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 | 311.31 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.2 |
$q$-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 | \(0.394700\pi\) | ||||
−0.324810 | + | 0.945779i | \(0.605300\pi\) | |||||||
\(3\) | −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 | \(0.221388\pi\) | ||||
−0.767727 | + | 0.640777i | \(0.778612\pi\) | |||||||
\(6\) | − | 4.46851i | − | 1.82426i | ||||||
\(7\) | 5.21058i | 1.96941i | 0.174217 | + | 0.984707i | \(0.444261\pi\) | ||||
−0.174217 | + | 0.984707i | \(0.555739\pi\) | |||||||
\(8\) | − | 8.44248i | − | 2.98487i | ||||||
\(9\) | −0.209666 | −0.0698885 | ||||||||
\(10\) | −7.66579 | −2.42413 | ||||||||
\(11\) | − | 0.107346i | − | 0.0323660i | −0.999869 | − | 0.0161830i | \(-0.994849\pi\) | ||
0.999869 | − | 0.0161830i | \(-0.00515143\pi\) | |||||||
\(12\) | 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 | \(0.102124\pi\) | ||||
−0.948974 | + | 0.315355i | \(0.897876\pi\) | |||||||
\(20\) | − | 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 | \(-0.799842\pi\) | ||
0.808724 | − | 0.588188i | \(-0.200158\pi\) | |||||||
\(38\) | −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 | \(0.258348\pi\) | ||||
−0.688320 | + | 0.725407i | \(0.741652\pi\) | |||||||
\(42\) | 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 | \(-0.888612\pi\) | ||
0.939395 | − | 0.342837i | \(-0.111388\pi\) | |||||||
\(48\) | −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 | \(0.267710\pi\) | ||||
−0.666692 | + | 0.745333i | \(0.732290\pi\) | |||||||
\(60\) | 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 | \(0.0312700\pi\) | ||||
−0.995179 | + | 0.0980796i | \(0.968730\pi\) | |||||||
\(68\) | 8.53323 | 1.03481 | ||||||||
\(69\) | −3.42490 | −0.412309 | ||||||||
\(70\) | − | 39.9432i | − | 4.77413i | ||||||
\(71\) | 8.50173i | 1.00897i | 0.863421 | + | 0.504485i | \(0.168318\pi\) | ||||
−0.863421 | + | 0.504485i | \(0.831682\pi\) | |||||||
\(72\) | 1.77010i | 0.208608i | ||||||||
\(73\) | − | 6.98159i | − | 0.817133i | −0.912729 | − | 0.408567i | \(-0.866029\pi\) | ||
0.912729 | − | 0.408567i | \(-0.133971\pi\) | |||||||
\(74\) | 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 | \(0.177582\pi\) | ||||
−0.848374 | + | 0.529398i | \(0.822418\pi\) | |||||||
\(84\) | 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 | \(-0.828118\pi\) | ||
0.857717 | − | 0.514122i | \(-0.171882\pi\) | |||||||
\(90\) | 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 | \(-0.744220\pi\) | ||
0.694150 | − | 0.719830i | \(-0.255780\pi\) | |||||||
\(98\) | − | 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 | \(-0.899222\pi\) | ||
0.950298 | − | 0.311341i | \(-0.100778\pi\) | |||||||
\(110\) | 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 | \(-0.932398\pi\) | ||
0.977532 | − | 0.210785i | \(-0.0676021\pi\) | |||||||
\(138\) | − | 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 | \(0.0161760\pi\) | ||||
−0.998709 | + | 0.0507967i | \(0.983824\pi\) | |||||||
\(150\) | 14.3524i | 1.17187i | ||||||||
\(151\) | 4.52510i | 0.368247i | 0.982903 | + | 0.184124i | \(0.0589447\pi\) | ||||
−0.982903 | + | 0.184124i | \(0.941055\pi\) | |||||||
\(152\) | 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 | \(0.0238317\pi\) | ||||
−0.997199 | + | 0.0747995i | \(0.976168\pi\) | |||||||
\(164\) | − | 47.8978i | − | 3.74019i | ||||||
\(165\) | −0.513849 | −0.0400031 | ||||||||
\(166\) | −25.8039 | −2.00277 | ||||||||
\(167\) | 20.1983i | 1.56299i | 0.623909 | + | 0.781497i | \(0.285543\pi\) | ||||
−0.623909 | + | 0.781497i | \(0.714457\pi\) | |||||||
