Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.8 | ||
Root | \(1.75036 + 1.75036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.493 |
Dual form | 570.2.m.a.37.8 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.253765 | + | 2.22162i | −0.113487 | + | 0.993539i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.47539 | + | 2.47539i | −0.935608 | + | 0.935608i | −0.998049 | − | 0.0624406i | \(-0.980112\pi\) |
0.0624406 | + | 0.998049i | \(0.480112\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.75036 | + | 1.39149i | −0.553513 | + | 0.440026i | ||||
\(11\) | 2.74367 | 0.827247 | 0.413624 | − | 0.910448i | \(-0.364263\pi\) | ||||
0.413624 | + | 0.910448i | \(0.364263\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −1.20178 | + | 1.20178i | −0.333314 | + | 0.333314i | −0.853844 | − | 0.520530i | \(-0.825735\pi\) |
0.520530 | + | 0.853844i | \(0.325735\pi\) | |||||||
\(14\) | −3.50073 | −0.935608 | ||||||||
\(15\) | 1.39149 | + | 1.75036i | 0.359280 | + | 0.451942i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.87121 | + | 4.87121i | −1.18144 | + | 1.18144i | −0.202070 | + | 0.979371i | \(0.564767\pi\) |
−0.979371 | + | 0.202070i | \(0.935233\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 1.94007 | − | 3.90335i | 0.445082 | − | 0.895490i | ||||
\(20\) | −2.22162 | − | 0.253765i | −0.496770 | − | 0.0567435i | ||||
\(21\) | 3.50073i | 0.763921i | ||||||||
\(22\) | 1.94007 | + | 1.94007i | 0.413624 | + | 0.413624i | ||||
\(23\) | 0.0321428 | + | 0.0321428i | 0.00670223 | + | 0.00670223i | 0.710450 | − | 0.703748i | \(-0.248491\pi\) |
−0.703748 | + | 0.710450i | \(0.748491\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −4.87121 | − | 1.12754i | −0.974241 | − | 0.225508i | ||||
\(26\) | −1.69957 | −0.333314 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −2.47539 | − | 2.47539i | −0.467804 | − | 0.467804i | ||||
\(29\) | 6.50952 | 1.20879 | 0.604394 | − | 0.796686i | \(-0.293415\pi\) | ||||
0.604394 | + | 0.796686i | \(0.293415\pi\) | |||||||
\(30\) | −0.253765 | + | 2.22162i | −0.0463309 | + | 0.405611i | ||||
\(31\) | 6.50952i | 1.16914i | 0.811342 | + | 0.584572i | \(0.198738\pi\) | ||||
−0.811342 | + | 0.584572i | \(0.801262\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 1.94007 | − | 1.94007i | 0.337722 | − | 0.337722i | ||||
\(34\) | −6.88893 | −1.18144 | ||||||||
\(35\) | −4.87121 | − | 6.12754i | −0.823384 | − | 1.03574i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.58998 | + | 4.58998i | 0.754589 | + | 0.754589i | 0.975332 | − | 0.220743i | \(-0.0708483\pi\) |
−0.220743 | + | 0.975332i | \(0.570848\pi\) | |||||||
\(38\) | 4.13192 | − | 1.38825i | 0.670286 | − | 0.225204i | ||||
\(39\) | 1.69957i | 0.272150i | ||||||||
\(40\) | −1.39149 | − | 1.75036i | −0.220013 | − | 0.276757i | ||||
\(41\) | − | 5.96665i | − | 0.931833i | −0.884829 | − | 0.465917i | \(-0.845725\pi\) | ||
0.884829 | − | 0.465917i | \(-0.154275\pi\) | |||||||
\(42\) | −2.47539 | + | 2.47539i | −0.381960 | + | 0.381960i | ||||
\(43\) | 5.39582 | + | 5.39582i | 0.822855 | + | 0.822855i | 0.986517 | − | 0.163662i | \(-0.0523305\pi\) |
−0.163662 | + | 0.986517i | \(0.552331\pi\) | |||||||
\(44\) | 2.74367i | 0.413624i | ||||||||
\(45\) | 2.22162 | + | 0.253765i | 0.331180 | + | 0.0378290i | ||||
\(46\) | 0.0454567i | 0.00670223i | ||||||||
\(47\) | 3.66743 | − | 3.66743i | 0.534950 | − | 0.534950i | −0.387091 | − | 0.922041i | \(-0.626520\pi\) |
0.922041 | + | 0.387091i | \(0.126520\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 5.25508i | − | 0.750725i | ||||||
\(50\) | −2.64717 | − | 4.24175i | −0.374367 | − | 0.599875i | ||||
\(51\) | 6.88893i | 0.964643i | ||||||||
\(52\) | −1.20178 | − | 1.20178i | −0.166657 | − | 0.166657i | ||||
\(53\) | 8.97544 | − | 8.97544i | 1.23287 | − | 1.23287i | 0.270015 | − | 0.962856i | \(-0.412971\pi\) |
0.962856 | − | 0.270015i | \(-0.0870288\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | −0.696246 | + | 6.09540i | −0.0938818 | + | 0.821903i | ||||
\(56\) | − | 3.50073i | − | 0.467804i | ||||||
\(57\) | −1.38825 | − | 4.13192i | −0.183878 | − | 0.547286i | ||||
\(58\) | 4.60292 | + | 4.60292i | 0.604394 | + | 0.604394i | ||||
\(59\) | 4.42301 | 0.575826 | 0.287913 | − | 0.957657i | \(-0.407039\pi\) | ||||
0.287913 | + | 0.957657i | \(0.407039\pi\) | |||||||
\(60\) | −1.75036 | + | 1.39149i | −0.225971 | + | 0.179640i | ||||
\(61\) | −2.95077 | −0.377808 | −0.188904 | − | 0.981996i | \(-0.560493\pi\) | ||||
−0.188904 | + | 0.981996i | \(0.560493\pi\) | |||||||
\(62\) | −4.60292 | + | 4.60292i | −0.584572 | + | 0.584572i | ||||
\(63\) | 2.47539 | + | 2.47539i | 0.311869 | + | 0.311869i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.36493 | − | 2.97487i | −0.293334 | − | 0.368987i | ||||
\(66\) | 2.74367 | 0.337722 | ||||||||
\(67\) | 7.00145 | + | 7.00145i | 0.855363 | + | 0.855363i | 0.990788 | − | 0.135424i | \(-0.0432398\pi\) |
−0.135424 | + | 0.990788i | \(0.543240\pi\) | |||||||
\(68\) | −4.87121 | − | 4.87121i | −0.590721 | − | 0.590721i | ||||
\(69\) | 0.0454567 | 0.00547235 | ||||||||
\(70\) | 0.888360 | − | 7.77729i | 0.106179 | − | 0.929564i | ||||
\(71\) | − | 5.56594i | − | 0.660556i | −0.943884 | − | 0.330278i | \(-0.892858\pi\) | ||
0.943884 | − | 0.330278i | \(-0.107142\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −2.19205 | − | 2.19205i | −0.256560 | − | 0.256560i | 0.567094 | − | 0.823653i | \(-0.308068\pi\) |
−0.823653 | + | 0.567094i | \(0.808068\pi\) | |||||||
\(74\) | 6.49122i | 0.754589i | ||||||||
\(75\) | −4.24175 | + | 2.64717i | −0.489795 | + | 0.305669i | ||||
\(76\) | 3.90335 | + | 1.94007i | 0.447745 | + | 0.222541i | ||||
\(77\) | −6.79164 | + | 6.79164i | −0.773979 | + | 0.773979i | ||||
\(78\) | −1.20178 | + | 1.20178i | −0.136075 | + | 0.136075i | ||||
\(79\) | −0.225823 | −0.0254070 | −0.0127035 | − | 0.999919i | \(-0.504044\pi\) | ||||
−0.0127035 | + | 0.999919i | \(0.504044\pi\) | |||||||
\(80\) | 0.253765 | − | 2.22162i | 0.0283717 | − | 0.248385i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.21906 | − | 4.21906i | 0.465917 | − | 0.465917i | ||||
\(83\) | −3.87246 | − | 3.87246i | −0.425058 | − | 0.425058i | 0.461883 | − | 0.886941i | \(-0.347174\pi\) |
−0.886941 | + | 0.461883i | \(0.847174\pi\) | |||||||
\(84\) | −3.50073 | −0.381960 | ||||||||
\(85\) | −9.58584 | − | 12.0581i | −1.03973 | − | 1.30789i | ||||
\(86\) | 7.63084i | 0.822855i | ||||||||
\(87\) | 4.60292 | − | 4.60292i | 0.493485 | − | 0.493485i | ||||
\(88\) | −1.94007 | + | 1.94007i | −0.206812 | + | 0.206812i | ||||
\(89\) | −9.13628 | −0.968444 | −0.484222 | − | 0.874945i | \(-0.660897\pi\) | ||||
−0.484222 | + | 0.874945i | \(0.660897\pi\) | |||||||
\(90\) | 1.39149 | + | 1.75036i | 0.146675 | + | 0.184504i | ||||
\(91\) | − | 5.94974i | − | 0.623703i | ||||||
\(92\) | −0.0321428 | + | 0.0321428i | −0.00335112 | + | 0.00335112i | ||||
\(93\) | 4.60292 | + | 4.60292i | 0.477301 | + | 0.477301i | ||||
\(94\) | 5.18653 | 0.534950 | ||||||||
\(95\) | 8.17945 | + | 5.30063i | 0.839194 | + | 0.543833i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −8.76663 | − | 8.76663i | −0.890117 | − | 0.890117i | 0.104417 | − | 0.994534i | \(-0.466702\pi\) |
−0.994534 | + | 0.104417i | \(0.966702\pi\) | |||||||
\(98\) | 3.71590 | − | 3.71590i | 0.375363 | − | 0.375363i | ||||
\(99\) | − | 2.74367i | − | 0.275749i | ||||||
\(100\) | 1.12754 | − | 4.87121i | 0.112754 | − | 0.487121i | ||||
\(101\) | 11.2650 | 1.12091 | 0.560455 | − | 0.828185i | \(-0.310626\pi\) | ||||
0.560455 | + | 0.828185i | \(0.310626\pi\) | |||||||
\(102\) | −4.87121 | + | 4.87121i | −0.482321 | + | 0.482321i | ||||
\(103\) | 0.762447 | − | 0.762447i | 0.0751262 | − | 0.0751262i | −0.668545 | − | 0.743671i | \(-0.733083\pi\) |
0.743671 | + | 0.668545i | \(0.233083\pi\) | |||||||
\(104\) | − | 1.69957i | − | 0.166657i | ||||||
\(105\) | −7.77729 | − | 0.888360i | −0.758986 | − | 0.0866951i | ||||
\(106\) | 12.6932 | 1.23287 | ||||||||
\(107\) | −13.5351 | − | 13.5351i | −1.30849 | − | 1.30849i | −0.922505 | − | 0.385985i | \(-0.873861\pi\) |
−0.385985 | − | 0.922505i | \(-0.626139\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | −4.37207 | −0.418768 | −0.209384 | − | 0.977833i | \(-0.567146\pi\) | ||||
−0.209384 | + | 0.977833i | \(0.567146\pi\) | |||||||
\(110\) | −4.80242 | + | 3.81777i | −0.457892 | + | 0.364011i | ||||
\(111\) | 6.49122 | 0.616119 | ||||||||
\(112\) | 2.47539 | − | 2.47539i | 0.233902 | − | 0.233902i | ||||
\(113\) | 6.95599 | − | 6.95599i | 0.654365 | − | 0.654365i | −0.299676 | − | 0.954041i | \(-0.596879\pi\) |
0.954041 | + | 0.299676i | \(0.0968786\pi\) | |||||||
\(114\) | 1.94007 | − | 3.90335i | 0.181704 | − | 0.365582i | ||||
\(115\) | −0.0795658 | + | 0.0632524i | −0.00741955 | + | 0.00589832i | ||||
\(116\) | 6.50952i | 0.604394i | ||||||||
\(117\) | 1.20178 | + | 1.20178i | 0.111105 | + | 0.111105i | ||||
\(118\) | 3.12754 | + | 3.12754i | 0.287913 | + | 0.287913i | ||||
\(119\) | − | 24.1162i | − | 2.21073i | ||||||
\(120\) | −2.22162 | − | 0.253765i | −0.202805 | − | 0.0231654i | ||||
\(121\) | −3.47228 | −0.315662 | ||||||||
\(122\) | −2.08651 | − | 2.08651i | −0.188904 | − | 0.188904i | ||||
\(123\) | −4.21906 | − | 4.21906i | −0.380419 | − | 0.380419i | ||||
\(124\) | −6.50952 | −0.584572 | ||||||||
\(125\) | 3.74110 | − | 10.5359i | 0.334614 | − | 0.942355i | ||||
