Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.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: | \(75.1232582216\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 4704) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.77462\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.13503 | 1.84924 | 0.924621 | − | 0.380888i | \(-0.124382\pi\) | ||||
0.924621 | + | 0.380888i | \(0.124382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29857 | 0.693046 | 0.346523 | − | 0.938042i | \(-0.387362\pi\) | ||||
0.346523 | + | 0.938042i | \(0.387362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.43361 | −0.674961 | −0.337480 | − | 0.941333i | \(-0.609575\pi\) | ||||
−0.337480 | + | 0.941333i | \(0.609575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.13503 | −1.06766 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.71279 | −0.900483 | −0.450241 | − | 0.892907i | \(-0.648662\pi\) | ||||
−0.450241 | + | 0.892907i | \(0.648662\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.84782 | −1.80041 | −0.900207 | − | 0.435463i | \(-0.856585\pi\) | ||||
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70143 | −0.354772 | −0.177386 | − | 0.984141i | \(-0.556764\pi\) | ||||
−0.177386 | + | 0.984141i | \(0.556764\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0985 | 2.41970 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.25067 | −0.603635 | −0.301817 | − | 0.953366i | \(-0.597593\pi\) | ||||
−0.301817 | + | 0.953366i | \(0.597593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.80904 | −0.324912 | −0.162456 | − | 0.986716i | \(-0.551942\pi\) | ||||
−0.162456 | + | 0.986716i | \(0.551942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.29857 | −0.400130 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | 0.929981 | 0.464991 | − | 0.885316i | \(-0.346058\pi\) | ||||
0.464991 | + | 0.885316i | \(0.346058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.43361 | 0.389689 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.81128 | 1.06374 | 0.531871 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531871 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.44164 | −0.829842 | −0.414921 | − | 0.909857i | \(-0.636191\pi\) | ||||
−0.414921 | + | 0.909857i | \(0.636191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.13503 | 0.616414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.2895 | −1.93847 | −0.969233 | − | 0.246144i | \(-0.920836\pi\) | ||||
−0.969233 | + | 0.246144i | \(0.920836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.71279 | 0.519894 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.09849 | −1.24977 | −0.624887 | − | 0.780715i | \(-0.714855\pi\) | ||||
−0.624887 | + | 0.780715i | \(0.714855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.50467 | 1.28161 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.84782 | 1.03947 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9463 | 1.94584 | 0.972922 | − | 0.231134i | \(-0.0742436\pi\) | ||||
0.972922 | + | 0.231134i | \(0.0742436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.16354 | 0.277013 | 0.138506 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138506 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.0630 | −1.24817 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2540 | −1.25273 | −0.626363 | − | 0.779532i | \(-0.715457\pi\) | ||||
−0.626363 | + | 0.779532i | \(0.715457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.70143 | 0.204828 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.95543 | 0.469423 | 0.234711 | − | 0.972065i | \(-0.424585\pi\) | ||||
0.234711 | + | 0.972065i | \(0.424585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.68428 | −1.13346 | −0.566730 | − | 0.823904i | \(-0.691792\pi\) | ||||
−0.566730 | + | 0.823904i | \(0.691792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0985 | −1.39701 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0388 | −1.12945 | −0.564726 | − | 0.825279i | \(-0.691018\pi\) | ||||
−0.564726 | + | 0.825279i | \(0.691018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6956 | 1.28376 | 0.641881 | − | 0.766804i | \(-0.278154\pi\) | ||||
0.641881 | + | 0.766804i | \(0.278154\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.3525 | −1.66521 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.25067 | 0.348509 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7725 | −1.35388 | −0.676941 | − | 0.736037i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736037i | \(0.736695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.80904 | 0.187588 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.4510 | −3.32940 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0274 | −1.22120 | −0.610600 | − | 0.791939i | \(-0.709072\pi\) | ||||
−0.610600 | + | 0.791939i | \(0.709072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.29857 | 0.231015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.30661 | 0.130012 | 0.0650060 | − | 0.997885i | \(-0.479293\pi\) | ||||
0.0650060 | + | 0.997885i | \(0.479293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0033 | −1.08419 | −0.542095 | − | 0.840317i | \(-0.682369\pi\) | ||||
−0.542095 | + | 0.840317i | \(0.682369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8387 | −1.04782 | −0.523908 | − | 0.851775i | \(-0.675527\pi\) | ||||
−0.523908 | + | 0.851775i | \(0.675527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.44164 | 0.904345 | 0.452172 | − | 0.891931i | \(-0.350649\pi\) | ||||
0.452172 | + | 0.891931i | \(0.350649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | −0.536925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.31371 | 0.876160 | 0.438080 | − | 0.898936i | \(-0.355659\pi\) | ||||
