Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} - 158 x^{7} + 8993 x^{6} + 265 x^{5} + 15176 x^{4} + 383 x^{3} + 12649 x^{2} + \cdots + 6400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.8 | ||
Root | \(-1.27611 - 2.21029i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.g.277.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.27611 | − | 2.21029i | 0.902347 | − | 1.56291i | 0.0779065 | − | 0.996961i | \(-0.475176\pi\) |
0.824440 | − | 0.565949i | \(-0.191490\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.25692 | − | 3.90910i | −1.12846 | − | 1.95455i | ||||
\(5\) | −0.324080 | + | 0.561322i | −0.144933 | + | 0.251031i | −0.929348 | − | 0.369205i | \(-0.879630\pi\) |
0.784415 | + | 0.620236i | \(0.212963\pi\) | |||||||
\(6\) | −2.55222 | −1.04194 | ||||||||
\(7\) | −2.38478 | − | 1.14579i | −0.901362 | − | 0.433066i | ||||
\(8\) | −6.41586 | −2.26835 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.827123 | + | 1.43262i | 0.261559 | + | 0.453034i | ||||
\(11\) | 1.49007 | + | 2.58088i | 0.449274 | + | 0.778166i | 0.998339 | − | 0.0576140i | \(-0.0183493\pi\) |
−0.549065 | + | 0.835780i | \(0.685016\pi\) | |||||||
\(12\) | −2.25692 | + | 3.90910i | −0.651516 | + | 1.12846i | ||||
\(13\) | −3.87158 | −1.07378 | −0.536892 | − | 0.843651i | \(-0.680402\pi\) | ||||
−0.536892 | + | 0.843651i | \(0.680402\pi\) | |||||||
\(14\) | −5.57576 | + | 3.80890i | −1.49018 | + | 1.01797i | ||||
\(15\) | 0.648159 | 0.167354 | ||||||||
\(16\) | −3.67352 | + | 6.36272i | −0.918379 | + | 1.59068i | ||||
\(17\) | −3.36610 | − | 5.83026i | −0.816400 | − | 1.41405i | −0.908318 | − | 0.418280i | \(-0.862633\pi\) |
0.0919178 | − | 0.995767i | \(-0.470700\pi\) | |||||||
\(18\) | 1.27611 | + | 2.21029i | 0.300782 | + | 0.520970i | ||||
\(19\) | 3.48863 | − | 6.04248i | 0.800346 | − | 1.38624i | −0.119043 | − | 0.992889i | \(-0.537982\pi\) |
0.919389 | − | 0.393351i | \(-0.128684\pi\) | |||||||
\(20\) | 2.92568 | 0.654203 | ||||||||
\(21\) | 0.200110 | + | 2.63817i | 0.0436676 | + | 0.575697i | ||||
\(22\) | 7.60600 | 1.62160 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 3.20793 | + | 5.55630i | 0.654816 | + | 1.13417i | ||||
\(25\) | 2.28994 | + | 3.96630i | 0.457989 | + | 0.793260i | ||||
\(26\) | −4.94057 | + | 8.55732i | −0.968925 | + | 1.67823i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.903263 | + | 11.9083i | 0.170701 | + | 2.25045i | ||||
\(29\) | 4.40182 | 0.817397 | 0.408699 | − | 0.912669i | \(-0.365983\pi\) | ||||
0.408699 | + | 0.912669i | \(0.365983\pi\) | |||||||
\(30\) | 0.827123 | − | 1.43262i | 0.151011 | − | 0.261559i | ||||
\(31\) | −1.10823 | − | 1.91951i | −0.199044 | − | 0.344754i | 0.749175 | − | 0.662372i | \(-0.230450\pi\) |
−0.948219 | + | 0.317618i | \(0.897117\pi\) | |||||||
\(32\) | 2.95976 | + | 5.12646i | 0.523217 | + | 0.906239i | ||||
\(33\) | 1.49007 | − | 2.58088i | 0.259389 | − | 0.449274i | ||||
\(34\) | −17.1821 | −2.94670 | ||||||||
\(35\) | 1.41601 | − | 0.967304i | 0.239350 | − | 0.163504i | ||||
\(36\) | 4.51383 | 0.752306 | ||||||||
\(37\) | 2.20547 | − | 3.81998i | 0.362576 | − | 0.628001i | −0.625808 | − | 0.779977i | \(-0.715231\pi\) |
0.988384 | + | 0.151977i | \(0.0485639\pi\) | |||||||
\(38\) | −8.90375 | − | 15.4217i | −1.44438 | − | 2.50174i | ||||
\(39\) | 1.93579 | + | 3.35289i | 0.309975 | + | 0.536892i | ||||
\(40\) | 2.07925 | − | 3.60137i | 0.328758 | − | 0.569426i | ||||
\(41\) | −0.194472 | −0.0303714 | −0.0151857 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151857 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(42\) | 6.08649 | + | 2.92430i | 0.939165 | + | 0.451229i | ||||
\(43\) | −1.37588 | −0.209819 | −0.104910 | − | 0.994482i | \(-0.533455\pi\) | ||||
−0.104910 | + | 0.994482i | \(0.533455\pi\) | |||||||
\(44\) | 6.72595 | − | 11.6497i | 1.01397 | − | 1.75626i | ||||
\(45\) | −0.324080 | − | 0.561322i | −0.0483109 | − | 0.0836770i | ||||
\(46\) | −1.27611 | − | 2.21029i | −0.188152 | − | 0.325889i | ||||
\(47\) | 1.24416 | − | 2.15495i | 0.181479 | − | 0.314332i | −0.760905 | − | 0.648863i | \(-0.775245\pi\) |
0.942385 | + | 0.334532i | \(0.108578\pi\) | |||||||
\(48\) | 7.34703 | 1.06045 | ||||||||
\(49\) | 4.37435 | + | 5.46489i | 0.624907 | + | 0.780699i | ||||
\(50\) | 11.6889 | 1.65306 | ||||||||
\(51\) | −3.36610 | + | 5.83026i | −0.471349 | + | 0.816400i | ||||
\(52\) | 8.73784 | + | 15.1344i | 1.21172 | + | 2.09876i | ||||
\(53\) | −4.73464 | − | 8.20065i | −0.650353 | − | 1.12645i | −0.983037 | − | 0.183407i | \(-0.941287\pi\) |
0.332684 | − | 0.943039i | \(-0.392046\pi\) | |||||||
\(54\) | 1.27611 | − | 2.21029i | 0.173657 | − | 0.300782i | ||||
\(55\) | −1.93161 | −0.260458 | ||||||||
\(56\) | 15.3004 | + | 7.35120i | 2.04460 | + | 0.982346i | ||||
\(57\) | −6.97725 | −0.924160 | ||||||||
\(58\) | 5.61721 | − | 9.72929i | 0.737575 | − | 1.27752i | ||||
\(59\) | −3.40017 | − | 5.88927i | −0.442664 | − | 0.766717i | 0.555222 | − | 0.831702i | \(-0.312633\pi\) |
−0.997886 | + | 0.0649851i | \(0.979300\pi\) | |||||||
\(60\) | −1.46284 | − | 2.53372i | −0.188852 | − | 0.327101i | ||||
\(61\) | −4.36166 | + | 7.55461i | −0.558453 | + | 0.967269i | 0.439173 | + | 0.898403i | \(0.355272\pi\) |
−0.997626 | + | 0.0688665i | \(0.978062\pi\) | |||||||
\(62\) | −5.65689 | −0.718426 | ||||||||
\(63\) | 2.18467 | − | 1.49239i | 0.275243 | − | 0.188023i | ||||
\(64\) | 0.413880 | 0.0517349 | ||||||||
\(65\) | 1.25470 | − | 2.17321i | 0.155627 | − | 0.269553i | ||||
\(66\) | −3.80300 | − | 6.58699i | −0.468117 | − | 0.810802i | ||||
\(67\) | 0.446927 | + | 0.774100i | 0.0546008 | + | 0.0945714i | 0.892034 | − | 0.451968i | \(-0.149278\pi\) |
−0.837433 | + | 0.546540i | \(0.815945\pi\) | |||||||
\(68\) | −15.1940 | + | 26.3168i | −1.84255 | + | 3.19139i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −0.331031 | − | 4.36419i | −0.0395658 | − | 0.521620i | ||||
\(71\) | 15.2489 | 1.80971 | 0.904856 | − | 0.425718i | \(-0.139979\pi\) | ||||
0.904856 | + | 0.425718i | \(0.139979\pi\) | |||||||
\(72\) | 3.20793 | − | 5.55630i | 0.378058 | − | 0.654816i | ||||
\(73\) | −0.471714 | − | 0.817032i | −0.0552099 | − | 0.0956264i | 0.837100 | − | 0.547051i | \(-0.184249\pi\) |
−0.892309 | + | 0.451424i | \(0.850916\pi\) | |||||||
\(74\) | −5.62884 | − | 9.74943i | −0.654339 | − | 1.13335i | ||||
\(75\) | 2.28994 | − | 3.96630i | 0.264420 | − | 0.457989i | ||||
\(76\) | −31.4942 | −3.61263 | ||||||||
\(77\) | −0.596357 | − | 7.86215i | −0.0679612 | − | 0.895975i | ||||
\(78\) | 9.88114 | 1.11882 | ||||||||
\(79\) | −7.07474 | + | 12.2538i | −0.795971 | + | 1.37866i | 0.126250 | + | 0.991998i | \(0.459706\pi\) |
−0.922221 | + | 0.386663i | \(0.873628\pi\) | |||||||
\(80\) | −2.38102 | − | 4.12405i | −0.266206 | − | 0.461083i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.248168 | + | 0.429839i | −0.0274055 | + | 0.0474678i | ||||
\(83\) | 14.6280 | 1.60563 | 0.802815 | − | 0.596228i | \(-0.203335\pi\) | ||||
0.802815 | + | 0.596228i | \(0.203335\pi\) | |||||||
\(84\) | 9.86124 | − | 6.73639i | 1.07595 | − | 0.735000i | ||||
\(85\) | 4.36354 | 0.473293 | ||||||||
\(86\) | −1.75577 | + | 3.04108i | −0.189330 | + | 0.327928i | ||||
\(87\) | −2.20091 | − | 3.81209i | −0.235962 | − | 0.408699i | ||||
\(88\) | −9.56011 | − | 16.5586i | −1.01911 | − | 1.76515i | ||||
\(89\) | 7.87304 | − | 13.6365i | 0.834541 | − | 1.44547i | −0.0598628 | − | 0.998207i | \(-0.519066\pi\) |
0.894404 | − | 0.447261i | \(-0.147600\pi\) | |||||||
\(90\) | −1.65425 | −0.174373 | ||||||||
\(91\) | 9.23287 | + | 4.43601i | 0.967868 | + | 0.465020i | ||||
\(92\) | −4.51383 | −0.470600 | ||||||||
\(93\) | −1.10823 | + | 1.91951i | −0.114918 | + | 0.199044i | ||||
\(94\) | −3.17537 | − | 5.49991i | −0.327515 | − | 0.567272i | ||||
\(95\) | 2.26119 | + | 3.91649i | 0.231993 | + | 0.401823i | ||||
\(96\) | 2.95976 | − | 5.12646i | 0.302080 | − | 0.523217i | ||||
\(97\) | 3.23421 | 0.328384 | 0.164192 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164192 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(98\) | 17.6611 | − | 2.69476i | 1.78405 | − | 0.272212i | ||||
\(99\) | −2.98015 | −0.299516 | ||||||||
\(100\) | 10.3364 | − | 17.9032i | 1.03364 | − | 1.79032i | ||||
\(101\) | −1.50331 | − | 2.60382i | −0.149585 | − | 0.259089i | 0.781489 | − | 0.623919i | \(-0.214461\pi\) |
−0.931074 | + | 0.364830i | \(0.881127\pi\) | |||||||
\(102\) | 8.59104 | + | 14.8801i | 0.850640 | + | 1.47335i | ||||
\(103\) | −6.97973 | + | 12.0892i | −0.687733 | + | 1.19119i | 0.284837 | + | 0.958576i | \(0.408061\pi\) |
−0.972570 | + | 0.232612i | \(0.925273\pi\) | |||||||
\(104\) | 24.8395 | 2.43572 | ||||||||
\(105\) | −1.54572 | − | 0.742652i | −0.150847 | − | 0.0724754i | ||||
\(106\) | −24.1677 | −2.34738 | ||||||||
\(107\) | 0.614369 | − | 1.06412i | 0.0593933 | − | 0.102872i | −0.834800 | − | 0.550553i | \(-0.814417\pi\) |
0.894193 | + | 0.447681i | \(0.147750\pi\) | |||||||
\(108\) | −2.25692 | − | 3.90910i | −0.217172 | − | 0.376153i | ||||
\(109\) | −8.08553 | − | 14.0046i | −0.774454 | − | 1.34139i | −0.935101 | − | 0.354381i | \(-0.884691\pi\) |
0.160647 | − | 0.987012i | \(-0.448642\pi\) | |||||||
\(110\) | −2.46495 | + | 4.26942i | −0.235024 | + | 0.407073i | ||||
\(111\) | −4.41093 | −0.418667 | ||||||||
\(112\) | 16.0508 | − | 10.9646i | 1.51666 | − | 1.03606i | ||||
\(113\) | −4.70467 | −0.442578 | −0.221289 | − | 0.975208i | \(-0.571026\pi\) | ||||
−0.221289 | + | 0.975208i | \(0.571026\pi\) | |||||||
\(114\) | −8.90375 | + | 15.4217i | −0.833912 | + | 1.44438i | ||||
\(115\) | 0.324080 | + | 0.561322i | 0.0302206 | + | 0.0523436i | ||||
