Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 351.1 | ||
Root | \(-0.566185 + 0.980662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.351 |
Dual form | 475.2.l.c.226.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.370282 | − | 2.09998i | −0.261829 | − | 1.48491i | −0.777915 | − | 0.628370i | \(-0.783723\pi\) |
0.516086 | − | 0.856537i | \(-0.327389\pi\) | |||||||
\(3\) | −1.70859 | + | 1.43367i | −0.986452 | + | 0.827732i | −0.985050 | − | 0.172267i | \(-0.944891\pi\) |
−0.00140187 | + | 0.999999i | \(0.500446\pi\) | |||||||
\(4\) | −2.39340 | + | 0.871127i | −1.19670 | + | 0.435563i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.64334 | + | 3.05712i | 1.48739 | + | 1.24807i | ||||
\(7\) | 0.742812 | − | 1.28659i | 0.280757 | − | 0.486285i | −0.690815 | − | 0.723032i | \(-0.742748\pi\) |
0.971571 | + | 0.236747i | \(0.0760813\pi\) | |||||||
\(8\) | 0.583208 | + | 1.01015i | 0.206195 | + | 0.357140i | ||||
\(9\) | 0.342900 | − | 1.94468i | 0.114300 | − | 0.648227i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34068 | − | 4.05417i | −0.705741 | − | 1.22238i | −0.966424 | − | 0.256954i | \(-0.917281\pi\) |
0.260683 | − | 0.965424i | \(-0.416052\pi\) | |||||||
\(12\) | 2.84042 | − | 4.91975i | 0.819958 | − | 1.42021i | ||||
\(13\) | 0.276562 | + | 0.232063i | 0.0767046 | + | 0.0643628i | 0.680334 | − | 0.732902i | \(-0.261835\pi\) |
−0.603629 | + | 0.797265i | \(0.706279\pi\) | |||||||
\(14\) | −2.97685 | − | 1.08349i | −0.795598 | − | 0.289574i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.99691 | + | 1.67560i | −0.499227 | + | 0.418901i | ||||
\(17\) | 0.951255 | + | 5.39483i | 0.230713 | + | 1.30844i | 0.851456 | + | 0.524425i | \(0.175720\pi\) |
−0.620743 | + | 0.784014i | \(0.713169\pi\) | |||||||
\(18\) | −4.21075 | −0.992484 | ||||||||
\(19\) | −1.68540 | + | 4.01988i | −0.386658 | + | 0.922223i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.575390 | + | 3.26320i | 0.125560 | + | 0.712088i | ||||
\(22\) | −7.64695 | + | 6.41655i | −1.63033 | + | 1.36801i | ||||
\(23\) | −5.79545 | + | 2.10937i | −1.20843 | + | 0.439834i | −0.866161 | − | 0.499766i | \(-0.833419\pi\) |
−0.342274 | + | 0.939600i | \(0.611197\pi\) | |||||||
\(24\) | −2.44468 | − | 0.889790i | −0.499018 | − | 0.181628i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.384921 | − | 0.666703i | 0.0754892 | − | 0.130751i | ||||
\(27\) | −1.14343 | − | 1.98049i | −0.220054 | − | 0.381145i | ||||
\(28\) | −0.657066 | + | 3.72641i | −0.124174 | + | 0.704225i | ||||
\(29\) | −0.155581 | + | 0.882346i | −0.0288907 | + | 0.163848i | −0.995840 | − | 0.0911225i | \(-0.970955\pi\) |
0.966949 | + | 0.254970i | \(0.0820656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.40012 | + | 4.15713i | −0.431074 | + | 0.746642i | −0.996966 | − | 0.0778374i | \(-0.975199\pi\) |
0.565892 | + | 0.824479i | \(0.308532\pi\) | |||||||
\(32\) | 6.04520 | + | 5.07252i | 1.06865 | + | 0.896704i | ||||
\(33\) | 9.81160 | + | 3.57113i | 1.70798 | + | 0.621654i | ||||
\(34\) | 10.9768 | − | 3.99522i | 1.88250 | − | 0.685175i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.873368 | + | 4.95311i | 0.145561 | + | 0.825519i | ||||
\(37\) | −11.3982 | −1.87385 | −0.936924 | − | 0.349534i | \(-0.886340\pi\) | ||||
−0.936924 | + | 0.349534i | \(0.886340\pi\) | |||||||
\(38\) | 9.06572 | + | 2.05081i | 1.47065 | + | 0.332686i | ||||
\(39\) | −0.805233 | −0.128941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.01104 | + | 3.36566i | −0.626419 | + | 0.525628i | −0.899814 | − | 0.436274i | \(-0.856298\pi\) |
0.273395 | + | 0.961902i | \(0.411853\pi\) | |||||||
\(42\) | 6.63958 | − | 2.41661i | 1.02451 | − | 0.372891i | ||||
\(43\) | 6.78295 | + | 2.46879i | 1.03439 | + | 0.376487i | 0.802751 | − | 0.596314i | \(-0.203369\pi\) |
0.231639 | + | 0.972802i | \(0.425591\pi\) | |||||||
\(44\) | 9.13387 | + | 7.66423i | 1.37698 | + | 1.15543i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.57558 | + | 11.3892i | 0.969516 | + | 1.67925i | ||||
\(47\) | 1.88678 | − | 10.7005i | 0.275215 | − | 1.56082i | −0.463062 | − | 0.886326i | \(-0.653249\pi\) |
0.738278 | − | 0.674497i | \(-0.235639\pi\) | |||||||
\(48\) | 1.00962 | − | 5.72583i | 0.145726 | − | 0.826452i | ||||
\(49\) | 2.39646 | + | 4.15079i | 0.342351 | + | 0.592970i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.35973 | − | 7.85374i | −1.31062 | − | 1.09974i | ||||
\(52\) | −0.864081 | − | 0.314500i | −0.119827 | − | 0.0436133i | ||||
\(53\) | −6.12941 | + | 2.23092i | −0.841940 | + | 0.306441i | −0.726750 | − | 0.686902i | \(-0.758970\pi\) |
−0.115190 | + | 0.993343i | \(0.536748\pi\) | |||||||
\(54\) | −3.73558 | + | 3.13452i | −0.508348 | + | 0.426555i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.73286 | 0.231563 | ||||||||
\(57\) | −2.88354 | − | 9.28462i | −0.381934 | − | 1.22978i | ||||
\(58\) | 1.91051 | 0.250863 | ||||||||
\(59\) | −1.70300 | − | 9.65818i | −0.221711 | − | 1.25739i | −0.868873 | − | 0.495035i | \(-0.835155\pi\) |
0.647162 | − | 0.762353i | \(-0.275956\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.20795 | + | 0.803626i | −0.282698 | + | 0.102894i | −0.479478 | − | 0.877554i | \(-0.659174\pi\) |
0.196779 | + | 0.980448i | \(0.436952\pi\) | |||||||
\(62\) | 9.61858 | + | 3.50088i | 1.22156 | + | 0.444612i | ||||
\(63\) | −2.24730 | − | 1.88571i | −0.283133 | − | 0.237577i | ||||
\(64\) | 5.80697 | − | 10.0580i | 0.725871 | − | 1.25725i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.86622 | − | 21.9264i | 0.475899 | − | 2.69896i | ||||
\(67\) | −1.53717 | + | 8.71774i | −0.187796 | + | 1.06504i | 0.734515 | + | 0.678592i | \(0.237410\pi\) |
−0.922311 | + | 0.386449i | \(0.873701\pi\) | |||||||
\(68\) | −6.97632 | − | 12.0833i | −0.846003 | − | 1.46532i | ||||
\(69\) | 6.87787 | − | 11.9128i | 0.827998 | − | 1.43414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.02538 | − | 2.19306i | −0.715081 | − | 0.260268i | −0.0412447 | − | 0.999149i | \(-0.513132\pi\) |
−0.673836 | + | 0.738881i | \(0.735355\pi\) | |||||||
\(72\) | 2.16439 | − | 0.787775i | 0.255076 | − | 0.0928402i | ||||
\(73\) | −2.19219 | + | 1.83946i | −0.256576 | + | 0.215293i | −0.761998 | − | 0.647580i | \(-0.775781\pi\) |
0.505422 | + | 0.862872i | \(0.331337\pi\) | |||||||
\(74\) | 4.22054 | + | 23.9359i | 0.490628 | + | 2.78249i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.532020 | − | 11.0894i | 0.0610268 | − | 1.27204i | ||||
\(77\) | −6.95473 | −0.792566 | ||||||||
\(78\) | 0.298164 | + | 1.69097i | 0.0337604 | + | 0.191465i | ||||
\(79\) | 1.58226 | − | 1.32767i | 0.178018 | − | 0.149375i | −0.549425 | − | 0.835543i | \(-0.685153\pi\) |
0.727443 | + | 0.686168i | \(0.240709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.3598 | + | 3.77066i | 1.15109 | + | 0.418962i | ||||
\(82\) | 8.55302 | + | 7.17684i | 0.944523 | + | 0.792549i | ||||
\(83\) | 3.08199 | − | 5.33816i | 0.338292 | − | 0.585939i | −0.645820 | − | 0.763490i | \(-0.723484\pi\) |
0.984112 | + | 0.177551i | \(0.0568176\pi\) | |||||||
\(84\) | −4.21980 | − | 7.30890i | −0.460418 | − | 0.797467i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.67280 | − | 15.1582i | 0.288215 | − | 1.63455i | ||||
\(87\) | −0.999172 | − | 1.73062i | −0.107122 | − | 0.185542i | ||||
\(88\) | 2.73020 | − | 4.72885i | 0.291040 | − | 0.504097i | ||||
\(89\) | −2.54338 | − | 2.13415i | −0.269598 | − | 0.226220i | 0.497959 | − | 0.867201i | \(-0.334083\pi\) |
−0.767556 | + | 0.640981i | \(0.778528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.504004 | − | 0.183442i | 0.0528340 | − | 0.0192300i | ||||
\(92\) | 12.0333 | − | 10.0971i | 1.25456 | − | 1.05270i | ||||
\(93\) | −1.85915 | − | 10.5438i | −0.192785 | − | 1.09334i | ||||
\(94\) | −23.1693 | −2.38974 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −17.6011 | −1.79640 | ||||||||
\(97\) | −0.819060 | − | 4.64512i | −0.0831630 | − | 0.471641i | −0.997738 | − | 0.0672241i | \(-0.978586\pi\) |
0.914575 | − | 0.404416i | \(-0.132525\pi\) | |||||||
\(98\) | 7.82919 | − | 6.56947i | 0.790867 | − | 0.663617i | ||||
\(99\) | −8.68669 | + | 3.16170i | −0.873045 | + | 0.317762i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.92692 | + | 5.81237i | 0.689254 | + | 0.578353i | 0.918694 | − | 0.394970i | \(-0.129245\pi\) |
−0.229440 | + | 0.973323i | \(0.573690\pi\) | |||||||
\(102\) | −13.0269 | + | 22.5633i | −1.28986 | + | 2.23410i | ||||
\(103\) | 3.89934 | + | 6.75385i | 0.384213 | + | 0.665476i | 0.991660 | − | 0.128884i | \(-0.0411395\pi\) |
−0.607447 | + | 0.794360i | \(0.707806\pi\) | |||||||
\(104\) | −0.0731245 | + | 0.414709i | −0.00717044 | + | 0.0406656i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.95450 | + | 12.0455i | 0.675481 | + | 1.16997i | ||||
\(107\) | 0.259152 | − | 0.448864i | 0.0250531 | − | 0.0433933i | −0.853227 | − | 0.521540i | \(-0.825358\pi\) |
0.878280 | + | 0.478146i | \(0.158691\pi\) | |||||||
\(108\) | 4.46195 | + | 3.74402i | 0.429352 | + | 0.360269i | ||||
\(109\) | 2.59771 | + | 0.945488i | 0.248815 | + | 0.0905614i | 0.463417 | − | 0.886140i | \(-0.346623\pi\) |
−0.214602 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.4747 | − | 16.3413i | 1.84846 | − | 1.55104i | ||||
\(112\) | 0.672486 | + | 3.81386i | 0.0635440 | + | 0.360376i | ||||
\(113\) | −12.4325 | −1.16955 | −0.584774 | − | 0.811197i | \(-0.698817\pi\) | ||||
−0.584774 | + | 0.811197i | \(0.698817\pi\) | |||||||
\(114\) | −18.4297 | + | 9.49329i | −1.72610 | + | 0.889128i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.396266 | − | 2.24734i | −0.0367924 | − | 0.208660i | ||||
