Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.6 | ||
Root | \(-1.40171i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.f.694.15 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.40171i | − | 0.991157i | −0.868563 | − | 0.495579i | \(-0.834956\pi\) | ||
0.868563 | − | 0.495579i | \(-0.165044\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.0352144 | 0.0176072 | ||||||||
\(5\) | −2.22487 | + | 0.223473i | −0.994993 | + | 0.0999401i | ||||
\(6\) | 1.40171 | 0.572245 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 2.85278i | − | 1.00861i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.313244 | + | 3.11862i | 0.0990563 | + | 0.986195i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.0352144i | 0.0101655i | ||||||||
\(13\) | 1.11469i | 0.309159i | 0.987980 | + | 0.154579i | \(0.0494022\pi\) | ||||
−0.987980 | + | 0.154579i | \(0.950598\pi\) | |||||||
\(14\) | 1.40171 | 0.374622 | ||||||||
\(15\) | −0.223473 | − | 2.22487i | −0.0577004 | − | 0.574460i | ||||
\(16\) | −3.92833 | −0.982083 | ||||||||
\(17\) | 3.90149i | 0.946251i | 0.880995 | + | 0.473126i | \(0.156874\pi\) | ||||
−0.880995 | + | 0.473126i | \(0.843126\pi\) | |||||||
\(18\) | 1.40171i | 0.330386i | ||||||||
\(19\) | 6.16229 | 1.41373 | 0.706863 | − | 0.707351i | \(-0.250110\pi\) | ||||
0.706863 | + | 0.707351i | \(0.250110\pi\) | |||||||
\(20\) | −0.0783475 | + | 0.00786945i | −0.0175190 | + | 0.00175966i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 1.40171i | − | 0.298845i | ||||||
\(23\) | 5.20203i | 1.08470i | 0.840153 | + | 0.542349i | \(0.182465\pi\) | ||||
−0.840153 | + | 0.542349i | \(0.817535\pi\) | |||||||
\(24\) | 2.85278 | 0.582321 | ||||||||
\(25\) | 4.90012 | − | 0.994397i | 0.980024 | − | 0.198879i | ||||
\(26\) | 1.56247 | 0.306425 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.0352144i | 0.00665489i | ||||||||
\(29\) | −8.42741 | −1.56493 | −0.782465 | − | 0.622695i | \(-0.786038\pi\) | ||||
−0.782465 | + | 0.622695i | \(0.786038\pi\) | |||||||
\(30\) | −3.11862 | + | 0.313244i | −0.569380 | + | 0.0571902i | ||||
\(31\) | 8.95281 | 1.60797 | 0.803986 | − | 0.594648i | \(-0.202709\pi\) | ||||
0.803986 | + | 0.594648i | \(0.202709\pi\) | |||||||
\(32\) | − | 0.199179i | − | 0.0352103i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 5.46876 | 0.937884 | ||||||||
\(35\) | −0.223473 | − | 2.22487i | −0.0377738 | − | 0.376072i | ||||
\(36\) | −0.0352144 | −0.00586906 | ||||||||
\(37\) | 0.540909i | 0.0889250i | 0.999011 | + | 0.0444625i | \(0.0141575\pi\) | ||||
−0.999011 | + | 0.0444625i | \(0.985842\pi\) | |||||||
\(38\) | − | 8.63773i | − | 1.40122i | ||||||
\(39\) | −1.11469 | −0.178493 | ||||||||
\(40\) | 0.637518 | + | 6.34707i | 0.100800 | + | 1.00356i | ||||
\(41\) | 3.36720 | 0.525869 | 0.262934 | − | 0.964814i | \(-0.415310\pi\) | ||||
0.262934 | + | 0.964814i | \(0.415310\pi\) | |||||||
\(42\) | 1.40171i | 0.216288i | ||||||||
\(43\) | 9.48334i | 1.44620i | 0.690746 | + | 0.723098i | \(0.257282\pi\) | ||||
−0.690746 | + | 0.723098i | \(0.742718\pi\) | |||||||
\(44\) | 0.0352144 | 0.00530877 | ||||||||
\(45\) | 2.22487 | − | 0.223473i | 0.331664 | − | 0.0333134i | ||||
\(46\) | 7.29173 | 1.07511 | ||||||||
\(47\) | 3.04186i | 0.443700i | 0.975081 | + | 0.221850i | \(0.0712096\pi\) | ||||
−0.975081 | + | 0.221850i | \(0.928790\pi\) | |||||||
\(48\) | − | 3.92833i | − | 0.567006i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.39385 | − | 6.86854i | −0.197121 | − | 0.971358i | ||||
\(51\) | −3.90149 | −0.546318 | ||||||||
\(52\) | 0.0392530i | 0.00544341i | ||||||||
\(53\) | 2.86404i | 0.393406i | 0.980463 | + | 0.196703i | \(0.0630234\pi\) | ||||
−0.980463 | + | 0.196703i | \(0.936977\pi\) | |||||||
\(54\) | −1.40171 | −0.190748 | ||||||||
\(55\) | −2.22487 | + | 0.223473i | −0.300002 | + | 0.0301331i | ||||
\(56\) | 2.85278 | 0.381218 | ||||||||
\(57\) | 6.16229i | 0.816215i | ||||||||
\(58\) | 11.8128i | 1.55109i | ||||||||
\(59\) | 11.5606 | 1.50506 | 0.752532 | − | 0.658556i | \(-0.228832\pi\) | ||||
0.752532 | + | 0.658556i | \(0.228832\pi\) | |||||||
\(60\) | −0.00786945 | − | 0.0783475i | −0.00101594 | − | 0.0101146i | ||||
\(61\) | 10.3786 | 1.32884 | 0.664420 | − | 0.747360i | \(-0.268679\pi\) | ||||
0.664420 | + | 0.747360i | \(0.268679\pi\) | |||||||
\(62\) | − | 12.5492i | − | 1.59375i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −8.13585 | −1.01698 | ||||||||
\(65\) | −0.249102 | − | 2.48004i | −0.0308973 | − | 0.307611i | ||||
\(66\) | 1.40171 | 0.172538 | ||||||||
