Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.04552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.40760 | −1.39003 | −0.695015 | − | 0.718995i | \(-0.744603\pi\) | ||||
−0.695015 | + | 0.718995i | \(0.744603\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.76144 | 0.787739 | 0.393870 | − | 0.919166i | \(-0.371136\pi\) | ||||
0.393870 | + | 0.919166i | \(0.371136\pi\) | |||||||
\(6\) | 2.40760 | 0.982900 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.79656 | 0.932186 | ||||||||
\(10\) | −1.76144 | −0.557016 | ||||||||
\(11\) | 1.18414 | 0.357033 | 0.178516 | − | 0.983937i | \(-0.442870\pi\) | ||||
0.178516 | + | 0.983937i | \(0.442870\pi\) | |||||||
\(12\) | −2.40760 | −0.695015 | ||||||||
\(13\) | −0.361568 | −0.100281 | −0.0501404 | − | 0.998742i | \(-0.515967\pi\) | ||||
−0.0501404 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −4.24085 | −1.09498 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.54532 | 0.859868 | 0.429934 | − | 0.902860i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902860i | \(0.358537\pi\) | |||||||
\(18\) | −2.79656 | −0.659155 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.76144 | 0.393870 | ||||||||
\(21\) | 2.40760 | 0.525382 | ||||||||
\(22\) | −1.18414 | −0.252460 | ||||||||
\(23\) | −2.87691 | −0.599877 | −0.299938 | − | 0.953959i | \(-0.596966\pi\) | ||||
−0.299938 | + | 0.953959i | \(0.596966\pi\) | |||||||
\(24\) | 2.40760 | 0.491450 | ||||||||
\(25\) | −1.89733 | −0.379467 | ||||||||
\(26\) | 0.361568 | 0.0709093 | ||||||||
\(27\) | 0.489807 | 0.0942634 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −5.10308 | −0.947618 | −0.473809 | − | 0.880628i | \(-0.657121\pi\) | ||||
−0.473809 | + | 0.880628i | \(0.657121\pi\) | |||||||
\(30\) | 4.24085 | 0.774269 | ||||||||
\(31\) | 1.38152 | 0.248129 | 0.124064 | − | 0.992274i | \(-0.460407\pi\) | ||||
0.124064 | + | 0.992274i | \(0.460407\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.85095 | −0.496286 | ||||||||
\(34\) | −3.54532 | −0.608018 | ||||||||
\(35\) | −1.76144 | −0.297737 | ||||||||
\(36\) | 2.79656 | 0.466093 | ||||||||
\(37\) | 3.35526 | 0.551602 | 0.275801 | − | 0.961215i | \(-0.411057\pi\) | ||||
0.275801 | + | 0.961215i | \(0.411057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.870512 | 0.139394 | ||||||||
\(40\) | −1.76144 | −0.278508 | ||||||||
\(41\) | −10.0120 | −1.56361 | −0.781803 | − | 0.623526i | \(-0.785700\pi\) | ||||
−0.781803 | + | 0.623526i | \(0.785700\pi\) | |||||||
\(42\) | −2.40760 | −0.371501 | ||||||||
\(43\) | 3.47246 | 0.529545 | 0.264772 | − | 0.964311i | \(-0.414703\pi\) | ||||
0.264772 | + | 0.964311i | \(0.414703\pi\) | |||||||
\(44\) | 1.18414 | 0.178516 | ||||||||
\(45\) | 4.92597 | 0.734320 | ||||||||
\(46\) | 2.87691 | 0.424177 | ||||||||
\(47\) | 11.6169 | 1.69451 | 0.847253 | − | 0.531190i | \(-0.178255\pi\) | ||||
0.847253 | + | 0.531190i | \(0.178255\pi\) | |||||||
\(48\) | −2.40760 | −0.347508 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.89733 | 0.268323 | ||||||||
\(51\) | −8.53574 | −1.19524 | ||||||||
\(52\) | −0.361568 | −0.0501404 | ||||||||
\(53\) | −12.0168 | −1.65063 | −0.825316 | − | 0.564672i | \(-0.809003\pi\) | ||||
−0.825316 | + | 0.564672i | \(0.809003\pi\) | |||||||
\(54\) | −0.489807 | −0.0666543 | ||||||||
\(55\) | 2.08580 | 0.281249 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.10308 | 0.670067 | ||||||||
\(59\) | 7.72735 | 1.00602 | 0.503008 | − | 0.864282i | \(-0.332227\pi\) | ||||
0.503008 | + | 0.864282i | \(0.332227\pi\) | |||||||
\(60\) | −4.24085 | −0.547491 | ||||||||
\(61\) | −1.99042 | −0.254848 | −0.127424 | − | 0.991848i | \(-0.540671\pi\) | ||||
−0.127424 | + | 0.991848i | \(0.540671\pi\) | |||||||
\(62\) | −1.38152 | −0.175453 | ||||||||
\(63\) | −2.79656 | −0.352333 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.636880 | −0.0789952 | ||||||||
\(66\) | 2.85095 | 0.350927 | ||||||||
\(67\) | −8.30406 | −1.01450 | −0.507251 | − | 0.861798i | \(-0.669338\pi\) | ||||
−0.507251 | + | 0.861798i | \(0.669338\pi\) | |||||||
\(68\) | 3.54532 | 0.429934 | ||||||||
\(69\) | 6.92645 | 0.833847 | ||||||||
\(70\) | 1.76144 | 0.210532 | ||||||||
\(71\) | 0.226733 | 0.0269083 | 0.0134541 | − | 0.999909i | \(-0.495717\pi\) | ||||
0.0134541 | + | 0.999909i | \(0.495717\pi\) | |||||||
\(72\) | −2.79656 | −0.329578 | ||||||||
\(73\) | −14.0163 | −1.64048 | −0.820242 | − | 0.572017i | \(-0.806161\pi\) | ||||
−0.820242 | + | 0.572017i | \(0.806161\pi\) | |||||||
\(74\) | −3.35526 | −0.390041 | ||||||||
\(75\) | 4.56803 | 0.527470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.18414 | −0.134946 | ||||||||
\(78\) | −0.870512 | −0.0985661 | ||||||||
\(79\) | −5.28063 | −0.594118 | −0.297059 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(80\) | 1.76144 | 0.196935 | ||||||||
\(81\) | −9.56894 | −1.06322 | ||||||||
\(82\) | 10.0120 | 1.10564 | ||||||||
\(83\) | 13.3912 | 1.46988 | 0.734939 | − | 0.678133i | \(-0.237211\pi\) | ||||
0.734939 | + | 0.678133i | \(0.237211\pi\) | |||||||
\(84\) | 2.40760 | 0.262691 | ||||||||
\(85\) | 6.24487 | 0.677351 | ||||||||
\(86\) | −3.47246 | −0.374445 | ||||||||
\(87\) | 12.2862 | 1.31722 | ||||||||
\(88\) | −1.18414 | −0.126230 | ||||||||
\(89\) | 1.87916 | 0.199191 | 0.0995954 | − | 0.995028i | \(-0.468245\pi\) | ||||
0.0995954 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(90\) | −4.92597 | −0.519242 | ||||||||
\(91\) | 0.361568 | 0.0379026 | ||||||||
\(92\) | −2.87691 | −0.299938 | ||||||||
\(93\) | −3.32616 | −0.344906 | ||||||||
\(94\) | −11.6169 | −1.19820 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.40760 | 0.245725 | ||||||||
\(97\) | 3.99766 | 0.405901 | 0.202950 | − | 0.979189i | \(-0.434947\pi\) | ||||
0.202950 | + | 0.979189i | \(0.434947\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.31153 | 0.332821 | ||||||||
\(100\) | −1.89733 | −0.189733 | ||||||||
\(101\) | −18.6641 | −1.85715 | −0.928575 | − | 0.371145i | \(-0.878965\pi\) | ||||
−0.928575 | + | 0.371145i | \(0.878965\pi\) | |||||||
\(102\) | 8.53574 | 0.845164 | ||||||||
\(103\) | 2.35245 | 0.231793 | 0.115897 | − | 0.993261i | \(-0.463026\pi\) | ||||
0.115897 | + | 0.993261i | \(0.463026\pi\) | |||||||
\(104\) | 0.361568 | 0.0354546 | ||||||||
\(105\) | 4.24085 | 0.413864 | ||||||||
\(106\) | 12.0168 | 1.16717 | ||||||||
\(107\) | 3.11852 | 0.301479 | 0.150739 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150739 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(108\) | 0.489807 | 0.0471317 | ||||||||
\(109\) | 14.1835 | 1.35853 | 0.679266 | − | 0.733892i | \(-0.262298\pi\) | ||||
0.679266 | + | 0.733892i | \(0.262298\pi\) | |||||||
\(110\) | −2.08580 | −0.198873 | ||||||||
\(111\) | −8.07815 | −0.766744 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.82085 | 0.359436 | 0.179718 | − | 0.983718i | \(-0.442482\pi\) | ||||
0.179718 | + | 0.983718i | \(0.442482\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.06749 | −0.472546 | ||||||||
\(116\) | −5.10308 | −0.473809 | ||||||||
\(117\) | −1.01115 | −0.0934804 | ||||||||
