Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.20 | ||
Character | \(\chi\) | \(=\) | 1110.43 |
Dual form | 1110.2.l.b.697.20 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.73553 | − | 1.40994i | 0.776154 | − | 0.630543i | ||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −3.05055 | + | 3.05055i | −1.15300 | + | 1.15300i | −0.167051 | + | 0.985948i | \(0.553424\pi\) |
−0.985948 | + | 0.167051i | \(0.946576\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.40994 | − | 1.73553i | −0.445861 | − | 0.548824i | ||||
\(11\) | 3.00583i | 0.906293i | 0.891436 | + | 0.453146i | \(0.149699\pi\) | ||||
−0.891436 | + | 0.453146i | \(0.850301\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 6.48482i | 1.79856i | 0.437369 | + | 0.899282i | \(0.355910\pi\) | ||||
−0.437369 | + | 0.899282i | \(0.644090\pi\) | |||||||
\(14\) | 3.05055 | + | 3.05055i | 0.815294 | + | 0.815294i | ||||
\(15\) | 0.230232 | − | 2.22418i | 0.0594456 | − | 0.574282i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00301 | 1.45594 | 0.727972 | − | 0.685607i | \(-0.240463\pi\) | ||||
0.727972 | + | 0.685607i | \(0.240463\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.44125 | + | 4.44125i | −1.01889 | + | 1.01889i | −0.0190753 | + | 0.999818i | \(0.506072\pi\) |
−0.999818 | + | 0.0190753i | \(0.993928\pi\) | |||||||
\(20\) | −1.73553 | + | 1.40994i | −0.388077 | + | 0.315272i | ||||
\(21\) | 4.31413i | 0.941420i | ||||||||
\(22\) | 3.00583 | 0.640846 | ||||||||
\(23\) | 4.23386i | 0.882821i | 0.897305 | + | 0.441410i | \(0.145522\pi\) | ||||
−0.897305 | + | 0.441410i | \(0.854478\pi\) | |||||||
\(24\) | 0.707107 | + | 0.707107i | 0.144338 | + | 0.144338i | ||||
\(25\) | 1.02416 | − | 4.89399i | 0.204831 | − | 0.978797i | ||||
\(26\) | 6.48482 | 1.27178 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 3.05055 | − | 3.05055i | 0.576500 | − | 0.576500i | ||||
\(29\) | 1.51474 | + | 1.51474i | 0.281280 | + | 0.281280i | 0.833619 | − | 0.552339i | \(-0.186265\pi\) |
−0.552339 | + | 0.833619i | \(0.686265\pi\) | |||||||
\(30\) | −2.22418 | − | 0.230232i | −0.406079 | − | 0.0420344i | ||||
\(31\) | 1.07252 | − | 1.07252i | 0.192631 | − | 0.192631i | −0.604201 | − | 0.796832i | \(-0.706508\pi\) |
0.796832 | + | 0.604201i | \(0.206508\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.12544 | + | 2.12544i | 0.369992 | + | 0.369992i | ||||
\(34\) | − | 6.00301i | − | 1.02951i | ||||||
\(35\) | −0.993249 | + | 9.59541i | −0.167890 | + | 1.62192i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −1.11161 | − | 5.98033i | −0.182747 | − | 0.983160i | ||||
\(38\) | 4.44125 | + | 4.44125i | 0.720466 | + | 0.720466i | ||||
\(39\) | 4.58546 | + | 4.58546i | 0.734261 | + | 0.734261i | ||||
\(40\) | 1.40994 | + | 1.73553i | 0.222931 | + | 0.274412i | ||||
\(41\) | − | 6.80482i | − | 1.06273i | −0.847142 | − | 0.531367i | \(-0.821678\pi\) | ||
0.847142 | − | 0.531367i | \(-0.178322\pi\) | |||||||
\(42\) | 4.31413 | 0.665684 | ||||||||
\(43\) | 11.7951i | 1.79874i | 0.437191 | + | 0.899369i | \(0.355973\pi\) | ||||
−0.437191 | + | 0.899369i | \(0.644027\pi\) | |||||||
\(44\) | − | 3.00583i | − | 0.453146i | ||||||
\(45\) | −1.40994 | − | 1.73553i | −0.210181 | − | 0.258718i | ||||
\(46\) | 4.23386 | 0.624249 | ||||||||
\(47\) | 5.31277 | − | 5.31277i | 0.774946 | − | 0.774946i | −0.204020 | − | 0.978967i | \(-0.565401\pi\) |
0.978967 | + | 0.204020i | \(0.0654008\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 11.6117i | − | 1.65881i | ||||||
\(50\) | −4.89399 | − | 1.02416i | −0.692114 | − | 0.144837i | ||||
\(51\) | 4.24477 | − | 4.24477i | 0.594387 | − | 0.594387i | ||||
\(52\) | − | 6.48482i | − | 0.899282i | ||||||
\(53\) | −5.63889 | − | 5.63889i | −0.774562 | − | 0.774562i | 0.204339 | − | 0.978900i | \(-0.434496\pi\) |
−0.978900 | + | 0.204339i | \(0.934496\pi\) | |||||||
\(54\) | −0.707107 | + | 0.707107i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | 4.23804 | + | 5.21672i | 0.571457 | + | 0.703423i | ||||
\(56\) | −3.05055 | − | 3.05055i | −0.407647 | − | 0.407647i | ||||
\(57\) | 6.28088i | 0.831923i | ||||||||
\(58\) | 1.51474 | − | 1.51474i | 0.198895 | − | 0.198895i | ||||
\(59\) | −4.46968 | + | 4.46968i | −0.581903 | + | 0.581903i | −0.935426 | − | 0.353523i | \(-0.884984\pi\) |
0.353523 | + | 0.935426i | \(0.384984\pi\) | |||||||
\(60\) | −0.230232 | + | 2.22418i | −0.0297228 | + | 0.287141i | ||||
\(61\) | −7.40088 | + | 7.40088i | −0.947586 | + | 0.947586i | −0.998693 | − | 0.0511071i | \(-0.983725\pi\) |
0.0511071 | + | 0.998693i | \(0.483725\pi\) | |||||||
\(62\) | −1.07252 | − | 1.07252i | −0.136210 | − | 0.136210i | ||||
\(63\) | 3.05055 | + | 3.05055i | 0.384333 | + | 0.384333i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 9.14318 | + | 11.2546i | 1.13407 | + | 1.39596i | ||||
\(66\) | 2.12544 | − | 2.12544i | 0.261624 | − | 0.261624i | ||||
\(67\) | −2.42395 | − | 2.42395i | −0.296132 | − | 0.296132i | 0.543364 | − | 0.839497i | \(-0.317150\pi\) |
−0.839497 | + | 0.543364i | \(0.817150\pi\) | |||||||
\(68\) | −6.00301 | −0.727972 | ||||||||
\(69\) | 2.99379 | + | 2.99379i | 0.360410 | + | 0.360410i | ||||
\(70\) | 9.59541 | + | 0.993249i | 1.14687 | + | 0.118716i | ||||
\(71\) | −9.18996 | −1.09065 | −0.545324 | − | 0.838225i | \(-0.683593\pi\) | ||||
−0.545324 | + | 0.838225i | \(0.683593\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.01404 | + | 2.01404i | −0.235725 | + | 0.235725i | −0.815077 | − | 0.579352i | \(-0.803306\pi\) |
0.579352 | + | 0.815077i | \(0.303306\pi\) | |||||||
\(74\) | −5.98033 | + | 1.11161i | −0.695199 | + | 0.129222i | ||||
\(75\) | −2.73638 | − | 4.18476i | −0.315970 | − | 0.483214i | ||||
\(76\) | 4.44125 | − | 4.44125i | 0.509447 | − | 0.509447i | ||||
\(77\) | −9.16944 | − | 9.16944i | −1.04495 | − | 1.04495i | ||||
\(78\) | 4.58546 | − | 4.58546i | 0.519201 | − | 0.519201i | ||||
\(79\) | 6.59707 | − | 6.59707i | 0.742228 | − | 0.742228i | −0.230778 | − | 0.973006i | \(-0.574127\pi\) |
0.973006 | + | 0.230778i | \(0.0741272\pi\) | |||||||
\(80\) | 1.73553 | − | 1.40994i | 0.194039 | − | 0.157636i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −6.80482 | −0.751467 | ||||||||
\(83\) | −0.481307 | − | 0.481307i | −0.0528303 | − | 0.0528303i | 0.680198 | − | 0.733028i | \(-0.261894\pi\) |
−0.733028 | + | 0.680198i | \(0.761894\pi\) | |||||||
\(84\) | − | 4.31413i | − | 0.470710i | ||||||
\(85\) | 10.4184 | − | 8.46387i | 1.13004 | − | 0.918036i | ||||
\(86\) | 11.7951 | 1.27190 | ||||||||
\(87\) | 2.14216 | 0.229664 | ||||||||
\(88\) | −3.00583 | −0.320423 | ||||||||
\(89\) | 4.35292 | + | 4.35292i | 0.461409 | + | 0.461409i | 0.899117 | − | 0.437708i | \(-0.144210\pi\) |
−0.437708 | + | 0.899117i | \(0.644210\pi\) | |||||||
\(90\) | −1.73553 | + | 1.40994i | −0.182941 | + | 0.148620i | ||||
\(91\) | −19.7823 | − | 19.7823i | −2.07374 | − | 2.07374i | ||||
\(92\) | − | 4.23386i | − | 0.441410i | ||||||
\(93\) | − | 1.51677i | − | 0.157282i | ||||||
\(94\) | −5.31277 | − | 5.31277i | −0.547970 | − | 0.547970i | ||||
\(95\) | −1.44606 | + | 13.9698i | −0.148362 | + | 1.43327i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 16.2572 | 1.65067 | 0.825336 | − | 0.564643i | \(-0.190986\pi\) | ||||
0.825336 | + | 0.564643i | \(0.190986\pi\) | |||||||
\(98\) | −11.6117 | −1.17296 | ||||||||
\(99\) | 3.00583 | 0.302098 | ||||||||
\(100\) | −1.02416 | + | 4.89399i | −0.102416 | + | 0.489399i | ||||
\(101\) | 16.3032i | 1.62223i | 0.584887 | + | 0.811115i | \(0.301139\pi\) | ||||
−0.584887 | + | 0.811115i | \(0.698861\pi\) | |||||||
\(102\) | −4.24477 | − | 4.24477i | −0.420295 | − | 0.420295i | ||||
\(103\) | 8.32869 | 0.820650 | 0.410325 | − | 0.911939i | \(-0.365415\pi\) | ||||
0.410325 | + | 0.911939i | \(0.365415\pi\) | |||||||
\(104\) | −6.48482 | −0.635889 | ||||||||
\(105\) | 6.08265 | + | 7.48731i | 0.593606 | + | 0.730687i | ||||
\(106\) | −5.63889 | + | 5.63889i | −0.547698 | + | 0.547698i | ||||
\(107\) | 7.63911 | − | 7.63911i | 0.738501 | − | 0.738501i | −0.233787 | − | 0.972288i | \(-0.575112\pi\) |
0.972288 | + | 0.233787i | \(0.0751119\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −6.00958 | + | 6.00958i | −0.575613 | + | 0.575613i | −0.933691 | − | 0.358079i | \(-0.883432\pi\) |
0.358079 | + | 0.933691i | \(0.383432\pi\) | |||||||
\(110\) | 5.21672 | − | 4.23804i | 0.497395 | − | 0.404081i | ||||
\(111\) | −5.01476 | − | 3.44271i | −0.475980 | − | 0.326767i | ||||
\(112\) | −3.05055 | + | 3.05055i | −0.288250 | + | 0.288250i | ||||
\(113\) | 9.17752 | 0.863348 | 0.431674 | − | 0.902030i | \(-0.357923\pi\) | ||||
0.431674 | + | 0.902030i | \(0.357923\pi\) | |||||||
\(114\) | 6.28088 | 0.588258 | ||||||||
\(115\) | 5.96948 | + | 7.34801i | 0.556657 | + | 0.685205i | ||||
\(116\) | −1.51474 | − | 1.51474i | −0.140640 | − | 0.140640i | ||||
\(117\) | 6.48482 | 0.599522 | ||||||||
\(118\) | 4.46968 | + | 4.46968i | 0.411467 | + | 0.411467i | ||||
\(119\) | −18.3125 | + | 18.3125i | −1.67870 | + | 1.67870i | ||||
\(120\) | 2.22418 | + | 0.230232i | 0.203039 | + | 0.0210172i | ||||
\(121\) | 1.96497 | 0.178634 | ||||||||
\(122\) | 7.40088 | + | 7.40088i | 0.670045 | + | 0.670045i | ||||
\(123\) | −4.81173 | − | 4.81173i | −0.433859 | − | 0.433859i | ||||