\(67\) | 5.35976i | 0.654799i | 0.944886 | + | 0.327399i | \(0.106172\pi\) | ||||
−0.944886 | + | 0.327399i | \(0.893828\pi\) | |||||||
\(68\) | 0.137389i | 0.0166608i | ||||||||
\(69\) | −5.20203 | −0.626251 | ||||||||
\(70\) | −3.11862 | + | 0.313244i | −0.372747 | + | 0.0374398i | ||||
\(71\) | 11.2413 | 1.33409 | 0.667047 | − | 0.745016i | \(-0.267558\pi\) | ||||
0.667047 | + | 0.745016i | \(0.267558\pi\) | |||||||
\(72\) | 2.85278i | 0.336203i | ||||||||
\(73\) | − | 0.333198i | − | 0.0389979i | −0.999810 | − | 0.0194989i | \(-0.993793\pi\) | ||
0.999810 | − | 0.0194989i | \(-0.00620710\pi\) | |||||||
\(74\) | 0.758197 | 0.0881386 | ||||||||
\(75\) | 0.994397 | + | 4.90012i | 0.114823 | + | 0.565817i | ||||
\(76\) | 0.217001 | 0.0248917 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 1.56247i | 0.176914i | ||||||||
\(79\) | −0.575756 | −0.0647776 | −0.0323888 | − | 0.999475i | \(-0.510311\pi\) | ||||
−0.0323888 | + | 0.999475i | \(0.510311\pi\) | |||||||
\(80\) | 8.74004 | − | 0.877875i | 0.977166 | − | 0.0981494i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 4.71984i | − | 0.521219i | ||||||
\(83\) | − | 0.318582i | − | 0.0349689i | −0.999847 | − | 0.0174844i | \(-0.994434\pi\) | ||
0.999847 | − | 0.0174844i | \(-0.00556575\pi\) | |||||||
\(84\) | −0.0352144 | −0.00384220 | ||||||||
\(85\) | −0.871878 | − | 8.68033i | −0.0945684 | − | 0.941514i | ||||
\(86\) | 13.2929 | 1.43341 | ||||||||
\(87\) | − | 8.42741i | − | 0.903513i | ||||||
\(88\) | − | 2.85278i | − | 0.304107i | ||||||
\(89\) | −6.02585 | −0.638739 | −0.319369 | − | 0.947630i | \(-0.603471\pi\) | ||||
−0.319369 | + | 0.947630i | \(0.603471\pi\) | |||||||
\(90\) | −0.313244 | − | 3.11862i | −0.0330188 | − | 0.328732i | ||||
\(91\) | −1.11469 | −0.116851 | ||||||||
\(92\) | 0.183186i | 0.0190985i | ||||||||
\(93\) | 8.95281i | 0.928363i | ||||||||
\(94\) | 4.26379 | 0.439777 | ||||||||
\(95\) | −13.7103 | + | 1.37710i | −1.40665 | + | 0.141288i | ||||
\(96\) | 0.199179 | 0.0203287 | ||||||||
\(97\) | 0.903942i | 0.0917814i | 0.998946 | + | 0.0458907i | \(0.0146126\pi\) | ||||
−0.998946 | + | 0.0458907i | \(0.985387\pi\) | |||||||
\(98\) | 1.40171i | 0.141594i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0.172555 | − | 0.0350171i | 0.0172555 | − | 0.00350171i | ||||
\(101\) | −0.151109 | −0.0150359 | −0.00751797 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751797 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(102\) | 5.46876i | 0.541487i | ||||||||
\(103\) | 16.1396i | 1.59028i | 0.606426 | + | 0.795140i | \(0.292603\pi\) | ||||
−0.606426 | + | 0.795140i | \(0.707397\pi\) | |||||||
\(104\) | 3.17995 | 0.311820 | ||||||||
\(105\) | 2.22487 | − | 0.223473i | 0.217125 | − | 0.0218087i | ||||
\(106\) | 4.01454 | 0.389927 | ||||||||
\(107\) | − | 7.81577i | − | 0.755579i | −0.925891 | − | 0.377790i | \(-0.876684\pi\) | ||
0.925891 | − | 0.377790i | \(-0.123316\pi\) | |||||||
\(108\) | − | 0.0352144i | − | 0.00338850i | ||||||
\(109\) | −18.2292 | −1.74604 | −0.873018 | − | 0.487687i | \(-0.837841\pi\) | ||||
−0.873018 | + | 0.487687i | \(0.837841\pi\) | |||||||
\(110\) | 0.313244 | + | 3.11862i | 0.0298666 | + | 0.297349i | ||||
\(111\) | −0.540909 | −0.0513409 | ||||||||
\(112\) | − | 3.92833i | − | 0.371192i | ||||||
\(113\) | − | 2.28487i | − | 0.214942i | −0.994208 | − | 0.107471i | \(-0.965725\pi\) | ||
0.994208 | − | 0.107471i | \(-0.0342753\pi\) | |||||||
\(114\) | 8.63773 | 0.808997 | ||||||||
\(115\) | −1.16251 | − | 11.5739i | −0.108405 | − | 1.07927i | ||||
\(116\) | −0.296766 | −0.0275540 | ||||||||
\(117\) | − | 1.11469i | − | 0.103053i | ||||||
\(118\) | − | 16.2046i | − | 1.49175i | ||||||
\(119\) | −3.90149 | −0.357649 | ||||||||
\(120\) | −6.34707 | + | 0.637518i | −0.579405 | + | 0.0581972i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 14.5477i | − | 1.31709i | ||||||
\(123\) | 3.36720i | 0.303611i | ||||||||
\(124\) | 0.315268 | 0.0283119 | ||||||||
\(125\) | −10.6799 | + | 3.30745i | −0.955241 | + | 0.295827i | ||||
\(126\) | −1.40171 | −0.124874 | ||||||||
\(127\) | − | 5.17876i | − | 0.459541i | −0.973245 | − | 0.229770i | \(-0.926202\pi\) | ||
0.973245 | − | 0.229770i | \(-0.0737975\pi\) | |||||||
\(128\) | 11.0057i | 0.972779i | ||||||||
\(129\) | −9.48334 | −0.834962 | ||||||||
\(130\) | −3.47629 | + | 0.349169i | −0.304891 | + | 0.0306241i | ||||
\(131\) | −9.72484 | −0.849663 | −0.424831 | − | 0.905272i | \(-0.639667\pi\) | ||||
−0.424831 | + | 0.905272i | \(0.639667\pi\) | |||||||
\(132\) | 0.0352144i | 0.00306502i | ||||||||
