Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(209,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.3 | ||
Character | \(\chi\) | \(=\) | 273.209 |
Dual form | 273.2.e.a.209.29 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.37766i | − | 1.68126i | −0.541613 | − | 0.840628i | \(-0.682186\pi\) | ||
0.541613 | − | 0.840628i | \(-0.317814\pi\) | |||||||
\(3\) | −1.58497 | + | 0.698482i | −0.915082 | + | 0.403269i | ||||
\(4\) | −3.65324 | −1.82662 | ||||||||
\(5\) | −1.30604 | −0.584077 | −0.292039 | − | 0.956407i | \(-0.594334\pi\) | ||||
−0.292039 | + | 0.956407i | \(0.594334\pi\) | |||||||
\(6\) | 1.66075 | + | 3.76851i | 0.677998 | + | 1.53849i | ||||
\(7\) | −0.0678621 | + | 2.64488i | −0.0256495 | + | 0.999671i | ||||
\(8\) | 3.93085i | 1.38976i | ||||||||
\(9\) | 2.02425 | − | 2.21414i | 0.674749 | − | 0.738048i | ||||
\(10\) | 3.10530i | 0.981983i | ||||||||
\(11\) | 5.27205i | 1.58958i | 0.606883 | + | 0.794791i | \(0.292420\pi\) | ||||
−0.606883 | + | 0.794791i | \(0.707580\pi\) | |||||||
\(12\) | 5.79027 | − | 2.55173i | 1.67151 | − | 0.736620i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 6.28861 | + | 0.161353i | 1.68070 | + | 0.0431233i | ||||
\(15\) | 2.07003 | − | 0.912243i | 0.534478 | − | 0.235540i | ||||
\(16\) | 2.03971 | 0.509926 | ||||||||
\(17\) | 0.801293 | 0.194342 | 0.0971711 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971711 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(18\) | −5.26447 | − | 4.81296i | −1.24085 | − | 1.13443i | ||||
\(19\) | 1.71006i | 0.392314i | 0.980573 | + | 0.196157i | \(0.0628462\pi\) | ||||
−0.980573 | + | 0.196157i | \(0.937154\pi\) | |||||||
\(20\) | 4.77127 | 1.06689 | ||||||||
\(21\) | −1.73984 | − | 4.23945i | −0.379665 | − | 0.925124i | ||||
\(22\) | 12.5351 | 2.67250 | ||||||||
\(23\) | 2.35494i | 0.491039i | 0.969392 | + | 0.245520i | \(0.0789585\pi\) | ||||
−0.969392 | + | 0.245520i | \(0.921041\pi\) | |||||||
\(24\) | −2.74562 | − | 6.23026i | −0.560448 | − | 1.27175i | ||||
\(25\) | −3.29427 | −0.658854 | ||||||||
\(26\) | −2.37766 | −0.466297 | ||||||||
\(27\) | −1.66183 | + | 4.92324i | −0.319819 | + | 0.947479i | ||||
\(28\) | 0.247917 | − | 9.66240i | 0.0468519 | − | 1.82602i | ||||
\(29\) | 6.71855i | 1.24760i | 0.781583 | + | 0.623802i | \(0.214413\pi\) | ||||
−0.781583 | + | 0.623802i | \(0.785587\pi\) | |||||||
\(30\) | −2.16900 | − | 4.92181i | −0.396003 | − | 0.898595i | ||||
\(31\) | 0.0594188i | 0.0106719i | 0.999986 | + | 0.00533597i | \(0.00169850\pi\) | ||||
−0.999986 | + | 0.00533597i | \(0.998301\pi\) | |||||||
\(32\) | 3.01197i | 0.532447i | ||||||||
\(33\) | −3.68243 | − | 8.35603i | −0.641029 | − | 1.45460i | ||||
\(34\) | − | 1.90520i | − | 0.326739i | ||||||
\(35\) | 0.0886304 | − | 3.45431i | 0.0149813 | − | 0.583885i | ||||
\(36\) | −7.39507 | + | 8.08880i | −1.23251 | + | 1.34813i | ||||
\(37\) | 6.59192 | 1.08371 | 0.541853 | − | 0.840473i | \(-0.317723\pi\) | ||||
0.541853 | + | 0.840473i | \(0.317723\pi\) | |||||||
\(38\) | 4.06592 | 0.659580 | ||||||||
\(39\) | 0.698482 | + | 1.58497i | 0.111847 | + | 0.253798i | ||||
\(40\) | − | 5.13383i | − | 0.811729i | ||||||
\(41\) | −11.0219 | −1.72133 | −0.860665 | − | 0.509172i | \(-0.829952\pi\) | ||||
−0.860665 | + | 0.509172i | \(0.829952\pi\) | |||||||
\(42\) | −10.0800 | + | 4.13675i | −1.55537 | + | 0.638314i | ||||
\(43\) | −4.90826 | −0.748503 | −0.374251 | − | 0.927327i | \(-0.622100\pi\) | ||||
−0.374251 | + | 0.927327i | \(0.622100\pi\) | |||||||
\(44\) | − | 19.2601i | − | 2.90357i | ||||||
\(45\) | −2.64374 | + | 2.89175i | −0.394105 | + | 0.431077i | ||||
\(46\) | 5.59924 | 0.825562 | ||||||||
\(47\) | −5.84623 | −0.852760 | −0.426380 | − | 0.904544i | \(-0.640211\pi\) | ||||
−0.426380 | + | 0.904544i | \(0.640211\pi\) | |||||||
\(48\) | −3.23287 | + | 1.42470i | −0.466624 | + | 0.205637i | ||||
\(49\) | −6.99079 | − | 0.358974i | −0.998684 | − | 0.0512821i | ||||
\(50\) | 7.83264i | 1.10770i | ||||||||
\(51\) | −1.27002 | + | 0.559689i | −0.177839 | + | 0.0783721i | ||||
\(52\) | 3.65324i | 0.506614i | ||||||||
\(53\) | − | 6.42005i | − | 0.881862i | −0.897541 | − | 0.440931i | \(-0.854648\pi\) | ||
0.897541 | − | 0.440931i | \(-0.145352\pi\) | |||||||
\(54\) | 11.7058 | + | 3.95125i | 1.59295 | + | 0.537697i | ||||
\(55\) | − | 6.88549i | − | 0.928439i | ||||||
\(56\) | −10.3966 | − | 0.266756i | −1.38931 | − | 0.0356467i | ||||
\(57\) | −1.19444 | − | 2.71038i | −0.158208 | − | 0.358999i | ||||
\(58\) | 15.9744 | 2.09754 | ||||||||
\(59\) | 10.7167 | 1.39520 | 0.697601 | − | 0.716487i | \(-0.254251\pi\) | ||||
0.697601 | + | 0.716487i | \(0.254251\pi\) | |||||||
\(60\) | −7.56231 | + | 3.33265i | −0.976290 | + | 0.430243i | ||||
\(61\) | 11.0415i | 1.41372i | 0.707354 | + | 0.706859i | \(0.249889\pi\) | ||||
−0.707354 | + | 0.706859i | \(0.750111\pi\) | |||||||
\(62\) | 0.141278 | 0.0179423 | ||||||||
\(63\) | 5.71877 | + | 5.50415i | 0.720498 | + | 0.693457i | ||||
\(64\) | 11.2408 | 1.40511 | ||||||||
\(65\) | 1.30604i | 0.161994i | ||||||||
\(66\) | −19.8678 | + | 8.75555i | −2.44555 | + | 1.07773i | ||||
\(67\) | 9.44978 | 1.15447 | 0.577237 | − | 0.816576i | \(-0.304131\pi\) | ||||
0.577237 | + | 0.816576i | \(0.304131\pi\) | |||||||
\(68\) | −2.92732 | −0.354990 | ||||||||
\(69\) | −1.64488 | − | 3.73250i | −0.198021 | − | 0.449341i | ||||
\(70\) | −8.21316 | − | 0.210733i | −0.981660 | − | 0.0251874i | ||||
\(71\) | 2.37782i | 0.282195i | 0.989996 | + | 0.141098i | \(0.0450632\pi\) | ||||
−0.989996 | + | 0.141098i | \(0.954937\pi\) | |||||||
\(72\) | 8.70345 | + | 7.95700i | 1.02571 | + | 0.937741i | ||||
\(73\) | 1.43970i | 0.168505i | 0.996444 | + | 0.0842523i | \(0.0268502\pi\) | ||||
−0.996444 | + | 0.0842523i | \(0.973150\pi\) | |||||||
\(74\) | − | 15.6733i | − | 1.82199i | ||||||
\(75\) | 5.22131 | − | 2.30099i | 0.602905 | − | 0.265695i | ||||
\(76\) | − | 6.24725i | − | 0.716609i | ||||||
\(77\) | −13.9439 | − | 0.357772i | −1.58906 | − | 0.0407720i | ||||
\(78\) | 3.76851 | − | 1.66075i | 0.426699 | − | 0.188043i | ||||
\(79\) | −15.2242 | −1.71286 | −0.856430 | − | 0.516263i | \(-0.827323\pi\) | ||||
−0.856430 | + | 0.516263i | \(0.827323\pi\) | |||||||
\(80\) | −2.66393 | −0.297836 | ||||||||
\(81\) | −0.804857 | − | 8.96394i | −0.0894285 | − | 0.995993i | ||||
\(82\) | 26.2062i | 2.89400i | ||||||||
\(83\) | 0.698538 | 0.0766745 | 0.0383373 | − | 0.999265i | \(-0.487794\pi\) | ||||
0.0383373 | + | 0.999265i | \(0.487794\pi\) | |||||||
\(84\) | 6.35607 | + | 15.4878i | 0.693504 | + | 1.68985i | ||||
\(85\) | −1.04652 | −0.113511 | ||||||||
\(86\) | 11.6701i | 1.25842i | ||||||||
\(87\) | −4.69278 | − | 10.6487i | −0.503119 | − | 1.14166i | ||||
\(88\) | −20.7236 | −2.20914 | ||||||||
\(89\) | 7.59165 | 0.804713 | 0.402357 | − | 0.915483i | \(-0.368191\pi\) | ||||
0.402357 | + | 0.915483i | \(0.368191\pi\) | |||||||
\(90\) | 6.87559 | + | 6.28590i | 0.724750 | + | 0.662592i | ||||
\(91\) | 2.64488 | + | 0.0678621i | 0.277259 | + | 0.00711388i | ||||
\(92\) | − | 8.60317i | − | 0.896943i | ||||||
\(93\) | −0.0415030 | − | 0.0941770i | −0.00430366 | − | 0.00976570i | ||||
\(94\) | 13.9003i | 1.43371i | ||||||||
\(95\) | − | 2.23339i | − | 0.229141i | ||||||
\(96\) | −2.10381 | − | 4.77388i | −0.214719 | − | 0.487232i | ||||
\(97\) | − | 14.3029i | − | 1.45224i | −0.687570 | − | 0.726118i | \(-0.741322\pi\) | ||
0.687570 | − | 0.726118i | \(-0.258678\pi\) | |||||||
\(98\) | −0.853518 | + | 16.6217i | −0.0862183 | + | 1.67904i | ||||
\(99\) | 11.6731 | + | 10.6719i | 1.17319 | + | 1.07257i | ||||
\(100\) | 12.0348 | 1.20348 | ||||||||
\(101\) | −5.97760 | −0.594794 | −0.297397 | − | 0.954754i | \(-0.596118\pi\) | ||||
−0.297397 | + | 0.954754i | \(0.596118\pi\) | |||||||
\(102\) | 1.33075 | + | 3.01968i | 0.131764 | + | 0.298993i | ||||
\(103\) | − | 17.9566i | − | 1.76932i | −0.466239 | − | 0.884659i | \(-0.654391\pi\) | ||
0.466239 | − | 0.884659i | \(-0.345609\pi\) | |||||||
\(104\) | 3.93085 | 0.385451 | ||||||||
\(105\) | 2.27230 | + | 5.53688i | 0.221753 | + | 0.540344i | ||||
\(106\) | −15.2647 | −1.48264 | ||||||||
\(107\) | − | 8.49082i | − | 0.820839i | −0.911897 | − | 0.410419i | \(-0.865382\pi\) | ||
0.911897 | − | 0.410419i | \(-0.134618\pi\) | |||||||
\(108\) | 6.07106 | − | 17.9858i | 0.584188 | − | 1.73069i | ||||
\(109\) | 4.48445 | 0.429533 | 0.214766 | − | 0.976665i | \(-0.431101\pi\) | ||||
0.214766 | + | 0.976665i | \(0.431101\pi\) | |||||||
\(110\) | −16.3713 | −1.56094 | ||||||||
\(111\) | −10.4480 | + | 4.60434i | −0.991679 | + | 0.437025i | ||||
\(112\) | −0.138419 | + | 5.39478i | −0.0130793 | + | 0.509759i | ||||
\(113\) | 11.8249i | 1.11239i | 0.831052 | + | 0.556195i | \(0.187739\pi\) | ||||
−0.831052 | + | 0.556195i | \(0.812261\pi\) | |||||||
\(114\) | −6.44436 | + | 2.83997i | −0.603569 | + | 0.265988i | ||||
