Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(71,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.cw (of order \(12\), degree \(4\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 71.3 | ||
Character | \(\chi\) | \(=\) | 585.71 |
Dual form | 585.2.cw.a.206.3 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59774 | + | 0.428113i | −1.12977 | + | 0.302721i | −0.774832 | − | 0.632168i | \(-0.782165\pi\) |
−0.354940 | + | 0.934889i | \(0.615499\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.637436 | − | 0.368024i | 0.318718 | − | 0.184012i | ||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.07084 | + | 3.99644i | −0.404741 | + | 1.51051i | 0.399793 | + | 0.916605i | \(0.369082\pi\) |
−0.804534 | + | 0.593907i | \(0.797585\pi\) | |||||||
\(8\) | 1.47835 | − | 1.47835i | 0.522676 | − | 0.522676i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.43249 | + | 0.827050i | 0.452994 | + | 0.261536i | ||||
\(11\) | −1.35793 | − | 5.06786i | −0.409431 | − | 1.52802i | −0.795735 | − | 0.605645i | \(-0.792915\pi\) |
0.386304 | − | 0.922371i | \(-0.373751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.741149 | − | 3.52855i | −0.205558 | − | 0.978645i | ||||
\(14\) | − | 6.84371i | − | 1.82906i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.46516 | + | 4.26979i | −0.616291 | + | 1.06745i | ||||
\(17\) | 2.05707 | + | 3.56295i | 0.498913 | + | 0.864143i | 0.999999 | − | 0.00125462i | \(-0.000399357\pi\) |
−0.501086 | + | 0.865397i | \(0.667066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19440 | + | 0.587987i | 0.503429 | + | 0.134893i | 0.501591 | − | 0.865105i | \(-0.332748\pi\) |
0.00183798 | + | 0.999998i | \(0.499415\pi\) | |||||||
\(20\) | −0.710968 | − | 0.190503i | −0.158977 | − | 0.0425978i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.33923 | + | 7.51576i | 0.925126 | + | 1.60237i | ||||
\(23\) | −0.647596 | + | 1.12167i | −0.135033 | + | 0.233884i | −0.925610 | − | 0.378478i | \(-0.876447\pi\) |
0.790577 | + | 0.612363i | \(0.209781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 2.69478 | + | 5.32041i | 0.528490 | + | 1.04342i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.788192 | + | 2.94157i | 0.148954 | + | 0.555905i | ||||
\(29\) | −3.29188 | − | 1.90057i | −0.611287 | − | 0.352927i | 0.162182 | − | 0.986761i | \(-0.448147\pi\) |
−0.773469 | + | 0.633834i | \(0.781480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.95022 | − | 3.95022i | 0.709480 | − | 0.709480i | −0.256946 | − | 0.966426i | \(-0.582716\pi\) |
0.966426 | + | 0.256946i | \(0.0827161\pi\) | |||||||
\(32\) | 1.02851 | − | 3.83845i | 0.181816 | − | 0.678548i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.81201 | − | 4.81201i | −0.825252 | − | 0.825252i | ||||
\(35\) | 3.58311 | − | 2.06871i | 0.605656 | − | 0.349676i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.14858 | − | 2.45136i | 1.50402 | − | 0.403000i | 0.589575 | − | 0.807714i | \(-0.299295\pi\) |
0.914444 | + | 0.404714i | \(0.132629\pi\) | |||||||
\(38\) | −3.75779 | −0.609595 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.09070 | −0.330569 | ||||||||
\(41\) | 1.89876 | − | 0.508772i | 0.296537 | − | 0.0794569i | −0.107483 | − | 0.994207i | \(-0.534279\pi\) |
0.404020 | + | 0.914750i | \(0.367613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0208 | − | 6.36286i | 1.68066 | − | 0.970327i | 0.719431 | − | 0.694564i | \(-0.244403\pi\) |
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(44\) | −2.73069 | − | 2.73069i | −0.411666 | − | 0.411666i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.554488 | − | 2.06938i | 0.0817549 | − | 0.305113i | ||||
\(47\) | 6.64428 | − | 6.64428i | 0.969169 | − | 0.969169i | −0.0303702 | − | 0.999539i | \(-0.509669\pi\) |
0.999539 | + | 0.0303702i | \(0.00966861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.76266 | − | 5.05912i | −1.25181 | − | 0.722732i | ||||
\(50\) | −0.428113 | − | 1.59774i | −0.0605443 | − | 0.225954i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.77103 | − | 1.97647i | −0.245597 | − | 0.274087i | ||||
\(53\) | 9.94699i | 1.36632i | 0.730267 | + | 0.683162i | \(0.239396\pi\) | ||||
−0.730267 | + | 0.683162i | \(0.760604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.62332 | + | 4.54372i | −0.353728 | + | 0.612675i | ||||
\(56\) | 4.32506 | + | 7.49122i | 0.577960 | + | 1.00106i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.07322 | + | 1.62731i | 0.797453 | + | 0.213677i | ||||
\(59\) | 4.55554 | + | 1.22065i | 0.593081 | + | 0.158916i | 0.542861 | − | 0.839823i | \(-0.317341\pi\) |
0.0502202 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.36172 | − | 2.35857i | −0.174350 | − | 0.301984i | 0.765586 | − | 0.643334i | \(-0.222449\pi\) |
−0.939936 | + | 0.341350i | \(0.889116\pi\) | |||||||
\(62\) | −4.62028 | + | 8.00256i | −0.586776 | + | 1.01633i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 3.28751i | − | 0.410939i | ||||||
\(65\) | −1.97099 | + | 3.01914i | −0.244472 | + | 0.374478i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92991 | + | 10.9346i | 0.357945 | + | 1.33587i | 0.876737 | + | 0.480969i | \(0.159715\pi\) |
−0.518792 | + | 0.854900i | \(0.673618\pi\) | |||||||
\(68\) | 2.62250 | + | 1.51410i | 0.318025 | + | 0.183612i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.83923 | + | 4.83923i | −0.578399 | + | 0.578399i | ||||
\(71\) | 3.72068 | − | 13.8858i | 0.441563 | − | 1.64794i | −0.283291 | − | 0.959034i | \(-0.591426\pi\) |
0.724854 | − | 0.688902i | \(-0.241907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.66372 | + | 4.66372i | 0.545847 | + | 0.545847i | 0.925237 | − | 0.379390i | \(-0.123866\pi\) |
−0.379390 | + | 0.925237i | \(0.623866\pi\) | |||||||
\(74\) | −13.5676 | + | 7.83325i | −1.57720 | + | 0.910597i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.61518 | − | 0.432786i | 0.185274 | − | 0.0496440i | ||||
\(77\) | 21.7075 | 2.47380 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.21562 | 0.249277 | 0.124638 | − | 0.992202i | \(-0.460223\pi\) | ||||
0.124638 | + | 0.992202i | \(0.460223\pi\) | |||||||
\(80\) | 4.76233 | − | 1.27606i | 0.532445 | − | 0.142668i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.81592 | + | 1.62577i | −0.310966 | + | 0.179536i | ||||
\(83\) | 1.87062 | + | 1.87062i | 0.205328 | + | 0.205328i | 0.802278 | − | 0.596951i | \(-0.203621\pi\) |
−0.596951 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.06482 | − | 3.97396i | 0.115496 | − | 0.431036i | ||||
\(86\) | −14.8843 | + | 14.8843i | −1.60502 | + | 1.60502i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.49956 | − | 5.48458i | −1.01266 | − | 0.584658i | ||||
\(89\) | −1.91392 | − | 7.14286i | −0.202876 | − | 0.757142i | −0.990087 | − | 0.140458i | \(-0.955142\pi\) |
0.787211 | − | 0.616684i | \(-0.211524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8953 | + | 0.816571i | 1.56145 | + | 0.0855999i | ||||
\(92\) | 0.953324i | 0.0993909i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.77133 | + | 13.4603i | −0.801551 | + | 1.38833i | ||||
\(95\) | −1.13590 | − | 1.96744i | −0.116541 | − | 0.201855i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6120 | − | 3.11142i | −1.17902 | − | 0.315917i | −0.384481 | − | 0.923133i | \(-0.625620\pi\) |
−0.794537 | + | 0.607216i | \(0.792286\pi\) | |||||||
\(98\) | 16.1663 | + | 4.33175i | 1.63304 | + | 0.437573i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.368024 | + | 0.637436i | 0.0368024 | + | 0.0637436i | ||||
\(101\) | 2.16281 | − | 3.74609i | 0.215207 | − | 0.372750i | −0.738129 | − | 0.674659i | \(-0.764291\pi\) |
0.953337 | + | 0.301909i | \(0.0976240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.3990i | − | 1.32024i | −0.751161 | − | 0.660119i | \(-0.770506\pi\) | ||
0.751161 | − | 0.660119i | \(-0.229494\pi\) | |||||||
\(104\) | −6.31212 | − | 4.12076i | −0.618954 | − | 0.404074i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.25843 | − | 15.8927i | −0.413615 | − | 1.54363i | ||||
\(107\) | −0.251377 | − | 0.145132i | −0.0243015 | − | 0.0140305i | 0.487800 | − | 0.872955i | \(-0.337800\pi\) |
−0.512102 | + | 0.858925i | \(0.671133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.70875 | − | 4.70875i | 0.451016 | − | 0.451016i | −0.444675 | − | 0.895692i | \(-0.646681\pi\) |
0.895692 | + | 0.444675i | \(0.146681\pi\) | |||||||
\(110\) | 2.24615 | − | 8.38274i | 0.214162 | − | 0.799263i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.4242 | − | 14.4242i | −1.36295 | − | 1.36295i | ||||
\(113\) | −11.1308 | + | 6.42637i | −1.04710 | + | 0.604542i | −0.921836 | − | 0.387581i | \(-0.873311\pi\) |
