 | −0.258542 | ||||||||
\(404\) | 26.8258 | 1.33463 | ||||||||
\(405\) | −1.75853 | −0.0873822 | ||||||||
\(406\) | −29.1154 | −1.44498 | ||||||||
\(407\) | −11.2479 | −0.557540 | ||||||||
\(408\) | 28.3078 | 1.40145 | ||||||||
\(409\) | −24.2817 | −1.20065 | −0.600326 | − | 0.799755i | \(-0.704963\pi\) | ||||
−0.600326 | + | 0.799755i | \(0.704963\pi\) | |||||||
\(410\) | −5.00025 | −0.246945 | ||||||||
\(411\) | 29.4147 | 1.45092 | ||||||||
\(412\) | −53.8072 | −2.65089 | ||||||||
\(413\) | −4.93103 | −0.242640 | ||||||||
\(414\) | −78.2450 | −3.84553 | ||||||||
\(415\) | −2.02764 | −0.0995327 | ||||||||
\(416\) | 10.5934 | 0.519383 | ||||||||
\(417\) | 10.0689 | 0.493075 | ||||||||
\(418\) | 17.7406 | 0.867723 | ||||||||
\(419\) | 13.1666 | 0.643232 | 0.321616 | − | 0.946870i | \(-0.395774\pi\) | ||||
0.321616 | + | 0.946870i | \(0.395774\pi\) | |||||||
\(420\) | −11.2224 | −0.547596 | ||||||||
\(421\) | 19.2883 | 0.940056 | 0.470028 | − | 0.882652i | \(-0.344244\pi\) | ||||
0.470028 | + | 0.882652i | \(0.344244\pi\) | |||||||
\(422\) | 8.16052 | 0.397248 | ||||||||
\(423\) | 26.2105 | 1.27440 | ||||||||
\(424\) | −17.5406 | −0.851849 | ||||||||
\(425\) | 18.5837 | 0.901444 | ||||||||
\(426\) | −56.0073 | −2.71356 | ||||||||
\(427\) | −8.14291 | −0.394063 | ||||||||
\(428\) | −39.8154 | −1.92455 | ||||||||
\(429\) | −4.96632 | −0.239776 | ||||||||
\(430\) | −0.185368 | −0.00893922 | ||||||||
\(431\) | 2.87707 | 0.138584 | 0.0692918 | − | 0.997596i | \(-0.477926\pi\) | ||||
0.0692918 | + | 0.997596i | \(0.477926\pi\) | |||||||
\(432\) | 0.200414 | 0.00964241 | ||||||||
\(433\) | −0.494116 | −0.0237457 | −0.0118728 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118728 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(434\) | −29.3460 | −1.40865 | ||||||||
\(435\) | −1.96377 | −0.0941554 | ||||||||
\(436\) | −5.36330 | −0.256856 | ||||||||
\(437\) | 70.6591 | 3.38009 | ||||||||
\(438\) | −10.7232 | −0.512373 | ||||||||
\(439\) | −3.82318 | −0.182470 | −0.0912352 | − | 0.995829i | \(-0.529082\pi\) | ||||
−0.0912352 | + | 0.995829i | \(0.529082\pi\) | |||||||
\(440\) | 0.812189 | 0.0387196 | ||||||||
\(441\) | 56.9963 | 2.71411 | ||||||||
\(442\) | 16.5735 | 0.788320 | ||||||||
\(443\) | 0.433596 | 0.0206007 | 0.0103004 | − | 0.999947i | \(-0.496721\pi\) | ||||
0.0103004 | + | 0.999947i | \(0.496721\pi\) | |||||||
\(444\) | 95.1462 | 4.51544 | ||||||||
\(445\) | 3.68503 | 0.174687 | ||||||||
\(446\) | 35.3869 | 1.67562 | ||||||||
\(447\) | 48.7514 | 2.30586 | ||||||||
\(448\) | 60.8873 | 2.87665 | ||||||||
\(449\) | −19.5141 | −0.920930 | −0.460465 | − | 0.887678i | \(-0.652317\pi\) | ||||
−0.460465 | + | 0.887678i | \(0.652317\pi\) | |||||||
\(450\) | 42.1536 | 1.98714 | ||||||||
\(451\) | −7.75370 | −0.365108 | ||||||||
\(452\) | 22.2011 | 1.04425 | ||||||||
\(453\) | 0.397339 | 0.0186686 | ||||||||
\(454\) | −8.37430 | −0.393026 | ||||||||
\(455\) | −2.53878 | −0.119020 | ||||||||
\(456\) | −57.9856 | −2.71543 | ||||||||
\(457\) | −15.9609 | −0.746617 | −0.373309 | − | 0.927707i | \(-0.621777\pi\) | ||||
−0.373309 | + | 0.927707i | \(0.621777\pi\) | |||||||
\(458\) | 61.4394 | 2.87087 | ||||||||
\(459\) | −7.20595 | −0.336345 | ||||||||
\(460\) | 8.37189 | 0.390341 | ||||||||
\(461\) | −36.4655 | −1.69837 | −0.849184 | − | 0.528097i | \(-0.822906\pi\) | ||||
−0.849184 | + | 0.528097i | \(0.822906\pi\) | |||||||
\(462\) | −28.0802 | −1.30641 | ||||||||
\(463\) | −23.9184 | −1.11158 | −0.555791 | − | 0.831322i | \(-0.687584\pi\) | ||||
−0.555791 | + | 0.831322i | \(0.687584\pi\) | |||||||
\(464\) | −0.282633 | −0.0131209 | ||||||||
\(465\) | −1.97932 | −0.0917886 | ||||||||
\(466\) | 50.1339 | 2.32241 | ||||||||
\(467\) | 31.9339 | 1.47773 | 0.738863 | − | 0.673856i | \(-0.235363\pi\) | ||||
0.738863 | + | 0.673856i | \(0.235363\pi\) | |||||||
\(468\) | 23.2980 | 1.07695 | ||||||||
\(469\) | −14.1791 | −0.654729 | ||||||||
\(470\) | −4.52522 | −0.208733 | ||||||||
\(471\) | −56.1883 | −2.58902 | ||||||||
\(472\) | −3.01875 | −0.138949 | ||||||||
\(473\) | −0.287443 | −0.0132166 | ||||||||
\(474\) | −23.5151 | −1.08008 | ||||||||
\(475\) | −38.0668 | −1.74663 | ||||||||
