Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(107,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("432.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.l (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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.15 | ||
Character | \(\chi\) | \(=\) | 432.107 |
Dual form | 432.2.l.a.323.15 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38130 | + | 0.303332i | 0.976727 | + | 0.214488i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.81598 | + | 0.837984i | 0.907990 | + | 0.418992i | ||||
\(5\) | −1.39178 | + | 1.39178i | −0.622423 | + | 0.622423i | −0.946150 | − | 0.323728i | \(-0.895064\pi\) |
0.323728 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.33599 | −0.504958 | −0.252479 | − | 0.967602i | \(-0.581246\pi\) | ||||
−0.252479 | + | 0.967602i | \(0.581246\pi\) | |||||||
\(8\) | 2.25423 | + | 1.70835i | 0.796989 | + | 0.603993i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.34464 | + | 1.50029i | −0.741439 | + | 0.474435i | ||||
\(11\) | 4.37602 | + | 4.37602i | 1.31942 | + | 1.31942i | 0.914236 | + | 0.405183i | \(0.132792\pi\) |
0.405183 | + | 0.914236i | \(0.367208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.20314 | − | 1.20314i | 0.333692 | − | 0.333692i | −0.520295 | − | 0.853987i | \(-0.674178\pi\) |
0.853987 | + | 0.520295i | \(0.174178\pi\) | |||||||
\(14\) | −1.84541 | − | 0.405249i | −0.493206 | − | 0.108307i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.59557 | + | 3.04352i | 0.648891 | + | 0.760881i | ||||
\(17\) | 1.84799i | 0.448204i | 0.974566 | + | 0.224102i | \(0.0719448\pi\) | ||||
−0.974566 | + | 0.224102i | \(0.928055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.19463 | − | 1.19463i | −0.274067 | − | 0.274067i | 0.556668 | − | 0.830735i | \(-0.312080\pi\) |
−0.830735 | + | 0.556668i | \(0.812080\pi\) | |||||||
\(20\) | −3.69373 | + | 1.36115i | −0.825944 | + | 0.304363i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.71721 | + | 7.37198i | 1.00571 | + | 1.57171i | ||||
\(23\) | − | 2.84298i | − | 0.592802i | −0.955064 | − | 0.296401i | \(-0.904213\pi\) | ||
0.955064 | − | 0.296401i | \(-0.0957865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.12590i | 0.225180i | ||||||||
\(26\) | 2.02686 | − | 1.29695i | 0.397499 | − | 0.254353i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.42614 | − | 1.11954i | −0.458497 | − | 0.211573i | ||||
\(29\) | −0.485646 | − | 0.485646i | −0.0901823 | − | 0.0901823i | 0.660576 | − | 0.750759i | \(-0.270312\pi\) |
−0.750759 | + | 0.660576i | \(0.770312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.61300i | − | 1.72654i | −0.504738 | − | 0.863272i | \(-0.668411\pi\) | ||
0.504738 | − | 0.863272i | \(-0.331589\pi\) | |||||||
\(32\) | 2.66206 | + | 4.99134i | 0.470590 | + | 0.882352i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.560554 | + | 2.55263i | −0.0961342 | + | 0.437772i | ||||
\(35\) | 1.85941 | − | 1.85941i | 0.314298 | − | 0.314298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.99709 | − | 6.99709i | −1.15031 | − | 1.15031i | −0.986489 | − | 0.163825i | \(-0.947617\pi\) |
−0.163825 | − | 0.986489i | \(-0.552383\pi\) | |||||||
\(38\) | −1.28778 | − | 2.01251i | −0.208905 | − | 0.326473i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.51503 | + | 0.759737i | −0.872004 | + | 0.120125i | ||||
\(41\) | −9.58349 | −1.49669 | −0.748345 | − | 0.663310i | \(-0.769151\pi\) | ||||
−0.748345 | + | 0.663310i | \(0.769151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.79108 | − | 5.79108i | 0.883132 | − | 0.883132i | −0.110720 | − | 0.993852i | \(-0.535316\pi\) |
0.993852 | + | 0.110720i | \(0.0353156\pi\) | |||||||
\(44\) | 4.27973 | + | 11.6138i | 0.645193 | + | 1.75084i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.862366 | − | 3.92701i | 0.127149 | − | 0.579006i | ||||
\(47\) | 8.06957 | 1.17707 | 0.588534 | − | 0.808473i | \(-0.299705\pi\) | ||||
0.588534 | + | 0.808473i | \(0.299705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.21512 | −0.745017 | ||||||||
\(50\) | −0.341521 | + | 1.55520i | −0.0482983 | + | 0.219939i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.19310 | − | 1.17667i | 0.442804 | − | 0.163175i | ||||
\(53\) | 3.25428 | − | 3.25428i | 0.447010 | − | 0.447010i | −0.447349 | − | 0.894359i | \(-0.647632\pi\) |
0.894359 | + | 0.447349i | \(0.147632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.1809 | −1.64247 | ||||||||
\(56\) | −3.01163 | − | 2.28235i | −0.402446 | − | 0.304992i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.523511 | − | 0.818135i | −0.0687404 | − | 0.107426i | ||||
\(59\) | 0.730119 | + | 0.730119i | 0.0950534 | + | 0.0950534i | 0.753034 | − | 0.657981i | \(-0.228589\pi\) |
−0.657981 | + | 0.753034i | \(0.728589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.32974 | − | 7.32974i | 0.938478 | − | 0.938478i | −0.0597365 | − | 0.998214i | \(-0.519026\pi\) |
0.998214 | + | 0.0597365i | \(0.0190261\pi\) | |||||||
\(62\) | 2.91593 | − | 13.2784i | 0.370323 | − | 1.68636i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.16307 | + | 7.70202i | 0.270384 | + | 0.962753i | ||||
\(65\) | 3.34902i | 0.415395i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.38696 | + | 7.38696i | 0.902461 | + | 0.902461i | 0.995649 | − | 0.0931880i | \(-0.0297057\pi\) |
−0.0931880 | + | 0.995649i | \(0.529706\pi\) | |||||||
\(68\) | −1.54859 | + | 3.35591i | −0.187794 | + | 0.406964i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.13242 | − | 2.00438i | 0.374396 | − | 0.239570i | ||||
\(71\) | 4.40733i | 0.523054i | 0.965196 | + | 0.261527i | \(0.0842260\pi\) | ||||
−0.965196 | + | 0.261527i | \(0.915774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.385877i | 0.0451635i | 0.999745 | + | 0.0225818i | \(0.00718861\pi\) | ||||
−0.999745 | + | 0.0225818i | \(0.992811\pi\) | |||||||
\(74\) | −7.54264 | − | 11.7875i | −0.876814 | − | 1.37027i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.16834 | − | 3.17051i | −0.134018 | − | 0.363682i | ||||
\(77\) | −5.84633 | − | 5.84633i | −0.666251 | − | 0.666251i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.84274i | 0.994886i | 0.867497 | + | 0.497443i | \(0.165728\pi\) | ||||
−0.867497 | + | 0.497443i | \(0.834272\pi\) | |||||||
\(80\) | −7.84837 | − | 0.623460i | −0.877474 | − | 0.0697049i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.2377 | − | 2.90698i | −1.46186 | − | 0.321022i | ||||
\(83\) | 6.75487 | − | 6.75487i | 0.741443 | − | 0.741443i | −0.231412 | − | 0.972856i | \(-0.574335\pi\) |
0.972856 | + | 0.231412i | \(0.0743347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.57200 | − | 2.57200i | −0.278972 | − | 0.278972i | ||||
\(86\) | 9.75584 | − | 6.24260i | 1.05200 | − | 0.673157i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.38876 | + | 17.3403i | 0.254642 | + | 1.84848i | ||||
\(89\) | −13.3980 | −1.42018 | −0.710091 | − | 0.704110i | \(-0.751346\pi\) | ||||
−0.710091 | + | 0.704110i | \(0.751346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.60739 | + | 1.60739i | −0.168501 | + | 0.168501i | ||||
\(92\) | 2.38237 | − | 5.16279i | 0.248379 | − | 0.538259i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.1465 | + | 2.44776i | 1.14967 | + | 0.252467i | ||||
\(95\) | 3.32533 | 0.341171 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.81458 | −0.285777 | −0.142889 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142889 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(98\) | −7.20365 | − | 1.58191i | −0.727678 | − | 0.159797i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.943486 | + | 2.04461i | −0.0943486 | + | 0.204461i | ||||
\(101\) | −9.18142 | + | 9.18142i | −0.913585 | + | 0.913585i | −0.996552 | − | 0.0829670i | \(-0.973560\pi\) |
0.0829670 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.32705 | 0.130758 | 0.0653791 | − | 0.997860i | \(-0.479174\pi\) | ||||
0.0653791 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(104\) | 4.76755 | − | 0.656766i | 0.467497 | − | 0.0644012i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.48227 | − | 3.50802i | 0.532485 | − | 0.340729i | ||||
\(107\) | −8.35676 | − | 8.35676i | −0.807879 | − | 0.807879i | 0.176434 | − | 0.984313i | \(-0.443544\pi\) |
−0.984313 | + | 0.176434i | \(0.943544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.82294 | − | 9.82294i | 0.940867 | − | 0.940867i | −0.0574793 | − | 0.998347i | \(-0.518306\pi\) |
0.998347 | + | 0.0574793i | \(0.0183063\pi\) | |||||||