\(133\) | 6.16229i | 0.534338i | ||||||||
\(134\) | 7.51282 | 0.649009 | ||||||||
\(135\) | 0.223473 | + | 2.22487i | 0.0192335 | + | 0.191487i | ||||
\(136\) | 11.1301 | 0.954397 | ||||||||
\(137\) | − | 10.0185i | − | 0.855939i | −0.903793 | − | 0.427969i | \(-0.859229\pi\) | ||
0.903793 | − | 0.427969i | \(-0.140771\pi\) | |||||||
\(138\) | 7.29173i | 0.620713i | ||||||||
\(139\) | 5.15308 | 0.437079 | 0.218539 | − | 0.975828i | \(-0.429871\pi\) | ||||
0.218539 | + | 0.975828i | \(0.429871\pi\) | |||||||
\(140\) | −0.00786945 | − | 0.0783475i | −0.000665090 | − | 0.00662157i | ||||
\(141\) | −3.04186 | −0.256170 | ||||||||
\(142\) | − | 15.7570i | − | 1.32230i | ||||||
\(143\) | 1.11469i | 0.0932148i | ||||||||
\(144\) | 3.92833 | 0.327361 | ||||||||
\(145\) | 18.7499 | − | 1.88330i | 1.55710 | − | 0.156399i | ||||
\(146\) | −0.467046 | −0.0386530 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0.0190478i | 0.00156572i | ||||||||
\(149\) | 6.59892 | 0.540604 | 0.270302 | − | 0.962776i | \(-0.412876\pi\) | ||||
0.270302 | + | 0.962776i | \(0.412876\pi\) | |||||||
\(150\) | 6.86854 | − | 1.39385i | 0.560814 | − | 0.113808i | ||||
\(151\) | −4.74431 | −0.386086 | −0.193043 | − | 0.981190i | \(-0.561836\pi\) | ||||
−0.193043 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(152\) | − | 17.5796i | − | 1.42590i | ||||||
\(153\) | − | 3.90149i | − | 0.315417i | ||||||
\(154\) | 1.40171 | 0.112953 | ||||||||
\(155\) | −19.9189 | + | 2.00071i | −1.59992 | + | 0.160701i | ||||
\(156\) | −0.0392530 | −0.00314276 | ||||||||
\(157\) | 11.3377i | 0.904847i | 0.891803 | + | 0.452424i | \(0.149441\pi\) | ||||
−0.891803 | + | 0.452424i | \(0.850559\pi\) | |||||||
\(158\) | 0.807042i | 0.0642048i | ||||||||
\(159\) | −2.86404 | −0.227133 | ||||||||
\(160\) | 0.0445112 | + | 0.443149i | 0.00351892 | + | 0.0350340i | ||||
\(161\) | −5.20203 | −0.409977 | ||||||||
\(162\) | − | 1.40171i | − | 0.110129i | ||||||
\(163\) | − | 20.0942i | − | 1.57390i | −0.617017 | − | 0.786950i | \(-0.711659\pi\) | ||
0.617017 | − | 0.786950i | \(-0.288341\pi\) | |||||||
\(164\) | 0.118574 | 0.00925907 | ||||||||
\(165\) | −0.223473 | − | 2.22487i | −0.0173973 | − | 0.173206i | ||||
\(166\) | −0.446558 | −0.0346597 | ||||||||
\(167\) | − | 20.2877i | − | 1.56991i | −0.619551 | − | 0.784956i | \(-0.712685\pi\) | ||
0.619551 | − | 0.784956i | \(-0.287315\pi\) | |||||||
\(168\) | 2.85278i | 0.220096i | ||||||||
\(169\) | 11.7575 | 0.904421 | ||||||||
\(170\) | −12.1673 | + | 1.22212i | −0.933188 | + | 0.0937322i | ||||
\(171\) | −6.16229 | −0.471242 | ||||||||
\(172\) | 0.333950i | 0.0254634i | ||||||||
\(173\) | − | 0.813028i | − | 0.0618134i | −0.999522 | − | 0.0309067i | \(-0.990161\pi\) | ||
0.999522 | − | 0.0309067i | \(-0.00983948\pi\) | |||||||
\(174\) | −11.8128 | −0.895523 | ||||||||
\(175\) | 0.994397 | + | 4.90012i | 0.0751694 | + | 0.370414i | ||||
\(176\) | −3.92833 | −0.296109 | ||||||||
\(177\) | 11.5606i | 0.868949i | ||||||||
\(178\) | 8.44648i | 0.633090i | ||||||||
\(179\) | 5.71923 | 0.427476 | 0.213738 | − | 0.976891i | \(-0.431436\pi\) | ||||
0.213738 | + | 0.976891i | \(0.431436\pi\) | |||||||
\(180\) | 0.0783475 | − | 0.00786945i | 0.00583968 | − | 0.000586555i | ||||
\(181\) | −19.2397 | −1.43008 | −0.715039 | − | 0.699085i | \(-0.753591\pi\) | ||||
−0.715039 | + | 0.699085i | \(0.753591\pi\) | |||||||
\(182\) | 1.56247i | 0.115818i | ||||||||
\(183\) | 10.3786i | 0.767206i | ||||||||
\(184\) | 14.8402 | 1.09404 | ||||||||
\(185\) | −0.120879 | − | 1.20345i | −0.00888717 | − | 0.0884798i | ||||
\(186\) | 12.5492 | 0.920154 | ||||||||
\(187\) | 3.90149i | 0.285305i | ||||||||
\(188\) | 0.107117i | 0.00781231i | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.93030 | + | 19.2178i | 0.140038 | + | 1.39421i | ||||
\(191\) | −12.3909 | −0.896572 | −0.448286 | − | 0.893890i | \(-0.647965\pi\) | ||||
−0.448286 | + | 0.893890i | \(0.647965\pi\) | |||||||
\(192\) | − | 8.13585i | − | 0.587155i | ||||||
\(193\) | − | 16.1704i | − | 1.16397i | −0.813198 | − | 0.581987i | \(-0.802276\pi\) | ||
0.813198 | − | 0.581987i | \(-0.197724\pi\) | |||||||
\(194\) | 1.26706 | 0.0909698 | ||||||||
\(195\) | 2.48004 | − | 0.249102i | 0.177599 | − | 0.0178386i | ||||
\(196\) | −0.0352144 | −0.00251531 | ||||||||
\(197\) | − | 16.7925i | − | 1.19641i | −0.801342 | − | 0.598207i | \(-0.795880\pi\) | ||
0.801342 | − | 0.598207i | \(-0.204120\pi\) | |||||||
\(198\) | 1.40171i | 0.0996151i | ||||||||
\(199\) | −24.1930 | −1.71500 | −0.857499 | − | 0.514486i | \(-0.827983\pi\) | ||||
