Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.1 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.b.367.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||
\(5\) | −1.98078 | + | 1.03755i | −0.885833 | + | 0.464005i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.124800 | + | 0.124800i | 0.0471701 | + | 0.0471701i | 0.730298 | − | 0.683128i | \(-0.239381\pi\) |
−0.683128 | + | 0.730298i | \(0.739381\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.666968 | − | 2.13428i | 0.210914 | − | 0.674919i | ||||
\(11\) | − | 0.552534i | − | 0.166595i | −0.996525 | − | 0.0832977i | \(-0.973455\pi\) | ||
0.996525 | − | 0.0832977i | \(-0.0265452\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 2.68793 | + | 2.68793i | 0.745497 | + | 0.745497i | 0.973630 | − | 0.228133i | \(-0.0732621\pi\) |
−0.228133 | + | 0.973630i | \(0.573262\pi\) | |||||||
\(14\) | −0.176495 | −0.0471701 | ||||||||
\(15\) | 2.13428 | + | 0.666968i | 0.551069 | + | 0.172210i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.61968 | − | 3.61968i | −0.877902 | − | 0.877902i | 0.115415 | − | 0.993317i | \(-0.463180\pi\) |
−0.993317 | + | 0.115415i | \(0.963180\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 1.08434 | 0.248764 | 0.124382 | − | 0.992234i | \(-0.460305\pi\) | ||||
0.124382 | + | 0.992234i | \(0.460305\pi\) | |||||||
\(20\) | 1.03755 | + | 1.98078i | 0.232002 | + | 0.442916i | ||||
\(21\) | − | 0.176495i | − | 0.0385143i | ||||||
\(22\) | 0.390701 | + | 0.390701i | 0.0832977 | + | 0.0832977i | ||||
\(23\) | −4.79526 | + | 0.0741463i | −0.999880 | + | 0.0154606i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 2.84699 | − | 4.11031i | 0.569399 | − | 0.822061i | ||||
\(26\) | −3.80130 | −0.745497 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.124800 | − | 0.124800i | 0.0235851 | − | 0.0235851i | ||||
\(29\) | − | 8.68275i | − | 1.61235i | −0.591679 | − | 0.806173i | \(-0.701535\pi\) | ||
0.591679 | − | 0.806173i | \(-0.298465\pi\) | |||||||
\(30\) | −1.98078 | + | 1.03755i | −0.361640 | + | 0.189429i | ||||
\(31\) | 2.45605 | 0.441119 | 0.220559 | − | 0.975374i | \(-0.429212\pi\) | ||||
0.220559 | + | 0.975374i | \(0.429212\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −0.390701 | + | 0.390701i | −0.0680123 | + | 0.0680123i | ||||
\(34\) | 5.11901 | 0.877902 | ||||||||
\(35\) | −0.376689 | − | 0.117716i | −0.0636720 | − | 0.0198977i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.79545 | − | 7.79545i | −1.28156 | − | 1.28156i | −0.939777 | − | 0.341787i | \(-0.888968\pi\) |
−0.341787 | − | 0.939777i | \(-0.611032\pi\) | |||||||
\(38\) | −0.766741 | + | 0.766741i | −0.124382 | + | 0.124382i | ||||
\(39\) | − | 3.80130i | − | 0.608696i | ||||||
\(40\) | −2.13428 | − | 0.666968i | −0.337459 | − | 0.105457i | ||||
\(41\) | −2.27486 | −0.355274 | −0.177637 | − | 0.984096i | \(-0.556845\pi\) | ||||
−0.177637 | + | 0.984096i | \(0.556845\pi\) | |||||||
\(42\) | 0.124800 | + | 0.124800i | 0.0192571 | + | 0.0192571i | ||||
\(43\) | 1.06804 | − | 1.06804i | 0.162874 | − | 0.162874i | −0.620965 | − | 0.783839i | \(-0.713259\pi\) |
0.783839 | + | 0.620965i | \(0.213259\pi\) | |||||||
\(44\) | −0.552534 | −0.0832977 | ||||||||
\(45\) | −1.03755 | − | 1.98078i | −0.154668 | − | 0.295278i | ||||
\(46\) | 3.33833 | − | 3.44319i | 0.492210 | − | 0.507671i | ||||
\(47\) | −0.597335 | + | 0.597335i | −0.0871302 | + | 0.0871302i | −0.749329 | − | 0.662198i | \(-0.769624\pi\) |
0.662198 | + | 0.749329i | \(0.269624\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 6.96885i | − | 0.995550i | ||||||
\(50\) | 0.893297 | + | 4.91955i | 0.126331 | + | 0.695730i | ||||
\(51\) | 5.11901i | 0.716804i | ||||||||
\(52\) | 2.68793 | − | 2.68793i | 0.372748 | − | 0.372748i | ||||
\(53\) | −5.95295 | + | 5.95295i | −0.817701 | + | 0.817701i | −0.985774 | − | 0.168073i | \(-0.946245\pi\) |
0.168073 | + | 0.985774i | \(0.446245\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0.573280 | + | 1.09445i | 0.0773011 | + | 0.147576i | ||||
\(56\) | 0.176495i | 0.0235851i | ||||||||
\(57\) | −0.766741 | − | 0.766741i | −0.101557 | − | 0.101557i | ||||
\(58\) | 6.13963 | + | 6.13963i | 0.806173 | + | 0.806173i | ||||
\(59\) | − | 10.4090i | − | 1.35514i | −0.735460 | − | 0.677569i | \(-0.763034\pi\) | ||
0.735460 | − | 0.677569i | \(-0.236966\pi\) | |||||||
\(60\) | 0.666968 | − | 2.13428i | 0.0861052 | − | 0.275534i | ||||
\(61\) | − | 9.12081i | − | 1.16780i | −0.811825 | − | 0.583900i | \(-0.801526\pi\) | ||
0.811825 | − | 0.583900i | \(-0.198474\pi\) | |||||||
\(62\) | −1.73669 | + | 1.73669i | −0.220559 | + | 0.220559i | ||||
\(63\) | −0.124800 | + | 0.124800i | −0.0157234 | + | 0.0157234i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −8.11305 | − | 2.53535i | −1.00630 | − | 0.314471i | ||||
\(66\) | − | 0.552534i | − | 0.0680123i | ||||||
\(67\) | −5.38491 | − | 5.38491i | −0.657871 | − | 0.657871i | 0.297005 | − | 0.954876i | \(-0.404012\pi\) |
−0.954876 | + | 0.297005i | \(0.904012\pi\) | |||||||
\(68\) | −3.61968 | + | 3.61968i | −0.438951 | + | 0.438951i | ||||
\(69\) | 3.44319 | + | 3.33833i | 0.414511 | + | 0.401888i | ||||
\(70\) | 0.349597 | − | 0.183121i | 0.0417849 | − | 0.0218872i | ||||
\(71\) | 8.16755 | 0.969309 | 0.484655 | − | 0.874706i | \(-0.338945\pi\) | ||||
0.484655 | + | 0.874706i | \(0.338945\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 3.12378 | + | 3.12378i | 0.365610 | + | 0.365610i | 0.865873 | − | 0.500263i | \(-0.166763\pi\) |
−0.500263 | + | 0.865873i | \(0.666763\pi\) | |||||||
\(74\) | 11.0244 | 1.28156 | ||||||||
\(75\) | −4.91955 | + | 0.893297i | −0.568061 | + | 0.103149i | ||||
\(76\) | − | 1.08434i | − | 0.124382i | ||||||
\(77\) | 0.0689566 | − | 0.0689566i | 0.00785833 | − | 0.00785833i | ||||
\(78\) | 2.68793 | + | 2.68793i | 0.304348 | + | 0.304348i | ||||
\(79\) | −6.76975 | −0.761656 | −0.380828 | − | 0.924646i | \(-0.624361\pi\) | ||||
−0.380828 | + | 0.924646i | \(0.624361\pi\) | |||||||
\(80\) | 1.98078 | − | 1.03755i | 0.221458 | − | 0.116001i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.60857 | − | 1.60857i | 0.177637 | − | 0.177637i | ||||
\(83\) | −0.190970 | + | 0.190970i | −0.0209616 | + | 0.0209616i | −0.717510 | − | 0.696548i | \(-0.754718\pi\) |
0.696548 | + | 0.717510i | \(0.254718\pi\) | |||||||
\(84\) | −0.176495 | −0.0192571 | ||||||||
\(85\) | 10.9254 | + | 3.41421i | 1.18503 | + | 0.370323i | ||||
\(86\) | 1.51043i | 0.162874i | ||||||||
\(87\) | −6.13963 | + | 6.13963i | −0.658238 | + | 0.658238i | ||||
\(88\) | 0.390701 | − | 0.390701i | 0.0416489 | − | 0.0416489i | ||||
\(89\) | 8.76193 | 0.928762 | 0.464381 | − | 0.885635i | \(-0.346277\pi\) | ||||
0.464381 | + | 0.885635i | \(0.346277\pi\) | |||||||
\(90\) | 2.13428 | + | 0.666968i | 0.224973 | + | 0.0703046i | ||||
\(91\) | 0.670909i | 0.0703304i | ||||||||
\(92\) | 0.0741463 | + | 4.79526i | 0.00773029 | + | 0.499940i | ||||
\(93\) | −1.73669 | − | 1.73669i | −0.180086 | − | 0.180086i | ||||
\(94\) | − | 0.844759i | − | 0.0871302i | ||||||
\(95\) | −2.14783 | + | 1.12505i | −0.220363 | + | 0.115428i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.62982 | − | 1.62982i | −0.165484 | − | 0.165484i | 0.619507 | − | 0.784991i | \(-0.287332\pi\) |
−0.784991 | + | 0.619507i | \(0.787332\pi\) | |||||||
\(98\) | 4.92772 | + | 4.92772i | 0.497775 | + | 0.497775i | ||||
\(99\) | 0.552534 | 0.0555318 | ||||||||
\(100\) | −4.11031 | − | 2.84699i | −0.411031 | − | 0.284699i | ||||
\(101\) | −5.93104 | −0.590161 | −0.295080 | − | 0.955472i | \(-0.595346\pi\) | ||||
−0.295080 | + | 0.955472i | \(0.595346\pi\) | |||||||
\(102\) | −3.61968 | − | 3.61968i | −0.358402 | − | 0.358402i | ||||
\(103\) | −3.77864 | + | 3.77864i | −0.372321 | + | 0.372321i | −0.868322 | − | 0.496001i | \(-0.834801\pi\) |
0.496001 | + | 0.868322i | \(0.334801\pi\) | |||||||
\(104\) | 3.80130i | 0.372748i | ||||||||
\(105\) | 0.183121 | + | 0.349597i | 0.0178708 | + | 0.0341172i | ||||
\(106\) | − | 8.41875i | − | 0.817701i | ||||||
\(107\) | 9.09321 | + | 9.09321i | 0.879074 | + | 0.879074i | 0.993439 | − | 0.114365i | \(-0.0364834\pi\) |
−0.114365 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 13.5947 | 1.30213 | 0.651067 | − | 0.759021i | \(-0.274322\pi\) | ||||
0.651067 | + | 0.759021i | \(0.274322\pi\) | |||||||
\(110\) | −1.17926 | − | 0.368523i | −0.112438 | − | 0.0351373i | ||||
\(111\) | 11.0244i | 1.04639i | ||||||||
\(112\) | −0.124800 | − | 0.124800i | −0.0117925 | − | 0.0117925i | ||||
\(113\) | 9.30335 | − | 9.30335i | 0.875186 | − | 0.875186i | −0.117846 | − | 0.993032i | \(-0.537599\pi\) |
0.993032 | + | 0.117846i | \(0.0375990\pi\) | |||||||
\(114\) | 1.08434 | 0.101557 | ||||||||
\(115\) | 9.42143 | − | 5.12217i | 0.878553 | − | 0.477645i | ||||
\(116\) | −8.68275 | −0.806173 | ||||||||
\(117\) | −2.68793 | + | 2.68793i | −0.248499 | + | 0.248499i | ||||
\(118\) | 7.36028 | + | 7.36028i | 0.677569 | + | 0.677569i | ||||
\(119\) | − | 0.903477i | − | 0.0828216i | ||||||
\(120\) | 1.03755 | + | 1.98078i | 0.0947146 | + | 0.180820i | ||||
\(121\) | 10.6947 | 0.972246 | ||||||||
\(122\) | 6.44939 | + | 6.44939i | 0.583900 | + | 0.583900i | ||||
\(123\) | 1.60857 | + | 1.60857i | 0.145040 | + | 0.145040i | ||||
\(124\) | − | 2.45605i | − | 0.220559i | ||||||
\(125\) | −1.37464 | + | 11.0955i | −0.122952 | + | 0.992413i | ||||
