Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(413,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.413");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 413.1 | ||
Character | \(\chi\) | \(=\) | 552.413 |
Dual form | 552.2.b.c.413.4 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41196 | − | 0.0797643i | −0.998408 | − | 0.0564019i | ||||
\(3\) | −0.807372 | − | 1.53237i | −0.466136 | − | 0.884713i | ||||
\(4\) | 1.98728 | + | 0.225248i | 0.993638 | + | 0.112624i | ||||
\(5\) | − | 2.83704i | − | 1.26876i | −0.773020 | − | 0.634382i | \(-0.781255\pi\) | ||
0.773020 | − | 0.634382i | \(-0.218745\pi\) | |||||||
\(6\) | 1.01775 | + | 2.22805i | 0.415495 | + | 0.909596i | ||||
\(7\) | 1.51036i | 0.570861i | 0.958399 | + | 0.285431i | \(0.0921366\pi\) | ||||
−0.958399 | + | 0.285431i | \(0.907863\pi\) | |||||||
\(8\) | −2.78799 | − | 0.476556i | −0.985704 | − | 0.168488i | ||||
\(9\) | −1.69630 | + | 2.47438i | −0.565434 | + | 0.824794i | ||||
\(10\) | −0.226295 | + | 4.00580i | −0.0715607 | + | 1.26674i | ||||
\(11\) | 5.25468i | 1.58434i | 0.610297 | + | 0.792172i | \(0.291050\pi\) | ||||
−0.610297 | + | 0.792172i | \(0.708950\pi\) | |||||||
\(12\) | −1.25931 | − | 3.22710i | −0.363530 | − | 0.931582i | ||||
\(13\) | 4.42296i | 1.22671i | 0.789808 | + | 0.613354i | \(0.210180\pi\) | ||||
−0.789808 | + | 0.613354i | \(0.789820\pi\) | |||||||
\(14\) | 0.120473 | − | 2.13257i | 0.0321976 | − | 0.569952i | ||||
\(15\) | −4.34739 | + | 2.29055i | −1.12249 | + | 0.591417i | ||||
\(16\) | 3.89853 | + | 0.895261i | 0.974632 | + | 0.223815i | ||||
\(17\) | −5.44908 | −1.32160 | −0.660798 | − | 0.750564i | \(-0.729782\pi\) | ||||
−0.660798 | + | 0.750564i | \(0.729782\pi\) | |||||||
\(18\) | 2.59248 | − | 3.35843i | 0.611054 | − | 0.791589i | ||||
\(19\) | −0.278059 | −0.0637912 | −0.0318956 | − | 0.999491i | \(-0.510154\pi\) | ||||
−0.0318956 | + | 0.999491i | \(0.510154\pi\) | |||||||
\(20\) | 0.639039 | − | 5.63799i | 0.142894 | − | 1.26069i | ||||
\(21\) | 2.31442 | − | 1.21942i | 0.505048 | − | 0.266099i | ||||
\(22\) | 0.419136 | − | 7.41941i | 0.0893600 | − | 1.58182i | ||||
\(23\) | 2.74274 | + | 3.93413i | 0.571900 | + | 0.820323i | ||||
\(24\) | 1.52069 | + | 4.65699i | 0.310409 | + | 0.950603i | ||||
\(25\) | −3.04882 | −0.609763 | ||||||||
\(26\) | 0.352794 | − | 6.24505i | 0.0691887 | − | 1.22476i | ||||
\(27\) | 5.16121 | + | 0.601614i | 0.993275 | + | 0.115781i | ||||
\(28\) | −0.340205 | + | 3.00149i | −0.0642928 | + | 0.567229i | ||||
\(29\) | 3.90617 | 0.725358 | 0.362679 | − | 0.931914i | \(-0.381862\pi\) | ||||
0.362679 | + | 0.931914i | \(0.381862\pi\) | |||||||
\(30\) | 6.32106 | − | 2.88740i | 1.15406 | − | 0.527165i | ||||
\(31\) | −0.0236931 | −0.00425542 | −0.00212771 | − | 0.999998i | \(-0.500677\pi\) | ||||
−0.00212771 | + | 0.999998i | \(0.500677\pi\) | |||||||
\(32\) | −5.43316 | − | 1.57504i | −0.960457 | − | 0.278430i | ||||
\(33\) | 8.05210 | − | 4.24248i | 1.40169 | − | 0.738521i | ||||
\(34\) | 7.69390 | + | 0.434642i | 1.31949 | + | 0.0745405i | ||||
\(35\) | 4.28495 | 0.724288 | ||||||||
\(36\) | −3.92837 | + | 4.53519i | −0.654728 | + | 0.755864i | ||||
\(37\) | −10.9457 | −1.79946 | −0.899732 | − | 0.436443i | \(-0.856238\pi\) | ||||
−0.899732 | + | 0.436443i | \(0.856238\pi\) | |||||||
\(38\) | 0.392609 | + | 0.0221792i | 0.0636896 | + | 0.00359794i | ||||
\(39\) | 6.77760 | − | 3.57097i | 1.08528 | − | 0.571813i | ||||
\(40\) | −1.35201 | + | 7.90965i | −0.213771 | + | 1.25063i | ||||
\(41\) | − | 7.21720i | − | 1.12714i | −0.826069 | − | 0.563569i | \(-0.809428\pi\) | ||
0.826069 | − | 0.563569i | \(-0.190572\pi\) | |||||||
\(42\) | −3.36514 | + | 1.53717i | −0.519253 | + | 0.237190i | ||||
\(43\) | −7.36445 | −1.12307 | −0.561534 | − | 0.827454i | \(-0.689789\pi\) | ||||
−0.561534 | + | 0.827454i | \(0.689789\pi\) | |||||||
\(44\) | −1.18361 | + | 10.4425i | −0.178436 | + | 1.57426i | ||||
\(45\) | 7.01993 | + | 4.81248i | 1.04647 | + | 0.717403i | ||||
\(46\) | −3.55884 | − | 5.77362i | −0.524722 | − | 0.851273i | ||||
\(47\) | 6.38523i | 0.931381i | 0.884948 | + | 0.465691i | \(0.154194\pi\) | ||||
−0.884948 | + | 0.465691i | \(0.845806\pi\) | |||||||
\(48\) | −1.77569 | − | 6.69678i | −0.256299 | − | 0.966598i | ||||
\(49\) | 4.71882 | 0.674118 | ||||||||
\(50\) | 4.30481 | + | 0.243187i | 0.608792 | + | 0.0343918i | ||||
\(51\) | 4.39943 | + | 8.35000i | 0.616044 | + | 1.16923i | ||||
\(52\) | −0.996265 | + | 8.78964i | −0.138157 | + | 1.21890i | ||||
\(53\) | 9.62419i | 1.32198i | 0.750393 | + | 0.660992i | \(0.229864\pi\) | ||||
−0.750393 | + | 0.660992i | \(0.770136\pi\) | |||||||
\(54\) | −7.23944 | − | 1.26114i | −0.985163 | − | 0.171619i | ||||
\(55\) | 14.9077 | 2.01016 | ||||||||
\(56\) | 0.719769 | − | 4.21086i | 0.0961832 | − | 0.562700i | ||||
\(57\) | 0.224497 | + | 0.426089i | 0.0297354 | + | 0.0564369i | ||||
\(58\) | −5.51537 | − | 0.311573i | −0.724203 | − | 0.0409115i | ||||
\(59\) | 9.58456 | 1.24780 | 0.623902 | − | 0.781503i | \(-0.285547\pi\) | ||||
0.623902 | + | 0.781503i | \(0.285547\pi\) | |||||||
\(60\) | −9.15541 | + | 3.57271i | −1.18196 | + | 0.461235i | ||||
\(61\) | −4.91803 | −0.629690 | −0.314845 | − | 0.949143i | \(-0.601952\pi\) | ||||
−0.314845 | + | 0.949143i | \(0.601952\pi\) | |||||||
\(62\) | 0.0334538 | + | 0.00188987i | 0.00424864 | + | 0.000240013i | ||||
\(63\) | −3.73720 | − | 2.56202i | −0.470843 | − | 0.322784i | ||||
\(64\) | 7.54579 | + | 2.65727i | 0.943224 | + | 0.332158i | ||||
\(65\) | 12.5481 | 1.55640 | ||||||||
\(66\) | −11.7077 | + | 5.34795i | −1.44111 | + | 0.658287i | ||||
\(67\) | 11.7718 | 1.43815 | 0.719074 | − | 0.694933i | \(-0.244566\pi\) | ||||
0.719074 | + | 0.694933i | \(0.244566\pi\) | |||||||
\(68\) | −10.8288 | − | 1.22740i | −1.31319 | − | 0.148844i | ||||
\(69\) | 3.81413 | − | 7.37919i | 0.459167 | − | 0.888350i | ||||
\(70\) | −6.05018 | − | 0.341786i | −0.723135 | − | 0.0408512i | ||||
\(71\) | 5.13535i | 0.609454i | 0.952440 | + | 0.304727i | \(0.0985653\pi\) | ||||
−0.952440 | + | 0.304727i | \(0.901435\pi\) | |||||||
\(72\) | 5.90846 | − | 6.09017i | 0.696318 | − | 0.717733i | ||||
\(73\) | −10.4463 | −1.22265 | −0.611325 | − | 0.791380i | \(-0.709363\pi\) | ||||
−0.611325 | + | 0.791380i | \(0.709363\pi\) | |||||||
\(74\) | 15.4549 | + | 0.873077i | 1.79660 | + | 0.101493i | ||||
\(75\) | 2.46153 | + | 4.67191i | 0.284233 | + | 0.539465i | ||||
\(76\) | −0.552580 | − | 0.0626324i | −0.0633853 | − | 0.00718443i | ||||
\(77\) | −7.93644 | −0.904441 | ||||||||
\(78\) | −9.85456 | + | 4.50147i | −1.11581 | + | 0.509691i | ||||
\(79\) | 13.3643i | 1.50360i | 0.659392 | + | 0.751799i | \(0.270814\pi\) | ||||
−0.659392 | + | 0.751799i | \(0.729186\pi\) | |||||||
\(80\) | 2.53989 | − | 11.0603i | 0.283969 | − | 1.23658i | ||||
\(81\) | −3.24512 | − | 8.39459i | −0.360569 | − | 0.932733i | ||||
\(82\) | −0.575675 | + | 10.1904i | −0.0635726 | + | 1.12534i | ||||
\(83\) | − | 2.01019i | − | 0.220647i | −0.993896 | − | 0.110323i | \(-0.964811\pi\) | ||
0.993896 | − | 0.110323i | \(-0.0351887\pi\) | |||||||
\(84\) | 4.87407 | − | 1.90200i | 0.531804 | − | 0.207525i | ||||
\(85\) | 15.4593i | 1.67679i | ||||||||
\(86\) | 10.3983 | + | 0.587420i | 1.12128 | + | 0.0633431i | ||||
\(87\) | −3.15373 | − | 5.98569i | −0.338115 | − | 0.641733i | ||||
\(88\) | 2.50415 | − | 14.6500i | 0.266943 | − | 1.56169i | ||||
\(89\) | −13.9059 | −1.47402 | −0.737012 | − | 0.675880i | \(-0.763764\pi\) | ||||
−0.737012 | + | 0.675880i | \(0.763764\pi\) | |||||||
\(90\) | −9.52801 | − | 7.35498i | −1.00434 | − | 0.775283i | ||||
\(91\) | −6.68025 | −0.700280 | ||||||||
\(92\) | 4.56442 | + | 8.43600i | 0.475874 | + | 0.879514i | ||||
\(93\) | 0.0191292 | + | 0.0363066i | 0.00198360 | + | 0.00376482i | ||||
\(94\) | 0.509313 | − | 9.01570i | 0.0525317 | − | 0.929899i | ||||
\(95\) | 0.788866i | 0.0809360i | ||||||||
\(96\) | 1.97304 | + | 9.59724i | 0.201373 | + | 0.979515i | ||||
\(97\) | − | 10.1465i | − | 1.03023i | −0.857123 | − | 0.515113i | \(-0.827750\pi\) | ||
0.857123 | − | 0.515113i | \(-0.172250\pi\) | |||||||
\(98\) | −6.66280 | − | 0.376394i | −0.673044 | − | 0.0380215i | ||||
\(99\) | −13.0021 | − | 8.91352i | −1.30676 | − | 0.895842i | ||||
\(100\) | −6.05884 | − | 0.686741i | −0.605884 | − | 0.0686741i | ||||
\(101\) | 7.70417 | 0.766594 | 0.383297 | − | 0.923625i | \(-0.374789\pi\) | ||||
0.383297 | + | 0.923625i | \(0.374789\pi\) | |||||||
\(102\) | −5.54580 | − | 12.1408i | −0.549116 | − | 1.20212i | ||||
\(103\) | − | 3.66936i | − | 0.361553i | −0.983524 | − | 0.180777i | \(-0.942139\pi\) | ||
0.983524 | − | 0.180777i | \(-0.0578611\pi\) | |||||||
\(104\) | 2.10779 | − | 12.3312i | 0.206686 | − | 1.20917i | ||||
\(105\) | −3.45954 | − | 6.56611i | −0.337617 | − | 0.640787i | ||||
\(106\) | 0.767667 | − | 13.5890i | 0.0745624 | − | 1.31988i | ||||
\(107\) | − | 6.54109i | − | 0.632352i | −0.948701 | − | 0.316176i | \(-0.897601\pi\) | ||
0.948701 | − | 0.316176i | \(-0.102399\pi\) | |||||||
\(108\) | 10.1212 | + | 2.35813i | 0.973916 | + | 0.226911i | ||||
\(109\) | 0.715038 | 0.0684882 | 0.0342441 | − | 0.999413i | \(-0.489098\pi\) | ||||
0.0342441 | + | 0.999413i | \(0.489098\pi\) | |||||||
\(110\) | −21.0492 | − | 1.18911i | −2.00696 | − | 0.113377i | ||||
\(111\) | 8.83725 | + | 16.7729i | 0.838795 | + | 1.59201i | ||||
\(112\) | −1.35216 | + | 5.88816i | −0.127767 | + | 0.556379i | ||||
\(113\) | −2.54869 | −0.239760 | −0.119880 | − | 0.992788i | \(-0.538251\pi\) | ||||
−0.119880 | + | 0.992788i | \(0.538251\pi\) | |||||||
\(114\) | −0.282995 | − | 0.619529i | −0.0265049 | − | 0.0580242i | ||||
\(115\) | 11.1613 | − | 7.78127i | 1.04080 | − | 0.725607i | ||||
\(116\) | 7.76264 | + | 0.879858i | 0.720743 | + | 0.0816928i | ||||
\(117\) | −10.9441 | − | 7.50268i | −1.01178 | − | 0.693623i | ||||
