Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, 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("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.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: | \(7.54586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | 1.23607 | 0.372689 | 0.186344 | − | 0.982485i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.47214 | −1.79505 | −0.897524 | − | 0.440966i | \(-0.854636\pi\) | ||||
−0.897524 | + | 0.440966i | \(0.854636\pi\) | |||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −0.236068 | −0.0572549 | −0.0286274 | − | 0.999590i | \(-0.509114\pi\) | ||||
−0.0286274 | + | 0.999590i | \(0.509114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.47214 | 0.337731 | 0.168866 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168866 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −1.76393 | −0.367805 | −0.183903 | − | 0.982944i | \(-0.558873\pi\) | ||||
−0.183903 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 10.4721 | 2.05375 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.618034 | −0.116797 | ||||||||
\(29\) | 5.70820 | 1.05999 | 0.529993 | − | 0.848002i | \(-0.322194\pi\) | ||||
0.529993 | + | 0.848002i | \(0.322194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.00000 | −1.61645 | −0.808224 | − | 0.588875i | \(-0.799571\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.381966 | 0.0655066 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70820 | 0.609625 | 0.304812 | − | 0.952412i | \(-0.401406\pi\) | ||||
0.304812 | + | 0.952412i | \(0.401406\pi\) | |||||||
\(38\) | −2.38197 | −0.386406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23607 | 0.353553 | ||||||||
\(41\) | −0.472136 | −0.0737352 | −0.0368676 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368676 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.472136 | 0.0720001 | 0.0360000 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360000 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(44\) | 0.763932 | 0.115167 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.85410 | 0.420814 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.61803 | −0.228825 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | −9.94427 | −1.36595 | −0.682975 | − | 0.730441i | \(-0.739314\pi\) | ||||
−0.682975 | + | 0.730441i | \(0.739314\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23607 | 0.166671 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.23607 | −1.21276 | ||||||||
\(59\) | −1.70820 | −0.222389 | −0.111195 | − | 0.993799i | \(-0.535468\pi\) | ||||
−0.111195 | + | 0.993799i | \(0.535468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7082 | −1.62712 | −0.813559 | − | 0.581482i | \(-0.802473\pi\) | ||||
−0.813559 | + | 0.581482i | \(0.802473\pi\) | |||||||
\(62\) | 14.5623 | 1.84941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −6.47214 | −0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.94427 | −0.848378 | −0.424189 | − | 0.905574i | \(-0.639441\pi\) | ||||
−0.424189 | + | 0.905574i | \(0.639441\pi\) | |||||||
\(68\) | −0.145898 | −0.0176927 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.61803 | 0.193392 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.47214 | −0.991589 | −0.495794 | − | 0.868440i | \(-0.665123\pi\) | ||||
−0.495794 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.909830 | 0.104365 | ||||||||
\(77\) | −1.23607 | −0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.18034 | 0.582834 | 0.291417 | − | 0.956596i | \(-0.405873\pi\) | ||||
0.291417 | + | 0.956596i | \(0.405873\pi\) | |||||||
\(80\) | −4.85410 | −0.542705 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.763932 | 0.0843622 | ||||||||
\(83\) | −11.0000 | −1.20741 | −0.603703 | − | 0.797209i | \(-0.706309\pi\) | ||||
−0.603703 | + | 0.797209i | \(0.706309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.236068 | −0.0256052 | ||||||||
\(86\) | −0.763932 | −0.0823769 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.76393 | 0.294636 | ||||||||
\(89\) | 14.1803 | 1.50311 | 0.751557 | − | 0.659669i | \(-0.229303\pi\) | ||||
0.751557 | + | 0.659669i | \(0.229303\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.47214 | 0.678464 | ||||||||
\(92\) | −1.09017 | −0.113658 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.47214 | 0.667550 | ||||||||
\(95\) | 1.47214 | 0.151038 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.763932 | −0.0775655 | −0.0387828 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387828 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(98\) | −1.61803 | −0.163446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.618034 | 0.0618034 | ||||||||
\(101\) | −16.1803 | −1.61000 | −0.805002 | − | 0.593272i | \(-0.797836\pi\) | ||||
−0.805002 | + | 0.593272i | \(0.797836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2361 | −1.50125 | −0.750627 | − | 0.660726i | \(-0.770249\pi\) | ||||
−0.750627 | + | 0.660726i | \(0.770249\pi\) | |||||||
\(104\) | −14.4721 | −1.41911 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.0902 | 1.56282 | ||||||||
\(107\) | −15.4164 | −1.49036 | −0.745180 | − | 0.666863i | \(-0.767637\pi\) | ||||
−0.745180 | + | 0.666863i | \(0.767637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | 0.0957826 | 0.0478913 | − | 0.998853i | \(-0.484750\pi\) | ||||
0.0478913 | + | 0.998853i | \(0.484750\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.85410 | 0.458670 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.76393 | −0.164488 | ||||||||
\(116\) | 3.52786 | 0.327554 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 0.236068 | 0.0216403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 20.5623 | 1.86162 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.56231 | −0.499510 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.18034 | −0.548416 | −0.274208 | − | 0.961670i | \(-0.588416\pi\) | ||||
−0.274208 | + | 0.961670i | \(0.588416\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.4721 | 0.918467 | ||||||||
\(131\) | 21.2361 | 1.85540 | 0.927702 | − | 0.373322i | \(-0.121781\pi\) | ||||
0.927702 | + | 0.373322i | \(0.121781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47214 | −0.127650 | ||||||||
\(134\) | 11.2361 | 0.970648 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.527864 | −0.0452640 | ||||||||