0.438080 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.03546 | −0.656060 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.43361 | −0.224987 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.71656 | −0.519688 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.81128 | −0.614152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 29.3525 | 2.62537 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1373 | −1.16574 | −0.582872 | − | 0.812564i | \(-0.698071\pi\) | ||||
−0.582872 | + | 0.812564i | \(0.698071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.44164 | 0.479109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.81236 | −0.769940 | −0.384970 | − | 0.922929i | \(-0.625788\pi\) | ||||
−0.384970 | + | 0.922929i | \(0.625788\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.13503 | −0.355887 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.367398 | 0.0313889 | 0.0156945 | − | 0.999877i | \(-0.495004\pi\) | ||||
0.0156945 | + | 0.999877i | \(0.495004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.2895 | 1.11917 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.59382 | −0.467779 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.4416 | −1.11627 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4122 | 1.34454 | 0.672270 | − | 0.740306i | \(-0.265319\pi\) | ||||
0.672270 | + | 0.740306i | \(0.265319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.78478 | 0.633517 | 0.316758 | − | 0.948506i | \(-0.397406\pi\) | ||||
0.316758 | + | 0.948506i | \(0.397406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.71279 | −0.300161 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.48042 | −0.600842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2050 | −1.37311 | −0.686555 | − | 0.727078i | \(-0.740878\pi\) | ||||
−0.686555 | + | 0.727078i | \(0.740878\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.09849 | 0.721557 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.71656 | 0.526082 | 0.263041 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263041 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.50467 | −0.739938 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.21189 | −0.0937789 | −0.0468894 | − | 0.998900i | \(-0.514931\pi\) | ||||
−0.0468894 | + | 0.998900i | \(0.514931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.07757 | −0.544428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.84782 | −0.600138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2772 | −0.781359 | −0.390679 | − | 0.920527i | \(-0.627760\pi\) | ||||
−0.390679 | + | 0.920527i | \(0.627760\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.9463 | −1.12343 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1221 | 0.906051 | 0.453026 | − | 0.891498i | \(-0.350345\pi\) | ||||
0.453026 | + | 0.891498i | \(0.350345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.2460 | 1.72786 | 0.863930 | − | 0.503613i | \(-0.167996\pi\) | ||||
0.863930 | + | 0.503613i | \(0.167996\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.16354 | −0.159934 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.3913 | 1.71976 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.53411 | −0.624076 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.2691 | 1.68370 | 0.841848 | − | 0.539715i | \(-0.181468\pi\) | ||||
0.841848 | + | 0.539715i | \(0.181468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.28613 | −0.308522 | −0.154261 | − | 0.988030i | \(-0.549300\pi\) | ||||
−0.154261 | + | 0.988030i | \(0.549300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.0630 | 0.720629 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9818 | 0.853666 | 0.426833 | − | 0.904331i | \(-0.359629\pi\) | ||||
0.426833 | + | 0.904331i | \(0.359629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.1970 | −1.57350 | −0.786751 | − | 0.617270i | \(-0.788239\pi\) | ||||
−0.786751 | + | 0.617270i | \(0.788239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2540 | 0.723261 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.1649 | 1.96712 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.70143 | −0.118257 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0388 | −1.24777 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.540129 | 0.0371840 | 0.0185920 | − | 0.999827i | \(-0.494082\pi\) | ||||
0.0185920 | + | 0.999827i | \(0.494082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.95543 | −0.271021 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.5013 | −1.53458 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.68428 | 0.654403 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.03546 | 0.607791 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1194 | 0.677646 | 0.338823 | − | 0.940850i | \(-0.389971\pi\) | ||||
0.338823 | + | 0.940850i | \(0.389971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.0985 | 0.806566 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.7587 | −1.84241 | −0.921204 | − | 0.389080i | \(-0.872793\pi\) | ||||
−0.921204 | + | 0.389080i | \(0.872793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8962 | 0.984366 | 0.492183 | − | 0.870492i | \(-0.336199\pi\) | ||||
0.492183 | + | 0.870492i | \(0.336199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5644 | −0.954144 | −0.477072 | − | 0.878864i | \(-0.658302\pi\) | ||||
−0.477072 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −54.9523 | −3.58469 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0388 | 0.652089 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.70143 | −0.110056 | −0.0550281 | − | 0.998485i | \(-0.517525\pi\) | ||||