\(124\) | −1.07252 | + | 1.07252i | −0.0963153 | + | 0.0963153i | ||||
\(125\) | −5.12276 | − | 9.93767i | −0.458193 | − | 0.888853i | ||||
\(126\) | 3.05055 | − | 3.05055i | 0.271765 | − | 0.271765i | ||||
\(127\) | 8.41071 | − | 8.41071i | 0.746330 | − | 0.746330i | −0.227458 | − | 0.973788i | \(-0.573042\pi\) |
0.973788 | + | 0.227458i | \(0.0730415\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 8.34040 | + | 8.34040i | 0.734331 | + | 0.734331i | ||||
\(130\) | 11.2546 | − | 9.14318i | 0.987095 | − | 0.801910i | ||||
\(131\) | 1.85417 | − | 1.85417i | 0.161999 | − | 0.161999i | −0.621452 | − | 0.783452i | \(-0.713457\pi\) |
0.783452 | + | 0.621452i | \(0.213457\pi\) | |||||||
\(132\) | −2.12544 | − | 2.12544i | −0.184996 | − | 0.184996i | ||||
\(133\) | − | 27.0965i | − | 2.34957i | ||||||
\(134\) | −2.42395 | + | 2.42395i | −0.209397 | + | 0.209397i | ||||
\(135\) | −2.22418 | − | 0.230232i | −0.191427 | − | 0.0198152i | ||||
\(136\) | 6.00301i | 0.514754i | ||||||||
\(137\) | 6.46226 | − | 6.46226i | 0.552108 | − | 0.552108i | −0.374941 | − | 0.927049i | \(-0.622337\pi\) |
0.927049 | + | 0.374941i | \(0.122337\pi\) | |||||||
\(138\) | 2.99379 | − | 2.99379i | 0.254848 | − | 0.254848i | ||||
\(139\) | 11.3845 | 0.965623 | 0.482812 | − | 0.875724i | \(-0.339616\pi\) | ||||
0.482812 | + | 0.875724i | \(0.339616\pi\) | |||||||
\(140\) | 0.993249 | − | 9.59541i | 0.0839449 | − | 0.810960i | ||||
\(141\) | − | 7.51338i | − | 0.632741i | ||||||
\(142\) | 9.18996i | 0.771204i | ||||||||
\(143\) | −19.4923 | −1.63003 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 4.76456 | + | 0.493194i | 0.395676 | + | 0.0409575i | ||||
\(146\) | 2.01404 | + | 2.01404i | 0.166683 | + | 0.166683i | ||||
\(147\) | −8.21071 | − | 8.21071i | −0.677208 | − | 0.677208i | ||||
\(148\) | 1.11161 | + | 5.98033i | 0.0913735 | + | 0.491580i | ||||
\(149\) | 21.2592i | 1.74162i | 0.491619 | + | 0.870811i | \(0.336405\pi\) | ||||
−0.491619 | + | 0.870811i | \(0.663595\pi\) | |||||||
\(150\) | −4.18476 | + | 2.73638i | −0.341684 | + | 0.223425i | ||||
\(151\) | − | 0.529983i | − | 0.0431294i | −0.999767 | − | 0.0215647i | \(-0.993135\pi\) | ||
0.999767 | − | 0.0215647i | \(-0.00686480\pi\) | |||||||
\(152\) | −4.44125 | − | 4.44125i | −0.360233 | − | 0.360233i | ||||
\(153\) | − | 6.00301i | − | 0.485315i | ||||||
\(154\) | −9.16944 | + | 9.16944i | −0.738895 | + | 0.738895i | ||||
\(155\) | 0.349210 | − | 3.37358i | 0.0280492 | − | 0.270973i | ||||
\(156\) | −4.58546 | − | 4.58546i | −0.367130 | − | 0.367130i | ||||
\(157\) | −9.06045 | + | 9.06045i | −0.723103 | + | 0.723103i | −0.969236 | − | 0.246133i | \(-0.920840\pi\) |
0.246133 | + | 0.969236i | \(0.420840\pi\) | |||||||
\(158\) | −6.59707 | − | 6.59707i | −0.524835 | − | 0.524835i | ||||
\(159\) | −7.97460 | −0.632427 | ||||||||
\(160\) | −1.40994 | − | 1.73553i | −0.111465 | − | 0.137206i | ||||
\(161\) | −12.9156 | − | 12.9156i | −1.01789 | − | 1.01789i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 21.1810 | 1.65902 | 0.829512 | − | 0.558489i | \(-0.188619\pi\) | ||||
0.829512 | + | 0.558489i | \(0.188619\pi\) | |||||||
\(164\) | 6.80482i | 0.531367i | ||||||||
\(165\) | 6.68552 | + | 0.692038i | 0.520467 | + | 0.0538751i | ||||
\(166\) | −0.481307 | + | 0.481307i | −0.0373567 | + | 0.0373567i | ||||
\(167\) | −12.7951 | −0.990113 | −0.495057 | − | 0.868861i | \(-0.664853\pi\) | ||||
−0.495057 | + | 0.868861i | \(0.664853\pi\) | |||||||
\(168\) | −4.31413 | −0.332842 | ||||||||
\(169\) | −29.0528 | −2.23483 | ||||||||
\(170\) | −8.46387 | − | 10.4184i | −0.649149 | − | 0.799057i | ||||
\(171\) | 4.44125 | + | 4.44125i | 0.339631 | + | 0.339631i | ||||
\(172\) | − | 11.7951i | − | 0.899369i | ||||||
\(173\) | 4.92625 | − | 4.92625i | 0.374536 | − | 0.374536i | −0.494590 | − | 0.869126i | \(-0.664682\pi\) |
0.869126 | + | 0.494590i | \(0.164682\pi\) | |||||||
\(174\) | − | 2.14216i | − | 0.162397i | ||||||
\(175\) | 11.8051 | + | 18.0536i | 0.892383 | + | 1.36472i | ||||
\(176\) | 3.00583i | 0.226573i | ||||||||
\(177\) | 6.32108i | 0.475122i | ||||||||
\(178\) | 4.35292 | − | 4.35292i | 0.326265 | − | 0.326265i | ||||
\(179\) | 7.25672 | + | 7.25672i | 0.542393 | + | 0.542393i | 0.924230 | − | 0.381837i | \(-0.124708\pi\) |
−0.381837 | + | 0.924230i | \(0.624708\pi\) | |||||||
\(180\) | 1.40994 | + | 1.73553i | 0.105091 | + | 0.129359i | ||||
\(181\) | 9.70338 | 0.721247 | 0.360623 | − | 0.932712i | \(-0.382564\pi\) | ||||
0.360623 | + | 0.932712i | \(0.382564\pi\) | |||||||
\(182\) | −19.7823 | + | 19.7823i | −1.46636 | + | 1.46636i | ||||
\(183\) | 10.4664i | 0.773701i | ||||||||
\(184\) | −4.23386 | −0.312124 | ||||||||
\(185\) | −10.3611 | − | 8.81177i | −0.761764 | − | 0.647854i | ||||
\(186\) | −1.51677 | −0.111215 | ||||||||
\(187\) | 18.0441i | 1.31951i | ||||||||
\(188\) | −5.31277 | + | 5.31277i | −0.387473 | + | 0.387473i | ||||
\(189\) | 4.31413 | 0.313807 | ||||||||
\(190\) | 13.9698 | + | 1.44606i | 1.01348 | + | 0.104908i | ||||
\(191\) | −7.13391 | − | 7.13391i | −0.516192 | − | 0.516192i | 0.400225 | − | 0.916417i | \(-0.368932\pi\) |
−0.916417 | + | 0.400225i | \(0.868932\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | − | 19.3360i | − | 1.39184i | −0.718121 | − | 0.695918i | \(-0.754998\pi\) | ||
0.718121 | − | 0.695918i | \(-0.245002\pi\) | |||||||
\(194\) | − | 16.2572i | − | 1.16720i | ||||||
\(195\) | 14.4234 | + | 1.49301i | 1.03288 | + | 0.106917i | ||||
\(196\) | 11.6117i | 0.829407i | ||||||||
\(197\) | −8.51405 | + | 8.51405i | −0.606601 | + | 0.606601i | −0.942056 | − | 0.335455i | \(-0.891110\pi\) |
0.335455 | + | 0.942056i | \(0.391110\pi\) | |||||||
\(198\) | − | 3.00583i | − | 0.213615i | ||||||
\(199\) | −4.71139 | − | 4.71139i | −0.333982 | − | 0.333982i | 0.520115 | − | 0.854096i | \(-0.325889\pi\) |
−0.854096 | + | 0.520115i | \(0.825889\pi\) | |||||||
\(200\) | 4.89399 | + | 1.02416i | 0.346057 | + | 0.0724187i | ||||
\(201\) | −3.42798 | −0.241791 | ||||||||
\(202\) | 16.3032 | 1.14709 | ||||||||
\(203\) | −9.24157 | −0.648631 | ||||||||
\(204\) | −4.24477 | + | 4.24477i | −0.297193 | + | 0.297193i | ||||
\(205\) | −9.59437 | − | 11.8100i | −0.670100 | − | 0.824846i | ||||
\(206\) | − | 8.32869i | − | 0.580287i | ||||||
\(207\) | 4.23386 | 0.294274 | ||||||||
\(208\) | 6.48482i | 0.449641i | ||||||||
\(209\) | −13.3497 | − | 13.3497i | −0.923416 | − | 0.923416i | ||||
\(210\) | 7.48731 | − | 6.08265i | 0.516674 | − | 0.419743i | ||||
\(211\) | −19.7786 | −1.36161 | −0.680806 | − | 0.732464i | \(-0.738370\pi\) | ||||
−0.680806 | + | 0.732464i | \(0.738370\pi\) | |||||||
\(212\) | 5.63889 | + | 5.63889i | 0.387281 | + | 0.387281i | ||||
\(213\) | −6.49828 | + | 6.49828i | −0.445255 | + | 0.445255i | ||||
\(214\) | −7.63911 | − | 7.63911i | −0.522199 | − | 0.522199i | ||||
\(215\) | 16.6304 | + | 20.4708i | 1.13418 | + | 1.39610i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 6.54356i | 0.444206i | ||||||||
\(218\) | 6.00958 | + | 6.00958i | 0.407020 | + | 0.407020i | ||||
\(219\) | 2.84828i | 0.192469i | ||||||||
\(220\) | −4.23804 | − | 5.21672i | −0.285728 | − | 0.351711i | ||||
\(221\) | 38.9284i | 2.61861i | ||||||||
\(222\) | −3.44271 | + | 5.01476i | −0.231059 | + | 0.336568i | ||||
\(223\) | 4.53283 | + | 4.53283i | 0.303540 | + | 0.303540i | 0.842397 | − | 0.538857i | \(-0.181144\pi\) |
−0.538857 | + | 0.842397i | \(0.681144\pi\) | |||||||
\(224\) | 3.05055 | + | 3.05055i | 0.203823 | + | 0.203823i | ||||
\(225\) | −4.89399 | − | 1.02416i | −0.326266 | − | 0.0682770i | ||||
\(226\) | − | 9.17752i | − | 0.610479i | ||||||
\(227\) | 12.5323 | 0.831799 | 0.415899 | − | 0.909411i | \(-0.363467\pi\) | ||||
0.415899 | + | 0.909411i | \(0.363467\pi\) | |||||||
\(228\) | − | 6.28088i | − | 0.415961i | ||||||
\(229\) | − | 20.0623i | − | 1.32575i | −0.748728 | − | 0.662877i | \(-0.769335\pi\) | ||
0.748728 | − | 0.662877i | \(-0.230665\pi\) | |||||||
\(230\) | 7.34801 | − | 5.96948i | 0.484513 | − | 0.393616i | ||||
\(231\) | −12.9675 | −0.853202 | ||||||||
\(232\) | −1.51474 | + | 1.51474i | −0.0994474 | + | 0.0994474i | ||||
\(233\) | −4.10021 | + | 4.10021i | −0.268614 | + | 0.268614i | −0.828542 | − | 0.559928i | \(-0.810829\pi\) |
0.559928 | + | 0.828542i | \(0.310829\pi\) | |||||||
\(234\) | − | 6.48482i | − | 0.423926i | ||||||
\(235\) | 1.72982 | − | 16.7111i | 0.112841 | − | 1.09012i | ||||
\(236\) | 4.46968 | − | 4.46968i | 0.290951 | − | 0.290951i | ||||
\(237\) | − | 9.32966i | − | 0.606027i | ||||||
\(238\) | 18.3125 | + | 18.3125i | 1.18702 | + | 1.18702i | ||||
\(239\) | −9.03944 | + | 9.03944i | −0.584713 | + | 0.584713i | −0.936195 | − | 0.351482i | \(-0.885678\pi\) |
0.351482 | + | 0.936195i | \(0.385678\pi\) | |||||||
\(240\) | 0.230232 | − | 2.22418i | 0.0148614 | − | 0.143570i | ||||
\(241\) | 7.69908 | + | 7.69908i | 0.495942 | + | 0.495942i | 0.910172 | − | 0.414230i | \(-0.135949\pi\) |
−0.414230 | + | 0.910172i | \(0.635949\pi\) | |||||||
\(242\) | − | 1.96497i | − | 0.126313i | ||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 7.40088 | − | 7.40088i | 0.473793 | − | 0.473793i | ||||
\(245\) | −16.3718 | − | 20.1525i | −1.04595 | − | 1.28750i | ||||
\(246\) | −4.81173 | + | 4.81173i | −0.306785 | + | 0.306785i | ||||
