Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(19,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.gh (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 262.4 | ||
Character | \(\chi\) | \(=\) | 819.262 |
Dual form | 819.2.gh.d.397.4 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.306419 | − | 1.14357i | −0.216671 | − | 0.808627i | −0.985572 | − | 0.169259i | \(-0.945863\pi\) |
0.768901 | − | 0.639368i | \(-0.220804\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.518187 | − | 0.299176i | 0.259094 | − | 0.149588i | ||||
\(5\) | 0.424345 | − | 1.58368i | 0.189773 | − | 0.708243i | −0.803785 | − | 0.594920i | \(-0.797184\pi\) |
0.993558 | − | 0.113323i | \(-0.0361495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65856 | − | 2.06135i | 0.626878 | − | 0.779118i | ||||
\(8\) | −2.17522 | − | 2.17522i | −0.769055 | − | 0.769055i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.94108 | −0.613823 | ||||||||
\(11\) | −2.06227 | − | 2.06227i | −0.621799 | − | 0.621799i | 0.324192 | − | 0.945991i | \(-0.394907\pi\) |
−0.945991 | + | 0.324192i | \(0.894907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.68202 | + | 2.40972i | −0.743860 | + | 0.668336i | ||||
\(14\) | −2.86552 | − | 1.26505i | −0.765842 | − | 0.338098i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.22264 | + | 2.11767i | −0.305659 | + | 0.529417i | ||||
\(17\) | 0.405682 | + | 0.702662i | 0.0983923 | + | 0.170420i | 0.911019 | − | 0.412364i | \(-0.135297\pi\) |
−0.812627 | + | 0.582784i | \(0.801963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.56252 | − | 4.56252i | −1.04671 | − | 1.04671i | −0.998854 | − | 0.0478587i | \(-0.984760\pi\) |
−0.0478587 | − | 0.998854i | \(-0.515240\pi\) | |||||||
\(20\) | −0.253908 | − | 0.947596i | −0.0567755 | − | 0.211889i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.72644 | + | 2.99028i | −0.368078 | + | 0.637529i | ||||
\(23\) | 1.58869 | + | 0.917230i | 0.331265 | + | 0.191256i | 0.656402 | − | 0.754411i | \(-0.272077\pi\) |
−0.325138 | + | 0.945667i | \(0.605411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00216 | + | 1.15595i | 0.400432 | + | 0.231189i | ||||
\(26\) | 3.57751 | + | 2.32870i | 0.701608 | + | 0.456696i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.242740 | − | 1.56437i | 0.0458736 | − | 0.295638i | ||||
\(29\) | 2.42827 | + | 4.20589i | 0.450918 | + | 0.781013i | 0.998443 | − | 0.0557760i | \(-0.0177633\pi\) |
−0.547525 | + | 0.836789i | \(0.684430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.78817 | − | 1.01504i | 0.680376 | − | 0.182306i | 0.0979517 | − | 0.995191i | \(-0.468771\pi\) |
0.582424 | + | 0.812885i | \(0.302104\pi\) | |||||||
\(32\) | −3.14646 | − | 0.843090i | −0.556220 | − | 0.149039i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.679235 | − | 0.679235i | 0.116488 | − | 0.116488i | ||||
\(35\) | −2.56071 | − | 3.50136i | −0.432840 | − | 0.591837i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.95665 | − | 1.06018i | 0.650470 | − | 0.174293i | 0.0815285 | − | 0.996671i | \(-0.474020\pi\) |
0.568941 | + | 0.822378i | \(0.307353\pi\) | |||||||
\(38\) | −3.81952 | + | 6.61561i | −0.619608 | + | 1.07319i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.36789 | + | 2.52180i | −0.690624 | + | 0.398732i | ||||
\(41\) | −0.392080 | + | 1.46326i | −0.0612326 | + | 0.228523i | −0.989760 | − | 0.142740i | \(-0.954409\pi\) |
0.928528 | + | 0.371263i | \(0.121075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.14648 | − | 1.23927i | −0.327335 | − | 0.188987i | 0.327322 | − | 0.944913i | \(-0.393854\pi\) |
−0.654657 | + | 0.755926i | \(0.727187\pi\) | |||||||
\(44\) | −1.68563 | − | 0.451662i | −0.254118 | − | 0.0680906i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.562114 | − | 2.09784i | 0.0828791 | − | 0.309309i | ||||
\(47\) | 1.21631 | + | 0.325908i | 0.177417 | + | 0.0475386i | 0.346434 | − | 0.938075i | \(-0.387393\pi\) |
−0.169017 | + | 0.985613i | \(0.554059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.49834 | − | 6.83776i | −0.214048 | − | 0.976823i | ||||
\(50\) | 0.708408 | − | 2.64382i | 0.100184 | − | 0.373892i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.668861 | + | 2.05108i | −0.0927544 | + | 0.284434i | ||||
\(53\) | 1.12609 | − | 1.95045i | 0.154681 | − | 0.267915i | −0.778262 | − | 0.627940i | \(-0.783898\pi\) |
0.932943 | + | 0.360025i | \(0.117232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.14109 | + | 2.39086i | −0.558385 | + | 0.322384i | ||||
\(56\) | −8.09162 | + | 0.876152i | −1.08129 | + | 0.117081i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.06566 | − | 4.06566i | 0.533848 | − | 0.533848i | ||||
\(59\) | −6.46664 | − | 1.73273i | −0.841885 | − | 0.225582i | −0.187993 | − | 0.982170i | \(-0.560198\pi\) |
−0.653892 | + | 0.756588i | \(0.726865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.516055i | 0.0660741i | 0.999454 | + | 0.0330370i | \(0.0105179\pi\) | ||||
−0.999454 | + | 0.0330370i | \(0.989482\pi\) | |||||||
\(62\) | −2.32154 | − | 4.02102i | −0.294836 | − | 0.510670i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.74708i | 1.09339i | ||||||||
\(65\) | 2.67812 | + | 5.27002i | 0.332180 | + | 0.653665i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.11247 | − | 9.11247i | 1.11327 | − | 1.11327i | 0.120560 | − | 0.992706i | \(-0.461531\pi\) |
0.992706 | − | 0.120560i | \(-0.0384689\pi\) | |||||||
\(68\) | 0.420438 | + | 0.242740i | 0.0509856 | + | 0.0294366i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.21940 | + | 4.00124i | −0.384792 | + | 0.478240i | ||||
\(71\) | 2.21845 | + | 8.27936i | 0.263281 | + | 0.982580i | 0.963294 | + | 0.268449i | \(0.0865111\pi\) |
−0.700012 | + | 0.714131i | \(0.746822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.64503 | − | 9.87139i | −0.309578 | − | 1.15536i | −0.928933 | − | 0.370248i | \(-0.879273\pi\) |
0.619355 | − | 0.785111i | \(-0.287394\pi\) | |||||||
\(74\) | −2.42479 | − | 4.19986i | −0.281876 | − | 0.488223i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72923 | − | 0.999244i | −0.427772 | − | 0.114621i | ||||
\(77\) | −7.67148 | + | 0.830660i | −0.874246 | + | 0.0946625i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.17152 | − | 3.76119i | −0.244315 | − | 0.423167i | 0.717623 | − | 0.696431i | \(-0.245230\pi\) |
−0.961939 | + | 0.273265i | \(0.911897\pi\) | |||||||
\(80\) | 2.83489 | + | 2.83489i | 0.316950 | + | 0.316950i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.79349 | 0.198058 | ||||||||
\(83\) | −7.44835 | − | 7.44835i | −0.817563 | − | 0.817563i | 0.168191 | − | 0.985754i | \(-0.446207\pi\) |
−0.985754 | + | 0.168191i | \(0.946207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.28494 | − | 0.344298i | 0.139371 | − | 0.0373444i | ||||
\(86\) | −0.759473 | + | 2.83439i | −0.0818961 | + | 0.305640i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.97178i | 0.956395i | ||||||||
\(89\) | 2.18907 | + | 8.16973i | 0.232041 | + | 0.865989i | 0.979460 | + | 0.201637i | \(0.0646260\pi\) |
−0.747419 | + | 0.664353i | \(0.768707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.518974 | + | 9.52526i | 0.0544033 | + | 0.998519i | ||||
\(92\) | 1.09765 | 0.114438 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1.49080i | − | 0.153764i | ||||||
\(95\) | −9.16164 | + | 5.28948i | −0.939964 | + | 0.542689i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5763 | + | 4.44161i | −1.68307 | + | 0.450978i | −0.968587 | − | 0.248674i | \(-0.920005\pi\) |
−0.714484 | + | 0.699652i | \(0.753339\pi\) | |||||||
\(98\) | −7.36035 | + | 3.80868i | −0.743508 | + | 0.384735i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.38332 | 0.138332 | ||||||||
\(101\) | 15.2229 | 1.51473 | 0.757365 | − | 0.652992i | \(-0.226486\pi\) | ||||
0.757365 | + | 0.652992i | \(0.226486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.54491 | + | 14.8002i | 0.841955 | + | 1.45831i | 0.888240 | + | 0.459380i | \(0.151928\pi\) |
−0.0462849 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(104\) | 11.0756 | + | 0.592320i | 1.08606 | + | 0.0580817i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.57554 | − | 0.690114i | −0.250159 | − | 0.0670298i | ||||
\(107\) | 8.82716 | − | 15.2891i | 0.853354 | − | 1.47805i | −0.0248100 | − | 0.999692i | \(-0.507898\pi\) |
0.878164 | − | 0.478360i | \(-0.158769\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21695 | − | 8.27379i | −0.212346 | − | 0.792485i | −0.987084 | − | 0.160203i | \(-0.948785\pi\) |
0.774738 | − | 0.632282i | \(-0.217882\pi\) | |||||||
\(110\) | 4.00303 | + | 4.00303i | 0.381674 | + | 0.381674i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.33744 | + | 6.03257i | 0.220867 | + | 0.570024i | ||||
\(113\) | 0.708253 | − | 1.22673i | 0.0666268 | − | 0.115401i | −0.830788 | − | 0.556589i | \(-0.812110\pi\) |
