Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.2 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.31 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.67507i | − | 1.89156i | −0.324810 | − | 0.945779i | \(-0.605300\pi\) | ||
0.324810 | − | 0.945779i | \(-0.394700\pi\) | |||||||
\(3\) | −1.67043 | −0.964423 | −0.482211 | − | 0.876055i | \(-0.660166\pi\) | ||||
−0.482211 | + | 0.876055i | \(0.660166\pi\) | |||||||
\(4\) | −5.15599 | −2.57799 | ||||||||
\(5\) | − | 2.86564i | − | 1.28155i | −0.767727 | − | 0.640777i | \(-0.778612\pi\) | ||
0.767727 | − | 0.640777i | \(-0.221388\pi\) | |||||||
\(6\) | 4.46851i | 1.82426i | ||||||||
\(7\) | − | 5.21058i | − | 1.96941i | −0.174217 | − | 0.984707i | \(-0.555739\pi\) | ||
0.174217 | − | 0.984707i | \(-0.444261\pi\) | |||||||
\(8\) | 8.44248i | 2.98487i | ||||||||
\(9\) | −0.209666 | −0.0698885 | ||||||||
\(10\) | −7.66579 | −2.42413 | ||||||||
\(11\) | 0.107346i | 0.0323660i | 0.999869 | + | 0.0161830i | \(0.00515143\pi\) | ||||
−0.999869 | + | 0.0161830i | \(0.994849\pi\) | |||||||
\(12\) | 8.61271 | 2.48628 | ||||||||
\(13\) | 3.42522 | + | 1.12598i | 0.949986 | + | 0.312292i | ||||
\(14\) | −13.9387 | −3.72526 | ||||||||
\(15\) | 4.78685i | 1.23596i | ||||||||
\(16\) | 12.2722 | 3.06805 | ||||||||
\(17\) | −1.65501 | −0.401400 | −0.200700 | − | 0.979653i | \(-0.564322\pi\) | ||||
−0.200700 | + | 0.979653i | \(0.564322\pi\) | |||||||
\(18\) | 0.560870i | 0.132198i | ||||||||
\(19\) | − | 2.74920i | − | 0.630710i | −0.948974 | − | 0.315355i | \(-0.897876\pi\) | ||
0.948974 | − | 0.315355i | \(-0.102124\pi\) | |||||||
\(20\) | 14.7752i | 3.30384i | ||||||||
\(21\) | 8.70391i | 1.89935i | ||||||||
\(22\) | 0.287157 | 0.0612221 | ||||||||
\(23\) | 2.05031 | 0.427519 | 0.213760 | − | 0.976886i | \(-0.431429\pi\) | ||||
0.213760 | + | 0.976886i | \(0.431429\pi\) | |||||||
\(24\) | − | 14.1026i | − | 2.87867i | ||||||
\(25\) | −3.21190 | −0.642381 | ||||||||
\(26\) | 3.01208 | − | 9.16271i | 0.590718 | − | 1.79695i | ||||
\(27\) | 5.36152 | 1.03182 | ||||||||
\(28\) | 26.8657i | 5.07714i | ||||||||
\(29\) | 8.54021 | 1.58588 | 0.792939 | − | 0.609302i | \(-0.208550\pi\) | ||||
0.792939 | + | 0.609302i | \(0.208550\pi\) | |||||||
\(30\) | 12.8052 | 2.33789 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | − | 15.9441i | − | 2.81854i | ||||||
\(33\) | − | 0.179314i | − | 0.0312145i | ||||||
\(34\) | 4.42728i | 0.759272i | ||||||||
\(35\) | −14.9317 | −2.52391 | ||||||||
\(36\) | 1.08103 | 0.180172 | ||||||||
\(37\) | 7.15561i | 1.17638i | 0.808724 | + | 0.588188i | \(0.200158\pi\) | ||||
−0.808724 | + | 0.588188i | \(0.799842\pi\) | |||||||
\(38\) | −7.35430 | −1.19302 | ||||||||
\(39\) | −5.72159 | − | 1.88088i | −0.916188 | − | 0.301181i | ||||
\(40\) | 24.1931 | 3.82527 | ||||||||
\(41\) | − | 9.28974i | − | 1.45081i | −0.688320 | − | 0.725407i | \(-0.741652\pi\) | ||
0.688320 | − | 0.725407i | \(-0.258348\pi\) | |||||||
\(42\) | 23.2835 | 3.59273 | ||||||||
\(43\) | −7.32217 | −1.11662 | −0.558311 | − | 0.829632i | \(-0.688550\pi\) | ||||
−0.558311 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(44\) | − | 0.553474i | − | 0.0834393i | ||||||
\(45\) | 0.600827i | 0.0895659i | ||||||||
\(46\) | − | 5.48472i | − | 0.808678i | ||||||
\(47\) | 4.70074i | 0.685674i | 0.939395 | + | 0.342837i | \(0.111388\pi\) | ||||
−0.939395 | + | 0.342837i | \(0.888612\pi\) | |||||||
\(48\) | −20.4999 | −2.95890 | ||||||||
\(49\) | −20.1502 | −2.87859 | ||||||||
\(50\) | 8.59206i | 1.21510i | ||||||||
\(51\) | 2.76459 | 0.387119 | ||||||||
\(52\) | −17.6604 | − | 5.80556i | −2.44906 | − | 0.805086i | ||||
\(53\) | −3.04370 | −0.418084 | −0.209042 | − | 0.977907i | \(-0.567035\pi\) | ||||
−0.209042 | + | 0.977907i | \(0.567035\pi\) | |||||||
\(54\) | − | 14.3424i | − | 1.95176i | ||||||
\(55\) | 0.307615 | 0.0414788 | ||||||||
\(56\) | 43.9902 | 5.87844 | ||||||||
\(57\) | 4.59235i | 0.608271i | ||||||||
\(58\) | − | 22.8456i | − | 2.99978i | ||||||
\(59\) | − | 11.4500i | − | 1.49067i | −0.666692 | − | 0.745333i | \(-0.732290\pi\) | ||
0.666692 | − | 0.745333i | \(-0.267710\pi\) | |||||||
\(60\) | − | 24.6809i | − | 3.18630i | ||||||
\(61\) | −5.46539 | −0.699772 | −0.349886 | − | 0.936792i | \(-0.613780\pi\) | ||||
−0.349886 | + | 0.936792i | \(0.613780\pi\) | |||||||
\(62\) | 2.67507 | 0.339734 | ||||||||
\(63\) | 1.09248i | 0.137640i | ||||||||
\(64\) | −18.1070 | −2.26338 | ||||||||
\(65\) | 3.22667 | − | 9.81547i | 0.400219 | − | 1.21746i | ||||
\(66\) | −0.479676 | −0.0590440 | ||||||||
\(67\) | − | 1.60563i | − | 0.196159i | −0.995179 | − | 0.0980796i | \(-0.968730\pi\) | ||
0.995179 | − | 0.0980796i | \(-0.0312700\pi\) | |||||||
\(68\) | 8.53323 | 1.03481 | ||||||||
\(69\) | −3.42490 | −0.412309 | ||||||||
\(70\) | 39.9432i | 4.77413i | ||||||||
\(71\) | − | 8.50173i | − | 1.00897i | −0.863421 | − | 0.504485i | \(-0.831682\pi\) | ||
0.863421 | − | 0.504485i | \(-0.168318\pi\) | |||||||
\(72\) | − | 1.77010i | − | 0.208608i | ||||||
\(73\) | 6.98159i | 0.817133i | 0.912729 | + | 0.408567i | \(0.133971\pi\) | ||||
−0.912729 | + | 0.408567i | \(0.866029\pi\) | |||||||
\(74\) | 19.1418 | 2.22518 | ||||||||
\(75\) | 5.36526 | 0.619527 | ||||||||
\(76\) | 14.1748i | 1.62597i | ||||||||
\(77\) | 0.559334 | 0.0637420 | ||||||||
\(78\) | −5.03148 | + | 15.3057i | −0.569702 | + | 1.73302i | ||||
\(79\) | −1.90261 | −0.214061 | −0.107030 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107030 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(80\) | − | 35.1678i | − | 3.93188i | ||||||
\(81\) | −8.32704 | −0.925227 | ||||||||
\(82\) | −24.8507 | −2.74430 | ||||||||
\(83\) | − | 9.64608i | − | 1.05880i | −0.848374 | − | 0.529398i | \(-0.822418\pi\) | ||
0.848374 | − | 0.529398i | \(-0.177582\pi\) | |||||||
\(84\) | − | 44.8772i | − | 4.89651i | ||||||
\(85\) | 4.74268i | 0.514416i | ||||||||
\(86\) | 19.5873i | 2.11215i | ||||||||
\(87\) | −14.2658 | −1.52946 | ||||||||
\(88\) | −0.906264 | −0.0966081 | ||||||||
\(89\) | 9.70043i | 1.02824i | 0.857717 | + | 0.514122i | \(0.171882\pi\) | ||||
−0.857717 | + | 0.514122i | \(0.828118\pi\) | |||||||
\(90\) | 1.60725 | 0.169419 | ||||||||
\(91\) | 5.86703 | − | 17.8474i | 0.615032 | − | 1.87092i | ||||
\(92\) | −10.5714 | −1.10214 | ||||||||
\(93\) | − | 1.67043i | − | 0.173215i | ||||||
\(94\) | 12.5748 | 1.29699 | ||||||||
\(95\) | −7.87823 | −0.808289 | ||||||||
\(96\) | 26.6334i | 2.71826i | ||||||||
\(97\) | 14.1790i | 1.43966i | 0.694150 | + | 0.719830i | \(0.255780\pi\) | ||||
−0.694150 | + | 0.719830i | \(0.744220\pi\) | |||||||
\(98\) | 53.9030i | 5.44503i | ||||||||
\(99\) | − | 0.0225067i | − | 0.00226201i | ||||||
\(100\) | 16.5605 | 1.65605 | ||||||||
\(101\) | 3.99013 | 0.397032 | 0.198516 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198516 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(102\) | − | 7.39545i | − | 0.732259i | ||||||
\(103\) | 7.24951 | 0.714316 | 0.357158 | − | 0.934044i | \(-0.383746\pi\) | ||||
0.357158 | + | 0.934044i | \(0.383746\pi\) | |||||||
\(104\) | −9.50610 | + | 28.9174i | −0.932150 | + | 2.83558i | ||||
\(105\) | 24.9423 | 2.43412 | ||||||||
\(106\) | 8.14210i | 0.790830i | ||||||||
\(107\) | 2.56526 | 0.247993 | 0.123997 | − | 0.992283i | \(-0.460429\pi\) | ||||
0.123997 | + | 0.992283i | \(0.460429\pi\) | |||||||
\(108\) | −27.6439 | −2.66004 | ||||||||
\(109\) | 6.50099i | 0.622682i | 0.950298 | + | 0.311341i | \(0.100778\pi\) | ||||
−0.950298 | + | 0.311341i | \(0.899222\pi\) | |||||||
\(110\) | − | 0.822890i | − | 0.0784595i | ||||||
\(111\) | − | 11.9529i | − | 1.13452i | ||||||
\(112\) | − | 63.9454i | − | 6.04227i | ||||||
