Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, 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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.179024.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.568906\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | 2.01243 | 1.16188 | 0.580938 | − | 0.813947i | \(-0.302686\pi\) | ||||
0.580938 | + | 0.813947i | \(0.302686\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.34851 | −1.49750 | −0.748751 | − | 0.662852i | \(-0.769346\pi\) | ||||
−0.748751 | + | 0.662852i | \(0.769346\pi\) | |||||||
\(6\) | 2.01243 | 0.821571 | ||||||||
\(7\) | −2.94661 | −1.11371 | −0.556857 | − | 0.830608i | \(-0.687993\pi\) | ||||
−0.556857 | + | 0.830608i | \(0.687993\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.04987 | 0.349958 | ||||||||
\(10\) | −3.34851 | −1.05889 | ||||||||
\(11\) | −4.10744 | −1.23844 | −0.619220 | − | 0.785218i | \(-0.712551\pi\) | ||||
−0.619220 | + | 0.785218i | \(0.712551\pi\) | |||||||
\(12\) | 2.01243 | 0.580938 | ||||||||
\(13\) | 0.449700 | 0.124724 | 0.0623622 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623622 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(14\) | −2.94661 | −0.787515 | ||||||||
\(15\) | −6.73865 | −1.73991 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.49340 | 0.362202 | 0.181101 | − | 0.983464i | \(-0.442034\pi\) | ||||
0.181101 | + | 0.983464i | \(0.442034\pi\) | |||||||
\(18\) | 1.04987 | 0.247458 | ||||||||
\(19\) | −7.57782 | −1.73847 | −0.869236 | − | 0.494398i | \(-0.835389\pi\) | ||||
−0.869236 | + | 0.494398i | \(0.835389\pi\) | |||||||
\(20\) | −3.34851 | −0.748751 | ||||||||
\(21\) | −5.92985 | −1.29400 | ||||||||
\(22\) | −4.10744 | −0.875709 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.01243 | 0.410786 | ||||||||
\(25\) | 6.21255 | 1.24251 | ||||||||
\(26\) | 0.449700 | 0.0881935 | ||||||||
\(27\) | −3.92449 | −0.755269 | ||||||||
\(28\) | −2.94661 | −0.556857 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −6.73865 | −1.23030 | ||||||||
\(31\) | −1.22039 | −0.219189 | −0.109594 | − | 0.993976i | \(-0.534955\pi\) | ||||
−0.109594 | + | 0.993976i | \(0.534955\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −8.26593 | −1.43891 | ||||||||
\(34\) | 1.49340 | 0.256116 | ||||||||
\(35\) | 9.86677 | 1.66779 | ||||||||
\(36\) | 1.04987 | 0.174979 | ||||||||
\(37\) | 7.68734 | 1.26379 | 0.631895 | − | 0.775054i | \(-0.282277\pi\) | ||||
0.631895 | + | 0.775054i | \(0.282277\pi\) | |||||||
\(38\) | −7.57782 | −1.22929 | ||||||||
\(39\) | 0.904990 | 0.144914 | ||||||||
\(40\) | −3.34851 | −0.529447 | ||||||||
\(41\) | 5.92160 | 0.924798 | 0.462399 | − | 0.886672i | \(-0.346989\pi\) | ||||
0.462399 | + | 0.886672i | \(0.346989\pi\) | |||||||
\(42\) | −5.92985 | −0.914996 | ||||||||
\(43\) | −8.61445 | −1.31369 | −0.656846 | − | 0.754025i | \(-0.728110\pi\) | ||||
−0.656846 | + | 0.754025i | \(0.728110\pi\) | |||||||
\(44\) | −4.10744 | −0.619220 | ||||||||
\(45\) | −3.51552 | −0.524063 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −7.72271 | −1.12647 | −0.563236 | − | 0.826296i | \(-0.690444\pi\) | ||||
−0.563236 | + | 0.826296i | \(0.690444\pi\) | |||||||
\(48\) | 2.01243 | 0.290469 | ||||||||
\(49\) | 1.68252 | 0.240360 | ||||||||
\(50\) | 6.21255 | 0.878587 | ||||||||
\(51\) | 3.00536 | 0.420834 | ||||||||
\(52\) | 0.449700 | 0.0623622 | ||||||||
\(53\) | 13.3982 | 1.84039 | 0.920194 | − | 0.391462i | \(-0.128030\pi\) | ||||
0.920194 | + | 0.391462i | \(0.128030\pi\) | |||||||
\(54\) | −3.92449 | −0.534056 | ||||||||
\(55\) | 13.7538 | 1.85456 | ||||||||
\(56\) | −2.94661 | −0.393758 | ||||||||
\(57\) | −15.2498 | −2.01989 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −7.90148 | −1.02868 | −0.514342 | − | 0.857585i | \(-0.671964\pi\) | ||||
−0.514342 | + | 0.857585i | \(0.671964\pi\) | |||||||
\(60\) | −6.73865 | −0.869956 | ||||||||
\(61\) | −3.37271 | −0.431831 | −0.215916 | − | 0.976412i | \(-0.569274\pi\) | ||||
−0.215916 | + | 0.976412i | \(0.569274\pi\) | |||||||
\(62\) | −1.22039 | −0.154990 | ||||||||
\(63\) | −3.09357 | −0.389753 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.50583 | −0.186775 | ||||||||
\(66\) | −8.26593 | −1.01747 | ||||||||
\(67\) | 1.93008 | 0.235797 | 0.117898 | − | 0.993026i | \(-0.462384\pi\) | ||||
0.117898 | + | 0.993026i | \(0.462384\pi\) | |||||||
\(68\) | 1.49340 | 0.181101 | ||||||||
\(69\) | −2.01243 | −0.242268 | ||||||||
\(70\) | 9.86677 | 1.17930 | ||||||||
\(71\) | −5.38155 | −0.638672 | −0.319336 | − | 0.947641i | \(-0.603460\pi\) | ||||
−0.319336 | + | 0.947641i | \(0.603460\pi\) | |||||||
\(72\) | 1.04987 | 0.123729 | ||||||||
\(73\) | −4.60202 | −0.538626 | −0.269313 | − | 0.963053i | \(-0.586797\pi\) | ||||
−0.269313 | + | 0.963053i | \(0.586797\pi\) | |||||||
\(74\) | 7.68734 | 0.893635 | ||||||||
\(75\) | 12.5023 | 1.44364 | ||||||||
\(76\) | −7.57782 | −0.869236 | ||||||||
\(77\) | 12.1030 | 1.37927 | ||||||||
\(78\) | 0.904990 | 0.102470 | ||||||||
\(79\) | 9.25601 | 1.04138 | 0.520691 | − | 0.853745i | \(-0.325674\pi\) | ||||
0.520691 | + | 0.853745i | \(0.325674\pi\) | |||||||
\(80\) | −3.34851 | −0.374375 | ||||||||
\(81\) | −11.0474 | −1.22749 | ||||||||
\(82\) | 5.92160 | 0.653931 | ||||||||
\(83\) | 3.54863 | 0.389513 | 0.194756 | − | 0.980852i | \(-0.437608\pi\) | ||||
0.194756 | + | 0.980852i | \(0.437608\pi\) | |||||||
\(84\) | −5.92985 | −0.647000 | ||||||||
\(85\) | −5.00066 | −0.542398 | ||||||||
\(86\) | −8.61445 | −0.928920 | ||||||||
\(87\) | 2.01243 | 0.215755 | ||||||||
\(88\) | −4.10744 | −0.437855 | ||||||||
\(89\) | 4.12612 | 0.437368 | 0.218684 | − | 0.975796i | \(-0.429824\pi\) | ||||
0.218684 | + | 0.975796i | \(0.429824\pi\) | |||||||
\(90\) | −3.51552 | −0.370568 | ||||||||
\(91\) | −1.32509 | −0.138907 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −2.45595 | −0.254671 | ||||||||
\(94\) | −7.72271 | −0.796536 | ||||||||
\(95\) | 25.3744 | 2.60336 | ||||||||
\(96\) | 2.01243 | 0.205393 | ||||||||
\(97\) | −8.83222 | −0.896776 | −0.448388 | − | 0.893839i | \(-0.648002\pi\) | ||||
−0.448388 | + | 0.893839i | \(0.648002\pi\) | |||||||
\(98\) | 1.68252 | 0.169960 | ||||||||
\(99\) | −4.31229 | −0.433402 | ||||||||
\(100\) | 6.21255 | 0.621255 | ||||||||
\(101\) | 17.2338 | 1.71483 | 0.857414 | − | 0.514627i | \(-0.172069\pi\) | ||||
0.857414 | + | 0.514627i | \(0.172069\pi\) | |||||||
\(102\) | 3.00536 | 0.297575 | ||||||||
\(103\) | −6.94133 | −0.683950 | −0.341975 | − | 0.939709i | \(-0.611096\pi\) | ||||
−0.341975 | + | 0.939709i | \(0.611096\pi\) | |||||||
\(104\) | 0.449700 | 0.0440967 | ||||||||
\(105\) | 19.8562 | 1.93777 | ||||||||
\(106\) | 13.3982 | 1.30135 | ||||||||
\(107\) | −4.72189 | −0.456482 | −0.228241 | − | 0.973605i | \(-0.573297\pi\) | ||||
−0.228241 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(108\) | −3.92449 | −0.377634 | ||||||||
\(109\) | 1.54601 | 0.148081 | 0.0740405 | − | 0.997255i | \(-0.476411\pi\) | ||||
0.0740405 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(110\) | 13.7538 | 1.31138 | ||||||||
\(111\) | 15.4702 | 1.46837 | ||||||||
\(112\) | −2.94661 | −0.278429 | ||||||||
