Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8014,2,Mod(1,8014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8014 = 2 \cdot 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8014.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: | \(63.9921121799\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.45668 | −1.41836 | −0.709181 | − | 0.705026i | \(-0.750935\pi\) | ||||
−0.709181 | + | 0.705026i | \(0.750935\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.657543 | −0.294062 | −0.147031 | − | 0.989132i | \(-0.546972\pi\) | ||||
−0.147031 | + | 0.989132i | \(0.546972\pi\) | |||||||
\(6\) | −2.45668 | −1.00293 | ||||||||
\(7\) | 4.85111 | 1.83355 | 0.916774 | − | 0.399405i | \(-0.130783\pi\) | ||||
0.916774 | + | 0.399405i | \(0.130783\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.03526 | 1.01175 | ||||||||
\(10\) | −0.657543 | −0.207933 | ||||||||
\(11\) | 4.65548 | 1.40368 | 0.701840 | − | 0.712334i | \(-0.252362\pi\) | ||||
0.701840 | + | 0.712334i | \(0.252362\pi\) | |||||||
\(12\) | −2.45668 | −0.709181 | ||||||||
\(13\) | −5.27842 | −1.46397 | −0.731985 | − | 0.681321i | \(-0.761406\pi\) | ||||
−0.731985 | + | 0.681321i | \(0.761406\pi\) | |||||||
\(14\) | 4.85111 | 1.29651 | ||||||||
\(15\) | 1.61537 | 0.417087 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.71623 | 0.901319 | 0.450660 | − | 0.892696i | \(-0.351189\pi\) | ||||
0.450660 | + | 0.892696i | \(0.351189\pi\) | |||||||
\(18\) | 3.03526 | 0.715417 | ||||||||
\(19\) | 7.87815 | 1.80737 | 0.903686 | − | 0.428197i | \(-0.140851\pi\) | ||||
0.903686 | + | 0.428197i | \(0.140851\pi\) | |||||||
\(20\) | −0.657543 | −0.147031 | ||||||||
\(21\) | −11.9176 | −2.60064 | ||||||||
\(22\) | 4.65548 | 0.992552 | ||||||||
\(23\) | −3.85376 | −0.803565 | −0.401782 | − | 0.915735i | \(-0.631609\pi\) | ||||
−0.401782 | + | 0.915735i | \(0.631609\pi\) | |||||||
\(24\) | −2.45668 | −0.501467 | ||||||||
\(25\) | −4.56764 | −0.913527 | ||||||||
\(26\) | −5.27842 | −1.03518 | ||||||||
\(27\) | −0.0866199 | −0.0166700 | ||||||||
\(28\) | 4.85111 | 0.916774 | ||||||||
\(29\) | 7.72413 | 1.43434 | 0.717168 | − | 0.696901i | \(-0.245438\pi\) | ||||
0.717168 | + | 0.696901i | \(0.245438\pi\) | |||||||
\(30\) | 1.61537 | 0.294925 | ||||||||
\(31\) | −1.67549 | −0.300928 | −0.150464 | − | 0.988616i | \(-0.548077\pi\) | ||||
−0.150464 | + | 0.988616i | \(0.548077\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −11.4370 | −1.99093 | ||||||||
\(34\) | 3.71623 | 0.637329 | ||||||||
\(35\) | −3.18982 | −0.539177 | ||||||||
\(36\) | 3.03526 | 0.505876 | ||||||||
\(37\) | 9.74450 | 1.60199 | 0.800993 | − | 0.598674i | \(-0.204305\pi\) | ||||
0.800993 | + | 0.598674i | \(0.204305\pi\) | |||||||
\(38\) | 7.87815 | 1.27800 | ||||||||
\(39\) | 12.9674 | 2.07644 | ||||||||
\(40\) | −0.657543 | −0.103967 | ||||||||
\(41\) | 8.25622 | 1.28941 | 0.644703 | − | 0.764433i | \(-0.276981\pi\) | ||||
0.644703 | + | 0.764433i | \(0.276981\pi\) | |||||||
\(42\) | −11.9176 | −1.83893 | ||||||||
\(43\) | 0.474388 | 0.0723435 | 0.0361718 | − | 0.999346i | \(-0.488484\pi\) | ||||
0.0361718 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(44\) | 4.65548 | 0.701840 | ||||||||
\(45\) | −1.99581 | −0.297518 | ||||||||
\(46\) | −3.85376 | −0.568206 | ||||||||
\(47\) | −3.65590 | −0.533268 | −0.266634 | − | 0.963798i | \(-0.585911\pi\) | ||||
−0.266634 | + | 0.963798i | \(0.585911\pi\) | |||||||
\(48\) | −2.45668 | −0.354591 | ||||||||
\(49\) | 16.5333 | 2.36190 | ||||||||
\(50\) | −4.56764 | −0.645961 | ||||||||
\(51\) | −9.12958 | −1.27840 | ||||||||
\(52\) | −5.27842 | −0.731985 | ||||||||
\(53\) | 1.25043 | 0.171760 | 0.0858802 | − | 0.996305i | \(-0.472630\pi\) | ||||
0.0858802 | + | 0.996305i | \(0.472630\pi\) | |||||||
\(54\) | −0.0866199 | −0.0117875 | ||||||||
\(55\) | −3.06118 | −0.412769 | ||||||||
\(56\) | 4.85111 | 0.648257 | ||||||||
\(57\) | −19.3541 | −2.56351 | ||||||||
\(58\) | 7.72413 | 1.01423 | ||||||||
\(59\) | −8.73589 | −1.13732 | −0.568658 | − | 0.822574i | \(-0.692537\pi\) | ||||
−0.568658 | + | 0.822574i | \(0.692537\pi\) | |||||||
\(60\) | 1.61537 | 0.208543 | ||||||||
\(61\) | −11.7977 | −1.51054 | −0.755272 | − | 0.655412i | \(-0.772495\pi\) | ||||
−0.755272 | + | 0.655412i | \(0.772495\pi\) | |||||||
\(62\) | −1.67549 | −0.212788 | ||||||||
\(63\) | 14.7244 | 1.85510 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.47079 | 0.430498 | ||||||||
\(66\) | −11.4370 | −1.40780 | ||||||||
\(67\) | −3.40005 | −0.415382 | −0.207691 | − | 0.978194i | \(-0.566595\pi\) | ||||
−0.207691 | + | 0.978194i | \(0.566595\pi\) | |||||||
\(68\) | 3.71623 | 0.450660 | ||||||||
\(69\) | 9.46744 | 1.13975 | ||||||||
\(70\) | −3.18982 | −0.381256 | ||||||||
\(71\) | 4.45021 | 0.528142 | 0.264071 | − | 0.964503i | \(-0.414935\pi\) | ||||
0.264071 | + | 0.964503i | \(0.414935\pi\) | |||||||
\(72\) | 3.03526 | 0.357709 | ||||||||
\(73\) | 5.84736 | 0.684382 | 0.342191 | − | 0.939630i | \(-0.388831\pi\) | ||||
0.342191 | + | 0.939630i | \(0.388831\pi\) | |||||||
\(74\) | 9.74450 | 1.13277 | ||||||||
\(75\) | 11.2212 | 1.29571 | ||||||||
\(76\) | 7.87815 | 0.903686 | ||||||||
\(77\) | 22.5843 | 2.57372 | ||||||||
\(78\) | 12.9674 | 1.46826 | ||||||||
\(79\) | 13.7681 | 1.54904 | 0.774518 | − | 0.632552i | \(-0.217992\pi\) | ||||
0.774518 | + | 0.632552i | \(0.217992\pi\) | |||||||
\(80\) | −0.657543 | −0.0735155 | ||||||||
\(81\) | −8.89298 | −0.988109 | ||||||||
\(82\) | 8.25622 | 0.911747 | ||||||||
\(83\) | −0.0309457 | −0.00339673 | −0.00169836 | − | 0.999999i | \(-0.500541\pi\) | ||||
−0.00169836 | + | 0.999999i | \(0.500541\pi\) | |||||||
\(84\) | −11.9176 | −1.30032 | ||||||||
\(85\) | −2.44358 | −0.265044 | ||||||||
\(86\) | 0.474388 | 0.0511546 | ||||||||
\(87\) | −18.9757 | −2.03441 | ||||||||
\(88\) | 4.65548 | 0.496276 | ||||||||
\(89\) | −11.2309 | −1.19047 | −0.595237 | − | 0.803550i | \(-0.702942\pi\) | ||||
−0.595237 | + | 0.803550i | \(0.702942\pi\) | |||||||
\(90\) | −1.99581 | −0.210377 | ||||||||
\(91\) | −25.6062 | −2.68426 | ||||||||
\(92\) | −3.85376 | −0.401782 | ||||||||
\(93\) | 4.11615 | 0.426824 | ||||||||
\(94\) | −3.65590 | −0.377077 | ||||||||
\(95\) | −5.18022 | −0.531479 | ||||||||
\(96\) | −2.45668 | −0.250733 | ||||||||
\(97\) | 4.35610 | 0.442295 | 0.221148 | − | 0.975240i | \(-0.429020\pi\) | ||||
0.221148 | + | 0.975240i | \(0.429020\pi\) | |||||||
\(98\) | 16.5333 | 1.67012 | ||||||||
\(99\) | 14.1306 | 1.42018 | ||||||||
\(100\) | −4.56764 | −0.456764 | ||||||||
\(101\) | −1.82482 | −0.181576 | −0.0907881 | − | 0.995870i | \(-0.528939\pi\) | ||||
−0.0907881 | + | 0.995870i | \(0.528939\pi\) | |||||||
\(102\) | −9.12958 | −0.903964 | ||||||||
\(103\) | −10.8846 | −1.07249 | −0.536245 | − | 0.844063i | \(-0.680158\pi\) | ||||
−0.536245 | + | 0.844063i | \(0.680158\pi\) | |||||||
\(104\) | −5.27842 | −0.517591 | ||||||||
\(105\) | 7.83635 | 0.764749 | ||||||||
\(106\) | 1.25043 | 0.121453 | ||||||||
\(107\) | −16.0350 | −1.55016 | −0.775081 | − | 0.631862i | \(-0.782291\pi\) | ||||
−0.775081 | + | 0.631862i | \(0.782291\pi\) | |||||||
\(108\) | −0.0866199 | −0.00833500 | ||||||||
\(109\) | 5.14174 | 0.492489 | 0.246244 | − | 0.969208i | \(-0.420803\pi\) | ||||
