Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.712717\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.712717 | 0.503967 | 0.251983 | − | 0.967732i | \(-0.418917\pi\) | ||||
0.251983 | + | 0.967732i | \(0.418917\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.49203 | −0.746017 | ||||||||
\(5\) | 0.415066 | 0.185623 | 0.0928115 | − | 0.995684i | \(-0.470415\pi\) | ||||
0.0928115 | + | 0.995684i | \(0.470415\pi\) | |||||||
\(6\) | −0.712717 | −0.290965 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.48883 | −0.879935 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.295824 | 0.0935479 | ||||||||
\(11\) | 2.75935 | 0.831975 | 0.415988 | − | 0.909370i | \(-0.363436\pi\) | ||||
0.415988 | + | 0.909370i | \(0.363436\pi\) | |||||||
\(12\) | 1.49203 | 0.430713 | ||||||||
\(13\) | 4.20250 | 1.16556 | 0.582782 | − | 0.812628i | \(-0.301964\pi\) | ||||
0.582782 | + | 0.812628i | \(0.301964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.415066 | −0.107169 | ||||||||
\(16\) | 1.21024 | 0.302559 | ||||||||
\(17\) | −4.39412 | −1.06573 | −0.532865 | − | 0.846200i | \(-0.678885\pi\) | ||||
−0.532865 | + | 0.846200i | \(0.678885\pi\) | |||||||
\(18\) | 0.712717 | 0.167989 | ||||||||
\(19\) | 1.26769 | 0.290828 | 0.145414 | − | 0.989371i | \(-0.453549\pi\) | ||||
0.145414 | + | 0.989371i | \(0.453549\pi\) | |||||||
\(20\) | −0.619292 | −0.138478 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.96663 | 0.419288 | ||||||||
\(23\) | 4.53011 | 0.944594 | 0.472297 | − | 0.881440i | \(-0.343425\pi\) | ||||
0.472297 | + | 0.881440i | \(0.343425\pi\) | |||||||
\(24\) | 2.48883 | 0.508031 | ||||||||
\(25\) | −4.82772 | −0.965544 | ||||||||
\(26\) | 2.99519 | 0.587406 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.42809 | −1.00797 | −0.503985 | − | 0.863712i | \(-0.668133\pi\) | ||||
−0.503985 | + | 0.863712i | \(0.668133\pi\) | |||||||
\(30\) | −0.295824 | −0.0540099 | ||||||||
\(31\) | 8.86379 | 1.59198 | 0.795992 | − | 0.605307i | \(-0.206950\pi\) | ||||
0.795992 | + | 0.605307i | \(0.206950\pi\) | |||||||
\(32\) | 5.84022 | 1.03241 | ||||||||
\(33\) | −2.75935 | −0.480341 | ||||||||
\(34\) | −3.13176 | −0.537093 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.49203 | −0.248672 | ||||||||
\(37\) | −2.60043 | −0.427508 | −0.213754 | − | 0.976887i | \(-0.568569\pi\) | ||||
−0.213754 | + | 0.976887i | \(0.568569\pi\) | |||||||
\(38\) | 0.903505 | 0.146568 | ||||||||
\(39\) | −4.20250 | −0.672939 | ||||||||
\(40\) | −1.03303 | −0.163336 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38379 | 0.668522 | 0.334261 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334261 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(44\) | −4.11704 | −0.620668 | ||||||||
\(45\) | 0.415066 | 0.0618743 | ||||||||
\(46\) | 3.22869 | 0.476044 | ||||||||
\(47\) | −10.9478 | −1.59691 | −0.798453 | − | 0.602057i | \(-0.794348\pi\) | ||||
−0.798453 | + | 0.602057i | \(0.794348\pi\) | |||||||
\(48\) | −1.21024 | −0.174683 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.44080 | −0.486602 | ||||||||
\(51\) | 4.39412 | 0.615300 | ||||||||
\(52\) | −6.27028 | −0.869531 | ||||||||
\(53\) | −2.30090 | −0.316053 | −0.158027 | − | 0.987435i | \(-0.550513\pi\) | ||||
−0.158027 | + | 0.987435i | \(0.550513\pi\) | |||||||
\(54\) | −0.712717 | −0.0969885 | ||||||||
\(55\) | 1.14531 | 0.154434 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.26769 | −0.167910 | ||||||||
\(58\) | −3.86869 | −0.507984 | ||||||||
\(59\) | 1.43254 | 0.186501 | 0.0932506 | − | 0.995643i | \(-0.470274\pi\) | ||||
0.0932506 | + | 0.995643i | \(0.470274\pi\) | |||||||
\(60\) | 0.619292 | 0.0799503 | ||||||||
\(61\) | 12.2775 | 1.57197 | 0.785986 | − | 0.618245i | \(-0.212156\pi\) | ||||
0.785986 | + | 0.618245i | \(0.212156\pi\) | |||||||
\(62\) | 6.31737 | 0.802307 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.74195 | 0.217744 | ||||||||
\(65\) | 1.74431 | 0.216356 | ||||||||
\(66\) | −1.96663 | −0.242076 | ||||||||
\(67\) | −1.10634 | −0.135161 | −0.0675806 | − | 0.997714i | \(-0.521528\pi\) | ||||
−0.0675806 | + | 0.997714i | \(0.521528\pi\) | |||||||
\(68\) | 6.55618 | 0.795054 | ||||||||
\(69\) | −4.53011 | −0.545361 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.83634 | 0.336611 | 0.168306 | − | 0.985735i | \(-0.446170\pi\) | ||||
0.168306 | + | 0.985735i | \(0.446170\pi\) | |||||||
\(72\) | −2.48883 | −0.293312 | ||||||||
\(73\) | 3.91272 | 0.457949 | 0.228975 | − | 0.973432i | \(-0.426463\pi\) | ||||
0.228975 | + | 0.973432i | \(0.426463\pi\) | |||||||
\(74\) | −1.85337 | −0.215450 | ||||||||
\(75\) | 4.82772 | 0.557457 | ||||||||
\(76\) | −1.89144 | −0.216963 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.99519 | −0.339139 | ||||||||
\(79\) | −15.3997 | −1.73260 | −0.866298 | − | 0.499527i | \(-0.833507\pi\) | ||||
−0.866298 | + | 0.499527i | \(0.833507\pi\) | |||||||
\(80\) | 0.502327 | 0.0561619 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.712717 | 0.0787064 | ||||||||
\(83\) | −4.04351 | −0.443833 | −0.221916 | − | 0.975066i | \(-0.571231\pi\) | ||||
−0.221916 | + | 0.975066i | \(0.571231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.82385 | −0.197824 | ||||||||
\(86\) | 3.12440 | 0.336913 | ||||||||
\(87\) | 5.42809 | 0.581952 | ||||||||
\(88\) | −6.86756 | −0.732084 | ||||||||
\(89\) | −1.02847 | −0.109018 | −0.0545090 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545090 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(90\) | 0.295824 | 0.0311826 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.75908 | −0.704683 | ||||||||
\(93\) | −8.86379 | −0.919132 | ||||||||
\(94\) | −7.80271 | −0.804788 | ||||||||
\(95\) | 0.526175 | 0.0539844 | ||||||||
\(96\) | −5.84022 | −0.596065 | ||||||||
\(97\) | −7.88278 | −0.800375 | −0.400187 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400187 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.75935 | 0.277325 | ||||||||
\(100\) | 7.20313 | 0.720313 | ||||||||
\(101\) | −8.38909 | −0.834746 | −0.417373 | − | 0.908735i | \(-0.637049\pi\) | ||||
−0.417373 | + | 0.908735i | \(0.637049\pi\) | |||||||
\(102\) | 3.13176 | 0.310091 | ||||||||
\(103\) | 17.2901 | 1.70365 | 0.851823 | − | 0.523830i | \(-0.175497\pi\) | ||||
0.851823 | + | 0.523830i | \(0.175497\pi\) | |||||||
\(104\) | −10.4593 | −1.02562 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.63989 | −0.159281 | ||||||||
\(107\) | −9.58485 | −0.926602 | −0.463301 | − | 0.886201i | \(-0.653335\pi\) | ||||
−0.463301 | + | 0.886201i | \(0.653335\pi\) | |||||||
\(108\) | 1.49203 | 0.143571 | ||||||||
\(109\) | −0.616655 | −0.0590648 | −0.0295324 | − | 0.999564i | \(-0.509402\pi\) | ||||
−0.0295324 | + | 0.999564i | \(0.509402\pi\) | |||||||
\(110\) | 0.816283 | 0.0778295 | ||||||||
\(111\) | 2.60043 | 0.246822 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7844 | 1.39080 | 0.695401 | − | 0.718622i | \(-0.255227\pi\) | ||||
0.695401 | + | 0.718622i | \(0.255227\pi\) | |||||||