\(247\) | −28.8007 | − | 28.8007i | −1.83255 | − | 1.83255i | ||||
\(248\) | 1.07252 | + | 1.07252i | 0.0681052 | + | 0.0681052i | ||||
\(249\) | −0.680671 | −0.0431358 | ||||||||
\(250\) | −9.93767 | + | 5.12276i | −0.628514 | + | 0.323992i | ||||
\(251\) | 9.83570 | − | 9.83570i | 0.620824 | − | 0.620824i | −0.324918 | − | 0.945742i | \(-0.605337\pi\) |
0.945742 | + | 0.324918i | \(0.105337\pi\) | |||||||
\(252\) | −3.05055 | − | 3.05055i | −0.192167 | − | 0.192167i | ||||
\(253\) | −12.7263 | −0.800094 | ||||||||
\(254\) | −8.41071 | − | 8.41071i | −0.527735 | − | 0.527735i | ||||
\(255\) | 1.38208 | − | 13.3518i | 0.0865495 | − | 0.836122i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.77576 | 0.235525 | 0.117763 | − | 0.993042i | \(-0.462428\pi\) | ||||
0.117763 | + | 0.993042i | \(0.462428\pi\) | |||||||
\(258\) | 8.34040 | − | 8.34040i | 0.519251 | − | 0.519251i | ||||
\(259\) | 21.6343 | + | 14.8523i | 1.34429 | + | 0.922876i | ||||
\(260\) | −9.14318 | − | 11.2546i | −0.567036 | − | 0.697982i | ||||
\(261\) | 1.51474 | − | 1.51474i | 0.0937599 | − | 0.0937599i | ||||
\(262\) | −1.85417 | − | 1.85417i | −0.114551 | − | 0.114551i | ||||
\(263\) | 9.85731 | − | 9.85731i | 0.607828 | − | 0.607828i | −0.334550 | − | 0.942378i | \(-0.608584\pi\) |
0.942378 | + | 0.334550i | \(0.108584\pi\) | |||||||
\(264\) | −2.12544 | + | 2.12544i | −0.130812 | + | 0.130812i | ||||
\(265\) | −17.7370 | − | 1.83601i | −1.08957 | − | 0.112785i | ||||
\(266\) | −27.0965 | −1.66139 | ||||||||
\(267\) | 6.15596 | 0.376739 | ||||||||
\(268\) | 2.42395 | + | 2.42395i | 0.148066 | + | 0.148066i | ||||
\(269\) | − | 25.0749i | − | 1.52884i | −0.644716 | − | 0.764422i | \(-0.723025\pi\) | ||
0.644716 | − | 0.764422i | \(-0.276975\pi\) | |||||||
\(270\) | −0.230232 | + | 2.22418i | −0.0140115 | + | 0.135360i | ||||
\(271\) | −24.0884 | −1.46326 | −0.731632 | − | 0.681700i | \(-0.761241\pi\) | ||||
−0.731632 | + | 0.681700i | \(0.761241\pi\) | |||||||
\(272\) | 6.00301 | 0.363986 | ||||||||
\(273\) | −27.9763 | −1.69320 | ||||||||
\(274\) | −6.46226 | − | 6.46226i | −0.390399 | − | 0.390399i | ||||
\(275\) | 14.7105 | + | 3.07844i | 0.887077 | + | 0.185637i | ||||
\(276\) | −2.99379 | − | 2.99379i | −0.180205 | − | 0.180205i | ||||
\(277\) | 16.3414i | 0.981859i | 0.871199 | + | 0.490929i | \(0.163343\pi\) | ||||
−0.871199 | + | 0.490929i | \(0.836657\pi\) | |||||||
\(278\) | − | 11.3845i | − | 0.682799i | ||||||
\(279\) | −1.07252 | − | 1.07252i | −0.0642102 | − | 0.0642102i | ||||
\(280\) | −9.59541 | − | 0.993249i | −0.573436 | − | 0.0593580i | ||||
\(281\) | −11.9540 | − | 11.9540i | −0.713117 | − | 0.713117i | 0.254069 | − | 0.967186i | \(-0.418231\pi\) |
−0.967186 | + | 0.254069i | \(0.918231\pi\) | |||||||
\(282\) | −7.51338 | −0.447416 | ||||||||
\(283\) | −10.0542 | −0.597658 | −0.298829 | − | 0.954307i | \(-0.596596\pi\) | ||||
−0.298829 | + | 0.954307i | \(0.596596\pi\) | |||||||
\(284\) | 9.18996 | 0.545324 | ||||||||
\(285\) | 8.85565 | + | 10.9007i | 0.524563 | + | 0.645701i | ||||
\(286\) | 19.4923i | 1.15260i | ||||||||
\(287\) | 20.7584 | + | 20.7584i | 1.22533 | + | 1.22533i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 19.0362 | 1.11977 | ||||||||
\(290\) | 0.493194 | − | 4.76456i | 0.0289613 | − | 0.279785i | ||||
\(291\) | 11.4956 | − | 11.4956i | 0.673884 | − | 0.673884i | ||||
\(292\) | 2.01404 | − | 2.01404i | 0.117863 | − | 0.117863i | ||||
\(293\) | 8.47560 | + | 8.47560i | 0.495150 | + | 0.495150i | 0.909924 | − | 0.414774i | \(-0.136139\pi\) |
−0.414774 | + | 0.909924i | \(0.636139\pi\) | |||||||
\(294\) | −8.21071 | + | 8.21071i | −0.478858 | + | 0.478858i | ||||
\(295\) | −1.45531 | + | 14.0592i | −0.0847316 | + | 0.818561i | ||||
\(296\) | 5.98033 | − | 1.11161i | 0.347600 | − | 0.0646108i | ||||
\(297\) | 2.12544 | − | 2.12544i | 0.123331 | − | 0.123331i | ||||
\(298\) | 21.2592 | 1.23151 | ||||||||
\(299\) | −27.4558 | −1.58781 | ||||||||
\(300\) | 2.73638 | + | 4.18476i | 0.157985 | + | 0.241607i | ||||
\(301\) | −35.9816 | − | 35.9816i | −2.07394 | − | 2.07394i | ||||
\(302\) | −0.529983 | −0.0304971 | ||||||||
\(303\) | 11.5281 | + | 11.5281i | 0.662273 | + | 0.662273i | ||||
\(304\) | −4.44125 | + | 4.44125i | −0.254723 | + | 0.254723i | ||||
\(305\) | −2.40970 | + | 23.2793i | −0.137979 | + | 1.33297i | ||||
\(306\) | −6.00301 | −0.343169 | ||||||||
\(307\) | −2.69632 | − | 2.69632i | −0.153887 | − | 0.153887i | 0.625964 | − | 0.779852i | \(-0.284706\pi\) |
−0.779852 | + | 0.625964i | \(0.784706\pi\) | |||||||
\(308\) | 9.16944 | + | 9.16944i | 0.522477 | + | 0.522477i | ||||
\(309\) | 5.88927 | − | 5.88927i | 0.335029 | − | 0.335029i | ||||
\(310\) | −3.37358 | − | 0.349210i | −0.191607 | − | 0.0198338i | ||||
\(311\) | −6.10837 | + | 6.10837i | −0.346374 | + | 0.346374i | −0.858757 | − | 0.512383i | \(-0.828763\pi\) |
0.512383 | + | 0.858757i | \(0.328763\pi\) | |||||||
\(312\) | −4.58546 | + | 4.58546i | −0.259600 | + | 0.259600i | ||||
\(313\) | 22.7166i | 1.28402i | 0.766697 | + | 0.642009i | \(0.221899\pi\) | ||||
−0.766697 | + | 0.642009i | \(0.778101\pi\) | |||||||
\(314\) | 9.06045 | + | 9.06045i | 0.511311 | + | 0.511311i | ||||
\(315\) | 9.59541 | + | 0.993249i | 0.540640 | + | 0.0559632i | ||||
\(316\) | −6.59707 | + | 6.59707i | −0.371114 | + | 0.371114i | ||||
\(317\) | 17.3373 | + | 17.3373i | 0.973762 | + | 0.973762i | 0.999664 | − | 0.0259029i | \(-0.00824608\pi\) |
−0.0259029 | + | 0.999664i | \(0.508246\pi\) | |||||||
\(318\) | 7.97460i | 0.447193i | ||||||||
\(319\) | −4.55305 | + | 4.55305i | −0.254922 | + | 0.254922i | ||||
\(320\) | −1.73553 | + | 1.40994i | −0.0970193 | + | 0.0788179i | ||||
\(321\) | − | 10.8033i | − | 0.602983i | ||||||
\(322\) | −12.9156 | + | 12.9156i | −0.719758 | + | 0.719758i | ||||
\(323\) | −26.6609 | + | 26.6609i | −1.48345 | + | 1.48345i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 31.7366 | + | 6.64146i | 1.76043 | + | 0.368402i | ||||
\(326\) | − | 21.1810i | − | 1.17311i | ||||||
\(327\) | 8.49882i | 0.469986i | ||||||||
\(328\) | 6.80482 | 0.375733 | ||||||||
\(329\) | 32.4137i | 1.78703i | ||||||||
\(330\) | 0.692038 | − | 6.68552i | 0.0380954 | − | 0.368026i | ||||
\(331\) | −0.296981 | − | 0.296981i | −0.0163236 | − | 0.0163236i | 0.698898 | − | 0.715221i | \(-0.253674\pi\) |
−0.715221 | + | 0.698898i | \(0.753674\pi\) | |||||||
\(332\) | 0.481307 | + | 0.481307i | 0.0264152 | + | 0.0264152i | ||||
\(333\) | −5.98033 | + | 1.11161i | −0.327720 | + | 0.0609157i | ||||
\(334\) | 12.7951i | 0.700116i | ||||||||
\(335\) | −7.62446 | − | 0.789230i | −0.416569 | − | 0.0431202i | ||||
\(336\) | 4.31413i | 0.235355i | ||||||||
\(337\) | −12.3894 | − | 12.3894i | −0.674892 | − | 0.674892i | 0.283948 | − | 0.958840i | \(-0.408356\pi\) |
−0.958840 | + | 0.283948i | \(0.908356\pi\) | |||||||
\(338\) | 29.0528i | 1.58027i | ||||||||
\(339\) | 6.48948 | − | 6.48948i | 0.352460 | − | 0.352460i | ||||
\(340\) | −10.4184 | + | 8.46387i | −0.565019 | + | 0.459018i | ||||
\(341\) | 3.22382 | + | 3.22382i | 0.174580 | + | 0.174580i | ||||
\(342\) | 4.44125 | − | 4.44125i | 0.240155 | − | 0.240155i | ||||
\(343\) | 14.0682 | + | 14.0682i | 0.759612 | + | 0.759612i | ||||
\(344\) | −11.7951 | −0.635950 | ||||||||
\(345\) | 9.41688 | + | 0.974769i | 0.506988 | + | 0.0524798i | ||||
\(346\) | −4.92625 | − | 4.92625i | −0.264837 | − | 0.264837i | ||||
\(347\) | − | 21.8151i | − | 1.17110i | −0.810637 | − | 0.585549i | \(-0.800879\pi\) | ||
0.810637 | − | 0.585549i | \(-0.199121\pi\) | |||||||
\(348\) | −2.14216 | −0.114832 | ||||||||
\(349\) | − | 0.296683i | − | 0.0158811i | −0.999968 | − | 0.00794054i | \(-0.997472\pi\) | ||
0.999968 | − | 0.00794054i | \(-0.00252758\pi\) | |||||||
\(350\) | 18.0536 | − | 11.8051i | 0.965005 | − | 0.631010i | ||||
\(351\) | 4.58546 | − | 4.58546i | 0.244754 | − | 0.244754i | ||||
\(352\) | 3.00583 | 0.160211 | ||||||||
\(353\) | −1.99266 | −0.106058 | −0.0530292 | − | 0.998593i | \(-0.516888\pi\) | ||||
−0.0530292 | + | 0.998593i | \(0.516888\pi\) | |||||||
\(354\) | 6.32108 | 0.335962 | ||||||||
\(355\) | −15.9495 | + | 12.9573i | −0.846511 | + | 0.687700i | ||||
\(356\) | −4.35292 | − | 4.35292i | −0.230704 | − | 0.230704i | ||||
\(357\) | 25.8978i | 1.37066i | ||||||||
\(358\) | 7.25672 | − | 7.25672i | 0.383530 | − | 0.383530i | ||||
\(359\) | − | 10.3520i | − | 0.546358i | −0.961963 | − | 0.273179i | \(-0.911925\pi\) | ||
0.961963 | − | 0.273179i | \(-0.0880752\pi\) | |||||||
\(360\) | 1.73553 | − | 1.40994i | 0.0914707 | − | 0.0743102i | ||||
\(361\) | − | 20.4495i | − | 1.07629i | ||||||
\(362\) | − | 9.70338i | − | 0.509998i | ||||||
\(363\) | 1.38944 | − | 1.38944i | 0.0729268 | − | 0.0729268i | ||||
\(364\) | 19.7823 | + | 19.7823i | 1.03687 | + | 1.03687i | ||||
\(365\) | −0.655764 | + | 6.33510i | −0.0343243 | + | 0.331594i | ||||
\(366\) | 10.4664 | 0.547089 | ||||||||
\(367\) | 0.446811 | − | 0.446811i | 0.0233233 | − | 0.0233233i | −0.695349 | − | 0.718672i | \(-0.744750\pi\) |
0.718672 | + | 0.695349i | \(0.244750\pi\) | |||||||
\(368\) | 4.23386i | 0.220705i | ||||||||
\(369\) | −6.80482 | −0.354245 | ||||||||
\(370\) | −8.81177 | + | 10.3611i | −0.458102 | + | 0.538649i | ||||
\(371\) | 34.4034 | 1.78614 | ||||||||
\(372\) | 1.51677i | 0.0786411i | ||||||||