\(116\) | −9.93454 | − | 17.2071i | −0.922399 | − | 1.59764i | ||||
\(117\) | 1.93579 | − | 3.35289i | 0.178964 | − | 0.309975i | ||||
\(118\) | −17.3560 | −1.59775 | ||||||||
\(119\) | 1.34718 | + | 17.7607i | 0.123496 | + | 1.62812i | ||||
\(120\) | −4.15850 | −0.379617 | ||||||||
\(121\) | 1.05936 | − | 1.83486i | 0.0963053 | − | 0.166806i | ||||
\(122\) | 11.1319 | + | 19.2810i | 1.00784 | + | 1.74562i | ||||
\(123\) | 0.0972360 | + | 0.168418i | 0.00876747 | + | 0.0151857i | ||||
\(124\) | −5.00236 | + | 8.66435i | −0.449226 | + | 0.778081i | ||||
\(125\) | −6.20929 | −0.555376 | ||||||||
\(126\) | −0.510725 | − | 6.73320i | −0.0454990 | − | 0.599841i | ||||
\(127\) | 15.9640 | 1.41657 | 0.708287 | − | 0.705924i | \(-0.249468\pi\) | ||||
0.708287 | + | 0.705924i | \(0.249468\pi\) | |||||||
\(128\) | −5.39137 | + | 9.33813i | −0.476534 | + | 0.825382i | ||||
\(129\) | 0.687938 | + | 1.19154i | 0.0605696 | + | 0.104910i | ||||
\(130\) | −3.20228 | − | 5.54650i | −0.280858 | − | 0.486461i | ||||
\(131\) | −7.79630 | + | 13.5036i | −0.681166 | + | 1.17981i | 0.293459 | + | 0.955972i | \(0.405194\pi\) |
−0.974625 | + | 0.223843i | \(0.928140\pi\) | |||||||
\(132\) | −13.4519 | −1.17084 | ||||||||
\(133\) | −15.2430 | + | 10.4128i | −1.32174 | + | 0.902901i | ||||
\(134\) | 2.28131 | 0.197075 | ||||||||
\(135\) | −0.324080 | + | 0.561322i | −0.0278923 | + | 0.0483109i | ||||
\(136\) | 21.5965 | + | 37.4062i | 1.85188 | + | 3.20755i | ||||
\(137\) | −5.36277 | − | 9.28859i | −0.458173 | − | 0.793578i | 0.540692 | − | 0.841221i | \(-0.318162\pi\) |
−0.998864 | + | 0.0476426i | \(0.984829\pi\) | |||||||
\(138\) | −1.27611 | + | 2.21029i | −0.108630 | + | 0.188152i | ||||
\(139\) | 21.4287 | 1.81756 | 0.908781 | − | 0.417273i | \(-0.137014\pi\) | ||||
0.908781 | + | 0.417273i | \(0.137014\pi\) | |||||||
\(140\) | −6.97711 | − | 3.35221i | −0.589673 | − | 0.283313i | ||||
\(141\) | −2.48832 | −0.209554 | ||||||||
\(142\) | 19.4593 | − | 33.7045i | 1.63299 | − | 2.82842i | ||||
\(143\) | −5.76895 | − | 9.99211i | −0.482424 | − | 0.835582i | ||||
\(144\) | −3.67352 | − | 6.36272i | −0.306126 | − | 0.530226i | ||||
\(145\) | −1.42654 | + | 2.47084i | −0.118468 | + | 0.205192i | ||||
\(146\) | −2.40784 | −0.199274 | ||||||||
\(147\) | 2.54556 | − | 6.52074i | 0.209955 | − | 0.537822i | ||||
\(148\) | −19.9102 | −1.63661 | ||||||||
\(149\) | 5.17626 | − | 8.96554i | 0.424055 | − | 0.734486i | −0.572276 | − | 0.820061i | \(-0.693939\pi\) |
0.996332 | + | 0.0855753i | \(0.0272728\pi\) | |||||||
\(150\) | −5.84445 | − | 10.1229i | −0.477197 | − | 0.826530i | ||||
\(151\) | 4.40288 | + | 7.62602i | 0.358302 | + | 0.620597i | 0.987677 | − | 0.156505i | \(-0.0500226\pi\) |
−0.629376 | + | 0.777101i | \(0.716689\pi\) | |||||||
\(152\) | −22.3825 | + | 38.7677i | −1.81546 | + | 3.14448i | ||||
\(153\) | 6.73221 | 0.544267 | ||||||||
\(154\) | −18.1386 | − | 8.71485i | −1.46165 | − | 0.702262i | ||||
\(155\) | 1.43662 | 0.115392 | ||||||||
\(156\) | 8.73784 | − | 15.1344i | 0.699587 | − | 1.21172i | ||||
\(157\) | 4.66548 | + | 8.08085i | 0.372346 | + | 0.644922i | 0.989926 | − | 0.141586i | \(-0.0452201\pi\) |
−0.617580 | + | 0.786508i | \(0.711887\pi\) | |||||||
\(158\) | 18.0563 | + | 31.2744i | 1.43648 | + | 2.48806i | ||||
\(159\) | −4.73464 | + | 8.20065i | −0.375482 | + | 0.650353i | ||||
\(160\) | −3.83679 | −0.303325 | ||||||||
\(161\) | −2.18467 | + | 1.49239i | −0.172176 | + | 0.117617i | ||||
\(162\) | −2.55222 | −0.200521 | ||||||||
\(163\) | −0.231561 | + | 0.401075i | −0.0181373 | + | 0.0314146i | −0.874952 | − | 0.484210i | \(-0.839107\pi\) |
0.856814 | + | 0.515625i | \(0.172440\pi\) | |||||||
\(164\) | 0.438907 | + | 0.760209i | 0.0342729 | + | 0.0593624i | ||||
\(165\) | 0.965805 | + | 1.67282i | 0.0751878 | + | 0.130229i | ||||
\(166\) | 18.6669 | − | 32.3321i | 1.44884 | − | 2.50946i | ||||
\(167\) | 2.40385 | 0.186015 | 0.0930076 | − | 0.995665i | \(-0.470352\pi\) | ||||
0.0930076 | + | 0.995665i | \(0.470352\pi\) | |||||||
\(168\) | −1.28388 | − | 16.9262i | −0.0990533 | − | 1.30588i | ||||
\(169\) | 1.98916 | 0.153012 | ||||||||
\(170\) | 5.56836 | − | 9.64469i | 0.427074 | − | 0.739714i | ||||
\(171\) | 3.48863 | + | 6.04248i | 0.266782 | + | 0.462080i | ||||
\(172\) | 3.10524 | + | 5.37843i | 0.236772 | + | 0.410101i | ||||
\(173\) | −2.57407 | + | 4.45842i | −0.195703 | + | 0.338967i | −0.947131 | − | 0.320848i | \(-0.896032\pi\) |
0.751428 | + | 0.659815i | \(0.229366\pi\) | |||||||
\(174\) | −11.2344 | −0.851679 | ||||||||
\(175\) | −0.916482 | − | 12.0825i | −0.0692795 | − | 0.913354i | ||||
\(176\) | −21.8952 | −1.65042 | ||||||||
\(177\) | −3.40017 | + | 5.88927i | −0.255572 | + | 0.442664i | ||||
\(178\) | −20.0937 | − | 34.8034i | −1.50609 | − | 2.60862i | ||||
\(179\) | 3.88943 | + | 6.73668i | 0.290709 | + | 0.503523i | 0.973978 | − | 0.226644i | \(-0.0727754\pi\) |
−0.683268 | + | 0.730167i | \(0.739442\pi\) | |||||||
\(180\) | −1.46284 | + | 2.53372i | −0.109034 | + | 0.188852i | ||||
\(181\) | −7.61327 | −0.565890 | −0.282945 | − | 0.959136i | \(-0.591311\pi\) | ||||
−0.282945 | + | 0.959136i | \(0.591311\pi\) | |||||||
\(182\) | 21.5870 | − | 14.7465i | 1.60014 | − | 1.09308i | ||||
\(183\) | 8.72332 | 0.644846 | ||||||||
\(184\) | −3.20793 | + | 5.55630i | −0.236492 | + | 0.409616i | ||||
\(185\) | 1.42949 | + | 2.47595i | 0.105098 | + | 0.182036i | ||||
\(186\) | 2.82845 | + | 4.89901i | 0.207392 | + | 0.359213i | ||||
\(187\) | 10.0315 | − | 17.3751i | 0.733575 | − | 1.27059i | ||||
\(188\) | −11.2319 | −0.819168 | ||||||||
\(189\) | −2.38478 | − | 1.14579i | −0.173467 | − | 0.0833437i | ||||
\(190\) | 11.5421 | 0.837351 | ||||||||
\(191\) | 0.369439 | − | 0.639887i | 0.0267317 | − | 0.0463006i | −0.852350 | − | 0.522972i | \(-0.824823\pi\) |
0.879082 | + | 0.476671i | \(0.158157\pi\) | |||||||
\(192\) | −0.206940 | − | 0.358430i | −0.0149346 | − | 0.0258675i | ||||
\(193\) | 7.98512 | + | 13.8306i | 0.574781 | + | 0.995551i | 0.996065 | + | 0.0886218i | \(0.0282463\pi\) |
−0.421284 | + | 0.906929i | \(0.638420\pi\) | |||||||
\(194\) | 4.12720 | − | 7.14853i | 0.296316 | − | 0.513234i | ||||
\(195\) | −2.50940 | −0.179702 | ||||||||
\(196\) | 11.4903 | − | 29.4336i | 0.820732 | − | 2.10240i | ||||
\(197\) | −9.50195 | −0.676986 | −0.338493 | − | 0.940969i | \(-0.609917\pi\) | ||||
−0.338493 | + | 0.940969i | \(0.609917\pi\) | |||||||
\(198\) | −3.80300 | + | 6.58699i | −0.270267 | + | 0.468117i | ||||
\(199\) | 8.32964 | + | 14.4274i | 0.590473 | + | 1.02273i | 0.994169 | + | 0.107836i | \(0.0343921\pi\) |
−0.403696 | + | 0.914893i | \(0.632275\pi\) | |||||||
\(200\) | −14.6920 | − | 25.4472i | −1.03888 | − | 1.79939i | ||||
\(201\) | 0.446927 | − | 0.774100i | 0.0315238 | − | 0.0546008i | ||||
\(202\) | −7.67358 | −0.539911 | ||||||||
\(203\) | −10.4974 | − | 5.04354i | −0.736771 | − | 0.353987i | ||||
\(204\) | 30.3881 | 2.12759 | ||||||||
\(205\) | 0.0630244 | − | 0.109161i | 0.00440181 | − | 0.00762417i | ||||
\(206\) | 17.8138 | + | 30.8544i | 1.24115 | + | 2.14973i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | 14.2223 | − | 24.6338i | 0.986141 | − | 1.70805i | ||||
\(209\) | 20.7933 | 1.43830 | ||||||||
\(210\) | −3.61398 | + | 2.46877i | −0.249388 | + | 0.170362i | ||||
\(211\) | 19.6449 | 1.35241 | 0.676207 | − | 0.736712i | \(-0.263623\pi\) | ||||
0.676207 | + | 0.736712i | \(0.263623\pi\) | |||||||
\(212\) | −21.3714 | + | 37.0164i | −1.46779 | + | 2.54229i | ||||
\(213\) | −7.62445 | − | 13.2059i | −0.522419 | − | 0.904856i | ||||
\(214\) | −1.56800 | − | 2.71586i | −0.107187 | − | 0.185653i | ||||
\(215\) | 0.445893 | − | 0.772310i | 0.0304097 | − | 0.0526711i | ||||
\(216\) | −6.41586 | −0.436544 | ||||||||
\(217\) | 0.443535 | + | 5.84740i | 0.0301092 | + | 0.396947i | ||||
\(218\) | −41.2721 | −2.79530 | ||||||||
\(219\) | −0.471714 | + | 0.817032i | −0.0318755 | + | 0.0552099i | ||||
\(220\) | 4.35948 | + | 7.55085i | 0.293916 | + | 0.509078i | ||||
\(221\) | 13.0322 | + | 22.5724i | 0.876638 | + | 1.51838i | ||||
\(222\) | −5.62884 | + | 9.74943i | −0.377783 | + | 0.654339i | ||||
\(223\) | −17.5246 | −1.17353 | −0.586766 | − | 0.809757i | \(-0.699599\pi\) | ||||
−0.586766 | + | 0.809757i | \(0.699599\pi\) | |||||||
\(224\) | −1.18456 | − | 15.6167i | −0.0791465 | − | 1.04344i | ||||
\(225\) | −4.57989 | −0.305326 | ||||||||
\(226\) | −6.00368 | + | 10.3987i | −0.399359 | + | 0.691710i | ||||
\(227\) | 5.34607 | + | 9.25966i | 0.354831 | + | 0.614585i | 0.987089 | − | 0.160172i | \(-0.0512050\pi\) |
−0.632258 | + | 0.774758i | \(0.717872\pi\) | |||||||
\(228\) | 15.7471 | + | 27.2747i | 1.04288 | + | 1.80631i | ||||
\(229\) | −4.65000 | + | 8.05404i | −0.307281 | + | 0.532226i | −0.977767 | − | 0.209697i | \(-0.932752\pi\) |
0.670486 | + | 0.741922i | \(0.266086\pi\) | |||||||
\(230\) | 1.65425 | 0.109078 | ||||||||
\(231\) | −6.51064 | + | 4.44753i | −0.428369 | + | 0.292626i | ||||
\(232\) | −28.2415 | −1.85414 | ||||||||
\(233\) | 11.8630 | − | 20.5474i | 0.777172 | − | 1.34610i | −0.156393 | − | 0.987695i | \(-0.549987\pi\) |
0.933565 | − | 0.358407i | \(-0.116680\pi\) | |||||||
\(234\) | −4.94057 | − | 8.55732i | −0.322975 | − | 0.559409i | ||||
\(235\) | 0.806414 | + | 1.39675i | 0.0526047 | + | 0.0911139i | ||||
\(236\) | −15.3478 | + | 26.5832i | −0.999057 | + | 1.73042i | ||||
\(237\) | 14.1495 | 0.919108 | ||||||||
\(238\) | 40.9755 | + | 19.6870i | 2.65605 | + | 1.27612i | ||||
\(239\) | 26.6326 | 1.72272 | 0.861360 | − | 0.507994i | \(-0.169613\pi\) | ||||
0.861360 | + | 0.507994i | \(0.169613\pi\) | |||||||