\(114\) | −0.903505 | −0.0846210 | ||||||||
\(115\) | 1.88029 | 0.175338 | ||||||||
\(116\) | 8.09889 | 0.751963 | ||||||||
\(117\) | 4.20250 | 0.388521 | ||||||||
\(118\) | 1.02100 | 0.0939904 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.03303 | 0.0943022 | ||||||||
\(121\) | −3.38599 | −0.307817 | ||||||||
\(122\) | 8.75037 | 0.792222 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −13.2251 | −1.18765 | ||||||||
\(125\) | −4.07915 | −0.364850 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0528 | 1.51319 | 0.756594 | − | 0.653885i | \(-0.226862\pi\) | ||||
0.756594 | + | 0.653885i | \(0.226862\pi\) | |||||||
\(128\) | −10.4389 | −0.922679 | ||||||||
\(129\) | −4.38379 | −0.385972 | ||||||||
\(130\) | 1.24320 | 0.109036 | ||||||||
\(131\) | 22.2167 | 1.94108 | 0.970540 | − | 0.240939i | \(-0.0774555\pi\) | ||||
0.970540 | + | 0.240939i | \(0.0774555\pi\) | |||||||
\(132\) | 4.11704 | 0.358343 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.788509 | −0.0681168 | ||||||||
\(135\) | −0.415066 | −0.0357232 | ||||||||
\(136\) | 10.9362 | 0.937774 | ||||||||
\(137\) | 8.05455 | 0.688147 | 0.344073 | − | 0.938943i | \(-0.388193\pi\) | ||||
0.344073 | + | 0.938943i | \(0.388193\pi\) | |||||||
\(138\) | −3.22869 | −0.274844 | ||||||||
\(139\) | 22.4539 | 1.90451 | 0.952257 | − | 0.305299i | \(-0.0987564\pi\) | ||||
0.952257 | + | 0.305299i | \(0.0987564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9478 | 0.921974 | ||||||||
\(142\) | 2.02150 | 0.169641 | ||||||||
\(143\) | 11.5962 | 0.969721 | ||||||||
\(144\) | 1.21024 | 0.100853 | ||||||||
\(145\) | −2.25301 | −0.187103 | ||||||||
\(146\) | 2.78866 | 0.230791 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.87993 | 0.318929 | ||||||||
\(149\) | −5.09508 | −0.417405 | −0.208702 | − | 0.977979i | \(-0.566924\pi\) | ||||
−0.208702 | + | 0.977979i | \(0.566924\pi\) | |||||||
\(150\) | 3.44080 | 0.280940 | ||||||||
\(151\) | −17.6500 | −1.43634 | −0.718168 | − | 0.695870i | \(-0.755019\pi\) | ||||
−0.718168 | + | 0.695870i | \(0.755019\pi\) | |||||||
\(152\) | −3.15507 | −0.255910 | ||||||||
\(153\) | −4.39412 | −0.355244 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.67906 | 0.295509 | ||||||||
\(156\) | 6.27028 | 0.502024 | ||||||||
\(157\) | −5.78121 | −0.461391 | −0.230695 | − | 0.973026i | \(-0.574100\pi\) | ||||
−0.230695 | + | 0.973026i | \(0.574100\pi\) | |||||||
\(158\) | −10.9756 | −0.873172 | ||||||||
\(159\) | 2.30090 | 0.182474 | ||||||||
\(160\) | 2.42407 | 0.191640 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.712717 | 0.0559963 | ||||||||
\(163\) | −0.157705 | −0.0123524 | −0.00617621 | − | 0.999981i | \(-0.501966\pi\) | ||||
−0.00617621 | + | 0.999981i | \(0.501966\pi\) | |||||||
\(164\) | −1.49203 | −0.116508 | ||||||||
\(165\) | −1.14531 | −0.0891623 | ||||||||
\(166\) | −2.88188 | −0.223677 | ||||||||
\(167\) | 22.1528 | 1.71424 | 0.857118 | − | 0.515120i | \(-0.172253\pi\) | ||||
0.857118 | + | 0.515120i | \(0.172253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.66102 | 0.358540 | ||||||||
\(170\) | −1.29989 | −0.0996969 | ||||||||
\(171\) | 1.26769 | 0.0969428 | ||||||||
\(172\) | −6.54077 | −0.498729 | ||||||||
\(173\) | 18.2812 | 1.38989 | 0.694947 | − | 0.719061i | \(-0.255428\pi\) | ||||
0.694947 | + | 0.719061i | \(0.255428\pi\) | |||||||
\(174\) | 3.86869 | 0.293285 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.33946 | 0.251722 | ||||||||
\(177\) | −1.43254 | −0.107677 | ||||||||
\(178\) | −0.733010 | −0.0549414 | ||||||||
\(179\) | −19.7583 | −1.47680 | −0.738402 | − | 0.674361i | \(-0.764419\pi\) | ||||
−0.738402 | + | 0.674361i | \(0.764419\pi\) | |||||||
\(180\) | −0.619292 | −0.0461593 | ||||||||
\(181\) | 13.0870 | 0.972748 | 0.486374 | − | 0.873751i | \(-0.338319\pi\) | ||||
0.486374 | + | 0.873751i | \(0.338319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2775 | −0.907578 | ||||||||
\(184\) | −11.2747 | −0.831181 | ||||||||
\(185\) | −1.07935 | −0.0793554 | ||||||||
\(186\) | −6.31737 | −0.463212 | ||||||||
\(187\) | −12.1249 | −0.886661 | ||||||||
\(188\) | 16.3345 | 1.19132 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.375014 | 0.0272064 | ||||||||
\(191\) | −22.8221 | −1.65135 | −0.825675 | − | 0.564146i | \(-0.809205\pi\) | ||||
−0.825675 | + | 0.564146i | \(0.809205\pi\) | |||||||
\(192\) | −1.74195 | −0.125715 | ||||||||
\(193\) | 13.0794 | 0.941472 | 0.470736 | − | 0.882274i | \(-0.343988\pi\) | ||||
0.470736 | + | 0.882274i | \(0.343988\pi\) | |||||||
\(194\) | −5.61819 | −0.403362 | ||||||||
\(195\) | −1.74431 | −0.124913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.844299 | −0.0601538 | −0.0300769 | − | 0.999548i | \(-0.509575\pi\) | ||||
−0.0300769 | + | 0.999548i | \(0.509575\pi\) | |||||||
\(198\) | 1.96663 | 0.139763 | ||||||||
\(199\) | 8.12795 | 0.576175 | 0.288088 | − | 0.957604i | \(-0.406981\pi\) | ||||
0.288088 | + | 0.957604i | \(0.406981\pi\) | |||||||
\(200\) | 12.0154 | 0.849616 | ||||||||
\(201\) | 1.10634 | 0.0780353 | ||||||||
\(202\) | −5.97905 | −0.420684 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.55618 | −0.459024 | ||||||||
\(205\) | 0.415066 | 0.0289894 | ||||||||
\(206\) | 12.3230 | 0.858581 | ||||||||
\(207\) | 4.53011 | 0.314865 | ||||||||
\(208\) | 5.08602 | 0.352652 | ||||||||
\(209\) | 3.49800 | 0.241962 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6549 | 0.802357 | 0.401178 | − | 0.916000i | \(-0.368601\pi\) | ||||
0.401178 | + | 0.916000i | \(0.368601\pi\) | |||||||
\(212\) | 3.43303 | 0.235781 | ||||||||
\(213\) | −2.83634 | −0.194342 | ||||||||
\(214\) | −6.83128 | −0.466977 | ||||||||
\(215\) | 1.81956 | 0.124093 | ||||||||
\(216\) | 2.48883 | 0.169344 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.439500 | −0.0297667 | ||||||||
\(219\) | −3.91272 | −0.264397 | ||||||||
\(220\) | −1.70884 | −0.115210 | ||||||||
\(221\) | −18.4663 | −1.24218 | ||||||||
\(222\) | 1.85337 | 0.124390 | ||||||||
\(223\) | 11.7288 | 0.785416 | 0.392708 | − | 0.919663i | \(-0.371538\pi\) | ||||
0.392708 | + | 0.919663i | \(0.371538\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.82772 | −0.321848 | ||||||||
\(226\) | 10.5371 | 0.700919 | ||||||||
\(227\) | −1.94495 | −0.129091 | −0.0645455 | − | 0.997915i | \(-0.520560\pi\) | ||||
−0.0645455 | + | 0.997915i | \(0.520560\pi\) | |||||||
\(228\) | 1.89144 | 0.125264 | ||||||||
\(229\) | 11.2389 | 0.742686 | 0.371343 | − | 0.928496i | \(-0.378897\pi\) | ||||
0.371343 | + | 0.928496i | \(0.378897\pi\) | |||||||
\(230\) | 1.34012 | 0.0883647 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.5096 | 0.886949 | ||||||||
\(233\) | 13.3117 | 0.872079 | 0.436039 | − | 0.899928i | \(-0.356381\pi\) | ||||
0.436039 | + | 0.899928i | \(0.356381\pi\) | |||||||
\(234\) | 2.99519 | 0.195802 | ||||||||
\(235\) | −4.54407 | −0.296423 | ||||||||
\(236\) | −2.13740 | −0.139133 | ||||||||