\(115\) | − | 3.07564i | − | 0.286805i | ||||||
\(116\) | − | 24.5445i | − | 2.27890i | ||||||
\(117\) | −2.21414 | − | 2.02425i | −0.204698 | − | 0.187142i | ||||
\(118\) | − | 25.4807i | − | 2.34569i | ||||||
\(119\) | −0.0543775 | + | 2.11933i | −0.00498477 | + | 0.194278i | ||||
\(120\) | 3.58588 | + | 8.13695i | 0.327345 | + | 0.742798i | ||||
\(121\) | −16.7945 | −1.52677 | ||||||||
\(122\) | 26.2529 | 2.37682 | ||||||||
\(123\) | 17.4693 | − | 7.69859i | 1.57516 | − | 0.694158i | ||||
\(124\) | − | 0.217072i | − | 0.0194936i | ||||||
\(125\) | 10.8326 | 0.968899 | ||||||||
\(126\) | 13.0870 | − | 13.5973i | 1.16588 | − | 1.21134i | ||||
\(127\) | 0.900158 | 0.0798761 | 0.0399380 | − | 0.999202i | \(-0.487284\pi\) | ||||
0.0399380 | + | 0.999202i | \(0.487284\pi\) | |||||||
\(128\) | − | 20.7029i | − | 1.82990i | ||||||
\(129\) | 7.77943 | − | 3.42833i | 0.684941 | − | 0.301848i | ||||
\(130\) | 3.10530 | 0.272353 | ||||||||
\(131\) | 20.8735 | 1.82373 | 0.911864 | − | 0.410491i | \(-0.134643\pi\) | ||||
0.911864 | + | 0.410491i | \(0.134643\pi\) | |||||||
\(132\) | 13.4528 | + | 30.5266i | 1.17092 | + | 2.65700i | ||||
\(133\) | −4.52289 | − | 0.116048i | −0.392185 | − | 0.0100626i | ||||
\(134\) | − | 22.4683i | − | 1.94097i | ||||||
\(135\) | 2.17040 | − | 6.42993i | 0.186799 | − | 0.553401i | ||||
\(136\) | 3.14976i | 0.270090i | ||||||||
\(137\) | 3.48336i | 0.297604i | 0.988867 | + | 0.148802i | \(0.0475416\pi\) | ||||
−0.988867 | + | 0.148802i | \(0.952458\pi\) | |||||||
\(138\) | −8.87461 | + | 3.91097i | −0.755457 | + | 0.332923i | ||||
\(139\) | 16.9530i | 1.43794i | 0.695042 | + | 0.718969i | \(0.255386\pi\) | ||||
−0.695042 | + | 0.718969i | \(0.744614\pi\) | |||||||
\(140\) | −0.323788 | + | 12.6194i | −0.0273651 | + | 1.06654i | ||||
\(141\) | 9.26608 | − | 4.08348i | 0.780345 | − | 0.343891i | ||||
\(142\) | 5.65364 | 0.474443 | ||||||||
\(143\) | 5.27205 | 0.440871 | ||||||||
\(144\) | 4.12887 | − | 4.51620i | 0.344072 | − | 0.376350i | ||||
\(145\) | − | 8.77467i | − | 0.728696i | ||||||
\(146\) | 3.42312 | 0.283299 | ||||||||
\(147\) | 11.3309 | − | 4.31398i | 0.934558 | − | 0.355811i | ||||
\(148\) | −24.0819 | −1.97952 | ||||||||
\(149\) | − | 5.95646i | − | 0.487972i | −0.969779 | − | 0.243986i | \(-0.921545\pi\) | ||
0.969779 | − | 0.243986i | \(-0.0784551\pi\) | |||||||
\(150\) | −5.47096 | − | 12.4145i | −0.446702 | − | 1.01364i | ||||
\(151\) | 2.73667 | 0.222707 | 0.111353 | − | 0.993781i | \(-0.464481\pi\) | ||||
0.111353 | + | 0.993781i | \(0.464481\pi\) | |||||||
\(152\) | −6.72197 | −0.545223 | ||||||||
\(153\) | 1.62201 | − | 1.77418i | 0.131132 | − | 0.143434i | ||||
\(154\) | −0.850660 | + | 33.1539i | −0.0685481 | + | 2.67162i | ||||
\(155\) | − | 0.0776032i | − | 0.00623324i | ||||||
\(156\) | −2.55173 | − | 5.79027i | −0.204302 | − | 0.463593i | ||||
\(157\) | − | 6.42503i | − | 0.512773i | −0.966574 | − | 0.256386i | \(-0.917468\pi\) | ||
0.966574 | − | 0.256386i | \(-0.0825320\pi\) | |||||||
\(158\) | 36.1980i | 2.87976i | ||||||||
\(159\) | 4.48429 | + | 10.1756i | 0.355627 | + | 0.806975i | ||||
\(160\) | − | 3.93375i | − | 0.310990i | ||||||
\(161\) | −6.22854 | − | 0.159811i | −0.490877 | − | 0.0125949i | ||||
\(162\) | −21.3132 | + | 1.91367i | −1.67452 | + | 0.150352i | ||||
\(163\) | −15.5138 | −1.21513 | −0.607567 | − | 0.794268i | \(-0.707855\pi\) | ||||
−0.607567 | + | 0.794268i | \(0.707855\pi\) | |||||||
\(164\) | 40.2656 | 3.14422 | ||||||||
\(165\) | 4.80939 | + | 10.9133i | 0.374410 | + | 0.849597i | ||||
\(166\) | − | 1.66088i | − | 0.128909i | ||||||
\(167\) | 8.77114 | 0.678731 | 0.339366 | − | 0.940655i | \(-0.389788\pi\) | ||||
0.339366 | + | 0.940655i | \(0.389788\pi\) | |||||||
\(168\) | 16.6646 | − | 6.83905i | 1.28570 | − | 0.527644i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 2.48826i | 0.190841i | ||||||||
\(171\) | 3.78631 | + | 3.46157i | 0.289546 | + | 0.264713i | ||||
\(172\) | 17.9311 | 1.36723 | ||||||||
\(173\) | −11.1707 | −0.849296 | −0.424648 | − | 0.905359i | \(-0.639602\pi\) | ||||
−0.424648 | + | 0.905359i | \(0.639602\pi\) | |||||||
\(174\) | −25.3189 | + | 11.1578i | −1.91942 | + | 0.845873i | ||||
\(175\) | 0.223556 | − | 8.71295i | 0.0168993 | − | 0.658637i | ||||
\(176\) | 10.7534i | 0.810570i | ||||||||
\(177\) | −16.9857 | + | 7.48545i | −1.27672 | + | 0.562641i | ||||
\(178\) | − | 18.0503i | − | 1.35293i | ||||||
\(179\) | 11.9012i | 0.889537i | 0.895646 | + | 0.444768i | \(0.146714\pi\) | ||||
−0.895646 | + | 0.444768i | \(0.853286\pi\) | |||||||
\(180\) | 9.65822 | − | 10.5643i | 0.719881 | − | 0.787414i | ||||
\(181\) | 6.53948i | 0.486075i | 0.970017 | + | 0.243038i | \(0.0781439\pi\) | ||||
−0.970017 | + | 0.243038i | \(0.921856\pi\) | |||||||
\(182\) | 0.161353 | − | 6.28861i | 0.0119603 | − | 0.466143i | ||||
\(183\) | −7.71229 | − | 17.5004i | −0.570109 | − | 1.29367i | ||||
\(184\) | −9.25691 | −0.682428 | ||||||||
\(185\) | −8.60929 | −0.632968 | ||||||||
\(186\) | −0.223920 | + | 0.0986798i | −0.0164186 | + | 0.00723555i | ||||
\(187\) | 4.22446i | 0.308923i | ||||||||
\(188\) | 21.3577 | 1.55767 | ||||||||
\(189\) | −12.9086 | − | 4.72943i | −0.938964 | − | 0.344016i | ||||
\(190\) | −5.31024 | −0.385245 | ||||||||
\(191\) | 17.2471i | 1.24796i | 0.781440 | + | 0.623980i | \(0.214485\pi\) | ||||
−0.781440 | + | 0.623980i | \(0.785515\pi\) | |||||||
\(192\) | −17.8164 | + | 7.85153i | −1.28579 | + | 0.566635i | ||||
\(193\) | 23.3740 | 1.68250 | 0.841250 | − | 0.540646i | \(-0.181820\pi\) | ||||
0.841250 | + | 0.540646i | \(0.181820\pi\) | |||||||
\(194\) | −34.0073 | −2.44158 | ||||||||
\(195\) | −0.912243 | − | 2.07003i | −0.0653270 | − | 0.148238i | ||||
\(196\) | 25.5391 | + | 1.31142i | 1.82422 | + | 0.0936730i | ||||
\(197\) | 7.54621i | 0.537645i | 0.963190 | + | 0.268823i | \(0.0866346\pi\) | ||||
−0.963190 | + | 0.268823i | \(0.913365\pi\) | |||||||
\(198\) | 25.3742 | − | 27.7545i | 1.80326 | − | 1.97243i | ||||
\(199\) | 10.6700i | 0.756376i | 0.925729 | + | 0.378188i | \(0.123453\pi\) | ||||
−0.925729 | + | 0.378188i | \(0.876547\pi\) | |||||||
\(200\) | − | 12.9493i | − | 0.915651i | ||||||
\(201\) | −14.9776 | + | 6.60050i | −1.05644 | + | 0.465564i | ||||
\(202\) | 14.2127i | 1.00000i | ||||||||
\(203\) | −17.7698 | − | 0.455935i | −1.24719 | − | 0.0320004i | ||||
\(204\) | 4.63971 | − | 2.04468i | 0.324845 | − | 0.143156i | ||||
\(205\) | 14.3950 | 1.00539 | ||||||||
\(206\) | −42.6946 | −2.97468 | ||||||||
\(207\) | 5.21417 | + | 4.76698i | 0.362410 | + | 0.331328i | ||||
\(208\) | − | 2.03971i | − | 0.141428i | ||||||
\(209\) | −9.01550 | −0.623615 | ||||||||
\(210\) | 13.1648 | − | 5.40274i | 0.908456 | − | 0.372824i | ||||
\(211\) | −15.2247 | −1.04811 | −0.524054 | − | 0.851685i | \(-0.675581\pi\) | ||||
−0.524054 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(212\) | 23.4540i | 1.61083i | ||||||||
\(213\) | −1.66086 | − | 3.76877i | −0.113801 | − | 0.258232i | ||||
\(214\) | −20.1882 | −1.38004 | ||||||||
\(215\) | 6.41036 | 0.437183 | ||||||||
\(216\) | −19.3525 | − | 6.53238i | −1.31677 | − | 0.444472i | ||||
\(217\) | −0.157156 | − | 0.00403229i | −0.0106684 | − | 0.000273730i | ||||
\(218\) | − | 10.6625i | − | 0.722155i | ||||||
\(219\) | −1.00561 | − | 2.28188i | −0.0679526 | − | 0.154195i | ||||
\(220\) | 25.1544i | 1.69591i | ||||||||
\(221\) | − | 0.801293i | − | 0.0539008i | ||||||
\(222\) | 10.9475 | + | 24.8417i | 0.734750 | + | 1.66727i | ||||
\(223\) | 19.0534i | 1.27591i | 0.770073 | + | 0.637956i | \(0.220220\pi\) | ||||
−0.770073 | + | 0.637956i | \(0.779780\pi\) | |||||||
\(224\) | −7.96631 | − | 0.204399i | −0.532271 | − | 0.0136570i | ||||
\(225\) | −6.66841 | + | 7.29398i | −0.444561 | + | 0.486266i | ||||
\(226\) | 28.1155 | 1.87021 | ||||||||
\(227\) | 26.1181 | 1.73352 | 0.866759 | − | 0.498727i | \(-0.166199\pi\) | ||||
0.866759 | + | 0.498727i | \(0.166199\pi\) | |||||||
\(228\) | 4.36359 | + | 9.90169i | 0.288986 | + | 0.655756i | ||||
\(229\) | − | 12.0895i | − | 0.798898i | −0.916756 | − | 0.399449i | \(-0.869202\pi\) | ||
0.916756 | − | 0.399449i | \(-0.130798\pi\) | |||||||
\(230\) | −7.31280 | −0.482192 | ||||||||
\(231\) | 22.3506 | − | 9.17253i | 1.47056 | − | 0.603508i | ||||
\(232\) | −26.4096 | −1.73387 | ||||||||
\(233\) | − | 12.8920i | − | 0.844584i | −0.906460 | − | 0.422292i | \(-0.861226\pi\) | ||
0.906460 | − | 0.422292i | \(-0.138774\pi\) | |||||||
\(234\) | −4.81296 | + | 5.26447i | −0.314633 | + | 0.344149i | ||||
\(235\) | 7.63538 | 0.498078 | ||||||||
\(236\) | −39.1509 | −2.54851 | ||||||||
\(237\) | 24.1299 | − | 10.6339i | 1.56741 | − | 0.690743i | ||||
\(238\) | 5.03902 | + | 0.129291i | 0.326631 | + | 0.00838068i | ||||
\(239\) | 14.9488i | 0.966960i | 0.875355 | + | 0.483480i | \(0.160627\pi\) | ||||
