Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(127,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.x (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.12 | ||
Character | \(\chi\) | \(=\) | 560.127 |
Dual form | 560.2.x.b.463.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.31224 | + | 2.31224i | 1.33497 | + | 1.33497i | 0.900860 | + | 0.434110i | \(0.142937\pi\) |
0.434110 | + | 0.900860i | \(0.357063\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.03291 | + | 0.931271i | 0.909146 | + | 0.416477i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.69286i | 2.56429i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.09628i | − | 1.83810i | −0.394144 | − | 0.919049i | \(-0.628959\pi\) | ||
0.394144 | − | 0.919049i | \(-0.371041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41796 | + | 1.41796i | −0.393271 | + | 0.393271i | −0.875852 | − | 0.482580i | \(-0.839700\pi\) |
0.482580 | + | 0.875852i | \(0.339700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.54726 | + | 6.85389i | 0.657699 | + | 1.76967i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.291645 | + | 0.291645i | 0.0707342 | + | 0.0707342i | 0.741589 | − | 0.670855i | \(-0.234073\pi\) |
−0.670855 | + | 0.741589i | \(0.734073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26091 | 0.748104 | 0.374052 | − | 0.927408i | \(-0.377968\pi\) | ||||
0.374052 | + | 0.927408i | \(0.377968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.26999 | −0.713571 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.29531 | − | 5.29531i | −1.10415 | − | 1.10415i | −0.993905 | − | 0.110243i | \(-0.964837\pi\) |
−0.110243 | − | 0.993905i | \(-0.535163\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.26547 | + | 3.78638i | 0.653094 | + | 0.757277i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.8510 | + | 10.8510i | −2.08828 | + | 2.08828i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.37807i | − | 0.441596i | −0.975320 | − | 0.220798i | \(-0.929134\pi\) | ||
0.975320 | − | 0.220798i | \(-0.0708661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.95390i | − | 0.710142i | −0.934839 | − | 0.355071i | \(-0.884457\pi\) | ||
0.934839 | − | 0.355071i | \(-0.115543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.0960 | − | 14.0960i | 2.45380 | − | 2.45380i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.09599 | + | 0.778979i | −0.354288 | + | 0.131671i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.09050 | − | 4.09050i | −0.672474 | − | 0.672474i | 0.285812 | − | 0.958286i | \(-0.407737\pi\) |
−0.958286 | + | 0.285812i | \(0.907737\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.55732 | −1.05001 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.03921 | 1.09934 | 0.549670 | − | 0.835382i | \(-0.314754\pi\) | ||||
0.549670 | + | 0.835382i | \(0.314754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.83184 | − | 1.83184i | −0.279352 | − | 0.279352i | 0.553498 | − | 0.832850i | \(-0.313293\pi\) |
−0.832850 | + | 0.553498i | \(0.813293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.16414 | + | 15.6389i | −1.06797 | + | 2.33131i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.50821 | + | 3.50821i | −0.511725 | + | 0.511725i | −0.915055 | − | 0.403330i | \(-0.867853\pi\) |
0.403330 | + | 0.915055i | \(0.367853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.34870i | 0.188856i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.49795 | + | 5.49795i | −0.755202 | + | 0.755202i | −0.975445 | − | 0.220243i | \(-0.929315\pi\) |
0.220243 | + | 0.975445i | \(0.429315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.67728 | − | 12.3932i | 0.765525 | − | 1.67110i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.53999 | + | 7.53999i | 0.998696 | + | 0.998696i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.02998 | 0.654847 | 0.327424 | − | 0.944878i | \(-0.393820\pi\) | ||||
0.327424 | + | 0.944878i | \(0.393820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.51192 | 0.577693 | 0.288846 | − | 0.957375i | \(-0.406728\pi\) | ||||
0.288846 | + | 0.957375i | \(0.406728\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.43968 | − | 5.43968i | −0.685335 | − | 0.685335i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.20309 | + | 1.56209i | −0.521330 | + | 0.193753i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.04639 | + | 4.04639i | −0.494345 | + | 0.494345i | −0.909672 | − | 0.415327i | \(-0.863667\pi\) |
0.415327 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 24.4880i | − | 2.94801i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.733929i | 0.0871014i | 0.999051 | + | 0.0435507i | \(0.0138670\pi\) | ||||
−0.999051 | + | 0.0435507i | \(0.986133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94871 | + | 2.94871i | −0.345120 | + | 0.345120i | −0.858288 | − | 0.513168i | \(-0.828472\pi\) |
0.513168 | + | 0.858288i | \(0.328472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.20448 | + | 16.3055i | −0.139081 | + | 1.88280i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.31072 | + | 4.31072i | 0.491252 | + | 0.491252i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.28925 | 0.145052 | 0.0725262 | − | 0.997367i | \(-0.476894\pi\) | ||||
0.0725262 | + | 0.997367i | \(0.476894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −27.1016 | −3.01128 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.84891 | + | 6.84891i | 0.751766 | + | 0.751766i | 0.974809 | − | 0.223043i | \(-0.0715991\pi\) |
−0.223043 | + | 0.974809i | \(0.571599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.321288 | + | 0.864488i | 0.0348486 | + | 0.0937669i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.49865 | − | 5.49865i | 0.589517 | − | 0.589517i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.21572i | − | 0.446866i | −0.974719 | − | 0.223433i | \(-0.928274\pi\) | ||
0.974719 | − | 0.223433i | \(-0.0717264\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.00530i | − | 0.210212i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.14235 | − | 9.14235i | 0.948018 | − | 0.948018i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.62914 | + | 3.03679i | 0.680136 | + | 0.311568i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.88225 | + | 2.88225i | 0.292648 | + | 0.292648i | 0.838126 | − | 0.545477i | \(-0.183652\pi\) |
−0.545477 | + | 0.838126i | \(0.683652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 46.8978 | 4.71341 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.03254 | 0.898772 | 0.449386 | − | 0.893338i | \(-0.351643\pi\) | ||||
0.449386 | + | 0.893338i | \(0.351643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.57683 | − | 2.57683i | −0.253903 | − | 0.253903i | 0.568666 | − | 0.822569i | \(-0.307460\pi\) |
−0.822569 | + | 0.568666i | \(0.807460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.64761 | − | 3.04525i | −0.648741 | − | 0.297186i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.11214 | − | 9.11214i | 0.880904 | − | 0.880904i | −0.112723 | − | 0.993626i | \(-0.535957\pi\) |
0.993626 | + | 0.112723i | \(0.0359572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0904i | 1.44540i | 0.691164 | + | 0.722698i | \(0.257098\pi\) | ||||
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 18.9164i | − | 1.79546i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.53162 | − | 5.53162i | 0.520371 | − | 0.520371i | −0.397313 | − | 0.917683i | \(-0.630057\pi\) |
