Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(71,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ba (of order \(6\), degree \(2\), not 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.10 | ||
Character | \(\chi\) | \(=\) | 756.575 |
Dual form | 756.2.ba.a.71.10 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.908765 | + | 1.08358i | −0.642594 | + | 0.766207i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.348292 | − | 1.96944i | −0.174146 | − | 0.984720i | ||||
\(5\) | −2.24261 | + | 1.29477i | −1.00293 | + | 0.579040i | −0.909113 | − | 0.416550i | \(-0.863239\pi\) |
−0.0938136 | + | 0.995590i | \(0.529906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | 2.45056 | + | 1.41236i | 0.866404 | + | 0.499343i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.635018 | − | 3.60669i | 0.200810 | − | 1.14054i | ||||
\(11\) | 0.124825 | − | 0.216204i | 0.0376363 | − | 0.0651879i | −0.846594 | − | 0.532240i | \(-0.821351\pi\) |
0.884230 | + | 0.467052i | \(0.154684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0646102 | − | 0.111908i | −0.0179197 | − | 0.0310377i | 0.856927 | − | 0.515439i | \(-0.172371\pi\) |
−0.874846 | + | 0.484401i | \(0.839038\pi\) | |||||||
\(14\) | 1.32880 | − | 0.484025i | 0.355138 | − | 0.129361i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75739 | + | 1.37188i | −0.939347 | + | 0.342970i | ||||
\(17\) | 0.554691i | 0.134532i | 0.997735 | + | 0.0672662i | \(0.0214277\pi\) | ||||
−0.997735 | + | 0.0672662i | \(0.978572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.58986i | − | 0.823571i | −0.911281 | − | 0.411786i | \(-0.864905\pi\) | ||
0.911281 | − | 0.411786i | \(-0.135095\pi\) | |||||||
\(20\) | 3.33106 | + | 3.96573i | 0.744847 | + | 0.886764i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.120837 | + | 0.331737i | 0.0257626 | + | 0.0707265i | ||||
\(23\) | −3.94814 | − | 6.83839i | −0.823245 | − | 1.42590i | −0.903253 | − | 0.429108i | \(-0.858828\pi\) |
0.0800083 | − | 0.996794i | \(-0.474505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.852871 | − | 1.47722i | 0.170574 | − | 0.295443i | ||||
\(26\) | 0.179977 | + | 0.0316879i | 0.0352964 | + | 0.00621451i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.683091 | + | 1.87973i | −0.129092 | + | 0.355236i | ||||
\(29\) | 5.90477 | + | 3.40912i | 1.09649 | + | 0.633058i | 0.935296 | − | 0.353865i | \(-0.115133\pi\) |
0.161192 | + | 0.986923i | \(0.448466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.96683 | − | 4.02230i | 1.25128 | − | 0.722427i | 0.279917 | − | 0.960024i | \(-0.409693\pi\) |
0.971364 | + | 0.237597i | \(0.0763598\pi\) | |||||||
\(32\) | 1.92804 | − | 5.31814i | 0.340833 | − | 0.940124i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.601052 | − | 0.504084i | −0.103080 | − | 0.0864497i | ||||
\(35\) | 2.58954 | 0.437713 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.96519 | 1.63827 | 0.819134 | − | 0.573603i | \(-0.194455\pi\) | ||||
0.819134 | + | 0.573603i | \(0.194455\pi\) | |||||||
\(38\) | 3.88991 | + | 3.26234i | 0.631026 | + | 0.529222i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.32434 | + | 0.00555133i | −1.15808 | + | 0.000877742i | ||||
\(41\) | −4.25964 | + | 2.45930i | −0.665244 | + | 0.384079i | −0.794272 | − | 0.607562i | \(-0.792148\pi\) |
0.129028 | + | 0.991641i | \(0.458814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.78791 | + | 2.18695i | 0.577651 | + | 0.333507i | 0.760199 | − | 0.649690i | \(-0.225101\pi\) |
−0.182549 | + | 0.983197i | \(0.558435\pi\) | |||||||
\(44\) | −0.469276 | − | 0.170534i | −0.0707460 | − | 0.0257090i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.9979 | + | 1.93636i | 1.62155 | + | 0.285500i | ||||
\(47\) | 2.41916 | − | 4.19011i | 0.352871 | − | 0.611190i | −0.633880 | − | 0.773431i | \(-0.718539\pi\) |
0.986751 | + | 0.162241i | \(0.0518721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 0.825622 | + | 2.26660i | 0.116761 | + | 0.320545i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.197893 | + | 0.166223i | −0.0274429 | + | 0.0230509i | ||||
\(53\) | − | 9.00057i | − | 1.23632i | −0.786051 | − | 0.618162i | \(-0.787878\pi\) | ||
0.786051 | − | 0.618162i | \(-0.212122\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.646482i | 0.0871715i | ||||||||
\(56\) | −1.41607 | − | 2.44842i | −0.189230 | − | 0.327184i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.06010 | + | 3.30020i | −1.18965 | + | 0.433338i | ||||
\(59\) | −3.71629 | − | 6.43680i | −0.483820 | − | 0.838001i | 0.516007 | − | 0.856584i | \(-0.327418\pi\) |
−0.999827 | + | 0.0185836i | \(0.994084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.42524 | − | 11.1288i | 0.822667 | − | 1.42490i | −0.0810220 | − | 0.996712i | \(-0.525818\pi\) |
0.903689 | − | 0.428189i | \(-0.140848\pi\) | |||||||
\(62\) | −1.97273 | + | 11.2045i | −0.250537 | + | 1.42297i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.01050 | + | 6.92213i | 0.501312 | + | 0.865266i | ||||
\(65\) | 0.289791 | + | 0.167311i | 0.0359442 | + | 0.0207524i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.23554 | − | 3.02274i | 0.639623 | − | 0.369287i | −0.144846 | − | 0.989454i | \(-0.546269\pi\) |
0.784469 | + | 0.620167i | \(0.212935\pi\) | |||||||
\(68\) | 1.09243 | − | 0.193194i | 0.132477 | − | 0.0234282i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.35329 | + | 2.80598i | −0.281272 | + | 0.335379i | ||||
\(71\) | 15.7820 | 1.87298 | 0.936489 | − | 0.350697i | \(-0.114055\pi\) | ||||
0.936489 | + | 0.350697i | \(0.114055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.1020 | −1.65051 | −0.825256 | − | 0.564759i | \(-0.808969\pi\) | ||||
−0.825256 | + | 0.564759i | \(0.808969\pi\) | |||||||
\(74\) | −9.05602 | + | 10.7981i | −1.05274 | + | 1.25525i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.07002 | + | 1.25032i | −0.810987 | + | 0.143421i | ||||
\(77\) | −0.216204 | + | 0.124825i | −0.0246387 | + | 0.0142252i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.04035 | + | 1.17800i | 0.229558 | + | 0.132535i | 0.610368 | − | 0.792118i | \(-0.291022\pi\) |
−0.380810 | + | 0.924653i | \(0.624355\pi\) | |||||||
\(80\) | 6.65009 | − | 7.94155i | 0.743502 | − | 0.887892i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.20616 | − | 6.85059i | 0.133198 | − | 0.756521i | ||||
\(83\) | 2.36518 | − | 4.09661i | 0.259612 | − | 0.449662i | −0.706526 | − | 0.707687i | \(-0.749739\pi\) |
0.966138 | + | 0.258026i | \(0.0830719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.718199 | − | 1.24396i | −0.0778996 | − | 0.134926i | ||||
\(86\) | −5.81205 | + | 2.11708i | −0.626730 | + | 0.228290i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.611249 | − | 0.353523i | 0.0651594 | − | 0.0376856i | ||||
\(89\) | 7.82233i | 0.829165i | 0.910012 | + | 0.414582i | \(0.136072\pi\) | ||||
−0.910012 | + | 0.414582i | \(0.863928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.129220i | 0.0135460i | ||||||||
\(92\) | −12.0927 | + | 10.1574i | −1.26075 | + | 1.05898i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.34187 | + | 6.42918i | 0.241545 | + | 0.663119i | ||||
\(95\) | 4.64806 | + | 8.05067i | 0.476881 | + | 0.825981i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67078 | + | 9.82208i | −0.575780 | + | 0.997281i | 0.420176 | + | 0.907443i | \(0.361968\pi\) |
−0.995956 | + | 0.0898382i | \(0.971365\pi\) | |||||||
\(98\) | −1.39279 | − | 0.245224i | −0.140693 | − | 0.0247713i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.20634 | − | 1.16518i | −0.320634 | − | 0.116518i | ||||
\(101\) | 3.16980 | + | 1.83009i | 0.315407 | + | 0.182100i | 0.649344 | − | 0.760495i | \(-0.275044\pi\) |
−0.333936 | + | 0.942596i | \(0.608377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.95960 | + | 3.44077i | −0.587216 | + | 0.339030i | −0.763996 | − | 0.645221i | \(-0.776765\pi\) |
0.176780 | + | 0.984250i | \(0.443432\pi\) | |||||||
\(104\) | −0.000277016 | − | 0.365490i | −2.71637e−5 | − | 0.0358393i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.75284 | + | 8.17941i | 0.947280 | + | 0.794454i | ||||
\(107\) | −7.43669 | −0.718932 | −0.359466 | − | 0.933158i | \(-0.617041\pi\) | ||||
−0.359466 | + | 0.933158i | \(0.617041\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.23684 | −0.788947 | −0.394473 | − | 0.918907i | \(-0.629073\pi\) | ||||
−0.394473 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(110\) | −0.700514 | − | 0.587500i | −0.0667914 | − | 0.0560159i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.93993 | + | 0.690611i | 0.372288 | + | 0.0652567i | ||||
\(113\) | 7.42933 | − | 4.28933i | 0.698893 | − | 0.403506i | −0.108042 | − | 0.994146i | \(-0.534458\pi\) |
