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.a.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 | \(-0.599575\pi\) | ||||
−0.307746 | + | 0.951468i | \(0.599575\pi\) | |||||||
\(20\) | 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 | \(0.276864\pi\) | ||||
−0.644985 | + | 0.764195i | \(0.723136\pi\) | |||||||
\(24\) | 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 | \(0.0421180\pi\) | ||||
−0.991259 | + | 0.131932i | \(0.957882\pi\) | |||||||
\(30\) | 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 | ||||||
\(35\) | 5.54136 | + | 2.07203i | 0.936661 | + | 0.350237i | ||||
\(36\) | 5.10065 | 0.850109 | ||||||||
\(37\) | 5.97120i | 0.981660i | 0.871255 | + | 0.490830i | \(0.163306\pi\) | ||||
−0.871255 | + | 0.490830i | \(0.836694\pi\) | |||||||
\(38\) | 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 | \(-0.484899\pi\) | ||||
0.0474224 | + | 0.998875i | \(0.484899\pi\) | |||||||
\(42\) | 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 | \(-0.709168\pi\) | ||||
−0.610841 | + | 0.791753i | \(0.709168\pi\) | |||||||
\(48\) | −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 | \(-0.809172\pi\) | ||
0.825616 | − | 0.564232i | \(-0.190828\pi\) | |||||||
\(54\) | 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 | \(-0.353035\pi\) | ||||
0.445473 | + | 0.895295i | \(0.353035\pi\) | |||||||
\(62\) | − | 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 | \(-0.842263\pi\) | ||
0.879710 | − | 0.475510i | \(-0.157737\pi\) | |||||||
\(68\) | 7.84099i | 0.950859i | ||||||||
\(69\) | − | 7.32990i | − | 0.882416i | ||||||
\(70\) | −14.7661 | − | 5.52135i | −1.76489 | − | 0.659928i | ||||
\(71\) | −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 | ||||||||
\(77\) | 8.36748 | + | 2.64297i | 0.953563 | + | 0.301195i | ||||
\(78\) | 2.30451i | 0.260934i | ||||||||
\(79\) | 8.94533i | 1.00643i | 0.864162 | + | 0.503214i | \(0.167849\pi\) | ||||
−0.864162 | + | 0.503214i | \(0.832151\pi\) | |||||||
\(80\) | 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 | \(-0.116544\pi\) | ||||
0.933719 | + | 0.358007i | \(0.116544\pi\) | |||||||
\(98\) | −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 | \(-0.844108\pi\) | ||||
−0.882451 | + | 0.470405i | \(0.844108\pi\) | |||||||
\(102\) | 4.09632i | 0.405596i | ||||||||
\(103\) | −15.5720 | −1.53436 | −0.767180 | − | 0.641432i | \(-0.778341\pi\) | ||||
−0.767180 | + | 0.641432i | \(0.778341\pi\) | |||||||
\(104\) | − | 7.14549i | − | 0.700673i | ||||||
\(105\) | −5.54136 | − | 2.07203i | −0.540782 | − | 0.202209i | ||||
\(106\) | 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 | \(0.184895\pi\) | ||||
−0.835988 | + | 0.548747i | \(0.815105\pi\) | |||||||
\(110\) | 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 | \(0.0584081\pi\) | ||||
−0.983212 | + | 0.182466i | \(0.941592\pi\) | |||||||
\(114\) | −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 | \(-0.613361\pi\) | ||||
−0.348653 | + | 0.937252i | \(0.613361\pi\) | |||||||
\(132\) | −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 | \(0.192684\pi\) | ||||
−0.822312 | + | 0.569037i | \(0.807316\pi\) | |||||||
\(138\) | 19.5320i | 1.66268i | ||||||||
\(139\) | −5.61484 | −0.476245 | −0.238122 | − | 0.971235i | \(-0.576532\pi\) | ||||
−0.238122 | + | 0.971235i | \(0.576532\pi\) | |||||||
\(140\) | 28.2646 | + | 10.5687i | 2.38879 | + | 0.893219i | ||||
\(141\) | 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 | \(0.0876172\pi\) | ||||
−0.962355 | + | 0.271795i | \(0.912383\pi\) | |||||||
\(150\) | −5.83640 | + | 11.9772i | −0.476540 | + | 0.977932i | ||||
\(151\) | − | 16.7964i | − | 1.36687i | −0.730010 | − | 0.683436i | \(-0.760485\pi\) | ||
0.730010 | − | 0.683436i | \(-0.239515\pi\) | |||||||
\(152\) | 22.1668 | 1.79796 | ||||||||
\(153\) | 1.53725i | 0.124279i | ||||||||