\(118\) | −13.5330 | − | 0.764506i | −1.24582 | − | 0.0703785i | ||||
\(119\) | − | 8.23005i | − | 0.754448i | ||||||
\(120\) | 13.2121 | − | 4.31425i | 1.20609 | − | 0.393836i | ||||
\(121\) | −16.6116 | −1.51015 | ||||||||
\(122\) | 6.94408 | + | 0.392283i | 0.628687 | + | 0.0355157i | ||||
\(123\) | −11.0594 | + | 5.82696i | −0.997193 | + | 0.525399i | ||||
\(124\) | −0.0470848 | − | 0.00533684i | −0.00422834 | − | 0.000479263i | ||||
\(125\) | − | 5.53560i | − | 0.495119i | ||||||
\(126\) | 5.07242 | + | 3.91557i | 0.451887 | + | 0.348827i | ||||
\(127\) | −1.27108 | −0.112790 | −0.0563950 | − | 0.998409i | \(-0.517961\pi\) | ||||
−0.0563950 | + | 0.998409i | \(0.517961\pi\) | |||||||
\(128\) | −10.4424 | − | 4.35385i | −0.922988 | − | 0.384829i | ||||
\(129\) | 5.94585 | + | 11.2850i | 0.523503 | + | 0.993593i | ||||
\(130\) | −17.7175 | − | 1.00089i | −1.55393 | − | 0.0877841i | ||||
\(131\) | −10.9007 | −0.952399 | −0.476199 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476199 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(132\) | 16.9573 | − | 6.61725i | 1.47595 | − | 0.575958i | ||||
\(133\) | − | 0.419969i | − | 0.0364159i | ||||||
\(134\) | −16.6213 | − | 0.938965i | −1.43586 | − | 0.0811143i | ||||
\(135\) | 1.70680 | − | 14.6426i | 0.146898 | − | 1.26023i | ||||
\(136\) | 15.1920 | + | 2.59679i | 1.30270 | + | 0.222673i | ||||
\(137\) | 9.56299 | 0.817021 | 0.408511 | − | 0.912754i | \(-0.366048\pi\) | ||||
0.408511 | + | 0.912754i | \(0.366048\pi\) | |||||||
\(138\) | −5.97400 | + | 10.1149i | −0.508541 | + | 0.861038i | ||||
\(139\) | 19.6353i | 1.66545i | 0.553690 | + | 0.832723i | \(0.313219\pi\) | ||||
−0.553690 | + | 0.832723i | \(0.686781\pi\) | |||||||
\(140\) | 8.51537 | + | 0.965177i | 0.719680 | + | 0.0815724i | ||||
\(141\) | 9.78452 | − | 5.15525i | 0.824005 | − | 0.434151i | ||||
\(142\) | 0.409618 | − | 7.25093i | 0.0343744 | − | 0.608484i | ||||
\(143\) | −23.2412 | −1.94353 | ||||||||
\(144\) | −8.82829 | + | 8.12781i | −0.735691 | + | 0.677317i | ||||
\(145\) | − | 11.0820i | − | 0.920308i | ||||||
\(146\) | 14.7498 | + | 0.833243i | 1.22070 | + | 0.0689597i | ||||
\(147\) | −3.80984 | − | 7.23097i | −0.314231 | − | 0.596401i | ||||
\(148\) | −21.7521 | − | 2.46550i | −1.78801 | − | 0.202663i | ||||
\(149\) | 13.2630i | 1.08655i | 0.839556 | + | 0.543274i | \(0.182815\pi\) | ||||
−0.839556 | + | 0.543274i | \(0.817185\pi\) | |||||||
\(150\) | −3.10293 | − | 6.79290i | −0.253353 | − | 0.554638i | ||||
\(151\) | 0.702221 | 0.0571460 | 0.0285730 | − | 0.999592i | \(-0.490904\pi\) | ||||
0.0285730 | + | 0.999592i | \(0.490904\pi\) | |||||||
\(152\) | 0.775227 | + | 0.132511i | 0.0628792 | + | 0.0107480i | ||||
\(153\) | 9.24329 | − | 13.4831i | 0.747275 | − | 1.09004i | ||||
\(154\) | 11.2059 | + | 0.633044i | 0.903001 | + | 0.0510122i | ||||
\(155\) | 0.0672185i | 0.00539912i | ||||||||
\(156\) | 14.2733 | − | 5.56986i | 1.14278 | − | 0.445946i | ||||
\(157\) | 7.53792 | 0.601592 | 0.300796 | − | 0.953689i | \(-0.402748\pi\) | ||||
0.300796 | + | 0.953689i | \(0.402748\pi\) | |||||||
\(158\) | 1.06599 | − | 18.8698i | 0.0848057 | − | 1.50120i | ||||
\(159\) | 14.7478 | − | 7.77030i | 1.16958 | − | 0.616225i | ||||
\(160\) | −4.46845 | + | 15.4141i | −0.353262 | + | 1.21859i | ||||
\(161\) | −5.94194 | + | 4.14251i | −0.468291 | + | 0.326476i | ||||
\(162\) | 3.91240 | + | 12.1117i | 0.307387 | + | 0.951585i | ||||
\(163\) | 4.73461i | 0.370843i | 0.982659 | + | 0.185421i | \(0.0593650\pi\) | ||||
−0.982659 | + | 0.185421i | \(0.940635\pi\) | |||||||
\(164\) | 1.62566 | − | 14.3426i | 0.126943 | − | 1.11997i | ||||
\(165\) | −12.0361 | − | 22.8442i | −0.937009 | − | 1.77841i | ||||
\(166\) | −0.160341 | + | 2.83831i | −0.0124449 | + | 0.220296i | ||||
\(167\) | 12.7163i | 0.984019i | 0.870590 | + | 0.492009i | \(0.163737\pi\) | ||||
−0.870590 | + | 0.492009i | \(0.836263\pi\) | |||||||
\(168\) | −7.03371 | + | 2.29678i | −0.542662 | + | 0.177200i | ||||
\(169\) | −6.56258 | −0.504814 | ||||||||
\(170\) | 1.23310 | − | 21.8279i | 0.0945743 | − | 1.67412i | ||||
\(171\) | 0.471673 | − | 0.688025i | 0.0360697 | − | 0.0526146i | ||||
\(172\) | −14.6352 | − | 1.65883i | −1.11592 | − | 0.126485i | ||||
\(173\) | 5.13533 | 0.390432 | 0.195216 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195216 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(174\) | 3.97551 | + | 8.70312i | 0.301382 | + | 0.659782i | ||||
\(175\) | − | 4.60480i | − | 0.348090i | ||||||
\(176\) | −4.70431 | + | 20.4855i | −0.354601 | + | 1.54415i | ||||
\(177\) | −7.73830 | − | 14.6871i | −0.581646 | − | 1.10395i | ||||
\(178\) | 19.6346 | + | 1.10920i | 1.47168 | + | 0.0831377i | ||||
\(179\) | −16.0763 | −1.20160 | −0.600799 | − | 0.799400i | \(-0.705151\pi\) | ||||
−0.600799 | + | 0.799400i | \(0.705151\pi\) | |||||||
\(180\) | 12.8665 | + | 11.1450i | 0.959014 | + | 0.830696i | ||||
\(181\) | 17.9778 | 1.33628 | 0.668138 | − | 0.744037i | \(-0.267091\pi\) | ||||
0.668138 | + | 0.744037i | \(0.267091\pi\) | |||||||
\(182\) | 9.43226 | + | 0.532845i | 0.699165 | + | 0.0394971i | ||||
\(183\) | 3.97068 | + | 7.53623i | 0.293521 | + | 0.557094i | ||||
\(184\) | −5.77190 | − | 12.2754i | −0.425510 | − | 0.904954i | ||||
\(185\) | 31.0535i | 2.28310i | ||||||||
\(186\) | −0.0241137 | − | 0.0527894i | −0.00176810 | − | 0.00387071i | ||||
\(187\) | − | 28.6332i | − | 2.09386i | ||||||
\(188\) | −1.43826 | + | 12.6892i | −0.104896 | + | 0.925456i | ||||
\(189\) | −0.908651 | + | 7.79526i | −0.0660946 | + | 0.567022i | ||||
\(190\) | 0.0629234 | − | 1.11385i | 0.00456494 | − | 0.0808071i | ||||
\(191\) | −17.2840 | −1.25063 | −0.625313 | − | 0.780374i | \(-0.715029\pi\) | ||||
−0.625313 | + | 0.780374i | \(0.715029\pi\) | |||||||
\(192\) | −2.02035 | − | 13.7083i | −0.145806 | − | 0.989313i | ||||
\(193\) | 6.00676 | 0.432376 | 0.216188 | − | 0.976352i | \(-0.430638\pi\) | ||||
0.216188 | + | 0.976352i | \(0.430638\pi\) | |||||||
\(194\) | −0.809332 | + | 14.3265i | −0.0581066 | + | 1.02859i | ||||
\(195\) | −10.1310 | − | 19.2284i | −0.725496 | − | 1.37697i | ||||
\(196\) | 9.37760 | + | 1.06291i | 0.669829 | + | 0.0759219i | ||||
\(197\) | −3.33454 | −0.237576 | −0.118788 | − | 0.992920i | \(-0.537901\pi\) | ||||
−0.118788 | + | 0.992920i | \(0.537901\pi\) | |||||||
\(198\) | 17.6475 | + | 13.6227i | 1.25415 | + | 0.968120i | ||||
\(199\) | 5.44215i | 0.385784i | 0.981220 | + | 0.192892i | \(0.0617867\pi\) | ||||
−0.981220 | + | 0.192892i | \(0.938213\pi\) | |||||||
\(200\) | 8.50007 | + | 1.45293i | 0.601046 | + | 0.102738i | ||||
\(201\) | −9.50418 | − | 18.0387i | −0.670373 | − | 1.27235i | ||||
\(202\) | −10.8780 | − | 0.614518i | −0.765373 | − | 0.0432373i | ||||
\(203\) | 5.89971i | 0.414078i | ||||||||
\(204\) | 6.86206 | + | 17.5847i | 0.480440 | + | 1.23118i | ||||
\(205\) | −20.4755 | −1.43007 | ||||||||
\(206\) | −0.292684 | + | 5.18100i | −0.0203923 | + | 0.360978i | ||||
\(207\) | −14.3871 | + | 0.113103i | −0.999969 | + | 0.00786119i | ||||
\(208\) | −3.95970 | + | 17.2430i | −0.274556 | + | 1.19559i | ||||
\(209\) | − | 1.46111i | − | 0.101067i | ||||||
\(210\) | 4.36101 | + | 9.54706i | 0.300938 | + | 0.658809i | ||||
\(211\) | − | 6.98441i | − | 0.480826i | −0.970671 | − | 0.240413i | \(-0.922717\pi\) | ||
0.970671 | − | 0.240413i | \(-0.0772829\pi\) | |||||||
\(212\) | −2.16783 | + | 19.1259i | −0.148887 | + | 1.31357i | ||||
\(213\) | 7.86925 | − | 4.14614i | 0.539192 | − | 0.284089i | ||||
\(214\) | −0.521746 | + | 9.23578i | −0.0356658 | + | 0.631345i | ||||
\(215\) | 20.8933i | 1.42491i | ||||||||
\(216\) | −14.1027 | − | 4.13690i | −0.959567 | − | 0.281480i | ||||
\(217\) | − | 0.0357851i | − | 0.00242925i | ||||||
\(218\) | −1.00961 | − | 0.0570345i | −0.0683792 | − | 0.00386286i | ||||
\(219\) | 8.43406 | + | 16.0076i | 0.569921 | + | 1.08169i | ||||
\(220\) | 29.6258 | + | 3.35795i | 1.99737 | + | 0.226393i | ||||
\(221\) | − | 24.1011i | − | 1.62121i | ||||||
\(222\) | −11.1400 | − | 24.3875i | −0.747668 | − | 1.63678i | ||||
\(223\) | 3.51479 | 0.235368 | 0.117684 | − | 0.993051i | \(-0.462453\pi\) | ||||
0.117684 | + | 0.993051i | \(0.462453\pi\) | |||||||
\(224\) | 2.37887 | − | 8.20601i | 0.158945 | − | 0.548287i | ||||
\(225\) | 5.17171 | − | 7.54393i | 0.344781 | − | 0.502929i | ||||
\(226\) | 3.59865 | + | 0.203294i | 0.239379 | + | 0.0135229i | ||||
\(227\) | − | 3.95674i | − | 0.262618i | −0.991341 | − | 0.131309i | \(-0.958082\pi\) | ||
0.991341 | − | 0.131309i | \(-0.0419180\pi\) | |||||||
\(228\) | 0.350162 | + | 0.897324i | 0.0231900 | + | 0.0594267i | ||||
\(229\) | 14.4693 | 0.956161 | 0.478081 | − | 0.878316i | \(-0.341333\pi\) | ||||
0.478081 | + | 0.878316i | \(0.341333\pi\) | |||||||
\(230\) | −16.3800 | + | 10.0966i | −1.08007 | + | 0.665749i | ||||
\(231\) | 6.40765 | + | 12.1615i | 0.421593 | + | 0.800171i | ||||
\(232\) | −10.8904 | − | 1.86151i | −0.714988 | − | 0.122214i | ||||
\(233\) | − | 6.38619i | − | 0.418373i | −0.977876 | − | 0.209186i | \(-0.932918\pi\) | ||
0.977876 | − | 0.209186i | \(-0.0670816\pi\) | |||||||
\(234\) | 14.8542 | + | 11.4664i | 0.971049 | + | 0.749585i | ||||
\(235\) | 18.1152 | 1.18170 | ||||||||
\(236\) | 19.0472 | + | 2.15891i | 1.23986 | + | 0.140533i | ||||
\(237\) | 20.4790 | − | 10.7899i | 1.33025 | − | 0.700882i | ||||
\(238\) | −0.656465 | + | 11.6205i | −0.0425523 | + | 0.753247i | ||||
\(239\) | 3.65421i | 0.236371i | 0.992992 | + | 0.118185i | \(0.0377077\pi\) | ||||
−0.992992 | + | 0.118185i | \(0.962292\pi\) | |||||||
\(240\) | −18.9991 | + | 5.03771i | −1.22638 | + | 0.325183i | ||||
\(241\) | 14.5478i | 0.937107i | 0.883435 | + | 0.468553i | \(0.155225\pi\) | ||||
−0.883435 | + | 0.468553i | \(0.844775\pi\) | |||||||
\(242\) | 23.4550 | + | 1.32502i | 1.50774 | + | 0.0851752i | ||||
