Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(-0.417865 + 1.68089i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.m.1601.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.417865 | − | 1.68089i | −0.241255 | − | 0.970462i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.25338 | − | 2.33003i | 0.473732 | − | 0.880669i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.65078 | + | 1.40477i | −0.883592 | + | 0.468257i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63831 | + | 2.67793i | 1.39850 | + | 0.807426i | 0.994236 | − | 0.107214i | \(-0.0341931\pi\) |
0.404268 | + | 0.914641i | \(0.367526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.13670i | 1.14732i | 0.819095 | + | 0.573658i | \(0.194476\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0773793 | − | 0.134025i | 0.0187672 | − | 0.0325058i | −0.856489 | − | 0.516165i | \(-0.827359\pi\) |
0.875257 | + | 0.483659i | \(0.160693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.40485 | + | 1.96579i | −0.781126 | + | 0.450983i | −0.836829 | − | 0.547464i | \(-0.815593\pi\) |
0.0557031 | + | 0.998447i | \(0.482260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.44027 | − | 1.13315i | −0.968946 | − | 0.247273i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19273 | − | 2.99803i | 1.08276 | − | 0.625132i | 0.151120 | − | 0.988515i | \(-0.451712\pi\) |
0.931640 | + | 0.363384i | \(0.118379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.46893 | + | 3.86866i | 0.667596 | + | 0.744524i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3150i | 1.91544i | 0.287703 | + | 0.957720i | \(0.407108\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.70071 | + | 3.86866i | 1.20348 | + | 0.694832i | 0.961328 | − | 0.275406i | \(-0.0888122\pi\) |
0.242156 | + | 0.970237i | \(0.422146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.56312 | − | 8.91550i | 0.446181 | − | 1.55199i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.24072 | + | 9.07719i | 0.861569 | + | 1.49228i | 0.870414 | + | 0.492320i | \(0.163851\pi\) |
−0.00884571 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.95334 | − | 1.72858i | 1.11343 | − | 0.276795i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.33876 | −0.365253 | −0.182627 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182627 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.78236 | −0.271807 | −0.135903 | − | 0.990722i | \(-0.543394\pi\) | ||||
−0.135903 | + | 0.990722i | \(0.543394\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.80118 | − | 3.11974i | −0.262729 | − | 0.455061i | 0.704237 | − | 0.709965i | \(-0.251289\pi\) |
−0.966966 | + | 0.254905i | \(0.917956\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.85809 | − | 5.84082i | −0.551156 | − | 0.834402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.257615 | − | 0.0740617i | −0.0360733 | − | 0.0103707i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.29470 | − | 2.47955i | −0.589923 | − | 0.340592i | 0.175144 | − | 0.984543i | \(-0.443961\pi\) |
−0.765067 | + | 0.643951i | \(0.777294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.72705 | + | 4.90174i | 0.626112 | + | 0.649251i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.27011 | + | 9.12810i | −0.686110 | + | 1.18838i | 0.286976 | + | 0.957938i | \(0.407350\pi\) |
−0.973087 | + | 0.230440i | \(0.925983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.25602 | + | 1.87987i | −0.416891 | + | 0.240692i | −0.693746 | − | 0.720219i | \(-0.744041\pi\) |
0.276855 | + | 0.960912i | \(0.410708\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0492651 | + | 7.93710i | −0.00620682 | + | 0.999981i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.444690 | + | 0.770225i | −0.0543275 | + | 0.0940980i | −0.891910 | − | 0.452213i | \(-0.850635\pi\) |
0.837583 | + | 0.546311i | \(0.183968\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.20921 | − | 7.47564i | −0.867887 | − | 0.899961i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.6200i | − | 1.37904i | −0.724269 | − | 0.689518i | \(-0.757822\pi\) | ||
0.724269 | − | 0.689518i | \(-0.242178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6097 | + | 6.12550i | 1.24177 | + | 0.716935i | 0.969454 | − | 0.245273i | \(-0.0788777\pi\) |
0.272314 | + | 0.962208i | \(0.412211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0532 | − | 7.45095i | 1.37359 | − | 0.849115i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.61147 | + | 6.25525i | 0.406322 | + | 0.703770i | 0.994474 | − | 0.104980i | \(-0.0334778\pi\) |
−0.588152 | + | 0.808750i | \(0.700144\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.05324 | − | 7.44747i | 0.561471 | − | 0.827496i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.14180 | 0.564386 | 0.282193 | − | 0.959358i | \(-0.408938\pi\) | ||||
0.282193 | + | 0.959358i | \(0.408938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.3383 | − | 4.31026i | 1.85886 | − | 0.462108i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.58428 | − | 14.8684i | −0.909932 | − | 1.57605i | −0.814156 | − | 0.580646i | \(-0.802800\pi\) |
−0.0957761 | − | 0.995403i | \(-0.530533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.63865 | + | 5.18485i | 1.01041 | + | 0.543520i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.70279 | − | 12.8797i | 0.383962 | − | 1.33557i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.28309i | − | 0.434882i | −0.976073 | − | 0.217441i | \(-0.930229\pi\) | ||
0.976073 | − | 0.217441i | \(-0.0697710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.0570 | − | 0.582836i | −1.61379 | − | 0.0585772i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.04794 | − | 5.27919i | 0.303282 | − | 0.525299i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.976877 | + | 0.213801i | \(0.0685844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.73132 | + | 2.15428i | −0.367658 | + | 0.212267i | −0.672435 | − | 0.740157i | \(-0.734751\pi\) |
0.304777 | + | 0.952424i | \(0.401418\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3579 | − | 8.28953i | 1.38803 | − | 0.801379i | 0.394936 | − | 0.918709i | \(-0.370767\pi\) |
0.993093 | + | 0.117330i | \(0.0374334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.92426 | + | 3.33292i | −0.184311 | + | 0.319236i | −0.943344 | − | 0.331816i | \(-0.892339\pi\) |
0.759033 | + | 0.651052i | \(0.225672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.0678 | − | 12.6021i | 1.24034 | − | 1.19614i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.94281i | − | 0.935341i | −0.883903 | − | 0.467671i | \(-0.845093\pi\) | ||
