Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2624,2,Mod(1,2624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2624, 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("2624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2624 = 2^{6} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2624.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: | \(20.9527454904\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 164) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.55466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2624.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.92968 | 1.69145 | 0.845726 | − | 0.533618i | \(-0.179168\pi\) | ||||
0.845726 | + | 0.533618i | \(0.179168\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.33307 | 1.49059 | 0.745296 | − | 0.666734i | \(-0.232308\pi\) | ||||
0.745296 | + | 0.666734i | \(0.232308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.77840 | −1.05014 | −0.525069 | − | 0.851060i | \(-0.675960\pi\) | ||||
−0.525069 | + | 0.851060i | \(0.675960\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.58303 | 1.86101 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.02837 | 0.611575 | 0.305788 | − | 0.952100i | \(-0.401080\pi\) | ||||
0.305788 | + | 0.952100i | \(0.401080\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.10932 | 0.862371 | 0.431186 | − | 0.902263i | \(-0.358095\pi\) | ||||
0.431186 | + | 0.902263i | \(0.358095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.76482 | 2.52126 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.91609 | −1.91993 | −0.959967 | − | 0.280112i | \(-0.909628\pi\) | ||||
−0.959967 | + | 0.280112i | \(0.909628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.17964 | 0.500044 | 0.250022 | − | 0.968240i | \(-0.419562\pi\) | ||||
0.250022 | + | 0.968240i | \(0.419562\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.13983 | −1.77626 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.75004 | 0.990451 | 0.495226 | − | 0.868764i | \(-0.335085\pi\) | ||||
0.495226 | + | 0.868764i | \(0.335085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.10932 | 1.22186 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.56744 | 1.45636 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.85936 | −0.716665 | −0.358333 | − | 0.933594i | \(-0.616655\pi\) | ||||
−0.358333 | + | 0.933594i | \(0.616655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6661 | 1.91569 | 0.957847 | − | 0.287280i | \(-0.0927509\pi\) | ||||
0.957847 | + | 0.287280i | \(0.0927509\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.94246 | 1.03445 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.26060 | −1.56533 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58303 | −1.08224 | −0.541122 | − | 0.840944i | \(-0.682000\pi\) | ||||
−0.541122 | + | 0.840944i | \(0.682000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.10932 | 1.45866 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.80677 | 0.733025 | 0.366513 | − | 0.930413i | \(-0.380552\pi\) | ||||
0.366513 | + | 0.930413i | \(0.380552\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.6086 | 2.77401 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.03900 | −0.589149 | −0.294575 | − | 0.955628i | \(-0.595178\pi\) | ||||
−0.294575 | + | 0.955628i | \(0.595178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.719526 | 0.102789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23.1916 | −3.24748 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.94327 | 0.266928 | 0.133464 | − | 0.991054i | \(-0.457390\pi\) | ||||
0.133464 | + | 0.991054i | \(0.457390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.76068 | 0.911609 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.38566 | 0.845801 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.75004 | 0.618402 | 0.309201 | − | 0.950997i | \(-0.399938\pi\) | ||||
0.309201 | + | 0.950997i | \(0.399938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.89068 | −0.370113 | −0.185057 | − | 0.982728i | \(-0.559247\pi\) | ||||
−0.185057 | + | 0.982728i | \(0.559247\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.5119 | −1.95432 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.3636 | 1.28544 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.97163 | 0.729551 | 0.364776 | − | 0.931095i | \(-0.381146\pi\) | ||||
0.364776 | + | 0.931095i | \(0.381146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.9161 | 1.67530 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4026 | −1.70927 | −0.854636 | − | 0.519228i | \(-0.826220\pi\) | ||||
−0.854636 | + | 0.519228i | \(0.826220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.24916 | −1.08253 | −0.541266 | − | 0.840851i | \(-0.682055\pi\) | ||||
−0.541266 | + | 0.840851i | \(0.682055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.8984 | 2.06673 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.63562 | −0.642238 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.320282 | 0.0360345 | 0.0180173 | − | 0.999838i | \(-0.494265\pi\) | ||||
0.0180173 | + | 0.999838i | \(0.494265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.42111 | 0.602346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.69745 | −0.405847 | −0.202924 | − | 0.979195i | \(-0.565044\pi\) | ||||
−0.202924 | + | 0.979195i | \(0.565044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.3849 | −2.86184 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.3067 | −1.21220 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.96868 | 0.950679 | 0.475339 | − | 0.879803i | \(-0.342325\pi\) | ||||
0.475339 | + | 0.879803i | \(0.342325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.63895 | −0.905608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 31.2484 | 3.24030 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.26489 | 0.745362 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8322 | 1.81058 | 0.905292 | − | 0.424790i | \(-0.139652\pi\) | ||||
0.905292 | + | 0.424790i | \(0.139652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.3244 | 1.13815 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0254 | 1.29608 | 0.648039 | − | 0.761607i | \(-0.275590\pi\) | ||||
0.648039 | + | 0.761607i | \(0.275590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.05673 | 0.793853 | 0.396927 | − | 0.917850i | \(-0.370077\pi\) | ||||
