Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76681 | −1.24933 | −0.624663 | − | 0.780894i | \(-0.714764\pi\) | ||||
−0.624663 | + | 0.780894i | \(0.714764\pi\) | |||||||
\(3\) | 2.93332 | 1.69356 | 0.846778 | − | 0.531947i | \(-0.178540\pi\) | ||||
0.846778 | + | 0.531947i | \(0.178540\pi\) | |||||||
\(4\) | 1.12163 | 0.560817 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −5.18264 | −2.11580 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.55191 | 0.548683 | ||||||||
\(9\) | 5.60439 | 1.86813 | ||||||||
\(10\) | 1.76681 | 0.558716 | ||||||||
\(11\) | 5.57251 | 1.68017 | 0.840087 | − | 0.542452i | \(-0.182504\pi\) | ||||
0.840087 | + | 0.542452i | \(0.182504\pi\) | |||||||
\(12\) | 3.29012 | 0.949775 | ||||||||
\(13\) | 2.46065 | 0.682461 | 0.341230 | − | 0.939980i | \(-0.389156\pi\) | ||||
0.341230 | + | 0.939980i | \(0.389156\pi\) | |||||||
\(14\) | 1.76681 | 0.472201 | ||||||||
\(15\) | −2.93332 | −0.757381 | ||||||||
\(16\) | −4.98520 | −1.24630 | ||||||||
\(17\) | 6.99936 | 1.69759 | 0.848797 | − | 0.528719i | \(-0.177327\pi\) | ||||
0.848797 | + | 0.528719i | \(0.177327\pi\) | |||||||
\(18\) | −9.90191 | −2.33390 | ||||||||
\(19\) | −7.29290 | −1.67311 | −0.836553 | − | 0.547886i | \(-0.815433\pi\) | ||||
−0.836553 | + | 0.547886i | \(0.815433\pi\) | |||||||
\(20\) | −1.12163 | −0.250805 | ||||||||
\(21\) | −2.93332 | −0.640104 | ||||||||
\(22\) | −9.84559 | −2.09909 | ||||||||
\(23\) | 7.80740 | 1.62795 | 0.813977 | − | 0.580896i | \(-0.197298\pi\) | ||||
0.813977 | + | 0.580896i | \(0.197298\pi\) | |||||||
\(24\) | 4.55225 | 0.929224 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.34751 | −0.852616 | ||||||||
\(27\) | 7.63951 | 1.47022 | ||||||||
\(28\) | −1.12163 | −0.211969 | ||||||||
\(29\) | −0.282924 | −0.0525376 | −0.0262688 | − | 0.999655i | \(-0.508363\pi\) | ||||
−0.0262688 | + | 0.999655i | \(0.508363\pi\) | |||||||
\(30\) | 5.18264 | 0.946216 | ||||||||
\(31\) | 9.08665 | 1.63201 | 0.816005 | − | 0.578044i | \(-0.196184\pi\) | ||||
0.816005 | + | 0.578044i | \(0.196184\pi\) | |||||||
\(32\) | 5.70412 | 1.00835 | ||||||||
\(33\) | 16.3460 | 2.84547 | ||||||||
\(34\) | −12.3666 | −2.12085 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 6.28607 | 1.04768 | ||||||||
\(37\) | 3.25443 | 0.535026 | 0.267513 | − | 0.963554i | \(-0.413798\pi\) | ||||
0.267513 | + | 0.963554i | \(0.413798\pi\) | |||||||
\(38\) | 12.8852 | 2.09026 | ||||||||
\(39\) | 7.21787 | 1.15578 | ||||||||
\(40\) | −1.55191 | −0.245378 | ||||||||
\(41\) | 5.90197 | 0.921733 | 0.460866 | − | 0.887470i | \(-0.347539\pi\) | ||||
0.460866 | + | 0.887470i | \(0.347539\pi\) | |||||||
\(42\) | 5.18264 | 0.799699 | ||||||||
\(43\) | −7.89879 | −1.20455 | −0.602277 | − | 0.798287i | \(-0.705740\pi\) | ||||
−0.602277 | + | 0.798287i | \(0.705740\pi\) | |||||||
\(44\) | 6.25032 | 0.942271 | ||||||||
\(45\) | −5.60439 | −0.835453 | ||||||||
\(46\) | −13.7942 | −2.03385 | ||||||||
\(47\) | 6.99295 | 1.02003 | 0.510014 | − | 0.860166i | \(-0.329640\pi\) | ||||
0.510014 | + | 0.860166i | \(0.329640\pi\) | |||||||
\(48\) | −14.6232 | −2.11068 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.76681 | −0.249865 | ||||||||
\(51\) | 20.5314 | 2.87497 | ||||||||
\(52\) | 2.75995 | 0.382736 | ||||||||
\(53\) | −9.58756 | −1.31695 | −0.658476 | − | 0.752602i | \(-0.728799\pi\) | ||||
−0.658476 | + | 0.752602i | \(0.728799\pi\) | |||||||
\(54\) | −13.4976 | −1.83679 | ||||||||
\(55\) | −5.57251 | −0.751397 | ||||||||
\(56\) | −1.55191 | −0.207383 | ||||||||
\(57\) | −21.3924 | −2.83350 | ||||||||
\(58\) | 0.499874 | 0.0656367 | ||||||||
\(59\) | −2.15310 | −0.280310 | −0.140155 | − | 0.990130i | \(-0.544760\pi\) | ||||
−0.140155 | + | 0.990130i | \(0.544760\pi\) | |||||||
\(60\) | −3.29012 | −0.424752 | ||||||||
\(61\) | 4.50495 | 0.576800 | 0.288400 | − | 0.957510i | \(-0.406877\pi\) | ||||
0.288400 | + | 0.957510i | \(0.406877\pi\) | |||||||
\(62\) | −16.0544 | −2.03891 | ||||||||
\(63\) | −5.60439 | −0.706086 | ||||||||
\(64\) | −0.107708 | −0.0134635 | ||||||||
\(65\) | −2.46065 | −0.305206 | ||||||||
\(66\) | −28.8803 | −3.55492 | ||||||||
\(67\) | −8.61501 | −1.05249 | −0.526245 | − | 0.850333i | \(-0.676401\pi\) | ||||
−0.526245 | + | 0.850333i | \(0.676401\pi\) | |||||||
\(68\) | 7.85073 | 0.952040 | ||||||||
\(69\) | 22.9016 | 2.75703 | ||||||||
\(70\) | −1.76681 | −0.211175 | ||||||||
\(71\) | 14.1801 | 1.68287 | 0.841434 | − | 0.540359i | \(-0.181712\pi\) | ||||
0.841434 | + | 0.540359i | \(0.181712\pi\) | |||||||
\(72\) | 8.69750 | 1.02501 | ||||||||
\(73\) | −12.7551 | −1.49287 | −0.746436 | − | 0.665457i | \(-0.768237\pi\) | ||||
−0.746436 | + | 0.665457i | \(0.768237\pi\) | |||||||
\(74\) | −5.74998 | −0.668422 | ||||||||
\(75\) | 2.93332 | 0.338711 | ||||||||
\(76\) | −8.17997 | −0.938307 | ||||||||
\(77\) | −5.57251 | −0.635046 | ||||||||
\(78\) | −12.7526 | −1.44395 | ||||||||
\(79\) | −10.9668 | −1.23386 | −0.616930 | − | 0.787018i | \(-0.711624\pi\) | ||||
−0.616930 | + | 0.787018i | \(0.711624\pi\) | |||||||
\(80\) | 4.98520 | 0.557363 | ||||||||
\(81\) | 5.59598 | 0.621776 | ||||||||
\(82\) | −10.4277 | −1.15155 | ||||||||
\(83\) | −0.554755 | −0.0608922 | −0.0304461 | − | 0.999536i | \(-0.509693\pi\) | ||||
−0.0304461 | + | 0.999536i | \(0.509693\pi\) | |||||||
\(84\) | −3.29012 | −0.358981 | ||||||||
\(85\) | −6.99936 | −0.759187 | ||||||||
\(86\) | 13.9557 | 1.50488 | ||||||||
\(87\) | −0.829907 | −0.0889754 | ||||||||
\(88\) | 8.64802 | 0.921882 | ||||||||
\(89\) | 11.4222 | 1.21075 | 0.605374 | − | 0.795941i | \(-0.293023\pi\) | ||||
0.605374 | + | 0.795941i | \(0.293023\pi\) | |||||||
\(90\) | 9.90191 | 1.04375 | ||||||||
\(91\) | −2.46065 | −0.257946 | ||||||||
\(92\) | 8.75705 | 0.912985 | ||||||||
\(93\) | 26.6541 | 2.76390 | ||||||||
\(94\) | −12.3553 | −1.27435 | ||||||||
\(95\) | 7.29290 | 0.748236 | ||||||||
\(96\) | 16.7320 | 1.70770 | ||||||||
\(97\) | 9.69786 | 0.984668 | 0.492334 | − | 0.870406i | \(-0.336144\pi\) | ||||
0.492334 | + | 0.870406i | \(0.336144\pi\) | |||||||
\(98\) | −1.76681 | −0.178475 | ||||||||
\(99\) | 31.2305 | 3.13878 | ||||||||
\(100\) | 1.12163 | 0.112163 | ||||||||
\(101\) | −3.30049 | −0.328411 | −0.164206 | − | 0.986426i | \(-0.552506\pi\) | ||||
−0.164206 | + | 0.986426i | \(0.552506\pi\) | |||||||
\(102\) | −36.2752 | −3.59178 | ||||||||
\(103\) | −11.3910 | −1.12239 | −0.561193 | − | 0.827685i | \(-0.689657\pi\) | ||||
−0.561193 | + | 0.827685i | \(0.689657\pi\) | |||||||
\(104\) | 3.81870 | 0.374454 | ||||||||
\(105\) | 2.93332 | 0.286263 | ||||||||
\(106\) | 16.9394 | 1.64530 | ||||||||
\(107\) | 14.6507 | 1.41634 | 0.708168 | − | 0.706044i | \(-0.249522\pi\) | ||||
0.708168 | + | 0.706044i | \(0.249522\pi\) | |||||||
\(108\) | 8.56873 | 0.824527 | ||||||||
\(109\) | −6.01512 | −0.576144 | −0.288072 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288072 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(110\) | 9.84559 | 0.938740 | ||||||||
\(111\) | 9.54631 | 0.906096 | ||||||||
\(112\) | 4.98520 | 0.471058 | ||||||||