0.883903 | − | 0.467671i | \(-0.154907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.81112 | − | 10.9655i | −0.537238 | − | 1.01376i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.215297 | − | 0.348280i | −0.0197362 | − | 0.0319268i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.84262 | + | 15.3159i | 0.803875 | + | 1.39235i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.977287 | + | 3.93120i | 0.0881190 | + | 0.354464i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.64472 | 0.412152 | 0.206076 | − | 0.978536i | \(-0.433931\pi\) | ||||
0.206076 | + | 0.978536i | \(0.433931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.744784 | + | 2.99594i | 0.0655746 | + | 0.263778i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.31417 | + | 5.74031i | 0.289561 | + | 0.501534i | 0.973705 | − | 0.227813i | \(-0.0731575\pi\) |
−0.684144 | + | 0.729347i | \(0.739824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.312794 | + | 10.3973i | 0.0271227 | + | 0.901559i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.08389 | + | 2.35783i | 0.348910 | + | 0.201443i | 0.664205 | − | 0.747550i | \(-0.268770\pi\) |
−0.315295 | + | 0.948994i | \(0.602103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.56273i | − | 0.811100i | −0.914073 | − | 0.405550i | \(-0.867080\pi\) | ||
0.914073 | − | 0.405550i | \(-0.132920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.49128 | + | 4.33122i | −0.378234 | + | 0.364754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0778 | + | 19.1873i | −0.926373 | + | 1.60452i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.20560 | + | 8.92570i | −0.676787 | + | 0.736179i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6339 | − | 10.1809i | 1.44462 | − | 0.834054i | 0.446471 | − | 0.894798i | \(-0.352681\pi\) |
0.998153 | + | 0.0607437i | \(0.0193472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.69396 | + | 9.86223i | −0.463368 | + | 0.802577i | −0.999126 | − | 0.0417947i | \(-0.986692\pi\) |
0.535758 | + | 0.844371i | \(0.320026\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0168412 | + | 0.463970i | −0.00136153 | + | 0.0375098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.89957 | − | 3.40612i | −0.470837 | − | 0.271838i | 0.245753 | − | 0.969332i | \(-0.420965\pi\) |
−0.716590 | + | 0.697495i | \(0.754298\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.37324 | + | 8.25504i | −0.188210 | + | 0.654667i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.477042 | − | 15.8569i | −0.0375962 | − | 1.24970i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.95589 | + | 6.85180i | 0.309849 | + | 0.536674i | 0.978329 | − | 0.207056i | \(-0.0663881\pi\) |
−0.668480 | + | 0.743730i | \(0.733055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2507 | −1.48966 | −0.744832 | − | 0.667252i | \(-0.767470\pi\) | ||||
−0.744832 | + | 0.667252i | \(0.767470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.11232 | −0.316332 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.26402 | − | 9.99391i | 0.479021 | − | 0.764253i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.07129 | − | 12.2478i | −0.537621 | − | 0.931186i | −0.999032 | − | 0.0439995i | \(-0.985990\pi\) |
0.461411 | − | 0.887186i | \(-0.347343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.5455 | + | 5.04416i | 1.31880 | + | 0.379142i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.79606 | − | 1.03696i | −0.134244 | − | 0.0775058i | 0.431374 | − | 0.902173i | \(-0.358029\pi\) |
−0.565618 | + | 0.824667i | \(0.691362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7401i | 1.61593i | 0.589231 | + | 0.807965i | \(0.299431\pi\) | ||||
−0.589231 | + | 0.807965i | \(0.700569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.52043 | + | 4.68749i | 0.334160 | + | 0.346509i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.717819 | − | 0.414433i | 0.0524921 | − | 0.0303063i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.3620 | − | 3.23383i | 0.971941 | − | 0.235226i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00687 | + | 1.15867i | −0.145212 | + | 0.0838383i | −0.570846 | − | 0.821057i | \(-0.693385\pi\) |
0.425634 | + | 0.904896i | \(0.360051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.93203 | − | 15.4707i | 0.642942 | − | 1.11361i | −0.341831 | − | 0.939761i | \(-0.611047\pi\) |
0.984773 | − | 0.173846i | \(-0.0556196\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.3849i | − | 1.30987i | −0.755685 | − | 0.654936i | \(-0.772696\pi\) | ||
0.755685 | − | 0.654936i | \(-0.227304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.70763 | − | 0.985902i | −0.121051 | − | 0.0698887i | 0.438252 | − | 0.898852i | \(-0.355598\pi\) |
−0.559303 | + | 0.828963i | \(0.688931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.48048 | + | 0.425624i | 0.104425 | + | 0.0300212i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0342 | + | 12.9285i | 1.68687 | + | 0.907405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.55324 | + | 15.2417i | −0.663996 | + | 1.05937i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0570 | −1.45654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07968 | 0.0743282 | 0.0371641 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371641 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.5319 | + | 4.85558i | −1.33830 | + | 0.332699i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.4126 | − | 10.7640i | 1.18205 | − | 0.730707i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.86287 | − | 20.3933i | 0.396176 | − | 1.37805i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.554421 | + | 0.320095i | 0.0372944 | + | 0.0215319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3841i | 1.03020i | 0.857131 | + | 0.515099i | \(0.172245\pi\) | ||||
−0.857131 | + | 0.515099i | \(0.827755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.975410 | + | 1.68946i | −0.0647402 | + | 0.112133i | −0.896579 | − | 0.442884i | \(-0.853955\pi\) |
0.831838 | + | 0.555018i | \(0.187289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.44750 | − | 1.41307i | 0.161735 | − | 0.0933780i | −0.416948 | − | 0.908930i | \(-0.636900\pi\) |
0.578683 | + | 0.815553i | \(0.303567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.5608 | − | 17.1466i | −1.15542 | − | 1.12817i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.80293 | − | 2.19563i | 0.249139 | − | 0.143840i | −0.370231 | − | 0.928940i | \(-0.620722\pi\) |
0.619370 | + | 0.785099i | \(0.287388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.00527 | − | 8.68433i | 0.584955 | − | 0.564108i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6724i | 1.14313i | 0.820556 | + | 0.571566i | \(0.193664\pi\) | ||||
−0.820556 | + | 0.571566i | \(0.806336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.69148 | − | 2.13128i | −0.237789 | − | 0.137288i | 0.376371 | − | 0.926469i | \(-0.377172\pi\) |
