Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35222 | −0.956167 | −0.478083 | − | 0.878314i | \(-0.658668\pi\) | ||||
−0.478083 | + | 0.878314i | \(0.658668\pi\) | |||||||
\(3\) | 2.90367 | 1.67644 | 0.838218 | − | 0.545335i | \(-0.183598\pi\) | ||||
0.838218 | + | 0.545335i | \(0.183598\pi\) | |||||||
\(4\) | −0.171490 | −0.0857452 | ||||||||
\(5\) | −2.71204 | −1.21286 | −0.606432 | − | 0.795136i | \(-0.707400\pi\) | ||||
−0.606432 | + | 0.795136i | \(0.707400\pi\) | |||||||
\(6\) | −3.92642 | −1.60295 | ||||||||
\(7\) | −3.82442 | −1.44550 | −0.722748 | − | 0.691111i | \(-0.757121\pi\) | ||||
−0.722748 | + | 0.691111i | \(0.757121\pi\) | |||||||
\(8\) | 2.93634 | 1.03815 | ||||||||
\(9\) | 5.43132 | 1.81044 | ||||||||
\(10\) | 3.66729 | 1.15970 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.497952 | −0.143746 | ||||||||
\(13\) | 6.55623 | 1.81837 | 0.909185 | − | 0.416393i | \(-0.136706\pi\) | ||||
0.909185 | + | 0.416393i | \(0.136706\pi\) | |||||||
\(14\) | 5.17148 | 1.38214 | ||||||||
\(15\) | −7.87489 | −2.03329 | ||||||||
\(16\) | −3.62761 | −0.906903 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −7.34436 | −1.73108 | ||||||||
\(19\) | −4.53389 | −1.04015 | −0.520073 | − | 0.854122i | \(-0.674095\pi\) | ||||
−0.520073 | + | 0.854122i | \(0.674095\pi\) | |||||||
\(20\) | 0.465090 | 0.103997 | ||||||||
\(21\) | −11.1049 | −2.42328 | ||||||||
\(22\) | 1.35222 | 0.288295 | ||||||||
\(23\) | −5.04566 | −1.05209 | −0.526047 | − | 0.850456i | \(-0.676326\pi\) | ||||
−0.526047 | + | 0.850456i | \(0.676326\pi\) | |||||||
\(24\) | 8.52618 | 1.74040 | ||||||||
\(25\) | 2.35519 | 0.471037 | ||||||||
\(26\) | −8.86548 | −1.73866 | ||||||||
\(27\) | 7.05975 | 1.35865 | ||||||||
\(28\) | 0.655852 | 0.123944 | ||||||||
\(29\) | 1.78233 | 0.330970 | 0.165485 | − | 0.986212i | \(-0.447081\pi\) | ||||
0.165485 | + | 0.986212i | \(0.447081\pi\) | |||||||
\(30\) | 10.6486 | 1.94416 | ||||||||
\(31\) | 5.17771 | 0.929944 | 0.464972 | − | 0.885325i | \(-0.346064\pi\) | ||||
0.464972 | + | 0.885325i | \(0.346064\pi\) | |||||||
\(32\) | −0.967341 | −0.171003 | ||||||||
\(33\) | −2.90367 | −0.505465 | ||||||||
\(34\) | 1.35222 | 0.231904 | ||||||||
\(35\) | 10.3720 | 1.75319 | ||||||||
\(36\) | −0.931419 | −0.155237 | ||||||||
\(37\) | −2.82360 | −0.464197 | −0.232098 | − | 0.972692i | \(-0.574559\pi\) | ||||
−0.232098 | + | 0.972692i | \(0.574559\pi\) | |||||||
\(38\) | 6.13084 | 0.994553 | ||||||||
\(39\) | 19.0371 | 3.04838 | ||||||||
\(40\) | −7.96349 | −1.25914 | ||||||||
\(41\) | −1.74874 | −0.273107 | −0.136553 | − | 0.990633i | \(-0.543603\pi\) | ||||
−0.136553 | + | 0.990633i | \(0.543603\pi\) | |||||||
\(42\) | 15.0163 | 2.31706 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0.171490 | 0.0258532 | ||||||||
\(45\) | −14.7300 | −2.19582 | ||||||||
\(46\) | 6.82286 | 1.00598 | ||||||||
\(47\) | 2.93681 | 0.428378 | 0.214189 | − | 0.976792i | \(-0.431289\pi\) | ||||
0.214189 | + | 0.976792i | \(0.431289\pi\) | |||||||
\(48\) | −10.5334 | −1.52036 | ||||||||
\(49\) | 7.62623 | 1.08946 | ||||||||
\(50\) | −3.18474 | −0.450390 | ||||||||
\(51\) | −2.90367 | −0.406596 | ||||||||
\(52\) | −1.12433 | −0.155916 | ||||||||
\(53\) | −7.42353 | −1.01970 | −0.509850 | − | 0.860263i | \(-0.670299\pi\) | ||||
−0.509850 | + | 0.860263i | \(0.670299\pi\) | |||||||
\(54\) | −9.54637 | −1.29910 | ||||||||
\(55\) | 2.71204 | 0.365692 | ||||||||
\(56\) | −11.2298 | −1.50065 | ||||||||
\(57\) | −13.1649 | −1.74374 | ||||||||
\(58\) | −2.41010 | −0.316462 | ||||||||
\(59\) | 7.83907 | 1.02056 | 0.510280 | − | 0.860008i | \(-0.329542\pi\) | ||||
0.510280 | + | 0.860008i | \(0.329542\pi\) | |||||||
\(60\) | 1.35047 | 0.174345 | ||||||||
\(61\) | −4.43647 | −0.568032 | −0.284016 | − | 0.958820i | \(-0.591667\pi\) | ||||
−0.284016 | + | 0.958820i | \(0.591667\pi\) | |||||||
\(62\) | −7.00142 | −0.889181 | ||||||||
\(63\) | −20.7717 | −2.61698 | ||||||||
\(64\) | 8.56328 | 1.07041 | ||||||||
\(65\) | −17.7808 | −2.20543 | ||||||||
\(66\) | 3.92642 | 0.483308 | ||||||||
\(67\) | −7.03016 | −0.858871 | −0.429435 | − | 0.903098i | \(-0.641287\pi\) | ||||
−0.429435 | + | 0.903098i | \(0.641287\pi\) | |||||||
\(68\) | 0.171490 | 0.0207963 | ||||||||
\(69\) | −14.6510 | −1.76377 | ||||||||
\(70\) | −14.0253 | −1.67634 | ||||||||
\(71\) | 9.18978 | 1.09063 | 0.545313 | − | 0.838232i | \(-0.316411\pi\) | ||||
0.545313 | + | 0.838232i | \(0.316411\pi\) | |||||||
\(72\) | 15.9482 | 1.87951 | ||||||||
\(73\) | −11.4059 | −1.33496 | −0.667482 | − | 0.744626i | \(-0.732628\pi\) | ||||
−0.667482 | + | 0.744626i | \(0.732628\pi\) | |||||||
\(74\) | 3.81814 | 0.443850 | ||||||||
\(75\) | 6.83869 | 0.789664 | ||||||||
\(76\) | 0.777519 | 0.0891875 | ||||||||
\(77\) | 3.82442 | 0.435834 | ||||||||
\(78\) | −25.7425 | −2.91476 | ||||||||
\(79\) | 11.9006 | 1.33892 | 0.669462 | − | 0.742846i | \(-0.266525\pi\) | ||||
0.669462 | + | 0.742846i | \(0.266525\pi\) | |||||||
\(80\) | 9.83824 | 1.09995 | ||||||||
\(81\) | 4.20526 | 0.467252 | ||||||||
\(82\) | 2.36468 | 0.261136 | ||||||||
\(83\) | −5.82134 | −0.638975 | −0.319488 | − | 0.947590i | \(-0.603511\pi\) | ||||
−0.319488 | + | 0.947590i | \(0.603511\pi\) | |||||||
\(84\) | 1.90438 | 0.207785 | ||||||||
\(85\) | 2.71204 | 0.294163 | ||||||||
\(86\) | −1.35222 | −0.145814 | ||||||||
\(87\) | 5.17529 | 0.554850 | ||||||||
\(88\) | −2.93634 | −0.313015 | ||||||||
\(89\) | 16.1023 | 1.70684 | 0.853422 | − | 0.521220i | \(-0.174523\pi\) | ||||
0.853422 | + | 0.521220i | \(0.174523\pi\) | |||||||
\(90\) | 19.9182 | 2.09957 | ||||||||
\(91\) | −25.0738 | −2.62845 | ||||||||
\(92\) | 0.865282 | 0.0902119 | ||||||||
\(93\) | 15.0344 | 1.55899 | ||||||||
\(94\) | −3.97123 | −0.409601 | ||||||||
\(95\) | 12.2961 | 1.26155 | ||||||||
\(96\) | −2.80884 | −0.286676 | ||||||||
\(97\) | 15.8546 | 1.60979 | 0.804894 | − | 0.593418i | \(-0.202222\pi\) | ||||
0.804894 | + | 0.593418i | \(0.202222\pi\) | |||||||
\(98\) | −10.3124 | −1.04171 | ||||||||
\(99\) | −5.43132 | −0.545868 | ||||||||
\(100\) | −0.403892 | −0.0403892 | ||||||||
\(101\) | 7.31163 | 0.727535 | 0.363767 | − | 0.931490i | \(-0.381490\pi\) | ||||
0.363767 | + | 0.931490i | \(0.381490\pi\) | |||||||
\(102\) | 3.92642 | 0.388773 | ||||||||
\(103\) | −16.6286 | −1.63847 | −0.819234 | − | 0.573460i | \(-0.805601\pi\) | ||||
−0.819234 | + | 0.573460i | \(0.805601\pi\) | |||||||
\(104\) | 19.2513 | 1.88775 | ||||||||
\(105\) | 30.1169 | 2.93911 | ||||||||
\(106\) | 10.0383 | 0.975004 | ||||||||
\(107\) | 12.3905 | 1.19783 | 0.598916 | − | 0.800812i | \(-0.295598\pi\) | ||||
0.598916 | + | 0.800812i | \(0.295598\pi\) | |||||||
\(108\) | −1.21068 | −0.116498 | ||||||||
\(109\) | 3.65262 | 0.349857 | 0.174929 | − | 0.984581i | \(-0.444031\pi\) | ||||
0.174929 | + | 0.984581i | \(0.444031\pi\) | |||||||
\(110\) | −3.66729 | −0.349663 | ||||||||
\(111\) | −8.19881 | −0.778197 | ||||||||
\(112\) | 13.8735 | 1.31092 | ||||||||
\(113\) | −8.03470 | −0.755841 | −0.377920 | − | 0.925838i | \(-0.623361\pi\) | ||||
−0.377920 | + | 0.925838i | \(0.623361\pi\) | |||||||
\(114\) | 17.8019 | 1.66730 | ||||||||