\(168\) | −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 | \(0.0221449\pi\) | ||||
−0.997581 | + | 0.0695142i | \(0.977855\pi\) | |||||||
\(194\) | 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 | \(-0.838969\pi\) | ||
0.874742 | − | 0.484588i | \(-0.161031\pi\) | |||||||
\(198\) | −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 | \(-0.795428\pi\) | ||
0.800491 | − | 0.599344i | \(-0.204572\pi\) | |||||||
\(224\) | −83.0779 | −5.55087 | ||||||||
\(225\) | 0.673426 | 0.0448951 | ||||||||
\(226\) | 16.5656i | 1.10193i | ||||||||
\(227\) | − | 1.72785i | − | 0.114681i | −0.998355 | − | 0.0573406i | \(-0.981738\pi\) | ||
0.998355 | − | 0.0573406i | \(-0.0182621\pi\) | |||||||
\(228\) | 23.6781i | 1.56812i | ||||||||
\(229\) | 13.4854i | 0.891141i | 0.895247 | + | 0.445570i | \(0.146999\pi\) | ||||
−0.895247 | + | 0.445570i | \(0.853001\pi\) | |||||||
\(230\) | −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 | \(0.158787\pi\) | ||||
−0.878136 | + | 0.478411i | \(0.841213\pi\) | |||||||
\(240\) | − | 58.7453i | − | 3.79199i | ||||||
\(241\) | − | 19.9764i | − | 1.28679i | −0.765532 | − | 0.643397i | \(-0.777524\pi\) | ||
0.765532 | − | 0.643397i | \(-0.222476\pi\) | |||||||
\(242\) | 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 | \(-0.867382\pi\) | ||
0.914457 | − | 0.404683i | \(-0.132618\pi\) | |||||||
\(272\) | −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 | \(0.0850241\pi\) | ||||
−0.964537 | + | 0.263946i | \(0.914976\pi\) | |||||||
\(282\) | −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 | \(0.259133\pi\) | ||||
−0.686529 | + | 0.727102i | \(0.740867\pi\) | |||||||
\(294\) | 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 | \(0.0407960\pi\) | ||||
−0.991798 | + | 0.127814i | \(0.959204\pi\) | |||||||
\(308\) | −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 | \(0.0812497\pi\) | ||||
−0.967599 | + | 0.252491i | \(0.918750\pi\) | |||||||
\(318\) | 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 | \(0.0828926\pi\) | ||||
−0.966283 | + | 0.257482i | \(0.917107\pi\) | |||||||
\(332\) | − | 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 | \(0.310801\pi\) | ||||
−0.560000 | + | 0.828492i | \(0.689199\pi\) | |||||||
\(350\) | 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 | \(0.0505808\pi\) | ||||
−0.987401 | + | 0.158236i | \(0.949419\pi\) | |||||||
\(354\) | 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 | \(-0.715182\pi\) | ||
0.625690 | − | 0.780072i | \(-0.284818\pi\) | |||||||
\(360\) | −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 | \(0.193963\pi\) | ||||
−0.820018 | + | 0.572338i | \(0.806037\pi\) | |||||||
\(380\) | 40.6200 | 2.08376 | ||||||||
\(381\) | −7.47788 | −0.383103 | ||||||||
\(382\) | − | 40.6561i | − | 2.08015i | ||||||
\(383\) | − | 21.8948i | − | 1.11877i | −0.828907 | − | 0.559387i | \(-0.811037\pi\) | ||
0.828907 | − | 0.559387i | \(-0.188963\pi\) | |||||||
\(384\) | 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 | \(0.0200599\pi\) | ||||
−0.998015 | + | 0.0629783i | \(0.979940\pi\) | |||||||
\(398\) | 30.3003i | 1.51882i | ||||||||
\(399\) | 23.9288 | 1.19794 | ||||||||
\(400\) | −39.4172 | −1.97086 | ||||||||
\(401\) | 1.92212i | 0.0959861i | 0.998848 | + | 0.0479930i | \(0.0152825\pi\) | ||||
−0.998848 | + | 0.0479930i | \(0.984717\pi\) | |||||||
\(402\) | 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 | \(0.283027\pi\) | ||||
−0.630068 | + | 0.776540i | \(0.716973\pi\) | |||||||
\(410\) | − | 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 | \(0.426290\pi\) | ||||
−0.229504 | + | 0.973308i | \(0.573710\pi\) | |||||||
