Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.44400625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.68704\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.68704 | 1.90003 | 0.950013 | − | 0.312211i | \(-0.101069\pi\) | ||||
0.950013 | + | 0.312211i | \(0.101069\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.22020 | 2.61010 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.68704 | 0.637642 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(8\) | 8.65280 | 3.05923 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.07882 | −0.325276 | −0.162638 | − | 0.986686i | \(-0.552000\pi\) | ||||
−0.162638 | + | 0.986686i | \(0.552000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67723 | 0.742531 | 0.371265 | − | 0.928527i | \(-0.378924\pi\) | ||||
0.371265 | + | 0.928527i | \(0.378924\pi\) | |||||||
\(14\) | 4.53315 | 1.21154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.8101 | 3.20251 | ||||||||
\(17\) | 3.93167 | 0.953570 | 0.476785 | − | 0.879020i | \(-0.341802\pi\) | ||||
0.476785 | + | 0.879020i | \(0.341802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.17755 | −0.270148 | −0.135074 | − | 0.990836i | \(-0.543127\pi\) | ||||
−0.135074 | + | 0.990836i | \(0.543127\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.89883 | −0.618032 | ||||||||
\(23\) | 4.06295 | 0.847183 | 0.423591 | − | 0.905853i | \(-0.360769\pi\) | ||||
0.423591 | + | 0.905853i | \(0.360769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.19384 | 1.41083 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.80669 | 1.66431 | ||||||||
\(29\) | −5.95595 | −1.10599 | −0.552996 | − | 0.833184i | \(-0.686516\pi\) | ||||
−0.552996 | + | 0.833184i | \(0.686516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.10310 | −1.27575 | −0.637877 | − | 0.770138i | \(-0.720187\pi\) | ||||
−0.637877 | + | 0.770138i | \(0.720187\pi\) | |||||||
\(32\) | 17.1155 | 3.02563 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.5646 | 1.81181 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.58187 | −0.753254 | −0.376627 | − | 0.926365i | \(-0.622916\pi\) | ||||
−0.376627 | + | 0.926365i | \(0.622916\pi\) | |||||||
\(38\) | −3.16412 | −0.513287 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2614 | 1.75874 | 0.879371 | − | 0.476137i | \(-0.157963\pi\) | ||||
0.879371 | + | 0.476137i | \(0.157963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.58587 | 0.394342 | 0.197171 | − | 0.980369i | \(-0.436825\pi\) | ||||
0.197171 | + | 0.980369i | \(0.436825\pi\) | |||||||
\(44\) | −5.63164 | −0.849002 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.9173 | 1.60967 | ||||||||
\(47\) | 1.91782 | 0.279743 | 0.139871 | − | 0.990170i | \(-0.455331\pi\) | ||||
0.139871 | + | 0.990170i | \(0.455331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.15389 | −0.593413 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.9757 | 1.93808 | ||||||||
\(53\) | 2.54861 | 0.350078 | 0.175039 | − | 0.984561i | \(-0.443995\pi\) | ||||
0.175039 | + | 0.984561i | \(0.443995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14.5976 | 1.95069 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.0039 | −2.10141 | ||||||||
\(59\) | −1.33599 | −0.173931 | −0.0869654 | − | 0.996211i | \(-0.527717\pi\) | ||||
−0.0869654 | + | 0.996211i | \(0.527717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.28106 | −0.932245 | −0.466122 | − | 0.884720i | \(-0.654349\pi\) | ||||
−0.466122 | + | 0.884720i | \(0.654349\pi\) | |||||||
\(62\) | −19.0863 | −2.42397 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 20.3701 | 2.54626 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4451 | 1.52041 | 0.760203 | − | 0.649686i | \(-0.225100\pi\) | ||||
0.760203 | + | 0.649686i | \(0.225100\pi\) | |||||||
\(68\) | 20.5241 | 2.48891 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.98480 | 0.710266 | 0.355133 | − | 0.934816i | \(-0.384436\pi\) | ||||
0.355133 | + | 0.934816i | \(0.384436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30065 | −0.386312 | −0.193156 | − | 0.981168i | \(-0.561872\pi\) | ||||
−0.193156 | + | 0.981168i | \(0.561872\pi\) | |||||||
\(74\) | −12.3117 | −1.43120 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.14702 | −0.705112 | ||||||||
\(77\) | −1.82001 | −0.207410 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00404 | −0.450490 | −0.225245 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225245 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 30.2600 | 3.34166 | ||||||||
\(83\) | −8.87482 | −0.974138 | −0.487069 | − | 0.873364i | \(-0.661934\pi\) | ||||
−0.487069 | + | 0.873364i | \(0.661934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.94834 | 0.749259 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.33480 | −0.995093 | ||||||||
\(89\) | −15.4436 | −1.63702 | −0.818509 | − | 0.574493i | \(-0.805199\pi\) | ||||
−0.818509 | + | 0.574493i | \(0.805199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.51660 | 0.473469 | ||||||||
\(92\) | 21.2094 | 2.21123 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.15327 | 0.531519 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7682 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(98\) | −11.1617 | −1.12750 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5654 | 1.34981 | 0.674905 | − | 0.737905i | \(-0.264185\pi\) | ||||
0.674905 | + | 0.737905i | \(0.264185\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.36904 | 0.134895 | 0.0674476 | − | 0.997723i | \(-0.478514\pi\) | ||||
0.0674476 | + | 0.997723i | \(0.478514\pi\) | |||||||
\(104\) | 23.1656 | 2.27157 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.84822 | 0.665158 | ||||||||
\(107\) | −11.0115 | −1.06452 | −0.532262 | − | 0.846579i | \(-0.678658\pi\) | ||||
−0.532262 | + | 0.846579i | \(0.678658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.44890 | 0.330344 | 0.165172 | − | 0.986265i | \(-0.447182\pi\) | ||||
0.165172 | + | 0.986265i | \(0.447182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 21.6111 | 2.04206 | ||||||||
