Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.2 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.b.769.1 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66471 | −1.88423 | −0.942116 | − | 0.335288i | \(-0.891166\pi\) | ||||
−0.942116 | + | 0.335288i | \(0.891166\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.10065 | 2.55033 | ||||||||
\(5\) | −1.18527 | + | 1.89608i | −0.530070 | + | 0.847954i | ||||
\(6\) | −2.66471 | −1.08786 | ||||||||
\(7\) | 2.09935 | − | 1.61019i | 0.793480 | − | 0.608596i | ||||
\(8\) | −8.26233 | −2.92118 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.15840 | − | 5.05250i | 0.998774 | − | 1.59774i | ||||
\(11\) | 1.90151 | − | 2.71740i | 0.573328 | − | 0.819326i | ||||
\(12\) | 5.10065 | 1.47243 | ||||||||
\(13\) | 0.864827i | 0.239860i | 0.992782 | + | 0.119930i | \(0.0382670\pi\) | ||||
−0.992782 | + | 0.119930i | \(0.961733\pi\) | |||||||
\(14\) | −5.59415 | + | 4.29069i | −1.49510 | + | 1.14673i | ||||
\(15\) | −1.18527 | + | 1.89608i | −0.306036 | + | 0.489567i | ||||
\(16\) | 11.8154 | 2.95384 | ||||||||
\(17\) | 1.53725i | 0.372838i | 0.982470 | + | 0.186419i | \(0.0596882\pi\) | ||||
−0.982470 | + | 0.186419i | \(0.940312\pi\) | |||||||
\(18\) | −2.66471 | −0.628077 | ||||||||
\(19\) | 2.68287 | 0.615493 | 0.307746 | − | 0.951468i | \(-0.400425\pi\) | ||||
0.307746 | + | 0.951468i | \(0.400425\pi\) | |||||||
\(20\) | −6.04566 | + | 9.67127i | −1.35185 | + | 2.16256i | ||||
\(21\) | 2.09935 | − | 1.61019i | 0.458116 | − | 0.351373i | ||||
\(22\) | −5.06697 | + | 7.24106i | −1.08028 | + | 1.54380i | ||||
\(23\) | − | 7.32990i | − | 1.52839i | −0.644985 | − | 0.764195i | \(-0.723136\pi\) | ||
0.644985 | − | 0.764195i | \(-0.276864\pi\) | |||||||
\(24\) | −8.26233 | −1.68654 | ||||||||
\(25\) | −2.19026 | − | 4.49475i | −0.438052 | − | 0.898949i | ||||
\(26\) | − | 2.30451i | − | 0.451951i | ||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 10.7081 | − | 8.21304i | 2.02364 | − | 1.55212i | ||||
\(29\) | − | 1.42095i | − | 0.263864i | −0.991259 | − | 0.131932i | \(-0.957882\pi\) | ||
0.991259 | − | 0.131932i | \(-0.0421180\pi\) | |||||||
\(30\) | 3.15840 | − | 5.05250i | 0.576642 | − | 0.922457i | ||||
\(31\) | 0.551846i | 0.0991145i | 0.998771 | + | 0.0495573i | \(0.0157810\pi\) | ||||
−0.998771 | + | 0.0495573i | \(0.984219\pi\) | |||||||
\(32\) | −14.9598 | −2.64455 | ||||||||
\(33\) | 1.90151 | − | 2.71740i | 0.331011 | − | 0.473038i | ||||
\(34\) | − | 4.09632i | − | 0.702513i | ||||||
\(35\) | 0.564757 | + | 5.88906i | 0.0954614 | + | 0.995433i | ||||
\(36\) | 5.10065 | 0.850109 | ||||||||
\(37\) | − | 5.97120i | − | 0.981660i | −0.871255 | − | 0.490830i | \(-0.836694\pi\) | ||
0.871255 | − | 0.490830i | \(-0.163306\pi\) | |||||||
\(38\) | −7.14906 | −1.15973 | ||||||||
\(39\) | 0.864827i | 0.138483i | ||||||||
\(40\) | 9.79311 | − | 15.6661i | 1.54843 | − | 2.47702i | ||||
\(41\) | −0.607303 | −0.0948447 | −0.0474224 | − | 0.998875i | \(-0.515101\pi\) | ||||
−0.0474224 | + | 0.998875i | \(0.515101\pi\) | |||||||
\(42\) | −5.59415 | + | 4.29069i | −0.863197 | + | 0.662068i | ||||
\(43\) | −0.823316 | −0.125554 | −0.0627772 | − | 0.998028i | \(-0.519996\pi\) | ||||
−0.0627772 | + | 0.998028i | \(0.519996\pi\) | |||||||
\(44\) | 9.69896 | − | 13.8605i | 1.46217 | − | 2.08955i | ||||
\(45\) | −1.18527 | + | 1.89608i | −0.176690 | + | 0.282651i | ||||
\(46\) | 19.5320i | 2.87984i | ||||||||
\(47\) | 8.37543 | 1.22168 | 0.610841 | − | 0.791753i | \(-0.290832\pi\) | ||||
0.610841 | + | 0.791753i | \(0.290832\pi\) | |||||||
\(48\) | 11.8154 | 1.70540 | ||||||||
\(49\) | 1.81456 | − | 6.76072i | 0.259223 | − | 0.965818i | ||||
\(50\) | 5.83640 | + | 11.9772i | 0.825392 | + | 1.69383i | ||||
\(51\) | 1.53725i | 0.215258i | ||||||||
\(52\) | 4.41118i | 0.611721i | ||||||||
\(53\) | 8.21534i | 1.12846i | 0.825616 | + | 0.564232i | \(0.190828\pi\) | ||||
−0.825616 | + | 0.564232i | \(0.809172\pi\) | |||||||
\(54\) | −2.66471 | −0.362620 | ||||||||
\(55\) | 2.89860 | + | 6.82628i | 0.390847 | + | 0.920455i | ||||
\(56\) | −17.3455 | + | 13.3039i | −2.31790 | + | 1.77781i | ||||
\(57\) | 2.68287 | 0.355355 | ||||||||
\(58\) | 3.78641i | 0.497180i | ||||||||
\(59\) | − | 14.3900i | − | 1.87341i | −0.350114 | − | 0.936707i | \(-0.613857\pi\) | ||
0.350114 | − | 0.936707i | \(-0.386143\pi\) | |||||||
\(60\) | −6.04566 | + | 9.67127i | −0.780492 | + | 1.24855i | ||||
\(61\) | −6.95852 | −0.890947 | −0.445473 | − | 0.895295i | \(-0.646965\pi\) | ||||
−0.445473 | + | 0.895295i | \(0.646965\pi\) | |||||||
\(62\) | − | 1.47051i | − | 0.186755i | ||||||
\(63\) | 2.09935 | − | 1.61019i | 0.264493 | − | 0.202865i | ||||
\(64\) | 16.2328 | 2.02910 | ||||||||
\(65\) | −1.63978 | − | 1.02505i | −0.203390 | − | 0.127142i | ||||
\(66\) | −5.06697 | + | 7.24106i | −0.623701 | + | 0.891313i | ||||
\(67\) | 7.78444i | 0.951021i | 0.879710 | + | 0.475510i | \(0.157737\pi\) | ||||
−0.879710 | + | 0.475510i | \(0.842263\pi\) | |||||||
\(68\) | 7.84099i | 0.950859i | ||||||||
\(69\) | − | 7.32990i | − | 0.882416i | ||||||
\(70\) | −1.50491 | − | 15.6926i | −0.179871 | − | 1.87563i | ||||
\(71\) | −4.38660 | −0.520594 | −0.260297 | − | 0.965529i | \(-0.583820\pi\) | ||||
−0.260297 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(72\) | −8.26233 | −0.973725 | ||||||||
\(73\) | 3.89027i | 0.455322i | 0.973740 | + | 0.227661i | \(0.0731078\pi\) | ||||
−0.973740 | + | 0.227661i | \(0.926892\pi\) | |||||||
\(74\) | 15.9115i | 1.84967i | ||||||||
\(75\) | −2.19026 | − | 4.49475i | −0.252910 | − | 0.519009i | ||||
\(76\) | 13.6844 | 1.56971 | ||||||||
\(77\) | −0.383589 | − | 8.76658i | −0.0437140 | − | 0.999044i | ||||
\(78\) | − | 2.30451i | − | 0.260934i | ||||||
\(79\) | − | 8.94533i | − | 1.00643i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) | ||
0.864162 | − | 0.503214i | \(-0.167849\pi\) | |||||||
\(80\) | −14.0044 | + | 22.4029i | −1.56574 | + | 2.50472i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.61828 | 0.178709 | ||||||||
\(83\) | 13.1440i | 1.44274i | 0.692549 | + | 0.721371i | \(0.256488\pi\) | ||||
−0.692549 | + | 0.721371i | \(0.743512\pi\) | |||||||
\(84\) | 10.7081 | − | 8.21304i | 1.16835 | − | 0.896116i | ||||
\(85\) | −2.91476 | − | 1.82206i | −0.316150 | − | 0.197630i | ||||
\(86\) | 2.19389 | 0.236574 | ||||||||
\(87\) | − | 1.42095i | − | 0.152342i | ||||||
\(88\) | −15.7109 | + | 22.4520i | −1.67479 | + | 2.39340i | ||||
\(89\) | 7.51433i | 0.796517i | 0.917273 | + | 0.398259i | \(0.130385\pi\) | ||||
−0.917273 | + | 0.398259i | \(0.869615\pi\) | |||||||
\(90\) | 3.15840 | − | 5.05250i | 0.332925 | − | 0.532581i | ||||
\(91\) | 1.39254 | + | 1.81558i | 0.145978 | + | 0.190324i | ||||
\(92\) | − | 37.3873i | − | 3.89790i | ||||||
\(93\) | 0.551846i | 0.0572238i | ||||||||
\(94\) | −22.3180 | −2.30193 | ||||||||
\(95\) | −3.17993 | + | 5.08694i | −0.326254 | + | 0.521909i | ||||
\(96\) | −14.9598 | −1.52683 | ||||||||
\(97\) | −18.3921 | −1.86744 | −0.933719 | − | 0.358007i | \(-0.883456\pi\) | ||||
−0.933719 | + | 0.358007i | \(0.883456\pi\) | |||||||
\(98\) | −4.83526 | + | 18.0153i | −0.488435 | + | 1.81982i | ||||
\(99\) | 1.90151 | − | 2.71740i | 0.191109 | − | 0.273109i | ||||
\(100\) | −11.1718 | − | 22.9262i | −1.11718 | − | 2.29262i | ||||
\(101\) | 17.7370 | 1.76490 | 0.882451 | − | 0.470405i | \(-0.155892\pi\) | ||||
0.882451 | + | 0.470405i | \(0.155892\pi\) | |||||||
\(102\) | − | 4.09632i | − | 0.405596i | ||||||
\(103\) | 15.5720 | 1.53436 | 0.767180 | − | 0.641432i | \(-0.221659\pi\) | ||||
0.767180 | + | 0.641432i | \(0.221659\pi\) | |||||||
\(104\) | − | 7.14549i | − | 0.700673i | ||||||
\(105\) | 0.564757 | + | 5.88906i | 0.0551146 | + | 0.574714i | ||||
\(106\) | − | 21.8915i | − | 2.12629i | ||||||
\(107\) | 16.4098 | 1.58639 | 0.793197 | − | 0.608965i | \(-0.208415\pi\) | ||||
0.793197 | + | 0.608965i | \(0.208415\pi\) | |||||||
\(108\) | 5.10065 | 0.490811 | ||||||||
\(109\) | − | 11.4582i | − | 1.09749i | −0.835988 | − | 0.548747i | \(-0.815105\pi\) | ||
0.835988 | − | 0.548747i | \(-0.184895\pi\) | |||||||
\(110\) | −7.72392 | − | 18.1900i | −0.736447 | − | 1.73435i | ||||
\(111\) | − | 5.97120i | − | 0.566762i | ||||||
\(112\) | 24.8046 | − | 19.0250i | 2.34382 | − | 1.79770i | ||||
\(113\) | − | 3.87929i | − | 0.364933i | −0.983212 | − | 0.182466i | \(-0.941592\pi\) | ||
0.983212 | − | 0.182466i | \(-0.0584081\pi\) | |||||||
\(114\) | −7.14906 | −0.669571 | ||||||||
\(115\) | 13.8981 | + | 8.68792i | 1.29600 | + | 0.810153i | ||||
\(116\) | − | 7.24777i | − | 0.672939i | ||||||
\(117\) | 0.864827i | 0.0799533i | ||||||||
\(118\) | 38.3450i | 3.52995i | ||||||||