0.917683 | + | 0.397313i | \(0.130057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.83353 | − | 15.6963i | −0.543980 | − | 1.46368i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.9082 | − | 10.9082i | −1.00846 | − | 1.00846i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.412448 | −0.0378090 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.1646 | −2.37860 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.2763 | + | 16.2763i | 1.46758 | + | 1.46758i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.11227 | + | 10.7384i | 0.278370 | + | 0.960474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.18696 | − | 2.18696i | 0.194061 | − | 0.194061i | −0.603387 | − | 0.797448i | \(-0.706183\pi\) |
0.797448 | + | 0.603387i | \(0.206183\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.47127i | − | 0.745854i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.1306i | − | 0.885116i | −0.896740 | − | 0.442558i | \(-0.854071\pi\) | ||
0.896740 | − | 0.442558i | \(-0.145929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.30581 | + | 2.30581i | −0.199939 | + | 0.199939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −32.1644 | + | 11.9539i | −2.76827 | + | 1.02883i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.91649 | − | 8.91649i | −0.761787 | − | 0.761787i | 0.214858 | − | 0.976645i | \(-0.431071\pi\) |
−0.976645 | + | 0.214858i | \(0.931071\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.5075 | −1.82424 | −0.912122 | − | 0.409918i | \(-0.865557\pi\) | ||||
−0.912122 | + | 0.409918i | \(0.865557\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.2236 | −1.36627 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.64428 | + | 8.64428i | 0.722871 | + | 0.722871i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.21462 | − | 4.83440i | 0.183914 | − | 0.401475i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.31224 | − | 2.31224i | 0.190710 | − | 0.190710i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.9408i | − | 0.978229i | −0.872220 | − | 0.489115i | \(-0.837320\pi\) | ||
0.872220 | − | 0.489115i | \(-0.162680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.2898i | − | 0.918747i | −0.888243 | − | 0.459374i | \(-0.848074\pi\) | ||
0.888243 | − | 0.459374i | \(-0.151926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.24358 | + | 2.24358i | −0.181383 | + | 0.181383i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.68215 | − | 8.03794i | 0.295758 | − | 0.645623i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.47755 | − | 6.47755i | −0.516965 | − | 0.516965i | 0.399687 | − | 0.916652i | \(-0.369119\pi\) |
−0.916652 | + | 0.399687i | \(0.869119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.4251 | −2.01634 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.48870 | 0.590192 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.712128 | − | 0.712128i | −0.0557782 | − | 0.0557782i | 0.678667 | − | 0.734446i | \(-0.262558\pi\) |
−0.734446 | + | 0.678667i | \(0.762558\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 41.7832 | − | 15.5288i | 3.25282 | − | 1.20891i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.07849 | + | 7.07849i | −0.547750 | + | 0.547750i | −0.925790 | − | 0.378039i | \(-0.876598\pi\) |
0.378039 | + | 0.925790i | \(0.376598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.97878i | 0.690675i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25.0857i | 1.91835i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.94380 | − | 2.94380i | 0.223813 | − | 0.223813i | −0.586289 | − | 0.810102i | \(-0.699412\pi\) |
0.810102 | + | 0.586289i | \(0.199412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.98641 | − | 0.368342i | −0.376937 | − | 0.0278440i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6305 | + | 11.6305i | 0.874201 | + | 0.874201i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5919 | −1.01591 | −0.507953 | − | 0.861385i | \(-0.669598\pi\) | ||||
−0.507953 | + | 0.861385i | \(0.669598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0560 | −1.04477 | −0.522386 | − | 0.852709i | \(-0.674958\pi\) | ||||
−0.522386 | + | 0.852709i | \(0.674958\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4326 | + | 10.4326i | 0.771202 | + | 0.771202i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.50627 | − | 12.1250i | −0.331307 | − | 0.891447i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.77795 | − | 1.77795i | 0.130016 | − | 0.130016i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 15.3456i | − | 1.11623i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.06875i | − | 0.149689i | −0.997195 | − | 0.0748446i | \(-0.976154\pi\) | ||
0.997195 | − | 0.0748446i | \(-0.0238461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8858 | − | 11.8858i | 0.855561 | − | 0.855561i | −0.135250 | − | 0.990811i | \(-0.543184\pi\) |
0.990811 | + | 0.135250i | \(0.0431838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.3305 | − | 6.10664i | −0.954613 | − | 0.437305i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3267 | + | 19.3267i | 1.37697 | + | 1.37697i | 0.849689 | + | 0.527285i | \(0.176790\pi\) |
0.527285 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.86247 | 0.344691 | 0.172346 | − | 0.985037i | \(-0.444865\pi\) | ||||
0.172346 | + | 0.985037i | \(0.444865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.7124 | −1.31987 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.68155 | + | 1.68155i | 0.118021 | + | 0.118021i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.3101 | + | 6.55540i | 0.999460 | + | 0.457849i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 40.7361 | − | 40.7361i | 2.83135 | − | 2.83135i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 19.8794i | − | 1.37509i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.21039i | 0.634070i | 0.948414 | + | 0.317035i | \(0.102687\pi\) | ||||
−0.948414 | + | 0.317035i | \(0.897313\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.69702 | + | 1.69702i | −0.116278 | + | 0.116278i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.01803 | − | 5.42990i | −0.137628 | − | 0.370316i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.79583 | + | 2.79583i | 0.189793 | + | 0.189793i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6362 | −0.921449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.827081 | −0.0556355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.93354 | + | 1.93354i | 0.129479 | + | 0.129479i | 0.768877 | − | 0.639397i | \(-0.220816\pi\) |
−0.639397 | + | 0.768877i | \(0.720816\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.1281 | + | 25.1208i | −1.94188 | + | 1.67472i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.89388 | + | 7.89388i | −0.523935 | + | 0.523935i | −0.918758 | − | 0.394822i | \(-0.870806\pi\) |
0.394822 | + | 0.918758i | \(0.370806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.1386i | 1.19863i | 0.800513 | + | 0.599316i | \(0.204561\pi\) | ||||
−0.800513 | + | 0.599316i | \(0.795439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.9348i | 1.31161i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.5097 | − | 11.5097i | 0.754027 | − | 0.754027i | −0.221201 | − | 0.975228i | \(-0.570998\pi\) |
0.975228 | + | 0.221201i | \(0.0709978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3990 | + | 3.86479i | −0.678354 | + | 0.252111i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.98106 | + | 2.98106i | 0.193641 | + | 0.193641i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.71436 | −0.434316 | −0.217158 | − | 0.976136i | \(-0.569679\pi\) | ||||