\(126\) | 3.50073i | 0.311869i | ||||||||
\(127\) | 13.7136 | + | 13.7136i | 1.21689 | + | 1.21689i | 0.968716 | + | 0.248173i | \(0.0798302\pi\) |
0.248173 | + | 0.968716i | \(0.420170\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 7.63084 | 0.671858 | ||||||||
\(130\) | 0.431292 | − | 3.77581i | 0.0378268 | − | 0.331161i | ||||
\(131\) | 8.01380 | 0.700169 | 0.350085 | − | 0.936718i | \(-0.386153\pi\) | ||||
0.350085 | + | 0.936718i | \(0.386153\pi\) | |||||||
\(132\) | 1.94007 | + | 1.94007i | 0.168861 | + | 0.168861i | ||||
\(133\) | 4.85988 | + | 14.4647i | 0.421405 | + | 1.25425i | ||||
\(134\) | 9.90155i | 0.855363i | ||||||||
\(135\) | 1.75036 | − | 1.39149i | 0.150647 | − | 0.119760i | ||||
\(136\) | − | 6.88893i | − | 0.590721i | ||||||
\(137\) | −12.6299 | + | 12.6299i | −1.07905 | + | 1.07905i | −0.0824532 | + | 0.996595i | \(0.526275\pi\) |
−0.996595 | + | 0.0824532i | \(0.973725\pi\) | |||||||
\(138\) | 0.0321428 | + | 0.0321428i | 0.00273617 | + | 0.00273617i | ||||
\(139\) | 10.3499i | 0.877869i | 0.898519 | + | 0.438934i | \(0.144644\pi\) | ||||
−0.898519 | + | 0.438934i | \(0.855356\pi\) | |||||||
\(140\) | 6.12754 | − | 4.87121i | 0.517871 | − | 0.411692i | ||||
\(141\) | − | 5.18653i | − | 0.436785i | ||||||
\(142\) | 3.93571 | − | 3.93571i | 0.330278 | − | 0.330278i | ||||
\(143\) | −3.29729 | + | 3.29729i | −0.275733 | + | 0.275733i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −1.65189 | + | 14.4617i | −0.137182 | + | 1.20098i | ||||
\(146\) | − | 3.10002i | − | 0.256560i | ||||||
\(147\) | −3.71590 | − | 3.71590i | −0.306482 | − | 0.306482i | ||||
\(148\) | −4.58998 | + | 4.58998i | −0.377294 | + | 0.377294i | ||||
\(149\) | − | 9.07466i | − | 0.743425i | −0.928348 | − | 0.371712i | \(-0.878771\pi\) | ||
0.928348 | − | 0.371712i | \(-0.121229\pi\) | |||||||
\(150\) | −4.87121 | − | 1.12754i | −0.397732 | − | 0.0920631i | ||||
\(151\) | 1.75287i | 0.142647i | 0.997453 | + | 0.0713234i | \(0.0227222\pi\) | ||||
−0.997453 | + | 0.0713234i | \(0.977278\pi\) | |||||||
\(152\) | 1.38825 | + | 4.13192i | 0.112602 | + | 0.335143i | ||||
\(153\) | 4.87121 | + | 4.87121i | 0.393814 | + | 0.393814i | ||||
\(154\) | −9.60483 | −0.773979 | ||||||||
\(155\) | −14.4617 | − | 1.65189i | −1.16159 | − | 0.132683i | ||||
\(156\) | −1.69957 | −0.136075 | ||||||||
\(157\) | 7.20733 | − | 7.20733i | 0.575207 | − | 0.575207i | −0.358372 | − | 0.933579i | \(-0.616668\pi\) |
0.933579 | + | 0.358372i | \(0.116668\pi\) | |||||||
\(158\) | −0.159681 | − | 0.159681i | −0.0127035 | − | 0.0127035i | ||||
\(159\) | − | 12.6932i | − | 1.00664i | ||||||
\(160\) | 1.75036 | − | 1.39149i | 0.138378 | − | 0.110007i | ||||
\(161\) | −0.159132 | −0.0125413 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 9.60292 | + | 9.60292i | 0.752159 | + | 0.752159i | 0.974882 | − | 0.222723i | \(-0.0714945\pi\) |
−0.222723 | + | 0.974882i | \(0.571494\pi\) | |||||||
\(164\) | 5.96665 | 0.465917 | ||||||||
\(165\) | 3.81777 | + | 4.80242i | 0.297213 | + | 0.373868i | ||||
\(166\) | − | 5.47649i | − | 0.425058i | ||||||
\(167\) | 12.9013 | + | 12.9013i | 0.998336 | + | 0.998336i | 0.999999 | − | 0.00166271i | \(-0.000529259\pi\) |
−0.00166271 | + | 0.999999i | \(0.500529\pi\) | |||||||
\(168\) | −2.47539 | − | 2.47539i | −0.190980 | − | 0.190980i | ||||
\(169\) | 10.1114i | 0.777804i | ||||||||
\(170\) | 1.74817 | − | 15.3046i | 0.134078 | − | 1.17381i | ||||
\(171\) | −3.90335 | − | 1.94007i | −0.298497 | − | 0.148361i | ||||
\(172\) | −5.39582 | + | 5.39582i | −0.411427 | + | 0.411427i | ||||
\(173\) | 0.271593 | − | 0.271593i | 0.0206488 | − | 0.0206488i | −0.696707 | − | 0.717356i | \(-0.745352\pi\) |
0.717356 | + | 0.696707i | \(0.245352\pi\) | |||||||
\(174\) | 6.50952 | 0.493485 | ||||||||
\(175\) | 14.8492 | − | 9.26703i | 1.12249 | − | 0.700521i | ||||
\(176\) | −2.74367 | −0.206812 | ||||||||
\(177\) | 3.12754 | − | 3.12754i | 0.235080 | − | 0.235080i | ||||
\(178\) | −6.46033 | − | 6.46033i | −0.484222 | − | 0.484222i | ||||
\(179\) | 16.1543 | 1.20743 | 0.603715 | − | 0.797200i | \(-0.293686\pi\) | ||||
0.603715 | + | 0.797200i | \(0.293686\pi\) | |||||||
\(180\) | −0.253765 | + | 2.22162i | −0.0189145 | + | 0.165590i | ||||
\(181\) | − | 16.1980i | − | 1.20399i | −0.798501 | − | 0.601994i | \(-0.794373\pi\) | ||
0.798501 | − | 0.601994i | \(-0.205627\pi\) | |||||||
\(182\) | 4.20710 | − | 4.20710i | 0.311851 | − | 0.311851i | ||||
\(183\) | −2.08651 | + | 2.08651i | −0.154239 | + | 0.154239i | ||||
\(184\) | −0.0454567 | −0.00335112 | ||||||||
\(185\) | −11.3620 | + | 9.03243i | −0.835349 | + | 0.664078i | ||||
\(186\) | 6.50952i | 0.477301i | ||||||||
\(187\) | −13.3650 | + | 13.3650i | −0.977344 | + | 0.977344i | ||||
\(188\) | 3.66743 | + | 3.66743i | 0.267475 | + | 0.267475i | ||||
\(189\) | 3.50073 | 0.254640 | ||||||||
\(190\) | 2.03563 | + | 9.53185i | 0.147680 | + | 0.691513i | ||||
\(191\) | 14.6162 | 1.05759 | 0.528795 | − | 0.848750i | \(-0.322644\pi\) | ||||
0.528795 | + | 0.848750i | \(0.322644\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 6.20432 | − | 6.20432i | 0.446597 | − | 0.446597i | −0.447625 | − | 0.894221i | \(-0.647730\pi\) |
0.894221 | + | 0.447625i | \(0.147730\pi\) | |||||||
\(194\) | − | 12.3979i | − | 0.890117i | ||||||
\(195\) | −3.77581 | − | 0.431292i | −0.270392 | − | 0.0308855i | ||||
\(196\) | 5.25508 | 0.375363 | ||||||||
\(197\) | −9.77456 | + | 9.77456i | −0.696408 | + | 0.696408i | −0.963634 | − | 0.267226i | \(-0.913893\pi\) |
0.267226 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(198\) | 1.94007 | − | 1.94007i | 0.137875 | − | 0.137875i | ||||
\(199\) | 7.77253i | 0.550980i | 0.961304 | + | 0.275490i | \(0.0888401\pi\) | ||||
−0.961304 | + | 0.275490i | \(0.911160\pi\) | |||||||
\(200\) | 4.24175 | − | 2.64717i | 0.299937 | − | 0.187183i | ||||
\(201\) | 9.90155 | 0.698401 | ||||||||
\(202\) | 7.96556 | + | 7.96556i | 0.560455 | + | 0.560455i | ||||
\(203\) | −16.1136 | + | 16.1136i | −1.13095 | + | 1.13095i | ||||
\(204\) | −6.88893 | −0.482321 | ||||||||
\(205\) | 13.2556 | + | 1.51412i | 0.925813 | + | 0.105751i | ||||
\(206\) | 1.07826 | 0.0751262 | ||||||||
\(207\) | 0.0321428 | − | 0.0321428i | 0.00223408 | − | 0.00223408i | ||||
\(208\) | 1.20178 | − | 1.20178i | 0.0833285 | − | 0.0833285i | ||||
\(209\) | 5.32290 | − | 10.7095i | 0.368193 | − | 0.740792i | ||||
\(210\) | −4.87121 | − | 6.12754i | −0.336145 | − | 0.422840i | ||||
\(211\) | − | 7.91902i | − | 0.545168i | −0.962132 | − | 0.272584i | \(-0.912122\pi\) | ||
0.962132 | − | 0.272584i | \(-0.0878783\pi\) | |||||||
\(212\) | 8.97544 | + | 8.97544i | 0.616436 | + | 0.616436i | ||||
\(213\) | −3.93571 | − | 3.93571i | −0.269671 | − | 0.269671i | ||||
\(214\) | − | 19.1416i | − | 1.30849i | ||||||
\(215\) | −13.3567 | + | 10.6182i | −0.910922 | + | 0.724156i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −16.1136 | − | 16.1136i | −1.09386 | − | 1.09386i | ||||
\(218\) | −3.09152 | − | 3.09152i | −0.209384 | − | 0.209384i | ||||
\(219\) | −3.10002 | −0.209480 | ||||||||
\(220\) | −6.09540 | − | 0.696246i | −0.410951 | − | 0.0469409i | ||||
\(221\) | − | 11.7082i | − | 0.787582i | ||||||
\(222\) | 4.58998 | + | 4.58998i | 0.308059 | + | 0.308059i | ||||
\(223\) | −14.3643 | + | 14.3643i | −0.961907 | + | 0.961907i | −0.999301 | − | 0.0373940i | \(-0.988094\pi\) |
0.0373940 | + | 0.999301i | \(0.488094\pi\) | |||||||
\(224\) | 3.50073 | 0.233902 | ||||||||
\(225\) | −1.12754 | + | 4.87121i | −0.0751692 | + | 0.324747i | ||||
\(226\) | 9.83726 | 0.654365 | ||||||||
\(227\) | −15.0385 | − | 15.0385i | −0.998139 | − | 0.998139i | 0.00185921 | − | 0.999998i | \(-0.499408\pi\) |
−0.999998 | + | 0.00185921i | \(0.999408\pi\) | |||||||
\(228\) | 4.13192 | − | 1.38825i | 0.273643 | − | 0.0919391i | ||||
\(229\) | 2.69570i | 0.178137i | 0.996026 | + | 0.0890683i | \(0.0283890\pi\) | ||||
−0.996026 | + | 0.0890683i | \(0.971611\pi\) | |||||||
\(230\) | −0.100988 | − | 0.0115353i | −0.00665893 | − | 0.000760616i | ||||
\(231\) | 9.60483i | 0.631951i | ||||||||
\(232\) | −4.60292 | + | 4.60292i | −0.302197 | + | 0.302197i | ||||
\(233\) | −12.4775 | − | 12.4775i | −0.817426 | − | 0.817426i | 0.168309 | − | 0.985734i | \(-0.446169\pi\) |
−0.985734 | + | 0.168309i | \(0.946169\pi\) | |||||||
\(234\) | 1.69957i | 0.111105i | ||||||||
\(235\) | 7.21698 | + | 9.07831i | 0.470784 | + | 0.592204i | ||||
\(236\) | 4.42301i | 0.287913i | ||||||||
\(237\) | −0.159681 | + | 0.159681i | −0.0103724 | + | 0.0103724i | ||||
\(238\) | 17.0528 | − | 17.0528i | 1.10537 | − | 1.10537i | ||||
\(239\) | 27.2150i | 1.76039i | 0.474613 | + | 0.880195i | \(0.342588\pi\) | ||||
−0.474613 | + | 0.880195i | \(0.657412\pi\) | |||||||
\(240\) | −1.39149 | − | 1.75036i | −0.0898200 | − | 0.112985i | ||||
\(241\) | − | 25.1111i | − | 1.61755i | −0.588120 | − | 0.808774i | \(-0.700132\pi\) | ||
0.588120 | − | 0.808774i | \(-0.299868\pi\) | |||||||
\(242\) | −2.45527 | − | 2.45527i | −0.157831 | − | 0.157831i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 2.95077i | − | 0.188904i | ||||||
\(245\) | 11.6748 | + | 1.33355i | 0.745875 | + | 0.0851975i | ||||
\(246\) | − | 5.96665i | − | 0.380419i | ||||||
\(247\) | 2.35944 | + | 7.02251i | 0.150127 | + | 0.446831i | ||||
\(248\) | −4.60292 | − | 4.60292i | −0.292286 | − | 0.292286i | ||||