\(118\) | −7.72735 | −0.711360 | ||||||||
\(119\) | −3.54532 | −0.324999 | ||||||||
\(120\) | 4.24085 | 0.387135 | ||||||||
\(121\) | −9.59781 | −0.872528 | ||||||||
\(122\) | 1.99042 | 0.180205 | ||||||||
\(123\) | 24.1048 | 2.17346 | ||||||||
\(124\) | 1.38152 | 0.124064 | ||||||||
\(125\) | −12.1492 | −1.08666 | ||||||||
\(126\) | 2.79656 | 0.249137 | ||||||||
\(127\) | 19.3815 | 1.71983 | 0.859917 | − | 0.510434i | \(-0.170515\pi\) | ||||
0.859917 | + | 0.510434i | \(0.170515\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.36030 | −0.736084 | ||||||||
\(130\) | 0.636880 | 0.0558580 | ||||||||
\(131\) | −4.99933 | −0.436794 | −0.218397 | − | 0.975860i | \(-0.570083\pi\) | ||||
−0.218397 | + | 0.975860i | \(0.570083\pi\) | |||||||
\(132\) | −2.85095 | −0.248143 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.30406 | 0.717362 | ||||||||
\(135\) | 0.862765 | 0.0742550 | ||||||||
\(136\) | −3.54532 | −0.304009 | ||||||||
\(137\) | 20.8876 | 1.78455 | 0.892276 | − | 0.451491i | \(-0.149108\pi\) | ||||
0.892276 | + | 0.451491i | \(0.149108\pi\) | |||||||
\(138\) | −6.92645 | −0.589619 | ||||||||
\(139\) | −13.2393 | −1.12294 | −0.561472 | − | 0.827496i | \(-0.689765\pi\) | ||||
−0.561472 | + | 0.827496i | \(0.689765\pi\) | |||||||
\(140\) | −1.76144 | −0.148869 | ||||||||
\(141\) | −27.9690 | −2.35541 | ||||||||
\(142\) | −0.226733 | −0.0190270 | ||||||||
\(143\) | −0.428148 | −0.0358035 | ||||||||
\(144\) | 2.79656 | 0.233047 | ||||||||
\(145\) | −8.98876 | −0.746476 | ||||||||
\(146\) | 14.0163 | 1.16000 | ||||||||
\(147\) | −2.40760 | −0.198576 | ||||||||
\(148\) | 3.35526 | 0.275801 | ||||||||
\(149\) | 3.08216 | 0.252500 | 0.126250 | − | 0.991998i | \(-0.459706\pi\) | ||||
0.126250 | + | 0.991998i | \(0.459706\pi\) | |||||||
\(150\) | −4.56803 | −0.372978 | ||||||||
\(151\) | 6.35364 | 0.517052 | 0.258526 | − | 0.966004i | \(-0.416763\pi\) | ||||
0.258526 | + | 0.966004i | \(0.416763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.91471 | 0.801557 | ||||||||
\(154\) | 1.18414 | 0.0954210 | ||||||||
\(155\) | 2.43347 | 0.195461 | ||||||||
\(156\) | 0.870512 | 0.0696968 | ||||||||
\(157\) | 4.20918 | 0.335929 | 0.167965 | − | 0.985793i | \(-0.446281\pi\) | ||||
0.167965 | + | 0.985793i | \(0.446281\pi\) | |||||||
\(158\) | 5.28063 | 0.420105 | ||||||||
\(159\) | 28.9316 | 2.29443 | ||||||||
\(160\) | −1.76144 | −0.139254 | ||||||||
\(161\) | 2.87691 | 0.226732 | ||||||||
\(162\) | 9.56894 | 0.751807 | ||||||||
\(163\) | 7.15678 | 0.560562 | 0.280281 | − | 0.959918i | \(-0.409572\pi\) | ||||
0.280281 | + | 0.959918i | \(0.409572\pi\) | |||||||
\(164\) | −10.0120 | −0.781803 | ||||||||
\(165\) | −5.02177 | −0.390944 | ||||||||
\(166\) | −13.3912 | −1.03936 | ||||||||
\(167\) | −22.1964 | −1.71761 | −0.858806 | − | 0.512300i | \(-0.828793\pi\) | ||||
−0.858806 | + | 0.512300i | \(0.828793\pi\) | |||||||
\(168\) | −2.40760 | −0.185751 | ||||||||
\(169\) | −12.8693 | −0.989944 | ||||||||
\(170\) | −6.24487 | −0.478960 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.47246 | 0.264772 | ||||||||
\(173\) | −10.8227 | −0.822835 | −0.411418 | − | 0.911447i | \(-0.634966\pi\) | ||||
−0.411418 | + | 0.911447i | \(0.634966\pi\) | |||||||
\(174\) | −12.2862 | −0.931414 | ||||||||
\(175\) | 1.89733 | 0.143425 | ||||||||
\(176\) | 1.18414 | 0.0892581 | ||||||||
\(177\) | −18.6044 | −1.39839 | ||||||||
\(178\) | −1.87916 | −0.140849 | ||||||||
\(179\) | 11.7586 | 0.878880 | 0.439440 | − | 0.898272i | \(-0.355177\pi\) | ||||
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(180\) | 4.92597 | 0.367160 | ||||||||
\(181\) | −1.62634 | −0.120885 | −0.0604426 | − | 0.998172i | \(-0.519251\pi\) | ||||
−0.0604426 | + | 0.998172i | \(0.519251\pi\) | |||||||
\(182\) | −0.361568 | −0.0268012 | ||||||||
\(183\) | 4.79215 | 0.354246 | ||||||||
\(184\) | 2.87691 | 0.212088 | ||||||||
\(185\) | 5.91009 | 0.434519 | ||||||||
\(186\) | 3.32616 | 0.243886 | ||||||||
\(187\) | 4.19817 | 0.307001 | ||||||||
\(188\) | 11.6169 | 0.847253 | ||||||||
\(189\) | −0.489807 | −0.0356282 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1136 | 1.09358 | 0.546792 | − | 0.837268i | \(-0.315849\pi\) | ||||
0.546792 | + | 0.837268i | \(0.315849\pi\) | |||||||
\(192\) | −2.40760 | −0.173754 | ||||||||
\(193\) | 21.0053 | 1.51200 | 0.755998 | − | 0.654574i | \(-0.227152\pi\) | ||||
0.755998 | + | 0.654574i | \(0.227152\pi\) | |||||||
\(194\) | −3.99766 | −0.287015 | ||||||||
\(195\) | 1.53335 | 0.109806 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.5580 | −1.74969 | −0.874844 | − | 0.484405i | \(-0.839036\pi\) | ||||
−0.874844 | + | 0.484405i | \(0.839036\pi\) | |||||||
\(198\) | −3.31153 | −0.235340 | ||||||||
\(199\) | 5.50367 | 0.390145 | 0.195073 | − | 0.980789i | \(-0.437506\pi\) | ||||
0.195073 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(200\) | 1.89733 | 0.134162 | ||||||||
\(201\) | 19.9929 | 1.41019 | ||||||||
\(202\) | 18.6641 | 1.31320 | ||||||||
\(203\) | 5.10308 | 0.358166 | ||||||||
\(204\) | −8.53574 | −0.597621 | ||||||||
\(205\) | −17.6355 | −1.23171 | ||||||||
\(206\) | −2.35245 | −0.163903 | ||||||||
\(207\) | −8.04544 | −0.559197 | ||||||||
\(208\) | −0.361568 | −0.0250702 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.24085 | −0.292646 | ||||||||
\(211\) | −4.53017 | −0.311870 | −0.155935 | − | 0.987767i | \(-0.549839\pi\) | ||||
−0.155935 | + | 0.987767i | \(0.549839\pi\) | |||||||
\(212\) | −12.0168 | −0.825316 | ||||||||
\(213\) | −0.545884 | −0.0374033 | ||||||||
\(214\) | −3.11852 | −0.213178 | ||||||||
\(215\) | 6.11652 | 0.417143 | ||||||||
\(216\) | −0.489807 | −0.0333271 | ||||||||
\(217\) | −1.38152 | −0.0937838 | ||||||||
\(218\) | −14.1835 | −0.960628 | ||||||||
\(219\) | 33.7457 | 2.28032 | ||||||||
\(220\) | 2.08580 | 0.140624 | ||||||||
\(221\) | −1.28188 | −0.0862283 | ||||||||
\(222\) | 8.07815 | 0.542170 | ||||||||
\(223\) | −10.0211 | −0.671066 | −0.335533 | − | 0.942029i | \(-0.608916\pi\) | ||||
−0.335533 | + | 0.942029i | \(0.608916\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −5.30600 | −0.353734 | ||||||||
\(226\) | −3.82085 | −0.254159 | ||||||||
\(227\) | 7.43478 | 0.493463 | 0.246732 | − | 0.969084i | \(-0.420643\pi\) | ||||
0.246732 | + | 0.969084i | \(0.420643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.96142 | 0.261778 | 0.130889 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130889 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(230\) | 5.06749 | 0.334141 | ||||||||
\(231\) | 2.85095 | 0.187579 | ||||||||
\(232\) | 5.10308 | 0.335034 | ||||||||
\(233\) | −14.3859 | −0.942452 | −0.471226 | − | 0.882012i | \(-0.656188\pi\) | ||||
−0.471226 | + | 0.882012i | \(0.656188\pi\) | |||||||
\(234\) | 1.01115 | 0.0661007 | ||||||||
\(235\) | 20.4625 | 1.33483 | ||||||||
\(236\) | 7.72735 | 0.503008 | ||||||||
\(237\) | 12.7137 | 0.825842 | ||||||||
\(238\) | 3.54532 | 0.229809 | ||||||||
\(239\) | −7.12027 | −0.460572 | −0.230286 | − | 0.973123i | \(-0.573966\pi\) | ||||
