Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(247,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.247");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 247.6 | ||
Character | \(\chi\) | \(=\) | 930.247 |
Dual form | 930.2.k.a.433.6 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.06824 | − | 1.96440i | 0.477731 | − | 0.878506i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.05833 | − | 1.05833i | −0.400009 | − | 0.400009i | 0.478227 | − | 0.878236i | \(-0.341280\pi\) |
−0.878236 | + | 0.478227i | \(0.841280\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −2.14440 | + | 0.633681i | −0.678119 | + | 0.200388i | ||||
\(11\) | − | 5.04212i | − | 1.52026i | −0.649774 | − | 0.760128i | \(-0.725136\pi\) | ||
0.649774 | − | 0.760128i | \(-0.274864\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −4.63173 | − | 4.63173i | −1.28461 | − | 1.28461i | −0.938014 | − | 0.346598i | \(-0.887337\pi\) |
−0.346598 | − | 0.938014i | \(-0.612663\pi\) | |||||||
\(14\) | 1.49670i | 0.400009i | ||||||||
\(15\) | 2.14440 | − | 0.633681i | 0.553682 | − | 0.163616i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.53121 | + | 2.53121i | −0.613910 | + | 0.613910i | −0.943962 | − | 0.330053i | \(-0.892933\pi\) |
0.330053 | + | 0.943962i | \(0.392933\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 7.83439i | 1.79733i | 0.438634 | + | 0.898666i | \(0.355463\pi\) | ||||
−0.438634 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(20\) | 1.96440 | + | 1.06824i | 0.439253 | + | 0.238866i | ||||
\(21\) | − | 1.49670i | − | 0.326606i | ||||||
\(22\) | −3.56532 | + | 3.56532i | −0.760128 | + | 0.760128i | ||||
\(23\) | −2.05623 | − | 2.05623i | −0.428755 | − | 0.428755i | 0.459449 | − | 0.888204i | \(-0.348047\pi\) |
−0.888204 | + | 0.459449i | \(0.848047\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.71773 | − | 4.19690i | −0.543546 | − | 0.839379i | ||||
\(26\) | 6.55026i | 1.28461i | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1.05833 | − | 1.05833i | 0.200005 | − | 0.200005i | ||||
\(29\) | −3.01575 | −0.560010 | −0.280005 | − | 0.959999i | \(-0.590336\pi\) | ||||
−0.280005 | + | 0.959999i | \(0.590336\pi\) | |||||||
\(30\) | −1.96440 | − | 1.06824i | −0.358649 | − | 0.195033i | ||||
\(31\) | −5.11803 | + | 2.19222i | −0.919224 | + | 0.393734i | ||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 3.56532 | − | 3.56532i | 0.620642 | − | 0.620642i | ||||
\(34\) | 3.57968 | 0.613910 | ||||||||
\(35\) | −3.20952 | + | 0.948429i | −0.542508 | + | 0.160314i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.29070 | − | 2.29070i | 0.376590 | − | 0.376590i | −0.493281 | − | 0.869870i | \(-0.664202\pi\) |
0.869870 | + | 0.493281i | \(0.164202\pi\) | |||||||
\(38\) | 5.53975 | − | 5.53975i | 0.898666 | − | 0.898666i | ||||
\(39\) | − | 6.55026i | − | 1.04888i | ||||||
\(40\) | −0.633681 | − | 2.14440i | −0.100194 | − | 0.339059i | ||||
\(41\) | 2.23428 | 0.348935 | 0.174468 | − | 0.984663i | \(-0.444180\pi\) | ||||
0.174468 | + | 0.984663i | \(0.444180\pi\) | |||||||
\(42\) | −1.05833 | + | 1.05833i | −0.163303 | + | 0.163303i | ||||
\(43\) | −4.87703 | − | 4.87703i | −0.743741 | − | 0.743741i | 0.229555 | − | 0.973296i | \(-0.426273\pi\) |
−0.973296 | + | 0.229555i | \(0.926273\pi\) | |||||||
\(44\) | 5.04212 | 0.760128 | ||||||||
\(45\) | 1.96440 | + | 1.06824i | 0.292835 | + | 0.159244i | ||||
\(46\) | 2.90795i | 0.428755i | ||||||||
\(47\) | 5.72583 | + | 5.72583i | 0.835198 | + | 0.835198i | 0.988222 | − | 0.153024i | \(-0.0489013\pi\) |
−0.153024 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 4.75989i | − | 0.679985i | ||||||
\(50\) | −1.04593 | + | 4.88938i | −0.147917 | + | 0.691463i | ||||
\(51\) | −3.57968 | −0.501255 | ||||||||
\(52\) | 4.63173 | − | 4.63173i | 0.642306 | − | 0.642306i | ||||
\(53\) | 5.97851 | + | 5.97851i | 0.821212 | + | 0.821212i | 0.986282 | − | 0.165070i | \(-0.0527850\pi\) |
−0.165070 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −9.90473 | − | 5.38619i | −1.33555 | − | 0.726273i | ||||
\(56\) | −1.49670 | −0.200005 | ||||||||
\(57\) | −5.53975 | + | 5.53975i | −0.733758 | + | 0.733758i | ||||
\(58\) | 2.13246 | + | 2.13246i | 0.280005 | + | 0.280005i | ||||
\(59\) | − | 5.06330i | − | 0.659186i | −0.944123 | − | 0.329593i | \(-0.893088\pi\) | ||
0.944123 | − | 0.329593i | \(-0.106912\pi\) | |||||||
\(60\) | 0.633681 | + | 2.14440i | 0.0818079 | + | 0.276841i | ||||
\(61\) | − | 4.63816i | − | 0.593855i | −0.954900 | − | 0.296928i | \(-0.904038\pi\) | ||
0.954900 | − | 0.296928i | \(-0.0959620\pi\) | |||||||
\(62\) | 5.16912 | + | 2.06886i | 0.656479 | + | 0.262745i | ||||
\(63\) | 1.05833 | − | 1.05833i | 0.133336 | − | 0.133336i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −14.0464 | + | 4.15078i | −1.74224 | + | 0.514840i | ||||
\(66\) | −5.04212 | −0.620642 | ||||||||
\(67\) | −5.44255 | − | 5.44255i | −0.664913 | − | 0.664913i | 0.291621 | − | 0.956534i | \(-0.405805\pi\) |
−0.956534 | + | 0.291621i | \(0.905805\pi\) | |||||||
\(68\) | −2.53121 | − | 2.53121i | −0.306955 | − | 0.306955i | ||||
\(69\) | − | 2.90795i | − | 0.350077i | ||||||
\(70\) | 2.94011 | + | 1.59883i | 0.351411 | + | 0.191097i | ||||
\(71\) | 15.4412 | 1.83253 | 0.916266 | − | 0.400570i | \(-0.131188\pi\) | ||||
0.916266 | + | 0.400570i | \(0.131188\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.66109 | − | 5.66109i | −0.662580 | − | 0.662580i | 0.293407 | − | 0.955988i | \(-0.405211\pi\) |
−0.955988 | + | 0.293407i | \(0.905211\pi\) | |||||||
\(74\) | −3.23955 | −0.376590 | ||||||||
\(75\) | 1.04593 | − | 4.88938i | 0.120773 | − | 0.564577i | ||||
\(76\) | −7.83439 | −0.898666 | ||||||||
\(77\) | −5.33620 | + | 5.33620i | −0.608117 | + | 0.608117i | ||||
\(78\) | −4.63173 | + | 4.63173i | −0.524440 | + | 0.524440i | ||||
\(79\) | 12.7043 | 1.42935 | 0.714673 | − | 0.699458i | \(-0.246575\pi\) | ||||
0.714673 | + | 0.699458i | \(0.246575\pi\) | |||||||
\(80\) | −1.06824 | + | 1.96440i | −0.119433 | + | 0.219627i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.57987 | − | 1.57987i | −0.174468 | − | 0.174468i | ||||
\(83\) | −8.45297 | − | 8.45297i | −0.927834 | − | 0.927834i | 0.0697314 | − | 0.997566i | \(-0.477786\pi\) |
−0.997566 | + | 0.0697314i | \(0.977786\pi\) | |||||||
\(84\) | 1.49670 | 0.163303 | ||||||||
\(85\) | 2.26837 | + | 7.67626i | 0.246040 | + | 0.832607i | ||||
\(86\) | 6.89717i | 0.743741i | ||||||||
\(87\) | −2.13246 | − | 2.13246i | −0.228623 | − | 0.228623i | ||||
\(88\) | −3.56532 | − | 3.56532i | −0.380064 | − | 0.380064i | ||||
\(89\) | −2.92224 | −0.309757 | −0.154878 | − | 0.987934i | \(-0.549499\pi\) | ||||
−0.154878 | + | 0.987934i | \(0.549499\pi\) | |||||||
\(90\) | −0.633681 | − | 2.14440i | −0.0667959 | − | 0.226040i | ||||
\(91\) | 9.80376i | 1.02771i | ||||||||
\(92\) | 2.05623 | − | 2.05623i | 0.214377 | − | 0.214377i | ||||
\(93\) | −5.16912 | − | 2.06886i | −0.536013 | − | 0.214531i | ||||
\(94\) | − | 8.09754i | − | 0.835198i | ||||||
\(95\) | 15.3899 | + | 8.36900i | 1.57897 | + | 0.858641i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −7.21512 | − | 7.21512i | −0.732584 | − | 0.732584i | 0.238547 | − | 0.971131i | \(-0.423329\pi\) |
−0.971131 | + | 0.238547i | \(0.923329\pi\) | |||||||
\(98\) | −3.36575 | + | 3.36575i | −0.339992 | + | 0.339992i | ||||
\(99\) | 5.04212 | 0.506752 | ||||||||
\(100\) | 4.19690 | − | 2.71773i | 0.419690 | − | 0.271773i | ||||
\(101\) | −8.30366 | −0.826245 | −0.413123 | − | 0.910675i | \(-0.635562\pi\) | ||||
−0.413123 | + | 0.910675i | \(0.635562\pi\) | |||||||
\(102\) | 2.53121 | + | 2.53121i | 0.250628 | + | 0.250628i | ||||
\(103\) | 11.0318 | − | 11.0318i | 1.08700 | − | 1.08700i | 0.0911602 | − | 0.995836i | \(-0.470942\pi\) |
0.995836 | − | 0.0911602i | \(-0.0290575\pi\) | |||||||
\(104\) | −6.55026 | −0.642306 | ||||||||
\(105\) | −2.94011 | − | 1.59883i | −0.286926 | − | 0.156030i | ||||
\(106\) | − | 8.45489i | − | 0.821212i | ||||||
\(107\) | 1.51957 | + | 1.51957i | 0.146903 | + | 0.146903i | 0.776733 | − | 0.629830i | \(-0.216875\pi\) |
−0.629830 | + | 0.776733i | \(0.716875\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 10.4479i | 1.00073i | 0.865815 | + | 0.500364i | \(0.166800\pi\) | ||||
−0.865815 | + | 0.500364i | \(0.833200\pi\) | |||||||
\(110\) | 3.19509 | + | 10.8123i | 0.304640 | + | 1.03091i | ||||
\(111\) | 3.23955 | 0.307484 | ||||||||
\(112\) | 1.05833 | + | 1.05833i | 0.100002 | + | 0.100002i | ||||
\(113\) | 14.5661 | − | 14.5661i | 1.37026 | − | 1.37026i | 0.510216 | − | 0.860046i | \(-0.329565\pi\) |
0.860046 | − | 0.510216i | \(-0.170435\pi\) | |||||||
\(114\) | 7.83439 | 0.733758 | ||||||||
\(115\) | −6.23582 | + | 1.84272i | −0.581493 | + | 0.171834i | ||||
\(116\) | − | 3.01575i | − | 0.280005i | ||||||
\(117\) | 4.63173 | − | 4.63173i | 0.428204 | − | 0.428204i | ||||
\(118\) | −3.58030 | + | 3.58030i | −0.329593 | + | 0.329593i | ||||
\(119\) | 5.35770 | 0.491139 | ||||||||
\(120\) | 1.06824 | − | 1.96440i | 0.0975164 | − | 0.179324i | ||||
\(121\) | −14.4230 | −1.31118 | ||||||||
\(122\) | −3.27967 | + | 3.27967i | −0.296928 | + | 0.296928i | ||||
\(123\) | 1.57987 | + | 1.57987i | 0.142452 | + | 0.142452i | ||||