0.246244 | + | 0.969208i | \(0.420803\pi\) | |||||||
\(110\) | −3.06118 | −0.291872 | ||||||||
\(111\) | −23.9391 | −2.27220 | ||||||||
\(112\) | 4.85111 | 0.458387 | ||||||||
\(113\) | 8.10135 | 0.762111 | 0.381055 | − | 0.924552i | \(-0.375561\pi\) | ||||
0.381055 | + | 0.924552i | \(0.375561\pi\) | |||||||
\(114\) | −19.3541 | −1.81267 | ||||||||
\(115\) | 2.53401 | 0.236298 | ||||||||
\(116\) | 7.72413 | 0.717168 | ||||||||
\(117\) | −16.0214 | −1.48118 | ||||||||
\(118\) | −8.73589 | −0.804203 | ||||||||
\(119\) | 18.0279 | 1.65261 | ||||||||
\(120\) | 1.61537 | 0.147462 | ||||||||
\(121\) | 10.6735 | 0.970319 | ||||||||
\(122\) | −11.7977 | −1.06812 | ||||||||
\(123\) | −20.2829 | −1.82884 | ||||||||
\(124\) | −1.67549 | −0.150464 | ||||||||
\(125\) | 6.29113 | 0.562696 | ||||||||
\(126\) | 14.7244 | 1.31175 | ||||||||
\(127\) | −8.49939 | −0.754199 | −0.377099 | − | 0.926173i | \(-0.623078\pi\) | ||||
−0.377099 | + | 0.926173i | \(0.623078\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.16542 | −0.102609 | ||||||||
\(130\) | 3.47079 | 0.304408 | ||||||||
\(131\) | −5.87777 | −0.513543 | −0.256772 | − | 0.966472i | \(-0.582659\pi\) | ||||
−0.256772 | + | 0.966472i | \(0.582659\pi\) | |||||||
\(132\) | −11.4370 | −0.995464 | ||||||||
\(133\) | 38.2178 | 3.31390 | ||||||||
\(134\) | −3.40005 | −0.293720 | ||||||||
\(135\) | 0.0569563 | 0.00490202 | ||||||||
\(136\) | 3.71623 | 0.318664 | ||||||||
\(137\) | 12.7165 | 1.08645 | 0.543223 | − | 0.839589i | \(-0.317204\pi\) | ||||
0.543223 | + | 0.839589i | \(0.317204\pi\) | |||||||
\(138\) | 9.46744 | 0.805922 | ||||||||
\(139\) | 8.41180 | 0.713480 | 0.356740 | − | 0.934204i | \(-0.383888\pi\) | ||||
0.356740 | + | 0.934204i | \(0.383888\pi\) | |||||||
\(140\) | −3.18982 | −0.269589 | ||||||||
\(141\) | 8.98136 | 0.756367 | ||||||||
\(142\) | 4.45021 | 0.373453 | ||||||||
\(143\) | −24.5736 | −2.05495 | ||||||||
\(144\) | 3.03526 | 0.252938 | ||||||||
\(145\) | −5.07895 | −0.421784 | ||||||||
\(146\) | 5.84736 | 0.483931 | ||||||||
\(147\) | −40.6170 | −3.35003 | ||||||||
\(148\) | 9.74450 | 0.800993 | ||||||||
\(149\) | 12.3235 | 1.00958 | 0.504790 | − | 0.863242i | \(-0.331570\pi\) | ||||
0.504790 | + | 0.863242i | \(0.331570\pi\) | |||||||
\(150\) | 11.2212 | 0.916208 | ||||||||
\(151\) | −11.7387 | −0.955285 | −0.477643 | − | 0.878554i | \(-0.658509\pi\) | ||||
−0.477643 | + | 0.878554i | \(0.658509\pi\) | |||||||
\(152\) | 7.87815 | 0.639002 | ||||||||
\(153\) | 11.2797 | 0.911912 | ||||||||
\(154\) | 22.5843 | 1.81989 | ||||||||
\(155\) | 1.10171 | 0.0884914 | ||||||||
\(156\) | 12.9674 | 1.03822 | ||||||||
\(157\) | 13.4078 | 1.07006 | 0.535028 | − | 0.844834i | \(-0.320301\pi\) | ||||
0.535028 | + | 0.844834i | \(0.320301\pi\) | |||||||
\(158\) | 13.7681 | 1.09533 | ||||||||
\(159\) | −3.07191 | −0.243618 | ||||||||
\(160\) | −0.657543 | −0.0519833 | ||||||||
\(161\) | −18.6950 | −1.47338 | ||||||||
\(162\) | −8.89298 | −0.698698 | ||||||||
\(163\) | −8.49718 | −0.665551 | −0.332775 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332775 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(164\) | 8.25622 | 0.644703 | ||||||||
\(165\) | 7.52033 | 0.585457 | ||||||||
\(166\) | −0.0309457 | −0.00240185 | ||||||||
\(167\) | −18.4665 | −1.42898 | −0.714490 | − | 0.699646i | \(-0.753341\pi\) | ||||
−0.714490 | + | 0.699646i | \(0.753341\pi\) | |||||||
\(168\) | −11.9176 | −0.919464 | ||||||||
\(169\) | 14.8617 | 1.14321 | ||||||||
\(170\) | −2.44358 | −0.187414 | ||||||||
\(171\) | 23.9122 | 1.82861 | ||||||||
\(172\) | 0.474388 | 0.0361718 | ||||||||
\(173\) | −7.14070 | −0.542897 | −0.271449 | − | 0.962453i | \(-0.587503\pi\) | ||||
−0.271449 | + | 0.962453i | \(0.587503\pi\) | |||||||
\(174\) | −18.9757 | −1.43854 | ||||||||
\(175\) | −22.1581 | −1.67500 | ||||||||
\(176\) | 4.65548 | 0.350920 | ||||||||
\(177\) | 21.4612 | 1.61313 | ||||||||
\(178\) | −11.2309 | −0.841793 | ||||||||
\(179\) | 0.549358 | 0.0410610 | 0.0205305 | − | 0.999789i | \(-0.493464\pi\) | ||||
0.0205305 | + | 0.999789i | \(0.493464\pi\) | |||||||
\(180\) | −1.99581 | −0.148759 | ||||||||
\(181\) | −23.6930 | −1.76108 | −0.880542 | − | 0.473967i | \(-0.842821\pi\) | ||||
−0.880542 | + | 0.473967i | \(0.842821\pi\) | |||||||
\(182\) | −25.6062 | −1.89806 | ||||||||
\(183\) | 28.9832 | 2.14250 | ||||||||
\(184\) | −3.85376 | −0.284103 | ||||||||
\(185\) | −6.40743 | −0.471083 | ||||||||
\(186\) | 4.11615 | 0.301810 | ||||||||
\(187\) | 17.3009 | 1.26516 | ||||||||
\(188\) | −3.65590 | −0.266634 | ||||||||
\(189\) | −0.420203 | −0.0305653 | ||||||||
\(190\) | −5.18022 | −0.375813 | ||||||||
\(191\) | −0.682066 | −0.0493525 | −0.0246763 | − | 0.999695i | \(-0.507855\pi\) | ||||
−0.0246763 | + | 0.999695i | \(0.507855\pi\) | |||||||
\(192\) | −2.45668 | −0.177295 | ||||||||
\(193\) | −25.0276 | −1.80153 | −0.900763 | − | 0.434312i | \(-0.856992\pi\) | ||||
−0.900763 | + | 0.434312i | \(0.856992\pi\) | |||||||
\(194\) | 4.35610 | 0.312750 | ||||||||
\(195\) | −8.52660 | −0.610602 | ||||||||
\(196\) | 16.5333 | 1.18095 | ||||||||
\(197\) | −19.0279 | −1.35568 | −0.677841 | − | 0.735209i | \(-0.737084\pi\) | ||||
−0.677841 | + | 0.735209i | \(0.737084\pi\) | |||||||
\(198\) | 14.1306 | 1.00422 | ||||||||
\(199\) | −5.36205 | −0.380106 | −0.190053 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190053 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(200\) | −4.56764 | −0.322981 | ||||||||
\(201\) | 8.35283 | 0.589163 | ||||||||
\(202\) | −1.82482 | −0.128394 | ||||||||
\(203\) | 37.4706 | 2.62992 | ||||||||
\(204\) | −9.12958 | −0.639199 | ||||||||
\(205\) | −5.42882 | −0.379165 | ||||||||
\(206\) | −10.8846 | −0.758365 | ||||||||
\(207\) | −11.6972 | −0.813009 | ||||||||
\(208\) | −5.27842 | −0.365992 | ||||||||
\(209\) | 36.6766 | 2.53697 | ||||||||
\(210\) | 7.83635 | 0.540759 | ||||||||
\(211\) | 27.9985 | 1.92750 | 0.963748 | − | 0.266815i | \(-0.0859714\pi\) | ||||
0.963748 | + | 0.266815i | \(0.0859714\pi\) | |||||||
\(212\) | 1.25043 | 0.0858802 | ||||||||
\(213\) | −10.9327 | −0.749098 | ||||||||
\(214\) | −16.0350 | −1.09613 | ||||||||
\(215\) | −0.311931 | −0.0212735 | ||||||||
\(216\) | −0.0866199 | −0.00589373 | ||||||||
\(217\) | −8.12801 | −0.551765 | ||||||||
\(218\) | 5.14174 | 0.348242 | ||||||||
\(219\) | −14.3651 | −0.970701 | ||||||||
\(220\) | −3.06118 | −0.206385 | ||||||||
\(221\) | −19.6158 | −1.31950 | ||||||||
\(222\) | −23.9391 | −1.60669 | ||||||||
\(223\) | −1.62148 | −0.108582 | −0.0542912 | − | 0.998525i | \(-0.517290\pi\) | ||||
−0.0542912 | + | 0.998525i | \(0.517290\pi\) | |||||||
\(224\) | 4.85111 | 0.324129 | ||||||||
\(225\) | −13.8640 | −0.924264 | ||||||||
\(226\) | 8.10135 | 0.538894 | ||||||||
\(227\) | 9.46216 | 0.628026 | 0.314013 | − | 0.949419i | \(-0.398327\pi\) | ||||
0.314013 | + | 0.949419i | \(0.398327\pi\) | |||||||
\(228\) | −19.3541 | −1.28175 | ||||||||
\(229\) | −1.53149 | −0.101204 | −0.0506019 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506019 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(230\) | 2.53401 | 0.167088 | ||||||||
\(231\) | −55.4823 | −3.65046 | ||||||||