\(113\) | −8.89955 | −0.837200 | −0.418600 | − | 0.908171i | \(-0.637479\pi\) | ||||
−0.418600 | + | 0.908171i | \(0.637479\pi\) | |||||||
\(114\) | −15.2498 | −1.42828 | ||||||||
\(115\) | 3.34851 | 0.312251 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 0.472129 | 0.0436483 | ||||||||
\(118\) | −7.90148 | −0.727390 | ||||||||
\(119\) | −4.40046 | −0.403390 | ||||||||
\(120\) | −6.73865 | −0.615152 | ||||||||
\(121\) | 5.87106 | 0.533733 | ||||||||
\(122\) | −3.37271 | −0.305351 | ||||||||
\(123\) | 11.9168 | 1.07450 | ||||||||
\(124\) | −1.22039 | −0.109594 | ||||||||
\(125\) | −4.06023 | −0.363158 | ||||||||
\(126\) | −3.09357 | −0.275597 | ||||||||
\(127\) | −2.22191 | −0.197162 | −0.0985812 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985812 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.3360 | −1.52635 | ||||||||
\(130\) | −1.50583 | −0.132070 | ||||||||
\(131\) | 14.5729 | 1.27324 | 0.636619 | − | 0.771179i | \(-0.280332\pi\) | ||||
0.636619 | + | 0.771179i | \(0.280332\pi\) | |||||||
\(132\) | −8.26593 | −0.719457 | ||||||||
\(133\) | 22.3289 | 1.93616 | ||||||||
\(134\) | 1.93008 | 0.166734 | ||||||||
\(135\) | 13.1412 | 1.13102 | ||||||||
\(136\) | 1.49340 | 0.128058 | ||||||||
\(137\) | −7.57308 | −0.647012 | −0.323506 | − | 0.946226i | \(-0.604862\pi\) | ||||
−0.323506 | + | 0.946226i | \(0.604862\pi\) | |||||||
\(138\) | −2.01243 | −0.171309 | ||||||||
\(139\) | −20.7952 | −1.76382 | −0.881912 | − | 0.471414i | \(-0.843744\pi\) | ||||
−0.881912 | + | 0.471414i | \(0.843744\pi\) | |||||||
\(140\) | 9.86677 | 0.833894 | ||||||||
\(141\) | −15.5414 | −1.30882 | ||||||||
\(142\) | −5.38155 | −0.451610 | ||||||||
\(143\) | −1.84712 | −0.154464 | ||||||||
\(144\) | 1.04987 | 0.0874895 | ||||||||
\(145\) | −3.34851 | −0.278079 | ||||||||
\(146\) | −4.60202 | −0.380866 | ||||||||
\(147\) | 3.38596 | 0.279269 | ||||||||
\(148\) | 7.68734 | 0.631895 | ||||||||
\(149\) | 15.2059 | 1.24571 | 0.622857 | − | 0.782336i | \(-0.285972\pi\) | ||||
0.622857 | + | 0.782336i | \(0.285972\pi\) | |||||||
\(150\) | 12.5023 | 1.02081 | ||||||||
\(151\) | 7.25184 | 0.590146 | 0.295073 | − | 0.955475i | \(-0.404656\pi\) | ||||
0.295073 | + | 0.955475i | \(0.404656\pi\) | |||||||
\(152\) | −7.57782 | −0.614643 | ||||||||
\(153\) | 1.56788 | 0.126756 | ||||||||
\(154\) | 12.1030 | 0.975290 | ||||||||
\(155\) | 4.08650 | 0.328236 | ||||||||
\(156\) | 0.904990 | 0.0724572 | ||||||||
\(157\) | −9.92692 | −0.792255 | −0.396127 | − | 0.918196i | \(-0.629646\pi\) | ||||
−0.396127 | + | 0.918196i | \(0.629646\pi\) | |||||||
\(158\) | 9.25601 | 0.736369 | ||||||||
\(159\) | 26.9630 | 2.13831 | ||||||||
\(160\) | −3.34851 | −0.264723 | ||||||||
\(161\) | 2.94661 | 0.232226 | ||||||||
\(162\) | −11.0474 | −0.867965 | ||||||||
\(163\) | 22.9592 | 1.79830 | 0.899152 | − | 0.437636i | \(-0.144184\pi\) | ||||
0.899152 | + | 0.437636i | \(0.144184\pi\) | |||||||
\(164\) | 5.92160 | 0.462399 | ||||||||
\(165\) | 27.6786 | 2.15478 | ||||||||
\(166\) | 3.54863 | 0.275427 | ||||||||
\(167\) | −3.46124 | −0.267838 | −0.133919 | − | 0.990992i | \(-0.542756\pi\) | ||||
−0.133919 | + | 0.990992i | \(0.542756\pi\) | |||||||
\(168\) | −5.92985 | −0.457498 | ||||||||
\(169\) | −12.7978 | −0.984444 | ||||||||
\(170\) | −5.00066 | −0.383533 | ||||||||
\(171\) | −7.95576 | −0.608392 | ||||||||
\(172\) | −8.61445 | −0.656846 | ||||||||
\(173\) | 2.40357 | 0.182740 | 0.0913701 | − | 0.995817i | \(-0.470875\pi\) | ||||
0.0913701 | + | 0.995817i | \(0.470875\pi\) | |||||||
\(174\) | 2.01243 | 0.152562 | ||||||||
\(175\) | −18.3060 | −1.38380 | ||||||||
\(176\) | −4.10744 | −0.309610 | ||||||||
\(177\) | −15.9012 | −1.19520 | ||||||||
\(178\) | 4.12612 | 0.309266 | ||||||||
\(179\) | −3.62288 | −0.270787 | −0.135393 | − | 0.990792i | \(-0.543230\pi\) | ||||
−0.135393 | + | 0.990792i | \(0.543230\pi\) | |||||||
\(180\) | −3.51552 | −0.262031 | ||||||||
\(181\) | −3.44626 | −0.256159 | −0.128079 | − | 0.991764i | \(-0.540881\pi\) | ||||
−0.128079 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(182\) | −1.32509 | −0.0982224 | ||||||||
\(183\) | −6.78734 | −0.501735 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −25.7412 | −1.89253 | ||||||||
\(186\) | −2.45595 | −0.180079 | ||||||||
\(187\) | −6.13404 | −0.448566 | ||||||||
\(188\) | −7.72271 | −0.563236 | ||||||||
\(189\) | 11.5640 | 0.841154 | ||||||||
\(190\) | 25.3744 | 1.84086 | ||||||||
\(191\) | −7.43775 | −0.538177 | −0.269088 | − | 0.963115i | \(-0.586722\pi\) | ||||
−0.269088 | + | 0.963115i | \(0.586722\pi\) | |||||||
\(192\) | 2.01243 | 0.145235 | ||||||||
\(193\) | −16.4333 | −1.18290 | −0.591449 | − | 0.806342i | \(-0.701444\pi\) | ||||
−0.591449 | + | 0.806342i | \(0.701444\pi\) | |||||||
\(194\) | −8.83222 | −0.634117 | ||||||||
\(195\) | −3.03037 | −0.217010 | ||||||||
\(196\) | 1.68252 | 0.120180 | ||||||||
\(197\) | −2.39554 | −0.170675 | −0.0853375 | − | 0.996352i | \(-0.527197\pi\) | ||||
−0.0853375 | + | 0.996352i | \(0.527197\pi\) | |||||||
\(198\) | −4.31229 | −0.306461 | ||||||||
\(199\) | 19.1929 | 1.36055 | 0.680273 | − | 0.732959i | \(-0.261861\pi\) | ||||
0.680273 | + | 0.732959i | \(0.261861\pi\) | |||||||
\(200\) | 6.21255 | 0.439293 | ||||||||
\(201\) | 3.88415 | 0.273967 | ||||||||
\(202\) | 17.2338 | 1.21257 | ||||||||
\(203\) | −2.94661 | −0.206812 | ||||||||
\(204\) | 3.00536 | 0.210417 | ||||||||
\(205\) | −19.8286 | −1.38489 | ||||||||
\(206\) | −6.94133 | −0.483625 | ||||||||
\(207\) | −1.04987 | −0.0729713 | ||||||||
\(208\) | 0.449700 | 0.0311811 | ||||||||
\(209\) | 31.1254 | 2.15299 | ||||||||
\(210\) | 19.8562 | 1.37021 | ||||||||
\(211\) | 12.9238 | 0.889711 | 0.444855 | − | 0.895602i | \(-0.353255\pi\) | ||||
0.444855 | + | 0.895602i | \(0.353255\pi\) | |||||||
\(212\) | 13.3982 | 0.920194 | ||||||||
\(213\) | −10.8300 | −0.742059 | ||||||||
\(214\) | −4.72189 | −0.322782 | ||||||||
\(215\) | 28.8456 | 1.96725 | ||||||||
\(216\) | −3.92449 | −0.267028 | ||||||||
\(217\) | 3.59602 | 0.244114 | ||||||||
\(218\) | 1.54601 | 0.104709 | ||||||||
\(219\) | −9.26124 | −0.625817 | ||||||||
\(220\) | 13.7538 | 0.927282 | ||||||||
\(221\) | 0.671581 | 0.0451755 | ||||||||
\(222\) | 15.4702 | 1.03829 | ||||||||
\(223\) | −5.01497 | −0.335827 | −0.167914 | − | 0.985802i | \(-0.553703\pi\) | ||||
−0.167914 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(224\) | −2.94661 | −0.196879 | ||||||||
\(225\) | 6.52239 | 0.434826 | ||||||||
\(226\) | −8.89955 | −0.591990 | ||||||||
\(227\) | −3.85327 | −0.255751 | −0.127875 | − | 0.991790i | \(-0.540816\pi\) | ||||
−0.127875 | + | 0.991790i | \(0.540816\pi\) | |||||||
\(228\) | −15.2498 | −1.00995 | ||||||||
\(229\) | −23.5676 | −1.55739 | −0.778697 | − | 0.627400i | \(-0.784119\pi\) | ||||
−0.778697 | + | 0.627400i | \(0.784119\pi\) | |||||||
\(230\) | 3.34851 | 0.220794 | ||||||||
\(231\) | 24.3565 | 1.60254 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −21.4376 | −1.40442 | −0.702212 | − | 0.711968i | \(-0.747804\pi\) | ||||
−0.702212 | + | 0.711968i | \(0.747804\pi\) | |||||||
\(234\) | 0.472129 | 0.0308640 | ||||||||
\(235\) | 25.8596 | 1.68689 | ||||||||
\(236\) | −7.90148 | −0.514342 | ||||||||