\(124\) | −2.19222 | − | 5.11803i | −0.196867 | − | 0.459612i | ||||
\(125\) | −11.1476 | + | 0.855419i | −0.997069 | + | 0.0765110i | ||||
\(126\) | −1.49670 | −0.133336 | ||||||||
\(127\) | −2.15923 | + | 2.15923i | −0.191601 | + | 0.191601i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.604787 | + | 0.796387i | \(0.293258\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 6.89717i | − | 0.607262i | ||||||
\(130\) | 12.8673 | + | 6.99724i | 1.12854 | + | 0.613699i | ||||
\(131\) | 0.0930152 | 0.00812678 | 0.00406339 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406339 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(132\) | 3.56532 | + | 3.56532i | 0.310321 | + | 0.310321i | ||||
\(133\) | 8.29133 | − | 8.29133i | 0.718950 | − | 0.718950i | ||||
\(134\) | 7.69692i | 0.664913i | ||||||||
\(135\) | 0.633681 | + | 2.14440i | 0.0545386 | + | 0.184561i | ||||
\(136\) | 3.57968i | 0.306955i | ||||||||
\(137\) | −4.24973 | + | 4.24973i | −0.363079 | + | 0.363079i | −0.864945 | − | 0.501866i | \(-0.832647\pi\) |
0.501866 | + | 0.864945i | \(0.332647\pi\) | |||||||
\(138\) | −2.05623 | + | 2.05623i | −0.175038 | + | 0.175038i | ||||
\(139\) | 4.79836 | 0.406991 | 0.203496 | − | 0.979076i | \(-0.434770\pi\) | ||||
0.203496 | + | 0.979076i | \(0.434770\pi\) | |||||||
\(140\) | −0.948429 | − | 3.20952i | −0.0801569 | − | 0.271254i | ||||
\(141\) | 8.09754i | 0.681936i | ||||||||
\(142\) | −10.9186 | − | 10.9186i | −0.916266 | − | 0.916266i | ||||
\(143\) | −23.3537 | + | 23.3537i | −1.95294 | + | 1.95294i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −3.22154 | + | 5.92413i | −0.267534 | + | 0.491972i | ||||
\(146\) | 8.00599i | 0.662580i | ||||||||
\(147\) | 3.36575 | − | 3.36575i | 0.277603 | − | 0.277603i | ||||
\(148\) | 2.29070 | + | 2.29070i | 0.188295 | + | 0.188295i | ||||
\(149\) | 11.4909i | 0.941373i | 0.882301 | + | 0.470686i | \(0.155994\pi\) | ||||
−0.882301 | + | 0.470686i | \(0.844006\pi\) | |||||||
\(150\) | −4.19690 | + | 2.71773i | −0.342675 | + | 0.221902i | ||||
\(151\) | 6.44191i | 0.524235i | 0.965036 | + | 0.262118i | \(0.0844209\pi\) | ||||
−0.965036 | + | 0.262118i | \(0.915579\pi\) | |||||||
\(152\) | 5.53975 | + | 5.53975i | 0.449333 | + | 0.449333i | ||||
\(153\) | −2.53121 | − | 2.53121i | −0.204637 | − | 0.204637i | ||||
\(154\) | 7.54653 | 0.608117 | ||||||||
\(155\) | −1.16088 | + | 12.3957i | −0.0932444 | + | 0.995643i | ||||
\(156\) | 6.55026 | 0.524440 | ||||||||
\(157\) | −3.09948 | − | 3.09948i | −0.247366 | − | 0.247366i | 0.572523 | − | 0.819889i | \(-0.305965\pi\) |
−0.819889 | + | 0.572523i | \(0.805965\pi\) | |||||||
\(158\) | −8.98330 | − | 8.98330i | −0.714673 | − | 0.714673i | ||||
\(159\) | 8.45489i | 0.670517i | ||||||||
\(160\) | 2.14440 | − | 0.633681i | 0.169530 | − | 0.0500969i | ||||
\(161\) | 4.35233i | 0.343012i | ||||||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −2.01708 | + | 2.01708i | −0.157990 | + | 0.157990i | −0.781675 | − | 0.623686i | \(-0.785635\pi\) |
0.623686 | + | 0.781675i | \(0.285635\pi\) | |||||||
\(164\) | 2.23428i | 0.174468i | ||||||||
\(165\) | −3.19509 | − | 10.8123i | −0.248738 | − | 0.841737i | ||||
\(166\) | 11.9543i | 0.927834i | ||||||||
\(167\) | 16.2544 | − | 16.2544i | 1.25780 | − | 1.25780i | 0.305666 | − | 0.952139i | \(-0.401121\pi\) |
0.952139 | − | 0.305666i | \(-0.0988791\pi\) | |||||||
\(168\) | −1.05833 | − | 1.05833i | −0.0816516 | − | 0.0816516i | ||||
\(169\) | 29.9059i | 2.30045i | ||||||||
\(170\) | 3.82395 | − | 7.03192i | 0.293284 | − | 0.539323i | ||||
\(171\) | −7.83439 | −0.599111 | ||||||||
\(172\) | 4.87703 | − | 4.87703i | 0.371870 | − | 0.371870i | ||||
\(173\) | 0.524672 | − | 0.524672i | 0.0398901 | − | 0.0398901i | −0.686880 | − | 0.726770i | \(-0.741020\pi\) |
0.726770 | + | 0.686880i | \(0.241020\pi\) | |||||||
\(174\) | 3.01575i | 0.228623i | ||||||||
\(175\) | −1.56544 | + | 7.31792i | −0.118336 | + | 0.553183i | ||||
\(176\) | 5.04212i | 0.380064i | ||||||||
\(177\) | 3.58030 | − | 3.58030i | 0.269112 | − | 0.269112i | ||||
\(178\) | 2.06634 | + | 2.06634i | 0.154878 | + | 0.154878i | ||||
\(179\) | 2.87084 | 0.214577 | 0.107288 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107288 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(180\) | −1.06824 | + | 1.96440i | −0.0796218 | + | 0.146418i | ||||
\(181\) | − | 25.7303i | − | 1.91252i | −0.292526 | − | 0.956258i | \(-0.594496\pi\) | ||
0.292526 | − | 0.956258i | \(-0.405504\pi\) | |||||||
\(182\) | 6.93231 | − | 6.93231i | 0.513857 | − | 0.513857i | ||||
\(183\) | 3.27967 | − | 3.27967i | 0.242440 | − | 0.242440i | ||||
\(184\) | −2.90795 | −0.214377 | ||||||||
\(185\) | −2.05284 | − | 6.94688i | −0.150928 | − | 0.510745i | ||||
\(186\) | 2.19222 | + | 5.11803i | 0.160741 | + | 0.375272i | ||||
\(187\) | 12.7627 | + | 12.7627i | 0.933299 | + | 0.933299i | ||||
\(188\) | −5.72583 | + | 5.72583i | −0.417599 | + | 0.417599i | ||||
\(189\) | 1.49670 | 0.108869 | ||||||||
\(190\) | −4.96450 | − | 16.8001i | −0.360163 | − | 1.21880i | ||||
\(191\) | 19.7130 | 1.42638 | 0.713192 | − | 0.700969i | \(-0.247249\pi\) | ||||
0.713192 | + | 0.700969i | \(0.247249\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −3.02398 | + | 3.02398i | −0.217671 | + | 0.217671i | −0.807516 | − | 0.589845i | \(-0.799189\pi\) |
0.589845 | + | 0.807516i | \(0.299189\pi\) | |||||||
\(194\) | 10.2037i | 0.732584i | ||||||||
\(195\) | −12.8673 | − | 6.99724i | −0.921448 | − | 0.501083i | ||||
\(196\) | 4.75989 | 0.339992 | ||||||||
\(197\) | 3.98103 | − | 3.98103i | 0.283636 | − | 0.283636i | −0.550921 | − | 0.834557i | \(-0.685723\pi\) |
0.834557 | + | 0.550921i | \(0.185723\pi\) | |||||||
\(198\) | −3.56532 | − | 3.56532i | −0.253376 | − | 0.253376i | ||||
\(199\) | 14.3596 | 1.01793 | 0.508964 | − | 0.860788i | \(-0.330029\pi\) | ||||
0.508964 | + | 0.860788i | \(0.330029\pi\) | |||||||
\(200\) | −4.88938 | − | 1.04593i | −0.345731 | − | 0.0739583i | ||||
\(201\) | − | 7.69692i | − | 0.542899i | ||||||
\(202\) | 5.87158 | + | 5.87158i | 0.413123 | + | 0.413123i | ||||
\(203\) | 3.19164 | + | 3.19164i | 0.224009 | + | 0.224009i | ||||
\(204\) | − | 3.57968i | − | 0.250628i | ||||||
\(205\) | 2.38674 | − | 4.38901i | 0.166697 | − | 0.306542i | ||||
\(206\) | −15.6013 | −1.08700 | ||||||||
\(207\) | 2.05623 | − | 2.05623i | 0.142918 | − | 0.142918i | ||||
\(208\) | 4.63173 | + | 4.63173i | 0.321153 | + | 0.321153i | ||||
\(209\) | 39.5019 | 2.73240 | ||||||||
\(210\) | 0.948429 | + | 3.20952i | 0.0654478 | + | 0.221478i | ||||
\(211\) | 9.13202 | 0.628674 | 0.314337 | − | 0.949311i | \(-0.398218\pi\) | ||||
0.314337 | + | 0.949311i | \(0.398218\pi\) | |||||||
\(212\) | −5.97851 | + | 5.97851i | −0.410606 | + | 0.410606i | ||||
\(213\) | 10.9186 | + | 10.9186i | 0.748128 | + | 0.748128i | ||||
\(214\) | − | 2.14900i | − | 0.146903i | ||||||
\(215\) | −14.7903 | + | 4.37060i | −1.00869 | + | 0.298073i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 7.73662 | + | 3.09646i | 0.525196 | + | 0.210201i | ||||
\(218\) | 7.38778 | − | 7.38778i | 0.500364 | − | 0.500364i | ||||
\(219\) | − | 8.00599i | − | 0.540994i | ||||||
\(220\) | 5.38619 | − | 9.90473i | 0.363137 | − | 0.667777i | ||||
\(221\) | 23.4478 | 1.57727 | ||||||||
\(222\) | −2.29070 | − | 2.29070i | −0.153742 | − | 0.153742i | ||||
\(223\) | 4.77518 | + | 4.77518i | 0.319770 | + | 0.319770i | 0.848679 | − | 0.528909i | \(-0.177399\pi\) |
−0.528909 | + | 0.848679i | \(0.677399\pi\) | |||||||
\(224\) | − | 1.49670i | − | 0.100002i | ||||||
\(225\) | 4.19690 | − | 2.71773i | 0.279793 | − | 0.181182i | ||||
\(226\) | −20.5996 | −1.37026 | ||||||||
\(227\) | −4.70595 | − | 4.70595i | −0.312345 | − | 0.312345i | 0.533473 | − | 0.845817i | \(-0.320887\pi\) |
−0.845817 | + | 0.533473i | \(0.820887\pi\) | |||||||
\(228\) | −5.53975 | − | 5.53975i | −0.366879 | − | 0.366879i | ||||
\(229\) | −25.0935 | −1.65823 | −0.829114 | − | 0.559080i | \(-0.811154\pi\) | ||||
−0.829114 | + | 0.559080i | \(0.811154\pi\) | |||||||
\(230\) | 5.71238 | + | 3.10639i | 0.376663 | + | 0.204829i | ||||
\(231\) | −7.54653 | −0.496525 | ||||||||
\(232\) | −2.13246 | + | 2.13246i | −0.140003 | + | 0.140003i | ||||
\(233\) | 19.4361 | − | 19.4361i | 1.27330 | − | 1.27330i | 0.328958 | − | 0.944345i | \(-0.393303\pi\) |
0.944345 | − | 0.328958i | \(-0.106697\pi\) | |||||||
\(234\) | −6.55026 | −0.428204 | ||||||||
\(235\) | 17.3644 | − | 5.13126i | 1.13273 | − | 0.334727i | ||||
\(236\) | 5.06330 | 0.329593 | ||||||||
\(237\) | 8.98330 | + | 8.98330i | 0.583528 | + | 0.583528i | ||||
\(238\) | −3.78846 | − | 3.78846i | −0.245570 | − | 0.245570i | ||||
\(239\) | 29.7199 | 1.92242 | 0.961211 | − | 0.275813i | \(-0.0889472\pi\) | ||||
0.961211 | + | 0.275813i | \(0.0889472\pi\) | |||||||
\(240\) | −2.14440 | + | 0.633681i | −0.138420 | + | 0.0409039i | ||||
\(241\) | 12.5924i | 0.811150i | 0.914062 | + | 0.405575i | \(0.132929\pi\) | ||||
−0.914062 | + | 0.405575i | \(0.867071\pi\) | |||||||
\(242\) | 10.1986 | + | 10.1986i | 0.655589 | + | 0.655589i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 4.63816 | 0.296928 | ||||||||
\(245\) | −9.35034 | − | 5.08471i | −0.597371 | − | 0.324850i | ||||
\(246\) | − | 2.23428i | − | 0.142452i | ||||||