\(117\) | 0.546123 | − | 0.458251i | 0.0504891 | − | 0.0423654i | ||||
\(118\) | −19.6513 | + | 7.15250i | −1.80905 | + | 0.658441i | ||||
\(119\) | 7.64754 | + | 2.78348i | 0.701049 | + | 0.255161i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.45753 | + | 9.45272i | −0.496139 | + | 0.859339i | ||||
\(122\) | 2.50516 | + | 4.33906i | 0.226806 | + | 0.392840i | ||||
\(123\) | 2.02794 | − | 11.5010i | 0.182853 | − | 1.03701i | ||||
\(124\) | 2.12306 | − | 12.0405i | 0.190656 | − | 1.08127i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.12780 | + | 5.41751i | −0.278647 | + | 0.482630i | ||||
\(127\) | 1.04258 | + | 0.874829i | 0.0925141 | + | 0.0776285i | 0.687872 | − | 0.725832i | \(-0.258545\pi\) |
−0.595358 | + | 0.803461i | \(0.702990\pi\) | |||||||
\(128\) | −8.44062 | − | 3.07213i | −0.746052 | − | 0.271541i | ||||
\(129\) | −15.1287 | + | 5.50639i | −1.33201 | + | 0.484811i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.39033 | − | 19.2275i | −0.296214 | − | 1.67991i | −0.662226 | − | 0.749305i | \(-0.730388\pi\) |
0.366011 | − | 0.930610i | \(-0.380723\pi\) | |||||||
\(132\) | −26.5940 | −2.31471 | ||||||||
\(133\) | 3.91999 | + | 5.15444i | 0.339907 | + | 0.446946i | ||||
\(134\) | 18.8762 | 1.63066 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.89479 | + | 4.10721i | −0.419725 | + | 0.352191i | ||||
\(137\) | 10.0363 | − | 3.65291i | 0.857458 | − | 0.312089i | 0.124381 | − | 0.992235i | \(-0.460306\pi\) |
0.733077 | + | 0.680145i | \(0.238083\pi\) | |||||||
\(138\) | −27.5634 | − | 10.0323i | −2.34635 | − | 0.854002i | ||||
\(139\) | −5.50879 | − | 4.62243i | −0.467250 | − | 0.392069i | 0.378541 | − | 0.925585i | \(-0.376426\pi\) |
−0.845790 | + | 0.533516i | \(0.820871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1172 | + | 20.9877i | 1.02046 | + | 1.76748i | ||||
\(142\) | −2.37428 | + | 13.4652i | −0.199245 | + | 1.12997i | ||||
\(143\) | 0.293481 | − | 1.66442i | 0.0245422 | − | 0.139185i | ||||
\(144\) | 2.57378 | + | 4.45792i | 0.214482 | + | 0.371493i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.67455 | + | 3.92241i | 0.386869 | + | 0.324621i | ||||
\(147\) | −10.0454 | − | 3.65624i | −0.828533 | − | 0.301561i | ||||
\(148\) | 27.2804 | − | 9.92925i | 2.24243 | − | 0.816179i | ||||
\(149\) | 3.25360 | − | 2.73009i | 0.266545 | − | 0.223658i | −0.499713 | − | 0.866191i | \(-0.666561\pi\) |
0.766258 | + | 0.642533i | \(0.222117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5373 | −1.58992 | −0.794961 | − | 0.606660i | \(-0.792509\pi\) | ||||
−0.794961 | + | 0.606660i | \(0.792509\pi\) | |||||||
\(152\) | −5.04360 | + | 0.641923i | −0.409090 | + | 0.0520668i | ||||
\(153\) | 10.8174 | 0.874537 | ||||||||
\(154\) | 2.57521 | + | 14.6048i | 0.207517 | + | 1.17689i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.92725 | − | 0.701460i | 0.154303 | − | 0.0561618i | ||||
\(157\) | 0.269149 | + | 0.0979622i | 0.0214804 | + | 0.00781823i | 0.352738 | − | 0.935722i | \(-0.385251\pi\) |
−0.331258 | + | 0.943540i | \(0.607473\pi\) | |||||||
\(158\) | −3.37396 | − | 2.83109i | −0.268418 | − | 0.225230i | ||||
\(159\) | 7.27421 | − | 12.5993i | 0.576882 | − | 0.999190i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.59104 | + | 9.02323i | −0.125391 | + | 0.711130i | ||||
\(162\) | 4.08224 | − | 23.1515i | 0.320731 | − | 1.81896i | ||||
\(163\) | −10.3128 | − | 17.8622i | −0.807759 | − | 1.39908i | −0.914413 | − | 0.404783i | \(-0.867347\pi\) |
0.106654 | − | 0.994296i | \(-0.465986\pi\) | |||||||
\(164\) | 6.66811 | − | 11.5495i | 0.520692 | − | 0.901864i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.3512 | − | 4.49547i | −0.958639 | − | 0.348916i | ||||
\(167\) | 10.1993 | − | 3.71223i | 0.789243 | − | 0.287261i | 0.0842218 | − | 0.996447i | \(-0.473160\pi\) |
0.705021 | + | 0.709186i | \(0.250937\pi\) | |||||||
\(168\) | −2.96073 | + | 2.48435i | −0.228425 | + | 0.191672i | ||||
\(169\) | −2.23479 | − | 12.6741i | −0.171907 | − | 0.974934i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.23946 | + | 4.65599i | 0.553615 | + | 0.356052i | ||||
\(172\) | −18.3850 | −1.40184 | ||||||||
\(173\) | 3.04734 | + | 17.2823i | 0.231685 | + | 1.31395i | 0.849483 | + | 0.527616i | \(0.176914\pi\) |
−0.617798 | + | 0.786337i | \(0.711975\pi\) | |||||||
\(174\) | −3.26428 | + | 2.73905i | −0.247464 | + | 0.207647i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.4673 | + | 4.17376i | 0.864380 | + | 0.314609i | ||||
\(177\) | 16.7564 | + | 14.0603i | 1.25949 | + | 1.05684i | ||||
\(178\) | −3.53989 | + | 6.13128i | −0.265326 | + | 0.459559i | ||||
\(179\) | −7.53220 | − | 13.0462i | −0.562983 | − | 0.975116i | −0.997234 | − | 0.0743239i | \(-0.976320\pi\) |
0.434251 | − | 0.900792i | \(-0.357013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.59091 | − | 14.6938i | 0.192581 | − | 1.09218i | −0.723241 | − | 0.690596i | \(-0.757348\pi\) |
0.915822 | − | 0.401585i | \(-0.131541\pi\) | |||||||
\(182\) | −0.571848 | − | 0.990471i | −0.0423882 | − | 0.0734186i | ||||
\(183\) | 2.62033 | − | 4.53854i | 0.193700 | − | 0.335498i | ||||
\(184\) | −5.51072 | − | 4.62405i | −0.406256 | − | 0.340889i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.4533 | + | 7.80836i | −1.57303 | + | 0.572536i | ||||
\(187\) | 19.6450 | − | 16.4841i | 1.43658 | − | 1.20544i | ||||
\(188\) | 4.80564 | + | 27.2541i | 0.350487 | + | 1.98771i | ||||
\(189\) | −3.39743 | −0.247127 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.00677854 | −0.000490478 | −0.000245239 | − | 1.00000i | \(-0.500078\pi\) | ||||
−0.000245239 | 1.00000i | \(0.500078\pi\) | ||||||||
\(192\) | 4.49813 | + | 25.5102i | 0.324625 | + | 1.84104i | ||||
\(193\) | −10.5149 | + | 8.82305i | −0.756880 | + | 0.635097i | −0.937313 | − | 0.348490i | \(-0.886695\pi\) |
0.180433 | + | 0.983587i | \(0.442250\pi\) | |||||||
\(194\) | −9.45136 | + | 3.44001i | −0.678568 | + | 0.246978i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.35155 | − | 7.84688i | −0.667968 | − | 0.560492i | ||||
\(197\) | 0.239890 | − | 0.415502i | 0.0170915 | − | 0.0296033i | −0.857353 | − | 0.514729i | \(-0.827893\pi\) |
0.874445 | + | 0.485125i | \(0.161226\pi\) | |||||||
\(198\) | 9.85601 | + | 17.0711i | 0.700436 | + | 1.21319i | ||||
\(199\) | −4.65737 | + | 26.4133i | −0.330152 | + | 1.87239i | 0.140517 | + | 0.990078i | \(0.455123\pi\) |
−0.470670 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.87200 | − | 17.0988i | −0.696317 | − | 1.20606i | ||||
\(202\) | 9.64092 | − | 16.6986i | 0.678333 | − | 1.17491i | ||||
\(203\) | 1.01965 | + | 0.855587i | 0.0715653 | + | 0.0600504i | ||||
\(204\) | 29.2432 | + | 10.6436i | 2.04743 | + | 0.745205i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.7391 | − | 10.6893i | 0.887572 | − | 0.744761i | ||||
\(207\) | 2.11480 | + | 11.9936i | 0.146989 | + | 0.833614i | ||||
\(208\) | −0.941116 | −0.0652547 | ||||||||
\(209\) | 20.2423 | − | 2.57633i | 1.40019 | − | 0.178208i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.43107 | + | 8.11599i | 0.0985188 | + | 0.558728i | 0.993612 | + | 0.112849i | \(0.0359976\pi\) |
−0.895093 | + | 0.445879i | \(0.852891\pi\) | |||||||
\(212\) | 12.7267 | − | 10.6790i | 0.874075 | − | 0.733436i | ||||
\(213\) | 13.4390 | − | 4.89139i | 0.920825 | − | 0.335153i | ||||
\(214\) | −1.03856 | − | 0.378006i | −0.0709946 | − | 0.0258399i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.33372 | − | 2.31007i | 0.0907481 | − | 0.157180i | ||||
\(217\) | 3.56567 | + | 6.17593i | 0.242054 | + | 0.419249i | ||||
\(218\) | 1.02362 | − | 5.80522i | 0.0693281 | − | 0.393179i | ||||
\(219\) | 1.10835 | − | 6.28576i | 0.0748952 | − | 0.424752i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.988862 | + | 1.71276i | −0.0665181 | + | 0.115213i | ||||
\(222\) | −41.5274 | − | 34.8456i | −2.78713 | − | 2.33868i | ||||
\(223\) | 1.61443 | + | 0.587605i | 0.108110 | + | 0.0393489i | 0.395509 | − | 0.918462i | \(-0.370568\pi\) |
−0.287399 | + | 0.957811i | \(0.592790\pi\) | |||||||
\(224\) | 11.0167 | − | 4.00975i | 0.736085 | − | 0.267913i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.60352 | + | 26.1079i | 0.306222 | + | 1.73667i | ||||
\(227\) | −4.22601 | −0.280490 | −0.140245 | − | 0.990117i | \(-0.544789\pi\) | ||||
−0.140245 | + | 0.990117i | \(0.544789\pi\) | |||||||
\(228\) | 14.9895 | + | 19.7099i | 0.992707 | + | 1.30532i | ||||
\(229\) | 5.52322 | 0.364985 | 0.182492 | − | 0.983207i | \(-0.441583\pi\) | ||||
0.182492 | + | 0.983207i | \(0.441583\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.8828 | − | 9.97082i | 0.781828 | − | 0.656032i | ||||
\(232\) | −0.982034 | + | 0.357431i | −0.0644737 | + | 0.0234665i | ||||
\(233\) | 26.4955 | + | 9.64357i | 1.73578 | + | 0.631771i | 0.999015 | − | 0.0443807i | \(-0.0141315\pi\) |
0.736762 | + | 0.676152i | \(0.236354\pi\) | |||||||
\(234\) | −1.16454 | − | 0.977162i | −0.0761281 | − | 0.0638791i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.4895 | + | 21.6324i | 0.812994 | + | 1.40815i | ||||
\(237\) | −0.799976 | + | 4.53689i | −0.0519640 | + | 0.294702i | ||||
\(238\) | 3.01348 | − | 17.0903i | 0.195335 | − | 1.10780i | ||||
\(239\) | 5.66020 | + | 9.80375i | 0.366128 | + | 0.634152i | 0.988956 | − | 0.148206i | \(-0.0473499\pi\) |
−0.622829 | + | 0.782358i | \(0.714017\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5356 | + | 10.5186i | 0.807488 | + | 0.677563i | 0.950007 | − | 0.312229i | \(-0.101076\pi\) |