\(126\) | − | 0.176495i | − | 0.0157234i | ||||||
\(127\) | −14.8431 | + | 14.8431i | −1.31711 | + | 1.31711i | −0.401054 | + | 0.916054i | \(0.631356\pi\) |
−0.916054 | + | 0.401054i | \(0.868644\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −1.51043 | −0.132986 | ||||||||
\(130\) | 7.52955 | − | 3.94403i | 0.660386 | − | 0.345914i | ||||
\(131\) | −8.69869 | −0.760008 | −0.380004 | − | 0.924985i | \(-0.624077\pi\) | ||||
−0.380004 | + | 0.924985i | \(0.624077\pi\) | |||||||
\(132\) | 0.390701 | + | 0.390701i | 0.0340061 | + | 0.0340061i | ||||
\(133\) | 0.135326 | + | 0.135326i | 0.0117342 | + | 0.0117342i | ||||
\(134\) | 7.61541 | 0.657871 | ||||||||
\(135\) | −0.666968 | + | 2.13428i | −0.0574035 | + | 0.183690i | ||||
\(136\) | − | 5.11901i | − | 0.438951i | ||||||
\(137\) | −6.93107 | − | 6.93107i | −0.592161 | − | 0.592161i | 0.346053 | − | 0.938215i | \(-0.387522\pi\) |
−0.938215 | + | 0.346053i | \(0.887522\pi\) | |||||||
\(138\) | −4.79526 | + | 0.0741463i | −0.408199 | + | 0.00631175i | ||||
\(139\) | − | 2.07505i | − | 0.176003i | −0.996120 | − | 0.0880017i | \(-0.971952\pi\) | ||
0.996120 | − | 0.0880017i | \(-0.0280481\pi\) | |||||||
\(140\) | −0.117716 | + | 0.376689i | −0.00994884 | + | 0.0318360i | ||||
\(141\) | 0.844759 | 0.0711415 | ||||||||
\(142\) | −5.77533 | + | 5.77533i | −0.484655 | + | 0.484655i | ||||
\(143\) | 1.48517 | − | 1.48517i | 0.124196 | − | 0.124196i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 9.00876 | + | 17.1986i | 0.748137 | + | 1.42827i | ||||
\(146\) | −4.41769 | −0.365610 | ||||||||
\(147\) | −4.92772 | + | 4.92772i | −0.406432 | + | 0.406432i | ||||
\(148\) | −7.79545 | + | 7.79545i | −0.640782 | + | 0.640782i | ||||
\(149\) | −12.3141 | −1.00881 | −0.504406 | − | 0.863466i | \(-0.668289\pi\) | ||||
−0.504406 | + | 0.863466i | \(0.668289\pi\) | |||||||
\(150\) | 2.84699 | − | 4.11031i | 0.232456 | − | 0.335605i | ||||
\(151\) | −10.0500 | −0.817860 | −0.408930 | − | 0.912566i | \(-0.634098\pi\) | ||||
−0.408930 | + | 0.912566i | \(0.634098\pi\) | |||||||
\(152\) | 0.766741 | + | 0.766741i | 0.0621909 | + | 0.0621909i | ||||
\(153\) | 3.61968 | − | 3.61968i | 0.292634 | − | 0.292634i | ||||
\(154\) | 0.0975193i | 0.00785833i | ||||||||
\(155\) | −4.86489 | + | 2.54826i | −0.390758 | + | 0.204681i | ||||
\(156\) | −3.80130 | −0.304348 | ||||||||
\(157\) | −3.40779 | − | 3.40779i | −0.271972 | − | 0.271972i | 0.557922 | − | 0.829893i | \(-0.311599\pi\) |
−0.829893 | + | 0.557922i | \(0.811599\pi\) | |||||||
\(158\) | 4.78694 | − | 4.78694i | 0.380828 | − | 0.380828i | ||||
\(159\) | 8.41875 | 0.667650 | ||||||||
\(160\) | −0.666968 | + | 2.13428i | −0.0527285 | + | 0.168730i | ||||
\(161\) | −0.607704 | − | 0.589197i | −0.0478938 | − | 0.0464352i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −10.9785 | − | 10.9785i | −0.859900 | − | 0.859900i | 0.131426 | − | 0.991326i | \(-0.458044\pi\) |
−0.991326 | + | 0.131426i | \(0.958044\pi\) | |||||||
\(164\) | 2.27486i | 0.177637i | ||||||||
\(165\) | 0.368523 | − | 1.17926i | 0.0286895 | − | 0.0918055i | ||||
\(166\) | − | 0.270072i | − | 0.0209616i | ||||||
\(167\) | 0.393053 | − | 0.393053i | 0.0304153 | − | 0.0304153i | −0.691736 | − | 0.722151i | \(-0.743154\pi\) |
0.722151 | + | 0.691736i | \(0.243154\pi\) | |||||||
\(168\) | 0.124800 | − | 0.124800i | 0.00962857 | − | 0.00962857i | ||||
\(169\) | 1.44991i | 0.111531i | ||||||||
\(170\) | −10.1396 | + | 5.31121i | −0.777674 | + | 0.407351i | ||||
\(171\) | 1.08434i | 0.0829212i | ||||||||
\(172\) | −1.06804 | − | 1.06804i | −0.0814370 | − | 0.0814370i | ||||
\(173\) | −6.09087 | − | 6.09087i | −0.463081 | − | 0.463081i | 0.436583 | − | 0.899664i | \(-0.356188\pi\) |
−0.899664 | + | 0.436583i | \(0.856188\pi\) | |||||||
\(174\) | − | 8.68275i | − | 0.658238i | ||||||
\(175\) | 0.868275 | − | 0.157662i | 0.0656354 | − | 0.0119181i | ||||
\(176\) | 0.552534i | 0.0416489i | ||||||||
\(177\) | −7.36028 | + | 7.36028i | −0.553233 | + | 0.553233i | ||||
\(178\) | −6.19562 | + | 6.19562i | −0.464381 | + | 0.464381i | ||||
\(179\) | 23.2150i | 1.73517i | 0.497291 | + | 0.867584i | \(0.334328\pi\) | ||||
−0.497291 | + | 0.867584i | \(0.665672\pi\) | |||||||
\(180\) | −1.98078 | + | 1.03755i | −0.147639 | + | 0.0773342i | ||||
\(181\) | 6.45396i | 0.479719i | 0.970808 | + | 0.239860i | \(0.0771014\pi\) | ||||
−0.970808 | + | 0.239860i | \(0.922899\pi\) | |||||||
\(182\) | −0.474405 | − | 0.474405i | −0.0351652 | − | 0.0351652i | ||||
\(183\) | −6.44939 | + | 6.44939i | −0.476753 | + | 0.476753i | ||||
\(184\) | −3.44319 | − | 3.33833i | −0.253835 | − | 0.246105i | ||||
\(185\) | 23.5292 | + | 7.35295i | 1.72990 | + | 0.540599i | ||||
\(186\) | 2.45605 | 0.180086 | ||||||||
\(187\) | −2.00000 | + | 2.00000i | −0.146254 | + | 0.146254i | ||||
\(188\) | 0.597335 | + | 0.597335i | 0.0435651 | + | 0.0435651i | ||||
\(189\) | 0.176495 | 0.0128381 | ||||||||
\(190\) | 0.723217 | − | 2.31428i | 0.0524677 | − | 0.167895i | ||||
\(191\) | 22.6724i | 1.64052i | 0.571991 | + | 0.820260i | \(0.306171\pi\) | ||||
−0.571991 | + | 0.820260i | \(0.693829\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 7.13533 | + | 7.13533i | 0.513612 | + | 0.513612i | 0.915631 | − | 0.402019i | \(-0.131692\pi\) |
−0.402019 | + | 0.915631i | \(0.631692\pi\) | |||||||
\(194\) | 2.30492 | 0.165484 | ||||||||
\(195\) | 3.94403 | + | 7.52955i | 0.282438 | + | 0.539203i | ||||
\(196\) | −6.96885 | −0.497775 | ||||||||
\(197\) | 2.41931 | − | 2.41931i | 0.172369 | − | 0.172369i | −0.615651 | − | 0.788019i | \(-0.711107\pi\) |
0.788019 | + | 0.615651i | \(0.211107\pi\) | |||||||
\(198\) | −0.390701 | + | 0.390701i | −0.0277659 | + | 0.0277659i | ||||
\(199\) | 22.7308 | 1.61134 | 0.805672 | − | 0.592362i | \(-0.201805\pi\) | ||||
0.805672 | + | 0.592362i | \(0.201805\pi\) | |||||||
\(200\) | 4.91955 | − | 0.893297i | 0.347865 | − | 0.0631656i | ||||
\(201\) | 7.61541i | 0.537149i | ||||||||
\(202\) | 4.19388 | − | 4.19388i | 0.295080 | − | 0.295080i | ||||
\(203\) | 1.08361 | − | 1.08361i | 0.0760546 | − | 0.0760546i | ||||
\(204\) | 5.11901 | 0.358402 | ||||||||
\(205\) | 4.50600 | − | 2.36027i | 0.314713 | − | 0.164849i | ||||
\(206\) | − | 5.34381i | − | 0.372321i | ||||||
\(207\) | −0.0741463 | − | 4.79526i | −0.00515352 | − | 0.333293i | ||||
\(208\) | −2.68793 | − | 2.68793i | −0.186374 | − | 0.186374i | ||||
\(209\) | − | 0.599133i | − | 0.0414429i | ||||||
\(210\) | −0.376689 | − | 0.117716i | −0.0259940 | − | 0.00812319i | ||||
\(211\) | −22.6042 | −1.55613 | −0.778067 | − | 0.628181i | \(-0.783800\pi\) | ||||
−0.778067 | + | 0.628181i | \(0.783800\pi\) | |||||||
\(212\) | 5.95295 | + | 5.95295i | 0.408851 | + | 0.408851i | ||||
\(213\) | −5.77533 | − | 5.77533i | −0.395719 | − | 0.395719i | ||||
\(214\) | −12.8597 | −0.879074 | ||||||||
\(215\) | −1.00741 | + | 3.22368i | −0.0687047 | + | 0.219853i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.306516 | + | 0.306516i | 0.0208076 | + | 0.0208076i | ||||
\(218\) | −9.61288 | + | 9.61288i | −0.651067 | + | 0.651067i | ||||
\(219\) | − | 4.41769i | − | 0.298520i | ||||||
\(220\) | 1.09445 | − | 0.573280i | 0.0737878 | − | 0.0386505i | ||||
\(221\) | − | 19.4589i | − | 1.30895i | ||||||
\(222\) | −7.79545 | − | 7.79545i | −0.523197 | − | 0.523197i | ||||
\(223\) | 10.6254 | + | 10.6254i | 0.711531 | + | 0.711531i | 0.966855 | − | 0.255325i | \(-0.0821823\pi\) |
−0.255325 | + | 0.966855i | \(0.582182\pi\) | |||||||
\(224\) | 0.176495 | 0.0117925 | ||||||||
\(225\) | 4.11031 | + | 2.84699i | 0.274020 | + | 0.189800i | ||||
\(226\) | 13.1569i | 0.875186i | ||||||||
\(227\) | −4.66128 | − | 4.66128i | −0.309380 | − | 0.309380i | 0.535289 | − | 0.844669i | \(-0.320203\pi\) |
−0.844669 | + | 0.535289i | \(0.820203\pi\) | |||||||
\(228\) | −0.766741 | + | 0.766741i | −0.0507787 | + | 0.0507787i | ||||
\(229\) | −6.63852 | −0.438686 | −0.219343 | − | 0.975648i | \(-0.570391\pi\) | ||||
−0.219343 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(230\) | −3.04004 | + | 10.2839i | −0.200454 | + | 0.678099i | ||||
\(231\) | −0.0975193 | −0.00641630 | ||||||||
\(232\) | 6.13963 | − | 6.13963i | 0.403087 | − | 0.403087i | ||||
\(233\) | −3.52576 | − | 3.52576i | −0.230980 | − | 0.230980i | 0.582122 | − | 0.813102i | \(-0.302223\pi\) |
−0.813102 | + | 0.582122i | \(0.802223\pi\) | |||||||
\(234\) | − | 3.80130i | − | 0.248499i | ||||||
\(235\) | 0.563427 | − | 1.80295i | 0.0367539 | − | 0.117612i | ||||
\(236\) | −10.4090 | −0.677569 | ||||||||
\(237\) | 4.78694 | + | 4.78694i | 0.310945 | + | 0.310945i | ||||
\(238\) | 0.638854 | + | 0.638854i | 0.0414108 | + | 0.0414108i | ||||
\(239\) | 19.3650i | 1.25262i | 0.779574 | + | 0.626310i | \(0.215436\pi\) | ||||
−0.779574 | + | 0.626310i | \(0.784564\pi\) | |||||||
\(240\) | −2.13428 | − | 0.666968i | −0.137767 | − | 0.0430526i | ||||
\(241\) | − | 20.0648i | − | 1.29248i | −0.763132 | − | 0.646242i | \(-0.776339\pi\) | ||
0.763132 | − | 0.646242i | \(-0.223661\pi\) | |||||||
\(242\) | −7.56230 | + | 7.56230i | −0.486123 | + | 0.486123i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −9.12081 | −0.583900 | ||||||||
\(245\) | 7.23051 | + | 13.8038i | 0.461940 | + | 0.881891i | ||||
\(246\) | −2.27486 | −0.145040 | ||||||||
\(247\) | 2.91461 | + | 2.91461i | 0.185452 | + | 0.185452i | ||||