0.806935 | + | 0.590640i | \(0.201125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.7083 | + | 10.2239i | 1.65131 | + | 0.953383i | ||||
\(116\) | 4.65748 | − | 12.8165i | 0.432436 | − | 1.18998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3520 | + | 1.82265i | 0.952981 | + | 0.167788i | ||||
\(119\) | 0.277346 | − | 0.480377i | 0.0254242 | − | 0.0440361i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.46884 | + | 9.47230i | 0.497167 | + | 0.861119i | ||||
\(122\) | 6.21995 | + | 17.0758i | 0.563128 | + | 1.54597i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.3482 | − | 12.3198i | −0.929294 | − | 1.10635i | ||||
\(125\) | − | 8.53063i | − | 0.763003i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.71023i | − | 0.417965i | −0.977919 | − | 0.208982i | \(-0.932985\pi\) | ||
0.977919 | − | 0.208982i | \(-0.0670152\pi\) | |||||||
\(128\) | −11.1453 | − | 1.94490i | −0.985113 | − | 0.171906i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.444647 | + | 0.161966i | −0.0389981 | + | 0.0142053i | ||||
\(131\) | −4.97136 | − | 8.61065i | −0.434350 | − | 0.752316i | 0.562893 | − | 0.826530i | \(-0.309688\pi\) |
−0.997242 | + | 0.0742144i | \(0.976355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.79493 | + | 3.10891i | −0.155640 | + | 0.269577i | ||||
\(134\) | −1.48250 | + | 8.42009i | −0.128068 | + | 0.727385i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.783422 | + | 1.35930i | −0.0671779 | + | 0.116559i | ||||
\(137\) | −13.1903 | − | 7.61545i | −1.12693 | − | 0.650632i | −0.183767 | − | 0.982970i | \(-0.558829\pi\) |
−0.943160 | + | 0.332338i | \(0.892162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.53695 | + | 0.887356i | −0.130362 | + | 0.0752645i | −0.563763 | − | 0.825937i | \(-0.690647\pi\) |
0.433401 | + | 0.901201i | \(0.357313\pi\) | |||||||
\(140\) | −0.901917 | − | 5.09995i | −0.0762259 | − | 0.431025i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3421 | + | 17.1011i | −1.20356 | + | 1.43509i | ||||
\(143\) | −0.0322600 | −0.00269771 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.6561 | −1.46626 | ||||||||
\(146\) | 12.8154 | − | 15.2806i | 1.06061 | − | 1.26463i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.47079 | − | 19.6258i | −0.285297 | − | 1.61323i | ||||
\(149\) | 14.3488 | − | 8.28427i | 1.17550 | − | 0.678674i | 0.220529 | − | 0.975380i | \(-0.429222\pi\) |
0.954969 | + | 0.296706i | \(0.0958882\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2363 | − | 8.79668i | −1.23991 | − | 0.715864i | −0.270836 | − | 0.962625i | \(-0.587300\pi\) |
−0.969076 | + | 0.246761i | \(0.920634\pi\) | |||||||
\(152\) | 5.07017 | − | 8.79718i | 0.411245 | − | 0.713546i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0612203 | − | 0.347711i | 0.00493327 | − | 0.0280194i | ||||
\(155\) | −10.4159 | + | 18.0409i | −0.836628 | + | 1.44908i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12675 | + | 1.95160i | 0.0899248 | + | 0.155754i | 0.907479 | − | 0.420097i | \(-0.138004\pi\) |
−0.817554 | + | 0.575851i | \(0.804671\pi\) | |||||||
\(158\) | −3.13066 | + | 1.14036i | −0.249062 | + | 0.0907223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.56194 | + | 14.4229i | 0.202539 | + | 1.14023i | ||||
\(161\) | 7.89629i | 0.622315i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.99511i | − | 0.547899i | −0.961744 | − | 0.273950i | \(-0.911670\pi\) | ||
0.961744 | − | 0.273950i | \(-0.0883302\pi\) | |||||||
\(164\) | 6.32705 | + | 7.53255i | 0.494060 | + | 0.588193i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.28961 | + | 6.28572i | 0.177709 | + | 0.487867i | ||||
\(167\) | −5.40220 | − | 9.35689i | −0.418035 | − | 0.724058i | 0.577707 | − | 0.816244i | \(-0.303948\pi\) |
−0.995742 | + | 0.0921866i | \(0.970614\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.49165 | − | 11.2439i | 0.499358 | − | 0.864913i | ||||
\(170\) | 2.00060 | + | 0.352239i | 0.153439 | + | 0.0270155i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.98777 | − | 8.22175i | 0.227815 | − | 0.626903i | ||||
\(173\) | −4.01988 | − | 2.32088i | −0.305626 | − | 0.176453i | 0.339341 | − | 0.940663i | \(-0.389796\pi\) |
−0.644968 | + | 0.764210i | \(0.723129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.47722 | + | 0.852871i | −0.111667 | + | 0.0644710i | ||||
\(176\) | −0.172412 | + | 0.983606i | −0.0129960 | + | 0.0741421i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.47612 | − | 7.10866i | −0.635312 | − | 0.532816i | ||||
\(179\) | −6.66668 | −0.498291 | −0.249145 | − | 0.968466i | \(-0.580150\pi\) | ||||
−0.249145 | + | 0.968466i | \(0.580150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.61248 | −0.565831 | −0.282916 | − | 0.959145i | \(-0.591302\pi\) | ||||
−0.282916 | + | 0.959145i | \(0.591302\pi\) | |||||||
\(182\) | −0.140021 | − | 0.117431i | −0.0103790 | − | 0.00870457i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0169276 | − | 22.3341i | −0.00124792 | − | 1.64649i | ||||
\(185\) | −22.3481 | + | 12.9027i | −1.64306 | + | 0.948622i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.119926 | + | 0.0692395i | 0.00876988 | + | 0.00506329i | ||||
\(188\) | −9.09474 | − | 3.30501i | −0.663302 | − | 0.241043i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.9475 | − | 2.27963i | −0.939313 | − | 0.165382i | ||||
\(191\) | 2.15506 | − | 3.73268i | 0.155935 | − | 0.270087i | −0.777464 | − | 0.628927i | \(-0.783494\pi\) |
0.933399 | + | 0.358840i | \(0.116828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.690908 | − | 1.19669i | −0.0497327 | − | 0.0861395i | 0.840087 | − | 0.542451i | \(-0.182504\pi\) |
−0.889820 | + | 0.456312i | \(0.849170\pi\) | |||||||
\(194\) | −5.48960 | − | 15.0707i | −0.394130 | − | 1.08201i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.53144 | − | 1.28635i | 0.109389 | − | 0.0918821i | ||||
\(197\) | 9.26481i | 0.660091i | 0.943965 | + | 0.330045i | \(0.107064\pi\) | ||||
−0.943965 | + | 0.330045i | \(0.892936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.5989i | 1.74377i | 0.489712 | + | 0.871884i | \(0.337102\pi\) | ||||
−0.489712 | + | 0.871884i | \(0.662898\pi\) | |||||||
\(200\) | 4.17637 | − | 2.41545i | 0.295314 | − | 0.170798i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.86365 | + | 1.77162i | −0.342205 | + | 0.124650i | ||||
\(203\) | −3.40912 | − | 5.90477i | −0.239273 | − | 0.414434i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.36848 | − | 11.0305i | 0.444794 | − | 0.770406i | ||||
\(206\) | 1.68752 | − | 9.58456i | 0.117575 | − | 0.667788i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.396290 | + | 0.331845i | 0.0274778 | + | 0.0230093i | ||||
\(209\) | −0.776142 | − | 0.448106i | −0.0536869 | − | 0.0309961i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.98731 | − | 5.18882i | 0.618712 | − | 0.357213i | −0.157655 | − | 0.987494i | \(-0.550394\pi\) |
0.776367 | + | 0.630281i | \(0.217060\pi\) | |||||||
\(212\) | −17.7261 | + | 3.13482i | −1.21743 | + | 0.215301i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.75820 | − | 8.05824i | 0.461981 | − | 0.550850i | ||||
\(215\) | −11.3264 | −0.772455 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.04461 | −0.546104 | ||||||||
\(218\) | 7.48536 | − | 8.92528i | 0.506972 | − | 0.604496i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.27321 | − | 0.225164i | 0.0858396 | − | 0.0151806i | ||||
\(221\) | 0.0620745 | − | 0.0358387i | 0.00417558 | − | 0.00241077i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3502 | − | 12.9039i | −1.49668 | − | 0.864109i | −0.496688 | − | 0.867929i | \(-0.665451\pi\) |
−0.999993 | + | 0.00382012i | \(0.998784\pi\) | |||||||
\(224\) | −4.32881 | + | 3.64163i | −0.289230 | + | 0.243316i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.10369 | + | 11.9483i | −0.139935 | + | 0.794787i | ||||
\(227\) | −6.74196 | + | 11.6774i | −0.447480 | + | 0.775057i | −0.998221 | − | 0.0596183i | \(-0.981012\pi\) |
0.550742 | + | 0.834676i | \(0.314345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.49974 | + | 11.2579i | 0.429515 | + | 0.743941i | 0.996830 | − | 0.0795594i | \(-0.0253513\pi\) |
−0.567315 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(230\) | −27.1711 | + | 9.89725i | −1.79161 | + | 0.652605i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.65510 | + | 16.6939i | 0.633889 | + | 1.09601i | ||||
\(233\) | − | 22.7845i | − | 1.49266i | −0.665575 | − | 0.746331i | \(-0.731814\pi\) | ||
0.665575 | − | 0.746331i | \(-0.268186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.5291i | 0.817305i | ||||||||
\(236\) | −11.3825 | + | 9.56089i | −0.740941 | + | 0.622361i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.268485 | + | 0.737076i | 0.0174033 | + | 0.0477775i | ||||