0.396927 | + | 0.917850i | \(0.370077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.1306 | −2.64768 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.41602 | −0.426912 | −0.213456 | − | 0.976953i | \(-0.568472\pi\) | ||||
−0.213456 | + | 0.976953i | \(0.568472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.5255 | −1.77442 | −0.887210 | − | 0.461366i | \(-0.847360\pi\) | ||||
−0.887210 | + | 0.461366i | \(0.847360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.2862 | −1.83056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.08310 | −0.760394 | −0.380197 | − | 0.924905i | \(-0.624144\pi\) | ||||
−0.380197 | + | 0.924905i | \(0.624144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8322 | 1.47636 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3594 | 1.60488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.9941 | 2.01620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.88573 | −0.625976 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.92968 | −0.264160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.69745 | 0.330710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.44748 | −0.394650 | −0.197325 | − | 0.980338i | \(-0.563225\pi\) | ||||
−0.197325 | + | 0.980338i | \(0.563225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.0823 | 1.23988 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.85936 | 0.861416 | 0.430708 | − | 0.902491i | \(-0.358264\pi\) | ||||
0.430708 | + | 0.902491i | \(0.358264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.05593 | −0.525115 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.2228 | 2.17083 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.30255 | −0.196720 | −0.0983602 | − | 0.995151i | \(-0.531360\pi\) | ||||
−0.0983602 | + | 0.995151i | \(0.531360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.16605 | 0.438179 | 0.219090 | − | 0.975705i | \(-0.429691\pi\) | ||||
0.219090 | + | 0.975705i | \(0.429691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8330 | −0.996517 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.30684 | 0.527405 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.8635 | −1.06826 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.10798 | 0.173863 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.85936 | −0.316171 | −0.158086 | − | 0.987425i | \(-0.550532\pi\) | ||||
−0.158086 | + | 0.987425i | \(0.550532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71103 | 0.383379 | 0.191689 | − | 0.981456i | \(-0.438603\pi\) | ||||
0.191689 | + | 0.981456i | \(0.438603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.1958 | −3.57302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 35.5509 | 2.85552 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.30684 | −0.662958 | −0.331479 | − | 0.943463i | \(-0.607548\pi\) | ||||
−0.331479 | + | 0.943463i | \(0.607548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.69316 | 0.451497 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.1975 | −1.04011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.6348 | −1.06796 | −0.533981 | − | 0.845497i | \(-0.679304\pi\) | ||||
−0.533981 | + | 0.845497i | \(0.679304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.8066 | 1.54194 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.97163 | −0.771628 | −0.385814 | − | 0.922577i | \(-0.626079\pi\) | ||||
−0.385814 | + | 0.922577i | \(0.626079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.33211 | −0.256316 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.1690 | 0.930587 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.11361 | −0.692895 | −0.346448 | − | 0.938069i | \(-0.612612\pi\) | ||||
−0.346448 | + | 0.938069i | \(0.612612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.9742 | −1.28313 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.9161 | 1.04600 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9403 | −0.967205 | −0.483602 | − | 0.875288i | \(-0.660672\pi\) | ||||
−0.483602 | + | 0.875288i | \(0.660672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.16191 | −0.606670 | −0.303335 | − | 0.952884i | \(-0.598100\pi\) | ||||
−0.303335 | + | 0.952884i | \(0.598100\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.46876 | −0.626029 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.9417 | −1.61318 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0567 | −1.17418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.0254 | −1.52937 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.52829 | −0.327656 | −0.163828 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163828 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1662 | −1.01971 | −0.509853 | − | 0.860262i | \(-0.670300\pi\) | ||||
−0.509853 | + | 0.860262i | \(0.670300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30.3620 | 2.17427 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5042 | 0.890888 | 0.445444 | − | 0.895310i | \(-0.353046\pi\) | ||||
0.445444 | + | 0.895310i | \(0.353046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5853 | 1.03393 | 0.516963 | − | 0.856008i | \(-0.327062\pi\) | ||||
0.516963 | + | 0.856008i | \(0.327062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.4950 | 1.23400 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7229 | 0.752597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.33307 | −0.232791 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.5196 | 1.84324 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.42111 | 0.305815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.3860 | −1.81649 | −0.908245 | − | 0.418439i | \(-0.862577\pi\) | ||||
−0.908245 | + | 0.418439i | \(0.862577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −42.1950 | −2.89115 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.0213 | 1.09264 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.6348 | −2.01174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.0971 | −1.83105 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.6137 | −1.65570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.89482 | 0.126886 | 0.0634432 | − | 0.997985i | \(-0.479792\pi\) | ||||
0.0634432 | + | 0.997985i | \(0.479792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 34.1085 | 2.27390 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.9805 | −1.65801 | −0.829007 | − | 0.559238i | \(-0.811094\pi\) | ||||