−0.614160 | + | 0.789181i | \(0.710505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6299 | − | 5.38190i | −0.938511 | − | 0.345249i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.13190 | − | 14.0849i | −0.517420 | − | 0.896198i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.14858 | − | 8.64280i | −0.136161 | − | 0.547715i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.87820 | −0.244790 | −0.122395 | − | 0.992481i | \(-0.539057\pi\) | ||||
−0.122395 | + | 0.992481i | \(0.539057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.1140 | 2.01899 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.85563 | + | 15.3384i | 0.552399 | + | 0.956784i | 0.998101 | + | 0.0616020i | \(0.0196209\pi\) |
−0.445702 | + | 0.895182i | \(0.647046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.7187 | − | 0.833896i | 1.72236 | − | 0.0518158i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.4901 | − | 27.3427i | −0.896917 | − | 1.69247i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.84912 | + | 2.79964i | 0.299010 | + | 0.172633i | 0.641998 | − | 0.766706i | \(-0.278106\pi\) |
−0.342988 | + | 0.939340i | \(0.611439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4051 | + | 20.6422i | −1.30997 | + | 1.26328i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.53335 | − | 14.7802i | 0.520288 | − | 0.901165i | −0.479434 | − | 0.877578i | \(-0.659158\pi\) |
0.999722 | − | 0.0235867i | \(-0.00750857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7661 | − | 8.52521i | 0.896977 | − | 0.517870i | 0.0207586 | − | 0.999785i | \(-0.493392\pi\) |
0.876218 | + | 0.481915i | \(0.160059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.68750 | − | 18.3681i | 0.283701 | − | 1.11169i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.26868 | − | 9.12563i | 0.316565 | − | 0.548306i | −0.663204 | − | 0.748438i | \(-0.730804\pi\) |
0.979769 | + | 0.200133i | \(0.0641373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.1967 | − | 0.841992i | −1.38875 | − | 0.0504087i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.2208i | 1.14662i | 0.819339 | + | 0.573309i | \(0.194340\pi\) | ||||
−0.819339 | + | 0.573309i | \(0.805660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5733 | − | 8.99126i | −0.925738 | − | 0.534475i | −0.0402770 | − | 0.999189i | \(-0.512824\pi\) |
−0.885461 | + | 0.464713i | \(0.846157\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.93135 | + | 5.44939i | −0.173032 | + | 0.321667i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48802 | + | 14.7017i | 0.499296 | + | 0.864805i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.19940 | + | 1.78975i | −0.422036 | + | 0.104917i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.2153 | −1.47309 | −0.736546 | − | 0.676388i | \(-0.763544\pi\) | ||||
−0.736546 | + | 0.676388i | \(0.763544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.72998 | + | 27.2336i | 0.332487 | + | 1.58025i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.4019 | + | 21.4808i | 0.717223 | + | 1.24227i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23396 | + | 4.15294i | −0.128764 | + | 0.239372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1474 | − | 2.91726i | −0.582951 | − | 0.167592i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.28693i | − | 0.472960i | −0.971636 | − | 0.236480i | \(-0.924006\pi\) | ||
0.971636 | − | 0.236480i | \(-0.0759938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.18029 | + | 5.37173i | 0.294696 | + | 0.305587i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.28958 | − | 7.42977i | 0.243240 | − | 0.421304i | −0.718395 | − | 0.695635i | \(-0.755123\pi\) |
0.961635 | + | 0.274331i | \(0.0884564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.807839 | + | 0.466406i | −0.0456617 | + | 0.0263628i | −0.522657 | − | 0.852543i | \(-0.675059\pi\) |
0.476995 | + | 0.878906i | \(0.341726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.58262 | + | 1.49108i | −0.145054 | + | 0.0837472i | −0.570771 | − | 0.821109i | \(-0.693355\pi\) |
0.425716 | + | 0.904857i | \(0.360022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.6227 | + | 47.8440i | −1.54658 | + | 2.67875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.9334 | − | 20.6701i | −1.11258 | − | 1.15369i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.608446i | 0.0338549i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.40636 | + | 1.84176i | 0.354272 | + | 0.101850i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.52665 | + | 0.286602i | −0.525221 | + | 0.0158009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9541 | + | 18.9730i | 0.602091 | + | 1.04285i | 0.992504 | + | 0.122213i | \(0.0389990\pi\) |
−0.390413 | + | 0.920640i | \(0.627668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.6433 | − | 16.6996i | −1.46005 | − | 0.915133i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.4696 | −1.98663 | −0.993314 | − | 0.115448i | \(-0.963170\pi\) | ||||
−0.993314 | + | 0.115448i | \(0.963170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.7128 | + | 4.15476i | −0.907713 | + | 0.225655i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7200 | + | 35.8881i | 1.12205 | + | 1.94345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4449 | + | 1.66873i | −0.995932 | + | 0.0901031i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.62881 | + | 2.09509i | 0.194805 | + | 0.112471i | 0.594230 | − | 0.804295i | \(-0.297457\pi\) |
−0.399425 | + | 0.916766i | \(0.630790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.2897i | − | 1.19314i | −0.802560 | − | 0.596571i | \(-0.796530\pi\) | ||
0.802560 | − | 0.596571i | \(-0.203470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0035 | + | 14.3499i | −0.854203 | + | 0.765943i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.72220 | − | 15.1073i | 0.464236 | − | 0.804080i | −0.534931 | − | 0.844896i | \(-0.679662\pi\) |
0.999167 | + | 0.0408157i | \(0.0129956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.495455 | + | 0.507424i | −0.0262223 | + | 0.0268557i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2564 | − | 14.5818i | 1.33298 | − | 0.769599i | 0.347228 | − | 0.937781i | \(-0.387123\pi\) |
0.985756 | + | 0.168182i | \(0.0537896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.77133 | + | 3.06803i | −0.0932279 | + | 0.161476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0493 | − | 21.2634i | 1.15729 | − | 1.11604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1633 | − | 13.3734i | −1.20912 | − | 0.698084i | −0.246550 | − | 0.969130i | \(-0.579297\pi\) |
−0.962566 | + | 0.271046i | \(0.912630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.19954 | − | 3.28542i | 0.322735 | − | 0.171032i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1603 | + | 6.89898i | −0.579414 | + | 0.358177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.56718 | − | 4.44649i | −0.132924 | − | 0.230231i | 0.791879 | − | 0.610678i | \(-0.209103\pi\) |