0.897414 | + | 0.441188i | \(0.145443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.12675 | − | 2.12675i | 0.198320 | − | 0.198320i | ||||
\(116\) | 2.51660 | + | 1.45296i | 0.233660 | + | 0.134904i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.92601i | 0.729649i | ||||||||
\(119\) | 2.12128 | + | 0.329156i | 0.194458 | + | 0.0301736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.49406i | − | 0.226733i | ||||||
\(122\) | 0.590146 | − | 0.158129i | 0.0534293 | − | 0.0143163i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.65931 | − | 1.65931i | 0.149010 | − | 0.149010i | ||||
\(125\) | 8.47692 | − | 8.47692i | 0.758199 | − | 0.758199i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.29671 | + | 3.05806i | −0.470007 | + | 0.271359i | −0.716243 | − | 0.697851i | \(-0.754140\pi\) |
0.246236 | + | 0.969210i | \(0.420806\pi\) | |||||||
\(128\) | 3.71001 | − | 0.994093i | 0.327921 | − | 0.0878662i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.20602 | − | 4.67745i | 0.456598 | − | 0.410240i | ||||
\(131\) | 14.8958 | − | 8.60009i | 1.30145 | − | 0.751393i | 0.320798 | − | 0.947148i | \(-0.396049\pi\) |
0.980653 | + | 0.195755i | \(0.0627156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.9722 | + | 1.83773i | −1.47167 | + | 0.159351i | ||||
\(134\) | −13.2130 | − | 7.62853i | −1.14143 | − | 0.659005i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.645995 | − | 2.41089i | 0.0553936 | − | 0.206732i | ||||
\(137\) | −4.40600 | + | 16.4434i | −0.376430 | + | 1.40486i | 0.474814 | + | 0.880086i | \(0.342515\pi\) |
−0.851244 | + | 0.524770i | \(0.824151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.74248 | + | 5.62482i | 0.826346 | + | 0.477091i | 0.852600 | − | 0.522564i | \(-0.175024\pi\) |
−0.0262538 | + | 0.999655i | \(0.508358\pi\) | |||||||
\(140\) | −2.37445 | − | 1.04825i | −0.200678 | − | 0.0885937i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.78827 | − | 5.07391i | 0.737495 | − | 0.425793i | ||||
\(143\) | 10.5006 | + | 0.561565i | 0.878101 | + | 0.0469604i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.69120 | − | 2.06085i | 0.638719 | − | 0.171144i | ||||
\(146\) | −10.4782 | + | 6.04957i | −0.867179 | + | 0.500666i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.73311 | − | 1.73311i | 0.142461 | − | 0.142461i | ||||
\(149\) | 16.6802 | − | 16.6802i | 1.36649 | − | 1.36649i | 0.501107 | − | 0.865386i | \(-0.332926\pi\) |
0.865386 | − | 0.501107i | \(-0.167074\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.75102 | + | 0.469184i | −0.142496 | + | 0.0381817i | −0.329362 | − | 0.944204i | \(-0.606834\pi\) |
0.186866 | + | 0.982385i | \(0.440167\pi\) | |||||||
\(152\) | 19.8489i | 1.60996i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.30061 | + | 8.51836i | 0.265970 | + | 0.686429i | ||||
\(155\) | − | 6.42998i | − | 0.516468i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0225395 | − | 0.0130132i | −0.00179885 | − | 0.00103857i | 0.499100 | − | 0.866544i | \(-0.333664\pi\) |
−0.500899 | + | 0.865506i | \(0.666997\pi\) | |||||||
\(158\) | −3.63579 | + | 3.63579i | −0.289248 | + | 0.289248i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.67037 | + | 4.62521i | −0.211111 | + | 0.365655i | ||||
\(161\) | 4.52567 | − | 1.75356i | 0.356673 | − | 0.138200i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2030 | + | 12.2030i | 0.955814 | + | 0.955814i | 0.999064 | − | 0.0432504i | \(-0.0137713\pi\) |
−0.0432504 | + | 0.999064i | \(0.513771\pi\) | |||||||
\(164\) | 0.234602 | + | 0.875545i | 0.0183193 | + | 0.0683686i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.23541 | + | 10.8000i | −0.483962 | + | 0.838246i | ||||
\(167\) | −8.63919 | − | 2.31486i | −0.668521 | − | 0.179130i | −0.0914324 | − | 0.995811i | \(-0.529145\pi\) |
−0.577088 | + | 0.816682i | \(0.695811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.38650 | − | 12.9259i | 0.106654 | − | 0.994296i | ||||
\(170\) | −0.787460 | − | 1.36392i | −0.0603954 | − | 0.104608i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.48304 | −0.113081 | ||||||||
\(173\) | −19.0267 | −1.44657 | −0.723287 | − | 0.690548i | \(-0.757369\pi\) | ||||
−0.723287 | + | 0.690548i | \(0.757369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.70352 | − | 2.20994i | 0.431145 | − | 0.167056i | ||||
\(176\) | 6.88862 | − | 1.84580i | 0.519249 | − | 0.139132i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.67189 | − | 5.00672i | 0.649986 | − | 0.375270i | ||||
\(179\) | − | 21.5069i | − | 1.60750i | −0.594967 | − | 0.803750i | \(-0.702835\pi\) | ||
0.594967 | − | 0.803750i | \(-0.297165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.08778 | −0.452501 | −0.226250 | − | 0.974069i | \(-0.572647\pi\) | ||||
−0.226250 | + | 0.974069i | \(0.572647\pi\) | |||||||
\(182\) | 10.7338 | − | 3.51221i | 0.795642 | − | 0.260342i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.46057 | − | 5.45092i | −0.107675 | − | 0.401847i | ||||
\(185\) | − | 6.71595i | − | 0.493767i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.612453 | − | 2.28571i | 0.0447870 | − | 0.167147i | ||||
\(188\) | 0.727779 | − | 0.195008i | 0.0530787 | − | 0.0142224i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.85620 | + | 8.85620i | 0.642496 | + | 0.642496i | ||||
\(191\) | 26.1213 | 1.89007 | 0.945034 | − | 0.326971i | \(-0.106028\pi\) | ||||
0.945034 | + | 0.326971i | \(0.106028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2997 | + | 15.2997i | 1.10129 | + | 1.10129i | 0.994255 | + | 0.107040i | \(0.0341371\pi\) |
0.107040 | + | 0.994255i | \(0.465863\pi\) | |||||||
\(194\) | 10.1586 | + | 17.5952i | 0.729346 | + | 1.26326i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.82211 | − | 3.09497i | −0.201579 | − | 0.221070i | ||||
\(197\) | −2.18156 | − | 0.584548i | −0.155430 | − | 0.0416473i | 0.180265 | − | 0.983618i | \(-0.442304\pi\) |
−0.335695 | + | 0.941971i | \(0.608971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.41153 | − | 5.90895i | −0.241837 | − | 0.418874i | 0.719400 | − | 0.694596i | \(-0.244417\pi\) |
−0.961238 | + | 0.275721i | \(0.911083\pi\) | |||||||
\(200\) | −1.84069 | − | 6.86956i | −0.130157 | − | 0.485751i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.66457 | − | 17.4084i | −0.328198 | − | 1.22485i | ||||
\(203\) | 12.6972 | + | 1.97021i | 0.891172 | + | 0.138282i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.15096 | + | 1.24186i | 0.150230 | + | 0.0867351i | ||||
\(206\) | 14.3068 | − | 14.3068i | 0.996801 | − | 0.996801i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.82385 | − | 8.62585i | −0.126461 | − | 0.598095i | ||||
\(209\) | 18.8183i | 1.30169i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.270154 | − | 0.467920i | −0.0185982 | − | 0.0322130i | 0.856577 | − | 0.516020i | \(-0.172587\pi\) |
−0.875175 | + | 0.483807i | \(0.839254\pi\) | |||||||
\(212\) | − | 1.34760i | − | 0.0925536i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.1890 | − | 5.40962i | −1.38009 | − | 0.369794i | ||||
\(215\) | −2.87346 | + | 2.87346i | −0.195968 | + | 0.195968i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.19057 | − | 9.49226i | 0.284475 | − | 0.644377i | ||||
\(218\) | −8.78235 | + | 5.07049i | −0.594816 | + | 0.343417i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.43057 | + | 2.47783i | −0.0964493 | + | 0.167055i | ||||
\(221\) | −2.78127 | − | 0.906975i | −0.187088 | − | 0.0610098i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.64421 | − | 6.13628i | 0.110105 | − | 0.410916i | −0.888770 | − | 0.458354i | \(-0.848439\pi\) |
0.998874 | + | 0.0474384i | \(0.0151058\pi\) | |||||||
\(224\) | −6.95650 | + | 5.08763i | −0.464801 | + | 0.339932i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.61988 | − | 0.434044i | −0.107753 | − | 0.0288722i | ||||
\(227\) | −5.68899 | + | 21.2316i | −0.377592 | + | 1.40919i | 0.471929 | + | 0.881636i | \(0.343558\pi\) |
−0.849521 | + | 0.527555i | \(0.823109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.8801 | + | 6.93454i | 1.71020 | + | 0.458247i | 0.975474 | − | 0.220115i | \(-0.0706431\pi\) |
0.734728 | + | 0.678362i | \(0.237310\pi\) | |||||||
\(230\) | −3.08377 | − | 1.78041i | −0.203338 | − | 0.117397i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.86670 | − | 14.4307i | 0.253861 | − | 0.947423i | ||||
\(233\) | 9.35685 | − | 5.40218i | 0.612988 | − | 0.353909i | −0.161146 | − | 0.986931i | \(-0.551519\pi\) |
0.774134 | + | 0.633022i | \(0.218186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.03227 | − | 1.78794i | 0.0673378 | − | 0.116632i | ||||
\(236\) | −3.86932 | + | 1.03678i | −0.251872 | + | 0.0674888i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.273588 | − | 2.52670i | −0.0177341 | − | 0.163781i | ||||