\(247\) | 36.2868 | − | 36.2868i | 2.30887 | − | 2.30887i | ||||
\(248\) | −2.06886 | + | 5.16912i | −0.131373 | + | 0.328240i | ||||
\(249\) | − | 11.9543i | − | 0.757574i | ||||||
\(250\) | 8.48739 | + | 7.27765i | 0.536790 | + | 0.460279i | ||||
\(251\) | 19.1678i | 1.20986i | 0.796279 | + | 0.604930i | \(0.206799\pi\) | ||||
−0.796279 | + | 0.604930i | \(0.793201\pi\) | |||||||
\(252\) | 1.05833 | + | 1.05833i | 0.0666682 | + | 0.0666682i | ||||
\(253\) | −10.3678 | + | 10.3678i | −0.651817 | + | 0.651817i | ||||
\(254\) | 3.05361 | 0.191601 | ||||||||
\(255\) | −3.82395 | + | 7.03192i | −0.239465 | + | 0.440356i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.79449 | − | 2.79449i | −0.174315 | − | 0.174315i | 0.614557 | − | 0.788872i | \(-0.289335\pi\) |
−0.788872 | + | 0.614557i | \(0.789335\pi\) | |||||||
\(258\) | −4.87703 | + | 4.87703i | −0.303631 | + | 0.303631i | ||||
\(259\) | −4.84862 | −0.301279 | ||||||||
\(260\) | −4.15078 | − | 14.0464i | −0.257420 | − | 0.871119i | ||||
\(261\) | − | 3.01575i | − | 0.186670i | ||||||
\(262\) | −0.0657717 | − | 0.0657717i | −0.00406339 | − | 0.00406339i | ||||
\(263\) | −5.66131 | − | 5.66131i | −0.349091 | − | 0.349091i | 0.510680 | − | 0.859771i | \(-0.329394\pi\) |
−0.859771 | + | 0.510680i | \(0.829394\pi\) | |||||||
\(264\) | − | 5.04212i | − | 0.310321i | ||||||
\(265\) | 18.1307 | − | 5.35771i | 1.11376 | − | 0.329121i | ||||
\(266\) | −11.7257 | −0.718950 | ||||||||
\(267\) | −2.06634 | − | 2.06634i | −0.126458 | − | 0.126458i | ||||
\(268\) | 5.44255 | − | 5.44255i | 0.332456 | − | 0.332456i | ||||
\(269\) | −5.20425 | −0.317309 | −0.158654 | − | 0.987334i | \(-0.550716\pi\) | ||||
−0.158654 | + | 0.987334i | \(0.550716\pi\) | |||||||
\(270\) | 1.06824 | − | 1.96440i | 0.0650110 | − | 0.119550i | ||||
\(271\) | − | 15.3617i | − | 0.933156i | −0.884480 | − | 0.466578i | \(-0.845487\pi\) | ||
0.884480 | − | 0.466578i | \(-0.154513\pi\) | |||||||
\(272\) | 2.53121 | − | 2.53121i | 0.153477 | − | 0.153477i | ||||
\(273\) | −6.93231 | + | 6.93231i | −0.419562 | + | 0.419562i | ||||
\(274\) | 6.01002 | 0.363079 | ||||||||
\(275\) | −21.1612 | + | 13.7031i | −1.27607 | + | 0.826329i | ||||
\(276\) | 2.90795 | 0.175038 | ||||||||
\(277\) | −8.05810 | + | 8.05810i | −0.484165 | + | 0.484165i | −0.906459 | − | 0.422294i | \(-0.861225\pi\) |
0.422294 | + | 0.906459i | \(0.361225\pi\) | |||||||
\(278\) | −3.39295 | − | 3.39295i | −0.203496 | − | 0.203496i | ||||
\(279\) | −2.19222 | − | 5.11803i | −0.131245 | − | 0.306408i | ||||
\(280\) | −1.59883 | + | 2.94011i | −0.0955484 | + | 0.175705i | ||||
\(281\) | −19.3095 | −1.15191 | −0.575956 | − | 0.817481i | \(-0.695370\pi\) | ||||
−0.575956 | + | 0.817481i | \(0.695370\pi\) | |||||||
\(282\) | 5.72583 | − | 5.72583i | 0.340968 | − | 0.340968i | ||||
\(283\) | −8.89357 | + | 8.89357i | −0.528668 | + | 0.528668i | −0.920175 | − | 0.391507i | \(-0.871954\pi\) |
0.391507 | + | 0.920175i | \(0.371954\pi\) | |||||||
\(284\) | 15.4412i | 0.916266i | ||||||||
\(285\) | 4.96450 | + | 16.8001i | 0.294072 | + | 0.995149i | ||||
\(286\) | 33.0272 | 1.95294 | ||||||||
\(287\) | −2.36459 | − | 2.36459i | −0.139577 | − | 0.139577i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 4.18591i | 0.246230i | ||||||||
\(290\) | 6.46697 | − | 1.91102i | 0.379753 | − | 0.112219i | ||||
\(291\) | − | 10.2037i | − | 0.598153i | ||||||
\(292\) | 5.66109 | − | 5.66109i | 0.331290 | − | 0.331290i | ||||
\(293\) | 8.83411 | − | 8.83411i | 0.516094 | − | 0.516094i | −0.400293 | − | 0.916387i | \(-0.631092\pi\) |
0.916387 | + | 0.400293i | \(0.131092\pi\) | |||||||
\(294\) | −4.75989 | −0.277603 | ||||||||
\(295\) | −9.94635 | − | 5.40882i | −0.579099 | − | 0.314914i | ||||
\(296\) | − | 3.23955i | − | 0.188295i | ||||||
\(297\) | 3.56532 | + | 3.56532i | 0.206881 | + | 0.206881i | ||||
\(298\) | 8.12531 | − | 8.12531i | 0.470686 | − | 0.470686i | ||||
\(299\) | 19.0479i | 1.10157i | ||||||||
\(300\) | 4.88938 | + | 1.04593i | 0.282288 | + | 0.0603867i | ||||
\(301\) | 10.3230i | 0.595006i | ||||||||
\(302\) | 4.55512 | − | 4.55512i | 0.262118 | − | 0.262118i | ||||
\(303\) | −5.87158 | − | 5.87158i | −0.337313 | − | 0.337313i | ||||
\(304\) | − | 7.83439i | − | 0.449333i | ||||||
\(305\) | −9.11119 | − | 4.95466i | −0.521705 | − | 0.283703i | ||||
\(306\) | 3.57968i | 0.204637i | ||||||||
\(307\) | 6.62807 | + | 6.62807i | 0.378284 | + | 0.378284i | 0.870483 | − | 0.492199i | \(-0.163807\pi\) |
−0.492199 | + | 0.870483i | \(0.663807\pi\) | |||||||
\(308\) | −5.33620 | − | 5.33620i | −0.304058 | − | 0.304058i | ||||
\(309\) | 15.6013 | 0.887529 | ||||||||
\(310\) | 9.58592 | − | 7.94419i | 0.544444 | − | 0.451199i | ||||
\(311\) | −1.91776 | −0.108746 | −0.0543730 | − | 0.998521i | \(-0.517316\pi\) | ||||
−0.0543730 | + | 0.998521i | \(0.517316\pi\) | |||||||
\(312\) | −4.63173 | − | 4.63173i | −0.262220 | − | 0.262220i | ||||
\(313\) | 7.23497 | + | 7.23497i | 0.408945 | + | 0.408945i | 0.881370 | − | 0.472426i | \(-0.156622\pi\) |
−0.472426 | + | 0.881370i | \(0.656622\pi\) | |||||||
\(314\) | 4.38333i | 0.247366i | ||||||||
\(315\) | −0.948429 | − | 3.20952i | −0.0534379 | − | 0.180836i | ||||
\(316\) | 12.7043i | 0.714673i | ||||||||
\(317\) | −14.1306 | − | 14.1306i | −0.793656 | − | 0.793656i | 0.188430 | − | 0.982087i | \(-0.439660\pi\) |
−0.982087 | + | 0.188430i | \(0.939660\pi\) | |||||||
\(318\) | 5.97851 | − | 5.97851i | 0.335258 | − | 0.335258i | ||||
\(319\) | 15.2058i | 0.851359i | ||||||||
\(320\) | −1.96440 | − | 1.06824i | −0.109813 | − | 0.0597164i | ||||
\(321\) | 2.14900i | 0.119946i | ||||||||
\(322\) | 3.07756 | − | 3.07756i | 0.171506 | − | 0.171506i | ||||
\(323\) | −19.8305 | − | 19.8305i | −1.10340 | − | 1.10340i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −6.85110 | + | 32.0267i | −0.380031 | + | 1.77652i | ||||
\(326\) | 2.85258 | 0.157990 | ||||||||
\(327\) | −7.38778 | + | 7.38778i | −0.408545 | + | 0.408545i | ||||
\(328\) | 1.57987 | − | 1.57987i | 0.0872338 | − | 0.0872338i | ||||
\(329\) | − | 12.1196i | − | 0.668174i | ||||||
\(330\) | −5.38619 | + | 9.90473i | −0.296500 | + | 0.545238i | ||||
\(331\) | − | 10.6923i | − | 0.587704i | −0.955851 | − | 0.293852i | \(-0.905063\pi\) | ||
0.955851 | − | 0.293852i | \(-0.0949372\pi\) | |||||||
\(332\) | 8.45297 | − | 8.45297i | 0.463917 | − | 0.463917i | ||||
\(333\) | 2.29070 | + | 2.29070i | 0.125530 | + | 0.125530i | ||||
\(334\) | −22.9872 | −1.25780 | ||||||||
\(335\) | −16.5053 | + | 4.87739i | −0.901779 | + | 0.266480i | ||||
\(336\) | 1.49670i | 0.0816516i | ||||||||
\(337\) | −8.95306 | + | 8.95306i | −0.487704 | + | 0.487704i | −0.907581 | − | 0.419877i | \(-0.862073\pi\) |
0.419877 | + | 0.907581i | \(0.362073\pi\) | |||||||
\(338\) | 21.1467 | − | 21.1467i | 1.15023 | − | 1.15023i | ||||
\(339\) | 20.5996 | 1.11881 | ||||||||
\(340\) | −7.67626 | + | 2.26837i | −0.416303 | + | 0.123020i | ||||
\(341\) | 11.0534 | + | 25.8057i | 0.598576 | + | 1.39746i | ||||
\(342\) | 5.53975 | + | 5.53975i | 0.299555 | + | 0.299555i | ||||
\(343\) | −12.4458 | + | 12.4458i | −0.672010 | + | 0.672010i | ||||
\(344\) | −6.89717 | −0.371870 | ||||||||
\(345\) | −5.71238 | − | 3.10639i | −0.307544 | − | 0.167242i | ||||
\(346\) | −0.741998 | −0.0398901 | ||||||||
\(347\) | −9.87072 | + | 9.87072i | −0.529888 | + | 0.529888i | −0.920539 | − | 0.390651i | \(-0.872250\pi\) |
0.390651 | + | 0.920539i | \(0.372250\pi\) | |||||||
\(348\) | 2.13246 | − | 2.13246i | 0.114312 | − | 0.114312i | ||||
\(349\) | 7.65781i | 0.409913i | 0.978771 | + | 0.204957i | \(0.0657053\pi\) | ||||
−0.978771 | + | 0.204957i | \(0.934295\pi\) | |||||||
\(350\) | 6.28149 | − | 4.06762i | 0.335760 | − | 0.217424i | ||||
\(351\) | 6.55026 | 0.349627 | ||||||||
\(352\) | 3.56532 | − | 3.56532i | 0.190032 | − | 0.190032i | ||||
\(353\) | 0.693301 | + | 0.693301i | 0.0369007 | + | 0.0369007i | 0.725316 | − | 0.688416i | \(-0.241693\pi\) |
−0.688416 | + | 0.725316i | \(0.741693\pi\) | |||||||
\(354\) | −5.06330 | −0.269112 | ||||||||
\(355\) | 16.4949 | − | 30.3327i | 0.875457 | − | 1.60989i | ||||
\(356\) | − | 2.92224i | − | 0.154878i | ||||||
\(357\) | 3.78846 | + | 3.78846i | 0.200507 | + | 0.200507i | ||||
\(358\) | −2.02999 | − | 2.02999i | −0.107288 | − | 0.107288i | ||||
\(359\) | − | 12.9348i | − | 0.682672i | −0.939941 | − | 0.341336i | \(-0.889121\pi\) | ||
0.939941 | − | 0.341336i | \(-0.110879\pi\) | |||||||
\(360\) | 2.14440 | − | 0.633681i | 0.113020 | − | 0.0333979i | ||||
\(361\) | −42.3776 | −2.23040 | ||||||||
\(362\) | −18.1940 | + | 18.1940i | −0.956258 | + | 0.956258i | ||||
\(363\) | −10.1986 | − | 10.1986i | −0.535286 | − | 0.535286i | ||||
\(364\) | −9.80376 | −0.513857 | ||||||||
\(365\) | −17.1680 | + | 5.07324i | −0.898616 | + | 0.265546i | ||||
\(366\) | −4.63816 | −0.242440 | ||||||||
\(367\) | −16.9386 | + | 16.9386i | −0.884189 | + | 0.884189i | −0.993957 | − | 0.109768i | \(-0.964989\pi\) |
0.109768 | + | 0.993957i | \(0.464989\pi\) | |||||||
\(368\) | 2.05623 | + | 2.05623i | 0.107189 | + | 0.107189i | ||||
\(369\) | 2.23428i | 0.116312i | ||||||||
\(370\) | −3.46061 | + | 6.36376i | −0.179909 | + | 0.330836i | ||||
\(371\) | − | 12.6544i | − | 0.656985i | ||||||
\(372\) | 2.06886 | − | 5.16912i | 0.107265 | − | 0.268007i | ||||