−0.0550281 | + | 0.998485i | \(0.517525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.0141 | −1.74013 | −0.870064 | − | 0.492939i | \(-0.835923\pi\) | ||||
−0.870064 | + | 0.492939i | \(0.835923\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.0985 | 1.21521 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6956 | −0.741181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.8269 | −0.809626 | −0.404813 | − | 0.914399i | \(-0.632663\pi\) | ||||
−0.404813 | + | 0.914399i | \(0.632663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.91085 | −0.245873 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.3525 | 0.961410 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.99892 | 0.124689 | 0.0623445 | − | 0.998055i | \(-0.480142\pi\) | ||||
0.0623445 | + | 0.998055i | \(0.480142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.25067 | −0.201212 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.07215 | −0.0661118 | −0.0330559 | − | 0.999454i | \(-0.510524\pi\) | ||||
−0.0330559 | + | 0.999454i | \(0.510524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.6226 | −2.31114 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.7725 | 0.781664 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.7188 | 1.93393 | 0.966965 | − | 0.254910i | \(-0.0820458\pi\) | ||||
0.966965 | + | 0.254910i | \(0.0820458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.614744 | −0.0373430 | −0.0186715 | − | 0.999826i | \(-0.505944\pi\) | ||||
−0.0186715 | + | 0.999826i | \(0.505944\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.8093 | 1.67696 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6747 | 0.881718 | 0.440859 | − | 0.897576i | \(-0.354674\pi\) | ||||
0.440859 | + | 0.897576i | \(0.354674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.80904 | −0.108304 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1406 | 0.724248 | 0.362124 | − | 0.932130i | \(-0.382052\pi\) | ||||
0.362124 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.54346 | 0.448412 | 0.224206 | − | 0.974542i | \(-0.428021\pi\) | ||||
0.224206 | + | 0.974542i | \(0.428021\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.4510 | 1.92223 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.21522 | −0.189130 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0274 | 0.705060 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.4648 | 1.25399 | 0.626994 | − | 0.779024i | \(-0.284285\pi\) | ||||
0.626994 | + | 0.779024i | \(0.284285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 61.8035 | 3.59834 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.29857 | −0.133377 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.14060 | 0.239457 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.30661 | −0.0750625 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.94631 | 0.512264 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.41738 | 0.423333 | 0.211666 | − | 0.977342i | \(-0.432111\pi\) | ||||
0.211666 | + | 0.977342i | \(0.432111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0033 | 0.625957 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7881 | −0.838557 | −0.419278 | − | 0.907858i | \(-0.637717\pi\) | ||||
−0.419278 | + | 0.907858i | \(0.637717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.95434 | 0.562653 | 0.281326 | − | 0.959612i | \(-0.409226\pi\) | ||||
0.281326 | + | 0.959612i | \(0.409226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.97907 | −0.167321 | −0.0836607 | − | 0.996494i | \(-0.526661\pi\) | ||||
−0.0836607 | + | 0.996494i | \(0.526661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.47191 | −0.418347 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.8387 | 0.604957 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.1373 | 1.62124 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.4430 | −1.63320 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.44164 | −0.522124 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.80571 | −0.374076 | −0.187038 | − | 0.982353i | \(-0.559889\pi\) | ||||
−0.187038 | + | 0.982353i | \(0.559889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.65685 | 0.309994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −42.4006 | −2.31659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.69564 | −0.419208 | −0.209604 | − | 0.977786i | \(-0.567217\pi\) | ||||
−0.209604 | + | 0.977786i | \(0.567217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.31371 | −0.505851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.15820 | −0.225179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.03546 | 0.378776 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2094 | −0.548071 | −0.274035 | − | 0.961720i | \(-0.588359\pi\) | ||||
−0.274035 | + | 0.961720i | \(0.588359\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.6742 | −1.48137 | −0.740684 | − | 0.671854i | \(-0.765498\pi\) | ||||
−0.740684 | + | 0.671854i | \(0.765498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.43361 | 0.129896 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.51849 | 0.134046 | 0.0670230 | − | 0.997751i | \(-0.478650\pi\) | ||||
0.0670230 | + | 0.997751i | \(0.478650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3558 | 0.868077 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.58470 | 0.241971 | 0.120986 | − | 0.992654i | \(-0.461394\pi\) | ||||