\(232\) | 7.72413 | 0.507114 | ||||||||
\(233\) | −13.1802 | −0.863461 | −0.431731 | − | 0.902003i | \(-0.642097\pi\) | ||||
−0.431731 | + | 0.902003i | \(0.642097\pi\) | |||||||
\(234\) | −16.0214 | −1.04735 | ||||||||
\(235\) | 2.40391 | 0.156814 | ||||||||
\(236\) | −8.73589 | −0.568658 | ||||||||
\(237\) | −33.8239 | −2.19710 | ||||||||
\(238\) | 18.0279 | 1.16857 | ||||||||
\(239\) | 19.4289 | 1.25675 | 0.628374 | − | 0.777911i | \(-0.283721\pi\) | ||||
0.628374 | + | 0.777911i | \(0.283721\pi\) | |||||||
\(240\) | 1.61537 | 0.104272 | ||||||||
\(241\) | −9.95609 | −0.641328 | −0.320664 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320664 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(242\) | 10.6735 | 0.686119 | ||||||||
\(243\) | 22.1070 | 1.41817 | ||||||||
\(244\) | −11.7977 | −0.755272 | ||||||||
\(245\) | −10.8714 | −0.694546 | ||||||||
\(246\) | −20.2829 | −1.29319 | ||||||||
\(247\) | −41.5841 | −2.64594 | ||||||||
\(248\) | −1.67549 | −0.106394 | ||||||||
\(249\) | 0.0760234 | 0.00481779 | ||||||||
\(250\) | 6.29113 | 0.397886 | ||||||||
\(251\) | 29.0730 | 1.83507 | 0.917535 | − | 0.397656i | \(-0.130176\pi\) | ||||
0.917535 | + | 0.397656i | \(0.130176\pi\) | |||||||
\(252\) | 14.7244 | 0.927549 | ||||||||
\(253\) | −17.9411 | −1.12795 | ||||||||
\(254\) | −8.49939 | −0.533299 | ||||||||
\(255\) | 6.00309 | 0.375928 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.63027 | −0.226450 | −0.113225 | − | 0.993569i | \(-0.536118\pi\) | ||||
−0.113225 | + | 0.993569i | \(0.536118\pi\) | |||||||
\(258\) | −1.16542 | −0.0725558 | ||||||||
\(259\) | 47.2717 | 2.93732 | ||||||||
\(260\) | 3.47079 | 0.215249 | ||||||||
\(261\) | 23.4447 | 1.45119 | ||||||||
\(262\) | −5.87777 | −0.363130 | ||||||||
\(263\) | 14.2500 | 0.878695 | 0.439347 | − | 0.898317i | \(-0.355210\pi\) | ||||
0.439347 | + | 0.898317i | \(0.355210\pi\) | |||||||
\(264\) | −11.4370 | −0.703899 | ||||||||
\(265\) | −0.822214 | −0.0505082 | ||||||||
\(266\) | 38.2178 | 2.34328 | ||||||||
\(267\) | 27.5907 | 1.68853 | ||||||||
\(268\) | −3.40005 | −0.207691 | ||||||||
\(269\) | −15.8136 | −0.964171 | −0.482085 | − | 0.876124i | \(-0.660121\pi\) | ||||
−0.482085 | + | 0.876124i | \(0.660121\pi\) | |||||||
\(270\) | 0.0569563 | 0.00346625 | ||||||||
\(271\) | −2.72575 | −0.165577 | −0.0827887 | − | 0.996567i | \(-0.526383\pi\) | ||||
−0.0827887 | + | 0.996567i | \(0.526383\pi\) | |||||||
\(272\) | 3.71623 | 0.225330 | ||||||||
\(273\) | 62.9062 | 3.80725 | ||||||||
\(274\) | 12.7165 | 0.768233 | ||||||||
\(275\) | −21.2646 | −1.28230 | ||||||||
\(276\) | 9.46744 | 0.569873 | ||||||||
\(277\) | −3.79366 | −0.227939 | −0.113970 | − | 0.993484i | \(-0.536357\pi\) | ||||
−0.113970 | + | 0.993484i | \(0.536357\pi\) | |||||||
\(278\) | 8.41180 | 0.504506 | ||||||||
\(279\) | −5.08556 | −0.304464 | ||||||||
\(280\) | −3.18982 | −0.190628 | ||||||||
\(281\) | 6.39000 | 0.381195 | 0.190598 | − | 0.981668i | \(-0.438957\pi\) | ||||
0.190598 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(282\) | 8.98136 | 0.534832 | ||||||||
\(283\) | 7.11658 | 0.423037 | 0.211518 | − | 0.977374i | \(-0.432159\pi\) | ||||
0.211518 | + | 0.977374i | \(0.432159\pi\) | |||||||
\(284\) | 4.45021 | 0.264071 | ||||||||
\(285\) | 12.7261 | 0.753831 | ||||||||
\(286\) | −24.5736 | −1.45307 | ||||||||
\(287\) | 40.0519 | 2.36419 | ||||||||
\(288\) | 3.03526 | 0.178854 | ||||||||
\(289\) | −3.18960 | −0.187624 | ||||||||
\(290\) | −5.07895 | −0.298246 | ||||||||
\(291\) | −10.7015 | −0.627335 | ||||||||
\(292\) | 5.84736 | 0.342191 | ||||||||
\(293\) | 23.5193 | 1.37401 | 0.687007 | − | 0.726651i | \(-0.258924\pi\) | ||||
0.687007 | + | 0.726651i | \(0.258924\pi\) | |||||||
\(294\) | −40.6170 | −2.36883 | ||||||||
\(295\) | 5.74422 | 0.334441 | ||||||||
\(296\) | 9.74450 | 0.566387 | ||||||||
\(297\) | −0.403257 | −0.0233994 | ||||||||
\(298\) | 12.3235 | 0.713881 | ||||||||
\(299\) | 20.3418 | 1.17639 | ||||||||
\(300\) | 11.2212 | 0.647857 | ||||||||
\(301\) | 2.30131 | 0.132645 | ||||||||
\(302\) | −11.7387 | −0.675489 | ||||||||
\(303\) | 4.48299 | 0.257541 | ||||||||
\(304\) | 7.87815 | 0.451843 | ||||||||
\(305\) | 7.75751 | 0.444194 | ||||||||
\(306\) | 11.2797 | 0.644819 | ||||||||
\(307\) | −4.26127 | −0.243203 | −0.121602 | − | 0.992579i | \(-0.538803\pi\) | ||||
−0.121602 | + | 0.992579i | \(0.538803\pi\) | |||||||
\(308\) | 22.5843 | 1.28686 | ||||||||
\(309\) | 26.7399 | 1.52118 | ||||||||
\(310\) | 1.10171 | 0.0625729 | ||||||||
\(311\) | −2.05998 | −0.116811 | −0.0584054 | − | 0.998293i | \(-0.518602\pi\) | ||||
−0.0584054 | + | 0.998293i | \(0.518602\pi\) | |||||||
\(312\) | 12.9674 | 0.734132 | ||||||||
\(313\) | −4.77654 | −0.269986 | −0.134993 | − | 0.990847i | \(-0.543101\pi\) | ||||
−0.134993 | + | 0.990847i | \(0.543101\pi\) | |||||||
\(314\) | 13.4078 | 0.756644 | ||||||||
\(315\) | −9.68192 | −0.545514 | ||||||||
\(316\) | 13.7681 | 0.774518 | ||||||||
\(317\) | 24.9167 | 1.39946 | 0.699731 | − | 0.714406i | \(-0.253303\pi\) | ||||
0.699731 | + | 0.714406i | \(0.253303\pi\) | |||||||
\(318\) | −3.07191 | −0.172264 | ||||||||
\(319\) | 35.9596 | 2.01335 | ||||||||
\(320\) | −0.657543 | −0.0367578 | ||||||||
\(321\) | 39.3928 | 2.19869 | ||||||||
\(322\) | −18.6950 | −1.04183 | ||||||||
\(323\) | 29.2770 | 1.62902 | ||||||||
\(324\) | −8.89298 | −0.494054 | ||||||||
\(325\) | 24.1099 | 1.33738 | ||||||||
\(326\) | −8.49718 | −0.470615 | ||||||||
\(327\) | −12.6316 | −0.698528 | ||||||||
\(328\) | 8.25622 | 0.455874 | ||||||||
\(329\) | −17.7352 | −0.977772 | ||||||||
\(330\) | 7.52033 | 0.413980 | ||||||||
\(331\) | 29.1738 | 1.60353 | 0.801767 | − | 0.597636i | \(-0.203893\pi\) | ||||
0.801767 | + | 0.597636i | \(0.203893\pi\) | |||||||
\(332\) | −0.0309457 | −0.00169836 | ||||||||
\(333\) | 29.5771 | 1.62081 | ||||||||
\(334\) | −18.4665 | −1.01044 | ||||||||
\(335\) | 2.23568 | 0.122148 | ||||||||
\(336\) | −11.9176 | −0.650159 | ||||||||
\(337\) | −5.77401 | −0.314530 | −0.157265 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157265 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(338\) | 14.8617 | 0.808369 | ||||||||
\(339\) | −19.9024 | −1.08095 | ||||||||
\(340\) | −2.44358 | −0.132522 | ||||||||
\(341\) | −7.80023 | −0.422406 | ||||||||
\(342\) | 23.9122 | 1.29302 | ||||||||
\(343\) | 46.2472 | 2.49711 | ||||||||
\(344\) | 0.474388 | 0.0255773 | ||||||||
\(345\) | −6.22525 | −0.335156 | ||||||||
\(346\) | −7.14070 | −0.383886 | ||||||||
\(347\) | 16.8513 | 0.904623 | 0.452311 | − | 0.891860i | \(-0.350600\pi\) | ||||
0.452311 | + | 0.891860i | \(0.350600\pi\) | |||||||
\(348\) | −18.9757 | −1.01720 | ||||||||
\(349\) | 18.2569 | 0.977272 | 0.488636 | − | 0.872488i | \(-0.337495\pi\) | ||||
0.488636 | + | 0.872488i | \(0.337495\pi\) | |||||||
\(350\) | −22.1581 | −1.18440 | ||||||||
\(351\) | 0.457216 | 0.0244044 | ||||||||
\(352\) | 4.65548 | 0.248138 | ||||||||
\(353\) | −19.7042 | −1.04875 | −0.524374 | − | 0.851488i | \(-0.675701\pi\) | ||||
−0.524374 | + | 0.851488i | \(0.675701\pi\) | |||||||
\(354\) | 21.4612 | 1.14065 | ||||||||
\(355\) | −2.92620 | −0.155307 | ||||||||
\(356\) | −11.2309 | −0.595237 | ||||||||
\(357\) | −44.2887 | −2.34400 | ||||||||