\(249\) | −5.47649 | −0.347058 | ||||||||
\(250\) | 10.0953 | − | 4.80461i | 0.638485 | − | 0.303870i | ||||
\(251\) | −2.30195 | −0.145298 | −0.0726489 | − | 0.997358i | \(-0.523145\pi\) | ||||
−0.0726489 | + | 0.997358i | \(0.523145\pi\) | |||||||
\(252\) | −2.47539 | + | 2.47539i | −0.155935 | + | 0.155935i | ||||
\(253\) | 0.0881891 | + | 0.0881891i | 0.00554440 | + | 0.00554440i | ||||
\(254\) | 19.3940i | 1.21689i | ||||||||
\(255\) | −15.3046 | − | 1.74817i | −0.958411 | − | 0.109474i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.7752 | + | 15.7752i | 0.984032 | + | 0.984032i | 0.999874 | − | 0.0158429i | \(-0.00504315\pi\) |
−0.0158429 | + | 0.999874i | \(0.505043\pi\) | |||||||
\(258\) | 5.39582 | + | 5.39582i | 0.335929 | + | 0.335929i | ||||
\(259\) | −22.7240 | −1.41200 | ||||||||
\(260\) | 2.97487 | − | 2.36493i | 0.184494 | − | 0.146667i | ||||
\(261\) | − | 6.50952i | − | 0.402929i | ||||||
\(262\) | 5.66661 | + | 5.66661i | 0.350085 | + | 0.350085i | ||||
\(263\) | −1.21906 | − | 1.21906i | −0.0751702 | − | 0.0751702i | 0.668522 | − | 0.743692i | \(-0.266927\pi\) |
−0.743692 | + | 0.668522i | \(0.766927\pi\) | |||||||
\(264\) | 2.74367i | 0.168861i | ||||||||
\(265\) | 17.6624 | + | 22.2177i | 1.08499 | + | 1.36482i | ||||
\(266\) | −6.79164 | + | 13.6646i | −0.416422 | + | 0.837828i | ||||
\(267\) | −6.46033 | + | 6.46033i | −0.395366 | + | 0.395366i | ||||
\(268\) | −7.00145 | + | 7.00145i | −0.427682 | + | 0.427682i | ||||
\(269\) | −7.58430 | −0.462423 | −0.231211 | − | 0.972904i | \(-0.574269\pi\) | ||||
−0.231211 | + | 0.972904i | \(0.574269\pi\) | |||||||
\(270\) | 2.22162 | + | 0.253765i | 0.135204 | + | 0.0154436i | ||||
\(271\) | −25.6741 | −1.55959 | −0.779795 | − | 0.626036i | \(-0.784676\pi\) | ||||
−0.779795 | + | 0.626036i | \(0.784676\pi\) | |||||||
\(272\) | 4.87121 | − | 4.87121i | 0.295360 | − | 0.295360i | ||||
\(273\) | −4.20710 | − | 4.20710i | −0.254626 | − | 0.254626i | ||||
\(274\) | −17.8614 | −1.07905 | ||||||||
\(275\) | −13.3650 | − | 3.09359i | −0.805939 | − | 0.186551i | ||||
\(276\) | 0.0454567i | 0.00273617i | ||||||||
\(277\) | −21.7414 | + | 21.7414i | −1.30631 | + | 1.30631i | −0.382257 | + | 0.924056i | \(0.624853\pi\) |
−0.924056 | + | 0.382257i | \(0.875147\pi\) | |||||||
\(278\) | −7.31850 | + | 7.31850i | −0.438934 | + | 0.438934i | ||||
\(279\) | 6.50952 | 0.389715 | ||||||||
\(280\) | 7.77729 | + | 0.888360i | 0.464782 | + | 0.0530897i | ||||
\(281\) | − | 21.9050i | − | 1.30674i | −0.757037 | − | 0.653372i | \(-0.773354\pi\) | ||
0.757037 | − | 0.653372i | \(-0.226646\pi\) | |||||||
\(282\) | 3.66743 | − | 3.66743i | 0.218392 | − | 0.218392i | ||||
\(283\) | 15.7217 | + | 15.7217i | 0.934557 | + | 0.934557i | 0.997986 | − | 0.0634298i | \(-0.0202039\pi\) |
−0.0634298 | + | 0.997986i | \(0.520204\pi\) | |||||||
\(284\) | 5.56594 | 0.330278 | ||||||||
\(285\) | 9.53185 | − | 2.03563i | 0.564618 | − | 0.120580i | ||||
\(286\) | −4.66307 | −0.275733 | ||||||||
\(287\) | 14.7698 | + | 14.7698i | 0.871831 | + | 0.871831i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 30.4573i | − | 1.79161i | ||||||
\(290\) | −11.3940 | + | 9.05790i | −0.669080 | + | 0.531898i | ||||
\(291\) | −12.3979 | −0.726777 | ||||||||
\(292\) | 2.19205 | − | 2.19205i | 0.128280 | − | 0.128280i | ||||
\(293\) | −8.25768 | + | 8.25768i | −0.482419 | + | 0.482419i | −0.905903 | − | 0.423484i | \(-0.860807\pi\) |
0.423484 | + | 0.905903i | \(0.360807\pi\) | |||||||
\(294\) | − | 5.25508i | − | 0.306482i | ||||||
\(295\) | −1.12240 | + | 9.82625i | −0.0653488 | + | 0.572106i | ||||
\(296\) | −6.49122 | −0.377294 | ||||||||
\(297\) | −1.94007 | − | 1.94007i | −0.112574 | − | 0.112574i | ||||
\(298\) | 6.41675 | − | 6.41675i | 0.371712 | − | 0.371712i | ||||
\(299\) | −0.0772571 | −0.00446790 | ||||||||
\(300\) | −2.64717 | − | 4.24175i | −0.152835 | − | 0.244898i | ||||
\(301\) | −26.7135 | −1.53974 | ||||||||
\(302\) | −1.23947 | + | 1.23947i | −0.0713234 | + | 0.0713234i | ||||
\(303\) | 7.96556 | − | 7.96556i | 0.457609 | − | 0.457609i | ||||
\(304\) | −1.94007 | + | 3.90335i | −0.111270 | + | 0.223872i | ||||
\(305\) | 0.748802 | − | 6.55550i | 0.0428763 | − | 0.375367i | ||||
\(306\) | 6.88893i | 0.393814i | ||||||||
\(307\) | −22.1239 | − | 22.1239i | −1.26268 | − | 1.26268i | −0.949790 | − | 0.312887i | \(-0.898704\pi\) |
−0.312887 | − | 0.949790i | \(-0.601296\pi\) | |||||||
\(308\) | −6.79164 | − | 6.79164i | −0.386990 | − | 0.386990i | ||||
\(309\) | − | 1.07826i | − | 0.0613403i | ||||||
\(310\) | −9.05790 | − | 11.3940i | −0.514454 | − | 0.647137i | ||||
\(311\) | 3.22108 | 0.182651 | 0.0913254 | − | 0.995821i | \(-0.470890\pi\) | ||||
0.0913254 | + | 0.995821i | \(0.470890\pi\) | |||||||
\(312\) | −1.20178 | − | 1.20178i | −0.0680374 | − | 0.0680374i | ||||
\(313\) | −14.9801 | − | 14.9801i | −0.846724 | − | 0.846724i | 0.142999 | − | 0.989723i | \(-0.454326\pi\) |
−0.989723 | + | 0.142999i | \(0.954326\pi\) | |||||||
\(314\) | 10.1927 | 0.575207 | ||||||||
\(315\) | −6.12754 | + | 4.87121i | −0.345248 | + | 0.274461i | ||||
\(316\) | − | 0.225823i | − | 0.0127035i | ||||||
\(317\) | −13.3317 | − | 13.3317i | −0.748782 | − | 0.748782i | 0.225468 | − | 0.974251i | \(-0.427609\pi\) |
−0.974251 | + | 0.225468i | \(0.927609\pi\) | |||||||
\(318\) | 8.97544 | − | 8.97544i | 0.503318 | − | 0.503318i | ||||
\(319\) | 17.8600 | 0.999966 | ||||||||
\(320\) | 2.22162 | + | 0.253765i | 0.124192 | + | 0.0141859i | ||||
\(321\) | −19.1416 | −1.06838 | ||||||||
\(322\) | −0.112523 | − | 0.112523i | −0.00627066 | − | 0.00627066i | ||||
\(323\) | 9.56356 | + | 28.4645i | 0.532131 | + | 1.58381i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 7.20918 | − | 4.49907i | 0.399893 | − | 0.249563i | ||||
\(326\) | 13.5806i | 0.752159i | ||||||||
\(327\) | −3.09152 | + | 3.09152i | −0.170961 | + | 0.170961i | ||||
\(328\) | 4.21906 | + | 4.21906i | 0.232958 | + | 0.232958i | ||||
\(329\) | 18.1566i | 1.00101i | ||||||||
\(330\) | −0.696246 | + | 6.09540i | −0.0383271 | + | 0.335540i | ||||
\(331\) | 6.73163i | 0.370004i | 0.982738 | + | 0.185002i | \(0.0592292\pi\) | ||||
−0.982738 | + | 0.185002i | \(0.940771\pi\) | |||||||
\(332\) | 3.87246 | − | 3.87246i | 0.212529 | − | 0.212529i | ||||
\(333\) | 4.58998 | − | 4.58998i | 0.251530 | − | 0.251530i | ||||
\(334\) | 18.2453i | 0.998336i | ||||||||
\(335\) | −17.3313 | + | 13.7779i | −0.946910 | + | 0.752765i | ||||
\(336\) | − | 3.50073i | − | 0.190980i | ||||||
\(337\) | 14.1501 | + | 14.1501i | 0.770806 | + | 0.770806i | 0.978247 | − | 0.207441i | \(-0.0665136\pi\) |
−0.207441 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(338\) | −7.14987 | + | 7.14987i | −0.388902 | + | 0.388902i | ||||
\(339\) | − | 9.83726i | − | 0.534287i | ||||||
\(340\) | 12.0581 | − | 9.58584i | 0.653943 | − | 0.519865i | ||||
\(341\) | 17.8600i | 0.967171i | ||||||||
\(342\) | −1.38825 | − | 4.13192i | −0.0750680 | − | 0.223429i | ||||
\(343\) | −4.31936 | − | 4.31936i | −0.233224 | − | 0.233224i | ||||
\(344\) | −7.63084 | −0.411427 | ||||||||
\(345\) | −0.0115353 | + | 0.100988i | −0.000621040 | + | 0.00543700i | ||||
\(346\) | 0.384091 | 0.0206488 | ||||||||
\(347\) | 6.84109 | − | 6.84109i | 0.367249 | − | 0.367249i | −0.499224 | − | 0.866473i | \(-0.666382\pi\) |
0.866473 | + | 0.499224i | \(0.166382\pi\) | |||||||
\(348\) | 4.60292 | + | 4.60292i | 0.246743 | + | 0.246743i | ||||
\(349\) | 33.2298i | 1.77875i | 0.457181 | + | 0.889374i | \(0.348859\pi\) | ||||
−0.457181 | + | 0.889374i | \(0.651141\pi\) | |||||||
\(350\) | 17.0528 | + | 3.94720i | 0.911508 | + | 0.210987i | ||||
\(351\) | 1.69957 | 0.0907166 | ||||||||
\(352\) | −1.94007 | − | 1.94007i | −0.103406 | − | 0.103406i | ||||
\(353\) | 25.3639 | + | 25.3639i | 1.34999 | + | 1.34999i | 0.885668 | + | 0.464318i | \(0.153701\pi\) |
0.464318 | + | 0.885668i | \(0.346299\pi\) | |||||||
\(354\) | 4.42301 | 0.235080 | ||||||||
\(355\) | 12.3654 | + | 1.41244i | 0.656288 | + | 0.0749645i | ||||
\(356\) | − | 9.13628i | − | 0.484222i | ||||||
\(357\) | −17.0528 | − | 17.0528i | −0.902528 | − | 0.902528i | ||||
\(358\) | 11.4228 | + | 11.4228i | 0.603715 | + | 0.603715i | ||||
\(359\) | − | 9.12994i | − | 0.481860i | −0.970543 | − | 0.240930i | \(-0.922548\pi\) | ||
0.970543 | − | 0.240930i | \(-0.0774524\pi\) | |||||||
\(360\) | −1.75036 | + | 1.39149i | −0.0922522 | + | 0.0733377i | ||||
\(361\) | −11.4723 | − | 15.1455i | −0.603804 | − | 0.797133i | ||||
\(362\) | 11.4537 | − | 11.4537i | 0.601994 | − | 0.601994i | ||||
\(363\) | −2.45527 | + | 2.45527i | −0.128868 | + | 0.128868i | ||||
\(364\) | 5.94974 | 0.311851 | ||||||||
\(365\) | 5.42616 | − | 4.31363i | 0.284018 | − | 0.225786i | ||||
\(366\) | −2.95077 | −0.154239 | ||||||||
\(367\) | 12.9778 | − | 12.9778i | 0.677435 | − | 0.677435i | −0.281984 | − | 0.959419i | \(-0.590993\pi\) |
0.959419 | + | 0.281984i | \(0.0909926\pi\) | |||||||
\(368\) | −0.0321428 | − | 0.0321428i | −0.00167556 | − | 0.00167556i | ||||
\(369\) | −5.96665 | −0.310611 | ||||||||
\(370\) | −14.4210 | − | 1.64724i | −0.749713 | − | 0.0856360i | ||||
\(371\) | 44.4354i | 2.30697i | ||||||||
\(372\) | −4.60292 | + | 4.60292i | −0.238651 | + | 0.238651i | ||||
\(373\) | 6.92570 | − | 6.92570i | 0.358599 | − | 0.358599i | −0.504697 | − | 0.863296i | \(-0.668396\pi\) |
0.863296 | + | 0.504697i | \(0.168396\pi\) | |||||||
