Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.63778 | −0.945574 | −0.472787 | − | 0.881177i | \(-0.656752\pi\) | ||||
−0.472787 | + | 0.881177i | \(0.656752\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.87336 | 1.28501 | 0.642504 | − | 0.766282i | \(-0.277896\pi\) | ||||
0.642504 | + | 0.766282i | \(0.277896\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.53418 | 0.957832 | 0.478916 | − | 0.877861i | \(-0.341030\pi\) | ||||
0.478916 | + | 0.877861i | \(0.341030\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.317671 | −0.105890 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.58220 | 1.08007 | 0.540037 | − | 0.841641i | \(-0.318410\pi\) | ||||
0.540037 | + | 0.841641i | \(0.318410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.49911 | 1.52518 | 0.762589 | − | 0.646883i | \(-0.223928\pi\) | ||||
0.762589 | + | 0.646883i | \(0.223928\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.70594 | −1.21507 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.64173 | 1.61086 | 0.805428 | − | 0.592694i | \(-0.201936\pi\) | ||||
0.805428 | + | 0.592694i | \(0.201936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16598 | 0.726325 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.15044 | −0.905700 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23185 | −0.465372 | −0.232686 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232686 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.25622 | 0.651245 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.43362 | 1.04570 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29424 | 0.983116 | 0.491558 | − | 0.870845i | \(-0.336428\pi\) | ||||
0.491558 | + | 0.870845i | \(0.336428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.91659 | −1.24226 | −0.621128 | − | 0.783709i | \(-0.713325\pi\) | ||||
−0.621128 | + | 0.783709i | \(0.713325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.86686 | −1.02129 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.28163 | 1.23082 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.97947 | 1.14742 | 0.573709 | − | 0.819059i | \(-0.305504\pi\) | ||||
0.573709 | + | 0.819059i | \(0.305504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00634 | −1.44217 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.56040 | 1.33691 | 0.668455 | − | 0.743753i | \(-0.266956\pi\) | ||||
0.668455 | + | 0.743753i | \(0.266956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.68921 | −1.17259 | −0.586297 | − | 0.810096i | \(-0.699415\pi\) | ||||
−0.586297 | + | 0.810096i | \(0.699415\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.912784 | −0.136070 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.74446 | 0.400321 | 0.200161 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200161 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.577911 | −0.0825587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8777 | −1.52318 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.46446 | −0.887962 | −0.443981 | − | 0.896036i | \(-0.646434\pi\) | ||||
−0.443981 | + | 0.896036i | \(0.646434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2930 | 1.38790 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.18518 | −0.686794 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.83419 | −0.368980 | −0.184490 | − | 0.982834i | \(-0.559063\pi\) | ||||
−0.184490 | + | 0.982834i | \(0.559063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72071 | −0.220315 | −0.110157 | − | 0.993914i | \(-0.535136\pi\) | ||||
−0.110157 | + | 0.993914i | \(0.535136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.805036 | −0.101425 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.8009 | 1.95987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.56400 | −0.801920 | −0.400960 | − | 0.916095i | \(-0.631323\pi\) | ||||
−0.400960 | + | 0.916095i | \(0.631323\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.65528 | 0.440043 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.23946 | −0.977844 | −0.488922 | − | 0.872327i | \(-0.662610\pi\) | ||||
−0.488922 | + | 0.872327i | \(0.662610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.78141 | 0.442581 | 0.221290 | − | 0.975208i | \(-0.428973\pi\) | ||||
0.221290 | + | 0.975208i | \(0.428973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.33299 | −0.615800 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.07795 | 1.03453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.99913 | −0.224920 | −0.112460 | − | 0.993656i | \(-0.535873\pi\) | ||||
−0.112460 | + | 0.993656i | \(0.535873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.94607 | −0.882897 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.83734 | 0.421202 | 0.210601 | − | 0.977572i | \(-0.432458\pi\) | ||||
0.210601 | + | 0.977572i | \(0.432458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.0841 | 2.06996 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.67081 | −0.929608 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.50063 | −0.265067 | −0.132533 | − | 0.991179i | \(-0.542311\pi\) | ||||
−0.132533 | + | 0.991179i | \(0.542311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9358 | 1.46086 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.3279 | 1.17465 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.09701 | 0.933334 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −19.1894 | −1.94839 | −0.974194 | − | 0.225712i | \(-0.927529\pi\) | ||||
−0.974194 | + | 0.225712i | \(0.927529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.13796 | −0.114369 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.3520 | −1.82609 | −0.913047 | − | 0.407855i | \(-0.866277\pi\) | ||||
−0.913047 | + | 0.407855i | \(0.866277\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.26082 | 0.222765 | 0.111382 | − | 0.993778i | \(-0.464472\pi\) | ||||
0.111382 | + | 0.993778i | \(0.464472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.9257 | −1.16383 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.98752 | 0.772182 | 0.386091 | − | 0.922461i | \(-0.373825\pi\) | ||||
0.386091 | + | 0.922461i | \(0.373825\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4937 | −1.00511 | −0.502556 | − | 0.864545i | \(-0.667607\pi\) | ||||
