Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(37,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, 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("1710.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.p (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: | \(13.6544187456\) |
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: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.8 | ||
Root | \(1.75036 - 1.75036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.37 |
Dual form | 1710.2.p.d.1063.8 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.253765 | + | 2.22162i | 0.113487 | + | 0.993539i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47539 | − | 2.47539i | −0.935608 | − | 0.935608i | 0.0624406 | − | 0.998049i | \(-0.480112\pi\) |
−0.998049 | + | 0.0624406i | \(0.980112\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.75036 | + | 1.39149i | 0.553513 | + | 0.440026i | ||||
\(11\) | −2.74367 | −0.827247 | −0.413624 | − | 0.910448i | \(-0.635737\pi\) | ||||
−0.413624 | + | 0.910448i | \(0.635737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.20178 | + | 1.20178i | 0.333314 | + | 0.333314i | 0.853844 | − | 0.520530i | \(-0.174265\pi\) |
−0.520530 | + | 0.853844i | \(0.674265\pi\) | |||||||
\(14\) | −3.50073 | −0.935608 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.87121 | + | 4.87121i | 1.18144 | + | 1.18144i | 0.979371 | + | 0.202070i | \(0.0647669\pi\) |
0.202070 | + | 0.979371i | \(0.435233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94007 | + | 3.90335i | −0.445082 | + | 0.895490i | ||||
\(20\) | 2.22162 | − | 0.253765i | 0.496770 | − | 0.0567435i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.94007 | + | 1.94007i | −0.413624 | + | 0.413624i | ||||
\(23\) | −0.0321428 | + | 0.0321428i | −0.00670223 | + | 0.00670223i | −0.710450 | − | 0.703748i | \(-0.751509\pi\) |
0.703748 | + | 0.710450i | \(0.251509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87121 | + | 1.12754i | −0.974241 | + | 0.225508i | ||||
\(26\) | 1.69957 | 0.333314 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −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 | 0 | ||||||||
\(31\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.88893 | 1.18144 | ||||||||
\(35\) | 4.87121 | − | 6.12754i | 0.823384 | − | 1.03574i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.58998 | + | 4.58998i | −0.754589 | + | 0.754589i | −0.975332 | − | 0.220743i | \(-0.929152\pi\) |
0.220743 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(38\) | 1.38825 | + | 4.13192i | 0.225204 | + | 0.670286i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.39149 | − | 1.75036i | 0.220013 | − | 0.276757i | ||||
\(41\) | 5.96665i | 0.931833i | 0.884829 | + | 0.465917i | \(0.154275\pi\) | ||||
−0.884829 | + | 0.465917i | \(0.845725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.39582 | − | 5.39582i | 0.822855 | − | 0.822855i | −0.163662 | − | 0.986517i | \(-0.552331\pi\) |
0.986517 | + | 0.163662i | \(0.0523305\pi\) | |||||||
\(44\) | 2.74367i | 0.413624i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0454567i | 0.00670223i | ||||||||
\(47\) | −3.66743 | − | 3.66743i | −0.534950 | − | 0.534950i | 0.387091 | − | 0.922041i | \(-0.373480\pi\) |
−0.922041 | + | 0.387091i | \(0.873480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.25508i | 0.750725i | ||||||||
\(50\) | −2.64717 | + | 4.24175i | −0.374367 | + | 0.599875i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.20178 | − | 1.20178i | 0.166657 | − | 0.166657i | ||||
\(53\) | 8.97544 | + | 8.97544i | 1.23287 | + | 1.23287i | 0.962856 | + | 0.270015i | \(0.0870288\pi\) |
0.270015 | + | 0.962856i | \(0.412971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.696246 | − | 6.09540i | −0.0938818 | − | 0.821903i | ||||
\(56\) | 3.50073i | 0.467804i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.60292 | − | 4.60292i | 0.604394 | − | 0.604394i | ||||
\(59\) | 4.42301 | 0.575826 | 0.287913 | − | 0.957657i | \(-0.407039\pi\) | ||||
0.287913 | + | 0.957657i | \(0.407039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.36493 | + | 2.97487i | −0.293334 | + | 0.368987i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00145 | + | 7.00145i | −0.855363 | + | 0.855363i | −0.990788 | − | 0.135424i | \(-0.956760\pi\) |
0.135424 | + | 0.990788i | \(0.456760\pi\) | |||||||
\(68\) | 4.87121 | − | 4.87121i | 0.590721 | − | 0.590721i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.888360 | − | 7.77729i | −0.106179 | − | 0.929564i | ||||
\(71\) | 5.56594i | 0.660556i | 0.943884 | + | 0.330278i | \(0.107142\pi\) | ||||
−0.943884 | + | 0.330278i | \(0.892858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.19205 | + | 2.19205i | −0.256560 | + | 0.256560i | −0.823653 | − | 0.567094i | \(-0.808068\pi\) |
0.567094 | + | 0.823653i | \(0.308068\pi\) | |||||||
\(74\) | 6.49122i | 0.754589i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.90335 | + | 1.94007i | 0.447745 | + | 0.222541i | ||||
\(77\) | 6.79164 | + | 6.79164i | 0.773979 | + | 0.773979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.225823 | 0.0254070 | 0.0127035 | − | 0.999919i | \(-0.495956\pi\) | ||||
0.0127035 | + | 0.999919i | \(0.495956\pi\) | |||||||
\(80\) | −0.253765 | − | 2.22162i | −0.0283717 | − | 0.248385i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.21906 | + | 4.21906i | 0.465917 | + | 0.465917i | ||||
\(83\) | 3.87246 | − | 3.87246i | 0.425058 | − | 0.425058i | −0.461883 | − | 0.886941i | \(-0.652826\pi\) |
0.886941 | + | 0.461883i | \(0.152826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.58584 | + | 12.0581i | −1.03973 | + | 1.30789i | ||||
\(86\) | − | 7.63084i | − | 0.822855i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.94007 | + | 1.94007i | 0.206812 | + | 0.206812i | ||||
\(89\) | −9.13628 | −0.968444 | −0.484222 | − | 0.874945i | \(-0.660897\pi\) | ||||
−0.484222 | + | 0.874945i | \(0.660897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.94974i | − | 0.623703i | ||||||
\(92\) | 0.0321428 | + | 0.0321428i | 0.00335112 | + | 0.00335112i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.18653 | −0.534950 | ||||||||
\(95\) | −9.16409 | − | 3.31956i | −0.940216 | − | 0.340580i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.76663 | − | 8.76663i | 0.890117 | − | 0.890117i | −0.104417 | − | 0.994534i | \(-0.533298\pi\) |
0.994534 | + | 0.104417i | \(0.0332976\pi\) | |||||||
\(98\) | 3.71590 | + | 3.71590i | 0.375363 | + | 0.375363i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.12754 | + | 4.87121i | 0.112754 | + | 0.487121i | ||||
\(101\) | −11.2650 | −1.12091 | −0.560455 | − | 0.828185i | \(-0.689374\pi\) | ||||
−0.560455 | + | 0.828185i | \(0.689374\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.762447 | − | 0.762447i | −0.0751262 | − | 0.0751262i | 0.668545 | − | 0.743671i | \(-0.266917\pi\) |
−0.743671 | + | 0.668545i | \(0.766917\pi\) | |||||||
\(104\) | − | 1.69957i | − | 0.166657i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.6932 | 1.23287 | ||||||||
\(107\) | −13.5351 | + | 13.5351i | −1.30849 | + | 1.30849i | −0.385985 | + | 0.922505i | \(0.626139\pi\) |
−0.922505 | + | 0.385985i | \(0.873861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.37207 | 0.418768 | 0.209384 | − | 0.977833i | \(-0.432854\pi\) | ||||
0.209384 | + | 0.977833i | \(0.432854\pi\) | |||||||
\(110\) | −4.80242 | − | 3.81777i | −0.457892 | − | 0.364011i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.47539 | + | 2.47539i | 0.233902 | + | 0.233902i | ||||
\(113\) | 6.95599 | + | 6.95599i | 0.654365 | + | 0.654365i | 0.954041 | − | 0.299676i | \(-0.0968786\pi\) |