\(358\) | 0.549358 | 0.0290345 | ||||||||
\(359\) | −22.2212 | −1.17279 | −0.586396 | − | 0.810024i | \(-0.699454\pi\) | ||||
−0.586396 | + | 0.810024i | \(0.699454\pi\) | |||||||
\(360\) | −1.99581 | −0.105189 | ||||||||
\(361\) | 43.0652 | 2.26659 | ||||||||
\(362\) | −23.6930 | −1.24527 | ||||||||
\(363\) | −26.2214 | −1.37626 | ||||||||
\(364\) | −25.6062 | −1.34213 | ||||||||
\(365\) | −3.84489 | −0.201251 | ||||||||
\(366\) | 28.9832 | 1.51498 | ||||||||
\(367\) | 31.0026 | 1.61832 | 0.809160 | − | 0.587588i | \(-0.199922\pi\) | ||||
0.809160 | + | 0.587588i | \(0.199922\pi\) | |||||||
\(368\) | −3.85376 | −0.200891 | ||||||||
\(369\) | 25.0598 | 1.30456 | ||||||||
\(370\) | −6.40743 | −0.333106 | ||||||||
\(371\) | 6.06600 | 0.314931 | ||||||||
\(372\) | 4.11615 | 0.213412 | ||||||||
\(373\) | 0.0557758 | 0.00288796 | 0.00144398 | − | 0.999999i | \(-0.499540\pi\) | ||||
0.00144398 | + | 0.999999i | \(0.499540\pi\) | |||||||
\(374\) | 17.3009 | 0.894606 | ||||||||
\(375\) | −15.4553 | −0.798107 | ||||||||
\(376\) | −3.65590 | −0.188539 | ||||||||
\(377\) | −40.7712 | −2.09982 | ||||||||
\(378\) | −0.420203 | −0.0216129 | ||||||||
\(379\) | −23.4822 | −1.20620 | −0.603099 | − | 0.797666i | \(-0.706068\pi\) | ||||
−0.603099 | + | 0.797666i | \(0.706068\pi\) | |||||||
\(380\) | −5.18022 | −0.265740 | ||||||||
\(381\) | 20.8802 | 1.06973 | ||||||||
\(382\) | −0.682066 | −0.0348975 | ||||||||
\(383\) | 28.1050 | 1.43610 | 0.718049 | − | 0.695992i | \(-0.245035\pi\) | ||||
0.718049 | + | 0.695992i | \(0.245035\pi\) | |||||||
\(384\) | −2.45668 | −0.125367 | ||||||||
\(385\) | −14.8501 | −0.756833 | ||||||||
\(386\) | −25.0276 | −1.27387 | ||||||||
\(387\) | 1.43989 | 0.0731938 | ||||||||
\(388\) | 4.35610 | 0.221148 | ||||||||
\(389\) | 27.4912 | 1.39386 | 0.696929 | − | 0.717140i | \(-0.254549\pi\) | ||||
0.696929 | + | 0.717140i | \(0.254549\pi\) | |||||||
\(390\) | −8.52660 | −0.431761 | ||||||||
\(391\) | −14.3215 | −0.724268 | ||||||||
\(392\) | 16.5333 | 0.835058 | ||||||||
\(393\) | 14.4398 | 0.728391 | ||||||||
\(394\) | −19.0279 | −0.958612 | ||||||||
\(395\) | −9.05314 | −0.455513 | ||||||||
\(396\) | 14.1306 | 0.710089 | ||||||||
\(397\) | 37.7034 | 1.89228 | 0.946141 | − | 0.323755i | \(-0.104946\pi\) | ||||
0.946141 | + | 0.323755i | \(0.104946\pi\) | |||||||
\(398\) | −5.36205 | −0.268775 | ||||||||
\(399\) | −93.8888 | −4.70032 | ||||||||
\(400\) | −4.56764 | −0.228382 | ||||||||
\(401\) | 0.289242 | 0.0144441 | 0.00722203 | − | 0.999974i | \(-0.497701\pi\) | ||||
0.00722203 | + | 0.999974i | \(0.497701\pi\) | |||||||
\(402\) | 8.35283 | 0.416601 | ||||||||
\(403\) | 8.84395 | 0.440549 | ||||||||
\(404\) | −1.82482 | −0.0907881 | ||||||||
\(405\) | 5.84752 | 0.290565 | ||||||||
\(406\) | 37.4706 | 1.85964 | ||||||||
\(407\) | 45.3653 | 2.24868 | ||||||||
\(408\) | −9.12958 | −0.451982 | ||||||||
\(409\) | 17.2439 | 0.852658 | 0.426329 | − | 0.904568i | \(-0.359807\pi\) | ||||
0.426329 | + | 0.904568i | \(0.359807\pi\) | |||||||
\(410\) | −5.42882 | −0.268110 | ||||||||
\(411\) | −31.2404 | −1.54097 | ||||||||
\(412\) | −10.8846 | −0.536245 | ||||||||
\(413\) | −42.3788 | −2.08532 | ||||||||
\(414\) | −11.6972 | −0.574884 | ||||||||
\(415\) | 0.0203481 | 0.000998849 0 | ||||||||
\(416\) | −5.27842 | −0.258796 | ||||||||
\(417\) | −20.6651 | −1.01197 | ||||||||
\(418\) | 36.6766 | 1.79391 | ||||||||
\(419\) | 11.8682 | 0.579798 | 0.289899 | − | 0.957057i | \(-0.406378\pi\) | ||||
0.289899 | + | 0.957057i | \(0.406378\pi\) | |||||||
\(420\) | 7.83635 | 0.382375 | ||||||||
\(421\) | 17.9260 | 0.873662 | 0.436831 | − | 0.899544i | \(-0.356101\pi\) | ||||
0.436831 | + | 0.899544i | \(0.356101\pi\) | |||||||
\(422\) | 27.9985 | 1.36294 | ||||||||
\(423\) | −11.0966 | −0.539535 | ||||||||
\(424\) | 1.25043 | 0.0607264 | ||||||||
\(425\) | −16.9744 | −0.823380 | ||||||||
\(426\) | −10.9327 | −0.529692 | ||||||||
\(427\) | −57.2321 | −2.76966 | ||||||||
\(428\) | −16.0350 | −0.775081 | ||||||||
\(429\) | 60.3693 | 2.91466 | ||||||||
\(430\) | −0.311931 | −0.0150426 | ||||||||
\(431\) | 23.7562 | 1.14430 | 0.572148 | − | 0.820150i | \(-0.306110\pi\) | ||||
0.572148 | + | 0.820150i | \(0.306110\pi\) | |||||||
\(432\) | −0.0866199 | −0.00416750 | ||||||||
\(433\) | −10.5516 | −0.507075 | −0.253538 | − | 0.967326i | \(-0.581594\pi\) | ||||
−0.253538 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(434\) | −8.12801 | −0.390157 | ||||||||
\(435\) | 12.4773 | 0.598242 | ||||||||
\(436\) | 5.14174 | 0.246244 | ||||||||
\(437\) | −30.3605 | −1.45234 | ||||||||
\(438\) | −14.3651 | −0.686390 | ||||||||
\(439\) | 13.2659 | 0.633148 | 0.316574 | − | 0.948568i | \(-0.397467\pi\) | ||||
0.316574 | + | 0.948568i | \(0.397467\pi\) | |||||||
\(440\) | −3.06118 | −0.145936 | ||||||||
\(441\) | 50.1829 | 2.38966 | ||||||||
\(442\) | −19.6158 | −0.933030 | ||||||||
\(443\) | −10.4100 | −0.494595 | −0.247298 | − | 0.968940i | \(-0.579543\pi\) | ||||
−0.247298 | + | 0.968940i | \(0.579543\pi\) | |||||||
\(444\) | −23.9391 | −1.13610 | ||||||||
\(445\) | 7.38481 | 0.350074 | ||||||||
\(446\) | −1.62148 | −0.0767793 | ||||||||
\(447\) | −30.2748 | −1.43195 | ||||||||
\(448\) | 4.85111 | 0.229194 | ||||||||
\(449\) | −17.3246 | −0.817597 | −0.408799 | − | 0.912625i | \(-0.634052\pi\) | ||||
−0.408799 | + | 0.912625i | \(0.634052\pi\) | |||||||
\(450\) | −13.8640 | −0.653553 | ||||||||
\(451\) | 38.4367 | 1.80991 | ||||||||
\(452\) | 8.10135 | 0.381055 | ||||||||
\(453\) | 28.8383 | 1.35494 | ||||||||
\(454\) | 9.46216 | 0.444081 | ||||||||
\(455\) | 16.8372 | 0.789339 | ||||||||
\(456\) | −19.3541 | −0.906337 | ||||||||
\(457\) | −20.1850 | −0.944215 | −0.472108 | − | 0.881541i | \(-0.656507\pi\) | ||||
−0.472108 | + | 0.881541i | \(0.656507\pi\) | |||||||
\(458\) | −1.53149 | −0.0715619 | ||||||||
\(459\) | −0.321900 | −0.0150250 | ||||||||
\(460\) | 2.53401 | 0.118149 | ||||||||
\(461\) | 1.41661 | 0.0659779 | 0.0329889 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329889 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(462\) | −55.4823 | −2.58127 | ||||||||
\(463\) | 19.8843 | 0.924101 | 0.462051 | − | 0.886854i | \(-0.347114\pi\) | ||||
0.462051 | + | 0.886854i | \(0.347114\pi\) | |||||||
\(464\) | 7.72413 | 0.358584 | ||||||||
\(465\) | −2.70654 | −0.125513 | ||||||||
\(466\) | −13.1802 | −0.610559 | ||||||||
\(467\) | −33.2983 | −1.54086 | −0.770431 | − | 0.637524i | \(-0.779959\pi\) | ||||
−0.770431 | + | 0.637524i | \(0.779959\pi\) | |||||||
\(468\) | −16.0214 | −0.740588 | ||||||||
\(469\) | −16.4940 | −0.761624 | ||||||||
\(470\) | 2.40391 | 0.110884 | ||||||||
\(471\) | −32.9385 | −1.51773 | ||||||||
\(472\) | −8.73589 | −0.402102 | ||||||||
\(473\) | 2.20851 | 0.101547 | ||||||||
\(474\) | −33.8239 | −1.55358 | ||||||||
\(475\) | −35.9845 | −1.65108 | ||||||||
\(476\) | 18.0279 | 0.826306 | ||||||||
\(477\) | 3.79539 | 0.173779 | ||||||||
\(478\) | 19.4289 | 0.888655 | ||||||||
\(479\) | −19.5149 | −0.891660 | −0.445830 | − | 0.895118i | \(-0.647091\pi\) | ||||
−0.445830 | + | 0.895118i | \(0.647091\pi\) | |||||||
\(480\) | 1.61537 | 0.0737312 | ||||||||
\(481\) | −51.4355 | −2.34526 | ||||||||