0.120986 | + | 0.992654i | \(0.461394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.5883 | 2.24149 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.71656 | 0.300042 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.0448 | −2.09604 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.38462 | 0.489873 | 0.244937 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244937 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.81128 | 0.354581 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0027 | 0.569698 | 0.284849 | − | 0.958572i | \(-0.408057\pi\) | ||||
0.284849 | + | 0.958572i | \(0.408057\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.3525 | −1.51576 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.91085 | 0.407430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7050 | 1.37174 | 0.685871 | − | 0.727723i | \(-0.259421\pi\) | ||||
0.685871 | + | 0.727723i | \(0.259421\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.1373 | 0.673043 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.3940 | 1.45086 | 0.725432 | − | 0.688294i | \(-0.241640\pi\) | ||||
0.725432 | + | 0.688294i | \(0.241640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.44164 | −0.276614 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.4450 | −1.03660 | −0.518300 | − | 0.855199i | \(-0.673435\pi\) | ||||
−0.518300 | + | 0.855199i | \(0.673435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.31704 | 0.319466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.81236 | 0.444525 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.5107 | −2.08863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.8752 | −0.796756 | −0.398378 | − | 0.917221i | \(-0.630427\pi\) | ||||
−0.398378 | + | 0.917221i | \(0.630427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.2507 | −0.961333 | −0.480666 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480666 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.40248 | 0.219303 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.13503 | 0.205471 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0027 | 0.644519 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.27963 | 0.0632737 | 0.0316368 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316368 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.367398 | −0.0181224 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.3618 | 2.37399 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.3137 | 0.749916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8754 | 0.824417 | 0.412209 | − | 0.911090i | \(-0.364758\pi\) | ||||
0.412209 | + | 0.911090i | \(0.364758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.6774 | −1.15397 | −0.576983 | − | 0.816756i | \(-0.695770\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.2895 | −0.646155 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.9191 | −2.17890 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.59382 | 0.270072 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8208 | −0.569390 | −0.284695 | − | 0.958618i | \(-0.591892\pi\) | ||||
−0.284695 | + | 0.958618i | \(0.591892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9771 | 1.05615 | 0.528075 | − | 0.849198i | \(-0.322914\pi\) | ||||
0.528075 | + | 0.849198i | \(0.322914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.4416 | 0.644477 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.3525 | 0.638736 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.3137 | −1.68543 | −0.842716 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842716 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1248 | 0.813625 | 0.406813 | − | 0.913512i | \(-0.366640\pi\) | ||||
0.406813 | + | 0.913512i | \(0.366640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −52.8147 | −2.50366 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.4122 | −0.776270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.6562 | 0.737223 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.78478 | −0.365761 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.80571 | 0.224802 | 0.112401 | − | 0.993663i | \(-0.464146\pi\) | ||||
0.112401 | + | 0.993663i | \(0.464146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.71279 | 0.173298 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0798 | −0.981785 | −0.490892 | − | 0.871220i | \(-0.663329\pi\) | ||||
−0.490892 | + | 0.871220i | \(0.663329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2861 | 0.663933 | 0.331966 | − | 0.943291i | \(-0.392288\pi\) | ||||
0.331966 | + | 0.943291i | \(0.392288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.48042 | 0.346896 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.5159 | −1.04191 | −0.520955 | − | 0.853584i | \(-0.674424\pi\) | ||||
−0.520955 | + | 0.853584i | \(0.674424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.2050 | 0.792765 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.5080 | −0.575118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −94.9468 | −4.35646 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.09849 | −0.416591 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.90753 | 0.406995 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7665 | −0.627701 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −49.7338 | −2.25829 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7848 | 1.07779 | 0.538896 | − | 0.842372i | \(-0.318842\pi\) | ||||
0.538896 | + | 0.842372i | \(0.318842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.71656 | −0.303733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1524 | 0.638689 | 0.319345 | − | 0.947639i | \(-0.396537\pi\) | ||||
0.319345 | + | 0.947639i | \(0.396537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0691 | 0.543563 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.50467 | 0.427203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4122 | 1.00331 | 0.501654 | − | 0.865068i | \(-0.332725\pi\) | ||||