−0.829007 | + | 0.559238i | \(0.811094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.52549 | 0.166889 | 0.0834446 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834446 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.5106 | −1.08632 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.24835 | 0.605880 | 0.302940 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302940 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4623 | −0.878181 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.938323 | 0.0609507 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.34746 | −0.151844 | −0.0759222 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759222 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.89068 | 0.186205 | 0.0931024 | − | 0.995657i | \(-0.470322\pi\) | ||||
0.0931024 | + | 0.995657i | \(0.470322\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.82021 | −0.437516 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.39823 | 0.153217 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.77721 | 0.431224 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.8323 | −0.686471 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9730 | 1.57628 | 0.788140 | − | 0.615496i | \(-0.211044\pi\) | ||||
0.788140 | + | 0.615496i | \(0.211044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.63481 | 0.605736 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −77.2992 | −4.84066 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7500 | 0.670569 | 0.335284 | − | 0.942117i | \(-0.391168\pi\) | ||||
0.335284 | + | 0.942117i | \(0.391168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.2903 | 1.13650 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.5469 | −1.33372 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.90250 | 0.302301 | 0.151151 | − | 0.988511i | \(-0.451702\pi\) | ||||
0.151151 | + | 0.988511i | \(0.451702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.47704 | 0.397881 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.2754 | 1.60803 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.32797 | −0.202910 | −0.101455 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101455 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.58222 | −0.278350 | −0.139175 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139175 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.3094 | −1.53179 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.3919 | 0.747262 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2178 | 1.45511 | 0.727555 | − | 0.686050i | \(-0.240657\pi\) | ||||
0.727555 | + | 0.686050i | \(0.240657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 59.5493 | 3.56512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.61369 | 0.394540 | 0.197270 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197270 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.16605 | 0.307090 | 0.153545 | − | 0.988142i | \(-0.450931\pi\) | ||||
0.153545 | + | 0.988142i | \(0.450931\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.2838 | 1.26074 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.77840 | 0.164004 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.6645 | 2.68615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.2426 | 3.06252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2458 | 0.598567 | 0.299284 | − | 0.954164i | \(-0.403252\pi\) | ||||
0.299284 | + | 0.954164i | \(0.403252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8322 | 0.921785 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.3495 | 0.890671 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.7694 | 0.854137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3551 | −0.769778 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.1603 | 2.19225 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.63481 | −0.551688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.2754 | −1.04303 | −0.521515 | − | 0.853242i | \(-0.674633\pi\) | ||||
−0.521515 | + | 0.853242i | \(0.674633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.6036 | 1.34276 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50303 | −0.255343 | −0.127672 | − | 0.991816i | \(-0.540750\pi\) | ||||
−0.127672 | + | 0.991816i | \(0.540750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.56095 | 0.370847 | 0.185423 | − | 0.982659i | \(-0.440634\pi\) | ||||
0.185423 | + | 0.982659i | \(0.440634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −51.7022 | −2.91309 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8363 | −0.720960 | −0.360480 | − | 0.932767i | \(-0.617387\pi\) | ||||
−0.360480 | + | 0.932767i | \(0.617387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.82820 | −0.438295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.9375 | −0.722102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.2543 | −0.960052 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.9959 | 1.05370 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −54.2738 | −3.00135 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2220 | 0.618688 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.99705 | −0.494523 | −0.247261 | − | 0.968949i | \(-0.579531\pi\) | ||||
−0.247261 | + | 0.968949i | \(0.579531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −36.7532 | −2.01406 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.9038 | 1.08746 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.0502 | −1.90930 | −0.954652 | − | 0.297723i | \(-0.903773\pi\) | ||||
−0.954652 | + | 0.297723i | \(0.903773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.6809 | −1.28617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.6348 | 1.17159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4497 | 0.942195 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 46.3832 | 2.49719 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8982 | 1.01451 | 0.507255 | − | 0.861796i | \(-0.330660\pi\) | ||||
0.507255 | + | 0.861796i | \(0.330660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1653 | 1.24001 | 0.620004 | − | 0.784599i | \(-0.287131\pi\) | ||||
0.620004 | + | 0.784599i | \(0.287131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.5296 | 1.25592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.55171 | −0.0825893 | −0.0412946 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412946 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.0047 | −2.54783 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 64.4357 | 3.41030 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.28128 | 0.225957 | 0.112979 | − | 0.993597i | \(-0.463961\pi\) | ||||