\(113\) | −10.9393 | −1.02908 | −0.514539 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514539 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(114\) | 37.7965 | 3.53996 | ||||||||
\(115\) | −7.80740 | −0.728044 | ||||||||
\(116\) | −0.317337 | −0.0294640 | ||||||||
\(117\) | 13.7904 | 1.27492 | ||||||||
\(118\) | 3.80413 | 0.350199 | ||||||||
\(119\) | −6.99936 | −0.641630 | ||||||||
\(120\) | −4.55225 | −0.415562 | ||||||||
\(121\) | 20.0528 | 1.82299 | ||||||||
\(122\) | −7.95942 | −0.720612 | ||||||||
\(123\) | 17.3124 | 1.56101 | ||||||||
\(124\) | 10.1919 | 0.915260 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.90191 | 0.882132 | ||||||||
\(127\) | −0.0780272 | −0.00692380 | −0.00346190 | − | 0.999994i | \(-0.501102\pi\) | ||||
−0.00346190 | + | 0.999994i | \(0.501102\pi\) | |||||||
\(128\) | −11.2179 | −0.991535 | ||||||||
\(129\) | −23.1697 | −2.03998 | ||||||||
\(130\) | 4.34751 | 0.381302 | ||||||||
\(131\) | −11.7880 | −1.02992 | −0.514960 | − | 0.857214i | \(-0.672193\pi\) | ||||
−0.514960 | + | 0.857214i | \(0.672193\pi\) | |||||||
\(132\) | 18.3342 | 1.59579 | ||||||||
\(133\) | 7.29290 | 0.632375 | ||||||||
\(134\) | 15.2211 | 1.31490 | ||||||||
\(135\) | −7.63951 | −0.657504 | ||||||||
\(136\) | 10.8624 | 0.931441 | ||||||||
\(137\) | 2.46593 | 0.210679 | 0.105339 | − | 0.994436i | \(-0.466407\pi\) | ||||
0.105339 | + | 0.994436i | \(0.466407\pi\) | |||||||
\(138\) | −40.4629 | −3.44443 | ||||||||
\(139\) | 12.0994 | 1.02626 | 0.513129 | − | 0.858312i | \(-0.328486\pi\) | ||||
0.513129 | + | 0.858312i | \(0.328486\pi\) | |||||||
\(140\) | 1.12163 | 0.0947954 | ||||||||
\(141\) | 20.5126 | 1.72747 | ||||||||
\(142\) | −25.0536 | −2.10245 | ||||||||
\(143\) | 13.7120 | 1.14665 | ||||||||
\(144\) | −27.9390 | −2.32825 | ||||||||
\(145\) | 0.282924 | 0.0234955 | ||||||||
\(146\) | 22.5359 | 1.86509 | ||||||||
\(147\) | 2.93332 | 0.241936 | ||||||||
\(148\) | 3.65029 | 0.300052 | ||||||||
\(149\) | −2.35083 | −0.192588 | −0.0962938 | − | 0.995353i | \(-0.530699\pi\) | ||||
−0.0962938 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(150\) | −5.18264 | −0.423161 | ||||||||
\(151\) | −11.8960 | −0.968086 | −0.484043 | − | 0.875044i | \(-0.660832\pi\) | ||||
−0.484043 | + | 0.875044i | \(0.660832\pi\) | |||||||
\(152\) | −11.3179 | −0.918004 | ||||||||
\(153\) | 39.2271 | 3.17132 | ||||||||
\(154\) | 9.84559 | 0.793380 | ||||||||
\(155\) | −9.08665 | −0.729857 | ||||||||
\(156\) | 8.09582 | 0.648184 | ||||||||
\(157\) | −16.0234 | −1.27880 | −0.639402 | − | 0.768873i | \(-0.720818\pi\) | ||||
−0.639402 | + | 0.768873i | \(0.720818\pi\) | |||||||
\(158\) | 19.3763 | 1.54149 | ||||||||
\(159\) | −28.1234 | −2.23033 | ||||||||
\(160\) | −5.70412 | −0.450950 | ||||||||
\(161\) | −7.80740 | −0.615309 | ||||||||
\(162\) | −9.88707 | −0.776801 | ||||||||
\(163\) | 2.75757 | 0.215989 | 0.107995 | − | 0.994151i | \(-0.465557\pi\) | ||||
0.107995 | + | 0.994151i | \(0.465557\pi\) | |||||||
\(164\) | 6.61985 | 0.516924 | ||||||||
\(165\) | −16.3460 | −1.27253 | ||||||||
\(166\) | 0.980149 | 0.0760743 | ||||||||
\(167\) | −22.0299 | −1.70472 | −0.852361 | − | 0.522953i | \(-0.824830\pi\) | ||||
−0.852361 | + | 0.522953i | \(0.824830\pi\) | |||||||
\(168\) | −4.55225 | −0.351214 | ||||||||
\(169\) | −6.94522 | −0.534248 | ||||||||
\(170\) | 12.3666 | 0.948473 | ||||||||
\(171\) | −40.8722 | −3.12558 | ||||||||
\(172\) | −8.85955 | −0.675535 | ||||||||
\(173\) | 23.7596 | 1.80641 | 0.903206 | − | 0.429207i | \(-0.141207\pi\) | ||||
0.903206 | + | 0.429207i | \(0.141207\pi\) | |||||||
\(174\) | 1.46629 | 0.111159 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −27.7801 | −2.09400 | ||||||||
\(177\) | −6.31574 | −0.474720 | ||||||||
\(178\) | −20.1809 | −1.51262 | ||||||||
\(179\) | 11.5524 | 0.863467 | 0.431734 | − | 0.902001i | \(-0.357902\pi\) | ||||
0.431734 | + | 0.902001i | \(0.357902\pi\) | |||||||
\(180\) | −6.28607 | −0.468536 | ||||||||
\(181\) | −25.8028 | −1.91791 | −0.958953 | − | 0.283565i | \(-0.908483\pi\) | ||||
−0.958953 | + | 0.283565i | \(0.908483\pi\) | |||||||
\(182\) | 4.34751 | 0.322259 | ||||||||
\(183\) | 13.2145 | 0.976843 | ||||||||
\(184\) | 12.1164 | 0.893231 | ||||||||
\(185\) | −3.25443 | −0.239271 | ||||||||
\(186\) | −47.0928 | −3.45301 | ||||||||
\(187\) | 39.0040 | 2.85225 | ||||||||
\(188\) | 7.84354 | 0.572049 | ||||||||
\(189\) | −7.63951 | −0.555692 | ||||||||
\(190\) | −12.8852 | −0.934791 | ||||||||
\(191\) | 27.0255 | 1.95549 | 0.977747 | − | 0.209786i | \(-0.0672768\pi\) | ||||
0.977747 | + | 0.209786i | \(0.0672768\pi\) | |||||||
\(192\) | −0.315942 | −0.0228012 | ||||||||
\(193\) | −8.88805 | −0.639776 | −0.319888 | − | 0.947455i | \(-0.603645\pi\) | ||||
−0.319888 | + | 0.947455i | \(0.603645\pi\) | |||||||
\(194\) | −17.1343 | −1.23017 | ||||||||
\(195\) | −7.21787 | −0.516883 | ||||||||
\(196\) | 1.12163 | 0.0801168 | ||||||||
\(197\) | −18.1670 | −1.29435 | −0.647173 | − | 0.762343i | \(-0.724049\pi\) | ||||
−0.647173 | + | 0.762343i | \(0.724049\pi\) | |||||||
\(198\) | −55.1785 | −3.92136 | ||||||||
\(199\) | −20.1135 | −1.42581 | −0.712904 | − | 0.701262i | \(-0.752620\pi\) | ||||
−0.712904 | + | 0.701262i | \(0.752620\pi\) | |||||||
\(200\) | 1.55191 | 0.109737 | ||||||||
\(201\) | −25.2706 | −1.78245 | ||||||||
\(202\) | 5.83136 | 0.410293 | ||||||||
\(203\) | 0.282924 | 0.0198574 | ||||||||
\(204\) | 23.0287 | 1.61233 | ||||||||
\(205\) | −5.90197 | −0.412211 | ||||||||
\(206\) | 20.1257 | 1.40223 | ||||||||
\(207\) | 43.7557 | 3.04123 | ||||||||
\(208\) | −12.2668 | −0.850551 | ||||||||
\(209\) | −40.6398 | −2.81111 | ||||||||
\(210\) | −5.18264 | −0.357636 | ||||||||
\(211\) | 25.6863 | 1.76832 | 0.884160 | − | 0.467183i | \(-0.154731\pi\) | ||||
0.884160 | + | 0.467183i | \(0.154731\pi\) | |||||||
\(212\) | −10.7537 | −0.738570 | ||||||||
\(213\) | 41.5948 | 2.85003 | ||||||||
\(214\) | −25.8851 | −1.76947 | ||||||||
\(215\) | 7.89879 | 0.538693 | ||||||||
\(216\) | 11.8558 | 0.806686 | ||||||||
\(217\) | −9.08665 | −0.616842 | ||||||||
\(218\) | 10.6276 | 0.719793 | ||||||||
\(219\) | −37.4148 | −2.52826 | ||||||||
\(220\) | −6.25032 | −0.421396 | ||||||||
\(221\) | 17.2230 | 1.15854 | ||||||||
\(222\) | −16.8666 | −1.13201 | ||||||||
\(223\) | 3.72658 | 0.249550 | 0.124775 | − | 0.992185i | \(-0.460179\pi\) | ||||
0.124775 | + | 0.992185i | \(0.460179\pi\) | |||||||
\(224\) | −5.70412 | −0.381122 | ||||||||
\(225\) | 5.60439 | 0.373626 | ||||||||
\(226\) | 19.3276 | 1.28566 | ||||||||
\(227\) | 10.1304 | 0.672379 | 0.336189 | − | 0.941794i | \(-0.390862\pi\) | ||||
0.336189 | + | 0.941794i | \(0.390862\pi\) | |||||||
\(228\) | −23.9945 | −1.58907 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 13.7942 | 0.909564 | ||||||||
\(231\) | −16.3460 | −1.07549 | ||||||||
\(232\) | −0.439072 | −0.0288265 | ||||||||
\(233\) | 1.22517 | 0.0802634 | 0.0401317 | − | 0.999194i | \(-0.487222\pi\) | ||||
0.0401317 | + | 0.999194i | \(0.487222\pi\) | |||||||
\(234\) | −24.3651 | −1.59280 | ||||||||
\(235\) | −6.99295 | −0.456170 | ||||||||
\(236\) | −2.41499 | −0.157203 | ||||||||
\(237\) | −32.1691 | −2.08961 | ||||||||
\(238\) | 12.3666 | 0.801606 | ||||||||