\(113\) | 6.19260 | 0.582551 | 0.291276 | − | 0.956639i | \(-0.405920\pi\) | ||||
0.291276 | + | 0.956639i | \(0.405920\pi\) | |||||||
\(114\) | 12.2848 | 1.15058 | ||||||||
\(115\) | − | 5.87546i | − | 0.547889i | ||||||
\(116\) | −44.0332 | −4.08838 | ||||||||
\(117\) | −0.718152 | − | 0.236080i | −0.0663931 | − | 0.0218256i | ||||
\(118\) | −30.6296 | −2.81968 | ||||||||
\(119\) | 8.62359i | 0.790523i | ||||||||
\(120\) | −40.4129 | −3.68918 | ||||||||
\(121\) | 10.9885 | 0.998952 | ||||||||
\(122\) | 14.6203i | 1.32366i | ||||||||
\(123\) | 15.5179i | 1.39920i | ||||||||
\(124\) | − | 5.15599i | − | 0.463021i | ||||||
\(125\) | − | 5.12404i | − | 0.458308i | ||||||
\(126\) | 2.92246 | 0.260353 | ||||||||
\(127\) | 4.47662 | 0.397236 | 0.198618 | − | 0.980077i | \(-0.436355\pi\) | ||||
0.198618 | + | 0.980077i | \(0.436355\pi\) | |||||||
\(128\) | 16.5493i | 1.46277i | ||||||||
\(129\) | 12.2312 | 1.07689 | ||||||||
\(130\) | −26.2570 | − | 8.63156i | −2.30289 | − | 0.757038i | ||||
\(131\) | 8.44606 | 0.737935 | 0.368968 | − | 0.929442i | \(-0.379711\pi\) | ||||
0.368968 | + | 0.929442i | \(0.379711\pi\) | |||||||
\(132\) | 0.924538i | 0.0804707i | ||||||||
\(133\) | −14.3249 | −1.24213 | ||||||||
\(134\) | −4.29518 | −0.371047 | ||||||||
\(135\) | − | 15.3642i | − | 1.32234i | ||||||
\(136\) | − | 13.9724i | − | 1.19813i | ||||||
\(137\) | 4.93436i | 0.421571i | 0.977532 | + | 0.210785i | \(0.0676021\pi\) | ||||
−0.977532 | + | 0.210785i | \(0.932398\pi\) | |||||||
\(138\) | 9.16184i | 0.779907i | ||||||||
\(139\) | −9.80769 | −0.831877 | −0.415938 | − | 0.909393i | \(-0.636547\pi\) | ||||
−0.415938 | + | 0.909393i | \(0.636547\pi\) | |||||||
\(140\) | 76.9874 | 6.50663 | ||||||||
\(141\) | − | 7.85226i | − | 0.661280i | ||||||
\(142\) | −22.7427 | −1.90852 | ||||||||
\(143\) | −0.120870 | + | 0.367683i | −0.0101076 | + | 0.0307472i | ||||
\(144\) | −2.57306 | −0.214422 | ||||||||
\(145\) | − | 24.4732i | − | 2.03239i | ||||||
\(146\) | 18.6762 | 1.54565 | ||||||||
\(147\) | 33.6594 | 2.77618 | ||||||||
\(148\) | − | 36.8943i | − | 3.03269i | ||||||
\(149\) | − | 1.24011i | − | 0.101593i | −0.998709 | − | 0.0507967i | \(-0.983824\pi\) | ||
0.998709 | − | 0.0507967i | \(-0.0161760\pi\) | |||||||
\(150\) | − | 14.3524i | − | 1.17187i | ||||||
\(151\) | − | 4.52510i | − | 0.368247i | −0.982903 | − | 0.184124i | \(-0.941055\pi\) | ||
0.982903 | − | 0.184124i | \(-0.0589447\pi\) | |||||||
\(152\) | 23.2101 | 1.88258 | ||||||||
\(153\) | 0.347000 | 0.0280533 | ||||||||
\(154\) | − | 1.49626i | − | 0.120572i | ||||||
\(155\) | 2.86564 | 0.230174 | ||||||||
\(156\) | 29.5005 | + | 9.69778i | 2.36193 | + | 0.776444i | ||||
\(157\) | 7.78510 | 0.621319 | 0.310659 | − | 0.950521i | \(-0.399450\pi\) | ||||
0.310659 | + | 0.950521i | \(0.399450\pi\) | |||||||
\(158\) | 5.08961i | 0.404908i | ||||||||
\(159\) | 5.08428 | 0.403210 | ||||||||
\(160\) | −45.6900 | −3.61211 | ||||||||
\(161\) | − | 10.6833i | − | 0.841963i | ||||||
\(162\) | 22.2754i | 1.75012i | ||||||||
\(163\) | − | 1.90995i | − | 0.149599i | −0.997199 | − | 0.0747995i | \(-0.976168\pi\) | ||
0.997199 | − | 0.0747995i | \(-0.0238317\pi\) | |||||||
\(164\) | 47.8978i | 3.74019i | ||||||||
\(165\) | −0.513849 | −0.0400031 | ||||||||
\(166\) | −25.8039 | −2.00277 | ||||||||
\(167\) | − | 20.1983i | − | 1.56299i | −0.623909 | − | 0.781497i | \(-0.714457\pi\) | ||
0.623909 | − | 0.781497i | \(-0.285543\pi\) | |||||||
\(168\) | −73.4825 | −5.66930 | ||||||||
\(169\) | 10.4643 | + | 7.71350i | 0.804947 | + | 0.593346i | ||||
\(170\) | 12.6870 | 0.973048 | ||||||||
\(171\) | 0.576413i | 0.0440794i | ||||||||
\(172\) | 37.7530 | 2.87864 | ||||||||
\(173\) | −2.87960 | −0.218932 | −0.109466 | − | 0.993991i | \(-0.534914\pi\) | ||||
−0.109466 | + | 0.993991i | \(0.534914\pi\) | |||||||
\(174\) | 38.1620i | 2.89306i | ||||||||
\(175\) | 16.7359i | 1.26511i | ||||||||
\(176\) | 1.31737i | 0.0993006i | ||||||||
\(177\) | 19.1265i | 1.43763i | ||||||||
\(178\) | 25.9493 | 1.94498 | ||||||||
\(179\) | −7.10080 | −0.530739 | −0.265369 | − | 0.964147i | \(-0.585494\pi\) | ||||
−0.265369 | + | 0.964147i | \(0.585494\pi\) | |||||||
\(180\) | − | 3.09785i | − | 0.230900i | ||||||
\(181\) | −12.7730 | −0.949409 | −0.474704 | − | 0.880145i | \(-0.657445\pi\) | ||||
−0.474704 | + | 0.880145i | \(0.657445\pi\) | |||||||
\(182\) | −47.7430 | − | 15.6947i | −3.53895 | − | 1.16337i | ||||
\(183\) | 9.12955 | 0.674876 | ||||||||
\(184\) | 17.3097i | 1.27609i | ||||||||
\(185\) | 20.5054 | 1.50759 | ||||||||
\(186\) | −4.46851 | −0.327647 | ||||||||
\(187\) | − | 0.177659i | − | 0.0129917i | ||||||
\(188\) | − | 24.2370i | − | 1.76766i | ||||||
\(189\) | − | 27.9366i | − | 2.03209i | ||||||
\(190\) | 21.0748i | 1.52893i | ||||||||
\(191\) | −15.1982 | −1.09970 | −0.549850 | − | 0.835263i | \(-0.685315\pi\) | ||||
−0.549850 | + | 0.835263i | \(0.685315\pi\) | |||||||
\(192\) | 30.2465 | 2.18285 | ||||||||
\(193\) | − | 1.93144i | − | 0.139028i | −0.997581 | − | 0.0695142i | \(-0.977855\pi\) | ||
0.997581 | − | 0.0695142i | \(-0.0221449\pi\) | |||||||
\(194\) | 37.9298 | 2.72320 | ||||||||
\(195\) | −5.38992 | + | 16.3960i | −0.385980 | + | 1.17415i | ||||
\(196\) | 103.894 | 7.42100 | ||||||||
\(197\) | 13.6030i | 0.969176i | 0.874742 | + | 0.484588i | \(0.161031\pi\) | ||||
−0.874742 | + | 0.484588i | \(0.838969\pi\) | |||||||
\(198\) | −0.0602070 | −0.00427873 | ||||||||
\(199\) | 11.3269 | 0.802946 | 0.401473 | − | 0.915871i | \(-0.368498\pi\) | ||||
0.401473 | + | 0.915871i | \(0.368498\pi\) | |||||||
\(200\) | − | 27.1164i | − | 1.91742i | ||||||
\(201\) | 2.68210i | 0.189180i | ||||||||
\(202\) | − | 10.6739i | − | 0.751010i | ||||||
\(203\) | − | 44.4995i | − | 3.12325i | ||||||
\(204\) | −14.2542 | −0.997991 | ||||||||
\(205\) | −26.6211 | −1.85930 | ||||||||
\(206\) | − | 19.3929i | − | 1.35117i | ||||||
\(207\) | −0.429880 | −0.0298787 | ||||||||
\(208\) | 42.0351 | + | 13.8183i | 2.91461 | + | 0.958129i | ||||
\(209\) | 0.295115 | 0.0204136 | ||||||||
\(210\) | − | 66.7223i | − | 4.60428i | ||||||
\(211\) | −9.96107 | −0.685749 | −0.342874 | − | 0.939381i | \(-0.611400\pi\) | ||||
−0.342874 | + | 0.939381i | \(0.611400\pi\) | |||||||
\(212\) | 15.6933 | 1.07782 | ||||||||
\(213\) | 14.2015i | 0.973073i | ||||||||
\(214\) | − | 6.86225i | − | 0.469094i | ||||||
\(215\) | 20.9827i | 1.43101i | ||||||||
\(216\) | 45.2645i | 3.07986i | ||||||||
\(217\) | 5.21058 | 0.353717 | ||||||||
\(218\) | 17.3906 | 1.17784 | ||||||||
\(219\) | − | 11.6623i | − | 0.788062i | ||||||
\(220\) | −1.58606 | −0.106932 | ||||||||
\(221\) | −5.66880 | − | 1.86352i | −0.381324 | − | 0.125354i | ||||
\(222\) | −31.9749 | −2.14602 | ||||||||
\(223\) | 17.9002i | 1.19869i | 0.800491 | + | 0.599344i | \(0.204572\pi\) | ||||
−0.800491 | + | 0.599344i | \(0.795428\pi\) | |||||||
\(224\) | −83.0779 | −5.55087 | ||||||||
\(225\) | 0.673426 | 0.0448951 | ||||||||
\(226\) | − | 16.5656i | − | 1.10193i | ||||||
\(227\) | 1.72785i | 0.114681i | 0.998355 | + | 0.0573406i | \(0.0182621\pi\) | ||||
−0.998355 | + | 0.0573406i | \(0.981738\pi\) | |||||||
\(228\) | − | 23.6781i | − | 1.56812i | ||||||
\(229\) | − | 13.4854i | − | 0.891141i | −0.895247 | − | 0.445570i | \(-0.853001\pi\) | ||
0.895247 | − | 0.445570i | \(-0.146999\pi\) | |||||||
\(230\) | −15.7172 | −1.03636 | ||||||||
\(231\) | −0.934328 | −0.0614743 | ||||||||
\(232\) | 72.1005i | 4.73363i | ||||||||
\(233\) | 2.06862 | 0.135520 | 0.0677600 | − | 0.997702i | \(-0.478415\pi\) | ||||
0.0677600 | + | 0.997702i | \(0.478415\pi\) | |||||||
\(234\) | −0.631531 | + | 1.92110i | −0.0412844 | + | 0.125587i | ||||
\(235\) | 13.4706 | 0.878728 | ||||||||