−0.299676 | + | 0.954041i | \(0.596879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0795658 | − | 0.0632524i | −0.00741955 | − | 0.00589832i | ||||
\(116\) | − | 6.50952i | − | 0.604394i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.12754 | − | 3.12754i | 0.287913 | − | 0.287913i | ||||
\(119\) | − | 24.1162i | − | 2.21073i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.47228 | −0.315662 | ||||||||
\(122\) | −2.08651 | + | 2.08651i | −0.188904 | + | 0.188904i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.50952 | 0.584572 | ||||||||
\(125\) | −3.74110 | − | 10.5359i | −0.334614 | − | 0.942355i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7136 | + | 13.7136i | −1.21689 | + | 1.21689i | −0.248173 | + | 0.968716i | \(0.579830\pi\) |
−0.968716 | + | 0.248173i | \(0.920170\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.431292 | + | 3.77581i | 0.0378268 | + | 0.331161i | ||||
\(131\) | −8.01380 | −0.700169 | −0.350085 | − | 0.936718i | \(-0.613847\pi\) | ||||
−0.350085 | + | 0.936718i | \(0.613847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4647 | − | 4.85988i | 1.25425 | − | 0.421405i | ||||
\(134\) | 9.90155i | 0.855363i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 6.88893i | − | 0.590721i | ||||||
\(137\) | 12.6299 | + | 12.6299i | 1.07905 | + | 1.07905i | 0.996595 | + | 0.0824532i | \(0.0262755\pi\) |
0.0824532 | + | 0.996595i | \(0.473725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.3499i | − | 0.877869i | −0.898519 | − | 0.438934i | \(-0.855356\pi\) | ||
0.898519 | − | 0.438934i | \(-0.144644\pi\) | |||||||
\(140\) | −6.12754 | − | 4.87121i | −0.517871 | − | 0.411692i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.93571 | + | 3.93571i | 0.330278 | + | 0.330278i | ||||
\(143\) | −3.29729 | − | 3.29729i | −0.275733 | − | 0.275733i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.65189 | + | 14.4617i | 0.137182 | + | 1.20098i | ||||
\(146\) | 3.10002i | 0.256560i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.58998 | + | 4.58998i | 0.377294 | + | 0.377294i | ||||
\(149\) | − | 9.07466i | − | 0.743425i | −0.928348 | − | 0.371712i | \(-0.878771\pi\) | ||
0.928348 | − | 0.371712i | \(-0.121229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.75287i | 0.142647i | 0.997453 | + | 0.0713234i | \(0.0227222\pi\) | ||||
−0.997453 | + | 0.0713234i | \(0.977278\pi\) | |||||||
\(152\) | 4.13192 | − | 1.38825i | 0.335143 | − | 0.112602i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.60483 | 0.773979 | ||||||||
\(155\) | −14.4617 | + | 1.65189i | −1.16159 | + | 0.132683i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.20733 | + | 7.20733i | 0.575207 | + | 0.575207i | 0.933579 | − | 0.358372i | \(-0.116668\pi\) |
−0.358372 | + | 0.933579i | \(0.616668\pi\) | |||||||
\(158\) | 0.159681 | − | 0.159681i | 0.0127035 | − | 0.0127035i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.75036 | − | 1.39149i | −0.138378 | − | 0.110007i | ||||
\(161\) | 0.159132 | 0.0125413 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.60292 | − | 9.60292i | 0.752159 | − | 0.752159i | −0.222723 | − | 0.974882i | \(-0.571494\pi\) |
0.974882 | + | 0.222723i | \(0.0714945\pi\) | |||||||
\(164\) | 5.96665 | 0.465917 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 5.47649i | − | 0.425058i | ||||||
\(167\) | 12.9013 | − | 12.9013i | 0.998336 | − | 0.998336i | −0.00166271 | − | 0.999999i | \(-0.500529\pi\) |
0.999999 | + | 0.00166271i | \(0.000529259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.1114i | − | 0.777804i | ||||||
\(170\) | 1.74817 | + | 15.3046i | 0.134078 | + | 1.17381i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.39582 | − | 5.39582i | −0.411427 | − | 0.411427i | ||||
\(173\) | 0.271593 | + | 0.271593i | 0.0206488 | + | 0.0206488i | 0.717356 | − | 0.696707i | \(-0.245352\pi\) |
−0.696707 | + | 0.717356i | \(0.745352\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.8492 | + | 9.26703i | 1.12249 | + | 0.700521i | ||||
\(176\) | 2.74367 | 0.206812 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −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 | 0 | ||||||||
\(181\) | − | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0454567 | 0.00335112 | ||||||||
\(185\) | −11.3620 | − | 9.03243i | −0.835349 | − | 0.664078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3650 | − | 13.3650i | −0.977344 | − | 0.977344i | ||||
\(188\) | −3.66743 | + | 3.66743i | −0.267475 | + | 0.267475i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.82727 | + | 4.13270i | −0.640398 | + | 0.299818i | ||||
\(191\) | −14.6162 | −1.05759 | −0.528795 | − | 0.848750i | \(-0.677356\pi\) | ||||
−0.528795 | + | 0.848750i | \(0.677356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.20432 | − | 6.20432i | −0.446597 | − | 0.446597i | 0.447625 | − | 0.894221i | \(-0.352270\pi\) |
−0.894221 | + | 0.447625i | \(0.852270\pi\) | |||||||
\(194\) | − | 12.3979i | − | 0.890117i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.25508 | 0.375363 | ||||||||
\(197\) | 9.77456 | + | 9.77456i | 0.696408 | + | 0.696408i | 0.963634 | − | 0.267226i | \(-0.0861069\pi\) |
−0.267226 | + | 0.963634i | \(0.586107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.77253i | − | 0.550980i | −0.961304 | − | 0.275490i | \(-0.911160\pi\) | ||
0.961304 | − | 0.275490i | \(-0.0888401\pi\) | |||||||
\(200\) | 4.24175 | + | 2.64717i | 0.299937 | + | 0.187183i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.96556 | + | 7.96556i | −0.560455 | + | 0.560455i | ||||
\(203\) | −16.1136 | − | 16.1136i | −1.13095 | − | 1.13095i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.2556 | + | 1.51412i | −0.925813 | + | 0.105751i | ||||
\(206\) | −1.07826 | −0.0751262 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.20178 | − | 1.20178i | −0.0833285 | − | 0.0833285i | ||||
\(209\) | 5.32290 | − | 10.7095i | 0.368193 | − | 0.740792i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.1416i | 1.30849i | ||||||||
\(215\) | 13.3567 | + | 10.6182i | 0.910922 | + | 0.724156i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1136 | − | 16.1136i | 1.09386 | − | 1.09386i | ||||
\(218\) | 3.09152 | − | 3.09152i | 0.209384 | − | 0.209384i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.09540 | + | 0.696246i | −0.410951 | + | 0.0469409i | ||||
\(221\) | 11.7082i | 0.787582i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3643 | + | 14.3643i | 0.961907 | + | 0.961907i | 0.999301 | − | 0.0373940i | \(-0.0119057\pi\) |
−0.0373940 | + | 0.999301i | \(0.511906\pi\) | |||||||
\(224\) | 3.50073 | 0.233902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.83726 | 0.654365 | ||||||||
\(227\) | −15.0385 | + | 15.0385i | −0.998139 | + | 0.998139i | −0.999998 | − | 0.00185921i | \(-0.999408\pi\) |
0.00185921 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.69570i | − | 0.178137i | −0.996026 | − | 0.0890683i | \(-0.971611\pi\) | ||
0.996026 | − | 0.0890683i | \(-0.0283890\pi\) | |||||||
\(230\) | −0.100988 | + | 0.0115353i | −0.00665893 | + | 0.000760616i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.60292 | − | 4.60292i | −0.302197 | − | 0.302197i | ||||
\(233\) | 12.4775 | − | 12.4775i | 0.817426 | − | 0.817426i | −0.168309 | − | 0.985734i | \(-0.553831\pi\) |
0.985734 | + | 0.168309i | \(0.0538306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.21698 | − | 9.07831i | 0.470784 | − | 0.592204i | ||||
\(236\) | − | 4.42301i | − | 0.287913i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.0528 | − | 17.0528i | −1.10537 | − | 1.10537i | ||||
\(239\) | 27.2150i | 1.76039i | 0.474613 | + | 0.880195i | \(0.342588\pi\) | ||||