\(422\) | − | 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 | \(0.127859\pi\) | ||||
−0.920405 | + | 0.390966i | \(0.872141\pi\) | |||||||
\(432\) | 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 | \(-0.946558\pi\) | ||
0.985939 | − | 0.167105i | \(-0.0534419\pi\) | |||||||
\(450\) | 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 | \(0.0283811\pi\) | ||||
−0.996028 | + | 0.0890437i | \(0.971619\pi\) | |||||||
\(458\) | −36.0744 | −1.68565 | ||||||||
\(459\) | −8.87339 | −0.414175 | ||||||||
\(460\) | − | 30.2938i | − | 1.41245i | ||||||
\(461\) | 4.09587i | 0.190764i | 0.995441 | + | 0.0953818i | \(0.0304072\pi\) | ||||
−0.995441 | + | 0.0953818i | \(0.969593\pi\) | |||||||
\(462\) | − | 2.49939i | − | 0.116282i | ||||||
\(463\) | − | 23.3795i | − | 1.08654i | −0.839559 | − | 0.543269i | \(-0.817186\pi\) | ||
0.839559 | − | 0.543269i | \(-0.182814\pi\) | |||||||
\(464\) | 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 | \(0.169475\pi\) | ||||
−0.861581 | + | 0.507621i | \(0.830525\pi\) | |||||||
\(480\) | 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 | \(0.0760628\pi\) | ||||
−0.971585 | + | 0.236691i | \(0.923937\pi\) | |||||||
\(488\) | 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 | \(0.351871\pi\) | ||||
−0.448747 | + | 0.893659i | \(0.648129\pi\) | |||||||
\(500\) | − | 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 | \(-0.990209\pi\) | ||
0.999527 | − | 0.0307544i | \(-0.00979098\pi\) | |||||||
\(510\) | −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 | \(-0.778686\pi\) | ||
0.767875 | − | 0.640600i | \(-0.221314\pi\) | |||||||
\(542\) | 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 | \(0.0856077\pi\) | ||||
−0.964052 | + | 0.265714i | \(0.914392\pi\) | |||||||
\(558\) | −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 | \(-0.923710\pi\) | ||
0.971416 | − | 0.237384i | \(-0.0762899\pi\) | |||||||
\(578\) | − | 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 | \(0.180487\pi\) | ||||
−0.843507 | + | 0.537119i | \(0.819513\pi\) | |||||||
\(588\) | −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 | \(0.233980\pi\) | ||||
−0.741785 | + | 0.670638i | \(0.766020\pi\) | |||||||
\(594\) | 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 | \(0.0482018\pi\) | ||||
−0.988556 | + | 0.150852i | \(0.951798\pi\) | |||||||
\(614\) | −11.9815 | −0.483535 | ||||||||
\(615\) | 44.4686 | 1.79315 | ||||||||
\(616\) | − | 4.72216i | − | 0.190261i | ||||||
\(617\) | − | 29.5623i | − | 1.19013i | −0.803676 | − | 0.595067i | \(-0.797125\pi\) | ||
0.803676 | − | 0.595067i | \(-0.202875\pi\) | |||||||
\(618\) | − | 32.3945i | − | 1.30310i | ||||||
\(619\) | − | 32.6410i | − | 1.31195i | −0.754782 | − | 0.655976i | \(-0.772257\pi\) | ||
0.754782 | − | 0.655976i | \(-0.227743\pi\) | |||||||
\(620\) | −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 | \(0.00720825\pi\) | ||||
−0.999744 | + | 0.0226435i | \(0.992792\pi\) | |||||||
\(632\) | 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 | \(0.0190486\pi\) | ||||
−0.998210 | + | 0.0598073i | \(0.980951\pi\) | |||||||
\(644\) | − | 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 | \(-0.757637\pi\) | ||
0.723868 | − | 0.689939i | \(-0.242363\pi\) | |||||||
\(662\) | −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 | \(-0.848693\pi\) | ||
0.889135 | − | 0.457644i | \(-0.151307\pi\) | |||||||
\(684\) | 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 | \(-0.892809\pi\) | ||
0.943834 | − | 0.330421i | \(-0.107191\pi\) | |||||||
\(692\) | 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 | \(-0.868524\pi\) | ||