−0.142519 | + | 0.989792i | \(0.545520\pi\) | |||||||
\(242\) | 21.8713 | + | 7.96051i | 1.40594 | + | 0.511721i | ||||
\(243\) | −16.6596 | + | 6.06362i | −1.06872 | + | 0.388981i | ||||
\(244\) | 4.58444 | − | 3.84680i | 0.293489 | − | 0.246266i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.9028 | −1.58774 | ||||||||
\(247\) | −1.39899 | + | 0.720627i | −0.0890153 | + | 0.0458524i | ||||
\(248\) | −5.59907 | −0.355541 | ||||||||
\(249\) | 2.38734 | + | 13.5393i | 0.151291 | + | 0.858015i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.90186 | − | 2.51207i | 0.435641 | − | 0.158560i | −0.114884 | − | 0.993379i | \(-0.536650\pi\) |
0.550525 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(252\) | 7.02137 | + | 2.55557i | 0.442305 | + | 0.160986i | ||||
\(253\) | 22.1170 | + | 18.5584i | 1.39049 | + | 1.16676i | ||||
\(254\) | 1.45107 | − | 2.51333i | 0.0910482 | − | 0.157700i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.707484 | − | 4.01234i | 0.0442178 | − | 0.250771i | ||||
\(257\) | 1.04416 | − | 5.92171i | 0.0651327 | − | 0.369386i | −0.934768 | − | 0.355260i | \(-0.884392\pi\) |
0.999900 | − | 0.0141259i | \(-0.00449655\pi\) | |||||||
\(258\) | 17.1652 | + | 29.7310i | 1.06866 | + | 1.85097i | ||||
\(259\) | −8.46670 | + | 14.6648i | −0.526095 | + | 0.911224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.66253 | + | 0.605113i | 0.102908 | + | 0.0374555i | ||||
\(262\) | −39.1219 | + | 14.2392i | −2.41696 | + | 0.879701i | ||||
\(263\) | −5.65251 | + | 4.74302i | −0.348549 | + | 0.292467i | −0.800207 | − | 0.599724i | \(-0.795277\pi\) |
0.451658 | + | 0.892191i | \(0.350833\pi\) | |||||||
\(264\) | 2.11484 | + | 11.9939i | 0.130159 | + | 0.738171i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.37268 | − | 10.1405i | 0.574676 | − | 0.621753i | ||||
\(267\) | 7.40526 | 0.453194 | ||||||||
\(268\) | −3.91519 | − | 22.2041i | −0.239158 | − | 1.35633i | ||||
\(269\) | −8.32148 | + | 6.98255i | −0.507370 | + | 0.425734i | −0.860203 | − | 0.509953i | \(-0.829663\pi\) |
0.352833 | + | 0.935686i | \(0.385218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.67693 | − | 0.974323i | −0.162612 | − | 0.0591859i | 0.259432 | − | 0.965762i | \(-0.416465\pi\) |
−0.422043 | + | 0.906576i | \(0.638687\pi\) | |||||||
\(272\) | −10.9392 | − | 9.17906i | −0.663285 | − | 0.556562i | ||||
\(273\) | −0.598137 | + | 1.03600i | −0.0362009 | + | 0.0627018i | ||||
\(274\) | −11.3873 | − | 19.7233i | −0.687931 | − | 1.19153i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.08393 | + | 34.5037i | −0.366209 | + | 2.07688i | ||||
\(277\) | −8.07213 | − | 13.9813i | −0.485008 | − | 0.840058i | 0.514844 | − | 0.857284i | \(-0.327850\pi\) |
−0.999852 | + | 0.0172261i | \(0.994516\pi\) | |||||||
\(278\) | −7.66717 | + | 13.2799i | −0.459846 | + | 0.796477i | ||||
\(279\) | 7.26129 | + | 6.09294i | 0.434722 | + | 0.364775i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.02211 | + | 1.09996i | −0.180284 | + | 0.0656179i | −0.430585 | − | 0.902550i | \(-0.641693\pi\) |
0.250301 | + | 0.968168i | \(0.419470\pi\) | |||||||
\(282\) | 39.5868 | − | 33.2173i | 2.35736 | − | 1.97806i | ||||
\(283\) | −2.23560 | − | 12.6787i | −0.132893 | − | 0.753671i | −0.976304 | − | 0.216403i | \(-0.930568\pi\) |
0.843412 | − | 0.537268i | \(-0.180544\pi\) | |||||||
\(284\) | 16.3316 | 0.969101 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.60390 | −0.213103 | ||||||||
\(287\) | 1.35077 | + | 7.66061i | 0.0797336 | + | 0.452192i | ||||
\(288\) | 11.9373 | − | 10.0166i | 0.703415 | − | 0.590235i | ||||
\(289\) | −12.2246 | + | 4.44938i | −0.719092 | + | 0.261728i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.05902 | + | 6.76232i | 0.472428 | + | 0.396414i | ||||
\(292\) | 3.64437 | − | 6.31224i | 0.213271 | − | 0.369396i | ||||
\(293\) | −15.4055 | − | 26.6831i | −0.899999 | − | 1.55884i | −0.827493 | − | 0.561476i | \(-0.810234\pi\) |
−0.0725066 | − | 0.997368i | \(-0.523100\pi\) | |||||||
\(294\) | −3.95836 | + | 22.4490i | −0.230856 | + | 1.30925i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.64750 | − | 11.5138i | −0.386378 | − | 0.669227i | ||||
\(297\) | −5.35282 | + | 9.27136i | −0.310602 | + | 0.537979i | ||||
\(298\) | −6.93788 | − | 5.82157i | −0.401900 | − | 0.337234i | ||||
\(299\) | −2.09231 | − | 0.761539i | −0.121001 | − | 0.0440409i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.21478 | − | 6.89302i | 0.473492 | − | 0.397307i | ||||
\(302\) | 7.23432 | + | 41.0278i | 0.416288 | + | 2.36089i | ||||
\(303\) | −20.1683 | −1.15864 | ||||||||
\(304\) | −3.37013 | − | 10.8514i | −0.193290 | − | 0.622370i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00550 | − | 22.7163i | −0.228979 | − | 1.29861i | ||||
\(307\) | −12.5488 | + | 10.5297i | −0.716196 | + | 0.600959i | −0.926330 | − | 0.376713i | \(-0.877054\pi\) |
0.210134 | + | 0.977673i | \(0.432610\pi\) | |||||||
\(308\) | 16.6455 | − | 6.05846i | 0.948464 | − | 0.345213i | ||||
\(309\) | −16.3452 | − | 5.94915i | −0.929844 | − | 0.338435i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3873 | + | 21.4555i | −0.702420 | + | 1.21663i | 0.265195 | + | 0.964195i | \(0.414564\pi\) |
−0.967615 | + | 0.252432i | \(0.918770\pi\) | |||||||
\(312\) | −0.469618 | − | 0.813403i | −0.0265869 | − | 0.0460499i | ||||
\(313\) | −1.78395 | + | 10.1173i | −0.100835 | + | 0.571863i | 0.891968 | + | 0.452099i | \(0.149325\pi\) |
−0.992802 | + | 0.119763i | \(0.961786\pi\) | |||||||
\(314\) | 0.106057 | − | 0.601480i | 0.00598515 | − | 0.0339435i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.63041 | + | 4.55600i | −0.147972 | + | 0.256295i | ||||
\(317\) | −4.65473 | − | 3.90578i | −0.261436 | − | 0.219371i | 0.502642 | − | 0.864495i | \(-0.332361\pi\) |
−0.764078 | + | 0.645124i | \(0.776806\pi\) | |||||||
\(318\) | −29.1517 | − | 10.6104i | −1.63475 | − | 0.595000i | ||||
\(319\) | 3.94135 | − | 1.43453i | 0.220673 | − | 0.0803184i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.200741 | + | 1.13846i | 0.0112043 | + | 0.0635427i | ||||
\(322\) | 19.5377 | 1.08879 | ||||||||
\(323\) | −23.2898 | − | 5.26854i | −1.29588 | − | 0.293149i | ||||
\(324\) | −28.0799 | −1.55999 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −33.6916 | + | 28.2706i | −1.86601 | + | 1.56577i | ||||
\(327\) | −5.79393 | + | 2.10882i | −0.320405 | + | 0.116618i | ||||
\(328\) | −5.73908 | − | 2.08885i | −0.316888 | − | 0.115338i | ||||
\(329\) | −12.3656 | − | 10.3759i | −0.681736 | − | 0.572044i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.90549 | − | 10.2286i | −0.324595 | − | 0.562215i | 0.656835 | − | 0.754034i | \(-0.271895\pi\) |
−0.981430 | + | 0.191819i | \(0.938561\pi\) | |||||||
\(332\) | −2.72622 | + | 15.4611i | −0.149621 | + | 0.848541i | ||||
\(333\) | −3.90843 | + | 22.1658i | −0.214181 | + | 1.21468i | ||||
\(334\) | −11.5722 | − | 20.0436i | −0.633203 | − | 1.09674i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.61683 | − | 5.55218i | −0.360978 | − | 0.302896i | ||||
\(337\) | 14.3082 | + | 5.20776i | 0.779417 | + | 0.283685i | 0.700930 | − | 0.713230i | \(-0.252769\pi\) |
0.0784877 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(338\) | −25.7879 | + | 9.38602i | −1.40268 | + | 0.510532i | ||||
\(339\) | 21.2419 | − | 17.8241i | 1.15370 | − | 0.968071i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.4716 | 1.21691 | ||||||||
\(342\) | 7.09681 | − | 16.9267i | 0.383752 | − | 0.915292i | ||||
\(343\) | 17.5199 | 0.945983 | ||||||||
\(344\) | 1.46203 | + | 8.29159i | 0.0788274 | + | 0.447052i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.1641 | − | 12.7987i | 1.89044 | − | 0.688062i | ||||
\(347\) | −28.3603 | − | 10.3223i | −1.52246 | − | 0.554131i | −0.560700 | − | 0.828019i | \(-0.689468\pi\) |
−0.961762 | + | 0.273888i | \(0.911690\pi\) | |||||||
\(348\) | 3.89900 | + | 3.27165i | 0.209009 | + | 0.175379i | ||||
\(349\) | 1.36886 | − | 2.37093i | 0.0732732 | − | 0.126913i | −0.827061 | − | 0.562112i | \(-0.809989\pi\) |
0.900334 | + | 0.435200i | \(0.143322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.143367 | − | 0.813077i | 0.00765239 | − | 0.0433989i | ||||
\(352\) | 6.41502 | − | 36.3814i | 0.341922 | − | 1.93914i | ||||
\(353\) | −2.30462 | − | 3.99172i | −0.122663 | − | 0.212458i | 0.798154 | − | 0.602453i | \(-0.205810\pi\) |
−0.920817 | + | 0.389995i | \(0.872477\pi\) | |||||||
\(354\) | 23.3216 | − | 40.3943i | 1.23953 | − | 2.14693i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.94645 | + | 2.89227i | 0.421161 | + | 0.153290i | ||||
\(357\) | −17.0571 | + | 6.20826i | −0.902755 | + | 0.328576i | ||||
\(358\) | −24.6076 | + | 20.6482i | −1.30055 | + | 1.09129i | ||||
\(359\) | 2.14281 | + | 12.1525i | 0.113093 | + | 0.641383i | 0.987677 | + | 0.156508i | \(0.0500237\pi\) |
−0.874584 | + | 0.484875i | \(0.838865\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3188 | − | 13.5502i | −0.700992 | − | 0.713170i | ||||
\(362\) | −31.8160 | −1.67221 | ||||||||
\(363\) | −4.22746 | − | 23.9751i | −0.221884 | − | 1.25837i | ||||
\(364\) | −1.04648 | + | 0.878103i | −0.0548506 | + | 0.0460251i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.5011 | − | 3.82208i | −0.548900 | − | 0.199783i | ||||
\(367\) | 1.25334 | + | 1.05168i | 0.0654239 | + | 0.0548972i | 0.674913 | − | 0.737897i | \(-0.264181\pi\) |
−0.609489 | + | 0.792794i | \(0.708625\pi\) | |||||||
\(368\) | 8.03851 | − | 13.9231i | 0.419036 | − | 0.725792i | ||||