\(476\) | 58.0740 | 2.66182 | ||||||||
\(477\) | 22.6840 | 1.03863 | ||||||||
\(478\) | −46.1468 | −2.11071 | ||||||||
\(479\) | −6.03824 | −0.275894 | −0.137947 | − | 0.990440i | \(-0.544050\pi\) | ||||
−0.137947 | + | 0.990440i | \(0.544050\pi\) | |||||||
\(480\) | 4.03986 | 0.184393 | ||||||||
\(481\) | 21.5244 | 0.981429 | ||||||||
\(482\) | −6.37190 | −0.290232 | ||||||||
\(483\) | −111.840 | −5.08891 | ||||||||
\(484\) | 3.25943 | 0.148156 | ||||||||
\(485\) | −5.01871 | −0.227888 | ||||||||
\(486\) | 50.3485 | 2.28386 | ||||||||
\(487\) | −12.8430 | −0.581970 | −0.290985 | − | 0.956728i | \(-0.593983\pi\) | ||||
−0.290985 | + | 0.956728i | \(0.593983\pi\) | |||||||
\(488\) | −4.98506 | −0.225663 | ||||||||
\(489\) | 18.4985 | 0.836532 | ||||||||
\(490\) | −9.84035 | −0.444542 | ||||||||
\(491\) | 18.6600 | 0.842116 | 0.421058 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421058 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(492\) | 65.5885 | 2.95696 | ||||||||
\(493\) | 10.1622 | 0.457681 | ||||||||
\(494\) | −33.9490 | −1.52744 | ||||||||
\(495\) | −1.05034 | −0.0472094 | ||||||||
\(496\) | −0.284871 | −0.0127911 | ||||||||
\(497\) | −44.3968 | −1.99147 | ||||||||
\(498\) | 42.9163 | 1.92313 | ||||||||
\(499\) | 29.3491 | 1.31385 | 0.656924 | − | 0.753957i | \(-0.271857\pi\) | ||||
0.656924 | + | 0.753957i | \(0.271857\pi\) | |||||||
\(500\) | −9.09300 | −0.406651 | ||||||||
\(501\) | 31.6021 | 1.41188 | ||||||||
\(502\) | 13.5431 | 0.604458 | ||||||||
\(503\) | 34.3816 | 1.53300 | 0.766500 | − | 0.642244i | \(-0.221996\pi\) | ||||
0.766500 | + | 0.642244i | \(0.221996\pi\) | |||||||
\(504\) | 50.8998 | 2.26726 | ||||||||
\(505\) | 2.31432 | 0.102986 | ||||||||
\(506\) | 20.9478 | 0.931242 | ||||||||
\(507\) | −24.2343 | −1.07628 | ||||||||
\(508\) | −14.8100 | −0.657088 | ||||||||
\(509\) | −5.59034 | −0.247787 | −0.123894 | − | 0.992296i | \(-0.539538\pi\) | ||||
−0.123894 | + | 0.992296i | \(0.539538\pi\) | |||||||
\(510\) | 6.32041 | 0.279872 | ||||||||
\(511\) | −8.50024 | −0.376029 | ||||||||
\(512\) | 1.18816 | 0.0525099 | ||||||||
\(513\) | 14.7606 | 0.651698 | ||||||||
\(514\) | 64.1395 | 2.82907 | ||||||||
\(515\) | −4.64207 | −0.204554 | ||||||||
\(516\) | 2.43147 | 0.107040 | ||||||||
\(517\) | −7.01709 | −0.308611 | ||||||||
\(518\) | 121.702 | 5.34726 | ||||||||
\(519\) | −2.34966 | −0.103138 | ||||||||
\(520\) | −1.55423 | −0.0681575 | ||||||||
\(521\) | −2.59655 | −0.113757 | −0.0568784 | − | 0.998381i | \(-0.518115\pi\) | ||||
−0.0568784 | + | 0.998381i | \(0.518115\pi\) | |||||||
\(522\) | 23.0509 | 1.00891 | ||||||||
\(523\) | 36.9088 | 1.61391 | 0.806955 | − | 0.590613i | \(-0.201114\pi\) | ||||
0.806955 | + | 0.590613i | \(0.201114\pi\) | |||||||
\(524\) | 3.25943 | 0.142389 | ||||||||
\(525\) | 60.2528 | 2.62965 | ||||||||
\(526\) | −28.0952 | −1.22501 | ||||||||
\(527\) | 10.2426 | 0.446176 | ||||||||
\(528\) | −0.272583 | −0.0118627 | ||||||||
\(529\) | 60.4329 | 2.62752 | ||||||||
\(530\) | −3.91637 | −0.170116 | ||||||||
\(531\) | 3.90393 | 0.169416 | ||||||||
\(532\) | −118.958 | −5.15750 | ||||||||
\(533\) | 14.8377 | 0.642693 | ||||||||
\(534\) | −77.9964 | −3.37523 | ||||||||
\(535\) | −3.43497 | −0.148507 | ||||||||
\(536\) | −8.68037 | −0.374935 | ||||||||
\(537\) | 26.5750 | 1.14679 | ||||||||
\(538\) | −45.4401 | −1.95906 | ||||||||
\(539\) | −15.2591 | −0.657255 | ||||||||
\(540\) | 1.74888 | 0.0752598 | ||||||||
\(541\) | −20.6830 | −0.889232 | −0.444616 | − | 0.895721i | \(-0.646660\pi\) | ||||
−0.444616 | + | 0.895721i | \(0.646660\pi\) | |||||||
\(542\) | −23.7957 | −1.02211 | ||||||||
\(543\) | 43.1768 | 1.85289 | ||||||||
\(544\) | −20.9056 | −0.896320 | ||||||||
\(545\) | −0.462704 | −0.0198201 | ||||||||
\(546\) | 53.7351 | 2.29965 | ||||||||
\(547\) | −39.8099 | −1.70215 | −0.851073 | − | 0.525047i | \(-0.824048\pi\) | ||||
−0.851073 | + | 0.525047i | \(0.824048\pi\) | |||||||
\(548\) | 36.9428 | 1.57812 | ||||||||
\(549\) | 6.44681 | 0.275143 | ||||||||
\(550\) | −11.2854 | −0.481210 | ||||||||
\(551\) | −20.8161 | −0.886797 | ||||||||
\(552\) | −68.4682 | −2.91420 | ||||||||