0.112979 | + | 0.993597i | \(0.463961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2492 | −0.749956 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.1730 | −1.05881 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.8280 | −1.61361 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3067 | 0.799003 | 0.399501 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399501 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.58303 | −0.290641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.39918 | −0.280312 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.39489 | 0.279337 | 0.139668 | − | 0.990198i | \(-0.455396\pi\) | ||||
0.139668 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8323 | 0.559379 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8009 | 1.37667 | 0.688334 | − | 0.725394i | \(-0.258342\pi\) | ||||
0.688334 | + | 0.725394i | \(0.258342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.0297 | −0.667532 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6675 | −1.10716 | −0.553578 | − | 0.832797i | \(-0.686738\pi\) | ||||
−0.553578 | + | 0.832797i | \(0.686738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.7839 | −0.957315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.8363 | 1.36417 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.7187 | −1.30399 | −0.651995 | − | 0.758223i | \(-0.726068\pi\) | ||||
−0.651995 | + | 0.758223i | \(0.726068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.6017 | −1.90160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.8848 | 1.45704 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.06752 | 0.0537128 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.1603 | −1.41333 | −0.706663 | − | 0.707551i | \(-0.749800\pi\) | ||||
−0.706663 | + | 0.707551i | \(0.749800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.7419 | −0.888208 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7178 | −0.535220 | −0.267610 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267610 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.1644 | 1.65204 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0689 | 0.897852 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3528 | −0.661873 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.7492 | 1.12488 | 0.562439 | − | 0.826839i | \(-0.309863\pi\) | ||||
0.562439 | + | 0.826839i | \(0.309863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.74575 | −0.332743 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.1975 | −0.649408 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.3238 | −0.604953 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.1349 | 0.741159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.02542 | −0.343214 | −0.171607 | − | 0.985165i | \(-0.554896\pi\) | ||||
−0.171607 | + | 0.985165i | \(0.554896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.5992 | −0.808996 | −0.404498 | − | 0.914539i | \(-0.632554\pi\) | ||||
−0.404498 | + | 0.914539i | \(0.632554\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.5499 | −1.09641 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −48.3620 | −2.34590 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.03147 | 0.388670 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.4770 | 0.892080 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7229 | 0.516502 | 0.258251 | − | 0.966078i | \(-0.416854\pi\) | ||||
0.258251 | + | 0.966078i | \(0.416854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.1644 | 1.49767 | 0.748834 | − | 0.662758i | \(-0.230614\pi\) | ||||
0.748834 | + | 0.662758i | \(0.230614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.6859 | −1.80690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3534 | 0.495270 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.7981 | 1.66082 | 0.830411 | − | 0.557152i | \(-0.188106\pi\) | ||||
0.830411 | + | 0.557152i | \(0.188106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.01714 | 0.191292 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.8806 | −1.22963 | −0.614813 | − | 0.788673i | \(-0.710769\pi\) | ||||
−0.614813 | + | 0.788673i | \(0.710769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.8932 | 1.41707 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.3067 | −0.534788 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.2231 | 1.28474 | 0.642368 | − | 0.766396i | \(-0.277952\pi\) | ||||
0.642368 | + | 0.766396i | \(0.277952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.02837 | −0.0955120 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8018 | 0.648466 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.7942 | −1.34989 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.19767 | −0.289915 | −0.144957 | − | 0.989438i | \(-0.546305\pi\) | ||||
−0.144957 | + | 0.989438i | \(0.546305\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.9046 | −2.79611 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9170 | 0.508458 | 0.254229 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254229 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.07047 | −0.189171 | −0.0945854 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945854 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 104.153 | 4.82997 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.63657 | −0.399653 | −0.199826 | − | 0.979831i | \(-0.564038\pi\) | ||||
−0.199826 | + | 0.979831i | \(0.564038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.5916 | −0.766129 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.3364 | −1.12136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.74989 | 0.448300 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.3161 | 0.610986 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8493 | 0.496756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.5537 | 1.07620 | 0.538098 | − | 0.842882i | \(-0.319143\pi\) | ||||
0.538098 | + | 0.842882i | \(0.319143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4688 | −0.933295 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38.6645 | −1.75930 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.4358 | 2.69884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9102 | −0.902217 | −0.451108 | − | 0.892469i | \(-0.648971\pi\) | ||||