\(248\) | 1.73669 | + | 1.73669i | 0.110280 | + | 0.110280i | ||||
\(249\) | 0.270072 | 0.0171151 | ||||||||
\(250\) | −6.87369 | − | 8.81773i | −0.434731 | − | 0.557682i | ||||
\(251\) | − | 29.2252i | − | 1.84468i | −0.386381 | − | 0.922339i | \(-0.626275\pi\) | ||
0.386381 | − | 0.922339i | \(-0.373725\pi\) | |||||||
\(252\) | 0.124800 | + | 0.124800i | 0.00786169 | + | 0.00786169i | ||||
\(253\) | 0.0409684 | + | 2.64955i | 0.00257566 | + | 0.166576i | ||||
\(254\) | − | 20.9913i | − | 1.31711i | ||||||
\(255\) | −5.31121 | − | 10.1396i | −0.332601 | − | 0.634969i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.47796 | − | 2.47796i | 0.154571 | − | 0.154571i | −0.625585 | − | 0.780156i | \(-0.715140\pi\) |
0.780156 | + | 0.625585i | \(0.215140\pi\) | |||||||
\(258\) | 1.06804 | − | 1.06804i | 0.0664930 | − | 0.0664930i | ||||
\(259\) | − | 1.94575i | − | 0.120903i | ||||||
\(260\) | −2.53535 | + | 8.11305i | −0.157236 | + | 0.503150i | ||||
\(261\) | 8.68275 | 0.537449 | ||||||||
\(262\) | 6.15090 | − | 6.15090i | 0.380004 | − | 0.380004i | ||||
\(263\) | 6.69369 | − | 6.69369i | 0.412751 | − | 0.412751i | −0.469945 | − | 0.882696i | \(-0.655726\pi\) |
0.882696 | + | 0.469945i | \(0.155726\pi\) | |||||||
\(264\) | −0.552534 | −0.0340061 | ||||||||
\(265\) | 5.61504 | − | 17.9680i | 0.344929 | − | 1.10376i | ||||
\(266\) | −0.191379 | −0.0117342 | ||||||||
\(267\) | −6.19562 | − | 6.19562i | −0.379166 | − | 0.379166i | ||||
\(268\) | −5.38491 | + | 5.38491i | −0.328935 | + | 0.328935i | ||||
\(269\) | − | 8.21211i | − | 0.500701i | −0.968155 | − | 0.250350i | \(-0.919454\pi\) | ||
0.968155 | − | 0.250350i | \(-0.0805459\pi\) | |||||||
\(270\) | −1.03755 | − | 1.98078i | −0.0631431 | − | 0.120547i | ||||
\(271\) | 8.60224 | 0.522549 | 0.261274 | − | 0.965265i | \(-0.415857\pi\) | ||||
0.261274 | + | 0.965265i | \(0.415857\pi\) | |||||||
\(272\) | 3.61968 | + | 3.61968i | 0.219476 | + | 0.219476i | ||||
\(273\) | 0.474405 | − | 0.474405i | 0.0287123 | − | 0.0287123i | ||||
\(274\) | 9.80202 | 0.592161 | ||||||||
\(275\) | −2.27109 | − | 1.57306i | −0.136952 | − | 0.0948592i | ||||
\(276\) | 3.33833 | − | 3.44319i | 0.200944 | − | 0.207256i | ||||
\(277\) | −9.28544 | + | 9.28544i | −0.557908 | + | 0.557908i | −0.928711 | − | 0.370803i | \(-0.879082\pi\) |
0.370803 | + | 0.928711i | \(0.379082\pi\) | |||||||
\(278\) | 1.46728 | + | 1.46728i | 0.0880017 | + | 0.0880017i | ||||
\(279\) | 2.45605i | 0.147040i | ||||||||
\(280\) | −0.183121 | − | 0.349597i | −0.0109436 | − | 0.0208924i | ||||
\(281\) | − | 15.2296i | − | 0.908521i | −0.890869 | − | 0.454261i | \(-0.849903\pi\) | ||
0.890869 | − | 0.454261i | \(-0.150097\pi\) | |||||||
\(282\) | −0.597335 | + | 0.597335i | −0.0355708 | + | 0.0355708i | ||||
\(283\) | −11.6676 | + | 11.6676i | −0.693566 | + | 0.693566i | −0.963015 | − | 0.269449i | \(-0.913158\pi\) |
0.269449 | + | 0.963015i | \(0.413158\pi\) | |||||||
\(284\) | − | 8.16755i | − | 0.484655i | ||||||
\(285\) | 2.31428 | + | 0.723217i | 0.137086 | + | 0.0428397i | ||||
\(286\) | 2.10035i | 0.124196i | ||||||||
\(287\) | −0.283904 | − | 0.283904i | −0.0167583 | − | 0.0167583i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 9.20422i | 0.541425i | ||||||||
\(290\) | −18.5314 | − | 5.79112i | −1.08820 | − | 0.340066i | ||||
\(291\) | 2.30492i | 0.135117i | ||||||||
\(292\) | 3.12378 | − | 3.12378i | 0.182805 | − | 0.182805i | ||||
\(293\) | 21.8568 | − | 21.8568i | 1.27689 | − | 1.27689i | 0.334484 | − | 0.942401i | \(-0.391438\pi\) |
0.942401 | − | 0.334484i | \(-0.108562\pi\) | |||||||
\(294\) | − | 6.96885i | − | 0.406432i | ||||||
\(295\) | 10.7998 | + | 20.6180i | 0.628790 | + | 1.20042i | ||||
\(296\) | − | 11.0244i | − | 0.640782i | ||||||
\(297\) | −0.390701 | − | 0.390701i | −0.0226708 | − | 0.0226708i | ||||
\(298\) | 8.70740 | − | 8.70740i | 0.504406 | − | 0.504406i | ||||
\(299\) | −13.0886 | − | 12.6900i | −0.756934 | − | 0.733882i | ||||
\(300\) | 0.893297 | + | 4.91955i | 0.0515745 | + | 0.284031i | ||||
\(301\) | 0.266583 | 0.0153656 | ||||||||
\(302\) | 7.10645 | − | 7.10645i | 0.408930 | − | 0.408930i | ||||
\(303\) | 4.19388 | + | 4.19388i | 0.240932 | + | 0.240932i | ||||
\(304\) | −1.08434 | −0.0621909 | ||||||||
\(305\) | 9.46327 | + | 18.0663i | 0.541865 | + | 1.03448i | ||||
\(306\) | 5.11901i | 0.292634i | ||||||||
\(307\) | −6.33351 | + | 6.33351i | −0.361473 | + | 0.361473i | −0.864355 | − | 0.502882i | \(-0.832273\pi\) |
0.502882 | + | 0.864355i | \(0.332273\pi\) | |||||||
\(308\) | −0.0689566 | − | 0.0689566i | −0.00392917 | − | 0.00392917i | ||||
\(309\) | 5.34381 | 0.303999 | ||||||||
\(310\) | 1.63810 | − | 5.24189i | 0.0930381 | − | 0.297719i | ||||
\(311\) | 21.7763 | 1.23482 | 0.617410 | − | 0.786641i | \(-0.288182\pi\) | ||||
0.617410 | + | 0.786641i | \(0.288182\pi\) | |||||||
\(312\) | 2.68793 | − | 2.68793i | 0.152174 | − | 0.152174i | ||||
\(313\) | 21.2955 | − | 21.2955i | 1.20369 | − | 1.20369i | 0.230658 | − | 0.973035i | \(-0.425912\pi\) |
0.973035 | − | 0.230658i | \(-0.0740877\pi\) | |||||||
\(314\) | 4.81935 | 0.271972 | ||||||||
\(315\) | 0.117716 | − | 0.376689i | 0.00663256 | − | 0.0212240i | ||||
\(316\) | 6.76975i | 0.380828i | ||||||||
\(317\) | 13.1005 | − | 13.1005i | 0.735797 | − | 0.735797i | −0.235965 | − | 0.971762i | \(-0.575825\pi\) |
0.971762 | + | 0.235965i | \(0.0758251\pi\) | |||||||
\(318\) | −5.95295 | + | 5.95295i | −0.333825 | + | 0.333825i | ||||
\(319\) | −4.79752 | −0.268610 | ||||||||
\(320\) | −1.03755 | − | 1.98078i | −0.0580006 | − | 0.110729i | ||||
\(321\) | − | 12.8597i | − | 0.717761i | ||||||
\(322\) | 0.846337 | − | 0.0130864i | 0.0471645 | − | 0.000729278i | ||||
\(323\) | −3.92495 | − | 3.92495i | −0.218390 | − | 0.218390i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 18.7007 | − | 3.39569i | 1.03733 | − | 0.188359i | ||||
\(326\) | 15.5259 | 0.859900 | ||||||||
\(327\) | −9.61288 | − | 9.61288i | −0.531594 | − | 0.531594i | ||||
\(328\) | −1.60857 | − | 1.60857i | −0.0888184 | − | 0.0888184i | ||||
\(329\) | −0.149095 | −0.00821989 | ||||||||
\(330\) | 0.573280 | + | 1.09445i | 0.0315580 | + | 0.0602475i | ||||
\(331\) | −18.0446 | −0.991822 | −0.495911 | − | 0.868373i | \(-0.665166\pi\) | ||||
−0.495911 | + | 0.868373i | \(0.665166\pi\) | |||||||
\(332\) | 0.190970 | + | 0.190970i | 0.0104808 | + | 0.0104808i | ||||
\(333\) | 7.79545 | − | 7.79545i | 0.427188 | − | 0.427188i | ||||
\(334\) | 0.555860i | 0.0304153i | ||||||||
\(335\) | 16.2534 | + | 5.07923i | 0.888019 | + | 0.277508i | ||||
\(336\) | 0.176495i | 0.00962857i | ||||||||
\(337\) | 11.3825 | + | 11.3825i | 0.620045 | + | 0.620045i | 0.945543 | − | 0.325498i | \(-0.105532\pi\) |
−0.325498 | + | 0.945543i | \(0.605532\pi\) | |||||||
\(338\) | −1.02524 | − | 1.02524i | −0.0557657 | − | 0.0557657i | ||||
\(339\) | −13.1569 | −0.714586 | ||||||||
\(340\) | 3.41421 | − | 10.9254i | 0.185162 | − | 0.592513i | ||||
\(341\) | − | 1.35705i | − | 0.0734884i | ||||||
\(342\) | −0.766741 | − | 0.766741i | −0.0414606 | − | 0.0414606i | ||||
\(343\) | 1.74332 | − | 1.74332i | 0.0941304 | − | 0.0941304i | ||||
\(344\) | 1.51043 | 0.0814370 | ||||||||
\(345\) | −10.2839 | − | 3.04004i | −0.553665 | − | 0.163670i | ||||
\(346\) | 8.61380 | 0.463081 | ||||||||
\(347\) | 0.783931 | − | 0.783931i | 0.0420836 | − | 0.0420836i | −0.685752 | − | 0.727835i | \(-0.740526\pi\) |
0.727835 | + | 0.685752i | \(0.240526\pi\) | |||||||
\(348\) | 6.13963 | + | 6.13963i | 0.329119 | + | 0.329119i | ||||
\(349\) | − | 2.79894i | − | 0.149824i | −0.997190 | − | 0.0749120i | \(-0.976132\pi\) | ||
0.997190 | − | 0.0749120i | \(-0.0238676\pi\) | |||||||
\(350\) | −0.502479 | + | 0.725447i | −0.0268586 | + | 0.0387768i | ||||
\(351\) | 3.80130 | 0.202899 | ||||||||
\(352\) | −0.390701 | − | 0.390701i | −0.0208244 | − | 0.0208244i | ||||
\(353\) | −8.28523 | − | 8.28523i | −0.440978 | − | 0.440978i | 0.451362 | − | 0.892341i | \(-0.350938\pi\) |
−0.892341 | + | 0.451362i | \(0.850938\pi\) | |||||||
\(354\) | − | 10.4090i | − | 0.553233i | ||||||
\(355\) | −16.1781 | + | 8.47421i | −0.858646 | + | 0.449764i | ||||
\(356\) | − | 8.76193i | − | 0.464381i | ||||||
\(357\) | −0.638854 | + | 0.638854i | −0.0338118 | + | 0.0338118i | ||||
\(358\) | −16.4155 | − | 16.4155i | −0.867584 | − | 0.867584i | ||||
\(359\) | 18.5465 | 0.978847 | 0.489424 | − | 0.872046i | \(-0.337207\pi\) | ||||
0.489424 | + | 0.872046i | \(0.337207\pi\) | |||||||
\(360\) | 0.666968 | − | 2.13428i | 0.0351523 | − | 0.112486i | ||||
\(361\) | −17.8242 | −0.938117 | ||||||||
\(362\) | −4.56364 | − | 4.56364i | −0.239860 | − | 0.239860i | ||||
\(363\) | −7.56230 | − | 7.56230i | −0.396918 | − | 0.396918i | ||||
\(364\) | 0.670909 | 0.0351652 | ||||||||
\(365\) | −9.42859 | − | 2.94646i | −0.493515 | − | 0.154225i | ||||
\(366\) | − | 9.12081i | − | 0.476753i | ||||||
\(367\) | −14.6933 | − | 14.6933i | −0.766985 | − | 0.766985i | 0.210590 | − | 0.977574i | \(-0.432462\pi\) |
−0.977574 | + | 0.210590i | \(0.932462\pi\) | |||||||
\(368\) | 4.79526 | − | 0.0741463i | 0.249970 | − | 0.00386514i | ||||
\(369\) | − | 2.27486i | − | 0.118425i | ||||||
\(370\) | −21.8370 | + | 11.4384i | −1.13525 | + | 0.594652i | ||||
\(371\) | −1.48586 | −0.0771422 | ||||||||
\(372\) | −1.73669 | + | 1.73669i | −0.0900430 | + | 0.0900430i | ||||