\(110\) | −16.8255 | − | 3.69485i | −1.60425 | − | 0.352290i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46766 | − | 4.06613i | −0.327663 | − | 0.384213i | ||||
\(113\) | − | 12.8196i | − | 1.20596i | −0.797755 | − | 0.602981i | \(-0.793979\pi\) | ||
0.797755 | − | 0.602981i | \(-0.206021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95680 | + | 3.95680i | 0.368974 | + | 0.368974i | ||||
\(116\) | −0.474960 | − | 1.28889i | −0.0440989 | − | 0.119670i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.787045 | + | 1.22998i | 0.0724534 | + | 0.113229i | ||||
\(119\) | − | 2.46890i | − | 0.226324i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.2990i | 2.48173i | ||||||||
\(122\) | 12.3479 | − | 7.90123i | 1.11793 | − | 0.715344i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.05554 | − | 17.4570i | 0.723409 | − | 1.56769i | ||||
\(125\) | −8.52590 | − | 8.52590i | −0.762580 | − | 0.762580i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.40699i | 0.124850i | 0.998050 | + | 0.0624249i | \(0.0198834\pi\) | ||||
−0.998050 | + | 0.0624249i | \(0.980117\pi\) | |||||||
\(128\) | 0.651582 | + | 11.2949i | 0.0575922 | + | 0.998340i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.01587 | + | 4.62601i | −0.0890973 | + | 0.405728i | ||||
\(131\) | 0.494626 | − | 0.494626i | 0.0432157 | − | 0.0432157i | −0.685169 | − | 0.728384i | \(-0.740272\pi\) |
0.728384 | + | 0.685169i | \(0.240272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.59602 | + | 1.59602i | 0.138393 | + | 0.138393i | ||||
\(134\) | 7.96291 | + | 12.4443i | 0.687890 | + | 1.07502i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.15702 | + | 4.16579i | −0.270712 | + | 0.357213i | ||||
\(137\) | 12.9156 | 1.10346 | 0.551728 | − | 0.834024i | \(-0.313969\pi\) | ||||
0.551728 | + | 0.834024i | \(0.313969\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1838 | − | 15.1838i | 1.28787 | − | 1.28787i | 0.351791 | − | 0.936078i | \(-0.385573\pi\) |
0.936078 | − | 0.351791i | \(-0.114427\pi\) | |||||||
\(140\) | 4.93480 | − | 1.81849i | 0.417067 | − | 0.153691i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.33688 | + | 6.08784i | −0.112189 | + | 0.510880i | ||||
\(143\) | 10.5300 | 0.880560 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.35183 | 0.112263 | ||||||||
\(146\) | −0.117049 | + | 0.533012i | −0.00968703 | + | 0.0441124i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.84312 | − | 18.5700i | −0.562501 | − | 1.52645i | ||||
\(149\) | −9.78679 | + | 9.78679i | −0.801765 | + | 0.801765i | −0.983371 | − | 0.181606i | \(-0.941870\pi\) |
0.181606 | + | 0.983371i | \(0.441870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9203 | −1.53971 | −0.769857 | − | 0.638216i | \(-0.779673\pi\) | ||||
−0.769857 | + | 0.638216i | \(0.779673\pi\) | |||||||
\(152\) | −0.652119 | − | 4.73382i | −0.0528938 | − | 0.383964i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.30216 | − | 9.84892i | −0.507843 | − | 0.793648i | ||||
\(155\) | 13.3792 | + | 13.3792i | 1.07464 | + | 1.07464i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3331 | + | 12.3331i | −0.984291 | + | 0.984291i | −0.999879 | − | 0.0155875i | \(-0.995038\pi\) |
0.0155875 | + | 0.999879i | \(0.495038\pi\) | |||||||
\(158\) | −2.68228 | + | 12.2145i | −0.213391 | + | 0.971732i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.6518 | − | 3.24184i | −0.842102 | − | 0.256290i | ||||
\(161\) | 3.79820i | 0.299340i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6186 | + | 13.6186i | 1.06669 | + | 1.06669i | 0.997611 | + | 0.0690796i | \(0.0220063\pi\) |
0.0690796 | + | 0.997611i | \(0.477994\pi\) | |||||||
\(164\) | −17.4034 | − | 8.03081i | −1.35898 | − | 0.627101i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3795 | − | 7.28154i | 0.883218 | − | 0.565157i | ||||
\(167\) | − | 6.27242i | − | 0.485374i | −0.970105 | − | 0.242687i | \(-0.921971\pi\) | ||
0.970105 | − | 0.242687i | \(-0.0780289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1049i | 0.777299i | ||||||||
\(170\) | −2.77253 | − | 4.33287i | −0.212643 | − | 0.332316i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.3693 | − | 5.66365i | 1.17190 | − | 0.431850i | ||||
\(173\) | 8.28143 | + | 8.28143i | 0.629625 | + | 0.629625i | 0.947974 | − | 0.318348i | \(-0.103128\pi\) |
−0.318348 | + | 0.947974i | \(0.603128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.50419i | − | 0.113706i | ||||||
\(176\) | −1.96028 | + | 24.6768i | −0.147761 | + | 1.86008i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.5066 | − | 4.06403i | −1.38713 | − | 0.304612i | ||||
\(179\) | 2.23413 | − | 2.23413i | 0.166986 | − | 0.166986i | −0.618667 | − | 0.785653i | \(-0.712327\pi\) |
0.785653 | + | 0.618667i | \(0.212327\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.60438 | + | 7.60438i | 0.565229 | + | 0.565229i | 0.930788 | − | 0.365559i | \(-0.119122\pi\) |
−0.365559 | + | 0.930788i | \(0.619122\pi\) | |||||||
\(182\) | −2.70787 | + | 1.73272i | −0.200720 | + | 0.128438i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.85681 | − | 6.40872i | 0.358049 | − | 0.472457i | ||||
\(185\) | 19.4768 | 1.43196 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.08684 | + | 8.08684i | −0.591368 | + | 0.591368i | ||||
\(188\) | 14.6542 | + | 6.76217i | 1.06877 | + | 0.493182i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.59328 | + | 1.00868i | 0.333231 | + | 0.0731771i | ||||
\(191\) | −6.09856 | −0.441276 | −0.220638 | − | 0.975356i | \(-0.570814\pi\) | ||||
−0.220638 | + | 0.975356i | \(0.570814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.42444 | 0.462441 | 0.231221 | − | 0.972901i | \(-0.425728\pi\) | ||||
0.231221 | + | 0.972901i | \(0.425728\pi\) | |||||||
\(194\) | −3.88778 | − | 0.853752i | −0.279126 | − | 0.0612958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.47055 | − | 4.37019i | −0.676468 | − | 0.312156i | ||||
\(197\) | 0.305089 | − | 0.305089i | 0.0217367 | − | 0.0217367i | −0.696155 | − | 0.717892i | \(-0.745107\pi\) |
0.717892 | + | 0.696155i | \(0.245107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.26500 | −0.656779 | −0.328389 | − | 0.944542i | \(-0.606506\pi\) | ||||
−0.328389 | + | 0.944542i | \(0.606506\pi\) | |||||||
\(200\) | −1.92343 | + | 2.53803i | −0.136007 | + | 0.179466i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.4673 | + | 9.89728i | −1.08828 | + | 0.696370i | ||||
\(203\) | 0.648821 | + | 0.648821i | 0.0455383 | + | 0.0455383i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.3381 | − | 13.3381i | 0.931574 | − | 0.931574i | ||||
\(206\) | 1.83306 | + | 0.402537i | 0.127715 | + | 0.0280460i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.78464 | + | 0.538959i | 0.470430 | + | 0.0373701i | ||||
\(209\) | − | 10.4555i | − | 0.723219i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.35580 | − | 1.35580i | −0.0933374 | − | 0.0933374i | 0.658896 | − | 0.752234i | \(-0.271024\pi\) |
−0.752234 | + | 0.658896i | \(0.771024\pi\) | |||||||
\(212\) | 8.63675 | − | 3.18268i | 0.593175 | − | 0.218587i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.00833 | − | 14.0781i | −0.615796 | − | 0.962357i | ||||
\(215\) | 16.1198i | 1.09936i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.8429i | 0.871833i | ||||||||
\(218\) | 16.5480 | − | 10.5888i | 1.12077 | − | 0.717166i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22.1203 | − | 10.2074i | −1.49135 | − | 0.688183i | ||||
\(221\) | 2.22340 | + | 2.22340i | 0.149562 | + | 0.149562i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.18959i | − | 0.0796606i | −0.999206 | − | 0.0398303i | \(-0.987318\pi\) | ||
0.999206 | − | 0.0398303i | \(-0.0126817\pi\) | |||||||
\(224\) | −3.55649 | − | 6.66840i | −0.237628 | − | 0.445551i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.88858 | − | 17.7077i | 0.258664 | − | 1.17790i | ||||
\(227\) | −12.7220 | + | 12.7220i | −0.844387 | + | 0.844387i | −0.989426 | − | 0.145039i | \(-0.953669\pi\) |
0.145039 | + | 0.989426i | \(0.453669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5661 | − | 12.5661i | −0.830393 | − | 0.830393i | 0.157177 | − | 0.987570i | \(-0.449761\pi\) |
−0.987570 | + | 0.157177i | \(0.949761\pi\) | |||||||
\(230\) | 4.26531 | + | 6.66575i | 0.281246 | + | 0.439527i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.265102 | − | 1.92441i | −0.0174048 | − | 0.126344i | ||||
\(233\) | −17.2312 | −1.12885 | −0.564427 | − | 0.825483i | \(-0.690903\pi\) | ||||
−0.564427 | + | 0.825483i | \(0.690903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2311 | + | 11.2311i | −0.732634 | + | 0.732634i | ||||