\(239\) | 10.1962 | + | 17.6603i | 0.659537 | + | 1.14235i | 0.980736 | + | 0.195340i | \(0.0625810\pi\) |
−0.321198 | + | 0.947012i | \(0.604086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.27539 | − | 5.67314i | 0.210986 | − | 0.365439i | −0.741037 | − | 0.671464i | \(-0.765666\pi\) |
0.952024 | + | 0.306025i | \(0.0989991\pi\) | |||||||
\(242\) | −15.2339 | − | 2.68218i | −0.979271 | − | 0.172417i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.1554 | − | 8.77804i | −1.54639 | − | 0.561956i | ||||
\(245\) | −2.24261 | − | 1.29477i | −0.143275 | − | 0.0827200i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.401735 | + | 0.231942i | −0.0255618 | + | 0.0147581i | ||||
\(248\) | 22.7536 | − | 0.0172456i | 1.44485 | − | 0.00109510i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.24362 | + | 7.75234i | 0.584618 | + | 0.490301i | ||||
\(251\) | 18.3086 | 1.15563 | 0.577814 | − | 0.816169i | \(-0.303906\pi\) | ||||
0.577814 | + | 0.816169i | \(0.303906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.97131 | −0.123935 | ||||||||
\(254\) | 5.10391 | + | 4.28049i | 0.320248 | + | 0.268582i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2359 | − | 10.3094i | 0.764744 | − | 0.644335i | ||||
\(257\) | −13.8378 | + | 7.98924i | −0.863176 | + | 0.498355i | −0.865075 | − | 0.501643i | \(-0.832729\pi\) |
0.00189858 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.63011 | − | 4.98260i | −0.536249 | − | 0.309603i | ||||
\(260\) | 0.228577 | − | 0.628999i | 0.0141758 | − | 0.0390089i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.8481 | + | 2.43819i | 0.855540 | + | 0.150632i | ||||
\(263\) | 1.92259 | − | 3.33002i | 0.118552 | − | 0.205338i | −0.800642 | − | 0.599143i | \(-0.795508\pi\) |
0.919194 | + | 0.393805i | \(0.128841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6537 | + | 20.1848i | 0.715881 | + | 1.23994i | ||||
\(266\) | −1.73758 | − | 4.77022i | −0.106538 | − | 0.292481i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.77660 | − | 9.25829i | −0.475032 | − | 0.565540i | ||||
\(269\) | − | 3.59531i | − | 0.219210i | −0.993975 | − | 0.109605i | \(-0.965041\pi\) | ||
0.993975 | − | 0.109605i | \(-0.0349585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.24361i | − | 0.257781i | −0.991659 | − | 0.128891i | \(-0.958858\pi\) | ||
0.991659 | − | 0.128891i | \(-0.0411416\pi\) | |||||||
\(272\) | −0.760969 | − | 2.08419i | −0.0461405 | − | 0.126373i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.2389 | − | 7.37214i | 1.22267 | − | 0.445367i | ||||
\(275\) | −0.212920 | − | 0.368788i | −0.0128395 | − | 0.0222387i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.88987 | − | 8.46950i | 0.293804 | − | 0.508883i | −0.680902 | − | 0.732374i | \(-0.738412\pi\) |
0.974706 | + | 0.223491i | \(0.0717454\pi\) | |||||||
\(278\) | 0.435201 | − | 2.47180i | 0.0261016 | − | 0.148249i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.34584 | + | 3.65736i | 0.379236 | + | 0.218569i | ||||
\(281\) | −20.3980 | − | 11.7768i | −1.21684 | − | 0.702544i | −0.252600 | − | 0.967571i | \(-0.581286\pi\) |
−0.964241 | + | 0.265027i | \(0.914619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.19988 | − | 2.42480i | 0.249657 | − | 0.144139i | −0.369950 | − | 0.929052i | \(-0.620625\pi\) |
0.619607 | + | 0.784912i | \(0.287292\pi\) | |||||||
\(284\) | −5.49673 | − | 31.0817i | −0.326171 | − | 1.84436i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0293167 | − | 0.0349563i | 0.00173353 | − | 0.00206701i | ||||
\(287\) | 4.91861 | 0.290336 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6923 | 0.981901 | ||||||||
\(290\) | 16.0453 | − | 19.1318i | 0.942212 | − | 1.12346i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.91160 | + | 27.7730i | 0.287430 | + | 1.62529i | ||||
\(293\) | 16.8856 | − | 9.74890i | 0.986467 | − | 0.569537i | 0.0822504 | − | 0.996612i | \(-0.473789\pi\) |
0.904216 | + | 0.427075i | \(0.140456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.6684 | + | 9.62350i | 0.970471 | + | 0.560302i | ||||
\(296\) | 24.4203 | + | 14.0744i | 1.41940 | + | 0.818058i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.06300 | + | 23.0765i | −0.235363 | + | 1.33679i | ||||
\(299\) | −0.510181 | + | 0.883659i | −0.0295045 | + | 0.0511033i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.18695 | − | 3.78791i | −0.126054 | − | 0.218331i | ||||
\(302\) | 23.3781 | − | 8.51563i | 1.34526 | − | 0.490020i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.92486 | + | 13.4885i | 0.282460 | + | 0.773619i | ||||
\(305\) | 33.2769i | 1.90543i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.21611i | 0.354772i | 0.984141 | + | 0.177386i | \(0.0567642\pi\) | ||||
−0.984141 | + | 0.177386i | \(0.943236\pi\) | |||||||
\(308\) | 0.321138 | + | 0.382325i | 0.0182985 | + | 0.0217850i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.0832 | − | 27.6815i | −0.572685 | − | 1.57220i | ||||
\(311\) | 11.2742 | + | 19.5275i | 0.639303 | + | 1.10731i | 0.985586 | + | 0.169176i | \(0.0541105\pi\) |
−0.346283 | + | 0.938130i | \(0.612556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.53213 | + | 13.0460i | −0.425741 | + | 0.737405i | −0.996489 | − | 0.0837201i | \(-0.973320\pi\) |
0.570748 | + | 0.821125i | \(0.306653\pi\) | |||||||
\(314\) | −3.13867 | − | 0.552614i | −0.177125 | − | 0.0311858i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60936 | − | 4.42864i | 0.0905335 | − | 0.249130i | ||||
\(317\) | 9.34442 | + | 5.39500i | 0.524835 | + | 0.303013i | 0.738911 | − | 0.673804i | \(-0.235341\pi\) |
−0.214076 | + | 0.976817i | \(0.568674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.47413 | − | 0.851089i | 0.0825354 | − | 0.0476518i | ||||
\(320\) | −17.9566 | − | 10.3310i | −1.00380 | − | 0.577519i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.55626 | − | 7.17587i | −0.476822 | − | 0.399896i | ||||
\(323\) | 1.99127 | 0.110797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.220417 | −0.0122265 | ||||||||
\(326\) | 7.57976 | + | 6.35691i | 0.419804 | + | 0.352077i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.9119 | + | 0.0105443i | −0.768158 | + | 0.000582209i | ||||
\(329\) | −4.19011 | + | 2.41916i | −0.231008 | + | 0.133373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.03466 | − | 5.21616i | −0.496590 | − | 0.286706i | 0.230714 | − | 0.973021i | \(-0.425894\pi\) |
−0.727304 | + | 0.686315i | \(0.759227\pi\) | |||||||
\(332\) | −8.89181 | − | 3.23127i | −0.488001 | − | 0.177339i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.0483 | + | 2.64950i | 0.823405 | + | 0.144974i | ||||
\(335\) | −7.82753 | + | 13.5577i | −0.427663 | + | 0.740735i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0986 | + | 26.1516i | 0.822475 | + | 1.42457i | 0.903834 | + | 0.427883i | \(0.140741\pi\) |
−0.0813590 | + | 0.996685i | \(0.525926\pi\) | |||||||
\(338\) | 6.28425 | + | 17.2523i | 0.341818 | + | 0.938399i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.19976 | + | 1.84771i | −0.119299 | + | 0.100206i | ||||
\(341\) | − | 2.00834i | − | 0.108758i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 6.19375 | + | 10.7091i | 0.333944 | + | 0.577398i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.16799 | − | 2.24673i | 0.331593 | − | 0.120785i | ||||
\(347\) | 12.7498 | + | 22.0832i | 0.684443 | + | 1.18549i | 0.973612 | + | 0.228212i | \(0.0732878\pi\) |
−0.289169 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4421 | − | 26.7465i | 0.826597 | − | 1.43171i | −0.0740953 | − | 0.997251i | \(-0.523607\pi\) |
0.900692 | − | 0.434457i | \(-0.143060\pi\) | |||||||
\(350\) | 0.418288 | − | 2.37574i | 0.0223585 | − | 0.126989i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.909134 | − | 1.08069i | −0.0484570 | − | 0.0576009i | ||||
\(353\) | 30.2542 | + | 17.4672i | 1.61027 | + | 0.929688i | 0.989308 | + | 0.145844i | \(0.0465898\pi\) |
0.620958 | + | 0.783843i | \(0.286744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.3929 | + | 20.4341i | −1.87846 | + | 1.08453i | ||||
\(356\) | 15.4056 | − | 2.72445i | 0.816495 | − | 0.144396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.05844 | − | 7.22388i | 0.320199 | − | 0.381794i | ||||
\(359\) | −5.92966 | −0.312956 | −0.156478 | − | 0.987681i | \(-0.550014\pi\) | ||||
−0.156478 | + | 0.987681i | \(0.550014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.11288 | 0.321730 | ||||||||
\(362\) | 6.91796 | − | 8.24873i | 0.363600 | − | 0.433544i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.254492 | − | 0.0450064i | 0.0133390 | − | 0.00235898i | ||||
\(365\) | 31.6253 | − | 18.2589i | 1.65534 | − | 0.955712i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.1820 | − | 15.1162i | −1.36669 | − | 0.789059i | −0.376187 | − | 0.926544i | \(-0.622765\pi\) |