−0.924802 | + | 0.380448i | \(0.875770\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.6699 | −2.19761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3320 | −0.890284 | −0.445142 | − | 0.895460i | \(-0.646847\pi\) | ||||
−0.445142 | + | 0.895460i | \(0.646847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.94087 | − | 7.80726i | −0.0994336 | − | 0.399978i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8457 | − | 18.7852i | −0.554188 | − | 0.959881i | −0.997966 | − | 0.0637447i | \(-0.979696\pi\) |
0.443779 | − | 0.896136i | \(-0.353638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.72463 | − | 2.50380i | 0.240166 | − | 0.127275i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6759 | + | 6.74110i | 0.591993 | + | 0.341787i | 0.765885 | − | 0.642977i | \(-0.222301\pi\) |
−0.173892 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.927941i | − | 0.0469280i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.26396 | − | 7.96943i | 0.416861 | − | 0.402005i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8800 | + | 6.85891i | −0.596240 | + | 0.344239i | −0.767561 | − | 0.640976i | \(-0.778530\pi\) |
0.171321 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.3460 | − | 4.87044i | 0.868385 | − | 0.243827i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4976 | + | 9.52487i | −0.823849 | + | 0.475649i | −0.851742 | − | 0.523962i | \(-0.824453\pi\) |
0.0278932 | + | 0.999611i | \(0.491120\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0035 | + | 27.7189i | −0.797191 | + | 1.38078i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.1371i | 2.78261i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1428 | + | 17.4030i | 1.49047 | + | 0.860521i | 0.999941 | − | 0.0109054i | \(-0.00347135\pi\) |
0.490526 | + | 0.871427i | \(0.336805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.25674 | − | 7.84982i | 0.111317 | − | 0.387203i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.6633 | + | 23.7205i | 0.721535 | + | 1.16721i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0739 | + | 3.99593i | −0.787142 | + | 0.195682i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.7934 | −0.966971 | −0.483486 | − | 0.875352i | \(-0.660629\pi\) | ||||
−0.483486 | + | 0.875352i | \(0.660629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2279 | −0.595951 | −0.297975 | − | 0.954574i | \(-0.596311\pi\) | ||||
−0.297975 | + | 0.954574i | \(0.596311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.15705 | + | 5.73949i | 0.445231 | + | 0.279063i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.299122 | + | 9.94282i | 0.0144755 | + | 0.481167i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.8808 | + | 10.6029i | 1.78062 | + | 0.511910i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.22781 | − | 5.32768i | −0.444488 | − | 0.256625i | 0.261012 | − | 0.965336i | \(-0.415944\pi\) |
−0.705499 | + | 0.708711i | \(0.749277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5027i | 1.22558i | 0.790245 | + | 0.612791i | \(0.209953\pi\) | ||||
−0.790245 | + | 0.612791i | \(0.790047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7870 | + | 20.4157i | −0.563848 | + | 0.976613i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8206 | − | 13.7528i | 1.13689 | − | 0.656386i | 0.191234 | − | 0.981544i | \(-0.438751\pi\) |
0.945660 | + | 0.325158i | \(0.105418\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4319 | + | 10.0630i | 0.877712 | + | 0.479189i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7785 | + | 9.68708i | −0.797171 | + | 0.460247i | −0.842481 | − | 0.538726i | \(-0.818906\pi\) |
0.0453099 | + | 0.998973i | \(0.485572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.4816 | − | 25.3864i | −1.15794 | − | 1.20073i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9504i | 1.27187i | 0.771744 | + | 0.635934i | \(0.219385\pi\) | ||||
−0.771744 | + | 0.635934i | \(0.780615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8479 | − | 6.26304i | −0.510808 | − | 0.294915i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.9566 | + | 5.44983i | 0.890660 | + | 0.256056i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.18704 | − | 15.9124i | −0.429752 | − | 0.744352i | 0.567099 | − | 0.823649i | \(-0.308066\pi\) |
−0.996851 | + | 0.0792977i | \(0.974732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.786920 | − | 0.165569i | 0.0367303 | − | 0.00772810i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2344 | −0.569814 | −0.284907 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284907 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4136 | −0.530433 | −0.265217 | − | 0.964189i | \(-0.585444\pi\) | ||||
−0.265217 | + | 0.964189i | \(0.585444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.665893 | − | 1.15336i | −0.0308138 | − | 0.0533711i | 0.850207 | − | 0.526448i | \(-0.176477\pi\) |
−0.881021 | + | 0.473077i | \(0.843143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23728 | + | 2.00152i | 0.0571325 | + | 0.0924218i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.26008 | + | 11.3398i | −0.150217 | + | 0.522511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.26712 | − | 4.77302i | −0.380123 | − | 0.219464i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.8675 | + | 0.539659i | 0.680736 | + | 0.0247093i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7342 | − | 18.5922i | 0.490458 | − | 0.849498i | −0.509482 | − | 0.860481i | \(-0.670163\pi\) |
0.999940 | + | 0.0109835i | \(0.00349621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.5496 | + | 21.6793i | −1.71212 | + | 0.988491i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.4543 | + | 7.42790i | −1.20371 | + | 0.337981i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.8630 | − | 24.0115i | 0.628195 | − | 1.08807i | −0.359719 | − | 0.933061i | \(-0.617127\pi\) |
0.987914 | − | 0.155004i | \(-0.0495392\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.86409 | − | 9.51254i | 0.446070 | − | 0.430172i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.536100i | 0.0241938i | 0.999927 | + | 0.0120969i | \(0.00385066\pi\) | ||||
−0.999927 | + | 0.0120969i | \(0.996149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.38246 | + | 0.798164i | 0.0622629 | + | 0.0359475i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.0749 | − | 14.5642i | −1.21447 | − | 0.653293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1191 | + | 26.1870i | 0.676823 | + | 1.17229i | 0.975933 | + | 0.218072i | \(0.0699769\pi\) |
−0.299110 | + | 0.954219i | \(0.596690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.04420 | + | 32.3583i | 0.359388 | + | 1.44566i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.5176 | 1.44989 | 0.724945 | − | 0.688807i | \(-0.241865\pi\) | ||||