\(553\) | −18.6404 | −0.792669 | ||||||||
\(554\) | −17.6163 | −0.748445 | ||||||||
\(555\) | 8.20848 | 0.348431 | ||||||||
\(556\) | 12.6458 | 0.536301 | ||||||||
\(557\) | −22.5385 | −0.954988 | −0.477494 | − | 0.878635i | \(-0.658455\pi\) | ||||
−0.477494 | + | 0.878635i | \(0.658455\pi\) | |||||||
\(558\) | 23.2334 | 0.983550 | ||||||||
\(559\) | 0.550059 | 0.0232650 | ||||||||
\(560\) | −0.139344 | −0.00588837 | ||||||||
\(561\) | 9.80082 | 0.413791 | ||||||||
\(562\) | 25.4410 | 1.07316 | ||||||||
\(563\) | −31.4014 | −1.32341 | −0.661706 | − | 0.749763i | \(-0.730167\pi\) | ||||
−0.661706 | + | 0.749763i | \(0.730167\pi\) | |||||||
\(564\) | 59.3575 | 2.49940 | ||||||||
\(565\) | 1.91534 | 0.0805788 | ||||||||
\(566\) | 22.7913 | 0.957991 | ||||||||
\(567\) | 29.5047 | 1.23908 | ||||||||
\(568\) | −27.1796 | −1.14043 | ||||||||
\(569\) | 1.68384 | 0.0705903 | 0.0352952 | − | 0.999377i | \(-0.488763\pi\) | ||||
0.0352952 | + | 0.999377i | \(0.488763\pi\) | |||||||
\(570\) | −12.9467 | −0.542277 | ||||||||
\(571\) | −22.2513 | −0.931189 | −0.465594 | − | 0.884998i | \(-0.654159\pi\) | ||||
−0.465594 | + | 0.884998i | \(0.654159\pi\) | |||||||
\(572\) | −6.23735 | −0.260797 | ||||||||
\(573\) | 8.67833 | 0.362542 | ||||||||
\(574\) | 83.8942 | 3.50168 | ||||||||
\(575\) | −44.9485 | −1.87448 | ||||||||
\(576\) | −48.2049 | −2.00854 | ||||||||
\(577\) | 3.19967 | 0.133204 | 0.0666021 | − | 0.997780i | \(-0.478784\pi\) | ||||
0.0666021 | + | 0.997780i | \(0.478784\pi\) | |||||||
\(578\) | 6.27981 | 0.261206 | ||||||||
\(579\) | 60.6887 | 2.52214 | ||||||||
\(580\) | −2.46635 | −0.102410 | ||||||||
\(581\) | 34.0197 | 1.41137 | ||||||||
\(582\) | 106.225 | 4.40315 | ||||||||
\(583\) | −6.07298 | −0.251517 | ||||||||
\(584\) | −5.20381 | −0.215335 | ||||||||
\(585\) | 2.00997 | 0.0831021 | ||||||||
\(586\) | −42.9215 | −1.77307 | ||||||||
\(587\) | 20.5662 | 0.848858 | 0.424429 | − | 0.905461i | \(-0.360475\pi\) | ||||
0.424429 | + | 0.905461i | \(0.360475\pi\) | |||||||
\(588\) | 129.076 | 5.32302 | ||||||||
\(589\) | −20.9810 | −0.864506 | ||||||||
\(590\) | −0.674010 | −0.0277485 | ||||||||
\(591\) | −58.1986 | −2.39397 | ||||||||
\(592\) | 1.18140 | 0.0485551 | ||||||||
\(593\) | −29.7853 | −1.22313 | −0.611567 | − | 0.791192i | \(-0.709461\pi\) | ||||
−0.611567 | + | 0.791192i | \(0.709461\pi\) | |||||||
\(594\) | 4.37597 | 0.179548 | ||||||||
\(595\) | 5.01017 | 0.205397 | ||||||||
\(596\) | 61.2284 | 2.50801 | ||||||||
\(597\) | −24.7815 | −1.01424 | ||||||||
\(598\) | −40.0863 | −1.63925 | ||||||||
\(599\) | 23.3136 | 0.952569 | 0.476284 | − | 0.879291i | \(-0.341983\pi\) | ||||
0.476284 | + | 0.879291i | \(0.341983\pi\) | |||||||
\(600\) | 36.8865 | 1.50589 | ||||||||
\(601\) | −14.5973 | −0.595438 | −0.297719 | − | 0.954654i | \(-0.596226\pi\) | ||||
−0.297719 | + | 0.954654i | \(0.596226\pi\) | |||||||
\(602\) | 3.11010 | 0.126758 | ||||||||
\(603\) | 11.2257 | 0.457145 | ||||||||
\(604\) | 0.499030 | 0.0203052 | ||||||||
\(605\) | 0.281199 | 0.0114323 | ||||||||
\(606\) | −48.9843 | −1.98985 | ||||||||
\(607\) | 0.598100 | 0.0242761 | 0.0121381 | − | 0.999926i | \(-0.496136\pi\) | ||||
0.0121381 | + | 0.999926i | \(0.496136\pi\) | |||||||
\(608\) | 42.8229 | 1.73670 | ||||||||
\(609\) | 32.9481 | 1.33512 | ||||||||
\(610\) | −1.11303 | −0.0450655 | ||||||||
\(611\) | 13.4281 | 0.543244 | ||||||||
\(612\) | −45.9776 | −1.85853 | ||||||||
\(613\) | 30.5921 | 1.23560 | 0.617802 | − | 0.786334i | \(-0.288023\pi\) | ||||
0.617802 | + | 0.786334i | \(0.288023\pi\) | |||||||
\(614\) | −70.8755 | −2.86030 | ||||||||
\(615\) | 5.65847 | 0.228171 | ||||||||
\(616\) | −13.6269 | −0.549044 | ||||||||
\(617\) | 13.3848 | 0.538851 | 0.269425 | − | 0.963021i | \(-0.413166\pi\) | ||||
0.269425 | + | 0.963021i | \(0.413166\pi\) | |||||||
\(618\) | 98.2526 | 3.95230 | ||||||||
\(619\) | −30.9914 | −1.24565 | −0.622825 | − | 0.782361i | \(-0.714015\pi\) | ||||
−0.622825 | + | 0.782361i | \(0.714015\pi\) | |||||||
\(620\) | −2.48588 | −0.0998355 | ||||||||
\(621\) | 17.4291 | 0.699404 | ||||||||
\(622\) | −39.8795 | −1.59902 | ||||||||
\(623\) | −61.8276 | −2.47707 | ||||||||
\(624\) | 0.521623 | 0.0208816 | ||||||||
