Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(16,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("195.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55708283941\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.61 |
Dual form | 195.2.i.a.16.1 |
$q$-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 \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | − | 1.73205i | −0.408248 | − | 0.707107i | ||||
\(7\) | −2.50000 | − | 4.33013i | −0.944911 | − | 1.63663i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
−0.188982 | − | 0.981981i | \(-0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | −2.50000 | + | 2.59808i | −0.693375 | + | 0.720577i | ||||
\(14\) | 10.0000 | 2.67261 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 2.00000 | 0.471405 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 5.00000 | 1.09109 | ||||||||
\(22\) | −2.00000 | − | 3.46410i | −0.426401 | − | 0.738549i | ||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.00000 | − | 6.92820i | −0.392232 | − | 1.35873i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.00000 | + | 8.66025i | −0.944911 | + | 1.63663i | ||||
\(29\) | 2.00000 | − | 3.46410i | 0.371391 | − | 0.643268i | −0.618389 | − | 0.785872i | \(-0.712214\pi\) |
0.989780 | + | 0.142605i | \(0.0455477\pi\) | |||||||
\(30\) | 1.00000 | + | 1.73205i | 0.182574 | + | 0.316228i | ||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 4.00000 | + | 6.92820i | 0.707107 | + | 1.22474i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 2.50000 | + | 4.33013i | 0.422577 | + | 0.731925i | ||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | −5.00000 | + | 8.66025i | −0.771517 | + | 1.33631i | ||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −6.00000 | − | 10.3923i | −0.884652 | − | 1.53226i | ||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 2.00000 | + | 3.46410i | 0.288675 | + | 0.500000i | ||||
\(49\) | −9.00000 | + | 15.5885i | −1.28571 | + | 2.22692i | ||||
\(50\) | −1.00000 | + | 1.73205i | −0.141421 | + | 0.244949i | ||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 7.00000 | + | 1.73205i | 0.970725 | + | 0.240192i | ||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | −1.00000 | + | 1.73205i | −0.136083 | + | 0.235702i | ||||
\(55\) | 1.00000 | − | 1.73205i | 0.134840 | − | 0.233550i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | + | 6.92820i | 0.525226 | + | 0.909718i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 7.00000 | − | 12.1244i | 0.889001 | − | 1.53979i | ||||
\(63\) | −2.50000 | + | 4.33013i | −0.314970 | + | 0.545545i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.50000 | − | 2.59808i | 0.310087 | − | 0.322252i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | −3.00000 | − | 5.19615i | −0.361158 | − | 0.625543i | ||||
\(70\) | −10.0000 | −1.19523 | ||||||||
\(71\) | −6.00000 | − | 10.3923i | −0.712069 | − | 1.23334i | −0.964079 | − | 0.265615i | \(-0.914425\pi\) |
0.252010 | − | 0.967725i | \(-0.418908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0000 | 1.75562 | 0.877809 | − | 0.479012i | \(-0.159005\pi\) | ||||
0.877809 | + | 0.479012i | \(0.159005\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.0000 | 1.13961 | ||||||||
\(78\) | 7.00000 | + | 1.73205i | 0.792594 | + | 0.196116i | ||||
\(79\) | 3.00000 | 0.337526 | 0.168763 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(80\) | −2.00000 | + | 3.46410i | −0.223607 | + | 0.387298i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.00000 | − | 10.3923i | −0.662589 | − | 1.14764i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −5.00000 | − | 8.66025i | −0.545545 | − | 0.944911i | ||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 2.00000 | + | 3.46410i | 0.214423 | + | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.00000 | + | 12.1244i | −0.741999 | + | 1.28518i | 0.209585 | + | 0.977790i | \(0.432789\pi\) |
−0.951584 | + | 0.307389i | \(0.900545\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 17.5000 | + | 4.33013i | 1.83450 | + | 0.453921i | ||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | 3.50000 | − | 6.06218i | 0.362933 | − | 0.628619i | ||||
\(94\) | 8.00000 | − | 13.8564i | 0.825137 | − | 1.42918i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.00000 | −0.816497 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | −18.0000 | − | 31.1769i | −1.81827 | − | 3.14934i | ||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −1.00000 | − | 1.73205i | −0.100000 | − | 0.173205i | ||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | −2.00000 | + | 3.46410i | −0.198030 | + | 0.342997i | ||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00000 | −0.487950 | ||||||||
\(106\) | 4.00000 | − | 6.92820i | 0.388514 | − | 0.672927i | ||||
\(107\) | −2.00000 | + | 3.46410i | −0.193347 | + | 0.334887i | −0.946357 | − | 0.323122i | \(-0.895268\pi\) |
0.753010 | + | 0.658009i | \(0.228601\pi\) | |||||||
\(108\) | −1.00000 | − | 1.73205i | −0.0962250 | − | 0.166667i | ||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 2.00000 | + | 3.46410i | 0.190693 | + | 0.330289i | ||||
\(111\) | 1.00000 | + | 1.73205i | 0.0949158 | + | 0.164399i | ||||
\(112\) | −20.0000 | −1.88982 | ||||||||
\(113\) | 1.00000 | + | 1.73205i | 0.0940721 | + | 0.162938i | 0.909221 | − | 0.416314i | \(-0.136678\pi\) |
−0.815149 | + | 0.579252i | \(0.803345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | − | 5.19615i | 0.279751 | − | 0.484544i | ||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 3.50000 | + | 0.866025i | 0.323575 | + | 0.0800641i | ||||
\(118\) | 24.0000 | 2.20938 | ||||||||
\(119\) | −5.00000 | + | 8.66025i | −0.458349 | + | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −26.0000 | −2.35393 | ||||||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | 7.00000 | + | 12.1244i | 0.628619 | + | 1.08880i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.00000 | − | 8.66025i | −0.445435 | − | 0.771517i | ||||
\(127\) | 5.50000 | − | 9.52628i | 0.488046 | − | 0.845321i | −0.511859 | − | 0.859069i | \(-0.671043\pi\) |
0.999905 | + | 0.0137486i | \(0.00437646\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 2.00000 | + | 6.92820i | 0.175412 | + | 0.607644i | ||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | −2.00000 | + | 3.46410i | −0.174078 | + | 0.301511i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.00000 | + | 12.1244i | 0.604708 | + | 1.04738i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | 1.50000 | + | 2.59808i | 0.127228 | + | 0.220366i | 0.922602 | − | 0.385754i | \(-0.126059\pi\) |
−0.795373 | + | 0.606120i | \(0.792725\pi\) | |||||||
\(140\) | 5.00000 | − | 8.66025i | 0.422577 | − | 0.731925i | ||||
\(141\) | 4.00000 | − | 6.92820i | 0.336861 | − | 0.583460i | ||||
\(142\) | 24.0000 | 2.01404 | ||||||||
\(143\) | −2.00000 | − | 6.92820i | −0.167248 | − | 0.579365i | ||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | −15.0000 | + | 25.9808i | −1.24141 | + | 2.15018i | ||||
\(147\) | −9.00000 | − | 15.5885i | −0.742307 | − | 1.28571i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | −1.00000 | − | 1.73205i | −0.0816497 | − | 0.141421i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | + | 1.73205i | −0.0808452 | + | 0.140028i | ||||
\(154\) | −10.0000 | + | 17.3205i | −0.805823 | + | 1.39573i | ||||
\(155\) | 7.00000 | 0.562254 | ||||||||
\(156\) | −5.00000 | + | 5.19615i | −0.400320 | + | 0.416025i | ||||
\(157\) | −15.0000 | −1.19713 | −0.598565 | − | 0.801074i | \(-0.704262\pi\) | ||||
−0.598565 | + | 0.801074i | \(0.704262\pi\) | |||||||
\(158\) | −3.00000 | + | 5.19615i | −0.238667 | + | 0.413384i | ||||
\(159\) | 2.00000 | − | 3.46410i | 0.158610 | − | 0.274721i | ||||
\(160\) | −4.00000 | − | 6.92820i | −0.316228 | − | 0.547723i | ||||
\(161\) | 30.0000 | 2.36433 | ||||||||
\(162\) | −1.00000 | − | 1.73205i | −0.0785674 | − | 0.136083i | ||||
\(163\) | 7.50000 | + | 12.9904i | 0.587445 | + | 1.01749i | 0.994566 | + | 0.104111i | \(0.0331996\pi\) |
−0.407120 | + | 0.913375i | \(0.633467\pi\) | |||||||
\(164\) | 12.0000 | 0.937043 | ||||||||
\(165\) | 1.00000 | + | 1.73205i | 0.0778499 | + | 0.134840i | ||||
\(166\) | −8.00000 | + | 13.8564i | −0.620920 | + | 1.07547i | ||||
\(167\) | −6.00000 | + | 10.3923i | −0.464294 | + | 0.804181i | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | −2.50000 | − | 4.33013i | −0.188982 | − | 0.327327i | ||||
\(176\) | 4.00000 | + | 6.92820i | 0.301511 | + | 0.522233i | ||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | −14.0000 | − | 24.2487i | −1.04934 | − | 1.81752i | ||||
\(179\) | 3.00000 | − | 5.19615i | 0.224231 | − | 0.388379i | −0.731858 | − | 0.681457i | \(-0.761346\pi\) |
0.956088 | + | 0.293079i | \(0.0946798\pi\) | |||||||
\(180\) | 1.00000 | − | 1.73205i | 0.0745356 | − | 0.129099i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | −25.0000 | + | 25.9808i | −1.85312 | + | 1.92582i | ||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | + | 1.73205i | −0.0735215 | + | 0.127343i | ||||
\(186\) | 7.00000 | + | 12.1244i | 0.513265 | + | 0.889001i | ||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 8.00000 | + | 13.8564i | 0.583460 | + | 1.01058i | ||||
\(189\) | −2.50000 | − | 4.33013i | −0.181848 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 4.00000 | − | 6.92820i | 0.288675 | − | 0.500000i | ||||
\(193\) | 5.50000 | − | 9.52628i | 0.395899 | − | 0.685717i | −0.597317 | − | 0.802005i | \(-0.703766\pi\) |
0.993215 | + | 0.116289i | \(0.0370998\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 1.00000 | + | 3.46410i | 0.0716115 | + | 0.248069i | ||||
\(196\) | 36.0000 | 2.57143 | ||||||||
\(197\) | 6.00000 | − | 10.3923i | 0.427482 | − | 0.740421i | −0.569166 | − | 0.822222i | \(-0.692734\pi\) |
0.996649 | + | 0.0818013i | \(0.0260673\pi\) | |||||||
\(198\) | −2.00000 | + | 3.46410i | −0.142134 | + | 0.246183i | ||||
\(199\) | −8.50000 | − | 14.7224i | −0.602549 | − | 1.04365i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | + | 6.06218i | 0.246871 | + | 0.427593i | ||||
\(202\) | 18.0000 | + | 31.1769i | 1.26648 | + | 2.19360i | ||||
\(203\) | −20.0000 | −1.40372 | ||||||||
\(204\) | −2.00000 | − | 3.46410i | −0.140028 | − | 0.242536i | ||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 4.00000 | + | 13.8564i | 0.277350 | + | 0.960769i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5.00000 | − | 8.66025i | 0.345033 | − | 0.597614i | ||||
\(211\) | −7.50000 | + | 12.9904i | −0.516321 | + | 0.894295i | 0.483499 | + | 0.875345i | \(0.339366\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(212\) | 4.00000 | + | 6.92820i | 0.274721 | + | 0.475831i | ||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | −4.00000 | − | 6.92820i | −0.273434 | − | 0.473602i | ||||
\(215\) | 0.500000 | + | 0.866025i | 0.0340997 | + | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.5000 | + | 30.3109i | 1.18798 | + | 2.05764i | ||||
\(218\) | 11.0000 | − | 19.0526i | 0.745014 | − | 1.29040i | ||||
\(219\) | −7.50000 | + | 12.9904i | −0.506803 | + | 0.877809i | ||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | 7.00000 | + | 1.73205i | 0.470871 | + | 0.116510i | ||||
\(222\) | −4.00000 | −0.268462 | ||||||||
\(223\) | 4.00000 | − | 6.92820i | 0.267860 | − | 0.463947i | −0.700449 | − | 0.713702i | \(-0.747017\pi\) |
0.968309 | + | 0.249756i | \(0.0803503\pi\) | |||||||
\(224\) | 20.0000 | − | 34.6410i | 1.33631 | − | 2.31455i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | −4.00000 | −0.266076 | ||||||||
\(227\) | −5.00000 | − | 8.66025i | −0.331862 | − | 0.574801i | 0.651015 | − | 0.759065i | \(-0.274343\pi\) |
−0.982877 | + | 0.184263i | \(0.941010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 6.00000 | + | 10.3923i | 0.395628 | + | 0.685248i | ||||
\(231\) | −5.00000 | + | 8.66025i | −0.328976 | + | 0.569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | −5.00000 | + | 5.19615i | −0.326860 | + | 0.339683i | ||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | −12.0000 | + | 20.7846i | −0.781133 | + | 1.35296i | ||||
\(237\) | −1.50000 | + | 2.59808i | −0.0974355 | + | 0.168763i | ||||
\(238\) | −10.0000 | − | 17.3205i | −0.648204 | − | 1.12272i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | −2.00000 | − | 3.46410i | −0.129099 | − | 0.223607i | ||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | −14.0000 | −0.899954 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 13.0000 | − | 22.5167i | 0.832240 | − | 1.44148i | ||||
\(245\) | 9.00000 | − | 15.5885i | 0.574989 | − | 0.995910i | ||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | + | 6.92820i | −0.253490 | + | 0.439057i | ||||
\(250\) | 1.00000 | − | 1.73205i | 0.0632456 | − | 0.109545i | ||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 10.0000 | 0.629941 | ||||||||
\(253\) | −6.00000 | − | 10.3923i | −0.377217 | − | 0.653359i | ||||
\(254\) | 11.0000 | + | 19.0526i | 0.690201 | + | 1.19546i | ||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 11.0000 | − | 19.0526i | 0.686161 | − | 1.18847i | −0.286909 | − | 0.957958i | \(-0.592628\pi\) |
0.973070 | − | 0.230508i | \(-0.0740389\pi\) | |||||||
\(258\) | −1.00000 | + | 1.73205i | −0.0622573 | + | 0.107833i | ||||
\(259\) | −10.0000 | −0.621370 | ||||||||
\(260\) | −7.00000 | − | 1.73205i | −0.434122 | − | 0.107417i | ||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | 4.00000 | − | 6.92820i | 0.247121 | − | 0.428026i | ||||
\(263\) | 5.00000 | − | 8.66025i | 0.308313 | − | 0.534014i | −0.669680 | − | 0.742650i | \(-0.733569\pi\) |
0.977993 | + | 0.208635i | \(0.0669022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.00000 | − | 12.1244i | −0.428393 | − | 0.741999i | ||||
\(268\) | −14.0000 | −0.855186 | ||||||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | 1.00000 | − | 1.73205i | 0.0608581 | − | 0.105409i | ||||
\(271\) | −14.5000 | + | 25.1147i | −0.880812 | + | 1.52561i | −0.0303728 | + | 0.999539i | \(0.509669\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | −12.5000 | + | 12.9904i | −0.756534 | + | 0.786214i | ||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | 3.50000 | + | 6.06218i | 0.209540 | + | 0.362933i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 8.00000 | + | 13.8564i | 0.476393 | + | 0.825137i | ||||
\(283\) | −2.50000 | + | 4.33013i | −0.148610 | + | 0.257399i | −0.930714 | − | 0.365748i | \(-0.880813\pi\) |
0.782104 | + | 0.623148i | \(0.214146\pi\) | |||||||
\(284\) | −12.0000 | + | 20.7846i | −0.712069 | + | 1.23334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0000 | + | 3.46410i | 0.827837 | + | 0.204837i | ||||
\(287\) | 30.0000 | 1.77084 | ||||||||
\(288\) | 4.00000 | − | 6.92820i | 0.235702 | − | 0.408248i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | −4.00000 | − | 6.92820i | −0.234888 | − | 0.406838i | ||||
\(291\) | −5.00000 | −0.293105 | ||||||||
\(292\) | −15.0000 | − | 25.9808i | −0.877809 | − | 1.52041i | ||||
\(293\) | −8.00000 | − | 13.8564i | −0.467365 | − | 0.809500i | 0.531940 | − | 0.846782i | \(-0.321463\pi\) |
−0.999305 | + | 0.0372823i | \(0.988130\pi\) | |||||||
\(294\) | 36.0000 | 2.09956 | ||||||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | −24.0000 | −1.39028 | ||||||||
\(299\) | −6.00000 | − | 20.7846i | −0.346989 | − | 1.20201i | ||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | −2.50000 | + | 4.33013i | −0.144098 | + | 0.249584i | ||||
\(302\) | 8.00000 | − | 13.8564i | 0.460348 | − | 0.797347i | ||||
\(303\) | 9.00000 | + | 15.5885i | 0.517036 | + | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.50000 | − | 11.2583i | −0.372189 | − | 0.644650i | ||||
\(306\) | −2.00000 | − | 3.46410i | −0.114332 | − | 0.198030i | ||||
\(307\) | −31.0000 | −1.76926 | −0.884632 | − | 0.466290i | \(-0.845590\pi\) | ||||
−0.884632 | + | 0.466290i | \(0.845590\pi\) | |||||||
\(308\) | −10.0000 | − | 17.3205i | −0.569803 | − | 0.986928i | ||||
\(309\) | 3.50000 | − | 6.06218i | 0.199108 | − | 0.344865i | ||||
\(310\) | −7.00000 | + | 12.1244i | −0.397573 | + | 0.688617i | ||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0000 | −1.75222 | −0.876112 | − | 0.482108i | \(-0.839871\pi\) | ||||
−0.876112 | + | 0.482108i | \(0.839871\pi\) | |||||||
\(314\) | 15.0000 | − | 25.9808i | 0.846499 | − | 1.46618i | ||||
\(315\) | 2.50000 | − | 4.33013i | 0.140859 | − | 0.243975i | ||||
\(316\) | −3.00000 | − | 5.19615i | −0.168763 | − | 0.292306i | ||||
\(317\) | 12.0000 | 0.673987 | 0.336994 | − | 0.941507i | \(-0.390590\pi\) | ||||
0.336994 | + | 0.941507i | \(0.390590\pi\) | |||||||
\(318\) | 4.00000 | + | 6.92820i | 0.224309 | + | 0.388514i | ||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | −2.00000 | − | 3.46410i | −0.111629 | − | 0.193347i | ||||
\(322\) | −30.0000 | + | 51.9615i | −1.67183 | + | 2.89570i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.00000 | 0.111111 | ||||||||
\(325\) | −2.50000 | + | 2.59808i | −0.138675 | + | 0.144115i | ||||
\(326\) | −30.0000 | −1.66155 | ||||||||
\(327\) | 5.50000 | − | 9.52628i | 0.304151 | − | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.0000 | + | 34.6410i | 1.10264 | + | 1.90982i | ||||
\(330\) | −4.00000 | −0.220193 | ||||||||
\(331\) | −4.50000 | − | 7.79423i | −0.247342 | − | 0.428410i | 0.715445 | − | 0.698669i | \(-0.246224\pi\) |
−0.962788 | + | 0.270259i | \(0.912891\pi\) | |||||||
\(332\) | −8.00000 | − | 13.8564i | −0.439057 | − | 0.760469i | ||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | −12.0000 | − | 20.7846i | −0.656611 | − | 1.13728i | ||||
\(335\) | −3.50000 | + | 6.06218i | −0.191225 | + | 0.331212i | ||||
\(336\) | 10.0000 | − | 17.3205i | 0.545545 | − | 0.944911i | ||||
\(337\) | −1.00000 | −0.0544735 | −0.0272367 | − | 0.999629i | \(-0.508671\pi\) | ||||
−0.0272367 | + | 0.999629i | \(0.508671\pi\) | |||||||
\(338\) | 23.0000 | + | 12.1244i | 1.25104 | + | 0.659478i | ||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | 7.00000 | − | 12.1244i | 0.379071 | − | 0.656571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55.0000 | 2.96972 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.00000 | + | 5.19615i | 0.161515 | + | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00000 | + | 13.8564i | 0.429463 | + | 0.743851i | 0.996826 | − | 0.0796169i | \(-0.0253697\pi\) |
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(348\) | 4.00000 | − | 6.92820i | 0.214423 | − | 0.371391i | ||||
\(349\) | −1.50000 | + | 2.59808i | −0.0802932 | + | 0.139072i | −0.903376 | − | 0.428850i | \(-0.858919\pi\) |
0.823083 | + | 0.567922i | \(0.192252\pi\) | |||||||
\(350\) | 10.0000 | 0.534522 | ||||||||
\(351\) | −2.50000 | + | 2.59808i | −0.133440 | + | 0.138675i | ||||
\(352\) | −16.0000 | −0.852803 | ||||||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | −12.0000 | + | 20.7846i | −0.637793 | + | 1.10469i | ||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 28.0000 | 1.48400 | ||||||||
\(357\) | −5.00000 | − | 8.66025i | −0.264628 | − | 0.458349i | ||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | 2.00000 | 0.105556 | 0.0527780 | − | 0.998606i | \(-0.483192\pi\) | ||||
0.0527780 | + | 0.998606i | \(0.483192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 22.0000 | − | 38.1051i | 1.15629 | − | 2.00276i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | −10.0000 | − | 34.6410i | −0.524142 | − | 1.81568i | ||||
\(365\) | −15.0000 | −0.785136 | ||||||||
\(366\) | 13.0000 | − | 22.5167i | 0.679521 | − | 1.17696i | ||||
\(367\) | −3.50000 | + | 6.06218i | −0.182699 | + | 0.316443i | −0.942799 | − | 0.333363i | \(-0.891817\pi\) |
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(368\) | 12.0000 | + | 20.7846i | 0.625543 | + | 1.08347i | ||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | −2.00000 | − | 3.46410i | −0.103975 | − | 0.180090i | ||||
\(371\) | 10.0000 | + | 17.3205i | 0.519174 | + | 0.899236i | ||||
\(372\) | −14.0000 | −0.725866 | ||||||||
\(373\) | −6.50000 | − | 11.2583i | −0.336557 | − | 0.582934i | 0.647225 | − | 0.762299i | \(-0.275929\pi\) |
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | + | 13.8564i | 0.206010 | + | 0.713641i | ||||
\(378\) | 10.0000 | 0.514344 | ||||||||
\(379\) | 2.50000 | − | 4.33013i | 0.128416 | − | 0.222424i | −0.794647 | − | 0.607072i | \(-0.792344\pi\) |
0.923063 | + | 0.384648i | \(0.125677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.50000 | + | 9.52628i | 0.281774 | + | 0.488046i | ||||
\(382\) | 24.0000 | 1.22795 | ||||||||
\(383\) | 9.00000 | + | 15.5885i | 0.459879 | + | 0.796533i | 0.998954 | − | 0.0457244i | \(-0.0145596\pi\) |
−0.539076 | + | 0.842257i | \(0.681226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | −0.509647 | ||||||||
\(386\) | 11.0000 | + | 19.0526i | 0.559885 | + | 0.969750i | ||||
\(387\) | −0.500000 | + | 0.866025i | −0.0254164 | + | 0.0440225i | ||||
\(388\) | 5.00000 | − | 8.66025i | 0.253837 | − | 0.439658i | ||||
\(389\) | 8.00000 | 0.405616 | 0.202808 | − | 0.979219i | \(-0.434993\pi\) | ||||
0.202808 | + | 0.979219i | \(0.434993\pi\) | |||||||
\(390\) | −7.00000 | − | 1.73205i | −0.354459 | − | 0.0877058i | ||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | − | 3.46410i | 0.100887 | − | 0.174741i | ||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | −3.00000 | −0.150946 | ||||||||
\(396\) | −2.00000 | − | 3.46410i | −0.100504 | − | 0.174078i | ||||
\(397\) | 7.50000 | + | 12.9904i | 0.376414 | + | 0.651969i | 0.990538 | − | 0.137241i | \(-0.0438236\pi\) |
−0.614123 | + | 0.789210i | \(0.710490\pi\) | |||||||
\(398\) | 34.0000 | 1.70427 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | −8.00000 | + | 13.8564i | −0.399501 | + | 0.691956i | −0.993664 | − | 0.112388i | \(-0.964150\pi\) |
0.594163 | + | 0.804344i | \(0.297483\pi\) | |||||||
\(402\) | −14.0000 | −0.698257 | ||||||||
\(403\) | 17.5000 | − | 18.1865i | 0.871737 | − | 0.905936i | ||||
\(404\) | −36.0000 | −1.79107 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 20.0000 | − | 34.6410i | 0.992583 | − | 1.71920i | ||||
\(407\) | 2.00000 | + | 3.46410i | 0.0991363 | + | 0.171709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | + | 12.9904i | 0.370851 | + | 0.642333i | 0.989697 | − | 0.143180i | \(-0.0457327\pi\) |
−0.618846 | + | 0.785513i | \(0.712399\pi\) | |||||||
\(410\) | 6.00000 | + | 10.3923i | 0.296319 | + | 0.513239i | ||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 7.00000 | + | 12.1244i | 0.344865 | + | 0.597324i | ||||
\(413\) | −30.0000 | + | 51.9615i | −1.47620 | + | 2.55686i | ||||
\(414\) | −6.00000 | + | 10.3923i | −0.294884 | + | 0.510754i | ||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | −28.0000 | − | 6.92820i | −1.37281 | − | 0.339683i | ||||
\(417\) | −3.00000 | −0.146911 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0000 | + | 32.9090i | −0.928211 | + | 1.60771i | −0.141896 | + | 0.989882i | \(0.545320\pi\) |
−0.786314 | + | 0.617827i | \(0.788013\pi\) | |||||||
\(420\) | 5.00000 | + | 8.66025i | 0.243975 | + | 0.422577i | ||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | −15.0000 | − | 25.9808i | −0.730189 | − | 1.26472i | ||||
\(423\) | 4.00000 | + | 6.92820i | 0.194487 | + | 0.336861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | −12.0000 | + | 20.7846i | −0.581402 | + | 1.00702i | ||||
\(427\) | 32.5000 | − | 56.2917i | 1.57279 | − | 2.72414i | ||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 7.00000 | + | 1.73205i | 0.337963 | + | 0.0836242i | ||||
\(430\) | −2.00000 | −0.0964486 | ||||||||
\(431\) | 14.0000 | − | 24.2487i | 0.674356 | − | 1.16802i | −0.302300 | − | 0.953213i | \(-0.597755\pi\) |
0.976657 | − | 0.214807i | \(-0.0689121\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | −0.500000 | − | 0.866025i | −0.0240285 | − | 0.0416185i | 0.853761 | − | 0.520665i | \(-0.174316\pi\) |
−0.877790 | + | 0.479046i | \(0.840983\pi\) | |||||||
\(434\) | −70.0000 | −3.36011 | ||||||||
\(435\) | −2.00000 | − | 3.46410i | −0.0958927 | − | 0.166091i | ||||
\(436\) | 11.0000 | + | 19.0526i | 0.526804 | + | 0.912452i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −15.0000 | − | 25.9808i | −0.716728 | − | 1.24141i | ||||
\(439\) | −7.50000 | + | 12.9904i | −0.357955 | + | 0.619997i | −0.987619 | − | 0.156871i | \(-0.949859\pi\) |
0.629664 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0000 | 0.857143 | ||||||||
\(442\) | −10.0000 | + | 10.3923i | −0.475651 | + | 0.494312i | ||||
\(443\) | 26.0000 | 1.23530 | 0.617649 | − | 0.786454i | \(-0.288085\pi\) | ||||
0.617649 | + | 0.786454i | \(0.288085\pi\) | |||||||
\(444\) | 2.00000 | − | 3.46410i | 0.0949158 | − | 0.164399i | ||||
\(445\) | 7.00000 | − | 12.1244i | 0.331832 | − | 0.574750i | ||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 20.0000 | + | 34.6410i | 0.944911 | + | 1.63663i | ||||
\(449\) | −9.00000 | − | 15.5885i | −0.424736 | − | 0.735665i | 0.571660 | − | 0.820491i | \(-0.306300\pi\) |
−0.996396 | + | 0.0848262i | \(0.972967\pi\) | |||||||
\(450\) | 2.00000 | 0.0942809 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 2.00000 | − | 3.46410i | 0.0940721 | − | 0.162938i | ||||
\(453\) | 4.00000 | − | 6.92820i | 0.187936 | − | 0.325515i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | −17.5000 | − | 4.33013i | −0.820413 | − | 0.202999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5000 | + | 30.3109i | −0.818615 | + | 1.41788i | 0.0880870 | + | 0.996113i | \(0.471925\pi\) |
−0.906702 | + | 0.421771i | \(0.861409\pi\) | |||||||
\(458\) | −14.0000 | + | 24.2487i | −0.654177 | + | 1.13307i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | 1.00000 | + | 1.73205i | 0.0465746 | + | 0.0806696i | 0.888373 | − | 0.459123i | \(-0.151836\pi\) |
−0.841798 | + | 0.539792i | \(0.818503\pi\) | |||||||
\(462\) | −10.0000 | − | 17.3205i | −0.465242 | − | 0.805823i | ||||
\(463\) | 3.00000 | 0.139422 | 0.0697109 | − | 0.997567i | \(-0.477792\pi\) | ||||
0.0697109 | + | 0.997567i | \(0.477792\pi\) | |||||||
\(464\) | −8.00000 | − | 13.8564i | −0.371391 | − | 0.643268i | ||||
\(465\) | −3.50000 | + | 6.06218i | −0.162309 | + | 0.281127i | ||||
\(466\) | 14.0000 | − | 24.2487i | 0.648537 | − | 1.12330i | ||||
\(467\) | −4.00000 | −0.185098 | −0.0925490 | − | 0.995708i | \(-0.529501\pi\) | ||||
−0.0925490 | + | 0.995708i | \(0.529501\pi\) | |||||||
\(468\) | −2.00000 | − | 6.92820i | −0.0924500 | − | 0.320256i | ||||
\(469\) | −35.0000 | −1.61615 | ||||||||
\(470\) | −8.00000 | + | 13.8564i | −0.369012 | + | 0.639148i | ||||
\(471\) | 7.50000 | − | 12.9904i | 0.345582 | − | 0.598565i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | −3.00000 | − | 5.19615i | −0.137795 | − | 0.238667i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 20.0000 | 0.916698 | ||||||||
\(477\) | 2.00000 | + | 3.46410i | 0.0915737 | + | 0.158610i | ||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | −21.0000 | + | 36.3731i | −0.959514 | + | 1.66193i | −0.235833 | + | 0.971794i | \(0.575782\pi\) |
−0.723681 | + | 0.690134i | \(0.757551\pi\) | |||||||
\(480\) | 8.00000 | 0.365148 | ||||||||
\(481\) | 2.00000 | + | 6.92820i | 0.0911922 | + | 0.315899i | ||||
\(482\) | 20.0000 | 0.910975 | ||||||||
\(483\) | −15.0000 | + | 25.9808i | −0.682524 | + | 1.18217i | ||||
\(484\) | 7.00000 | − | 12.1244i | 0.318182 | − | 0.551107i | ||||
\(485\) | −2.50000 | − | 4.33013i | −0.113519 | − | 0.196621i | ||||
\(486\) | 2.00000 | 0.0907218 | ||||||||
\(487\) | 14.0000 | + | 24.2487i | 0.634401 | + | 1.09881i | 0.986642 | + | 0.162905i | \(0.0520863\pi\) |
−0.352241 | + | 0.935909i | \(0.614580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.0000 | −0.678323 | ||||||||
\(490\) | 18.0000 | + | 31.1769i | 0.813157 | + | 1.40843i | ||||
\(491\) | 12.0000 | − | 20.7846i | 0.541552 | − | 0.937996i | −0.457263 | − | 0.889332i | \(-0.651170\pi\) |
0.998815 | − | 0.0486647i | \(-0.0154966\pi\) | |||||||
\(492\) | −6.00000 | + | 10.3923i | −0.270501 | + | 0.468521i | ||||
\(493\) | −8.00000 | −0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −14.0000 | + | 24.2487i | −0.628619 | + | 1.08880i | ||||
\(497\) | −30.0000 | + | 51.9615i | −1.34568 | + | 2.33079i | ||||
\(498\) | −8.00000 | − | 13.8564i | −0.358489 | − | 0.620920i | ||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 1.00000 | + | 1.73205i | 0.0447214 | + | 0.0774597i | ||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.00000 | + | 5.19615i | 0.133763 | + | 0.231685i | 0.925124 | − | 0.379664i | \(-0.123960\pi\) |
−0.791361 | + | 0.611349i | \(0.790627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | + | 15.5885i | −0.400495 | + | 0.693677i | ||||
\(506\) | 24.0000 | 1.06693 | ||||||||
\(507\) | 11.5000 | + | 6.06218i | 0.510733 | + | 0.269231i | ||||
\(508\) | −22.0000 | −0.976092 | ||||||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 2.00000 | − | 3.46410i | 0.0885615 | − | 0.153393i | ||||
\(511\) | −37.5000 | − | 64.9519i | −1.65890 | − | 2.87330i | ||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.0000 | + | 38.1051i | 0.970378 | + | 1.68074i | ||||
\(515\) | 7.00000 | 0.308457 | ||||||||
\(516\) | −1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | ||||
\(517\) | 8.00000 | − | 13.8564i | 0.351840 | − | 0.609404i | ||||
\(518\) | 10.0000 | − | 17.3205i | 0.439375 | − | 0.761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 4.00000 | − | 6.92820i | 0.175075 | − | 0.303239i | ||||
\(523\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(524\) | 4.00000 | + | 6.92820i | 0.174741 | + | 0.302660i | ||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 10.0000 | + | 17.3205i | 0.436021 | + | 0.755210i | ||||
\(527\) | 7.00000 | + | 12.1244i | 0.304925 | + | 0.528145i | ||||
\(528\) | −8.00000 | −0.348155 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −4.00000 | + | 6.92820i | −0.173749 | + | 0.300942i | ||||
\(531\) | −6.00000 | + | 10.3923i | −0.260378 | + | 0.450988i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | − | 20.7846i | −0.259889 | − | 0.900281i | ||||
\(534\) | 28.0000 | 1.21168 | ||||||||
\(535\) | 2.00000 | − | 3.46410i | 0.0864675 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.00000 | + | 5.19615i | 0.129460 | + | 0.224231i | ||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | −18.0000 | − | 31.1769i | −0.775315 | − | 1.34288i | ||||
\(540\) | 1.00000 | + | 1.73205i | 0.0430331 | + | 0.0745356i | ||||
\(541\) | 29.0000 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | −29.0000 | − | 50.2295i | −1.24566 | − | 2.15754i | ||||
\(543\) | 11.0000 | − | 19.0526i | 0.472055 | − | 0.817624i | ||||
\(544\) | 8.00000 | − | 13.8564i | 0.342997 | − | 0.594089i | ||||
\(545\) | 11.0000 | 0.471188 | ||||||||
\(546\) | −10.0000 | − | 34.6410i | −0.427960 | − | 1.48250i | ||||
\(547\) | −9.00000 | −0.384812 | −0.192406 | − | 0.981315i | \(-0.561629\pi\) | ||||
−0.192406 | + | 0.981315i | \(0.561629\pi\) | |||||||
\(548\) | 2.00000 | − | 3.46410i | 0.0854358 | − | 0.147979i | ||||
\(549\) | 6.50000 | − | 11.2583i | 0.277413 | − | 0.480494i | ||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50000 | − | 12.9904i | −0.318932 | − | 0.552407i | ||||
\(554\) | 20.0000 | 0.849719 | ||||||||
\(555\) | −1.00000 | − | 1.73205i | −0.0424476 | − | 0.0735215i | ||||
\(556\) | 3.00000 | − | 5.19615i | 0.127228 | − | 0.220366i | ||||
\(557\) | 10.0000 | − | 17.3205i | 0.423714 | − | 0.733893i | −0.572586 | − | 0.819845i | \(-0.694060\pi\) |
0.996299 | + | 0.0859514i | \(0.0273930\pi\) | |||||||
\(558\) | −14.0000 | −0.592667 | ||||||||
\(559\) | 3.50000 | + | 0.866025i | 0.148034 | + | 0.0366290i | ||||
\(560\) | 20.0000 | 0.845154 | ||||||||
\(561\) | −2.00000 | + | 3.46410i | −0.0844401 | + | 0.146254i | ||||
\(562\) | 12.0000 | − | 20.7846i | 0.506189 | − | 0.876746i | ||||
\(563\) | −13.0000 | − | 22.5167i | −0.547885 | − | 0.948964i | −0.998419 | − | 0.0562051i | \(-0.982100\pi\) |
0.450535 | − | 0.892759i | \(-0.351233\pi\) | |||||||
\(564\) | −16.0000 | −0.673722 | ||||||||
\(565\) | −1.00000 | − | 1.73205i | −0.0420703 | − | 0.0728679i | ||||
\(566\) | −5.00000 | − | 8.66025i | −0.210166 | − | 0.364018i | ||||
\(567\) | 5.00000 | 0.209980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | − | 17.3205i | 0.419222 | − | 0.726113i | −0.576640 | − | 0.816999i | \(-0.695636\pi\) |
0.995861 | + | 0.0908852i | \(0.0289696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | −10.0000 | + | 10.3923i | −0.418121 | + | 0.434524i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −30.0000 | + | 51.9615i | −1.25218 | + | 2.16883i | ||||
\(575\) | −3.00000 | + | 5.19615i | −0.125109 | + | 0.216695i | ||||
\(576\) | 4.00000 | + | 6.92820i | 0.166667 | + | 0.288675i | ||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 13.0000 | + | 22.5167i | 0.540729 | + | 0.936570i | ||||
\(579\) | 5.50000 | + | 9.52628i | 0.228572 | + | 0.395899i | ||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | −20.0000 | − | 34.6410i | −0.829740 | − | 1.43715i | ||||
\(582\) | 5.00000 | − | 8.66025i | 0.207257 | − | 0.358979i | ||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.50000 | − | 0.866025i | −0.144707 | − | 0.0358057i | ||||
\(586\) | 32.0000 | 1.32191 | ||||||||
\(587\) | −14.0000 | + | 24.2487i | −0.577842 | + | 1.00085i | 0.417885 | + | 0.908500i | \(0.362772\pi\) |
−0.995726 | + | 0.0923513i | \(0.970562\pi\) | |||||||
\(588\) | −18.0000 | + | 31.1769i | −0.742307 | + | 1.28571i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −24.0000 | −0.988064 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | −10.0000 | −0.410651 | −0.205325 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205325 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(594\) | −2.00000 | − | 3.46410i | −0.0820610 | − | 0.142134i | ||||
\(595\) | 5.00000 | − | 8.66025i | 0.204980 | − | 0.355036i | ||||
\(596\) | 12.0000 | − | 20.7846i | 0.491539 | − | 0.851371i | ||||
\(597\) | 17.0000 | 0.695764 | ||||||||
\(598\) | 42.0000 | + | 10.3923i | 1.71751 | + | 0.424973i | ||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | + | 19.0526i | −0.448699 | + | 0.777170i | −0.998302 | − | 0.0582563i | \(-0.981446\pi\) |
0.549602 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(602\) | −5.00000 | − | 8.66025i | −0.203785 | − | 0.352966i | ||||
\(603\) | −7.00000 | −0.285062 | ||||||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | −36.0000 | −1.46240 | ||||||||
\(607\) | −8.00000 | − | 13.8564i | −0.324710 | − | 0.562414i | 0.656744 | − | 0.754114i | \(-0.271933\pi\) |
−0.981454 | + | 0.191700i | \(0.938600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0000 | − | 17.3205i | 0.405220 | − | 0.701862i | ||||
\(610\) | 26.0000 | 1.05271 | ||||||||
\(611\) | 20.0000 | − | 20.7846i | 0.809113 | − | 0.840855i | ||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 7.50000 | − | 12.9904i | 0.302922 | − | 0.524677i | −0.673874 | − | 0.738846i | \(-0.735371\pi\) |
0.976797 | + | 0.214169i | \(0.0687045\pi\) | |||||||
\(614\) | 31.0000 | − | 53.6936i | 1.25106 | − | 2.16690i | ||||
\(615\) | 3.00000 | + | 5.19615i | 0.120972 | + | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | − | 5.19615i | −0.120775 | − | 0.209189i | 0.799298 | − | 0.600935i | \(-0.205205\pi\) |
−0.920074 | + | 0.391745i | \(0.871871\pi\) | |||||||
\(618\) | 7.00000 | + | 12.1244i | 0.281581 | + | 0.487713i | ||||
\(619\) | 37.0000 | 1.48716 | 0.743578 | − | 0.668649i | \(-0.233127\pi\) | ||||
0.743578 | + | 0.668649i | \(0.233127\pi\) | |||||||
\(620\) | −7.00000 | − | 12.1244i | −0.281127 | − | 0.486926i | ||||
\(621\) | −3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | ||||
\(622\) | 22.0000 | − | 38.1051i | 0.882120 | − | 1.52788i | ||||
\(623\) | 70.0000 | 2.80449 | ||||||||
\(624\) | −14.0000 | − | 3.46410i | −0.560449 | − | 0.138675i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.0000 | − | 53.6936i | 1.23901 | − | 2.14603i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.0000 | + | 25.9808i | 0.598565 | + | 1.03675i | ||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 5.00000 | + | 8.66025i | 0.199205 | + | 0.345033i | ||||
\(631\) | −3.50000 | − | 6.06218i | −0.139333 | − | 0.241331i | 0.787911 | − | 0.615789i | \(-0.211162\pi\) |
−0.927244 | + | 0.374457i | \(0.877829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.50000 | − | 12.9904i | −0.298098 | − | 0.516321i | ||||
\(634\) | −12.0000 | + | 20.7846i | −0.476581 | + | 0.825462i | ||||
\(635\) | −5.50000 | + | 9.52628i | −0.218261 | + | 0.378039i | ||||
\(636\) | −8.00000 | −0.317221 | ||||||||
\(637\) | −18.0000 | − | 62.3538i | −0.713186 | − | 2.47055i | ||||
\(638\) | −16.0000 | −0.633446 | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | − | 1.73205i | −0.0394976 | − | 0.0684119i | 0.845601 | − | 0.533816i | \(-0.179242\pi\) |
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(642\) | 8.00000 | 0.315735 | ||||||||
\(643\) | 9.50000 | + | 16.4545i | 0.374643 | + | 0.648901i | 0.990274 | − | 0.139134i | \(-0.0444318\pi\) |
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(644\) | −30.0000 | − | 51.9615i | −1.18217 | − | 2.04757i | ||||
\(645\) | −1.00000 | −0.0393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0000 | + | 32.9090i | −0.746967 | + | 1.29378i | 0.202303 | + | 0.979323i | \(0.435157\pi\) |
−0.949270 | + | 0.314462i | \(0.898176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | −2.00000 | − | 6.92820i | −0.0784465 | − | 0.271746i | ||||
\(651\) | −35.0000 | −1.37176 | ||||||||
\(652\) | 15.0000 | − | 25.9808i | 0.587445 | − | 1.01749i | ||||
\(653\) | −21.0000 | + | 36.3731i | −0.821794 | + | 1.42339i | 0.0825519 | + | 0.996587i | \(0.473693\pi\) |
−0.904345 | + | 0.426801i | \(0.859640\pi\) | |||||||
\(654\) | 11.0000 | + | 19.0526i | 0.430134 | + | 0.745014i | ||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 12.0000 | + | 20.7846i | 0.468521 | + | 0.811503i | ||||
\(657\) | −7.50000 | − | 12.9904i | −0.292603 | − | 0.506803i | ||||
\(658\) | −80.0000 | −3.11872 | ||||||||
\(659\) | 12.0000 | + | 20.7846i | 0.467454 | + | 0.809653i | 0.999309 | − | 0.0371821i | \(-0.0118382\pi\) |
−0.531855 | + | 0.846836i | \(0.678505\pi\) | |||||||
\(660\) | 2.00000 | − | 3.46410i | 0.0778499 | − | 0.134840i | ||||
\(661\) | −17.5000 | + | 30.3109i | −0.680671 | + | 1.17896i | 0.294105 | + | 0.955773i | \(0.404978\pi\) |
−0.974776 | + | 0.223184i | \(0.928355\pi\) | |||||||
\(662\) | 18.0000 | 0.699590 | ||||||||
\(663\) | −5.00000 | + | 5.19615i | −0.194184 | + | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.00000 | − | 3.46410i | 0.0774984 | − | 0.134231i | ||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 24.0000 | 0.928588 | ||||||||
\(669\) | 4.00000 | + | 6.92820i | 0.154649 | + | 0.267860i | ||||
\(670\) | −7.00000 | − | 12.1244i | −0.270434 | − | 0.468405i | ||||
\(671\) | −26.0000 | −1.00372 | ||||||||
\(672\) | 20.0000 | + | 34.6410i | 0.771517 | + | 1.33631i | ||||
\(673\) | −16.5000 | + | 28.5788i | −0.636028 | + | 1.10163i | 0.350268 | + | 0.936650i | \(0.386091\pi\) |
−0.986296 | + | 0.164984i | \(0.947243\pi\) | |||||||
\(674\) | 1.00000 | − | 1.73205i | 0.0385186 | − | 0.0667161i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −22.0000 | + | 13.8564i | −0.846154 | + | 0.532939i | ||||
\(677\) | −12.0000 | −0.461197 | −0.230599 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230599 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(678\) | 2.00000 | − | 3.46410i | 0.0768095 | − | 0.133038i | ||||
\(679\) | 12.5000 | − | 21.6506i | 0.479706 | − | 0.830875i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | 0.383201 | ||||||||
\(682\) | 14.0000 | + | 24.2487i | 0.536088 | + | 0.928531i | ||||
\(683\) | 10.0000 | + | 17.3205i | 0.382639 | + | 0.662751i | 0.991439 | − | 0.130573i | \(-0.0416818\pi\) |
−0.608799 | + | 0.793324i | \(0.708349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00000 | − | 1.73205i | −0.0382080 | − | 0.0661783i | ||||
\(686\) | −55.0000 | + | 95.2628i | −2.09991 | + | 3.63715i | ||||
\(687\) | −7.00000 | + | 12.1244i | −0.267067 | + | 0.462573i | ||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 10.0000 | − | 10.3923i | 0.380970 | − | 0.395915i | ||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | −18.5000 | + | 32.0429i | −0.703773 | + | 1.21897i | 0.263359 | + | 0.964698i | \(0.415170\pi\) |
−0.967132 | + | 0.254273i | \(0.918164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.00000 | − | 8.66025i | −0.189934 | − | 0.328976i | ||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | −1.50000 | − | 2.59808i | −0.0568982 | − | 0.0985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | 0.454532 | ||||||||
\(698\) | −3.00000 | − | 5.19615i | −0.113552 | − | 0.196677i | ||||
\(699\) | 7.00000 | − | 12.1244i | 0.264764 | − | 0.458585i | ||||
\(700\) | −5.00000 | + | 8.66025i | −0.188982 | + | 0.327327i | ||||
\(701\) | 40.0000 | 1.51078 | 0.755390 | − | 0.655276i | \(-0.227448\pi\) | ||||
0.755390 | + | 0.655276i | \(0.227448\pi\) | |||||||
\(702\) | −2.00000 | − | 6.92820i | −0.0754851 | − | 0.261488i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 8.00000 | − | 13.8564i | 0.301511 | − | 0.522233i | ||||
\(705\) | −4.00000 | + | 6.92820i | −0.150649 | + | 0.260931i | ||||
\(706\) | −6.00000 | − | 10.3923i | −0.225813 | − | 0.391120i | ||||
\(707\) | −90.0000 | −3.38480 | ||||||||
\(708\) | −12.0000 | − | 20.7846i | −0.450988 | − | 0.781133i | ||||
\(709\) | 11.5000 | + | 19.9186i | 0.431892 | + | 0.748058i | 0.997036 | − | 0.0769337i | \(-0.0245130\pi\) |
−0.565145 | + | 0.824992i | \(0.691180\pi\) | |||||||
\(710\) | −24.0000 | −0.900704 | ||||||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0000 | − | 36.3731i | 0.786456 | − | 1.36218i | ||||
\(714\) | 20.0000 | 0.748481 | ||||||||
\(715\) | 2.00000 | + | 6.92820i | 0.0747958 | + | 0.259100i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −6.00000 | + | 10.3923i | −0.224074 | + | 0.388108i | ||||
\(718\) | −2.00000 | + | 3.46410i | −0.0746393 | + | 0.129279i | ||||
\(719\) | −20.0000 | − | 34.6410i | −0.745874 | − | 1.29189i | −0.949785 | − | 0.312903i | \(-0.898699\pi\) |
0.203911 | − | 0.978989i | \(-0.434635\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | 17.5000 | + | 30.3109i | 0.651734 | + | 1.12884i | ||||
\(722\) | 19.0000 | + | 32.9090i | 0.707107 | + | 1.22474i | ||||
\(723\) | 10.0000 | 0.371904 | ||||||||
\(724\) | 22.0000 | + | 38.1051i | 0.817624 | + | 1.41617i | ||||
\(725\) | 2.00000 | − | 3.46410i | 0.0742781 | − | 0.128654i | ||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | 9.00000 | 0.333792 | 0.166896 | − | 0.985975i | \(-0.446626\pi\) | ||||
0.166896 | + | 0.985975i | \(0.446626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.0000 | − | 25.9808i | 0.555175 | − | 0.961591i | ||||
\(731\) | −1.00000 | + | 1.73205i | −0.0369863 | + | 0.0640622i | ||||
\(732\) | 13.0000 | + | 22.5167i | 0.480494 | + | 0.832240i | ||||
\(733\) | 7.00000 | 0.258551 | 0.129275 | − | 0.991609i | \(-0.458735\pi\) | ||||
0.129275 | + | 0.991609i | \(0.458735\pi\) | |||||||
\(734\) | −7.00000 | − | 12.1244i | −0.258375 | − | 0.447518i | ||||
\(735\) | 9.00000 | + | 15.5885i | 0.331970 | + | 0.574989i | ||||
\(736\) | −48.0000 | −1.76930 | ||||||||
\(737\) | 7.00000 | + | 12.1244i | 0.257848 | + | 0.446606i | ||||
\(738\) | −6.00000 | + | 10.3923i | −0.220863 | + | 0.382546i | ||||
\(739\) | 18.0000 | − | 31.1769i | 0.662141 | − | 1.14686i | −0.317911 | − | 0.948120i | \(-0.602981\pi\) |
0.980052 | − | 0.198741i | \(-0.0636852\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −40.0000 | −1.46845 | ||||||||
\(743\) | −12.0000 | + | 20.7846i | −0.440237 | + | 0.762513i | −0.997707 | − | 0.0676840i | \(-0.978439\pi\) |
0.557470 | + | 0.830197i | \(0.311772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | −4.00000 | − | 6.92820i | −0.146352 | − | 0.253490i | ||||
\(748\) | −4.00000 | − | 6.92820i | −0.146254 | − | 0.253320i | ||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 1.00000 | + | 1.73205i | 0.0365148 | + | 0.0632456i | ||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | −16.0000 | + | 27.7128i | −0.583460 | + | 1.01058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.0000 | − | 6.92820i | −1.01970 | − | 0.252310i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | −5.00000 | + | 8.66025i | −0.181848 | + | 0.314970i | ||||
\(757\) | −1.00000 | + | 1.73205i | −0.0363456 | + | 0.0629525i | −0.883626 | − | 0.468193i | \(-0.844905\pi\) |
0.847280 | + | 0.531146i | \(0.178238\pi\) | |||||||
\(758\) | 5.00000 | + | 8.66025i | 0.181608 | + | 0.314555i | ||||
\(759\) | 12.0000 | 0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | + | 31.1769i | 0.652499 | + | 1.13016i | 0.982514 | + | 0.186187i | \(0.0596129\pi\) |
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(762\) | −22.0000 | −0.796976 | ||||||||
\(763\) | 27.5000 | + | 47.6314i | 0.995567 | + | 1.72437i | ||||
\(764\) | −12.0000 | + | 20.7846i | −0.434145 | + | 0.751961i | ||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 42.0000 | + | 10.3923i | 1.51653 | + | 0.375244i | ||||
\(768\) | 16.0000 | 0.577350 | ||||||||
\(769\) | 17.0000 | − | 29.4449i | 0.613036 | − | 1.06181i | −0.377690 | − | 0.925932i | \(-0.623282\pi\) |
0.990726 | − | 0.135877i | \(-0.0433852\pi\) | |||||||
\(770\) | 10.0000 | − | 17.3205i | 0.360375 | − | 0.624188i | ||||
\(771\) | 11.0000 | + | 19.0526i | 0.396155 | + | 0.686161i | ||||
\(772\) | −22.0000 | −0.791797 | ||||||||
\(773\) | −23.0000 | − | 39.8372i | −0.827253 | − | 1.43284i | −0.900186 | − | 0.435507i | \(-0.856569\pi\) |
0.0729331 | − | 0.997337i | \(-0.476764\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | −7.00000 | −0.251447 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00000 | − | 8.66025i | 0.179374 | − | 0.310685i | ||||
\(778\) | −8.00000 | + | 13.8564i | −0.286814 | + | 0.496776i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 5.00000 | − | 5.19615i | 0.179029 | − | 0.186052i | ||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | −12.0000 | + | 20.7846i | −0.429119 | + | 0.743256i | ||||
\(783\) | 2.00000 | − | 3.46410i | 0.0714742 | − | 0.123797i | ||||
\(784\) | 36.0000 | + | 62.3538i | 1.28571 | + | 2.22692i | ||||
\(785\) | 15.0000 | 0.535373 | ||||||||
\(786\) | 4.00000 | + | 6.92820i | 0.142675 | + | 0.247121i | ||||
\(787\) | −8.50000 | − | 14.7224i | −0.302992 | − | 0.524798i | 0.673820 | − | 0.738896i | \(-0.264652\pi\) |
−0.976812 | + | 0.214097i | \(0.931319\pi\) | |||||||
\(788\) | −24.0000 | −0.854965 | ||||||||
\(789\) | 5.00000 | + | 8.66025i | 0.178005 | + | 0.308313i | ||||
\(790\) | 3.00000 | − | 5.19615i | 0.106735 | − | 0.184871i | ||||
\(791\) | 5.00000 | − | 8.66025i | 0.177780 | − | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.5000 | − | 11.2583i | −1.61575 | − | 0.399795i | ||||
\(794\) | −30.0000 | −1.06466 | ||||||||
\(795\) | −2.00000 | + | 3.46410i | −0.0709327 | + | 0.122859i | ||||
\(796\) | −17.0000 | + | 29.4449i | −0.602549 | + | 1.04365i | ||||
\(797\) | −15.0000 | − | 25.9808i | −0.531327 | − | 0.920286i | −0.999331 | − | 0.0365596i | \(-0.988360\pi\) |
0.468004 | − | 0.883726i | \(-0.344973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | + | 13.8564i | 0.283020 | + | 0.490204i | ||||
\(800\) | 4.00000 | + | 6.92820i | 0.141421 | + | 0.244949i | ||||
\(801\) | 14.0000 | 0.494666 | ||||||||
\(802\) | −16.0000 | − | 27.7128i | −0.564980 | − | 0.978573i | ||||
\(803\) | −15.0000 | + | 25.9808i | −0.529339 | + | 0.916841i | ||||
\(804\) | 7.00000 | − | 12.1244i | 0.246871 | − | 0.427593i | ||||
\(805\) | −30.0000 | −1.05736 | ||||||||
\(806\) | 14.0000 | + | 48.4974i | 0.493129 | + | 1.70825i | ||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.00000 | + | 3.46410i | −0.0703163 | + | 0.121791i | −0.899040 | − | 0.437867i | \(-0.855734\pi\) |
0.828724 | + | 0.559658i | \(0.189068\pi\) | |||||||
\(810\) | 1.00000 | + | 1.73205i | 0.0351364 | + | 0.0608581i | ||||
\(811\) | 45.0000 | 1.58016 | 0.790082 | − | 0.613001i | \(-0.210038\pi\) | ||||
0.790082 | + | 0.613001i | \(0.210038\pi\) | |||||||
\(812\) | 20.0000 | + | 34.6410i | 0.701862 | + | 1.21566i | ||||
\(813\) | −14.5000 | − | 25.1147i | −0.508537 | − | 0.880812i | ||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | −7.50000 | − | 12.9904i | −0.262714 | − | 0.455033i | ||||
\(816\) | 4.00000 | − | 6.92820i | 0.140028 | − | 0.242536i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −30.0000 | −1.04893 | ||||||||
\(819\) | −5.00000 | − | 17.3205i | −0.174714 | − | 0.605228i | ||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | 11.0000 | − | 19.0526i | 0.383903 | − | 0.664939i | −0.607714 | − | 0.794156i | \(-0.707913\pi\) |
0.991616 | + | 0.129217i | \(0.0412465\pi\) | |||||||
\(822\) | 2.00000 | − | 3.46410i | 0.0697580 | − | 0.120824i | ||||
\(823\) | −10.0000 | − | 17.3205i | −0.348578 | − | 0.603755i | 0.637419 | − | 0.770517i | \(-0.280002\pi\) |
−0.985997 | + | 0.166762i | \(0.946669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00000 | − | 1.73205i | −0.0348155 | − | 0.0603023i | ||||
\(826\) | −60.0000 | − | 103.923i | −2.08767 | − | 3.61595i | ||||
\(827\) | 46.0000 | 1.59958 | 0.799788 | − | 0.600282i | \(-0.204945\pi\) | ||||
0.799788 | + | 0.600282i | \(0.204945\pi\) | |||||||
\(828\) | −6.00000 | − | 10.3923i | −0.208514 | − | 0.361158i | ||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 8.00000 | − | 13.8564i | 0.277684 | − | 0.480963i | ||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | 20.0000 | − | 20.7846i | 0.693375 | − | 0.720577i | ||||
\(833\) | 36.0000 | 1.24733 | ||||||||
\(834\) | 3.00000 | − | 5.19615i | 0.103882 | − | 0.179928i | ||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.00000 | −0.241955 | ||||||||
\(838\) | −38.0000 | − | 65.8179i | −1.31269 | − | 2.27364i | ||||
\(839\) | 17.0000 | + | 29.4449i | 0.586905 | + | 1.01655i | 0.994635 | + | 0.103447i | \(0.0329872\pi\) |
−0.407730 | + | 0.913103i | \(0.633679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 23.0000 | − | 39.8372i | 0.792632 | − | 1.37288i | ||||
\(843\) | 6.00000 | − | 10.3923i | 0.206651 | − | 0.357930i | ||||
\(844\) | 30.0000 | 1.03264 | ||||||||
\(845\) | 0.500000 | + | 12.9904i | 0.0172005 | + | 0.446883i | ||||
\(846\) | −16.0000 | −0.550091 | ||||||||
\(847\) | 17.5000 | − | 30.3109i | 0.601307 | − | 1.04149i | ||||
\(848\) | −8.00000 | + | 13.8564i | −0.274721 | + | 0.475831i | ||||
\(849\) | −2.50000 | − | 4.33013i | −0.0857998 | − | 0.148610i | ||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −12.0000 | − | 20.7846i | −0.411113 | − | 0.712069i | ||||
\(853\) | 9.00000 | 0.308154 | 0.154077 | − | 0.988059i | \(-0.450760\pi\) | ||||
0.154077 | + | 0.988059i | \(0.450760\pi\) | |||||||
\(854\) | 65.0000 | + | 112.583i | 2.22425 | + | 3.85252i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0000 | −0.409912 | −0.204956 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204956 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(858\) | −10.0000 | + | 10.3923i | −0.341394 | + | 0.354787i | ||||
\(859\) | 43.0000 | 1.46714 | 0.733571 | − | 0.679613i | \(-0.237852\pi\) | ||||
0.733571 | + | 0.679613i | \(0.237852\pi\) | |||||||
\(860\) | 1.00000 | − | 1.73205i | 0.0340997 | − | 0.0590624i | ||||
\(861\) | −15.0000 | + | 25.9808i | −0.511199 | + | 0.885422i | ||||
\(862\) | 28.0000 | + | 48.4974i | 0.953684 | + | 1.65183i | ||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 4.00000 | + | 6.92820i | 0.136083 | + | 0.235702i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | 6.50000 | + | 11.2583i | 0.220752 | + | 0.382353i | ||||
\(868\) | 35.0000 | − | 60.6218i | 1.18798 | − | 2.05764i | ||||
\(869\) | −3.00000 | + | 5.19615i | −0.101768 | + | 0.176267i | ||||
\(870\) | 8.00000 | 0.271225 | ||||||||
\(871\) | 7.00000 | + | 24.2487i | 0.237186 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.50000 | − | 4.33013i | 0.0846122 | − | 0.146553i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.50000 | + | 4.33013i | 0.0845154 | + | 0.146385i | ||||
\(876\) | 30.0000 | 1.01361 | ||||||||
\(877\) | −3.00000 | − | 5.19615i | −0.101303 | − | 0.175462i | 0.810919 | − | 0.585159i | \(-0.198968\pi\) |
−0.912222 | + | 0.409697i | \(0.865634\pi\) | |||||||
\(878\) | −15.0000 | − | 25.9808i | −0.506225 | − | 0.876808i | ||||
\(879\) | 16.0000 | 0.539667 | ||||||||
\(880\) | −4.00000 | − | 6.92820i | −0.134840 | − | 0.233550i | ||||
\(881\) | −10.0000 | + | 17.3205i | −0.336909 | + | 0.583543i | −0.983850 | − | 0.178997i | \(-0.942715\pi\) |
0.646941 | + | 0.762540i | \(0.276048\pi\) | |||||||
\(882\) | −18.0000 | + | 31.1769i | −0.606092 | + | 1.04978i | ||||
\(883\) | −25.0000 | −0.841317 | −0.420658 | − | 0.907219i | \(-0.638201\pi\) | ||||
−0.420658 | + | 0.907219i | \(0.638201\pi\) | |||||||
\(884\) | −4.00000 | − | 13.8564i | −0.134535 | − | 0.466041i | ||||
\(885\) | −12.0000 | −0.403376 | ||||||||
\(886\) | −26.0000 | + | 45.0333i | −0.873487 | + | 1.51292i | ||||
\(887\) | 22.0000 | − | 38.1051i | 0.738688 | − | 1.27944i | −0.214399 | − | 0.976746i | \(-0.568779\pi\) |
0.953086 | − | 0.302698i | \(-0.0978875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55.0000 | −1.84464 | ||||||||
\(890\) | 14.0000 | + | 24.2487i | 0.469281 | + | 0.812819i | ||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 12.0000 | − | 20.7846i | 0.401340 | − | 0.695141i | ||||
\(895\) | −3.00000 | + | 5.19615i | −0.100279 | + | 0.173688i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.0000 | + | 5.19615i | 0.701170 | + | 0.173494i | ||||
\(898\) | 36.0000 | 1.20134 | ||||||||
\(899\) | −14.0000 | + | 24.2487i | −0.466926 | + | 0.808740i | ||||
\(900\) | −1.00000 | + | 1.73205i | −0.0333333 | + | 0.0577350i | ||||
\(901\) | 4.00000 | + | 6.92820i | 0.133259 | + | 0.230812i | ||||
\(902\) | 24.0000 | 0.799113 | ||||||||
\(903\) | −2.50000 | − | 4.33013i | −0.0831948 | − | 0.144098i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0000 | 0.731305 | ||||||||
\(906\) | 8.00000 | + | 13.8564i | 0.265782 | + | 0.460348i | ||||
\(907\) | −10.0000 | + | 17.3205i | −0.332045 | + | 0.575118i | −0.982913 | − | 0.184073i | \(-0.941072\pi\) |
0.650868 | + | 0.759191i | \(0.274405\pi\) | |||||||
\(908\) | −10.0000 | + | 17.3205i | −0.331862 | + | 0.574801i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 25.0000 | − | 25.9808i | 0.828742 | − | 0.861254i | ||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | −35.0000 | − | 60.6218i | −1.15770 | − | 2.00519i | ||||
\(915\) | 13.0000 | 0.429767 | ||||||||
\(916\) | −14.0000 | − | 24.2487i | −0.462573 | − | 0.801200i | ||||
\(917\) | 10.0000 | + | 17.3205i | 0.330229 | + | 0.571974i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −4.00000 | − | 6.92820i | −0.131948 | − | 0.228540i | 0.792480 | − | 0.609898i | \(-0.208790\pi\) |
−0.924427 | + | 0.381358i | \(0.875456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.5000 | − | 26.8468i | 0.510742 | − | 0.884632i | ||||
\(922\) | −4.00000 | −0.131733 | ||||||||
\(923\) | 42.0000 | + | 10.3923i | 1.38245 | + | 0.342067i | ||||
\(924\) | 20.0000 | 0.657952 | ||||||||
\(925\) | 1.00000 | − | 1.73205i | 0.0328798 | − | 0.0569495i | ||||
\(926\) | −3.00000 | + | 5.19615i | −0.0985861 | + | 0.170756i | ||||
\(927\) | 3.50000 | + | 6.06218i | 0.114955 | + | 0.199108i | ||||
\(928\) | 32.0000 | 1.05045 | ||||||||
\(929\) | −26.0000 | − | 45.0333i | −0.853032 | − | 1.47750i | −0.878459 | − | 0.477819i | \(-0.841428\pi\) |
0.0254262 | − | 0.999677i | \(-0.491906\pi\) | |||||||
\(930\) | −7.00000 | − | 12.1244i | −0.229539 | − | 0.397573i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.0000 | + | 24.2487i | 0.458585 | + | 0.794293i | ||||
\(933\) | 11.0000 | − | 19.0526i | 0.360124 | − | 0.623753i | ||||
\(934\) | 4.00000 | − | 6.92820i | 0.130884 | − | 0.226698i | ||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 35.0000 | − | 60.6218i | 1.14279 | − | 1.97937i | ||||
\(939\) | 15.5000 | − | 26.8468i | 0.505823 | − | 0.876112i | ||||
\(940\) | −8.00000 | − | 13.8564i | −0.260931 | − | 0.451946i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 15.0000 | + | 25.9808i | 0.488726 | + | 0.846499i | ||||
\(943\) | −18.0000 | − | 31.1769i | −0.586161 | − | 1.01526i | ||||
\(944\) | −48.0000 | −1.56227 | ||||||||
\(945\) | 2.50000 | + | 4.33013i | 0.0813250 | + | 0.140859i | ||||
\(946\) | −2.00000 | + | 3.46410i | −0.0650256 | + | 0.112628i | ||||
\(947\) | −9.00000 | + | 15.5885i | −0.292461 | + | 0.506557i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) |
0.681930 | + | 0.731417i | \(0.261141\pi\) | |||||||
\(948\) | 6.00000 | 0.194871 | ||||||||
\(949\) | −37.5000 | + | 38.9711i | −1.21730 | + | 1.26506i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | + | 10.3923i | −0.194563 | + | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | \(-0.197649\pi\) |
−0.910516 | + | 0.413473i | \(0.864315\pi\) | |||||||
\(954\) | −8.00000 | −0.259010 | ||||||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | −42.0000 | − | 72.7461i | −1.35696 | − | 2.35032i | ||||
\(959\) | 5.00000 | − | 8.66025i | 0.161458 | − | 0.279654i | ||||
\(960\) | −4.00000 | + | 6.92820i | −0.129099 | + | 0.223607i | ||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | −14.0000 | − | 3.46410i | −0.451378 | − | 0.111687i | ||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | −10.0000 | + | 17.3205i | −0.322078 | + | 0.557856i | ||||
\(965\) | −5.50000 | + | 9.52628i | −0.177051 | + | 0.306662i | ||||
\(966\) | −30.0000 | − | 51.9615i | −0.965234 | − | 1.67183i | ||||
\(967\) | −56.0000 | −1.80084 | −0.900419 | − | 0.435023i | \(-0.856740\pi\) | ||||
−0.900419 | + | 0.435023i | \(0.856740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | −10.0000 | − | 17.3205i | −0.320915 | − | 0.555842i | 0.659762 | − | 0.751475i | \(-0.270657\pi\) |
−0.980677 | + | 0.195633i | \(0.937324\pi\) | |||||||
\(972\) | −1.00000 | + | 1.73205i | −0.0320750 | + | 0.0555556i | ||||
\(973\) | 7.50000 | − | 12.9904i | 0.240439 | − | 0.416452i | ||||
\(974\) | −56.0000 | −1.79436 | ||||||||
\(975\) | −1.00000 | − | 3.46410i | −0.0320256 | − | 0.110940i | ||||
\(976\) | 52.0000 | 1.66448 | ||||||||
\(977\) | −30.0000 | + | 51.9615i | −0.959785 | + | 1.66240i | −0.236768 | + | 0.971566i | \(0.576088\pi\) |
−0.723017 | + | 0.690830i | \(0.757245\pi\) | |||||||
\(978\) | 15.0000 | − | 25.9808i | 0.479647 | − | 0.830773i | ||||
\(979\) | −14.0000 | − | 24.2487i | −0.447442 | − | 0.774992i | ||||
\(980\) | −36.0000 | −1.14998 | ||||||||
\(981\) | 5.50000 | + | 9.52628i | 0.175601 | + | 0.304151i | ||||
\(982\) | 24.0000 | + | 41.5692i | 0.765871 | + | 1.32653i | ||||
\(983\) | 38.0000 | 1.21201 | 0.606006 | − | 0.795460i | \(-0.292771\pi\) | ||||
0.606006 | + | 0.795460i | \(0.292771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 8.00000 | − | 13.8564i | 0.254772 | − | 0.441278i | ||||
\(987\) | −40.0000 | −1.27321 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 2.00000 | − | 3.46410i | 0.0635642 | − | 0.110096i | ||||
\(991\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(992\) | −28.0000 | − | 48.4974i | −0.889001 | − | 1.53979i | ||||
\(993\) | 9.00000 | 0.285606 | ||||||||
\(994\) | −60.0000 | − | 103.923i | −1.90308 | − | 3.29624i | ||||
\(995\) | 8.50000 | + | 14.7224i | 0.269468 | + | 0.466732i | ||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | −14.5000 | − | 25.1147i | −0.459220 | − | 0.795392i | 0.539700 | − | 0.841857i | \(-0.318538\pi\) |
−0.998920 | + | 0.0464655i | \(0.985204\pi\) | |||||||
\(998\) | −4.00000 | + | 6.92820i | −0.126618 | + | 0.219308i | ||||
\(999\) | 1.00000 | − | 1.73205i | 0.0316386 | − | 0.0547997i |
(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 | 195.2.i.a.61.1 | yes | 2 | |
3.2 | odd | 2 | 585.2.j.b.451.1 | 2 | |||
5.2 | odd | 4 | 975.2.bb.f.724.1 | 4 | |||
5.3 | odd | 4 | 975.2.bb.f.724.2 | 4 | |||
5.4 | even | 2 | 975.2.i.i.451.1 | 2 | |||
13.3 | even | 3 | inner | 195.2.i.a.16.1 | ✓ | 2 | |
13.4 | even | 6 | 2535.2.a.c.1.1 | 1 | |||
13.9 | even | 3 | 2535.2.a.m.1.1 | 1 | |||
39.17 | odd | 6 | 7605.2.a.s.1.1 | 1 | |||
39.29 | odd | 6 | 585.2.j.b.406.1 | 2 | |||
39.35 | odd | 6 | 7605.2.a.a.1.1 | 1 | |||
65.3 | odd | 12 | 975.2.bb.f.874.1 | 4 | |||
65.29 | even | 6 | 975.2.i.i.601.1 | 2 | |||
65.42 | odd | 12 | 975.2.bb.f.874.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.a.16.1 | ✓ | 2 | 13.3 | even | 3 | inner | |
195.2.i.a.61.1 | yes | 2 | 1.1 | even | 1 | trivial | |
585.2.j.b.406.1 | 2 | 39.29 | odd | 6 | |||
585.2.j.b.451.1 | 2 | 3.2 | odd | 2 | |||
975.2.i.i.451.1 | 2 | 5.4 | even | 2 | |||
975.2.i.i.601.1 | 2 | 65.29 | even | 6 | |||
975.2.bb.f.724.1 | 4 | 5.2 | odd | 4 | |||
975.2.bb.f.724.2 | 4 | 5.3 | odd | 4 | |||
975.2.bb.f.874.1 | 4 | 65.3 | odd | 12 | |||
975.2.bb.f.874.2 | 4 | 65.42 | odd | 12 | |||
2535.2.a.c.1.1 | 1 | 13.4 | even | 6 | |||
2535.2.a.m.1.1 | 1 | 13.9 | even | 3 | |||
7605.2.a.a.1.1 | 1 | 39.35 | odd | 6 | |||
7605.2.a.s.1.1 | 1 | 39.17 | odd | 6 |