−0.125263 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.25106 | − | 0.335221i | 0.116662 | − | 0.0312595i | ||||
\(116\) | −2.79782 | −0.259771 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.80114 | −0.718154 | ||||||||
\(119\) | −16.4419 | + | 4.40560i | −1.50723 | + | 0.403861i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.3129 | + | 8.26357i | −1.30118 | + | 0.751234i | ||||
\(122\) | 3.18541 | + | 3.18541i | 0.288393 | + | 0.288393i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.06424 | − | 3.97179i | 0.0955713 | − | 0.356677i | ||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.99150 | − | 1.14979i | −0.176717 | − | 0.102028i | 0.409032 | − | 0.912520i | \(-0.365866\pi\) |
−0.585749 | + | 0.810492i | \(0.699200\pi\) | |||||||
\(128\) | 3.46444 | + | 12.9295i | 0.306216 | + | 1.14281i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.85660 | − | 5.66760i | 0.162835 | − | 0.497081i | ||||
\(131\) | 22.6535i | 1.97925i | 0.143687 | + | 0.989623i | \(0.454104\pi\) | ||||
−0.143687 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.69971 | + | 8.14013i | −0.407516 | + | 0.705839i | ||||
\(134\) | −9.36245 | − | 16.2162i | −0.808793 | − | 1.40087i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.30837 | + | 2.22622i | 0.712436 | + | 0.190897i | ||||
\(137\) | −6.67984 | − | 1.78986i | −0.570697 | − | 0.152918i | −0.0380809 | − | 0.999275i | \(-0.512124\pi\) |
−0.532616 | + | 0.846357i | \(0.678791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.22191 | − | 5.58051i | −0.273279 | − | 0.473332i | 0.696421 | − | 0.717634i | \(-0.254775\pi\) |
−0.969699 | + | 0.244301i | \(0.921441\pi\) | |||||||
\(140\) | 1.52267 | − | 2.63734i | 0.128689 | − | 0.222896i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 23.7787i | 1.99546i | ||||||||
\(143\) | −16.8758 | + | 8.54756i | −1.41122 | + | 0.714783i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.983806 | + | 3.67162i | 0.0817007 | + | 0.304911i | ||||
\(146\) | −9.44800 | − | 5.45480i | −0.781922 | − | 0.451443i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.92948 | − | 4.92948i | 0.405201 | − | 0.405201i | ||||
\(149\) | 4.32010 | − | 16.1228i | 0.353916 | − | 1.32083i | −0.527927 | − | 0.849290i | \(-0.677030\pi\) |
0.881843 | − | 0.471543i | \(-0.156303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.942270 | − | 0.942270i | −0.0766808 | − | 0.0766808i | 0.667726 | − | 0.744407i | \(-0.267268\pi\) |
−0.744407 | + | 0.667726i | \(0.767268\pi\) | |||||||
\(152\) | 4.11334 | − | 2.37484i | 0.333636 | − | 0.192625i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −34.6829 | + | 9.29326i | −2.79483 | + | 0.748873i | ||||
\(155\) | −5.58645 | −0.448715 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.43419 | 0.194269 | 0.0971347 | − | 0.995271i | \(-0.469032\pi\) | ||||
0.0971347 | + | 0.995271i | \(0.469032\pi\) | |||||||
\(158\) | −3.53998 | + | 0.948534i | −0.281626 | + | 0.0754613i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.44146 | + | 1.98693i | −0.272071 | + | 0.157080i | ||||
\(161\) | −3.78921 | − | 3.78921i | −0.298632 | − | 0.298632i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.44589 | − | 9.12819i | 0.191577 | − | 0.714975i | −0.801549 | − | 0.597929i | \(-0.795991\pi\) |
0.993126 | − | 0.117047i | \(-0.0373427\pi\) | |||||||
\(164\) | 1.02310 | − | 1.02310i | 0.0798907 | − | 0.0798907i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.78960 | − | 2.18793i | −0.294130 | − | 0.169816i | ||||
\(167\) | −2.46644 | − | 9.20489i | −0.190859 | − | 0.712296i | −0.993300 | − | 0.115564i | \(-0.963132\pi\) |
0.802441 | − | 0.596732i | \(-0.203534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9014 | + | 5.23037i | −0.915492 | + | 0.402336i | ||||
\(170\) | 6.80520i | 0.521935i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.68337 | − | 8.11184i | 0.357104 | − | 0.618522i | ||||
\(173\) | 2.34441 | + | 4.06063i | 0.178242 | + | 0.308724i | 0.941278 | − | 0.337631i | \(-0.109626\pi\) |
−0.763036 | + | 0.646356i | \(0.776292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.99644 | − | 1.07084i | −0.302103 | − | 0.0809481i | ||||
\(176\) | 24.9862 | + | 6.69503i | 1.88341 | + | 0.504657i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.11590 | + | 10.5931i | 0.458406 | + | 0.793983i | ||||
\(179\) | 7.24675 | − | 12.5517i | 0.541648 | − | 0.938161i | −0.457162 | − | 0.889383i | \(-0.651134\pi\) |
0.998810 | − | 0.0487777i | \(-0.0155326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0245i | 1.19109i | 0.803320 | + | 0.595547i | \(0.203065\pi\) | ||||
−0.803320 | + | 0.595547i | \(0.796935\pi\) | |||||||
\(182\) | −24.1484 | + | 5.07221i | −1.79000 | + | 0.375977i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.700847 | + | 2.61560i | 0.0516671 | + | 0.192824i | ||||
\(185\) | −8.20240 | − | 4.73566i | −0.603052 | − | 0.348172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2632 | − | 15.2632i | 1.11615 | − | 1.11615i | ||||
\(188\) | 1.79005 | − | 6.68056i | 0.130553 | − | 0.487230i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.65716 | + | 2.65716i | 0.192771 | + | 0.192771i | ||||
\(191\) | −8.21436 | + | 4.74256i | −0.594370 | + | 0.343160i | −0.766824 | − | 0.641858i | \(-0.778164\pi\) |
0.172454 | + | 0.985018i | \(0.444831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4296 | + | 3.06256i | −0.822723 | + | 0.220448i | −0.645537 | − | 0.763729i | \(-0.723366\pi\) |
−0.177187 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(194\) | 19.8850 | 1.42766 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.44751 | −0.531965 | ||||||||
\(197\) | −16.5438 | + | 4.43290i | −1.17870 | + | 0.315831i | −0.794410 | − | 0.607382i | \(-0.792220\pi\) |
−0.384288 | + | 0.923213i | \(0.625553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4801 | − | 11.8242i | 1.45179 | − | 0.838194i | 0.453211 | − | 0.891403i | \(-0.350278\pi\) |
0.998583 | + | 0.0532089i | \(0.0169449\pi\) | |||||||
\(200\) | 1.47835 | + | 1.47835i | 0.104535 | + | 0.104535i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.85185 | + | 6.91119i | −0.130296 | + | 0.486270i | ||||
\(203\) | 11.1206 | − | 11.1206i | 0.780513 | − | 0.780513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.70239 | − | 0.982873i | −0.118900 | − | 0.0686468i | ||||
\(206\) | 5.73626 | + | 21.4080i | 0.399664 | + | 1.49157i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.8932 | + | 5.53392i | 1.17134 | + | 0.383708i | ||||
\(209\) | − | 11.9193i | − | 0.824477i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.04720 | + | 15.6702i | −0.622835 | + | 1.07878i | 0.366120 | + | 0.930568i | \(0.380686\pi\) |
−0.988955 | + | 0.148215i | \(0.952647\pi\) | |||||||
\(212\) | 3.66073 | + | 6.34057i | 0.251420 | + | 0.435472i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.463767 | + | 0.124266i | 0.0317025 | + | 0.00849465i | ||||
\(215\) | −12.2921 | − | 3.29366i | −0.838315 | − | 0.224626i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5568 | + | 20.0169i | 0.784524 | + | 1.35883i | ||||
\(218\) | −5.50747 | + | 9.53922i | −0.373013 | + | 0.646078i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.86177i | 0.260361i | ||||||||
\(221\) | 11.0475 | − | 9.89917i | 0.743134 | − | 0.665890i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.14711 | − | 11.7452i | −0.210746 | − | 0.786514i | −0.987621 | − | 0.156859i | \(-0.949863\pi\) |
0.776875 | − | 0.629655i | \(-0.216804\pi\) | |||||||
\(224\) | 14.2388 | + | 8.22075i | 0.951367 | + | 0.549272i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0329 | − | 15.0329i | 0.999974 | − | 0.999974i | ||||
\(227\) | −2.43208 | + | 9.07665i | −0.161423 | + | 0.602438i | 0.837047 | + | 0.547132i | \(0.184280\pi\) |
−0.998469 | + | 0.0553067i | \(0.982386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.78915 | − | 4.78915i | −0.316476 | − | 0.316476i | 0.530936 | − | 0.847412i | \(-0.321840\pi\) |
−0.847412 | + | 0.530936i | \(0.821840\pi\) | |||||||
\(230\) | −1.85535 | + | 1.07119i | −0.122338 | + | 0.0706321i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.67626 | + | 2.05685i | −0.503971 | + | 0.135039i | ||||
\(233\) | 24.1853 | 1.58443 | 0.792217 | − | 0.610240i | \(-0.208927\pi\) | ||||
0.792217 | + | 0.610240i | \(0.208927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.39644 | −0.612956 | ||||||||
\(236\) | 3.35310 | − | 0.898460i | 0.218268 | − | 0.0584848i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.3838 | − | 14.0780i | 1.58057 | − | 0.912541i | ||||
\(239\) | 3.65280 | + | 3.65280i | 0.236280 | + | 0.236280i | 0.815308 | − | 0.579028i | \(-0.196568\pi\) |