−0.857499 | + | 0.514486i | \(0.827983\pi\) | |||||||
\(200\) | −2.83679 | − | 13.9789i | −0.200592 | − | 0.988461i | ||||
\(201\) | −5.35976 | −0.378048 | ||||||||
\(202\) | 0.211811i | 0.0149030i | ||||||||
\(203\) | − | 8.42741i | − | 0.591488i | ||||||
\(204\) | −0.137389 | −0.00961913 | ||||||||
\(205\) | −7.49160 | + | 0.752479i | −0.523236 | + | 0.0525554i | ||||
\(206\) | 22.6230 | 1.57622 | ||||||||
\(207\) | − | 5.20203i | − | 0.361566i | ||||||
\(208\) | − | 4.37886i | − | 0.303619i | ||||||
\(209\) | 6.16229 | 0.426254 | ||||||||
\(210\) | −0.313244 | − | 3.11862i | −0.0216159 | − | 0.215205i | ||||
\(211\) | −4.37957 | −0.301502 | −0.150751 | − | 0.988572i | \(-0.548169\pi\) | ||||
−0.150751 | + | 0.988572i | \(0.548169\pi\) | |||||||
\(212\) | 0.100855i | 0.00692677i | ||||||||
\(213\) | 11.2413i | 0.770239i | ||||||||
\(214\) | −10.9554 | −0.748898 | ||||||||
\(215\) | −2.11927 | − | 21.0992i | −0.144533 | − | 1.43896i | ||||
\(216\) | −2.85278 | −0.194107 | ||||||||
\(217\) | 8.95281i | 0.607756i | ||||||||
\(218\) | 25.5520i | 1.73060i | ||||||||
\(219\) | 0.333198 | 0.0225154 | ||||||||
\(220\) | −0.0783475 | + | 0.00786945i | −0.00528219 | + | 0.000530559i | ||||
\(221\) | −4.34894 | −0.292542 | ||||||||
\(222\) | 0.758197i | 0.0508869i | ||||||||
\(223\) | − | 15.7451i | − | 1.05437i | −0.849750 | − | 0.527186i | \(-0.823247\pi\) | ||
0.849750 | − | 0.527186i | \(-0.176753\pi\) | |||||||
\(224\) | 0.199179 | 0.0133082 | ||||||||
\(225\) | −4.90012 | + | 0.994397i | −0.326675 | + | 0.0662931i | ||||
\(226\) | −3.20272 | −0.213042 | ||||||||
\(227\) | 26.6766i | 1.77059i | 0.465032 | + | 0.885294i | \(0.346043\pi\) | ||||
−0.465032 | + | 0.885294i | \(0.653957\pi\) | |||||||
\(228\) | 0.217001i | 0.0143712i | ||||||||
\(229\) | −12.4550 | −0.823052 | −0.411526 | − | 0.911398i | \(-0.635004\pi\) | ||||
−0.411526 | + | 0.911398i | \(0.635004\pi\) | |||||||
\(230\) | −16.2232 | + | 1.62950i | −1.06972 | + | 0.107446i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 24.0415i | 1.57840i | ||||||||
\(233\) | 19.4102i | 1.27160i | 0.771853 | + | 0.635801i | \(0.219330\pi\) | ||||
−0.771853 | + | 0.635801i | \(0.780670\pi\) | |||||||
\(234\) | −1.56247 | −0.102142 | ||||||||
\(235\) | −0.679772 | − | 6.76774i | −0.0443434 | − | 0.441479i | ||||
\(236\) | 0.407100 | 0.0264999 | ||||||||
\(237\) | − | 0.575756i | − | 0.0373994i | ||||||
\(238\) | 5.46876i | 0.354487i | ||||||||
\(239\) | −15.8535 | −1.02548 | −0.512740 | − | 0.858544i | \(-0.671369\pi\) | ||||
−0.512740 | + | 0.858544i | \(0.671369\pi\) | |||||||
\(240\) | 0.877875 | + | 8.74004i | 0.0566666 | + | 0.564167i | ||||
\(241\) | 18.1106 | 1.16661 | 0.583304 | − | 0.812254i | \(-0.301760\pi\) | ||||
0.583304 | + | 0.812254i | \(0.301760\pi\) | |||||||
\(242\) | − | 1.40171i | − | 0.0901052i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0.365475 | 0.0233971 | ||||||||
\(245\) | 2.22487 | − | 0.223473i | 0.142142 | − | 0.0142772i | ||||
\(246\) | 4.71984 | 0.300926 | ||||||||
\(247\) | 6.86902i | 0.437065i | ||||||||
\(248\) | − | 25.5404i | − | 1.62182i | ||||||
\(249\) | 0.318582 | 0.0201893 | ||||||||
\(250\) | 4.63608 | + | 14.9701i | 0.293212 | + | 0.946795i | ||||
\(251\) | −3.24386 | −0.204751 | −0.102375 | − | 0.994746i | \(-0.532644\pi\) | ||||
−0.102375 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(252\) | − | 0.0352144i | − | 0.00221830i | ||||||
\(253\) | 5.20203i | 0.327049i | ||||||||
\(254\) | −7.25911 | −0.455477 | ||||||||
\(255\) | 8.68033 | − | 0.871878i | 0.543583 | − | 0.0545991i | ||||
\(256\) | −0.844881 | −0.0528051 | ||||||||
\(257\) | 23.6248i | 1.47367i | 0.676071 | + | 0.736837i | \(0.263681\pi\) | ||||
−0.676071 | + | 0.736837i | \(0.736319\pi\) | |||||||
\(258\) | 13.2929i | 0.827578i | ||||||||
\(259\) | −0.540909 | −0.0336105 | ||||||||
\(260\) | −0.00877198 | − | 0.0873329i | −0.000544015 | − | 0.00541616i | ||||
\(261\) | 8.42741 | 0.521643 | ||||||||
\(262\) | 13.6314i | 0.842150i | ||||||||
\(263\) | − | 3.88432i | − | 0.239517i | −0.992803 | − | 0.119759i | \(-0.961788\pi\) | ||
0.992803 | − | 0.119759i | \(-0.0382121\pi\) | |||||||
\(264\) | 2.85278 | 0.175576 | ||||||||
\(265\) | −0.640034 | − | 6.37212i | −0.0393170 | − | 0.391436i | ||||
\(266\) | 8.63773 | 0.529613 | ||||||||
\(267\) | − | 6.02585i | − | 0.368776i | ||||||
\(268\) | 0.188741i | 0.0115292i | ||||||||
\(269\) | −0.573778 | −0.0349839 | −0.0174919 | − | 0.999847i | \(-0.505568\pi\) | ||||