\(373\) | −3.14679 | + | 3.14679i | −0.162935 | + | 0.162935i | −0.783865 | − | 0.620931i | \(-0.786755\pi\) |
0.620931 | + | 0.783865i | \(0.286755\pi\) | |||||||
\(374\) | − | 2.82843i | − | 0.146254i | ||||||
\(375\) | 8.81773 | − | 6.87369i | 0.455346 | − | 0.354956i | ||||
\(376\) | −0.844759 | −0.0435651 | ||||||||
\(377\) | 23.3386 | − | 23.3386i | 1.20200 | − | 1.20200i | ||||
\(378\) | −0.124800 | + | 0.124800i | −0.00641904 | + | 0.00641904i | ||||
\(379\) | −16.5615 | −0.850706 | −0.425353 | − | 0.905028i | \(-0.639850\pi\) | ||||
−0.425353 | + | 0.905028i | \(0.639850\pi\) | |||||||
\(380\) | 1.12505 | + | 2.14783i | 0.0577138 | + | 0.110181i | ||||
\(381\) | 20.9913 | 1.07541 | ||||||||
\(382\) | −16.0318 | − | 16.0318i | −0.820260 | − | 0.820260i | ||||
\(383\) | 11.2204 | − | 11.2204i | 0.573338 | − | 0.573338i | −0.359722 | − | 0.933060i | \(-0.617128\pi\) |
0.933060 | + | 0.359722i | \(0.117128\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −0.0650423 | + | 0.208134i | −0.00331486 | + | 0.0106075i | ||||
\(386\) | −10.0909 | −0.513612 | ||||||||
\(387\) | 1.06804 | + | 1.06804i | 0.0542913 | + | 0.0542913i | ||||
\(388\) | −1.62982 | + | 1.62982i | −0.0827418 | + | 0.0827418i | ||||
\(389\) | −26.6584 | −1.35164 | −0.675818 | − | 0.737068i | \(-0.736210\pi\) | ||||
−0.675818 | + | 0.737068i | \(0.736210\pi\) | |||||||
\(390\) | −8.11305 | − | 2.53535i | −0.410820 | − | 0.128382i | ||||
\(391\) | 17.6257 | + | 17.0889i | 0.891370 | + | 0.864224i | ||||
\(392\) | 4.92772 | − | 4.92772i | 0.248887 | − | 0.248887i | ||||
\(393\) | 6.15090 | + | 6.15090i | 0.310272 | + | 0.310272i | ||||
\(394\) | 3.42142i | 0.172369i | ||||||||
\(395\) | 13.4094 | − | 7.02393i | 0.674700 | − | 0.353412i | ||||
\(396\) | − | 0.552534i | − | 0.0277659i | ||||||
\(397\) | 1.03788 | − | 1.03788i | 0.0520899 | − | 0.0520899i | −0.680582 | − | 0.732672i | \(-0.738273\pi\) |
0.732672 | + | 0.680582i | \(0.238273\pi\) | |||||||
\(398\) | −16.0731 | + | 16.0731i | −0.805672 | + | 0.805672i | ||||
\(399\) | − | 0.191379i | − | 0.00958095i | ||||||
\(400\) | −2.84699 | + | 4.11031i | −0.142350 | + | 0.205515i | ||||
\(401\) | 24.1332i | 1.20516i | 0.798060 | + | 0.602578i | \(0.205860\pi\) | ||||
−0.798060 | + | 0.602578i | \(0.794140\pi\) | |||||||
\(402\) | −5.38491 | − | 5.38491i | −0.268575 | − | 0.268575i | ||||
\(403\) | 6.60168 | + | 6.60168i | 0.328853 | + | 0.328853i | ||||
\(404\) | 5.93104i | 0.295080i | ||||||||
\(405\) | 1.98078 | − | 1.03755i | 0.0984258 | − | 0.0515561i | ||||
\(406\) | 1.53246i | 0.0760546i | ||||||||
\(407\) | −4.30726 | + | 4.30726i | −0.213503 | + | 0.213503i | ||||
\(408\) | −3.61968 | + | 3.61968i | −0.179201 | + | 0.179201i | ||||
\(409\) | 17.2612i | 0.853511i | 0.904367 | + | 0.426756i | \(0.140344\pi\) | ||||
−0.904367 | + | 0.426756i | \(0.859656\pi\) | |||||||
\(410\) | −1.51726 | + | 4.85519i | −0.0749321 | + | 0.239781i | ||||
\(411\) | 9.80202i | 0.483498i | ||||||||
\(412\) | 3.77864 | + | 3.77864i | 0.186160 | + | 0.186160i | ||||
\(413\) | 1.29905 | − | 1.29905i | 0.0639220 | − | 0.0639220i | ||||
\(414\) | 3.44319 | + | 3.33833i | 0.169224 | + | 0.164070i | ||||
\(415\) | 0.180129 | − | 0.576409i | 0.00884220 | − | 0.0282948i | ||||
\(416\) | 3.80130 | 0.186374 | ||||||||
\(417\) | −1.46728 | + | 1.46728i | −0.0718531 | + | 0.0718531i | ||||
\(418\) | 0.423651 | + | 0.423651i | 0.0207214 | + | 0.0207214i | ||||
\(419\) | −8.83329 | −0.431534 | −0.215767 | − | 0.976445i | \(-0.569225\pi\) | ||||
−0.215767 | + | 0.976445i | \(0.569225\pi\) | |||||||
\(420\) | 0.349597 | − | 0.183121i | 0.0170586 | − | 0.00893540i | ||||
\(421\) | 22.9157i | 1.11684i | 0.829558 | + | 0.558421i | \(0.188592\pi\) | ||||
−0.829558 | + | 0.558421i | \(0.811408\pi\) | |||||||
\(422\) | 15.9836 | − | 15.9836i | 0.778067 | − | 0.778067i | ||||
\(423\) | −0.597335 | − | 0.597335i | −0.0290434 | − | 0.0290434i | ||||
\(424\) | −8.41875 | −0.408851 | ||||||||
\(425\) | −25.1832 | + | 4.57279i | −1.22157 | + | 0.221813i | ||||
\(426\) | 8.16755 | 0.395719 | ||||||||
\(427\) | 1.13828 | − | 1.13828i | 0.0550853 | − | 0.0550853i | ||||
\(428\) | 9.09321 | − | 9.09321i | 0.439537 | − | 0.439537i | ||||
\(429\) | −2.10035 | −0.101406 | ||||||||
\(430\) | −1.56714 | − | 2.99183i | −0.0755743 | − | 0.144279i | ||||
\(431\) | − | 4.11877i | − | 0.198394i | −0.995068 | − | 0.0991970i | \(-0.968373\pi\) | ||
0.995068 | − | 0.0991970i | \(-0.0316274\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −13.2007 | + | 13.2007i | −0.634383 | + | 0.634383i | −0.949164 | − | 0.314781i | \(-0.898069\pi\) |
0.314781 | + | 0.949164i | \(0.398069\pi\) | |||||||
\(434\) | −0.433479 | −0.0208076 | ||||||||
\(435\) | 5.79112 | − | 18.5314i | 0.277663 | − | 0.888514i | ||||
\(436\) | − | 13.5947i | − | 0.651067i | ||||||
\(437\) | −5.19967 | + | 0.0803995i | −0.248734 | + | 0.00384603i | ||||
\(438\) | 3.12378 | + | 3.12378i | 0.149260 | + | 0.149260i | ||||
\(439\) | 13.3446i | 0.636905i | 0.947939 | + | 0.318452i | \(0.103163\pi\) | ||||
−0.947939 | + | 0.318452i | \(0.896837\pi\) | |||||||
\(440\) | −0.368523 | + | 1.17926i | −0.0175686 | + | 0.0562192i | ||||
\(441\) | 6.96885 | 0.331850 | ||||||||
\(442\) | 13.7595 | + | 13.7595i | 0.654473 | + | 0.654473i | ||||
\(443\) | −17.1528 | − | 17.1528i | −0.814955 | − | 0.814955i | 0.170417 | − | 0.985372i | \(-0.445489\pi\) |
−0.985372 | + | 0.170417i | \(0.945489\pi\) | |||||||
\(444\) | 11.0244 | 0.523197 | ||||||||
\(445\) | −17.3555 | + | 9.09091i | −0.822728 | + | 0.430950i | ||||
\(446\) | −15.0266 | −0.711531 | ||||||||
\(447\) | 8.70740 | + | 8.70740i | 0.411846 | + | 0.411846i | ||||
\(448\) | −0.124800 | + | 0.124800i | −0.00589627 | + | 0.00589627i | ||||
\(449\) | 7.35156i | 0.346942i | 0.984839 | + | 0.173471i | \(0.0554982\pi\) | ||||
−0.984839 | + | 0.173471i | \(0.944502\pi\) | |||||||
\(450\) | −4.91955 | + | 0.893297i | −0.231910 | + | 0.0421104i | ||||
\(451\) | 1.25694i | 0.0591870i | ||||||||
\(452\) | −9.30335 | − | 9.30335i | −0.437593 | − | 0.437593i | ||||
\(453\) | 7.10645 | + | 7.10645i | 0.333890 | + | 0.333890i | ||||
\(454\) | 6.59205 | 0.309380 | ||||||||
\(455\) | −0.696100 | − | 1.32893i | −0.0326337 | − | 0.0623010i | ||||
\(456\) | − | 1.08434i | − | 0.0507787i | ||||||
\(457\) | 1.61697 | + | 1.61697i | 0.0756388 | + | 0.0756388i | 0.743914 | − | 0.668275i | \(-0.232967\pi\) |
−0.668275 | + | 0.743914i | \(0.732967\pi\) | |||||||
\(458\) | 4.69415 | − | 4.69415i | 0.219343 | − | 0.219343i | ||||
\(459\) | −5.11901 | −0.238935 | ||||||||
\(460\) | −5.12217 | − | 9.42143i | −0.238822 | − | 0.439276i | ||||
\(461\) | −19.4223 | −0.904586 | −0.452293 | − | 0.891869i | \(-0.649394\pi\) | ||||
−0.452293 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(462\) | 0.0689566 | − | 0.0689566i | 0.00320815 | − | 0.00320815i | ||||
\(463\) | −16.6725 | − | 16.6725i | −0.774836 | − | 0.774836i | 0.204112 | − | 0.978948i | \(-0.434569\pi\) |
−0.978948 | + | 0.204112i | \(0.934569\pi\) | |||||||
\(464\) | 8.68275i | 0.403087i | ||||||||
\(465\) | 5.24189 | + | 1.63810i | 0.243087 | + | 0.0759653i | ||||
\(466\) | 4.98618 | 0.230980 | ||||||||
\(467\) | 18.7427 | + | 18.7427i | 0.867310 | + | 0.867310i | 0.992174 | − | 0.124864i | \(-0.0398495\pi\) |
−0.124864 | + | 0.992174i | \(0.539850\pi\) | |||||||
\(468\) | 2.68793 | + | 2.68793i | 0.124249 | + | 0.124249i | ||||
\(469\) | − | 1.34408i | − | 0.0620637i | ||||||
\(470\) | 0.876477 | + | 1.67328i | 0.0404289 | + | 0.0771828i | ||||
\(471\) | 4.81935i | 0.222064i | ||||||||
\(472\) | 7.36028 | − | 7.36028i | 0.338784 | − | 0.338784i | ||||
\(473\) | −0.590127 | − | 0.590127i | −0.0271341 | − | 0.0271341i | ||||
\(474\) | −6.76975 | −0.310945 | ||||||||
\(475\) | 3.08710 | − | 4.45695i | 0.141646 | − | 0.204499i | ||||
\(476\) | −0.903477 | −0.0414108 | ||||||||
\(477\) | −5.95295 | − | 5.95295i | −0.272567 | − | 0.272567i | ||||
\(478\) | −13.6932 | − | 13.6932i | −0.626310 | − | 0.626310i | ||||
\(479\) | 4.02931 | 0.184104 | 0.0920520 | − | 0.995754i | \(-0.470657\pi\) | ||||
0.0920520 | + | 0.995754i | \(0.470657\pi\) | |||||||
\(480\) | 1.98078 | − | 1.03755i | 0.0904099 | − | 0.0473573i | ||||
\(481\) | − | 41.9072i | − | 1.91081i | ||||||
\(482\) | 14.1879 | + | 14.1879i | 0.646242 | + | 0.646242i | ||||
\(483\) | 0.0130864 | + | 0.846337i | 0.000595453 | + | 0.0385097i | ||||
\(484\) | − | 10.6947i | − | 0.486123i | ||||||
\(485\) | 4.91935 | + | 1.53731i | 0.223376 | + | 0.0698056i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −15.4120 | + | 15.4120i | −0.698385 | + | 0.698385i | −0.964062 | − | 0.265677i | \(-0.914404\pi\) |
0.265677 | + | 0.964062i | \(0.414404\pi\) | |||||||
\(488\) | 6.44939 | − | 6.44939i | 0.291950 | − | 0.291950i | ||||
\(489\) | 15.5259i | 0.702105i | ||||||||
\(490\) | −14.8735 | − | 4.64800i | −0.671915 | − | 0.209975i | ||||
\(491\) | 2.44078 | 0.110151 | 0.0550755 | − | 0.998482i | \(-0.482460\pi\) | ||||
0.0550755 | + | 0.998482i | \(0.482460\pi\) | |||||||
\(492\) | 1.60857 | − | 1.60857i | 0.0725199 | − | 0.0725199i | ||||
\(493\) | −31.4288 | + | 31.4288i | −1.41548 | + | 1.41548i | ||||
\(494\) | −4.12189 | −0.185452 | ||||||||
\(495\) | −1.09445 | + | 0.573280i | −0.0491919 | + | 0.0257670i | ||||
\(496\) | −2.45605 | −0.110280 | ||||||||
\(497\) | 1.01931 | + | 1.01931i | 0.0457225 | + | 0.0457225i | ||||