\(374\) | −18.9009 | −0.977344 | ||||||||
\(375\) | −4.80461 | − | 10.0953i | −0.248109 | − | 0.521321i | ||||
\(376\) | 5.18653i | 0.267475i | ||||||||
\(377\) | −7.82301 | + | 7.82301i | −0.402906 | + | 0.402906i | ||||
\(378\) | 2.47539 | + | 2.47539i | 0.127320 | + | 0.127320i | ||||
\(379\) | 22.4882 | 1.15514 | 0.577570 | − | 0.816341i | \(-0.304001\pi\) | ||||
0.577570 | + | 0.816341i | \(0.304001\pi\) | |||||||
\(380\) | −5.30063 | + | 8.17945i | −0.271916 | + | 0.419597i | ||||
\(381\) | 19.3940 | 0.993586 | ||||||||
\(382\) | 10.3352 | + | 10.3352i | 0.528795 | + | 0.528795i | ||||
\(383\) | 14.9680 | − | 14.9680i | 0.764830 | − | 0.764830i | −0.212361 | − | 0.977191i | \(-0.568115\pi\) |
0.977191 | + | 0.212361i | \(0.0681153\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −13.3650 | − | 16.8119i | −0.681142 | − | 0.856816i | ||||
\(386\) | 8.77423 | 0.446597 | ||||||||
\(387\) | 5.39582 | − | 5.39582i | 0.274285 | − | 0.274285i | ||||
\(388\) | 8.76663 | − | 8.76663i | 0.445058 | − | 0.445058i | ||||
\(389\) | − | 10.1897i | − | 0.516639i | −0.966060 | − | 0.258319i | \(-0.916831\pi\) | ||
0.966060 | − | 0.258319i | \(-0.0831687\pi\) | |||||||
\(390\) | −2.36493 | − | 2.97487i | −0.119753 | − | 0.150638i | ||||
\(391\) | −0.313148 | −0.0158366 | ||||||||
\(392\) | 3.71590 | + | 3.71590i | 0.187681 | + | 0.187681i | ||||
\(393\) | 5.66661 | − | 5.66661i | 0.285843 | − | 0.285843i | ||||
\(394\) | −13.8233 | −0.696408 | ||||||||
\(395\) | 0.0573058 | − | 0.501693i | 0.00288337 | − | 0.0252429i | ||||
\(396\) | 2.74367 | 0.137875 | ||||||||
\(397\) | 14.9493 | − | 14.9493i | 0.750284 | − | 0.750284i | −0.224248 | − | 0.974532i | \(-0.571993\pi\) |
0.974532 | + | 0.224248i | \(0.0719927\pi\) | |||||||
\(398\) | −5.49601 | + | 5.49601i | −0.275490 | + | 0.275490i | ||||
\(399\) | 13.6646 | + | 6.79164i | 0.684083 | + | 0.340007i | ||||
\(400\) | 4.87121 | + | 1.12754i | 0.243560 | + | 0.0563769i | ||||
\(401\) | − | 17.1894i | − | 0.858400i | −0.903210 | − | 0.429200i | \(-0.858796\pi\) | ||
0.903210 | − | 0.429200i | \(-0.141204\pi\) | |||||||
\(402\) | 7.00145 | + | 7.00145i | 0.349201 | + | 0.349201i | ||||
\(403\) | −7.82301 | − | 7.82301i | −0.389692 | − | 0.389692i | ||||
\(404\) | 11.2650i | 0.560455i | ||||||||
\(405\) | 0.253765 | − | 2.22162i | 0.0126097 | − | 0.110393i | ||||
\(406\) | −22.7880 | −1.13095 | ||||||||
\(407\) | 12.5934 | + | 12.5934i | 0.624231 | + | 0.624231i | ||||
\(408\) | −4.87121 | − | 4.87121i | −0.241161 | − | 0.241161i | ||||
\(409\) | −23.9489 | −1.18420 | −0.592099 | − | 0.805865i | \(-0.701701\pi\) | ||||
−0.592099 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(410\) | 8.30250 | + | 10.4438i | 0.410031 | + | 0.515782i | ||||
\(411\) | 17.8614i | 0.881039i | ||||||||
\(412\) | 0.762447 | + | 0.762447i | 0.0375631 | + | 0.0375631i | ||||
\(413\) | −10.9487 | + | 10.9487i | −0.538748 | + | 0.538748i | ||||
\(414\) | 0.0454567 | 0.00223408 | ||||||||
\(415\) | 9.58584 | − | 7.62045i | 0.470550 | − | 0.374073i | ||||
\(416\) | 1.69957 | 0.0833285 | ||||||||
\(417\) | 7.31850 | + | 7.31850i | 0.358388 | + | 0.358388i | ||||
\(418\) | 11.3366 | − | 3.80890i | 0.554492 | − | 0.186299i | ||||
\(419\) | 21.4134i | 1.04611i | 0.852298 | + | 0.523056i | \(0.175208\pi\) | ||||
−0.852298 | + | 0.523056i | \(0.824792\pi\) | |||||||
\(420\) | 0.888360 | − | 7.77729i | 0.0433475 | − | 0.379493i | ||||
\(421\) | 1.72609i | 0.0841246i | 0.999115 | + | 0.0420623i | \(0.0133928\pi\) | ||||
−0.999115 | + | 0.0420623i | \(0.986607\pi\) | |||||||
\(422\) | 5.59960 | − | 5.59960i | 0.272584 | − | 0.272584i | ||||
\(423\) | −3.66743 | − | 3.66743i | −0.178317 | − | 0.178317i | ||||
\(424\) | 12.6932i | 0.616436i | ||||||||
\(425\) | 29.2211 | − | 18.2362i | 1.41743 | − | 0.884585i | ||||
\(426\) | − | 5.56594i | − | 0.269671i | ||||||
\(427\) | 7.30430 | − | 7.30430i | 0.353480 | − | 0.353480i | ||||
\(428\) | 13.5351 | − | 13.5351i | 0.654245 | − | 0.654245i | ||||
\(429\) | 4.66307i | 0.225135i | ||||||||
\(430\) | −16.9528 | − | 1.93644i | −0.817539 | − | 0.0933833i | ||||
\(431\) | 29.5770i | 1.42467i | 0.701838 | + | 0.712337i | \(0.252363\pi\) | ||||
−0.701838 | + | 0.712337i | \(0.747637\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −18.7711 | + | 18.7711i | −0.902081 | + | 0.902081i | −0.995616 | − | 0.0935354i | \(-0.970183\pi\) |
0.0935354 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(434\) | − | 22.7880i | − | 1.09386i | ||||||
\(435\) | 9.05790 | + | 11.3940i | 0.434293 | + | 0.546301i | ||||
\(436\) | − | 4.37207i | − | 0.209384i | ||||||
\(437\) | 0.187824 | − | 0.0631054i | 0.00898482 | − | 0.00301874i | ||||
\(438\) | −2.19205 | − | 2.19205i | −0.104740 | − | 0.104740i | ||||
\(439\) | 8.66125 | 0.413379 | 0.206690 | − | 0.978407i | \(-0.433731\pi\) | ||||
0.206690 | + | 0.978407i | \(0.433731\pi\) | |||||||
\(440\) | −3.81777 | − | 4.80242i | −0.182005 | − | 0.228946i | ||||
\(441\) | −5.25508 | −0.250242 | ||||||||
\(442\) | 8.27898 | − | 8.27898i | 0.393791 | − | 0.393791i | ||||
\(443\) | −19.5669 | − | 19.5669i | −0.929652 | − | 0.929652i | 0.0680315 | − | 0.997683i | \(-0.478328\pi\) |
−0.997683 | + | 0.0680315i | \(0.978328\pi\) | |||||||
\(444\) | 6.49122i | 0.308059i | ||||||||
\(445\) | 2.31847 | − | 20.2974i | 0.109906 | − | 0.962187i | ||||
\(446\) | −20.3142 | −0.961907 | ||||||||
\(447\) | −6.41675 | − | 6.41675i | −0.303502 | − | 0.303502i | ||||
\(448\) | 2.47539 | + | 2.47539i | 0.116951 | + | 0.116951i | ||||
\(449\) | 21.3429 | 1.00724 | 0.503618 | − | 0.863927i | \(-0.332002\pi\) | ||||
0.503618 | + | 0.863927i | \(0.332002\pi\) | |||||||
\(450\) | −4.24175 | + | 2.64717i | −0.199958 | + | 0.124789i | ||||
\(451\) | − | 16.3705i | − | 0.770857i | ||||||
\(452\) | 6.95599 | + | 6.95599i | 0.327182 | + | 0.327182i | ||||
\(453\) | 1.23947 | + | 1.23947i | 0.0582353 | + | 0.0582353i | ||||
\(454\) | − | 21.2676i | − | 0.998139i | ||||||
\(455\) | 13.2181 | + | 1.50983i | 0.619673 | + | 0.0707821i | ||||
\(456\) | 3.90335 | + | 1.94007i | 0.182791 | + | 0.0908520i | ||||
\(457\) | 21.3371 | − | 21.3371i | 0.998110 | − | 0.998110i | −0.00188859 | − | 0.999998i | \(-0.500601\pi\) |
0.999998 | + | 0.00188859i | \(0.000601157\pi\) | |||||||
\(458\) | −1.90615 | + | 1.90615i | −0.0890683 | + | 0.0890683i | ||||
\(459\) | 6.88893 | 0.321548 | ||||||||
\(460\) | −0.0632524 | − | 0.0795658i | −0.00294916 | − | 0.00370977i | ||||
\(461\) | 0.603474 | 0.0281066 | 0.0140533 | − | 0.999901i | \(-0.495527\pi\) | ||||
0.0140533 | + | 0.999901i | \(0.495527\pi\) | |||||||
\(462\) | −6.79164 | + | 6.79164i | −0.315976 | + | 0.315976i | ||||
\(463\) | −13.8679 | − | 13.8679i | −0.644495 | − | 0.644495i | 0.307162 | − | 0.951657i | \(-0.400621\pi\) |
−0.951657 | + | 0.307162i | \(0.900621\pi\) | |||||||
\(464\) | −6.50952 | −0.302197 | ||||||||
\(465\) | −11.3940 | + | 9.05790i | −0.528385 | + | 0.420050i | ||||
\(466\) | − | 17.6458i | − | 0.817426i | ||||||
\(467\) | 5.10843 | − | 5.10843i | 0.236390 | − | 0.236390i | −0.578964 | − | 0.815353i | \(-0.696543\pi\) |
0.815353 | + | 0.578964i | \(0.196543\pi\) | |||||||
\(468\) | −1.20178 | + | 1.20178i | −0.0555523 | + | 0.0555523i | ||||
\(469\) | −34.6626 | −1.60057 | ||||||||
\(470\) | −1.31616 | + | 11.5225i | −0.0607098 | + | 0.531494i | ||||
\(471\) | − | 10.1927i | − | 0.469655i | ||||||
\(472\) | −3.12754 | + | 3.12754i | −0.143957 | + | 0.143957i | ||||
\(473\) | 14.8043 | + | 14.8043i | 0.680705 | + | 0.680705i | ||||
\(474\) | −0.225823 | −0.0103724 | ||||||||
\(475\) | −13.8516 | + | 16.8265i | −0.635557 | + | 0.772054i | ||||
\(476\) | 24.1162 | 1.10537 | ||||||||
\(477\) | −8.97544 | − | 8.97544i | −0.410957 | − | 0.410957i | ||||
\(478\) | −19.2439 | + | 19.2439i | −0.880195 | + | 0.880195i | ||||
\(479\) | − | 0.676761i | − | 0.0309220i | −0.999880 | − | 0.0154610i | \(-0.995078\pi\) | ||
0.999880 | − | 0.0154610i | \(-0.00492158\pi\) | |||||||
\(480\) | 0.253765 | − | 2.22162i | 0.0115827 | − | 0.101403i | ||||
\(481\) | −11.0323 | −0.503030 | ||||||||
\(482\) | 17.7562 | − | 17.7562i | 0.808774 | − | 0.808774i | ||||
\(483\) | −0.112523 | + | 0.112523i | −0.00511997 | + | 0.00511997i | ||||
\(484\) | − | 3.47228i | − | 0.157831i | ||||||
\(485\) | 21.7008 | − | 17.2515i | 0.985383 | − | 0.783350i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.31334 | − | 2.31334i | −0.104828 | − | 0.104828i | 0.652748 | − | 0.757575i | \(-0.273616\pi\) |
−0.757575 | + | 0.652748i | \(0.773616\pi\) | |||||||
\(488\) | 2.08651 | − | 2.08651i | 0.0944519 | − | 0.0944519i | ||||
\(489\) | 13.5806 | 0.614135 | ||||||||
\(490\) | 7.31236 | + | 9.19829i | 0.330339 | + | 0.415536i | ||||
\(491\) | −0.0138034 | −0.000622939 | −0.000311469 | − | 1.00000i | \(-0.500099\pi\) | ||||
−0.000311469 | 1.00000i | \(0.500099\pi\) | ||||||||
\(492\) | 4.21906 | − | 4.21906i | 0.190210 | − | 0.190210i | ||||
\(493\) | −31.7092 | + | 31.7092i | −1.42811 | + | 1.42811i | ||||
\(494\) | −3.29729 | + | 6.63403i | −0.148352 | + | 0.298479i | ||||
\(495\) | 6.09540 | + | 0.696246i | 0.273968 | + | 0.0312939i | ||||
\(496\) | − | 6.50952i | − | 0.292286i | ||||||
\(497\) | 13.7779 | + | 13.7779i | 0.618021 | + | 0.618021i | ||||
\(498\) | −3.87246 | − | 3.87246i | −0.173529 | − | 0.173529i | ||||