\(137\) | −15.9443 | −1.36221 | −0.681106 | − | 0.732185i | \(-0.738501\pi\) | ||||
−0.681106 | + | 0.732185i | \(0.738501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4721 | 1.22751 | 0.613755 | − | 0.789496i | \(-0.289658\pi\) | ||||
0.613755 | + | 0.789496i | \(0.289658\pi\) | |||||||
\(140\) | −0.618034 | −0.0522334 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.23607 | −0.271565 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.70820 | 0.474041 | ||||||||
\(146\) | 13.7082 | 1.13450 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.29180 | 0.188384 | ||||||||
\(149\) | −10.9443 | −0.896590 | −0.448295 | − | 0.893886i | \(-0.647969\pi\) | ||||
−0.448295 | + | 0.893886i | \(0.647969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8885 | −1.45575 | −0.727875 | − | 0.685710i | \(-0.759492\pi\) | ||||
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(152\) | 3.29180 | 0.267000 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | −9.00000 | −0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.23607 | −0.417884 | −0.208942 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208942 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(158\) | −8.38197 | −0.666833 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.38197 | 0.267368 | ||||||||
\(161\) | 1.76393 | 0.139017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.76393 | 0.529792 | 0.264896 | − | 0.964277i | \(-0.414662\pi\) | ||||
0.264896 | + | 0.964277i | \(0.414662\pi\) | |||||||
\(164\) | −0.291796 | −0.0227854 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7984 | 1.38142 | ||||||||
\(167\) | 11.9443 | 0.924276 | 0.462138 | − | 0.886808i | \(-0.347083\pi\) | ||||
0.462138 | + | 0.886808i | \(0.347083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 0.381966 | 0.0292955 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.291796 | 0.0222492 | ||||||||
\(173\) | 9.18034 | 0.697968 | 0.348984 | − | 0.937129i | \(-0.386527\pi\) | ||||
0.348984 | + | 0.937129i | \(0.386527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.9443 | −1.71975 | ||||||||
\(179\) | −11.4164 | −0.853302 | −0.426651 | − | 0.904416i | \(-0.640307\pi\) | ||||
−0.426651 | + | 0.904416i | \(0.640307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.23607 | 0.612182 | 0.306091 | − | 0.952002i | \(-0.400979\pi\) | ||||
0.306091 | + | 0.952002i | \(0.400979\pi\) | |||||||
\(182\) | −10.4721 | −0.776246 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.94427 | −0.290776 | ||||||||
\(185\) | 3.70820 | 0.272633 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.291796 | −0.0213382 | ||||||||
\(188\) | −2.47214 | −0.180299 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.38197 | −0.172806 | ||||||||
\(191\) | 25.2361 | 1.82602 | 0.913009 | − | 0.407940i | \(-0.133753\pi\) | ||||
0.913009 | + | 0.407940i | \(0.133753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.4164 | 1.68555 | 0.842775 | − | 0.538266i | \(-0.180920\pi\) | ||||
0.842775 | + | 0.538266i | \(0.180920\pi\) | |||||||
\(194\) | 1.23607 | 0.0887445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 17.9443 | 1.27848 | 0.639238 | − | 0.769009i | \(-0.279250\pi\) | ||||
0.639238 | + | 0.769009i | \(0.279250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5279 | −1.24252 | −0.621259 | − | 0.783606i | \(-0.713378\pi\) | ||||
−0.621259 | + | 0.783606i | \(0.713378\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.1803 | 1.84204 | ||||||||
\(203\) | −5.70820 | −0.400637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.472136 | −0.0329754 | ||||||||
\(206\) | 24.6525 | 1.71762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 31.4164 | 2.17834 | ||||||||
\(209\) | 1.81966 | 0.125869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7082 | −0.874869 | −0.437434 | − | 0.899250i | \(-0.644113\pi\) | ||||
−0.437434 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(212\) | −6.14590 | −0.422102 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.9443 | 1.70516 | ||||||||
\(215\) | 0.472136 | 0.0321994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | 0.610960 | ||||||||
\(218\) | −1.61803 | −0.109587 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.763932 | 0.0515043 | ||||||||
\(221\) | 1.52786 | 0.102775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6525 | −0.847272 | −0.423636 | − | 0.905832i | \(-0.639247\pi\) | ||||
−0.423636 | + | 0.905832i | \(0.639247\pi\) | |||||||
\(224\) | −3.38197 | −0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.23607 | 0.215260 | ||||||||
\(227\) | −11.0000 | −0.730096 | −0.365048 | − | 0.930989i | \(-0.618947\pi\) | ||||
−0.365048 | + | 0.930989i | \(0.618947\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.76393 | 0.248728 | 0.124364 | − | 0.992237i | \(-0.460311\pi\) | ||||
0.124364 | + | 0.992237i | \(0.460311\pi\) | |||||||
\(230\) | 2.85410 | 0.188194 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.7639 | 0.837993 | ||||||||
\(233\) | 26.3607 | 1.72695 | 0.863473 | − | 0.504395i | \(-0.168285\pi\) | ||||
0.863473 | + | 0.504395i | \(0.168285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | −1.05573 | −0.0687220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.381966 | −0.0247592 | ||||||||
\(239\) | 3.52786 | 0.228199 | 0.114099 | − | 0.993469i | \(-0.463602\pi\) | ||||
0.114099 | + | 0.993469i | \(0.463602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.6525 | 1.65242 | 0.826211 | − | 0.563361i | \(-0.190492\pi\) | ||||
0.826211 | + | 0.563361i | \(0.190492\pi\) | |||||||
\(242\) | 15.3262 | 0.985208 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.85410 | −0.502807 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.52786 | −0.606243 | ||||||||
\(248\) | −20.1246 | −1.27791 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.61803 | −0.102333 | ||||||||
\(251\) | 7.23607 | 0.456737 | 0.228368 | − | 0.973575i | \(-0.426661\pi\) | ||||
0.228368 | + | 0.973575i | \(0.426661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.18034 | −0.137077 | ||||||||
\(254\) | 10.0000 | 0.627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 24.5967 | 1.53430 | 0.767151 | − | 0.641466i | \(-0.221673\pi\) | ||||
0.767151 | + | 0.641466i | \(0.221673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.70820 | −0.230417 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −34.3607 | −2.12281 | ||||||||