\(115\) | 13.6841 | 1.27604 | ||||||||
\(116\) | −0.305652 | −0.0283791 | ||||||||
\(117\) | 35.6089 | 3.29205 | ||||||||
\(118\) | −10.6002 | −0.975826 | ||||||||
\(119\) | 3.82442 | 0.350584 | ||||||||
\(120\) | −23.1234 | −2.11087 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.99910 | 0.543133 | ||||||||
\(123\) | −5.07776 | −0.457846 | ||||||||
\(124\) | −0.887927 | −0.0797382 | ||||||||
\(125\) | 7.17286 | 0.641560 | ||||||||
\(126\) | 28.0879 | 2.50227 | ||||||||
\(127\) | −20.9777 | −1.86147 | −0.930734 | − | 0.365697i | \(-0.880831\pi\) | ||||
−0.930734 | + | 0.365697i | \(0.880831\pi\) | |||||||
\(128\) | −9.64479 | −0.852487 | ||||||||
\(129\) | 2.90367 | 0.255654 | ||||||||
\(130\) | 24.0436 | 2.10876 | ||||||||
\(131\) | 11.9181 | 1.04129 | 0.520643 | − | 0.853774i | \(-0.325692\pi\) | ||||
0.520643 | + | 0.853774i | \(0.325692\pi\) | |||||||
\(132\) | 0.497952 | 0.0433412 | ||||||||
\(133\) | 17.3395 | 1.50353 | ||||||||
\(134\) | 9.50635 | 0.821224 | ||||||||
\(135\) | −19.1464 | −1.64786 | ||||||||
\(136\) | −2.93634 | −0.251789 | ||||||||
\(137\) | −11.0622 | −0.945107 | −0.472554 | − | 0.881302i | \(-0.656668\pi\) | ||||
−0.472554 | + | 0.881302i | \(0.656668\pi\) | |||||||
\(138\) | 19.8114 | 1.68646 | ||||||||
\(139\) | −7.60424 | −0.644984 | −0.322492 | − | 0.946572i | \(-0.604520\pi\) | ||||
−0.322492 | + | 0.946572i | \(0.604520\pi\) | |||||||
\(140\) | −1.77870 | −0.150328 | ||||||||
\(141\) | 8.52755 | 0.718149 | ||||||||
\(142\) | −12.4266 | −1.04282 | ||||||||
\(143\) | −6.55623 | −0.548259 | ||||||||
\(144\) | −19.7027 | −1.64189 | ||||||||
\(145\) | −4.83375 | −0.401421 | ||||||||
\(146\) | 15.4234 | 1.27645 | ||||||||
\(147\) | 22.1441 | 1.82641 | ||||||||
\(148\) | 0.484220 | 0.0398027 | ||||||||
\(149\) | 5.71999 | 0.468600 | 0.234300 | − | 0.972164i | \(-0.424720\pi\) | ||||
0.234300 | + | 0.972164i | \(0.424720\pi\) | |||||||
\(150\) | −9.24744 | −0.755050 | ||||||||
\(151\) | 3.15808 | 0.257001 | 0.128500 | − | 0.991709i | \(-0.458984\pi\) | ||||
0.128500 | + | 0.991709i | \(0.458984\pi\) | |||||||
\(152\) | −13.3130 | −1.07983 | ||||||||
\(153\) | −5.43132 | −0.439096 | ||||||||
\(154\) | −5.17148 | −0.416730 | ||||||||
\(155\) | −14.0422 | −1.12789 | ||||||||
\(156\) | −3.26469 | −0.261384 | ||||||||
\(157\) | −10.3010 | −0.822105 | −0.411053 | − | 0.911612i | \(-0.634839\pi\) | ||||
−0.411053 | + | 0.911612i | \(0.634839\pi\) | |||||||
\(158\) | −16.0923 | −1.28024 | ||||||||
\(159\) | −21.5555 | −1.70946 | ||||||||
\(160\) | 2.62347 | 0.207404 | ||||||||
\(161\) | 19.2968 | 1.52080 | ||||||||
\(162\) | −5.68646 | −0.446770 | ||||||||
\(163\) | −10.3686 | −0.812129 | −0.406064 | − | 0.913845i | \(-0.633099\pi\) | ||||
−0.406064 | + | 0.913845i | \(0.633099\pi\) | |||||||
\(164\) | 0.299892 | 0.0234176 | ||||||||
\(165\) | 7.87489 | 0.613059 | ||||||||
\(166\) | 7.87176 | 0.610967 | ||||||||
\(167\) | 14.9716 | 1.15854 | 0.579270 | − | 0.815136i | \(-0.303338\pi\) | ||||
0.579270 | + | 0.815136i | \(0.303338\pi\) | |||||||
\(168\) | −32.6077 | −2.51574 | ||||||||
\(169\) | 29.9841 | 2.30647 | ||||||||
\(170\) | −3.66729 | −0.281268 | ||||||||
\(171\) | −24.6250 | −1.88312 | ||||||||
\(172\) | −0.171490 | −0.0130760 | ||||||||
\(173\) | −2.32655 | −0.176884 | −0.0884422 | − | 0.996081i | \(-0.528189\pi\) | ||||
−0.0884422 | + | 0.996081i | \(0.528189\pi\) | |||||||
\(174\) | −6.99815 | −0.530529 | ||||||||
\(175\) | −9.00723 | −0.680882 | ||||||||
\(176\) | 3.62761 | 0.273441 | ||||||||
\(177\) | 22.7621 | 1.71090 | ||||||||
\(178\) | −21.7740 | −1.63203 | ||||||||
\(179\) | −10.4681 | −0.782426 | −0.391213 | − | 0.920300i | \(-0.627944\pi\) | ||||
−0.391213 | + | 0.920300i | \(0.627944\pi\) | |||||||
\(180\) | 2.52605 | 0.188281 | ||||||||
\(181\) | 0.0409755 | 0.00304568 | 0.00152284 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152284 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(182\) | 33.9054 | 2.51323 | ||||||||
\(183\) | −12.8821 | −0.952269 | ||||||||
\(184\) | −14.8158 | −1.09223 | ||||||||
\(185\) | 7.65773 | 0.563007 | ||||||||
\(186\) | −20.3298 | −1.49066 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −0.503635 | −0.0367314 | ||||||||
\(189\) | −26.9995 | −1.96392 | ||||||||
\(190\) | −16.6271 | −1.20626 | ||||||||
\(191\) | −11.8179 | −0.855116 | −0.427558 | − | 0.903988i | \(-0.640626\pi\) | ||||
−0.427558 | + | 0.903988i | \(0.640626\pi\) | |||||||
\(192\) | 24.8650 | 1.79447 | ||||||||
\(193\) | −6.21284 | −0.447210 | −0.223605 | − | 0.974680i | \(-0.571783\pi\) | ||||
−0.223605 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(194\) | −21.4389 | −1.53923 | ||||||||
\(195\) | −51.6296 | −3.69727 | ||||||||
\(196\) | −1.30782 | −0.0934160 | ||||||||
\(197\) | 15.7562 | 1.12259 | 0.561293 | − | 0.827617i | \(-0.310304\pi\) | ||||
0.561293 | + | 0.827617i | \(0.310304\pi\) | |||||||
\(198\) | 7.34436 | 0.521941 | ||||||||
\(199\) | 15.6522 | 1.10955 | 0.554776 | − | 0.832000i | \(-0.312804\pi\) | ||||
0.554776 | + | 0.832000i | \(0.312804\pi\) | |||||||
\(200\) | 6.91563 | 0.489009 | ||||||||
\(201\) | −20.4133 | −1.43984 | ||||||||
\(202\) | −9.88697 | −0.695644 | ||||||||
\(203\) | −6.81637 | −0.478416 | ||||||||
\(204\) | 0.497952 | 0.0348636 | ||||||||
\(205\) | 4.74265 | 0.331241 | ||||||||
\(206\) | 22.4856 | 1.56665 | ||||||||
\(207\) | −27.4046 | −1.90475 | ||||||||
\(208\) | −23.7834 | −1.64908 | ||||||||
\(209\) | 4.53389 | 0.313616 | ||||||||
\(210\) | −40.7248 | −2.81028 | ||||||||
\(211\) | 23.2399 | 1.59990 | 0.799952 | − | 0.600064i | \(-0.204858\pi\) | ||||
0.799952 | + | 0.600064i | \(0.204858\pi\) | |||||||
\(212\) | 1.27306 | 0.0874345 | ||||||||
\(213\) | 26.6841 | 1.82837 | ||||||||
\(214\) | −16.7547 | −1.14533 | ||||||||
\(215\) | −2.71204 | −0.184960 | ||||||||
\(216\) | 20.7298 | 1.41049 | ||||||||
\(217\) | −19.8018 | −1.34423 | ||||||||
\(218\) | −4.93916 | −0.334522 | ||||||||
\(219\) | −33.1191 | −2.23798 | ||||||||
\(220\) | −0.465090 | −0.0313563 | ||||||||
\(221\) | −6.55623 | −0.441019 | ||||||||
\(222\) | 11.0866 | 0.744086 | ||||||||
\(223\) | 24.1804 | 1.61924 | 0.809621 | − | 0.586953i | \(-0.199673\pi\) | ||||
0.809621 | + | 0.586953i | \(0.199673\pi\) | |||||||
\(224\) | 3.69952 | 0.247185 | ||||||||
\(225\) | 12.7918 | 0.852784 | ||||||||
\(226\) | 10.8647 | 0.722710 | ||||||||
\(227\) | 4.56931 | 0.303276 | 0.151638 | − | 0.988436i | \(-0.451545\pi\) | ||||
0.151638 | + | 0.988436i | \(0.451545\pi\) | |||||||
\(228\) | 2.25766 | 0.149517 | ||||||||
\(229\) | 1.22928 | 0.0812329 | 0.0406164 | − | 0.999175i | \(-0.487068\pi\) | ||||
0.0406164 | + | 0.999175i | \(0.487068\pi\) | |||||||
\(230\) | −18.5039 | −1.22011 | ||||||||
\(231\) | 11.1049 | 0.730647 | ||||||||
\(232\) | 5.23352 | 0.343597 | ||||||||
\(233\) | −26.9387 | −1.76481 | −0.882407 | − | 0.470487i | \(-0.844078\pi\) | ||||
−0.882407 | + | 0.470487i | \(0.844078\pi\) | |||||||
\(234\) | −48.1513 | −3.14775 | ||||||||
\(235\) | −7.96477 | −0.519564 | ||||||||
\(236\) | −1.34433 | −0.0875082 | ||||||||
\(237\) | 34.5555 | 2.24462 | ||||||||
\(238\) | −5.17148 | −0.335217 | ||||||||