\(369\) | 5.16976 | + | 8.95428i | 0.269127 | + | 0.466141i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68272 | + | 9.54319i | −0.0873626 | + | 0.495458i | ||||
\(372\) | 13.6347 | + | 23.6160i | 0.706925 | + | 1.22443i | ||||
\(373\) | −7.37936 | + | 12.7814i | −0.382089 | + | 0.661797i | −0.991361 | − | 0.131164i | \(-0.958129\pi\) |
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(374\) | −41.8904 | − | 35.1502i | −2.16610 | − | 1.81758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.9094 | − | 4.33467i | 0.614181 | − | 0.223544i | ||||
\(377\) | −0.247788 | + | 0.207919i | −0.0127617 | + | 0.0107084i | ||||
\(378\) | 1.25801 | + | 7.13452i | 0.0647049 | + | 0.366960i | ||||
\(379\) | −1.75865 | −0.0903358 | −0.0451679 | − | 0.998979i | \(-0.514382\pi\) | ||||
−0.0451679 | + | 0.998979i | \(0.514382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.03556 | −0.155516 | ||||||||
\(382\) | 0.00250997 | + | 0.0142348i | 0.000128421 | + | 0.000728314i | ||||
\(383\) | 6.51031 | − | 5.46280i | 0.332661 | − | 0.279136i | −0.461122 | − | 0.887337i | \(-0.652553\pi\) |
0.793783 | + | 0.608201i | \(0.208108\pi\) | |||||||
\(384\) | 18.8259 | − | 6.85209i | 0.960708 | − | 0.349669i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.4217 | + | 18.8140i | 1.14123 | + | 0.957609i | ||||
\(387\) | 7.12689 | − | 12.3441i | 0.362280 | − | 0.627488i | ||||
\(388\) | 6.00683 | + | 10.4041i | 0.304951 | + | 0.528190i | ||||
\(389\) | −5.89390 | + | 33.4260i | −0.298833 | + | 1.69476i | 0.352370 | + | 0.935861i | \(0.385376\pi\) |
−0.651203 | + | 0.758904i | \(0.725735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8927 | − | 29.2589i | −0.854298 | − | 1.47969i | ||||
\(392\) | −2.79527 | + | 4.84155i | −0.141182 | + | 0.244535i | ||||
\(393\) | 33.3586 | + | 27.9912i | 1.68272 | + | 1.41197i | ||||
\(394\) | −0.961370 | − | 0.349910i | −0.0484331 | − | 0.0176282i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.0365 | − | 15.1344i | 0.906368 | − | 0.760533i | ||||
\(397\) | −1.35048 | − | 7.65893i | −0.0677785 | − | 0.384391i | −0.999760 | − | 0.0218863i | \(-0.993033\pi\) |
0.931982 | − | 0.362505i | \(-0.118078\pi\) | |||||||
\(398\) | 57.1918 | 2.86676 | ||||||||
\(399\) | −14.0874 | − | 3.18680i | −0.705253 | − | 0.159540i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.41570 | + | 30.7140i | 0.270447 | + | 1.53378i | 0.753062 | + | 0.657950i | \(0.228576\pi\) |
−0.482615 | + | 0.875833i | \(0.660313\pi\) | |||||||
\(402\) | −32.2516 | + | 27.0623i | −1.60857 | + | 1.34975i | ||||
\(403\) | −1.62850 | + | 0.592725i | −0.0811213 | + | 0.0295257i | ||||
\(404\) | −21.6422 | − | 7.87712i | −1.07674 | − | 0.391901i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.41915 | − | 2.45805i | 0.0704314 | − | 0.121991i | ||||
\(407\) | 26.6794 | + | 46.2101i | 1.32245 | + | 2.29055i | ||||
\(408\) | 2.47476 | − | 14.0351i | 0.122519 | − | 0.694839i | ||||
\(409\) | −2.54836 | + | 14.4525i | −0.126008 | + | 0.714629i | 0.854695 | + | 0.519130i | \(0.173744\pi\) |
−0.980704 | + | 0.195499i | \(0.937367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9108 | + | 20.6301i | −0.587515 | + | 1.01761i | ||||
\(412\) | −15.2161 | − | 12.7679i | −0.749645 | − | 0.629027i | ||||
\(413\) | −13.6911 | − | 4.98316i | −0.673696 | − | 0.245205i | ||||
\(414\) | 24.4032 | − | 8.88204i | 1.19935 | − | 0.436529i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.494727 | + | 2.80574i | 0.0242560 | + | 0.137563i | ||||
\(417\) | 16.0393 | 0.785447 | ||||||||
\(418\) | −12.9056 | − | 41.5543i | −0.631232 | − | 2.03249i | ||||
\(419\) | −20.6063 | −1.00668 | −0.503341 | − | 0.864088i | \(-0.667896\pi\) | ||||
−0.503341 | + | 0.864088i | \(0.667896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.2034 | − | 17.7918i | 1.03339 | − | 0.867119i | 0.0421416 | − | 0.999112i | \(-0.486582\pi\) |
0.991251 | + | 0.131993i | \(0.0421375\pi\) | |||||||
\(422\) | 16.5135 | − | 6.01041i | 0.803864 | − | 0.292582i | ||||
\(423\) | −20.1620 | − | 7.33837i | −0.980311 | − | 0.356804i | ||||
\(424\) | −5.82828 | − | 4.89051i | −0.283046 | − | 0.237504i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.2480 | − | 26.4104i | −0.738769 | − | 1.27959i | ||||
\(427\) | −0.606153 | + | 3.43766i | −0.0293338 | + | 0.166360i | ||||
\(428\) | −0.229237 | + | 1.30007i | −0.0110806 | + | 0.0628410i | ||||
\(429\) | 1.88479 | + | 3.26455i | 0.0909986 | + | 0.157614i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0072 | − | 13.4317i | −0.771042 | − | 0.646981i | 0.169934 | − | 0.985455i | \(-0.445645\pi\) |
−0.940976 | + | 0.338475i | \(0.890089\pi\) | |||||||
\(432\) | 5.60185 | + | 2.03891i | 0.269519 | + | 0.0980969i | ||||
\(433\) | 1.80980 | − | 0.658712i | 0.0869732 | − | 0.0316557i | −0.298167 | − | 0.954514i | \(-0.596375\pi\) |
0.385140 | + | 0.922858i | \(0.374153\pi\) | |||||||
\(434\) | 11.6490 | − | 9.77467i | 0.559170 | − | 0.469199i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.04100 | −0.337203 | ||||||||
\(437\) | 1.28825 | − | 26.8521i | 0.0616252 | − | 1.28451i | ||||
\(438\) | −13.6103 | −0.650327 | ||||||||
\(439\) | 6.02549 | + | 34.1723i | 0.287581 | + | 1.63095i | 0.695918 | + | 0.718121i | \(0.254998\pi\) |
−0.408337 | + | 0.912831i | \(0.633891\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.89371 | − | 3.23705i | 0.423510 | − | 0.154145i | ||||
\(442\) | 3.96291 | + | 1.44238i | 0.188496 | + | 0.0686071i | ||||
\(443\) | −20.1629 | − | 16.9187i | −0.957970 | − | 0.803832i | 0.0226514 | − | 0.999743i | \(-0.492789\pi\) |
−0.980622 | + | 0.195911i | \(0.937234\pi\) | |||||||
\(444\) | −32.3756 | + | 56.0761i | −1.53648 | + | 2.66126i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.636160 | − | 3.60784i | 0.0301231 | − | 0.170836i | ||||
\(447\) | −1.64499 | + | 9.32919i | −0.0778053 | + | 0.441256i | ||||
\(448\) | −8.62698 | − | 14.9424i | −0.407586 | − | 0.705960i | ||||
\(449\) | 6.71581 | − | 11.6321i | 0.316939 | − | 0.548954i | −0.662909 | − | 0.748700i | \(-0.730678\pi\) |
0.979848 | + | 0.199746i | \(0.0640117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.0335 | + | 8.38351i | 1.08461 | + | 0.394764i | ||||
\(452\) | 29.7559 | − | 10.8302i | 1.39960 | − | 0.509412i | ||||
\(453\) | 33.3811 | − | 28.0101i | 1.56838 | − | 1.31603i | ||||
\(454\) | 1.56482 | + | 8.87452i | 0.0734405 | + | 0.416502i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.69712 | − | 8.32766i | 0.360450 | − | 0.389978i | ||||
\(457\) | −0.205882 | −0.00963073 | −0.00481537 | − | 0.999988i | \(-0.501533\pi\) | ||||
−0.00481537 | + | 0.999988i | \(0.501533\pi\) | |||||||
\(458\) | −2.04515 | − | 11.5986i | −0.0955637 | − | 0.541969i | ||||
\(459\) | 9.59670 | − | 8.05259i | 0.447935 | − | 0.375863i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.6739 | − | 13.3482i | −1.70807 | − | 0.621688i | −0.711371 | − | 0.702817i | \(-0.751925\pi\) |
−0.996704 | + | 0.0811290i | \(0.974147\pi\) | |||||||
\(462\) | −25.3384 | − | 21.2615i | −1.17885 | − | 0.989173i | ||||
\(463\) | −3.71234 | + | 6.42997i | −0.172527 | + | 0.298826i | −0.939303 | − | 0.343089i | \(-0.888527\pi\) |
0.766776 | + | 0.641915i | \(0.221860\pi\) | |||||||
\(464\) | −1.16778 | − | 2.02266i | −0.0542129 | − | 0.0938995i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.4404 | − | 59.2107i | 0.483644 | − | 2.74288i | ||||
\(467\) | 10.9627 | + | 18.9880i | 0.507295 | + | 0.878660i | 0.999964 | + | 0.00844368i | \(0.00268774\pi\) |
−0.492670 | + | 0.870216i | \(0.663979\pi\) | |||||||
\(468\) | −0.907896 | + | 1.57252i | −0.0419675 | + | 0.0726898i | ||||
\(469\) | 10.0743 | + | 8.45336i | 0.465189 | + | 0.390340i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.600309 | + | 0.218495i | −0.0276608 | + | 0.0100677i | ||||
\(472\) | 8.76296 | − | 7.35300i | 0.403348 | − | 0.338449i | ||||
\(473\) | −5.86779 | − | 33.2779i | −0.269801 | − | 1.53012i | ||||
\(474\) | 9.82357 | 0.451211 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −20.7284 | −0.950084 | ||||||||
\(477\) | 2.23666 | + | 12.6847i | 0.102410 | + | 0.580795i | ||||
\(478\) | 18.4918 | − | 15.5164i | 0.845794 | − | 0.709705i | ||||
\(479\) | 26.3861 | − | 9.60376i | 1.20561 | − | 0.438807i | 0.340433 | − | 0.940269i | \(-0.389427\pi\) |
0.865180 | + | 0.501462i | \(0.167204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.15230 | − | 2.64510i | −0.143733 | − | 0.120606i | ||||
\(482\) | 17.4471 | − | 30.2193i | 0.794694 | − | 1.37645i | ||||
\(483\) | −10.2179 | − | 17.6980i | −0.464932 | − | 0.805286i | ||||
\(484\) | 4.82754 | − | 27.3784i | 0.219434 | − | 1.24447i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.9022 | + | 32.7396i | 0.857422 | + | 1.48510i | ||||
\(487\) | −7.06739 | + | 12.2411i | −0.320254 | + | 0.554697i | −0.980540 | − | 0.196318i | \(-0.937102\pi\) |
0.660286 | + | 0.751014i | \(0.270435\pi\) | |||||||
\(488\) | −2.09947 | − | 1.76167i | −0.0950386 | − | 0.0797468i | ||||
\(489\) | 43.2289 | + | 15.7340i | 1.95488 | + | 0.711517i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7677 | + | 14.9089i | −0.801847 | + | 0.672830i | −0.948647 | − | 0.316337i | \(-0.897547\pi\) |
0.146800 | + | 0.989166i | \(0.453103\pi\) | |||||||
\(492\) | 5.16518 | + | 29.2932i | 0.232864 | + | 1.32064i | ||||
\(493\) | −4.90811 | −0.221050 | ||||||||
\(494\) | 2.03132 | + | 2.67100i | 0.0913933 | + | 0.120174i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.17289 | − | 12.3230i | −0.0975654 | − | 0.553321i | ||||
\(497\) | −7.29729 | + | 6.12315i | −0.327328 | + | 0.274661i | ||||
