Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-1.89507\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89507 | 1.34001 | 0.670007 | − | 0.742355i | \(-0.266291\pi\) | ||||
0.670007 | + | 0.742355i | \(0.266291\pi\) | |||||||
\(3\) | −1.57790 | −0.911000 | −0.455500 | − | 0.890236i | \(-0.650539\pi\) | ||||
−0.455500 | + | 0.890236i | \(0.650539\pi\) | |||||||
\(4\) | 1.59127 | 0.795637 | ||||||||
\(5\) | 3.12194 | 1.39617 | 0.698086 | − | 0.716013i | \(-0.254035\pi\) | ||||
0.698086 | + | 0.716013i | \(0.254035\pi\) | |||||||
\(6\) | −2.99022 | −1.22075 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.774564 | −0.273850 | ||||||||
\(9\) | −0.510238 | −0.170079 | ||||||||
\(10\) | 5.91628 | 1.87089 | ||||||||
\(11\) | −2.47721 | −0.746906 | −0.373453 | − | 0.927649i | \(-0.621826\pi\) | ||||
−0.373453 | + | 0.927649i | \(0.621826\pi\) | |||||||
\(12\) | −2.51087 | −0.724825 | ||||||||
\(13\) | −3.58819 | −0.995185 | −0.497592 | − | 0.867411i | \(-0.665782\pi\) | ||||
−0.497592 | + | 0.867411i | \(0.665782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.92610 | −1.27191 | ||||||||
\(16\) | −4.65040 | −1.16260 | ||||||||
\(17\) | 7.11446 | 1.72551 | 0.862755 | − | 0.505622i | \(-0.168737\pi\) | ||||
0.862755 | + | 0.505622i | \(0.168737\pi\) | |||||||
\(18\) | −0.966935 | −0.227909 | ||||||||
\(19\) | 5.99670 | 1.37574 | 0.687868 | − | 0.725836i | \(-0.258547\pi\) | ||||
0.687868 | + | 0.725836i | \(0.258547\pi\) | |||||||
\(20\) | 4.96786 | 1.11085 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.69447 | −1.00086 | ||||||||
\(23\) | 9.03548 | 1.88403 | 0.942014 | − | 0.335574i | \(-0.108930\pi\) | ||||
0.942014 | + | 0.335574i | \(0.108930\pi\) | |||||||
\(24\) | 1.22218 | 0.249477 | ||||||||
\(25\) | 4.74649 | 0.949299 | ||||||||
\(26\) | −6.79985 | −1.33356 | ||||||||
\(27\) | 5.53880 | 1.06594 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.03999 | 1.67868 | 0.839342 | − | 0.543604i | \(-0.182941\pi\) | ||||
0.839342 | + | 0.543604i | \(0.182941\pi\) | |||||||
\(30\) | −9.33528 | −1.70438 | ||||||||
\(31\) | 8.92613 | 1.60318 | 0.801590 | − | 0.597874i | \(-0.203988\pi\) | ||||
0.801590 | + | 0.597874i | \(0.203988\pi\) | |||||||
\(32\) | −7.26368 | −1.28405 | ||||||||
\(33\) | 3.90878 | 0.680431 | ||||||||
\(34\) | 13.4824 | 2.31221 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.811929 | −0.135321 | ||||||||
\(37\) | −3.61418 | −0.594168 | −0.297084 | − | 0.954851i | \(-0.596014\pi\) | ||||
−0.297084 | + | 0.954851i | \(0.596014\pi\) | |||||||
\(38\) | 11.3641 | 1.84351 | ||||||||
\(39\) | 5.66180 | 0.906613 | ||||||||
\(40\) | −2.41814 | −0.382341 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37070 | −1.27652 | −0.638260 | − | 0.769821i | \(-0.720346\pi\) | ||||
−0.638260 | + | 0.769821i | \(0.720346\pi\) | |||||||
\(44\) | −3.94191 | −0.594266 | ||||||||
\(45\) | −1.59293 | −0.237460 | ||||||||
\(46\) | 17.1228 | 2.52462 | ||||||||
\(47\) | 1.53886 | 0.224465 | 0.112233 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112233 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(48\) | 7.33785 | 1.05913 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.99492 | 1.27207 | ||||||||
\(51\) | −11.2259 | −1.57194 | ||||||||
\(52\) | −5.70979 | −0.791805 | ||||||||
\(53\) | −0.436569 | −0.0599673 | −0.0299837 | − | 0.999550i | \(-0.509546\pi\) | ||||
−0.0299837 | + | 0.999550i | \(0.509546\pi\) | |||||||
\(54\) | 10.4964 | 1.42838 | ||||||||
\(55\) | −7.73369 | −1.04281 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.46217 | −1.25330 | ||||||||
\(58\) | 17.1314 | 2.24946 | ||||||||
\(59\) | 9.21554 | 1.19976 | 0.599880 | − | 0.800090i | \(-0.295215\pi\) | ||||
0.599880 | + | 0.800090i | \(0.295215\pi\) | |||||||
\(60\) | −7.83877 | −1.01198 | ||||||||
\(61\) | −11.5476 | −1.47851 | −0.739257 | − | 0.673423i | \(-0.764823\pi\) | ||||
−0.739257 | + | 0.673423i | \(0.764823\pi\) | |||||||
\(62\) | 16.9156 | 2.14828 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.46435 | −0.558044 | ||||||||
\(65\) | −11.2021 | −1.38945 | ||||||||
\(66\) | 7.40739 | 0.911787 | ||||||||
\(67\) | 2.71201 | 0.331325 | 0.165662 | − | 0.986183i | \(-0.447024\pi\) | ||||
0.165662 | + | 0.986183i | \(0.447024\pi\) | |||||||
\(68\) | 11.3211 | 1.37288 | ||||||||
\(69\) | −14.2571 | −1.71635 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.30671 | 0.511113 | 0.255556 | − | 0.966794i | \(-0.417741\pi\) | ||||
0.255556 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(72\) | 0.395212 | 0.0465762 | ||||||||
\(73\) | −6.16745 | −0.721846 | −0.360923 | − | 0.932596i | \(-0.617538\pi\) | ||||
−0.360923 | + | 0.932596i | \(0.617538\pi\) | |||||||
\(74\) | −6.84911 | −0.796193 | ||||||||
\(75\) | −7.48948 | −0.864811 | ||||||||
\(76\) | 9.54238 | 1.09459 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.7295 | 1.21487 | ||||||||
\(79\) | 0.388867 | 0.0437510 | 0.0218755 | − | 0.999761i | \(-0.493036\pi\) | ||||
0.0218755 | + | 0.999761i | \(0.493036\pi\) | |||||||
\(80\) | −14.5182 | −1.62319 | ||||||||
\(81\) | −7.20894 | −0.800993 | ||||||||
\(82\) | 1.89507 | 0.209275 | ||||||||
\(83\) | −7.05134 | −0.773985 | −0.386993 | − | 0.922083i | \(-0.626486\pi\) | ||||
−0.386993 | + | 0.922083i | \(0.626486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.2109 | 2.40911 | ||||||||
\(86\) | −15.8630 | −1.71055 | ||||||||
\(87\) | −14.2642 | −1.52928 | ||||||||
\(88\) | 1.91875 | 0.204540 | ||||||||
\(89\) | 11.6241 | 1.23215 | 0.616074 | − | 0.787688i | \(-0.288722\pi\) | ||||
0.616074 | + | 0.787688i | \(0.288722\pi\) | |||||||
\(90\) | −3.01871 | −0.318200 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.3779 | 1.49900 | ||||||||
\(93\) | −14.0845 | −1.46050 | ||||||||
\(94\) | 2.91623 | 0.300787 | ||||||||
\(95\) | 18.7213 | 1.92077 | ||||||||
\(96\) | 11.4613 | 1.16977 | ||||||||
\(97\) | −10.4689 | −1.06295 | −0.531476 | − | 0.847073i | \(-0.678362\pi\) | ||||
−0.531476 | + | 0.847073i | \(0.678362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.26397 | 0.127033 | ||||||||
\(100\) | 7.55297 | 0.755297 | ||||||||
\(101\) | −9.43867 | −0.939183 | −0.469591 | − | 0.882884i | \(-0.655599\pi\) | ||||
−0.469591 | + | 0.882884i | \(0.655599\pi\) | |||||||
\(102\) | −21.2738 | −2.10642 | ||||||||
\(103\) | 7.20731 | 0.710157 | 0.355079 | − | 0.934836i | \(-0.384454\pi\) | ||||
0.355079 | + | 0.934836i | \(0.384454\pi\) | |||||||
\(104\) | 2.77928 | 0.272531 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.827326 | −0.0803570 | ||||||||
\(107\) | −7.17570 | −0.693702 | −0.346851 | − | 0.937920i | \(-0.612749\pi\) | ||||
−0.346851 | + | 0.937920i | \(0.612749\pi\) | |||||||
\(108\) | 8.81374 | 0.848103 | ||||||||
\(109\) | −12.8300 | −1.22889 | −0.614447 | − | 0.788958i | \(-0.710621\pi\) | ||||
−0.614447 | + | 0.788958i | \(0.710621\pi\) | |||||||
\(110\) | −14.6558 | −1.39738 | ||||||||