\(113\) | −6.05194 | −0.569319 | −0.284660 | − | 0.958629i | \(-0.591881\pi\) | ||||
−0.284660 | + | 0.958629i | \(0.591881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −31.0912 | −2.88675 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.58986 | −0.330473 | ||||||||
\(119\) | 6.63289 | 0.608036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.83615 | −0.894196 | ||||||||
\(122\) | −19.5645 | −1.77129 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −37.0796 | −3.32984 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.2362 | −1.79567 | −0.897835 | − | 0.440332i | \(-0.854861\pi\) | ||||
−0.897835 | + | 0.440332i | \(0.854861\pi\) | |||||||
\(128\) | 20.5042 | 1.81233 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.05011 | 0.266490 | 0.133245 | − | 0.991083i | \(-0.457460\pi\) | ||||
0.133245 | + | 0.991083i | \(0.457460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.98657 | −0.172257 | ||||||||
\(134\) | 33.4404 | 2.88881 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34.0200 | 2.91719 | ||||||||
\(137\) | 20.5100 | 1.75229 | 0.876145 | − | 0.482048i | \(-0.160107\pi\) | ||||
0.876145 | + | 0.482048i | \(0.160107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3184 | 1.55374 | 0.776871 | − | 0.629659i | \(-0.216806\pi\) | ||||
0.776871 | + | 0.629659i | \(0.216806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.0814 | 1.34952 | ||||||||
\(143\) | −2.88825 | −0.241527 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.86899 | −0.734003 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.9182 | −1.96607 | ||||||||
\(149\) | −0.705938 | −0.0578327 | −0.0289163 | − | 0.999582i | \(-0.509206\pi\) | ||||
−0.0289163 | + | 0.999582i | \(0.509206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.04538 | 0.573345 | 0.286673 | − | 0.958029i | \(-0.407451\pi\) | ||||
0.286673 | + | 0.958029i | \(0.407451\pi\) | |||||||
\(152\) | −10.1891 | −0.826443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.89045 | −0.394083 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12880 | −0.409323 | −0.204662 | − | 0.978833i | \(-0.565609\pi\) | ||||
−0.204662 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(158\) | −10.7590 | −0.855942 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.85436 | 0.540199 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.2613 | −1.90029 | −0.950146 | − | 0.311806i | \(-0.899066\pi\) | ||||
−0.950146 | + | 0.311806i | \(0.899066\pi\) | |||||||
\(164\) | 58.7869 | 4.59049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23.8470 | −1.85089 | ||||||||
\(167\) | −4.54890 | −0.352004 | −0.176002 | − | 0.984390i | \(-0.556317\pi\) | ||||
−0.176002 | + | 0.984390i | \(0.556317\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83243 | −0.448648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.4988 | 1.02927 | ||||||||
\(173\) | 2.67729 | 0.203550 | 0.101775 | − | 0.994807i | \(-0.467548\pi\) | ||||
0.101775 | + | 0.994807i | \(0.467548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.8197 | −1.04170 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −41.4976 | −3.11038 | ||||||||
\(179\) | 15.6266 | 1.16799 | 0.583995 | − | 0.811757i | \(-0.301489\pi\) | ||||
0.583995 | + | 0.811757i | \(0.301489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.202843 | 0.0150772 | 0.00753859 | − | 0.999972i | \(-0.497600\pi\) | ||||
0.00753859 | + | 0.999972i | \(0.497600\pi\) | |||||||
\(182\) | 12.1363 | 0.899603 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 35.1559 | 2.59172 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.24155 | −0.310173 | ||||||||
\(188\) | 10.0114 | 0.730156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.91975 | 0.573053 | 0.286526 | − | 0.958072i | \(-0.407499\pi\) | ||||
0.286526 | + | 0.958072i | \(0.407499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4269 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(194\) | 28.9346 | 2.07738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.6841 | −1.54887 | ||||||||
\(197\) | 17.1369 | 1.22095 | 0.610475 | − | 0.792035i | \(-0.290978\pi\) | ||||
0.610475 | + | 0.792035i | \(0.290978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.01848 | −0.143086 | −0.0715430 | − | 0.997438i | \(-0.522792\pi\) | ||||
−0.0715430 | + | 0.997438i | \(0.522792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 36.4509 | 2.56467 | ||||||||
\(203\) | −10.0479 | −0.705227 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.67866 | 0.256304 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 34.2955 | 2.37796 | ||||||||
\(209\) | 1.27036 | 0.0878725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8213 | −1.63993 | −0.819963 | − | 0.572416i | \(-0.806006\pi\) | ||||
−0.819963 | + | 0.572416i | \(0.806006\pi\) | |||||||
\(212\) | 13.3042 | 0.913738 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −29.5884 | −2.02262 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9832 | −0.813475 | ||||||||
\(218\) | 9.26733 | 0.627663 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.5260 | 0.708055 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1112 | 0.877989 | 0.438995 | − | 0.898490i | \(-0.355335\pi\) | ||||
0.438995 | + | 0.898490i | \(0.355335\pi\) | |||||||
\(224\) | 28.8746 | 1.92927 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.2618 | −1.08172 | ||||||||
\(227\) | 26.2807 | 1.74431 | 0.872155 | − | 0.489229i | \(-0.162722\pi\) | ||||
0.872155 | + | 0.489229i | \(0.162722\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.99605 | 0.131903 | 0.0659513 | − | 0.997823i | \(-0.478992\pi\) | ||||
0.0659513 | + | 0.997823i | \(0.478992\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −51.5357 | −3.38348 | ||||||||
\(233\) | 0.525548 | 0.0344298 | 0.0172149 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172149 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.97412 | −0.453976 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.8229 | 1.15528 | ||||||||
\(239\) | 7.00971 | 0.453421 | 0.226710 | − | 0.973962i | \(-0.427203\pi\) | ||||