\(154\) | −22.2969 | − | 7.04274i | −1.79673 | − | 0.567520i | ||||
\(155\) | −1.04635 | + | 0.654088i | −0.0840446 | + | 0.0525376i | ||||
\(156\) | − | 4.41118i | − | 0.353177i | ||||||
\(157\) | −6.52197 | −0.520510 | −0.260255 | − | 0.965540i | \(-0.583807\pi\) | ||||
−0.260255 | + | 0.965540i | \(0.583807\pi\) | |||||||
\(158\) | − | 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 | \(-0.956042\pi\) | ||
0.990480 | − | 0.137659i | \(-0.0439578\pi\) | |||||||
\(164\) | 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 | ||||||||
\(175\) | 2.63928 | + | 12.9628i | 0.199511 | + | 0.979896i | ||||
\(176\) | 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 | ||||
\(210\) | 14.7661 | + | 5.52135i | 1.01896 | + | 0.381009i | ||||
\(211\) | 17.3558i | 1.19482i | 0.801934 | + | 0.597412i | \(0.203804\pi\) | ||||
−0.801934 | + | 0.597412i | \(0.796196\pi\) | |||||||
\(212\) | − | 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 | \(-0.595094\pi\) | ||||
−0.294322 | + | 0.955706i | \(0.595094\pi\) | |||||||
\(224\) | −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 | ||||
\(231\) | −8.36748 | − | 2.64297i | −0.550540 | − | 0.173895i | ||||
\(232\) | − | 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 | \(0.0268868\pi\) | ||||
−0.996435 | + | 0.0843671i | \(0.973113\pi\) | |||||||
\(240\) | −14.0044 | − | 22.4029i | −0.903982 | − | 1.44610i | ||||
\(241\) | 1.02093 | 0.0657638 | 0.0328819 | − | 0.999459i | \(-0.489531\pi\) | ||||
0.0328819 | + | 0.999459i | \(0.489531\pi\) | |||||||
\(242\) | 10.0419 | − | 27.5380i | 0.645520 | − | 1.77021i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 35.4930 | 2.27221 | ||||||||
\(245\) | 14.9696 | − | 4.57274i | 0.956375 | − | 0.292142i | ||||
\(246\) | 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 | \(-0.229436\pi\) | ||||
0.751282 | + | 0.659981i | \(0.229436\pi\) | |||||||
\(258\) | −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 | \(-0.245517\pi\) | ||||
0.716995 | + | 0.697078i | \(0.245517\pi\) | |||||||
\(272\) | 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 | ||||||||
\(280\) | −45.7846 | − | 17.1198i | −2.73615 | − | 1.02310i | ||||
\(281\) | − | 31.7030i | − | 1.89124i | −0.325272 | − | 0.945620i | \(-0.605456\pi\) | ||
0.325272 | − | 0.945620i | \(-0.394544\pi\) | |||||||
\(282\) | −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 | \(0.870964\pi\) | |||||||
\(308\) | 42.6796 | + | 13.4809i | 2.43190 | + | 0.768145i | ||||
\(309\) | 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 | \(-0.768323\pi\) | ||||
−0.746616 | + | 0.665256i | \(0.768323\pi\) | |||||||
\(314\) | 17.3791 | 0.980762 | ||||||||
\(315\) | 5.54136 | + | 2.07203i | 0.312220 | + | 0.116746i | ||||
\(316\) | 45.6270i | 2.56672i | ||||||||
\(317\) | 7.88446i | 0.442835i | 0.975179 | + | 0.221418i | \(0.0710684\pi\) | ||||
−0.975179 | + | 0.221418i | \(0.928932\pi\) | |||||||
\(318\) | − | 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 | \(-0.560329\pi\) | ||||
−0.188396 | + | 0.982093i | \(0.560329\pi\) | |||||||
\(350\) | −7.03290 | − | 34.5420i | −0.375924 | − | 1.84635i | ||||
\(351\) | − | 0.864827i | − | 0.0461610i | ||||||
\(352\) | −28.4463 | − | 40.6518i | −1.51619 | − | 2.16675i | ||||
\(353\) | 10.8364 | 0.576766 | 0.288383 | − | 0.957515i | \(-0.406882\pi\) | ||||
0.288383 | + | 0.957515i | \(0.406882\pi\) | |||||||
\(354\) | − | 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 | \(-0.962131\pi\) | ||
0.992931 | − | 0.118689i | \(-0.0378692\pi\) | |||||||
\(360\) | −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 | \(-0.485769\pi\) | ||||
0.0446924 | + | 0.999001i | \(0.485769\pi\) | |||||||
\(368\) | 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 | \(-0.242456\pi\) | ||||
0.723665 | + | 0.690152i | \(0.242456\pi\) | |||||||