−0.451108 | + | 0.892469i | \(0.648971\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −39.9456 | −1.80640 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.7585 | 1.34298 | 0.671490 | − | 0.741013i | \(-0.265654\pi\) | ||||
0.671490 | + | 0.741013i | \(0.265654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.5511 | 1.37595 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 37.7450 | 1.69651 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.0162 | 1.79497 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9297 | 0.847409 | 0.423704 | − | 0.905801i | \(-0.360730\pi\) | ||||
0.423704 | + | 0.905801i | \(0.360730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.2137 | −1.30517 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.93382 | 0.0862248 | 0.0431124 | − | 0.999070i | \(-0.486273\pi\) | ||||
0.0431124 | + | 0.999070i | \(0.486273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.4146 | 1.93192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.76202 | −0.433546 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.6602 | −1.53629 | −0.768144 | − | 0.640277i | \(-0.778819\pi\) | ||||
−0.768144 | + | 0.640277i | \(0.778819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.6979 | 1.13681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.4943 | 0.728242 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.8536 | 1.18331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.19258 | −0.360309 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.7000 | −1.17200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.33402 | −0.277498 | −0.138749 | − | 0.990328i | \(-0.544308\pi\) | ||||
−0.138749 | + | 0.990328i | \(0.544308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.9460 | −1.30944 | −0.654722 | − | 0.755869i | \(-0.727215\pi\) | ||||
−0.654722 | + | 0.755869i | \(0.727215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −49.7289 | −2.17035 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −84.4341 | −3.67801 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.437142 | −0.0190062 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.5196 | 1.15085 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.10932 | −0.134680 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.7189 | −0.636352 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.9110 | −1.63598 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45946 | 0.0628635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.834750 | −0.0358887 | −0.0179443 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179443 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.9118 | −1.02615 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −61.7467 | −2.64494 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.6527 | −0.883045 | −0.441523 | − | 0.897250i | \(-0.645562\pi\) | ||||
−0.441523 | + | 0.897250i | \(0.645562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.1387 | −0.688784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.41203 | −0.358364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.889872 | −0.0378412 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −64.2820 | −2.72862 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.72447 | 0.369668 | 0.184834 | − | 0.982770i | \(-0.440825\pi\) | ||||
0.184834 | + | 0.982770i | \(0.440825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9458 | 0.632140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −47.0411 | −1.98608 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.80144 | 0.413081 | 0.206541 | − | 0.978438i | \(-0.433779\pi\) | ||||
0.206541 | + | 0.978438i | \(0.433779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.9415 | −1.13344 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.0620 | −0.632546 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.1570 | 1.05464 | 0.527318 | − | 0.849668i | \(-0.323198\pi\) | ||||
0.527318 | + | 0.849668i | \(0.323198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1928 | 1.13798 | 0.568992 | − | 0.822343i | \(-0.307334\pi\) | ||||
0.568992 | + | 0.822343i | \(0.307334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.2664 | −0.554214 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.0195 | 1.21020 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.365186 | −0.0152029 | −0.00760144 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760144 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.5025 | −1.72478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2730 | 0.426196 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.94166 | 0.163247 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 57.8601 | 2.39222 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.7242 | −1.55704 | −0.778522 | − | 0.627617i | \(-0.784030\pi\) | ||||
−0.778522 | + | 0.627617i | \(0.784030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.2484 | 0.957932 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.6334 | 1.50689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.1333 | −1.85340 | −0.926701 | − | 0.375800i | \(-0.877368\pi\) | ||||
−0.926701 | + | 0.375800i | \(0.877368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 73.3078 | 3.00533 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 42.7303 | 1.74884 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4982 | −0.633238 | −0.316619 | − | 0.948553i | \(-0.602548\pi\) | ||||
−0.316619 | + | 0.948553i | \(0.602548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.18924 | −0.211674 | −0.105837 | − | 0.994384i | \(-0.533752\pi\) | ||||
−0.105837 | + | 0.994384i | \(0.533752\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.3398 | 1.35770 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.9506 | −0.933074 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8280 | 0.683029 | 0.341515 | − | 0.939876i | \(-0.389060\pi\) | ||||
0.341515 | + | 0.939876i | \(0.389060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.4146 | 1.27298 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.5586 | −0.508065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1042 | −1.01395 | −0.506975 | − | 0.861961i | \(-0.669236\pi\) | ||||
−0.506975 | + | 0.861961i | \(0.669236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.76482 | −0.393755 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3324 | 0.577001 | 0.288501 | − | 0.957480i | \(-0.406843\pi\) | ||||