\(237\) | 15.3997 | 1.00032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1521 | 0.980106 | 0.490053 | − | 0.871693i | \(-0.336977\pi\) | ||||
0.490053 | + | 0.871693i | \(0.336977\pi\) | |||||||
\(240\) | −0.502327 | −0.0324251 | ||||||||
\(241\) | 25.5139 | 1.64350 | 0.821749 | − | 0.569850i | \(-0.192999\pi\) | ||||
0.821749 | + | 0.569850i | \(0.192999\pi\) | |||||||
\(242\) | −2.41325 | −0.155130 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.3184 | −1.17272 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.712717 | −0.0454412 | ||||||||
\(247\) | 5.32748 | 0.338979 | ||||||||
\(248\) | −22.0605 | −1.40084 | ||||||||
\(249\) | 4.04351 | 0.256247 | ||||||||
\(250\) | −2.90728 | −0.183872 | ||||||||
\(251\) | 9.41888 | 0.594514 | 0.297257 | − | 0.954797i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954797i | \(0.403928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.5002 | 0.785878 | ||||||||
\(254\) | 12.1538 | 0.762597 | ||||||||
\(255\) | 1.82385 | 0.114214 | ||||||||
\(256\) | −10.9239 | −0.682744 | ||||||||
\(257\) | 1.07261 | 0.0669075 | 0.0334537 | − | 0.999440i | \(-0.489349\pi\) | ||||
0.0334537 | + | 0.999440i | \(0.489349\pi\) | |||||||
\(258\) | −3.12440 | −0.194517 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.60258 | −0.161405 | ||||||||
\(261\) | −5.42809 | −0.335990 | ||||||||
\(262\) | 15.8342 | 0.978240 | ||||||||
\(263\) | 26.2752 | 1.62020 | 0.810100 | − | 0.586292i | \(-0.199413\pi\) | ||||
0.810100 | + | 0.586292i | \(0.199413\pi\) | |||||||
\(264\) | 6.86756 | 0.422669 | ||||||||
\(265\) | −0.955026 | −0.0586668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.02847 | 0.0629415 | ||||||||
\(268\) | 1.65070 | 0.100833 | ||||||||
\(269\) | 19.8799 | 1.21210 | 0.606049 | − | 0.795427i | \(-0.292753\pi\) | ||||
0.606049 | + | 0.795427i | \(0.292753\pi\) | |||||||
\(270\) | −0.295824 | −0.0180033 | ||||||||
\(271\) | −15.1791 | −0.922062 | −0.461031 | − | 0.887384i | \(-0.652520\pi\) | ||||
−0.461031 | + | 0.887384i | \(0.652520\pi\) | |||||||
\(272\) | −5.31792 | −0.322446 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.74062 | 0.346803 | ||||||||
\(275\) | −13.3214 | −0.803309 | ||||||||
\(276\) | 6.75908 | 0.406849 | ||||||||
\(277\) | 14.8072 | 0.889681 | 0.444840 | − | 0.895610i | \(-0.353260\pi\) | ||||
0.444840 | + | 0.895610i | \(0.353260\pi\) | |||||||
\(278\) | 16.0033 | 0.959812 | ||||||||
\(279\) | 8.86379 | 0.530661 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5292 | 0.747429 | 0.373715 | − | 0.927544i | \(-0.378084\pi\) | ||||
0.373715 | + | 0.927544i | \(0.378084\pi\) | |||||||
\(282\) | 7.80271 | 0.464645 | ||||||||
\(283\) | 0.286081 | 0.0170058 | 0.00850289 | − | 0.999964i | \(-0.497293\pi\) | ||||
0.00850289 | + | 0.999964i | \(0.497293\pi\) | |||||||
\(284\) | −4.23191 | −0.251118 | ||||||||
\(285\) | −0.526175 | −0.0311679 | ||||||||
\(286\) | 8.26479 | 0.488707 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.84022 | 0.344138 | ||||||||
\(289\) | 2.30830 | 0.135782 | ||||||||
\(290\) | −1.60576 | −0.0942935 | ||||||||
\(291\) | 7.88278 | 0.462096 | ||||||||
\(292\) | −5.83792 | −0.341638 | ||||||||
\(293\) | 16.1124 | 0.941299 | 0.470650 | − | 0.882320i | \(-0.344020\pi\) | ||||
0.470650 | + | 0.882320i | \(0.344020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.594599 | 0.0346189 | ||||||||
\(296\) | 6.47204 | 0.376180 | ||||||||
\(297\) | −2.75935 | −0.160114 | ||||||||
\(298\) | −3.63135 | −0.210358 | ||||||||
\(299\) | 19.0378 | 1.10098 | ||||||||
\(300\) | −7.20313 | −0.415873 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.5794 | −0.723866 | ||||||||
\(303\) | 8.38909 | 0.481941 | ||||||||
\(304\) | 1.53421 | 0.0879927 | ||||||||
\(305\) | 5.09596 | 0.291794 | ||||||||
\(306\) | −3.13176 | −0.179031 | ||||||||
\(307\) | −8.82967 | −0.503936 | −0.251968 | − | 0.967736i | \(-0.581078\pi\) | ||||
−0.251968 | + | 0.967736i | \(0.581078\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.2901 | −0.983600 | ||||||||
\(310\) | 2.62213 | 0.148927 | ||||||||
\(311\) | 6.70085 | 0.379971 | 0.189985 | − | 0.981787i | \(-0.439156\pi\) | ||||
0.189985 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(312\) | 10.4593 | 0.592143 | ||||||||
\(313\) | 2.34758 | 0.132693 | 0.0663465 | − | 0.997797i | \(-0.478866\pi\) | ||||
0.0663465 | + | 0.997797i | \(0.478866\pi\) | |||||||
\(314\) | −4.12037 | −0.232526 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.9768 | 1.29255 | ||||||||
\(317\) | 22.8746 | 1.28477 | 0.642384 | − | 0.766383i | \(-0.277945\pi\) | ||||
0.642384 | + | 0.766383i | \(0.277945\pi\) | |||||||
\(318\) | 1.63989 | 0.0919606 | ||||||||
\(319\) | −14.9780 | −0.838606 | ||||||||
\(320\) | 0.723024 | 0.0404183 | ||||||||
\(321\) | 9.58485 | 0.534974 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.57039 | −0.309945 | ||||||||
\(324\) | −1.49203 | −0.0828908 | ||||||||
\(325\) | −20.2885 | −1.12540 | ||||||||
\(326\) | −0.112399 | −0.00622521 | ||||||||
\(327\) | 0.616655 | 0.0341011 | ||||||||
\(328\) | −2.48883 | −0.137423 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.816283 | −0.0449349 | ||||||||
\(331\) | −10.6287 | −0.584209 | −0.292104 | − | 0.956386i | \(-0.594355\pi\) | ||||
−0.292104 | + | 0.956386i | \(0.594355\pi\) | |||||||
\(332\) | 6.03306 | 0.331107 | ||||||||
\(333\) | −2.60043 | −0.142503 | ||||||||
\(334\) | 15.7887 | 0.863918 | ||||||||
\(335\) | −0.459205 | −0.0250890 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0676 | −0.875259 | −0.437630 | − | 0.899155i | \(-0.644182\pi\) | ||||
−0.437630 | + | 0.899155i | \(0.644182\pi\) | |||||||
\(338\) | 3.32199 | 0.180692 | ||||||||
\(339\) | −14.7844 | −0.802980 | ||||||||
\(340\) | 2.72125 | 0.147580 | ||||||||
\(341\) | 24.4583 | 1.32449 | ||||||||
\(342\) | 0.903505 | 0.0488560 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.9105 | −0.588256 | ||||||||
\(345\) | −1.88029 | −0.101232 | ||||||||
\(346\) | 13.0293 | 0.700460 | ||||||||
\(347\) | 31.3886 | 1.68503 | 0.842515 | − | 0.538674i | \(-0.181074\pi\) | ||||
0.842515 | + | 0.538674i | \(0.181074\pi\) | |||||||
\(348\) | −8.09889 | −0.434146 | ||||||||
\(349\) | −24.1638 | −1.29346 | −0.646728 | − | 0.762720i | \(-0.723863\pi\) | ||||
−0.646728 | + | 0.762720i | \(0.723863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.20250 | −0.224313 | ||||||||
\(352\) | 16.1152 | 0.858943 | ||||||||
\(353\) | −26.2342 | −1.39631 | −0.698153 | − | 0.715949i | \(-0.745994\pi\) | ||||
−0.698153 | + | 0.715949i | \(0.745994\pi\) | |||||||
\(354\) | −1.02100 | −0.0542654 | ||||||||
\(355\) | 1.17727 | 0.0624828 | ||||||||
\(356\) | 1.53452 | 0.0813293 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.0821 | −0.744260 | ||||||||
\(359\) | 20.7642 | 1.09589 | 0.547945 | − | 0.836514i | \(-0.315410\pi\) | ||||
0.547945 | + | 0.836514i | \(0.315410\pi\) | |||||||
\(360\) | −1.03303 | −0.0544454 | ||||||||
\(361\) | −17.3930 | −0.915419 | ||||||||
\(362\) | 9.32732 | 0.490233 | ||||||||