\(263\) | −18.4721 | −1.13904 | −0.569520 | − | 0.821977i | \(-0.692871\pi\) | ||||
−0.569520 | + | 0.821977i | \(0.692871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.94427 | −0.610872 | ||||||||
\(266\) | 2.38197 | 0.146048 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.29180 | −0.262163 | ||||||||
\(269\) | 7.70820 | 0.469977 | 0.234989 | − | 0.971998i | \(-0.424495\pi\) | ||||
0.234989 | + | 0.971998i | \(0.424495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.4164 | −1.24021 | −0.620104 | − | 0.784519i | \(-0.712910\pi\) | ||||
−0.620104 | + | 0.784519i | \(0.712910\pi\) | |||||||
\(272\) | 1.14590 | 0.0694803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.7984 | 1.55854 | ||||||||
\(275\) | 1.23607 | 0.0745377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3607 | 1.82420 | 0.912098 | − | 0.409972i | \(-0.134461\pi\) | ||||
0.912098 | + | 0.409972i | \(0.134461\pi\) | |||||||
\(278\) | −23.4164 | −1.40442 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.23607 | −0.133631 | ||||||||
\(281\) | 10.6525 | 0.635473 | 0.317737 | − | 0.948179i | \(-0.397077\pi\) | ||||
0.317737 | + | 0.948179i | \(0.397077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0000 | −1.30776 | −0.653882 | − | 0.756596i | \(-0.726861\pi\) | ||||
−0.653882 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(284\) | 1.23607 | 0.0733471 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.9443 | 0.765411 | ||||||||
\(287\) | 0.472136 | 0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9443 | −0.996722 | ||||||||
\(290\) | −9.23607 | −0.542361 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.23607 | −0.306418 | ||||||||
\(293\) | −9.29180 | −0.542833 | −0.271416 | − | 0.962462i | \(-0.587492\pi\) | ||||
−0.271416 | + | 0.962462i | \(0.587492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.70820 | −0.0994555 | ||||||||
\(296\) | 8.29180 | 0.481951 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.7082 | 1.02581 | ||||||||
\(299\) | 11.4164 | 0.660228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.472136 | −0.0272135 | ||||||||
\(302\) | 28.9443 | 1.66556 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.14590 | −0.409845 | ||||||||
\(305\) | −12.7082 | −0.727670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1246 | 1.31979 | 0.659896 | − | 0.751357i | \(-0.270600\pi\) | ||||
0.659896 | + | 0.751357i | \(0.270600\pi\) | |||||||
\(308\) | −0.763932 | −0.0435291 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.5623 | 0.827083 | ||||||||
\(311\) | −0.944272 | −0.0535447 | −0.0267724 | − | 0.999642i | \(-0.508523\pi\) | ||||
−0.0267724 | + | 0.999642i | \(0.508523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4721 | −0.591920 | −0.295960 | − | 0.955200i | \(-0.595640\pi\) | ||||
−0.295960 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(314\) | 8.47214 | 0.478110 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.20163 | 0.180106 | ||||||||
\(317\) | 11.9443 | 0.670857 | 0.335429 | − | 0.942066i | \(-0.391119\pi\) | ||||
0.335429 | + | 0.942066i | \(0.391119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.05573 | 0.395045 | ||||||||
\(320\) | 4.23607 | 0.236803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.85410 | −0.159053 | ||||||||
\(323\) | −0.347524 | −0.0193368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.47214 | −0.359010 | ||||||||
\(326\) | −10.9443 | −0.606147 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.05573 | −0.0582928 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4164 | −1.06722 | −0.533611 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533611 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(332\) | −6.79837 | −0.373109 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.3262 | −1.05748 | ||||||||
\(335\) | −6.94427 | −0.379406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9443 | 1.14091 | 0.570454 | − | 0.821330i | \(-0.306767\pi\) | ||||
0.570454 | + | 0.821330i | \(0.306767\pi\) | |||||||
\(338\) | −46.7426 | −2.54246 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.145898 | −0.00791243 | ||||||||
\(341\) | −11.1246 | −0.602432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.05573 | 0.0569210 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.8541 | −0.798561 | ||||||||
\(347\) | 20.9443 | 1.12435 | 0.562174 | − | 0.827019i | \(-0.309965\pi\) | ||||
0.562174 | + | 0.827019i | \(0.309965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1803 | −0.598470 | −0.299235 | − | 0.954179i | \(-0.596731\pi\) | ||||
−0.299235 | + | 0.954179i | \(0.596731\pi\) | |||||||
\(350\) | 1.61803 | 0.0864876 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.18034 | 0.222813 | ||||||||
\(353\) | −4.47214 | −0.238028 | −0.119014 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119014 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00000 | 0.106149 | ||||||||
\(356\) | 8.76393 | 0.464487 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.4721 | 0.976283 | ||||||||
\(359\) | −17.4164 | −0.919203 | −0.459601 | − | 0.888125i | \(-0.652008\pi\) | ||||
−0.459601 | + | 0.888125i | \(0.652008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8328 | −0.885938 | ||||||||
\(362\) | −13.3262 | −0.700412 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −8.47214 | −0.443452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.41641 | 0.178335 | 0.0891675 | − | 0.996017i | \(-0.471579\pi\) | ||||
0.0891675 | + | 0.996017i | \(0.471579\pi\) | |||||||
\(368\) | 8.56231 | 0.446341 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 9.94427 | 0.516281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4164 | 0.798231 | 0.399116 | − | 0.916901i | \(-0.369317\pi\) | ||||
0.399116 | + | 0.916901i | \(0.369317\pi\) | |||||||
\(374\) | 0.472136 | 0.0244136 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.94427 | −0.461266 | ||||||||
\(377\) | −36.9443 | −1.90273 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6525 | −1.72861 | −0.864306 | − | 0.502967i | \(-0.832242\pi\) | ||||
−0.864306 | + | 0.502967i | \(0.832242\pi\) | |||||||
\(380\) | 0.909830 | 0.0466733 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −40.8328 | −2.08919 | ||||||||
\(383\) | 10.0557 | 0.513824 | 0.256912 | − | 0.966435i | \(-0.417295\pi\) | ||||