−0.230286 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(240\) | −4.24085 | −0.273746 | ||||||||
\(241\) | 14.9816 | 0.965051 | 0.482525 | − | 0.875882i | \(-0.339720\pi\) | ||||
0.482525 | + | 0.875882i | \(0.339720\pi\) | |||||||
\(242\) | 9.59781 | 0.616970 | ||||||||
\(243\) | 21.5688 | 1.38364 | ||||||||
\(244\) | −1.99042 | −0.127424 | ||||||||
\(245\) | 1.76144 | 0.112534 | ||||||||
\(246\) | −24.1048 | −1.53687 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.38152 | −0.0877267 | ||||||||
\(249\) | −32.2408 | −2.04318 | ||||||||
\(250\) | 12.1492 | 0.768385 | ||||||||
\(251\) | −28.2614 | −1.78385 | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||||
−0.891923 | + | 0.452187i | \(0.850644\pi\) | |||||||
\(252\) | −2.79656 | −0.176167 | ||||||||
\(253\) | −3.40667 | −0.214175 | ||||||||
\(254\) | −19.3815 | −1.21611 | ||||||||
\(255\) | −15.0352 | −0.941540 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.5197 | 0.718576 | 0.359288 | − | 0.933227i | \(-0.383020\pi\) | ||||
0.359288 | + | 0.933227i | \(0.383020\pi\) | |||||||
\(258\) | 8.36030 | 0.520490 | ||||||||
\(259\) | −3.35526 | −0.208486 | ||||||||
\(260\) | −0.636880 | −0.0394976 | ||||||||
\(261\) | −14.2711 | −0.883357 | ||||||||
\(262\) | 4.99933 | 0.308860 | ||||||||
\(263\) | 26.6852 | 1.64548 | 0.822740 | − | 0.568418i | \(-0.192445\pi\) | ||||
0.822740 | + | 0.568418i | \(0.192445\pi\) | |||||||
\(264\) | 2.85095 | 0.175464 | ||||||||
\(265\) | −21.1668 | −1.30027 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.52428 | −0.276881 | ||||||||
\(268\) | −8.30406 | −0.507251 | ||||||||
\(269\) | 2.07333 | 0.126413 | 0.0632065 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632065 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(270\) | −0.862765 | −0.0525062 | ||||||||
\(271\) | −23.0985 | −1.40314 | −0.701568 | − | 0.712602i | \(-0.747516\pi\) | ||||
−0.701568 | + | 0.712602i | \(0.747516\pi\) | |||||||
\(272\) | 3.54532 | 0.214967 | ||||||||
\(273\) | −0.870512 | −0.0526858 | ||||||||
\(274\) | −20.8876 | −1.26187 | ||||||||
\(275\) | −2.24671 | −0.135482 | ||||||||
\(276\) | 6.92645 | 0.416923 | ||||||||
\(277\) | 20.3780 | 1.22440 | 0.612198 | − | 0.790705i | \(-0.290286\pi\) | ||||
0.612198 | + | 0.790705i | \(0.290286\pi\) | |||||||
\(278\) | 13.2393 | 0.794042 | ||||||||
\(279\) | 3.86351 | 0.231302 | ||||||||
\(280\) | 1.76144 | 0.105266 | ||||||||
\(281\) | −15.6633 | −0.934394 | −0.467197 | − | 0.884153i | \(-0.654736\pi\) | ||||
−0.467197 | + | 0.884153i | \(0.654736\pi\) | |||||||
\(282\) | 27.9690 | 1.66553 | ||||||||
\(283\) | 2.37228 | 0.141017 | 0.0705086 | − | 0.997511i | \(-0.477538\pi\) | ||||
0.0705086 | + | 0.997511i | \(0.477538\pi\) | |||||||
\(284\) | 0.226733 | 0.0134541 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.428148 | 0.0253169 | ||||||||
\(287\) | 10.0120 | 0.590987 | ||||||||
\(288\) | −2.79656 | −0.164789 | ||||||||
\(289\) | −4.43067 | −0.260628 | ||||||||
\(290\) | 8.98876 | 0.527838 | ||||||||
\(291\) | −9.62478 | −0.564215 | ||||||||
\(292\) | −14.0163 | −0.820242 | ||||||||
\(293\) | 0.586563 | 0.0342674 | 0.0171337 | − | 0.999853i | \(-0.494546\pi\) | ||||
0.0171337 | + | 0.999853i | \(0.494546\pi\) | |||||||
\(294\) | 2.40760 | 0.140414 | ||||||||
\(295\) | 13.6113 | 0.792478 | ||||||||
\(296\) | −3.35526 | −0.195021 | ||||||||
\(297\) | 0.580001 | 0.0336551 | ||||||||
\(298\) | −3.08216 | −0.178545 | ||||||||
\(299\) | 1.04020 | 0.0601561 | ||||||||
\(300\) | 4.56803 | 0.263735 | ||||||||
\(301\) | −3.47246 | −0.200149 | ||||||||
\(302\) | −6.35364 | −0.365611 | ||||||||
\(303\) | 44.9358 | 2.58150 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.50601 | −0.200754 | ||||||||
\(306\) | −9.91471 | −0.566786 | ||||||||
\(307\) | −19.9202 | −1.13690 | −0.568452 | − | 0.822717i | \(-0.692457\pi\) | ||||
−0.568452 | + | 0.822717i | \(0.692457\pi\) | |||||||
\(308\) | −1.18414 | −0.0674728 | ||||||||
\(309\) | −5.66376 | −0.322200 | ||||||||
\(310\) | −2.43347 | −0.138212 | ||||||||
\(311\) | −14.6345 | −0.829849 | −0.414925 | − | 0.909856i | \(-0.636192\pi\) | ||||
−0.414925 | + | 0.909856i | \(0.636192\pi\) | |||||||
\(312\) | −0.870512 | −0.0492831 | ||||||||
\(313\) | −26.9261 | −1.52195 | −0.760975 | − | 0.648781i | \(-0.775279\pi\) | ||||
−0.760975 | + | 0.648781i | \(0.775279\pi\) | |||||||
\(314\) | −4.20918 | −0.237538 | ||||||||
\(315\) | −4.92597 | −0.277547 | ||||||||
\(316\) | −5.28063 | −0.297059 | ||||||||
\(317\) | −30.5772 | −1.71739 | −0.858694 | − | 0.512489i | \(-0.828724\pi\) | ||||
−0.858694 | + | 0.512489i | \(0.828724\pi\) | |||||||
\(318\) | −28.9316 | −1.62241 | ||||||||
\(319\) | −6.04278 | −0.338331 | ||||||||
\(320\) | 1.76144 | 0.0984674 | ||||||||
\(321\) | −7.50816 | −0.419065 | ||||||||
\(322\) | −2.87691 | −0.160324 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.56894 | −0.531608 | ||||||||
\(325\) | 0.686015 | 0.0380533 | ||||||||
\(326\) | −7.15678 | −0.396377 | ||||||||
\(327\) | −34.1483 | −1.88840 | ||||||||
\(328\) | 10.0120 | 0.552818 | ||||||||
\(329\) | −11.6169 | −0.640463 | ||||||||
\(330\) | 5.02177 | 0.276439 | ||||||||
\(331\) | −20.3542 | −1.11877 | −0.559384 | − | 0.828909i | \(-0.688962\pi\) | ||||
−0.559384 | + | 0.828909i | \(0.688962\pi\) | |||||||
\(332\) | 13.3912 | 0.734939 | ||||||||
\(333\) | 9.38319 | 0.514196 | ||||||||
\(334\) | 22.1964 | 1.21454 | ||||||||
\(335\) | −14.6271 | −0.799164 | ||||||||
\(336\) | 2.40760 | 0.131346 | ||||||||
\(337\) | 14.8090 | 0.806700 | 0.403350 | − | 0.915046i | \(-0.367846\pi\) | ||||
0.403350 | + | 0.915046i | \(0.367846\pi\) | |||||||
\(338\) | 12.8693 | 0.699996 | ||||||||
\(339\) | −9.19910 | −0.499627 | ||||||||
\(340\) | 6.24487 | 0.338676 | ||||||||
\(341\) | 1.63592 | 0.0885900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.47246 | −0.187222 | ||||||||
\(345\) | 12.2005 | 0.656854 | ||||||||
\(346\) | 10.8227 | 0.581832 | ||||||||
\(347\) | −19.0467 | −1.02248 | −0.511241 | − | 0.859438i | \(-0.670814\pi\) | ||||
−0.511241 | + | 0.859438i | \(0.670814\pi\) | |||||||
\(348\) | 12.2862 | 0.658609 | ||||||||
\(349\) | −21.1239 | −1.13074 | −0.565368 | − | 0.824839i | \(-0.691266\pi\) | ||||
−0.565368 | + | 0.824839i | \(0.691266\pi\) | |||||||
\(350\) | −1.89733 | −0.101417 | ||||||||
\(351\) | −0.177098 | −0.00945282 | ||||||||
\(352\) | −1.18414 | −0.0631150 | ||||||||
\(353\) | 2.24313 | 0.119390 | 0.0596949 | − | 0.998217i | \(-0.480987\pi\) | ||||
0.0596949 | + | 0.998217i | \(0.480987\pi\) | |||||||
\(354\) | 18.6044 | 0.988813 | ||||||||
\(355\) | 0.399377 | 0.0211967 | ||||||||
\(356\) | 1.87916 | 0.0995954 | ||||||||
\(357\) | 8.53574 | 0.451759 | ||||||||
\(358\) | −11.7586 | −0.621462 | ||||||||
\(359\) | 3.31981 | 0.175213 | 0.0876066 | − | 0.996155i | \(-0.472078\pi\) | ||||
0.0876066 | + | 0.996155i | \(0.472078\pi\) | |||||||
\(360\) | −4.92597 | −0.259621 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.62634 | 0.0854787 | ||||||||
\(363\) | 23.1077 | 1.21284 | ||||||||
\(364\) | 0.361568 | 0.0189513 | ||||||||
\(365\) | −24.6888 | −1.29227 | ||||||||