0.226710 | + | 0.973962i | \(0.427203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.31554 | 0.149157 | 0.0745786 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745786 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(242\) | −26.4302 | −1.69899 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −38.0086 | −2.43325 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.15257 | −0.200593 | ||||||||
\(248\) | −61.4617 | −3.90282 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.17885 | 0.390005 | 0.195003 | − | 0.980803i | \(-0.437528\pi\) | ||||
0.195003 | + | 0.980803i | \(0.437528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.38318 | −0.275568 | ||||||||
\(254\) | −54.3755 | −3.41182 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.3555 | 0.897217 | ||||||||
\(257\) | −13.2239 | −0.824882 | −0.412441 | − | 0.910984i | \(-0.635324\pi\) | ||||
−0.412441 | + | 0.910984i | \(0.635324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.72980 | −0.480306 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.19578 | 0.506337 | ||||||||
\(263\) | 6.97643 | 0.430185 | 0.215092 | − | 0.976594i | \(-0.430995\pi\) | ||||
0.215092 | + | 0.976594i | \(0.430995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.33800 | −0.327294 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 64.9656 | 3.96841 | ||||||||
\(269\) | −23.7199 | −1.44623 | −0.723113 | − | 0.690730i | \(-0.757289\pi\) | ||||
−0.723113 | + | 0.690730i | \(0.757289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9910 | 1.76108 | 0.880539 | − | 0.473975i | \(-0.157181\pi\) | ||||
0.880539 | + | 0.473975i | \(0.157181\pi\) | |||||||
\(272\) | 50.3649 | 3.05382 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 55.1113 | 3.32940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.58667 | −0.515923 | −0.257962 | − | 0.966155i | \(-0.583051\pi\) | ||||
−0.257962 | + | 0.966155i | \(0.583051\pi\) | |||||||
\(278\) | 49.2222 | 2.95215 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.1661 | −1.02405 | −0.512023 | − | 0.858972i | \(-0.671104\pi\) | ||||
−0.512023 | + | 0.858972i | \(0.671104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.62005 | −0.571853 | −0.285926 | − | 0.958252i | \(-0.592301\pi\) | ||||
−0.285926 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(284\) | 31.2419 | 1.85386 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.76084 | −0.458908 | ||||||||
\(287\) | 18.9985 | 1.12145 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.54198 | −0.0907048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.2301 | −1.00831 | ||||||||
\(293\) | −16.8202 | −0.982649 | −0.491324 | − | 0.870977i | \(-0.663487\pi\) | ||||
−0.491324 | + | 0.870977i | \(0.663487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.6460 | −2.30438 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.89688 | −0.109884 | ||||||||
\(299\) | 10.8775 | 0.629059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.36247 | 0.251449 | ||||||||
\(302\) | 18.9312 | 1.08937 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.0844 | −0.865151 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3212 | 0.646134 | 0.323067 | − | 0.946376i | \(-0.395286\pi\) | ||||
0.323067 | + | 0.946376i | \(0.395286\pi\) | |||||||
\(308\) | −9.50081 | −0.541359 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5635 | −1.05264 | −0.526318 | − | 0.850288i | \(-0.676428\pi\) | ||||
−0.526318 | + | 0.850288i | \(0.676428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.69951 | −0.548249 | −0.274124 | − | 0.961694i | \(-0.588388\pi\) | ||||
−0.274124 | + | 0.961694i | \(0.588388\pi\) | |||||||
\(314\) | −13.7813 | −0.777724 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.9019 | −1.17582 | ||||||||
\(317\) | −7.47647 | −0.419920 | −0.209960 | − | 0.977710i | \(-0.567333\pi\) | ||||
−0.209960 | + | 0.977710i | \(0.567333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.42538 | 0.359752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.4180 | 1.02639 | ||||||||
\(323\) | −4.62972 | −0.257605 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −65.1911 | −3.61060 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 97.4430 | 5.38039 | ||||||||
\(329\) | 3.23544 | 0.178376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.2570 | −1.38825 | −0.694125 | − | 0.719854i | \(-0.744209\pi\) | ||||
−0.694125 | + | 0.719854i | \(0.744209\pi\) | |||||||
\(332\) | −46.3283 | −2.54259 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2231 | −0.668817 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0240 | −0.709463 | −0.354731 | − | 0.934968i | \(-0.615428\pi\) | ||||
−0.354731 | + | 0.934968i | \(0.615428\pi\) | |||||||
\(338\) | −15.6720 | −0.852443 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.66295 | 0.414972 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8171 | −1.01603 | ||||||||
\(344\) | 22.3750 | 1.20638 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.19398 | 0.386751 | ||||||||
\(347\) | 6.00149 | 0.322177 | 0.161089 | − | 0.986940i | \(-0.448500\pi\) | ||||
0.161089 | + | 0.986940i | \(0.448500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7183 | −1.21608 | −0.608042 | − | 0.793905i | \(-0.708045\pi\) | ||||
−0.608042 | + | 0.793905i | \(0.708045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.4646 | −0.984164 | ||||||||
\(353\) | 4.85493 | 0.258402 | 0.129201 | − | 0.991618i | \(-0.458759\pi\) | ||||
0.129201 | + | 0.991618i | \(0.458759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −80.6186 | −4.27278 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 41.9895 | 2.21921 | ||||||||
\(359\) | −28.8910 | −1.52481 | −0.762403 | − | 0.647102i | \(-0.775981\pi\) | ||||
−0.762403 | + | 0.647102i | \(0.775981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6134 | −0.927020 | ||||||||
\(362\) | 0.545047 | 0.0286470 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.5776 | 1.23580 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7089 | −0.767800 | −0.383900 | − | 0.923375i | \(-0.625419\pi\) | ||||
−0.383900 | + | 0.923375i | \(0.625419\pi\) | |||||||