0.256912 | + | 0.966435i | \(0.417295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.23607 | −0.0629959 | ||||||||
\(386\) | −37.8885 | −1.92848 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.472136 | −0.0239691 | ||||||||
\(389\) | 24.6525 | 1.24993 | 0.624965 | − | 0.780653i | \(-0.285113\pi\) | ||||
0.624965 | + | 0.780653i | \(0.285113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.416408 | 0.0210587 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.0344 | −1.46273 | ||||||||
\(395\) | 5.18034 | 0.260651 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2361 | −0.563922 | −0.281961 | − | 0.959426i | \(-0.590985\pi\) | ||||
−0.281961 | + | 0.959426i | \(0.590985\pi\) | |||||||
\(398\) | 28.3607 | 1.42159 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85410 | −0.242705 | ||||||||
\(401\) | −15.5279 | −0.775425 | −0.387712 | − | 0.921780i | \(-0.626735\pi\) | ||||
−0.387712 | + | 0.921780i | \(0.626735\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 58.2492 | 2.90160 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.23607 | 0.458378 | ||||||||
\(407\) | 4.58359 | 0.227200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.23607 | 0.209460 | 0.104730 | − | 0.994501i | \(-0.466602\pi\) | ||||
0.104730 | + | 0.994501i | \(0.466602\pi\) | |||||||
\(410\) | 0.763932 | 0.0377279 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.41641 | −0.463913 | ||||||||
\(413\) | 1.70820 | 0.0840552 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0000 | −0.539969 | ||||||||
\(416\) | −21.8885 | −1.07317 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.94427 | −0.144009 | ||||||||
\(419\) | −12.6525 | −0.618114 | −0.309057 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309057 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.8328 | 1.25901 | 0.629507 | − | 0.776995i | \(-0.283257\pi\) | ||||
0.629507 | + | 0.776995i | \(0.283257\pi\) | |||||||
\(422\) | 20.5623 | 1.00096 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.2361 | −1.07988 | ||||||||
\(425\) | −0.236068 | −0.0114510 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.7082 | 0.614993 | ||||||||
\(428\) | −9.52786 | −0.460547 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.763932 | −0.0368401 | ||||||||
\(431\) | −9.52786 | −0.458941 | −0.229471 | − | 0.973316i | \(-0.573699\pi\) | ||||
−0.229471 | + | 0.973316i | \(0.573699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.763932 | 0.0367122 | 0.0183561 | − | 0.999832i | \(-0.494157\pi\) | ||||
0.0183561 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(434\) | −14.5623 | −0.699013 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.618034 | 0.0295985 | ||||||||
\(437\) | −2.59675 | −0.124219 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.0000 | −1.00228 | −0.501138 | − | 0.865368i | \(-0.667085\pi\) | ||||
−0.501138 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(440\) | 2.76393 | 0.131765 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.47214 | −0.117588 | ||||||||
\(443\) | 30.7082 | 1.45899 | 0.729495 | − | 0.683986i | \(-0.239755\pi\) | ||||
0.729495 | + | 0.683986i | \(0.239755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1803 | 0.672213 | ||||||||
\(446\) | 20.4721 | 0.969384 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.23607 | −0.200135 | ||||||||
\(449\) | 7.05573 | 0.332980 | 0.166490 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166490 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.583592 | −0.0274803 | ||||||||
\(452\) | −1.23607 | −0.0581397 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.7984 | 0.835319 | ||||||||
\(455\) | 6.47214 | 0.303418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0689 | −0.845227 | −0.422613 | − | 0.906310i | \(-0.638887\pi\) | ||||
−0.422613 | + | 0.906310i | \(0.638887\pi\) | |||||||
\(458\) | −6.09017 | −0.284575 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.09017 | −0.0508294 | ||||||||
\(461\) | 28.4721 | 1.32608 | 0.663040 | − | 0.748584i | \(-0.269266\pi\) | ||||
0.663040 | + | 0.748584i | \(0.269266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.4721 | −1.50911 | −0.754554 | − | 0.656238i | \(-0.772147\pi\) | ||||
−0.754554 | + | 0.656238i | \(0.772147\pi\) | |||||||
\(464\) | −27.7082 | −1.28632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42.6525 | −1.97584 | ||||||||
\(467\) | −41.4721 | −1.91910 | −0.959551 | − | 0.281536i | \(-0.909156\pi\) | ||||
−0.959551 | + | 0.281536i | \(0.909156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.94427 | 0.320657 | ||||||||
\(470\) | 6.47214 | 0.298537 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.81966 | −0.175814 | ||||||||
\(473\) | 0.583592 | 0.0268336 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.47214 | 0.0675462 | ||||||||
\(476\) | 0.145898 | 0.00668723 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.70820 | −0.261087 | ||||||||
\(479\) | 21.5967 | 0.986781 | 0.493390 | − | 0.869808i | \(-0.335757\pi\) | ||||
0.493390 | + | 0.869808i | \(0.335757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | −41.5066 | −1.89057 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.85410 | −0.266096 | ||||||||
\(485\) | −0.763932 | −0.0346884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.23607 | −0.0560116 | −0.0280058 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280058 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(488\) | −28.4164 | −1.28635 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.61803 | −0.0730953 | ||||||||
\(491\) | 3.88854 | 0.175488 | 0.0877438 | − | 0.996143i | \(-0.472034\pi\) | ||||
0.0877438 | + | 0.996143i | \(0.472034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.34752 | −0.0606894 | ||||||||
\(494\) | 15.4164 | 0.693617 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.6869 | 1.96160 | ||||||||
\(497\) | −2.00000 | −0.0897123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2361 | 0.458229 | 0.229115 | − | 0.973399i | \(-0.426417\pi\) | ||||
0.229115 | + | 0.973399i | \(0.426417\pi\) | |||||||
\(500\) | 0.618034 | 0.0276393 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.7082 | −0.522563 | ||||||||
\(503\) | −9.94427 | −0.443393 | −0.221697 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221697 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1803 | −0.720016 | ||||||||