\(384\) | 13.3359 | 0.680545 | ||||||||
\(385\) | 4.90644 | + | 18.9981i | 0.250055 | + | 0.968232i | ||||
\(386\) | 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 | \(-0.512898\pi\) | ||||
−0.0405081 | + | 0.999179i | \(0.512898\pi\) | |||||||
\(398\) | 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 | \(-0.0760968\pi\) | ||||
0.971560 | + | 0.236794i | \(0.0760968\pi\) | |||||||
\(410\) | −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 | \(-0.0336537\pi\) | |||||||
\(420\) | −28.2646 | − | 10.5687i | −1.37917 | − | 0.515700i | ||||
\(421\) | −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 | \(-0.586146\pi\) | ||
0.267344 | − | 0.963601i | \(-0.413854\pi\) | |||||||
\(432\) | −11.8154 | −0.568467 | ||||||||
\(433\) | −8.18707 | −0.393445 | −0.196723 | − | 0.980459i | \(-0.563030\pi\) | ||||
−0.196723 | + | 0.980459i | \(0.563030\pi\) | |||||||
\(434\) | −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 | \(-0.371733\pi\) | ||||
0.392144 | + | 0.919904i | \(0.371733\pi\) | |||||||
\(440\) | 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 | \(0.111355\pi\) | ||||
−0.939430 | + | 0.342741i | \(0.888645\pi\) | |||||||
\(444\) | − | 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 | ||||||||
\(455\) | −1.79195 | + | 4.79232i | −0.0840078 | + | 0.224667i | ||||
\(456\) | −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 | \(-0.369018\pi\) | ||||
0.399978 | + | 0.916525i | \(0.369018\pi\) | |||||||
\(462\) | 22.2969 | + | 7.04274i | 1.03734 | + | 0.327658i | ||||
\(463\) | − | 23.7081i | − | 1.10181i | −0.834568 | − | 0.550905i | \(-0.814283\pi\) | ||
0.834568 | − | 0.550905i | \(-0.185717\pi\) | |||||||
\(464\) | 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 | \(-0.334360\pi\) | ||||
0.497204 | + | 0.867634i | \(0.334360\pi\) | |||||||
\(468\) | 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 | \(-0.560994\pi\) | ||||
−0.190448 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(480\) | 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 | \(0.0437961\pi\) | ||||
−0.990550 | + | 0.137156i | \(0.956204\pi\) | |||||||
\(488\) | −57.4936 | −2.60261 | ||||||||
\(489\) | 3.51503i | 0.158955i | ||||||||
\(490\) | −39.8897 | + | 12.1850i | −1.80203 | + | 0.550462i | ||||
\(491\) | − | 25.3715i | − | 1.14500i | −0.819905 | − | 0.572500i | \(-0.805974\pi\) | ||
0.819905 | − | 0.572500i | \(-0.194026\pi\) | |||||||
\(492\) | −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 | ||||||||
\(525\) | −2.63928 | − | 12.9628i | −0.115188 | − | 0.565743i | ||||
\(526\) | −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 | ||||||||
\(539\) | 21.8220 | − | 7.92473i | 0.939939 | − | 0.341342i | ||||
\(540\) | −6.04566 | − | 9.67127i | −0.260164 | − | 0.416185i | ||||
\(541\) | 18.5873i | 0.799129i | 0.916705 | + | 0.399565i | \(0.130839\pi\) | ||||
−0.916705 | + | 0.399565i | \(0.869161\pi\) | |||||||
\(542\) | −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 | ||||||
\(560\) | 65.4732 | + | 24.4818i | 2.76675 | + | 1.03454i | ||||
\(561\) | 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 | \(0.161573\pi\) | ||||
−0.873916 | + | 0.486077i | \(0.838427\pi\) | |||||||
\(570\) | −8.47358 | − | 13.5552i | −0.354919 | − | 0.567765i | ||||
\(571\) | 18.0124i | 0.753794i | 0.926255 | + | 0.376897i | \(0.123009\pi\) | ||||
−0.926255 | + | 0.376897i | \(0.876991\pi\) | |||||||
\(572\) | −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 | \(-0.311842\pi\) | ||||
0.557288 | + | 0.830319i | \(0.311842\pi\) | |||||||
\(578\) | −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 | \(-0.187436\pi\) | ||||
0.831581 | + | 0.555403i | \(0.187436\pi\) | |||||||
\(588\) | −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 | ||||
\(595\) | −3.18523 | + | 8.51847i | −0.130582 | + | 0.349223i | ||||