\(499\) | − | 19.0461i | − | 0.852619i | −0.904577 | − | 0.426309i | \(-0.859813\pi\) | ||
0.904577 | − | 0.426309i | \(-0.140187\pi\) | |||||||
\(500\) | 10.5359 | + | 3.74110i | 0.471178 | + | 0.167307i | ||||
\(501\) | 18.2453 | 0.815138 | ||||||||
\(502\) | −1.62772 | − | 1.62772i | −0.0726489 | − | 0.0726489i | ||||
\(503\) | −15.5475 | − | 15.5475i | −0.693230 | − | 0.693230i | 0.269711 | − | 0.962941i | \(-0.413072\pi\) |
−0.962941 | + | 0.269711i | \(0.913072\pi\) | |||||||
\(504\) | −3.50073 | −0.155935 | ||||||||
\(505\) | −2.85866 | + | 25.0266i | −0.127209 | + | 1.11367i | ||||
\(506\) | 0.124718i | 0.00554440i | ||||||||
\(507\) | 7.14987 | + | 7.14987i | 0.317537 | + | 0.317537i | ||||
\(508\) | −13.7136 | + | 13.7136i | −0.608444 | + | 0.608444i | ||||
\(509\) | 4.08859 | 0.181224 | 0.0906118 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906118 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(510\) | −9.58584 | − | 12.0581i | −0.424468 | − | 0.533943i | ||||
\(511\) | 10.8523 | 0.480078 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.13192 | + | 1.38825i | −0.182429 | + | 0.0612928i | ||||
\(514\) | 22.3095i | 0.984032i | ||||||||
\(515\) | 1.50039 | + | 1.88735i | 0.0661150 | + | 0.0831667i | ||||
\(516\) | 7.63084i | 0.335929i | ||||||||
\(517\) | 10.0622 | − | 10.0622i | 0.442536 | − | 0.442536i | ||||
\(518\) | −16.0683 | − | 16.0683i | −0.705999 | − | 0.705999i | ||||
\(519\) | − | 0.384091i | − | 0.0168597i | ||||||
\(520\) | 3.77581 | + | 0.431292i | 0.165580 | + | 0.0189134i | ||||
\(521\) | 29.8730i | 1.30876i | 0.756166 | + | 0.654380i | \(0.227070\pi\) | ||||
−0.756166 | + | 0.654380i | \(0.772930\pi\) | |||||||
\(522\) | 4.60292 | − | 4.60292i | 0.201465 | − | 0.201465i | ||||
\(523\) | −20.1935 | + | 20.1935i | −0.883001 | + | 0.883001i | −0.993839 | − | 0.110837i | \(-0.964647\pi\) |
0.110837 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(524\) | 8.01380i | 0.350085i | ||||||||
\(525\) | 3.94720 | − | 17.0528i | 0.172270 | − | 0.744243i | ||||
\(526\) | − | 1.72400i | − | 0.0751702i | ||||||
\(527\) | −31.7092 | − | 31.7092i | −1.38127 | − | 1.38127i | ||||
\(528\) | −1.94007 | + | 1.94007i | −0.0844306 | + | 0.0844306i | ||||
\(529\) | − | 22.9979i | − | 0.999910i | ||||||
\(530\) | −3.22108 | + | 28.1995i | −0.139915 | + | 1.22491i | ||||
\(531\) | − | 4.42301i | − | 0.191942i | ||||||
\(532\) | −14.4647 | + | 4.85988i | −0.627125 | + | 0.210703i | ||||
\(533\) | 7.17060 | + | 7.17060i | 0.310593 | + | 0.310593i | ||||
\(534\) | −9.13628 | −0.395366 | ||||||||
\(535\) | 33.5047 | − | 26.6352i | 1.44853 | − | 1.15154i | ||||
\(536\) | −9.90155 | −0.427682 | ||||||||
\(537\) | 11.4228 | − | 11.4228i | 0.492932 | − | 0.492932i | ||||
\(538\) | −5.36291 | − | 5.36291i | −0.231211 | − | 0.231211i | ||||
\(539\) | − | 14.4182i | − | 0.621035i | ||||||
\(540\) | 1.39149 | + | 1.75036i | 0.0598800 | + | 0.0753236i | ||||
\(541\) | −25.3583 | −1.09024 | −0.545120 | − | 0.838358i | \(-0.683516\pi\) | ||||
−0.545120 | + | 0.838358i | \(0.683516\pi\) | |||||||
\(542\) | −18.1543 | − | 18.1543i | −0.779795 | − | 0.779795i | ||||
\(543\) | −11.4537 | − | 11.4537i | −0.491526 | − | 0.491526i | ||||
\(544\) | 6.88893 | 0.295360 | ||||||||
\(545\) | 1.10948 | − | 9.71308i | 0.0475247 | − | 0.416063i | ||||
\(546\) | − | 5.94974i | − | 0.254626i | ||||||
\(547\) | −13.3457 | − | 13.3457i | −0.570622 | − | 0.570622i | 0.361680 | − | 0.932302i | \(-0.382203\pi\) |
−0.932302 | + | 0.361680i | \(0.882203\pi\) | |||||||
\(548\) | −12.6299 | − | 12.6299i | −0.539524 | − | 0.539524i | ||||
\(549\) | 2.95077i | 0.125936i | ||||||||
\(550\) | −7.26297 | − | 11.6380i | −0.309694 | − | 0.496245i | ||||
\(551\) | 12.6289 | − | 25.4089i | 0.538009 | − | 1.08246i | ||||
\(552\) | −0.0321428 | + | 0.0321428i | −0.00136809 | + | 0.00136809i | ||||
\(553\) | 0.558998 | − | 0.558998i | 0.0237710 | − | 0.0237710i | ||||
\(554\) | −30.7470 | −1.30631 | ||||||||
\(555\) | −1.64724 | + | 14.4210i | −0.0699215 | + | 0.612138i | ||||
\(556\) | −10.3499 | −0.438934 | ||||||||
\(557\) | −8.05867 | + | 8.05867i | −0.341457 | + | 0.341457i | −0.856915 | − | 0.515458i | \(-0.827622\pi\) |
0.515458 | + | 0.856915i | \(0.327622\pi\) | |||||||
\(558\) | 4.60292 | + | 4.60292i | 0.194857 | + | 0.194857i | ||||
\(559\) | −12.9692 | −0.548538 | ||||||||
\(560\) | 4.87121 | + | 6.12754i | 0.205846 | + | 0.258936i | ||||
\(561\) | 18.9009i | 0.797998i | ||||||||
\(562\) | 15.4892 | − | 15.4892i | 0.653372 | − | 0.653372i | ||||
\(563\) | 28.6648 | − | 28.6648i | 1.20808 | − | 1.20808i | 0.236430 | − | 0.971648i | \(-0.424022\pi\) |
0.971648 | − | 0.236430i | \(-0.0759775\pi\) | |||||||
\(564\) | 5.18653 | 0.218392 | ||||||||
\(565\) | 13.6884 | + | 17.2188i | 0.575875 | + | 0.724399i | ||||
\(566\) | 22.2338i | 0.934557i | ||||||||
\(567\) | 2.47539 | − | 2.47539i | 0.103956 | − | 0.103956i | ||||
\(568\) | 3.93571 | + | 3.93571i | 0.165139 | + | 0.165139i | ||||
\(569\) | −8.54540 | −0.358242 | −0.179121 | − | 0.983827i | \(-0.557325\pi\) | ||||
−0.179121 | + | 0.983827i | \(0.557325\pi\) | |||||||
\(570\) | 8.17945 | + | 5.30063i | 0.342599 | + | 0.222019i | ||||
\(571\) | 45.4169 | 1.90064 | 0.950320 | − | 0.311275i | \(-0.100756\pi\) | ||||
0.950320 | + | 0.311275i | \(0.100756\pi\) | |||||||
\(572\) | −3.29729 | − | 3.29729i | −0.137867 | − | 0.137867i | ||||
\(573\) | 10.3352 | − | 10.3352i | 0.431759 | − | 0.431759i | ||||
\(574\) | 20.8876i | 0.871831i | ||||||||
\(575\) | −0.120332 | − | 0.192816i | −0.00501819 | − | 0.00804100i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 12.1650 | − | 12.1650i | 0.506437 | − | 0.506437i | −0.406994 | − | 0.913431i | \(-0.633423\pi\) |
0.913431 | + | 0.406994i | \(0.133423\pi\) | |||||||
\(578\) | 21.5366 | − | 21.5366i | 0.895803 | − | 0.895803i | ||||
\(579\) | − | 8.77423i | − | 0.364645i | ||||||
\(580\) | −14.4617 | − | 1.65189i | −0.600489 | − | 0.0685908i | ||||
\(581\) | 19.1717 | 0.795375 | ||||||||
\(582\) | −8.76663 | − | 8.76663i | −0.363389 | − | 0.363389i | ||||
\(583\) | 24.6256 | − | 24.6256i | 1.01989 | − | 1.01989i | ||||
\(584\) | 3.10002 | 0.128280 | ||||||||
\(585\) | −2.97487 | + | 2.36493i | −0.122996 | + | 0.0977779i | ||||
\(586\) | −11.6781 | −0.482419 | ||||||||
\(587\) | −5.32968 | + | 5.32968i | −0.219980 | + | 0.219980i | −0.808490 | − | 0.588510i | \(-0.799715\pi\) |
0.588510 | + | 0.808490i | \(0.299715\pi\) | |||||||
\(588\) | 3.71590 | − | 3.71590i | 0.153241 | − | 0.153241i | ||||
\(589\) | 25.4089 | + | 12.6289i | 1.04696 | + | 0.520365i | ||||
\(590\) | −7.74186 | + | 6.15455i | −0.318728 | + | 0.253379i | ||||
\(591\) | 13.8233i | 0.568615i | ||||||||
\(592\) | −4.58998 | − | 4.58998i | −0.188647 | − | 0.188647i | ||||
\(593\) | −1.80818 | − | 1.80818i | −0.0742529 | − | 0.0742529i | 0.669005 | − | 0.743258i | \(-0.266720\pi\) |
−0.743258 | + | 0.669005i | \(0.766720\pi\) | |||||||
\(594\) | − | 2.74367i | − | 0.112574i | ||||||
\(595\) | 53.5772 | + | 6.11985i | 2.19645 | + | 0.250889i | ||||
\(596\) | 9.07466 | 0.371712 | ||||||||
\(597\) | 5.49601 | + | 5.49601i | 0.224937 | + | 0.224937i | ||||
\(598\) | −0.0546290 | − | 0.0546290i | −0.00223395 | − | 0.00223395i | ||||
\(599\) | 25.3131 | 1.03426 | 0.517132 | − | 0.855906i | \(-0.327000\pi\) | ||||
0.517132 | + | 0.855906i | \(0.327000\pi\) | |||||||
\(600\) | 1.12754 | − | 4.87121i | 0.0460315 | − | 0.198866i | ||||
\(601\) | − | 18.5367i | − | 0.756126i | −0.925780 | − | 0.378063i | \(-0.876590\pi\) | ||
0.925780 | − | 0.378063i | \(-0.123410\pi\) | |||||||
\(602\) | −18.8893 | − | 18.8893i | −0.769870 | − | 0.769870i | ||||
\(603\) | 7.00145 | − | 7.00145i | 0.285121 | − | 0.285121i | ||||
\(604\) | −1.75287 | −0.0713234 | ||||||||
\(605\) | 0.881142 | − | 7.71409i | 0.0358235 | − | 0.313622i | ||||
\(606\) | 11.2650 | 0.457609 | ||||||||
\(607\) | −11.5164 | − | 11.5164i | −0.467435 | − | 0.467435i | 0.433647 | − | 0.901083i | \(-0.357226\pi\) |
−0.901083 | + | 0.433647i | \(0.857226\pi\) | |||||||
\(608\) | −4.13192 | + | 1.38825i | −0.167571 | + | 0.0563010i | ||||
\(609\) | 22.7880i | 0.923418i | ||||||||
\(610\) | 5.16492 | − | 4.10596i | 0.209122 | − | 0.166245i | ||||
\(611\) | 8.81490i | 0.356613i | ||||||||
\(612\) | −4.87121 | + | 4.87121i | −0.196907 | + | 0.196907i | ||||
\(613\) | −7.66890 | − | 7.66890i | −0.309744 | − | 0.309744i | 0.535066 | − | 0.844810i | \(-0.320287\pi\) |
−0.844810 | + | 0.535066i | \(0.820287\pi\) | |||||||
\(614\) | − | 31.2879i | − | 1.26268i | ||||||
\(615\) | 10.4438 | − | 8.30250i | 0.421134 | − | 0.334789i | ||||
\(616\) | − | 9.60483i | − | 0.386990i | ||||||
\(617\) | 33.2792 | − | 33.2792i | 1.33977 | − | 1.33977i | 0.443492 | − | 0.896278i | \(-0.353740\pi\) |
0.896278 | − | 0.443492i | \(-0.146260\pi\) | |||||||
\(618\) | 0.762447 | − | 0.762447i | 0.0306701 | − | 0.0306701i | ||||
\(619\) | 3.87513i | 0.155755i | 0.996963 | + | 0.0778774i | \(0.0248143\pi\) | ||||
−0.996963 | + | 0.0778774i | \(0.975186\pi\) | |||||||
\(620\) | 1.65189 | − | 14.4617i | 0.0663413 | − | 0.580795i | ||||
\(621\) | − | 0.0454567i | − | 0.00182412i | ||||||
\(622\) | 2.27765 | + | 2.27765i | 0.0913254 | + | 0.0913254i | ||||
\(623\) | 22.6158 | − | 22.6158i | 0.906084 | − | 0.906084i | ||||
\(624\) | − | 1.69957i | − | 0.0680374i | ||||||
\(625\) | 22.4573 | + | 10.9849i | 0.898293 | + | 0.439398i | ||||