−0.875355 | + | 0.483480i | \(0.839373\pi\) | |||||||
\(240\) | 4.22224 | − | 1.86071i | 0.272545 | − | 0.120108i | ||||
\(241\) | 12.8418i | 0.827216i | 0.910455 | + | 0.413608i | \(0.135732\pi\) | ||||
−0.910455 | + | 0.413608i | \(0.864268\pi\) | |||||||
\(242\) | 39.9315i | 2.56690i | ||||||||
\(243\) | 7.53682 | + | 13.6454i | 0.483487 | + | 0.875351i | ||||
\(244\) | − | 40.3373i | − | 2.58233i | ||||||
\(245\) | 9.13022 | + | 0.468834i | 0.583309 | + | 0.0299527i | ||||
\(246\) | −18.3046 | − | 41.5361i | −1.16706 | − | 2.64824i | ||||
\(247\) | 1.71006 | 0.108808 | ||||||||
\(248\) | −0.233566 | −0.0148315 | ||||||||
\(249\) | −1.10716 | + | 0.487916i | −0.0701634 | + | 0.0309204i | ||||
\(250\) | − | 25.7562i | − | 1.62897i | ||||||
\(251\) | 1.01030 | 0.0637695 | 0.0318848 | − | 0.999492i | \(-0.489849\pi\) | ||||
0.0318848 | + | 0.999492i | \(0.489849\pi\) | |||||||
\(252\) | −20.8921 | − | 20.1080i | −1.31608 | − | 1.26668i | ||||
\(253\) | −12.4154 | −0.780547 | ||||||||
\(254\) | − | 2.14026i | − | 0.134292i | ||||||
\(255\) | 1.65870 | − | 0.730974i | 0.103872 | − | 0.0457754i | ||||
\(256\) | −26.7427 | −1.67142 | ||||||||
\(257\) | 26.1478 | 1.63105 | 0.815527 | − | 0.578720i | \(-0.196447\pi\) | ||||
0.815527 | + | 0.578720i | \(0.196447\pi\) | |||||||
\(258\) | −8.15139 | − | 18.4968i | −0.507483 | − | 1.15156i | ||||
\(259\) | −0.447342 | + | 17.4349i | −0.0277965 | + | 1.08335i | ||||
\(260\) | − | 4.77127i | − | 0.295902i | ||||||
\(261\) | 14.8758 | + | 13.6000i | 0.920791 | + | 0.841819i | ||||
\(262\) | − | 49.6301i | − | 3.06616i | ||||||
\(263\) | − | 3.56322i | − | 0.219717i | −0.993947 | − | 0.109859i | \(-0.964960\pi\) | ||
0.993947 | − | 0.109859i | \(-0.0350398\pi\) | |||||||
\(264\) | 32.8463 | − | 14.4751i | 2.02155 | − | 0.890879i | ||||
\(265\) | 8.38482i | 0.515075i | ||||||||
\(266\) | −0.275922 | + | 10.7539i | −0.0169179 | + | 0.659363i | ||||
\(267\) | −12.0325 | + | 5.30263i | −0.736379 | + | 0.324516i | ||||
\(268\) | −34.5224 | −2.10879 | ||||||||
\(269\) | −21.6665 | −1.32103 | −0.660514 | − | 0.750814i | \(-0.729661\pi\) | ||||
−0.660514 | + | 0.750814i | \(0.729661\pi\) | |||||||
\(270\) | −15.2882 | − | 5.16047i | −0.930408 | − | 0.314056i | ||||
\(271\) | 5.64273i | 0.342772i | 0.985204 | + | 0.171386i | \(0.0548245\pi\) | ||||
−0.985204 | + | 0.171386i | \(0.945176\pi\) | |||||||
\(272\) | 1.63440 | 0.0991002 | ||||||||
\(273\) | −4.23945 | + | 1.73984i | −0.256583 | + | 0.105300i | ||||
\(274\) | 8.28223 | 0.500348 | ||||||||
\(275\) | − | 17.3676i | − | 1.04730i | ||||||
\(276\) | 6.00916 | + | 13.6358i | 0.361709 | + | 0.820776i | ||||
\(277\) | 14.8371 | 0.891472 | 0.445736 | − | 0.895164i | \(-0.352942\pi\) | ||||
0.445736 | + | 0.895164i | \(0.352942\pi\) | |||||||
\(278\) | 40.3085 | 2.41754 | ||||||||
\(279\) | 0.131562 | + | 0.120278i | 0.00787640 | + | 0.00720088i | ||||
\(280\) | 13.5784 | + | 0.348392i | 0.811462 | + | 0.0208204i | ||||
\(281\) | − | 20.4548i | − | 1.22023i | −0.792313 | − | 0.610115i | \(-0.791123\pi\) | ||
0.792313 | − | 0.610115i | \(-0.208877\pi\) | |||||||
\(282\) | −9.70912 | − | 22.0316i | −0.578170 | − | 1.31196i | ||||
\(283\) | 17.8012i | 1.05817i | 0.848569 | + | 0.529084i | \(0.177464\pi\) | ||||
−0.848569 | + | 0.529084i | \(0.822536\pi\) | |||||||
\(284\) | − | 8.68676i | − | 0.515464i | ||||||
\(285\) | 1.55999 | + | 3.53986i | 0.0924056 | + | 0.209683i | ||||
\(286\) | − | 12.5351i | − | 0.741217i | ||||||
\(287\) | 0.747969 | − | 29.1516i | 0.0441512 | − | 1.72076i | ||||
\(288\) | 6.66894 | + | 6.09697i | 0.392971 | + | 0.359268i | ||||
\(289\) | −16.3579 | −0.962231 | ||||||||
\(290\) | −20.8631 | −1.22513 | ||||||||
\(291\) | 9.99030 | + | 22.6696i | 0.585642 | + | 1.32892i | ||||
\(292\) | − | 5.25959i | − | 0.307794i | ||||||
\(293\) | −13.9111 | −0.812697 | −0.406348 | − | 0.913718i | \(-0.633198\pi\) | ||||
−0.406348 | + | 0.913718i | \(0.633198\pi\) | |||||||
\(294\) | −10.2572 | − | 26.9410i | −0.598209 | − | 1.57123i | ||||
\(295\) | −13.9965 | −0.814905 | ||||||||
\(296\) | 25.9118i | 1.50609i | ||||||||
\(297\) | −25.9556 | − | 8.76123i | −1.50610 | − | 0.508378i | ||||
\(298\) | −14.1624 | −0.820406 | ||||||||
\(299\) | 2.35494 | 0.136190 | ||||||||
\(300\) | −19.0747 | + | 8.40607i | −1.10128 | + | 0.485325i | ||||
\(301\) | 0.333085 | − | 12.9818i | 0.0191987 | − | 0.748256i | ||||
\(302\) | − | 6.50685i | − | 0.374427i | ||||||
\(303\) | 9.47431 | − | 4.17525i | 0.544285 | − | 0.239862i | ||||
\(304\) | 3.48801i | 0.200051i | ||||||||
\(305\) | − | 14.4206i | − | 0.825721i | ||||||
\(306\) | −4.21838 | − | 3.85659i | −0.241149 | − | 0.220467i | ||||
\(307\) | 21.4056i | 1.22168i | 0.791752 | + | 0.610842i | \(0.209169\pi\) | ||||
−0.791752 | + | 0.610842i | \(0.790831\pi\) | |||||||
\(308\) | 50.9406 | + | 1.30703i | 2.90261 | + | 0.0744750i | ||||
\(309\) | 12.5424 | + | 28.4607i | 0.713511 | + | 1.61907i | ||||
\(310\) | −0.184514 | −0.0104797 | ||||||||
\(311\) | 6.98339 | 0.395992 | 0.197996 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197996 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(312\) | −6.23026 | + | 2.74562i | −0.352719 | + | 0.155440i | ||||
\(313\) | 2.38679i | 0.134909i | 0.997722 | + | 0.0674547i | \(0.0214878\pi\) | ||||
−0.997722 | + | 0.0674547i | \(0.978512\pi\) | |||||||
\(314\) | −15.2765 | −0.862102 | ||||||||
\(315\) | −7.46893 | − | 7.18861i | −0.420826 | − | 0.405032i | ||||
\(316\) | 55.6179 | 3.12875 | ||||||||
\(317\) | 8.07054i | 0.453287i | 0.973978 | + | 0.226643i | \(0.0727751\pi\) | ||||
−0.973978 | + | 0.226643i | \(0.927225\pi\) | |||||||
\(318\) | 24.1940 | − | 10.6621i | 1.35673 | − | 0.597900i | ||||
\(319\) | −35.4205 | −1.98317 | ||||||||
\(320\) | −14.6809 | −0.820690 | ||||||||
\(321\) | 5.93068 | + | 13.4577i | 0.331019 | + | 0.751134i | ||||
\(322\) | −0.379976 | + | 14.8093i | −0.0211752 | + | 0.825291i | ||||
\(323\) | 1.37026i | 0.0762431i | ||||||||
\(324\) | 2.94034 | + | 32.7475i | 0.163352 | + | 1.81930i | ||||
\(325\) | 3.29427i | 0.182733i | ||||||||
\(326\) | 36.8865i | 2.04295i | ||||||||
\(327\) | −7.10771 | + | 3.13231i | −0.393057 | + | 0.173217i | ||||
\(328\) | − | 43.3253i | − | 2.39224i | ||||||
\(329\) | 0.396737 | − | 15.4626i | 0.0218728 | − | 0.852479i | ||||
\(330\) | 25.9480 | − | 11.4351i | 1.42839 | − | 0.629480i | ||||
\(331\) | 0.989255 | 0.0543744 | 0.0271872 | − | 0.999630i | \(-0.491345\pi\) | ||||
0.0271872 | + | 0.999630i | \(0.491345\pi\) | |||||||
\(332\) | −2.55193 | −0.140055 | ||||||||
\(333\) | 13.3437 | − | 14.5955i | 0.731229 | − | 0.799826i | ||||
\(334\) | − | 20.8548i | − | 1.14112i | ||||||
\(335\) | −12.3418 | −0.674302 | ||||||||
\(336\) | −3.54877 | − | 8.64723i | −0.193601 | − | 0.471745i | ||||
\(337\) | 14.3737 | 0.782984 | 0.391492 | − | 0.920181i | \(-0.371959\pi\) | ||||
0.391492 | + | 0.920181i | \(0.371959\pi\) | |||||||
\(338\) | 2.37766i | 0.129327i | ||||||||
\(339\) | −8.25946 | − | 18.7420i | −0.448592 | − | 1.01793i | ||||
\(340\) | 3.82319 | 0.207341 | ||||||||
\(341\) | −0.313259 | −0.0169639 | ||||||||
\(342\) | 8.23043 | − | 9.00254i | 0.445051 | − | 0.486801i | ||||
\(343\) | 1.42385 | − | 18.4654i | 0.0768809 | − | 0.997040i | ||||
\(344\) | − | 19.2936i | − | 1.04024i | ||||||
\(345\) | 2.14828 | + | 4.87479i | 0.115659 | + | 0.262450i | ||||
\(346\) | 26.5602i | 1.42788i | ||||||||
\(347\) | − | 21.3809i | − | 1.14779i | −0.818929 | − | 0.573895i | \(-0.805432\pi\) | ||
0.818929 | − | 0.573895i | \(-0.194568\pi\) | |||||||
\(348\) | 17.1439 | + | 38.9022i | 0.919009 | + | 2.08538i | ||||
\(349\) | − | 20.1489i | − | 1.07855i | −0.842131 | − | 0.539274i | \(-0.818699\pi\) | ||
0.842131 | − | 0.539274i | \(-0.181301\pi\) | |||||||
\(350\) | −20.7164 | − | 0.531540i | −1.10734 | − | 0.0284120i | ||||
\(351\) | 4.92324 | + | 1.66183i | 0.262783 | + | 0.0887017i | ||||
\(352\) | −15.8793 | −0.846368 | ||||||||
\(353\) | 5.59804 | 0.297954 | 0.148977 | − | 0.988841i | \(-0.452402\pi\) | ||||
0.148977 | + | 0.988841i | \(0.452402\pi\) | |||||||
\(354\) | 17.7978 | + | 40.3861i | 0.945944 | + | 2.14650i | ||||
\(355\) | − | 3.10552i | − | 0.164824i | ||||||
\(356\) | −27.7342 | −1.46991 | ||||||||
\(357\) | −1.39412 | − | 3.39704i | −0.0737849 | − | 0.179791i | ||||
\(358\) | 28.2969 | 1.49554 | ||||||||
\(359\) | − | 11.9080i | − | 0.628482i | −0.949343 | − | 0.314241i | \(-0.898250\pi\) | ||
0.949343 | − | 0.314241i | \(-0.101750\pi\) | |||||||
\(360\) | −11.3670 | − | 10.3921i | −0.599095 | − | 0.547713i | ||||
\(361\) | 16.0757 | 0.846090 | ||||||||
\(362\) | 15.5486 | 0.817217 | ||||||||
\(363\) | 26.6187 | − | 11.7307i | 1.39712 | − | 0.615700i | ||||
\(364\) | −9.66240 | − | 0.247917i | −0.506447 | − | 0.0129944i | ||||
\(365\) | − | 1.88030i | − | 0.0984197i | ||||||
\(366\) | −41.6100 | + | 18.3372i | −2.17499 | + | 0.958499i | ||||
\(367\) | − | 2.77210i | − | 0.144702i | −0.997379 | − | 0.0723511i | \(-0.976950\pi\) | ||
0.997379 | − | 0.0723511i | \(-0.0230502\pi\) | |||||||
\(368\) | 4.80339i | 0.250394i | ||||||||
\(369\) | −22.3110 | + | 24.4040i | −1.16146 | + | 1.27042i | ||||
\(370\) | 20.4699i | 1.06418i | ||||||||
\(371\) | 16.9803 | + | 0.435678i | 0.881572 | + | 0.0226193i | ||||
\(372\) | 0.151621 | + | 0.344051i | 0.00786116 | + | 0.0178382i | ||||
\(373\) | −17.6790 | −0.915384 | −0.457692 | − | 0.889111i | \(-0.651324\pi\) | ||||
−0.457692 | + | 0.889111i | \(0.651324\pi\) | |||||||
\(374\) | 10.0443 | 0.519379 | ||||||||
\(375\) | −17.1693 | + | 7.56639i | −0.886621 | + | 0.390727i | ||||
\(376\) | − | 22.9806i | − | 1.18513i | ||||||
\(377\) | 6.71855 | 0.346023 | ||||||||
\(378\) | −11.2450 | + | 30.6922i | −0.578378 | + | 1.57864i | ||||
\(379\) | 9.10040 | 0.467456 | 0.233728 | − | 0.972302i | \(-0.424907\pi\) | ||||
0.233728 | + | 0.972302i | \(0.424907\pi\) | |||||||
\(380\) | 8.15914i | 0.418555i | ||||||||
\(381\) | −1.42672 | + | 0.628744i | −0.0730931 | + | 0.0322115i | ||||
\(382\) | 41.0078 | 2.09814 | ||||||||
\(383\) | −12.3375 | −0.630419 | −0.315209 | − | 0.949022i | \(-0.602075\pi\) | ||||
−0.315209 | + | 0.949022i | \(0.602075\pi\) | |||||||
\(384\) | 14.4606 | + | 32.8134i | 0.737940 | + | 1.67450i | ||||
\(385\) | 18.2113 | + | 0.467264i | 0.928133 | + | 0.0238140i | ||||
\(386\) | − | 55.5754i | − | 2.82872i | ||||||
\(387\) | −9.93552 | + | 10.8676i | −0.505051 | + | 0.552431i | ||||
\(388\) | 52.2519i | 2.65269i | ||||||||
\(389\) | 1.00846i | 0.0511308i | 0.999673 | + | 0.0255654i | \(0.00813861\pi\) | ||||
−0.999673 | + | 0.0255654i | \(0.991861\pi\) | |||||||
\(390\) | −4.92181 | + | 2.16900i | −0.249225 | + | 0.109832i | ||||
\(391\) | 1.88700i | 0.0954296i | ||||||||
\(392\) | 1.41107 | − | 27.4797i | 0.0712700 | − | 1.38794i | ||||
\(393\) | −33.0839 | + | 14.5798i | −1.66886 | + | 0.735453i | ||||
\(394\) | 17.9423 | 0.903920 | ||||||||
\(395\) | 19.8834 | 1.00044 | ||||||||
\(396\) | −42.6446 | − | 38.9871i | −2.14297 | − | 1.95918i | ||||
\(397\) | − | 7.16645i | − | 0.359674i | −0.983696 | − | 0.179837i | \(-0.942443\pi\) | ||
0.983696 | − | 0.179837i | \(-0.0575570\pi\) | |||||||
\(398\) | 25.3696 | 1.27166 | ||||||||
\(399\) | 7.24970 | − | 2.97523i | 0.362939 | − | 0.148948i | ||||
\(400\) | −6.71934 | −0.335967 | ||||||||
\(401\) | 11.7059i | 0.584567i | 0.956332 | + | 0.292284i | \(0.0944151\pi\) | ||||
−0.956332 | + | 0.292284i | \(0.905585\pi\) | |||||||
\(402\) | 15.6937 | + | 35.6116i | 0.782732 | + | 1.77614i | ||||
\(403\) | 0.0594188 | 0.00295986 | ||||||||
\(404\) | 21.8376 | 1.08646 | ||||||||
\(405\) | 1.05117 | + | 11.7072i | 0.0522332 | + | 0.581737i | ||||
\(406\) | −1.08406 | + | 42.2504i | −0.0538008 | + | 2.09685i | ||||
\(407\) | 34.7530i | 1.72264i | ||||||||
\(408\) | −2.20005 | − | 4.99227i | −0.108919 | − | 0.247154i | ||||
\(409\) | 33.0347i | 1.63346i | 0.577020 | + | 0.816730i | \(0.304216\pi\) | ||||
−0.577020 | + | 0.816730i | \(0.695784\pi\) | |||||||
\(410\) | − | 34.2263i | − | 1.69032i | ||||||
\(411\) | −2.43307 | − | 5.52102i | −0.120014 | − | 0.272332i | ||||
\(412\) | 65.5999i | 3.23188i | ||||||||
\(413\) | −0.727261 | + | 28.3445i | −0.0357862 | + | 1.39474i | ||||
\(414\) | 11.3342 | − | 12.3975i | 0.557047 | − | 0.609304i | ||||
\(415\) | −0.912316 | −0.0447838 | ||||||||
\(416\) | 3.01197 | 0.147674 | ||||||||
\(417\) | −11.8414 | − | 26.8700i | −0.579876 | − | 1.31583i | ||||
\(418\) | 21.4357i | 1.04846i | ||||||||
\(419\) | −6.62409 | −0.323608 | −0.161804 | − | 0.986823i | \(-0.551731\pi\) | ||||
−0.161804 | + | 0.986823i | \(0.551731\pi\) | |||||||
\(420\) | −8.30126 | − | 20.2276i | −0.405060 | − | 0.987004i | ||||
\(421\) | 29.5920 | 1.44222 | 0.721112 | − | 0.692818i | \(-0.243631\pi\) | ||||
0.721112 | + | 0.692818i | \(0.243631\pi\) | |||||||
\(422\) | 36.1990i | 1.76214i | ||||||||
\(423\) | −11.8342 | + | 12.9444i | −0.575399 | + | 0.629377i | ||||
\(424\) | 25.2362 | 1.22558 | ||||||||
\(425\) | −2.63968 | −0.128043 | ||||||||
\(426\) | −8.96083 | + | 3.94896i | −0.434154 | + | 0.191328i | ||||
\(427\) | −29.2034 | − | 0.749300i | −1.41325 | − | 0.0362611i | ||||
\(428\) | 31.0190i | 1.49936i | ||||||||
\(429\) | −8.35603 | + | 3.68243i | −0.403433 | + | 0.177789i | ||||
\(430\) | − | 15.2416i | − | 0.735017i | ||||||
\(431\) | − | 20.8160i | − | 1.00267i | −0.865253 | − | 0.501335i | \(-0.832842\pi\) | ||
0.865253 | − | 0.501335i | \(-0.167158\pi\) | |||||||
\(432\) | −3.38964 | + | 10.0420i | −0.163084 | + | 0.483145i | ||||
\(433\) | − | 0.784792i | − | 0.0377147i | −0.999822 | − | 0.0188573i | \(-0.993997\pi\) | ||
0.999822 | − | 0.0188573i | \(-0.00600283\pi\) | |||||||
\(434\) | −0.00958739 | + | 0.373662i | −0.000460210 | + | 0.0179364i | ||||
\(435\) | 6.12895 | + | 13.9076i | 0.293860 | + | 0.666817i | ||||
\(436\) | −16.3828 | −0.784594 | ||||||||
\(437\) | −4.02708 | −0.192641 | ||||||||
\(438\) | −5.42553 | + | 2.39099i | −0.259242 | + | 0.114246i | ||||
\(439\) | − | 23.6486i | − | 1.12869i | −0.825540 | − | 0.564343i | \(-0.809129\pi\) | ||
0.825540 | − | 0.564343i | \(-0.190871\pi\) | |||||||
\(440\) | 27.0658 | 1.29031 | ||||||||
\(441\) | −14.9459 | + | 14.7520i | −0.711709 | + | 0.702474i | ||||
\(442\) | −1.90520 | −0.0906211 | ||||||||
\(443\) | − | 11.7837i | − | 0.559859i | −0.960021 | − | 0.279930i | \(-0.909689\pi\) | ||
0.960021 | − | 0.279930i | \(-0.0903111\pi\) | |||||||
\(444\) | 38.1691 | − | 16.8208i | 1.81142 | − | 0.798279i | ||||
\(445\) | −9.91497 | −0.470015 | ||||||||
\(446\) | 45.3025 | 2.14514 | ||||||||
\(447\) | 4.16048 | + | 9.44079i | 0.196784 | + | 0.446534i | ||||
\(448\) | −0.762828 | + | 29.7307i | −0.0360402 | + | 1.40464i | ||||
\(449\) | − | 13.3714i | − | 0.631035i | −0.948920 | − | 0.315517i | \(-0.897822\pi\) | ||
0.948920 | − | 0.315517i | \(-0.102178\pi\) | |||||||
\(450\) | 17.3426 | + | 15.8552i | 0.817537 | + | 0.747421i | ||||
\(451\) | − | 58.1079i | − | 2.73620i | ||||||
\(452\) | − | 43.1992i | − | 2.03192i | ||||||
\(453\) | −4.33753 | + | 1.91151i | −0.203795 | + | 0.0898106i | ||||
\(454\) | − | 62.0998i | − | 2.91449i | ||||||
\(455\) | −3.45431 | − | 0.0886304i | −0.161941 | − | 0.00415506i | ||||
\(456\) | 10.6541 | − | 4.69517i | 0.498924 | − | 0.219872i | ||||
\(457\) | 33.8545 | 1.58365 | 0.791824 | − | 0.610750i | \(-0.209132\pi\) | ||||
0.791824 | + | 0.610750i | \(0.209132\pi\) | |||||||
\(458\) | −28.7447 | −1.34315 | ||||||||
\(459\) | −1.33161 | + | 3.94496i | −0.0621542 | + | 0.184135i | ||||
\(460\) | 11.2361i | 0.523884i | ||||||||
\(461\) | 8.88641 | 0.413881 | 0.206941 | − | 0.978354i | \(-0.433649\pi\) | ||||
0.206941 | + | 0.978354i | \(0.433649\pi\) | |||||||
\(462\) | −21.8091 | − | 53.1420i | −1.01465 | − | 2.47239i | ||||
\(463\) | −11.2494 | −0.522803 | −0.261401 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261401 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(464\) | 13.7039i | 0.636186i | ||||||||
\(465\) | 0.0542044 | + | 0.122999i | 0.00251367 | + | 0.00570392i | ||||
\(466\) | −30.6528 | −1.41996 | ||||||||
\(467\) | 1.60871 | 0.0744423 | 0.0372212 | − | 0.999307i | \(-0.488149\pi\) | ||||
0.0372212 | + | 0.999307i | \(0.488149\pi\) | |||||||
\(468\) | 8.08880 | + | 7.39507i | 0.373905 | + | 0.341837i | ||||
\(469\) | −0.641282 | + | 24.9935i | −0.0296117 | + | 1.15409i | ||||
\(470\) | − | 18.1543i | − | 0.837396i | ||||||
\(471\) | 4.48776 | + | 10.1835i | 0.206785 | + | 0.469229i | ||||
\(472\) | 42.1259i | 1.93900i | ||||||||
\(473\) | − | 25.8766i | − | 1.18981i | ||||||
\(474\) | −25.2836 | − | 57.3727i | −1.16132 | − | 2.63521i | ||||
\(475\) | − | 5.63339i | − | 0.258477i | ||||||
\(476\) | 0.198654 | − | 7.74241i | 0.00910530 | − | 0.354873i | ||||
\(477\) | −14.2149 | − | 12.9958i | −0.650856 | − | 0.595035i | ||||
\(478\) | 35.5432 | 1.62571 | ||||||||
\(479\) | −28.2154 | −1.28920 | −0.644598 | − | 0.764522i | \(-0.722975\pi\) | ||||
−0.644598 | + | 0.764522i | \(0.722975\pi\) | |||||||
\(480\) | 2.74765 | + | 6.23486i | 0.125412 | + | 0.284581i | ||||
\(481\) | − | 6.59192i | − | 0.300566i | ||||||
\(482\) | 30.5335 | 1.39076 | ||||||||
\(483\) | 9.98366 | − | 4.09722i | 0.454272 | − | 0.186430i | ||||
\(484\) | 61.3544 | 2.78884 | ||||||||
\(485\) | 18.6801i | 0.848218i | ||||||||
\(486\) | 32.4440 | − | 17.9200i | 1.47169 | − | 0.812866i | ||||
\(487\) | −3.13667 | −0.142136 | −0.0710680 | − | 0.997471i | \(-0.522641\pi\) | ||||
−0.0710680 | + | 0.997471i | \(0.522641\pi\) | |||||||
\(488\) | −43.4024 | −1.96474 | ||||||||
\(489\) | 24.5889 | − | 10.8361i | 1.11195 | − | 0.490026i | ||||
\(490\) | 1.11472 | − | 21.7085i | 0.0503581 | − | 0.980691i | ||||