\(596\) | 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 | \(-0.443563\pi\) | ||||
0.176374 | + | 0.984323i | \(0.443563\pi\) | |||||||
\(602\) | 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 | ||||
\(616\) | −69.1349 | − | 21.8371i | −2.78552 | − | 0.879842i | ||||
\(617\) | − | 4.90065i | − | 0.197293i | −0.995123 | − | 0.0986465i | \(-0.968549\pi\) | ||
0.995123 | − | 0.0986465i | \(-0.0314513\pi\) | |||||||
\(618\) | −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 | ||||||||
\(630\) | −14.7661 | − | 5.52135i | −0.588295 | − | 0.219976i | ||||
\(631\) | −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 | \(-0.375384\pi\) | ||||
0.381570 | + | 0.924340i | \(0.375384\pi\) | |||||||
\(644\) | 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 | \(-0.248799\pi\) | ||||
0.709770 | + | 0.704434i | \(0.248799\pi\) | |||||||
\(648\) | −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 | \(-0.769580\pi\) | ||
0.749238 | − | 0.662301i | \(-0.230420\pi\) | |||||||
\(654\) | 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 | \(-0.806005\pi\) | ||
0.819962 | − | 0.572418i | \(-0.193995\pi\) | |||||||
\(660\) | 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 | ||||||
\(665\) | −14.8668 | − | 5.55899i | −0.576508 | − | 0.215568i | ||||
\(666\) | − | 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 | \(0.280612\pi\) | ||||
−0.635942 | + | 0.771737i | \(0.719388\pi\) | |||||||
\(684\) | −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 | ||||||
\(693\) | 8.36748 | + | 2.64297i | 0.317854 | + | 0.100398i | ||||
\(694\) | 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 | ||||||||
\(700\) | 13.4620 | + | 66.1188i | 0.508817 | + | 2.49905i | ||||
\(701\) | − | 15.8130i | − | 0.597250i | −0.954370 | − | 0.298625i | \(-0.903472\pi\) | ||
0.954370 | − | 0.298625i | \(-0.0965280\pi\) | |||||||
\(702\) | 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 | \(-0.479889\pi\) | ||||
0.0631377 | + | 0.998005i | \(0.479889\pi\) | |||||||
\(728\) | −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 | ||||||||
\(735\) | −14.9696 | + | 4.57274i | −0.552163 | + | 0.168668i | ||||
\(736\) | − | 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 | \(0.0140687\pi\) | ||||
−0.999023 | + | 0.0441837i | \(0.985931\pi\) | |||||||
\(740\) | −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 | \(-0.750523\pi\) | ||
0.708268 | − | 0.705944i | \(-0.249477\pi\) | |||||||
\(758\) | 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 | \(-0.177710\pi\) | ||||
0.848161 | + | 0.529738i | \(0.177710\pi\) | |||||||
\(762\) | 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 | \(-0.511280\pi\) | ||||
−0.0354303 | + | 0.999372i | \(0.511280\pi\) | |||||||
\(770\) | −13.0742 | − | 50.6243i | −0.471162 | − | 1.82437i | ||||
\(771\) | −24.0879 | −0.867506 | ||||||||
\(772\) | −42.4515 | −1.52786 | ||||||||
\(773\) | −12.5159 | −0.450166 | −0.225083 | − | 0.974340i | \(-0.572265\pi\) | ||||
−0.225083 | + | 0.974340i | \(0.572265\pi\) | |||||||
\(774\) | 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 | \(-0.678673\pi\) | ||||
−0.532303 | + | 0.846554i | \(0.678673\pi\) | |||||||
\(798\) | −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 | ||||||||
\(805\) | −15.1878 | + | 40.6176i | −0.535299 | + | 1.43158i | ||||
\(806\) | 1.27173 | 0.0447949 | ||||||||
\(807\) | 10.2977i | 0.362496i | ||||||||
\(808\) | 146.549 | 5.15559 | ||||||||
\(809\) | 33.2719i | 1.16978i | 0.811114 | + | 0.584888i | \(0.198862\pi\) | ||||
−0.811114 | + | 0.584888i | \(0.801138\pi\) | |||||||
\(810\) | −3.15840 | − | 5.05250i | −0.110975 | − | 0.177527i | ||||
\(811\) | −7.58505 | −0.266347 | −0.133174 | − | 0.991093i | \(-0.542517\pi\) | ||||
−0.133174 | + | 0.991093i | \(0.542517\pi\) | |||||||
\(812\) | 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 | \(-0.948602\pi\) | ||