\(119\) | 2.47527 | + | 3.22723i | 0.226908 | + | 0.295840i | ||||
\(120\) | 9.79311 | − | 15.6661i | 0.893984 | − | 1.43011i | ||||
\(121\) | −3.76850 | − | 10.3343i | −0.342591 | − | 0.939485i | ||||
\(122\) | 18.5424 | 1.67875 | ||||||||
\(123\) | −0.607303 | −0.0547586 | ||||||||
\(124\) | 2.81478i | 0.252774i | ||||||||
\(125\) | 11.1185 | + | 1.17458i | 0.994466 | + | 0.105057i | ||||
\(126\) | −5.59415 | + | 4.29069i | −0.498367 | + | 0.382245i | ||||
\(127\) | 16.1339 | 1.43165 | 0.715825 | − | 0.698279i | \(-0.246051\pi\) | ||||
0.715825 | + | 0.698279i | \(0.246051\pi\) | |||||||
\(128\) | −13.3359 | −1.17874 | ||||||||
\(129\) | −0.823316 | −0.0724889 | ||||||||
\(130\) | 4.36954 | + | 2.73147i | 0.383234 | + | 0.239566i | ||||
\(131\) | 7.98104 | 0.697307 | 0.348653 | − | 0.937252i | \(-0.386639\pi\) | ||||
0.348653 | + | 0.937252i | \(0.386639\pi\) | |||||||
\(132\) | 9.69896 | − | 13.8605i | 0.844186 | − | 1.20640i | ||||
\(133\) | 5.63229 | − | 4.31994i | 0.488381 | − | 0.374586i | ||||
\(134\) | − | 20.7432i | − | 1.79194i | ||||||
\(135\) | −1.18527 | + | 1.89608i | −0.102012 | + | 0.163189i | ||||
\(136\) | − | 12.7013i | − | 1.08913i | ||||||
\(137\) | − | 13.3208i | − | 1.13807i | −0.822312 | − | 0.569037i | \(-0.807316\pi\) | ||
0.822312 | − | 0.569037i | \(-0.192684\pi\) | |||||||
\(138\) | 19.5320i | 1.66268i | ||||||||
\(139\) | 5.61484 | 0.476245 | 0.238122 | − | 0.971235i | \(-0.423468\pi\) | ||||
0.238122 | + | 0.971235i | \(0.423468\pi\) | |||||||
\(140\) | 2.88063 | + | 30.0381i | 0.243458 | + | 2.53868i | ||||
\(141\) | 8.37543 | 0.705338 | ||||||||
\(142\) | 11.6890 | 0.980919 | ||||||||
\(143\) | 2.35008 | + | 1.64448i | 0.196523 | + | 0.137518i | ||||
\(144\) | 11.8154 | 0.984614 | ||||||||
\(145\) | 2.69424 | + | 1.68421i | 0.223744 | + | 0.139866i | ||||
\(146\) | − | 10.3664i | − | 0.857932i | ||||||
\(147\) | 1.81456 | − | 6.76072i | 0.149662 | − | 0.557615i | ||||
\(148\) | − | 30.4571i | − | 2.50355i | ||||||
\(149\) | − | 6.63536i | − | 0.543590i | −0.962355 | − | 0.271795i | \(-0.912383\pi\) | ||
0.962355 | − | 0.271795i | \(-0.0876172\pi\) | |||||||
\(150\) | 5.83640 | + | 11.9772i | 0.476540 | + | 0.977932i | ||||
\(151\) | 16.7964i | 1.36687i | 0.730010 | + | 0.683436i | \(0.239515\pi\) | ||||
−0.730010 | + | 0.683436i | \(0.760485\pi\) | |||||||
\(152\) | −22.1668 | −1.79796 | ||||||||
\(153\) | 1.53725i | 0.124279i | ||||||||
\(154\) | 1.02215 | + | 23.3603i | 0.0823674 | + | 1.88243i | ||||
\(155\) | −1.04635 | − | 0.654088i | −0.0840446 | − | 0.0525376i | ||||
\(156\) | 4.41118i | 0.353177i | ||||||||
\(157\) | 6.52197 | 0.520510 | 0.260255 | − | 0.965540i | \(-0.416193\pi\) | ||||
0.260255 | + | 0.965540i | \(0.416193\pi\) | |||||||
\(158\) | 23.8367i | 1.89634i | ||||||||
\(159\) | 8.21534i | 0.651519i | ||||||||
\(160\) | 17.7314 | − | 28.3651i | 1.40179 | − | 2.24245i | ||||
\(161\) | −11.8026 | − | 15.3880i | −0.930172 | − | 1.21275i | ||||
\(162\) | −2.66471 | −0.209359 | ||||||||
\(163\) | 3.51503i | 0.275318i | 0.990480 | + | 0.137659i | \(0.0439578\pi\) | ||||
−0.990480 | + | 0.137659i | \(0.956042\pi\) | |||||||
\(164\) | −3.09764 | −0.241885 | ||||||||
\(165\) | 2.89860 | + | 6.82628i | 0.225656 | + | 0.531425i | ||||
\(166\) | − | 35.0249i | − | 2.71846i | ||||||
\(167\) | − | 16.2402i | − | 1.25671i | −0.777928 | − | 0.628354i | \(-0.783729\pi\) | ||
0.777928 | − | 0.628354i | \(-0.216271\pi\) | |||||||
\(168\) | −17.3455 | + | 13.3039i | −1.33824 | + | 1.02642i | ||||
\(169\) | 12.2521 | 0.942467 | ||||||||
\(170\) | 7.76697 | + | 4.85525i | 0.595699 | + | 0.372381i | ||||
\(171\) | 2.68287 | 0.205164 | ||||||||
\(172\) | −4.19945 | −0.320205 | ||||||||
\(173\) | − | 9.54156i | − | 0.725432i | −0.931900 | − | 0.362716i | \(-0.881850\pi\) | ||
0.931900 | − | 0.362716i | \(-0.118150\pi\) | |||||||
\(174\) | 3.78641i | 0.287047i | ||||||||
\(175\) | −11.8355 | − | 5.90931i | −0.894683 | − | 0.446702i | ||||
\(176\) | 22.4671 | − | 32.1071i | 1.69352 | − | 2.42016i | ||||
\(177\) | − | 14.3900i | − | 1.08162i | ||||||
\(178\) | − | 20.0235i | − | 1.50082i | ||||||
\(179\) | −14.7615 | −1.10333 | −0.551664 | − | 0.834066i | \(-0.686007\pi\) | ||||
−0.551664 | + | 0.834066i | \(0.686007\pi\) | |||||||
\(180\) | −6.04566 | + | 9.67127i | −0.450617 | + | 0.720854i | ||||
\(181\) | 23.2469i | 1.72793i | 0.503555 | + | 0.863963i | \(0.332025\pi\) | ||||
−0.503555 | + | 0.863963i | \(0.667975\pi\) | |||||||
\(182\) | −3.71070 | − | 4.83798i | −0.275056 | − | 0.358615i | ||||
\(183\) | −6.95852 | −0.514388 | ||||||||
\(184\) | 60.5621i | 4.46470i | ||||||||
\(185\) | 11.3219 | + | 7.07750i | 0.832403 | + | 0.520348i | ||||
\(186\) | − | 1.47051i | − | 0.107823i | ||||||
\(187\) | 4.17732 | + | 2.92310i | 0.305476 | + | 0.213758i | ||||
\(188\) | 42.7202 | 3.11569 | ||||||||
\(189\) | 2.09935 | − | 1.61019i | 0.152705 | − | 0.117124i | ||||
\(190\) | 8.47358 | − | 13.5552i | 0.614738 | − | 0.983398i | ||||
\(191\) | 15.8968 | 1.15025 | 0.575125 | − | 0.818066i | \(-0.304953\pi\) | ||||
0.575125 | + | 0.818066i | \(0.304953\pi\) | |||||||
\(192\) | 16.2328 | 1.17150 | ||||||||
\(193\) | −8.32276 | −0.599085 | −0.299543 | − | 0.954083i | \(-0.596834\pi\) | ||||
−0.299543 | + | 0.954083i | \(0.596834\pi\) | |||||||
\(194\) | 49.0096 | 3.51868 | ||||||||
\(195\) | −1.63978 | − | 1.02505i | −0.117427 | − | 0.0734057i | ||||
\(196\) | 9.25543 | − | 34.4841i | 0.661102 | − | 2.46315i | ||||
\(197\) | −13.2323 | −0.942762 | −0.471381 | − | 0.881930i | \(-0.656244\pi\) | ||||
−0.471381 | + | 0.881930i | \(0.656244\pi\) | |||||||
\(198\) | −5.06697 | + | 7.24106i | −0.360094 | + | 0.514600i | ||||
\(199\) | − | 3.83430i | − | 0.271806i | −0.990722 | − | 0.135903i | \(-0.956606\pi\) | ||
0.990722 | − | 0.135903i | \(-0.0433936\pi\) | |||||||
\(200\) | 18.0967 | + | 37.1371i | 1.27963 | + | 2.62599i | ||||
\(201\) | 7.78444i | 0.549072i | ||||||||
\(202\) | −47.2640 | −3.32548 | ||||||||
\(203\) | −2.28800 | − | 2.98307i | −0.160586 | − | 0.209371i | ||||
\(204\) | 7.84099i | 0.548979i | ||||||||
\(205\) | 0.719819 | − | 1.15150i | 0.0502743 | − | 0.0804240i | ||||
\(206\) | −41.4949 | −2.89109 | ||||||||
\(207\) | − | 7.32990i | − | 0.509463i | ||||||
\(208\) | 10.2182i | 0.708508i | ||||||||
\(209\) | 5.10151 | − | 7.29042i | 0.352879 | − | 0.504289i | ||||
\(210\) | −1.50491 | − | 15.6926i | −0.103849 | − | 1.08289i | ||||
\(211\) | − | 17.3558i | − | 1.19482i | −0.801934 | − | 0.597412i | \(-0.796196\pi\) | ||
0.801934 | − | 0.597412i | \(-0.203804\pi\) | |||||||
\(212\) | 41.9036i | 2.87795i | ||||||||
\(213\) | −4.38660 | −0.300565 | ||||||||
\(214\) | −43.7273 | −2.98913 | ||||||||
\(215\) | 0.975853 | − | 1.56107i | 0.0665526 | − | 0.106464i | ||||
\(216\) | −8.26233 | −0.562180 | ||||||||
\(217\) | 0.888579 | + | 1.15852i | 0.0603207 | + | 0.0786454i | ||||
\(218\) | 30.5327i | 2.06793i | ||||||||
\(219\) | 3.89027i | 0.262880i | ||||||||
\(220\) | 14.7848 | + | 34.8185i | 0.996789 | + | 2.34746i | ||||
\(221\) | −1.32946 | −0.0894289 | ||||||||
\(222\) | 15.9115i | 1.06791i | ||||||||
\(223\) | 8.79032 | 0.588644 | 0.294322 | − | 0.955706i | \(-0.404906\pi\) | ||||
0.294322 | + | 0.955706i | \(0.404906\pi\) | |||||||
\(224\) | −31.4059 | + | 24.0882i | −2.09840 | + | 1.60946i | ||||
\(225\) | −2.19026 | − | 4.49475i | −0.146017 | − | 0.299650i | ||||
\(226\) | 10.3372i | 0.687618i | ||||||||
\(227\) | − | 16.2488i | − | 1.07847i | −0.842155 | − | 0.539236i | \(-0.818713\pi\) | ||
0.842155 | − | 0.539236i | \(-0.181287\pi\) | |||||||
\(228\) | 13.6844 | 0.906271 | ||||||||
\(229\) | 24.5602i | 1.62299i | 0.584362 | + | 0.811493i | \(0.301345\pi\) | ||||
−0.584362 | + | 0.811493i | \(0.698655\pi\) | |||||||
\(230\) | −37.0343 | − | 23.1508i | −2.44197 | − | 1.52652i | ||||
\(231\) | −0.383589 | − | 8.76658i | −0.0252383 | − | 0.576798i | ||||
\(232\) | 11.7404i | 0.770792i | ||||||||
\(233\) | −17.2426 | −1.12960 | −0.564802 | − | 0.825227i | \(-0.691047\pi\) | ||||
−0.564802 | + | 0.825227i | \(0.691047\pi\) | |||||||
\(234\) | − | 2.30451i | − | 0.150650i | ||||||
\(235\) | −9.92716 | + | 15.8805i | −0.647576 | + | 1.03593i | ||||
\(236\) | − | 73.3983i | − | 4.77782i | ||||||
\(237\) | − | 8.94533i | − | 0.581061i | ||||||
\(238\) | −6.59587 | − | 8.59962i | −0.427547 | − | 0.557431i | ||||
\(239\) | − | 2.60857i | − | 0.168734i | −0.996435 | − | 0.0843671i | \(-0.973113\pi\) | ||
0.996435 | − | 0.0843671i | \(-0.0268868\pi\) | |||||||
\(240\) | −14.0044 | + | 22.4029i | −0.903982 | + | 1.44610i | ||||
\(241\) | −1.02093 | −0.0657638 | −0.0328819 | − | 0.999459i | \(-0.510469\pi\) | ||||
−0.0328819 | + | 0.999459i | \(0.510469\pi\) | |||||||