\(498\) | 27.5481 | − | 10.0267i | 1.23446 | − | 0.449307i | ||||
\(499\) | 39.8744 | + | 14.5131i | 1.78502 | + | 0.649695i | 0.999525 | + | 0.0308294i | \(0.00981485\pi\) |
0.785497 | + | 0.618865i | \(0.212407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.1042 | + | 20.9651i | −0.540776 | + | 0.936651i | ||||
\(502\) | −7.83092 | − | 13.5635i | −0.349511 | − | 0.605371i | ||||
\(503\) | −1.01542 | + | 5.75873i | −0.0452753 | + | 0.256769i | −0.999041 | − | 0.0437817i | \(-0.986059\pi\) |
0.953766 | + | 0.300551i | \(0.0971705\pi\) | |||||||
\(504\) | 0.594196 | − | 3.36985i | 0.0264676 | − | 0.150105i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.7826 | − | 53.3170i | 1.36845 | − | 2.37023i | ||||
\(507\) | 21.9889 | + | 18.4509i | 0.976562 | + | 0.819433i | ||||
\(508\) | −3.25740 | − | 1.18560i | −0.144524 | − | 0.0526023i | ||||
\(509\) | −7.84135 | + | 2.85402i | −0.347562 | + | 0.126502i | −0.509902 | − | 0.860233i | \(-0.670318\pi\) |
0.162340 | + | 0.986735i | \(0.448096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.738249 | + | 4.18682i | 0.0326582 | + | 0.185214i | ||||
\(512\) | −26.6524 | −1.17788 | ||||||||
\(513\) | 9.88846 | − | 1.25855i | 0.436586 | − | 0.0555664i | ||||
\(514\) | −12.8221 | −0.565557 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 31.4123 | − | 26.3580i | 1.38285 | − | 1.16035i | ||||
\(517\) | −47.7978 | + | 17.3970i | −2.10215 | + | 0.765119i | ||||
\(518\) | 33.9307 | + | 12.3498i | 1.49083 | + | 0.542618i | ||||
\(519\) | −29.9839 | − | 25.1595i | −1.31615 | − | 1.10438i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.4419 | − | 26.7461i | −0.676521 | − | 1.17177i | −0.976022 | − | 0.217673i | \(-0.930154\pi\) |
0.299501 | − | 0.954096i | \(-0.403180\pi\) | |||||||
\(522\) | 0.655115 | − | 3.71534i | 0.0286736 | − | 0.162616i | ||||
\(523\) | −3.97753 | + | 22.5577i | −0.173925 | + | 0.986380i | 0.765452 | + | 0.643494i | \(0.222516\pi\) |
−0.939377 | + | 0.342886i | \(0.888595\pi\) | |||||||
\(524\) | 24.8640 | + | 43.0657i | 1.08619 | + | 1.88134i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0532 | + | 10.1139i | 0.525547 | + | 0.440986i | ||||
\(527\) | −24.7101 | − | 8.99375i | −1.07639 | − | 0.391774i | ||||
\(528\) | −25.5767 | + | 9.30914i | −1.11308 | + | 0.405129i | ||||
\(529\) | 11.5188 | − | 9.66540i | 0.500816 | − | 0.420235i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.3660 | −0.840415 | ||||||||
\(532\) | −13.8723 | − | 8.92182i | −0.601440 | − | 0.386810i | ||||
\(533\) | −1.89035 | −0.0818801 | ||||||||
\(534\) | −2.74204 | − | 15.5509i | −0.118659 | − | 0.672951i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.70268 | + | 3.53149i | −0.419092 | + | 0.152537i | ||||
\(537\) | 31.5733 | + | 11.4918i | 1.36249 | + | 0.495906i | ||||
\(538\) | 17.7445 | + | 14.8894i | 0.765019 | + | 0.641927i | ||||
\(539\) | 11.2187 | − | 19.4313i | 0.483222 | − | 0.836966i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.695195 | + | 3.94265i | −0.0298888 | + | 0.169508i | −0.996098 | − | 0.0882501i | \(-0.971873\pi\) |
0.966210 | + | 0.257758i | \(0.0829837\pi\) | |||||||
\(542\) | −1.05483 | + | 5.98226i | −0.0453090 | + | 0.256960i | ||||
\(543\) | 16.6393 | + | 28.8201i | 0.714061 | + | 1.23679i | ||||
\(544\) | −21.6149 | + | 37.4381i | −0.926731 | + | 1.60515i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.39706 | + | 0.872460i | 0.102585 | + | 0.0373378i | ||||
\(547\) | 39.1590 | − | 14.2527i | 1.67432 | − | 0.609402i | 0.681804 | − | 0.731535i | \(-0.261196\pi\) |
0.992514 | + | 0.122133i | \(0.0389735\pi\) | |||||||
\(548\) | −20.8387 | + | 17.4858i | −0.890186 | + | 0.746954i | ||||
\(549\) | 0.805694 | + | 4.56932i | 0.0343862 | + | 0.195014i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.28471 | − | 2.11253i | −0.139933 | − | 0.0899966i | ||||
\(552\) | 16.0449 | 0.682917 | ||||||||
\(553\) | −0.532848 | − | 3.02193i | −0.0226590 | − | 0.128506i | ||||
\(554\) | −26.3715 | + | 22.1283i | −1.12042 | + | 0.940142i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.2115 | + | 6.26446i | 0.729929 | + | 0.265672i | ||||
\(557\) | 2.43219 | + | 2.04085i | 0.103055 | + | 0.0864735i | 0.692859 | − | 0.721073i | \(-0.256351\pi\) |
−0.589804 | + | 0.807546i | \(0.700795\pi\) | |||||||
\(558\) | 10.1063 | − | 17.5046i | 0.427834 | − | 0.741030i | ||||
\(559\) | 1.30299 | + | 2.25685i | 0.0551107 | + | 0.0954546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.93232 | + | 56.3290i | −0.419343 | + | 2.37821i | ||||
\(562\) | 3.42891 | + | 5.93905i | 0.144640 | + | 0.250524i | ||||
\(563\) | 7.20295 | − | 12.4759i | 0.303568 | − | 0.525796i | −0.673373 | − | 0.739303i | \(-0.735155\pi\) |
0.976942 | + | 0.213507i | \(0.0684886\pi\) | |||||||
\(564\) | −47.2843 | − | 39.6763i | −1.99103 | − | 1.67067i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.7972 | + | 9.38940i | −1.08434 | + | 0.394666i | ||||
\(567\) | 12.5467 | − | 10.5279i | 0.526911 | − | 0.442131i | ||||
\(568\) | −1.29874 | − | 7.36552i | −0.0544939 | − | 0.309050i | ||||
\(569\) | 24.9795 | 1.04719 | 0.523597 | − | 0.851966i | \(-0.324590\pi\) | ||||
0.523597 | + | 0.851966i | \(0.324590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1086 | 0.548579 | 0.274289 | − | 0.961647i | \(-0.411557\pi\) | ||||
0.274289 | + | 0.961647i | \(0.411557\pi\) | |||||||
\(572\) | 0.747499 | + | 4.23928i | 0.0312545 | + | 0.177253i | ||||
\(573\) | 0.0115817 | − | 0.00971822i | 0.000483833 | − | 0.000405984i | ||||
\(574\) | 15.5869 | − | 5.67318i | 0.650586 | − | 0.236794i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −17.5683 | − | 14.7416i | −0.732014 | − | 0.614233i | ||||
\(577\) | 4.12748 | − | 7.14901i | 0.171829 | − | 0.297617i | −0.767230 | − | 0.641372i | \(-0.778366\pi\) |
0.939059 | + | 0.343755i | \(0.111699\pi\) | |||||||
\(578\) | 13.8701 | + | 24.0238i | 0.576921 | + | 0.999257i | ||||
\(579\) | 5.31624 | − | 30.1499i | 0.220935 | − | 1.25299i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.57867 | − | 7.93050i | −0.189955 | − | 0.329012i | ||||
\(582\) | 11.2166 | − | 19.4277i | 0.464943 | − | 0.805304i | ||||
\(583\) | 23.3915 | + | 19.6278i | 0.968778 | + | 0.812901i | ||||
\(584\) | −3.13662 | − | 1.14164i | −0.129794 | − | 0.0472413i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.3295 | + | 42.2315i | −2.07909 | + | 1.74457i | ||||
\(587\) | 1.37287 | + | 7.78595i | 0.0566646 | + | 0.321361i | 0.999943 | − | 0.0106409i | \(-0.00338717\pi\) |
−0.943279 | + | 0.332002i | \(0.892276\pi\) | |||||||
\(588\) | 27.2278 | 1.12286 | ||||||||
\(589\) | −12.6660 | − | 16.6546i | −0.521892 | − | 0.686241i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.185821 | + | 1.05384i | 0.00764366 | + | 0.0433493i | ||||
\(592\) | 22.7611 | − | 19.0988i | 0.935475 | − | 0.784957i | ||||
\(593\) | −3.34124 | + | 1.21611i | −0.137208 | + | 0.0499398i | −0.409712 | − | 0.912215i | \(-0.634371\pi\) |
0.272503 | + | 0.962155i | \(0.412148\pi\) | |||||||
\(594\) | 21.4517 | + | 7.80777i | 0.880173 | + | 0.320357i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.40891 | + | 9.36850i | −0.221557 | + | 0.383749i | ||||
\(597\) | −29.9105 | − | 51.8065i | −1.22415 | − | 2.12030i | ||||
\(598\) | −0.824467 | + | 4.67579i | −0.0337150 | + | 0.191207i | ||||
\(599\) | 1.91987 | − | 10.8881i | 0.0784437 | − | 0.444876i | −0.920136 | − | 0.391599i | \(-0.871922\pi\) |
0.998580 | − | 0.0532774i | \(-0.0169668\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7722 | − | 39.4426i | 0.928898 | − | 1.60890i | 0.143728 | − | 0.989617i | \(-0.454091\pi\) |
0.785170 | − | 0.619281i | \(-0.212576\pi\) | |||||||
\(602\) | −17.5170 | − | 14.6985i | −0.713938 | − | 0.599065i | ||||
\(603\) | 16.4261 | + | 5.97863i | 0.668924 | + | 0.243468i | ||||
\(604\) | 46.7606 | − | 17.0195i | 1.90266 | − | 0.692512i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.46795 | + | 42.3529i | 0.303365 | + | 1.72047i | ||||
\(607\) | −36.4498 | −1.47945 | −0.739727 | − | 0.672907i | \(-0.765045\pi\) | ||||
−0.739727 | + | 0.672907i | \(0.765045\pi\) | |||||||
\(608\) | −30.5795 | + | 15.7517i | −1.24016 | + | 0.638817i | ||||
\(609\) | −2.96879 | −0.120301 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00500 | − | 2.52149i | 0.121569 | − | 0.102009i | ||||
\(612\) | −25.8904 | + | 9.42334i | −1.04656 | + | 0.380916i | ||||
\(613\) | 6.33713 | + | 2.30653i | 0.255954 | + | 0.0931597i | 0.466811 | − | 0.884357i | \(-0.345403\pi\) |
−0.210856 | + | 0.977517i | \(0.567625\pi\) | |||||||
\(614\) | 26.7586 | + | 22.4531i | 1.07989 | + | 0.906135i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.05606 | − | 7.02529i | −0.163423 | − | 0.283057i | ||||
\(617\) | −4.38423 | + | 24.8642i | −0.176503 | + | 1.00100i | 0.759893 | + | 0.650049i | \(0.225252\pi\) |
−0.936395 | + | 0.350947i | \(0.885860\pi\) | |||||||
\(618\) | −6.44075 | + | 36.5273i | −0.259085 | + | 1.46934i | ||||
\(619\) | −11.1611 | − | 19.3317i | −0.448604 | − | 0.777006i | 0.549691 | − | 0.835368i | \(-0.314745\pi\) |
−0.998295 | + | 0.0583624i | \(0.981412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8043 | + | 9.06588i | 0.433562 | + | 0.363801i | ||||
\(622\) | 49.6427 | + | 18.0685i | 1.99049 | + | 0.724480i | ||||
\(623\) | −4.63503 | + | 1.68701i | −0.185699 | + | 0.0675887i | ||||
\(624\) | 1.60798 | − | 1.34925i | 0.0643706 | − | 0.0540133i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.9066 | 0.875564 | ||||||||