0.724945 | + | 0.688807i | \(0.241865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.71839 | + | 6.91235i | 0.0763166 | + | 0.306988i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1885 | − | 22.8432i | −0.584570 | − | 1.01251i | −0.994929 | − | 0.100581i | \(-0.967930\pi\) |
0.410359 | − | 0.911924i | \(-0.365403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5705 | − | 17.0433i | 1.21965 | − | 0.753952i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.4162 | − | 6.35301i | −0.857245 | − | 0.280492i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.2938i | − | 0.848538i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6324 | + | 17.0040i | −0.773977 | + | 0.746393i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.39842 | + | 9.35035i | −0.236509 | + | 0.409646i | −0.959710 | − | 0.280992i | \(-0.909337\pi\) |
0.723201 | + | 0.690638i | \(0.242670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.206455 | + | 0.119197i | −0.00902764 | + | 0.00521211i | −0.504507 | − | 0.863408i | \(-0.668326\pi\) |
0.495479 | + | 0.868620i | \(0.334992\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03699 | − | 0.598708i | 0.0451721 | − | 0.0260801i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.47632 | − | 11.2173i | 0.281579 | − | 0.487709i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.14701 | − | 31.5999i | 0.0497760 | − | 1.37132i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.67476i | − | 0.419061i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.992498 | + | 3.45229i | −0.0428294 | + | 0.148977i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.25374 | − | 37.4232i | −0.0970753 | − | 1.61193i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.28056 | − | 2.21799i | −0.0550555 | − | 0.0953588i | 0.837184 | − | 0.546921i | \(-0.184200\pi\) |
−0.892240 | + | 0.451562i | \(0.850867\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.5427 | − | 9.08444i | 1.56820 | − | 0.389850i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1549 | −1.16106 | −0.580529 | − | 0.814239i | \(-0.697154\pi\) | ||||
−0.580529 | + | 0.814239i | \(0.697154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.99022 | − | 9.55707i | 0.255656 | − | 0.407886i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.2770 | − | 35.1209i | −0.863831 | − | 1.49620i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.1015 | − | 0.574652i | 0.812277 | − | 0.0244367i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7984 | + | 12.0080i | 0.881257 | + | 0.508794i | 0.871073 | − | 0.491154i | \(-0.163425\pi\) |
0.0101846 | + | 0.999948i | \(0.496758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.37308i | − | 0.311848i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.996567 | − | 1.03340i | −0.0420751 | − | 0.0436300i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.1487 | + | 34.8986i | −0.849168 | + | 1.47080i | 0.0327839 | + | 0.999462i | \(0.489563\pi\) |
−0.881952 | + | 0.471340i | \(0.843771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.0192 | − | 21.1087i | −0.462763 | − | 0.886482i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.46883 | + | 2.58008i | −0.187343 | + | 0.108163i | −0.590738 | − | 0.806863i | \(-0.701163\pi\) |
0.403395 | + | 0.915026i | \(0.367830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.841937 | − | 1.45828i | 0.0352340 | − | 0.0610270i | −0.847871 | − | 0.530203i | \(-0.822116\pi\) |
0.883105 | + | 0.469176i | \(0.155449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.78620 | + | 2.88916i | 0.116395 | + | 0.120697i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5104 | − | 14.7284i | −1.06201 | − | 0.613153i | −0.136024 | − | 0.990706i | \(-0.543432\pi\) |
−0.925988 | + | 0.377552i | \(0.876766\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.7370 | − | 8.54907i | −1.23583 | − | 0.355287i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.44461 | − | 11.9806i | 0.267368 | − | 0.497037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.2801 | − | 23.0018i | −0.550006 | − | 0.952638i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.9862 | 1.89805 | 0.949027 | − | 0.315195i | \(-0.102070\pi\) | ||||
0.949027 | + | 0.315195i | \(0.102070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.4199 | −1.25343 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.9030 | + | 7.68242i | −1.27118 | + | 0.316012i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.954084 | + | 1.65252i | 0.0391795 | + | 0.0678610i | 0.884950 | − | 0.465686i | \(-0.154192\pi\) |
−0.845771 | + | 0.533547i | \(0.820859\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.943632 | + | 3.28231i | −0.0386203 | + | 0.134336i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2188 | + | 10.5186i | 0.744401 | + | 0.429780i | 0.823667 | − | 0.567073i | \(-0.191924\pi\) |
−0.0792661 | + | 0.996853i | \(0.525258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.3573i | − | 1.23830i | −0.785273 | − | 0.619150i | \(-0.787477\pi\) | ||
0.785273 | − | 0.619150i | \(-0.212523\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0967842 | − | 2.66638i | 0.00394136 | − | 0.108583i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4049 | + | 8.89399i | −0.625264 | + | 0.360996i | −0.778915 | − | 0.627129i | \(-0.784230\pi\) |
0.153652 | + | 0.988125i | \(0.450897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.6884 | − | 45.8012i | 0.473637 | − | 1.85596i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9054 | − | 7.45095i | 0.522098 | − | 0.301433i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5074 | − | 25.1276i | 0.585950 | − | 1.01490i | −0.408806 | − | 0.912621i | \(-0.634055\pi\) |
0.994756 | − | 0.102274i | \(-0.0326118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.32967i | − | 0.134047i | −0.997751 | − | 0.0670237i | \(-0.978650\pi\) | ||
0.997751 | − | 0.0670237i | \(-0.0213503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.6135 | + | 24.0256i | 1.67259 | + | 0.965669i | 0.966182 | + | 0.257863i | \(0.0830182\pi\) |
0.706406 | + | 0.707806i | \(0.250315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.6116 | + | 9.68897i | 1.18827 | + | 0.388805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.4032 | + | 1.36592i | −1.81904 | + | 0.0547244i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.79899 | + | 35.3945i | 0.351398 | + | 1.41352i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.62209 | 0.0646771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8726 | 0.631878 | 0.315939 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315939 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.451160 | − | 1.81482i | −0.0179320 | − | 0.0721327i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.1617 | − | 15.9598i | 0.957322 | − | 0.632350i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.3234 | + | 30.8019i | 0.645743 | + | 1.21851i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.34785 | + | 1.93288i | 0.132232 | + | 0.0763443i | 0.564657 | − | 0.825326i | \(-0.309009\pi\) |