\(506\) | 3.52786 | 0.156833 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.81966 | −0.169470 | ||||||||
\(509\) | −36.3607 | −1.61166 | −0.805829 | − | 0.592148i | \(-0.798280\pi\) | ||||
−0.805829 | + | 0.592148i | \(0.798280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.47214 | 0.374785 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −39.7984 | −1.75543 | ||||||||
\(515\) | −15.2361 | −0.671381 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.94427 | −0.217449 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4721 | −0.634645 | ||||||||
\(521\) | −28.2918 | −1.23949 | −0.619743 | − | 0.784805i | \(-0.712763\pi\) | ||||
−0.619743 | + | 0.784805i | \(0.712763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.0689 | 1.66464 | 0.832318 | − | 0.554298i | \(-0.187013\pi\) | ||||
0.832318 | + | 0.554298i | \(0.187013\pi\) | |||||||
\(524\) | 13.1246 | 0.573351 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.8885 | 1.30320 | ||||||||
\(527\) | 2.12461 | 0.0925495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8885 | −0.864719 | ||||||||
\(530\) | 16.0902 | 0.698912 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.909830 | −0.0394461 | ||||||||
\(533\) | 3.05573 | 0.132358 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4164 | −0.666509 | ||||||||
\(536\) | −15.5279 | −0.670702 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.4721 | −0.537712 | ||||||||
\(539\) | 1.23607 | 0.0532412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.47214 | 0.364246 | 0.182123 | − | 0.983276i | \(-0.441703\pi\) | ||||
0.182123 | + | 0.983276i | \(0.441703\pi\) | |||||||
\(542\) | 33.0344 | 1.41895 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.798374 | −0.0342300 | ||||||||
\(545\) | 1.00000 | 0.0428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.76393 | −0.289205 | −0.144602 | − | 0.989490i | \(-0.546190\pi\) | ||||
−0.144602 | + | 0.989490i | \(0.546190\pi\) | |||||||
\(548\) | −9.85410 | −0.420946 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 8.40325 | 0.357991 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.18034 | −0.220290 | ||||||||
\(554\) | −49.1246 | −2.08710 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.94427 | 0.379322 | ||||||||
\(557\) | −14.9443 | −0.633209 | −0.316605 | − | 0.948558i | \(-0.602543\pi\) | ||||
−0.316605 | + | 0.948558i | \(0.602543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.05573 | −0.129244 | ||||||||
\(560\) | 4.85410 | 0.205123 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.2361 | −0.727060 | ||||||||
\(563\) | 27.4164 | 1.15546 | 0.577732 | − | 0.816227i | \(-0.303938\pi\) | ||||
0.577732 | + | 0.816227i | \(0.303938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 35.5967 | 1.49624 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.47214 | 0.187647 | ||||||||
\(569\) | 33.5279 | 1.40556 | 0.702781 | − | 0.711407i | \(-0.251942\pi\) | ||||
0.702781 | + | 0.711407i | \(0.251942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.18034 | −0.216790 | −0.108395 | − | 0.994108i | \(-0.534571\pi\) | ||||
−0.108395 | + | 0.994108i | \(0.534571\pi\) | |||||||
\(572\) | −4.94427 | −0.206730 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.763932 | −0.0318859 | ||||||||
\(575\) | −1.76393 | −0.0735611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.5410 | 1.60448 | 0.802242 | − | 0.596999i | \(-0.203640\pi\) | ||||
0.802242 | + | 0.596999i | \(0.203640\pi\) | |||||||
\(578\) | 27.4164 | 1.14037 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.52786 | 0.146487 | ||||||||
\(581\) | 11.0000 | 0.456357 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.2918 | −0.509074 | ||||||||
\(584\) | −18.9443 | −0.783920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0344 | 0.621067 | ||||||||
\(587\) | −46.3050 | −1.91121 | −0.955605 | − | 0.294651i | \(-0.904797\pi\) | ||||
−0.955605 | + | 0.294651i | \(0.904797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.2492 | −0.545925 | ||||||||
\(590\) | 2.76393 | 0.113789 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.0000 | −0.739795 | ||||||||
\(593\) | −23.1803 | −0.951902 | −0.475951 | − | 0.879472i | \(-0.657896\pi\) | ||||
−0.475951 | + | 0.879472i | \(0.657896\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.236068 | 0.00967784 | ||||||||
\(596\) | −6.76393 | −0.277061 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.4721 | −0.755382 | ||||||||
\(599\) | 41.8885 | 1.71152 | 0.855760 | − | 0.517373i | \(-0.173090\pi\) | ||||
0.855760 | + | 0.517373i | \(0.173090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.23607 | 0.172793 | 0.0863964 | − | 0.996261i | \(-0.472465\pi\) | ||||
0.0863964 | + | 0.996261i | \(0.472465\pi\) | |||||||
\(602\) | 0.763932 | 0.0311355 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0557 | −0.449851 | ||||||||
\(605\) | −9.47214 | −0.385097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.58359 | −0.104865 | −0.0524324 | − | 0.998624i | \(-0.516697\pi\) | ||||
−0.0524324 | + | 0.998624i | \(0.516697\pi\) | |||||||
\(608\) | 4.97871 | 0.201914 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.5623 | 0.832543 | ||||||||
\(611\) | 25.8885 | 1.04734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.7082 | 1.03834 | 0.519172 | − | 0.854670i | \(-0.326240\pi\) | ||||
0.519172 | + | 0.854670i | \(0.326240\pi\) | |||||||
\(614\) | −37.4164 | −1.51000 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.76393 | −0.111362 | ||||||||
\(617\) | 8.88854 | 0.357839 | 0.178920 | − | 0.983864i | \(-0.442740\pi\) | ||||
0.178920 | + | 0.983864i | \(0.442740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8328 | −0.435408 | −0.217704 | − | 0.976015i | \(-0.569857\pi\) | ||||
−0.217704 | + | 0.976015i | \(0.569857\pi\) | |||||||
\(620\) | −5.56231 | −0.223388 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.52786 | 0.0612618 | ||||||||
\(623\) | −14.1803 | −0.568123 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.9443 | 0.677229 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.23607 | −0.129133 | ||||||||
\(629\) | −0.875388 | −0.0349040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1803 | 0.683939 | 0.341969 | − | 0.939711i | \(-0.388906\pi\) | ||||