\(363\) | 3.38599 | 0.177718 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.62404 | 0.0850060 | ||||||||
\(366\) | −8.75037 | −0.457389 | ||||||||
\(367\) | 25.4996 | 1.33107 | 0.665534 | − | 0.746368i | \(-0.268204\pi\) | ||||
0.665534 | + | 0.746368i | \(0.268204\pi\) | |||||||
\(368\) | 5.48250 | 0.285795 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −0.769271 | −0.0399925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.2251 | 0.685689 | ||||||||
\(373\) | −24.8633 | −1.28737 | −0.643685 | − | 0.765290i | \(-0.722595\pi\) | ||||
−0.643685 | + | 0.765290i | \(0.722595\pi\) | |||||||
\(374\) | −8.64163 | −0.446848 | ||||||||
\(375\) | 4.07915 | 0.210646 | ||||||||
\(376\) | 27.2473 | 1.40517 | ||||||||
\(377\) | −22.8115 | −1.17485 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7940 | 0.811285 | 0.405642 | − | 0.914032i | \(-0.367048\pi\) | ||||
0.405642 | + | 0.914032i | \(0.367048\pi\) | |||||||
\(380\) | −0.785072 | −0.0402733 | ||||||||
\(381\) | −17.0528 | −0.873639 | ||||||||
\(382\) | −16.2657 | −0.832226 | ||||||||
\(383\) | 13.6516 | 0.697563 | 0.348781 | − | 0.937204i | \(-0.386596\pi\) | ||||
0.348781 | + | 0.937204i | \(0.386596\pi\) | |||||||
\(384\) | 10.4389 | 0.532709 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.32188 | 0.474471 | ||||||||
\(387\) | 4.38379 | 0.222841 | ||||||||
\(388\) | 11.7614 | 0.597093 | ||||||||
\(389\) | −15.8822 | −0.805260 | −0.402630 | − | 0.915363i | \(-0.631904\pi\) | ||||
−0.402630 | + | 0.915363i | \(0.631904\pi\) | |||||||
\(390\) | −1.24320 | −0.0629520 | ||||||||
\(391\) | −19.9059 | −1.00668 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.2167 | −1.12068 | ||||||||
\(394\) | −0.601746 | −0.0303155 | ||||||||
\(395\) | −6.39187 | −0.321610 | ||||||||
\(396\) | −4.11704 | −0.206889 | ||||||||
\(397\) | −0.506673 | −0.0254292 | −0.0127146 | − | 0.999919i | \(-0.504047\pi\) | ||||
−0.0127146 | + | 0.999919i | \(0.504047\pi\) | |||||||
\(398\) | 5.79293 | 0.290373 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.84268 | −0.292134 | ||||||||
\(401\) | −11.8880 | −0.593660 | −0.296830 | − | 0.954930i | \(-0.595929\pi\) | ||||
−0.296830 | + | 0.954930i | \(0.595929\pi\) | |||||||
\(402\) | 0.788509 | 0.0393272 | ||||||||
\(403\) | 37.2501 | 1.85556 | ||||||||
\(404\) | 12.5168 | 0.622735 | ||||||||
\(405\) | 0.415066 | 0.0206248 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.17550 | −0.355676 | ||||||||
\(408\) | −10.9362 | −0.541424 | ||||||||
\(409\) | 27.4784 | 1.35872 | 0.679359 | − | 0.733806i | \(-0.262258\pi\) | ||||
0.679359 | + | 0.733806i | \(0.262258\pi\) | |||||||
\(410\) | 0.295824 | 0.0146097 | ||||||||
\(411\) | −8.05455 | −0.397302 | ||||||||
\(412\) | −25.7974 | −1.27095 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.22869 | 0.158681 | ||||||||
\(415\) | −1.67832 | −0.0823856 | ||||||||
\(416\) | 24.5435 | 1.20335 | ||||||||
\(417\) | −22.4539 | −1.09957 | ||||||||
\(418\) | 2.49309 | 0.121941 | ||||||||
\(419\) | −3.97916 | −0.194394 | −0.0971972 | − | 0.995265i | \(-0.530988\pi\) | ||||
−0.0971972 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5438 | −0.513874 | −0.256937 | − | 0.966428i | \(-0.582713\pi\) | ||||
−0.256937 | + | 0.966428i | \(0.582713\pi\) | |||||||
\(422\) | 8.30665 | 0.404361 | ||||||||
\(423\) | −10.9478 | −0.532302 | ||||||||
\(424\) | 5.72656 | 0.278107 | ||||||||
\(425\) | 21.2136 | 1.02901 | ||||||||
\(426\) | −2.02150 | −0.0979422 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.3009 | 0.691261 | ||||||||
\(429\) | −11.5962 | −0.559868 | ||||||||
\(430\) | 1.29683 | 0.0625389 | ||||||||
\(431\) | −14.7089 | −0.708503 | −0.354252 | − | 0.935150i | \(-0.615264\pi\) | ||||
−0.354252 | + | 0.935150i | \(0.615264\pi\) | |||||||
\(432\) | −1.21024 | −0.0582275 | ||||||||
\(433\) | 4.20424 | 0.202043 | 0.101021 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101021 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.25301 | 0.108024 | ||||||||
\(436\) | 0.920070 | 0.0440634 | ||||||||
\(437\) | 5.74278 | 0.274715 | ||||||||
\(438\) | −2.78866 | −0.133247 | ||||||||
\(439\) | −9.46738 | −0.451854 | −0.225927 | − | 0.974144i | \(-0.572541\pi\) | ||||
−0.225927 | + | 0.974144i | \(0.572541\pi\) | |||||||
\(440\) | −2.85049 | −0.135892 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.1612 | −0.626017 | ||||||||
\(443\) | −14.5808 | −0.692753 | −0.346377 | − | 0.938096i | \(-0.612588\pi\) | ||||
−0.346377 | + | 0.938096i | \(0.612588\pi\) | |||||||
\(444\) | −3.87993 | −0.184134 | ||||||||
\(445\) | −0.426884 | −0.0202362 | ||||||||
\(446\) | 8.35929 | 0.395824 | ||||||||
\(447\) | 5.09508 | 0.240989 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0362 | 0.945567 | 0.472783 | − | 0.881179i | \(-0.343249\pi\) | ||||
0.472783 | + | 0.881179i | \(0.343249\pi\) | |||||||
\(450\) | −3.44080 | −0.162201 | ||||||||
\(451\) | 2.75935 | 0.129933 | ||||||||
\(452\) | −22.0589 | −1.03756 | ||||||||
\(453\) | 17.6500 | 0.829269 | ||||||||
\(454\) | −1.38620 | −0.0650576 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.15507 | 0.147750 | ||||||||
\(457\) | 27.5760 | 1.28995 | 0.644975 | − | 0.764204i | \(-0.276868\pi\) | ||||
0.644975 | + | 0.764204i | \(0.276868\pi\) | |||||||
\(458\) | 8.01014 | 0.374289 | ||||||||
\(459\) | 4.39412 | 0.205100 | ||||||||
\(460\) | −2.80546 | −0.130805 | ||||||||
\(461\) | −27.9697 | −1.30268 | −0.651340 | − | 0.758786i | \(-0.725793\pi\) | ||||
−0.651340 | + | 0.758786i | \(0.725793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.96307 | 0.416549 | 0.208275 | − | 0.978070i | \(-0.433215\pi\) | ||||
0.208275 | + | 0.978070i | \(0.433215\pi\) | |||||||
\(464\) | −6.56927 | −0.304971 | ||||||||
\(465\) | −3.67906 | −0.170612 | ||||||||
\(466\) | 9.48748 | 0.439499 | ||||||||
\(467\) | −20.6797 | −0.956944 | −0.478472 | − | 0.878103i | \(-0.658809\pi\) | ||||
−0.478472 | + | 0.878103i | \(0.658809\pi\) | |||||||
\(468\) | −6.27028 | −0.289844 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.23864 | −0.149387 | ||||||||
\(471\) | 5.78121 | 0.266384 | ||||||||
\(472\) | −3.56536 | −0.164109 | ||||||||
\(473\) | 12.0964 | 0.556194 | ||||||||
\(474\) | 10.9756 | 0.504126 | ||||||||
\(475\) | −6.12006 | −0.280808 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.30090 | −0.105351 | ||||||||
\(478\) | 10.7991 | 0.493941 | ||||||||
\(479\) | 0.0182962 | 0.000835976 0 | 0.000417988 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000417988 | 1.00000i | \(0.499867\pi\) | ||||||||
\(480\) | −2.42407 | −0.110643 | ||||||||
\(481\) | −10.9283 | −0.498289 | ||||||||
\(482\) | 18.1842 | 0.828268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.05202 | 0.229637 | ||||||||
\(485\) | −3.27187 | −0.148568 | ||||||||
\(486\) | −0.712717 | −0.0323295 | ||||||||
\(487\) | 26.5955 | 1.20516 | 0.602579 | − | 0.798059i | \(-0.294140\pi\) | ||||
0.602579 | + | 0.798059i | \(0.294140\pi\) | |||||||
\(488\) | −30.5566 | −1.38323 | ||||||||