\(242\) | 10.0419 | + | 27.5380i | 0.645520 | + | 1.77021i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −35.4930 | −2.27221 | ||||||||
\(245\) | 10.6681 | + | 11.4538i | 0.681563 | + | 0.731759i | ||||
\(246\) | 1.61828 | 0.103178 | ||||||||
\(247\) | 2.32022i | 0.147632i | ||||||||
\(248\) | − | 4.55954i | − | 0.289531i | ||||||
\(249\) | 13.1440i | 0.832967i | ||||||||
\(250\) | −29.6274 | − | 3.12990i | −1.87380 | − | 0.197952i | ||||
\(251\) | 15.9683i | 1.00791i | 0.863730 | + | 0.503955i | \(0.168122\pi\) | ||||
−0.863730 | + | 0.503955i | \(0.831878\pi\) | |||||||
\(252\) | 10.7081 | − | 8.21304i | 0.674545 | − | 0.517373i | ||||
\(253\) | −19.9183 | − | 13.9379i | −1.25225 | − | 0.876268i | ||||
\(254\) | −42.9920 | −2.69756 | ||||||||
\(255\) | −2.91476 | − | 1.82206i | −0.182529 | − | 0.114102i | ||||
\(256\) | 3.07071 | 0.191919 | ||||||||
\(257\) | −24.0879 | −1.50256 | −0.751282 | − | 0.659981i | \(-0.770564\pi\) | ||||
−0.751282 | + | 0.659981i | \(0.770564\pi\) | |||||||
\(258\) | 2.19389 | 0.136586 | ||||||||
\(259\) | −9.61479 | − | 12.5357i | −0.597434 | − | 0.778928i | ||||
\(260\) | −8.36397 | − | 5.22845i | −0.518711 | − | 0.324255i | ||||
\(261\) | − | 1.42095i | − | 0.0879546i | ||||||
\(262\) | −21.2671 | −1.31389 | ||||||||
\(263\) | 18.4313 | 1.13652 | 0.568260 | − | 0.822849i | \(-0.307617\pi\) | ||||
0.568260 | + | 0.822849i | \(0.307617\pi\) | |||||||
\(264\) | −15.7109 | + | 22.4520i | −0.966941 | + | 1.38183i | ||||
\(265\) | −15.5770 | − | 9.73741i | −0.956885 | − | 0.598164i | ||||
\(266\) | −15.0084 | + | 11.5114i | −0.920223 | + | 0.705807i | ||||
\(267\) | 7.51433i | 0.459870i | ||||||||
\(268\) | 39.7057i | 2.42541i | ||||||||
\(269\) | − | 10.2977i | − | 0.627861i | −0.949446 | − | 0.313931i | \(-0.898354\pi\) | ||
0.949446 | − | 0.313931i | \(-0.101646\pi\) | |||||||
\(270\) | 3.15840 | − | 5.05250i | 0.192214 | − | 0.307486i | ||||
\(271\) | −23.6065 | −1.43399 | −0.716995 | − | 0.697078i | \(-0.754483\pi\) | ||||
−0.716995 | + | 0.697078i | \(0.754483\pi\) | |||||||
\(272\) | 18.1632i | 1.10131i | ||||||||
\(273\) | 1.39254 | + | 1.81558i | 0.0842802 | + | 0.109884i | ||||
\(274\) | 35.4960i | 2.14439i | ||||||||
\(275\) | −16.3788 | − | 2.59501i | −0.987680 | − | 0.156485i | ||||
\(276\) | − | 37.3873i | − | 2.25045i | ||||||
\(277\) | 26.2554 | 1.57754 | 0.788768 | − | 0.614691i | \(-0.210719\pi\) | ||||
0.788768 | + | 0.614691i | \(0.210719\pi\) | |||||||
\(278\) | −14.9619 | −0.897356 | ||||||||
\(279\) | 0.551846i | 0.0330382i | ||||||||
\(280\) | −4.66621 | − | 48.6574i | −0.278859 | − | 2.90783i | ||||
\(281\) | 31.7030i | 1.89124i | 0.325272 | + | 0.945620i | \(0.394544\pi\) | ||||
−0.325272 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(282\) | −22.3180 | −1.32902 | ||||||||
\(283\) | 7.26679i | 0.431966i | 0.976397 | + | 0.215983i | \(0.0692955\pi\) | ||||
−0.976397 | + | 0.215983i | \(0.930704\pi\) | |||||||
\(284\) | −22.3745 | −1.32768 | ||||||||
\(285\) | −3.17993 | + | 5.08694i | −0.188363 | + | 0.301325i | ||||
\(286\) | −6.26227 | − | 4.38205i | −0.370296 | − | 0.259116i | ||||
\(287\) | −1.27494 | + | 0.977874i | −0.0752575 | + | 0.0577221i | ||||
\(288\) | −14.9598 | −0.881516 | ||||||||
\(289\) | 14.6369 | 0.860992 | ||||||||
\(290\) | −7.17935 | − | 4.48793i | −0.421586 | − | 0.263540i | ||||
\(291\) | −18.3921 | −1.07817 | ||||||||
\(292\) | 19.8429i | 1.16122i | ||||||||
\(293\) | 31.4376i | 1.83661i | 0.395877 | + | 0.918303i | \(0.370441\pi\) | ||||
−0.395877 | + | 0.918303i | \(0.629559\pi\) | |||||||
\(294\) | −4.83526 | + | 18.0153i | −0.281998 | + | 1.05068i | ||||
\(295\) | 27.2846 | + | 17.0560i | 1.58857 | + | 0.993040i | ||||
\(296\) | 49.3361i | 2.86760i | ||||||||
\(297\) | 1.90151 | − | 2.71740i | 0.110337 | − | 0.157679i | ||||
\(298\) | 17.6813i | 1.02425i | ||||||||
\(299\) | 6.33910 | 0.366599 | ||||||||
\(300\) | −11.1718 | − | 22.9262i | −0.645003 | − | 1.32364i | ||||
\(301\) | −1.72843 | + | 1.32570i | −0.0996250 | + | 0.0764119i | ||||
\(302\) | − | 44.7575i | − | 2.57550i | ||||||
\(303\) | 17.7370 | 1.01897 | ||||||||
\(304\) | 31.6991 | 1.81807 | ||||||||
\(305\) | 8.24773 | − | 13.1939i | 0.472264 | − | 0.755482i | ||||
\(306\) | − | 4.09632i | − | 0.234171i | ||||||
\(307\) | 13.8197i | 0.788733i | 0.918953 | + | 0.394366i | \(0.129036\pi\) | ||||
−0.918953 | + | 0.394366i | \(0.870964\pi\) | |||||||
\(308\) | −1.95656 | − | 44.7153i | −0.111485 | − | 2.54789i | ||||
\(309\) | 15.5720 | 0.885863 | ||||||||
\(310\) | 2.78820 | + | 1.74295i | 0.158359 | + | 0.0989930i | ||||
\(311\) | 4.57177i | 0.259241i | 0.991564 | + | 0.129621i | \(0.0413759\pi\) | ||||
−0.991564 | + | 0.129621i | \(0.958624\pi\) | |||||||
\(312\) | − | 7.14549i | − | 0.404533i | ||||||
\(313\) | 26.4180 | 1.49323 | 0.746616 | − | 0.665256i | \(-0.231677\pi\) | ||||
0.746616 | + | 0.665256i | \(0.231677\pi\) | |||||||
\(314\) | −17.3791 | −0.980762 | ||||||||
\(315\) | 0.564757 | + | 5.88906i | 0.0318205 | + | 0.331811i | ||||
\(316\) | − | 45.6270i | − | 2.56672i | ||||||
\(317\) | − | 7.88446i | − | 0.442835i | −0.975179 | − | 0.221418i | \(-0.928932\pi\) | ||
0.975179 | − | 0.221418i | \(-0.0710684\pi\) | |||||||
\(318\) | − | 21.8915i | − | 1.22761i | ||||||
\(319\) | −3.86129 | − | 2.70195i | −0.216190 | − | 0.151280i | ||||
\(320\) | −19.2402 | + | 30.7787i | −1.07556 | + | 1.72058i | ||||
\(321\) | 16.4098 | 0.915905 | ||||||||
\(322\) | 31.4503 | + | 41.0046i | 1.75266 | + | 2.28510i | ||||
\(323\) | 4.12424i | 0.229479i | ||||||||
\(324\) | 5.10065 | 0.283370 | ||||||||
\(325\) | 3.88718 | − | 1.89420i | 0.215622 | − | 0.105071i | ||||
\(326\) | − | 9.36651i | − | 0.518763i | ||||||
\(327\) | − | 11.4582i | − | 0.633639i | ||||||
\(328\) | 5.01774 | 0.277058 | ||||||||
\(329\) | 17.5830 | − | 13.4861i | 0.969381 | − | 0.743510i | ||||
\(330\) | −7.72392 | − | 18.1900i | −0.425188 | − | 1.00133i | ||||
\(331\) | −5.20944 | −0.286337 | −0.143168 | − | 0.989698i | \(-0.545729\pi\) | ||||
−0.143168 | + | 0.989698i | \(0.545729\pi\) | |||||||
\(332\) | 67.0430i | 3.67946i | ||||||||
\(333\) | − | 5.97120i | − | 0.327220i | ||||||
\(334\) | 43.2755i | 2.36793i | ||||||||
\(335\) | −14.7599 | − | 9.22668i | −0.806422 | − | 0.504107i | ||||
\(336\) | 24.8046 | − | 19.0250i | 1.35320 | − | 1.03790i | ||||
\(337\) | 0.820269 | 0.0446829 | 0.0223414 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223414 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(338\) | −32.6482 | −1.77583 | ||||||||
\(339\) | − | 3.87929i | − | 0.210694i | ||||||
\(340\) | −14.8672 | − | 9.29370i | −0.806285 | − | 0.504022i | ||||
\(341\) | 1.49959 | + | 1.04934i | 0.0812071 | + | 0.0568251i | ||||
\(342\) | −7.14906 | −0.386577 | ||||||||
\(343\) | −7.07667 | − | 17.1149i | −0.382104 | − | 0.924119i | ||||
\(344\) | 6.80251 | 0.366767 | ||||||||
\(345\) | 13.8981 | + | 8.68792i | 0.748249 | + | 0.467742i | ||||
\(346\) | 25.4255i | 1.36688i | ||||||||
\(347\) | −9.64321 | −0.517675 | −0.258837 | − | 0.965921i | \(-0.583339\pi\) | ||||
−0.258837 | + | 0.965921i | \(0.583339\pi\) | |||||||
\(348\) | − | 7.24777i | − | 0.388521i | ||||||
\(349\) | 7.03905 | 0.376792 | 0.188396 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188396 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(350\) | 31.5382 | + | 15.7466i | 1.68579 | + | 0.841690i | ||||
\(351\) | 0.864827i | 0.0461610i | ||||||||
\(352\) | −28.4463 | + | 40.6518i | −1.51619 | + | 2.16675i | ||||
\(353\) | −10.8364 | −0.576766 | −0.288383 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288383 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(354\) | 38.3450i | 2.03802i | ||||||||
\(355\) | 5.19931 | − | 8.31736i | 0.275951 | − | 0.441440i | ||||
\(356\) | 38.3280i | 2.03138i | ||||||||
\(357\) | 2.47527 | + | 3.22723i | 0.131005 | + | 0.170803i | ||||
\(358\) | 39.3351 | 2.07893 | ||||||||
\(359\) | 4.49768i | 0.237378i | 0.992931 | + | 0.118689i | \(0.0378692\pi\) | ||||
−0.992931 | + | 0.118689i | \(0.962131\pi\) | |||||||
\(360\) | 9.79311 | − | 15.6661i | 0.516142 | − | 0.825674i | ||||
\(361\) | −11.8022 | −0.621169 | ||||||||
\(362\) | − | 61.9460i | − | 3.25581i | ||||||
\(363\) | −3.76850 | − | 10.3343i | −0.197795 | − | 0.542412i | ||||
\(364\) | 7.10286 | + | 9.26063i | 0.372291 | + | 0.485389i | ||||
\(365\) | −7.37628 | − | 4.61103i | −0.386092 | − | 0.241352i | ||||
\(366\) | 18.5424 | 0.969227 | ||||||||
\(367\) | −1.71236 | −0.0893847 | −0.0446924 | − | 0.999001i | \(-0.514231\pi\) | ||||
−0.0446924 | + | 0.999001i | \(0.514231\pi\) | |||||||
\(368\) | − | 86.6055i | − | 4.51462i | ||||||