\(236\) | 0.714053 | + | 1.93771i | 0.0464809 | + | 0.126134i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.748897 | − | 3.41030i | 0.0485438 | − | 0.221057i | ||||
\(239\) | −17.6216 | −1.13985 | −0.569925 | − | 0.821697i | \(-0.693028\pi\) | ||||
−0.569925 | + | 0.821697i | \(0.693028\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.55260 | −0.293259 | −0.146629 | − | 0.989191i | \(-0.546842\pi\) | ||||
−0.146629 | + | 0.989191i | \(0.546842\pi\) | |||||||
\(242\) | −8.28066 | + | 37.7082i | −0.532301 | + | 2.42397i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.4529 | − | 7.16846i | 1.24534 | − | 0.458914i | ||||
\(245\) | 7.25830 | − | 7.25830i | 0.463716 | − | 0.463716i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.87463 | −0.182908 | ||||||||
\(248\) | 16.4224 | − | 21.6699i | 1.04282 | − | 1.37604i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.19065 | − | 14.3630i | −0.581268 | − | 0.908396i | ||||
\(251\) | −13.6040 | − | 13.6040i | −0.858677 | − | 0.858677i | 0.132505 | − | 0.991182i | \(-0.457698\pi\) |
−0.991182 | + | 0.132505i | \(0.957698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4409 | − | 12.4409i | 0.782154 | − | 0.782154i | ||||
\(254\) | −0.426783 | + | 1.94347i | −0.0267788 | + | 0.121944i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.52608 | + | 15.7993i | −0.157880 | + | 0.987458i | ||||
\(257\) | 21.0374i | 1.31228i | 0.754640 | + | 0.656139i | \(0.227811\pi\) | ||||
−0.754640 | + | 0.656139i | \(0.772189\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.34807 | + | 9.34807i | 0.580861 | + | 0.580861i | ||||
\(260\) | −2.80643 | + | 6.08176i | −0.174047 | + | 0.377175i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.833263 | − | 0.533191i | 0.0514792 | − | 0.0329407i | ||||
\(263\) | 5.35347i | 0.330109i | 0.986284 | + | 0.165055i | \(0.0527800\pi\) | ||||
−0.986284 | + | 0.165055i | \(0.947220\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.05849i | 0.556459i | ||||||||
\(266\) | 1.72046 | + | 2.68871i | 0.105488 | + | 0.164855i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.22441 | + | 19.6047i | 0.441301 | + | 1.19755i | ||||
\(269\) | 18.2302 | + | 18.2302i | 1.11151 | + | 1.11151i | 0.992946 | + | 0.118569i | \(0.0378306\pi\) |
0.118569 | + | 0.992946i | \(0.462169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32505i | 0.384219i | 0.981373 | + | 0.192110i | \(0.0615329\pi\) | ||||
−0.981373 | + | 0.192110i | \(0.938467\pi\) | |||||||
\(272\) | −5.62441 | + | 4.79658i | −0.341030 | + | 0.290835i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8404 | + | 3.91772i | 1.07778 | + | 0.236678i | ||||
\(275\) | −4.92695 | + | 4.92695i | −0.297107 | + | 0.297107i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.50389 | − | 4.50389i | −0.270612 | − | 0.270612i | 0.558734 | − | 0.829347i | \(-0.311287\pi\) |
−0.829347 | + | 0.558734i | \(0.811287\pi\) | |||||||
\(278\) | 25.5790 | − | 16.3676i | 1.53413 | − | 0.981664i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.36805 | − | 1.01500i | 0.440325 | − | 0.0606581i | ||||
\(281\) | 20.6398 | 1.23127 | 0.615634 | − | 0.788033i | \(-0.288900\pi\) | ||||
0.615634 | + | 0.788033i | \(0.288900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8888 | − | 16.8888i | 1.00393 | − | 1.00393i | 0.00394063 | − | 0.999992i | \(-0.498746\pi\) |
0.999992 | − | 0.00394063i | \(-0.00125434\pi\) | |||||||
\(284\) | −3.69327 | + | 8.00362i | −0.219155 | + | 0.474927i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.5450 | + | 3.19407i | 0.860066 | + | 0.188869i | ||||
\(287\) | 12.8035 | 0.755766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5849 | 0.799113 | ||||||||
\(290\) | 1.86728 | + | 0.410051i | 0.109650 | + | 0.0240790i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.323359 | + | 0.700745i | −0.0189232 | + | 0.0410080i | ||||
\(293\) | 10.0125 | − | 10.0125i | 0.584934 | − | 0.584934i | −0.351321 | − | 0.936255i | \(-0.614267\pi\) |
0.936255 | + | 0.351321i | \(0.114267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.03233 | −0.118327 | ||||||||
\(296\) | −3.81953 | − | 27.7265i | −0.222006 | − | 1.61157i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.4871 | + | 10.5498i | −0.955074 | + | 0.611136i | ||||
\(299\) | −3.42052 | − | 3.42052i | −0.197814 | − | 0.197814i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.73685 | + | 7.73685i | −0.445945 | + | 0.445945i | ||||
\(302\) | −26.1346 | − | 5.73913i | −1.50388 | − | 0.330250i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.535146 | − | 6.73664i | 0.0306927 | − | 0.386373i | ||||
\(305\) | 20.4028i | 1.16826i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0816 | + | 13.0816i | 0.746607 | + | 0.746607i | 0.973840 | − | 0.227233i | \(-0.0729679\pi\) |
−0.227233 | + | 0.973840i | \(0.572968\pi\) | |||||||
\(308\) | −5.71769 | − | 15.5160i | −0.325796 | − | 0.884104i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.4223 | + | 22.5390i | 0.819133 | + | 1.28013i | ||||
\(311\) | − | 2.77454i | − | 0.157330i | −0.996901 | − | 0.0786648i | \(-0.974934\pi\) | ||
0.996901 | − | 0.0786648i | \(-0.0250657\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.90643i | − | 0.220804i | −0.993887 | − | 0.110402i | \(-0.964786\pi\) | ||
0.993887 | − | 0.110402i | \(-0.0352139\pi\) | |||||||
\(314\) | −20.7768 | + | 13.2947i | −1.17250 | + | 0.750265i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.41008 | + | 16.0582i | −0.416849 | + | 0.903347i | ||||
\(317\) | −4.99649 | − | 4.99649i | −0.280631 | − | 0.280631i | 0.552730 | − | 0.833361i | \(-0.313586\pi\) |
−0.833361 | + | 0.552730i | \(0.813586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.25039i | − | 0.237976i | ||||||
\(320\) | −13.7300 | − | 7.70900i | −0.767532 | − | 0.430946i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.15212 | + | 5.24646i | −0.0642049 | + | 0.292374i | ||||
\(323\) | 2.20767 | − | 2.20767i | 0.122838 | − | 0.122838i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.35462 | + | 1.35462i | 0.0751408 | + | 0.0751408i | ||||
\(326\) | 14.6804 | + | 22.9423i | 0.813073 | + | 1.27066i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.6034 | − | 16.3720i | −1.19285 | − | 0.903991i | ||||
\(329\) | −10.7809 | −0.594370 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.18235 | + | 3.18235i | −0.174918 | + | 0.174918i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(332\) | 17.9272 | − | 6.60623i | 0.983882 | − | 0.362564i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.90262 | − | 8.66409i | 0.104107 | − | 0.474078i | ||||
\(335\) | −20.5620 | −1.12342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8660 | −1.84480 | −0.922399 | − | 0.386238i | \(-0.873774\pi\) | ||||
−0.922399 | + | 0.386238i | \(0.873774\pi\) | |||||||
\(338\) | −3.06513 | + | 13.9579i | −0.166721 | + | 0.759209i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.51540 | − | 6.82598i | −0.136417 | − | 0.370191i | ||||
\(341\) | 42.0666 | − | 42.0666i | 2.27804 | − | 2.27804i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3193 | 0.881161 | ||||||||
\(344\) | 22.9476 | − | 3.16120i | 1.23725 | − | 0.170441i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.92712 | + | 13.9512i | 0.479925 | + | 0.750019i | ||||
\(347\) | −0.987636 | − | 0.987636i | −0.0530191 | − | 0.0530191i | 0.680100 | − | 0.733119i | \(-0.261936\pi\) |
−0.733119 | + | 0.680100i | \(0.761936\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8420 | + | 17.8420i | −0.955060 | + | 0.955060i | −0.999033 | − | 0.0439726i | \(-0.985999\pi\) |
0.0439726 | + | 0.999033i | \(0.485999\pi\) | |||||||
\(350\) | 0.456270 | − | 2.07774i | 0.0243886 | − | 0.111060i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.1930 | + | 33.4914i | −0.543287 | + | 1.78510i | ||||
\(353\) | − | 10.3421i | − | 0.550455i | −0.961379 | − | 0.275228i | \(-0.911247\pi\) | ||
0.961379 | − | 0.275228i | \(-0.0887532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.13403 | − | 6.13403i | −0.325560 | − | 0.325560i | ||||
\(356\) | −24.3305 | − | 11.2273i | −1.28951 | − | 0.595045i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.76368 | − | 2.40832i | 0.198917 | − | 0.127284i | ||||
\(359\) | 9.51484i | 0.502174i | 0.967965 | + | 0.251087i | \(0.0807880\pi\) | ||||
−0.967965 | + | 0.251087i | \(0.919212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 16.1457i | − | 0.849774i | ||||||
\(362\) | 8.19729 | + | 12.8106i | 0.430840 | + | 0.673309i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.26597 | + | 1.57202i | −0.223597 | + | 0.0823965i | ||||