0.341969 | + | 0.939711i | \(0.388906\pi\) | |||||||
\(632\) | 11.5836 | 0.460771 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.3262 | −0.767543 | ||||||||
\(635\) | −6.18034 | −0.245259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.47214 | −0.256435 | ||||||||
\(638\) | −11.4164 | −0.451980 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.6180 | −0.538300 | ||||||||
\(641\) | 13.1246 | 0.518391 | 0.259195 | − | 0.965825i | \(-0.416543\pi\) | ||||
0.259195 | + | 0.965825i | \(0.416543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.6525 | −0.577837 | −0.288919 | − | 0.957354i | \(-0.593296\pi\) | ||||
−0.288919 | + | 0.957354i | \(0.593296\pi\) | |||||||
\(644\) | 1.09017 | 0.0429587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.562306 | 0.0221236 | ||||||||
\(647\) | −11.4721 | −0.451016 | −0.225508 | − | 0.974241i | \(-0.572404\pi\) | ||||
−0.225508 | + | 0.974241i | \(0.572404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.11146 | −0.0828819 | ||||||||
\(650\) | 10.4721 | 0.410751 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.18034 | 0.163715 | ||||||||
\(653\) | 4.88854 | 0.191304 | 0.0956518 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956518 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.2361 | 0.829762 | ||||||||
\(656\) | 2.29180 | 0.0894796 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.47214 | −0.252310 | ||||||||
\(659\) | 13.5279 | 0.526971 | 0.263485 | − | 0.964663i | \(-0.415128\pi\) | ||||
0.263485 | + | 0.964663i | \(0.415128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.3607 | −1.02531 | −0.512656 | − | 0.858594i | \(-0.671338\pi\) | ||||
−0.512656 | + | 0.858594i | \(0.671338\pi\) | |||||||
\(662\) | 31.4164 | 1.22103 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.5967 | −0.954539 | ||||||||
\(665\) | −1.47214 | −0.0570870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0689 | −0.389869 | ||||||||
\(668\) | 7.38197 | 0.285617 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.2361 | 0.434087 | ||||||||
\(671\) | −15.7082 | −0.606408 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2361 | 1.35825 | 0.679125 | − | 0.734022i | \(-0.262359\pi\) | ||||
0.679125 | + | 0.734022i | \(0.262359\pi\) | |||||||
\(674\) | −33.8885 | −1.30534 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8541 | 0.686696 | ||||||||
\(677\) | −15.5279 | −0.596784 | −0.298392 | − | 0.954443i | \(-0.596450\pi\) | ||||
−0.298392 | + | 0.954443i | \(0.596450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.763932 | 0.0293170 | ||||||||
\(680\) | −0.527864 | −0.0202427 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.0000 | 0.689256 | ||||||||
\(683\) | 38.1246 | 1.45880 | 0.729399 | − | 0.684089i | \(-0.239800\pi\) | ||||
0.729399 | + | 0.684089i | \(0.239800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9443 | −0.609199 | ||||||||
\(686\) | 1.61803 | 0.0617768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.29180 | −0.0873739 | ||||||||
\(689\) | 64.3607 | 2.45195 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3607 | −1.04085 | −0.520425 | − | 0.853908i | \(-0.674226\pi\) | ||||
−0.520425 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(692\) | 5.67376 | 0.215684 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.8885 | −1.28639 | ||||||||
\(695\) | 14.4721 | 0.548959 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.111456 | 0.00422170 | ||||||||
\(698\) | 18.0902 | 0.684723 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.618034 | −0.0233595 | ||||||||
\(701\) | −46.9443 | −1.77306 | −0.886530 | − | 0.462670i | \(-0.846891\pi\) | ||||
−0.886530 | + | 0.462670i | \(0.846891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.45898 | 0.205889 | ||||||||
\(704\) | 5.23607 | 0.197342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.23607 | 0.272333 | ||||||||
\(707\) | 16.1803 | 0.608524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.9443 | 1.46258 | 0.731291 | − | 0.682065i | \(-0.238918\pi\) | ||||
0.731291 | + | 0.682065i | \(0.238918\pi\) | |||||||
\(710\) | −3.23607 | −0.121447 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.7082 | 1.18832 | ||||||||
\(713\) | 15.8754 | 0.594538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | −7.05573 | −0.263685 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.1803 | 1.05168 | ||||||||
\(719\) | 37.7771 | 1.40885 | 0.704424 | − | 0.709780i | \(-0.251205\pi\) | ||||
0.704424 | + | 0.709780i | \(0.251205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2361 | 0.567421 | ||||||||
\(722\) | 27.2361 | 1.01362 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.09017 | 0.189175 | ||||||||
\(725\) | 5.70820 | 0.211997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.0557 | −0.558386 | −0.279193 | − | 0.960235i | \(-0.590067\pi\) | ||||
−0.279193 | + | 0.960235i | \(0.590067\pi\) | |||||||
\(728\) | 14.4721 | 0.536373 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.7082 | 0.507363 | ||||||||
\(731\) | −0.111456 | −0.00412236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.1246 | 0.927999 | 0.463999 | − | 0.885836i | \(-0.346414\pi\) | ||||
0.463999 | + | 0.885836i | \(0.346414\pi\) | |||||||
\(734\) | −5.52786 | −0.204037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.96556 | −0.219893 | ||||||||
\(737\) | −8.58359 | −0.316181 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.2361 | −0.376540 | −0.188270 | − | 0.982117i | \(-0.560288\pi\) | ||||
−0.188270 | + | 0.982117i | \(0.560288\pi\) | |||||||
\(740\) | 2.29180 | 0.0842481 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.0902 | −0.590689 | ||||||||
\(743\) | 6.11146 | 0.224208 | 0.112104 | − | 0.993697i | \(-0.464241\pi\) | ||||
0.112104 | + | 0.993697i | \(0.464241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9443 | −0.400967 | ||||||||
\(746\) | −24.9443 | −0.913275 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.180340 | −0.00659388 | ||||||||
\(749\) | 15.4164 | 0.563303 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.34752 | −0.304605 | −0.152303 | − | 0.988334i | \(-0.548669\pi\) | ||||
−0.152303 | + | 0.988334i | \(0.548669\pi\) | |||||||