\(366\) | −4.79215 | −0.250490 | ||||||||
\(367\) | −18.3886 | −0.959875 | −0.479938 | − | 0.877303i | \(-0.659341\pi\) | ||||
−0.479938 | + | 0.877303i | \(0.659341\pi\) | |||||||
\(368\) | −2.87691 | −0.149969 | ||||||||
\(369\) | −27.9990 | −1.45757 | ||||||||
\(370\) | −5.91009 | −0.307251 | ||||||||
\(371\) | 12.0168 | 0.623880 | ||||||||
\(372\) | −3.32616 | −0.172453 | ||||||||
\(373\) | 3.33060 | 0.172452 | 0.0862259 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862259 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(374\) | −4.19817 | −0.217082 | ||||||||
\(375\) | 29.2505 | 1.51049 | ||||||||
\(376\) | −11.6169 | −0.599098 | ||||||||
\(377\) | 1.84511 | 0.0950280 | ||||||||
\(378\) | 0.489807 | 0.0251929 | ||||||||
\(379\) | −30.8785 | −1.58612 | −0.793061 | − | 0.609142i | \(-0.791514\pi\) | ||||
−0.793061 | + | 0.609142i | \(0.791514\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.6631 | −2.39062 | ||||||||
\(382\) | −15.1136 | −0.773281 | ||||||||
\(383\) | 4.18785 | 0.213989 | 0.106995 | − | 0.994260i | \(-0.465877\pi\) | ||||
0.106995 | + | 0.994260i | \(0.465877\pi\) | |||||||
\(384\) | 2.40760 | 0.122863 | ||||||||
\(385\) | −2.08580 | −0.106302 | ||||||||
\(386\) | −21.0053 | −1.06914 | ||||||||
\(387\) | 9.71093 | 0.493634 | ||||||||
\(388\) | 3.99766 | 0.202950 | ||||||||
\(389\) | 13.7229 | 0.695779 | 0.347890 | − | 0.937536i | \(-0.386898\pi\) | ||||
0.347890 | + | 0.937536i | \(0.386898\pi\) | |||||||
\(390\) | −1.53335 | −0.0776444 | ||||||||
\(391\) | −10.1996 | −0.515814 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 12.0364 | 0.607157 | ||||||||
\(394\) | 24.5580 | 1.23722 | ||||||||
\(395\) | −9.30151 | −0.468010 | ||||||||
\(396\) | 3.31153 | 0.166410 | ||||||||
\(397\) | −12.7243 | −0.638614 | −0.319307 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319307 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(398\) | −5.50367 | −0.275874 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.89733 | −0.0948667 | ||||||||
\(401\) | −27.5174 | −1.37415 | −0.687077 | − | 0.726585i | \(-0.741106\pi\) | ||||
−0.687077 | + | 0.726585i | \(0.741106\pi\) | |||||||
\(402\) | −19.9929 | −0.997155 | ||||||||
\(403\) | −0.499514 | −0.0248826 | ||||||||
\(404\) | −18.6641 | −0.928575 | ||||||||
\(405\) | −16.8551 | −0.837536 | ||||||||
\(406\) | −5.10308 | −0.253262 | ||||||||
\(407\) | 3.97311 | 0.196940 | ||||||||
\(408\) | 8.53574 | 0.422582 | ||||||||
\(409\) | −30.1566 | −1.49115 | −0.745574 | − | 0.666423i | \(-0.767825\pi\) | ||||
−0.745574 | + | 0.666423i | \(0.767825\pi\) | |||||||
\(410\) | 17.6355 | 0.870953 | ||||||||
\(411\) | −50.2892 | −2.48058 | ||||||||
\(412\) | 2.35245 | 0.115897 | ||||||||
\(413\) | −7.72735 | −0.380238 | ||||||||
\(414\) | 8.04544 | 0.395412 | ||||||||
\(415\) | 23.5878 | 1.15788 | ||||||||
\(416\) | 0.361568 | 0.0177273 | ||||||||
\(417\) | 31.8750 | 1.56093 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.2631 | 1.23418 | 0.617092 | − | 0.786891i | \(-0.288311\pi\) | ||||
0.617092 | + | 0.786891i | \(0.288311\pi\) | |||||||
\(420\) | 4.24085 | 0.206932 | ||||||||
\(421\) | 38.0387 | 1.85389 | 0.926945 | − | 0.375197i | \(-0.122425\pi\) | ||||
0.926945 | + | 0.375197i | \(0.122425\pi\) | |||||||
\(422\) | 4.53017 | 0.220525 | ||||||||
\(423\) | 32.4875 | 1.57959 | ||||||||
\(424\) | 12.0168 | 0.583586 | ||||||||
\(425\) | −6.72666 | −0.326291 | ||||||||
\(426\) | 0.545884 | 0.0264482 | ||||||||
\(427\) | 1.99042 | 0.0963234 | ||||||||
\(428\) | 3.11852 | 0.150739 | ||||||||
\(429\) | 1.03081 | 0.0497680 | ||||||||
\(430\) | −6.11652 | −0.294965 | ||||||||
\(431\) | −18.9095 | −0.910837 | −0.455419 | − | 0.890277i | \(-0.650510\pi\) | ||||
−0.455419 | + | 0.890277i | \(0.650510\pi\) | |||||||
\(432\) | 0.489807 | 0.0235658 | ||||||||
\(433\) | 12.6102 | 0.606009 | 0.303005 | − | 0.952989i | \(-0.402010\pi\) | ||||
0.303005 | + | 0.952989i | \(0.402010\pi\) | |||||||
\(434\) | 1.38152 | 0.0663152 | ||||||||
\(435\) | 21.6414 | 1.03763 | ||||||||
\(436\) | 14.1835 | 0.679266 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −33.7457 | −1.61243 | ||||||||
\(439\) | −33.9256 | −1.61918 | −0.809591 | − | 0.586994i | \(-0.800311\pi\) | ||||
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(440\) | −2.08580 | −0.0994364 | ||||||||
\(441\) | 2.79656 | 0.133169 | ||||||||
\(442\) | 1.28188 | 0.0609726 | ||||||||
\(443\) | −4.69792 | −0.223205 | −0.111602 | − | 0.993753i | \(-0.535598\pi\) | ||||
−0.111602 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(444\) | −8.07815 | −0.383372 | ||||||||
\(445\) | 3.31003 | 0.156910 | ||||||||
\(446\) | 10.0211 | 0.474515 | ||||||||
\(447\) | −7.42061 | −0.350983 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −25.3251 | −1.19517 | −0.597583 | − | 0.801807i | \(-0.703872\pi\) | ||||
−0.597583 | + | 0.801807i | \(0.703872\pi\) | |||||||
\(450\) | 5.30600 | 0.250127 | ||||||||
\(451\) | −11.8556 | −0.558258 | ||||||||
\(452\) | 3.82085 | 0.179718 | ||||||||
\(453\) | −15.2970 | −0.718718 | ||||||||
\(454\) | −7.43478 | −0.348931 | ||||||||
\(455\) | 0.636880 | 0.0298574 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.3466 | −1.88734 | −0.943668 | − | 0.330894i | \(-0.892650\pi\) | ||||
−0.943668 | + | 0.330894i | \(0.892650\pi\) | |||||||
\(458\) | −3.96142 | −0.185105 | ||||||||
\(459\) | 1.73652 | 0.0810540 | ||||||||
\(460\) | −5.06749 | −0.236273 | ||||||||
\(461\) | 8.28479 | 0.385861 | 0.192931 | − | 0.981212i | \(-0.438201\pi\) | ||||
0.192931 | + | 0.981212i | \(0.438201\pi\) | |||||||
\(462\) | −2.85095 | −0.132638 | ||||||||
\(463\) | −26.7426 | −1.24283 | −0.621416 | − | 0.783481i | \(-0.713442\pi\) | ||||
−0.621416 | + | 0.783481i | \(0.713442\pi\) | |||||||
\(464\) | −5.10308 | −0.236905 | ||||||||
\(465\) | −5.85882 | −0.271696 | ||||||||
\(466\) | 14.3859 | 0.666414 | ||||||||
\(467\) | 7.29907 | 0.337761 | 0.168880 | − | 0.985637i | \(-0.445985\pi\) | ||||
0.168880 | + | 0.985637i | \(0.445985\pi\) | |||||||
\(468\) | −1.01115 | −0.0467402 | ||||||||
\(469\) | 8.30406 | 0.383446 | ||||||||
\(470\) | −20.4625 | −0.943866 | ||||||||
\(471\) | −10.1340 | −0.466952 | ||||||||
\(472\) | −7.72735 | −0.355680 | ||||||||
\(473\) | 4.11189 | 0.189065 | ||||||||
\(474\) | −12.7137 | −0.583959 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.54532 | −0.162500 | ||||||||
\(477\) | −33.6056 | −1.53870 | ||||||||
\(478\) | 7.12027 | 0.325673 | ||||||||
\(479\) | −27.1804 | −1.24191 | −0.620953 | − | 0.783848i | \(-0.713254\pi\) | ||||
−0.620953 | + | 0.783848i | \(0.713254\pi\) | |||||||
\(480\) | 4.24085 | 0.193567 | ||||||||
\(481\) | −1.21316 | −0.0553151 | ||||||||
\(482\) | −14.9816 | −0.682394 | ||||||||
\(483\) | −6.92645 | −0.315165 | ||||||||
\(484\) | −9.59781 | −0.436264 | ||||||||
\(485\) | 7.04163 | 0.319744 | ||||||||
\(486\) | −21.5688 | −0.978380 | ||||||||
\(487\) | −6.88190 | −0.311849 | −0.155924 | − | 0.987769i | \(-0.549836\pi\) | ||||
−0.155924 | + | 0.987769i | \(0.549836\pi\) | |||||||
\(488\) | 1.99042 | 0.0901023 | ||||||||