\(368\) | 52.0465 | 2.71311 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.29961 | 0.223225 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.0391 | −1.71070 | −0.855350 | − | 0.518051i | \(-0.826658\pi\) | ||||
−0.855350 | + | 0.518051i | \(0.826658\pi\) | |||||||
\(374\) | −11.3972 | −0.589337 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.5945 | 0.855797 | ||||||||
\(377\) | −15.9455 | −0.821233 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1556 | −0.778493 | −0.389247 | − | 0.921134i | \(-0.627265\pi\) | ||||
−0.389247 | + | 0.921134i | \(0.627265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.2807 | 1.08882 | ||||||||
\(383\) | 8.00811 | 0.409195 | 0.204598 | − | 0.978846i | \(-0.434411\pi\) | ||||
0.204598 | + | 0.978846i | \(0.434411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −44.1397 | −2.24665 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 56.2121 | 2.85374 | ||||||||
\(389\) | −1.07463 | −0.0544858 | −0.0272429 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272429 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9742 | 0.807848 | ||||||||
\(392\) | −35.9428 | −1.81538 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 46.0475 | 2.31984 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2139 | −1.21526 | −0.607630 | − | 0.794220i | \(-0.707880\pi\) | ||||
−0.607630 | + | 0.794220i | \(0.707880\pi\) | |||||||
\(398\) | −5.42373 | −0.271867 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.99317 | 0.0995340 | 0.0497670 | − | 0.998761i | \(-0.484152\pi\) | ||||
0.0497670 | + | 0.998761i | \(0.484152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0166 | −0.947287 | ||||||||
\(404\) | 70.8142 | 3.52314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.9992 | −1.33995 | ||||||||
\(407\) | 4.94300 | 0.245015 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.66478 | 0.329552 | 0.164776 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164776 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.14664 | 0.352090 | ||||||||
\(413\) | −2.25387 | −0.110906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 45.8223 | 2.24662 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.41351 | 0.166960 | ||||||||
\(419\) | −21.3540 | −1.04321 | −0.521606 | − | 0.853186i | \(-0.674667\pi\) | ||||
−0.521606 | + | 0.853186i | \(0.674667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3367 | 1.08863 | 0.544313 | − | 0.838882i | \(-0.316790\pi\) | ||||
0.544313 | + | 0.838882i | \(0.316790\pi\) | |||||||
\(422\) | −64.0088 | −3.11590 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.0526 | 1.07097 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2835 | −0.594438 | ||||||||
\(428\) | −57.4823 | −2.77851 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4129 | 1.46494 | 0.732469 | − | 0.680800i | \(-0.238368\pi\) | ||||
0.732469 | + | 0.680800i | \(0.238368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.576639 | 0.0277115 | 0.0138558 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138558 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(434\) | −32.1994 | −1.54562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0039 | 0.862231 | ||||||||
\(437\) | −4.78431 | −0.228864 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.8045 | 0.611125 | 0.305563 | − | 0.952172i | \(-0.401155\pi\) | ||||
0.305563 | + | 0.952172i | \(0.401155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.2838 | 1.34532 | ||||||||
\(443\) | −14.3147 | −0.680110 | −0.340055 | − | 0.940405i | \(-0.610446\pi\) | ||||
−0.340055 | + | 0.940405i | \(0.610446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 35.2303 | 1.66820 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 34.3652 | 1.62360 | ||||||||
\(449\) | 11.9663 | 0.564724 | 0.282362 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282362 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1490 | −0.572076 | ||||||||
\(452\) | −31.5923 | −1.48598 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 70.6173 | 3.31424 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.22154 | −0.384587 | −0.192294 | − | 0.981337i | \(-0.561593\pi\) | ||||
−0.192294 | + | 0.981337i | \(0.561593\pi\) | |||||||
\(458\) | 5.36346 | 0.250618 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.27216 | −0.0592505 | −0.0296253 | − | 0.999561i | \(-0.509431\pi\) | ||||
−0.0296253 | + | 0.999561i | \(0.509431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.6764 | 1.51860 | 0.759300 | − | 0.650740i | \(-0.225541\pi\) | ||||
0.759300 | + | 0.650740i | \(0.225541\pi\) | |||||||
\(464\) | −76.2960 | −3.54195 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.41217 | 0.0654175 | ||||||||
\(467\) | −14.4347 | −0.667958 | −0.333979 | − | 0.942581i | \(-0.608391\pi\) | ||||
−0.333979 | + | 0.942581i | \(0.608391\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.9953 | 0.969474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.5600 | −0.532094 | ||||||||
\(473\) | −2.78968 | −0.128270 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 34.6250 | 1.58703 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8354 | 0.861511 | ||||||||
\(479\) | 16.8618 | 0.770436 | 0.385218 | − | 0.922826i | \(-0.374126\pi\) | ||||
0.385218 | + | 0.922826i | \(0.374126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2667 | −0.559314 | ||||||||
\(482\) | 6.22196 | 0.283403 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −51.3466 | −2.33394 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.8235 | 1.80457 | 0.902287 | − | 0.431135i | \(-0.141887\pi\) | ||||
0.902287 | + | 0.431135i | \(0.141887\pi\) | |||||||
\(488\) | −63.0016 | −2.85195 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.0255 | −0.632961 | −0.316480 | − | 0.948599i | \(-0.602501\pi\) | ||||
−0.316480 | + | 0.948599i | \(0.602501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.4168 | −1.05464 | ||||||||
\(494\) | −8.47108 | −0.381132 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −90.9911 | −4.08562 | ||||||||