−0.217158 | + | 0.976136i | \(0.569679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.79406 | −0.630891 | −0.315446 | − | 0.948944i | \(-0.602154\pi\) | ||||
−0.315446 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −30.1122 | − | 30.1122i | −1.93170 | − | 1.93170i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.931271 | − | 2.03291i | 0.0594967 | − | 0.129878i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.62384 | + | 4.62384i | −0.294208 | + | 0.294208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.6726i | 2.00717i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.7582i | 1.68896i | 0.535587 | + | 0.844480i | \(0.320091\pi\) | ||||
−0.535587 | + | 0.844480i | \(0.679909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.2817 | + | 32.2817i | −2.02953 | + | 2.02953i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.25601 | + | 2.74179i | −0.0786542 | + | 0.171698i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.67234 | − | 7.67234i | −0.478588 | − | 0.478588i | 0.426092 | − | 0.904680i | \(-0.359890\pi\) |
−0.904680 | + | 0.426092i | \(0.859890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.78484 | 0.359452 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.2941 | 1.13238 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.7919 | + | 16.7919i | 1.03543 | + | 1.03543i | 0.999349 | + | 0.0360845i | \(0.0114885\pi\) |
0.0360845 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.2969 | + | 6.05678i | −1.00111 | + | 0.372065i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.74775 | − | 9.74775i | 0.596552 | − | 0.596552i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 21.5442i | − | 1.31357i | −0.754076 | − | 0.656787i | \(-0.771915\pi\) | ||
0.754076 | − | 0.656787i | \(-0.228085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.3853i | − | 1.35981i | −0.733300 | − | 0.679905i | \(-0.762021\pi\) | ||
0.733300 | − | 0.679905i | \(-0.237979\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.63672 | − | 4.63672i | 0.280627 | − | 0.280627i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.0829 | − | 19.9072i | 1.39195 | − | 1.20045i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.40580 | + | 6.40580i | 0.384887 | + | 0.384887i | 0.872859 | − | 0.487972i | \(-0.162263\pi\) |
−0.487972 | + | 0.872859i | \(0.662263\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.4168 | 1.82101 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1228 | 1.43904 | 0.719522 | − | 0.694469i | \(-0.244361\pi\) | ||||
0.719522 | + | 0.694469i | \(0.244361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7620 | + | 10.7620i | 0.639734 | + | 0.639734i | 0.950490 | − | 0.310755i | \(-0.100582\pi\) |
−0.310755 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.30637 | + | 22.3499i | 0.492027 | + | 1.32389i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.97747 | + | 4.97747i | −0.293811 | + | 0.293811i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.8299i | − | 0.989993i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.3289i | 0.781353i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7195 | + | 10.7195i | −0.626238 | + | 0.626238i | −0.947119 | − | 0.320881i | \(-0.896021\pi\) |
0.320881 | + | 0.947119i | \(0.396021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2255 | + | 4.68427i | 0.595352 | + | 0.272729i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 66.1507 | + | 66.1507i | 3.83846 | + | 3.83846i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0171 | 0.868460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.59061 | 0.149320 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.8854 | + | 20.8854i | 1.19983 | + | 1.19983i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.17235 | + | 4.20182i | 0.525207 | + | 0.240596i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.8605 | + | 11.8605i | −0.676914 | + | 0.676914i | −0.959301 | − | 0.282386i | \(-0.908874\pi\) |
0.282386 | + | 0.959301i | \(0.408874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 11.9165i | − | 0.677905i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.75781i | 0.156381i | 0.996938 | + | 0.0781905i | \(0.0249142\pi\) | ||||
−0.996938 | + | 0.0781905i | \(0.975086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5624 | + | 19.5624i | −1.10573 | + | 1.10573i | −0.112030 | + | 0.993705i | \(0.535735\pi\) |
−0.993705 | + | 0.112030i | \(0.964265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.99258 | − | 16.1242i | −0.337644 | − | 0.908496i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.66348 | − | 3.66348i | −0.205761 | − | 0.205761i | 0.596702 | − | 0.802463i | \(-0.296478\pi\) |
−0.802463 | + | 0.596702i | \(0.796478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.4974 | −0.811696 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 42.1388 | 2.35196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.951027 | + | 0.951027i | 0.0529165 | + | 0.0529165i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.99925 | − | 0.738635i | −0.554659 | − | 0.0409721i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −34.8925 | + | 34.8925i | −1.92956 | + | 1.92956i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.96136i | − | 0.273528i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8355i | 1.42005i | 0.704178 | + | 0.710024i | \(0.251316\pi\) | ||||
−0.704178 | + | 0.710024i | \(0.748684\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.4677 | − | 31.4677i | 1.72442 | − | 1.72442i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9942 | + | 4.45768i | −0.655316 | + | 0.243549i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8537 | − | 13.8537i | −0.754661 | − | 0.754661i | 0.220684 | − | 0.975345i | \(-0.429171\pi\) |
−0.975345 | + | 0.220684i | \(0.929171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.5808 | 1.38936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.1041 | −1.30531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.8049 | − | 49.7820i | 1.22778 | − | 2.68017i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.81196 | + | 7.81196i | −0.419368 | + | 0.419368i | −0.884986 | − | 0.465618i | \(-0.845832\pi\) |
0.465618 | + | 0.884986i | \(0.345832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0157i | 0.857302i | 0.903470 | + | 0.428651i | \(0.141011\pi\) | ||||
−0.903470 | + | 0.428651i | \(0.858989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 30.7726i | − | 1.64252i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.3102 | + | 15.3102i | −0.814881 | + | 0.814881i | −0.985361 | − | 0.170480i | \(-0.945468\pi\) |
0.170480 | + | 0.985361i | \(0.445468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.683487 | + | 1.49201i | −0.0362757 | + | 0.0791879i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.953677 | − | 0.953677i | −0.0504739 | − | 0.0504739i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.1586 | −1.06393 | −0.531964 | − | 0.846767i | \(-0.678546\pi\) | ||||
−0.531964 | + | 0.846767i | \(0.678546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.36647 | −0.440341 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −60.4987 | − | 60.4987i | −3.17536 | − | 3.17536i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.74051 | + | 3.24842i | −0.457499 | + | 0.170030i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8443 | − | 12.8443i | 0.670466 | − | 0.670466i | −0.287358 | − | 0.957823i | \(-0.592777\pi\) |