\(489\) | −17.2307 | −0.779199 | ||||||||
\(490\) | −1.76144 | −0.0795737 | ||||||||
\(491\) | −9.47678 | −0.427681 | −0.213841 | − | 0.976869i | \(-0.568597\pi\) | ||||
−0.213841 | + | 0.976869i | \(0.568597\pi\) | |||||||
\(492\) | 24.1048 | 1.08673 | ||||||||
\(493\) | −18.0921 | −0.814826 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.83305 | 0.262176 | ||||||||
\(496\) | 1.38152 | 0.0620322 | ||||||||
\(497\) | −0.226733 | −0.0101704 | ||||||||
\(498\) | 32.2408 | 1.44474 | ||||||||
\(499\) | −5.58793 | −0.250150 | −0.125075 | − | 0.992147i | \(-0.539917\pi\) | ||||
−0.125075 | + | 0.992147i | \(0.539917\pi\) | |||||||
\(500\) | −12.1492 | −0.543330 | ||||||||
\(501\) | 53.4403 | 2.38753 | ||||||||
\(502\) | 28.2614 | 1.26137 | ||||||||
\(503\) | −9.98556 | −0.445234 | −0.222617 | − | 0.974906i | \(-0.571460\pi\) | ||||
−0.222617 | + | 0.974906i | \(0.571460\pi\) | |||||||
\(504\) | 2.79656 | 0.124569 | ||||||||
\(505\) | −32.8757 | −1.46295 | ||||||||
\(506\) | 3.40667 | 0.151445 | ||||||||
\(507\) | 30.9841 | 1.37605 | ||||||||
\(508\) | 19.3815 | 0.859917 | ||||||||
\(509\) | 35.5061 | 1.57378 | 0.786890 | − | 0.617093i | \(-0.211690\pi\) | ||||
0.786890 | + | 0.617093i | \(0.211690\pi\) | |||||||
\(510\) | 15.0352 | 0.665769 | ||||||||
\(511\) | 14.0163 | 0.620044 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.5197 | −0.508110 | ||||||||
\(515\) | 4.14369 | 0.182593 | ||||||||
\(516\) | −8.36030 | −0.368042 | ||||||||
\(517\) | 13.7561 | 0.604993 | ||||||||
\(518\) | 3.35526 | 0.147422 | ||||||||
\(519\) | 26.0568 | 1.14377 | ||||||||
\(520\) | 0.636880 | 0.0279290 | ||||||||
\(521\) | −4.29772 | −0.188287 | −0.0941433 | − | 0.995559i | \(-0.530011\pi\) | ||||
−0.0941433 | + | 0.995559i | \(0.530011\pi\) | |||||||
\(522\) | 14.2711 | 0.624627 | ||||||||
\(523\) | −31.1762 | −1.36324 | −0.681620 | − | 0.731707i | \(-0.738724\pi\) | ||||
−0.681620 | + | 0.731707i | \(0.738724\pi\) | |||||||
\(524\) | −4.99933 | −0.218397 | ||||||||
\(525\) | −4.56803 | −0.199365 | ||||||||
\(526\) | −26.6852 | −1.16353 | ||||||||
\(527\) | 4.89794 | 0.213358 | ||||||||
\(528\) | −2.85095 | −0.124072 | ||||||||
\(529\) | −14.7234 | −0.640148 | ||||||||
\(530\) | 21.1668 | 0.919428 | ||||||||
\(531\) | 21.6100 | 0.937794 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.62000 | 0.156800 | ||||||||
\(534\) | 4.52428 | 0.195785 | ||||||||
\(535\) | 5.49308 | 0.237487 | ||||||||
\(536\) | 8.30406 | 0.358681 | ||||||||
\(537\) | −28.3101 | −1.22167 | ||||||||
\(538\) | −2.07333 | −0.0893874 | ||||||||
\(539\) | 1.18414 | 0.0510047 | ||||||||
\(540\) | 0.862765 | 0.0371275 | ||||||||
\(541\) | −5.51854 | −0.237261 | −0.118630 | − | 0.992938i | \(-0.537850\pi\) | ||||
−0.118630 | + | 0.992938i | \(0.537850\pi\) | |||||||
\(542\) | 23.0985 | 0.992167 | ||||||||
\(543\) | 3.91559 | 0.168034 | ||||||||
\(544\) | −3.54532 | −0.152005 | ||||||||
\(545\) | 24.9834 | 1.07017 | ||||||||
\(546\) | 0.870512 | 0.0372545 | ||||||||
\(547\) | −8.52743 | −0.364607 | −0.182303 | − | 0.983242i | \(-0.558355\pi\) | ||||
−0.182303 | + | 0.983242i | \(0.558355\pi\) | |||||||
\(548\) | 20.8876 | 0.892276 | ||||||||
\(549\) | −5.56634 | −0.237565 | ||||||||
\(550\) | 2.24671 | 0.0958002 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −6.92645 | −0.294809 | ||||||||
\(553\) | 5.28063 | 0.224555 | ||||||||
\(554\) | −20.3780 | −0.865778 | ||||||||
\(555\) | −14.2292 | −0.603994 | ||||||||
\(556\) | −13.2393 | −0.561472 | ||||||||
\(557\) | 22.8183 | 0.966843 | 0.483422 | − | 0.875388i | \(-0.339394\pi\) | ||||
0.483422 | + | 0.875388i | \(0.339394\pi\) | |||||||
\(558\) | −3.86351 | −0.163555 | ||||||||
\(559\) | −1.25553 | −0.0531032 | ||||||||
\(560\) | −1.76144 | −0.0744344 | ||||||||
\(561\) | −10.1075 | −0.426740 | ||||||||
\(562\) | 15.6633 | 0.660716 | ||||||||
\(563\) | −10.7974 | −0.455056 | −0.227528 | − | 0.973772i | \(-0.573064\pi\) | ||||
−0.227528 | + | 0.973772i | \(0.573064\pi\) | |||||||
\(564\) | −27.9690 | −1.17771 | ||||||||
\(565\) | 6.73020 | 0.283142 | ||||||||
\(566\) | −2.37228 | −0.0997142 | ||||||||
\(567\) | 9.56894 | 0.401858 | ||||||||
\(568\) | −0.226733 | −0.00951351 | ||||||||
\(569\) | −5.10510 | −0.214017 | −0.107008 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107008 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.62174 | 0.193414 | 0.0967070 | − | 0.995313i | \(-0.469169\pi\) | ||||
0.0967070 | + | 0.995313i | \(0.469169\pi\) | |||||||
\(572\) | −0.428148 | −0.0179018 | ||||||||
\(573\) | −36.3877 | −1.52012 | ||||||||
\(574\) | −10.0120 | −0.417891 | ||||||||
\(575\) | 5.45845 | 0.227633 | ||||||||
\(576\) | 2.79656 | 0.116523 | ||||||||
\(577\) | −32.4426 | −1.35060 | −0.675302 | − | 0.737541i | \(-0.735987\pi\) | ||||
−0.675302 | + | 0.737541i | \(0.735987\pi\) | |||||||
\(578\) | 4.43067 | 0.184292 | ||||||||
\(579\) | −50.5725 | −2.10172 | ||||||||
\(580\) | −8.98876 | −0.373238 | ||||||||
\(581\) | −13.3912 | −0.555562 | ||||||||
\(582\) | 9.62478 | 0.398960 | ||||||||
\(583\) | −14.2296 | −0.589329 | ||||||||
\(584\) | 14.0163 | 0.579998 | ||||||||
\(585\) | −1.78107 | −0.0736382 | ||||||||
\(586\) | −0.586563 | −0.0242307 | ||||||||
\(587\) | −7.36820 | −0.304118 | −0.152059 | − | 0.988371i | \(-0.548590\pi\) | ||||
−0.152059 | + | 0.988371i | \(0.548590\pi\) | |||||||
\(588\) | −2.40760 | −0.0992879 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −13.6113 | −0.560367 | ||||||||
\(591\) | 59.1261 | 2.43212 | ||||||||
\(592\) | 3.35526 | 0.137900 | ||||||||
\(593\) | 3.98443 | 0.163621 | 0.0818105 | − | 0.996648i | \(-0.473930\pi\) | ||||
0.0818105 | + | 0.996648i | \(0.473930\pi\) | |||||||
\(594\) | −0.580001 | −0.0237977 | ||||||||
\(595\) | −6.24487 | −0.256015 | ||||||||
\(596\) | 3.08216 | 0.126250 | ||||||||
\(597\) | −13.2507 | −0.542314 | ||||||||
\(598\) | −1.04020 | −0.0425368 | ||||||||
\(599\) | −4.19582 | −0.171436 | −0.0857182 | − | 0.996319i | \(-0.527318\pi\) | ||||
−0.0857182 | + | 0.996319i | \(0.527318\pi\) | |||||||
\(600\) | −4.56803 | −0.186489 | ||||||||
\(601\) | −30.5991 | −1.24816 | −0.624081 | − | 0.781360i | \(-0.714526\pi\) | ||||
−0.624081 | + | 0.781360i | \(0.714526\pi\) | |||||||
\(602\) | 3.47246 | 0.141527 | ||||||||
\(603\) | −23.2228 | −0.945706 | ||||||||
\(604\) | 6.35364 | 0.258526 | ||||||||
\(605\) | −16.9059 | −0.687324 | ||||||||
\(606\) | −44.9358 | −1.82539 | ||||||||
\(607\) | −42.8583 | −1.73957 | −0.869783 | − | 0.493435i | \(-0.835741\pi\) | ||||
−0.869783 | + | 0.493435i | \(0.835741\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.2862 | −0.497862 | ||||||||
\(610\) | 3.50601 | 0.141954 | ||||||||
\(611\) | −4.20031 | −0.169926 | ||||||||
\(612\) | 9.91471 | 0.400778 | ||||||||
\(613\) | 24.8978 | 1.00561 | 0.502806 | − | 0.864399i | \(-0.332301\pi\) | ||||
0.502806 | + | 0.864399i | \(0.332301\pi\) | |||||||
\(614\) | 19.9202 | 0.803912 | ||||||||
\(615\) | 42.4592 | 1.71212 | ||||||||
\(616\) | 1.18414 | 0.0477105 | ||||||||