−0.579028 | + | 0.815308i | \(0.696568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.60991 | − | 6.00827i | 0.103704 | − | 0.387027i | −0.894491 | − | 0.447085i | \(-0.852462\pi\) |
0.998195 | + | 0.0600585i | \(0.0191287\pi\) | |||||||
\(242\) | 19.3306 | − | 19.3306i | 1.24262 | − | 1.24262i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.73602 | − | 1.00229i | −0.111137 | − | 0.0641651i | ||||
\(245\) | 2.61879 | + | 9.77347i | 0.167309 | + | 0.624404i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.448369 | − | 8.17883i | 0.0285290 | − | 0.520407i | ||||
\(248\) | − | 11.6796i | − | 0.741657i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.827050 | + | 1.43249i | −0.0523072 | + | 0.0905988i | ||||
\(251\) | −5.84012 | − | 10.1154i | −0.368625 | − | 0.638477i | 0.620726 | − | 0.784028i | \(-0.286838\pi\) |
−0.989351 | + | 0.145550i | \(0.953505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.56385 | + | 1.75878i | 0.412666 | + | 0.110573i | ||||
\(254\) | 3.67414 | + | 0.984483i | 0.230536 | + | 0.0617719i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.78303 | − | 13.4806i | −0.486439 | − | 0.842538i | ||||
\(257\) | −6.57188 | + | 11.3828i | −0.409942 | + | 0.710041i | −0.994883 | − | 0.101035i | \(-0.967785\pi\) |
0.584940 | + | 0.811076i | \(0.301118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.1868i | 2.43495i | ||||||||
\(260\) | −0.145268 | + | 2.64988i | −0.00900915 | + | 0.164339i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.69825 | − | 36.1944i | −0.599160 | − | 2.23610i | ||||
\(263\) | −11.4962 | − | 6.63734i | −0.708886 | − | 0.409276i | 0.101762 | − | 0.994809i | \(-0.467552\pi\) |
−0.810649 | + | 0.585533i | \(0.800885\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.03358 | − | 7.03358i | 0.432070 | − | 0.432070i | ||||
\(266\) | 4.02401 | − | 15.0178i | 0.246728 | − | 0.920800i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.89181 | + | 5.89181i | 0.359900 | + | 0.359900i | ||||
\(269\) | −2.39287 | + | 1.38152i | −0.145896 | + | 0.0842331i | −0.571171 | − | 0.820831i | \(-0.693511\pi\) |
0.425275 | + | 0.905064i | \(0.360177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3643 | − | 4.38480i | 0.994060 | − | 0.266358i | 0.275105 | − | 0.961414i | \(-0.411287\pi\) |
0.718955 | + | 0.695057i | \(0.244621\pi\) | |||||||
\(272\) | −20.2841 | −1.22990 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4389 | 0.691049 | ||||||||
\(275\) | 5.06786 | − | 1.35793i | 0.305603 | − | 0.0818862i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.8030 | − | 14.8974i | 1.55035 | − | 0.895097i | 0.552241 | − | 0.833685i | \(-0.313773\pi\) |
0.998113 | − | 0.0614120i | \(-0.0195603\pi\) | |||||||
\(278\) | 7.53685 | + | 7.53685i | 0.452030 | + | 0.452030i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.23882 | − | 8.35537i | 0.133795 | − | 0.499329i | ||||
\(281\) | −2.39701 | + | 2.39701i | −0.142993 | + | 0.142993i | −0.774980 | − | 0.631986i | \(-0.782240\pi\) |
0.631986 | + | 0.774980i | \(0.282240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.44627 | + | 3.72175i | 0.383191 | + | 0.221235i | 0.679206 | − | 0.733948i | \(-0.262324\pi\) |
−0.296015 | + | 0.955183i | \(0.595658\pi\) | |||||||
\(284\) | −2.73860 | − | 10.2206i | −0.162506 | − | 0.606480i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.3038 | − | 20.8815i | 1.37798 | − | 1.23475i | ||||
\(287\) | 8.13311i | 0.480083i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0369152 | − | 0.0639390i | 0.00217148 | − | 0.00376112i | ||||
\(290\) | −3.14373 | − | 5.44510i | −0.184606 | − | 0.319747i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.68918 | + | 1.25646i | 0.274414 | + | 0.0735289i | ||||
\(293\) | 4.57609 | + | 1.22616i | 0.267338 | + | 0.0716330i | 0.389998 | − | 0.920816i | \(-0.372476\pi\) |
−0.122660 | + | 0.992449i | \(0.539142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.35812 | − | 4.08439i | −0.137295 | − | 0.237802i | ||||
\(296\) | 9.90085 | − | 17.1488i | 0.575475 | − | 0.996753i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.6095i | 1.59938i | ||||||||
\(299\) | 4.43784 | + | 1.45376i | 0.256647 | + | 0.0840728i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.6273 | + | 50.8576i | 0.785462 | + | 2.93138i | ||||
\(302\) | 1.90890 | + | 1.10210i | 0.109845 | + | 0.0634189i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.92013 | + | 7.92013i | −0.454250 | + | 0.454250i | ||||
\(305\) | −0.704878 | + | 2.63064i | −0.0403612 | + | 0.150630i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9183 | − | 20.9183i | −1.19387 | − | 1.19387i | −0.975971 | − | 0.217899i | \(-0.930080\pi\) |
−0.217899 | − | 0.975971i | \(-0.569920\pi\) | |||||||
\(308\) | 13.8372 | − | 7.98889i | 0.788445 | − | 0.455209i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.92569 | − | 2.39163i | 0.506945 | − | 0.135836i | ||||
\(311\) | 15.2872 | 0.866860 | 0.433430 | − | 0.901187i | \(-0.357303\pi\) | ||||
0.433430 | + | 0.901187i | \(0.357303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.5240 | −1.38618 | −0.693089 | − | 0.720852i | \(-0.743751\pi\) | ||||
−0.693089 | + | 0.720852i | \(0.743751\pi\) | |||||||
\(314\) | −3.88920 | + | 1.04211i | −0.219480 | + | 0.0588095i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.41232 | − | 0.815401i | 0.0794489 | − | 0.0458699i | ||||
\(317\) | 13.3264 | + | 13.3264i | 0.748488 | + | 0.748488i | 0.974195 | − | 0.225707i | \(-0.0724693\pi\) |
−0.225707 | + | 0.974195i | \(0.572469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.16167 | + | 19.2636i | −0.288998 | + | 1.07856i | ||||
\(320\) | −2.32462 | + | 2.32462i | −0.129950 | + | 0.129950i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.67638 | + | 4.43196i | 0.427788 | + | 0.246984i | ||||
\(323\) | 2.41906 | + | 9.02806i | 0.134600 | + | 0.502334i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.52855 | − | 0.741149i | 0.195729 | − | 0.0411115i | ||||
\(326\) | 15.6316i | 0.865753i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.05490 | − | 3.55918i | 0.113463 | − | 0.196523i | ||||
\(329\) | 19.4385 | + | 33.6685i | 1.07168 | + | 1.85620i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2535 | + | 2.74741i | 0.563582 | + | 0.151011i | 0.529351 | − | 0.848403i | \(-0.322435\pi\) |
0.0342304 | + | 0.999414i | \(0.489102\pi\) | |||||||
\(332\) | 1.88084 | + | 0.503969i | 0.103224 | + | 0.0276589i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.88146 | + | 13.6511i | 0.431254 | + | 0.746954i | ||||
\(335\) | 5.66015 | − | 9.80366i | 0.309247 | − | 0.535631i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6276i | 1.23261i | 0.787509 | + | 0.616303i | \(0.211370\pi\) | ||||
−0.787509 | + | 0.616303i | \(0.788630\pi\) | |||||||
\(338\) | 16.7761 | − | 13.4519i | 0.912501 | − | 0.731687i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.783757 | − | 2.92502i | −0.0425052 | − | 0.158632i | ||||
\(341\) | −25.3833 | − | 14.6550i | −1.37458 | − | 0.793615i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.12273 | − | 9.12273i | 0.492581 | − | 0.492581i | ||||
\(344\) | 6.88607 | − | 25.6992i | 0.371272 | − | 1.38561i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.48416 | − | 5.48416i | −0.294830 | − | 0.294830i | ||||
\(347\) | 10.4795 | − | 6.05032i | 0.562567 | − | 0.324798i | −0.191608 | − | 0.981471i | \(-0.561370\pi\) |
0.754175 | + | 0.656674i | \(0.228037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4836 | − | 3.88087i | 0.775289 | − | 0.207738i | 0.150582 | − | 0.988597i | \(-0.451885\pi\) |
0.624707 | + | 0.780859i | \(0.285218\pi\) | |||||||
\(350\) | 6.84371 | 0.365812 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.8493 | −1.11127 | ||||||||
\(353\) | 1.43209 | − | 0.383729i | 0.0762227 | − | 0.0204238i | −0.220506 | − | 0.975386i | \(-0.570771\pi\) |
0.296729 | + | 0.954962i | \(0.404104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4496 | + | 7.18780i | −0.660758 | + | 0.381489i | ||||
\(356\) | −3.84875 | − | 3.84875i | −0.203983 | − | 0.203983i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.20485 | + | 23.1568i | −0.327937 | + | 1.22388i | ||||
\(359\) | −5.51307 | + | 5.51307i | −0.290968 | + | 0.290968i | −0.837463 | − | 0.546494i | \(-0.815962\pi\) |
0.546494 | + | 0.837463i | \(0.315962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9848 | − | 6.91945i | −0.630781 | − | 0.364182i | ||||
\(362\) | −6.86031 | − | 25.6030i | −0.360570 | − | 1.34566i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.79533 | − | 4.96132i | 0.513415 | − | 0.260044i | ||||
\(365\) | − | 6.59549i | − | 0.345224i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.92106 | − | 11.9876i | 0.361276 | − | 0.625749i | −0.626895 | − | 0.779104i | \(-0.715674\pi\) |