\(236\) | 59.0362i | 3.84293i | ||||||||
\(237\) | 3.17818 | 0.206445 | ||||||||
\(238\) | 23.0687 | 1.49532 | ||||||||
\(239\) | − | 14.7921i | − | 0.956823i | −0.878136 | − | 0.478411i | \(-0.841213\pi\) | ||
0.878136 | − | 0.478411i | \(-0.158787\pi\) | |||||||
\(240\) | 58.7453i | 3.79199i | ||||||||
\(241\) | 19.9764i | 1.28679i | 0.765532 | + | 0.643397i | \(0.222476\pi\) | ||||
−0.765532 | + | 0.643397i | \(0.777524\pi\) | |||||||
\(242\) | − | 29.3949i | − | 1.88958i | ||||||
\(243\) | −2.17482 | −0.139515 | ||||||||
\(244\) | 28.1795 | 1.80401 | ||||||||
\(245\) | 57.7431i | 3.68907i | ||||||||
\(246\) | 41.5113 | 2.64666 | ||||||||
\(247\) | 3.09556 | − | 9.41663i | 0.196966 | − | 0.599166i | ||||
\(248\) | −8.44248 | −0.536098 | ||||||||
\(249\) | 16.1131i | 1.02113i | ||||||||
\(250\) | −13.7072 | −0.866917 | ||||||||
\(251\) | −4.64690 | −0.293310 | −0.146655 | − | 0.989188i | \(-0.546851\pi\) | ||||
−0.146655 | + | 0.989188i | \(0.546851\pi\) | |||||||
\(252\) | − | 5.63281i | − | 0.354834i | ||||||
\(253\) | 0.220092i | 0.0138371i | ||||||||
\(254\) | − | 11.9753i | − | 0.751394i | ||||||
\(255\) | − | 7.92231i | − | 0.496114i | ||||||
\(256\) | 8.05659 | 0.503537 | ||||||||
\(257\) | 9.54021 | 0.595102 | 0.297551 | − | 0.954706i | \(-0.403830\pi\) | ||||
0.297551 | + | 0.954706i | \(0.403830\pi\) | |||||||
\(258\) | − | 32.7192i | − | 2.03701i | ||||||
\(259\) | 37.2849 | 2.31677 | ||||||||
\(260\) | −16.6367 | + | 50.6084i | −1.03176 | + | 3.13860i | ||||
\(261\) | −1.79059 | −0.110835 | ||||||||
\(262\) | − | 22.5938i | − | 1.39585i | ||||||
\(263\) | −14.4929 | −0.893672 | −0.446836 | − | 0.894616i | \(-0.647449\pi\) | ||||
−0.446836 | + | 0.894616i | \(0.647449\pi\) | |||||||
\(264\) | 1.51385 | 0.0931711 | ||||||||
\(265\) | 8.72215i | 0.535797i | ||||||||
\(266\) | 38.3202i | 2.34956i | ||||||||
\(267\) | − | 16.2039i | − | 0.991662i | ||||||
\(268\) | 8.27862i | 0.505697i | ||||||||
\(269\) | 27.3814 | 1.66947 | 0.834737 | − | 0.550648i | \(-0.185619\pi\) | ||||
0.834737 | + | 0.550648i | \(0.185619\pi\) | |||||||
\(270\) | −41.1003 | −2.50128 | ||||||||
\(271\) | 13.3239i | 0.809367i | 0.914457 | + | 0.404683i | \(0.132618\pi\) | ||||
−0.914457 | + | 0.404683i | \(0.867382\pi\) | |||||||
\(272\) | −20.3107 | −1.23152 | ||||||||
\(273\) | −9.80047 | + | 29.8128i | −0.593151 | + | 1.80435i | ||||
\(274\) | 13.1997 | 0.797426 | ||||||||
\(275\) | − | 0.344785i | − | 0.0207913i | ||||||
\(276\) | 17.6587 | 1.06293 | ||||||||
\(277\) | −30.1947 | −1.81422 | −0.907112 | − | 0.420890i | \(-0.861718\pi\) | ||||
−0.907112 | + | 0.420890i | \(0.861718\pi\) | |||||||
\(278\) | 26.2362i | 1.57354i | ||||||||
\(279\) | − | 0.209666i | − | 0.0125524i | ||||||
\(280\) | − | 126.060i | − | 7.53354i | ||||||
\(281\) | − | 8.84908i | − | 0.527892i | −0.964537 | − | 0.263946i | \(-0.914976\pi\) | ||
0.964537 | − | 0.263946i | \(-0.0850241\pi\) | |||||||
\(282\) | −21.0053 | −1.25085 | ||||||||
\(283\) | −3.32142 | −0.197438 | −0.0987190 | − | 0.995115i | \(-0.531474\pi\) | ||||
−0.0987190 | + | 0.995115i | \(0.531474\pi\) | |||||||
\(284\) | 43.8348i | 2.60112i | ||||||||
\(285\) | 13.1600 | 0.779532 | ||||||||
\(286\) | 0.983578 | + | 0.323335i | 0.0581602 | + | 0.0191192i | ||||
\(287\) | −48.4049 | −2.85725 | ||||||||
\(288\) | 3.34292i | 0.196984i | ||||||||
\(289\) | −14.2609 | −0.838878 | ||||||||
\(290\) | −65.4674 | −3.84438 | ||||||||
\(291\) | − | 23.6850i | − | 1.38844i | ||||||
\(292\) | − | 35.9970i | − | 2.10656i | ||||||
\(293\) | − | 24.8920i | − | 1.45420i | −0.686529 | − | 0.727102i | \(-0.740867\pi\) | ||
0.686529 | − | 0.727102i | \(-0.259133\pi\) | |||||||
\(294\) | − | 90.0412i | − | 5.25131i | ||||||
\(295\) | −32.8117 | −1.91037 | ||||||||
\(296\) | −60.4111 | −3.51132 | ||||||||
\(297\) | 0.575537i | 0.0333960i | ||||||||
\(298\) | −3.31736 | −0.192170 | ||||||||
\(299\) | 7.02277 | + | 2.30862i | 0.406137 | + | 0.133511i | ||||
\(300\) | −27.6632 | −1.59714 | ||||||||
\(301\) | 38.1528i | 2.19909i | ||||||||
\(302\) | −12.1049 | −0.696561 | ||||||||
\(303\) | −6.66522 | −0.382907 | ||||||||
\(304\) | − | 33.7388i | − | 1.93505i | ||||||
\(305\) | 15.6619i | 0.896796i | ||||||||
\(306\) | − | 0.928247i | − | 0.0530644i | ||||||
\(307\) | − | 4.47896i | − | 0.255628i | −0.991798 | − | 0.127814i | \(-0.959204\pi\) | ||
0.991798 | − | 0.127814i | \(-0.0407960\pi\) | |||||||
\(308\) | −2.88392 | −0.164327 | ||||||||
\(309\) | −12.1098 | −0.688902 | ||||||||
\(310\) | − | 7.66579i | − | 0.435387i | ||||||
\(311\) | 24.8980 | 1.41184 | 0.705918 | − | 0.708294i | \(-0.250535\pi\) | ||||
0.705918 | + | 0.708294i | \(0.250535\pi\) | |||||||
\(312\) | 15.8793 | − | 48.3044i | 0.898986 | − | 2.73470i | ||||
\(313\) | 21.0469 | 1.18964 | 0.594819 | − | 0.803860i | \(-0.297224\pi\) | ||||
0.594819 | + | 0.803860i | \(0.297224\pi\) | |||||||
\(314\) | − | 20.8257i | − | 1.17526i | ||||||
\(315\) | 3.13066 | 0.176392 | ||||||||
\(316\) | 9.80984 | 0.551847 | ||||||||
\(317\) | − | 8.99093i | − | 0.504981i | −0.967599 | − | 0.252491i | \(-0.918750\pi\) | ||
0.967599 | − | 0.252491i | \(-0.0812497\pi\) | |||||||
\(318\) | − | 13.6008i | − | 0.762695i | ||||||
\(319\) | 0.916756i | 0.0513285i | ||||||||
\(320\) | 51.8882i | 2.90064i | ||||||||
\(321\) | −4.28509 | −0.239170 | ||||||||
\(322\) | −28.5786 | −1.59262 | ||||||||
\(323\) | 4.54997i | 0.253167i | ||||||||
\(324\) | 42.9341 | 2.38523 | ||||||||
\(325\) | −11.0015 | − | 3.61656i | −0.610253 | − | 0.200610i | ||||
\(326\) | −5.10925 | −0.282975 | ||||||||
\(327\) | − | 10.8594i | − | 0.600529i | ||||||
\(328\) | 78.4284 | 4.33048 | ||||||||
\(329\) | 24.4936 | 1.35038 | ||||||||
\(330\) | 1.37458i | 0.0756681i | ||||||||
\(331\) | − | 9.36893i | − | 0.514963i | −0.966283 | − | 0.257482i | \(-0.917107\pi\) | ||
0.966283 | − | 0.257482i | \(-0.0828926\pi\) | |||||||
\(332\) | 49.7351i | 2.72957i | ||||||||
\(333\) | − | 1.50029i | − | 0.0822152i | ||||||
\(334\) | −54.0319 | −2.95649 | ||||||||
\(335\) | −4.60117 | −0.251389 | ||||||||
\(336\) | 106.816i | 5.82731i | ||||||||
\(337\) | −20.3475 | −1.10840 | −0.554199 | − | 0.832384i | \(-0.686975\pi\) | ||||
−0.554199 | + | 0.832384i | \(0.686975\pi\) | |||||||
\(338\) | 20.6341 | − | 27.9928i | 1.12235 | − | 1.52261i | ||||
\(339\) | −10.3443 | −0.561826 | ||||||||
\(340\) | − | 24.4532i | − | 1.32616i | ||||||
\(341\) | −0.107346 | −0.00581310 | ||||||||
\(342\) | 1.54194 | 0.0833788 | ||||||||
\(343\) | 68.5200i | 3.69973i | ||||||||
\(344\) | − | 61.8173i | − | 3.33296i | ||||||
\(345\) | 9.81454i | 0.528397i | ||||||||
\(346\) | 7.70312i | 0.414122i | ||||||||
\(347\) | −12.1586 | −0.652709 | −0.326354 | − | 0.945248i | \(-0.605820\pi\) | ||||
−0.326354 | + | 0.945248i | \(0.605820\pi\) | |||||||
\(348\) | 73.5544 | 3.94293 | ||||||||
\(349\) | − | 30.9550i | − | 1.65698i | −0.560000 | − | 0.828492i | \(-0.689199\pi\) | ||
0.560000 | − | 0.828492i | \(-0.310801\pi\) | |||||||
\(350\) | 44.7696 | 2.39304 | ||||||||
\(351\) | 18.3644 | + | 6.03699i | 0.980219 | + | 0.322231i | ||||
\(352\) | 1.71153 | 0.0912248 | ||||||||
\(353\) | − | 5.94598i | − | 0.316472i | −0.987401 | − | 0.158236i | \(-0.949419\pi\) | ||
0.987401 | − | 0.158236i | \(-0.0505808\pi\) | |||||||
\(354\) | 51.1646 | 2.71937 | ||||||||
\(355\) | −24.3629 | −1.29305 | ||||||||
\(356\) | − | 50.0153i | − | 2.65081i | ||||||
\(357\) | − | 14.4051i | − | 0.762399i | ||||||
\(358\) | 18.9951i | 1.00392i | ||||||||
\(359\) | 29.5605i | 1.56014i | 0.625690 | + | 0.780072i | \(0.284818\pi\) | ||||
−0.625690 | + | 0.780072i | \(0.715182\pi\) | |||||||
\(360\) | −5.07246 | −0.267342 | ||||||||
\(361\) | 11.4419 | 0.602205 | ||||||||