−0.0174919 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(270\) | 3.11862 | − | 0.313244i | 0.189793 | − | 0.0190634i | ||||
\(271\) | 24.9842 | 1.51768 | 0.758842 | − | 0.651275i | \(-0.225766\pi\) | ||||
0.758842 | + | 0.651275i | \(0.225766\pi\) | |||||||
\(272\) | − | 15.3264i | − | 0.929297i | ||||||
\(273\) | − | 1.11469i | − | 0.0674639i | ||||||
\(274\) | −14.0430 | −0.848370 | ||||||||
\(275\) | 4.90012 | − | 0.994397i | 0.295488 | − | 0.0599644i | ||||
\(276\) | −0.183186 | −0.0110265 | ||||||||
\(277\) | − | 18.7064i | − | 1.12396i | −0.827151 | − | 0.561979i | \(-0.810040\pi\) | ||
0.827151 | − | 0.561979i | \(-0.189960\pi\) | |||||||
\(278\) | − | 7.22312i | − | 0.433214i | ||||||
\(279\) | −8.95281 | −0.535991 | ||||||||
\(280\) | −6.34707 | + | 0.637518i | −0.379310 | + | 0.0380990i | ||||
\(281\) | 10.8364 | 0.646446 | 0.323223 | − | 0.946323i | \(-0.395234\pi\) | ||||
0.323223 | + | 0.946323i | \(0.395234\pi\) | |||||||
\(282\) | 4.26379i | 0.253905i | ||||||||
\(283\) | 11.1910i | 0.665237i | 0.943061 | + | 0.332619i | \(0.107932\pi\) | ||||
−0.943061 | + | 0.332619i | \(0.892068\pi\) | |||||||
\(284\) | 0.395854 | 0.0234896 | ||||||||
\(285\) | −1.37710 | − | 13.7103i | −0.0815726 | − | 0.812128i | ||||
\(286\) | 1.56247 | 0.0923905 | ||||||||
\(287\) | 3.36720i | 0.198760i | ||||||||
\(288\) | 0.199179i | 0.0117368i | ||||||||
\(289\) | 1.77835 | 0.104609 | ||||||||
\(290\) | −2.63983 | − | 26.2819i | −0.155016 | − | 1.54333i | ||||
\(291\) | −0.903942 | −0.0529900 | ||||||||
\(292\) | − | 0.0117334i | − | 0.000686643i | ||||||
\(293\) | 3.82893i | 0.223689i | 0.993726 | + | 0.111844i | \(0.0356758\pi\) | ||||
−0.993726 | + | 0.111844i | \(0.964324\pi\) | |||||||
\(294\) | −1.40171 | −0.0817493 | ||||||||
\(295\) | −25.7209 | + | 2.58348i | −1.49753 | + | 0.150416i | ||||
\(296\) | 1.54309 | 0.0896905 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | − | 9.24975i | − | 0.535824i | ||||||
\(299\) | −5.79864 | −0.335344 | ||||||||
\(300\) | 0.0350171 | + | 0.172555i | 0.00202171 | + | 0.00996245i | ||||
\(301\) | −9.48334 | −0.546611 | ||||||||
\(302\) | 6.65013i | 0.382672i | ||||||||
\(303\) | − | 0.151109i | − | 0.00868101i | ||||||
\(304\) | −24.2075 | −1.38840 | ||||||||
\(305\) | −23.0910 | + | 2.31933i | −1.32219 | + | 0.132804i | ||||
\(306\) | −5.46876 | −0.312628 | ||||||||
\(307\) | − | 22.7405i | − | 1.29787i | −0.760844 | − | 0.648934i | \(-0.775215\pi\) | ||
0.760844 | − | 0.648934i | \(-0.224785\pi\) | |||||||
\(308\) | 0.0352144i | 0.00200653i | ||||||||
\(309\) | −16.1396 | −0.918149 | ||||||||
\(310\) | 2.80441 | + | 27.9204i | 0.159280 | + | 1.58577i | ||||
\(311\) | 22.6476 | 1.28423 | 0.642115 | − | 0.766608i | \(-0.278057\pi\) | ||||
0.642115 | + | 0.766608i | \(0.278057\pi\) | |||||||
\(312\) | 3.17995i | 0.180029i | ||||||||
\(313\) | 22.8832i | 1.29344i | 0.762729 | + | 0.646719i | \(0.223859\pi\) | ||||
−0.762729 | + | 0.646719i | \(0.776141\pi\) | |||||||
\(314\) | 15.8922 | 0.896846 | ||||||||
\(315\) | 0.223473 | + | 2.22487i | 0.0125913 | + | 0.125357i | ||||
\(316\) | −0.0202749 | −0.00114055 | ||||||||
\(317\) | 28.2934i | 1.58911i | 0.607189 | + | 0.794557i | \(0.292297\pi\) | ||||
−0.607189 | + | 0.794557i | \(0.707703\pi\) | |||||||
\(318\) | 4.01454i | 0.225124i | ||||||||
\(319\) | −8.42741 | −0.471844 | ||||||||
\(320\) | 18.1012 | − | 1.81814i | 1.01189 | − | 0.101637i | ||||
\(321\) | 7.81577 | 0.436234 | ||||||||
\(322\) | 7.29173i | 0.406352i | ||||||||
\(323\) | 24.0421i | 1.33774i | ||||||||
\(324\) | 0.0352144 | 0.00195635 | ||||||||
\(325\) | 1.10844 | + | 5.46210i | 0.0614853 | + | 0.302983i | ||||
\(326\) | −28.1662 | −1.55998 | ||||||||
\(327\) | − | 18.2292i | − | 1.00807i | ||||||
\(328\) | − | 9.60588i | − | 0.530396i | ||||||
\(329\) | −3.04186 | −0.167703 | ||||||||
\(330\) | −3.11862 | + | 0.313244i | −0.171675 | + | 0.0172435i | ||||
\(331\) | −1.50467 | −0.0827042 | −0.0413521 | − | 0.999145i | \(-0.513167\pi\) | ||||
−0.0413521 | + | 0.999145i | \(0.513167\pi\) | |||||||
\(332\) | − | 0.0112187i | − | 0.000615704i | ||||||
\(333\) | − | 0.540909i | − | 0.0296417i | ||||||
\(334\) | −28.4375 | −1.55603 | ||||||||
\(335\) | −1.19776 | − | 11.9248i | −0.0654407 | − | 0.651521i | ||||
\(336\) | 3.92833 | 0.214308 | ||||||||
\(337\) | 7.26220i | 0.395597i | 0.980243 | + | 0.197799i | \(0.0633792\pi\) | ||||
−0.980243 | + | 0.197799i | \(0.936621\pi\) | |||||||
\(338\) | − | 16.4805i | − | 0.896423i | ||||||
\(339\) | 2.28487 | 0.124097 | ||||||||
\(340\) | −0.0307026 | − | 0.305672i | −0.00166508 | − | 0.0165774i | ||||