\(243\) | −10.2436 | + | 11.7503i | −0.657126 | + | 0.753780i | ||||
\(244\) | −9.77348 | − | 1.10778i | −0.625683 | − | 0.0709183i | ||||
\(245\) | − | 13.3875i | − | 0.855296i | ||||||
\(246\) | 16.0802 | − | 7.34531i | 1.02524 | − | 0.468320i | ||||
\(247\) | − | 1.22985i | − | 0.0782532i | ||||||
\(248\) | 0.0660563 | + | 0.0112911i | 0.00419458 | + | 0.000716986i | ||||
\(249\) | −3.08035 | + | 1.62297i | −0.195209 | + | 0.102851i | ||||
\(250\) | −0.441543 | + | 7.81605i | −0.0279256 | + | 0.494331i | ||||
\(251\) | 5.58993i | 0.352833i | 0.984316 | + | 0.176417i | \(0.0564506\pi\) | ||||
−0.984316 | + | 0.176417i | \(0.943549\pi\) | |||||||
\(252\) | −6.84975 | − | 5.93324i | −0.431494 | − | 0.373759i | ||||
\(253\) | −20.6726 | + | 14.4122i | −1.29967 | + | 0.906087i | ||||
\(254\) | 1.79471 | + | 0.101387i | 0.112610 | + | 0.00636156i | ||||
\(255\) | 23.6893 | − | 12.4814i | 1.48348 | − | 0.781615i | ||||
\(256\) | 14.3970 | + | 6.98040i | 0.899813 | + | 0.436275i | ||||
\(257\) | − | 3.98354i | − | 0.248486i | −0.992252 | − | 0.124243i | \(-0.960350\pi\) | ||
0.992252 | − | 0.124243i | \(-0.0396503\pi\) | |||||||
\(258\) | −7.49517 | − | 16.4083i | −0.466629 | − | 1.02154i | ||||
\(259\) | − | 16.5319i | − | 1.02724i | ||||||
\(260\) | 24.9366 | + | 2.82645i | 1.54650 | + | 0.175289i | ||||
\(261\) | −6.62604 | + | 9.66535i | −0.410142 | + | 0.598270i | ||||
\(262\) | 15.3914 | + | 0.869487i | 0.950883 | + | 0.0537171i | ||||
\(263\) | 8.31685 | 0.512839 | 0.256419 | − | 0.966566i | \(-0.417457\pi\) | ||||
0.256419 | + | 0.966566i | \(0.417457\pi\) | |||||||
\(264\) | −24.4710 | + | 7.99072i | −1.50608 | + | 0.491795i | ||||
\(265\) | 27.3042 | 1.67729 | ||||||||
\(266\) | −0.0334985 | + | 0.592980i | −0.00205393 | + | 0.0363579i | ||||
\(267\) | 11.2272 | + | 21.3090i | 0.687096 | + | 1.30409i | ||||
\(268\) | 23.3937 | + | 2.65157i | 1.42900 | + | 0.161970i | ||||
\(269\) | 6.72690 | 0.410146 | 0.205073 | − | 0.978747i | \(-0.434257\pi\) | ||||
0.205073 | + | 0.978747i | \(0.434257\pi\) | |||||||
\(270\) | −3.57790 | + | 20.5386i | −0.217744 | + | 1.24994i | ||||
\(271\) | −11.4000 | −0.692500 | −0.346250 | − | 0.938142i | \(-0.612545\pi\) | ||||
−0.346250 | + | 0.938142i | \(0.612545\pi\) | |||||||
\(272\) | −21.2434 | − | 4.87835i | −1.28807 | − | 0.295793i | ||||
\(273\) | 5.39344 | + | 10.2366i | 0.326426 | + | 0.619547i | ||||
\(274\) | −13.5026 | − | 0.762785i | −0.815721 | − | 0.0460815i | ||||
\(275\) | − | 16.0205i | − | 0.966075i | ||||||
\(276\) | 9.24187 | − | 13.8054i | 0.556295 | − | 0.830985i | ||||
\(277\) | 24.3492i | 1.46300i | 0.681842 | + | 0.731500i | \(0.261179\pi\) | ||||
−0.681842 | + | 0.731500i | \(0.738821\pi\) | |||||||
\(278\) | 1.56620 | − | 27.7243i | 0.0939343 | − | 1.66279i | ||||
\(279\) | 0.0401907 | − | 0.0586259i | 0.00240616 | − | 0.00350984i | ||||
\(280\) | −11.9464 | − | 2.04202i | −0.713934 | − | 0.122034i | ||||
\(281\) | 3.27622 | 0.195443 | 0.0977215 | − | 0.995214i | \(-0.468845\pi\) | ||||
0.0977215 | + | 0.995214i | \(0.468845\pi\) | |||||||
\(282\) | −14.2266 | + | 6.49857i | −0.847180 | + | 0.386984i | ||||
\(283\) | −20.5517 | −1.22167 | −0.610836 | − | 0.791757i | \(-0.709167\pi\) | ||||
−0.610836 | + | 0.791757i | \(0.709167\pi\) | |||||||
\(284\) | −1.15673 | + | 10.2054i | −0.0686393 | + | 0.605577i | ||||
\(285\) | 1.20883 | − | 0.636908i | 0.0716051 | − | 0.0377272i | ||||
\(286\) | 32.8157 | + | 1.85382i | 1.94044 | + | 0.109619i | ||||
\(287\) | 10.9005 | 0.643439 | ||||||||
\(288\) | 13.1135 | − | 10.7720i | 0.772722 | − | 0.634745i | ||||
\(289\) | 12.6925 | 0.746616 | ||||||||
\(290\) | −0.883946 | + | 15.6473i | −0.0519071 | + | 0.918843i | ||||
\(291\) | −15.5482 | + | 8.19203i | −0.911453 | + | 0.480225i | ||||
\(292\) | −20.7597 | − | 2.35302i | −1.21487 | − | 0.137700i | ||||
\(293\) | 2.96154i | 0.173015i | 0.996251 | + | 0.0865076i | \(0.0275707\pi\) | ||||
−0.996251 | + | 0.0865076i | \(0.972429\pi\) | |||||||
\(294\) | 4.80258 | + | 10.5138i | 0.280092 | + | 0.613174i | ||||
\(295\) | − | 27.1918i | − | 1.58317i | ||||||
\(296\) | 30.5165 | + | 5.21624i | 1.77374 | + | 0.303188i | ||||
\(297\) | −3.16129 | + | 27.1205i | −0.183436 | + | 1.57369i | ||||
\(298\) | 1.05791 | − | 18.7269i | 0.0612833 | − | 1.08482i | ||||
\(299\) | −17.4005 | + | 12.1310i | −1.00630 | + | 0.701555i | ||||
\(300\) | 3.83939 | + | 9.83882i | 0.221667 | + | 0.568045i | ||||
\(301\) | − | 11.1229i | − | 0.641116i | ||||||
\(302\) | −0.991510 | − | 0.0560122i | −0.0570550 | − | 0.00322314i | ||||
\(303\) | −6.22013 | − | 11.8056i | −0.357337 | − | 0.678215i | ||||
\(304\) | −1.08402 | − | 0.248936i | −0.0621729 | − | 0.0142774i | ||||
\(305\) | 13.9527i | 0.798928i | ||||||||
\(306\) | −14.1266 | + | 18.3003i | −0.807566 | + | 1.04616i | ||||
\(307\) | − | 16.2366i | − | 0.926672i | −0.886183 | − | 0.463336i | \(-0.846652\pi\) | ||
0.886183 | − | 0.463336i | \(-0.153348\pi\) | |||||||
\(308\) | −15.7719 | − | 1.78767i | −0.898687 | − | 0.101862i | ||||
\(309\) | −5.62282 | + | 2.96254i | −0.319871 | + | 0.168533i | ||||
\(310\) | 0.00536164 | − | 0.0949100i | 0.000304520 | − | 0.00539052i | ||||
\(311\) | 5.86765i | 0.332724i | 0.986065 | + | 0.166362i | \(0.0532020\pi\) | ||||
−0.986065 | + | 0.166362i | \(0.946798\pi\) | |||||||
\(312\) | −20.5977 | + | 6.72594i | −1.16611 | + | 0.380781i | ||||
\(313\) | − | 11.2752i | − | 0.637313i | −0.947870 | − | 0.318656i | \(-0.896768\pi\) | ||
0.947870 | − | 0.318656i | \(-0.103232\pi\) | |||||||
\(314\) | −10.6433 | − | 0.601257i | −0.600634 | − | 0.0339309i | ||||
\(315\) | −7.26856 | + | 10.6026i | −0.409537 | + | 0.597388i | ||||
\(316\) | −3.01028 | + | 26.5585i | −0.169341 | + | 1.49403i | ||||
\(317\) | −29.8569 | −1.67693 | −0.838466 | − | 0.544954i | \(-0.816547\pi\) | ||||
−0.838466 | + | 0.544954i | \(0.816547\pi\) | |||||||
\(318\) | −21.4431 | + | 9.79502i | −1.20247 | + | 0.549277i | ||||
\(319\) | 20.5257i | 1.14922i | ||||||||
\(320\) | 7.53878 | − | 21.4077i | 0.421431 | − | 1.19673i | ||||
\(321\) | −10.0234 | + | 5.28109i | −0.559450 | + | 0.294762i | ||||
\(322\) | 8.72022 | − | 5.37512i | 0.485959 | − | 0.299544i | ||||
\(323\) | 1.51517 | 0.0843062 | ||||||||
\(324\) | −4.55808 | − | 17.4133i | −0.253226 | − | 0.967407i | ||||
\(325\) | − | 13.4848i | − | 0.748002i | ||||||
\(326\) | 0.377653 | − | 6.68509i | 0.0209162 | − | 0.370253i | ||||
\(327\) | −0.577301 | − | 1.09570i | −0.0319248 | − | 0.0605924i | ||||
\(328\) | −3.43940 | + | 20.1215i | −0.189909 | + | 1.11102i | ||||
\(329\) | −9.64397 | −0.531689 | ||||||||
\(330\) | 15.1724 | + | 33.2151i | 0.835211 | + | 1.82843i | ||||
\(331\) | − | 29.3591i | − | 1.61372i | −0.590740 | − | 0.806862i | \(-0.701164\pi\) | ||
0.590740 | − | 0.806862i | \(-0.298836\pi\) | |||||||
\(332\) | 0.452792 | − | 3.99480i | 0.0248502 | − | 0.219243i | ||||
\(333\) | 18.5672 | − | 27.0838i | 1.01748 | − | 1.48419i | ||||
\(334\) | 1.01431 | − | 17.9550i | 0.0555005 | − | 0.982452i | ||||
\(335\) | − | 33.3970i | − | 1.82467i | ||||||
\(336\) | 10.1145 | − | 2.68193i | 0.551793 | − | 0.146311i | ||||
\(337\) | 35.2740i | 1.92150i | 0.277417 | + | 0.960750i | \(0.410522\pi\) | ||||
−0.277417 | + | 0.960750i | \(0.589478\pi\) | |||||||
\(338\) | 9.26612 | + | 0.523460i | 0.504010 | + | 0.0284724i | ||||
\(339\) | 2.05774 | + | 3.90553i | 0.111761 | + | 0.212119i | ||||
\(340\) | −3.48218 | + | 30.7218i | −0.188848 | + | 1.66613i | ||||
\(341\) | − | 0.124500i | − | 0.00674205i | ||||||
\(342\) | −0.720864 | + | 0.933842i | −0.0389798 | + | 0.0504964i | ||||
\(343\) | 17.6996i | 0.955689i | ||||||||
\(344\) | 20.5320 | + | 3.50957i | 1.10701 | + | 0.189223i | ||||
\(345\) | −20.9351 | − | 10.8208i | −1.12711 | − | 0.582575i | ||||
\(346\) | −7.25090 | − | 0.409616i | −0.389811 | − | 0.0220211i | ||||
\(347\) | 13.5906 | 0.729581 | 0.364790 | − | 0.931090i | \(-0.381141\pi\) | ||||
0.364790 | + | 0.931090i | \(0.381141\pi\) | |||||||
\(348\) | −4.91907 | − | 12.6056i | −0.263690 | − | 0.675730i | ||||
\(349\) | − | 22.5138i | − | 1.20514i | −0.798067 | − | 0.602568i | \(-0.794144\pi\) | ||
0.798067 | − | 0.602568i | \(-0.205856\pi\) | |||||||
\(350\) | −0.367299 | + | 6.50180i | −0.0196329 | + | 0.347536i | ||||
\(351\) | −2.66091 | + | 22.8278i | −0.142029 | + | 1.21846i | ||||
\(352\) | 8.27632 | − | 28.5495i | 0.441129 | − | 1.52169i | ||||
\(353\) | − | 12.0054i | − | 0.638984i | −0.947589 | − | 0.319492i | \(-0.896488\pi\) | ||
0.947589 | − | 0.319492i | \(-0.103512\pi\) | |||||||
\(354\) | 9.75469 | + | 21.3548i | 0.518456 | + | 1.13500i | ||||
\(355\) | 14.5692 | 0.773254 | ||||||||
\(356\) | −27.6349 | − | 3.13228i | −1.46465 | − | 0.166011i | ||||
\(357\) | −12.6115 | + | 6.64471i | −0.667470 | + | 0.351675i | ||||
\(358\) | 22.6991 | + | 1.28231i | 1.19969 | + | 0.0677724i | ||||
\(359\) | −12.3407 | −0.651317 | −0.325658 | − | 0.945488i | \(-0.605586\pi\) | ||||
−0.325658 | + | 0.945488i | \(0.605586\pi\) | |||||||
\(360\) | −17.2781 | − | 16.7625i | −0.910634 | − | 0.883464i | ||||
\(361\) | −18.9227 | −0.995931 | ||||||||
\(362\) | −25.3839 | − | 1.43398i | −1.33415 | − | 0.0753685i | ||||
\(363\) | 13.4118 | + | 25.4551i | 0.703935 | + | 1.33605i | ||||
\(364\) | −13.2755 | − | 1.50471i | −0.695825 | − | 0.0788685i | ||||
\(365\) | 29.6367i | 1.55125i | ||||||||
\(366\) | −5.00533 | − | 10.9576i | −0.261633 | − | 0.572763i | ||||
\(367\) | − | 10.4677i | − | 0.546408i | −0.961956 | − | 0.273204i | \(-0.911917\pi\) | ||
0.961956 | − | 0.273204i | \(-0.0880834\pi\) | |||||||
\(368\) | 7.17056 | + | 17.7928i | 0.373791 | + | 0.927513i | ||||
\(369\) | 17.8581 | + | 12.2425i | 0.929655 | + | 0.637322i | ||||
\(370\) | 2.47696 | − | 43.8463i | 0.128771 | − | 2.27946i | ||||
\(371\) | −14.5360 | −0.754669 | ||||||||