\(373\) | 19.8830 | − | 19.8830i | 1.02950 | − | 1.02950i | 0.0299526 | − | 0.999551i | \(-0.490464\pi\) |
0.999551 | − | 0.0299526i | \(-0.00953562\pi\) | |||||||
\(374\) | 18.0441 | 0.933036 | ||||||||
\(375\) | −10.6493 | − | 3.40466i | −0.549929 | − | 0.175816i | ||||
\(376\) | 5.31277 | + | 5.31277i | 0.273985 | + | 0.273985i | ||||
\(377\) | −9.82280 | + | 9.82280i | −0.505900 | + | 0.505900i | ||||
\(378\) | − | 4.31413i | − | 0.221895i | ||||||
\(379\) | − | 2.16219i | − | 0.111064i | −0.998457 | − | 0.0555322i | \(-0.982314\pi\) | ||
0.998457 | − | 0.0555322i | \(-0.0176855\pi\) | |||||||
\(380\) | 1.44606 | − | 13.9698i | 0.0741812 | − | 0.716637i | ||||
\(381\) | − | 11.8945i | − | 0.609376i | ||||||
\(382\) | −7.13391 | + | 7.13391i | −0.365003 | + | 0.365003i | ||||
\(383\) | 28.0841i | 1.43503i | 0.696543 | + | 0.717515i | \(0.254721\pi\) | ||||
−0.696543 | + | 0.717515i | \(0.745279\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | −28.8422 | − | 2.98554i | −1.46994 | − | 0.152157i | ||||
\(386\) | −19.3360 | −0.984177 | ||||||||
\(387\) | 11.7951 | 0.599579 | ||||||||
\(388\) | −16.2572 | −0.825336 | ||||||||
\(389\) | −8.88959 | + | 8.88959i | −0.450720 | + | 0.450720i | −0.895594 | − | 0.444873i | \(-0.853249\pi\) |
0.444873 | + | 0.895594i | \(0.353249\pi\) | |||||||
\(390\) | 1.49301 | − | 14.4234i | 0.0756015 | − | 0.730358i | ||||
\(391\) | 25.4159i | 1.28534i | ||||||||
\(392\) | 11.6117 | 0.586479 | ||||||||
\(393\) | − | 2.62219i | − | 0.132272i | ||||||
\(394\) | 8.51405 | + | 8.51405i | 0.428932 | + | 0.428932i | ||||
\(395\) | 2.14798 | − | 20.7509i | 0.108077 | − | 1.04409i | ||||
\(396\) | −3.00583 | −0.151049 | ||||||||
\(397\) | −2.71530 | − | 2.71530i | −0.136277 | − | 0.136277i | 0.635678 | − | 0.771955i | \(-0.280721\pi\) |
−0.771955 | + | 0.635678i | \(0.780721\pi\) | |||||||
\(398\) | −4.71139 | + | 4.71139i | −0.236161 | + | 0.236161i | ||||
\(399\) | −19.1601 | − | 19.1601i | −0.959206 | − | 0.959206i | ||||
\(400\) | 1.02416 | − | 4.89399i | 0.0512078 | − | 0.244699i | ||||
\(401\) | 12.5140 | − | 12.5140i | 0.624919 | − | 0.624919i | −0.321866 | − | 0.946785i | \(-0.604310\pi\) |
0.946785 | + | 0.321866i | \(0.104310\pi\) | |||||||
\(402\) | 3.42798i | 0.170972i | ||||||||
\(403\) | 6.95511 | + | 6.95511i | 0.346458 | + | 0.346458i | ||||
\(404\) | − | 16.3032i | − | 0.811115i | ||||||
\(405\) | −1.73553 | + | 1.40994i | −0.0862394 | + | 0.0700603i | ||||
\(406\) | 9.24157i | 0.458651i | ||||||||
\(407\) | 17.9759 | − | 3.34130i | 0.891031 | − | 0.165622i | ||||
\(408\) | 4.24477 | + | 4.24477i | 0.210148 | + | 0.210148i | ||||
\(409\) | −19.7886 | − | 19.7886i | −0.978486 | − | 0.978486i | 0.0212876 | − | 0.999773i | \(-0.493223\pi\) |
−0.999773 | + | 0.0212876i | \(0.993223\pi\) | |||||||
\(410\) | −11.8100 | + | 9.59437i | −0.583254 | + | 0.473832i | ||||
\(411\) | − | 9.13901i | − | 0.450794i | ||||||
\(412\) | −8.32869 | −0.410325 | ||||||||
\(413\) | − | 27.2700i | − | 1.34187i | ||||||
\(414\) | − | 4.23386i | − | 0.208083i | ||||||
\(415\) | −1.51394 | − | 0.156712i | −0.0743163 | − | 0.00769269i | ||||
\(416\) | 6.48482 | 0.317944 | ||||||||
\(417\) | 8.05008 | − | 8.05008i | 0.394214 | − | 0.394214i | ||||
\(418\) | −13.3497 | + | 13.3497i | −0.652953 | + | 0.652953i | ||||
\(419\) | − | 21.0888i | − | 1.03026i | −0.857113 | − | 0.515129i | \(-0.827744\pi\) | ||
0.857113 | − | 0.515129i | \(-0.172256\pi\) | |||||||
\(420\) | −6.08265 | − | 7.48731i | −0.296803 | − | 0.365344i | ||||
\(421\) | 0.620287 | − | 0.620287i | 0.0302309 | − | 0.0302309i | −0.691830 | − | 0.722061i | \(-0.743195\pi\) |
0.722061 | + | 0.691830i | \(0.243195\pi\) | |||||||
\(422\) | 19.7786i | 0.962805i | ||||||||
\(423\) | −5.31277 | − | 5.31277i | −0.258315 | − | 0.258315i | ||||
\(424\) | 5.63889 | − | 5.63889i | 0.273849 | − | 0.273849i | ||||
\(425\) | 6.14802 | − | 29.3787i | 0.298223 | − | 1.42507i | ||||
\(426\) | 6.49828 | + | 6.49828i | 0.314843 | + | 0.314843i | ||||
\(427\) | − | 45.1535i | − | 2.18513i | ||||||
\(428\) | −7.63911 | + | 7.63911i | −0.369250 | + | 0.369250i | ||||
\(429\) | −13.7831 | + | 13.7831i | −0.665455 | + | 0.665455i | ||||
\(430\) | 20.4708 | − | 16.6304i | 0.987190 | − | 0.801987i | ||||
\(431\) | 19.6454 | − | 19.6454i | 0.946286 | − | 0.946286i | −0.0523433 | − | 0.998629i | \(-0.516669\pi\) |
0.998629 | + | 0.0523433i | \(0.0166690\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −26.4568 | − | 26.4568i | −1.27143 | − | 1.27143i | −0.945337 | − | 0.326095i | \(-0.894267\pi\) |
−0.326095 | − | 0.945337i | \(-0.605733\pi\) | |||||||
\(434\) | 6.54356 | 0.314101 | ||||||||
\(435\) | 3.71780 | − | 3.02032i | 0.178255 | − | 0.144813i | ||||
\(436\) | 6.00958 | − | 6.00958i | 0.287806 | − | 0.287806i | ||||
\(437\) | −18.8036 | − | 18.8036i | −0.899500 | − | 0.899500i | ||||
\(438\) | 2.84828 | 0.136096 | ||||||||
\(439\) | 15.3968 | + | 15.3968i | 0.734850 | + | 0.734850i | 0.971576 | − | 0.236726i | \(-0.0760744\pi\) |
−0.236726 | + | 0.971576i | \(0.576074\pi\) | |||||||
\(440\) | −5.21672 | + | 4.23804i | −0.248698 | + | 0.202040i | ||||
\(441\) | −11.6117 | −0.552938 | ||||||||
\(442\) | 38.9284 | 1.85164 | ||||||||
\(443\) | 13.4474 | − | 13.4474i | 0.638907 | − | 0.638907i | −0.311379 | − | 0.950286i | \(-0.600791\pi\) |
0.950286 | + | 0.311379i | \(0.100791\pi\) | |||||||
\(444\) | 5.01476 | + | 3.44271i | 0.237990 | + | 0.163384i | ||||
\(445\) | 13.6920 | + | 1.41730i | 0.649062 | + | 0.0671863i | ||||
\(446\) | 4.53283 | − | 4.53283i | 0.214636 | − | 0.214636i | ||||
\(447\) | 15.0325 | + | 15.0325i | 0.711014 | + | 0.711014i | ||||
\(448\) | 3.05055 | − | 3.05055i | 0.144125 | − | 0.144125i | ||||
\(449\) | 0.109620 | − | 0.109620i | 0.00517328 | − | 0.00517328i | −0.704515 | − | 0.709689i | \(-0.748836\pi\) |
0.709689 | + | 0.704515i | \(0.248836\pi\) | |||||||
\(450\) | −1.02416 | + | 4.89399i | −0.0482791 | + | 0.230705i | ||||
\(451\) | 20.4542 | 0.963148 | ||||||||
\(452\) | −9.17752 | −0.431674 | ||||||||
\(453\) | −0.374755 | − | 0.374755i | −0.0176075 | − | 0.0176075i | ||||
\(454\) | − | 12.5323i | − | 0.588170i | ||||||
\(455\) | −62.2245 | − | 6.44104i | −2.91713 | − | 0.301960i | ||||
\(456\) | −6.28088 | −0.294129 | ||||||||
\(457\) | −7.05088 | −0.329826 | −0.164913 | − | 0.986308i | \(-0.552734\pi\) | ||||
−0.164913 | + | 0.986308i | \(0.552734\pi\) | |||||||
\(458\) | −20.0623 | −0.937450 | ||||||||
\(459\) | −4.24477 | − | 4.24477i | −0.198129 | − | 0.198129i | ||||
\(460\) | −5.96948 | − | 7.34801i | −0.278328 | − | 0.342603i | ||||
\(461\) | 0.0298156 | + | 0.0298156i | 0.00138865 | + | 0.00138865i | 0.707801 | − | 0.706412i | \(-0.249687\pi\) |
−0.706412 | + | 0.707801i | \(0.749687\pi\) | |||||||
\(462\) | 12.9675i | 0.603305i | ||||||||
\(463\) | − | 5.26855i | − | 0.244850i | −0.992478 | − | 0.122425i | \(-0.960933\pi\) | ||
0.992478 | − | 0.122425i | \(-0.0390671\pi\) | |||||||
\(464\) | 1.51474 | + | 1.51474i | 0.0703200 | + | 0.0703200i | ||||
\(465\) | −2.13856 | − | 2.63241i | −0.0991732 | − | 0.122075i | ||||
\(466\) | 4.10021 | + | 4.10021i | 0.189939 | + | 0.189939i | ||||
\(467\) | 8.16999 | 0.378062 | 0.189031 | − | 0.981971i | \(-0.439465\pi\) | ||||
0.189031 | + | 0.981971i | \(0.439465\pi\) | |||||||
\(468\) | −6.48482 | −0.299761 | ||||||||
\(469\) | 14.7887 | 0.682881 | ||||||||
\(470\) | −16.7111 | − | 1.72982i | −0.770828 | − | 0.0797906i | ||||
\(471\) | 12.8134i | 0.590411i | ||||||||
\(472\) | −4.46968 | − | 4.46968i | −0.205734 | − | 0.205734i | ||||
\(473\) | −35.4541 | −1.63018 | ||||||||
\(474\) | −9.32966 | −0.428526 | ||||||||
\(475\) | 17.1869 | + | 26.2840i | 0.788589 | + | 1.20599i | ||||
\(476\) | 18.3125 | − | 18.3125i | 0.839352 | − | 0.839352i | ||||
\(477\) | −5.63889 | + | 5.63889i | −0.258187 | + | 0.258187i | ||||
\(478\) | 9.03944 | + | 9.03944i | 0.413454 | + | 0.413454i | ||||
\(479\) | 8.69240 | − | 8.69240i | 0.397166 | − | 0.397166i | −0.480066 | − | 0.877232i | \(-0.659387\pi\) |
0.877232 | + | 0.480066i | \(0.159387\pi\) | |||||||
\(480\) | −2.22418 | − | 0.230232i | −0.101520 | − | 0.0105086i | ||||
\(481\) | 38.7813 | − | 7.20856i | 1.76828 | − | 0.328682i | ||||
\(482\) | 7.69908 | − | 7.69908i | 0.350684 | − | 0.350684i | ||||
\(483\) | −18.2654 | −0.831105 | ||||||||
\(484\) | −1.96497 | −0.0893168 | ||||||||
\(485\) | 28.2150 | − | 22.9217i | 1.28118 | − | 1.04082i | ||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 25.3749 | 1.14984 | 0.574922 | − | 0.818208i | \(-0.305032\pi\) | ||||
0.574922 | + | 0.818208i | \(0.305032\pi\) | |||||||
\(488\) | −7.40088 | − | 7.40088i | −0.335022 | − | 0.335022i | ||||
\(489\) | 14.9772 | − | 14.9772i | 0.677294 | − | 0.677294i | ||||
\(490\) | −20.1525 | + | 16.3718i | −0.910397 | + | 0.739601i | ||||
\(491\) | −34.9666 | −1.57802 | −0.789009 | − | 0.614381i | \(-0.789406\pi\) | ||||
−0.789009 | + | 0.614381i | \(0.789406\pi\) | |||||||
\(492\) | 4.81173 | + | 4.81173i | 0.216930 | + | 0.216930i | ||||
\(493\) | 9.09299 | + | 9.09299i | 0.409528 | + | 0.409528i | ||||
\(494\) | −28.8007 | + | 28.8007i | −1.29581 | + | 1.29581i | ||||
\(495\) | 5.21672 | − | 4.23804i | 0.234474 | − | 0.190486i | ||||
\(496\) | 1.07252 | − | 1.07252i | 0.0481576 | − | 0.0481576i | ||||