0.988171 | + | 0.153355i | \(0.0490078\pi\) | |||||||
\(368\) | −3.19286 | − | 5.53020i | −0.166440 | − | 0.288282i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.1327 | + | 4.05479i | 0.786710 | + | 0.210798i | ||||
\(371\) | −39.7525 | − | 10.6517i | −2.06385 | − | 0.553007i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.28298 | + | 10.8824i | 0.325320 | + | 0.563472i | 0.981577 | − | 0.191066i | \(-0.0611945\pi\) |
−0.656257 | + | 0.754538i | \(0.727861\pi\) | |||||||
\(374\) | −17.8522 | + | 30.9209i | −0.923115 | + | 1.59888i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 19.6452i | − | 1.01312i | ||||||
\(377\) | −4.26649 | + | 13.0242i | −0.219735 | + | 0.670780i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0547530 | − | 0.204341i | −0.00281247 | − | 0.0104963i | 0.964505 | − | 0.264063i | \(-0.0850628\pi\) |
−0.967318 | + | 0.253567i | \(0.918396\pi\) | |||||||
\(380\) | −1.44813 | − | 0.836079i | −0.0742875 | − | 0.0428899i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0940 | − | 11.0940i | 0.567621 | − | 0.567621i | ||||
\(383\) | 2.73178 | − | 10.1951i | 0.139587 | − | 0.520948i | −0.860349 | − | 0.509705i | \(-0.829755\pi\) |
0.999937 | − | 0.0112427i | \(-0.00357874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.3495 | − | 15.3495i | −0.782285 | − | 0.782285i | ||||
\(386\) | 16.9504 | − | 9.78635i | 0.862755 | − | 0.498112i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.54698 | + | 2.29016i | −0.433907 | + | 0.116265i | ||||
\(389\) | 19.6503 | 0.996311 | 0.498155 | − | 0.867088i | \(-0.334011\pi\) | ||||
0.498155 | + | 0.867088i | \(0.334011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.32861 | −0.269479 | ||||||||
\(392\) | −20.4334 | + | 5.47512i | −1.03204 | + | 0.276535i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.5349 | − | 14.1652i | 1.23605 | − | 0.713634i | ||||
\(395\) | −1.56668 | − | 1.56668i | −0.0788282 | − | 0.0788282i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.16997 | − | 11.8305i | 0.159096 | − | 0.593756i | −0.839623 | − | 0.543169i | \(-0.817224\pi\) |
0.998720 | − | 0.0505866i | \(-0.0161091\pi\) | |||||||
\(398\) | −27.6597 | + | 27.6597i | −1.38646 | + | 1.38646i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.26979 | − | 2.46516i | −0.213490 | − | 0.123258i | ||||
\(401\) | 6.82125 | + | 25.4572i | 0.340637 | + | 1.27127i | 0.897627 | + | 0.440755i | \(0.145289\pi\) |
−0.556991 | + | 0.830519i | \(0.688044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.8663 | − | 11.0109i | −0.840169 | − | 0.548490i | ||||
\(404\) | − | 3.18386i | − | 0.158403i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.0069 | + | 22.5287i | −0.645523 | + | 1.11808i | ||||
\(407\) | −24.8462 | − | 43.0350i | −1.23158 | − | 2.13316i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3442 | + | 3.84351i | 0.709274 | + | 0.190050i | 0.595381 | − | 0.803443i | \(-0.297001\pi\) |
0.113893 | + | 0.993493i | \(0.463668\pi\) | |||||||
\(410\) | 3.14075 | + | 0.841560i | 0.155110 | + | 0.0415617i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.93114 | − | 8.54098i | −0.242940 | − | 0.420784i | ||||
\(413\) | −9.75655 | + | 16.8988i | −0.480088 | + | 0.831537i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.64546i | − | 0.129861i | ||||||
\(416\) | −14.3064 | − | 0.784289i | −0.701431 | − | 0.0384529i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.10281 | + | 19.0440i | 0.249587 | + | 0.931471i | ||||
\(419\) | −14.1443 | − | 8.16623i | −0.690995 | − | 0.398946i | 0.112990 | − | 0.993596i | \(-0.463957\pi\) |
−0.803985 | + | 0.594650i | \(0.797291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9020 | + | 19.9020i | −0.969964 | + | 0.969964i | −0.999562 | − | 0.0295975i | \(-0.990577\pi\) |
0.0295975 | + | 0.999562i | \(0.490577\pi\) | |||||||
\(422\) | 7.74645 | − | 28.9101i | 0.377091 | − | 1.40732i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.7051 | + | 14.7051i | 0.714145 | + | 0.714145i | ||||
\(425\) | −3.56295 | + | 2.05707i | −0.172829 | + | 0.0997826i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8841 | − | 2.91638i | 0.526717 | − | 0.141133i | ||||
\(428\) | −0.213649 | −0.0103271 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.0496 | 1.01510 | ||||||||
\(431\) | 11.3153 | − | 3.03192i | 0.545037 | − | 0.146042i | 0.0242139 | − | 0.999707i | \(-0.492292\pi\) |
0.520823 | + | 0.853665i | \(0.325625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.9523 | + | 17.2930i | −1.43942 | + | 0.831048i | −0.997809 | − | 0.0661593i | \(-0.978925\pi\) |
−0.441609 | + | 0.897208i | \(0.645592\pi\) | |||||||
\(434\) | −27.0341 | − | 27.0341i | −1.29768 | − | 1.29768i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.26859 | − | 4.73446i | 0.0607546 | − | 0.226739i | ||||
\(437\) | −2.08061 | + | 2.08061i | −0.0995291 | + | 0.0995291i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8729 | + | 13.7830i | 1.13939 | + | 0.657829i | 0.946280 | − | 0.323348i | \(-0.104808\pi\) |
0.193113 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(440\) | 2.83903 | + | 10.5954i | 0.135345 | + | 0.505115i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.4130 | + | 20.5458i | −0.637992 | + | 0.977266i | ||||
\(443\) | 5.03590i | 0.239263i | 0.992818 | + | 0.119631i | \(0.0381713\pi\) | ||||
−0.992818 | + | 0.119631i | \(0.961829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.69742 | + | 6.40412i | −0.175274 | + | 0.303584i | ||||
\(446\) | 10.0565 | + | 17.4184i | 0.476189 | + | 0.824784i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.1383 | + | 3.52041i | 0.620728 | + | 0.166324i | ||||
\(449\) | 22.5403 | + | 6.03965i | 1.06374 | + | 0.285029i | 0.747920 | − | 0.663789i | \(-0.231053\pi\) |
0.315823 | + | 0.948818i | \(0.397720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.15677 | − | 8.93179i | −0.242823 | − | 0.420582i | ||||
\(452\) | −4.73012 | + | 8.19280i | −0.222486 | + | 0.385357i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 15.5433i | − | 0.729484i | ||||||
\(455\) | −9.95517 | − | 11.1100i | −0.466706 | − | 0.520844i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.11569 | − | 15.3599i | −0.192524 | − | 0.718508i | −0.992894 | − | 0.119002i | \(-0.962030\pi\) |
0.800370 | − | 0.599506i | \(-0.204636\pi\) | |||||||
\(458\) | 9.70210 | + | 5.60151i | 0.453350 | + | 0.261742i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.674102 | − | 0.674102i | 0.0314302 | − | 0.0314302i | ||||
\(461\) | 6.80355 | − | 25.3912i | 0.316873 | − | 1.18259i | −0.605360 | − | 0.795952i | \(-0.706971\pi\) |
0.922233 | − | 0.386634i | \(-0.126362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7236 | − | 14.7236i | −0.684262 | − | 0.684262i | 0.276696 | − | 0.960958i | \(-0.410761\pi\) |
−0.960958 | + | 0.276696i | \(0.910761\pi\) | |||||||
\(464\) | 16.2301 | − | 9.37043i | 0.753461 | − | 0.435011i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −38.6418 | + | 10.3540i | −1.79005 | + | 0.479642i | ||||
\(467\) | −5.89065 | −0.272587 | −0.136293 | − | 0.990669i | \(-0.543519\pi\) | ||||
−0.136293 | + | 0.990669i | \(0.543519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.8368 | −2.16272 | ||||||||
\(470\) | 15.0130 | − | 4.02273i | 0.692500 | − | 0.185555i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.53925 | − | 4.93014i | 0.393051 | − | 0.226928i | ||||
\(473\) | −47.2115 | − | 47.2115i | −2.17079 | − | 2.17079i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.587987 | + | 2.19440i | −0.0269787 | + | 0.100686i | ||||
\(476\) | −8.85931 | + | 8.85931i | −0.406066 | + | 0.406066i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.40002 | − | 4.27240i | −0.338469 | − | 0.195415i | ||||
\(479\) | 5.30113 | + | 19.7841i | 0.242215 | + | 0.903958i | 0.974763 | + | 0.223242i | \(0.0716642\pi\) |
−0.732548 | + | 0.680715i | \(0.761669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.4302 | − | 30.4645i | −0.703557 | − | 1.38906i | ||||
\(482\) | 10.2889i | 0.468645i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.08238 | + | 10.5350i | −0.276472 | + | 0.478864i | ||||
\(485\) | 6.01081 | + | 10.4110i | 0.272937 | + | 0.472740i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2243 | − | 4.34729i | −0.735193 | − | 0.196994i | −0.128252 | − | 0.991742i | \(-0.540937\pi\) |
−0.606941 | + | 0.794747i | \(0.707603\pi\) | |||||||
\(488\) | −5.49989 | − | 1.47369i | −0.248968 | − | 0.0667109i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.36829 | − | 14.4943i | −0.378041 | − | 0.654786i | ||||