\(237\) | 18.6271 | 1.20996 | ||||||||
\(238\) | −4.40046 | −0.285240 | ||||||||
\(239\) | −28.6339 | −1.85217 | −0.926086 | − | 0.377312i | \(-0.876849\pi\) | ||||
−0.926086 | + | 0.377312i | \(0.876849\pi\) | |||||||
\(240\) | −6.73865 | −0.434978 | ||||||||
\(241\) | −12.4373 | −0.801160 | −0.400580 | − | 0.916262i | \(-0.631191\pi\) | ||||
−0.400580 | + | 0.916262i | \(0.631191\pi\) | |||||||
\(242\) | 5.87106 | 0.377406 | ||||||||
\(243\) | −10.4586 | −0.670921 | ||||||||
\(244\) | −3.37271 | −0.215916 | ||||||||
\(245\) | −5.63395 | −0.359940 | ||||||||
\(246\) | 11.9168 | 0.759787 | ||||||||
\(247\) | −3.40775 | −0.216830 | ||||||||
\(248\) | −1.22039 | −0.0774950 | ||||||||
\(249\) | 7.14137 | 0.452566 | ||||||||
\(250\) | −4.06023 | −0.256791 | ||||||||
\(251\) | 12.5035 | 0.789215 | 0.394608 | − | 0.918850i | \(-0.370881\pi\) | ||||
0.394608 | + | 0.918850i | \(0.370881\pi\) | |||||||
\(252\) | −3.09357 | −0.194877 | ||||||||
\(253\) | 4.10744 | 0.258233 | ||||||||
\(254\) | −2.22191 | −0.139415 | ||||||||
\(255\) | −10.0635 | −0.630200 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.1475 | −1.31914 | −0.659571 | − | 0.751642i | \(-0.729262\pi\) | ||||
−0.659571 | + | 0.751642i | \(0.729262\pi\) | |||||||
\(258\) | −17.3360 | −1.07929 | ||||||||
\(259\) | −22.6516 | −1.40750 | ||||||||
\(260\) | −1.50583 | −0.0933875 | ||||||||
\(261\) | 1.04987 | 0.0649856 | ||||||||
\(262\) | 14.5729 | 0.900315 | ||||||||
\(263\) | −13.8786 | −0.855792 | −0.427896 | − | 0.903828i | \(-0.640745\pi\) | ||||
−0.427896 | + | 0.903828i | \(0.640745\pi\) | |||||||
\(264\) | −8.26593 | −0.508733 | ||||||||
\(265\) | −44.8642 | −2.75598 | ||||||||
\(266\) | 22.3289 | 1.36907 | ||||||||
\(267\) | 8.30353 | 0.508168 | ||||||||
\(268\) | 1.93008 | 0.117898 | ||||||||
\(269\) | 18.7274 | 1.14183 | 0.570915 | − | 0.821009i | \(-0.306589\pi\) | ||||
0.570915 | + | 0.821009i | \(0.306589\pi\) | |||||||
\(270\) | 13.1412 | 0.799749 | ||||||||
\(271\) | −29.6416 | −1.80060 | −0.900300 | − | 0.435271i | \(-0.856653\pi\) | ||||
−0.900300 | + | 0.435271i | \(0.856653\pi\) | |||||||
\(272\) | 1.49340 | 0.0905505 | ||||||||
\(273\) | −2.66666 | −0.161393 | ||||||||
\(274\) | −7.57308 | −0.457507 | ||||||||
\(275\) | −25.5177 | −1.53877 | ||||||||
\(276\) | −2.01243 | −0.121134 | ||||||||
\(277\) | −28.1416 | −1.69086 | −0.845432 | − | 0.534083i | \(-0.820657\pi\) | ||||
−0.845432 | + | 0.534083i | \(0.820657\pi\) | |||||||
\(278\) | −20.7952 | −1.24721 | ||||||||
\(279\) | −1.28126 | −0.0767069 | ||||||||
\(280\) | 9.86677 | 0.589652 | ||||||||
\(281\) | 25.4697 | 1.51940 | 0.759698 | − | 0.650276i | \(-0.225347\pi\) | ||||
0.759698 | + | 0.650276i | \(0.225347\pi\) | |||||||
\(282\) | −15.5414 | −0.925477 | ||||||||
\(283\) | −20.7801 | −1.23525 | −0.617625 | − | 0.786472i | \(-0.711905\pi\) | ||||
−0.617625 | + | 0.786472i | \(0.711905\pi\) | |||||||
\(284\) | −5.38155 | −0.319336 | ||||||||
\(285\) | 51.0643 | 3.02479 | ||||||||
\(286\) | −1.84712 | −0.109222 | ||||||||
\(287\) | −17.4487 | −1.02996 | ||||||||
\(288\) | 1.04987 | 0.0618644 | ||||||||
\(289\) | −14.7698 | −0.868810 | ||||||||
\(290\) | −3.34851 | −0.196632 | ||||||||
\(291\) | −17.7742 | −1.04194 | ||||||||
\(292\) | −4.60202 | −0.269313 | ||||||||
\(293\) | 21.7496 | 1.27062 | 0.635312 | − | 0.772256i | \(-0.280872\pi\) | ||||
0.635312 | + | 0.772256i | \(0.280872\pi\) | |||||||
\(294\) | 3.38596 | 0.197473 | ||||||||
\(295\) | 26.4582 | 1.54046 | ||||||||
\(296\) | 7.68734 | 0.446817 | ||||||||
\(297\) | 16.1196 | 0.935355 | ||||||||
\(298\) | 15.2059 | 0.880853 | ||||||||
\(299\) | −0.449700 | −0.0260068 | ||||||||
\(300\) | 12.5023 | 0.721821 | ||||||||
\(301\) | 25.3834 | 1.46308 | ||||||||
\(302\) | 7.25184 | 0.417296 | ||||||||
\(303\) | 34.6818 | 1.99242 | ||||||||
\(304\) | −7.57782 | −0.434618 | ||||||||
\(305\) | 11.2936 | 0.646668 | ||||||||
\(306\) | 1.56788 | 0.0896297 | ||||||||
\(307\) | −30.9335 | −1.76547 | −0.882734 | − | 0.469873i | \(-0.844300\pi\) | ||||
−0.882734 | + | 0.469873i | \(0.844300\pi\) | |||||||
\(308\) | 12.1030 | 0.689634 | ||||||||
\(309\) | −13.9689 | −0.794665 | ||||||||
\(310\) | 4.08650 | 0.232098 | ||||||||
\(311\) | 19.0093 | 1.07792 | 0.538960 | − | 0.842331i | \(-0.318817\pi\) | ||||
0.538960 | + | 0.842331i | \(0.318817\pi\) | |||||||
\(312\) | 0.904990 | 0.0512350 | ||||||||
\(313\) | 23.3187 | 1.31805 | 0.659026 | − | 0.752120i | \(-0.270969\pi\) | ||||
0.659026 | + | 0.752120i | \(0.270969\pi\) | |||||||
\(314\) | −9.92692 | −0.560209 | ||||||||
\(315\) | 10.3589 | 0.583656 | ||||||||
\(316\) | 9.25601 | 0.520691 | ||||||||
\(317\) | 0.472925 | 0.0265621 | 0.0132811 | − | 0.999912i | \(-0.495772\pi\) | ||||
0.0132811 | + | 0.999912i | \(0.495772\pi\) | |||||||
\(318\) | 26.9630 | 1.51201 | ||||||||
\(319\) | −4.10744 | −0.229972 | ||||||||
\(320\) | −3.34851 | −0.187188 | ||||||||
\(321\) | −9.50247 | −0.530376 | ||||||||
\(322\) | 2.94661 | 0.164208 | ||||||||
\(323\) | −11.3167 | −0.629678 | ||||||||
\(324\) | −11.0474 | −0.613744 | ||||||||
\(325\) | 2.79378 | 0.154971 | ||||||||
\(326\) | 22.9592 | 1.27159 | ||||||||
\(327\) | 3.11124 | 0.172052 | ||||||||
\(328\) | 5.92160 | 0.326966 | ||||||||
\(329\) | 22.7558 | 1.25457 | ||||||||
\(330\) | 27.6786 | 1.52366 | ||||||||
\(331\) | 11.1247 | 0.611471 | 0.305735 | − | 0.952116i | \(-0.401098\pi\) | ||||
0.305735 | + | 0.952116i | \(0.401098\pi\) | |||||||
\(332\) | 3.54863 | 0.194756 | ||||||||
\(333\) | 8.07074 | 0.442274 | ||||||||
\(334\) | −3.46124 | −0.189390 | ||||||||
\(335\) | −6.46290 | −0.353106 | ||||||||
\(336\) | −5.92985 | −0.323500 | ||||||||
\(337\) | −2.61571 | −0.142487 | −0.0712433 | − | 0.997459i | \(-0.522697\pi\) | ||||
−0.0712433 | + | 0.997459i | \(0.522697\pi\) | |||||||
\(338\) | −12.7978 | −0.696107 | ||||||||
\(339\) | −17.9097 | −0.972723 | ||||||||
\(340\) | −5.00066 | −0.271199 | ||||||||
\(341\) | 5.01269 | 0.271452 | ||||||||
\(342\) | −7.95576 | −0.430198 | ||||||||
\(343\) | 15.6685 | 0.846022 | ||||||||
\(344\) | −8.61445 | −0.464460 | ||||||||
\(345\) | 6.73865 | 0.362797 | ||||||||
\(346\) | 2.40357 | 0.129217 | ||||||||
\(347\) | 26.9380 | 1.44611 | 0.723054 | − | 0.690792i | \(-0.242738\pi\) | ||||
0.723054 | + | 0.690792i | \(0.242738\pi\) | |||||||
\(348\) | 2.01243 | 0.107878 | ||||||||
\(349\) | −19.0367 | −1.01901 | −0.509506 | − | 0.860467i | \(-0.670172\pi\) | ||||
−0.509506 | + | 0.860467i | \(0.670172\pi\) | |||||||
\(350\) | −18.3060 | −0.978495 | ||||||||
\(351\) | −1.76485 | −0.0942005 | ||||||||
\(352\) | −4.10744 | −0.218927 | ||||||||
\(353\) | 18.8385 | 1.00267 | 0.501335 | − | 0.865253i | \(-0.332842\pi\) | ||||
0.501335 | + | 0.865253i | \(0.332842\pi\) | |||||||
\(354\) | −15.9012 | −0.845138 | ||||||||
\(355\) | 18.0202 | 0.956413 | ||||||||
\(356\) | 4.12612 | 0.218684 | ||||||||
\(357\) | −8.85563 | −0.468689 | ||||||||
\(358\) | −3.62288 | −0.191475 | ||||||||
\(359\) | −16.6130 | −0.876803 | −0.438401 | − | 0.898779i | \(-0.644455\pi\) | ||||
−0.438401 | + | 0.898779i | \(0.644455\pi\) | |||||||
\(360\) | −3.51552 | −0.185284 | ||||||||
\(361\) | 38.4234 | 2.02228 | ||||||||