\(627\) | −30.8920 | + | 33.4226i | −1.23371 | + | 1.33477i | ||||
\(628\) | −0.729519 | −0.0291110 | ||||||||
\(629\) | −10.8426 | − | 61.4912i | −0.432321 | − | 2.45182i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.32590 | + | 1.21053i | −0.132402 | + | 0.0481904i | −0.407371 | − | 0.913263i | \(-0.633555\pi\) |
0.274969 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(632\) | 2.26393 | + | 0.824003i | 0.0900543 | + | 0.0327771i | ||||
\(633\) | −14.0808 | − | 11.8152i | −0.559661 | − | 0.469611i | ||||
\(634\) | −6.47848 | + | 11.2211i | −0.257293 | + | 0.445645i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.43451 | + | 36.4919i | −0.255145 | + | 1.44700i | ||||
\(637\) | −0.300476 | + | 1.70408i | −0.0119053 | + | 0.0675182i | ||||
\(638\) | −4.47189 | − | 7.74555i | −0.177044 | − | 0.306649i | ||||
\(639\) | −6.33090 | + | 10.9654i | −0.250447 | + | 0.433786i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.7767 | − | 9.01799i | −0.978622 | − | 0.356189i | −0.197318 | − | 0.980340i | \(-0.563223\pi\) |
−0.781304 | + | 0.624150i | \(0.785445\pi\) | |||||||
\(642\) | 2.31641 | − | 0.843104i | 0.0914213 | − | 0.0332746i | ||||
\(643\) | 11.2983 | − | 9.48043i | 0.445563 | − | 0.373872i | −0.392223 | − | 0.919870i | \(-0.628294\pi\) |
0.837786 | + | 0.545998i | \(0.183850\pi\) | |||||||
\(644\) | −4.05238 | − | 22.9822i | −0.159686 | − | 0.905626i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.43999 | + | 50.8589i | −0.0960000 | + | 2.00102i | ||||
\(647\) | −5.04555 | −0.198361 | −0.0991804 | − | 0.995069i | \(-0.531622\pi\) | ||||
−0.0991804 | + | 0.995069i | \(0.531622\pi\) | |||||||
\(648\) | 2.23300 | + | 12.6640i | 0.0877207 | + | 0.497489i | ||||
\(649\) | −35.1697 | + | 29.5109i | −1.38053 | + | 1.15840i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.9465 | − | 5.44009i | −0.585800 | − | 0.213214i | ||||
\(652\) | 40.2429 | + | 33.7678i | 1.57603 | + | 1.32245i | ||||
\(653\) | −22.3362 | + | 38.6875i | −0.874084 | + | 1.51396i | −0.0163488 | + | 0.999866i | \(0.505204\pi\) |
−0.857735 | + | 0.514092i | \(0.828129\pi\) | |||||||
\(654\) | 6.57385 | + | 11.3862i | 0.257058 | + | 0.445237i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.37016 | − | 13.4418i | 0.0925391 | − | 0.524815i | ||||
\(657\) | 2.82547 | + | 4.89386i | 0.110232 | + | 0.190927i | ||||
\(658\) | −17.2105 | + | 29.8094i | −0.670934 | + | 1.16209i | ||||
\(659\) | 22.5147 | + | 18.8921i | 0.877049 | + | 0.735931i | 0.965570 | − | 0.260143i | \(-0.0837697\pi\) |
−0.0885212 | + | 0.996074i | \(0.528214\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0049 | − | 6.91721i | 0.739204 | − | 0.269048i | 0.0551486 | − | 0.998478i | \(-0.482437\pi\) |
0.684056 | + | 0.729430i | \(0.260215\pi\) | |||||||
\(662\) | −19.2931 | + | 16.1889i | −0.749849 | + | 0.629198i | ||||
\(663\) | −0.765982 | − | 4.34410i | −0.0297483 | − | 0.168711i | ||||
\(664\) | 7.18975 | 0.279016 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 47.9949 | 1.85976 | ||||||||
\(667\) | −0.959531 | − | 5.44177i | −0.0371532 | − | 0.210706i | ||||
\(668\) | −21.1771 | + | 17.7697i | −0.819367 | + | 0.687531i | ||||
\(669\) | −3.60083 | + | 1.31059i | −0.139216 | + | 0.0506705i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.42612 | + | 7.07036i | 0.325287 | + | 0.272948i | ||||
\(672\) | −13.0743 | + | 22.6454i | −0.504352 | + | 0.873564i | ||||
\(673\) | −13.8331 | − | 23.9597i | −0.533227 | − | 0.923577i | −0.999247 | − | 0.0388026i | \(-0.987646\pi\) |
0.466019 | − | 0.884774i | \(-0.345688\pi\) | |||||||
\(674\) | 5.63809 | − | 31.9752i | 0.217171 | − | 1.23164i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.3895 | + | 28.3875i | 0.630367 | + | 1.09183i | ||||
\(677\) | 15.8370 | − | 27.4305i | 0.608665 | − | 1.05424i | −0.382796 | − | 0.923833i | \(-0.625039\pi\) |
0.991461 | − | 0.130405i | \(-0.0416279\pi\) | |||||||
\(678\) | −45.2956 | − | 38.0075i | −1.73957 | − | 1.45967i | ||||
\(679\) | −6.58477 | − | 2.39666i | −0.252700 | − | 0.0919754i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.22050 | − | 6.05872i | 0.276690 | − | 0.232171i | ||||
\(682\) | −8.32083 | − | 47.1898i | −0.318621 | − | 1.80699i | ||||
\(683\) | 4.75181 | 0.181823 | 0.0909114 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909114 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(684\) | −21.3829 | − | 4.83716i | −0.817595 | − | 0.184953i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.48729 | − | 36.7913i | −0.247686 | − | 1.40470i | ||||
\(687\) | −9.43690 | + | 7.91850i | −0.360040 | + | 0.302110i | ||||
\(688\) | −17.6816 | + | 6.43559i | −0.674106 | + | 0.245355i | ||||
\(689\) | −2.21288 | − | 0.805423i | −0.0843040 | − | 0.0306842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.211770 | − | 0.366797i | 0.00805613 | − | 0.0139536i | −0.861969 | − | 0.506961i | \(-0.830769\pi\) |
0.870025 | + | 0.493007i | \(0.164102\pi\) | |||||||
\(692\) | −22.3486 | − | 38.7090i | −0.849568 | − | 1.47149i | ||||
\(693\) | −2.38478 | + | 13.5247i | −0.0905902 | + | 0.513763i | ||||
\(694\) | −11.1753 | + | 63.3781i | −0.424208 | + | 2.40580i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.16545 | − | 2.01862i | 0.0441762 | − | 0.0765155i | ||||
\(697\) | −21.9727 | − | 18.4373i | −0.832275 | − | 0.698362i | ||||
\(698\) | −5.48575 | − | 1.99665i | −0.207639 | − | 0.0755743i | ||||
\(699\) | −59.0955 | + | 21.5090i | −2.23520 | + | 0.813545i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.37980 | + | 7.82526i | 0.0521145 | + | 0.295556i | 0.999714 | − | 0.0239040i | \(-0.00760962\pi\) |
−0.947600 | + | 0.319460i | \(0.896499\pi\) | |||||||
\(702\) | −1.76053 | −0.0664469 | ||||||||
\(703\) | 19.2105 | − | 45.8193i | 0.724538 | − | 1.72811i | ||||
\(704\) | −54.3689 | −2.04911 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.52915 | + | 6.31771i | −0.283363 | + | 0.237770i | ||||
\(707\) | 12.6235 | − | 4.59459i | 0.474757 | − | 0.172797i | ||||
\(708\) | −52.3530 | − | 19.0549i | −1.96755 | − | 0.716129i | ||||
\(709\) | 8.99170 | + | 7.54493i | 0.337690 | + | 0.283356i | 0.795825 | − | 0.605527i | \(-0.207038\pi\) |
−0.458134 | + | 0.888883i | \(0.651482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.03935 | − | 3.53225i | −0.0764815 | − | 0.132470i | ||||
\(712\) | 0.672483 | − | 3.81384i | 0.0252024 | − | 0.142930i | ||||
\(713\) | 5.14084 | − | 29.1552i | 0.192526 | − | 1.09187i | ||||
\(714\) | 19.3531 | + | 33.5206i | 0.724272 | + | 1.25448i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.3924 | + | 24.6632i | 1.09845 | + | 0.921707i | ||||
\(717\) | −23.7263 | − | 8.63567i | −0.886075 | − | 0.322505i | ||||
\(718\) | 24.7264 | − | 8.99969i | 0.922783 | − | 0.335865i | ||||
\(719\) | −38.6452 | + | 32.4272i | −1.44122 | + | 1.20933i | −0.502536 | + | 0.864556i | \(0.667600\pi\) |
−0.938686 | + | 0.344773i | \(0.887956\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5859 | 0.431481 | ||||||||
\(722\) | −23.5234 | + | 32.9866i | −0.875450 | + | 1.22764i | ||||
\(723\) | −36.4983 | −1.35739 | ||||||||
\(724\) | 6.59907 | + | 37.4252i | 0.245252 | + | 1.39090i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −48.7818 | + | 17.7551i | −1.81046 | + | 0.658954i | ||||
\(727\) | 24.4935 | + | 8.91490i | 0.908414 | + | 0.330636i | 0.753619 | − | 0.657311i | \(-0.228306\pi\) |
0.154794 | + | 0.987947i | \(0.450529\pi\) | |||||||
\(728\) | 0.479243 | + | 0.402132i | 0.0177619 | + | 0.0149040i | ||||
\(729\) | 3.23417 | − | 5.60174i | 0.119784 | − | 0.207472i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.86641 | + | 38.9413i | −0.253963 | + | 1.44030i | ||||
\(732\) | −2.31785 | + | 13.1452i | −0.0856702 | + | 0.485860i | ||||
\(733\) | 8.54306 | + | 14.7970i | 0.315545 | + | 0.546540i | 0.979553 | − | 0.201185i | \(-0.0644793\pi\) |
−0.664008 | + | 0.747725i | \(0.731146\pi\) | |||||||
\(734\) | 1.74441 | − | 3.02141i | 0.0643873 | − | 0.111522i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45.7345 | − | 16.6460i | −1.68580 | − | 0.613580i | ||||
\(737\) | 38.9412 | − | 14.1734i | 1.43442 | − | 0.522086i | ||||
\(738\) | 16.8895 | − | 14.1720i | 0.621711 | − | 0.521677i | ||||
\(739\) | −4.27432 | − | 24.2409i | −0.157233 | − | 0.891715i | −0.956715 | − | 0.291025i | \(-0.906004\pi\) |
0.799482 | − | 0.600690i | \(-0.205107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.35714 | − | 3.23694i | 0.0498559 | − | 0.118912i | ||||
\(742\) | 20.6636 | 0.758583 | ||||||||
\(743\) | 1.33186 | + | 7.55333i | 0.0488610 | + | 0.277105i | 0.999443 | − | 0.0333687i | \(-0.0106236\pi\) |
−0.950582 | + | 0.310473i | \(0.899512\pi\) | |||||||
\(744\) | 9.56649 | − | 8.02724i | 0.350724 | − | 0.294293i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.5731 | + | 10.7637i | 1.08275 | + | 0.394089i | ||||
\(747\) | −9.32420 | − | 7.82393i | −0.341155 | − | 0.286263i | ||||
\(748\) | −32.6586 | + | 56.5664i | −1.19412 | + | 2.06827i | ||||
\(749\) | −0.385002 | − | 0.666843i | −0.0140677 | − | 0.0243659i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.65755 | − | 20.7430i | 0.133466 | − | 0.756923i | −0.842450 | − | 0.538775i | \(-0.818887\pi\) |
0.975916 | − | 0.218148i | \(-0.0700017\pi\) | |||||||
\(752\) | 14.1620 | + | 24.5293i | 0.516436 | + | 0.894493i | ||||
\(753\) | −8.19092 | + | 14.1871i | −0.298494 | + | 0.517006i | ||||
\(754\) | 0.528376 | + | 0.443360i | 0.0192423 | + | 0.0161462i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.13141 | − | 2.95959i | 0.295737 | − | 0.107639i | ||||