\(369\) | −0.607303 | −0.0316149 | ||||||||
\(370\) | −30.1695 | − | 18.8594i | −1.56844 | − | 0.980456i | ||||
\(371\) | 13.2283 | + | 17.2469i | 0.686778 | + | 0.895414i | ||||
\(372\) | 2.81478i | 0.145939i | ||||||||
\(373\) | −27.0598 | −1.40110 | −0.700552 | − | 0.713601i | \(-0.747063\pi\) | ||||
−0.700552 | + | 0.713601i | \(0.747063\pi\) | |||||||
\(374\) | −11.1313 | − | 7.78921i | −0.575588 | − | 0.402770i | ||||
\(375\) | 11.1185 | + | 1.17458i | 0.574155 | + | 0.0606549i | ||||
\(376\) | −69.2006 | −3.56875 | ||||||||
\(377\) | 1.22888 | 0.0632903 | ||||||||
\(378\) | −5.59415 | + | 4.29069i | −0.287732 | + | 0.220689i | ||||
\(379\) | −21.3719 | −1.09780 | −0.548899 | − | 0.835889i | \(-0.684953\pi\) | ||||
−0.548899 | + | 0.835889i | \(0.684953\pi\) | |||||||
\(380\) | −16.2197 | + | 25.9467i | −0.832054 | + | 1.33104i | ||||
\(381\) | 16.1339 | 0.826564 | ||||||||
\(382\) | −42.3602 | −2.16734 | ||||||||
\(383\) | −28.3248 | −1.44733 | −0.723665 | − | 0.690152i | \(-0.757544\pi\) | ||||
−0.723665 | + | 0.690152i | \(0.757544\pi\) | |||||||
\(384\) | −13.3359 | −0.680545 | ||||||||
\(385\) | 17.0768 | + | 9.66346i | 0.870315 | + | 0.492495i | ||||
\(386\) | 22.1777 | 1.12881 | ||||||||
\(387\) | −0.823316 | −0.0418515 | ||||||||
\(388\) | −93.8119 | −4.76258 | ||||||||
\(389\) | 15.0506 | 0.763095 | 0.381547 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381547 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(390\) | 4.36954 | + | 2.73147i | 0.221260 | + | 0.138313i | ||||
\(391\) | 11.2679 | 0.569842 | ||||||||
\(392\) | −14.9925 | + | 55.8593i | −0.757235 | + | 2.82132i | ||||
\(393\) | 7.98104 | 0.402590 | ||||||||
\(394\) | 35.2602 | 1.77638 | ||||||||
\(395\) | 16.9611 | + | 10.6026i | 0.853405 | + | 0.533477i | ||||
\(396\) | 9.69896 | − | 13.8605i | 0.487391 | − | 0.696517i | ||||
\(397\) | 1.61424 | 0.0810162 | 0.0405081 | − | 0.999179i | \(-0.487102\pi\) | ||||
0.0405081 | + | 0.999179i | \(0.487102\pi\) | |||||||
\(398\) | 10.2173i | 0.512146i | ||||||||
\(399\) | 5.63229 | − | 4.31994i | 0.281967 | − | 0.216267i | ||||
\(400\) | −25.8788 | − | 53.1071i | −1.29394 | − | 2.65535i | ||||
\(401\) | 11.4134 | 0.569956 | 0.284978 | − | 0.958534i | \(-0.408014\pi\) | ||||
0.284978 | + | 0.958534i | \(0.408014\pi\) | |||||||
\(402\) | − | 20.7432i | − | 1.03458i | ||||||
\(403\) | −0.477251 | −0.0237736 | ||||||||
\(404\) | 90.4705 | 4.50108 | ||||||||
\(405\) | −1.18527 | + | 1.89608i | −0.0588966 | + | 0.0942171i | ||||
\(406\) | 6.09685 | + | 7.94901i | 0.302582 | + | 0.394503i | ||||
\(407\) | −16.2261 | − | 11.3543i | −0.804300 | − | 0.562813i | ||||
\(408\) | − | 12.7013i | − | 0.628807i | ||||||
\(409\) | −39.2972 | −1.94312 | −0.971560 | − | 0.236794i | \(-0.923903\pi\) | ||||
−0.971560 | + | 0.236794i | \(0.923903\pi\) | |||||||
\(410\) | −1.91810 | + | 3.06840i | −0.0947284 | + | 0.151537i | ||||
\(411\) | − | 13.3208i | − | 0.657067i | ||||||
\(412\) | 79.4276 | 3.91312 | ||||||||
\(413\) | −23.1706 | − | 30.2096i | −1.14015 | − | 1.48652i | ||||
\(414\) | 19.5320i | 0.959947i | ||||||||
\(415\) | −24.9221 | − | 15.5792i | −1.22338 | − | 0.764754i | ||||
\(416\) | − | 12.9376i | − | 0.634320i | ||||||
\(417\) | 5.61484 | 0.274960 | ||||||||
\(418\) | −13.5940 | + | 19.4268i | −0.664905 | + | 0.950197i | ||||
\(419\) | − | 4.32026i | − | 0.211059i | −0.994416 | − | 0.105529i | \(-0.966346\pi\) | ||
0.994416 | − | 0.105529i | \(-0.0336537\pi\) | |||||||
\(420\) | 2.88063 | + | 30.0381i | 0.140560 | + | 1.46571i | ||||
\(421\) | −5.64413 | −0.275078 | −0.137539 | − | 0.990496i | \(-0.543919\pi\) | ||||
−0.137539 | + | 0.990496i | \(0.543919\pi\) | |||||||
\(422\) | 46.2482i | 2.25133i | ||||||||
\(423\) | 8.37543 | 0.407227 | ||||||||
\(424\) | − | 67.8779i | − | 3.29644i | ||||||
\(425\) | 6.90956 | − | 3.36698i | 0.335163 | − | 0.163323i | ||||
\(426\) | 11.6890 | 0.566334 | ||||||||
\(427\) | −14.6084 | + | 11.2046i | −0.706949 | + | 0.542226i | ||||
\(428\) | 83.7007 | 4.04582 | ||||||||
\(429\) | 2.35008 | + | 1.64448i | 0.113463 | + | 0.0793962i | ||||
\(430\) | −2.60036 | + | 4.15980i | −0.125400 | + | 0.200604i | ||||
\(431\) | 40.0098i | 1.92720i | 0.267344 | + | 0.963601i | \(0.413854\pi\) | ||||
−0.267344 | + | 0.963601i | \(0.586146\pi\) | |||||||
\(432\) | 11.8154 | 0.568467 | ||||||||
\(433\) | 8.18707 | 0.393445 | 0.196723 | − | 0.980459i | \(-0.436970\pi\) | ||||
0.196723 | + | 0.980459i | \(0.436970\pi\) | |||||||
\(434\) | −2.36780 | − | 3.08711i | −0.113658 | − | 0.148186i | ||||
\(435\) | 2.69424 | + | 1.68421i | 0.129179 | + | 0.0807518i | ||||
\(436\) | − | 58.4442i | − | 2.79897i | ||||||
\(437\) | − | 19.6652i | − | 0.940713i | ||||||
\(438\) | − | 10.3664i | − | 0.495327i | ||||||
\(439\) | −16.4327 | −0.784289 | −0.392144 | − | 0.919904i | \(-0.628267\pi\) | ||||
−0.392144 | + | 0.919904i | \(0.628267\pi\) | |||||||
\(440\) | −23.9492 | − | 56.4010i | −1.14173 | − | 2.68881i | ||||
\(441\) | 1.81456 | − | 6.76072i | 0.0864075 | − | 0.321939i | ||||
\(442\) | 3.54261 | 0.168505 | ||||||||
\(443\) | − | 14.4277i | − | 0.685482i | −0.939430 | − | 0.342741i | \(-0.888645\pi\) | ||
0.939430 | − | 0.342741i | \(-0.111355\pi\) | |||||||
\(444\) | − | 30.4571i | − | 1.44543i | ||||||
\(445\) | −14.2478 | − | 8.90652i | −0.675410 | − | 0.422210i | ||||
\(446\) | −23.4236 | −1.10914 | ||||||||
\(447\) | − | 6.63536i | − | 0.313842i | ||||||
\(448\) | 34.0783 | − | 26.1379i | 1.61005 | − | 1.23490i | ||||
\(449\) | 1.50128 | 0.0708500 | 0.0354250 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354250 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(450\) | 5.83640 | + | 11.9772i | 0.275131 | + | 0.564610i | ||||
\(451\) | −1.15479 | + | 1.65028i | −0.0543771 | + | 0.0777088i | ||||
\(452\) | − | 19.7869i | − | 0.930698i | ||||||
\(453\) | 16.7964i | 0.789164i | ||||||||
\(454\) | 43.2983i | 2.03209i | ||||||||
\(455\) | −5.09302 | + | 0.488417i | −0.238764 | + | 0.0228973i | ||||
\(456\) | −22.1668 | −1.03805 | ||||||||
\(457\) | −19.1770 | −0.897061 | −0.448531 | − | 0.893767i | \(-0.648053\pi\) | ||||
−0.448531 | + | 0.893767i | \(0.648053\pi\) | |||||||
\(458\) | − | 65.4458i | − | 3.05808i | ||||||
\(459\) | 1.53725i | 0.0717527i | ||||||||
\(460\) | 70.8894 | + | 44.3141i | 3.30524 | + | 2.06616i | ||||
\(461\) | −17.1758 | −0.799956 | −0.399978 | − | 0.916525i | \(-0.630982\pi\) | ||||
−0.399978 | + | 0.916525i | \(0.630982\pi\) | |||||||
\(462\) | 1.02215 | + | 23.3603i | 0.0475548 | + | 1.08682i | ||||
\(463\) | 23.7081i | 1.10181i | 0.834568 | + | 0.550905i | \(0.185717\pi\) | ||||
−0.834568 | + | 0.550905i | \(0.814283\pi\) | |||||||
\(464\) | − | 16.7890i | − | 0.779412i | ||||||
\(465\) | −1.04635 | − | 0.654088i | −0.0485231 | − | 0.0303326i | ||||
\(466\) | 45.9466 | 2.12843 | ||||||||
\(467\) | −21.4893 | −0.994408 | −0.497204 | − | 0.867634i | \(-0.665640\pi\) | ||||
−0.497204 | + | 0.867634i | \(0.665640\pi\) | |||||||
\(468\) | 4.41118i | 0.203907i | ||||||||
\(469\) | 12.5344 | + | 16.3423i | 0.578787 | + | 0.754616i | ||||
\(470\) | 26.4529 | − | 42.3169i | 1.22018 | − | 1.95193i | ||||
\(471\) | 6.52197 | 0.300517 | ||||||||
\(472\) | 118.895i | 5.47257i | ||||||||
\(473\) | −1.56555 | + | 2.23728i | −0.0719838 | + | 0.102870i | ||||
\(474\) | 23.8367i | 1.09485i | ||||||||
\(475\) | −5.87619 | − | 12.0588i | −0.269618 | − | 0.553297i | ||||
\(476\) | 12.6255 | + | 16.4610i | 0.578689 | + | 0.754488i | ||||
\(477\) | 8.21534i | 0.376155i | ||||||||
\(478\) | 6.95106i | 0.317934i | ||||||||
\(479\) | 8.33633 | 0.380897 | 0.190448 | − | 0.981697i | \(-0.439006\pi\) | ||||
0.190448 | + | 0.981697i | \(0.439006\pi\) | |||||||
\(480\) | 17.7314 | − | 28.3651i | 0.809326 | − | 1.29468i | ||||
\(481\) | 5.16406 | 0.235461 | ||||||||
\(482\) | 2.72047 | 0.123914 | ||||||||
\(483\) | −11.8026 | − | 15.3880i | −0.537035 | − | 0.700180i | ||||
\(484\) | −19.2218 | − | 52.7119i | −0.873719 | − | 2.39599i | ||||
\(485\) | 21.7997 | − | 34.8730i | 0.989872 | − | 1.58350i | ||||
\(486\) | −2.66471 | −0.120873 | ||||||||
\(487\) | − | 6.05352i | − | 0.274311i | −0.990550 | − | 0.137156i | \(-0.956204\pi\) | ||
0.990550 | − | 0.137156i | \(-0.0437961\pi\) | |||||||
\(488\) | 57.4936 | 2.60261 | ||||||||
\(489\) | 3.51503i | 0.158955i | ||||||||
\(490\) | −28.4275 | − | 30.5211i | −1.28422 | − | 1.37880i | ||||
\(491\) | 25.3715i | 1.14500i | 0.819905 | + | 0.572500i | \(0.194026\pi\) | ||||
−0.819905 | + | 0.572500i | \(0.805974\pi\) | |||||||
\(492\) | −3.09764 | −0.139652 | ||||||||
\(493\) | 2.18436 | 0.0983785 | ||||||||
\(494\) | − | 6.18270i | − | 0.278173i | ||||||
\(495\) | 2.89860 | + | 6.82628i | 0.130282 | + | 0.306818i | ||||