−0.474613 | + | 0.880195i | \(0.657412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 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 | 0 | ||||||||
\(244\) | 2.95077i | 0.188904i | ||||||||
\(245\) | −11.6748 | + | 1.33355i | −0.745875 | + | 0.0851975i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.02251 | + | 2.35944i | −0.446831 | + | 0.150127i | ||||
\(248\) | 4.60292 | − | 4.60292i | 0.292286 | − | 0.292286i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0953 | − | 4.80461i | −0.638485 | − | 0.303870i | ||||
\(251\) | 2.30195 | 0.145298 | 0.0726489 | − | 0.997358i | \(-0.476855\pi\) | ||||
0.0726489 | + | 0.997358i | \(0.476855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0881891 | − | 0.0881891i | 0.00554440 | − | 0.00554440i | ||||
\(254\) | 19.3940i | 1.21689i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.7752 | − | 15.7752i | 0.984032 | − | 0.984032i | −0.0158429 | − | 0.999874i | \(-0.505043\pi\) |
0.999874 | + | 0.0158429i | \(0.00504315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.7240 | 1.41200 | ||||||||
\(260\) | 2.97487 | + | 2.36493i | 0.184494 | + | 0.146667i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.66661 | + | 5.66661i | −0.350085 | + | 0.350085i | ||||
\(263\) | 1.21906 | − | 1.21906i | 0.0751702 | − | 0.0751702i | −0.668522 | − | 0.743692i | \(-0.733073\pi\) |
0.743692 | + | 0.668522i | \(0.233073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.6624 | + | 22.2177i | −1.08499 | + | 1.36482i | ||||
\(266\) | 6.79164 | − | 13.6646i | 0.416422 | − | 0.837828i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00145 | + | 7.00145i | 0.427682 | + | 0.427682i | ||||
\(269\) | −7.58430 | −0.462423 | −0.231211 | − | 0.972904i | \(-0.574269\pi\) | ||||
−0.231211 | + | 0.972904i | \(0.574269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8614 | 1.07905 | ||||||||
\(275\) | 13.3650 | − | 3.09359i | 0.805939 | − | 0.186551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7414 | − | 21.7414i | −1.30631 | − | 1.30631i | −0.924056 | − | 0.382257i | \(-0.875147\pi\) |
−0.382257 | − | 0.924056i | \(-0.624853\pi\) | |||||||
\(278\) | −7.31850 | − | 7.31850i | −0.438934 | − | 0.438934i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.77729 | + | 0.888360i | −0.464782 | + | 0.0530897i | ||||
\(281\) | 21.9050i | 1.30674i | 0.757037 | + | 0.653372i | \(0.226646\pi\) | ||||
−0.757037 | + | 0.653372i | \(0.773354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7217 | − | 15.7217i | 0.934557 | − | 0.934557i | −0.0634298 | − | 0.997986i | \(-0.520204\pi\) |
0.997986 | + | 0.0634298i | \(0.0202039\pi\) | |||||||
\(284\) | 5.56594 | 0.330278 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.66307 | −0.275733 | ||||||||
\(287\) | 14.7698 | − | 14.7698i | 0.871831 | − | 0.871831i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.4573i | 1.79161i | ||||||||
\(290\) | 11.3940 | + | 9.05790i | 0.669080 | + | 0.531898i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.19205 | + | 2.19205i | 0.128280 | + | 0.128280i | ||||
\(293\) | −8.25768 | − | 8.25768i | −0.482419 | − | 0.482419i | 0.423484 | − | 0.905903i | \(-0.360807\pi\) |
−0.905903 | + | 0.423484i | \(0.860807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.12240 | + | 9.82625i | 0.0653488 | + | 0.572106i | ||||
\(296\) | 6.49122 | 0.377294 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.41675 | − | 6.41675i | −0.371712 | − | 0.371712i | ||||
\(299\) | −0.0772571 | −0.00446790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.7135 | −1.53974 | ||||||||
\(302\) | 1.23947 | + | 1.23947i | 0.0713234 | + | 0.0713234i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.94007 | − | 3.90335i | 0.111270 | − | 0.223872i | ||||
\(305\) | −0.748802 | − | 6.55550i | −0.0428763 | − | 0.375367i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1239 | − | 22.1239i | 1.26268 | − | 1.26268i | 0.312887 | − | 0.949790i | \(-0.398704\pi\) |
0.949790 | − | 0.312887i | \(-0.101296\pi\) | |||||||
\(308\) | 6.79164 | − | 6.79164i | 0.386990 | − | 0.386990i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.05790 | + | 11.3940i | −0.514454 | + | 0.647137i | ||||
\(311\) | −3.22108 | −0.182651 | −0.0913254 | − | 0.995821i | \(-0.529110\pi\) | ||||
−0.0913254 | + | 0.995821i | \(0.529110\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9801 | + | 14.9801i | −0.846724 | + | 0.846724i | −0.989723 | − | 0.142999i | \(-0.954326\pi\) |
0.142999 | + | 0.989723i | \(0.454326\pi\) | |||||||
\(314\) | 10.1927 | 0.575207 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 0.225823i | − | 0.0127035i | ||||||
\(317\) | −13.3317 | + | 13.3317i | −0.748782 | + | 0.748782i | −0.974251 | − | 0.225468i | \(-0.927609\pi\) |
0.225468 | + | 0.974251i | \(0.427609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.8600 | −0.999966 | ||||||||
\(320\) | −2.22162 | + | 0.253765i | −0.124192 | + | 0.0141859i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.112523 | − | 0.112523i | 0.00627066 | − | 0.00627066i | ||||
\(323\) | −28.4645 | + | 9.56356i | −1.58381 | + | 0.532131i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.20918 | − | 4.49907i | −0.399893 | − | 0.249563i | ||||
\(326\) | − | 13.5806i | − | 0.752159i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.21906 | − | 4.21906i | 0.232958 | − | 0.232958i | ||||
\(329\) | 18.1566i | 1.00101i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 18.2453i | − | 0.998336i | ||||||
\(335\) | −17.3313 | − | 13.7779i | −0.946910 | − | 0.752765i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1501 | + | 14.1501i | −0.770806 | + | 0.770806i | −0.978247 | − | 0.207441i | \(-0.933486\pi\) |
0.207441 | + | 0.978247i | \(0.433486\pi\) | |||||||
\(338\) | −7.14987 | − | 7.14987i | −0.388902 | − | 0.388902i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.0581 | + | 9.58584i | 0.653943 | + | 0.519865i | ||||
\(341\) | − | 17.8600i | − | 0.967171i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.31936 | + | 4.31936i | −0.233224 | + | 0.233224i | ||||
\(344\) | −7.63084 | −0.411427 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.384091 | 0.0206488 | ||||||||
\(347\) | −6.84109 | − | 6.84109i | −0.367249 | − | 0.367249i | 0.499224 | − | 0.866473i | \(-0.333618\pi\) |
−0.866473 | + | 0.499224i | \(0.833618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 33.2298i | − | 1.77875i | −0.457181 | − | 0.889374i | \(-0.651141\pi\) | ||
0.457181 | − | 0.889374i | \(-0.348859\pi\) | |||||||
\(350\) | 17.0528 | − | 3.94720i | 0.911508 | − | 0.210987i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.94007 | − | 1.94007i | 0.103406 | − | 0.103406i | ||||
\(353\) | −25.3639 | + | 25.3639i | −1.34999 | + | 1.34999i | −0.464318 | + | 0.885668i | \(0.653701\pi\) |
−0.885668 | + | 0.464318i | \(0.846299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3654 | + | 1.41244i | −0.656288 | + | 0.0749645i | ||||
\(356\) | 9.13628i | 0.484222i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.4228 | − | 11.4228i | 0.603715 | − | 0.603715i | ||||
\(359\) | − | 9.12994i | − | 0.481860i | −0.970543 | − | 0.240930i | \(-0.922548\pi\) | ||
0.970543 | − | 0.240930i | \(-0.0774524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4723 | − | 15.1455i | −0.603804 | − | 0.797133i | ||||
\(362\) | −11.4537 | − | 11.4537i | −0.601994 | − | 0.601994i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.94974 | −0.311851 | ||||||||
\(365\) | −5.42616 | − | 4.31363i | −0.284018 | − | 0.225786i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9778 | + | 12.9778i | 0.677435 | + | 0.677435i | 0.959419 | − | 0.281984i | \(-0.0909926\pi\) |
−0.281984 | + | 0.959419i | \(0.590993\pi\) | |||||||
