Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6561,2,Mod(1,6561)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6561, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6561.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6561 = 3^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6561.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: | \(52.3898487662\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | no (minimal twist has level 81) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6561.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11413 | −1.49491 | −0.747456 | − | 0.664311i | \(-0.768725\pi\) | ||||
−0.747456 | + | 0.664311i | \(0.768725\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.46953 | 1.23476 | ||||||||
\(5\) | −2.98999 | −1.33716 | −0.668582 | − | 0.743638i | \(-0.733099\pi\) | ||||
−0.668582 | + | 0.743638i | \(0.733099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.51273 | −1.32769 | −0.663843 | − | 0.747872i | \(-0.731076\pi\) | ||||
−0.663843 | + | 0.747872i | \(0.731076\pi\) | |||||||
\(8\) | −0.992637 | −0.350950 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.32121 | 1.99894 | ||||||||
\(11\) | 1.96066 | 0.591162 | 0.295581 | − | 0.955318i | \(-0.404487\pi\) | ||||
0.295581 | + | 0.955318i | \(0.404487\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.66702 | 0.462349 | 0.231175 | − | 0.972912i | \(-0.425743\pi\) | ||||
0.231175 | + | 0.972912i | \(0.425743\pi\) | |||||||
\(14\) | 7.42634 | 1.98477 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.84049 | −0.710123 | ||||||||
\(17\) | 3.89091 | 0.943683 | 0.471842 | − | 0.881683i | \(-0.343589\pi\) | ||||
0.471842 | + | 0.881683i | \(0.343589\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0165720 | 0.00380187 | 0.00190094 | − | 0.999998i | \(-0.499395\pi\) | ||||
0.00190094 | + | 0.999998i | \(0.499395\pi\) | |||||||
\(20\) | −7.38386 | −1.65108 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.14509 | −0.883735 | ||||||||
\(23\) | 7.72480 | 1.61073 | 0.805366 | − | 0.592778i | \(-0.201969\pi\) | ||||
0.805366 | + | 0.592778i | \(0.201969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.94004 | 0.788009 | ||||||||
\(26\) | −3.52430 | −0.691171 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.67477 | −1.63938 | ||||||||
\(29\) | −4.62155 | −0.858200 | −0.429100 | − | 0.903257i | \(-0.641169\pi\) | ||||
−0.429100 | + | 0.903257i | \(0.641169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2650 | −1.84365 | −0.921826 | − | 0.387604i | \(-0.873303\pi\) | ||||
−0.921826 | + | 0.387604i | \(0.873303\pi\) | |||||||
\(32\) | 7.99043 | 1.41252 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.22586 | −1.41072 | ||||||||
\(35\) | 10.5030 | 1.77533 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.15788 | 1.17675 | 0.588374 | − | 0.808589i | \(-0.299768\pi\) | ||||
0.588374 | + | 0.808589i | \(0.299768\pi\) | |||||||
\(38\) | −0.0350352 | −0.00568346 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.96798 | 0.469278 | ||||||||
\(41\) | 5.65673 | 0.883433 | 0.441716 | − | 0.897155i | \(-0.354370\pi\) | ||||
0.441716 | + | 0.897155i | \(0.354370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.56357 | −0.695938 | −0.347969 | − | 0.937506i | \(-0.613129\pi\) | ||||
−0.347969 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(44\) | 4.84191 | 0.729945 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.3312 | −2.40790 | ||||||||
\(47\) | 2.87659 | 0.419594 | 0.209797 | − | 0.977745i | \(-0.432720\pi\) | ||||
0.209797 | + | 0.977745i | \(0.432720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.33925 | 0.762750 | ||||||||
\(50\) | −8.32975 | −1.17800 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.11676 | 0.570892 | ||||||||
\(53\) | −2.80825 | −0.385743 | −0.192872 | − | 0.981224i | \(-0.561780\pi\) | ||||
−0.192872 | + | 0.981224i | \(0.561780\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.86236 | −0.790481 | ||||||||
\(56\) | 3.48686 | 0.465952 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.77053 | 1.28293 | ||||||||
\(59\) | 4.95688 | 0.645331 | 0.322666 | − | 0.946513i | \(-0.395421\pi\) | ||||
0.322666 | + | 0.946513i | \(0.395421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.38279 | 1.20134 | 0.600672 | − | 0.799496i | \(-0.294900\pi\) | ||||
0.600672 | + | 0.799496i | \(0.294900\pi\) | |||||||
\(62\) | 21.7015 | 2.75610 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.2118 | −1.40147 | ||||||||
\(65\) | −4.98438 | −0.618237 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48321 | −0.547711 | −0.273856 | − | 0.961771i | \(-0.588299\pi\) | ||||
−0.273856 | + | 0.961771i | \(0.588299\pi\) | |||||||
\(68\) | 9.60870 | 1.16523 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −22.2047 | −2.65397 | ||||||||
\(71\) | 7.70195 | 0.914053 | 0.457026 | − | 0.889453i | \(-0.348914\pi\) | ||||
0.457026 | + | 0.889453i | \(0.348914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00919 | −0.469240 | −0.234620 | − | 0.972087i | \(-0.575385\pi\) | ||||
−0.234620 | + | 0.972087i | \(0.575385\pi\) | |||||||
\(74\) | −15.1327 | −1.75914 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0409249 | 0.00469441 | ||||||||
\(77\) | −6.88727 | −0.784877 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.15157 | 0.917123 | 0.458562 | − | 0.888663i | \(-0.348365\pi\) | ||||
0.458562 | + | 0.888663i | \(0.348365\pi\) | |||||||
\(80\) | 8.49305 | 0.949552 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.9590 | −1.32065 | ||||||||
\(83\) | −5.15607 | −0.565953 | −0.282976 | − | 0.959127i | \(-0.591322\pi\) | ||||
−0.282976 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6338 | −1.26186 | ||||||||
\(86\) | 9.64796 | 1.04037 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.94623 | −0.207468 | ||||||||
\(89\) | −4.77831 | −0.506500 | −0.253250 | − | 0.967401i | \(-0.581500\pi\) | ||||
−0.253250 | + | 0.967401i | \(0.581500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.85580 | −0.613854 | ||||||||
\(92\) | 19.0766 | 1.98887 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.08148 | −0.627257 | ||||||||
\(95\) | −0.0495500 | −0.00508373 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6308 | −1.18093 | −0.590463 | − | 0.807065i | \(-0.701055\pi\) | ||||
−0.590463 | + | 0.807065i | \(0.701055\pi\) | |||||||
\(98\) | −11.2878 | −1.14024 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.73004 | 0.973004 | ||||||||
\(101\) | −2.85928 | −0.284509 | −0.142254 | − | 0.989830i | \(-0.545435\pi\) | ||||
−0.142254 | + | 0.989830i | \(0.545435\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.86090 | −0.281893 | −0.140947 | − | 0.990017i | \(-0.545015\pi\) | ||||
−0.140947 | + | 0.990017i | \(0.545015\pi\) | |||||||
\(104\) | −1.65475 | −0.162261 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.93700 | 0.576652 | ||||||||