\(496\) | 6.52027i | 0.292769i | ||||||||
\(497\) | −9.20902 | + | 7.06327i | −0.413081 | + | 0.316831i | ||||
\(498\) | − | 35.0249i | − | 1.56950i | ||||||
\(499\) | 31.5146 | 1.41079 | 0.705394 | − | 0.708815i | \(-0.250770\pi\) | ||||
0.705394 | + | 0.708815i | \(0.250770\pi\) | |||||||
\(500\) | 56.7115 | + | 5.99111i | 2.53621 | + | 0.267931i | ||||
\(501\) | − | 16.2402i | − | 0.725560i | ||||||
\(502\) | − | 42.5508i | − | 1.89913i | ||||||
\(503\) | − | 19.5773i | − | 0.872907i | −0.899727 | − | 0.436454i | \(-0.856234\pi\) | ||
0.899727 | − | 0.436454i | \(-0.143766\pi\) | |||||||
\(504\) | −17.3455 | + | 13.3039i | −0.772632 | + | 0.592605i | ||||
\(505\) | −21.0232 | + | 33.6309i | −0.935520 | + | 1.49656i | ||||
\(506\) | 53.0763 | + | 37.1404i | 2.35953 | + | 1.65109i | ||||
\(507\) | 12.2521 | 0.544134 | ||||||||
\(508\) | 82.2934 | 3.65118 | ||||||||
\(509\) | 24.6470i | 1.09246i | 0.837635 | + | 0.546230i | \(0.183937\pi\) | ||||
−0.837635 | + | 0.546230i | \(0.816063\pi\) | |||||||
\(510\) | 7.76697 | + | 4.85525i | 0.343927 | + | 0.214994i | ||||
\(511\) | 6.26409 | + | 8.16705i | 0.277107 | + | 0.361289i | ||||
\(512\) | 18.4893 | 0.817117 | ||||||||
\(513\) | 2.68287 | 0.118452 | ||||||||
\(514\) | 64.1873 | 2.83118 | ||||||||
\(515\) | −18.4571 | + | 29.5259i | −0.813317 | + | 1.30107i | ||||
\(516\) | −4.19945 | −0.184870 | ||||||||
\(517\) | 15.9260 | − | 22.7594i | 0.700424 | − | 1.00096i | ||||
\(518\) | 25.6206 | + | 33.4038i | 1.12570 | + | 1.46768i | ||||
\(519\) | − | 9.54156i | − | 0.418828i | ||||||
\(520\) | 13.5484 | + | 8.46934i | 0.594138 | + | 0.371405i | ||||
\(521\) | 7.65022i | 0.335162i | 0.985858 | + | 0.167581i | \(0.0535956\pi\) | ||||
−0.985858 | + | 0.167581i | \(0.946404\pi\) | |||||||
\(522\) | 3.78641i | 0.165727i | ||||||||
\(523\) | 22.3884i | 0.978978i | 0.872010 | + | 0.489489i | \(0.162817\pi\) | ||||
−0.872010 | + | 0.489489i | \(0.837183\pi\) | |||||||
\(524\) | 40.7085 | 1.77836 | ||||||||
\(525\) | −11.8355 | − | 5.90931i | −0.516545 | − | 0.257904i | ||||
\(526\) | −49.1139 | −2.14147 | ||||||||
\(527\) | −0.848326 | −0.0369537 | ||||||||
\(528\) | 22.4671 | − | 32.1071i | 0.977754 | − | 1.39728i | ||||
\(529\) | −30.7275 | −1.33598 | ||||||||
\(530\) | 41.5080 | + | 25.9473i | 1.80299 | + | 1.12708i | ||||
\(531\) | − | 14.3900i | − | 0.624471i | ||||||
\(532\) | 28.7284 | − | 22.0345i | 1.24553 | − | 0.955317i | ||||
\(533\) | − | 0.525212i | − | 0.0227494i | ||||||
\(534\) | − | 20.0235i | − | 0.866501i | ||||||
\(535\) | −19.4501 | + | 31.1143i | −0.840899 | + | 1.34519i | ||||
\(536\) | − | 64.3176i | − | 2.77810i | ||||||
\(537\) | −14.7615 | −0.637007 | ||||||||
\(538\) | 27.4403i | 1.18304i | ||||||||
\(539\) | −14.9212 | − | 17.7865i | −0.642700 | − | 0.766118i | ||||
\(540\) | −6.04566 | + | 9.67127i | −0.260164 | + | 0.416185i | ||||
\(541\) | − | 18.5873i | − | 0.799129i | −0.916705 | − | 0.399565i | \(-0.869161\pi\) | ||
0.916705 | − | 0.399565i | \(-0.130839\pi\) | |||||||
\(542\) | 62.9042 | 2.70197 | ||||||||
\(543\) | 23.2469i | 0.997618i | ||||||||
\(544\) | − | 22.9970i | − | 0.985988i | ||||||
\(545\) | 21.7257 | + | 13.5811i | 0.930625 | + | 0.581748i | ||||
\(546\) | −3.71070 | − | 4.83798i | −0.158803 | − | 0.207046i | ||||
\(547\) | 3.02733 | 0.129439 | 0.0647197 | − | 0.997903i | \(-0.479385\pi\) | ||||
0.0647197 | + | 0.997903i | \(0.479385\pi\) | |||||||
\(548\) | − | 67.9448i | − | 2.90246i | ||||||
\(549\) | −6.95852 | −0.296982 | ||||||||
\(550\) | 43.6447 | + | 6.91493i | 1.86102 | + | 0.294853i | ||||
\(551\) | − | 3.81222i | − | 0.162406i | ||||||
\(552\) | 60.5621i | 2.57769i | ||||||||
\(553\) | −14.4037 | − | 18.7794i | −0.612508 | − | 0.798581i | ||||
\(554\) | −69.9630 | −2.97244 | ||||||||
\(555\) | 11.3219 | + | 7.07750i | 0.480588 | + | 0.300423i | ||||
\(556\) | 28.6394 | 1.21458 | ||||||||
\(557\) | 37.3665 | 1.58327 | 0.791634 | − | 0.610996i | \(-0.209231\pi\) | ||||
0.791634 | + | 0.610996i | \(0.209231\pi\) | |||||||
\(558\) | − | 1.47051i | − | 0.0622516i | ||||||
\(559\) | − | 0.712025i | − | 0.0301155i | ||||||
\(560\) | 6.67281 | + | 69.5814i | 0.281978 | + | 2.94035i | ||||
\(561\) | 4.17732 | + | 2.92310i | 0.176367 | + | 0.123414i | ||||
\(562\) | − | 84.4791i | − | 3.56354i | ||||||
\(563\) | 3.28145i | 0.138297i | 0.997606 | + | 0.0691483i | \(0.0220282\pi\) | ||||
−0.997606 | + | 0.0691483i | \(0.977972\pi\) | |||||||
\(564\) | 42.7202 | 1.79884 | ||||||||
\(565\) | 7.35545 | + | 4.59801i | 0.309446 | + | 0.193440i | ||||
\(566\) | − | 19.3639i | − | 0.813923i | ||||||
\(567\) | 2.09935 | − | 1.61019i | 0.0881645 | − | 0.0676217i | ||||
\(568\) | 36.2436 | 1.52075 | ||||||||
\(569\) | − | 23.1895i | − | 0.972154i | −0.873916 | − | 0.486077i | \(-0.838427\pi\) | ||
0.873916 | − | 0.486077i | \(-0.161573\pi\) | |||||||
\(570\) | 8.47358 | − | 13.5552i | 0.354919 | − | 0.567765i | ||||
\(571\) | − | 18.0124i | − | 0.753794i | −0.926255 | − | 0.376897i | \(-0.876991\pi\) | ||
0.926255 | − | 0.376897i | \(-0.123009\pi\) | |||||||
\(572\) | 11.9869 | + | 8.38792i | 0.501199 | + | 0.350717i | ||||
\(573\) | 15.8968 | 0.664097 | ||||||||
\(574\) | 3.39735 | − | 2.60575i | 0.141802 | − | 0.108762i | ||||
\(575\) | −32.9461 | + | 16.0544i | −1.37395 | + | 0.669515i | ||||
\(576\) | 16.2328 | 0.676365 | ||||||||
\(577\) | −26.7730 | −1.11458 | −0.557288 | − | 0.830319i | \(-0.688158\pi\) | ||||
−0.557288 | + | 0.830319i | \(0.688158\pi\) | |||||||
\(578\) | −39.0029 | −1.62231 | ||||||||
\(579\) | −8.32276 | −0.345882 | ||||||||
\(580\) | 13.7424 | + | 8.59058i | 0.570621 | + | 0.356704i | ||||
\(581\) | 21.1644 | + | 27.5939i | 0.878047 | + | 1.14479i | ||||
\(582\) | 49.0096 | 2.03151 | ||||||||
\(583\) | 22.3243 | + | 15.6216i | 0.924580 | + | 0.646979i | ||||
\(584\) | − | 32.1427i | − | 1.33008i | ||||||
\(585\) | −1.63978 | − | 1.02505i | −0.0677967 | − | 0.0423808i | ||||
\(586\) | − | 83.7721i | − | 3.46059i | ||||||
\(587\) | −40.2952 | −1.66316 | −0.831581 | − | 0.555403i | \(-0.812564\pi\) | ||||
−0.831581 | + | 0.555403i | \(0.812564\pi\) | |||||||
\(588\) | 9.25543 | − | 34.4841i | 0.381688 | − | 1.42210i | ||||
\(589\) | 1.48053i | 0.0610042i | ||||||||
\(590\) | −72.7054 | − | 45.4493i | −2.99323 | − | 1.87112i | ||||
\(591\) | −13.2323 | −0.544304 | ||||||||
\(592\) | − | 70.5520i | − | 2.89967i | ||||||
\(593\) | 29.8747i | 1.22681i | 0.789769 | + | 0.613404i | \(0.210200\pi\) | ||||
−0.789769 | + | 0.613404i | \(0.789800\pi\) | |||||||
\(594\) | −5.06697 | + | 7.24106i | −0.207900 | + | 0.297104i | ||||
\(595\) | −9.05297 | + | 0.868173i | −0.371135 | + | 0.0355916i | ||||
\(596\) | − | 33.8447i | − | 1.38633i | ||||||
\(597\) | − | 3.83430i | − | 0.156928i | ||||||
\(598\) | −16.8918 | −0.690758 | ||||||||
\(599\) | 5.01487 | 0.204902 | 0.102451 | − | 0.994738i | \(-0.467332\pi\) | ||||
0.102451 | + | 0.994738i | \(0.467332\pi\) | |||||||
\(600\) | 18.0967 | + | 37.1371i | 0.738794 | + | 1.51612i | ||||
\(601\) | −8.64771 | −0.352748 | −0.176374 | − | 0.984323i | \(-0.556437\pi\) | ||||
−0.176374 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(602\) | 4.60575 | − | 3.53259i | 0.187717 | − | 0.143978i | ||||
\(603\) | 7.78444i | 0.317007i | ||||||||
\(604\) | 85.6727i | 3.48597i | ||||||||
\(605\) | 24.0614 | + | 5.10360i | 0.978237 | + | 0.207491i | ||||
\(606\) | −47.2640 | −1.91997 | ||||||||
\(607\) | − | 48.8060i | − | 1.98098i | −0.137601 | − | 0.990488i | \(-0.543939\pi\) | ||
0.137601 | − | 0.990488i | \(-0.456061\pi\) | |||||||
\(608\) | −40.1352 | −1.62770 | ||||||||
\(609\) | −2.28800 | − | 2.98307i | −0.0927146 | − | 0.120880i | ||||
\(610\) | −21.9778 | + | 35.1579i | −0.889854 | + | 1.42350i | ||||
\(611\) | 7.24329i | 0.293032i | ||||||||
\(612\) | 7.84099i | 0.316953i | ||||||||
\(613\) | 18.4910 | 0.746846 | 0.373423 | − | 0.927661i | \(-0.378184\pi\) | ||||
0.373423 | + | 0.927661i | \(0.378184\pi\) | |||||||
\(614\) | − | 36.8255i | − | 1.48616i | ||||||
\(615\) | 0.719819 | − | 1.15150i | 0.0290259 | − | 0.0464328i | ||||
\(616\) | 3.16934 | + | 72.4324i | 0.127696 | + | 2.91838i | ||||
\(617\) | 4.90065i | 0.197293i | 0.995123 | + | 0.0986465i | \(0.0314513\pi\) | ||||
−0.995123 | + | 0.0986465i | \(0.968549\pi\) | |||||||
\(618\) | −41.4949 | −1.66917 | ||||||||
\(619\) | − | 22.3396i | − | 0.897902i | −0.893556 | − | 0.448951i | \(-0.851798\pi\) | ||
0.893556 | − | 0.448951i | \(-0.148202\pi\) | |||||||
\(620\) | −5.33705 | − | 3.33628i | −0.214341 | − | 0.133988i | ||||
\(621\) | − | 7.32990i | − | 0.294139i | ||||||
\(622\) | − | 12.1824i | − | 0.488470i | ||||||