\(368\) | 0.0321428 | − | 0.0321428i | 0.00167556 | − | 0.00167556i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.4210 | + | 1.64724i | −0.749713 | + | 0.0856360i | ||||
\(371\) | − | 44.4354i | − | 2.30697i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.92570 | − | 6.92570i | −0.358599 | − | 0.358599i | 0.504697 | − | 0.863296i | \(-0.331604\pi\) |
−0.863296 | + | 0.504697i | \(0.831604\pi\) | |||||||
\(374\) | −18.9009 | −0.977344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.18653i | 0.267475i | ||||||||
\(377\) | 7.82301 | + | 7.82301i | 0.402906 | + | 0.402906i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4882 | −1.15514 | −0.577570 | − | 0.816341i | \(-0.695999\pi\) | ||||
−0.577570 | + | 0.816341i | \(0.695999\pi\) | |||||||
\(380\) | −3.31956 | + | 9.16409i | −0.170290 | + | 0.470108i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.3352 | + | 10.3352i | −0.528795 | + | 0.528795i | ||||
\(383\) | 14.9680 | + | 14.9680i | 0.764830 | + | 0.764830i | 0.977191 | − | 0.212361i | \(-0.0681153\pi\) |
−0.212361 | + | 0.977191i | \(0.568115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.3650 | + | 16.8119i | −0.681142 | + | 0.856816i | ||||
\(386\) | −8.77423 | −0.446597 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.76663 | − | 8.76663i | −0.445058 | − | 0.445058i | ||||
\(389\) | − | 10.1897i | − | 0.516639i | −0.966060 | − | 0.258319i | \(-0.916831\pi\) | ||
0.966060 | − | 0.258319i | \(-0.0831687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.313148 | −0.0158366 | ||||||||
\(392\) | 3.71590 | − | 3.71590i | 0.187681 | − | 0.187681i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.8233 | 0.696408 | ||||||||
\(395\) | 0.0573058 | + | 0.501693i | 0.00288337 | + | 0.0252429i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9493 | + | 14.9493i | 0.750284 | + | 0.750284i | 0.974532 | − | 0.224248i | \(-0.0719927\pi\) |
−0.224248 | + | 0.974532i | \(0.571993\pi\) | |||||||
\(398\) | −5.49601 | − | 5.49601i | −0.275490 | − | 0.275490i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.87121 | − | 1.12754i | 0.243560 | − | 0.0563769i | ||||
\(401\) | 17.1894i | 0.858400i | 0.903210 | + | 0.429200i | \(0.141204\pi\) | ||||
−0.903210 | + | 0.429200i | \(0.858796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.82301 | + | 7.82301i | −0.389692 | + | 0.389692i | ||||
\(404\) | 11.2650i | 0.560455i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.7880 | −1.13095 | ||||||||
\(407\) | 12.5934 | − | 12.5934i | 0.624231 | − | 0.624231i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9489 | 1.18420 | 0.592099 | − | 0.805865i | \(-0.298299\pi\) | ||||
0.592099 | + | 0.805865i | \(0.298299\pi\) | |||||||
\(410\) | −8.30250 | + | 10.4438i | −0.410031 | + | 0.515782i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.762447 | + | 0.762447i | −0.0375631 | + | 0.0375631i | ||||
\(413\) | −10.9487 | − | 10.9487i | −0.538748 | − | 0.538748i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.58584 | + | 7.62045i | 0.470550 | + | 0.374073i | ||||
\(416\) | −1.69957 | −0.0833285 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.80890 | − | 11.3366i | −0.186299 | − | 0.554492i | ||||
\(419\) | 21.4134i | 1.04611i | 0.852298 | + | 0.523056i | \(0.175208\pi\) | ||||
−0.852298 | + | 0.523056i | \(0.824792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.6932i | − | 0.616436i | ||||||
\(425\) | −29.2211 | − | 18.2362i | −1.41743 | − | 0.884585i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.30430 | + | 7.30430i | 0.353480 | + | 0.353480i | ||||
\(428\) | 13.5351 | + | 13.5351i | 0.654245 | + | 0.654245i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.9528 | − | 1.93644i | 0.817539 | − | 0.0933833i | ||||
\(431\) | − | 29.5770i | − | 1.42467i | −0.701838 | − | 0.712337i | \(-0.747637\pi\) | ||
0.701838 | − | 0.712337i | \(-0.252363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7711 | + | 18.7711i | 0.902081 | + | 0.902081i | 0.995616 | − | 0.0935354i | \(-0.0298168\pi\) |
−0.0935354 | + | 0.995616i | \(0.529817\pi\) | |||||||
\(434\) | − | 22.7880i | − | 1.09386i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.37207i | − | 0.209384i | ||||||
\(437\) | −0.0631054 | − | 0.187824i | −0.00301874 | − | 0.00898482i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.66125 | −0.413379 | −0.206690 | − | 0.978407i | \(-0.566269\pi\) | ||||
−0.206690 | + | 0.978407i | \(0.566269\pi\) | |||||||
\(440\) | −3.81777 | + | 4.80242i | −0.182005 | + | 0.228946i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.27898 | + | 8.27898i | 0.393791 | + | 0.393791i | ||||
\(443\) | 19.5669 | − | 19.5669i | 0.929652 | − | 0.929652i | −0.0680315 | − | 0.997683i | \(-0.521672\pi\) |
0.997683 | + | 0.0680315i | \(0.0216718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.31847 | − | 20.2974i | −0.109906 | − | 0.962187i | ||||
\(446\) | 20.3142 | 0.961907 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.47539 | − | 2.47539i | 0.116951 | − | 0.116951i | ||||
\(449\) | 21.3429 | 1.00724 | 0.503618 | − | 0.863927i | \(-0.332002\pi\) | ||||
0.503618 | + | 0.863927i | \(0.332002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.3705i | − | 0.770857i | ||||||
\(452\) | 6.95599 | − | 6.95599i | 0.327182 | − | 0.327182i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.2676i | 0.998139i | ||||||||
\(455\) | 13.2181 | − | 1.50983i | 0.619673 | − | 0.0707821i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.3371 | + | 21.3371i | 0.998110 | + | 0.998110i | 0.999998 | − | 0.00188859i | \(-0.000601157\pi\) |
−0.00188859 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(458\) | −1.90615 | − | 1.90615i | −0.0890683 | − | 0.0890683i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0632524 | + | 0.0795658i | −0.00294916 | + | 0.00370977i | ||||
\(461\) | −0.603474 | −0.0281066 | −0.0140533 | − | 0.999901i | \(-0.504473\pi\) | ||||
−0.0140533 | + | 0.999901i | \(0.504473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8679 | + | 13.8679i | −0.644495 | + | 0.644495i | −0.951657 | − | 0.307162i | \(-0.900621\pi\) |
0.307162 | + | 0.951657i | \(0.400621\pi\) | |||||||
\(464\) | −6.50952 | −0.302197 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 17.6458i | − | 0.817426i | ||||||
\(467\) | −5.10843 | − | 5.10843i | −0.236390 | − | 0.236390i | 0.578964 | − | 0.815353i | \(-0.303457\pi\) |
−0.815353 | + | 0.578964i | \(0.803457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.6626 | 1.60057 | ||||||||
\(470\) | −1.31616 | − | 11.5225i | −0.0607098 | − | 0.531494i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.12754 | − | 3.12754i | −0.143957 | − | 0.143957i | ||||
\(473\) | −14.8043 | + | 14.8043i | −0.680705 | + | 0.680705i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.04929 | − | 21.2015i | 0.231677 | − | 0.972793i | ||||
\(476\) | −24.1162 | −1.10537 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | 0 | ||||||||
\(481\) | −11.0323 | −0.503030 | ||||||||
\(482\) | −17.7562 | − | 17.7562i | −0.808774 | − | 0.808774i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.47228i | 0.157831i | ||||||||
\(485\) | 21.7008 | + | 17.2515i | 0.985383 | + | 0.783350i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.31334 | − | 2.31334i | 0.104828 | − | 0.104828i | −0.652748 | − | 0.757575i | \(-0.726384\pi\) |
0.757575 | + | 0.652748i | \(0.226384\pi\) | |||||||
\(488\) | 2.08651 | + | 2.08651i | 0.0944519 | + | 0.0944519i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.31236 | + | 9.19829i | −0.330339 | + | 0.415536i | ||||
\(491\) | 0.0138034 | 0.000622939 | 0.000311469 | − | 1.00000i | \(-0.499901\pi\) | ||||