0.915904 | − | 0.401398i | \(-0.131476\pi\) | |||||||
\(710\) | − | 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 | \(0.0932476\pi\) | ||||
−0.957397 | + | 0.288774i | \(0.906752\pi\) | |||||||
\(734\) | 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 | \(0.0215786\pi\) | ||||
−0.997703 | + | 0.0677392i | \(0.978421\pi\) | |||||||
\(740\) | −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 | \(-0.626961\pi\) | ||
0.388367 | − | 0.921505i | \(-0.373039\pi\) | |||||||
\(744\) | 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 | \(0.136472\pi\) | ||||
−0.909490 | + | 0.415726i | \(0.863528\pi\) | |||||||
\(762\) | − | 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 | \(-0.857403\pi\) | ||
0.901323 | − | 0.433148i | \(-0.142597\pi\) | |||||||
\(770\) | −4.28774 | −0.154519 | ||||||||
\(771\) | −15.9362 | −0.573930 | ||||||||
\(772\) | − | 9.95850i | − | 0.358414i | ||||||
\(773\) | − | 24.5940i | − | 0.884585i | −0.896871 | − | 0.442292i | \(-0.854165\pi\) | ||
0.896871 | − | 0.442292i | \(-0.145835\pi\) | |||||||
\(774\) | 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 | \(0.255876\pi\) | ||||
−0.693934 | + | 0.720039i | \(0.744124\pi\) | |||||||
\(788\) | 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 | \(-0.875406\pi\) | ||
0.924367 | − | 0.381505i | \(-0.124594\pi\) | |||||||
\(812\) | − | 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 | \(0.297913\pi\) | ||||
−0.593077 | + | 0.805146i | \(0.702087\pi\) | |||||||
\(822\) | −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 | \(-0.867049\pi\) | ||
0.914034 | − | 0.405638i | \(-0.132951\pi\) | |||||||
\(828\) | 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 | \(-0.963789\pi\) | ||
0.993536 | − | 0.113515i | \(-0.0362110\pi\) | |||||||
\(840\) | − | 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 | \(-0.705197\pi\) | ||
0.600914 | − | 0.799314i | \(-0.294803\pi\) | |||||||
\(854\) | 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 | \(-0.910464\pi\) | ||
0.960699 | − | 0.277591i | \(-0.0895360\pi\) | |||||||
\(864\) | 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 | \(0.0386946\pi\) | ||||
−0.992620 | + | 0.121264i | \(0.961305\pi\) | |||||||
\(878\) | 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 | \(0.171424\pi\) | ||||
−0.858456 | + | 0.512887i | \(0.828576\pi\) | |||||||
\(930\) | − | 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 | \(-0.949532\pi\) | ||
0.987457 | − | 0.157888i | \(-0.0504685\pi\) | |||||||
\(942\) | − | 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 | \(-0.952133\pi\) | ||
0.988714 | − | 0.149813i | \(-0.0478671\pi\) | |||||||
\(948\) | −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 | \(-0.923532\pi\) | ||
0.971283 | − | 0.237927i | \(-0.0764680\pi\) | |||||||
\(968\) | − | 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 | \(-0.944843\pi\) | ||
0.985024 | − | 0.172415i | \(-0.0551572\pi\) | |||||||
\(978\) | 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 | \(-0.983393\pi\) | ||
0.998639 | − | 0.0521490i | \(-0.0166071\pi\) | |||||||
\(984\) | −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.311.31 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.15 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.2 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.2 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.2 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.31 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.2 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.15 | 16 | 13.5 | odd | 4 |