\(362\) | −3.44626 | −0.181132 | ||||||||
\(363\) | 11.8151 | 0.620132 | ||||||||
\(364\) | −1.32509 | −0.0694537 | ||||||||
\(365\) | 15.4099 | 0.806592 | ||||||||
\(366\) | −6.78734 | −0.354780 | ||||||||
\(367\) | 10.2844 | 0.536843 | 0.268421 | − | 0.963302i | \(-0.413498\pi\) | ||||
0.268421 | + | 0.963302i | \(0.413498\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 6.21693 | 0.323641 | ||||||||
\(370\) | −25.7412 | −1.33822 | ||||||||
\(371\) | −39.4794 | −2.04967 | ||||||||
\(372\) | −2.45595 | −0.127335 | ||||||||
\(373\) | 2.86104 | 0.148139 | 0.0740695 | − | 0.997253i | \(-0.476401\pi\) | ||||
0.0740695 | + | 0.997253i | \(0.476401\pi\) | |||||||
\(374\) | −6.13404 | −0.317184 | ||||||||
\(375\) | −8.17092 | −0.421945 | ||||||||
\(376\) | −7.72271 | −0.398268 | ||||||||
\(377\) | 0.449700 | 0.0231607 | ||||||||
\(378\) | 11.5640 | 0.594786 | ||||||||
\(379\) | 4.57836 | 0.235175 | 0.117587 | − | 0.993063i | \(-0.462484\pi\) | ||||
0.117587 | + | 0.993063i | \(0.462484\pi\) | |||||||
\(380\) | 25.3744 | 1.30168 | ||||||||
\(381\) | −4.47143 | −0.229078 | ||||||||
\(382\) | −7.43775 | −0.380549 | ||||||||
\(383\) | −13.4638 | −0.687966 | −0.343983 | − | 0.938976i | \(-0.611776\pi\) | ||||
−0.343983 | + | 0.938976i | \(0.611776\pi\) | |||||||
\(384\) | 2.01243 | 0.102696 | ||||||||
\(385\) | −40.5272 | −2.06546 | ||||||||
\(386\) | −16.4333 | −0.836435 | ||||||||
\(387\) | −9.04409 | −0.459737 | ||||||||
\(388\) | −8.83222 | −0.448388 | ||||||||
\(389\) | −3.92455 | −0.198982 | −0.0994912 | − | 0.995038i | \(-0.531722\pi\) | ||||
−0.0994912 | + | 0.995038i | \(0.531722\pi\) | |||||||
\(390\) | −3.03037 | −0.153449 | ||||||||
\(391\) | −1.49340 | −0.0755244 | ||||||||
\(392\) | 1.68252 | 0.0849802 | ||||||||
\(393\) | 29.3269 | 1.47935 | ||||||||
\(394\) | −2.39554 | −0.120685 | ||||||||
\(395\) | −30.9939 | −1.55947 | ||||||||
\(396\) | −4.31229 | −0.216701 | ||||||||
\(397\) | 30.7736 | 1.54448 | 0.772242 | − | 0.635328i | \(-0.219135\pi\) | ||||
0.772242 | + | 0.635328i | \(0.219135\pi\) | |||||||
\(398\) | 19.1929 | 0.962051 | ||||||||
\(399\) | 44.9353 | 2.24958 | ||||||||
\(400\) | 6.21255 | 0.310627 | ||||||||
\(401\) | 2.60010 | 0.129843 | 0.0649213 | − | 0.997890i | \(-0.479320\pi\) | ||||
0.0649213 | + | 0.997890i | \(0.479320\pi\) | |||||||
\(402\) | 3.88415 | 0.193724 | ||||||||
\(403\) | −0.548811 | −0.0273382 | ||||||||
\(404\) | 17.2338 | 0.857414 | ||||||||
\(405\) | 36.9923 | 1.83816 | ||||||||
\(406\) | −2.94661 | −0.146238 | ||||||||
\(407\) | −31.5753 | −1.56513 | ||||||||
\(408\) | 3.00536 | 0.148787 | ||||||||
\(409\) | 1.80606 | 0.0893037 | 0.0446518 | − | 0.999003i | \(-0.485782\pi\) | ||||
0.0446518 | + | 0.999003i | \(0.485782\pi\) | |||||||
\(410\) | −19.8286 | −0.979262 | ||||||||
\(411\) | −15.2403 | −0.751749 | ||||||||
\(412\) | −6.94133 | −0.341975 | ||||||||
\(413\) | 23.2826 | 1.14566 | ||||||||
\(414\) | −1.04987 | −0.0515985 | ||||||||
\(415\) | −11.8826 | −0.583296 | ||||||||
\(416\) | 0.449700 | 0.0220484 | ||||||||
\(417\) | −41.8488 | −2.04935 | ||||||||
\(418\) | 31.1254 | 1.52240 | ||||||||
\(419\) | 16.3847 | 0.800444 | 0.400222 | − | 0.916418i | \(-0.368933\pi\) | ||||
0.400222 | + | 0.916418i | \(0.368933\pi\) | |||||||
\(420\) | 19.8562 | 0.968883 | ||||||||
\(421\) | −29.9884 | −1.46155 | −0.730773 | − | 0.682621i | \(-0.760840\pi\) | ||||
−0.730773 | + | 0.682621i | \(0.760840\pi\) | |||||||
\(422\) | 12.9238 | 0.629120 | ||||||||
\(423\) | −8.10787 | −0.394218 | ||||||||
\(424\) | 13.3982 | 0.650676 | ||||||||
\(425\) | 9.27780 | 0.450040 | ||||||||
\(426\) | −10.8300 | −0.524715 | ||||||||
\(427\) | 9.93807 | 0.480937 | ||||||||
\(428\) | −4.72189 | −0.228241 | ||||||||
\(429\) | −3.71719 | −0.179468 | ||||||||
\(430\) | 28.8456 | 1.39106 | ||||||||
\(431\) | −20.2190 | −0.973916 | −0.486958 | − | 0.873425i | \(-0.661894\pi\) | ||||
−0.486958 | + | 0.873425i | \(0.661894\pi\) | |||||||
\(432\) | −3.92449 | −0.188817 | ||||||||
\(433\) | 29.7211 | 1.42831 | 0.714153 | − | 0.699989i | \(-0.246812\pi\) | ||||
0.714153 | + | 0.699989i | \(0.246812\pi\) | |||||||
\(434\) | 3.59602 | 0.172615 | ||||||||
\(435\) | −6.73865 | −0.323094 | ||||||||
\(436\) | 1.54601 | 0.0740405 | ||||||||
\(437\) | 7.57782 | 0.362496 | ||||||||
\(438\) | −9.26124 | −0.442519 | ||||||||
\(439\) | 28.3637 | 1.35373 | 0.676864 | − | 0.736108i | \(-0.263339\pi\) | ||||
0.676864 | + | 0.736108i | \(0.263339\pi\) | |||||||
\(440\) | 13.7538 | 0.655688 | ||||||||
\(441\) | 1.76644 | 0.0841160 | ||||||||
\(442\) | 0.671581 | 0.0319439 | ||||||||
\(443\) | 33.1054 | 1.57289 | 0.786443 | − | 0.617662i | \(-0.211920\pi\) | ||||
0.786443 | + | 0.617662i | \(0.211920\pi\) | |||||||
\(444\) | 15.4702 | 0.734185 | ||||||||
\(445\) | −13.8164 | −0.654959 | ||||||||
\(446\) | −5.01497 | −0.237466 | ||||||||
\(447\) | 30.6008 | 1.44737 | ||||||||
\(448\) | −2.94661 | −0.139214 | ||||||||
\(449\) | −8.66957 | −0.409142 | −0.204571 | − | 0.978852i | \(-0.565580\pi\) | ||||
−0.204571 | + | 0.978852i | \(0.565580\pi\) | |||||||
\(450\) | 6.52239 | 0.307468 | ||||||||
\(451\) | −24.3226 | −1.14531 | ||||||||
\(452\) | −8.89955 | −0.418600 | ||||||||
\(453\) | 14.5938 | 0.685677 | ||||||||
\(454\) | −3.85327 | −0.180843 | ||||||||
\(455\) | 4.43709 | 0.208014 | ||||||||
\(456\) | −15.2498 | −0.714139 | ||||||||
\(457\) | 14.1426 | 0.661563 | 0.330781 | − | 0.943707i | \(-0.392688\pi\) | ||||
0.330781 | + | 0.943707i | \(0.392688\pi\) | |||||||
\(458\) | −23.5676 | −1.10124 | ||||||||
\(459\) | −5.86083 | −0.273560 | ||||||||
\(460\) | 3.34851 | 0.156125 | ||||||||
\(461\) | −37.5912 | −1.75080 | −0.875398 | − | 0.483402i | \(-0.839401\pi\) | ||||
−0.875398 | + | 0.483402i | \(0.839401\pi\) | |||||||
\(462\) | 24.3565 | 1.13317 | ||||||||
\(463\) | 24.3916 | 1.13357 | 0.566786 | − | 0.823865i | \(-0.308187\pi\) | ||||
0.566786 | + | 0.823865i | \(0.308187\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 8.22380 | 0.381369 | ||||||||
\(466\) | −21.4376 | −0.993078 | ||||||||
\(467\) | −1.71268 | −0.0792532 | −0.0396266 | − | 0.999215i | \(-0.512617\pi\) | ||||
−0.0396266 | + | 0.999215i | \(0.512617\pi\) | |||||||
\(468\) | 0.472129 | 0.0218242 | ||||||||
\(469\) | −5.68720 | −0.262611 | ||||||||
\(470\) | 25.8596 | 1.19281 | ||||||||
\(471\) | −19.9772 | −0.920502 | ||||||||
\(472\) | −7.90148 | −0.363695 | ||||||||
\(473\) | 35.3833 | 1.62693 | ||||||||
\(474\) | 18.6271 | 0.855570 | ||||||||
\(475\) | −47.0776 | −2.16007 | ||||||||
\(476\) | −4.40046 | −0.201695 | ||||||||
\(477\) | 14.0665 | 0.644059 | ||||||||
\(478\) | −28.6339 | −1.30968 | ||||||||
\(479\) | −31.2291 | −1.42689 | −0.713446 | − | 0.700710i | \(-0.752867\pi\) | ||||
−0.713446 | + | 0.700710i | \(0.752867\pi\) | |||||||
\(480\) | −6.73865 | −0.307576 | ||||||||
\(481\) | 3.45700 | 0.157626 | ||||||||
\(482\) | −12.4373 | −0.566506 | ||||||||
\(483\) | 5.92985 | 0.269818 | ||||||||
\(484\) | 5.87106 | 0.266866 | ||||||||
\(485\) | 29.5748 | 1.34292 | ||||||||
\(486\) | −10.4586 | −0.474412 | ||||||||
\(487\) | 2.28762 | 0.103662 | 0.0518310 | − | 0.998656i | \(-0.483494\pi\) | ||||