−0.990504 | + | 0.137485i | \(0.956098\pi\) | |||||||
\(368\) | 24.2161 | + | 20.2781i | 1.26235 | + | 1.05707i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.32807 | − | 35.9414i | 0.328981 | − | 1.86850i | ||||
\(371\) | −4.50029 | + | 7.79472i | −0.233643 | + | 0.404682i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.54373 | + | 4.40588i | 0.131710 | + | 0.228128i | 0.924336 | − | 0.381580i | \(-0.124620\pi\) |
−0.792626 | + | 0.609708i | \(0.791287\pi\) | |||||||
\(374\) | −0.184011 | + | 0.0670273i | −0.00951501 | + | 0.00346590i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.8462 | − | 6.85140i | 0.610923 | − | 0.353334i | ||||
\(377\) | − | 0.881056i | − | 0.0453767i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.6036i | − | 0.955600i | −0.878469 | − | 0.477800i | \(-0.841434\pi\) | ||
0.878469 | − | 0.477800i | \(-0.158566\pi\) | |||||||
\(380\) | 14.2364 | − | 11.9580i | 0.730314 | − | 0.613435i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.08621 | + | 5.72731i | 0.106740 | + | 0.293035i | ||||
\(383\) | 5.98305 | + | 10.3630i | 0.305720 | + | 0.529522i | 0.977421 | − | 0.211300i | \(-0.0677696\pi\) |
−0.671702 | + | 0.740822i | \(0.734436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.323241 | − | 0.559869i | 0.0164739 | − | 0.0285336i | ||||
\(386\) | 1.92458 | + | 0.338854i | 0.0979586 | + | 0.0172472i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.3191 | + | 7.74731i | 1.08231 | + | 0.393310i | ||||
\(389\) | 16.3655 | + | 9.44864i | 0.829765 | + | 0.479065i | 0.853772 | − | 0.520647i | \(-0.174309\pi\) |
−0.0240072 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.79319 | − | 2.19000i | 0.191830 | − | 0.110753i | ||||
\(392\) | 0.00214375 | + | 2.82843i | 0.000108276 | + | 0.142857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0392 | − | 8.41954i | −0.505766 | − | 0.424170i | ||||
\(395\) | −6.10096 | −0.306973 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3234 | −1.32113 | −0.660566 | − | 0.750768i | \(-0.729684\pi\) | ||||
−0.660566 | + | 0.750768i | \(0.729684\pi\) | |||||||
\(398\) | −26.6549 | − | 22.3546i | −1.33609 | − | 1.12054i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.17801 | + | 6.72051i | −0.0589003 | + | 0.336025i | ||||
\(401\) | 7.64521 | − | 4.41396i | 0.381783 | − | 0.220423i | −0.296811 | − | 0.954936i | \(-0.595923\pi\) |
0.678594 | + | 0.734514i | \(0.262590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.900257 | − | 0.519764i | −0.0448450 | − | 0.0258913i | ||||
\(404\) | 2.50023 | − | 6.88014i | 0.124391 | − | 0.342300i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.49638 | + | 1.67199i | 0.471297 | + | 0.0829797i | ||||
\(407\) | 1.24391 | − | 2.15451i | 0.0616582 | − | 0.106795i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.4524 | − | 19.8361i | −0.566283 | − | 0.980831i | −0.996929 | − | 0.0783100i | \(-0.975048\pi\) |
0.430646 | − | 0.902521i | \(-0.358286\pi\) | |||||||
\(410\) | 6.16501 | + | 16.9249i | 0.304468 | + | 0.835862i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.85207 | + | 10.5387i | 0.436110 | + | 0.519203i | ||||
\(413\) | 7.43258i | 0.365733i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2495i | 0.601304i | ||||||||
\(416\) | −0.719715 | + | 0.127843i | −0.0352869 | + | 0.00626801i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.19089 | − | 0.433789i | 0.0582483 | − | 0.0212173i | ||||
\(419\) | −5.10769 | − | 8.84679i | −0.249527 | − | 0.432194i | 0.713868 | − | 0.700281i | \(-0.246942\pi\) |
−0.963395 | + | 0.268087i | \(0.913609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.95328 | − | 10.3114i | 0.290145 | − | 0.502546i | −0.683699 | − | 0.729765i | \(-0.739630\pi\) |
0.973844 | + | 0.227218i | \(0.0729630\pi\) | |||||||
\(422\) | −2.54485 | + | 14.4539i | −0.123881 | + | 0.703604i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.7120 | − | 22.0565i | 0.617350 | − | 1.07116i | ||||
\(425\) | 0.819399 | + | 0.473080i | 0.0397467 | + | 0.0229478i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1288 | + | 6.42524i | −0.538562 | + | 0.310939i | ||||
\(428\) | 2.59013 | + | 14.6461i | 0.125199 | + | 0.707946i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.2930 | − | 12.2731i | 0.496375 | − | 0.591860i | ||||
\(431\) | −4.26567 | −0.205470 | −0.102735 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102735 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.7838 | 1.76772 | 0.883858 | − | 0.467756i | \(-0.154937\pi\) | ||||
0.883858 | + | 0.467756i | \(0.154937\pi\) | |||||||
\(434\) | 7.31066 | − | 8.71698i | 0.350923 | − | 0.418428i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.86882 | + | 16.2220i | 0.137392 | + | 0.776891i | ||||
\(437\) | −24.5489 | + | 14.1733i | −1.17433 | + | 0.678001i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2806 | + | 7.66755i | 0.633848 | + | 0.365952i | 0.782241 | − | 0.622976i | \(-0.214077\pi\) |
−0.148393 | + | 0.988928i | \(0.547410\pi\) | |||||||
\(440\) | −0.913062 | + | 1.58424i | −0.0435285 | + | 0.0755258i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0175770 | + | 0.0998317i | −0.000836053 | + | 0.00474851i | ||||
\(443\) | 5.27986 | − | 9.14498i | 0.250854 | − | 0.434491i | −0.712907 | − | 0.701258i | \(-0.752622\pi\) |
0.963761 | + | 0.266767i | \(0.0859554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1281 | − | 17.5424i | −0.480119 | − | 0.831591i | ||||
\(446\) | 34.2935 | − | 12.4916i | 1.62384 | − | 0.591496i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0121269 | − | 7.99999i | −0.000572940 | − | 0.377964i | ||||
\(449\) | − | 16.5280i | − | 0.780006i | −0.920813 | − | 0.390003i | \(-0.872474\pi\) | ||
0.920813 | − | 0.390003i | \(-0.127526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.22793i | 0.0578212i | ||||||||
\(452\) | −11.0351 | − | 13.1377i | −0.519050 | − | 0.617945i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.52656 | − | 17.9175i | −0.306307 | − | 0.840909i | ||||
\(455\) | −0.167311 | − | 0.289791i | −0.00784366 | − | 0.0135856i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.27095 | + | 9.12955i | −0.246564 | + | 0.427062i | −0.962570 | − | 0.271032i | \(-0.912635\pi\) |
0.716006 | + | 0.698094i | \(0.245968\pi\) | |||||||
\(458\) | −18.1055 | − | 3.18778i | −0.846016 | − | 0.148955i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.9677 | − | 38.4363i | 0.651247 | − | 1.79210i | ||||
\(461\) | 21.5838 | + | 12.4614i | 1.00526 | + | 0.580387i | 0.909800 | − | 0.415046i | \(-0.136235\pi\) |
0.0954593 | + | 0.995433i | \(0.469568\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8446 | + | 16.0761i | −1.29405 | + | 0.747119i | −0.979369 | − | 0.202079i | \(-0.935230\pi\) |
−0.314679 | + | 0.949198i | \(0.601897\pi\) | |||||||
\(464\) | −26.8634 | − | 4.70876i | −1.24710 | − | 0.218598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.6888 | + | 20.7058i | 1.14369 | + | 0.959176i | ||||
\(467\) | −8.54957 | −0.395627 | −0.197813 | − | 0.980240i | \(-0.563384\pi\) | ||||
−0.197813 | + | 0.980240i | \(0.563384\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.04548 | −0.279155 | ||||||||
\(470\) | −13.5762 | − | 11.3860i | −0.626225 | − | 0.525195i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0159336 | − | 21.0225i | −0.000733402 | − | 0.967639i | ||||
\(473\) | 0.945654 | − | 0.545973i | 0.0434812 | − | 0.0251039i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.30300 | − | 3.06169i | −0.243319 | − | 0.140480i | ||||
\(476\) | −1.04267 | − | 0.378904i | −0.0477907 | − | 0.0173671i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.4023 | − | 5.00070i | −1.29909 | − | 0.228727i | ||||
\(479\) | 8.25859 | − | 14.3043i | 0.377345 | − | 0.653580i | −0.613330 | − | 0.789826i | \(-0.710171\pi\) |
0.990675 | + | 0.136247i | \(0.0435039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.643853 | − | 1.11519i | −0.0293572 | − | 0.0508481i | ||||
\(482\) | 3.17074 | + | 8.70470i | 0.144423 | + | 0.396488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.7504 | − | 14.0697i | 0.761381 | − | 0.639530i | ||||
\(485\) | − | 29.3695i | − | 1.33360i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.93519i | 0.359578i | 0.983705 | + | 0.179789i | \(0.0575415\pi\) | ||||
−0.983705 | + | 0.179789i | \(0.942459\pi\) | |||||||
\(488\) | 31.4633 | − | 18.1972i | 1.42428 | − | 0.823747i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.44100 | − | 1.25341i | 0.155448 | − | 0.0566231i | ||||
\(491\) | −1.83003 | − | 3.16970i | −0.0825880 | − | 0.143047i | 0.821773 | − | 0.569815i | \(-0.192985\pi\) |
−0.904361 | + | 0.426769i | \(0.859652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.89101 | + | 3.27532i | −0.0851668 | + | 0.147513i | ||||