\(482\) | −9.95609 | −0.453487 | ||||||||
\(483\) | 45.9277 | 2.08978 | ||||||||
\(484\) | 10.6735 | 0.485159 | ||||||||
\(485\) | −2.86432 | −0.130062 | ||||||||
\(486\) | 22.1070 | 1.00280 | ||||||||
\(487\) | 2.43265 | 0.110234 | 0.0551169 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551169 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(488\) | −11.7977 | −0.534058 | ||||||||
\(489\) | 20.8748 | 0.943992 | ||||||||
\(490\) | −10.8714 | −0.491118 | ||||||||
\(491\) | 26.1573 | 1.18046 | 0.590231 | − | 0.807234i | \(-0.299036\pi\) | ||||
0.590231 | + | 0.807234i | \(0.299036\pi\) | |||||||
\(492\) | −20.2829 | −0.914422 | ||||||||
\(493\) | 28.7047 | 1.29279 | ||||||||
\(494\) | −41.5841 | −1.87096 | ||||||||
\(495\) | −9.29147 | −0.417621 | ||||||||
\(496\) | −1.67549 | −0.0752319 | ||||||||
\(497\) | 21.5885 | 0.968375 | ||||||||
\(498\) | 0.0760234 | 0.00340669 | ||||||||
\(499\) | 13.2342 | 0.592444 | 0.296222 | − | 0.955119i | \(-0.404273\pi\) | ||||
0.296222 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(500\) | 6.29113 | 0.281348 | ||||||||
\(501\) | 45.3662 | 2.02681 | ||||||||
\(502\) | 29.0730 | 1.29759 | ||||||||
\(503\) | −29.2876 | −1.30587 | −0.652934 | − | 0.757415i | \(-0.726462\pi\) | ||||
−0.652934 | + | 0.757415i | \(0.726462\pi\) | |||||||
\(504\) | 14.7244 | 0.655876 | ||||||||
\(505\) | 1.19990 | 0.0533947 | ||||||||
\(506\) | −17.9411 | −0.797580 | ||||||||
\(507\) | −36.5103 | −1.62148 | ||||||||
\(508\) | −8.49939 | −0.377099 | ||||||||
\(509\) | 27.6933 | 1.22748 | 0.613742 | − | 0.789507i | \(-0.289664\pi\) | ||||
0.613742 | + | 0.789507i | \(0.289664\pi\) | |||||||
\(510\) | 6.00309 | 0.265821 | ||||||||
\(511\) | 28.3662 | 1.25485 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.682404 | −0.0301289 | ||||||||
\(514\) | −3.63027 | −0.160124 | ||||||||
\(515\) | 7.15708 | 0.315379 | ||||||||
\(516\) | −1.16542 | −0.0513047 | ||||||||
\(517\) | −17.0200 | −0.748537 | ||||||||
\(518\) | 47.2717 | 2.07700 | ||||||||
\(519\) | 17.5424 | 0.770025 | ||||||||
\(520\) | 3.47079 | 0.152204 | ||||||||
\(521\) | −30.6888 | −1.34450 | −0.672250 | − | 0.740324i | \(-0.734672\pi\) | ||||
−0.672250 | + | 0.740324i | \(0.734672\pi\) | |||||||
\(522\) | 23.4447 | 1.02615 | ||||||||
\(523\) | −0.0449696 | −0.00196638 | −0.000983191 | − | 1.00000i | \(-0.500313\pi\) | ||||
−0.000983191 | 1.00000i | \(0.500313\pi\) | ||||||||
\(524\) | −5.87777 | −0.256772 | ||||||||
\(525\) | 54.4354 | 2.37575 | ||||||||
\(526\) | 14.2500 | 0.621331 | ||||||||
\(527\) | −6.22653 | −0.271232 | ||||||||
\(528\) | −11.4370 | −0.497732 | ||||||||
\(529\) | −8.14852 | −0.354284 | ||||||||
\(530\) | −0.822214 | −0.0357147 | ||||||||
\(531\) | −26.5157 | −1.15068 | ||||||||
\(532\) | 38.2178 | 1.65695 | ||||||||
\(533\) | −43.5798 | −1.88765 | ||||||||
\(534\) | 27.5907 | 1.19397 | ||||||||
\(535\) | 10.5437 | 0.455844 | ||||||||
\(536\) | −3.40005 | −0.146860 | ||||||||
\(537\) | −1.34960 | −0.0582393 | ||||||||
\(538\) | −15.8136 | −0.681772 | ||||||||
\(539\) | 76.9705 | 3.31536 | ||||||||
\(540\) | 0.0569563 | 0.00245101 | ||||||||
\(541\) | 30.4047 | 1.30720 | 0.653599 | − | 0.756841i | \(-0.273258\pi\) | ||||
0.653599 | + | 0.756841i | \(0.273258\pi\) | |||||||
\(542\) | −2.72575 | −0.117081 | ||||||||
\(543\) | 58.2060 | 2.49786 | ||||||||
\(544\) | 3.71623 | 0.159332 | ||||||||
\(545\) | −3.38091 | −0.144822 | ||||||||
\(546\) | 62.9062 | 2.69213 | ||||||||
\(547\) | −3.01713 | −0.129003 | −0.0645015 | − | 0.997918i | \(-0.520546\pi\) | ||||
−0.0645015 | + | 0.997918i | \(0.520546\pi\) | |||||||
\(548\) | 12.7165 | 0.543223 | ||||||||
\(549\) | −35.8091 | −1.52830 | ||||||||
\(550\) | −21.2646 | −0.906723 | ||||||||
\(551\) | 60.8519 | 2.59238 | ||||||||
\(552\) | 9.46744 | 0.402961 | ||||||||
\(553\) | 66.7908 | 2.84023 | ||||||||
\(554\) | −3.79366 | −0.161177 | ||||||||
\(555\) | 15.7410 | 0.668167 | ||||||||
\(556\) | 8.41180 | 0.356740 | ||||||||
\(557\) | 28.2522 | 1.19708 | 0.598541 | − | 0.801092i | \(-0.295747\pi\) | ||||
0.598541 | + | 0.801092i | \(0.295747\pi\) | |||||||
\(558\) | −5.08556 | −0.215289 | ||||||||
\(559\) | −2.50402 | −0.105909 | ||||||||
\(560\) | −3.18982 | −0.134794 | ||||||||
\(561\) | −42.5026 | −1.79446 | ||||||||
\(562\) | 6.39000 | 0.269546 | ||||||||
\(563\) | −0.798961 | −0.0336722 | −0.0168361 | − | 0.999858i | \(-0.505359\pi\) | ||||
−0.0168361 | + | 0.999858i | \(0.505359\pi\) | |||||||
\(564\) | 8.98136 | 0.378184 | ||||||||
\(565\) | −5.32698 | −0.224108 | ||||||||
\(566\) | 7.11658 | 0.299132 | ||||||||
\(567\) | −43.1409 | −1.81175 | ||||||||
\(568\) | 4.45021 | 0.186727 | ||||||||
\(569\) | −26.0163 | −1.09066 | −0.545331 | − | 0.838221i | \(-0.683596\pi\) | ||||
−0.545331 | + | 0.838221i | \(0.683596\pi\) | |||||||
\(570\) | 12.7261 | 0.533039 | ||||||||
\(571\) | −33.2937 | −1.39330 | −0.696650 | − | 0.717411i | \(-0.745327\pi\) | ||||
−0.696650 | + | 0.717411i | \(0.745327\pi\) | |||||||
\(572\) | −24.5736 | −1.02747 | ||||||||
\(573\) | 1.67561 | 0.0699998 | ||||||||
\(574\) | 40.0519 | 1.67173 | ||||||||
\(575\) | 17.6026 | 0.734078 | ||||||||
\(576\) | 3.03526 | 0.126469 | ||||||||
\(577\) | −5.13287 | −0.213684 | −0.106842 | − | 0.994276i | \(-0.534074\pi\) | ||||
−0.106842 | + | 0.994276i | \(0.534074\pi\) | |||||||
\(578\) | −3.18960 | −0.132670 | ||||||||
\(579\) | 61.4847 | 2.55522 | ||||||||
\(580\) | −5.07895 | −0.210892 | ||||||||
\(581\) | −0.150121 | −0.00622806 | ||||||||
\(582\) | −10.7015 | −0.443593 | ||||||||
\(583\) | 5.82137 | 0.241097 | ||||||||
\(584\) | 5.84736 | 0.241965 | ||||||||
\(585\) | 10.5347 | 0.435558 | ||||||||
\(586\) | 23.5193 | 0.971574 | ||||||||
\(587\) | 3.97512 | 0.164071 | 0.0820354 | − | 0.996629i | \(-0.473858\pi\) | ||||
0.0820354 | + | 0.996629i | \(0.473858\pi\) | |||||||
\(588\) | −40.6170 | −1.67502 | ||||||||
\(589\) | −13.1998 | −0.543888 | ||||||||
\(590\) | 5.74422 | 0.236486 | ||||||||
\(591\) | 46.7454 | 1.92285 | ||||||||
\(592\) | 9.74450 | 0.400496 | ||||||||
\(593\) | −12.3895 | −0.508776 | −0.254388 | − | 0.967102i | \(-0.581874\pi\) | ||||
−0.254388 | + | 0.967102i | \(0.581874\pi\) | |||||||
\(594\) | −0.403257 | −0.0165458 | ||||||||
\(595\) | −11.8541 | −0.485971 | ||||||||
\(596\) | 12.3235 | 0.504790 | ||||||||
\(597\) | 13.1728 | 0.539128 | ||||||||
\(598\) | 20.3418 | 0.831836 | ||||||||
\(599\) | 28.5977 | 1.16847 | 0.584236 | − | 0.811584i | \(-0.301394\pi\) | ||||
0.584236 | + | 0.811584i | \(0.301394\pi\) | |||||||
\(600\) | 11.2212 | 0.458104 | ||||||||
\(601\) | −24.5799 | −1.00264 | −0.501318 | − | 0.865263i | \(-0.667151\pi\) | ||||
−0.501318 | + | 0.865263i | \(0.667151\pi\) | |||||||
\(602\) | 2.30131 | 0.0937945 | ||||||||
\(603\) | −10.3200 | −0.420264 | ||||||||
\(604\) | −11.7387 | −0.477643 | ||||||||
\(605\) | −7.01829 | −0.285334 | ||||||||
\(606\) | 4.48299 | 0.182109 | ||||||||
\(607\) | −43.2003 | −1.75345 | −0.876723 | − | 0.480995i | \(-0.840275\pi\) | ||||
−0.876723 | + | 0.480995i | \(0.840275\pi\) | |||||||
\(608\) | 7.87815 | 0.319501 | ||||||||
\(609\) | −92.0533 | −3.73019 | ||||||||
\(610\) | 7.75751 | 0.314092 | ||||||||
\(611\) | 19.2974 | 0.780688 | ||||||||
\(612\) | 11.2797 | 0.455956 | ||||||||
\(613\) | −20.8148 | −0.840703 | −0.420351 | − | 0.907361i | \(-0.638093\pi\) | ||||
−0.420351 | + | 0.907361i | \(0.638093\pi\) | |||||||
\(614\) | −4.26127 | −0.171971 | ||||||||
\(615\) | 13.3369 | 0.537794 | ||||||||
\(616\) | 22.5843 | 0.909946 | ||||||||
\(617\) | 14.5617 | 0.586233 | 0.293117 | − | 0.956077i | \(-0.405308\pi\) | ||||
0.293117 | + | 0.956077i | \(0.405308\pi\) | |||||||
\(618\) | 26.7399 | 1.07564 | ||||||||
\(619\) | −33.2360 | −1.33587 | −0.667934 | − | 0.744221i | \(-0.732821\pi\) | ||||
−0.667934 | + | 0.744221i | \(0.732821\pi\) | |||||||
\(620\) | 1.10171 | 0.0442457 | ||||||||
\(621\) | 0.333812 | 0.0133954 | ||||||||
\(622\) | −2.05998 | −0.0825977 | ||||||||
\(623\) | −54.4825 | −2.18279 | ||||||||
\(624\) | 12.9674 | 0.519110 | ||||||||
\(625\) | 18.7015 | 0.748060 | ||||||||
\(626\) | −4.77654 | −0.190909 | ||||||||
\(627\) | −90.1025 | −3.59835 | ||||||||
\(628\) | 13.4078 | 0.535028 | ||||||||
\(629\) | 36.2128 | 1.44390 | ||||||||
\(630\) | −9.68192 | −0.385737 | ||||||||
\(631\) | 21.7958 | 0.867679 | 0.433839 | − | 0.900990i | \(-0.357158\pi\) | ||||
0.433839 | + | 0.900990i | \(0.357158\pi\) | |||||||
\(632\) | 13.7681 | 0.547667 | ||||||||
\(633\) | −68.7832 | −2.73389 | ||||||||
\(634\) | 24.9167 | 0.989569 | ||||||||
\(635\) | 5.58871 | 0.221781 | ||||||||
\(636\) | −3.07191 | −0.121809 | ||||||||
\(637\) | −87.2697 | −3.45775 | ||||||||
\(638\) | 35.9596 | 1.42365 | ||||||||
\(639\) | 13.5075 | 0.534350 | ||||||||
\(640\) | −0.657543 | −0.0259917 | ||||||||
\(641\) | 13.0221 | 0.514344 | 0.257172 | − | 0.966366i | \(-0.417209\pi\) | ||||
0.257172 | + | 0.966366i | \(0.417209\pi\) | |||||||
\(642\) | 39.3928 | 1.55471 | ||||||||
\(643\) | −24.7405 | −0.975670 | −0.487835 | − | 0.872936i | \(-0.662213\pi\) | ||||
−0.487835 | + | 0.872936i | \(0.662213\pi\) | |||||||
\(644\) | −18.6950 | −0.736688 | ||||||||
\(645\) | 0.766313 | 0.0301735 | ||||||||
\(646\) | 29.2770 | 1.15189 | ||||||||
\(647\) | 48.5747 | 1.90967 | 0.954835 | − | 0.297137i | \(-0.0960318\pi\) | ||||
0.954835 | + | 0.297137i | \(0.0960318\pi\) | |||||||
\(648\) | −8.89298 | −0.349349 | ||||||||
\(649\) | −40.6698 | −1.59643 | ||||||||
\(650\) | 24.1099 | 0.945668 | ||||||||
\(651\) | 19.9679 | 0.782604 | ||||||||
\(652\) | −8.49718 | −0.332775 | ||||||||
\(653\) | −28.2937 | −1.10722 | −0.553609 | − | 0.832777i | \(-0.686750\pi\) | ||||
−0.553609 | + | 0.832777i | \(0.686750\pi\) | |||||||
\(654\) | −12.6316 | −0.493934 | ||||||||
\(655\) | 3.86489 | 0.151014 | ||||||||
\(656\) | 8.25622 | 0.322351 | ||||||||
\(657\) | 17.7482 | 0.692425 | ||||||||
\(658\) | −17.7352 | −0.691390 | ||||||||
\(659\) | −20.0225 | −0.779966 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(660\) | 7.52033 | 0.292728 | ||||||||
\(661\) | 8.46135 | 0.329108 | 0.164554 | − | 0.986368i | \(-0.447381\pi\) | ||||
0.164554 | + | 0.986368i | \(0.447381\pi\) | |||||||
\(662\) | 29.1738 | 1.13387 | ||||||||
\(663\) | 48.1897 | 1.87153 | ||||||||
\(664\) | −0.0309457 | −0.00120092 | ||||||||
\(665\) | −25.1298 | −0.974494 | ||||||||
\(666\) | 29.5771 | 1.14609 | ||||||||
\(667\) | −29.7670 | −1.15258 | ||||||||
\(668\) | −18.4665 | −0.714490 | ||||||||
\(669\) | 3.98345 | 0.154009 | ||||||||
\(670\) | 2.23568 | 0.0863718 | ||||||||
\(671\) | −54.9241 | −2.12032 | ||||||||
\(672\) | −11.9176 | −0.459732 | ||||||||
\(673\) | −13.2386 | −0.510311 | −0.255155 | − | 0.966900i | \(-0.582127\pi\) | ||||
−0.255155 | + | 0.966900i | \(0.582127\pi\) | |||||||
\(674\) | −5.77401 | −0.222407 | ||||||||
\(675\) | 0.395648 | 0.0152285 | ||||||||
\(676\) | 14.8617 | 0.571603 | ||||||||
\(677\) | 28.0768 | 1.07908 | 0.539540 | − | 0.841960i | \(-0.318598\pi\) | ||||
0.539540 | + | 0.841960i | \(0.318598\pi\) | |||||||
\(678\) | −19.9024 | −0.764347 | ||||||||
\(679\) | 21.1319 | 0.810970 | ||||||||
\(680\) | −2.44358 | −0.0937072 | ||||||||
\(681\) | −23.2455 | −0.890768 | ||||||||
\(682\) | −7.80023 | −0.298686 | ||||||||
\(683\) | −16.6571 | −0.637366 | −0.318683 | − | 0.947861i | \(-0.603241\pi\) | ||||
−0.318683 | + | 0.947861i | \(0.603241\pi\) | |||||||
\(684\) | 23.9122 | 0.914307 | ||||||||
\(685\) | −8.36166 | −0.319482 | ||||||||
\(686\) | 46.2472 | 1.76573 | ||||||||
\(687\) | 3.76238 | 0.143544 | ||||||||
\(688\) | 0.474388 | 0.0180859 | ||||||||
\(689\) | −6.60031 | −0.251452 | ||||||||
\(690\) | −6.22525 | −0.236991 | ||||||||
\(691\) | 45.7787 | 1.74150 | 0.870752 | − | 0.491722i | \(-0.163632\pi\) | ||||
0.870752 | + | 0.491722i | \(0.163632\pi\) | |||||||
\(692\) | −7.14070 | −0.271449 | ||||||||
\(693\) | 68.5491 | 2.60397 | ||||||||
\(694\) | 16.8513 | 0.639665 | ||||||||
\(695\) | −5.53112 | −0.209807 | ||||||||
\(696\) | −18.9757 | −0.719272 | ||||||||
\(697\) | 30.6821 | 1.16217 | ||||||||
\(698\) | 18.2569 | 0.691035 | ||||||||
\(699\) | 32.3794 | 1.22470 | ||||||||
\(700\) | −22.1581 | −0.837499 | ||||||||
\(701\) | 5.42076 | 0.204739 | 0.102370 | − | 0.994746i | \(-0.467358\pi\) | ||||
0.102370 | + | 0.994746i | \(0.467358\pi\) | |||||||
\(702\) | 0.457216 | 0.0172565 | ||||||||
\(703\) | 76.7686 | 2.89538 | ||||||||
\(704\) | 4.65548 | 0.175460 | ||||||||
\(705\) | −5.90563 | −0.222419 | ||||||||
\(706\) | −19.7042 | −0.741577 | ||||||||
\(707\) | −8.85240 | −0.332929 | ||||||||
\(708\) | 21.4612 | 0.806563 | ||||||||
\(709\) | −19.8950 | −0.747173 | −0.373587 | − | 0.927595i | \(-0.621872\pi\) | ||||
−0.373587 | + | 0.927595i | \(0.621872\pi\) | |||||||
\(710\) | −2.92620 | −0.109818 | ||||||||
\(711\) | 41.7899 | 1.56724 | ||||||||
\(712\) | −11.2309 | −0.420896 | ||||||||
\(713\) | 6.45695 | 0.241815 | ||||||||
\(714\) | −44.2887 | −1.65746 | ||||||||
\(715\) | 16.1582 | 0.604282 | ||||||||
\(716\) | 0.549358 | 0.0205305 | ||||||||
\(717\) | −47.7304 | −1.78252 | ||||||||
\(718\) | −22.2212 | −0.829289 | ||||||||
\(719\) | 16.2096 | 0.604517 | 0.302259 | − | 0.953226i | \(-0.402259\pi\) | ||||
0.302259 | + | 0.953226i | \(0.402259\pi\) | |||||||
\(720\) | −1.99581 | −0.0743796 | ||||||||
\(721\) | −52.8023 | −1.96646 | ||||||||
\(722\) | 43.0652 | 1.60272 | ||||||||
\(723\) | 24.4589 | 0.909636 | ||||||||
\(724\) | −23.6930 | −0.880542 | ||||||||
\(725\) | −35.2810 | −1.31030 | ||||||||
\(726\) | −26.2214 | −0.973166 | ||||||||
\(727\) | −25.5839 | −0.948854 | −0.474427 | − | 0.880295i | \(-0.657345\pi\) | ||||
−0.474427 | + | 0.880295i | \(0.657345\pi\) | |||||||
\(728\) | −25.6062 | −0.949029 | ||||||||
\(729\) | −27.6309 | −1.02337 | ||||||||
\(730\) | −3.84489 | −0.142306 | ||||||||
\(731\) | 1.76294 | 0.0652046 | ||||||||
\(732\) | 28.9832 | 1.07125 | ||||||||
\(733\) | −26.4630 | −0.977432 | −0.488716 | − | 0.872443i | \(-0.662535\pi\) | ||||
−0.488716 | + | 0.872443i | \(0.662535\pi\) | |||||||
\(734\) | 31.0026 | 1.14433 | ||||||||
\(735\) | 26.7074 | 0.985118 | ||||||||
\(736\) | −3.85376 | −0.142052 | ||||||||
\(737\) | −15.8289 | −0.583064 | ||||||||
\(738\) | 25.0598 | 0.922463 | ||||||||
\(739\) | 4.76143 | 0.175152 | 0.0875760 | − | 0.996158i | \(-0.472088\pi\) | ||||
0.0875760 | + | 0.996158i | \(0.472088\pi\) | |||||||
\(740\) | −6.40743 | −0.235542 | ||||||||
\(741\) | 102.159 | 3.75290 | ||||||||
\(742\) | 6.06600 | 0.222690 | ||||||||
\(743\) | −42.7383 | −1.56791 | −0.783957 | − | 0.620815i | \(-0.786802\pi\) | ||||
−0.783957 | + | 0.620815i | \(0.786802\pi\) | |||||||
\(744\) | 4.11615 | 0.150905 | ||||||||
\(745\) | −8.10323 | −0.296879 | ||||||||
\(746\) | 0.0557758 | 0.00204210 | ||||||||
\(747\) | −0.0939281 | −0.00343665 | ||||||||
\(748\) | 17.3009 | 0.632582 | ||||||||
\(749\) | −77.7876 | −2.84230 | ||||||||
\(750\) | −15.4553 | −0.564347 | ||||||||
\(751\) | 0.0611600 | 0.00223176 | 0.00111588 | − | 0.999999i | \(-0.499645\pi\) | ||||
0.00111588 | + | 0.999999i | \(0.499645\pi\) | |||||||
\(752\) | −3.65590 | −0.133317 | ||||||||
\(753\) | −71.4229 | −2.60279 | ||||||||
\(754\) | −40.7712 | −1.48480 | ||||||||
\(755\) | 7.71873 | 0.280913 | ||||||||
\(756\) | −0.420203 | −0.0152826 | ||||||||
\(757\) | 28.9890 | 1.05362 | 0.526811 | − | 0.849982i | \(-0.323388\pi\) | ||||
0.526811 | + | 0.849982i | \(0.323388\pi\) | |||||||
\(758\) | −23.4822 | −0.852911 | ||||||||
\(759\) | 44.0755 | 1.59984 | ||||||||
\(760\) | −5.18022 | −0.187906 | ||||||||
\(761\) | 6.54394 | 0.237218 | 0.118609 | − | 0.992941i | \(-0.462157\pi\) | ||||
0.118609 | + | 0.992941i | \(0.462157\pi\) | |||||||
\(762\) | 20.8802 | 0.756411 | ||||||||
\(763\) | 24.9432 | 0.903003 | ||||||||
\(764\) | −0.682066 | −0.0246763 | ||||||||
\(765\) | −7.41691 | −0.268159 | ||||||||
\(766\) | 28.1050 | 1.01548 | ||||||||
\(767\) | 46.1116 | 1.66499 | ||||||||
\(768\) | −2.45668 | −0.0886477 | ||||||||
\(769\) | −48.0782 | −1.73374 | −0.866872 | − | 0.498530i | \(-0.833873\pi\) | ||||
−0.866872 | + | 0.498530i | \(0.833873\pi\) | |||||||
\(770\) | −14.8501 | −0.535162 | ||||||||
\(771\) | 8.91840 | 0.321188 | ||||||||
\(772\) | −25.0276 | −0.900763 | ||||||||
\(773\) | 13.0824 | 0.470541 | 0.235271 | − | 0.971930i | \(-0.424402\pi\) | ||||
0.235271 | + | 0.971930i | \(0.424402\pi\) | |||||||
\(774\) | 1.43989 | 0.0517558 | ||||||||
\(775\) | 7.65305 | 0.274906 | ||||||||
\(776\) | 4.35610 | 0.156375 | ||||||||
\(777\) | −116.131 | −4.16618 | ||||||||
\(778\) | 27.4912 | 0.985606 | ||||||||
\(779\) | 65.0437 | 2.33043 | ||||||||
\(780\) | −8.52660 | −0.305301 | ||||||||
\(781\) | 20.7179 | 0.741343 | ||||||||
\(782\) | −14.3215 | −0.512135 | ||||||||
\(783\) | −0.669063 | −0.0239104 | ||||||||
\(784\) | 16.5333 | 0.590475 | ||||||||
\(785\) | −8.81618 | −0.314663 | ||||||||
\(786\) | 14.4398 | 0.515050 | ||||||||
\(787\) | −49.4331 | −1.76210 | −0.881050 | − | 0.473022i | \(-0.843163\pi\) | ||||
−0.881050 | + | 0.473022i | \(0.843163\pi\) | |||||||
\(788\) | −19.0279 | −0.677841 | ||||||||
\(789\) | −35.0077 | −1.24631 | ||||||||
\(790\) | −9.05314 | −0.322096 | ||||||||
\(791\) | 39.3006 | 1.39737 | ||||||||
\(792\) | 14.1306 | 0.502109 | ||||||||
\(793\) | 62.2733 | 2.21139 | ||||||||
\(794\) | 37.7034 | 1.33805 | ||||||||
\(795\) | 2.01991 | 0.0716390 | ||||||||
\(796\) | −5.36205 | −0.190053 | ||||||||
\(797\) | 37.6259 | 1.33278 | 0.666389 | − | 0.745605i | \(-0.267839\pi\) | ||||
0.666389 | + | 0.745605i | \(0.267839\pi\) | |||||||
\(798\) | −93.8888 | −3.32363 | ||||||||
\(799\) | −13.5862 | −0.480644 | ||||||||
\(800\) | −4.56764 | −0.161490 | ||||||||
\(801\) | −34.0887 | −1.20447 | ||||||||
\(802\) | 0.289242 | 0.0102135 | ||||||||
\(803\) | 27.2223 | 0.960653 | ||||||||
\(804\) | 8.35283 | 0.294581 | ||||||||
\(805\) | 12.2928 | 0.433264 | ||||||||
\(806\) | 8.84395 | 0.311515 | ||||||||
\(807\) | 38.8488 | 1.36754 | ||||||||
\(808\) | −1.82482 | −0.0641969 | ||||||||
\(809\) | −12.0141 | −0.422395 | −0.211197 | − | 0.977443i | \(-0.567736\pi\) | ||||
−0.211197 | + | 0.977443i | \(0.567736\pi\) | |||||||
\(810\) | 5.84752 | 0.205461 | ||||||||
\(811\) | 6.50765 | 0.228515 | 0.114257 | − | 0.993451i | \(-0.463551\pi\) | ||||
0.114257 | + | 0.993451i | \(0.463551\pi\) | |||||||
\(812\) | 37.4706 | 1.31496 | ||||||||
\(813\) | 6.69628 | 0.234849 | ||||||||
\(814\) | 45.3653 | 1.59005 | ||||||||
\(815\) | 5.58726 | 0.195713 | ||||||||
\(816\) | −9.12958 | −0.319599 | ||||||||
\(817\) | 3.73730 | 0.130752 | ||||||||
\(818\) | 17.2439 | 0.602921 | ||||||||
\(819\) | −77.7215 | −2.71581 | ||||||||
\(820\) | −5.42882 | −0.189583 | ||||||||
\(821\) | −13.4854 | −0.470644 | −0.235322 | − | 0.971917i | \(-0.575614\pi\) | ||||
−0.235322 | + | 0.971917i | \(0.575614\pi\) | |||||||
\(822\) | −31.2404 | −1.08963 | ||||||||
\(823\) | 17.5977 | 0.613417 | 0.306708 | − | 0.951804i | \(-0.400772\pi\) | ||||
0.306708 | + | 0.951804i | \(0.400772\pi\) | |||||||
\(824\) | −10.8846 | −0.379182 | ||||||||
\(825\) | 52.2401 | 1.81877 | ||||||||
\(826\) | −42.3788 | −1.47455 | ||||||||
\(827\) | −7.38576 | −0.256828 | −0.128414 | − | 0.991721i | \(-0.540989\pi\) | ||||
−0.128414 | + | 0.991721i | \(0.540989\pi\) | |||||||
\(828\) | −11.6972 | −0.406505 | ||||||||
\(829\) | 23.0075 | 0.799083 | 0.399541 | − | 0.916715i | \(-0.369169\pi\) | ||||
0.399541 | + | 0.916715i | \(0.369169\pi\) | |||||||
\(830\) | 0.0203481 | 0.000706293 0 | ||||||||
\(831\) | 9.31981 | 0.323300 | ||||||||
\(832\) | −5.27842 | −0.182996 | ||||||||
\(833\) | 61.4417 | 2.12883 | ||||||||
\(834\) | −20.6651 | −0.715573 | ||||||||
\(835\) | 12.1425 | 0.420209 | ||||||||
\(836\) | 36.6766 | 1.26849 | ||||||||
\(837\) | 0.145131 | 0.00501646 | ||||||||
\(838\) | 11.8682 | 0.409979 | ||||||||
\(839\) | 37.2965 | 1.28762 | 0.643810 | − | 0.765186i | \(-0.277353\pi\) | ||||
0.643810 | + | 0.765186i | \(0.277353\pi\) | |||||||
\(840\) | 7.83635 | 0.270380 | ||||||||
\(841\) | 30.6622 | 1.05732 | ||||||||
\(842\) | 17.9260 | 0.617772 | ||||||||
\(843\) | −15.6982 | −0.540673 | ||||||||
\(844\) | 27.9985 | 0.963748 | ||||||||
\(845\) | −9.77219 | −0.336174 | ||||||||
\(846\) | −11.0966 | −0.381509 | ||||||||
\(847\) | 51.7784 | 1.77913 | ||||||||
\(848\) | 1.25043 | 0.0429401 | ||||||||
\(849\) | −17.4831 | −0.600020 | ||||||||
\(850\) | −16.9744 | −0.582217 | ||||||||
\(851\) | −37.5530 | −1.28730 | ||||||||
\(852\) | −10.9327 | −0.374549 | ||||||||
\(853\) | 14.7541 | 0.505170 | 0.252585 | − | 0.967575i | \(-0.418719\pi\) | ||||
0.252585 | + | 0.967575i | \(0.418719\pi\) | |||||||
\(854\) | −57.2321 | −1.95844 | ||||||||
\(855\) | −15.7233 | −0.537726 | ||||||||
\(856\) | −16.0350 | −0.548065 | ||||||||
\(857\) | 2.80112 | 0.0956844 | 0.0478422 | − | 0.998855i | \(-0.484766\pi\) | ||||
0.0478422 | + | 0.998855i | \(0.484766\pi\) | |||||||
\(858\) | 60.3693 | 2.06097 | ||||||||
\(859\) | −20.7412 | −0.707679 | −0.353840 | − | 0.935306i | \(-0.615124\pi\) | ||||
−0.353840 | + | 0.935306i | \(0.615124\pi\) | |||||||
\(860\) | −0.311931 | −0.0106367 | ||||||||
\(861\) | −98.3945 | −3.35328 | ||||||||
\(862\) | 23.7562 | 0.809140 | ||||||||
\(863\) | −28.2525 | −0.961726 | −0.480863 | − | 0.876796i | \(-0.659676\pi\) | ||||
−0.480863 | + | 0.876796i | \(0.659676\pi\) | |||||||
\(864\) | −0.0866199 | −0.00294687 | ||||||||
\(865\) | 4.69532 | 0.159646 | ||||||||
\(866\) | −10.5516 | −0.358556 | ||||||||
\(867\) | 7.83583 | 0.266119 | ||||||||
\(868\) | −8.12801 | −0.275883 | ||||||||
\(869\) | 64.0973 | 2.17435 | ||||||||
\(870\) | 12.4773 | 0.423021 | ||||||||
\(871\) | 17.9469 | 0.608107 | ||||||||