\(373\) | −12.2249 | + | 12.2249i | −0.632981 | + | 0.632981i | −0.948815 | − | 0.315833i | \(-0.897716\pi\) |
0.315833 | + | 0.948815i | \(0.397716\pi\) | |||||||
\(374\) | − | 18.0492i | − | 0.933299i | ||||||
\(375\) | −8.48739 | − | 7.27765i | −0.438287 | − | 0.375816i | ||||
\(376\) | 8.09754 | 0.417599 | ||||||||
\(377\) | 13.9681 | + | 13.9681i | 0.719395 | + | 0.719395i | ||||
\(378\) | −1.05833 | − | 1.05833i | −0.0544344 | − | 0.0544344i | ||||
\(379\) | 20.4677i | 1.05135i | 0.850685 | + | 0.525676i | \(0.176188\pi\) | ||||
−0.850685 | + | 0.525676i | \(0.823812\pi\) | |||||||
\(380\) | −8.36900 | + | 15.3899i | −0.429321 | + | 0.789484i | ||||
\(381\) | −3.05361 | −0.156441 | ||||||||
\(382\) | −13.9392 | − | 13.9392i | −0.713192 | − | 0.713192i | ||||
\(383\) | 25.2058 | + | 25.2058i | 1.28796 | + | 1.28796i | 0.936027 | + | 0.351928i | \(0.114474\pi\) |
0.351928 | + | 0.936027i | \(0.385526\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.78209 | + | 16.1828i | 0.243718 | + | 0.824750i | ||||
\(386\) | 4.27656 | 0.217671 | ||||||||
\(387\) | 4.87703 | − | 4.87703i | 0.247914 | − | 0.247914i | ||||
\(388\) | 7.21512 | − | 7.21512i | 0.366292 | − | 0.366292i | ||||
\(389\) | 18.4973 | 0.937849 | 0.468924 | − | 0.883238i | \(-0.344642\pi\) | ||||
0.468924 | + | 0.883238i | \(0.344642\pi\) | |||||||
\(390\) | 4.15078 | + | 14.0464i | 0.210183 | + | 0.711266i | ||||
\(391\) | 10.4095 | 0.526433 | ||||||||
\(392\) | −3.36575 | − | 3.36575i | −0.169996 | − | 0.169996i | ||||
\(393\) | 0.0657717 | + | 0.0657717i | 0.00331774 | + | 0.00331774i | ||||
\(394\) | −5.63002 | −0.283636 | ||||||||
\(395\) | 13.5712 | − | 24.9563i | 0.682843 | − | 1.25569i | ||||
\(396\) | 5.04212i | 0.253376i | ||||||||
\(397\) | −8.45450 | − | 8.45450i | −0.424319 | − | 0.424319i | 0.462368 | − | 0.886688i | \(-0.347000\pi\) |
−0.886688 | + | 0.462368i | \(0.847000\pi\) | |||||||
\(398\) | −10.1538 | − | 10.1538i | −0.508964 | − | 0.508964i | ||||
\(399\) | 11.7257 | 0.587020 | ||||||||
\(400\) | 2.71773 | + | 4.19690i | 0.135887 | + | 0.209845i | ||||
\(401\) | − | 7.64200i | − | 0.381623i | −0.981627 | − | 0.190812i | \(-0.938888\pi\) | ||
0.981627 | − | 0.190812i | \(-0.0611119\pi\) | |||||||
\(402\) | −5.44255 | + | 5.44255i | −0.271450 | + | 0.271450i | ||||
\(403\) | 33.8591 | + | 13.5516i | 1.68664 | + | 0.675051i | ||||
\(404\) | − | 8.30366i | − | 0.413123i | ||||||
\(405\) | −1.06824 | + | 1.96440i | −0.0530812 | + | 0.0976118i | ||||
\(406\) | − | 4.51366i | − | 0.224009i | ||||||
\(407\) | −11.5500 | − | 11.5500i | −0.572512 | − | 0.572512i | ||||
\(408\) | −2.53121 | + | 2.53121i | −0.125314 | + | 0.125314i | ||||
\(409\) | −22.9311 | −1.13387 | −0.566935 | − | 0.823762i | \(-0.691871\pi\) | ||||
−0.566935 | + | 0.823762i | \(0.691871\pi\) | |||||||
\(410\) | −4.79118 | + | 1.41582i | −0.236619 | + | 0.0699223i | ||||
\(411\) | −6.01002 | −0.296453 | ||||||||
\(412\) | 11.0318 | + | 11.0318i | 0.543498 | + | 0.543498i | ||||
\(413\) | −5.35862 | + | 5.35862i | −0.263681 | + | 0.263681i | ||||
\(414\) | −2.90795 | −0.142918 | ||||||||
\(415\) | −25.6348 | + | 7.57522i | −1.25836 | + | 0.371853i | ||||
\(416\) | − | 6.55026i | − | 0.321153i | ||||||
\(417\) | 3.39295 | + | 3.39295i | 0.166154 | + | 0.166154i | ||||
\(418\) | −27.9321 | − | 27.9321i | −1.36620 | − | 1.36620i | ||||
\(419\) | − | 30.5175i | − | 1.49088i | −0.666575 | − | 0.745438i | \(-0.732240\pi\) | ||
0.666575 | − | 0.745438i | \(-0.267760\pi\) | |||||||
\(420\) | 1.59883 | − | 2.94011i | 0.0780150 | − | 0.143463i | ||||
\(421\) | 21.7751 | 1.06125 | 0.530627 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530627 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(422\) | −6.45731 | − | 6.45731i | −0.314337 | − | 0.314337i | ||||
\(423\) | −5.72583 | + | 5.72583i | −0.278399 | + | 0.278399i | ||||
\(424\) | 8.45489 | 0.410606 | ||||||||
\(425\) | 17.5024 | + | 3.74409i | 0.848991 | + | 0.181615i | ||||
\(426\) | − | 15.4412i | − | 0.748128i | ||||||
\(427\) | −4.90868 | + | 4.90868i | −0.237548 | + | 0.237548i | ||||
\(428\) | −1.51957 | + | 1.51957i | −0.0734514 | + | 0.0734514i | ||||
\(429\) | −33.0272 | −1.59457 | ||||||||
\(430\) | 13.5488 | + | 7.36782i | 0.653381 | + | 0.355308i | ||||
\(431\) | 0.781118 | 0.0376251 | 0.0188126 | − | 0.999823i | \(-0.494011\pi\) | ||||
0.0188126 | + | 0.999823i | \(0.494011\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −4.95534 | − | 4.95534i | −0.238138 | − | 0.238138i | 0.577941 | − | 0.816079i | \(-0.303857\pi\) |
−0.816079 | + | 0.577941i | \(0.803857\pi\) | |||||||
\(434\) | −3.28109 | − | 7.66014i | −0.157497 | − | 0.367698i | ||||
\(435\) | −6.46697 | + | 1.91102i | −0.310067 | + | 0.0916265i | ||||
\(436\) | −10.4479 | −0.500364 | ||||||||
\(437\) | 16.1093 | − | 16.1093i | 0.770614 | − | 0.770614i | ||||
\(438\) | −5.66109 | + | 5.66109i | −0.270497 | + | 0.270497i | ||||
\(439\) | 4.02017i | 0.191872i | 0.995387 | + | 0.0959362i | \(0.0305845\pi\) | ||||
−0.995387 | + | 0.0959362i | \(0.969416\pi\) | |||||||
\(440\) | −10.8123 | + | 3.19509i | −0.515457 | + | 0.152320i | ||||
\(441\) | 4.75989 | 0.226662 | ||||||||
\(442\) | −16.5801 | − | 16.5801i | −0.788635 | − | 0.788635i | ||||
\(443\) | 15.2507 | − | 15.2507i | 0.724582 | − | 0.724582i | −0.244953 | − | 0.969535i | \(-0.578773\pi\) |
0.969535 | + | 0.244953i | \(0.0787726\pi\) | |||||||
\(444\) | 3.23955i | 0.153742i | ||||||||
\(445\) | −3.12165 | + | 5.74045i | −0.147980 | + | 0.272123i | ||||
\(446\) | − | 6.75312i | − | 0.319770i | ||||||
\(447\) | −8.12531 | + | 8.12531i | −0.384314 | + | 0.384314i | ||||
\(448\) | −1.05833 | + | 1.05833i | −0.0500012 | + | 0.0500012i | ||||
\(449\) | −14.0081 | −0.661085 | −0.330542 | − | 0.943791i | \(-0.607232\pi\) | ||||
−0.330542 | + | 0.943791i | \(0.607232\pi\) | |||||||
\(450\) | −4.88938 | − | 1.04593i | −0.230488 | − | 0.0493055i | ||||
\(451\) | − | 11.2655i | − | 0.530471i | ||||||
\(452\) | 14.5661 | + | 14.5661i | 0.685131 | + | 0.685131i | ||||
\(453\) | −4.55512 | + | 4.55512i | −0.214018 | + | 0.214018i | ||||
\(454\) | 6.65522i | 0.312345i | ||||||||
\(455\) | 19.2585 | + | 10.4728i | 0.902853 | + | 0.490971i | ||||
\(456\) | 7.83439i | 0.366879i | ||||||||
\(457\) | −21.3948 | + | 21.3948i | −1.00081 | + | 1.00081i | −0.000807496 | 1.00000i | \(0.500257\pi\) | |
−1.00000 | 0.000807496i | \(0.999743\pi\) | ||||||||
\(458\) | 17.7438 | + | 17.7438i | 0.829114 | + | 0.829114i | ||||
\(459\) | − | 3.57968i | − | 0.167085i | ||||||
\(460\) | −1.84272 | − | 6.23582i | −0.0859171 | − | 0.290746i | ||||
\(461\) | 13.2812i | 0.618569i | 0.950970 | + | 0.309284i | \(0.100089\pi\) | ||||
−0.950970 | + | 0.309284i | \(0.899911\pi\) | |||||||
\(462\) | 5.33620 | + | 5.33620i | 0.248263 | + | 0.248263i | ||||
\(463\) | −5.97931 | − | 5.97931i | −0.277882 | − | 0.277882i | 0.554381 | − | 0.832263i | \(-0.312955\pi\) |
−0.832263 | + | 0.554381i | \(0.812955\pi\) | |||||||
\(464\) | 3.01575 | 0.140003 | ||||||||
\(465\) | −9.58592 | + | 7.94419i | −0.444537 | + | 0.368403i | ||||
\(466\) | −27.4868 | −1.27330 | ||||||||
\(467\) | −9.72180 | − | 9.72180i | −0.449871 | − | 0.449871i | 0.445440 | − | 0.895312i | \(-0.353047\pi\) |
−0.895312 | + | 0.445440i | \(0.853047\pi\) | |||||||
\(468\) | 4.63173 | + | 4.63173i | 0.214102 | + | 0.214102i | ||||
\(469\) | 11.5200i | 0.531943i | ||||||||
\(470\) | −15.9068 | − | 8.65011i | −0.733727 | − | 0.399000i | ||||
\(471\) | − | 4.38333i | − | 0.201973i | ||||||
\(472\) | −3.58030 | − | 3.58030i | −0.164797 | − | 0.164797i | ||||
\(473\) | −24.5906 | + | 24.5906i | −1.13068 | + | 1.13068i | ||||
\(474\) | − | 12.7043i | − | 0.583528i | ||||||
\(475\) | 32.8801 | − | 21.2918i | 1.50864 | − | 0.976933i | ||||
\(476\) | 5.35770i | 0.245570i | ||||||||
\(477\) | −5.97851 | + | 5.97851i | −0.273737 | + | 0.273737i | ||||
\(478\) | −21.0152 | − | 21.0152i | −0.961211 | − | 0.961211i | ||||
\(479\) | − | 15.8991i | − | 0.726446i | −0.931702 | − | 0.363223i | \(-0.881676\pi\) | ||
0.931702 | − | 0.363223i | \(-0.118324\pi\) | |||||||
\(480\) | 1.96440 | + | 1.06824i | 0.0896622 | + | 0.0487582i | ||||
\(481\) | −21.2199 | −0.967543 | ||||||||
\(482\) | 8.90420 | − | 8.90420i | 0.405575 | − | 0.405575i | ||||
\(483\) | −3.07756 | + | 3.07756i | −0.140034 | + | 0.140034i | ||||
\(484\) | − | 14.4230i | − | 0.655589i | ||||||
\(485\) | −21.8809 | + | 6.46590i | −0.993558 | + | 0.293602i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −2.16804 | + | 2.16804i | −0.0982432 | + | 0.0982432i | −0.754520 | − | 0.656277i | \(-0.772130\pi\) |
0.656277 | + | 0.754520i | \(0.272130\pi\) | |||||||
\(488\) | −3.27967 | − | 3.27967i | −0.148464 | − | 0.148464i | ||||
\(489\) | −2.85258 | −0.128998 | ||||||||
\(490\) | 3.01626 | + | 10.2071i | 0.136261 | + | 0.461110i | ||||
\(491\) | 19.8973i | 0.897951i | 0.893544 | + | 0.448975i | \(0.148211\pi\) | ||||
−0.893544 | + | 0.448975i | \(0.851789\pi\) | |||||||
\(492\) | −1.57987 | + | 1.57987i | −0.0712261 | + | 0.0712261i | ||||
\(493\) | 7.63350 | − | 7.63350i | 0.343796 | − | 0.343796i | ||||
\(494\) | −51.3173 | −2.30887 | ||||||||
\(495\) | 5.38619 | − | 9.90473i | 0.242091 | − | 0.445185i | ||||