\(372\) | 0.0298369 | + | 0.0764601i | 0.00154697 | + | 0.00396427i | ||||
\(373\) | −19.0982 | −0.988867 | −0.494433 | − | 0.869216i | \(-0.664624\pi\) | ||||
−0.494433 | + | 0.869216i | \(0.664624\pi\) | |||||||
\(374\) | −2.28390 | + | 40.4289i | −0.118098 | + | 2.09053i | ||||
\(375\) | −8.48257 | + | 4.46928i | −0.438038 | + | 0.230793i | ||||
\(376\) | 3.04292 | − | 17.8020i | 0.156927 | − | 0.918066i | ||||
\(377\) | 17.2768i | 0.889802i | ||||||||
\(378\) | 1.90476 | − | 10.9341i | 0.0979705 | − | 0.562391i | ||||
\(379\) | 27.6320 | 1.41936 | 0.709680 | − | 0.704524i | \(-0.248839\pi\) | ||||
0.709680 | + | 0.704524i | \(0.248839\pi\) | |||||||
\(380\) | −0.177691 | + | 1.56769i | −0.00911535 | + | 0.0804210i | ||||
\(381\) | 1.02623 | + | 1.94776i | 0.0525755 | + | 0.0997867i | ||||
\(382\) | 24.4044 | + | 1.37865i | 1.24864 | + | 0.0705377i | ||||
\(383\) | 24.5172 | 1.25277 | 0.626384 | − | 0.779514i | \(-0.284534\pi\) | ||||
0.626384 | + | 0.779514i | \(0.284534\pi\) | |||||||
\(384\) | 1.75922 | + | 19.5168i | 0.0897747 | + | 0.995962i | ||||
\(385\) | 22.5160i | 1.14752i | ||||||||
\(386\) | −8.48132 | − | 0.479125i | −0.431688 | − | 0.0243868i | ||||
\(387\) | 12.4923 | − | 18.2224i | 0.635021 | − | 0.926299i | ||||
\(388\) | 2.28549 | − | 20.1640i | 0.116028 | − | 1.02367i | ||||
\(389\) | − | 17.6113i | − | 0.892929i | −0.894801 | − | 0.446465i | \(-0.852683\pi\) | ||
0.894801 | − | 0.446465i | \(-0.147317\pi\) | |||||||
\(390\) | 12.7709 | + | 27.9578i | 0.646678 | + | 1.41570i | ||||
\(391\) | −14.9454 | − | 21.4374i | −0.755821 | − | 1.08414i | ||||
\(392\) | −13.1560 | − | 2.24878i | −0.664480 | − | 0.113581i | ||||
\(393\) | 8.80092 | + | 16.7039i | 0.443948 | + | 0.842600i | ||||
\(394\) | 4.70824 | + | 0.265977i | 0.237198 | + | 0.0133997i | ||||
\(395\) | 37.9150 | 1.90771 | ||||||||
\(396\) | −23.8309 | − | 20.6423i | −1.19755 | − | 1.03732i | ||||
\(397\) | − | 26.0926i | − | 1.30955i | −0.755825 | − | 0.654774i | \(-0.772764\pi\) | ||
0.755825 | − | 0.654774i | \(-0.227236\pi\) | |||||||
\(398\) | 0.434090 | − | 7.68412i | 0.0217589 | − | 0.385170i | ||||
\(399\) | −0.643547 | + | 0.339071i | −0.0322176 | + | 0.0169748i | ||||
\(400\) | −11.8859 | − | 2.72949i | −0.594294 | − | 0.136474i | ||||
\(401\) | −5.82998 | −0.291135 | −0.145568 | − | 0.989348i | \(-0.546501\pi\) | ||||
−0.145568 | + | 0.989348i | \(0.546501\pi\) | |||||||
\(402\) | 11.9807 | + | 26.2280i | 0.597543 | + | 1.30813i | ||||
\(403\) | − | 0.104794i | − | 0.00522015i | ||||||
\(404\) | 15.3103 | + | 1.73535i | 0.761716 | + | 0.0863370i | ||||
\(405\) | −23.8158 | + | 9.20654i | −1.18342 | + | 0.457477i | ||||
\(406\) | 0.470586 | − | 8.33017i | 0.0233548 | − | 0.413419i | ||||
\(407\) | − | 57.5162i | − | 2.85097i | ||||||
\(408\) | −8.28634 | − | 25.3763i | −0.410235 | − | 1.25631i | ||||
\(409\) | 33.6916 | 1.66594 | 0.832971 | − | 0.553317i | \(-0.186638\pi\) | ||||
0.832971 | + | 0.553317i | \(0.186638\pi\) | |||||||
\(410\) | 28.9106 | + | 1.63321i | 1.42779 | + | 0.0806587i | ||||
\(411\) | −7.72089 | − | 14.6540i | −0.380843 | − | 0.722829i | ||||
\(412\) | 0.826518 | − | 7.29204i | 0.0407196 | − | 0.359253i | ||||
\(413\) | 14.4761i | 0.712323i | ||||||||
\(414\) | 20.3230 | + | 0.987876i | 0.998821 | + | 0.0485515i | ||||
\(415\) | −5.70299 | −0.279949 | ||||||||
\(416\) | 6.96633 | − | 24.0307i | 0.341552 | − | 1.17820i | ||||
\(417\) | 30.0885 | − | 15.8530i | 1.47344 | − | 0.776325i | ||||
\(418\) | −0.116545 | + | 2.06304i | −0.00570038 | + | 0.100906i | ||||
\(419\) | − | 17.4910i | − | 0.854490i | −0.904136 | − | 0.427245i | \(-0.859484\pi\) | ||
0.904136 | − | 0.427245i | \(-0.140516\pi\) | |||||||
\(420\) | −5.39606 | − | 13.8279i | −0.263301 | − | 0.674734i | ||||
\(421\) | 18.6829 | 0.910550 | 0.455275 | − | 0.890351i | \(-0.349541\pi\) | ||||
0.455275 | + | 0.890351i | \(0.349541\pi\) | |||||||
\(422\) | −0.557106 | + | 9.86172i | −0.0271195 | + | 0.480061i | ||||
\(423\) | −15.7995 | − | 10.8313i | −0.768197 | − | 0.526635i | ||||
\(424\) | 4.58646 | − | 26.8322i | 0.222738 | − | 1.30308i | ||||
\(425\) | 16.6132 | 0.805861 | ||||||||
\(426\) | −11.4418 | + | 5.22651i | −0.554357 | + | 0.253225i | ||||
\(427\) | − | 7.42798i | − | 0.359465i | ||||||
\(428\) | 1.47337 | − | 12.9990i | 0.0712181 | − | 0.628328i | ||||
\(429\) | 18.7643 | + | 35.6141i | 0.905950 | + | 1.71947i | ||||
\(430\) | 1.66654 | − | 29.5005i | 0.0803675 | − | 1.42264i | ||||
\(431\) | 3.99271 | 0.192322 | 0.0961610 | − | 0.995366i | \(-0.469344\pi\) | ||||
0.0961610 | + | 0.995366i | \(0.469344\pi\) | |||||||
\(432\) | 19.5825 | + | 6.96603i | 0.942164 | + | 0.335153i | ||||
\(433\) | 20.4619i | 0.983336i | 0.870783 | + | 0.491668i | \(0.163613\pi\) | ||||
−0.870783 | + | 0.491668i | \(0.836387\pi\) | |||||||
\(434\) | −0.00285437 | + | 0.0505272i | −0.000137014 | + | 0.00242538i | ||||
\(435\) | −16.9817 | + | 8.94727i | −0.814208 | + | 0.428989i | ||||
\(436\) | 1.42098 | + | 0.161061i | 0.0680525 | + | 0.00771343i | ||||
\(437\) | −0.762644 | − | 1.09392i | −0.0364822 | − | 0.0523294i | ||||
\(438\) | −10.6317 | − | 23.2749i | −0.508004 | − | 1.11212i | ||||
\(439\) | 13.4074 | 0.639900 | 0.319950 | − | 0.947434i | \(-0.396334\pi\) | ||||
0.319950 | + | 0.947434i | \(0.396334\pi\) | |||||||
\(440\) | −41.5627 | − | 7.10437i | −1.98142 | − | 0.338688i | ||||
\(441\) | −8.00455 | + | 11.6762i | −0.381169 | + | 0.556008i | ||||
\(442\) | −1.92240 | + | 34.0298i | −0.0914395 | + | 1.61863i | ||||
\(443\) | 35.7620 | 1.69910 | 0.849552 | − | 0.527505i | \(-0.176873\pi\) | ||||
0.849552 | + | 0.527505i | \(0.176873\pi\) | |||||||
\(444\) | 13.7840 | + | 35.3229i | 0.654160 | + | 1.67635i | ||||
\(445\) | 39.4517i | 1.87019i | ||||||||
\(446\) | −4.96275 | − | 0.280355i | −0.234993 | − | 0.0132752i | ||||
\(447\) | 20.3238 | − | 10.7082i | 0.961283 | − | 0.506479i | ||||
\(448\) | −4.01342 | + | 11.3968i | −0.189616 | + | 0.538450i | ||||
\(449\) | 12.9815i | 0.612636i | 0.951929 | + | 0.306318i | \(0.0990971\pi\) | ||||
−0.951929 | + | 0.306318i | \(0.900903\pi\) | |||||||
\(450\) | −7.90400 | + | 10.2392i | −0.372598 | + | 0.482682i | ||||
\(451\) | 37.9241 | 1.78577 | ||||||||
\(452\) | −5.06494 | − | 0.574088i | −0.238235 | − | 0.0270028i | ||||
\(453\) | −0.566954 | − | 1.07606i | −0.0266378 | − | 0.0505578i | ||||
\(454\) | −0.315607 | + | 5.58677i | −0.0148122 | + | 0.262200i | ||||
\(455\) | 18.9522i | 0.888491i | ||||||||
\(456\) | −0.422841 | − | 1.29492i | −0.0198013 | − | 0.0606401i | ||||
\(457\) | − | 23.2473i | − | 1.08746i | −0.839259 | − | 0.543732i | \(-0.817011\pi\) | ||
0.839259 | − | 0.543732i | \(-0.182989\pi\) | |||||||
\(458\) | −20.4302 | − | 1.15414i | −0.954639 | − | 0.0539293i | ||||
\(459\) | −28.1238 | − | 3.27824i | −1.31271 | − | 0.153015i | ||||
\(460\) | 23.9333 | − | 12.9495i | 1.11590 | − | 0.603771i | ||||
\(461\) | −26.5945 | −1.23863 | −0.619314 | − | 0.785143i | \(-0.712589\pi\) | ||||
−0.619314 | + | 0.785143i | \(0.712589\pi\) | |||||||
\(462\) | −8.07731 | − | 17.6827i | −0.375790 | − | 0.822675i | ||||
\(463\) | −22.2831 | −1.03558 | −0.517791 | − | 0.855507i | \(-0.673246\pi\) | ||||
−0.517791 | + | 0.855507i | \(0.673246\pi\) | |||||||
\(464\) | 15.2283 | + | 3.49704i | 0.706956 | + | 0.162346i | ||||
\(465\) | 0.103003 | − | 0.0542703i | 0.00477667 | − | 0.00251673i | ||||
\(466\) | −0.509390 | + | 9.01705i | −0.0235970 | + | 0.417707i | ||||
\(467\) | − | 9.03811i | − | 0.418234i | −0.977891 | − | 0.209117i | \(-0.932941\pi\) | ||
0.977891 | − | 0.209117i | \(-0.0670589\pi\) | |||||||
\(468\) | −20.0590 | − | 17.3750i | −0.927225 | − | 0.803161i | ||||
\(469\) | 17.7795i | 0.820983i | ||||||||
\(470\) | −25.5779 | − | 1.44494i | −1.17982 | − | 0.0666503i | ||||
\(471\) | −6.08590 | − | 11.5509i | −0.280424 | − | 0.532236i | ||||
\(472\) | −26.7217 | − | 4.56758i | −1.22996 | − | 0.210240i | ||||
\(473\) | − | 38.6978i | − | 1.77933i | ||||||
\(474\) | −29.7762 | + | 13.6015i | −1.36767 | + | 0.624737i | ||||
\(475\) | 0.847752 | 0.0388975 | ||||||||
\(476\) | 1.85381 | − | 16.3554i | 0.0849691 | − | 0.749648i | ||||
\(477\) | −23.8139 | − | 16.3255i | −1.09036 | − | 0.747495i | ||||
\(478\) | 0.291475 | − | 5.15960i | 0.0133318 | − | 0.235995i | ||||
\(479\) | 9.04841 | 0.413432 | 0.206716 | − | 0.978401i | \(-0.433722\pi\) | ||||
0.206716 | + | 0.978401i | \(0.433722\pi\) | |||||||
\(480\) | 27.2278 | − | 5.59761i | 1.24277 | − | 0.255495i | ||||
\(481\) | − | 48.4124i | − | 2.20742i | ||||||
\(482\) | 1.16040 | − | 20.5410i | 0.0528546 | − | 0.935615i | ||||
\(483\) | 11.1452 | + | 5.76069i | 0.507124 | + | 0.262121i | ||||
\(484\) | −33.0119 | − | 3.74174i | −1.50054 | − | 0.170079i | ||||
\(485\) | −28.7862 | −1.30711 | ||||||||
\(486\) | 15.4008 | − | 15.7739i | 0.698595 | − | 0.715517i | ||||
\(487\) | −12.0729 | −0.547076 | −0.273538 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273538 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(488\) | 13.7114 | + | 2.34372i | 0.620687 | + | 0.106095i | ||||
\(489\) | 7.25516 | − | 3.82259i | 0.328090 | − | 0.172863i | ||||
\(490\) | −1.06785 | + | 18.9027i | −0.0482403 | + | 0.853935i | ||||
\(491\) | −1.06548 | −0.0480844 | −0.0240422 | − | 0.999711i | \(-0.507654\pi\) | ||||
−0.0240422 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(492\) | −23.2906 | + | 9.08867i | −1.05002 | + | 0.409749i | ||||
\(493\) | −21.2850 | −0.958630 | ||||||||
\(494\) | −0.0980978 | + | 1.73650i | −0.00441363 | + | 0.0781286i | ||||
\(495\) | −25.2880 | + | 36.8874i | −1.13661 | + | 1.65797i | ||||
\(496\) | −0.0923684 | − | 0.0212116i | −0.00414746 | − | 0.000952427i | ||||
\(497\) | −7.75622 | −0.347914 | ||||||||
\(498\) | 4.47879 | − | 2.04587i | 0.200699 | − | 0.0916776i | ||||
\(499\) | 15.7374i | 0.704501i | 0.935906 | + | 0.352250i | \(0.114583\pi\) | ||||
