Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69011 | −1.90220 | −0.951098 | − | 0.308890i | \(-0.900043\pi\) | ||||
−0.951098 | + | 0.308890i | \(0.900043\pi\) | |||||||
\(3\) | 0.353602 | 0.204152 | 0.102076 | − | 0.994777i | \(-0.467451\pi\) | ||||
0.102076 | + | 0.994777i | \(0.467451\pi\) | |||||||
\(4\) | 5.23670 | 2.61835 | ||||||||
\(5\) | −0.999886 | −0.447163 | −0.223581 | − | 0.974685i | \(-0.571775\pi\) | ||||
−0.223581 | + | 0.974685i | \(0.571775\pi\) | |||||||
\(6\) | −0.951229 | −0.388338 | ||||||||
\(7\) | 3.25121 | 1.22884 | 0.614421 | − | 0.788978i | \(-0.289390\pi\) | ||||
0.614421 | + | 0.788978i | \(0.289390\pi\) | |||||||
\(8\) | −8.70707 | −3.07842 | ||||||||
\(9\) | −2.87497 | −0.958322 | ||||||||
\(10\) | 2.68981 | 0.850591 | ||||||||
\(11\) | −3.92179 | −1.18246 | −0.591232 | − | 0.806502i | \(-0.701358\pi\) | ||||
−0.591232 | + | 0.806502i | \(0.701358\pi\) | |||||||
\(12\) | 1.85171 | 0.534542 | ||||||||
\(13\) | 2.55128 | 0.707597 | 0.353798 | − | 0.935322i | \(-0.384890\pi\) | ||||
0.353798 | + | 0.935322i | \(0.384890\pi\) | |||||||
\(14\) | −8.74612 | −2.33750 | ||||||||
\(15\) | −0.353562 | −0.0912894 | ||||||||
\(16\) | 12.9496 | 3.23740 | ||||||||
\(17\) | −3.24551 | −0.787153 | −0.393576 | − | 0.919292i | \(-0.628762\pi\) | ||||
−0.393576 | + | 0.919292i | \(0.628762\pi\) | |||||||
\(18\) | 7.73398 | 1.82292 | ||||||||
\(19\) | −6.18143 | −1.41812 | −0.709059 | − | 0.705149i | \(-0.750880\pi\) | ||||
−0.709059 | + | 0.705149i | \(0.750880\pi\) | |||||||
\(20\) | −5.23610 | −1.17083 | ||||||||
\(21\) | 1.14964 | 0.250871 | ||||||||
\(22\) | 10.5500 | 2.24928 | ||||||||
\(23\) | −6.21887 | −1.29672 | −0.648362 | − | 0.761332i | \(-0.724546\pi\) | ||||
−0.648362 | + | 0.761332i | \(0.724546\pi\) | |||||||
\(24\) | −3.07884 | −0.628466 | ||||||||
\(25\) | −4.00023 | −0.800045 | ||||||||
\(26\) | −6.86322 | −1.34599 | ||||||||
\(27\) | −2.07740 | −0.399796 | ||||||||
\(28\) | 17.0256 | 3.21754 | ||||||||
\(29\) | 2.78073 | 0.516368 | 0.258184 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258184 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(30\) | 0.951121 | 0.173650 | ||||||||
\(31\) | −2.88281 | −0.517767 | −0.258884 | − | 0.965909i | \(-0.583355\pi\) | ||||
−0.258884 | + | 0.965909i | \(0.583355\pi\) | |||||||
\(32\) | −17.4217 | −3.07975 | ||||||||
\(33\) | −1.38675 | −0.241403 | ||||||||
\(34\) | 8.73079 | 1.49732 | ||||||||
\(35\) | −3.25084 | −0.549492 | ||||||||
\(36\) | −15.0553 | −2.50922 | ||||||||
\(37\) | 7.41193 | 1.21851 | 0.609257 | − | 0.792973i | \(-0.291468\pi\) | ||||
0.609257 | + | 0.792973i | \(0.291468\pi\) | |||||||
\(38\) | 16.6287 | 2.69754 | ||||||||
\(39\) | 0.902137 | 0.144458 | ||||||||
\(40\) | 8.70609 | 1.37655 | ||||||||
\(41\) | −2.56356 | −0.400361 | −0.200181 | − | 0.979759i | \(-0.564153\pi\) | ||||
−0.200181 | + | 0.979759i | \(0.564153\pi\) | |||||||
\(42\) | −3.09265 | −0.477206 | ||||||||
\(43\) | −7.30959 | −1.11470 | −0.557351 | − | 0.830277i | \(-0.688182\pi\) | ||||
−0.557351 | + | 0.830277i | \(0.688182\pi\) | |||||||
\(44\) | −20.5372 | −3.09610 | ||||||||
\(45\) | 2.87464 | 0.428526 | ||||||||
\(46\) | 16.7295 | 2.46662 | ||||||||
\(47\) | −0.0357877 | −0.00522017 | −0.00261009 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00261009 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(48\) | 4.57901 | 0.660923 | ||||||||
\(49\) | 3.57036 | 0.510052 | ||||||||
\(50\) | 10.7611 | 1.52184 | ||||||||
\(51\) | −1.14762 | −0.160699 | ||||||||
\(52\) | 13.3603 | 1.85273 | ||||||||
\(53\) | 12.9978 | 1.78539 | 0.892695 | − | 0.450662i | \(-0.148812\pi\) | ||||
0.892695 | + | 0.450662i | \(0.148812\pi\) | |||||||
\(54\) | 5.58844 | 0.760490 | ||||||||
\(55\) | 3.92134 | 0.528754 | ||||||||
\(56\) | −28.3085 | −3.78289 | ||||||||
\(57\) | −2.18577 | −0.289512 | ||||||||
\(58\) | −7.48046 | −0.982233 | ||||||||
\(59\) | −7.42610 | −0.966796 | −0.483398 | − | 0.875401i | \(-0.660598\pi\) | ||||
−0.483398 | + | 0.875401i | \(0.660598\pi\) | |||||||
\(60\) | −1.85150 | −0.239027 | ||||||||
\(61\) | 1.59266 | 0.203920 | 0.101960 | − | 0.994789i | \(-0.467489\pi\) | ||||
0.101960 | + | 0.994789i | \(0.467489\pi\) | |||||||
\(62\) | 7.75507 | 0.984895 | ||||||||
\(63\) | −9.34712 | −1.17763 | ||||||||
\(64\) | 20.9671 | 2.62089 | ||||||||
\(65\) | −2.55099 | −0.316411 | ||||||||
\(66\) | 3.73052 | 0.459195 | ||||||||
\(67\) | −5.79715 | −0.708234 | −0.354117 | − | 0.935201i | \(-0.615219\pi\) | ||||
−0.354117 | + | 0.935201i | \(0.615219\pi\) | |||||||
\(68\) | −16.9958 | −2.06104 | ||||||||
\(69\) | −2.19901 | −0.264729 | ||||||||
\(70\) | 8.74512 | 1.04524 | ||||||||
\(71\) | −0.814408 | −0.0966524 | −0.0483262 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483262 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(72\) | 25.0325 | 2.95011 | ||||||||
\(73\) | 13.1201 | 1.53559 | 0.767794 | − | 0.640697i | \(-0.221355\pi\) | ||||
0.767794 | + | 0.640697i | \(0.221355\pi\) | |||||||
\(74\) | −19.9389 | −2.31785 | ||||||||
\(75\) | −1.41449 | −0.163331 | ||||||||
\(76\) | −32.3703 | −3.71313 | ||||||||
\(77\) | −12.7506 | −1.45306 | ||||||||
\(78\) | −2.42685 | −0.274787 | ||||||||
\(79\) | 9.45733 | 1.06403 | 0.532016 | − | 0.846734i | \(-0.321434\pi\) | ||||
0.532016 | + | 0.846734i | \(0.321434\pi\) | |||||||
\(80\) | −12.9481 | −1.44765 | ||||||||
\(81\) | 7.89032 | 0.876702 | ||||||||
\(82\) | 6.89627 | 0.761565 | ||||||||
\(83\) | −1.90763 | −0.209390 | −0.104695 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104695 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(84\) | 6.02029 | 0.656868 | ||||||||
\(85\) | 3.24514 | 0.351985 | ||||||||
\(86\) | 19.6636 | 2.12038 | ||||||||
\(87\) | 0.983271 | 0.105418 | ||||||||
\(88\) | 34.1473 | 3.64012 | ||||||||
\(89\) | 18.3507 | 1.94517 | 0.972587 | − | 0.232541i | \(-0.0747039\pi\) | ||||
0.972587 | + | 0.232541i | \(0.0747039\pi\) | |||||||
\(90\) | −7.73310 | −0.815140 | ||||||||
\(91\) | 8.29473 | 0.869524 | ||||||||
\(92\) | −32.5663 | −3.39528 | ||||||||
\(93\) | −1.01937 | −0.105703 | ||||||||
\(94\) | 0.0962729 | 0.00992979 | ||||||||
\(95\) | 6.18073 | 0.634129 | ||||||||
\(96\) | −6.16036 | −0.628739 | ||||||||
\(97\) | 3.98815 | 0.404935 | 0.202468 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202468 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(98\) | −9.60468 | −0.970219 | ||||||||
\(99\) | 11.2750 | 1.13318 | ||||||||
\(100\) | −20.9480 | −2.09480 | ||||||||
\(101\) | 9.07095 | 0.902594 | 0.451297 | − | 0.892374i | \(-0.350962\pi\) | ||||
0.451297 | + | 0.892374i | \(0.350962\pi\) | |||||||
\(102\) | 3.08723 | 0.305681 | ||||||||
\(103\) | 9.80257 | 0.965876 | 0.482938 | − | 0.875655i | \(-0.339570\pi\) | ||||
0.482938 | + | 0.875655i | \(0.339570\pi\) | |||||||
\(104\) | −22.2142 | −2.17828 | ||||||||
\(105\) | −1.14950 | −0.112180 | ||||||||
\(106\) | −34.9656 | −3.39616 | ||||||||
\(107\) | 14.2465 | 1.37726 | 0.688628 | − | 0.725115i | \(-0.258213\pi\) | ||||
0.688628 | + | 0.725115i | \(0.258213\pi\) | |||||||
\(108\) | −10.8787 | −1.04681 | ||||||||
\(109\) | 10.3058 | 0.987112 | 0.493556 | − | 0.869714i | \(-0.335697\pi\) | ||||
0.493556 | + | 0.869714i | \(0.335697\pi\) | |||||||
\(110\) | −10.5488 | −1.00579 | ||||||||
\(111\) | 2.62088 | 0.248762 | ||||||||
\(112\) | 42.1019 | 3.97825 | ||||||||
\(113\) | 12.1223 | 1.14037 | 0.570183 | − | 0.821518i | \(-0.306872\pi\) | ||||
0.570183 | + | 0.821518i | \(0.306872\pi\) | |||||||
\(114\) | 5.87996 | 0.550709 | ||||||||
\(115\) | 6.21816 | 0.579847 | ||||||||
\(116\) | 14.5618 | 1.35203 | ||||||||
\(117\) | −7.33483 | −0.678105 | ||||||||
\(118\) | 19.9770 | 1.83903 | ||||||||
\(119\) | −10.5518 | −0.967286 | ||||||||
\(120\) | 3.07849 | 0.281027 | ||||||||
\(121\) | 4.38043 | 0.398221 | ||||||||
\(122\) | −4.28444 | −0.387895 | ||||||||
\(123\) | −0.906482 | −0.0817347 | ||||||||
\(124\) | −15.0964 | −1.35570 | ||||||||
\(125\) | 8.99921 | 0.804913 | ||||||||
\(126\) | 25.1448 | 2.24007 | ||||||||
\(127\) | −8.05780 | −0.715014 | −0.357507 | − | 0.933910i | \(-0.616373\pi\) | ||||
−0.357507 | + | 0.933910i | \(0.616373\pi\) | |||||||
\(128\) | −21.5605 | −1.90570 | ||||||||
\(129\) | −2.58469 | −0.227569 | ||||||||
\(130\) | 6.86244 | 0.601876 | ||||||||
\(131\) | −8.09546 | −0.707304 | −0.353652 | − | 0.935377i | \(-0.615060\pi\) | ||||
−0.353652 | + | 0.935377i | \(0.615060\pi\) | |||||||
\(132\) | −7.26201 | −0.632077 | ||||||||
\(133\) | −20.0971 | −1.74264 | ||||||||
\(134\) | 15.5950 | 1.34720 | ||||||||
\(135\) | 2.07717 | 0.178774 | ||||||||
\(136\) | 28.2589 | 2.42318 | ||||||||
\(137\) | 22.1702 | 1.89413 | 0.947066 | − | 0.321039i | \(-0.104032\pi\) | ||||
0.947066 | + | 0.321039i | \(0.104032\pi\) | |||||||
\(138\) | 5.91557 | 0.503567 | ||||||||
\(139\) | 5.71832 | 0.485022 | 0.242511 | − | 0.970149i | \(-0.422029\pi\) | ||||
0.242511 | + | 0.970149i | \(0.422029\pi\) | |||||||
\(140\) | −17.0237 | −1.43876 | ||||||||
\(141\) | −0.0126546 | −0.00106571 | ||||||||
\(142\) | 2.19085 | 0.183852 | ||||||||
\(143\) | −10.0056 | −0.836708 | ||||||||
\(144\) | −37.2297 | −3.10247 | ||||||||
\(145\) | −2.78041 | −0.230901 | ||||||||
\(146\) | −35.2944 | −2.92099 | ||||||||
\(147\) | 1.26249 | 0.104128 | ||||||||
\(148\) | 38.8140 | 3.19049 | ||||||||
\(149\) | −11.6974 | −0.958284 | −0.479142 | − | 0.877737i | \(-0.659052\pi\) | ||||
−0.479142 | + | 0.877737i | \(0.659052\pi\) | |||||||
\(150\) | 3.80513 | 0.310688 | ||||||||
\(151\) | 5.06610 | 0.412273 | 0.206137 | − | 0.978523i | \(-0.433911\pi\) | ||||
0.206137 | + | 0.978523i | \(0.433911\pi\) | |||||||
\(152\) | 53.8222 | 4.36556 | ||||||||
\(153\) | 9.33074 | 0.754345 | ||||||||
\(154\) | 34.3004 | 2.76401 | ||||||||
\(155\) | 2.88248 | 0.231526 | ||||||||
\(156\) | 4.72422 | 0.378240 | ||||||||
\(157\) | 4.41311 | 0.352205 | 0.176102 | − | 0.984372i | \(-0.443651\pi\) | ||||
0.176102 | + | 0.984372i | \(0.443651\pi\) | |||||||
\(158\) | −25.4413 | −2.02400 | ||||||||
\(159\) | 4.59606 | 0.364491 | ||||||||
\(160\) | 17.4197 | 1.37715 | ||||||||
\(161\) | −20.2189 | −1.59347 | ||||||||
\(162\) | −21.2258 | −1.66766 | ||||||||
\(163\) | −6.15144 | −0.481818 | −0.240909 | − | 0.970548i | \(-0.577446\pi\) | ||||
−0.240909 | + | 0.970548i | \(0.577446\pi\) | |||||||
\(164\) | −13.4246 | −1.04829 | ||||||||
\(165\) | 1.38660 | 0.107946 | ||||||||
\(166\) | 5.13174 | 0.398300 | ||||||||
\(167\) | −2.18316 | −0.168938 | −0.0844690 | − | 0.996426i | \(-0.526919\pi\) | ||||
−0.0844690 | + | 0.996426i | \(0.526919\pi\) | |||||||
\(168\) | −10.0100 | −0.772285 | ||||||||
\(169\) | −6.49099 | −0.499307 | ||||||||
\(170\) | −8.72980 | −0.669545 | ||||||||
\(171\) | 17.7714 | 1.35901 | ||||||||
\(172\) | −38.2781 | −2.91868 | ||||||||
\(173\) | −7.39065 | −0.561901 | −0.280950 | − | 0.959722i | \(-0.590650\pi\) | ||||
−0.280950 | + | 0.959722i | \(0.590650\pi\) | |||||||
\(174\) | −2.64511 | −0.200525 | ||||||||
\(175\) | −13.0056 | −0.983129 | ||||||||
\(176\) | −50.7856 | −3.82811 | ||||||||
\(177\) | −2.62589 | −0.197374 | ||||||||
\(178\) | −49.3655 | −3.70010 | ||||||||
\(179\) | −4.52767 | −0.338414 | −0.169207 | − | 0.985581i | \(-0.554121\pi\) | ||||
−0.169207 | + | 0.985581i | \(0.554121\pi\) | |||||||
\(180\) | 15.0536 | 1.12203 | ||||||||
\(181\) | 2.35496 | 0.175043 | 0.0875216 | − | 0.996163i | \(-0.472105\pi\) | ||||
0.0875216 | + | 0.996163i | \(0.472105\pi\) | |||||||
\(182\) | −22.3138 | −1.65401 | ||||||||
\(183\) | 0.563169 | 0.0416307 | ||||||||
\(184\) | 54.1482 | 3.99186 | ||||||||
\(185\) | −7.41109 | −0.544874 | ||||||||
\(186\) | 2.74221 | 0.201069 | ||||||||
\(187\) | 12.7282 | 0.930779 | ||||||||
\(188\) | −0.187409 | −0.0136682 | ||||||||
\(189\) | −6.75407 | −0.491286 | ||||||||
\(190\) | −16.6268 | −1.20624 | ||||||||
\(191\) | −15.2688 | −1.10481 | −0.552406 | − | 0.833575i | \(-0.686290\pi\) | ||||
−0.552406 | + | 0.833575i | \(0.686290\pi\) | |||||||
\(192\) | 7.41403 | 0.535062 | ||||||||
\(193\) | 6.24930 | 0.449835 | 0.224917 | − | 0.974378i | \(-0.427789\pi\) | ||||
0.224917 | + | 0.974378i | \(0.427789\pi\) | |||||||
\(194\) | −10.7286 | −0.770266 | ||||||||
\(195\) | −0.902035 | −0.0645961 | ||||||||
\(196\) | 18.6969 | 1.33549 | ||||||||
\(197\) | −7.42210 | −0.528803 | −0.264401 | − | 0.964413i | \(-0.585174\pi\) | ||||
−0.264401 | + | 0.964413i | \(0.585174\pi\) | |||||||
\(198\) | −30.3310 | −2.15553 | ||||||||
\(199\) | −8.90657 | −0.631370 | −0.315685 | − | 0.948864i | \(-0.602234\pi\) | ||||
−0.315685 | + | 0.948864i | \(0.602234\pi\) | |||||||
\(200\) | 34.8303 | 2.46287 | ||||||||
\(201\) | −2.04988 | −0.144588 | ||||||||
\(202\) | −24.4019 | −1.71691 | ||||||||
\(203\) | 9.04073 | 0.634535 | ||||||||
\(204\) | −6.00974 | −0.420766 | ||||||||
\(205\) | 2.56327 | 0.179027 | ||||||||
\(206\) | −26.3700 | −1.83728 | ||||||||
\(207\) | 17.8790 | 1.24268 | ||||||||
\(208\) | 33.0380 | 2.29077 | ||||||||
\(209\) | 24.2423 | 1.67687 | ||||||||
\(210\) | 3.09230 | 0.213389 | ||||||||
\(211\) | −0.682757 | −0.0470029 | −0.0235015 | − | 0.999724i | \(-0.507481\pi\) | ||||
−0.0235015 | + | 0.999724i | \(0.507481\pi\) | |||||||
\(212\) | 68.0657 | 4.67477 | ||||||||
\(213\) | −0.287976 | −0.0197318 | ||||||||
\(214\) | −38.3245 | −2.61981 | ||||||||
\(215\) | 7.30876 | 0.498453 | ||||||||
\(216\) | 18.0881 | 1.23074 | ||||||||
\(217\) | −9.37261 | −0.636254 | ||||||||
\(218\) | −27.7236 | −1.87768 | ||||||||
\(219\) | 4.63928 | 0.313494 | ||||||||
\(220\) | 20.5349 | 1.38446 | ||||||||
\(221\) | −8.28020 | −0.556987 | ||||||||
\(222\) | −7.05044 | −0.473195 | ||||||||
\(223\) | −19.2400 | −1.28841 | −0.644204 | − | 0.764854i | \(-0.722811\pi\) | ||||
−0.644204 | + | 0.764854i | \(0.722811\pi\) | |||||||
\(224\) | −56.6417 | −3.78453 | ||||||||
\(225\) | 11.5005 | 0.766701 | ||||||||
\(226\) | −32.6102 | −2.16920 | ||||||||
\(227\) | 22.9038 | 1.52018 | 0.760088 | − | 0.649820i | \(-0.225156\pi\) | ||||
0.760088 | + | 0.649820i | \(0.225156\pi\) | |||||||
\(228\) | −11.4462 | −0.758044 | ||||||||
\(229\) | 1.05414 | 0.0696598 | 0.0348299 | − | 0.999393i | \(-0.488911\pi\) | ||||
0.0348299 | + | 0.999393i | \(0.488911\pi\) | |||||||
\(230\) | −16.7276 | −1.10298 | ||||||||
\(231\) | −4.50863 | −0.296646 | ||||||||
\(232\) | −24.2120 | −1.58960 | ||||||||
\(233\) | −15.9142 | −1.04258 | −0.521288 | − | 0.853381i | \(-0.674548\pi\) | ||||
−0.521288 | + | 0.853381i | \(0.674548\pi\) | |||||||
\(234\) | 19.7315 | 1.28989 | ||||||||
\(235\) | 0.0357836 | 0.00233427 | ||||||||
\(236\) | −38.8882 | −2.53141 | ||||||||
\(237\) | 3.34413 | 0.217225 | ||||||||
\(238\) | 28.3856 | 1.83997 | ||||||||
\(239\) | 4.44642 | 0.287615 | 0.143808 | − | 0.989606i | \(-0.454065\pi\) | ||||
0.143808 | + | 0.989606i | \(0.454065\pi\) | |||||||
\(240\) | −4.57849 | −0.295540 | ||||||||
\(241\) | 4.66671 | 0.300609 | 0.150304 | − | 0.988640i | \(-0.451975\pi\) | ||||
0.150304 | + | 0.988640i | \(0.451975\pi\) | |||||||
\(242\) | −11.7838 | −0.757494 | ||||||||
\(243\) | 9.02224 | 0.578777 | ||||||||
\(244\) | 8.34029 | 0.533933 | ||||||||
\(245\) | −3.56996 | −0.228076 | ||||||||
\(246\) | 2.43854 | 0.155475 | ||||||||
\(247\) | −15.7705 | −1.00346 | ||||||||
\(248\) | 25.1008 | 1.59390 | ||||||||
\(249\) | −0.674542 | −0.0427474 | ||||||||
\(250\) | −24.2089 | −1.53110 | ||||||||
\(251\) | 18.6306 | 1.17595 | 0.587976 | − | 0.808879i | \(-0.299925\pi\) | ||||
0.587976 | + | 0.808879i | \(0.299925\pi\) | |||||||
\(252\) | −48.9480 | −3.08343 | ||||||||
\(253\) | 24.3891 | 1.53333 | ||||||||
\(254\) | 21.6764 | 1.36010 | ||||||||
\(255\) | 1.14749 | 0.0718587 | ||||||||
\(256\) | 16.0659 | 1.00412 | ||||||||
\(257\) | 5.18730 | 0.323575 | 0.161787 | − | 0.986826i | \(-0.448274\pi\) | ||||
0.161787 | + | 0.986826i | \(0.448274\pi\) | |||||||
\(258\) | 6.95309 | 0.432881 | ||||||||
\(259\) | 24.0977 | 1.49736 | ||||||||
\(260\) | −13.3587 | −0.828474 | ||||||||
\(261\) | −7.99449 | −0.494847 | ||||||||
\(262\) | 21.7777 | 1.34543 | ||||||||
\(263\) | 0.929089 | 0.0572901 | 0.0286450 | − | 0.999590i | \(-0.490881\pi\) | ||||
0.0286450 | + | 0.999590i | \(0.490881\pi\) | |||||||
\(264\) | 12.0746 | 0.743138 | ||||||||
\(265\) | −12.9964 | −0.798360 | ||||||||
\(266\) | 54.0635 | 3.31485 | ||||||||
\(267\) | 6.48886 | 0.397112 | ||||||||
\(268\) | −30.3579 | −1.85440 | ||||||||
\(269\) | 7.96326 | 0.485528 | 0.242764 | − | 0.970085i | \(-0.421946\pi\) | ||||
0.242764 | + | 0.970085i | \(0.421946\pi\) | |||||||
\(270\) | −5.58781 | −0.340063 | ||||||||
\(271\) | 1.94501 | 0.118151 | 0.0590754 | − | 0.998254i | \(-0.481185\pi\) | ||||
0.0590754 | + | 0.998254i | \(0.481185\pi\) | |||||||
\(272\) | −42.0281 | −2.54833 | ||||||||
\(273\) | 2.93304 | 0.177515 | ||||||||
\(274\) | −59.6404 | −3.60301 | ||||||||
\(275\) | 15.6880 | 0.946025 | ||||||||
\(276\) | −11.5155 | −0.693154 | ||||||||
\(277\) | 12.0364 | 0.723195 | 0.361597 | − | 0.932334i | \(-0.382232\pi\) | ||||
0.361597 | + | 0.932334i | \(0.382232\pi\) | |||||||
\(278\) | −15.3829 | −0.922606 | ||||||||
\(279\) | 8.28797 | 0.496188 | ||||||||
\(280\) | 28.3053 | 1.69157 | ||||||||
\(281\) | −10.4581 | −0.623878 | −0.311939 | − | 0.950102i | \(-0.600979\pi\) | ||||
−0.311939 | + | 0.950102i | \(0.600979\pi\) | |||||||
\(282\) | 0.0340423 | 0.00202719 | ||||||||
\(283\) | −1.06203 | −0.0631310 | −0.0315655 | − | 0.999502i | \(-0.510049\pi\) | ||||
−0.0315655 | + | 0.999502i | \(0.510049\pi\) | |||||||
\(284\) | −4.26481 | −0.253070 | ||||||||
\(285\) | 2.18552 | 0.129459 | ||||||||
\(286\) | 26.9161 | 1.59158 | ||||||||
\(287\) | −8.33468 | −0.491981 | ||||||||
\(288\) | 50.0868 | 2.95139 | ||||||||
\(289\) | −6.46664 | −0.380391 | ||||||||
\(290\) | 7.47961 | 0.439218 | ||||||||
\(291\) | 1.41022 | 0.0826685 | ||||||||
\(292\) | 68.7058 | 4.02070 | ||||||||
\(293\) | 8.35925 | 0.488352 | 0.244176 | − | 0.969731i | \(-0.421482\pi\) | ||||
0.244176 | + | 0.969731i | \(0.421482\pi\) | |||||||
\(294\) | −3.39624 | −0.198073 | ||||||||
\(295\) | 7.42525 | 0.432315 | ||||||||
\(296\) | −64.5362 | −3.75109 | ||||||||
\(297\) | 8.14713 | 0.472744 | ||||||||
\(298\) | 31.4672 | 1.82284 | ||||||||
\(299\) | −15.8661 | −0.917558 | ||||||||
\(300\) | −7.40725 | −0.427658 | ||||||||
\(301\) | −23.7650 | −1.36979 | ||||||||
\(302\) | −13.6284 | −0.784224 | ||||||||
\(303\) | 3.20751 | 0.184267 | ||||||||
\(304\) | −80.0471 | −4.59101 | ||||||||
\(305\) | −1.59248 | −0.0911853 | ||||||||
\(306\) | −25.1007 | −1.43491 | ||||||||
\(307\) | −22.3856 | −1.27762 | −0.638808 | − | 0.769366i | \(-0.720572\pi\) | ||||
−0.638808 | + | 0.769366i | \(0.720572\pi\) | |||||||
\(308\) | −66.7708 | −3.80462 | ||||||||
\(309\) | 3.46621 | 0.197186 | ||||||||
\(310\) | −7.75419 | −0.440408 | ||||||||
\(311\) | −15.4306 | −0.874989 | −0.437494 | − | 0.899221i | \(-0.644134\pi\) | ||||
−0.437494 | + | 0.899221i | \(0.644134\pi\) | |||||||
\(312\) | −7.85498 | −0.444700 | ||||||||
\(313\) | −12.7769 | −0.722195 | −0.361097 | − | 0.932528i | \(-0.617598\pi\) | ||||
−0.361097 | + | 0.932528i | \(0.617598\pi\) | |||||||
\(314\) | −11.8718 | −0.669962 | ||||||||
\(315\) | 9.34605 | 0.526591 | ||||||||
\(316\) | 49.5252 | 2.78601 | ||||||||
\(317\) | −6.96753 | −0.391336 | −0.195668 | − | 0.980670i | \(-0.562687\pi\) | ||||
−0.195668 | + | 0.980670i | \(0.562687\pi\) | |||||||
\(318\) | −12.3639 | −0.693334 | ||||||||
\(319\) | −10.9054 | −0.610586 | ||||||||
\(320\) | −20.9648 | −1.17197 | ||||||||
\(321\) | 5.03758 | 0.281170 | ||||||||
\(322\) | 54.3910 | 3.03109 | ||||||||
\(323\) | 20.0619 | 1.11627 | ||||||||
\(324\) | 41.3192 | 2.29551 | ||||||||
\(325\) | −10.2057 | −0.566110 | ||||||||
\(326\) | 16.5481 | 0.916513 | ||||||||
\(327\) | 3.64414 | 0.201521 | ||||||||
\(328\) | 22.3211 | 1.23248 | ||||||||
\(329\) | −0.116353 | −0.00641477 | ||||||||
\(330\) | −3.73010 | −0.205335 | ||||||||
\(331\) | 35.3489 | 1.94295 | 0.971476 | − | 0.237139i | \(-0.0762098\pi\) | ||||
0.971476 | + | 0.237139i | \(0.0762098\pi\) | |||||||
\(332\) | −9.98968 | −0.548255 | ||||||||
\(333\) | −21.3090 | −1.16773 | ||||||||
\(334\) | 5.87294 | 0.321353 | ||||||||
\(335\) | 5.79649 | 0.316696 | ||||||||
\(336\) | 14.8873 | 0.812170 | ||||||||
\(337\) | −3.83616 | −0.208969 | −0.104484 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104484 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(338\) | 17.4615 | 0.949779 | ||||||||
\(339\) | 4.28646 | 0.232808 | ||||||||
\(340\) | 16.9938 | 0.921620 | ||||||||
\(341\) | 11.3058 | 0.612241 | ||||||||
\(342\) | −47.8070 | −2.58511 | ||||||||
\(343\) | −11.1505 | −0.602068 | ||||||||
\(344\) | 63.6451 | 3.43151 | ||||||||
\(345\) | 2.19876 | 0.118377 | ||||||||
\(346\) | 19.8817 | 1.06884 | ||||||||
\(347\) | −21.8511 | −1.17303 | −0.586515 | − | 0.809938i | \(-0.699500\pi\) | ||||
−0.586515 | + | 0.809938i | \(0.699500\pi\) | |||||||
\(348\) | 5.14909 | 0.276020 | ||||||||
\(349\) | 6.87369 | 0.367940 | 0.183970 | − | 0.982932i | \(-0.441105\pi\) | ||||
0.183970 | + | 0.982932i | \(0.441105\pi\) | |||||||
\(350\) | 34.9864 | 1.87010 | ||||||||
\(351\) | −5.30002 | −0.282894 | ||||||||
\(352\) | 68.3243 | 3.64170 | ||||||||
\(353\) | −22.6485 | −1.20546 | −0.602728 | − | 0.797946i | \(-0.705920\pi\) | ||||
−0.602728 | + | 0.797946i | \(0.705920\pi\) | |||||||
\(354\) | 7.06392 | 0.375443 | ||||||||
\(355\) | 0.814315 | 0.0432194 | ||||||||
\(356\) | 96.0972 | 5.09314 | ||||||||
\(357\) | −3.73116 | −0.197474 | ||||||||
\(358\) | 12.1799 | 0.643729 | ||||||||
\(359\) | −12.9264 | −0.682228 | −0.341114 | − | 0.940022i | \(-0.610804\pi\) | ||||
−0.341114 | + | 0.940022i | \(0.610804\pi\) | |||||||
\(360\) | −25.0297 | −1.31918 | ||||||||
\(361\) | 19.2101 | 1.01106 | ||||||||
\(362\) | −6.33512 | −0.332966 | ||||||||
\(363\) | 1.54893 | 0.0812977 | ||||||||
\(364\) | 43.4370 | 2.27672 | ||||||||
\(365\) | −13.1186 | −0.686658 | ||||||||
\(366\) | −1.51499 | −0.0791897 | ||||||||
\(367\) | −2.24222 | −0.117043 | −0.0585215 | − | 0.998286i | \(-0.518639\pi\) | ||||
−0.0585215 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(368\) | −80.5319 | −4.19802 | ||||||||
\(369\) | 7.37015 | 0.383675 | ||||||||
\(370\) | 19.9366 | 1.03646 | ||||||||
\(371\) | 42.2587 | 2.19396 | ||||||||
\(372\) | −5.33812 | −0.276768 | ||||||||
\(373\) | −35.5116 | −1.83872 | −0.919361 | − | 0.393414i | \(-0.871294\pi\) | ||||
−0.919361 | + | 0.393414i | \(0.871294\pi\) | |||||||
\(374\) | −34.2403 | −1.77052 | ||||||||
\(375\) | 3.18214 | 0.164325 | ||||||||
\(376\) | 0.311606 | 0.0160699 | ||||||||
\(377\) | 7.09440 | 0.365380 | ||||||||
\(378\) | 18.1692 | 0.934522 | ||||||||
\(379\) | −11.5009 | −0.590762 | −0.295381 | − | 0.955380i | \(-0.595447\pi\) | ||||
−0.295381 | + | 0.955380i | \(0.595447\pi\) | |||||||
\(380\) | 32.3666 | 1.66037 | ||||||||
\(381\) | −2.84926 | −0.145972 | ||||||||
\(382\) | 41.0748 | 2.10157 | ||||||||
\(383\) | 19.5259 | 0.997729 | 0.498864 | − | 0.866680i | \(-0.333751\pi\) | ||||
0.498864 | + | 0.866680i | \(0.333751\pi\) | |||||||
\(384\) | −7.62385 | −0.389053 | ||||||||
\(385\) | 12.7491 | 0.649755 | ||||||||
\(386\) | −16.8113 | −0.855674 | ||||||||
\(387\) | 21.0148 | 1.06824 | ||||||||
\(388\) | 20.8847 | 1.06026 | ||||||||
\(389\) | 13.3406 | 0.676395 | 0.338198 | − | 0.941075i | \(-0.390183\pi\) | ||||
0.338198 | + | 0.941075i | \(0.390183\pi\) | |||||||
\(390\) | 2.42657 | 0.122874 | ||||||||
\(391\) | 20.1834 | 1.02072 | ||||||||
\(392\) | −31.0874 | −1.57015 | ||||||||
\(393\) | −2.86257 | −0.144398 | ||||||||
\(394\) | 19.9663 | 1.00589 | ||||||||
\(395\) | −9.45626 | −0.475796 | ||||||||
\(396\) | 59.0438 | 2.96706 | ||||||||
\(397\) | −36.1041 | −1.81202 | −0.906008 | − | 0.423262i | \(-0.860885\pi\) | ||||
−0.906008 | + | 0.423262i | \(0.860885\pi\) | |||||||
\(398\) | 23.9597 | 1.20099 | ||||||||
\(399\) | −7.10639 | −0.355765 | ||||||||
\(400\) | −51.8013 | −2.59007 | ||||||||
\(401\) | 20.3990 | 1.01868 | 0.509340 | − | 0.860566i | \(-0.329890\pi\) | ||||
0.509340 | + | 0.860566i | \(0.329890\pi\) | |||||||
\(402\) | 5.51442 | 0.275034 | ||||||||
\(403\) | −7.35484 | −0.366370 | ||||||||
\(404\) | 47.5018 | 2.36330 | ||||||||
\(405\) | −7.88943 | −0.392029 | ||||||||
\(406\) | −24.3206 | −1.20701 | ||||||||
\(407\) | −29.0680 | −1.44085 | ||||||||
\(408\) | 9.99242 | 0.494699 | ||||||||
\(409\) | 25.8625 | 1.27882 | 0.639409 | − | 0.768867i | \(-0.279179\pi\) | ||||
0.639409 | + | 0.768867i | \(0.279179\pi\) | |||||||
\(410\) | −6.89548 | −0.340544 | ||||||||
\(411\) | 7.83945 | 0.386692 | ||||||||
\(412\) | 51.3331 | 2.52900 | ||||||||
\(413\) | −24.1438 | −1.18804 | ||||||||
\(414\) | −48.0966 | −2.36382 | ||||||||
\(415\) | 1.90741 | 0.0936313 | ||||||||
\(416\) | −44.4476 | −2.17922 | ||||||||
\(417\) | 2.02201 | 0.0990184 | ||||||||
\(418\) | −65.2144 | −3.18974 | ||||||||
\(419\) | −2.01758 | −0.0985652 | −0.0492826 | − | 0.998785i | \(-0.515693\pi\) | ||||
−0.0492826 | + | 0.998785i | \(0.515693\pi\) | |||||||
\(420\) | −6.01961 | −0.293727 | ||||||||
\(421\) | 20.4455 | 0.996454 | 0.498227 | − | 0.867047i | \(-0.333985\pi\) | ||||
0.498227 | + | 0.867047i | \(0.333985\pi\) | |||||||
\(422\) | 1.83669 | 0.0894088 | ||||||||
\(423\) | 0.102888 | 0.00500260 | ||||||||
\(424\) | −113.173 | −5.49617 | ||||||||
\(425\) | 12.9828 | 0.629758 | ||||||||
\(426\) | 0.774689 | 0.0375338 | ||||||||
\(427\) | 5.17808 | 0.250585 | ||||||||
\(428\) | 74.6043 | 3.60614 | ||||||||
\(429\) | −3.53799 | −0.170816 | ||||||||
\(430\) | −19.6614 | −0.948155 | ||||||||
\(431\) | 26.3069 | 1.26716 | 0.633580 | − | 0.773677i | \(-0.281585\pi\) | ||||
0.633580 | + | 0.773677i | \(0.281585\pi\) | |||||||
\(432\) | −26.9015 | −1.29430 | ||||||||
\(433\) | −4.77867 | −0.229648 | −0.114824 | − | 0.993386i | \(-0.536630\pi\) | ||||
−0.114824 | + | 0.993386i | \(0.536630\pi\) | |||||||
\(434\) | 25.2134 | 1.21028 | ||||||||
\(435\) | −0.983160 | −0.0471389 | ||||||||
\(436\) | 53.9681 | 2.58460 | ||||||||
\(437\) | 38.4415 | 1.83891 | ||||||||
\(438\) | −12.4802 | −0.596327 | ||||||||
\(439\) | 36.1670 | 1.72616 | 0.863078 | − | 0.505071i | \(-0.168534\pi\) | ||||
0.863078 | + | 0.505071i | \(0.168534\pi\) | |||||||
\(440\) | −34.1434 | −1.62772 | ||||||||
\(441\) | −10.2647 | −0.488794 | ||||||||
\(442\) | 22.2747 | 1.05950 | ||||||||
\(443\) | −11.3463 | −0.539080 | −0.269540 | − | 0.962989i | \(-0.586872\pi\) | ||||
−0.269540 | + | 0.962989i | \(0.586872\pi\) | |||||||
\(444\) | 13.7247 | 0.651347 | ||||||||
\(445\) | −18.3486 | −0.869809 | ||||||||
\(446\) | 51.7578 | 2.45080 | ||||||||
\(447\) | −4.13621 | −0.195636 | ||||||||
\(448\) | 68.1686 | 3.22066 | ||||||||
\(449\) | 40.6597 | 1.91885 | 0.959425 | − | 0.281965i | \(-0.0909862\pi\) | ||||
0.959425 | + | 0.281965i | \(0.0909862\pi\) | |||||||
\(450\) | −30.9377 | −1.45842 | ||||||||
\(451\) | 10.0538 | 0.473413 | ||||||||
\(452\) | 63.4806 | 2.98587 | ||||||||
\(453\) | 1.79138 | 0.0841665 | ||||||||
\(454\) | −61.6137 | −2.89167 | ||||||||
\(455\) | −8.29379 | −0.388819 | ||||||||
\(456\) | 19.0316 | 0.891239 | ||||||||
\(457\) | 36.6821 | 1.71592 | 0.857958 | − | 0.513720i | \(-0.171733\pi\) | ||||
0.857958 | + | 0.513720i | \(0.171733\pi\) | |||||||
\(458\) | −2.83576 | −0.132507 | ||||||||
\(459\) | 6.74223 | 0.314701 | ||||||||
\(460\) | 32.5626 | 1.51824 | ||||||||
\(461\) | 14.3424 | 0.667990 | 0.333995 | − | 0.942575i | \(-0.391603\pi\) | ||||
0.333995 | + | 0.942575i | \(0.391603\pi\) | |||||||
\(462\) | 12.1287 | 0.564278 | ||||||||
\(463\) | 20.5777 | 0.956326 | 0.478163 | − | 0.878271i | \(-0.341303\pi\) | ||||
0.478163 | + | 0.878271i | \(0.341303\pi\) | |||||||
\(464\) | 36.0093 | 1.67169 | ||||||||
\(465\) | 1.01925 | 0.0472666 | ||||||||
\(466\) | 42.8110 | 1.98318 | ||||||||
\(467\) | 10.8678 | 0.502902 | 0.251451 | − | 0.967870i | \(-0.419092\pi\) | ||||
0.251451 | + | 0.967870i | \(0.419092\pi\) | |||||||
\(468\) | −38.4103 | −1.77552 | ||||||||
\(469\) | −18.8477 | −0.870308 | ||||||||
\(470\) | −0.0962619 | −0.00444023 | ||||||||
\(471\) | 1.56049 | 0.0719035 | ||||||||
\(472\) | 64.6596 | 2.97620 | ||||||||
\(473\) | 28.6667 | 1.31809 | ||||||||
\(474\) | −8.99609 | −0.413204 | ||||||||
\(475\) | 24.7271 | 1.13456 | ||||||||
\(476\) | −55.2568 | −2.53269 | ||||||||
\(477\) | −37.3683 | −1.71098 | ||||||||
\(478\) | −11.9614 | −0.547100 | ||||||||
\(479\) | 14.5044 | 0.662723 | 0.331362 | − | 0.943504i | \(-0.392492\pi\) | ||||
0.331362 | + | 0.943504i | \(0.392492\pi\) | |||||||
\(480\) | 6.15966 | 0.281149 | ||||||||
\(481\) | 18.9099 | 0.862216 | ||||||||
\(482\) | −12.5540 | −0.571817 | ||||||||
\(483\) | −7.14943 | −0.325310 | ||||||||
\(484\) | 22.9390 | 1.04268 | ||||||||
\(485\) | −3.98770 | −0.181072 | ||||||||
\(486\) | −24.2708 | −1.10095 | ||||||||
\(487\) | −22.3017 | −1.01059 | −0.505294 | − | 0.862947i | \(-0.668616\pi\) | ||||
−0.505294 | + | 0.862947i | \(0.668616\pi\) | |||||||
\(488\) | −13.8674 | −0.627749 | ||||||||
\(489\) | −2.17516 | −0.0983644 | ||||||||
\(490\) | 9.60359 | 0.433846 | ||||||||
\(491\) | 7.30407 | 0.329628 | 0.164814 | − | 0.986325i | \(-0.447298\pi\) | ||||
0.164814 | + | 0.986325i | \(0.447298\pi\) | |||||||
\(492\) | −4.74697 | −0.214010 | ||||||||
\(493\) | −9.02489 | −0.406460 | ||||||||
\(494\) | 42.4245 | 1.90877 | ||||||||
\(495\) | −11.2737 | −0.506716 | ||||||||
\(496\) | −37.3312 | −1.67622 | ||||||||
\(497\) | −2.64781 | −0.118771 | ||||||||
\(498\) | 1.81459 | 0.0813139 | ||||||||
\(499\) | 28.9663 | 1.29671 | 0.648355 | − | 0.761338i | \(-0.275457\pi\) | ||||
0.648355 | + | 0.761338i | \(0.275457\pi\) | |||||||
\(500\) | 47.1261 | 2.10754 | ||||||||
\(501\) | −0.771971 | −0.0344891 | ||||||||
\(502\) | −50.1183 | −2.23689 | ||||||||
\(503\) | 17.6833 | 0.788459 | 0.394230 | − | 0.919012i | \(-0.371011\pi\) | ||||
0.394230 | + | 0.919012i | \(0.371011\pi\) | |||||||
\(504\) | 81.3860 | 3.62522 | ||||||||
\(505\) | −9.06992 | −0.403606 | ||||||||
\(506\) | −65.6094 | −2.91669 | ||||||||
\(507\) | −2.29523 | −0.101935 | ||||||||
\(508\) | −42.1963 | −1.87216 | ||||||||
\(509\) | −22.5151 | −0.997966 | −0.498983 | − | 0.866612i | \(-0.666293\pi\) | ||||
−0.498983 | + | 0.866612i | \(0.666293\pi\) | |||||||
\(510\) | −3.08688 | −0.136689 | ||||||||
\(511\) | 42.6561 | 1.88699 | ||||||||
\(512\) | −0.0980122 | −0.00433157 | ||||||||
\(513\) | 12.8413 | 0.566958 | ||||||||
\(514\) | −13.9544 | −0.615502 | ||||||||
\(515\) | −9.80145 | −0.431904 | ||||||||
\(516\) | −13.5352 | −0.595855 | ||||||||
\(517\) | 0.140352 | 0.00617267 | ||||||||
\(518\) | −64.8256 | −2.84827 | ||||||||
\(519\) | −2.61335 | −0.114713 | ||||||||
\(520\) | 22.2116 | 0.974044 | ||||||||
\(521\) | 29.1819 | 1.27848 | 0.639240 | − | 0.769007i | \(-0.279249\pi\) | ||||
0.639240 | + | 0.769007i | \(0.279249\pi\) | |||||||
\(522\) | 21.5061 | 0.941295 | ||||||||
\(523\) | −23.3445 | −1.02078 | −0.510392 | − | 0.859942i | \(-0.670500\pi\) | ||||
−0.510392 | + | 0.859942i | \(0.670500\pi\) | |||||||
\(524\) | −42.3935 | −1.85197 | ||||||||
\(525\) | −4.59880 | −0.200708 | ||||||||
\(526\) | −2.49935 | −0.108977 | ||||||||
\(527\) | 9.35619 | 0.407562 | ||||||||
\(528\) | −17.9579 | −0.781518 | ||||||||
\(529\) | 15.6744 | 0.681494 | ||||||||
\(530\) | 34.9616 | 1.51864 | ||||||||
\(531\) | 21.3498 | 0.926501 | ||||||||
\(532\) | −105.243 | −4.56284 | ||||||||
\(533\) | −6.54036 | −0.283294 | ||||||||
\(534\) | −17.4558 | −0.755384 | ||||||||
\(535\) | −14.2448 | −0.615858 | ||||||||
\(536\) | 50.4762 | 2.18024 | ||||||||
\(537\) | −1.60099 | −0.0690879 | ||||||||
\(538\) | −21.4220 | −0.923570 | ||||||||
\(539\) | −14.0022 | −0.603118 | ||||||||
\(540\) | 10.8775 | 0.468092 | ||||||||
\(541\) | −9.84022 | −0.423064 | −0.211532 | − | 0.977371i | \(-0.567845\pi\) | ||||
−0.211532 | + | 0.977371i | \(0.567845\pi\) | |||||||
\(542\) | −5.23229 | −0.224746 | ||||||||
\(543\) | 0.832721 | 0.0357355 | ||||||||
\(544\) | 56.5424 | 2.42424 | ||||||||
\(545\) | −10.3046 | −0.441400 | ||||||||
\(546\) | −7.89020 | −0.337669 | ||||||||
\(547\) | 12.5086 | 0.534828 | 0.267414 | − | 0.963582i | \(-0.413831\pi\) | ||||
0.267414 | + | 0.963582i | \(0.413831\pi\) | |||||||
\(548\) | 116.099 | 4.95950 | ||||||||
\(549\) | −4.57885 | −0.195421 | ||||||||
\(550\) | −42.2026 | −1.79952 | ||||||||
\(551\) | −17.1889 | −0.732271 | ||||||||
\(552\) | 19.1469 | 0.814947 | ||||||||
\(553\) | 30.7478 | 1.30753 | ||||||||
\(554\) | −32.3791 | −1.37566 | ||||||||
\(555\) | −2.62058 | −0.111237 | ||||||||
\(556\) | 29.9451 | 1.26996 | ||||||||
\(557\) | −13.1604 | −0.557625 | −0.278813 | − | 0.960346i | \(-0.589941\pi\) | ||||
−0.278813 | + | 0.960346i | \(0.589941\pi\) | |||||||
\(558\) | −22.2956 | −0.943846 | ||||||||
\(559\) | −18.6488 | −0.788759 | ||||||||
\(560\) | −42.0971 | −1.77893 | ||||||||
\(561\) | 4.50073 | 0.190021 | ||||||||
\(562\) | 28.1335 | 1.18674 | ||||||||
\(563\) | 10.4178 | 0.439059 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(564\) | −0.0662684 | −0.00279040 | ||||||||
\(565\) | −12.1209 | −0.509929 | ||||||||
\(566\) | 2.85697 | 0.120087 | ||||||||
\(567\) | 25.6531 | 1.07733 | ||||||||
\(568\) | 7.09111 | 0.297536 | ||||||||
\(569\) | 33.3673 | 1.39883 | 0.699415 | − | 0.714716i | \(-0.253444\pi\) | ||||
0.699415 | + | 0.714716i | \(0.253444\pi\) | |||||||
\(570\) | −5.87929 | −0.246256 | ||||||||
\(571\) | 4.00863 | 0.167756 | 0.0838779 | − | 0.996476i | \(-0.473269\pi\) | ||||
0.0838779 | + | 0.996476i | \(0.473269\pi\) | |||||||
\(572\) | −52.3961 | −2.19079 | ||||||||
\(573\) | −5.39909 | −0.225550 | ||||||||
\(574\) | 22.4212 | 0.935843 | ||||||||
\(575\) | 24.8769 | 1.03744 | ||||||||
\(576\) | −60.2798 | −2.51166 | ||||||||
\(577\) | −12.4877 | −0.519868 | −0.259934 | − | 0.965626i | \(-0.583701\pi\) | ||||
−0.259934 | + | 0.965626i | \(0.583701\pi\) | |||||||
\(578\) | 17.3960 | 0.723578 | ||||||||
\(579\) | 2.20977 | 0.0918348 | ||||||||
\(580\) | −14.5602 | −0.604578 | ||||||||
\(581\) | −6.20211 | −0.257307 | ||||||||
\(582\) | −3.79364 | −0.157252 | ||||||||
\(583\) | −50.9747 | −2.11116 | ||||||||
\(584\) | −114.237 | −4.72718 | ||||||||
\(585\) | 7.33400 | 0.303224 | ||||||||
\(586\) | −22.4873 | −0.928942 | ||||||||
\(587\) | −36.3147 | −1.49887 | −0.749434 | − | 0.662079i | \(-0.769674\pi\) | ||||
−0.749434 | + | 0.662079i | \(0.769674\pi\) | |||||||
\(588\) | 6.61127 | 0.272644 | ||||||||
\(589\) | 17.8199 | 0.734255 | ||||||||
\(590\) | −19.9748 | −0.822348 | ||||||||
\(591\) | −2.62447 | −0.107956 | ||||||||
\(592\) | 95.9815 | 3.94482 | ||||||||
\(593\) | −21.4713 | −0.881719 | −0.440859 | − | 0.897576i | \(-0.645326\pi\) | ||||
−0.440859 | + | 0.897576i | \(0.645326\pi\) | |||||||
\(594\) | −21.9167 | −0.899252 | ||||||||
\(595\) | 10.5506 | 0.432534 | ||||||||
\(596\) | −61.2555 | −2.50912 | ||||||||
\(597\) | −3.14938 | −0.128896 | ||||||||
\(598\) | 42.6815 | 1.74537 | ||||||||
\(599\) | 41.4723 | 1.69451 | 0.847255 | − | 0.531186i | \(-0.178253\pi\) | ||||
0.847255 | + | 0.531186i | \(0.178253\pi\) | |||||||
\(600\) | 12.3161 | 0.502801 | ||||||||
\(601\) | −21.7104 | −0.885586 | −0.442793 | − | 0.896624i | \(-0.646012\pi\) | ||||
−0.442793 | + | 0.896624i | \(0.646012\pi\) | |||||||
\(602\) | 63.9305 | 2.60561 | ||||||||
\(603\) | 16.6666 | 0.678716 | ||||||||
\(604\) | 26.5296 | 1.07947 | ||||||||
\(605\) | −4.37993 | −0.178070 | ||||||||
\(606\) | −8.62856 | −0.350511 | ||||||||
\(607\) | −16.2310 | −0.658795 | −0.329397 | − | 0.944191i | \(-0.606846\pi\) | ||||
−0.329397 | + | 0.944191i | \(0.606846\pi\) | |||||||
\(608\) | 107.691 | 4.36745 | ||||||||
\(609\) | 3.19682 | 0.129542 | ||||||||
\(610\) | 4.28395 | 0.173452 | ||||||||
\(611\) | −0.0913043 | −0.00369378 | ||||||||
\(612\) | 48.8622 | 1.97514 | ||||||||
\(613\) | −9.52547 | −0.384730 | −0.192365 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192365 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(614\) | 60.2199 | 2.43028 | ||||||||
\(615\) | 0.906379 | 0.0365487 | ||||||||
\(616\) | 111.020 | 4.47313 | ||||||||
\(617\) | −22.0116 | −0.886154 | −0.443077 | − | 0.896484i | \(-0.646113\pi\) | ||||
−0.443077 | + | 0.896484i | \(0.646113\pi\) | |||||||
\(618\) | −9.32449 | −0.375086 | ||||||||
\(619\) | 2.39082 | 0.0960952 | 0.0480476 | − | 0.998845i | \(-0.484700\pi\) | ||||
0.0480476 | + | 0.998845i | \(0.484700\pi\) | |||||||
\(620\) | 15.0947 | 0.606217 | ||||||||
\(621\) | 12.9191 | 0.518425 | ||||||||
\(622\) | 41.5100 | 1.66440 | ||||||||
\(623\) | 59.6621 | 2.39031 | ||||||||
\(624\) | 11.6823 | 0.467667 | ||||||||
\(625\) | 11.0030 | 0.440118 | ||||||||
\(626\) | 34.3714 | 1.37376 | ||||||||
\(627\) | 8.57212 | 0.342338 | ||||||||
\(628\) | 23.1101 | 0.922195 | ||||||||
\(629\) | −24.0555 | −0.959156 | ||||||||
\(630\) | −25.1419 | −1.00168 | ||||||||
\(631\) | −7.37154 | −0.293456 | −0.146728 | − | 0.989177i | \(-0.546874\pi\) | ||||
−0.146728 | + | 0.989177i | \(0.546874\pi\) | |||||||
\(632\) | −82.3457 | −3.27554 | ||||||||
\(633\) | −0.241425 | −0.00959576 | ||||||||
\(634\) | 18.7434 | 0.744397 | ||||||||
\(635\) | 8.05689 | 0.319728 | ||||||||
\(636\) | 24.0682 | 0.954366 | ||||||||
\(637\) | 9.10899 | 0.360911 | ||||||||
\(638\) | 29.3368 | 1.16145 | ||||||||
\(639\) | 2.34139 | 0.0926241 | ||||||||
\(640\) | 21.5581 | 0.852158 | ||||||||
\(641\) | 14.4403 | 0.570358 | 0.285179 | − | 0.958474i | \(-0.407947\pi\) | ||||
0.285179 | + | 0.958474i | \(0.407947\pi\) | |||||||
\(642\) | −13.5516 | −0.534841 | ||||||||
\(643\) | −33.7128 | −1.32950 | −0.664751 | − | 0.747065i | \(-0.731462\pi\) | ||||
−0.664751 | + | 0.747065i | \(0.731462\pi\) | |||||||
\(644\) | −105.880 | −4.17226 | ||||||||
\(645\) | 2.58439 | 0.101760 | ||||||||
\(646\) | −53.9688 | −2.12337 | ||||||||
\(647\) | 2.48216 | 0.0975839 | 0.0487920 | − | 0.998809i | \(-0.484463\pi\) | ||||
0.0487920 | + | 0.998809i | \(0.484463\pi\) | |||||||
\(648\) | −68.7016 | −2.69885 | ||||||||
\(649\) | 29.1236 | 1.14320 | ||||||||
\(650\) | 27.4544 | 1.07685 | ||||||||
\(651\) | −3.31418 | −0.129893 | ||||||||
\(652\) | −32.2133 | −1.26157 | ||||||||
\(653\) | 16.5022 | 0.645782 | 0.322891 | − | 0.946436i | \(-0.395345\pi\) | ||||
0.322891 | + | 0.946436i | \(0.395345\pi\) | |||||||
\(654\) | −9.80314 | −0.383333 | ||||||||
\(655\) | 8.09454 | 0.316280 | ||||||||
\(656\) | −33.1971 | −1.29613 | ||||||||
\(657\) | −37.7197 | −1.47159 | ||||||||
\(658\) | 0.313003 | 0.0122021 | ||||||||
\(659\) | −46.8300 | −1.82424 | −0.912119 | − | 0.409925i | \(-0.865555\pi\) | ||||
−0.912119 | + | 0.409925i | \(0.865555\pi\) | |||||||
\(660\) | 7.26118 | 0.282641 | ||||||||
\(661\) | 27.1955 | 1.05778 | 0.528891 | − | 0.848689i | \(-0.322608\pi\) | ||||
0.528891 | + | 0.848689i | \(0.322608\pi\) | |||||||
\(662\) | −95.0925 | −3.69587 | ||||||||
\(663\) | −2.92790 | −0.113710 | ||||||||
\(664\) | 16.6099 | 0.644588 | ||||||||
\(665\) | 20.0948 | 0.779245 | ||||||||
\(666\) | 57.3237 | 2.22125 | ||||||||
\(667\) | −17.2930 | −0.669587 | ||||||||
\(668\) | −11.4326 | −0.442339 | ||||||||
\(669\) | −6.80332 | −0.263031 | ||||||||
\(670\) | −15.5932 | −0.602418 | ||||||||
\(671\) | −6.24609 | −0.241128 | ||||||||
\(672\) | −20.0286 | −0.772621 | ||||||||
\(673\) | −16.8344 | −0.648917 | −0.324458 | − | 0.945900i | \(-0.605182\pi\) | ||||
−0.324458 | + | 0.945900i | \(0.605182\pi\) | |||||||
\(674\) | 10.3197 | 0.397500 | ||||||||
\(675\) | 8.31008 | 0.319855 | ||||||||
\(676\) | −33.9913 | −1.30736 | ||||||||
\(677\) | 41.9534 | 1.61240 | 0.806201 | − | 0.591642i | \(-0.201520\pi\) | ||||
0.806201 | + | 0.591642i | \(0.201520\pi\) | |||||||
\(678\) | −11.5310 | −0.442847 | ||||||||
\(679\) | 12.9663 | 0.497601 | ||||||||
\(680\) | −28.2557 | −1.08356 | ||||||||
\(681\) | 8.09883 | 0.310348 | ||||||||
\(682\) | −30.4137 | −1.16460 | ||||||||
\(683\) | 29.2647 | 1.11978 | 0.559892 | − | 0.828566i | \(-0.310843\pi\) | ||||
0.559892 | + | 0.828566i | \(0.310843\pi\) | |||||||
\(684\) | 93.0634 | 3.55837 | ||||||||
\(685\) | −22.1677 | −0.846985 | ||||||||
\(686\) | 29.9960 | 1.14525 | ||||||||
\(687\) | 0.372748 | 0.0142212 | ||||||||
\(688\) | −94.6562 | −3.60873 | ||||||||
\(689\) | 33.1611 | 1.26334 | ||||||||
\(690\) | −5.91490 | −0.225176 | ||||||||
\(691\) | 24.0618 | 0.915354 | 0.457677 | − | 0.889119i | \(-0.348682\pi\) | ||||
0.457677 | + | 0.889119i | \(0.348682\pi\) | |||||||
\(692\) | −38.7026 | −1.47125 | ||||||||
\(693\) | 36.6574 | 1.39250 | ||||||||
\(694\) | 58.7819 | 2.23133 | ||||||||
\(695\) | −5.71767 | −0.216884 | ||||||||
\(696\) | −8.56142 | −0.324520 | ||||||||
\(697\) | 8.32008 | 0.315145 | ||||||||
\(698\) | −18.4910 | −0.699894 | ||||||||
\(699\) | −5.62731 | −0.212844 | ||||||||
\(700\) | −68.1063 | −2.57417 | ||||||||
\(701\) | −45.2373 | −1.70859 | −0.854294 | − | 0.519790i | \(-0.826010\pi\) | ||||
−0.854294 | + | 0.519790i | \(0.826010\pi\) | |||||||
\(702\) | 14.2577 | 0.538121 | ||||||||
\(703\) | −45.8163 | −1.72800 | ||||||||
\(704\) | −82.2287 | −3.09911 | ||||||||
\(705\) | 0.0126532 | 0.000476546 0 | ||||||||
\(706\) | 60.9269 | 2.29301 | ||||||||
\(707\) | 29.4916 | 1.10914 | ||||||||
\(708\) | −13.7510 | −0.516793 | ||||||||
\(709\) | −34.1604 | −1.28292 | −0.641461 | − | 0.767156i | \(-0.721671\pi\) | ||||
−0.641461 | + | 0.767156i | \(0.721671\pi\) | |||||||
\(710\) | −2.19060 | −0.0822117 | ||||||||
\(711\) | −27.1895 | −1.01969 | ||||||||
\(712\) | −159.781 | −5.98805 | ||||||||
\(713\) | 17.9278 | 0.671401 | ||||||||
\(714\) | 10.0372 | 0.375634 | ||||||||
\(715\) | 10.0044 | 0.374145 | ||||||||
\(716\) | −23.7100 | −0.886085 | ||||||||
\(717\) | 1.57227 | 0.0587173 | ||||||||
\(718\) | 34.7734 | 1.29773 | ||||||||
\(719\) | −41.1197 | −1.53350 | −0.766752 | − | 0.641943i | \(-0.778129\pi\) | ||||
−0.766752 | + | 0.641943i | \(0.778129\pi\) | |||||||
\(720\) | 37.2254 | 1.38731 | ||||||||
\(721\) | 31.8702 | 1.18691 | ||||||||
\(722\) | −51.6773 | −1.92323 | ||||||||
\(723\) | 1.65016 | 0.0613700 | ||||||||
\(724\) | 12.3322 | 0.458324 | ||||||||
\(725\) | −11.1235 | −0.413118 | ||||||||
\(726\) | −4.16679 | −0.154644 | ||||||||
\(727\) | 27.0131 | 1.00186 | 0.500931 | − | 0.865487i | \(-0.332991\pi\) | ||||
0.500931 | + | 0.865487i | \(0.332991\pi\) | |||||||
\(728\) | −72.2229 | −2.67676 | ||||||||
\(729\) | −20.4807 | −0.758544 | ||||||||
\(730\) | 35.2904 | 1.30616 | ||||||||
\(731\) | 23.7234 | 0.877440 | ||||||||
\(732\) | 2.94915 | 0.109004 | ||||||||
\(733\) | −42.6350 | −1.57476 | −0.787380 | − | 0.616468i | \(-0.788563\pi\) | ||||
−0.787380 | + | 0.616468i | \(0.788563\pi\) | |||||||
\(734\) | 6.03182 | 0.222639 | ||||||||
\(735\) | −1.26235 | −0.0465623 | ||||||||
\(736\) | 108.343 | 3.99359 | ||||||||
\(737\) | 22.7352 | 0.837461 | ||||||||
\(738\) | −19.8265 | −0.729825 | ||||||||
\(739\) | −2.49327 | −0.0917163 | −0.0458582 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458582 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(740\) | −38.8096 | −1.42667 | ||||||||
\(741\) | −5.57650 | −0.204858 | ||||||||
\(742\) | −113.681 | −4.17334 | ||||||||
\(743\) | 1.90224 | 0.0697865 | 0.0348932 | − | 0.999391i | \(-0.488891\pi\) | ||||
0.0348932 | + | 0.999391i | \(0.488891\pi\) | |||||||
\(744\) | 8.87570 | 0.325399 | ||||||||
\(745\) | 11.6960 | 0.428509 | ||||||||
\(746\) | 95.5302 | 3.49761 | ||||||||
\(747\) | 5.48437 | 0.200663 | ||||||||
\(748\) | 66.6538 | 2.43711 | ||||||||
\(749\) | 46.3182 | 1.69243 | ||||||||
\(750\) | −8.56031 | −0.312578 | ||||||||
\(751\) | −26.0973 | −0.952303 | −0.476152 | − | 0.879363i | \(-0.657969\pi\) | ||||
−0.476152 | + | 0.879363i | \(0.657969\pi\) | |||||||
\(752\) | −0.463436 | −0.0168998 | ||||||||
\(753\) | 6.58782 | 0.240073 | ||||||||
\(754\) | −19.0847 | −0.695025 | ||||||||
\(755\) | −5.06552 | −0.184353 | ||||||||
\(756\) | −35.3690 | −1.28636 | ||||||||
\(757\) | 18.2526 | 0.663403 | 0.331701 | − | 0.943384i | \(-0.392377\pi\) | ||||
0.331701 | + | 0.943384i | \(0.392377\pi\) | |||||||
\(758\) | 30.9387 | 1.12374 | ||||||||
\(759\) | 8.62404 | 0.313033 | ||||||||
\(760\) | −53.8161 | −1.95211 | ||||||||
\(761\) | −33.4256 | −1.21168 | −0.605838 | − | 0.795588i | \(-0.707162\pi\) | ||||
−0.605838 | + | 0.795588i | \(0.707162\pi\) | |||||||
\(762\) | 7.66482 | 0.277667 | ||||||||
\(763\) | 33.5062 | 1.21300 | ||||||||
\(764\) | −79.9582 | −2.89278 | ||||||||
\(765\) | −9.32968 | −0.337315 | ||||||||
\(766\) | −52.5269 | −1.89788 | ||||||||
\(767\) | −18.9460 | −0.684101 | ||||||||
\(768\) | 5.68094 | 0.204993 | ||||||||
\(769\) | 15.3937 | 0.555112 | 0.277556 | − | 0.960709i | \(-0.410476\pi\) | ||||
0.277556 | + | 0.960709i | \(0.410476\pi\) | |||||||
\(770\) | −34.2965 | −1.23596 | ||||||||
\(771\) | 1.83424 | 0.0660585 | ||||||||
\(772\) | 32.7257 | 1.17782 | ||||||||
\(773\) | 20.3970 | 0.733631 | 0.366815 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366815 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(774\) | −56.5322 | −2.03201 | ||||||||
\(775\) | 11.5319 | 0.414237 | ||||||||
\(776\) | −34.7251 | −1.24656 | ||||||||
\(777\) | 8.52101 | 0.305690 | ||||||||
\(778\) | −35.8877 | −1.28664 | ||||||||
\(779\) | 15.8465 | 0.567759 | ||||||||
\(780\) | −4.72368 | −0.169135 | ||||||||
\(781\) | 3.19394 | 0.114288 | ||||||||
\(782\) | −54.2957 | −1.94161 | ||||||||
\(783\) | −5.77669 | −0.206442 | ||||||||
\(784\) | 46.2348 | 1.65124 | ||||||||
\(785\) | −4.41261 | −0.157493 | ||||||||
\(786\) | 7.70064 | 0.274673 | ||||||||
\(787\) | 9.49213 | 0.338358 | 0.169179 | − | 0.985585i | \(-0.445888\pi\) | ||||
0.169179 | + | 0.985585i | \(0.445888\pi\) | |||||||
\(788\) | −38.8673 | −1.38459 | ||||||||
\(789\) | 0.328528 | 0.0116959 | ||||||||
\(790\) | 25.4384 | 0.905057 | ||||||||
\(791\) | 39.4120 | 1.40133 | ||||||||
\(792\) | −98.1723 | −3.48840 | ||||||||
\(793\) | 4.06332 | 0.144293 | ||||||||
\(794\) | 97.1242 | 3.44681 | ||||||||
\(795\) | −4.59554 | −0.162987 | ||||||||
\(796\) | −46.6410 | −1.65315 | ||||||||
\(797\) | 10.2928 | 0.364590 | 0.182295 | − | 0.983244i | \(-0.441647\pi\) | ||||
0.182295 | + | 0.983244i | \(0.441647\pi\) | |||||||
\(798\) | 19.1170 | 0.676734 | ||||||||
\(799\) | 0.116149 | 0.00410907 | ||||||||
\(800\) | 69.6908 | 2.46394 | ||||||||
\(801\) | −52.7577 | −1.86410 | ||||||||
\(802\) | −54.8757 | −1.93773 | ||||||||
\(803\) | −51.4541 | −1.81578 | ||||||||
\(804\) | −10.7346 | −0.378581 | ||||||||
\(805\) | 20.2166 | 0.712540 | ||||||||
\(806\) | 19.7853 | 0.696908 | ||||||||
\(807\) | 2.81583 | 0.0991218 | ||||||||
\(808\) | −78.9815 | −2.77856 | ||||||||
\(809\) | −22.8025 | −0.801693 | −0.400847 | − | 0.916145i | \(-0.631284\pi\) | ||||
−0.400847 | + | 0.916145i | \(0.631284\pi\) | |||||||
\(810\) | 21.2234 | 0.745715 | ||||||||
\(811\) | 50.9046 | 1.78750 | 0.893751 | − | 0.448564i | \(-0.148065\pi\) | ||||
0.893751 | + | 0.448564i | \(0.148065\pi\) | |||||||
\(812\) | 47.3435 | 1.66143 | ||||||||
\(813\) | 0.687759 | 0.0241208 | ||||||||
\(814\) | 78.1962 | 2.74078 | ||||||||
\(815\) | 6.15075 | 0.215451 | ||||||||
\(816\) | −14.8612 | −0.520247 | ||||||||
\(817\) | 45.1837 | 1.58078 | ||||||||
\(818\) | −69.5730 | −2.43256 | ||||||||
\(819\) | −23.8471 | −0.833284 | ||||||||
\(820\) | 13.4231 | 0.468754 | ||||||||
\(821\) | 48.5255 | 1.69355 | 0.846776 | − | 0.531949i | \(-0.178540\pi\) | ||||
0.846776 | + | 0.531949i | \(0.178540\pi\) | |||||||
\(822\) | −21.0890 | −0.735563 | ||||||||
\(823\) | 37.8842 | 1.32056 | 0.660280 | − | 0.751020i | \(-0.270438\pi\) | ||||
0.660280 | + | 0.751020i | \(0.270438\pi\) | |||||||
\(824\) | −85.3517 | −2.97337 | ||||||||
\(825\) | 5.54733 | 0.193133 | ||||||||
\(826\) | 64.9495 | 2.25988 | ||||||||
\(827\) | −0.662653 | −0.0230427 | −0.0115214 | − | 0.999934i | \(-0.503667\pi\) | ||||
−0.0115214 | + | 0.999934i | \(0.503667\pi\) | |||||||
\(828\) | 93.6271 | 3.25377 | ||||||||
\(829\) | 55.5636 | 1.92981 | 0.964903 | − | 0.262608i | \(-0.0845826\pi\) | ||||
0.964903 | + | 0.262608i | \(0.0845826\pi\) | |||||||
\(830\) | −5.13115 | −0.178105 | ||||||||
\(831\) | 4.25608 | 0.147642 | ||||||||
\(832\) | 53.4930 | 1.85454 | ||||||||
\(833\) | −11.5877 | −0.401489 | ||||||||
\(834\) | −5.43944 | −0.188352 | ||||||||
\(835\) | 2.18291 | 0.0755428 | ||||||||
\(836\) | 126.949 | 4.39064 | ||||||||
\(837\) | 5.98875 | 0.207001 | ||||||||
\(838\) | 5.42751 | 0.187490 | ||||||||
\(839\) | 9.46898 | 0.326906 | 0.163453 | − | 0.986551i | \(-0.447737\pi\) | ||||
0.163453 | + | 0.986551i | \(0.447737\pi\) | |||||||
\(840\) | 10.0088 | 0.345337 | ||||||||
\(841\) | −21.2676 | −0.733364 | ||||||||
\(842\) | −55.0008 | −1.89545 | ||||||||
\(843\) | −3.69801 | −0.127366 | ||||||||
\(844\) | −3.57539 | −0.123070 | ||||||||
\(845\) | 6.49025 | 0.223271 | ||||||||
\(846\) | −0.276781 | −0.00951593 | ||||||||
\(847\) | 14.2417 | 0.489350 | ||||||||
\(848\) | 168.317 | 5.78002 | ||||||||
\(849\) | −0.375535 | −0.0128883 | ||||||||
\(850\) | −34.9251 | −1.19792 | ||||||||
\(851\) | −46.0938 | −1.58008 | ||||||||
\(852\) | −1.50805 | −0.0516648 | ||||||||
\(853\) | 13.3248 | 0.456231 | 0.228116 | − | 0.973634i | \(-0.426744\pi\) | ||||
0.228116 | + | 0.973634i | \(0.426744\pi\) | |||||||
\(854\) | −13.9296 | −0.476662 | ||||||||
\(855\) | −17.7694 | −0.607700 | ||||||||
\(856\) | −124.045 | −4.23977 | ||||||||
\(857\) | −23.0047 | −0.785826 | −0.392913 | − | 0.919576i | \(-0.628533\pi\) | ||||
−0.392913 | + | 0.919576i | \(0.628533\pi\) | |||||||
\(858\) | 9.51759 | 0.324925 | ||||||||
\(859\) | 40.7816 | 1.39145 | 0.695725 | − | 0.718309i | \(-0.255083\pi\) | ||||
0.695725 | + | 0.718309i | \(0.255083\pi\) | |||||||
\(860\) | 38.2737 | 1.30512 | ||||||||
\(861\) | −2.94716 | −0.100439 | ||||||||
\(862\) | −70.7686 | −2.41039 | ||||||||
\(863\) | −14.3339 | −0.487933 | −0.243966 | − | 0.969784i | \(-0.578449\pi\) | ||||
−0.243966 | + | 0.969784i | \(0.578449\pi\) | |||||||
\(864\) | 36.1919 | 1.23127 | ||||||||
\(865\) | 7.38981 | 0.251261 | ||||||||
\(866\) | 12.8551 | 0.436835 | ||||||||
\(867\) | −2.28662 | −0.0776577 | ||||||||
\(868\) | −49.0815 | −1.66594 | ||||||||
\(869\) | −37.0897 | −1.25818 | ||||||||
\(870\) | 2.64481 | 0.0896674 | ||||||||
\(871\) | −14.7901 | −0.501144 | ||||||||
\(872\) | −89.7330 | −3.03874 | ||||||||
\(873\) | −11.4658 | −0.388058 | ||||||||
\(874\) | −103.412 | −3.49796 | ||||||||
\(875\) | 29.2583 | 0.989111 | ||||||||
\(876\) | 24.2945 | 0.820836 | ||||||||
\(877\) | −12.2334 | −0.413094 | −0.206547 | − | 0.978437i | \(-0.566223\pi\) | ||||
−0.206547 | + | 0.978437i | \(0.566223\pi\) | |||||||
\(878\) | −97.2932 | −3.28349 | ||||||||
\(879\) | 2.95585 | 0.0996983 | ||||||||
\(880\) | 50.7798 | 1.71179 | ||||||||
\(881\) | −40.0849 | −1.35049 | −0.675247 | − | 0.737592i | \(-0.735963\pi\) | ||||
−0.675247 | + | 0.737592i | \(0.735963\pi\) | |||||||
\(882\) | 27.6131 | 0.929782 | ||||||||
\(883\) | 30.9326 | 1.04096 | 0.520482 | − | 0.853873i | \(-0.325752\pi\) | ||||
0.520482 | + | 0.853873i | \(0.325752\pi\) | |||||||
\(884\) | −43.3609 | −1.45839 | ||||||||
\(885\) | 2.62559 | 0.0882581 | ||||||||
\(886\) | 30.5228 | 1.02543 | ||||||||
\(887\) | −56.7326 | −1.90490 | −0.952448 | − | 0.304702i | \(-0.901443\pi\) | ||||
−0.952448 | + | 0.304702i | \(0.901443\pi\) | |||||||
\(888\) | −22.8202 | −0.765794 | ||||||||
\(889\) | −26.1976 | −0.878639 | ||||||||
\(890\) | 49.3599 | 1.65455 | ||||||||
\(891\) | −30.9442 | −1.03667 | ||||||||
\(892\) | −100.754 | −3.37350 | ||||||||
\(893\) | 0.221219 | 0.00740282 | ||||||||
\(894\) | 11.1269 | 0.372138 | ||||||||
\(895\) | 4.52715 | 0.151326 | ||||||||
\(896\) | −70.0978 | −2.34180 | ||||||||
\(897\) | −5.61027 | −0.187322 | ||||||||
\(898\) | −109.379 | −3.65003 | ||||||||
\(899\) | −8.01630 | −0.267358 | ||||||||
\(900\) | 60.2247 | 2.00749 | ||||||||
\(901\) | −42.1846 | −1.40537 | ||||||||
\(902\) | −27.0457 | −0.900524 | ||||||||
\(903\) | −8.40336 | −0.279646 | ||||||||
\(904\) | −105.549 | −3.51052 | ||||||||
\(905\) | −2.35470 | −0.0782728 | ||||||||
\(906\) | −4.81902 | −0.160101 | ||||||||
\(907\) | −30.8420 | −1.02409 | −0.512047 | − | 0.858958i | \(-0.671112\pi\) | ||||
−0.512047 | + | 0.858958i | \(0.671112\pi\) | |||||||
\(908\) | 119.940 | 3.98035 | ||||||||
\(909\) | −26.0787 | −0.864975 | ||||||||
\(910\) | 22.3112 | 0.739610 | ||||||||
\(911\) | −16.2193 | −0.537370 | −0.268685 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268685 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(912\) | −28.3048 | −0.937267 | ||||||||
\(913\) | 7.48132 | 0.247596 | ||||||||
\(914\) | −98.6789 | −3.26401 | ||||||||
\(915\) | −0.563105 | −0.0186157 | ||||||||
\(916\) | 5.52023 | 0.182394 | ||||||||
\(917\) | −26.3200 | −0.869164 | ||||||||
\(918\) | −18.1374 | −0.598622 | ||||||||
\(919\) | −4.34727 | −0.143403 | −0.0717015 | − | 0.997426i | \(-0.522843\pi\) | ||||
−0.0717015 | + | 0.997426i | \(0.522843\pi\) | |||||||
\(920\) | −54.1420 | −1.78501 | ||||||||
\(921\) | −7.91561 | −0.260828 | ||||||||
\(922\) | −38.5825 | −1.27065 | ||||||||
\(923\) | −2.07778 | −0.0683909 | ||||||||
\(924\) | −23.6103 | −0.776722 | ||||||||
\(925\) | −29.6494 | −0.974866 | ||||||||
\(926\) | −55.3563 | −1.81912 | ||||||||
\(927\) | −28.1820 | −0.925620 | ||||||||
\(928\) | −48.4450 | −1.59029 | ||||||||
\(929\) | −2.22372 | −0.0729580 | −0.0364790 | − | 0.999334i | \(-0.511614\pi\) | ||||
−0.0364790 | + | 0.999334i | \(0.511614\pi\) | |||||||
\(930\) | −2.74190 | −0.0899104 | ||||||||
\(931\) | −22.0700 | −0.723314 | ||||||||
\(932\) | −83.3380 | −2.72983 | ||||||||
\(933\) | −5.45629 | −0.178631 | ||||||||
\(934\) | −29.2356 | −0.956618 | ||||||||
\(935\) | −12.7268 | −0.416210 | ||||||||
\(936\) | 63.8649 | 2.08749 | ||||||||
\(937\) | −27.6279 | −0.902564 | −0.451282 | − | 0.892381i | \(-0.649033\pi\) | ||||
−0.451282 | + | 0.892381i | \(0.649033\pi\) | |||||||
\(938\) | 50.7025 | 1.65550 | ||||||||
\(939\) | −4.51795 | −0.147438 | ||||||||
\(940\) | 0.187388 | 0.00611192 | ||||||||
\(941\) | 26.9990 | 0.880144 | 0.440072 | − | 0.897963i | \(-0.354953\pi\) | ||||
0.440072 | + | 0.897963i | \(0.354953\pi\) | |||||||
\(942\) | −4.19788 | −0.136774 | ||||||||
\(943\) | 15.9425 | 0.519158 | ||||||||
\(944\) | −96.1650 | −3.12990 | ||||||||
\(945\) | 6.75330 | 0.219685 | ||||||||
\(946\) | −77.1165 | −2.50727 | ||||||||
\(947\) | 15.4751 | 0.502872 | 0.251436 | − | 0.967874i | \(-0.419097\pi\) | ||||
0.251436 | + | 0.967874i | \(0.419097\pi\) | |||||||
\(948\) | 17.5122 | 0.568770 | ||||||||
\(949\) | 33.4729 | 1.08658 | ||||||||
\(950\) | −66.5187 | −2.15815 | ||||||||
\(951\) | −2.46374 | −0.0798921 | ||||||||
\(952\) | 91.8757 | 2.97771 | ||||||||
\(953\) | 2.03284 | 0.0658501 | 0.0329250 | − | 0.999458i | \(-0.489518\pi\) | ||||
0.0329250 | + | 0.999458i | \(0.489518\pi\) | |||||||
\(954\) | 100.525 | 3.25461 | ||||||||
\(955\) | 15.2671 | 0.494031 | ||||||||
\(956\) | 23.2846 | 0.753077 | ||||||||
\(957\) | −3.85618 | −0.124653 | ||||||||
\(958\) | −39.0185 | −1.26063 | ||||||||
\(959\) | 72.0801 | 2.32759 | ||||||||
\(960\) | −7.41319 | −0.239260 | ||||||||
\(961\) | −22.6894 | −0.731917 | ||||||||
\(962\) | −50.8697 | −1.64010 | ||||||||
\(963\) | −40.9581 | −1.31985 | ||||||||
\(964\) | 24.4381 | 0.787099 | ||||||||
\(965\) | −6.24859 | −0.201149 | ||||||||
\(966\) | 19.2328 | 0.618804 | ||||||||
\(967\) | −48.7916 | −1.56903 | −0.784516 | − | 0.620109i | \(-0.787088\pi\) | ||||
−0.784516 | + | 0.620109i | \(0.787088\pi\) | |||||||
\(968\) | −38.1407 | −1.22589 | ||||||||
\(969\) | 7.09394 | 0.227890 | ||||||||
\(970\) | 10.7273 | 0.344434 | ||||||||
\(971\) | 39.4950 | 1.26746 | 0.633728 | − | 0.773556i | \(-0.281524\pi\) | ||||
0.633728 | + | 0.773556i | \(0.281524\pi\) | |||||||
\(972\) | 47.2467 | 1.51544 | ||||||||
\(973\) | 18.5915 | 0.596015 | ||||||||
\(974\) | 59.9941 | 1.92234 | ||||||||
\(975\) | −3.60875 | −0.115573 | ||||||||
\(976\) | 20.6243 | 0.660169 | ||||||||
\(977\) | −22.4125 | −0.717039 | −0.358519 | − | 0.933522i | \(-0.616718\pi\) | ||||
−0.358519 | + | 0.933522i | \(0.616718\pi\) | |||||||
\(978\) | 5.85144 | 0.187108 | ||||||||
\(979\) | −71.9677 | −2.30010 | ||||||||
\(980\) | −18.6948 | −0.597183 | ||||||||
\(981\) | −29.6287 | −0.945971 | ||||||||
\(982\) | −19.6488 | −0.627017 | ||||||||
\(983\) | 37.5986 | 1.19921 | 0.599605 | − | 0.800296i | \(-0.295324\pi\) | ||||
0.599605 | + | 0.800296i | \(0.295324\pi\) | |||||||
\(984\) | 7.89280 | 0.251613 | ||||||||
\(985\) | 7.42126 | 0.236461 | ||||||||
\(986\) | 24.2779 | 0.773167 | ||||||||
\(987\) | −0.0411428 | −0.00130959 | ||||||||
\(988\) | −82.5855 | −2.62740 | ||||||||
\(989\) | 45.4574 | 1.44546 | ||||||||
\(990\) | 30.3276 | 0.963874 | ||||||||
\(991\) | −25.3130 | −0.804094 | −0.402047 | − | 0.915619i | \(-0.631701\pi\) | ||||
−0.402047 | + | 0.915619i | \(0.631701\pi\) | |||||||
\(992\) | 50.2234 | 1.59460 | ||||||||
\(993\) | 12.4995 | 0.396658 | ||||||||
\(994\) | 7.12290 | 0.225925 | ||||||||
\(995\) | 8.90556 | 0.282325 | ||||||||
\(996\) | −3.53237 | −0.111928 | ||||||||
\(997\) | 40.1089 | 1.27026 | 0.635130 | − | 0.772405i | \(-0.280946\pi\) | ||||
0.635130 | + | 0.772405i | \(0.280946\pi\) | |||||||
\(998\) | −77.9226 | −2.46660 | ||||||||
\(999\) | −15.3976 | −0.487157 |
(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 | 4019.2.a.b.1.7 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.7 | ✓ | 186 | 1.1 | even | 1 | trivial |