0.000311469 | 1.00000i | \(0.499901\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.7092 | + | 31.7092i | 1.42811 | + | 1.42811i | ||||
\(494\) | −3.29729 | + | 6.63403i | −0.148352 | + | 0.298479i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.50952i | − | 0.292286i | ||||||
\(497\) | 13.7779 | − | 13.7779i | 0.618021 | − | 0.618021i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0461i | 0.852619i | 0.904577 | + | 0.426309i | \(0.140187\pi\) | ||||
−0.904577 | + | 0.426309i | \(0.859813\pi\) | |||||||
\(500\) | −10.5359 | + | 3.74110i | −0.471178 | + | 0.167307i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.62772 | − | 1.62772i | 0.0726489 | − | 0.0726489i | ||||
\(503\) | 15.5475 | − | 15.5475i | 0.693230 | − | 0.693230i | −0.269711 | − | 0.962941i | \(-0.586928\pi\) |
0.962941 | + | 0.269711i | \(0.0869282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.85866 | − | 25.0266i | −0.127209 | − | 1.11367i | ||||
\(506\) | − | 0.124718i | − | 0.00554440i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.7136 | + | 13.7136i | 0.608444 | + | 0.608444i | ||||
\(509\) | 4.08859 | 0.181224 | 0.0906118 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906118 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8523 | 0.480078 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 22.3095i | − | 0.984032i | ||||||
\(515\) | 1.50039 | − | 1.88735i | 0.0661150 | − | 0.0831667i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0622 | + | 10.0622i | 0.442536 | + | 0.442536i | ||||
\(518\) | 16.0683 | − | 16.0683i | 0.705999 | − | 0.705999i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.77581 | − | 0.431292i | 0.165580 | − | 0.0189134i | ||||
\(521\) | − | 29.8730i | − | 1.30876i | −0.756166 | − | 0.654380i | \(-0.772930\pi\) | ||
0.756166 | − | 0.654380i | \(-0.227070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.1935 | + | 20.1935i | 0.883001 | + | 0.883001i | 0.993839 | − | 0.110837i | \(-0.0353532\pi\) |
−0.110837 | + | 0.993839i | \(0.535353\pi\) | |||||||
\(524\) | 8.01380i | 0.350085i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1.72400i | − | 0.0751702i | ||||||
\(527\) | −31.7092 | + | 31.7092i | −1.38127 | + | 1.38127i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9979i | 0.999910i | ||||||||
\(530\) | 3.22108 | + | 28.1995i | 0.139915 | + | 1.22491i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.85988 | − | 14.4647i | −0.210703 | − | 0.627125i | ||||
\(533\) | −7.17060 | + | 7.17060i | −0.310593 | + | 0.310593i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.5047 | − | 26.6352i | −1.44853 | − | 1.15154i | ||||
\(536\) | 9.90155 | 0.427682 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.36291 | + | 5.36291i | −0.231211 | + | 0.231211i | ||||
\(539\) | − | 14.4182i | − | 0.621035i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.88893 | −0.295360 | ||||||||
\(545\) | 1.10948 | + | 9.71308i | 0.0475247 | + | 0.416063i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.3457 | − | 13.3457i | 0.570622 | − | 0.570622i | −0.361680 | − | 0.932302i | \(-0.617797\pi\) |
0.932302 | + | 0.361680i | \(0.117797\pi\) | |||||||
\(548\) | 12.6299 | − | 12.6299i | 0.539524 | − | 0.539524i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.26297 | − | 11.6380i | 0.309694 | − | 0.496245i | ||||
\(551\) | −12.6289 | + | 25.4089i | −0.538009 | + | 1.08246i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.558998 | − | 0.558998i | −0.0237710 | − | 0.0237710i | ||||
\(554\) | −30.7470 | −1.30631 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.3499 | −0.438934 | ||||||||
\(557\) | 8.05867 | + | 8.05867i | 0.341457 | + | 0.341457i | 0.856915 | − | 0.515458i | \(-0.172378\pi\) |
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9692 | 0.548538 | ||||||||
\(560\) | −4.87121 | + | 6.12754i | −0.205846 | + | 0.258936i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.4892 | + | 15.4892i | 0.653372 | + | 0.653372i | ||||
\(563\) | 28.6648 | + | 28.6648i | 1.20808 | + | 1.20808i | 0.971648 | + | 0.236430i | \(0.0759775\pi\) |
0.236430 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6884 | + | 17.2188i | −0.575875 | + | 0.724399i | ||||
\(566\) | − | 22.2338i | − | 0.934557i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.93571 | − | 3.93571i | 0.165139 | − | 0.165139i | ||||
\(569\) | −8.54540 | −0.358242 | −0.179121 | − | 0.983827i | \(-0.557325\pi\) | ||||
−0.179121 | + | 0.983827i | \(0.557325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 20.8876i | − | 0.871831i | ||||||
\(575\) | 0.120332 | − | 0.192816i | 0.00501819 | − | 0.00804100i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1650 | + | 12.1650i | 0.506437 | + | 0.506437i | 0.913431 | − | 0.406994i | \(-0.133423\pi\) |
−0.406994 | + | 0.913431i | \(0.633423\pi\) | |||||||
\(578\) | 21.5366 | + | 21.5366i | 0.895803 | + | 0.895803i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.4617 | − | 1.65189i | 0.600489 | − | 0.0685908i | ||||
\(581\) | −19.1717 | −0.795375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.6256 | − | 24.6256i | −1.01989 | − | 1.01989i | ||||
\(584\) | 3.10002 | 0.128280 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6781 | −0.482419 | ||||||||
\(587\) | 5.32968 | + | 5.32968i | 0.219980 | + | 0.219980i | 0.808490 | − | 0.588510i | \(-0.200285\pi\) |
−0.588510 | + | 0.808490i | \(0.700285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.4089 | − | 12.6289i | −1.04696 | − | 0.520365i | ||||
\(590\) | 7.74186 | + | 6.15455i | 0.318728 | + | 0.253379i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.58998 | − | 4.58998i | 0.188647 | − | 0.188647i | ||||
\(593\) | 1.80818 | − | 1.80818i | 0.0742529 | − | 0.0742529i | −0.669005 | − | 0.743258i | \(-0.733280\pi\) |
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 53.5772 | − | 6.11985i | 2.19645 | − | 0.250889i | ||||
\(596\) | −9.07466 | −0.371712 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0546290 | + | 0.0546290i | −0.00223395 | + | 0.00223395i | ||||
\(599\) | 25.3131 | 1.03426 | 0.517132 | − | 0.855906i | \(-0.327000\pi\) | ||||
0.517132 | + | 0.855906i | \(0.327000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.75287 | 0.0713234 | ||||||||
\(605\) | −0.881142 | − | 7.71409i | −0.0358235 | − | 0.313622i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5164 | − | 11.5164i | 0.467435 | − | 0.467435i | −0.433647 | − | 0.901083i | \(-0.642774\pi\) |
0.901083 | + | 0.433647i | \(0.142774\pi\) | |||||||
\(608\) | −1.38825 | − | 4.13192i | −0.0563010 | − | 0.167571i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.16492 | − | 4.10596i | −0.209122 | − | 0.166245i | ||||
\(611\) | − | 8.81490i | − | 0.356613i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.66890 | + | 7.66890i | −0.309744 | + | 0.309744i | −0.844810 | − | 0.535066i | \(-0.820287\pi\) |
0.535066 | + | 0.844810i | \(0.320287\pi\) | |||||||
\(614\) | − | 31.2879i | − | 1.26268i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 9.60483i | − | 0.386990i | ||||||
\(617\) | −33.2792 | − | 33.2792i | −1.33977 | − | 1.33977i | −0.896278 | − | 0.443492i | \(-0.853740\pi\) |
−0.443492 | − | 0.896278i | \(-0.646260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.87513i | − | 0.155755i | −0.996963 | − | 0.0778774i | \(-0.975186\pi\) | ||
0.996963 | − | 0.0778774i | \(-0.0248143\pi\) | |||||||
\(620\) | 1.65189 | + | 14.4617i | 0.0663413 | + | 0.580795i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.27765 | + | 2.27765i | −0.0913254 | + | 0.0913254i | ||||
\(623\) | 22.6158 | + | 22.6158i | 0.906084 | + | 0.906084i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4573 | − | 10.9849i | 0.898293 | − | 0.439398i | ||||
\(626\) | 21.1850i | 0.846724i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.20733 | − | 7.20733i | 0.287604 | − | 0.287604i | ||||
\(629\) | −44.7175 | −1.78300 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.8539i | 0.748782i | ||||||||
\(635\) | −33.9466 | − | 26.9865i | −1.34713 | − | 1.07093i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.31545 | + | 6.31545i | −0.250227 | + | 0.250227i | ||||
\(638\) | −12.6289 | + | 12.6289i | −0.499983 | + | 0.499983i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.39149 | + | 1.75036i | −0.0550033 | + | 0.0691892i | ||||
\(641\) | 6.61503i | 0.261278i | 0.991430 | + | 0.130639i | \(0.0417029\pi\) | ||||
−0.991430 | + | 0.130639i | \(0.958297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.3608 | + | 30.3608i | −1.19731 | + | 1.19731i | −0.222347 | + | 0.974968i | \(0.571372\pi\) |
−0.974968 | + | 0.222347i | \(0.928628\pi\) | |||||||
\(644\) | − | 0.159132i | − | 0.00627066i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.3650 | + | 26.8899i | −0.525838 | + | 1.05797i | ||||
\(647\) | −5.83884 | − | 5.83884i | −0.229549 | − | 0.229549i | 0.582956 | − | 0.812504i | \(-0.301896\pi\) |
−0.812504 | + | 0.582956i | \(0.801896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.1353 | −0.476351 | ||||||||
\(650\) | −8.27898 | + | 1.91633i | −0.324728 | + | 0.0751648i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.60292 | − | 9.60292i | −0.376080 | − | 0.376080i | ||||
\(653\) | 19.7797 | − | 19.7797i | 0.774039 | − | 0.774039i | −0.204771 | − | 0.978810i | \(-0.565645\pi\) |
0.978810 | + | 0.204771i | \(0.0656449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.03362 | − | 17.8036i | −0.0794601 | − | 0.695646i | ||||
\(656\) | − | 5.96665i | − | 0.232958i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.8387 | + | 12.8387i | 0.500503 | + | 0.500503i | ||||
\(659\) | 8.44761 | 0.329072 | 0.164536 | − | 0.986371i | \(-0.447387\pi\) | ||||
0.164536 | + | 0.986371i | \(0.447387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.47649 | −0.212529 | ||||||||
\(665\) | 14.4675 | + | 30.9019i | 0.561024 | + | 1.19832i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.209234 | + | 0.209234i | −0.00810157 | + | 0.00810157i | ||||
\(668\) | −12.9013 | − | 12.9013i | −0.499168 | − | 0.499168i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.9975 | + | 2.51266i | −0.849837 | + | 0.0970726i | ||||
\(671\) | 8.09594 | 0.312540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.9422 | + | 31.9422i | 1.23128 | + | 1.23128i | 0.963471 | + | 0.267812i | \(0.0863005\pi\) |
0.267812 | + | 0.963471i | \(0.413700\pi\) | |||||||
\(674\) | 20.0113i | 0.770806i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1114 | −0.388902 | ||||||||
\(677\) | −11.7115 | + | 11.7115i | −0.450111 | + | 0.450111i | −0.895391 | − | 0.445280i | \(-0.853104\pi\) |
0.445280 | + | 0.895391i | \(0.353104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.4016 | −1.66560 | ||||||||
\(680\) | 15.3046 | − | 1.74817i | 0.586904 | − | 0.0670391i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.6289 | − | 12.6289i | −0.483586 | − | 0.483586i | ||||
\(683\) | −3.55375 | − | 3.55375i | −0.135981 | − | 0.135981i | 0.635840 | − | 0.771821i | \(-0.280654\pi\) |
−0.771821 | + | 0.635840i | \(0.780654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.8539 | + | 31.2640i | −0.949619 | + | 1.19453i | ||||
\(686\) | 6.10850i | 0.233224i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.39582 | + | 5.39582i | −0.205714 | + | 0.205714i | ||||
\(689\) | 21.5730i | 0.821867i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 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 | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.67476 | −0.367249 | ||||||||
\(695\) | 22.9936 | − | 2.62644i | 0.872197 | − | 0.0996267i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.0648 | + | 29.0648i | −1.10091 | + | 1.10091i | ||||
\(698\) | −23.4970 | − | 23.4970i | −0.889374 | − | 0.889374i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.26703 | − | 14.8492i | 0.350261 | − | 0.561247i | ||||
\(701\) | 10.3224 | 0.389873 | 0.194936 | − | 0.980816i | \(-0.437550\pi\) | ||||
0.194936 | + | 0.980816i | \(0.437550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.01143 | − | 26.8212i | −0.339873 | − | 1.01158i | ||||
\(704\) | − | 2.74367i | − | 0.103406i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.8700i | 1.34999i | ||||||||
\(707\) | 27.8852 | + | 27.8852i | 1.04873 | + | 1.04873i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.3223i | − | 0.387663i | −0.981035 | − | 0.193831i | \(-0.937909\pi\) | ||
0.981035 | − | 0.193831i | \(-0.0620915\pi\) | |||||||
\(710\) | −7.74492 | + | 9.74241i | −0.290662 | + | 0.365626i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.46033 | + | 6.46033i | 0.242111 | + | 0.242111i | ||||
\(713\) | −0.209234 | − | 0.209234i | −0.00783587 | − | 0.00783587i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.48859 | − | 8.16206i | 0.242660 | − | 0.305244i | ||||
\(716\) | − | 16.1543i | − | 0.603715i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.45584 | − | 6.45584i | −0.240930 | − | 0.240930i | ||||
\(719\) | − | 34.9029i | − | 1.30166i | −0.759224 | − | 0.650830i | \(-0.774421\pi\) | ||
0.759224 | − | 0.650830i | \(-0.225579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.77470i | 0.140577i | ||||||||
\(722\) | −18.8216 | − | 2.59737i | −0.700468 | − | 0.0966642i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.1980 | −0.601994 | ||||||||
\(725\) | −31.7092 | + | 7.33973i | −1.17765 | + | 0.272591i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8595 | + | 12.8595i | 0.476932 | + | 0.476932i | 0.904149 | − | 0.427217i | \(-0.140506\pi\) |
−0.427217 | + | 0.904149i | \(0.640506\pi\) | |||||||
\(728\) | −4.20710 | + | 4.20710i | −0.155926 | + | 0.155926i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.88707 | + | 0.786675i | −0.254902 | + | 0.0291162i | ||||
\(731\) | 52.5683 | 1.94431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1047 | − | 11.1047i | 0.410162 | − | 0.410162i | −0.471633 | − | 0.881795i | \(-0.656335\pi\) |
0.881795 | + | 0.471633i | \(0.156335\pi\) | |||||||
\(734\) | 18.3534 | 0.677435 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.0454567i | − | 0.00167556i | ||||||
\(737\) | 19.2097 | − | 19.2097i | 0.707597 | − | 0.707597i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.1001i | − | 0.665823i | −0.942958 | − | 0.332911i | \(-0.891969\pi\) | ||
0.942958 | − | 0.332911i | \(-0.108031\pi\) | |||||||
\(740\) | −9.03243 | + | 11.3620i | −0.332039 | + | 0.417675i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.4205 | − | 31.4205i | −1.15348 | − | 1.15348i | ||||
\(743\) | 26.9208 | + | 26.9208i | 0.987630 | + | 0.987630i | 0.999924 | − | 0.0122949i | \(-0.00391368\pi\) |
−0.0122949 | + | 0.999924i | \(0.503914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1605 | − | 2.30283i | 0.738622 | − | 0.0843690i | ||||
\(746\) | −9.79442 | −0.358599 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.3650 | + | 13.3650i | −0.488672 | + | 0.488672i | ||||
\(749\) | 67.0093 | 2.44847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.0634 | 0.402906 | ||||||||
\(755\) | −3.89422 | + | 0.444817i | −0.141725 | + | 0.0161886i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.01763 | + | 3.01763i | 0.109678 | + | 0.109678i | 0.759816 | − | 0.650138i | \(-0.225289\pi\) |
−0.650138 | + | 0.759816i | \(0.725289\pi\) | |||||||
\(758\) | −15.9015 | + | 15.9015i | −0.577570 | + | 0.577570i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.13270 | + | 8.82727i | 0.149909 | + | 0.320199i | ||||