\(617\) | 13.1675 | 0.530102 | 0.265051 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265051 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(618\) | 5.66376 | 0.227830 | ||||||||
\(619\) | −5.34109 | −0.214676 | −0.107338 | − | 0.994223i | \(-0.534233\pi\) | ||||
−0.107338 | + | 0.994223i | \(0.534233\pi\) | |||||||
\(620\) | 2.43347 | 0.0977303 | ||||||||
\(621\) | −1.40913 | −0.0565464 | ||||||||
\(622\) | 14.6345 | 0.586792 | ||||||||
\(623\) | −1.87916 | −0.0752870 | ||||||||
\(624\) | 0.870512 | 0.0348484 | ||||||||
\(625\) | −11.9135 | −0.476538 | ||||||||
\(626\) | 26.9261 | 1.07618 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.20918 | 0.167965 | ||||||||
\(629\) | 11.8955 | 0.474305 | ||||||||
\(630\) | 4.92597 | 0.196255 | ||||||||
\(631\) | −49.2604 | −1.96103 | −0.980513 | − | 0.196453i | \(-0.937058\pi\) | ||||
−0.980513 | + | 0.196453i | \(0.937058\pi\) | |||||||
\(632\) | 5.28063 | 0.210052 | ||||||||
\(633\) | 10.9069 | 0.433509 | ||||||||
\(634\) | 30.5772 | 1.21438 | ||||||||
\(635\) | 34.1394 | 1.35478 | ||||||||
\(636\) | 28.9316 | 1.14721 | ||||||||
\(637\) | −0.361568 | −0.0143258 | ||||||||
\(638\) | 6.04278 | 0.239236 | ||||||||
\(639\) | 0.634073 | 0.0250835 | ||||||||
\(640\) | −1.76144 | −0.0696270 | ||||||||
\(641\) | 34.2166 | 1.35147 | 0.675737 | − | 0.737143i | \(-0.263826\pi\) | ||||
0.675737 | + | 0.737143i | \(0.263826\pi\) | |||||||
\(642\) | 7.50816 | 0.296324 | ||||||||
\(643\) | −44.9211 | −1.77152 | −0.885758 | − | 0.464148i | \(-0.846361\pi\) | ||||
−0.885758 | + | 0.464148i | \(0.846361\pi\) | |||||||
\(644\) | 2.87691 | 0.113366 | ||||||||
\(645\) | −14.7262 | −0.579842 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1593 | 0.753230 | 0.376615 | − | 0.926370i | \(-0.377088\pi\) | ||||
0.376615 | + | 0.926370i | \(0.377088\pi\) | |||||||
\(648\) | 9.56894 | 0.375903 | ||||||||
\(649\) | 9.15029 | 0.359180 | ||||||||
\(650\) | −0.686015 | −0.0269077 | ||||||||
\(651\) | 3.32616 | 0.130362 | ||||||||
\(652\) | 7.15678 | 0.280281 | ||||||||
\(653\) | 26.2846 | 1.02860 | 0.514299 | − | 0.857611i | \(-0.328052\pi\) | ||||
0.514299 | + | 0.857611i | \(0.328052\pi\) | |||||||
\(654\) | 34.1483 | 1.33530 | ||||||||
\(655\) | −8.80602 | −0.344079 | ||||||||
\(656\) | −10.0120 | −0.390901 | ||||||||
\(657\) | −39.1974 | −1.52924 | ||||||||
\(658\) | 11.6169 | 0.452876 | ||||||||
\(659\) | 37.2268 | 1.45015 | 0.725074 | − | 0.688671i | \(-0.241805\pi\) | ||||
0.725074 | + | 0.688671i | \(0.241805\pi\) | |||||||
\(660\) | −5.02177 | −0.195472 | ||||||||
\(661\) | −10.9786 | −0.427018 | −0.213509 | − | 0.976941i | \(-0.568489\pi\) | ||||
−0.213509 | + | 0.976941i | \(0.568489\pi\) | |||||||
\(662\) | 20.3542 | 0.791089 | ||||||||
\(663\) | 3.08625 | 0.119860 | ||||||||
\(664\) | −13.3912 | −0.519681 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.38319 | −0.363591 | ||||||||
\(667\) | 14.6811 | 0.568454 | ||||||||
\(668\) | −22.1964 | −0.858806 | ||||||||
\(669\) | 24.1270 | 0.932802 | ||||||||
\(670\) | 14.6271 | 0.565094 | ||||||||
\(671\) | −2.35695 | −0.0909889 | ||||||||
\(672\) | −2.40760 | −0.0928754 | ||||||||
\(673\) | −7.09081 | −0.273331 | −0.136665 | − | 0.990617i | \(-0.543638\pi\) | ||||
−0.136665 | + | 0.990617i | \(0.543638\pi\) | |||||||
\(674\) | −14.8090 | −0.570423 | ||||||||
\(675\) | −0.929327 | −0.0357698 | ||||||||
\(676\) | −12.8693 | −0.494972 | ||||||||
\(677\) | 4.66569 | 0.179317 | 0.0896584 | − | 0.995973i | \(-0.471422\pi\) | ||||
0.0896584 | + | 0.995973i | \(0.471422\pi\) | |||||||
\(678\) | 9.19910 | 0.353289 | ||||||||
\(679\) | −3.99766 | −0.153416 | ||||||||
\(680\) | −6.24487 | −0.239480 | ||||||||
\(681\) | −17.9000 | −0.685930 | ||||||||
\(682\) | −1.63592 | −0.0626426 | ||||||||
\(683\) | 33.2650 | 1.27285 | 0.636425 | − | 0.771338i | \(-0.280412\pi\) | ||||
0.636425 | + | 0.771338i | \(0.280412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.7923 | 1.40576 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −9.53753 | −0.363880 | ||||||||
\(688\) | 3.47246 | 0.132386 | ||||||||
\(689\) | 4.34488 | 0.165527 | ||||||||
\(690\) | −12.2005 | −0.464466 | ||||||||
\(691\) | 27.5209 | 1.04694 | 0.523472 | − | 0.852043i | \(-0.324637\pi\) | ||||
0.523472 | + | 0.852043i | \(0.324637\pi\) | |||||||
\(692\) | −10.8227 | −0.411418 | ||||||||
\(693\) | −3.31153 | −0.125794 | ||||||||
\(694\) | 19.0467 | 0.723004 | ||||||||
\(695\) | −23.3203 | −0.884588 | ||||||||
\(696\) | −12.2862 | −0.465707 | ||||||||
\(697\) | −35.4956 | −1.34449 | ||||||||
\(698\) | 21.1239 | 0.799550 | ||||||||
\(699\) | 34.6356 | 1.31004 | ||||||||
\(700\) | 1.89733 | 0.0717125 | ||||||||
\(701\) | 6.21171 | 0.234613 | 0.117306 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117306 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(702\) | 0.177098 | 0.00668415 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.18414 | 0.0446291 | ||||||||
\(705\) | −49.2657 | −1.85545 | ||||||||
\(706\) | −2.24313 | −0.0844213 | ||||||||
\(707\) | 18.6641 | 0.701937 | ||||||||
\(708\) | −18.6044 | −0.699196 | ||||||||
\(709\) | −1.17736 | −0.0442167 | −0.0221083 | − | 0.999756i | \(-0.507038\pi\) | ||||
−0.0221083 | + | 0.999756i | \(0.507038\pi\) | |||||||
\(710\) | −0.399377 | −0.0149883 | ||||||||
\(711\) | −14.7676 | −0.553828 | ||||||||
\(712\) | −1.87916 | −0.0704246 | ||||||||
\(713\) | −3.97451 | −0.148847 | ||||||||
\(714\) | −8.53574 | −0.319442 | ||||||||
\(715\) | −0.754157 | −0.0282039 | ||||||||
\(716\) | 11.7586 | 0.439440 | ||||||||
\(717\) | 17.1428 | 0.640209 | ||||||||
\(718\) | −3.31981 | −0.123894 | ||||||||
\(719\) | 37.2872 | 1.39058 | 0.695289 | − | 0.718730i | \(-0.255276\pi\) | ||||
0.695289 | + | 0.718730i | \(0.255276\pi\) | |||||||
\(720\) | 4.92597 | 0.183580 | ||||||||
\(721\) | −2.35245 | −0.0876097 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.0698 | −1.34145 | ||||||||
\(724\) | −1.62634 | −0.0604426 | ||||||||
\(725\) | 9.68225 | 0.359590 | ||||||||
\(726\) | −23.1077 | −0.857608 | ||||||||
\(727\) | 17.8760 | 0.662983 | 0.331492 | − | 0.943458i | \(-0.392448\pi\) | ||||
0.331492 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(728\) | −0.361568 | −0.0134006 | ||||||||
\(729\) | −23.2223 | −0.860085 | ||||||||
\(730\) | 24.6888 | 0.913775 | ||||||||
\(731\) | 12.3110 | 0.455338 | ||||||||
\(732\) | 4.79215 | 0.177123 | ||||||||
\(733\) | 7.02123 | 0.259335 | 0.129667 | − | 0.991558i | \(-0.458609\pi\) | ||||
0.129667 | + | 0.991558i | \(0.458609\pi\) | |||||||
\(734\) | 18.3886 | 0.678734 | ||||||||
\(735\) | −4.24085 | −0.156426 | ||||||||
\(736\) | 2.87691 | 0.106044 | ||||||||
\(737\) | −9.83320 | −0.362211 | ||||||||
\(738\) | 27.9990 | 1.03066 | ||||||||
\(739\) | −46.3549 | −1.70519 | −0.852596 | − | 0.522570i | \(-0.824973\pi\) | ||||
−0.852596 | + | 0.522570i | \(0.824973\pi\) | |||||||
\(740\) | 5.91009 | 0.217259 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0168 | −0.441150 | ||||||||
\(743\) | −11.0899 | −0.406850 | −0.203425 | − | 0.979091i | \(-0.565207\pi\) | ||||
−0.203425 | + | 0.979091i | \(0.565207\pi\) | |||||||