\(497\) | 10.0966 | 0.452895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.2315 | 0.681857 | 0.340929 | − | 0.940089i | \(-0.389259\pi\) | ||||
0.340929 | + | 0.940089i | \(0.389259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.6028 | 0.741020 | ||||||||
\(503\) | −23.7330 | −1.05820 | −0.529101 | − | 0.848559i | \(-0.677471\pi\) | ||||
−0.529101 | + | 0.848559i | \(0.677471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.7778 | −0.523586 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −105.637 | −4.68688 | ||||||||
\(509\) | 12.5097 | 0.554482 | 0.277241 | − | 0.960800i | \(-0.410580\pi\) | ||||
0.277241 | + | 0.960800i | \(0.410580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.56834 | −0.246329 | ||||||||
\(512\) | −2.43464 | −0.107597 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −35.5331 | −1.56730 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.06898 | −0.0909936 | ||||||||
\(518\) | −20.7703 | −0.912595 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.9638 | 1.22512 | 0.612559 | − | 0.790425i | \(-0.290140\pi\) | ||||
0.612559 | + | 0.790425i | \(0.290140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7013 | 0.686569 | 0.343285 | − | 0.939231i | \(-0.388460\pi\) | ||||
0.343285 | + | 0.939231i | \(0.388460\pi\) | |||||||
\(524\) | 15.9222 | 0.695564 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7460 | 0.817362 | ||||||||
\(527\) | −27.9270 | −1.21652 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.49247 | −0.282281 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.3703 | −0.449609 | ||||||||
\(533\) | 30.1495 | 1.30592 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 107.685 | 4.65127 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −63.7363 | −2.74787 | ||||||||
\(539\) | 4.48129 | 0.193023 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9783 | −1.03091 | −0.515455 | − | 0.856917i | \(-0.672377\pi\) | ||||
−0.515455 | + | 0.856917i | \(0.672377\pi\) | |||||||
\(542\) | 77.9000 | 3.34609 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 67.2927 | 2.88515 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.62681 | −0.240585 | −0.120293 | − | 0.992738i | \(-0.538383\pi\) | ||||
−0.120293 | + | 0.992738i | \(0.538383\pi\) | |||||||
\(548\) | 107.066 | 4.57365 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.01341 | 0.298781 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.75498 | −0.287251 | ||||||||
\(554\) | −23.0728 | −0.980268 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 95.6254 | 4.05542 | ||||||||
\(557\) | 42.4247 | 1.79759 | 0.898796 | − | 0.438366i | \(-0.144443\pi\) | ||||
0.898796 | + | 0.438366i | \(0.144443\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.92298 | 0.292811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −46.1261 | −1.94571 | ||||||||
\(563\) | −5.78597 | −0.243850 | −0.121925 | − | 0.992539i | \(-0.538907\pi\) | ||||
−0.121925 | + | 0.992539i | \(0.538907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.8495 | −1.08653 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 51.7853 | 2.17286 | ||||||||
\(569\) | 22.0056 | 0.922522 | 0.461261 | − | 0.887265i | \(-0.347397\pi\) | ||||
0.461261 | + | 0.887265i | \(0.347397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6143 | 1.40672 | 0.703358 | − | 0.710835i | \(-0.251683\pi\) | ||||
0.703358 | + | 0.710835i | \(0.251683\pi\) | |||||||
\(572\) | −15.0772 | −0.630410 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 51.0499 | 2.13078 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.2350 | 1.67501 | 0.837503 | − | 0.546433i | \(-0.184015\pi\) | ||||
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(578\) | −4.14337 | −0.172341 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9722 | −0.621151 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.74948 | −0.113872 | ||||||||
\(584\) | −28.5599 | −1.18182 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −45.1967 | −1.86706 | ||||||||
\(587\) | 2.82299 | 0.116517 | 0.0582587 | − | 0.998302i | \(-0.481445\pi\) | ||||
0.0582587 | + | 0.998302i | \(0.481445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.36423 | 0.344642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −58.6939 | −2.41231 | ||||||||
\(593\) | 24.6805 | 1.01351 | 0.506754 | − | 0.862091i | \(-0.330845\pi\) | ||||
0.506754 | + | 0.862091i | \(0.330845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.68513 | −0.150949 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.2282 | 1.19523 | ||||||||
\(599\) | 7.71547 | 0.315245 | 0.157623 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157623 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6506 | 0.923938 | 0.461969 | − | 0.886896i | \(-0.347143\pi\) | ||||
0.461969 | + | 0.886896i | \(0.347143\pi\) | |||||||
\(602\) | 11.7222 | 0.477759 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.7783 | 1.49649 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6423 | −1.00020 | −0.500099 | − | 0.865968i | \(-0.666703\pi\) | ||||
−0.500099 | + | 0.865968i | \(0.666703\pi\) | |||||||
\(608\) | −20.1543 | −0.817367 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.13445 | 0.207718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.8034 | −1.68842 | −0.844211 | − | 0.536011i | \(-0.819931\pi\) | ||||
−0.844211 | + | 0.536011i | \(0.819931\pi\) | |||||||
\(614\) | 30.4205 | 1.22767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.7482 | −0.634513 | ||||||||
\(617\) | −15.9390 | −0.641680 | −0.320840 | − | 0.947133i | \(-0.603965\pi\) | ||||
−0.320840 | + | 0.947133i | \(0.603965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.1700 | −1.89592 | −0.947961 | − | 0.318385i | \(-0.896859\pi\) | ||||
−0.947961 | + | 0.318385i | \(0.896859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −49.8808 | −2.00004 | ||||||||
\(623\) | −26.0540 | −1.04383 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.0630 | −1.04169 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.7734 | −1.06837 | ||||||||