\(239\) | −25.2747 | −1.63489 | −0.817443 | − | 0.576009i | \(-0.804609\pi\) | ||||
−0.817443 | + | 0.576009i | \(0.804609\pi\) | |||||||
\(240\) | 14.6232 | 0.943925 | ||||||||
\(241\) | −2.54854 | −0.164166 | −0.0820831 | − | 0.996625i | \(-0.526157\pi\) | ||||
−0.0820831 | + | 0.996625i | \(0.526157\pi\) | |||||||
\(242\) | −35.4297 | −2.27750 | ||||||||
\(243\) | −6.50369 | −0.417212 | ||||||||
\(244\) | 5.05291 | 0.323480 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −30.5878 | −1.95021 | ||||||||
\(247\) | −17.9453 | −1.14183 | ||||||||
\(248\) | 14.1017 | 0.895456 | ||||||||
\(249\) | −1.62728 | −0.103124 | ||||||||
\(250\) | 1.76681 | 0.111743 | ||||||||
\(251\) | 4.34906 | 0.274510 | 0.137255 | − | 0.990536i | \(-0.456172\pi\) | ||||
0.137255 | + | 0.990536i | \(0.456172\pi\) | |||||||
\(252\) | −6.28607 | −0.395985 | ||||||||
\(253\) | 43.5068 | 2.73525 | ||||||||
\(254\) | 0.137860 | 0.00865009 | ||||||||
\(255\) | −20.5314 | −1.28573 | ||||||||
\(256\) | 20.0354 | 1.25221 | ||||||||
\(257\) | 16.0884 | 1.00356 | 0.501782 | − | 0.864994i | \(-0.332678\pi\) | ||||
0.501782 | + | 0.864994i | \(0.332678\pi\) | |||||||
\(258\) | 40.9366 | 2.54860 | ||||||||
\(259\) | −3.25443 | −0.202221 | ||||||||
\(260\) | −2.75995 | −0.171165 | ||||||||
\(261\) | −1.58561 | −0.0981471 | ||||||||
\(262\) | 20.8272 | 1.28671 | ||||||||
\(263\) | 15.1036 | 0.931330 | 0.465665 | − | 0.884961i | \(-0.345815\pi\) | ||||
0.465665 | + | 0.884961i | \(0.345815\pi\) | |||||||
\(264\) | 25.3674 | 1.56126 | ||||||||
\(265\) | 9.58756 | 0.588959 | ||||||||
\(266\) | −12.8852 | −0.790043 | ||||||||
\(267\) | 33.5049 | 2.05047 | ||||||||
\(268\) | −9.66289 | −0.590255 | ||||||||
\(269\) | −21.9389 | −1.33764 | −0.668820 | − | 0.743424i | \(-0.733200\pi\) | ||||
−0.668820 | + | 0.743424i | \(0.733200\pi\) | |||||||
\(270\) | 13.4976 | 0.821437 | ||||||||
\(271\) | −21.9172 | −1.33138 | −0.665689 | − | 0.746230i | \(-0.731862\pi\) | ||||
−0.665689 | + | 0.746230i | \(0.731862\pi\) | |||||||
\(272\) | −34.8932 | −2.11571 | ||||||||
\(273\) | −7.21787 | −0.436845 | ||||||||
\(274\) | −4.35685 | −0.263207 | ||||||||
\(275\) | 5.57251 | 0.336035 | ||||||||
\(276\) | 25.6873 | 1.54619 | ||||||||
\(277\) | −1.46742 | −0.0881685 | −0.0440843 | − | 0.999028i | \(-0.514037\pi\) | ||||
−0.0440843 | + | 0.999028i | \(0.514037\pi\) | |||||||
\(278\) | −21.3774 | −1.28213 | ||||||||
\(279\) | 50.9251 | 3.04881 | ||||||||
\(280\) | 1.55191 | 0.0927443 | ||||||||
\(281\) | 9.73542 | 0.580766 | 0.290383 | − | 0.956910i | \(-0.406217\pi\) | ||||
0.290383 | + | 0.956910i | \(0.406217\pi\) | |||||||
\(282\) | −36.2420 | −2.15818 | ||||||||
\(283\) | −4.69544 | −0.279115 | −0.139558 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139558 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(284\) | 15.9049 | 0.943782 | ||||||||
\(285\) | 21.3924 | 1.26718 | ||||||||
\(286\) | −24.2265 | −1.43254 | ||||||||
\(287\) | −5.90197 | −0.348382 | ||||||||
\(288\) | 31.9681 | 1.88374 | ||||||||
\(289\) | 31.9911 | 1.88183 | ||||||||
\(290\) | −0.499874 | −0.0293536 | ||||||||
\(291\) | 28.4470 | 1.66759 | ||||||||
\(292\) | −14.3066 | −0.837229 | ||||||||
\(293\) | 19.8129 | 1.15748 | 0.578740 | − | 0.815512i | \(-0.303545\pi\) | ||||
0.578740 | + | 0.815512i | \(0.303545\pi\) | |||||||
\(294\) | −5.18264 | −0.302258 | ||||||||
\(295\) | 2.15310 | 0.125358 | ||||||||
\(296\) | 5.05059 | 0.293559 | ||||||||
\(297\) | 42.5712 | 2.47023 | ||||||||
\(298\) | 4.15348 | 0.240605 | ||||||||
\(299\) | 19.2112 | 1.11101 | ||||||||
\(300\) | 3.29012 | 0.189955 | ||||||||
\(301\) | 7.89879 | 0.455279 | ||||||||
\(302\) | 21.0181 | 1.20946 | ||||||||
\(303\) | −9.68141 | −0.556182 | ||||||||
\(304\) | 36.3566 | 2.08519 | ||||||||
\(305\) | −4.50495 | −0.257953 | ||||||||
\(306\) | −69.3071 | −3.96202 | ||||||||
\(307\) | −22.2882 | −1.27206 | −0.636028 | − | 0.771666i | \(-0.719424\pi\) | ||||
−0.636028 | + | 0.771666i | \(0.719424\pi\) | |||||||
\(308\) | −6.25032 | −0.356145 | ||||||||
\(309\) | −33.4134 | −1.90082 | ||||||||
\(310\) | 16.0544 | 0.911830 | ||||||||
\(311\) | −8.81128 | −0.499642 | −0.249821 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249821 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(312\) | 11.2015 | 0.634159 | ||||||||
\(313\) | 17.5808 | 0.993724 | 0.496862 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496862 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(314\) | 28.3103 | 1.59764 | ||||||||
\(315\) | 5.60439 | 0.315771 | ||||||||
\(316\) | −12.3007 | −0.691970 | ||||||||
\(317\) | −24.6180 | −1.38269 | −0.691343 | − | 0.722526i | \(-0.742981\pi\) | ||||
−0.691343 | + | 0.722526i | \(0.742981\pi\) | |||||||
\(318\) | 49.6888 | 2.78641 | ||||||||
\(319\) | −1.57660 | −0.0882724 | ||||||||
\(320\) | 0.107708 | 0.00602106 | ||||||||
\(321\) | 42.9752 | 2.39864 | ||||||||
\(322\) | 13.7942 | 0.768722 | ||||||||
\(323\) | −51.0457 | −2.84026 | ||||||||
\(324\) | 6.27665 | 0.348703 | ||||||||
\(325\) | 2.46065 | 0.136492 | ||||||||
\(326\) | −4.87211 | −0.269841 | ||||||||
\(327\) | −17.6443 | −0.975732 | ||||||||
\(328\) | 9.15932 | 0.505739 | ||||||||
\(329\) | −6.99295 | −0.385534 | ||||||||
\(330\) | 28.8803 | 1.58981 | ||||||||
\(331\) | 17.0015 | 0.934484 | 0.467242 | − | 0.884129i | \(-0.345248\pi\) | ||||
0.467242 | + | 0.884129i | \(0.345248\pi\) | |||||||
\(332\) | −0.622232 | −0.0341494 | ||||||||
\(333\) | 18.2391 | 0.999497 | ||||||||
\(334\) | 38.9227 | 2.12976 | ||||||||
\(335\) | 8.61501 | 0.470688 | ||||||||
\(336\) | 14.6232 | 0.797762 | ||||||||
\(337\) | −6.26804 | −0.341442 | −0.170721 | − | 0.985319i | \(-0.554610\pi\) | ||||
−0.170721 | + | 0.985319i | \(0.554610\pi\) | |||||||
\(338\) | 12.2709 | 0.667450 | ||||||||
\(339\) | −32.0884 | −1.74280 | ||||||||
\(340\) | −7.85073 | −0.425765 | ||||||||
\(341\) | 50.6354 | 2.74206 | ||||||||
\(342\) | 72.2137 | 3.90487 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −12.2582 | −0.660918 | ||||||||
\(345\) | −22.9016 | −1.23298 | ||||||||
\(346\) | −41.9789 | −2.25680 | ||||||||
\(347\) | 11.0320 | 0.592230 | 0.296115 | − | 0.955152i | \(-0.404309\pi\) | ||||
0.296115 | + | 0.955152i | \(0.404309\pi\) | |||||||
\(348\) | −0.930853 | −0.0498989 | ||||||||
\(349\) | −23.9723 | −1.28321 | −0.641603 | − | 0.767037i | \(-0.721730\pi\) | ||||
−0.641603 | + | 0.767037i | \(0.721730\pi\) | |||||||
\(350\) | 1.76681 | 0.0944402 | ||||||||
\(351\) | 18.7981 | 1.00337 | ||||||||
\(352\) | 31.7862 | 1.69421 | ||||||||
\(353\) | −14.6943 | −0.782101 | −0.391051 | − | 0.920369i | \(-0.627888\pi\) | ||||
−0.391051 | + | 0.920369i | \(0.627888\pi\) | |||||||
\(354\) | 11.1587 | 0.593081 | ||||||||
\(355\) | −14.1801 | −0.752602 | ||||||||
\(356\) | 12.8115 | 0.679009 | ||||||||
\(357\) | −20.5314 | −1.08664 | ||||||||
\(358\) | −20.4110 | −1.07875 | ||||||||
\(359\) | 8.60763 | 0.454294 | 0.227147 | − | 0.973861i | \(-0.427060\pi\) | ||||
0.227147 | + | 0.973861i | \(0.427060\pi\) | |||||||
\(360\) | −8.69750 | −0.458398 | ||||||||
\(361\) | 34.1864 | 1.79929 | ||||||||
\(362\) | 45.5887 | 2.39609 | ||||||||