\(626\) | − | 21.1850i | − | 0.846724i | ||||||
\(627\) | −3.80890 | − | 11.3366i | −0.152113 | − | 0.452741i | ||||
\(628\) | 7.20733 | + | 7.20733i | 0.287604 | + | 0.287604i | ||||
\(629\) | −44.7175 | −1.78300 | ||||||||
\(630\) | −7.77729 | − | 0.888360i | −0.309855 | − | 0.0353931i | ||||
\(631\) | 1.80965 | 0.0720412 | 0.0360206 | − | 0.999351i | \(-0.488532\pi\) | ||||
0.0360206 | + | 0.999351i | \(0.488532\pi\) | |||||||
\(632\) | 0.159681 | − | 0.159681i | 0.00635176 | − | 0.00635176i | ||||
\(633\) | −5.59960 | − | 5.59960i | −0.222564 | − | 0.222564i | ||||
\(634\) | − | 18.8539i | − | 0.748782i | ||||||
\(635\) | −33.9466 | + | 26.9865i | −1.34713 | + | 1.07093i | ||||
\(636\) | 12.6932 | 0.503318 | ||||||||
\(637\) | 6.31545 | + | 6.31545i | 0.250227 | + | 0.250227i | ||||
\(638\) | 12.6289 | + | 12.6289i | 0.499983 | + | 0.499983i | ||||
\(639\) | −5.56594 | −0.220185 | ||||||||
\(640\) | 1.39149 | + | 1.75036i | 0.0550033 | + | 0.0691892i | ||||
\(641\) | − | 6.61503i | − | 0.261278i | −0.991430 | − | 0.130639i | \(-0.958297\pi\) | ||
0.991430 | − | 0.130639i | \(-0.0417029\pi\) | |||||||
\(642\) | −13.5351 | − | 13.5351i | −0.534189 | − | 0.534189i | ||||
\(643\) | −30.3608 | − | 30.3608i | −1.19731 | − | 1.19731i | −0.974968 | − | 0.222347i | \(-0.928628\pi\) |
−0.222347 | − | 0.974968i | \(-0.571372\pi\) | |||||||
\(644\) | − | 0.159132i | − | 0.00627066i | ||||||
\(645\) | −1.93644 | + | 16.9528i | −0.0762472 | + | 0.667518i | ||||
\(646\) | −13.3650 | + | 26.8899i | −0.525838 | + | 1.05797i | ||||
\(647\) | 5.83884 | − | 5.83884i | 0.229549 | − | 0.229549i | −0.582956 | − | 0.812504i | \(-0.698104\pi\) |
0.812504 | + | 0.582956i | \(0.198104\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 12.1353 | 0.476351 | ||||||||
\(650\) | 8.27898 | + | 1.91633i | 0.324728 | + | 0.0751648i | ||||
\(651\) | −22.7880 | −0.893133 | ||||||||
\(652\) | −9.60292 | + | 9.60292i | −0.376080 | + | 0.376080i | ||||
\(653\) | −19.7797 | − | 19.7797i | −0.774039 | − | 0.774039i | 0.204771 | − | 0.978810i | \(-0.434355\pi\) |
−0.978810 | + | 0.204771i | \(0.934355\pi\) | |||||||
\(654\) | −4.37207 | −0.170961 | ||||||||
\(655\) | −2.03362 | + | 17.8036i | −0.0794601 | + | 0.695646i | ||||
\(656\) | 5.96665i | 0.232958i | ||||||||
\(657\) | −2.19205 | + | 2.19205i | −0.0855198 | + | 0.0855198i | ||||
\(658\) | −12.8387 | + | 12.8387i | −0.500503 | + | 0.500503i | ||||
\(659\) | 8.44761 | 0.329072 | 0.164536 | − | 0.986371i | \(-0.447387\pi\) | ||||
0.164536 | + | 0.986371i | \(0.447387\pi\) | |||||||
\(660\) | −4.80242 | + | 3.81777i | −0.186934 | + | 0.148607i | ||||
\(661\) | − | 23.8283i | − | 0.926814i | −0.886146 | − | 0.463407i | \(-0.846627\pi\) | ||
0.886146 | − | 0.463407i | \(-0.153373\pi\) | |||||||
\(662\) | −4.75998 | + | 4.75998i | −0.185002 | + | 0.185002i | ||||
\(663\) | −8.27898 | − | 8.27898i | −0.321529 | − | 0.321529i | ||||
\(664\) | 5.47649 | 0.212529 | ||||||||
\(665\) | −33.3684 | + | 7.12619i | −1.29397 | + | 0.276342i | ||||
\(666\) | 6.49122 | 0.251530 | ||||||||
\(667\) | 0.209234 | + | 0.209234i | 0.00810157 | + | 0.00810157i | ||||
\(668\) | −12.9013 | + | 12.9013i | −0.499168 | + | 0.499168i | ||||
\(669\) | 20.3142i | 0.785393i | ||||||||
\(670\) | −21.9975 | − | 2.51266i | −0.849837 | − | 0.0970726i | ||||
\(671\) | −8.09594 | −0.312540 | ||||||||
\(672\) | 2.47539 | − | 2.47539i | 0.0954901 | − | 0.0954901i | ||||
\(673\) | −31.9422 | + | 31.9422i | −1.23128 | + | 1.23128i | −0.267812 | + | 0.963471i | \(0.586300\pi\) |
−0.963471 | + | 0.267812i | \(0.913700\pi\) | |||||||
\(674\) | 20.0113i | 0.770806i | ||||||||
\(675\) | 2.64717 | + | 4.24175i | 0.101890 | + | 0.163265i | ||||
\(676\) | −10.1114 | −0.388902 | ||||||||
\(677\) | −11.7115 | − | 11.7115i | −0.450111 | − | 0.450111i | 0.445280 | − | 0.895391i | \(-0.353104\pi\) |
−0.895391 | + | 0.445280i | \(0.853104\pi\) | |||||||
\(678\) | 6.95599 | − | 6.95599i | 0.267143 | − | 0.267143i | ||||
\(679\) | 43.4016 | 1.66560 | ||||||||
\(680\) | 15.3046 | + | 1.74817i | 0.586904 | + | 0.0670391i | ||||
\(681\) | −21.2676 | −0.814977 | ||||||||
\(682\) | −12.6289 | + | 12.6289i | −0.483586 | + | 0.483586i | ||||
\(683\) | −3.55375 | + | 3.55375i | −0.135981 | + | 0.135981i | −0.771821 | − | 0.635840i | \(-0.780654\pi\) |
0.635840 | + | 0.771821i | \(0.280654\pi\) | |||||||
\(684\) | 1.94007 | − | 3.90335i | 0.0741803 | − | 0.149248i | ||||
\(685\) | −24.8539 | − | 31.2640i | −0.949619 | − | 1.19453i | ||||
\(686\) | − | 6.10850i | − | 0.233224i | ||||||
\(687\) | 1.90615 | + | 1.90615i | 0.0727240 | + | 0.0727240i | ||||
\(688\) | −5.39582 | − | 5.39582i | −0.205714 | − | 0.205714i | ||||
\(689\) | 21.5730i | 0.821867i | ||||||||
\(690\) | −0.0795658 | + | 0.0632524i | −0.00302902 | + | 0.00240798i | ||||
\(691\) | 9.74241 | 0.370619 | 0.185309 | − | 0.982680i | \(-0.440671\pi\) | ||||
0.185309 | + | 0.982680i | \(0.440671\pi\) | |||||||
\(692\) | 0.271593 | + | 0.271593i | 0.0103244 | + | 0.0103244i | ||||
\(693\) | 6.79164 | + | 6.79164i | 0.257993 | + | 0.257993i | ||||
\(694\) | 9.67476 | 0.367249 | ||||||||
\(695\) | −22.9936 | − | 2.62644i | −0.872197 | − | 0.0996267i | ||||
\(696\) | 6.50952i | 0.246743i | ||||||||
\(697\) | 29.0648 | + | 29.0648i | 1.10091 | + | 1.10091i | ||||
\(698\) | −23.4970 | + | 23.4970i | −0.889374 | + | 0.889374i | ||||
\(699\) | −17.6458 | −0.667425 | ||||||||
\(700\) | 9.26703 | + | 14.8492i | 0.350261 | + | 0.561247i | ||||
\(701\) | −10.3224 | −0.389873 | −0.194936 | − | 0.980816i | \(-0.562450\pi\) | ||||
−0.194936 | + | 0.980816i | \(0.562450\pi\) | |||||||
\(702\) | 1.20178 | + | 1.20178i | 0.0453583 | + | 0.0453583i | ||||
\(703\) | 26.8212 | − | 9.01143i | 1.01158 | − | 0.339873i | ||||
\(704\) | − | 2.74367i | − | 0.103406i | ||||||
\(705\) | 11.5225 | + | 1.31616i | 0.433963 | + | 0.0495694i | ||||
\(706\) | 35.8700i | 1.34999i | ||||||||
\(707\) | −27.8852 | + | 27.8852i | −1.04873 | + | 1.04873i | ||||
\(708\) | 3.12754 | + | 3.12754i | 0.117540 | + | 0.117540i | ||||
\(709\) | 10.3223i | 0.387663i | 0.981035 | + | 0.193831i | \(0.0620915\pi\) | ||||
−0.981035 | + | 0.193831i | \(0.937909\pi\) | |||||||
\(710\) | 7.74492 | + | 9.74241i | 0.290662 | + | 0.365626i | ||||
\(711\) | 0.225823i | 0.00846901i | ||||||||
\(712\) | 6.46033 | − | 6.46033i | 0.242111 | − | 0.242111i | ||||
\(713\) | −0.209234 | + | 0.209234i | −0.00783587 | + | 0.00783587i | ||||
\(714\) | − | 24.1162i | − | 0.902528i | ||||||
\(715\) | −6.48859 | − | 8.16206i | −0.242660 | − | 0.305244i | ||||
\(716\) | 16.1543i | 0.603715i | ||||||||
\(717\) | 19.2439 | + | 19.2439i | 0.718676 | + | 0.718676i | ||||
\(718\) | 6.45584 | − | 6.45584i | 0.240930 | − | 0.240930i | ||||
\(719\) | − | 34.9029i | − | 1.30166i | −0.759224 | − | 0.650830i | \(-0.774421\pi\) | ||
0.759224 | − | 0.650830i | \(-0.225579\pi\) | |||||||
\(720\) | −2.22162 | − | 0.253765i | −0.0827950 | − | 0.00945725i | ||||
\(721\) | 3.77470i | 0.140577i | ||||||||
\(722\) | 2.59737 | − | 18.8216i | 0.0966642 | − | 0.700468i | ||||
\(723\) | −17.7562 | − | 17.7562i | −0.660361 | − | 0.660361i | ||||
\(724\) | 16.1980 | 0.601994 | ||||||||
\(725\) | −31.7092 | − | 7.33973i | −1.17765 | − | 0.272591i | ||||
\(726\) | −3.47228 | −0.128868 | ||||||||
\(727\) | 12.8595 | − | 12.8595i | 0.476932 | − | 0.476932i | −0.427217 | − | 0.904149i | \(-0.640506\pi\) |
0.904149 | + | 0.427217i | \(0.140506\pi\) | |||||||
\(728\) | 4.20710 | + | 4.20710i | 0.155926 | + | 0.155926i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 6.88707 | + | 0.786675i | 0.254902 | + | 0.0291162i | ||||
\(731\) | −52.5683 | −1.94431 | ||||||||
\(732\) | −2.08651 | − | 2.08651i | −0.0771197 | − | 0.0771197i | ||||
\(733\) | 11.1047 | + | 11.1047i | 0.410162 | + | 0.410162i | 0.881795 | − | 0.471633i | \(-0.156335\pi\) |
−0.471633 | + | 0.881795i | \(0.656335\pi\) | |||||||
\(734\) | 18.3534 | 0.677435 | ||||||||
\(735\) | 9.19829 | − | 7.31236i | 0.339284 | − | 0.269720i | ||||
\(736\) | − | 0.0454567i | − | 0.00167556i | ||||||
\(737\) | 19.2097 | + | 19.2097i | 0.707597 | + | 0.707597i | ||||
\(738\) | −4.21906 | − | 4.21906i | −0.155306 | − | 0.155306i | ||||
\(739\) | 18.1001i | 0.665823i | 0.942958 | + | 0.332911i | \(0.108031\pi\) | ||||
−0.942958 | + | 0.332911i | \(0.891969\pi\) | |||||||
\(740\) | −9.03243 | − | 11.3620i | −0.332039 | − | 0.417675i | ||||
\(741\) | 6.63403 | + | 3.29729i | 0.243707 | + | 0.121129i | ||||
\(742\) | −31.4205 | + | 31.4205i | −1.15348 | + | 1.15348i | ||||
\(743\) | 26.9208 | − | 26.9208i | 0.987630 | − | 0.987630i | −0.0122949 | − | 0.999924i | \(-0.503914\pi\) |
0.999924 | + | 0.0122949i | \(0.00391368\pi\) | |||||||
\(744\) | −6.50952 | −0.238651 | ||||||||
\(745\) | 20.1605 | + | 2.30283i | 0.738622 | + | 0.0843690i | ||||
\(746\) | 9.79442 | 0.358599 | ||||||||
\(747\) | −3.87246 | + | 3.87246i | −0.141686 | + | 0.141686i | ||||
\(748\) | −13.3650 | − | 13.3650i | −0.488672 | − | 0.488672i | ||||
\(749\) | 67.0093 | 2.44847 | ||||||||
\(750\) | 3.74110 | − | 10.5359i | 0.136606 | − | 0.384715i | ||||
\(751\) | − | 9.91849i | − | 0.361931i | −0.983489 | − | 0.180965i | \(-0.942078\pi\) | ||
0.983489 | − | 0.180965i | \(-0.0579222\pi\) | |||||||
\(752\) | −3.66743 | + | 3.66743i | −0.133737 | + | 0.133737i | ||||
\(753\) | −1.62772 | + | 1.62772i | −0.0593176 | + | 0.0593176i | ||||