−0.502556 | + | 0.864545i | \(0.667607\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4308 | −1.08497 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2368 | −1.05707 | −0.528535 | − | 0.848911i | \(-0.677259\pi\) | ||||
−0.528535 | + | 0.848911i | \(0.677259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.41291 | −0.598006 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.74691 | −0.161501 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.8314 | 1.54293 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83216 | 0.166560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0201 | −1.26415 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.01050 | −0.448153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4562 | 1.37152 | 0.685758 | − | 0.727829i | \(-0.259471\pi\) | ||||
0.685758 | + | 0.727829i | \(0.259471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5933 | 1.10877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.77547 | −0.417235 | −0.208617 | − | 0.977997i | \(-0.566896\pi\) | ||||
−0.208617 | + | 0.977997i | \(0.566896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.02317 | 0.695697 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.6128 | 1.34373 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.915844 | 0.0782458 | 0.0391229 | − | 0.999234i | \(-0.487544\pi\) | ||||
0.0391229 | + | 0.999234i | \(0.487544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3649 | −0.879142 | −0.439571 | − | 0.898208i | \(-0.644869\pi\) | ||||
−0.439571 | + | 0.898208i | \(0.644869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.49483 | −0.378533 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.6989 | 1.64731 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2123 | 1.26331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.946492 | 0.0780654 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.02783 | −0.248050 | −0.124025 | − | 0.992279i | \(-0.539580\pi\) | ||||
−0.124025 | + | 0.992279i | \(0.539580\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3704 | 1.08807 | 0.544034 | − | 0.839063i | \(-0.316896\pi\) | ||||
0.544034 | + | 0.839063i | \(0.316896\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.10988 | −0.170574 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.8739 | −1.59631 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6842 | 0.932502 | 0.466251 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466251 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5874 | 0.839633 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65591 | −0.445748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.7450 | −1.54655 | −0.773273 | − | 0.634073i | \(-0.781382\pi\) | ||||
−0.773273 | + | 0.634073i | \(0.781382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.8576 | −1.31237 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2898 | 0.951012 | 0.475506 | − | 0.879712i | \(-0.342265\pi\) | ||||
0.475506 | + | 0.879712i | \(0.342265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.2402 | 1.32617 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00574 | −0.0769108 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.17998 | 0.621913 | 0.310956 | − | 0.950424i | \(-0.399351\pi\) | ||||
0.310956 | + | 0.950424i | \(0.399351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.25187 | 0.623783 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.64178 | 0.348898 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4848 | −0.933158 | −0.466579 | − | 0.884480i | \(-0.654514\pi\) | ||||
−0.466579 | + | 0.884480i | \(0.654514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3557 | −1.06705 | −0.533524 | − | 0.845785i | \(-0.679132\pi\) | ||||
−0.533524 | + | 0.845785i | \(0.679132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.81816 | 0.208324 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0546 | 1.47444 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.7920 | 1.73984 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7698 | 1.00161 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3815 | −1.11296 | −0.556482 | − | 0.830860i | \(-0.687849\pi\) | ||||
−0.556482 | + | 0.830860i | \(0.687849\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8713 | −1.43037 | −0.715183 | − | 0.698938i | \(-0.753656\pi\) | ||||
−0.715183 | + | 0.698938i | \(0.753656\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25.8785 | −1.85320 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6912 | −1.26045 | −0.630225 | − | 0.776413i | \(-0.717037\pi\) | ||||
−0.630225 | + | 0.776413i | \(0.717037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5377 | 1.10144 | 0.550720 | − | 0.834690i | \(-0.314353\pi\) | ||||
0.550720 | + | 0.834690i | \(0.314353\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7504 | 0.758275 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.4166 | 0.941659 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.5972 | 1.71794 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.708992 | 0.0492783 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3412 | 0.784485 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.3588 | −1.40156 | −0.700780 | − | 0.713378i | \(-0.747164\pi\) | ||||
−0.700780 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.4944 | 0.924624 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.0939 | −1.50679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.5279 | −1.18987 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.19313 | −0.418493 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.5236 | 2.45684 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.77751 | 0.119031 | 0.0595156 | − | 0.998227i | \(-0.481044\pi\) | ||||
0.0595156 | + | 0.998227i | \(0.481044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.03441 | −0.0689605 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.2202 | 1.60755 | 0.803777 | − | 0.594931i | \(-0.202821\pi\) | ||||
0.803777 | + | 0.594931i | \(0.202821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9310 | 1.64749 | 0.823745 | − | 0.566960i | \(-0.191881\pi\) | ||||
0.823745 | + | 0.566960i | \(0.191881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.8677 | −0.978223 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.63799 | 0.238333 | 0.119166 | − | 0.992874i | \(-0.461978\pi\) | ||||