\(363\) | 58.8215 | 3.08733 | ||||||||
\(364\) | −2.75995 | −0.144660 | ||||||||
\(365\) | 12.7551 | 0.667633 | ||||||||
\(366\) | −23.3476 | −1.22040 | ||||||||
\(367\) | −0.831519 | −0.0434049 | −0.0217025 | − | 0.999764i | \(-0.506909\pi\) | ||||
−0.0217025 | + | 0.999764i | \(0.506909\pi\) | |||||||
\(368\) | −38.9215 | −2.02892 | ||||||||
\(369\) | 33.0769 | 1.72192 | ||||||||
\(370\) | 5.74998 | 0.298927 | ||||||||
\(371\) | 9.58756 | 0.497761 | ||||||||
\(372\) | 29.8961 | 1.55004 | ||||||||
\(373\) | 9.85102 | 0.510066 | 0.255033 | − | 0.966932i | \(-0.417914\pi\) | ||||
0.255033 | + | 0.966932i | \(0.417914\pi\) | |||||||
\(374\) | −68.9128 | −3.56340 | ||||||||
\(375\) | −2.93332 | −0.151476 | ||||||||
\(376\) | 10.8524 | 0.559671 | ||||||||
\(377\) | −0.696176 | −0.0358549 | ||||||||
\(378\) | 13.4976 | 0.694241 | ||||||||
\(379\) | 4.68612 | 0.240710 | 0.120355 | − | 0.992731i | \(-0.461597\pi\) | ||||
0.120355 | + | 0.992731i | \(0.461597\pi\) | |||||||
\(380\) | 8.17997 | 0.419624 | ||||||||
\(381\) | −0.228879 | −0.0117258 | ||||||||
\(382\) | −47.7490 | −2.44305 | ||||||||
\(383\) | 20.9263 | 1.06928 | 0.534641 | − | 0.845079i | \(-0.320447\pi\) | ||||
0.534641 | + | 0.845079i | \(0.320447\pi\) | |||||||
\(384\) | −32.9058 | −1.67922 | ||||||||
\(385\) | 5.57251 | 0.284001 | ||||||||
\(386\) | 15.7035 | 0.799289 | ||||||||
\(387\) | −44.2678 | −2.25026 | ||||||||
\(388\) | 10.8775 | 0.552219 | ||||||||
\(389\) | 12.4828 | 0.632905 | 0.316452 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316452 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(390\) | 12.7526 | 0.645755 | ||||||||
\(391\) | 54.6468 | 2.76361 | ||||||||
\(392\) | 1.55191 | 0.0783832 | ||||||||
\(393\) | −34.5779 | −1.74423 | ||||||||
\(394\) | 32.0978 | 1.61706 | ||||||||
\(395\) | 10.9668 | 0.551799 | ||||||||
\(396\) | 35.0292 | 1.76028 | ||||||||
\(397\) | 23.1029 | 1.15950 | 0.579751 | − | 0.814794i | \(-0.303150\pi\) | ||||
0.579751 | + | 0.814794i | \(0.303150\pi\) | |||||||
\(398\) | 35.5368 | 1.78130 | ||||||||
\(399\) | 21.3924 | 1.07096 | ||||||||
\(400\) | −4.98520 | −0.249260 | ||||||||
\(401\) | −0.559463 | −0.0279382 | −0.0139691 | − | 0.999902i | \(-0.504447\pi\) | ||||
−0.0139691 | + | 0.999902i | \(0.504447\pi\) | |||||||
\(402\) | 44.6485 | 2.22686 | ||||||||
\(403\) | 22.3590 | 1.11378 | ||||||||
\(404\) | −3.70195 | −0.184179 | ||||||||
\(405\) | −5.59598 | −0.278067 | ||||||||
\(406\) | −0.499874 | −0.0248083 | ||||||||
\(407\) | 18.1354 | 0.898936 | ||||||||
\(408\) | 31.8628 | 1.57745 | ||||||||
\(409\) | 17.5238 | 0.866498 | 0.433249 | − | 0.901274i | \(-0.357367\pi\) | ||||
0.433249 | + | 0.901274i | \(0.357367\pi\) | |||||||
\(410\) | 10.4277 | 0.514987 | ||||||||
\(411\) | 7.23338 | 0.356796 | ||||||||
\(412\) | −12.7765 | −0.629453 | ||||||||
\(413\) | 2.15310 | 0.105947 | ||||||||
\(414\) | −77.3082 | −3.79949 | ||||||||
\(415\) | 0.554755 | 0.0272318 | ||||||||
\(416\) | 14.0358 | 0.688162 | ||||||||
\(417\) | 35.4915 | 1.73802 | ||||||||
\(418\) | 71.8029 | 3.51200 | ||||||||
\(419\) | −30.6310 | −1.49642 | −0.748210 | − | 0.663462i | \(-0.769086\pi\) | ||||
−0.748210 | + | 0.663462i | \(0.769086\pi\) | |||||||
\(420\) | 3.29012 | 0.160541 | ||||||||
\(421\) | −4.02979 | −0.196400 | −0.0981999 | − | 0.995167i | \(-0.531308\pi\) | ||||
−0.0981999 | + | 0.995167i | \(0.531308\pi\) | |||||||
\(422\) | −45.3830 | −2.20921 | ||||||||
\(423\) | 39.1912 | 1.90554 | ||||||||
\(424\) | −14.8790 | −0.722589 | ||||||||
\(425\) | 6.99936 | 0.339519 | ||||||||
\(426\) | −73.4904 | −3.56062 | ||||||||
\(427\) | −4.50495 | −0.218010 | ||||||||
\(428\) | 16.4327 | 0.794306 | ||||||||
\(429\) | 40.2216 | 1.94192 | ||||||||
\(430\) | −13.9557 | −0.673003 | ||||||||
\(431\) | −24.0938 | −1.16056 | −0.580279 | − | 0.814418i | \(-0.697056\pi\) | ||||
−0.580279 | + | 0.814418i | \(0.697056\pi\) | |||||||
\(432\) | −38.0845 | −1.83234 | ||||||||
\(433\) | 6.12482 | 0.294340 | 0.147170 | − | 0.989111i | \(-0.452984\pi\) | ||||
0.147170 | + | 0.989111i | \(0.452984\pi\) | |||||||
\(434\) | 16.0544 | 0.770637 | ||||||||
\(435\) | 0.829907 | 0.0397910 | ||||||||
\(436\) | −6.74677 | −0.323112 | ||||||||
\(437\) | −56.9386 | −2.72374 | ||||||||
\(438\) | 66.1051 | 3.15862 | ||||||||
\(439\) | −10.8531 | −0.517990 | −0.258995 | − | 0.965879i | \(-0.583391\pi\) | ||||
−0.258995 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(440\) | −8.64802 | −0.412278 | ||||||||
\(441\) | 5.60439 | 0.266876 | ||||||||
\(442\) | −30.4298 | −1.44740 | ||||||||
\(443\) | 16.6982 | 0.793354 | 0.396677 | − | 0.917958i | \(-0.370163\pi\) | ||||
0.396677 | + | 0.917958i | \(0.370163\pi\) | |||||||
\(444\) | 10.7075 | 0.508154 | ||||||||
\(445\) | −11.4222 | −0.541463 | ||||||||
\(446\) | −6.58417 | −0.311770 | ||||||||
\(447\) | −6.89575 | −0.326158 | ||||||||
\(448\) | 0.107708 | 0.00508872 | ||||||||
\(449\) | 13.9150 | 0.656691 | 0.328345 | − | 0.944558i | \(-0.393509\pi\) | ||||
0.328345 | + | 0.944558i | \(0.393509\pi\) | |||||||
\(450\) | −9.90191 | −0.466781 | ||||||||
\(451\) | 32.8888 | 1.54867 | ||||||||
\(452\) | −12.2698 | −0.577125 | ||||||||
\(453\) | −34.8949 | −1.63951 | ||||||||
\(454\) | −17.8986 | −0.840021 | ||||||||
\(455\) | 2.46065 | 0.115357 | ||||||||
\(456\) | −33.1991 | −1.55469 | ||||||||
\(457\) | 23.5948 | 1.10372 | 0.551859 | − | 0.833937i | \(-0.313919\pi\) | ||||
0.551859 | + | 0.833937i | \(0.313919\pi\) | |||||||
\(458\) | −1.76681 | −0.0825578 | ||||||||
\(459\) | 53.4717 | 2.49584 | ||||||||
\(460\) | −8.75705 | −0.408299 | ||||||||
\(461\) | 7.28675 | 0.339378 | 0.169689 | − | 0.985498i | \(-0.445724\pi\) | ||||
0.169689 | + | 0.985498i | \(0.445724\pi\) | |||||||
\(462\) | 28.8803 | 1.34363 | ||||||||
\(463\) | −2.00582 | −0.0932182 | −0.0466091 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466091 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(464\) | 1.41043 | 0.0654777 | ||||||||
\(465\) | −26.6541 | −1.23605 | ||||||||
\(466\) | −2.16465 | −0.100275 | ||||||||
\(467\) | −13.6741 | −0.632760 | −0.316380 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316380 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(468\) | 15.4678 | 0.715000 | ||||||||
\(469\) | 8.61501 | 0.397804 | ||||||||
\(470\) | 12.3553 | 0.569905 | ||||||||
\(471\) | −47.0017 | −2.16572 | ||||||||
\(472\) | −3.34142 | −0.153801 | ||||||||
\(473\) | −44.0160 | −2.02386 | ||||||||
\(474\) | 56.8369 | 2.61061 | ||||||||
\(475\) | −7.29290 | −0.334621 | ||||||||
\(476\) | −7.85073 | −0.359837 | ||||||||
\(477\) | −53.7324 | −2.46024 | ||||||||
\(478\) | 44.6558 | 2.04251 | ||||||||
\(479\) | −15.8846 | −0.725787 | −0.362893 | − | 0.931831i | \(-0.618211\pi\) | ||||
−0.362893 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(480\) | −16.7320 | −0.763709 | ||||||||
\(481\) | 8.00801 | 0.365134 | ||||||||
\(482\) | 4.50280 | 0.205097 | ||||||||
\(483\) | −22.9016 | −1.04206 | ||||||||
\(484\) | 22.4920 | 1.02236 | ||||||||
\(485\) | −9.69786 | −0.440357 | ||||||||
\(486\) | 11.4908 | 0.521234 | ||||||||
\(487\) | 35.2183 | 1.59589 | 0.797947 | − | 0.602727i | \(-0.205919\pi\) | ||||