\(239\) | 9.76651 | 0.631743 | 0.315872 | − | 0.948802i | \(-0.397703\pi\) | ||||
0.315872 | + | 0.948802i | \(0.397703\pi\) | |||||||
\(240\) | 28.5670 | 1.84399 | ||||||||
\(241\) | 23.8483 | 1.53621 | 0.768103 | − | 0.640326i | \(-0.221201\pi\) | ||||
0.768103 | + | 0.640326i | \(0.221201\pi\) | |||||||
\(242\) | −1.35222 | −0.0869242 | ||||||||
\(243\) | −8.96855 | −0.575333 | ||||||||
\(244\) | 0.760812 | 0.0487060 | ||||||||
\(245\) | −20.6827 | −1.32137 | ||||||||
\(246\) | 6.86627 | 0.437777 | ||||||||
\(247\) | −29.7252 | −1.89137 | ||||||||
\(248\) | 15.2035 | 0.965424 | ||||||||
\(249\) | −16.9033 | −1.07120 | ||||||||
\(250\) | −9.69931 | −0.613438 | ||||||||
\(251\) | 3.33534 | 0.210525 | 0.105262 | − | 0.994444i | \(-0.466432\pi\) | ||||
0.105262 | + | 0.994444i | \(0.466432\pi\) | |||||||
\(252\) | 3.56214 | 0.224394 | ||||||||
\(253\) | 5.04566 | 0.317218 | ||||||||
\(254\) | 28.3665 | 1.77987 | ||||||||
\(255\) | 7.87489 | 0.493145 | ||||||||
\(256\) | −4.08464 | −0.255290 | ||||||||
\(257\) | −26.3396 | −1.64302 | −0.821510 | − | 0.570194i | \(-0.806868\pi\) | ||||
−0.821510 | + | 0.570194i | \(0.806868\pi\) | |||||||
\(258\) | −3.92642 | −0.244448 | ||||||||
\(259\) | 10.7986 | 0.670995 | ||||||||
\(260\) | 3.04923 | 0.189105 | ||||||||
\(261\) | 9.68038 | 0.599201 | ||||||||
\(262\) | −16.1159 | −0.995644 | ||||||||
\(263\) | −3.19647 | −0.197103 | −0.0985514 | − | 0.995132i | \(-0.531421\pi\) | ||||
−0.0985514 | + | 0.995132i | \(0.531421\pi\) | |||||||
\(264\) | −8.52618 | −0.524750 | ||||||||
\(265\) | 20.1330 | 1.23676 | ||||||||
\(266\) | −23.4469 | −1.43762 | ||||||||
\(267\) | 46.7559 | 2.86142 | ||||||||
\(268\) | 1.20561 | 0.0736440 | ||||||||
\(269\) | 8.15122 | 0.496989 | 0.248494 | − | 0.968633i | \(-0.420064\pi\) | ||||
0.248494 | + | 0.968633i | \(0.420064\pi\) | |||||||
\(270\) | 25.8902 | 1.57563 | ||||||||
\(271\) | 10.5868 | 0.643102 | 0.321551 | − | 0.946892i | \(-0.395796\pi\) | ||||
0.321551 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(272\) | 3.62761 | 0.219956 | ||||||||
\(273\) | −72.8061 | −4.40643 | ||||||||
\(274\) | 14.9586 | 0.903680 | ||||||||
\(275\) | −2.35519 | −0.142023 | ||||||||
\(276\) | 2.51250 | 0.151235 | ||||||||
\(277\) | 15.0750 | 0.905772 | 0.452886 | − | 0.891569i | \(-0.350395\pi\) | ||||
0.452886 | + | 0.891569i | \(0.350395\pi\) | |||||||
\(278\) | 10.2826 | 0.616712 | ||||||||
\(279\) | 28.1218 | 1.68361 | ||||||||
\(280\) | 30.4558 | 1.82008 | ||||||||
\(281\) | −15.5869 | −0.929835 | −0.464917 | − | 0.885354i | \(-0.653916\pi\) | ||||
−0.464917 | + | 0.885354i | \(0.653916\pi\) | |||||||
\(282\) | −11.5312 | −0.686670 | ||||||||
\(283\) | 13.8275 | 0.821962 | 0.410981 | − | 0.911644i | \(-0.365186\pi\) | ||||
0.410981 | + | 0.911644i | \(0.365186\pi\) | |||||||
\(284\) | −1.57596 | −0.0935160 | ||||||||
\(285\) | 35.7039 | 2.11492 | ||||||||
\(286\) | 8.86548 | 0.524227 | ||||||||
\(287\) | 6.68791 | 0.394775 | ||||||||
\(288\) | −5.25394 | −0.309591 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.53631 | 0.383825 | ||||||||
\(291\) | 46.0365 | 2.69871 | ||||||||
\(292\) | 1.95601 | 0.114467 | ||||||||
\(293\) | 9.79451 | 0.572201 | 0.286101 | − | 0.958200i | \(-0.407641\pi\) | ||||
0.286101 | + | 0.958200i | \(0.407641\pi\) | |||||||
\(294\) | −29.9437 | −1.74635 | ||||||||
\(295\) | −21.2599 | −1.23780 | ||||||||
\(296\) | −8.29105 | −0.481908 | ||||||||
\(297\) | −7.05975 | −0.409648 | ||||||||
\(298\) | −7.73471 | −0.448059 | ||||||||
\(299\) | −33.0805 | −1.91309 | ||||||||
\(300\) | −1.17277 | −0.0677099 | ||||||||
\(301\) | −3.82442 | −0.220436 | ||||||||
\(302\) | −4.27042 | −0.245735 | ||||||||
\(303\) | 21.2306 | 1.21967 | ||||||||
\(304\) | 16.4472 | 0.943311 | ||||||||
\(305\) | 12.0319 | 0.688945 | ||||||||
\(306\) | 7.34436 | 0.419849 | ||||||||
\(307\) | 23.2372 | 1.32622 | 0.663109 | − | 0.748523i | \(-0.269237\pi\) | ||||
0.663109 | + | 0.748523i | \(0.269237\pi\) | |||||||
\(308\) | −0.655852 | −0.0373706 | ||||||||
\(309\) | −48.2841 | −2.74679 | ||||||||
\(310\) | 18.9882 | 1.07846 | ||||||||
\(311\) | 15.4005 | 0.873283 | 0.436642 | − | 0.899636i | \(-0.356168\pi\) | ||||
0.436642 | + | 0.899636i | \(0.356168\pi\) | |||||||
\(312\) | 55.8995 | 3.16469 | ||||||||
\(313\) | 0.459283 | 0.0259602 | 0.0129801 | − | 0.999916i | \(-0.495868\pi\) | ||||
0.0129801 | + | 0.999916i | \(0.495868\pi\) | |||||||
\(314\) | 13.9292 | 0.786070 | ||||||||
\(315\) | 56.3337 | 3.17404 | ||||||||
\(316\) | −2.04084 | −0.114806 | ||||||||
\(317\) | 23.3642 | 1.31226 | 0.656131 | − | 0.754647i | \(-0.272192\pi\) | ||||
0.656131 | + | 0.754647i | \(0.272192\pi\) | |||||||
\(318\) | 29.1479 | 1.63453 | ||||||||
\(319\) | −1.78233 | −0.0997911 | ||||||||
\(320\) | −23.2240 | −1.29826 | ||||||||
\(321\) | 35.9779 | 2.00809 | ||||||||
\(322\) | −26.0935 | −1.45414 | ||||||||
\(323\) | 4.53389 | 0.252272 | ||||||||
\(324\) | −0.721162 | −0.0400646 | ||||||||
\(325\) | 15.4411 | 0.856519 | ||||||||
\(326\) | 14.0206 | 0.776530 | ||||||||
\(327\) | 10.6060 | 0.586514 | ||||||||
\(328\) | −5.13489 | −0.283527 | ||||||||
\(329\) | −11.2316 | −0.619219 | ||||||||
\(330\) | −10.6486 | −0.586187 | ||||||||
\(331\) | −2.33660 | −0.128431 | −0.0642155 | − | 0.997936i | \(-0.520454\pi\) | ||||
−0.0642155 | + | 0.997936i | \(0.520454\pi\) | |||||||
\(332\) | 0.998305 | 0.0547891 | ||||||||
\(333\) | −15.3359 | −0.840400 | ||||||||
\(334\) | −20.2450 | −1.10776 | ||||||||
\(335\) | 19.0661 | 1.04169 | ||||||||
\(336\) | 40.2842 | 2.19768 | ||||||||
\(337\) | 13.5136 | 0.736132 | 0.368066 | − | 0.929800i | \(-0.380020\pi\) | ||||
0.368066 | + | 0.929800i | \(0.380020\pi\) | |||||||
\(338\) | −40.5452 | −2.20537 | ||||||||
\(339\) | −23.3301 | −1.26712 | ||||||||
\(340\) | −0.465090 | −0.0252230 | ||||||||
\(341\) | −5.17771 | −0.280389 | ||||||||
\(342\) | 33.2985 | 1.80058 | ||||||||
\(343\) | −2.39495 | −0.129315 | ||||||||
\(344\) | 2.93634 | 0.158317 | ||||||||
\(345\) | 39.7340 | 2.13921 | ||||||||
\(346\) | 3.14602 | 0.169131 | ||||||||
\(347\) | −1.24924 | −0.0670630 | −0.0335315 | − | 0.999438i | \(-0.510675\pi\) | ||||
−0.0335315 | + | 0.999438i | \(0.510675\pi\) | |||||||
\(348\) | −0.887513 | −0.0475757 | ||||||||
\(349\) | 29.8629 | 1.59853 | 0.799263 | − | 0.600982i | \(-0.205224\pi\) | ||||
0.799263 | + | 0.600982i | \(0.205224\pi\) | |||||||
\(350\) | 12.1798 | 0.651037 | ||||||||
\(351\) | 46.2853 | 2.47053 | ||||||||
\(352\) | 0.967341 | 0.0515595 | ||||||||
\(353\) | 26.3886 | 1.40452 | 0.702262 | − | 0.711918i | \(-0.252173\pi\) | ||||
0.702262 | + | 0.711918i | \(0.252173\pi\) | |||||||
\(354\) | −30.7795 | −1.63591 | ||||||||
\(355\) | −24.9231 | −1.32278 | ||||||||
\(356\) | −2.76140 | −0.146354 | ||||||||
\(357\) | 11.1049 | 0.587733 | ||||||||
\(358\) | 14.1553 | 0.748130 | ||||||||
\(359\) | 32.1089 | 1.69464 | 0.847322 | − | 0.531079i | \(-0.178213\pi\) | ||||
0.847322 | + | 0.531079i | \(0.178213\pi\) | |||||||
\(360\) | −43.2522 | −2.27959 | ||||||||
\(361\) | 1.55616 | 0.0819032 | ||||||||
\(362\) | −0.0554080 | −0.00291218 | ||||||||