\(494\) | 0.113755 | − | 0.646093i | 0.00511809 | − | 0.0290691i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.6590 | + | 24.6710i | −0.927615 | + | 1.10776i | ||||
\(497\) | −13.6676 | − | 7.89100i | −0.613076 | − | 0.353960i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.46689 | + | 4.31101i | −0.334264 | + | 0.192987i | −0.657733 | − | 0.753252i | \(-0.728484\pi\) |
0.323469 | + | 0.946239i | \(0.395151\pi\) | |||||||
\(500\) | −16.8006 | + | 2.97115i | −0.751344 | + | 0.132874i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.6382 | + | 19.8388i | −0.742599 | + | 0.885449i | ||||
\(503\) | −44.0191 | −1.96271 | −0.981357 | − | 0.192194i | \(-0.938440\pi\) | ||||
−0.981357 | + | 0.192194i | \(0.938440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.47818 | −0.421773 | ||||||||
\(506\) | 1.79146 | − | 2.13608i | 0.0796402 | − | 0.0949602i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.27651 | + | 1.64053i | −0.411578 | + | 0.0727868i | ||||
\(509\) | −9.48279 | + | 5.47489i | −0.420317 | + | 0.242670i | −0.695213 | − | 0.718804i | \(-0.744690\pi\) |
0.274896 | + | 0.961474i | \(0.411357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2127 | + | 7.05099i | 0.540257 | + | 0.311917i | ||||
\(512\) | 0.0514499 | + | 22.6274i | 0.00227379 | + | 0.999997i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.91830 | − | 22.2547i | 0.172829 | − | 0.981611i | ||||
\(515\) | 8.91004 | − | 15.4326i | 0.392623 | − | 0.680043i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.603945 | − | 1.04606i | −0.0265615 | − | 0.0460058i | ||||
\(518\) | 13.2418 | − | 4.82340i | 0.581811 | − | 0.211928i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.473848 | + | 0.819295i | 0.0207796 | + | 0.0359284i | ||||
\(521\) | 6.26841i | 0.274624i | 0.990528 | + | 0.137312i | \(0.0438463\pi\) | ||||
−0.990528 | + | 0.137312i | \(0.956154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.7279i | − | 0.818913i | −0.912330 | − | 0.409456i | \(-0.865718\pi\) | ||
0.912330 | − | 0.409456i | \(-0.134282\pi\) | |||||||
\(524\) | −15.2267 | + | 12.7898i | −0.665180 | + | 0.558725i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.86116 | + | 5.10948i | 0.0811505 | + | 0.222784i | ||||
\(527\) | 2.23114 | + | 3.86444i | 0.0971898 | + | 0.168338i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6757 | + | 34.0793i | −0.855465 | + | 1.48171i | ||||
\(530\) | −32.4623 | − | 5.71552i | −1.41007 | − | 0.248267i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.74798 | + | 2.45220i | 0.292562 | + | 0.106316i | ||||
\(533\) | 0.550433 | + | 0.317792i | 0.0238419 | + | 0.0137651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.6776 | − | 9.62882i | 0.721035 | − | 0.416290i | ||||
\(536\) | 17.0992 | − | 0.0129600i | 0.738573 | − | 0.000559786i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.89580 | + | 3.26729i | 0.167960 | + | 0.140863i | ||||
\(539\) | 0.249651 | 0.0107532 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7122 | 1.06246 | 0.531230 | − | 0.847228i | \(-0.321730\pi\) | ||||
0.531230 | + | 0.847228i | \(0.321730\pi\) | |||||||
\(542\) | 4.59830 | + | 3.85645i | 0.197514 | + | 0.165649i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.94993 | + | 1.06947i | 0.126477 | + | 0.0458531i | ||||
\(545\) | 18.4720 | − | 10.6648i | 0.791255 | − | 0.456832i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.9787 | + | 13.8441i | 1.02525 | + | 0.591930i | 0.915621 | − | 0.402042i | \(-0.131699\pi\) |
0.109632 | + | 0.993972i | \(0.465033\pi\) | |||||||
\(548\) | −10.4041 | + | 28.6300i | −0.444440 | + | 1.22301i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.593105 | + | 0.104426i | 0.0252901 | + | 0.00445274i | ||||
\(551\) | 12.2383 | − | 21.1973i | 0.521368 | − | 0.903036i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.17800 | − | 2.04035i | −0.0500936 | − | 0.0867646i | ||||
\(554\) | 4.73364 | + | 12.9954i | 0.201113 | + | 0.552120i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.28290 | + | 2.71786i | 0.0968165 | + | 0.115263i | ||||
\(557\) | 43.5015i | 1.84322i | 0.388119 | + | 0.921609i | \(0.373125\pi\) | ||||
−0.388119 | + | 0.921609i | \(0.626875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.565197i | − | 0.0239053i | ||||||
\(560\) | −9.72992 | + | 3.55254i | −0.411164 | + | 0.150122i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.2981 | − | 11.4005i | 1.32023 | − | 0.480902i | ||||
\(563\) | 0.525773 | + | 0.910665i | 0.0221587 | + | 0.0383800i | 0.876892 | − | 0.480687i | \(-0.159613\pi\) |
−0.854733 | + | 0.519067i | \(0.826279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1074 | + | 19.2386i | −0.467292 | + | 0.809374i | ||||
\(566\) | −1.18924 | + | 6.75448i | −0.0499874 | + | 0.283912i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.6747 | + | 22.2898i | 1.62276 | + | 0.935259i | ||||
\(569\) | 4.94731 | + | 2.85633i | 0.207402 | + | 0.119744i | 0.600103 | − | 0.799922i | \(-0.295126\pi\) |
−0.392701 | + | 0.919666i | \(0.628459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2710 | − | 8.81671i | 0.639071 | − | 0.368968i | −0.145185 | − | 0.989404i | \(-0.546378\pi\) |
0.784257 | + | 0.620436i | \(0.213045\pi\) | |||||||
\(572\) | 0.0112359 | + | 0.0635341i | 0.000469795 | + | 0.00265649i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.46986 | + | 5.32971i | −0.186568 | + | 0.222458i | ||||
\(575\) | −13.4690 | −0.561697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3399 | −0.763501 | −0.381751 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381751 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(578\) | −15.1694 | + | 18.0875i | −0.630964 | + | 0.752339i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.14948 | + | 34.7727i | 0.255343 | + | 1.44386i | ||||
\(581\) | −4.09661 | + | 2.36518i | −0.169956 | + | 0.0981243i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.94596 | − | 1.12350i | −0.0805933 | − | 0.0465306i | ||||
\(584\) | −34.5578 | − | 19.9170i | −1.43001 | − | 0.824172i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.78132 | + | 27.1563i | −0.197515 | + | 1.12182i | ||||
\(587\) | 8.18823 | − | 14.1824i | 0.337965 | − | 0.585372i | −0.646085 | − | 0.763265i | \(-0.723595\pi\) |
0.984050 | + | 0.177893i | \(0.0569282\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4395 | − | 25.0100i | −0.594970 | − | 1.03052i | ||||
\(590\) | −25.5755 | + | 9.31603i | −1.05293 | + | 0.383535i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −37.4431 | + | 13.6710i | −1.53890 | + | 0.561876i | ||||
\(593\) | 2.86950i | 0.117836i | 0.998263 | + | 0.0589181i | \(0.0187651\pi\) | ||||
−0.998263 | + | 0.0589181i | \(0.981235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.43640i | 0.0588866i | ||||||||
\(596\) | −21.3129 | − | 25.3737i | −0.873012 | − | 1.03935i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.493881 | − | 1.35586i | −0.0201963 | − | 0.0554453i | ||||
\(599\) | −0.530101 | − | 0.918163i | −0.0216594 | − | 0.0375151i | 0.854993 | − | 0.518640i | \(-0.173562\pi\) |
−0.876652 | + | 0.481125i | \(0.840228\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.48648 | − | 11.2349i | 0.264589 | − | 0.458282i | −0.702867 | − | 0.711322i | \(-0.748097\pi\) |
0.967456 | + | 0.253040i | \(0.0814303\pi\) | |||||||
\(602\) | 6.09192 | + | 1.07258i | 0.248288 | + | 0.0437153i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.0179 | + | 33.0708i | −0.489000 | + | 1.34563i | ||||
\(605\) | −24.5290 | − | 14.1618i | −0.997244 | − | 0.575759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3945 | − | 14.0842i | 0.990144 | − | 0.571660i | 0.0848266 | − | 0.996396i | \(-0.472966\pi\) |
0.905317 | + | 0.424736i | \(0.139633\pi\) | |||||||
\(608\) | −19.0914 | − | 6.92141i | −0.774259 | − | 0.280700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.0582 | − | 30.2409i | −1.45995 | − | 1.22442i | ||||
\(611\) | −0.625210 | −0.0252933 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1934 | −0.896381 | −0.448191 | − | 0.893938i | \(-0.647931\pi\) | ||||
−0.448191 | + | 0.893938i | \(0.647931\pi\) | |||||||
\(614\) | −6.73566 | − | 5.64899i | −0.271829 | − | 0.227975i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.706118 | 0.000535188i | −0.0284503 | 2.15633e-5i | ||||||
\(617\) | −12.7221 | + | 7.34512i | −0.512173 | + | 0.295703i | −0.733726 | − | 0.679445i | \(-0.762221\pi\) |
0.221553 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2161 | − | 8.20765i | −0.571392 | − | 0.329893i | 0.186313 | − | 0.982490i | \(-0.440346\pi\) |
−0.757705 | + | 0.652597i | \(0.773679\pi\) | |||||||