0.986992 | − | 0.160769i | \(-0.0513976\pi\) | |||||||
\(822\) | 35.4960i | 1.23807i | ||||||||
\(823\) | − | 31.0541i | − | 1.08248i | −0.840869 | − | 0.541239i | \(-0.817955\pi\) | ||
0.840869 | − | 0.541239i | \(-0.182045\pi\) | |||||||
\(824\) | 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 | \(-0.0215086\pi\) | |||||||
\(840\) | 45.7846 | + | 17.1198i | 1.57972 | + | 0.590689i | ||||
\(841\) | 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 | ||||||||
\(847\) | 8.72886 | + | 27.7634i | 0.299927 | + | 0.953962i | ||||
\(848\) | − | 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 | \(-0.982523\pi\) | ||
0.998493 | − | 0.0548785i | \(-0.0174772\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | −21.4503 | + | 20.3687i | −0.725152 | + | 0.688589i | ||||
\(876\) | − | 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 | \(0.0476294\pi\) | ||||
−0.988826 | + | 0.149074i | \(0.952371\pi\) | |||||||
\(884\) | −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 | \(-0.808442\pi\) | ||
0.824320 | − | 0.566125i | \(-0.191558\pi\) | |||||||
\(908\) | − | 82.8796i | − | 2.75046i | ||||||
\(909\) | −17.7370 | −0.588300 | ||||||||
\(910\) | 4.77501 | − | 12.7701i | 0.158290 | − | 0.423325i | ||||
\(911\) | 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 | \(0.171997\pi\) | ||||
−0.857531 | + | 0.514433i | \(0.828003\pi\) | |||||||
\(920\) | 114.831 | − | 71.7825i | 3.78586 | − | 2.36660i | ||||
\(921\) | − | 13.8197i | − | 0.455375i | ||||||
\(922\) | −45.7684 | −1.50730 | ||||||||
\(923\) | − | 3.79365i | − | 0.124870i | ||||||
\(924\) | −42.6796 | − | 13.4809i | −1.40406 | − | 0.443489i | ||||
\(925\) | −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 | \(-0.642316\pi\) | ||||
−0.432351 | + | 0.901705i | \(0.642316\pi\) | |||||||
\(942\) | −17.3791 | −0.566243 | ||||||||
\(943\) | 4.45147i | 0.144960i | ||||||||
\(944\) | − | 170.023i | − | 5.53377i | ||||||
\(945\) | −5.54136 | − | 2.07203i | −0.180261 | − | 0.0674031i | ||||
\(946\) | 4.17172 | + | 5.96168i | 0.135634 | + | 0.193831i | ||||
\(947\) | − | 6.15057i | − | 0.199867i | −0.994994 | − | 0.0999333i | \(-0.968137\pi\) | ||
0.994994 | − | 0.0999333i | \(-0.0318630\pi\) | |||||||
\(948\) | − | 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 | \(-0.879096\pi\) | ||
0.928727 | − | 0.370764i | \(-0.120904\pi\) | |||||||
\(978\) | − | 9.36651i | − | 0.299508i | ||||||
\(979\) | −20.4194 | + | 14.2886i | −0.652608 | + | 0.456666i | ||||
\(980\) | 76.3550 | − | 23.3240i | 2.43907 | − | 0.745057i | ||||
\(981\) | 11.4582i | 0.365832i | ||||||||
\(982\) | 67.6076i | 2.15744i | ||||||||
\(983\) | 11.1133 | 0.354459 | 0.177230 | − | 0.984170i | \(-0.443286\pi\) | ||||
0.177230 | + | 0.984170i | \(0.443286\pi\) | |||||||
\(984\) | 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.a.769.2 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.b.769.47 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.b.769.1 | yes | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.a.769.47 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.a.769.48 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.b.769.2 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.b.769.48 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.a.769.1 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.1 | ✓ | 48 | 385.384 | even | 2 | inner | |
1155.2.k.a.769.2 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.a.769.47 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.a.769.48 | yes | 48 | 35.34 | odd | 2 | inner | |
1155.2.k.b.769.1 | yes | 48 | 7.6 | odd | 2 | ||
1155.2.k.b.769.2 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.b.769.47 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.b.769.48 | yes | 48 | 77.76 | even | 2 |