\(491\) | 14.5488 | − | 25.1992i | 0.656577 | − | 1.13723i | −0.324918 | − | 0.945742i | \(-0.605337\pi\) |
0.981496 | − | 0.191483i | \(-0.0613298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 15.6384i | − | 0.704319i | ||||||
\(494\) | 2.78508 | + | 13.2596i | 0.125307 | + | 0.596577i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.12867 | + | 26.6046i | 0.320087 | + | 1.19458i | ||||
\(497\) | 51.5094 | + | 29.7389i | 2.31051 | + | 1.33397i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.00053 | − | 3.00053i | 0.134322 | − | 0.134322i | −0.636749 | − | 0.771071i | \(-0.719721\pi\) |
0.771071 | + | 0.636749i | \(0.219721\pi\) | |||||||
\(500\) | 0.190503 | − | 0.710968i | 0.00851956 | − | 0.0317954i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.6615 | + | 13.6615i | 0.609743 | + | 0.609743i | ||||
\(503\) | 5.95857 | − | 3.44018i | 0.265680 | − | 0.153390i | −0.361243 | − | 0.932472i | \(-0.617648\pi\) |
0.626923 | + | 0.779082i | \(0.284314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.17822 | + | 1.11955i | −0.185928 | + | 0.0498193i | ||||
\(506\) | −11.2403 | −0.499691 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.69261 | −0.0750973 | ||||||||
\(509\) | −8.07544 | + | 2.16381i | −0.357937 | + | 0.0959090i | −0.433306 | − | 0.901247i | \(-0.642653\pi\) |
0.0753690 | + | 0.997156i | \(0.475987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.6324 | + | 13.6442i | −1.04544 | + | 0.603582i | ||||
\(512\) | −0.723595 | − | 0.723595i | −0.0319787 | − | 0.0319787i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.62701 | − | 21.0003i | 0.248197 | − | 0.926282i | ||||
\(515\) | −9.47449 | + | 9.47449i | −0.417496 | + | 0.417496i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.6947 | − | 24.6498i | −1.87771 | − | 1.08410i | ||||
\(518\) | −16.7764 | − | 62.6102i | −0.737111 | − | 2.75094i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.54952 | + | 7.37716i | 0.0679511 | + | 0.323510i | ||||
\(521\) | 15.7170i | 0.688573i | 0.938865 | + | 0.344287i | \(0.111879\pi\) | ||||
−0.938865 | + | 0.344287i | \(0.888121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7516 | + | 22.0864i | −0.557589 | + | 0.965772i | 0.440109 | + | 0.897945i | \(0.354940\pi\) |
−0.997697 | + | 0.0678271i | \(0.978393\pi\) | |||||||
\(524\) | 8.33703 | + | 14.4402i | 0.364205 | + | 0.630822i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2095 | + | 5.68306i | 0.924776 | + | 0.247793i | ||||
\(527\) | 22.2003 | + | 5.94856i | 0.967061 | + | 0.259123i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6612 | + | 18.4658i | 0.463532 | + | 0.802861i | ||||
\(530\) | −8.22666 | + | 14.2490i | −0.357343 | + | 0.618937i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.91842i | 0.299951i | ||||||||
\(533\) | −3.20250 | − | 6.32282i | −0.138716 | − | 0.273872i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0751260 | + | 0.280374i | 0.00324798 | + | 0.0121216i | ||||
\(536\) | 20.4966 | + | 11.8337i | 0.885316 | + | 0.511138i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.23173 | − | 3.23173i | 0.139330 | − | 0.139330i | ||||
\(539\) | −13.7398 | + | 51.2778i | −0.591817 | + | 2.20869i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8129 | + | 16.8129i | 0.722842 | + | 0.722842i | 0.969183 | − | 0.246341i | \(-0.0792283\pi\) |
−0.246341 | + | 0.969183i | \(0.579228\pi\) | |||||||
\(542\) | −24.2687 | + | 14.0115i | −1.04243 | + | 0.601846i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.7919 | − | 4.23143i | 0.677073 | − | 0.181421i | ||||
\(545\) | −6.65918 | −0.285248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5401 | 0.621690 | 0.310845 | − | 0.950461i | \(-0.399388\pi\) | ||||
0.310845 | + | 0.950461i | \(0.399388\pi\) | |||||||
\(548\) | −4.91668 | + | 1.31742i | −0.210030 | + | 0.0562774i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.51576 | + | 4.33923i | −0.320473 | + | 0.185025i | ||||
\(551\) | −6.10618 | − | 6.10618i | −0.260132 | − | 0.260132i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.37258 | + | 8.85459i | −0.100892 | + | 0.376535i | ||||
\(554\) | −34.8487 | + | 34.8487i | −1.48058 | + | 1.48058i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.10752 | − | 2.37148i | −0.174198 | − | 0.100573i | ||||
\(557\) | 8.21593 | + | 30.6622i | 0.348120 | + | 1.29920i | 0.888925 | + | 0.458053i | \(0.151453\pi\) |
−0.540805 | + | 0.841148i | \(0.681880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.6198 | − | 34.1717i | −1.29508 | − | 1.44531i | ||||
\(560\) | 20.3988i | 0.862008i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.80360 | − | 4.85598i | 0.118263 | − | 0.204837i | ||||
\(563\) | 12.2594 | + | 21.2339i | 0.516672 | + | 0.894903i | 0.999813 | + | 0.0193597i | \(0.00616276\pi\) |
−0.483140 | + | 0.875543i | \(0.660504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4148 | + | 3.32654i | 0.522295 | + | 0.139948i | ||||
\(566\) | −11.8928 | − | 3.18666i | −0.499891 | − | 0.133945i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.0276 | − | 26.0285i | −0.630542 | − | 1.09213i | ||||
\(569\) | −7.14531 | + | 12.3760i | −0.299547 | + | 0.518831i | −0.976032 | − | 0.217626i | \(-0.930169\pi\) |
0.676485 | + | 0.736456i | \(0.263502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.3591i | − | 1.56343i | −0.623636 | − | 0.781715i | \(-0.714345\pi\) | ||
0.623636 | − | 0.781715i | \(-0.285655\pi\) | |||||||
\(572\) | −7.61153 | + | 11.6592i | −0.318254 | + | 0.487496i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.48189 | − | 12.9946i | −0.145331 | − | 0.542384i | ||||
\(575\) | −1.12167 | − | 0.647596i | −0.0467769 | − | 0.0270066i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.25987 | + | 9.25987i | −0.385494 | + | 0.385494i | −0.873077 | − | 0.487583i | \(-0.837879\pi\) |
0.487583 | + | 0.873077i | \(0.337879\pi\) | |||||||
\(578\) | −0.0316077 | + | 0.117962i | −0.00131471 | + | 0.00490656i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.97836 | + | 1.97836i | 0.0821468 | + | 0.0821468i | ||||
\(581\) | −9.47898 | + | 5.47269i | −0.393254 | + | 0.227045i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.4099 | − | 13.5073i | 2.08777 | − | 0.559415i | ||||
\(584\) | 13.7892 | 0.570602 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.83632 | −0.323716 | ||||||||
\(587\) | 21.1431 | − | 5.66527i | 0.872668 | − | 0.233831i | 0.205427 | − | 0.978673i | \(-0.434142\pi\) |
0.667241 | + | 0.744842i | \(0.267475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9910 | − | 6.34567i | 0.452877 | − | 0.261469i | ||||
\(590\) | 5.51624 | + | 5.51624i | 0.227100 | + | 0.227100i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0860 | + | 45.1055i | −0.496731 | + | 1.85383i | ||||
\(593\) | −7.96501 | + | 7.96501i | −0.327084 | + | 0.327084i | −0.851476 | − | 0.524393i | \(-0.824292\pi\) |
0.524393 | + | 0.851476i | \(0.324292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7414 | + | 8.51097i | 0.604340 | + | 0.348916i | ||||
\(596\) | −3.17980 | − | 11.8672i | −0.130250 | − | 0.486098i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.71288 | − | 0.422825i | −0.315403 | − | 0.0172906i | ||||
\(599\) | 2.08260i | 0.0850926i | 0.999094 | + | 0.0425463i | \(0.0135470\pi\) | ||||
−0.999094 | + | 0.0425463i | \(0.986453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0978 | − | 24.4180i | 0.575060 | − | 0.996033i | −0.420975 | − | 0.907072i | \(-0.638312\pi\) |
0.996035 | − | 0.0889605i | \(-0.0283545\pi\) | |||||||
\(602\) | −43.5456 | − | 75.4231i | −1.77479 | − | 3.07402i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.947415 | − | 0.253859i | −0.0385498 | − | 0.0103294i | ||||
\(605\) | 15.9640 | + | 4.27754i | 0.649029 | + | 0.173907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6540 | + | 27.1134i | 0.635374 | + | 1.10050i | 0.986436 | + | 0.164148i | \(0.0524875\pi\) |
−0.351061 | + | 0.936352i | \(0.614179\pi\) | |||||||
\(608\) | 4.51391 | − | 7.81832i | 0.183063 | − | 0.317075i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 4.50484i | − | 0.182396i | ||||||
\(611\) | −28.3691 | − | 18.5203i | −1.14769 | − | 0.749252i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0358 | − | 44.9183i | −0.486122 | − | 1.81423i | −0.574955 | − | 0.818185i | \(-0.694981\pi\) |
0.0888337 | − | 0.996046i | \(-0.471686\pi\) | |||||||
\(614\) | 42.3774 | + | 24.4666i | 1.71021 | + | 0.987391i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 32.0913 | − | 32.0913i | 1.29300 | − | 1.29300i | ||||
\(617\) | −8.22581 | + | 30.6991i | −0.331159 | + | 1.23590i | 0.576815 | + | 0.816874i | \(0.304295\pi\) |