\(496\) | 5.11803 | − | 2.19222i | 0.229806 | − | 0.0984335i | ||||
\(497\) | −16.3418 | − | 16.3418i | −0.733030 | − | 0.733030i | ||||
\(498\) | −8.45297 | + | 8.45297i | −0.378787 | + | 0.378787i | ||||
\(499\) | 3.74882 | 0.167820 | 0.0839100 | − | 0.996473i | \(-0.473259\pi\) | ||||
0.0839100 | + | 0.996473i | \(0.473259\pi\) | |||||||
\(500\) | −0.855419 | − | 11.1476i | −0.0382555 | − | 0.498534i | ||||
\(501\) | 22.9872 | 1.02699 | ||||||||
\(502\) | 13.5537 | − | 13.5537i | 0.604930 | − | 0.604930i | ||||
\(503\) | −26.1897 | + | 26.1897i | −1.16774 | + | 1.16774i | −0.185003 | + | 0.982738i | \(0.559229\pi\) |
−0.982738 | + | 0.185003i | \(0.940771\pi\) | |||||||
\(504\) | − | 1.49670i | − | 0.0666682i | ||||||
\(505\) | −8.87030 | + | 16.3117i | −0.394723 | + | 0.725861i | ||||
\(506\) | 14.6623 | 0.651817 | ||||||||
\(507\) | −21.1467 | + | 21.1467i | −0.939156 | + | 0.939156i | ||||
\(508\) | −2.15923 | − | 2.15923i | −0.0958003 | − | 0.0958003i | ||||
\(509\) | −40.5226 | −1.79613 | −0.898067 | − | 0.439859i | \(-0.855028\pi\) | ||||
−0.898067 | + | 0.439859i | \(0.855028\pi\) | |||||||
\(510\) | 7.67626 | − | 2.26837i | 0.339910 | − | 0.100445i | ||||
\(511\) | 11.9825i | 0.530077i | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.53975 | − | 5.53975i | −0.244586 | − | 0.244586i | ||||
\(514\) | 3.95200i | 0.174315i | ||||||||
\(515\) | −9.88627 | − | 33.4555i | −0.435641 | − | 1.47422i | ||||
\(516\) | 6.89717 | 0.303631 | ||||||||
\(517\) | 28.8703 | − | 28.8703i | 1.26971 | − | 1.26971i | ||||
\(518\) | 3.42849 | + | 3.42849i | 0.150639 | + | 0.150639i | ||||
\(519\) | 0.741998 | 0.0325701 | ||||||||
\(520\) | −6.99724 | + | 12.8673i | −0.306849 | + | 0.564270i | ||||
\(521\) | 13.8583 | 0.607142 | 0.303571 | − | 0.952809i | \(-0.401821\pi\) | ||||
0.303571 | + | 0.952809i | \(0.401821\pi\) | |||||||
\(522\) | −2.13246 | + | 2.13246i | −0.0933350 | + | 0.0933350i | ||||
\(523\) | −17.8505 | − | 17.8505i | −0.780546 | − | 0.780546i | 0.199377 | − | 0.979923i | \(-0.436108\pi\) |
−0.979923 | + | 0.199377i | \(0.936108\pi\) | |||||||
\(524\) | 0.0930152i | 0.00406339i | ||||||||
\(525\) | −6.28149 | + | 4.06762i | −0.274147 | + | 0.177526i | ||||
\(526\) | 8.00630i | 0.349091i | ||||||||
\(527\) | 7.40584 | − | 18.5038i | 0.322604 | − | 0.806038i | ||||
\(528\) | −3.56532 | + | 3.56532i | −0.155160 | + | 0.155160i | ||||
\(529\) | − | 14.5438i | − | 0.632339i | ||||||
\(530\) | −16.6088 | − | 9.03185i | −0.721440 | − | 0.392318i | ||||
\(531\) | 5.06330 | 0.219729 | ||||||||
\(532\) | 8.29133 | + | 8.29133i | 0.359475 | + | 0.359475i | ||||
\(533\) | −10.3486 | − | 10.3486i | −0.448246 | − | 0.448246i | ||||
\(534\) | 2.92224i | 0.126458i | ||||||||
\(535\) | 4.60832 | − | 1.36178i | 0.199235 | − | 0.0588750i | ||||
\(536\) | −7.69692 | −0.332456 | ||||||||
\(537\) | 2.02999 | + | 2.02999i | 0.0876007 | + | 0.0876007i | ||||
\(538\) | 3.67996 | + | 3.67996i | 0.158654 | + | 0.158654i | ||||
\(539\) | −24.0000 | −1.03375 | ||||||||
\(540\) | −2.14440 | + | 0.633681i | −0.0922803 | + | 0.0272693i | ||||
\(541\) | 35.7301 | 1.53616 | 0.768078 | − | 0.640356i | \(-0.221213\pi\) | ||||
0.768078 | + | 0.640356i | \(0.221213\pi\) | |||||||
\(542\) | −10.8624 | + | 10.8624i | −0.466578 | + | 0.466578i | ||||
\(543\) | 18.1940 | − | 18.1940i | 0.780781 | − | 0.780781i | ||||
\(544\) | −3.57968 | −0.153477 | ||||||||
\(545\) | 20.5239 | + | 11.1609i | 0.879145 | + | 0.478079i | ||||
\(546\) | 9.80376 | 0.419562 | ||||||||
\(547\) | 30.1622 | + | 30.1622i | 1.28964 | + | 1.28964i | 0.935002 | + | 0.354642i | \(0.115397\pi\) |
0.354642 | + | 0.935002i | \(0.384603\pi\) | |||||||
\(548\) | −4.24973 | − | 4.24973i | −0.181539 | − | 0.181539i | ||||
\(549\) | 4.63816 | 0.197952 | ||||||||
\(550\) | 24.6528 | + | 5.27369i | 1.05120 | + | 0.224871i | ||||
\(551\) | − | 23.6265i | − | 1.00652i | ||||||
\(552\) | −2.05623 | − | 2.05623i | −0.0875192 | − | 0.0875192i | ||||
\(553\) | −13.4453 | − | 13.4453i | −0.571752 | − | 0.571752i | ||||
\(554\) | 11.3959 | 0.484165 | ||||||||
\(555\) | 3.46061 | − | 6.36376i | 0.146895 | − | 0.270127i | ||||
\(556\) | 4.79836i | 0.203496i | ||||||||
\(557\) | 16.5286 | − | 16.5286i | 0.700339 | − | 0.700339i | −0.264144 | − | 0.964483i | \(-0.585090\pi\) |
0.964483 | + | 0.264144i | \(0.0850896\pi\) | |||||||
\(558\) | −2.06886 | + | 5.16912i | −0.0875818 | + | 0.218826i | ||||
\(559\) | 45.1782i | 1.91084i | ||||||||
\(560\) | 3.20952 | − | 0.948429i | 0.135627 | − | 0.0400784i | ||||
\(561\) | 18.0492i | 0.762036i | ||||||||
\(562\) | 13.6539 | + | 13.6539i | 0.575956 | + | 0.575956i | ||||
\(563\) | −4.44405 | + | 4.44405i | −0.187294 | + | 0.187294i | −0.794525 | − | 0.607231i | \(-0.792280\pi\) |
0.607231 | + | 0.794525i | \(0.292280\pi\) | |||||||
\(564\) | −8.09754 | −0.340968 | ||||||||
\(565\) | −13.0536 | − | 44.1737i | −0.549167 | − | 1.85840i | ||||
\(566\) | 12.5774 | 0.528668 | ||||||||
\(567\) | 1.05833 | + | 1.05833i | 0.0444455 | + | 0.0444455i | ||||
\(568\) | 10.9186 | − | 10.9186i | 0.458133 | − | 0.458133i | ||||
\(569\) | −25.1454 | −1.05415 | −0.527075 | − | 0.849819i | \(-0.676711\pi\) | ||||
−0.527075 | + | 0.849819i | \(0.676711\pi\) | |||||||
\(570\) | 8.36900 | − | 15.3899i | 0.350539 | − | 0.644611i | ||||
\(571\) | − | 16.7647i | − | 0.701581i | −0.936454 | − | 0.350790i | \(-0.885913\pi\) | ||
0.936454 | − | 0.350790i | \(-0.114087\pi\) | |||||||
\(572\) | −23.3537 | − | 23.3537i | −0.976469 | − | 0.976469i | ||||
\(573\) | 13.9392 | + | 13.9392i | 0.582319 | + | 0.582319i | ||||
\(574\) | 3.34404i | 0.139577i | ||||||||
\(575\) | −3.04151 | + | 14.2181i | −0.126840 | + | 0.592936i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −2.00618 | − | 2.00618i | −0.0835185 | − | 0.0835185i | 0.664113 | − | 0.747632i | \(-0.268809\pi\) |
−0.747632 | + | 0.664113i | \(0.768809\pi\) | |||||||
\(578\) | 2.95989 | − | 2.95989i | 0.123115 | − | 0.123115i | ||||
\(579\) | −4.27656 | −0.177728 | ||||||||
\(580\) | −5.92413 | − | 3.22154i | −0.245986 | − | 0.133767i | ||||
\(581\) | 17.8920i | 0.742285i | ||||||||
\(582\) | −7.21512 | + | 7.21512i | −0.299076 | + | 0.299076i | ||||
\(583\) | 30.1444 | − | 30.1444i | 1.24845 | − | 1.24845i | ||||
\(584\) | −8.00599 | −0.331290 | ||||||||
\(585\) | −4.15078 | − | 14.0464i | −0.171613 | − | 0.580746i | ||||
\(586\) | −12.4933 | −0.516094 | ||||||||
\(587\) | −0.268866 | + | 0.268866i | −0.0110973 | + | 0.0110973i | −0.712634 | − | 0.701536i | \(-0.752498\pi\) |
0.701536 | + | 0.712634i | \(0.252498\pi\) | |||||||
\(588\) | 3.36575 | + | 3.36575i | 0.138801 | + | 0.138801i | ||||
\(589\) | −17.1747 | − | 40.0966i | −0.707670 | − | 1.65215i | ||||
\(590\) | 3.20852 | + | 10.8577i | 0.132093 | + | 0.447006i | ||||
\(591\) | 5.63002 | 0.231588 | ||||||||
\(592\) | −2.29070 | + | 2.29070i | −0.0941474 | + | 0.0941474i | ||||
\(593\) | −11.4240 | + | 11.4240i | −0.469128 | + | 0.469128i | −0.901632 | − | 0.432504i | \(-0.857630\pi\) |
0.432504 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(594\) | − | 5.04212i | − | 0.206881i | ||||||
\(595\) | 5.72330 | − | 10.5247i | 0.234632 | − | 0.431469i | ||||
\(596\) | −11.4909 | −0.470686 | ||||||||
\(597\) | 10.1538 | + | 10.1538i | 0.415567 | + | 0.415567i | ||||
\(598\) | 13.4689 | − | 13.4689i | 0.550783 | − | 0.550783i | ||||
\(599\) | 19.1063i | 0.780662i | 0.920675 | + | 0.390331i | \(0.127639\pi\) | ||||
−0.920675 | + | 0.390331i | \(0.872361\pi\) | |||||||
\(600\) | −2.71773 | − | 4.19690i | −0.110951 | − | 0.171338i | ||||
\(601\) | − | 43.1864i | − | 1.76161i | −0.473479 | − | 0.880805i | \(-0.657002\pi\) | ||
0.473479 | − | 0.880805i | \(-0.342998\pi\) | |||||||
\(602\) | 7.29945 | − | 7.29945i | 0.297503 | − | 0.297503i | ||||
\(603\) | 5.44255 | − | 5.44255i | 0.221638 | − | 0.221638i | ||||
\(604\) | −6.44191 | −0.262118 | ||||||||
\(605\) | −15.4072 | + | 28.3324i | −0.626390 | + | 1.15188i | ||||
\(606\) | 8.30366i | 0.337313i | ||||||||
\(607\) | −26.2758 | − | 26.2758i | −1.06650 | − | 1.06650i | −0.997625 | − | 0.0688749i | \(-0.978059\pi\) |
−0.0688749 | − | 0.997625i | \(-0.521941\pi\) | |||||||
\(608\) | −5.53975 | + | 5.53975i | −0.224666 | + | 0.224666i | ||||
\(609\) | 4.51366i | 0.182903i | ||||||||
\(610\) | 2.93911 | + | 9.94606i | 0.119001 | + | 0.402704i | ||||
\(611\) | − | 53.0410i | − | 2.14581i | ||||||
\(612\) | 2.53121 | − | 2.53121i | 0.102318 | − | 0.102318i | ||||
\(613\) | 9.84589 | + | 9.84589i | 0.397672 | + | 0.397672i | 0.877411 | − | 0.479739i | \(-0.159269\pi\) |
−0.479739 | + | 0.877411i | \(0.659269\pi\) | |||||||
\(614\) | − | 9.37351i | − | 0.378284i | ||||||
\(615\) | 4.79118 | − | 1.41582i | 0.193199 | − | 0.0570913i | ||||
\(616\) | 7.54653i | 0.304058i | ||||||||
\(617\) | 0.731349 | + | 0.731349i | 0.0294430 | + | 0.0294430i | 0.721675 | − | 0.692232i | \(-0.243373\pi\) |
−0.692232 | + | 0.721675i | \(0.743373\pi\) | |||||||
\(618\) | −11.0318 | − | 11.0318i | −0.443764 | − | 0.443764i | ||||
\(619\) | 47.6445 | 1.91500 | 0.957498 | − | 0.288441i | \(-0.0931371\pi\) | ||||
0.957498 | + | 0.288441i | \(0.0931371\pi\) | |||||||
\(620\) | −12.3957 | − | 1.16088i | −0.497822 | − | 0.0466222i | ||||
\(621\) | 2.90795 | 0.116692 | ||||||||