\(498\) | −0.190970 | + | 0.190970i | −0.00855756 | + | 0.00855756i | ||||
\(499\) | − | 42.3741i | − | 1.89693i | −0.316889 | − | 0.948463i | \(-0.602638\pi\) | ||
0.316889 | − | 0.948463i | \(-0.397362\pi\) | |||||||
\(500\) | 11.0955 | + | 1.37464i | 0.496206 | + | 0.0614758i | ||||
\(501\) | −0.555860 | −0.0248340 | ||||||||
\(502\) | 20.6653 | + | 20.6653i | 0.922339 | + | 0.922339i | ||||
\(503\) | 28.9820 | − | 28.9820i | 1.29224 | − | 1.29224i | 0.358846 | − | 0.933397i | \(-0.383170\pi\) |
0.933397 | − | 0.358846i | \(-0.116830\pi\) | |||||||
\(504\) | −0.176495 | −0.00786169 | ||||||||
\(505\) | 11.7481 | − | 6.15373i | 0.522784 | − | 0.273838i | ||||
\(506\) | −1.90248 | − | 1.84454i | −0.0845756 | − | 0.0819999i | ||||
\(507\) | 1.02524 | − | 1.02524i | 0.0455325 | − | 0.0455325i | ||||
\(508\) | 14.8431 | + | 14.8431i | 0.658554 | + | 0.658554i | ||||
\(509\) | − | 3.86372i | − | 0.171257i | −0.996327 | − | 0.0856283i | \(-0.972710\pi\) | ||
0.996327 | − | 0.0856283i | \(-0.0272897\pi\) | |||||||
\(510\) | 10.9254 | + | 3.41421i | 0.483785 | + | 0.151184i | ||||
\(511\) | 0.779698i | 0.0344918i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0.766741 | − | 0.766741i | 0.0338524 | − | 0.0338524i | ||||
\(514\) | 3.50437i | 0.154571i | ||||||||
\(515\) | 3.56415 | − | 11.4052i | 0.157055 | − | 0.502573i | ||||
\(516\) | 1.51043i | 0.0664930i | ||||||||
\(517\) | 0.330048 | + | 0.330048i | 0.0145155 | + | 0.0145155i | ||||
\(518\) | 1.37586 | + | 1.37586i | 0.0604516 | + | 0.0604516i | ||||
\(519\) | 8.61380i | 0.378104i | ||||||||
\(520\) | −3.94403 | − | 7.52955i | −0.172957 | − | 0.330193i | ||||
\(521\) | 19.8403i | 0.869221i | 0.900619 | + | 0.434610i | \(0.143114\pi\) | ||||
−0.900619 | + | 0.434610i | \(0.856886\pi\) | |||||||
\(522\) | −6.13963 | + | 6.13963i | −0.268724 | + | 0.268724i | ||||
\(523\) | −13.6045 | + | 13.6045i | −0.594883 | + | 0.594883i | −0.938946 | − | 0.344063i | \(-0.888197\pi\) |
0.344063 | + | 0.938946i | \(0.388197\pi\) | |||||||
\(524\) | 8.69869i | 0.380004i | ||||||||
\(525\) | −0.725447 | − | 0.502479i | −0.0316611 | − | 0.0219300i | ||||
\(526\) | 9.46631i | 0.412751i | ||||||||
\(527\) | −8.89011 | − | 8.89011i | −0.387259 | − | 0.387259i | ||||
\(528\) | 0.390701 | − | 0.390701i | 0.0170031 | − | 0.0170031i | ||||
\(529\) | 22.9890 | − | 0.711101i | 0.999522 | − | 0.0309175i | ||||
\(530\) | 8.73484 | + | 16.6757i | 0.379417 | + | 0.724346i | ||||
\(531\) | 10.4090 | 0.451712 | ||||||||
\(532\) | 0.135326 | − | 0.135326i | 0.00586711 | − | 0.00586711i | ||||
\(533\) | −6.11466 | − | 6.11466i | −0.264855 | − | 0.264855i | ||||
\(534\) | 8.76193 | 0.379166 | ||||||||
\(535\) | −27.4463 | − | 8.57704i | −1.18661 | − | 0.370818i | ||||
\(536\) | − | 7.61541i | − | 0.328935i | ||||||
\(537\) | 16.4155 | − | 16.4155i | 0.708379 | − | 0.708379i | ||||
\(538\) | 5.80684 | + | 5.80684i | 0.250350 | + | 0.250350i | ||||
\(539\) | −3.85053 | −0.165854 | ||||||||
\(540\) | 2.13428 | + | 0.666968i | 0.0918448 | + | 0.0287017i | ||||
\(541\) | −21.3249 | −0.916828 | −0.458414 | − | 0.888739i | \(-0.651582\pi\) | ||||
−0.458414 | + | 0.888739i | \(0.651582\pi\) | |||||||
\(542\) | −6.08270 | + | 6.08270i | −0.261274 | + | 0.261274i | ||||
\(543\) | 4.56364 | − | 4.56364i | 0.195845 | − | 0.195845i | ||||
\(544\) | −5.11901 | −0.219476 | ||||||||
\(545\) | −26.9281 | + | 14.1051i | −1.15347 | + | 0.604196i | ||||
\(546\) | 0.670909i | 0.0287123i | ||||||||
\(547\) | 21.0991 | − | 21.0991i | 0.902131 | − | 0.902131i | −0.0934889 | − | 0.995620i | \(-0.529802\pi\) |
0.995620 | + | 0.0934889i | \(0.0298020\pi\) | |||||||
\(548\) | −6.93107 | + | 6.93107i | −0.296081 | + | 0.296081i | ||||
\(549\) | 9.12081 | 0.389267 | ||||||||
\(550\) | 2.71822 | − | 0.493577i | 0.115905 | − | 0.0210462i | ||||
\(551\) | − | 9.41502i | − | 0.401093i | ||||||
\(552\) | 0.0741463 | + | 4.79526i | 0.00315588 | + | 0.204100i | ||||
\(553\) | −0.844868 | − | 0.844868i | −0.0359274 | − | 0.0359274i | ||||
\(554\) | − | 13.1316i | − | 0.557908i | ||||||
\(555\) | −11.4384 | − | 21.8370i | −0.485532 | − | 0.926929i | ||||
\(556\) | −2.07505 | −0.0880017 | ||||||||
\(557\) | 27.8064 | + | 27.8064i | 1.17820 | + | 1.17820i | 0.980203 | + | 0.197993i | \(0.0634423\pi\) |
0.197993 | + | 0.980203i | \(0.436558\pi\) | |||||||
\(558\) | −1.73669 | − | 1.73669i | −0.0735198 | − | 0.0735198i | ||||
\(559\) | 5.74161 | 0.242844 | ||||||||
\(560\) | 0.376689 | + | 0.117716i | 0.0159180 | + | 0.00497442i | ||||
\(561\) | 2.82843 | 0.119416 | ||||||||
\(562\) | 10.7689 | + | 10.7689i | 0.454261 | + | 0.454261i | ||||
\(563\) | −22.4843 | + | 22.4843i | −0.947602 | + | 0.947602i | −0.998694 | − | 0.0510924i | \(-0.983730\pi\) |
0.0510924 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(564\) | − | 0.844759i | − | 0.0355708i | ||||||
\(565\) | −8.77525 | + | 28.0806i | −0.369178 | + | 1.18136i | ||||
\(566\) | − | 16.5005i | − | 0.693566i | ||||||
\(567\) | −0.124800 | − | 0.124800i | −0.00524113 | − | 0.00524113i | ||||
\(568\) | 5.77533 | + | 5.77533i | 0.242327 | + | 0.242327i | ||||
\(569\) | −33.7165 | −1.41347 | −0.706735 | − | 0.707479i | \(-0.749832\pi\) | ||||
−0.706735 | + | 0.707479i | \(0.749832\pi\) | |||||||
\(570\) | −2.14783 | + | 1.12505i | −0.0899628 | + | 0.0471231i | ||||
\(571\) | 36.2733i | 1.51799i | 0.651097 | + | 0.758995i | \(0.274309\pi\) | ||||
−0.651097 | + | 0.758995i | \(0.725691\pi\) | |||||||
\(572\) | −1.48517 | − | 1.48517i | −0.0620982 | − | 0.0620982i | ||||
\(573\) | 16.0318 | − | 16.0318i | 0.669740 | − | 0.669740i | ||||
\(574\) | 0.401501 | 0.0167583 | ||||||||
\(575\) | −13.3473 | + | 19.9211i | −0.556621 | + | 0.830766i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −21.9088 | + | 21.9088i | −0.912076 | + | 0.912076i | −0.996435 | − | 0.0843592i | \(-0.973116\pi\) |
0.0843592 | + | 0.996435i | \(0.473116\pi\) | |||||||
\(578\) | −6.50837 | − | 6.50837i | −0.270712 | − | 0.270712i | ||||
\(579\) | − | 10.0909i | − | 0.419362i | ||||||
\(580\) | 17.1986 | − | 9.00876i | 0.714135 | − | 0.374068i | ||||
\(581\) | −0.0476662 | −0.00197753 | ||||||||
\(582\) | −1.62982 | − | 1.62982i | −0.0675584 | − | 0.0675584i | ||||
\(583\) | 3.28921 | + | 3.28921i | 0.136225 | + | 0.136225i | ||||
\(584\) | 4.41769i | 0.182805i | ||||||||
\(585\) | 2.53535 | − | 8.11305i | 0.104824 | − | 0.335433i | ||||
\(586\) | 30.9101i | 1.27689i | ||||||||
\(587\) | 28.8834 | − | 28.8834i | 1.19215 | − | 1.19215i | 0.215684 | − | 0.976463i | \(-0.430802\pi\) |
0.976463 | − | 0.215684i | \(-0.0691980\pi\) | |||||||
\(588\) | 4.92772 | + | 4.92772i | 0.203216 | + | 0.203216i | ||||
\(589\) | 2.66318 | 0.109734 | ||||||||
\(590\) | −22.2157 | − | 6.94248i | −0.914608 | − | 0.285817i | ||||
\(591\) | −3.42142 | −0.140738 | ||||||||
\(592\) | 7.79545 | + | 7.79545i | 0.320391 | + | 0.320391i | ||||
\(593\) | −21.3435 | − | 21.3435i | −0.876474 | − | 0.876474i | 0.116694 | − | 0.993168i | \(-0.462770\pi\) |
−0.993168 | + | 0.116694i | \(0.962770\pi\) | |||||||
\(594\) | 0.552534 | 0.0226708 | ||||||||
\(595\) | 0.937399 | + | 1.78959i | 0.0384296 | + | 0.0733660i | ||||
\(596\) | 12.3141i | 0.504406i | ||||||||
\(597\) | −16.0731 | − | 16.0731i | −0.657828 | − | 0.657828i | ||||
\(598\) | 18.2282 | − | 0.281853i | 0.745408 | − | 0.0115258i | ||||
\(599\) | 38.3444i | 1.56671i | 0.621576 | + | 0.783354i | \(0.286493\pi\) | ||||
−0.621576 | + | 0.783354i | \(0.713507\pi\) | |||||||
\(600\) | −4.11031 | − | 2.84699i | −0.167803 | − | 0.116228i | ||||
\(601\) | 16.2980 | 0.664808 | 0.332404 | − | 0.943137i | \(-0.392140\pi\) | ||||
0.332404 | + | 0.943137i | \(0.392140\pi\) | |||||||
\(602\) | −0.188502 | + | 0.188502i | −0.00768279 | + | 0.00768279i | ||||
\(603\) | 5.38491 | − | 5.38491i | 0.219290 | − | 0.219290i | ||||
\(604\) | 10.0500i | 0.408930i | ||||||||
\(605\) | −21.1839 | + | 11.0963i | −0.861247 | + | 0.451127i | ||||
\(606\) | −5.93104 | −0.240932 | ||||||||
\(607\) | 1.17706 | − | 1.17706i | 0.0477754 | − | 0.0477754i | −0.682815 | − | 0.730591i | \(-0.739245\pi\) |
0.730591 | + | 0.682815i | \(0.239245\pi\) | |||||||
\(608\) | 0.766741 | − | 0.766741i | 0.0310954 | − | 0.0310954i | ||||
\(609\) | −1.53246 | −0.0620984 | ||||||||
\(610\) | −19.4664 | − | 6.08329i | −0.788171 | − | 0.246305i | ||||
\(611\) | −3.21119 | −0.129911 | ||||||||
\(612\) | −3.61968 | − | 3.61968i | −0.146317 | − | 0.146317i | ||||
\(613\) | 20.0004 | − | 20.0004i | 0.807808 | − | 0.807808i | −0.176494 | − | 0.984302i | \(-0.556476\pi\) |
0.984302 | + | 0.176494i | \(0.0564756\pi\) | |||||||
\(614\) | − | 8.95694i | − | 0.361473i | ||||||
\(615\) | −4.85519 | − | 1.51726i | −0.195780 | − | 0.0611818i | ||||
\(616\) | 0.0975193 | 0.00392917 | ||||||||
\(617\) | 18.9554 | + | 18.9554i | 0.763117 | + | 0.763117i | 0.976885 | − | 0.213767i | \(-0.0685734\pi\) |
−0.213767 | + | 0.976885i | \(0.568573\pi\) | |||||||
\(618\) | −3.77864 | + | 3.77864i | −0.151999 | + | 0.151999i | ||||
\(619\) | −3.91634 | −0.157411 | −0.0787055 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787055 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(620\) | 2.54826 | + | 4.86489i | 0.102341 | + | 0.195379i | ||||
\(621\) | −3.33833 | + | 3.44319i | −0.133963 | + | 0.138170i | ||||
\(622\) | −15.3982 | + | 15.3982i | −0.617410 | + | 0.617410i | ||||