\(365\) | −0.537056 | − | 0.537056i | −0.0281108 | − | 0.0281108i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 15.9015i | − | 0.830051i | −0.909810 | − | 0.415026i | \(-0.863773\pi\) | ||
0.909810 | − | 0.415026i | \(-0.136227\pi\) | |||||||
\(368\) | 8.65268 | − | 7.37914i | 0.451052 | − | 0.384664i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.9033 | + | 5.90793i | 1.39864 | + | 0.307139i | ||||
\(371\) | −4.34770 | + | 4.34770i | −0.225722 | + | 0.225722i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.33818 | + | 8.33818i | 0.431735 | + | 0.431735i | 0.889218 | − | 0.457483i | \(-0.151249\pi\) |
−0.457483 | + | 0.889218i | \(0.651249\pi\) | |||||||
\(374\) | −13.6233 | + | 8.71736i | −0.704446 | + | 0.450764i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.1906 | + | 13.7857i | 0.938110 | + | 0.710941i | ||||
\(377\) | −1.16861 | −0.0601863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.86499 | − | 9.86499i | 0.506731 | − | 0.506731i | −0.406791 | − | 0.913521i | \(-0.633352\pi\) |
0.913521 | + | 0.406791i | \(0.133352\pi\) | |||||||
\(380\) | 6.03873 | + | 2.78657i | 0.309780 | + | 0.142948i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.42394 | − | 1.84988i | −0.431006 | − | 0.0946483i | ||||
\(383\) | −24.8050 | −1.26748 | −0.633738 | − | 0.773548i | \(-0.718480\pi\) | ||||
−0.633738 | + | 0.773548i | \(0.718480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.2736 | 0.829380 | ||||||||
\(386\) | 8.87407 | + | 1.94873i | 0.451679 | + | 0.0991880i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.11122 | − | 2.35857i | −0.259483 | − | 0.119738i | ||||
\(389\) | −18.5481 | + | 18.5481i | −0.940428 | + | 0.940428i | −0.998323 | − | 0.0578943i | \(-0.981561\pi\) |
0.0578943 | + | 0.998323i | \(0.481561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.25380 | 0.265696 | ||||||||
\(392\) | −11.7561 | − | 8.90926i | −0.593771 | − | 0.449985i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.513962 | − | 0.328876i | 0.0258930 | − | 0.0165685i | ||||
\(395\) | −12.3071 | − | 12.3071i | −0.619240 | − | 0.619240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.27587 | − | 9.27587i | 0.465542 | − | 0.465542i | −0.434924 | − | 0.900467i | \(-0.643225\pi\) |
0.900467 | + | 0.434924i | \(0.143225\pi\) | |||||||
\(398\) | −12.7977 | − | 2.81037i | −0.641493 | − | 0.140871i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.42670 | + | 2.92235i | −0.171335 | + | 0.146117i | ||||
\(401\) | − | 32.5487i | − | 1.62540i | −0.582680 | − | 0.812702i | \(-0.697996\pi\) | ||
0.582680 | − | 0.812702i | \(-0.302004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.5658 | − | 11.5658i | −0.576135 | − | 0.576135i | ||||
\(404\) | −24.3672 | + | 8.97939i | −1.21231 | + | 0.446741i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.699408 | + | 1.09302i | 0.0347110 | + | 0.0542459i | ||||
\(407\) | − | 61.2387i | − | 3.03549i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.8204i | − | 0.732819i | −0.930454 | − | 0.366410i | \(-0.880587\pi\) | ||
0.930454 | − | 0.366410i | \(-0.119413\pi\) | |||||||
\(410\) | 22.4698 | − | 14.3781i | 1.10970 | − | 0.710082i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.40990 | + | 1.11205i | 0.118727 | + | 0.0547866i | ||||
\(413\) | −0.975434 | − | 0.975434i | −0.0479980 | − | 0.0479980i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.8026i | 0.922982i | ||||||||
\(416\) | 9.20814 | + | 2.80246i | 0.451466 | + | 0.137402i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.17147 | − | 14.4421i | 0.155122 | − | 0.706387i | ||||
\(419\) | −0.857617 | + | 0.857617i | −0.0418973 | + | 0.0418973i | −0.727745 | − | 0.685848i | \(-0.759432\pi\) |
0.685848 | + | 0.727745i | \(0.259432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1613 | − | 23.1613i | −1.12881 | − | 1.12881i | −0.990370 | − | 0.138445i | \(-0.955790\pi\) |
−0.138445 | − | 0.990370i | \(-0.544210\pi\) | |||||||
\(422\) | −1.46151 | − | 2.28403i | −0.0711454 | − | 0.111185i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.8954 | − | 1.77643i | 0.626254 | − | 0.0862711i | ||||
\(425\) | −2.08065 | −0.100926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.79250 | + | 9.79250i | −0.473892 | + | 0.473892i | ||||
\(428\) | −8.17288 | − | 22.1785i | −0.395051 | − | 1.07204i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.88965 | + | 22.2663i | −0.235800 | + | 1.07378i | ||||
\(431\) | −2.42928 | −0.117014 | −0.0585072 | − | 0.998287i | \(-0.518634\pi\) | ||||
−0.0585072 | + | 0.998287i | \(0.518634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.16178 | 0.392230 | 0.196115 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196115 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(434\) | −3.89566 | + | 17.7399i | −0.186998 | + | 0.851543i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.0697 | − | 9.60680i | 1.24851 | − | 0.460082i | ||||
\(437\) | −3.39631 | + | 3.39631i | −0.162468 | + | 0.162468i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.09986 | 0.100221 | 0.0501104 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501104 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(440\) | −27.4585 | − | 20.8093i | −1.30903 | − | 0.992043i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.39676 | + | 3.74561i | 0.114002 | + | 0.178161i | ||||
\(443\) | 7.58622 | + | 7.58622i | 0.360432 | + | 0.360432i | 0.863972 | − | 0.503540i | \(-0.167969\pi\) |
−0.503540 | + | 0.863972i | \(0.667969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.6470 | − | 18.6470i | 0.883954 | − | 0.883954i | ||||
\(446\) | 0.360839 | − | 1.64317i | 0.0170862 | − | 0.0778066i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.88985 | − | 10.2899i | −0.136532 | − | 0.486150i | ||||
\(449\) | 1.07314i | 0.0506445i | 0.999679 | + | 0.0253223i | \(0.00806119\pi\) | ||||
−0.999679 | + | 0.0253223i | \(0.991939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.9375 | − | 41.9375i | −1.97476 | − | 1.97476i | ||||
\(452\) | 10.7426 | − | 23.2801i | 0.505289 | − | 1.09500i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.4318 | + | 13.7139i | −1.00585 | + | 0.643624i | ||||
\(455\) | − | 4.47428i | − | 0.209757i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.2121i | − | 1.03904i | −0.854459 | − | 0.519519i | \(-0.826111\pi\) | ||
0.854459 | − | 0.519519i | \(-0.173889\pi\) | |||||||
\(458\) | −13.5459 | − | 21.1693i | −0.632958 | − | 0.989176i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.86974 | + | 10.5012i | 0.180427 | + | 0.489621i | ||||
\(461\) | −0.113003 | − | 0.113003i | −0.00526308 | − | 0.00526308i | 0.704470 | − | 0.709733i | \(-0.251185\pi\) |
−0.709733 | + | 0.704470i | \(0.751185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.8420i | − | 1.01509i | −0.861627 | − | 0.507543i | \(-0.830554\pi\) | ||
0.861627 | − | 0.507543i | \(-0.169446\pi\) | |||||||
\(464\) | 0.217550 | − | 2.73860i | 0.0100995 | − | 0.127136i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.8015 | − | 5.22677i | −1.10258 | − | 0.242126i | ||||
\(467\) | −16.6910 | + | 16.6910i | −0.772366 | + | 0.772366i | −0.978520 | − | 0.206154i | \(-0.933905\pi\) |
0.206154 | + | 0.978520i | \(0.433905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.86893 | − | 9.86893i | −0.455705 | − | 0.455705i | ||||
\(470\) | −18.9202 | + | 12.1067i | −0.872724 | + | 0.558442i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.398553 | + | 2.89315i | 0.0183449 | + | 0.133168i | ||||
\(473\) | 50.6838 | 2.33044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34504 | − | 1.34504i | 0.0617144 | − | 0.0617144i | ||||
\(476\) | 2.06890 | − | 4.48348i | 0.0948280 | − | 0.205500i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.3408 | − | 5.34520i | −1.11332 | − | 0.244484i | ||||
\(479\) | −38.9267 | −1.77861 | −0.889304 | − | 0.457317i | \(-0.848811\pi\) | ||||
−0.889304 | + | 0.457317i | \(0.848811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8370 | −0.767702 | ||||||||
\(482\) | −6.28851 | − | 1.38095i | −0.286434 | − | 0.0629005i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.8762 | + | 49.5745i | −1.03983 | + | 2.25339i | ||||
\(485\) | 3.91728 | − | 3.91728i | 0.177874 | − | 0.177874i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6434 | −1.56984 | −0.784921 | − | 0.619595i | \(-0.787297\pi\) | ||||
−0.784921 | + | 0.619595i | \(0.787297\pi\) | |||||||
\(488\) | 29.0447 | − | 4.00112i | 1.31479 | − | 0.181122i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.2276 | − | 7.82422i | 0.552385 | − | 0.353462i | ||||