−0.907974 | + | 0.419026i | \(0.862371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.4733 | − | 21.4733i | −0.863085 | − | 0.863085i | 0.128610 | − | 0.991695i | \(-0.458948\pi\) |
−0.991695 | + | 0.128610i | \(0.958948\pi\) | |||||||
\(620\) | −3.56101 | + | 2.05595i | −0.143014 | + | 0.0825689i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.4250 | + | 6.54466i | −0.979354 | + | 0.262417i | ||||
\(623\) | 30.5955 | 1.22578 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 39.1829 | − | 10.4990i | 1.56607 | − | 0.419626i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.55164 | − | 0.895839i | 0.0619172 | − | 0.0357479i | ||||
\(629\) | 27.5534 | + | 27.5534i | 1.09862 | + | 1.09862i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.86108 | + | 6.94563i | −0.0740883 | + | 0.276501i | −0.993025 | − | 0.117904i | \(-0.962383\pi\) |
0.918937 | + | 0.394405i | \(0.129049\pi\) | |||||||
\(632\) | 3.27546 | − | 3.27546i | 0.130291 | − | 0.130291i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.9974 | − | 15.5869i | −1.07220 | − | 0.619037i | ||||
\(635\) | 0.595177 | + | 2.22123i | 0.0236189 | + | 0.0881469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3570 | + | 34.6691i | −0.449979 | + | 1.37364i | ||||
\(638\) | − | 32.9880i | − | 1.30601i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.69279 | − | 11.5922i | 0.264556 | − | 0.458224i | ||||
\(641\) | 4.46307 | + | 7.73027i | 0.176281 | + | 0.305327i | 0.940604 | − | 0.339506i | \(-0.110260\pi\) |
−0.764323 | + | 0.644834i | \(0.776927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.6675 | − | 7.68142i | −1.13053 | − | 0.302926i | −0.355395 | − | 0.934716i | \(-0.615654\pi\) |
−0.775139 | + | 0.631791i | \(0.782320\pi\) | |||||||
\(644\) | −3.80990 | − | 1.02086i | −0.150131 | − | 0.0402275i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.73005 | − | 13.3888i | −0.304135 | − | 0.526777i | ||||
\(647\) | −9.62938 | + | 16.6786i | −0.378570 | + | 0.655703i | −0.990854 | − | 0.134935i | \(-0.956917\pi\) |
0.612284 | + | 0.790638i | \(0.290251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.7444i | − | 0.971303i | ||||||
\(650\) | −5.32041 | + | 2.69478i | −0.208684 | + | 0.105698i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.80029 | − | 6.71879i | −0.0705049 | − | 0.263128i | ||||
\(653\) | −11.3645 | − | 6.56128i | −0.444726 | − | 0.256763i | 0.260874 | − | 0.965373i | \(-0.415989\pi\) |
−0.705600 | + | 0.708610i | \(0.749323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0185 | − | 16.0185i | 0.625893 | − | 0.625893i | ||||
\(656\) | −2.50842 | + | 9.36153i | −0.0979372 | + | 0.365506i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −45.4715 | − | 45.4715i | −1.77267 | − | 1.77267i | ||||
\(659\) | 21.1474 | − | 12.2094i | 0.823785 | − | 0.475612i | −0.0279350 | − | 0.999610i | \(-0.508893\pi\) |
0.851720 | + | 0.523997i | \(0.175560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3078 | + | 6.51327i | −0.945466 | + | 0.253337i | −0.698437 | − | 0.715671i | \(-0.746121\pi\) |
−0.247029 | + | 0.969008i | \(0.579454\pi\) | |||||||
\(662\) | −17.5586 | −0.682433 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.53087 | 0.214640 | ||||||||
\(665\) | 9.07914 | − | 2.43275i | 0.352074 | − | 0.0943379i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.26362 | − | 2.46160i | 0.165088 | − | 0.0953136i | ||||
\(668\) | −4.95982 | − | 4.95982i | −0.191901 | − | 0.191901i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.84636 | + | 18.0869i | −0.187231 | + | 0.698757i | ||||
\(671\) | −10.1038 | + | 10.1038i | −0.390052 | + | 0.390052i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.54380 | − | 2.62336i | −0.175151 | − | 0.101123i | 0.409862 | − | 0.912148i | \(-0.365577\pi\) |
−0.585012 | + | 0.811024i | \(0.698910\pi\) | |||||||
\(674\) | −9.68718 | − | 36.1531i | −0.373136 | − | 1.39256i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.66148 | + | 7.71402i | −0.217749 | + | 0.296693i | ||||
\(677\) | 1.76098i | 0.0676799i | 0.999427 | + | 0.0338399i | \(0.0107736\pi\) | ||||
−0.999427 | + | 0.0338399i | \(0.989226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.8692 | − | 43.0748i | 0.954393 | − | 1.65306i | ||||
\(680\) | −4.30073 | − | 7.44908i | −0.164925 | − | 0.285659i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46.8298 | + | 12.5480i | 1.79321 | + | 0.480488i | ||||
\(683\) | 27.7031 | + | 7.42302i | 1.06003 | + | 0.284034i | 0.746391 | − | 0.665508i | \(-0.231785\pi\) |
0.313639 | + | 0.949542i | \(0.398452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.45774 | + | 5.98898i | 0.132113 | + | 0.228827i | ||||
\(686\) | −10.6702 | + | 18.4813i | −0.407389 | + | 0.705619i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 62.7420i | 2.39202i | ||||||||
\(689\) | 35.0985 | − | 7.37220i | 1.33715 | − | 0.280858i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.25298 | + | 30.8005i | 0.313958 | + | 1.17171i | 0.924956 | + | 0.380075i | \(0.124102\pi\) |
−0.610998 | + | 0.791632i | \(0.709232\pi\) | |||||||
\(692\) | 2.98882 | + | 1.72560i | 0.113618 | + | 0.0655973i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.1532 | + | 14.1532i | −0.537248 | + | 0.537248i | ||||
\(695\) | −1.66778 | + | 6.22425i | −0.0632626 | + | 0.236099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.71862 | + | 5.71862i | 0.216608 | + | 0.216608i | ||||
\(698\) | −21.4796 | + | 12.4012i | −0.813013 | + | 0.469393i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.94157 | + | 0.788192i | −0.111181 | + | 0.0297908i | ||||
\(701\) | −23.0986 | −0.872421 | −0.436211 | − | 0.899845i | \(-0.643680\pi\) | ||||
−0.436211 | + | 0.899845i | \(0.643680\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.5170 | 0.811528 | ||||||||
\(704\) | −16.6606 | + | 4.46420i | −0.627921 | + | 0.168251i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.12383 | + | 1.22620i | −0.0799315 | + | 0.0461485i | ||||
\(707\) | 12.6550 | + | 12.6550i | 0.475940 | + | 0.475940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.86877 | − | 18.1705i | 0.182850 | − | 0.682407i | −0.812230 | − | 0.583337i | \(-0.801747\pi\) |
0.995081 | − | 0.0990696i | \(-0.0315867\pi\) | |||||||
\(710\) | 16.8141 | − | 16.8141i | 0.631021 | − | 0.631021i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.3891 | − | 7.73021i | −0.501778 | − | 0.289702i | ||||
\(713\) | 1.87269 | + | 6.98899i | 0.0701330 | + | 0.261740i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9770 | + | 5.88894i | 0.672302 | + | 0.220234i | ||||
\(716\) | − | 10.6679i | − | 0.398678i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.44822 | − | 11.1686i | 0.240645 | − | 0.416810i | ||||
\(719\) | −7.71367 | − | 13.3605i | −0.287671 | − | 0.498261i | 0.685582 | − | 0.727995i | \(-0.259548\pi\) |
−0.973253 | + | 0.229734i | \(0.926214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.5481 | + | 14.3482i | 1.99424 | + | 0.534354i | ||||
\(722\) | 22.1109 | + | 5.92461i | 0.822884 | + | 0.220491i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.89741 | + | 10.2146i | 0.219176 | + | 0.379623i | ||||
\(725\) | 1.90057 | − | 3.29188i | 0.0705853 | − | 0.122257i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4554i | 0.387769i | 0.981024 | + | 0.193885i | \(0.0621088\pi\) | ||||
−0.981024 | + | 0.193885i | \(0.937891\pi\) | |||||||
\(728\) | 23.2277 | − | 20.8133i | 0.860875 | − | 0.771393i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.82361 | + | 10.5379i | 0.104507 | + | 0.390024i | ||||
\(731\) | 45.3412 | + | 26.1777i | 1.67700 | + | 0.968218i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4480 | + | 27.4480i | −1.01382 | + | 1.01382i | −0.0139129 | + | 0.999903i | \(0.504429\pi\) |
−0.999903 | + | 0.0139129i | \(0.995571\pi\) | |||||||
\(734\) | −5.92598 | + | 22.1161i | −0.218732 | + | 0.816319i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.63941 | + | 3.63941i | 0.134150 | + | 0.134150i | ||||
\(737\) | 51.4362 | − | 29.6967i | 1.89468 | − | 1.09389i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.6134 | − | 7.66694i | 1.05256 | − | 0.282033i | 0.309252 | − | 0.950980i | \(-0.399922\pi\) |
0.743310 | + | 0.668947i | \(0.233255\pi\) | |||||||
\(740\) | −6.97134 | −0.256271 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 68.0743 | 2.49909 | ||||||||
\(743\) | −25.2630 | + | 6.76921i | −0.926811 | + | 0.248338i | −0.690494 | − | 0.723338i | \(-0.742607\pi\) |
−0.236317 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4553 | + | 8.34579i | −0.529602 | + | 0.305766i | ||||
\(746\) | −14.6975 | − | 14.6975i | −0.538113 | − | 0.538113i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.11209 | − | 15.3465i | 0.150353 | − | 0.561124i | ||||