\(623\) | 1.09349 | + | 1.09349i | 0.0438099 | + | 0.0438099i | ||||
\(624\) | 3.80130i | 0.152174i | ||||||||
\(625\) | −8.78925 | − | 23.4040i | −0.351570 | − | 0.936162i | ||||
\(626\) | 30.1164i | 1.20369i | ||||||||
\(627\) | −0.423651 | + | 0.423651i | −0.0169190 | + | 0.0169190i | ||||
\(628\) | −3.40779 | + | 3.40779i | −0.135986 | + | 0.135986i | ||||
\(629\) | 56.4342i | 2.25018i | ||||||||
\(630\) | 0.183121 | + | 0.349597i | 0.00729573 | + | 0.0139283i | ||||
\(631\) | 34.6601i | 1.37980i | 0.723906 | + | 0.689899i | \(0.242345\pi\) | ||||
−0.723906 | + | 0.689899i | \(0.757655\pi\) | |||||||
\(632\) | −4.78694 | − | 4.78694i | −0.190414 | − | 0.190414i | ||||
\(633\) | 15.9836 | + | 15.9836i | 0.635289 | + | 0.635289i | ||||
\(634\) | 18.5269i | 0.735797i | ||||||||
\(635\) | 14.0005 | − | 44.8012i | 0.555593 | − | 1.77788i | ||||
\(636\) | − | 8.41875i | − | 0.333825i | ||||||
\(637\) | 18.7318 | − | 18.7318i | 0.742179 | − | 0.742179i | ||||
\(638\) | 3.39236 | − | 3.39236i | 0.134305 | − | 0.134305i | ||||
\(639\) | 8.16755i | 0.323103i | ||||||||
\(640\) | 2.13428 | + | 0.666968i | 0.0843648 | + | 0.0263642i | ||||
\(641\) | − | 39.3379i | − | 1.55375i | −0.629653 | − | 0.776876i | \(-0.716803\pi\) | ||
0.629653 | − | 0.776876i | \(-0.283197\pi\) | |||||||
\(642\) | 9.09321 | + | 9.09321i | 0.358880 | + | 0.358880i | ||||
\(643\) | 16.8975 | − | 16.8975i | 0.666371 | − | 0.666371i | −0.290503 | − | 0.956874i | \(-0.593823\pi\) |
0.956874 | + | 0.290503i | \(0.0938226\pi\) | |||||||
\(644\) | −0.589197 | + | 0.607704i | −0.0232176 | + | 0.0239469i | ||||
\(645\) | 2.99183 | − | 1.56714i | 0.117803 | − | 0.0617062i | ||||
\(646\) | 5.55072 | 0.218390 | ||||||||
\(647\) | −29.2297 | + | 29.2297i | −1.14914 | + | 1.14914i | −0.162414 | + | 0.986723i | \(0.551928\pi\) |
−0.986723 | + | 0.162414i | \(0.948072\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | −5.75134 | −0.225760 | ||||||||
\(650\) | −10.8223 | + | 15.6245i | −0.424485 | + | 0.612844i | ||||
\(651\) | − | 0.433479i | − | 0.0169894i | ||||||
\(652\) | −10.9785 | + | 10.9785i | −0.429950 | + | 0.429950i | ||||
\(653\) | −17.2954 | − | 17.2954i | −0.676820 | − | 0.676820i | 0.282459 | − | 0.959279i | \(-0.408850\pi\) |
−0.959279 | + | 0.282459i | \(0.908850\pi\) | |||||||
\(654\) | 13.5947 | 0.531594 | ||||||||
\(655\) | 17.2302 | − | 9.02529i | 0.673240 | − | 0.352647i | ||||
\(656\) | 2.27486 | 0.0888184 | ||||||||
\(657\) | −3.12378 | + | 3.12378i | −0.121870 | + | 0.121870i | ||||
\(658\) | 0.105426 | − | 0.105426i | 0.00410995 | − | 0.00410995i | ||||
\(659\) | −12.9859 | −0.505860 | −0.252930 | − | 0.967485i | \(-0.581394\pi\) | ||||
−0.252930 | + | 0.967485i | \(0.581394\pi\) | |||||||
\(660\) | −1.17926 | − | 0.368523i | −0.0459028 | − | 0.0143447i | ||||
\(661\) | − | 30.6022i | − | 1.19029i | −0.803620 | − | 0.595143i | \(-0.797095\pi\) | ||
0.803620 | − | 0.595143i | \(-0.202905\pi\) | |||||||
\(662\) | 12.7595 | − | 12.7595i | 0.495911 | − | 0.495911i | ||||
\(663\) | −13.7595 | + | 13.7595i | −0.534375 | + | 0.534375i | ||||
\(664\) | −0.270072 | −0.0104808 | ||||||||
\(665\) | −0.408457 | − | 0.127644i | −0.0158393 | − | 0.00494982i | ||||
\(666\) | 11.0244i | 0.427188i | ||||||||
\(667\) | 0.643794 | + | 41.6360i | 0.0249278 | + | 1.61215i | ||||
\(668\) | −0.393053 | − | 0.393053i | −0.0152077 | − | 0.0152077i | ||||
\(669\) | − | 15.0266i | − | 0.580963i | ||||||
\(670\) | −15.0845 | + | 7.90134i | −0.582764 | + | 0.305255i | ||||
\(671\) | −5.03956 | −0.194550 | ||||||||
\(672\) | −0.124800 | − | 0.124800i | −0.00481428 | − | 0.00481428i | ||||
\(673\) | 6.26582 | + | 6.26582i | 0.241530 | + | 0.241530i | 0.817483 | − | 0.575953i | \(-0.195369\pi\) |
−0.575953 | + | 0.817483i | \(0.695369\pi\) | |||||||
\(674\) | −16.0973 | −0.620045 | ||||||||
\(675\) | −0.893297 | − | 4.91955i | −0.0343830 | − | 0.189354i | ||||
\(676\) | 1.44991 | 0.0557657 | ||||||||
\(677\) | 31.0473 | + | 31.0473i | 1.19325 | + | 1.19325i | 0.976150 | + | 0.217096i | \(0.0696583\pi\) |
0.217096 | + | 0.976150i | \(0.430342\pi\) | |||||||
\(678\) | 9.30335 | − | 9.30335i | 0.357293 | − | 0.357293i | ||||
\(679\) | − | 0.406806i | − | 0.0156118i | ||||||
\(680\) | 5.31121 | + | 10.1396i | 0.203675 | + | 0.388837i | ||||
\(681\) | 6.59205i | 0.252608i | ||||||||
\(682\) | 0.959580 | + | 0.959580i | 0.0367442 | + | 0.0367442i | ||||
\(683\) | 36.0336 | + | 36.0336i | 1.37879 | + | 1.37879i | 0.846669 | + | 0.532120i | \(0.178605\pi\) |
0.532120 | + | 0.846669i | \(0.321395\pi\) | |||||||
\(684\) | 1.08434 | 0.0414606 | ||||||||
\(685\) | 20.9203 | + | 6.53763i | 0.799322 | + | 0.249790i | ||||
\(686\) | 2.46543i | 0.0941304i | ||||||||
\(687\) | 4.69415 | + | 4.69415i | 0.179093 | + | 0.179093i | ||||
\(688\) | −1.06804 | + | 1.06804i | −0.0407185 | + | 0.0407185i | ||||
\(689\) | −32.0022 | −1.21919 | ||||||||
\(690\) | 9.42143 | − | 5.12217i | 0.358668 | − | 0.194998i | ||||
\(691\) | 13.8803 | 0.528031 | 0.264016 | − | 0.964518i | \(-0.414953\pi\) | ||||
0.264016 | + | 0.964518i | \(0.414953\pi\) | |||||||
\(692\) | −6.09087 | + | 6.09087i | −0.231540 | + | 0.231540i | ||||
\(693\) | 0.0689566 | + | 0.0689566i | 0.00261944 | + | 0.00261944i | ||||
\(694\) | 1.10865i | 0.0420836i | ||||||||
\(695\) | 2.15296 | + | 4.11022i | 0.0816664 | + | 0.155910i | ||||
\(696\) | −8.68275 | −0.329119 | ||||||||
\(697\) | 8.23428 | + | 8.23428i | 0.311896 | + | 0.311896i | ||||
\(698\) | 1.97915 | + | 1.97915i | 0.0749120 | + | 0.0749120i | ||||
\(699\) | 4.98618i | 0.188595i | ||||||||
\(700\) | −0.157662 | − | 0.868275i | −0.00595907 | − | 0.0328177i | ||||
\(701\) | 18.1607i | 0.685920i | 0.939350 | + | 0.342960i | \(0.111430\pi\) | ||||
−0.939350 | + | 0.342960i | \(0.888570\pi\) | |||||||
\(702\) | −2.68793 | + | 2.68793i | −0.101449 | + | 0.101449i | ||||
\(703\) | −8.45289 | − | 8.45289i | −0.318807 | − | 0.318807i | ||||
\(704\) | 0.552534 | 0.0208244 | ||||||||
\(705\) | −1.67328 | + | 0.876477i | −0.0630195 | + | 0.0330100i | ||||
\(706\) | 11.7171 | 0.440978 | ||||||||
\(707\) | −0.740197 | − | 0.740197i | −0.0278380 | − | 0.0278380i | ||||
\(708\) | 7.36028 | + | 7.36028i | 0.276616 | + | 0.276616i | ||||
\(709\) | −7.89324 | −0.296437 | −0.148218 | − | 0.988955i | \(-0.547354\pi\) | ||||
−0.148218 | + | 0.988955i | \(0.547354\pi\) | |||||||
\(710\) | 5.44749 | − | 17.4318i | 0.204441 | − | 0.654205i | ||||
\(711\) | − | 6.76975i | − | 0.253885i | ||||||
\(712\) | 6.19562 | + | 6.19562i | 0.232191 | + | 0.232191i | ||||
\(713\) | −11.7774 | + | 0.182107i | −0.441066 | + | 0.00681995i | ||||
\(714\) | − | 0.903477i | − | 0.0338118i | ||||||
\(715\) | −1.40087 | + | 4.48274i | −0.0523895 | + | 0.167645i | ||||
\(716\) | 23.2150 | 0.867584 | ||||||||
\(717\) | 13.6932 | − | 13.6932i | 0.511380 | − | 0.511380i | ||||
\(718\) | −13.1144 | + | 13.1144i | −0.489424 | + | 0.489424i | ||||
\(719\) | 21.8935i | 0.816490i | 0.912872 | + | 0.408245i | \(0.133859\pi\) | ||||
−0.912872 | + | 0.408245i | \(0.866141\pi\) | |||||||
\(720\) | 1.03755 | + | 1.98078i | 0.0386671 | + | 0.0738194i | ||||
\(721\) | −0.943153 | −0.0351249 | ||||||||
\(722\) | 12.6036 | − | 12.6036i | 0.469058 | − | 0.469058i | ||||
\(723\) | −14.1879 | + | 14.1879i | −0.527655 | + | 0.527655i | ||||
\(724\) | 6.45396 | 0.239860 | ||||||||
\(725\) | −35.6888 | − | 24.7197i | −1.32545 | − | 0.918068i | ||||
\(726\) | 10.6947 | 0.396918 | ||||||||
\(727\) | 2.54984 | + | 2.54984i | 0.0945684 | + | 0.0945684i | 0.752808 | − | 0.658240i | \(-0.228699\pi\) |
−0.658240 | + | 0.752808i | \(0.728699\pi\) | |||||||
\(728\) | −0.474405 | + | 0.474405i | −0.0175826 | + | 0.0175826i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 8.75048 | − | 4.58356i | 0.323870 | − | 0.169645i | ||||
\(731\) | −7.73190 | −0.285975 | ||||||||
\(732\) | 6.44939 | + | 6.44939i | 0.238376 | + | 0.238376i | ||||
\(733\) | −22.3443 | + | 22.3443i | −0.825304 | + | 0.825304i | −0.986863 | − | 0.161559i | \(-0.948348\pi\) |
0.161559 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(734\) | 20.7795 | 0.766985 | ||||||||
\(735\) | 4.64800 | − | 14.8735i | 0.171444 | − | 0.548617i | ||||
\(736\) | −3.33833 | + | 3.44319i | −0.123052 | + | 0.126918i | ||||
\(737\) | −2.97535 | + | 2.97535i | −0.109598 | + | 0.109598i | ||||
\(738\) | 1.60857 | + | 1.60857i | 0.0592123 | + | 0.0592123i | ||||
\(739\) | 11.6646i | 0.429089i | 0.976714 | + | 0.214545i | \(0.0688267\pi\) | ||||
−0.976714 | + | 0.214545i | \(0.931173\pi\) | |||||||
\(740\) | 7.35295 | − | 23.5292i | 0.270300 | − | 0.864952i | ||||
\(741\) | − | 4.12189i | − | 0.151421i | ||||||
\(742\) | 1.05066 | − | 1.05066i | 0.0385711 | − | 0.0385711i | ||||
\(743\) | 1.05995 | − | 1.05995i | 0.0388859 | − | 0.0388859i | −0.687396 | − | 0.726282i | \(-0.741246\pi\) |
0.726282 | + | 0.687396i | \(0.241246\pi\) | |||||||
\(744\) | − | 2.45605i | − | 0.0900430i | ||||||
\(745\) | 24.3916 | − | 12.7765i | 0.893639 | − | 0.468094i | ||||
\(746\) | − | 4.45023i | − | 0.162935i | ||||||
\(747\) | −0.190970 | − | 0.190970i | −0.00698722 | − | 0.00698722i | ||||
\(748\) | 2.00000 | + | 2.00000i | 0.0731272 | + | 0.0731272i | ||||
\(749\) | 2.26967i | 0.0829321i | ||||||||
\(750\) | −1.37464 | + | 11.0955i | −0.0501947 | + | 0.405151i | ||||