\(491\) | 25.0776 | + | 25.0776i | 1.13174 | + | 1.13174i | 0.989888 | + | 0.141848i | \(0.0453044\pi\) |
0.141848 | + | 0.989888i | \(0.454696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.897470 | − | 0.897470i | 0.0404200 | − | 0.0404200i | ||||
\(494\) | −3.97073 | − | 0.871966i | −0.178651 | − | 0.0392316i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.2574 | − | 24.9512i | 1.31370 | − | 1.12034i | ||||
\(497\) | − | 5.88816i | − | 0.264120i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.744492 | + | 0.744492i | 0.0333280 | + | 0.0333280i | 0.723574 | − | 0.690246i | \(-0.242498\pi\) |
−0.690246 | + | 0.723574i | \(0.742498\pi\) | |||||||
\(500\) | −8.33830 | − | 22.6274i | −0.372900 | − | 1.01193i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.6647 | − | 22.9177i | −0.654517 | − | 1.02287i | ||||
\(503\) | 25.4114i | 1.13304i | 0.824049 | + | 0.566518i | \(0.191710\pi\) | ||||
−0.824049 | + | 0.566518i | \(0.808290\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.5570i | − | 1.13727i | ||||||
\(506\) | 20.9584 | − | 13.4109i | 0.931714 | − | 0.596188i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.17903 | + | 2.55506i | −0.0523110 | + | 0.113362i | ||||
\(509\) | 6.08160 | + | 6.08160i | 0.269562 | + | 0.269562i | 0.828924 | − | 0.559362i | \(-0.188954\pi\) |
−0.559362 | + | 0.828924i | \(0.688954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.515530i | − | 0.0228057i | ||||||
\(512\) | −8.28171 | + | 21.0574i | −0.366003 | + | 0.930614i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.38131 | + | 29.0590i | −0.281468 | + | 1.28174i | ||||
\(515\) | −1.84696 | + | 1.84696i | −0.0813869 | + | 0.0813869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3126 | + | 35.3126i | 1.55305 | + | 1.55305i | ||||
\(518\) | 10.0769 | + | 15.7481i | 0.442755 | + | 0.691930i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.72131 | + | 7.54946i | −0.250896 | + | 0.331066i | ||||
\(521\) | −2.71599 | −0.118990 | −0.0594949 | − | 0.998229i | \(-0.518949\pi\) | ||||
−0.0594949 | + | 0.998229i | \(0.518949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.25885 | − | 3.25885i | 0.142500 | − | 0.142500i | −0.632258 | − | 0.774758i | \(-0.717872\pi\) |
0.774758 | + | 0.632258i | \(0.217872\pi\) | |||||||
\(524\) | 1.31272 | − | 0.483742i | 0.0573464 | − | 0.0211324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.62388 | + | 7.39475i | −0.0708044 | + | 0.322426i | ||||
\(527\) | 17.7647 | 0.773844 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.9175 | 0.648585 | ||||||||
\(530\) | −2.74773 | + | 12.5125i | −0.119354 | + | 0.543508i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.56090 | + | 4.23578i | 0.0676737 | + | 0.183644i | ||||
\(533\) | −11.5303 | + | 11.5303i | −0.499434 | + | 0.499434i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2615 | 1.00568 | ||||||||
\(536\) | 4.03235 | + | 29.2714i | 0.174171 | + | 1.26433i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.6516 | + | 30.7112i | 0.847240 | + | 1.32405i | ||||
\(539\) | −22.8215 | − | 22.8215i | −0.982990 | − | 0.982990i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.1883 | + | 25.1883i | −1.08293 | + | 1.08293i | −0.0866938 | + | 0.996235i | \(0.527630\pi\) |
−0.996235 | + | 0.0866938i | \(0.972370\pi\) | |||||||
\(542\) | −1.91859 | + | 8.73679i | −0.0824104 | + | 0.375277i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.22395 | + | 4.91946i | −0.395473 | + | 0.210920i | ||||
\(545\) | 27.3427i | 1.17123i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.9678 | − | 13.9678i | −0.597220 | − | 0.597220i | 0.342352 | − | 0.939572i | \(-0.388776\pi\) |
−0.939572 | + | 0.342352i | \(0.888776\pi\) | |||||||
\(548\) | 23.4545 | + | 10.8231i | 1.00193 | + | 0.462340i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.30010 | + | 5.31110i | −0.353918 | + | 0.226466i | ||||
\(551\) | 1.16034i | 0.0494320i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.8139i | − | 0.502376i | ||||||
\(554\) | −4.85505 | − | 7.58739i | −0.206271 | − | 0.322357i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 40.2972 | − | 14.8497i | 1.70898 | − | 0.629766i | ||||
\(557\) | 24.4470 | + | 24.4470i | 1.03585 | + | 1.03585i | 0.999333 | + | 0.0365217i | \(0.0116278\pi\) |
0.0365217 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.9350i | − | 0.589389i | ||||||
\(560\) | 10.4854 | + | 0.832939i | 0.443088 | + | 0.0351981i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.5098 | + | 6.26070i | 1.20261 | + | 0.264092i | ||||
\(563\) | 1.69941 | − | 1.69941i | 0.0716217 | − | 0.0716217i | −0.670389 | − | 0.742010i | \(-0.733873\pi\) |
0.742010 | + | 0.670389i | \(0.233873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.8420 | + | 17.8420i | 0.750618 | + | 0.750618i | ||||
\(566\) | 28.4513 | − | 18.2056i | 1.19590 | − | 0.765237i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.52927 | + | 9.93511i | −0.315921 | + | 0.416868i | ||||
\(569\) | 2.63311 | 0.110386 | 0.0551929 | − | 0.998476i | \(-0.482423\pi\) | ||||
0.0551929 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.58069 | + | 7.58069i | −0.317242 | + | 0.317242i | −0.847707 | − | 0.530465i | \(-0.822017\pi\) |
0.530465 | + | 0.847707i | \(0.322017\pi\) | |||||||
\(572\) | 19.1222 | + | 8.82394i | 0.799539 | + | 0.368948i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.6855 | + | 3.88370i | 0.738177 | + | 0.162103i | ||||
\(575\) | 3.20091 | 0.133487 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4358 | −0.975643 | −0.487822 | − | 0.872943i | \(-0.662208\pi\) | ||||
−0.487822 | + | 0.872943i | \(0.662208\pi\) | |||||||
\(578\) | 18.7649 | + | 4.12074i | 0.780515 | + | 0.171400i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.45489 | + | 1.13281i | 0.101934 | + | 0.0470373i | ||||
\(581\) | −9.02447 | + | 9.02447i | −0.374398 | + | 0.374398i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4816 | 1.17959 | ||||||||
\(584\) | −0.659214 | + | 0.869855i | −0.0272785 | + | 0.0359948i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.8673 | − | 10.7931i | 0.696782 | − | 0.445860i | ||||
\(587\) | −12.5335 | − | 12.5335i | −0.517313 | − | 0.517313i | 0.399445 | − | 0.916757i | \(-0.369203\pi\) |
−0.916757 | + | 0.399445i | \(0.869203\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4840 | + | 11.4840i | −0.473190 | + | 0.473190i | ||||
\(590\) | −2.80726 | − | 0.616470i | −0.115573 | − | 0.0253796i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.13441 | − | 39.4572i | 0.128823 | − | 1.62168i | ||||
\(593\) | 0.818182i | 0.0335987i | 0.999859 | + | 0.0167994i | \(0.00534765\pi\) | ||||
−0.999859 | + | 0.0167994i | \(0.994652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.43617 | + | 3.43617i | 0.140869 | + | 0.140869i | ||||
\(596\) | −25.9738 | + | 9.57144i | −1.06393 | + | 0.392061i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.68721 | − | 5.76231i | −0.150781 | − | 0.235638i | ||||
\(599\) | 26.8601i | 1.09747i | 0.835995 | + | 0.548737i | \(0.184891\pi\) | ||||
−0.835995 | + | 0.548737i | \(0.815109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.9878i | 0.570573i | 0.958442 | + | 0.285286i | \(0.0920887\pi\) | ||||
−0.958442 | + | 0.285286i | \(0.907911\pi\) | |||||||
\(602\) | −13.0337 | + | 8.34008i | −0.531216 | + | 0.339916i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.3589 | − | 15.8549i | −1.39804 | − | 0.645128i | ||||
\(605\) | −37.9943 | − | 37.9943i | −1.54469 | − | 1.54469i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5530i | 0.509512i | 0.967005 | + | 0.254756i | \(0.0819952\pi\) | ||||
−0.967005 | + | 0.254756i | \(0.918005\pi\) | |||||||
\(608\) | 2.78263 | − | 9.14299i | 0.112851 | − | 0.370797i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.18881 | + | 28.1824i | −0.250578 | + | 1.14107i | ||||
\(611\) | 9.70886 | − | 9.70886i | 0.392778 | − | 0.392778i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.35533 | + | 1.35533i | 0.0547411 | + | 0.0547411i | 0.733947 | − | 0.679206i | \(-0.237676\pi\) |
−0.679206 | + | 0.733947i | \(0.737676\pi\) | |||||||
\(614\) | 14.1016 | + | 22.0377i | 0.569093 | + | 0.889369i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.19136 | − | 23.1665i | −0.128584 | − | 0.933407i | ||||
\(617\) | −3.03958 | −0.122369 | −0.0611845 | − | 0.998126i | \(-0.519488\pi\) | ||||
−0.0611845 | + | 0.998126i | \(0.519488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8492 | + | 12.8492i | −0.516453 | + | 0.516453i | −0.916496 | − | 0.400043i | \(-0.868995\pi\) |