\(107\) | −15.7860 | −1.52609 | −0.763045 | − | 0.646345i | \(-0.776297\pi\) | ||||
−0.763045 | + | 0.646345i | \(0.776297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.290786 | −0.0278522 | −0.0139261 | − | 0.999903i | \(-0.504433\pi\) | ||||
−0.0139261 | + | 0.999903i | \(0.504433\pi\) | |||||||
\(110\) | 12.3938 | 1.18170 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.97788 | 0.942821 | ||||||||
\(113\) | 3.23362 | 0.304193 | 0.152097 | − | 0.988366i | \(-0.451397\pi\) | ||||
0.152097 | + | 0.988366i | \(0.451397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.0971 | −2.15381 | ||||||||
\(116\) | −11.4130 | −1.05967 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.4795 | −0.964714 | ||||||||
\(119\) | −13.6677 | −1.25292 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.15580 | −0.650528 | ||||||||
\(122\) | −19.8364 | −1.79590 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −25.3497 | −2.27647 | ||||||||
\(125\) | 3.16926 | 0.283467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1293 | 1.16503 | 0.582517 | − | 0.812818i | \(-0.302068\pi\) | ||||
0.582517 | + | 0.812818i | \(0.302068\pi\) | |||||||
\(128\) | 7.72227 | 0.682558 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.5376 | 0.924210 | ||||||||
\(131\) | 0.000322743 0 | 2.81982e−5 0 | 1.40991e−5 | − | 1.00000i | \(-0.499996\pi\) | ||||
1.40991e−5 | 1.00000i | \(0.499996\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0582128 | −0.00504769 | ||||||||
\(134\) | 9.47807 | 0.818781 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.86226 | −0.331186 | ||||||||
\(137\) | −12.8945 | −1.10165 | −0.550825 | − | 0.834620i | \(-0.685687\pi\) | ||||
−0.550825 | + | 0.834620i | \(0.685687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.641356 | 0.0543991 | 0.0271996 | − | 0.999630i | \(-0.491341\pi\) | ||||
0.0271996 | + | 0.999630i | \(0.491341\pi\) | |||||||
\(140\) | 25.9375 | 2.19212 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.2829 | −1.36643 | ||||||||
\(143\) | 3.26847 | 0.273323 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8184 | 1.14755 | ||||||||
\(146\) | 8.47593 | 0.701473 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.6766 | 1.45301 | ||||||||
\(149\) | −12.9227 | −1.05867 | −0.529336 | − | 0.848412i | \(-0.677559\pi\) | ||||
−0.529336 | + | 0.848412i | \(0.677559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7832 | −1.36579 | −0.682897 | − | 0.730514i | \(-0.739280\pi\) | ||||
−0.682897 | + | 0.730514i | \(0.739280\pi\) | |||||||
\(152\) | −0.0164500 | −0.00133427 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.5606 | 1.17332 | ||||||||
\(155\) | 30.6923 | 2.46527 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.60099 | −0.686434 | −0.343217 | − | 0.939256i | \(-0.611517\pi\) | ||||
−0.343217 | + | 0.939256i | \(0.611517\pi\) | |||||||
\(158\) | −17.2334 | −1.37102 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23.8913 | −1.88877 | ||||||||
\(161\) | −27.1351 | −2.13855 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.674482 | 0.0528295 | 0.0264148 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264148 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(164\) | 13.9694 | 1.09083 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9006 | 0.846050 | ||||||||
\(167\) | 16.1197 | 1.24738 | 0.623690 | − | 0.781672i | \(-0.285633\pi\) | ||||
0.623690 | + | 0.781672i | \(0.285633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.2210 | −0.786233 | ||||||||
\(170\) | 24.5953 | 1.88637 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.2699 | −0.859318 | ||||||||
\(173\) | −16.1302 | −1.22635 | −0.613177 | − | 0.789946i | \(-0.710109\pi\) | ||||
−0.613177 | + | 0.789946i | \(0.710109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8403 | −1.04623 | ||||||||
\(176\) | −5.56925 | −0.419798 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.1020 | 0.757173 | ||||||||
\(179\) | 7.93866 | 0.593363 | 0.296682 | − | 0.954976i | \(-0.404120\pi\) | ||||
0.296682 | + | 0.954976i | \(0.404120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8345 | −1.02831 | −0.514153 | − | 0.857698i | \(-0.671894\pi\) | ||||
−0.514153 | + | 0.857698i | \(0.671894\pi\) | |||||||
\(182\) | 12.3799 | 0.917658 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.66792 | −0.565287 | ||||||||
\(185\) | −21.4020 | −1.57351 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.62875 | 0.557870 | ||||||||
\(188\) | 7.10382 | 0.518100 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.104755 | 0.00759972 | ||||||||
\(191\) | 14.3742 | 1.04008 | 0.520042 | − | 0.854141i | \(-0.325916\pi\) | ||||
0.520042 | + | 0.854141i | \(0.325916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.18390 | −0.301163 | −0.150582 | − | 0.988598i | \(-0.548115\pi\) | ||||
−0.150582 | + | 0.988598i | \(0.548115\pi\) | |||||||
\(194\) | 24.5889 | 1.76538 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1854 | 0.941815 | ||||||||
\(197\) | 0.236490 | 0.0168492 | 0.00842461 | − | 0.999965i | \(-0.497318\pi\) | ||||
0.00842461 | + | 0.999965i | \(0.497318\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0899 | 1.84946 | 0.924731 | − | 0.380622i | \(-0.124290\pi\) | ||||
0.924731 | + | 0.380622i | \(0.124290\pi\) | |||||||
\(200\) | −3.91103 | −0.276552 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.04487 | 0.425316 | ||||||||
\(203\) | 16.2342 | 1.13942 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.9136 | −1.18130 | ||||||||
\(206\) | 6.04831 | 0.421406 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.73517 | −0.328325 | ||||||||
\(209\) | 0.0324920 | 0.00224752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7991 | −0.812285 | −0.406143 | − | 0.913810i | \(-0.633126\pi\) | ||||
−0.406143 | + | 0.913810i | \(0.633126\pi\) | |||||||
\(212\) | −6.93505 | −0.476301 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 33.3736 | 2.28137 | ||||||||
\(215\) | 13.6450 | 0.930583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.0582 | 2.44779 | ||||||||
\(218\) | 0.614757 | 0.0416366 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.4773 | −0.976056 | ||||||||
\(221\) | 6.48623 | 0.436311 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.3361 | −1.76359 | −0.881797 | − | 0.471630i | \(-0.843666\pi\) | ||||
−0.881797 | + | 0.471630i | \(0.843666\pi\) | |||||||
\(224\) | −28.0682 | −1.87539 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.83628 | −0.454742 | ||||||||
\(227\) | 1.01951 | 0.0676673 | 0.0338337 | − | 0.999427i | \(-0.489228\pi\) | ||||
0.0338337 | + | 0.999427i | \(0.489228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0815 | 1.72352 | 0.861758 | − | 0.507320i | \(-0.169364\pi\) | ||||
0.861758 | + | 0.507320i | \(0.169364\pi\) | |||||||
\(230\) | 48.8301 | 3.21976 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.58752 | 0.301185 | ||||||||
\(233\) | −4.48925 | −0.294101 | −0.147050 | − | 0.989129i | \(-0.546978\pi\) | ||||
−0.147050 | + | 0.989129i | \(0.546978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.60099 | −0.561067 | ||||||||
\(236\) | 12.2412 | 0.796831 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.8952 | 1.87300 | ||||||||
\(239\) | 1.52499 | 0.0986431 | 0.0493216 | − | 0.998783i | \(-0.484294\pi\) | ||||
0.0493216 | + | 0.998783i | \(0.484294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.842169 | 0.0542488 | 0.0271244 | − | 0.999632i | \(-0.491365\pi\) | ||||
0.0271244 | + | 0.999632i | \(0.491365\pi\) | |||||||
\(242\) | 15.1283 | 0.972482 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.1711 | 1.48337 | ||||||||
\(245\) | −15.9643 | −1.01992 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0276259 | 0.00175779 | ||||||||
\(248\) | 10.1894 | 0.647030 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.70022 | −0.423759 | ||||||||
\(251\) | −14.9225 | −0.941899 | −0.470950 | − | 0.882160i | \(-0.656089\pi\) | ||||
−0.470950 | + | 0.882160i | \(0.656089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.1457 | 0.952203 | ||||||||
\(254\) | −27.7569 | −1.74162 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.09774 | 0.381109 | ||||||||
\(257\) | 9.22403 | 0.575379 | 0.287690 | − | 0.957724i | \(-0.407113\pi\) | ||||
0.287690 | + | 0.957724i | \(0.407113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.1437 | −1.56235 | ||||||||
\(260\) | −12.3091 | −0.763376 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.000682320 0 | −4.21539e−5 0 | ||||||||
\(263\) | −0.238033 | −0.0146777 | −0.00733886 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733886 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.39665 | 0.515802 | ||||||||
\(266\) | 0.123069 | 0.00754585 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.0714 | −0.676294 | ||||||||
\(269\) | 14.4205 | 0.879234 | 0.439617 | − | 0.898185i | \(-0.355114\pi\) | ||||
0.439617 | + | 0.898185i | \(0.355114\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6640 | 1.01227 | 0.506133 | − | 0.862456i | \(-0.331075\pi\) | ||||
0.506133 | + | 0.862456i | \(0.331075\pi\) | |||||||
\(272\) | −11.0521 | −0.670132 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.2606 | 1.64687 | ||||||||
\(275\) | 7.72509 | 0.465841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8172 | 1.49112 | 0.745561 | − | 0.666438i | \(-0.232182\pi\) | ||||
0.745561 | + | 0.666438i | \(0.232182\pi\) | |||||||
\(278\) | −1.35591 | −0.0813219 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4257 | −0.623054 | ||||||||
\(281\) | 19.3251 | 1.15284 | 0.576418 | − | 0.817155i | \(-0.304450\pi\) | ||||
0.576418 | + | 0.817155i | \(0.304450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.11626 | 0.0663547 | 0.0331773 | − | 0.999449i | \(-0.489437\pi\) | ||||
0.0331773 | + | 0.999449i | \(0.489437\pi\) | |||||||
\(284\) | 19.0202 | 1.12864 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.90995 | −0.408594 | ||||||||
\(287\) | −19.8705 | −1.17292 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.86084 | −0.109461 | ||||||||
\(290\) | −29.2138 | −1.71549 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.90080 | −0.579400 | ||||||||
\(293\) | 8.03767 | 0.469566 | 0.234783 | − | 0.972048i | \(-0.424562\pi\) | ||||
0.234783 | + | 0.972048i | \(0.424562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.8210 | −0.862914 | ||||||||
\(296\) | −7.10518 | −0.412980 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.3203 | 1.58262 | ||||||||
\(299\) | 12.8774 | 0.744721 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0306 | 0.923987 | ||||||||
\(302\) | 35.4817 | 2.04174 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0470726 | −0.00269980 | ||||||||
\(305\) | −28.0545 | −1.60639 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7923 | 0.958388 | 0.479194 | − | 0.877709i | \(-0.340929\pi\) | ||||
0.479194 | + | 0.877709i | \(0.340929\pi\) | |||||||
\(308\) | −17.0083 | −0.969137 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −64.8874 | −3.68536 | ||||||||
\(311\) | 5.15497 | 0.292312 | 0.146156 | − | 0.989262i | \(-0.453310\pi\) | ||||
0.146156 | + | 0.989262i | \(0.453310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9400 | 1.57926 | 0.789632 | − | 0.613580i | \(-0.210271\pi\) | ||||
0.789632 | + | 0.613580i | \(0.210271\pi\) | |||||||
\(314\) | 18.1836 | 1.02616 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.1305 | 1.13243 | ||||||||
\(317\) | 9.19431 | 0.516404 | 0.258202 | − | 0.966091i | \(-0.416870\pi\) | ||||
0.258202 | + | 0.966091i | \(0.416870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.06130 | −0.507335 | ||||||||
\(320\) | 33.5231 | 1.87400 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 57.3670 | 3.19694 | ||||||||
\(323\) | 0.0644800 | 0.00358776 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.56814 | 0.364335 | ||||||||
\(326\) | −1.42594 | −0.0789755 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.61508 | −0.310041 | ||||||||
\(329\) | −10.1047 | −0.557090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.9510 | 0.931711 | 0.465855 | − | 0.884861i | \(-0.345747\pi\) | ||||
0.465855 | + | 0.884861i | \(0.345747\pi\) | |||||||
\(332\) | −12.7331 | −0.698817 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −34.0791 | −1.86472 | ||||||||
\(335\) | 13.4048 | 0.732380 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0457 | 0.710644 | 0.355322 | − | 0.934744i | \(-0.384371\pi\) | ||||
0.355322 | + | 0.934744i | \(0.384371\pi\) | |||||||
\(338\) | 21.6085 | 1.17535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −28.7299 | −1.55810 | ||||||||
\(341\) | −20.1262 | −1.08990 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.83377 | 0.314994 | ||||||||
\(344\) | 4.52997 | 0.244240 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.1012 | 1.83329 | ||||||||
\(347\) | 14.3935 | 0.772682 | 0.386341 | − | 0.922356i | \(-0.373739\pi\) | ||||
0.386341 | + | 0.922356i | \(0.373739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.13327 | 0.435364 | 0.217682 | − | 0.976020i | \(-0.430150\pi\) | ||||
0.217682 | + | 0.976020i | \(0.430150\pi\) | |||||||
\(350\) | 29.2601 | 1.56402 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.6665 | 0.835029 | ||||||||
\(353\) | 27.1058 | 1.44270 | 0.721348 | − | 0.692572i | \(-0.243523\pi\) | ||||
0.721348 | + | 0.692572i | \(0.243523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.0287 | −1.22224 | ||||||||
\(356\) | −11.8002 | −0.625408 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.7833 | −0.887026 | ||||||||
\(359\) | −24.9323 | −1.31587 | −0.657937 | − | 0.753073i | \(-0.728571\pi\) | ||||
−0.657937 | + | 0.753073i | \(0.728571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9997 | −0.999986 | ||||||||
\(362\) | 29.2478 | 1.53723 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.4610 | −0.757965 | ||||||||
\(365\) | 11.9874 | 0.627451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0921 | 0.683403 | 0.341702 | − | 0.939809i | \(-0.388997\pi\) | ||||
0.341702 | + | 0.939809i | \(0.388997\pi\) | |||||||
\(368\) | −21.9422 | −1.14382 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 45.2465 | 2.35225 | ||||||||
\(371\) | 9.86462 | 0.512146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.7755 | −1.48994 | −0.744969 | − | 0.667099i | \(-0.767536\pi\) | ||||
−0.744969 | + | 0.667099i | \(0.767536\pi\) | |||||||
\(374\) | −16.1281 | −0.833966 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.85541 | −0.147257 | ||||||||
\(377\) | −7.70423 | −0.396788 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9830 | −1.07782 | −0.538912 | − | 0.842362i | \(-0.681164\pi\) | ||||
−0.538912 | + | 0.842362i | \(0.681164\pi\) | |||||||
\(380\) | −0.122365 | −0.00627720 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −30.3890 | −1.55483 | ||||||||
\(383\) | −24.4951 | −1.25164 | −0.625820 | − | 0.779968i | \(-0.715236\pi\) | ||||
−0.625820 | + | 0.779968i | \(0.715236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.5929 | 1.04951 | ||||||||
\(386\) | 8.84528 | 0.450213 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.7225 | −1.45816 | ||||||||
\(389\) | 15.7668 | 0.799411 | 0.399705 | − | 0.916644i | \(-0.369112\pi\) | ||||
0.399705 | + | 0.916644i | \(0.369112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0565 | 1.52002 | ||||||||
\(392\) | −5.29994 | −0.267687 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.499970 | −0.0251881 | ||||||||
\(395\) | −24.3731 | −1.22634 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8264 | −1.29619 | −0.648095 | − | 0.761560i | \(-0.724434\pi\) | ||||
−0.648095 | + | 0.761560i | \(0.724434\pi\) | |||||||
\(398\) | −55.1572 | −2.76478 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.1917 | −0.559583 | ||||||||
\(401\) | −16.3786 | −0.817909 | −0.408954 | − | 0.912555i | \(-0.634106\pi\) | ||||
−0.408954 | + | 0.912555i | \(0.634106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1120 | −0.852411 | ||||||||
\(404\) | −7.06106 | −0.351301 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.3212 | −1.70333 | ||||||||
\(407\) | 14.0342 | 0.695649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.3561 | −1.25378 | −0.626888 | − | 0.779109i | \(-0.715672\pi\) | ||||
−0.626888 | + | 0.779109i | \(0.715672\pi\) | |||||||
\(410\) | 35.7574 | 1.76593 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.06508 | −0.348071 | ||||||||
\(413\) | −17.4122 | −0.856797 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4166 | 0.756772 | ||||||||
\(416\) | 13.3202 | 0.653078 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0686922 | −0.00335985 | ||||||||
\(419\) | 6.35976 | 0.310695 | 0.155347 | − | 0.987860i | \(-0.450350\pi\) | ||||
0.155347 | + | 0.987860i | \(0.450350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2648 | 1.28007 | 0.640033 | − | 0.768347i | \(-0.278921\pi\) | ||||
0.640033 | + | 0.768347i | \(0.278921\pi\) | |||||||
\(422\) | 24.9448 | 1.21430 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.78757 | 0.135377 | ||||||||
\(425\) | 15.3303 | 0.743631 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.9592 | −1.59501 | ||||||||
\(428\) | −38.9839 | −1.88436 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −28.8473 | −1.39114 | ||||||||
\(431\) | 12.3288 | 0.593858 | 0.296929 | − | 0.954900i | \(-0.404038\pi\) | ||||
0.296929 | + | 0.954900i | \(0.404038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.75112 | −0.324438 | −0.162219 | − | 0.986755i | \(-0.551865\pi\) | ||||
−0.162219 | + | 0.986755i | \(0.551865\pi\) | |||||||
\(434\) | −76.2316 | −3.65923 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.718103 | −0.0343909 | ||||||||
\(437\) | 0.128015 | 0.00612380 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.46643 | −0.213171 | −0.106586 | − | 0.994304i | \(-0.533992\pi\) | ||||
−0.106586 | + | 0.994304i | \(0.533992\pi\) | |||||||
\(440\) | 5.81920 | 0.277419 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.7127 | −0.652247 | ||||||||
\(443\) | −28.2113 | −1.34036 | −0.670179 | − | 0.742199i | \(-0.733783\pi\) | ||||
−0.670179 | + | 0.742199i | \(0.733783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.2871 | 0.677274 | ||||||||
\(446\) | 55.6777 | 2.63642 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 39.3840 | 1.86072 | ||||||||
\(449\) | 26.2299 | 1.23787 | 0.618933 | − | 0.785444i | \(-0.287565\pi\) | ||||
0.618933 | + | 0.785444i | \(0.287565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.0909 | 0.522252 | ||||||||
\(452\) | 7.98551 | 0.375607 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.15537 | −0.101157 | ||||||||
\(455\) | 17.5088 | 0.820824 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.1349 | −1.12898 | −0.564492 | − | 0.825438i | \(-0.690928\pi\) | ||||
−0.564492 | + | 0.825438i | \(0.690928\pi\) | |||||||
\(458\) | −55.1396 | −2.57650 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −57.0388 | −2.65945 | ||||||||
\(461\) | 18.9067 | 0.880572 | 0.440286 | − | 0.897858i | \(-0.354877\pi\) | ||||
0.440286 | + | 0.897858i | \(0.354877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.69898 | 0.0789581 | 0.0394790 | − | 0.999220i | \(-0.487430\pi\) | ||||
0.0394790 | + | 0.999220i | \(0.487430\pi\) | |||||||
\(464\) | 13.1275 | 0.609428 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.49084 | 0.439655 | ||||||||
\(467\) | −1.53809 | −0.0711744 | −0.0355872 | − | 0.999367i | \(-0.511330\pi\) | ||||
−0.0355872 | + | 0.999367i | \(0.511330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.7483 | 0.727189 | ||||||||
\(470\) | 18.1836 | 0.838746 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.92039 | −0.226479 | ||||||||
\(473\) | −8.94762 | −0.411412 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0652943 | 0.00299591 | ||||||||
\(476\) | −33.7527 | −1.54705 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.22401 | −0.147463 | ||||||||
\(479\) | −15.8904 | −0.726052 | −0.363026 | − | 0.931779i | \(-0.618256\pi\) | ||||
−0.363026 | + | 0.931779i | \(0.618256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9324 | 0.544068 | ||||||||
\(482\) | −1.78045 | −0.0810973 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.6714 | −0.803248 | ||||||||
\(485\) | 34.7759 | 1.57909 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0750 | 1.77066 | 0.885330 | − | 0.464964i | \(-0.153933\pi\) | ||||
0.885330 | + | 0.464964i | \(0.153933\pi\) | |||||||
\(488\) | −9.31371 | −0.421612 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 33.7505 | 1.52469 | ||||||||
\(491\) | 38.5841 | 1.74128 | 0.870638 | − | 0.491925i | \(-0.163706\pi\) | ||||
0.870638 | + | 0.491925i | \(0.163706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.9820 | −0.809869 | ||||||||
\(494\) | −0.0584045 | −0.00262774 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.1577 | 1.30922 | ||||||||
\(497\) | −27.0548 | −1.21358 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.32929 | 0.238572 | 0.119286 | − | 0.992860i | \(-0.461940\pi\) | ||||
0.119286 | + | 0.992860i | \(0.461940\pi\) | |||||||
\(500\) | 7.82657 | 0.350015 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.5480 | 1.40806 | ||||||||
\(503\) | 22.6519 | 1.01000 | 0.505000 | − | 0.863119i | \(-0.331492\pi\) | ||||
0.505000 | + | 0.863119i | \(0.331492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.54921 | 0.380435 | ||||||||
\(506\) | −32.0200 | −1.42346 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.4231 | 1.43854 | ||||||||
\(509\) | −31.2829 | −1.38659 | −0.693295 | − | 0.720654i | \(-0.743842\pi\) | ||||
−0.693295 | + | 0.720654i | \(0.743842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0832 | 0.623003 | ||||||||
\(512\) | −28.3359 | −1.25228 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.5008 | −0.860141 | ||||||||
\(515\) | 8.55408 | 0.376938 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.64003 | 0.248048 | ||||||||
\(518\) | 53.1569 | 2.33558 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.94768 | 0.216970 | ||||||||
\(521\) | 28.7603 | 1.26001 | 0.630006 | − | 0.776590i | \(-0.283052\pi\) | ||||
0.630006 | + | 0.776590i | \(0.283052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.36746 | −0.322156 | −0.161078 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161078 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(524\) | 0.000797023 0 | 3.48181e−5 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.503231 | 0.0219419 | ||||||||
\(527\) | −39.9402 | −1.73982 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.6725 | 1.59446 | ||||||||
\(530\) | −17.7516 | −0.771079 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.143758 | −0.00623270 | ||||||||
\(533\) | 9.42990 | 0.408454 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.2000 | 2.04063 | ||||||||
\(536\) | 4.45020 | 0.192219 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.4868 | −1.31438 | ||||||||
\(539\) | 10.4685 | 0.450909 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.2403 | −1.08517 | −0.542583 | − | 0.840002i | \(-0.682554\pi\) | ||||
−0.542583 | + | 0.840002i | \(0.682554\pi\) | |||||||
\(542\) | −35.2298 | −1.51325 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 31.0900 | 1.33297 | ||||||||
\(545\) | 0.869446 | 0.0372430 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1106 | 0.774355 | 0.387178 | − | 0.922005i | \(-0.373450\pi\) | ||||
0.387178 | + | 0.922005i | \(0.373450\pi\) | |||||||
\(548\) | −31.8433 | −1.36028 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.3318 | −0.696391 | ||||||||
\(551\) | −0.0765882 | −0.00326277 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.6342 | −1.21765 | ||||||||
\(554\) | −52.4667 | −2.22910 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.58385 | 0.0671700 | ||||||||
\(557\) | −9.10466 | −0.385777 | −0.192888 | − | 0.981221i | \(-0.561786\pi\) | ||||
−0.192888 | + | 0.981221i | \(0.561786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.60758 | −0.321766 | ||||||||
\(560\) | −29.8338 | −1.26071 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.8556 | −1.72339 | ||||||||
\(563\) | 17.6895 | 0.745522 | 0.372761 | − | 0.927927i | \(-0.378411\pi\) | ||||
0.372761 | + | 0.927927i | \(0.378411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.66849 | −0.406757 | ||||||||
\(566\) | −2.35991 | −0.0991944 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.64524 | −0.320787 | ||||||||
\(569\) | 41.7760 | 1.75134 | 0.875670 | − | 0.482909i | \(-0.160420\pi\) | ||||
0.875670 | + | 0.482909i | \(0.160420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.7073 | 0.824726 | 0.412363 | − | 0.911020i | \(-0.364704\pi\) | ||||
0.412363 | + | 0.911020i | \(0.364704\pi\) | |||||||
\(572\) | 8.07157 | 0.337489 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 42.0088 | 1.75341 | ||||||||
\(575\) | 30.4360 | 1.26927 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.80701 | −0.325010 | −0.162505 | − | 0.986708i | \(-0.551957\pi\) | ||||
−0.162505 | + | 0.986708i | \(0.551957\pi\) | |||||||
\(578\) | 3.93406 | 0.163635 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 34.1249 | 1.41696 | ||||||||
\(581\) | 18.1119 | 0.751407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.50603 | −0.228037 | ||||||||
\(584\) | 3.97967 | 0.164680 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.9926 | −0.701960 | ||||||||
\(587\) | −20.9714 | −0.865582 | −0.432791 | − | 0.901494i | \(-0.642471\pi\) | ||||
−0.432791 | + | 0.901494i | \(0.642471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.170112 | −0.00700933 | ||||||||
\(590\) | 31.3335 | 1.28998 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.3319 | −0.835636 | ||||||||
\(593\) | −23.6392 | −0.970747 | −0.485373 | − | 0.874307i | \(-0.661316\pi\) | ||||
−0.485373 | + | 0.874307i | \(0.661316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.8663 | 1.67535 | ||||||||
\(596\) | −31.9131 | −1.30721 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.2245 | −1.11329 | ||||||||
\(599\) | 1.59764 | 0.0652777 | 0.0326389 | − | 0.999467i | \(-0.489609\pi\) | ||||
0.0326389 | + | 0.999467i | \(0.489609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7194 | 1.29386 | 0.646931 | − | 0.762548i | \(-0.276052\pi\) | ||||
0.646931 | + | 0.762548i | \(0.276052\pi\) | |||||||
\(602\) | −33.8906 | −1.38128 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −41.4465 | −1.68643 | ||||||||
\(605\) | 21.3958 | 0.869862 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.6373 | 0.431755 | 0.215877 | − | 0.976421i | \(-0.430739\pi\) | ||||
0.215877 | + | 0.976421i | \(0.430739\pi\) | |||||||
\(608\) | 0.132417 | 0.00537023 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 59.3107 | 2.40142 | ||||||||
\(611\) | 4.79535 | 0.193999 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.3797 | −1.83287 | −0.916434 | − | 0.400185i | \(-0.868946\pi\) | ||||
−0.916434 | + | 0.400185i | \(0.868946\pi\) | |||||||
\(614\) | −35.5011 | −1.43271 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.83656 | 0.275453 | ||||||||
\(617\) | −23.0932 | −0.929699 | −0.464850 | − | 0.885390i | \(-0.653892\pi\) | ||||
−0.464850 | + | 0.885390i | \(0.653892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.96634 | 0.0790337 | 0.0395168 | − | 0.999219i | \(-0.487418\pi\) | ||||
0.0395168 | + | 0.999219i | \(0.487418\pi\) | |||||||
\(620\) | 75.7955 | 3.04402 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.8983 | −0.436980 | ||||||||
\(623\) | 16.7849 | 0.672473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1763 | −1.16705 | ||||||||
\(626\) | −59.0688 | −2.36086 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.2404 | −0.847583 | ||||||||
\(629\) | 27.8506 | 1.11048 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.7084 | 1.93905 | 0.969526 | − | 0.244990i | \(-0.0787845\pi\) | ||||
0.969526 | + | 0.244990i | \(0.0787845\pi\) | |||||||
\(632\) | −8.09155 | −0.321865 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.4379 | −0.771979 | ||||||||
\(635\) | −39.2564 | −1.55784 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.90065 | 0.352657 | ||||||||
\(638\) | 19.1567 | 0.758422 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.0895 | −0.912693 | ||||||||
\(641\) | 24.6679 | 0.974325 | 0.487162 | − | 0.873311i | \(-0.338032\pi\) | ||||
0.487162 | + | 0.873311i | \(0.338032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5915 | −0.417686 | −0.208843 | − | 0.977949i | \(-0.566970\pi\) | ||||
−0.208843 | + | 0.977949i | \(0.566970\pi\) | |||||||
\(644\) | −67.0109 | −2.64060 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.136319 | −0.00536339 | ||||||||
\(647\) | 12.2785 | 0.482716 | 0.241358 | − | 0.970436i | \(-0.422407\pi\) | ||||
0.241358 | + | 0.970436i | \(0.422407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.71877 | 0.381495 | ||||||||
\(650\) | −13.8859 | −0.544649 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.66565 | 0.0652320 | ||||||||
\(653\) | 2.86324 | 0.112047 | 0.0560235 | − | 0.998429i | \(-0.482158\pi\) | ||||
0.0560235 | + | 0.998429i | \(0.482158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.000965000 0 | −3.77057e−5 0 | ||||||||
\(656\) | −16.0679 | −0.627346 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.3626 | 0.832800 | ||||||||
\(659\) | 46.7125 | 1.81966 | 0.909831 | − | 0.414979i | \(-0.136211\pi\) | ||||
0.909831 | + | 0.414979i | \(0.136211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8425 | 0.927366 | 0.463683 | − | 0.886001i | \(-0.346528\pi\) | ||||
0.463683 | + | 0.886001i | \(0.346528\pi\) | |||||||
\(662\) | −35.8365 | −1.39283 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.11811 | 0.198621 | ||||||||
\(665\) | 0.174056 | 0.00674959 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.7005 | −1.38233 | ||||||||
\(668\) | 39.8080 | 1.54022 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.3393 | −1.09484 | ||||||||
\(671\) | 18.3965 | 0.710188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.51325 | 0.173973 | 0.0869864 | − | 0.996209i | \(-0.472276\pi\) | ||||
0.0869864 | + | 0.996209i | \(0.472276\pi\) | |||||||
\(674\) | −27.5802 | −1.06235 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.2411 | −0.970812 | ||||||||
\(677\) | −12.6120 | −0.484720 | −0.242360 | − | 0.970186i | \(-0.577922\pi\) | ||||
−0.242360 | + | 0.970186i | \(0.577922\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.8557 | 1.56790 | ||||||||
\(680\) | 11.5481 | 0.442850 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42.5494 | 1.62930 | ||||||||
\(683\) | 18.0420 | 0.690358 | 0.345179 | − | 0.938537i | \(-0.387818\pi\) | ||||
0.345179 | + | 0.938537i | \(0.387818\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.5544 | 1.47309 | ||||||||
\(686\) | −12.3333 | −0.470888 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.9628 | 0.494202 | ||||||||
\(689\) | −4.68142 | −0.178348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.2733 | −1.26578 | −0.632888 | − | 0.774243i | \(-0.718131\pi\) | ||||
−0.632888 | + | 0.774243i | \(0.718131\pi\) | |||||||
\(692\) | −39.8339 | −1.51426 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4296 | −1.15509 | ||||||||
\(695\) | −1.91765 | −0.0727406 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0098 | 0.833681 | ||||||||
\(698\) | −17.1948 | −0.650831 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −34.1790 | −1.29184 | ||||||||
\(701\) | −18.2677 | −0.689961 | −0.344981 | − | 0.938610i | \(-0.612115\pi\) | ||||
−0.344981 | + | 0.938610i | \(0.612115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.118620 | 0.00447384 | ||||||||
\(704\) | −21.9825 | −0.828498 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57.3051 | −2.15671 | ||||||||
\(707\) | 10.0439 | 0.377738 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.97841 | 0.0743006 | 0.0371503 | − | 0.999310i | \(-0.488172\pi\) | ||||
0.0371503 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(710\) | 48.6857 | 1.82714 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.74313 | 0.177756 | ||||||||
\(713\) | −79.2952 | −2.96963 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.77269 | −0.365478 | ||||||||
\(716\) | 19.6047 | 0.732663 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 52.7099 | 1.96712 | ||||||||
\(719\) | −13.9854 | −0.521566 | −0.260783 | − | 0.965397i | \(-0.583981\pi\) | ||||
−0.260783 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0496 | 0.374266 | ||||||||
\(722\) | 40.1678 | 1.49489 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.1645 | −1.26972 | ||||||||
\(725\) | −18.2091 | −0.676269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.3803 | 1.38636 | 0.693180 | − | 0.720764i | \(-0.256209\pi\) | ||||
0.693180 | + | 0.720764i | \(0.256209\pi\) | |||||||
\(728\) | 5.81268 | 0.215432 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.3429 | −0.937984 | ||||||||
\(731\) | −17.7564 | −0.656745 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6081 | 0.982793 | 0.491397 | − | 0.870936i | \(-0.336487\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336487\pi\) | |||||||
\(734\) | −27.6784 | −1.02163 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 61.7245 | 2.27520 | ||||||||
\(737\) | −8.79006 | −0.323786 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5914 | 1.60353 | 0.801767 | − | 0.597636i | \(-0.203893\pi\) | ||||
0.801767 | + | 0.597636i | \(0.203893\pi\) | |||||||
\(740\) | −52.8528 | −1.94291 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.8550 | −0.765613 | ||||||||
\(743\) | −50.8670 | −1.86613 | −0.933065 | − | 0.359709i | \(-0.882876\pi\) | ||||
−0.933065 | + | 0.359709i | \(0.882876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.6389 | 1.41562 | ||||||||
\(746\) | 60.8350 | 2.22733 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.8394 | 0.688837 | ||||||||
\(749\) | 55.4519 | 2.02617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6722 | 0.462416 | 0.231208 | − | 0.972904i | \(-0.425732\pi\) | ||||
0.231208 | + | 0.972904i | \(0.425732\pi\) | |||||||
\(752\) | −8.17095 | −0.297964 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.2877 | 0.593163 | ||||||||
\(755\) | 50.1815 | 1.82629 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.9877 | −0.544737 | −0.272368 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272368 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(758\) | 44.3607 | 1.61125 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0491852 | 0.00178413 | ||||||||
\(761\) | −10.5506 | −0.382458 | −0.191229 | − | 0.981545i | \(-0.561247\pi\) | ||||
−0.191229 | + | 0.981545i | \(0.561247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.02145 | 0.0369790 | ||||||||
\(764\) | 35.4976 | 1.28426 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 51.7857 | 1.87109 | ||||||||
\(767\) | 8.26324 | 0.298368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.3336 | −1.41840 | −0.709202 | − | 0.705005i | \(-0.750945\pi\) | ||||
−0.709202 | + | 0.705005i | \(0.750945\pi\) | |||||||
\(770\) | −43.5359 | −1.56893 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.3322 | −0.371865 | ||||||||
\(773\) | 48.4610 | 1.74302 | 0.871511 | − | 0.490376i | \(-0.163140\pi\) | ||||
0.871511 | + | 0.490376i | \(0.163140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.4446 | −1.45281 | ||||||||
\(776\) | 11.5451 | 0.414446 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.3331 | −1.19505 | ||||||||
\(779\) | 0.0937432 | 0.00335870 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1009 | 0.540353 | ||||||||
\(782\) | −63.5432 | −2.27230 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.1661 | −0.541646 | ||||||||
\(785\) | 25.7169 | 0.917875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1310 | 0.681946 | 0.340973 | − | 0.940073i | \(-0.389243\pi\) | ||||
0.340973 | + | 0.940073i | \(0.389243\pi\) | |||||||
\(788\) | 0.584019 | 0.0208048 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 51.5278 | 1.83328 | ||||||||
\(791\) | −11.3588 | −0.403873 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6413 | 0.555440 | ||||||||
\(794\) | 54.6002 | 1.93769 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 64.4296 | 2.28365 | ||||||||
\(797\) | 53.1941 | 1.88423 | 0.942116 | − | 0.335288i | \(-0.108834\pi\) | ||||
0.942116 | + | 0.335288i | \(0.108834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1926 | 0.395964 | ||||||||
\(800\) | 31.4826 | 1.11308 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.6264 | 1.22270 | ||||||||
\(803\) | −7.86066 | −0.277397 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.1337 | 2.85959 | ||||||||
\(806\) | 36.1770 | 1.27428 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.83822 | 0.0998484 | ||||||||
\(809\) | −52.4325 | −1.84343 | −0.921715 | − | 0.387868i | \(-0.873211\pi\) | ||||
−0.921715 | + | 0.387868i | \(0.873211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1664 | −0.567679 | −0.283839 | − | 0.958872i | \(-0.591608\pi\) | ||||
−0.283839 | + | 0.958872i | \(0.591608\pi\) | |||||||
\(812\) | 40.0909 | 1.40691 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.6700 | −1.03993 | ||||||||
\(815\) | −2.01670 | −0.0706418 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0756273 | −0.00264587 | ||||||||
\(818\) | 53.6059 | 1.87429 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −41.7685 | −1.45862 | ||||||||
\(821\) | 56.3605 | 1.96700 | 0.983498 | − | 0.180918i | \(-0.0579069\pi\) | ||||
0.983498 | + | 0.180918i | \(0.0579069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.8461 | −1.38895 | −0.694473 | − | 0.719518i | \(-0.744363\pi\) | ||||
−0.694473 | + | 0.719518i | \(0.744363\pi\) | |||||||
\(824\) | 2.83984 | 0.0989305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.8115 | 1.28084 | ||||||||
\(827\) | −26.8004 | −0.931942 | −0.465971 | − | 0.884800i | \(-0.654295\pi\) | ||||
−0.465971 | + | 0.884800i | \(0.654295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.9647 | 1.83954 | 0.919769 | − | 0.392460i | \(-0.128376\pi\) | ||||
0.919769 | + | 0.392460i | \(0.128376\pi\) | |||||||
\(830\) | −32.5926 | −1.13131 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18.6903 | −0.647970 | ||||||||
\(833\) | 20.7745 | 0.719794 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.1978 | −1.66795 | ||||||||
\(836\) | 0.0802399 | 0.00277516 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.4453 | −0.464461 | ||||||||
\(839\) | 36.5919 | 1.26329 | 0.631647 | − | 0.775256i | \(-0.282379\pi\) | ||||
0.631647 | + | 0.775256i | \(0.282379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.64129 | −0.263493 | ||||||||
\(842\) | −55.5270 | −1.91359 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29.1382 | −1.00298 | ||||||||
\(845\) | 30.5608 | 1.05132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.1364 | 0.863696 | ||||||||
\(848\) | 7.97682 | 0.273925 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −32.4103 | −1.11166 | ||||||||
\(851\) | 55.2932 | 1.89543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.8342 | 1.87749 | 0.938743 | − | 0.344617i | \(-0.111991\pi\) | ||||
0.938743 | + | 0.344617i | \(0.111991\pi\) | |||||||
\(854\) | 69.6799 | 2.38440 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.6698 | 0.535582 | ||||||||
\(857\) | 43.3706 | 1.48151 | 0.740757 | − | 0.671774i | \(-0.234467\pi\) | ||||
0.740757 | + | 0.671774i | \(0.234467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2926 | −0.385298 | −0.192649 | − | 0.981268i | \(-0.561708\pi\) | ||||
−0.192649 | + | 0.981268i | \(0.561708\pi\) | |||||||
\(860\) | 33.6968 | 1.14905 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.0646 | −0.887765 | ||||||||
\(863\) | 11.5449 | 0.392991 | 0.196496 | − | 0.980505i | \(-0.437044\pi\) | ||||
0.196496 | + | 0.980505i | \(0.437044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.2291 | 1.63984 | ||||||||
\(866\) | 14.2727 | 0.485007 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 89.0467 | 3.02244 | ||||||||
\(869\) | 15.9825 | 0.542168 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.47362 | −0.253234 | ||||||||
\(872\) | 0.288645 | 0.00977474 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.270640 | −0.00915454 | ||||||||
\(875\) | −11.1327 | −0.376356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.8656 | −1.14356 | −0.571780 | − | 0.820407i | \(-0.693747\pi\) | ||||
−0.571780 | + | 0.820407i | \(0.693747\pi\) | |||||||
\(878\) | 9.44259 | 0.318672 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.6520 | 0.561339 | ||||||||
\(881\) | 25.2356 | 0.850210 | 0.425105 | − | 0.905144i | \(-0.360237\pi\) | ||||
0.425105 | + | 0.905144i | \(0.360237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.56124 | −0.220803 | −0.110402 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110402 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(884\) | 16.0179 | 0.538741 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.6422 | 2.00372 | ||||||||
\(887\) | 47.7246 | 1.60243 | 0.801217 | − | 0.598374i | \(-0.204186\pi\) | ||||
0.801217 | + | 0.598374i | \(0.204186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.1195 | −1.54680 | ||||||||
\(890\) | −30.2047 | −1.01247 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −65.0376 | −2.17762 | ||||||||
\(893\) | 0.0476708 | 0.00159524 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.7365 | −0.793424 | ||||||||
\(896\) | −27.1262 | −0.906223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.4533 | −1.85050 | ||||||||
\(899\) | 47.4403 | 1.58222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9266 | −0.364019 | ||||||||
\(902\) | −23.4476 | −0.780721 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.20981 | −0.106757 | ||||||||
\(905\) | 41.3649 | 1.37502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1207 | 0.668098 | 0.334049 | − | 0.942556i | \(-0.391585\pi\) | ||||
0.334049 | + | 0.942556i | \(0.391585\pi\) | |||||||
\(908\) | 2.51771 | 0.0835531 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −37.0157 | −1.22706 | ||||||||
\(911\) | 43.6896 | 1.44750 | 0.723751 | − | 0.690061i | \(-0.242416\pi\) | ||||
0.723751 | + | 0.690061i | \(0.242416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1093 | −0.334570 | ||||||||
\(914\) | 51.0243 | 1.68773 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 64.4090 | 2.12813 | ||||||||
\(917\) | −0.00113371 | −3.74384e−5 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5424 | −0.413734 | −0.206867 | − | 0.978369i | \(-0.566327\pi\) | ||||
−0.206867 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(920\) | 22.9270 | 0.755881 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.9711 | −1.31638 | ||||||||
\(923\) | 12.8393 | 0.422612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.2024 | 0.927288 | ||||||||
\(926\) | −3.59185 | −0.118035 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36.9282 | −1.21223 | ||||||||
\(929\) | −31.6414 | −1.03812 | −0.519060 | − | 0.854738i | \(-0.673718\pi\) | ||||
−0.519060 | + | 0.854738i | \(0.673718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0884818 | 0.00289988 | ||||||||
\(932\) | −11.0863 | −0.363145 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.25172 | 0.106399 | ||||||||
\(935\) | −22.8099 | −0.745963 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.3437 | 1.15463 | 0.577315 | − | 0.816522i | \(-0.304101\pi\) | ||||
0.577315 | + | 0.816522i | \(0.304101\pi\) | |||||||
\(938\) | −33.2939 | −1.08708 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.2404 | −0.692784 | ||||||||
\(941\) | 27.8837 | 0.908982 | 0.454491 | − | 0.890751i | \(-0.349821\pi\) | ||||
0.454491 | + | 0.890751i | \(0.349821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.6971 | 1.42297 | ||||||||
\(944\) | −14.0800 | −0.458265 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.9164 | 0.615025 | ||||||||
\(947\) | −17.6519 | −0.573609 | −0.286804 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286804 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.68341 | −0.216953 | ||||||||
\(950\) | −0.138040 | −0.00447862 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.5671 | 0.439711 | ||||||||
\(953\) | 1.16016 | 0.0375813 | 0.0187907 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187907 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.9789 | −1.39076 | ||||||||
\(956\) | 3.76599 | 0.121801 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.5943 | 1.08538 | ||||||||
\(959\) | 45.2948 | 1.46265 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.3707 | 2.39905 | ||||||||
\(962\) | −25.2265 | −0.813335 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.07976 | 0.0669845 | ||||||||
\(965\) | 12.5098 | 0.402705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.5213 | −1.20660 | −0.603302 | − | 0.797513i | \(-0.706149\pi\) | ||||
−0.603302 | + | 0.797513i | \(0.706149\pi\) | |||||||
\(968\) | 7.10312 | 0.228303 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −73.5205 | −2.36060 | ||||||||
\(971\) | 13.1664 | 0.422531 | 0.211265 | − | 0.977429i | \(-0.432242\pi\) | ||||
0.211265 | + | 0.977429i | \(0.432242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.25291 | −0.0722250 | ||||||||
\(974\) | −82.6096 | −2.64698 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6518 | −0.853102 | ||||||||
\(977\) | −26.8056 | −0.857587 | −0.428793 | − | 0.903403i | \(-0.641061\pi\) | ||||
−0.428793 | + | 0.903403i | \(0.641061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.36866 | −0.299424 | ||||||||
\(980\) | −39.4243 | −1.25936 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −81.5716 | −2.60305 | ||||||||
\(983\) | −12.0965 | −0.385819 | −0.192910 | − | 0.981217i | \(-0.561792\pi\) | ||||
−0.192910 | + | 0.981217i | \(0.561792\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.707103 | −0.0225302 | ||||||||
\(986\) | 38.0162 | 1.21068 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0682228 | 0.00217046 | ||||||||
\(989\) | −35.2527 | −1.12097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.9307 | −0.791950 | −0.395975 | − | 0.918261i | \(-0.629593\pi\) | ||||
−0.395975 | + | 0.918261i | \(0.629593\pi\) | |||||||
\(992\) | −82.0220 | −2.60420 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 57.1973 | 1.81419 | ||||||||
\(995\) | −78.0084 | −2.47303 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4776 | −1.06025 | −0.530124 | − | 0.847920i | \(-0.677855\pi\) | ||||
−0.530124 | + | 0.847920i | \(0.677855\pi\) | |||||||
\(998\) | −11.2668 | −0.356644 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6561.2.a.d.1.11 | 72 | ||
3.2 | odd | 2 | 6561.2.a.c.1.62 | 72 | |||
81.5 | odd | 54 | 729.2.g.c.460.8 | 144 | |||
81.11 | odd | 54 | 81.2.g.a.40.1 | ✓ | 144 | ||
81.16 | even | 27 | 729.2.g.b.271.1 | 144 | |||
81.22 | even | 27 | 243.2.g.a.235.8 | 144 | |||
81.32 | odd | 54 | 729.2.g.d.703.1 | 144 | |||
81.38 | odd | 54 | 729.2.g.d.28.1 | 144 | |||
81.43 | even | 27 | 729.2.g.a.28.8 | 144 | |||
81.49 | even | 27 | 729.2.g.a.703.8 | 144 | |||
81.59 | odd | 54 | 81.2.g.a.79.1 | yes | 144 | ||
81.65 | odd | 54 | 729.2.g.c.271.8 | 144 | |||
81.70 | even | 27 | 243.2.g.a.91.8 | 144 | |||
81.76 | even | 27 | 729.2.g.b.460.1 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.40.1 | ✓ | 144 | 81.11 | odd | 54 | ||
81.2.g.a.79.1 | yes | 144 | 81.59 | odd | 54 | ||
243.2.g.a.91.8 | 144 | 81.70 | even | 27 | |||
243.2.g.a.235.8 | 144 | 81.22 | even | 27 | |||
729.2.g.a.28.8 | 144 | 81.43 | even | 27 | |||
729.2.g.a.703.8 | 144 | 81.49 | even | 27 | |||
729.2.g.b.271.1 | 144 | 81.16 | even | 27 | |||
729.2.g.b.460.1 | 144 | 81.76 | even | 27 | |||
729.2.g.c.271.8 | 144 | 81.65 | odd | 54 | |||
729.2.g.c.460.8 | 144 | 81.5 | odd | 54 | |||
729.2.g.d.28.1 | 144 | 81.38 | odd | 54 | |||
729.2.g.d.703.1 | 144 | 81.32 | odd | 54 | |||
6561.2.a.c.1.62 | 72 | 3.2 | odd | 2 | |||
6561.2.a.d.1.11 | 72 | 1.1 | even | 1 | trivial |