\(751\) | 20.0466i | 0.731510i | 0.930711 | + | 0.365755i | \(0.119189\pi\) | ||||
−0.930711 | + | 0.365755i | \(0.880811\pi\) | |||||||
\(752\) | 0.597335 | − | 0.597335i | 0.0217826 | − | 0.0217826i | ||||
\(753\) | −20.6653 | + | 20.6653i | −0.753087 | + | 0.753087i | ||||
\(754\) | 33.0058i | 1.20200i | ||||||||
\(755\) | 19.9069 | − | 10.4274i | 0.724487 | − | 0.379491i | ||||
\(756\) | − | 0.176495i | − | 0.00641904i | ||||||
\(757\) | −35.9979 | − | 35.9979i | −1.30837 | − | 1.30837i | −0.922595 | − | 0.385770i | \(-0.873936\pi\) |
−0.385770 | − | 0.922595i | \(-0.626064\pi\) | |||||||
\(758\) | 11.7107 | − | 11.7107i | 0.425353 | − | 0.425353i | ||||
\(759\) | 1.84454 | − | 1.90248i | 0.0669527 | − | 0.0690557i | ||||
\(760\) | −2.31428 | − | 0.723217i | −0.0839476 | − | 0.0262338i | ||||
\(761\) | −13.7196 | −0.497334 | −0.248667 | − | 0.968589i | \(-0.579992\pi\) | ||||
−0.248667 | + | 0.968589i | \(0.579992\pi\) | |||||||
\(762\) | −14.8431 | + | 14.8431i | −0.537707 | + | 0.537707i | ||||
\(763\) | 1.69662 | + | 1.69662i | 0.0614218 | + | 0.0614218i | ||||
\(764\) | 22.6724 | 0.820260 | ||||||||
\(765\) | −3.41421 | + | 10.9254i | −0.123441 | + | 0.395008i | ||||
\(766\) | 15.8681i | 0.573338i | ||||||||
\(767\) | 27.9787 | − | 27.9787i | 1.01025 | − | 1.01025i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 2.88500 | 0.104036 | 0.0520179 | − | 0.998646i | \(-0.483435\pi\) | ||||
0.0520179 | + | 0.998646i | \(0.483435\pi\) | |||||||
\(770\) | −0.101181 | − | 0.193165i | −0.00364630 | − | 0.00696117i | ||||
\(771\) | −3.50437 | −0.126207 | ||||||||
\(772\) | 7.13533 | − | 7.13533i | 0.256806 | − | 0.256806i | ||||
\(773\) | 26.4041 | − | 26.4041i | 0.949689 | − | 0.949689i | −0.0491046 | − | 0.998794i | \(-0.515637\pi\) |
0.998794 | + | 0.0491046i | \(0.0156368\pi\) | |||||||
\(774\) | −1.51043 | −0.0542913 | ||||||||
\(775\) | 6.99235 | − | 10.0951i | 0.251173 | − | 0.362627i | ||||
\(776\) | − | 2.30492i | − | 0.0827418i | ||||||
\(777\) | −1.37586 | + | 1.37586i | −0.0493585 | + | 0.0493585i | ||||
\(778\) | 18.8504 | − | 18.8504i | 0.675818 | − | 0.675818i | ||||
\(779\) | −2.46671 | −0.0883791 | ||||||||
\(780\) | 7.52955 | − | 3.94403i | 0.269601 | − | 0.141219i | ||||
\(781\) | − | 4.51285i | − | 0.161483i | ||||||
\(782\) | −24.5470 | + | 0.379555i | −0.877797 | + | 0.0135729i | ||||
\(783\) | −6.13963 | − | 6.13963i | −0.219413 | − | 0.219413i | ||||
\(784\) | 6.96885i | 0.248887i | ||||||||
\(785\) | 10.2858 | + | 3.21435i | 0.367117 | + | 0.114725i | ||||
\(786\) | −8.69869 | −0.310272 | ||||||||
\(787\) | −36.1586 | − | 36.1586i | −1.28891 | − | 1.28891i | −0.935447 | − | 0.353466i | \(-0.885003\pi\) |
−0.353466 | − | 0.935447i | \(-0.614997\pi\) | |||||||
\(788\) | −2.41931 | − | 2.41931i | −0.0861844 | − | 0.0861844i | ||||
\(789\) | −9.46631 | −0.337010 | ||||||||
\(790\) | −4.51521 | + | 14.4485i | −0.160644 | + | 0.514056i | ||||
\(791\) | 2.32213 | 0.0825653 | ||||||||
\(792\) | 0.390701 | + | 0.390701i | 0.0138830 | + | 0.0138830i | ||||
\(793\) | 24.5161 | − | 24.5161i | 0.870592 | − | 0.870592i | ||||
\(794\) | 1.46779i | 0.0520899i | ||||||||
\(795\) | −16.6757 | + | 8.73484i | −0.591426 | + | 0.309793i | ||||
\(796\) | − | 22.7308i | − | 0.805672i | ||||||
\(797\) | 19.2279 | + | 19.2279i | 0.681088 | + | 0.681088i | 0.960245 | − | 0.279157i | \(-0.0900551\pi\) |
−0.279157 | + | 0.960245i | \(0.590055\pi\) | |||||||
\(798\) | 0.135326 | + | 0.135326i | 0.00479047 | + | 0.00479047i | ||||
\(799\) | 4.32433 | 0.152984 | ||||||||
\(800\) | −0.893297 | − | 4.91955i | −0.0315828 | − | 0.173933i | ||||
\(801\) | 8.76193i | 0.309587i | ||||||||
\(802\) | −17.0648 | − | 17.0648i | −0.602578 | − | 0.602578i | ||||
\(803\) | 1.72599 | − | 1.72599i | 0.0609090 | − | 0.0609090i | ||||
\(804\) | 7.61541 | 0.268575 | ||||||||
\(805\) | 1.81505 | + | 0.536550i | 0.0639721 | + | 0.0189109i | ||||
\(806\) | −9.33618 | −0.328853 | ||||||||
\(807\) | −5.80684 | + | 5.80684i | −0.204410 | + | 0.204410i | ||||
\(808\) | −4.19388 | − | 4.19388i | −0.147540 | − | 0.147540i | ||||
\(809\) | 5.62570i | 0.197789i | 0.995098 | + | 0.0988946i | \(0.0315307\pi\) | ||||
−0.995098 | + | 0.0988946i | \(0.968469\pi\) | |||||||
\(810\) | −0.666968 | + | 2.13428i | −0.0234349 | + | 0.0749910i | ||||
\(811\) | 47.8518 | 1.68030 | 0.840151 | − | 0.542352i | \(-0.182466\pi\) | ||||
0.840151 | + | 0.542352i | \(0.182466\pi\) | |||||||
\(812\) | −1.08361 | − | 1.08361i | −0.0380273 | − | 0.0380273i | ||||
\(813\) | −6.08270 | − | 6.08270i | −0.213330 | − | 0.213330i | ||||
\(814\) | − | 6.09138i | − | 0.213503i | ||||||
\(815\) | 33.1366 | + | 10.3553i | 1.16072 | + | 0.362729i | ||||
\(816\) | − | 5.11901i | − | 0.179201i | ||||||
\(817\) | 1.15811 | − | 1.15811i | 0.0405171 | − | 0.0405171i | ||||
\(818\) | −12.2055 | − | 12.2055i | −0.426756 | − | 0.426756i | ||||
\(819\) | −0.670909 | −0.0234435 | ||||||||
\(820\) | −2.36027 | − | 4.50600i | −0.0824244 | − | 0.157356i | ||||
\(821\) | −11.4696 | −0.400291 | −0.200145 | − | 0.979766i | \(-0.564141\pi\) | ||||
−0.200145 | + | 0.979766i | \(0.564141\pi\) | |||||||
\(822\) | −6.93107 | − | 6.93107i | −0.241749 | − | 0.241749i | ||||
\(823\) | −8.97892 | − | 8.97892i | −0.312985 | − | 0.312985i | 0.533080 | − | 0.846065i | \(-0.321035\pi\) |
−0.846065 | + | 0.533080i | \(0.821035\pi\) | |||||||
\(824\) | −5.34381 | −0.186160 | ||||||||
\(825\) | 0.493577 | + | 2.71822i | 0.0171842 | + | 0.0946364i | ||||
\(826\) | 1.83713i | 0.0639220i | ||||||||
\(827\) | −20.4092 | − | 20.4092i | −0.709697 | − | 0.709697i | 0.256775 | − | 0.966471i | \(-0.417340\pi\) |
−0.966471 | + | 0.256775i | \(0.917340\pi\) | |||||||
\(828\) | −4.79526 | + | 0.0741463i | −0.166647 | + | 0.00257676i | ||||
\(829\) | − | 29.9611i | − | 1.04059i | −0.853985 | − | 0.520297i | \(-0.825821\pi\) | ||
0.853985 | − | 0.520297i | \(-0.174179\pi\) | |||||||
\(830\) | 0.280212 | + | 0.534954i | 0.00972631 | + | 0.0185685i | ||||
\(831\) | 13.1316 | 0.455530 | ||||||||
\(832\) | −2.68793 | + | 2.68793i | −0.0931871 | + | 0.0931871i | ||||
\(833\) | −25.2250 | + | 25.2250i | −0.873996 | + | 0.873996i | ||||
\(834\) | − | 2.07505i | − | 0.0718531i | ||||||
\(835\) | −0.370741 | + | 1.18636i | −0.0128300 | + | 0.0410558i | ||||
\(836\) | −0.599133 | −0.0207214 | ||||||||
\(837\) | 1.73669 | − | 1.73669i | 0.0600287 | − | 0.0600287i | ||||
\(838\) | 6.24608 | − | 6.24608i | 0.215767 | − | 0.215767i | ||||
\(839\) | −12.7197 | −0.439133 | −0.219566 | − | 0.975598i | \(-0.570464\pi\) | ||||
−0.219566 | + | 0.975598i | \(0.570464\pi\) | |||||||
\(840\) | −0.117716 | + | 0.376689i | −0.00406160 | + | 0.0129970i | ||||
\(841\) | −46.3902 | −1.59966 | ||||||||
\(842\) | −16.2038 | − | 16.2038i | −0.558421 | − | 0.558421i | ||||
\(843\) | −10.7689 | + | 10.7689i | −0.370902 | + | 0.370902i | ||||
\(844\) | 22.6042i | 0.778067i | ||||||||
\(845\) | −1.50435 | − | 2.87195i | −0.0517511 | − | 0.0987982i | ||||
\(846\) | 0.844759 | 0.0290434 | ||||||||
\(847\) | 1.33470 | + | 1.33470i | 0.0458610 | + | 0.0458610i | ||||
\(848\) | 5.95295 | − | 5.95295i | 0.204425 | − | 0.204425i | ||||
\(849\) | 16.5005 | 0.566294 | ||||||||
\(850\) | 14.5738 | − | 21.0407i | 0.499877 | − | 0.721690i | ||||
\(851\) | 37.9592 | + | 36.8032i | 1.30123 | + | 1.26160i | ||||
\(852\) | −5.77533 | + | 5.77533i | −0.197859 | + | 0.197859i | ||||
\(853\) | 4.45279 | + | 4.45279i | 0.152461 | + | 0.152461i | 0.779216 | − | 0.626755i | \(-0.215617\pi\) |
−0.626755 | + | 0.779216i | \(0.715617\pi\) | |||||||
\(854\) | 1.60977i | 0.0550853i | ||||||||
\(855\) | −1.12505 | − | 2.14783i | −0.0384758 | − | 0.0734543i | ||||
\(856\) | 12.8597i | 0.439537i | ||||||||
\(857\) | 31.4578 | − | 31.4578i | 1.07458 | − | 1.07458i | 0.0775921 | − | 0.996985i | \(-0.475277\pi\) |
0.996985 | − | 0.0775921i | \(-0.0247232\pi\) | |||||||
\(858\) | 1.48517 | − | 1.48517i | 0.0507030 | − | 0.0507030i | ||||
\(859\) | − | 37.1082i | − | 1.26611i | −0.774105 | − | 0.633057i | \(-0.781800\pi\) | ||
0.774105 | − | 0.633057i | \(-0.218200\pi\) | |||||||
\(860\) | 3.22368 | + | 1.00741i | 0.109927 | + | 0.0343524i | ||||
\(861\) | 0.401501i | 0.0136831i | ||||||||
\(862\) | 2.91241 | + | 2.91241i | 0.0991970 | + | 0.0991970i | ||||
\(863\) | 6.80762 | + | 6.80762i | 0.231734 | + | 0.231734i | 0.813416 | − | 0.581682i | \(-0.197605\pi\) |
−0.581682 | + | 0.813416i | \(0.697605\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 18.3843 | + | 5.74513i | 0.625084 | + | 0.195340i | ||||
\(866\) | − | 18.6686i | − | 0.634383i | ||||||
\(867\) | 6.50837 | − | 6.50837i | 0.221036 | − | 0.221036i | ||||
\(868\) | 0.306516 | − | 0.306516i | 0.0104038 | − | 0.0104038i | ||||
\(869\) | 3.74052i | 0.126888i | ||||||||
\(870\) | 9.00876 | + | 17.1986i | 0.305426 | + | 0.583089i | ||||
\(871\) | − | 28.9485i | − | 0.980882i | ||||||
\(872\) | 9.61288 | + | 9.61288i | 0.325533 | + | 0.325533i | ||||
\(873\) | 1.62982 | − | 1.62982i | 0.0551612 | − | 0.0551612i | ||||
\(874\) | 3.61987 | − | 3.73357i | 0.122444 | − | 0.126290i | ||||
\(875\) | −1.55628 | + | 1.21317i | −0.0526119 | + | 0.0410126i | ||||
\(876\) | −4.41769 | −0.149260 | ||||||||
\(877\) | −2.87923 | + | 2.87923i | −0.0972247 | + | 0.0972247i | −0.754046 | − | 0.656821i | \(-0.771901\pi\) |
0.656821 | + | 0.754046i | \(0.271901\pi\) | |||||||