0.400043 | + | 0.916496i | \(0.368995\pi\) | |||||||
\(620\) | 13.0848 | + | 35.5078i | 0.525497 | + | 1.42603i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.841605 | − | 3.83247i | 0.0337453 | − | 0.153668i | ||||
\(623\) | 17.8996 | 0.717133 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1029 | 0.724114 | ||||||||
\(626\) | 1.18494 | − | 5.39595i | 0.0473599 | − | 0.215666i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7317 | + | 12.0617i | −1.30614 | + | 0.481316i | ||||
\(629\) | 12.9306 | − | 12.9306i | 0.515575 | − | 0.515575i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7376 | 1.74117 | 0.870583 | − | 0.492022i | \(-0.163742\pi\) | ||||
0.870583 | + | 0.492022i | \(0.163742\pi\) | |||||||
\(632\) | −15.1065 | + | 19.9335i | −0.600905 | + | 0.792914i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.38606 | − | 8.41725i | −0.213908 | − | 0.334292i | ||||
\(635\) | −1.95821 | − | 1.95821i | −0.0777093 | − | 0.0777093i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.27454 | + | 6.27454i | −0.248606 | + | 0.248606i | ||||
\(638\) | 1.28928 | − | 5.87107i | 0.0510430 | − | 0.232438i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.6269 | − | 14.8132i | −0.657236 | − | 0.585543i | ||||
\(641\) | − | 17.4093i | − | 0.687628i | −0.939038 | − | 0.343814i | \(-0.888281\pi\) | ||
0.939038 | − | 0.343814i | \(-0.111719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.85280 | − | 4.85280i | −0.191376 | − | 0.191376i | 0.604915 | − | 0.796290i | \(-0.293207\pi\) |
−0.796290 | + | 0.604915i | \(0.793207\pi\) | |||||||
\(644\) | −3.18283 | + | 6.89746i | −0.125421 | + | 0.271798i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.71911 | − | 2.37980i | 0.146326 | − | 0.0936319i | ||||
\(647\) | 19.3043i | 0.758930i | 0.925206 | + | 0.379465i | \(0.123892\pi\) | ||||
−0.925206 | + | 0.379465i | \(0.876108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.39002i | 0.250830i | ||||||||
\(650\) | 1.46024 | + | 2.28204i | 0.0572752 | + | 0.0895088i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.3189 | + | 36.1433i | 0.521610 | + | 1.41548i | ||||
\(653\) | 22.7421 | + | 22.7421i | 0.889968 | + | 0.889968i | 0.994519 | − | 0.104552i | \(-0.0333407\pi\) |
−0.104552 | + | 0.994519i | \(0.533341\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.37682i | 0.0537969i | ||||||||
\(656\) | −24.8746 | − | 29.1676i | −0.971189 | − | 1.13880i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.8917 | − | 3.27019i | −0.580537 | − | 0.127485i | ||||
\(659\) | 1.27511 | − | 1.27511i | 0.0496711 | − | 0.0496711i | −0.681835 | − | 0.731506i | \(-0.738818\pi\) |
0.731506 | + | 0.681835i | \(0.238818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.1257 | − | 15.1257i | −0.588323 | − | 0.588323i | 0.348854 | − | 0.937177i | \(-0.386571\pi\) |
−0.937177 | + | 0.348854i | \(0.886571\pi\) | |||||||
\(662\) | −5.36109 | + | 3.43047i | −0.208365 | + | 0.133329i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.7667 | − | 3.68731i | 1.03875 | − | 0.143095i | ||||
\(665\) | −4.44262 | −0.172277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.38068 | + | 1.38068i | −0.0534603 | + | 0.0534603i | ||||
\(668\) | 5.25619 | − | 11.3906i | 0.203368 | − | 0.440715i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.4023 | − | 6.23712i | −1.09728 | − | 0.240961i | ||||
\(671\) | 64.1502 | 2.47649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7749 | 0.762265 | 0.381133 | − | 0.924520i | \(-0.375534\pi\) | ||||
0.381133 | + | 0.924520i | \(0.375534\pi\) | |||||||
\(674\) | −46.7791 | − | 10.2726i | −1.80186 | − | 0.395687i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.46773 | + | 18.3503i | −0.325682 | + | 0.705780i | ||||
\(677\) | −14.8386 | + | 14.8386i | −0.570295 | + | 0.570295i | −0.932211 | − | 0.361916i | \(-0.882123\pi\) |
0.361916 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.76026 | 0.144306 | ||||||||
\(680\) | −1.40399 | − | 10.1917i | −0.0538404 | − | 0.390835i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 70.8668 | − | 45.3465i | 2.71363 | − | 1.73641i | ||||
\(683\) | −5.57200 | − | 5.57200i | −0.213207 | − | 0.213207i | 0.592422 | − | 0.805628i | \(-0.298172\pi\) |
−0.805628 | + | 0.592422i | \(0.798172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9757 | + | 17.9757i | −0.686816 | + | 0.686816i | ||||
\(686\) | 22.5419 | + | 4.95017i | 0.860653 | + | 0.188998i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 32.6564 | + | 2.59417i | 1.24501 | + | 0.0989017i | ||||
\(689\) | − | 7.83075i | − | 0.298328i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.1504 | + | 21.1504i | 0.804598 | + | 0.804598i | 0.983810 | − | 0.179212i | \(-0.0573549\pi\) |
−0.179212 | + | 0.983810i | \(0.557355\pi\) | |||||||
\(692\) | 8.09920 | + | 21.9786i | 0.307885 | + | 0.835502i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.06464 | − | 1.66380i | −0.0404132 | − | 0.0631571i | ||||
\(695\) | 42.2649i | 1.60320i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 17.7102i | − | 0.670822i | ||||||
\(698\) | −30.0572 | + | 19.2331i | −1.13768 | + | 0.727984i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.26049 | − | 2.73159i | 0.0476421 | − | 0.103244i | ||||
\(701\) | −16.7025 | − | 16.7025i | −0.630846 | − | 0.630846i | 0.317434 | − | 0.948280i | \(-0.397179\pi\) |
−0.948280 | + | 0.317434i | \(0.897179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7179i | 0.630527i | ||||||||
\(704\) | −24.2385 | + | 43.1698i | −0.913525 | + | 1.62702i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.13709 | − | 14.2856i | 0.118066 | − | 0.537644i | ||||
\(707\) | 12.2663 | − | 12.2663i | 0.461322 | − | 0.461322i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.2575 | + | 15.2575i | 0.573009 | + | 0.573009i | 0.932968 | − | 0.359959i | \(-0.117209\pi\) |
−0.359959 | + | 0.932968i | \(0.617209\pi\) | |||||||
\(710\) | −6.61229 | − | 10.3336i | −0.248155 | − | 0.387812i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.2021 | − | 22.8885i | −1.13187 | − | 0.857781i | ||||
\(713\) | −27.3296 | −1.02350 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6554 | + | 14.6554i | −0.548080 | + | 0.548080i | ||||
\(716\) | 5.92929 | − | 2.18497i | 0.221588 | − | 0.0816560i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.88615 | + | 13.1428i | −0.107710 | + | 0.490487i | ||||
\(719\) | 16.7129 | 0.623287 | 0.311643 | − | 0.950199i | \(-0.399121\pi\) | ||||
0.311643 | + | 0.950199i | \(0.399121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.77293 | −0.0660274 | ||||||||
\(722\) | 4.89750 | − | 22.3021i | 0.182266 | − | 0.829997i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.43705 | + | 20.1818i | 0.276396 | + | 0.750049i | ||||
\(725\) | 0.546789 | − | 0.546789i | 0.0203072 | − | 0.0203072i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.4451 | 0.906619 | 0.453309 | − | 0.891353i | \(-0.350243\pi\) | ||||
0.453309 | + | 0.891353i | \(0.350243\pi\) | |||||||
\(728\) | −6.36942 | + | 0.877435i | −0.236067 | + | 0.0325199i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.578930 | − | 0.904742i | −0.0214271 | − | 0.0334860i | ||||
\(731\) | 10.7019 | + | 10.7019i | 0.395823 | + | 0.395823i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.43009 | + | 7.43009i | −0.274437 | + | 0.274437i | −0.830883 | − | 0.556447i | \(-0.812164\pi\) |
0.556447 | + | 0.830883i | \(0.312164\pi\) | |||||||
\(734\) | 4.82343 | − | 21.9647i | 0.178036 | − | 0.810733i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1903 | − | 7.56818i | 0.523060 | − | 0.278967i | ||||
\(737\) | 64.6509i | 2.38145i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.91352 | − | 8.91352i | −0.327889 | − | 0.327889i | 0.523894 | − | 0.851783i | \(-0.324479\pi\) |
−0.851783 | + | 0.523894i | \(0.824479\pi\) | |||||||
\(740\) | 35.3695 | + | 16.3213i | 1.30021 | + | 0.599981i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.32428 | + | 4.68669i | −0.268883 | + | 0.172054i | ||||
\(743\) | − | 40.2146i | − | 1.47533i | −0.675167 | − | 0.737665i | \(-0.735928\pi\) | ||
0.675167 | − | 0.737665i | \(-0.264072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 27.2421i | − | 0.998073i | ||||||
\(746\) | 8.98830 | + | 14.0468i | 0.329085 | + | 0.514289i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.4622 | + | 7.90889i | −0.784735 | + | 0.289178i | ||||
\(749\) | 11.1646 | + | 11.1646i | 0.407945 | + | 0.407945i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.3705i | 1.69209i | 0.533115 | + | 0.846043i | \(0.321021\pi\) | ||||