\(744\) | 3.32616 | 0.121943 | ||||||||
\(745\) | 5.42903 | 0.198904 | ||||||||
\(746\) | −3.33060 | −0.121942 | ||||||||
\(747\) | 37.4494 | 1.37020 | ||||||||
\(748\) | 4.19817 | 0.153500 | ||||||||
\(749\) | −3.11852 | −0.113948 | ||||||||
\(750\) | −29.2505 | −1.06808 | ||||||||
\(751\) | −16.6367 | −0.607080 | −0.303540 | − | 0.952819i | \(-0.598169\pi\) | ||||
−0.303540 | + | 0.952819i | \(0.598169\pi\) | |||||||
\(752\) | 11.6169 | 0.423626 | ||||||||
\(753\) | 68.0424 | 2.47960 | ||||||||
\(754\) | −1.84511 | −0.0671949 | ||||||||
\(755\) | 11.1915 | 0.407302 | ||||||||
\(756\) | −0.489807 | −0.0178141 | ||||||||
\(757\) | −23.9144 | −0.869185 | −0.434592 | − | 0.900627i | \(-0.643108\pi\) | ||||
−0.434592 | + | 0.900627i | \(0.643108\pi\) | |||||||
\(758\) | 30.8785 | 1.12156 | ||||||||
\(759\) | 8.20191 | 0.297711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.6040 | 1.83439 | 0.917196 | − | 0.398435i | \(-0.130447\pi\) | ||||
0.917196 | + | 0.398435i | \(0.130447\pi\) | |||||||
\(762\) | 46.6631 | 1.69042 | ||||||||
\(763\) | −14.1835 | −0.513477 | ||||||||
\(764\) | 15.1136 | 0.546792 | ||||||||
\(765\) | 17.4641 | 0.631418 | ||||||||
\(766\) | −4.18785 | −0.151313 | ||||||||
\(767\) | −2.79396 | −0.100884 | ||||||||
\(768\) | −2.40760 | −0.0868769 | ||||||||
\(769\) | −8.66228 | −0.312370 | −0.156185 | − | 0.987728i | \(-0.549920\pi\) | ||||
−0.156185 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(770\) | 2.08580 | 0.0751669 | ||||||||
\(771\) | −27.7348 | −0.998843 | ||||||||
\(772\) | 21.0053 | 0.755998 | ||||||||
\(773\) | −28.4345 | −1.02272 | −0.511358 | − | 0.859368i | \(-0.670858\pi\) | ||||
−0.511358 | + | 0.859368i | \(0.670858\pi\) | |||||||
\(774\) | −9.71093 | −0.349052 | ||||||||
\(775\) | −2.62121 | −0.0941566 | ||||||||
\(776\) | −3.99766 | −0.143508 | ||||||||
\(777\) | 8.07815 | 0.289802 | ||||||||
\(778\) | −13.7229 | −0.491990 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.53335 | 0.0549029 | ||||||||
\(781\) | 0.268485 | 0.00960713 | ||||||||
\(782\) | 10.1996 | 0.364736 | ||||||||
\(783\) | −2.49952 | −0.0893257 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 7.41422 | 0.264625 | ||||||||
\(786\) | −12.0364 | −0.429325 | ||||||||
\(787\) | −7.80328 | −0.278157 | −0.139078 | − | 0.990281i | \(-0.544414\pi\) | ||||
−0.139078 | + | 0.990281i | \(0.544414\pi\) | |||||||
\(788\) | −24.5580 | −0.874844 | ||||||||
\(789\) | −64.2474 | −2.28727 | ||||||||
\(790\) | 9.30151 | 0.330933 | ||||||||
\(791\) | −3.82085 | −0.135854 | ||||||||
\(792\) | −3.31153 | −0.117670 | ||||||||
\(793\) | 0.719673 | 0.0255564 | ||||||||
\(794\) | 12.7243 | 0.451568 | ||||||||
\(795\) | 50.9613 | 1.80741 | ||||||||
\(796\) | 5.50367 | 0.195073 | ||||||||
\(797\) | −22.7219 | −0.804849 | −0.402425 | − | 0.915453i | \(-0.631832\pi\) | ||||
−0.402425 | + | 0.915453i | \(0.631832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.1858 | 1.45705 | ||||||||
\(800\) | 1.89733 | 0.0670809 | ||||||||
\(801\) | 5.25519 | 0.185683 | ||||||||
\(802\) | 27.5174 | 0.971673 | ||||||||
\(803\) | −16.5973 | −0.585706 | ||||||||
\(804\) | 19.9929 | 0.705095 | ||||||||
\(805\) | 5.06749 | 0.178606 | ||||||||
\(806\) | 0.499514 | 0.0175946 | ||||||||
\(807\) | −4.99175 | −0.175718 | ||||||||
\(808\) | 18.6641 | 0.656602 | ||||||||
\(809\) | −4.48771 | −0.157779 | −0.0788897 | − | 0.996883i | \(-0.525137\pi\) | ||||
−0.0788897 | + | 0.996883i | \(0.525137\pi\) | |||||||
\(810\) | 16.8551 | 0.592228 | ||||||||
\(811\) | 17.5040 | 0.614648 | 0.307324 | − | 0.951605i | \(-0.400566\pi\) | ||||
0.307324 | + | 0.951605i | \(0.400566\pi\) | |||||||
\(812\) | 5.10308 | 0.179083 | ||||||||
\(813\) | 55.6121 | 1.95040 | ||||||||
\(814\) | −3.97311 | −0.139258 | ||||||||
\(815\) | 12.6062 | 0.441577 | ||||||||
\(816\) | −8.53574 | −0.298811 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 30.1566 | 1.05440 | ||||||||
\(819\) | 1.01115 | 0.0353323 | ||||||||
\(820\) | −17.6355 | −0.615857 | ||||||||
\(821\) | 9.51661 | 0.332132 | 0.166066 | − | 0.986115i | \(-0.446893\pi\) | ||||
0.166066 | + | 0.986115i | \(0.446893\pi\) | |||||||
\(822\) | 50.2892 | 1.75404 | ||||||||
\(823\) | 31.8532 | 1.11033 | 0.555167 | − | 0.831739i | \(-0.312654\pi\) | ||||
0.555167 | + | 0.831739i | \(0.312654\pi\) | |||||||
\(824\) | −2.35245 | −0.0819513 | ||||||||
\(825\) | 5.40920 | 0.188324 | ||||||||
\(826\) | 7.72735 | 0.268869 | ||||||||
\(827\) | −10.9457 | −0.380620 | −0.190310 | − | 0.981724i | \(-0.560949\pi\) | ||||
−0.190310 | + | 0.981724i | \(0.560949\pi\) | |||||||
\(828\) | −8.04544 | −0.279598 | ||||||||
\(829\) | 30.2531 | 1.05073 | 0.525366 | − | 0.850876i | \(-0.323928\pi\) | ||||
0.525366 | + | 0.850876i | \(0.323928\pi\) | |||||||
\(830\) | −23.5878 | −0.818746 | ||||||||
\(831\) | −49.0622 | −1.70195 | ||||||||
\(832\) | −0.361568 | −0.0125351 | ||||||||
\(833\) | 3.54532 | 0.122838 | ||||||||
\(834\) | −31.8750 | −1.10374 | ||||||||
\(835\) | −39.0977 | −1.35303 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.676679 | 0.0233894 | ||||||||
\(838\) | −25.2631 | −0.872699 | ||||||||
\(839\) | −38.9311 | −1.34405 | −0.672025 | − | 0.740528i | \(-0.734575\pi\) | ||||
−0.672025 | + | 0.740528i | \(0.734575\pi\) | |||||||
\(840\) | −4.24085 | −0.146323 | ||||||||
\(841\) | −2.95857 | −0.102020 | ||||||||
\(842\) | −38.0387 | −1.31090 | ||||||||
\(843\) | 37.7110 | 1.29884 | ||||||||
\(844\) | −4.53017 | −0.155935 | ||||||||
\(845\) | −22.6684 | −0.779818 | ||||||||
\(846\) | −32.4875 | −1.11694 | ||||||||
\(847\) | 9.59781 | 0.329784 | ||||||||
\(848\) | −12.0168 | −0.412658 | ||||||||
\(849\) | −5.71150 | −0.196018 | ||||||||
\(850\) | 6.72666 | 0.230723 | ||||||||
\(851\) | −9.65278 | −0.330893 | ||||||||
\(852\) | −0.545884 | −0.0187017 | ||||||||
\(853\) | −40.9671 | −1.40269 | −0.701344 | − | 0.712823i | \(-0.747416\pi\) | ||||
−0.701344 | + | 0.712823i | \(0.747416\pi\) | |||||||
\(854\) | −1.99042 | −0.0681109 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.11852 | −0.106589 | ||||||||
\(857\) | 13.0672 | 0.446367 | 0.223184 | − | 0.974776i | \(-0.428355\pi\) | ||||
0.223184 | + | 0.974776i | \(0.428355\pi\) | |||||||
\(858\) | −1.03081 | −0.0351913 | ||||||||
\(859\) | 14.8518 | 0.506735 | 0.253368 | − | 0.967370i | \(-0.418462\pi\) | ||||
0.253368 | + | 0.967370i | \(0.418462\pi\) | |||||||
\(860\) | 6.11652 | 0.208572 | ||||||||
\(861\) | −24.1048 | −0.821491 | ||||||||
\(862\) | 18.9095 | 0.644059 | ||||||||
\(863\) | 56.6176 | 1.92729 | 0.963643 | − | 0.267193i | \(-0.0860962\pi\) | ||||
0.963643 | + | 0.267193i | \(0.0860962\pi\) | |||||||
\(864\) | −0.489807 | −0.0166636 | ||||||||
\(865\) | −19.0635 | −0.648180 | ||||||||
\(866\) | −12.6102 | −0.428513 | ||||||||
\(867\) | 10.6673 | 0.362281 | ||||||||
\(868\) | −1.38152 | −0.0468919 | ||||||||
\(869\) | −6.25303 | −0.212119 | ||||||||
\(870\) | −21.6414 | −0.733712 | ||||||||
\(871\) | 3.00248 | 0.101735 | ||||||||
\(872\) | −14.1835 | −0.480314 | ||||||||
\(873\) | 11.1797 | 0.378375 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1492 | 0.410719 | ||||||||