\(239\) | 20.4504 | − | 20.4504i | 1.32282 | − | 1.32282i | 0.411345 | − | 0.911480i | \(-0.365059\pi\) |
0.911480 | − | 0.411345i | \(-0.134941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.71785 | − | 2.06799i | −0.497150 | − | 0.133211i | 0.00152691 | − | 0.999999i | \(-0.499514\pi\) |
−0.498677 | + | 0.866788i | \(0.666181\pi\) | |||||||
\(242\) | −2.85214 | + | 0.764227i | −0.183342 | + | 0.0491264i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.154391 | + | 0.267413i | 0.00988388 | + | 0.0171194i | ||||
\(245\) | −11.4646 | − | 0.528686i | −0.732448 | − | 0.0337765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.2312 | + | 1.24239i | 1.47816 | + | 0.0790514i | ||||
\(248\) | −10.4480 | − | 6.03217i | −0.663450 | − | 0.383043i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.2915 | − | 7.09648i | −0.777380 | − | 0.448821i | ||||
\(251\) | −3.59872 | + | 6.23316i | −0.227149 | + | 0.393434i | −0.956962 | − | 0.290213i | \(-0.906274\pi\) |
0.729813 | + | 0.683647i | \(0.239607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.38473 | − | 5.16789i | −0.0870573 | − | 0.324902i | ||||
\(254\) | 5.12012 | + | 5.12012i | 0.321265 | + | 0.321265i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.47345 | + | 11.2123i | 0.404591 | + | 0.700772i | ||||
\(257\) | −9.95744 | + | 17.2468i | −0.621128 | + | 1.07583i | 0.368148 | + | 0.929767i | \(0.379992\pi\) |
−0.989276 | + | 0.146058i | \(0.953341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.37695 | − | 9.91443i | 0.271970 | − | 0.616053i | ||||
\(260\) | 2.96443 | + | 1.92963i | 0.183846 | + | 0.119670i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.3992 | − | 14.3992i | −0.889584 | − | 0.889584i | ||||
\(263\) | −13.6905 | −0.844194 | −0.422097 | − | 0.906551i | \(-0.638706\pi\) | ||||
−0.422097 | + | 0.906551i | \(0.638706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.61104 | − | 2.61104i | −0.160395 | − | 0.160395i | ||||
\(266\) | 7.30217 | + | 18.8458i | 0.447725 | + | 1.15551i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.99574 | − | 7.44820i | 0.121909 | − | 0.454971i | ||||
\(269\) | 1.73392 | − | 1.00108i | 0.105719 | − | 0.0610368i | −0.446208 | − | 0.894929i | \(-0.647226\pi\) |
0.551927 | + | 0.833892i | \(0.313893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.53795 | + | 20.6679i | 0.336407 | + | 1.25549i | 0.902336 | + | 0.431033i | \(0.141851\pi\) |
−0.565930 | + | 0.824454i | \(0.691483\pi\) | |||||||
\(272\) | −1.98401 | −0.120298 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.1543 | 1.21757 | ||||||||
\(275\) | −1.74512 | − | 6.51287i | −0.105235 | − | 0.392741i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3585 | + | 8.86722i | −0.922801 | + | 0.532780i | −0.884528 | − | 0.466488i | \(-0.845519\pi\) |
−0.0382736 | + | 0.999267i | \(0.512186\pi\) | |||||||
\(278\) | 3.44711 | − | 12.8648i | 0.206744 | − | 0.771578i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.04610 | + | 13.1863i | −0.122278 | + | 0.788033i | ||||
\(281\) | 20.0393 | + | 20.0393i | 1.19545 | + | 1.19545i | 0.975515 | + | 0.219932i | \(0.0705834\pi\) |
0.219932 | + | 0.975515i | \(0.429417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.43296 | 0.441843 | 0.220922 | − | 0.975292i | \(-0.429093\pi\) | ||||
0.220922 | + | 0.975292i | \(0.429093\pi\) | |||||||
\(284\) | 3.62656 | + | 3.62656i | 0.215196 | + | 0.215196i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.57538 | − | 12.1802i | −0.152286 | − | 0.720232i | ||||
\(287\) | 2.36601 | + | 3.23513i | 0.139661 | + | 0.190964i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17084 | − | 14.1523i | 0.480638 | − | 0.832489i | ||||
\(290\) | −4.71346 | − | 8.16395i | −0.276784 | − | 0.479404i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.32390 | − | 4.32390i | −0.253037 | − | 0.253037i | ||||
\(293\) | 1.93278 | + | 7.21323i | 0.112914 | + | 0.421401i | 0.999122 | − | 0.0418859i | \(-0.0133366\pi\) |
−0.886208 | + | 0.463287i | \(0.846670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.48818 | + | 9.50581i | −0.319534 | + | 0.553450i | ||||
\(296\) | −10.9127 | − | 6.30045i | −0.634288 | − | 0.366206i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.1861 | − | 13.9638i | −1.40106 | − | 0.808904i | ||||
\(299\) | −6.47117 | + | 1.36826i | −0.374237 | + | 0.0791287i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.11465 | + | 2.36924i | −0.352442 | + | 0.136561i | ||||
\(302\) | 1.07309 | + | 1.85865i | 0.0617495 | + | 0.106953i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.2402 | − | 4.08360i | 0.874085 | − | 0.234210i | ||||
\(305\) | 0.817265 | + | 0.218986i | 0.0467965 | + | 0.0125391i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3746 | − | 14.3746i | 0.820400 | − | 0.820400i | −0.165765 | − | 0.986165i | \(-0.553009\pi\) |
0.986165 | + | 0.165765i | \(0.0530094\pi\) | |||||||
\(308\) | −3.72675 | + | 2.72556i | −0.212351 | + | 0.155303i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.35314 | + | 1.97027i | −0.417630 | + | 0.111904i | ||||
\(311\) | −2.05346 | + | 3.55670i | −0.116441 | + | 0.201682i | −0.918355 | − | 0.395758i | \(-0.870482\pi\) |
0.801914 | + | 0.597440i | \(0.203815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5196 | + | 11.8470i | −1.15984 | + | 0.669632i | −0.951265 | − | 0.308375i | \(-0.900215\pi\) |
−0.208572 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(314\) | −0.00797499 | + | 0.0297631i | −0.000450055 | + | 0.00167963i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.25051 | − | 1.29933i | −0.126601 | − | 0.0730932i | ||||
\(317\) | 10.7209 | + | 2.87265i | 0.602144 | + | 0.161344i | 0.546998 | − | 0.837134i | \(-0.315771\pi\) |
0.0551466 | + | 0.998478i | \(0.482437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.66593 | − | 13.6814i | 0.205253 | − | 0.766013i | ||||
\(320\) | 13.8526 | + | 3.71178i | 0.774382 | + | 0.207495i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.39208 | − | 4.63811i | −0.189033 | − | 0.258472i | ||||
\(323\) | 1.35497 | − | 5.05683i | 0.0753928 | − | 0.281370i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.15534 | + | 1.72436i | −0.452377 | + | 0.0956505i | ||||
\(326\) | 10.2158 | − | 17.6943i | 0.565800 | − | 0.979994i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.03577 | − | 2.33005i | 0.222838 | − | 0.128656i | ||||
\(329\) | 2.68913 | − | 1.96670i | 0.148257 | − | 0.108427i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2743 | + | 10.2743i | −0.564729 | + | 0.564729i | −0.930647 | − | 0.365918i | \(-0.880755\pi\) |
0.365918 | + | 0.930647i | \(0.380755\pi\) | |||||||
\(332\) | −6.08801 | − | 1.63128i | −0.334123 | − | 0.0895280i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5889i | 0.579396i | ||||||||
\(335\) | −10.5644 | − | 18.2981i | −0.577194 | − | 0.999730i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.20930i | 0.447189i | 0.974682 | + | 0.223594i | \(0.0717791\pi\) | ||||
−0.974682 | + | 0.223594i | \(0.928221\pi\) | |||||||
\(338\) | −15.2065 | + | 2.37516i | −0.827124 | + | 0.129192i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.562834 | − | 0.562834i | 0.0305239 | − | 0.0305239i | ||||
\(341\) | −9.90553 | − | 5.71896i | −0.536415 | − | 0.309699i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.5801 | − | 8.25225i | −0.895242 | − | 0.445580i | ||||
\(344\) | 1.97338 | + | 7.36475i | 0.106397 | + | 0.397080i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.83014 | + | 21.7584i | 0.313430 | + | 1.16974i | ||||
\(347\) | −6.17589 | − | 10.6970i | −0.331539 | − | 0.574243i | 0.651275 | − | 0.758842i | \(-0.274235\pi\) |
−0.982814 | + | 0.184599i | \(0.940901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.95084 | − | 1.05862i | −0.211483 | − | 0.0566668i | 0.151522 | − | 0.988454i | \(-0.451583\pi\) |
−0.363005 | + | 0.931787i | \(0.618249\pi\) | |||||||
\(350\) | −4.27489 | − | 5.84521i | −0.228503 | − | 0.312440i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.75017 | + | 8.22753i | 0.253185 | + | 0.438529i | ||||
\(353\) | −17.6691 | − | 17.6691i | −0.940431 | − | 0.940431i | 0.0578922 | − | 0.998323i | \(-0.481562\pi\) |
−0.998323 | + | 0.0578922i | \(0.981562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0532 | 0.745869 | ||||||||
\(356\) | 3.57853 | + | 3.57853i | 0.189662 | + | 0.189662i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.5947 | + | 6.59012i | −1.29987 | + | 0.348299i | ||||
\(359\) | −5.24373 | + | 19.5699i | −0.276753 | + | 1.03286i | 0.677904 | + | 0.735151i | \(0.262889\pi\) |
−0.954657 | + | 0.297707i | \(0.903778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.6331i | 1.19122i | ||||||||
\(362\) | 1.86541 | + | 6.96181i | 0.0980438 | + | 0.365905i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.11865 | + | 4.78061i | 0.163462 | + | 0.250572i | ||||
\(365\) | −16.7555 | −0.877024 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6562i | 1.18265i | 0.806435 | + | 0.591323i | \(0.201394\pi\) | ||||
−0.806435 | + | 0.591323i | \(0.798606\pi\) | |||||||
\(368\) | −3.88478 | + | 2.24288i | −0.202508 | + | 0.116918i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.68017 | + | 2.05790i | −0.399273 | + | 0.106985i | ||||
\(371\) | −2.15287 | − | 5.55623i | −0.111771 | − | 0.288465i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2022 | −0.787140 | −0.393570 | − | 0.919295i | \(-0.628760\pi\) | ||||
−0.393570 | + | 0.919295i | \(0.628760\pi\) | |||||||
\(374\) | −2.80154 | −0.144864 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.93681 | − | 3.35465i | −0.0998833 | − | 0.173003i | ||||
\(377\) | −16.6477 | − | 5.42884i | −0.857399 | − | 0.279599i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1074 | + | 7.79931i | 1.49515 | + | 0.400623i | 0.911471 | − | 0.411364i | \(-0.134947\pi\) |
0.583676 | + | 0.811987i | \(0.301614\pi\) | |||||||
\(380\) | −3.16496 | + | 5.48188i | −0.162359 | + | 0.281214i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.00406 | − | 29.8715i | −0.409523 | − | 1.52836i | ||||
\(383\) | −2.01992 | − | 2.01992i | −0.103213 | − | 0.103213i | 0.653614 | − | 0.756828i | \(-0.273252\pi\) |
−0.756828 | + | 0.653614i | \(0.773252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.93986 | + | 12.5016i | −0.0988643 | + | 0.637143i | ||||
\(386\) | 12.8082 | − | 22.1844i | 0.651918 | − | 1.12916i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.26082 | + | 7.26082i | −0.368612 | + | 0.368612i | ||||
\(389\) | 8.56918 | + | 4.94742i | 0.434474 | + | 0.250844i | 0.701251 | − | 0.712914i | \(-0.252625\pi\) |
−0.266777 | + | 0.963758i | \(0.585959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.48841i | 0.0752723i | ||||||||
\(392\) | −11.6144 | + | 18.1328i | −0.586616 | + | 0.915846i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.67389i | 0.134709i | ||||||||
\(395\) | −6.87799 | + | 1.84295i | −0.346069 | + | 0.0927290i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.23489 | + | 8.23489i | −0.413297 | + | 0.413297i | −0.882886 | − | 0.469588i | \(-0.844402\pi\) |
0.469588 | + | 0.882886i | \(0.344402\pi\) | |||||||
\(398\) | −5.71195 | + | 5.71195i | −0.286314 | + | 0.286314i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.89582 | + | 2.82661i | −0.244791 | + | 0.141330i | ||||
\(401\) | −8.23517 | + | 2.20661i | −0.411245 | + | 0.110193i | −0.458509 | − | 0.888690i | \(-0.651616\pi\) |
0.0472642 | + | 0.998882i | \(0.484950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.71401 | + | 11.8508i | −0.384262 | + | 0.590330i | ||||
\(404\) | 7.88829 | − | 4.55431i | 0.392457 | − | 0.226585i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.63760 | − | 15.1239i | −0.0812728 | − | 0.750587i | ||||
\(407\) | −10.3461 | − | 5.97332i | −0.512836 | − | 0.296086i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.67045 | + | 28.6265i | −0.379280 | + | 1.41549i | 0.467710 | + | 0.883882i | \(0.345079\pi\) |
−0.846990 | + | 0.531609i | \(0.821588\pi\) | |||||||
\(410\) | 0.761058 | − | 2.84031i | 0.0375860 | − | 0.140273i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.85573 | + | 5.11286i | 0.436290 | + | 0.251892i | ||||
\(413\) | −14.2971 | + | 10.4562i | −0.703514 | + | 0.514515i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9565 | + | 8.63512i | −0.734184 | + | 0.423882i | ||||
\(416\) | 10.4705 | − | 5.32089i | 0.513358 | − | 0.260878i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.5201 | − | 5.76629i | 1.05258 | − | 0.282038i | ||||
\(419\) | −5.87227 | + | 3.39035i | −0.286879 | + | 0.165630i | −0.636533 | − | 0.771249i | \(-0.719632\pi\) |
0.349655 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.568530 | + | 0.568530i | −0.0277084 | + | 0.0277084i | −0.720825 | − | 0.693117i | \(-0.756237\pi\) |
0.693117 | + | 0.720825i | \(0.256237\pi\) | |||||||
\(422\) | −0.452320 | + | 0.452320i | −0.0220186 | + | 0.0220186i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.69216 | + | 1.79316i | −0.325000 | + | 0.0870835i | ||||
\(425\) | 1.87579i | 0.0909890i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.06377 | + | 0.855910i | 0.0514795 | + | 0.0414204i | ||||
\(428\) | − | 10.5635i | − | 0.510605i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.16649 | + | 2.40552i | 0.200926 | + | 0.116005i | ||||
\(431\) | 27.9494 | − | 27.9494i | 1.34628 | − | 1.34628i | 0.456609 | − | 0.889668i | \(-0.349064\pi\) |
0.889668 | − | 0.456609i | \(-0.150936\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.52576 | + | 11.3030i | −0.313608 | + | 0.543185i | −0.979141 | − | 0.203184i | \(-0.934871\pi\) |
0.665533 | + | 0.746369i | \(0.268204\pi\) | |||||||
\(434\) | −12.1392 | − | 1.88361i | −0.582698 | − | 0.0904162i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.62411 | − | 3.62411i | −0.173564 | − | 0.173564i | ||||
\(437\) | −3.06354 | − | 11.4333i | −0.146549 | − | 0.546929i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.52378 | − | 11.2995i | 0.311363 | − | 0.539297i | −0.667295 | − | 0.744794i | \(-0.732548\pi\) |
0.978658 | + | 0.205497i | \(0.0658811\pi\) | |||||||
\(440\) | 14.2084 | + | 3.80713i | 0.677360 | + | 0.181498i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.184958 | + | 3.45849i | −0.00879757 | + | 0.164504i | ||||
\(443\) | −6.21784 | − | 10.7696i | −0.295418 | − | 0.511680i | 0.679664 | − | 0.733524i | \(-0.262126\pi\) |
−0.975082 | + | 0.221844i | \(0.928792\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8671 | 0.657366 | ||||||||
\(446\) | −7.52110 | −0.356134 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.0308 | + | 14.5076i | 0.851876 | + | 0.685419i | ||||
\(449\) | −34.8689 | + | 9.34311i | −1.64557 | + | 0.440928i | −0.958367 | − | 0.285539i | \(-0.907827\pi\) |
−0.687200 | + | 0.726468i | \(0.741161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.82622 | − | 2.20907i | 0.180170 | − | 0.104021i | ||||
\(452\) | − | 0.847568i | − | 0.0398662i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.0231 | 1.22132 | ||||||||
\(455\) | 15.3052 | + | 3.22011i | 0.717518 | + | 0.150961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.53955 | + | 28.1380i | 0.352685 | + | 1.31624i | 0.883372 | + | 0.468672i | \(0.155267\pi\) |
−0.530687 | + | 0.847568i | \(0.678066\pi\) | |||||||
\(458\) | − | 31.7206i | − | 1.48220i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.465783 | − | 1.73833i | 0.0217173 | − | 0.0810499i | ||||
\(461\) | −9.16537 | + | 2.45585i | −0.426874 | + | 0.114381i | −0.465858 | − | 0.884859i | \(-0.654254\pi\) |
0.0389845 | + | 0.999240i | \(0.487588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6084 | − | 20.6084i | −0.957754 | − | 0.957754i | 0.0413889 | − | 0.999143i | \(-0.486822\pi\) |
−0.999143 | + | 0.0413889i | \(0.986822\pi\) | |||||||
\(464\) | −11.8756 | −0.551309 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.04490 | − | 9.04490i | −0.418997 | − | 0.418997i | ||||
\(467\) | 16.5197 | + | 28.6129i | 0.764440 | + | 1.32405i | 0.940542 | + | 0.339677i | \(0.110318\pi\) |
−0.176102 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.67040 | − | 33.8976i | −0.169483 | − | 1.56525i | ||||
\(470\) | −2.36095 | − | 0.632614i | −0.108902 | − | 0.0291803i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.2973 | + | 17.8354i | 0.473971 | + | 0.820942i | ||||
\(473\) | 1.87091 | + | 6.98235i | 0.0860247 | + | 0.321049i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.86085 | − | 14.4089i | −0.177148 | − | 0.661126i | ||||
\(476\) | 1.19770 | − | 0.464071i | 0.0548963 | − | 0.0212707i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.6529 | − | 17.1201i | −1.35629 | − | 0.783054i | ||||
\(479\) | −18.1414 | + | 18.1414i | −0.828903 | + | 0.828903i | −0.987365 | − | 0.158462i | \(-0.949346\pi\) |
0.158462 | + | 0.987365i | \(0.449346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.05710 | + | 12.3779i | −0.367372 | + | 0.564382i | ||||
\(482\) | 9.45958i | 0.430872i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.746162 | − | 1.29239i | −0.0339164 | − | 0.0587450i | ||||
\(485\) | 28.1364i | 1.27761i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.15499 | − | 1.64923i | −0.278909 | − | 0.0747336i | 0.116653 | − | 0.993173i | \(-0.462784\pi\) |
−0.395562 | + | 0.918439i | \(0.629450\pi\) | |||||||
\(488\) | 1.12253 | − | 1.12253i | 0.0508146 | − | 0.0508146i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.90839 | + | 13.2726i | 0.131388 | + | 0.599596i | ||||
\(491\) | −23.9297 | + | 13.8158i | −1.07993 | + | 0.623500i | −0.930878 | − | 0.365329i | \(-0.880956\pi\) |
−0.149055 | + | 0.988829i | \(0.547623\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.97021 | + | 3.41250i | −0.0887338 | + | 0.153691i | ||||