\(341\) | 8.95281 | 0.484822 | ||||||||
\(342\) | 8.63773i | 0.467075i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 27.0538 | 1.45865 | ||||||||
\(345\) | 11.5739 | − | 1.16251i | 0.623116 | − | 0.0625876i | ||||
\(346\) | −1.13963 | −0.0612668 | ||||||||
\(347\) | − | 12.1412i | − | 0.651772i | −0.945409 | − | 0.325886i | \(-0.894337\pi\) | ||
0.945409 | − | 0.325886i | \(-0.105663\pi\) | |||||||
\(348\) | − | 0.296766i | − | 0.0159083i | ||||||
\(349\) | −23.1231 | −1.23775 | −0.618875 | − | 0.785490i | \(-0.712411\pi\) | ||||
−0.618875 | + | 0.785490i | \(0.712411\pi\) | |||||||
\(350\) | 6.86854 | − | 1.39385i | 0.367139 | − | 0.0745047i | ||||
\(351\) | 1.11469 | 0.0594976 | ||||||||
\(352\) | − | 0.199179i | − | 0.0106163i | ||||||
\(353\) | 0.0323931i | 0.00172411i | 1.00000 | 0.000862055i | \(0.000274401\pi\) | |||||
−1.00000 | 0.000862055i | \(0.999726\pi\) | ||||||||
\(354\) | 16.2046 | 0.861265 | ||||||||
\(355\) | −25.0104 | + | 2.51212i | −1.32741 | + | 0.133329i | ||||
\(356\) | −0.212196 | −0.0112464 | ||||||||
\(357\) | − | 3.90149i | − | 0.206489i | ||||||
\(358\) | − | 8.01670i | − | 0.423696i | ||||||
\(359\) | −5.14259 | −0.271415 | −0.135708 | − | 0.990749i | \(-0.543331\pi\) | ||||
−0.135708 | + | 0.990749i | \(0.543331\pi\) | |||||||
\(360\) | −0.637518 | − | 6.34707i | −0.0336001 | − | 0.334520i | ||||
\(361\) | 18.9738 | 0.998620 | ||||||||
\(362\) | 26.9685i | 1.41743i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −0.0392530 | −0.00205742 | ||||||||
\(365\) | 0.0744607 | + | 0.741323i | 0.00389745 | + | 0.0388026i | ||||
\(366\) | 14.5477 | 0.760422 | ||||||||
\(367\) | 25.9376i | 1.35393i | 0.736014 | + | 0.676966i | \(0.236706\pi\) | ||||
−0.736014 | + | 0.676966i | \(0.763294\pi\) | |||||||
\(368\) | − | 20.4353i | − | 1.06526i | ||||||
\(369\) | −3.36720 | −0.175290 | ||||||||
\(370\) | −1.68689 | + | 0.169436i | −0.0876974 | + | 0.00880858i | ||||
\(371\) | −2.86404 | −0.148693 | ||||||||
\(372\) | 0.315268i | 0.0163459i | ||||||||
\(373\) | − | 26.4045i | − | 1.36717i | −0.729870 | − | 0.683586i | \(-0.760419\pi\) | ||
0.729870 | − | 0.683586i | \(-0.239581\pi\) | |||||||
\(374\) | 5.46876 | 0.282783 | ||||||||
\(375\) | −3.30745 | − | 10.6799i | −0.170796 | − | 0.551509i | ||||
\(376\) | 8.67774 | 0.447520 | ||||||||
\(377\) | − | 9.39392i | − | 0.483811i | ||||||
\(378\) | − | 1.40171i | − | 0.0720961i | ||||||
\(379\) | −7.96861 | −0.409320 | −0.204660 | − | 0.978833i | \(-0.565609\pi\) | ||||
−0.204660 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(380\) | −0.482800 | + | 0.0484938i | −0.0247671 | + | 0.00248768i | ||||
\(381\) | 5.17876 | 0.265316 | ||||||||
\(382\) | 17.3684i | 0.888644i | ||||||||
\(383\) | 0.0488882i | 0.00249807i | 0.999999 | + | 0.00124904i | \(0.000397581\pi\) | ||||
−0.999999 | + | 0.00124904i | \(0.999602\pi\) | |||||||
\(384\) | −11.0057 | −0.561634 | ||||||||
\(385\) | −0.223473 | − | 2.22487i | −0.0113892 | − | 0.113390i | ||||
\(386\) | −22.6662 | −1.15368 | ||||||||
\(387\) | − | 9.48334i | − | 0.482065i | ||||||
\(388\) | 0.0318317i | 0.00161601i | ||||||||
\(389\) | −12.8737 | −0.652721 | −0.326360 | − | 0.945245i | \(-0.605822\pi\) | ||||
−0.326360 | + | 0.945245i | \(0.605822\pi\) | |||||||
\(390\) | −0.349169 | − | 3.47629i | −0.0176808 | − | 0.176029i | ||||
\(391\) | −20.2957 | −1.02640 | ||||||||
\(392\) | 2.85278i | 0.144087i | ||||||||
\(393\) | − | 9.72484i | − | 0.490553i | ||||||
\(394\) | −23.5381 | −1.18583 | ||||||||
\(395\) | 1.28098 | − | 0.128666i | 0.0644533 | − | 0.00647388i | ||||
\(396\) | −0.0352144 | −0.00176959 | ||||||||
\(397\) | 18.7983i | 0.943460i | 0.881743 | + | 0.471730i | \(0.156370\pi\) | ||||
−0.881743 | + | 0.471730i | \(0.843630\pi\) | |||||||
\(398\) | 33.9115i | 1.69983i | ||||||||
\(399\) | −6.16229 | −0.308500 | ||||||||
\(400\) | −19.2493 | + | 3.90632i | −0.962465 | + | 0.195316i | ||||
\(401\) | −26.0692 | −1.30183 | −0.650917 | − | 0.759149i | \(-0.725615\pi\) | ||||
−0.650917 | + | 0.759149i | \(0.725615\pi\) | |||||||
\(402\) | 7.51282i | 0.374705i | ||||||||
\(403\) | 9.97958i | 0.497118i | ||||||||
\(404\) | −0.00532122 | −0.000264741 | ||||||||
\(405\) | −2.22487 | + | 0.223473i | −0.110555 | + | 0.0111045i | ||||
\(406\) | −11.8128 | −0.586258 | ||||||||
\(407\) | 0.540909i | 0.0268119i | ||||||||
\(408\) | 11.1301i | 0.551022i | ||||||||
\(409\) | −5.77357 | −0.285484 | −0.142742 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142742 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(410\) | 1.05476 | + | 10.5010i | 0.0520907 | + | 0.518609i | ||||