\(362\) | 34.1686i | 1.79586i | ||||||||
\(363\) | −18.3555 | −0.963413 | ||||||||
\(364\) | −30.2503 | + | 92.0210i | −1.58555 | + | 4.82321i | ||||
\(365\) | 20.0067 | 1.04720 | ||||||||
\(366\) | − | 24.4222i | − | 1.27657i | ||||||
\(367\) | 26.1640 | 1.36575 | 0.682874 | − | 0.730536i | \(-0.260730\pi\) | ||||
0.682874 | + | 0.730536i | \(0.260730\pi\) | |||||||
\(368\) | 25.1619 | 1.31165 | ||||||||
\(369\) | 1.94774i | 0.101395i | ||||||||
\(370\) | − | 54.8534i | − | 2.85169i | ||||||
\(371\) | 15.8594i | 0.823381i | ||||||||
\(372\) | 8.61271i | 0.446548i | ||||||||
\(373\) | 8.69976 | 0.450456 | 0.225228 | − | 0.974306i | \(-0.427687\pi\) | ||||
0.225228 | + | 0.974306i | \(0.427687\pi\) | |||||||
\(374\) | −0.475250 | −0.0245746 | ||||||||
\(375\) | 8.55935i | 0.442003i | ||||||||
\(376\) | −39.6859 | −2.04664 | ||||||||
\(377\) | 29.2521 | + | 9.61614i | 1.50656 | + | 0.495257i | ||||
\(378\) | −74.7324 | −3.84382 | ||||||||
\(379\) | − | 22.2845i | − | 1.14468i | −0.820018 | − | 0.572338i | \(-0.806037\pi\) | ||
0.820018 | − | 0.572338i | \(-0.193963\pi\) | |||||||
\(380\) | 40.6200 | 2.08376 | ||||||||
\(381\) | −7.47788 | −0.383103 | ||||||||
\(382\) | 40.6561i | 2.08015i | ||||||||
\(383\) | 21.8948i | 1.11877i | 0.828907 | + | 0.559387i | \(0.188963\pi\) | ||||
−0.828907 | + | 0.559387i | \(0.811037\pi\) | |||||||
\(384\) | − | 27.6445i | − | 1.41073i | ||||||
\(385\) | − | 1.60285i | − | 0.0816889i | ||||||
\(386\) | −5.16674 | −0.262980 | ||||||||
\(387\) | 1.53521 | 0.0780390 | ||||||||
\(388\) | − | 73.1068i | − | 3.71143i | ||||||
\(389\) | 18.6807 | 0.947150 | 0.473575 | − | 0.880754i | \(-0.342963\pi\) | ||||
0.473575 | + | 0.880754i | \(0.342963\pi\) | |||||||
\(390\) | 43.8605 | + | 14.4184i | 2.22096 | + | 0.730104i | ||||
\(391\) | −3.39329 | −0.171606 | ||||||||
\(392\) | − | 170.117i | − | 8.59222i | ||||||
\(393\) | −14.1085 | −0.711682 | ||||||||
\(394\) | 36.3891 | 1.83325 | ||||||||
\(395\) | 5.45220i | 0.274330i | ||||||||
\(396\) | 0.116044i | 0.00583145i | ||||||||
\(397\) | − | 2.50967i | − | 0.125957i | −0.998015 | − | 0.0629783i | \(-0.979940\pi\) | ||
0.998015 | − | 0.0629783i | \(-0.0200599\pi\) | |||||||
\(398\) | − | 30.3003i | − | 1.51882i | ||||||
\(399\) | 23.9288 | 1.19794 | ||||||||
\(400\) | −39.4172 | −1.97086 | ||||||||
\(401\) | − | 1.92212i | − | 0.0959861i | −0.998848 | − | 0.0479930i | \(-0.984717\pi\) | ||
0.998848 | − | 0.0479930i | \(-0.0152825\pi\) | |||||||
\(402\) | 7.17479 | 0.357846 | ||||||||
\(403\) | −1.12598 | + | 3.42522i | −0.0560893 | + | 0.170623i | ||||
\(404\) | −20.5730 | −1.02355 | ||||||||
\(405\) | 23.8623i | 1.18573i | ||||||||
\(406\) | −119.039 | −5.90781 | ||||||||
\(407\) | −0.768125 | −0.0380746 | ||||||||
\(408\) | 23.3399i | 1.15550i | ||||||||
\(409\) | − | 31.4091i | − | 1.55308i | −0.630068 | − | 0.776540i | \(-0.716973\pi\) | ||
0.630068 | − | 0.776540i | \(-0.283027\pi\) | |||||||
\(410\) | 71.2132i | 3.51697i | ||||||||
\(411\) | − | 8.24250i | − | 0.406572i | ||||||
\(412\) | −37.3784 | −1.84150 | ||||||||
\(413\) | −59.6613 | −2.93574 | ||||||||
\(414\) | 1.14996i | 0.0565173i | ||||||||
\(415\) | −27.6422 | −1.35690 | ||||||||
\(416\) | 17.9528 | − | 54.6120i | 0.880207 | − | 2.67757i | ||||
\(417\) | 16.3830 | 0.802281 | ||||||||
\(418\) | − | 0.789453i | − | 0.0386134i | ||||||
\(419\) | 30.6922 | 1.49941 | 0.749707 | − | 0.661770i | \(-0.230195\pi\) | ||||
0.749707 | + | 0.661770i | \(0.230195\pi\) | |||||||
\(420\) | −128.602 | −6.27514 | ||||||||
\(421\) | − | 39.9412i | − | 1.94662i | −0.229504 | − | 0.973308i | \(-0.573710\pi\) | ||
0.229504 | − | 0.973308i | \(-0.426290\pi\) | |||||||
\(422\) | 26.6465i | 1.29713i | ||||||||
\(423\) | − | 0.985584i | − | 0.0479207i | ||||||
\(424\) | − | 25.6963i | − | 1.24792i | ||||||
\(425\) | 5.31575 | 0.257852 | ||||||||
\(426\) | 37.9901 | 1.84062 | ||||||||
\(427\) | 28.4779i | 1.37814i | ||||||||
\(428\) | −13.2265 | −0.639325 | ||||||||
\(429\) | 0.201904 | − | 0.614189i | 0.00974804 | − | 0.0296533i | ||||
\(430\) | 56.1302 | 2.70684 | ||||||||
\(431\) | − | 16.2333i | − | 0.781931i | −0.920405 | − | 0.390966i | \(-0.872141\pi\) | ||
0.920405 | − | 0.390966i | \(-0.127859\pi\) | |||||||
\(432\) | 65.7978 | 3.16570 | ||||||||
\(433\) | 31.2313 | 1.50088 | 0.750439 | − | 0.660939i | \(-0.229842\pi\) | ||||
0.750439 | + | 0.660939i | \(0.229842\pi\) | |||||||
\(434\) | − | 13.9387i | − | 0.669077i | ||||||
\(435\) | 40.8807i | 1.96008i | ||||||||
\(436\) | − | 33.5190i | − | 1.60527i | ||||||
\(437\) | − | 5.63672i | − | 0.269641i | ||||||
\(438\) | −31.1973 | −1.49066 | ||||||||
\(439\) | 8.10748 | 0.386949 | 0.193475 | − | 0.981105i | \(-0.438024\pi\) | ||||
0.193475 | + | 0.981105i | \(0.438024\pi\) | |||||||
\(440\) | 2.59703i | 0.123809i | ||||||||
\(441\) | 4.22480 | 0.201181 | ||||||||
\(442\) | −4.98504 | + | 15.1644i | −0.237114 | + | 0.721297i | ||||
\(443\) | −1.90009 | −0.0902762 | −0.0451381 | − | 0.998981i | \(-0.514373\pi\) | ||||
−0.0451381 | + | 0.998981i | \(0.514373\pi\) | |||||||
\(444\) | 61.6292i | 2.92479i | ||||||||
\(445\) | 27.7980 | 1.31775 | ||||||||
\(446\) | 47.8843 | 2.26739 | ||||||||
\(447\) | 2.07151i | 0.0979790i | ||||||||
\(448\) | 94.3481i | 4.45753i | ||||||||
\(449\) | 7.08178i | 0.334210i | 0.985939 | + | 0.167105i | \(0.0534419\pi\) | ||||
−0.985939 | + | 0.167105i | \(0.946558\pi\) | |||||||
\(450\) | − | 1.80146i | − | 0.0849216i | ||||||
\(451\) | 0.997215 | 0.0469570 | ||||||||
\(452\) | −31.9290 | −1.50181 | ||||||||
\(453\) | 7.55885i | 0.355146i | ||||||||
\(454\) | 4.62210 | 0.216926 | ||||||||
\(455\) | −51.1443 | − | 16.8128i | −2.39768 | − | 0.788197i | ||||
\(456\) | −38.7708 | −1.81561 | ||||||||
\(457\) | − | 3.80707i | − | 0.178087i | −0.996028 | − | 0.0890437i | \(-0.971619\pi\) | ||
0.996028 | − | 0.0890437i | \(-0.0283811\pi\) | |||||||
\(458\) | −36.0744 | −1.68565 | ||||||||
\(459\) | −8.87339 | −0.414175 | ||||||||
\(460\) | 30.2938i | 1.41245i | ||||||||
\(461\) | − | 4.09587i | − | 0.190764i | −0.995441 | − | 0.0953818i | \(-0.969593\pi\) | ||
0.995441 | − | 0.0953818i | \(-0.0304072\pi\) | |||||||
\(462\) | 2.49939i | 0.116282i | ||||||||
\(463\) | 23.3795i | 1.08654i | 0.839559 | + | 0.543269i | \(0.182814\pi\) | ||||
−0.839559 | + | 0.543269i | \(0.817186\pi\) | |||||||
\(464\) | 104.807 | 4.86556 | ||||||||
\(465\) | −4.78685 | −0.221985 | ||||||||
\(466\) | − | 5.53371i | − | 0.256344i | ||||||
\(467\) | 12.5818 | 0.582217 | 0.291108 | − | 0.956690i | \(-0.405976\pi\) | ||||
0.291108 | + | 0.956690i | \(0.405976\pi\) | |||||||
\(468\) | 3.70278 | + | 1.21723i | 0.171161 | + | 0.0562663i | ||||
\(469\) | −8.36628 | −0.386319 | ||||||||
\(470\) | − | 36.0349i | − | 1.66217i | ||||||
\(471\) | −13.0045 | −0.599214 | ||||||||
\(472\) | 96.6666 | 4.44944 | ||||||||
\(473\) | − | 0.786005i | − | 0.0361405i | ||||||
\(474\) | − | 8.50184i | − | 0.390502i | ||||||
\(475\) | 8.83017i | 0.405156i | ||||||||
\(476\) | − | 44.4631i | − | 2.03796i | ||||||
\(477\) | 0.638159 | 0.0292193 | ||||||||
\(478\) | −39.5699 | −1.80989 | ||||||||
\(479\) | − | 22.2197i | − | 1.01524i | −0.861581 | − | 0.507621i | \(-0.830525\pi\) | ||
0.861581 | − | 0.507621i | \(-0.169475\pi\) | |||||||
\(480\) | 76.3219 | 3.48360 | ||||||||
\(481\) | −8.05711 | + | 24.5096i | −0.367373 | + | 1.11754i | ||||
\(482\) | 53.4383 | 2.43405 | ||||||||
\(483\) | 17.8457i | 0.812008i | ||||||||
\(484\) | −56.6564 | −2.57529 | ||||||||
\(485\) | 40.6320 | 1.84500 | ||||||||
\(486\) | 5.81779i | 0.263900i | ||||||||
\(487\) | − | 10.4466i | − | 0.473381i | −0.971585 | − | 0.236691i | \(-0.923937\pi\) | ||
0.971585 | − | 0.236691i | \(-0.0760628\pi\) | |||||||