\(240\) | −2.38102 | + | 4.12405i | −0.153694 | + | 0.266206i | ||||
\(241\) | −5.84295 | − | 10.1203i | −0.376377 | − | 0.651905i | 0.614155 | − | 0.789186i | \(-0.289497\pi\) |
−0.990532 | + | 0.137281i | \(0.956164\pi\) | |||||||
\(242\) | −2.70372 | − | 4.68297i | −0.173801 | − | 0.301033i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 39.3756 | 2.52076 | ||||||||
\(245\) | −4.48520 | + | 0.684358i | −0.286549 | + | 0.0437221i | ||||
\(246\) | 0.496336 | 0.0316452 | ||||||||
\(247\) | −13.5065 | + | 23.3940i | −0.859399 | + | 1.48852i | ||||
\(248\) | 7.11025 | + | 12.3153i | 0.451501 | + | 0.782023i | ||||
\(249\) | −7.31399 | − | 12.6682i | −0.463506 | − | 0.802815i | ||||
\(250\) | −7.92375 | + | 13.7243i | −0.501142 | + | 0.868003i | ||||
\(251\) | −12.0271 | −0.759142 | −0.379571 | − | 0.925163i | \(-0.623928\pi\) | ||||
−0.379571 | + | 0.925163i | \(0.623928\pi\) | |||||||
\(252\) | −10.7645 | − | 5.17189i | −0.678100 | − | 0.325798i | ||||
\(253\) | 2.98015 | 0.187360 | ||||||||
\(254\) | 20.3718 | − | 35.2850i | 1.27824 | − | 2.21398i | ||||
\(255\) | −2.18177 | − | 3.77894i | −0.136628 | − | 0.236646i | ||||
\(256\) | 14.1738 | + | 24.5498i | 0.885866 | + | 1.53436i | ||||
\(257\) | 5.09201 | − | 8.81961i | 0.317631 | − | 0.550152i | −0.662363 | − | 0.749183i | \(-0.730446\pi\) |
0.979993 | + | 0.199031i | \(0.0637795\pi\) | |||||||
\(258\) | 3.51154 | 0.218619 | ||||||||
\(259\) | −9.63643 | + | 6.58281i | −0.598778 | + | 0.409036i | ||||
\(260\) | −11.3270 | −0.702472 | ||||||||
\(261\) | −2.20091 | + | 3.81209i | −0.136233 | + | 0.235962i | ||||
\(262\) | 19.8979 | + | 34.4642i | 1.22930 | + | 2.12920i | ||||
\(263\) | −10.4282 | − | 18.0622i | −0.643033 | − | 1.11377i | −0.984752 | − | 0.173964i | \(-0.944342\pi\) |
0.341719 | − | 0.939802i | \(-0.388991\pi\) | |||||||
\(264\) | −9.56011 | + | 16.5586i | −0.588384 | + | 1.01911i | ||||
\(265\) | 6.13761 | 0.377030 | ||||||||
\(266\) | 3.56346 | + | 46.9793i | 0.218490 | + | 2.88048i | ||||
\(267\) | −15.7461 | −0.963645 | ||||||||
\(268\) | 2.01735 | − | 3.49416i | 0.123230 | − | 0.213440i | ||||
\(269\) | 10.2355 | + | 17.7284i | 0.624071 | + | 1.08092i | 0.988720 | + | 0.149777i | \(0.0478557\pi\) |
−0.364649 | + | 0.931145i | \(0.618811\pi\) | |||||||
\(270\) | 0.827123 | + | 1.43262i | 0.0503371 | + | 0.0871864i | ||||
\(271\) | 9.42784 | − | 16.3295i | 0.572700 | − | 0.991946i | −0.423587 | − | 0.905855i | \(-0.639229\pi\) |
0.996287 | − | 0.0860907i | \(-0.0274375\pi\) | |||||||
\(272\) | 49.4617 | 2.99906 | ||||||||
\(273\) | −0.774742 | − | 10.2139i | −0.0468895 | − | 0.618174i | ||||
\(274\) | −27.3740 | −1.65372 | ||||||||
\(275\) | −6.82438 | + | 11.8202i | −0.411525 | + | 0.712783i | ||||
\(276\) | 2.25692 | + | 3.90910i | 0.135850 | + | 0.235300i | ||||
\(277\) | 2.48103 | + | 4.29727i | 0.149070 | + | 0.258198i | 0.930884 | − | 0.365314i | \(-0.119039\pi\) |
−0.781814 | + | 0.623512i | \(0.785705\pi\) | |||||||
\(278\) | 27.3454 | − | 47.3637i | 1.64007 | − | 2.84069i | ||||
\(279\) | 2.21646 | 0.132696 | ||||||||
\(280\) | −9.08495 | + | 6.20609i | −0.542929 | + | 0.370885i | ||||
\(281\) | 9.56605 | 0.570663 | 0.285331 | − | 0.958429i | \(-0.407896\pi\) | ||||
0.285331 | + | 0.958429i | \(0.407896\pi\) | |||||||
\(282\) | −3.17537 | + | 5.49991i | −0.189091 | + | 0.327515i | ||||
\(283\) | −3.70917 | − | 6.42447i | −0.220487 | − | 0.381895i | 0.734469 | − | 0.678642i | \(-0.237431\pi\) |
−0.954956 | + | 0.296748i | \(0.904098\pi\) | |||||||
\(284\) | −34.4155 | − | 59.6094i | −2.04218 | − | 3.53717i | ||||
\(285\) | 2.26119 | − | 3.91649i | 0.133941 | − | 0.231993i | ||||
\(286\) | −29.4473 | −1.74125 | ||||||||
\(287\) | 0.463773 | + | 0.222823i | 0.0273756 | + | 0.0131528i | ||||
\(288\) | −5.91953 | −0.348811 | ||||||||
\(289\) | −14.1613 | + | 24.5281i | −0.833019 | + | 1.44283i | ||||
\(290\) | 3.64084 | + | 6.30613i | 0.213798 | + | 0.370309i | ||||
\(291\) | −1.61710 | − | 2.80090i | −0.0947963 | − | 0.164192i | ||||
\(292\) | −2.12924 | + | 3.68795i | −0.124604 | + | 0.215821i | ||||
\(293\) | 9.37108 | 0.547464 | 0.273732 | − | 0.961806i | \(-0.411742\pi\) | ||||
0.273732 | + | 0.961806i | \(0.411742\pi\) | |||||||
\(294\) | −11.1643 | − | 13.9476i | −0.651116 | − | 0.813442i | ||||
\(295\) | 4.40770 | 0.256626 | ||||||||
\(296\) | −14.1500 | + | 24.5085i | −0.822450 | + | 1.42452i | ||||
\(297\) | 1.49007 | + | 2.58088i | 0.0864629 | + | 0.149758i | ||||
\(298\) | −13.2110 | − | 22.8820i | −0.765290 | − | 1.32552i | ||||
\(299\) | −1.93579 | + | 3.35289i | −0.111950 | + | 0.193903i | ||||
\(300\) | −20.6729 | −1.19355 | ||||||||
\(301\) | 3.28116 | + | 1.57646i | 0.189123 | + | 0.0908656i | ||||
\(302\) | 22.4743 | 1.29325 | ||||||||
\(303\) | −1.50331 | + | 2.60382i | −0.0863631 | + | 0.149585i | ||||
\(304\) | 25.6310 | + | 44.3943i | 1.47004 | + | 2.54619i | ||||
\(305\) | −2.82705 | − | 4.89659i | −0.161876 | − | 0.280378i | ||||
\(306\) | 8.59104 | − | 14.8801i | 0.491117 | − | 0.850640i | ||||
\(307\) | −0.0388797 | −0.00221898 | −0.00110949 | − | 0.999999i | \(-0.500353\pi\) | ||||
−0.00110949 | + | 0.999999i | \(0.500353\pi\) | |||||||
\(308\) | −29.3879 | + | 20.0754i | −1.67453 | + | 1.14390i | ||||
\(309\) | 13.9595 | 0.794125 | ||||||||
\(310\) | 1.83328 | − | 3.17534i | 0.104124 | − | 0.180347i | ||||
\(311\) | −4.56923 | − | 7.91415i | −0.259098 | − | 0.448770i | 0.706903 | − | 0.707311i | \(-0.250092\pi\) |
−0.966000 | + | 0.258541i | \(0.916758\pi\) | |||||||
\(312\) | −12.4198 | − | 21.5117i | −0.703131 | − | 1.21786i | ||||
\(313\) | 6.43808 | − | 11.1511i | 0.363902 | − | 0.630296i | −0.624698 | − | 0.780867i | \(-0.714778\pi\) |
0.988599 | + | 0.150571i | \(0.0481111\pi\) | |||||||
\(314\) | 23.8147 | 1.34394 | ||||||||
\(315\) | 0.129703 | + | 1.70996i | 0.00730794 | + | 0.0963451i | ||||
\(316\) | 63.8684 | 3.59288 | ||||||||
\(317\) | −5.39355 | + | 9.34191i | −0.302932 | + | 0.524694i | −0.976799 | − | 0.214159i | \(-0.931299\pi\) |
0.673867 | + | 0.738853i | \(0.264632\pi\) | |||||||
\(318\) | 12.0839 | + | 20.9299i | 0.677629 | + | 1.17369i | ||||
\(319\) | 6.55904 | + | 11.3606i | 0.367235 | + | 0.636071i | ||||
\(320\) | −0.134130 | + | 0.232320i | −0.00749809 | + | 0.0129871i | ||||
\(321\) | −1.22874 | −0.0685814 | ||||||||
\(322\) | 0.510725 | + | 6.73320i | 0.0284616 | + | 0.375227i | ||||
\(323\) | −46.9723 | −2.61361 | ||||||||
\(324\) | −2.25692 | + | 3.90910i | −0.125384 | + | 0.217172i | ||||
\(325\) | −8.86571 | − | 15.3559i | −0.491781 | − | 0.851790i | ||||
\(326\) | 0.590995 | + | 1.02363i | 0.0327322 | + | 0.0566938i | ||||
\(327\) | −8.08553 | + | 14.0046i | −0.447131 | + | 0.774454i | ||||
\(328\) | 1.24771 | 0.0688930 | ||||||||
\(329\) | −5.43616 | + | 3.71354i | −0.299705 | + | 0.204734i | ||||
\(330\) | 4.92990 | 0.271382 | ||||||||
\(331\) | −11.2883 | + | 19.5519i | −0.620461 | + | 1.07467i | 0.368939 | + | 0.929454i | \(0.379721\pi\) |
−0.989400 | + | 0.145216i | \(0.953612\pi\) | |||||||
\(332\) | −33.0142 | − | 57.1822i | −1.81189 | − | 3.13828i | ||||
\(333\) | 2.20547 | + | 3.81998i | 0.120859 | + | 0.209334i | ||||
\(334\) | 3.06757 | − | 5.31319i | 0.167850 | − | 0.290725i | ||||
\(335\) | −0.579360 | −0.0316538 | ||||||||
\(336\) | −17.5210 | − | 8.41813i | −0.955852 | − | 0.459246i | ||||
\(337\) | −6.39947 | −0.348601 | −0.174301 | − | 0.984693i | \(-0.555766\pi\) | ||||
−0.174301 | + | 0.984693i | \(0.555766\pi\) | |||||||
\(338\) | 2.53839 | − | 4.39662i | 0.138070 | − | 0.239144i | ||||
\(339\) | 2.35234 | + | 4.07437i | 0.127761 | + | 0.221289i | ||||
\(340\) | −9.84815 | − | 17.0575i | −0.534091 | − | 0.925073i | ||||
\(341\) | 3.30269 | − | 5.72042i | 0.178851 | − | 0.309778i | ||||
\(342\) | 17.8075 | 0.962919 | ||||||||
\(343\) | −4.17026 | − | 18.0446i | −0.225173 | − | 0.974319i | ||||
\(344\) | 8.82743 | 0.475943 | ||||||||
\(345\) | 0.324080 | − | 0.561322i | 0.0174479 | − | 0.0302206i | ||||
\(346\) | 6.56960 | + | 11.3789i | 0.353184 | + | 0.611732i | ||||
\(347\) | −16.6599 | − | 28.8558i | −0.894351 | − | 1.54906i | −0.834606 | − | 0.550848i | \(-0.814305\pi\) |
−0.0597451 | − | 0.998214i | \(-0.519029\pi\) | |||||||
\(348\) | −9.93454 | + | 17.2071i | −0.532547 | + | 0.922399i | ||||
\(349\) | −28.5439 | −1.52792 | −0.763961 | − | 0.645262i | \(-0.776748\pi\) | ||||
−0.763961 | + | 0.645262i | \(0.776748\pi\) | |||||||
\(350\) | −27.8754 | − | 13.3930i | −1.49000 | − | 0.715884i | ||||
\(351\) | −3.87158 | −0.206650 | ||||||||
\(352\) | −8.82053 | + | 15.2776i | −0.470136 | + | 0.814299i | ||||
\(353\) | 0.0765559 | + | 0.132599i | 0.00407466 | + | 0.00705752i | 0.868056 | − | 0.496467i | \(-0.165370\pi\) |
−0.863981 | + | 0.503525i | \(0.832036\pi\) | |||||||
\(354\) | 8.67798 | + | 15.0307i | 0.461230 | + | 0.798873i | ||||
\(355\) | −4.94186 | + | 8.55955i | −0.262287 | + | 0.454294i | ||||
\(356\) | −71.0752 | −3.76698 | ||||||||
\(357\) | 14.7077 | − | 10.0471i | 0.778412 | − | 0.531747i | ||||
\(358\) | 19.8534 | 1.04928 | ||||||||
\(359\) | −10.8426 | + | 18.7799i | −0.572250 | + | 0.991166i | 0.424084 | + | 0.905623i | \(0.360596\pi\) |
−0.996334 | + | 0.0855436i | \(0.972737\pi\) | |||||||
\(360\) | 2.07925 | + | 3.60137i | 0.109586 | + | 0.189809i | ||||
\(361\) | −14.8410 | − | 25.7054i | −0.781107 | − | 1.35292i | ||||
\(362\) | −9.71537 | + | 16.8275i | −0.510629 | + | 0.884435i | ||||
\(363\) | −2.11872 | −0.111204 | ||||||||
\(364\) | −3.49706 | − | 46.1039i | −0.183296 | − | 2.41650i | ||||
\(365\) | 0.611491 | 0.0320069 | ||||||||
\(366\) | 11.1319 | − | 19.2810i | 0.581875 | − | 1.00784i | ||||
\(367\) | −1.52104 | − | 2.63451i | −0.0793974 | − | 0.137520i | 0.823593 | − | 0.567182i | \(-0.191966\pi\) |
−0.902990 | + | 0.429661i | \(0.858633\pi\) | |||||||
\(368\) | 3.67352 | + | 6.36272i | 0.191495 | + | 0.331679i | ||||
\(369\) | 0.0972360 | − | 0.168418i | 0.00506190 | − | 0.00876747i | ||||
\(370\) | 7.29676 | 0.379341 | ||||||||
\(371\) | 1.89490 | + | 24.9816i | 0.0983783 | + | 1.29698i | ||||
\(372\) | 10.0047 | 0.518721 | ||||||||
\(373\) | −13.8069 | + | 23.9142i | −0.714892 | + | 1.23823i | 0.248109 | + | 0.968732i | \(0.420191\pi\) |
−0.963001 | + | 0.269497i | \(0.913142\pi\) | |||||||
\(374\) | −25.6026 | − | 44.3450i | −1.32388 | − | 2.29302i | ||||
\(375\) | 3.10465 | + | 5.37741i | 0.160323 | + | 0.277688i | ||||
\(376\) | −7.98236 | + | 13.8259i | −0.411659 | + | 0.713014i | ||||
\(377\) | −17.0420 | −0.877708 | ||||||||
\(378\) | −5.57576 | + | 3.80890i | −0.286786 | + | 0.195909i | ||||
\(379\) | 24.0119 | 1.23341 | 0.616705 | − | 0.787194i | \(-0.288467\pi\) | ||||
0.616705 | + | 0.787194i | \(0.288467\pi\) | |||||||
\(380\) | 10.2066 | − | 17.6784i | 0.523588 | − | 0.906882i | ||||
\(381\) | −7.98199 | − | 13.8252i | −0.408930 | − | 0.708287i | ||||
\(382\) | −0.942890 | − | 1.63313i | −0.0482424 | − | 0.0835583i | ||||
\(383\) | 5.50591 | − | 9.53651i | 0.281339 | − | 0.487293i | −0.690376 | − | 0.723451i | \(-0.742555\pi\) |
0.971715 | + | 0.236158i | \(0.0758882\pi\) | |||||||
\(384\) | 10.7827 | 0.550254 | ||||||||
\(385\) | 4.60647 | + | 2.21321i | 0.234767 | + | 0.112796i | ||||
\(386\) | 40.7596 | 2.07461 | ||||||||
\(387\) | 0.687938 | − | 1.19154i | 0.0349699 | − | 0.0605696i | ||||
\(388\) | −7.29933 | − | 12.6428i | −0.370568 | − | 0.641842i | ||||
\(389\) | −17.5477 | − | 30.3935i | −0.889704 | − | 1.54101i | −0.840226 | − | 0.542237i | \(-0.817577\pi\) |
−0.0494782 | − | 0.998775i | \(-0.515756\pi\) | |||||||
\(390\) | −3.20228 | + | 5.54650i | −0.162154 | + | 0.280858i | ||||
\(391\) | −6.73221 | −0.340462 | ||||||||
\(392\) | −28.0652 | − | 35.0620i | −1.41751 | − | 1.77090i | ||||
\(393\) | 15.5926 | 0.786543 | ||||||||
\(394\) | −12.1255 | + | 21.0020i | −0.610876 | + | 1.05807i | ||||
\(395\) | −4.58556 | − | 7.94242i | −0.230725 | − | 0.399627i | ||||
\(396\) | 6.72595 | + | 11.6497i | 0.337992 | + | 0.585419i | ||||
\(397\) | −7.61416 | + | 13.1881i | −0.382144 | + | 0.661892i | −0.991368 | − | 0.131106i | \(-0.958147\pi\) |
0.609225 | + | 0.792997i | \(0.291481\pi\) | |||||||
\(398\) | 42.5182 | 2.13124 | ||||||||
\(399\) | 16.6392 | + | 7.99444i | 0.833003 | + | 0.400223i | ||||
\(400\) | −33.6486 | −1.68243 | ||||||||
\(401\) | 9.49301 | − | 16.4424i | 0.474058 | − | 0.821093i | −0.525501 | − | 0.850793i | \(-0.676122\pi\) |
0.999559 | + | 0.0297003i | \(0.00945529\pi\) | |||||||
\(402\) | −1.14066 | − | 1.97567i | −0.0568908 | − | 0.0985377i | ||||
\(403\) | 4.29060 | + | 7.43154i | 0.213730 | + | 0.370191i | ||||
\(404\) | −6.78571 | + | 11.7532i | −0.337602 | + | 0.584743i | ||||
\(405\) | 0.648159 | 0.0322073 | ||||||||
\(406\) | −24.5435 | + | 16.7661i | −1.21807 | + | 0.832087i | ||||
\(407\) | 13.1452 | 0.651585 | ||||||||
\(408\) | 21.5965 | − | 37.4062i | 1.06918 | − | 1.85188i | ||||
\(409\) | −3.72738 | − | 6.45601i | −0.184307 | − | 0.319229i | 0.759036 | − | 0.651049i | \(-0.225671\pi\) |
−0.943343 | + | 0.331820i | \(0.892337\pi\) | |||||||
\(410\) | −0.160852 | − | 0.278604i | −0.00794392 | − | 0.0137593i | ||||
\(411\) | −5.36277 | + | 9.28859i | −0.264526 | + | 0.458173i | ||||
\(412\) | 63.0106 | 3.10431 | ||||||||
\(413\) | 1.36082 | + | 17.9405i | 0.0669614 | + | 0.882793i | ||||
\(414\) | 2.55222 | 0.125435 | ||||||||
\(415\) | −4.74063 | + | 8.21102i | −0.232708 | + | 0.403063i | ||||
\(416\) | −11.4590 | − | 19.8475i | −0.561822 | − | 0.973105i | ||||
\(417\) | −10.7144 | − | 18.5578i | −0.524685 | − | 0.908781i | ||||
\(418\) | 26.5345 | − | 45.9591i | 1.29784 | − | 2.24793i | ||||
\(419\) | 3.17379 | 0.155050 | 0.0775248 | − | 0.996990i | \(-0.475298\pi\) | ||||
0.0775248 | + | 0.996990i | \(0.475298\pi\) | |||||||
\(420\) | 0.585458 | + | 7.71846i | 0.0285674 | + | 0.376622i | ||||
\(421\) | 15.1064 | 0.736239 | 0.368120 | − | 0.929778i | \(-0.380002\pi\) | ||||
0.368120 | + | 0.929778i | \(0.380002\pi\) | |||||||
\(422\) | 25.0691 | − | 43.4210i | 1.22035 | − | 2.11370i | ||||
\(423\) | 1.24416 | + | 2.15495i | 0.0604932 | + | 0.104777i | ||||
\(424\) | 30.3768 | + | 52.6142i | 1.47523 | + | 2.55517i | ||||
\(425\) | 15.4164 | − | 26.7020i | 0.747805 | − | 1.29524i | ||||
\(426\) | −38.9186 | −1.88561 | ||||||||
\(427\) | 19.0576 | − | 13.0186i | 0.922260 | − | 0.630012i | ||||
\(428\) | −5.54632 | −0.268091 | ||||||||
\(429\) | −5.76895 | + | 9.99211i | −0.278527 | + | 0.482424i | ||||
\(430\) | −1.13802 | − | 1.97111i | −0.0548801 | − | 0.0950552i | ||||
\(431\) | −12.5136 | − | 21.6742i | −0.602760 | − | 1.04401i | −0.992401 | − | 0.123044i | \(-0.960734\pi\) |
0.389641 | − | 0.920967i | \(-0.372599\pi\) | |||||||
\(432\) | −3.67352 | + | 6.36272i | −0.176742 | + | 0.306126i | ||||
\(433\) | −27.5871 | −1.32575 | −0.662876 | − | 0.748729i | \(-0.730664\pi\) | ||||
−0.662876 | + | 0.748729i | \(0.730664\pi\) | |||||||
\(434\) | 13.4904 | + | 6.48159i | 0.647562 | + | 0.311126i | ||||
\(435\) | 2.85308 | 0.136795 | ||||||||
\(436\) | −36.4968 | + | 63.2142i | −1.74788 | + | 3.02741i | ||||
\(437\) | −3.48863 | − | 6.04248i | −0.166884 | − | 0.289051i | ||||
\(438\) | 1.20392 | + | 2.08525i | 0.0575254 | + | 0.0996370i | ||||
\(439\) | 10.1933 | − | 17.6554i | 0.486501 | − | 0.842645i | −0.513378 | − | 0.858162i | \(-0.671606\pi\) |
0.999880 | + | 0.0155176i | \(0.00493960\pi\) | |||||||
\(440\) | 12.3929 | 0.590810 | ||||||||
\(441\) | −6.91991 | + | 1.05585i | −0.329520 | + | 0.0502785i | ||||
\(442\) | 66.5219 | 3.16412 | ||||||||
\(443\) | −13.9371 | + | 24.1398i | −0.662173 | + | 1.14692i | 0.317871 | + | 0.948134i | \(0.397032\pi\) |
−0.980044 | + | 0.198783i | \(0.936301\pi\) | |||||||
\(444\) | 9.95511 | + | 17.2427i | 0.472448 | + | 0.818305i | ||||
\(445\) | 5.10298 | + | 8.83863i | 0.241905 | + | 0.418991i | ||||
\(446\) | −22.3633 | + | 38.7343i | −1.05893 | + | 1.83412i | ||||
\(447\) | −10.3525 | −0.489657 | ||||||||
\(448\) | −0.987012 | − | 0.474217i | −0.0466319 | − | 0.0224047i | ||||
\(449\) | −12.5841 | −0.593882 | −0.296941 | − | 0.954896i | \(-0.595966\pi\) | ||||
−0.296941 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(450\) | −5.84445 | + | 10.1229i | −0.275510 | + | 0.477197i | ||||
\(451\) | −0.289778 | − | 0.501910i | −0.0136451 | − | 0.0236340i | ||||
\(452\) | 10.6181 | + | 18.3910i | 0.499431 | + | 0.865041i | ||||
\(453\) | 4.40288 | − | 7.62602i | 0.206866 | − | 0.358302i | ||||
\(454\) | 27.2887 | 1.28072 | ||||||||
\(455\) | −5.48222 | + | 3.74500i | −0.257010 | + | 0.175568i | ||||
\(456\) | 44.7651 | 2.09632 | ||||||||
\(457\) | 10.6464 | − | 18.4401i | 0.498019 | − | 0.862594i | −0.501979 | − | 0.864880i | \(-0.667394\pi\) |
0.999997 | + | 0.00228642i | \(0.000727790\pi\) | |||||||
\(458\) | 11.8678 | + | 20.5557i | 0.554547 | + | 0.960504i | ||||
\(459\) | −3.36610 | − | 5.83026i | −0.157116 | − | 0.272133i | ||||
\(460\) | 1.46284 | − | 2.53372i | 0.0682053 | − | 0.118135i | ||||
\(461\) | −3.83733 | −0.178722 | −0.0893612 | − | 0.995999i | \(-0.528483\pi\) | ||||
−0.0893612 | + | 0.995999i | \(0.528483\pi\) | |||||||
\(462\) | 1.52204 | + | 20.0659i | 0.0708115 | + | 0.933552i | ||||
\(463\) | −40.4632 | −1.88048 | −0.940242 | − | 0.340508i | \(-0.889401\pi\) | ||||
−0.940242 | + | 0.340508i | \(0.889401\pi\) | |||||||
\(464\) | −16.1701 | + | 28.0075i | −0.750680 | + | 1.30022i | ||||
\(465\) | −0.718309 | − | 1.24415i | −0.0333108 | − | 0.0576960i | ||||
\(466\) | −30.2771 | − | 52.4414i | −1.40256 | − | 2.42930i | ||||
\(467\) | 0.886015 | − | 1.53462i | 0.0409999 | − | 0.0710139i | −0.844797 | − | 0.535087i | \(-0.820279\pi\) |
0.885797 | + | 0.464073i | \(0.153612\pi\) | |||||||
\(468\) | −17.4757 | −0.807814 | ||||||||
\(469\) | −0.178869 | − | 2.35814i | −0.00825941 | − | 0.108889i | ||||
\(470\) | 4.11629 | 0.189870 | ||||||||
\(471\) | 4.66548 | − | 8.08085i | 0.214974 | − | 0.372346i | ||||
\(472\) | 21.8150 | + | 37.7847i | 1.00412 | + | 1.73918i | ||||
\(473\) | −2.05016 | − | 3.55098i | −0.0942663 | − | 0.163274i | ||||
\(474\) | 18.0563 | − | 31.2744i | 0.829354 | − | 1.43648i | ||||
\(475\) | 31.9551 | 1.46620 | ||||||||
\(476\) | 66.3879 | − | 45.3508i | 3.04288 | − | 2.07865i | ||||
\(477\) | 9.46929 | 0.433569 | ||||||||
\(478\) | 33.9862 | − | 58.8658i | 1.55449 | − | 2.69246i | ||||
\(479\) | 7.00989 | + | 12.1415i | 0.320290 | + | 0.554759i | 0.980548 | − | 0.196280i | \(-0.0628863\pi\) |
−0.660258 | + | 0.751039i | \(0.729553\pi\) | |||||||
\(480\) | 1.91840 | + | 3.32276i | 0.0875625 | + | 0.151663i | ||||
\(481\) | −8.53864 | + | 14.7894i | −0.389329 | + | 0.674337i | ||||
\(482\) | −29.8250 | −1.35849 | ||||||||
\(483\) | 2.38478 | + | 1.14579i | 0.108511 | + | 0.0521351i | ||||
\(484\) | −9.56353 | −0.434706 | ||||||||
\(485\) | −1.04814 | + | 1.81543i | −0.0475936 | + | 0.0824345i | ||||
\(486\) | 1.27611 | + | 2.21029i | 0.0578856 | + | 0.100261i | ||||
\(487\) | 13.3895 | + | 23.1913i | 0.606736 | + | 1.05090i | 0.991775 | + | 0.127997i | \(0.0408549\pi\) |
−0.385038 | + | 0.922901i | \(0.625812\pi\) | |||||||
\(488\) | 27.9838 | − | 48.4693i | 1.26677 | − | 2.19410i | ||||
\(489\) | 0.463122 | 0.0209431 | ||||||||
\(490\) | −4.21099 | + | 10.7869i | −0.190233 | + | 0.487303i | ||||
\(491\) | 36.1444 | 1.63117 | 0.815587 | − | 0.578635i | \(-0.196414\pi\) | ||||
0.815587 | + | 0.578635i | \(0.196414\pi\) | |||||||
\(492\) | 0.438907 | − | 0.760209i | 0.0197875 | − | 0.0342729i | ||||
\(493\) | −14.8170 | − | 25.6638i | −0.667323 | − | 1.15584i | ||||
\(494\) | 34.4716 | + | 59.7066i | 1.55095 | + | 2.68633i | ||||
\(495\) | 0.965805 | − | 1.67282i | 0.0434097 | − | 0.0751878i | ||||
\(496\) | 16.2844 | 0.731191 | ||||||||
\(497\) | −36.3653 | − | 17.4720i | −1.63121 | − | 0.783725i | ||||
\(498\) | −37.3339 | −1.67297 | ||||||||
\(499\) | −19.0160 | + | 32.9367i | −0.851274 | + | 1.47445i | 0.0287847 | + | 0.999586i | \(0.490836\pi\) |
−0.880059 | + | 0.474865i | \(0.842497\pi\) | |||||||
\(500\) | 14.0139 | + | 24.2727i | 0.626719 | + | 1.08551i | ||||
\(501\) | −1.20192 | − | 2.08179i | −0.0536980 | − | 0.0930076i | ||||
\(502\) | −15.3479 | + | 26.5833i | −0.685009 | + | 1.18647i | ||||
\(503\) | −13.8143 | −0.615947 | −0.307974 | − | 0.951395i | \(-0.599651\pi\) | ||||
−0.307974 | + | 0.951395i | \(0.599651\pi\) | |||||||
\(504\) | −14.0165 | + | 9.57495i | −0.624346 | + | 0.426502i | ||||
\(505\) | 1.94877 | 0.0867193 | ||||||||
\(506\) | 3.80300 | − | 6.58699i | 0.169064 | − | 0.292827i | ||||
\(507\) | −0.994580 | − | 1.72266i | −0.0441708 | − | 0.0765061i | ||||
\(508\) | −36.0294 | − | 62.4047i | −1.59855 | − | 2.76876i | ||||
\(509\) | −4.19047 | + | 7.25811i | −0.185739 | + | 0.321710i | −0.943825 | − | 0.330445i | \(-0.892801\pi\) |
0.758086 | + | 0.652154i | \(0.226135\pi\) | |||||||
\(510\) | −11.1367 | −0.493143 | ||||||||
\(511\) | 0.188789 | + | 2.48892i | 0.00835154 | + | 0.110104i | ||||
\(512\) | 50.7841 | 2.24436 | ||||||||
\(513\) | 3.48863 | − | 6.04248i | 0.154027 | − | 0.266782i | ||||
\(514\) | −12.9959 | − | 22.5096i | −0.573226 | − | 0.992856i | ||||
\(515\) | −4.52397 | − | 7.83575i | −0.199350 | − | 0.345284i | ||||
\(516\) | 3.10524 | − | 5.37843i | 0.136700 | − | 0.236772i | ||||
\(517\) | 7.41557 | 0.326136 | ||||||||
\(518\) | 2.25277 | + | 29.6997i | 0.0989811 | + | 1.30493i | ||||
\(519\) | 5.14814 | 0.225978 | ||||||||
\(520\) | −8.04999 | + | 13.9430i | −0.353015 | + | 0.611441i | ||||
\(521\) | 0.175171 | + | 0.303404i | 0.00767436 | + | 0.0132924i | 0.869837 | − | 0.493339i | \(-0.164224\pi\) |
−0.862163 | + | 0.506631i | \(0.830890\pi\) | |||||||
\(522\) | 5.61721 | + | 9.72929i | 0.245858 | + | 0.425839i | ||||
\(523\) | 19.6404 | − | 34.0181i | 0.858813 | − | 1.48751i | −0.0142487 | − | 0.999898i | \(-0.504536\pi\) |
0.873062 | − | 0.487609i | \(-0.162131\pi\) | |||||||
\(524\) | 70.3824 | 3.07467 | ||||||||
\(525\) | −10.0055 | + | 6.83497i | −0.436678 | + | 0.298302i | ||||
\(526\) | −53.2304 | −2.32095 | ||||||||
\(527\) | −7.46083 | + | 12.9225i | −0.324999 | + | 0.562915i | ||||
\(528\) | 10.9476 | + | 18.9618i | 0.476434 | + | 0.825208i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 7.83227 | − | 13.5659i | 0.340212 | − | 0.589264i | ||||
\(531\) | 6.80034 | 0.295110 | ||||||||
\(532\) | 75.1067 | + | 36.0856i | 3.25629 | + | 1.56451i | ||||
\(533\) | 0.752915 | 0.0326123 | ||||||||
\(534\) | −20.0937 | + | 34.8034i | −0.869542 | + | 1.50609i | ||||
\(535\) | 0.398209 | + | 0.689718i | 0.0172161 | + | 0.0298191i | ||||
\(536\) | −2.86742 | − | 4.96652i | −0.123854 | − | 0.214521i | ||||
\(537\) | 3.88943 | − | 6.73668i | 0.167841 | − | 0.290709i | ||||
\(538\) | 52.2466 | 2.25251 | ||||||||
\(539\) | −7.58616 | + | 19.4328i | −0.326759 | + | 0.837029i | ||||
\(540\) | 2.92568 | 0.125901 | ||||||||
\(541\) | 9.54946 | − | 16.5401i | 0.410563 | − | 0.711116i | −0.584388 | − | 0.811474i | \(-0.698665\pi\) |
0.994951 | + | 0.100358i | \(0.0319988\pi\) | |||||||
\(542\) | −24.0619 | − | 41.6765i | −1.03355 | − | 1.79016i | ||||
\(543\) | 3.80663 | + | 6.59328i | 0.163358 | + | 0.282945i | ||||
\(544\) | 19.9257 | − | 34.5124i | 0.854309 | − | 1.47971i | ||||
\(545\) | 10.4814 | 0.448975 | ||||||||
\(546\) | −23.5643 | − | 11.3217i | −1.00846 | − | 0.484523i | ||||
\(547\) | −14.2276 | −0.608330 | −0.304165 | − | 0.952619i | \(-0.598377\pi\) | ||||
−0.304165 | + | 0.952619i | \(0.598377\pi\) | |||||||
\(548\) | −24.2067 | + | 41.9272i | −1.03406 | + | 1.79104i | ||||
\(549\) | −4.36166 | − | 7.55461i | −0.186151 | − | 0.322423i | ||||
\(550\) | 17.4173 | + | 30.1677i | 0.742677 | + | 1.28635i | ||||
\(551\) | 15.3563 | − | 26.5979i | 0.654200 | − | 1.13311i | ||||
\(552\) | 6.41586 | 0.273077 | ||||||||
\(553\) | 30.9120 | − | 21.1165i | 1.31451 | − | 0.897965i | ||||
\(554\) | 12.6643 | 0.538053 | ||||||||
\(555\) | 1.42949 | − | 2.47595i | 0.0606786 | − | 0.105098i | ||||
\(556\) | −48.3629 | − | 83.7670i | −2.05104 | − | 3.55251i | ||||
\(557\) | 6.88024 | + | 11.9169i | 0.291525 | + | 0.504936i | 0.974171 | − | 0.225813i | \(-0.0725040\pi\) |
−0.682645 | + | 0.730750i | \(0.739171\pi\) | |||||||
\(558\) | 2.82845 | − | 4.89901i | 0.119738 | − | 0.207392i | ||||
\(559\) | 5.32682 | 0.225300 | ||||||||
\(560\) | 0.952933 | + | 12.5631i | 0.0402688 | + | 0.530888i | ||||
\(561\) | −20.0630 | −0.847060 | ||||||||
\(562\) | 12.2073 | − | 21.1437i | 0.514935 | − | 0.891894i | ||||
\(563\) | 11.7109 | + | 20.2839i | 0.493555 | + | 0.854863i | 0.999972 | − | 0.00742562i | \(-0.00236367\pi\) |
−0.506417 | + | 0.862289i | \(0.669030\pi\) | |||||||
\(564\) | 5.61593 | + | 9.72708i | 0.236473 | + | 0.409584i | ||||
\(565\) | 1.52469 | − | 2.64084i | 0.0641441 | − | 0.111101i | ||||
\(566\) | −18.9332 | −0.795823 | ||||||||
\(567\) | 0.200110 | + | 2.63817i | 0.00840383 | + | 0.110793i | ||||
\(568\) | −97.8348 | −4.10506 | ||||||||
\(569\) | −8.47391 | + | 14.6773i | −0.355245 | + | 0.615302i | −0.987160 | − | 0.159735i | \(-0.948936\pi\) |
0.631915 | + | 0.775038i | \(0.282269\pi\) | |||||||
\(570\) | −5.77105 | − | 9.99575i | −0.241723 | − | 0.418676i | ||||
\(571\) | −11.6928 | − | 20.2526i | −0.489330 | − | 0.847545i | 0.510594 | − | 0.859822i | \(-0.329425\pi\) |
−0.999925 | + | 0.0122769i | \(0.996092\pi\) | |||||||
\(572\) | −26.0401 | + | 45.1027i | −1.08879 | + | 1.88584i | ||||
\(573\) | −0.738878 | −0.0308671 | ||||||||
\(574\) | 1.08433 | − | 0.740725i | 0.0452590 | − | 0.0309172i | ||||
\(575\) | 4.57989 | 0.190995 | ||||||||
\(576\) | −0.206940 | + | 0.358430i | −0.00862249 | + | 0.0149346i | ||||
\(577\) | 9.33006 | + | 16.1601i | 0.388415 | + | 0.672755i | 0.992237 | − | 0.124365i | \(-0.0396892\pi\) |
−0.603821 | + | 0.797120i | \(0.706356\pi\) | |||||||
\(578\) | 36.1428 | + | 62.6012i | 1.50334 | + | 2.60387i | ||||
\(579\) | 7.98512 | − | 13.8306i | 0.331850 | − | 0.574781i | ||||
\(580\) | 12.8783 | 0.534743 | ||||||||
\(581\) | −34.8845 | − | 16.7605i | −1.44725 | − | 0.695345i | ||||
\(582\) | −8.25441 | −0.342156 | ||||||||
\(583\) | 14.1099 | − | 24.4391i | 0.584374 | − | 1.01217i | ||||
\(584\) | 3.02645 | + | 5.24197i | 0.125235 | + | 0.216914i | ||||
\(585\) | 1.25470 | + | 2.17321i | 0.0518755 | + | 0.0898510i | ||||
\(586\) | 11.9585 | − | 20.7128i | 0.494003 | − | 0.855638i | ||||
\(587\) | 36.1742 | 1.49307 | 0.746535 | − | 0.665346i | \(-0.231716\pi\) | ||||
0.746535 | + | 0.665346i | \(0.231716\pi\) | |||||||
\(588\) | −31.2353 | + | 4.76593i | −1.28812 | + | 0.196544i | ||||
\(589\) | −15.4648 | −0.637216 | ||||||||
\(590\) | 5.62472 | − | 9.74229i | 0.231566 | − | 0.401084i | ||||
\(591\) | 4.75097 | + | 8.22893i | 0.195429 | + | 0.338493i | ||||
\(592\) | 16.2036 | + | 28.0655i | 0.665965 | + | 1.15348i | ||||
\(593\) | −14.5370 | + | 25.1788i | −0.596961 | + | 1.03397i | 0.396305 | + | 0.918119i | \(0.370292\pi\) |
−0.993267 | + | 0.115849i | \(0.963041\pi\) | |||||||
\(594\) | 7.60600 | 0.312078 | ||||||||
\(595\) | −10.4061 | − | 4.99969i | −0.426608 | − | 0.204967i | ||||
\(596\) | −46.7295 | −1.91412 | ||||||||
\(597\) | 8.32964 | − | 14.4274i | 0.340910 | − | 0.590473i | ||||
\(598\) | 4.94057 | + | 8.55732i | 0.202035 | + | 0.349935i | ||||
\(599\) | −19.6546 | − | 34.0428i | −0.803066 | − | 1.39095i | −0.917589 | − | 0.397531i | \(-0.869867\pi\) |
0.114522 | − | 0.993421i | \(-0.463466\pi\) | |||||||
\(600\) | −14.6920 | + | 25.4472i | −0.599797 | + | 1.03888i | ||||
\(601\) | 45.2577 | 1.84610 | 0.923049 | − | 0.384682i | \(-0.125689\pi\) | ||||
0.923049 | + | 0.384682i | \(0.125689\pi\) | |||||||
\(602\) | 7.67155 | − | 5.24058i | 0.312669 | − | 0.213590i | ||||
\(603\) | −0.893854 | −0.0364005 | ||||||||
\(604\) | 19.8739 | − | 34.4226i | 0.808657 | − | 1.40063i | ||||
\(605\) | 0.686632 | + | 1.18928i | 0.0279156 | + | 0.0483512i | ||||
\(606\) | 3.83679 | + | 6.64551i | 0.155859 | + | 0.269956i | ||||
\(607\) | 22.7764 | − | 39.4499i | 0.924466 | − | 1.60122i | 0.132047 | − | 0.991243i | \(-0.457845\pi\) |
0.792418 | − | 0.609978i | \(-0.208822\pi\) | |||||||
\(608\) | 41.3020 | 1.67502 | ||||||||
\(609\) | 0.880848 | + | 11.6128i | 0.0356937 | + | 0.470573i | ||||
\(610\) | −14.4305 | −0.584274 | ||||||||
\(611\) | −4.81687 | + | 8.34307i | −0.194870 | + | 0.337524i | ||||
\(612\) | −15.1940 | − | 26.3168i | −0.614183 | − | 1.06380i | ||||
\(613\) | −2.97103 | − | 5.14597i | −0.119999 | − | 0.207844i | 0.799768 | − | 0.600309i | \(-0.204956\pi\) |
−0.919767 | + | 0.392465i | \(0.871622\pi\) | |||||||
\(614\) | −0.0496148 | + | 0.0859354i | −0.00200229 | + | 0.00346807i | ||||
\(615\) | −0.126049 | −0.00508278 | ||||||||
\(616\) | 3.82615 | + | 50.4424i | 0.154160 | + | 2.03238i | ||||
\(617\) | 7.63295 | 0.307291 | 0.153646 | − | 0.988126i | \(-0.450899\pi\) | ||||
0.153646 | + | 0.988126i | \(0.450899\pi\) | |||||||
\(618\) | 17.8138 | − | 30.8544i | 0.716576 | − | 1.24115i | ||||
\(619\) | −6.38206 | − | 11.0541i | −0.256517 | − | 0.444300i | 0.708790 | − | 0.705420i | \(-0.249242\pi\) |
−0.965306 | + | 0.261120i | \(0.915908\pi\) | |||||||
\(620\) | −3.24233 | − | 5.61588i | −0.130215 | − | 0.225539i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | −23.3234 | −0.935183 | ||||||||
\(623\) | −34.4000 | + | 23.4993i | −1.37821 | + | 0.941478i | ||||
\(624\) | −28.4446 | −1.13870 | ||||||||
\(625\) | −9.43742 | + | 16.3461i | −0.377497 | + | 0.653844i | ||||
\(626\) | −16.4314 | − | 28.4600i | −0.656731 | − | 1.13749i | ||||
\(627\) | −10.3966 | − | 18.0075i | −0.415201 | − | 0.719150i | ||||
\(628\) | 21.0592 | − | 36.4756i | 0.840354 | − | 1.45554i | ||||
\(629\) | −29.6953 | −1.18403 | ||||||||
\(630\) | 3.94501 | + | 1.89541i | 0.157173 | + | 0.0755150i | ||||
\(631\) | −23.8685 | −0.950192 | −0.475096 | − | 0.879934i | \(-0.657587\pi\) | ||||
−0.475096 | + | 0.879934i | \(0.657587\pi\) | |||||||
\(632\) | 45.3906 | − | 78.6188i | 1.80554 | − | 3.12729i | ||||
\(633\) | −9.82247 | − | 17.0130i | −0.390408 | − | 0.676207i | ||||
\(634\) | 13.7655 | + | 23.8426i | 0.546699 | + | 0.946911i | ||||
\(635\) | −5.17360 | + | 8.96094i | −0.205308 | + | 0.355604i | ||||
\(636\) | 42.7428 | 1.69486 | ||||||||
\(637\) | −16.9357 | − | 21.1578i | −0.671015 | − | 0.838302i | ||||
\(638\) | 33.4802 | 1.32549 | ||||||||
\(639\) | −7.62445 | + | 13.2059i | −0.301619 | + | 0.522419i | ||||
\(640\) | −3.49447 | − | 6.05259i | −0.138131 | − | 0.239250i | ||||
\(641\) | −12.3957 | − | 21.4700i | −0.489601 | − | 0.848014i | 0.510327 | − | 0.859980i | \(-0.329524\pi\) |
−0.999928 | + | 0.0119663i | \(0.996191\pi\) | |||||||
\(642\) | −1.56800 | + | 2.71586i | −0.0618842 | + | 0.107187i | ||||
\(643\) | 40.8527 | 1.61107 | 0.805537 | − | 0.592546i | \(-0.201877\pi\) | ||||
0.805537 | + | 0.592546i | \(0.201877\pi\) | |||||||
\(644\) | 10.7645 | + | 5.17189i | 0.424181 | + | 0.203801i | ||||
\(645\) | −0.891787 | −0.0351141 | ||||||||
\(646\) | −59.9419 | + | 103.822i | −2.35838 | + | 4.08484i | ||||
\(647\) | 14.3158 | + | 24.7957i | 0.562811 | + | 0.974818i | 0.997250 | + | 0.0741161i | \(0.0236135\pi\) |
−0.434438 | + | 0.900702i | \(0.643053\pi\) | |||||||
\(648\) | 3.20793 | + | 5.55630i | 0.126019 | + | 0.218272i | ||||
\(649\) | 10.1330 | − | 17.5509i | 0.397755 | − | 0.688933i | ||||
\(650\) | −45.2545 | −1.77503 | ||||||||
\(651\) | 4.84223 | − | 3.30781i | 0.189782 | − | 0.129643i | ||||
\(652\) | 2.09046 | 0.0818686 | ||||||||
\(653\) | 10.4627 | − | 18.1219i | 0.409437 | − | 0.709166i | −0.585390 | − | 0.810752i | \(-0.699059\pi\) |
0.994827 | + | 0.101586i | \(0.0323919\pi\) | |||||||
\(654\) | 20.6361 | + | 35.7427i | 0.806934 | + | 1.39765i | ||||
\(655\) | −5.05325 | − | 8.75248i | −0.197447 | − | 0.341988i | ||||
\(656\) | 0.714396 | − | 1.23737i | 0.0278925 | − | 0.0483112i | ||||
\(657\) | 0.943428 | 0.0368066 | ||||||||
\(658\) | 1.27085 | + | 16.7544i | 0.0495428 | + | 0.653153i | ||||
\(659\) | −12.2792 | −0.478329 | −0.239165 | − | 0.970979i | \(-0.576874\pi\) | ||||
−0.239165 | + | 0.970979i | \(0.576874\pi\) | |||||||
\(660\) | 4.35948 | − | 7.55085i | 0.169693 | − | 0.293916i | ||||
\(661\) | −13.6631 | − | 23.6652i | −0.531432 | − | 0.920468i | −0.999327 | − | 0.0366836i | \(-0.988321\pi\) |
0.467895 | − | 0.883784i | \(-0.345013\pi\) | |||||||
\(662\) | 28.8102 | + | 49.9008i | 1.11974 | + | 1.93945i | ||||
\(663\) | 13.0322 | − | 22.5724i | 0.506127 | − | 0.876638i | ||||
\(664\) | −93.8512 | −3.64213 | ||||||||
\(665\) | −0.904971 | − | 11.9308i | −0.0350933 | − | 0.462656i | ||||
\(666\) | 11.2577 | 0.436226 | ||||||||
\(667\) | 2.20091 | − | 3.81209i | 0.0852195 | − | 0.147605i | ||||
\(668\) | −5.42528 | − | 9.39686i | −0.209910 | − | 0.363576i | ||||
\(669\) | 8.76228 | + | 15.1767i | 0.338769 | + | 0.586766i | ||||
\(670\) | −0.739327 | + | 1.28055i | −0.0285627 | + | 0.0494720i | ||||
\(671\) | −25.9968 | −1.00359 | ||||||||
\(672\) | −12.9322 | + | 8.83422i | −0.498871 | + | 0.340788i | ||||
\(673\) | 9.75358 | 0.375973 | 0.187986 | − | 0.982172i | \(-0.439804\pi\) | ||||
0.187986 | + | 0.982172i | \(0.439804\pi\) | |||||||
\(674\) | −8.16643 | + | 14.1447i | −0.314559 | + | 0.544832i | ||||
\(675\) | 2.28994 | + | 3.96630i | 0.0881400 | + | 0.152663i | ||||
\(676\) | −4.48937 | − | 7.77581i | −0.172668 | − | 0.299070i | ||||
\(677\) | −1.63166 | + | 2.82612i | −0.0627097 | + | 0.108616i | −0.895676 | − | 0.444708i | \(-0.853308\pi\) |
0.832966 | + | 0.553324i | \(0.186641\pi\) | |||||||
\(678\) | 12.0074 | 0.461140 | ||||||||
\(679\) | −7.71287 | − | 3.70571i | −0.295993 | − | 0.142212i | ||||
\(680\) | −27.9959 | −1.07359 | ||||||||
\(681\) | 5.34607 | − | 9.25966i | 0.204862 | − | 0.354831i | ||||
\(682\) | −8.42919 | − | 14.5998i | −0.322770 | − | 0.559055i | ||||
\(683\) | 14.2770 | + | 24.7285i | 0.546294 | + | 0.946209i | 0.998524 | + | 0.0543076i | \(0.0172951\pi\) |
−0.452230 | + | 0.891901i | \(0.649372\pi\) | |||||||
\(684\) | 15.7471 | − | 27.2747i | 0.602105 | − | 1.04288i | ||||
\(685\) | 6.95186 | 0.265617 | ||||||||
\(686\) | −45.2056 | − | 13.8095i | −1.72596 | − | 0.527249i | ||||
\(687\) | 9.30000 | 0.354817 | ||||||||
\(688\) | 5.05430 | − | 8.75431i | 0.192693 | − | 0.333755i | ||||
\(689\) | 18.3306 | + | 31.7495i | 0.698339 | + | 1.20956i | ||||
\(690\) | −0.827123 | − | 1.43262i | −0.0314880 | − | 0.0545389i | ||||
\(691\) | −23.1058 | + | 40.0204i | −0.878985 | + | 1.52245i | −0.0265298 | + | 0.999648i | \(0.508446\pi\) |
−0.852456 | + | 0.522800i | \(0.824888\pi\) | |||||||
\(692\) | 23.2379 | 0.883371 | ||||||||
\(693\) | 7.10700 | + | 3.41461i | 0.269973 | + | 0.129710i | ||||
\(694\) | −85.0396 | −3.22806 | ||||||||
\(695\) | −6.94462 | + | 12.0284i | −0.263424 | + | 0.456264i | ||||
\(696\) | 14.1207 | + | 24.4578i | 0.535245 | + | 0.927071i | ||||
\(697\) | 0.654613 | + | 1.13382i | 0.0247952 | + | 0.0429466i | ||||
\(698\) | −36.4252 | + | 63.0903i | −1.37872 | + | 2.38800i | ||||
\(699\) | −23.7260 | −0.897401 | ||||||||
\(700\) | −45.1634 | + | 30.8519i | −1.70702 | + | 1.16609i | ||||
\(701\) | 29.0091 | 1.09566 | 0.547830 | − | 0.836590i | \(-0.315454\pi\) | ||||
0.547830 | + | 0.836590i | \(0.315454\pi\) | |||||||
\(702\) | −4.94057 | + | 8.55732i | −0.186470 | + | 0.322975i | ||||
\(703\) | −15.3881 | − | 26.6530i | −0.580373 | − | 1.00524i | ||||
\(704\) | 0.616711 | + | 1.06818i | 0.0232432 | + | 0.0402584i | ||||
\(705\) | 0.806414 | − | 1.39675i | 0.0303713 | − | 0.0526047i | ||||
\(706\) | 0.390775 | 0.0147070 | ||||||||
\(707\) | 0.601656 | + | 7.93200i | 0.0226276 | + | 0.298314i | ||||
\(708\) | 30.6956 | 1.15361 | ||||||||
\(709\) | −24.6074 | + | 42.6213i | −0.924150 | + | 1.60067i | −0.131228 | + | 0.991352i | \(0.541892\pi\) |
−0.792923 | + | 0.609322i | \(0.791441\pi\) | |||||||
\(710\) | 12.6127 | + | 21.8459i | 0.473347 | + | 0.819861i | ||||
\(711\) | −7.07474 | − | 12.2538i | −0.265324 | − | 0.459554i | ||||
\(712\) | −50.5124 | + | 87.4900i | −1.89303 | + | 3.27883i | ||||
\(713\) | −2.21646 | −0.0830070 | ||||||||
\(714\) | −3.43831 | − | 45.3293i | −0.128675 | − | 1.69641i | ||||
\(715\) | 7.47839 | 0.279676 | ||||||||
\(716\) | 17.5562 | − | 30.4083i | 0.656107 | − | 1.13641i | ||||
\(717\) | −13.3163 | − | 23.0645i | −0.497307 | − | 0.861360i | ||||
\(718\) | 27.6727 | + | 47.9305i | 1.03274 | + | 1.78875i | ||||
\(719\) | −9.55428 | + | 16.5485i | −0.356314 | + | 0.617155i | −0.987342 | − | 0.158606i | \(-0.949300\pi\) |
0.631028 | + | 0.775760i | \(0.282633\pi\) | |||||||
\(720\) | 4.76204 | 0.177471 | ||||||||
\(721\) | 30.4968 | − | 20.8329i | 1.13576 | − | 0.775858i | ||||
\(722\) | −75.7552 | −2.81932 | ||||||||
\(723\) | −5.84295 | + | 10.1203i | −0.217302 | + | 0.376377i | ||||
\(724\) | 17.1825 | + | 29.7610i | 0.638583 | + | 1.10606i | ||||
\(725\) | 10.0799 | + | 17.4589i | 0.374359 | + | 0.648409i | ||||
\(726\) | −2.70372 | + | 4.68297i | −0.100344 | + | 0.173801i | ||||
\(727\) | 3.03289 | 0.112483 | 0.0562417 | − | 0.998417i | \(-0.482088\pi\) | ||||
0.0562417 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(728\) | −59.2368 | − | 28.4608i | −2.19546 | − | 1.05483i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.780330 | − | 1.35157i | 0.0288813 | − | 0.0500239i | ||||
\(731\) | 4.63134 | + | 8.02172i | 0.171296 | + | 0.296694i | ||||
\(732\) | −19.6878 | − | 34.1003i | −0.727682 | − | 1.26038i | ||||
\(733\) | 0.412163 | − | 0.713887i | 0.0152236 | − | 0.0263680i | −0.858313 | − | 0.513126i | \(-0.828487\pi\) |
0.873537 | + | 0.486758i | \(0.161821\pi\) | |||||||
\(734\) | −7.76404 | −0.286576 | ||||||||
\(735\) | 2.83527 | + | 3.54212i | 0.104581 | + | 0.130653i | ||||
\(736\) | 5.91953 | 0.218197 | ||||||||
\(737\) | −1.33191 | + | 2.30693i | −0.0490615 | + | 0.0849770i | ||||
\(738\) | −0.248168 | − | 0.429839i | −0.00913518 | − | 0.0158226i | ||||
\(739\) | 5.10966 | + | 8.85019i | 0.187962 | + | 0.325560i | 0.944571 | − | 0.328308i | \(-0.106479\pi\) |
−0.756609 | + | 0.653868i | \(0.773145\pi\) | |||||||
\(740\) | 6.45249 | − | 11.1760i | 0.237198 | − | 0.410840i | ||||
\(741\) | 27.0130 | 0.992348 | ||||||||
\(742\) | 57.6347 | + | 27.6910i | 2.11584 | + | 1.01657i | ||||
\(743\) | 10.5624 | 0.387496 | 0.193748 | − | 0.981051i | \(-0.437936\pi\) | ||||
0.193748 | + | 0.981051i | \(0.437936\pi\) | |||||||
\(744\) | 7.11025 | − | 12.3153i | 0.260674 | − | 0.451501i | ||||
\(745\) | 3.35504 | + | 5.81110i | 0.122919 | + | 0.212902i | ||||
\(746\) | 35.2382 | + | 61.0343i | 1.29016 | + | 2.23462i | ||||
\(747\) | −7.31399 | + | 12.6682i | −0.267605 | + | 0.463506i | ||||
\(748\) | −90.5610 | −3.31124 | ||||||||
\(749\) | −2.68439 | + | 1.83375i | −0.0980853 | + | 0.0670038i | ||||
\(750\) | 15.8475 | 0.578669 | ||||||||
\(751\) | 20.5518 | − | 35.5967i | 0.749944 | − | 1.29894i | −0.197905 | − | 0.980221i | \(-0.563414\pi\) |
0.947849 | − | 0.318720i | \(-0.103253\pi\) | |||||||
\(752\) | 9.14089 | + | 15.8325i | 0.333334 | + | 0.577351i | ||||
\(753\) | 6.01353 | + | 10.4157i | 0.219145 | + | 0.379571i | ||||
\(754\) | −21.7475 | + | 37.6678i | −0.791997 | + | 1.37178i | ||||
\(755\) | −5.70754 | −0.207719 | ||||||||
\(756\) | 0.903263 | + | 11.9083i | 0.0328514 | + | 0.433100i | ||||
\(757\) | −34.3157 | −1.24723 | −0.623613 | − | 0.781733i | \(-0.714336\pi\) | ||||
−0.623613 | + | 0.781733i | \(0.714336\pi\) | |||||||
\(758\) | 30.6419 | − | 53.0733i | 1.11296 | − | 1.92771i | ||||
\(759\) | −1.49007 | − | 2.58088i | −0.0540863 | − | 0.0936802i | ||||
\(760\) | −14.5075 | − | 25.1276i | −0.526241 | − | 0.911476i | ||||
\(761\) | 2.89620 | − | 5.01637i | 0.104987 | − | 0.181843i | −0.808746 | − | 0.588158i | \(-0.799853\pi\) |
0.913733 | + | 0.406315i | \(0.133186\pi\) | |||||||
\(762\) | −40.7436 | −1.47599 | ||||||||
\(763\) | 3.23599 | + | 42.6621i | 0.117151 | + | 1.54447i | ||||
\(764\) | −3.33517 | −0.120662 | ||||||||
\(765\) | −2.18177 | + | 3.77894i | −0.0788821 | + | 0.136628i | ||||
\(766\) | −14.0523 | − | 24.3393i | −0.507730 | − | 0.879414i | ||||
\(767\) | 13.1640 | + | 22.8008i | 0.475326 | + | 0.823289i | ||||
\(768\) | 14.1738 | − | 24.5498i | 0.511455 | − | 0.885866i | ||||
\(769\) | −27.9852 | −1.00917 | −0.504586 | − | 0.863361i | \(-0.668355\pi\) | ||||
−0.504586 | + | 0.863361i | \(0.668355\pi\) | |||||||
\(770\) | 10.7702 | − | 7.35731i | 0.388131 | − | 0.265139i | ||||
\(771\) | −10.1840 | −0.366768 | ||||||||
\(772\) | 36.0435 | − | 62.4292i | 1.29723 | − | 2.24688i | ||||
\(773\) | 17.6635 | + | 30.5941i | 0.635313 | + | 1.10039i | 0.986449 | + | 0.164069i | \(0.0524621\pi\) |
−0.351136 | + | 0.936324i | \(0.614205\pi\) | |||||||
\(774\) | −1.75577 | − | 3.04108i | −0.0631098 | − | 0.109309i | ||||
\(775\) | 5.07557 | − | 8.79114i | 0.182320 | − | 0.315787i | ||||
\(776\) | −20.7502 | −0.744889 | ||||||||
\(777\) | 10.5191 | + | 5.05398i | 0.377371 | + | 0.181311i | ||||
\(778\) | −89.5712 | −3.21128 | ||||||||
\(779\) | −0.678440 | + | 1.17509i | −0.0243076 | + | 0.0421021i | ||||
\(780\) | 5.66351 | + | 9.80949i | 0.202786 | + | 0.351236i | ||||
\(781\) | 22.7220 | + | 39.3556i | 0.813057 | + | 1.40826i | ||||
\(782\) | −8.59104 | + | 14.8801i | −0.307215 | + | 0.532112i | ||||
\(783\) | 4.40182 | 0.157308 | ||||||||
\(784\) | −50.8408 | + | 7.75736i | −1.81574 | + | 0.277048i | ||||
\(785\) | −6.04795 | −0.215861 | ||||||||
\(786\) | 19.8979 | − | 34.4642i | 0.709734 | − | 1.22930i | ||||
\(787\) | 17.1994 | + | 29.7903i | 0.613094 | + | 1.06191i | 0.990716 | + | 0.135950i | \(0.0434085\pi\) |
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(788\) | 21.4451 | + | 37.1440i | 0.763950 | + | 1.32320i | ||||
\(789\) | −10.4282 | + | 18.0622i | −0.371255 | + | 0.643033i | ||||
\(790\) | −23.4067 | −0.832774 | ||||||||
\(791\) | 11.2196 | + | 5.39055i | 0.398923 | + | 0.191666i | ||||
\(792\) | 19.1202 | 0.679407 | ||||||||
\(793\) | 16.8865 | − | 29.2483i | 0.599658 | − | 1.03864i | ||||
\(794\) | 19.4330 | + | 33.6590i | 0.689652 | + | 1.19451i | ||||
\(795\) | −3.06880 | − | 5.31532i | −0.108839 | − | 0.188515i | ||||
\(796\) | 37.5986 | − | 65.1227i | 1.33265 | − | 2.30821i | ||||
\(797\) | −22.2714 | −0.788894 | −0.394447 | − | 0.918919i | \(-0.629064\pi\) | ||||
−0.394447 | + | 0.918919i | \(0.629064\pi\) | |||||||
\(798\) | 38.9035 | − | 26.5757i | 1.37717 | − | 0.940769i | ||||
\(799\) | −16.7519 | −0.592640 | ||||||||
\(800\) | −13.5554 | + | 23.4786i | −0.479255 | + | 0.830095i | ||||
\(801\) | 7.87304 | + | 13.6365i | 0.278180 | + | 0.481822i | ||||
\(802\) | −24.2283 | − | 41.9646i | −0.855530 | − | 1.48182i | ||||
\(803\) | 1.40578 | − | 2.43488i | 0.0496088 | − | 0.0859250i | ||||
\(804\) | −4.03471 | −0.142293 | ||||||||
\(805\) | −0.129703 | − | 1.70996i | −0.00457143 | − | 0.0602680i | ||||
\(806\) | 21.9011 | 0.771435 | ||||||||
\(807\) | 10.2355 | − | 17.7284i | 0.360307 | − | 0.624071i | ||||
\(808\) | 9.64505 | + | 16.7057i | 0.339312 | + | 0.587705i | ||||
\(809\) | 17.1349 | + | 29.6785i | 0.602431 | + | 1.04344i | 0.992452 | + | 0.122635i | \(0.0391346\pi\) |
−0.390021 | + | 0.920806i | \(0.627532\pi\) | |||||||
\(810\) | 0.827123 | − | 1.43262i | 0.0290621 | − | 0.0503371i | ||||
\(811\) | −52.1588 | −1.83154 | −0.915772 | − | 0.401698i | \(-0.868420\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(812\) | 3.97600 | + | 52.4181i | 0.139530 | + | 1.83951i | ||||
\(813\) | −18.8557 | −0.661297 | ||||||||
\(814\) | 16.7748 | − | 29.0547i | 0.587955 | − | 1.01837i | ||||
\(815\) | −0.150088 | − | 0.259961i | −0.00525737 | − | 0.00910602i | ||||
\(816\) | −24.7309 | − | 42.8351i | −0.865754 | − | 1.49953i | ||||
\(817\) | −4.79992 | + | 8.31370i | −0.167928 | + | 0.290860i | ||||
\(818\) | −19.0262 | −0.665235 | ||||||||
\(819\) | −8.45813 | + | 5.77790i | −0.295551 | + | 0.201896i | ||||
\(820\) | −0.568963 | −0.0198691 | ||||||||
\(821\) | 8.86817 | − | 15.3601i | 0.309501 | − | 0.536072i | −0.668752 | − | 0.743486i | \(-0.733171\pi\) |
0.978253 | + | 0.207413i | \(0.0665045\pi\) | |||||||
\(822\) | 13.6870 | + | 23.7065i | 0.477388 | + | 0.826861i | ||||
\(823\) | 0.295059 | + | 0.511057i | 0.0102851 | + | 0.0178143i | 0.871122 | − | 0.491066i | \(-0.163393\pi\) |
−0.860837 | + | 0.508881i | \(0.830059\pi\) | |||||||
\(824\) | 44.7810 | − | 77.5629i | 1.56002 | − | 2.70203i | ||||
\(825\) | 13.6488 | 0.475189 | ||||||||
\(826\) | 41.3902 | + | 19.8862i | 1.44015 | + | 0.691930i | ||||
\(827\) | 50.4841 | 1.75550 | 0.877752 | − | 0.479114i | \(-0.159042\pi\) | ||||
0.877752 | + | 0.479114i | \(0.159042\pi\) | |||||||
\(828\) | 2.25692 | − | 3.90910i | 0.0784333 | − | 0.135850i | ||||
\(829\) | 14.0542 | + | 24.3427i | 0.488124 | + | 0.845456i | 0.999907 | − | 0.0136592i | \(-0.00434798\pi\) |
−0.511783 | + | 0.859115i | \(0.671015\pi\) | |||||||
\(830\) | 12.0991 | + | 20.9563i | 0.419967 | + | 0.727405i | ||||
\(831\) | 2.48103 | − | 4.29727i | 0.0860659 | − | 0.149070i | ||||
\(832\) | −1.60237 | −0.0555522 | ||||||||
\(833\) | 17.1373 | − | 43.8990i | 0.593771 | − | 1.52101i | ||||
\(834\) | −54.6909 | −1.89379 | ||||||||
\(835\) | −0.779037 | + | 1.34933i | −0.0269597 | + | 0.0466956i | ||||
\(836\) | −46.9286 | − | 81.2828i | −1.62306 | − | 2.81122i | ||||
\(837\) | −1.10823 | − | 1.91951i | −0.0383060 | − | 0.0663480i | ||||
\(838\) | 4.05011 | − | 7.01499i | 0.139909 | − | 0.242329i | ||||
\(839\) | −22.3730 | −0.772401 | −0.386200 | − | 0.922415i | \(-0.626213\pi\) | ||||
−0.386200 | + | 0.922415i | \(0.626213\pi\) | |||||||
\(840\) | 9.91710 | + | 4.76475i | 0.342173 | + | 0.164400i | ||||
\(841\) | −9.62400 | −0.331862 | ||||||||
\(842\) | 19.2774 | − | 33.3894i | 0.664343 | − | 1.15068i | ||||
\(843\) | −4.78302 | − | 8.28444i | −0.164736 | − | 0.285331i | ||||
\(844\) | −44.3370 | − | 76.7939i | −1.52614 | − | 2.64336i | ||||
\(845\) | −0.644646 | + | 1.11656i | −0.0221765 | + | 0.0384108i | ||||
\(846\) | 6.35075 | 0.218343 | ||||||||
\(847\) | −4.62869 | + | 3.16194i | −0.159044 | + | 0.108646i | ||||
\(848\) | 69.5712 | 2.38908 | ||||||||
\(849\) | −3.70917 | + | 6.42447i | −0.127298 | + | 0.220487i | ||||
\(850\) | −39.3460 | − | 68.1493i | −1.34956 | − | 2.33750i | ||||
\(851\) | −2.20547 | − | 3.81998i | −0.0756024 | − | 0.130947i | ||||
\(852\) | −34.4155 | + | 59.6094i | −1.17906 | + | 2.04218i | ||||
\(853\) | 39.3664 | 1.34788 | 0.673940 | − | 0.738786i | \(-0.264601\pi\) | ||||
0.673940 | + | 0.738786i | \(0.264601\pi\) | |||||||
\(854\) | −4.45521 | − | 58.7358i | −0.152454 | − | 2.00990i | ||||
\(855\) | −4.52237 | −0.154662 | ||||||||
\(856\) | −3.94170 | + | 6.82723i | −0.134725 | + | 0.233350i | ||||
\(857\) | −11.9660 | − | 20.7257i | −0.408751 | − | 0.707977i | 0.585999 | − | 0.810311i | \(-0.300702\pi\) |
−0.994750 | + | 0.102335i | \(0.967369\pi\) | |||||||
\(858\) | 14.7236 | + | 25.5021i | 0.502656 | + | 0.870626i | ||||
\(859\) | −13.0940 | + | 22.6794i | −0.446761 | + | 0.773812i | −0.998173 | − | 0.0604207i | \(-0.980756\pi\) |
0.551412 | + | 0.834233i | \(0.314089\pi\) | |||||||
\(860\) | −4.02538 | −0.137264 | ||||||||
\(861\) | −0.0389158 | − | 0.513051i | −0.00132625 | − | 0.0174847i | ||||
\(862\) | −63.8751 | −2.17559 | ||||||||
\(863\) | 8.87506 | − | 15.3721i | 0.302111 | − | 0.523271i | −0.674503 | − | 0.738272i | \(-0.735642\pi\) |
0.976614 | + | 0.215001i | \(0.0689755\pi\) | |||||||
\(864\) | 2.95976 | + | 5.12646i | 0.100693 | + | 0.174406i | ||||
\(865\) | −1.66841 | − | 2.88977i | −0.0567276 | − | 0.0982550i | ||||
\(866\) | −35.2042 | + | 60.9755i | −1.19629 | + | 2.07203i | ||||
\(867\) | 28.3226 | 0.961887 | ||||||||
\(868\) | 21.8570 | − | 14.9309i | 0.741876 | − | 0.506789i | ||||
\(869\) | −42.1676 | −1.43044 | ||||||||
\(870\) | 3.64084 | − | 6.30613i | 0.123436 | − | 0.213798i | ||||
\(871\) | −1.73031 | − | 2.99699i | −0.0586295 | − | 0.101549i | ||||
\(872\) | 51.8757 | + | 89.8513i | 1.75673 | + | 3.04275i | ||||
\(873\) | −1.61710 | + | 2.80090i | −0.0547306 | + | 0.0947963i | ||||
\(874\) | −17.8075 | −0.602348 | ||||||||
\(875\) | 14.8078 | + | 7.11452i | 0.500595 | + | 0.240515i | ||||
\(876\) | 4.25848 | 0.143881 | ||||||||
\(877\) | −0.490644 | + | 0.849820i | −0.0165679 | + | 0.0286964i | −0.874190 | − | 0.485583i | \(-0.838607\pi\) |
0.857623 | + | 0.514280i | \(0.171941\pi\) | |||||||
\(878\) | −26.0156 | − | 45.0604i | −0.877985 | − | 1.52072i | ||||
\(879\) | −4.68554 | − | 8.11559i | −0.158039 | − | 0.273732i | ||||
\(880\) | 7.09580 | − | 12.2903i | 0.239199 | − | 0.414305i | ||||
\(881\) | 52.6379 | 1.77341 | 0.886707 | − | 0.462331i | \(-0.152987\pi\) | ||||
0.886707 | + | 0.462331i | \(0.152987\pi\) | |||||||
\(882\) | −6.49684 | + | 16.6424i | −0.218760 | + | 0.560378i | ||||
\(883\) | 22.2550 | 0.748939 | 0.374469 | − | 0.927239i | \(-0.377825\pi\) | ||||
0.374469 | + | 0.927239i | \(0.377825\pi\) | |||||||
\(884\) | 58.8250 | − | 101.888i | 1.97850 | − | 3.42686i | ||||
\(885\) | −2.20385 | − | 3.81718i | −0.0740816 | − | 0.128313i | ||||
\(886\) | 35.5706 | + | 61.6101i | 1.19502 | + | 2.06983i | ||||
\(887\) | 16.6489 | − | 28.8367i | 0.559014 | − | 0.968241i | −0.438565 | − | 0.898700i | \(-0.644513\pi\) |
0.997579 | − | 0.0695415i | \(-0.0221536\pi\) | |||||||
\(888\) | 28.2999 | 0.949683 | ||||||||
\(889\) | −38.0706 | − | 18.2913i | −1.27685 | − | 0.613471i | ||||
\(890\) | 26.0479 | 0.873127 | ||||||||
\(891\) | 1.49007 | − | 2.58088i | 0.0499194 | − | 0.0864629i | ||||
\(892\) | 39.5515 | + | 68.5052i | 1.32428 | + | 2.29372i | ||||
\(893\) | −8.68082 | − | 15.0356i | −0.290493 | − | 0.503148i | ||||
\(894\) | −13.2110 | + | 22.8820i | −0.441840 | + | 0.765290i | ||||
\(895\) | −5.04193 | −0.168533 | ||||||||
\(896\) | 23.5567 | − | 16.0920i | 0.786975 | − | 0.537597i | ||||
\(897\) | 3.87158 | 0.129268 | ||||||||
\(898\) | −16.0587 | + | 27.8145i | −0.535887 | + | 0.928183i | ||||
\(899\) | −4.87822 | − | 8.44933i | −0.162698 | − | 0.281801i | ||||
\(900\) | 10.3364 | + | 17.9032i | 0.344548 | + | 0.596774i | ||||
\(901\) | −31.8746 | + | 55.2085i | −1.06190 | + | 1.83926i | ||||
\(902\) | −1.47915 | −0.0492504 | ||||||||
\(903\) | −0.275326 | − | 3.62980i | −0.00916229 | − | 0.120792i | ||||
\(904\) | 30.1845 | 1.00392 | ||||||||
\(905\) | 2.46730 | − | 4.27350i | 0.0820160 | − | 0.142056i | ||||
\(906\) | −11.2371 | − | 19.4633i | −0.373329 | − | 0.646624i | ||||
\(907\) | −3.09177 | − | 5.35511i | −0.102661 | − | 0.177814i | 0.810119 | − | 0.586265i | \(-0.199402\pi\) |
−0.912780 | + | 0.408451i | \(0.866069\pi\) | |||||||
\(908\) | 24.1313 | − | 41.7966i | 0.800824 | − | 1.38707i | ||||
\(909\) | 3.00663 | 0.0997235 | ||||||||
\(910\) | 1.28161 | + | 16.8963i | 0.0424851 | + | 0.560107i | ||||
\(911\) | 15.7337 | 0.521282 | 0.260641 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260641 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(912\) | 25.6310 | − | 44.3943i | 0.848729 | − | 1.47004i | ||||
\(913\) | 21.7968 | + | 37.7531i | 0.721368 | + | 1.24945i | ||||
\(914\) | −27.1720 | − | 47.0633i | −0.898771 | − | 1.55672i | ||||
\(915\) | −2.82705 | + | 4.89659i | −0.0934593 | + | 0.161876i | ||||
\(916\) | 41.9787 | 1.38701 | ||||||||
\(917\) | 34.0647 | − | 23.2702i | 1.12492 | − | 0.768450i | ||||
\(918\) | −17.1821 | −0.567093 | ||||||||
\(919\) | −5.74393 | + | 9.94877i | −0.189475 | + | 0.328180i | −0.945075 | − | 0.326853i | \(-0.894012\pi\) |
0.755601 | + | 0.655033i | \(0.227345\pi\) | |||||||
\(920\) | −2.07925 | − | 3.60137i | −0.0685508 | − | 0.118734i | ||||
\(921\) | 0.0194399 | + | 0.0336708i | 0.000640565 | + | 0.00110949i | ||||
\(922\) | −4.89686 | + | 8.48161i | −0.161270 | + | 0.279327i | ||||
\(923\) | −59.0374 | −1.94324 | ||||||||
\(924\) | 32.0798 | + | 15.4130i | 1.05535 | + | 0.507050i | ||||
\(925\) | 20.2016 | 0.664224 | ||||||||
\(926\) | −51.6355 | + | 89.4353i | −1.69685 | + | 2.93903i | ||||
\(927\) | −6.97973 | − | 12.0892i | −0.229244 | − | 0.397063i | ||||
\(928\) | 13.0283 | + | 22.5657i | 0.427676 | + | 0.740757i | ||||
\(929\) | −5.14417 | + | 8.90996i | −0.168775 | + | 0.292326i | −0.937989 | − | 0.346664i | \(-0.887314\pi\) |
0.769215 | + | 0.638991i | \(0.220648\pi\) | |||||||
\(930\) | −3.66657 | −0.120231 | ||||||||
\(931\) | 48.2820 | − | 7.36693i | 1.58238 | − | 0.241441i | ||||
\(932\) | −107.095 | −3.50803 | ||||||||
\(933\) | −4.56923 | + | 7.91415i | −0.149590 | + | 0.259098i | ||||
\(934\) | −2.26131 | − | 3.91670i | −0.0739922 | − | 0.128158i | ||||
\(935\) | 6.50200 | + | 11.2618i | 0.212638 | + | 0.368300i | ||||
\(936\) | −12.4198 | + | 21.5117i | −0.405953 | + | 0.703131i | ||||
\(937\) | −5.44863 | −0.177999 | −0.0889994 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0889994 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(938\) | −5.44043 | − | 2.61390i | −0.177636 | − | 0.0853467i | ||||
\(939\) | −12.8762 | −0.420197 | ||||||||
\(940\) | 3.64002 | − | 6.30470i | 0.118724 | − | 0.205637i | ||||
\(941\) | 13.9243 | + | 24.1177i | 0.453921 | + | 0.786214i | 0.998625 | − | 0.0524143i | \(-0.0166916\pi\) |
−0.544705 | + | 0.838628i | \(0.683358\pi\) | |||||||
\(942\) | −11.9073 | − | 20.6241i | −0.387962 | − | 0.671970i | ||||
\(943\) | −0.0972360 | + | 0.168418i | −0.00316644 | + | 0.00548443i | ||||
\(944\) | 49.9623 | 1.62613 | ||||||||
\(945\) | 1.41601 | − | 0.967304i | 0.0460629 | − | 0.0314664i | ||||
\(946\) | −10.4649 | −0.340244 | ||||||||
\(947\) | 24.1522 | − | 41.8328i | 0.784840 | − | 1.35938i | −0.144255 | − | 0.989541i | \(-0.546079\pi\) |
0.929095 | − | 0.369842i | \(-0.120588\pi\) | |||||||
\(948\) | −31.9342 | − | 55.3117i | −1.03718 | − | 1.79644i | ||||
\(949\) | 1.82628 | + | 3.16321i | 0.0592835 | + | 0.102682i | ||||
\(950\) | 40.7782 | − | 70.6299i | 1.32302 | − | 2.29154i | ||||
\(951\) | 10.7871 | 0.349796 | ||||||||
\(952\) | −8.64333 | − | 113.950i | −0.280132 | − | 3.69315i | ||||
\(953\) | −17.0509 | −0.552334 | −0.276167 | − | 0.961110i | \(-0.589064\pi\) | ||||
−0.276167 | + | 0.961110i | \(0.589064\pi\) | |||||||
\(954\) | 12.0839 | − | 20.9299i | 0.391229 | − | 0.677629i | ||||
\(955\) | 0.239455 | + | 0.414748i | 0.00774859 | + | 0.0134209i | ||||
\(956\) | −60.1076 | − | 104.109i | −1.94402 | − | 3.36714i | ||||
\(957\) | 6.55904 | − | 11.3606i | 0.212024 | − | 0.367235i | ||||
\(958\) | 35.7816 | 1.15605 | ||||||||
\(959\) | 2.14629 | + | 28.2958i | 0.0693073 | + | 0.913720i | ||||
\(960\) | 0.268260 | 0.00865805 | ||||||||
\(961\) | 13.0437 | − | 22.5923i | 0.420763 | − | 0.728783i | ||||
\(962\) | 21.7925 | + | 37.7457i | 0.702619 | + | 1.21697i | ||||
\(963\) | 0.614369 | + | 1.06412i | 0.0197978 | + | 0.0342907i | ||||
\(964\) | −26.3741 | + | 45.6813i | −0.849452 | + | 1.47129i | ||||
\(965\) | −10.3513 | −0.333219 | ||||||||
\(966\) | 5.57576 | − | 3.80890i | 0.179397 | − | 0.122549i | ||||
\(967\) | 46.1833 | 1.48515 | 0.742577 | − | 0.669761i | \(-0.233603\pi\) | ||||
0.742577 | + | 0.669761i | \(0.233603\pi\) | |||||||
\(968\) | −6.79669 | + | 11.7722i | −0.218454 | + | 0.378373i | ||||
\(969\) | 23.4862 | + | 40.6792i | 0.754484 | + | 1.30681i | ||||
\(970\) | 2.67509 | + | 4.63338i | 0.0858918 | + | 0.148769i | ||||
\(971\) | 1.11493 | − | 1.93111i | 0.0357797 | − | 0.0619723i | −0.847581 | − | 0.530666i | \(-0.821942\pi\) |
0.883361 | + | 0.468694i | \(0.155275\pi\) | |||||||
\(972\) | 4.51383 | 0.144781 | ||||||||
\(973\) | −51.1028 | − | 24.5528i | −1.63828 | − | 0.787125i | ||||
\(974\) | 68.3459 | 2.18995 | ||||||||
\(975\) | −8.86571 | + | 15.3559i | −0.283930 | + | 0.491781i | ||||
\(976\) | −32.0452 | − | 55.5040i | −1.02574 | − | 1.77664i | ||||
\(977\) | 23.9884 | + | 41.5491i | 0.767456 | + | 1.32927i | 0.938938 | + | 0.344085i | \(0.111811\pi\) |
−0.171482 | + | 0.985187i | \(0.554856\pi\) | |||||||
\(978\) | 0.590995 | − | 1.02363i | 0.0188979 | − | 0.0327322i | ||||
\(979\) | 46.9257 | 1.49975 | ||||||||
\(980\) | 12.7980 | + | 15.9885i | 0.408816 | + | 0.510735i | ||||
\(981\) | 16.1711 | 0.516302 | ||||||||
\(982\) | 46.1243 | − | 79.8895i | 1.47188 | − | 2.54938i | ||||
\(983\) | 28.2299 | + | 48.8956i | 0.900393 | + | 1.55953i | 0.826985 | + | 0.562224i | \(0.190054\pi\) |
0.0734081 | + | 0.997302i | \(0.476612\pi\) | |||||||
\(984\) | −0.623853 | − | 1.08054i | −0.0198877 | − | 0.0344465i | ||||
\(985\) | 3.07939 | − | 5.33365i | 0.0981174 | − | 0.169944i | ||||
\(986\) | −75.6324 | −2.40863 | ||||||||
\(987\) | 5.93410 | + | 2.85108i | 0.188884 | + | 0.0907510i | ||||
\(988\) | 121.932 | 3.87918 | ||||||||
\(989\) | −0.687938 | + | 1.19154i | −0.0218752 | + | 0.0378889i | ||||
\(990\) | −2.46495 | − | 4.26942i | −0.0783412 | − | 0.135691i | ||||
\(991\) | −11.6212 | − | 20.1286i | −0.369161 | − | 0.639405i | 0.620274 | − | 0.784385i | \(-0.287021\pi\) |
−0.989435 | + | 0.144980i | \(0.953688\pi\) | |||||||
\(992\) | 6.56019 | − | 11.3626i | 0.208286 | − | 0.360762i | ||||
\(993\) | 22.5766 | 0.716447 | ||||||||
\(994\) | −85.0242 | + | 58.0816i | −2.69680 | + | 1.84224i | ||||
\(995\) | −10.7979 | −0.342316 | ||||||||
\(996\) | −33.0142 | + | 57.1822i | −1.04609 | + | 1.81189i | ||||
\(997\) | 27.8638 | + | 48.2615i | 0.882454 | + | 1.52846i | 0.848604 | + | 0.529029i | \(0.177444\pi\) |
0.0338505 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(998\) | 48.5331 | + | 84.0618i | 1.53629 | + | 2.66093i | ||||
\(999\) | 2.20547 | − | 3.81998i | 0.0697778 | − | 0.120859i |
(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 | 483.2.i.g.415.8 | yes | 16 | |
7.2 | even | 3 | 3381.2.a.bf.1.1 | 8 | |||
7.4 | even | 3 | inner | 483.2.i.g.277.8 | ✓ | 16 | |
7.5 | odd | 6 | 3381.2.a.be.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.g.277.8 | ✓ | 16 | 7.4 | even | 3 | inner | |
483.2.i.g.415.8 | yes | 16 | 1.1 | even | 1 | trivial | |
3381.2.a.be.1.1 | 8 | 7.5 | odd | 6 | |||
3381.2.a.bf.1.1 | 8 | 7.2 | even | 3 |