\(629\) | −18.0144 | −0.718280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3634 | 1.28836 | 0.644182 | − | 0.764872i | \(-0.277198\pi\) | ||||
0.644182 | + | 0.764872i | \(0.277198\pi\) | |||||||
\(632\) | −34.6462 | −1.37815 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.0896 | −0.797859 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.1209 | −0.440627 | ||||||||
\(638\) | 17.2653 | 0.683539 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0042 | −0.711122 | −0.355561 | − | 0.934653i | \(-0.615710\pi\) | ||||
−0.355561 | + | 0.934653i | \(0.615710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8891 | 0.863224 | 0.431612 | − | 0.902059i | \(-0.357945\pi\) | ||||
0.431612 | + | 0.902059i | \(0.357945\pi\) | |||||||
\(644\) | 35.7811 | 1.40997 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.4403 | −0.489455 | ||||||||
\(647\) | −19.0263 | −0.748003 | −0.374001 | − | 0.927428i | \(-0.622015\pi\) | ||||
−0.374001 | + | 0.927428i | \(0.622015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.44129 | 0.0565755 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −126.649 | −4.95995 | ||||||||
\(653\) | 2.31971 | 0.0907774 | 0.0453887 | − | 0.998969i | \(-0.485547\pi\) | ||||
0.0453887 | + | 0.998969i | \(0.485547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 144.260 | 5.63239 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.69378 | 0.338919 | ||||||||
\(659\) | −7.19180 | −0.280153 | −0.140076 | − | 0.990141i | \(-0.544735\pi\) | ||||
−0.140076 | + | 0.990141i | \(0.544735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.0214 | 1.67334 | 0.836669 | − | 0.547709i | \(-0.184500\pi\) | ||||
0.836669 | + | 0.547709i | \(0.184500\pi\) | |||||||
\(662\) | −67.8666 | −2.63771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −76.7920 | −2.98011 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.1987 | −0.936977 | ||||||||
\(668\) | −23.7461 | −0.918765 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.85494 | 0.303237 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.8031 | −1.14882 | −0.574412 | − | 0.818566i | \(-0.694769\pi\) | ||||
−0.574412 | + | 0.818566i | \(0.694769\pi\) | |||||||
\(674\) | −34.9961 | −1.34800 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.4464 | −1.17102 | ||||||||
\(677\) | 26.7346 | 1.02749 | 0.513746 | − | 0.857942i | \(-0.328257\pi\) | ||||
0.513746 | + | 0.857942i | \(0.328257\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.1664 | 0.697163 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.5907 | 0.788457 | ||||||||
\(683\) | −28.4950 | −1.09033 | −0.545165 | − | 0.838329i | \(-0.683533\pi\) | ||||
−0.545165 | + | 0.838329i | \(0.683533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −50.5623 | −1.93048 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 33.1251 | 1.26288 | ||||||||
\(689\) | 6.82321 | 0.259944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6469 | 1.31803 | 0.659015 | − | 0.752130i | \(-0.270973\pi\) | ||||
0.659015 | + | 0.752130i | \(0.270973\pi\) | |||||||
\(692\) | 13.9760 | 0.531286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.1263 | 0.612145 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44.2763 | 1.67708 | ||||||||
\(698\) | −61.0451 | −2.31059 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.973305 | −0.0367612 | −0.0183806 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183806 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.39536 | 0.203490 | ||||||||
\(704\) | −21.9756 | −0.828237 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.0454 | 0.490971 | ||||||||
\(707\) | 22.8854 | 0.860696 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3242 | −0.425291 | −0.212645 | − | 0.977129i | \(-0.568208\pi\) | ||||
−0.212645 | + | 0.977129i | \(0.568208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −133.630 | −5.00801 | ||||||||
\(713\) | −28.8595 | −1.08080 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 81.5742 | 3.04857 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −77.6312 | −2.89717 | ||||||||
\(719\) | 30.7320 | 1.14611 | 0.573056 | − | 0.819516i | \(-0.305758\pi\) | ||||
0.573056 | + | 0.819516i | \(0.305758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.30962 | 0.0860149 | ||||||||
\(722\) | −47.3279 | −1.76136 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.05888 | 0.0393529 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.56836 | −0.243607 | −0.121803 | − | 0.992554i | \(-0.538868\pi\) | ||||
−0.121803 | + | 0.992554i | \(0.538868\pi\) | |||||||
\(728\) | 39.0813 | 1.44845 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1668 | 0.376032 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.9276 | −1.17927 | −0.589636 | − | 0.807669i | \(-0.700729\pi\) | ||||
−0.589636 | + | 0.807669i | \(0.700729\pi\) | |||||||
\(734\) | −39.5235 | −1.45884 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 69.5395 | 2.56326 | ||||||||
\(737\) | −13.4259 | −0.494551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3072 | −0.563083 | −0.281542 | − | 0.959549i | \(-0.590846\pi\) | ||||
−0.281542 | + | 0.959549i | \(0.590846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.5532 | 0.424132 | ||||||||
\(743\) | −16.5455 | −0.606995 | −0.303498 | − | 0.952832i | \(-0.598154\pi\) | ||||
−0.303498 | + | 0.952832i | \(0.598154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −88.7774 | −3.25037 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.1417 | −0.809582 | ||||||||
\(749\) | −18.5769 | −0.678786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0279 | 1.67958 | 0.839791 | − | 0.542911i | \(-0.182678\pi\) | ||||
0.839791 | + | 0.542911i | \(0.182678\pi\) | |||||||
\(752\) | 24.5674 | 0.895880 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −42.8461 | −1.56036 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.5282 | −0.964184 | −0.482092 | − | 0.876121i | \(-0.660123\pi\) | ||||
−0.482092 | + | 0.876121i | \(0.660123\pi\) | |||||||
\(758\) | −40.7239 | −1.47916 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4241 | 1.03037 | 0.515187 | − | 0.857078i | \(-0.327723\pi\) | ||||
0.515187 | + | 0.857078i | \(0.327723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.81843 | 0.210641 | ||||||||
\(764\) | 41.3426 | 1.49572 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5181 | 0.777481 | ||||||||
\(767\) | −3.57675 | −0.129149 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.95952 | −0.323089 | −0.161544 | − | 0.986865i | \(-0.551647\pi\) | ||||
−0.161544 | + | 0.986865i | \(0.551647\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −85.7515 | −3.08626 | ||||||||
\(773\) | −23.1042 | −0.831001 | −0.415500 | − | 0.909593i | \(-0.636393\pi\) | ||||
−0.415500 | + | 0.909593i | \(0.636393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 93.1752 | 3.34479 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.88757 | −0.103524 | ||||||||
\(779\) | −13.2609 | −0.475120 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.45651 | −0.231032 | ||||||||
\(782\) | 42.9232 | 1.53493 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −53.2115 | −1.90041 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.03390 | −0.0725009 | −0.0362504 | − | 0.999343i | \(-0.511541\pi\) | ||||
−0.0362504 | + | 0.999343i | \(0.511541\pi\) | |||||||
\(788\) | 89.4578 | 3.18680 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2099 | −0.363022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.4931 | −0.692220 | ||||||||
\(794\) | −65.0637 | −2.30902 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.5368 | −0.373469 | ||||||||
\(797\) | 12.1923 | 0.431874 | 0.215937 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215937 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.54024 | 0.266754 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.35572 | 0.189117 | ||||||||
\(803\) | 3.56080 | 0.125658 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −51.0985 | −1.79987 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 117.379 | 4.12938 | ||||||||
\(809\) | −8.83355 | −0.310571 | −0.155286 | − | 0.987870i | \(-0.549630\pi\) | ||||
−0.155286 | + | 0.987870i | \(0.549630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9184 | −0.488741 | −0.244370 | − | 0.969682i | \(-0.578581\pi\) | ||||
−0.244370 | + | 0.969682i | \(0.578581\pi\) | |||||||
\(812\) | −52.4522 | −1.84071 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.2820 | 0.465535 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.04498 | −0.106530 | ||||||||
\(818\) | 17.9085 | 0.626158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.4930 | 1.02931 | 0.514656 | − | 0.857397i | \(-0.327920\pi\) | ||||
0.514656 | + | 0.857397i | \(0.327920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.9661 | −1.46285 | −0.731423 | − | 0.681924i | \(-0.761143\pi\) | ||||
−0.731423 | + | 0.681924i | \(0.761143\pi\) | |||||||
\(824\) | 11.8460 | 0.412675 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.05624 | −0.210724 | ||||||||
\(827\) | −37.4674 | −1.30287 | −0.651435 | − | 0.758704i | \(-0.725833\pi\) | ||||
−0.651435 | + | 0.758704i | \(0.725833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.55614 | −0.331899 | −0.165949 | − | 0.986134i | \(-0.553069\pi\) | ||||
−0.165949 | + | 0.986134i | \(0.553069\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 54.5355 | 1.89068 | ||||||||
\(833\) | −16.3317 | −0.565860 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.63152 | 0.229356 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −57.3792 | −1.98213 | ||||||||
\(839\) | −54.7310 | −1.88952 | −0.944761 | − | 0.327759i | \(-0.893707\pi\) | ||||
−0.944761 | + | 0.327759i | \(0.893707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.47334 | 0.223219 | ||||||||
\(842\) | 60.0197 | 2.06842 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −124.352 | −4.28037 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.5940 | −0.570177 | ||||||||
\(848\) | 32.6478 | 1.12113 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.6159 | −0.638144 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3067 | −0.524092 | −0.262046 | − | 0.965055i | \(-0.584397\pi\) | ||||
−0.262046 | + | 0.965055i | \(0.584397\pi\) | |||||||
\(854\) | −33.0062 | −1.12945 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −95.2806 | −3.25662 | ||||||||
\(857\) | 8.66910 | 0.296131 | 0.148065 | − | 0.988978i | \(-0.452695\pi\) | ||||
0.148065 | + | 0.988978i | \(0.452695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4078 | −1.03750 | −0.518750 | − | 0.854926i | \(-0.673603\pi\) | ||||
−0.518750 | + | 0.854926i | \(0.673603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 81.7208 | 2.78342 | ||||||||
\(863\) | 18.0425 | 0.614175 | 0.307088 | − | 0.951681i | \(-0.400646\pi\) | ||||
0.307088 | + | 0.951681i | \(0.400646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.54945 | 0.0526526 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −62.5548 | −2.12325 | ||||||||
\(869\) | 4.31963 | 0.146533 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3183 | 1.12895 | ||||||||
\(872\) | 29.8426 | 1.01060 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.8556 | −0.434848 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3057 | 0.753211 | 0.376605 | − | 0.926374i | \(-0.377091\pi\) | ||||
0.376605 | + | 0.926374i | \(0.377091\pi\) | |||||||
\(878\) | 34.4062 | 1.16115 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.75956 | −0.261426 | −0.130713 | − | 0.991420i | \(-0.541727\pi\) | ||||
−0.130713 | + | 0.991420i | \(0.541727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.9527 | −0.671462 | −0.335731 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335731 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(884\) | 54.9477 | 1.84809 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.4641 | −1.29223 | ||||||||
\(887\) | −8.60289 | −0.288857 | −0.144428 | − | 0.989515i | \(-0.546134\pi\) | ||||
−0.144428 | + | 0.989515i | \(0.546134\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.1393 | −1.14499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 68.4429 | 2.29164 | ||||||||
\(893\) | −2.25832 | −0.0755719 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 34.5915 | 1.15562 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.1539 | 1.07299 | ||||||||
\(899\) | 42.3057 | 1.41097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0203 | 0.333824 | ||||||||
\(902\) | −32.6450 | −1.08696 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.3663 | −1.74168 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.26125 | 0.207902 | 0.103951 | − | 0.994582i | \(-0.466852\pi\) | ||||
0.103951 | + | 0.994582i | \(0.466852\pi\) | |||||||
\(908\) | 137.190 | 4.55282 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.905575 | −0.0300030 | −0.0150015 | − | 0.999887i | \(-0.504775\pi\) | ||||
−0.0150015 | + | 0.999887i | \(0.504775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.57431 | 0.316863 | ||||||||
\(914\) | −22.0916 | −0.730726 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.4198 | 0.344279 | ||||||||
\(917\) | 5.14567 | 0.169925 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9933 | 1.45120 | 0.725602 | − | 0.688114i | \(-0.241561\pi\) | ||||
0.725602 | + | 0.688114i | \(0.241561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.41836 | −0.112578 | ||||||||
\(923\) | 16.0227 | 0.527394 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 87.8029 | 2.88538 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −101.939 | −3.34632 | ||||||||
\(929\) | 36.7447 | 1.20555 | 0.602777 | − | 0.797910i | \(-0.294061\pi\) | ||||
0.602777 | + | 0.797910i | \(0.294061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89140 | 0.160309 | ||||||||
\(932\) | 2.74347 | 0.0898652 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.7866 | −1.26914 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.6490 | 0.805248 | 0.402624 | − | 0.915366i | \(-0.368098\pi\) | ||||
0.402624 | + | 0.915366i | \(0.368098\pi\) | |||||||
\(938\) | 56.4153 | 1.84203 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.1479 | 1.92817 | 0.964083 | − | 0.265602i | \(-0.0855706\pi\) | ||||
0.964083 | + | 0.265602i | \(0.0855706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.7546 | 1.48998 | ||||||||
\(944\) | −17.1141 | −0.557016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.49600 | −0.243716 | ||||||||
\(947\) | 30.0960 | 0.977989 | 0.488995 | − | 0.872287i | \(-0.337364\pi\) | ||||
0.488995 | + | 0.872287i | \(0.337364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.83661 | −0.286849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 57.3931 | 1.86012 | ||||||||
\(953\) | 20.6393 | 0.668572 | 0.334286 | − | 0.942472i | \(-0.391505\pi\) | ||||
0.334286 | + | 0.942472i | \(0.391505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.5921 | 1.18347 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45.3084 | 1.46385 | ||||||||
\(959\) | 34.6013 | 1.11733 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4540 | 0.627549 | ||||||||
\(962\) | −32.9612 | −1.06271 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.0876 | 0.389315 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.6016 | −0.726817 | −0.363408 | − | 0.931630i | \(-0.618387\pi\) | ||||
−0.363408 | + | 0.931630i | \(0.618387\pi\) | |||||||
\(968\) | −85.1103 | −2.73555 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1381 | −0.774628 | −0.387314 | − | 0.921948i | \(-0.626597\pi\) | ||||
−0.387314 | + | 0.921948i | \(0.626597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.9038 | 0.990732 | ||||||||
\(974\) | 107.007 | 3.42874 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −93.2708 | −2.98553 | ||||||||
\(977\) | −23.0506 | −0.737454 | −0.368727 | − | 0.929538i | \(-0.620206\pi\) | ||||
−0.368727 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.6608 | 0.532483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.6870 | −1.20264 | ||||||||
\(983\) | −29.8713 | −0.952745 | −0.476373 | − | 0.879243i | \(-0.658049\pi\) | ||||
−0.476373 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −62.9220 | −2.00384 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.4570 | −0.523567 | ||||||||
\(989\) | 10.5063 | 0.334079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.6560 | 0.529096 | 0.264548 | − | 0.964372i | \(-0.414777\pi\) | ||||
0.264548 | + | 0.964372i | \(0.414777\pi\) | |||||||
\(992\) | −121.573 | −3.85996 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27.1300 | 0.860513 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.4934 | 0.395669 | 0.197835 | − | 0.980235i | \(-0.436609\pi\) | ||||
0.197835 | + | 0.980235i | \(0.436609\pi\) | |||||||
\(998\) | 40.9278 | 1.29555 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.p.1.6 | 6 | ||
3.2 | odd | 2 | 1875.2.a.j.1.1 | 6 | |||
5.4 | even | 2 | 5625.2.a.q.1.1 | 6 | |||
15.2 | even | 4 | 1875.2.b.f.1249.1 | 12 | |||
15.8 | even | 4 | 1875.2.b.f.1249.12 | 12 | |||
15.14 | odd | 2 | 1875.2.a.k.1.6 | 6 | |||
25.11 | even | 5 | 225.2.h.d.46.3 | 12 | |||
25.16 | even | 5 | 225.2.h.d.181.3 | 12 | |||
75.2 | even | 20 | 375.2.i.d.274.1 | 24 | |||
75.11 | odd | 10 | 75.2.g.c.46.1 | yes | 12 | ||
75.14 | odd | 10 | 375.2.g.c.226.3 | 12 | |||
75.23 | even | 20 | 375.2.i.d.274.6 | 24 | |||
75.38 | even | 20 | 375.2.i.d.349.1 | 24 | |||
75.41 | odd | 10 | 75.2.g.c.31.1 | ✓ | 12 | ||
75.59 | odd | 10 | 375.2.g.c.151.3 | 12 | |||
75.62 | even | 20 | 375.2.i.d.349.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.1 | ✓ | 12 | 75.41 | odd | 10 | ||
75.2.g.c.46.1 | yes | 12 | 75.11 | odd | 10 | ||
225.2.h.d.46.3 | 12 | 25.11 | even | 5 | |||
225.2.h.d.181.3 | 12 | 25.16 | even | 5 | |||
375.2.g.c.151.3 | 12 | 75.59 | odd | 10 | |||
375.2.g.c.226.3 | 12 | 75.14 | odd | 10 | |||
375.2.i.d.274.1 | 24 | 75.2 | even | 20 | |||
375.2.i.d.274.6 | 24 | 75.23 | even | 20 | |||
375.2.i.d.349.1 | 24 | 75.38 | even | 20 | |||
375.2.i.d.349.6 | 24 | 75.62 | even | 20 | |||
1875.2.a.j.1.1 | 6 | 3.2 | odd | 2 | |||
1875.2.a.k.1.6 | 6 | 15.14 | odd | 2 | |||
1875.2.b.f.1249.1 | 12 | 15.2 | even | 4 | |||
1875.2.b.f.1249.12 | 12 | 15.8 | even | 4 | |||
5625.2.a.p.1.6 | 6 | 1.1 | even | 1 | trivial | ||
5625.2.a.q.1.1 | 6 | 5.4 | even | 2 |