\(761\) | 11.1416 | 0.403881 | 0.201941 | − | 0.979398i | \(-0.435275\pi\) | ||||
0.201941 | + | 0.979398i | \(0.435275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8226 | − | 10.8226i | −0.391803 | − | 0.391803i | ||||
\(764\) | 14.6162i | 0.528795i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.1680 | 0.764830 | ||||||||
\(767\) | 5.31548 | + | 5.31548i | 0.191931 | + | 0.191931i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.8840i | 1.18583i | 0.805266 | + | 0.592913i | \(0.202022\pi\) | ||||
−0.805266 | + | 0.592913i | \(0.797978\pi\) | |||||||
\(770\) | 2.43737 | + | 21.3383i | 0.0878366 | + | 0.768979i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.20432 | + | 6.20432i | −0.223298 | + | 0.223298i | ||||
\(773\) | −31.2573 | − | 31.2573i | −1.12425 | − | 1.12425i | −0.991096 | − | 0.133152i | \(-0.957490\pi\) |
−0.133152 | − | 0.991096i | \(-0.542510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.33973 | − | 31.7092i | −0.263651 | − | 1.13903i | ||||
\(776\) | −12.3979 | −0.445058 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.20521 | − | 7.20521i | −0.258319 | − | 0.258319i | ||||
\(779\) | −23.2899 | − | 11.5757i | −0.834447 | − | 0.414742i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 15.2711i | − | 0.546443i | ||||||
\(782\) | −0.221429 | + | 0.221429i | −0.00791829 | + | 0.00791829i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.25508i | − | 0.187681i | ||||||
\(785\) | −14.1830 | + | 17.8409i | −0.506213 | + | 0.636770i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.28524 | + | 2.28524i | −0.0814600 | + | 0.0814600i | −0.746663 | − | 0.665203i | \(-0.768345\pi\) |
0.665203 | + | 0.746663i | \(0.268345\pi\) | |||||||
\(788\) | 9.77456 | − | 9.77456i | 0.348204 | − | 0.348204i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.395271 | + | 0.314229i | 0.0140631 | + | 0.0111798i | ||||
\(791\) | − | 34.4375i | − | 1.22446i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.54618 | − | 3.54618i | −0.125929 | − | 0.125929i | ||||
\(794\) | 21.1415 | 0.750284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.77253 | −0.275490 | ||||||||
\(797\) | 20.1327 | − | 20.1327i | 0.713137 | − | 0.713137i | −0.254054 | − | 0.967190i | \(-0.581764\pi\) |
0.967190 | + | 0.254054i | \(0.0817639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 35.7296i | − | 1.26402i | ||||||
\(800\) | 2.64717 | − | 4.24175i | 0.0935917 | − | 0.149969i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.1548 | + | 12.1548i | 0.429200 | + | 0.429200i | ||||
\(803\) | 6.01425 | − | 6.01425i | 0.212238 | − | 0.212238i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0403820 | + | 0.353530i | 0.00142328 | + | 0.0124603i | ||||
\(806\) | 11.0634i | 0.389692i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.96556 | + | 7.96556i | 0.280227 | + | 0.280227i | ||||
\(809\) | − | 19.9089i | − | 0.699958i | −0.936758 | − | 0.349979i | \(-0.886189\pi\) | ||
0.936758 | − | 0.349979i | \(-0.113811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 17.8097i | − | 0.624231i | ||||||
\(815\) | 23.7709 | + | 18.8972i | 0.832660 | + | 0.661939i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5935 | + | 31.5300i | 0.370620 | + | 1.10310i | ||||
\(818\) | 16.9345 | − | 16.9345i | 0.592099 | − | 0.592099i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.51412 | + | 13.2556i | 0.0528755 | + | 0.462907i | ||||
\(821\) | 16.0769 | 0.561089 | 0.280545 | − | 0.959841i | \(-0.409485\pi\) | ||||
0.280545 | + | 0.959841i | \(0.409485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.761023 | − | 0.761023i | 0.0265276 | − | 0.0265276i | −0.693719 | − | 0.720246i | \(-0.744029\pi\) |
0.720246 | + | 0.693719i | \(0.244029\pi\) | |||||||
\(824\) | 1.07826i | 0.0375631i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.4837 | −0.538748 | ||||||||
\(827\) | −20.8201 | + | 20.8201i | −0.723984 | + | 0.723984i | −0.969414 | − | 0.245430i | \(-0.921071\pi\) |
0.245430 | + | 0.969414i | \(0.421071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.8887 | −1.10754 | −0.553771 | − | 0.832669i | \(-0.686812\pi\) | ||||
−0.553771 | + | 0.832669i | \(0.686812\pi\) | |||||||
\(830\) | 12.1667 | − | 1.38974i | 0.422312 | − | 0.0482385i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.20178 | + | 1.20178i | −0.0416642 | + | 0.0416642i | ||||
\(833\) | −25.5986 | + | 25.5986i | −0.886938 | + | 0.886938i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.9358 | + | 25.3880i | 1.10518 | + | 0.878588i | ||||
\(836\) | −10.7095 | − | 5.32290i | −0.370396 | − | 0.184096i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.1416 | + | 15.1416i | 0.523056 | + | 0.523056i | ||||
\(839\) | −39.4110 | −1.36062 | −0.680310 | − | 0.732924i | \(-0.738155\pi\) | ||||
−0.680310 | + | 0.732924i | \(0.738155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.3738 | 0.461166 | ||||||||
\(842\) | 1.22053 | + | 1.22053i | 0.0420623 | + | 0.0420623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.91902 | −0.272584 | ||||||||
\(845\) | 22.4638 | − | 2.56593i | 0.772779 | − | 0.0882706i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.59523 | + | 8.59523i | 0.295336 | + | 0.295336i | ||||
\(848\) | −8.97544 | − | 8.97544i | −0.308218 | − | 0.308218i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.5574 | + | 7.76753i | −1.15101 | + | 0.266424i | ||||
\(851\) | − | 0.295070i | − | 0.0101149i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.3272 | − | 29.3272i | 1.00414 | − | 1.00414i | 0.00415191 | − | 0.999991i | \(-0.498678\pi\) |
0.999991 | − | 0.00415191i | \(-0.00132160\pi\) | |||||||
\(854\) | 10.3298 | 0.353480 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1416 | 0.654245 | ||||||||
\(857\) | −22.6621 | + | 22.6621i | −0.774121 | + | 0.774121i | −0.978824 | − | 0.204703i | \(-0.934377\pi\) |
0.204703 | + | 0.978824i | \(0.434377\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.13130i | 0.311556i | 0.987792 | + | 0.155778i | \(0.0497884\pi\) | ||||
−0.987792 | + | 0.155778i | \(0.950212\pi\) | |||||||
\(860\) | 10.6182 | − | 13.3567i | 0.362078 | − | 0.455461i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.9141 | − | 20.9141i | −0.712337 | − | 0.712337i | ||||
\(863\) | 31.2115 | + | 31.2115i | 1.06245 | + | 1.06245i | 0.997915 | + | 0.0645382i | \(0.0205574\pi\) |
0.0645382 | + | 0.997915i | \(0.479443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.534456 | + | 0.672298i | −0.0181721 | + | 0.0228588i | ||||
\(866\) | 26.5463 | 0.902081 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.1136 | − | 16.1136i | −0.546930 | − | 0.546930i | ||||
\(869\) | −0.619583 | −0.0210179 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8284 | −0.570209 | ||||||||
\(872\) | −3.09152 | − | 3.09152i | −0.104692 | − | 0.104692i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.177434 | − | 0.0881891i | −0.00600178 | − | 0.00298304i | ||||
\(875\) | −16.8196 | + | 35.3410i | −0.568607 | + | 1.19474i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7226 | + | 15.7226i | −0.530916 | + | 0.530916i | −0.920845 | − | 0.389929i | \(-0.872500\pi\) |
0.389929 | + | 0.920845i | \(0.372500\pi\) | |||||||
\(878\) | −6.12443 | + | 6.12443i | −0.206690 | + | 0.206690i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.696246 | + | 6.09540i | 0.0234705 | + | 0.205476i | ||||
\(881\) | 12.7472 | 0.429464 | 0.214732 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214732 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.1600 | − | 26.1600i | 0.880352 | − | 0.880352i | −0.113218 | − | 0.993570i | \(-0.536116\pi\) |
0.993570 | + | 0.113218i | \(0.0361158\pi\) | |||||||