\(111\) | 5.70281 | 0.541287 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8789 | 1.49376 | 0.746879 | − | 0.664960i | \(-0.231552\pi\) | ||||
0.746879 | + | 0.664960i | \(0.231552\pi\) | |||||||
\(114\) | −17.9314 | −1.67943 | ||||||||
\(115\) | 28.2082 | 2.63043 | ||||||||
\(116\) | 14.3851 | 1.33562 | ||||||||
\(117\) | 1.83083 | 0.169260 | ||||||||
\(118\) | 17.4640 | 1.60770 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.81558 | 0.348313 | ||||||||
\(121\) | −4.86345 | −0.442131 | ||||||||
\(122\) | −21.8834 | −1.98123 | ||||||||
\(123\) | −1.57790 | −0.142274 | ||||||||
\(124\) | 14.2039 | 1.27555 | ||||||||
\(125\) | −0.791427 | −0.0707874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7032 | −1.74838 | −0.874189 | − | 0.485585i | \(-0.838607\pi\) | ||||
−0.874189 | + | 0.485585i | \(0.838607\pi\) | |||||||
\(128\) | 6.06711 | 0.536262 | ||||||||
\(129\) | 13.2081 | 1.16291 | ||||||||
\(130\) | −21.2287 | −1.86188 | ||||||||
\(131\) | 8.98260 | 0.784814 | 0.392407 | − | 0.919792i | \(-0.371643\pi\) | ||||
0.392407 | + | 0.919792i | \(0.371643\pi\) | |||||||
\(132\) | 6.21994 | 0.541376 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.13943 | 0.443979 | ||||||||
\(135\) | 17.2918 | 1.48824 | ||||||||
\(136\) | −5.51060 | −0.472530 | ||||||||
\(137\) | 8.94745 | 0.764432 | 0.382216 | − | 0.924073i | \(-0.375161\pi\) | ||||
0.382216 | + | 0.924073i | \(0.375161\pi\) | |||||||
\(138\) | −27.0181 | −2.29993 | ||||||||
\(139\) | −4.85149 | −0.411498 | −0.205749 | − | 0.978605i | \(-0.565963\pi\) | ||||
−0.205749 | + | 0.978605i | \(0.565963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.42816 | −0.204488 | ||||||||
\(142\) | 8.16150 | 0.684898 | ||||||||
\(143\) | 8.88869 | 0.743309 | ||||||||
\(144\) | 2.37281 | 0.197734 | ||||||||
\(145\) | 28.2223 | 2.34373 | ||||||||
\(146\) | −11.6877 | −0.967283 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.75115 | −0.472742 | ||||||||
\(149\) | −1.14539 | −0.0938337 | −0.0469168 | − | 0.998899i | \(-0.514940\pi\) | ||||
−0.0469168 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(150\) | −14.1931 | −1.15886 | ||||||||
\(151\) | 14.5501 | 1.18407 | 0.592035 | − | 0.805912i | \(-0.298325\pi\) | ||||
0.592035 | + | 0.805912i | \(0.298325\pi\) | |||||||
\(152\) | −4.64482 | −0.376745 | ||||||||
\(153\) | −3.63007 | −0.293474 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.8668 | 2.23832 | ||||||||
\(156\) | 9.00947 | 0.721335 | ||||||||
\(157\) | 6.23465 | 0.497579 | 0.248789 | − | 0.968558i | \(-0.419967\pi\) | ||||
0.248789 | + | 0.968558i | \(0.419967\pi\) | |||||||
\(158\) | 0.736929 | 0.0586269 | ||||||||
\(159\) | 0.688861 | 0.0546302 | ||||||||
\(160\) | −22.6767 | −1.79275 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13.6614 | −1.07334 | ||||||||
\(163\) | 8.73385 | 0.684088 | 0.342044 | − | 0.939684i | \(-0.388881\pi\) | ||||
0.342044 | + | 0.939684i | \(0.388881\pi\) | |||||||
\(164\) | 1.59127 | 0.124258 | ||||||||
\(165\) | 12.2030 | 0.950000 | ||||||||
\(166\) | −13.3628 | −1.03715 | ||||||||
\(167\) | 7.37954 | 0.571046 | 0.285523 | − | 0.958372i | \(-0.407833\pi\) | ||||
0.285523 | + | 0.958372i | \(0.407833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.124898 | −0.00960750 | ||||||||
\(170\) | 42.0911 | 3.22824 | ||||||||
\(171\) | −3.05975 | −0.233985 | ||||||||
\(172\) | −13.3201 | −1.01565 | ||||||||
\(173\) | −21.1685 | −1.60941 | −0.804705 | − | 0.593675i | \(-0.797676\pi\) | ||||
−0.804705 | + | 0.593675i | \(0.797676\pi\) | |||||||
\(174\) | −27.0315 | −2.04926 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.5200 | 0.868352 | ||||||||
\(177\) | −14.5412 | −1.09298 | ||||||||
\(178\) | 22.0284 | 1.65110 | ||||||||
\(179\) | −5.13375 | −0.383715 | −0.191857 | − | 0.981423i | \(-0.561451\pi\) | ||||
−0.191857 | + | 0.981423i | \(0.561451\pi\) | |||||||
\(180\) | −2.53479 | −0.188932 | ||||||||
\(181\) | 4.56104 | 0.339019 | 0.169510 | − | 0.985529i | \(-0.445782\pi\) | ||||
0.169510 | + | 0.985529i | \(0.445782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.2209 | 1.34693 | ||||||||
\(184\) | −6.99855 | −0.515940 | ||||||||
\(185\) | −11.2833 | −0.829561 | ||||||||
\(186\) | −26.6911 | −1.95708 | ||||||||
\(187\) | −17.6240 | −1.28879 | ||||||||
\(188\) | 2.44874 | 0.178593 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 35.4781 | 2.57385 | ||||||||
\(191\) | 3.47482 | 0.251429 | 0.125715 | − | 0.992066i | \(-0.459878\pi\) | ||||
0.125715 | + | 0.992066i | \(0.459878\pi\) | |||||||
\(192\) | 7.04429 | 0.508378 | ||||||||
\(193\) | −16.2855 | −1.17225 | −0.586127 | − | 0.810219i | \(-0.699348\pi\) | ||||
−0.586127 | + | 0.810219i | \(0.699348\pi\) | |||||||
\(194\) | −19.8392 | −1.42437 | ||||||||
\(195\) | 17.6758 | 1.26579 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.44475 | −0.459169 | −0.229585 | − | 0.973289i | \(-0.573737\pi\) | ||||
−0.229585 | + | 0.973289i | \(0.573737\pi\) | |||||||
\(198\) | 2.39530 | 0.170226 | ||||||||
\(199\) | 1.35506 | 0.0960575 | 0.0480287 | − | 0.998846i | \(-0.484706\pi\) | ||||
0.0480287 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(200\) | −3.67646 | −0.259965 | ||||||||
\(201\) | −4.27927 | −0.301837 | ||||||||
\(202\) | −17.8869 | −1.25852 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −17.8635 | −1.25069 | ||||||||
\(205\) | 3.12194 | 0.218046 | ||||||||
\(206\) | 13.6583 | 0.951621 | ||||||||
\(207\) | −4.61025 | −0.320434 | ||||||||
\(208\) | 16.6865 | 1.15700 | ||||||||
\(209\) | −14.8551 | −1.02755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0138 | −1.30896 | −0.654482 | − | 0.756078i | \(-0.727113\pi\) | ||||
−0.654482 | + | 0.756078i | \(0.727113\pi\) | |||||||
\(212\) | −0.694700 | −0.0477122 | ||||||||
\(213\) | −6.79555 | −0.465623 | ||||||||
\(214\) | −13.5984 | −0.929570 | ||||||||
\(215\) | −26.1328 | −1.78224 | ||||||||
\(216\) | −4.29015 | −0.291908 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −24.3138 | −1.64674 | ||||||||
\(219\) | 9.73161 | 0.657601 | ||||||||
\(220\) | −12.3064 | −0.829698 | ||||||||
\(221\) | −25.5280 | −1.71720 | ||||||||
\(222\) | 10.8072 | 0.725332 | ||||||||
\(223\) | 2.62540 | 0.175810 | 0.0879049 | − | 0.996129i | \(-0.471983\pi\) | ||||
0.0879049 | + | 0.996129i | \(0.471983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.42184 | −0.161456 | ||||||||
\(226\) | 30.0915 | 2.00166 | ||||||||
\(227\) | 7.07709 | 0.469723 | 0.234862 | − | 0.972029i | \(-0.424536\pi\) | ||||
0.234862 | + | 0.972029i | \(0.424536\pi\) | |||||||
\(228\) | −15.0569 | −0.997168 | ||||||||
\(229\) | 6.78303 | 0.448235 | 0.224118 | − | 0.974562i | \(-0.428050\pi\) | ||||
0.224118 | + | 0.974562i | \(0.428050\pi\) | |||||||
\(230\) | 53.4564 | 3.52481 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.00204 | −0.459707 | ||||||||
\(233\) | −7.98179 | −0.522904 | −0.261452 | − | 0.965216i | \(-0.584201\pi\) | ||||
−0.261452 | + | 0.965216i | \(0.584201\pi\) | |||||||
\(234\) | 3.46955 | 0.226811 | ||||||||
\(235\) | 4.80421 | 0.313392 | ||||||||
\(236\) | 14.6644 | 0.954574 | ||||||||
\(237\) | −0.613593 | −0.0398572 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2781 | 0.858887 | 0.429444 | − | 0.903094i | \(-0.358710\pi\) | ||||
0.429444 | + | 0.903094i | \(0.358710\pi\) | |||||||
\(240\) | 22.9083 | 1.47872 | ||||||||
\(241\) | −9.73257 | −0.626930 | −0.313465 | − | 0.949600i | \(-0.601490\pi\) | ||||
−0.313465 | + | 0.949600i | \(0.601490\pi\) | |||||||
\(242\) | −9.21655 | −0.592462 | ||||||||
\(243\) | −5.24142 | −0.336237 | ||||||||
\(244\) | −18.3753 | −1.17636 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.99022 | −0.190649 | ||||||||
\(247\) | −21.5173 | −1.36911 | ||||||||
\(248\) | −6.91385 | −0.439030 | ||||||||
\(249\) | 11.1263 | 0.705100 | ||||||||
\(250\) | −1.49981 | −0.0948561 | ||||||||
\(251\) | −10.0364 | −0.633492 | −0.316746 | − | 0.948510i | \(-0.602590\pi\) | ||||
−0.316746 | + | 0.948510i | \(0.602590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.3828 | −1.40719 | ||||||||
\(254\) | −37.3389 | −2.34285 | ||||||||
\(255\) | −35.0465 | −2.19470 | ||||||||
\(256\) | 20.4263 | 1.27664 | ||||||||
\(257\) | 23.3460 | 1.45628 | 0.728142 | − | 0.685426i | \(-0.240384\pi\) | ||||
0.728142 | + | 0.685426i | \(0.240384\pi\) | |||||||
\(258\) | 25.0302 | 1.55831 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −17.8256 | −1.10550 | ||||||||
\(261\) | −4.61255 | −0.285510 | ||||||||
\(262\) | 17.0226 | 1.05166 | ||||||||
\(263\) | 7.46153 | 0.460098 | 0.230049 | − | 0.973179i | \(-0.426111\pi\) | ||||
0.230049 | + | 0.973179i | \(0.426111\pi\) | |||||||
\(264\) | −3.02760 | −0.186336 | ||||||||
\(265\) | −1.36294 | −0.0837247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.3416 | −1.12249 | ||||||||
\(268\) | 4.31555 | 0.263614 | ||||||||
\(269\) | 2.41427 | 0.147200 | 0.0736002 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0736002 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(270\) | 32.7691 | 1.99426 | ||||||||
\(271\) | 17.7171 | 1.07624 | 0.538118 | − | 0.842870i | \(-0.319136\pi\) | ||||
0.538118 | + | 0.842870i | \(0.319136\pi\) | |||||||
\(272\) | −33.0851 | −2.00608 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9560 | 1.02435 | ||||||||
\(275\) | −11.7580 | −0.709037 | ||||||||
\(276\) | −22.6869 | −1.36559 | ||||||||
\(277\) | 13.2764 | 0.797703 | 0.398852 | − | 0.917015i | \(-0.369409\pi\) | ||||
0.398852 | + | 0.917015i | \(0.369409\pi\) | |||||||
\(278\) | −9.19388 | −0.551413 | ||||||||
\(279\) | −4.55445 | −0.272668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.58617 | −0.333243 | −0.166621 | − | 0.986021i | \(-0.553286\pi\) | ||||
−0.166621 | + | 0.986021i | \(0.553286\pi\) | |||||||
\(282\) | −4.60152 | −0.274017 | ||||||||
\(283\) | 18.4441 | 1.09639 | 0.548194 | − | 0.836351i | \(-0.315316\pi\) | ||||
0.548194 | + | 0.836351i | \(0.315316\pi\) | |||||||
\(284\) | 6.85315 | 0.406660 | ||||||||
\(285\) | −29.5403 | −1.74982 | ||||||||
\(286\) | 16.8446 | 0.996045 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.70621 | 0.218390 | ||||||||
\(289\) | 33.6156 | 1.97739 | ||||||||
\(290\) | 53.4831 | 3.14063 | ||||||||
\(291\) | 16.5188 | 0.968349 | ||||||||
\(292\) | −9.81410 | −0.574327 | ||||||||
\(293\) | 25.2343 | 1.47420 | 0.737101 | − | 0.675783i | \(-0.236194\pi\) | ||||
0.737101 | + | 0.675783i | \(0.236194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7703 | 1.67507 | ||||||||
\(296\) | 2.79941 | 0.162713 | ||||||||
\(297\) | −13.7207 | −0.796159 | ||||||||
\(298\) | −2.17058 | −0.125738 | ||||||||
\(299\) | −32.4210 | −1.87496 | ||||||||
\(300\) | −11.9178 | −0.688075 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.5734 | 1.58667 | ||||||||
\(303\) | 14.8933 | 0.855595 | ||||||||
\(304\) | −27.8870 | −1.59943 | ||||||||
\(305\) | −36.0508 | −2.06426 | ||||||||
\(306\) | −6.87923 | −0.393259 | ||||||||
\(307\) | −6.32587 | −0.361037 | −0.180518 | − | 0.983572i | \(-0.557778\pi\) | ||||
−0.180518 | + | 0.983572i | \(0.557778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3724 | −0.646953 | ||||||||
\(310\) | 52.8094 | 2.99937 | ||||||||
\(311\) | −13.5024 | −0.765649 | −0.382824 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382824 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(312\) | −4.38542 | −0.248276 | ||||||||
\(313\) | 5.10715 | 0.288673 | 0.144337 | − | 0.989529i | \(-0.453895\pi\) | ||||
0.144337 | + | 0.989529i | \(0.453895\pi\) | |||||||
\(314\) | 11.8151 | 0.666763 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.618794 | 0.0348099 | ||||||||
\(317\) | 10.1152 | 0.568123 | 0.284062 | − | 0.958806i | \(-0.408318\pi\) | ||||
0.284062 | + | 0.958806i | \(0.408318\pi\) | |||||||
\(318\) | 1.30544 | 0.0732052 | ||||||||
\(319\) | −22.3939 | −1.25382 | ||||||||
\(320\) | −13.9374 | −0.779126 | ||||||||
\(321\) | 11.3225 | 0.631962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.6633 | 2.37385 | ||||||||
\(324\) | −11.4714 | −0.637300 | ||||||||
\(325\) | −17.0313 | −0.944728 | ||||||||
\(326\) | 16.5512 | 0.916687 | ||||||||
\(327\) | 20.2445 | 1.11952 | ||||||||
\(328\) | −0.774564 | −0.0427681 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 23.1254 | 1.27301 | ||||||||
\(331\) | −18.3598 | −1.00915 | −0.504574 | − | 0.863369i | \(-0.668350\pi\) | ||||
−0.504574 | + | 0.863369i | \(0.668350\pi\) | |||||||
\(332\) | −11.2206 | −0.615811 | ||||||||
\(333\) | 1.84409 | 0.101056 | ||||||||
\(334\) | 13.9847 | 0.765209 | ||||||||
\(335\) | 8.46672 | 0.462586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.5700 | −1.77420 | −0.887099 | − | 0.461578i | \(-0.847283\pi\) | ||||
−0.887099 | + | 0.461578i | \(0.847283\pi\) | |||||||
\(338\) | −0.236689 | −0.0128742 | ||||||||
\(339\) | −25.0552 | −1.36081 | ||||||||
\(340\) | 35.3436 | 1.91678 | ||||||||
\(341\) | −22.1119 | −1.19742 | ||||||||
\(342\) | −5.79842 | −0.313543 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.48364 | 0.349575 | ||||||||
\(345\) | −44.5097 | −2.39632 | ||||||||
\(346\) | −40.1157 | −2.15663 | ||||||||
\(347\) | 27.9803 | 1.50206 | 0.751031 | − | 0.660267i | \(-0.229557\pi\) | ||||
0.751031 | + | 0.660267i | \(0.229557\pi\) | |||||||
\(348\) | −22.6982 | −1.21675 | ||||||||
\(349\) | −10.0218 | −0.536455 | −0.268228 | − | 0.963356i | \(-0.586438\pi\) | ||||
−0.268228 | + | 0.963356i | \(0.586438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8743 | −1.06081 | ||||||||
\(352\) | 17.9936 | 0.959064 | ||||||||
\(353\) | 3.92033 | 0.208658 | 0.104329 | − | 0.994543i | \(-0.466731\pi\) | ||||
0.104329 | + | 0.994543i | \(0.466731\pi\) | |||||||
\(354\) | −27.5565 | −1.46461 | ||||||||
\(355\) | 13.4453 | 0.713602 | ||||||||
\(356\) | 18.4971 | 0.980343 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.72879 | −0.514183 | ||||||||
\(359\) | −19.1431 | −1.01034 | −0.505168 | − | 0.863021i | \(-0.668569\pi\) | ||||
−0.505168 | + | 0.863021i | \(0.668569\pi\) | |||||||
\(360\) | 1.23383 | 0.0650284 | ||||||||
\(361\) | 16.9604 | 0.892651 | ||||||||
\(362\) | 8.64347 | 0.454291 | ||||||||
\(363\) | 7.67402 | 0.402782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.2544 | −1.00782 | ||||||||
\(366\) | 34.5298 | 1.80490 | ||||||||
\(367\) | 12.5790 | 0.656616 | 0.328308 | − | 0.944571i | \(-0.393522\pi\) | ||||
0.328308 | + | 0.944571i | \(0.393522\pi\) | |||||||
\(368\) | −42.0186 | −2.19037 | ||||||||
\(369\) | −0.510238 | −0.0265620 | ||||||||
\(370\) | −21.3825 | −1.11162 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.4123 | −1.16202 | ||||||||
\(373\) | −35.4026 | −1.83308 | −0.916540 | − | 0.399943i | \(-0.869030\pi\) | ||||
−0.916540 | + | 0.399943i | \(0.869030\pi\) | |||||||
\(374\) | −33.3986 | −1.72700 | ||||||||
\(375\) | 1.24879 | 0.0644873 | ||||||||
\(376\) | −1.19194 | −0.0614697 | ||||||||
\(377\) | −32.4372 | −1.67060 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.1951 | −0.934619 | −0.467310 | − | 0.884094i | \(-0.654777\pi\) | ||||
−0.467310 | + | 0.884094i | \(0.654777\pi\) | |||||||
\(380\) | 29.7907 | 1.52823 | ||||||||
\(381\) | 31.0897 | 1.59277 | ||||||||
\(382\) | 6.58501 | 0.336919 | ||||||||
\(383\) | 33.3543 | 1.70432 | 0.852162 | − | 0.523277i | \(-0.175291\pi\) | ||||
0.852162 | + | 0.523277i | \(0.175291\pi\) | |||||||
\(384\) | −9.57328 | −0.488535 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.8620 | −1.57084 | ||||||||
\(387\) | 4.27105 | 0.217110 | ||||||||
\(388\) | −16.6588 | −0.845724 | ||||||||
\(389\) | 4.26120 | 0.216052 | 0.108026 | − | 0.994148i | \(-0.465547\pi\) | ||||
0.108026 | + | 0.994148i | \(0.465547\pi\) | |||||||
\(390\) | 33.4968 | 1.69617 | ||||||||
\(391\) | 64.2826 | 3.25091 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1736 | −0.714965 | ||||||||
\(394\) | −12.2132 | −0.615293 | ||||||||
\(395\) | 1.21402 | 0.0610840 | ||||||||
\(396\) | 2.01132 | 0.101072 | ||||||||
\(397\) | −2.13534 | −0.107170 | −0.0535849 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535849 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(398\) | 2.56792 | 0.128718 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.0731 | −1.10365 | ||||||||
\(401\) | −3.75522 | −0.187527 | −0.0937634 | − | 0.995595i | \(-0.529890\pi\) | ||||
−0.0937634 | + | 0.995595i | \(0.529890\pi\) | |||||||
\(402\) | −8.10950 | −0.404465 | ||||||||
\(403\) | −32.0286 | −1.59546 | ||||||||
\(404\) | −15.0195 | −0.747248 | ||||||||
\(405\) | −22.5059 | −1.11833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.95308 | 0.443788 | ||||||||
\(408\) | 8.69517 | 0.430475 | ||||||||
\(409\) | −17.3950 | −0.860127 | −0.430063 | − | 0.902799i | \(-0.641509\pi\) | ||||
−0.430063 | + | 0.902799i | \(0.641509\pi\) | |||||||
\(410\) | 5.91628 | 0.292184 | ||||||||
\(411\) | −14.1182 | −0.696398 | ||||||||
\(412\) | 11.4688 | 0.565027 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.73672 | −0.429387 | ||||||||
\(415\) | −22.0138 | −1.08062 | ||||||||
\(416\) | 26.0634 | 1.27787 | ||||||||
\(417\) | 7.65515 | 0.374874 | ||||||||
\(418\) | −28.1513 | −1.37693 | ||||||||
\(419\) | −11.4568 | −0.559701 | −0.279850 | − | 0.960044i | \(-0.590285\pi\) | ||||
−0.279850 | + | 0.960044i | \(0.590285\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.481034 | −0.0234441 | −0.0117221 | − | 0.999931i | \(-0.503731\pi\) | ||||
−0.0117221 | + | 0.999931i | \(0.503731\pi\) | |||||||
\(422\) | −36.0324 | −1.75403 | ||||||||
\(423\) | −0.785184 | −0.0381769 | ||||||||
\(424\) | 0.338150 | 0.0164220 | ||||||||
\(425\) | 33.7688 | 1.63803 | ||||||||
\(426\) | −12.8780 | −0.623942 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.4185 | −0.551934 | ||||||||
\(429\) | −14.0254 | −0.677155 | ||||||||
\(430\) | −49.5234 | −2.38823 | ||||||||
\(431\) | 5.92032 | 0.285172 | 0.142586 | − | 0.989782i | \(-0.454458\pi\) | ||||
0.142586 | + | 0.989782i | \(0.454458\pi\) | |||||||
\(432\) | −25.7576 | −1.23926 | ||||||||
\(433\) | −6.92900 | −0.332987 | −0.166493 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166493 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −44.5319 | −2.13514 | ||||||||
\(436\) | −20.4161 | −0.977754 | ||||||||
\(437\) | 54.1830 | 2.59193 | ||||||||
\(438\) | 18.4420 | 0.881195 | ||||||||
\(439\) | −27.3202 | −1.30392 | −0.651960 | − | 0.758253i | \(-0.726053\pi\) | ||||
−0.651960 | + | 0.758253i | \(0.726053\pi\) | |||||||
\(440\) | 5.99023 | 0.285573 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.3773 | −2.30107 | ||||||||
\(443\) | 32.2590 | 1.53267 | 0.766335 | − | 0.642441i | \(-0.222078\pi\) | ||||
0.766335 | + | 0.642441i | \(0.222078\pi\) | |||||||
\(444\) | 9.07473 | 0.430668 | ||||||||
\(445\) | 36.2896 | 1.72029 | ||||||||
\(446\) | 4.97531 | 0.235588 | ||||||||
\(447\) | 1.80730 | 0.0854824 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0930 | −0.806670 | −0.403335 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403335 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(450\) | −4.58955 | −0.216354 | ||||||||
\(451\) | −2.47721 | −0.116647 | ||||||||
\(452\) | 25.2676 | 1.18849 | ||||||||
\(453\) | −22.9586 | −1.07869 | ||||||||
\(454\) | 13.4116 | 0.629435 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.32906 | 0.343214 | ||||||||
\(457\) | −13.2781 | −0.621125 | −0.310563 | − | 0.950553i | \(-0.600517\pi\) | ||||
−0.310563 | + | 0.950553i | \(0.600517\pi\) | |||||||
\(458\) | 12.8543 | 0.600641 | ||||||||
\(459\) | 39.4056 | 1.83929 | ||||||||
\(460\) | 44.8870 | 2.09287 | ||||||||
\(461\) | −10.7809 | −0.502115 | −0.251058 | − | 0.967972i | \(-0.580778\pi\) | ||||
−0.251058 | + | 0.967972i | \(0.580778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7876 | −1.19845 | −0.599226 | − | 0.800580i | \(-0.704525\pi\) | ||||
−0.599226 | + | 0.800580i | \(0.704525\pi\) | |||||||
\(464\) | −42.0395 | −1.95164 | ||||||||
\(465\) | −43.9710 | −2.03911 | ||||||||
\(466\) | −15.1260 | −0.700699 | ||||||||
\(467\) | 24.5678 | 1.13686 | 0.568430 | − | 0.822731i | \(-0.307551\pi\) | ||||
0.568430 | + | 0.822731i | \(0.307551\pi\) | |||||||
\(468\) | 2.91335 | 0.134670 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.10430 | 0.419950 | ||||||||
\(471\) | −9.83763 | −0.453294 | ||||||||
\(472\) | −7.13802 | −0.328554 | ||||||||
\(473\) | 20.7360 | 0.953441 | ||||||||
\(474\) | −1.16280 | −0.0534091 | ||||||||
\(475\) | 28.4633 | 1.30599 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.222754 | 0.0101992 | ||||||||
\(478\) | 25.1628 | 1.15092 | ||||||||
\(479\) | 10.6687 | 0.487464 | 0.243732 | − | 0.969843i | \(-0.421628\pi\) | ||||
0.243732 | + | 0.969843i | \(0.421628\pi\) | |||||||
\(480\) | 35.7816 | 1.63320 | ||||||||
\(481\) | 12.9684 | 0.591307 | ||||||||
\(482\) | −18.4439 | −0.840095 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.73907 | −0.351776 | ||||||||
\(485\) | −32.6831 | −1.48406 | ||||||||
\(486\) | −9.93283 | −0.450563 | ||||||||
\(487\) | −7.74207 | −0.350827 | −0.175413 | − | 0.984495i | \(-0.556126\pi\) | ||||
−0.175413 | + | 0.984495i | \(0.556126\pi\) | |||||||
\(488\) | 8.94432 | 0.404890 | ||||||||
\(489\) | −13.7811 | −0.623204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.97531 | −0.134274 | −0.0671370 | − | 0.997744i | \(-0.521386\pi\) | ||||
−0.0671370 | + | 0.997744i | \(0.521386\pi\) | |||||||
\(492\) | −2.51087 | −0.113199 | ||||||||
\(493\) | 64.3146 | 2.89659 | ||||||||
\(494\) | −40.7767 | −1.83463 | ||||||||
\(495\) | 3.94602 | 0.177361 | ||||||||
\(496\) | −41.5100 | −1.86385 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 21.0851 | 0.944844 | ||||||||
\(499\) | 1.45634 | 0.0651947 | 0.0325973 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325973 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(500\) | −1.25938 | −0.0563211 | ||||||||
\(501\) | −11.6442 | −0.520223 | ||||||||
\(502\) | −19.0196 | −0.848887 | ||||||||
\(503\) | −37.5010 | −1.67209 | −0.836043 | − | 0.548664i | \(-0.815137\pi\) | ||||
−0.836043 | + | 0.548664i | \(0.815137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.4669 | −1.31126 | ||||||||
\(506\) | −42.4168 | −1.88566 | ||||||||
\(507\) | 0.197076 | 0.00875243 | ||||||||
\(508\) | −31.3532 | −1.39107 | ||||||||
\(509\) | 6.21143 | 0.275317 | 0.137658 | − | 0.990480i | \(-0.456042\pi\) | ||||
0.137658 | + | 0.990480i | \(0.456042\pi\) | |||||||
\(510\) | −66.4155 | −2.94093 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 26.5749 | 1.17446 | ||||||||
\(513\) | 33.2145 | 1.46646 | ||||||||
\(514\) | 44.2422 | 1.95144 | ||||||||
\(515\) | 22.5008 | 0.991503 | ||||||||
\(516\) | 21.0177 | 0.925254 | ||||||||
\(517\) | −3.81207 | −0.167655 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.4017 | 1.46617 | ||||||||
\(520\) | 8.67674 | 0.380500 | ||||||||
\(521\) | 33.0896 | 1.44968 | 0.724841 | − | 0.688917i | \(-0.241913\pi\) | ||||
0.724841 | + | 0.688917i | \(0.241913\pi\) | |||||||
\(522\) | −8.74108 | −0.382587 | ||||||||
\(523\) | −29.5269 | −1.29112 | −0.645560 | − | 0.763710i | \(-0.723376\pi\) | ||||
−0.645560 | + | 0.763710i | \(0.723376\pi\) | |||||||
\(524\) | 14.2938 | 0.624427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.1401 | 0.616537 | ||||||||
\(527\) | 63.5046 | 2.76630 | ||||||||
\(528\) | −18.1774 | −0.791069 | ||||||||
\(529\) | 58.6399 | 2.54956 | ||||||||
\(530\) | −2.58286 | −0.112192 | ||||||||
\(531\) | −4.70212 | −0.204055 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.58819 | −0.155422 | ||||||||
\(534\) | −34.7585 | −1.50415 | ||||||||
\(535\) | −22.4021 | −0.968527 | ||||||||
\(536\) | −2.10062 | −0.0907331 | ||||||||
\(537\) | 8.10053 | 0.349564 | ||||||||
\(538\) | 4.57519 | 0.197251 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 27.5160 | 1.18410 | ||||||||
\(541\) | −29.5888 | −1.27212 | −0.636060 | − | 0.771639i | \(-0.719437\pi\) | ||||
−0.636060 | + | 0.771639i | \(0.719437\pi\) | |||||||
\(542\) | 33.5750 | 1.44217 | ||||||||
\(543\) | −7.19686 | −0.308847 | ||||||||
\(544\) | −51.6772 | −2.21564 | ||||||||
\(545\) | −40.0546 | −1.71575 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.8516 | −1.61842 | −0.809208 | − | 0.587522i | \(-0.800103\pi\) | ||||
−0.809208 | + | 0.587522i | \(0.800103\pi\) | |||||||
\(548\) | 14.2378 | 0.608210 | ||||||||
\(549\) | 5.89201 | 0.251465 | ||||||||
\(550\) | −22.2823 | −0.950119 | ||||||||
\(551\) | 54.2101 | 2.30943 | ||||||||
\(552\) | 11.0430 | 0.470021 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.1597 | 1.06893 | ||||||||
\(555\) | 17.8038 | 0.755730 | ||||||||
\(556\) | −7.72004 | −0.327403 | ||||||||
\(557\) | −44.0069 | −1.86463 | −0.932315 | − | 0.361647i | \(-0.882215\pi\) | ||||
−0.932315 | + | 0.361647i | \(0.882215\pi\) | |||||||
\(558\) | −8.63099 | −0.365379 | ||||||||
\(559\) | 30.0357 | 1.27037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.8089 | 1.17409 | ||||||||
\(562\) | −10.5862 | −0.446550 | ||||||||
\(563\) | 23.5580 | 0.992852 | 0.496426 | − | 0.868079i | \(-0.334645\pi\) | ||||
0.496426 | + | 0.868079i | \(0.334645\pi\) | |||||||
\(564\) | −3.86386 | −0.162698 | ||||||||
\(565\) | 49.5728 | 2.08554 | ||||||||
\(566\) | 34.9528 | 1.46917 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.33582 | −0.139968 | ||||||||
\(569\) | 31.6342 | 1.32618 | 0.663088 | − | 0.748542i | \(-0.269246\pi\) | ||||
0.663088 | + | 0.748542i | \(0.269246\pi\) | |||||||
\(570\) | −55.9808 | −2.34478 | ||||||||
\(571\) | 8.77077 | 0.367045 | 0.183523 | − | 0.983015i | \(-0.441250\pi\) | ||||
0.183523 | + | 0.983015i | \(0.441250\pi\) | |||||||
\(572\) | 14.1443 | 0.591404 | ||||||||
\(573\) | −5.48291 | −0.229052 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.8869 | 1.78851 | ||||||||
\(576\) | 2.27788 | 0.0949119 | ||||||||
\(577\) | −29.3406 | −1.22147 | −0.610733 | − | 0.791837i | \(-0.709125\pi\) | ||||
−0.610733 | + | 0.791837i | \(0.709125\pi\) | |||||||
\(578\) | 63.7037 | 2.64973 | ||||||||
\(579\) | 25.6968 | 1.06792 | ||||||||
\(580\) | 44.9094 | 1.86476 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 31.3042 | 1.29760 | ||||||||
\(583\) | 1.08147 | 0.0447899 | ||||||||
\(584\) | 4.77708 | 0.197677 | ||||||||
\(585\) | 5.71574 | 0.236317 | ||||||||
\(586\) | 47.8206 | 1.97545 | ||||||||
\(587\) | −0.497739 | −0.0205439 | −0.0102719 | − | 0.999947i | \(-0.503270\pi\) | ||||
−0.0102719 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.5273 | 2.20555 | ||||||||
\(590\) | 54.5217 | 2.24462 | ||||||||
\(591\) | 10.1692 | 0.418303 | ||||||||
\(592\) | 16.8074 | 0.690779 | ||||||||
\(593\) | −15.2791 | −0.627437 | −0.313719 | − | 0.949516i | \(-0.601575\pi\) | ||||
−0.313719 | + | 0.949516i | \(0.601575\pi\) | |||||||
\(594\) | −26.0017 | −1.06686 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.82262 | −0.0746575 | ||||||||
\(597\) | −2.13814 | −0.0875083 | ||||||||
\(598\) | −61.4399 | −2.51247 | ||||||||
\(599\) | 34.9568 | 1.42830 | 0.714148 | − | 0.699995i | \(-0.246814\pi\) | ||||
0.714148 | + | 0.699995i | \(0.246814\pi\) | |||||||
\(600\) | 5.80108 | 0.236828 | ||||||||
\(601\) | 45.0759 | 1.83868 | 0.919342 | − | 0.393459i | \(-0.128722\pi\) | ||||
0.919342 | + | 0.393459i | \(0.128722\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.38377 | −0.0563515 | ||||||||
\(604\) | 23.1532 | 0.942089 | ||||||||
\(605\) | −15.1834 | −0.617292 | ||||||||
\(606\) | 28.2237 | 1.14651 | ||||||||
\(607\) | 6.55822 | 0.266190 | 0.133095 | − | 0.991103i | \(-0.457508\pi\) | ||||
0.133095 | + | 0.991103i | \(0.457508\pi\) | |||||||
\(608\) | −43.5581 | −1.76651 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −68.3186 | −2.76614 | ||||||||
\(611\) | −5.52171 | −0.223384 | ||||||||
\(612\) | −5.77644 | −0.233499 | ||||||||
\(613\) | −10.4603 | −0.422489 | −0.211245 | − | 0.977433i | \(-0.567752\pi\) | ||||
−0.211245 | + | 0.977433i | \(0.567752\pi\) | |||||||
\(614\) | −11.9879 | −0.483794 | ||||||||
\(615\) | −4.92610 | −0.198639 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1861 | −0.530852 | −0.265426 | − | 0.964131i | \(-0.585513\pi\) | ||||
−0.265426 | + | 0.964131i | \(0.585513\pi\) | |||||||
\(618\) | −21.5514 | −0.866926 | ||||||||
\(619\) | 23.2046 | 0.932670 | 0.466335 | − | 0.884608i | \(-0.345574\pi\) | ||||
0.466335 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(620\) | 44.3437 | 1.78089 | ||||||||
\(621\) | 50.0457 | 2.00826 | ||||||||
\(622\) | −25.5879 | −1.02598 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −26.3296 | −1.05403 | ||||||||
\(625\) | −26.2033 | −1.04813 | ||||||||
\(626\) | 9.67839 | 0.386826 | ||||||||
\(627\) | 23.4398 | 0.936094 | ||||||||
\(628\) | 9.92103 | 0.395892 | ||||||||
\(629\) | −25.7130 | −1.02524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.7919 | −1.02676 | −0.513379 | − | 0.858162i | \(-0.671607\pi\) | ||||
−0.513379 | + | 0.858162i | \(0.671607\pi\) | |||||||
\(632\) | −0.301203 | −0.0119812 | ||||||||
\(633\) | 30.0018 | 1.19247 | ||||||||
\(634\) | 19.1689 | 0.761293 | ||||||||
\(635\) | −61.5122 | −2.44104 | ||||||||
\(636\) | 1.09617 | 0.0434658 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −42.4379 | −1.68013 | ||||||||
\(639\) | −2.19745 | −0.0869298 | ||||||||
\(640\) | 18.9411 | 0.748715 | ||||||||
\(641\) | −18.3270 | −0.723873 | −0.361936 | − | 0.932203i | \(-0.617884\pi\) | ||||
−0.361936 | + | 0.932203i | \(0.617884\pi\) | |||||||
\(642\) | 21.4569 | 0.846838 | ||||||||
\(643\) | −32.9938 | −1.30115 | −0.650575 | − | 0.759442i | \(-0.725472\pi\) | ||||
−0.650575 | + | 0.759442i | \(0.725472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.2349 | 1.62362 | ||||||||
\(646\) | 80.8497 | 3.18099 | ||||||||
\(647\) | −23.7648 | −0.934290 | −0.467145 | − | 0.884181i | \(-0.654717\pi\) | ||||
−0.467145 | + | 0.884181i | \(0.654717\pi\) | |||||||
\(648\) | 5.58378 | 0.219352 | ||||||||
\(649\) | −22.8288 | −0.896109 | ||||||||
\(650\) | −32.2755 | −1.26595 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.8979 | 0.544285 | ||||||||
\(653\) | 2.32882 | 0.0911336 | 0.0455668 | − | 0.998961i | \(-0.485491\pi\) | ||||
0.0455668 | + | 0.998961i | \(0.485491\pi\) | |||||||
\(654\) | 38.3646 | 1.50018 | ||||||||
\(655\) | 28.0431 | 1.09574 | ||||||||
\(656\) | −4.65040 | −0.181567 | ||||||||
\(657\) | 3.14687 | 0.122771 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0113 | −0.389985 | −0.194992 | − | 0.980805i | \(-0.562468\pi\) | ||||
−0.194992 | + | 0.980805i | \(0.562468\pi\) | |||||||
\(660\) | 19.4183 | 0.755855 | ||||||||
\(661\) | −22.8365 | −0.888235 | −0.444118 | − | 0.895969i | \(-0.646483\pi\) | ||||
−0.444118 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(662\) | −34.7931 | −1.35227 | ||||||||
\(663\) | 40.2806 | 1.56437 | ||||||||
\(664\) | 5.46171 | 0.211956 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.49468 | 0.135416 | ||||||||
\(667\) | 81.6806 | 3.16269 | ||||||||
\(668\) | 11.7429 | 0.454345 | ||||||||
\(669\) | −4.14262 | −0.160163 | ||||||||
\(670\) | 16.0450 | 0.619872 | ||||||||
\(671\) | 28.6057 | 1.10431 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.59421 | −0.254188 | −0.127094 | − | 0.991891i | \(-0.540565\pi\) | ||||
−0.127094 | + | 0.991891i | \(0.540565\pi\) | |||||||
\(674\) | −61.7222 | −2.37745 | ||||||||
\(675\) | 26.2899 | 1.01190 | ||||||||
\(676\) | −0.198746 | −0.00764408 | ||||||||
\(677\) | −30.6496 | −1.17796 | −0.588980 | − | 0.808147i | \(-0.700470\pi\) | ||||
−0.588980 | + | 0.808147i | \(0.700470\pi\) | |||||||
\(678\) | −47.4813 | −1.82351 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −17.2038 | −0.659734 | ||||||||
\(681\) | −11.1669 | −0.427918 | ||||||||
\(682\) | −41.9034 | −1.60457 | ||||||||
\(683\) | 0.229687 | 0.00878873 | 0.00439437 | − | 0.999990i | \(-0.498601\pi\) | ||||
0.00439437 | + | 0.999990i | \(0.498601\pi\) | |||||||
\(684\) | −4.86889 | −0.186167 | ||||||||
\(685\) | 27.9334 | 1.06728 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7029 | −0.408342 | ||||||||
\(688\) | 38.9271 | 1.48408 | ||||||||
\(689\) | 1.56649 | 0.0596785 | ||||||||
\(690\) | −84.3487 | −3.21110 | ||||||||
\(691\) | −1.61668 | −0.0615013 | −0.0307506 | − | 0.999527i | \(-0.509790\pi\) | ||||
−0.0307506 | + | 0.999527i | \(0.509790\pi\) | |||||||
\(692\) | −33.6848 | −1.28051 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53.0246 | 2.01278 | ||||||||
\(695\) | −15.1460 | −0.574522 | ||||||||
\(696\) | 11.0485 | 0.418793 | ||||||||
\(697\) | 7.11446 | 0.269479 | ||||||||
\(698\) | −18.9920 | −0.718858 | ||||||||
\(699\) | 12.5944 | 0.476366 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.0273 | 1.05858 | 0.529288 | − | 0.848442i | \(-0.322459\pi\) | ||||
0.529288 | + | 0.848442i | \(0.322459\pi\) | |||||||
\(702\) | −37.6630 | −1.42150 | ||||||||
\(703\) | −21.6732 | −0.817418 | ||||||||
\(704\) | 11.0591 | 0.416807 | ||||||||
\(705\) | −7.58056 | −0.285500 | ||||||||
\(706\) | 7.42928 | 0.279605 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −23.1390 | −0.869616 | ||||||||
\(709\) | 48.9214 | 1.83728 | 0.918642 | − | 0.395091i | \(-0.129287\pi\) | ||||
0.918642 | + | 0.395091i | \(0.129287\pi\) | |||||||
\(710\) | 25.4797 | 0.956236 | ||||||||
\(711\) | −0.198415 | −0.00744115 | ||||||||
\(712\) | −9.00358 | −0.337423 | ||||||||
\(713\) | 80.6518 | 3.02043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.7499 | 1.03779 | ||||||||
\(716\) | −8.16920 | −0.305297 | ||||||||
\(717\) | −20.9514 | −0.782446 | ||||||||
\(718\) | −36.2775 | −1.35386 | ||||||||
\(719\) | −32.5456 | −1.21375 | −0.606874 | − | 0.794798i | \(-0.707577\pi\) | ||||
−0.606874 | + | 0.794798i | \(0.707577\pi\) | |||||||
\(720\) | 7.40777 | 0.276071 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 32.1410 | 1.19616 | ||||||||
\(723\) | 15.3570 | 0.571133 | ||||||||
\(724\) | 7.25786 | 0.269736 | ||||||||
\(725\) | 42.9082 | 1.59357 | ||||||||
\(726\) | 14.5428 | 0.539733 | ||||||||
\(727\) | 24.4090 | 0.905278 | 0.452639 | − | 0.891694i | \(-0.350483\pi\) | ||||
0.452639 | + | 0.891694i | \(0.350483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8972 | 1.10731 | ||||||||
\(730\) | −36.4883 | −1.35049 | ||||||||
\(731\) | −59.5531 | −2.20265 | ||||||||
\(732\) | 28.9944 | 1.07166 | ||||||||
\(733\) | 23.0042 | 0.849680 | 0.424840 | − | 0.905268i | \(-0.360330\pi\) | ||||
0.424840 | + | 0.905268i | \(0.360330\pi\) | |||||||
\(734\) | 23.8380 | 0.879875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −65.6308 | −2.41918 | ||||||||
\(737\) | −6.71821 | −0.247468 | ||||||||
\(738\) | −0.966935 | −0.0355934 | ||||||||
\(739\) | 6.28473 | 0.231188 | 0.115594 | − | 0.993297i | \(-0.463123\pi\) | ||||
0.115594 | + | 0.993297i | \(0.463123\pi\) | |||||||
\(740\) | −17.9547 | −0.660029 | ||||||||
\(741\) | 33.9521 | 1.24726 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.355429 | −0.0130394 | −0.00651971 | − | 0.999979i | \(-0.502075\pi\) | ||||
−0.00651971 | + | 0.999979i | \(0.502075\pi\) | |||||||
\(744\) | 10.9094 | 0.399956 | ||||||||
\(745\) | −3.57582 | −0.131008 | ||||||||
\(746\) | −67.0903 | −2.45635 | ||||||||
\(747\) | 3.59787 | 0.131639 | ||||||||
\(748\) | −28.0446 | −1.02541 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.36654 | 0.0864139 | ||||||||
\(751\) | 16.0914 | 0.587183 | 0.293592 | − | 0.955931i | \(-0.405149\pi\) | ||||
0.293592 | + | 0.955931i | \(0.405149\pi\) | |||||||
\(752\) | −7.15629 | −0.260963 | ||||||||
\(753\) | 15.8364 | 0.577111 | ||||||||
\(754\) | −61.4706 | −2.23863 | ||||||||
\(755\) | 45.4245 | 1.65317 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.45992 | −0.198444 | −0.0992221 | − | 0.995065i | \(-0.531635\pi\) | ||||
−0.0992221 | + | 0.995065i | \(0.531635\pi\) | |||||||
\(758\) | −34.4809 | −1.25240 | ||||||||
\(759\) | 35.3177 | 1.28195 | ||||||||
\(760\) | −14.5008 | −0.526001 | ||||||||
\(761\) | −25.1724 | −0.912497 | −0.456249 | − | 0.889852i | \(-0.650807\pi\) | ||||
−0.456249 | + | 0.889852i | \(0.650807\pi\) | |||||||
\(762\) | 58.9170 | 2.13434 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.52939 | 0.200046 | ||||||||
\(765\) | −11.3329 | −0.409740 | ||||||||
\(766\) | 63.2086 | 2.28382 | ||||||||
\(767\) | −33.0671 | −1.19398 | ||||||||
\(768\) | −32.2306 | −1.16302 | ||||||||
\(769\) | −14.8717 | −0.536286 | −0.268143 | − | 0.963379i | \(-0.586410\pi\) | ||||
−0.268143 | + | 0.963379i | \(0.586410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.8376 | −1.32667 | ||||||||
\(772\) | −25.9146 | −0.932689 | ||||||||
\(773\) | −11.8929 | −0.427758 | −0.213879 | − | 0.976860i | \(-0.568610\pi\) | ||||
−0.213879 | + | 0.976860i | \(0.568610\pi\) | |||||||
\(774\) | 8.09393 | 0.290930 | ||||||||
\(775\) | 42.3678 | 1.52190 | ||||||||
\(776\) | 8.10880 | 0.291089 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.07526 | 0.289512 | ||||||||
\(779\) | 5.99670 | 0.214854 | ||||||||
\(780\) | 28.1270 | 1.00711 | ||||||||
\(781\) | −10.6686 | −0.381753 | ||||||||
\(782\) | 121.820 | 4.35626 | ||||||||
\(783\) | 50.0707 | 1.78938 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.4642 | 0.694706 | ||||||||
\(786\) | −26.8600 | −0.958063 | ||||||||
\(787\) | −1.56890 | −0.0559254 | −0.0279627 | − | 0.999609i | \(-0.508902\pi\) | ||||
−0.0279627 | + | 0.999609i | \(0.508902\pi\) | |||||||
\(788\) | −10.2554 | −0.365332 | ||||||||
\(789\) | −11.7735 | −0.419149 | ||||||||
\(790\) | 2.30065 | 0.0818534 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.979022 | −0.0347880 | ||||||||
\(793\) | 41.4348 | 1.47139 | ||||||||
\(794\) | −4.04661 | −0.143609 | ||||||||
\(795\) | 2.15058 | 0.0762732 | ||||||||
\(796\) | 2.15627 | 0.0764269 | ||||||||
\(797\) | 8.77673 | 0.310888 | 0.155444 | − | 0.987845i | \(-0.450319\pi\) | ||||
0.155444 | + | 0.987845i | \(0.450319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9481 | 0.387317 | ||||||||
\(800\) | −34.4770 | −1.21895 | ||||||||
\(801\) | −5.93105 | −0.209563 | ||||||||
\(802\) | −7.11639 | −0.251288 | ||||||||
\(803\) | 15.2781 | 0.539151 | ||||||||
\(804\) | −6.80949 | −0.240152 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −60.6964 | −2.13794 | ||||||||
\(807\) | −3.80947 | −0.134100 | ||||||||
\(808\) | 7.31085 | 0.257195 | ||||||||
\(809\) | −16.4611 | −0.578743 | −0.289371 | − | 0.957217i | \(-0.593446\pi\) | ||||
−0.289371 | + | 0.957217i | \(0.593446\pi\) | |||||||
\(810\) | −42.6501 | −1.49857 | ||||||||
\(811\) | −19.6126 | −0.688692 | −0.344346 | − | 0.938843i | \(-0.611899\pi\) | ||||
−0.344346 | + | 0.938843i | \(0.611899\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.9557 | −0.980450 | ||||||||
\(814\) | 16.9667 | 0.594681 | ||||||||
\(815\) | 27.2665 | 0.955105 | ||||||||
\(816\) | 52.2049 | 1.82754 | ||||||||
\(817\) | −50.1966 | −1.75616 | ||||||||
\(818\) | −32.9646 | −1.15258 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.96786 | 0.173485 | ||||||||
\(821\) | 46.3721 | 1.61840 | 0.809199 | − | 0.587535i | \(-0.199902\pi\) | ||||
0.809199 | + | 0.587535i | \(0.199902\pi\) | |||||||
\(822\) | −26.7548 | −0.933182 | ||||||||
\(823\) | −36.9837 | −1.28917 | −0.644586 | − | 0.764532i | \(-0.722970\pi\) | ||||
−0.644586 | + | 0.764532i | \(0.722970\pi\) | |||||||
\(824\) | −5.58252 | −0.194476 | ||||||||
\(825\) | 18.5530 | 0.645933 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.16974 | −0.249316 | −0.124658 | − | 0.992200i | \(-0.539783\pi\) | ||||
−0.124658 | + | 0.992200i | \(0.539783\pi\) | |||||||
\(828\) | −7.33617 | −0.254949 | ||||||||
\(829\) | −10.5683 | −0.367053 | −0.183526 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183526 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(830\) | −41.7177 | −1.44804 | ||||||||
\(831\) | −20.9488 | −0.726707 | ||||||||
\(832\) | 16.0189 | 0.555357 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.5070 | 0.502337 | ||||||||
\(835\) | 23.0385 | 0.797279 | ||||||||
\(836\) | −23.6385 | −0.817553 | ||||||||
\(837\) | 49.4400 | 1.70890 | ||||||||
\(838\) | −21.7114 | −0.750006 | ||||||||
\(839\) | −22.4068 | −0.773568 | −0.386784 | − | 0.922170i | \(-0.626414\pi\) | ||||
−0.386784 | + | 0.922170i | \(0.626414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.7214 | 1.81798 | ||||||||
\(842\) | −0.911590 | −0.0314155 | ||||||||
\(843\) | 8.81440 | 0.303584 | ||||||||
\(844\) | −30.2562 | −1.04146 | ||||||||
\(845\) | −0.389922 | −0.0134137 | ||||||||
\(846\) | −1.48797 | −0.0511576 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.03022 | 0.0697179 | ||||||||
\(849\) | −29.1029 | −0.998808 | ||||||||
\(850\) | 63.9940 | 2.19498 | ||||||||
\(851\) | −32.6559 | −1.11943 | ||||||||
\(852\) | −10.8136 | −0.370467 | ||||||||
\(853\) | 17.1768 | 0.588122 | 0.294061 | − | 0.955787i | \(-0.404993\pi\) | ||||
0.294061 | + | 0.955787i | \(0.404993\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.55233 | −0.326683 | ||||||||
\(856\) | 5.55804 | 0.189970 | ||||||||
\(857\) | −43.1901 | −1.47535 | −0.737673 | − | 0.675159i | \(-0.764075\pi\) | ||||
−0.737673 | + | 0.675159i | \(0.764075\pi\) | |||||||
\(858\) | −26.5791 | −0.907397 | ||||||||
\(859\) | 18.4603 | 0.629858 | 0.314929 | − | 0.949115i | \(-0.398019\pi\) | ||||
0.314929 | + | 0.949115i | \(0.398019\pi\) | |||||||
\(860\) | −41.5845 | −1.41802 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.2194 | 0.382134 | ||||||||
\(863\) | −11.8699 | −0.404055 | −0.202028 | − | 0.979380i | \(-0.564753\pi\) | ||||
−0.202028 | + | 0.979380i | \(0.564753\pi\) | |||||||
\(864\) | −40.2320 | −1.36872 | ||||||||
\(865\) | −66.0867 | −2.24701 | ||||||||
\(866\) | −13.1309 | −0.446207 | ||||||||
\(867\) | −53.0420 | −1.80140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.963305 | −0.0326779 | ||||||||
\(870\) | −84.3908 | −2.86112 | ||||||||
\(871\) | −9.73120 | −0.329729 | ||||||||
\(872\) | 9.93768 | 0.336532 | ||||||||
\(873\) | 5.34162 | 0.180786 | ||||||||
\(874\) | 102.680 | 3.47322 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.4856 | 0.523212 | ||||||||
\(877\) | −45.3383 | −1.53097 | −0.765483 | − | 0.643457i | \(-0.777500\pi\) | ||||
−0.765483 | + | 0.643457i | \(0.777500\pi\) | |||||||
\(878\) | −51.7735 | −1.74727 | ||||||||
\(879\) | −39.8171 | −1.34300 | ||||||||
\(880\) | 35.9647 | 1.21237 | ||||||||
\(881\) | 32.8550 | 1.10691 | 0.553457 | − | 0.832878i | \(-0.313308\pi\) | ||||
0.553457 | + | 0.832878i | \(0.313308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6424 | 0.829282 | 0.414641 | − | 0.909985i | \(-0.363907\pi\) | ||||
0.414641 | + | 0.909985i | \(0.363907\pi\) | |||||||
\(884\) | −40.6221 | −1.36627 | ||||||||
\(885\) | −45.3966 | −1.52599 | ||||||||
\(886\) | 61.1328 | 2.05380 | ||||||||
\(887\) | −40.4767 | −1.35908 | −0.679538 | − | 0.733640i | \(-0.737820\pi\) | ||||
−0.679538 | + | 0.733640i | \(0.737820\pi\) | |||||||
\(888\) | −4.41719 | −0.148231 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 68.7712 | 2.30522 | ||||||||
\(891\) | 17.8580 | 0.598267 | ||||||||
\(892\) | 4.17773 | 0.139881 | ||||||||
\(893\) | 9.22806 | 0.308805 | ||||||||
\(894\) | 3.42496 | 0.114548 | ||||||||
\(895\) | −16.0273 | −0.535732 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.1570 | 1.70808 | ||||||||
\(898\) | −32.3924 | −1.08095 | ||||||||
\(899\) | 80.6921 | 2.69123 | ||||||||
\(900\) | −3.85382 | −0.128461 | ||||||||
\(901\) | −3.10595 | −0.103474 | ||||||||
\(902\) | −4.69447 | −0.156309 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2992 | −0.409065 | ||||||||
\(905\) | 14.2393 | 0.473330 | ||||||||
\(906\) | −43.5080 | −1.44546 | ||||||||
\(907\) | −26.8838 | −0.892661 | −0.446331 | − | 0.894868i | \(-0.647269\pi\) | ||||
−0.446331 | + | 0.894868i | \(0.647269\pi\) | |||||||
\(908\) | 11.2616 | 0.373729 | ||||||||
\(909\) | 4.81597 | 0.159736 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.7158 | −0.520688 | −0.260344 | − | 0.965516i | \(-0.583836\pi\) | ||||
−0.260344 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(912\) | 44.0029 | 1.45708 | ||||||||
\(913\) | 17.4676 | 0.578094 | ||||||||
\(914\) | −25.1629 | −0.832316 | ||||||||
\(915\) | 56.8844 | 1.88054 | ||||||||
\(916\) | 10.7937 | 0.356632 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 74.6761 | 2.46468 | ||||||||
\(919\) | −14.3753 | −0.474197 | −0.237098 | − | 0.971486i | \(-0.576196\pi\) | ||||
−0.237098 | + | 0.971486i | \(0.576196\pi\) | |||||||
\(920\) | −21.8490 | −0.720342 | ||||||||
\(921\) | 9.98158 | 0.328904 | ||||||||
\(922\) | −20.4305 | −0.672841 | ||||||||
\(923\) | −15.4533 | −0.508651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1547 | −0.564043 | ||||||||
\(926\) | −48.8692 | −1.60594 | ||||||||
\(927\) | −3.67745 | −0.120783 | ||||||||
\(928\) | −65.6635 | −2.15551 | ||||||||
\(929\) | 20.4613 | 0.671312 | 0.335656 | − | 0.941985i | \(-0.391042\pi\) | ||||
0.335656 | + | 0.941985i | \(0.391042\pi\) | |||||||
\(930\) | −83.3279 | −2.73243 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.7012 | −0.416042 | ||||||||
\(933\) | 21.3053 | 0.697506 | ||||||||
\(934\) | 46.5575 | 1.52341 | ||||||||
\(935\) | −55.0210 | −1.79938 | ||||||||
\(936\) | −1.41810 | −0.0463519 | ||||||||
\(937\) | −9.48803 | −0.309960 | −0.154980 | − | 0.987918i | \(-0.549531\pi\) | ||||
−0.154980 | + | 0.987918i | \(0.549531\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.05856 | −0.262981 | ||||||||
\(940\) | 7.64482 | 0.249347 | ||||||||
\(941\) | −7.95394 | −0.259291 | −0.129645 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129645 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(942\) | −18.6430 | −0.607421 | ||||||||
\(943\) | 9.03548 | 0.294236 | ||||||||
\(944\) | −42.8559 | −1.39484 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.2960 | 1.27762 | ||||||||
\(947\) | 36.5486 | 1.18767 | 0.593835 | − | 0.804587i | \(-0.297613\pi\) | ||||
0.593835 | + | 0.804587i | \(0.297613\pi\) | |||||||
\(948\) | −0.976394 | −0.0317118 | ||||||||
\(949\) | 22.1300 | 0.718370 | ||||||||
\(950\) | 53.9398 | 1.75004 | ||||||||
\(951\) | −15.9607 | −0.517560 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.5565 | −1.57290 | −0.786450 | − | 0.617655i | \(-0.788083\pi\) | ||||
−0.786450 | + | 0.617655i | \(0.788083\pi\) | |||||||
\(954\) | 0.422134 | 0.0136671 | ||||||||
\(955\) | 10.8482 | 0.351039 | ||||||||
\(956\) | 21.1290 | 0.683362 | ||||||||
\(957\) | 35.3353 | 1.14223 | ||||||||
\(958\) | 20.2178 | 0.653209 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 21.9918 | 0.709784 | ||||||||
\(961\) | 48.6757 | 1.57018 | ||||||||
\(962\) | 24.5759 | 0.792359 | ||||||||
\(963\) | 3.66132 | 0.117984 | ||||||||
\(964\) | −15.4872 | −0.498809 | ||||||||
\(965\) | −50.8422 | −1.63667 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.81990 | −0.0906817 | −0.0453409 | − | 0.998972i | \(-0.514437\pi\) | ||||
−0.0453409 | + | 0.998972i | \(0.514437\pi\) | |||||||
\(968\) | 3.76705 | 0.121078 | ||||||||
\(969\) | −67.3183 | −2.16257 | ||||||||
\(970\) | −61.9367 | −1.98867 | ||||||||
\(971\) | 30.2345 | 0.970272 | 0.485136 | − | 0.874439i | \(-0.338770\pi\) | ||||
0.485136 | + | 0.874439i | \(0.338770\pi\) | |||||||
\(972\) | −8.34053 | −0.267523 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.6717 | −0.470113 | ||||||||
\(975\) | 26.8737 | 0.860647 | ||||||||
\(976\) | 53.7007 | 1.71892 | ||||||||
\(977\) | −22.6696 | −0.725263 | −0.362632 | − | 0.931933i | \(-0.618122\pi\) | ||||
−0.362632 | + | 0.931933i | \(0.618122\pi\) | |||||||
\(978\) | −26.1161 | −0.835101 | ||||||||
\(979\) | −28.7952 | −0.920299 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.54638 | 0.209010 | ||||||||
\(982\) | −5.63841 | −0.179929 | ||||||||
\(983\) | −9.70795 | −0.309636 | −0.154818 | − | 0.987943i | \(-0.549479\pi\) | ||||
−0.154818 | + | 0.987943i | \(0.549479\pi\) | |||||||
\(984\) | 1.22218 | 0.0389617 | ||||||||
\(985\) | −20.1201 | −0.641079 | ||||||||
\(986\) | 121.880 | 3.88146 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −34.2399 | −1.08932 | ||||||||
\(989\) | −75.6333 | −2.40500 | ||||||||
\(990\) | 7.47797 | 0.237666 | ||||||||
\(991\) | 4.56981 | 0.145165 | 0.0725824 | − | 0.997362i | \(-0.476876\pi\) | ||||
0.0725824 | + | 0.997362i | \(0.476876\pi\) | |||||||
\(992\) | −64.8365 | −2.05856 | ||||||||
\(993\) | 28.9699 | 0.919333 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.23040 | 0.134113 | ||||||||
\(996\) | 17.7050 | 0.561004 | ||||||||
\(997\) | 4.92320 | 0.155919 | 0.0779597 | − | 0.996957i | \(-0.475159\pi\) | ||||
0.0779597 | + | 0.996957i | \(0.475159\pi\) | |||||||
\(998\) | 2.75986 | 0.0873618 | ||||||||
\(999\) | −20.0182 | −0.633348 |
(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 | 2009.2.a.u.1.17 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.17 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.17 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.17 | yes | 20 | 1.1 | even | 1 | trivial |