0.797947 | + | 0.602727i | \(0.205919\pi\) | |||||||
\(488\) | 6.99128 | 0.316480 | ||||||||
\(489\) | 8.08884 | 0.365790 | ||||||||
\(490\) | 1.76681 | 0.0798166 | ||||||||
\(491\) | 0.185421 | 0.00836795 | 0.00418398 | − | 0.999991i | \(-0.498668\pi\) | ||||
0.00418398 | + | 0.999991i | \(0.498668\pi\) | |||||||
\(492\) | 19.4182 | 0.875439 | ||||||||
\(493\) | −1.98029 | −0.0891876 | ||||||||
\(494\) | 31.7059 | 1.42652 | ||||||||
\(495\) | −31.2305 | −1.40371 | ||||||||
\(496\) | −45.2988 | −2.03398 | ||||||||
\(497\) | −14.1801 | −0.636065 | ||||||||
\(498\) | 2.87509 | 0.128836 | ||||||||
\(499\) | 15.3955 | 0.689199 | 0.344599 | − | 0.938750i | \(-0.388015\pi\) | ||||
0.344599 | + | 0.938750i | \(0.388015\pi\) | |||||||
\(500\) | −1.12163 | −0.0501610 | ||||||||
\(501\) | −64.6207 | −2.88704 | ||||||||
\(502\) | −7.68398 | −0.342953 | ||||||||
\(503\) | −12.4786 | −0.556394 | −0.278197 | − | 0.960524i | \(-0.589737\pi\) | ||||
−0.278197 | + | 0.960524i | \(0.589737\pi\) | |||||||
\(504\) | −8.69750 | −0.387417 | ||||||||
\(505\) | 3.30049 | 0.146870 | ||||||||
\(506\) | −76.8684 | −3.41722 | ||||||||
\(507\) | −20.3726 | −0.904778 | ||||||||
\(508\) | −0.0875181 | −0.00388299 | ||||||||
\(509\) | 23.9865 | 1.06318 | 0.531592 | − | 0.847001i | \(-0.321594\pi\) | ||||
0.531592 | + | 0.847001i | \(0.321594\pi\) | |||||||
\(510\) | 36.2752 | 1.60629 | ||||||||
\(511\) | 12.7551 | 0.564253 | ||||||||
\(512\) | −12.9630 | −0.572890 | ||||||||
\(513\) | −55.7142 | −2.45984 | ||||||||
\(514\) | −28.4251 | −1.25378 | ||||||||
\(515\) | 11.3910 | 0.501946 | ||||||||
\(516\) | −25.9879 | −1.14406 | ||||||||
\(517\) | 38.9683 | 1.71382 | ||||||||
\(518\) | 5.74998 | 0.252640 | ||||||||
\(519\) | 69.6947 | 3.05926 | ||||||||
\(520\) | −3.81870 | −0.167461 | ||||||||
\(521\) | 2.06211 | 0.0903427 | 0.0451713 | − | 0.998979i | \(-0.485617\pi\) | ||||
0.0451713 | + | 0.998979i | \(0.485617\pi\) | |||||||
\(522\) | 2.80149 | 0.122618 | ||||||||
\(523\) | −16.8449 | −0.736577 | −0.368288 | − | 0.929712i | \(-0.620056\pi\) | ||||
−0.368288 | + | 0.929712i | \(0.620056\pi\) | |||||||
\(524\) | −13.2218 | −0.577597 | ||||||||
\(525\) | −2.93332 | −0.128021 | ||||||||
\(526\) | −26.6853 | −1.16354 | ||||||||
\(527\) | 63.6007 | 2.77049 | ||||||||
\(528\) | −81.4880 | −3.54631 | ||||||||
\(529\) | 37.9555 | 1.65024 | ||||||||
\(530\) | −16.9394 | −0.735802 | ||||||||
\(531\) | −12.0668 | −0.523655 | ||||||||
\(532\) | 8.17997 | 0.354647 | ||||||||
\(533\) | 14.5227 | 0.629046 | ||||||||
\(534\) | −59.1970 | −2.56171 | ||||||||
\(535\) | −14.6507 | −0.633405 | ||||||||
\(536\) | −13.3697 | −0.577483 | ||||||||
\(537\) | 33.8869 | 1.46233 | ||||||||
\(538\) | 38.7620 | 1.67115 | ||||||||
\(539\) | 5.57251 | 0.240025 | ||||||||
\(540\) | −8.56873 | −0.368740 | ||||||||
\(541\) | −2.13928 | −0.0919747 | −0.0459874 | − | 0.998942i | \(-0.514643\pi\) | ||||
−0.0459874 | + | 0.998942i | \(0.514643\pi\) | |||||||
\(542\) | 38.7237 | 1.66333 | ||||||||
\(543\) | −75.6879 | −3.24808 | ||||||||
\(544\) | 39.9252 | 1.71178 | ||||||||
\(545\) | 6.01512 | 0.257660 | ||||||||
\(546\) | 12.7526 | 0.545763 | ||||||||
\(547\) | −38.9611 | −1.66585 | −0.832927 | − | 0.553382i | \(-0.813337\pi\) | ||||
−0.832927 | + | 0.553382i | \(0.813337\pi\) | |||||||
\(548\) | 2.76588 | 0.118152 | ||||||||
\(549\) | 25.2475 | 1.07754 | ||||||||
\(550\) | −9.84559 | −0.419817 | ||||||||
\(551\) | 2.06334 | 0.0879011 | ||||||||
\(552\) | 35.5412 | 1.51274 | ||||||||
\(553\) | 10.9668 | 0.466355 | ||||||||
\(554\) | 2.59265 | 0.110151 | ||||||||
\(555\) | −9.54631 | −0.405218 | ||||||||
\(556\) | 13.5711 | 0.575543 | ||||||||
\(557\) | 24.3258 | 1.03072 | 0.515359 | − | 0.856974i | \(-0.327658\pi\) | ||||
0.515359 | + | 0.856974i | \(0.327658\pi\) | |||||||
\(558\) | −89.9752 | −3.80895 | ||||||||
\(559\) | −19.4361 | −0.822060 | ||||||||
\(560\) | −4.98520 | −0.210663 | ||||||||
\(561\) | 114.411 | 4.83045 | ||||||||
\(562\) | −17.2007 | −0.725567 | ||||||||
\(563\) | 33.5731 | 1.41494 | 0.707469 | − | 0.706744i | \(-0.249837\pi\) | ||||
0.707469 | + | 0.706744i | \(0.249837\pi\) | |||||||
\(564\) | 23.0076 | 0.968796 | ||||||||
\(565\) | 10.9393 | 0.460218 | ||||||||
\(566\) | 8.29598 | 0.348706 | ||||||||
\(567\) | −5.59598 | −0.235009 | ||||||||
\(568\) | 22.0062 | 0.923361 | ||||||||
\(569\) | −7.83718 | −0.328552 | −0.164276 | − | 0.986414i | \(-0.552529\pi\) | ||||
−0.164276 | + | 0.986414i | \(0.552529\pi\) | |||||||
\(570\) | −37.7965 | −1.58312 | ||||||||
\(571\) | −27.0736 | −1.13299 | −0.566497 | − | 0.824064i | \(-0.691702\pi\) | ||||
−0.566497 | + | 0.824064i | \(0.691702\pi\) | |||||||
\(572\) | 15.3798 | 0.643063 | ||||||||
\(573\) | 79.2744 | 3.31174 | ||||||||
\(574\) | 10.4277 | 0.435243 | ||||||||
\(575\) | 7.80740 | 0.325591 | ||||||||
\(576\) | −0.603637 | −0.0251515 | ||||||||
\(577\) | 4.95258 | 0.206179 | 0.103089 | − | 0.994672i | \(-0.467127\pi\) | ||||
0.103089 | + | 0.994672i | \(0.467127\pi\) | |||||||
\(578\) | −56.5223 | −2.35102 | ||||||||
\(579\) | −26.0715 | −1.08350 | ||||||||
\(580\) | 0.317337 | 0.0131767 | ||||||||
\(581\) | 0.554755 | 0.0230151 | ||||||||
\(582\) | −50.2605 | −2.08337 | ||||||||
\(583\) | −53.4267 | −2.21271 | ||||||||
\(584\) | −19.7948 | −0.819113 | ||||||||
\(585\) | −13.7904 | −0.570163 | ||||||||
\(586\) | −35.0057 | −1.44607 | ||||||||
\(587\) | 23.0449 | 0.951163 | 0.475581 | − | 0.879672i | \(-0.342238\pi\) | ||||
0.475581 | + | 0.879672i | \(0.342238\pi\) | |||||||
\(588\) | 3.29012 | 0.135682 | ||||||||
\(589\) | −66.2681 | −2.73053 | ||||||||
\(590\) | −3.80413 | −0.156614 | ||||||||
\(591\) | −53.2897 | −2.19205 | ||||||||
\(592\) | −16.2240 | −0.666803 | ||||||||
\(593\) | 13.5697 | 0.557242 | 0.278621 | − | 0.960401i | \(-0.410123\pi\) | ||||
0.278621 | + | 0.960401i | \(0.410123\pi\) | |||||||
\(594\) | −75.2154 | −3.08613 | ||||||||
\(595\) | 6.99936 | 0.286946 | ||||||||
\(596\) | −2.63677 | −0.108006 | ||||||||
\(597\) | −58.9994 | −2.41468 | ||||||||
\(598\) | −33.9427 | −1.38802 | ||||||||
\(599\) | −33.6379 | −1.37441 | −0.687203 | − | 0.726465i | \(-0.741162\pi\) | ||||
−0.687203 | + | 0.726465i | \(0.741162\pi\) | |||||||
\(600\) | 4.55225 | 0.185845 | ||||||||
\(601\) | 38.3161 | 1.56295 | 0.781474 | − | 0.623938i | \(-0.214468\pi\) | ||||
0.781474 | + | 0.623938i | \(0.214468\pi\) | |||||||
\(602\) | −13.9557 | −0.568792 | ||||||||
\(603\) | −48.2818 | −1.96619 | ||||||||
\(604\) | −13.3430 | −0.542919 | ||||||||
\(605\) | −20.0528 | −0.815264 | ||||||||
\(606\) | 17.1053 | 0.694854 | ||||||||
\(607\) | 3.05677 | 0.124071 | 0.0620353 | − | 0.998074i | \(-0.480241\pi\) | ||||
0.0620353 | + | 0.998074i | \(0.480241\pi\) | |||||||
\(608\) | −41.5996 | −1.68709 | ||||||||
\(609\) | 0.829907 | 0.0336295 | ||||||||
\(610\) | 7.95942 | 0.322267 | ||||||||
\(611\) | 17.2072 | 0.696128 | ||||||||
\(612\) | 43.9985 | 1.77853 | ||||||||
\(613\) | 19.0380 | 0.768936 | 0.384468 | − | 0.923138i | \(-0.374385\pi\) | ||||
0.384468 | + | 0.923138i | \(0.374385\pi\) | |||||||
\(614\) | 39.3791 | 1.58921 | ||||||||