\(488\) | − | 46.1415i | − | 2.08873i | ||||||
\(489\) | 3.19044i | 0.144277i | ||||||||
\(490\) | 154.467 | 6.97810 | ||||||||
\(491\) | −30.7514 | −1.38779 | −0.693895 | − | 0.720076i | \(-0.744107\pi\) | ||||
−0.693895 | + | 0.720076i | \(0.744107\pi\) | |||||||
\(492\) | − | 80.0098i | − | 3.60712i | ||||||
\(493\) | −14.1342 | −0.636571 | ||||||||
\(494\) | −25.1901 | − | 8.28083i | −1.13336 | − | 0.372572i | ||||
\(495\) | −0.0644962 | −0.00289889 | ||||||||
\(496\) | 12.2722i | 0.551039i | ||||||||
\(497\) | −44.2989 | −1.98708 | ||||||||
\(498\) | 43.1036 | 1.93152 | ||||||||
\(499\) | − | 39.9257i | − | 1.78732i | −0.448747 | − | 0.893659i | \(-0.648129\pi\) | ||
0.448747 | − | 0.893659i | \(-0.351871\pi\) | |||||||
\(500\) | 26.4195i | 1.18152i | ||||||||
\(501\) | 33.7399i | 1.50739i | ||||||||
\(502\) | 12.4308i | 0.554812i | ||||||||
\(503\) | −37.8842 | −1.68917 | −0.844586 | − | 0.535420i | \(-0.820153\pi\) | ||||
−0.844586 | + | 0.535420i | \(0.820153\pi\) | |||||||
\(504\) | −9.22323 | −0.410835 | ||||||||
\(505\) | − | 11.4343i | − | 0.508819i | ||||||
\(506\) | 0.588762 | 0.0261737 | ||||||||
\(507\) | −17.4799 | − | 12.8849i | −0.776310 | − | 0.572237i | ||||
\(508\) | −23.0814 | −1.02407 | ||||||||
\(509\) | 1.38770i | 0.0615089i | 0.999527 | + | 0.0307544i | \(0.00979098\pi\) | ||||
−0.999527 | + | 0.0307544i | \(0.990209\pi\) | |||||||
\(510\) | −21.1927 | −0.938429 | ||||||||
\(511\) | 36.3781 | 1.60927 | ||||||||
\(512\) | 11.5468i | 0.510299i | ||||||||
\(513\) | − | 14.7399i | − | 0.650782i | ||||||
\(514\) | − | 25.5207i | − | 1.12567i | ||||||
\(515\) | − | 20.7745i | − | 0.915434i | ||||||
\(516\) | −63.0638 | −2.77623 | ||||||||
\(517\) | −0.504605 | −0.0221925 | ||||||||
\(518\) | − | 99.7397i | − | 4.38231i | ||||||
\(519\) | 4.81016 | 0.211143 | ||||||||
\(520\) | 82.8668 | + | 27.2411i | 3.63395 | + | 1.19460i | ||||
\(521\) | 17.5495 | 0.768857 | 0.384428 | − | 0.923155i | \(-0.374399\pi\) | ||||
0.384428 | + | 0.923155i | \(0.374399\pi\) | |||||||
\(522\) | 4.78994i | 0.209650i | ||||||||
\(523\) | −14.5271 | −0.635224 | −0.317612 | − | 0.948221i | \(-0.602881\pi\) | ||||
−0.317612 | + | 0.948221i | \(0.602881\pi\) | |||||||
\(524\) | −43.5478 | −1.90239 | ||||||||
\(525\) | − | 27.9561i | − | 1.22011i | ||||||
\(526\) | 38.7695i | 1.69043i | ||||||||
\(527\) | − | 1.65501i | − | 0.0720936i | ||||||
\(528\) | − | 2.20058i | − | 0.0957678i | ||||||
\(529\) | −18.7962 | −0.817227 | ||||||||
\(530\) | 23.3323 | 1.01349 | ||||||||
\(531\) | 2.40068i | 0.104180i | ||||||||
\(532\) | 73.8592 | 3.20220 | ||||||||
\(533\) | 10.4601 | − | 31.8194i | 0.453077 | − | 1.37825i | ||||
\(534\) | −43.3465 | −1.87579 | ||||||||
\(535\) | − | 7.35112i | − | 0.317817i | ||||||
\(536\) | 13.5555 | 0.585509 | ||||||||
\(537\) | 11.8614 | 0.511857 | ||||||||
\(538\) | − | 73.2471i | − | 3.15791i | ||||||
\(539\) | − | 2.16304i | − | 0.0931685i | ||||||
\(540\) | 79.2176i | 3.40898i | ||||||||
\(541\) | 29.8000i | 1.28120i | 0.767875 | + | 0.640600i | \(0.221314\pi\) | ||||
−0.767875 | + | 0.640600i | \(0.778686\pi\) | |||||||
\(542\) | 35.6422 | 1.53096 | ||||||||
\(543\) | 21.3364 | 0.915632 | ||||||||
\(544\) | 26.3877i | 1.13136i | ||||||||
\(545\) | 18.6295 | 0.798001 | ||||||||
\(546\) | 79.7513 | + | 26.2169i | 3.41304 | + | 1.12198i | ||||
\(547\) | −22.7158 | −0.971256 | −0.485628 | − | 0.874166i | \(-0.661409\pi\) | ||||
−0.485628 | + | 0.874166i | \(0.661409\pi\) | |||||||
\(548\) | − | 25.4415i | − | 1.08681i | ||||||
\(549\) | 1.14591 | 0.0489060 | ||||||||
\(550\) | −0.922322 | −0.0393279 | ||||||||
\(551\) | − | 23.4788i | − | 1.00023i | ||||||
\(552\) | − | 28.9146i | − | 1.23069i | ||||||
\(553\) | 9.91371i | 0.421574i | ||||||||
\(554\) | 80.7728i | 3.43171i | ||||||||
\(555\) | −34.2529 | −1.45395 | ||||||||
\(556\) | 50.5683 | 2.14457 | ||||||||
\(557\) | − | 12.5422i | − | 0.531428i | −0.964052 | − | 0.265714i | \(-0.914392\pi\) | ||
0.964052 | − | 0.265714i | \(-0.0856077\pi\) | |||||||
\(558\) | −0.560870 | −0.0237435 | ||||||||
\(559\) | −25.0801 | − | 8.24466i | −1.06077 | − | 0.348712i | ||||
\(560\) | −183.245 | −7.74350 | ||||||||
\(561\) | 0.296767i | 0.0125295i | ||||||||
\(562\) | −23.6719 | −0.998538 | ||||||||
\(563\) | 2.74698 | 0.115771 | 0.0578857 | − | 0.998323i | \(-0.481564\pi\) | ||||
0.0578857 | + | 0.998323i | \(0.481564\pi\) | |||||||
\(564\) | 40.4861i | 1.70477i | ||||||||
\(565\) | − | 17.7458i | − | 0.746571i | ||||||
\(566\) | 8.88502i | 0.373465i | ||||||||
\(567\) | 43.3887i | 1.82216i | ||||||||
\(568\) | 71.7756 | 3.01164 | ||||||||
\(569\) | −5.85158 | −0.245311 | −0.122655 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122655 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(570\) | − | 35.2039i | − | 1.47453i | ||||||
\(571\) | 7.17387 | 0.300217 | 0.150109 | − | 0.988670i | \(-0.452038\pi\) | ||||
0.150109 | + | 0.988670i | \(0.452038\pi\) | |||||||
\(572\) | 0.623203 | − | 1.89577i | 0.0260574 | − | 0.0792662i | ||||
\(573\) | 25.3874 | 1.06058 | ||||||||
\(574\) | 129.486i | 5.40466i | ||||||||
\(575\) | −6.58540 | −0.274630 | ||||||||
\(576\) | 3.79642 | 0.158184 | ||||||||
\(577\) | 11.4043i | 0.474768i | 0.971416 | + | 0.237384i | \(0.0762899\pi\) | ||||
−0.971416 | + | 0.237384i | \(0.923710\pi\) | |||||||
\(578\) | 38.1489i | 1.58679i | ||||||||
\(579\) | 3.22634i | 0.134082i | ||||||||
\(580\) | 126.183i | 5.23948i | ||||||||
\(581\) | −50.2617 | −2.08521 | ||||||||
\(582\) | −63.3590 | −2.62632 | ||||||||
\(583\) | − | 0.326728i | − | 0.0135317i | ||||||
\(584\) | −58.9419 | −2.43903 | ||||||||
\(585\) | −0.676522 | + | 2.05797i | −0.0279707 | + | 0.0850864i | ||||
\(586\) | −66.5877 | −2.75071 | ||||||||
\(587\) | − | 26.0267i | − | 1.07424i | −0.843507 | − | 0.537119i | \(-0.819513\pi\) | ||
0.843507 | − | 0.537119i | \(-0.180487\pi\) | |||||||
\(588\) | −173.547 | −7.15698 | ||||||||
\(589\) | 2.74920 | 0.113279 | ||||||||
\(590\) | 87.7734i | 3.61358i | ||||||||
\(591\) | − | 22.7229i | − | 0.934696i | ||||||
\(592\) | 87.8153i | 3.60919i | ||||||||
\(593\) | − | 32.6622i | − | 1.34128i | −0.741785 | − | 0.670638i | \(-0.766020\pi\) | ||
0.741785 | − | 0.670638i | \(-0.233980\pi\) | |||||||
\(594\) | 1.53960 | 0.0631705 | ||||||||
\(595\) | 24.7121 | 1.01310 | ||||||||
\(596\) | 6.39396i | 0.261907i | ||||||||
\(597\) | −18.9209 | −0.774379 | ||||||||
\(598\) | 6.17571 | − | 18.7864i | 0.252544 | − | 0.768233i | ||||
\(599\) | −39.3376 | −1.60729 | −0.803646 | − | 0.595108i | \(-0.797109\pi\) | ||||
−0.803646 | + | 0.595108i | \(0.797109\pi\) | |||||||
\(600\) | 45.2961i | 1.84920i | ||||||||
\(601\) | −41.5732 | −1.69580 | −0.847902 | − | 0.530153i | \(-0.822135\pi\) | ||||
−0.847902 | + | 0.530153i | \(0.822135\pi\) | |||||||
\(602\) | 102.061 | 4.15971 | ||||||||
\(603\) | 0.336646i | 0.0137093i | ||||||||
\(604\) | 23.3313i | 0.949339i | ||||||||
\(605\) | − | 31.4890i | − | 1.28021i | ||||||
\(606\) | 17.8299i | 0.724291i | ||||||||
\(607\) | 8.85069 | 0.359238 | 0.179619 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179619 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(608\) | −43.8334 | −1.77768 | ||||||||
\(609\) | 74.3332i | 3.01213i | ||||||||
\(610\) | 41.8965 | 1.69634 | ||||||||
\(611\) | −5.29296 | + | 16.1011i | −0.214130 | + | 0.651381i | ||||
\(612\) | −1.78913 | −0.0723211 | ||||||||
\(613\) | − | 7.46986i | − | 0.301705i | −0.988556 | − | 0.150852i | \(-0.951798\pi\) | ||
0.988556 | − | 0.150852i | \(-0.0482018\pi\) | |||||||
\(614\) | −11.9815 | −0.483535 | ||||||||
\(615\) | 44.4686 | 1.79315 | ||||||||
\(616\) | 4.72216i | 0.190261i | ||||||||