−0.533115 | + | 0.846043i | \(0.678979\pi\) | |||||||
\(752\) | 20.9451 | + | 24.5599i | 0.763789 | + | 0.895609i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.61420 | − | 0.354475i | −0.0587855 | − | 0.0129092i | ||||
\(755\) | 26.3329 | − | 26.3329i | 0.958353 | − | 0.958353i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1930 | + | 16.1930i | 0.588546 | + | 0.588546i | 0.937237 | − | 0.348692i | \(-0.113374\pi\) |
−0.348692 | + | 0.937237i | \(0.613374\pi\) | |||||||
\(758\) | 16.6189 | − | 10.6341i | 0.603625 | − | 0.386250i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.49604 | + | 5.68083i | 0.271910 | + | 0.206065i | ||||
\(761\) | −10.8371 | −0.392843 | −0.196422 | − | 0.980520i | \(-0.562932\pi\) | ||||
−0.196422 | + | 0.980520i | \(0.562932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.1234 | + | 13.1234i | −0.475099 | + | 0.475099i | ||||
\(764\) | −11.0749 | − | 5.11049i | −0.400674 | − | 0.184891i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.2632 | − | 7.52414i | −1.23798 | − | 0.271858i | ||||
\(767\) | 1.75688 | 0.0634371 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0426 | 1.08336 | 0.541681 | − | 0.840584i | \(-0.317788\pi\) | ||||
0.541681 | + | 0.840584i | \(0.317788\pi\) | |||||||
\(770\) | 22.4787 | + | 4.93630i | 0.810078 | + | 0.177892i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.6666 | + | 5.38358i | 0.419892 | + | 0.193759i | ||||
\(773\) | −7.38305 | + | 7.38305i | −0.265550 | + | 0.265550i | −0.827304 | − | 0.561754i | \(-0.810127\pi\) |
0.561754 | + | 0.827304i | \(0.310127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8233 | 0.388783 | ||||||||
\(776\) | −6.34470 | − | 4.80830i | −0.227762 | − | 0.172608i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.2468 | + | 19.9943i | −1.12025 | + | 0.716831i | ||||
\(779\) | 11.4487 | + | 11.4487i | 0.410194 | + | 0.410194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2865 | + | 19.2865i | −0.690127 | + | 0.690127i | ||||
\(782\) | 7.25708 | + | 1.59364i | 0.259513 | + | 0.0569886i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.5362 | − | 15.8723i | −0.483435 | − | 0.566869i | ||||
\(785\) | − | 34.3300i | − | 1.22529i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8336 | − | 19.8336i | −0.706990 | − | 0.706990i | 0.258911 | − | 0.965901i | \(-0.416636\pi\) |
−0.965901 | + | 0.258911i | \(0.916636\pi\) | |||||||
\(788\) | 0.809694 | − | 0.298375i | 0.0288442 | − | 0.0106292i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.2667 | − | 20.7330i | −0.472009 | − | 0.737648i | ||||
\(791\) | 17.1269i | 0.608961i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.6375i | − | 0.626326i | ||||||
\(794\) | 15.6264 | − | 9.99909i | 0.554561 | − | 0.354855i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.8251 | − | 7.76392i | −0.596348 | − | 0.275185i | ||||
\(797\) | −12.3065 | − | 12.3065i | −0.435918 | − | 0.435918i | 0.454718 | − | 0.890636i | \(-0.349740\pi\) |
−0.890636 | + | 0.454718i | \(0.849740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.9125i | 0.527566i | ||||||||
\(800\) | −5.61974 | + | 2.99721i | −0.198688 | + | 0.105967i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.87304 | − | 44.9595i | 0.348629 | − | 1.58757i | ||||
\(803\) | −1.68861 | + | 1.68861i | −0.0595896 | + | 0.0595896i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.28626 | − | 5.28626i | −0.186316 | − | 0.186316i | ||||
\(806\) | −12.4676 | − | 19.4842i | −0.439152 | − | 0.686300i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.3821 | + | 5.01190i | −1.27992 | + | 0.176318i | ||||
\(809\) | −38.4080 | −1.35035 | −0.675176 | − | 0.737657i | \(-0.735932\pi\) | ||||
−0.675176 | + | 0.737657i | \(0.735932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1507 | + | 35.1507i | −1.23431 | + | 1.23431i | −0.272013 | + | 0.962294i | \(0.587689\pi\) |
−0.962294 | + | 0.272013i | \(0.912311\pi\) | |||||||
\(812\) | 0.634544 | + | 1.72195i | 0.0222681 | + | 0.0604285i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.5757 | − | 84.5891i | 0.651076 | − | 2.96485i | ||||
\(815\) | −37.9082 | −1.32787 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8364 | −0.484075 | ||||||||
\(818\) | 4.49548 | − | 20.4714i | 0.157181 | − | 0.715764i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.3989 | − | 13.0446i | 1.23618 | − | 0.455538i | ||||
\(821\) | −0.263864 | + | 0.263864i | −0.00920890 | + | 0.00920890i | −0.711696 | − | 0.702487i | \(-0.752073\pi\) |
0.702487 | + | 0.711696i | \(0.252073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.00341 | 0.209266 | 0.104633 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104633 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(824\) | 2.99147 | + | 2.26707i | 0.104213 | + | 0.0789771i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.05149 | − | 1.64325i | −0.0365859 | − | 0.0571759i | ||||
\(827\) | 5.50493 | + | 5.50493i | 0.191425 | + | 0.191425i | 0.796312 | − | 0.604887i | \(-0.206782\pi\) |
−0.604887 | + | 0.796312i | \(0.706782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.2457 | + | 13.2457i | −0.460041 | + | 0.460041i | −0.898669 | − | 0.438628i | \(-0.855465\pi\) |
0.438628 | + | 0.898669i | \(0.355465\pi\) | |||||||
\(830\) | −5.70342 | + | 25.9720i | −0.197969 | + | 0.901502i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.8691 | + | 6.66416i | 0.411488 | + | 0.231038i | ||||
\(833\) | − | 9.63749i | − | 0.333919i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.72982 | + | 8.72982i | 0.302108 | + | 0.302108i | ||||
\(836\) | 8.76151 | − | 18.9869i | 0.303023 | − | 0.656676i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.44477 | + | 0.924484i | −0.0499087 | + | 0.0319358i | ||||
\(839\) | − | 25.5283i | − | 0.881334i | −0.897671 | − | 0.440667i | \(-0.854742\pi\) | ||
0.897671 | − | 0.440667i | \(-0.145258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.5283i | − | 0.983734i | ||||||
\(842\) | −24.9672 | − | 39.0183i | −0.860426 | − | 1.34466i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.32597 | − | 3.59826i | −0.0456418 | − | 0.123857i | ||||
\(845\) | −14.0638 | − | 14.0638i | −0.483809 | − | 0.483809i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 36.4714i | − | 1.25317i | ||||||
\(848\) | 18.3512 | + | 1.45779i | 0.630183 | + | 0.0500606i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.87400 | − | 0.631127i | −0.0985775 | − | 0.0216475i | ||||
\(851\) | −19.8926 | + | 19.8926i | −0.681909 | + | 0.681909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7071 | + | 13.7071i | 0.469321 | + | 0.469321i | 0.901695 | − | 0.432373i | \(-0.142324\pi\) |
−0.432373 | + | 0.901695i | \(0.642324\pi\) | |||||||
\(854\) | −16.4967 | + | 10.5560i | −0.564507 | + | 0.361219i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.56174 | − | 33.1143i | −0.155917 | − | 1.13182i | ||||
\(857\) | 16.8324 | 0.574982 | 0.287491 | − | 0.957783i | \(-0.407179\pi\) | ||||
0.287491 | + | 0.957783i | \(0.407179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.49208 | + | 9.49208i | −0.323866 | + | 0.323866i | −0.850248 | − | 0.526382i | \(-0.823548\pi\) |
0.526382 | + | 0.850248i | \(0.323548\pi\) | |||||||
\(860\) | −13.5082 | + | 29.2733i | −0.460624 | + | 0.998210i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.35557 | − | 0.736878i | −0.114291 | − | 0.0250982i | ||||
\(863\) | 51.2834 | 1.74571 | 0.872853 | − | 0.487982i | \(-0.162267\pi\) | ||||
0.872853 | + | 0.487982i | \(0.162267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.0518 | −0.783786 | ||||||||
\(866\) | 11.2739 | + | 2.47573i | 0.383101 | + | 0.0841286i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.7621 | + | 23.3225i | −0.365291 | + | 0.791616i | ||||
\(869\) | −38.6960 | + | 38.6960i | −1.31267 | + | 1.31267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7752 | 0.602288 | ||||||||
\(872\) | 38.9242 | − | 5.36209i | 1.31814 | − | 0.181583i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.72154 | + | 3.66112i | −0.193534 | + | 0.123839i | ||||
\(875\) | 11.3906 | + | 11.3906i | 0.385071 | + | 0.385071i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.23767 | + | 9.23767i | −0.311934 | + | 0.311934i | −0.845658 | − | 0.533724i | \(-0.820792\pi\) |
0.533724 | + | 0.845658i | \(0.320792\pi\) | |||||||
\(878\) | 2.90054 | + | 0.636954i | 0.0978884 | + | 0.0214962i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.6163 | − | 37.0729i | −1.06579 | − | 1.24973i | ||||
\(881\) | − | 44.2215i | − | 1.48986i | −0.667143 | − | 0.744929i | \(-0.732483\pi\) | ||