\(625\) | 23.8202 | 0.952807 | ||||||||
\(626\) | 54.2225 | 2.16717 | ||||||||
\(627\) | −20.0760 | −0.801757 | ||||||||
\(628\) | −70.5685 | −2.81599 | ||||||||
\(629\) | −42.4775 | −1.69369 | ||||||||
\(630\) | 11.3646 | 0.452777 | ||||||||
\(631\) | −3.15523 | −0.125608 | −0.0628038 | − | 0.998026i | \(-0.520004\pi\) | ||||
−0.0628038 | + | 0.998026i | \(0.520004\pi\) | |||||||
\(632\) | −11.4116 | −0.453928 | ||||||||
\(633\) | −9.23474 | −0.367048 | ||||||||
\(634\) | −10.1372 | −0.402599 | ||||||||
\(635\) | −1.27769 | −0.0507037 | ||||||||
\(636\) | 51.3712 | 2.03700 | ||||||||
\(637\) | 29.2002 | 1.15696 | ||||||||
\(638\) | −6.17120 | −0.244320 | ||||||||
\(639\) | 35.1493 | 1.39049 | ||||||||
\(640\) | 5.20924 | 0.205913 | ||||||||
\(641\) | −37.4841 | −1.48053 | −0.740267 | − | 0.672313i | \(-0.765301\pi\) | ||||
−0.740267 | + | 0.672313i | \(0.765301\pi\) | |||||||
\(642\) | 72.7035 | 2.86938 | ||||||||
\(643\) | −16.7203 | −0.659383 | −0.329692 | − | 0.944089i | \(-0.606945\pi\) | ||||
−0.329692 | + | 0.944089i | \(0.606945\pi\) | |||||||
\(644\) | −140.464 | −5.53504 | ||||||||
\(645\) | 0.209769 | 0.00825964 | ||||||||
\(646\) | 66.9970 | 2.63596 | ||||||||
\(647\) | −35.3518 | −1.38982 | −0.694911 | − | 0.719096i | \(-0.744556\pi\) | ||||
−0.694911 | + | 0.719096i | \(0.744556\pi\) | |||||||
\(648\) | 18.0627 | 0.709568 | ||||||||
\(649\) | −1.04516 | −0.0410262 | ||||||||
\(650\) | 21.5961 | 0.847067 | ||||||||
\(651\) | 33.2090 | 1.30156 | ||||||||
\(652\) | 23.2329 | 0.909869 | ||||||||
\(653\) | −29.4459 | −1.15231 | −0.576153 | − | 0.817342i | \(-0.695447\pi\) | ||||
−0.576153 | + | 0.817342i | \(0.695447\pi\) | |||||||
\(654\) | 9.79346 | 0.382955 | ||||||||
\(655\) | 0.281199 | 0.0109873 | ||||||||
\(656\) | 0.814388 | 0.0317965 | ||||||||
\(657\) | 6.72971 | 0.262551 | ||||||||
\(658\) | 75.9242 | 2.95983 | ||||||||
\(659\) | −4.37056 | −0.170253 | −0.0851264 | − | 0.996370i | \(-0.527129\pi\) | ||||
−0.0851264 | + | 0.996370i | \(0.527129\pi\) | |||||||
\(660\) | −2.37866 | −0.0925890 | ||||||||
\(661\) | −14.4908 | −0.563625 | −0.281812 | − | 0.959469i | \(-0.590936\pi\) | ||||
−0.281812 | + | 0.959469i | \(0.590936\pi\) | |||||||
\(662\) | −1.62748 | −0.0632539 | ||||||||
\(663\) | −18.7552 | −0.728390 | ||||||||
\(664\) | 20.8267 | 0.808233 | ||||||||
\(665\) | −10.2628 | −0.397975 | ||||||||
\(666\) | −96.3521 | −3.73357 | ||||||||
\(667\) | −24.5793 | −0.951713 | ||||||||
\(668\) | 39.6900 | 1.53565 | ||||||||
\(669\) | −40.0452 | −1.54824 | ||||||||
\(670\) | −1.93810 | −0.0748755 | ||||||||
\(671\) | −1.72594 | −0.0666293 | ||||||||
\(672\) | −67.7808 | −2.61470 | ||||||||
\(673\) | −8.72397 | −0.336284 | −0.168142 | − | 0.985763i | \(-0.553777\pi\) | ||||
−0.168142 | + | 0.985763i | \(0.553777\pi\) | |||||||
\(674\) | 3.34776 | 0.128951 | ||||||||
\(675\) | −9.38971 | −0.361410 | ||||||||
\(676\) | −30.4366 | −1.17064 | ||||||||
\(677\) | −27.4394 | −1.05458 | −0.527291 | − | 0.849685i | \(-0.676792\pi\) | ||||
−0.527291 | + | 0.849685i | \(0.676792\pi\) | |||||||
\(678\) | −40.5394 | −1.55691 | ||||||||
\(679\) | 84.2040 | 3.23145 | ||||||||
\(680\) | 3.06721 | 0.117622 | ||||||||
\(681\) | 9.47667 | 0.363147 | ||||||||
\(682\) | −6.22007 | −0.238179 | ||||||||
\(683\) | −16.6117 | −0.635631 | −0.317815 | − | 0.948153i | \(-0.602949\pi\) | ||||
−0.317815 | + | 0.948153i | \(0.602949\pi\) | |||||||
\(684\) | 94.1803 | 3.60107 | ||||||||
\(685\) | 3.18714 | 0.121774 | ||||||||
\(686\) | 89.3623 | 3.41187 | ||||||||
\(687\) | −69.5271 | −2.65262 | ||||||||
\(688\) | 0.0301907 | 0.00115101 | ||||||||
\(689\) | 11.6214 | 0.442741 | ||||||||
\(690\) | −15.2872 | −0.581973 | ||||||||
\(691\) | 2.06559 | 0.0785788 | 0.0392894 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392894 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(692\) | −2.95100 | −0.112180 | ||||||||
\(693\) | 17.6227 | 0.669430 | ||||||||
\(694\) | 0.672193 | 0.0255161 | ||||||||
\(695\) | 1.09098 | 0.0413833 | ||||||||
\(696\) | 20.1707 | 0.764569 | ||||||||
\(697\) | −29.2816 | −1.10912 | ||||||||
\(698\) | −70.6841 | −2.67543 | ||||||||