\(615\) | −17.3124 | −0.698103 | ||||||||
\(616\) | −8.64802 | −0.348439 | ||||||||
\(617\) | −1.04915 | −0.0422371 | −0.0211185 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211185 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(618\) | 59.0353 | 2.37475 | ||||||||
\(619\) | 2.01296 | 0.0809076 | 0.0404538 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404538 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(620\) | −10.1919 | −0.409317 | ||||||||
\(621\) | 59.6447 | 2.39346 | ||||||||
\(622\) | 15.5679 | 0.624216 | ||||||||
\(623\) | −11.4222 | −0.457620 | ||||||||
\(624\) | −35.9826 | −1.44046 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −31.0620 | −1.24149 | ||||||||
\(627\) | −119.210 | −4.76077 | ||||||||
\(628\) | −17.9724 | −0.717175 | ||||||||
\(629\) | 22.7790 | 0.908257 | ||||||||
\(630\) | −9.90191 | −0.394502 | ||||||||
\(631\) | −19.6968 | −0.784117 | −0.392059 | − | 0.919940i | \(-0.628237\pi\) | ||||
−0.392059 | + | 0.919940i | \(0.628237\pi\) | |||||||
\(632\) | −17.0195 | −0.676998 | ||||||||
\(633\) | 75.3463 | 2.99475 | ||||||||
\(634\) | 43.4955 | 1.72743 | ||||||||
\(635\) | 0.0780272 | 0.00309642 | ||||||||
\(636\) | −31.5442 | −1.25081 | ||||||||
\(637\) | 2.46065 | 0.0974944 | ||||||||
\(638\) | 2.78555 | 0.110281 | ||||||||
\(639\) | 79.4708 | 3.14381 | ||||||||
\(640\) | 11.2179 | 0.443428 | ||||||||
\(641\) | −8.70703 | −0.343907 | −0.171954 | − | 0.985105i | \(-0.555008\pi\) | ||||
−0.171954 | + | 0.985105i | \(0.555008\pi\) | |||||||
\(642\) | −75.9293 | −2.99669 | ||||||||
\(643\) | 17.7885 | 0.701511 | 0.350756 | − | 0.936467i | \(-0.385925\pi\) | ||||
0.350756 | + | 0.936467i | \(0.385925\pi\) | |||||||
\(644\) | −8.75705 | −0.345076 | ||||||||
\(645\) | 23.1697 | 0.912306 | ||||||||
\(646\) | 90.1882 | 3.54841 | ||||||||
\(647\) | −31.1355 | −1.22406 | −0.612032 | − | 0.790833i | \(-0.709648\pi\) | ||||
−0.612032 | + | 0.790833i | \(0.709648\pi\) | |||||||
\(648\) | 8.68445 | 0.341158 | ||||||||
\(649\) | −11.9982 | −0.470969 | ||||||||
\(650\) | −4.34751 | −0.170523 | ||||||||
\(651\) | −26.6541 | −1.04466 | ||||||||
\(652\) | 3.09298 | 0.121131 | ||||||||
\(653\) | −11.9099 | −0.466069 | −0.233035 | − | 0.972468i | \(-0.574866\pi\) | ||||
−0.233035 | + | 0.972468i | \(0.574866\pi\) | |||||||
\(654\) | 31.1742 | 1.21901 | ||||||||
\(655\) | 11.7880 | 0.460594 | ||||||||
\(656\) | −29.4225 | −1.14876 | ||||||||
\(657\) | −71.4845 | −2.78888 | ||||||||
\(658\) | 12.3553 | 0.481658 | ||||||||
\(659\) | −12.2728 | −0.478079 | −0.239040 | − | 0.971010i | \(-0.576833\pi\) | ||||
−0.239040 | + | 0.971010i | \(0.576833\pi\) | |||||||
\(660\) | −18.3342 | −0.713658 | ||||||||
\(661\) | 21.5059 | 0.836481 | 0.418240 | − | 0.908336i | \(-0.362647\pi\) | ||||
0.418240 | + | 0.908336i | \(0.362647\pi\) | |||||||
\(662\) | −30.0384 | −1.16748 | ||||||||
\(663\) | 50.5205 | 1.96205 | ||||||||
\(664\) | −0.860929 | −0.0334105 | ||||||||
\(665\) | −7.29290 | −0.282807 | ||||||||
\(666\) | −32.2251 | −1.24870 | ||||||||
\(667\) | −2.20890 | −0.0855289 | ||||||||
\(668\) | −24.7095 | −0.956038 | ||||||||
\(669\) | 10.9313 | 0.422627 | ||||||||
\(670\) | −15.2211 | −0.588043 | ||||||||
\(671\) | 25.1039 | 0.969125 | ||||||||
\(672\) | −16.7320 | −0.645452 | ||||||||
\(673\) | −15.2023 | −0.586006 | −0.293003 | − | 0.956111i | \(-0.594655\pi\) | ||||
−0.293003 | + | 0.956111i | \(0.594655\pi\) | |||||||
\(674\) | 11.0745 | 0.426572 | ||||||||
\(675\) | 7.63951 | 0.294045 | ||||||||
\(676\) | −7.79000 | −0.299615 | ||||||||
\(677\) | 28.2617 | 1.08618 | 0.543092 | − | 0.839673i | \(-0.317253\pi\) | ||||
0.543092 | + | 0.839673i | \(0.317253\pi\) | |||||||
\(678\) | 56.6942 | 2.17733 | ||||||||
\(679\) | −9.69786 | −0.372170 | ||||||||
\(680\) | −10.8624 | −0.416553 | ||||||||
\(681\) | 29.7158 | 1.13871 | ||||||||
\(682\) | −89.4634 | −3.42573 | ||||||||
\(683\) | −21.5966 | −0.826372 | −0.413186 | − | 0.910647i | \(-0.635584\pi\) | ||||
−0.413186 | + | 0.910647i | \(0.635584\pi\) | |||||||
\(684\) | −45.8437 | −1.75288 | ||||||||
\(685\) | −2.46593 | −0.0942185 | ||||||||
\(686\) | 1.76681 | 0.0674573 | ||||||||
\(687\) | 2.93332 | 0.111913 | ||||||||
\(688\) | 39.3771 | 1.50124 | ||||||||
\(689\) | −23.5916 | −0.898768 | ||||||||
\(690\) | 40.4629 | 1.54040 | ||||||||
\(691\) | 2.53457 | 0.0964197 | 0.0482098 | − | 0.998837i | \(-0.484648\pi\) | ||||
0.0482098 | + | 0.998837i | \(0.484648\pi\) | |||||||
\(692\) | 26.6496 | 1.01307 | ||||||||
\(693\) | −31.2305 | −1.18635 | ||||||||
\(694\) | −19.4916 | −0.739889 | ||||||||
\(695\) | −12.0994 | −0.458957 | ||||||||
\(696\) | −1.28794 | −0.0488193 | ||||||||
\(697\) | 41.3100 | 1.56473 | ||||||||
\(698\) | 42.3546 | 1.60314 | ||||||||
\(699\) | 3.59381 | 0.135931 | ||||||||
\(700\) | −1.12163 | −0.0423938 | ||||||||
\(701\) | −34.1597 | −1.29019 | −0.645097 | − | 0.764100i | \(-0.723183\pi\) | ||||
−0.645097 | + | 0.764100i | \(0.723183\pi\) | |||||||
\(702\) | −33.2128 | −1.25354 | ||||||||
\(703\) | −23.7343 | −0.895155 | ||||||||
\(704\) | −0.600203 | −0.0226210 | ||||||||
\(705\) | −20.5126 | −0.772549 | ||||||||
\(706\) | 25.9622 | 0.977100 | ||||||||
\(707\) | 3.30049 | 0.124128 | ||||||||
\(708\) | −7.08396 | −0.266231 | ||||||||
\(709\) | −32.1055 | −1.20575 | −0.602875 | − | 0.797836i | \(-0.705978\pi\) | ||||
−0.602875 | + | 0.797836i | \(0.705978\pi\) | |||||||
\(710\) | 25.0536 | 0.940245 | ||||||||
\(711\) | −61.4621 | −2.30501 | ||||||||
\(712\) | 17.7262 | 0.664317 | ||||||||
\(713\) | 70.9431 | 2.65684 | ||||||||
\(714\) | 36.2752 | 1.35756 | ||||||||
\(715\) | −13.7120 | −0.512799 | ||||||||
\(716\) | 12.9576 | 0.484247 | ||||||||
\(717\) | −74.1390 | −2.76877 | ||||||||
\(718\) | −15.2081 | −0.567561 | ||||||||
\(719\) | 8.31992 | 0.310280 | 0.155140 | − | 0.987892i | \(-0.450417\pi\) | ||||
0.155140 | + | 0.987892i | \(0.450417\pi\) | |||||||
\(720\) | 27.9390 | 1.04123 | ||||||||
\(721\) | 11.3910 | 0.424222 | ||||||||
\(722\) | −60.4011 | −2.24790 | ||||||||
\(723\) | −7.47570 | −0.278024 | ||||||||
\(724\) | −28.9413 | −1.07560 | ||||||||
\(725\) | −0.282924 | −0.0105075 | ||||||||
\(726\) | −103.927 | −3.85708 | ||||||||
\(727\) | 9.85286 | 0.365422 | 0.182711 | − | 0.983167i | \(-0.441513\pi\) | ||||
0.182711 | + | 0.983167i | \(0.441513\pi\) | |||||||
\(728\) | −3.81870 | −0.141530 | ||||||||
\(729\) | −35.8654 | −1.32835 | ||||||||
\(730\) | −22.5359 | −0.834091 | ||||||||
\(731\) | −55.2865 | −2.04484 | ||||||||
\(732\) | 14.8218 | 0.547830 | ||||||||
\(733\) | 18.2883 | 0.675494 | 0.337747 | − | 0.941237i | \(-0.390335\pi\) | ||||
0.337747 | + | 0.941237i | \(0.390335\pi\) | |||||||
\(734\) | 1.46914 | 0.0542270 | ||||||||
\(735\) | −2.93332 | −0.108197 | ||||||||
\(736\) | 44.5343 | 1.64156 | ||||||||
\(737\) | −48.0072 | −1.76837 | ||||||||
\(738\) | −58.4408 | −2.15124 | ||||||||
\(739\) | 33.3823 | 1.22799 | 0.613994 | − | 0.789311i | \(-0.289562\pi\) | ||||
0.613994 | + | 0.789311i | \(0.289562\pi\) | |||||||
\(740\) | −3.65029 | −0.134187 | ||||||||
\(741\) | −52.6392 | −1.93375 | ||||||||
\(742\) | −16.9394 | −0.621866 | ||||||||