\(622\) | 1.35606 | + | 1.35606i | 0.0543730 | + | 0.0543730i | ||||
\(623\) | 3.09268 | + | 3.09268i | 0.123906 | + | 0.123906i | ||||
\(624\) | 6.55026i | 0.262220i | ||||||||
\(625\) | −10.2279 | + | 22.8121i | −0.409115 | + | 0.912483i | ||||
\(626\) | − | 10.2318i | − | 0.408945i | ||||||
\(627\) | 27.9321 | + | 27.9321i | 1.11550 | + | 1.11550i | ||||
\(628\) | 3.09948 | − | 3.09948i | 0.123683 | − | 0.123683i | ||||
\(629\) | 11.5965i | 0.462384i | ||||||||
\(630\) | −1.59883 | + | 2.94011i | −0.0636990 | + | 0.117137i | ||||
\(631\) | − | 9.24375i | − | 0.367988i | −0.982927 | − | 0.183994i | \(-0.941097\pi\) | ||
0.982927 | − | 0.183994i | \(-0.0589027\pi\) | |||||||
\(632\) | 8.98330 | − | 8.98330i | 0.357337 | − | 0.357337i | ||||
\(633\) | 6.45731 | + | 6.45731i | 0.256655 | + | 0.256655i | ||||
\(634\) | 19.9838i | 0.793656i | ||||||||
\(635\) | 1.93502 | + | 6.54816i | 0.0767888 | + | 0.259856i | ||||
\(636\) | −8.45489 | −0.335258 | ||||||||
\(637\) | −22.0466 | + | 22.0466i | −0.873517 | + | 0.873517i | ||||
\(638\) | 10.7521 | − | 10.7521i | 0.425679 | − | 0.425679i | ||||
\(639\) | 15.4412i | 0.610844i | ||||||||
\(640\) | 0.633681 | + | 2.14440i | 0.0250484 | + | 0.0847648i | ||||
\(641\) | − | 38.8629i | − | 1.53499i | −0.641055 | − | 0.767495i | \(-0.721503\pi\) | ||
0.641055 | − | 0.767495i | \(-0.278497\pi\) | |||||||
\(642\) | 1.51957 | − | 1.51957i | 0.0599728 | − | 0.0599728i | ||||
\(643\) | 16.8017 | + | 16.8017i | 0.662595 | + | 0.662595i | 0.955991 | − | 0.293396i | \(-0.0947854\pi\) |
−0.293396 | + | 0.955991i | \(0.594785\pi\) | |||||||
\(644\) | −4.35233 | −0.171506 | ||||||||
\(645\) | −13.5488 | − | 7.36782i | −0.533483 | − | 0.290108i | ||||
\(646\) | 28.0446i | 1.10340i | ||||||||
\(647\) | 10.8269 | − | 10.8269i | 0.425650 | − | 0.425650i | −0.461494 | − | 0.887144i | \(-0.652686\pi\) |
0.887144 | + | 0.461494i | \(0.152686\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | −25.5298 | −1.00213 | ||||||||
\(650\) | 27.4908 | − | 17.8018i | 1.07828 | − | 0.698246i | ||||
\(651\) | 3.28109 | + | 7.66014i | 0.128596 | + | 0.300224i | ||||
\(652\) | −2.01708 | − | 2.01708i | −0.0789949 | − | 0.0789949i | ||||
\(653\) | 2.85826 | − | 2.85826i | 0.111852 | − | 0.111852i | −0.648965 | − | 0.760818i | \(-0.724798\pi\) |
0.760818 | + | 0.648965i | \(0.224798\pi\) | |||||||
\(654\) | 10.4479 | 0.408545 | ||||||||
\(655\) | 0.0993625 | − | 0.182719i | 0.00388241 | − | 0.00713942i | ||||
\(656\) | −2.23428 | −0.0872338 | ||||||||
\(657\) | 5.66109 | − | 5.66109i | 0.220860 | − | 0.220860i | ||||
\(658\) | −8.56984 | + | 8.56984i | −0.334087 | + | 0.334087i | ||||
\(659\) | − | 31.5214i | − | 1.22790i | −0.789345 | − | 0.613950i | \(-0.789580\pi\) | ||
0.789345 | − | 0.613950i | \(-0.210420\pi\) | |||||||
\(660\) | 10.8123 | − | 3.19509i | 0.420869 | − | 0.124369i | ||||
\(661\) | −16.6869 | −0.649047 | −0.324523 | − | 0.945878i | \(-0.605204\pi\) | ||||
−0.324523 | + | 0.945878i | \(0.605204\pi\) | |||||||
\(662\) | −7.56062 | + | 7.56062i | −0.293852 | + | 0.293852i | ||||
\(663\) | 16.5801 | + | 16.5801i | 0.643918 | + | 0.643918i | ||||
\(664\) | −11.9543 | −0.463917 | ||||||||
\(665\) | −7.43036 | − | 25.1446i | −0.288137 | − | 0.975066i | ||||
\(666\) | − | 3.23955i | − | 0.125530i | ||||||
\(667\) | 6.20108 | + | 6.20108i | 0.240107 | + | 0.240107i | ||||
\(668\) | 16.2544 | + | 16.2544i | 0.628902 | + | 0.628902i | ||||
\(669\) | 6.75312i | 0.261091i | ||||||||
\(670\) | 15.1198 | + | 8.22215i | 0.584130 | + | 0.317649i | ||||
\(671\) | −23.3861 | −0.902812 | ||||||||
\(672\) | 1.05833 | − | 1.05833i | 0.0408258 | − | 0.0408258i | ||||
\(673\) | 27.7515 | + | 27.7515i | 1.06974 | + | 1.06974i | 0.997378 | + | 0.0723632i | \(0.0230541\pi\) |
0.0723632 | + | 0.997378i | \(0.476946\pi\) | |||||||
\(674\) | 12.6615 | 0.487704 | ||||||||
\(675\) | 4.88938 | + | 1.04593i | 0.188192 | + | 0.0402578i | ||||
\(676\) | −29.9059 | −1.15023 | ||||||||
\(677\) | −25.1068 | + | 25.1068i | −0.964933 | + | 0.964933i | −0.999406 | − | 0.0344722i | \(-0.989025\pi\) |
0.0344722 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(678\) | −14.5661 | − | 14.5661i | −0.559407 | − | 0.559407i | ||||
\(679\) | 15.2719i | 0.586081i | ||||||||
\(680\) | 7.03192 | + | 3.82395i | 0.269662 | + | 0.146642i | ||||
\(681\) | − | 6.65522i | − | 0.255028i | ||||||
\(682\) | 10.4314 | − | 26.0633i | 0.399440 | − | 0.998016i | ||||
\(683\) | 4.29572 | − | 4.29572i | 0.164371 | − | 0.164371i | −0.620129 | − | 0.784500i | \(-0.712920\pi\) |
0.784500 | + | 0.620129i | \(0.212920\pi\) | |||||||
\(684\) | − | 7.83439i | − | 0.299555i | ||||||
\(685\) | 3.80844 | + | 12.8879i | 0.145513 | + | 0.492421i | ||||
\(686\) | 17.6010 | 0.672010 | ||||||||
\(687\) | −17.7438 | − | 17.7438i | −0.676968 | − | 0.676968i | ||||
\(688\) | 4.87703 | + | 4.87703i | 0.185935 | + | 0.185935i | ||||
\(689\) | − | 55.3817i | − | 2.10988i | ||||||
\(690\) | 1.84272 | + | 6.23582i | 0.0701510 | + | 0.237393i | ||||
\(691\) | −39.6224 | −1.50731 | −0.753654 | − | 0.657271i | \(-0.771711\pi\) | ||||
−0.753654 | + | 0.657271i | \(0.771711\pi\) | |||||||
\(692\) | 0.524672 | + | 0.524672i | 0.0199450 | + | 0.0199450i | ||||
\(693\) | −5.33620 | − | 5.33620i | −0.202706 | − | 0.202706i | ||||
\(694\) | 13.9593 | 0.529888 | ||||||||
\(695\) | 5.12579 | − | 9.42589i | 0.194432 | − | 0.357544i | ||||
\(696\) | −3.01575 | −0.114312 | ||||||||
\(697\) | −5.65543 | + | 5.65543i | −0.214215 | + | 0.214215i | ||||
\(698\) | 5.41489 | − | 5.41489i | 0.204957 | − | 0.204957i | ||||
\(699\) | 27.4868 | 1.03965 | ||||||||
\(700\) | −7.31792 | − | 1.56544i | −0.276592 | − | 0.0591680i | ||||
\(701\) | 27.1869 | 1.02683 | 0.513417 | − | 0.858139i | \(-0.328379\pi\) | ||||
0.513417 | + | 0.858139i | \(0.328379\pi\) | |||||||
\(702\) | −4.63173 | − | 4.63173i | −0.174813 | − | 0.174813i | ||||
\(703\) | 17.9463 | + | 17.9463i | 0.676856 | + | 0.676856i | ||||
\(704\) | −5.04212 | −0.190032 | ||||||||
\(705\) | 15.9068 | + | 8.65011i | 0.599085 | + | 0.325782i | ||||
\(706\) | − | 0.980476i | − | 0.0369007i | ||||||
\(707\) | 8.78798 | + | 8.78798i | 0.330506 | + | 0.330506i | ||||
\(708\) | 3.58030 | + | 3.58030i | 0.134556 | + | 0.134556i | ||||
\(709\) | 18.1008 | 0.679790 | 0.339895 | − | 0.940463i | \(-0.389608\pi\) | ||||
0.339895 | + | 0.940463i | \(0.389608\pi\) | |||||||
\(710\) | −33.1121 | + | 9.78479i | −1.24267 | + | 0.367217i | ||||
\(711\) | 12.7043i | 0.476449i | ||||||||
\(712\) | −2.06634 | + | 2.06634i | −0.0774392 | + | 0.0774392i | ||||
\(713\) | 15.0316 | + | 6.01615i | 0.562937 | + | 0.225306i | ||||
\(714\) | − | 5.35770i | − | 0.200507i | ||||||
\(715\) | 20.9287 | + | 70.8235i | 0.782689 | + | 2.64865i | ||||
\(716\) | 2.87084i | 0.107288i | ||||||||
\(717\) | 21.0152 | + | 21.0152i | 0.784826 | + | 0.784826i | ||||
\(718\) | −9.14628 | + | 9.14628i | −0.341336 | + | 0.341336i | ||||
\(719\) | 38.6292 | 1.44062 | 0.720312 | − | 0.693650i | \(-0.243998\pi\) | ||||
0.720312 | + | 0.693650i | \(0.243998\pi\) | |||||||
\(720\) | −1.96440 | − | 1.06824i | −0.0732088 | − | 0.0398109i | ||||
\(721\) | −23.3505 | −0.869618 | ||||||||
\(722\) | 29.9655 | + | 29.9655i | 1.11520 | + | 1.11520i | ||||
\(723\) | −8.90420 | + | 8.90420i | −0.331151 | + | 0.331151i | ||||
\(724\) | 25.7303 | 0.956258 | ||||||||
\(725\) | 8.19599 | + | 12.6568i | 0.304391 | + | 0.470061i | ||||
\(726\) | 14.4230i | 0.535286i | ||||||||
\(727\) | −11.1771 | − | 11.1771i | −0.414537 | − | 0.414537i | 0.468779 | − | 0.883316i | \(-0.344694\pi\) |
−0.883316 | + | 0.468779i | \(0.844694\pi\) | |||||||
\(728\) | 6.93231 | + | 6.93231i | 0.256928 | + | 0.256928i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 15.7270 | + | 8.55231i | 0.582081 | + | 0.316535i | ||||
\(731\) | 24.6896 | 0.913179 | ||||||||
\(732\) | 3.27967 | + | 3.27967i | 0.121220 | + | 0.121220i | ||||
\(733\) | 24.3154 | − | 24.3154i | 0.898109 | − | 0.898109i | −0.0971596 | − | 0.995269i | \(-0.530976\pi\) |
0.995269 | + | 0.0971596i | \(0.0309757\pi\) | |||||||
\(734\) | 23.9548 | 0.884189 | ||||||||
\(735\) | −3.01626 | − | 10.2071i | −0.111256 | − | 0.376495i | ||||
\(736\) | − | 2.90795i | − | 0.107189i | ||||||
\(737\) | −27.4420 | + | 27.4420i | −1.01084 | + | 1.01084i | ||||
\(738\) | 1.57987 | − | 1.57987i | 0.0581559 | − | 0.0581559i | ||||
\(739\) | −49.5046 | −1.82106 | −0.910528 | − | 0.413447i | \(-0.864325\pi\) | ||||
−0.910528 | + | 0.413447i | \(0.864325\pi\) | |||||||
\(740\) | 6.94688 | − | 2.05284i | 0.255372 | − | 0.0754639i | ||||
\(741\) | 51.3173 | 1.88519 | ||||||||
\(742\) | −8.94803 | + | 8.94803i | −0.328492 | + | 0.328492i | ||||
\(743\) | 31.5991 | + | 31.5991i | 1.15926 | + | 1.15926i | 0.984635 | + | 0.174624i | \(0.0558711\pi\) |
0.174624 | + | 0.984635i | \(0.444129\pi\) | |||||||
\(744\) | −5.11803 | + | 2.19222i | −0.187636 | + | 0.0803706i | ||||
\(745\) | 22.5728 | + | 12.2751i | 0.827002 | + | 0.449723i | ||||
\(746\) | 17.2886 | 0.632981 | ||||||||
\(747\) | 8.45297 | − | 8.45297i | 0.309278 | − | 0.309278i | ||||
\(748\) | −12.7627 | + | 12.7627i | −0.466650 | + | 0.466650i | ||||
\(749\) | − | 3.21641i | − | 0.117525i | ||||||
\(750\) | 0.855419 | + | 11.1476i | 0.0312355 | + | 0.407052i | ||||