\(617\) | 29.5623i | 1.19013i | 0.803676 | + | 0.595067i | \(0.202875\pi\) | ||||
−0.803676 | + | 0.595067i | \(0.797125\pi\) | |||||||
\(618\) | 32.3945i | 1.30310i | ||||||||
\(619\) | 32.6410i | 1.31195i | 0.754782 | + | 0.655976i | \(0.227743\pi\) | ||||
−0.754782 | + | 0.655976i | \(0.772257\pi\) | |||||||
\(620\) | −14.7752 | −0.593387 | ||||||||
\(621\) | 10.9928 | 0.441125 | ||||||||
\(622\) | − | 66.6038i | − | 2.67057i | ||||||
\(623\) | 50.5449 | 2.02504 | ||||||||
\(624\) | −70.2167 | − | 23.0825i | −2.81092 | − | 0.924041i | ||||
\(625\) | −30.7432 | −1.22973 | ||||||||
\(626\) | − | 56.3017i | − | 2.25027i | ||||||
\(627\) | −0.492969 | −0.0196873 | ||||||||
\(628\) | −40.1399 | −1.60176 | ||||||||
\(629\) | − | 11.8426i | − | 0.472197i | ||||||
\(630\) | − | 8.37472i | − | 0.333657i | ||||||
\(631\) | − | 1.13759i | − | 0.0452869i | −0.999744 | − | 0.0226435i | \(-0.992792\pi\) | ||
0.999744 | − | 0.0226435i | \(-0.00720825\pi\) | |||||||
\(632\) | − | 16.0628i | − | 0.638942i | ||||||
\(633\) | 16.6393 | 0.661352 | ||||||||
\(634\) | −24.0513 | −0.955201 | ||||||||
\(635\) | − | 12.8284i | − | 0.509079i | ||||||
\(636\) | −26.2145 | −1.03947 | ||||||||
\(637\) | −69.0188 | − | 22.6888i | −2.73462 | − | 0.898962i | ||||
\(638\) | 2.45238 | 0.0970908 | ||||||||
\(639\) | 1.78252i | 0.0705154i | ||||||||
\(640\) | 47.4245 | 1.87462 | ||||||||
\(641\) | −14.9135 | −0.589049 | −0.294525 | − | 0.955644i | \(-0.595161\pi\) | ||||
−0.294525 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(642\) | 11.4629i | 0.452405i | ||||||||
\(643\) | − | 3.03312i | − | 0.119615i | −0.998210 | − | 0.0598073i | \(-0.980951\pi\) | ||
0.998210 | − | 0.0598073i | \(-0.0190486\pi\) | |||||||
\(644\) | 55.0830i | 2.17057i | ||||||||
\(645\) | − | 35.0502i | − | 1.38010i | ||||||
\(646\) | 12.1715 | 0.478880 | ||||||||
\(647\) | 28.4704 | 1.11929 | 0.559643 | − | 0.828734i | \(-0.310938\pi\) | ||||
0.559643 | + | 0.828734i | \(0.310938\pi\) | |||||||
\(648\) | − | 70.3009i | − | 2.76168i | ||||||
\(649\) | 1.22911 | 0.0482469 | ||||||||
\(650\) | −9.67453 | + | 29.4297i | −0.379466 | + | 1.15433i | ||||
\(651\) | −8.70391 | −0.341133 | ||||||||
\(652\) | 9.84769i | 0.385665i | ||||||||
\(653\) | 21.9746 | 0.859931 | 0.429966 | − | 0.902845i | \(-0.358526\pi\) | ||||
0.429966 | + | 0.902845i | \(0.358526\pi\) | |||||||
\(654\) | −29.0498 | −1.13594 | ||||||||
\(655\) | − | 24.2034i | − | 0.945704i | ||||||
\(656\) | − | 114.006i | − | 4.45118i | ||||||
\(657\) | − | 1.46380i | − | 0.0571082i | ||||||
\(658\) | − | 65.5220i | − | 2.55432i | ||||||
\(659\) | 42.4003 | 1.65168 | 0.825841 | − | 0.563903i | \(-0.190701\pi\) | ||||
0.825841 | + | 0.563903i | \(0.190701\pi\) | |||||||
\(660\) | 2.64940 | 0.103128 | ||||||||
\(661\) | 35.4765i | 1.37988i | 0.723868 | + | 0.689939i | \(0.242363\pi\) | ||||
−0.723868 | + | 0.689939i | \(0.757637\pi\) | |||||||
\(662\) | −25.0625 | −0.974083 | ||||||||
\(663\) | 9.46932 | + | 3.11288i | 0.367758 | + | 0.120894i | ||||
\(664\) | 81.4368 | 3.16036 | ||||||||
\(665\) | 41.0501i | 1.59186i | ||||||||
\(666\) | −4.01337 | −0.155515 | ||||||||
\(667\) | 17.5101 | 0.677993 | ||||||||
\(668\) | 104.142i | 4.02939i | ||||||||
\(669\) | − | 29.9011i | − | 1.15604i | ||||||
\(670\) | 12.3084i | 0.475516i | ||||||||
\(671\) | − | 0.586687i | − | 0.0226488i | ||||||
\(672\) | 138.776 | 5.35339 | ||||||||
\(673\) | 45.4861 | 1.75336 | 0.876680 | − | 0.481074i | \(-0.159753\pi\) | ||||
0.876680 | + | 0.481074i | \(0.159753\pi\) | |||||||
\(674\) | 54.4309i | 2.09660i | ||||||||
\(675\) | −17.2207 | −0.662825 | ||||||||
\(676\) | −53.9539 | − | 39.7707i | −2.07515 | − | 1.52964i | ||||
\(677\) | −11.7990 | −0.453471 | −0.226735 | − | 0.973956i | \(-0.572805\pi\) | ||||
−0.226735 | + | 0.973956i | \(0.572805\pi\) | |||||||
\(678\) | 27.6717i | 1.06273i | ||||||||
\(679\) | 73.8809 | 2.83529 | ||||||||
\(680\) | −40.0400 | −1.53546 | ||||||||
\(681\) | − | 2.88624i | − | 0.110601i | ||||||
\(682\) | 0.287157i | 0.0109958i | ||||||||
\(683\) | 23.9204i | 0.915288i | 0.889135 | + | 0.457644i | \(0.151307\pi\) | ||||
−0.889135 | + | 0.457644i | \(0.848693\pi\) | |||||||
\(684\) | − | 2.97198i | − | 0.113636i | ||||||
\(685\) | 14.1401 | 0.540266 | ||||||||
\(686\) | 183.296 | 6.99826 | ||||||||
\(687\) | 22.5264i | 0.859437i | ||||||||
\(688\) | −89.8593 | −3.42585 | ||||||||
\(689\) | −10.4253 | − | 3.42716i | −0.397174 | − | 0.130564i | ||||
\(690\) | 26.2545 | 0.999493 | ||||||||
\(691\) | 17.3715i | 0.660842i | 0.943834 | + | 0.330421i | \(0.107191\pi\) | ||||
−0.943834 | + | 0.330421i | \(0.892809\pi\) | |||||||
\(692\) | 14.8472 | 0.564405 | ||||||||
\(693\) | −0.117273 | −0.00445484 | ||||||||
\(694\) | 32.5251i | 1.23464i | ||||||||
\(695\) | 28.1053i | 1.06610i | ||||||||
\(696\) | − | 120.439i | − | 4.56522i | ||||||
\(697\) | 15.3747i | 0.582357i | ||||||||
\(698\) | −82.8068 | −3.13428 | ||||||||
\(699\) | −3.45549 | −0.130699 | ||||||||
\(700\) | − | 86.2900i | − | 3.26146i | ||||||
\(701\) | 32.9874 | 1.24592 | 0.622958 | − | 0.782256i | \(-0.285931\pi\) | ||||
0.622958 | + | 0.782256i | \(0.285931\pi\) | |||||||
\(702\) | 16.1494 | − | 49.1260i | 0.609518 | − | 1.85414i | ||||
\(703\) | 19.6722 | 0.741952 | ||||||||
\(704\) | − | 1.94371i | − | 0.0732564i | ||||||
\(705\) | −22.5018 | −0.847465 | ||||||||
\(706\) | −15.9059 | −0.598626 | ||||||||
\(707\) | − | 20.7909i | − | 0.781921i | ||||||
\(708\) | − | 98.6158i | − | 3.70621i | ||||||
\(709\) | 21.3761i | 0.802797i | 0.915904 | + | 0.401398i | \(0.131476\pi\) | ||||
−0.915904 | + | 0.401398i | \(0.868524\pi\) | |||||||
\(710\) | 65.1724i | 2.44588i | ||||||||
\(711\) | 0.398912 | 0.0149604 | ||||||||
\(712\) | −81.8957 | −3.06917 | ||||||||
\(713\) | 2.05031i | 0.0767847i | ||||||||
\(714\) | −38.5346 | −1.44212 | ||||||||
\(715\) | 1.05365 | + | 0.346369i | 0.0394042 | + | 0.0129535i | ||||
\(716\) | 36.6116 | 1.36824 | ||||||||
\(717\) | 24.7092i | 0.922782i | ||||||||
\(718\) | 79.0764 | 2.95110 | ||||||||
\(719\) | 42.6299 | 1.58983 | 0.794913 | − | 0.606723i | \(-0.207516\pi\) | ||||
0.794913 | + | 0.606723i | \(0.207516\pi\) | |||||||
\(720\) | 7.37348i | 0.274793i | ||||||||
\(721\) | − | 37.7742i | − | 1.40678i | ||||||
\(722\) | − | 30.6078i | − | 1.13911i | ||||||
\(723\) | − | 33.3692i | − | 1.24101i | ||||||
\(724\) | 65.8574 | 2.44757 | ||||||||
\(725\) | −27.4303 | −1.01874 | ||||||||
\(726\) | 49.1021i | 1.82235i | ||||||||
\(727\) | 38.9647 | 1.44512 | 0.722561 | − | 0.691308i | \(-0.242965\pi\) | ||||
0.722561 | + | 0.691308i | \(0.242965\pi\) | |||||||
\(728\) | 150.676 | + | 49.5323i | 5.58444 | + | 1.83579i | ||||
\(729\) | 28.6140 | 1.05978 | ||||||||
\(730\) | − | 53.5194i | − | 1.98084i | ||||||
\(731\) | 12.1183 | 0.448212 | ||||||||
\(732\) | −47.0719 | −1.73983 | ||||||||
\(733\) | − | 15.6365i | − | 0.577548i | −0.957397 | − | 0.288774i | \(-0.906752\pi\) | ||
0.957397 | − | 0.288774i | \(-0.0932476\pi\) | |||||||
\(734\) | − | 69.9904i | − | 2.58339i | ||||||
\(735\) | − | 96.4558i | − | 3.55783i | ||||||
\(736\) | − | 32.6903i | − | 1.20498i | ||||||
\(737\) | 0.172358 | 0.00634889 | ||||||||
\(738\) | 5.21033 | 0.191795 | ||||||||
\(739\) | − | 3.68292i | − | 0.135478i | −0.997703 | − | 0.0677392i | \(-0.978421\pi\) | ||
0.997703 | − | 0.0677392i | \(-0.0215786\pi\) | |||||||
\(740\) | −105.726 | −3.88655 | ||||||||
\(741\) | −5.17091 | + | 15.7298i | −0.189958 | + | 0.577849i | ||||
\(742\) | 42.4251 | 1.55747 | ||||||||
\(743\) | 50.2368i | 1.84301i | 0.388367 | + | 0.921505i | \(0.373039\pi\) | ||||
−0.388367 | + | 0.921505i | \(0.626961\pi\) | |||||||
\(744\) | 14.1026 | 0.517025 | ||||||||