−0.432425 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.7423i | 1.48841i | 0.667950 | + | 0.744206i | \(0.267172\pi\) | ||||
−0.667950 | + | 0.744206i | \(0.732828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.9230 | − | 18.9193i | 0.429429 | − | 0.743793i | −0.567393 | − | 0.823447i | \(-0.692048\pi\) |
0.996823 | + | 0.0796536i | \(0.0253814\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.8888 | + | 28.2260i | −1.91905 | + | 1.10797i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.3692 | − | 24.7708i | −0.994297 | − | 0.970844i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.14321 | + | 1.81473i | −0.123003 | + | 0.0710159i | −0.560239 | − | 0.828331i | \(-0.689291\pi\) |
0.437236 | + | 0.899347i | \(0.355957\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.7288 | − | 1.33318i | −1.43293 | − | 0.0520123i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.4040i | − | 0.872737i | −0.899768 | − | 0.436369i | \(-0.856264\pi\) | ||
0.899768 | − | 0.436369i | \(-0.143736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6525 | + | 7.88230i | 0.531023 | + | 0.306586i | 0.741433 | − | 0.671027i | \(-0.234147\pi\) |
−0.210410 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.306371 | − | 1.06568i | 0.0118985 | − | 0.0413875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.9245 | + | 53.5628i | 1.19740 | + | 2.07396i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.8590 | − | 6.42849i | 0.999767 | − | 0.248540i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.1366 | −0.777365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.84031 | −0.340769 | −0.170385 | − | 0.985378i | \(-0.554501\pi\) | ||||
−0.170385 | + | 0.985378i | \(0.554501\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.82417 | − | 13.5519i | −0.300707 | − | 0.520840i | 0.675589 | − | 0.737278i | \(-0.263889\pi\) |
−0.976296 | + | 0.216438i | \(0.930556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.97974 | − | 5.36833i | −0.382987 | − | 0.206018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.24738 | + | 0.933590i | 0.124440 | + | 0.0357752i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7691 | − | 18.9193i | −1.25388 | − | 0.723926i | −0.281999 | − | 0.959415i | \(-0.590998\pi\) |
−0.971877 | + | 0.235489i | \(0.924331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.39793 | − | 3.52351i | −0.129639 | − | 0.134430i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2572 | − | 17.7659i | 0.390766 | − | 0.676827i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5792 | + | 8.41732i | −0.554620 | + | 0.320210i | −0.750983 | − | 0.660321i | \(-0.770420\pi\) |
0.196363 | + | 0.980531i | \(0.437087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.4835 | + | 36.6828i | −0.816091 | + | 1.39347i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.180972 | + | 0.313452i | −0.00685480 | + | 0.0118729i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.27972 | − | 5.47484i | −0.199697 | − | 0.207077i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.2554i | 1.06719i | 0.845740 | + | 0.533596i | \(0.179160\pi\) | ||||
−0.845740 | + | 0.533596i | \(0.820840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.6877 | − | 20.6043i | −1.34599 | − | 0.777106i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.48046 | − | 13.7186i | −0.318940 | − | 0.515942i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.40632 | − | 12.8281i | −0.278150 | − | 0.481770i | 0.692775 | − | 0.721154i | \(-0.256388\pi\) |
−0.970925 | + | 0.239384i | \(0.923055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.3604 | − | 11.5080i | −0.688568 | − | 0.431583i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.3934 | 1.73744 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.7053 | − | 7.38467i | 1.10937 | − | 0.275786i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1406 | + | 17.5640i | 0.378179 | + | 0.655025i | 0.990797 | − | 0.135353i | \(-0.0432170\pi\) |
−0.612618 | + | 0.790379i | \(0.709884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.342786 | + | 11.3942i | 0.0127660 | + | 0.424342i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.03990 | + | 7.09555i | −0.0758646 | + | 0.263886i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.81854i | − | 0.104534i | −0.998633 | − | 0.0522670i | \(-0.983355\pi\) | ||
0.998633 | − | 0.0522670i | \(-0.0166447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.93304 | + | 26.8402i | −0.108631 | + | 0.994082i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.137917 | + | 0.238880i | −0.00510106 | + | 0.00883530i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2169 | − | 17.4457i | 1.11609 | − | 0.644372i | 0.175687 | − | 0.984446i | \(-0.443785\pi\) |
0.940399 | + | 0.340074i | \(0.110452\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.12522 | + | 2.38170i | −0.151954 | + | 0.0877309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4220 | − | 23.2476i | 0.493737 | − | 0.855177i | −0.506237 | − | 0.862394i | \(-0.668964\pi\) |
0.999974 | + | 0.00721695i | \(0.00229725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.2770 | + | 19.5544i | −0.744896 | + | 0.718348i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.24499i | − | 0.0823607i | −0.999152 | − | 0.0411804i | \(-0.986888\pi\) | ||
0.999152 | − | 0.0411804i | \(-0.0131118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.6298 | + | 7.22305i | −0.498687 | + | 0.264277i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.31902 | − | 43.8442i | −0.0481959 | − | 1.60203i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.56634 | − | 2.71297i | −0.0571564 | − | 0.0989978i | 0.836031 | − | 0.548682i | \(-0.184870\pi\) |
−0.893188 | + | 0.449684i | \(0.851537\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.62056 | + | 6.51882i | 0.0590566 | + | 0.237559i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.5473 | −0.928532 | −0.464266 | − | 0.885696i | \(-0.653682\pi\) | ||||
−0.464266 | + | 0.885696i | \(0.653682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.4193 | − | 53.9801i | −0.487091 | − | 1.95935i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.16163 | − | 3.74406i | −0.0783591 | − | 0.135722i | 0.824183 | − | 0.566324i | \(-0.191635\pi\) |