\(699\) | −56.7333 | −2.14585 | ||||||||
\(700\) | 75.6733 | 2.86018 | ||||||||
\(701\) | 19.3780 | 0.731899 | 0.365949 | − | 0.930635i | \(-0.380744\pi\) | ||||
0.365949 | + | 0.930635i | \(0.380744\pi\) | |||||||
\(702\) | −8.37400 | −0.316056 | ||||||||
\(703\) | 87.0108 | 3.28167 | ||||||||
\(704\) | 12.9054 | 0.486392 | ||||||||
\(705\) | 5.12090 | 0.192864 | ||||||||
\(706\) | 66.2201 | 2.49223 | ||||||||
\(707\) | −38.8298 | −1.46034 | ||||||||
\(708\) | 8.84101 | 0.332266 | ||||||||
\(709\) | 44.7917 | 1.68219 | 0.841094 | − | 0.540888i | \(-0.181912\pi\) | ||||
0.841094 | + | 0.540888i | \(0.181912\pi\) | |||||||
\(710\) | −6.06849 | −0.227747 | ||||||||
\(711\) | 14.7577 | 0.553458 | ||||||||
\(712\) | −37.8506 | −1.41851 | ||||||||
\(713\) | −24.7739 | −0.927790 | ||||||||
\(714\) | −106.044 | −3.96859 | ||||||||
\(715\) | −0.538110 | −0.0201242 | ||||||||
\(716\) | 33.3763 | 1.24733 | ||||||||
\(717\) | 52.2214 | 1.95024 | ||||||||
\(718\) | −67.5713 | −2.52174 | ||||||||
\(719\) | 11.5863 | 0.432095 | 0.216047 | − | 0.976383i | \(-0.430683\pi\) | ||||
0.216047 | + | 0.976383i | \(0.430683\pi\) | |||||||
\(720\) | 0.110320 | 0.00411138 | ||||||||
\(721\) | 77.8846 | 2.90058 | ||||||||
\(722\) | −93.6627 | −3.48577 | ||||||||
\(723\) | 7.21067 | 0.268168 | ||||||||
\(724\) | 54.2271 | 2.01533 | ||||||||
\(725\) | 13.2418 | 0.491789 | ||||||||
\(726\) | −5.95177 | −0.220891 | ||||||||
\(727\) | −4.65474 | −0.172635 | −0.0863174 | − | 0.996268i | \(-0.527510\pi\) | ||||
−0.0863174 | + | 0.996268i | \(0.527510\pi\) | |||||||
\(728\) | 26.0769 | 0.966474 | ||||||||
\(729\) | −38.2151 | −1.41537 | ||||||||
\(730\) | −1.16188 | −0.0430030 | ||||||||
\(731\) | −1.08552 | −0.0401494 | ||||||||
\(732\) | 14.5997 | 0.539621 | ||||||||
\(733\) | 32.5589 | 1.20259 | 0.601296 | − | 0.799027i | \(-0.294651\pi\) | ||||
0.601296 | + | 0.799027i | \(0.294651\pi\) | |||||||
\(734\) | −48.0676 | −1.77421 | ||||||||
\(735\) | 11.1357 | 0.410747 | ||||||||
\(736\) | 50.5644 | 1.86383 | ||||||||
\(737\) | −3.00535 | −0.110703 | ||||||||
\(738\) | −66.4197 | −2.44494 | ||||||||
\(739\) | −0.993856 | −0.0365596 | −0.0182798 | − | 0.999833i | \(-0.505819\pi\) | ||||
−0.0182798 | + | 0.999833i | \(0.505819\pi\) | |||||||
\(740\) | 10.3093 | 0.378977 | ||||||||
\(741\) | 38.4180 | 1.41132 | ||||||||
\(742\) | 65.7089 | 2.41225 | ||||||||
\(743\) | −24.6731 | −0.905167 | −0.452584 | − | 0.891722i | \(-0.649498\pi\) | ||||
−0.452584 | + | 0.891722i | \(0.649498\pi\) | |||||||
\(744\) | 20.3304 | 0.745349 | ||||||||
\(745\) | 5.28231 | 0.193529 | ||||||||
\(746\) | −23.0747 | −0.844823 | ||||||||
\(747\) | −26.9336 | −0.985451 | ||||||||
\(748\) | 12.3091 | 0.450067 | ||||||||
\(749\) | 57.6319 | 2.10582 | ||||||||
\(750\) | 16.6039 | 0.606290 | ||||||||
\(751\) | 6.33138 | 0.231035 | 0.115518 | − | 0.993305i | \(-0.463147\pi\) | ||||
0.115518 | + | 0.993305i | \(0.463147\pi\) | |||||||
\(752\) | 0.737020 | 0.0268764 | ||||||||
\(753\) | −15.3259 | −0.558506 | ||||||||
\(754\) | 11.8094 | 0.430073 | ||||||||
\(755\) | 0.0430524 | 0.00156684 | ||||||||
\(756\) | −29.3427 | −1.06719 | ||||||||
\(757\) | −9.13651 | −0.332072 | −0.166036 | − | 0.986120i | \(-0.553097\pi\) | ||||
−0.166036 | + | 0.986120i | \(0.553097\pi\) | |||||||
\(758\) | 85.2018 | 3.09467 | ||||||||
\(759\) | −23.7053 | −0.860447 | ||||||||
\(760\) | −6.28285 | −0.227903 | ||||||||
\(761\) | −13.1478 | −0.476609 | −0.238305 | − | 0.971190i | \(-0.576592\pi\) | ||||
−0.238305 | + | 0.971190i | \(0.576592\pi\) | |||||||
\(762\) | 27.0433 | 0.979675 | ||||||||
\(763\) | 7.76325 | 0.281049 | ||||||||
\(764\) | 10.8994 | 0.394326 | ||||||||
\(765\) | −3.96659 | −0.143412 | ||||||||
\(766\) | 53.7882 | 1.94345 | ||||||||
\(767\) | 2.00005 | 0.0722178 | ||||||||
\(768\) | −43.2720 | −1.56145 | ||||||||
\(769\) | −50.8048 | −1.83207 | −0.916034 | − | 0.401102i | \(-0.868627\pi\) | ||||
−0.916034 | + | 0.401102i | \(0.868627\pi\) | |||||||
\(770\) | −3.04254 | −0.109645 | ||||||||
\(771\) | −72.5826 | −2.61400 | ||||||||
\(772\) | 76.2208 | 2.74325 | ||||||||
\(773\) | 34.8943 | 1.25506 | 0.627530 | − | 0.778592i | \(-0.284066\pi\) | ||||