\(743\) | −11.9424 | −0.438123 | −0.219062 | − | 0.975711i | \(-0.570300\pi\) | ||||
−0.219062 | + | 0.975711i | \(0.570300\pi\) | |||||||
\(744\) | 41.3647 | 1.51650 | ||||||||
\(745\) | 2.35083 | 0.0861278 | ||||||||
\(746\) | −17.4049 | −0.637239 | ||||||||
\(747\) | −3.10906 | −0.113755 | ||||||||
\(748\) | 43.7482 | 1.59959 | ||||||||
\(749\) | −14.6507 | −0.535325 | ||||||||
\(750\) | 5.18264 | 0.189243 | ||||||||
\(751\) | −8.69916 | −0.317437 | −0.158718 | − | 0.987324i | \(-0.550736\pi\) | ||||
−0.158718 | + | 0.987324i | \(0.550736\pi\) | |||||||
\(752\) | −34.8613 | −1.27126 | ||||||||
\(753\) | 12.7572 | 0.464898 | ||||||||
\(754\) | 1.23001 | 0.0447944 | ||||||||
\(755\) | 11.8960 | 0.432941 | ||||||||
\(756\) | −8.56873 | −0.311642 | ||||||||
\(757\) | −19.9289 | −0.724327 | −0.362164 | − | 0.932115i | \(-0.617962\pi\) | ||||
−0.362164 | + | 0.932115i | \(0.617962\pi\) | |||||||
\(758\) | −8.27950 | −0.300725 | ||||||||
\(759\) | 127.619 | 4.63229 | ||||||||
\(760\) | 11.3179 | 0.410544 | ||||||||
\(761\) | −22.0167 | −0.798104 | −0.399052 | − | 0.916928i | \(-0.630661\pi\) | ||||
−0.399052 | + | 0.916928i | \(0.630661\pi\) | |||||||
\(762\) | 0.404387 | 0.0146494 | ||||||||
\(763\) | 6.01512 | 0.217762 | ||||||||
\(764\) | 30.3127 | 1.09668 | ||||||||
\(765\) | −39.2271 | −1.41826 | ||||||||
\(766\) | −36.9728 | −1.33588 | ||||||||
\(767\) | −5.29802 | −0.191300 | ||||||||
\(768\) | 58.7704 | 2.12069 | ||||||||
\(769\) | 10.3014 | 0.371477 | 0.185738 | − | 0.982599i | \(-0.440532\pi\) | ||||
0.185738 | + | 0.982599i | \(0.440532\pi\) | |||||||
\(770\) | −9.84559 | −0.354810 | ||||||||
\(771\) | 47.1923 | 1.69959 | ||||||||
\(772\) | −9.96914 | −0.358797 | ||||||||
\(773\) | 1.42750 | 0.0513435 | 0.0256717 | − | 0.999670i | \(-0.491828\pi\) | ||||
0.0256717 | + | 0.999670i | \(0.491828\pi\) | |||||||
\(774\) | 78.2131 | 2.81131 | ||||||||
\(775\) | 9.08665 | 0.326402 | ||||||||
\(776\) | 15.0502 | 0.540270 | ||||||||
\(777\) | −9.54631 | −0.342472 | ||||||||
\(778\) | −22.0549 | −0.790705 | ||||||||
\(779\) | −43.0425 | −1.54216 | ||||||||
\(780\) | −8.09582 | −0.289877 | ||||||||
\(781\) | 79.0187 | 2.82751 | ||||||||
\(782\) | −96.5508 | −3.45265 | ||||||||
\(783\) | −2.16140 | −0.0772421 | ||||||||
\(784\) | −4.98520 | −0.178043 | ||||||||
\(785\) | 16.0234 | 0.571898 | ||||||||
\(786\) | 61.0928 | 2.17911 | ||||||||
\(787\) | 53.7310 | 1.91530 | 0.957652 | − | 0.287927i | \(-0.0929660\pi\) | ||||
0.957652 | + | 0.287927i | \(0.0929660\pi\) | |||||||
\(788\) | −20.3768 | −0.725892 | ||||||||
\(789\) | 44.3039 | 1.57726 | ||||||||
\(790\) | −19.3763 | −0.689377 | ||||||||
\(791\) | 10.9393 | 0.388955 | ||||||||
\(792\) | 48.4669 | 1.72219 | ||||||||
\(793\) | 11.0851 | 0.393643 | ||||||||
\(794\) | −40.8185 | −1.44860 | ||||||||
\(795\) | 28.1234 | 0.997434 | ||||||||
\(796\) | −22.5600 | −0.799618 | ||||||||
\(797\) | −38.5582 | −1.36580 | −0.682900 | − | 0.730512i | \(-0.739282\pi\) | ||||
−0.682900 | + | 0.730512i | \(0.739282\pi\) | |||||||
\(798\) | −37.7965 | −1.33798 | ||||||||
\(799\) | 48.9462 | 1.73159 | ||||||||
\(800\) | 5.70412 | 0.201671 | ||||||||
\(801\) | 64.0143 | 2.26183 | ||||||||
\(802\) | 0.988467 | 0.0349040 | ||||||||
\(803\) | −71.0779 | −2.50829 | ||||||||
\(804\) | −28.3444 | −0.999629 | ||||||||
\(805\) | 7.80740 | 0.275175 | ||||||||
\(806\) | −39.5043 | −1.39148 | ||||||||
\(807\) | −64.3540 | −2.26537 | ||||||||
\(808\) | −5.12206 | −0.180194 | ||||||||
\(809\) | 8.74409 | 0.307426 | 0.153713 | − | 0.988116i | \(-0.450877\pi\) | ||||
0.153713 | + | 0.988116i | \(0.450877\pi\) | |||||||
\(810\) | 9.88707 | 0.347396 | ||||||||
\(811\) | −6.36588 | −0.223536 | −0.111768 | − | 0.993734i | \(-0.535651\pi\) | ||||
−0.111768 | + | 0.993734i | \(0.535651\pi\) | |||||||
\(812\) | 0.317337 | 0.0111364 | ||||||||
\(813\) | −64.2903 | −2.25476 | ||||||||
\(814\) | −32.0418 | −1.12307 | ||||||||
\(815\) | −2.75757 | −0.0965934 | ||||||||
\(816\) | −102.353 | −3.58308 | ||||||||
\(817\) | 57.6051 | 2.01535 | ||||||||
\(818\) | −30.9614 | −1.08254 | ||||||||
\(819\) | −13.7904 | −0.481876 | ||||||||
\(820\) | −6.61985 | −0.231175 | ||||||||
\(821\) | −28.5401 | −0.996057 | −0.498028 | − | 0.867161i | \(-0.665942\pi\) | ||||
−0.498028 | + | 0.867161i | \(0.665942\pi\) | |||||||
\(822\) | −12.7800 | −0.445755 | ||||||||
\(823\) | 29.1255 | 1.01525 | 0.507626 | − | 0.861578i | \(-0.330523\pi\) | ||||
0.507626 | + | 0.861578i | \(0.330523\pi\) | |||||||
\(824\) | −17.6777 | −0.615833 | ||||||||
\(825\) | 16.3460 | 0.569093 | ||||||||
\(826\) | −3.80413 | −0.132363 | ||||||||
\(827\) | −31.5453 | −1.09694 | −0.548468 | − | 0.836172i | \(-0.684789\pi\) | ||||
−0.548468 | + | 0.836172i | \(0.684789\pi\) | |||||||
\(828\) | 49.0779 | 1.70557 | ||||||||
\(829\) | 21.9470 | 0.762251 | 0.381126 | − | 0.924523i | \(-0.375537\pi\) | ||||
0.381126 | + | 0.924523i | \(0.375537\pi\) | |||||||
\(830\) | −0.980149 | −0.0340215 | ||||||||
\(831\) | −4.30441 | −0.149318 | ||||||||
\(832\) | −0.265031 | −0.00918830 | ||||||||
\(833\) | 6.99936 | 0.242513 | ||||||||
\(834\) | −62.7068 | −2.17136 | ||||||||
\(835\) | 22.0299 | 0.762375 | ||||||||
\(836\) | −45.5830 | −1.57652 | ||||||||
\(837\) | 69.4175 | 2.39942 | ||||||||
\(838\) | 54.1192 | 1.86952 | ||||||||
\(839\) | 13.1665 | 0.454558 | 0.227279 | − | 0.973830i | \(-0.427017\pi\) | ||||
0.227279 | + | 0.973830i | \(0.427017\pi\) | |||||||
\(840\) | 4.55225 | 0.157068 | ||||||||
\(841\) | −28.9200 | −0.997240 | ||||||||
\(842\) | 7.11989 | 0.245368 | ||||||||
\(843\) | 28.5571 | 0.983560 | ||||||||
\(844\) | 28.8107 | 0.991705 | ||||||||
\(845\) | 6.94522 | 0.238923 | ||||||||
\(846\) | −69.2436 | −2.38064 | ||||||||
\(847\) | −20.0528 | −0.689024 | ||||||||
\(848\) | 47.7959 | 1.64132 | ||||||||
\(849\) | −13.7733 | −0.472697 | ||||||||
\(850\) | −12.3666 | −0.424170 | ||||||||
\(851\) | 25.4087 | 0.870998 | ||||||||
\(852\) | 46.6542 | 1.59835 | ||||||||
\(853\) | 9.97282 | 0.341463 | 0.170731 | − | 0.985318i | \(-0.445387\pi\) | ||||
0.170731 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(854\) | 7.95942 | 0.272366 | ||||||||
\(855\) | 40.8722 | 1.39780 | ||||||||
\(856\) | 22.7366 | 0.777119 | ||||||||
\(857\) | −13.1891 | −0.450533 | −0.225266 | − | 0.974297i | \(-0.572325\pi\) | ||||
−0.225266 | + | 0.974297i | \(0.572325\pi\) | |||||||
\(858\) | −71.0642 | −2.42609 | ||||||||
\(859\) | 1.16310 | 0.0396844 | 0.0198422 | − | 0.999803i | \(-0.493684\pi\) | ||||
0.0198422 | + | 0.999803i | \(0.493684\pi\) | |||||||
\(860\) | 8.85955 | 0.302108 | ||||||||
\(861\) | −17.3124 | −0.590005 | ||||||||
\(862\) | 42.5693 | 1.44992 | ||||||||
\(863\) | 55.1620 | 1.87774 | 0.938868 | − | 0.344278i | \(-0.111876\pi\) | ||||
0.938868 | + | 0.344278i | \(0.111876\pi\) | |||||||
\(864\) | 43.5766 | 1.48251 | ||||||||
\(865\) | −23.7596 | −0.807852 | ||||||||
\(866\) | −10.8214 | −0.367727 | ||||||||
\(867\) | 93.8401 | 3.18698 | ||||||||
\(868\) | −10.1919 | −0.345936 | ||||||||
\(869\) | −61.1125 | −2.07310 | ||||||||
\(870\) | −1.46629 | −0.0497120 | ||||||||
\(871\) | −21.1985 | −0.718283 | ||||||||