0.288501 | + | 0.957480i | \(0.406843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.2712 | 0.774576 | 0.387288 | − | 0.921959i | \(-0.373412\pi\) | ||||
0.387288 | + | 0.921959i | \(0.373412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.9456 | 1.44245 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.9186 | −0.998344 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.2228 | −0.728911 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9524 | 0.517271 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.1119 | 2.07784 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1856 | 1.20167 | 0.600834 | − | 0.799374i | \(-0.294835\pi\) | ||||
0.600834 | + | 0.799374i | \(0.294835\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −77.3027 | −3.07251 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.8238 | −0.588263 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.23724 | 0.0886427 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −80.4100 | −3.18097 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.9984 | −1.02687 | −0.513437 | − | 0.858127i | \(-0.671628\pi\) | ||||
−0.513437 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4402 | 0.451159 | 0.225580 | − | 0.974225i | \(-0.427572\pi\) | ||||
0.225580 | + | 0.974225i | \(0.427572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 46.9372 | 1.84815 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.6915 | −1.48181 | −0.740904 | − | 0.671611i | \(-0.765603\pi\) | ||||
−0.740904 | + | 0.671611i | \(0.765603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.63481 | 0.378200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −86.8205 | −3.40277 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.6814 | 1.70938 | 0.854692 | − | 0.519136i | \(-0.173746\pi\) | ||||
0.854692 | + | 0.519136i | \(0.173746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.8619 | 1.28402 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −51.6383 | −2.01460 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.0900 | 0.977367 | 0.488684 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488684 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7392 | 1.46788 | 0.733942 | − | 0.679212i | \(-0.237678\pi\) | ||||
0.733942 | + | 0.679212i | \(0.237678\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −72.1102 | −2.80053 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.1848 | −0.782733 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3321 | −0.709822 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.55121 | 0.214622 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.86335 | −0.226352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.63642 | 0.140174 | 0.0700869 | − | 0.997541i | \(-0.477672\pi\) | ||||
0.0700869 | + | 0.997541i | \(0.477672\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 46.2320 | 1.77947 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.1948 | −1.12205 | −0.561024 | − | 0.827800i | \(-0.689592\pi\) | ||||
−0.561024 | + | 0.827800i | \(0.689592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.5450 | −1.90136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −73.1849 | −2.80445 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.6527 | −1.09636 | −0.548182 | − | 0.836359i | \(-0.684680\pi\) | ||||
−0.548182 | + | 0.836359i | \(0.684680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.67456 | −0.293230 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.39888 | 0.282285 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.04225 | 0.230191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6880 | 0.672883 | 0.336442 | − | 0.941704i | \(-0.390777\pi\) | ||||
0.336442 | + | 0.941704i | \(0.390777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.4638 | −1.19521 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.2188 | 0.653146 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.91609 | 0.299843 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.0947 | 1.02482 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.79339 | −0.105505 | −0.0527525 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527525 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3486 | −0.541169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.4401 | −1.48540 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.1899 | −1.36106 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4117 | −0.766578 | −0.383289 | − | 0.923628i | \(-0.625209\pi\) | ||||
−0.383289 | + | 0.923628i | \(0.625209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.78814 | 0.0670606 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.6645 | 1.89740 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0211 | 0.786145 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.87730 | −0.256838 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.9848 | −1.30471 | −0.652356 | − | 0.757912i | \(-0.726219\pi\) | ||||
−0.652356 | + | 0.757912i | \(0.726219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3849 | −0.833655 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.46876 | 0.314957 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.5781 | −0.875668 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.8796 | 0.922734 | 0.461367 | − | 0.887209i | \(-0.347359\pi\) | ||||
0.461367 | + | 0.887209i | \(0.347359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.2444 | −1.34238 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.0508 | −1.40736 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.7737 | 1.06278 | 0.531390 | − | 0.847127i | \(-0.321670\pi\) | ||||
0.531390 | + | 0.847127i | \(0.321670\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.02604 | 0.259159 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.1127 | 0.446176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.1856 | −1.11039 | −0.555197 | − | 0.831719i | \(-0.687357\pi\) | ||||
−0.555197 | + | 0.831719i | \(0.687357\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.8551 | 0.729394 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.7127 | 0.833247 | 0.416624 | − | 0.909079i | \(-0.363213\pi\) | ||||
0.416624 | + | 0.909079i | \(0.363213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8635 | −0.471282 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.6429 | −0.755286 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2695 | 0.448317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0200854 | 0.000732927 0 | 0.000366463 | − | 1.00000i | \(-0.499883\pi\) | ||||