\(751\) | 25.3950 | 0.926677 | 0.463338 | − | 0.886181i | \(-0.346651\pi\) | ||||
0.463338 | + | 0.886181i | \(0.346651\pi\) | |||||||
\(752\) | −5.72583 | − | 5.72583i | −0.208799 | − | 0.208799i | ||||
\(753\) | −13.5537 | + | 13.5537i | −0.493923 | + | 0.493923i | ||||
\(754\) | − | 19.7539i | − | 0.719395i | ||||||
\(755\) | 12.6545 | + | 6.88150i | 0.460544 | + | 0.250444i | ||||
\(756\) | 1.49670i | 0.0544344i | ||||||||
\(757\) | 0.171583 | − | 0.171583i | 0.00623630 | − | 0.00623630i | −0.703982 | − | 0.710218i | \(-0.748596\pi\) |
0.710218 | + | 0.703982i | \(0.248596\pi\) | |||||||
\(758\) | 14.4728 | − | 14.4728i | 0.525676 | − | 0.525676i | ||||
\(759\) | −14.6623 | −0.532206 | ||||||||
\(760\) | 16.8001 | − | 4.96450i | 0.609402 | − | 0.180081i | ||||
\(761\) | − | 0.0579901i | − | 0.00210214i | −0.999999 | − | 0.00105107i | \(-0.999665\pi\) | ||
0.999999 | − | 0.00105107i | \(-0.000334566\pi\) | |||||||
\(762\) | 2.15923 | + | 2.15923i | 0.0782206 | + | 0.0782206i | ||||
\(763\) | 11.0573 | − | 11.0573i | 0.400300 | − | 0.400300i | ||||
\(764\) | 19.7130i | 0.713192i | ||||||||
\(765\) | −7.67626 | + | 2.26837i | −0.277536 | + | 0.0820132i | ||||
\(766\) | − | 35.6464i | − | 1.28796i | ||||||
\(767\) | −23.4519 | + | 23.4519i | −0.846798 | + | 0.846798i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 3.84574i | − | 0.138681i | −0.997593 | − | 0.0693405i | \(-0.977911\pi\) | ||
0.997593 | − | 0.0693405i | \(-0.0220895\pi\) | |||||||
\(770\) | 8.06150 | − | 14.8244i | 0.290516 | − | 0.534234i | ||||
\(771\) | − | 3.95200i | − | 0.142328i | ||||||
\(772\) | −3.02398 | − | 3.02398i | −0.108836 | − | 0.108836i | ||||
\(773\) | −5.69371 | − | 5.69371i | −0.204788 | − | 0.204788i | 0.597260 | − | 0.802048i | \(-0.296256\pi\) |
−0.802048 | + | 0.597260i | \(0.796256\pi\) | |||||||
\(774\) | −6.89717 | −0.247914 | ||||||||
\(775\) | 23.1099 | + | 15.5220i | 0.830133 | + | 0.557565i | ||||
\(776\) | −10.2037 | −0.366292 | ||||||||
\(777\) | −3.42849 | − | 3.42849i | −0.122997 | − | 0.122997i | ||||
\(778\) | −13.0795 | − | 13.0795i | −0.468924 | − | 0.468924i | ||||
\(779\) | 17.5042i | 0.627152i | ||||||||
\(780\) | 6.99724 | − | 12.8673i | 0.250541 | − | 0.460724i | ||||
\(781\) | − | 77.8563i | − | 2.78592i | ||||||
\(782\) | −7.36066 | − | 7.36066i | −0.263216 | − | 0.263216i | ||||
\(783\) | 2.13246 | − | 2.13246i | 0.0762077 | − | 0.0762077i | ||||
\(784\) | 4.75989i | 0.169996i | ||||||||
\(785\) | −9.39961 | + | 2.77763i | −0.335487 | + | 0.0991380i | ||||
\(786\) | − | 0.0930152i | − | 0.00331774i | ||||||
\(787\) | −31.0306 | + | 31.0306i | −1.10612 | + | 1.10612i | −0.112467 | + | 0.993655i | \(0.535875\pi\) |
−0.993655 | + | 0.112467i | \(0.964125\pi\) | |||||||
\(788\) | 3.98103 | + | 3.98103i | 0.141818 | + | 0.141818i | ||||
\(789\) | − | 8.00630i | − | 0.285032i | ||||||
\(790\) | −27.2431 | + | 8.05048i | −0.969267 | + | 0.286423i | ||||
\(791\) | −30.8313 | −1.09624 | ||||||||
\(792\) | 3.56532 | − | 3.56532i | 0.126688 | − | 0.126688i | ||||
\(793\) | −21.4827 | + | 21.4827i | −0.762873 | + | 0.762873i | ||||
\(794\) | 11.9565i | 0.424319i | ||||||||
\(795\) | 16.6088 | + | 9.03185i | 0.589053 | + | 0.320327i | ||||
\(796\) | 14.3596i | 0.508964i | ||||||||
\(797\) | 12.8535 | − | 12.8535i | 0.455296 | − | 0.455296i | −0.441812 | − | 0.897108i | \(-0.645664\pi\) |
0.897108 | + | 0.441812i | \(0.145664\pi\) | |||||||
\(798\) | −8.29133 | − | 8.29133i | −0.293510 | − | 0.293510i | ||||
\(799\) | −28.9866 | −1.02547 | ||||||||
\(800\) | 1.04593 | − | 4.88938i | 0.0369792 | − | 0.172866i | ||||
\(801\) | − | 2.92224i | − | 0.103252i | ||||||
\(802\) | −5.40371 | + | 5.40371i | −0.190812 | + | 0.190812i | ||||
\(803\) | −28.5439 | + | 28.5439i | −1.00729 | + | 1.00729i | ||||
\(804\) | 7.69692 | 0.271450 | ||||||||
\(805\) | 8.54971 | + | 4.64933i | 0.301338 | + | 0.163867i | ||||
\(806\) | −14.3596 | − | 33.5244i | −0.505795 | − | 1.18085i | ||||
\(807\) | −3.67996 | − | 3.67996i | −0.129541 | − | 0.129541i | ||||
\(808\) | −5.87158 | + | 5.87158i | −0.206561 | + | 0.206561i | ||||
\(809\) | 32.9889 | 1.15983 | 0.579913 | − | 0.814678i | \(-0.303086\pi\) | ||||
0.579913 | + | 0.814678i | \(0.303086\pi\) | |||||||
\(810\) | 2.14440 | − | 0.633681i | 0.0753465 | − | 0.0222653i | ||||
\(811\) | −51.3364 | −1.80267 | −0.901333 | − | 0.433127i | \(-0.857410\pi\) | ||||
−0.901333 | + | 0.433127i | \(0.857410\pi\) | |||||||
\(812\) | −3.19164 | + | 3.19164i | −0.112005 | + | 0.112005i | ||||
\(813\) | 10.8624 | − | 10.8624i | 0.380959 | − | 0.380959i | ||||
\(814\) | 16.3342i | 0.572512i | ||||||||
\(815\) | 1.80763 | + | 6.11707i | 0.0633184 | + | 0.214272i | ||||
\(816\) | 3.57968 | 0.125314 | ||||||||
\(817\) | 38.2086 | − | 38.2086i | 1.33675 | − | 1.33675i | ||||
\(818\) | 16.2147 | + | 16.2147i | 0.566935 | + | 0.566935i | ||||
\(819\) | −9.80376 | −0.342571 | ||||||||
\(820\) | 4.38901 | + | 2.38674i | 0.153271 | + | 0.0833486i | ||||
\(821\) | − | 3.93571i | − | 0.137357i | −0.997639 | − | 0.0686786i | \(-0.978122\pi\) | ||
0.997639 | − | 0.0686786i | \(-0.0218783\pi\) | |||||||
\(822\) | 4.24973 | + | 4.24973i | 0.148226 | + | 0.148226i | ||||
\(823\) | 31.8846 | + | 31.8846i | 1.11143 | + | 1.11143i | 0.992958 | + | 0.118468i | \(0.0377982\pi\) |
0.118468 | + | 0.992958i | \(0.462202\pi\) | |||||||
\(824\) | − | 15.6013i | − | 0.543498i | ||||||
\(825\) | −24.6528 | − | 5.27369i | −0.858301 | − | 0.183606i | ||||
\(826\) | 7.57824 | 0.263681 | ||||||||
\(827\) | 33.8426 | − | 33.8426i | 1.17682 | − | 1.17682i | 0.196272 | − | 0.980549i | \(-0.437116\pi\) |
0.980549 | − | 0.196272i | \(-0.0628837\pi\) | |||||||
\(828\) | 2.05623 | + | 2.05623i | 0.0714591 | + | 0.0714591i | ||||
\(829\) | 39.8409 | 1.38373 | 0.691866 | − | 0.722026i | \(-0.256789\pi\) | ||||
0.691866 | + | 0.722026i | \(0.256789\pi\) | |||||||
\(830\) | 23.4830 | + | 12.7701i | 0.815108 | + | 0.443255i | ||||
\(831\) | −11.3959 | −0.395319 | ||||||||
\(832\) | −4.63173 | + | 4.63173i | −0.160576 | + | 0.160576i | ||||
\(833\) | 12.0483 | + | 12.0483i | 0.417449 | + | 0.417449i | ||||
\(834\) | − | 4.79836i | − | 0.166154i | ||||||
\(835\) | −14.5666 | − | 49.2938i | −0.504097 | − | 1.70588i | ||||
\(836\) | 39.5019i | 1.36620i | ||||||||
\(837\) | 2.06886 | − | 5.16912i | 0.0715102 | − | 0.178671i | ||||
\(838\) | −21.5791 | + | 21.5791i | −0.745438 | + | 0.745438i | ||||
\(839\) | − | 35.9863i | − | 1.24239i | −0.783657 | − | 0.621193i | \(-0.786648\pi\) | ||
0.783657 | − | 0.621193i | \(-0.213352\pi\) | |||||||
\(840\) | −3.20952 | + | 0.948429i | −0.110739 | + | 0.0327239i | ||||
\(841\) | −19.9053 | −0.686389 | ||||||||
\(842\) | −15.3973 | − | 15.3973i | −0.530627 | − | 0.530627i | ||||
\(843\) | −13.6539 | − | 13.6539i | −0.470266 | − | 0.470266i | ||||
\(844\) | 9.13202i | 0.314337i | ||||||||
\(845\) | 58.7471 | + | 31.9467i | 2.02096 | + | 1.09900i | ||||
\(846\) | 8.09754 | 0.278399 | ||||||||
\(847\) | 15.2642 | + | 15.2642i | 0.524483 | + | 0.524483i | ||||
\(848\) | −5.97851 | − | 5.97851i | −0.205303 | − | 0.205303i | ||||
\(849\) | −12.5774 | −0.431655 | ||||||||
\(850\) | −9.72860 | − | 15.0235i | −0.333688 | − | 0.515303i | ||||
\(851\) | −9.42045 | −0.322929 | ||||||||
\(852\) | −10.9186 | + | 10.9186i | −0.374064 | + | 0.374064i | ||||
\(853\) | 34.2863 | − | 34.2863i | 1.17394 | − | 1.17394i | 0.192680 | − | 0.981262i | \(-0.438282\pi\) |
0.981262 | − | 0.192680i | \(-0.0617181\pi\) | |||||||
\(854\) | 6.94192 | 0.237548 | ||||||||
\(855\) | −8.36900 | + | 15.3899i | −0.286214 | + | 0.526322i | ||||
\(856\) | 2.14900 | 0.0734514 | ||||||||
\(857\) | 1.05382 | + | 1.05382i | 0.0359978 | + | 0.0359978i | 0.724877 | − | 0.688879i | \(-0.241897\pi\) |
−0.688879 | + | 0.724877i | \(0.741897\pi\) | |||||||
\(858\) | 23.3537 | + | 23.3537i | 0.797284 | + | 0.797284i | ||||
\(859\) | −7.56805 | −0.258219 | −0.129109 | − | 0.991630i | \(-0.541212\pi\) | ||||
−0.129109 | + | 0.991630i | \(0.541212\pi\) | |||||||
\(860\) | −4.37060 | − | 14.7903i | −0.149036 | − | 0.504344i | ||||
\(861\) | − | 3.34404i | − | 0.113964i | ||||||
\(862\) | −0.552334 | − | 0.552334i | −0.0188126 | − | 0.0188126i | ||||
\(863\) | −20.5693 | − | 20.5693i | −0.700187 | − | 0.700187i | 0.264264 | − | 0.964450i | \(-0.414871\pi\) |
−0.964450 | + | 0.264264i | \(0.914871\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −0.470190 | − | 1.59114i | −0.0159869 | − | 0.0541004i | ||||
\(866\) | 7.00791i | 0.238138i | ||||||||
\(867\) | −2.95989 | + | 2.95989i | −0.100523 | + | 0.100523i | ||||
\(868\) | −3.09646 | + | 7.73662i | −0.105101 | + | 0.262598i | ||||
\(869\) | − | 64.0566i | − | 2.17297i | ||||||
\(870\) | 5.92413 | + | 3.22154i | 0.200847 | + | 0.109220i | ||||
\(871\) | 50.4168i | 1.70831i | ||||||||
\(872\) | 7.38778 | + | 7.38778i | 0.250182 | + | 0.250182i | ||||
\(873\) | 7.21512 | − | 7.21512i | 0.244195 | − | 0.244195i | ||||
\(874\) | −22.7820 | −0.770614 | ||||||||
\(875\) | 12.7031 | + | 10.8924i | 0.429442 | + | 0.368232i | ||||
\(876\) | 8.00599 | 0.270497 | ||||||||
\(877\) | −34.9011 | − | 34.9011i | −1.17853 | − | 1.17853i | −0.980120 | − | 0.198406i | \(-0.936424\pi\) |
−0.198406 | − | 0.980120i | \(-0.563576\pi\) | |||||||