\(872\) | −9.33492 | −0.316120 | ||||||||
\(873\) | 54.3505 | 1.83949 | ||||||||
\(874\) | 100.600 | 3.40284 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −41.9658 | −1.41789 | ||||||||
\(877\) | −8.97353 | −0.303015 | −0.151507 | − | 0.988456i | \(-0.548413\pi\) | ||||
−0.151507 | + | 0.988456i | \(0.548413\pi\) | |||||||
\(878\) | 19.1754 | 0.647139 | ||||||||
\(879\) | 58.1175 | 1.96026 | ||||||||
\(880\) | 27.7801 | 0.936467 | ||||||||
\(881\) | 52.7878 | 1.77847 | 0.889233 | − | 0.457454i | \(-0.151239\pi\) | ||||
0.889233 | + | 0.457454i | \(0.151239\pi\) | |||||||
\(882\) | −9.90191 | −0.333415 | ||||||||
\(883\) | 7.46113 | 0.251087 | 0.125544 | − | 0.992088i | \(-0.459933\pi\) | ||||
0.125544 | + | 0.992088i | \(0.459933\pi\) | |||||||
\(884\) | 19.3179 | 0.649730 | ||||||||
\(885\) | 6.31574 | 0.212301 | ||||||||
\(886\) | −29.5026 | −0.991158 | ||||||||
\(887\) | 5.05704 | 0.169799 | 0.0848995 | − | 0.996390i | \(-0.472943\pi\) | ||||
0.0848995 | + | 0.996390i | \(0.472943\pi\) | |||||||
\(888\) | 14.8150 | 0.497159 | ||||||||
\(889\) | 0.0780272 | 0.00261695 | ||||||||
\(890\) | 20.1809 | 0.676464 | ||||||||
\(891\) | 31.1837 | 1.04469 | ||||||||
\(892\) | 4.17986 | 0.139952 | ||||||||
\(893\) | −50.9989 | −1.70661 | ||||||||
\(894\) | 12.1835 | 0.407478 | ||||||||
\(895\) | −11.5524 | −0.386154 | ||||||||
\(896\) | 11.2179 | 0.374765 | ||||||||
\(897\) | 56.3528 | 1.88156 | ||||||||
\(898\) | −24.5853 | −0.820421 | ||||||||
\(899\) | −2.57083 | −0.0857420 | ||||||||
\(900\) | 6.28607 | 0.209536 | ||||||||
\(901\) | −67.1068 | −2.23565 | ||||||||
\(902\) | −58.1084 | −1.93480 | ||||||||
\(903\) | 23.1697 | 0.771039 | ||||||||
\(904\) | −16.9767 | −0.564638 | ||||||||
\(905\) | 25.8028 | 0.857714 | ||||||||
\(906\) | 61.6529 | 2.04828 | ||||||||
\(907\) | −21.4264 | −0.711453 | −0.355726 | − | 0.934590i | \(-0.615767\pi\) | ||||
−0.355726 | + | 0.934590i | \(0.615767\pi\) | |||||||
\(908\) | 11.3626 | 0.377082 | ||||||||
\(909\) | −18.4972 | −0.613514 | ||||||||
\(910\) | −4.34751 | −0.144118 | ||||||||
\(911\) | 11.2098 | 0.371398 | 0.185699 | − | 0.982607i | \(-0.440545\pi\) | ||||
0.185699 | + | 0.982607i | \(0.440545\pi\) | |||||||
\(912\) | 106.646 | 3.53139 | ||||||||
\(913\) | −3.09138 | −0.102310 | ||||||||
\(914\) | −41.6877 | −1.37891 | ||||||||
\(915\) | −13.2145 | −0.436857 | ||||||||
\(916\) | 1.12163 | 0.0370599 | ||||||||
\(917\) | 11.7880 | 0.389273 | ||||||||
\(918\) | −94.4745 | −3.11812 | ||||||||
\(919\) | 33.1011 | 1.09191 | 0.545953 | − | 0.837816i | \(-0.316168\pi\) | ||||
0.545953 | + | 0.837816i | \(0.316168\pi\) | |||||||
\(920\) | −12.1164 | −0.399465 | ||||||||
\(921\) | −65.3785 | −2.15430 | ||||||||
\(922\) | −12.8743 | −0.423994 | ||||||||
\(923\) | 34.8922 | 1.14849 | ||||||||
\(924\) | −18.3342 | −0.603151 | ||||||||
\(925\) | 3.25443 | 0.107005 | ||||||||
\(926\) | 3.54391 | 0.116460 | ||||||||
\(927\) | −63.8394 | −2.09676 | ||||||||
\(928\) | −1.61383 | −0.0529766 | ||||||||
\(929\) | 20.2164 | 0.663278 | 0.331639 | − | 0.943406i | \(-0.392398\pi\) | ||||
0.331639 | + | 0.943406i | \(0.392398\pi\) | |||||||
\(930\) | 47.0928 | 1.54423 | ||||||||
\(931\) | −7.29290 | −0.239015 | ||||||||
\(932\) | 1.37419 | 0.0450131 | ||||||||
\(933\) | −25.8463 | −0.846171 | ||||||||
\(934\) | 24.1595 | 0.790524 | ||||||||
\(935\) | −39.0040 | −1.27557 | ||||||||
\(936\) | 21.4015 | 0.699529 | ||||||||
\(937\) | 1.88144 | 0.0614639 | 0.0307319 | − | 0.999528i | \(-0.490216\pi\) | ||||
0.0307319 | + | 0.999528i | \(0.490216\pi\) | |||||||
\(938\) | −15.2211 | −0.496987 | ||||||||
\(939\) | 51.5701 | 1.68293 | ||||||||
\(940\) | −7.84354 | −0.255828 | ||||||||
\(941\) | −16.9898 | −0.553851 | −0.276925 | − | 0.960891i | \(-0.589316\pi\) | ||||
−0.276925 | + | 0.960891i | \(0.589316\pi\) | |||||||
\(942\) | 83.0433 | 2.70570 | ||||||||
\(943\) | 46.0790 | 1.50054 | ||||||||
\(944\) | 10.7337 | 0.349351 | ||||||||
\(945\) | 7.63951 | 0.248513 | ||||||||
\(946\) | 77.7682 | 2.52846 | ||||||||
\(947\) | 19.4492 | 0.632013 | 0.316007 | − | 0.948757i | \(-0.397658\pi\) | ||||
0.316007 | + | 0.948757i | \(0.397658\pi\) | |||||||
\(948\) | −36.0820 | −1.17189 | ||||||||
\(949\) | −31.3858 | −1.01883 | ||||||||
\(950\) | 12.8852 | 0.418051 | ||||||||
\(951\) | −72.2127 | −2.34166 | ||||||||
\(952\) | −10.8624 | −0.352051 | ||||||||
\(953\) | 15.6168 | 0.505877 | 0.252939 | − | 0.967482i | \(-0.418603\pi\) | ||||
0.252939 | + | 0.967482i | \(0.418603\pi\) | |||||||
\(954\) | 94.9351 | 3.07364 | ||||||||
\(955\) | −27.0255 | −0.874524 | ||||||||
\(956\) | −28.3490 | −0.916873 | ||||||||
\(957\) | −4.62466 | −0.149494 | ||||||||
\(958\) | 28.0652 | 0.906745 | ||||||||
\(959\) | −2.46593 | −0.0796292 | ||||||||
\(960\) | 0.315942 | 0.0101970 | ||||||||
\(961\) | 51.5672 | 1.66346 | ||||||||
\(962\) | −14.1487 | −0.456172 | ||||||||
\(963\) | 82.1082 | 2.64590 | ||||||||
\(964\) | −2.85853 | −0.0920672 | ||||||||
\(965\) | 8.88805 | 0.286116 | ||||||||
\(966\) | 40.4629 | 1.30187 | ||||||||
\(967\) | 6.17907 | 0.198705 | 0.0993527 | − | 0.995052i | \(-0.468323\pi\) | ||||
0.0993527 | + | 0.995052i | \(0.468323\pi\) | |||||||
\(968\) | 31.1202 | 1.00024 | ||||||||
\(969\) | −149.733 | −4.81013 | ||||||||
\(970\) | 17.1343 | 0.550150 | ||||||||
\(971\) | −42.0542 | −1.34958 | −0.674791 | − | 0.738008i | \(-0.735766\pi\) | ||||
−0.674791 | + | 0.738008i | \(0.735766\pi\) | |||||||
\(972\) | −7.29476 | −0.233980 | ||||||||
\(973\) | −12.0994 | −0.387889 | ||||||||
\(974\) | −62.2243 | −1.99379 | ||||||||
\(975\) | 7.21787 | 0.231157 | ||||||||
\(976\) | −22.4581 | −0.718867 | ||||||||
\(977\) | −1.79994 | −0.0575851 | −0.0287925 | − | 0.999585i | \(-0.509166\pi\) | ||||
−0.0287925 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(978\) | −14.2915 | −0.456991 | ||||||||
\(979\) | 63.6502 | 2.03427 | ||||||||
\(980\) | −1.12163 | −0.0358293 | ||||||||
\(981\) | −33.7111 | −1.07631 | ||||||||
\(982\) | −0.327605 | −0.0104543 | ||||||||
\(983\) | 3.13320 | 0.0999336 | 0.0499668 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499668 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(984\) | 26.8672 | 0.856496 | ||||||||
\(985\) | 18.1670 | 0.578849 | ||||||||
\(986\) | 3.49880 | 0.111424 | ||||||||
\(987\) | −20.5126 | −0.652923 | ||||||||
\(988\) | −20.1280 | −0.640358 | ||||||||
\(989\) | −61.6690 | −1.96096 | ||||||||
\(990\) | 55.1785 | 1.75369 | ||||||||
\(991\) | 8.04171 | 0.255453 | 0.127727 | − | 0.991809i | \(-0.459232\pi\) | ||||
0.127727 | + | 0.991809i | \(0.459232\pi\) | |||||||
\(992\) | 51.8313 | 1.64565 | ||||||||
\(993\) | 49.8708 | 1.58260 | ||||||||
\(994\) | 25.0536 | 0.794652 | ||||||||
\(995\) | 20.1135 | 0.637641 | ||||||||
\(996\) | −1.82521 | −0.0578339 | ||||||||
\(997\) | 36.6604 | 1.16105 | 0.580523 | − | 0.814244i | \(-0.302848\pi\) | ||||
0.580523 | + | 0.814244i | \(0.302848\pi\) | |||||||
\(998\) | −27.2011 | −0.861035 | ||||||||
\(999\) | 24.8623 | 0.786607 |
(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 | 8015.2.a.l.1.14 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.14 | ✓ | 62 | 1.1 | even | 1 | trivial |