\(620\) | 39.1583 | + | 14.2301i | 1.57264 | + | 0.571493i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.4053 | − | 5.52942i | −1.25924 | − | 0.221710i | ||||
\(623\) | 3.91116 | − | 6.77433i | 0.156697 | − | 0.271408i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3096 | + | 26.5170i | 0.612383 | + | 1.06068i | ||||
\(626\) | −7.29148 | − | 20.0174i | −0.291426 | − | 0.800058i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.45111 | − | 2.89880i | 0.137714 | − | 0.115675i | ||||
\(629\) | 5.52760i | 0.220400i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7711i | 0.508411i | 0.967150 | + | 0.254205i | \(0.0818139\pi\) | ||||
−0.967150 | + | 0.254205i | \(0.918186\pi\) | |||||||
\(632\) | 3.33626 | + | 5.76846i | 0.132709 | + | 0.229457i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.3378 | + | 5.22263i | −0.569427 | + | 0.207417i | ||||
\(635\) | 6.09867 | + | 10.5632i | 0.242018 | + | 0.419188i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0646102 | − | 0.111908i | 0.00255995 | − | 0.00443396i | ||||
\(638\) | −0.417414 | + | 2.37078i | −0.0165256 | + | 0.0938600i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.5127 | − | 10.0690i | 1.08754 | − | 0.398010i | ||||
\(641\) | −13.2162 | − | 7.63040i | −0.522010 | − | 0.301383i | 0.215746 | − | 0.976449i | \(-0.430782\pi\) |
−0.737757 | + | 0.675067i | \(0.764115\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.5137 | − | 19.3492i | 1.32165 | − | 0.763057i | 0.337661 | − | 0.941268i | \(-0.390364\pi\) |
0.983992 | + | 0.178211i | \(0.0570311\pi\) | |||||||
\(644\) | 15.5513 | − | 2.75021i | 0.612806 | − | 0.108373i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.80959 | + | 2.15770i | −0.0711975 | + | 0.0848934i | ||||
\(647\) | 0.564326 | 0.0221860 | 0.0110930 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110930 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.85555 | −0.0728367 | ||||||||
\(650\) | 0.200307 | − | 0.238839i | 0.00785669 | − | 0.00936804i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.7765 | + | 2.43634i | −0.539527 | + | 0.0954144i | ||||
\(653\) | 3.90030 | − | 2.25184i | 0.152631 | − | 0.0881214i | −0.421740 | − | 0.906717i | \(-0.638580\pi\) |
0.574370 | + | 0.818596i | \(0.305247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.2977 | + | 12.8736i | 0.871241 | + | 0.503011i | ||||
\(656\) | 12.6312 | − | 15.0843i | 0.493167 | − | 0.588942i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.18647 | − | 6.73877i | 0.0462535 | − | 0.262705i | ||||
\(659\) | −7.02737 | + | 12.1718i | −0.273747 | + | 0.474144i | −0.969818 | − | 0.243829i | \(-0.921597\pi\) |
0.696071 | + | 0.717973i | \(0.254930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.4242 | − | 30.1797i | −0.677724 | − | 1.17385i | −0.975665 | − | 0.219269i | \(-0.929633\pi\) |
0.297940 | − | 0.954585i | \(-0.403700\pi\) | |||||||
\(662\) | 13.8625 | − | 5.04951i | 0.538782 | − | 0.196255i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.5819 | − | 6.69852i | 0.449465 | − | 0.259953i | ||||
\(665\) | − | 9.29611i | − | 0.360488i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 53.8388i | − | 2.08465i | ||||||
\(668\) | −16.5463 | + | 13.8982i | −0.640195 | + | 0.537739i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.57744 | − | 20.8025i | −0.292742 | − | 0.803670i | ||||
\(671\) | −1.60406 | − | 2.77832i | −0.0619242 | − | 0.107256i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.76133 | + | 16.9071i | −0.376272 | + | 0.651722i | −0.990516 | − | 0.137394i | \(-0.956127\pi\) |
0.614245 | + | 0.789115i | \(0.289461\pi\) | |||||||
\(674\) | −42.0585 | − | 7.40509i | −1.62003 | − | 0.285233i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.4051 | − | 8.86877i | −0.938658 | − | 0.341107i | ||||
\(677\) | −7.35277 | − | 4.24512i | −0.282590 | − | 0.163153i | 0.352005 | − | 0.935998i | \(-0.385500\pi\) |
−0.634595 | + | 0.772845i | \(0.718833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.82208 | − | 5.67078i | 0.376937 | − | 0.217625i | ||||
\(680\) | −0.00307927 | − | 4.06275i | −0.000118085 | − | 0.155799i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.17620 | + | 1.82511i | 0.0833310 | + | 0.0698871i | ||||
\(683\) | 16.0399 | 0.613751 | 0.306876 | − | 0.951750i | \(-0.400716\pi\) | ||||
0.306876 | + | 0.951750i | \(0.400716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.4411 | 1.50697 | ||||||||
\(686\) | 1.08358 | + | 0.908765i | 0.0413713 | + | 0.0346968i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.2329 | − | 3.02066i | −0.656997 | − | 0.115162i | ||||
\(689\) | −1.00724 | + | 0.581529i | −0.0383727 | + | 0.0221545i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.7036 | + | 10.2212i | 0.673476 | + | 0.388831i | 0.797392 | − | 0.603461i | \(-0.206212\pi\) |
−0.123917 | + | 0.992293i | \(0.539546\pi\) | |||||||
\(692\) | −3.17074 | + | 8.72526i | −0.120534 | + | 0.331685i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.5155 | − | 6.25309i | −1.34815 | − | 0.237364i | ||||
\(695\) | 2.29785 | − | 3.97999i | 0.0871623 | − | 0.150970i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36415 | − | 2.36279i | −0.0516710 | − | 0.0894969i | ||||
\(698\) | 14.9487 | + | 41.0391i | 0.565818 | + | 1.55335i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.19418 | + | 2.61224i | 0.0829322 | + | 0.0987334i | ||||
\(701\) | − | 11.4242i | − | 0.431488i | −0.976450 | − | 0.215744i | \(-0.930782\pi\) | ||
0.976450 | − | 0.215744i | \(-0.0692176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 35.7737i | − | 1.34923i | ||||||
\(704\) | 1.99720 | − | 0.00302748i | 0.0752724 | − | 0.000114102i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −46.4211 | + | 16.9092i | −1.74708 | + | 0.636385i | ||||
\(707\) | −1.83009 | − | 3.16980i | −0.0688275 | − | 0.119213i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.08955 | − | 8.81537i | 0.191142 | − | 0.331068i | −0.754487 | − | 0.656315i | \(-0.772114\pi\) |
0.945629 | + | 0.325247i | \(0.105447\pi\) | |||||||
\(710\) | 10.0218 | − | 56.9208i | 0.376113 | − | 2.13620i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.0479 | + | 19.1691i | −0.414038 | + | 0.718392i | ||||
\(713\) | −55.0121 | − | 31.7613i | −2.06022 | − | 1.18947i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0723466 | − | 0.0417693i | 0.00270561 | − | 0.00156208i | ||||
\(716\) | 2.32195 | + | 13.1296i | 0.0867752 | + | 0.490677i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.38867 | − | 6.42526i | 0.201103 | − | 0.239789i | ||||
\(719\) | 25.4397 | 0.948741 | 0.474370 | − | 0.880325i | \(-0.342676\pi\) | ||||
0.474370 | + | 0.880325i | \(0.342676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.88155 | 0.256282 | ||||||||
\(722\) | −5.55517 | + | 6.62379i | −0.206742 | + | 0.246512i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.65136 | + | 14.9923i | 0.0985371 | + | 0.557185i | ||||
\(725\) | 10.0720 | − | 5.81508i | 0.374065 | − | 0.215967i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2142 | − | 8.20655i | −0.527174 | − | 0.304364i | 0.212691 | − | 0.977120i | \(-0.431777\pi\) |
−0.739865 | + | 0.672756i | \(0.765111\pi\) | |||||||
\(728\) | −0.182505 | + | 0.316663i | −0.00676410 | + | 0.0117363i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.95501 | + | 50.8615i | −0.331440 | + | 1.88247i | ||||
\(731\) | −1.21308 | + | 2.10112i | −0.0448674 | + | 0.0777127i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2362 | − | 31.5859i | −0.673568 | − | 1.16665i | −0.976885 | − | 0.213764i | \(-0.931428\pi\) |
0.303318 | − | 0.952889i | \(-0.401906\pi\) | |||||||
\(734\) | 40.1729 | − | 14.6332i | 1.48281 | − | 0.540123i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.9797 | + | 7.81211i | −1.62111 | + | 0.287958i | ||||
\(737\) | − | 1.50926i | − | 0.0555943i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0747i | 1.58453i | 0.610177 | + | 0.792265i | \(0.291098\pi\) | ||||
−0.610177 | + | 0.792265i | \(0.708902\pi\) | |||||||
\(740\) | 33.1946 | + | 39.5193i | 1.22026 | + | 1.45276i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.35650 | − | 11.9600i | −0.159932 | − | 0.439065i | ||||
\(743\) | −21.0352 | − | 36.4340i | −0.771705 | − | 1.33663i | −0.936628 | − | 0.350326i | \(-0.886071\pi\) |
0.164922 | − | 0.986307i | \(-0.447263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.4525 | + | 37.1568i | −0.785959 | + | 1.36132i | ||||
\(746\) | −7.08578 | − | 1.24757i | −0.259429 | − | 0.0456767i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0945937 | − | 0.260303i | 0.00345869 | − | 0.00951763i | ||||
\(749\) | 6.44036 | + | 3.71834i | 0.235326 | + | 0.135865i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.20236 | + | 1.84888i | −0.116856 | + | 0.0674667i | −0.557289 | − | 0.830319i | \(-0.688158\pi\) |
0.440433 | + | 0.897786i | \(0.354825\pi\) | |||||||
\(752\) | −3.34140 | + | 19.0627i | −0.121848 | + | 0.695144i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.954695 | + | 0.800673i | 0.0347679 | + | 0.0291588i | ||||
\(755\) | 45.5588 | 1.65805 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8240 | 0.466097 | 0.233048 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233048 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(758\) | 20.1584 | + | 16.9063i | 0.732188 | + | 0.614063i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0199285 | + | 26.2934i | 0.000722883 | + | 0.953761i | ||||
\(761\) | −30.7741 | + | 17.7674i | −1.11556 | + | 0.644069i | −0.940264 | − | 0.340447i | \(-0.889422\pi\) |
−0.175296 | + | 0.984516i | \(0.556088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.13332 | + | 4.11842i | 0.258243 | + | 0.149097i | ||||
\(764\) | −8.10188 | − | 2.94421i | −0.293116 | − | 0.106518i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6663 | − | 2.93437i | −0.602177 | − | 0.106023i | ||||
\(767\) | −0.480221 | + | 0.831767i | −0.0173398 | + | 0.0300334i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.57085 | − | 6.18489i | −0.128768 | − | 0.223033i | 0.794431 | − | 0.607354i | \(-0.207769\pi\) |
−0.923200 | + | 0.384321i | \(0.874436\pi\) | |||||||
\(770\) | 0.312913 | + | 0.859047i | 0.0112766 | + | 0.0309579i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.11617 | + | 1.77750i | −0.0761626 | + | 0.0639736i | ||||
\(773\) | − | 39.5269i | − | 1.42168i | −0.703351 | − | 0.710842i | \(-0.748314\pi\) | ||
0.703351 | − | 0.710842i | \(-0.251686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 13.7220i | − | 0.492910i | ||||||
\(776\) | −27.7689 | + | 16.0604i | −0.996844 | + | 0.576536i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.1108 | + | 9.14676i | −0.900265 | + | 0.327927i | ||||
\(779\) | 8.82857 | + | 15.2915i | 0.316316 | + | 0.547876i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.96999 | − | 3.41213i | 0.0704919 | − | 0.122095i | ||||
\(782\) | −1.07408 | + | 6.10042i | −0.0384090 | + | 0.218151i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.06677 | − | 2.56805i | −0.109528 | − | 0.0917162i | ||||
\(785\) | −5.05375 | − | 2.91778i | −0.180376 | − | 0.104140i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.4865 | + | 21.6428i | −1.33625 | + | 0.771484i | −0.986249 | − | 0.165266i | \(-0.947152\pi\) |
−0.350000 | + | 0.936750i | \(0.613818\pi\) | |||||||
\(788\) | 18.2465 | − | 3.22686i | 0.650004 | − | 0.114952i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.54434 | − | 6.61088i | 0.197259 | − | 0.235204i | ||||
\(791\) | −8.57866 | −0.305022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.66054 | −0.0589676 | ||||||||
\(794\) | 23.9218 | − | 28.5235i | 0.848952 | − | 1.01226i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.4460 | − | 8.56758i | 1.71712 | − | 0.303670i | ||||
\(797\) | 8.31298 | − | 4.79950i | 0.294461 | − | 0.170007i | −0.345491 | − | 0.938422i | \(-0.612288\pi\) |
0.639952 | + | 0.768415i | \(0.278954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32422 | + | 1.34189i | 0.0822249 | + | 0.0474726i | ||||
\(800\) | −6.21168 | − | 7.38383i | −0.219616 | − | 0.261058i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.16482 | + | 12.2954i | −0.0764423 | + | 0.434167i | ||||
\(803\) | −1.76028 | + | 3.04890i | −0.0621191 | + | 0.107593i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2239 | − | 17.7083i | −0.360345 | − | 0.624136i | ||||
\(806\) | 1.38133 | − | 0.503158i | 0.0486552 | − | 0.0177230i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.18306 | + | 8.96163i | 0.182339 | + | 0.315269i | ||||
\(809\) | − | 29.1906i | − | 1.02629i | −0.858303 | − | 0.513144i | \(-0.828481\pi\) | ||
0.858303 | − | 0.513144i | \(-0.171519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.7718i | 1.95841i | 0.202866 | + | 0.979207i | \(0.434974\pi\) | ||||
−0.202866 | + | 0.979207i | \(0.565026\pi\) | |||||||
\(812\) | −10.4417 | + | 8.77064i | −0.366433 | + | 0.307789i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.20417 | + | 3.30582i | 0.0422060 | + | 0.115869i | ||||
\(815\) | 9.05708 | + | 15.6873i | 0.317256 | + | 0.549503i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.85085 | − | 13.5981i | 0.274667 | − | 0.475736i | ||||
\(818\) | 31.9015 | + | 5.61678i | 1.11541 | + | 0.196386i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.9421 | − | 8.70050i | −0.836093 | − | 0.303835i | ||||
\(821\) | −1.49795 | − | 0.864842i | −0.0522788 | − | 0.0301832i | 0.473633 | − | 0.880722i | \(-0.342942\pi\) |
−0.525912 | + | 0.850539i | \(0.676276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6424 | − | 15.3820i | 0.928697 | − | 0.536184i | 0.0422978 | − | 0.999105i | \(-0.486532\pi\) |
0.886399 | + | 0.462922i | \(0.153199\pi\) | |||||||
\(824\) | −19.4640 | + | 0.0147523i | −0.678059 | + | 0.000513921i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.05380 | − | 6.75447i | −0.280227 | − | 0.235018i | ||||
\(827\) | −18.2699 | −0.635305 | −0.317653 | − | 0.948207i | \(-0.602895\pi\) | ||||
−0.317653 | + | 0.948207i | \(0.602895\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.8459 | 1.17552 | 0.587758 | − | 0.809037i | \(-0.300011\pi\) | ||||
0.587758 | + | 0.809037i | \(0.300011\pi\) | |||||||
\(830\) | −13.2733 | − | 11.1319i | −0.460723 | − | 0.386394i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.515524 | − | 0.896048i | 0.0178726 | − | 0.0310649i | ||||
\(833\) | −0.480377 | + | 0.277346i | −0.0166441 | + | 0.00960946i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.2301 | + | 13.9892i | 0.838517 | + | 0.484118i | ||||
\(836\) | −0.612194 | + | 1.68464i | −0.0211732 | + | 0.0582644i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.2279 | + | 2.50506i | 0.491494 | + | 0.0865357i | ||||
\(839\) | −8.32917 | + | 14.4265i | −0.287555 | + | 0.498060i | −0.973226 | − | 0.229852i | \(-0.926176\pi\) |
0.685671 | + | 0.727912i | \(0.259509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.74420 | + | 15.1454i | 0.301524 | + | 0.522255i | ||||
\(842\) | 5.76308 | + | 15.8215i | 0.198609 | + | 0.545245i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3493 | − | 15.8927i | −0.459501 | − | 0.547051i | ||||
\(845\) | 33.6208i | 1.15659i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.9377i | − | 0.375823i | ||||||
\(848\) | 12.3477 | + | 33.8186i | 0.424021 | + | 1.16134i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.25726 | + | 0.457965i | −0.0431237 | + | 0.0157081i | ||||
\(851\) | −39.3440 | − | 68.1458i | −1.34870 | − | 2.33601i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.7026 | + | 30.6618i | −0.606126 | + | 1.04984i | 0.385747 | + | 0.922605i | \(0.373944\pi\) |
−0.991872 | + | 0.127236i | \(0.959390\pi\) | |||||||
\(854\) | 3.15124 | − | 17.8980i | 0.107833 | − | 0.612457i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.2241 | − | 10.5033i | −0.622885 | − | 0.358994i | ||||
\(857\) | 7.62418 | + | 4.40182i | 0.260437 | + | 0.150363i | 0.624534 | − | 0.780998i | \(-0.285289\pi\) |
−0.364097 | + | 0.931361i | \(0.618622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0092 | + | 12.7070i | −0.750944 | + | 0.433558i | −0.826035 | − | 0.563619i | \(-0.809409\pi\) |
0.0750910 | + | 0.997177i | \(0.476075\pi\) | |||||||
\(860\) | 3.94489 | + | 22.3067i | 0.134520 | + | 0.760651i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.87649 | − | 4.62219i | 0.132034 | − | 0.157432i | ||||
\(863\) | −31.5520 | −1.07404 | −0.537021 | − | 0.843569i | \(-0.680451\pi\) | ||||
−0.537021 | + | 0.843569i | \(0.680451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0200 | 0.408694 | ||||||||
\(866\) | −33.4278 | + | 39.8582i | −1.13592 | + | 1.35444i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.80187 | + | 15.8434i | 0.0951016 | + | 0.537759i | ||||
\(869\) | 0.509375 | − | 0.294088i | 0.0172794 | − | 0.00997625i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.676539 | − | 0.390600i | −0.0229237 | − | 0.0132350i | ||||
\(872\) | −20.1849 | − | 11.6334i | −0.683547 | − | 0.393955i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.95126 | − | 39.4809i | 0.235130 | − | 1.33546i | ||||
\(875\) | −4.26531 | + | 7.38774i | −0.144194 | + | 0.249751i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.1063 | + | 29.6290i | 0.577639 | + | 1.00050i | 0.995749 | + | 0.0921044i | \(0.0293593\pi\) |
−0.418110 | + | 0.908396i | \(0.637307\pi\) | |||||||
\(878\) | −20.3773 | + | 7.42257i | −0.687702 | + | 0.250500i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.886894 | − | 2.42908i | −0.0298972 | − | 0.0818843i | ||||
\(881\) | 4.09172i | 0.137854i | 0.997622 | + | 0.0689268i | \(0.0219575\pi\) | ||||
−0.997622 | + | 0.0689268i | \(0.978043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.1247i | − | 1.11474i | −0.830266 | − | 0.557368i | \(-0.811811\pi\) | ||
0.830266 | − | 0.557368i | \(-0.188189\pi\) | |||||||
\(884\) | −0.0922022 | − | 0.109770i | −0.00310110 | − | 0.00369195i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.11117 | + | 14.0318i | 0.171713 | + | 0.471407i | ||||
\(887\) | 9.55299 | + | 16.5463i | 0.320758 | + | 0.555569i | 0.980645 | − | 0.195796i | \(-0.0627290\pi\) |
−0.659887 | + | 0.751365i | \(0.729396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.35511 | + | 4.07918i | −0.0789879 | + | 0.136811i | ||||
\(890\) | 28.2127 | + | 4.96732i | 0.945693 | + | 0.166505i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.6291 | + | 48.5117i | −0.590265 | + | 1.62429i | ||||
\(893\) | −15.0419 | − | 8.68446i | −0.503359 | − | 0.290614i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.9508 | − | 8.63183i | 0.499749 | − | 0.288530i | ||||
\(896\) | 8.67965 | + | 7.25697i | 0.289967 | + | 0.242438i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.9095 | + | 15.0201i | 0.597646 | + | 0.501227i | ||||
\(899\) | 54.8501 | 1.82935 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.99254 | 0.166326 | ||||||||
\(902\) | −1.33056 | − | 1.11590i | −0.0443030 | − | 0.0371555i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.2641 | − | 0.0183905i | 0.807012 | − | 0.000611658i | ||||
\(905\) | 17.0718 | − | 9.85643i | 0.567487 | − | 0.327639i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.4678 | − | 8.35301i | −0.480397 | − | 0.277357i | 0.240185 | − | 0.970727i | \(-0.422792\pi\) |
−0.720582 | + | 0.693370i | \(0.756125\pi\) | |||||||
\(908\) | 25.3461 | + | 9.21074i | 0.841141 | + | 0.305669i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.466058 | + | 0.0820573i | 0.0154497 | + | 0.00272017i | ||||
\(911\) | 23.3136 | − | 40.3803i | 0.772414 | − | 1.33786i | −0.163823 | − | 0.986490i | \(-0.552382\pi\) |
0.936237 | − | 0.351370i | \(-0.114284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.590469 | − | 1.02272i | −0.0195417 | − | 0.0338472i | ||||
\(914\) | −5.10254 | − | 14.0081i | −0.168777 | − | 0.463347i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.9079 | − | 16.7219i | 0.657776 | − | 0.552506i | ||||
\(917\) | 9.94272i | 0.328337i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.8829i | 0.919771i | 0.887978 | + | 0.459885i | \(0.152110\pi\) | ||||
−0.887978 | + | 0.459885i | \(0.847890\pi\) | |||||||
\(920\) | 28.9555 | + | 50.0647i | 0.954635 | + | 1.65059i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.1176 | + | 12.0633i | −1.09067 | + | 0.397284i | ||||
\(923\) | −1.01968 | − | 1.76613i | −0.0335631 | − | 0.0581330i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.49902 | − | 14.7207i | 0.279446 | − | 0.484015i | ||||
\(926\) | 7.88448 | − | 44.7812i | 0.259100 | − | 1.47160i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.5148 | − | 24.8295i | 0.968872 | − | 0.815068i | ||||
\(929\) | 19.5047 | + | 11.2610i | 0.639929 | + | 0.369463i | 0.784587 | − | 0.620019i | \(-0.212875\pi\) |
−0.144658 | + | 0.989482i | \(0.546208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.10891 | − | 1.79493i | 0.101891 | − | 0.0588265i | ||||
\(932\) | −44.8727 | + | 7.93565i | −1.46985 | + | 0.259941i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.76955 | − | 9.26414i | 0.254227 | − | 0.303132i | ||||
\(935\) | −0.358598 | −0.0117274 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.6374 | −1.00088 | −0.500440 | − | 0.865771i | \(-0.666828\pi\) | ||||
−0.500440 | + | 0.865771i | \(0.666828\pi\) | |||||||
\(938\) | 5.49393 | − | 6.55077i | 0.179383 | − | 0.213890i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.6752 | − | 4.36376i | 0.804817 | − | 0.142330i | ||||
\(941\) | −14.0870 | + | 8.13315i | −0.459224 | + | 0.265133i | −0.711718 | − | 0.702465i | \(-0.752083\pi\) |
0.252494 | + | 0.967598i | \(0.418749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.6354 | + | 19.4194i | 1.09532 | + | 0.632382i | ||||
\(944\) | 22.7941 | + | 19.0873i | 0.741883 | + | 0.621237i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.267771 | + | 1.52085i | −0.00870599 | + | 0.0494472i | ||||
\(947\) | 0.924500 | − | 1.60128i | 0.0300422 | − | 0.0520347i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157102\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.911132 | + | 1.57813i | 0.0295766 | + | 0.0512282i | ||||
\(950\) | 8.13677 | − | 2.96387i | 0.263992 | − | 0.0961607i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.35812 | − | 0.785481i | 0.0440168 | − | 0.0254576i | ||||
\(953\) | 58.7162i | 1.90200i | 0.309186 | + | 0.951002i | \(0.399944\pi\) | ||||
−0.309186 | + | 0.951002i | \(0.600056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.1613i | 0.361170i | ||||||||
\(956\) | 31.2297 | − | 26.2317i | 1.01004 | − | 0.848395i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.99473 | + | 21.9481i | 0.258298 | + | 0.709110i | ||||
\(959\) | 7.61545 | + | 13.1903i | 0.245916 | + | 0.425938i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.8579 | − | 29.1987i | 0.543802 | − | 0.941892i | ||||
\(962\) | 1.79351 | + | 0.315776i | 0.0578249 | + | 0.0101810i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.3137 | − | 4.47478i | −0.396598 | − | 0.144123i | ||||
\(965\) | 3.09888 | + | 1.78914i | 0.0997564 | + | 0.0575944i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2999 | − | 5.94663i | 0.331221 | − | 0.191231i | −0.325162 | − | 0.945658i | \(-0.605419\pi\) |
0.656383 | + | 0.754428i | \(0.272085\pi\) | |||||||
\(968\) | 0.0234476 | + | 30.9364i | 0.000753635 | + | 0.994334i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.8242 | + | 26.6900i | 1.02181 | + | 0.856963i | ||||
\(971\) | 9.56549 | 0.306971 | 0.153486 | − | 0.988151i | \(-0.450950\pi\) | ||||
0.153486 | + | 0.988151i | \(0.450950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.77471 | 0.0568946 | ||||||||
\(974\) | −8.59842 | − | 7.21123i | −0.275511 | − | 0.231063i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.87468 | + | 50.6300i | −0.284072 | + | 1.62063i | ||||
\(977\) | −31.6762 | + | 18.2882i | −1.01341 | + | 0.585093i | −0.912188 | − | 0.409771i | \(-0.865608\pi\) |
−0.101222 | + | 0.994864i | \(0.532275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.69122 | + | 0.976424i | 0.0540515 | + | 0.0312067i | ||||
\(980\) | −1.76889 | + | 4.86765i | −0.0565052 | + | 0.155491i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.09769 | + | 0.897532i | 0.162674 | + | 0.0286414i | ||||
\(983\) | 14.3674 | − | 24.8851i | 0.458250 | − | 0.793712i | −0.540619 | − | 0.841268i | \(-0.681810\pi\) |
0.998869 | + | 0.0475560i | \(0.0151432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9958 | − | 20.7774i | −0.382219 | − | 0.662022i | ||||
\(986\) | −1.83059 | − | 5.02556i | −0.0582979 | − | 0.160046i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.596717 | + | 0.710410i | 0.0189841 | + | 0.0226011i | ||||
\(989\) | − | 34.5376i | − | 1.09823i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 23.6126i | − | 0.750078i | −0.927009 | − | 0.375039i | \(-0.877629\pi\) | ||
0.927009 | − | 0.375039i | \(-0.122371\pi\) | |||||||
\(992\) | −7.95884 | − | 44.8058i | −0.252694 | − | 1.42259i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.9712 | − | 7.63888i | 0.665165 | − | 0.242291i | ||||
\(995\) | −31.8500 | − | 55.1657i | −1.00971 | − | 1.74887i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.49998 | + | 9.52625i | −0.174186 | + | 0.301699i | −0.939879 | − | 0.341507i | \(-0.889063\pi\) |
0.765693 | + | 0.643206i | \(0.222396\pi\) | |||||||
\(998\) | 2.11432 | − | 12.0087i | 0.0669278 | − | 0.380128i | ||||
\(999\) | 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 | 756.2.ba.a.575.10 | 72 | ||
3.2 | odd | 2 | 252.2.ba.a.155.27 | yes | 72 | ||
4.3 | odd | 2 | inner | 756.2.ba.a.575.22 | 72 | ||
9.4 | even | 3 | 252.2.ba.a.239.15 | yes | 72 | ||
9.5 | odd | 6 | inner | 756.2.ba.a.71.22 | 72 | ||
12.11 | even | 2 | 252.2.ba.a.155.15 | ✓ | 72 | ||
36.23 | even | 6 | inner | 756.2.ba.a.71.10 | 72 | ||
36.31 | odd | 6 | 252.2.ba.a.239.27 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.ba.a.155.15 | ✓ | 72 | 12.11 | even | 2 | ||
252.2.ba.a.155.27 | yes | 72 | 3.2 | odd | 2 | ||
252.2.ba.a.239.15 | yes | 72 | 9.4 | even | 3 | ||
252.2.ba.a.239.27 | yes | 72 | 36.31 | odd | 6 | ||
756.2.ba.a.71.10 | 72 | 36.23 | even | 6 | inner | ||
756.2.ba.a.71.22 | 72 | 9.5 | odd | 6 | inner | ||
756.2.ba.a.575.10 | 72 | 1.1 | even | 1 | trivial | ||
756.2.ba.a.575.22 | 72 | 4.3 | odd | 2 | inner |