\(494\) | −5.69771 | − | 26.9472i | −0.256352 | − | 1.21241i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.48205 | + | 9.26312i | −0.111447 | + | 0.415926i | ||||
\(497\) | 20.7461 | + | 9.15884i | 0.930590 | + | 0.410830i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.78545 | + | 0.478410i | 0.0799278 | + | 0.0214166i | 0.298561 | − | 0.954390i | \(-0.403493\pi\) |
−0.218634 | + | 0.975807i | \(0.570160\pi\) | |||||||
\(500\) | 1.85654 | − | 6.92872i | 0.0830272 | − | 0.309862i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.23078 | + | 2.20543i | 0.367358 | + | 0.0984332i | ||||
\(503\) | −1.57204 | − | 0.907615i | −0.0700936 | − | 0.0404686i | 0.464544 | − | 0.885550i | \(-0.346218\pi\) |
−0.534637 | + | 0.845082i | \(0.679552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.45975 | − | 24.1081i | 0.287455 | − | 1.07280i | ||||
\(506\) | −5.48554 | + | 3.16708i | −0.243862 | + | 0.140794i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.82979 | + | 3.16929i | −0.0811838 | + | 0.140615i | ||||
\(509\) | 17.3620 | − | 4.65215i | 0.769559 | − | 0.206203i | 0.147382 | − | 0.989080i | \(-0.452915\pi\) |
0.622177 | + | 0.782877i | \(0.286249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7354 | − | 10.9200i | −1.09423 | − | 0.483072i | ||||
\(512\) | 16.2704 | − | 16.2704i | 0.719055 | − | 0.719055i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.7741 | + | 6.10230i | 1.00452 | + | 0.269161i | ||||
\(515\) | 27.0648 | − | 7.25199i | 1.19262 | − | 0.319561i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.83624 | − | 3.18047i | −0.0807580 | − | 0.139877i | ||||
\(518\) | −12.6790 | − | 1.96739i | −0.557085 | − | 0.0864420i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.63794 | − | 17.2889i | 0.247240 | − | 0.758169i | ||||
\(521\) | 13.2345 | + | 7.64094i | 0.579814 | + | 0.334756i | 0.761059 | − | 0.648682i | \(-0.224680\pi\) |
−0.181245 | + | 0.983438i | \(0.558013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9830 | − | 16.1560i | −1.22361 | − | 0.706452i | −0.257925 | − | 0.966165i | \(-0.583039\pi\) |
−0.965686 | + | 0.259713i | \(0.916372\pi\) | |||||||
\(524\) | 5.14587 | − | 8.91291i | 0.224798 | − | 0.389362i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.19504 | + | 15.6561i | 0.182912 | + | 0.682638i | ||||
\(527\) | 2.25002 | + | 2.25002i | 0.0980125 | + | 0.0980125i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.81738 | − | 17.0042i | −0.426843 | − | 0.739313i | ||||
\(530\) | −2.18584 | + | 3.78598i | −0.0949467 | + | 0.164453i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.24496 | + | 6.02995i | −0.357464 | + | 0.261431i | ||||
\(533\) | −2.47449 | − | 4.86931i | −0.107182 | − | 0.210913i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.4672 | − | 20.4672i | −0.884876 | − | 0.884876i | ||||
\(536\) | −39.6432 | −1.71233 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.67611 | − | 1.67611i | −0.0722622 | − | 0.0722622i | ||||
\(539\) | −11.0113 | + | 17.1913i | −0.474292 | + | 0.740482i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.91231 | − | 18.3330i | 0.211197 | − | 0.788197i | −0.776274 | − | 0.630396i | \(-0.782893\pi\) |
0.987471 | − | 0.157802i | \(-0.0504407\pi\) | |||||||
\(542\) | 21.9383 | − | 12.6661i | 0.942331 | − | 0.544055i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.684053 | − | 2.55292i | −0.0293285 | − | 0.109456i | ||||
\(545\) | −14.0438 | −0.601569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.64107 | −0.369465 | −0.184733 | − | 0.982789i | \(-0.559142\pi\) | ||||
−0.184733 | + | 0.982789i | \(0.559142\pi\) | |||||||
\(548\) | 2.63633 | + | 9.83894i | 0.112619 | + | 0.420299i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.91320 | + | 3.99134i | −0.294780 | + | 0.170191i | ||||
\(551\) | 8.11040 | − | 30.2684i | 0.345515 | − | 1.28948i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.3547 | − | 1.76190i | −0.482853 | − | 0.0749234i | ||||
\(554\) | 14.8464 | + | 14.8464i | 0.630764 | + | 0.630764i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.73124 | 0.285468 | ||||||||
\(557\) | 12.8552 | + | 12.8552i | 0.544694 | + | 0.544694i | 0.924901 | − | 0.380207i | \(-0.124147\pi\) |
−0.380207 | + | 0.924901i | \(0.624147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.74321 | − | 1.84866i | 0.369798 | − | 0.0781901i | ||||
\(560\) | 10.5455 | − | 1.14186i | 0.445630 | − | 0.0482524i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.7760 | − | 29.0569i | 0.707652 | − | 1.22569i | ||||
\(563\) | −7.38562 | − | 12.7923i | −0.311267 | − | 0.539130i | 0.667370 | − | 0.744726i | \(-0.267420\pi\) |
−0.978637 | + | 0.205596i | \(0.934087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.64220 | − | 1.64220i | −0.0690880 | − | 0.0690880i | ||||
\(566\) | −2.27760 | − | 8.50012i | −0.0957347 | − | 0.357287i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.1838 | − | 22.8350i | 0.553180 | − | 0.958136i | ||||
\(569\) | 23.1049 | + | 13.3396i | 0.968607 | + | 0.559226i | 0.898811 | − | 0.438335i | \(-0.144432\pi\) |
0.0697961 | + | 0.997561i | \(0.477765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3259 | + | 10.0031i | 0.725067 | + | 0.418618i | 0.816615 | − | 0.577183i | \(-0.195848\pi\) |
−0.0915476 | + | 0.995801i | \(0.529181\pi\) | |||||||
\(572\) | 5.60927 | − | 2.85052i | 0.234535 | − | 0.119186i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.97461 | − | 3.69701i | 0.124158 | − | 0.154310i | ||||
\(575\) | 2.12054 | + | 3.67288i | 0.0884325 | + | 0.153170i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8386 | − | 11.2106i | 1.74177 | − | 0.466705i | 0.758928 | − | 0.651175i | \(-0.225724\pi\) |
0.982838 | + | 0.184470i | \(0.0590569\pi\) | |||||||
\(578\) | −18.6879 | − | 5.00741i | −0.777314 | − | 0.208281i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.36892 | − | 3.36892i | 0.139887 | − | 0.139887i | ||||
\(581\) | −27.7072 | + | 3.00011i | −1.14949 | + | 0.124466i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.34468 | + | 1.70005i | −0.262770 | + | 0.0704090i | ||||
\(584\) | −15.7189 | + | 27.2259i | −0.650453 | + | 1.12662i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.65660 | − | 4.42054i | 0.316291 | − | 0.182611i | ||||
\(587\) | 9.76067 | − | 36.4273i | 0.402866 | − | 1.50352i | −0.405091 | − | 0.914276i | \(-0.632760\pi\) |
0.807958 | − | 0.589241i | \(-0.200573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.9147 | − | 12.6525i | −0.902980 | − | 0.521336i | ||||
\(590\) | 12.5523 | + | 3.36337i | 0.516768 | + | 0.138468i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.59244 | + | 9.67510i | −0.106548 | + | 0.397644i | ||||
\(593\) | −10.7514 | − | 2.88084i | −0.441508 | − | 0.118302i | 0.0312150 | − | 0.999513i | \(-0.490062\pi\) |
−0.472723 | + | 0.881211i | \(0.656729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.42143 | − | 3.21975i | 0.0582731 | − | 0.131997i | ||||
\(596\) | 3.65315 | − | 13.6337i | 0.149639 | − | 0.558460i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.54760 | + | 6.98098i | 0.145072 | + | 0.285474i | ||||
\(599\) | −10.6818 | + | 18.5015i | −0.436447 | + | 0.755949i | −0.997413 | − | 0.0718904i | \(-0.977097\pi\) |
0.560965 | + | 0.827839i | \(0.310430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0625 | − | 7.54164i | 0.532830 | − | 0.307630i | −0.209338 | − | 0.977843i | \(-0.567131\pi\) |
0.742168 | + | 0.670214i | \(0.233798\pi\) | |||||||
\(602\) | 4.58304 | + | 6.26656i | 0.186791 | + | 0.255406i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.766987 | + | 0.766987i | −0.0312083 | + | 0.0312083i | ||||
\(605\) | −3.94979 | − | 1.05834i | −0.160582 | − | 0.0430277i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 44.7577i | − | 1.81666i | −0.418254 | − | 0.908330i | \(-0.637358\pi\) | ||
0.418254 | − | 0.908330i | \(-0.362642\pi\) | |||||||
\(608\) | 10.5091 | + | 18.2024i | 0.426202 | + | 0.738203i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 1.00170i | − | 0.0405578i | ||||||
\(611\) | −4.04751 | + | 2.05686i | −0.163745 | + | 0.0832118i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.0127 | + | 32.0127i | −1.29298 | + | 1.29298i | −0.360044 | + | 0.932935i | \(0.617238\pi\) |
−0.932935 | + | 0.360044i | \(0.882762\pi\) | |||||||
\(614\) | −20.8430 | − | 12.0337i | −0.841155 | − | 0.485641i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.4940 | + | 14.8803i | 0.745144 | + | 0.599543i | ||||
\(617\) | −6.09471 | − | 22.7458i | −0.245364 | − | 0.915710i | −0.973200 | − | 0.229959i | \(-0.926141\pi\) |
0.727837 | − | 0.685751i | \(-0.240526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.944826 | − | 3.52614i | −0.0379758 | − | 0.141727i | 0.944335 | − | 0.328985i | \(-0.106707\pi\) |
−0.982311 | + | 0.187258i | \(0.940040\pi\) | |||||||
\(620\) | −1.92369 | − | 3.33193i | −0.0772573 | − | 0.133814i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.69656 | + | 1.25844i | 0.188315 | + | 0.0504588i | ||||
\(623\) | 20.4714 | + | 9.03756i | 0.820169 | + | 0.362082i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.04784 | − | 7.01107i | −0.161914 | − | 0.280443i | ||||
\(626\) | 19.8355 | + | 19.8355i | 0.792786 | + | 0.792786i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0155729 | −0.000621427 | ||||||||
\(629\) | 2.35009 | + | 2.35009i | 0.0937043 | + | 0.0937043i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.03886 | + | 2.42196i | −0.359831 | + | 0.0964165i | −0.434205 | − | 0.900814i | \(-0.642971\pi\) |
0.0743741 | + | 0.997230i | \(0.476304\pi\) | |||||||
\(632\) | −3.45787 | + | 12.9049i | −0.137547 | + | 0.513331i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 13.1403i | − | 0.521869i | ||||||
\(635\) | 2.59534 | + | 9.68595i | 0.102993 | + | 0.384375i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.4957 | + | 14.7285i | 0.812068 | + | 0.583563i | ||||
\(638\) | −16.7690 | −0.663892 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 6.29729i | − | 0.248922i | ||||||
\(641\) | −7.59400 | + | 4.38440i | −0.299945 | + | 0.173173i | −0.642418 | − | 0.766354i | \(-0.722069\pi\) |
0.342473 | + | 0.939528i | \(0.388735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.4077 | − | 12.4349i | 1.83014 | − | 0.490384i | 0.832196 | − | 0.554481i | \(-0.187083\pi\) |
0.997944 | + | 0.0640969i | \(0.0204167\pi\) | |||||||
\(644\) | 1.82052 | − | 2.26264i | 0.0717387 | − | 0.0891607i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.19804 | −0.243859 | ||||||||
\(647\) | 13.7843 | 0.541918 | 0.270959 | − | 0.962591i | \(-0.412659\pi\) | ||||
0.270959 | + | 0.962591i | \(0.412659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.76262 | + | 16.9094i | 0.383216 | + | 0.663750i | ||||
\(650\) | 4.47089 | + | 8.79784i | 0.175363 | + | 0.345080i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.97429 | + | 2.67260i | 0.390623 | + | 0.104667i | ||||
\(653\) | 20.3999 | − | 35.3337i | 0.798311 | − | 1.38271i | −0.122405 | − | 0.992480i | \(-0.539061\pi\) |
0.920716 | − | 0.390234i | \(-0.127606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.29881 | − | 27.2395i | −0.285188 | − | 1.06434i | ||||
\(656\) | −2.61934 | − | 2.61934i | −0.102268 | − | 0.102268i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.07306 | − | 2.47258i | −0.119800 | − | 0.0963913i | ||||
\(659\) | 10.0428 | − | 17.3947i | 0.391213 | − | 0.677601i | −0.601396 | − | 0.798951i | \(-0.705389\pi\) |
0.992610 | + | 0.121349i | \(0.0387221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.18282 | + | 6.18282i | −0.240484 | + | 0.240484i | −0.817050 | − | 0.576566i | \(-0.804392\pi\) |
0.576566 | + | 0.817050i | \(0.304392\pi\) | |||||||
\(662\) | 14.8977 | + | 8.60119i | 0.579016 | + | 0.334295i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.4036i | 1.25750i | ||||||||
\(665\) | −4.29169 | + | 27.6583i | −0.166425 | + | 1.07254i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.90912i | 0.344963i | ||||||||
\(668\) | −5.16927 | + | 1.38510i | −0.200005 | + | 0.0535912i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.6880 | + | 17.6880i | −0.683348 | + | 0.683348i | ||||
\(671\) | 1.06425 | − | 1.06425i | 0.0410848 | − | 0.0410848i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9793 | − | 12.6898i | 0.847240 | − | 0.489154i | −0.0124786 | − | 0.999922i | \(-0.503972\pi\) |
0.859719 | + | 0.510768i | \(0.170639\pi\) | |||||||
\(674\) | 9.38792 | − | 2.51549i | 0.361609 | − | 0.0968929i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.14863 | − | 7.11282i | −0.121101 | − | 0.273570i | ||||
\(677\) | −21.5441 | + | 12.4385i | −0.828009 | + | 0.478051i | −0.853170 | − | 0.521632i | \(-0.825323\pi\) |
0.0251616 | + | 0.999683i | \(0.491990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.3372 | + | 41.5363i | −0.703716 | + | 1.59402i | ||||
\(680\) | −3.54394 | − | 2.04610i | −0.135904 | − | 0.0784643i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.50480 | + | 13.0801i | −0.134206 | + | 0.500862i | ||||
\(683\) | −10.9521 | + | 40.8739i | −0.419072 | + | 1.56400i | 0.357467 | + | 0.933926i | \(0.383641\pi\) |
−0.776538 | + | 0.630070i | \(0.783026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1714 | + | 13.9554i | 0.923542 | + | 0.533207i | ||||
\(686\) | −4.35658 | + | 21.4892i | −0.166335 | + | 0.820462i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.24873 | − | 3.03036i | 0.200106 | − | 0.115531i | ||||
\(689\) | 1.67983 | + | 7.94474i | 0.0639966 | + | 0.302670i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9598 | + | 3.20461i | −0.454971 | + | 0.121909i | −0.479024 | − | 0.877802i | \(-0.659009\pi\) |
0.0240536 | + | 0.999711i | \(0.492343\pi\) | |||||||
\(692\) | −9.85939 | + | 5.69232i | −0.374798 | + | 0.216390i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.3403 | + | 10.3403i | −0.392514 | + | 0.392514i | ||||
\(695\) | 13.0421 | − | 13.0421i | 0.494714 | − | 0.494714i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.18724 | + | 0.318120i | −0.0449699 | + | 0.0120496i | ||||
\(698\) | 4.84245i | 0.183289i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.29433 | − | 2.85152i | 0.0867175 | − | 0.107777i | ||||
\(701\) | 42.4269i | 1.60244i | 0.598369 | + | 0.801220i | \(0.295816\pi\) | ||||
−0.598369 | + | 0.801220i | \(0.704184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.8894 | − | 13.2152i | −0.863290 | − | 0.498421i | ||||
\(704\) | 18.0389 | − | 18.0389i | 0.679866 | − | 0.679866i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.7917 | + | 25.6200i | −0.556694 | + | 0.964222i | ||||
\(707\) | 25.2481 | − | 31.3796i | 0.949551 | − | 1.18015i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.897457 | − | 0.897457i | −0.0337047 | − | 0.0337047i | 0.690054 | − | 0.723758i | \(-0.257587\pi\) |
−0.723758 | + | 0.690054i | \(0.757587\pi\) | |||||||
\(710\) | −4.30618 | − | 16.0709i | −0.161608 | − | 0.603130i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.0092 | − | 22.5326i | 0.487541 | − | 0.844446i | ||||
\(713\) | 6.94925 | + | 1.86205i | 0.260251 | + | 0.0697342i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.34520 | − | 16.3912i | 0.199899 | − | 0.612997i | ||||
\(716\) | −6.43433 | − | 11.1446i | −0.240462 | − | 0.416493i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.9863 | 0.895162 | ||||||||
\(719\) | −5.80365 | −0.216439 | −0.108220 | − | 0.994127i | \(-0.534515\pi\) | ||||
−0.108220 | + | 0.994127i | \(0.534515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.6807 | + | 6.93303i | 1.66400 | + | 0.258199i | ||||
\(722\) | 25.8826 | − | 6.93521i | 0.963249 | − | 0.258102i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.15461 | + | 1.82131i | −0.117240 | + | 0.0676886i | ||||
\(725\) | 11.2278i | 0.416990i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.625577 | 0.0232014 | 0.0116007 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116007 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(728\) | 19.5906 | − | 21.8484i | 0.726077 | − | 0.809755i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.13421 | + | 19.1611i | 0.190026 | + | 0.709186i | ||||
\(731\) | − | 2.01100i | − | 0.0743795i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.44991 | − | 9.14319i | 0.0904895 | − | 0.337711i | −0.905808 | − | 0.423689i | \(-0.860735\pi\) |
0.996297 | + | 0.0859780i | \(0.0274015\pi\) | |||||||
\(734\) | 25.9090 | − | 6.94230i | 0.956319 | − | 0.256245i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.22543 | − | 4.22543i | −0.155751 | − | 0.155751i | ||||
\(737\) | −37.5848 | −1.38445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.82186 | − | 8.82186i | −0.324517 | − | 0.324517i | 0.525980 | − | 0.850497i | \(-0.323699\pi\) |
−0.850497 | + | 0.525980i | \(0.823699\pi\) | |||||||
\(740\) | −2.00925 | − | 3.48012i | −0.0738614 | − | 0.127932i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.69426 | + | 4.16450i | −0.209043 | + | 0.152883i | ||||
\(743\) | −28.7095 | − | 7.69268i | −1.05325 | − | 0.282217i | −0.309655 | − | 0.950849i | \(-0.600214\pi\) |
−0.743594 | + | 0.668632i | \(0.766880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.3379 | − | 33.4942i | −0.708485 | − | 1.22713i | ||||
\(746\) | 4.65825 | + | 17.3848i | 0.170550 | + | 0.636503i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.366462 | − | 1.36766i | −0.0133992 | − | 0.0500064i | ||||
\(749\) | −16.8758 | − | 43.5538i | −0.616628 | − | 1.59142i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5612 | + | 8.40693i | 0.531347 | + | 0.306773i | 0.741565 | − | 0.670881i | \(-0.234084\pi\) |
−0.210218 | + | 0.977655i | \(0.567417\pi\) | |||||||
\(752\) | −2.17727 | + | 2.17727i | −0.0793968 | + | 0.0793968i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.10710 | + | 20.7013i | −0.0403180 | + | 0.753897i | ||||
\(755\) | 2.97215i | 0.108168i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9748 | + | 19.0089i | 0.398886 | + | 0.690890i | 0.993589 | − | 0.113055i | \(-0.0360637\pi\) |
−0.594703 | + | 0.803945i | \(0.702730\pi\) | |||||||
\(758\) | − | 35.6763i | − | 1.29582i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 31.4343 | + | 8.42280i | 1.14024 | + | 0.305527i | ||||
\(761\) | 28.1192 | − | 28.1192i | 1.01932 | − | 1.01932i | 0.0195119 | − | 0.999810i | \(-0.493789\pi\) |
0.999810 | − | 0.0195119i | \(-0.00621123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7321 | − | 9.15267i | −0.750554 | − | 0.331349i | ||||
\(764\) | 13.5357 | − | 7.81485i | 0.489705 | − | 0.282731i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.69099 | + | 2.92887i | −0.0610978 | + | 0.105824i | ||||
\(767\) | 21.5191 | − | 10.9356i | 0.777009 | − | 0.394861i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.10710 | − | 7.86381i | 0.0759840 | − | 0.283576i | −0.917471 | − | 0.397804i | \(-0.869773\pi\) |
0.993455 | + | 0.114227i | \(0.0364392\pi\) | |||||||
\(770\) | 14.8909 | − | 1.61238i | 0.536632 | − | 0.0581060i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.5054 | + | 3.35081i | 0.450079 | + | 0.120598i | ||||
\(773\) | −6.23533 | + | 23.2706i | −0.224269 | + | 0.836985i | 0.758427 | + | 0.651759i | \(0.225968\pi\) |
−0.982696 | + | 0.185226i | \(0.940698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.75785 | + | 2.34666i | 0.314591 | + | 0.0842945i | ||||
\(776\) | 45.7186 | + | 26.3956i | 1.64120 | + | 0.947548i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.03197 | − | 11.3154i | 0.108701 | − | 0.405679i | ||||
\(779\) | 8.46503 | − | 4.88729i | 0.303291 | − | 0.175105i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4993 | − | 21.6494i | 0.447259 | − | 0.774675i | ||||
\(782\) | 1.70211 | − | 0.456079i | 0.0608673 | − | 0.0163093i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.3120 | + | 5.18711i | 0.582573 | + | 0.185254i | ||||
\(785\) | −0.0301733 | + | 0.0301733i | −0.00107693 | + | 0.00107693i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8590 | + | 5.05325i | 0.672250 | + | 0.180129i | 0.578768 | − | 0.815492i | \(-0.303534\pi\) |
0.0934820 | + | 0.995621i | \(0.470200\pi\) | |||||||
\(788\) | −1.30534 | + | 0.349765i | −0.0465008 | + | 0.0124599i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.21509 | + | 7.30076i | 0.149966 | + | 0.259749i | ||||
\(791\) | −1.35404 | − | 3.49457i | −0.0481441 | − | 0.124252i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.24355 | − | 1.38407i | −0.0441597 | − | 0.0491498i | ||||
\(794\) | 11.9405 | + | 6.89386i | 0.423753 | + | 0.244654i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.53563 | − | 2.04130i | −0.125317 | − | 0.0723518i | ||||
\(797\) | −3.93665 | + | 6.81848i | −0.139443 | + | 0.241523i | −0.927286 | − | 0.374354i | \(-0.877865\pi\) |
0.787843 | + | 0.615877i | \(0.211198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.264430 | + | 0.986867i | 0.00935487 | + | 0.0349129i | ||||
\(800\) | −5.32514 | − | 5.32514i | −0.188272 | − | 0.188272i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.04683 | + | 8.74136i | 0.178210 | + | 0.308668i | ||||
\(803\) | −14.9027 | + | 25.8123i | −0.525906 | + | 0.910896i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.856631 | − | 7.91133i | −0.0301923 | − | 0.278838i | ||||
\(806\) | 15.9159 | + | 5.19022i | 0.560615 | + | 0.182818i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.1130 | − | 33.1130i | −1.16491 | − | 1.16491i | ||||
\(809\) | −23.9648 | −0.842557 | −0.421279 | − | 0.906931i | \(-0.638419\pi\) | ||||
−0.421279 | + | 0.906931i | \(0.638419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.15807 | + | 9.15807i | 0.321583 | + | 0.321583i | 0.849374 | − | 0.527791i | \(-0.176980\pi\) |
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(812\) | 7.16899 | − | 2.77777i | 0.251582 | − | 0.0974805i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.66068 | + | 13.6618i | −0.128307 | + | 0.478847i | ||||
\(815\) | 24.5039 | − | 14.1474i | 0.858336 | − | 0.495560i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.13916 | + | 15.4476i | 0.144811 | + | 0.540441i | ||||
\(818\) | 35.0869 | 1.22678 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.48613 | 0.0518981 | ||||||||
\(821\) | 1.96582 | + | 7.33655i | 0.0686077 | + | 0.256047i | 0.991708 | − | 0.128512i | \(-0.0410201\pi\) |
−0.923100 | + | 0.384559i | \(0.874353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53409 | + | 0.885704i | −0.0534748 | + | 0.0308737i | −0.526499 | − | 0.850176i | \(-0.676496\pi\) |
0.473024 | + | 0.881049i | \(0.343162\pi\) | |||||||
\(824\) | 13.6066 | − | 50.7807i | 0.474010 | − | 1.76903i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.3383 | + | 13.1458i | 0.568482 | + | 0.457401i | ||||
\(827\) | 7.08670 | + | 7.08670i | 0.246429 | + | 0.246429i | 0.819503 | − | 0.573074i | \(-0.194249\pi\) |
−0.573074 | + | 0.819503i | \(0.694249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.9548 | −0.901447 | −0.450723 | − | 0.892664i | \(-0.648834\pi\) | ||||
−0.450723 | + | 0.892664i | \(0.648834\pi\) | |||||||
\(830\) | 14.4578 | + | 14.4578i | 0.501839 | + | 0.501839i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.0780 | − | 23.4599i | −0.730749 | − | 0.813325i | ||||
\(833\) | 4.19678 | − | 3.82678i | 0.145410 | − | 0.132590i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.33200 | + | 12.6994i | −0.253734 | + | 0.439481i | ||||
\(836\) | 5.62998 | + | 9.75141i | 0.194717 | + | 0.337259i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.67649 | + | 5.67649i | 0.196091 | + | 0.196091i | ||||
\(839\) | −1.15171 | − | 4.29822i | −0.0397613 | − | 0.148391i | 0.943191 | − | 0.332250i | \(-0.107808\pi\) |
−0.982953 | + | 0.183859i | \(0.941141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.70702 | − | 4.68870i | 0.0933455 | − | 0.161679i | ||||
\(842\) | 0.824363 | + | 0.475946i | 0.0284094 | + | 0.0164022i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.279981 | − | 0.161647i | −0.00963733 | − | 0.00556412i | ||||
\(845\) | −19.8820 | − | 7.68080i | −0.683963 | − | 0.264227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.14113 | − | 4.13655i | −0.176651 | − | 0.142134i | ||||
\(848\) | 2.75361 | + | 4.76939i | 0.0945594 | + | 0.163782i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.14510 | − | 0.574777i | 0.0735762 | − | 0.0197147i | ||||
\(851\) | 7.25832 | + | 1.94486i | 0.248812 | + | 0.0666690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4636 | + | 20.4636i | −0.700660 | + | 0.700660i | −0.964552 | − | 0.263892i | \(-0.914994\pi\) |
0.263892 | + | 0.964552i | \(0.414994\pi\) | |||||||
\(854\) | 0.652834 | − | 1.47877i | 0.0223395 | − | 0.0506023i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −52.4581 | + | 14.0561i | −1.79298 | + | 0.480427i | ||||
\(857\) | −13.0829 | + | 22.6603i | −0.446904 | + | 0.774060i | −0.998183 | − | 0.0602609i | \(-0.980807\pi\) |
0.551279 | + | 0.834321i | \(0.314140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0690 | − | 16.7830i | 0.991820 | − | 0.572627i | 0.0860021 | − | 0.996295i | \(-0.472591\pi\) |
0.905818 | + | 0.423667i | \(0.139257\pi\) | |||||||
\(860\) | −0.629321 | + | 2.34866i | −0.0214597 | + | 0.0800886i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.5264 | − | 23.3979i | −1.38033 | − | 0.796937i | ||||
\(863\) | 12.6280 | + | 3.38366i | 0.429862 | + | 0.115181i | 0.467261 | − | 0.884119i | \(-0.345241\pi\) |
−0.0373995 | + | 0.999300i | \(0.511907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.07389 | + | 30.1322i | −0.274521 | + | 1.02452i | ||||
\(866\) | 14.9254 | + | 3.99924i | 0.507184 | + | 0.135900i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.668350 | − | 6.17249i | −0.0226853 | − | 0.209508i | ||||
\(869\) | −3.27832 | + | 12.2349i | −0.111210 | + | 0.415040i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.48136 | + | 46.3984i | −0.0840777 | + | 1.57215i | ||||
\(872\) | −13.1749 | + | 22.8196i | −0.446159 | + | 0.772770i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.1361 | + | 7.00676i | −0.410508 | + | 0.237007i | ||||
\(875\) | −3.41441 | − | 31.5334i | −0.115428 | − | 1.06602i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.105858 | + | 0.105858i | −0.00357457 | + | 0.00357457i | −0.708892 | − | 0.705317i | \(-0.750805\pi\) |
0.705317 | + | 0.708892i | \(0.250805\pi\) | |||||||
\(878\) | −14.9208 | − | 3.99802i | −0.503554 | − | 0.134927i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 11.6926i | − | 0.394158i | ||||||
\(881\) | 15.6550 | + | 27.1152i | 0.527429 | + | 0.913534i | 0.999489 | + | 0.0319677i | \(0.0101774\pi\) |
−0.472060 | + | 0.881567i | \(0.656489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.8521i | 0.499812i | 0.968270 | + | 0.249906i | \(0.0803998\pi\) | ||||
−0.968270 | + | 0.249906i | \(0.919600\pi\) | |||||||
\(884\) | −1.71256 | + | 0.362104i | −0.0575997 | + | 0.0121789i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.4106 | + | 10.4106i | −0.349749 | + | 0.349749i | ||||
\(887\) | 37.1161 | + | 21.4290i | 1.24624 | + | 0.719515i | 0.970357 | − | 0.241677i | \(-0.0776976\pi\) |
0.275879 | + | 0.961192i | \(0.411031\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.48119 | + | 15.9904i | −0.0832166 | + | 0.536299i | ||||
\(890\) | −4.24916 | − | 15.8581i | −0.142432 | − | 0.531564i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.983816 | − | 3.67165i | −0.0329406 | − | 0.122936i | ||||
\(893\) | −4.06246 | − | 7.03638i | −0.135945 | − | 0.235464i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.0600 | − | 9.12635i | −1.13850 | − | 0.305060i | ||||
\(896\) | 4.10410 | − | 9.29639i | 0.137108 | − | 0.310571i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.3690 | + | 37.0122i | 0.713094 | + | 1.23511i | ||||
\(899\) | 13.4678 | + | 13.4678i | 0.449177 | + | 0.449177i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.82735 | 0.0608777 | ||||||||
\(902\) | −3.69866 | − | 3.69866i | −0.123152 | − | 0.123152i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.20901 | + | 1.12780i | −0.139989 | + | 0.0375101i | ||||
\(905\) | −2.58332 | + | 9.64108i | −0.0858725 | + | 0.320480i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3951i | 0.743619i | 0.928309 | + | 0.371809i | \(0.121262\pi\) | ||||
−0.928309 | + | 0.371809i | \(0.878738\pi\) | |||||||
\(908\) | 3.40402 | + | 12.7040i | 0.112966 | + | 0.421596i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.00737 | − | 18.4893i | −0.0333940 | − | 0.612914i | ||||
\(911\) | −27.2540 | −0.902965 | −0.451483 | − | 0.892280i | \(-0.649105\pi\) | ||||
−0.451483 | + | 0.892280i | \(0.649105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.7211i | 1.01672i | ||||||||
\(914\) | 29.8676 | − | 17.2440i | 0.987931 | − | 0.570382i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.4854 | − | 4.14929i | 0.511651 | − | 0.137096i | ||||
\(917\) | 6.97780 | − | 44.9692i | 0.230427 | − | 1.48501i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4376 | −0.905083 | −0.452541 | − | 0.891743i | \(-0.649482\pi\) | ||||
−0.452541 | + | 0.891743i | \(0.649482\pi\) | |||||||
\(920\) | −9.25228 | −0.305039 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.61689 | + | 9.72874i | 0.184982 | + | 0.320399i | ||||
\(923\) | −25.9009 | − | 16.8596i | −0.852538 | − | 0.554941i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.14736 | + | 2.45103i | 0.300763 | + | 0.0805893i | ||||
\(926\) | −17.2524 | + | 29.8820i | −0.566949 | + | 0.981984i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.09450 | − | 15.2809i | −0.134409 | − | 0.501620i | ||||
\(929\) | −34.8854 | − | 34.8854i | −1.14455 | − | 1.14455i | −0.987607 | − | 0.156946i | \(-0.949835\pi\) |
−0.156946 | − | 0.987607i | \(-0.550165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3612 | + | 38.0336i | −0.798406 | + | 1.24650i | ||||
\(932\) | 3.23240 | − | 5.59868i | 0.105881 | − | 0.183391i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.6590 | − | 27.6590i | 0.905030 | − | 0.905030i | ||||
\(935\) | −3.35993 | − | 1.93986i | −0.109882 | − | 0.0634402i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.9902i | − | 0.620384i | −0.950674 | − | 0.310192i | \(-0.899607\pi\) | ||
0.950674 | − | 0.310192i | \(-0.100393\pi\) | |||||||
\(938\) | −37.6397 | + | 14.5842i | −1.22898 | + | 0.476192i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 1.23532i | − | 0.0402916i | ||||||
\(941\) | −29.3705 | + | 7.86979i | −0.957450 | + | 0.256548i | −0.703521 | − | 0.710675i | \(-0.748390\pi\) |
−0.253929 | + | 0.967223i | \(0.581723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.96504 | + | 1.96504i | −0.0639906 | + | 0.0639906i | ||||
\(944\) | 11.5757 | − | 11.5757i | 0.376757 | − | 0.376757i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.41153 | − | 4.27905i | 0.240970 | − | 0.139124i | ||||
\(947\) | −54.1565 | + | 14.5112i | −1.75985 | + | 0.471550i | −0.986683 | − | 0.162653i | \(-0.947995\pi\) |
−0.773166 | + | 0.634204i | \(0.781328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.8813 | + | 20.1015i | 1.00245 | + | 0.652523i | ||||
\(950\) | −15.2946 | + | 8.83033i | −0.496221 | + | 0.286494i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.89826 | − | 5.33023i | −0.126343 | − | 0.172754i | ||||
\(953\) | 12.5739 | + | 7.25952i | 0.407307 | + | 0.235159i | 0.689632 | − | 0.724160i | \(-0.257772\pi\) |
−0.282325 | + | 0.959319i | \(0.591106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0844 | − | 41.3677i | 0.358684 | − | 1.33863i | ||||
\(956\) | 4.47887 | − | 16.7154i | 0.144857 | − | 0.540614i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.3049 | + | 15.1871i | 0.849873 | + | 0.490674i | ||||
\(959\) | 26.5880 | + | 36.3547i | 0.858572 | + | 1.17396i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5268 | + | 7.80972i | −0.436350 | + | 0.251927i | ||||
\(962\) | 16.6238 | + | 5.42105i | 0.535973 | + | 0.174782i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.61798 | + | 1.23738i | −0.148735 | + | 0.0398535i | ||||
\(965\) | 30.7221 | − | 17.7374i | 0.988979 | − | 0.570988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.9101 | + | 35.9101i | −1.15479 | + | 1.15479i | −0.169212 | + | 0.985580i | \(0.554122\pi\) |
−0.985580 | + | 0.169212i | \(0.945878\pi\) | |||||||
\(968\) | −5.42512 | + | 5.42512i | −0.174370 | + | 0.174370i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.1759 | − | 8.62152i | 1.03311 | − | 0.276820i | ||||
\(971\) | 4.67903i | 0.150157i | 0.997178 | + | 0.0750785i | \(0.0239207\pi\) | ||||
−0.997178 | + | 0.0750785i | \(0.976079\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.7532 | − | 10.7535i | 0.889728 | − | 0.344743i | ||||
\(974\) | 7.54403i | 0.241726i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.09283 | − | 0.630948i | −0.0349808 | − | 0.0201961i | ||||
\(977\) | −31.2664 | + | 31.2664i | −1.00030 | + | 1.00030i | −0.000299689 | 1.00000i | \(0.500095\pi\) | |
−1.00000 | 0.000299689i | \(0.999905\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3337 | − | 21.3627i | 0.394188 | − | 0.682754i | ||||
\(980\) | −6.09900 | + | 3.15598i | −0.194825 | + | 0.100814i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.1319 | + | 23.1319i | 0.738169 | + | 0.738169i | ||||
\(983\) | −3.59836 | − | 13.4293i | −0.114770 | − | 0.428327i | 0.884500 | − | 0.466541i | \(-0.154500\pi\) |
−0.999270 | + | 0.0382139i | \(0.987833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.85147 | + | 3.20684i | −0.0589928 | + | 0.102178i | ||||
\(986\) | 4.50615 | + | 1.20742i | 0.143505 | + | 0.0384521i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.4098 | − | 6.30640i | 0.394808 | − | 0.200633i | ||||
\(989\) | −2.27339 | − | 3.93763i | −0.0722897 | − | 0.125209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.4158 | 1.12502 | 0.562510 | − | 0.826791i | \(-0.309836\pi\) | ||||
0.562510 | + | 0.826791i | \(0.309836\pi\) | |||||||
\(992\) | −12.7751 | −0.405609 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.11679 | − | 26.5311i | 0.130577 | − | 0.841516i | ||||
\(995\) | −10.8055 | + | 2.89534i | −0.342559 | + | 0.0917884i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.2024 | + | 14.5506i | −0.798167 | + | 0.460822i | −0.842830 | − | 0.538180i | \(-0.819112\pi\) |
0.0446626 | + | 0.999002i | \(0.485779\pi\) | |||||||
\(998\) | − | 2.18839i | − | 0.0692721i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.gh.d.262.4 | 40 | ||
3.2 | odd | 2 | 273.2.cg.b.262.7 | yes | 40 | ||
7.5 | odd | 6 | 819.2.et.d.145.4 | 40 | |||
13.7 | odd | 12 | 819.2.et.d.514.4 | 40 | |||
21.5 | even | 6 | 273.2.bt.b.145.7 | ✓ | 40 | ||
39.20 | even | 12 | 273.2.bt.b.241.7 | yes | 40 | ||
91.33 | even | 12 | inner | 819.2.gh.d.397.4 | 40 | ||
273.215 | odd | 12 | 273.2.cg.b.124.7 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.b.145.7 | ✓ | 40 | 21.5 | even | 6 | ||
273.2.bt.b.241.7 | yes | 40 | 39.20 | even | 12 | ||
273.2.cg.b.124.7 | yes | 40 | 273.215 | odd | 12 | ||
273.2.cg.b.262.7 | yes | 40 | 3.2 | odd | 2 | ||
819.2.et.d.145.4 | 40 | 7.5 | odd | 6 | |||
819.2.et.d.514.4 | 40 | 13.7 | odd | 12 | |||
819.2.gh.d.262.4 | 40 | 1.1 | even | 1 | trivial | ||
819.2.gh.d.397.4 | 40 | 91.33 | even | 12 | inner |