\(752\) | 19.4164 | 0.708044 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 59.7771 | 2.17695 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.41641 | 0.0514802 | 0.0257401 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257401 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(758\) | 54.4508 | 1.97774 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.29180 | 0.119406 | ||||||||
\(761\) | 2.47214 | 0.0896149 | 0.0448074 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448074 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | −0.0362024 | ||||||||
\(764\) | 15.5967 | 0.564271 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.2705 | −0.587877 | ||||||||
\(767\) | 11.0557 | 0.399199 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.5967 | 1.03123 | 0.515613 | − | 0.856822i | \(-0.327564\pi\) | ||||
0.515613 | + | 0.856822i | \(0.327564\pi\) | |||||||
\(770\) | 2.00000 | 0.0720750 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.4721 | 0.520864 | ||||||||
\(773\) | 47.1803 | 1.69696 | 0.848479 | − | 0.529228i | \(-0.177519\pi\) | ||||
0.848479 | + | 0.529228i | \(0.177519\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.00000 | −0.323290 | ||||||||
\(776\) | −1.70820 | −0.0613209 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.8885 | −1.43007 | ||||||||
\(779\) | −0.695048 | −0.0249027 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.47214 | 0.0884600 | ||||||||
\(782\) | −0.673762 | −0.0240937 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | −5.23607 | −0.186883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1803 | 1.21840 | 0.609199 | − | 0.793018i | \(-0.291491\pi\) | ||||
0.609199 | + | 0.793018i | \(0.291491\pi\) | |||||||
\(788\) | 11.0902 | 0.395071 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.38197 | −0.298217 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 82.2492 | 2.92076 | ||||||||
\(794\) | 18.1803 | 0.645196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.8328 | −0.383959 | ||||||||
\(797\) | −25.2918 | −0.895881 | −0.447941 | − | 0.894063i | \(-0.647842\pi\) | ||||
−0.447941 | + | 0.894063i | \(0.647842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.944272 | 0.0334059 | ||||||||
\(800\) | 3.38197 | 0.119571 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.1246 | 0.887181 | ||||||||
\(803\) | −10.4721 | −0.369554 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.76393 | 0.0621704 | ||||||||
\(806\) | −94.2492 | −3.31979 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.1803 | −1.27282 | ||||||||
\(809\) | −29.0557 | −1.02154 | −0.510772 | − | 0.859716i | \(-0.670641\pi\) | ||||
−0.510772 | + | 0.859716i | \(0.670641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0557 | 1.23097 | 0.615487 | − | 0.788147i | \(-0.288960\pi\) | ||||
0.615487 | + | 0.788147i | \(0.288960\pi\) | |||||||
\(812\) | −3.52786 | −0.123804 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.41641 | −0.259945 | ||||||||
\(815\) | 6.76393 | 0.236930 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.695048 | 0.0243167 | ||||||||
\(818\) | −6.85410 | −0.239648 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.291796 | −0.0101900 | ||||||||
\(821\) | −5.41641 | −0.189034 | −0.0945170 | − | 0.995523i | \(-0.530131\pi\) | ||||
−0.0945170 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3050 | 0.812360 | 0.406180 | − | 0.913793i | \(-0.366861\pi\) | ||||
0.406180 | + | 0.913793i | \(0.366861\pi\) | |||||||
\(824\) | −34.0689 | −1.18685 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.76393 | −0.0961695 | ||||||||
\(827\) | 21.2918 | 0.740388 | 0.370194 | − | 0.928954i | \(-0.379291\pi\) | ||||
0.370194 | + | 0.928954i | \(0.379291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.4721 | 0.988878 | 0.494439 | − | 0.869212i | \(-0.335374\pi\) | ||||
0.494439 | + | 0.869212i | \(0.335374\pi\) | |||||||
\(830\) | 17.7984 | 0.617791 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.4164 | −0.950493 | ||||||||
\(833\) | −0.236068 | −0.00817927 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9443 | 0.413349 | ||||||||
\(836\) | 1.12461 | 0.0388955 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.4721 | 0.707198 | ||||||||
\(839\) | 3.81966 | 0.131869 | 0.0659347 | − | 0.997824i | \(-0.478997\pi\) | ||||
0.0659347 | + | 0.997824i | \(0.478997\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.58359 | 0.123572 | ||||||||
\(842\) | −41.7984 | −1.44047 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.85410 | −0.270349 | ||||||||
\(845\) | 28.8885 | 0.993796 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.47214 | 0.325466 | ||||||||
\(848\) | 48.2705 | 1.65762 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.381966 | 0.0131013 | ||||||||
\(851\) | −6.54102 | −0.224223 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.2492 | −1.44659 | −0.723293 | − | 0.690541i | \(-0.757372\pi\) | ||||
−0.723293 | + | 0.690541i | \(0.757372\pi\) | |||||||
\(854\) | −20.5623 | −0.703628 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34.4721 | −1.17823 | ||||||||
\(857\) | −0.819660 | −0.0279991 | −0.0139995 | − | 0.999902i | \(-0.504456\pi\) | ||||
−0.0139995 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9443 | −0.407533 | −0.203767 | − | 0.979019i | \(-0.565318\pi\) | ||||
−0.203767 | + | 0.979019i | \(0.565318\pi\) | |||||||
\(860\) | 0.291796 | 0.00995016 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.4164 | 0.525085 | ||||||||
\(863\) | −4.81966 | −0.164063 | −0.0820316 | − | 0.996630i | \(-0.526141\pi\) | ||||
−0.0820316 | + | 0.996630i | \(0.526141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.18034 | 0.312141 | ||||||||
\(866\) | −1.23607 | −0.0420033 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.56231 | 0.188797 | ||||||||
\(869\) | 6.40325 | 0.217215 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.9443 | 1.52288 | ||||||||
\(872\) | 2.23607 | 0.0757228 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.20163 | 0.142122 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.6525 | 1.77795 | 0.888974 | − | 0.457958i | \(-0.151419\pi\) | ||||
0.888974 | + | 0.457958i | \(0.151419\pi\) | |||||||
\(878\) | 33.9787 | 1.14673 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | −37.4853 | −1.26291 | −0.631456 | − | 0.775412i | \(-0.717542\pi\) | ||||
−0.631456 | + | 0.775412i | \(0.717542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6525 | −1.16615 | −0.583074 | − | 0.812419i | \(-0.698150\pi\) | ||||