−0.935906 | + | 0.352250i | \(0.885417\pi\) | |||||||
\(500\) | 1.24688 | − | 11.0008i | 0.0557623 | − | 0.491969i | ||||
\(501\) | 19.4861 | − | 10.2668i | 0.870574 | − | 0.458687i | ||||
\(502\) | 0.445877 | − | 7.89277i | 0.0199004 | − | 0.352271i | ||||
\(503\) | 0.610236 | 0.0272091 | 0.0136045 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136045 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(504\) | 9.19833 | + | 8.92387i | 0.409726 | + | 0.397501i | ||||
\(505\) | − | 21.8571i | − | 0.972627i | ||||||
\(506\) | 30.3385 | − | 18.7006i | 1.34871 | − | 0.831341i | ||||
\(507\) | 5.29844 | + | 10.0563i | 0.235312 | + | 0.446615i | ||||
\(508\) | −2.52598 | − | 0.286308i | −0.112072 | − | 0.0127029i | ||||
\(509\) | 34.2520 | 1.51819 | 0.759095 | − | 0.650979i | \(-0.225642\pi\) | ||||
0.759095 | + | 0.650979i | \(0.225642\pi\) | |||||||
\(510\) | −34.4440 | + | 15.7337i | −1.52520 | + | 0.696699i | ||||
\(511\) | − | 15.7777i | − | 0.697963i | ||||||
\(512\) | −19.7713 | − | 11.0044i | −0.873774 | − | 0.486332i | ||||
\(513\) | −1.43512 | − | 0.167284i | −0.0633622 | − | 0.00738578i | ||||
\(514\) | −0.317744 | + | 5.62461i | −0.0140151 | + | 0.248091i | ||||
\(515\) | −10.4101 | −0.458726 | ||||||||
\(516\) | 9.27410 | + | 23.7658i | 0.408269 | + | 1.04623i | ||||
\(517\) | −33.5523 | −1.47563 | ||||||||
\(518\) | −1.31866 | + | 23.3425i | −0.0579385 | + | 1.02561i | ||||
\(519\) | −4.14612 | − | 7.86922i | −0.181995 | − | 0.345420i | ||||
\(520\) | −34.9841 | − | 5.97989i | −1.53415 | − | 0.262235i | ||||
\(521\) | 12.3295 | 0.540165 | 0.270083 | − | 0.962837i | \(-0.412949\pi\) | ||||
0.270083 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(522\) | 10.1267 | − | 13.1186i | 0.443233 | − | 0.574185i | ||||
\(523\) | −0.786343 | −0.0343844 | −0.0171922 | − | 0.999852i | \(-0.505473\pi\) | ||||
−0.0171922 | + | 0.999852i | \(0.505473\pi\) | |||||||
\(524\) | −21.6627 | − | 2.45537i | −0.946339 | − | 0.107263i | ||||
\(525\) | −7.05624 | + | 3.71778i | −0.307960 | + | 0.162257i | ||||
\(526\) | −11.7431 | − | 0.663387i | −0.512022 | − | 0.0289251i | ||||
\(527\) | 0.129106 | 0.00562394 | ||||||||
\(528\) | 35.1894 | − | 9.33068i | 1.53142 | − | 0.406066i | ||||
\(529\) | −7.95478 | + | 21.5806i | −0.345860 | + | 0.938286i | ||||
\(530\) | −38.5526 | − | 2.17790i | −1.67462 | − | 0.0946021i | ||||
\(531\) | −16.2583 | + | 23.7159i | −0.705551 | + | 1.02918i | ||||
\(532\) | 0.0945973 | − | 0.834593i | 0.00410131 | − | 0.0361842i | ||||
\(533\) | 31.9214 | 1.38267 | ||||||||
\(534\) | −14.1527 | − | 30.9830i | −0.612449 | − | 1.34077i | ||||
\(535\) | −18.5574 | −0.802305 | ||||||||
\(536\) | −32.8195 | − | 5.60990i | −1.41759 | − | 0.242311i | ||||
\(537\) | 12.9795 | + | 24.6348i | 0.560109 | + | 1.06307i | ||||
\(538\) | −9.49813 | − | 0.536566i | −0.409493 | − | 0.0231330i | ||||
\(539\) | 24.7959i | 1.06803i | ||||||||
\(540\) | 6.69010 | − | 28.7144i | 0.287896 | − | 1.23567i | ||||
\(541\) | 14.9417i | 0.642394i | 0.947012 | + | 0.321197i | \(0.104085\pi\) | ||||
−0.947012 | + | 0.321197i | \(0.895915\pi\) | |||||||
\(542\) | 16.0964 | + | 0.909313i | 0.691398 | + | 0.0390583i | ||||
\(543\) | −14.5147 | − | 27.5485i | −0.622887 | − | 1.18222i | ||||
\(544\) | 29.6057 | + | 8.58251i | 1.26934 | + | 0.367972i | ||||
\(545\) | − | 2.02859i | − | 0.0868954i | ||||||
\(546\) | −6.79882 | − | 14.8839i | −0.290963 | − | 0.636972i | ||||
\(547\) | 26.1652i | 1.11874i | 0.828917 | + | 0.559371i | \(0.188957\pi\) | ||||
−0.828917 | + | 0.559371i | \(0.811043\pi\) | |||||||
\(548\) | 19.0043 | + | 2.15405i | 0.811823 | + | 0.0920164i | ||||
\(549\) | 8.34247 | − | 12.1691i | 0.356048 | − | 0.519364i | ||||
\(550\) | −1.27787 | + | 22.6204i | −0.0544884 | + | 0.964537i | ||||
\(551\) | −1.08615 | −0.0462714 | ||||||||
\(552\) | −14.1503 | + | 18.7555i | −0.602279 | + | 0.798286i | ||||
\(553\) | −20.1848 | −0.858346 | ||||||||
\(554\) | 1.94219 | − | 34.3801i | 0.0825159 | − | 1.46067i | ||||
\(555\) | 47.5853 | − | 25.0717i | 2.01988 | − | 1.06423i | ||||
\(556\) | −4.42282 | + | 39.0208i | −0.187569 | + | 1.65485i | ||||
\(557\) | − | 31.3190i | − | 1.32703i | −0.748164 | − | 0.663513i | \(-0.769065\pi\) | ||
0.748164 | − | 0.663513i | \(-0.230935\pi\) | |||||||
\(558\) | −0.0614241 | + | 0.0795717i | −0.00260029 | + | 0.00336854i | ||||
\(559\) | − | 32.5727i | − | 1.37768i | ||||||
\(560\) | 16.7050 | + | 3.83615i | 0.705914 | + | 0.162107i | ||||
\(561\) | −43.8765 | + | 23.1176i | −1.85247 | + | 0.976026i | ||||
\(562\) | −4.62590 | − | 0.261325i | −0.195132 | − | 0.0110233i | ||||
\(563\) | 43.2187i | 1.82145i | 0.413014 | + | 0.910725i | \(0.364476\pi\) | ||||
−0.413014 | + | 0.910725i | \(0.635524\pi\) | |||||||
\(564\) | 20.6057 | − | 8.04096i | 0.867658 | − | 0.338585i | ||||
\(565\) | 7.23074i | 0.304199i | ||||||||
\(566\) | 29.0182 | + | 1.63929i | 1.21973 | + | 0.0689046i | ||||
\(567\) | 12.6788 | − | 4.90129i | 0.532461 | − | 0.205835i | ||||
\(568\) | 2.44728 | − | 14.3173i | 0.102686 | − | 0.600741i | ||||
\(569\) | 9.00515 | 0.377515 | 0.188758 | − | 0.982024i | \(-0.439554\pi\) | ||||
0.188758 | + | 0.982024i | \(0.439554\pi\) | |||||||
\(570\) | −1.75763 | + | 0.802869i | −0.0736190 | + | 0.0336285i | ||||
\(571\) | −39.7928 | −1.66528 | −0.832639 | − | 0.553816i | \(-0.813171\pi\) | ||||
−0.832639 | + | 0.553816i | \(0.813171\pi\) | |||||||
\(572\) | −46.1867 | − | 5.23505i | −1.93116 | − | 0.218888i | ||||
\(573\) | 13.9546 | + | 26.4855i | 0.582963 | + | 1.10645i | ||||
\(574\) | −15.3912 | − | 0.869474i | −0.642414 | − | 0.0362912i | ||||
\(575\) | −8.36210 | − | 11.9944i | −0.348724 | − | 0.500203i | ||||
\(576\) | −19.3750 | + | 14.1636i | −0.807293 | + | 0.590151i | ||||
\(577\) | 26.7652 | 1.11425 | 0.557126 | − | 0.830428i | \(-0.311904\pi\) | ||||
0.557126 | + | 0.830428i | \(0.311904\pi\) | |||||||
\(578\) | −17.9213 | − | 1.01241i | −0.745428 | − | 0.0421106i | ||||
\(579\) | −4.84969 | − | 9.20456i | −0.201546 | − | 0.382529i | ||||
\(580\) | 2.49620 | − | 22.0229i | 0.103649 | − | 0.914453i | ||||
\(581\) | 3.03610 | 0.125959 | ||||||||
\(582\) | 22.6069 | − | 10.3266i | 0.937088 | − | 0.428053i | ||||
\(583\) | −50.5720 | −2.09448 | ||||||||
\(584\) | 29.1242 | + | 4.97825i | 1.20517 | + | 0.206002i | ||||
\(585\) | −21.2854 | + | 31.0489i | −0.880044 | + | 1.28371i | ||||
\(586\) | 0.236225 | − | 4.18159i | 0.00975838 | − | 0.172740i | ||||
\(587\) | −31.7614 | −1.31094 | −0.655468 | − | 0.755223i | \(-0.727528\pi\) | ||||
−0.655468 | + | 0.755223i | \(0.727528\pi\) | |||||||
\(588\) | −5.94244 | − | 15.2281i | −0.245062 | − | 0.627996i | ||||
\(589\) | 0.00658810 | 0.000271458 | ||||||||
\(590\) | −2.16894 | + | 38.3938i | −0.0892937 | + | 1.58065i | ||||
\(591\) | 2.69221 | + | 5.10974i | 0.110743 | + | 0.210187i | ||||
\(592\) | −42.6721 | − | 9.79927i | −1.75381 | − | 0.402747i | ||||
\(593\) | − | 22.6400i | − | 0.929712i | −0.885386 | − | 0.464856i | \(-0.846106\pi\) | ||
0.885386 | − | 0.464856i | \(-0.153894\pi\) | |||||||
\(594\) | 6.62686 | − | 38.0409i | 0.271903 | − | 1.56084i | ||||
\(595\) | −23.3490 | −0.957217 | ||||||||
\(596\) | −2.98747 | + | 26.3572i | −0.122372 | + | 1.07963i | ||||
\(597\) | 8.33938 | − | 4.39384i | 0.341308 | − | 0.179828i | ||||
\(598\) | 25.5365 | − | 15.7406i | 1.04426 | − | 0.643681i | ||||
\(599\) | − | 14.8241i | − | 0.605697i | −0.953039 | − | 0.302848i | \(-0.902062\pi\) | ||
0.953039 | − | 0.302848i | \(-0.0979376\pi\) | |||||||
\(600\) | −4.63629 | − | 14.1983i | −0.189276 | − | 0.579643i | ||||
\(601\) | 4.48110 | 0.182788 | 0.0913939 | − | 0.995815i | \(-0.470868\pi\) | ||||
0.0913939 | + | 0.995815i | \(0.470868\pi\) | |||||||
\(602\) | −0.887214 | + | 15.7052i | −0.0361601 | + | 0.640095i | ||||
\(603\) | −19.9684 | + | 29.1278i | −0.813178 | + | 1.18618i | ||||
\(604\) | 1.39551 | + | 0.158174i | 0.0567824 | + | 0.00643602i | ||||
\(605\) | 47.1279i | 1.91602i | ||||||||
\(606\) | 7.84092 | + | 17.1652i | 0.318516 | + | 0.697290i | ||||
\(607\) | 38.8731 | 1.57781 | 0.788905 | − | 0.614516i | \(-0.210648\pi\) | ||||
0.788905 | + | 0.614516i | \(0.210648\pi\) | |||||||
\(608\) | 1.51074 | + | 0.437954i | 0.0612687 | + | 0.0177614i | ||||
\(609\) | 9.04052 | − | 4.76326i | 0.366341 | − | 0.193017i | ||||
\(610\) | 1.11293 | − | 19.7006i | 0.0450610 | − | 0.797656i | ||||
\(611\) | −28.2416 | −1.14253 | ||||||||
\(612\) | 21.4060 | − | 24.7126i | 0.865286 | − | 0.998947i | ||||
\(613\) | 47.3280 | 1.91156 | 0.955780 | − | 0.294084i | \(-0.0950144\pi\) | ||||
0.955780 | + | 0.294084i | \(0.0950144\pi\) | |||||||
\(614\) | −1.29510 | + | 22.9255i | −0.0522661 | + | 0.925197i | ||||
\(615\) | 16.5313 | + | 31.3760i | 0.666608 | + | 1.26520i | ||||
\(616\) | 22.1267 | + | 3.78216i | 0.891511 | + | 0.152387i | ||||
\(617\) | −18.2646 | −0.735307 | −0.367653 | − | 0.929963i | \(-0.619839\pi\) | ||||
−0.367653 | + | 0.929963i | \(0.619839\pi\) | |||||||
\(618\) | 8.17551 | − | 3.73450i | 0.328867 | − | 0.150223i | ||||
\(619\) | −5.94337 | −0.238884 | −0.119442 | − | 0.992841i | \(-0.538111\pi\) | ||||
−0.119442 | + | 0.992841i | \(0.538111\pi\) | |||||||
\(620\) | −0.0151409 | + | 0.133582i | −0.000608071 | + | 0.00536477i | ||||
\(621\) | 11.7890 | + | 21.9549i | 0.473077 | + | 0.881021i | ||||
\(622\) | 0.468029 | − | 8.28490i | 0.0187663 | − | 0.332194i | ||||
\(623\) | − | 21.0029i | − | 0.841463i | ||||||
\(624\) | 29.6196 | − | 7.85381i | 1.18573 | − | 0.314404i | ||||
\(625\) | −30.9488 | −1.23795 | ||||||||
\(626\) | −0.899359 | + | 15.9202i | −0.0359456 | + | 0.636298i | ||||
\(627\) | −2.23896 | + | 1.17966i | −0.0894155 | + | 0.0471111i | ||||
\(628\) | 14.9799 | + | 1.69790i | 0.597764 | + | 0.0677538i | ||||
\(629\) | 59.6440 | 2.37816 | ||||||||
\(630\) | 11.1086 | − | 14.3907i | 0.442579 | − | 0.573339i | ||||
\(631\) | − | 12.8561i | − | 0.511794i | −0.966704 | − | 0.255897i | \(-0.917629\pi\) | ||
0.966704 | − | 0.255897i | \(-0.0823709\pi\) | |||||||
\(632\) | 6.36882 | − | 37.2595i | 0.253338 | − | 1.48210i | ||||
\(633\) | −10.7027 | + | 5.63901i | −0.425393 | + | 0.224131i | ||||
\(634\) | 42.1569 | + | 2.38152i | 1.67426 | + | 0.0945821i | ||||
\(635\) | 3.60610i | 0.143104i | ||||||||
\(636\) | 31.0582 | − | 12.1198i | 1.23154 | − | 0.480581i | ||||
\(637\) | 20.8712i | 0.826946i | ||||||||
\(638\) | 1.63722 | − | 28.9815i | 0.0648180 | − | 1.14739i | ||||
\(639\) | −12.7068 | − | 8.71111i | −0.502674 | − | 0.344606i | ||||
\(640\) | −12.3520 | + | 29.6256i | −0.488258 | + | 1.17105i | ||||
\(641\) | 37.2339 | 1.47065 | 0.735326 | − | 0.677714i | \(-0.237029\pi\) | ||||
0.735326 | + | 0.677714i | \(0.237029\pi\) | |||||||
\(642\) | 14.5739 | − | 6.65720i | 0.575184 | − | 0.262739i | ||||
\(643\) | −4.26786 | −0.168308 | −0.0841541 | − | 0.996453i | \(-0.526819\pi\) | ||||
−0.0841541 | + | 0.996453i | \(0.526819\pi\) | |||||||
\(644\) | −12.7414 | + | 6.89390i | −0.502080 | + | 0.271658i | ||||
\(645\) | 32.0162 | − | 16.8686i | 1.26064 | − | 0.664202i | ||||
\(646\) | −2.13936 | − | 0.120856i | −0.0841720 | − | 0.00475503i | ||||
\(647\) | − | 1.13278i | − | 0.0445340i | −0.999752 | − | 0.0222670i | \(-0.992912\pi\) | ||
0.999752 | − | 0.0222670i | \(-0.00708839\pi\) | |||||||
\(648\) | 5.04687 | + | 24.9505i | 0.198260 | + | 0.980150i | ||||
\(649\) | 50.3638i | 1.97695i | ||||||||
\(650\) | −1.07560 | + | 19.0400i | −0.0421887 | + | 0.746811i | ||||
\(651\) | −0.0548359 | + | 0.0288919i | −0.00214919 | + | 0.00113236i | ||||
\(652\) | −1.06646 | + | 9.40897i | −0.0417659 | + | 0.368484i | ||||
\(653\) | 27.5832 | 1.07941 | 0.539707 | − | 0.841853i | \(-0.318535\pi\) | ||||
0.539707 | + | 0.841853i | \(0.318535\pi\) | |||||||
\(654\) | 0.727730 | + | 1.59314i | 0.0284565 | + | 0.0622966i | ||||
\(655\) | 30.9258i | 1.20837i | ||||||||
\(656\) | 6.46128 | − | 28.1364i | 0.252270 | − | 1.09854i | ||||
\(657\) | 17.7201 | − | 25.8482i | 0.691327 | − | 1.00843i | ||||
\(658\) | 13.6169 | + | 0.769245i | 0.530843 | + | 0.0299883i | ||||
\(659\) | − | 27.3110i | − | 1.06388i | −0.846781 | − | 0.531942i | \(-0.821462\pi\) | ||
0.846781 | − | 0.531942i | \(-0.178538\pi\) | |||||||
\(660\) | −18.7734 | − | 48.1087i | −0.730755 | − | 1.87263i | ||||
\(661\) | −8.45225 | −0.328754 | −0.164377 | − | 0.986398i | \(-0.552561\pi\) | ||||
−0.164377 | + | 0.986398i | \(0.552561\pi\) | |||||||
\(662\) | −2.34181 | + | 41.4540i | −0.0910171 | + | 1.61116i | ||||
\(663\) | −36.9317 | + | 19.4585i | −1.43431 | + | 0.755706i | ||||
\(664\) | −0.957967 | + | 5.60439i | −0.0371763 | + | 0.217492i | ||||
\(665\) | −1.19147 | −0.0462032 | ||||||||
\(666\) | −28.3765 | + | 36.7604i | −1.09957 | + | 1.42444i | ||||
\(667\) | 10.7136 | + | 15.3674i | 0.414832 | + | 0.595028i | ||||
\(668\) | −2.86433 | + | 25.2708i | −0.110824 | + | 0.977758i | ||||
\(669\) | −2.83774 | − | 5.38595i | −0.109713 | − | 0.208233i | ||||
\(670\) | −2.66389 | + | 47.1553i | −0.102915 | + | 1.82177i | ||||
\(671\) | − | 25.8427i | − | 0.997645i | ||||||
\(672\) | −14.4953 | + | 2.98000i | −0.559167 | + | 0.114956i | ||||
\(673\) | 28.7225 | 1.10717 | 0.553585 | − | 0.832793i | \(-0.313260\pi\) | ||||
0.553585 | + | 0.832793i | \(0.313260\pi\) | |||||||
\(674\) | 2.81361 | − | 49.8056i | 0.108376 | − | 1.91844i | ||||
\(675\) | −15.7356 | − | 1.83421i | −0.605662 | − | 0.0705987i | ||||
\(676\) | −13.0417 | − | 1.47821i | −0.501602 | − | 0.0568542i | ||||
\(677\) | − | 7.23891i | − | 0.278214i | −0.990277 | − | 0.139107i | \(-0.955577\pi\) | ||
0.990277 | − | 0.139107i | \(-0.0444232\pi\) | |||||||
\(678\) | −2.59393 | − | 5.67859i | −0.0996191 | − | 0.218085i | ||||
\(679\) | 15.3249 | 0.588115 | ||||||||
\(680\) | 7.36721 | − | 43.1003i | 0.282520 | − | 1.65282i | ||||
\(681\) | −6.06318 | + | 3.19456i | −0.232342 | + | 0.122416i | ||||
\(682\) | −0.00993064 | + | 0.175789i | −0.000380264 | + | 0.00673131i | ||||
\(683\) | 11.1797 | 0.427778 | 0.213889 | − | 0.976858i | \(-0.431387\pi\) | ||||
0.213889 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(684\) | 1.09232 | − | 1.26105i | 0.0417659 | − | 0.0482175i | ||||
\(685\) | − | 27.1306i | − | 1.03661i | ||||||
\(686\) | 1.41180 | − | 24.9912i | 0.0539026 | − | 0.954167i | ||||
\(687\) | −11.6821 | − | 22.1724i | −0.445701 | − | 0.845928i | ||||
\(688\) | −28.7105 | − | 6.59310i | −1.09458 | − | 0.251360i | ||||
\(689\) | −42.5674 | −1.62169 | ||||||||
\(690\) | 28.6964 | + | 16.9485i | 1.09245 | + | 0.645218i | ||||
\(691\) | − | 9.57423i | − | 0.364221i | −0.983278 | − | 0.182110i | \(-0.941707\pi\) | ||
0.983278 | − | 0.182110i | \(-0.0582928\pi\) | |||||||
\(692\) | 10.2053 | + | 1.15673i | 0.387948 | + | 0.0439721i | ||||
\(693\) | 13.4626 | − | 19.6378i | 0.511402 | − | 0.745977i | ||||
\(694\) | −19.1894 | − | 1.08404i | −0.728419 | − | 0.0411497i | ||||
\(695\) | 55.7062 | 2.11306 | ||||||||
\(696\) | 5.94006 | + | 18.1910i | 0.225157 | + | 0.689527i | ||||
\(697\) | 39.3271i | 1.48962i | ||||||||
\(698\) | −1.79580 | + | 31.7886i | −0.0679719 | + | 1.20322i | ||||
\(699\) | −9.78599 | + | 5.15603i | −0.370140 | + | 0.195019i | ||||
\(700\) | 1.03722 | − | 9.15100i | 0.0392034 | − | 0.345875i | ||||
\(701\) | − | 12.8330i | − | 0.484697i | −0.970189 | − | 0.242349i | \(-0.922082\pi\) | ||
0.970189 | − | 0.242349i | \(-0.0779178\pi\) | |||||||
\(702\) | 5.57795 | − | 32.0198i | 0.210526 | − | 1.20851i | ||||
\(703\) | 3.04356 | 0.114790 | ||||||||
\(704\) | −13.9631 | + | 39.6507i | −0.526253 | + | 1.49439i | ||||
\(705\) | −14.6257 | − | 27.7591i | −0.550835 | − | 1.04547i | ||||
\(706\) | −0.957603 | + | 16.9512i | −0.0360399 | + | 0.637966i | ||||
\(707\) | 11.6360i | 0.437618i | ||||||||
\(708\) | −12.0699 | − | 30.9303i | −0.453615 | − | 1.16243i | ||||
\(709\) | −2.20392 | −0.0827701 | −0.0413850 | − | 0.999143i | \(-0.513177\pi\) | ||||
−0.0413850 | + | 0.999143i | \(0.513177\pi\) | |||||||
\(710\) | −20.5712 | − | 1.16210i | −0.772023 | − | 0.0436130i | ||||
\(711\) | −33.0683 | − | 22.6698i | −1.24016 | − | 0.850185i | ||||
\(712\) | 38.7696 | + | 6.62694i | 1.45295 | + | 0.248355i | ||||
\(713\) | −0.0649841 | − | 0.0932120i | −0.00243367 | − | 0.00349082i | ||||
\(714\) | 18.3369 | − | 8.37614i | 0.686242 | − | 0.313469i | ||||
\(715\) | 65.9364i | 2.46588i | ||||||||
\(716\) | −31.9480 | − | 3.62116i | −1.19395 | − | 0.135329i | ||||
\(717\) | 5.59959 | − | 2.95030i | 0.209120 | − | 0.110181i | ||||
\(718\) | 17.4246 | + | 0.984346i | 0.650280 | + | 0.0367355i | ||||
\(719\) | 45.9821i | 1.71484i | 0.514616 | + | 0.857421i | \(0.327935\pi\) | ||||
−0.514616 | + | 0.857421i | \(0.672065\pi\) | |||||||
\(720\) | 23.0589 | + | 25.0463i | 0.859356 | + | 0.933419i | ||||
\(721\) | 5.54205 | 0.206397 | ||||||||
\(722\) | 26.7181 | + | 1.50935i | 0.994345 | + | 0.0561724i | ||||
\(723\) | 22.2926 | − | 11.7455i | 0.829071 | − | 0.436820i | ||||
\(724\) | 35.7268 | + | 4.04946i | 1.32778 | + | 0.150497i | ||||
\(725\) | −11.9092 | −0.442296 | ||||||||
\(726\) | −16.9065 | − | 37.0115i | −0.627459 | − | 1.37362i | ||||
\(727\) | 40.8296i | 1.51428i | 0.653250 | + | 0.757142i | \(0.273405\pi\) | ||||
−0.653250 | + | 0.757142i | \(0.726595\pi\) | |||||||
\(728\) | 18.6245 | + | 3.18351i | 0.690269 | + | 0.117989i | ||||
\(729\) | 26.2761 | + | 6.21011i | 0.973190 | + | 0.230004i | ||||
\(730\) | 2.36395 | − | 41.8459i | 0.0874936 | − | 1.54878i | ||||
\(731\) | 40.1295 | 1.48424 | ||||||||
\(732\) | 6.19331 | + | 15.8710i | 0.228911 | + | 0.586608i | ||||
\(733\) | 10.9115 | 0.403024 | 0.201512 | − | 0.979486i | \(-0.435414\pi\) | ||||
0.201512 | + | 0.979486i | \(0.435414\pi\) | |||||||
\(734\) | −0.834946 | + | 14.7800i | −0.0308184 | + | 0.545538i | ||||
\(735\) | −20.5146 | + | 10.8087i | −0.756692 | + | 0.398685i | ||||
\(736\) | −8.70533 | − | 25.6947i | −0.320883 | − | 0.947119i | ||||
\(737\) | 61.8568i | 2.27852i | ||||||||
\(738\) | −24.2384 | − | 18.7105i | −0.892229 | − | 0.688741i | ||||
\(739\) | − | 39.1912i | − | 1.44167i | −0.693105 | − | 0.720836i | \(-0.743758\pi\) | ||
0.693105 | − | 0.720836i | \(-0.256242\pi\) | |||||||
\(740\) | −6.99474 | + | 61.7118i | −0.257132 | + | 2.26857i | ||||
\(741\) | −1.88458 | + | 0.992942i | −0.0692316 | + | 0.0364766i | ||||
\(742\) | 20.5242 | + | 1.15945i | 0.753468 | + | 0.0425648i | ||||
\(743\) | 53.5532 | 1.96468 | 0.982338 | − | 0.187113i | \(-0.0599132\pi\) | ||||
0.982338 | + | 0.187113i | \(0.0599132\pi\) | |||||||
\(744\) | −0.0360298 | − | 0.110339i | −0.00132092 | − | 0.00404521i | ||||
\(745\) | 37.6277 | 1.37857 | ||||||||
\(746\) | 26.9659 | + | 1.52335i | 0.987293 | + | 0.0557739i | ||||
\(747\) | 4.97397 | + | 3.40989i | 0.181988 | + | 0.124761i | ||||
\(748\) | 6.44957 | − | 56.9020i | 0.235820 | − | 2.08054i | ||||
\(749\) | 9.87939 | 0.360985 | ||||||||
\(750\) | 12.3336 | − | 5.63385i | 0.450358 | − | 0.205719i | ||||
\(751\) | − | 13.1585i | − | 0.480161i | −0.970753 | − | 0.240081i | \(-0.922826\pi\) | ||
0.970753 | − | 0.240081i | \(-0.0771739\pi\) | |||||||
\(752\) | −5.71645 | + | 24.8930i | −0.208457 | + | 0.907754i | ||||
\(753\) | 8.56582 | − | 4.51315i | 0.312156 | − | 0.164468i | ||||
\(754\) | 1.37807 | − | 24.3942i | 0.0501865 | − | 0.888386i | ||||
\(755\) | − | 1.99223i | − | 0.0725048i | ||||||
\(756\) | −3.56161 | + | 15.2867i | −0.129535 | + | 0.555971i | ||||
\(757\) | 16.8295 | 0.611680 | 0.305840 | − | 0.952083i | \(-0.401063\pi\) | ||||
0.305840 | + | 0.952083i | \(0.401063\pi\) | |||||||
\(758\) | −39.0153 | − | 2.20405i | −1.41710 | − | 0.0800546i | ||||
\(759\) | 38.7753 | + | 20.0420i | 1.40745 | + | 0.727479i | ||||
\(760\) | 0.375939 | − | 2.19935i | 0.0136367 | − | 0.0797789i | ||||
\(761\) | − | 49.7398i | − | 1.80307i | −0.432708 | − | 0.901534i | \(-0.642442\pi\) | ||
0.432708 | − | 0.901534i | \(-0.357558\pi\) | |||||||
\(762\) | −1.29364 | − | 2.83202i | −0.0468636 | − | 0.102593i | ||||
\(763\) | 1.07996i | 0.0390973i | ||||||||
\(764\) | −34.3481 | − | 3.89319i | −1.24267 | − | 0.140851i | ||||
\(765\) | −38.2521 | − | 26.2236i | −1.38301 | − | 0.948116i | ||||
\(766\) | −34.6173 | − | 1.95559i | −1.25077 | − | 0.0706585i | ||||
\(767\) | 42.3921i | 1.53069i | ||||||||
\(768\) | −0.927206 | − | 27.6973i | −0.0334577 | − | 0.999440i | ||||
\(769\) | − | 13.3506i | − | 0.481434i | −0.970595 | − | 0.240717i | \(-0.922617\pi\) | ||
0.970595 | − | 0.240717i | \(-0.0773825\pi\) | |||||||
\(770\) | 1.79597 | − | 31.7918i | 0.0647224 | − | 1.14570i | ||||
\(771\) | −6.10425 | + | 3.21620i | −0.219839 | + | 0.115829i | ||||
\(772\) | 11.9371 | + | 1.35301i | 0.429625 | + | 0.0486960i | ||||
\(773\) | 27.4662i | 0.987890i | 0.869493 | + | 0.493945i | \(0.164446\pi\) | ||||
−0.869493 | + | 0.493945i | \(0.835554\pi\) | |||||||
\(774\) | −19.0922 | + | 24.7330i | −0.686255 | + | 0.889008i | ||||
\(775\) | 0.0722360 | 0.00259480 | ||||||||
\(776\) | −4.83539 | + | 28.2885i | −0.173580 | + | 1.01550i | ||||
\(777\) | −25.3330 | + | 13.3474i | −0.908816 | + | 0.478836i | ||||
\(778\) | −1.40475 | + | 24.8665i | −0.0503629 | + | 0.891508i | ||||
\(779\) | 2.00681i | 0.0719014i | ||||||||
\(780\) | −15.8019 | − | 40.4940i | −0.565800 | − | 1.44992i | ||||
\(781\) | −26.9846 | −0.965586 | ||||||||
\(782\) | 19.3924 | + | 31.4609i | 0.693471 | + | 1.12504i | ||||
\(783\) | 20.1606 | + | 2.35001i | 0.720479 | + | 0.0839823i | ||||
\(784\) | 18.3965 | + | 4.22458i | 0.657016 | + | 0.150878i | ||||
\(785\) | − | 21.3854i | − | 0.763278i | ||||||
\(786\) | −11.0942 | − | 24.2873i | −0.395717 | − | 0.866298i | ||||
\(787\) | −41.9113 | −1.49398 | −0.746988 | − | 0.664837i | \(-0.768501\pi\) | ||||
−0.746988 | + | 0.664837i | \(0.768501\pi\) | |||||||
\(788\) | −6.62665 | − | 0.751100i | −0.236065 | − | 0.0267568i | ||||
\(789\) | −6.71479 | − | 12.7445i | −0.239053 | − | 0.453715i | ||||
\(790\) | −53.5346 | − | 3.02426i | −1.90467 | − | 0.107599i | ||||
\(791\) | − | 3.84943i | − | 0.136870i | ||||||
\(792\) | 32.0019 | + | 31.0470i | 1.13714 | + | 1.10321i | ||||
\(793\) | − | 21.7523i | − | 0.772446i | ||||||
\(794\) | −2.08125 | + | 36.8417i | −0.0738610 | + | 1.30746i | ||||
\(795\) | −22.0447 | − | 41.8401i | −0.781844 | − | 1.48392i | ||||
\(796\) | −1.22584 | + | 10.8151i | −0.0434486 | + | 0.383330i | ||||
\(797\) | 1.43260i | 0.0507454i | 0.999678 | + | 0.0253727i | \(0.00807725\pi\) | ||||
−0.999678 | + | 0.0253727i | \(0.991923\pi\) | |||||||
\(798\) | 0.935709 | − | 0.427423i | 0.0331237 | − | 0.0151306i | ||||
\(799\) | − | 34.7936i | − | 1.23091i | ||||||
\(800\) | 16.5647 | + | 4.80200i | 0.585651 | + | 0.169776i | ||||
\(801\) | 23.5886 | − | 34.4085i | 0.833463 | − | 1.21577i | ||||
\(802\) | 8.23171 | + | 0.465024i | 0.290672 | + | 0.0164206i | ||||
\(803\) | − | 54.8920i | − | 1.93710i | ||||||
\(804\) | −14.8242 | − | 37.9886i | −0.522811 | − | 1.33975i | ||||
\(805\) | 11.7525 | + | 16.8575i | 0.414221 | + | 0.594150i | ||||
\(806\) | −0.00835881 | + | 0.147965i | −0.000294426 | + | 0.00521184i | ||||
\(807\) | −5.43111 | − | 10.3081i | −0.191184 | − | 0.362862i | ||||
\(808\) | −21.4792 | − | 3.67147i | −0.755634 | − | 0.129162i | ||||
\(809\) | 41.7684i | 1.46850i | 0.678881 | + | 0.734248i | \(0.262465\pi\) | ||||
−0.678881 | + | 0.734248i | \(0.737535\pi\) | |||||||
\(810\) | 34.3614 | − | 11.0996i | 1.20734 | − | 0.390002i | ||||
\(811\) | 10.2543i | 0.360078i | 0.983659 | + | 0.180039i | \(0.0576223\pi\) | ||||
−0.983659 | + | 0.180039i | \(0.942378\pi\) | |||||||
\(812\) | −1.32890 | + | 11.7243i | −0.0466352 | + | 0.411444i | ||||
\(813\) | 9.20403 | + | 17.4690i | 0.322800 | + | 0.612664i | ||||
\(814\) | −4.58774 | + | 81.2107i | −0.160800 | + | 2.84643i | ||||
\(815\) | 13.4323 | 0.470512 | ||||||||
\(816\) | 9.67588 | + | 36.4913i | 0.338724 | + | 1.27745i | ||||
\(817\) | 2.04775 | 0.0716418 | ||||||||
\(818\) | −47.5712 | − | 2.68739i | −1.66329 | − | 0.0939622i | ||||
\(819\) | 11.3317 | − | 16.5295i | 0.395962 | − | 0.577587i | ||||
\(820\) | −40.6905 | − | 4.61207i | −1.42097 | − | 0.161061i | ||||
\(821\) | −35.9779 | −1.25564 | −0.627819 | − | 0.778359i | \(-0.716052\pi\) | ||||
−0.627819 | + | 0.778359i | \(0.716052\pi\) | |||||||
\(822\) | 9.73274 | + | 21.3068i | 0.339468 | + | 0.743159i | ||||
\(823\) | 31.1038 | 1.08421 | 0.542106 | − | 0.840310i | \(-0.317627\pi\) | ||||
0.542106 | + | 0.840310i | \(0.317627\pi\) | |||||||
\(824\) | −1.74866 | + | 10.2302i | −0.0609173 | + | 0.356384i | ||||
\(825\) | −24.5494 | + | 12.9345i | −0.854699 | + | 0.450323i | ||||
\(826\) | 1.15468 | − | 20.4397i | 0.0401763 | − | 0.711189i | ||||
\(827\) | 44.8962i | 1.56119i | 0.625036 | + | 0.780596i | \(0.285084\pi\) | ||||
−0.625036 | + | 0.780596i | \(0.714916\pi\) | |||||||
\(828\) | −28.6165 | − | 3.01589i | −0.994492 | − | 0.104810i | ||||
\(829\) | − | 24.4025i | − | 0.847535i | −0.905771 | − | 0.423768i | \(-0.860707\pi\) | ||
0.905771 | − | 0.423768i | \(-0.139293\pi\) | |||||||
\(830\) | 8.05241 | + | 0.454895i | 0.279503 | + | 0.0157896i | ||||
\(831\) | 37.3119 | − | 19.6588i | 1.29433 | − | 0.681957i | ||||
\(832\) | −11.7530 | + | 33.3747i | −0.407461 | + | 1.15706i | ||||
\(833\) | −25.7132 | −0.890911 | ||||||||
\(834\) | −43.7484 | + | 19.9838i | −1.51488 | + | 0.691984i | ||||
\(835\) | 36.0768 | 1.24849 | ||||||||
\(836\) | 0.329113 | − | 2.90363i | 0.0113826 | − | 0.100424i | ||||
\(837\) | −0.122285 | − | 0.0142541i | −0.00422680 | − | 0.000492695i | ||||
\(838\) | −1.39516 | + | 24.6966i | −0.0481949 | + | 0.853130i | ||||
\(839\) | −42.3798 | −1.46311 | −0.731557 | − | 0.681780i | \(-0.761206\pi\) | ||||
−0.731557 | + | 0.681780i | \(0.761206\pi\) | |||||||
\(840\) | 6.51606 | + | 19.9549i | 0.224825 | + | 0.688511i | ||||
\(841\) | −13.7418 | −0.473856 | ||||||||
\(842\) | −26.3796 | − | 1.49023i | −0.909100 | − | 0.0513567i | ||||
\(843\) | −2.64513 | − | 5.02038i | −0.0911030 | − | 0.172911i | ||||
\(844\) | 1.57323 | − | 13.8799i | 0.0541527 | − | 0.477767i | ||||
\(845\) | 18.6183i | 0.640490i | ||||||||
\(846\) | 21.4443 | + | 16.5536i | 0.737271 | + | 0.569124i | ||||
\(847\) | − | 25.0895i | − | 0.862085i | ||||||
\(848\) | −8.61616 | + | 37.5202i | −0.295880 | + | 1.28845i | ||||
\(849\) | 16.5929 | + | 31.4928i | 0.569466 | + | 1.08083i | ||||
\(850\) | −23.4573 | − | 1.32514i | −0.804578 | − | 0.0454520i | ||||
\(851\) | −30.0212 | − | 43.0619i | −1.02911 | − | 1.47614i | ||||
\(852\) | 16.5723 | − | 6.46698i | 0.567757 | − | 0.221555i | ||||
\(853\) | 39.5979i | 1.35581i | 0.735151 | + | 0.677903i | \(0.237111\pi\) | ||||
−0.735151 | + | 0.677903i | \(0.762889\pi\) | |||||||
\(854\) | −0.592488 | + | 10.4880i | −0.0202745 | + | 0.358893i | ||||
\(855\) | −1.95196 | − | 1.33816i | −0.0667555 | − | 0.0457640i | ||||
\(856\) | −3.11720 | + | 18.2365i | −0.106544 | + | 0.623311i | ||||
\(857\) | − | 45.3290i | − | 1.54841i | −0.632935 | − | 0.774205i | \(-0.718150\pi\) | ||
0.632935 | − | 0.774205i | \(-0.281850\pi\) | |||||||
\(858\) | −23.6538 | − | 51.7825i | −0.807526 | − | 1.76783i | ||||
\(859\) | 24.6318i | 0.840426i | 0.907426 | + | 0.420213i | \(0.138045\pi\) | ||||
−0.907426 | + | 0.420213i | \(0.861955\pi\) | |||||||
\(860\) | −4.70617 | + | 41.5207i | −0.160479 | + | 1.41584i | ||||
\(861\) | −8.80079 | − | 16.7036i | −0.299930 | − | 0.569259i | ||||
\(862\) | −5.63755 | − | 0.318475i | −0.192016 | − | 0.0108473i | ||||
\(863\) | 21.3840i | 0.727921i | 0.931414 | + | 0.363960i | \(0.118576\pi\) | ||||
−0.931414 | + | 0.363960i | \(0.881424\pi\) | |||||||
\(864\) | −27.0941 | − | 11.3978i | −0.921760 | − | 0.387760i | ||||
\(865\) | − | 14.5692i | − | 0.495366i | ||||||
\(866\) | 1.63213 | − | 28.8914i | 0.0554620 | − | 0.981770i | ||||
\(867\) | −10.2475 | − | 19.4495i | −0.348025 | − | 0.660541i | ||||
\(868\) | 0.00806054 | − | 0.0711149i | 0.000273592 | − | 0.00241380i | ||||
\(869\) | −70.2249 | −2.38222 | ||||||||
\(870\) | 24.6911 | − | 11.2787i | 0.837108 | − | 0.382383i | ||||
\(871\) | 52.0660i | 1.76419i | ||||||||
\(872\) | −1.99352 | − | 0.340755i | −0.0675091 | − | 0.0115394i | ||||
\(873\) | 25.1064 | + | 17.2116i | 0.849723 | + | 0.582524i | ||||
\(874\) | 0.989568 | + | 1.60541i | 0.0334727 | + | 0.0543037i | ||||
\(875\) | 8.36072 | 0.282644 | ||||||||
\(876\) | 13.1551 | + | 33.7113i | 0.444470 | + | 1.13900i | ||||
\(877\) | − | 7.10030i | − | 0.239760i | −0.992788 | − | 0.119880i | \(-0.961749\pi\) | ||
0.992788 | − | 0.119880i | \(-0.0382510\pi\) | |||||||
\(878\) | −18.9307 | − | 1.06943i | −0.638881 | − | 0.0360915i | ||||
\(879\) | 4.53817 | − | 2.39107i | 0.153069 | − | 0.0806487i | ||||
\(880\) | 58.1183 | + | 13.3463i | 1.95917 | + | 0.449905i | ||||
\(881\) | 21.8256 | 0.735323 | 0.367661 | − | 0.929960i | \(-0.380159\pi\) | ||||
0.367661 | + | 0.929960i | \(0.380159\pi\) | |||||||
\(882\) | 12.2335 | − | 15.8478i | 0.411922 | − | 0.533624i | ||||
\(883\) | − | 34.5350i | − | 1.16220i | −0.813834 | − | 0.581098i | \(-0.802623\pi\) | ||
0.813834 | − | 0.581098i | \(-0.197377\pi\) | |||||||
\(884\) | 5.42873 | − | 47.8955i | 0.182588 | − | 1.61090i | ||||
\(885\) | −41.6679 | + | 21.9539i | −1.40065 | + | 0.737972i | ||||
\(886\) | −50.4946 | − | 2.85253i | −1.69640 | − | 0.0958326i | ||||
\(887\) | − | 23.9052i | − | 0.802660i | −0.915934 | − | 0.401330i | \(-0.868548\pi\) | ||
0.915934 | − | 0.401330i | \(-0.131452\pi\) | |||||||
\(888\) | −16.6450 | − | 50.9740i | −0.558569 | − | 1.71058i | ||||
\(889\) | − | 1.91978i | − | 0.0643874i | ||||||