\(884\) | 11.7082 | 0.393791 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 27.6718i | − | 0.929652i | ||||||
\(887\) | 3.63787 | − | 3.63787i | 0.122148 | − | 0.122148i | −0.643390 | − | 0.765538i | \(-0.722473\pi\) |
0.765538 | + | 0.643390i | \(0.222473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.8931 | 2.27706 | ||||||||
\(890\) | −15.9918 | − | 12.7130i | −0.536047 | − | 0.426141i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.3643 | − | 14.3643i | 0.480953 | − | 0.480953i | ||||
\(893\) | 21.4303 | − | 7.20021i | 0.717139 | − | 0.240946i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.09940 | + | 35.8888i | 0.137028 | + | 1.19963i | ||||
\(896\) | − | 3.50073i | − | 0.116951i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0917 | − | 15.0917i | 0.503618 | − | 0.503618i | ||||
\(899\) | 42.3738i | 1.41325i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 87.4424i | 2.91313i | ||||||||
\(902\) | −11.5757 | − | 11.5757i | −0.385428 | − | 0.385428i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 9.83726i | − | 0.327182i | ||||||
\(905\) | 35.9858 | − | 4.11048i | 1.19621 | − | 0.136637i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.2643 | − | 27.2643i | 0.905298 | − | 0.905298i | −0.0905904 | − | 0.995888i | \(-0.528875\pi\) |
0.995888 | + | 0.0905904i | \(0.0288754\pi\) | |||||||
\(908\) | 15.0385 | + | 15.0385i | 0.499070 | + | 0.499070i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.27898 | − | 10.4142i | 0.274445 | − | 0.345228i | ||||
\(911\) | − | 1.42099i | − | 0.0470796i | −0.999723 | − | 0.0235398i | \(-0.992506\pi\) | ||
0.999723 | − | 0.0235398i | \(-0.00749364\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.6248 | + | 10.6248i | −0.351628 | + | 0.351628i | ||||
\(914\) | 30.1753 | 0.998110 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.69570 | −0.0890683 | ||||||||
\(917\) | 19.8373 | + | 19.8373i | 0.655084 | + | 0.655084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.9380i | − | 1.28445i | −0.766518 | − | 0.642223i | \(-0.778012\pi\) | ||
0.766518 | − | 0.642223i | \(-0.221988\pi\) | |||||||
\(920\) | 0.0115353 | + | 0.100988i | 0.000380308 | + | 0.00332947i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.426720 | + | 0.426720i | −0.0140533 | + | 0.0140533i | ||||
\(923\) | −6.68904 | + | 6.68904i | −0.220172 | + | 0.220172i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1834 | − | 27.5341i | 0.564986 | − | 0.905317i | ||||
\(926\) | 19.6121i | 0.644495i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.60292 | + | 4.60292i | −0.151098 | + | 0.151098i | ||||
\(929\) | 23.8414i | 0.782211i | 0.920346 | + | 0.391106i | \(0.127907\pi\) | ||||
−0.920346 | + | 0.391106i | \(0.872093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.5124 | − | 10.1952i | −0.672267 | − | 0.334134i | ||||
\(932\) | −12.4775 | − | 12.4775i | −0.408713 | − | 0.408713i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.22441 | −0.236390 | ||||||||
\(935\) | 26.3004 | − | 33.0835i | 0.860114 | − | 1.08195i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2718 | − | 13.2718i | −0.433572 | − | 0.433572i | 0.456270 | − | 0.889842i | \(-0.349185\pi\) |
−0.889842 | + | 0.456270i | \(0.849185\pi\) | |||||||
\(938\) | 24.5102 | − | 24.5102i | 0.800285 | − | 0.800285i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.07831 | − | 7.21698i | −0.296102 | − | 0.235392i | ||||
\(941\) | 27.1173i | 0.884000i | 0.897015 | + | 0.442000i | \(0.145731\pi\) | ||||
−0.897015 | + | 0.442000i | \(0.854269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.191785 | − | 0.191785i | −0.00624536 | − | 0.00624536i | ||||
\(944\) | −4.42301 | −0.143957 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.9365i | 0.680705i | ||||||||
\(947\) | 12.0469 | + | 12.0469i | 0.391473 | + | 0.391473i | 0.875212 | − | 0.483739i | \(-0.160722\pi\) |
−0.483739 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.26872 | −0.171030 | ||||||||
\(950\) | −11.4214 | − | 18.5621i | −0.370558 | − | 0.602235i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.0528 | + | 17.0528i | −0.552683 | + | 0.552683i | ||||
\(953\) | 33.0593 | + | 33.0593i | 1.07090 | + | 1.07090i | 0.997287 | + | 0.0736082i | \(0.0234514\pi\) |
0.0736082 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.70907 | − | 32.4716i | −0.120023 | − | 1.05076i | ||||
\(956\) | 27.2150 | 0.880195 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.478542 | − | 0.478542i | −0.0154610 | − | 0.0154610i | ||||
\(959\) | − | 62.5279i | − | 2.01913i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3738 | −0.366898 | ||||||||
\(962\) | −7.80102 | + | 7.80102i | −0.251515 | + | 0.251515i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.1111 | −0.808774 | ||||||||
\(965\) | 12.2092 | − | 15.3581i | 0.393028 | − | 0.494394i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.66093 | + | 4.66093i | 0.149885 | + | 0.149885i | 0.778067 | − | 0.628181i | \(-0.216200\pi\) |
−0.628181 | + | 0.778067i | \(0.716200\pi\) | |||||||
\(968\) | 2.45527 | + | 2.45527i | 0.0789155 | + | 0.0789155i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27.5434 | − | 3.14615i | 0.884366 | − | 0.101017i | ||||
\(971\) | 11.8515i | 0.380332i | 0.981752 | + | 0.190166i | \(0.0609026\pi\) | ||||
−0.981752 | + | 0.190166i | \(0.939097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.6201 | + | 25.6201i | −0.821341 | + | 0.821341i | ||||
\(974\) | − | 3.27156i | − | 0.104828i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.95077 | 0.0944519 | ||||||||
\(977\) | 26.7920 | − | 26.7920i | 0.857153 | − | 0.857153i | −0.133849 | − | 0.991002i | \(-0.542734\pi\) |
0.991002 | + | 0.133849i | \(0.0427336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.0669 | 0.801143 | ||||||||
\(980\) | 1.33355 | + | 11.6748i | 0.0425988 | + | 0.372938i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.00976048 | − | 0.00976048i | 0.000311469 | − | 0.000311469i | ||||
\(983\) | −11.6066 | − | 11.6066i | −0.370193 | − | 0.370193i | 0.497354 | − | 0.867547i | \(-0.334305\pi\) |
−0.867547 | + | 0.497354i | \(0.834305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2349 | + | 24.1958i | −0.612876 | + | 0.770942i | ||||
\(986\) | 44.8436 | 1.42811 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.35944 | + | 7.02251i | 0.0750636 | + | 0.223416i | ||||
\(989\) | 0.346873i | 0.0110299i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 19.4848i | − | 0.618021i | ||||||
\(995\) | 17.2676 | − | 1.97239i | 0.547420 | − | 0.0625291i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.5242 | − | 21.5242i | −0.681678 | − | 0.681678i | 0.278701 | − | 0.960378i | \(-0.410096\pi\) |
−0.960378 | + | 0.278701i | \(0.910096\pi\) | |||||||
\(998\) | 13.4676 | + | 13.4676i | 0.426309 | + | 0.426309i | ||||
\(999\) | 0 | 0 |
(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 | 1710.2.p.d.37.8 | 20 | ||
3.2 | odd | 2 | 570.2.m.a.37.3 | ✓ | 20 | ||
5.3 | odd | 4 | inner | 1710.2.p.d.1063.3 | 20 | ||
15.8 | even | 4 | 570.2.m.a.493.8 | yes | 20 | ||
19.18 | odd | 2 | inner | 1710.2.p.d.37.3 | 20 | ||
57.56 | even | 2 | 570.2.m.a.37.8 | yes | 20 | ||
95.18 | even | 4 | inner | 1710.2.p.d.1063.8 | 20 | ||
285.113 | odd | 4 | 570.2.m.a.493.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.3 | ✓ | 20 | 3.2 | odd | 2 | ||
570.2.m.a.37.8 | yes | 20 | 57.56 | even | 2 | ||
570.2.m.a.493.3 | yes | 20 | 285.113 | odd | 4 | ||
570.2.m.a.493.8 | yes | 20 | 15.8 | even | 4 | ||
1710.2.p.d.37.3 | 20 | 19.18 | odd | 2 | inner | ||
1710.2.p.d.37.8 | 20 | 1.1 | even | 1 | trivial | ||
1710.2.p.d.1063.3 | 20 | 5.3 | odd | 4 | inner | ||
1710.2.p.d.1063.8 | 20 | 95.18 | even | 4 | inner |