\(411\) | 10.0185 | 0.494176 | ||||||||
\(412\) | 0.568345i | 0.0280004i | ||||||||
\(413\) | 11.5606i | 0.568861i | ||||||||
\(414\) | −7.29173 | −0.358369 | ||||||||
\(415\) | 0.0711943 | + | 0.708804i | 0.00349479 | + | 0.0347938i | ||||
\(416\) | 0.222023 | 0.0108856 | ||||||||
\(417\) | 5.15308i | 0.252348i | ||||||||
\(418\) | − | 8.63773i | − | 0.422485i | ||||||
\(419\) | 20.7104 | 1.01177 | 0.505884 | − | 0.862602i | \(-0.331166\pi\) | ||||
0.505884 | + | 0.862602i | \(0.331166\pi\) | |||||||
\(420\) | 0.0783475 | − | 0.00786945i | 0.00382297 | − | 0.000383990i | ||||
\(421\) | 22.0655 | 1.07540 | 0.537702 | − | 0.843135i | \(-0.319292\pi\) | ||||
0.537702 | + | 0.843135i | \(0.319292\pi\) | |||||||
\(422\) | 6.13887i | 0.298836i | ||||||||
\(423\) | − | 3.04186i | − | 0.147900i | ||||||
\(424\) | 8.17046 | 0.396793 | ||||||||
\(425\) | 3.87963 | + | 19.1178i | 0.188190 | + | 0.927349i | ||||
\(426\) | 15.7570 | 0.763428 | ||||||||
\(427\) | 10.3786i | 0.502254i | ||||||||
\(428\) | − | 0.275228i | − | 0.0133036i | ||||||
\(429\) | −1.11469 | −0.0538176 | ||||||||
\(430\) | −29.5750 | + | 2.97060i | −1.42623 | + | 0.143255i | ||||
\(431\) | 5.07517 | 0.244463 | 0.122231 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122231 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(432\) | 3.92833i | 0.189002i | ||||||||
\(433\) | − | 36.8250i | − | 1.76970i | −0.465879 | − | 0.884849i | \(-0.654262\pi\) | ||
0.465879 | − | 0.884849i | \(-0.345738\pi\) | |||||||
\(434\) | 12.5492 | 0.602382 | ||||||||
\(435\) | 1.88330 | + | 18.7499i | 0.0902971 | + | 0.898989i | ||||
\(436\) | −0.641928 | −0.0307428 | ||||||||
\(437\) | 32.0564i | 1.53347i | ||||||||
\(438\) | − | 0.467046i | − | 0.0223163i | ||||||
\(439\) | 22.4927 | 1.07352 | 0.536758 | − | 0.843736i | \(-0.319649\pi\) | ||||
0.536758 | + | 0.843736i | \(0.319649\pi\) | |||||||
\(440\) | 0.637518 | + | 6.34707i | 0.0303925 | + | 0.302584i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 6.09595i | 0.289955i | ||||||||
\(443\) | − | 10.6128i | − | 0.504229i | −0.967697 | − | 0.252114i | \(-0.918874\pi\) | ||
0.967697 | − | 0.252114i | \(-0.0811259\pi\) | |||||||
\(444\) | −0.0190478 | −0.000903968 | ||||||||
\(445\) | 13.4067 | − | 1.34661i | 0.635541 | − | 0.0638356i | ||||
\(446\) | −22.0701 | −1.04505 | ||||||||
\(447\) | 6.59892i | 0.312118i | ||||||||
\(448\) | − | 8.13585i | − | 0.384383i | ||||||
\(449\) | 21.7038 | 1.02427 | 0.512133 | − | 0.858906i | \(-0.328856\pi\) | ||||
0.512133 | + | 0.858906i | \(0.328856\pi\) | |||||||
\(450\) | 1.39385 | + | 6.86854i | 0.0657069 | + | 0.323786i | ||||
\(451\) | 3.36720 | 0.158555 | ||||||||
\(452\) | − | 0.0804602i | − | 0.00378453i | ||||||
\(453\) | − | 4.74431i | − | 0.222907i | ||||||
\(454\) | 37.3928 | 1.75493 | ||||||||
\(455\) | 2.48004 | − | 0.249102i | 0.116266 | − | 0.0116781i | ||||
\(456\) | 17.5796 | 0.823241 | ||||||||
\(457\) | − | 18.8122i | − | 0.879999i | −0.897998 | − | 0.439999i | \(-0.854979\pi\) | ||
0.897998 | − | 0.439999i | \(-0.145021\pi\) | |||||||
\(458\) | 17.4583i | 0.815774i | ||||||||
\(459\) | 3.90149 | 0.182106 | ||||||||
\(460\) | −0.0409371 | − | 0.407566i | −0.00190870 | − | 0.0190029i | ||||
\(461\) | 11.8650 | 0.552610 | 0.276305 | − | 0.961070i | \(-0.410890\pi\) | ||||
0.276305 | + | 0.961070i | \(0.410890\pi\) | |||||||
\(462\) | 1.40171i | 0.0652134i | ||||||||
\(463\) | − | 21.3418i | − | 0.991839i | −0.868368 | − | 0.495920i | \(-0.834831\pi\) | ||
0.868368 | − | 0.495920i | \(-0.165169\pi\) | |||||||
\(464\) | 33.1056 | 1.53689 | ||||||||
\(465\) | −2.00071 | − | 19.9189i | −0.0927807 | − | 0.923715i | ||||
\(466\) | 27.2074 | 1.26036 | ||||||||
\(467\) | − | 36.9132i | − | 1.70814i | −0.520158 | − | 0.854070i | \(-0.674127\pi\) | ||
0.520158 | − | 0.854070i | \(-0.325873\pi\) | |||||||
\(468\) | − | 0.0392530i | − | 0.00181447i | ||||||
\(469\) | −5.35976 | −0.247491 | ||||||||
\(470\) | −9.48640 | + | 0.952842i | −0.437575 | + | 0.0439513i | ||||
\(471\) | −11.3377 | −0.522414 | ||||||||
\(472\) | − | 32.9798i | − | 1.51802i | ||||||
\(473\) | 9.48334i | 0.436044i | ||||||||
\(474\) | −0.807042 | −0.0370687 | ||||||||
\(475\) | 30.1959 | − | 6.12776i | 1.38548 | − | 0.281161i | ||||
\(476\) | −0.137389 | −0.00629720 | ||||||||
\(477\) | − | 2.86404i | − | 0.131135i | ||||||
\(478\) | 22.2220i | 1.01641i | ||||||||
\(479\) | −21.3170 | −0.973998 | −0.486999 | − | 0.873402i | \(-0.661908\pi\) | ||||