0.000366463 | 1.00000i | \(0.499883\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 73.1628 | 2.66620 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.7022 | 0.571461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.9002 | −1.63192 | −0.815962 | − | 0.578106i | \(-0.803792\pi\) | ||||
−0.815962 | + | 0.578106i | \(0.803792\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.2269 | 1.02457 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0203 | −0.689486 | −0.344743 | − | 0.938697i | \(-0.612034\pi\) | ||||
−0.344743 | + | 0.938697i | \(0.612034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.4713 | 1.86339 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −147.307 | −5.32591 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.7694 | 0.533292 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1220 | 1.51896 | 0.759480 | − | 0.650531i | \(-0.225454\pi\) | ||||
0.759480 | + | 0.650531i | \(0.225454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.4942 | 1.13424 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.7753 | −0.387561 | −0.193780 | − | 0.981045i | \(-0.562075\pi\) | ||||
−0.193780 | + | 0.981045i | \(0.562075\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.1628 | 2.34072 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 53.5848 | 1.92234 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.17964 | −0.0780938 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.2137 | −1.04535 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.2055 | −1.04372 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.6873 | −0.988201 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.8592 | 0.814843 | 0.407421 | − | 0.913240i | \(-0.366428\pi\) | ||||
0.407421 | + | 0.913240i | \(0.366428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.3628 | 0.511328 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.4581 | 0.798519 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.98805 | −0.319175 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.9757 | 0.672997 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.00444 | 0.177266 | 0.0886332 | − | 0.996064i | \(-0.471750\pi\) | ||||
0.0886332 | + | 0.996064i | \(0.471750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9731 | 1.13113 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.0724 | 1.76922 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.7607 | −0.662050 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.9882 | −1.55038 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.74989 | −0.343212 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.52135 | 0.264437 | 0.132218 | − | 0.991221i | \(-0.457790\pi\) | ||||
0.132218 | + | 0.991221i | \(0.457790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4103 | 1.03273 | 0.516367 | − | 0.856367i | \(-0.327284\pi\) | ||||
0.516367 | + | 0.856367i | \(0.327284\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.4244 | −0.470816 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45.4457 | −1.59189 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4770 | 0.366545 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48.2315 | −1.68535 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.0205 | −1.32692 | −0.663462 | − | 0.748210i | \(-0.730913\pi\) | ||||
−0.663462 | + | 0.748210i | \(0.730913\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7849 | −0.898805 | −0.449403 | − | 0.893329i | \(-0.648363\pi\) | ||||
−0.449403 | + | 0.893329i | \(0.648363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.3044 | 1.26396 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.00295 | 0.243516 | 0.121758 | − | 0.992560i | \(-0.461147\pi\) | ||||
0.121758 | + | 0.992560i | \(0.461147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.166709 | −0.00579003 | −0.00289501 | − | 0.999996i | \(-0.500922\pi\) | ||||
−0.00289501 | + | 0.999996i | \(0.500922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 70.9505 | 2.46125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.69584 | −0.197349 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.2361 | −1.15018 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 80.7154 | 2.78993 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.1105 | 0.452625 | 0.226313 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226313 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1053 | −0.486391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.3760 | 0.667345 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1061 | −0.382063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.1313 | 0.657361 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1349 | 0.519428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.2696 | −1.07191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.445573 | 0.0152561 | 0.00762806 | − | 0.999971i | \(-0.497572\pi\) | ||||
0.00762806 | + | 0.999971i | \(0.497572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.5601 | 1.38713 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.5519 | −0.702038 | −0.351019 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351019 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8891 | −0.644487 | −0.322243 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322243 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.13983 | 0.277405 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.9204 | 1.63123 | 0.815614 | − | 0.578596i | \(-0.196399\pi\) | ||||
0.815614 | + | 0.578596i | \(0.196399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.3763 | −1.03282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 133.782 | 4.54349 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.649649 | 0.0220378 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5677 | 0.629144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 99.5576 | 3.36951 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2730 | −0.347291 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.2738 | 1.69762 | 0.848812 | − | 0.528694i | \(-0.177318\pi\) | ||||
0.848812 | + | 0.528694i | \(0.177318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.0170 | 1.01245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6019 | −1.30053 | −0.650265 | − | 0.759707i | \(-0.725342\pi\) | ||||
−0.650265 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.07860 | 0.103603 | 0.0518016 | − | 0.998657i | \(-0.483504\pi\) | ||||