\(489\) | 0.157705 | 0.00713168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.4915 | −1.19555 | −0.597773 | − | 0.801665i | \(-0.703948\pi\) | ||||
−0.597773 | + | 0.801665i | \(0.703948\pi\) | |||||||
\(492\) | 1.49203 | 0.0672661 | ||||||||
\(493\) | 23.8517 | 1.07423 | ||||||||
\(494\) | 3.79698 | 0.170834 | ||||||||
\(495\) | 1.14531 | 0.0514779 | ||||||||
\(496\) | 10.7273 | 0.481669 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.88188 | 0.129140 | ||||||||
\(499\) | −2.14122 | −0.0958541 | −0.0479270 | − | 0.998851i | \(-0.515261\pi\) | ||||
−0.0479270 | + | 0.998851i | \(0.515261\pi\) | |||||||
\(500\) | 6.08623 | 0.272185 | ||||||||
\(501\) | −22.1528 | −0.989715 | ||||||||
\(502\) | 6.71299 | 0.299616 | ||||||||
\(503\) | −14.0491 | −0.626417 | −0.313209 | − | 0.949684i | \(-0.601404\pi\) | ||||
−0.313209 | + | 0.949684i | \(0.601404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.48203 | −0.154948 | ||||||||
\(506\) | 8.90908 | 0.396057 | ||||||||
\(507\) | −4.66102 | −0.207003 | ||||||||
\(508\) | −25.4433 | −1.12886 | ||||||||
\(509\) | 8.88531 | 0.393834 | 0.196917 | − | 0.980420i | \(-0.436907\pi\) | ||||
0.196917 | + | 0.980420i | \(0.436907\pi\) | |||||||
\(510\) | 1.29989 | 0.0575600 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.0922 | 0.578599 | ||||||||
\(513\) | −1.26769 | −0.0559699 | ||||||||
\(514\) | 0.764466 | 0.0337192 | ||||||||
\(515\) | 7.17653 | 0.316236 | ||||||||
\(516\) | 6.54077 | 0.287941 | ||||||||
\(517\) | −30.2089 | −1.32859 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.2812 | −0.802455 | ||||||||
\(520\) | −4.34131 | −0.190379 | ||||||||
\(521\) | −12.9008 | −0.565194 | −0.282597 | − | 0.959239i | \(-0.591196\pi\) | ||||
−0.282597 | + | 0.959239i | \(0.591196\pi\) | |||||||
\(522\) | −3.86869 | −0.169328 | ||||||||
\(523\) | 8.93640 | 0.390762 | 0.195381 | − | 0.980727i | \(-0.437406\pi\) | ||||
0.195381 | + | 0.980727i | \(0.437406\pi\) | |||||||
\(524\) | −33.1481 | −1.44808 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7268 | 0.816527 | ||||||||
\(527\) | −38.9486 | −1.69663 | ||||||||
\(528\) | −3.33946 | −0.145332 | ||||||||
\(529\) | −2.47809 | −0.107743 | ||||||||
\(530\) | −0.680663 | −0.0295661 | ||||||||
\(531\) | 1.43254 | 0.0621671 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.20250 | 0.182031 | ||||||||
\(534\) | 0.733010 | 0.0317205 | ||||||||
\(535\) | −3.97834 | −0.171999 | ||||||||
\(536\) | 2.75350 | 0.118933 | ||||||||
\(537\) | 19.7583 | 0.852633 | ||||||||
\(538\) | 14.1687 | 0.610858 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.619292 | 0.0266501 | ||||||||
\(541\) | 30.4024 | 1.30710 | 0.653550 | − | 0.756884i | \(-0.273279\pi\) | ||||
0.653550 | + | 0.756884i | \(0.273279\pi\) | |||||||
\(542\) | −10.8184 | −0.464689 | ||||||||
\(543\) | −13.0870 | −0.561616 | ||||||||
\(544\) | −25.6626 | −1.10028 | ||||||||
\(545\) | −0.255952 | −0.0109638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.5850 | −1.39323 | −0.696617 | − | 0.717443i | \(-0.745312\pi\) | ||||
−0.696617 | + | 0.717443i | \(0.745312\pi\) | |||||||
\(548\) | −12.0177 | −0.513369 | ||||||||
\(549\) | 12.2775 | 0.523990 | ||||||||
\(550\) | −9.49436 | −0.404841 | ||||||||
\(551\) | −6.88114 | −0.293146 | ||||||||
\(552\) | 11.2747 | 0.479883 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.5534 | 0.448370 | ||||||||
\(555\) | 1.07935 | 0.0458159 | ||||||||
\(556\) | −33.5020 | −1.42080 | ||||||||
\(557\) | −16.0876 | −0.681654 | −0.340827 | − | 0.940126i | \(-0.610707\pi\) | ||||
−0.340827 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(558\) | 6.31737 | 0.267436 | ||||||||
\(559\) | 18.4229 | 0.779206 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1249 | 0.511914 | ||||||||
\(562\) | 8.92977 | 0.376680 | ||||||||
\(563\) | −33.1478 | −1.39701 | −0.698507 | − | 0.715603i | \(-0.746152\pi\) | ||||
−0.698507 | + | 0.715603i | \(0.746152\pi\) | |||||||
\(564\) | −16.3345 | −0.687809 | ||||||||
\(565\) | 6.13651 | 0.258165 | ||||||||
\(566\) | 0.203895 | 0.00857035 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.05916 | −0.296196 | ||||||||
\(569\) | 19.8175 | 0.830791 | 0.415396 | − | 0.909641i | \(-0.363643\pi\) | ||||
0.415396 | + | 0.909641i | \(0.363643\pi\) | |||||||
\(570\) | −0.375014 | −0.0157076 | ||||||||
\(571\) | 29.5390 | 1.23617 | 0.618085 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618085 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(572\) | −17.3019 | −0.723428 | ||||||||
\(573\) | 22.8221 | 0.953407 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.8701 | −0.912047 | ||||||||
\(576\) | 1.74195 | 0.0725813 | ||||||||
\(577\) | 32.6770 | 1.36036 | 0.680181 | − | 0.733044i | \(-0.261901\pi\) | ||||
0.680181 | + | 0.733044i | \(0.261901\pi\) | |||||||
\(578\) | 1.64516 | 0.0684298 | ||||||||
\(579\) | −13.0794 | −0.543559 | ||||||||
\(580\) | 3.36157 | 0.139582 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.61819 | 0.232881 | ||||||||
\(583\) | −6.34900 | −0.262949 | ||||||||
\(584\) | −9.73811 | −0.402966 | ||||||||
\(585\) | 1.74431 | 0.0721185 | ||||||||
\(586\) | 11.4836 | 0.474384 | ||||||||
\(587\) | −40.6133 | −1.67629 | −0.838146 | − | 0.545447i | \(-0.816360\pi\) | ||||
−0.838146 | + | 0.545447i | \(0.816360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2366 | 0.462994 | ||||||||
\(590\) | 0.423781 | 0.0174468 | ||||||||
\(591\) | 0.844299 | 0.0347298 | ||||||||
\(592\) | −3.14714 | −0.129347 | ||||||||
\(593\) | 11.9727 | 0.491660 | 0.245830 | − | 0.969313i | \(-0.420940\pi\) | ||||
0.245830 | + | 0.969313i | \(0.420940\pi\) | |||||||
\(594\) | −1.96663 | −0.0806920 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.60203 | 0.311391 | ||||||||
\(597\) | −8.12795 | −0.332655 | ||||||||
\(598\) | 13.5686 | 0.554860 | ||||||||
\(599\) | −6.16091 | −0.251728 | −0.125864 | − | 0.992048i | \(-0.540170\pi\) | ||||
−0.125864 | + | 0.992048i | \(0.540170\pi\) | |||||||
\(600\) | −12.0154 | −0.490526 | ||||||||
\(601\) | −33.4325 | −1.36374 | −0.681871 | − | 0.731473i | \(-0.738833\pi\) | ||||
−0.681871 | + | 0.731473i | \(0.738833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.10634 | −0.0450537 | ||||||||
\(604\) | 26.3344 | 1.07153 | ||||||||
\(605\) | −1.40541 | −0.0571380 | ||||||||
\(606\) | 5.97905 | 0.242882 | ||||||||
\(607\) | −39.8822 | −1.61877 | −0.809385 | − | 0.587279i | \(-0.800199\pi\) | ||||
−0.809385 | + | 0.587279i | \(0.800199\pi\) | |||||||
\(608\) | 7.40360 | 0.300256 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.63198 | 0.147055 | ||||||||
\(611\) | −46.0083 | −1.86130 | ||||||||
\(612\) | 6.55618 | 0.265018 | ||||||||
\(613\) | 9.30534 | 0.375839 | 0.187920 | − | 0.982184i | \(-0.439826\pi\) | ||||
0.187920 | + | 0.982184i | \(0.439826\pi\) | |||||||
\(614\) | −6.29306 | −0.253967 | ||||||||
\(615\) | −0.415066 | −0.0167371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.3926 | 1.42485 | 0.712426 | − | 0.701747i | \(-0.247596\pi\) | ||||