\(491\) | − | 13.8904i | − | 0.626865i | −0.949611 | − | 0.313432i | \(-0.898521\pi\) | ||
0.949611 | − | 0.313432i | \(-0.101479\pi\) | |||||||
\(492\) | −63.8198 | + | 28.1248i | −2.87722 | + | 1.26797i | ||||
\(493\) | 5.38353i | 0.242462i | ||||||||
\(494\) | − | 4.06592i | − | 0.182935i | ||||||
\(495\) | −15.2454 | − | 13.9379i | −0.685232 | − | 0.626463i | ||||
\(496\) | 0.121197i | 0.00544190i | ||||||||
\(497\) | −6.28905 | − | 0.161364i | −0.282103 | − | 0.00723816i | ||||
\(498\) | 1.16010 | + | 2.63245i | 0.0519852 | + | 0.117963i | ||||
\(499\) | 17.7660 | 0.795314 | 0.397657 | − | 0.917534i | \(-0.369823\pi\) | ||||
0.397657 | + | 0.917534i | \(0.369823\pi\) | |||||||
\(500\) | −39.5742 | −1.76981 | ||||||||
\(501\) | −13.9020 | + | 6.12649i | −0.621095 | + | 0.273711i | ||||
\(502\) | − | 2.40214i | − | 0.107213i | ||||||
\(503\) | −32.3589 | −1.44281 | −0.721407 | − | 0.692512i | \(-0.756504\pi\) | ||||
−0.721407 | + | 0.692512i | \(0.756504\pi\) | |||||||
\(504\) | −21.6359 | + | 22.4796i | −0.963742 | + | 1.00132i | ||||
\(505\) | 7.80696 | 0.347405 | ||||||||
\(506\) | 29.5194i | 1.31230i | ||||||||
\(507\) | 1.58497 | − | 0.698482i | 0.0703909 | − | 0.0310207i | ||||
\(508\) | −3.28850 | −0.145903 | ||||||||
\(509\) | 21.0344 | 0.932334 | 0.466167 | − | 0.884697i | \(-0.345635\pi\) | ||||
0.466167 | + | 0.884697i | \(0.345635\pi\) | |||||||
\(510\) | −1.73800 | − | 3.94381i | −0.0769601 | − | 0.174635i | ||||
\(511\) | −3.80784 | − | 0.0977014i | −0.168449 | − | 0.00432205i | ||||
\(512\) | 22.1791i | 0.980186i | ||||||||
\(513\) | −8.41902 | − | 2.84182i | −0.371709 | − | 0.125469i | ||||
\(514\) | − | 62.1704i | − | 2.74222i | ||||||
\(515\) | 23.4520i | 1.03342i | ||||||||
\(516\) | −28.4202 | + | 12.5245i | −1.25113 | + | 0.551362i | ||||
\(517\) | − | 30.8216i | − | 1.35553i | ||||||
\(518\) | 41.4541 | + | 1.06363i | 1.82139 | + | 0.0467330i | ||||
\(519\) | 17.7053 | − | 7.80256i | 0.777175 | − | 0.342494i | ||||
\(520\) | −5.13383 | −0.225133 | ||||||||
\(521\) | −18.8906 | −0.827614 | −0.413807 | − | 0.910365i | \(-0.635801\pi\) | ||||
−0.413807 | + | 0.910365i | \(0.635801\pi\) | |||||||
\(522\) | 32.3361 | − | 35.3696i | 1.41531 | − | 1.54808i | ||||
\(523\) | 5.64594i | 0.246880i | 0.992352 | + | 0.123440i | \(0.0393926\pi\) | ||||
−0.992352 | + | 0.123440i | \(0.960607\pi\) | |||||||
\(524\) | −76.2561 | −3.33126 | ||||||||
\(525\) | 5.73151 | + | 13.9659i | 0.250144 | + | 0.609522i | ||||
\(526\) | −8.47210 | −0.369401 | ||||||||
\(527\) | 0.0476119i | 0.00207401i | ||||||||
\(528\) | −7.51108 | − | 17.0438i | −0.326878 | − | 0.741738i | ||||
\(529\) | 17.4543 | 0.758881 | ||||||||
\(530\) | 19.9362 | 0.865973 | ||||||||
\(531\) | 21.6933 | − | 23.7284i | 0.941410 | − | 1.02973i | ||||
\(532\) | 16.5232 | + | 0.423952i | 0.716373 | + | 0.0183806i | ||||
\(533\) | 11.0219i | 0.477411i | ||||||||
\(534\) | 12.6078 | + | 28.6092i | 0.545594 | + | 1.23804i | ||||
\(535\) | 11.0893i | 0.479433i | ||||||||
\(536\) | 37.1456i | 1.60445i | ||||||||
\(537\) | −8.31277 | − | 18.8630i | −0.358722 | − | 0.813999i | ||||
\(538\) | 51.5154i | 2.22098i | ||||||||
\(539\) | 1.89253 | − | 36.8558i | 0.0815171 | − | 1.58749i | ||||
\(540\) | −7.92902 | + | 23.4901i | −0.341211 | + | 1.01085i | ||||
\(541\) | 17.4067 | 0.748372 | 0.374186 | − | 0.927354i | \(-0.377922\pi\) | ||||
0.374186 | + | 0.927354i | \(0.377922\pi\) | |||||||
\(542\) | 13.4165 | 0.576287 | ||||||||
\(543\) | −4.56771 | − | 10.3649i | −0.196019 | − | 0.444799i | ||||
\(544\) | 2.41347i | 0.103477i | ||||||||
\(545\) | −5.85686 | −0.250880 | ||||||||
\(546\) | 4.13675 | + | 10.0800i | 0.177036 | + | 0.431382i | ||||
\(547\) | 8.17213 | 0.349415 | 0.174707 | − | 0.984620i | \(-0.444102\pi\) | ||||
0.174707 | + | 0.984620i | \(0.444102\pi\) | |||||||
\(548\) | − | 12.7256i | − | 0.543609i | ||||||
\(549\) | 24.4475 | + | 22.3507i | 1.04339 | + | 0.953905i | ||||
\(550\) | −41.2941 | −1.76078 | ||||||||
\(551\) | −11.4891 | −0.489452 | ||||||||
\(552\) | 14.6719 | − | 6.46578i | 0.624477 | − | 0.275202i | ||||
\(553\) | 1.03315 | − | 40.2663i | 0.0439340 | − | 1.71230i | ||||
\(554\) | − | 35.2774i | − | 1.49879i | ||||||
\(555\) | 13.6454 | − | 6.01343i | 0.579217 | − | 0.255256i | ||||
\(556\) | − | 61.9336i | − | 2.62657i | ||||||
\(557\) | 12.1045i | 0.512882i | 0.966560 | + | 0.256441i | \(0.0825500\pi\) | ||||
−0.966560 | + | 0.256441i | \(0.917450\pi\) | |||||||
\(558\) | 0.285980 | − | 0.312809i | 0.0121065 | − | 0.0132422i | ||||
\(559\) | 4.90826i | 0.207597i | ||||||||
\(560\) | 0.180780 | − | 7.04578i | 0.00763935 | − | 0.297738i | ||||
\(561\) | −2.95071 | − | 6.69563i | −0.124579 | − | 0.282690i | ||||
\(562\) | −48.6344 | −2.05152 | ||||||||
\(563\) | 26.8237 | 1.13048 | 0.565242 | − | 0.824925i | \(-0.308783\pi\) | ||||
0.565242 | + | 0.824925i | \(0.308783\pi\) | |||||||
\(564\) | −33.8513 | + | 14.9180i | −1.42540 | + | 0.628160i | ||||
\(565\) | − | 15.4437i | − | 0.649722i | ||||||
\(566\) | 42.3250 | 1.77905 | ||||||||
\(567\) | 23.7632 | − | 1.52044i | 0.997959 | − | 0.0638524i | ||||
\(568\) | −9.34684 | −0.392185 | ||||||||
\(569\) | 31.7789i | 1.33224i | 0.745845 | + | 0.666120i | \(0.232046\pi\) | ||||
−0.745845 | + | 0.666120i | \(0.767954\pi\) | |||||||
\(570\) | 8.41656 | − | 3.70911i | 0.352531 | − | 0.155357i | ||||
\(571\) | −39.8161 | −1.66625 | −0.833127 | − | 0.553082i | \(-0.813452\pi\) | ||||
−0.833127 | + | 0.553082i | \(0.813452\pi\) | |||||||
\(572\) | −19.2601 | −0.805305 | ||||||||
\(573\) | −12.0468 | − | 27.3362i | −0.503263 | − | 1.14198i | ||||
\(574\) | −69.3124 | − | 1.77841i | −2.89304 | − | 0.0742295i | ||||
\(575\) | − | 7.75781i | − | 0.323523i | ||||||
\(576\) | 22.7542 | − | 24.8888i | 0.948093 | − | 1.03703i | ||||
\(577\) | − | 36.3628i | − | 1.51380i | −0.653530 | − | 0.756901i | \(-0.726713\pi\) | ||
0.653530 | − | 0.756901i | \(-0.273287\pi\) | |||||||
\(578\) | 38.8935i | 1.61776i | ||||||||
\(579\) | −37.0471 | + | 16.3264i | −1.53963 | + | 0.678500i | ||||
\(580\) | 32.0560i | 1.33105i | ||||||||
\(581\) | −0.0474043 | + | 1.84755i | −0.00196666 | + | 0.0766493i | ||||
\(582\) | 53.9005 | − | 23.7535i | 2.23425 | − | 0.984614i | ||||
\(583\) | 33.8468 | 1.40179 | ||||||||
\(584\) | −5.65925 | −0.234182 | ||||||||
\(585\) | 2.89175 | + | 2.64374i | 0.119559 | + | 0.109305i | ||||
\(586\) | 33.0759i | 1.36635i | ||||||||
\(587\) | −10.3902 | −0.428851 | −0.214426 | − | 0.976740i | \(-0.568788\pi\) | ||||
−0.214426 | + | 0.976740i | \(0.568788\pi\) | |||||||
\(588\) | −41.3946 | + | 15.7600i | −1.70708 | + | 0.649932i | ||||
\(589\) | −0.101610 | −0.00418675 | ||||||||
\(590\) | 33.2787i | 1.37006i | ||||||||
\(591\) | −5.27089 | − | 11.9605i | −0.216816 | − | 0.491989i | ||||
\(592\) | 13.4456 | 0.552610 | ||||||||
\(593\) | 6.17427 | 0.253547 | 0.126773 | − | 0.991932i | \(-0.459538\pi\) | ||||
0.126773 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(594\) | −20.8312 | + | 61.7134i | −0.854714 | + | 2.53213i | ||||
\(595\) | 0.0710189 | − | 2.76791i | 0.00291149 | − | 0.113473i | ||||
\(596\) | 21.7604i | 0.891340i | ||||||||
\(597\) | −7.45280 | − | 16.9116i | −0.305023 | − | 0.692146i | ||||
\(598\) | − | 5.59924i | − | 0.228970i | ||||||
\(599\) | 15.6452i | 0.639244i | 0.947545 | + | 0.319622i | \(0.103556\pi\) | ||||
−0.947545 | + | 0.319622i | \(0.896444\pi\) | |||||||
\(600\) | 9.04483 | + | 20.5242i | 0.369254 | + | 0.837896i | ||||
\(601\) | − | 40.1236i | − | 1.63668i | −0.574736 | − | 0.818339i | \(-0.694895\pi\) | ||
0.574736 | − | 0.818339i | \(-0.305105\pi\) | |||||||
\(602\) | −30.8662 | − | 0.791961i | −1.25801 | − | 0.0322779i | ||||
\(603\) | 19.1287 | − | 20.9232i | 0.778980 | − | 0.852057i | ||||
\(604\) | −9.99771 | −0.406801 | ||||||||
\(605\) | 21.9342 | 0.891753 | ||||||||
\(606\) | −9.92730 | − | 22.5266i | −0.403269 | − | 0.915082i | ||||
\(607\) | − | 6.91437i | − | 0.280646i | −0.990106 | − | 0.140323i | \(-0.955186\pi\) | ||
0.990106 | − | 0.140323i | \(-0.0448140\pi\) | |||||||
\(608\) | −5.15064 | −0.208886 | ||||||||
\(609\) | 28.4830 | − | 11.6892i | 1.15419 | − | 0.473671i | ||||
\(610\) | −34.2872 | −1.38825 | ||||||||
\(611\) | 5.84623i | 0.236513i | ||||||||
\(612\) | −5.92562 | + | 6.48150i | −0.239529 | + | 0.261999i | ||||
\(613\) | −3.98925 | −0.161124 | −0.0805622 | − | 0.996750i | \(-0.525672\pi\) | ||||
−0.0805622 | + | 0.996750i | \(0.525672\pi\) | |||||||
\(614\) | 50.8952 | 2.05396 | ||||||||
\(615\) | −22.8156 | + | 10.0546i | −0.920013 | + | 0.405442i | ||||
\(616\) | 1.40635 | − | 54.8115i | 0.0566634 | − | 2.20842i | ||||
\(617\) | − | 2.94791i | − | 0.118678i | −0.998238 | − | 0.0593391i | \(-0.981101\pi\) | ||
0.998238 | − | 0.0593391i | \(-0.0188993\pi\) | |||||||
\(618\) | 67.6696 | − | 29.8214i | 2.72207 | − | 1.19959i | ||||
\(619\) | 26.3053i | 1.05730i | 0.848841 | + | 0.528649i | \(0.177301\pi\) | ||||
−0.848841 | + | 0.528649i | \(0.822699\pi\) | |||||||
\(620\) | 0.283503i | 0.0113858i | ||||||||
\(621\) | −11.5939 | − | 3.91350i | −0.465249 | − | 0.157043i | ||||
\(622\) | − | 16.6041i | − | 0.665763i | ||||||
\(623\) | −0.515186 | + | 20.0790i | −0.0206405 | + | 0.804449i | ||||
\(624\) | 1.42470 | + | 3.23287i | 0.0570336 | + | 0.129418i | ||||
\(625\) | 2.32356 | 0.0929426 | ||||||||
\(626\) | 5.67497 | 0.226817 | ||||||||
\(627\) | 14.2893 | − | 6.29716i | 0.570659 | − | 0.251484i | ||||
\(628\) | 23.4722i | 0.936642i | ||||||||
\(629\) | 5.28206 | 0.210610 | ||||||||
\(630\) | −17.0920 | + | 17.7585i | −0.680963 | + | 0.707517i | ||||
\(631\) | 24.0536 | 0.957558 | 0.478779 | − | 0.877935i | \(-0.341080\pi\) | ||||
0.478779 | + | 0.877935i | \(0.341080\pi\) | |||||||
\(632\) | − | 59.8441i | − | 2.38047i | ||||||
\(633\) | 24.1306 | − | 10.6341i | 0.959105 | − | 0.422669i | ||||
\(634\) | 19.1890 | 0.762091 | ||||||||
\(635\) | −1.17564 | −0.0466538 | ||||||||
\(636\) | −16.3822 | − | 37.1739i | −0.649597 | − | 1.47404i | ||||
\(637\) | −0.358974 | + | 6.99079i | −0.0142231 | + | 0.276985i | ||||
\(638\) | 84.2178i | 3.33421i | ||||||||
\(639\) | 5.26483 | + | 4.81329i | 0.208274 | + | 0.190411i | ||||
\(640\) | 27.0387i | 1.06880i | ||||||||
\(641\) | − | 23.0473i | − | 0.910313i | −0.890411 | − | 0.455156i | \(-0.849583\pi\) | ||
0.890411 | − | 0.455156i | \(-0.150417\pi\) | |||||||
\(642\) | 31.9977 | − | 14.1011i | 1.26285 | − | 0.556527i | ||||
\(643\) | 24.7695i | 0.976814i | 0.872616 | + | 0.488407i | \(0.162422\pi\) | ||||
−0.872616 | + | 0.488407i | \(0.837578\pi\) | |||||||
\(644\) | 22.7544 | + | 0.583830i | 0.896648 | + | 0.0230061i | ||||
\(645\) | −10.1602 | + | 4.47752i | −0.400058 | + | 0.176302i | ||||
\(646\) | 3.25800 | 0.128184 | ||||||||
\(647\) | −38.5439 | −1.51532 | −0.757659 | − | 0.652650i | \(-0.773657\pi\) | ||||
−0.757659 | + | 0.652650i | \(0.773657\pi\) | |||||||
\(648\) | 35.2359 | − | 3.16377i | 1.38420 | − | 0.124285i | ||||
\(649\) | 56.4992i | 2.21779i | ||||||||
\(650\) | 7.83264 | 0.307221 | ||||||||
\(651\) | 0.251903 | − | 0.103379i | 0.00987287 | − | 0.00405176i | ||||
\(652\) | 56.6757 | 2.21959 | ||||||||
\(653\) | − | 11.3301i | − | 0.443380i | −0.975117 | − | 0.221690i | \(-0.928843\pi\) | ||
0.975117 | − | 0.221690i | \(-0.0711573\pi\) | |||||||
\(654\) | 7.44755 | + | 16.8997i | 0.291222 | + | 0.660830i | ||||
\(655\) | −27.2616 | −1.06520 | ||||||||
\(656\) | −22.4814 | −0.877751 | ||||||||
\(657\) | 3.18771 | + | 2.91431i | 0.124364 | + | 0.113698i | ||||
\(658\) | −36.7647 | − | 0.943305i | −1.43324 | − | 0.0367739i | ||||
\(659\) | 43.9153i | 1.71070i | 0.518052 | + | 0.855349i | \(0.326657\pi\) | ||||
−0.518052 | + | 0.855349i | \(0.673343\pi\) | |||||||
\(660\) | −17.5699 | − | 39.8689i | −0.683906 | − | 1.55189i | ||||
\(661\) | 22.8566i | 0.889019i | 0.895774 | + | 0.444510i | \(0.146622\pi\) | ||||
−0.895774 | + | 0.444510i | \(0.853378\pi\) | |||||||
\(662\) | − | 2.35211i | − | 0.0914173i | ||||||
\(663\) | 0.559689 | + | 1.27002i | 0.0217365 | + | 0.0493236i | ||||
\(664\) | 2.74585i | 0.106559i | ||||||||
\(665\) | 5.90706 | + | 0.151563i | 0.229066 | + | 0.00587736i | ||||
\(666\) | −34.7030 | − | 31.7267i | −1.34471 | − | 1.22938i | ||||
\(667\) | −15.8218 | −0.612622 | ||||||||
\(668\) | −32.0431 | −1.23979 | ||||||||
\(669\) | −13.3085 | − | 30.1991i | −0.514536 | − | 1.16756i | ||||
\(670\) | 29.3444i | 1.13367i | ||||||||
\(671\) | −58.2113 | −2.24722 | ||||||||
\(672\) | 12.7691 | − | 5.24036i | 0.492579 | − | 0.202151i | ||||
\(673\) | −43.6869 | −1.68400 | −0.842002 | − | 0.539474i | \(-0.818623\pi\) | ||||
−0.842002 | + | 0.539474i | \(0.818623\pi\) | |||||||
\(674\) | − | 34.1757i | − | 1.31640i | ||||||
\(675\) | 5.47450 | − | 16.2185i | 0.210714 | − | 0.624250i | ||||
\(676\) | 3.65324 | 0.140509 | ||||||||
\(677\) | −1.75811 | −0.0675696 | −0.0337848 | − | 0.999429i | \(-0.510756\pi\) | ||||
−0.0337848 | + | 0.999429i | \(0.510756\pi\) | |||||||
\(678\) | −44.5621 | + | 19.6382i | −1.71140 | + | 0.754199i | ||||
\(679\) | 37.8294 | + | 0.970623i | 1.45176 | + | 0.0372491i | ||||
\(680\) | − | 4.11370i | − | 0.157753i | ||||||
\(681\) | −41.3963 | + | 18.2430i | −1.58631 | + | 0.699074i | ||||
\(682\) | 0.744822i | 0.0285207i | ||||||||
\(683\) | 19.7054i | 0.754008i | 0.926212 | + | 0.377004i | \(0.123046\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(684\) | −13.8323 | − | 12.6460i | −0.528892 | − | 0.483531i | ||||
\(685\) | − | 4.54940i | − | 0.173823i | ||||||
\(686\) | −43.9045 | − | 3.38544i | −1.67628 | − | 0.129257i | ||||
\(687\) | 8.44431 | + | 19.1615i | 0.322170 | + | 0.731056i | ||||
\(688\) | −10.0114 | −0.381681 | ||||||||
\(689\) | −6.42005 | −0.244584 | ||||||||
\(690\) | 11.5906 | − | 5.10786i | 0.441245 | − | 0.194453i | ||||
\(691\) | 16.9590i | 0.645149i | 0.946544 | + | 0.322575i | \(0.104548\pi\) | ||||
−0.946544 | + | 0.322575i | \(0.895452\pi\) | |||||||
\(692\) | 40.8095 | 1.55134 | ||||||||
\(693\) | −29.0181 | + | 30.1497i | −1.10231 | + | 1.14529i | ||||
\(694\) | −50.8365 | −1.92973 | ||||||||
\(695\) | − | 22.1413i | − | 0.839867i | ||||||
\(696\) | 41.8583 | − | 18.4466i | 1.58664 | − | 0.699217i | ||||
\(697\) | −8.83176 | −0.334527 | ||||||||
\(698\) | −47.9072 | −1.81331 | ||||||||
\(699\) | 9.00484 | + | 20.4334i | 0.340594 | + | 0.772863i | ||||
\(700\) | −0.816705 | + | 31.8305i | −0.0308686 | + | 1.20308i | ||||
\(701\) | 12.4182i | 0.469029i | 0.972113 | + | 0.234514i | \(0.0753500\pi\) | ||||
−0.972113 | + | 0.234514i | \(0.924650\pi\) | |||||||
\(702\) | 3.95125 | − | 11.7058i | 0.149130 | − | 0.441806i | ||||
\(703\) | 11.2726i | 0.425153i | ||||||||
\(704\) | 59.2623i | 2.23353i | ||||||||
\(705\) | −12.1018 | + | 5.33318i | −0.455782 | + | 0.200859i | ||||
\(706\) | − | 13.3102i | − | 0.500937i | ||||||
\(707\) | 0.405653 | − | 15.8100i | 0.0152561 | − | 0.594598i | ||||
\(708\) | 62.0529 | − | 27.3462i | 2.33209 | − | 1.02773i | ||||
\(709\) | −40.6691 | −1.52736 | −0.763679 | − | 0.645596i | \(-0.776609\pi\) | ||||
−0.763679 | + | 0.645596i | \(0.776609\pi\) | |||||||
\(710\) | −7.38385 | −0.277111 | ||||||||
\(711\) | −30.8176 | + | 33.7086i | −1.15575 | + | 1.26417i | ||||
\(712\) | 29.8416i | 1.11836i | ||||||||
\(713\) | −0.139928 | −0.00524034 | ||||||||
\(714\) | −8.07700 | + | 3.31475i | −0.302274 | + | 0.124051i | ||||
\(715\) | −6.88549 | −0.257503 | ||||||||
\(716\) | − | 43.4780i | − | 1.62485i | ||||||
\(717\) | −10.4415 | − | 23.6934i | −0.389945 | − | 0.884847i | ||||
\(718\) | −28.3132 | −1.05664 | ||||||||
\(719\) | 45.8031 | 1.70817 | 0.854084 | − | 0.520136i | \(-0.174119\pi\) | ||||
0.854084 | + | 0.520136i | \(0.174119\pi\) | |||||||
\(720\) | −5.39245 | + | 5.89832i | −0.200965 | + | 0.219817i | ||||
\(721\) | 47.4931 | + | 1.21857i | 1.76874 | + | 0.0453821i | ||||
\(722\) | − | 38.2225i | − | 1.42249i | ||||||
\(723\) | −8.96979 | − | 20.3539i | −0.333590 | − | 0.756970i | ||||
\(724\) | − | 23.8903i | − | 0.887876i | ||||||
\(725\) | − | 22.1327i | − | 0.821988i | ||||||
\(726\) | −27.8915 | − | 63.2902i | −1.03515 | − | 2.34892i | ||||
\(727\) | − | 45.2897i | − | 1.67970i | −0.542816 | − | 0.839851i | \(-0.682642\pi\) | ||
0.542816 | − | 0.839851i | \(-0.317358\pi\) | |||||||
\(728\) | −0.266756 | + | 10.3966i | −0.00988662 | + | 0.385324i | ||||
\(729\) | −21.4767 | − | 16.3631i | −0.795432 | − | 0.606043i | ||||
\(730\) | −4.47072 | −0.165469 | ||||||||
\(731\) | −3.93296 | −0.145466 | ||||||||
\(732\) | 28.1749 | + | 63.9333i | 1.04137 | + | 2.36304i | ||||
\(733\) | 35.0859i | 1.29593i | 0.761672 | + | 0.647963i | \(0.224379\pi\) | ||||
−0.761672 | + | 0.647963i | \(0.775621\pi\) | |||||||
\(734\) | −6.59109 | −0.243282 | ||||||||
\(735\) | −14.7986 | + | 5.63421i | −0.545854 | + | 0.207821i | ||||
\(736\) | −7.09302 | −0.261452 | ||||||||
\(737\) | 49.8197i | 1.83513i | ||||||||
\(738\) | 58.0244 | + | 53.0479i | 2.13591 | + | 1.95272i | ||||
\(739\) | 27.5255 | 1.01254 | 0.506271 | − | 0.862374i | \(-0.331023\pi\) | ||||
0.506271 | + | 0.862374i | \(0.331023\pi\) | |||||||
\(740\) | 31.4518 | 1.15619 | ||||||||
\(741\) | −2.71038 | + | 1.19444i | −0.0995684 | + | 0.0438790i | ||||
\(742\) | 1.03589 | − | 40.3732i | 0.0380288 | − | 1.48215i | ||||
\(743\) | 13.0242i | 0.477810i | 0.971043 | + | 0.238905i | \(0.0767884\pi\) | ||||
−0.971043 | + | 0.238905i | \(0.923212\pi\) | |||||||
\(744\) | 0.370195 | − | 0.163142i | 0.0135720 | − | 0.00598107i | ||||
\(745\) | 7.77935i | 0.285013i | ||||||||
\(746\) | 42.0346i | 1.53899i | ||||||||
\(747\) | 1.41401 | − | 1.54666i | 0.0517360 | − | 0.0565894i | ||||
\(748\) | − | 15.4330i | − | 0.564285i | ||||||
\(749\) | 22.4572 | + | 0.576205i | 0.820568 | + | 0.0210541i | ||||
\(750\) | 17.9903 | + | 40.8228i | 0.656911 | + | 1.49064i | ||||
\(751\) | 27.1767 | 0.991691 | 0.495846 | − | 0.868411i | \(-0.334858\pi\) | ||||
0.495846 | + | 0.868411i | \(0.334858\pi\) | |||||||
\(752\) | −11.9246 | −0.434845 | ||||||||
\(753\) | −1.60129 | + | 0.705676i | −0.0583543 | + | 0.0257163i | ||||
\(754\) | − | 15.9744i | − | 0.581753i | ||||||
\(755\) | −3.57418 | −0.130078 | ||||||||
\(756\) | 47.1583 | + | 17.2778i | 1.71513 | + | 0.628387i | ||||
\(757\) | 31.6636 | 1.15083 | 0.575417 | − | 0.817860i | \(-0.304840\pi\) | ||||
0.575417 | + | 0.817860i | \(0.304840\pi\) | |||||||
\(758\) | − | 21.6376i | − | 0.785913i | ||||||
\(759\) | 19.6779 | − | 8.67191i | 0.714264 | − | 0.314770i | ||||
\(760\) | 8.77913 | 0.318452 | ||||||||
\(761\) | 17.1558 | 0.621898 | 0.310949 | − | 0.950427i | \(-0.399353\pi\) | ||||
0.310949 | + | 0.950427i | \(0.399353\pi\) | |||||||
\(762\) | 1.49494 | + | 3.39225i | 0.0541558 | + | 0.122888i | ||||
\(763\) | −0.304325 | + | 11.8608i | −0.0110173 | + | 0.429391i | ||||
\(764\) | − | 63.0080i | − | 2.27955i | ||||||
\(765\) | −2.11841 | + | 2.31714i | −0.0765913 | + | 0.0837764i | ||||
\(766\) | 29.3344i | 1.05990i | ||||||||
\(767\) | − | 10.7167i | − | 0.386959i | ||||||
\(768\) | 42.3863 | − | 18.6793i | 1.52948 | − | 0.674031i | ||||
\(769\) | 23.9313i | 0.862986i | 0.902116 | + | 0.431493i | \(0.142013\pi\) | ||||
−0.902116 | + | 0.431493i | \(0.857987\pi\) | |||||||
\(770\) | 1.11099 | − | 43.3002i | 0.0400374 | − | 1.56043i | ||||
\(771\) | −41.4434 | + | 18.2637i | −1.49255 | + | 0.657753i | ||||
\(772\) | −85.3911 | −3.07329 | ||||||||
\(773\) | −34.5517 | −1.24274 | −0.621368 | − | 0.783519i | \(-0.713423\pi\) | ||||
−0.621368 | + | 0.783519i | \(0.713423\pi\) | |||||||
\(774\) | 25.8394 | + | 23.6233i | 0.928777 | + | 0.849120i | ||||
\(775\) | − | 0.195742i | − | 0.00703125i | ||||||
\(776\) | 56.2224 | 2.01827 | ||||||||
\(777\) | −11.4689 | − | 27.9461i | −0.411445 | − | 1.00256i | ||||
\(778\) | 2.39776 | 0.0859640 | ||||||||
\(779\) | − | 18.8480i | − | 0.675301i | ||||||
\(780\) | 3.33265 | + | 7.56231i | 0.119328 | + | 0.270774i | ||||
\(781\) | −12.5360 | −0.448573 | ||||||||
\(782\) | 4.48663 | 0.160442 | ||||||||
\(783\) | −33.0771 | − | 11.1651i | −1.18208 | − | 0.399007i | ||||
\(784\) | −14.2592 | − | 0.732202i | −0.509256 | − | 0.0261501i | ||||
\(785\) | 8.39131i | 0.299499i | ||||||||
\(786\) | 34.6657 | + | 78.6621i | 1.23648 | + | 2.80578i | ||||
\(787\) | 37.7756i | 1.34655i | 0.739391 | + | 0.673277i | \(0.235114\pi\) | ||||
−0.739391 | + | 0.673277i | \(0.764886\pi\) | |||||||
\(788\) | − | 27.5682i | − | 0.982075i | ||||||
\(789\) | 2.48884 | + | 5.64759i | 0.0886052 | + | 0.201059i | ||||
\(790\) | − | 47.2759i | − | 1.68200i | ||||||
\(791\) | −31.2754 | − | 0.802461i | −1.11202 | − | 0.0285322i | ||||
\(792\) | −41.9497 | + | 45.8850i | −1.49062 | + | 1.63045i | ||||
\(793\) | 11.0415 | 0.392095 | ||||||||
\(794\) | −17.0393 | −0.604704 | ||||||||
\(795\) | −5.85664 | − | 13.2897i | −0.207714 | − | 0.471336i | ||||
\(796\) | − | 38.9801i | − | 1.38161i | ||||||
\(797\) | 17.5665 | 0.622239 | 0.311119 | − | 0.950371i | \(-0.399296\pi\) | ||||
0.311119 | + | 0.950371i | \(0.399296\pi\) | |||||||
\(798\) | −7.07407 | − | 17.2373i | −0.250419 | − | 0.610193i | ||||
\(799\) | −4.68454 | −0.165727 | ||||||||
\(800\) | − | 9.92225i | − | 0.350805i | ||||||
\(801\) | 15.3674 | − | 16.8090i | 0.542979 | − | 0.593917i | ||||
\(802\) | 27.8327 | 0.982807 | ||||||||
\(803\) | −7.59019 | −0.267852 | ||||||||
\(804\) | 54.7168 | − | 24.1132i | 1.92971 | − | 0.850409i | ||||
\(805\) | 8.13469 | + | 0.208719i | 0.286710 | + | 0.00735639i | ||||
\(806\) | − | 0.141278i | − | 0.00497629i | ||||||
\(807\) | 34.3406 | − | 15.1336i | 1.20885 | − | 0.532729i | ||||
\(808\) | − | 23.4970i | − | 0.826623i | ||||||
\(809\) | 4.95280i | 0.174131i | 0.996203 | + | 0.0870656i | \(0.0277490\pi\) | ||||
−0.996203 | + | 0.0870656i | \(0.972251\pi\) | |||||||
\(810\) | 27.8358 | − | 2.49932i | 0.978049 | − | 0.0878173i | ||||
\(811\) | − | 20.6467i | − | 0.725004i | −0.931983 | − | 0.362502i | \(-0.881923\pi\) | ||
0.931983 | − | 0.362502i | \(-0.118077\pi\) | |||||||
\(812\) | 64.9173 | + | 1.66564i | 2.27815 | + | 0.0584526i | ||||
\(813\) | −3.94135 | − | 8.94355i | −0.138229 | − | 0.313664i | ||||
\(814\) | 82.6305 | 2.89620 | ||||||||
\(815\) | 20.2616 | 0.709732 | ||||||||
\(816\) | −2.59048 | + | 1.14160i | −0.0906848 | + | 0.0399640i | ||||
\(817\) | − | 8.39340i | − | 0.293648i | ||||||
\(818\) | 78.5451 | 2.74627 | ||||||||
\(819\) | 5.50415 | − | 5.71877i | 0.192330 | − | 0.199830i | ||||
\(820\) | −52.5884 | −1.83647 | ||||||||
\(821\) | − | 13.4087i | − | 0.467966i | −0.972241 | − | 0.233983i | \(-0.924824\pi\) | ||
0.972241 | − | 0.233983i | \(-0.0751760\pi\) | |||||||
\(822\) | −13.1271 | + | 5.78499i | −0.457859 | + | 0.201775i | ||||
\(823\) | 4.81544 | 0.167856 | 0.0839279 | − | 0.996472i | \(-0.473253\pi\) | ||||
0.0839279 | + | 0.996472i | \(0.473253\pi\) | |||||||
\(824\) | 70.5847 | 2.45893 | ||||||||
\(825\) | 12.1309 | + | 27.5270i | 0.422345 | + | 0.958368i | ||||
\(826\) | 67.3935 | + | 1.72918i | 2.34492 | + | 0.0601657i | ||||
\(827\) | 27.6726i | 0.962272i | 0.876646 | + | 0.481136i | \(0.159776\pi\) | ||||
−0.876646 | + | 0.481136i | \(0.840224\pi\) | |||||||
\(828\) | −19.0487 | − | 17.4149i | −0.661986 | − | 0.605211i | ||||
\(829\) | 47.4183i | 1.64691i | 0.567385 | + | 0.823453i | \(0.307955\pi\) | ||||
−0.567385 | + | 0.823453i | \(0.692045\pi\) | |||||||
\(830\) | 2.16917i | 0.0752931i | ||||||||
\(831\) | −23.5163 | + | 10.3634i | −0.815770 | + | 0.359503i | ||||
\(832\) | − | 11.2408i | − | 0.389706i | ||||||
\(833\) | −5.60167 | − | 0.287644i | −0.194086 | − | 0.00996627i | ||||
\(834\) | −63.8877 | + | 28.1548i | −2.21225 | + | 0.974920i | ||||
\(835\) | −11.4554 | −0.396431 | ||||||||
\(836\) | 32.9358 | 1.13911 | ||||||||
\(837\) | −0.292534 | − | 0.0987438i | −0.0101114 | − | 0.00341308i | ||||
\(838\) | 15.7498i | 0.544068i | ||||||||
\(839\) | 13.9589 | 0.481915 | 0.240958 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240958 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(840\) | −21.7646 | + | 8.93205i | −0.750950 | + | 0.308185i | ||||
\(841\) | −16.1389 | −0.556514 | ||||||||
\(842\) | − | 70.3595i | − | 2.42475i | ||||||
\(843\) | 14.2873 | + | 32.4202i | 0.492081 | + | 1.11661i | ||||
\(844\) | 55.6194 | 1.91450 | ||||||||
\(845\) | 1.30604 | 0.0449290 | ||||||||
\(846\) | 30.7773 | + | 28.1377i | 1.05814 | + | 0.967392i | ||||
\(847\) | 1.13971 | − | 44.4195i | 0.0391609 | − | 1.52627i | ||||
\(848\) | − | 13.0950i | − | 0.449685i | ||||||
\(849\) | −12.4338 | − | 28.2143i | −0.426726 | − | 0.968311i | ||||
\(850\) | 6.27624i | 0.215273i | ||||||||
\(851\) | 15.5236i | 0.532142i | ||||||||
\(852\) | 6.06754 | + | 13.7682i | 0.207871 | + | 0.471692i | ||||
\(853\) | 12.9150i | 0.442202i | 0.975251 | + | 0.221101i | \(0.0709651\pi\) | ||||
−0.975251 | + | 0.221101i | \(0.929035\pi\) | |||||||
\(854\) | −1.78158 | + | 69.4357i | −0.0609643 | + | 2.37604i | ||||
\(855\) | −4.94505 | − | 4.52094i | −0.169117 | − | 0.154613i | ||||
\(856\) | 33.3761 | 1.14077 | ||||||||
\(857\) | 6.20273 | 0.211881 | 0.105941 | − | 0.994372i | \(-0.466215\pi\) | ||||
0.105941 | + | 0.994372i | \(0.466215\pi\) | |||||||
\(858\) | 8.75555 | + | 19.8678i | 0.298910 | + | 0.678274i | ||||
\(859\) | − | 8.24498i | − | 0.281315i | −0.990058 | − | 0.140657i | \(-0.955078\pi\) | ||
0.990058 | − | 0.140657i | \(-0.0449216\pi\) | |||||||
\(860\) | −23.4186 | −0.798568 | ||||||||
\(861\) | 19.1763 | + | 46.7268i | 0.653528 | + | 1.59244i | ||||
\(862\) | −49.4932 | −1.68574 | ||||||||
\(863\) | 11.6422i | 0.396305i | 0.980171 | + | 0.198153i | \(0.0634942\pi\) | ||||
−0.980171 | + | 0.198153i | \(0.936506\pi\) | |||||||
\(864\) | −14.8287 | − | 5.00537i | −0.504482 | − | 0.170286i | ||||
\(865\) | 14.5894 | 0.496054 | ||||||||
\(866\) | −1.86596 | −0.0634080 | ||||||||
\(867\) | 25.9268 | − | 11.4257i | 0.880520 | − | 0.388038i | ||||
\(868\) | 0.574128 | + | 0.0147309i | 0.0194872 | + | 0.000500001i | ||||
\(869\) | − | 80.2629i | − | 2.72273i | ||||||
\(870\) | 33.0674 | − | 14.5725i | 1.12109 | − | 0.494055i | ||||
\(871\) | − | 9.44978i | − | 0.320194i | ||||||
\(872\) | 17.6277i | 0.596949i | ||||||||
\(873\) | −31.6686 | − | 28.9525i | −1.07182 | − | 0.979895i | ||||
\(874\) | 9.57501i | 0.323879i | ||||||||
\(875\) | −0.735124 | + | 28.6510i | −0.0248517 | + | 0.968580i | ||||
\(876\) | 3.67373 | + | 8.33628i | 0.124124 | + | 0.281657i | ||||
\(877\) | −4.32934 | −0.146191 | −0.0730956 | − | 0.997325i | \(-0.523288\pi\) | ||||
−0.0730956 | + | 0.997325i | \(0.523288\pi\) | |||||||