0.0518310 | + | 0.998656i | \(0.483494\pi\) | |||||||
\(488\) | −3.37271 | −0.152675 | ||||||||
\(489\) | 46.2038 | 2.08941 | ||||||||
\(490\) | −5.63395 | −0.254516 | ||||||||
\(491\) | 29.5094 | 1.33174 | 0.665870 | − | 0.746068i | \(-0.268061\pi\) | ||||
0.665870 | + | 0.746068i | \(0.268061\pi\) | |||||||
\(492\) | 11.9168 | 0.537251 | ||||||||
\(493\) | 1.49340 | 0.0672593 | ||||||||
\(494\) | −3.40775 | −0.153322 | ||||||||
\(495\) | 14.4398 | 0.649020 | ||||||||
\(496\) | −1.22039 | −0.0547972 | ||||||||
\(497\) | 15.8573 | 0.711299 | ||||||||
\(498\) | 7.14137 | 0.320012 | ||||||||
\(499\) | −24.7717 | −1.10893 | −0.554467 | − | 0.832206i | \(-0.687078\pi\) | ||||
−0.554467 | + | 0.832206i | \(0.687078\pi\) | |||||||
\(500\) | −4.06023 | −0.181579 | ||||||||
\(501\) | −6.96549 | −0.311195 | ||||||||
\(502\) | 12.5035 | 0.558059 | ||||||||
\(503\) | −2.51484 | −0.112131 | −0.0560655 | − | 0.998427i | \(-0.517856\pi\) | ||||
−0.0560655 | + | 0.998427i | \(0.517856\pi\) | |||||||
\(504\) | −3.09357 | −0.137799 | ||||||||
\(505\) | −57.7077 | −2.56796 | ||||||||
\(506\) | 4.10744 | 0.182598 | ||||||||
\(507\) | −25.7546 | −1.14380 | ||||||||
\(508\) | −2.22191 | −0.0985812 | ||||||||
\(509\) | 19.3823 | 0.859107 | 0.429554 | − | 0.903041i | \(-0.358671\pi\) | ||||
0.429554 | + | 0.903041i | \(0.358671\pi\) | |||||||
\(510\) | −10.0635 | −0.445619 | ||||||||
\(511\) | 13.5604 | 0.599875 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 29.7391 | 1.31301 | ||||||||
\(514\) | −21.1475 | −0.932775 | ||||||||
\(515\) | 23.2431 | 1.02422 | ||||||||
\(516\) | −17.3360 | −0.763174 | ||||||||
\(517\) | 31.7205 | 1.39507 | ||||||||
\(518\) | −22.6516 | −0.995254 | ||||||||
\(519\) | 4.83702 | 0.212322 | ||||||||
\(520\) | −1.50583 | −0.0660349 | ||||||||
\(521\) | 1.35159 | 0.0592141 | 0.0296071 | − | 0.999562i | \(-0.490574\pi\) | ||||
0.0296071 | + | 0.999562i | \(0.490574\pi\) | |||||||
\(522\) | 1.04987 | 0.0459517 | ||||||||
\(523\) | −11.3329 | −0.495555 | −0.247777 | − | 0.968817i | \(-0.579700\pi\) | ||||
−0.247777 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(524\) | 14.5729 | 0.636619 | ||||||||
\(525\) | −36.8395 | −1.60781 | ||||||||
\(526\) | −13.8786 | −0.605136 | ||||||||
\(527\) | −1.82253 | −0.0793907 | ||||||||
\(528\) | −8.26593 | −0.359729 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −44.8642 | −1.94878 | ||||||||
\(531\) | −8.29556 | −0.359996 | ||||||||
\(532\) | 22.3289 | 0.968081 | ||||||||
\(533\) | 2.66294 | 0.115345 | ||||||||
\(534\) | 8.30353 | 0.359329 | ||||||||
\(535\) | 15.8113 | 0.683582 | ||||||||
\(536\) | 1.93008 | 0.0833668 | ||||||||
\(537\) | −7.29079 | −0.314621 | ||||||||
\(538\) | 18.7274 | 0.807396 | ||||||||
\(539\) | −6.91086 | −0.297672 | ||||||||
\(540\) | 13.1412 | 0.565508 | ||||||||
\(541\) | −10.2323 | −0.439921 | −0.219961 | − | 0.975509i | \(-0.570593\pi\) | ||||
−0.219961 | + | 0.975509i | \(0.570593\pi\) | |||||||
\(542\) | −29.6416 | −1.27322 | ||||||||
\(543\) | −6.93536 | −0.297625 | ||||||||
\(544\) | 1.49340 | 0.0640289 | ||||||||
\(545\) | −5.17684 | −0.221751 | ||||||||
\(546\) | −2.66666 | −0.114122 | ||||||||
\(547\) | −35.6571 | −1.52459 | −0.762293 | − | 0.647232i | \(-0.775926\pi\) | ||||
−0.762293 | + | 0.647232i | \(0.775926\pi\) | |||||||
\(548\) | −7.57308 | −0.323506 | ||||||||
\(549\) | −3.54092 | −0.151123 | ||||||||
\(550\) | −25.5177 | −1.08808 | ||||||||
\(551\) | −7.57782 | −0.322826 | ||||||||
\(552\) | −2.01243 | −0.0856547 | ||||||||
\(553\) | −27.2739 | −1.15980 | ||||||||
\(554\) | −28.1416 | −1.19562 | ||||||||
\(555\) | −51.8023 | −2.19888 | ||||||||
\(556\) | −20.7952 | −0.881912 | ||||||||
\(557\) | 10.9917 | 0.465732 | 0.232866 | − | 0.972509i | \(-0.425190\pi\) | ||||
0.232866 | + | 0.972509i | \(0.425190\pi\) | |||||||
\(558\) | −1.28126 | −0.0542400 | ||||||||
\(559\) | −3.87392 | −0.163849 | ||||||||
\(560\) | 9.86677 | 0.416947 | ||||||||
\(561\) | −12.3443 | −0.521178 | ||||||||
\(562\) | 25.4697 | 1.07437 | ||||||||
\(563\) | 5.43294 | 0.228971 | 0.114486 | − | 0.993425i | \(-0.463478\pi\) | ||||
0.114486 | + | 0.993425i | \(0.463478\pi\) | |||||||
\(564\) | −15.5414 | −0.654411 | ||||||||
\(565\) | 29.8003 | 1.25371 | ||||||||
\(566\) | −20.7801 | −0.873454 | ||||||||
\(567\) | 32.5524 | 1.36707 | ||||||||
\(568\) | −5.38155 | −0.225805 | ||||||||
\(569\) | −11.0418 | −0.462894 | −0.231447 | − | 0.972847i | \(-0.574346\pi\) | ||||
−0.231447 | + | 0.972847i | \(0.574346\pi\) | |||||||
\(570\) | 51.0643 | 2.13885 | ||||||||
\(571\) | 8.52720 | 0.356852 | 0.178426 | − | 0.983953i | \(-0.442899\pi\) | ||||
0.178426 | + | 0.983953i | \(0.442899\pi\) | |||||||
\(572\) | −1.84712 | −0.0772318 | ||||||||
\(573\) | −14.9680 | −0.625295 | ||||||||
\(574\) | −17.4487 | −0.728293 | ||||||||
\(575\) | −6.21255 | −0.259081 | ||||||||
\(576\) | 1.04987 | 0.0437448 | ||||||||
\(577\) | −35.8618 | −1.49294 | −0.746472 | − | 0.665416i | \(-0.768254\pi\) | ||||
−0.746472 | + | 0.665416i | \(0.768254\pi\) | |||||||
\(578\) | −14.7698 | −0.614341 | ||||||||
\(579\) | −33.0710 | −1.37438 | ||||||||
\(580\) | −3.34851 | −0.139039 | ||||||||
\(581\) | −10.4564 | −0.433806 | ||||||||
\(582\) | −17.7742 | −0.736765 | ||||||||
\(583\) | −55.0324 | −2.27921 | ||||||||
\(584\) | −4.60202 | −0.190433 | ||||||||
\(585\) | −1.58093 | −0.0653634 | ||||||||
\(586\) | 21.7496 | 0.898466 | ||||||||
\(587\) | −24.2605 | −1.00134 | −0.500669 | − | 0.865639i | \(-0.666913\pi\) | ||||
−0.500669 | + | 0.865639i | \(0.666913\pi\) | |||||||
\(588\) | 3.38596 | 0.139635 | ||||||||
\(589\) | 9.24791 | 0.381054 | ||||||||
\(590\) | 26.4582 | 1.08927 | ||||||||
\(591\) | −4.82085 | −0.198303 | ||||||||
\(592\) | 7.68734 | 0.315948 | ||||||||
\(593\) | −33.7632 | −1.38649 | −0.693243 | − | 0.720704i | \(-0.743819\pi\) | ||||
−0.693243 | + | 0.720704i | \(0.743819\pi\) | |||||||
\(594\) | 16.1196 | 0.661396 | ||||||||
\(595\) | 14.7350 | 0.604077 | ||||||||
\(596\) | 15.2059 | 0.622857 | ||||||||
\(597\) | 38.6243 | 1.58079 | ||||||||
\(598\) | −0.449700 | −0.0183896 | ||||||||
\(599\) | −7.63298 | −0.311875 | −0.155938 | − | 0.987767i | \(-0.549840\pi\) | ||||
−0.155938 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(600\) | 12.5023 | 0.510405 | ||||||||
\(601\) | −25.3357 | −1.03347 | −0.516733 | − | 0.856147i | \(-0.672852\pi\) | ||||
−0.516733 | + | 0.856147i | \(0.672852\pi\) | |||||||
\(602\) | 25.3834 | 1.03455 | ||||||||
\(603\) | 2.02634 | 0.0825190 | ||||||||
\(604\) | 7.25184 | 0.295073 | ||||||||
\(605\) | −19.6593 | −0.799265 | ||||||||
\(606\) | 34.6818 | 1.40885 | ||||||||
\(607\) | 5.59433 | 0.227067 | 0.113533 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113533 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(608\) | −7.57782 | −0.307321 | ||||||||
\(609\) | −5.92985 | −0.240290 | ||||||||
\(610\) | 11.2936 | 0.457263 | ||||||||
\(611\) | −3.47290 | −0.140499 | ||||||||
\(612\) | 1.56788 | 0.0633778 | ||||||||
\(613\) | 29.1101 | 1.17575 | 0.587873 | − | 0.808953i | \(-0.299965\pi\) | ||||
0.587873 | + | 0.808953i | \(0.299965\pi\) | |||||||
\(614\) | −30.9335 | −1.24837 | ||||||||
\(615\) | −39.9036 | −1.60907 | ||||||||