\(757\) | −3.29957 | + | 2.76867i | −0.119925 | + | 0.100629i | −0.700778 | − | 0.713379i | \(-0.747164\pi\) |
0.580853 | + | 0.814009i | \(0.302719\pi\) | |||||||
\(758\) | 0.651197 | + | 3.69312i | 0.0236525 | + | 0.134140i | ||||
\(759\) | −64.3955 | −2.33741 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.11318 | −0.0403529 | −0.0201764 | − | 0.999796i | \(-0.506423\pi\) | ||||
−0.0201764 | + | 0.999796i | \(0.506423\pi\) | |||||||
\(762\) | 1.12401 | + | 6.37459i | 0.0407187 | + | 0.230927i | ||||
\(763\) | 3.14606 | − | 2.63986i | 0.113895 | − | 0.0955694i | ||||
\(764\) | 0.0162238 | − | 0.00590497i | 0.000586956 | − | 0.000213634i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.8824 | − | 11.6487i | −0.501591 | − | 0.420885i | ||||
\(767\) | 1.77032 | − | 3.06629i | 0.0639227 | − | 0.110717i | ||||
\(768\) | 4.54359 | + | 7.86973i | 0.163953 | + | 0.283975i | ||||
\(769\) | 1.71410 | − | 9.72113i | 0.0618119 | − | 0.350553i | −0.938178 | − | 0.346152i | \(-0.887488\pi\) |
0.999990 | − | 0.00440066i | \(-0.00140078\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.70576 | + | 11.6147i | 0.241502 | + | 0.418294i | ||||
\(772\) | 17.4804 | − | 30.2769i | 0.629133 | − | 1.08969i | ||||
\(773\) | 13.0788 | + | 10.9744i | 0.470410 | + | 0.394721i | 0.846944 | − | 0.531682i | \(-0.178440\pi\) |
−0.376534 | + | 0.926403i | \(0.622884\pi\) | |||||||
\(774\) | −28.5613 | − | 10.3955i | −1.02662 | − | 0.373658i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.21457 | − | 3.53644i | 0.151294 | − | 0.126951i | ||||
\(777\) | −6.55839 | − | 37.1945i | −0.235281 | − | 1.33434i | ||||
\(778\) | 72.3761 | 2.59481 | ||||||||
\(779\) | −6.76933 | − | 21.7964i | −0.242537 | − | 0.780936i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.21243 | + | 29.5611i | 0.186515 | + | 1.05778i | ||||
\(782\) | −55.1880 | + | 46.3082i | −1.97352 | + | 1.65598i | ||||
\(783\) | 1.92537 | − | 0.700778i | 0.0688072 | − | 0.0250438i | ||||
\(784\) | −11.7406 | − | 4.27323i | −0.419307 | − | 0.152615i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 46.4287 | − | 80.4169i | 1.65606 | − | 2.86838i | ||||
\(787\) | −5.82825 | − | 10.0948i | −0.207755 | − | 0.359842i | 0.743252 | − | 0.669011i | \(-0.233282\pi\) |
−0.951007 | + | 0.309170i | \(0.899949\pi\) | |||||||
\(788\) | −0.212198 | + | 1.20344i | −0.00755925 | + | 0.0428707i | ||||
\(789\) | 2.85786 | − | 16.2077i | 0.101742 | − | 0.577010i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.23498 | + | 15.9955i | −0.328358 | + | 0.568733i | ||||
\(792\) | −8.25992 | − | 6.93090i | −0.293503 | − | 0.246279i | ||||
\(793\) | −0.797127 | − | 0.290130i | −0.0283068 | − | 0.0103028i | ||||
\(794\) | −15.5835 | + | 5.67194i | −0.553038 | + | 0.201289i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8624 | − | 67.2747i | −0.420450 | − | 2.38449i | ||||
\(797\) | 29.8609 | 1.05773 | 0.528864 | − | 0.848707i | \(-0.322618\pi\) | ||||
0.528864 | + | 0.848707i | \(0.322618\pi\) | |||||||
\(798\) | −1.47589 | + | 30.7632i | −0.0522458 | + | 1.08901i | ||||
\(799\) | 59.5220 | 2.10574 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.02237 | + | 4.21427i | −0.177457 | + | 0.148904i | ||||
\(802\) | 62.4932 | − | 22.7457i | 2.20671 | − | 0.803178i | ||||
\(803\) | 12.5887 | + | 4.58191i | 0.444245 | + | 0.161692i | ||||
\(804\) | 38.5229 | + | 32.3245i | 1.35860 | + | 1.14000i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.84771 | + | 3.20033i | 0.0650829 | + | 0.112727i | ||||
\(807\) | 4.20726 | − | 23.8606i | 0.148103 | − | 0.839932i | ||||
\(808\) | −1.83151 | + | 10.3870i | −0.0644323 | + | 0.365414i | ||||
\(809\) | 19.1756 | + | 33.2132i | 0.674180 | + | 1.16771i | 0.976708 | + | 0.214573i | \(0.0688360\pi\) |
−0.302528 | + | 0.953140i | \(0.597831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.55127 | + | 7.17537i | 0.300276 | + | 0.251961i | 0.780459 | − | 0.625207i | \(-0.214985\pi\) |
−0.480183 | + | 0.877168i | \(0.659430\pi\) | |||||||
\(812\) | −3.18575 | − | 1.15952i | −0.111798 | − | 0.0406911i | ||||
\(813\) | 5.97062 | − | 2.17313i | 0.209399 | − | 0.0762150i | ||||
\(814\) | 87.1612 | − | 73.1369i | 3.05500 | − | 2.56345i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 31.8503 | 1.11498 | ||||||||
\(817\) | −21.3562 | + | 23.1057i | −0.747160 | + | 0.808367i | ||||
\(818\) | 31.2935 | 1.09415 | ||||||||
\(819\) | −0.183914 | − | 1.04303i | −0.00642649 | − | 0.0364464i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.18934 | + | 2.61671i | −0.250910 | + | 0.0913236i | −0.464413 | − | 0.885619i | \(-0.653735\pi\) |
0.213504 | + | 0.976942i | \(0.431513\pi\) | |||||||
\(822\) | 47.7330 | + | 17.3734i | 1.66488 | + | 0.605966i | ||||
\(823\) | −25.4494 | − | 21.3546i | −0.887110 | − | 0.744373i | 0.0805185 | − | 0.996753i | \(-0.474342\pi\) |
−0.967628 | + | 0.252380i | \(0.918787\pi\) | |||||||
\(824\) | −4.54825 | + | 7.87779i | −0.158446 | + | 0.274436i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.39493 | + | 30.5962i | −0.187714 | + | 1.06458i | ||||
\(827\) | 0.591681 | − | 3.35559i | 0.0205748 | − | 0.116685i | −0.972791 | − | 0.231686i | \(-0.925576\pi\) |
0.993365 | + | 0.115001i | \(0.0366870\pi\) | |||||||
\(828\) | −15.5095 | − | 26.8633i | −0.538993 | − | 0.933563i | ||||
\(829\) | −2.21217 | + | 3.83160i | −0.0768320 | + | 0.133077i | −0.901881 | − | 0.431984i | \(-0.857814\pi\) |
0.825049 | + | 0.565060i | \(0.191147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.8366 | + | 12.3155i | 1.17378 | + | 0.427221i | ||||
\(832\) | 3.94007 | − | 1.43407i | 0.136597 | − | 0.0497174i | ||||
\(833\) | −20.1132 | + | 16.8770i | −0.696880 | + | 0.584752i | ||||
\(834\) | −5.93906 | − | 33.6821i | −0.205653 | − | 1.16632i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −46.2035 | + | 23.7998i | −1.59798 | + | 0.823132i | ||||
\(837\) | 10.9775 | 0.379438 | ||||||||
\(838\) | 7.63013 | + | 43.2726i | 0.263579 | + | 1.49483i | ||||
\(839\) | −18.2406 | + | 15.3057i | −0.629736 | + | 0.528411i | −0.900847 | − | 0.434137i | \(-0.857053\pi\) |
0.271111 | + | 0.962548i | \(0.412609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4968 | + | 9.64403i | 0.913681 | + | 0.332553i | ||||
\(842\) | −45.2136 | − | 37.9387i | −1.55816 | − | 1.30745i | ||||
\(843\) | 3.58655 | − | 6.21208i | 0.123527 | − | 0.213956i | ||||
\(844\) | −10.4952 | − | 18.1782i | −0.361259 | − | 0.625719i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.94477 | + | 45.0570i | −0.273147 | + | 1.54909i | ||||
\(847\) | 8.10785 | + | 14.0432i | 0.278589 | + | 0.482530i | ||||
\(848\) | 8.50173 | − | 14.7254i | 0.291951 | − | 0.505673i | ||||
\(849\) | 21.9968 | + | 18.4575i | 0.754929 | + | 0.633461i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66.0575 | − | 24.0430i | 2.26442 | − | 0.824183i | ||||
\(852\) | −27.9039 | + | 23.4141i | −0.955971 | + | 0.802155i | ||||
\(853\) | 0.769903 | + | 4.36634i | 0.0263610 | + | 0.149501i | 0.995147 | − | 0.0983970i | \(-0.0313715\pi\) |
−0.968786 | + | 0.247898i | \(0.920260\pi\) | |||||||
\(854\) | 7.44345 | 0.254710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.604557 | 0.0206633 | ||||||||
\(857\) | −4.68808 | − | 26.5874i | −0.160142 | − | 0.908208i | −0.953933 | − | 0.300019i | \(-0.903007\pi\) |
0.793792 | − | 0.608190i | \(-0.208104\pi\) | |||||||
\(858\) | 6.15758 | − | 5.16682i | 0.210216 | − | 0.176392i | ||||
\(859\) | 12.8850 | − | 4.68976i | 0.439631 | − | 0.160013i | −0.112715 | − | 0.993627i | \(-0.535955\pi\) |
0.552346 | + | 0.833615i | \(0.313733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2907 | − | 11.1522i | −0.452947 | − | 0.380067i | ||||
\(862\) | −22.2790 | + | 38.5883i | −0.758825 | + | 1.31432i | ||||
\(863\) | 26.2240 | + | 45.4213i | 0.892676 | + | 1.54616i | 0.836655 | + | 0.547730i | \(0.184508\pi\) |
0.0560208 | + | 0.998430i | \(0.482159\pi\) | |||||||
\(864\) | 3.13378 | − | 17.7725i | 0.106613 | − | 0.604634i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.05341 | − | 3.55662i | −0.0697778 | − | 0.120859i | ||||
\(867\) | 14.5078 | − | 25.1282i | 0.492709 | − | 0.853398i | ||||
\(868\) | −13.9141 | − | 11.6753i | −0.472276 | − | 0.396286i | ||||
\(869\) | −9.08617 | − | 3.30710i | −0.308227 | − | 0.112186i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.44819 | + | 2.05428i | −0.0829538 | + | 0.0696065i | ||||
\(872\) | 0.559923 | + | 3.17548i | 0.0189614 | + | 0.107535i | ||||
\(873\) | −9.31414 | −0.315236 | ||||||||
\(874\) | −56.8658 | + | 7.23758i | −1.92352 | + | 0.244815i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.82297 | + | 16.0098i | 0.0953792 | + | 0.540923i | ||||
\(877\) | 31.2742 | − | 26.2422i | 1.05606 | − | 0.886136i | 0.0623382 | − | 0.998055i | \(-0.480144\pi\) |
0.993717 | + | 0.111919i | \(0.0356998\pi\) | |||||||
\(878\) | 69.5298 | − | 25.3068i | 2.34652 | − | 0.854062i | ||||
\(879\) | 64.5765 | + | 23.5039i | 2.17811 | + | 0.792768i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8807 | − | 41.3627i | 0.804563 | − | 1.39354i | −0.112023 | − | 0.993706i | \(-0.535733\pi\) |
0.916586 | − | 0.399838i | \(-0.130934\pi\) | |||||||
\(882\) | −10.0909 | − | 17.4780i | −0.339778 | − | 0.588513i | ||||
\(883\) | −5.57488 | + | 31.6167i | −0.187610 | + | 1.06399i | 0.734946 | + | 0.678125i | \(0.237207\pi\) |
−0.922556 | + | 0.385863i | \(0.873904\pi\) | |||||||
\(884\) | 0.874713 | − | 4.96074i | 0.0294198 | − | 0.166848i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.0629 | + | 48.6064i | −0.942792 | + | 1.63296i | ||||