\(497\) | 28.0344 | − | 28.0344i | 1.25752 | − | 1.25752i | ||||
\(498\) | 0.680671i | 0.0305016i | ||||||||
\(499\) | −0.199787 | − | 0.199787i | −0.00894368 | − | 0.00894368i | 0.702621 | − | 0.711564i | \(-0.252013\pi\) |
−0.711564 | + | 0.702621i | \(0.752013\pi\) | |||||||
\(500\) | 5.12276 | + | 9.93767i | 0.229097 | + | 0.444426i | ||||
\(501\) | −9.04749 | + | 9.04749i | −0.404212 | + | 0.404212i | ||||
\(502\) | −9.83570 | − | 9.83570i | −0.438989 | − | 0.438989i | ||||
\(503\) | − | 16.3722i | − | 0.729999i | −0.931008 | − | 0.365000i | \(-0.881069\pi\) | ||
0.931008 | − | 0.365000i | \(-0.118931\pi\) | |||||||
\(504\) | −3.05055 | + | 3.05055i | −0.135882 | + | 0.135882i | ||||
\(505\) | 22.9865 | + | 28.2948i | 1.02289 | + | 1.25910i | ||||
\(506\) | 12.7263i | 0.565752i | ||||||||
\(507\) | −20.5435 | + | 20.5435i | −0.912367 | + | 0.912367i | ||||
\(508\) | −8.41071 | + | 8.41071i | −0.373165 | + | 0.373165i | ||||
\(509\) | 32.3903 | 1.43568 | 0.717838 | − | 0.696210i | \(-0.245132\pi\) | ||||
0.717838 | + | 0.696210i | \(0.245132\pi\) | |||||||
\(510\) | −13.3518 | − | 1.38208i | −0.591228 | − | 0.0611997i | ||||
\(511\) | − | 12.2878i | − | 0.543582i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.28088 | 0.277308 | ||||||||
\(514\) | − | 3.77576i | − | 0.166541i | ||||||
\(515\) | 14.4547 | − | 11.7429i | 0.636951 | − | 0.517455i | ||||
\(516\) | −8.34040 | − | 8.34040i | −0.367166 | − | 0.367166i | ||||
\(517\) | 15.9693 | + | 15.9693i | 0.702328 | + | 0.702328i | ||||
\(518\) | 14.8523 | − | 21.6343i | 0.652572 | − | 0.950556i | ||||
\(519\) | − | 6.96677i | − | 0.305807i | ||||||
\(520\) | −11.2546 | + | 9.14318i | −0.493548 | + | 0.400955i | ||||
\(521\) | − | 17.4138i | − | 0.762914i | −0.924387 | − | 0.381457i | \(-0.875422\pi\) | ||
0.924387 | − | 0.381457i | \(-0.124578\pi\) | |||||||
\(522\) | −1.51474 | − | 1.51474i | −0.0662983 | − | 0.0662983i | ||||
\(523\) | 38.1149i | 1.66665i | 0.552784 | + | 0.833325i | \(0.313566\pi\) | ||||
−0.552784 | + | 0.833325i | \(0.686434\pi\) | |||||||
\(524\) | −1.85417 | + | 1.85417i | −0.0809997 | + | 0.0809997i | ||||
\(525\) | 21.1133 | + | 4.41834i | 0.921459 | + | 0.192832i | ||||
\(526\) | −9.85731 | − | 9.85731i | −0.429799 | − | 0.429799i | ||||
\(527\) | 6.43836 | − | 6.43836i | 0.280459 | − | 0.280459i | ||||
\(528\) | 2.12544 | + | 2.12544i | 0.0924981 | + | 0.0924981i | ||||
\(529\) | 5.07442 | 0.220627 | ||||||||
\(530\) | −1.83601 | + | 17.7370i | −0.0797510 | + | 0.770445i | ||||
\(531\) | 4.46968 | + | 4.46968i | 0.193968 | + | 0.193968i | ||||
\(532\) | 27.0965i | 1.17478i | ||||||||
\(533\) | 44.1280 | 1.91140 | ||||||||
\(534\) | − | 6.15596i | − | 0.266394i | ||||||
\(535\) | 2.48727 | − | 24.0286i | 0.107534 | − | 1.03885i | ||||
\(536\) | 2.42395 | − | 2.42395i | 0.104699 | − | 0.104699i | ||||
\(537\) | 10.2626 | 0.442862 | ||||||||
\(538\) | −25.0749 | −1.08106 | ||||||||
\(539\) | 34.9028 | 1.50337 | ||||||||
\(540\) | 2.22418 | + | 0.230232i | 0.0957136 | + | 0.00990759i | ||||
\(541\) | −27.4040 | − | 27.4040i | −1.17819 | − | 1.17819i | −0.980205 | − | 0.197986i | \(-0.936560\pi\) |
−0.197986 | − | 0.980205i | \(-0.563440\pi\) | |||||||
\(542\) | 24.0884i | 1.03468i | ||||||||
\(543\) | 6.86133 | − | 6.86133i | 0.294448 | − | 0.294448i | ||||
\(544\) | − | 6.00301i | − | 0.257377i | ||||||
\(545\) | −1.95670 | + | 18.9029i | −0.0838158 | + | 0.809713i | ||||
\(546\) | 27.9763i | 1.19728i | ||||||||
\(547\) | − | 4.61554i | − | 0.197346i | −0.995120 | − | 0.0986731i | \(-0.968540\pi\) | ||
0.995120 | − | 0.0986731i | \(-0.0314598\pi\) | |||||||
\(548\) | −6.46226 | + | 6.46226i | −0.276054 | + | 0.276054i | ||||
\(549\) | 7.40088 | + | 7.40088i | 0.315862 | + | 0.315862i | ||||
\(550\) | 3.07844 | − | 14.7105i | 0.131265 | − | 0.627258i | ||||
\(551\) | −13.4547 | −0.573188 | ||||||||
\(552\) | −2.99379 | + | 2.99379i | −0.127424 | + | 0.127424i | ||||
\(553\) | 40.2494i | 1.71158i | ||||||||
\(554\) | 16.3414 | 0.694279 | ||||||||
\(555\) | −13.5573 | + | 1.09556i | −0.575474 | + | 0.0465037i | ||||
\(556\) | −11.3845 | −0.482812 | ||||||||
\(557\) | − | 6.03445i | − | 0.255688i | −0.991794 | − | 0.127844i | \(-0.959194\pi\) | ||
0.991794 | − | 0.127844i | \(-0.0408056\pi\) | |||||||
\(558\) | −1.07252 | + | 1.07252i | −0.0454035 | + | 0.0454035i | ||||
\(559\) | −76.4891 | −3.23514 | ||||||||
\(560\) | −0.993249 | + | 9.59541i | −0.0419724 | + | 0.405480i | ||||
\(561\) | 12.7591 | + | 12.7591i | 0.538689 | + | 0.538689i | ||||
\(562\) | −11.9540 | + | 11.9540i | −0.504250 | + | 0.504250i | ||||
\(563\) | − | 16.8876i | − | 0.711727i | −0.934538 | − | 0.355863i | \(-0.884187\pi\) | ||
0.934538 | − | 0.355863i | \(-0.115813\pi\) | |||||||
\(564\) | 7.51338i | 0.316371i | ||||||||
\(565\) | 15.9279 | − | 12.9397i | 0.670091 | − | 0.544378i | ||||
\(566\) | 10.0542i | 0.422608i | ||||||||
\(567\) | 3.05055 | − | 3.05055i | 0.128111 | − | 0.128111i | ||||
\(568\) | − | 9.18996i | − | 0.385602i | ||||||
\(569\) | 22.0925 | + | 22.0925i | 0.926168 | + | 0.926168i | 0.997456 | − | 0.0712881i | \(-0.0227110\pi\) |
−0.0712881 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(570\) | 10.9007 | − | 8.85565i | 0.456579 | − | 0.370922i | ||||
\(571\) | 28.0375 | 1.17333 | 0.586666 | − | 0.809829i | \(-0.300440\pi\) | ||||
0.586666 | + | 0.809829i | \(0.300440\pi\) | |||||||
\(572\) | 19.4923 | 0.815013 | ||||||||
\(573\) | −10.0889 | −0.421469 | ||||||||
\(574\) | 20.7584 | − | 20.7584i | 0.866440 | − | 0.866440i | ||||
\(575\) | 20.7205 | + | 4.33613i | 0.864103 | + | 0.180829i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 27.2016 | 1.13242 | 0.566208 | − | 0.824262i | \(-0.308410\pi\) | ||||
0.566208 | + | 0.824262i | \(0.308410\pi\) | |||||||
\(578\) | − | 19.0362i | − | 0.791800i | ||||||
\(579\) | −13.6726 | − | 13.6726i | −0.568215 | − | 0.568215i | ||||
\(580\) | −4.76456 | − | 0.493194i | −0.197838 | − | 0.0204788i | ||||
\(581\) | 2.93650 | 0.121827 | ||||||||
\(582\) | −11.4956 | − | 11.4956i | −0.476508 | − | 0.476508i | ||||
\(583\) | 16.9496 | − | 16.9496i | 0.701979 | − | 0.701979i | ||||
\(584\) | −2.01404 | − | 2.01404i | −0.0833415 | − | 0.0833415i | ||||
\(585\) | 11.2546 | − | 9.14318i | 0.465321 | − | 0.378024i | ||||
\(586\) | 8.47560 | − | 8.47560i | 0.350124 | − | 0.350124i | ||||
\(587\) | 8.46791i | 0.349508i | 0.984612 | + | 0.174754i | \(0.0559131\pi\) | ||||
−0.984612 | + | 0.174754i | \(0.944087\pi\) | |||||||
\(588\) | 8.21071 | + | 8.21071i | 0.338604 | + | 0.338604i | ||||
\(589\) | 9.52668i | 0.392540i | ||||||||
\(590\) | 14.0592 | + | 1.45531i | 0.578810 | + | 0.0599143i | ||||
\(591\) | 12.0407i | 0.495288i | ||||||||
\(592\) | −1.11161 | − | 5.98033i | −0.0456867 | − | 0.245790i | ||||
\(593\) | 6.22133 | + | 6.22133i | 0.255479 | + | 0.255479i | 0.823213 | − | 0.567733i | \(-0.192179\pi\) |
−0.567733 | + | 0.823213i | \(0.692179\pi\) | |||||||
\(594\) | −2.12544 | − | 2.12544i | −0.0872081 | − | 0.0872081i | ||||
\(595\) | −5.96249 | + | 57.6014i | −0.244438 | + | 2.36143i | ||||
\(596\) | − | 21.2592i | − | 0.870811i | ||||||
\(597\) | −6.66291 | −0.272695 | ||||||||
\(598\) | 27.4558i | 1.12275i | ||||||||
\(599\) | 31.7305i | 1.29647i | 0.761439 | + | 0.648236i | \(0.224493\pi\) | ||||
−0.761439 | + | 0.648236i | \(0.775507\pi\) | |||||||
\(600\) | 4.18476 | − | 2.73638i | 0.170842 | − | 0.111712i | ||||
\(601\) | −7.01914 | −0.286317 | −0.143158 | − | 0.989700i | \(-0.545726\pi\) | ||||
−0.143158 | + | 0.989700i | \(0.545726\pi\) | |||||||
\(602\) | −35.9816 | + | 35.9816i | −1.46650 | + | 1.46650i | ||||
\(603\) | −2.42395 | + | 2.42395i | −0.0987108 | + | 0.0987108i | ||||
\(604\) | 0.529983i | 0.0215647i | ||||||||
\(605\) | 3.41027 | − | 2.77048i | 0.138647 | − | 0.112636i | ||||
\(606\) | 11.5281 | − | 11.5281i | 0.468297 | − | 0.468297i | ||||
\(607\) | − | 20.9319i | − | 0.849600i | −0.905287 | − | 0.424800i | \(-0.860344\pi\) | ||
0.905287 | − | 0.424800i | \(-0.139656\pi\) | |||||||
\(608\) | 4.44125 | + | 4.44125i | 0.180117 | + | 0.180117i | ||||
\(609\) | −6.53477 | + | 6.53477i | −0.264802 | + | 0.264802i | ||||
\(610\) | 23.2793 | + | 2.40970i | 0.942550 | + | 0.0975661i | ||||
\(611\) | 34.4523 | + | 34.4523i | 1.39379 | + | 1.39379i | ||||
\(612\) | 6.00301i | 0.242657i | ||||||||
\(613\) | −3.66683 | + | 3.66683i | −0.148102 | + | 0.148102i | −0.777270 | − | 0.629168i | \(-0.783396\pi\) |
0.629168 | + | 0.777270i | \(0.283396\pi\) | |||||||
\(614\) | −2.69632 | + | 2.69632i | −0.108815 | + | 0.108815i | ||||
\(615\) | −15.1352 | − | 1.56669i | −0.610309 | − | 0.0631748i | ||||
\(616\) | 9.16944 | − | 9.16944i | 0.369447 | − | 0.369447i | ||||
\(617\) | −3.93991 | − | 3.93991i | −0.158615 | − | 0.158615i | 0.623338 | − | 0.781953i | \(-0.285776\pi\) |
−0.781953 | + | 0.623338i | \(0.785776\pi\) | |||||||
\(618\) | −5.88927 | − | 5.88927i | −0.236901 | − | 0.236901i | ||||
\(619\) | −17.6521 | −0.709496 | −0.354748 | − | 0.934962i | \(-0.615433\pi\) | ||||
−0.354748 | + | 0.934962i | \(0.615433\pi\) | |||||||
\(620\) | −0.349210 | + | 3.37358i | −0.0140246 | + | 0.135486i | ||||
\(621\) | 2.99379 | − | 2.99379i | 0.120137 | − | 0.120137i | ||||
\(622\) | 6.10837 | + | 6.10837i | 0.244924 | + | 0.244924i | ||||
\(623\) | −26.5576 | −1.06401 | ||||||||
\(624\) | 4.58546 | + | 4.58546i | 0.183565 | + | 0.183565i | ||||
\(625\) | −22.9022 | − | 10.0244i | −0.916088 | − | 0.400976i | ||||
\(626\) | 22.7166 | 0.907938 | ||||||||
\(627\) | −18.8793 | −0.753966 | ||||||||
\(628\) | 9.06045 | − | 9.06045i | 0.361551 | − | 0.361551i | ||||
\(629\) | −6.67299 | − | 35.9000i | −0.266069 | − | 1.43143i | ||||
\(630\) | 0.993249 | − | 9.59541i | 0.0395720 | − | 0.382290i | ||||
\(631\) | −14.6419 | + | 14.6419i | −0.582883 | + | 0.582883i | −0.935695 | − | 0.352811i | \(-0.885226\pi\) |
0.352811 | + | 0.935695i | \(0.385226\pi\) | |||||||
\(632\) | 6.59707 | + | 6.59707i | 0.262417 | + | 0.262417i | ||||
\(633\) | −13.9855 | + | 13.9855i | −0.555876 | + | 0.555876i | ||||
\(634\) | 17.3373 | − | 17.3373i | 0.688553 | − | 0.688553i | ||||
\(635\) | 2.73850 | − | 26.4556i | 0.108674 | − | 1.04986i | ||||
\(636\) | 7.97460 | 0.316213 | ||||||||
\(637\) | 75.2997 | 2.98348 | ||||||||
\(638\) | 4.55305 | + | 4.55305i | 0.180257 | + | 0.180257i | ||||
\(639\) | 9.18996i | 0.363549i | ||||||||
\(640\) | 1.40994 | + | 1.73553i | 0.0557327 | + | 0.0686030i | ||||
\(641\) | 41.2135 | 1.62783 | 0.813917 | − | 0.580981i | \(-0.197331\pi\) | ||||
0.813917 | + | 0.580981i | \(0.197331\pi\) | |||||||
\(642\) | −10.8033 | −0.426374 | ||||||||
\(643\) | −16.5141 | −0.651254 | −0.325627 | − | 0.945498i | \(-0.605575\pi\) | ||||
−0.325627 | + | 0.945498i | \(0.605575\pi\) | |||||||
\(644\) | 12.9156 | + | 12.9156i | 0.508946 | + | 0.508946i | ||||
\(645\) | 26.2345 | + | 2.71561i | 1.03298 | + | 0.106927i | ||||
\(646\) | 26.6609 | + | 26.6609i | 1.04896 | + | 1.04896i | ||||
\(647\) | 48.9342i | 1.92380i | 0.273401 | + | 0.961900i | \(0.411851\pi\) | ||||
−0.273401 | + | 0.961900i | \(0.588149\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −13.4351 | − | 13.4351i | −0.527374 | − | 0.527374i | ||||
\(650\) | 6.64146 | − | 31.7366i | 0.260499 | − | 1.24481i | ||||
\(651\) | 4.62699 | + | 4.62699i | 0.181346 | + | 0.181346i | ||||
\(652\) | −21.1810 | −0.829512 | ||||||||
\(653\) | 15.4749 | 0.605581 | 0.302791 | − | 0.953057i | \(-0.402082\pi\) | ||||
0.302791 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(654\) | 8.49882 | 0.332330 | ||||||||
\(655\) | 0.603711 | − | 5.83223i | 0.0235889 | − | 0.227884i | ||||
\(656\) | − | 6.80482i | − | 0.265684i | ||||||
\(657\) | 2.01404 | + | 2.01404i | 0.0785751 | + | 0.0785751i | ||||
\(658\) | 32.4137 | 1.26362 | ||||||||
\(659\) | 36.9284 | 1.43853 | 0.719264 | − | 0.694737i | \(-0.244479\pi\) | ||||
0.719264 | + | 0.694737i | \(0.244479\pi\) | |||||||
\(660\) | −6.68552 | − | 0.692038i | −0.260234 | − | 0.0269375i | ||||
\(661\) | −11.4256 | + | 11.4256i | −0.444405 | + | 0.444405i | −0.893489 | − | 0.449084i | \(-0.851750\pi\) |
0.449084 | + | 0.893489i | \(0.351750\pi\) | |||||||
\(662\) | −0.296981 | + | 0.296981i | −0.0115425 | + | 0.0115425i | ||||
\(663\) | 27.5266 | + | 27.5266i | 1.06904 | + | 1.06904i | ||||
\(664\) | 0.481307 | − | 0.481307i | 0.0186783 | − | 0.0186783i | ||||
\(665\) | −38.2044 | − | 47.0269i | −1.48150 | − | 1.82363i | ||||
\(666\) | 1.11161 | + | 5.98033i | 0.0430739 | + | 0.231733i | ||||
\(667\) | −6.41319 | + | 6.41319i | −0.248320 | + | 0.248320i | ||||
\(668\) | 12.7951 | 0.495057 | ||||||||
\(669\) | 6.41038 | 0.247840 | ||||||||
\(670\) | −0.789230 | + | 7.62446i | −0.0304906 | + | 0.294559i | ||||
\(671\) | −22.2458 | − | 22.2458i | −0.858790 | − | 0.858790i | ||||
\(672\) | 4.31413 | 0.166421 | ||||||||
\(673\) | 21.5091 | + | 21.5091i | 0.829113 | + | 0.829113i | 0.987394 | − | 0.158281i | \(-0.0505952\pi\) |
−0.158281 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(674\) | −12.3894 | + | 12.3894i | −0.477220 | + | 0.477220i | ||||
\(675\) | −4.18476 | + | 2.73638i | −0.161071 | + | 0.105323i | ||||
\(676\) | 29.0528 | 1.11742 | ||||||||
\(677\) | 10.9295 | + | 10.9295i | 0.420053 | + | 0.420053i | 0.885222 | − | 0.465169i | \(-0.154006\pi\) |
−0.465169 | + | 0.885222i | \(0.654006\pi\) | |||||||
\(678\) | −6.48948 | − | 6.48948i | −0.249227 | − | 0.249227i | ||||
\(679\) | −49.5935 | + | 49.5935i | −1.90322 | + | 1.90322i | ||||
\(680\) | 8.46387 | + | 10.4184i | 0.324575 | + | 0.399529i | ||||
\(681\) | 8.86168 | − | 8.86168i | 0.339580 | − | 0.339580i | ||||
\(682\) | 3.22382 | − | 3.22382i | 0.123446 | − | 0.123446i | ||||
\(683\) | − | 14.1654i | − | 0.542024i | −0.962576 | − | 0.271012i | \(-0.912642\pi\) | ||
0.962576 | − | 0.271012i | \(-0.0873584\pi\) | |||||||
\(684\) | −4.44125 | − | 4.44125i | −0.169816 | − | 0.169816i | ||||
\(685\) | 2.10409 | − | 20.3268i | 0.0803932 | − | 0.776649i | ||||
\(686\) | 14.0682 | − | 14.0682i | 0.537127 | − | 0.537127i | ||||
\(687\) | −14.1862 | − | 14.1862i | −0.541237 | − | 0.541237i | ||||
\(688\) | 11.7951i | 0.449684i | ||||||||
\(689\) | 36.5672 | − | 36.5672i | 1.39310 | − | 1.39310i | ||||
\(690\) | 0.974769 | − | 9.41688i | 0.0371088 | − | 0.358495i | ||||
\(691\) | 3.21102i | 0.122153i | 0.998133 | + | 0.0610765i | \(0.0194533\pi\) | ||||
−0.998133 | + | 0.0610765i | \(0.980547\pi\) | |||||||
\(692\) | −4.92625 | + | 4.92625i | −0.187268 | + | 0.187268i | ||||
\(693\) | −9.16944 | + | 9.16944i | −0.348318 | + | 0.348318i | ||||
\(694\) | −21.8151 | −0.828091 | ||||||||
\(695\) | 19.7582 | − | 16.0515i | 0.749473 | − | 0.608867i | ||||
\(696\) | 2.14216i | 0.0811985i | ||||||||
\(697\) | − | 40.8494i | − | 1.54728i | ||||||
\(698\) | −0.296683 | −0.0112296 | ||||||||
\(699\) | 5.79858i | 0.219322i | ||||||||
\(700\) | −11.8051 | − | 18.0536i | −0.446191 | − | 0.682361i | ||||
\(701\) | 7.77755 | + | 7.77755i | 0.293754 | + | 0.293754i | 0.838561 | − | 0.544807i | \(-0.183397\pi\) |
−0.544807 | + | 0.838561i | \(0.683397\pi\) | |||||||
\(702\) | −4.58546 | − | 4.58546i | −0.173067 | − | 0.173067i | ||||
\(703\) | 31.4971 | + | 21.6232i | 1.18793 | + | 0.815536i | ||||
\(704\) | − | 3.00583i | − | 0.113287i | ||||||
\(705\) | −10.5934 | − | 13.0397i | −0.398970 | − | 0.491105i | ||||
\(706\) | 1.99266i | 0.0749946i | ||||||||
\(707\) | −49.7337 | − | 49.7337i | −1.87043 | − | 1.87043i | ||||
\(708\) | − | 6.32108i | − | 0.237561i | ||||||
\(709\) | 23.8317 | − | 23.8317i | 0.895018 | − | 0.895018i | −0.0999719 | − | 0.994990i | \(-0.531875\pi\) |
0.994990 | + | 0.0999719i | \(0.0318753\pi\) | |||||||
\(710\) | 12.9573 | + | 15.9495i | 0.486278 | + | 0.598574i | ||||
\(711\) | −6.59707 | − | 6.59707i | −0.247409 | − | 0.247409i | ||||
\(712\) | −4.35292 | + | 4.35292i | −0.163133 | + | 0.163133i | ||||
\(713\) | 4.54091 | + | 4.54091i | 0.170058 | + | 0.170058i | ||||
\(714\) | 25.8978 | 0.969200 | ||||||||
\(715\) | −33.8295 | + | 27.4829i | −1.26515 | + | 1.02780i | ||||
\(716\) | −7.25672 | − | 7.25672i | −0.271196 | − | 0.271196i | ||||
\(717\) | 12.7837i | 0.477416i | ||||||||
\(718\) | −10.3520 | −0.386334 | ||||||||
\(719\) | 35.0794i | 1.30824i | 0.756391 | + | 0.654120i | \(0.226961\pi\) | ||||
−0.756391 | + | 0.654120i | \(0.773039\pi\) | |||||||
\(720\) | −1.40994 | − | 1.73553i | −0.0525453 | − | 0.0646795i | ||||
\(721\) | −25.4071 | + | 25.4071i | −0.946209 | + | 0.946209i | ||||
\(722\) | −20.4495 | −0.761050 | ||||||||
\(723\) | 10.8881 | 0.404935 | ||||||||
\(724\) | −9.70338 | −0.360623 | ||||||||
\(725\) | 8.96444 | − | 5.86178i | 0.332931 | − | 0.217701i | ||||
\(726\) | −1.38944 | − | 1.38944i | −0.0515671 | − | 0.0515671i | ||||
\(727\) | 8.98773i | 0.333336i | 0.986013 | + | 0.166668i | \(0.0533009\pi\) | ||||
−0.986013 | + | 0.166668i | \(0.946699\pi\) | |||||||
\(728\) | 19.7823 | − | 19.7823i | 0.733179 | − | 0.733179i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 6.33510 | + | 0.655764i | 0.234473 | + | 0.0242709i | ||||
\(731\) | 70.8062i | 2.61886i | ||||||||
\(732\) | − | 10.4664i | − | 0.386850i | ||||||
\(733\) | 1.69194 | − | 1.69194i | 0.0624931 | − | 0.0624931i | −0.675170 | − | 0.737663i | \(-0.735930\pi\) |
0.737663 | + | 0.675170i | \(0.235930\pi\) | |||||||
\(734\) | −0.446811 | − | 0.446811i | −0.0164921 | − | 0.0164921i | ||||
\(735\) | −25.8266 | − | 2.67338i | −0.952627 | − | 0.0986092i | ||||
\(736\) | 4.23386 | 0.156062 | ||||||||
\(737\) | 7.28598 | − | 7.28598i | 0.268383 | − | 0.268383i | ||||
\(738\) | 6.80482i | 0.250489i | ||||||||
\(739\) | 8.19699 | 0.301531 | 0.150765 | − | 0.988570i | \(-0.451826\pi\) | ||||
0.150765 | + | 0.988570i | \(0.451826\pi\) | |||||||
\(740\) | 10.3611 | + | 8.81177i | 0.380882 | + | 0.323927i | ||||
\(741\) | −40.7304 | −1.49627 | ||||||||
\(742\) | − | 34.4034i | − | 1.26299i | ||||||
\(743\) | −5.18593 | + | 5.18593i | −0.190253 | + | 0.190253i | −0.795806 | − | 0.605552i | \(-0.792952\pi\) |
0.605552 | + | 0.795806i | \(0.292952\pi\) | |||||||
\(744\) | 1.51677 | 0.0556076 | ||||||||
\(745\) | 29.9741 | + | 36.8961i | 1.09817 | + | 1.35177i | ||||
\(746\) | −19.8830 | − | 19.8830i | −0.727969 | − | 0.727969i | ||||
\(747\) | −0.481307 | + | 0.481307i | −0.0176101 | + | 0.0176101i | ||||
\(748\) | − | 18.0441i | − | 0.659756i | ||||||
\(749\) | 46.6070i | 1.70298i | ||||||||
\(750\) | −3.40466 | + | 10.6493i | −0.124321 | + | 0.388859i | ||||
\(751\) | − | 7.11165i | − | 0.259508i | −0.991546 | − | 0.129754i | \(-0.958581\pi\) | ||
0.991546 | − | 0.129754i | \(-0.0414187\pi\) | |||||||
\(752\) | 5.31277 | − | 5.31277i | 0.193737 | − | 0.193737i | ||||
\(753\) | − | 13.9098i | − | 0.506901i | ||||||
\(754\) | 9.82280 | + | 9.82280i | 0.357725 | + | 0.357725i | ||||
\(755\) | −0.747243 | − | 0.919804i | −0.0271950 | − | 0.0334751i | ||||
\(756\) | −4.31413 | −0.156903 | ||||||||
\(757\) | 23.4049 | 0.850665 | 0.425332 | − | 0.905037i | \(-0.360157\pi\) | ||||
0.425332 | + | 0.905037i | \(0.360157\pi\) | |||||||
\(758\) | −2.16219 | −0.0785343 | ||||||||
\(759\) | −8.99884 | + | 8.99884i | −0.326637 | + | 0.326637i | ||||
\(760\) | −13.9698 | − | 1.44606i | −0.506739 | − | 0.0524540i | ||||
\(761\) | 10.2257i | 0.370683i | 0.982674 | + | 0.185341i | \(0.0593391\pi\) | ||||
−0.982674 | + | 0.185341i | \(0.940661\pi\) | |||||||
\(762\) | −11.8945 | −0.430894 | ||||||||
\(763\) | − | 36.6650i | − | 1.32736i | ||||||
\(764\) | 7.13391 | + | 7.13391i | 0.258096 | + | 0.258096i | ||||
\(765\) | −8.46387 | − | 10.4184i | −0.306012 | − | 0.376679i | ||||
\(766\) | 28.0841 | 1.01472 | ||||||||
\(767\) | −28.9851 | − | 28.9851i | −1.04659 | − | 1.04659i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −35.6398 | − | 35.6398i | −1.28520 | − | 1.28520i | −0.937666 | − | 0.347537i | \(-0.887018\pi\) |
−0.347537 | − | 0.937666i | \(-0.612982\pi\) | |||||||
\(770\) | −2.98554 | + | 28.8422i | −0.107591 | + | 1.03940i | ||||
\(771\) | 2.66986 | − | 2.66986i | 0.0961528 | − | 0.0961528i | ||||
\(772\) | 19.3360i | 0.695918i | ||||||||
\(773\) | −9.02172 | − | 9.02172i | −0.324489 | − | 0.324489i | 0.525997 | − | 0.850486i | \(-0.323692\pi\) |
−0.850486 | + | 0.525997i | \(0.823692\pi\) | |||||||
\(774\) | − | 11.7951i | − | 0.423966i | ||||||
\(775\) | −4.15048 | − | 6.34733i | −0.149090 | − | 0.228003i | ||||
\(776\) | 16.2572i | 0.583600i | ||||||||
\(777\) | 25.7999 | − | 4.79561i | 0.925566 | − | 0.172042i | ||||
\(778\) | 8.88959 | + | 8.88959i | 0.318707 | + | 0.318707i | ||||
\(779\) | 30.2219 | + | 30.2219i | 1.08281 | + | 1.08281i | ||||
\(780\) | −14.4234 | − | 1.49301i | −0.516441 | − | 0.0534583i | ||||
\(781\) | − | 27.6235i | − | 0.988446i | ||||||
\(782\) | 25.4159 | 0.908872 | ||||||||
\(783\) | − | 2.14216i | − | 0.0765547i | ||||||
\(784\) | − | 11.6117i | − | 0.414704i | ||||||
\(785\) | −2.95005 | + | 28.4994i | −0.105292 | + | 1.01719i | ||||
\(786\) | −2.62219 | −0.0935304 | ||||||||
\(787\) | −2.54597 | + | 2.54597i | −0.0907541 | + | 0.0907541i | −0.751026 | − | 0.660272i | \(-0.770441\pi\) |
0.660272 | + | 0.751026i | \(0.270441\pi\) | |||||||
\(788\) | 8.51405 | − | 8.51405i | 0.303301 | − | 0.303301i | ||||
\(789\) | − | 13.9403i | − | 0.496289i | ||||||
\(790\) | −20.7509 | − | 2.14798i | −0.738283 | − | 0.0764218i | ||||
\(791\) | −27.9965 | + | 27.9965i | −0.995440 | + | 0.995440i | ||||
\(792\) | 3.00583i | 0.106808i | ||||||||
\(793\) | −47.9934 | − | 47.9934i | −1.70429 | − | 1.70429i | ||||
\(794\) | −2.71530 | + | 2.71530i | −0.0963625 | + | 0.0963625i | ||||
\(795\) | −13.8402 | + | 11.2437i | −0.490861 | + | 0.398772i | ||||
\(796\) | 4.71139 | + | 4.71139i | 0.166991 | + | 0.166991i | ||||
\(797\) | 27.8103i | 0.985091i | 0.870287 | + | 0.492545i | \(0.163933\pi\) | ||||
−0.870287 | + | 0.492545i | \(0.836067\pi\) | |||||||
\(798\) | −19.1601 | + | 19.1601i | −0.678261 | + | 0.678261i | ||||
\(799\) | 31.8926 | − | 31.8926i | 1.12828 | − | 1.12828i | ||||
\(800\) | −4.89399 | − | 1.02416i | −0.173029 | − | 0.0362094i | ||||
\(801\) | 4.35292 | − | 4.35292i | 0.153803 | − | 0.153803i | ||||
\(802\) | −12.5140 | − | 12.5140i | −0.441884 | − | 0.441884i | ||||
\(803\) | −6.05386 | − | 6.05386i | −0.213636 | − | 0.213636i | ||||
\(804\) | 3.42798 | 0.120896 | ||||||||
\(805\) | −40.6256 | − | 4.20528i | −1.43187 | − | 0.148217i | ||||
\(806\) | 6.95511 | − | 6.95511i | 0.244983 | − | 0.244983i | ||||
\(807\) | −17.7306 | − | 17.7306i | −0.624148 | − | 0.624148i | ||||
\(808\) | −16.3032 | −0.573545 | ||||||||
\(809\) | −8.62575 | − | 8.62575i | −0.303265 | − | 0.303265i | 0.539025 | − | 0.842290i | \(-0.318793\pi\) |
−0.842290 | + | 0.539025i | \(0.818793\pi\) | |||||||
\(810\) | 1.40994 | + | 1.73553i | 0.0495401 | + | 0.0609804i | ||||
\(811\) | −32.5674 | −1.14359 | −0.571797 | − | 0.820395i | \(-0.693754\pi\) | ||||
−0.571797 | + | 0.820395i | \(0.693754\pi\) | |||||||
\(812\) | 9.24157 | 0.324315 | ||||||||
\(813\) | −17.0331 | + | 17.0331i | −0.597375 | + | 0.597375i | ||||
\(814\) | −3.34130 | − | 17.9759i | −0.117113 | − | 0.630054i | ||||
\(815\) | 36.7603 | − | 29.8639i | 1.28766 | − | 1.04609i | ||||
\(816\) | 4.24477 | − | 4.24477i | 0.148597 | − | 0.148597i | ||||
\(817\) | −52.3851 | − | 52.3851i | −1.83272 | − | 1.83272i | ||||
\(818\) | −19.7886 | + | 19.7886i | −0.691894 | + | 0.691894i | ||||
\(819\) | −19.7823 | + | 19.7823i | −0.691248 | + | 0.691248i | ||||
\(820\) | 9.59437 | + | 11.8100i | 0.335050 | + | 0.412423i | ||||
\(821\) | 4.42305 | 0.154365 | 0.0771827 | − | 0.997017i | \(-0.475408\pi\) | ||||
0.0771827 | + | 0.997017i | \(0.475408\pi\) | |||||||
\(822\) | −9.13901 | −0.318760 | ||||||||
\(823\) | −18.0088 | − | 18.0088i | −0.627749 | − | 0.627749i | 0.319752 | − | 0.947501i | \(-0.396400\pi\) |
−0.947501 | + | 0.319752i | \(0.896400\pi\) | |||||||
\(824\) | 8.32869i | 0.290144i | ||||||||
\(825\) | 12.5787 | − | 8.22511i | 0.437934 | − | 0.286362i | ||||
\(826\) | −27.2700 | −0.948843 | ||||||||
\(827\) | 12.8455 | 0.446682 | 0.223341 | − | 0.974740i | \(-0.428304\pi\) | ||||
0.223341 | + | 0.974740i | \(0.428304\pi\) | |||||||
\(828\) | −4.23386 | −0.147137 | ||||||||
\(829\) | 8.43842 | + | 8.43842i | 0.293078 | + | 0.293078i | 0.838295 | − | 0.545217i | \(-0.183553\pi\) |
−0.545217 | + | 0.838295i | \(0.683553\pi\) | |||||||
\(830\) | −0.156712 | + | 1.51394i | −0.00543956 | + | 0.0525496i | ||||
\(831\) | 11.5551 | + | 11.5551i | 0.400842 | + | 0.400842i | ||||
\(832\) | − | 6.48482i | − | 0.224821i | ||||||
\(833\) | − | 69.7052i | − | 2.41514i | ||||||
\(834\) | −8.05008 | − | 8.05008i | −0.278751 | − | 0.278751i | ||||
\(835\) | −22.2063 | + | 18.0403i | −0.768481 | + | 0.624309i | ||||
\(836\) | 13.3497 | + | 13.3497i | 0.461708 | + | 0.461708i | ||||
\(837\) | −1.51677 | −0.0524274 | ||||||||
\(838\) | −21.0888 | −0.728502 | ||||||||
\(839\) | −12.7028 | −0.438548 | −0.219274 | − | 0.975663i | \(-0.570369\pi\) | ||||
−0.219274 | + | 0.975663i | \(0.570369\pi\) | |||||||
\(840\) | −7.48731 | + | 6.08265i | −0.258337 | + | 0.209871i | ||||
\(841\) | − | 24.4111i | − | 0.841763i | ||||||
\(842\) | −0.620287 | − | 0.620287i | −0.0213765 | − | 0.0213765i | ||||
\(843\) | −16.9055 | −0.582257 | ||||||||
\(844\) | 19.7786 | 0.680806 | ||||||||
\(845\) | −50.4222 | + | 40.9627i | −1.73458 | + | 1.40916i | ||||
\(846\) | −5.31277 | + | 5.31277i | −0.182657 | + | 0.182657i | ||||
\(847\) | −5.99423 | + | 5.99423i | −0.205964 | + | 0.205964i | ||||
\(848\) | −5.63889 | − | 5.63889i | −0.193640 | − | 0.193640i | ||||
\(849\) | −7.10937 | + | 7.10937i | −0.243993 | + | 0.243993i | ||||
\(850\) | −29.3787 | − | 6.14802i | −1.00768 | − | 0.210875i | ||||
\(851\) | 25.3199 | − | 4.70639i | 0.867954 | − | 0.161333i | ||||
\(852\) | 6.49828 | − | 6.49828i | 0.222628 | − | 0.222628i | ||||
\(853\) | 0.629737 | 0.0215618 | 0.0107809 | − | 0.999942i | \(-0.496568\pi\) | ||||
0.0107809 | + | 0.999942i | \(0.496568\pi\) | |||||||
\(854\) | −45.1535 | −1.54512 | ||||||||
\(855\) | 13.9698 | + | 1.44606i | 0.477758 | + | 0.0494541i | ||||
\(856\) | 7.63911 | + | 7.63911i | 0.261099 | + | 0.261099i | ||||
\(857\) | 20.1915 | 0.689729 | 0.344865 | − | 0.938652i | \(-0.387925\pi\) | ||||
0.344865 | + | 0.938652i | \(0.387925\pi\) | |||||||
\(858\) | 13.7831 | + | 13.7831i | 0.470548 | + | 0.470548i | ||||
\(859\) | 0.0308185 | − | 0.0308185i | 0.00105151 | − | 0.00105151i | −0.706581 | − | 0.707632i | \(-0.749763\pi\) |
0.707632 | + | 0.706581i | \(0.249763\pi\) | |||||||
\(860\) | −16.6304 | − | 20.4708i | −0.567091 | − | 0.698049i | ||||
\(861\) | 29.3569 | 1.00048 | ||||||||
\(862\) | −19.6454 | − | 19.6454i | −0.669125 | − | 0.669125i | ||||
\(863\) | 16.7213 | + | 16.7213i | 0.569201 | + | 0.569201i | 0.931904 | − | 0.362704i | \(-0.118146\pi\) |
−0.362704 | + | 0.931904i | \(0.618146\pi\) | |||||||
\(864\) | −0.707107 | + | 0.707107i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | 1.60397 | − | 15.4954i | 0.0545367 | − | 0.526859i | ||||
\(866\) | −26.4568 | + | 26.4568i | −0.899038 | + | 0.899038i | ||||
\(867\) | 13.4606 | − | 13.4606i | 0.457146 | − | 0.457146i | ||||
\(868\) | − | 6.54356i | − | 0.222103i | ||||||
\(869\) | 19.8297 | + | 19.8297i | 0.672676 | + | 0.672676i | ||||
\(870\) | −3.02032 | − | 3.71780i | −0.102398 | − | 0.126045i | ||||
\(871\) | 15.7189 | − | 15.7189i | 0.532613 | − | 0.532613i | ||||
\(872\) | −6.00958 | − | 6.00958i | −0.203510 | − | 0.203510i | ||||
\(873\) | − | 16.2572i | − | 0.550224i | ||||||
\(874\) | −18.8036 | + | 18.8036i | −0.636043 | + | 0.636043i | ||||
\(875\) | 45.9426 | + | 14.6881i | 1.55314 | + | 0.496550i | ||||
\(876\) | − | 2.84828i | − | 0.0962345i | ||||||
\(877\) | −11.9469 | + | 11.9469i | −0.403419 | + | 0.403419i | −0.879436 | − | 0.476017i | \(-0.842080\pi\) |