\(623\) | 12.0995 | + | 15.7752i | 0.484757 | + | 0.632021i | ||||
\(624\) | 10.2182i | 0.409057i | ||||||||
\(625\) | −15.4055 | + | 19.6894i | −0.616220 | + | 0.787574i | ||||
\(626\) | −70.3961 | −2.81359 | ||||||||
\(627\) | 5.10151 | − | 7.29042i | 0.203735 | − | 0.291151i | ||||
\(628\) | 33.2663 | 1.32747 | ||||||||
\(629\) | 9.17924 | 0.366000 | ||||||||
\(630\) | −1.50491 | − | 15.6926i | −0.0599571 | − | 0.625209i | ||||
\(631\) | −14.9662 | −0.595796 | −0.297898 | − | 0.954598i | \(-0.596286\pi\) | ||||
−0.297898 | + | 0.954598i | \(0.596286\pi\) | |||||||
\(632\) | 73.9093i | 2.93995i | ||||||||
\(633\) | − | 17.3558i | − | 0.689832i | ||||||
\(634\) | 21.0098i | 0.834404i | ||||||||
\(635\) | −19.1230 | + | 30.5912i | −0.758874 | + | 1.21397i | ||||
\(636\) | 41.9036i | 1.66159i | ||||||||
\(637\) | 5.84685 | + | 1.56928i | 0.231661 | + | 0.0621771i | ||||
\(638\) | 10.2892 | + | 7.19991i | 0.407353 | + | 0.285047i | ||||
\(639\) | −4.38660 | −0.173531 | ||||||||
\(640\) | 15.8067 | − | 25.2860i | 0.624813 | − | 0.999516i | ||||
\(641\) | −13.6017 | −0.537233 | −0.268617 | − | 0.963247i | \(-0.586566\pi\) | ||||
−0.268617 | + | 0.963247i | \(0.586566\pi\) | |||||||
\(642\) | −43.7273 | −1.72578 | ||||||||
\(643\) | −19.3513 | −0.763140 | −0.381570 | − | 0.924340i | \(-0.624616\pi\) | ||||
−0.381570 | + | 0.924340i | \(0.624616\pi\) | |||||||
\(644\) | −60.2008 | − | 78.4891i | −2.37224 | − | 3.09290i | ||||
\(645\) | 0.975853 | − | 1.56107i | 0.0384242 | − | 0.0614673i | ||||
\(646\) | − | 10.9899i | − | 0.432392i | ||||||
\(647\) | −36.1077 | −1.41954 | −0.709770 | − | 0.704434i | \(-0.751201\pi\) | ||||
−0.709770 | + | 0.704434i | \(0.751201\pi\) | |||||||
\(648\) | −8.26233 | −0.324575 | ||||||||
\(649\) | −39.1033 | − | 27.3627i | −1.53494 | − | 1.07408i | ||||
\(650\) | −10.3582 | + | 5.04748i | −0.406281 | + | 0.197978i | ||||
\(651\) | 0.888579 | + | 1.15852i | 0.0348262 | + | 0.0454060i | ||||
\(652\) | 17.9289i | 0.702151i | ||||||||
\(653\) | 33.8487i | 1.32460i | 0.749238 | + | 0.662301i | \(0.230420\pi\) | ||||
−0.749238 | + | 0.662301i | \(0.769580\pi\) | |||||||
\(654\) | 30.5327i | 1.19392i | ||||||||
\(655\) | −9.45970 | + | 15.1327i | −0.369621 | + | 0.591284i | ||||
\(656\) | −7.17551 | −0.280156 | ||||||||
\(657\) | 3.89027i | 0.151774i | ||||||||
\(658\) | −46.8534 | + | 35.9364i | −1.82654 | + | 1.40095i | ||||
\(659\) | 29.3891i | 1.14484i | 0.819962 | + | 0.572418i | \(0.193995\pi\) | ||||
−0.819962 | + | 0.572418i | \(0.806005\pi\) | |||||||
\(660\) | 14.7848 | + | 34.8185i | 0.575496 | + | 1.35531i | ||||
\(661\) | 16.7396i | 0.651096i | 0.945526 | + | 0.325548i | \(0.105549\pi\) | ||||
−0.945526 | + | 0.325548i | \(0.894451\pi\) | |||||||
\(662\) | 13.8816 | 0.539525 | ||||||||
\(663\) | −1.32946 | −0.0516318 | ||||||||
\(664\) | − | 108.600i | − | 4.21450i | ||||||
\(665\) | 1.51517 | + | 15.7996i | 0.0587558 | + | 0.612682i | ||||
\(666\) | 15.9115i | 0.616558i | ||||||||
\(667\) | −10.4154 | −0.403287 | ||||||||
\(668\) | − | 82.8359i | − | 3.20502i | ||||||
\(669\) | 8.79032 | 0.339854 | ||||||||
\(670\) | 39.3309 | + | 24.5864i | 1.51949 | + | 0.949854i | ||||
\(671\) | −13.2317 | + | 18.9091i | −0.510805 | + | 0.729976i | ||||
\(672\) | −31.4059 | + | 24.0882i | −1.21151 | + | 0.929222i | ||||
\(673\) | −15.6776 | −0.604327 | −0.302163 | − | 0.953256i | \(-0.597709\pi\) | ||||
−0.302163 | + | 0.953256i | \(0.597709\pi\) | |||||||
\(674\) | −2.18578 | −0.0841929 | ||||||||
\(675\) | −2.19026 | − | 4.49475i | −0.0843032 | − | 0.173003i | ||||
\(676\) | 62.4936 | 2.40360 | ||||||||
\(677\) | − | 16.2016i | − | 0.622679i | −0.950299 | − | 0.311340i | \(-0.899222\pi\) | ||
0.950299 | − | 0.311340i | \(-0.100778\pi\) | |||||||
\(678\) | 10.3372i | 0.396996i | ||||||||
\(679\) | −38.6116 | + | 29.6149i | −1.48178 | + | 1.13651i | ||||
\(680\) | 24.0827 | + | 15.0545i | 0.923529 | + | 0.577312i | ||||
\(681\) | − | 16.2488i | − | 0.622656i | ||||||
\(682\) | −3.99595 | − | 2.79619i | −0.153013 | − | 0.107072i | ||||
\(683\) | − | 40.3376i | − | 1.54347i | −0.635942 | − | 0.771737i | \(-0.719388\pi\) | ||
0.635942 | − | 0.771737i | \(-0.280612\pi\) | |||||||
\(684\) | 13.6844 | 0.523236 | ||||||||
\(685\) | 25.2574 | + | 15.7888i | 0.965034 | + | 0.603258i | ||||
\(686\) | 18.8572 | + | 45.6062i | 0.719973 | + | 1.74125i | ||||
\(687\) | 24.5602i | 0.937032i | ||||||||
\(688\) | −9.72778 | −0.370868 | ||||||||
\(689\) | −7.10485 | −0.270673 | ||||||||
\(690\) | −37.0343 | − | 23.1508i | −1.40987 | − | 0.881334i | ||||
\(691\) | − | 19.3016i | − | 0.734268i | −0.930168 | − | 0.367134i | \(-0.880339\pi\) | ||
0.930168 | − | 0.367134i | \(-0.119661\pi\) | |||||||
\(692\) | − | 48.6682i | − | 1.85009i | ||||||
\(693\) | −0.383589 | − | 8.76658i | −0.0145713 | − | 0.333015i | ||||
\(694\) | 25.6963 | 0.975419 | ||||||||
\(695\) | −6.65512 | + | 10.6462i | −0.252443 | + | 0.403834i | ||||
\(696\) | 11.7404i | 0.445017i | ||||||||
\(697\) | − | 0.933577i | − | 0.0353617i | ||||||
\(698\) | −18.7570 | −0.709963 | ||||||||
\(699\) | −17.2426 | −0.652177 | ||||||||
\(700\) | −60.3690 | − | 30.1414i | −2.28173 | − | 1.13924i | ||||
\(701\) | 15.8130i | 0.597250i | 0.954370 | + | 0.298625i | \(0.0965280\pi\) | ||||
−0.954370 | + | 0.298625i | \(0.903472\pi\) | |||||||
\(702\) | − | 2.30451i | − | 0.0869781i | ||||||
\(703\) | − | 16.0200i | − | 0.604204i | ||||||
\(704\) | 30.8668 | − | 44.1109i | 1.16334 | − | 1.66249i | ||||
\(705\) | −9.92716 | + | 15.8805i | −0.373878 | + | 0.598094i | ||||
\(706\) | 28.8759 | 1.08676 | ||||||||
\(707\) | 37.2363 | − | 28.5600i | 1.40041 | − | 1.07411i | ||||
\(708\) | − | 73.3983i | − | 2.75848i | ||||||
\(709\) | 17.8940 | 0.672025 | 0.336012 | − | 0.941858i | \(-0.390922\pi\) | ||||
0.336012 | + | 0.941858i | \(0.390922\pi\) | |||||||
\(710\) | −13.8546 | + | 22.1633i | −0.519955 | + | 0.831774i | ||||
\(711\) | − | 8.94533i | − | 0.335476i | ||||||
\(712\) | − | 62.0859i | − | 2.32677i | ||||||
\(713\) | 4.04498 | 0.151486 | ||||||||
\(714\) | −6.59587 | − | 8.59962i | −0.246844 | − | 0.321833i | ||||
\(715\) | −5.90355 | + | 2.50679i | −0.220780 | + | 0.0937486i | ||||
\(716\) | −75.2935 | −2.81385 | ||||||||
\(717\) | − | 2.60857i | − | 0.0974187i | ||||||
\(718\) | − | 11.9850i | − | 0.447276i | ||||||
\(719\) | 4.73442i | 0.176564i | 0.996096 | + | 0.0882821i | \(0.0281377\pi\) | ||||
−0.996096 | + | 0.0882821i | \(0.971862\pi\) | |||||||
\(720\) | −14.0044 | + | 22.4029i | −0.521914 | + | 0.834908i | ||||
\(721\) | 32.6912 | − | 25.0740i | 1.21748 | − | 0.933805i | ||||
\(722\) | 31.4494 | 1.17043 | ||||||||
\(723\) | −1.02093 | −0.0379687 | ||||||||
\(724\) | 118.574i | 4.40678i | ||||||||
\(725\) | −6.38681 | + | 3.11225i | −0.237200 | + | 0.115586i | ||||
\(726\) | 10.0419 | + | 27.5380i | 0.372691 | + | 1.02203i | ||||
\(727\) | −3.40475 | −0.126275 | −0.0631377 | − | 0.998005i | \(-0.520111\pi\) | ||||
−0.0631377 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(728\) | −11.5056 | − | 15.0009i | −0.426426 | − | 0.555970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.6556 | + | 12.2870i | 0.727487 | + | 0.454764i | ||||
\(731\) | − | 1.26564i | − | 0.0468115i | ||||||
\(732\) | −35.4930 | −1.31186 | ||||||||
\(733\) | − | 51.5861i | − | 1.90537i | −0.303953 | − | 0.952687i | \(-0.598306\pi\) | ||
0.303953 | − | 0.952687i | \(-0.401694\pi\) | |||||||
\(734\) | 4.56295 | 0.168421 | ||||||||
\(735\) | 10.6681 | + | 11.4538i | 0.393501 | + | 0.422481i | ||||
\(736\) | 109.654i | 4.04190i | ||||||||
\(737\) | 21.1534 | + | 14.8022i | 0.779196 | + | 0.545246i | ||||
\(738\) | 1.61828 | 0.0595698 | ||||||||
\(739\) | − | 2.40223i | − | 0.0883674i | −0.999023 | − | 0.0441837i | \(-0.985931\pi\) | ||
0.999023 | − | 0.0441837i | \(-0.0140687\pi\) | |||||||
\(740\) | 57.7491 | + | 36.0999i | 2.12290 | + | 1.32706i | ||||
\(741\) | 2.32022i | 0.0852353i | ||||||||
\(742\) | −35.2495 | − | 45.9579i | −1.29405 | − | 1.68717i | ||||
\(743\) | −20.2751 | −0.743823 | −0.371911 | − | 0.928268i | \(-0.621297\pi\) | ||||
−0.371911 | + | 0.928268i | \(0.621297\pi\) | |||||||
\(744\) | − | 4.55954i | − | 0.167161i | ||||||
\(745\) | 12.5812 | + | 7.86470i | 0.460939 | + | 0.288140i | ||||
\(746\) | 72.1064 | 2.64000 | ||||||||
\(747\) | 13.1440i | 0.480914i | ||||||||
\(748\) | 21.3071 | + | 14.9097i | 0.779064 | + | 0.545154i | ||||
\(749\) | 34.4499 | − | 26.4229i | 1.25877 | − | 0.965473i | ||||
\(750\) | −29.6274 | − | 3.12990i | −1.08184 | − | 0.114288i | ||||
\(751\) | −25.0938 | −0.915685 | −0.457843 | − | 0.889033i | \(-0.651378\pi\) | ||||
−0.457843 | + | 0.889033i | \(0.651378\pi\) | |||||||