−0.583074 | + | 0.812419i | \(0.698150\pi\) | |||||||
\(884\) | 0.944272 | 0.0317593 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.6869 | −1.66926 | ||||||||
\(887\) | −37.7214 | −1.26656 | −0.633280 | − | 0.773923i | \(-0.718292\pi\) | ||||
−0.633280 | + | 0.773923i | \(0.718292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.18034 | 0.207282 | ||||||||
\(890\) | −22.9443 | −0.769094 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.81966 | −0.261822 | ||||||||
\(893\) | −5.88854 | −0.197053 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.4164 | −0.381608 | ||||||||
\(896\) | 13.6180 | 0.454947 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.4164 | −0.380970 | ||||||||
\(899\) | −51.3738 | −1.71341 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.34752 | 0.0782074 | ||||||||
\(902\) | 0.944272 | 0.0314408 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.47214 | −0.148741 | ||||||||
\(905\) | 8.23607 | 0.273776 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.1246 | −0.435796 | −0.217898 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217898 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(908\) | −6.79837 | −0.225612 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.4721 | −0.347148 | ||||||||
\(911\) | −59.2361 | −1.96258 | −0.981289 | − | 0.192539i | \(-0.938328\pi\) | ||||
−0.981289 | + | 0.192539i | \(0.938328\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5967 | −0.449987 | ||||||||
\(914\) | 29.2361 | 0.967043 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.32624 | 0.0768611 | ||||||||
\(917\) | −21.2361 | −0.701277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.3050 | 0.438890 | 0.219445 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219445 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(920\) | −3.94427 | −0.130039 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −46.0689 | −1.51720 | ||||||||
\(923\) | −12.9443 | −0.426066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.70820 | 0.121925 | ||||||||
\(926\) | 52.5410 | 1.72661 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.3050 | 0.633716 | ||||||||
\(929\) | −35.1246 | −1.15240 | −0.576201 | − | 0.817308i | \(-0.695465\pi\) | ||||
−0.576201 | + | 0.817308i | \(0.695465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.47214 | 0.0482473 | ||||||||
\(932\) | 16.2918 | 0.533656 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.1033 | 2.19569 | ||||||||
\(935\) | −0.291796 | −0.00954275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5279 | 0.441936 | 0.220968 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220968 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(938\) | −11.2361 | −0.366871 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.47214 | −0.0806322 | ||||||||
\(941\) | −30.7639 | −1.00288 | −0.501438 | − | 0.865194i | \(-0.667195\pi\) | ||||
−0.501438 | + | 0.865194i | \(0.667195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.832816 | 0.0271202 | ||||||||
\(944\) | 8.29180 | 0.269875 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.944272 | −0.0307009 | ||||||||
\(947\) | 25.5410 | 0.829972 | 0.414986 | − | 0.909828i | \(-0.363787\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.8328 | 1.77995 | ||||||||
\(950\) | −2.38197 | −0.0772812 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.527864 | 0.0171082 | ||||||||
\(953\) | −13.7771 | −0.446284 | −0.223142 | − | 0.974786i | \(-0.571631\pi\) | ||||
−0.223142 | + | 0.974786i | \(0.571631\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.2361 | 0.816620 | ||||||||
\(956\) | 2.18034 | 0.0705172 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.9443 | −1.12900 | ||||||||
\(959\) | 15.9443 | 0.514867 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.0000 | 1.61290 | ||||||||
\(962\) | 38.8328 | 1.25202 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.8541 | 0.510626 | ||||||||
\(965\) | 23.4164 | 0.753801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.5967 | 0.951767 | 0.475884 | − | 0.879508i | \(-0.342128\pi\) | ||||
0.475884 | + | 0.879508i | \(0.342128\pi\) | |||||||
\(968\) | −21.1803 | −0.680762 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.23607 | 0.0396878 | ||||||||
\(971\) | −30.0000 | −0.962746 | −0.481373 | − | 0.876516i | \(-0.659862\pi\) | ||||
−0.481373 | + | 0.876516i | \(0.659862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4721 | −0.463955 | ||||||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61.6869 | 1.97455 | ||||||||
\(977\) | −55.8885 | −1.78803 | −0.894016 | − | 0.448034i | \(-0.852124\pi\) | ||||
−0.894016 | + | 0.448034i | \(0.852124\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5279 | 0.560193 | ||||||||
\(980\) | 0.618034 | 0.0197424 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.29180 | −0.200779 | ||||||||
\(983\) | −41.0000 | −1.30770 | −0.653848 | − | 0.756626i | \(-0.726847\pi\) | ||||
−0.653848 | + | 0.756626i | \(0.726847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.9443 | 0.571752 | ||||||||
\(986\) | 2.18034 | 0.0694362 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.88854 | −0.187340 | ||||||||
\(989\) | −0.832816 | −0.0264820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0132 | −1.33459 | −0.667296 | − | 0.744793i | \(-0.732548\pi\) | ||||
−0.667296 | + | 0.744793i | \(0.732548\pi\) | |||||||
\(992\) | −30.4377 | −0.966398 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.23607 | 0.102642 | ||||||||
\(995\) | −17.5279 | −0.555671 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4164 | 1.05831 | 0.529154 | − | 0.848526i | \(-0.322509\pi\) | ||||
0.529154 | + | 0.848526i | \(0.322509\pi\) | |||||||
\(998\) | −16.5623 | −0.524271 | ||||||||
\(999\) | 0 | 0 |
(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 | 945.2.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 945.2.a.h.1.2 | yes | 2 | ||
5.4 | even | 2 | 4725.2.a.bd.1.2 | 2 | |||
7.6 | odd | 2 | 6615.2.a.n.1.1 | 2 | |||
15.14 | odd | 2 | 4725.2.a.y.1.1 | 2 | |||
21.20 | even | 2 | 6615.2.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
945.2.a.h.1.2 | yes | 2 | 3.2 | odd | 2 | ||
4725.2.a.y.1.1 | 2 | 15.14 | odd | 2 | |||
4725.2.a.bd.1.2 | 2 | 5.4 | even | 2 | |||
6615.2.a.n.1.1 | 2 | 7.6 | odd | 2 | |||
6615.2.a.t.1.2 | 2 | 21.20 | even | 2 |