\(745\) | −3.55370 | −0.130197 | ||||||||
\(746\) | − | 23.2724i | − | 0.852065i | ||||||
\(747\) | 2.02245i | 0.0739977i | ||||||||
\(748\) | 0.916007i | 0.0334925i | ||||||||
\(749\) | − | 13.3665i | − | 0.488402i | ||||||
\(750\) | 22.8968 | 0.836074 | ||||||||
\(751\) | −5.96827 | −0.217785 | −0.108893 | − | 0.994054i | \(-0.534730\pi\) | ||||
−0.108893 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(752\) | 57.6885i | 2.10368i | ||||||||
\(753\) | 7.76232 | 0.282875 | ||||||||
\(754\) | 25.7238 | − | 78.2514i | 0.936807 | − | 2.84975i | ||||
\(755\) | −12.9673 | −0.471929 | ||||||||
\(756\) | 144.041i | 5.23872i | ||||||||
\(757\) | −37.6489 | −1.36837 | −0.684187 | − | 0.729307i | \(-0.739843\pi\) | ||||
−0.684187 | + | 0.729307i | \(0.739843\pi\) | |||||||
\(758\) | −59.6124 | −2.16522 | ||||||||
\(759\) | − | 0.367649i | − | 0.0133448i | ||||||
\(760\) | − | 66.5117i | − | 2.41263i | ||||||
\(761\) | − | 22.9366i | − | 0.831451i | −0.909490 | − | 0.415726i | \(-0.863528\pi\) | ||
0.909490 | − | 0.415726i | \(-0.136472\pi\) | |||||||
\(762\) | 20.0038i | 0.724662i | ||||||||
\(763\) | 33.8739 | 1.22632 | ||||||||
\(764\) | 78.3615 | 2.83502 | ||||||||
\(765\) | − | 0.994377i | − | 0.0359518i | ||||||
\(766\) | 58.5702 | 2.11623 | ||||||||
\(767\) | 12.8926 | − | 39.2189i | 0.465523 | − | 1.41611i | ||||
\(768\) | −13.4580 | −0.485623 | ||||||||
\(769\) | 24.0231i | 0.866295i | 0.901323 | + | 0.433148i | \(0.142597\pi\) | ||||
−0.901323 | + | 0.433148i | \(0.857403\pi\) | |||||||
\(770\) | −4.28774 | −0.154519 | ||||||||
\(771\) | −15.9362 | −0.573930 | ||||||||
\(772\) | 9.95850i | 0.358414i | ||||||||
\(773\) | 24.5940i | 0.884585i | 0.896871 | + | 0.442292i | \(0.145835\pi\) | ||||
−0.896871 | + | 0.442292i | \(0.854165\pi\) | |||||||
\(774\) | − | 4.10679i | − | 0.147615i | ||||||
\(775\) | − | 3.21190i | − | 0.115375i | ||||||
\(776\) | −119.706 | −4.29719 | ||||||||
\(777\) | −62.2818 | −2.23435 | ||||||||
\(778\) | − | 49.9722i | − | 1.79159i | ||||||
\(779\) | −25.5394 | −0.915043 | ||||||||
\(780\) | 27.7904 | − | 84.5378i | 0.995055 | − | 3.02694i | ||||
\(781\) | 0.912625 | 0.0326563 | ||||||||
\(782\) | 9.07729i | 0.324603i | ||||||||
\(783\) | 45.7885 | 1.63635 | ||||||||
\(784\) | −247.287 | −8.83168 | ||||||||
\(785\) | − | 22.3093i | − | 0.796254i | ||||||
\(786\) | 37.7413i | 1.34619i | ||||||||
\(787\) | − | 40.3993i | − | 1.44008i | −0.693934 | − | 0.720039i | \(-0.744124\pi\) | ||
0.693934 | − | 0.720039i | \(-0.255876\pi\) | |||||||
\(788\) | − | 70.1371i | − | 2.49853i | ||||||
\(789\) | 24.2094 | 0.861878 | ||||||||
\(790\) | 14.5850 | 0.518911 | ||||||||
\(791\) | − | 32.2671i | − | 1.14728i | ||||||
\(792\) | 0.190012 | 0.00675180 | ||||||||
\(793\) | −18.7202 | − | 6.15395i | −0.664774 | − | 0.218533i | ||||
\(794\) | −6.71352 | −0.238254 | ||||||||
\(795\) | − | 14.5697i | − | 0.516735i | ||||||
\(796\) | −58.4016 | −2.06999 | ||||||||
\(797\) | 40.4038 | 1.43118 | 0.715589 | − | 0.698522i | \(-0.246159\pi\) | ||||
0.715589 | + | 0.698522i | \(0.246159\pi\) | |||||||
\(798\) | − | 64.0111i | − | 2.26597i | ||||||
\(799\) | − | 7.77980i | − | 0.275229i | ||||||
\(800\) | 51.2108i | 1.81058i | ||||||||
\(801\) | − | 2.03385i | − | 0.0718624i | ||||||
\(802\) | −5.14180 | −0.181563 | ||||||||
\(803\) | −0.749444 | −0.0264473 | ||||||||
\(804\) | − | 13.8289i | − | 0.487706i | ||||||
\(805\) | −30.6145 | −1.07902 | ||||||||
\(806\) | 9.16271 | + | 3.01208i | 0.322743 | + | 0.106096i | ||||
\(807\) | −45.7387 | −1.61008 | ||||||||
\(808\) | 33.6865i | 1.18509i | ||||||||
\(809\) | −45.5611 | −1.60184 | −0.800922 | − | 0.598768i | \(-0.795657\pi\) | ||||
−0.800922 | + | 0.598768i | \(0.795657\pi\) | |||||||
\(810\) | 63.8333 | 2.24287 | ||||||||
\(811\) | 21.7290i | 0.763010i | 0.924367 | + | 0.381505i | \(0.124594\pi\) | ||||
−0.924367 | + | 0.381505i | \(0.875406\pi\) | |||||||
\(812\) | 229.439i | 8.05172i | ||||||||
\(813\) | − | 22.2566i | − | 0.780572i | ||||||
\(814\) | 2.05479i | 0.0720203i | ||||||||
\(815\) | −5.47324 | −0.191719 | ||||||||
\(816\) | 33.9276 | 1.18770 | ||||||||
\(817\) | 20.1301i | 0.704264i | ||||||||
\(818\) | −84.0215 | −2.93774 | ||||||||
\(819\) | −1.23012 | + | 3.74199i | −0.0429837 | + | 0.130756i | ||||
\(820\) | 137.258 | 4.79325 | ||||||||
\(821\) | − | 46.1398i | − | 1.61029i | −0.593077 | − | 0.805146i | \(-0.702087\pi\) | ||
0.593077 | − | 0.805146i | \(-0.297913\pi\) | |||||||
\(822\) | −22.0492 | −0.769055 | ||||||||
\(823\) | −31.2220 | −1.08833 | −0.544165 | − | 0.838978i | \(-0.683154\pi\) | ||||
−0.544165 | + | 0.838978i | \(0.683154\pi\) | |||||||
\(824\) | 61.2038i | 2.13214i | ||||||||
\(825\) | 0.575938i | 0.0200516i | ||||||||
\(826\) | 159.598i | 5.55312i | ||||||||
\(827\) | 23.3304i | 0.811276i | 0.914034 | + | 0.405638i | \(0.132951\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867049\pi\) | |||||||
\(828\) | 2.21645 | 0.0770271 | ||||||||
\(829\) | −6.95045 | −0.241399 | −0.120700 | − | 0.992689i | \(-0.538514\pi\) | ||||
−0.120700 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(830\) | 73.9448i | 2.56666i | ||||||||
\(831\) | 50.4381 | 1.74968 | ||||||||
\(832\) | −62.0206 | − | 20.3882i | −2.15018 | − | 0.706834i | ||||
\(833\) | 33.3488 | 1.15547 | ||||||||
\(834\) | − | 43.8258i | − | 1.51756i | ||||||
\(835\) | −57.8812 | −2.00306 | ||||||||
\(836\) | −1.52161 | −0.0526260 | ||||||||
\(837\) | 5.36152i | 0.185321i | ||||||||
\(838\) | − | 82.1038i | − | 2.83623i | ||||||
\(839\) | 6.57603i | 0.227030i | 0.993536 | + | 0.113515i | \(0.0362110\pi\) | ||||
−0.993536 | + | 0.113515i | \(0.963789\pi\) | |||||||
\(840\) | 210.575i | 7.26552i | ||||||||
\(841\) | 43.9352 | 1.51501 | ||||||||
\(842\) | −106.845 | −3.68214 | ||||||||
\(843\) | 14.7818i | 0.509111i | ||||||||
\(844\) | 51.3592 | 1.76785 | ||||||||
\(845\) | 22.1041 | − | 29.9870i | 0.760405 | − | 1.03158i | ||||
\(846\) | −2.63650 | −0.0906449 | ||||||||
\(847\) | − | 57.2564i | − | 1.96735i | ||||||
\(848\) | −37.3529 | −1.28270 | ||||||||
\(849\) | 5.54820 | 0.190414 | ||||||||
\(850\) | − | 14.2200i | − | 0.487742i | ||||||
\(851\) | 14.6712i | 0.502923i | ||||||||
\(852\) | − | 73.2229i | − | 2.50858i | ||||||
\(853\) | 46.6898i | 1.59863i | 0.600914 | + | 0.799314i | \(0.294803\pi\) | ||||
−0.600914 | + | 0.799314i | \(0.705197\pi\) | |||||||
\(854\) | 76.1802 | 2.60683 | ||||||||
\(855\) | 1.65179 | 0.0564901 | ||||||||
\(856\) | 21.6572i | 0.740227i | ||||||||
\(857\) | 15.1188 | 0.516448 | 0.258224 | − | 0.966085i | \(-0.416863\pi\) | ||||
0.258224 | + | 0.966085i | \(0.416863\pi\) | |||||||
\(858\) | −1.64300 | − | 0.540108i | −0.0560910 | − | 0.0184390i | ||||
\(859\) | −14.9342 | −0.509547 | −0.254774 | − | 0.967001i | \(-0.582001\pi\) | ||||
−0.254774 | + | 0.967001i | \(0.582001\pi\) | |||||||
\(860\) | − | 108.187i | − | 3.68913i | ||||||
\(861\) | 80.8570 | 2.75560 | ||||||||
\(862\) | −43.4252 | −1.47907 | ||||||||
\(863\) | 16.3095i | 0.555182i | 0.960699 | + | 0.277591i | \(0.0895360\pi\) | ||||
−0.960699 | + | 0.277591i | \(0.910464\pi\) | |||||||
\(864\) | − | 85.4844i | − | 2.90824i | ||||||
\(865\) | 8.25190i | 0.280573i | ||||||||
\(866\) | − | 83.5458i | − | 2.83900i | ||||||
\(867\) | 23.8219 | 0.809033 | ||||||||
\(868\) | −26.8657 | −0.911881 | ||||||||
\(869\) | − | 0.204237i | − | 0.00692828i | ||||||
\(870\) | 109.359 | 3.70761 | ||||||||
\(871\) | 1.80792 | − | 5.49965i | 0.0612590 | − | 0.186349i | ||||
\(872\) | −54.8845 | −1.85862 | ||||||||
\(873\) | − | 2.97285i | − | 0.100616i | ||||||
\(874\) | −15.0786 | −0.510041 | ||||||||
\(875\) | −26.6992 | −0.902599 | ||||||||
\(876\) | 60.1304i | 2.03162i | ||||||||