−0.902542 | + | 0.430602i | \(0.858301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.35399 | + | 8.66100i | 0.193827 | + | 0.313549i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.7603 | − | 21.8009i | −1.36344 | − | 0.787185i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.4529i | − | 1.24240i | −0.783650 | − | 0.621202i | \(-0.786645\pi\) | ||
0.783650 | − | 0.621202i | \(-0.213355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0817 | − | 21.2947i | 0.795253 | − | 0.766911i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.19273 | − | 8.99408i | 0.186770 | − | 0.323494i | −0.757402 | − | 0.652949i | \(-0.773532\pi\) |
0.944171 | + | 0.329455i | \(0.106865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.9844 | − | 46.2437i | −0.465812 | − | 1.65898i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.96313 | − | 4.59752i | 0.285309 | − | 0.164723i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.1174 | − | 53.8970i | 1.11347 | − | 1.92859i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.9050 | + | 35.7819i | −1.42609 | + | 1.27874i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1681 | + | 21.4590i | 1.32490 | + | 0.764931i | 0.984506 | − | 0.175352i | \(-0.0561064\pi\) |
0.340394 | + | 0.940283i | \(0.389440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.67961 | − | 9.32071i | 0.0953966 | − | 0.331826i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.1671 | − | 12.4621i | −0.823726 | − | 0.443101i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.77645 | − | 13.4692i | −0.276150 | − | 0.478306i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3628 | −0.685866 | −0.342933 | − | 0.939360i | \(-0.611420\pi\) | ||||
−0.342933 | + | 0.939360i | \(0.611420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.557497 | −0.0197228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43.6417 | + | 27.3539i | 1.54200 | + | 0.966503i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.8073 | + | 56.8239i | 1.15774 | + | 2.00527i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.4097 | − | 8.16749i | −1.00007 | − | 0.287509i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.120667 | − | 0.0696669i | −0.00424241 | − | 0.00244936i | 0.497877 | − | 0.867247i | \(-0.334113\pi\) |
−0.502120 | + | 0.864798i | \(0.667446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5559i | 1.52945i | 0.644354 | + | 0.764727i | \(0.277126\pi\) | ||||
−0.644354 | + | 0.764727i | \(0.722874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.5002 | − | 21.2578i | −0.718973 | − | 0.745543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.06865 | − | 3.50374i | 0.212315 | − | 0.122580i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −32.8334 | − | 0.203795i | −1.14729 | − | 0.00712118i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.9212 | − | 23.0485i | 1.39326 | − | 0.804400i | 0.399586 | − | 0.916696i | \(-0.369154\pi\) |
0.993675 | + | 0.112296i | \(0.0358204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2425 | − | 19.4726i | 0.391889 | − | 0.678772i | −0.600809 | − | 0.799392i | \(-0.705155\pi\) |
0.992699 | + | 0.120620i | \(0.0384882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2536i | 1.81704i | 0.417846 | + | 0.908518i | \(0.362785\pi\) | ||||
−0.417846 | + | 0.908518i | \(0.637215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.26705 | + | 1.88623i | 0.113469 | + | 0.0655115i | 0.555661 | − | 0.831409i | \(-0.312465\pi\) |
−0.442191 | + | 0.896921i | \(0.645799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5408 | − | 5.04279i | −0.608483 | − | 0.174933i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.08135 | + | 0.0651222i | −0.0374666 | + | 0.00225635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.27779 | + | 39.3429i | 0.286122 | + | 1.35989i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.7191 | −1.40578 | −0.702890 | − | 0.711299i | \(-0.748107\pi\) | ||||
−0.702890 | + | 0.711299i | \(0.748107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.3983 | −2.66891 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.3081 | − | 8.03171i | 1.11275 | − | 0.276627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.7696 | − | 1.40703i | 1.60702 | − | 0.0483460i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.60577 | + | 29.9342i | −0.295349 | + | 1.02734i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.4273 | + | 31.4236i | 1.86574 | + | 1.07719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.21298i | − | 0.110010i | −0.998486 | − | 0.0550051i | \(-0.982482\pi\) | ||
0.998486 | − | 0.0550051i | \(-0.0175175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0555 | − | 41.6653i | 0.821720 | − | 1.42326i | −0.0826803 | − | 0.996576i | \(-0.526348\pi\) |
0.904400 | − | 0.426685i | \(-0.140319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4266 | − | 6.01978i | 0.355750 | − | 0.205392i | −0.311465 | − | 0.950258i | \(-0.600820\pi\) |
0.667215 | + | 0.744865i | \(0.267486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3847 | + | 2.65017i | 0.353911 | + | 0.0903174i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.51239 | + | 3.75993i | −0.221684 | + | 0.127989i | −0.606730 | − | 0.794908i | \(-0.707519\pi\) |
0.385046 | + | 0.922898i | \(0.374186\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.1651 | − | 20.4108i | 0.718803 | − | 0.693186i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.6851i | 1.31230i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.18619 | − | 1.83955i | −0.107960 | − | 0.0623308i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.01676 | + | 11.3535i | 0.203636 | + | 0.384259i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.6367 | + | 28.8156i | 0.561781 | + | 0.973033i | 0.997341 | + | 0.0728736i | \(0.0232170\pi\) |
−0.435560 | + | 0.900160i | \(0.643450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5366 | + | 42.3841i | 0.355390 | + | 1.42958i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9614 | 0.672515 | 0.336258 | − | 0.941770i | \(-0.390839\pi\) | ||||
0.336258 | + | 0.941770i | \(0.390839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3120 | 1.72679 | 0.863393 | − | 0.504533i | \(-0.168335\pi\) | ||||
0.863393 | + | 0.504533i | \(0.168335\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.94659 | − | 17.2280i | −0.333974 | − | 0.578460i | 0.649313 | − | 0.760521i | \(-0.275056\pi\) |
−0.983287 | + | 0.182061i | \(0.941723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.82158 | − | 10.8223i | 0.195250 | − | 0.362970i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.3823 | − | 21.0114i | 1.45336 | − | 0.703910i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2655 | + | 7.08149i | 0.410450 | + | 0.236973i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.9245 | − | 29.8224i | 1.03254 | − | 0.995740i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.9050 | + | 69.1176i | −1.33091 | + | 2.30520i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.664642 | + | 0.383731i | −0.0221424 | + | 0.0127839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.91414 | + | 2.01967i | 0.263366 | + | 0.0672106i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4200 | − | 37.1005i | 0.711239 | − | 1.23190i | −0.253153 | − | 0.967426i | \(-0.581468\pi\) |