\(749\) | 0.849198 | − | 0.849198i | 0.0310290 | − | 0.0310290i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.04739 | − | 0.604708i | −0.0382196 | − | 0.0220661i | 0.480768 | − | 0.876848i | \(-0.340358\pi\) |
−0.518988 | + | 0.854781i | \(0.673691\pi\) | |||||||
\(752\) | 11.9904 | + | 44.7490i | 0.437247 | + | 1.63183i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.24091 | − | 22.6358i | 0.0451912 | − | 0.824346i | ||||
\(755\) | 1.33257i | 0.0484972i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.9100 | + | 29.2890i | −0.614605 | + | 1.06453i | 0.375848 | + | 0.926681i | \(0.377351\pi\) |
−0.990454 | + | 0.137847i | \(0.955982\pi\) | |||||||
\(758\) | 0.174962 | + | 0.303043i | 0.00635490 | + | 0.0110070i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.58783 | − | 1.22931i | −0.166418 | − | 0.0445916i | ||||
\(761\) | −26.7925 | − | 7.17903i | −0.971227 | − | 0.260240i | −0.261881 | − | 0.965100i | \(-0.584343\pi\) |
−0.709346 | + | 0.704860i | \(0.751010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7759 | + | 23.8606i | 0.498721 | + | 0.863810i | ||||
\(764\) | −3.49075 | + | 6.04616i | −0.126291 | + | 0.218742i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.4587i | 0.630808i | ||||||||
\(767\) | 0.930810 | − | 16.9792i | 0.0336096 | − | 0.613082i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.369770 | − | 1.38000i | −0.0133343 | − | 0.0497641i | 0.958938 | − | 0.283615i | \(-0.0915338\pi\) |
−0.972272 | + | 0.233851i | \(0.924867\pi\) | |||||||
\(770\) | 31.0959 | + | 17.9532i | 1.12062 | + | 0.646989i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.15857 | + | 6.15857i | −0.221652 | + | 0.221652i | ||||
\(773\) | −9.03253 | + | 33.7099i | −0.324878 | + | 1.21246i | 0.589557 | + | 0.807726i | \(0.299302\pi\) |
−0.914435 | + | 0.404733i | \(0.867364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.95022 | + | 3.95022i | 0.141896 | + | 0.141896i | ||||
\(776\) | −21.7664 | + | 12.5668i | −0.781367 | + | 0.451122i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.3961 | + | 8.41255i | −1.12560 | + | 0.301605i | ||||
\(779\) | 4.46579 | 0.160004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.4235 | −2.69886 | ||||||||
\(782\) | 8.51372 | − | 2.28124i | 0.304450 | − | 0.0815771i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 43.2028 | − | 24.9431i | 1.54296 | − | 0.890826i | ||||
\(785\) | −1.72123 | − | 1.72123i | −0.0614334 | − | 0.0614334i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.7444 | + | 47.5627i | −0.454288 | + | 1.69543i | 0.235884 | + | 0.971781i | \(0.424201\pi\) |
−0.690172 | + | 0.723645i | \(0.742465\pi\) | |||||||
\(788\) | −8.91421 | + | 8.91421i | −0.317556 | + | 0.317556i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.17386 | + | 1.83243i | 0.112921 | + | 0.0651949i | ||||
\(791\) | −13.7633 | − | 51.3652i | −0.489366 | − | 1.82634i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.31310 | + | 6.55296i | −0.259696 | + | 0.232702i | ||||
\(794\) | 20.2591i | 0.718970i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.70316 | − | 15.0743i | 0.308475 | − | 0.534295i | ||||
\(797\) | −24.6703 | − | 42.7302i | −0.873866 | − | 1.51358i | −0.857966 | − | 0.513706i | \(-0.828272\pi\) |
−0.0158996 | − | 0.999874i | \(-0.505061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.3410 | + | 10.0055i | 1.32103 | + | 0.353969i | ||||
\(800\) | 3.83845 | + | 1.02851i | 0.135710 | + | 0.0363633i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.7971 | − | 37.7537i | −0.769684 | − | 1.33313i | ||||
\(803\) | 17.3021 | − | 29.9681i | 0.610577 | − | 1.05755i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.35876i | 0.188871i | ||||||||
\(806\) | 31.6618 | + | 10.3718i | 1.11524 | + | 0.365332i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.34065 | − | 8.73542i | −0.0823437 | − | 0.307311i | ||||
\(809\) | −39.9550 | − | 23.0680i | −1.40474 | − | 0.811029i | −0.409869 | − | 0.912144i | \(-0.634426\pi\) |
−0.994875 | + | 0.101115i | \(0.967759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6219 | + | 29.6219i | −1.04017 | + | 1.04017i | −0.0410063 | + | 0.999159i | \(0.513056\pi\) |
−0.999159 | + | 0.0410063i | \(0.986944\pi\) | |||||||
\(812\) | 2.99602 | − | 11.1813i | 0.105140 | − | 0.392387i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 58.1216 | + | 58.1216i | 2.03716 | + | 2.03716i | ||||
\(815\) | −8.18411 | + | 4.72510i | −0.286677 | + | 0.165513i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.9253 | − | 7.48256i | 0.976982 | − | 0.261781i | ||||
\(818\) | −24.5637 | −0.858850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.44688 | −0.0505273 | ||||||||
\(821\) | 18.2435 | − | 4.88833i | 0.636702 | − | 0.170604i | 0.0739928 | − | 0.997259i | \(-0.476426\pi\) |
0.562709 | + | 0.826655i | \(0.309759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.59188 | + | 3.80582i | −0.229779 | + | 0.132663i | −0.610470 | − | 0.792039i | \(-0.709019\pi\) |
0.380691 | + | 0.924702i | \(0.375686\pi\) | |||||||
\(824\) | −19.8084 | − | 19.8084i | −0.690057 | − | 0.690057i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.35380 | − | 31.1768i | 0.290666 | − | 1.08478i | ||||
\(827\) | 34.7183 | − | 34.7183i | 1.20727 | − | 1.20727i | 0.235367 | − | 0.971907i | \(-0.424371\pi\) |
0.971907 | − | 0.235367i | \(-0.0756291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.7503 | − | 20.0631i | −1.20693 | − | 0.696821i | −0.244842 | − | 0.969563i | \(-0.578736\pi\) |
−0.962087 | + | 0.272742i | \(0.912069\pi\) | |||||||
\(830\) | 1.13255 | + | 4.22675i | 0.0393116 | + | 0.146713i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.6002 | + | 2.43653i | −0.402163 | + | 0.0844716i | ||||
\(833\) | − | 41.6279i | − | 1.44232i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.76480 | + | 8.25288i | −0.164893 | + | 0.285603i | ||||
\(836\) | −4.38660 | − | 7.59781i | −0.151714 | − | 0.262776i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.0950 | + | 6.99213i | 0.901436 | + | 0.241539i | ||||
\(839\) | −50.8437 | − | 13.6235i | −1.75532 | − | 0.470336i | −0.769570 | − | 0.638563i | \(-0.779529\pi\) |
−0.985748 | + | 0.168227i | \(0.946196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.27568 | − | 12.6019i | −0.250886 | − | 0.434547i | ||||
\(842\) | 23.2779 | − | 40.3185i | 0.802209 | − | 1.38947i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.3184i | 0.458437i | ||||||||
\(845\) | 12.1140 | + | 4.71713i | 0.416734 | + | 0.162274i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.6980 | − | 66.0498i | −0.608110 | − | 2.26950i | ||||
\(848\) | −42.4716 | − | 24.5210i | −1.45848 | − | 0.842053i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.81201 | − | 4.81201i | 0.165050 | − | 0.165050i | ||||
\(851\) | −3.17498 | + | 11.8492i | −0.108837 | + | 0.406185i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.4352 | + | 32.4352i | 1.11056 | + | 1.11056i | 0.993074 | + | 0.117487i | \(0.0374837\pi\) |
0.117487 | + | 0.993074i | \(0.462516\pi\) | |||||||
\(854\) | −16.1414 | + | 9.31922i | −0.552346 | + | 0.318897i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.586179 | + | 0.157066i | −0.0200352 | + | 0.00536841i | ||||
\(857\) | 23.5952 | 0.805995 | 0.402998 | − | 0.915201i | \(-0.367968\pi\) | ||||
0.402998 | + | 0.915201i | \(0.367968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5309 | 0.564027 | 0.282013 | − | 0.959410i | \(-0.408998\pi\) | ||||
0.282013 | + | 0.959410i | \(0.408998\pi\) | |||||||
\(860\) | −9.04758 | + | 2.42429i | −0.308520 | + | 0.0826677i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.7808 | + | 9.68842i | −0.571557 | + | 0.329989i | ||||
\(863\) | 6.22093 | + | 6.22093i | 0.211763 | + | 0.211763i | 0.805016 | − | 0.593253i | \(-0.202157\pi\) |
−0.593253 | + | 0.805016i | \(0.702157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.21356 | − | 4.52905i | 0.0412621 | − | 0.153992i | ||||
\(866\) | 40.4527 | − | 40.4527i | 1.37464 | − | 1.37464i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.7334 | + | 8.50632i | 0.500084 | + | 0.288723i | ||||
\(869\) | −3.00865 | − | 11.2284i | −0.102062 | − | 0.380899i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.4117 | − | 18.4425i | 1.23376 | − | 0.624900i | ||||
\(872\) | − | 13.9224i | − | 0.471471i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.43353 | − | 4.21500i | 0.0823155 | − | 0.142575i | ||||
\(875\) | 2.06871 | + | 3.58311i | 0.0699352 | + | 0.121131i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.68900 | − | 0.452567i | −0.0570336 | − | 0.0152821i | 0.230189 | − | 0.973146i | \(-0.426065\pi\) |