0.627530 | + | 0.778592i | \(0.284066\pi\) | |||||||
\(774\) | −2.46229 | −0.0885052 | ||||||||
\(775\) | 13.3467 | 0.479426 | ||||||||
\(776\) | 51.5494 | 1.85051 | ||||||||
\(777\) | −137.722 | −4.94075 | ||||||||
\(778\) | −0.434246 | −0.0155685 | ||||||||
\(779\) | 59.9803 | 2.14902 | ||||||||
\(780\) | 4.55187 | 0.162983 | ||||||||
\(781\) | −9.41019 | −0.336723 | ||||||||
\(782\) | 79.1087 | 2.82892 | ||||||||
\(783\) | −5.13459 | −0.183495 | ||||||||
\(784\) | 1.60269 | 0.0572391 | ||||||||
\(785\) | −6.08811 | −0.217294 | ||||||||
\(786\) | −5.95177 | −0.212293 | ||||||||
\(787\) | 22.1160 | 0.788349 | 0.394175 | − | 0.919036i | \(-0.371030\pi\) | ||||
0.394175 | + | 0.919036i | \(0.371030\pi\) | |||||||
\(788\) | −73.0934 | −2.60384 | ||||||||
\(789\) | 31.7935 | 1.13188 | ||||||||
\(790\) | −2.54791 | −0.0906505 | ||||||||
\(791\) | −32.1355 | −1.14261 | ||||||||
\(792\) | 10.7885 | 0.383354 | ||||||||
\(793\) | 3.30282 | 0.117286 | ||||||||
\(794\) | 27.7201 | 0.983748 | ||||||||
\(795\) | 4.43191 | 0.157184 | ||||||||
\(796\) | −31.1238 | −1.10315 | ||||||||
\(797\) | −46.7936 | −1.65752 | −0.828758 | − | 0.559608i | \(-0.810952\pi\) | ||||
−0.828758 | + | 0.559608i | \(0.810952\pi\) | |||||||
\(798\) | 217.220 | 7.68950 | ||||||||
\(799\) | −26.4998 | −0.937497 | ||||||||
\(800\) | −27.2410 | −0.963115 | ||||||||
\(801\) | 48.9493 | 1.72954 | ||||||||
\(802\) | 26.8994 | 0.949851 | ||||||||
\(803\) | −1.80168 | −0.0635799 | ||||||||
\(804\) | 25.4222 | 0.896571 | ||||||||
\(805\) | −12.1181 | −0.427108 | ||||||||
\(806\) | 11.9029 | 0.419262 | ||||||||
\(807\) | 51.4217 | 1.81013 | ||||||||
\(808\) | −23.7714 | −0.836276 | ||||||||
\(809\) | −3.84347 | −0.135129 | −0.0675647 | − | 0.997715i | \(-0.521523\pi\) | ||||
−0.0675647 | + | 0.997715i | \(0.521523\pi\) | |||||||
\(810\) | 4.03292 | 0.141702 | ||||||||
\(811\) | 18.2764 | 0.641770 | 0.320885 | − | 0.947118i | \(-0.396020\pi\) | ||||
0.320885 | + | 0.947118i | \(0.396020\pi\) | |||||||
\(812\) | 41.3805 | 1.45217 | ||||||||
\(813\) | 26.9281 | 0.944409 | ||||||||
\(814\) | 25.7954 | 0.904129 | ||||||||
\(815\) | 2.00435 | 0.0702093 | ||||||||
\(816\) | −1.02940 | −0.0360363 | ||||||||
\(817\) | 2.22357 | 0.0777929 | ||||||||
\(818\) | 55.6863 | 1.94703 | ||||||||
\(819\) | −33.7233 | −1.17839 | ||||||||
\(820\) | 7.10664 | 0.248175 | ||||||||
\(821\) | 4.42889 | 0.154569 | 0.0772846 | − | 0.997009i | \(-0.475375\pi\) | ||||
0.0772846 | + | 0.997009i | \(0.475375\pi\) | |||||||
\(822\) | −67.4581 | −2.35287 | ||||||||
\(823\) | 31.7806 | 1.10780 | 0.553901 | − | 0.832583i | \(-0.313139\pi\) | ||||
0.553901 | + | 0.832583i | \(0.313139\pi\) | |||||||
\(824\) | 47.6807 | 1.66103 | ||||||||
\(825\) | 12.7710 | 0.444628 | ||||||||
\(826\) | 11.3085 | 0.393475 | ||||||||
\(827\) | 2.98838 | 0.103916 | 0.0519580 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519580 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(828\) | 111.206 | 3.86468 | ||||||||
\(829\) | 7.18961 | 0.249706 | 0.124853 | − | 0.992175i | \(-0.460154\pi\) | ||||
0.124853 | + | 0.992175i | \(0.460154\pi\) | |||||||
\(830\) | 4.65007 | 0.161406 | ||||||||
\(831\) | 19.9353 | 0.691547 | ||||||||
\(832\) | −24.6963 | −0.856189 | ||||||||
\(833\) | −57.6254 | −1.99660 | ||||||||
\(834\) | −23.0914 | −0.799590 | ||||||||
\(835\) | 3.42415 | 0.118498 | ||||||||
\(836\) | −25.2140 | −0.872044 | ||||||||
\(837\) | −5.17525 | −0.178883 | ||||||||
\(838\) | −30.1956 | −1.04309 | ||||||||
\(839\) | 3.31630 | 0.114491 | 0.0572457 | − | 0.998360i | \(-0.481768\pi\) | ||||
0.0572457 | + | 0.998360i | \(0.481768\pi\) | |||||||
\(840\) | 9.94460 | 0.343121 | ||||||||
\(841\) | −21.7590 | −0.750309 | ||||||||
\(842\) | −44.2348 | −1.52443 | ||||||||
\(843\) | −28.7900 | −0.991579 | ||||||||
\(844\) | −11.5982 | −0.399226 | ||||||||
\(845\) | −2.62584 | −0.0903315 | ||||||||
\(846\) | −60.1097 | −2.06662 | ||||||||
\(847\) | −4.71795 | −0.162111 | ||||||||
\(848\) | 0.637858 | 0.0219041 | ||||||||
\(849\) | −25.7915 | −0.885162 | ||||||||
\(850\) | −42.6189 | −1.46182 | ||||||||
\(851\) | 102.741 | 3.52190 | ||||||||
\(852\) | 79.6007 | 2.72708 | ||||||||