0.0518016 | + | 0.998657i | \(0.483504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.3832 | 1.55916 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.0770 | 1.04346 | 0.521731 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521731 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3569 | 0.414437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9960 | 0.368380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.80358 | −0.294601 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.1309 | −1.44171 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.2696 | 1.44473 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.1644 | −1.37291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3831 | −0.512485 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.1263 | −1.30204 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.2042 | −0.904298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.5534 | 1.41296 | 0.706482 | − | 0.707731i | \(-0.250281\pi\) | ||||
0.706482 | + | 0.707731i | \(0.250281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.7213 | 2.41201 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8694 | 0.492645 | 0.246323 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246323 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.49977 | −0.248206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.2269 | −0.933153 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.3933 | −0.904606 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5539 | −0.875931 | −0.437965 | − | 0.898992i | \(-0.644301\pi\) | ||||
−0.437965 | + | 0.898992i | \(0.644301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.5410 | −1.76424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.7823 | −1.47403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.2178 | −1.32235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.9810 | 1.47737 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.70749 | 0.0888298 | 0.0444149 | − | 0.999013i | \(-0.485858\pi\) | ||||
0.0444149 | + | 0.999013i | \(0.485858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.56831 | 0.0513993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.1924 | −0.431901 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −53.5181 | −1.75023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.0067 | −1.17629 | −0.588143 | − | 0.808757i | \(-0.700141\pi\) | ||||
−0.588143 | + | 0.808757i | \(0.700141\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2215 | 0.627269 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6135 | −0.378591 | −0.189295 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189295 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.75004 | −0.154683 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70.0791 | −2.27967 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.9061 | −0.679355 | −0.339678 | − | 0.940542i | \(-0.610318\pi\) | ||||
−0.339678 | + | 0.940542i | \(0.610318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.7586 | −0.933544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.6063 | −1.21947 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7510 | −0.445438 | −0.222719 | − | 0.974883i | \(-0.571493\pi\) | ||||
−0.222719 | + | 0.974883i | \(0.571493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0931 | −0.488401 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.9341 | −0.741355 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.39742 | 0.206584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.7663 | 2.66988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.6547 | −0.794488 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.2169 | −1.51997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.07935 | −0.227656 | −0.113828 | − | 0.993500i | \(-0.536311\pi\) | ||||
−0.113828 | + | 0.993500i | \(0.536311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50.5494 | −1.62388 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7382 | −0.601338 | −0.300669 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3534 | −0.460148 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 55.6518 | 1.78228 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60.6756 | 1.94118 | 0.970592 | − | 0.240729i | \(-0.0773866\pi\) | ||||
0.970592 | + | 0.240729i | \(0.0773866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.1918 | 0.581412 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −103.428 | −3.30221 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.3720 | −1.51093 | −0.755466 | − | 0.655188i | \(-0.772590\pi\) | ||||
−0.755466 | + | 0.655188i | \(0.772590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.6774 | 1.32795 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.8768 | 1.04648 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.8323 | 0.726026 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2110 | 0.610256 | 0.305128 | − | 0.952311i | \(-0.401301\pi\) | ||||
0.305128 | + | 0.952311i | \(0.401301\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.3585 | −0.836461 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.6138 | 1.54116 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.1077 | 1.87196 | 0.935980 | − | 0.352053i | \(-0.114516\pi\) | ||||
0.935980 | + | 0.352053i | \(0.114516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.8167 | −1.57613 |
(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 | 2624.2.a.y.1.4 | 4 | ||
4.3 | odd | 2 | 2624.2.a.v.1.1 | 4 | |||
8.3 | odd | 2 | 164.2.a.a.1.4 | ✓ | 4 | ||
8.5 | even | 2 | 656.2.a.i.1.1 | 4 | |||
24.5 | odd | 2 | 5904.2.a.bp.1.4 | 4 | |||
24.11 | even | 2 | 1476.2.a.g.1.4 | 4 | |||
40.3 | even | 4 | 4100.2.d.c.1149.7 | 8 | |||
40.19 | odd | 2 | 4100.2.a.c.1.1 | 4 | |||
40.27 | even | 4 | 4100.2.d.c.1149.2 | 8 | |||
56.27 | even | 2 | 8036.2.a.i.1.1 | 4 | |||
328.163 | odd | 2 | 6724.2.a.c.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.4 | ✓ | 4 | 8.3 | odd | 2 | ||
656.2.a.i.1.1 | 4 | 8.5 | even | 2 | |||
1476.2.a.g.1.4 | 4 | 24.11 | even | 2 | |||
2624.2.a.v.1.1 | 4 | 4.3 | odd | 2 | |||
2624.2.a.y.1.4 | 4 | 1.1 | even | 1 | trivial | ||
4100.2.a.c.1.1 | 4 | 40.19 | odd | 2 | |||
4100.2.d.c.1149.2 | 8 | 40.27 | even | 4 | |||
4100.2.d.c.1149.7 | 8 | 40.3 | even | 4 | |||
5904.2.a.bp.1.4 | 4 | 24.5 | odd | 2 | |||
6724.2.a.c.1.1 | 4 | 328.163 | odd | 2 | |||
8036.2.a.i.1.1 | 4 | 56.27 | even | 2 |