0.119166 | + | 0.992874i | \(0.461978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.88584 | 0.514416 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.27414 | 0.212678 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.55109 | 0.359070 | 0.179535 | − | 0.983752i | \(-0.442541\pi\) | ||||
0.179535 | + | 0.983752i | \(0.442541\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6127 | 1.45661 | 0.728307 | − | 0.685251i | \(-0.240308\pi\) | ||||
0.728307 | + | 0.685251i | \(0.240308\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.28693 | −0.210857 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.66055 | −0.106089 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.4101 | 1.10778 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.28472 | −0.398278 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.99492 | −0.502636 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.2556 | −1.95730 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.81945 | −0.238250 | −0.119125 | − | 0.992879i | \(-0.538009\pi\) | ||||
−0.119125 | + | 0.992879i | \(0.538009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6873 | 1.09903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.68182 | −0.104102 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.7787 | −0.911293 | −0.455647 | − | 0.890161i | \(-0.650592\pi\) | ||||
−0.455647 | + | 0.890161i | \(0.650592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.5747 | −1.14104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.09549 | 0.250640 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.19011 | −0.194505 | −0.0972523 | − | 0.995260i | \(-0.531005\pi\) | ||||
−0.0972523 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80281 | 0.109513 | 0.0547566 | − | 0.998500i | \(-0.482562\pi\) | ||||
0.0547566 | + | 0.998500i | \(0.482562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.8237 | −1.38135 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.6644 | 0.703393 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.4958 | −1.77223 | −0.886117 | − | 0.463462i | \(-0.846607\pi\) | ||||
−0.886117 | + | 0.463462i | \(0.846607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.19720 | 0.131543 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8365 | −0.825417 | −0.412709 | − | 0.910863i | \(-0.635417\pi\) | ||||
−0.412709 | + | 0.910863i | \(0.635417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1061 | 1.13574 | 0.567870 | − | 0.823119i | \(-0.307768\pi\) | ||||
0.567870 | + | 0.823119i | \(0.307768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.8989 | −0.882536 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.6936 | 1.28053 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.1125 | 1.59485 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.4280 | 1.84234 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.8992 | 1.27936 | 0.639682 | − | 0.768640i | \(-0.279066\pi\) | ||||
0.639682 | + | 0.768640i | \(0.279066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.14365 | −0.474142 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.4643 | 1.12943 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.2732 | −0.709775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.4859 | −1.12315 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.0566 | 1.72671 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.94424 | −0.283106 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5125 | −0.999489 | −0.499745 | − | 0.866173i | \(-0.666573\pi\) | ||||
−0.499745 | + | 0.866173i | \(0.666573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.70272 | −0.210641 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.54200 | −0.0874386 | −0.0437193 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437193 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.7634 | 1.28667 | 0.643333 | − | 0.765587i | \(-0.277551\pi\) | ||||
0.643333 | + | 0.765587i | \(0.277551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.31316 | −0.130332 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.17875 | 0.347033 | 0.173517 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173517 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9650 | 1.06184 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.0818 | −0.730155 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0276 | 1.17001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.9063 | 0.993264 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.1864 | 0.950408 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.95497 | 0.383440 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0907 | 0.829460 | 0.414730 | − | 0.909944i | \(-0.363876\pi\) | ||||
0.414730 | + | 0.909944i | \(0.363876\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.21717 | −0.121500 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.8608 | −1.03047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7597 | 0.695063 | 0.347532 | − | 0.937668i | \(-0.387020\pi\) | ||||
0.347532 | + | 0.937668i | \(0.387020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.4035 | 0.999538 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.7766 | −1.34173 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2038 | −1.03691 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5029 | 0.565459 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.65152 | −0.464438 | −0.232219 | − | 0.972664i | \(-0.574599\pi\) | ||||
−0.232219 | + | 0.972664i | \(0.574599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.4064 | 1.14586 | 0.572928 | − | 0.819606i | \(-0.305807\pi\) | ||||
0.572928 | + | 0.819606i | \(0.305807\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.8801 | 1.59488 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.184444 | −0.00981694 | −0.00490847 | − | 0.999988i | \(-0.501562\pi\) | ||||
−0.00490847 | + | 0.999988i | \(0.501562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.6750 | −1.25654 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.5661 | −1.45895 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.8516 | −1.41718 | −0.708588 | − | 0.705623i | \(-0.750667\pi\) | ||||