0.712426 | + | 0.701747i | \(0.247596\pi\) | |||||||
\(618\) | −12.3230 | −0.495702 | ||||||||
\(619\) | −5.72703 | −0.230189 | −0.115094 | − | 0.993355i | \(-0.536717\pi\) | ||||
−0.115094 | + | 0.993355i | \(0.536717\pi\) | |||||||
\(620\) | −5.48928 | −0.220455 | ||||||||
\(621\) | −4.53011 | −0.181787 | ||||||||
\(622\) | 4.77581 | 0.191493 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.08602 | −0.203604 | ||||||||
\(625\) | 22.4455 | 0.897820 | ||||||||
\(626\) | 1.67316 | 0.0668729 | ||||||||
\(627\) | −3.49800 | −0.139697 | ||||||||
\(628\) | 8.62576 | 0.344205 | ||||||||
\(629\) | 11.4266 | 0.455609 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.10310 | 0.0837233 | 0.0418616 | − | 0.999123i | \(-0.486671\pi\) | ||||
0.0418616 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(632\) | 38.3272 | 1.52457 | ||||||||
\(633\) | −11.6549 | −0.463241 | ||||||||
\(634\) | 16.3031 | 0.647481 | ||||||||
\(635\) | 7.07802 | 0.280882 | ||||||||
\(636\) | −3.43303 | −0.136128 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.6751 | −0.422630 | ||||||||
\(639\) | 2.83634 | 0.112204 | ||||||||
\(640\) | −4.33284 | −0.171270 | ||||||||
\(641\) | −7.39557 | −0.292107 | −0.146054 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146054 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(642\) | 6.83128 | 0.269609 | ||||||||
\(643\) | 13.9177 | 0.548861 | 0.274431 | − | 0.961607i | \(-0.411511\pi\) | ||||
0.274431 | + | 0.961607i | \(0.411511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.81956 | −0.0716452 | ||||||||
\(646\) | −3.97011 | −0.156202 | ||||||||
\(647\) | 22.1622 | 0.871287 | 0.435643 | − | 0.900119i | \(-0.356521\pi\) | ||||
0.435643 | + | 0.900119i | \(0.356521\pi\) | |||||||
\(648\) | −2.48883 | −0.0977706 | ||||||||
\(649\) | 3.95289 | 0.155164 | ||||||||
\(650\) | −14.4600 | −0.567166 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.235302 | 0.00921512 | ||||||||
\(653\) | −9.10805 | −0.356425 | −0.178213 | − | 0.983992i | \(-0.557032\pi\) | ||||
−0.178213 | + | 0.983992i | \(0.557032\pi\) | |||||||
\(654\) | 0.439500 | 0.0171858 | ||||||||
\(655\) | 9.22138 | 0.360309 | ||||||||
\(656\) | 1.21024 | 0.0472518 | ||||||||
\(657\) | 3.91272 | 0.152650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.1797 | −0.591318 | −0.295659 | − | 0.955294i | \(-0.595539\pi\) | ||||
−0.295659 | + | 0.955294i | \(0.595539\pi\) | |||||||
\(660\) | 1.70884 | 0.0665167 | ||||||||
\(661\) | −19.9463 | −0.775823 | −0.387911 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387911 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(662\) | −7.57529 | −0.294422 | ||||||||
\(663\) | 18.4663 | 0.717172 | ||||||||
\(664\) | 10.0636 | 0.390544 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.85337 | −0.0718167 | ||||||||
\(667\) | −24.5898 | −0.952123 | ||||||||
\(668\) | −33.0528 | −1.27885 | ||||||||
\(669\) | −11.7288 | −0.453460 | ||||||||
\(670\) | −0.327283 | −0.0126440 | ||||||||
\(671\) | 33.8779 | 1.30784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.3373 | 0.938136 | 0.469068 | − | 0.883162i | \(-0.344590\pi\) | ||||
0.469068 | + | 0.883162i | \(0.344590\pi\) | |||||||
\(674\) | −11.4517 | −0.441102 | ||||||||
\(675\) | 4.82772 | 0.185819 | ||||||||
\(676\) | −6.95441 | −0.267477 | ||||||||
\(677\) | −16.7296 | −0.642971 | −0.321485 | − | 0.946915i | \(-0.604182\pi\) | ||||
−0.321485 | + | 0.946915i | \(0.604182\pi\) | |||||||
\(678\) | −10.5371 | −0.404676 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.53925 | 0.174072 | ||||||||
\(681\) | 1.94495 | 0.0745307 | ||||||||
\(682\) | 17.4318 | 0.667500 | ||||||||
\(683\) | −13.7682 | −0.526827 | −0.263413 | − | 0.964683i | \(-0.584848\pi\) | ||||
−0.263413 | + | 0.964683i | \(0.584848\pi\) | |||||||
\(684\) | −1.89144 | −0.0723210 | ||||||||
\(685\) | 3.34317 | 0.127736 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.2389 | −0.428790 | ||||||||
\(688\) | 5.30543 | 0.202268 | ||||||||
\(689\) | −9.66955 | −0.368381 | ||||||||
\(690\) | −1.34012 | −0.0510174 | ||||||||
\(691\) | 14.5283 | 0.552684 | 0.276342 | − | 0.961059i | \(-0.410878\pi\) | ||||
0.276342 | + | 0.961059i | \(0.410878\pi\) | |||||||
\(692\) | −27.2762 | −1.03688 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3712 | 0.849199 | ||||||||
\(695\) | 9.31983 | 0.353521 | ||||||||
\(696\) | −13.5096 | −0.512080 | ||||||||
\(697\) | −4.39412 | −0.166439 | ||||||||
\(698\) | −17.2219 | −0.651860 | ||||||||
\(699\) | −13.3117 | −0.503495 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.6703 | 1.57386 | 0.786932 | − | 0.617040i | \(-0.211668\pi\) | ||||
0.786932 | + | 0.617040i | \(0.211668\pi\) | |||||||
\(702\) | −2.99519 | −0.113046 | ||||||||
\(703\) | −3.29655 | −0.124332 | ||||||||
\(704\) | 4.80665 | 0.181158 | ||||||||
\(705\) | 4.54407 | 0.171140 | ||||||||
\(706\) | −18.6976 | −0.703692 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.13740 | 0.0803285 | ||||||||
\(709\) | 9.18522 | 0.344958 | 0.172479 | − | 0.985013i | \(-0.444822\pi\) | ||||
0.172479 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(710\) | 0.839057 | 0.0314892 | ||||||||
\(711\) | −15.3997 | −0.577532 | ||||||||
\(712\) | 2.55970 | 0.0959287 | ||||||||
\(713\) | 40.1540 | 1.50378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.81317 | 0.180002 | ||||||||
\(716\) | 29.4800 | 1.10172 | ||||||||
\(717\) | −15.1521 | −0.565864 | ||||||||
\(718\) | 14.7990 | 0.552292 | ||||||||
\(719\) | −9.93068 | −0.370352 | −0.185176 | − | 0.982705i | \(-0.559286\pi\) | ||||
−0.185176 | + | 0.982705i | \(0.559286\pi\) | |||||||
\(720\) | 0.502327 | 0.0187206 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.3963 | −0.461341 | ||||||||
\(723\) | −25.5139 | −0.948874 | ||||||||
\(724\) | −19.5262 | −0.725687 | ||||||||
\(725\) | 26.2053 | 0.973240 | ||||||||
\(726\) | 2.41325 | 0.0895643 | ||||||||
\(727\) | −34.7960 | −1.29051 | −0.645256 | − | 0.763966i | \(-0.723249\pi\) | ||||
−0.645256 | + | 0.763966i | \(0.723249\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.15748 | 0.0428402 | ||||||||
\(731\) | −19.2629 | −0.712465 | ||||||||
\(732\) | 18.3184 | 0.677069 | ||||||||
\(733\) | 3.15245 | 0.116438 | 0.0582192 | − | 0.998304i | \(-0.481458\pi\) | ||||
0.0582192 | + | 0.998304i | \(0.481458\pi\) | |||||||
\(734\) | 18.1740 | 0.670814 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.4569 | 0.975212 | ||||||||
\(737\) | −3.05278 | −0.112451 | ||||||||
\(738\) | 0.712717 | 0.0262355 | ||||||||
\(739\) | 46.0474 | 1.69388 | 0.846941 | − | 0.531686i | \(-0.178441\pi\) | ||||
0.846941 | + | 0.531686i | \(0.178441\pi\) | |||||||
\(740\) | 1.61043 | 0.0592005 | ||||||||
\(741\) | −5.32748 | −0.195710 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.9816 | 1.32004 | 0.660019 | − | 0.751249i | \(-0.270548\pi\) | ||||
0.660019 | + | 0.751249i | \(0.270548\pi\) | |||||||
\(744\) | 22.0605 | 0.808777 | ||||||||
\(745\) | −2.11479 | −0.0774799 | ||||||||