\(853\) | −6.97923 | −0.238964 | −0.119482 | − | 0.992836i | \(-0.538123\pi\) | ||||
−0.119482 | + | 0.992836i | \(0.538123\pi\) | |||||||
\(854\) | 18.6745 | 0.639029 | ||||||||
\(855\) | 8.12515 | 0.277874 | ||||||||
\(856\) | 35.2820 | 1.20591 | ||||||||
\(857\) | −38.0811 | −1.30083 | −0.650413 | − | 0.759581i | \(-0.725404\pi\) | ||||
−0.650413 | + | 0.759581i | \(0.725404\pi\) | |||||||
\(858\) | 11.3895 | 0.388831 | ||||||||
\(859\) | 30.4877 | 1.04023 | 0.520113 | − | 0.854097i | \(-0.325890\pi\) | ||||
0.520113 | + | 0.854097i | \(0.325890\pi\) | |||||||
\(860\) | 0.263455 | 0.00898374 | ||||||||
\(861\) | −94.9378 | −3.23547 | ||||||||
\(862\) | −6.59812 | −0.224733 | ||||||||
\(863\) | 35.7615 | 1.21734 | 0.608669 | − | 0.793425i | \(-0.291704\pi\) | ||||
0.608669 | + | 0.793425i | \(0.291704\pi\) | |||||||
\(864\) | 10.5629 | 0.359356 | ||||||||
\(865\) | −0.254590 | −0.00865631 | ||||||||
\(866\) | 1.13318 | 0.0385070 | ||||||||
\(867\) | −7.10646 | −0.241348 | ||||||||
\(868\) | 41.7082 | 1.41567 | ||||||||
\(869\) | −3.95095 | −0.134027 | ||||||||
\(870\) | 4.50360 | 0.152686 | ||||||||
\(871\) | 5.75112 | 0.194869 | ||||||||
\(872\) | 4.75263 | 0.160944 | ||||||||
\(873\) | −66.6650 | −2.25627 | ||||||||
\(874\) | −162.046 | −5.48128 | ||||||||
\(875\) | 13.1619 | 0.444954 | ||||||||
\(876\) | 15.2404 | 0.514925 | ||||||||
\(877\) | −45.5722 | −1.53887 | −0.769433 | − | 0.638728i | \(-0.779461\pi\) | ||||
−0.769433 | + | 0.638728i | \(0.779461\pi\) | |||||||
\(878\) | 8.76787 | 0.295901 | ||||||||
\(879\) | 48.5715 | 1.63828 | ||||||||
\(880\) | −0.0295349 | −0.000995621 0 | ||||||||
\(881\) | 21.5688 | 0.726671 | 0.363335 | − | 0.931658i | \(-0.381638\pi\) | ||||
0.363335 | + | 0.931658i | \(0.381638\pi\) | |||||||
\(882\) | −130.712 | −4.40131 | ||||||||
\(883\) | 24.6983 | 0.831164 | 0.415582 | − | 0.909556i | \(-0.363578\pi\) | ||||
0.415582 | + | 0.909556i | \(0.363578\pi\) | |||||||
\(884\) | −23.5552 | −0.792246 | ||||||||
\(885\) | 0.762734 | 0.0256390 | ||||||||
\(886\) | −0.994384 | −0.0334070 | ||||||||
\(887\) | −31.6362 | −1.06224 | −0.531121 | − | 0.847296i | \(-0.678229\pi\) | ||||
−0.531121 | + | 0.847296i | \(0.678229\pi\) | |||||||
\(888\) | −84.3129 | −2.82935 | ||||||||
\(889\) | 21.4372 | 0.718979 | ||||||||
\(890\) | −8.45106 | −0.283280 | ||||||||
\(891\) | 6.25371 | 0.209507 | ||||||||
\(892\) | −50.2939 | −1.68396 | ||||||||
\(893\) | 54.2821 | 1.81648 | ||||||||
\(894\) | −111.804 | −3.73928 | ||||||||
\(895\) | 2.87945 | 0.0962494 | ||||||||
\(896\) | −87.4008 | −2.91985 | ||||||||
\(897\) | 45.3632 | 1.51463 | ||||||||
\(898\) | 44.7527 | 1.49342 | ||||||||
\(899\) | 7.29838 | 0.243414 | ||||||||
\(900\) | −59.9111 | −1.99704 | ||||||||
\(901\) | −22.9344 | −0.764056 | ||||||||
\(902\) | 17.7819 | 0.592073 | ||||||||
\(903\) | −3.51950 | −0.117122 | ||||||||
\(904\) | −19.6732 | −0.654322 | ||||||||
\(905\) | 4.67829 | 0.155512 | ||||||||
\(906\) | −0.911235 | −0.0302738 | ||||||||
\(907\) | 19.1385 | 0.635482 | 0.317741 | − | 0.948178i | \(-0.397076\pi\) | ||||
0.317741 | + | 0.948178i | \(0.397076\pi\) | |||||||
\(908\) | 11.9020 | 0.394983 | ||||||||
\(909\) | 30.7418 | 1.01964 | ||||||||
\(910\) | 5.82230 | 0.193007 | ||||||||
\(911\) | −9.58711 | −0.317635 | −0.158818 | − | 0.987308i | \(-0.550768\pi\) | ||||
−0.158818 | + | 0.987308i | \(0.550768\pi\) | |||||||
\(912\) | 2.10862 | 0.0698234 | ||||||||
\(913\) | 7.21069 | 0.238639 | ||||||||
\(914\) | 36.6037 | 1.21074 | ||||||||
\(915\) | 1.25955 | 0.0416395 | ||||||||
\(916\) | −87.3211 | −2.88517 | ||||||||
\(917\) | −4.71795 | −0.155801 | ||||||||
\(918\) | 16.5257 | 0.545430 | ||||||||
\(919\) | −18.7872 | −0.619733 | −0.309867 | − | 0.950780i | \(-0.600284\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600284\pi\) | |||||||
\(920\) | −7.41867 | −0.244586 | ||||||||
\(921\) | 80.2053 | 2.64285 | ||||||||
\(922\) | 83.6280 | 2.75414 | ||||||||
\(923\) | 18.0076 | 0.592729 | ||||||||
\(924\) | 39.9091 | 1.31291 | ||||||||
\(925\) | −55.3503 | −1.81991 | ||||||||
\(926\) | 54.8531 | 1.80258 | ||||||||
\(927\) | −61.6619 | −2.02524 | ||||||||
\(928\) | −14.8962 | −0.488993 | ||||||||
\(929\) | 10.9349 | 0.358763 | 0.179381 | − | 0.983780i | \(-0.442590\pi\) | ||||
0.179381 | + | 0.983780i | \(0.442590\pi\) | |||||||
\(930\) | 4.53926 | 0.148848 | ||||||||
\(931\) | 118.040 | 3.86859 | ||||||||
\(932\) | −71.2531 | −2.33397 | ||||||||
\(933\) | 45.1291 | 1.47746 | ||||||||
\(934\) | −73.2355 | −2.39634 | ||||||||
\(935\) | 1.06194 | 0.0347291 | ||||||||
\(936\) | −20.6453 | −0.674812 | ||||||||
\(937\) | −0.156151 | −0.00510123 | −0.00255061 | − | 0.999997i | \(-0.500812\pi\) | ||||
−0.00255061 | + | 0.999997i | \(0.500812\pi\) | |||||||
\(938\) | 32.5175 | 1.06173 | ||||||||
\(939\) | −61.3601 | −2.00241 | ||||||||
\(940\) | 6.43150 | 0.209772 | ||||||||
\(941\) | −22.6423 | −0.738119 | −0.369059 | − | 0.929406i | \(-0.620320\pi\) | ||||
−0.369059 | + | 0.929406i | \(0.620320\pi\) | |||||||
\(942\) | 128.859 | 4.19846 | ||||||||
\(943\) | 70.8236 | 2.30633 | ||||||||
\(944\) | 0.109776 | 0.00357289 | ||||||||
\(945\) | −2.53146 | −0.0823485 | ||||||||
\(946\) | 0.659205 | 0.0214326 | ||||||||
\(947\) | 56.5202 | 1.83666 | 0.918330 | − | 0.395815i | \(-0.129538\pi\) | ||||
0.918330 | + | 0.395815i | \(0.129538\pi\) | |||||||
\(948\) | 33.4210 | 1.08546 | ||||||||
\(949\) | 3.44775 | 0.111919 | ||||||||
\(950\) | 87.3004 | 2.83240 | ||||||||
\(951\) | 11.4716 | 0.371993 | ||||||||
\(952\) | −51.4616 | −1.66788 | ||||||||
\(953\) | −17.4436 | −0.565054 | −0.282527 | − | 0.959259i | \(-0.591173\pi\) | ||||
−0.282527 | + | 0.959259i | \(0.591173\pi\) | |||||||
\(954\) | −52.0223 | −1.68428 | ||||||||
\(955\) | 0.940314 | 0.0304278 | ||||||||
\(956\) | 65.5864 | 2.12122 | ||||||||
\(957\) | 6.98356 | 0.225746 | ||||||||
\(958\) | 13.8478 | 0.447401 | ||||||||
\(959\) | −53.4739 | −1.72676 | ||||||||
\(960\) | −9.41809 | −0.303967 | ||||||||
\(961\) | −23.6438 | −0.762704 | ||||||||
\(962\) | −49.3629 | −1.59152 | ||||||||
\(963\) | −45.6276 | −1.47033 | ||||||||
\(964\) | 9.05610 | 0.291677 | ||||||||
\(965\) | 6.57574 | 0.211681 | ||||||||
\(966\) | 256.489 | 8.25239 | ||||||||
\(967\) | 23.2732 | 0.748416 | 0.374208 | − | 0.927345i | \(-0.377915\pi\) | ||||
0.374208 | + | 0.927345i | \(0.377915\pi\) | |||||||
\(968\) | −2.88831 | −0.0928339 | ||||||||
\(969\) | −75.8163 | −2.43557 | ||||||||
\(970\) | 11.5096 | 0.369552 | ||||||||
\(971\) | −17.0540 | −0.547290 | −0.273645 | − | 0.961831i | \(-0.588229\pi\) | ||||
−0.273645 | + | 0.961831i | \(0.588229\pi\) | |||||||
\(972\) | −71.5582 | −2.29523 | ||||||||
\(973\) | −18.3045 | −0.586816 | ||||||||
\(974\) | 29.4533 | 0.943746 | ||||||||
\(975\) | −24.4389 | −0.782671 | ||||||||
\(976\) | 0.181279 | 0.00580261 | ||||||||
\(977\) | −25.8638 | −0.827458 | −0.413729 | − | 0.910400i | \(-0.635774\pi\) | ||||
−0.413729 | + | 0.910400i | \(0.635774\pi\) | |||||||
\(978\) | −42.4235 | −1.35655 | ||||||||
\(979\) | −13.1047 | −0.418829 | ||||||||
\(980\) | 13.9857 | 0.446756 | ||||||||
\(981\) | −6.14623 | −0.196234 | ||||||||
\(982\) | −42.7939 | −1.36561 | ||||||||
\(983\) | −37.8775 | −1.20810 | −0.604052 | − | 0.796945i | \(-0.706448\pi\) | ||||
−0.604052 | + | 0.796945i | \(0.706448\pi\) | |||||||
\(984\) | −58.1206 | −1.85282 | ||||||||
\(985\) | −6.30593 | −0.200924 | ||||||||
\(986\) | −23.3054 | −0.742194 | ||||||||
\(987\) | −85.9186 | −2.73482 | ||||||||
\(988\) | 48.2503 | 1.53505 | ||||||||
\(989\) | 2.62555 | 0.0834876 | ||||||||
\(990\) | 2.40880 | 0.0765567 | ||||||||
\(991\) | 35.2843 | 1.12084 | 0.560421 | − | 0.828208i | \(-0.310639\pi\) | ||||
0.560421 | + | 0.828208i | \(0.310639\pi\) | |||||||
\(992\) | −15.0142 | −0.476701 | ||||||||
\(993\) | 1.84172 | 0.0584452 | ||||||||
\(994\) | 101.817 | 3.22945 | ||||||||
\(995\) | −2.68512 | −0.0851241 | ||||||||
\(996\) | −60.9951 | −1.93270 | ||||||||
\(997\) | 16.7122 | 0.529280 | 0.264640 | − | 0.964347i | \(-0.414747\pi\) | ||||
0.264640 | + | 0.964347i | \(0.414747\pi\) | |||||||
\(998\) | −67.3077 | −2.13059 | ||||||||
\(999\) | 21.4624 | 0.679040 |
(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 | 1441.2.a.f.1.3 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.f.1.3 | ✓ | 31 | 1.1 | even | 1 | trivial |