\(616\) | 12.1030 | 0.487645 | ||||||||
\(617\) | −11.1186 | −0.447617 | −0.223809 | − | 0.974633i | \(-0.571849\pi\) | ||||
−0.223809 | + | 0.974633i | \(0.571849\pi\) | |||||||
\(618\) | −13.9689 | −0.561913 | ||||||||
\(619\) | −36.4026 | −1.46315 | −0.731573 | − | 0.681763i | \(-0.761213\pi\) | ||||
−0.731573 | + | 0.681763i | \(0.761213\pi\) | |||||||
\(620\) | 4.08650 | 0.164118 | ||||||||
\(621\) | 3.92449 | 0.157484 | ||||||||
\(622\) | 19.0093 | 0.762204 | ||||||||
\(623\) | −12.1581 | −0.487103 | ||||||||
\(624\) | 0.904990 | 0.0362286 | ||||||||
\(625\) | −17.4670 | −0.698680 | ||||||||
\(626\) | 23.3187 | 0.932004 | ||||||||
\(627\) | 62.6378 | 2.50151 | ||||||||
\(628\) | −9.92692 | −0.396127 | ||||||||
\(629\) | 11.4803 | 0.457748 | ||||||||
\(630\) | 10.3589 | 0.412707 | ||||||||
\(631\) | 3.55998 | 0.141720 | 0.0708602 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708602 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(632\) | 9.25601 | 0.368184 | ||||||||
\(633\) | 26.0082 | 1.03373 | ||||||||
\(634\) | 0.472925 | 0.0187822 | ||||||||
\(635\) | 7.44009 | 0.295251 | ||||||||
\(636\) | 26.9630 | 1.06915 | ||||||||
\(637\) | 0.756631 | 0.0299788 | ||||||||
\(638\) | −4.10744 | −0.162615 | ||||||||
\(639\) | −5.64995 | −0.223509 | ||||||||
\(640\) | −3.34851 | −0.132362 | ||||||||
\(641\) | −5.02032 | −0.198291 | −0.0991453 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991453 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(642\) | −9.50247 | −0.375033 | ||||||||
\(643\) | −8.07710 | −0.318530 | −0.159265 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159265 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(644\) | 2.94661 | 0.116113 | ||||||||
\(645\) | 58.0497 | 2.28571 | ||||||||
\(646\) | −11.3167 | −0.445250 | ||||||||
\(647\) | −12.4312 | −0.488720 | −0.244360 | − | 0.969685i | \(-0.578578\pi\) | ||||
−0.244360 | + | 0.969685i | \(0.578578\pi\) | |||||||
\(648\) | −11.0474 | −0.433982 | ||||||||
\(649\) | 32.4548 | 1.27396 | ||||||||
\(650\) | 2.79378 | 0.109581 | ||||||||
\(651\) | 7.23674 | 0.283630 | ||||||||
\(652\) | 22.9592 | 0.899152 | ||||||||
\(653\) | −8.09108 | −0.316629 | −0.158314 | − | 0.987389i | \(-0.550606\pi\) | ||||
−0.158314 | + | 0.987389i | \(0.550606\pi\) | |||||||
\(654\) | 3.11124 | 0.121659 | ||||||||
\(655\) | −48.7975 | −1.90667 | ||||||||
\(656\) | 5.92160 | 0.231200 | ||||||||
\(657\) | −4.83154 | −0.188496 | ||||||||
\(658\) | 22.7558 | 0.887114 | ||||||||
\(659\) | 1.58997 | 0.0619366 | 0.0309683 | − | 0.999520i | \(-0.490141\pi\) | ||||
0.0309683 | + | 0.999520i | \(0.490141\pi\) | |||||||
\(660\) | 27.6786 | 1.07739 | ||||||||
\(661\) | −43.2396 | −1.68182 | −0.840912 | − | 0.541171i | \(-0.817981\pi\) | ||||
−0.840912 | + | 0.541171i | \(0.817981\pi\) | |||||||
\(662\) | 11.1247 | 0.432375 | ||||||||
\(663\) | 1.35151 | 0.0524883 | ||||||||
\(664\) | 3.54863 | 0.137714 | ||||||||
\(665\) | −74.7686 | −2.89940 | ||||||||
\(666\) | 8.07074 | 0.312735 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −3.46124 | −0.133919 | ||||||||
\(669\) | −10.0923 | −0.390190 | ||||||||
\(670\) | −6.46290 | −0.249684 | ||||||||
\(671\) | 13.8532 | 0.534797 | ||||||||
\(672\) | −5.92985 | −0.228749 | ||||||||
\(673\) | 11.8305 | 0.456030 | 0.228015 | − | 0.973658i | \(-0.426776\pi\) | ||||
0.228015 | + | 0.973658i | \(0.426776\pi\) | |||||||
\(674\) | −2.61571 | −0.100753 | ||||||||
\(675\) | −24.3811 | −0.938428 | ||||||||
\(676\) | −12.7978 | −0.492222 | ||||||||
\(677\) | 7.36323 | 0.282992 | 0.141496 | − | 0.989939i | \(-0.454809\pi\) | ||||
0.141496 | + | 0.989939i | \(0.454809\pi\) | |||||||
\(678\) | −17.9097 | −0.687819 | ||||||||
\(679\) | 26.0251 | 0.998753 | ||||||||
\(680\) | −5.00066 | −0.191767 | ||||||||
\(681\) | −7.75444 | −0.297151 | ||||||||
\(682\) | 5.01269 | 0.191946 | ||||||||
\(683\) | 9.49956 | 0.363490 | 0.181745 | − | 0.983346i | \(-0.441825\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441825\pi\) | |||||||
\(684\) | −7.95576 | −0.304196 | ||||||||
\(685\) | 25.3586 | 0.968901 | ||||||||
\(686\) | 15.6685 | 0.598228 | ||||||||
\(687\) | −47.4282 | −1.80950 | ||||||||
\(688\) | −8.61445 | −0.328423 | ||||||||
\(689\) | 6.02519 | 0.229541 | ||||||||
\(690\) | 6.73865 | 0.256536 | ||||||||
\(691\) | −23.5689 | −0.896601 | −0.448301 | − | 0.893883i | \(-0.647971\pi\) | ||||
−0.448301 | + | 0.893883i | \(0.647971\pi\) | |||||||
\(692\) | 2.40357 | 0.0913701 | ||||||||
\(693\) | 12.7067 | 0.482686 | ||||||||
\(694\) | 26.9380 | 1.02255 | ||||||||
\(695\) | 69.6330 | 2.64133 | ||||||||
\(696\) | 2.01243 | 0.0762810 | ||||||||
\(697\) | 8.84330 | 0.334964 | ||||||||
\(698\) | −19.0367 | −0.720551 | ||||||||
\(699\) | −43.1417 | −1.63177 | ||||||||
\(700\) | −18.3060 | −0.691900 | ||||||||
\(701\) | −1.92411 | −0.0726725 | −0.0363363 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363363 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(702\) | −1.76485 | −0.0666098 | ||||||||
\(703\) | −58.2533 | −2.19706 | ||||||||
\(704\) | −4.10744 | −0.154805 | ||||||||
\(705\) | 52.0406 | 1.95996 | ||||||||
\(706\) | 18.8385 | 0.708995 | ||||||||
\(707\) | −50.7814 | −1.90983 | ||||||||
\(708\) | −15.9012 | −0.597602 | ||||||||
\(709\) | 43.0363 | 1.61626 | 0.808130 | − | 0.589004i | \(-0.200480\pi\) | ||||
0.808130 | + | 0.589004i | \(0.200480\pi\) | |||||||
\(710\) | 18.0202 | 0.676286 | ||||||||
\(711\) | 9.71765 | 0.364440 | ||||||||
\(712\) | 4.12612 | 0.154633 | ||||||||
\(713\) | 1.22039 | 0.0457040 | ||||||||
\(714\) | −8.85563 | −0.331413 | ||||||||
\(715\) | 6.18510 | 0.231309 | ||||||||
\(716\) | −3.62288 | −0.135393 | ||||||||
\(717\) | −57.6237 | −2.15200 | ||||||||
\(718\) | −16.6130 | −0.619993 | ||||||||
\(719\) | 42.7397 | 1.59392 | 0.796961 | − | 0.604030i | \(-0.206439\pi\) | ||||
0.796961 | + | 0.604030i | \(0.206439\pi\) | |||||||
\(720\) | −3.51552 | −0.131016 | ||||||||
\(721\) | 20.4534 | 0.761725 | ||||||||
\(722\) | 38.4234 | 1.42997 | ||||||||
\(723\) | −25.0293 | −0.930849 | ||||||||
\(724\) | −3.44626 | −0.128079 | ||||||||
\(725\) | 6.21255 | 0.230728 | ||||||||
\(726\) | 11.8151 | 0.438499 | ||||||||
\(727\) | −50.2135 | −1.86231 | −0.931157 | − | 0.364618i | \(-0.881200\pi\) | ||||
−0.931157 | + | 0.364618i | \(0.881200\pi\) | |||||||
\(728\) | −1.32509 | −0.0491112 | ||||||||
\(729\) | 12.0949 | 0.447960 | ||||||||
\(730\) | 15.4099 | 0.570347 | ||||||||
\(731\) | −12.8648 | −0.475822 | ||||||||
\(732\) | −6.78734 | −0.250867 | ||||||||
\(733\) | 19.6376 | 0.725332 | 0.362666 | − | 0.931919i | \(-0.381867\pi\) | ||||
0.362666 | + | 0.931919i | \(0.381867\pi\) | |||||||
\(734\) | 10.2844 | 0.379605 | ||||||||
\(735\) | −11.3379 | −0.418206 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −7.92769 | −0.292020 | ||||||||
\(738\) | 6.21693 | 0.228848 | ||||||||
\(739\) | 44.2013 | 1.62597 | 0.812985 | − | 0.582285i | \(-0.197841\pi\) | ||||
0.812985 | + | 0.582285i | \(0.197841\pi\) | |||||||
\(740\) | −25.7412 | −0.946264 | ||||||||
\(741\) | −6.85786 | −0.251930 | ||||||||
\(742\) | −39.4794 | −1.44933 | ||||||||