\(872\) | 5.14174 | 0.174121 | ||||||||
\(873\) | 13.2219 | 0.447493 | ||||||||
\(874\) | −30.3605 | −1.02696 | ||||||||
\(875\) | 30.5190 | 1.03173 | ||||||||
\(876\) | −14.3651 | −0.485351 | ||||||||
\(877\) | 13.8321 | 0.467078 | 0.233539 | − | 0.972347i | \(-0.424969\pi\) | ||||
0.233539 | + | 0.972347i | \(0.424969\pi\) | |||||||
\(878\) | 13.2659 | 0.447703 | ||||||||
\(879\) | −57.7794 | −1.94885 | ||||||||
\(880\) | −3.06118 | −0.103192 | ||||||||
\(881\) | 15.1747 | 0.511248 | 0.255624 | − | 0.966776i | \(-0.417719\pi\) | ||||
0.255624 | + | 0.966776i | \(0.417719\pi\) | |||||||
\(882\) | 50.1829 | 1.68975 | ||||||||
\(883\) | −43.4233 | −1.46131 | −0.730656 | − | 0.682746i | \(-0.760786\pi\) | ||||
−0.730656 | + | 0.682746i | \(0.760786\pi\) | |||||||
\(884\) | −19.6158 | −0.659752 | ||||||||
\(885\) | −14.1117 | −0.474359 | ||||||||
\(886\) | −10.4100 | −0.349732 | ||||||||
\(887\) | −31.6996 | −1.06437 | −0.532184 | − | 0.846629i | \(-0.678628\pi\) | ||||
−0.532184 | + | 0.846629i | \(0.678628\pi\) | |||||||
\(888\) | −23.9391 | −0.803343 | ||||||||
\(889\) | −41.2315 | −1.38286 | ||||||||
\(890\) | 7.38481 | 0.247539 | ||||||||
\(891\) | −41.4011 | −1.38699 | ||||||||
\(892\) | −1.62148 | −0.0542912 | ||||||||
\(893\) | −28.8017 | −0.963813 | ||||||||
\(894\) | −30.2748 | −1.01254 | ||||||||
\(895\) | −0.361227 | −0.0120745 | ||||||||
\(896\) | 4.85111 | 0.162064 | ||||||||
\(897\) | −49.9731 | −1.66855 | ||||||||
\(898\) | −17.3246 | −0.578129 | ||||||||
\(899\) | −12.9417 | −0.431631 | ||||||||
\(900\) | −13.8640 | −0.462132 | ||||||||
\(901\) | 4.64691 | 0.154811 | ||||||||
\(902\) | 38.4367 | 1.27980 | ||||||||
\(903\) | −5.65358 | −0.188139 | ||||||||
\(904\) | 8.10135 | 0.269447 | ||||||||
\(905\) | 15.5791 | 0.517868 | ||||||||
\(906\) | 28.8383 | 0.958088 | ||||||||
\(907\) | −20.0221 | −0.664822 | −0.332411 | − | 0.943135i | \(-0.607862\pi\) | ||||
−0.332411 | + | 0.943135i | \(0.607862\pi\) | |||||||
\(908\) | 9.46216 | 0.314013 | ||||||||
\(909\) | −5.53879 | −0.183710 | ||||||||
\(910\) | 16.8372 | 0.558147 | ||||||||
\(911\) | −57.5661 | −1.90725 | −0.953625 | − | 0.300996i | \(-0.902681\pi\) | ||||
−0.953625 | + | 0.300996i | \(0.902681\pi\) | |||||||
\(912\) | −19.3541 | −0.640877 | ||||||||
\(913\) | −0.144067 | −0.00476792 | ||||||||
\(914\) | −20.1850 | −0.667661 | ||||||||
\(915\) | −19.0577 | −0.630028 | ||||||||
\(916\) | −1.53149 | −0.0506019 | ||||||||
\(917\) | −28.5137 | −0.941607 | ||||||||
\(918\) | −0.321900 | −0.0106243 | ||||||||
\(919\) | −35.7330 | −1.17872 | −0.589362 | − | 0.807869i | \(-0.700621\pi\) | ||||
−0.589362 | + | 0.807869i | \(0.700621\pi\) | |||||||
\(920\) | 2.53401 | 0.0835440 | ||||||||
\(921\) | 10.4686 | 0.344951 | ||||||||
\(922\) | 1.41661 | 0.0466534 | ||||||||
\(923\) | −23.4900 | −0.773184 | ||||||||
\(924\) | −55.4823 | −1.82523 | ||||||||
\(925\) | −44.5093 | −1.46346 | ||||||||
\(926\) | 19.8843 | 0.653438 | ||||||||
\(927\) | −33.0375 | −1.08509 | ||||||||
\(928\) | 7.72413 | 0.253557 | ||||||||
\(929\) | 43.7375 | 1.43498 | 0.717490 | − | 0.696568i | \(-0.245291\pi\) | ||||
0.717490 | + | 0.696568i | \(0.245291\pi\) | |||||||
\(930\) | −2.70654 | −0.0887510 | ||||||||
\(931\) | 130.252 | 4.26883 | ||||||||
\(932\) | −13.1802 | −0.431731 | ||||||||
\(933\) | 5.06071 | 0.165680 | ||||||||
\(934\) | −33.2983 | −1.08955 | ||||||||
\(935\) | −11.3761 | −0.372037 | ||||||||
\(936\) | −16.0214 | −0.523675 | ||||||||
\(937\) | −9.17833 | −0.299843 | −0.149922 | − | 0.988698i | \(-0.547902\pi\) | ||||
−0.149922 | + | 0.988698i | \(0.547902\pi\) | |||||||
\(938\) | −16.4940 | −0.538549 | ||||||||
\(939\) | 11.7344 | 0.382938 | ||||||||
\(940\) | 2.40391 | 0.0784069 | ||||||||
\(941\) | −10.8151 | −0.352561 | −0.176280 | − | 0.984340i | \(-0.556407\pi\) | ||||
−0.176280 | + | 0.984340i | \(0.556407\pi\) | |||||||
\(942\) | −32.9385 | −1.07320 | ||||||||
\(943\) | −31.8175 | −1.03612 | ||||||||
\(944\) | −8.73589 | −0.284329 | ||||||||
\(945\) | 0.276301 | 0.00898809 | ||||||||
\(946\) | 2.20851 | 0.0718047 | ||||||||
\(947\) | 39.6293 | 1.28778 | 0.643889 | − | 0.765119i | \(-0.277320\pi\) | ||||
0.643889 | + | 0.765119i | \(0.277320\pi\) | |||||||
\(948\) | −33.8239 | −1.09855 | ||||||||
\(949\) | −30.8648 | −1.00191 | ||||||||
\(950\) | −35.9845 | −1.16749 | ||||||||
\(951\) | −61.2123 | −1.98495 | ||||||||
\(952\) | 18.0279 | 0.584287 | ||||||||
\(953\) | −51.2464 | −1.66004 | −0.830018 | − | 0.557737i | \(-0.811670\pi\) | ||||
−0.830018 | + | 0.557737i | \(0.811670\pi\) | |||||||
\(954\) | 3.79539 | 0.122880 | ||||||||
\(955\) | 0.448487 | 0.0145127 | ||||||||
\(956\) | 19.4289 | 0.628374 | ||||||||
\(957\) | −88.3410 | −2.85566 | ||||||||
\(958\) | −19.5149 | −0.630499 | ||||||||
\(959\) | 61.6893 | 1.99205 | ||||||||
\(960\) | 1.61537 | 0.0521359 | ||||||||
\(961\) | −28.1927 | −0.909443 | ||||||||
\(962\) | −51.4355 | −1.65835 | ||||||||
\(963\) | −48.6704 | −1.56838 | ||||||||
\(964\) | −9.95609 | −0.320664 | ||||||||
\(965\) | 16.4567 | 0.529760 | ||||||||
\(966\) | 45.9277 | 1.47770 | ||||||||
\(967\) | −45.8410 | −1.47415 | −0.737074 | − | 0.675812i | \(-0.763793\pi\) | ||||
−0.737074 | + | 0.675812i | \(0.763793\pi\) | |||||||
\(968\) | 10.6735 | 0.343060 | ||||||||
\(969\) | −71.9242 | −2.31054 | ||||||||
\(970\) | −2.86432 | −0.0919679 | ||||||||
\(971\) | 37.6783 | 1.20916 | 0.604578 | − | 0.796546i | \(-0.293342\pi\) | ||||
0.604578 | + | 0.796546i | \(0.293342\pi\) | |||||||
\(972\) | 22.1070 | 0.709083 | ||||||||
\(973\) | 40.8066 | 1.30820 | ||||||||
\(974\) | 2.43265 | 0.0779470 | ||||||||
\(975\) | −59.2302 | −1.89688 | ||||||||
\(976\) | −11.7977 | −0.377636 | ||||||||
\(977\) | 2.94293 | 0.0941527 | 0.0470764 | − | 0.998891i | \(-0.485010\pi\) | ||||
0.0470764 | + | 0.998891i | \(0.485010\pi\) | |||||||
\(978\) | 20.8748 | 0.667503 | ||||||||
\(979\) | −52.2853 | −1.67105 | ||||||||
\(980\) | −10.8714 | −0.347273 | ||||||||
\(981\) | 15.6065 | 0.498277 | ||||||||
\(982\) | 26.1573 | 0.834713 | ||||||||
\(983\) | 21.5954 | 0.688787 | 0.344393 | − | 0.938825i | \(-0.388085\pi\) | ||||
0.344393 | + | 0.938825i | \(0.388085\pi\) | |||||||
\(984\) | −20.2829 | −0.646594 | ||||||||
\(985\) | 12.5117 | 0.398655 | ||||||||
\(986\) | 28.7047 | 0.914143 | ||||||||
\(987\) | 43.5696 | 1.38684 | ||||||||
\(988\) | −41.5841 | −1.32297 | ||||||||
\(989\) | −1.82818 | −0.0581327 | ||||||||
\(990\) | −9.29147 | −0.295302 | ||||||||
\(991\) | 21.1106 | 0.670599 | 0.335299 | − | 0.942112i | \(-0.391163\pi\) | ||||
0.335299 | + | 0.942112i | \(0.391163\pi\) | |||||||
\(992\) | −1.67549 | −0.0531970 | ||||||||
\(993\) | −71.6705 | −2.27439 | ||||||||
\(994\) | 21.5885 | 0.684744 | ||||||||
\(995\) | 3.52578 | 0.111775 | ||||||||
\(996\) | 0.0760234 | 0.00240890 | ||||||||
\(997\) | −8.65940 | −0.274246 | −0.137123 | − | 0.990554i | \(-0.543786\pi\) | ||||
−0.137123 | + | 0.990554i | \(0.543786\pi\) | |||||||
\(998\) | 13.2342 | 0.418921 | ||||||||
\(999\) | −0.844067 | −0.0267051 |
(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 | 8014.2.a.d.1.11 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8014.2.a.d.1.11 | ✓ | 88 | 1.1 | even | 1 | trivial |