0.501654 | + | 0.865068i | \(0.332725\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.21189 | 0.0541432 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.61538 | −0.294965 | −0.147483 | − | 0.989065i | \(-0.547117\pi\) | ||||
−0.147483 | + | 0.989065i | \(0.547117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.40285 | 0.240424 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.07757 | 0.314326 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.93588 | 0.0858064 | 0.0429032 | − | 0.999079i | \(-0.486339\pi\) | ||||
0.0429032 | + | 0.999079i | \(0.486339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.84782 | 0.346490 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.4991 | −2.00493 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.5468 | −1.34345 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.2772 | 0.451118 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.7079 | −0.469123 | −0.234561 | − | 0.972101i | \(-0.575365\pi\) | ||||
−0.234561 | + | 0.972101i | \(0.575365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0896 | 1.40318 | 0.701590 | − | 0.712581i | \(-0.252474\pi\) | ||||
0.701590 | + | 0.712581i | \(0.252474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.71656 | 0.292578 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1051 | −0.874137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.9463 | 0.648615 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.5760 | −0.717985 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.8184 | −1.93767 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.1221 | −0.523109 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.4804 | 0.751542 | 0.375771 | − | 0.926713i | \(-0.377378\pi\) | ||||
0.375771 | + | 0.926713i | \(0.377378\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.2460 | −0.997580 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.0415 | 1.67235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.6243 | −1.48043 | −0.740215 | − | 0.672370i | \(-0.765276\pi\) | ||||
−0.740215 | + | 0.672370i | \(0.765276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.16354 | 0.0923377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.5107 | 1.08679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.3913 | −0.992904 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.9042 | −0.504397 | −0.252199 | − | 0.967676i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967676i | \(0.581154\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.2428 | 0.560111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.53411 | 0.360310 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.1339 | −0.764255 | −0.382127 | − | 0.924110i | \(-0.624808\pi\) | ||||
−0.382127 | + | 0.924110i | \(0.624808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.5125 | 1.62023 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7102 | −0.826293 | −0.413147 | − | 0.910665i | \(-0.635570\pi\) | ||||
−0.413147 | + | 0.910665i | \(0.635570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.96122 | −0.249469 | −0.124735 | − | 0.992190i | \(-0.539808\pi\) | ||||
−0.124735 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.2691 | −0.972082 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.5847 | −0.858441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.9249 | −1.45394 | −0.726971 | − | 0.686668i | \(-0.759073\pi\) | ||||
−0.726971 | + | 0.686668i | \(0.759073\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.28613 | 0.178125 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.9135 | −0.866151 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0630 | −0.416055 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.05369 | −0.373686 | −0.186843 | − | 0.982390i | \(-0.559826\pi\) | ||||
−0.186843 | + | 0.982390i | \(0.559826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1970 | 0.584977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9818 | −0.492864 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.129013 | 0.00529795 | 0.00264897 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264897 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.1970 | 0.908462 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0357 | 0.859495 | 0.429747 | − | 0.902949i | \(-0.358603\pi\) | ||||
0.429747 | + | 0.902949i | \(0.358603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.67307 | −0.190619 | −0.0953093 | − | 0.995448i | \(-0.530384\pi\) | ||||
−0.0953093 | + | 0.995448i | \(0.530384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2540 | −0.417575 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.6382 | −0.961028 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.3164 | −1.31168 | −0.655841 | − | 0.754899i | \(-0.727686\pi\) | ||||
−0.655841 | + | 0.754899i | \(0.727686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.3413 | 1.30839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.6480 | 1.72254 | 0.861268 | − | 0.508152i | \(-0.169671\pi\) | ||||
0.861268 | + | 0.508152i | \(0.169671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.1649 | −1.13572 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.3741 | −0.900745 | −0.450373 | − | 0.892841i | \(-0.648709\pi\) | ||||
−0.450373 | + | 0.892841i | \(0.648709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3428 | −1.25977 | −0.629886 | − | 0.776687i | \(-0.716898\pi\) | ||||