\(743\) | −30.0155 | −1.10116 | −0.550581 | − | 0.834781i | \(-0.685594\pi\) | ||||
−0.550581 | + | 0.834781i | \(0.685594\pi\) | |||||||
\(744\) | −2.45595 | −0.0900396 | ||||||||
\(745\) | −50.9171 | −1.86546 | ||||||||
\(746\) | 2.86104 | 0.104750 | ||||||||
\(747\) | 3.72562 | 0.136313 | ||||||||
\(748\) | −6.13404 | −0.224283 | ||||||||
\(749\) | 13.9136 | 0.508391 | ||||||||
\(750\) | −8.17092 | −0.298360 | ||||||||
\(751\) | 11.5227 | 0.420469 | 0.210235 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210235 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(752\) | −7.72271 | −0.281618 | ||||||||
\(753\) | 25.1625 | 0.916971 | ||||||||
\(754\) | 0.449700 | 0.0163771 | ||||||||
\(755\) | −24.2829 | −0.883744 | ||||||||
\(756\) | 11.5640 | 0.420577 | ||||||||
\(757\) | −19.1922 | −0.697554 | −0.348777 | − | 0.937206i | \(-0.613403\pi\) | ||||
−0.348777 | + | 0.937206i | \(0.613403\pi\) | |||||||
\(758\) | 4.57836 | 0.166294 | ||||||||
\(759\) | 8.26593 | 0.300034 | ||||||||
\(760\) | 25.3744 | 0.920428 | ||||||||
\(761\) | −12.0269 | −0.435973 | −0.217987 | − | 0.975952i | \(-0.569949\pi\) | ||||
−0.217987 | + | 0.975952i | \(0.569949\pi\) | |||||||
\(762\) | −4.47143 | −0.161983 | ||||||||
\(763\) | −4.55550 | −0.164920 | ||||||||
\(764\) | −7.43775 | −0.269088 | ||||||||
\(765\) | −5.25007 | −0.189817 | ||||||||
\(766\) | −13.4638 | −0.486466 | ||||||||
\(767\) | −3.55330 | −0.128302 | ||||||||
\(768\) | 2.01243 | 0.0726173 | ||||||||
\(769\) | 42.2556 | 1.52378 | 0.761889 | − | 0.647708i | \(-0.224272\pi\) | ||||
0.761889 | + | 0.647708i | \(0.224272\pi\) | |||||||
\(770\) | −40.5272 | −1.46050 | ||||||||
\(771\) | −42.5578 | −1.53268 | ||||||||
\(772\) | −16.4333 | −0.591449 | ||||||||
\(773\) | 6.53047 | 0.234885 | 0.117442 | − | 0.993080i | \(-0.462530\pi\) | ||||
0.117442 | + | 0.993080i | \(0.462530\pi\) | |||||||
\(774\) | −9.04409 | −0.325083 | ||||||||
\(775\) | −7.58174 | −0.272344 | ||||||||
\(776\) | −8.83222 | −0.317058 | ||||||||
\(777\) | −45.5848 | −1.63534 | ||||||||
\(778\) | −3.92455 | −0.140702 | ||||||||
\(779\) | −44.8728 | −1.60774 | ||||||||
\(780\) | −3.03037 | −0.108505 | ||||||||
\(781\) | 22.1044 | 0.790957 | ||||||||
\(782\) | −1.49340 | −0.0534038 | ||||||||
\(783\) | −3.92449 | −0.140250 | ||||||||
\(784\) | 1.68252 | 0.0600901 | ||||||||
\(785\) | 33.2404 | 1.18640 | ||||||||
\(786\) | 29.3269 | 1.04606 | ||||||||
\(787\) | 31.6289 | 1.12745 | 0.563724 | − | 0.825963i | \(-0.309368\pi\) | ||||
0.563724 | + | 0.825963i | \(0.309368\pi\) | |||||||
\(788\) | −2.39554 | −0.0853375 | ||||||||
\(789\) | −27.9297 | −0.994325 | ||||||||
\(790\) | −30.9939 | −1.10271 | ||||||||
\(791\) | 26.2235 | 0.932401 | ||||||||
\(792\) | −4.31229 | −0.153231 | ||||||||
\(793\) | −1.51671 | −0.0538599 | ||||||||
\(794\) | 30.7736 | 1.09212 | ||||||||
\(795\) | −90.2860 | −3.20211 | ||||||||
\(796\) | 19.1929 | 0.680273 | ||||||||
\(797\) | −54.5784 | −1.93327 | −0.966634 | − | 0.256162i | \(-0.917542\pi\) | ||||
−0.966634 | + | 0.256162i | \(0.917542\pi\) | |||||||
\(798\) | 44.9353 | 1.59069 | ||||||||
\(799\) | −11.5331 | −0.408011 | ||||||||
\(800\) | 6.21255 | 0.219647 | ||||||||
\(801\) | 4.33191 | 0.153060 | ||||||||
\(802\) | 2.60010 | 0.0918126 | ||||||||
\(803\) | 18.9025 | 0.667055 | ||||||||
\(804\) | 3.88415 | 0.136984 | ||||||||
\(805\) | −9.86677 | −0.347758 | ||||||||
\(806\) | −0.548811 | −0.0193310 | ||||||||
\(807\) | 37.6876 | 1.32667 | ||||||||
\(808\) | 17.2338 | 0.606284 | ||||||||
\(809\) | 33.0661 | 1.16254 | 0.581270 | − | 0.813710i | \(-0.302556\pi\) | ||||
0.581270 | + | 0.813710i | \(0.302556\pi\) | |||||||
\(810\) | 36.9923 | 1.29978 | ||||||||
\(811\) | 28.7021 | 1.00787 | 0.503933 | − | 0.863742i | \(-0.331886\pi\) | ||||
0.503933 | + | 0.863742i | \(0.331886\pi\) | |||||||
\(812\) | −2.94661 | −0.103406 | ||||||||
\(813\) | −59.6516 | −2.09207 | ||||||||
\(814\) | −31.5753 | −1.10671 | ||||||||
\(815\) | −76.8793 | −2.69296 | ||||||||
\(816\) | 3.00536 | 0.105209 | ||||||||
\(817\) | 65.2788 | 2.28381 | ||||||||
\(818\) | 1.80606 | 0.0631472 | ||||||||
\(819\) | −1.39118 | −0.0486118 | ||||||||
\(820\) | −19.8286 | −0.692443 | ||||||||
\(821\) | −2.02510 | −0.0706766 | −0.0353383 | − | 0.999375i | \(-0.511251\pi\) | ||||
−0.0353383 | + | 0.999375i | \(0.511251\pi\) | |||||||
\(822\) | −15.2403 | −0.531567 | ||||||||
\(823\) | 7.59197 | 0.264639 | 0.132320 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132320 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(824\) | −6.94133 | −0.241813 | ||||||||
\(825\) | −51.3525 | −1.78786 | ||||||||
\(826\) | 23.2826 | 0.810105 | ||||||||
\(827\) | 8.34687 | 0.290249 | 0.145124 | − | 0.989413i | \(-0.453642\pi\) | ||||
0.145124 | + | 0.989413i | \(0.453642\pi\) | |||||||
\(828\) | −1.04987 | −0.0364856 | ||||||||
\(829\) | 3.08964 | 0.107308 | 0.0536538 | − | 0.998560i | \(-0.482913\pi\) | ||||
0.0536538 | + | 0.998560i | \(0.482913\pi\) | |||||||
\(830\) | −11.8826 | −0.412452 | ||||||||
\(831\) | −56.6330 | −1.96458 | ||||||||
\(832\) | 0.449700 | 0.0155906 | ||||||||
\(833\) | 2.51268 | 0.0870590 | ||||||||
\(834\) | −41.8488 | −1.44911 | ||||||||
\(835\) | 11.5900 | 0.401088 | ||||||||
\(836\) | 31.1254 | 1.07650 | ||||||||
\(837\) | 4.78942 | 0.165547 | ||||||||
\(838\) | 16.3847 | 0.565999 | ||||||||
\(839\) | −17.4894 | −0.603802 | −0.301901 | − | 0.953339i | \(-0.597621\pi\) | ||||
−0.301901 | + | 0.953339i | \(0.597621\pi\) | |||||||
\(840\) | 19.8562 | 0.685104 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −29.9884 | −1.03347 | ||||||||
\(843\) | 51.2560 | 1.76535 | ||||||||
\(844\) | 12.9238 | 0.444855 | ||||||||
\(845\) | 42.8535 | 1.47421 | ||||||||
\(846\) | −8.10787 | −0.278754 | ||||||||
\(847\) | −17.2997 | −0.594426 | ||||||||
\(848\) | 13.3982 | 0.460097 | ||||||||
\(849\) | −41.8186 | −1.43521 | ||||||||
\(850\) | 9.27780 | 0.318226 | ||||||||
\(851\) | −7.68734 | −0.263519 | ||||||||
\(852\) | −10.8300 | −0.371029 | ||||||||
\(853\) | −10.0668 | −0.344679 | −0.172340 | − | 0.985038i | \(-0.555133\pi\) | ||||
−0.172340 | + | 0.985038i | \(0.555133\pi\) | |||||||
\(854\) | 9.93807 | 0.340074 | ||||||||
\(855\) | 26.6400 | 0.911068 | ||||||||
\(856\) | −4.72189 | −0.161391 | ||||||||
\(857\) | −13.0068 | −0.444305 | −0.222153 | − | 0.975012i | \(-0.571308\pi\) | ||||
−0.222153 | + | 0.975012i | \(0.571308\pi\) | |||||||
\(858\) | −3.71719 | −0.126903 | ||||||||
\(859\) | −34.5801 | −1.17986 | −0.589928 | − | 0.807456i | \(-0.700844\pi\) | ||||
−0.589928 | + | 0.807456i | \(0.700844\pi\) | |||||||
\(860\) | 28.8456 | 0.983627 | ||||||||
\(861\) | −35.1142 | −1.19669 | ||||||||
\(862\) | −20.2190 | −0.688663 | ||||||||
\(863\) | 51.1433 | 1.74094 | 0.870470 | − | 0.492222i | \(-0.163815\pi\) | ||||
0.870470 | + | 0.492222i | \(0.163815\pi\) | |||||||
\(864\) | −3.92449 | −0.133514 | ||||||||
\(865\) | −8.04839 | −0.273654 | ||||||||
\(866\) | 29.7211 | 1.00997 | ||||||||
\(867\) | −29.7231 | −1.00945 | ||||||||
\(868\) | 3.59602 | 0.122057 | ||||||||
\(869\) | −38.0185 | −1.28969 | ||||||||
\(870\) | −6.73865 | −0.228462 | ||||||||
\(871\) | 0.867958 | 0.0294096 | ||||||||