\(752\) | 98.9588 | 3.60865 | ||||||||
\(753\) | 15.9683i | 0.581917i | ||||||||
\(754\) | −3.27459 | −0.119254 | ||||||||
\(755\) | −31.8474 | − | 19.9083i | −1.15904 | − | 0.724537i | ||||
\(756\) | 10.7081 | − | 8.21304i | 0.389449 | − | 0.298705i | ||||
\(757\) | 38.8462i | 1.41189i | 0.708268 | + | 0.705944i | \(0.249477\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(758\) | 56.9497 | 2.06851 | ||||||||
\(759\) | −19.9183 | − | 13.9379i | −0.722987 | − | 0.505914i | ||||
\(760\) | 26.2736 | − | 42.0300i | 0.953045 | − | 1.52459i | ||||
\(761\) | −46.7951 | −1.69632 | −0.848161 | − | 0.529738i | \(-0.822290\pi\) | ||||
−0.848161 | + | 0.529738i | \(0.822290\pi\) | |||||||
\(762\) | −42.9920 | −1.55744 | ||||||||
\(763\) | −18.4499 | − | 24.0548i | −0.667930 | − | 0.870841i | ||||
\(764\) | 81.0839 | 2.93351 | ||||||||
\(765\) | −2.91476 | − | 1.82206i | −0.105383 | − | 0.0658767i | ||||
\(766\) | 75.4772 | 2.72710 | ||||||||
\(767\) | 12.4448 | 0.449357 | ||||||||
\(768\) | 3.07071 | 0.110805 | ||||||||
\(769\) | 1.96503 | 0.0708606 | 0.0354303 | − | 0.999372i | \(-0.488720\pi\) | ||||
0.0354303 | + | 0.999372i | \(0.488720\pi\) | |||||||
\(770\) | −45.5047 | − | 25.7503i | −1.63987 | − | 0.927975i | ||||
\(771\) | −24.0879 | −0.867506 | ||||||||
\(772\) | −42.4515 | −1.52786 | ||||||||
\(773\) | 12.5159 | 0.450166 | 0.225083 | − | 0.974340i | \(-0.427735\pi\) | ||||
0.225083 | + | 0.974340i | \(0.427735\pi\) | |||||||
\(774\) | 2.19389 | 0.0788579 | ||||||||
\(775\) | 2.48041 | − | 1.20869i | 0.0890989 | − | 0.0434174i | ||||
\(776\) | 151.962 | 5.45511 | ||||||||
\(777\) | −9.61479 | − | 12.5357i | −0.344929 | − | 0.449714i | ||||
\(778\) | −40.1054 | −1.43785 | ||||||||
\(779\) | −1.62931 | −0.0583762 | ||||||||
\(780\) | −8.36397 | − | 5.22845i | −0.299478 | − | 0.187209i | ||||
\(781\) | −8.34118 | + | 11.9201i | −0.298471 | + | 0.426536i | ||||
\(782\) | −30.0256 | −1.07371 | ||||||||
\(783\) | − | 1.42095i | − | 0.0507806i | ||||||
\(784\) | 21.4397 | − | 79.8804i | 0.765703 | − | 2.85287i | ||||
\(785\) | −7.73031 | + | 12.3662i | −0.275907 | + | 0.441369i | ||||
\(786\) | −21.2671 | −0.758573 | ||||||||
\(787\) | − | 22.0607i | − | 0.786379i | −0.919457 | − | 0.393190i | \(-0.871372\pi\) | ||
0.919457 | − | 0.393190i | \(-0.128628\pi\) | |||||||
\(788\) | −67.4934 | −2.40435 | ||||||||
\(789\) | 18.4313 | 0.656170 | ||||||||
\(790\) | −45.1963 | − | 28.2529i | −1.60801 | − | 1.00519i | ||||
\(791\) | −6.24640 | − | 8.14399i | −0.222096 | − | 0.289567i | ||||
\(792\) | −15.7109 | + | 22.4520i | −0.558264 | + | 0.797798i | ||||
\(793\) | − | 6.01791i | − | 0.213702i | ||||||
\(794\) | −4.30146 | −0.152653 | ||||||||
\(795\) | −15.5770 | − | 9.73741i | −0.552458 | − | 0.345350i | ||||
\(796\) | − | 19.5575i | − | 0.693195i | ||||||
\(797\) | 30.0551 | 1.06461 | 0.532303 | − | 0.846554i | \(-0.321327\pi\) | ||||
0.532303 | + | 0.846554i | \(0.321327\pi\) | |||||||
\(798\) | −15.0084 | + | 11.5114i | −0.531291 | + | 0.407498i | ||||
\(799\) | 12.8751i | 0.455490i | ||||||||
\(800\) | 32.7659 | + | 67.2406i | 1.15845 | + | 2.37731i | ||||
\(801\) | 7.51433i | 0.265506i | ||||||||
\(802\) | −30.4132 | −1.07393 | ||||||||
\(803\) | 10.5714 | + | 7.39740i | 0.373057 | + | 0.261049i | ||||
\(804\) | 39.7057i | 1.40031i | ||||||||
\(805\) | 43.1662 | − | 4.13961i | 1.52141 | − | 0.145902i | ||||
\(806\) | 1.27173 | 0.0447949 | ||||||||
\(807\) | − | 10.2977i | − | 0.362496i | ||||||
\(808\) | −146.549 | −5.15559 | ||||||||
\(809\) | − | 33.2719i | − | 1.16978i | −0.811114 | − | 0.584888i | \(-0.801138\pi\) | ||
0.811114 | − | 0.584888i | \(-0.198862\pi\) | |||||||
\(810\) | 3.15840 | − | 5.05250i | 0.110975 | − | 0.177527i | ||||
\(811\) | 7.58505 | 0.266347 | 0.133174 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133174 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(812\) | −11.6703 | − | 15.2156i | −0.409548 | − | 0.533964i | ||||
\(813\) | −23.6065 | −0.827915 | ||||||||
\(814\) | 43.2379 | + | 30.2559i | 1.51549 | + | 1.06047i | ||||
\(815\) | −6.66478 | − | 4.16626i | −0.233457 | − | 0.145938i | ||||
\(816\) | 18.1632i | 0.635839i | ||||||||
\(817\) | −2.20885 | −0.0772778 | ||||||||
\(818\) | 104.715 | 3.66129 | ||||||||
\(819\) | 1.39254 | + | 1.81558i | 0.0486592 | + | 0.0634414i | ||||
\(820\) | 3.67155 | − | 5.87339i | 0.128216 | − | 0.205108i | ||||
\(821\) | 9.21308i | 0.321539i | 0.986992 | + | 0.160769i | \(0.0513976\pi\) | ||||
−0.986992 | + | 0.160769i | \(0.948602\pi\) | |||||||
\(822\) | 35.4960i | 1.23807i | ||||||||
\(823\) | 31.0541i | 1.08248i | 0.840869 | + | 0.541239i | \(0.182045\pi\) | ||||
−0.840869 | + | 0.541239i | \(0.817955\pi\) | |||||||
\(824\) | −128.661 | −4.48213 | ||||||||
\(825\) | −16.3788 | − | 2.59501i | −0.570238 | − | 0.0903465i | ||||
\(826\) | 61.7429 | + | 80.4997i | 2.14831 | + | 2.80094i | ||||
\(827\) | −25.0716 | −0.871823 | −0.435912 | − | 0.899989i | \(-0.643574\pi\) | ||||
−0.435912 | + | 0.899989i | \(0.643574\pi\) | |||||||
\(828\) | − | 37.3873i | − | 1.29930i | ||||||
\(829\) | 20.3332i | 0.706201i | 0.935585 | + | 0.353101i | \(0.114873\pi\) | ||||
−0.935585 | + | 0.353101i | \(0.885127\pi\) | |||||||
\(830\) | 66.4101 | + | 41.5140i | 2.30513 | + | 1.44097i | ||||
\(831\) | 26.2554 | 0.910791 | ||||||||
\(832\) | 14.0385i | 0.486698i | ||||||||
\(833\) | 10.3929 | + | 2.78943i | 0.360094 | + | 0.0966481i | ||||
\(834\) | −14.9619 | −0.518088 | ||||||||
\(835\) | 30.7928 | + | 19.2491i | 1.06563 | + | 0.666142i | ||||
\(836\) | 26.0210 | − | 37.1859i | 0.899957 | − | 1.28610i | ||||
\(837\) | 0.551846i | 0.0190746i | ||||||||
\(838\) | 11.5122i | 0.397683i | ||||||||
\(839\) | − | 3.91149i | − | 0.135040i | −0.997718 | − | 0.0675198i | \(-0.978491\pi\) | ||
0.997718 | − | 0.0675198i | \(-0.0215086\pi\) | |||||||
\(840\) | −4.66621 | − | 48.6574i | −0.161000 | − | 1.67884i | ||||
\(841\) | 26.9809 | 0.930376 | ||||||||
\(842\) | 15.0400 | 0.518311 | ||||||||
\(843\) | 31.7030i | 1.09191i | ||||||||
\(844\) | − | 88.5261i | − | 3.04719i | ||||||
\(845\) | −14.5220 | + | 23.2310i | −0.499573 | + | 0.799169i | ||||
\(846\) | −22.3180 | −0.767310 | ||||||||
\(847\) | −24.5517 | − | 15.6274i | −0.843605 | − | 0.536964i | ||||
\(848\) | 97.0673i | 3.33330i | ||||||||
\(849\) | 7.26679i | 0.249396i | ||||||||
\(850\) | −18.4119 | + | 8.97202i | −0.631524 | + | 0.307738i | ||||
\(851\) | −43.7683 | −1.50036 | ||||||||
\(852\) | −22.3745 | −0.766539 | ||||||||
\(853\) | 1.00626i | 0.0344538i | 0.999852 | + | 0.0172269i | \(0.00548377\pi\) | ||||
−0.999852 | + | 0.0172269i | \(0.994516\pi\) | |||||||
\(854\) | 38.9270 | − | 29.8568i | 1.33206 | − | 1.02168i | ||||
\(855\) | −3.17993 | + | 5.08694i | −0.108751 | + | 0.173970i | ||||
\(856\) | −135.583 | −4.63414 | ||||||||
\(857\) | − | 33.8944i | − | 1.15781i | −0.815395 | − | 0.578905i | \(-0.803480\pi\) | ||
0.815395 | − | 0.578905i | \(-0.196520\pi\) | |||||||
\(858\) | −6.26227 | − | 4.38205i | −0.213790 | − | 0.149601i | ||||
\(859\) | − | 34.4495i | − | 1.17540i | −0.809078 | − | 0.587701i | \(-0.800033\pi\) | ||
0.809078 | − | 0.587701i | \(-0.199967\pi\) | |||||||
\(860\) | 4.97749 | − | 7.96250i | 0.169731 | − | 0.271519i | ||||
\(861\) | −1.27494 | + | 0.977874i | −0.0434499 | + | 0.0333259i | ||||
\(862\) | − | 106.614i | − | 3.63129i | ||||||
\(863\) | 3.22432i | 0.109757i | 0.998493 | + | 0.0548785i | \(0.0174772\pi\) | ||||
−0.998493 | + | 0.0548785i | \(0.982523\pi\) | |||||||
\(864\) | −14.9598 | −0.508943 | ||||||||
\(865\) | 18.0916 | + | 11.3093i | 0.615133 | + | 0.384529i | ||||
\(866\) | −21.8161 | −0.741342 | ||||||||
\(867\) | 14.6369 | 0.497094 | ||||||||
\(868\) | 4.53233 | + | 5.90921i | 0.153837 | + | 0.200572i | ||||
\(869\) | −24.3080 | − | 17.0097i | −0.824593 | − | 0.577013i | ||||
\(870\) | −7.17935 | − | 4.48793i | −0.243403 | − | 0.152155i | ||||
\(871\) | −6.73219 | −0.228112 | ||||||||
\(872\) | 94.6713i | 3.20597i | ||||||||
\(873\) | −18.3921 | −0.622479 | ||||||||
\(874\) | 52.4019i | 1.77252i | ||||||||
\(875\) | 25.2329 | − | 15.4370i | 0.853027 | − | 0.521867i | ||||
\(876\) | 19.8429i | 0.670431i | ||||||||
\(877\) | −7.74745 | −0.261613 | −0.130806 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130806 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(878\) | 43.7882 | 1.47778 | ||||||||
\(879\) | 31.4376i | 1.06037i | ||||||||
\(880\) | 34.2481 | + | 80.6550i | 1.15450 | + | 2.71888i | ||||
\(881\) | − | 22.6712i | − | 0.763813i | −0.924201 | − | 0.381907i | \(-0.875268\pi\) | ||
0.924201 | − | 0.381907i | \(-0.124732\pi\) | |||||||
\(882\) | −4.83526 | + | 18.0153i | −0.162812 | + | 0.606608i | ||||