0.957823 | + | 0.287358i | \(0.0927769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 54.1516i | 2.81902i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.77528i | − | 0.403672i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4076 | + | 21.4076i | −1.10845 | + | 1.10845i | −0.115090 | + | 0.993355i | \(0.536716\pi\) |
−0.993355 | + | 0.115090i | \(0.963284\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.6335 | + | 32.0261i | −0.910588 | + | 1.65382i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.37200 | + | 3.37200i | 0.173667 | + | 0.173667i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3326 | −1.14715 | −0.573574 | − | 0.819154i | \(-0.694444\pi\) | ||||
−0.573574 | + | 0.819154i | \(0.694444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1135 | 0.518132 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72177 | + | 4.72177i | 0.241271 | + | 0.241271i | 0.817376 | − | 0.576105i | \(-0.195428\pi\) |
−0.576105 | + | 0.817376i | \(0.695428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.74887 | + | 12.7778i | 0.242025 | + | 0.651215i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.0921 | − | 14.0921i | 0.716340 | − | 0.716340i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.78307i | 0.394617i | 0.980341 | + | 0.197309i | \(0.0632201\pi\) | ||||
−0.980341 | + | 0.197309i | \(0.936780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.08870i | − | 0.156202i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.4244 | − | 23.4244i | 1.18160 | − | 1.18160i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.62094 | + | 1.20064i | 0.131874 | + | 0.0604110i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6270 | − | 23.6270i | −1.18581 | − | 1.18581i | −0.978216 | − | 0.207590i | \(-0.933438\pi\) |
−0.207590 | − | 0.978216i | \(-0.566562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6632 | −0.533825 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9410 | 0.696180 | 0.348090 | − | 0.937461i | \(-0.386830\pi\) | ||||
0.348090 | + | 0.937461i | \(0.386830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.60648 | + | 5.60648i | 0.279279 | + | 0.279279i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −55.0951 | − | 25.2389i | −2.73770 | − | 1.25413i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.9368 | + | 24.9368i | −1.23607 | + | 1.23607i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.1994i | − | 1.59216i | −0.605194 | − | 0.796078i | \(-0.706904\pi\) | ||
0.605194 | − | 0.796078i | \(-0.293096\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 41.2340i | − | 2.03392i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.55673 | + | 3.55673i | −0.175015 | + | 0.175015i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.54505 | + | 20.3014i | 0.370372 | + | 0.996558i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −49.7305 | − | 49.7305i | −2.43531 | − | 2.43531i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.5442 | 1.34562 | 0.672810 | − | 0.739815i | \(-0.265087\pi\) | ||||
0.672810 | + | 0.739815i | \(0.265087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1609 | 1.46995 | 0.734977 | − | 0.678092i | \(-0.237193\pi\) | ||||
0.734977 | + | 0.678092i | \(0.237193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.9882 | − | 26.9882i | −1.31221 | − | 1.31221i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.151922 | + | 2.05664i | −0.00736929 | + | 0.0997615i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.19041 | + | 3.19041i | −0.154395 | + | 0.154395i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 39.9752i | 1.93002i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.7177i | 1.91313i | 0.291515 | + | 0.956566i | \(0.405841\pi\) | ||||
−0.291515 | + | 0.956566i | \(0.594159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2101 | − | 26.2101i | 1.25958 | − | 1.25958i | 0.308280 | − | 0.951296i | \(-0.400247\pi\) |
0.951296 | − | 0.308280i | \(-0.0997534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.2990 | − | 6.05754i | 0.781477 | − | 0.290437i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.2675 | − | 17.2675i | −0.826017 | − | 0.826017i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0808 | −1.29249 | −0.646247 | − | 0.763128i | \(-0.723662\pi\) | ||||
−0.646247 | + | 0.763128i | \(0.723662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.69286 | 0.366327 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.742047 | + | 0.742047i | 0.0352557 | + | 0.0352557i | 0.724515 | − | 0.689259i | \(-0.242064\pi\) |
−0.689259 | + | 0.724515i | \(0.742064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.92598 | − | 8.57020i | 0.186109 | − | 0.406267i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.6100 | − | 27.6100i | 1.30591 | − | 1.30591i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7917i | 0.745258i | 0.927980 | + | 0.372629i | \(0.121544\pi\) | ||||
−0.927980 | + | 0.372629i | \(0.878456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 42.9130i | − | 2.02069i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.1046 | − | 26.1046i | 1.22650 | − | 1.22650i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.86748 | − | 4.07660i | 0.0875486 | − | 0.191114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5908 | − | 14.5908i | −0.682527 | − | 0.682527i | 0.278042 | − | 0.960569i | \(-0.410314\pi\) |
−0.960569 | + | 0.278042i | \(0.910314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.32928 | −0.295425 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.77291 | 0.455170 | 0.227585 | − | 0.973758i | \(-0.426917\pi\) | ||||
0.227585 | + | 0.973758i | \(0.426917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.32678 | − | 2.32678i | −0.108135 | − | 0.108135i | 0.650969 | − | 0.759104i | \(-0.274363\pi\) |
−0.759104 | + | 0.650969i | \(0.774363\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.0996 | − | 10.0716i | 1.25671 | − | 0.467059i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7558 | + | 19.7558i | −0.914192 | + | 0.914192i | −0.996599 | − | 0.0824071i | \(-0.973739\pi\) |
0.0824071 | + | 0.996599i | \(0.473739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.72246i | − | 0.264239i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 29.9552i | − | 1.38026i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.1674 | + | 11.1674i | −0.513477 | + | 0.513477i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6484 | + | 12.3471i | 0.488582 | + | 0.566522i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.2950 | − | 42.2950i | −1.93655 | − | 1.93655i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.9223 | 1.68702 | 0.843511 | − | 0.537112i | \(-0.180485\pi\) | ||||
0.843511 | + | 0.537112i | \(0.180485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6003 | 0.528930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.3156 | + | 17.3156i | 0.787888 | + | 0.787888i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.17521 | + | 8.54353i | 0.144179 | + | 0.387942i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1499 | − | 16.1499i | 0.731822 | − | 0.731822i | −0.239159 | − | 0.970980i | \(-0.576872\pi\) |
0.970980 | + | 0.239159i | \(0.0768716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.29321i | − | 0.148924i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.901752i | 0.0406955i | 0.999793 | + | 0.0203477i | \(0.00647734\pi\) | ||||