\(890\) | 3.14684 | − | 55.7043i | 0.105482 | − | 1.86721i | ||||
\(891\) | 44.1109 | − | 17.0521i | 1.47777 | − | 0.571265i | ||||
\(892\) | 6.98485 | + | 0.791700i | 0.233870 | + | 0.0265081i | ||||
\(893\) | − | 1.77547i | − | 0.0594139i | ||||||
\(894\) | −29.5506 | + | 13.4984i | −0.988319 | + | 0.451455i | ||||
\(895\) | 45.6091i | 1.52455i | ||||||||
\(896\) | 6.57586 | − | 15.7718i | 0.219684 | − | 0.526898i | ||||
\(897\) | 32.6379 | + | 16.8697i | 1.08975 | + | 0.563264i | ||||
\(898\) | 1.03546 | − | 18.3294i | 0.0345538 | − | 0.611661i | ||||
\(899\) | −0.0925495 | −0.00308670 | ||||||||
\(900\) | 11.9769 | − | 13.8269i | 0.399229 | − | 0.460898i | ||||
\(901\) | − | 52.4430i | − | 1.74713i | ||||||
\(902\) | −53.5473 | − | 3.02499i | −1.78293 | − | 0.100721i | ||||
\(903\) | −17.0444 | + | 8.98035i | −0.567203 | + | 0.298847i | ||||
\(904\) | 7.10572 | + | 1.21459i | 0.236333 | + | 0.0403967i | ||||
\(905\) | − | 51.0037i | − | 1.69542i | ||||||
\(906\) | 0.714686 | + | 1.56458i | 0.0237438 | + | 0.0519797i | ||||
\(907\) | 20.9902 | 0.696967 | 0.348484 | − | 0.937315i | \(-0.386697\pi\) | ||||
0.348484 | + | 0.937315i | \(0.386697\pi\) | |||||||
\(908\) | 0.891249 | − | 7.86313i | 0.0295771 | − | 0.260947i | ||||
\(909\) | −13.0686 | + | 19.0630i | −0.433458 | + | 0.632281i | ||||
\(910\) | 1.51171 | − | 26.7597i | 0.0501125 | − | 0.887076i | ||||
\(911\) | 19.5906 | 0.649064 | 0.324532 | − | 0.945875i | \(-0.394793\pi\) | ||||
0.324532 | + | 0.945875i | \(0.394793\pi\) | |||||||
\(912\) | 0.493747 | + | 1.86210i | 0.0163496 | + | 0.0616604i | ||||
\(913\) | 10.5629 | 0.349581 | ||||||||
\(914\) | −1.85431 | + | 32.8243i | −0.0613350 | + | 1.08573i | ||||
\(915\) | 21.3806 | − | 11.2650i | 0.706822 | − | 0.372409i | ||||
\(916\) | 28.7546 | + | 3.25920i | 0.950078 | + | 0.107687i | ||||
\(917\) | − | 16.4639i | − | 0.543688i | ||||||
\(918\) | 39.4483 | + | 6.87203i | 1.30199 | + | 0.226811i | ||||
\(919\) | 5.56361i | 0.183527i | 0.995781 | + | 0.0917633i | \(0.0292503\pi\) | ||||
−0.995781 | + | 0.0917633i | \(0.970750\pi\) | |||||||
\(920\) | −34.8258 | + | 16.3751i | −1.14817 | + | 0.539872i | ||||
\(921\) | −24.8805 | + | 13.1090i | −0.819839 | + | 0.431956i | ||||
\(922\) | 37.5504 | + | 2.12129i | 1.23666 | + | 0.0698610i | ||||
\(923\) | −22.7135 | −0.747623 | ||||||||
\(924\) | 9.99441 | + | 25.6116i | 0.328792 | + | 0.842561i | ||||
\(925\) | 33.3714 | 1.09725 | ||||||||
\(926\) | 31.4629 | + | 1.77739i | 1.03393 | + | 0.0584088i | ||||
\(927\) | 9.07940 | + | 6.22435i | 0.298207 | + | 0.204434i | ||||
\(928\) | −21.2229 | − | 6.15237i | −0.696674 | − | 0.201961i | ||||
\(929\) | 15.4930i | 0.508309i | 0.967164 | + | 0.254155i | \(0.0817972\pi\) | ||||
−0.967164 | + | 0.254155i | \(0.918203\pi\) | |||||||
\(930\) | −0.149766 | + | 0.0684116i | −0.00491101 | + | 0.00224331i | ||||
\(931\) | −1.31211 | −0.0430028 | ||||||||
\(932\) | 1.43848 | − | 12.6911i | 0.0471189 | − | 0.415711i | ||||
\(933\) | 8.99140 | − | 4.73738i | 0.294365 | − | 0.155095i | ||||
\(934\) | −0.720918 | + | 12.7615i | −0.0235892 | + | 0.417568i | ||||
\(935\) | −81.2335 | −2.65662 | ||||||||
\(936\) | 26.9366 | + | 26.1329i | 0.880450 | + | 0.854179i | ||||
\(937\) | − | 3.40862i | − | 0.111355i | −0.998449 | − | 0.0556774i | \(-0.982268\pi\) | ||
0.998449 | − | 0.0556774i | \(-0.0177318\pi\) | |||||||
\(938\) | 1.41817 | − | 25.1040i | 0.0463050 | − | 0.819676i | ||||
\(939\) | −17.2778 | + | 9.10329i | −0.563839 | + | 0.297075i | ||||
\(940\) | 35.9998 | + | 4.08041i | 1.17419 | + | 0.133088i | ||||
\(941\) | − | 14.3553i | − | 0.467969i | −0.972240 | − | 0.233985i | \(-0.924823\pi\) | ||
0.972240 | − | 0.233985i | \(-0.0751765\pi\) | |||||||
\(942\) | 7.67172 | + | 16.7948i | 0.249958 | + | 0.547205i | ||||
\(943\) | 28.3934 | − | 19.7949i | 0.924617 | − | 0.644610i | ||||
\(944\) | 37.3657 | + | 8.58068i | 1.21615 | + | 0.279277i | ||||
\(945\) | 22.1155 | + | 2.57788i | 0.719417 | + | 0.0838585i | ||||
\(946\) | −3.08670 | + | 54.6398i | −0.100357 | + | 1.77649i | ||||
\(947\) | −10.2010 | −0.331490 | −0.165745 | − | 0.986169i | \(-0.553003\pi\) | ||||
−0.165745 | + | 0.986169i | \(0.553003\pi\) | |||||||
\(948\) | 43.1278 | − | 16.8297i | 1.40073 | − | 0.546604i | ||||
\(949\) | − | 46.2037i | − | 1.49983i | ||||||
\(950\) | −1.19699 | − | 0.0676203i | −0.0388356 | − | 0.00219389i | ||||
\(951\) | 24.1056 | + | 45.7518i | 0.781679 | + | 1.48360i | ||||
\(952\) | −3.92208 | + | 22.9453i | −0.127115 | + | 0.743662i | ||||
\(953\) | 10.7012 | 0.346645 | 0.173323 | − | 0.984865i | \(-0.444550\pi\) | ||||
0.173323 | + | 0.984865i | \(0.444550\pi\) | |||||||
\(954\) | 32.3221 | + | 24.9505i | 1.04647 | + | 0.807803i | ||||
\(955\) | 49.0355i | 1.58675i | ||||||||
\(956\) | −0.823104 | + | 7.26191i | −0.0266211 | + | 0.234867i | ||||
\(957\) | 31.4529 | − | 16.5718i | 1.01673 | − | 0.535692i | ||||
\(958\) | −12.7760 | − | 0.721740i | −0.412774 | − | 0.0233184i | ||||
\(959\) | 14.4435i | 0.466406i | ||||||||
\(960\) | −38.8911 | + | 5.73181i | −1.25521 | + | 0.184993i | ||||
\(961\) | −30.9994 | −0.999982 | ||||||||
\(962\) | −3.86158 | + | 68.3565i | −0.124502 | + | 2.20390i | ||||
\(963\) | 16.1852 | + | 11.0957i | 0.521559 | + | 0.357553i | ||||
\(964\) | −3.27687 | + | 28.9105i | −0.105541 | + | 0.931145i | ||||
\(965\) | − | 17.0414i | − | 0.548583i | ||||||
\(966\) | −15.2771 | − | 9.02287i | −0.491533 | − | 0.290306i | ||||
\(967\) | 6.66228 | 0.214244 | 0.107122 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107122 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(968\) | 46.3131 | + | 7.91637i | 1.48856 | + | 0.254442i | ||||
\(969\) | −1.22330 | − | 2.32179i | −0.0392982 | − | 0.0745868i | ||||
\(970\) | 40.6450 | + | 2.29611i | 1.30503 | + | 0.0737236i | ||||
\(971\) | − | 46.2279i | − | 1.48352i | −0.670663 | − | 0.741762i | \(-0.733990\pi\) | ||
0.670663 | − | 0.741762i | \(-0.266010\pi\) | |||||||
\(972\) | −23.0036 | + | 21.0437i | −0.737839 | + | 0.674976i | ||||
\(973\) | −29.6563 | −0.950738 | ||||||||
\(974\) | 17.0465 | + | 0.962987i | 0.546205 | + | 0.0308561i | ||||
\(975\) | −20.6637 | + | 10.8872i | −0.661767 | + | 0.348671i | ||||
\(976\) | −19.1731 | − | 4.40292i | −0.613715 | − | 0.140934i | ||||
\(977\) | 3.77134 | 0.120656 | 0.0603280 | − | 0.998179i | \(-0.480785\pi\) | ||||
0.0603280 | + | 0.998179i | \(0.480785\pi\) | |||||||
\(978\) | −10.5489 | + | 4.81865i | −0.337317 | + | 0.154083i | ||||
\(979\) | − | 73.0711i | − | 2.33536i | ||||||
\(980\) | 3.01551 | − | 26.6047i | 0.0963271 | − | 0.849855i | ||||
\(981\) | −1.21292 | + | 1.76928i | −0.0387256 | + | 0.0564886i | ||||
\(982\) | 1.50442 | + | 0.0849872i | 0.0480079 | + | 0.00271205i | ||||
\(983\) | 10.4725 | 0.334021 | 0.167010 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167010 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(984\) | 33.6104 | − | 10.9751i | 1.07146 | − | 0.349873i | ||||
\(985\) | 9.46023i | 0.301428i | ||||||||
\(986\) | 30.0537 | + | 1.69779i | 0.957104 | + | 0.0540685i | ||||
\(987\) | 7.78627 | + | 14.7781i | 0.247840 | + | 0.470392i | ||||
\(988\) | 0.277021 | − | 2.44404i | 0.00881320 | − | 0.0777553i | ||||
\(989\) | −20.1988 | − | 28.9727i | −0.642283 | − | 0.921279i | ||||
\(990\) | 38.6481 | − | 50.0666i | 1.22832 | − | 1.59122i | ||||
\(991\) | 15.3490 | 0.487576 | 0.243788 | − | 0.969829i | \(-0.421610\pi\) | ||||
0.243788 | + | 0.969829i | \(0.421610\pi\) | |||||||
\(992\) | 0.128729 | + | 0.0373176i | 0.00408714 | + | 0.00118484i | ||||
\(993\) | −44.9890 | + | 23.7037i | −1.42768 | + | 0.752215i | ||||
\(994\) | 10.9515 | + | 0.618669i | 0.347360 | + | 0.0196230i | ||||
\(995\) | 15.4396 | 0.489469 | ||||||||
\(996\) | −6.48707 | + | 2.53144i | −0.205551 | + | 0.0802118i | ||||
\(997\) | 49.8784i | 1.57967i | 0.613323 | + | 0.789833i | \(0.289833\pi\) | ||||
−0.613323 | + | 0.789833i | \(0.710167\pi\) | |||||||
\(998\) | 1.25528 | − | 22.2206i | 0.0397352 | − | 0.703379i | ||||
\(999\) | −56.4931 | − | 6.58509i | −1.78736 | − | 0.208343i |
(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 | 552.2.b.c.413.1 | ✓ | 80 | |
3.2 | odd | 2 | inner | 552.2.b.c.413.80 | yes | 80 | |
4.3 | odd | 2 | 2208.2.b.c.689.55 | 80 | |||
8.3 | odd | 2 | 2208.2.b.c.689.26 | 80 | |||
8.5 | even | 2 | inner | 552.2.b.c.413.78 | yes | 80 | |
12.11 | even | 2 | 2208.2.b.c.689.28 | 80 | |||
23.22 | odd | 2 | inner | 552.2.b.c.413.2 | yes | 80 | |
24.5 | odd | 2 | inner | 552.2.b.c.413.3 | yes | 80 | |
24.11 | even | 2 | 2208.2.b.c.689.53 | 80 | |||
69.68 | even | 2 | inner | 552.2.b.c.413.79 | yes | 80 | |
92.91 | even | 2 | 2208.2.b.c.689.56 | 80 | |||
184.45 | odd | 2 | inner | 552.2.b.c.413.77 | yes | 80 | |
184.91 | even | 2 | 2208.2.b.c.689.25 | 80 | |||
276.275 | odd | 2 | 2208.2.b.c.689.27 | 80 | |||
552.275 | odd | 2 | 2208.2.b.c.689.54 | 80 | |||
552.413 | even | 2 | inner | 552.2.b.c.413.4 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.b.c.413.1 | ✓ | 80 | 1.1 | even | 1 | trivial | |
552.2.b.c.413.2 | yes | 80 | 23.22 | odd | 2 | inner | |
552.2.b.c.413.3 | yes | 80 | 24.5 | odd | 2 | inner | |
552.2.b.c.413.4 | yes | 80 | 552.413 | even | 2 | inner | |
552.2.b.c.413.77 | yes | 80 | 184.45 | odd | 2 | inner | |
552.2.b.c.413.78 | yes | 80 | 8.5 | even | 2 | inner | |
552.2.b.c.413.79 | yes | 80 | 69.68 | even | 2 | inner | |
552.2.b.c.413.80 | yes | 80 | 3.2 | odd | 2 | inner | |
2208.2.b.c.689.25 | 80 | 184.91 | even | 2 | |||
2208.2.b.c.689.26 | 80 | 8.3 | odd | 2 | |||
2208.2.b.c.689.27 | 80 | 276.275 | odd | 2 | |||
2208.2.b.c.689.28 | 80 | 12.11 | even | 2 | |||
2208.2.b.c.689.53 | 80 | 24.11 | even | 2 | |||
2208.2.b.c.689.54 | 80 | 552.275 | odd | 2 | |||
2208.2.b.c.689.55 | 80 | 4.3 | odd | 2 | |||
2208.2.b.c.689.56 | 80 | 92.91 | even | 2 |