\(878\) | 2.84269 | − | 2.84269i | 0.0959362 | − | 0.0959362i | ||||
\(879\) | 12.4933 | 0.421389 | ||||||||
\(880\) | 9.90473 | + | 5.38619i | 0.333889 | + | 0.181568i | ||||
\(881\) | − | 15.2410i | − | 0.513484i | −0.966480 | − | 0.256742i | \(-0.917351\pi\) | ||
0.966480 | − | 0.256742i | \(-0.0826490\pi\) | |||||||
\(882\) | −3.36575 | − | 3.36575i | −0.113331 | − | 0.113331i | ||||
\(883\) | 6.41003 | + | 6.41003i | 0.215715 | + | 0.215715i | 0.806690 | − | 0.590975i | \(-0.201257\pi\) |
−0.590975 | + | 0.806690i | \(0.701257\pi\) | |||||||
\(884\) | 23.4478i | 0.788635i | ||||||||
\(885\) | −3.20852 | − | 10.8577i | −0.107853 | − | 0.364979i | ||||
\(886\) | −21.5677 | −0.724582 | ||||||||
\(887\) | −23.7037 | − | 23.7037i | −0.795893 | − | 0.795893i | 0.186552 | − | 0.982445i | \(-0.440269\pi\) |
−0.982445 | + | 0.186552i | \(0.940269\pi\) | |||||||
\(888\) | 2.29070 | − | 2.29070i | 0.0768710 | − | 0.0768710i | ||||
\(889\) | 4.57033 | 0.153284 | ||||||||
\(890\) | 6.26645 | − | 1.85177i | 0.210052 | − | 0.0620714i | ||||
\(891\) | 5.04212i | 0.168917i | ||||||||
\(892\) | −4.77518 | + | 4.77518i | −0.159885 | + | 0.159885i | ||||
\(893\) | −44.8584 | + | 44.8584i | −1.50113 | + | 1.50113i | ||||
\(894\) | 11.4909 | 0.384314 | ||||||||
\(895\) | 3.06675 | − | 5.63948i | 0.102510 | − | 0.188507i | ||||
\(896\) | 1.49670 | 0.0500012 | ||||||||
\(897\) | −13.4689 | + | 13.4689i | −0.449712 | + | 0.449712i | ||||
\(898\) | 9.90525 | + | 9.90525i | 0.330542 | + | 0.330542i | ||||
\(899\) | 15.4347 | − | 6.61117i | 0.514775 | − | 0.220495i | ||||
\(900\) | 2.71773 | + | 4.19690i | 0.0905910 | + | 0.139897i | ||||
\(901\) | −30.2658 | −1.00830 | ||||||||
\(902\) | −7.96590 | + | 7.96590i | −0.265235 | + | 0.265235i | ||||
\(903\) | −7.29945 | + | 7.29945i | −0.242910 | + | 0.242910i | ||||
\(904\) | − | 20.5996i | − | 0.685131i | ||||||
\(905\) | −50.5445 | − | 27.4861i | −1.68016 | − | 0.913668i | ||||
\(906\) | 6.44191 | 0.214018 | ||||||||
\(907\) | −12.9844 | − | 12.9844i | −0.431139 | − | 0.431139i | 0.457877 | − | 0.889016i | \(-0.348610\pi\) |
−0.889016 | + | 0.457877i | \(0.848610\pi\) | |||||||
\(908\) | 4.70595 | − | 4.70595i | 0.156172 | − | 0.156172i | ||||
\(909\) | − | 8.30366i | − | 0.275415i | ||||||
\(910\) | −6.21246 | − | 21.0232i | −0.205941 | − | 0.696912i | ||||
\(911\) | − | 10.0038i | − | 0.331441i | −0.986173 | − | 0.165720i | \(-0.947005\pi\) | ||
0.986173 | − | 0.165720i | \(-0.0529949\pi\) | |||||||
\(912\) | 5.53975 | − | 5.53975i | 0.183439 | − | 0.183439i | ||||
\(913\) | −42.6209 | + | 42.6209i | −1.41055 | + | 1.41055i | ||||
\(914\) | 30.2568 | 1.00081 | ||||||||
\(915\) | −2.93911 | − | 9.94606i | −0.0971640 | − | 0.328807i | ||||
\(916\) | − | 25.0935i | − | 0.829114i | ||||||
\(917\) | −0.0984403 | − | 0.0984403i | −0.00325079 | − | 0.00325079i | ||||
\(918\) | −2.53121 | + | 2.53121i | −0.0835425 | + | 0.0835425i | ||||
\(919\) | − | 26.5931i | − | 0.877224i | −0.898676 | − | 0.438612i | \(-0.855470\pi\) | ||
0.898676 | − | 0.438612i | \(-0.144530\pi\) | |||||||
\(920\) | −3.10639 | + | 5.71238i | −0.102415 | + | 0.188332i | ||||
\(921\) | 9.37351i | 0.308868i | ||||||||
\(922\) | 9.39125 | − | 9.39125i | 0.309284 | − | 0.309284i | ||||
\(923\) | −71.5195 | − | 71.5195i | −2.35409 | − | 2.35409i | ||||
\(924\) | − | 7.54653i | − | 0.248263i | ||||||
\(925\) | −15.8394 | − | 3.38833i | −0.520795 | − | 0.111408i | ||||
\(926\) | 8.45602i | 0.277882i | ||||||||
\(927\) | 11.0318 | + | 11.0318i | 0.362332 | + | 0.362332i | ||||
\(928\) | −2.13246 | − | 2.13246i | −0.0700013 | − | 0.0700013i | ||||
\(929\) | 26.4741 | 0.868588 | 0.434294 | − | 0.900771i | \(-0.356998\pi\) | ||||
0.434294 | + | 0.900771i | \(0.356998\pi\) | |||||||
\(930\) | 12.3957 | + | 1.16088i | 0.406470 | + | 0.0380669i | ||||
\(931\) | 37.2909 | 1.22216 | ||||||||
\(932\) | 19.4361 | + | 19.4361i | 0.636651 | + | 0.636651i | ||||
\(933\) | −1.35606 | − | 1.35606i | −0.0443954 | − | 0.0443954i | ||||
\(934\) | 13.7487i | 0.449871i | ||||||||
\(935\) | 38.7046 | − | 11.4374i | 1.26578 | − | 0.374043i | ||||
\(936\) | − | 6.55026i | − | 0.214102i | ||||||
\(937\) | 23.7864 | + | 23.7864i | 0.777067 | + | 0.777067i | 0.979331 | − | 0.202264i | \(-0.0648298\pi\) |
−0.202264 | + | 0.979331i | \(0.564830\pi\) | |||||||
\(938\) | 8.14585 | − | 8.14585i | 0.265971 | − | 0.265971i | ||||
\(939\) | 10.2318i | 0.333902i | ||||||||
\(940\) | 5.13126 | + | 17.3644i | 0.167363 | + | 0.566363i | ||||
\(941\) | − | 1.41436i | − | 0.0461067i | −0.999734 | − | 0.0230534i | \(-0.992661\pi\) | ||
0.999734 | − | 0.0230534i | \(-0.00733877\pi\) | |||||||
\(942\) | −3.09948 | + | 3.09948i | −0.100987 | + | 0.100987i | ||||
\(943\) | −4.59419 | − | 4.59419i | −0.149608 | − | 0.149608i | ||||
\(944\) | 5.06330i | 0.164797i | ||||||||
\(945\) | 1.59883 | − | 2.94011i | 0.0520100 | − | 0.0956419i | ||||
\(946\) | 34.7763 | 1.13068 | ||||||||
\(947\) | 19.7136 | − | 19.7136i | 0.640605 | − | 0.640605i | −0.310100 | − | 0.950704i | \(-0.600362\pi\) |
0.950704 | + | 0.310100i | \(0.100362\pi\) | |||||||
\(948\) | −8.98330 | + | 8.98330i | −0.291764 | + | 0.291764i | ||||
\(949\) | 52.4413i | 1.70232i | ||||||||
\(950\) | −38.3053 | − | 8.19421i | −1.24279 | − | 0.265855i | ||||
\(951\) | − | 19.9838i | − | 0.648018i | ||||||
\(952\) | 3.78846 | − | 3.78846i | 0.122785 | − | 0.122785i | ||||
\(953\) | 34.0418 | + | 34.0418i | 1.10272 | + | 1.10272i | 0.994081 | + | 0.108642i | \(0.0346501\pi\) |
0.108642 | + | 0.994081i | \(0.465350\pi\) | |||||||
\(954\) | 8.45489 | 0.273737 | ||||||||
\(955\) | 21.0582 | − | 38.7242i | 0.681428 | − | 1.25309i | ||||
\(956\) | 29.7199i | 0.961211i | ||||||||
\(957\) | −10.7521 | + | 10.7521i | −0.347566 | + | 0.347566i | ||||
\(958\) | −11.2423 | + | 11.2423i | −0.363223 | + | 0.363223i | ||||
\(959\) | 8.99519 | 0.290470 | ||||||||
\(960\) | −0.633681 | − | 2.14440i | −0.0204520 | − | 0.0692102i | ||||
\(961\) | 21.3884 | − | 22.4396i | 0.689947 | − | 0.723860i | ||||
\(962\) | 15.0047 | + | 15.0047i | 0.483771 | + | 0.483771i | ||||
\(963\) | −1.51957 | + | 1.51957i | −0.0489676 | + | 0.0489676i | ||||
\(964\) | −12.5924 | −0.405575 | ||||||||
\(965\) | 2.70997 | + | 9.17065i | 0.0872371 | + | 0.295214i | ||||
\(966\) | 4.35233 | 0.140034 | ||||||||
\(967\) | 7.33819 | − | 7.33819i | 0.235980 | − | 0.235980i | −0.579203 | − | 0.815183i | \(-0.696636\pi\) |
0.815183 | + | 0.579203i | \(0.196636\pi\) | |||||||
\(968\) | −10.1986 | + | 10.1986i | −0.327794 | + | 0.327794i | ||||
\(969\) | − | 28.0446i | − | 0.900922i | ||||||
\(970\) | 20.0442 | + | 10.9000i | 0.643580 | + | 0.349978i | ||||
\(971\) | −3.20869 | −0.102972 | −0.0514858 | − | 0.998674i | \(-0.516396\pi\) | ||||
−0.0514858 | + | 0.998674i | \(0.516396\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −5.07822 | − | 5.07822i | −0.162800 | − | 0.162800i | ||||
\(974\) | 3.06607 | 0.0982432 | ||||||||
\(975\) | −27.4908 | + | 17.8018i | −0.880409 | + | 0.570115i | ||||
\(976\) | 4.63816i | 0.148464i | ||||||||
\(977\) | 21.2352 | + | 21.2352i | 0.679373 | + | 0.679373i | 0.959858 | − | 0.280485i | \(-0.0904955\pi\) |
−0.280485 | + | 0.959858i | \(0.590495\pi\) | |||||||
\(978\) | 2.01708 | + | 2.01708i | 0.0644990 | + | 0.0644990i | ||||
\(979\) | 14.7343i | 0.470909i | ||||||||
\(980\) | 5.08471 | − | 9.35034i | 0.162425 | − | 0.298686i | ||||
\(981\) | −10.4479 | −0.333576 | ||||||||
\(982\) | 14.0695 | − | 14.0695i | 0.448975 | − | 0.448975i | ||||
\(983\) | 14.4629 | + | 14.4629i | 0.461294 | + | 0.461294i | 0.899080 | − | 0.437785i | \(-0.144237\pi\) |
−0.437785 | + | 0.899080i | \(0.644237\pi\) | |||||||
\(984\) | 2.23428 | 0.0712261 | ||||||||
\(985\) | −3.56764 | − | 12.0730i | −0.113674 | − | 0.384678i | ||||
\(986\) | −10.7954 | −0.343796 | ||||||||
\(987\) | 8.56984 | − | 8.56984i | 0.272781 | − | 0.272781i | ||||
\(988\) | 36.2868 | + | 36.2868i | 1.15444 | + | 1.15444i | ||||
\(989\) | 20.0567i | 0.637764i | ||||||||
\(990\) | −10.8123 | + | 3.19509i | −0.343638 | + | 0.101547i | ||||
\(991\) | 34.1173i | 1.08377i | 0.840452 | + | 0.541886i | \(0.182290\pi\) | ||||
−0.840452 | + | 0.541886i | \(0.817710\pi\) | |||||||
\(992\) | −5.16912 | − | 2.06886i | −0.164120 | − | 0.0656863i | ||||
\(993\) | 7.56062 | − | 7.56062i | 0.239929 | − | 0.239929i | ||||
\(994\) | 23.1108i | 0.733030i | ||||||||
\(995\) | 15.3395 | − | 28.2081i | 0.486296 | − | 0.894256i | ||||
\(996\) | 11.9543 | 0.378787 | ||||||||
\(997\) | 10.4258 | + | 10.4258i | 0.330188 | + | 0.330188i | 0.852658 | − | 0.522470i | \(-0.174989\pi\) |
−0.522470 | + | 0.852658i | \(0.674989\pi\) | |||||||
\(998\) | −2.65081 | − | 2.65081i | −0.0839100 | − | 0.0839100i | ||||
\(999\) | 3.23955i | 0.102495i |
(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 | 930.2.k.a.247.6 | ✓ | 32 | |
5.3 | odd | 4 | 930.2.k.b.433.6 | yes | 32 | ||
31.30 | odd | 2 | 930.2.k.b.247.6 | yes | 32 | ||
155.123 | even | 4 | inner | 930.2.k.a.433.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.k.a.247.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
930.2.k.a.433.6 | yes | 32 | 155.123 | even | 4 | inner | |
930.2.k.b.247.6 | yes | 32 | 31.30 | odd | 2 | ||
930.2.k.b.433.6 | yes | 32 | 5.3 | odd | 4 |