0.667143 | − | 0.744929i | \(-0.267517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.93847 | + | 3.93847i | 0.132540 | + | 0.132540i | 0.770265 | − | 0.637724i | \(-0.220124\pi\) |
−0.637724 | + | 0.770265i | \(0.720124\pi\) | |||||||
\(884\) | 2.17448 | + | 5.90082i | 0.0731356 | + | 0.198466i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.17771 | + | 12.7800i | 0.274735 | + | 0.429352i | ||||
\(887\) | − | 18.4211i | − | 0.618518i | −0.950978 | − | 0.309259i | \(-0.899919\pi\) | ||
0.950978 | − | 0.309259i | \(-0.100081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.87972i | − | 0.0630439i | ||||||
\(890\) | 31.4134 | − | 20.1009i | 1.05298 | − | 0.673784i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.996854 | − | 2.16026i | 0.0333771 | − | 0.0723310i | ||||
\(893\) | −9.64016 | − | 9.64016i | −0.322596 | − | 0.322596i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.21882i | 0.207872i | ||||||||
\(896\) | −0.870509 | − | 15.0900i | −0.0290817 | − | 0.504120i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.325517 | + | 1.48233i | −0.0108626 | + | 0.0494659i | ||||
\(899\) | −4.66852 | + | 4.66852i | −0.155704 | + | 0.155704i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.01389 | + | 6.01389i | 0.200352 | + | 0.200352i | ||||
\(902\) | −45.2073 | − | 70.6493i | −1.50524 | − | 2.35236i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.9003 | − | 28.8982i | 0.728393 | − | 0.961139i | ||||
\(905\) | −21.1673 | −0.703623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.4813 | − | 24.4813i | 0.812887 | − | 0.812887i | −0.172179 | − | 0.985066i | \(-0.555081\pi\) |
0.985066 | + | 0.172179i | \(0.0550806\pi\) | |||||||
\(908\) | −33.7637 | + | 12.4420i | −1.12049 | + | 0.412903i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.35719 | − | 6.18032i | 0.0449904 | − | 0.204876i | ||||
\(911\) | −17.6487 | −0.584728 | −0.292364 | − | 0.956307i | \(-0.594442\pi\) | ||||
−0.292364 | + | 0.956307i | \(0.594442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.1189 | 1.95655 | ||||||||
\(914\) | 6.73763 | − | 30.6816i | 0.222861 | − | 1.01486i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.2896 | − | 33.3500i | −0.406060 | − | 1.10192i | ||||
\(917\) | −0.660818 | + | 0.660818i | −0.0218221 | + | 0.0218221i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.6259 | 0.515452 | 0.257726 | − | 0.966218i | \(-0.417027\pi\) | ||||
0.257726 | + | 0.966218i | \(0.417027\pi\) | |||||||
\(920\) | 2.15992 | + | 15.6791i | 0.0712103 | + | 0.516926i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.121814 | − | 0.190369i | −0.00401172 | − | 0.00626946i | ||||
\(923\) | 5.30265 | + | 5.30265i | 0.174539 | + | 0.174539i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.87802 | − | 7.87802i | 0.259028 | − | 0.259028i | ||||
\(926\) | 6.62538 | − | 30.1704i | 0.217724 | − | 0.991461i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.13121 | − | 3.71684i | 0.0371337 | − | 0.122011i | ||||
\(929\) | 45.6109i | 1.49644i | 0.663448 | + | 0.748222i | \(0.269092\pi\) | ||||
−0.663448 | + | 0.748222i | \(0.730908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.23015 | + | 6.23015i | 0.204185 | + | 0.204185i | ||||
\(932\) | −31.2915 | − | 14.4395i | −1.02499 | − | 0.472981i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.1181 | + | 17.9923i | −0.920053 | + | 0.588727i | ||||
\(935\) | − | 22.5102i | − | 0.736162i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.9133i | 1.46725i | 0.679553 | + | 0.733626i | \(0.262174\pi\) | ||||
−0.679553 | + | 0.733626i | \(0.737826\pi\) | |||||||
\(938\) | −10.6384 | − | 16.6255i | −0.347356 | − | 0.542842i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29.8068 | + | 10.9839i | −0.972192 | + | 0.358256i | ||||
\(941\) | −19.7625 | − | 19.7625i | −0.644241 | − | 0.644241i | 0.307355 | − | 0.951595i | \(-0.400556\pi\) |
−0.951595 | + | 0.307355i | \(0.900556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.2457i | 0.887241i | ||||||||
\(944\) | −0.327063 | + | 4.11720i | −0.0106450 | + | 0.134004i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.0095 | + | 15.3740i | 2.27620 | + | 0.499851i | ||||
\(947\) | 28.1515 | − | 28.1515i | 0.914802 | − | 0.914802i | −0.0818429 | − | 0.996645i | \(-0.526081\pi\) |
0.996645 | + | 0.0818429i | \(0.0260806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.464266 | + | 0.464266i | 0.0150707 | + | 0.0150707i | ||||
\(950\) | 2.26589 | − | 1.44991i | 0.0735151 | − | 0.0470411i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.21776 | − | 5.56547i | 0.136698 | − | 0.180378i | ||||
\(953\) | 5.21912 | 0.169064 | 0.0845319 | − | 0.996421i | \(-0.473061\pi\) | ||||
0.0845319 | + | 0.996421i | \(0.473061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.48785 | − | 8.48785i | 0.274660 | − | 0.274660i | ||||
\(956\) | −32.0005 | − | 14.7667i | −1.03497 | − | 0.477588i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −53.7695 | − | 11.8077i | −1.73721 | − | 0.381490i | ||||
\(959\) | −17.2552 | −0.557200 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −61.4097 | −1.98096 | ||||||||
\(962\) | −23.2570 | − | 5.10720i | −0.749835 | − | 0.164663i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.26743 | − | 3.81501i | −0.266276 | − | 0.122873i | ||||
\(965\) | −8.94140 | + | 8.94140i | −0.287834 | + | 0.287834i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.57917 | 0.0507827 | 0.0253914 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253914 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(968\) | −46.6364 | + | 61.5382i | −1.49895 | + | 1.97791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.59917 | − | 4.22270i | 0.211887 | − | 0.135583i | ||||
\(971\) | 27.7225 | + | 27.7225i | 0.889658 | + | 0.889658i | 0.994490 | − | 0.104832i | \(-0.0334304\pi\) |
−0.104832 | + | 0.994490i | \(0.533430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.2854 | + | 20.2854i | −0.650321 | + | 0.650321i | ||||
\(974\) | −47.8530 | − | 10.5084i | −1.53331 | − | 0.336712i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.3331 | + | 3.28342i | 1.32304 | + | 0.105100i | ||||
\(977\) | − | 19.1443i | − | 0.612480i | −0.951954 | − | 0.306240i | \(-0.900929\pi\) | ||
0.951954 | − | 0.306240i | \(-0.0990711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.6298 | − | 58.6298i | −1.87382 | − | 1.87382i | ||||
\(980\) | 19.2633 | − | 7.09858i | 0.615342 | − | 0.226756i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.0329 | + | 42.2465i | 0.862653 | + | 1.34814i | ||||
\(983\) | − | 59.3747i | − | 1.89376i | −0.321588 | − | 0.946880i | \(-0.604217\pi\) | ||
0.321588 | − | 0.946880i | \(-0.395783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.849233i | 0.0270588i | ||||||||
\(986\) | 1.51191 | − | 0.967444i | 0.0481489 | − | 0.0308097i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.22027 | − | 2.40889i | −0.166079 | − | 0.0766371i | ||||
\(989\) | −16.4639 | − | 16.4639i | −0.523523 | − | 0.523523i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.2515i | − | 0.484481i | −0.970216 | − | 0.242241i | \(-0.922118\pi\) | ||
0.970216 | − | 0.242241i | \(-0.0778823\pi\) | |||||||
\(992\) | 47.9817 | − | 25.5903i | 1.52342 | − | 0.812494i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.78607 | − | 8.13332i | 0.0566506 | − | 0.257973i | ||||
\(995\) | 12.8948 | − | 12.8948i | 0.408794 | − | 0.408794i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2388 | + | 31.2388i | 0.989344 | + | 0.989344i | 0.999944 | − | 0.0106003i | \(-0.00337423\pi\) |
−0.0106003 | + | 0.999944i | \(0.503374\pi\) | |||||||
\(998\) | 0.802539 | + | 1.25419i | 0.0254039 | + | 0.0397008i | ||||
\(999\) | 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 | 432.2.l.a.107.15 | yes | 32 | |
3.2 | odd | 2 | inner | 432.2.l.a.107.2 | ✓ | 32 | |
4.3 | odd | 2 | 1728.2.l.a.1295.4 | 32 | |||
12.11 | even | 2 | 1728.2.l.a.1295.13 | 32 | |||
16.3 | odd | 4 | inner | 432.2.l.a.323.2 | yes | 32 | |
16.13 | even | 4 | 1728.2.l.a.431.13 | 32 | |||
48.29 | odd | 4 | 1728.2.l.a.431.4 | 32 | |||
48.35 | even | 4 | inner | 432.2.l.a.323.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.l.a.107.2 | ✓ | 32 | 3.2 | odd | 2 | inner | |
432.2.l.a.107.15 | yes | 32 | 1.1 | even | 1 | trivial | |
432.2.l.a.323.2 | yes | 32 | 16.3 | odd | 4 | inner | |
432.2.l.a.323.15 | yes | 32 | 48.35 | even | 4 | inner | |
1728.2.l.a.431.4 | 32 | 48.29 | odd | 4 | |||
1728.2.l.a.431.13 | 32 | 16.13 | even | 4 | |||
1728.2.l.a.1295.4 | 32 | 4.3 | odd | 2 | |||
1728.2.l.a.1295.13 | 32 | 12.11 | even | 2 |