\(746\) | −17.7205 | −0.648792 | ||||||||
\(747\) | −4.04351 | −0.147944 | ||||||||
\(748\) | 18.0908 | 0.661465 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.90728 | 0.106159 | ||||||||
\(751\) | −29.6433 | −1.08170 | −0.540850 | − | 0.841119i | \(-0.681897\pi\) | ||||
−0.540850 | + | 0.841119i | \(0.681897\pi\) | |||||||
\(752\) | −13.2495 | −0.483158 | ||||||||
\(753\) | −9.41888 | −0.343243 | ||||||||
\(754\) | −16.2582 | −0.592088 | ||||||||
\(755\) | −7.32590 | −0.266617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7775 | 0.609790 | 0.304895 | − | 0.952386i | \(-0.401379\pi\) | ||||
0.304895 | + | 0.952386i | \(0.401379\pi\) | |||||||
\(758\) | 11.2567 | 0.408861 | ||||||||
\(759\) | −12.5002 | −0.453727 | ||||||||
\(760\) | −1.30956 | −0.0475028 | ||||||||
\(761\) | −23.0227 | −0.834574 | −0.417287 | − | 0.908775i | \(-0.637019\pi\) | ||||
−0.417287 | + | 0.908775i | \(0.637019\pi\) | |||||||
\(762\) | −12.1538 | −0.440285 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 34.0514 | 1.23194 | ||||||||
\(765\) | −1.82385 | −0.0659414 | ||||||||
\(766\) | 9.72971 | 0.351549 | ||||||||
\(767\) | 6.02026 | 0.217379 | ||||||||
\(768\) | 10.9239 | 0.394182 | ||||||||
\(769\) | 6.17449 | 0.222658 | 0.111329 | − | 0.993784i | \(-0.464489\pi\) | ||||
0.111329 | + | 0.993784i | \(0.464489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.07261 | −0.0386291 | ||||||||
\(772\) | −19.5148 | −0.702355 | ||||||||
\(773\) | 37.5482 | 1.35051 | 0.675257 | − | 0.737583i | \(-0.264033\pi\) | ||||
0.675257 | + | 0.737583i | \(0.264033\pi\) | |||||||
\(774\) | 3.12440 | 0.112304 | ||||||||
\(775\) | −42.7919 | −1.53713 | ||||||||
\(776\) | 19.6189 | 0.704278 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.3195 | −0.405825 | ||||||||
\(779\) | 1.26769 | 0.0454198 | ||||||||
\(780\) | 2.60258 | 0.0931872 | ||||||||
\(781\) | 7.82644 | 0.280052 | ||||||||
\(782\) | −14.1872 | −0.507335 | ||||||||
\(783\) | 5.42809 | 0.193984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.39958 | −0.0856447 | ||||||||
\(786\) | −15.8342 | −0.564787 | ||||||||
\(787\) | 37.2802 | 1.32890 | 0.664448 | − | 0.747335i | \(-0.268667\pi\) | ||||
0.664448 | + | 0.747335i | \(0.268667\pi\) | |||||||
\(788\) | 1.25972 | 0.0448758 | ||||||||
\(789\) | −26.2752 | −0.935422 | ||||||||
\(790\) | −4.55559 | −0.162081 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.86756 | −0.244028 | ||||||||
\(793\) | 51.5962 | 1.83223 | ||||||||
\(794\) | −0.361114 | −0.0128155 | ||||||||
\(795\) | 0.955026 | 0.0338713 | ||||||||
\(796\) | −12.1272 | −0.429837 | ||||||||
\(797\) | 22.0377 | 0.780617 | 0.390308 | − | 0.920684i | \(-0.372368\pi\) | ||||
0.390308 | + | 0.920684i | \(0.372368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.1061 | 1.70187 | ||||||||
\(800\) | −28.1950 | −0.996842 | ||||||||
\(801\) | −1.02847 | −0.0363393 | ||||||||
\(802\) | −8.47280 | −0.299185 | ||||||||
\(803\) | 10.7966 | 0.381003 | ||||||||
\(804\) | −1.65070 | −0.0582157 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.5488 | 0.935141 | ||||||||
\(807\) | −19.8799 | −0.699806 | ||||||||
\(808\) | 20.8790 | 0.734522 | ||||||||
\(809\) | 34.8178 | 1.22413 | 0.612065 | − | 0.790807i | \(-0.290339\pi\) | ||||
0.612065 | + | 0.790807i | \(0.290339\pi\) | |||||||
\(810\) | 0.295824 | 0.0103942 | ||||||||
\(811\) | −9.01482 | −0.316553 | −0.158277 | − | 0.987395i | \(-0.550594\pi\) | ||||
−0.158277 | + | 0.987395i | \(0.550594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.1791 | 0.532353 | ||||||||
\(814\) | −5.11410 | −0.179249 | ||||||||
\(815\) | −0.0654580 | −0.00229289 | ||||||||
\(816\) | 5.31792 | 0.186165 | ||||||||
\(817\) | 5.55730 | 0.194425 | ||||||||
\(818\) | 19.5843 | 0.684749 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.619292 | −0.0216266 | ||||||||
\(821\) | −15.2878 | −0.533547 | −0.266774 | − | 0.963759i | \(-0.585958\pi\) | ||||
−0.266774 | + | 0.963759i | \(0.585958\pi\) | |||||||
\(822\) | −5.74062 | −0.200227 | ||||||||
\(823\) | −32.2809 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(824\) | −43.0322 | −1.49910 | ||||||||
\(825\) | 13.3214 | 0.463790 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.5227 | −1.44389 | −0.721943 | − | 0.691952i | \(-0.756751\pi\) | ||||
−0.721943 | + | 0.691952i | \(0.756751\pi\) | |||||||
\(828\) | −6.75908 | −0.234894 | ||||||||
\(829\) | 5.55425 | 0.192907 | 0.0964535 | − | 0.995337i | \(-0.469250\pi\) | ||||
0.0964535 | + | 0.995337i | \(0.469250\pi\) | |||||||
\(830\) | −1.19617 | −0.0415196 | ||||||||
\(831\) | −14.8072 | −0.513657 | ||||||||
\(832\) | 7.32056 | 0.253795 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.0033 | −0.554148 | ||||||||
\(835\) | 9.19487 | 0.318202 | ||||||||
\(836\) | −5.21914 | −0.180508 | ||||||||
\(837\) | −8.86379 | −0.306377 | ||||||||
\(838\) | −2.83601 | −0.0979684 | ||||||||
\(839\) | −40.4477 | −1.39641 | −0.698204 | − | 0.715899i | \(-0.746017\pi\) | ||||
−0.698204 | + | 0.715899i | \(0.746017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.464135 | 0.0160046 | ||||||||
\(842\) | −7.51476 | −0.258976 | ||||||||
\(843\) | −12.5292 | −0.431528 | ||||||||
\(844\) | −17.3895 | −0.598572 | ||||||||
\(845\) | 1.93463 | 0.0665533 | ||||||||
\(846\) | −7.80271 | −0.268263 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.78464 | −0.0956248 | ||||||||
\(849\) | −0.286081 | −0.00981829 | ||||||||
\(850\) | 15.1193 | 0.518587 | ||||||||
\(851\) | −11.7802 | −0.403822 | ||||||||
\(852\) | 4.23191 | 0.144983 | ||||||||
\(853\) | 16.5141 | 0.565431 | 0.282715 | − | 0.959204i | \(-0.408765\pi\) | ||||
0.282715 | + | 0.959204i | \(0.408765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.526175 | 0.0179948 | ||||||||
\(856\) | 23.8551 | 0.815350 | ||||||||
\(857\) | 14.7078 | 0.502410 | 0.251205 | − | 0.967934i | \(-0.419173\pi\) | ||||
0.251205 | + | 0.967934i | \(0.419173\pi\) | |||||||
\(858\) | −8.26479 | −0.282155 | ||||||||
\(859\) | 42.3688 | 1.44561 | 0.722803 | − | 0.691055i | \(-0.242854\pi\) | ||||
0.722803 | + | 0.691055i | \(0.242854\pi\) | |||||||
\(860\) | −2.71485 | −0.0925756 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.4833 | −0.357062 | ||||||||
\(863\) | −57.6490 | −1.96239 | −0.981197 | − | 0.193009i | \(-0.938175\pi\) | ||||
−0.981197 | + | 0.193009i | \(0.938175\pi\) | |||||||
\(864\) | −5.84022 | −0.198688 | ||||||||
\(865\) | 7.58790 | 0.257996 | ||||||||
\(866\) | 2.99643 | 0.101823 | ||||||||
\(867\) | −2.30830 | −0.0783939 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.4930 | −1.44148 | ||||||||
\(870\) | 1.60576 | 0.0544404 | ||||||||
\(871\) | −4.64940 | −0.157539 | ||||||||
\(872\) | 1.53475 | 0.0519732 | ||||||||
\(873\) | −7.88278 | −0.266792 | ||||||||
\(874\) | 4.09298 | 0.138447 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.83792 | 0.197245 | ||||||||
\(877\) | −40.9161 | −1.38164 | −0.690819 | − | 0.723028i | \(-0.742750\pi\) | ||||