−0.629886 | + | 0.776687i | \(0.716898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.70143 | 0.0682759 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 60.8810 | 2.43524 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.0388 | 0.720400 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0027 | −0.837432 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.79413 | −0.111233 | −0.0556163 | − | 0.998452i | \(-0.517712\pi\) | ||||
−0.0556163 | + | 0.998452i | \(0.517712\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.540129 | −0.0214682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −54.3231 | −2.15574 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.95543 | 0.156474 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.17042 | −0.0857262 | −0.0428631 | − | 0.999081i | \(-0.513648\pi\) | ||||
−0.0428631 | + | 0.999081i | \(0.513648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.91604 | 0.351614 | 0.175807 | − | 0.984425i | \(-0.443746\pi\) | ||||
0.175807 | + | 0.984425i | \(0.443746\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.5013 | 0.885990 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1018 | 0.711656 | 0.355828 | − | 0.934551i | \(-0.384199\pi\) | ||||
0.355828 | + | 0.934551i | \(0.384199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.3552 | 1.34856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.826893 | 0.0323588 | 0.0161794 | − | 0.999869i | \(-0.494850\pi\) | ||||
0.0161794 | + | 0.999869i | \(0.494850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.4394 | −1.42381 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.68428 | −0.377820 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.4956 | 1.26585 | 0.632924 | − | 0.774214i | \(-0.281855\pi\) | ||||
0.632924 | + | 0.774214i | \(0.281855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4127 | 1.06623 | 0.533115 | − | 0.846043i | \(-0.321021\pi\) | ||||
0.533115 | + | 0.846043i | \(0.321021\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.03546 | −0.350908 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.53078 | 0.214153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1194 | −0.391239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.97306 | 0.191983 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.9884 | 1.23306 | 0.616531 | − | 0.787330i | \(-0.288537\pi\) | ||||
0.616531 | + | 0.787330i | \(0.288537\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0985 | −0.465671 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.6979 | −1.56415 | −0.782073 | − | 0.623186i | \(-0.785838\pi\) | ||||
−0.782073 | + | 0.623186i | \(0.785838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.7587 | 1.06371 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.0357 | −0.651852 | −0.325926 | − | 0.945395i | \(-0.605676\pi\) | ||||
−0.325926 | + | 0.945395i | \(0.605676\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.51920 | 0.0580458 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8962 | −0.568324 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.1421 | 0.843548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8926 | −0.985002 | −0.492501 | − | 0.870312i | \(-0.663917\pi\) | ||||
−0.492501 | + | 0.870312i | \(0.663917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −63.3227 | −2.40197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.2888 | −0.957882 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.5644 | 0.550875 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8781 | 0.977402 | 0.488701 | − | 0.872451i | \(-0.337471\pi\) | ||||
0.488701 | + | 0.872451i | \(0.337471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.3940 | −1.67435 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 54.9523 | 2.06962 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.2660 | −1.13666 | −0.568332 | − | 0.822799i | \(-0.692411\pi\) | ||||
−0.568332 | + | 0.822799i | \(0.692411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0388 | −0.376484 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.07794 | 0.115270 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.1306 | −0.865036 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.70143 | 0.0635410 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2652 | 0.569296 | 0.284648 | − | 0.958632i | \(-0.408123\pi\) | ||||
0.284648 | + | 0.958632i | \(0.408123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.0141 | 1.00466 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.3282 | −1.46061 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0154 | 0.705241 | 0.352620 | − | 0.935766i | \(-0.385291\pi\) | ||||
0.352620 | + | 0.935766i | \(0.385291\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.2036 | 0.747259 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.21353 | −0.340309 | −0.170155 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170155 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.5696 | −0.868196 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.1078 | −1.40182 | −0.700910 | − | 0.713250i | \(-0.747222\pi\) | ||||
−0.700910 | + | 0.713250i | \(0.747222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.0985 | −0.701601 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.46528 | −0.0904425 | −0.0452213 | − | 0.998977i | \(-0.514399\pi\) | ||||
−0.0452213 | + | 0.998977i | \(0.514399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 67.8650 | 2.48638 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6956 | 0.427921 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2843 | 1.03211 | 0.516054 | − | 0.856556i | \(-0.327400\pi\) | ||||
0.516054 | + | 0.856556i | \(0.327400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.8269 | 0.467438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.1903 | 1.17153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0691 | 1.16557 | 0.582785 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582785 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.91085 | 0.141955 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.99136 | 0.144687 | 0.0723434 | − | 0.997380i | \(-0.476952\pi\) | ||||
0.0723434 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.3525 | −0.555071 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.3734 | −1.31337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8082 | −0.786423 | −0.393212 | − | 0.919448i | \(-0.628636\pi\) | ||||
−0.393212 | + | 0.919448i | \(0.628636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.99892 | −0.0719892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.9956 | −0.683224 | −0.341612 | − | 0.939841i | \(-0.610973\pi\) | ||||
−0.341612 | + | 0.939841i | \(0.610973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.8866 | −0.786190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.4537 | −1.91518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.09184 | 0.325332 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.25067 | 0.116170 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −71.1433 | −2.53921 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2063 | 1.61143 | 0.805716 | − | 0.592302i | \(-0.201781\pi\) | ||||
0.805716 | + | 0.592302i | \(0.201781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.07215 | 0.0381696 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.26520 | −0.186973 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.6226 | 1.33433 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.5517 | 1.29473 | 0.647364 | − | 0.762181i | \(-0.275871\pi\) | ||||
0.647364 | + | 0.762181i | \(0.275871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.3409 | 1.74556 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7725 | −0.451294 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.2600 | −0.785539 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.7188 | −1.11655 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0829 | −1.26861 | −0.634304 | − | 0.773083i | \(-0.718713\pi\) | ||||
−0.634304 | + | 0.773083i | \(0.718713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.6565 | 0.936036 | 0.468018 | − | 0.883719i | \(-0.344968\pi\) | ||||
0.468018 | + | 0.883719i | \(0.344968\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.614744 | 0.0215600 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.7732 | 0.972853 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.7050 | 1.49406 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.0369 | −1.46710 | −0.733549 | − | 0.679636i | \(-0.762138\pi\) | ||||
−0.733549 | + | 0.679636i | \(0.762138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4692 | 0.922659 | 0.461329 | − | 0.887229i | \(-0.347373\pi\) | ||||
0.461329 | + | 0.887229i | \(0.347373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.8093 | −0.968194 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.8663 | 1.94266 | 0.971330 | − | 0.237733i | \(-0.0764044\pi\) | ||||
0.971330 | + | 0.237733i | \(0.0764044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.394822 | −0.0137127 | −0.00685637 | − | 0.999976i | \(-0.502182\pi\) | ||||
−0.00685637 | + | 0.999976i | \(0.502182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6747 | −0.509060 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.01120 | −0.173420 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.80904 | 0.0625294 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9851 | 0.724486 | 0.362243 | − | 0.932084i | \(-0.382011\pi\) | ||||
0.362243 | + | 0.932084i | \(0.382011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4331 | −0.635625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1406 | −0.418145 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.2660 | −1.00678 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.54346 | −0.258891 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.62473 | −0.329931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.76517 | 0.300114 | 0.150057 | − | 0.988677i | \(-0.452054\pi\) | ||||
0.150057 | + | 0.988677i | \(0.452054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.4510 | −1.10980 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.45879 | −0.323106 | −0.161553 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161553 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.7377 | −1.11700 | −0.558499 | − | 0.829505i | \(-0.688622\pi\) | ||||
−0.558499 | + | 0.829505i | \(0.688622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.73086 | −0.297202 | −0.148601 | − | 0.988897i | \(-0.547477\pi\) | ||||
−0.148601 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.4964 | −1.44492 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.21522 | 0.109194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.0749 | −0.782762 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9542 | 0.845540 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0274 | −0.407067 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.8814 | −1.24540 | −0.622698 | − | 0.782462i | \(-0.713964\pi\) | ||||
−0.622698 | + | 0.782462i | \(0.713964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.4648 | −0.723990 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.7543 | −0.362320 | −0.181160 | − | 0.983454i | \(-0.557985\pi\) | ||||
−0.181160 | + | 0.983454i | \(0.557985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8266 | −0.465303 | −0.232652 | − | 0.972560i | \(-0.574740\pi\) | ||||