\(883\) | − | 8.85959i | − | 0.298149i | −0.988826 | − | 0.149074i | \(-0.952371\pi\) | ||
0.988826 | − | 0.149074i | \(-0.0476294\pi\) | |||||||
\(884\) | −6.78110 | −0.228073 | ||||||||
\(885\) | 27.2846 | + | 17.0560i | 0.917161 | + | 0.573332i | ||||
\(886\) | 38.4456i | 1.29161i | ||||||||
\(887\) | 50.8004i | 1.70571i | 0.522147 | + | 0.852856i | \(0.325131\pi\) | ||||
−0.522147 | + | 0.852856i | \(0.674869\pi\) | |||||||
\(888\) | 49.3361i | 1.65561i | ||||||||
\(889\) | 33.8707 | − | 25.9787i | 1.13599 | − | 0.871296i | ||||
\(890\) | 37.9662 | + | 23.7333i | 1.27263 | + | 0.795541i | ||||
\(891\) | 1.90151 | − | 2.71740i | 0.0637031 | − | 0.0910362i | ||||
\(892\) | 44.8364 | 1.50123 | ||||||||
\(893\) | 22.4702 | 0.751936 | ||||||||
\(894\) | 17.6813i | 0.591350i | ||||||||
\(895\) | 17.4964 | − | 27.9891i | 0.584841 | − | 0.935572i | ||||
\(896\) | −27.9967 | + | 21.4734i | −0.935305 | + | 0.717375i | ||||
\(897\) | 6.33910 | 0.211656 | ||||||||
\(898\) | −4.00048 | −0.133498 | ||||||||
\(899\) | 0.784146 | 0.0261527 | ||||||||
\(900\) | −11.1718 | − | 22.9262i | −0.372392 | − | 0.764205i | ||||
\(901\) | −12.6290 | −0.420734 | ||||||||
\(902\) | 3.07719 | − | 4.39752i | 0.102459 | − | 0.146421i | ||||
\(903\) | −1.72843 | + | 1.32570i | −0.0575185 | + | 0.0441164i | ||||
\(904\) | 32.0520i | 1.06603i | ||||||||
\(905\) | −44.0780 | − | 27.5538i | −1.46520 | − | 0.915921i | ||||
\(906\) | − | 44.7575i | − | 1.48697i | ||||||
\(907\) | 34.0993i | 1.13225i | 0.824320 | + | 0.566125i | \(0.191558\pi\) | ||||
−0.824320 | + | 0.566125i | \(0.808442\pi\) | |||||||
\(908\) | − | 82.8796i | − | 2.75046i | ||||||
\(909\) | 17.7370 | 0.588300 | ||||||||
\(910\) | 13.5714 | − | 1.30149i | 0.449887 | − | 0.0431439i | ||||
\(911\) | 13.9029 | 0.460622 | 0.230311 | − | 0.973117i | \(-0.426026\pi\) | ||||
0.230311 | + | 0.973117i | \(0.426026\pi\) | |||||||
\(912\) | 31.6991 | 1.04966 | ||||||||
\(913\) | 35.7175 | + | 24.9935i | 1.18208 | + | 0.827164i | ||||
\(914\) | 51.1010 | 1.69027 | ||||||||
\(915\) | 8.24773 | − | 13.1939i | 0.272662 | − | 0.436178i | ||||
\(916\) | 125.273i | 4.13915i | ||||||||
\(917\) | 16.7550 | − | 12.8510i | 0.553299 | − | 0.424378i | ||||
\(918\) | − | 4.09632i | − | 0.135199i | ||||||
\(919\) | − | 31.1901i | − | 1.02887i | −0.857531 | − | 0.514433i | \(-0.828003\pi\) | ||
0.857531 | − | 0.514433i | \(-0.171997\pi\) | |||||||
\(920\) | −114.831 | − | 71.7825i | −3.78586 | − | 2.36660i | ||||
\(921\) | 13.8197i | 0.455375i | ||||||||
\(922\) | 45.7684 | 1.50730 | ||||||||
\(923\) | − | 3.79365i | − | 0.124870i | ||||||
\(924\) | −1.95656 | − | 44.7153i | −0.0643660 | − | 1.47102i | ||||
\(925\) | −26.8391 | + | 13.0785i | −0.882463 | + | 0.430019i | ||||
\(926\) | − | 63.1752i | − | 2.07607i | ||||||
\(927\) | 15.5720 | 0.511453 | ||||||||
\(928\) | 21.2571i | 0.697800i | ||||||||
\(929\) | − | 30.5461i | − | 1.00218i | −0.865394 | − | 0.501092i | \(-0.832932\pi\) | ||
0.865394 | − | 0.501092i | \(-0.167068\pi\) | |||||||
\(930\) | 2.78820 | + | 1.74295i | 0.0914288 | + | 0.0571536i | ||||
\(931\) | 4.86822 | − | 18.1381i | 0.159550 | − | 0.594454i | ||||
\(932\) | −87.9488 | −2.88086 | ||||||||
\(933\) | 4.57177i | 0.149673i | ||||||||
\(934\) | 57.2628 | 1.87370 | ||||||||
\(935\) | −10.4937 | + | 4.45588i | −0.343181 | + | 0.145723i | ||||
\(936\) | − | 7.14549i | − | 0.233558i | ||||||
\(937\) | − | 2.87984i | − | 0.0940802i | −0.998893 | − | 0.0470401i | \(-0.985021\pi\) | ||
0.998893 | − | 0.0470401i | \(-0.0149789\pi\) | |||||||
\(938\) | −33.4006 | − | 43.5474i | −1.09057 | − | 1.42187i | ||||
\(939\) | 26.4180 | 0.862117 | ||||||||
\(940\) | −50.6350 | + | 81.0010i | −1.65153 | + | 2.64196i | ||||
\(941\) | 26.5254 | 0.864702 | 0.432351 | − | 0.901705i | \(-0.357684\pi\) | ||||
0.432351 | + | 0.901705i | \(0.357684\pi\) | |||||||
\(942\) | −17.3791 | −0.566243 | ||||||||
\(943\) | 4.45147i | 0.144960i | ||||||||
\(944\) | − | 170.023i | − | 5.53377i | ||||||
\(945\) | 0.564757 | + | 5.88906i | 0.0183715 | + | 0.191571i | ||||
\(946\) | 4.17172 | − | 5.96168i | 0.135634 | − | 0.193831i | ||||
\(947\) | 6.15057i | 0.199867i | 0.994994 | + | 0.0999333i | \(0.0318630\pi\) | ||||
−0.994994 | + | 0.0999333i | \(0.968137\pi\) | |||||||
\(948\) | − | 45.6270i | − | 1.48190i | ||||||
\(949\) | −3.36441 | −0.109213 | ||||||||
\(950\) | 15.6583 | + | 32.1332i | 0.508023 | + | 1.04254i | ||||
\(951\) | − | 7.88446i | − | 0.255671i | ||||||
\(952\) | −20.4515 | − | 26.6645i | −0.662837 | − | 0.864200i | ||||
\(953\) | −11.6177 | −0.376333 | −0.188166 | − | 0.982137i | \(-0.560254\pi\) | ||||
−0.188166 | + | 0.982137i | \(0.560254\pi\) | |||||||
\(954\) | − | 21.8915i | − | 0.708762i | ||||||
\(955\) | −18.8420 | + | 30.1416i | −0.609712 | + | 0.975359i | ||||
\(956\) | − | 13.3054i | − | 0.430327i | ||||||
\(957\) | −3.86129 | − | 2.70195i | −0.124818 | − | 0.0873418i | ||||
\(958\) | −22.2139 | −0.717697 | ||||||||
\(959\) | −21.4491 | − | 27.9651i | −0.692627 | − | 0.903039i | ||||
\(960\) | −19.2402 | + | 30.7787i | −0.620976 | + | 0.993377i | ||||
\(961\) | 30.6955 | 0.990176 | ||||||||
\(962\) | −13.7607 | −0.443663 | ||||||||
\(963\) | 16.4098 | 0.528798 | ||||||||
\(964\) | −5.20740 | −0.167719 | ||||||||
\(965\) | 9.86473 | − | 15.7806i | 0.317557 | − | 0.507997i | ||||
\(966\) | 31.4503 | + | 41.0046i | 1.01190 | + | 1.31930i | ||||
\(967\) | 36.8220 | 1.18412 | 0.592058 | − | 0.805895i | \(-0.298316\pi\) | ||||
0.592058 | + | 0.805895i | \(0.298316\pi\) | |||||||
\(968\) | 31.1366 | + | 85.3857i | 1.00077 | + | 2.74440i | ||||
\(969\) | 4.12424i | 0.132490i | ||||||||
\(970\) | −58.0897 | + | 92.9263i | −1.86515 | + | 2.98368i | ||||
\(971\) | 19.0710i | 0.612019i | 0.952029 | + | 0.306009i | \(0.0989939\pi\) | ||||
−0.952029 | + | 0.306009i | \(0.901006\pi\) | |||||||
\(972\) | 5.10065 | 0.163604 | ||||||||
\(973\) | 11.7875 | − | 9.04098i | 0.377891 | − | 0.289841i | ||||
\(974\) | 16.1309i | 0.516866i | ||||||||
\(975\) | 3.88718 | − | 1.89420i | 0.124489 | − | 0.0606629i | ||||
\(976\) | −82.2175 | −2.63172 | ||||||||
\(977\) | 23.1779i | 0.741527i | 0.928727 | + | 0.370764i | \(0.120904\pi\) | ||||
−0.928727 | + | 0.370764i | \(0.879096\pi\) | |||||||
\(978\) | − | 9.36651i | − | 0.299508i | ||||||
\(979\) | 20.4194 | + | 14.2886i | 0.652608 | + | 0.456666i | ||||
\(980\) | 54.4145 | + | 58.4221i | 1.73821 | + | 1.86623i | ||||
\(981\) | − | 11.4582i | − | 0.365832i | ||||||
\(982\) | − | 67.6076i | − | 2.15744i | ||||||
\(983\) | −11.1133 | −0.354459 | −0.177230 | − | 0.984170i | \(-0.556714\pi\) | ||||
−0.177230 | + | 0.984170i | \(0.556714\pi\) | |||||||
\(984\) | 5.01774 | 0.159960 | ||||||||
\(985\) | 15.6839 | − | 25.0895i | 0.499730 | − | 0.799419i | ||||
\(986\) | −5.82067 | −0.185368 | ||||||||
\(987\) | 17.5830 | − | 13.4861i | 0.559672 | − | 0.429266i | ||||
\(988\) | 11.8346i | 0.376510i | ||||||||
\(989\) | 6.03482i | 0.191896i | ||||||||
\(990\) | −7.72392 | − | 18.1900i | −0.245482 | − | 0.578117i | ||||
\(991\) | −21.0898 | −0.669939 | −0.334969 | − | 0.942229i | \(-0.608726\pi\) | ||||
−0.334969 | + | 0.942229i | \(0.608726\pi\) | |||||||
\(992\) | − | 8.25552i | − | 0.262113i | ||||||
\(993\) | −5.20944 | −0.165317 | ||||||||
\(994\) | 24.5393 | − | 18.8215i | 0.778340 | − | 0.596983i | ||||
\(995\) | 7.27016 | + | 4.54469i | 0.230479 | + | 0.144076i | ||||
\(996\) | 67.0430i | 2.12434i | ||||||||
\(997\) | 32.2736i | 1.02212i | 0.859546 | + | 0.511058i | \(0.170746\pi\) | ||||
−0.859546 | + | 0.511058i | \(0.829254\pi\) | |||||||
\(998\) | −83.9772 | −2.65825 | ||||||||
\(999\) | − | 5.97120i | − | 0.188921i |
(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 | 1155.2.k.b.769.2 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.a.769.47 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.a.769.1 | ✓ | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.b.769.47 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.b.769.48 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.a.769.2 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.a.769.48 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.b.769.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.1 | ✓ | 48 | 7.6 | odd | 2 | ||
1155.2.k.a.769.2 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.a.769.47 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.a.769.48 | yes | 48 | 77.76 | even | 2 | ||
1155.2.k.b.769.1 | yes | 48 | 385.384 | even | 2 | inner | |
1155.2.k.b.769.2 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.b.769.47 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.b.769.48 | yes | 48 | 35.34 | odd | 2 | inner |