\(878\) | −56.2283 | −1.89761 | ||||||||
\(879\) | 22.0487 | − | 9.71667i | 0.743684 | − | 0.327735i | ||||
\(880\) | − | 14.0444i | − | 0.473435i | ||||||
\(881\) | 45.9169 | 1.54698 | 0.773490 | − | 0.633808i | \(-0.218509\pi\) | ||||
0.773490 | + | 0.633808i | \(0.218509\pi\) | |||||||
\(882\) | 35.0751 | + | 35.5362i | 1.18104 | + | 1.19657i | ||||
\(883\) | 3.98052 | 0.133955 | 0.0669776 | − | 0.997754i | \(-0.478664\pi\) | ||||
0.0669776 | + | 0.997754i | \(0.478664\pi\) | |||||||
\(884\) | 2.92732i | 0.0984564i | ||||||||
\(885\) | 22.1839 | − | 9.77627i | 0.745705 | − | 0.328626i | ||||
\(886\) | −28.0175 | −0.941267 | ||||||||
\(887\) | −20.2330 | −0.679357 | −0.339679 | − | 0.940542i | \(-0.610318\pi\) | ||||
−0.339679 | + | 0.940542i | \(0.610318\pi\) | |||||||
\(888\) | −18.0989 | − | 41.0694i | −0.607361 | − | 1.37820i | ||||
\(889\) | −0.0610866 | + | 2.38081i | −0.00204878 | + | 0.0798498i | ||||
\(890\) | 23.5744i | 0.790215i | ||||||||
\(891\) | 47.2583 | − | 4.24325i | 1.58321 | − | 0.142154i | ||||
\(892\) | − | 69.6069i | − | 2.33061i | ||||||
\(893\) | − | 9.99738i | − | 0.334549i | ||||||
\(894\) | 22.4469 | − | 9.89218i | 0.750738 | − | 0.330844i | ||||
\(895\) | − | 15.5434i | − | 0.519558i | ||||||
\(896\) | 54.7567 | + | 1.40494i | 1.82929 | + | 0.0469359i | ||||
\(897\) | −3.73250 | + | 1.64488i | −0.124625 | + | 0.0549211i | ||||
\(898\) | −31.7925 | −1.06093 | ||||||||
\(899\) | −0.399208 | −0.0133143 | ||||||||
\(900\) | 24.3613 | − | 26.6467i | 0.812045 | − | 0.888224i | ||||
\(901\) | − | 5.14434i | − | 0.171383i | ||||||
\(902\) | −138.161 | −4.60025 | ||||||||
\(903\) | 8.53960 | + | 20.8083i | 0.284180 | + | 0.692458i | ||||
\(904\) | −46.4818 | −1.54596 | ||||||||
\(905\) | − | 8.54079i | − | 0.283905i | ||||||
\(906\) | 4.54491 | + | 10.3131i | 0.150995 | + | 0.342631i | ||||
\(907\) | −13.1754 | −0.437481 | −0.218741 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218741 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(908\) | −95.4157 | −3.16648 | ||||||||
\(909\) | −12.1001 | + | 13.2353i | −0.401336 | + | 0.438986i | ||||
\(910\) | −0.210733 | + | 8.21316i | −0.00698571 | + | 0.272264i | ||||
\(911\) | − | 25.5221i | − | 0.845586i | −0.906226 | − | 0.422793i | \(-0.861050\pi\) | ||
0.906226 | − | 0.422793i | \(-0.138950\pi\) | |||||||
\(912\) | −2.43631 | − | 5.52839i | −0.0806744 | − | 0.183063i | ||||
\(913\) | 3.68273i | 0.121880i | ||||||||
\(914\) | − | 80.4944i | − | 2.66252i | ||||||
\(915\) | 10.0725 | + | 22.8562i | 0.332987 | + | 0.755602i | ||||
\(916\) | 44.1660i | 1.45928i | ||||||||
\(917\) | −1.41652 | + | 55.2080i | −0.0467777 | + | 1.82313i | ||||
\(918\) | 9.37976 | + | 3.16611i | 0.309578 | + | 0.104497i | ||||
\(919\) | 24.8561 | 0.819926 | 0.409963 | − | 0.912102i | \(-0.365542\pi\) | ||||
0.409963 | + | 0.912102i | \(0.365542\pi\) | |||||||
\(920\) | 12.0899 | 0.398591 | ||||||||
\(921\) | −14.9515 | − | 33.9273i | −0.492667 | − | 1.11794i | ||||
\(922\) | − | 21.1288i | − | 0.695840i | ||||||
\(923\) | 2.37782 | 0.0782669 | ||||||||
\(924\) | −81.6522 | + | 33.5095i | −2.68616 | + | 1.10238i | ||||
\(925\) | −21.7156 | −0.714004 | ||||||||
\(926\) | 26.7471i | 0.878965i | ||||||||
\(927\) | −39.7585 | − | 36.3486i | −1.30584 | − | 1.19384i | ||||
\(928\) | −20.2361 | −0.664282 | ||||||||
\(929\) | 44.7158 | 1.46708 | 0.733538 | − | 0.679648i | \(-0.237867\pi\) | ||||
0.733538 | + | 0.679648i | \(0.237867\pi\) | |||||||
\(930\) | 0.292448 | − | 0.128879i | 0.00958975 | − | 0.00422612i | ||||
\(931\) | 0.613866 | − | 11.9546i | 0.0201187 | − | 0.391798i | ||||
\(932\) | 47.0977i | 1.54274i | ||||||||
\(933\) | −11.0684 | + | 4.87777i | −0.362365 | + | 0.159691i | ||||
\(934\) | − | 3.82496i | − | 0.125157i | ||||||
\(935\) | − | 5.51729i | − | 0.180435i | ||||||
\(936\) | 7.95700 | − | 8.70345i | 0.260083 | − | 0.284481i | ||||
\(937\) | 16.9933i | 0.555146i | 0.960704 | + | 0.277573i | \(0.0895301\pi\) | ||||
−0.960704 | + | 0.277573i | \(0.910470\pi\) | |||||||
\(938\) | 59.4260 | + | 1.52475i | 1.94033 | + | 0.0497848i | ||||
\(939\) | −1.66713 | − | 3.78299i | −0.0544048 | − | 0.123453i | ||||
\(940\) | −27.8939 | −0.909800 | ||||||||
\(941\) | −0.151960 | −0.00495374 | −0.00247687 | − | 0.999997i | \(-0.500788\pi\) | ||||
−0.00247687 | + | 0.999997i | \(0.500788\pi\) | |||||||
\(942\) | 24.2128 | − | 10.6704i | 0.788894 | − | 0.347659i | ||||
\(943\) | − | 25.9559i | − | 0.845240i | ||||||
\(944\) | 21.8590 | 0.711450 | ||||||||
\(945\) | 16.8591 | + | 6.17681i | 0.548427 | + | 0.200932i | ||||
\(946\) | −61.5256 | −2.00037 | ||||||||
\(947\) | 40.0680i | 1.30203i | 0.759063 | + | 0.651017i | \(0.225657\pi\) | ||||
−0.759063 | + | 0.651017i | \(0.774343\pi\) | |||||||
\(948\) | −88.1525 | + | 38.8481i | −2.86306 | + | 1.26173i | ||||
\(949\) | 1.43970 | 0.0467348 | ||||||||
\(950\) | −13.3942 | −0.434567 | ||||||||
\(951\) | −5.63712 | − | 12.7915i | −0.182796 | − | 0.414794i | ||||
\(952\) | −8.33074 | − | 0.213749i | −0.270001 | − | 0.00692766i | ||||
\(953\) | − | 29.9201i | − | 0.969206i | −0.874734 | − | 0.484603i | \(-0.838964\pi\) | ||
0.874734 | − | 0.484603i | \(-0.161036\pi\) | |||||||
\(954\) | −30.8994 | + | 33.7981i | −1.00041 | + | 1.09426i | ||||
\(955\) | − | 22.5254i | − | 0.728905i | ||||||
\(956\) | − | 54.6118i | − | 1.76627i | ||||||
\(957\) | 56.1404 | − | 24.7406i | 1.81476 | − | 0.799750i | ||||
\(958\) | 67.0866i | 2.16747i | ||||||||
\(959\) | −9.21308 | − | 0.236388i | −0.297506 | − | 0.00763338i | ||||
\(960\) | 23.2688 | − | 10.2544i | 0.750998 | − | 0.330959i | ||||
\(961\) | 30.9965 | 0.999886 | ||||||||
\(962\) | −15.6733 | −0.505328 | ||||||||
\(963\) | −18.7999 | − | 17.1875i | −0.605818 | − | 0.553860i | ||||
\(964\) | − | 46.9144i | − | 1.51101i | ||||||
\(965\) | −30.5274 | −0.982710 | ||||||||
\(966\) | −9.74179 | − | 23.7377i | −0.313437 | − | 0.763748i | ||||
\(967\) | −51.8928 | −1.66876 | −0.834379 | − | 0.551191i | \(-0.814174\pi\) | ||||
−0.834379 | + | 0.551191i | \(0.814174\pi\) | |||||||
\(968\) | − | 66.0166i | − | 2.12185i | ||||||
\(969\) | −0.957099 | − | 2.17181i | −0.0307465 | − | 0.0697687i | ||||
\(970\) | 44.4148 | 1.42607 | ||||||||
\(971\) | −22.7141 | −0.728929 | −0.364464 | − | 0.931217i | \(-0.618748\pi\) | ||||
−0.364464 | + | 0.931217i | \(0.618748\pi\) | |||||||
\(972\) | −27.5339 | − | 49.8499i | −0.883149 | − | 1.59894i | ||||
\(973\) | −44.8388 | − | 1.15047i | −1.43747 | − | 0.0368824i | ||||
\(974\) | 7.45791i | 0.238967i | ||||||||
\(975\) | −2.30099 | − | 5.22131i | −0.0736906 | − | 0.167216i | ||||
\(976\) | 22.5214i | 0.720893i | ||||||||
\(977\) | 10.6566i | 0.340935i | 0.985363 | + | 0.170468i | \(0.0545278\pi\) | ||||
−0.985363 | + | 0.170468i | \(0.945472\pi\) | |||||||
\(978\) | −25.7645 | − | 58.4639i | −0.823859 | − | 1.86947i | ||||
\(979\) | 40.0236i | 1.27916i | ||||||||
\(980\) | −33.3549 | − | 1.71276i | −1.06548 | − | 0.0547122i | ||||
\(981\) | 9.07764 | − | 9.92922i | 0.289827 | − | 0.317016i | ||||
\(982\) | −33.0266 | −1.05392 | ||||||||
\(983\) | −37.1111 | −1.18366 | −0.591829 | − | 0.806063i | \(-0.701594\pi\) | ||||
−0.591829 | + | 0.806063i | \(0.701594\pi\) | |||||||
\(984\) | 30.2620 | + | 68.6693i | 0.964716 | + | 2.18910i | ||||
\(985\) | − | 9.85562i | − | 0.314026i | ||||||
\(986\) | 12.8002 | 0.407641 | ||||||||
\(987\) | 10.1715 | + | 24.7848i | 0.323763 | + | 0.788909i | ||||
\(988\) | −6.24725 | −0.198752 | ||||||||
\(989\) | − | 11.5587i | − | 0.367544i | ||||||
\(990\) | −33.1396 | + | 36.2484i | −1.05324 | + | 1.15205i | ||||
\(991\) | −30.8059 | −0.978583 | −0.489292 | − | 0.872120i | \(-0.662745\pi\) | ||||
−0.489292 | + | 0.872120i | \(0.662745\pi\) | |||||||
\(992\) | −0.178968 | −0.00568224 | ||||||||
\(993\) | −1.56794 | + | 0.690977i | −0.0497570 | + | 0.0219275i | ||||
\(994\) | −0.383668 | + | 14.9532i | −0.0121692 | + | 0.474287i | ||||
\(995\) | − | 13.9354i | − | 0.441782i | ||||||
\(996\) | 4.04473 | − | 1.78248i | 0.128162 | − | 0.0564800i | ||||
\(997\) | 30.2312i | 0.957433i | 0.877970 | + | 0.478716i | \(0.158898\pi\) | ||||
−0.877970 | + | 0.478716i | \(0.841102\pi\) | |||||||
\(998\) | − | 42.2413i | − | 1.33713i | ||||||
\(999\) | −10.9546 | + | 32.4537i | −0.346589 | + | 1.02679i |
(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 | 273.2.e.a.209.3 | ✓ | 32 | |
3.2 | odd | 2 | inner | 273.2.e.a.209.30 | yes | 32 | |
7.6 | odd | 2 | inner | 273.2.e.a.209.4 | yes | 32 | |
21.20 | even | 2 | inner | 273.2.e.a.209.29 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.e.a.209.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
273.2.e.a.209.4 | yes | 32 | 7.6 | odd | 2 | inner | |
273.2.e.a.209.29 | yes | 32 | 21.20 | even | 2 | inner | |
273.2.e.a.209.30 | yes | 32 | 3.2 | odd | 2 | inner |