\(878\) | −9.43609 | − | 9.43609i | −0.318452 | − | 0.318452i | ||||
\(879\) | −30.9101 | −1.04257 | ||||||||
\(880\) | −0.573280 | − | 1.09445i | −0.0193253 | − | 0.0368939i | ||||
\(881\) | 34.1144i | 1.14934i | 0.818384 | + | 0.574672i | \(0.194870\pi\) | ||||
−0.818384 | + | 0.574672i | \(0.805130\pi\) | |||||||
\(882\) | −4.92772 | + | 4.92772i | −0.165925 | + | 0.165925i | ||||
\(883\) | 9.96963 | + | 9.96963i | 0.335505 | + | 0.335505i | 0.854672 | − | 0.519168i | \(-0.173758\pi\) |
−0.519168 | + | 0.854672i | \(0.673758\pi\) | |||||||
\(884\) | −19.4589 | −0.654473 | ||||||||
\(885\) | 6.94248 | − | 22.2157i | 0.233369 | − | 0.746774i | ||||
\(886\) | 24.2577 | 0.814955 | ||||||||
\(887\) | −0.170309 | + | 0.170309i | −0.00571841 | + | 0.00571841i | −0.709960 | − | 0.704242i | \(-0.751287\pi\) |
0.704242 | + | 0.709960i | \(0.251287\pi\) | |||||||
\(888\) | −7.79545 | + | 7.79545i | −0.261598 | + | 0.261598i | ||||
\(889\) | −3.70484 | −0.124256 | ||||||||
\(890\) | 5.84393 | − | 18.7004i | 0.195889 | − | 0.626839i | ||||
\(891\) | 0.552534i | 0.0185106i | ||||||||
\(892\) | 10.6254 | − | 10.6254i | 0.355765 | − | 0.355765i | ||||
\(893\) | −0.647711 | + | 0.647711i | −0.0216748 | + | 0.0216748i | ||||
\(894\) | −12.3141 | −0.411846 | ||||||||
\(895\) | −24.0866 | − | 45.9838i | −0.805126 | − | 1.53707i | ||||
\(896\) | − | 0.176495i | − | 0.00589627i | ||||||
\(897\) | 0.281853 | + | 18.2282i | 0.00941079 | + | 0.608623i | ||||
\(898\) | −5.19834 | − | 5.19834i | −0.173471 | − | 0.173471i | ||||
\(899\) | − | 21.3252i | − | 0.711237i | ||||||
\(900\) | 2.84699 | − | 4.11031i | 0.0948998 | − | 0.137010i | ||||
\(901\) | 43.0956 | 1.43572 | ||||||||
\(902\) | −0.888790 | − | 0.888790i | −0.0295935 | − | 0.0295935i | ||||
\(903\) | −0.188502 | − | 0.188502i | −0.00627297 | − | 0.00627297i | ||||
\(904\) | 13.1569 | 0.437593 | ||||||||
\(905\) | −6.69629 | − | 12.7839i | −0.222592 | − | 0.424951i | ||||
\(906\) | −10.0500 | −0.333890 | ||||||||
\(907\) | −11.8107 | − | 11.8107i | −0.392168 | − | 0.392168i | 0.483292 | − | 0.875459i | \(-0.339441\pi\) |
−0.875459 | + | 0.483292i | \(0.839441\pi\) | |||||||
\(908\) | −4.66128 | + | 4.66128i | −0.154690 | + | 0.154690i | ||||
\(909\) | − | 5.93104i | − | 0.196720i | ||||||
\(910\) | 1.43191 | + | 0.447475i | 0.0474673 | + | 0.0148337i | ||||
\(911\) | − | 35.6840i | − | 1.18226i | −0.806575 | − | 0.591132i | \(-0.798681\pi\) | ||
0.806575 | − | 0.591132i | \(-0.201319\pi\) | |||||||
\(912\) | 0.766741 | + | 0.766741i | 0.0253893 | + | 0.0253893i | ||||
\(913\) | 0.105517 | + | 0.105517i | 0.00349211 | + | 0.00349211i | ||||
\(914\) | −2.28675 | −0.0756388 | ||||||||
\(915\) | 6.08329 | − | 19.4664i | 0.201107 | − | 0.643539i | ||||
\(916\) | 6.63852i | 0.219343i | ||||||||
\(917\) | −1.08560 | − | 1.08560i | −0.0358497 | − | 0.0358497i | ||||
\(918\) | 3.61968 | − | 3.61968i | 0.119467 | − | 0.119467i | ||||
\(919\) | 33.7384 | 1.11293 | 0.556463 | − | 0.830872i | \(-0.312158\pi\) | ||||
0.556463 | + | 0.830872i | \(0.312158\pi\) | |||||||
\(920\) | 10.2839 | + | 3.04004i | 0.339049 | + | 0.100227i | ||||
\(921\) | 8.95694 | 0.295141 | ||||||||
\(922\) | 13.7336 | − | 13.7336i | 0.452293 | − | 0.452293i | ||||
\(923\) | 21.9538 | + | 21.9538i | 0.722617 | + | 0.722617i | ||||
\(924\) | 0.0975193i | 0.00320815i | ||||||||
\(925\) | −54.2353 | + | 9.84810i | −1.78325 | + | 0.323803i | ||||
\(926\) | 23.5785 | 0.774836 | ||||||||
\(927\) | −3.77864 | − | 3.77864i | −0.124107 | − | 0.124107i | ||||
\(928\) | −6.13963 | − | 6.13963i | −0.201543 | − | 0.201543i | ||||
\(929\) | − | 21.5707i | − | 0.707711i | −0.935300 | − | 0.353856i | \(-0.884870\pi\) | ||
0.935300 | − | 0.353856i | \(-0.115130\pi\) | |||||||
\(930\) | −4.86489 | + | 2.54826i | −0.159526 | + | 0.0835608i | ||||
\(931\) | − | 7.55657i | − | 0.247657i | ||||||
\(932\) | −3.52576 | + | 3.52576i | −0.115490 | + | 0.115490i | ||||
\(933\) | −15.3982 | − | 15.3982i | −0.504113 | − | 0.504113i | ||||
\(934\) | −26.5062 | −0.867310 | ||||||||
\(935\) | 1.88647 | − | 6.03666i | 0.0616942 | − | 0.197420i | ||||
\(936\) | −3.80130 | −0.124249 | ||||||||
\(937\) | −2.45269 | − | 2.45269i | −0.0801260 | − | 0.0801260i | 0.665908 | − | 0.746034i | \(-0.268044\pi\) |
−0.746034 | + | 0.665908i | \(0.768044\pi\) | |||||||
\(938\) | 0.950406 | + | 0.950406i | 0.0310319 | + | 0.0310319i | ||||
\(939\) | −30.1164 | −0.982811 | ||||||||
\(940\) | −1.80295 | − | 0.563427i | −0.0588058 | − | 0.0183770i | ||||
\(941\) | 41.3511i | 1.34801i | 0.738729 | + | 0.674003i | \(0.235427\pi\) | ||||
−0.738729 | + | 0.674003i | \(0.764573\pi\) | |||||||
\(942\) | −3.40779 | − | 3.40779i | −0.111032 | − | 0.111032i | ||||
\(943\) | 10.9085 | − | 0.168673i | 0.355231 | − | 0.00549273i | ||||
\(944\) | 10.4090i | 0.338784i | ||||||||
\(945\) | −0.349597 | + | 0.183121i | −0.0113724 | + | 0.00595694i | ||||
\(946\) | 0.834565 | 0.0271341 | ||||||||
\(947\) | −10.8386 | + | 10.8386i | −0.352208 | + | 0.352208i | −0.860930 | − | 0.508723i | \(-0.830118\pi\) |
0.508723 | + | 0.860930i | \(0.330118\pi\) | |||||||
\(948\) | 4.78694 | − | 4.78694i | 0.155472 | − | 0.155472i | ||||
\(949\) | 16.7930i | 0.545123i | ||||||||
\(950\) | 0.968634 | + | 5.33445i | 0.0314266 | + | 0.173072i | ||||
\(951\) | −18.5269 | −0.600775 | ||||||||
\(952\) | 0.638854 | − | 0.638854i | 0.0207054 | − | 0.0207054i | ||||
\(953\) | 22.1223 | − | 22.1223i | 0.716612 | − | 0.716612i | −0.251298 | − | 0.967910i | \(-0.580857\pi\) |
0.967910 | + | 0.251298i | \(0.0808573\pi\) | |||||||
\(954\) | 8.41875 | 0.272567 | ||||||||
\(955\) | −23.5237 | − | 44.9092i | −0.761210 | − | 1.45323i | ||||
\(956\) | 19.3650 | 0.626310 | ||||||||
\(957\) | 3.39236 | + | 3.39236i | 0.109659 | + | 0.109659i | ||||
\(958\) | −2.84915 | + | 2.84915i | −0.0920520 | + | 0.0920520i | ||||
\(959\) | − | 1.73000i | − | 0.0558647i | ||||||
\(960\) | −0.666968 | + | 2.13428i | −0.0215263 | + | 0.0688836i | ||||
\(961\) | −24.9678 | −0.805414 | ||||||||
\(962\) | 29.6329 | + | 29.6329i | 0.955403 | + | 0.955403i | ||||
\(963\) | −9.09321 | + | 9.09321i | −0.293025 | + | 0.293025i | ||||
\(964\) | −20.0648 | −0.646242 | ||||||||
\(965\) | −21.5368 | − | 6.73029i | −0.693293 | − | 0.216656i | ||||
\(966\) | −0.607704 | − | 0.589197i | −0.0195526 | − | 0.0189571i | ||||
\(967\) | 4.75663 | − | 4.75663i | 0.152963 | − | 0.152963i | −0.626477 | − | 0.779440i | \(-0.715504\pi\) |
0.779440 | + | 0.626477i | \(0.215504\pi\) | |||||||
\(968\) | 7.56230 | + | 7.56230i | 0.243061 | + | 0.243061i | ||||
\(969\) | 5.55072i | 0.178315i | ||||||||
\(970\) | −4.56554 | + | 2.39146i | −0.146591 | + | 0.0767852i | ||||
\(971\) | 7.39491i | 0.237314i | 0.992935 | + | 0.118657i | \(0.0378589\pi\) | ||||
−0.992935 | + | 0.118657i | \(0.962141\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 0.258967 | − | 0.258967i | 0.00830211 | − | 0.00830211i | ||||
\(974\) | − | 21.7959i | − | 0.698385i | ||||||
\(975\) | −15.6245 | − | 10.8223i | −0.500385 | − | 0.346591i | ||||
\(976\) | 9.12081i | 0.291950i | ||||||||
\(977\) | 1.90875 | + | 1.90875i | 0.0610662 | + | 0.0610662i | 0.736980 | − | 0.675914i | \(-0.236251\pi\) |
−0.675914 | + | 0.736980i | \(0.736251\pi\) | |||||||
\(978\) | −10.9785 | − | 10.9785i | −0.351053 | − | 0.351053i | ||||
\(979\) | − | 4.84127i | − | 0.154728i | ||||||
\(980\) | 13.8038 | − | 7.23051i | 0.440945 | − | 0.230970i | ||||
\(981\) | 13.5947i | 0.434044i | ||||||||
\(982\) | −1.72590 | + | 1.72590i | −0.0550755 | + | 0.0550755i | ||||
\(983\) | 2.58513 | − | 2.58513i | 0.0824528 | − | 0.0824528i | −0.664678 | − | 0.747130i | \(-0.731431\pi\) |
0.747130 | + | 0.664678i | \(0.231431\pi\) | |||||||
\(984\) | 2.27486i | 0.0725199i | ||||||||
\(985\) | −2.28198 | + | 7.30227i | −0.0727099 | + | 0.232670i | ||||
\(986\) | − | 44.4471i | − | 1.41548i | ||||||
\(987\) | 0.105426 | + | 0.105426i | 0.00335576 | + | 0.00335576i | ||||
\(988\) | 2.91461 | − | 2.91461i | 0.0927262 | − | 0.0927262i | ||||
\(989\) | −5.04232 | + | 5.20070i | −0.160336 | + | 0.165373i | ||||
\(990\) | 0.368523 | − | 1.17926i | 0.0117124 | − | 0.0374795i | ||||
\(991\) | 48.3443 | 1.53571 | 0.767853 | − | 0.640626i | \(-0.221325\pi\) | ||||
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(992\) | 1.73669 | − | 1.73669i | 0.0551399 | − | 0.0551399i | ||||
\(993\) | 12.7595 | + | 12.7595i | 0.404910 | + | 0.404910i | ||||
\(994\) | −1.44153 | −0.0457225 | ||||||||
\(995\) | −45.0248 | + | 23.5843i | −1.42738 | + | 0.747671i | ||||
\(996\) | − | 0.270072i | − | 0.00855756i | ||||||
\(997\) | 6.62156 | − | 6.62156i | 0.209707 | − | 0.209707i | −0.594436 | − | 0.804143i | \(-0.702625\pi\) |
0.804143 | + | 0.594436i | \(0.202625\pi\) | |||||||
\(998\) | 29.9630 | + | 29.9630i | 0.948463 | + | 0.948463i | ||||
\(999\) | −11.0244 | −0.348798 |
(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 | 690.2.j.b.643.1 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.b.367.6 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.643.6 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.b.367.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.1 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.b.367.6 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.b.643.1 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.643.6 | yes | 24 | 23.22 | odd | 2 | inner |