−0.690819 | + | 0.723028i | \(0.742750\pi\) | |||||||
\(878\) | −6.74757 | −0.227719 | ||||||||
\(879\) | −16.1124 | −0.543459 | ||||||||
\(880\) | 1.38610 | 0.0467253 | ||||||||
\(881\) | 4.58413 | 0.154443 | 0.0772216 | − | 0.997014i | \(-0.475395\pi\) | ||||
0.0772216 | + | 0.997014i | \(0.475395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.8738 | −1.30821 | −0.654104 | − | 0.756404i | \(-0.726954\pi\) | ||||
−0.654104 | + | 0.756404i | \(0.726954\pi\) | |||||||
\(884\) | 27.5524 | 0.926686 | ||||||||
\(885\) | −0.594599 | −0.0199872 | ||||||||
\(886\) | −10.3920 | −0.349125 | ||||||||
\(887\) | −8.32382 | −0.279487 | −0.139743 | − | 0.990188i | \(-0.544628\pi\) | ||||
−0.139743 | + | 0.990188i | \(0.544628\pi\) | |||||||
\(888\) | −6.47204 | −0.217187 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.304247 | −0.0101984 | ||||||||
\(891\) | 2.75935 | 0.0924417 | ||||||||
\(892\) | −17.4997 | −0.585934 | ||||||||
\(893\) | −13.8785 | −0.464426 | ||||||||
\(894\) | 3.63135 | 0.121450 | ||||||||
\(895\) | −8.20098 | −0.274129 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.0378 | −0.635654 | ||||||||
\(898\) | 14.2801 | 0.476534 | ||||||||
\(899\) | −48.1134 | −1.60467 | ||||||||
\(900\) | 7.20313 | 0.240104 | ||||||||
\(901\) | 10.1104 | 0.336828 | ||||||||
\(902\) | 1.96663 | 0.0654818 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.7960 | −1.22382 | ||||||||
\(905\) | 5.43196 | 0.180564 | ||||||||
\(906\) | 12.5794 | 0.417924 | ||||||||
\(907\) | 28.0918 | 0.932772 | 0.466386 | − | 0.884581i | \(-0.345556\pi\) | ||||
0.466386 | + | 0.884581i | \(0.345556\pi\) | |||||||
\(908\) | 2.90194 | 0.0963041 | ||||||||
\(909\) | −8.38909 | −0.278249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.7190 | −1.84605 | −0.923027 | − | 0.384736i | \(-0.874292\pi\) | ||||
−0.923027 | + | 0.384736i | \(0.874292\pi\) | |||||||
\(912\) | −1.53421 | −0.0508026 | ||||||||
\(913\) | −11.1575 | −0.369258 | ||||||||
\(914\) | 19.6539 | 0.650092 | ||||||||
\(915\) | −5.09596 | −0.168467 | ||||||||
\(916\) | −16.7688 | −0.554057 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.13176 | 0.103364 | ||||||||
\(919\) | −12.6642 | −0.417752 | −0.208876 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208876 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(920\) | −4.67974 | −0.154286 | ||||||||
\(921\) | 8.82967 | 0.290948 | ||||||||
\(922\) | −19.9345 | −0.656508 | ||||||||
\(923\) | 11.9197 | 0.392342 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5542 | 0.412778 | ||||||||
\(926\) | 6.38813 | 0.209927 | ||||||||
\(927\) | 17.2901 | 0.567882 | ||||||||
\(928\) | −31.7012 | −1.04064 | ||||||||
\(929\) | 38.2432 | 1.25472 | 0.627359 | − | 0.778730i | \(-0.284136\pi\) | ||||
0.627359 | + | 0.778730i | \(0.284136\pi\) | |||||||
\(930\) | −2.62213 | −0.0859829 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.8615 | −0.650586 | ||||||||
\(933\) | −6.70085 | −0.219376 | ||||||||
\(934\) | −14.7388 | −0.482268 | ||||||||
\(935\) | −5.03264 | −0.164585 | ||||||||
\(936\) | −10.4593 | −0.341874 | ||||||||
\(937\) | 49.0781 | 1.60331 | 0.801656 | − | 0.597785i | \(-0.203952\pi\) | ||||
0.801656 | + | 0.597785i | \(0.203952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.34758 | −0.0766103 | ||||||||
\(940\) | 6.77991 | 0.221136 | ||||||||
\(941\) | 31.8341 | 1.03776 | 0.518882 | − | 0.854846i | \(-0.326349\pi\) | ||||
0.518882 | + | 0.854846i | \(0.326349\pi\) | |||||||
\(942\) | 4.12037 | 0.134249 | ||||||||
\(943\) | 4.53011 | 0.147521 | ||||||||
\(944\) | 1.73372 | 0.0564276 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.62132 | 0.280303 | ||||||||
\(947\) | 33.8537 | 1.10010 | 0.550049 | − | 0.835132i | \(-0.314609\pi\) | ||||
0.550049 | + | 0.835132i | \(0.314609\pi\) | |||||||
\(948\) | −22.9768 | −0.746252 | ||||||||
\(949\) | 16.4432 | 0.533770 | ||||||||
\(950\) | −4.36187 | −0.141518 | ||||||||
\(951\) | −22.8746 | −0.741761 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.1049 | −1.33152 | −0.665759 | − | 0.746167i | \(-0.731892\pi\) | ||||
−0.665759 | + | 0.746167i | \(0.731892\pi\) | |||||||
\(954\) | −1.63989 | −0.0530935 | ||||||||
\(955\) | −9.47267 | −0.306528 | ||||||||
\(956\) | −22.6074 | −0.731176 | ||||||||
\(957\) | 14.9780 | 0.484170 | ||||||||
\(958\) | 0.0130400 | 0.000421304 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.723024 | −0.0233355 | ||||||||
\(961\) | 47.5668 | 1.53441 | ||||||||
\(962\) | −7.78880 | −0.251121 | ||||||||
\(963\) | −9.58485 | −0.308867 | ||||||||
\(964\) | −38.0677 | −1.22608 | ||||||||
\(965\) | 5.42879 | 0.174759 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3207 | 1.42526 | 0.712628 | − | 0.701542i | \(-0.247505\pi\) | ||||
0.712628 | + | 0.701542i | \(0.247505\pi\) | |||||||
\(968\) | 8.42717 | 0.270859 | ||||||||
\(969\) | 5.57039 | 0.178947 | ||||||||
\(970\) | −2.33192 | −0.0748733 | ||||||||
\(971\) | 24.4418 | 0.784374 | 0.392187 | − | 0.919885i | \(-0.371719\pi\) | ||||
0.392187 | + | 0.919885i | \(0.371719\pi\) | |||||||
\(972\) | 1.49203 | 0.0478570 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.9551 | 0.607360 | ||||||||
\(975\) | 20.2885 | 0.649752 | ||||||||
\(976\) | 14.8587 | 0.475614 | ||||||||
\(977\) | 15.7803 | 0.504857 | 0.252429 | − | 0.967615i | \(-0.418771\pi\) | ||||
0.252429 | + | 0.967615i | \(0.418771\pi\) | |||||||
\(978\) | 0.112399 | 0.00359413 | ||||||||
\(979\) | −2.83792 | −0.0907002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.616655 | −0.0196883 | ||||||||
\(982\) | −18.8810 | −0.602516 | ||||||||
\(983\) | −25.3592 | −0.808832 | −0.404416 | − | 0.914575i | \(-0.632525\pi\) | ||||
−0.404416 | + | 0.914575i | \(0.632525\pi\) | |||||||
\(984\) | 2.48883 | 0.0793411 | ||||||||
\(985\) | −0.350439 | −0.0111659 | ||||||||
\(986\) | 16.9995 | 0.541374 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.94878 | −0.252884 | ||||||||
\(989\) | 19.8591 | 0.631482 | ||||||||
\(990\) | 0.816283 | 0.0259432 | ||||||||
\(991\) | −9.51391 | −0.302219 | −0.151110 | − | 0.988517i | \(-0.548285\pi\) | ||||
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(992\) | 51.7665 | 1.64359 | ||||||||
\(993\) | 10.6287 | 0.337293 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.37363 | 0.106951 | ||||||||
\(996\) | −6.03306 | −0.191165 | ||||||||
\(997\) | 44.0831 | 1.39612 | 0.698062 | − | 0.716037i | \(-0.254046\pi\) | ||||
0.698062 | + | 0.716037i | \(0.254046\pi\) | |||||||
\(998\) | −1.52608 | −0.0483073 | ||||||||
\(999\) | 2.60043 | 0.0822740 |
(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 | 6027.2.a.bj.1.9 | 14 | ||
7.2 | even | 3 | 861.2.i.g.739.6 | yes | 28 | ||
7.4 | even | 3 | 861.2.i.g.247.6 | ✓ | 28 | ||
7.6 | odd | 2 | 6027.2.a.bk.1.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.6 | ✓ | 28 | 7.4 | even | 3 | ||
861.2.i.g.739.6 | yes | 28 | 7.2 | even | 3 | ||
6027.2.a.bj.1.9 | 14 | 1.1 | even | 1 | trivial | ||
6027.2.a.bk.1.9 | 14 | 7.6 | odd | 2 |