\(877\) | − | 7.18224i | − | 0.242527i | −0.992620 | − | 0.121264i | \(-0.961305\pi\) | ||
0.992620 | − | 0.121264i | \(-0.0386946\pi\) | |||||||
\(878\) | − | 21.6881i | − | 0.731937i | ||||||
\(879\) | 41.5803i | 1.40247i | ||||||||
\(880\) | 3.77512 | 0.127259 | ||||||||
\(881\) | −28.4293 | −0.957806 | −0.478903 | − | 0.877868i | \(-0.658965\pi\) | ||||
−0.478903 | + | 0.877868i | \(0.658965\pi\) | |||||||
\(882\) | − | 11.3016i | − | 0.380545i | ||||||
\(883\) | −4.98962 | −0.167914 | −0.0839570 | − | 0.996469i | \(-0.526756\pi\) | ||||
−0.0839570 | + | 0.996469i | \(0.526756\pi\) | |||||||
\(884\) | 29.2282 | + | 9.60829i | 0.983052 | + | 0.323162i | ||||
\(885\) | 54.8096 | 1.84240 | ||||||||
\(886\) | 5.08288i | 0.170763i | ||||||||
\(887\) | −6.01723 | −0.202039 | −0.101019 | − | 0.994884i | \(-0.532210\pi\) | ||||
−0.101019 | + | 0.994884i | \(0.532210\pi\) | |||||||
\(888\) | 100.912 | 3.38640 | ||||||||
\(889\) | − | 23.3258i | − | 0.782322i | ||||||
\(890\) | − | 74.3614i | − | 2.49260i | ||||||
\(891\) | − | 0.893873i | − | 0.0299459i | ||||||
\(892\) | − | 92.2934i | − | 3.09021i | ||||||
\(893\) | 12.9233 | 0.432461 | ||||||||
\(894\) | 5.54142 | 0.185333 | ||||||||
\(895\) | 20.3484i | 0.680171i | ||||||||
\(896\) | 86.2317 | 2.88080 | ||||||||
\(897\) | −11.7310 | − | 3.85638i | −0.391688 | − | 0.128761i | ||||
\(898\) | 18.9442 | 0.632177 | ||||||||
\(899\) | 8.54021i | 0.284832i | ||||||||
\(900\) | −3.47217 | −0.115739 | ||||||||
\(901\) | 5.03737 | 0.167819 | ||||||||
\(902\) | − | 2.66762i | − | 0.0888219i | ||||||
\(903\) | − | 63.7315i | − | 2.12085i | ||||||
\(904\) | 52.2809i | 1.73884i | ||||||||
\(905\) | 36.6028i | 1.21672i | ||||||||
\(906\) | 20.2204 | 0.671779 | ||||||||
\(907\) | 7.82026 | 0.259667 | 0.129834 | − | 0.991536i | \(-0.458556\pi\) | ||||
0.129834 | + | 0.991536i | \(0.458556\pi\) | |||||||
\(908\) | − | 8.90875i | − | 0.295647i | ||||||
\(909\) | −0.836592 | −0.0277480 | ||||||||
\(910\) | −44.9754 | + | 136.814i | −1.49092 | + | 4.53535i | ||||
\(911\) | 28.0064 | 0.927894 | 0.463947 | − | 0.885863i | \(-0.346433\pi\) | ||||
0.463947 | + | 0.885863i | \(0.346433\pi\) | |||||||
\(912\) | 56.3583i | 1.86621i | ||||||||
\(913\) | 1.03547 | 0.0342689 | ||||||||
\(914\) | −10.1842 | −0.336863 | ||||||||
\(915\) | − | 26.1620i | − | 0.864890i | ||||||
\(916\) | 69.5306i | 2.29736i | ||||||||
\(917\) | − | 44.0089i | − | 1.45330i | ||||||
\(918\) | 23.7369i | 0.783435i | ||||||||
\(919\) | 37.6488 | 1.24192 | 0.620960 | − | 0.783842i | \(-0.286743\pi\) | ||||
0.620960 | + | 0.783842i | \(0.286743\pi\) | |||||||
\(920\) | 49.6034 | 1.63538 | ||||||||
\(921\) | 7.48179i | 0.246533i | ||||||||
\(922\) | −10.9567 | −0.360840 | ||||||||
\(923\) | 9.57281 | − | 29.1203i | 0.315093 | − | 0.958507i | ||||
\(924\) | 4.81738 | 0.158480 | ||||||||
\(925\) | − | 22.9832i | − | 0.755681i | ||||||
\(926\) | 62.5418 | 2.05525 | ||||||||
\(927\) | −1.51997 | −0.0499225 | ||||||||
\(928\) | − | 136.166i | − | 4.46986i | ||||||
\(929\) | − | 31.2651i | − | 1.02577i | −0.858456 | − | 0.512887i | \(-0.828576\pi\) | ||
0.858456 | − | 0.512887i | \(-0.171424\pi\) | |||||||
\(930\) | 12.8052i | 0.419898i | ||||||||
\(931\) | 55.3968i | 1.81556i | ||||||||
\(932\) | −10.6658 | −0.349370 | ||||||||
\(933\) | −41.5903 | −1.36161 | ||||||||
\(934\) | − | 33.6572i | − | 1.10130i | ||||||
\(935\) | −0.509107 | −0.0166496 | ||||||||
\(936\) | 1.99310 | − | 6.06298i | 0.0651466 | − | 0.198175i | ||||
\(937\) | −11.2719 | −0.368238 | −0.184119 | − | 0.982904i | \(-0.558943\pi\) | ||||
−0.184119 | + | 0.982904i | \(0.558943\pi\) | |||||||
\(938\) | 22.3804i | 0.730745i | ||||||||
\(939\) | −35.1573 | −1.14731 | ||||||||
\(940\) | −69.4545 | −2.26535 | ||||||||
\(941\) | 9.68665i | 0.315776i | 0.987457 | + | 0.157888i | \(0.0504685\pi\) | ||||
−0.987457 | + | 0.157888i | \(0.949532\pi\) | |||||||
\(942\) | 34.7878i | 1.13345i | ||||||||
\(943\) | − | 19.0469i | − | 0.620251i | ||||||
\(944\) | − | 140.517i | − | 4.57345i | ||||||
\(945\) | −80.0564 | −2.60423 | ||||||||
\(946\) | −2.10262 | −0.0683619 | ||||||||
\(947\) | 9.22048i | 0.299625i | 0.988714 | + | 0.149813i | \(0.0478671\pi\) | ||||
−0.988714 | + | 0.149813i | \(0.952133\pi\) | |||||||
\(948\) | −16.3866 | −0.532213 | ||||||||
\(949\) | −7.86116 | + | 23.9135i | −0.255184 | + | 0.776265i | ||||
\(950\) | 23.6213 | 0.766376 | ||||||||
\(951\) | 15.0187i | 0.487015i | ||||||||
\(952\) | −72.8044 | −2.35961 | ||||||||
\(953\) | 17.9528 | 0.581548 | 0.290774 | − | 0.956792i | \(-0.406087\pi\) | ||||
0.290774 | + | 0.956792i | \(0.406087\pi\) | |||||||
\(954\) | − | 1.70712i | − | 0.0552700i | ||||||
\(955\) | 43.5525i | 1.40933i | ||||||||
\(956\) | 76.2680i | 2.46668i | ||||||||
\(957\) | − | 1.53138i | − | 0.0495023i | ||||||
\(958\) | −59.4391 | −1.92039 | ||||||||
\(959\) | 25.7109 | 0.830248 | ||||||||
\(960\) | − | 86.6756i | − | 2.79744i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 65.5648 | + | 21.5533i | 2.11389 | + | 0.694907i | ||||
\(963\) | −0.537847 | −0.0173319 | ||||||||
\(964\) | − | 102.998i | − | 3.31735i | ||||||
\(965\) | −5.53483 | −0.178172 | ||||||||
\(966\) | 47.7385 | 1.53596 | ||||||||
\(967\) | 14.7975i | 0.475855i | 0.971283 | + | 0.237927i | \(0.0764680\pi\) | ||||
−0.971283 | + | 0.237927i | \(0.923532\pi\) | |||||||
\(968\) | 92.7699i | 2.98174i | ||||||||
\(969\) | − | 7.60040i | − | 0.244160i | ||||||
\(970\) | − | 108.693i | − | 3.48993i | ||||||
\(971\) | −24.8066 | −0.796082 | −0.398041 | − | 0.917368i | \(-0.630310\pi\) | ||||
−0.398041 | + | 0.917368i | \(0.630310\pi\) | |||||||
\(972\) | 11.2133 | 0.359668 | ||||||||
\(973\) | 51.1037i | 1.63831i | ||||||||
\(974\) | −27.9454 | −0.895428 | ||||||||
\(975\) | 18.3772 | + | 6.04120i | 0.588542 | + | 0.193473i | ||||
\(976\) | −67.0725 | −2.14694 | ||||||||
\(977\) | 10.7784i | 0.344831i | 0.985024 | + | 0.172415i | \(0.0551572\pi\) | ||||
−0.985024 | + | 0.172415i | \(0.944843\pi\) | |||||||
\(978\) | 8.53464 | 0.272908 | ||||||||
\(979\) | −1.04130 | −0.0332801 | ||||||||
\(980\) | − | 297.723i | − | 9.51041i | ||||||
\(981\) | − | 1.36303i | − | 0.0435183i | ||||||
\(982\) | 82.2620i | 2.62509i | ||||||||
\(983\) | 3.27003i | 0.104298i | 0.998639 | + | 0.0521490i | \(0.0166071\pi\) | ||||
−0.998639 | + | 0.0521490i | \(0.983393\pi\) | |||||||
\(984\) | −131.009 | −4.17642 | ||||||||
\(985\) | 38.9814 | 1.24205 | ||||||||
\(986\) | 37.8099i | 1.20411i | ||||||||
\(987\) | −40.9148 | −1.30233 | ||||||||
\(988\) | −15.9607 | + | 48.5520i | −0.507776 | + | 1.54465i | ||||
\(989\) | −15.0127 | −0.477377 | ||||||||
\(990\) | 0.172532i | 0.00548342i | ||||||||
\(991\) | 14.6836 | 0.466440 | 0.233220 | − | 0.972424i | \(-0.425074\pi\) | ||||
0.233220 | + | 0.972424i | \(0.425074\pi\) | |||||||
\(992\) | 15.9441 | 0.506225 | ||||||||
\(993\) | 15.6501i | 0.496642i | ||||||||
\(994\) | 118.503i | 3.75868i | ||||||||
\(995\) | − | 32.4590i | − | 1.02902i | ||||||
\(996\) | − | 83.0789i | − | 2.63246i | ||||||
\(997\) | −37.2324 | −1.17916 | −0.589580 | − | 0.807710i | \(-0.700707\pi\) | ||||
−0.589580 | + | 0.807710i | \(0.700707\pi\) | |||||||
\(998\) | −106.804 | −3.38082 | ||||||||
\(999\) | 38.3650i | 1.21381i |
(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 | 403.2.c.b.311.2 | ✓ | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.2 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.15 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.31 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
403.2.c.b.311.31 | yes | 32 | 13.12 | even | 2 | inner | |
5239.2.a.k.1.2 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.15 | 16 | 13.8 | odd | 4 |