\(363\) | 2.90367 | 0.152403 | ||||||||
\(364\) | 4.29991 | 0.225377 | ||||||||
\(365\) | 30.9334 | 1.61913 | ||||||||
\(366\) | 17.4194 | 0.910528 | ||||||||
\(367\) | −25.2704 | −1.31910 | −0.659551 | − | 0.751660i | \(-0.729253\pi\) | ||||
−0.659551 | + | 0.751660i | \(0.729253\pi\) | |||||||
\(368\) | 18.3037 | 0.954146 | ||||||||
\(369\) | −9.49795 | −0.494444 | ||||||||
\(370\) | −10.3550 | −0.538329 | ||||||||
\(371\) | 28.3907 | 1.47397 | ||||||||
\(372\) | −2.57825 | −0.133676 | ||||||||
\(373\) | 7.58114 | 0.392536 | 0.196268 | − | 0.980550i | \(-0.437118\pi\) | ||||
0.196268 | + | 0.980550i | \(0.437118\pi\) | |||||||
\(374\) | −1.35222 | −0.0699218 | ||||||||
\(375\) | 20.8276 | 1.07553 | ||||||||
\(376\) | 8.62349 | 0.444722 | ||||||||
\(377\) | 11.6853 | 0.601825 | ||||||||
\(378\) | 36.5094 | 1.87784 | ||||||||
\(379\) | −6.41419 | −0.329475 | −0.164737 | − | 0.986337i | \(-0.552678\pi\) | ||||
−0.164737 | + | 0.986337i | \(0.552678\pi\) | |||||||
\(380\) | −2.10867 | −0.108172 | ||||||||
\(381\) | −60.9123 | −3.12063 | ||||||||
\(382\) | 15.9805 | 0.817633 | ||||||||
\(383\) | 2.02837 | 0.103645 | 0.0518225 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518225 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(384\) | −28.0053 | −1.42914 | ||||||||
\(385\) | −10.3720 | −0.528607 | ||||||||
\(386\) | 8.40115 | 0.427607 | ||||||||
\(387\) | 5.43132 | 0.276089 | ||||||||
\(388\) | −2.71891 | −0.138032 | ||||||||
\(389\) | −3.17019 | −0.160735 | −0.0803675 | − | 0.996765i | \(-0.525609\pi\) | ||||
−0.0803675 | + | 0.996765i | \(0.525609\pi\) | |||||||
\(390\) | 69.8147 | 3.53521 | ||||||||
\(391\) | 5.04566 | 0.255170 | ||||||||
\(392\) | 22.3932 | 1.13103 | ||||||||
\(393\) | 34.6062 | 1.74565 | ||||||||
\(394\) | −21.3060 | −1.07338 | ||||||||
\(395\) | −32.2750 | −1.62393 | ||||||||
\(396\) | 0.931419 | 0.0468056 | ||||||||
\(397\) | −23.7766 | −1.19331 | −0.596656 | − | 0.802497i | \(-0.703504\pi\) | ||||
−0.596656 | + | 0.802497i | \(0.703504\pi\) | |||||||
\(398\) | −21.1652 | −1.06092 | ||||||||
\(399\) | 50.3483 | 2.52057 | ||||||||
\(400\) | −8.54369 | −0.427185 | ||||||||
\(401\) | 7.66774 | 0.382909 | 0.191454 | − | 0.981502i | \(-0.438680\pi\) | ||||
0.191454 | + | 0.981502i | \(0.438680\pi\) | |||||||
\(402\) | 27.6033 | 1.37673 | ||||||||
\(403\) | 33.9462 | 1.69098 | ||||||||
\(404\) | −1.25388 | −0.0623826 | ||||||||
\(405\) | −11.4049 | −0.566712 | ||||||||
\(406\) | 9.21726 | 0.457445 | ||||||||
\(407\) | 2.82360 | 0.139961 | ||||||||
\(408\) | −8.52618 | −0.422109 | ||||||||
\(409\) | −5.68880 | −0.281293 | −0.140646 | − | 0.990060i | \(-0.544918\pi\) | ||||
−0.140646 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(410\) | −6.41313 | −0.316722 | ||||||||
\(411\) | −32.1210 | −1.58441 | ||||||||
\(412\) | 2.85165 | 0.140491 | ||||||||
\(413\) | −29.9799 | −1.47522 | ||||||||
\(414\) | 37.0571 | 1.82126 | ||||||||
\(415\) | 15.7877 | 0.774990 | ||||||||
\(416\) | −6.34211 | −0.310947 | ||||||||
\(417\) | −22.0802 | −1.08127 | ||||||||
\(418\) | −6.13084 | −0.299869 | ||||||||
\(419\) | 9.57191 | 0.467619 | 0.233809 | − | 0.972282i | \(-0.424881\pi\) | ||||
0.233809 | + | 0.972282i | \(0.424881\pi\) | |||||||
\(420\) | −5.16476 | −0.252015 | ||||||||
\(421\) | −10.0032 | −0.487524 | −0.243762 | − | 0.969835i | \(-0.578382\pi\) | ||||
−0.243762 | + | 0.969835i | \(0.578382\pi\) | |||||||
\(422\) | −31.4256 | −1.52977 | ||||||||
\(423\) | 15.9508 | 0.775553 | ||||||||
\(424\) | −21.7980 | −1.05861 | ||||||||
\(425\) | −2.35519 | −0.114243 | ||||||||
\(426\) | −36.0829 | −1.74822 | ||||||||
\(427\) | 16.9669 | 0.821088 | ||||||||
\(428\) | −2.12485 | −0.102708 | ||||||||
\(429\) | −19.0371 | −0.919122 | ||||||||
\(430\) | 3.66729 | 0.176852 | ||||||||
\(431\) | −9.25481 | −0.445789 | −0.222894 | − | 0.974843i | \(-0.571550\pi\) | ||||
−0.222894 | + | 0.974843i | \(0.571550\pi\) | |||||||
\(432\) | −25.6100 | −1.23216 | ||||||||
\(433\) | 31.3603 | 1.50708 | 0.753539 | − | 0.657403i | \(-0.228345\pi\) | ||||
0.753539 | + | 0.657403i | \(0.228345\pi\) | |||||||
\(434\) | 26.7764 | 1.28531 | ||||||||
\(435\) | −14.0356 | −0.672957 | ||||||||
\(436\) | −0.626389 | −0.0299986 | ||||||||
\(437\) | 22.8765 | 1.09433 | ||||||||
\(438\) | 44.7845 | 2.13988 | ||||||||
\(439\) | 33.2415 | 1.58653 | 0.793265 | − | 0.608877i | \(-0.208380\pi\) | ||||
0.793265 | + | 0.608877i | \(0.208380\pi\) | |||||||
\(440\) | 7.96349 | 0.379644 | ||||||||
\(441\) | 41.4205 | 1.97240 | ||||||||
\(442\) | 8.86548 | 0.421688 | ||||||||
\(443\) | 16.3964 | 0.779018 | 0.389509 | − | 0.921023i | \(-0.372645\pi\) | ||||
0.389509 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(444\) | 1.40602 | 0.0667266 | ||||||||
\(445\) | −43.6703 | −2.07017 | ||||||||
\(446\) | −32.6974 | −1.54827 | ||||||||
\(447\) | 16.6090 | 0.785578 | ||||||||
\(448\) | −32.7496 | −1.54727 | ||||||||
\(449\) | 30.3808 | 1.43376 | 0.716880 | − | 0.697197i | \(-0.245570\pi\) | ||||
0.716880 | + | 0.697197i | \(0.245570\pi\) | |||||||
\(450\) | −17.2973 | −0.815404 | ||||||||
\(451\) | 1.74874 | 0.0823448 | ||||||||
\(452\) | 1.37787 | 0.0648097 | ||||||||
\(453\) | 9.17002 | 0.430845 | ||||||||
\(454\) | −6.17873 | −0.289982 | ||||||||
\(455\) | 68.0012 | 3.18795 | ||||||||
\(456\) | −38.6567 | −1.81027 | ||||||||
\(457\) | 3.65130 | 0.170801 | 0.0854003 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854003 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(458\) | −1.66226 | −0.0776722 | ||||||||
\(459\) | −7.05975 | −0.329521 | ||||||||
\(460\) | −2.34668 | −0.109415 | ||||||||
\(461\) | 10.9631 | 0.510602 | 0.255301 | − | 0.966862i | \(-0.417825\pi\) | ||||
0.255301 | + | 0.966862i | \(0.417825\pi\) | |||||||
\(462\) | −15.0163 | −0.698621 | ||||||||
\(463\) | 31.1279 | 1.44663 | 0.723317 | − | 0.690516i | \(-0.242616\pi\) | ||||
0.723317 | + | 0.690516i | \(0.242616\pi\) | |||||||
\(464\) | −6.46558 | −0.300157 | ||||||||
\(465\) | −40.7739 | −1.89084 | ||||||||
\(466\) | 36.4272 | 1.68746 | ||||||||
\(467\) | 36.0960 | 1.67033 | 0.835163 | − | 0.550003i | \(-0.185373\pi\) | ||||
0.835163 | + | 0.550003i | \(0.185373\pi\) | |||||||
\(468\) | −6.10659 | −0.282277 | ||||||||
\(469\) | 26.8863 | 1.24149 | ||||||||
\(470\) | 10.7702 | 0.496790 | ||||||||
\(471\) | −29.9106 | −1.37821 | ||||||||
\(472\) | 23.0182 | 1.05950 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −46.7268 | −2.14623 | ||||||||
\(475\) | −10.6782 | −0.489947 | ||||||||
\(476\) | −0.655852 | −0.0300609 | ||||||||
\(477\) | −40.3196 | −1.84611 | ||||||||
\(478\) | −13.2065 | −0.604052 | ||||||||
\(479\) | 36.5287 | 1.66904 | 0.834519 | − | 0.550979i | \(-0.185745\pi\) | ||||
0.834519 | + | 0.550979i | \(0.185745\pi\) | |||||||
\(480\) | 7.61771 | 0.347699 | ||||||||
\(481\) | −18.5122 | −0.844082 | ||||||||
\(482\) | −32.2483 | −1.46887 | ||||||||
\(483\) | 56.0315 | 2.54952 | ||||||||
\(484\) | −0.171490 | −0.00779502 | ||||||||
\(485\) | −42.9983 | −1.95245 | ||||||||
\(486\) | 12.1275 | 0.550114 | ||||||||
\(487\) | 23.1007 | 1.04679 | 0.523397 | − | 0.852089i | \(-0.324664\pi\) | ||||
0.523397 | + | 0.852089i | \(0.324664\pi\) | |||||||
\(488\) | −13.0270 | −0.589704 | ||||||||
\(489\) | −30.1069 | −1.36148 | ||||||||
\(490\) | 27.9676 | 1.26345 | ||||||||
\(491\) | −15.8353 | −0.714639 | −0.357319 | − | 0.933982i | \(-0.616309\pi\) | ||||
−0.357319 | + | 0.933982i | \(0.616309\pi\) | |||||||
\(492\) | 0.870788 | 0.0392581 | ||||||||
\(493\) | −1.78233 | −0.0802719 | ||||||||
\(494\) | 40.1951 | 1.80846 | ||||||||
\(495\) | 14.7300 | 0.662063 | ||||||||
\(496\) | −18.7827 | −0.843368 | ||||||||
\(497\) | −35.1456 | −1.57650 | ||||||||
\(498\) | 22.8570 | 1.02425 | ||||||||
\(499\) | −3.86130 | −0.172855 | −0.0864277 | − | 0.996258i | \(-0.527545\pi\) | ||||
−0.0864277 | + | 0.996258i | \(0.527545\pi\) | |||||||
\(500\) | −1.23008 | −0.0550107 | ||||||||
\(501\) | 43.4727 | 1.94222 | ||||||||
\(502\) | −4.51013 | −0.201297 | ||||||||
\(503\) | 35.3284 | 1.57521 | 0.787607 | − | 0.616177i | \(-0.211320\pi\) | ||||
0.787607 | + | 0.616177i | \(0.211320\pi\) | |||||||
\(504\) | −60.9927 | −2.71683 | ||||||||
\(505\) | −19.8295 | −0.882400 | ||||||||
\(506\) | −6.82286 | −0.303313 | ||||||||
\(507\) | 87.0640 | 3.86665 | ||||||||
\(508\) | 3.59747 | 0.159612 | ||||||||
\(509\) | −37.6483 | −1.66873 | −0.834365 | − | 0.551212i | \(-0.814166\pi\) | ||||
−0.834365 | + | 0.551212i | \(0.814166\pi\) | |||||||
\(510\) | −10.6486 | −0.471529 | ||||||||
\(511\) | 43.6211 | 1.92969 | ||||||||
\(512\) | 24.8129 | 1.09659 | ||||||||
\(513\) | −32.0082 | −1.41319 | ||||||||
\(514\) | 35.6171 | 1.57100 | ||||||||
\(515\) | 45.0976 | 1.98724 | ||||||||
\(516\) | −0.497952 | −0.0219211 | ||||||||
\(517\) | −2.93681 | −0.129161 | ||||||||
\(518\) | −14.6022 | −0.641583 | ||||||||
\(519\) | −6.75555 | −0.296536 | ||||||||
\(520\) | −52.2104 | −2.28958 | ||||||||
\(521\) | 27.0494 | 1.18506 | 0.592528 | − | 0.805550i | \(-0.298130\pi\) | ||||
0.592528 | + | 0.805550i | \(0.298130\pi\) | |||||||
\(522\) | −13.0900 | −0.572936 | ||||||||
\(523\) | 13.2877 | 0.581030 | 0.290515 | − | 0.956870i | \(-0.406173\pi\) | ||||
0.290515 | + | 0.956870i | \(0.406173\pi\) | |||||||
\(524\) | −2.04384 | −0.0892854 | ||||||||
\(525\) | −26.1540 | −1.14146 | ||||||||
\(526\) | 4.32235 | 0.188463 | ||||||||
\(527\) | −5.17771 | −0.225544 | ||||||||
\(528\) | 10.5334 | 0.458407 | ||||||||
\(529\) | 2.45870 | 0.106900 | ||||||||
\(530\) | −27.2243 | −1.18255 | ||||||||
\(531\) | 42.5765 | 1.84766 | ||||||||
\(532\) | −2.97356 | −0.128920 | ||||||||
\(533\) | −11.4651 | −0.496609 | ||||||||
\(534\) | −63.2245 | −2.73599 | ||||||||
\(535\) | −33.6035 | −1.45281 | ||||||||
\(536\) | −20.6429 | −0.891640 | ||||||||
\(537\) | −30.3961 | −1.31169 | ||||||||
\(538\) | −11.0223 | −0.475204 | ||||||||
\(539\) | −7.62623 | −0.328485 | ||||||||
\(540\) | 3.28342 | 0.141296 | ||||||||
\(541\) | 34.3858 | 1.47836 | 0.739180 | − | 0.673508i | \(-0.235213\pi\) | ||||
0.739180 | + | 0.673508i | \(0.235213\pi\) | |||||||
\(542\) | −14.3157 | −0.614913 | ||||||||
\(543\) | 0.118979 | 0.00510589 | ||||||||
\(544\) | 0.967341 | 0.0414744 | ||||||||
\(545\) | −9.90606 | −0.424329 | ||||||||
\(546\) | 98.4501 | 4.21328 | ||||||||
\(547\) | −11.3789 | −0.486529 | −0.243264 | − | 0.969960i | \(-0.578218\pi\) | ||||
−0.243264 | + | 0.969960i | \(0.578218\pi\) | |||||||
\(548\) | 1.89706 | 0.0810384 | ||||||||
\(549\) | −24.0959 | −1.02839 | ||||||||
\(550\) | 3.18474 | 0.135798 | ||||||||
\(551\) | −8.08087 | −0.344257 | ||||||||
\(552\) | −43.0202 | −1.83106 | ||||||||
\(553\) | −45.5130 | −1.93541 | ||||||||
\(554\) | −20.3848 | −0.866069 | ||||||||
\(555\) | 22.2355 | 0.943846 | ||||||||
\(556\) | 1.30406 | 0.0553043 | ||||||||
\(557\) | 15.0746 | 0.638729 | 0.319365 | − | 0.947632i | \(-0.396531\pi\) | ||||
0.319365 | + | 0.947632i | \(0.396531\pi\) | |||||||
\(558\) | −38.0269 | −1.60981 | ||||||||
\(559\) | 6.55623 | 0.277299 | ||||||||
\(560\) | −37.6256 | −1.58997 | ||||||||
\(561\) | 2.90367 | 0.122593 | ||||||||
\(562\) | 21.0769 | 0.889077 | ||||||||
\(563\) | 0.978991 | 0.0412595 | 0.0206298 | − | 0.999787i | \(-0.493433\pi\) | ||||
0.0206298 | + | 0.999787i | \(0.493433\pi\) | |||||||
\(564\) | −1.46239 | −0.0615778 | ||||||||
\(565\) | 21.7905 | 0.916731 | ||||||||
\(566\) | −18.6979 | −0.785933 | ||||||||
\(567\) | −16.0827 | −0.675411 | ||||||||
\(568\) | 26.9843 | 1.13224 | ||||||||
\(569\) | 20.9669 | 0.878977 | 0.439489 | − | 0.898248i | \(-0.355160\pi\) | ||||
0.439489 | + | 0.898248i | \(0.355160\pi\) | |||||||
\(570\) | −48.2797 | −2.02221 | ||||||||
\(571\) | 6.84194 | 0.286326 | 0.143163 | − | 0.989699i | \(-0.454273\pi\) | ||||
0.143163 | + | 0.989699i | \(0.454273\pi\) | |||||||
\(572\) | 1.12433 | 0.0470106 | ||||||||
\(573\) | −34.3154 | −1.43355 | ||||||||
\(574\) | −9.04356 | −0.377471 | ||||||||
\(575\) | −11.8835 | −0.495575 | ||||||||
\(576\) | 46.5099 | 1.93791 | ||||||||
\(577\) | 22.2671 | 0.926990 | 0.463495 | − | 0.886099i | \(-0.346595\pi\) | ||||
0.463495 | + | 0.886099i | \(0.346595\pi\) | |||||||
\(578\) | −1.35222 | −0.0562451 | ||||||||
\(579\) | −18.0401 | −0.749719 | ||||||||
\(580\) | 0.828941 | 0.0344199 | ||||||||
\(581\) | 22.2633 | 0.923637 | ||||||||
\(582\) | −62.2517 | −2.58042 | ||||||||
\(583\) | 7.42353 | 0.307451 | ||||||||
\(584\) | −33.4917 | −1.38590 | ||||||||
\(585\) | −96.5730 | −3.99280 | ||||||||
\(586\) | −13.2444 | −0.547120 | ||||||||
\(587\) | −32.1014 | −1.32497 | −0.662483 | − | 0.749077i | \(-0.730497\pi\) | ||||
−0.662483 | + | 0.749077i | \(0.730497\pi\) | |||||||
\(588\) | −3.79749 | −0.156606 | ||||||||
\(589\) | −23.4752 | −0.967277 | ||||||||
\(590\) | 28.7482 | 1.18354 | ||||||||
\(591\) | 45.7510 | 1.88194 | ||||||||
\(592\) | 10.2429 | 0.420981 | ||||||||
\(593\) | 3.78570 | 0.155460 | 0.0777300 | − | 0.996974i | \(-0.475233\pi\) | ||||
0.0777300 | + | 0.996974i | \(0.475233\pi\) | |||||||
\(594\) | 9.54637 | 0.391692 | ||||||||
\(595\) | −10.3720 | −0.425211 | ||||||||
\(596\) | −0.980923 | −0.0401802 | ||||||||
\(597\) | 45.4487 | 1.86009 | ||||||||
\(598\) | 44.7322 | 1.82924 | ||||||||
\(599\) | 13.6792 | 0.558918 | 0.279459 | − | 0.960158i | \(-0.409845\pi\) | ||||
0.279459 | + | 0.960158i | \(0.409845\pi\) | |||||||
\(600\) | 20.0807 | 0.819792 | ||||||||
\(601\) | −39.8451 | −1.62531 | −0.812657 | − | 0.582742i | \(-0.801980\pi\) | ||||
−0.812657 | + | 0.582742i | \(0.801980\pi\) | |||||||
\(602\) | 5.17148 | 0.210774 | ||||||||
\(603\) | −38.1830 | −1.55493 | ||||||||
\(604\) | −0.541580 | −0.0220366 | ||||||||
\(605\) | −2.71204 | −0.110260 | ||||||||
\(606\) | −28.7085 | −1.16620 | ||||||||
\(607\) | 37.1126 | 1.50636 | 0.753178 | − | 0.657817i | \(-0.228520\pi\) | ||||
0.753178 | + | 0.657817i | \(0.228520\pi\) | |||||||
\(608\) | 4.38582 | 0.177868 | ||||||||
\(609\) | −19.7925 | −0.802033 | ||||||||
\(610\) | −16.2698 | −0.658746 | ||||||||
\(611\) | 19.2544 | 0.778950 | ||||||||
\(612\) | 0.931419 | 0.0376504 | ||||||||
\(613\) | −0.0657236 | −0.00265455 | −0.00132728 | − | 0.999999i | \(-0.500422\pi\) | ||||
−0.00132728 | + | 0.999999i | \(0.500422\pi\) | |||||||
\(614\) | −31.4219 | −1.26808 | ||||||||
\(615\) | 13.7711 | 0.555305 | ||||||||
\(616\) | 11.2298 | 0.452462 | ||||||||
\(617\) | −29.9394 | −1.20531 | −0.602657 | − | 0.798000i | \(-0.705891\pi\) | ||||
−0.602657 | + | 0.798000i | \(0.705891\pi\) | |||||||
\(618\) | 65.2909 | 2.62639 | ||||||||
\(619\) | −44.6983 | −1.79658 | −0.898288 | − | 0.439407i | \(-0.855188\pi\) | ||||
−0.898288 | + | 0.439407i | \(0.855188\pi\) | |||||||
\(620\) | 2.40810 | 0.0967115 | ||||||||
\(621\) | −35.6211 | −1.42943 | ||||||||
\(622\) | −20.8249 | −0.835004 | ||||||||
\(623\) | −61.5822 | −2.46724 | ||||||||
\(624\) | −69.0593 | −2.76458 | ||||||||
\(625\) | −31.2290 | −1.24916 | ||||||||
\(626\) | −0.621053 | −0.0248223 | ||||||||
\(627\) | 13.1649 | 0.525757 | ||||||||
\(628\) | 1.76651 | 0.0704916 | ||||||||
\(629\) | 2.82360 | 0.112584 | ||||||||
\(630\) | −76.1758 | −3.03492 | ||||||||
\(631\) | −12.6505 | −0.503610 | −0.251805 | − | 0.967778i | \(-0.581024\pi\) | ||||
−0.251805 | + | 0.967778i | \(0.581024\pi\) | |||||||
\(632\) | 34.9443 | 1.39001 | ||||||||
\(633\) | 67.4812 | 2.68214 | ||||||||
\(634\) | −31.5936 | −1.25474 | ||||||||
\(635\) | 56.8924 | 2.25771 | ||||||||
\(636\) | 3.69656 | 0.146578 | ||||||||
\(637\) | 49.9993 | 1.98104 | ||||||||
\(638\) | 2.41010 | 0.0954169 | ||||||||
\(639\) | 49.9126 | 1.97451 | ||||||||
\(640\) | 26.1571 | 1.03395 | ||||||||
\(641\) | −23.7748 | −0.939047 | −0.469524 | − | 0.882920i | \(-0.655574\pi\) | ||||
−0.469524 | + | 0.882920i | \(0.655574\pi\) | |||||||
\(642\) | −48.6502 | −1.92007 | ||||||||
\(643\) | −30.5374 | −1.20428 | −0.602138 | − | 0.798392i | \(-0.705684\pi\) | ||||
−0.602138 | + | 0.798392i | \(0.705684\pi\) | |||||||
\(644\) | −3.30921 | −0.130401 | ||||||||
\(645\) | −7.87489 | −0.310074 | ||||||||
\(646\) | −6.13084 | −0.241214 | ||||||||
\(647\) | 8.56003 | 0.336529 | 0.168265 | − | 0.985742i | \(-0.446184\pi\) | ||||
0.168265 | + | 0.985742i | \(0.446184\pi\) | |||||||
\(648\) | 12.3481 | 0.485079 | ||||||||
\(649\) | −7.83907 | −0.307711 | ||||||||
\(650\) | −20.8799 | −0.818975 | ||||||||
\(651\) | −57.4978 | −2.25352 | ||||||||
\(652\) | 1.77811 | 0.0696361 | ||||||||
\(653\) | 4.82113 | 0.188666 | 0.0943328 | − | 0.995541i | \(-0.469928\pi\) | ||||
0.0943328 | + | 0.995541i | \(0.469928\pi\) | |||||||
\(654\) | −14.3417 | −0.560805 | ||||||||
\(655\) | −32.3223 | −1.26294 | ||||||||
\(656\) | 6.34374 | 0.247681 | ||||||||
\(657\) | −61.9493 | −2.41687 | ||||||||
\(658\) | 15.1877 | 0.592077 | ||||||||
\(659\) | 28.9821 | 1.12898 | 0.564490 | − | 0.825440i | \(-0.309073\pi\) | ||||
0.564490 | + | 0.825440i | \(0.309073\pi\) | |||||||
\(660\) | −1.35047 | −0.0525669 | ||||||||
\(661\) | −38.1439 | −1.48362 | −0.741812 | − | 0.670608i | \(-0.766033\pi\) | ||||
−0.741812 | + | 0.670608i | \(0.766033\pi\) | |||||||
\(662\) | 3.15960 | 0.122801 | ||||||||
\(663\) | −19.0371 | −0.739341 | ||||||||
\(664\) | −17.0935 | −0.663355 | ||||||||
\(665\) | −47.0256 | −1.82357 | ||||||||
\(666\) | 20.7375 | 0.803563 | ||||||||
\(667\) | −8.99301 | −0.348211 | ||||||||
\(668\) | −2.56749 | −0.0993392 | ||||||||
\(669\) | 70.2121 | 2.71456 | ||||||||
\(670\) | −25.7816 | −0.996032 | ||||||||
\(671\) | 4.43647 | 0.171268 | ||||||||
\(672\) | 10.7422 | 0.414390 | ||||||||
\(673\) | −39.5529 | −1.52465 | −0.762326 | − | 0.647194i | \(-0.775943\pi\) | ||||
−0.762326 | + | 0.647194i | \(0.775943\pi\) | |||||||
\(674\) | −18.2734 | −0.703865 | ||||||||
\(675\) | 16.6270 | 0.639975 | ||||||||
\(676\) | −5.14198 | −0.197769 | ||||||||
\(677\) | 23.1792 | 0.890849 | 0.445425 | − | 0.895319i | \(-0.353053\pi\) | ||||
0.445425 | + | 0.895319i | \(0.353053\pi\) | |||||||
\(678\) | 31.5476 | 1.21158 | ||||||||
\(679\) | −60.6347 | −2.32694 | ||||||||
\(680\) | 7.96349 | 0.305386 | ||||||||
\(681\) | 13.2678 | 0.508422 | ||||||||
\(682\) | 7.00142 | 0.268098 | ||||||||
\(683\) | 45.3107 | 1.73377 | 0.866883 | − | 0.498511i | \(-0.166120\pi\) | ||||
0.866883 | + | 0.498511i | \(0.166120\pi\) | |||||||
\(684\) | 4.22295 | 0.161469 | ||||||||
\(685\) | 30.0012 | 1.14629 | ||||||||
\(686\) | 3.23851 | 0.123647 | ||||||||
\(687\) | 3.56942 | 0.136182 | ||||||||
\(688\) | −3.62761 | −0.138301 | ||||||||
\(689\) | −48.6704 | −1.85419 | ||||||||
\(690\) | −53.7293 | −2.04544 | ||||||||
\(691\) | −20.6230 | −0.784535 | −0.392267 | − | 0.919851i | \(-0.628309\pi\) | ||||
−0.392267 | + | 0.919851i | \(0.628309\pi\) | |||||||
\(692\) | 0.398981 | 0.0151670 | ||||||||
\(693\) | 20.7717 | 0.789050 | ||||||||
\(694\) | 1.68926 | 0.0641234 | ||||||||
\(695\) | 20.6230 | 0.782277 | ||||||||
\(696\) | 15.1964 | 0.576019 | ||||||||
\(697\) | 1.74874 | 0.0662382 | ||||||||
\(698\) | −40.3813 | −1.52846 | ||||||||
\(699\) | −78.2212 | −2.95860 | ||||||||
\(700\) | 1.54465 | 0.0583824 | ||||||||
\(701\) | 31.7742 | 1.20010 | 0.600048 | − | 0.799964i | \(-0.295148\pi\) | ||||
0.600048 | + | 0.799964i | \(0.295148\pi\) | |||||||
\(702\) | −62.5881 | −2.36224 | ||||||||
\(703\) | 12.8019 | 0.482832 | ||||||||
\(704\) | −8.56328 | −0.322741 | ||||||||
\(705\) | −23.1271 | −0.871016 | ||||||||
\(706\) | −35.6833 | −1.34296 | ||||||||
\(707\) | −27.9628 | −1.05165 | ||||||||
\(708\) | −3.90348 | −0.146702 | ||||||||
\(709\) | −44.7416 | −1.68030 | −0.840152 | − | 0.542351i | \(-0.817534\pi\) | ||||
−0.840152 | + | 0.542351i | \(0.817534\pi\) | |||||||
\(710\) | 33.7016 | 1.26480 | ||||||||
\(711\) | 64.6361 | 2.42404 | ||||||||
\(712\) | 47.2820 | 1.77197 | ||||||||
\(713\) | −26.1250 | −0.978387 | ||||||||
\(714\) | −15.0163 | −0.561970 | ||||||||
\(715\) | 17.7808 | 0.664963 | ||||||||
\(716\) | 1.79519 | 0.0670893 | ||||||||
\(717\) | 28.3588 | 1.05908 | ||||||||
\(718\) | −43.4185 | −1.62036 | ||||||||
\(719\) | 36.9506 | 1.37803 | 0.689013 | − | 0.724749i | \(-0.258044\pi\) | ||||
0.689013 | + | 0.724749i | \(0.258044\pi\) | |||||||
\(720\) | 53.4346 | 1.99139 | ||||||||
\(721\) | 63.5949 | 2.36840 | ||||||||
\(722\) | −2.10428 | −0.0783131 | ||||||||
\(723\) | 69.2478 | 2.57535 | ||||||||
\(724\) | −0.00702690 | −0.000261153 0 | ||||||||
\(725\) | 4.19771 | 0.155899 | ||||||||
\(726\) | −3.92642 | −0.145723 | ||||||||
\(727\) | −20.3689 | −0.755440 | −0.377720 | − | 0.925920i | \(-0.623292\pi\) | ||||
−0.377720 | + | 0.925920i | \(0.623292\pi\) | |||||||
\(728\) | −73.6252 | −2.72873 | ||||||||
\(729\) | −38.6575 | −1.43176 | ||||||||
\(730\) | −41.8289 | −1.54816 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 2.20915 | 0.0816525 | ||||||||
\(733\) | −17.1672 | −0.634085 | −0.317042 | − | 0.948411i | \(-0.602690\pi\) | ||||
−0.317042 | + | 0.948411i | \(0.602690\pi\) | |||||||
\(734\) | 34.1712 | 1.26128 | ||||||||
\(735\) | −60.0557 | −2.21519 | ||||||||
\(736\) | 4.88088 | 0.179911 | ||||||||
\(737\) | 7.03016 | 0.258959 | ||||||||
\(738\) | 12.8434 | 0.472770 | ||||||||
\(739\) | −35.9594 | −1.32279 | −0.661394 | − | 0.750039i | \(-0.730035\pi\) | ||||
−0.661394 | + | 0.750039i | \(0.730035\pi\) | |||||||
\(740\) | −1.31323 | −0.0482752 | ||||||||
\(741\) | −86.3123 | −3.17076 | ||||||||
\(742\) | −38.3907 | −1.40937 | ||||||||
\(743\) | −19.3251 | −0.708968 | −0.354484 | − | 0.935062i | \(-0.615343\pi\) | ||||
−0.354484 | + | 0.935062i | \(0.615343\pi\) | |||||||
\(744\) | 44.1460 | 1.61847 | ||||||||
\(745\) | −15.5129 | −0.568347 | ||||||||
\(746\) | −10.2514 | −0.375330 | ||||||||
\(747\) | −31.6176 | −1.15683 | ||||||||
\(748\) | −0.171490 | −0.00627031 | ||||||||
\(749\) | −47.3864 | −1.73146 | ||||||||
\(750\) | −28.1636 | −1.02839 | ||||||||
\(751\) | −46.7552 | −1.70612 | −0.853060 | − | 0.521813i | \(-0.825256\pi\) | ||||
−0.853060 | + | 0.521813i | \(0.825256\pi\) | |||||||
\(752\) | −10.6536 | −0.388497 | ||||||||
\(753\) | 9.68474 | 0.352932 | ||||||||
\(754\) | −15.8012 | −0.575445 | ||||||||
\(755\) | −8.56484 | −0.311706 | ||||||||
\(756\) | 4.63016 | 0.168397 | ||||||||
\(757\) | −45.1596 | −1.64135 | −0.820676 | − | 0.571393i | \(-0.806403\pi\) | ||||
−0.820676 | + | 0.571393i | \(0.806403\pi\) | |||||||
\(758\) | 8.67342 | 0.315033 | ||||||||
\(759\) | 14.6510 | 0.531796 | ||||||||
\(760\) | 36.1056 | 1.30969 | ||||||||
\(761\) | −6.60063 | −0.239273 | −0.119636 | − | 0.992818i | \(-0.538173\pi\) | ||||
−0.119636 | + | 0.992818i | \(0.538173\pi\) | |||||||
\(762\) | 82.3671 | 2.98384 | ||||||||
\(763\) | −13.9692 | −0.505718 | ||||||||
\(764\) | 2.02666 | 0.0733221 | ||||||||
\(765\) | 14.7300 | 0.532563 | ||||||||
\(766\) | −2.74281 | −0.0991019 | ||||||||
\(767\) | 51.3947 | 1.85576 | ||||||||
\(768\) | −11.8605 | −0.427978 | ||||||||
\(769\) | 39.1599 | 1.41214 | 0.706071 | − | 0.708141i | \(-0.250466\pi\) | ||||
0.706071 | + | 0.708141i | \(0.250466\pi\) | |||||||
\(770\) | 14.0253 | 0.505436 | ||||||||
\(771\) | −76.4817 | −2.75442 | ||||||||
\(772\) | 1.06544 | 0.0383461 | ||||||||
\(773\) | −32.7745 | −1.17882 | −0.589409 | − | 0.807835i | \(-0.700639\pi\) | ||||
−0.589409 | + | 0.807835i | \(0.700639\pi\) | |||||||
\(774\) | −7.34436 | −0.263988 | ||||||||
\(775\) | 12.1945 | 0.438038 | ||||||||
\(776\) | 46.5545 | 1.67121 | ||||||||
\(777\) | 31.3557 | 1.12488 | ||||||||
\(778\) | 4.28681 | 0.153689 | ||||||||
\(779\) | 7.92858 | 0.284071 | ||||||||
\(780\) | 8.85397 | 0.317023 | ||||||||
\(781\) | −9.18978 | −0.328836 | ||||||||
\(782\) | −6.82286 | −0.243985 | ||||||||
\(783\) | 12.5828 | 0.449672 | ||||||||
\(784\) | −27.6650 | −0.988035 | ||||||||
\(785\) | 27.9366 | 0.997101 | ||||||||
\(786\) | −46.7953 | −1.66913 | ||||||||
\(787\) | −16.9436 | −0.603973 | −0.301986 | − | 0.953312i | \(-0.597650\pi\) | ||||
−0.301986 | + | 0.953312i | \(0.597650\pi\) | |||||||
\(788\) | −2.70205 | −0.0962564 | ||||||||
\(789\) | −9.28151 | −0.330430 | ||||||||
\(790\) | 43.6431 | 1.55275 | ||||||||
\(791\) | 30.7281 | 1.09257 | ||||||||
\(792\) | −15.9482 | −0.566695 | ||||||||
\(793\) | −29.0865 | −1.03289 | ||||||||
\(794\) | 32.1512 | 1.14100 | ||||||||
\(795\) | 58.4595 | 2.07335 | ||||||||
\(796\) | −2.68419 | −0.0951387 | ||||||||
\(797\) | 50.6406 | 1.79378 | 0.896891 | − | 0.442252i | \(-0.145820\pi\) | ||||
0.896891 | + | 0.442252i | \(0.145820\pi\) | |||||||
\(798\) | −68.0822 | −2.41008 | ||||||||
\(799\) | −2.93681 | −0.103897 | ||||||||
\(800\) | −2.27827 | −0.0805489 | ||||||||
\(801\) | 87.4569 | 3.09014 | ||||||||
\(802\) | −10.3685 | −0.366125 | ||||||||
\(803\) | 11.4059 | 0.402507 | ||||||||
\(804\) | 3.50068 | 0.123460 | ||||||||
\(805\) | −52.3336 | −1.84452 | ||||||||
\(806\) | −45.9029 | −1.61686 | ||||||||
\(807\) | 23.6685 | 0.833170 | ||||||||
\(808\) | 21.4695 | 0.755293 | ||||||||
\(809\) | 17.9321 | 0.630457 | 0.315229 | − | 0.949016i | \(-0.397919\pi\) | ||||
0.315229 | + | 0.949016i | \(0.397919\pi\) | |||||||
\(810\) | 15.4219 | 0.541871 | ||||||||
\(811\) | 33.7816 | 1.18623 | 0.593117 | − | 0.805117i | \(-0.297897\pi\) | ||||
0.593117 | + | 0.805117i | \(0.297897\pi\) | |||||||
\(812\) | 1.16894 | 0.0410218 | ||||||||
\(813\) | 30.7406 | 1.07812 | ||||||||
\(814\) | −3.81814 | −0.133826 | ||||||||
\(815\) | 28.1200 | 0.985001 | ||||||||
\(816\) | 10.5334 | 0.368743 | ||||||||
\(817\) | −4.53389 | −0.158621 | ||||||||
\(818\) | 7.69253 | 0.268963 | ||||||||
\(819\) | −136.184 | −4.75865 | ||||||||
\(820\) | −0.813320 | −0.0284024 | ||||||||
\(821\) | −3.46824 | −0.121042 | −0.0605211 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605211 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(822\) | 43.4348 | 1.51496 | ||||||||
\(823\) | −30.3712 | −1.05867 | −0.529336 | − | 0.848412i | \(-0.677559\pi\) | ||||
−0.529336 | + | 0.848412i | \(0.677559\pi\) | |||||||
\(824\) | −48.8273 | −1.70098 | ||||||||
\(825\) | −6.83869 | −0.238093 | ||||||||
\(826\) | 40.5396 | 1.41055 | ||||||||
\(827\) | −34.9041 | −1.21374 | −0.606868 | − | 0.794803i | \(-0.707574\pi\) | ||||
−0.606868 | + | 0.794803i | \(0.707574\pi\) | |||||||
\(828\) | 4.69962 | 0.163323 | ||||||||
\(829\) | 12.3081 | 0.427479 | 0.213739 | − | 0.976891i | \(-0.431436\pi\) | ||||
0.213739 | + | 0.976891i | \(0.431436\pi\) | |||||||
\(830\) | −21.3486 | −0.741019 | ||||||||
\(831\) | 43.7730 | 1.51847 | ||||||||
\(832\) | 56.1428 | 1.94640 | ||||||||
\(833\) | −7.62623 | −0.264233 | ||||||||
\(834\) | 29.8574 | 1.03388 | ||||||||
\(835\) | −40.6037 | −1.40515 | ||||||||
\(836\) | −0.777519 | −0.0268910 | ||||||||
\(837\) | 36.5533 | 1.26347 | ||||||||
\(838\) | −12.9434 | −0.447121 | ||||||||
\(839\) | 15.3505 | 0.529958 | 0.264979 | − | 0.964254i | \(-0.414635\pi\) | ||||
0.264979 | + | 0.964254i | \(0.414635\pi\) | |||||||
\(840\) | 88.4336 | 3.05125 | ||||||||
\(841\) | −25.8233 | −0.890459 | ||||||||
\(842\) | 13.5265 | 0.466155 | ||||||||
\(843\) | −45.2592 | −1.55881 | ||||||||
\(844\) | −3.98543 | −0.137184 | ||||||||
\(845\) | −81.3182 | −2.79743 | ||||||||
\(846\) | −21.5690 | −0.741558 | ||||||||
\(847\) | −3.82442 | −0.131409 | ||||||||
\(848\) | 26.9297 | 0.924769 | ||||||||
\(849\) | 40.1507 | 1.37797 | ||||||||
\(850\) | 3.18474 | 0.109236 | ||||||||
\(851\) | 14.2469 | 0.488378 | ||||||||
\(852\) | −4.57607 | −0.156774 | ||||||||
\(853\) | 3.13432 | 0.107317 | 0.0536585 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536585 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(854\) | −22.9431 | −0.785097 | ||||||||
\(855\) | 66.7841 | 2.28397 | ||||||||
\(856\) | 36.3827 | 1.24353 | ||||||||
\(857\) | −36.4168 | −1.24397 | −0.621987 | − | 0.783027i | \(-0.713674\pi\) | ||||
−0.621987 | + | 0.783027i | \(0.713674\pi\) | |||||||
\(858\) | 25.7425 | 0.878833 | ||||||||
\(859\) | −48.5351 | −1.65599 | −0.827997 | − | 0.560732i | \(-0.810520\pi\) | ||||
−0.827997 | + | 0.560732i | \(0.810520\pi\) | |||||||
\(860\) | 0.465090 | 0.0158594 | ||||||||
\(861\) | 19.4195 | 0.661815 | ||||||||
\(862\) | 12.5146 | 0.426248 | ||||||||
\(863\) | 25.9828 | 0.884463 | 0.442232 | − | 0.896901i | \(-0.354187\pi\) | ||||
0.442232 | + | 0.896901i | \(0.354187\pi\) | |||||||
\(864\) | −6.82919 | −0.232334 | ||||||||
\(865\) | 6.30971 | 0.214537 | ||||||||
\(866\) | −42.4061 | −1.44102 | ||||||||
\(867\) | 2.90367 | 0.0986139 | ||||||||
\(868\) | 3.39581 | 0.115261 | ||||||||
\(869\) | −11.9006 | −0.403701 | ||||||||
\(870\) | 18.9793 | 0.643459 | ||||||||
\(871\) | −46.0913 | −1.56174 | ||||||||
\(872\) | 10.7253 | 0.363206 | ||||||||
\(873\) | 86.1113 | 2.91443 | ||||||||
\(874\) | −30.9341 | −1.04636 | ||||||||
\(875\) | −27.4320 | −0.927372 | ||||||||
\(876\) | 5.67961 | 0.191896 | ||||||||
\(877\) | −9.31643 | −0.314594 | −0.157297 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157297 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(878\) | −44.9499 | −1.51699 | ||||||||
\(879\) | 28.4400 | 0.959259 | ||||||||
\(880\) | −9.83824 | −0.331647 | ||||||||
\(881\) | 4.88254 | 0.164497 | 0.0822485 | − | 0.996612i | \(-0.473790\pi\) | ||||
0.0822485 | + | 0.996612i | \(0.473790\pi\) | |||||||
\(882\) | −56.0097 | −1.88595 | ||||||||
\(883\) | −25.2231 | −0.848824 | −0.424412 | − | 0.905469i | \(-0.639519\pi\) | ||||
−0.424412 | + | 0.905469i | \(0.639519\pi\) | |||||||
\(884\) | 1.12433 | 0.0378153 | ||||||||
\(885\) | −61.7318 | −2.07509 | ||||||||
\(886\) | −22.1716 | −0.744871 | ||||||||
\(887\) | 58.7875 | 1.97389 | 0.986946 | − | 0.161054i | \(-0.0514895\pi\) | ||||
0.986946 | + | 0.161054i | \(0.0514895\pi\) | |||||||
\(888\) | −24.0745 | −0.807887 | ||||||||
\(889\) | 80.2275 | 2.69075 | ||||||||
\(890\) | 59.0520 | 1.97943 | ||||||||
\(891\) | −4.20526 | −0.140882 | ||||||||
\(892\) | −4.14671 | −0.138842 | ||||||||
\(893\) | −13.3152 | −0.445576 | ||||||||
\(894\) | −22.4591 | −0.751143 | ||||||||
\(895\) | 28.3901 | 0.948975 | ||||||||
\(896\) | 36.8858 | 1.23227 | ||||||||
\(897\) | −96.0549 | −3.20718 | ||||||||
\(898\) | −41.0817 | −1.37091 | ||||||||
\(899\) | 9.22836 | 0.307783 | ||||||||
\(900\) | −2.19366 | −0.0731221 | ||||||||
\(901\) | 7.42353 | 0.247314 | ||||||||
\(902\) | −2.36468 | −0.0787354 | ||||||||
\(903\) | −11.1049 | −0.369547 | ||||||||
\(904\) | −23.5926 | −0.784679 | ||||||||
\(905\) | −0.111127 | −0.00369399 | ||||||||
\(906\) | −12.3999 | −0.411960 | ||||||||
\(907\) | −9.26028 | −0.307483 | −0.153741 | − | 0.988111i | \(-0.549132\pi\) | ||||
−0.153741 | + | 0.988111i | \(0.549132\pi\) | |||||||
\(908\) | −0.783592 | −0.0260044 | ||||||||
\(909\) | 39.7118 | 1.31716 | ||||||||
\(910\) | −91.9529 | −3.04821 | ||||||||
\(911\) | 9.85948 | 0.326659 | 0.163329 | − | 0.986572i | \(-0.447777\pi\) | ||||
0.163329 | + | 0.986572i | \(0.447777\pi\) | |||||||
\(912\) | 47.7573 | 1.58140 | ||||||||
\(913\) | 5.82134 | 0.192658 | ||||||||
\(914\) | −4.93737 | −0.163314 | ||||||||
\(915\) | 34.9367 | 1.15497 | ||||||||
\(916\) | −0.210809 | −0.00696533 | ||||||||
\(917\) | −45.5798 | −1.50518 | ||||||||
\(918\) | 9.54637 | 0.315077 | ||||||||
\(919\) | −11.4635 | −0.378147 | −0.189073 | − | 0.981963i | \(-0.560548\pi\) | ||||
−0.189073 | + | 0.981963i | \(0.560548\pi\) | |||||||
\(920\) | 40.1811 | 1.32473 | ||||||||
\(921\) | 67.4732 | 2.22332 | ||||||||
\(922\) | −14.8245 | −0.488220 | ||||||||
\(923\) | 60.2503 | 1.98316 | ||||||||
\(924\) | −1.90438 | −0.0626495 | ||||||||
\(925\) | −6.65010 | −0.218654 | ||||||||
\(926\) | −42.0918 | −1.38322 | ||||||||
\(927\) | −90.3154 | −2.96635 | ||||||||
\(928\) | −1.72412 | −0.0565969 | ||||||||
\(929\) | −9.94867 | −0.326405 | −0.163203 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163203 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(930\) | 55.1354 | 1.80796 | ||||||||
\(931\) | −34.5765 | −1.13320 | ||||||||
\(932\) | 4.61973 | 0.151324 | ||||||||
\(933\) | 44.7181 | 1.46400 | ||||||||
\(934\) | −48.8099 | −1.59711 | ||||||||
\(935\) | −2.71204 | −0.0886933 | ||||||||
\(936\) | 104.560 | 3.41765 | ||||||||
\(937\) | −12.6998 | −0.414884 | −0.207442 | − | 0.978247i | \(-0.566514\pi\) | ||||
−0.207442 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(938\) | −36.3563 | −1.18708 | ||||||||
\(939\) | 1.33361 | 0.0435206 | ||||||||
\(940\) | 1.36588 | 0.0445501 | ||||||||
\(941\) | −16.0382 | −0.522829 | −0.261415 | − | 0.965227i | \(-0.584189\pi\) | ||||
−0.261415 | + | 0.965227i | \(0.584189\pi\) | |||||||
\(942\) | 40.4458 | 1.31780 | ||||||||
\(943\) | 8.82354 | 0.287334 | ||||||||
\(944\) | −28.4371 | −0.925549 | ||||||||
\(945\) | 73.2238 | 2.38197 | ||||||||
\(946\) | 1.35222 | 0.0439646 | ||||||||
\(947\) | 8.65237 | 0.281164 | 0.140582 | − | 0.990069i | \(-0.455103\pi\) | ||||
0.140582 | + | 0.990069i | \(0.455103\pi\) | |||||||
\(948\) | −5.92594 | −0.192466 | ||||||||
\(949\) | −74.7799 | −2.42746 | ||||||||
\(950\) | 14.4393 | 0.468471 | ||||||||
\(951\) | 67.8419 | 2.19992 | ||||||||
\(952\) | 11.2298 | 0.363960 | ||||||||
\(953\) | −23.0662 | −0.747188 | −0.373594 | − | 0.927592i | \(-0.621875\pi\) | ||||
−0.373594 | + | 0.927592i | \(0.621875\pi\) | |||||||
\(954\) | 54.5211 | 1.76519 | ||||||||
\(955\) | 32.0508 | 1.03714 | ||||||||
\(956\) | −1.67486 | −0.0541690 | ||||||||
\(957\) | −5.17529 | −0.167293 | ||||||||
\(958\) | −49.3950 | −1.59588 | ||||||||
\(959\) | 42.3065 | 1.36615 | ||||||||
\(960\) | −67.4349 | −2.17645 | ||||||||
\(961\) | −4.19135 | −0.135205 | ||||||||
\(962\) | 25.0326 | 0.807083 | ||||||||
\(963\) | 67.2966 | 2.16860 | ||||||||
\(964\) | −4.08976 | −0.131722 | ||||||||
\(965\) | 16.8495 | 0.542405 | ||||||||
\(966\) | −75.7671 | −2.43777 | ||||||||
\(967\) | −8.01458 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(968\) | 2.93634 | 0.0943776 | ||||||||
\(969\) | 13.1649 | 0.422919 | ||||||||
\(970\) | 58.1434 | 1.86687 | ||||||||
\(971\) | 12.8506 | 0.412396 | 0.206198 | − | 0.978510i | \(-0.433891\pi\) | ||||
0.206198 | + | 0.978510i | \(0.433891\pi\) | |||||||
\(972\) | 1.53802 | 0.0493320 | ||||||||
\(973\) | 29.0819 | 0.932322 | ||||||||
\(974\) | −31.2374 | −1.00091 | ||||||||
\(975\) | 44.8360 | 1.43590 | ||||||||
\(976\) | 16.0938 | 0.515149 | ||||||||
\(977\) | 41.3415 | 1.32263 | 0.661316 | − | 0.750108i | \(-0.269998\pi\) | ||||
0.661316 | + | 0.750108i | \(0.269998\pi\) | |||||||
\(978\) | 40.7113 | 1.30180 | ||||||||
\(979\) | −16.1023 | −0.514633 | ||||||||
\(980\) | 3.54688 | 0.113301 | ||||||||
\(981\) | 19.8385 | 0.633396 | ||||||||
\(982\) | 21.4129 | 0.683314 | ||||||||
\(983\) | 4.55883 | 0.145404 | 0.0727021 | − | 0.997354i | \(-0.476838\pi\) | ||||
0.0727021 | + | 0.997354i | \(0.476838\pi\) | |||||||
\(984\) | −14.9100 | −0.475315 | ||||||||
\(985\) | −42.7316 | −1.36154 | ||||||||
\(986\) | 2.41010 | 0.0767533 | ||||||||
\(987\) | −32.6130 | −1.03808 | ||||||||
\(988\) | 5.09759 | 0.162176 | ||||||||
\(989\) | −5.04566 | −0.160443 | ||||||||
\(990\) | −19.9182 | −0.633043 | ||||||||
\(991\) | 43.3979 | 1.37858 | 0.689290 | − | 0.724486i | \(-0.257923\pi\) | ||||
0.689290 | + | 0.724486i | \(0.257923\pi\) | |||||||
\(992\) | −5.00861 | −0.159024 | ||||||||
\(993\) | −6.78471 | −0.215306 | ||||||||
\(994\) | 47.5248 | 1.50739 | ||||||||
\(995\) | −42.4493 | −1.34573 | ||||||||
\(996\) | 2.89875 | 0.0918504 | ||||||||
\(997\) | 20.2454 | 0.641178 | 0.320589 | − | 0.947218i | \(-0.396119\pi\) | ||||
0.320589 | + | 0.947218i | \(0.396119\pi\) | |||||||
\(998\) | 5.22134 | 0.165279 | ||||||||
\(999\) | −19.9339 | −0.630681 |
(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 | 8041.2.a.e.1.17 | ✓ | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.e.1.17 | ✓ | 66 | 1.1 | even | 1 | trivial |