−0.708588 | + | 0.705623i | \(0.750667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.97658 | −0.472451 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00068 | −0.157495 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8654 | 0.568720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.8931 | 1.76920 | 0.884602 | − | 0.466347i | \(-0.154430\pi\) | ||||
0.884602 | + | 0.466347i | \(0.154430\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.71939 | −0.141566 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.3821 | −0.850518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3751 | −0.640757 | −0.320378 | − | 0.947290i | \(-0.603810\pi\) | ||||
−0.320378 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.20611 | 0.423762 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.1136 | 1.49943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0864 | 0.826302 | 0.413151 | − | 0.910662i | \(-0.364428\pi\) | ||||
0.413151 | + | 0.910662i | \(0.364428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.3139 | −1.29687 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.2145 | 0.777423 | 0.388712 | − | 0.921359i | \(-0.372920\pi\) | ||||
0.388712 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.0843 | 1.32938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.44264 | 0.124166 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1557 | −0.717720 | −0.358860 | − | 0.933391i | \(-0.616835\pi\) | ||||
−0.358860 | + | 0.933391i | \(0.616835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8233 | −0.749647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.82118 | 0.394526 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.74424 | −0.289024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.221665 | 0.0111250 | 0.00556252 | − | 0.999985i | \(-0.498229\pi\) | ||||
0.00556252 | + | 0.999985i | \(0.498229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.1402 | −0.657833 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8688 | 1.39170 | 0.695850 | − | 0.718187i | \(-0.255028\pi\) | ||||
0.695850 | + | 0.718187i | \(0.255028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.0351 | −1.89466 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.8320 | −1.13453 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0019 | 1.23930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.197291 | 0.00975540 | 0.00487770 | − | 0.999988i | \(-0.498447\pi\) | ||||
0.00487770 | + | 0.999988i | \(0.498447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.49995 | −0.0739872 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.18235 | −0.353420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0261 | 0.541248 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9755 | 0.831293 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7060 | 1.35352 | 0.676762 | − | 0.736202i | \(-0.263383\pi\) | ||||
0.676762 | + | 0.736202i | \(0.263383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6023 | −1.05283 | −0.526415 | − | 0.850227i | \(-0.676464\pi\) | ||||
−0.526415 | + | 0.850227i | \(0.676464\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.871835 | −0.0423901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.6270 | 1.04906 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.36061 | −0.211025 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32.2625 | −1.55765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9317 | 0.526563 | 0.263282 | − | 0.964719i | \(-0.415195\pi\) | ||||
0.263282 | + | 0.964719i | \(0.415195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.9311 | 0.957829 | 0.478914 | − | 0.877862i | \(-0.341030\pi\) | ||||
0.478914 | + | 0.877862i | \(0.341030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.9144 | −1.19455 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.06597 | −0.338011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.46326 | −0.403930 | −0.201965 | − | 0.979393i | \(-0.564733\pi\) | ||||
−0.201965 | + | 0.979393i | \(0.564733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.183585 | 0.00874216 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5587 | 0.786725 | 0.393363 | − | 0.919383i | \(-0.371312\pi\) | ||||
0.393363 | + | 0.919383i | \(0.371312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.18523 | −0.340613 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.95893 | 0.234549 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.25857 | 0.0593956 | 0.0296978 | − | 0.999559i | \(-0.490546\pi\) | ||||
0.0296978 | + | 0.999559i | \(0.490546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.6651 | 1.44396 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.8978 | −1.02885 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 40.0425 | 1.87722 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.9487 | −1.54128 | −0.770638 | − | 0.637273i | \(-0.780062\pi\) | ||||
−0.770638 | + | 0.637273i | \(0.780062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.0886 | 1.68447 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.2657 | 1.22332 | 0.611658 | − | 0.791122i | \(-0.290503\pi\) | ||||
0.611658 | + | 0.791122i | \(0.290503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1906 | 0.798915 | 0.399458 | − | 0.916752i | \(-0.369198\pi\) | ||||
0.399458 | + | 0.916752i | \(0.369198\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.5491 | 1.50943 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.188356 | −0.00871607 | −0.00435804 | − | 0.999991i | \(-0.501387\pi\) | ||||
−0.00435804 | + | 0.999991i | \(0.501387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.6344 | −0.768105 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.1362 | −0.881750 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5443 | −1.26649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3091 | 0.473016 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.05357 | 0.0940265 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.44361 | 0.431490 | 0.215745 | − | 0.976450i | \(-0.430782\pi\) | ||||
0.215745 | + | 0.976450i | \(0.430782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.3809 | 1.75002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.26314 | 0.421488 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −55.1381 | −2.50369 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.41931 | −0.290887 | −0.145443 | − | 0.989367i | \(-0.546461\pi\) | ||||
−0.145443 | + | 0.989367i | \(0.546461\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.3380 | 1.46237 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9623 | 0.584978 | 0.292489 | − | 0.956269i | \(-0.405516\pi\) | ||||
0.292489 | + | 0.956269i | \(0.405516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.1629 | 1.58366 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.26977 | −0.146965 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.8803 | −0.936610 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.8989 | −1.24893 | −0.624464 | − | 0.781054i | \(-0.714682\pi\) | ||||
−0.624464 | + | 0.781054i | \(0.714682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1280 | −0.899252 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.590849 | 0.0263446 | 0.0131723 | − | 0.999913i | \(-0.495807\pi\) | ||||
0.0131723 | + | 0.999913i | \(0.495807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.7320 | −2.34654 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.2357 | −1.25399 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.845673 | 0.0374838 | 0.0187419 | − | 0.999824i | \(-0.494034\pi\) | ||||
0.0187419 | + | 0.999824i | \(0.494034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.58279 | 0.423918 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.2027 | 0.759519 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.49615 | 0.286255 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.83122 | 0.432376 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.3970 | −0.588064 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.78980 | 0.0784127 | 0.0392064 | − | 0.999231i | \(-0.487517\pi\) | ||||
0.0392064 | + | 0.999231i | \(0.487517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8079 | 0.472598 | 0.236299 | − | 0.971680i | \(-0.424065\pi\) | ||||
0.236299 | + | 0.971680i | \(0.424065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.5148 | −0.589833 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.9381 | −2.00110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.0189 | −0.783429 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.900338 | 0.0390713 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.0746 | 2.03903 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.9511 | 0.992260 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.4474 | 0.882370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.07019 | −0.0891695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.2633 | −1.68806 | −0.844031 | − | 0.536294i | \(-0.819824\pi\) | ||||
−0.844031 | + | 0.536294i | \(0.819824\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.5114 | 1.00897 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.1522 | −1.29158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3676 | 0.486042 | 0.243021 | − | 0.970021i | \(-0.421862\pi\) | ||||
0.243021 | + | 0.970021i | \(0.421862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.546621 | 0.0233292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7615 | 0.714062 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.06617 | −0.215435 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.8450 | −1.39419 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.2532 | −0.858157 | −0.429078 | − | 0.903267i | \(-0.641162\pi\) | ||||
−0.429078 | + | 0.903267i | \(0.641162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.2838 | −1.78841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.9661 | −1.64515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.0446 | −1.39266 | −0.696332 | − | 0.717720i | \(-0.745186\pi\) | ||||
−0.696332 | + | 0.717720i | \(0.745186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.2875 | −1.35834 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.1368 | −0.845667 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.96182 | −0.249933 | −0.124966 | − | 0.992161i | \(-0.539882\pi\) | ||||
−0.124966 | + | 0.992161i | \(0.539882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.3032 | 1.05891 | 0.529453 | − | 0.848339i | \(-0.322397\pi\) | ||||
0.529453 | + | 0.848339i | \(0.322397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.1915 | 1.05239 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.26739 | −0.303071 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2078 | 1.17431 | 0.587154 | − | 0.809475i | \(-0.300248\pi\) | ||||
0.587154 | + | 0.809475i | \(0.300248\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32.5448 | 1.35252 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.72451 | 0.403441 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.1570 | −0.959064 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.01950 | −0.207531 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −47.1038 | −1.94418 | −0.972091 | − | 0.234606i | \(-0.924620\pi\) | ||||
−0.972091 | + | 0.234606i | \(0.924620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.8978 | −0.902283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.9744 | 1.19185 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0019 | 0.821378 | 0.410689 | − | 0.911775i | \(-0.365288\pi\) | ||||
0.410689 | + | 0.911775i | \(0.365288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.3626 | 1.98267 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.4474 | −1.04149 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.2555 | −1.72651 | −0.863256 | − | 0.504767i | \(-0.831578\pi\) | ||||
−0.863256 | + | 0.504767i | \(0.831578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0107 | −0.979418 | −0.489709 | − | 0.871886i | \(-0.662897\pi\) | ||||
−0.489709 | + | 0.871886i | \(0.662897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.08519 | 0.0849155 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.26446 | 0.214031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.42764 | 0.301479 | 0.150739 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150739 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.9734 | −0.890408 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0921 | 0.610561 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.4174 | −1.59205 | −0.796027 | − | 0.605261i | \(-0.793069\pi\) | ||||
−0.796027 | + | 0.605261i | \(0.793069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −40.2848 | −1.62444 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5931 | −0.466720 | −0.233360 | − | 0.972390i | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.3934 | −1.42258 | −0.711291 | − | 0.702897i | \(-0.751889\pi\) | ||||
−0.711291 | + | 0.702897i | \(0.751889\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.1270 | −0.486640 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.33707 | −0.253889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6781 | −1.22712 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.5744 | −0.741789 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 46.3557 | 1.84832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4900 | 1.21379 | 0.606894 | − | 0.794783i | \(-0.292415\pi\) | ||||
0.606894 | + | 0.794783i | \(0.292415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.3433 | 1.32528 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44.4113 | 1.76241 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.17799 | −0.125917 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.61744 | 0.103544 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.2358 | 1.82620 | 0.913102 | − | 0.407732i | \(-0.133680\pi\) | ||||
0.913102 | + | 0.407732i | \(0.133680\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.45425 | 0.254531 | 0.127265 | − | 0.991869i | \(-0.459380\pi\) | ||||
0.127265 | + | 0.991869i | \(0.459380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.1850 | 1.42478 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.7050 | −1.28577 | −0.642883 | − | 0.765964i | \(-0.722262\pi\) | ||||
−0.642883 | + | 0.765964i | \(0.722262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1526 | −0.398525 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.7069 | 1.12511 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.9520 | −0.467719 | −0.233860 | − | 0.972270i | \(-0.575136\pi\) | ||||
−0.233860 | + | 0.972270i | \(0.575136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.7217 | −0.536150 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.20124 | −0.0468650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.87073 | −0.111828 | −0.0559139 | − | 0.998436i | \(-0.517807\pi\) | ||||
−0.0559139 | + | 0.998436i | \(0.517807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7741 | −1.66372 | −0.831860 | − | 0.554985i | \(-0.812724\pi\) | ||||
−0.831860 | + | 0.554985i | \(0.812724\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −59.8176 | −2.32312 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.0535 | 0.893977 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8159 | −0.457514 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.91118 | −0.112553 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.16395 | −0.237956 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.73708 | 0.259695 | 0.129848 | − | 0.991534i | \(-0.458551\pi\) | ||||
0.129848 | + | 0.991534i | \(0.458551\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.6931 | 0.681007 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.3391 | −1.28133 | −0.640663 | − | 0.767822i | \(-0.721341\pi\) | ||||
−0.640663 | + | 0.767822i | \(0.721341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.6295 | −1.86623 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.6675 | −1.52006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0975 | −1.64908 | −0.824539 | − | 0.565805i | \(-0.808566\pi\) | ||||
−0.824539 | + | 0.565805i | \(0.808566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.63155 | 0.100547 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.8316 | −1.55782 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.5488 | −1.35430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.89619 | 0.262343 | 0.131172 | − | 0.991360i | \(-0.458126\pi\) | ||||
0.131172 | + | 0.991360i | \(0.458126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.88380 | −0.109547 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.7822 | −1.12970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.8558 | 2.15357 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.95824 | −0.225361 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.40633 | −0.355272 | −0.177636 | − | 0.984096i | \(-0.556845\pi\) | ||||
−0.177636 | + | 0.984096i | \(0.556845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0969 | 0.833399 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9153 | −0.486418 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.5074 | −1.74909 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.3168 | 1.70191 | 0.850954 | − | 0.525241i | \(-0.176025\pi\) | ||||
0.850954 | + | 0.525241i | \(0.176025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.635066 | 0.0238168 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.4368 | 0.578111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.6021 | 2.11680 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.09148 | −0.339528 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9044 | 1.26442 | 0.632211 | − | 0.774796i | \(-0.282148\pi\) | ||||
0.632211 | + | 0.774796i | \(0.282148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.72932 | 0.213371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.0347 | −1.37734 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.2392 | 0.640249 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4489 | 0.424615 | 0.212307 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212307 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2215 | 1.08228 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.0696 | −1.88888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.3623 | −0.715163 | −0.357582 | − | 0.933882i | \(-0.616399\pi\) | ||||
−0.357582 | + | 0.933882i | \(0.616399\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.71962 | 0.100315 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.5136 | −0.866133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.5699 | 1.67631 | 0.838157 | − | 0.545429i | \(-0.183633\pi\) | ||||
0.838157 | + | 0.545429i | \(0.183633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.5139 | −1.04748 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −53.5695 | −1.96527 | −0.982637 | − | 0.185536i | \(-0.940598\pi\) | ||||
−0.982637 | + | 0.185536i | \(0.940598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.70007 | −0.318746 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.21901 | −0.0446012 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.2418 | 0.739621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0518 | 0.804683 | 0.402341 | − | 0.915490i | \(-0.368197\pi\) | ||||
0.402341 | + | 0.915490i | \(0.368197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.63778 | −0.0596841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.4181 | 1.39818 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.4488 | −0.488804 | −0.244402 | − | 0.969674i | \(-0.578592\pi\) | ||||
−0.244402 | + | 0.969674i | \(0.578592\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.0939 | 0.475280 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.1601 | −0.767052 | −0.383526 | − | 0.923530i | \(-0.625290\pi\) | ||||
−0.383526 | + | 0.923530i | \(0.625290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.5929 | −0.962728 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.06246 | −0.219189 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5855 | −0.562760 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.7960 | −1.54326 | −0.771632 | − | 0.636069i | \(-0.780559\pi\) | ||||
−0.771632 | + | 0.636069i | \(0.780559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.25542 | 0.225283 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.2783 | −0.909196 | −0.454598 | − | 0.890697i | \(-0.650217\pi\) | ||||
−0.454598 | + | 0.890697i | \(0.650217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.5220 | −0.809013 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.9679 | −1.03922 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.1020 | 0.971032 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.5154 | −1.05614 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.7669 | 1.02804 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.5730 | 1.19827 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.9621 | 0.889804 | 0.444902 | − | 0.895579i | \(-0.353239\pi\) | ||||
0.444902 | + | 0.895579i | \(0.353239\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.2043 | 0.861695 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.4762 | −1.01250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.46240 | −0.336020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.4214 | 1.07894 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.7836 | 0.452819 | 0.226409 | − | 0.974032i | \(-0.427301\pi\) | ||||
0.226409 | + | 0.974032i | \(0.427301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.2280 | 0.644859 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.794378 | 0.0280680 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5458 | 0.478020 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.2515 | −0.572789 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.22471 | 0.183919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.7716 | −1.60924 | −0.804621 | − | 0.593788i | \(-0.797632\pi\) | ||||
−0.804621 | + | 0.593788i | \(0.797632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.2043 | −1.51711 | −0.758554 | − | 0.651611i | \(-0.774094\pi\) | ||||
−0.758554 | + | 0.651611i | \(0.774094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.95262 | −0.103553 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −56.7345 | −1.98732 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.3439 | −0.851685 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.42698 | −0.154691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.0066 | 1.50094 | 0.750470 | − | 0.660905i | \(-0.229827\pi\) | ||||
0.750470 | + | 0.660905i | \(0.229827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6275 | 0.684172 | 0.342086 | − | 0.939669i | \(-0.388867\pi\) | ||||
0.342086 | + | 0.939669i | \(0.388867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.1038 | −0.665110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.3503 | −1.29880 | −0.649399 | − | 0.760448i | \(-0.724980\pi\) | ||||
−0.649399 | + | 0.760448i | \(0.724980\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.5687 | −1.89525 | −0.947625 | − | 0.319385i | \(-0.896524\pi\) | ||||
−0.947625 | + | 0.319385i | \(0.896524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.3077 | 1.67578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.83833 | −0.132990 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.3130 | 1.22206 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.5821 | −1.29903 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.4475 | −0.809496 | −0.404748 | − | 0.914428i | \(-0.632641\pi\) | ||||
−0.404748 | + | 0.914428i | \(0.632641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.971019 | −0.0334834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.6612 | 0.780493 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.5373 | 1.70414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.64303 | 0.159536 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.2916 | −1.07393 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5771 | −0.533976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9988 | 0.582028 | 0.291014 | − | 0.956719i | \(-0.406007\pi\) | ||||
0.291014 | + | 0.956719i | \(0.406007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.88985 | −0.0988309 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.4443 | 0.971639 | 0.485820 | − | 0.874059i | \(-0.338521\pi\) | ||||
0.485820 | + | 0.874059i | \(0.338521\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.6892 | −1.04710 | −0.523551 | − | 0.851994i | \(-0.675393\pi\) | ||||
−0.523551 | + | 0.851994i | \(0.675393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.5294 | −1.21084 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.15386 | 0.209480 | 0.104740 | − | 0.994500i | \(-0.466599\pi\) | ||||
0.104740 | + | 0.994500i | \(0.466599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5041 | 0.799163 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.4044 | −1.50805 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.16129 | −0.242930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0962 | −1.22307 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.09591 | 0.206315 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.6975 | −0.429255 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8524 | 0.569064 | 0.284532 | − | 0.958667i | \(-0.408162\pi\) | ||||
0.284532 | + | 0.958667i | \(0.408162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −35.8661 | −1.20973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0892 | 0.407295 | 0.203648 | − | 0.979044i | \(-0.434720\pi\) | ||||
0.203648 | + | 0.979044i | \(0.434720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8973 | 1.07343 | 0.536715 | − | 0.843764i | \(-0.319665\pi\) | ||||
0.536715 | + | 0.843764i | \(0.319665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.3375 | 0.448336 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7775 | −0.429026 | −0.214513 | − | 0.976721i | \(-0.568816\pi\) | ||||
−0.214513 | + | 0.976721i | \(0.568816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.1689 | 1.31368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.4644 | −0.953594 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.68891 | 0.290763 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.8734 | −1.19912 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.1008 | 0.671145 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.6181 | −1.22128 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.9352 | −1.43038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.9136 | 1.06202 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.2490 | −1.37116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.24689 | 0.174220 | 0.0871101 | − | 0.996199i | \(-0.472237\pi\) | ||||
0.0871101 | + | 0.996199i | \(0.472237\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.82990 | 0.193365 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.1166 | −1.82609 | −0.913047 | − | 0.407855i | \(-0.866277\pi\) | ||||
−0.913047 | + | 0.407855i | \(0.866277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.7461 | 0.454930 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.09759 | 0.267698 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.1019 | −0.399641 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.9249 | 1.38297 | 0.691487 | − | 0.722389i | \(-0.256956\pi\) | ||||
0.691487 | + | 0.722389i | \(0.256956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.6816 | 0.945091 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.3097 | −1.49139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.7267 | 0.747250 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.718195 | −0.0235886 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.71805 | 0.253221 | 0.126611 | − | 0.991953i | \(-0.459590\pi\) | ||||
0.126611 | + | 0.991953i | \(0.459590\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82965 | −0.0599645 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.52545 | 0.0826796 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 68.3631 | 2.23571 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3638 | −1.18795 | −0.593977 | − | 0.804482i | \(-0.702443\pi\) | ||||
−0.593977 | + | 0.804482i | \(0.702443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.2815 | −1.21664 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.36459 | −0.109682 | −0.0548412 | − | 0.998495i | \(-0.517465\pi\) | ||||
−0.0548412 | + | 0.998495i | \(0.517465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.1055 | −0.622160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.5656 | 1.28707 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.6697 | 0.769161 | 0.384581 | − | 0.923091i | \(-0.374346\pi\) | ||||
0.384581 | + | 0.923091i | \(0.374346\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7944 | 0.675014 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.1194 | −0.328145 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.20371 | 0.168565 | 0.0842823 | − | 0.996442i | \(-0.473140\pi\) | ||||
0.0842823 | + | 0.996442i | \(0.473140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.1965 | −1.43017 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.0606 | −1.00405 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.32092 | 0.0749463 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.8392 | 0.543202 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.53740 | −0.0817666 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57.0974 | −1.83803 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.5099 | 1.17408 | 0.587040 | − | 0.809558i | \(-0.300293\pi\) | ||||
0.587040 | + | 0.809558i | \(0.300293\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.4386 | −1.10633 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.6329 | 0.437502 | 0.218751 | − | 0.975781i | \(-0.429802\pi\) | ||||
0.218751 | + | 0.975781i | \(0.429802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.2666 | −0.842070 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.3267 | −0.939205 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.1343 | 0.740132 | 0.370066 | − | 0.929005i | \(-0.379335\pi\) | ||||
0.370066 | + | 0.929005i | \(0.379335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.95777 | −0.286292 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.33354 | 0.106432 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.7685 | −1.77874 | −0.889369 | − | 0.457190i | \(-0.848856\pi\) | ||||
−0.889369 | + | 0.457190i | \(0.848856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.8334 | −1.61969 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3907 | −0.362571 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.1611 | 0.545692 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.6117 | 1.00418 | 0.502090 | − | 0.864816i | \(-0.332565\pi\) | ||||
0.502090 | + | 0.864816i | \(0.332565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.7153 | −0.784316 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.6456 | 1.41536 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.90161 | −0.186906 | −0.0934530 | − | 0.995624i | \(-0.529790\pi\) | ||||
−0.0934530 | + | 0.995624i | \(0.529790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.9238 | 1.19986 |
(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 | 4016.2.a.m.1.8 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.16 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.16 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.8 | 23 | 1.1 | even | 1 | trivial |