0.964392 | − | 0.264476i | \(-0.0851990\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.663367 | + | 18.2756i | −0.0220025 | + | 0.606164i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5359i | 0.945437i | 0.881213 | + | 0.472719i | \(0.156727\pi\) | ||||
−0.881213 | + | 0.472719i | \(0.843273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.8493 | + | 13.7694i | 0.789296 | + | 0.455700i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5290 | − | 0.527347i | 0.578859 | − | 0.0174145i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.41160 | + | 7.64112i | 0.145525 | + | 0.252057i | 0.929569 | − | 0.368649i | \(-0.120179\pi\) |
−0.784043 | + | 0.620706i | \(0.786846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9294 | + | 3.46282i | −0.458990 | + | 0.114104i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0683 | 1.58219 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.86463 | − | 10.9521i | 0.225464 | − | 0.359716i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.1691 | + | 47.0583i | 0.891389 | + | 1.54393i | 0.838211 | + | 0.545346i | \(0.183602\pi\) |
0.0531782 | + | 0.998585i | \(0.483065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6180 | + | 12.3029i | 0.806824 | + | 0.403211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.2811 | − | 4.10567i | −0.467542 | − | 0.134414i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.3198i | 0.533144i | 0.963815 | + | 0.266572i | \(0.0858911\pi\) | ||||
−0.963815 | + | 0.266572i | \(0.914109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12154 | + | 1.16299i | 0.0366002 | + | 0.0379528i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.80594 | − | 6.59208i | 0.124070 | − | 0.214896i | −0.797299 | − | 0.603585i | \(-0.793739\pi\) |
0.921369 | + | 0.388689i | \(0.127072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.1446 | + | 7.01167i | −0.395481 | + | 0.228331i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9034 | − | 11.4912i | 0.646774 | − | 0.373415i | −0.140445 | − | 0.990088i | \(-0.544853\pi\) |
0.787219 | + | 0.616673i | \(0.211520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3394 | + | 43.8891i | −0.822551 | + | 1.42470i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.58552 | + | 3.71803i | 0.116269 | + | 0.120565i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.5633i | − | 1.31397i | −0.753902 | − | 0.656986i | \(-0.771831\pi\) | ||
0.753902 | − | 0.656986i | \(-0.228169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 91.9630 | + | 26.4384i | 2.97274 | + | 0.854633i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.6125 | − | 6.56034i | 0.342695 | − | 0.211844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4330 | + | 24.9988i | 0.465582 | + | 0.806412i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.4147 | + | 42.1432i | −0.851201 | + | 1.35805i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.10140 | 0.0997343 | 0.0498672 | − | 0.998756i | \(-0.484120\pi\) | ||||
0.0498672 | + | 0.998756i | \(0.484120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.02273 | − | 0.254249i | 0.0328549 | − | 0.00816764i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5212 | − | 39.0078i | −0.722739 | − | 1.25182i | −0.959898 | − | 0.280350i | \(-0.909550\pi\) |
0.237159 | − | 0.971471i | \(-0.423784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.2815 | − | 11.9857i | −0.714311 | − | 0.384244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8598 | + | 12.6207i | 0.699356 | + | 0.403773i | 0.807108 | − | 0.590404i | \(-0.201032\pi\) |
−0.107751 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 91.9525i | − | 2.93881i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.418805 | − | 11.5380i | 0.0133714 | − | 0.368379i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1759 | − | 52.2661i | 0.962461 | − | 1.66703i | 0.246173 | − | 0.969226i | \(-0.420827\pi\) |
0.716288 | − | 0.697805i | \(-0.245840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.46260 | + | 15.8935i | 0.142046 | + | 0.505895i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.25530 | + | 5.34355i | −0.294301 | + | 0.169915i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.93445 | − | 8.54672i | 0.156748 | − | 0.271495i | −0.776946 | − | 0.629567i | \(-0.783232\pi\) |
0.933694 | + | 0.358072i | \(0.116566\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.3142 | − | 26.3408i | 0.866792 | − | 0.835900i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.3385 | − | 13.4745i | −0.739138 | − | 0.426742i | 0.0826177 | − | 0.996581i | \(-0.473672\pi\) |
−0.821756 | + | 0.569840i | \(0.807005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.9369 | + | 51.7627i | −0.535859 | + | 1.63770i |
(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 | 2100.2.bi.m.101.3 | yes | 16 | |
3.2 | odd | 2 | inner | 2100.2.bi.m.101.1 | yes | 16 | |
5.2 | odd | 4 | 2100.2.bo.i.1949.2 | 32 | |||
5.3 | odd | 4 | 2100.2.bo.i.1949.15 | 32 | |||
5.4 | even | 2 | 2100.2.bi.l.101.6 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 2100.2.bi.m.1601.1 | yes | 16 | |
15.2 | even | 4 | 2100.2.bo.i.1949.10 | 32 | |||
15.8 | even | 4 | 2100.2.bo.i.1949.7 | 32 | |||
15.14 | odd | 2 | 2100.2.bi.l.101.8 | yes | 16 | ||
21.5 | even | 6 | inner | 2100.2.bi.m.1601.3 | yes | 16 | |
35.12 | even | 12 | 2100.2.bo.i.1349.7 | 32 | |||
35.19 | odd | 6 | 2100.2.bi.l.1601.8 | yes | 16 | ||
35.33 | even | 12 | 2100.2.bo.i.1349.10 | 32 | |||
105.47 | odd | 12 | 2100.2.bo.i.1349.15 | 32 | |||
105.68 | odd | 12 | 2100.2.bo.i.1349.2 | 32 | |||
105.89 | even | 6 | 2100.2.bi.l.1601.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.6 | ✓ | 16 | 5.4 | even | 2 | ||
2100.2.bi.l.101.8 | yes | 16 | 15.14 | odd | 2 | ||
2100.2.bi.l.1601.6 | yes | 16 | 105.89 | even | 6 | ||
2100.2.bi.l.1601.8 | yes | 16 | 35.19 | odd | 6 | ||
2100.2.bi.m.101.1 | yes | 16 | 3.2 | odd | 2 | inner | |
2100.2.bi.m.101.3 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.bi.m.1601.1 | yes | 16 | 7.5 | odd | 6 | inner | |
2100.2.bi.m.1601.3 | yes | 16 | 21.5 | even | 6 | inner | |
2100.2.bo.i.1349.2 | 32 | 105.68 | odd | 12 | |||
2100.2.bo.i.1349.7 | 32 | 35.12 | even | 12 | |||
2100.2.bo.i.1349.10 | 32 | 35.33 | even | 12 | |||
2100.2.bo.i.1349.15 | 32 | 105.47 | odd | 12 | |||
2100.2.bo.i.1949.2 | 32 | 5.2 | odd | 4 | |||
2100.2.bo.i.1949.7 | 32 | 15.8 | even | 4 | |||
2100.2.bo.i.1949.10 | 32 | 15.2 | even | 4 | |||
2100.2.bo.i.1949.15 | 32 | 5.3 | odd | 4 |