\(754\) | −11.0634 | −0.402906 | ||||||||
\(755\) | −3.89422 | − | 0.444817i | −0.141725 | − | 0.0161886i | ||||
\(756\) | 3.50073i | 0.127320i | ||||||||
\(757\) | 3.01763 | − | 3.01763i | 0.109678 | − | 0.109678i | −0.650138 | − | 0.759816i | \(-0.725289\pi\) |
0.759816 | + | 0.650138i | \(0.225289\pi\) | |||||||
\(758\) | 15.9015 | + | 15.9015i | 0.577570 | + | 0.577570i | ||||
\(759\) | 0.124718 | 0.00452699 | ||||||||
\(760\) | −9.53185 | + | 2.03563i | −0.345757 | + | 0.0738402i | ||||
\(761\) | −11.1416 | −0.403881 | −0.201941 | − | 0.979398i | \(-0.564725\pi\) | ||||
−0.201941 | + | 0.979398i | \(0.564725\pi\) | |||||||
\(762\) | 13.7136 | + | 13.7136i | 0.496793 | + | 0.496793i | ||||
\(763\) | 10.8226 | − | 10.8226i | 0.391803 | − | 0.391803i | ||||
\(764\) | 14.6162i | 0.528795i | ||||||||
\(765\) | −12.0581 | + | 9.58584i | −0.435962 | + | 0.346577i | ||||
\(766\) | 21.1680 | 0.764830 | ||||||||
\(767\) | −5.31548 | + | 5.31548i | −0.191931 | + | 0.191931i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 32.8840i | − | 1.18583i | −0.805266 | − | 0.592913i | \(-0.797978\pi\) | ||
0.805266 | − | 0.592913i | \(-0.202022\pi\) | |||||||
\(770\) | 2.43737 | − | 21.3383i | 0.0878366 | − | 0.768979i | ||||
\(771\) | 22.3095 | 0.803458 | ||||||||
\(772\) | 6.20432 | + | 6.20432i | 0.223298 | + | 0.223298i | ||||
\(773\) | −31.2573 | + | 31.2573i | −1.12425 | + | 1.12425i | −0.133152 | + | 0.991096i | \(0.542510\pi\) |
−0.991096 | + | 0.133152i | \(0.957490\pi\) | |||||||
\(774\) | 7.63084 | 0.274285 | ||||||||
\(775\) | 7.33973 | − | 31.7092i | 0.263651 | − | 1.13903i | ||||
\(776\) | 12.3979 | 0.445058 | ||||||||
\(777\) | −16.0683 | + | 16.0683i | −0.576446 | + | 0.576446i | ||||
\(778\) | 7.20521 | − | 7.20521i | 0.258319 | − | 0.258319i | ||||
\(779\) | −23.2899 | − | 11.5757i | −0.834447 | − | 0.414742i | ||||
\(780\) | 0.431292 | − | 3.77581i | 0.0154427 | − | 0.135196i | ||||
\(781\) | − | 15.2711i | − | 0.546443i | ||||||
\(782\) | −0.221429 | − | 0.221429i | −0.00791829 | − | 0.00791829i | ||||
\(783\) | −4.60292 | − | 4.60292i | −0.164495 | − | 0.164495i | ||||
\(784\) | 5.25508i | 0.187681i | ||||||||
\(785\) | 14.1830 | + | 17.8409i | 0.506213 | + | 0.636770i | ||||
\(786\) | 8.01380 | 0.285843 | ||||||||
\(787\) | 2.28524 | + | 2.28524i | 0.0814600 | + | 0.0814600i | 0.746663 | − | 0.665203i | \(-0.231655\pi\) |
−0.665203 | + | 0.746663i | \(0.731655\pi\) | |||||||
\(788\) | −9.77456 | − | 9.77456i | −0.348204 | − | 0.348204i | ||||
\(789\) | −1.72400 | −0.0613762 | ||||||||
\(790\) | 0.395271 | − | 0.314229i | 0.0140631 | − | 0.0111798i | ||||
\(791\) | 34.4375i | 1.22446i | ||||||||
\(792\) | 1.94007 | + | 1.94007i | 0.0689373 | + | 0.0689373i | ||||
\(793\) | 3.54618 | − | 3.54618i | 0.125929 | − | 0.125929i | ||||
\(794\) | 21.1415 | 0.750284 | ||||||||
\(795\) | 28.1995 | + | 3.22108i | 1.00013 | + | 0.114240i | ||||
\(796\) | −7.77253 | −0.275490 | ||||||||
\(797\) | 20.1327 | + | 20.1327i | 0.713137 | + | 0.713137i | 0.967190 | − | 0.254054i | \(-0.0817639\pi\) |
−0.254054 | + | 0.967190i | \(0.581764\pi\) | |||||||
\(798\) | 4.85988 | + | 14.4647i | 0.172038 | + | 0.512045i | ||||
\(799\) | 35.7296i | 1.26402i | ||||||||
\(800\) | 2.64717 | + | 4.24175i | 0.0935917 | + | 0.149969i | ||||
\(801\) | 9.13628i | 0.322815i | ||||||||
\(802\) | 12.1548 | − | 12.1548i | 0.429200 | − | 0.429200i | ||||
\(803\) | −6.01425 | − | 6.01425i | −0.212238 | − | 0.212238i | ||||
\(804\) | 9.90155i | 0.349201i | ||||||||
\(805\) | 0.0403820 | − | 0.353530i | 0.00142328 | − | 0.0124603i | ||||
\(806\) | − | 11.0634i | − | 0.389692i | ||||||
\(807\) | −5.36291 | + | 5.36291i | −0.188783 | + | 0.188783i | ||||
\(808\) | −7.96556 | + | 7.96556i | −0.280227 | + | 0.280227i | ||||
\(809\) | − | 19.9089i | − | 0.699958i | −0.936758 | − | 0.349979i | \(-0.886189\pi\) | ||
0.936758 | − | 0.349979i | \(-0.113811\pi\) | |||||||
\(810\) | 1.75036 | − | 1.39149i | 0.0615015 | − | 0.0488918i | ||||
\(811\) | 27.5845i | 0.968623i | 0.874896 | + | 0.484312i | \(0.160930\pi\) | ||||
−0.874896 | + | 0.484312i | \(0.839070\pi\) | |||||||
\(812\) | −16.1136 | − | 16.1136i | −0.565476 | − | 0.565476i | ||||
\(813\) | −18.1543 | + | 18.1543i | −0.636700 | + | 0.636700i | ||||
\(814\) | 17.8097i | 0.624231i | ||||||||
\(815\) | −23.7709 | + | 18.8972i | −0.832660 | + | 0.661939i | ||||
\(816\) | − | 6.88893i | − | 0.241161i | ||||||
\(817\) | 31.5300 | − | 10.5935i | 1.10310 | − | 0.370620i | ||||
\(818\) | −16.9345 | − | 16.9345i | −0.592099 | − | 0.592099i | ||||
\(819\) | −5.94974 | −0.207901 | ||||||||
\(820\) | −1.51412 | + | 13.2556i | −0.0528755 | + | 0.462907i | ||||
\(821\) | −16.0769 | −0.561089 | −0.280545 | − | 0.959841i | \(-0.590515\pi\) | ||||
−0.280545 | + | 0.959841i | \(0.590515\pi\) | |||||||
\(822\) | −12.6299 | + | 12.6299i | −0.440520 | + | 0.440520i | ||||
\(823\) | 0.761023 | + | 0.761023i | 0.0265276 | + | 0.0265276i | 0.720246 | − | 0.693719i | \(-0.244029\pi\) |
−0.693719 | + | 0.720246i | \(0.744029\pi\) | |||||||
\(824\) | 1.07826i | 0.0375631i | ||||||||
\(825\) | −11.6380 | + | 7.26297i | −0.405182 | + | 0.252864i | ||||
\(826\) | −15.4837 | −0.538748 | ||||||||
\(827\) | −20.8201 | − | 20.8201i | −0.723984 | − | 0.723984i | 0.245430 | − | 0.969414i | \(-0.421071\pi\) |
−0.969414 | + | 0.245430i | \(0.921071\pi\) | |||||||
\(828\) | 0.0321428 | + | 0.0321428i | 0.00111704 | + | 0.00111704i | ||||
\(829\) | 31.8887 | 1.10754 | 0.553771 | − | 0.832669i | \(-0.313188\pi\) | ||||
0.553771 | + | 0.832669i | \(0.313188\pi\) | |||||||
\(830\) | 12.1667 | + | 1.38974i | 0.422312 | + | 0.0482385i | ||||
\(831\) | 30.7470i | 1.06660i | ||||||||
\(832\) | 1.20178 | + | 1.20178i | 0.0416642 | + | 0.0416642i | ||||
\(833\) | 25.5986 | + | 25.5986i | 0.886938 | + | 0.886938i | ||||
\(834\) | 10.3499i | 0.358388i | ||||||||
\(835\) | −31.9358 | + | 25.3880i | −1.10518 | + | 0.878588i | ||||
\(836\) | 10.7095 | + | 5.32290i | 0.370396 | + | 0.184096i | ||||
\(837\) | 4.60292 | − | 4.60292i | 0.159100 | − | 0.159100i | ||||
\(838\) | −15.1416 | + | 15.1416i | −0.523056 | + | 0.523056i | ||||
\(839\) | −39.4110 | −1.36062 | −0.680310 | − | 0.732924i | \(-0.738155\pi\) | ||||
−0.680310 | + | 0.732924i | \(0.738155\pi\) | |||||||
\(840\) | 6.12754 | − | 4.87121i | 0.211420 | − | 0.168073i | ||||
\(841\) | 13.3738 | 0.461166 | ||||||||
\(842\) | −1.22053 | + | 1.22053i | −0.0420623 | + | 0.0420623i | ||||
\(843\) | −15.4892 | − | 15.4892i | −0.533476 | − | 0.533476i | ||||
\(844\) | 7.91902 | 0.272584 | ||||||||
\(845\) | −22.4638 | − | 2.56593i | −0.772779 | − | 0.0882706i | ||||
\(846\) | − | 5.18653i | − | 0.178317i | ||||||
\(847\) | 8.59523 | − | 8.59523i | 0.295336 | − | 0.295336i | ||||
\(848\) | −8.97544 | + | 8.97544i | −0.308218 | + | 0.308218i | ||||
\(849\) | 22.2338 | 0.763062 | ||||||||
\(850\) | 33.5574 | + | 7.76753i | 1.15101 | + | 0.266424i | ||||
\(851\) | 0.295070i | 0.0101149i | ||||||||
\(852\) | 3.93571 | − | 3.93571i | 0.134835 | − | 0.134835i | ||||
\(853\) | 29.3272 | + | 29.3272i | 1.00414 | + | 1.00414i | 0.999991 | + | 0.00415191i | \(0.00132160\pi\) |
0.00415191 | + | 0.999991i | \(0.498678\pi\) | |||||||
\(854\) | 10.3298 | 0.353480 | ||||||||
\(855\) | 5.30063 | − | 8.17945i | 0.181278 | − | 0.279731i | ||||
\(856\) | 19.1416 | 0.654245 | ||||||||
\(857\) | −22.6621 | − | 22.6621i | −0.774121 | − | 0.774121i | 0.204703 | − | 0.978824i | \(-0.434377\pi\) |
−0.978824 | + | 0.204703i | \(0.934377\pi\) | |||||||
\(858\) | −3.29729 | + | 3.29729i | −0.112568 | + | 0.112568i | ||||
\(859\) | − | 9.13130i | − | 0.311556i | −0.987792 | − | 0.155778i | \(-0.950212\pi\) | ||
0.987792 | − | 0.155778i | \(-0.0497884\pi\) | |||||||
\(860\) | −10.6182 | − | 13.3567i | −0.362078 | − | 0.455461i | ||||
\(861\) | 20.8876 | 0.711847 | ||||||||
\(862\) | −20.9141 | + | 20.9141i | −0.712337 | + | 0.712337i | ||||
\(863\) | 31.2115 | − | 31.2115i | 1.06245 | − | 1.06245i | 0.0645382 | − | 0.997915i | \(-0.479443\pi\) |
0.997915 | − | 0.0645382i | \(-0.0205574\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 0.534456 | + | 0.672298i | 0.0181721 | + | 0.0228588i | ||||
\(866\) | −26.5463 | −0.902081 | ||||||||
\(867\) | −21.5366 | − | 21.5366i | −0.731420 | − | 0.731420i | ||||
\(868\) | 16.1136 | − | 16.1136i | 0.546930 | − | 0.546930i | ||||
\(869\) | −0.619583 | −0.0210179 | ||||||||
\(870\) | −1.65189 | + | 14.4617i | −0.0560042 | + | 0.490297i | ||||
\(871\) | −16.8284 | −0.570209 | ||||||||
\(872\) | 3.09152 | − | 3.09152i | 0.104692 | − | 0.104692i | ||||
\(873\) | −8.76663 | + | 8.76663i | −0.296706 | + | 0.296706i | ||||
\(874\) | 0.177434 | + | 0.0881891i | 0.00600178 | + | 0.00298304i | ||||
\(875\) | 16.8196 | + | 35.3410i | 0.568607 | + | 1.19474i | ||||
\(876\) | − | 3.10002i | − | 0.104740i | ||||||
\(877\) | 15.7226 | + | 15.7226i | 0.530916 | + | 0.530916i | 0.920845 | − | 0.389929i | \(-0.127500\pi\) |
−0.389929 | + | 0.920845i | \(0.627500\pi\) | |||||||
\(878\) | 6.12443 | + | 6.12443i | 0.206690 | + | 0.206690i | ||||
\(879\) | 11.6781i | 0.393894i | ||||||||
\(880\) | 0.696246 | − | 6.09540i | 0.0234705 | − | 0.205476i | ||||
\(881\) | −12.7472 | −0.429464 | −0.214732 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214732 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(882\) | −3.71590 | − | 3.71590i | −0.125121 | − | 0.125121i | ||||
