Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(277,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("552.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.f (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.40774219157\) |
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: | \( x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 277.18 | ||
Root | \(-1.14290 - 0.832928i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.277 |
Dual form | 552.2.f.d.277.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14290 | + | 0.832928i | 0.808156 | + | 0.588969i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.612462 | + | 1.90391i | 0.306231 | + | 0.951957i | ||||
\(5\) | 1.03589i | 0.463264i | 0.972803 | + | 0.231632i | \(0.0744065\pi\) | ||||
−0.972803 | + | 0.231632i | \(0.925593\pi\) | |||||||
\(6\) | −0.832928 | + | 1.14290i | −0.340041 | + | 0.466589i | ||||
\(7\) | −3.71260 | −1.40323 | −0.701616 | − | 0.712556i | \(-0.747538\pi\) | ||||
−0.701616 | + | 0.712556i | \(0.747538\pi\) | |||||||
\(8\) | −0.885838 | + | 2.68613i | −0.313191 | + | 0.949690i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.862822 | + | 1.18392i | −0.272848 | + | 0.374389i | ||||
\(11\) | − | 1.98292i | − | 0.597873i | −0.954273 | − | 0.298936i | \(-0.903368\pi\) | ||
0.954273 | − | 0.298936i | \(-0.0966319\pi\) | |||||||
\(12\) | −1.90391 | + | 0.612462i | −0.549613 | + | 0.176803i | ||||
\(13\) | 4.05749i | 1.12534i | 0.826680 | + | 0.562672i | \(0.190227\pi\) | ||||
−0.826680 | + | 0.562672i | \(0.809773\pi\) | |||||||
\(14\) | −4.24315 | − | 3.09233i | −1.13403 | − | 0.826460i | ||||
\(15\) | −1.03589 | −0.267466 | ||||||||
\(16\) | −3.24978 | + | 2.33215i | −0.812445 | + | 0.583038i | ||||
\(17\) | 0.0352924 | 0.00855966 | 0.00427983 | − | 0.999991i | \(-0.498638\pi\) | ||||
0.00427983 | + | 0.999991i | \(0.498638\pi\) | |||||||
\(18\) | −1.14290 | − | 0.832928i | −0.269385 | − | 0.196323i | ||||
\(19\) | − | 0.839050i | − | 0.192491i | −0.995358 | − | 0.0962456i | \(-0.969317\pi\) | ||
0.995358 | − | 0.0962456i | \(-0.0306834\pi\) | |||||||
\(20\) | −1.97225 | + | 0.634443i | −0.441007 | + | 0.141866i | ||||
\(21\) | − | 3.71260i | − | 0.810156i | ||||||
\(22\) | 1.65163 | − | 2.26629i | 0.352129 | − | 0.483174i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.68613 | − | 0.885838i | −0.548304 | − | 0.180821i | ||||
\(25\) | 3.92693 | 0.785386 | ||||||||
\(26\) | −3.37959 | + | 4.63732i | −0.662793 | + | 0.909453i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.27383 | − | 7.06847i | −0.429713 | − | 1.33582i | ||||
\(29\) | 8.98442i | 1.66836i | 0.551489 | + | 0.834182i | \(0.314060\pi\) | ||||
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(30\) | −1.18392 | − | 0.862822i | −0.216154 | − | 0.157529i | ||||
\(31\) | 5.65271 | 1.01526 | 0.507628 | − | 0.861576i | \(-0.330522\pi\) | ||||
0.507628 | + | 0.861576i | \(0.330522\pi\) | |||||||
\(32\) | −5.65670 | − | 0.0414082i | −0.999973 | − | 0.00732001i | ||||
\(33\) | 1.98292 | 0.345182 | ||||||||
\(34\) | 0.0403358 | + | 0.0293960i | 0.00691753 | + | 0.00504137i | ||||
\(35\) | − | 3.84584i | − | 0.650066i | ||||||
\(36\) | −0.612462 | − | 1.90391i | −0.102077 | − | 0.317319i | ||||
\(37\) | − | 1.63184i | − | 0.268272i | −0.990963 | − | 0.134136i | \(-0.957174\pi\) | ||
0.990963 | − | 0.134136i | \(-0.0428260\pi\) | |||||||
\(38\) | 0.698868 | − | 0.958954i | 0.113371 | − | 0.155563i | ||||
\(39\) | −4.05749 | −0.649718 | ||||||||
\(40\) | −2.78253 | − | 0.917631i | −0.439957 | − | 0.145090i | ||||
\(41\) | −1.65181 | −0.257969 | −0.128984 | − | 0.991647i | \(-0.541172\pi\) | ||||
−0.128984 | + | 0.991647i | \(0.541172\pi\) | |||||||
\(42\) | 3.09233 | − | 4.24315i | 0.477157 | − | 0.654732i | ||||
\(43\) | − | 2.17414i | − | 0.331554i | −0.986163 | − | 0.165777i | \(-0.946987\pi\) | ||
0.986163 | − | 0.165777i | \(-0.0530131\pi\) | |||||||
\(44\) | 3.77531 | − | 1.21446i | 0.569149 | − | 0.183087i | ||||
\(45\) | − | 1.03589i | − | 0.154421i | ||||||
\(46\) | 1.14290 | + | 0.832928i | 0.168512 | + | 0.122809i | ||||
\(47\) | 9.26034 | 1.35076 | 0.675380 | − | 0.737470i | \(-0.263980\pi\) | ||||
0.675380 | + | 0.737470i | \(0.263980\pi\) | |||||||
\(48\) | −2.33215 | − | 3.24978i | −0.336617 | − | 0.469065i | ||||
\(49\) | 6.78340 | 0.969058 | ||||||||
\(50\) | 4.48811 | + | 3.27085i | 0.634714 | + | 0.462568i | ||||
\(51\) | 0.0352924i | 0.00494192i | ||||||||
\(52\) | −7.72511 | + | 2.48506i | −1.07128 | + | 0.344615i | ||||
\(53\) | 9.53235i | 1.30937i | 0.755902 | + | 0.654684i | \(0.227198\pi\) | ||||
−0.755902 | + | 0.654684i | \(0.772802\pi\) | |||||||
\(54\) | 0.832928 | − | 1.14290i | 0.113347 | − | 0.155530i | ||||
\(55\) | 2.05409 | 0.276973 | ||||||||
\(56\) | 3.28876 | − | 9.97253i | 0.439479 | − | 1.33263i | ||||
\(57\) | 0.839050 | 0.111135 | ||||||||
\(58\) | −7.48337 | + | 10.2683i | −0.982615 | + | 1.34830i | ||||
\(59\) | − | 0.521307i | − | 0.0678684i | −0.999424 | − | 0.0339342i | \(-0.989196\pi\) | ||
0.999424 | − | 0.0339342i | \(-0.0108037\pi\) | |||||||
\(60\) | −0.634443 | − | 1.97225i | −0.0819062 | − | 0.254616i | ||||
\(61\) | − | 1.08170i | − | 0.138498i | −0.997599 | − | 0.0692488i | \(-0.977940\pi\) | ||
0.997599 | − | 0.0692488i | \(-0.0220602\pi\) | |||||||
\(62\) | 6.46050 | + | 4.70830i | 0.820485 | + | 0.597954i | ||||
\(63\) | 3.71260 | 0.467744 | ||||||||
\(64\) | −6.43058 | − | 4.75895i | −0.803823 | − | 0.594869i | ||||
\(65\) | −4.20311 | −0.521331 | ||||||||
\(66\) | 2.26629 | + | 1.65163i | 0.278961 | + | 0.203302i | ||||
\(67\) | − | 3.82606i | − | 0.467427i | −0.972305 | − | 0.233714i | \(-0.924912\pi\) | ||
0.972305 | − | 0.233714i | \(-0.0750878\pi\) | |||||||
\(68\) | 0.0216152 | + | 0.0671936i | 0.00262123 | + | 0.00814843i | ||||
\(69\) | 1.00000i | 0.120386i | ||||||||
\(70\) | 3.20331 | − | 4.39543i | 0.382869 | − | 0.525355i | ||||
\(71\) | −0.0570741 | −0.00677345 | −0.00338673 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338673 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(72\) | 0.885838 | − | 2.68613i | 0.104397 | − | 0.316563i | ||||
\(73\) | 2.11118 | 0.247095 | 0.123548 | − | 0.992339i | \(-0.460573\pi\) | ||||
0.123548 | + | 0.992339i | \(0.460573\pi\) | |||||||
\(74\) | 1.35920 | − | 1.86503i | 0.158004 | − | 0.216806i | ||||
\(75\) | 3.92693i | 0.453443i | ||||||||
\(76\) | 1.59748 | − | 0.513886i | 0.183243 | − | 0.0589468i | ||||
\(77\) | 7.36179i | 0.838954i | ||||||||
\(78\) | −4.63732 | − | 3.37959i | −0.525073 | − | 0.382664i | ||||
\(79\) | −10.6052 | −1.19318 | −0.596590 | − | 0.802546i | \(-0.703478\pi\) | ||||
−0.596590 | + | 0.802546i | \(0.703478\pi\) | |||||||
\(80\) | −2.41585 | − | 3.36641i | −0.270100 | − | 0.376377i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.88786 | − | 1.37584i | −0.208479 | − | 0.151936i | ||||
\(83\) | 12.9986i | 1.42678i | 0.700766 | + | 0.713391i | \(0.252842\pi\) | ||||
−0.700766 | + | 0.713391i | \(0.747158\pi\) | |||||||
\(84\) | 7.06847 | − | 2.27383i | 0.771234 | − | 0.248095i | ||||
\(85\) | 0.0365590i | 0.00396538i | ||||||||
\(86\) | 1.81090 | − | 2.48484i | 0.195275 | − | 0.267947i | ||||
\(87\) | −8.98442 | −0.963231 | ||||||||
\(88\) | 5.32638 | + | 1.75655i | 0.567794 | + | 0.187248i | ||||
\(89\) | −8.32127 | −0.882053 | −0.441026 | − | 0.897494i | \(-0.645385\pi\) | ||||
−0.441026 | + | 0.897494i | \(0.645385\pi\) | |||||||
\(90\) | 0.862822 | − | 1.18392i | 0.0909494 | − | 0.124796i | ||||
\(91\) | − | 15.0638i | − | 1.57912i | ||||||
\(92\) | 0.612462 | + | 1.90391i | 0.0638536 | + | 0.198497i | ||||
\(93\) | 5.65271i | 0.586158i | ||||||||
\(94\) | 10.5837 | + | 7.71320i | 1.09162 | + | 0.795556i | ||||
\(95\) | 0.869163 | 0.0891742 | ||||||||
\(96\) | 0.0414082 | − | 5.65670i | 0.00422621 | − | 0.577335i | ||||
\(97\) | 17.4131 | 1.76803 | 0.884016 | − | 0.467456i | \(-0.154829\pi\) | ||||
0.884016 | + | 0.467456i | \(0.154829\pi\) | |||||||
\(98\) | 7.75278 | + | 5.65009i | 0.783149 | + | 0.570745i | ||||
\(99\) | 1.98292i | 0.199291i | ||||||||
\(100\) | 2.40510 | + | 7.47654i | 0.240510 | + | 0.747654i | ||||
\(101\) | − | 3.74361i | − | 0.372503i | −0.982502 | − | 0.186252i | \(-0.940366\pi\) | ||
0.982502 | − | 0.186252i | \(-0.0596340\pi\) | |||||||
\(102\) | −0.0293960 | + | 0.0403358i | −0.00291064 | + | 0.00399384i | ||||
\(103\) | 13.8609 | 1.36575 | 0.682877 | − | 0.730533i | \(-0.260728\pi\) | ||||
0.682877 | + | 0.730533i | \(0.260728\pi\) | |||||||
\(104\) | −10.8989 | − | 3.59428i | −1.06873 | − | 0.352448i | ||||
\(105\) | 3.84584 | 0.375316 | ||||||||
\(106\) | −7.93976 | + | 10.8946i | −0.771178 | + | 1.05817i | ||||
\(107\) | 0.628866i | 0.0607947i | 0.999538 | + | 0.0303974i | \(0.00967727\pi\) | ||||
−0.999538 | + | 0.0303974i | \(0.990323\pi\) | |||||||
\(108\) | 1.90391 | − | 0.612462i | 0.183204 | − | 0.0589342i | ||||
\(109\) | − | 17.4967i | − | 1.67588i | −0.545763 | − | 0.837939i | \(-0.683760\pi\) | ||
0.545763 | − | 0.837939i | \(-0.316240\pi\) | |||||||
\(110\) | 2.34763 | + | 1.71091i | 0.223837 | + | 0.163129i | ||||
\(111\) | 1.63184 | 0.154887 | ||||||||
\(112\) | 12.0651 | − | 8.65834i | 1.14005 | − | 0.818136i | ||||
\(113\) | 18.6143 | 1.75108 | 0.875541 | − | 0.483144i | \(-0.160505\pi\) | ||||
0.875541 | + | 0.483144i | \(0.160505\pi\) | |||||||
\(114\) | 0.958954 | + | 0.698868i | 0.0898142 | + | 0.0654550i | ||||
\(115\) | 1.03589i | 0.0965972i | ||||||||
\(116\) | −17.1056 | + | 5.50261i | −1.58821 | + | 0.510905i | ||||
\(117\) | − | 4.05749i | − | 0.375115i | ||||||
\(118\) | 0.434211 | − | 0.595804i | 0.0399724 | − | 0.0548482i | ||||
\(119\) | −0.131026 | −0.0120112 | ||||||||
\(120\) | 0.917631 | − | 2.78253i | 0.0837678 | − | 0.254009i | ||||
\(121\) | 7.06803 | 0.642548 | ||||||||
\(122\) | 0.900979 | − | 1.23628i | 0.0815708 | − | 0.111928i | ||||
\(123\) | − | 1.65181i | − | 0.148938i | ||||||
\(124\) | 3.46207 | + | 10.7623i | 0.310903 | + | 0.966480i | ||||
\(125\) | 9.24732i | 0.827105i | ||||||||
\(126\) | 4.24315 | + | 3.09233i | 0.378010 | + | 0.275487i | ||||
\(127\) | −17.9648 | −1.59412 | −0.797060 | − | 0.603900i | \(-0.793613\pi\) | ||||
−0.797060 | + | 0.603900i | \(0.793613\pi\) | |||||||
\(128\) | −3.38568 | − | 10.7952i | −0.299254 | − | 0.954173i | ||||
\(129\) | 2.17414 | 0.191423 | ||||||||
\(130\) | −4.80375 | − | 3.50089i | −0.421317 | − | 0.307048i | ||||
\(131\) | − | 11.4395i | − | 0.999475i | −0.866177 | − | 0.499737i | \(-0.833430\pi\) | ||
0.866177 | − | 0.499737i | \(-0.166570\pi\) | |||||||
\(132\) | 1.21446 | + | 3.77531i | 0.105705 | + | 0.328599i | ||||
\(133\) | 3.11506i | 0.270110i | ||||||||
\(134\) | 3.18683 | − | 4.37282i | 0.275300 | − | 0.377754i | ||||
\(135\) | 1.03589 | 0.0891552 | ||||||||
\(136\) | −0.0312633 | + | 0.0947999i | −0.00268081 | + | 0.00812902i | ||||
\(137\) | −1.46165 | −0.124877 | −0.0624387 | − | 0.998049i | \(-0.519888\pi\) | ||||
−0.0624387 | + | 0.998049i | \(0.519888\pi\) | |||||||
\(138\) | −0.832928 | + | 1.14290i | −0.0709035 | + | 0.0972905i | ||||
\(139\) | − | 18.8020i | − | 1.59477i | −0.603473 | − | 0.797383i | \(-0.706217\pi\) | ||
0.603473 | − | 0.797383i | \(-0.293783\pi\) | |||||||
\(140\) | 7.32216 | − | 2.35543i | 0.618835 | − | 0.199070i | ||||
\(141\) | 9.26034i | 0.779862i | ||||||||
\(142\) | −0.0652303 | − | 0.0475386i | −0.00547400 | − | 0.00398935i | ||||
\(143\) | 8.04567 | 0.672813 | ||||||||
\(144\) | 3.24978 | − | 2.33215i | 0.270815 | − | 0.194346i | ||||
\(145\) | −9.30687 | −0.772893 | ||||||||
\(146\) | 2.41288 | + | 1.75846i | 0.199691 | + | 0.145531i | ||||
\(147\) | 6.78340i | 0.559486i | ||||||||
\(148\) | 3.10688 | − | 0.999438i | 0.255384 | − | 0.0821533i | ||||
\(149\) | 7.30712i | 0.598622i | 0.954156 | + | 0.299311i | \(0.0967568\pi\) | ||||
−0.954156 | + | 0.299311i | \(0.903243\pi\) | |||||||
\(150\) | −3.27085 | + | 4.48811i | −0.267064 | + | 0.366453i | ||||
\(151\) | 6.67219 | 0.542975 | 0.271488 | − | 0.962442i | \(-0.412484\pi\) | ||||
0.271488 | + | 0.962442i | \(0.412484\pi\) | |||||||
\(152\) | 2.25380 | + | 0.743262i | 0.182807 | + | 0.0602865i | ||||
\(153\) | −0.0352924 | −0.00285322 | ||||||||
\(154\) | −6.13184 | + | 8.41382i | −0.494118 | + | 0.678005i | ||||
\(155\) | 5.85558i | 0.470332i | ||||||||
\(156\) | −2.48506 | − | 7.72511i | −0.198964 | − | 0.618503i | ||||
\(157\) | 4.12484i | 0.329198i | 0.986361 | + | 0.164599i | \(0.0526330\pi\) | ||||
−0.986361 | + | 0.164599i | \(0.947367\pi\) | |||||||
\(158\) | −12.1208 | − | 8.83338i | −0.964275 | − | 0.702746i | ||||
\(159\) | −9.53235 | −0.755964 | ||||||||
\(160\) | 0.0428944 | − | 5.85972i | 0.00339110 | − | 0.463252i | ||||
\(161\) | −3.71260 | −0.292594 | ||||||||
\(162\) | 1.14290 | + | 0.832928i | 0.0897951 | + | 0.0654410i | ||||
\(163\) | − | 13.7415i | − | 1.07632i | −0.842842 | − | 0.538160i | \(-0.819119\pi\) | ||
0.842842 | − | 0.538160i | \(-0.180881\pi\) | |||||||
\(164\) | −1.01167 | − | 3.14490i | −0.0789980 | − | 0.245575i | ||||
\(165\) | 2.05409i | 0.159910i | ||||||||
\(166\) | −10.8269 | + | 14.8562i | −0.840331 | + | 1.15306i | ||||
\(167\) | 3.23975 | 0.250699 | 0.125350 | − | 0.992113i | \(-0.459995\pi\) | ||||
0.125350 | + | 0.992113i | \(0.459995\pi\) | |||||||
\(168\) | 9.97253 | + | 3.28876i | 0.769397 | + | 0.253734i | ||||
\(169\) | −3.46319 | −0.266399 | ||||||||
\(170\) | −0.0304510 | + | 0.0417834i | −0.00233549 | + | 0.00320464i | ||||
\(171\) | 0.839050i | 0.0641637i | ||||||||
\(172\) | 4.13938 | − | 1.33158i | 0.315625 | − | 0.101532i | ||||
\(173\) | 18.1261i | 1.37810i | 0.724713 | + | 0.689051i | \(0.241972\pi\) | ||||
−0.724713 | + | 0.689051i | \(0.758028\pi\) | |||||||
\(174\) | −10.2683 | − | 7.48337i | −0.778440 | − | 0.567313i | ||||
\(175\) | −14.5791 | −1.10208 | ||||||||
\(176\) | 4.62447 | + | 6.44406i | 0.348582 | + | 0.485739i | ||||
\(177\) | 0.521307 | 0.0391838 | ||||||||
\(178\) | −9.51041 | − | 6.93102i | −0.712836 | − | 0.519502i | ||||
\(179\) | 6.25406i | 0.467450i | 0.972303 | + | 0.233725i | \(0.0750916\pi\) | ||||
−0.972303 | + | 0.233725i | \(0.924908\pi\) | |||||||
\(180\) | 1.97225 | − | 0.634443i | 0.147002 | − | 0.0472886i | ||||
\(181\) | − | 12.6374i | − | 0.939330i | −0.882845 | − | 0.469665i | \(-0.844375\pi\) | ||
0.882845 | − | 0.469665i | \(-0.155625\pi\) | |||||||
\(182\) | 12.5471 | − | 17.2165i | 0.930051 | − | 1.27617i | ||||
\(183\) | 1.08170 | 0.0799616 | ||||||||
\(184\) | −0.885838 | + | 2.68613i | −0.0653049 | + | 0.198024i | ||||
\(185\) | 1.69040 | 0.124281 | ||||||||
\(186\) | −4.70830 | + | 6.46050i | −0.345229 | + | 0.473707i | ||||
\(187\) | − | 0.0699819i | − | 0.00511759i | ||||||
\(188\) | 5.67161 | + | 17.6309i | 0.413645 | + | 1.28587i | ||||
\(189\) | 3.71260i | 0.270052i | ||||||||
\(190\) | 0.993370 | + | 0.723950i | 0.0720666 | + | 0.0525209i | ||||
\(191\) | −17.8806 | −1.29380 | −0.646898 | − | 0.762576i | \(-0.723934\pi\) | ||||
−0.646898 | + | 0.762576i | \(0.723934\pi\) | |||||||
\(192\) | 4.75895 | − | 6.43058i | 0.343448 | − | 0.464087i | ||||
\(193\) | −2.56140 | −0.184374 | −0.0921870 | − | 0.995742i | \(-0.529386\pi\) | ||||
−0.0921870 | + | 0.995742i | \(0.529386\pi\) | |||||||
\(194\) | 19.9015 | + | 14.5039i | 1.42885 | + | 1.04132i | ||||
\(195\) | − | 4.20311i | − | 0.300991i | ||||||
\(196\) | 4.15458 | + | 12.9150i | 0.296755 | + | 0.922501i | ||||
\(197\) | − | 8.36352i | − | 0.595876i | −0.954585 | − | 0.297938i | \(-0.903701\pi\) | ||
0.954585 | − | 0.297938i | \(-0.0962989\pi\) | |||||||
\(198\) | −1.65163 | + | 2.26629i | −0.117376 | + | 0.161058i | ||||
\(199\) | −4.24697 | −0.301059 | −0.150530 | − | 0.988605i | \(-0.548098\pi\) | ||||
−0.150530 | + | 0.988605i | \(0.548098\pi\) | |||||||
\(200\) | −3.47863 | + | 10.5482i | −0.245976 | + | 0.745874i | ||||
\(201\) | 3.82606 | 0.269869 | ||||||||
\(202\) | 3.11816 | − | 4.27859i | 0.219393 | − | 0.301041i | ||||
\(203\) | − | 33.3556i | − | 2.34110i | ||||||
\(204\) | −0.0671936 | + | 0.0216152i | −0.00470450 | + | 0.00151337i | ||||
\(205\) | − | 1.71109i | − | 0.119508i | ||||||
\(206\) | 15.8417 | + | 11.5451i | 1.10374 | + | 0.804387i | ||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −9.46267 | − | 13.1859i | −0.656118 | − | 0.914280i | ||||
\(209\) | −1.66377 | −0.115085 | ||||||||
\(210\) | 4.39543 | + | 3.20331i | 0.303314 | + | 0.221050i | ||||
\(211\) | 23.2483i | 1.60048i | 0.599680 | + | 0.800240i | \(0.295295\pi\) | ||||
−0.599680 | + | 0.800240i | \(0.704705\pi\) | |||||||
\(212\) | −18.1488 | + | 5.83820i | −1.24646 | + | 0.400969i | ||||
\(213\) | − | 0.0570741i | − | 0.00391065i | ||||||
\(214\) | −0.523800 | + | 0.718733i | −0.0358062 | + | 0.0491316i | ||||
\(215\) | 2.25217 | 0.153597 | ||||||||
\(216\) | 2.68613 | + | 0.885838i | 0.182768 | + | 0.0602737i | ||||
\(217\) | −20.9862 | −1.42464 | ||||||||
\(218\) | 14.5735 | − | 19.9970i | 0.987041 | − | 1.35437i | ||||
\(219\) | 2.11118i | 0.142660i | ||||||||
\(220\) | 1.25805 | + | 3.91081i | 0.0848177 | + | 0.263666i | ||||
\(221\) | 0.143198i | 0.00963256i | ||||||||
\(222\) | 1.86503 | + | 1.35920i | 0.125173 | + | 0.0912237i | ||||
\(223\) | −27.1897 | −1.82075 | −0.910377 | − | 0.413779i | \(-0.864209\pi\) | ||||
−0.910377 | + | 0.413779i | \(0.864209\pi\) | |||||||
\(224\) | 21.0011 | + | 0.153732i | 1.40319 | + | 0.0102717i | ||||
\(225\) | −3.92693 | −0.261795 | ||||||||
\(226\) | 21.2743 | + | 15.5043i | 1.41515 | + | 1.03133i | ||||
\(227\) | 8.83046i | 0.586098i | 0.956097 | + | 0.293049i | \(0.0946700\pi\) | ||||
−0.956097 | + | 0.293049i | \(0.905330\pi\) | |||||||
\(228\) | 0.513886 | + | 1.59748i | 0.0340329 | + | 0.105796i | ||||
\(229\) | − | 25.0163i | − | 1.65313i | −0.562844 | − | 0.826563i | \(-0.690293\pi\) | ||
0.562844 | − | 0.826563i | \(-0.309707\pi\) | |||||||
\(230\) | −0.862822 | + | 1.18392i | −0.0568928 | + | 0.0780656i | ||||
\(231\) | −7.36179 | −0.484370 | ||||||||
\(232\) | −24.1333 | − | 7.95874i | −1.58443 | − | 0.522517i | ||||
\(233\) | 22.2640 | 1.45856 | 0.729282 | − | 0.684213i | \(-0.239854\pi\) | ||||
0.729282 | + | 0.684213i | \(0.239854\pi\) | |||||||
\(234\) | 3.37959 | − | 4.63732i | 0.220931 | − | 0.303151i | ||||
\(235\) | 9.59270i | 0.625758i | ||||||||
\(236\) | 0.992524 | − | 0.319281i | 0.0646078 | − | 0.0207834i | ||||
\(237\) | − | 10.6052i | − | 0.688883i | ||||||
\(238\) | −0.149751 | − | 0.109136i | −0.00970690 | − | 0.00707421i | ||||
\(239\) | −4.66752 | −0.301917 | −0.150958 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150958 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(240\) | 3.36641 | − | 2.41585i | 0.217301 | − | 0.155942i | ||||
\(241\) | 17.6837 | 1.13911 | 0.569555 | − | 0.821953i | \(-0.307116\pi\) | ||||
0.569555 | + | 0.821953i | \(0.307116\pi\) | |||||||
\(242\) | 8.07808 | + | 5.88716i | 0.519279 | + | 0.378441i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 2.05947 | − | 0.662500i | 0.131844 | − | 0.0424122i | ||||
\(245\) | 7.02686i | 0.448930i | ||||||||
\(246\) | 1.37584 | − | 1.88786i | 0.0877200 | − | 0.120365i | ||||
\(247\) | 3.40443 | 0.216619 | ||||||||
\(248\) | −5.00738 | + | 15.1839i | −0.317969 | + | 0.964179i | ||||
\(249\) | −12.9986 | −0.823753 | ||||||||
\(250\) | −7.70235 | + | 10.5688i | −0.487139 | + | 0.668430i | ||||
\(251\) | − | 4.11640i | − | 0.259825i | −0.991525 | − | 0.129912i | \(-0.958530\pi\) | ||
0.991525 | − | 0.129912i | \(-0.0414696\pi\) | |||||||
\(252\) | 2.27383 | + | 7.06847i | 0.143238 | + | 0.445272i | ||||
\(253\) | − | 1.98292i | − | 0.124665i | ||||||
\(254\) | −20.5321 | − | 14.9634i | −1.28830 | − | 0.938888i | ||||
\(255\) | −0.0365590 | −0.00228941 | ||||||||
\(256\) | 5.12215 | − | 15.1580i | 0.320134 | − | 0.947372i | ||||
\(257\) | −19.7060 | −1.22923 | −0.614614 | − | 0.788828i | \(-0.710688\pi\) | ||||
−0.614614 | + | 0.788828i | \(0.710688\pi\) | |||||||
\(258\) | 2.48484 | + | 1.81090i | 0.154699 | + | 0.112742i | ||||
\(259\) | 6.05836i | 0.376448i | ||||||||
\(260\) | −2.57424 | − | 8.00236i | −0.159648 | − | 0.496285i | ||||
\(261\) | − | 8.98442i | − | 0.556122i | ||||||
\(262\) | 9.52829 | − | 13.0743i | 0.588660 | − | 0.807731i | ||||
\(263\) | −12.1168 | −0.747155 | −0.373577 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373577 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(264\) | −1.75655 | + | 5.32638i | −0.108108 | + | 0.327816i | ||||
\(265\) | −9.87446 | −0.606583 | ||||||||
\(266\) | −2.59462 | + | 3.56021i | −0.159086 | + | 0.218291i | ||||
\(267\) | − | 8.32127i | − | 0.509253i | ||||||
\(268\) | 7.28449 | − | 2.34331i | 0.444971 | − | 0.143141i | ||||
\(269\) | − | 16.2608i | − | 0.991441i | −0.868482 | − | 0.495720i | \(-0.834904\pi\) | ||
0.868482 | − | 0.495720i | \(-0.165096\pi\) | |||||||
\(270\) | 1.18392 | + | 0.862822i | 0.0720513 | + | 0.0525096i | ||||
\(271\) | 15.3045 | 0.929685 | 0.464843 | − | 0.885393i | \(-0.346111\pi\) | ||||
0.464843 | + | 0.885393i | \(0.346111\pi\) | |||||||
\(272\) | −0.114692 | + | 0.0823071i | −0.00695425 | + | 0.00499060i | ||||
\(273\) | 15.0638 | 0.911704 | ||||||||
\(274\) | −1.67053 | − | 1.21745i | −0.100920 | − | 0.0735489i | ||||
\(275\) | − | 7.78679i | − | 0.469561i | ||||||
\(276\) | −1.90391 | + | 0.612462i | −0.114602 | + | 0.0368659i | ||||
\(277\) | 11.1209i | 0.668188i | 0.942540 | + | 0.334094i | \(0.108430\pi\) | ||||
−0.942540 | + | 0.334094i | \(0.891570\pi\) | |||||||
\(278\) | 15.6607 | − | 21.4889i | 0.939268 | − | 1.28882i | ||||
\(279\) | −5.65271 | −0.338419 | ||||||||
\(280\) | 10.3304 | + | 3.40680i | 0.617362 | + | 0.203595i | ||||
\(281\) | −31.5006 | −1.87917 | −0.939584 | − | 0.342317i | \(-0.888788\pi\) | ||||
−0.939584 | + | 0.342317i | \(0.888788\pi\) | |||||||
\(282\) | −7.71320 | + | 10.5837i | −0.459314 | + | 0.630250i | ||||
\(283\) | − | 19.1846i | − | 1.14041i | −0.821504 | − | 0.570203i | \(-0.806865\pi\) | ||
0.821504 | − | 0.570203i | \(-0.193135\pi\) | |||||||
\(284\) | −0.0349557 | − | 0.108664i | −0.00207424 | − | 0.00644804i | ||||
\(285\) | 0.869163i | 0.0514848i | ||||||||
\(286\) | 9.19543 | + | 6.70146i | 0.543737 | + | 0.396266i | ||||
\(287\) | 6.13249 | 0.361990 | ||||||||
\(288\) | 5.65670 | + | 0.0414082i | 0.333324 | + | 0.00244000i | ||||
\(289\) | −16.9988 | −0.999927 | ||||||||
\(290\) | −10.6369 | − | 7.75195i | −0.624618 | − | 0.455210i | ||||
\(291\) | 17.4131i | 1.02077i | ||||||||
\(292\) | 1.29302 | + | 4.01951i | 0.0756682 | + | 0.235224i | ||||
\(293\) | − | 29.1881i | − | 1.70519i | −0.522574 | − | 0.852594i | \(-0.675028\pi\) | ||
0.522574 | − | 0.852594i | \(-0.324972\pi\) | |||||||
\(294\) | −5.65009 | + | 7.75278i | −0.329520 | + | 0.452152i | ||||
\(295\) | 0.540017 | 0.0314410 | ||||||||
\(296\) | 4.38333 | + | 1.44554i | 0.254776 | + | 0.0840205i | ||||
\(297\) | −1.98292 | −0.115061 | ||||||||
\(298\) | −6.08630 | + | 8.35134i | −0.352570 | + | 0.483780i | ||||
\(299\) | 4.05749i | 0.234650i | ||||||||
\(300\) | −7.47654 | + | 2.40510i | −0.431658 | + | 0.138858i | ||||
\(301\) | 8.07172i | 0.465246i | ||||||||
\(302\) | 7.62568 | + | 5.55745i | 0.438808 | + | 0.319796i | ||||
\(303\) | 3.74361 | 0.215065 | ||||||||
\(304\) | 1.95679 | + | 2.72673i | 0.112230 | + | 0.156389i | ||||
\(305\) | 1.12052 | 0.0641609 | ||||||||
\(306\) | −0.0403358 | − | 0.0293960i | −0.00230584 | − | 0.00168046i | ||||
\(307\) | 15.3866i | 0.878160i | 0.898448 | + | 0.439080i | \(0.144696\pi\) | ||||
−0.898448 | + | 0.439080i | \(0.855304\pi\) | |||||||
\(308\) | −14.0162 | + | 4.50882i | −0.798648 | + | 0.256914i | ||||
\(309\) | 13.8609i | 0.788519i | ||||||||
\(310\) | −4.87728 | + | 6.69237i | −0.277011 | + | 0.380101i | ||||
\(311\) | −22.4890 | −1.27523 | −0.637616 | − | 0.770354i | \(-0.720079\pi\) | ||||
−0.637616 | + | 0.770354i | \(0.720079\pi\) | |||||||
\(312\) | 3.59428 | − | 10.8989i | 0.203486 | − | 0.617030i | ||||
\(313\) | 24.1804 | 1.36676 | 0.683379 | − | 0.730064i | \(-0.260510\pi\) | ||||
0.683379 | + | 0.730064i | \(0.260510\pi\) | |||||||
\(314\) | −3.43570 | + | 4.71430i | −0.193888 | + | 0.266043i | ||||
\(315\) | 3.84584i | 0.216689i | ||||||||
\(316\) | −6.49529 | − | 20.1914i | −0.365389 | − | 1.13586i | ||||
\(317\) | 8.16834i | 0.458780i | 0.973335 | + | 0.229390i | \(0.0736731\pi\) | ||||
−0.973335 | + | 0.229390i | \(0.926327\pi\) | |||||||
\(318\) | −10.8946 | − | 7.93976i | −0.610937 | − | 0.445240i | ||||
\(319\) | 17.8154 | 0.997470 | ||||||||
\(320\) | 4.92975 | − | 6.66137i | 0.275581 | − | 0.372382i | ||||
\(321\) | −0.628866 | −0.0350998 | ||||||||
\(322\) | −4.24315 | − | 3.09233i | −0.236461 | − | 0.172329i | ||||
\(323\) | − | 0.0296120i | − | 0.00164766i | ||||||
\(324\) | 0.612462 | + | 1.90391i | 0.0340257 | + | 0.105773i | ||||
\(325\) | 15.9335i | 0.883830i | ||||||||
\(326\) | 11.4457 | − | 15.7053i | 0.633920 | − | 0.869835i | ||||
\(327\) | 17.4967 | 0.967569 | ||||||||
\(328\) | 1.46323 | − | 4.43696i | 0.0807935 | − | 0.244990i | ||||
\(329\) | −34.3800 | −1.89543 | ||||||||
\(330\) | −1.71091 | + | 2.34763i | −0.0941823 | + | 0.129233i | ||||
\(331\) | 26.7727i | 1.47156i | 0.677220 | + | 0.735781i | \(0.263185\pi\) | ||||
−0.677220 | + | 0.735781i | \(0.736815\pi\) | |||||||
\(332\) | −24.7482 | + | 7.96115i | −1.35824 | + | 0.436925i | ||||
\(333\) | 1.63184i | 0.0894241i | ||||||||
\(334\) | 3.70272 | + | 2.69848i | 0.202604 | + | 0.147654i | ||||
\(335\) | 3.96337 | 0.216542 | ||||||||
\(336\) | 8.65834 | + | 12.0651i | 0.472351 | + | 0.658207i | ||||
\(337\) | −33.0578 | −1.80077 | −0.900386 | − | 0.435092i | \(-0.856716\pi\) | ||||
−0.900386 | + | 0.435092i | \(0.856716\pi\) | |||||||
\(338\) | −3.95809 | − | 2.88459i | −0.215292 | − | 0.156901i | ||||
\(339\) | 18.6143i | 1.01099i | ||||||||
\(340\) | −0.0696052 | + | 0.0223910i | −0.00377487 | + | 0.00121432i | ||||
\(341\) | − | 11.2089i | − | 0.606994i | ||||||
\(342\) | −0.698868 | + | 0.958954i | −0.0377904 | + | 0.0518543i | ||||
\(343\) | 0.804135 | 0.0434192 | ||||||||
\(344\) | 5.84003 | + | 1.92594i | 0.314873 | + | 0.103840i | ||||
\(345\) | −1.03589 | −0.0557704 | ||||||||
\(346\) | −15.0977 | + | 20.7164i | −0.811659 | + | 1.11372i | ||||
\(347\) | 21.8355i | 1.17219i | 0.810242 | + | 0.586095i | \(0.199336\pi\) | ||||
−0.810242 | + | 0.586095i | \(0.800664\pi\) | |||||||
\(348\) | −5.50261 | − | 17.1056i | −0.294971 | − | 0.916954i | ||||
\(349\) | − | 26.5464i | − | 1.42099i | −0.703700 | − | 0.710497i | \(-0.748470\pi\) | ||
0.703700 | − | 0.710497i | \(-0.251530\pi\) | |||||||
\(350\) | −16.6626 | − | 12.1434i | −0.890651 | − | 0.649090i | ||||
\(351\) | 4.05749 | 0.216573 | ||||||||
\(352\) | −0.0821092 | + | 11.2168i | −0.00437644 | + | 0.597857i | ||||
\(353\) | −1.79765 | −0.0956794 | −0.0478397 | − | 0.998855i | \(-0.515234\pi\) | ||||
−0.0478397 | + | 0.998855i | \(0.515234\pi\) | |||||||
\(354\) | 0.595804 | + | 0.434211i | 0.0316666 | + | 0.0230781i | ||||
\(355\) | − | 0.0591225i | − | 0.00313790i | ||||||
\(356\) | −5.09646 | − | 15.8430i | −0.270112 | − | 0.839676i | ||||
\(357\) | − | 0.131026i | − | 0.00693466i | ||||||
\(358\) | −5.20918 | + | 7.14780i | −0.275314 | + | 0.377773i | ||||
\(359\) | 29.4648 | 1.55509 | 0.777547 | − | 0.628824i | \(-0.216464\pi\) | ||||
0.777547 | + | 0.628824i | \(0.216464\pi\) | |||||||
\(360\) | 2.78253 | + | 0.917631i | 0.146652 | + | 0.0483634i | ||||
\(361\) | 18.2960 | 0.962947 | ||||||||
\(362\) | 10.5260 | − | 14.4433i | 0.553236 | − | 0.759125i | ||||
\(363\) | 7.06803i | 0.370975i | ||||||||
\(364\) | 28.6802 | − | 9.22602i | 1.50325 | − | 0.483575i | ||||
\(365\) | 2.18695i | 0.114470i | ||||||||
\(366\) | 1.23628 | + | 0.900979i | 0.0646214 | + | 0.0470949i | ||||
\(367\) | −4.47265 | −0.233470 | −0.116735 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116735 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(368\) | −3.24978 | + | 2.33215i | −0.169407 | + | 0.121572i | ||||
\(369\) | 1.65181 | 0.0859896 | ||||||||
\(370\) | 1.93197 | + | 1.40798i | 0.100438 | + | 0.0731976i | ||||
\(371\) | − | 35.3898i | − | 1.83735i | ||||||
\(372\) | −10.7623 | + | 3.46207i | −0.557998 | + | 0.179500i | ||||
\(373\) | 9.38766i | 0.486075i | 0.970017 | + | 0.243037i | \(0.0781438\pi\) | ||||
−0.970017 | + | 0.243037i | \(0.921856\pi\) | |||||||
\(374\) | 0.0582899 | − | 0.0799827i | 0.00301410 | − | 0.00413581i | ||||
\(375\) | −9.24732 | −0.477529 | ||||||||
\(376\) | −8.20317 | + | 24.8745i | −0.423046 | + | 1.28280i | ||||
\(377\) | −36.4541 | −1.87748 | ||||||||
\(378\) | −3.09233 | + | 4.24315i | −0.159052 | + | 0.218244i | ||||
\(379\) | − | 9.91274i | − | 0.509183i | −0.967049 | − | 0.254592i | \(-0.918059\pi\) | ||
0.967049 | − | 0.254592i | \(-0.0819410\pi\) | |||||||
\(380\) | 0.532329 | + | 1.65481i | 0.0273079 | + | 0.0848900i | ||||
\(381\) | − | 17.9648i | − | 0.920366i | ||||||
\(382\) | −20.4358 | − | 14.8933i | −1.04559 | − | 0.762006i | ||||
\(383\) | 34.2745 | 1.75134 | 0.875672 | − | 0.482907i | \(-0.160419\pi\) | ||||
0.875672 | + | 0.482907i | \(0.160419\pi\) | |||||||
\(384\) | 10.7952 | − | 3.38568i | 0.550892 | − | 0.172775i | ||||
\(385\) | −7.62600 | −0.388657 | ||||||||
\(386\) | −2.92744 | − | 2.13347i | −0.149003 | − | 0.108591i | ||||
\(387\) | 2.17414i | 0.110518i | ||||||||
\(388\) | 10.6649 | + | 33.1531i | 0.541426 | + | 1.68309i | ||||
\(389\) | 17.0908i | 0.866539i | 0.901264 | + | 0.433269i | \(0.142640\pi\) | ||||
−0.901264 | + | 0.433269i | \(0.857360\pi\) | |||||||
\(390\) | 3.50089 | − | 4.80375i | 0.177274 | − | 0.243247i | ||||
\(391\) | 0.0352924 | 0.00178481 | ||||||||
\(392\) | −6.00900 | + | 18.2211i | −0.303500 | + | 0.920305i | ||||
\(393\) | 11.4395 | 0.577047 | ||||||||
\(394\) | 6.96621 | − | 9.55871i | 0.350953 | − | 0.481561i | ||||
\(395\) | − | 10.9858i | − | 0.552757i | ||||||
\(396\) | −3.77531 | + | 1.21446i | −0.189716 | + | 0.0610291i | ||||
\(397\) | − | 14.1217i | − | 0.708750i | −0.935103 | − | 0.354375i | \(-0.884694\pi\) | ||
0.935103 | − | 0.354375i | \(-0.115306\pi\) | |||||||
\(398\) | −4.85388 | − | 3.53742i | −0.243303 | − | 0.177315i | ||||
\(399\) | −3.11506 | −0.155948 | ||||||||
\(400\) | −12.7617 | + | 9.15820i | −0.638083 | + | 0.457910i | ||||
\(401\) | −20.8984 | −1.04362 | −0.521808 | − | 0.853063i | \(-0.674742\pi\) | ||||
−0.521808 | + | 0.853063i | \(0.674742\pi\) | |||||||
\(402\) | 4.37282 | + | 3.18683i | 0.218096 | + | 0.158945i | ||||
\(403\) | 22.9358i | 1.14251i | ||||||||
\(404\) | 7.12752 | − | 2.29282i | 0.354607 | − | 0.114072i | ||||
\(405\) | 1.03589i | 0.0514738i | ||||||||
\(406\) | 27.7828 | − | 38.1222i | 1.37884 | − | 1.89197i | ||||
\(407\) | −3.23580 | −0.160393 | ||||||||
\(408\) | −0.0947999 | − | 0.0312633i | −0.00469329 | − | 0.00154777i | ||||
\(409\) | 20.5558 | 1.01642 | 0.508209 | − | 0.861234i | \(-0.330308\pi\) | ||||
0.508209 | + | 0.861234i | \(0.330308\pi\) | |||||||
\(410\) | 1.42521 | − | 1.95561i | 0.0703863 | − | 0.0965807i | ||||
\(411\) | − | 1.46165i | − | 0.0720980i | ||||||
\(412\) | 8.48927 | + | 26.3900i | 0.418236 | + | 1.30014i | ||||
\(413\) | 1.93541i | 0.0952351i | ||||||||
\(414\) | −1.14290 | − | 0.832928i | −0.0561707 | − | 0.0409362i | ||||
\(415\) | −13.4651 | −0.660977 | ||||||||
\(416\) | 0.168013 | − | 22.9520i | 0.00823753 | − | 1.12531i | ||||
\(417\) | 18.8020 | 0.920739 | ||||||||
\(418\) | −1.90153 | − | 1.38580i | −0.0930068 | − | 0.0677817i | ||||
\(419\) | − | 16.3140i | − | 0.796990i | −0.917171 | − | 0.398495i | \(-0.869533\pi\) | ||
0.917171 | − | 0.398495i | \(-0.130467\pi\) | |||||||
\(420\) | 2.35543 | + | 7.32216i | 0.114933 | + | 0.357285i | ||||
\(421\) | 19.9773i | 0.973636i | 0.873503 | + | 0.486818i | \(0.161843\pi\) | ||||
−0.873503 | + | 0.486818i | \(0.838157\pi\) | |||||||
\(422\) | −19.3642 | + | 26.5706i | −0.942633 | + | 1.29344i | ||||
\(423\) | −9.26034 | −0.450253 | ||||||||
\(424\) | −25.6051 | − | 8.44412i | −1.24349 | − | 0.410083i | ||||
\(425\) | 0.138591 | 0.00672264 | ||||||||
\(426\) | 0.0475386 | − | 0.0652303i | 0.00230325 | − | 0.00316042i | ||||
\(427\) | 4.01592i | 0.194344i | ||||||||
\(428\) | −1.19731 | + | 0.385156i | −0.0578740 | + | 0.0186172i | ||||
\(429\) | 8.04567i | 0.388449i | ||||||||
\(430\) | 2.57402 | + | 1.87590i | 0.124130 | + | 0.0904638i | ||||
\(431\) | 6.28068 | 0.302530 | 0.151265 | − | 0.988493i | \(-0.451665\pi\) | ||||
0.151265 | + | 0.988493i | \(0.451665\pi\) | |||||||
\(432\) | 2.33215 | + | 3.24978i | 0.112206 | + | 0.156355i | ||||
\(433\) | 16.6871 | 0.801929 | 0.400964 | − | 0.916094i | \(-0.368675\pi\) | ||||
0.400964 | + | 0.916094i | \(0.368675\pi\) | |||||||
\(434\) | −23.9853 | − | 17.4800i | −1.15133 | − | 0.839068i | ||||
\(435\) | − | 9.30687i | − | 0.446230i | ||||||
\(436\) | 33.3122 | − | 10.7161i | 1.59536 | − | 0.513206i | ||||
\(437\) | − | 0.839050i | − | 0.0401372i | ||||||
\(438\) | −1.75846 | + | 2.41288i | −0.0840226 | + | 0.115292i | ||||
\(439\) | 10.5597 | 0.503985 | 0.251993 | − | 0.967729i | \(-0.418914\pi\) | ||||
0.251993 | + | 0.967729i | \(0.418914\pi\) | |||||||
\(440\) | −1.81959 | + | 5.51754i | −0.0867455 | + | 0.263039i | ||||
\(441\) | −6.78340 | −0.323019 | ||||||||
\(442\) | −0.119274 | + | 0.163662i | −0.00567328 | + | 0.00778461i | ||||
\(443\) | 2.31761i | 0.110113i | 0.998483 | + | 0.0550564i | \(0.0175339\pi\) | ||||
−0.998483 | + | 0.0550564i | \(0.982466\pi\) | |||||||
\(444\) | 0.999438 | + | 3.10688i | 0.0474312 | + | 0.147446i | ||||
\(445\) | − | 8.61992i | − | 0.408623i | ||||||
\(446\) | −31.0752 | − | 22.6470i | −1.47145 | − | 1.07237i | ||||
\(447\) | −7.30712 | −0.345615 | ||||||||
\(448\) | 23.8742 | + | 17.6681i | 1.12795 | + | 0.834739i | ||||
\(449\) | −8.86194 | −0.418221 | −0.209111 | − | 0.977892i | \(-0.567057\pi\) | ||||
−0.209111 | + | 0.977892i | \(0.567057\pi\) | |||||||
\(450\) | −4.48811 | − | 3.27085i | −0.211571 | − | 0.154189i | ||||
\(451\) | 3.27540i | 0.154232i | ||||||||
\(452\) | 11.4005 | + | 35.4399i | 0.536235 | + | 1.66695i | ||||
\(453\) | 6.67219i | 0.313487i | ||||||||
\(454\) | −7.35514 | + | 10.0924i | −0.345194 | + | 0.473659i | ||||
\(455\) | 15.6045 | 0.731548 | ||||||||
\(456\) | −0.743262 | + | 2.25380i | −0.0348064 | + | 0.105544i | ||||
\(457\) | −11.1767 | −0.522823 | −0.261411 | − | 0.965228i | \(-0.584188\pi\) | ||||
−0.261411 | + | 0.965228i | \(0.584188\pi\) | |||||||
\(458\) | 20.8368 | − | 28.5913i | 0.973640 | − | 1.33598i | ||||
\(459\) | − | 0.0352924i | − | 0.00164731i | ||||||
\(460\) | −1.97225 | + | 0.634443i | −0.0919564 | + | 0.0295811i | ||||
\(461\) | 14.5453i | 0.677443i | 0.940887 | + | 0.338722i | \(0.109995\pi\) | ||||
−0.940887 | + | 0.338722i | \(0.890005\pi\) | |||||||
\(462\) | −8.41382 | − | 6.13184i | −0.391447 | − | 0.285279i | ||||
\(463\) | 13.3702 | 0.621366 | 0.310683 | − | 0.950514i | \(-0.399442\pi\) | ||||
0.310683 | + | 0.950514i | \(0.399442\pi\) | |||||||
\(464\) | −20.9530 | − | 29.1974i | −0.972719 | − | 1.35545i | ||||
\(465\) | −5.85558 | −0.271546 | ||||||||
\(466\) | 25.4457 | + | 18.5443i | 1.17875 | + | 0.859049i | ||||
\(467\) | 21.0042i | 0.971960i | 0.873970 | + | 0.485980i | \(0.161537\pi\) | ||||
−0.873970 | + | 0.485980i | \(0.838463\pi\) | |||||||
\(468\) | 7.72511 | − | 2.48506i | 0.357093 | − | 0.114872i | ||||
\(469\) | 14.2046i | 0.655909i | ||||||||
\(470\) | −7.99002 | + | 10.9635i | −0.368552 | + | 0.505710i | ||||
\(471\) | −4.12484 | −0.190063 | ||||||||
\(472\) | 1.40030 | + | 0.461794i | 0.0644540 | + | 0.0212558i | ||||
\(473\) | −4.31115 | −0.198227 | ||||||||
\(474\) | 8.83338 | − | 12.1208i | 0.405731 | − | 0.556725i | ||||
\(475\) | − | 3.29489i | − | 0.151180i | ||||||
\(476\) | −0.0802487 | − | 0.249463i | −0.00367819 | − | 0.0114341i | ||||
\(477\) | − | 9.53235i | − | 0.436456i | ||||||
\(478\) | −5.33453 | − | 3.88770i | −0.243996 | − | 0.177819i | ||||
\(479\) | 6.39527 | 0.292207 | 0.146104 | − | 0.989269i | \(-0.453327\pi\) | ||||
0.146104 | + | 0.989269i | \(0.453327\pi\) | |||||||
\(480\) | 5.85972 | + | 0.0428944i | 0.267458 | + | 0.00195785i | ||||
\(481\) | 6.62116 | 0.301899 | ||||||||
\(482\) | 20.2108 | + | 14.7293i | 0.920578 | + | 0.670900i | ||||
\(483\) | − | 3.71260i | − | 0.168929i | ||||||
\(484\) | 4.32890 | + | 13.4569i | 0.196768 | + | 0.611678i | ||||
\(485\) | 18.0381i | 0.819066i | ||||||||
\(486\) | −0.832928 | + | 1.14290i | −0.0377824 | + | 0.0518432i | ||||
\(487\) | 25.2354 | 1.14352 | 0.571762 | − | 0.820420i | \(-0.306260\pi\) | ||||
0.571762 | + | 0.820420i | \(0.306260\pi\) | |||||||
\(488\) | 2.90559 | + | 0.958212i | 0.131530 | + | 0.0433762i | ||||
\(489\) | 13.7415 | 0.621414 | ||||||||
\(490\) | −5.85287 | + | 8.03103i | −0.264406 | + | 0.362805i | ||||
\(491\) | − | 38.6086i | − | 1.74238i | −0.490945 | − | 0.871191i | \(-0.663348\pi\) | ||
0.490945 | − | 0.871191i | \(-0.336652\pi\) | |||||||
\(492\) | 3.14490 | − | 1.01167i | 0.141783 | − | 0.0456095i | ||||
\(493\) | 0.317081i | 0.0142806i | ||||||||
\(494\) | 3.89094 | + | 2.83565i | 0.175062 | + | 0.127582i | ||||
\(495\) | −2.05409 | −0.0923243 | ||||||||
\(496\) | −18.3701 | + | 13.1830i | −0.824840 | + | 0.591932i | ||||
\(497\) | 0.211893 | 0.00950472 | ||||||||
\(498\) | −14.8562 | − | 10.8269i | −0.665721 | − | 0.485165i | ||||
\(499\) | 42.0927i | 1.88433i | 0.335153 | + | 0.942164i | \(0.391212\pi\) | ||||
−0.335153 | + | 0.942164i | \(0.608788\pi\) | |||||||
\(500\) | −17.6061 | + | 5.66363i | −0.787369 | + | 0.253285i | ||||
\(501\) | 3.23975i | 0.144741i | ||||||||
\(502\) | 3.42866 | − | 4.70465i | 0.153029 | − | 0.209979i | ||||
\(503\) | 37.8332 | 1.68690 | 0.843449 | − | 0.537210i | \(-0.180522\pi\) | ||||
0.843449 | + | 0.537210i | \(0.180522\pi\) | |||||||
\(504\) | −3.28876 | + | 9.97253i | −0.146493 | + | 0.444212i | ||||
\(505\) | 3.87797 | 0.172567 | ||||||||
\(506\) | 1.65163 | − | 2.26629i | 0.0734239 | − | 0.100749i | ||||
\(507\) | − | 3.46319i | − | 0.153806i | ||||||
\(508\) | −11.0028 | − | 34.2035i | −0.488169 | − | 1.51753i | ||||
\(509\) | − | 19.8782i | − | 0.881088i | −0.897731 | − | 0.440544i | \(-0.854786\pi\) | ||
0.897731 | − | 0.440544i | \(-0.145214\pi\) | |||||||
\(510\) | −0.0417834 | − | 0.0304510i | −0.00185020 | − | 0.00134839i | ||||
\(511\) | −7.83798 | −0.346732 | ||||||||
\(512\) | 18.4796 | − | 13.0577i | 0.816691 | − | 0.577075i | ||||
\(513\) | −0.839050 | −0.0370449 | ||||||||
\(514\) | −22.5221 | − | 16.4137i | −0.993407 | − | 0.723977i | ||||
\(515\) | 14.3584i | 0.632705i | ||||||||
\(516\) | 1.33158 | + | 4.13938i | 0.0586195 | + | 0.182226i | ||||
\(517\) | − | 18.3625i | − | 0.807583i | ||||||
\(518\) | −5.04618 | + | 6.92413i | −0.221716 | + | 0.304229i | ||||
\(519\) | −18.1261 | −0.795647 | ||||||||
\(520\) | 3.72327 | − | 11.2901i | 0.163276 | − | 0.495103i | ||||
\(521\) | 24.0911 | 1.05545 | 0.527726 | − | 0.849415i | \(-0.323045\pi\) | ||||
0.527726 | + | 0.849415i | \(0.323045\pi\) | |||||||
\(522\) | 7.48337 | − | 10.2683i | 0.327538 | − | 0.449433i | ||||
\(523\) | 6.89987i | 0.301710i | 0.988556 | + | 0.150855i | \(0.0482027\pi\) | ||||
−0.988556 | + | 0.150855i | \(0.951797\pi\) | |||||||
\(524\) | 21.7798 | − | 7.00626i | 0.951457 | − | 0.306070i | ||||
\(525\) | − | 14.5791i | − | 0.636285i | ||||||
\(526\) | −13.8484 | − | 10.0924i | −0.603817 | − | 0.440051i | ||||
\(527\) | 0.199497 | 0.00869024 | ||||||||
\(528\) | −6.44406 | + | 4.62447i | −0.280442 | + | 0.201254i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −11.2856 | − | 8.22471i | −0.490214 | − | 0.357259i | ||||
\(531\) | 0.521307i | 0.0226228i | ||||||||
\(532\) | −5.93080 | + | 1.90785i | −0.257133 | + | 0.0827159i | ||||
\(533\) | − | 6.70218i | − | 0.290304i | ||||||
\(534\) | 6.93102 | − | 9.51041i | 0.299934 | − | 0.411556i | ||||
\(535\) | −0.651435 | −0.0281640 | ||||||||
\(536\) | 10.2773 | + | 3.38927i | 0.443911 | + | 0.146394i | ||||
\(537\) | −6.25406 | −0.269883 | ||||||||
\(538\) | 13.5441 | − | 18.5846i | 0.583928 | − | 0.801238i | ||||
\(539\) | − | 13.4509i | − | 0.579373i | ||||||
\(540\) | 0.634443 | + | 1.97225i | 0.0273021 | + | 0.0848719i | ||||
\(541\) | − | 31.7799i | − | 1.36633i | −0.730266 | − | 0.683163i | \(-0.760604\pi\) | ||
0.730266 | − | 0.683163i | \(-0.239396\pi\) | |||||||
\(542\) | 17.4916 | + | 12.7476i | 0.751330 | + | 0.547556i | ||||
\(543\) | 12.6374 | 0.542323 | ||||||||
\(544\) | −0.199638 | − | 0.00146139i | −0.00855943 | − | 6.26568e-5i | ||||
\(545\) | 18.1246 | 0.776374 | ||||||||
\(546\) | 17.2165 | + | 12.5471i | 0.736799 | + | 0.536965i | ||||
\(547\) | 3.03957i | 0.129963i | 0.997886 | + | 0.0649814i | \(0.0206988\pi\) | ||||
−0.997886 | + | 0.0649814i | \(0.979301\pi\) | |||||||
\(548\) | −0.895206 | − | 2.78286i | −0.0382413 | − | 0.118878i | ||||
\(549\) | 1.08170i | 0.0461659i | ||||||||
\(550\) | 6.48584 | − | 8.89956i | 0.276557 | − | 0.379479i | ||||
\(551\) | 7.53837 | 0.321145 | ||||||||
\(552\) | −2.68613 | − | 0.885838i | −0.114329 | − | 0.0377038i | ||||
\(553\) | 39.3729 | 1.67431 | ||||||||
\(554\) | −9.26288 | + | 12.7101i | −0.393542 | + | 0.540000i | ||||
\(555\) | 1.69040i | 0.0717536i | ||||||||
\(556\) | 35.7974 | − | 11.5155i | 1.51815 | − | 0.488367i | ||||
\(557\) | 1.27269i | 0.0539258i | 0.999636 | + | 0.0269629i | \(0.00858360\pi\) | ||||
−0.999636 | + | 0.0269629i | \(0.991416\pi\) | |||||||
\(558\) | −6.46050 | − | 4.70830i | −0.273495 | − | 0.199318i | ||||
\(559\) | 8.82155 | 0.373112 | ||||||||
\(560\) | 8.96909 | + | 12.4982i | 0.379013 | + | 0.528143i | ||||
\(561\) | 0.0699819 | 0.00295464 | ||||||||
\(562\) | −36.0022 | − | 26.2377i | −1.51866 | − | 1.10677i | ||||
\(563\) | 28.3319i | 1.19405i | 0.802223 | + | 0.597024i | \(0.203650\pi\) | ||||
−0.802223 | + | 0.597024i | \(0.796350\pi\) | |||||||
\(564\) | −17.6309 | + | 5.67161i | −0.742395 | + | 0.238818i | ||||
\(565\) | 19.2823i | 0.811213i | ||||||||
\(566\) | 15.9794 | − | 21.9262i | 0.671664 | − | 0.921625i | ||||
\(567\) | −3.71260 | −0.155915 | ||||||||
\(568\) | 0.0505584 | − | 0.153308i | 0.00212138 | − | 0.00643268i | ||||
\(569\) | −22.2098 | −0.931082 | −0.465541 | − | 0.885026i | \(-0.654140\pi\) | ||||
−0.465541 | + | 0.885026i | \(0.654140\pi\) | |||||||
\(570\) | −0.723950 | + | 0.993370i | −0.0303229 | + | 0.0416077i | ||||
\(571\) | − | 5.60588i | − | 0.234599i | −0.993097 | − | 0.117299i | \(-0.962576\pi\) | ||
0.993097 | − | 0.117299i | \(-0.0374237\pi\) | |||||||
\(572\) | 4.92767 | + | 15.3183i | 0.206036 | + | 0.640489i | ||||
\(573\) | − | 17.8806i | − | 0.746974i | ||||||
\(574\) | 7.00886 | + | 5.10793i | 0.292544 | + | 0.213201i | ||||
\(575\) | 3.92693 | 0.163764 | ||||||||
\(576\) | 6.43058 | + | 4.75895i | 0.267941 | + | 0.198290i | ||||
\(577\) | 8.63486 | 0.359474 | 0.179737 | − | 0.983715i | \(-0.442475\pi\) | ||||
0.179737 | + | 0.983715i | \(0.442475\pi\) | |||||||
\(578\) | −19.4280 | − | 14.1587i | −0.808096 | − | 0.588926i | ||||
\(579\) | − | 2.56140i | − | 0.106448i | ||||||
\(580\) | −5.70010 | − | 17.7195i | −0.236684 | − | 0.735761i | ||||
\(581\) | − | 48.2586i | − | 2.00211i | ||||||
\(582\) | −14.5039 | + | 19.9015i | −0.601204 | + | 0.824944i | ||||
\(583\) | 18.9019 | 0.782836 | ||||||||
\(584\) | −1.87017 | + | 5.67091i | −0.0773880 | + | 0.234664i | ||||
\(585\) | 4.20311 | 0.173777 | ||||||||
\(586\) | 24.3116 | − | 33.3592i | 1.00430 | − | 1.37806i | ||||
\(587\) | − | 5.46776i | − | 0.225679i | −0.993613 | − | 0.112839i | \(-0.964005\pi\) | ||
0.993613 | − | 0.112839i | \(-0.0359946\pi\) | |||||||
\(588\) | −12.9150 | + | 4.15458i | −0.532606 | + | 0.171332i | ||||
\(589\) | − | 4.74290i | − | 0.195428i | ||||||
\(590\) | 0.617188 | + | 0.449795i | 0.0254092 | + | 0.0185178i | ||||
\(591\) | 8.36352 | 0.344029 | ||||||||
\(592\) | 3.80569 | + | 5.30311i | 0.156413 | + | 0.217957i | ||||
\(593\) | 40.5175 | 1.66385 | 0.831927 | − | 0.554884i | \(-0.187238\pi\) | ||||
0.831927 | + | 0.554884i | \(0.187238\pi\) | |||||||
\(594\) | −2.26629 | − | 1.65163i | −0.0929869 | − | 0.0677672i | ||||
\(595\) | − | 0.135729i | − | 0.00556435i | ||||||
\(596\) | −13.9121 | + | 4.47533i | −0.569863 | + | 0.183317i | ||||
\(597\) | − | 4.24697i | − | 0.173817i | ||||||
\(598\) | −3.37959 | + | 4.63732i | −0.138202 | + | 0.189634i | ||||
\(599\) | −4.37851 | −0.178901 | −0.0894505 | − | 0.995991i | \(-0.528511\pi\) | ||||
−0.0894505 | + | 0.995991i | \(0.528511\pi\) | |||||||
\(600\) | −10.5482 | − | 3.47863i | −0.430630 | − | 0.142014i | ||||
\(601\) | 3.04134 | 0.124059 | 0.0620294 | − | 0.998074i | \(-0.480243\pi\) | ||||
0.0620294 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(602\) | −6.72317 | + | 9.22521i | −0.274016 | + | 0.375992i | ||||
\(603\) | 3.82606i | 0.155809i | ||||||||
\(604\) | 4.08646 | + | 12.7033i | 0.166276 | + | 0.516889i | ||||
\(605\) | 7.32170i | 0.297669i | ||||||||
\(606\) | 4.27859 | + | 3.11816i | 0.173806 | + | 0.126667i | ||||
\(607\) | 14.2779 | 0.579520 | 0.289760 | − | 0.957099i | \(-0.406424\pi\) | ||||
0.289760 | + | 0.957099i | \(0.406424\pi\) | |||||||
\(608\) | −0.0347436 | + | 4.74625i | −0.00140904 | + | 0.192486i | ||||
\(609\) | 33.3556 | 1.35164 | ||||||||
\(610\) | 1.28065 | + | 0.933315i | 0.0518520 | + | 0.0377888i | ||||
\(611\) | 37.5737i | 1.52007i | ||||||||
\(612\) | −0.0216152 | − | 0.0671936i | −0.000873744 | − | 0.00271614i | ||||
\(613\) | 2.22906i | 0.0900308i | 0.998986 | + | 0.0450154i | \(0.0143337\pi\) | ||||
−0.998986 | + | 0.0450154i | \(0.985666\pi\) | |||||||
\(614\) | −12.8159 | + | 17.5854i | −0.517209 | + | 0.709690i | ||||
\(615\) | 1.71109 | 0.0689977 | ||||||||
\(616\) | −19.7747 | − | 6.52136i | −0.796746 | − | 0.262753i | ||||
\(617\) | 9.07230 | 0.365237 | 0.182618 | − | 0.983184i | \(-0.441543\pi\) | ||||
0.182618 | + | 0.983184i | \(0.441543\pi\) | |||||||
\(618\) | −11.5451 | + | 15.8417i | −0.464413 | + | 0.637246i | ||||
\(619\) | − | 3.24295i | − | 0.130345i | −0.997874 | − | 0.0651726i | \(-0.979240\pi\) | ||
0.997874 | − | 0.0651726i | \(-0.0207598\pi\) | |||||||
\(620\) | −11.1485 | + | 3.58632i | −0.447735 | + | 0.144030i | ||||
\(621\) | − | 1.00000i | − | 0.0401286i | ||||||
\(622\) | −25.7027 | − | 18.7317i | −1.03059 | − | 0.751072i | ||||
\(623\) | 30.8935 | 1.23772 | ||||||||
\(624\) | 13.1859 | − | 9.46267i | 0.527860 | − | 0.378810i | ||||
\(625\) | 10.0555 | 0.402218 | ||||||||
\(626\) | 27.6359 | + | 20.1405i | 1.10455 | + | 0.804978i | ||||
\(627\) | − | 1.66377i | − | 0.0664445i | ||||||
\(628\) | −7.85334 | + | 2.52631i | −0.313383 | + | 0.100811i | ||||
\(629\) | − | 0.0575914i | − | 0.00229632i | ||||||
\(630\) | −3.20331 | + | 4.39543i | −0.127623 | + | 0.175118i | ||||
\(631\) | 5.73771 | 0.228415 | 0.114207 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114207 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(632\) | 9.39451 | − | 28.4870i | 0.373693 | − | 1.13315i | ||||
\(633\) | −23.2483 | −0.924038 | ||||||||
\(634\) | −6.80364 | + | 9.33564i | −0.270207 | + | 0.370766i | ||||
\(635\) | − | 18.6096i | − | 0.738499i | ||||||
\(636\) | −5.83820 | − | 18.1488i | −0.231500 | − | 0.719646i | ||||
\(637\) | 27.5236i | 1.09052i | ||||||||
\(638\) | 20.3613 | + | 14.8389i | 0.806111 | + | 0.587479i | ||||
\(639\) | 0.0570741 | 0.00225782 | ||||||||
\(640\) | 11.1827 | − | 3.50719i | 0.442034 | − | 0.138634i | ||||
\(641\) | 44.4992 | 1.75761 | 0.878807 | − | 0.477178i | \(-0.158340\pi\) | ||||
0.878807 | + | 0.477178i | \(0.158340\pi\) | |||||||
\(642\) | −0.718733 | − | 0.523800i | −0.0283661 | − | 0.0206727i | ||||
\(643\) | − | 13.4068i | − | 0.528714i | −0.964425 | − | 0.264357i | \(-0.914840\pi\) | ||
0.964425 | − | 0.264357i | \(-0.0851598\pi\) | |||||||
\(644\) | −2.27383 | − | 7.06847i | −0.0896013 | − | 0.278537i | ||||
\(645\) | 2.25217i | 0.0886792i | ||||||||
\(646\) | 0.0246647 | − | 0.0338437i | 0.000970420 | − | 0.00133156i | ||||
\(647\) | 18.2256 | 0.716521 | 0.358261 | − | 0.933622i | \(-0.383370\pi\) | ||||
0.358261 | + | 0.933622i | \(0.383370\pi\) | |||||||
\(648\) | −0.885838 | + | 2.68613i | −0.0347990 | + | 0.105521i | ||||
\(649\) | −1.03371 | −0.0405767 | ||||||||
\(650\) | −13.2714 | + | 18.2104i | −0.520548 | + | 0.714272i | ||||
\(651\) | − | 20.9862i | − | 0.822516i | ||||||
\(652\) | 26.1627 | − | 8.41617i | 1.02461 | − | 0.329603i | ||||
\(653\) | − | 49.1873i | − | 1.92485i | −0.271551 | − | 0.962424i | \(-0.587537\pi\) | ||
0.271551 | − | 0.962424i | \(-0.412463\pi\) | |||||||
\(654\) | 19.9970 | + | 14.5735i | 0.781946 | + | 0.569868i | ||||
\(655\) | 11.8501 | 0.463021 | ||||||||
\(656\) | 5.36801 | − | 3.85226i | 0.209585 | − | 0.150405i | ||||
\(657\) | −2.11118 | −0.0823651 | ||||||||
\(658\) | −39.2930 | − | 28.6360i | −1.53180 | − | 1.11635i | ||||
\(659\) | 11.5711i | 0.450746i | 0.974273 | + | 0.225373i | \(0.0723601\pi\) | ||||
−0.974273 | + | 0.225373i | \(0.927640\pi\) | |||||||
\(660\) | −3.91081 | + | 1.25805i | −0.152228 | + | 0.0489695i | ||||
\(661\) | − | 12.5878i | − | 0.489609i | −0.969572 | − | 0.244804i | \(-0.921276\pi\) | ||
0.969572 | − | 0.244804i | \(-0.0787237\pi\) | |||||||
\(662\) | −22.2997 | + | 30.5987i | −0.866704 | + | 1.18925i | ||||
\(663\) | −0.143198 | −0.00556136 | ||||||||
\(664\) | −34.9159 | − | 11.5147i | −1.35500 | − | 0.446856i | ||||
\(665\) | −3.22685 | −0.125132 | ||||||||
\(666\) | −1.35920 | + | 1.86503i | −0.0526680 | + | 0.0722686i | ||||
\(667\) | 8.98442i | 0.347878i | ||||||||
\(668\) | 1.98422 | + | 6.16820i | 0.0767718 | + | 0.238655i | ||||
\(669\) | − | 27.1897i | − | 1.05121i | ||||||
\(670\) | 4.52976 | + | 3.30121i | 0.175000 | + | 0.127537i | ||||
\(671\) | −2.14493 | −0.0828039 | ||||||||
\(672\) | −0.153732 | + | 21.0011i | −0.00593035 | + | 0.810134i | ||||
\(673\) | −27.6053 | −1.06411 | −0.532054 | − | 0.846710i | \(-0.678580\pi\) | ||||
−0.532054 | + | 0.846710i | \(0.678580\pi\) | |||||||
\(674\) | −37.7819 | − | 27.5347i | −1.45530 | − | 1.06060i | ||||
\(675\) | − | 3.92693i | − | 0.151148i | ||||||
\(676\) | −2.12107 | − | 6.59362i | −0.0815797 | − | 0.253601i | ||||
\(677\) | − | 4.67781i | − | 0.179783i | −0.995952 | − | 0.0898914i | \(-0.971348\pi\) | ||
0.995952 | − | 0.0898914i | \(-0.0286520\pi\) | |||||||
\(678\) | −15.5043 | + | 21.2743i | −0.595440 | + | 0.817035i | ||||
\(679\) | −64.6479 | −2.48096 | ||||||||
\(680\) | −0.0982022 | − | 0.0323854i | −0.00376588 | − | 0.00124192i | ||||
\(681\) | −8.83046 | −0.338384 | ||||||||
\(682\) | 9.33618 | − | 12.8107i | 0.357501 | − | 0.490546i | ||||
\(683\) | − | 17.8023i | − | 0.681185i | −0.940211 | − | 0.340592i | \(-0.889372\pi\) | ||
0.940211 | − | 0.340592i | \(-0.110628\pi\) | |||||||
\(684\) | −1.59748 | + | 0.513886i | −0.0610811 | + | 0.0196489i | ||||
\(685\) | − | 1.51411i | − | 0.0578512i | ||||||
\(686\) | 0.919050 | + | 0.669787i | 0.0350895 | + | 0.0255726i | ||||
\(687\) | 25.0163 | 0.954433 | ||||||||
\(688\) | 5.07043 | + | 7.06549i | 0.193308 | + | 0.269369i | ||||
\(689\) | −38.6774 | −1.47349 | ||||||||
\(690\) | −1.18392 | − | 0.862822i | −0.0450712 | − | 0.0328471i | ||||
\(691\) | 29.6148i | 1.12660i | 0.826253 | + | 0.563300i | \(0.190468\pi\) | ||||
−0.826253 | + | 0.563300i | \(0.809532\pi\) | |||||||
\(692\) | −34.5105 | + | 11.1015i | −1.31189 | + | 0.422017i | ||||
\(693\) | − | 7.36179i | − | 0.279651i | ||||||
\(694\) | −18.1874 | + | 24.9559i | −0.690384 | + | 0.947312i | ||||
\(695\) | 19.4768 | 0.738798 | ||||||||
\(696\) | 7.95874 | − | 24.1333i | 0.301675 | − | 0.914771i | ||||
\(697\) | −0.0582961 | −0.00220812 | ||||||||
\(698\) | 22.1112 | − | 30.3400i | 0.836922 | − | 1.14838i | ||||
\(699\) | 22.2640i | 0.842103i | ||||||||
\(700\) | −8.92916 | − | 27.7574i | −0.337491 | − | 1.04913i | ||||
\(701\) | 16.2594i | 0.614109i | 0.951692 | + | 0.307054i | \(0.0993433\pi\) | ||||
−0.951692 | + | 0.307054i | \(0.900657\pi\) | |||||||
\(702\) | 4.63732 | + | 3.37959i | 0.175024 | + | 0.127555i | ||||
\(703\) | −1.36919 | −0.0516401 | ||||||||
\(704\) | −9.43662 | + | 12.7513i | −0.355656 | + | 0.480584i | ||||
\(705\) | −9.59270 | −0.361282 | ||||||||
\(706\) | −2.05455 | − | 1.49731i | −0.0773238 | − | 0.0563522i | ||||
\(707\) | 13.8985i | 0.522708i | ||||||||
\(708\) | 0.319281 | + | 0.992524i | 0.0119993 | + | 0.0373013i | ||||
\(709\) | − | 4.30800i | − | 0.161790i | −0.996723 | − | 0.0808952i | \(-0.974222\pi\) | ||
0.996723 | − | 0.0808952i | \(-0.0257779\pi\) | |||||||
\(710\) | 0.0492448 | − | 0.0675714i | 0.00184812 | − | 0.00253591i | ||||
\(711\) | 10.6052 | 0.397727 | ||||||||
\(712\) | 7.37130 | − | 22.3520i | 0.276251 | − | 0.837677i | ||||
\(713\) | 5.65271 | 0.211696 | ||||||||
\(714\) | 0.109136 | − | 0.149751i | 0.00408430 | − | 0.00560428i | ||||
\(715\) | 8.33443i | 0.311690i | ||||||||
\(716\) | −11.9072 | + | 3.83037i | −0.444993 | + | 0.143148i | ||||
\(717\) | − | 4.66752i | − | 0.174312i | ||||||
\(718\) | 33.6755 | + | 24.5421i | 1.25676 | + | 0.915903i | ||||
\(719\) | 12.9861 | 0.484301 | 0.242150 | − | 0.970239i | \(-0.422147\pi\) | ||||
0.242150 | + | 0.970239i | \(0.422147\pi\) | |||||||
\(720\) | 2.41585 | + | 3.36641i | 0.0900334 | + | 0.125459i | ||||
\(721\) | −51.4600 | −1.91647 | ||||||||
\(722\) | 20.9106 | + | 15.2392i | 0.778211 | + | 0.567146i | ||||
\(723\) | 17.6837i | 0.657665i | ||||||||
\(724\) | 24.0605 | − | 7.73992i | 0.894202 | − | 0.287652i | ||||
\(725\) | 35.2812i | 1.31031i | ||||||||
\(726\) | −5.88716 | + | 8.07808i | −0.218493 | + | 0.299806i | ||||
\(727\) | −32.5529 | −1.20732 | −0.603660 | − | 0.797242i | \(-0.706291\pi\) | ||||
−0.603660 | + | 0.797242i | \(0.706291\pi\) | |||||||
\(728\) | 40.4634 | + | 13.3441i | 1.49967 | + | 0.494566i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.82157 | + | 2.49948i | −0.0674195 | + | 0.0925098i | ||||
\(731\) | − | 0.0767306i | − | 0.00283799i | ||||||
\(732\) | 0.662500 | + | 2.05947i | 0.0244867 | + | 0.0761200i | ||||
\(733\) | 27.4265i | 1.01302i | 0.862233 | + | 0.506511i | \(0.169065\pi\) | ||||
−0.862233 | + | 0.506511i | \(0.830935\pi\) | |||||||
\(734\) | −5.11181 | − | 3.72539i | −0.188680 | − | 0.137507i | ||||
\(735\) | −7.02686 | −0.259190 | ||||||||
\(736\) | −5.65670 | − | 0.0414082i | −0.208509 | − | 0.00152633i | ||||
\(737\) | −7.58677 | −0.279462 | ||||||||
\(738\) | 1.88786 | + | 1.37584i | 0.0694929 | + | 0.0506452i | ||||
\(739\) | 21.1976i | 0.779767i | 0.920864 | + | 0.389884i | \(0.127485\pi\) | ||||
−0.920864 | + | 0.389884i | \(0.872515\pi\) | |||||||
\(740\) | 1.03531 | + | 3.21838i | 0.0380587 | + | 0.118310i | ||||
\(741\) | 3.40443i | 0.125065i | ||||||||
\(742\) | 29.4772 | − | 40.4472i | 1.08214 | − | 1.48486i | ||||
\(743\) | −28.4918 | −1.04526 | −0.522631 | − | 0.852559i | \(-0.675049\pi\) | ||||
−0.522631 | + | 0.852559i | \(0.675049\pi\) | |||||||
\(744\) | −15.1839 | − | 5.00738i | −0.556669 | − | 0.183580i | ||||
\(745\) | −7.56937 | −0.277320 | ||||||||
\(746\) | −7.81925 | + | 10.7292i | −0.286283 | + | 0.392824i | ||||
\(747\) | − | 12.9986i | − | 0.475594i | ||||||
\(748\) | 0.133240 | − | 0.0428613i | 0.00487172 | − | 0.00156716i | ||||
\(749\) | − | 2.33473i | − | 0.0853091i | ||||||
\(750\) | −10.5688 | − | 7.70235i | −0.385918 | − | 0.281250i | ||||
\(751\) | −43.8582 | −1.60041 | −0.800205 | − | 0.599727i | \(-0.795276\pi\) | ||||
−0.800205 | + | 0.599727i | \(0.795276\pi\) | |||||||
\(752\) | −30.0941 | + | 21.5965i | −1.09742 | + | 0.787544i | ||||
\(753\) | 4.11640 | 0.150010 | ||||||||
\(754\) | −41.6636 | − | 30.3637i | −1.51730 | − | 1.10578i | ||||
\(755\) | 6.91165i | 0.251541i | ||||||||
\(756\) | −7.06847 | + | 2.27383i | −0.257078 | + | 0.0826983i | ||||
\(757\) | 23.8058i | 0.865238i | 0.901577 | + | 0.432619i | \(0.142411\pi\) | ||||
−0.901577 | + | 0.432619i | \(0.857589\pi\) | |||||||
\(758\) | 8.25660 | − | 11.3293i | 0.299893 | − | 0.411499i | ||||
\(759\) | 1.98292 | 0.0719754 | ||||||||
\(760\) | −0.769938 | + | 2.33468i | −0.0279286 | + | 0.0846879i | ||||
\(761\) | 51.1304 | 1.85348 | 0.926738 | − | 0.375709i | \(-0.122601\pi\) | ||||
0.926738 | + | 0.375709i | \(0.122601\pi\) | |||||||
\(762\) | 14.9634 | − | 20.5321i | 0.542067 | − | 0.743799i | ||||
\(763\) | 64.9582i | 2.35165i | ||||||||
\(764\) | −10.9512 | − | 34.0432i | −0.396201 | − | 1.23164i | ||||
\(765\) | − | 0.0365590i | − | 0.00132179i | ||||||
\(766\) | 39.1724 | + | 28.5482i | 1.41536 | + | 1.03149i | ||||
\(767\) | 2.11520 | 0.0763753 | ||||||||
\(768\) | 15.1580 | + | 5.12215i | 0.546966 | + | 0.184830i | ||||
\(769\) | −39.8744 | −1.43791 | −0.718954 | − | 0.695058i | \(-0.755379\pi\) | ||||
−0.718954 | + | 0.695058i | \(0.755379\pi\) | |||||||
\(770\) | −8.71579 | − | 6.35191i | −0.314095 | − | 0.228907i | ||||
\(771\) | − | 19.7060i | − | 0.709695i | ||||||
\(772\) | −1.56876 | − | 4.87669i | −0.0564610 | − | 0.175516i | ||||
\(773\) | 28.3459i | 1.01953i | 0.860314 | + | 0.509765i | \(0.170268\pi\) | ||||
−0.860314 | + | 0.509765i | \(0.829732\pi\) | |||||||
\(774\) | −1.81090 | + | 2.48484i | −0.0650916 | + | 0.0893157i | ||||
\(775\) | 22.1978 | 0.797368 | ||||||||
\(776\) | −15.4252 | + | 46.7738i | −0.553732 | + | 1.67908i | ||||
\(777\) | −6.05836 | −0.217342 | ||||||||
\(778\) | −14.2354 | + | 19.5332i | −0.510364 | + | 0.700298i | ||||
\(779\) | 1.38595i | 0.0496567i | ||||||||
\(780\) | 8.00236 | − | 2.57424i | 0.286530 | − | 0.0921727i | ||||
\(781\) | 0.113173i | 0.00404966i | ||||||||
\(782\) | 0.0403358 | + | 0.0293960i | 0.00144241 | + | 0.00105120i | ||||
\(783\) | 8.98442 | 0.321077 | ||||||||
\(784\) | −22.0446 | + | 15.8199i | −0.787306 | + | 0.564997i | ||||
\(785\) | −4.27288 | −0.152506 | ||||||||
\(786\) | 13.0743 | + | 9.52829i | 0.466344 | + | 0.339863i | ||||
\(787\) | 21.7598i | 0.775653i | 0.921732 | + | 0.387827i | \(0.126774\pi\) | ||||
−0.921732 | + | 0.387827i | \(0.873226\pi\) | |||||||
\(788\) | 15.9234 | − | 5.12234i | 0.567249 | − | 0.182476i | ||||
\(789\) | − | 12.1168i | − | 0.431370i | ||||||
\(790\) | 9.15041 | − | 12.5558i | 0.325557 | − | 0.446714i | ||||
\(791\) | −69.1073 | −2.45717 | ||||||||
\(792\) | −5.32638 | − | 1.75655i | −0.189265 | − | 0.0624162i | ||||
\(793\) | 4.38898 | 0.155857 | ||||||||
\(794\) | 11.7624 | − | 16.1398i | 0.417432 | − | 0.572780i | ||||
\(795\) | − | 9.87446i | − | 0.350211i | ||||||
\(796\) | −2.60110 | − | 8.08586i | −0.0921937 | − | 0.286596i | ||||
\(797\) | − | 28.2980i | − | 1.00237i | −0.865341 | − | 0.501184i | \(-0.832898\pi\) | ||
0.865341 | − | 0.501184i | \(-0.167102\pi\) | |||||||
\(798\) | −3.56021 | − | 2.59462i | −0.126030 | − | 0.0918485i | ||||
\(799\) | 0.326819 | 0.0115620 | ||||||||
\(800\) | −22.2135 | − | 0.162607i | −0.785365 | − | 0.00574904i | ||||
\(801\) | 8.32127 | 0.294018 | ||||||||
\(802\) | −23.8849 | − | 17.4069i | −0.843404 | − | 0.614658i | ||||
\(803\) | − | 4.18631i | − | 0.147732i | ||||||
\(804\) | 2.34331 | + | 7.28449i | 0.0826423 | + | 0.256904i | ||||
\(805\) | − | 3.84584i | − | 0.135548i | ||||||
\(806\) | −19.1038 | + | 26.2134i | −0.672904 | + | 0.923328i | ||||
\(807\) | 16.2608 | 0.572409 | ||||||||
\(808\) | 10.0558 | + | 3.31623i | 0.353763 | + | 0.116665i | ||||
\(809\) | −14.9378 | −0.525186 | −0.262593 | − | 0.964907i | \(-0.584578\pi\) | ||||
−0.262593 | + | 0.964907i | \(0.584578\pi\) | |||||||
\(810\) | −0.862822 | + | 1.18392i | −0.0303165 | + | 0.0415988i | ||||
\(811\) | − | 52.6398i | − | 1.84843i | −0.381868 | − | 0.924217i | \(-0.624719\pi\) | ||
0.381868 | − | 0.924217i | \(-0.375281\pi\) | |||||||
\(812\) | 63.5061 | − | 20.4290i | 2.22863 | − | 0.716918i | ||||
\(813\) | 15.3045i | 0.536754i | ||||||||
\(814\) | −3.69821 | − | 2.69519i | −0.129622 | − | 0.0944664i | ||||
\(815\) | 14.2347 | 0.498621 | ||||||||
\(816\) | −0.0823071 | − | 0.114692i | −0.00288132 | − | 0.00401504i | ||||
\(817\) | −1.82421 | −0.0638212 | ||||||||
\(818\) | 23.4933 | + | 17.1215i | 0.821423 | + | 0.598638i | ||||
\(819\) | 15.0638i | 0.526373i | ||||||||
\(820\) | 3.25777 | − | 1.04798i | 0.113766 | − | 0.0365969i | ||||
\(821\) | − | 7.88739i | − | 0.275272i | −0.990483 | − | 0.137636i | \(-0.956050\pi\) | ||
0.990483 | − | 0.137636i | \(-0.0439504\pi\) | |||||||
\(822\) | 1.21745 | − | 1.67053i | 0.0424635 | − | 0.0582664i | ||||
\(823\) | −13.2341 | −0.461313 | −0.230657 | − | 0.973035i | \(-0.574087\pi\) | ||||
−0.230657 | + | 0.973035i | \(0.574087\pi\) | |||||||
\(824\) | −12.2785 | + | 37.2322i | −0.427742 | + | 1.29704i | ||||
\(825\) | 7.78679 | 0.271101 | ||||||||
\(826\) | −1.61205 | + | 2.21198i | −0.0560905 | + | 0.0769648i | ||||
\(827\) | 36.3427i | 1.26376i | 0.775066 | + | 0.631880i | \(0.217717\pi\) | ||||
−0.775066 | + | 0.631880i | \(0.782283\pi\) | |||||||
\(828\) | −0.612462 | − | 1.90391i | −0.0212845 | − | 0.0661656i | ||||
\(829\) | 24.4887i | 0.850528i | 0.905069 | + | 0.425264i | \(0.139819\pi\) | ||||
−0.905069 | + | 0.425264i | \(0.860181\pi\) | |||||||
\(830\) | −15.3894 | − | 11.2155i | −0.534172 | − | 0.389295i | ||||
\(831\) | −11.1209 | −0.385779 | ||||||||
\(832\) | 19.3094 | − | 26.0920i | 0.669432 | − | 0.904577i | ||||
\(833\) | 0.239402 | 0.00829480 | ||||||||
\(834\) | 21.4889 | + | 15.6607i | 0.744100 | + | 0.542287i | ||||
\(835\) | 3.35602i | 0.116140i | ||||||||
\(836\) | −1.01899 | − | 3.16767i | −0.0352427 | − | 0.109556i | ||||
\(837\) | − | 5.65271i | − | 0.195386i | ||||||
\(838\) | 13.5884 | − | 18.6453i | 0.469402 | − | 0.644092i | ||||
\(839\) | −38.1236 | −1.31617 | −0.658087 | − | 0.752942i | \(-0.728634\pi\) | ||||
−0.658087 | + | 0.752942i | \(0.728634\pi\) | |||||||
\(840\) | −3.40680 | + | 10.3304i | −0.117546 | + | 0.356434i | ||||
\(841\) | −51.7198 | −1.78344 | ||||||||
\(842\) | −16.6397 | + | 22.8322i | −0.573442 | + | 0.786850i | ||||
\(843\) | − | 31.5006i | − | 1.08494i | ||||||
\(844\) | −44.2628 | + | 14.2387i | −1.52359 | + | 0.490116i | ||||
\(845\) | − | 3.58748i | − | 0.123413i | ||||||
\(846\) | −10.5837 | − | 7.71320i | −0.363875 | − | 0.265185i | ||||
\(847\) | −26.2408 | −0.901643 | ||||||||
\(848\) | −22.2309 | − | 30.9780i | −0.763411 | − | 1.06379i | ||||
\(849\) | 19.1846 | 0.658414 | ||||||||
\(850\) | 0.158396 | + | 0.115436i | 0.00543294 | + | 0.00395943i | ||||
\(851\) | − | 1.63184i | − | 0.0559387i | ||||||
\(852\) | 0.108664 | − | 0.0349557i | 0.00372278 | − | 0.00119756i | ||||
\(853\) | − | 28.3191i | − | 0.969627i | −0.874618 | − | 0.484813i | \(-0.838887\pi\) | ||
0.874618 | − | 0.484813i | \(-0.161113\pi\) | |||||||
\(854\) | −3.34497 | + | 4.58982i | −0.114463 | + | 0.157060i | ||||
\(855\) | −0.869163 | −0.0297247 | ||||||||
\(856\) | −1.68921 | − | 0.557073i | −0.0577361 | − | 0.0190404i | ||||
\(857\) | −5.00409 | −0.170937 | −0.0854683 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854683 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(858\) | −6.70146 | + | 9.19543i | −0.228784 | + | 0.313927i | ||||
\(859\) | − | 43.3989i | − | 1.48075i | −0.672194 | − | 0.740375i | \(-0.734648\pi\) | ||
0.672194 | − | 0.740375i | \(-0.265352\pi\) | |||||||
\(860\) | 1.37937 | + | 4.28794i | 0.0470361 | + | 0.146218i | ||||
\(861\) | 6.13249i | 0.208995i | ||||||||
\(862\) | 7.17822 | + | 5.23135i | 0.244491 | + | 0.178181i | ||||
\(863\) | −56.3132 | −1.91692 | −0.958462 | − | 0.285220i | \(-0.907933\pi\) | ||||
−0.958462 | + | 0.285220i | \(0.907933\pi\) | |||||||
\(864\) | −0.0414082 | + | 5.65670i | −0.00140874 | + | 0.192445i | ||||
\(865\) | −18.7766 | −0.638425 | ||||||||
\(866\) | 19.0717 | + | 13.8991i | 0.648083 | + | 0.472311i | ||||
\(867\) | − | 16.9988i | − | 0.577308i | ||||||
\(868\) | −12.8533 | − | 39.9560i | −0.436269 | − | 1.35620i | ||||
\(869\) | 21.0293i | 0.713370i | ||||||||
\(870\) | 7.75195 | − | 10.6369i | 0.262816 | − | 0.360623i | ||||
\(871\) | 15.5242 | 0.526017 | ||||||||
\(872\) | 46.9984 | + | 15.4992i | 1.59157 | + | 0.524870i | ||||
\(873\) | −17.4131 | −0.589344 | ||||||||
\(874\) | 0.698868 | − | 0.958954i | 0.0236396 | − | 0.0324371i | ||||
\(875\) | − | 34.3316i | − | 1.16062i | ||||||
\(876\) | −4.01951 | + | 1.29302i | −0.135807 | + | 0.0436871i | ||||
\(877\) | 36.0118i | 1.21603i | 0.793924 | + | 0.608017i | \(0.208035\pi\) | ||||
−0.793924 | + | 0.608017i | \(0.791965\pi\) | |||||||
\(878\) | 12.0687 | + | 8.79544i | 0.407298 | + | 0.296832i | ||||
\(879\) | 29.1881 | 0.984491 | ||||||||
\(880\) | −6.67533 | + | 4.79044i | −0.225025 | + | 0.161486i | ||||
\(881\) | −7.27238 | −0.245013 | −0.122506 | − | 0.992468i | \(-0.539093\pi\) | ||||
−0.122506 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(882\) | −7.75278 | − | 5.65009i | −0.261050 | − | 0.190248i | ||||
\(883\) | − | 53.3083i | − | 1.79397i | −0.442065 | − | 0.896983i | \(-0.645754\pi\) | ||
0.442065 | − | 0.896983i | \(-0.354246\pi\) | |||||||
\(884\) | −0.272637 | + | 0.0877035i | −0.00916978 | + | 0.00294979i | ||||
\(885\) | 0.540017i | 0.0181525i | ||||||||
\(886\) | −1.93040 | + | 2.64880i | −0.0648530 | + | 0.0889883i | ||||
\(887\) | 9.02645 | 0.303079 | 0.151539 | − | 0.988451i | \(-0.451577\pi\) | ||||
0.151539 | + | 0.988451i | \(0.451577\pi\) | |||||||
\(888\) | −1.44554 | + | 4.38333i | −0.0485093 | + | 0.147095i | ||||
\(889\) | 66.6962 | 2.23692 | ||||||||
\(890\) | 7.17977 | − | 9.85174i | 0.240666 | − | 0.330231i | ||||
\(891\) | − | 1.98292i | − | 0.0664303i | ||||||
\(892\) | −16.6526 | − | 51.7668i | −0.557571 | − | 1.73328i | ||||
\(893\) | − | 7.76989i | − | 0.260009i | ||||||
\(894\) | −8.35134 | − | 6.08630i | −0.279310 | − | 0.203556i | ||||
\(895\) | −6.47852 | −0.216553 | ||||||||
\(896\) | 12.5697 | + | 40.0784i | 0.419923 | + | 1.33893i | ||||
\(897\) | −4.05749 | −0.135475 | ||||||||
\(898\) | −10.1284 | − | 7.38136i | −0.337988 | − | 0.246319i | ||||
\(899\) | 50.7863i | 1.69382i | ||||||||
\(900\) | −2.40510 | − | 7.47654i | −0.0801699 | − | 0.249218i | ||||
\(901\) | 0.336419i | 0.0112077i | ||||||||
\(902\) | −2.72817 | + | 3.74347i | −0.0908382 | + | 0.124644i | ||||
\(903\) | −8.07172 | −0.268610 | ||||||||
\(904\) | −16.4892 | + | 50.0003i | −0.548423 | + | 1.66298i | ||||
\(905\) | 13.0909 | 0.435158 | ||||||||
\(906\) | −5.55745 | + | 7.62568i | −0.184634 | + | 0.253346i | ||||
\(907\) | − | 18.6291i | − | 0.618568i | −0.950970 | − | 0.309284i | \(-0.899911\pi\) | ||
0.950970 | − | 0.309284i | \(-0.100089\pi\) | |||||||
\(908\) | −16.8124 | + | 5.40832i | −0.557941 | + | 0.179481i | ||||
\(909\) | 3.74361i | 0.124168i | ||||||||
\(910\) | 17.8344 | + | 12.9974i | 0.591205 | + | 0.430859i | ||||
\(911\) | −19.8933 | −0.659094 | −0.329547 | − | 0.944139i | \(-0.606896\pi\) | ||||
−0.329547 | + | 0.944139i | \(0.606896\pi\) | |||||||
\(912\) | −2.72673 | + | 1.95679i | −0.0902910 | + | 0.0647958i | ||||
\(913\) | 25.7752 | 0.853035 | ||||||||
\(914\) | −12.7739 | − | 9.30936i | −0.422522 | − | 0.307926i | ||||
\(915\) | 1.12052i | 0.0370433i | ||||||||
\(916\) | 47.6290 | − | 15.3216i | 1.57371 | − | 0.506239i | ||||
\(917\) | 42.4703i | 1.40249i | ||||||||
\(918\) | 0.0293960 | − | 0.0403358i | 0.000970213 | − | 0.00133128i | ||||
\(919\) | −44.6518 | −1.47293 | −0.736463 | − | 0.676477i | \(-0.763506\pi\) | ||||
−0.736463 | + | 0.676477i | \(0.763506\pi\) | |||||||
\(920\) | −2.78253 | − | 0.917631i | −0.0917374 | − | 0.0302534i | ||||
\(921\) | −15.3866 | −0.507006 | ||||||||
\(922\) | −12.1152 | + | 16.6239i | −0.398993 | + | 0.547480i | ||||
\(923\) | − | 0.231577i | − | 0.00762246i | ||||||
\(924\) | −4.50882 | − | 14.0162i | −0.148329 | − | 0.461100i | ||||
\(925\) | − | 6.40812i | − | 0.210698i | ||||||
\(926\) | 15.2809 | + | 11.1364i | 0.502161 | + | 0.365966i | ||||
\(927\) | −13.8609 | −0.455252 | ||||||||
\(928\) | 0.372029 | − | 50.8222i | 0.0122124 | − | 1.66832i | ||||
\(929\) | 45.7107 | 1.49972 | 0.749860 | − | 0.661597i | \(-0.230121\pi\) | ||||
0.749860 | + | 0.661597i | \(0.230121\pi\) | |||||||
\(930\) | −6.69237 | − | 4.87728i | −0.219451 | − | 0.159932i | ||||
\(931\) | − | 5.69161i | − | 0.186535i | ||||||
\(932\) | 13.6359 | + | 42.3888i | 0.446658 | + | 1.38849i | ||||
\(933\) | − | 22.4890i | − | 0.736255i | ||||||
\(934\) | −17.4950 | + | 24.0058i | −0.572455 | + | 0.785495i | ||||
\(935\) | 0.0724936 | 0.00237079 | ||||||||
\(936\) | 10.8989 | + | 3.59428i | 0.356243 | + | 0.117483i | ||||
\(937\) | −54.7330 | −1.78805 | −0.894024 | − | 0.448018i | \(-0.852130\pi\) | ||||
−0.894024 | + | 0.448018i | \(0.852130\pi\) | |||||||
\(938\) | −11.8314 | + | 16.2345i | −0.386310 | + | 0.530076i | ||||
\(939\) | 24.1804i | 0.789098i | ||||||||
\(940\) | −18.2637 | + | 5.87516i | −0.595695 | + | 0.191627i | ||||
\(941\) | 36.7184i | 1.19699i | 0.801128 | + | 0.598493i | \(0.204233\pi\) | ||||
−0.801128 | + | 0.598493i | \(0.795767\pi\) | |||||||
\(942\) | −4.71430 | − | 3.43570i | −0.153600 | − | 0.111941i | ||||
\(943\) | −1.65181 | −0.0537902 | ||||||||
\(944\) | 1.21577 | + | 1.69413i | 0.0395698 | + | 0.0551394i | ||||
\(945\) | −3.84584 | −0.125105 | ||||||||
\(946\) | −4.92724 | − | 3.59088i | −0.160198 | − | 0.116750i | ||||
\(947\) | 26.4766i | 0.860374i | 0.902740 | + | 0.430187i | \(0.141552\pi\) | ||||
−0.902740 | + | 0.430187i | \(0.858448\pi\) | |||||||
\(948\) | 20.1914 | − | 6.49529i | 0.655787 | − | 0.210957i | ||||
\(949\) | 8.56609i | 0.278067i | ||||||||
\(950\) | 2.74441 | − | 3.76575i | 0.0890403 | − | 0.122177i | ||||
\(951\) | −8.16834 | −0.264877 | ||||||||
\(952\) | 0.116068 | − | 0.351954i | 0.00376179 | − | 0.0114069i | ||||
\(953\) | −5.66869 | −0.183627 | −0.0918134 | − | 0.995776i | \(-0.529266\pi\) | ||||
−0.0918134 | + | 0.995776i | \(0.529266\pi\) | |||||||
\(954\) | 7.93976 | − | 10.8946i | 0.257059 | − | 0.352725i | ||||
\(955\) | − | 18.5224i | − | 0.599369i | ||||||
\(956\) | −2.85868 | − | 8.88655i | −0.0924562 | − | 0.287412i | ||||
\(957\) | 17.8154i | 0.575890i | ||||||||
\(958\) | 7.30918 | + | 5.32680i | 0.236149 | + | 0.172101i | ||||
\(959\) | 5.42653 | 0.175232 | ||||||||
\(960\) | 6.66137 | + | 4.92975i | 0.214995 | + | 0.159107i | ||||
\(961\) | 0.953085 | 0.0307447 | ||||||||
\(962\) | 7.56735 | + | 5.51495i | 0.243981 | + | 0.177809i | ||||
\(963\) | − | 0.628866i | − | 0.0202649i | ||||||
\(964\) | 10.8306 | + | 33.6683i | 0.348831 | + | 1.08438i | ||||
\(965\) | − | 2.65333i | − | 0.0854138i | ||||||
\(966\) | 3.09233 | − | 4.24315i | 0.0994941 | − | 0.136521i | ||||
\(967\) | 3.36120 | 0.108089 | 0.0540445 | − | 0.998539i | \(-0.482789\pi\) | ||||
0.0540445 | + | 0.998539i | \(0.482789\pi\) | |||||||
\(968\) | −6.26113 | + | 18.9856i | −0.201240 | + | 0.610221i | ||||
\(969\) | 0.0296120 | 0.000951276 | ||||||||
\(970\) | −15.0244 | + | 20.6158i | −0.482404 | + | 0.661933i | ||||
\(971\) | 9.91531i | 0.318197i | 0.987263 | + | 0.159099i | \(0.0508588\pi\) | ||||
−0.987263 | + | 0.159099i | \(0.949141\pi\) | |||||||
\(972\) | −1.90391 | + | 0.612462i | −0.0610681 | + | 0.0196447i | ||||
\(973\) | 69.8044i | 2.23783i | ||||||||
\(974\) | 28.8416 | + | 21.0193i | 0.924145 | + | 0.673500i | ||||
\(975\) | −15.9335 | −0.510279 | ||||||||
\(976\) | 2.52269 | + | 3.51529i | 0.0807493 | + | 0.112522i | ||||
\(977\) | 27.2308 | 0.871191 | 0.435596 | − | 0.900142i | \(-0.356538\pi\) | ||||
0.435596 | + | 0.900142i | \(0.356538\pi\) | |||||||
\(978\) | 15.7053 | + | 11.4457i | 0.502199 | + | 0.365994i | ||||
\(979\) | 16.5004i | 0.527355i | ||||||||
\(980\) | −13.3785 | + | 4.30368i | −0.427362 | + | 0.137476i | ||||
\(981\) | 17.4967i | 0.558626i | ||||||||
\(982\) | 32.1582 | − | 44.1259i | 1.02621 | − | 1.40812i | ||||
\(983\) | −12.7325 | −0.406103 | −0.203051 | − | 0.979168i | \(-0.565086\pi\) | ||||
−0.203051 | + | 0.979168i | \(0.565086\pi\) | |||||||
\(984\) | 4.43696 | + | 1.46323i | 0.141445 | + | 0.0466461i | ||||
\(985\) | 8.66369 | 0.276048 | ||||||||
\(986\) | −0.264106 | + | 0.362394i | −0.00841085 | + | 0.0115410i | ||||
\(987\) | − | 34.3800i | − | 1.09433i | ||||||
\(988\) | 2.08508 | + | 6.48175i | 0.0663354 | + | 0.206212i | ||||
\(989\) | − | 2.17414i | − | 0.0691337i | ||||||
\(990\) | −2.34763 | − | 1.71091i | −0.0746124 | − | 0.0543762i | ||||
\(991\) | 56.1787 | 1.78458 | 0.892288 | − | 0.451467i | \(-0.149099\pi\) | ||||
0.892288 | + | 0.451467i | \(0.149099\pi\) | |||||||
\(992\) | −31.9757 | − | 0.234069i | −1.01523 | − | 0.00743168i | ||||
\(993\) | −26.7727 | −0.849606 | ||||||||
\(994\) | 0.242174 | + | 0.176492i | 0.00768129 | + | 0.00559799i | ||||
\(995\) | − | 4.39939i | − | 0.139470i | ||||||
\(996\) | −7.96115 | − | 24.7482i | −0.252259 | − | 0.784178i | ||||
\(997\) | 1.37812i | 0.0436456i | 0.999762 | + | 0.0218228i | \(0.00694696\pi\) | ||||
−0.999762 | + | 0.0218228i | \(0.993053\pi\) | |||||||
\(998\) | −35.0602 | + | 48.1079i | −1.10981 | + | 1.52283i | ||||
\(999\) | −1.63184 | −0.0516290 |
(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 | 552.2.f.d.277.18 | yes | 20 | |
4.3 | odd | 2 | 2208.2.f.d.1105.6 | 20 | |||
8.3 | odd | 2 | 2208.2.f.d.1105.15 | 20 | |||
8.5 | even | 2 | inner | 552.2.f.d.277.17 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.f.d.277.17 | ✓ | 20 | 8.5 | even | 2 | inner | |
552.2.f.d.277.18 | yes | 20 | 1.1 | even | 1 | trivial | |
2208.2.f.d.1105.6 | 20 | 4.3 | odd | 2 | |||
2208.2.f.d.1105.15 | 20 | 8.3 | odd | 2 |