0.476017 | + | 0.879436i | \(0.342080\pi\) | |||||||
\(878\) | 15.3968 | − | 15.3968i | 0.519618 | − | 0.519618i | ||||
\(879\) | 11.9863 | 0.404288 | ||||||||
\(880\) | 4.23804 | + | 5.21672i | 0.142864 | + | 0.175856i | ||||
\(881\) | − | 3.77343i | − | 0.127130i | −0.997978 | − | 0.0635651i | \(-0.979753\pi\) | ||
0.997978 | − | 0.0635651i | \(-0.0202471\pi\) | |||||||
\(882\) | 11.6117i | 0.390986i | ||||||||
\(883\) | 22.2616 | 0.749163 | 0.374582 | − | 0.927194i | \(-0.377786\pi\) | ||||
0.374582 | + | 0.927194i | \(0.377786\pi\) | |||||||
\(884\) | − | 38.9284i | − | 1.30931i | ||||||
\(885\) | 8.91233 | + | 10.9705i | 0.299585 | + | 0.368768i | ||||
\(886\) | −13.4474 | − | 13.4474i | −0.451776 | − | 0.451776i | ||||
\(887\) | −19.5694 | − | 19.5694i | −0.657078 | − | 0.657078i | 0.297610 | − | 0.954688i | \(-0.403810\pi\) |
−0.954688 | + | 0.297610i | \(0.903810\pi\) | |||||||
\(888\) | 3.44271 | − | 5.01476i | 0.115530 | − | 0.168284i | ||||
\(889\) | 51.3146i | 1.72103i | ||||||||
\(890\) | 1.41730 | − | 13.6920i | 0.0475079 | − | 0.458956i | ||||
\(891\) | − | 3.00583i | − | 0.100699i | ||||||
\(892\) | −4.53283 | − | 4.53283i | −0.151770 | − | 0.151770i | ||||
\(893\) | 47.1907i | 1.57918i | ||||||||
\(894\) | 15.0325 | − | 15.0325i | 0.502763 | − | 0.502763i | ||||
\(895\) | 22.8258 | + | 2.36276i | 0.762982 | + | 0.0789785i | ||||
\(896\) | −3.05055 | − | 3.05055i | −0.101912 | − | 0.101912i | ||||
\(897\) | −19.4142 | + | 19.4142i | −0.648221 | + | 0.648221i | ||||
\(898\) | −0.109620 | − | 0.109620i | −0.00365806 | − | 0.00365806i | ||||
\(899\) | 3.24918 | 0.108366 | ||||||||
\(900\) | 4.89399 | + | 1.02416i | 0.163133 | + | 0.0341385i | ||||
\(901\) | −33.8504 | − | 33.8504i | −1.12772 | − | 1.12772i | ||||
\(902\) | − | 20.4542i | − | 0.681049i | ||||||
\(903\) | −50.8856 | −1.69337 | ||||||||
\(904\) | 9.17752i | 0.305240i | ||||||||
\(905\) | 16.8405 | − | 13.6812i | 0.559799 | − | 0.454777i | ||||
\(906\) | −0.374755 | + | 0.374755i | −0.0124504 | + | 0.0124504i | ||||
\(907\) | 12.9608 | 0.430357 | 0.215178 | − | 0.976575i | \(-0.430967\pi\) | ||||
0.215178 | + | 0.976575i | \(0.430967\pi\) | |||||||
\(908\) | −12.5323 | −0.415899 | ||||||||
\(909\) | 16.3032 | 0.540743 | ||||||||
\(910\) | −6.44104 | + | 62.2245i | −0.213518 | + | 2.06272i | ||||
\(911\) | −26.6292 | − | 26.6292i | −0.882265 | − | 0.882265i | 0.111500 | − | 0.993764i | \(-0.464435\pi\) |
−0.993764 | + | 0.111500i | \(0.964435\pi\) | |||||||
\(912\) | 6.28088i | 0.207981i | ||||||||
\(913\) | 1.44673 | − | 1.44673i | 0.0478798 | − | 0.0478798i | ||||
\(914\) | 7.05088i | 0.233222i | ||||||||
\(915\) | 14.7570 | + | 18.1648i | 0.487852 | + | 0.600511i | ||||
\(916\) | 20.0623i | 0.662877i | ||||||||
\(917\) | 11.3125i | 0.373570i | ||||||||
\(918\) | −4.24477 | + | 4.24477i | −0.140098 | + | 0.140098i | ||||
\(919\) | 17.8611 | + | 17.8611i | 0.589183 | + | 0.589183i | 0.937410 | − | 0.348227i | \(-0.113216\pi\) |
−0.348227 | + | 0.937410i | \(0.613216\pi\) | |||||||
\(920\) | −7.34801 | + | 5.96948i | −0.242257 | + | 0.196808i | ||||
\(921\) | −3.81318 | −0.125649 | ||||||||
\(922\) | 0.0298156 | − | 0.0298156i | 0.000981926 | − | 0.000981926i | ||||
\(923\) | − | 59.5952i | − | 1.96160i | ||||||
\(924\) | 12.9675 | 0.426601 | ||||||||
\(925\) | −30.4061 | − | 0.684598i | −0.999747 | − | 0.0225094i | ||||
\(926\) | −5.26855 | −0.173135 | ||||||||
\(927\) | − | 8.32869i | − | 0.273550i | ||||||
\(928\) | 1.51474 | − | 1.51474i | 0.0497237 | − | 0.0497237i | ||||
\(929\) | 49.7187 | 1.63122 | 0.815609 | − | 0.578604i | \(-0.196402\pi\) | ||||
0.815609 | + | 0.578604i | \(0.196402\pi\) | |||||||
\(930\) | −2.63241 | + | 2.13856i | −0.0863202 | + | 0.0701260i | ||||
\(931\) | 51.5705 | + | 51.5705i | 1.69015 | + | 1.69015i | ||||
\(932\) | 4.10021 | − | 4.10021i | 0.134307 | − | 0.134307i | ||||
\(933\) | 8.63855i | 0.282813i | ||||||||
\(934\) | − | 8.16999i | − | 0.267330i | ||||||
\(935\) | 25.4410 | + | 31.3161i | 0.832009 | + | 1.02414i | ||||
\(936\) | 6.48482i | 0.211963i | ||||||||
\(937\) | 21.5400 | − | 21.5400i | 0.703682 | − | 0.703682i | −0.261517 | − | 0.965199i | \(-0.584223\pi\) |
0.965199 | + | 0.261517i | \(0.0842228\pi\) | |||||||
\(938\) | − | 14.7887i | − | 0.482870i | ||||||
\(939\) | 16.0631 | + | 16.0631i | 0.524199 | + | 0.524199i | ||||
\(940\) | −1.72982 | + | 16.7111i | −0.0564205 | + | 0.545058i | ||||
\(941\) | −45.1384 | −1.47147 | −0.735735 | − | 0.677270i | \(-0.763163\pi\) | ||||
−0.735735 | + | 0.677270i | \(0.763163\pi\) | |||||||
\(942\) | 12.8134 | 0.417484 | ||||||||
\(943\) | 28.8107 | 0.938204 | ||||||||
\(944\) | −4.46968 | + | 4.46968i | −0.145476 | + | 0.145476i | ||||
\(945\) | 7.48731 | − | 6.08265i | 0.243562 | − | 0.197869i | ||||
\(946\) | 35.4541i | 1.15271i | ||||||||
\(947\) | −42.8211 | −1.39150 | −0.695750 | − | 0.718284i | \(-0.744928\pi\) | ||||
−0.695750 | + | 0.718284i | \(0.744928\pi\) | |||||||
\(948\) | 9.32966i | 0.303013i | ||||||||
\(949\) | −13.0607 | − | 13.0607i | −0.423967 | − | 0.423967i | ||||
\(950\) | 26.2840 | − | 17.1869i | 0.852764 | − | 0.557617i | ||||
\(951\) | 24.5187 | 0.795073 | ||||||||
\(952\) | −18.3125 | − | 18.3125i | −0.593511 | − | 0.593511i | ||||
\(953\) | −19.4170 | + | 19.4170i | −0.628978 | + | 0.628978i | −0.947811 | − | 0.318833i | \(-0.896709\pi\) |
0.318833 | + | 0.947811i | \(0.396709\pi\) | |||||||
\(954\) | 5.63889 | + | 5.63889i | 0.182566 | + | 0.182566i | ||||
\(955\) | −22.4395 | − | 2.32278i | −0.726126 | − | 0.0751634i | ||||
\(956\) | 9.03944 | − | 9.03944i | 0.292356 | − | 0.292356i | ||||
\(957\) | 6.43898i | 0.208143i | ||||||||
\(958\) | −8.69240 | − | 8.69240i | −0.280839 | − | 0.280839i | ||||
\(959\) | 39.4269i | 1.27316i | ||||||||
\(960\) | −0.230232 | + | 2.22418i | −0.00743070 | + | 0.0717852i | ||||
\(961\) | 28.6994i | 0.925787i | ||||||||
\(962\) | −7.20856 | − | 38.7813i | −0.232413 | − | 1.25036i | ||||
\(963\) | −7.63911 | − | 7.63911i | −0.246167 | − | 0.246167i | ||||
\(964\) | −7.69908 | − | 7.69908i | −0.247971 | − | 0.247971i | ||||
\(965\) | −27.2626 | − | 33.5583i | −0.877613 | − | 1.08028i | ||||
\(966\) | 18.2654i | 0.587680i | ||||||||
\(967\) | −1.21142 | −0.0389565 | −0.0194782 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194782 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(968\) | 1.96497i | 0.0631565i | ||||||||
\(969\) | 37.7042i | 1.21123i | ||||||||
\(970\) | −22.9217 | − | 28.2150i | −0.735970 | − | 0.905928i | ||||
\(971\) | −36.7851 | −1.18049 | −0.590245 | − | 0.807224i | \(-0.700969\pi\) | ||||
−0.590245 | + | 0.807224i | \(0.700969\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −34.7291 | + | 34.7291i | −1.11336 | + | 1.11336i | ||||
\(974\) | − | 25.3749i | − | 0.813063i | ||||||
\(975\) | 27.1374 | − | 17.7449i | 0.869092 | − | 0.568293i | ||||
\(976\) | −7.40088 | + | 7.40088i | −0.236897 | + | 0.236897i | ||||
\(977\) | − | 4.59322i | − | 0.146950i | −0.997297 | − | 0.0734750i | \(-0.976591\pi\) | ||
0.997297 | − | 0.0734750i | \(-0.0234089\pi\) | |||||||
\(978\) | −14.9772 | − | 14.9772i | −0.478919 | − | 0.478919i | ||||
\(979\) | −13.0842 | + | 13.0842i | −0.418171 | + | 0.418171i | ||||
\(980\) | 16.3718 | + | 20.1525i | 0.522977 | + | 0.643748i | ||||
\(981\) | 6.00958 | + | 6.00958i | 0.191871 | + | 0.191871i | ||||
\(982\) | 34.9666i | 1.11583i | ||||||||
\(983\) | 13.5819 | − | 13.5819i | 0.433196 | − | 0.433196i | −0.456518 | − | 0.889714i | \(-0.650904\pi\) |
0.889714 | + | 0.456518i | \(0.150904\pi\) | |||||||
\(984\) | 4.81173 | − | 4.81173i | 0.153392 | − | 0.153392i | ||||
\(985\) | −2.77215 | + | 26.7807i | −0.0883280 | + | 0.853304i | ||||
\(986\) | 9.09299 | − | 9.09299i | 0.289580 | − | 0.289580i | ||||
\(987\) | 22.9199 | + | 22.9199i | 0.729550 | + | 0.729550i | ||||
\(988\) | 28.8007 | + | 28.8007i | 0.916273 | + | 0.916273i | ||||
\(989\) | −49.9388 | −1.58796 | ||||||||
\(990\) | −4.23804 | − | 5.21672i | −0.134694 | − | 0.165798i | ||||
\(991\) | −14.6078 | + | 14.6078i | −0.464032 | + | 0.464032i | −0.899975 | − | 0.435942i | \(-0.856415\pi\) |
0.435942 | + | 0.899975i | \(0.356415\pi\) | |||||||
\(992\) | −1.07252 | − | 1.07252i | −0.0340526 | − | 0.0340526i | ||||
\(993\) | −0.419995 | −0.0133281 | ||||||||
\(994\) | −28.0344 | − | 28.0344i | −0.889198 | − | 0.889198i | ||||
\(995\) | −14.8195 | − | 1.53401i | −0.469811 | − | 0.0486315i | ||||
\(996\) | 0.680671 | 0.0215679 | ||||||||
\(997\) | 10.1411 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448661\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448661\pi\) | |||||||
\(998\) | −0.199787 | + | 0.199787i | −0.00632414 | + | 0.00632414i | ||||
\(999\) | −3.44271 | + | 5.01476i | −0.108922 | + | 0.158660i |
(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 | 1110.2.l.b.43.20 | ✓ | 40 | |
5.2 | odd | 4 | 1110.2.o.b.487.1 | yes | 40 | ||
37.31 | odd | 4 | 1110.2.o.b.253.1 | yes | 40 | ||
185.142 | even | 4 | inner | 1110.2.l.b.697.20 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.20 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.l.b.697.20 | yes | 40 | 185.142 | even | 4 | inner | |
1110.2.o.b.253.1 | yes | 40 | 37.31 | odd | 4 | ||
1110.2.o.b.487.1 | yes | 40 | 5.2 | odd | 4 |