\(887\) | 6.75510 | + | 5.66820i | 0.226814 | + | 0.190319i | 0.749112 | − | 0.662444i | \(-0.230481\pi\) |
−0.522298 | + | 0.852763i | \(0.674925\pi\) | |||||||
\(888\) | 27.8649 | + | 10.1420i | 0.935084 | + | 0.340343i | ||||
\(889\) | 1.89999 | − | 0.691539i | 0.0637235 | − | 0.0231935i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.96205 | − | 50.8263i | −0.300240 | − | 1.70275i | ||||
\(892\) | −4.37586 | −0.146515 | ||||||||
\(893\) | 39.8346 | + | 25.6192i | 1.33301 | + | 0.857314i | ||||
\(894\) | 20.2002 | 0.675595 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.2224 | + | 8.57759i | −0.341505 | + | 0.286557i | ||||
\(897\) | 4.66669 | − | 1.69854i | 0.155816 | − | 0.0567125i | ||||
\(898\) | −26.9139 | − | 9.79587i | −0.898130 | − | 0.326892i | ||||
\(899\) | −3.29461 | − | 2.76451i | −0.109881 | − | 0.0922014i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8661 | − | 30.9450i | −0.595206 | − | 1.03093i | ||||
\(902\) | 9.07627 | − | 51.4741i | 0.302207 | − | 1.71390i | ||||
\(903\) | −4.15332 | + | 23.5546i | −0.138214 | + | 0.783849i | ||||
\(904\) | −7.25071 | − | 12.5586i | −0.241155 | − | 0.417693i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −71.1810 | − | 59.7279i | −2.36483 | − | 1.98433i | ||||
\(907\) | 9.71693 | + | 3.53667i | 0.322645 | + | 0.117433i | 0.498265 | − | 0.867025i | \(-0.333971\pi\) |
−0.175620 | + | 0.984458i | \(0.556193\pi\) | |||||||
\(908\) | 10.1145 | − | 3.68139i | 0.335663 | − | 0.122171i | ||||
\(909\) | 13.6785 | − | 11.4776i | 0.453686 | − | 0.380688i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.25941 | 0.174252 | 0.0871260 | − | 0.996197i | \(-0.472232\pi\) | ||||
0.0871260 | + | 0.996197i | \(0.472232\pi\) | |||||||
\(912\) | 21.3155 | + | 13.7089i | 0.705827 | + | 0.453946i | ||||
\(913\) | −28.8557 | −0.954985 | ||||||||
\(914\) | 0.0762343 | + | 0.432346i | 0.00252161 | + | 0.0143007i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.2193 | + | 4.81143i | −0.436778 | + | 0.158974i | ||||
\(917\) | −27.2563 | − | 9.92047i | −0.900081 | − | 0.327603i | ||||
\(918\) | −20.4637 | − | 17.1711i | −0.675403 | − | 0.566731i | ||||
\(919\) | −0.101184 | + | 0.175255i | −0.00333774 | + | 0.00578114i | −0.867689 | − | 0.497107i | \(-0.834396\pi\) |
0.864352 | + | 0.502888i | \(0.167729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.34453 | − | 35.9816i | 0.209060 | − | 1.18564i | ||||
\(922\) | −14.4512 | + | 81.9569i | −0.475925 | + | 2.69911i | ||||
\(923\) | −1.15746 | − | 2.00479i | −0.0380984 | − | 0.0659883i | ||||
\(924\) | −19.7544 | + | 34.2155i | −0.649871 | + | 1.12561i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.8774 | + | 5.41492i | 0.488901 | + | 0.177945i | ||||
\(927\) | 14.4712 | − | 5.26707i | 0.475296 | − | 0.172993i | ||||
\(928\) | −5.41624 | + | 4.54477i | −0.177797 | + | 0.149189i | ||||
\(929\) | 3.23698 | + | 18.3578i | 0.106202 | + | 0.602301i | 0.990733 | + | 0.135821i | \(0.0433671\pi\) |
−0.884532 | + | 0.466480i | \(0.845522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7247 | + | 2.63773i | −0.679223 | + | 0.0864480i | ||||
\(932\) | −71.8151 | −2.35238 | ||||||||
\(933\) | −9.59533 | − | 54.4178i | −0.314137 | − | 1.78156i | ||||
\(934\) | 35.8150 | − | 30.0524i | 1.17190 | − | 0.983344i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.781404 | + | 0.284408i | 0.0255410 | + | 0.00929615i | ||||
\(937\) | 38.6935 | + | 32.4677i | 1.26406 | + | 1.06067i | 0.995237 | + | 0.0974836i | \(0.0310794\pi\) |
0.268824 | + | 0.963189i | \(0.413365\pi\) | |||||||
\(938\) | 14.0215 | − | 24.2859i | 0.457818 | − | 0.792964i | ||||
\(939\) | −11.4568 | − | 19.8438i | −0.373880 | − | 0.647579i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.87903 | + | 16.3278i | −0.0938538 | + | 0.532271i | 0.901239 | + | 0.433323i | \(0.142659\pi\) |
−0.995093 | + | 0.0989484i | \(0.968452\pi\) | |||||||
\(942\) | 0.681118 | + | 1.17973i | 0.0221920 | + | 0.0384377i | ||||
\(943\) | 16.1463 | − | 27.9663i | 0.525797 | − | 0.910708i | ||||
\(944\) | 19.5840 | + | 16.4329i | 0.637405 | + | 0.534847i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −67.7100 | + | 24.6444i | −2.20144 | + | 0.801259i | ||||
\(947\) | −28.6765 | + | 24.0625i | −0.931862 | + | 0.781925i | −0.976151 | − | 0.217094i | \(-0.930342\pi\) |
0.0442887 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(948\) | −2.03754 | − | 11.5555i | −0.0661763 | − | 0.375304i | ||||
\(949\) | −1.03315 | −0.0335374 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.5526 | 0.439474 | ||||||||
\(952\) | 1.64839 | + | 9.34847i | 0.0534245 | + | 0.302986i | ||||
\(953\) | −32.5326 | + | 27.2981i | −1.05384 | + | 0.884273i | −0.993492 | − | 0.113905i | \(-0.963664\pi\) |
−0.0603438 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(954\) | 25.8095 | − | 9.39387i | 0.835612 | − | 0.304138i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.0874 | − | 18.5336i | −0.714359 | − | 0.599418i | ||||
\(957\) | −4.67748 | + | 8.10162i | −0.151201 | + | 0.261888i | ||||
\(958\) | −29.9380 | − | 51.8541i | −0.967252 | − | 1.67533i | ||||
\(959\) | 2.75529 | − | 15.6260i | 0.0889728 | − | 0.504590i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.97887 | + | 6.89160i | 0.128351 | + | 0.222310i | ||||
\(962\) | −4.38740 | + | 7.59919i | −0.141455 | + | 0.245008i | ||||
\(963\) | −0.784034 | − | 0.657883i | −0.0252652 | − | 0.0212000i | ||||
\(964\) | −39.1657 | − | 14.2552i | −1.26144 | − | 0.459128i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −33.3818 | + | 28.0107i | −1.07404 | + | 0.901228i | ||||
\(967\) | −2.81797 | − | 15.9815i | −0.0906197 | − | 0.513930i | −0.996002 | − | 0.0893324i | \(-0.971527\pi\) |
0.905382 | − | 0.424598i | \(-0.139584\pi\) | |||||||
\(968\) | −12.7315 | −0.409206 | ||||||||
\(969\) | 47.3460 | − | 24.3882i | 1.52097 | − | 0.783463i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.05833 | − | 17.3447i | −0.0981465 | − | 0.556617i | −0.993738 | − | 0.111738i | \(-0.964358\pi\) |
0.895591 | − | 0.444878i | \(-0.146753\pi\) | |||||||
\(972\) | 34.5910 | − | 29.0253i | 1.10951 | − | 0.930988i | ||||
\(973\) | −10.0392 | + | 3.65396i | −0.321841 | + | 0.117140i | ||||
\(974\) | 28.3229 | + | 10.3087i | 0.907524 | + | 0.330312i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.06250 | − | 5.30441i | 0.0980283 | − | 0.169790i | ||||
\(977\) | 0.0604375 | + | 0.104681i | 0.00193357 | + | 0.00334903i | 0.866991 | − | 0.498325i | \(-0.166051\pi\) |
−0.865057 | + | 0.501674i | \(0.832718\pi\) | |||||||
\(978\) | 17.0342 | − | 96.6056i | 0.544693 | − | 3.08911i | ||||
\(979\) | −2.69898 | + | 15.3067i | −0.0862597 | + | 0.489203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.72943 | − | 4.72751i | 0.0871439 | − | 0.150938i | ||||
\(982\) | 37.8874 | + | 31.7913i | 1.20904 | + | 1.01450i | ||||
\(983\) | 21.3108 | + | 7.75648i | 0.679708 | + | 0.247393i | 0.658722 | − | 0.752386i | \(-0.271097\pi\) |
0.0209857 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(984\) | 12.8004 | − | 4.65898i | 0.408063 | − | 0.148523i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.81738 | + | 10.3069i | 0.0578773 | + | 0.328239i | ||||
\(987\) | 36.0033 | 1.14600 | ||||||||
\(988\) | 2.72058 | − | 2.94344i | 0.0865530 | − | 0.0936434i | ||||
\(989\) | −44.5179 | −1.41559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.1874 | + | 34.5603i | −1.30836 | + | 1.09784i | −0.319725 | + | 0.947510i | \(0.603591\pi\) |
−0.988635 | + | 0.150334i | \(0.951965\pi\) | |||||||
\(992\) | −35.5963 | + | 12.9560i | −1.13018 | + | 0.411353i | ||||
\(993\) | 24.7545 | + | 9.00991i | 0.785561 | + | 0.285921i | ||||
\(994\) | 15.5605 | + | 13.0568i | 0.493550 | + | 0.414137i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.5083 | − | 30.3252i | −0.554770 | − | 0.960890i | ||||
\(997\) | −6.38045 | + | 36.1853i | −0.202071 | + | 1.14600i | 0.699912 | + | 0.714229i | \(0.253223\pi\) |
−0.901983 | + | 0.431772i | \(0.857889\pi\) | |||||||
\(998\) | 15.7123 | − | 89.1091i | 0.497365 | − | 2.82070i | ||||
\(999\) | 13.0331 | + | 22.5739i | 0.412348 | + | 0.714207i |
(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 | 475.2.l.c.351.1 | 18 | ||
5.2 | odd | 4 | 475.2.u.b.199.5 | 36 | |||
5.3 | odd | 4 | 475.2.u.b.199.2 | 36 | |||
5.4 | even | 2 | 95.2.k.a.66.3 | yes | 18 | ||
15.14 | odd | 2 | 855.2.bs.c.541.1 | 18 | |||
19.6 | even | 9 | 9025.2.a.cc.1.3 | 9 | |||
19.13 | odd | 18 | 9025.2.a.cf.1.7 | 9 | |||
19.17 | even | 9 | inner | 475.2.l.c.226.1 | 18 | ||
95.17 | odd | 36 | 475.2.u.b.74.2 | 36 | |||
95.44 | even | 18 | 1805.2.a.v.1.7 | 9 | |||
95.74 | even | 18 | 95.2.k.a.36.3 | ✓ | 18 | ||
95.89 | odd | 18 | 1805.2.a.s.1.3 | 9 | |||
95.93 | odd | 36 | 475.2.u.b.74.5 | 36 | |||
285.74 | odd | 18 | 855.2.bs.c.226.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.36.3 | ✓ | 18 | 95.74 | even | 18 | ||
95.2.k.a.66.3 | yes | 18 | 5.4 | even | 2 | ||
475.2.l.c.226.1 | 18 | 19.17 | even | 9 | inner | ||
475.2.l.c.351.1 | 18 | 1.1 | even | 1 | trivial | ||
475.2.u.b.74.2 | 36 | 95.17 | odd | 36 | |||
475.2.u.b.74.5 | 36 | 95.93 | odd | 36 | |||
475.2.u.b.199.2 | 36 | 5.3 | odd | 4 | |||
475.2.u.b.199.5 | 36 | 5.2 | odd | 4 | |||
855.2.bs.c.226.1 | 18 | 285.74 | odd | 18 | |||
855.2.bs.c.541.1 | 18 | 15.14 | odd | 2 | |||
1805.2.a.s.1.3 | 9 | 95.89 | odd | 18 | |||
1805.2.a.v.1.7 | 9 | 95.44 | even | 18 | |||
9025.2.a.cc.1.3 | 9 | 19.6 | even | 9 | |||
9025.2.a.cf.1.7 | 9 | 19.13 | odd | 18 |