\(872\) | 1.54601 | 0.0523546 | ||||||||
\(873\) | −9.27272 | −0.313834 | ||||||||
\(874\) | 7.57782 | 0.256324 | ||||||||
\(875\) | 11.9639 | 0.404454 | ||||||||
\(876\) | −9.26124 | −0.312908 | ||||||||
\(877\) | 52.8468 | 1.78451 | 0.892255 | − | 0.451531i | \(-0.149122\pi\) | ||||
0.892255 | + | 0.451531i | \(0.149122\pi\) | |||||||
\(878\) | 28.3637 | 0.957230 | ||||||||
\(879\) | 43.7695 | 1.47631 | ||||||||
\(880\) | 13.7538 | 0.463641 | ||||||||
\(881\) | 0.405614 | 0.0136655 | 0.00683274 | − | 0.999977i | \(-0.497825\pi\) | ||||
0.00683274 | + | 0.999977i | \(0.497825\pi\) | |||||||
\(882\) | 1.76644 | 0.0594790 | ||||||||
\(883\) | −30.3038 | −1.01980 | −0.509901 | − | 0.860233i | \(-0.670318\pi\) | ||||
−0.509901 | + | 0.860233i | \(0.670318\pi\) | |||||||
\(884\) | 0.671581 | 0.0225877 | ||||||||
\(885\) | 53.2453 | 1.78982 | ||||||||
\(886\) | 33.1054 | 1.11220 | ||||||||
\(887\) | 30.8406 | 1.03553 | 0.517763 | − | 0.855524i | \(-0.326765\pi\) | ||||
0.517763 | + | 0.855524i | \(0.326765\pi\) | |||||||
\(888\) | 15.4702 | 0.519147 | ||||||||
\(889\) | 6.54710 | 0.219583 | ||||||||
\(890\) | −13.8164 | −0.463126 | ||||||||
\(891\) | 45.3765 | 1.52017 | ||||||||
\(892\) | −5.01497 | −0.167914 | ||||||||
\(893\) | 58.5213 | 1.95834 | ||||||||
\(894\) | 30.6008 | 1.02344 | ||||||||
\(895\) | 12.1313 | 0.405504 | ||||||||
\(896\) | −2.94661 | −0.0984394 | ||||||||
\(897\) | −0.904990 | −0.0302167 | ||||||||
\(898\) | −8.66957 | −0.289307 | ||||||||
\(899\) | −1.22039 | −0.0407024 | ||||||||
\(900\) | 6.52239 | 0.217413 | ||||||||
\(901\) | 20.0089 | 0.666593 | ||||||||
\(902\) | −24.3226 | −0.809854 | ||||||||
\(903\) | 51.0824 | 1.69992 | ||||||||
\(904\) | −8.89955 | −0.295995 | ||||||||
\(905\) | 11.5399 | 0.383598 | ||||||||
\(906\) | 14.5938 | 0.484847 | ||||||||
\(907\) | 8.62844 | 0.286503 | 0.143251 | − | 0.989686i | \(-0.454244\pi\) | ||||
0.143251 | + | 0.989686i | \(0.454244\pi\) | |||||||
\(908\) | −3.85327 | −0.127875 | ||||||||
\(909\) | 18.0933 | 0.600118 | ||||||||
\(910\) | 4.43709 | 0.147088 | ||||||||
\(911\) | 36.6066 | 1.21283 | 0.606416 | − | 0.795148i | \(-0.292607\pi\) | ||||
0.606416 | + | 0.795148i | \(0.292607\pi\) | |||||||
\(912\) | −15.2498 | −0.504973 | ||||||||
\(913\) | −14.5758 | −0.482388 | ||||||||
\(914\) | 14.1426 | 0.467795 | ||||||||
\(915\) | 22.7275 | 0.751348 | ||||||||
\(916\) | −23.5676 | −0.778697 | ||||||||
\(917\) | −42.9406 | −1.41802 | ||||||||
\(918\) | −5.86083 | −0.193436 | ||||||||
\(919\) | 45.0971 | 1.48762 | 0.743808 | − | 0.668394i | \(-0.233018\pi\) | ||||
0.743808 | + | 0.668394i | \(0.233018\pi\) | |||||||
\(920\) | 3.34851 | 0.110397 | ||||||||
\(921\) | −62.2515 | −2.05126 | ||||||||
\(922\) | −37.5912 | −1.23800 | ||||||||
\(923\) | −2.42008 | −0.0796580 | ||||||||
\(924\) | 24.3565 | 0.801270 | ||||||||
\(925\) | 47.7579 | 1.57027 | ||||||||
\(926\) | 24.3916 | 0.801557 | ||||||||
\(927\) | −7.28752 | −0.239354 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −21.3839 | −0.701583 | −0.350792 | − | 0.936454i | \(-0.614087\pi\) | ||||
−0.350792 | + | 0.936454i | \(0.614087\pi\) | |||||||
\(930\) | 8.22380 | 0.269669 | ||||||||
\(931\) | −12.7499 | −0.417860 | ||||||||
\(932\) | −21.4376 | −0.702212 | ||||||||
\(933\) | 38.2549 | 1.25241 | ||||||||
\(934\) | −1.71268 | −0.0560405 | ||||||||
\(935\) | 20.5399 | 0.671727 | ||||||||
\(936\) | 0.472129 | 0.0154320 | ||||||||
\(937\) | −34.5974 | −1.13025 | −0.565124 | − | 0.825006i | \(-0.691172\pi\) | ||||
−0.565124 | + | 0.825006i | \(0.691172\pi\) | |||||||
\(938\) | −5.68720 | −0.185694 | ||||||||
\(939\) | 46.9273 | 1.53141 | ||||||||
\(940\) | 25.8596 | 0.843447 | ||||||||
\(941\) | −44.1629 | −1.43967 | −0.719835 | − | 0.694145i | \(-0.755782\pi\) | ||||
−0.719835 | + | 0.694145i | \(0.755782\pi\) | |||||||
\(942\) | −19.9772 | −0.650894 | ||||||||
\(943\) | −5.92160 | −0.192834 | ||||||||
\(944\) | −7.90148 | −0.257171 | ||||||||
\(945\) | −38.7221 | −1.25963 | ||||||||
\(946\) | 35.3833 | 1.15041 | ||||||||
\(947\) | 21.6888 | 0.704791 | 0.352395 | − | 0.935851i | \(-0.385367\pi\) | ||||
0.352395 | + | 0.935851i | \(0.385367\pi\) | |||||||
\(948\) | 18.6271 | 0.604979 | ||||||||
\(949\) | −2.06953 | −0.0671798 | ||||||||
\(950\) | −47.0776 | −1.52740 | ||||||||
\(951\) | 0.951728 | 0.0308619 | ||||||||
\(952\) | −4.40046 | −0.142620 | ||||||||
\(953\) | 0.441114 | 0.0142891 | 0.00714454 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714454 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(954\) | 14.0665 | 0.455418 | ||||||||
\(955\) | 24.9054 | 0.805921 | ||||||||
\(956\) | −28.6339 | −0.926086 | ||||||||
\(957\) | −8.26593 | −0.267200 | ||||||||
\(958\) | −31.2291 | −1.00897 | ||||||||
\(959\) | 22.3149 | 0.720587 | ||||||||
\(960\) | −6.73865 | −0.217489 | ||||||||
\(961\) | −29.5106 | −0.951956 | ||||||||
\(962\) | 3.45700 | 0.111458 | ||||||||
\(963\) | −4.95739 | −0.159750 | ||||||||
\(964\) | −12.4373 | −0.400580 | ||||||||
\(965\) | 55.0273 | 1.77139 | ||||||||
\(966\) | 5.92985 | 0.190790 | ||||||||
\(967\) | 43.3851 | 1.39517 | 0.697586 | − | 0.716501i | \(-0.254258\pi\) | ||||
0.697586 | + | 0.716501i | \(0.254258\pi\) | |||||||
\(968\) | 5.87106 | 0.188703 | ||||||||
\(969\) | −22.7741 | −0.731609 | ||||||||
\(970\) | 29.5748 | 0.949590 | ||||||||
\(971\) | 7.68638 | 0.246668 | 0.123334 | − | 0.992365i | \(-0.460641\pi\) | ||||
0.123334 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(972\) | −10.4586 | −0.335460 | ||||||||
\(973\) | 61.2753 | 1.96440 | ||||||||
\(974\) | 2.28762 | 0.0733001 | ||||||||
\(975\) | 5.62229 | 0.180058 | ||||||||
\(976\) | −3.37271 | −0.107958 | ||||||||
\(977\) | −1.22029 | −0.0390405 | −0.0195203 | − | 0.999809i | \(-0.506214\pi\) | ||||
−0.0195203 | + | 0.999809i | \(0.506214\pi\) | |||||||
\(978\) | 46.2038 | 1.47744 | ||||||||
\(979\) | −16.9478 | −0.541654 | ||||||||
\(980\) | −5.63395 | −0.179970 | ||||||||
\(981\) | 1.62312 | 0.0518221 | ||||||||
\(982\) | 29.5094 | 0.941682 | ||||||||
\(983\) | 24.2195 | 0.772483 | 0.386241 | − | 0.922398i | \(-0.373773\pi\) | ||||
0.386241 | + | 0.922398i | \(0.373773\pi\) | |||||||
\(984\) | 11.9168 | 0.379894 | ||||||||
\(985\) | 8.02149 | 0.255586 | ||||||||
\(986\) | 1.49340 | 0.0475595 | ||||||||
\(987\) | 45.7945 | 1.45765 | ||||||||
\(988\) | −3.40775 | −0.108415 | ||||||||
\(989\) | 8.61445 | 0.273924 | ||||||||
\(990\) | 14.4398 | 0.458926 | ||||||||
\(991\) | −18.9870 | −0.603143 | −0.301571 | − | 0.953444i | \(-0.597511\pi\) | ||||
−0.301571 | + | 0.953444i | \(0.597511\pi\) | |||||||
\(992\) | −1.22039 | −0.0387475 | ||||||||
\(993\) | 22.3878 | 0.710454 | ||||||||
\(994\) | 15.8573 | 0.502964 | ||||||||
\(995\) | −64.2676 | −2.03742 | ||||||||
\(996\) | 7.14137 | 0.226283 | ||||||||
\(997\) | −13.0196 | −0.412333 | −0.206167 | − | 0.978517i | \(-0.566099\pi\) | ||||
−0.206167 | + | 0.978517i | \(0.566099\pi\) | |||||||
\(998\) | −24.7717 | −0.784134 | ||||||||
\(999\) | −30.1689 | −0.954502 |
(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 | 1334.2.a.h.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.h.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |