Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9301.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.60312\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.77625 | 1.42729 | 0.713643 | − | 0.700509i | \(-0.247044\pi\) | ||||
0.713643 | + | 0.700509i | \(0.247044\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.60312 | 1.08638 | 0.543191 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543191 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.22690 | −1.44968 | −0.724841 | − | 0.688916i | \(-0.758087\pi\) | ||||
−0.724841 | + | 0.688916i | \(0.758087\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.62378 | 0.393825 | 0.196913 | − | 0.980421i | \(-0.436908\pi\) | ||||
0.196913 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.15246 | −0.723224 | −0.361612 | − | 0.932329i | \(-0.617774\pi\) | ||||
−0.361612 | + | 0.932329i | \(0.617774\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.77625 | −0.824044 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.55249 | −1.36629 | −0.683144 | − | 0.730283i | \(-0.739388\pi\) | ||||
−0.683144 | + | 0.730283i | \(0.739388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.87493 | 0.348165 | 0.174082 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174082 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.40003 | −1.68829 | −0.844147 | − | 0.536111i | \(-0.819893\pi\) | ||||
−0.844147 | + | 0.536111i | \(0.819893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.60312 | −0.627223 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.77625 | −0.638302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.90132 | 0.312575 | 0.156288 | − | 0.987712i | \(-0.450047\pi\) | ||||
0.156288 | + | 0.987712i | \(0.450047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.22690 | 0.836975 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8036 | −1.68724 | −0.843622 | − | 0.536938i | \(-0.819581\pi\) | ||||
−0.843622 | + | 0.536938i | \(0.819581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.674415 | 0.102847 | 0.0514237 | − | 0.998677i | \(-0.483624\pi\) | ||||
0.0514237 | + | 0.998677i | \(0.483624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.78198 | −0.259928 | −0.129964 | − | 0.991519i | \(-0.541486\pi\) | ||||
−0.129964 | + | 0.991519i | \(0.541486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.26003 | 1.03715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.62378 | −0.227375 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.01246 | 0.825875 | 0.412938 | − | 0.910759i | \(-0.364503\pi\) | ||||
0.412938 | + | 0.910759i | \(0.364503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.60312 | −0.485845 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.15246 | 0.417554 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.839338 | −0.109273 | −0.0546363 | − | 0.998506i | \(-0.517400\pi\) | ||||
−0.0546363 | + | 0.998506i | \(0.517400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.26261 | −0.289698 | −0.144849 | − | 0.989454i | \(-0.546270\pi\) | ||||
−0.144849 | + | 0.989454i | \(0.546270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.77625 | 0.475762 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.22690 | 0.648318 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.55249 | 0.788827 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9433 | −1.77345 | −0.886723 | − | 0.462301i | \(-0.847024\pi\) | ||||
−0.886723 | + | 0.462301i | \(0.847024\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34378 | 0.859524 | 0.429762 | − | 0.902942i | \(-0.358597\pi\) | ||||
0.429762 | + | 0.902942i | \(0.358597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6063 | 1.55058 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.98822 | 0.898745 | 0.449373 | − | 0.893344i | \(-0.351648\pi\) | ||||
0.449373 | + | 0.893344i | \(0.351648\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.72820 | 0.518987 | 0.259494 | − | 0.965745i | \(-0.416444\pi\) | ||||
0.259494 | + | 0.965745i | \(0.416444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.62378 | −0.176124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.87493 | −0.201013 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.96688 | −0.314488 | −0.157244 | − | 0.987560i | \(-0.550261\pi\) | ||||
−0.157244 | + | 0.987560i | \(0.550261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.7381 | −2.06911 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.40003 | 0.974737 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.15246 | 0.323436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.1556 | −1.64035 | −0.820177 | − | 0.572110i | \(-0.806125\pi\) | ||||
−0.820177 | + | 0.572110i | \(0.806125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.60312 | 0.362127 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.33736 | −0.232576 | −0.116288 | − | 0.993216i | \(-0.537100\pi\) | ||||
−0.116288 | + | 0.993216i | \(0.537100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.674415 | −0.0664521 | −0.0332260 | − | 0.999448i | \(-0.510578\pi\) | ||||
−0.0332260 | + | 0.999448i | \(0.510578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.77625 | 0.368524 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.72573 | 0.553527 | 0.276764 | − | 0.960938i | \(-0.410738\pi\) | ||||
0.276764 | + | 0.960938i | \(0.410738\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.89312 | −0.947589 | −0.473795 | − | 0.880635i | \(-0.657116\pi\) | ||||
−0.473795 | + | 0.880635i | \(0.657116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.90132 | −0.180465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.70742 | 0.819125 | 0.409562 | − | 0.912282i | \(-0.365681\pi\) | ||||
0.409562 | + | 0.912282i | \(0.365681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.55249 | 0.611023 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.22690 | −0.483228 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.13180 | 0.562101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.98249 | 0.180226 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.8036 | 0.974131 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5582 | −1.29183 | −0.645917 | − | 0.763408i | \(-0.723525\pi\) | ||||
−0.645917 | + | 0.763408i | \(0.723525\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.674415 | −0.0593789 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.3501 | 1.86537 | 0.932683 | − | 0.360698i | \(-0.117462\pi\) | ||||
0.932683 | + | 0.360698i | \(0.117462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.9045 | −1.03225 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.53195 | −0.387190 | −0.193595 | − | 0.981081i | \(-0.562015\pi\) | ||||
−0.193595 | + | 0.981081i | \(0.562015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.08117 | 0.346160 | 0.173080 | − | 0.984908i | \(-0.444628\pi\) | ||||
0.173080 | + | 0.984908i | \(0.444628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.78198 | 0.150070 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8332 | −1.57491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.87493 | −0.155704 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.26003 | −0.598797 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0099 | 1.06581 | 0.532905 | − | 0.846175i | \(-0.321100\pi\) | ||||
0.532905 | + | 0.846175i | \(0.321100\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.90952 | −0.725046 | −0.362523 | − | 0.931975i | \(-0.618085\pi\) | ||||
−0.362523 | + | 0.931975i | \(0.618085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.62378 | 0.131275 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.40003 | 0.755028 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1798 | −0.972058 | −0.486029 | − | 0.873943i | \(-0.661555\pi\) | ||||
−0.486029 | + | 0.873943i | \(0.661555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.01246 | −0.476819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.7438 | −1.95009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.4730 | −1.68189 | −0.840947 | − | 0.541117i | \(-0.818002\pi\) | ||||
−0.840947 | + | 0.541117i | \(0.818002\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.60312 | 0.280503 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.11330 | 0.627826 | 0.313913 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313913 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.3205 | 1.10158 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.15246 | −0.241075 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.16393 | −0.392606 | −0.196303 | − | 0.980543i | \(-0.562894\pi\) | ||||
−0.196303 | + | 0.980543i | \(0.562894\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.77625 | 0.285457 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.839338 | 0.0630885 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8905 | −0.888740 | −0.444370 | − | 0.895843i | \(-0.646573\pi\) | ||||
−0.444370 | + | 0.895843i | \(0.646573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0123 | −1.48751 | −0.743753 | − | 0.668455i | \(-0.766956\pi\) | ||||
−0.743753 | + | 0.668455i | \(0.766956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.26261 | 0.167257 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.90132 | −0.139788 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.85069 | 0.427845 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.77625 | −0.274681 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.63525 | 0.118323 | 0.0591613 | − | 0.998248i | \(-0.481157\pi\) | ||||
0.0591613 | + | 0.998248i | \(0.481157\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.90805 | 0.353289 | 0.176644 | − | 0.984275i | \(-0.443476\pi\) | ||||
0.176644 | + | 0.984275i | \(0.443476\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.22690 | −0.374306 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.5681 | 1.67916 | 0.839579 | − | 0.543238i | \(-0.182802\pi\) | ||||
0.839579 | + | 0.543238i | \(0.182802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.1887 | −1.85647 | −0.928235 | − | 0.371994i | \(-0.878674\pi\) | ||||
−0.928235 | + | 0.371994i | \(0.878674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.08018 | 0.496931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.8036 | 0.754558 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.55249 | −0.455430 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3587 | −0.785698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.31054 | 0.296750 | 0.148375 | − | 0.988931i | \(-0.452596\pi\) | ||||
0.148375 | + | 0.988931i | \(0.452596\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.9433 | 1.02390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.674415 | −0.0459947 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −35.4968 | −2.40968 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.34378 | −0.496247 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.48736 | −0.570921 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6662 | −0.848193 | −0.424096 | − | 0.905617i | \(-0.639408\pi\) | ||||
−0.424096 | + | 0.905617i | \(0.639408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0812 | 0.669111 | 0.334555 | − | 0.942376i | \(-0.391414\pi\) | ||||
0.334555 | + | 0.942376i | \(0.391414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.91063 | −0.390585 | −0.195293 | − | 0.980745i | \(-0.562566\pi\) | ||||
−0.195293 | + | 0.980745i | \(0.562566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.6063 | −0.895227 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1073 | 0.793173 | 0.396586 | − | 0.917997i | \(-0.370195\pi\) | ||||
0.396586 | + | 0.917997i | \(0.370195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.78198 | 0.116243 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.98822 | −0.518891 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.08105 | −0.587404 | −0.293702 | − | 0.955897i | \(-0.594887\pi\) | ||||
−0.293702 | + | 0.955897i | \(0.594887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0627 | −1.67884 | −0.839422 | − | 0.543480i | \(-0.817106\pi\) | ||||
−0.839422 | + | 0.543480i | \(0.817106\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.26003 | −0.463826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4776 | 1.04845 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.72820 | −0.299637 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.877201 | −0.0553684 | −0.0276842 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276842 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.6094 | −1.48431 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.62378 | 0.101685 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0413 | −0.688739 | −0.344369 | − | 0.938834i | \(-0.611907\pi\) | ||||
−0.344369 | + | 0.938834i | \(0.611907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.17985 | 0.446134 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.87493 | 0.116055 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.65018 | −0.225080 | −0.112540 | − | 0.993647i | \(-0.535899\pi\) | ||||
−0.112540 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.01246 | −0.369343 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96688 | 0.181570 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9112 | −1.15304 | −0.576518 | − | 0.817084i | \(-0.695589\pi\) | ||||
−0.576518 | + | 0.817084i | \(0.695589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1827 | 0.983028 | 0.491514 | − | 0.870870i | \(-0.336444\pi\) | ||||
0.491514 | + | 0.870870i | \(0.336444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.7381 | 1.19460 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.60312 | 0.217276 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3557 | −1.76381 | −0.881906 | − | 0.471425i | \(-0.843740\pi\) | ||||
−0.881906 | + | 0.471425i | \(0.843740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.40003 | −0.562765 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.14957 | 0.187888 | 0.0939438 | − | 0.995578i | \(-0.470053\pi\) | ||||
0.0939438 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.73955 | 0.519512 | 0.259756 | − | 0.965674i | \(-0.416358\pi\) | ||||
0.259756 | + | 0.965674i | \(0.416358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.15246 | −0.186736 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.7972 | −2.40818 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3633 | −0.844902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1556 | 0.947059 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.2250 | −1.88260 | −0.941302 | − | 0.337564i | \(-0.890397\pi\) | ||||
−0.941302 | + | 0.337564i | \(0.890397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.839338 | 0.0488681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.60312 | −0.209074 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.2492 | 1.98068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54676 | 0.146793 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.33736 | 0.134278 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.26261 | 0.129557 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.2079 | 0.982108 | 0.491054 | − | 0.871129i | \(-0.336612\pi\) | ||||
0.491054 | + | 0.871129i | \(0.336612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.674415 | 0.0383661 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.2154 | 1.03290 | 0.516451 | − | 0.856317i | \(-0.327253\pi\) | ||||
0.516451 | + | 0.856317i | \(0.327253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.66363 | −0.489697 | −0.244849 | − | 0.969561i | \(-0.578738\pi\) | ||||
−0.244849 | + | 0.969561i | \(0.578738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.77625 | −0.212767 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.8591 | 1.90172 | 0.950858 | − | 0.309627i | \(-0.100204\pi\) | ||||
0.950858 | + | 0.309627i | \(0.100204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.75558 | 0.378240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.72573 | −0.319579 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.11891 | −0.284824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.22690 | −0.289937 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.89312 | 0.547091 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.72919 | −0.370992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.34625 | −0.293856 | −0.146928 | − | 0.989147i | \(-0.546939\pi\) | ||||
−0.146928 | + | 0.989147i | \(0.546939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.90132 | 0.104192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1638 | −0.608132 | −0.304066 | − | 0.952651i | \(-0.598344\pi\) | ||||
−0.304066 | + | 0.952651i | \(0.598344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.70742 | −0.472922 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.8694 | −1.83413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.981924 | 0.0530189 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.55249 | −0.352774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.8414 | 1.17251 | 0.586253 | − | 0.810128i | \(-0.300602\pi\) | ||||
0.586253 | + | 0.810128i | \(0.300602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3056 | 0.658704 | 0.329352 | − | 0.944207i | \(-0.393170\pi\) | ||||
0.329352 | + | 0.944207i | \(0.393170\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.22690 | 0.278992 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.2258 | −0.863612 | −0.431806 | − | 0.901967i | \(-0.642123\pi\) | ||||
−0.431806 | + | 0.901967i | \(0.642123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.9433 | 0.793109 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.13180 | −0.324529 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4341 | −0.550693 | −0.275346 | − | 0.961345i | \(-0.588793\pi\) | ||||
−0.275346 | + | 0.961345i | \(0.588793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.06198 | −0.476946 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.98249 | −0.104054 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.34378 | −0.384391 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.90459 | −0.308217 | −0.154108 | − | 0.988054i | \(-0.549251\pi\) | ||||
−0.154108 | + | 0.988054i | \(0.549251\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.8036 | −0.562415 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.7045 | 1.17876 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5743 | −0.651071 | −0.325535 | − | 0.945530i | \(-0.605544\pi\) | ||||
−0.325535 | + | 0.945530i | \(0.605544\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.80006 | −0.504729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4124 | 1.15125 | 0.575623 | − | 0.817715i | \(-0.304760\pi\) | ||||
0.575623 | + | 0.817715i | \(0.304760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.5582 | 0.745840 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.87739 | 0.402516 | 0.201258 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201258 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6063 | −0.693440 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.674415 | 0.0342824 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0405 | −0.610479 | −0.305240 | − | 0.952276i | \(-0.598737\pi\) | ||||
−0.305240 | + | 0.952276i | \(0.598737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.6398 | −0.538079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.3501 | −1.07697 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.98822 | −0.401931 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.6133 | 1.48625 | 0.743123 | − | 0.669154i | \(-0.233344\pi\) | ||||
0.743123 | + | 0.669154i | \(0.233344\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.9045 | 0.595969 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2243 | −0.660391 | −0.330196 | − | 0.943913i | \(-0.607115\pi\) | ||||
−0.330196 | + | 0.943913i | \(0.607115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.1331 | 2.44749 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.85069 | 0.339576 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.8798 | −1.67525 | −0.837623 | − | 0.546249i | \(-0.816055\pi\) | ||||
−0.837623 | + | 0.546249i | \(0.816055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.53195 | 0.223545 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.16955 | −0.155963 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.72820 | −0.232098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.08117 | −0.199856 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.71931 | 0.0839939 | 0.0419970 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419970 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.37233 | 0.213094 | 0.106547 | − | 0.994308i | \(-0.466020\pi\) | ||||
0.106547 | + | 0.994308i | \(0.466020\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.78198 | −0.0866428 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.62378 | 0.0787650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.54417 | −0.413481 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.8332 | 0.909274 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.67887 | −0.466215 | −0.233107 | − | 0.972451i | \(-0.574889\pi\) | ||||
−0.233107 | + | 0.972451i | \(0.574889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.4480 | 1.12684 | 0.563418 | − | 0.826172i | \(-0.309486\pi\) | ||||
0.563418 | + | 0.826172i | \(0.309486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.87493 | 0.0898958 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.6565 | 0.988133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.45727 | 0.117279 | 0.0586395 | − | 0.998279i | \(-0.481324\pi\) | ||||
0.0586395 | + | 0.998279i | \(0.481324\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.26003 | 0.345716 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.88682 | 0.137157 | 0.0685785 | − | 0.997646i | \(-0.478154\pi\) | ||||
0.0685785 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.96688 | 0.140644 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.0099 | −0.615346 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6595 | 0.691824 | 0.345912 | − | 0.938267i | \(-0.387570\pi\) | ||||
0.345912 | + | 0.938267i | \(0.387570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.9268 | −1.83299 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.90952 | 0.418606 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7381 | 0.925335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.6905 | 1.43564 | 0.717820 | − | 0.696229i | \(-0.245140\pi\) | ||||
0.717820 | + | 0.696229i | \(0.245140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.62378 | −0.0757917 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.85820 | −0.0865451 | −0.0432726 | − | 0.999063i | \(-0.513778\pi\) | ||||
−0.0432726 | + | 0.999063i | \(0.513778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9450 | 1.15929 | 0.579646 | − | 0.814868i | \(-0.303191\pi\) | ||||
0.579646 | + | 0.814868i | \(0.303191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.40003 | −0.435916 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4090 | −0.666770 | −0.333385 | − | 0.942791i | \(-0.608191\pi\) | ||||
−0.333385 | + | 0.942791i | \(0.608191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.77625 | 0.174371 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1798 | 0.561218 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.43000 | 0.111731 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.15246 | −0.144645 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.01246 | 0.275292 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.4255 | 1.34449 | 0.672243 | − | 0.740331i | \(-0.265331\pi\) | ||||
0.672243 | + | 0.740331i | \(0.265331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.93802 | −0.453135 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.7438 | 1.12588 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.1556 | 0.733589 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.17571 | −0.189219 | −0.0946097 | − | 0.995514i | \(-0.530160\pi\) | ||||
−0.0946097 | + | 0.995514i | \(0.530160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.4730 | 0.971043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.9816 | 1.75921 | 0.879607 | − | 0.475701i | \(-0.157806\pi\) | ||||
0.879607 | + | 0.475701i | \(0.157806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.04447 | 0.137116 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.60312 | −0.161948 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −56.4297 | −2.53122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.9639 | −1.60996 | −0.804982 | − | 0.593299i | \(-0.797825\pi\) | ||||
−0.804982 | + | 0.593299i | \(0.797825\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.11330 | −0.362475 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50018 | 0.245241 | 0.122620 | − | 0.992454i | \(-0.460870\pi\) | ||||
0.122620 | + | 0.992454i | \(0.460870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.33736 | 0.104011 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.3205 | −0.635997 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.0234 | −1.02049 | −0.510247 | − | 0.860028i | \(-0.670446\pi\) | ||||
−0.510247 | + | 0.860028i | \(0.670446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.7319 | 1.22679 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.15246 | 0.139185 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.674415 | 0.0297183 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.42069 | −0.282382 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.16393 | 0.226671 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2379 | −1.28094 | −0.640469 | − | 0.767984i | \(-0.721260\pi\) | ||||
−0.640469 | + | 0.767984i | \(0.721260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 45.3475 | 1.98291 | 0.991454 | − | 0.130458i | \(-0.0416449\pi\) | ||||
0.991454 | + | 0.130458i | \(0.0416449\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.77625 | −0.164809 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.2636 | −0.664893 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9351 | 0.866745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.839338 | −0.0364242 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.4696 | 2.44597 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.72573 | −0.247545 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.8905 | 0.513115 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.1588 | 1.12674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.97915 | −0.214070 | −0.107035 | − | 0.994255i | \(-0.534136\pi\) | ||||
−0.107035 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0123 | 0.858812 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.89312 | 0.423775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.7029 | −1.14174 | −0.570868 | − | 0.821042i | \(-0.693393\pi\) | ||||
−0.570868 | + | 0.821042i | \(0.693393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.26261 | −0.0965659 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.91063 | −0.251801 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.1655 | 1.28277 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.90132 | 0.0807065 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.3824 | 1.07549 | 0.537743 | − | 0.843109i | \(-0.319277\pi\) | ||||
0.537743 | + | 0.843109i | \(0.319277\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.52510 | −0.149096 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.85069 | −0.247016 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.6969 | −1.37801 | −0.689005 | − | 0.724757i | \(-0.741952\pi\) | ||||
−0.689005 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.70742 | −0.366324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.77625 | 0.158587 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.4469 | −1.73754 | −0.868771 | − | 0.495213i | \(-0.835090\pi\) | ||||
−0.868771 | + | 0.495213i | \(0.835090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0228 | 0.796080 | 0.398040 | − | 0.917368i | \(-0.369690\pi\) | ||||
0.398040 | + | 0.917368i | \(0.369690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.63525 | −0.0683136 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.55249 | −0.273258 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.22937 | 0.176071 | 0.0880355 | − | 0.996117i | \(-0.471941\pi\) | ||||
0.0880355 | + | 0.996117i | \(0.471941\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.90805 | −0.203971 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.8548 | 0.740743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.6636 | 0.897216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.22690 | 0.216106 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.85069 | 0.365307 | 0.182653 | − | 0.983177i | \(-0.441531\pi\) | ||||
0.182653 | + | 0.983177i | \(0.441531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.6332 | 1.22102 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.5681 | −0.969462 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4167 | −0.509895 | −0.254947 | − | 0.966955i | \(-0.582058\pi\) | ||||
−0.254947 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.13180 | −0.251379 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.1887 | 1.07183 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6469 | 0.516739 | 0.258369 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258369 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.06809 | 0.329104 | 0.164552 | − | 0.986368i | \(-0.447382\pi\) | ||||
0.164552 | + | 0.986368i | \(0.447382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.98249 | −0.0805997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.8958 | 0.726370 | 0.363185 | − | 0.931717i | \(-0.381689\pi\) | ||||
0.363185 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.08018 | −0.286903 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.31424 | 0.376814 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3202 | 0.901505 | 0.450753 | − | 0.892649i | \(-0.351156\pi\) | ||||
0.450753 | + | 0.892649i | \(0.351156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.8036 | −0.435645 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.0658 | 1.25066 | 0.625331 | − | 0.780359i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780359i | \(0.284964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.4628 | 1.30479 | 0.652395 | − | 0.757879i | \(-0.273764\pi\) | ||||
0.652395 | + | 0.757879i | \(0.273764\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.55249 | 0.262942 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.2037 | −0.448865 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.3587 | 0.453623 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.08733 | 0.123100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.89102 | −0.115090 | −0.0575448 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575448 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.31054 | −0.171329 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.5582 | 0.577726 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.9475 | −1.50353 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.9433 | −0.591149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.8389 | −1.37605 | −0.688027 | − | 0.725685i | \(-0.741523\pi\) | ||||
−0.688027 | + | 0.725685i | \(0.741523\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.86068 | −0.270559 | −0.135279 | − | 0.990807i | \(-0.543193\pi\) | ||||
−0.135279 | + | 0.990807i | \(0.543193\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.674415 | 0.0265551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.55014 | 0.336141 | 0.168070 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168070 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.02424 | −0.118712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.4968 | 1.39123 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.1123 | −1.49145 | −0.745724 | − | 0.666255i | \(-0.767896\pi\) | ||||
−0.745724 | + | 0.666255i | \(0.767896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.3501 | −0.834217 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.34378 | 0.286508 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8356 | 0.733732 | 0.366866 | − | 0.930274i | \(-0.380431\pi\) | ||||
0.366866 | + | 0.930274i | \(0.380431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0398 | 1.24621 | 0.623103 | − | 0.782140i | \(-0.285872\pi\) | ||||
0.623103 | + | 0.782140i | \(0.285872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.48736 | 0.329622 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.9045 | 0.461636 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2854 | −0.475694 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.6662 | 0.489704 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.15246 | −0.314722 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9297 | 1.46208 | 0.731041 | − | 0.682333i | \(-0.239035\pi\) | ||||
0.731041 | + | 0.682333i | \(0.239035\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.06323 | 0.233029 | 0.116514 | − | 0.993189i | \(-0.462828\pi\) | ||||
0.116514 | + | 0.993189i | \(0.462828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −61.0076 | −2.34125 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0812 | −0.386311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.7163 | 0.945743 | 0.472872 | − | 0.881131i | \(-0.343217\pi\) | ||||
0.472872 | + | 0.881131i | \(0.343217\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.53195 | 0.173157 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.91063 | 0.225505 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.4266 | −1.19726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.7806 | −1.74158 | −0.870789 | − | 0.491657i | \(-0.836391\pi\) | ||||
−0.870789 | + | 0.491657i | \(0.836391\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.6063 | 0.516860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.08117 | −0.154808 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5428 | −0.664479 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1073 | −0.457938 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.2338 | −1.63292 | −0.816458 | − | 0.577404i | \(-0.804066\pi\) | ||||
−0.816458 | + | 0.577404i | \(0.804066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.99384 | −0.226062 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.78198 | −0.0671132 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.82645 | −0.331953 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.40219 | 0.165328 | 0.0826638 | − | 0.996577i | \(-0.473657\pi\) | ||||
0.0826638 | + | 0.996577i | \(0.473657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.98822 | 0.299582 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 61.5936 | 2.30670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8332 | 0.704321 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.08105 | 0.339138 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.8469 | −1.33686 | −0.668432 | − | 0.743774i | \(-0.733034\pi\) | ||||
−0.668432 | + | 0.743774i | \(0.733034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.54676 | −0.0948461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.0627 | 0.969281 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.87493 | 0.0696330 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6395 | 0.431686 | 0.215843 | − | 0.976428i | \(-0.430750\pi\) | ||||
0.215843 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.09510 | 0.0405039 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.6633 | 1.02177 | 0.510884 | − | 0.859650i | \(-0.329318\pi\) | ||||
0.510884 | + | 0.859650i | \(0.329318\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.26003 | 0.267790 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.60312 | 0.132723 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.8592 | −0.914461 | −0.457230 | − | 0.889348i | \(-0.651159\pi\) | ||||
−0.457230 | + | 0.889348i | \(0.651159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.4776 | −0.605321 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.7609 | 1.27525 | 0.637627 | − | 0.770345i | \(-0.279916\pi\) | ||||
0.637627 | + | 0.770345i | \(0.279916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.0099 | −0.476645 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72820 | 0.172996 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.6218 | 0.790042 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.1218 | −1.68301 | −0.841503 | − | 0.540252i | \(-0.818329\pi\) | ||||
−0.841503 | + | 0.540252i | \(0.818329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.877201 | 0.0319670 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.90952 | 0.324251 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.7737 | −1.80906 | −0.904528 | − | 0.426413i | \(-0.859777\pi\) | ||||
−0.904528 | + | 0.426413i | \(0.859777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.6094 | 0.856968 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.4073 | 0.631015 | 0.315507 | − | 0.948923i | \(-0.397825\pi\) | ||||
0.315507 | + | 0.948923i | \(0.397825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.3588 | −1.35248 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.62378 | −0.0587080 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.38714 | 0.158410 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.2180 | −1.19787 | −0.598935 | − | 0.800797i | \(-0.704409\pi\) | ||||
−0.598935 | + | 0.800797i | \(0.704409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0413 | 0.397643 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.0868 | −0.902309 | −0.451154 | − | 0.892446i | \(-0.648988\pi\) | ||||
−0.451154 | + | 0.892446i | \(0.648988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.40003 | −0.337659 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.17985 | −0.257576 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.0580 | 1.22026 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.8426 | −1.92664 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.87493 | −0.0670044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1798 | 0.434717 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.6568 | −0.700689 | −0.350344 | − | 0.936621i | \(-0.613935\pi\) | ||||
−0.350344 | + | 0.936621i | \(0.613935\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.65018 | 0.129950 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8813 | 1.16913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.8265 | 0.419970 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.01246 | 0.213240 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3425 | −0.755990 | −0.377995 | − | 0.925808i | \(-0.623386\pi\) | ||||
−0.377995 | + | 0.925808i | \(0.623386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.89355 | −0.102366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.96688 | −0.104829 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.4605 | 0.933772 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.7438 | 0.872105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.9112 | 0.665706 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8446 | 0.732859 | 0.366429 | − | 0.930446i | \(-0.380580\pi\) | ||||
0.366429 | + | 0.930446i | \(0.380580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5594 | −0.441020 | −0.220510 | − | 0.975385i | \(-0.570772\pi\) | ||||
−0.220510 | + | 0.975385i | \(0.570772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.1827 | −0.567552 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.4730 | 0.752166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.12607 | −0.0743817 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.7381 | −0.689704 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.51352 | 0.297124 | 0.148562 | − | 0.988903i | \(-0.452536\pi\) | ||||
0.148562 | + | 0.988903i | \(0.452536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.89589 | 0.275234 | 0.137617 | − | 0.990486i | \(-0.456056\pi\) | ||||
0.137617 | + | 0.990486i | \(0.456056\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.60312 | −0.125445 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1443 | 1.11777 | 0.558883 | − | 0.829247i | \(-0.311230\pi\) | ||||
0.558883 | + | 0.829247i | \(0.311230\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6986 | 0.614698 | 0.307349 | − | 0.951597i | \(-0.400558\pi\) | ||||
0.307349 | + | 0.951597i | \(0.400558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.3557 | 1.01834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.7887 | 0.408454 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.11330 | −0.280772 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.40003 | 0.324912 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.8281 | 1.68573 | 0.842867 | − | 0.538122i | \(-0.180866\pi\) | ||||
0.842867 | + | 0.538122i | \(0.180866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.4847 | −0.878781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.14957 | −0.108477 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.3205 | −0.492641 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.48637 | 0.257235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.73955 | −0.299940 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.4584 | −0.427068 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.5404 | −0.737529 | −0.368765 | − | 0.929523i | \(-0.620219\pi\) | ||||
−0.368765 | + | 0.929523i | \(0.620219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.15246 | 0.107812 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.5713 | 0.873497 | 0.436749 | − | 0.899584i | \(-0.356130\pi\) | ||||
0.436749 | + | 0.899584i | \(0.356130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4722 | −0.834981 | −0.417490 | − | 0.908681i | \(-0.637090\pi\) | ||||
−0.417490 | + | 0.908681i | \(0.637090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.7972 | 1.39036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.16054 | 0.107586 | 0.0537931 | − | 0.998552i | \(-0.482869\pi\) | ||||
0.0537931 | + | 0.998552i | \(0.482869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.16393 | 0.175579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.3633 | 0.487804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.7825 | 0.976381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.22690 | −0.177107 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.1556 | −0.546785 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.77625 | −0.127660 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.25292 | 0.0760758 | 0.0380379 | − | 0.999276i | \(-0.487889\pi\) | ||||
0.0380379 | + | 0.999276i | \(0.487889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.2250 | 1.08692 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.7432 | −0.564094 | −0.282047 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282047 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7769 | −1.60782 | −0.803910 | − | 0.594751i | \(-0.797251\pi\) | ||||
−0.803910 | + | 0.594751i | \(0.797251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.839338 | −0.0282140 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.9579 | −0.804429 | −0.402215 | − | 0.915545i | \(-0.631759\pi\) | ||||
−0.402215 | + | 0.915545i | \(0.631759\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.9754 | −1.84382 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.60312 | 0.120709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.61762 | 0.187987 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.8905 | 0.397457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.2492 | −1.14355 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.6243 | −0.587805 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.76293 | 0.325250 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.54676 | −0.0847507 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0123 | 0.665233 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.3367 | 0.708475 | 0.354237 | − | 0.935155i | \(-0.384740\pi\) | ||||
0.354237 | + | 0.935155i | \(0.384740\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.33736 | −0.0775254 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.53867 | −0.316030 | −0.158015 | − | 0.987437i | \(-0.550509\pi\) | ||||
−0.158015 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0363 | 0.563818 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.26261 | −0.0747996 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.6231 | 2.66241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.6636 | 1.07747 | 0.538736 | − | 0.842475i | \(-0.318902\pi\) | ||||
0.538736 | + | 0.842475i | \(0.318902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2079 | −0.567020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 78.1073 | 2.57093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.90132 | 0.0625150 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.674415 | −0.0221507 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.0801 | 1.67588 | 0.837941 | − | 0.545760i | \(-0.183759\pi\) | ||||
0.837941 | + | 0.545760i | \(0.183759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.8870 | −0.750090 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.2154 | −0.596347 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.85069 | −0.191338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.88651 | 0.0616297 | 0.0308148 | − | 0.999525i | \(-0.490190\pi\) | ||||
0.0308148 | + | 0.999525i | \(0.490190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.66363 | 0.282727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.91748 | 0.323300 | 0.161650 | − | 0.986848i | \(-0.448318\pi\) | ||||
0.161650 | + | 0.986848i | \(0.448318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.7907 | 2.30526 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.77625 | 0.122841 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.5684 | −1.09083 | −0.545413 | − | 0.838168i | \(-0.683627\pi\) | ||||
−0.545413 | + | 0.838168i | \(0.683627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.3852 | −1.24604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.8591 | −1.09796 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.9301 | 1.19628 | 0.598142 | − | 0.801390i | \(-0.295906\pi\) | ||||
0.598142 | + | 0.801390i | \(0.295906\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.63525 | −0.0529155 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.75558 | −0.218377 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1137 | −0.552632 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.3605 | 1.85034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.72573 | 0.184509 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.90805 | −0.157996 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.84706 | 0.0915552 | 0.0457776 | − | 0.998952i | \(-0.485423\pi\) | ||||
0.0457776 | + | 0.998952i | \(0.485423\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.11891 | 0.164443 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.8727 | 1.56840 | 0.784200 | − | 0.620508i | \(-0.213074\pi\) | ||||
0.784200 | + | 0.620508i | \(0.213074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.4115 | 0.494070 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.22690 | 0.167395 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.2666 | 0.968315 | 0.484158 | − | 0.874981i | \(-0.339126\pi\) | ||||
0.484158 | + | 0.874981i | \(0.339126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6900 | −0.341655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.89312 | −0.315863 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.7693 | 1.10897 | 0.554484 | − | 0.832194i | \(-0.312916\pi\) | ||||
0.554484 | + | 0.832194i | \(0.312916\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.5681 | −0.750942 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.72919 | 0.214192 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.41910 | −0.140519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.3396 | 1.63085 | 0.815427 | − | 0.578859i | \(-0.196502\pi\) | ||||
0.815427 | + | 0.578859i | \(0.196502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.34625 | 0.169658 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.1887 | 0.830239 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.3360 | 1.84752 | 0.923760 | − | 0.382971i | \(-0.125099\pi\) | ||||
0.923760 | + | 0.382971i | \(0.125099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.90132 | −0.0601551 |
(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 | 4020.2.a.b.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |