Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [744,2,Mod(557,744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("744.557");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 744 = 2^{3} \cdot 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 744.o (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: | \(5.94086991038\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 557.15 | ||
Character | \(\chi\) | \(=\) | 744.557 |
Dual form | 744.2.o.e.557.13 |
$q$-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 \(\left(\mathbb{Z}/744\mathbb{Z}\right)^\times\).
\(n\) | \(313\) | \(373\) | \(497\) | \(559\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30178 | + | 0.552593i | −0.920500 | + | 0.390742i | ||||
\(3\) | −1.50847 | + | 0.851189i | −0.870915 | + | 0.491434i | ||||
\(4\) | 1.38928 | − | 1.43871i | 0.694641 | − | 0.719357i | ||||
\(5\) | −2.01938 | −0.903095 | −0.451548 | − | 0.892247i | \(-0.649128\pi\) | ||||
−0.451548 | + | 0.892247i | \(0.649128\pi\) | |||||||
\(6\) | 1.49334 | − | 1.94163i | 0.609653 | − | 0.792668i | ||||
\(7\) | −0.359027 | −0.135700 | −0.0678498 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678498 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(8\) | −1.01352 | + | 2.64060i | −0.358334 | + | 0.933593i | ||||
\(9\) | 1.55095 | − | 2.56798i | 0.516985 | − | 0.855994i | ||||
\(10\) | 2.62880 | − | 1.11590i | 0.831299 | − | 0.352877i | ||||
\(11\) | 1.25539i | 0.378514i | 0.981928 | + | 0.189257i | \(0.0606080\pi\) | ||||
−0.981928 | + | 0.189257i | \(0.939392\pi\) | |||||||
\(12\) | −0.871072 | + | 3.35279i | −0.251457 | + | 0.967869i | ||||
\(13\) | 4.90527 | 1.36048 | 0.680239 | − | 0.732990i | \(-0.261876\pi\) | ||||
0.680239 | + | 0.732990i | \(0.261876\pi\) | |||||||
\(14\) | 0.467376 | − | 0.198396i | 0.124912 | − | 0.0530236i | ||||
\(15\) | 3.04617 | − | 1.71888i | 0.786519 | − | 0.443812i | ||||
\(16\) | −0.139790 | − | 3.99756i | −0.0349476 | − | 0.999389i | ||||
\(17\) | 0.530078 | 0.128563 | 0.0642814 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642814 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(18\) | −0.599958 | + | 4.20001i | −0.141412 | + | 0.989951i | ||||
\(19\) | − | 1.51514i | − | 0.347597i | −0.984781 | − | 0.173798i | \(-0.944396\pi\) | ||
0.984781 | − | 0.173798i | \(-0.0556041\pi\) | |||||||
\(20\) | −2.80549 | + | 2.90531i | −0.627327 | + | 0.649647i | ||||
\(21\) | 0.541582 | − | 0.305600i | 0.118183 | − | 0.0666874i | ||||
\(22\) | −0.693720 | − | 1.63425i | −0.147902 | − | 0.348422i | ||||
\(23\) | 0.370588 | 0.0772729 | 0.0386364 | − | 0.999253i | \(-0.487699\pi\) | ||||
0.0386364 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(24\) | −0.718783 | − | 4.84596i | −0.146721 | − | 0.989178i | ||||
\(25\) | −0.922095 | −0.184419 | ||||||||
\(26\) | −6.38561 | + | 2.71062i | −1.25232 | + | 0.531596i | ||||
\(27\) | −0.153728 | + | 5.19388i | −0.0295849 | + | 0.999562i | ||||
\(28\) | −0.498790 | + | 0.516538i | −0.0942625 | + | 0.0976164i | ||||
\(29\) | 4.00910i | 0.744471i | 0.928138 | + | 0.372236i | \(0.121409\pi\) | ||||
−0.928138 | + | 0.372236i | \(0.878591\pi\) | |||||||
\(30\) | −3.01562 | + | 3.92090i | −0.550575 | + | 0.715855i | ||||
\(31\) | −3.24407 | + | 4.52505i | −0.582651 | + | 0.812722i | ||||
\(32\) | 2.39100 | + | 5.12671i | 0.422673 | + | 0.906282i | ||||
\(33\) | −1.06857 | − | 1.89372i | −0.186015 | − | 0.329654i | ||||
\(34\) | −0.690047 | + | 0.292917i | −0.118342 | + | 0.0502349i | ||||
\(35\) | 0.725014 | 0.122550 | ||||||||
\(36\) | −1.53988 | − | 5.79903i | −0.256646 | − | 0.966505i | ||||
\(37\) | 6.16631 | 1.01373 | 0.506867 | − | 0.862024i | \(-0.330803\pi\) | ||||
0.506867 | + | 0.862024i | \(0.330803\pi\) | |||||||
\(38\) | 0.837255 | + | 1.97238i | 0.135821 | + | 0.319963i | ||||
\(39\) | −7.39945 | + | 4.17531i | −1.18486 | + | 0.668585i | ||||
\(40\) | 2.04669 | − | 5.33238i | 0.323610 | − | 0.843124i | ||||
\(41\) | − | 3.27399i | − | 0.511311i | −0.966768 | − | 0.255655i | \(-0.917709\pi\) | ||
0.966768 | − | 0.255655i | \(-0.0822912\pi\) | |||||||
\(42\) | −0.536150 | + | 0.697100i | −0.0827297 | + | 0.107565i | ||||
\(43\) | −4.57537 | −0.697738 | −0.348869 | − | 0.937172i | \(-0.613434\pi\) | ||||
−0.348869 | + | 0.937172i | \(0.613434\pi\) | |||||||
\(44\) | 1.80615 | + | 1.74409i | 0.272287 | + | 0.262932i | ||||
\(45\) | −3.13197 | + | 5.18574i | −0.466887 | + | 0.773044i | ||||
\(46\) | −0.482425 | + | 0.204784i | −0.0711297 | + | 0.0301938i | ||||
\(47\) | 6.81027i | 0.993381i | 0.867928 | + | 0.496690i | \(0.165451\pi\) | ||||
−0.867928 | + | 0.496690i | \(0.834549\pi\) | |||||||
\(48\) | 3.61355 | + | 5.91120i | 0.521570 | + | 0.853208i | ||||
\(49\) | −6.87110 | −0.981586 | ||||||||
\(50\) | 1.20037 | − | 0.509543i | 0.169758 | − | 0.0720603i | ||||
\(51\) | −0.799606 | + | 0.451196i | −0.111967 | + | 0.0631801i | ||||
\(52\) | 6.81481 | − | 7.05728i | 0.945044 | − | 0.978669i | ||||
\(53\) | − | 0.592046i | − | 0.0813238i | −0.999173 | − | 0.0406619i | \(-0.987053\pi\) | ||
0.999173 | − | 0.0406619i | \(-0.0129467\pi\) | |||||||
\(54\) | −2.66998 | − | 6.84625i | −0.363338 | − | 0.931657i | ||||
\(55\) | − | 2.53511i | − | 0.341834i | ||||||
\(56\) | 0.363882 | − | 0.948048i | 0.0486258 | − | 0.126688i | ||||
\(57\) | 1.28967 | + | 2.28554i | 0.170821 | + | 0.302727i | ||||
\(58\) | −2.21540 | − | 5.21898i | −0.290896 | − | 0.685286i | ||||
\(59\) | −12.5066 | −1.62823 | −0.814114 | − | 0.580706i | \(-0.802777\pi\) | ||||
−0.814114 | + | 0.580706i | \(0.802777\pi\) | |||||||
\(60\) | 1.75903 | − | 6.77057i | 0.227089 | − | 0.874077i | ||||
\(61\) | −6.24528 | −0.799626 | −0.399813 | − | 0.916597i | \(-0.630925\pi\) | ||||
−0.399813 | + | 0.916597i | \(0.630925\pi\) | |||||||
\(62\) | 1.72256 | − | 7.68328i | 0.218766 | − | 0.975777i | ||||
\(63\) | −0.556835 | + | 0.921977i | −0.0701547 | + | 0.116158i | ||||
\(64\) | −5.94554 | − | 5.35262i | −0.743193 | − | 0.669077i | ||||
\(65\) | −9.90562 | −1.22864 | ||||||||
\(66\) | 2.43751 | + | 1.87472i | 0.300036 | + | 0.230762i | ||||
\(67\) | 9.87091i | 1.20592i | 0.797770 | + | 0.602962i | \(0.206013\pi\) | ||||
−0.797770 | + | 0.602962i | \(0.793987\pi\) | |||||||
\(68\) | 0.736428 | − | 0.762630i | 0.0893050 | − | 0.0924825i | ||||
\(69\) | −0.559020 | + | 0.315440i | −0.0672981 | + | 0.0379745i | ||||
\(70\) | −0.943811 | + | 0.400637i | −0.112807 | + | 0.0478853i | ||||
\(71\) | − | 2.37470i | − | 0.281826i | −0.990022 | − | 0.140913i | \(-0.954996\pi\) | ||
0.990022 | − | 0.140913i | \(-0.0450037\pi\) | |||||||
\(72\) | 5.20909 | + | 6.69816i | 0.613897 | + | 0.789386i | ||||
\(73\) | 6.69918i | 0.784079i | 0.919948 | + | 0.392040i | \(0.128230\pi\) | ||||
−0.919948 | + | 0.392040i | \(0.871770\pi\) | |||||||
\(74\) | −8.02720 | + | 3.40746i | −0.933143 | + | 0.396109i | ||||
\(75\) | 1.39095 | − | 0.784877i | 0.160613 | − | 0.0906298i | ||||
\(76\) | −2.17985 | − | 2.10496i | −0.250046 | − | 0.241455i | ||||
\(77\) | − | 0.450719i | − | 0.0513643i | ||||||
\(78\) | 7.32524 | − | 9.52424i | 0.829420 | − | 1.07841i | ||||
\(79\) | 9.72903i | 1.09460i | 0.836936 | + | 0.547301i | \(0.184345\pi\) | ||||
−0.836936 | + | 0.547301i | \(0.815655\pi\) | |||||||
\(80\) | 0.282290 | + | 8.07259i | 0.0315610 | + | 0.902544i | ||||
\(81\) | −4.18908 | − | 7.96565i | −0.465453 | − | 0.885073i | ||||
\(82\) | 1.80918 | + | 4.26202i | 0.199791 | + | 0.470662i | ||||
\(83\) | 7.22344i | 0.792876i | 0.918062 | + | 0.396438i | \(0.129754\pi\) | ||||
−0.918062 | + | 0.396438i | \(0.870246\pi\) | |||||||
\(84\) | 0.312739 | − | 1.20375i | 0.0341226 | − | 0.131339i | ||||
\(85\) | −1.07043 | −0.116104 | ||||||||
\(86\) | 5.95615 | − | 2.52832i | 0.642268 | − | 0.272636i | ||||
\(87\) | −3.41250 | − | 6.04760i | −0.365859 | − | 0.648371i | ||||
\(88\) | −3.31498 | − | 1.27237i | −0.353378 | − | 0.135635i | ||||
\(89\) | −7.20666 | −0.763904 | −0.381952 | − | 0.924182i | \(-0.624748\pi\) | ||||
−0.381952 | + | 0.924182i | \(0.624748\pi\) | |||||||
\(90\) | 1.21155 | − | 8.48142i | 0.127708 | − | 0.894020i | ||||
\(91\) | −1.76113 | −0.184616 | ||||||||
\(92\) | 0.514851 | − | 0.533169i | 0.0536769 | − | 0.0555867i | ||||
\(93\) | 1.04190 | − | 9.58720i | 0.108040 | − | 0.994147i | ||||
\(94\) | −3.76331 | − | 8.86550i | −0.388156 | − | 0.914407i | ||||
\(95\) | 3.05965i | 0.313913i | ||||||||
\(96\) | −7.97054 | − | 5.69829i | −0.813490 | − | 0.581579i | ||||
\(97\) | 4.22348 | 0.428829 | 0.214415 | − | 0.976743i | \(-0.431216\pi\) | ||||
0.214415 | + | 0.976743i | \(0.431216\pi\) | |||||||
\(98\) | 8.94469 | − | 3.79692i | 0.903550 | − | 0.383547i | ||||
\(99\) | 3.22382 | + | 1.94705i | 0.324006 | + | 0.195686i | ||||
\(100\) | −1.28105 | + | 1.32663i | −0.128105 | + | 0.132663i | ||||
\(101\) | −6.18926 | −0.615854 | −0.307927 | − | 0.951410i | \(-0.599635\pi\) | ||||
−0.307927 | + | 0.951410i | \(0.599635\pi\) | |||||||
\(102\) | 0.791586 | − | 1.02922i | 0.0783787 | − | 0.101908i | ||||
\(103\) | −2.20770 | −0.217531 | −0.108766 | − | 0.994067i | \(-0.534690\pi\) | ||||
−0.108766 | + | 0.994067i | \(0.534690\pi\) | |||||||
\(104\) | −4.97160 | + | 12.9529i | −0.487506 | + | 1.27013i | ||||
\(105\) | −1.09366 | + | 0.617124i | −0.106730 | + | 0.0602251i | ||||
\(106\) | 0.327161 | + | 0.770716i | 0.0317766 | + | 0.0748586i | ||||
\(107\) | 0.436108 | 0.0421602 | 0.0210801 | − | 0.999778i | \(-0.493290\pi\) | ||||
0.0210801 | + | 0.999778i | \(0.493290\pi\) | |||||||
\(108\) | 7.25893 | + | 7.43693i | 0.698491 | + | 0.715619i | ||||
\(109\) | 3.38785i | 0.324497i | 0.986750 | + | 0.162249i | \(0.0518746\pi\) | ||||
−0.986750 | + | 0.162249i | \(0.948125\pi\) | |||||||
\(110\) | 1.40088 | + | 3.30017i | 0.133569 | + | 0.314659i | ||||
\(111\) | −9.30168 | + | 5.24869i | −0.882876 | + | 0.498184i | ||||
\(112\) | 0.0501886 | + | 1.43523i | 0.00474237 | + | 0.135617i | ||||
\(113\) | − | 11.4455i | − | 1.07670i | −0.842721 | − | 0.538351i | \(-0.819047\pi\) | ||
0.842721 | − | 0.538351i | \(-0.180953\pi\) | |||||||
\(114\) | −2.94184 | − | 2.26262i | −0.275529 | − | 0.211913i | ||||
\(115\) | −0.748358 | −0.0697848 | ||||||||
\(116\) | 5.76795 | + | 5.56977i | 0.535540 | + | 0.517140i | ||||
\(117\) | 7.60786 | − | 12.5967i | 0.703347 | − | 1.16456i | ||||
\(118\) | 16.2810 | − | 6.91109i | 1.49878 | − | 0.636217i | ||||
\(119\) | −0.190313 | −0.0174459 | ||||||||
\(120\) | 1.45150 | + | 9.78585i | 0.132503 | + | 0.893322i | ||||
\(121\) | 9.42400 | 0.856727 | ||||||||
\(122\) | 8.13001 | − | 3.45110i | 0.736056 | − | 0.312448i | ||||
\(123\) | 2.78678 | + | 4.93870i | 0.251275 | + | 0.445308i | ||||
\(124\) | 2.00332 | + | 10.9538i | 0.179903 | + | 0.983684i | ||||
\(125\) | 11.9590 | 1.06964 | ||||||||
\(126\) | 0.215402 | − | 1.50792i | 0.0191895 | − | 0.134336i | ||||
\(127\) | 18.8970i | 1.67684i | 0.545028 | + | 0.838418i | \(0.316519\pi\) | ||||
−0.545028 | + | 0.838418i | \(0.683481\pi\) | |||||||
\(128\) | 10.6976 | + | 3.68248i | 0.945546 | + | 0.325489i | ||||
\(129\) | 6.90180 | − | 3.89451i | 0.607670 | − | 0.342892i | ||||
\(130\) | 12.8950 | − | 5.47378i | 1.13096 | − | 0.480082i | ||||
\(131\) | −5.46430 | −0.477418 | −0.238709 | − | 0.971091i | \(-0.576724\pi\) | ||||
−0.238709 | + | 0.971091i | \(0.576724\pi\) | |||||||
\(132\) | −4.20906 | − | 1.09353i | −0.366352 | − | 0.0951800i | ||||
\(133\) | 0.543977i | 0.0471688i | ||||||||
\(134\) | −5.45460 | − | 12.8498i | −0.471205 | − | 1.11005i | ||||
\(135\) | 0.310435 | − | 10.4884i | 0.0267180 | − | 0.902700i | ||||
\(136\) | −0.537246 | + | 1.39972i | −0.0460685 | + | 0.120025i | ||||
\(137\) | −13.5837 | −1.16054 | −0.580268 | − | 0.814425i | \(-0.697052\pi\) | ||||
−0.580268 | + | 0.814425i | \(0.697052\pi\) | |||||||
\(138\) | 0.553413 | − | 0.719545i | 0.0471096 | − | 0.0612518i | ||||
\(139\) | −0.453491 | −0.0384646 | −0.0192323 | − | 0.999815i | \(-0.506122\pi\) | ||||
−0.0192323 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(140\) | 1.00725 | − | 1.04309i | 0.0851280 | − | 0.0881569i | ||||
\(141\) | −5.79683 | − | 10.2731i | −0.488181 | − | 0.865150i | ||||
\(142\) | 1.31224 | + | 3.09135i | 0.110121 | + | 0.259421i | ||||
\(143\) | 6.15803i | 0.514960i | ||||||||
\(144\) | −10.4825 | − | 5.84105i | −0.873539 | − | 0.486754i | ||||
\(145\) | − | 8.09591i | − | 0.672329i | ||||||
\(146\) | −3.70192 | − | 8.72088i | −0.306373 | − | 0.721745i | ||||
\(147\) | 10.3648 | − | 5.84860i | 0.854877 | − | 0.482385i | ||||
\(148\) | 8.56674 | − | 8.87154i | 0.704182 | − | 0.729236i | ||||
\(149\) | 19.6286 | 1.60804 | 0.804018 | − | 0.594605i | \(-0.202692\pi\) | ||||
0.804018 | + | 0.594605i | \(0.202692\pi\) | |||||||
\(150\) | −1.37700 | + | 1.79037i | −0.112432 | + | 0.146183i | ||||
\(151\) | 2.86421i | 0.233086i | 0.993186 | + | 0.116543i | \(0.0371813\pi\) | ||||
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(152\) | 4.00088 | + | 1.53563i | 0.324514 | + | 0.124556i | ||||
\(153\) | 0.822127 | − | 1.36123i | 0.0664650 | − | 0.110049i | ||||
\(154\) | 0.249064 | + | 0.586739i | 0.0200702 | + | 0.0472808i | ||||
\(155\) | 6.55101 | − | 9.13780i | 0.526190 | − | 0.733965i | ||||
\(156\) | −4.27285 | + | 16.4464i | −0.342101 | + | 1.31676i | ||||
\(157\) | 17.5419i | 1.39999i | 0.714146 | + | 0.699997i | \(0.246815\pi\) | ||||
−0.714146 | + | 0.699997i | \(0.753185\pi\) | |||||||
\(158\) | −5.37620 | − | 12.6651i | −0.427707 | − | 1.00758i | ||||
\(159\) | 0.503943 | + | 0.893083i | 0.0399653 | + | 0.0708261i | ||||
\(160\) | −4.82834 | − | 10.3528i | −0.381714 | − | 0.818459i | ||||
\(161\) | −0.133051 | −0.0104859 | ||||||||
\(162\) | 9.85504 | + | 8.05470i | 0.774285 | + | 0.632837i | ||||
\(163\) | 20.5511i | 1.60969i | 0.593486 | + | 0.804845i | \(0.297751\pi\) | ||||
−0.593486 | + | 0.804845i | \(0.702249\pi\) | |||||||
\(164\) | −4.71033 | − | 4.54849i | −0.367815 | − | 0.355177i | ||||
\(165\) | 2.15786 | + | 3.82414i | 0.167989 | + | 0.297709i | ||||
\(166\) | −3.99162 | − | 9.40336i | −0.309810 | − | 0.729842i | ||||
\(167\) | 8.17750 | 0.632794 | 0.316397 | − | 0.948627i | \(-0.397527\pi\) | ||||
0.316397 | + | 0.948627i | \(0.397527\pi\) | |||||||
\(168\) | 0.258063 | + | 1.73983i | 0.0199100 | + | 0.134231i | ||||
\(169\) | 11.0617 | 0.850901 | ||||||||
\(170\) | 1.39347 | − | 0.591512i | 0.106874 | − | 0.0453669i | ||||
\(171\) | −3.89085 | − | 2.34991i | −0.297541 | − | 0.179702i | ||||
\(172\) | −6.35648 | + | 6.58265i | −0.484677 | + | 0.501922i | ||||
\(173\) | 15.2964 | 1.16296 | 0.581480 | − | 0.813560i | \(-0.302474\pi\) | ||||
0.581480 | + | 0.813560i | \(0.302474\pi\) | |||||||
\(174\) | 7.78420 | + | 5.98695i | 0.590119 | + | 0.453869i | ||||
\(175\) | 0.331058 | 0.0250256 | ||||||||
\(176\) | 5.01849 | − | 0.175491i | 0.378283 | − | 0.0132282i | ||||
\(177\) | 18.8659 | − | 10.6455i | 1.41805 | − | 0.800166i | ||||
\(178\) | 9.38151 | − | 3.98235i | 0.703174 | − | 0.298490i | ||||
\(179\) | − | 19.0378i | − | 1.42296i | −0.702709 | − | 0.711478i | \(-0.748026\pi\) | ||
0.702709 | − | 0.711478i | \(-0.251974\pi\) | |||||||
\(180\) | 3.10960 | + | 11.7105i | 0.231776 | + | 0.872846i | ||||
\(181\) | −4.49019 | −0.333753 | −0.166877 | − | 0.985978i | \(-0.553368\pi\) | ||||
−0.166877 | + | 0.985978i | \(0.553368\pi\) | |||||||
\(182\) | 2.29261 | − | 0.973187i | 0.169939 | − | 0.0721374i | ||||
\(183\) | 9.42081 | − | 5.31591i | 0.696406 | − | 0.392964i | ||||
\(184\) | −0.375599 | + | 0.978574i | −0.0276895 | + | 0.0721414i | ||||
\(185\) | −12.4521 | −0.915499 | ||||||||
\(186\) | 3.94149 | + | 13.0562i | 0.289004 | + | 0.957328i | ||||
\(187\) | 0.665455i | 0.0486629i | ||||||||
\(188\) | 9.79803 | + | 9.46139i | 0.714595 | + | 0.690043i | ||||
\(189\) | 0.0551925 | − | 1.86474i | 0.00401466 | − | 0.135640i | ||||
\(190\) | −1.69074 | − | 3.98300i | −0.122659 | − | 0.288957i | ||||
\(191\) | 15.6920i | 1.13543i | 0.823224 | + | 0.567716i | \(0.192173\pi\) | ||||
−0.823224 | + | 0.567716i | \(0.807827\pi\) | |||||||
\(192\) | 13.5248 | + | 3.01347i | 0.976065 | + | 0.217479i | ||||
\(193\) | 10.0352 | 0.722350 | 0.361175 | − | 0.932498i | \(-0.382376\pi\) | ||||
0.361175 | + | 0.932498i | \(0.382376\pi\) | |||||||
\(194\) | −5.49806 | + | 2.33386i | −0.394737 | + | 0.167562i | ||||
\(195\) | 14.9423 | − | 8.43156i | 1.07004 | − | 0.603796i | ||||
\(196\) | −9.54590 | + | 9.88554i | −0.681850 | + | 0.706110i | ||||
\(197\) | 8.62105i | 0.614224i | 0.951673 | + | 0.307112i | \(0.0993627\pi\) | ||||
−0.951673 | + | 0.307112i | \(0.900637\pi\) | |||||||
\(198\) | −5.27265 | − | 0.753182i | −0.374711 | − | 0.0535263i | ||||
\(199\) | 12.2556i | 0.868779i | 0.900725 | + | 0.434389i | \(0.143036\pi\) | ||||
−0.900725 | + | 0.434389i | \(0.856964\pi\) | |||||||
\(200\) | 0.934564 | − | 2.43489i | 0.0660837 | − | 0.172172i | ||||
\(201\) | −8.40201 | − | 14.8900i | −0.592632 | − | 1.05026i | ||||
\(202\) | 8.05708 | − | 3.42014i | 0.566894 | − | 0.240640i | ||||
\(203\) | − | 1.43938i | − | 0.101024i | ||||||
\(204\) | −0.461736 | + | 1.77724i | −0.0323280 | + | 0.124432i | ||||
\(205\) | 6.61143i | 0.461762i | ||||||||
\(206\) | 2.87395 | − | 1.21996i | 0.200238 | − | 0.0849987i | ||||
\(207\) | 0.574765 | − | 0.951663i | 0.0399489 | − | 0.0661452i | ||||
\(208\) | −0.685710 | − | 19.6091i | −0.0475454 | − | 1.35965i | ||||
\(209\) | 1.90209 | 0.131570 | ||||||||
\(210\) | 1.08269 | − | 1.40771i | 0.0747128 | − | 0.0971413i | ||||
\(211\) | − | 17.4011i | − | 1.19794i | −0.800770 | − | 0.598972i | \(-0.795576\pi\) | ||
0.800770 | − | 0.598972i | \(-0.204424\pi\) | |||||||
\(212\) | −0.851785 | − | 0.822519i | −0.0585008 | − | 0.0564909i | ||||
\(213\) | 2.02132 | + | 3.58217i | 0.138499 | + | 0.245446i | ||||
\(214\) | −0.567719 | + | 0.240990i | −0.0388084 | + | 0.0164738i | ||||
\(215\) | 9.23942 | 0.630124 | ||||||||
\(216\) | −13.5592 | − | 5.67004i | −0.922583 | − | 0.385798i | ||||
\(217\) | 1.16471 | − | 1.62462i | 0.0790656 | − | 0.110286i | ||||
\(218\) | −1.87210 | − | 4.41025i | −0.126795 | − | 0.298700i | ||||
\(219\) | −5.70226 | − | 10.1055i | −0.385323 | − | 0.682866i | ||||
\(220\) | −3.64730 | − | 3.52199i | −0.245901 | − | 0.237452i | ||||
\(221\) | 2.60018 | 0.174907 | ||||||||
\(222\) | 9.20838 | − | 11.9727i | 0.618026 | − | 0.803555i | ||||
\(223\) | − | 13.3927i | − | 0.896840i | −0.893823 | − | 0.448420i | \(-0.851987\pi\) | ||
0.893823 | − | 0.448420i | \(-0.148013\pi\) | |||||||
\(224\) | −0.858434 | − | 1.84063i | −0.0573565 | − | 0.122982i | ||||
\(225\) | −1.43013 | + | 2.36793i | −0.0953419 | + | 0.157862i | ||||
\(226\) | 6.32470 | + | 14.8996i | 0.420713 | + | 0.991105i | ||||
\(227\) | −14.6335 | −0.971260 | −0.485630 | − | 0.874164i | \(-0.661410\pi\) | ||||
−0.485630 | + | 0.874164i | \(0.661410\pi\) | |||||||
\(228\) | 5.07995 | + | 1.31980i | 0.336428 | + | 0.0874056i | ||||
\(229\) | −17.1847 | −1.13560 | −0.567799 | − | 0.823167i | \(-0.692205\pi\) | ||||
−0.567799 | + | 0.823167i | \(0.692205\pi\) | |||||||
\(230\) | 0.974201 | − | 0.413537i | 0.0642369 | − | 0.0272679i | ||||
\(231\) | 0.383647 | + | 0.679896i | 0.0252421 | + | 0.0447339i | ||||
\(232\) | −10.5864 | − | 4.06331i | −0.695034 | − | 0.266770i | ||||
\(233\) | − | 4.28624i | − | 0.280801i | −0.990095 | − | 0.140401i | \(-0.955161\pi\) | ||
0.990095 | − | 0.140401i | \(-0.0448390\pi\) | |||||||
\(234\) | −2.94296 | + | 20.6022i | −0.192387 | + | 1.34681i | ||||
\(235\) | − | 13.7525i | − | 0.897117i | ||||||
\(236\) | −17.3753 | + | 17.9935i | −1.13103 | + | 1.17128i | ||||
\(237\) | −8.28125 | − | 14.6759i | −0.537925 | − | 0.953305i | ||||
\(238\) | 0.247746 | − | 0.105165i | 0.0160590 | − | 0.00681686i | ||||
\(239\) | 26.9964 | 1.74625 | 0.873125 | − | 0.487497i | \(-0.162090\pi\) | ||||
0.873125 | + | 0.487497i | \(0.162090\pi\) | |||||||
\(240\) | −7.29713 | − | 11.9370i | −0.471028 | − | 0.770528i | ||||
\(241\) | − | 22.0932i | − | 1.42315i | −0.702610 | − | 0.711575i | \(-0.747982\pi\) | ||
0.702610 | − | 0.711575i | \(-0.252018\pi\) | |||||||
\(242\) | −12.2680 | + | 5.20763i | −0.788617 | + | 0.334759i | ||||
\(243\) | 13.0994 | + | 8.45024i | 0.840325 | + | 0.542083i | ||||
\(244\) | −8.67646 | + | 8.98517i | −0.555453 | + | 0.575216i | ||||
\(245\) | 13.8754 | 0.886465 | ||||||||
\(246\) | −6.35688 | − | 4.88917i | −0.405300 | − | 0.311722i | ||||
\(247\) | − | 7.43217i | − | 0.472898i | ||||||
\(248\) | −8.66090 | − | 13.1525i | −0.549968 | − | 0.835186i | ||||
\(249\) | −6.14851 | − | 10.8963i | −0.389646 | − | 0.690527i | ||||
\(250\) | −15.5680 | + | 6.60844i | −0.984607 | + | 0.417955i | ||||
\(251\) | 15.4005i | 0.972072i | 0.873939 | + | 0.486036i | \(0.161558\pi\) | ||||
−0.873939 | + | 0.486036i | \(0.838442\pi\) | |||||||
\(252\) | 0.552858 | + | 2.08201i | 0.0348268 | + | 0.131154i | ||||
\(253\) | 0.465232i | 0.0292489i | ||||||||
\(254\) | −10.4423 | − | 24.5998i | −0.655210 | − | 1.54353i | ||||
\(255\) | 1.61471 | − | 0.911138i | 0.101117 | − | 0.0570577i | ||||
\(256\) | −15.9609 | + | 1.11764i | −0.997557 | + | 0.0698525i | ||||
\(257\) | − | 9.32155i | − | 0.581462i | −0.956805 | − | 0.290731i | \(-0.906102\pi\) | ||
0.956805 | − | 0.290731i | \(-0.0938985\pi\) | |||||||
\(258\) | −6.83258 | + | 8.88369i | −0.425378 | + | 0.553075i | ||||
\(259\) | −2.21387 | −0.137563 | ||||||||
\(260\) | −13.7617 | + | 14.2513i | −0.853465 | + | 0.883831i | ||||
\(261\) | 10.2953 | + | 6.21793i | 0.637263 | + | 0.384881i | ||||
\(262\) | 7.11333 | − | 3.01953i | 0.439463 | − | 0.186547i | ||||
\(263\) | −24.2167 | −1.49327 | −0.746634 | − | 0.665235i | \(-0.768331\pi\) | ||||
−0.746634 | + | 0.665235i | \(0.768331\pi\) | |||||||
\(264\) | 6.08357 | − | 0.902354i | 0.374418 | − | 0.0555360i | ||||
\(265\) | 1.19557i | 0.0734432i | ||||||||
\(266\) | −0.300598 | − | 0.708140i | −0.0184308 | − | 0.0434189i | ||||
\(267\) | 10.8710 | − | 6.13423i | 0.665295 | − | 0.375408i | ||||
\(268\) | 14.2014 | + | 13.7135i | 0.867489 | + | 0.837684i | ||||
\(269\) | 32.2092i | 1.96383i | 0.189326 | + | 0.981914i | \(0.439370\pi\) | ||||
−0.189326 | + | 0.981914i | \(0.560630\pi\) | |||||||
\(270\) | 5.39171 | + | 13.8252i | 0.328129 | + | 0.841375i | ||||
\(271\) | − | 17.2940i | − | 1.05054i | −0.850936 | − | 0.525269i | \(-0.823965\pi\) | ||
0.850936 | − | 0.525269i | \(-0.176035\pi\) | |||||||
\(272\) | −0.0740998 | − | 2.11902i | −0.00449296 | − | 0.128484i | ||||
\(273\) | 2.65661 | − | 1.49905i | 0.160785 | − | 0.0907268i | ||||
\(274\) | 17.6831 | − | 7.50627i | 1.06827 | − | 0.453471i | ||||
\(275\) | − | 1.15759i | − | 0.0698053i | ||||||
\(276\) | −0.322809 | + | 1.24250i | −0.0194308 | + | 0.0747900i | ||||
\(277\) | −20.2977 | −1.21957 | −0.609786 | − | 0.792566i | \(-0.708745\pi\) | ||||
−0.609786 | + | 0.792566i | \(0.708745\pi\) | |||||||
\(278\) | 0.590347 | − | 0.250596i | 0.0354066 | − | 0.0150297i | ||||
\(279\) | 6.58884 | + | 15.3488i | 0.394464 | + | 0.918912i | ||||
\(280\) | −0.734818 | + | 1.91447i | −0.0439138 | + | 0.114412i | ||||
\(281\) | 31.5946i | 1.88477i | 0.334526 | + | 0.942386i | \(0.391424\pi\) | ||||
−0.334526 | + | 0.942386i | \(0.608576\pi\) | |||||||
\(282\) | 13.2231 | + | 10.1700i | 0.787421 | + | 0.605617i | ||||
\(283\) | − | 10.2707i | − | 0.610530i | −0.952267 | − | 0.305265i | \(-0.901255\pi\) | ||
0.952267 | − | 0.305265i | \(-0.0987451\pi\) | |||||||
\(284\) | −3.41652 | − | 3.29913i | −0.202733 | − | 0.195768i | ||||
\(285\) | −2.60434 | − | 4.61538i | −0.154268 | − | 0.273392i | ||||
\(286\) | −3.40288 | − | 8.01642i | −0.201217 | − | 0.474021i | ||||
\(287\) | 1.17545i | 0.0693847i | ||||||||
\(288\) | 16.8736 | + | 1.81125i | 0.994288 | + | 0.106729i | ||||
\(289\) | −16.7190 | −0.983472 | ||||||||
\(290\) | 4.47374 | + | 10.5391i | 0.262707 | + | 0.618879i | ||||
\(291\) | −6.37099 | + | 3.59498i | −0.373474 | + | 0.210741i | ||||
\(292\) | 9.63819 | + | 9.30704i | 0.564032 | + | 0.544654i | ||||
\(293\) | −13.9548 | −0.815250 | −0.407625 | − | 0.913149i | \(-0.633643\pi\) | ||||
−0.407625 | + | 0.913149i | \(0.633643\pi\) | |||||||
\(294\) | −10.2609 | + | 13.3412i | −0.598427 | + | 0.778072i | ||||
\(295\) | 25.2557 | 1.47044 | ||||||||
\(296\) | −6.24969 | + | 16.2828i | −0.363256 | + | 0.946416i | ||||
\(297\) | −6.52034 | − | 0.192988i | −0.378349 | − | 0.0111983i | ||||
\(298\) | −25.5522 | + | 10.8466i | −1.48020 | + | 0.628327i | ||||
\(299\) | 1.81783 | 0.105128 | ||||||||
\(300\) | 0.803211 | − | 3.09160i | 0.0463734 | − | 0.178493i | ||||
\(301\) | 1.64268 | 0.0946827 | ||||||||
\(302\) | −1.58274 | − | 3.72858i | −0.0910765 | − | 0.214556i | ||||
\(303\) | 9.33630 | − | 5.26823i | 0.536357 | − | 0.302652i | ||||
\(304\) | −6.05686 | + | 0.211802i | −0.347385 | + | 0.0121477i | ||||
\(305\) | 12.6116 | 0.722139 | ||||||||
\(306\) | −0.318025 | + | 2.22633i | −0.0181803 | + | 0.127271i | ||||
\(307\) | − | 6.39879i | − | 0.365198i | −0.983187 | − | 0.182599i | \(-0.941549\pi\) | ||
0.983187 | − | 0.182599i | \(-0.0584510\pi\) | |||||||
\(308\) | −0.648456 | − | 0.626177i | −0.0369492 | − | 0.0356797i | ||||
\(309\) | 3.33025 | − | 1.87917i | 0.189451 | − | 0.106902i | ||||
\(310\) | −3.47852 | + | 15.5155i | −0.197566 | + | 0.881220i | ||||
\(311\) | 4.40781i | 0.249944i | 0.992160 | + | 0.124972i | \(0.0398841\pi\) | ||||
−0.992160 | + | 0.124972i | \(0.960116\pi\) | |||||||
\(312\) | −3.52583 | − | 23.7708i | −0.199611 | − | 1.34575i | ||||
\(313\) | 16.7888i | 0.948959i | 0.880266 | + | 0.474480i | \(0.157364\pi\) | ||||
−0.880266 | + | 0.474480i | \(0.842636\pi\) | |||||||
\(314\) | −9.69352 | − | 22.8357i | −0.547037 | − | 1.28869i | ||||
\(315\) | 1.12446 | − | 1.86182i | 0.0633563 | − | 0.104902i | ||||
\(316\) | 13.9973 | + | 13.5164i | 0.787409 | + | 0.760355i | ||||
\(317\) | −11.3323 | −0.636484 | −0.318242 | − | 0.948009i | \(-0.603092\pi\) | ||||
−0.318242 | + | 0.948009i | \(0.603092\pi\) | |||||||
\(318\) | −1.14954 | − | 0.884126i | −0.0644628 | − | 0.0495793i | ||||
\(319\) | −5.03299 | −0.281793 | ||||||||
\(320\) | 12.0063 | + | 10.8090i | 0.671174 | + | 0.604240i | ||||
\(321\) | −0.657856 | + | 0.371210i | −0.0367179 | + | 0.0207189i | ||||
\(322\) | 0.173204 | − | 0.0735231i | 0.00965227 | − | 0.00409728i | ||||
\(323\) | − | 0.803142i | − | 0.0446880i | ||||||
\(324\) | −17.2801 | − | 5.03966i | −0.960006 | − | 0.279981i | ||||
\(325\) | −4.52313 | −0.250898 | ||||||||
\(326\) | −11.3564 | − | 26.7531i | −0.628973 | − | 1.48172i | ||||
\(327\) | −2.88370 | − | 5.11047i | −0.159469 | − | 0.282609i | ||||
\(328\) | 8.64529 | + | 3.31826i | 0.477356 | + | 0.183220i | ||||
\(329\) | − | 2.44508i | − | 0.134801i | ||||||
\(330\) | −4.92226 | − | 3.78578i | −0.270961 | − | 0.208400i | ||||
\(331\) | −28.9555 | −1.59154 | −0.795769 | − | 0.605601i | \(-0.792933\pi\) | ||||
−0.795769 | + | 0.605601i | \(0.792933\pi\) | |||||||
\(332\) | 10.3925 | + | 10.0354i | 0.570360 | + | 0.550764i | ||||
\(333\) | 9.56366 | − | 15.8350i | 0.524085 | − | 0.867751i | ||||
\(334\) | −10.6453 | + | 4.51883i | −0.582487 | + | 0.247259i | ||||
\(335\) | − | 19.9331i | − | 1.08906i | ||||||
\(336\) | −1.29736 | − | 2.12228i | −0.0707769 | − | 0.115780i | ||||
\(337\) | 31.5174i | 1.71686i | 0.512931 | + | 0.858430i | \(0.328560\pi\) | ||||
−0.512931 | + | 0.858430i | \(0.671440\pi\) | |||||||
\(338\) | −14.4000 | + | 6.11262i | −0.783254 | + | 0.332483i | ||||
\(339\) | 9.74228 | + | 17.2652i | 0.529128 | + | 0.937716i | ||||
\(340\) | −1.48713 | + | 1.54004i | −0.0806509 | + | 0.0835205i | ||||
\(341\) | −5.68070 | − | 4.07257i | −0.307627 | − | 0.220542i | ||||
\(342\) | 6.36360 | + | 0.909021i | 0.344104 | + | 0.0491542i | ||||
\(343\) | 4.98011 | 0.268900 | ||||||||
\(344\) | 4.63724 | − | 12.0817i | 0.250023 | − | 0.651403i | ||||
\(345\) | 1.12887 | − | 0.636994i | 0.0607766 | − | 0.0342946i | ||||
\(346\) | −19.9126 | + | 8.45266i | −1.07051 | + | 0.454418i | ||||
\(347\) | − | 33.3853i | − | 1.79222i | −0.443833 | − | 0.896109i | \(-0.646382\pi\) | ||
0.443833 | − | 0.896109i | \(-0.353618\pi\) | |||||||
\(348\) | −13.4417 | − | 3.49222i | −0.720550 | − | 0.187202i | ||||
\(349\) | − | 2.59037i | − | 0.138659i | −0.997594 | − | 0.0693296i | \(-0.977914\pi\) | ||
0.997594 | − | 0.0693296i | \(-0.0220860\pi\) | |||||||
\(350\) | −0.430965 | + | 0.182940i | −0.0230361 | + | 0.00977856i | ||||
\(351\) | −0.754076 | + | 25.4774i | −0.0402496 | + | 1.35988i | ||||
\(352\) | −6.43602 | + | 3.00164i | −0.343041 | + | 0.159988i | ||||
\(353\) | −1.41331 | −0.0752228 | −0.0376114 | − | 0.999292i | \(-0.511975\pi\) | ||||
−0.0376114 | + | 0.999292i | \(0.511975\pi\) | |||||||
\(354\) | −18.6767 | + | 24.2833i | −0.992654 | + | 1.29064i | ||||
\(355\) | 4.79544i | 0.254515i | ||||||||
\(356\) | −10.0121 | + | 10.3683i | −0.530639 | + | 0.549519i | ||||
\(357\) | 0.287080 | − | 0.161992i | 0.0151939 | − | 0.00857352i | ||||
\(358\) | 10.5202 | + | 24.7832i | 0.556009 | + | 1.30983i | ||||
\(359\) | − | 17.6500i | − | 0.931529i | −0.884909 | − | 0.465765i | \(-0.845779\pi\) | ||
0.884909 | − | 0.465765i | \(-0.154221\pi\) | |||||||
\(360\) | −10.5191 | − | 13.5261i | −0.554408 | − | 0.712891i | ||||
\(361\) | 16.7044 | 0.879176 | ||||||||
\(362\) | 5.84526 | − | 2.48125i | 0.307220 | − | 0.130412i | ||||
\(363\) | −14.2158 | + | 8.02160i | −0.746136 | + | 0.421025i | ||||
\(364\) | −2.44670 | + | 2.53376i | −0.128242 | + | 0.132805i | ||||
\(365\) | − | 13.5282i | − | 0.708098i | ||||||
\(366\) | −9.32632 | + | 12.1260i | −0.487495 | + | 0.633838i | ||||
\(367\) | 13.3942i | 0.699169i | 0.936905 | + | 0.349585i | \(0.113677\pi\) | ||||
−0.936905 | + | 0.349585i | \(0.886323\pi\) | |||||||
\(368\) | −0.0518046 | − | 1.48145i | −0.00270050 | − | 0.0772257i | ||||
\(369\) | −8.40754 | − | 5.07780i | −0.437679 | − | 0.264340i | ||||
\(370\) | 16.2100 | − | 6.88096i | 0.842717 | − | 0.357724i | ||||
\(371\) | 0.212561i | 0.0110356i | ||||||||
\(372\) | −12.3457 | − | 14.8183i | −0.640096 | − | 0.768295i | ||||
\(373\) | − | 23.7437i | − | 1.22940i | −0.788760 | − | 0.614702i | \(-0.789276\pi\) | ||
0.788760 | − | 0.614702i | \(-0.210724\pi\) | |||||||
\(374\) | −0.367725 | − | 0.866278i | −0.0190146 | − | 0.0447942i | ||||
\(375\) | −18.0397 | + | 10.1793i | −0.931568 | + | 0.525659i | ||||
\(376\) | −17.9832 | − | 6.90236i | −0.927413 | − | 0.355962i | ||||
\(377\) | 19.6657i | 1.01284i | ||||||||
\(378\) | 0.958596 | + | 2.45799i | 0.0493049 | + | 0.126426i | ||||
\(379\) | − | 14.9481i | − | 0.767833i | −0.923368 | − | 0.383916i | \(-0.874575\pi\) | ||
0.923368 | − | 0.383916i | \(-0.125425\pi\) | |||||||
\(380\) | 4.40195 | + | 4.25071i | 0.225815 | + | 0.218057i | ||||
\(381\) | −16.0849 | − | 28.5055i | −0.824054 | − | 1.46038i | ||||
\(382\) | −8.67129 | − | 20.4276i | −0.443662 | − | 1.04517i | ||||
\(383\) | 15.5799 | 0.796094 | 0.398047 | − | 0.917365i | \(-0.369688\pi\) | ||||
0.398047 | + | 0.917365i | \(0.369688\pi\) | |||||||
\(384\) | −19.2715 | + | 3.55080i | −0.983446 | + | 0.181201i | ||||
\(385\) | 0.910175i | 0.0463868i | ||||||||
\(386\) | −13.0637 | + | 5.54538i | −0.664923 | + | 0.282252i | ||||
\(387\) | −7.09620 | + | 11.7495i | −0.360720 | + | 0.597260i | ||||
\(388\) | 5.86760 | − | 6.07637i | 0.297882 | − | 0.308481i | ||||
\(389\) | 1.11800i | 0.0566850i | 0.999598 | + | 0.0283425i | \(0.00902291\pi\) | ||||
−0.999598 | + | 0.0283425i | \(0.990977\pi\) | |||||||
\(390\) | −14.7925 | + | 19.2331i | −0.749045 | + | 0.973905i | ||||
\(391\) | 0.196440 | 0.00993442 | ||||||||
\(392\) | 6.96401 | − | 18.1438i | 0.351736 | − | 0.916402i | ||||
\(393\) | 8.24272 | − | 4.65115i | 0.415790 | − | 0.234619i | ||||
\(394\) | −4.76393 | − | 11.2227i | −0.240003 | − | 0.565394i | ||||
\(395\) | − | 19.6466i | − | 0.988530i | ||||||
\(396\) | 7.28005 | − | 1.93315i | 0.365836 | − | 0.0971443i | ||||
\(397\) | − | 1.26271i | − | 0.0633738i | −0.999498 | − | 0.0316869i | \(-0.989912\pi\) | ||
0.999498 | − | 0.0316869i | \(-0.0100879\pi\) | |||||||
\(398\) | −6.77238 | − | 15.9542i | −0.339469 | − | 0.799711i | ||||
\(399\) | −0.463027 | − | 0.820572i | −0.0231803 | − | 0.0410800i | ||||
\(400\) | 0.128900 | + | 3.68613i | 0.00644500 | + | 0.184306i | ||||
\(401\) | 22.4892 | 1.12306 | 0.561529 | − | 0.827457i | \(-0.310213\pi\) | ||||
0.561529 | + | 0.827457i | \(0.310213\pi\) | |||||||
\(402\) | 19.1657 | + | 14.7406i | 0.955898 | + | 0.735195i | ||||
\(403\) | −15.9130 | + | 22.1966i | −0.792685 | + | 1.10569i | ||||
\(404\) | −8.59863 | + | 8.90457i | −0.427798 | + | 0.443019i | ||||
\(405\) | 8.45935 | + | 16.0857i | 0.420348 | + | 0.799305i | ||||
\(406\) | 0.795390 | + | 1.87376i | 0.0394745 | + | 0.0929931i | ||||
\(407\) | 7.74112i | 0.383713i | ||||||||
\(408\) | −0.381011 | − | 2.56874i | −0.0188629 | − | 0.127171i | ||||
\(409\) | 22.8174i | 1.12825i | 0.825690 | + | 0.564125i | \(0.190786\pi\) | ||||
−0.825690 | + | 0.564125i | \(0.809214\pi\) | |||||||
\(410\) | −3.65343 | − | 8.60665i | −0.180430 | − | 0.425052i | ||||
\(411\) | 20.4906 | − | 11.5623i | 1.01073 | − | 0.570327i | ||||
\(412\) | −3.06712 | + | 3.17625i | −0.151106 | + | 0.156483i | ||||
\(413\) | 4.49023 | 0.220950 | ||||||||
\(414\) | −0.222337 | + | 1.55647i | −0.0109273 | + | 0.0764964i | ||||
\(415\) | − | 14.5869i | − | 0.716042i | ||||||
\(416\) | 11.7285 | + | 25.1479i | 0.575037 | + | 1.23298i | ||||
\(417\) | 0.684076 | − | 0.386006i | 0.0334994 | − | 0.0189028i | ||||
\(418\) | −2.47611 | + | 1.05108i | −0.121111 | + | 0.0514101i | ||||
\(419\) | −17.7592 | −0.867596 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(420\) | −0.631539 | + | 2.43082i | −0.0308159 | + | 0.118612i | ||||
\(421\) | 2.99995i | 0.146209i | 0.997324 | + | 0.0731043i | \(0.0232906\pi\) | ||||
−0.997324 | + | 0.0731043i | \(0.976709\pi\) | |||||||
\(422\) | 9.61575 | + | 22.6525i | 0.468087 | + | 1.10271i | ||||
\(423\) | 17.4887 | + | 10.5624i | 0.850328 | + | 0.513563i | ||||
\(424\) | 1.56336 | + | 0.600052i | 0.0759234 | + | 0.0291411i | ||||
\(425\) | −0.488782 | −0.0237094 | ||||||||
\(426\) | −4.61080 | − | 3.54624i | −0.223394 | − | 0.171816i | ||||
\(427\) | 2.24223 | 0.108509 | ||||||||
\(428\) | 0.605877 | − | 0.627435i | 0.0292862 | − | 0.0303282i | ||||
\(429\) | −5.24165 | − | 9.28920i | −0.253069 | − | 0.448487i | ||||
\(430\) | −12.0277 | + | 5.10564i | −0.580029 | + | 0.246216i | ||||
\(431\) | − | 14.5862i | − | 0.702595i | −0.936264 | − | 0.351297i | \(-0.885741\pi\) | ||
0.936264 | − | 0.351297i | \(-0.114259\pi\) | |||||||
\(432\) | 20.7843 | − | 0.111519i | 0.999986 | − | 0.00536545i | ||||
\(433\) | − | 40.3152i | − | 1.93743i | −0.248182 | − | 0.968713i | \(-0.579833\pi\) | ||
0.248182 | − | 0.968713i | \(-0.420167\pi\) | |||||||
\(434\) | −0.618448 | + | 2.75851i | −0.0296865 | + | 0.132413i | ||||
\(435\) | 6.89115 | + | 12.2124i | 0.330405 | + | 0.585541i | ||||
\(436\) | 4.87414 | + | 4.70668i | 0.233429 | + | 0.225409i | ||||
\(437\) | − | 0.561492i | − | 0.0268598i | ||||||
\(438\) | 13.0073 | + | 10.0041i | 0.621515 | + | 0.478016i | ||||
\(439\) | −1.28668 | −0.0614097 | −0.0307049 | − | 0.999528i | \(-0.509775\pi\) | ||||
−0.0307049 | + | 0.999528i | \(0.509775\pi\) | |||||||
\(440\) | 6.69422 | + | 2.56939i | 0.319134 | + | 0.122491i | ||||
\(441\) | −10.6568 | + | 17.6449i | −0.507465 | + | 0.840232i | ||||
\(442\) | −3.38487 | + | 1.43684i | −0.161002 | + | 0.0683435i | ||||
\(443\) | 24.5573 | 1.16675 | 0.583375 | − | 0.812203i | \(-0.301732\pi\) | ||||
0.583375 | + | 0.812203i | \(0.301732\pi\) | |||||||
\(444\) | −5.37130 | + | 20.6744i | −0.254910 | + | 0.981162i | ||||
\(445\) | 14.5530 | 0.689878 | ||||||||
\(446\) | 7.40070 | + | 17.4344i | 0.350433 | + | 0.825541i | ||||
\(447\) | −29.6091 | + | 16.7076i | −1.40046 | + | 0.790244i | ||||
\(448\) | 2.13461 | + | 1.92174i | 0.100851 | + | 0.0907935i | ||||
\(449\) | 15.8486 | 0.747944 | 0.373972 | − | 0.927440i | \(-0.377996\pi\) | ||||
0.373972 | + | 0.927440i | \(0.377996\pi\) | |||||||
\(450\) | 0.553219 | − | 3.87281i | 0.0260790 | − | 0.182566i | ||||
\(451\) | 4.11013 | 0.193538 | ||||||||
\(452\) | −16.4668 | − | 15.9010i | −0.774533 | − | 0.747922i | ||||
\(453\) | −2.43798 | − | 4.32057i | −0.114546 | − | 0.202998i | ||||
\(454\) | 19.0497 | − | 8.08637i | 0.894045 | − | 0.379512i | ||||
\(455\) | 3.55639 | 0.166726 | ||||||||
\(456\) | −7.34231 | + | 1.08906i | −0.343835 | + | 0.0509998i | ||||
\(457\) | 20.3442i | 0.951661i | 0.879537 | + | 0.475830i | \(0.157852\pi\) | ||||
−0.879537 | + | 0.475830i | \(0.842148\pi\) | |||||||
\(458\) | 22.3708 | − | 9.49615i | 1.04532 | − | 0.443726i | ||||
\(459\) | −0.0814877 | + | 2.75316i | −0.00380352 | + | 0.128507i | ||||
\(460\) | −1.03968 | + | 1.07667i | −0.0484754 | + | 0.0502001i | ||||
\(461\) | 24.3721i | 1.13512i | 0.823332 | + | 0.567560i | \(0.192113\pi\) | ||||
−0.823332 | + | 0.567560i | \(0.807887\pi\) | |||||||
\(462\) | −0.875132 | − | 0.673077i | −0.0407148 | − | 0.0313144i | ||||
\(463\) | − | 23.7526i | − | 1.10388i | −0.833885 | − | 0.551939i | \(-0.813888\pi\) | ||
0.833885 | − | 0.551939i | \(-0.186112\pi\) | |||||||
\(464\) | 16.0266 | − | 0.560434i | 0.744017 | − | 0.0260175i | ||||
\(465\) | −2.10400 | + | 19.3602i | −0.0975707 | + | 0.897809i | ||||
\(466\) | 2.36855 | + | 5.57976i | 0.109721 | + | 0.258477i | ||||
\(467\) | −29.7836 | −1.37822 | −0.689110 | − | 0.724656i | \(-0.741999\pi\) | ||||
−0.689110 | + | 0.724656i | \(0.741999\pi\) | |||||||
\(468\) | −7.55352 | − | 28.4458i | −0.349162 | − | 1.31491i | ||||
\(469\) | − | 3.54393i | − | 0.163643i | ||||||
\(470\) | 7.59956 | + | 17.9028i | 0.350542 | + | 0.825796i | ||||
\(471\) | −14.9315 | − | 26.4614i | −0.688005 | − | 1.21928i | ||||
\(472\) | 12.6758 | − | 33.0251i | 0.583450 | − | 1.52010i | ||||
\(473\) | − | 5.74388i | − | 0.264104i | ||||||
\(474\) | 18.8902 | + | 14.5287i | 0.867656 | + | 0.667327i | ||||
\(475\) | 1.39710i | 0.0641035i | ||||||||
\(476\) | −0.264398 | + | 0.273805i | −0.0121187 | + | 0.0125498i | ||||
\(477\) | −1.52037 | − | 0.918237i | −0.0696127 | − | 0.0420432i | ||||
\(478\) | −35.1434 | + | 14.9180i | −1.60742 | + | 0.682333i | ||||
\(479\) | − | 17.3877i | − | 0.794466i | −0.917718 | − | 0.397233i | \(-0.869970\pi\) | ||
0.917718 | − | 0.397233i | \(-0.130030\pi\) | |||||||
\(480\) | 16.0956 | + | 11.5070i | 0.734659 | + | 0.525221i | ||||
\(481\) | 30.2474 | 1.37916 | ||||||||
\(482\) | 12.2086 | + | 28.7606i | 0.556085 | + | 1.31001i | ||||
\(483\) | 0.200704 | − | 0.113252i | 0.00913233 | − | 0.00515313i | ||||
\(484\) | 13.0926 | − | 13.5584i | 0.595118 | − | 0.616292i | ||||
\(485\) | −8.52882 | −0.387274 | ||||||||
\(486\) | −21.7221 | − | 3.76177i | −0.985334 | − | 0.170637i | ||||
\(487\) | 14.3592i | 0.650679i | 0.945597 | + | 0.325339i | \(0.105479\pi\) | ||||
−0.945597 | + | 0.325339i | \(0.894521\pi\) | |||||||
\(488\) | 6.32973 | − | 16.4913i | 0.286533 | − | 0.746526i | ||||
\(489\) | −17.4929 | − | 31.0007i | −0.791056 | − | 1.40190i | ||||
\(490\) | −18.0627 | + | 7.66743i | −0.815991 | + | 0.346379i | ||||
\(491\) | − | 11.3456i | − | 0.512019i | −0.966674 | − | 0.256009i | \(-0.917592\pi\) | ||
0.966674 | − | 0.256009i | \(-0.0824078\pi\) | |||||||
\(492\) | 10.9770 | + | 2.85188i | 0.494881 | + | 0.128573i | ||||
\(493\) | 2.12514i | 0.0957113i | ||||||||
\(494\) | 4.10697 | + | 9.67508i | 0.184781 | + | 0.435303i | ||||
\(495\) | −6.51013 | − | 3.93184i | −0.292608 | − | 0.176723i | ||||
\(496\) | 18.5426 | + | 12.3358i | 0.832588 | + | 0.553893i | ||||
\(497\) | 0.852584i | 0.0382436i | ||||||||
\(498\) | 14.0253 | + | 10.7870i | 0.628488 | + | 0.483379i | ||||
\(499\) | 34.9340 | 1.56386 | 0.781931 | − | 0.623365i | \(-0.214235\pi\) | ||||
0.781931 | + | 0.623365i | \(0.214235\pi\) | |||||||
\(500\) | 16.6144 | − | 17.2055i | 0.743018 | − | 0.769455i | ||||
\(501\) | −12.3355 | + | 6.96060i | −0.551110 | + | 0.310977i | ||||
\(502\) | −8.51021 | − | 20.0481i | −0.379829 | − | 0.894792i | ||||
\(503\) | − | 4.42949i | − | 0.197501i | −0.995112 | − | 0.0987506i | \(-0.968515\pi\) | ||
0.995112 | − | 0.0987506i | \(-0.0314846\pi\) | |||||||
\(504\) | −1.87021 | − | 2.40482i | −0.0833056 | − | 0.107119i | ||||
\(505\) | 12.4985 | 0.556175 | ||||||||
\(506\) | −0.257084 | − | 0.605632i | −0.0114288 | − | 0.0269236i | ||||
\(507\) | −16.6862 | + | 9.41560i | −0.741062 | + | 0.418162i | ||||
\(508\) | 27.1873 | + | 26.2532i | 1.20624 | + | 1.16480i | ||||
\(509\) | 22.3665i | 0.991377i | 0.868500 | + | 0.495688i | \(0.165084\pi\) | ||||
−0.868500 | + | 0.495688i | \(0.834916\pi\) | |||||||
\(510\) | −1.59851 | + | 2.07838i | −0.0707834 | + | 0.0920323i | ||||
\(511\) | − | 2.40519i | − | 0.106399i | ||||||
\(512\) | 20.1601 | − | 10.2748i | 0.890957 | − | 0.454087i | ||||
\(513\) | 7.86945 | + | 0.232919i | 0.347445 | + | 0.0102836i | ||||
\(514\) | 5.15102 | + | 12.1346i | 0.227202 | + | 0.535236i | ||||
\(515\) | 4.45819 | 0.196451 | ||||||||
\(516\) | 3.98548 | − | 15.3403i | 0.175451 | − | 0.675318i | ||||
\(517\) | −8.54955 | −0.376009 | ||||||||
\(518\) | 2.88198 | − | 1.22337i | 0.126627 | − | 0.0537518i | ||||
\(519\) | −23.0741 | + | 13.0201i | −1.01284 | + | 0.571519i | ||||
\(520\) | 10.0396 | − | 26.1568i | 0.440264 | − | 1.14705i | ||||
\(521\) | − | 0.310368i | − | 0.0135975i | −0.999977 | − | 0.00679874i | \(-0.997836\pi\) | ||
0.999977 | − | 0.00679874i | \(-0.00216412\pi\) | |||||||
\(522\) | −16.8382 | − | 2.40529i | −0.736990 | − | 0.105277i | ||||
\(523\) | −3.12326 | −0.136570 | −0.0682852 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682852 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(524\) | −7.59145 | + | 7.86155i | −0.331634 | + | 0.343434i | ||||
\(525\) | −0.499390 | + | 0.281793i | −0.0217952 | + | 0.0122984i | ||||
\(526\) | 31.5250 | − | 13.3820i | 1.37455 | − | 0.583483i | ||||
\(527\) | −1.71961 | + | 2.39863i | −0.0749073 | + | 0.104486i | ||||
\(528\) | −7.42086 | + | 4.53641i | −0.322952 | + | 0.197422i | ||||
\(529\) | −22.8627 | −0.994029 | ||||||||
\(530\) | −0.660662 | − | 1.55637i | −0.0286973 | − | 0.0676044i | ||||
\(531\) | −19.3972 | + | 32.1169i | −0.841769 | + | 1.39375i | ||||
\(532\) | 0.782626 | + | 0.755737i | 0.0339312 | + | 0.0327654i | ||||
\(533\) | − | 16.0598i | − | 0.695627i | ||||||
\(534\) | −10.7620 | + | 13.9927i | −0.465716 | + | 0.605523i | ||||
\(535\) | −0.880669 | −0.0380747 | ||||||||
\(536\) | −26.0651 | − | 10.0044i | −1.12584 | − | 0.432124i | ||||
\(537\) | 16.2048 | + | 28.7180i | 0.699289 | + | 1.23927i | ||||
\(538\) | −17.7986 | − | 41.9294i | −0.767351 | − | 1.80770i | ||||
\(539\) | − | 8.62591i | − | 0.371544i | ||||||
\(540\) | −14.6586 | − | 15.0180i | −0.630804 | − | 0.646272i | ||||
\(541\) | − | 37.9126i | − | 1.62999i | −0.579467 | − | 0.814996i | \(-0.696739\pi\) | ||
0.579467 | − | 0.814996i | \(-0.303261\pi\) | |||||||
\(542\) | 9.55656 | + | 22.5131i | 0.410489 | + | 0.967020i | ||||
\(543\) | 6.77331 | − | 3.82200i | 0.290671 | − | 0.164018i | ||||
\(544\) | 1.26742 | + | 2.71755i | 0.0543400 | + | 0.116514i | ||||
\(545\) | − | 6.84136i | − | 0.293052i | ||||||
\(546\) | −2.62996 | + | 3.41946i | −0.112552 | + | 0.146340i | ||||
\(547\) | 24.7663i | 1.05893i | 0.848331 | + | 0.529466i | \(0.177608\pi\) | ||||
−0.848331 | + | 0.529466i | \(0.822392\pi\) | |||||||
\(548\) | −18.8716 | + | 19.5431i | −0.806156 | + | 0.834839i | ||||
\(549\) | −9.68615 | + | 16.0378i | −0.413395 | + | 0.684476i | ||||
\(550\) | 0.639676 | + | 1.50693i | 0.0272759 | + | 0.0642558i | ||||
\(551\) | 6.07435 | 0.258776 | ||||||||
\(552\) | −0.266372 | − | 1.79585i | −0.0113376 | − | 0.0764366i | ||||
\(553\) | − | 3.49299i | − | 0.148537i | ||||||
\(554\) | 26.4232 | − | 11.2164i | 1.12262 | − | 0.476538i | ||||
\(555\) | 18.7836 | − | 10.5991i | 0.797321 | − | 0.449907i | ||||
\(556\) | −0.630026 | + | 0.652443i | −0.0267191 | + | 0.0276697i | ||||
\(557\) | − | 25.0783i | − | 1.06260i | −0.847183 | − | 0.531302i | \(-0.821703\pi\) | ||
0.847183 | − | 0.531302i | \(-0.178297\pi\) | |||||||
\(558\) | −17.0589 | − | 16.3399i | −0.722161 | − | 0.691725i | ||||
\(559\) | −22.4435 | −0.949257 | ||||||||
\(560\) | −0.101350 | − | 2.89828i | −0.00428282 | − | 0.122475i | ||||
\(561\) | −0.566427 | − | 1.00382i | −0.0239146 | − | 0.0423812i | ||||
\(562\) | −17.4589 | − | 41.1293i | −0.736460 | − | 1.73493i | ||||
\(563\) | −22.1982 | −0.935541 | −0.467770 | − | 0.883850i | \(-0.654943\pi\) | ||||
−0.467770 | + | 0.883850i | \(0.654943\pi\) | |||||||
\(564\) | −22.8335 | − | 5.93224i | −0.961462 | − | 0.249792i | ||||
\(565\) | 23.1128i | 0.972365i | ||||||||
\(566\) | 5.67552 | + | 13.3702i | 0.238560 | + | 0.561993i | ||||
\(567\) | 1.50399 | + | 2.85989i | 0.0631618 | + | 0.120104i | ||||
\(568\) | 6.27065 | + | 2.40682i | 0.263111 | + | 0.100988i | ||||
\(569\) | 3.66233 | 0.153533 | 0.0767665 | − | 0.997049i | \(-0.475540\pi\) | ||||
0.0767665 | + | 0.997049i | \(0.475540\pi\) | |||||||
\(570\) | 5.94071 | + | 4.56909i | 0.248829 | + | 0.191378i | ||||
\(571\) | −29.0424 | −1.21539 | −0.607693 | − | 0.794172i | \(-0.707905\pi\) | ||||
−0.607693 | + | 0.794172i | \(0.707905\pi\) | |||||||
\(572\) | 8.85964 | + | 8.55524i | 0.370440 | + | 0.357713i | ||||
\(573\) | −13.3569 | − | 23.6709i | −0.557990 | − | 0.988865i | ||||
\(574\) | −0.649546 | − | 1.53018i | −0.0271115 | − | 0.0638686i | ||||
\(575\) | −0.341717 | −0.0142506 | ||||||||
\(576\) | −22.9667 | + | 6.96640i | −0.956946 | + | 0.290266i | ||||
\(577\) | −28.7589 | −1.19725 | −0.598624 | − | 0.801030i | \(-0.704286\pi\) | ||||
−0.598624 | + | 0.801030i | \(0.704286\pi\) | |||||||
\(578\) | 21.7645 | − | 9.23881i | 0.905286 | − | 0.384284i | ||||
\(579\) | −15.1378 | + | 8.54185i | −0.629105 | + | 0.354987i | ||||
\(580\) | −11.6477 | − | 11.2475i | −0.483644 | − | 0.467027i | ||||
\(581\) | − | 2.59341i | − | 0.107593i | ||||||
\(582\) | 6.30709 | − | 8.20045i | 0.261437 | − | 0.339919i | ||||
\(583\) | 0.743249 | 0.0307822 | ||||||||
\(584\) | −17.6898 | − | 6.78976i | −0.732011 | − | 0.280962i | ||||
\(585\) | −15.3632 | + | 25.4375i | −0.635189 | + | 1.05171i | ||||
\(586\) | 18.1662 | − | 7.71135i | 0.750438 | − | 0.318553i | ||||
\(587\) | 15.3051i | 0.631710i | 0.948807 | + | 0.315855i | \(0.102291\pi\) | ||||
−0.948807 | + | 0.315855i | \(0.897709\pi\) | |||||||
\(588\) | 5.98522 | − | 23.0374i | 0.246826 | − | 0.950046i | ||||
\(589\) | 6.85608 | + | 4.91521i | 0.282500 | + | 0.202528i | ||||
\(590\) | −32.8775 | + | 13.9561i | −1.35354 | + | 0.574565i | ||||
\(591\) | −7.33814 | − | 13.0046i | −0.301851 | − | 0.534937i | ||||
\(592\) | −0.861990 | − | 24.6502i | −0.0354276 | − | 1.01312i | ||||
\(593\) | 34.4043i | 1.41282i | 0.707804 | + | 0.706409i | \(0.249686\pi\) | ||||
−0.707804 | + | 0.706409i | \(0.750314\pi\) | |||||||
\(594\) | 8.59472 | − | 3.35187i | 0.352646 | − | 0.137529i | ||||
\(595\) | 0.384314 | 0.0157553 | ||||||||
\(596\) | 27.2696 | − | 28.2399i | 1.11701 | − | 1.15675i | ||||
\(597\) | −10.4319 | − | 18.4872i | −0.426948 | − | 0.756632i | ||||
\(598\) | −2.36643 | + | 1.00452i | −0.0967704 | + | 0.0410780i | ||||
\(599\) | − | 35.1757i | − | 1.43724i | −0.695402 | − | 0.718621i | \(-0.744774\pi\) | ||
0.695402 | − | 0.718621i | \(-0.255226\pi\) | |||||||
\(600\) | 0.662787 | + | 4.46844i | 0.0270582 | + | 0.182423i | ||||
\(601\) | 12.1715i | 0.496487i | 0.968698 | + | 0.248244i | \(0.0798533\pi\) | ||||
−0.968698 | + | 0.248244i | \(0.920147\pi\) | |||||||
\(602\) | −2.13842 | + | 0.907736i | −0.0871555 | + | 0.0369965i | ||||
\(603\) | 25.3483 | + | 15.3093i | 1.03226 | + | 0.623444i | ||||
\(604\) | 4.12077 | + | 3.97919i | 0.167672 | + | 0.161911i | ||||
\(605\) | −19.0307 | −0.773706 | ||||||||
\(606\) | −9.24266 | + | 12.0173i | −0.375457 | + | 0.488168i | ||||
\(607\) | 11.2629 | 0.457147 | 0.228573 | − | 0.973527i | \(-0.426594\pi\) | ||||
0.228573 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(608\) | 7.76768 | − | 3.62270i | 0.315021 | − | 0.146920i | ||||
\(609\) | 1.22518 | + | 2.17126i | 0.0496469 | + | 0.0879837i | ||||
\(610\) | −16.4176 | + | 6.96909i | −0.664729 | + | 0.282170i | ||||
\(611\) | 33.4063i | 1.35147i | ||||||||
\(612\) | −0.816255 | − | 3.07394i | −0.0329952 | − | 0.124257i | ||||
\(613\) | 47.1446 | 1.90415 | 0.952076 | − | 0.305860i | \(-0.0989440\pi\) | ||||
0.952076 | + | 0.305860i | \(0.0989440\pi\) | |||||||
\(614\) | 3.53592 | + | 8.32984i | 0.142698 | + | 0.336165i | ||||
\(615\) | −5.62757 | − | 9.97313i | −0.226926 | − | 0.402155i | ||||
\(616\) | 1.19017 | + | 0.456814i | 0.0479533 | + | 0.0184056i | ||||
\(617\) | − | 0.713094i | − | 0.0287081i | −0.999897 | − | 0.0143540i | \(-0.995431\pi\) | ||
0.999897 | − | 0.0143540i | \(-0.00456919\pi\) | |||||||
\(618\) | −3.29685 | + | 4.28655i | −0.132619 | + | 0.172430i | ||||
\(619\) | 21.4057 | 0.860367 | 0.430184 | − | 0.902741i | \(-0.358449\pi\) | ||||
0.430184 | + | 0.902741i | \(0.358449\pi\) | |||||||
\(620\) | −4.04547 | − | 22.1200i | −0.162470 | − | 0.888361i | ||||
\(621\) | −0.0569696 | + | 1.92479i | −0.00228611 | + | 0.0772391i | ||||
\(622\) | −2.43573 | − | 5.73802i | −0.0976637 | − | 0.230074i | ||||
\(623\) | 2.58739 | 0.103661 | ||||||||
\(624\) | 17.7254 | + | 28.9961i | 0.709585 | + | 1.16077i | ||||
\(625\) | −19.5393 | −0.781571 | ||||||||
\(626\) | −9.27737 | − | 21.8554i | −0.370798 | − | 0.873517i | ||||
\(627\) | −2.86924 | + | 1.61904i | −0.114587 | + | 0.0646582i | ||||
\(628\) | 25.2377 | + | 24.3706i | 1.00709 | + | 0.972494i | ||||
\(629\) | 3.26862 | 0.130329 | ||||||||
\(630\) | −0.434978 | + | 3.04506i | −0.0173299 | + | 0.121318i | ||||
\(631\) | − | 24.5796i | − | 0.978497i | −0.872144 | − | 0.489248i | \(-0.837271\pi\) | ||
0.872144 | − | 0.489248i | \(-0.162729\pi\) | |||||||
\(632\) | −25.6905 | − | 9.86059i | −1.02191 | − | 0.392233i | ||||
\(633\) | 14.8117 | + | 26.2491i | 0.588711 | + | 1.04331i | ||||
\(634\) | 14.7522 | − | 6.26214i | 0.585884 | − | 0.248701i | ||||
\(635\) | − | 38.1602i | − | 1.51434i | ||||||
\(636\) | 1.98501 | + | 0.515715i | 0.0787108 | + | 0.0204494i | ||||
\(637\) | −33.7046 | −1.33543 | ||||||||
\(638\) | 6.55186 | − | 2.78119i | 0.259391 | − | 0.110108i | ||||
\(639\) | −6.09820 | − | 3.68306i | −0.241241 | − | 0.145700i | ||||
\(640\) | −21.6026 | − | 7.43634i | −0.853918 | − | 0.293947i | ||||
\(641\) | 28.8232 | 1.13845 | 0.569225 | − | 0.822182i | \(-0.307243\pi\) | ||||
0.569225 | + | 0.822182i | \(0.307243\pi\) | |||||||
\(642\) | 0.651257 | − | 0.846762i | 0.0257031 | − | 0.0334190i | ||||
\(643\) | 45.5128 | 1.79485 | 0.897424 | − | 0.441169i | \(-0.145436\pi\) | ||||
0.897424 | + | 0.441169i | \(0.145436\pi\) | |||||||
\(644\) | −0.184846 | + | 0.191422i | −0.00728394 | + | 0.00754310i | ||||
\(645\) | −13.9374 | + | 7.86450i | −0.548784 | + | 0.309664i | ||||
\(646\) | 0.443811 | + | 1.04552i | 0.0174615 | + | 0.0411353i | ||||
\(647\) | −19.2950 | −0.758563 | −0.379281 | − | 0.925281i | \(-0.623829\pi\) | ||||
−0.379281 | + | 0.925281i | \(0.623829\pi\) | |||||||
\(648\) | 25.2798 | − | 2.98832i | 0.993086 | − | 0.117392i | ||||
\(649\) | − | 15.7007i | − | 0.616307i | ||||||
\(650\) | 5.88814 | − | 2.49945i | 0.230952 | − | 0.0980365i | ||||
\(651\) | −0.374072 | + | 3.44207i | −0.0146610 | + | 0.134905i | ||||
\(652\) | 29.5672 | + | 28.5513i | 1.15794 | + | 1.11816i | ||||
\(653\) | 20.6505 | 0.808116 | 0.404058 | − | 0.914733i | \(-0.367599\pi\) | ||||
0.404058 | + | 0.914733i | \(0.367599\pi\) | |||||||
\(654\) | 6.57796 | + | 5.05921i | 0.257219 | + | 0.197831i | ||||
\(655\) | 11.0345 | 0.431154 | ||||||||
\(656\) | −13.0879 | + | 0.457671i | −0.510998 | + | 0.0178691i | ||||
\(657\) | 17.2034 | + | 10.3901i | 0.671167 | + | 0.405357i | ||||
\(658\) | 1.35113 | + | 3.18296i | 0.0526726 | + | 0.124085i | ||||
\(659\) | 17.0833 | 0.665470 | 0.332735 | − | 0.943020i | \(-0.392029\pi\) | ||||
0.332735 | + | 0.943020i | \(0.392029\pi\) | |||||||
\(660\) | 8.49971 | + | 2.20826i | 0.330851 | + | 0.0859566i | ||||
\(661\) | − | 34.9359i | − | 1.35885i | −0.733745 | − | 0.679425i | \(-0.762229\pi\) | ||
0.733745 | − | 0.679425i | \(-0.237771\pi\) | |||||||
\(662\) | 37.6938 | − | 16.0006i | 1.46501 | − | 0.621881i | ||||
\(663\) | −3.92229 | + | 2.21324i | −0.152329 | + | 0.0859552i | ||||
\(664\) | −19.0742 | − | 7.32112i | −0.740224 | − | 0.284115i | ||||
\(665\) | − | 1.09850i | − | 0.0425979i | ||||||
\(666\) | −3.69953 | + | 25.8985i | −0.143354 | + | 1.00355i | ||||
\(667\) | 1.48572i | 0.0575274i | ||||||||
\(668\) | 11.3609 | − | 11.7651i | 0.439565 | − | 0.455205i | ||||
\(669\) | 11.3997 | + | 20.2024i | 0.440738 | + | 0.781071i | ||||
\(670\) | 11.0149 | + | 25.9486i | 0.425543 | + | 1.00248i | ||||
\(671\) | − | 7.84026i | − | 0.302670i | ||||||
\(672\) | 2.86164 | + | 2.04584i | 0.110390 | + | 0.0789200i | ||||
\(673\) | 9.63430i | 0.371375i | 0.982609 | + | 0.185687i | \(0.0594512\pi\) | ||||
−0.982609 | + | 0.185687i | \(0.940549\pi\) | |||||||
\(674\) | −17.4163 | − | 41.0288i | −0.670850 | − | 1.58037i | ||||
\(675\) | 0.141752 | − | 4.78925i | 0.00545602 | − | 0.184338i | ||||
\(676\) | 15.3678 | − | 15.9146i | 0.591071 | − | 0.612101i | ||||
\(677\) | 8.42522i | 0.323808i | 0.986807 | + | 0.161904i | \(0.0517634\pi\) | ||||
−0.986807 | + | 0.161904i | \(0.948237\pi\) | |||||||
\(678\) | −22.2230 | − | 17.0920i | −0.853468 | − | 0.656415i | ||||
\(679\) | −1.51635 | −0.0581920 | ||||||||
\(680\) | 1.08490 | − | 2.82658i | 0.0416042 | − | 0.108394i | ||||
\(681\) | 22.0742 | − | 12.4559i | 0.845885 | − | 0.477310i | ||||
\(682\) | 9.64551 | + | 2.16249i | 0.369346 | + | 0.0828060i | ||||
\(683\) | 35.2639 | 1.34934 | 0.674669 | − | 0.738121i | \(-0.264287\pi\) | ||||
0.674669 | + | 0.738121i | \(0.264287\pi\) | |||||||
\(684\) | −8.78634 | + | 2.33313i | −0.335954 | + | 0.0892094i | ||||
\(685\) | 27.4307 | 1.04807 | ||||||||
\(686\) | −6.48302 | + | 2.75197i | −0.247523 | + | 0.105071i | ||||
\(687\) | 25.9226 | − | 14.6274i | 0.989009 | − | 0.558072i | ||||
\(688\) | 0.639593 | + | 18.2903i | 0.0243842 | + | 0.697311i | ||||
\(689\) | − | 2.90415i | − | 0.110639i | ||||||
\(690\) | −1.11755 | + | 1.45304i | −0.0425445 | + | 0.0553162i | ||||
\(691\) | 32.6503i | 1.24208i | 0.783780 | + | 0.621038i | \(0.213289\pi\) | ||||
−0.783780 | + | 0.621038i | \(0.786711\pi\) | |||||||
\(692\) | 21.2510 | − | 22.0071i | 0.807840 | − | 0.836583i | ||||
\(693\) | −1.15744 | − | 0.699046i | −0.0439675 | − | 0.0265545i | ||||
\(694\) | 18.4485 | + | 43.4605i | 0.700296 | + | 1.64974i | ||||
\(695\) | 0.915771 | 0.0347372 | ||||||||
\(696\) | 19.4280 | − | 2.88168i | 0.736415 | − | 0.109230i | ||||
\(697\) | − | 1.73547i | − | 0.0657355i | ||||||
\(698\) | 1.43142 | + | 3.37210i | 0.0541800 | + | 0.127636i | ||||
\(699\) | 3.64840 | + | 6.46566i | 0.137995 | + | 0.244554i | ||||
\(700\) | 0.459932 | − | 0.476297i | 0.0173838 | − | 0.0180023i | ||||
\(701\) | 30.5160 | 1.15257 | 0.576287 | − | 0.817248i | \(-0.304501\pi\) | ||||
0.576287 | + | 0.817248i | \(0.304501\pi\) | |||||||
\(702\) | −13.0970 | − | 33.5828i | −0.494314 | − | 1.26750i | ||||
\(703\) | − | 9.34281i | − | 0.352371i | ||||||
\(704\) | 6.71962 | − | 7.46398i | 0.253255 | − | 0.281309i | ||||
\(705\) | 11.7060 | + | 20.7453i | 0.440874 | + | 0.781313i | ||||
\(706\) | 1.83982 | − | 0.780984i | 0.0692426 | − | 0.0293927i | ||||
\(707\) | 2.22211 | 0.0835712 | ||||||||
\(708\) | 10.8942 | − | 41.9322i | 0.409429 | − | 1.57591i | ||||
\(709\) | 12.8448 | 0.482396 | 0.241198 | − | 0.970476i | \(-0.422460\pi\) | ||||
0.241198 | + | 0.970476i | \(0.422460\pi\) | |||||||
\(710\) | −2.64992 | − | 6.24262i | −0.0994499 | − | 0.234281i | ||||
\(711\) | 24.9840 | + | 15.0893i | 0.936973 | + | 0.565893i | ||||
\(712\) | 7.30411 | − | 19.0299i | 0.273733 | − | 0.713176i | ||||
\(713\) | −1.20221 | + | 1.67693i | −0.0450232 | + | 0.0628014i | ||||
\(714\) | −0.284201 | + | 0.369517i | −0.0106360 | + | 0.0138288i | ||||
\(715\) | − | 12.4354i | − | 0.465058i | ||||||
\(716\) | −27.3900 | − | 26.4489i | −1.02361 | − | 0.988443i | ||||
\(717\) | −40.7232 | + | 22.9790i | −1.52083 | + | 0.858167i | ||||
\(718\) | 9.75324 | + | 22.9764i | 0.363988 | + | 0.857473i | ||||
\(719\) | −0.729364 | −0.0272007 | −0.0136003 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0136003 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(720\) | 21.1681 | + | 11.7953i | 0.788889 | + | 0.439585i | ||||
\(721\) | 0.792626 | 0.0295189 | ||||||||
\(722\) | −21.7455 | + | 9.23071i | −0.809282 | + | 0.343531i | ||||
\(723\) | 18.8055 | + | 33.3269i | 0.699384 | + | 1.23944i | ||||
\(724\) | −6.23814 | + | 6.46010i | −0.231839 | + | 0.240088i | ||||
\(725\) | − | 3.69677i | − | 0.137295i | ||||||
\(726\) | 14.0732 | − | 18.2979i | 0.522306 | − | 0.679100i | ||||
\(727\) | −28.9918 | −1.07525 | −0.537624 | − | 0.843185i | \(-0.680678\pi\) | ||||
−0.537624 | + | 0.843185i | \(0.680678\pi\) | |||||||
\(728\) | 1.78494 | − | 4.65044i | 0.0661544 | − | 0.172357i | ||||
\(729\) | −26.9527 | − | 1.59689i | −0.998249 | − | 0.0591439i | ||||
\(730\) | 7.47559 | + | 17.6108i | 0.276684 | + | 0.651804i | ||||
\(731\) | −2.42530 | −0.0897031 | ||||||||
\(732\) | 5.44009 | − | 20.9391i | 0.201071 | − | 0.773933i | ||||
\(733\) | 9.05166i | 0.334331i | 0.985929 | + | 0.167165i | \(0.0534614\pi\) | ||||
−0.985929 | + | 0.167165i | \(0.946539\pi\) | |||||||
\(734\) | −7.40152 | − | 17.4363i | −0.273195 | − | 0.643586i | ||||
\(735\) | −20.9306 | + | 11.8106i | −0.772036 | + | 0.435639i | ||||
\(736\) | 0.886075 | + | 1.89989i | 0.0326611 | + | 0.0700310i | ||||
\(737\) | −12.3918 | −0.456459 | ||||||||
\(738\) | 13.7508 | + | 1.96426i | 0.506172 | + | 0.0723052i | ||||
\(739\) | 45.0935 | 1.65879 | 0.829396 | − | 0.558661i | \(-0.188685\pi\) | ||||
0.829396 | + | 0.558661i | \(0.188685\pi\) | |||||||
\(740\) | −17.2995 | + | 17.9150i | −0.635943 | + | 0.658570i | ||||
\(741\) | 6.32618 | + | 11.2112i | 0.232398 | + | 0.411854i | ||||
\(742\) | −0.117460 | − | 0.276708i | −0.00431208 | − | 0.0101583i | ||||
\(743\) | 40.4715 | 1.48475 | 0.742377 | − | 0.669983i | \(-0.233698\pi\) | ||||
0.742377 | + | 0.669983i | \(0.233698\pi\) | |||||||
\(744\) | 24.2600 | + | 12.4681i | 0.889414 | + | 0.457103i | ||||
\(745\) | −39.6376 | −1.45221 | ||||||||
\(746\) | 13.1206 | + | 30.9092i | 0.480380 | + | 1.13167i | ||||
\(747\) | 18.5497 | + | 11.2032i | 0.678697 | + | 0.409905i | ||||
\(748\) | 0.957398 | + | 0.924504i | 0.0350059 | + | 0.0338032i | ||||
\(749\) | −0.156575 | −0.00572112 | ||||||||
\(750\) | 17.8588 | − | 23.2199i | 0.652111 | − | 0.847872i | ||||
\(751\) | 27.5619 | 1.00575 | 0.502873 | − | 0.864360i | \(-0.332276\pi\) | ||||
0.502873 | + | 0.864360i | \(0.332276\pi\) | |||||||
\(752\) | 27.2245 | − | 0.952010i | 0.992774 | − | 0.0347162i | ||||
\(753\) | −13.1087 | − | 23.2312i | −0.477709 | − | 0.846592i | ||||
\(754\) | −10.8671 | − | 25.6005i | −0.395758 | − | 0.932317i | ||||
\(755\) | − | 5.78393i | − | 0.210499i | ||||||
\(756\) | −2.60615 | − | 2.67006i | −0.0947849 | − | 0.0971092i | ||||
\(757\) | 24.0859 | 0.875417 | 0.437708 | − | 0.899117i | \(-0.355790\pi\) | ||||
0.437708 | + | 0.899117i | \(0.355790\pi\) | |||||||
\(758\) | 8.26022 | + | 19.4592i | 0.300025 | + | 0.706790i | ||||
\(759\) | −0.396000 | − | 0.701788i | −0.0143739 | − | 0.0254733i | ||||
\(760\) | −8.07930 | − | 3.10102i | −0.293067 | − | 0.112486i | ||||
\(761\) | 16.0015 | 0.580056 | 0.290028 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290028 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(762\) | 36.6910 | + | 28.2196i | 1.32917 | + | 1.02229i | ||||
\(763\) | − | 1.21633i | − | 0.0440341i | ||||||
\(764\) | 22.5763 | + | 21.8006i | 0.816781 | + | 0.788718i | ||||
\(765\) | −1.66019 | + | 2.74885i | −0.0600242 | + | 0.0993848i | ||||
\(766\) | −20.2816 | + | 8.60933i | −0.732805 | + | 0.311068i | ||||
\(767\) | −61.3485 | −2.21517 | ||||||||
\(768\) | 23.1252 | − | 15.2717i | 0.834459 | − | 0.551069i | ||||
\(769\) | 0.443249 | 0.0159840 | 0.00799199 | − | 0.999968i | \(-0.497456\pi\) | ||||
0.00799199 | + | 0.999968i | \(0.497456\pi\) | |||||||
\(770\) | −0.502956 | − | 1.18485i | −0.0181253 | − | 0.0426991i | ||||
\(771\) | 7.93440 | + | 14.0613i | 0.285750 | + | 0.506404i | ||||
\(772\) | 13.9417 | − | 14.4378i | 0.501774 | − | 0.519627i | ||||
\(773\) | 25.3696i | 0.912482i | 0.889856 | + | 0.456241i | \(0.150805\pi\) | ||||
−0.889856 | + | 0.456241i | \(0.849195\pi\) | |||||||
\(774\) | 2.74503 | − | 19.2166i | 0.0986682 | − | 0.690726i | ||||
\(775\) | 2.99134 | − | 4.17252i | 0.107452 | − | 0.149881i | ||||
\(776\) | −4.28059 | + | 11.1525i | −0.153664 | + | 0.400352i | ||||
\(777\) | 3.33956 | − | 1.88442i | 0.119806 | − | 0.0676033i | ||||
\(778\) | −0.617801 | − | 1.45540i | −0.0221492 | − | 0.0521786i | ||||
\(779\) | −4.96054 | −0.177730 | ||||||||
\(780\) | 8.62851 | − | 33.2115i | 0.308950 | − | 1.18916i | ||||
\(781\) | 2.98118 | 0.106675 | ||||||||
\(782\) | −0.255723 | + | 0.108552i | −0.00914463 | + | 0.00388180i | ||||
\(783\) | −20.8228 | − | 0.616310i | −0.744146 | − | 0.0220251i | ||||
\(784\) | 0.960513 | + | 27.4676i | 0.0343040 | + | 0.980986i | ||||
\(785\) | − | 35.4238i | − | 1.26433i | ||||||
\(786\) | −8.16005 | + | 10.6097i | −0.291059 | + | 0.378434i | ||||
\(787\) | −16.6822 | −0.594656 | −0.297328 | − | 0.954775i | \(-0.596096\pi\) | ||||
−0.297328 | + | 0.954775i | \(0.596096\pi\) | |||||||
\(788\) | 12.4032 | + | 11.9771i | 0.441846 | + | 0.426665i | ||||
\(789\) | 36.5302 | − | 20.6130i | 1.30051 | − | 0.733843i | ||||
\(790\) | 10.8566 | + | 25.5757i | 0.386260 | + | 0.909942i | ||||
\(791\) | 4.10925i | 0.146108i | ||||||||
\(792\) | −8.40880 | + | 6.53944i | −0.298794 | + | 0.232369i | ||||
\(793\) | −30.6348 | −1.08787 | ||||||||
\(794\) | 0.697767 | + | 1.64378i | 0.0247628 | + | 0.0583356i | ||||
\(795\) | −1.01765 | − | 1.80348i | −0.0360925 | − | 0.0639627i | ||||
\(796\) | 17.6323 | + | 17.0265i | 0.624962 | + | 0.603490i | ||||
\(797\) | 48.0774i | 1.70299i | 0.524364 | + | 0.851494i | \(0.324303\pi\) | ||||
−0.524364 | + | 0.851494i | \(0.675697\pi\) | |||||||
\(798\) | 1.05620 | + | 0.812342i | 0.0373892 | + | 0.0287566i | ||||
\(799\) | 3.60998i | 0.127712i | ||||||||
\(800\) | −2.20473 | − | 4.72731i | −0.0779489 | − | 0.167136i | ||||
\(801\) | −11.1772 | + | 18.5066i | −0.394927 | + | 0.653898i | ||||
\(802\) | −29.2761 | + | 12.4274i | −1.03377 | + | 0.438826i | ||||
\(803\) | −8.41008 | −0.296785 | ||||||||
\(804\) | −33.0951 | − | 8.59827i | −1.16718 | − | 0.303238i | ||||
\(805\) | 0.268681 | 0.00946977 | ||||||||
\(806\) | 8.44965 | − | 37.6886i | 0.297626 | − | 1.32752i | ||||
\(807\) | −27.4161 | − | 48.5865i | −0.965092 | − | 1.71033i | ||||
\(808\) | 6.27295 | − | 16.3434i | 0.220682 | − | 0.574958i | ||||
\(809\) | −37.0743 | −1.30346 | −0.651732 | − | 0.758449i | \(-0.725957\pi\) | ||||
−0.651732 | + | 0.758449i | \(0.725957\pi\) | |||||||
\(810\) | −19.9011 | − | 16.2655i | −0.699253 | − | 0.571512i | ||||
\(811\) | − | 38.5331i | − | 1.35308i | −0.736407 | − | 0.676539i | \(-0.763479\pi\) | ||
0.736407 | − | 0.676539i | \(-0.236521\pi\) | |||||||
\(812\) | −2.07085 | − | 1.99970i | −0.0726726 | − | 0.0701758i | ||||
\(813\) | 14.7205 | + | 26.0875i | 0.516270 | + | 0.914928i | ||||
\(814\) | −4.27769 | − | 10.0773i | −0.149933 | − | 0.353208i | ||||
\(815\) | − | 41.5006i | − | 1.45370i | ||||||
\(816\) | 1.91546 | + | 3.13340i | 0.0670545 | + | 0.109691i | ||||
\(817\) | 6.93233i | 0.242531i | ||||||||
\(818\) | −12.6087 | − | 29.7034i | −0.440855 | − | 1.03855i | ||||
\(819\) | −2.73143 | + | 4.52255i | −0.0954439 | + | 0.158031i | ||||
\(820\) | 9.51195 | + | 9.18514i | 0.332172 | + | 0.320759i | ||||
\(821\) | 3.00235i | 0.104783i | 0.998627 | + | 0.0523914i | \(0.0166843\pi\) | ||||
−0.998627 | + | 0.0523914i | \(0.983316\pi\) | |||||||
\(822\) | −20.2851 | + | 26.3746i | −0.707525 | + | 0.919920i | ||||
\(823\) | − | 5.26380i | − | 0.183485i | −0.995783 | − | 0.0917423i | \(-0.970756\pi\) | ||
0.995783 | − | 0.0917423i | \(-0.0292436\pi\) | |||||||
\(824\) | 2.23756 | − | 5.82966i | 0.0779489 | − | 0.203086i | ||||
\(825\) | 0.985327 | + | 1.74619i | 0.0343047 | + | 0.0607944i | ||||
\(826\) | −5.84531 | + | 2.48127i | −0.203384 | + | 0.0863344i | ||||
\(827\) | − | 30.2469i | − | 1.05179i | −0.850550 | − | 0.525894i | \(-0.823731\pi\) | ||
0.850550 | − | 0.525894i | \(-0.176269\pi\) | |||||||
\(828\) | −0.570660 | − | 2.14905i | −0.0198318 | − | 0.0746847i | ||||
\(829\) | 1.09771 | 0.0381251 | 0.0190625 | − | 0.999818i | \(-0.493932\pi\) | ||||
0.0190625 | + | 0.999818i | \(0.493932\pi\) | |||||||
\(830\) | 8.06061 | + | 18.9890i | 0.279788 | + | 0.659117i | ||||
\(831\) | 30.6185 | − | 17.2772i | 1.06214 | − | 0.599339i | ||||
\(832\) | −29.1645 | − | 26.2560i | −1.01110 | − | 0.910265i | ||||
\(833\) | −3.64222 | −0.126195 | ||||||||
\(834\) | −0.677215 | + | 0.880512i | −0.0234500 | + | 0.0304896i | ||||
\(835\) | −16.5135 | −0.571473 | ||||||||
\(836\) | 2.64254 | − | 2.73656i | 0.0913942 | − | 0.0946460i | ||||
\(837\) | −23.0038 | − | 17.5449i | −0.795129 | − | 0.606441i | ||||
\(838\) | 23.1187 | − | 9.81363i | 0.798622 | − | 0.339006i | ||||
\(839\) | 8.04282i | 0.277669i | 0.990316 | + | 0.138834i | \(0.0443356\pi\) | ||||
−0.990316 | + | 0.138834i | \(0.955664\pi\) | |||||||
\(840\) | −0.521128 | − | 3.51339i | −0.0179806 | − | 0.121223i | ||||
\(841\) | 12.9271 | 0.445762 | ||||||||
\(842\) | −1.65775 | − | 3.90529i | −0.0571299 | − | 0.134585i | ||||
\(843\) | −26.8929 | − | 47.6594i | −0.926242 | − | 1.64148i | ||||
\(844\) | −25.0353 | − | 24.1751i | −0.861749 | − | 0.832141i | ||||
\(845\) | −22.3378 | −0.768444 | ||||||||
\(846\) | −28.6032 | − | 4.08588i | −0.983398 | − | 0.140475i | ||||
\(847\) | −3.38347 | −0.116258 | ||||||||
\(848\) | −2.36674 | + | 0.0827624i | −0.0812741 | + | 0.00284207i | ||||
\(849\) | 8.74232 | + | 15.4930i | 0.300036 | + | 0.531720i | ||||
\(850\) | 0.636289 | − | 0.270098i | 0.0218245 | − | 0.00926427i | ||||
\(851\) | 2.28516 | 0.0783342 | ||||||||
\(852\) | 7.96190 | + | 2.06854i | 0.272770 | + | 0.0708670i | ||||
\(853\) | 17.1359i | 0.586723i | 0.956002 | + | 0.293362i | \(0.0947740\pi\) | ||||
−0.956002 | + | 0.293362i | \(0.905226\pi\) | |||||||
\(854\) | −2.91890 | + | 1.23904i | −0.0998825 | + | 0.0423990i | ||||
\(855\) | 7.85712 | + | 4.74537i | 0.268708 | + | 0.162288i | ||||
\(856\) | −0.442005 | + | 1.15159i | −0.0151074 | + | 0.0393605i | ||||
\(857\) | 31.4277i | 1.07355i | 0.843725 | + | 0.536775i | \(0.180358\pi\) | ||||
−0.843725 | + | 0.536775i | \(0.819642\pi\) | |||||||
\(858\) | 11.9566 | + | 9.19603i | 0.408193 | + | 0.313947i | ||||
\(859\) | 0.472050 | 0.0161061 | 0.00805306 | − | 0.999968i | \(-0.497437\pi\) | ||||
0.00805306 | + | 0.999968i | \(0.497437\pi\) | |||||||
\(860\) | 12.8362 | − | 13.2929i | 0.437710 | − | 0.453283i | ||||
\(861\) | −1.00053 | − | 1.77313i | −0.0340980 | − | 0.0604281i | ||||
\(862\) | 8.06026 | + | 18.9881i | 0.274533 | + | 0.646739i | ||||
\(863\) | −57.8887 | −1.97055 | −0.985276 | − | 0.170969i | \(-0.945310\pi\) | ||||
−0.985276 | + | 0.170969i | \(0.945310\pi\) | |||||||
\(864\) | −26.9951 | + | 11.6304i | −0.918390 | + | 0.395675i | ||||
\(865\) | −30.8892 | −1.05026 | ||||||||
\(866\) | 22.2779 | + | 52.4817i | 0.757034 | + | 1.78340i | ||||
\(867\) | 25.2201 | − | 14.2310i | 0.856520 | − | 0.483312i | ||||
\(868\) | −0.719246 | − | 3.93273i | −0.0244128 | − | 0.133486i | ||||
\(869\) | −12.2137 | −0.414322 | ||||||||
\(870\) | −15.7193 | − | 12.0899i | −0.532934 | − | 0.409887i | ||||
\(871\) | 48.4195i | 1.64063i | ||||||||
\(872\) | −8.94596 | − | 3.43366i | −0.302948 | − | 0.116278i | ||||
\(873\) | 6.55043 | − | 10.8458i | 0.221698 | − | 0.367076i | ||||
\(874\) | 0.310277 | + | 0.730941i | 0.0104953 | + | 0.0247245i | ||||
\(875\) | −4.29360 | −0.145150 | ||||||||
\(876\) | −22.4610 | − | 5.83546i | −0.758886 | − | 0.197162i | ||||
\(877\) | 23.6764i | 0.799494i | 0.916626 | + | 0.399747i | \(0.130902\pi\) | ||||
−0.916626 | + | 0.399747i | \(0.869098\pi\) | |||||||
\(878\) | 1.67497 | − | 0.711008i | 0.0565277 | − | 0.0239954i | ||||
\(879\) | 21.0504 | − | 11.8782i | 0.710014 | − | 0.400642i | ||||
\(880\) | −10.1343 | + | 0.354384i | −0.341626 | + | 0.0119463i | ||||
\(881\) | −18.1245 | −0.610631 | −0.305316 | − | 0.952251i | \(-0.598762\pi\) | ||||
−0.305316 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(882\) | 4.12237 | − | 28.8587i | 0.138808 | − | 0.971722i | ||||
\(883\) | 26.1465 | 0.879900 | 0.439950 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439950 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(884\) | 3.61238 | − | 3.74091i | 0.121497 | − | 0.125820i | ||||
\(885\) | −38.0974 | + | 21.4974i | −1.28063 | + | 0.722626i | ||||
\(886\) | −31.9682 | + | 13.5702i | −1.07399 | + | 0.455899i | ||||
\(887\) | − | 24.0982i | − | 0.809140i | −0.914507 | − | 0.404570i | \(-0.867421\pi\) | ||
0.914507 | − | 0.404570i | \(-0.132579\pi\) | |||||||
\(888\) | −4.43224 | − | 29.8817i | −0.148736 | − | 1.00276i | ||||
\(889\) | − | 6.78453i | − | 0.227546i | ||||||
\(890\) | −18.9448 | + | 8.04188i | −0.635033 | + | 0.269564i | ||||
\(891\) | 10.0000 | − | 5.25893i | 0.335013 | − | 0.176181i | ||||
\(892\) | −19.2682 | − | 18.6062i | −0.645147 | − | 0.622982i | ||||
\(893\) | 10.3185 | 0.345296 | ||||||||
\(894\) | 29.3121 | − | 38.1115i | 0.980344 | − | 1.27464i | ||||
\(895\) | 38.4447i | 1.28506i | ||||||||
\(896\) | −3.84074 | − | 1.32211i | −0.128310 | − | 0.0441687i | ||||
\(897\) | −2.74215 | + | 1.54732i | −0.0915576 | + | 0.0516635i | ||||
\(898\) | −20.6315 | + | 8.75785i | −0.688483 | + | 0.292253i | ||||
\(899\) | −18.1414 | − | 13.0058i | −0.605048 | − | 0.433767i | ||||
\(900\) | 1.41991 | + | 5.34726i | 0.0473305 | + | 0.178242i | ||||
\(901\) | − | 0.313831i | − | 0.0104552i | ||||||
\(902\) | −5.35050 | + | 2.27123i | −0.178152 | + | 0.0756236i | ||||
\(903\) | −2.47794 | + | 1.39823i | −0.0824606 | + | 0.0465303i | ||||
\(904\) | 30.2230 | + | 11.6003i | 1.00520 | + | 0.385819i | ||||
\(905\) | 9.06741 | 0.301411 | ||||||||
\(906\) | 5.56124 | + | 4.27723i | 0.184760 | + | 0.142102i | ||||
\(907\) | 15.9864i | 0.530820i | 0.964136 | + | 0.265410i | \(0.0855074\pi\) | ||||
−0.964136 | + | 0.265410i | \(0.914493\pi\) | |||||||
\(908\) | −20.3301 | + | 21.0534i | −0.674677 | + | 0.698682i | ||||
\(909\) | −9.59926 | + | 15.8939i | −0.318387 | + | 0.527168i | ||||
\(910\) | −4.62965 | + | 1.96524i | −0.153471 | + | 0.0651469i | ||||
\(911\) | 25.8041 | 0.854927 | 0.427464 | − | 0.904033i | \(-0.359407\pi\) | ||||
0.427464 | + | 0.904033i | \(0.359407\pi\) | |||||||
\(912\) | 8.95629 | − | 5.47503i | 0.296573 | − | 0.181296i | ||||
\(913\) | −9.06824 | −0.300115 | ||||||||
\(914\) | −11.2421 | − | 26.4837i | −0.371854 | − | 0.876004i | ||||
\(915\) | −19.0242 | + | 10.7349i | −0.628921 | + | 0.354884i | ||||
\(916\) | −23.8744 | + | 24.7239i | −0.788833 | + | 0.816900i | ||||
\(917\) | 1.96183 | 0.0647854 | ||||||||
\(918\) | −1.41530 | − | 3.62905i | −0.0467118 | − | 0.119776i | ||||
\(919\) | −14.2523 | −0.470139 | −0.235070 | − | 0.971979i | \(-0.575532\pi\) | ||||
−0.235070 | + | 0.971979i | \(0.575532\pi\) | |||||||
\(920\) | 0.758478 | − | 1.97612i | 0.0250063 | − | 0.0651506i | ||||
\(921\) | 5.44658 | + | 9.65237i | 0.179471 | + | 0.318056i | ||||
\(922\) | −13.4678 | − | 31.7272i | −0.443539 | − | 1.04488i | ||||
\(923\) | − | 11.6486i | − | 0.383418i | ||||||
\(924\) | 1.51117 | + | 0.392609i | 0.0497138 | + | 0.0129159i | ||||
\(925\) | −5.68592 | −0.186952 | ||||||||
\(926\) | 13.1255 | + | 30.9208i | 0.431332 | + | 1.01612i | ||||
\(927\) | −3.42405 | + | 5.66934i | −0.112460 | + | 0.186206i | ||||
\(928\) | −20.5535 | + | 9.58575i | −0.674701 | + | 0.314668i | ||||
\(929\) | −30.2498 | −0.992464 | −0.496232 | − | 0.868190i | \(-0.665283\pi\) | ||||
−0.496232 | + | 0.868190i | \(0.665283\pi\) | |||||||
\(930\) | −7.95937 | − | 26.3655i | −0.260998 | − | 0.864558i | ||||
\(931\) | 10.4107i | 0.341196i | ||||||||
\(932\) | −6.16667 | − | 5.95480i | −0.201996 | − | 0.195056i | ||||
\(933\) | −3.75188 | − | 6.64904i | −0.122831 | − | 0.217680i | ||||
\(934\) | 38.7718 | − | 16.4582i | 1.26865 | − | 0.538529i | ||||
\(935\) | − | 1.34381i | − | 0.0439472i | ||||||
\(936\) | 25.5520 | + | 32.8563i | 0.835194 | + | 1.07394i | ||||
\(937\) | −19.8096 | −0.647152 | −0.323576 | − | 0.946202i | \(-0.604885\pi\) | ||||
−0.323576 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(938\) | 1.95835 | + | 4.61343i | 0.0639424 | + | 0.150634i | ||||
\(939\) | −14.2904 | − | 25.3254i | −0.466351 | − | 0.826463i | ||||
\(940\) | −19.7860 | − | 19.1062i | −0.645347 | − | 0.623174i | ||||
\(941\) | 42.9009i | 1.39853i | 0.714862 | + | 0.699265i | \(0.246489\pi\) | ||||
−0.714862 | + | 0.699265i | \(0.753511\pi\) | |||||||
\(942\) | 34.0599 | + | 26.1960i | 1.10973 | + | 0.853511i | ||||
\(943\) | − | 1.21330i | − | 0.0395104i | ||||||
\(944\) | 1.74831 | + | 49.9960i | 0.0569026 | + | 1.62723i | ||||
\(945\) | −0.111455 | + | 3.76563i | −0.00362562 | + | 0.122496i | ||||
\(946\) | 3.17403 | + | 7.47728i | 0.103196 | + | 0.243107i | ||||
\(947\) | 38.1906i | 1.24103i | 0.784196 | + | 0.620514i | \(0.213076\pi\) | ||||
−0.784196 | + | 0.620514i | \(0.786924\pi\) | |||||||
\(948\) | −32.6195 | − | 8.47469i | −1.05943 | − | 0.275245i | ||||
\(949\) | 32.8613i | 1.06672i | ||||||||
\(950\) | −0.772029 | − | 1.81873i | −0.0250479 | − | 0.0590073i | ||||
\(951\) | 17.0944 | − | 9.64591i | 0.554323 | − | 0.312790i | ||||
\(952\) | 0.192886 | − | 0.502539i | 0.00625147 | − | 0.0162874i | ||||
\(953\) | −18.7141 | −0.606208 | −0.303104 | − | 0.952957i | \(-0.598023\pi\) | ||||
−0.303104 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(954\) | 2.48660 | + | 0.355203i | 0.0805066 | + | 0.0115001i | ||||
\(955\) | − | 31.6881i | − | 1.02540i | ||||||
\(956\) | 37.5056 | − | 38.8400i | 1.21302 | − | 1.25618i | ||||
\(957\) | 7.59210 | − | 4.28402i | 0.245418 | − | 0.138483i | ||||
\(958\) | 9.60834 | + | 22.6351i | 0.310431 | + | 0.731306i | ||||
\(959\) | 4.87693 | 0.157484 | ||||||||
\(960\) | −27.3116 | − | 6.08535i | −0.881480 | − | 0.196404i | ||||
\(961\) | −9.95207 | − | 29.3591i | −0.321034 | − | 0.947068i | ||||
\(962\) | −39.3756 | + | 16.7145i | −1.26952 | + | 0.538897i | ||||
\(963\) | 0.676384 | − | 1.11992i | 0.0217962 | − | 0.0360889i | ||||
\(964\) | −31.7858 | − | 30.6937i | −1.02375 | − | 0.988578i | ||||
\(965\) | −20.2649 | −0.652350 | ||||||||
\(966\) | −0.198690 | + | 0.258337i | −0.00639276 | + | 0.00831184i | ||||
\(967\) | − | 41.4972i | − | 1.33446i | −0.744852 | − | 0.667229i | \(-0.767480\pi\) | ||
0.744852 | − | 0.667229i | \(-0.232520\pi\) | |||||||
\(968\) | −9.55143 | + | 24.8850i | −0.306995 | + | 0.799835i | ||||
\(969\) | 0.683626 | + | 1.21151i | 0.0219612 | + | 0.0389195i | ||||
\(970\) | 11.1027 | − | 4.71296i | 0.356486 | − | 0.151324i | ||||
\(971\) | 19.0234 | 0.610490 | 0.305245 | − | 0.952274i | \(-0.401262\pi\) | ||||
0.305245 | + | 0.952274i | \(0.401262\pi\) | |||||||
\(972\) | 30.3562 | − | 7.10646i | 0.973675 | − | 0.227940i | ||||
\(973\) | 0.162816 | 0.00521963 | ||||||||
\(974\) | −7.93481 | − | 18.6926i | −0.254248 | − | 0.598950i | ||||
\(975\) | 6.82300 | − | 3.85004i | 0.218511 | − | 0.123300i | ||||
\(976\) | 0.873030 | + | 24.9659i | 0.0279450 | + | 0.799138i | ||||
\(977\) | 47.2319i | 1.51108i | 0.655100 | + | 0.755542i | \(0.272626\pi\) | ||||
−0.655100 | + | 0.755542i | \(0.727374\pi\) | |||||||
\(978\) | 39.9028 | + | 30.6898i | 1.27595 | + | 0.981352i | ||||
\(979\) | − | 9.04716i | − | 0.289149i | ||||||
\(980\) | 19.2768 | − | 19.9627i | 0.615775 | − | 0.637685i | ||||
\(981\) | 8.69994 | + | 5.25440i | 0.277768 | + | 0.167760i | ||||
\(982\) | 6.26949 | + | 14.7695i | 0.200067 | + | 0.471314i | ||||
\(983\) | −17.4021 | −0.555040 | −0.277520 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277520 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(984\) | −15.8656 | + | 2.35329i | −0.505777 | + | 0.0750200i | ||||
\(985\) | − | 17.4092i | − | 0.554703i | ||||||
\(986\) | −1.17434 | − | 2.76647i | −0.0373985 | − | 0.0881023i | ||||
\(987\) | 2.08122 | + | 3.68832i | 0.0662460 | + | 0.117400i | ||||
\(988\) | −10.6928 | − | 10.3254i | −0.340182 | − | 0.328494i | ||||
\(989\) | −1.69558 | −0.0539162 | ||||||||
\(990\) | 10.6475 | + | 1.52096i | 0.338399 | + | 0.0483393i | ||||
\(991\) | − | 8.19232i | − | 0.260238i | −0.991498 | − | 0.130119i | \(-0.958464\pi\) | ||
0.991498 | − | 0.130119i | \(-0.0415359\pi\) | |||||||
\(992\) | −30.9551 | − | 5.81200i | −0.982827 | − | 0.184531i | ||||
\(993\) | 43.6784 | − | 24.6466i | 1.38609 | − | 0.782136i | ||||
\(994\) | −0.471132 | − | 1.10988i | −0.0149434 | − | 0.0352033i | ||||
\(995\) | − | 24.7488i | − | 0.784590i | ||||||
\(996\) | −24.2187 | − | 6.29214i | −0.767400 | − | 0.199374i | ||||
\(997\) | 35.0130i | 1.10887i | 0.832226 | + | 0.554437i | \(0.187066\pi\) | ||||
−0.832226 | + | 0.554437i | \(0.812934\pi\) | |||||||
\(998\) | −45.4765 | + | 19.3043i | −1.43953 | + | 0.611067i | ||||
\(999\) | −0.947932 | + | 32.0270i | −0.0299912 | + | 1.01329i |
(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 | 744.2.o.e.557.15 | yes | 96 | |
3.2 | odd | 2 | inner | 744.2.o.e.557.81 | yes | 96 | |
8.5 | even | 2 | inner | 744.2.o.e.557.84 | yes | 96 | |
24.5 | odd | 2 | inner | 744.2.o.e.557.14 | yes | 96 | |
31.30 | odd | 2 | inner | 744.2.o.e.557.16 | yes | 96 | |
93.92 | even | 2 | inner | 744.2.o.e.557.82 | yes | 96 | |
248.61 | odd | 2 | inner | 744.2.o.e.557.83 | yes | 96 | |
744.557 | even | 2 | inner | 744.2.o.e.557.13 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
744.2.o.e.557.13 | ✓ | 96 | 744.557 | even | 2 | inner | |
744.2.o.e.557.14 | yes | 96 | 24.5 | odd | 2 | inner | |
744.2.o.e.557.15 | yes | 96 | 1.1 | even | 1 | trivial | |
744.2.o.e.557.16 | yes | 96 | 31.30 | odd | 2 | inner | |
744.2.o.e.557.81 | yes | 96 | 3.2 | odd | 2 | inner | |
744.2.o.e.557.82 | yes | 96 | 93.92 | even | 2 | inner | |
744.2.o.e.557.83 | yes | 96 | 248.61 | odd | 2 | inner | |
744.2.o.e.557.84 | yes | 96 | 8.5 | even | 2 | inner |