−0.999793 | + | 0.0203477i | \(0.993523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.693550 | − | 0.693550i | 0.0312359 | − | 0.0312359i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 95.3392 | + | 43.6746i | 4.28518 | + | 1.96303i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.518966 | − | 0.518966i | −0.0232788 | − | 0.0232788i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.1739 | −1.08217 | −0.541085 | − | 0.840968i | \(-0.681986\pi\) | ||||
−0.541085 | + | 0.840968i | \(0.681986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.7343 | −1.46246 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.72002 | − | 5.72002i | −0.255043 | − | 0.255043i | 0.567991 | − | 0.823034i | \(-0.307721\pi\) |
−0.823034 | + | 0.567991i | \(0.807721\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3624 | + | 8.41174i | 0.817115 | + | 0.374318i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.7610 | + | 20.7610i | −0.922030 | + | 0.922030i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 27.3014i | − | 1.21011i | −0.796183 | − | 0.605056i | \(-0.793151\pi\) | ||
0.796183 | − | 0.605056i | \(-0.206849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.17010i | − | 0.184474i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.3841 | + | 35.3841i | −1.56225 | + | 1.56225i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.83875 | − | 7.63821i | −0.125090 | − | 0.336580i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.3870 | + | 21.3870i | 0.940600 | + | 0.940600i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6135 | 0.597567 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5026 | −0.460129 | −0.230065 | − | 0.973175i | \(-0.573894\pi\) | ||||
−0.230065 | + | 0.973175i | \(0.573894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7721 | + | 11.7721i | 0.514757 | + | 0.514757i | 0.915980 | − | 0.401223i | \(-0.131415\pi\) |
−0.401223 | + | 0.915980i | \(0.631415\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.6781 | − | 12.3815i | −0.466029 | − | 0.540371i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15313 | − | 1.15313i | 0.0502313 | − | 0.0502313i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.0806i | 1.43829i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.6949i | 1.67922i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.98131 | + | 9.98131i | −0.432339 | + | 0.432339i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.0101 | − | 10.0383i | 1.16775 | − | 0.433994i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.4276 | − | 31.4276i | −1.35620 | − | 1.35620i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.09628 | −0.262585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3649 | −1.00453 | −0.502267 | − | 0.864712i | \(-0.667501\pi\) | ||||
−0.502267 | + | 0.864712i | \(0.667501\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.5007 | − | 32.5007i | −1.39474 | − | 1.39474i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0532 | + | 30.6774i | −0.601974 | + | 1.31408i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.8564 | + | 25.8564i | −1.10554 | + | 1.10554i | −0.111808 | + | 0.993730i | \(0.535664\pi\) |
−0.993730 | + | 0.111808i | \(0.964336\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.7096i | 1.48137i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.75466i | − | 0.330359i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.911640 | + | 0.911640i | −0.0387669 | + | 0.0387669i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.6163 | − | 38.4554i | 0.747769 | − | 1.63234i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.7534 | + | 30.7534i | 1.30307 | + | 1.30307i | 0.926315 | + | 0.376750i | \(0.122959\pi\) |
0.376750 | + | 0.926315i | \(0.377041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.19494 | 0.219723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.22206 | 0.347136 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.2257 | − | 17.2257i | −0.725978 | − | 0.725978i | 0.243838 | − | 0.969816i | \(-0.421594\pi\) |
−0.969816 | + | 0.243838i | \(0.921594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.3967 | − | 6.09386i | 0.689815 | − | 0.256371i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.1637 | − | 19.1637i | 0.804800 | − | 0.804800i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.71562i | − | 0.323455i | −0.986835 | − | 0.161728i | \(-0.948293\pi\) | ||
0.986835 | − | 0.161728i | \(-0.0517066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.7991i | − | 1.45630i | −0.685419 | − | 0.728149i | \(-0.740381\pi\) | ||
0.685419 | − | 0.728149i | \(-0.259619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.78343 | − | 4.78343i | 0.199831 | − | 0.199831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.75840 | − | 37.3417i | 0.115033 | − | 1.55726i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.91727 | − | 9.91727i | −0.412861 | − | 0.412861i | 0.469873 | − | 0.882734i | \(-0.344300\pi\) |
−0.882734 | + | 0.469873i | \(0.844300\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54.9657 | 2.28430 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.68582 | −0.401836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.5170 | + | 33.5170i | 1.38813 | + | 1.38813i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0169 | − | 32.3338i | −0.496838 | − | 1.33684i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.719263 | + | 0.719263i | −0.0296872 | + | 0.0296872i | −0.721795 | − | 0.692107i | \(-0.756682\pi\) |
0.692107 | + | 0.721795i | \(0.256682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.8933i | − | 0.531260i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 89.3760i | 3.67644i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.54021 | − | 7.54021i | 0.309639 | − | 0.309639i | −0.535130 | − | 0.844770i | \(-0.679737\pi\) |
0.844770 | + | 0.535130i | \(0.179737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.838471 | − | 0.384101i | −0.0343739 | − | 0.0157466i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.2432 | + | 11.2432i | 0.460152 | + | 0.460152i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.70994 | −0.233302 | −0.116651 | − | 0.993173i | \(-0.537216\pi\) | ||||
−0.116651 | + | 0.993173i | \(0.537216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.67836 | 0.231625 | 0.115813 | − | 0.993271i | \(-0.463053\pi\) | ||||
0.115813 | + | 0.993271i | \(0.463053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.1283 | − | 31.1283i | −1.26764 | − | 1.26764i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −53.1904 | − | 24.3663i | −2.16250 | − | 0.990632i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5239 | − | 21.5239i | 0.873627 | − | 0.873627i | −0.119239 | − | 0.992866i | \(-0.538045\pi\) |
0.992866 | + | 0.119239i | \(0.0380455\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.77626i | 0.315110i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.94900i | − | 0.402493i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.14168 | + | 4.14168i | −0.167281 | + | 0.167281i | −0.785783 | − | 0.618502i | \(-0.787740\pi\) |
0.618502 | + | 0.785783i | \(0.287740\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.9307 | + | 48.2459i | 0.723034 | + | 1.94546i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9214 | − | 15.9214i | −0.640973 | − | 0.640973i | 0.309822 | − | 0.950795i | \(-0.399731\pi\) |
−0.950795 | + | 0.309822i | \(0.899731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.5060 | −0.784011 | −0.392006 | − | 0.919963i | \(-0.628219\pi\) | ||||
−0.392006 | + | 0.919963i | \(0.628219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 114.919 | 4.61153 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.98097 | + | 2.98097i | 0.119430 | + | 0.119430i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.67341 | + | 24.7286i | −0.146936 | + | 0.989146i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.9659 | − | 45.9659i | 1.83570 | − | 1.83570i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.38594i | − | 0.0951338i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.3766i | 1.24908i | 0.780991 | + | 0.624542i | \(0.214714\pi\) | ||||
−0.780991 | + | 0.624542i | \(0.785286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.2966 | + | 21.2966i | −0.846464 | + | 0.846464i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.48255 | − | 2.40925i | 0.257252 | − | 0.0956080i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.41796 | + | 1.41796i | 0.0561816 | + | 0.0561816i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.64602 | −0.223353 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.8373 | 0.783525 | 0.391762 | − | 0.920066i | \(-0.371865\pi\) | ||||
0.391762 | + | 0.920066i | \(0.371865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4092 | + | 18.4092i | 0.725988 | + | 0.725988i | 0.969818 | − | 0.243830i | \(-0.0784038\pi\) |
−0.243830 | + | 0.969818i | \(0.578404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.88905 | − | 17.2214i | 0.310631 | − | 0.678090i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9741 | − | 12.9741i | 0.510065 | − | 0.510065i | −0.404481 | − | 0.914546i | \(-0.632548\pi\) |
0.914546 | + | 0.404481i | \(0.132548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.6641i | − | 1.20367i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9292i | 0.506737i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.9963 | − | 13.9963i | 0.547717 | − | 0.547717i | −0.378063 | − | 0.925780i | \(-0.623410\pi\) |
0.925780 | + | 0.378063i | \(0.123410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.43435 | − | 20.5947i | 0.368630 | − | 0.804700i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.6840 | − | 22.6840i | −0.884987 | − | 0.884987i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.44981 | −0.368112 | −0.184056 | − | 0.982916i | \(-0.558923\pi\) | ||||
−0.184056 | + | 0.982916i | \(0.558923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.58645 | 0.333974 | 0.166987 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166987 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.91241 | − | 1.91241i | −0.0742717 | − | 0.0742717i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.83485 | + | 2.54018i | −0.265044 | + | 0.0985039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.5926 | + | 12.5926i | −0.487587 | + | 0.487587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.94158i | 0.345702i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 27.5059i | − | 1.06186i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.63136 | − | 2.63136i | 0.101432 | − | 0.101432i | −0.654570 | − | 0.756001i | \(-0.727150\pi\) |
0.756001 | + | 0.654570i | \(0.227150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −76.5197 | − | 5.65244i | −2.94524 | − | 0.217562i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.8779 | + | 33.8779i | 1.30203 | + | 1.30203i | 0.927020 | + | 0.375012i | \(0.122361\pi\) |
0.375012 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.07612 | −0.156427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.5050 | −1.39888 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.6544 | − | 21.6544i | −0.828582 | − | 0.828582i | 0.158738 | − | 0.987321i | \(-0.449257\pi\) |
−0.987321 | + | 0.158738i | \(0.949257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.82278 | − | 26.4301i | −0.375309 | − | 1.00984i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.9407 | + | 41.9407i | −1.60014 | + | 1.60014i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.5918i | − | 0.593999i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.95056i | 0.112245i | 0.998424 | + | 0.0561224i | \(0.0178737\pi\) | ||||
−0.998424 | + | 0.0561224i | \(0.982126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −33.1618 | + | 33.1618i | −1.25971 | + | 1.25971i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.7229 | − | 20.0293i | −1.65851 | − | 0.759756i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05295 | + | 2.05295i | 0.0777609 | + | 0.0777609i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.2263 | 2.01321 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0970 | 1.36336 | 0.681682 | − | 0.731649i | \(-0.261249\pi\) | ||||
0.681682 | + | 0.731649i | \(0.261249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3387 | − | 13.3387i | −0.503080 | − | 0.503080i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.9812 | − | 15.1086i | −1.24214 | − | 0.569021i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.38697 | + | 6.38697i | −0.240207 | + | 0.240207i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.6727i | − | 1.30216i | −0.759008 | − | 0.651081i | \(-0.774316\pi\) | ||
0.759008 | − | 0.651081i | \(-0.225684\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.91805i | 0.371956i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.9371 | + | 20.9371i | −0.784102 | + | 0.784102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.52291 | + | 25.6232i | 0.356137 | + | 0.958255i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5252 | − | 15.5252i | −0.579798 | − | 0.579798i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.21998 | −0.269260 | −0.134630 | − | 0.990896i | \(-0.542985\pi\) | ||||
−0.134630 | + | 0.990896i | \(0.542985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.64419 | 0.135717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.6462 | − | 22.6462i | −0.842221 | − | 0.842221i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00427 | − | 7.76550i | 0.334410 | − | 0.288404i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.0772 | + | 25.0772i | −0.930061 | + | 0.930061i | −0.997709 | − | 0.0676479i | \(-0.978451\pi\) |
0.0676479 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 57.9482i | − | 2.14623i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.06849i | − | 0.0395196i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.7234 | − | 16.7234i | 0.617692 | − | 0.617692i | −0.327247 | − | 0.944939i | \(-0.606121\pi\) |
0.944939 | + | 0.327247i | \(0.106121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.85389 | − | 2.54726i | 0.252810 | − | 0.0939570i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.6679 | + | 24.6679i | 0.908655 | + | 0.908655i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.4665 | −0.679300 | −0.339650 | − | 0.940552i | \(-0.610309\pi\) | ||||
−0.339650 | + | 0.940552i | \(0.610309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3828 | −0.785517 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.9865 | + | 10.9865i | 0.403054 | + | 0.403054i | 0.879308 | − | 0.476254i | \(-0.158006\pi\) |
−0.476254 | + | 0.879308i | \(0.658006\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1201 | − | 24.2746i | 0.407410 | − | 0.889353i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.6877 | + | 52.6877i | −1.92774 | + | 1.92774i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.8865i | 0.470863i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.02969i | − | 0.110555i | −0.998471 | − | 0.0552775i | \(-0.982396\pi\) | ||
0.998471 | − | 0.0552775i | \(-0.0176044\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.8712 | + | 61.8712i | −2.25471 | + | 2.25471i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5138 | − | 22.9511i | 0.382637 | − | 0.835276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.4638 | + | 21.4638i | 0.780114 | + | 0.780114i | 0.979850 | − | 0.199736i | \(-0.0640085\pi\) |
−0.199736 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −149.286 | −5.41872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.4590 | 0.596640 | 0.298320 | − | 0.954466i | \(-0.403574\pi\) | ||||
0.298320 | + | 0.954466i | \(0.403574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6705 | − | 10.6705i | −0.386299 | − | 0.386299i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.65039 | + | 2.47163i | −0.240445 | + | 0.0893618i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.13231 | + | 7.13231i | −0.257533 | + | 0.257533i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.4933i | 1.49629i | 0.663537 | + | 0.748143i | \(0.269054\pi\) | ||||
−0.663537 | + | 0.748143i | \(0.730946\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 35.4805i | − | 1.27780i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.2071 | + | 10.2071i | −0.367125 | + | 0.367125i | −0.866428 | − | 0.499303i | \(-0.833590\pi\) |
0.499303 | + | 0.866428i | \(0.333590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.9710 | − | 12.9114i | 0.537774 | − | 0.463789i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.3759 | + | 13.3759i | 0.479858 | + | 0.479858i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.9542 | 0.822420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.47424 | 0.160101 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.8044 | + | 25.8044i | 0.922174 | + | 0.922174i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.13595 | − | 19.2007i | −0.254693 | − | 0.685301i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4080 | − | 25.4080i | 0.905697 | − | 0.905697i | −0.0902245 | − | 0.995921i | \(-0.528758\pi\) |
0.995921 | + | 0.0902245i | \(0.0287585\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 77.6537i | 2.76454i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.82289i | 0.278150i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.39773 | + | 6.39773i | −0.227190 | + | 0.227190i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −51.6871 | − | 23.6777i | −1.83315 | − | 0.839760i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.41505 | + | 1.41505i | 0.0501236 | + | 0.0501236i | 0.731724 | − | 0.681601i | \(-0.238716\pi\) |
−0.681601 | + | 0.731724i | \(0.738716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.04630 | −0.0723929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.4310 | 1.14589 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.9761 | + | 17.9761i | 0.634364 | + | 0.634364i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2239 | + | 6.97400i | 0.536571 | + | 0.245801i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 49.8153 | − | 49.8153i | 1.75358 | − | 1.75358i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 29.5078i | − | 1.03744i | −0.854945 | − | 0.518719i | \(-0.826409\pi\) | ||
0.854945 | − | 0.518719i | \(-0.173591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.08089i | 0.0730699i | 0.999332 | + | 0.0365350i | \(0.0116320\pi\) | ||||
−0.999332 | + | 0.0365350i | \(0.988368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.7601 | − | 51.7601i | 1.81530 | − | 1.81530i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.784510 | − | 2.11088i | −0.0274802 | − | 0.0739408i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.97345 | − | 5.97345i | −0.208985 | − | 0.208985i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.4265 | 0.539045 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.51361 | 0.157526 | 0.0787631 | − | 0.996893i | \(-0.474903\pi\) | ||||
0.0787631 | + | 0.996893i | \(0.474903\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.8753 | + | 19.8753i | 0.692811 | + | 0.692811i | 0.962850 | − | 0.270038i | \(-0.0870364\pi\) |
−0.270038 | + | 0.962850i | \(0.587036\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 99.4031 | + | 7.34282i | 3.46077 | + | 0.255644i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.6393 | − | 17.6393i | 0.613377 | − | 0.613377i | −0.330447 | − | 0.943824i | \(-0.607200\pi\) |
0.943824 | + | 0.330447i | \(0.107200\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.8366i | 1.38358i | 0.722097 | + | 0.691791i | \(0.243178\pi\) | ||||
−0.722097 | + | 0.691791i | \(0.756822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6234i | 1.02763i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.291645 | − | 0.291645i | 0.0101049 | − | 0.0101049i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.9820 | + | 7.79797i | −0.726110 | + | 0.269860i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.9038 | + | 42.9038i | 1.48297 | + | 1.48297i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.58183 | −0.330802 | −0.165401 | − | 0.986226i | \(-0.552892\pi\) | ||||
−0.165401 | + | 0.986226i | \(0.552892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3448 | 0.804993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.7776 | + | 55.7776i | 1.92108 | + | 1.92108i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.36167 | + | 18.2531i | −0.287650 | + | 0.627925i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.5012 | − | 18.5012i | 0.635708 | − | 0.635708i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.7685i | 1.70805i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.3209i | 1.48502i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7835 | − | 27.7835i | 0.951290 | − | 0.951290i | −0.0475780 | − | 0.998868i | \(-0.515150\pi\) |
0.998868 | + | 0.0475780i | \(0.0151503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.3616 | + | 50.9971i | −0.798950 | + | 1.74406i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.8089 | − | 10.8089i | −0.369224 | − | 0.369224i | 0.497970 | − | 0.867194i | \(-0.334079\pi\) |
−0.867194 | + | 0.497970i | \(0.834079\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.0374 | 1.53666 | 0.768328 | − | 0.640057i | \(-0.221089\pi\) | ||||
0.768328 | + | 0.640057i | \(0.221089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.0182 | −0.784457 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.21367 | + | 6.21367i | 0.211516 | + | 0.211516i | 0.804911 | − | 0.593395i | \(-0.202213\pi\) |
−0.593395 | + | 0.804911i | \(0.702213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.72596 | − | 3.24301i | 0.296691 | − | 0.110266i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.9147 | − | 38.9147i | 1.32161 | − | 1.32161i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.85965i | − | 0.266620i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11.4752i | − | 0.388824i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.1728 | + | 22.1728i | −0.750435 | + | 0.750435i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.79392 | − | 5.39251i | −0.331095 | − | 0.182300i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5695 | − | 25.5695i | −0.863419 | − | 0.863419i | 0.128315 | − | 0.991734i | \(-0.459043\pi\) |
−0.991734 | + | 0.128315i | \(0.959043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.5719 | −1.67202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3716 | 0.551572 | 0.275786 | − | 0.961219i | \(-0.411062\pi\) | ||||
0.275786 | + | 0.961219i | \(0.411062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.1512 | − | 28.1512i | −0.947365 | − | 0.947365i | 0.0513175 | − | 0.998682i | \(-0.483658\pi\) |
−0.998682 | + | 0.0513175i | \(0.983658\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.8126 | + | 34.4749i | 0.430692 | + | 1.15886i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5121 | − | 20.5121i | 0.688730 | − | 0.688730i | −0.273221 | − | 0.961951i | \(-0.588089\pi\) |
0.961951 | + | 0.273221i | \(0.0880891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.09283i | 0.103730i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 165.219i | 5.53503i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.4399 | + | 11.4399i | −0.382823 | + | 0.382823i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.6311 | − | 12.6577i | −0.923607 | − | 0.423101i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.7230 | + | 34.7230i | 1.15937 | + | 1.15937i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.40264 | −0.313596 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.20690 | −0.106837 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.99009 | + | 5.99009i | 0.199338 | + | 0.199338i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.5746 | − | 13.0899i | −0.949851 | − | 0.435124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.17842 | + | 7.17842i | −0.238356 | + | 0.238356i | −0.816169 | − | 0.577813i | \(-0.803906\pi\) |
0.577813 | + | 0.816169i | \(0.303906\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 69.4861i | 2.30471i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.6686i | − | 1.21488i | −0.794364 | − | 0.607442i | \(-0.792196\pi\) | ||
0.794364 | − | 0.607442i | \(-0.207804\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.7529 | − | 41.7529i | 1.38182 | − | 1.38182i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4930 | + | 30.9242i | 0.379948 | + | 1.02232i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.16343 | + | 7.16343i | 0.236557 | + | 0.236557i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.9984 | 1.91319 | 0.956595 | − | 0.291420i | \(-0.0941278\pi\) | ||||
0.956595 | + | 0.291420i | \(0.0941278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.8485 | −1.80732 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.04068 | − | 1.04068i | −0.0342545 | − | 0.0342545i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.13080 | − | 28.8456i | 0.0700602 | − | 0.948438i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.8232 | − | 19.8232i | 0.651080 | − | 0.651080i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 18.4743i | − | 0.606122i | −0.952971 | − | 0.303061i | \(-0.901991\pi\) | ||
0.952971 | − | 0.303061i | \(-0.0980086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.26091i | − | 0.106872i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.37670 | + | 6.37670i | −0.208764 | + | 0.208764i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.27016 | − | 1.95866i | 0.172353 | − | 0.0640551i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7475 | + | 10.7475i | 0.351107 | + | 0.351107i | 0.860521 | − | 0.509415i | \(-0.170138\pi\) |
−0.509415 | + | 0.860521i | \(0.670138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −90.4659 | −2.95224 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.6701 | −1.13021 | −0.565106 | − | 0.825018i | \(-0.691165\pi\) | ||||
−0.565106 | + | 0.825018i | \(0.691165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.2748 | − | 37.2748i | −1.21383 | − | 1.21383i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.2909 | − | 31.1963i | 0.464884 | − | 1.01482i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.8525 | − | 24.8525i | 0.807598 | − | 0.807598i | −0.176672 | − | 0.984270i | \(-0.556533\pi\) |
0.984270 | + | 0.176672i | \(0.0565331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.36230i | − | 0.271452i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 16.9416i | − | 0.549370i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.0869 | + | 29.0869i | −0.942218 | + | 0.942218i | −0.998419 | − | 0.0562014i | \(-0.982101\pi\) |
0.0562014 | + | 0.998419i | \(0.482101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.92656 | − | 4.20558i | 0.0623421 | − | 0.136089i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −33.5213 | − | 33.5213i | −1.08359 | − | 1.08359i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6098 | 0.407192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3667 | 0.495698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 70.0984 | + | 70.0984i | 2.25889 | + | 2.25889i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.2318 | − | 13.0939i | 1.13415 | − | 0.421509i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9518 | − | 40.9518i | 1.31692 | − | 1.31692i | 0.400718 | − | 0.916201i | \(-0.368761\pi\) |
0.916201 | − | 0.400718i | \(-0.131239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.39800i | 0.141284i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.8745i | 1.24754i | 0.781608 | + | 0.623770i | \(0.214400\pi\) | ||||
−0.781608 | + | 0.623770i | \(0.785600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.2081 | − | 15.2081i | 0.487550 | − | 0.487550i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.4127 | − | 24.8285i | −0.685756 | − | 0.795149i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.22366 | + | 2.22366i | 0.0711412 | + | 0.0711412i | 0.741782 | − | 0.670641i | \(-0.233981\pi\) |
−0.670641 | + | 0.741782i | \(0.733981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.7002 | −0.821383 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −116.088 | −3.70641 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.13209 | − | 8.13209i | −0.259373 | − | 0.259373i | 0.565426 | − | 0.824799i | \(-0.308712\pi\) |
−0.824799 | + | 0.565426i | \(0.808712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.2912 | + | 57.2880i | 0.678393 | + | 1.82535i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.4718 | − | 11.4718i | 0.365152 | − | 0.365152i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.4003i | 0.616893i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7134i | 0.530917i | 0.964122 | + | 0.265459i | \(0.0855234\pi\) | ||||
−0.964122 | + | 0.265459i | \(0.914477\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.7378 | + | 59.7378i | −1.89572 | + | 1.89572i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.88498 | + | 4.52827i | 0.313375 | + | 0.143556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.52263 | + | 7.52263i | 0.238244 | + | 0.238244i | 0.816123 | − | 0.577879i | \(-0.196119\pi\) |
−0.577879 | + | 0.816123i | \(0.696119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 88.7721 | 2.80862 |
(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 | 560.2.x.b.127.12 | yes | 24 | |
4.3 | odd | 2 | inner | 560.2.x.b.127.1 | ✓ | 24 | |
5.3 | odd | 4 | inner | 560.2.x.b.463.1 | yes | 24 | |
20.3 | even | 4 | inner | 560.2.x.b.463.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.x.b.127.1 | ✓ | 24 | 4.3 | odd | 2 | inner | |
560.2.x.b.127.12 | yes | 24 | 1.1 | even | 1 | trivial | |
560.2.x.b.463.1 | yes | 24 | 5.3 | odd | 4 | inner | |
560.2.x.b.463.12 | yes | 24 | 20.3 | even | 4 | inner |