−0.232652 | + | 0.972560i | \(0.574740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −61.8035 | −2.07750 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.8657 | −1.17067 | −0.585337 | − | 0.810790i | \(-0.699038\pi\) | ||||
−0.585337 | + | 0.810790i | \(0.699038\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.29857 | 0.0770051 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 104.293 | 3.49004 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.1254 | 1.67551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.14060 | −0.138251 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.88058 | 0.196128 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.7808 | 1.12540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 96.1228 | 3.19523 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9202 | 0.893871 | 0.446935 | − | 0.894566i | \(-0.352515\pi\) | ||||
0.446935 | + | 0.894566i | \(0.352515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.30661 | 0.0433374 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3288 | −0.540999 | −0.270499 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270499 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.8833 | 0.889707 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.94631 | −0.295756 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.51920 | 0.0501139 | 0.0250570 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250570 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.41738 | −0.244411 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.62595 | −0.316842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 68.4394 | 2.25027 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.0033 | −0.361397 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.39057 | −0.275286 | −0.137643 | − | 0.990482i | \(-0.543953\pi\) | ||||
−0.137643 | + | 0.990482i | \(0.543953\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7881 | 0.484141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.2888 | −1.15407 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6019 | 0.934382 | 0.467191 | − | 0.884156i | \(-0.345266\pi\) | ||||
0.467191 | + | 0.884156i | \(0.345266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.95434 | −0.324848 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8743 | 1.00647 | 0.503237 | − | 0.864148i | \(-0.332142\pi\) | ||||
0.503237 | + | 0.864148i | \(0.332142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5889 | −0.377386 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.0151 | 0.812883 | 0.406441 | − | 0.913677i | \(-0.366770\pi\) | ||||
0.406441 | + | 0.913677i | \(0.366770\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.5677 | 0.765040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97907 | 0.0966031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.11942 | 0.133441 | 0.0667205 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667205 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 96.2186 | 3.11356 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.47191 | 0.241533 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.7274 | −0.894432 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.8387 | −0.349272 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.7233 | −0.570533 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.5901 | −0.758607 | −0.379303 | − | 0.925272i | \(-0.623836\pi\) | ||||
−0.379303 | + | 0.925272i | \(0.623836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.1373 | −0.936024 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8833 | −0.477627 | −0.238814 | − | 0.971065i | \(-0.576758\pi\) | ||||
−0.238814 | + | 0.971065i | \(0.576758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.4430 | 0.942929 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.6353 | −1.42801 | −0.714005 | − | 0.700141i | \(-0.753121\pi\) | ||||
−0.714005 | + | 0.700141i | \(0.753121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.3585 | −0.938302 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.44164 | 0.301448 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.1167 | −0.418359 | −0.209179 | − | 0.977877i | \(-0.567079\pi\) | ||||
−0.209179 | + | 0.977877i | \(0.567079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.5450 | 1.57863 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.25855 | 0.294405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5968 | 1.19430 | 0.597150 | − | 0.802129i | \(-0.296300\pi\) | ||||
0.597150 | + | 0.802129i | \(0.296300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.80571 | 0.215973 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −91.7852 | −2.90979 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.1044 | 0.826733 | 0.413367 | − | 0.910565i | \(-0.364353\pi\) | ||||
0.413367 | + | 0.910565i | \(0.364353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.65685 | −0.178975 |
(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 | 9408.2.a.el.1.4 | 4 | ||
4.3 | odd | 2 | 9408.2.a.en.1.4 | 4 | |||
7.6 | odd | 2 | 9408.2.a.em.1.1 | 4 | |||
8.3 | odd | 2 | 4704.2.a.bw.1.1 | ✓ | 4 | ||
8.5 | even | 2 | 4704.2.a.by.1.1 | yes | 4 | ||
28.27 | even | 2 | 9408.2.a.ek.1.1 | 4 | |||
56.13 | odd | 2 | 4704.2.a.bx.1.4 | yes | 4 | ||
56.27 | even | 2 | 4704.2.a.bz.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4704.2.a.bw.1.1 | ✓ | 4 | 8.3 | odd | 2 | ||
4704.2.a.bx.1.4 | yes | 4 | 56.13 | odd | 2 | ||
4704.2.a.by.1.1 | yes | 4 | 8.5 | even | 2 | ||
4704.2.a.bz.1.4 | yes | 4 | 56.27 | even | 2 | ||
9408.2.a.ek.1.1 | 4 | 28.27 | even | 2 | |||
9408.2.a.el.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9408.2.a.em.1.1 | 4 | 7.6 | odd | 2 | |||
9408.2.a.en.1.4 | 4 | 4.3 | odd | 2 |