\(876\) | 33.7457 | 1.14016 | ||||||||
\(877\) | 29.6812 | 1.00226 | 0.501131 | − | 0.865372i | \(-0.332918\pi\) | ||||
0.501131 | + | 0.865372i | \(0.332918\pi\) | |||||||
\(878\) | 33.9256 | 1.14494 | ||||||||
\(879\) | −1.41221 | −0.0476327 | ||||||||
\(880\) | 2.08580 | 0.0703122 | ||||||||
\(881\) | −21.9013 | −0.737875 | −0.368937 | − | 0.929454i | \(-0.620278\pi\) | ||||
−0.368937 | + | 0.929454i | \(0.620278\pi\) | |||||||
\(882\) | −2.79656 | −0.0941650 | ||||||||
\(883\) | −22.8216 | −0.768008 | −0.384004 | − | 0.923331i | \(-0.625455\pi\) | ||||
−0.384004 | + | 0.923331i | \(0.625455\pi\) | |||||||
\(884\) | −1.28188 | −0.0431141 | ||||||||
\(885\) | −32.7705 | −1.10157 | ||||||||
\(886\) | 4.69792 | 0.157830 | ||||||||
\(887\) | −19.8209 | −0.665519 | −0.332760 | − | 0.943012i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943012i | \(0.607980\pi\) | |||||||
\(888\) | 8.07815 | 0.271085 | ||||||||
\(889\) | −19.3815 | −0.650036 | ||||||||
\(890\) | −3.31003 | −0.110952 | ||||||||
\(891\) | −11.3310 | −0.379602 | ||||||||
\(892\) | −10.0211 | −0.335533 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.42061 | 0.248182 | ||||||||
\(895\) | 20.7121 | 0.692329 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −2.50438 | −0.0836189 | ||||||||
\(898\) | 25.3251 | 0.845109 | ||||||||
\(899\) | −7.05002 | −0.235131 | ||||||||
\(900\) | −5.30600 | −0.176867 | ||||||||
\(901\) | −42.6034 | −1.41932 | ||||||||
\(902\) | 11.8556 | 0.394748 | ||||||||
\(903\) | 8.36030 | 0.278213 | ||||||||
\(904\) | −3.82085 | −0.127080 | ||||||||
\(905\) | −2.86470 | −0.0952260 | ||||||||
\(906\) | 15.2970 | 0.508210 | ||||||||
\(907\) | 51.2543 | 1.70187 | 0.850936 | − | 0.525270i | \(-0.176035\pi\) | ||||
0.850936 | + | 0.525270i | \(0.176035\pi\) | |||||||
\(908\) | 7.43478 | 0.246732 | ||||||||
\(909\) | −52.1953 | −1.73121 | ||||||||
\(910\) | −0.636880 | −0.0211124 | ||||||||
\(911\) | 31.5849 | 1.04646 | 0.523228 | − | 0.852193i | \(-0.324728\pi\) | ||||
0.523228 | + | 0.852193i | \(0.324728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.8571 | 0.524795 | ||||||||
\(914\) | 40.3466 | 1.33455 | ||||||||
\(915\) | 8.44108 | 0.279054 | ||||||||
\(916\) | 3.96142 | 0.130889 | ||||||||
\(917\) | 4.99933 | 0.165092 | ||||||||
\(918\) | −1.73652 | −0.0573138 | ||||||||
\(919\) | −9.70848 | −0.320253 | −0.160127 | − | 0.987096i | \(-0.551190\pi\) | ||||
−0.160127 | + | 0.987096i | \(0.551190\pi\) | |||||||
\(920\) | 5.06749 | 0.167070 | ||||||||
\(921\) | 47.9599 | 1.58033 | ||||||||
\(922\) | −8.28479 | −0.272845 | ||||||||
\(923\) | −0.0819794 | −0.00269839 | ||||||||
\(924\) | 2.85095 | 0.0937893 | ||||||||
\(925\) | −6.36605 | −0.209315 | ||||||||
\(926\) | 26.7426 | 0.878815 | ||||||||
\(927\) | 6.57875 | 0.216075 | ||||||||
\(928\) | 5.10308 | 0.167517 | ||||||||
\(929\) | −11.8253 | −0.387977 | −0.193988 | − | 0.981004i | \(-0.562142\pi\) | ||||
−0.193988 | + | 0.981004i | \(0.562142\pi\) | |||||||
\(930\) | 5.85882 | 0.192118 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.3859 | −0.471226 | ||||||||
\(933\) | 35.2342 | 1.15352 | ||||||||
\(934\) | −7.29907 | −0.238833 | ||||||||
\(935\) | 7.39482 | 0.241837 | ||||||||
\(936\) | 1.01115 | 0.0330503 | ||||||||
\(937\) | 39.1239 | 1.27812 | 0.639062 | − | 0.769155i | \(-0.279323\pi\) | ||||
0.639062 | + | 0.769155i | \(0.279323\pi\) | |||||||
\(938\) | −8.30406 | −0.271137 | ||||||||
\(939\) | 64.8273 | 2.11556 | ||||||||
\(940\) | 20.4625 | 0.667414 | ||||||||
\(941\) | −16.5733 | −0.540274 | −0.270137 | − | 0.962822i | \(-0.587069\pi\) | ||||
−0.270137 | + | 0.962822i | \(0.587069\pi\) | |||||||
\(942\) | 10.1340 | 0.330185 | ||||||||
\(943\) | 28.8035 | 0.937970 | ||||||||
\(944\) | 7.72735 | 0.251504 | ||||||||
\(945\) | −0.862765 | −0.0280657 | ||||||||
\(946\) | −4.11189 | −0.133689 | ||||||||
\(947\) | 27.0746 | 0.879805 | 0.439902 | − | 0.898046i | \(-0.355013\pi\) | ||||
0.439902 | + | 0.898046i | \(0.355013\pi\) | |||||||
\(948\) | 12.7137 | 0.412921 | ||||||||
\(949\) | 5.06784 | 0.164509 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.6178 | 2.38722 | ||||||||
\(952\) | 3.54532 | 0.114905 | ||||||||
\(953\) | 23.7483 | 0.769284 | 0.384642 | − | 0.923066i | \(-0.374325\pi\) | ||||
0.384642 | + | 0.923066i | \(0.374325\pi\) | |||||||
\(954\) | 33.6056 | 1.08802 | ||||||||
\(955\) | 26.6218 | 0.861460 | ||||||||
\(956\) | −7.12027 | −0.230286 | ||||||||
\(957\) | 14.5486 | 0.470290 | ||||||||
\(958\) | 27.1804 | 0.878160 | ||||||||
\(959\) | −20.8876 | −0.674497 | ||||||||
\(960\) | −4.24085 | −0.136873 | ||||||||
\(961\) | −29.0914 | −0.938432 | ||||||||
\(962\) | 1.21316 | 0.0391137 | ||||||||
\(963\) | 8.72113 | 0.281034 | ||||||||
\(964\) | 14.9816 | 0.482525 | ||||||||
\(965\) | 36.9996 | 1.19106 | ||||||||
\(966\) | 6.92645 | 0.222855 | ||||||||
\(967\) | 43.7978 | 1.40844 | 0.704221 | − | 0.709981i | \(-0.251297\pi\) | ||||
0.704221 | + | 0.709981i | \(0.251297\pi\) | |||||||
\(968\) | 9.59781 | 0.308485 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.04163 | −0.226093 | ||||||||
\(971\) | −17.3224 | −0.555901 | −0.277951 | − | 0.960595i | \(-0.589655\pi\) | ||||
−0.277951 | + | 0.960595i | \(0.589655\pi\) | |||||||
\(972\) | 21.5688 | 0.691819 | ||||||||
\(973\) | 13.2393 | 0.424433 | ||||||||
\(974\) | 6.88190 | 0.220510 | ||||||||
\(975\) | −1.65165 | −0.0528952 | ||||||||
\(976\) | −1.99042 | −0.0637119 | ||||||||
\(977\) | 55.2674 | 1.76816 | 0.884080 | − | 0.467336i | \(-0.154786\pi\) | ||||
0.884080 | + | 0.467336i | \(0.154786\pi\) | |||||||
\(978\) | 17.2307 | 0.550977 | ||||||||
\(979\) | 2.22520 | 0.0711176 | ||||||||
\(980\) | 1.76144 | 0.0562671 | ||||||||
\(981\) | 39.6650 | 1.26641 | ||||||||
\(982\) | 9.47678 | 0.302416 | ||||||||
\(983\) | 15.1410 | 0.482922 | 0.241461 | − | 0.970411i | \(-0.422373\pi\) | ||||
0.241461 | + | 0.970411i | \(0.422373\pi\) | |||||||
\(984\) | −24.1048 | −0.768434 | ||||||||
\(985\) | −43.2575 | −1.37830 | ||||||||
\(986\) | 18.0921 | 0.576169 | ||||||||
\(987\) | 27.9690 | 0.890263 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.98994 | −0.317662 | ||||||||
\(990\) | −5.83305 | −0.185386 | ||||||||
\(991\) | 32.4171 | 1.02976 | 0.514882 | − | 0.857261i | \(-0.327836\pi\) | ||||
0.514882 | + | 0.857261i | \(0.327836\pi\) | |||||||
\(992\) | −1.38152 | −0.0438634 | ||||||||
\(993\) | 49.0049 | 1.55512 | ||||||||
\(994\) | 0.226733 | 0.00719154 | ||||||||
\(995\) | 9.69439 | 0.307333 | ||||||||
\(996\) | −32.2408 | −1.02159 | ||||||||
\(997\) | 49.4268 | 1.56536 | 0.782681 | − | 0.622423i | \(-0.213852\pi\) | ||||
0.782681 | + | 0.622423i | \(0.213852\pi\) | |||||||
\(998\) | 5.58793 | 0.176883 | ||||||||
\(999\) | 1.64343 | 0.0519959 |
(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 | 5054.2.a.bf.1.2 | ✓ | 8 | |
19.18 | odd | 2 | 5054.2.a.bi.1.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bf.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5054.2.a.bi.1.7 | yes | 8 | 19.18 | odd | 2 |