−0.287223 | + | 0.957864i | \(0.592732\pi\) | |||||||
\(878\) | −44.0434 | − | 11.8014i | −1.48639 | − | 0.398278i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.9338 | − | 22.4020i | −0.435999 | − | 0.755172i | ||||
\(881\) | −19.1433 | + | 33.1572i | −0.644955 | + | 1.11710i | 0.339356 | + | 0.940658i | \(0.389791\pi\) |
−0.984312 | + | 0.176438i | \(0.943543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.61695i | − | 0.121720i | −0.998146 | − | 0.0608601i | \(-0.980616\pi\) | ||
0.998146 | − | 0.0608601i | \(-0.0193843\pi\) | |||||||
\(884\) | 3.39893 | − | 10.3758i | 0.114318 | − | 0.348977i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.15593 | − | 8.04605i | −0.0724299 | − | 0.270312i | ||||
\(887\) | −13.8194 | − | 7.97865i | −0.464011 | − | 0.267897i | 0.249718 | − | 0.968319i | \(-0.419662\pi\) |
−0.713729 | + | 0.700422i | \(0.752995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.72767 | − | 6.72767i | 0.225639 | − | 0.225639i | ||||
\(890\) | 3.16582 | − | 11.8150i | 0.106119 | − | 0.396040i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.32858 | − | 6.32858i | −0.211896 | − | 0.211896i | ||||
\(893\) | 18.4869 | − | 10.6734i | 0.618642 | − | 0.357173i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.9996 | + | 3.75119i | −0.467957 | + | 0.125389i | ||||
\(896\) | −55.3817 | −1.85017 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.5991 | −1.28807 | ||||||||
\(899\) | −20.5113 | + | 5.49599i | −0.684091 | + | 0.183302i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.4406 | + | 20.4617i | −1.18070 | + | 0.681677i | ||||
\(902\) | 12.0630 | + | 12.0630i | 0.401653 | + | 0.401653i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.95480 | + | 25.9557i | −0.231313 | + | 0.863273i | ||||
\(905\) | 11.3311 | − | 11.3311i | 0.376657 | − | 0.376657i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.8532 | + | 9.73022i | 0.559602 | + | 0.323087i | 0.752986 | − | 0.658037i | \(-0.228613\pi\) |
−0.193383 | + | 0.981123i | \(0.561946\pi\) | |||||||
\(908\) | 1.79013 | + | 6.68085i | 0.0594075 | + | 0.221712i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.6621 | + | 13.4889i | 0.684941 | + | 0.447153i | ||||
\(911\) | − | 15.3382i | − | 0.508176i | −0.967181 | − | 0.254088i | \(-0.918225\pi\) | ||
0.967181 | − | 0.254088i | \(-0.0817752\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.93988 | − | 12.0202i | 0.229676 | − | 0.397811i | ||||
\(914\) | 13.1516 | + | 22.7792i | 0.435015 | + | 0.753469i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.81530 | − | 1.29026i | −0.159102 | − | 0.0426312i | ||||
\(917\) | −90.5334 | − | 24.2584i | −2.98968 | − | 0.801081i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1330 | + | 21.0150i | 0.400232 | + | 0.693222i | 0.993754 | − | 0.111596i | \(-0.0355963\pi\) |
−0.593522 | + | 0.804818i | \(0.702263\pi\) | |||||||
\(920\) | 1.35393 | − | 2.34508i | 0.0446378 | − | 0.0773150i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 43.4812i | 1.43198i | ||||||||
\(923\) | −51.7542 | − | 2.83720i | −1.70351 | − | 0.0933876i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.45136 | + | 9.14858i | 0.0806001 | + | 0.300804i | ||||
\(926\) | 29.8277 | + | 17.2210i | 0.980200 | + | 0.565919i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.6810 | + | 10.6810i | −0.350620 | + | 0.350620i | ||||
\(929\) | −14.4986 | + | 54.1094i | −0.475683 | + | 1.77527i | 0.143098 | + | 0.989708i | \(0.454293\pi\) |
−0.618781 | + | 0.785563i | \(0.712373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.2540 | − | 16.2540i | −0.532705 | − | 0.532705i | ||||
\(932\) | 15.4166 | − | 8.90078i | 0.504987 | − | 0.291555i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.41172 | − | 2.52186i | 0.307961 | − | 0.0825179i | ||||
\(935\) | −21.5854 | −0.705918 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.5441 | 1.74921 | 0.874605 | − | 0.484837i | \(-0.161121\pi\) | ||||
0.874605 | + | 0.484837i | \(0.161121\pi\) | |||||||
\(938\) | 74.8330 | − | 20.0514i | 2.44338 | − | 0.654703i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.98963 | + | 3.45811i | −0.195360 | + | 0.112791i | ||||
\(941\) | −12.8048 | − | 12.8048i | −0.417426 | − | 0.417426i | 0.466890 | − | 0.884316i | \(-0.345375\pi\) |
−0.884316 | + | 0.466890i | \(0.845375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.658958 | + | 2.45927i | −0.0214586 | + | 0.0800847i | ||||
\(944\) | −16.4421 | + | 16.4421i | −0.535145 | + | 0.535145i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 95.6435 | + | 55.2198i | 3.10964 | + | 1.79535i | ||||
\(947\) | 11.2602 | + | 42.0237i | 0.365907 | + | 1.36559i | 0.866186 | + | 0.499721i | \(0.166564\pi\) |
−0.500279 | + | 0.865864i | \(0.666769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9997 | − | 19.9127i | 0.421987 | − | 0.646393i | ||||
\(950\) | − | 3.75779i | − | 0.121919i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.7939 | + | 30.8200i | −0.576704 | + | 0.998881i | ||||
\(953\) | −7.37765 | − | 12.7785i | −0.238986 | − | 0.413935i | 0.721438 | − | 0.692479i | \(-0.243482\pi\) |
−0.960423 | + | 0.278544i | \(0.910148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.16193 | + | 2.45493i | 0.296473 | + | 0.0794397i | ||||
\(956\) | 3.67274 | + | 0.984108i | 0.118785 | + | 0.0318283i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.9396 | − | 29.3403i | −0.547295 | − | 0.947942i | ||||
\(959\) | 14.3061 | − | 24.7789i | 0.461969 | − | 0.800153i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 0.208469i | − | 0.00672482i | ||||||
\(962\) | 37.6957 | + | 42.0684i | 1.21536 | + | 1.35634i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.18497 | − | 4.42238i | −0.0381654 | − | 0.142435i | ||||
\(965\) | 10.2475 | + | 5.91642i | 0.329880 | + | 0.190456i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.33868 | − | 7.33868i | 0.235996 | − | 0.235996i | −0.579194 | − | 0.815190i | \(-0.696633\pi\) |
0.815190 | + | 0.579194i | \(0.196633\pi\) | |||||||
\(968\) | −8.94307 | + | 33.3760i | −0.287441 | + | 1.07274i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0608 | − | 14.0608i | −0.451465 | − | 0.451465i | ||||
\(971\) | 16.1557 | − | 9.32751i | 0.518461 | − | 0.299334i | −0.217843 | − | 0.975984i | \(-0.569902\pi\) |
0.736305 | + | 0.676650i | \(0.236569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.7523 | − | 6.90031i | 0.825582 | − | 0.221214i | ||||
\(974\) | 27.7833 | 0.890234 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.4275 | 0.429803 | ||||||||
\(977\) | 25.2431 | − | 6.76388i | 0.807600 | − | 0.216396i | 0.168682 | − | 0.985671i | \(-0.446049\pi\) |
0.638918 | + | 0.769275i | \(0.279382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.6000 | + | 19.3990i | −1.07386 | + | 0.619995i | ||||
\(980\) | 5.26619 | + | 5.26619i | 0.168222 | + | 0.168222i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.4570 | + | 46.4903i | −0.397520 | + | 1.48356i | ||||
\(983\) | −9.08894 | + | 9.08894i | −0.289892 | + | 0.289892i | −0.837038 | − | 0.547145i | \(-0.815714\pi\) |
0.547145 | + | 0.837038i | \(0.315714\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8328 | + | 8.56371i | 0.472612 | + | 0.272862i | ||||
\(986\) | 6.69500 | + | 24.9861i | 0.213212 | + | 0.795719i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.72420 | − | 5.37849i | −0.0866683 | − | 0.171113i | ||||
\(989\) | 16.4823i | 0.524106i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.02952 | − | 5.24728i | 0.0962358 | − | 0.166685i | −0.813888 | − | 0.581022i | \(-0.802653\pi\) |
0.910124 | + | 0.414337i | \(0.135986\pi\) | |||||||
\(992\) | −11.0999 | − | 19.2255i | −0.352421 | − | 0.610411i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −95.0301 | − | 25.4632i | −3.01417 | − | 0.807645i | ||||
\(995\) | −22.8426 | − | 6.12065i | −0.724158 | − | 0.194038i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.5104 | − | 21.6686i | −0.396208 | − | 0.686252i | 0.597047 | − | 0.802206i | \(-0.296341\pi\) |
−0.993255 | + | 0.115955i | \(0.963007\pi\) | |||||||
\(998\) | −3.50950 | + | 6.07863i | −0.111091 | + | 0.192416i | ||||
\(999\) | 0 | 0 |
(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 | 585.2.cw.a.71.3 | ✓ | 40 | |
3.2 | odd | 2 | inner | 585.2.cw.a.71.8 | yes | 40 | |
13.11 | odd | 12 | inner | 585.2.cw.a.206.8 | yes | 40 | |
39.11 | even | 12 | inner | 585.2.cw.a.206.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.cw.a.71.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
585.2.cw.a.71.8 | yes | 40 | 3.2 | odd | 2 | inner | |
585.2.cw.a.206.3 | yes | 40 | 39.11 | even | 12 | inner | |
585.2.cw.a.206.8 | yes | 40 | 13.11 | odd | 12 | inner |