\(883\) | 26.1600 | + | 26.1600i | 0.880352 | + | 0.880352i | 0.993570 | − | 0.113218i | \(-0.0361158\pi\) |
−0.113218 | + | 0.993570i | \(0.536116\pi\) | |||||||
\(884\) | 11.7082 | 0.393791 | ||||||||
\(885\) | 6.15455 | + | 7.74186i | 0.206883 | + | 0.260240i | ||||
\(886\) | − | 27.6718i | − | 0.929652i | ||||||
\(887\) | 3.63787 | + | 3.63787i | 0.122148 | + | 0.122148i | 0.765538 | − | 0.643390i | \(-0.222473\pi\) |
−0.643390 | + | 0.765538i | \(0.722473\pi\) | |||||||
\(888\) | −4.58998 | + | 4.58998i | −0.154030 | + | 0.154030i | ||||
\(889\) | −67.8931 | −2.27706 | ||||||||
\(890\) | 15.9918 | − | 12.7130i | 0.536047 | − | 0.426141i | ||||
\(891\) | −2.74367 | −0.0919164 | ||||||||
\(892\) | −14.3643 | − | 14.3643i | −0.480953 | − | 0.480953i | ||||
\(893\) | −7.20021 | − | 21.4303i | −0.240946 | − | 0.717139i | ||||
\(894\) | − | 9.07466i | − | 0.303502i | ||||||
\(895\) | −4.09940 | + | 35.8888i | −0.137028 | + | 1.19963i | ||||
\(896\) | 3.50073i | 0.116951i | ||||||||
\(897\) | −0.0546290 | + | 0.0546290i | −0.00182401 | + | 0.00182401i | ||||
\(898\) | 15.0917 | + | 15.0917i | 0.503618 | + | 0.503618i | ||||
\(899\) | 42.3738i | 1.41325i | ||||||||
\(900\) | −4.87121 | − | 1.12754i | −0.162374 | − | 0.0375846i | ||||
\(901\) | 87.4424i | 2.91313i | ||||||||
\(902\) | 11.5757 | − | 11.5757i | 0.385428 | − | 0.385428i | ||||
\(903\) | −18.8893 | + | 18.8893i | −0.628596 | + | 0.628596i | ||||
\(904\) | 9.83726i | 0.327182i | ||||||||
\(905\) | 35.9858 | + | 4.11048i | 1.19621 | + | 0.136637i | ||||
\(906\) | 1.75287i | 0.0582353i | ||||||||
\(907\) | −27.2643 | − | 27.2643i | −0.905298 | − | 0.905298i | 0.0905904 | − | 0.995888i | \(-0.471125\pi\) |
−0.995888 | + | 0.0905904i | \(0.971125\pi\) | |||||||
\(908\) | 15.0385 | − | 15.0385i | 0.499070 | − | 0.499070i | ||||
\(909\) | − | 11.2650i | − | 0.373637i | ||||||
\(910\) | 8.27898 | + | 10.4142i | 0.274445 | + | 0.345228i | ||||
\(911\) | 1.42099i | 0.0470796i | 0.999723 | + | 0.0235398i | \(0.00749364\pi\) | ||||
−0.999723 | + | 0.0235398i | \(0.992506\pi\) | |||||||
\(912\) | 1.38825 | + | 4.13192i | 0.0459696 | + | 0.136822i | ||||
\(913\) | −10.6248 | − | 10.6248i | −0.351628 | − | 0.351628i | ||||
\(914\) | 30.1753 | 0.998110 | ||||||||
\(915\) | −4.10596 | − | 5.16492i | −0.135739 | − | 0.170747i | ||||
\(916\) | −2.69570 | −0.0890683 | ||||||||
\(917\) | −19.8373 | + | 19.8373i | −0.655084 | + | 0.655084i | ||||
\(918\) | 4.87121 | + | 4.87121i | 0.160774 | + | 0.160774i | ||||
\(919\) | 38.9380i | 1.28445i | 0.766518 | + | 0.642223i | \(0.221988\pi\) | ||||
−0.766518 | + | 0.642223i | \(0.778012\pi\) | |||||||
\(920\) | 0.0115353 | − | 0.100988i | 0.000380308 | − | 0.00332947i | ||||
\(921\) | −31.2879 | −1.03097 | ||||||||
\(922\) | 0.426720 | + | 0.426720i | 0.0140533 | + | 0.0140533i | ||||
\(923\) | 6.68904 | + | 6.68904i | 0.220172 | + | 0.220172i | ||||
\(924\) | −9.60483 | −0.315976 | ||||||||
\(925\) | −17.1834 | − | 27.5341i | −0.564986 | − | 0.905317i | ||||
\(926\) | − | 19.6121i | − | 0.644495i | ||||||
\(927\) | −0.762447 | − | 0.762447i | −0.0250421 | − | 0.0250421i | ||||
\(928\) | −4.60292 | − | 4.60292i | −0.151098 | − | 0.151098i | ||||
\(929\) | 23.8414i | 0.782211i | 0.920346 | + | 0.391106i | \(0.127907\pi\) | ||||
−0.920346 | + | 0.391106i | \(0.872093\pi\) | |||||||
\(930\) | −14.4617 | − | 1.65189i | −0.474217 | − | 0.0541675i | ||||
\(931\) | −20.5124 | − | 10.1952i | −0.672267 | − | 0.334134i | ||||
\(932\) | 12.4775 | − | 12.4775i | 0.408713 | − | 0.408713i | ||||
\(933\) | 2.27765 | − | 2.27765i | 0.0745669 | − | 0.0745669i | ||||
\(934\) | 7.22441 | 0.236390 | ||||||||
\(935\) | −26.3004 | − | 33.0835i | −0.860114 | − | 1.08195i | ||||
\(936\) | −1.69957 | −0.0555523 | ||||||||
\(937\) | −13.2718 | + | 13.2718i | −0.433572 | + | 0.433572i | −0.889842 | − | 0.456270i | \(-0.849185\pi\) |
0.456270 | + | 0.889842i | \(0.349185\pi\) | |||||||
\(938\) | −24.5102 | − | 24.5102i | −0.800285 | − | 0.800285i | ||||
\(939\) | −21.1850 | −0.691347 | ||||||||
\(940\) | −9.07831 | + | 7.21698i | −0.296102 | + | 0.235392i | ||||
\(941\) | − | 27.1173i | − | 0.884000i | −0.897015 | − | 0.442000i | \(-0.854269\pi\) | ||
0.897015 | − | 0.442000i | \(-0.145731\pi\) | |||||||
\(942\) | 7.20733 | − | 7.20733i | 0.234827 | − | 0.234827i | ||||
\(943\) | 0.191785 | − | 0.191785i | 0.00624536 | − | 0.00624536i | ||||
\(944\) | −4.42301 | −0.143957 | ||||||||
\(945\) | −0.888360 | + | 7.77729i | −0.0288984 | + | 0.252995i | ||||
\(946\) | 20.9365i | 0.680705i | ||||||||
\(947\) | −12.0469 | + | 12.0469i | −0.391473 | + | 0.391473i | −0.875212 | − | 0.483739i | \(-0.839278\pi\) |
0.483739 | + | 0.875212i | \(0.339278\pi\) | |||||||
\(948\) | −0.159681 | − | 0.159681i | −0.00518619 | − | 0.00518619i | ||||
\(949\) | 5.26872 | 0.171030 | ||||||||
\(950\) | −21.6927 | + | 2.10356i | −0.703805 | + | 0.0682485i | ||||
\(951\) | −18.8539 | −0.611378 | ||||||||
\(952\) | 17.0528 | + | 17.0528i | 0.552683 | + | 0.552683i | ||||
\(953\) | 33.0593 | − | 33.0593i | 1.07090 | − | 1.07090i | 0.0736082 | − | 0.997287i | \(-0.476549\pi\) |
0.997287 | − | 0.0736082i | \(-0.0234514\pi\) | |||||||
\(954\) | − | 12.6932i | − | 0.410957i | ||||||
\(955\) | −3.70907 | + | 32.4716i | −0.120023 | + | 1.05076i | ||||
\(956\) | −27.2150 | −0.880195 | ||||||||
\(957\) | 12.6289 | − | 12.6289i | 0.408234 | − | 0.408234i | ||||
\(958\) | 0.478542 | − | 0.478542i | 0.0154610 | − | 0.0154610i | ||||
\(959\) | − | 62.5279i | − | 2.01913i | ||||||
\(960\) | 1.75036 | − | 1.39149i | 0.0564927 | − | 0.0449100i | ||||
\(961\) | −11.3738 | −0.366898 | ||||||||
\(962\) | −7.80102 | − | 7.80102i | −0.251515 | − | 0.251515i | ||||
\(963\) | −13.5351 | + | 13.5351i | −0.436163 | + | 0.436163i | ||||
\(964\) | 25.1111 | 0.808774 | ||||||||
\(965\) | 12.2092 | + | 15.3581i | 0.393028 | + | 0.494394i | ||||
\(966\) | −0.159132 | −0.00511997 | ||||||||
\(967\) | 4.66093 | − | 4.66093i | 0.149885 | − | 0.149885i | −0.628181 | − | 0.778067i | \(-0.716200\pi\) |
0.778067 | + | 0.628181i | \(0.216200\pi\) | |||||||
\(968\) | 2.45527 | − | 2.45527i | 0.0789155 | − | 0.0789155i | ||||
\(969\) | 26.8899 | + | 13.3650i | 0.863828 | + | 0.429345i | ||||
\(970\) | 27.5434 | + | 3.14615i | 0.884366 | + | 0.101017i | ||||
\(971\) | − | 11.8515i | − | 0.380332i | −0.981752 | − | 0.190166i | \(-0.939097\pi\) | ||
0.981752 | − | 0.190166i | \(-0.0609026\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −25.6201 | − | 25.6201i | −0.821341 | − | 0.821341i | ||||
\(974\) | − | 3.27156i | − | 0.104828i | ||||||
\(975\) | 1.91633 | − | 8.27898i | 0.0613718 | − | 0.265140i | ||||
\(976\) | 2.95077 | 0.0944519 | ||||||||
\(977\) | 26.7920 | + | 26.7920i | 0.857153 | + | 0.857153i | 0.991002 | − | 0.133849i | \(-0.0427336\pi\) |
−0.133849 | + | 0.991002i | \(0.542734\pi\) | |||||||
\(978\) | 9.60292 | + | 9.60292i | 0.307068 | + | 0.307068i | ||||
\(979\) | −25.0669 | −0.801143 | ||||||||
\(980\) | −1.33355 | + | 11.6748i | −0.0425988 | + | 0.372938i | ||||
\(981\) | 4.37207i | 0.139589i | ||||||||
\(982\) | −0.00976048 | − | 0.00976048i | −0.000311469 | − | 0.000311469i | ||||
\(983\) | −11.6066 | + | 11.6066i | −0.370193 | + | 0.370193i | −0.867547 | − | 0.497354i | \(-0.834305\pi\) |
0.497354 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(984\) | 5.96665 | 0.190210 | ||||||||
\(985\) | −19.2349 | − | 24.1958i | −0.612876 | − | 0.770942i | ||||
\(986\) | −44.8436 | −1.42811 | ||||||||
\(987\) | 12.8387 | + | 12.8387i | 0.408659 | + | 0.408659i | ||||
\(988\) | −7.02251 | + | 2.35944i | −0.223416 | + | 0.0750636i | ||||
\(989\) | 0.346873i | 0.0110299i | ||||||||
\(990\) | 3.81777 | + | 4.80242i | 0.121337 | + | 0.152631i | ||||
\(991\) | 58.1707i | 1.84785i | 0.382568 | + | 0.923927i | \(0.375040\pi\) | ||||
−0.382568 | + | 0.923927i | \(0.624960\pi\) | |||||||
\(992\) | 4.60292 | − | 4.60292i | 0.146143 | − | 0.146143i | ||||
\(993\) | 4.75998 | + | 4.75998i | 0.151053 | + | 0.151053i | ||||
\(994\) | 19.4848i | 0.618021i | ||||||||
\(995\) | −17.2676 | − | 1.97239i | −0.547420 | − | 0.0625291i | ||||
\(996\) | − | 5.47649i | − | 0.173529i | ||||||
\(997\) | −21.5242 | + | 21.5242i | −0.681678 | + | 0.681678i | −0.960378 | − | 0.278701i | \(-0.910096\pi\) |
0.278701 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(998\) | 13.4676 | − | 13.4676i | 0.426309 | − | 0.426309i | ||||
\(999\) | − | 6.49122i | − | 0.205373i |
(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 | 570.2.m.a.493.8 | yes | 20 | |
3.2 | odd | 2 | 1710.2.p.d.1063.3 | 20 | |||
5.2 | odd | 4 | inner | 570.2.m.a.37.3 | ✓ | 20 | |
15.2 | even | 4 | 1710.2.p.d.37.8 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.a.493.3 | yes | 20 | |
57.56 | even | 2 | 1710.2.p.d.1063.8 | 20 | |||
95.37 | even | 4 | inner | 570.2.m.a.37.8 | yes | 20 | |
285.227 | odd | 4 | 1710.2.p.d.37.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.3 | ✓ | 20 | 5.2 | odd | 4 | inner | |
570.2.m.a.37.8 | yes | 20 | 95.37 | even | 4 | inner | |
570.2.m.a.493.3 | yes | 20 | 19.18 | odd | 2 | inner | |
570.2.m.a.493.8 | yes | 20 | 1.1 | even | 1 | trivial | |
1710.2.p.d.37.3 | 20 | 285.227 | odd | 4 | |||
1710.2.p.d.37.8 | 20 | 15.2 | even | 4 | |||
1710.2.p.d.1063.3 | 20 | 3.2 | odd | 2 | |||
1710.2.p.d.1063.8 | 20 | 57.56 | even | 2 |