−0.486999 | + | 0.873402i | \(0.661908\pi\) | |||||||
\(480\) | −0.443149 | + | 0.0445112i | −0.0202269 | + | 0.00203165i | ||||
\(481\) | −0.602945 | −0.0274919 | ||||||||
\(482\) | − | 25.3858i | − | 1.15629i | ||||||
\(483\) | − | 5.20203i | − | 0.236701i | ||||||
\(484\) | 0.0352144 | 0.00160065 | ||||||||
\(485\) | −0.202006 | − | 2.01116i | −0.00917264 | − | 0.0913219i | ||||
\(486\) | 1.40171 | 0.0635828 | ||||||||
\(487\) | 40.6900i | 1.84384i | 0.387379 | + | 0.921921i | \(0.373381\pi\) | ||||
−0.387379 | + | 0.921921i | \(0.626619\pi\) | |||||||
\(488\) | − | 29.6077i | − | 1.34028i | ||||||
\(489\) | 20.0942 | 0.908692 | ||||||||
\(490\) | −0.313244 | − | 3.11862i | −0.0141509 | − | 0.140885i | ||||
\(491\) | 37.0297 | 1.67113 | 0.835563 | − | 0.549395i | \(-0.185142\pi\) | ||||
0.835563 | + | 0.549395i | \(0.185142\pi\) | |||||||
\(492\) | 0.118574i | 0.00534573i | ||||||||
\(493\) | − | 32.8795i | − | 1.48082i | ||||||
\(494\) | 9.62836 | 0.433200 | ||||||||
\(495\) | 2.22487 | − | 0.223473i | 0.100001 | − | 0.0100444i | ||||
\(496\) | −35.1696 | −1.57916 | ||||||||
\(497\) | 11.2413i | 0.504240i | ||||||||
\(498\) | − | 0.446558i | − | 0.0200108i | ||||||
\(499\) | −10.9316 | −0.489366 | −0.244683 | − | 0.969603i | \(-0.578684\pi\) | ||||
−0.244683 | + | 0.969603i | \(0.578684\pi\) | |||||||
\(500\) | −0.376087 | + | 0.116470i | −0.0168191 | + | 0.00520869i | ||||
\(501\) | 20.2877 | 0.906389 | ||||||||
\(502\) | 4.54695i | 0.202940i | ||||||||
\(503\) | − | 35.6225i | − | 1.58833i | −0.607703 | − | 0.794164i | \(-0.707909\pi\) | ||
0.607703 | − | 0.794164i | \(-0.292091\pi\) | |||||||
\(504\) | −2.85278 | −0.127073 | ||||||||
\(505\) | 0.336199 | − | 0.0337688i | 0.0149607 | − | 0.00150269i | ||||
\(506\) | 7.29173 | 0.324157 | ||||||||
\(507\) | 11.7575i | 0.522168i | ||||||||
\(508\) | − | 0.182367i | − | 0.00809122i | ||||||
\(509\) | 39.3126 | 1.74250 | 0.871251 | − | 0.490838i | \(-0.163309\pi\) | ||||
0.871251 | + | 0.490838i | \(0.163309\pi\) | |||||||
\(510\) | −1.22212 | − | 12.1673i | −0.0541163 | − | 0.538776i | ||||
\(511\) | 0.333198 | 0.0147398 | ||||||||
\(512\) | 23.1957i | 1.02512i | ||||||||
\(513\) | − | 6.16229i | − | 0.272072i | ||||||
\(514\) | 33.1151 | 1.46064 | ||||||||
\(515\) | −3.60676 | − | 35.9085i | −0.158933 | − | 1.58232i | ||||
\(516\) | −0.333950 | −0.0147013 | ||||||||
\(517\) | 3.04186i | 0.133781i | ||||||||
\(518\) | 0.758197i | 0.0333133i | ||||||||
\(519\) | 0.813028 | 0.0356880 | ||||||||
\(520\) | −7.07499 | + | 0.710633i | −0.310259 | + | 0.0311633i | ||||
\(521\) | 15.7075 | 0.688157 | 0.344078 | − | 0.938941i | \(-0.388191\pi\) | ||||
0.344078 | + | 0.938941i | \(0.388191\pi\) | |||||||
\(522\) | − | 11.8128i | − | 0.517031i | ||||||
\(523\) | − | 23.6574i | − | 1.03447i | −0.855845 | − | 0.517233i | \(-0.826962\pi\) | ||
0.855845 | − | 0.517233i | \(-0.173038\pi\) | |||||||
\(524\) | −0.342454 | −0.0149602 | ||||||||
\(525\) | −4.90012 | + | 0.994397i | −0.213859 | + | 0.0433991i | ||||
\(526\) | −5.44468 | −0.237399 | ||||||||
\(527\) | 34.9293i | 1.52155i | ||||||||
\(528\) | − | 3.92833i | − | 0.170959i | ||||||
\(529\) | −4.06112 | −0.176571 | ||||||||
\(530\) | −8.93185 | + | 0.897141i | −0.387975 | + | 0.0389693i | ||||
\(531\) | −11.5606 | −0.501688 | ||||||||
\(532\) | 0.217001i | 0.00940819i | ||||||||
\(533\) | 3.75338i | 0.162577i | ||||||||
\(534\) | −8.44648 | −0.365515 | ||||||||
\(535\) | 1.74661 | + | 17.3891i | 0.0755126 | + | 0.751796i | ||||
\(536\) | 15.2902 | 0.660436 | ||||||||
\(537\) | 5.71923i | 0.246803i | ||||||||
\(538\) | 0.804269i | 0.0346745i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0.00786945 | + | 0.0783475i | 0.000338647 | + | 0.00337154i | ||||
\(541\) | 41.0294 | 1.76399 | 0.881995 | − | 0.471258i | \(-0.156200\pi\) | ||||
0.881995 | + | 0.471258i | \(0.156200\pi\) | |||||||
\(542\) | − | 35.0206i | − | 1.50426i | ||||||
\(543\) | − | 19.2397i | − | 0.825655i | ||||||
\(544\) | 0.777097 | 0.0333177 | ||||||||
\(545\) | 40.5576 | − | 4.07372i | 1.73730 | − | 0.174499i | ||||
\(546\) | −1.56247 | −0.0668674 | ||||||||
\(547\) | − | 20.3175i | − | 0.868716i | −0.900740 | − | 0.434358i | \(-0.856975\pi\) | ||
0.900740 | − | 0.434358i | \(-0.143025\pi\) | |||||||
\(548\) | − | 0.352795i | − | 0.0150707i | ||||||
\(549\) | −10.3786 | −0.442946 | ||||||||
\(550\) | −1.39385 | − | 6.86854i | −0.0594342 | − | 0.292875i | ||||
\(551\) | −51.9321 | −2.21238 | ||||||||
\(552\) | 14.8402i | 0.631642i | ||||||||
\(553\) | − | 0.575756i | − | 0.0244836i | ||||||
\(554\) | −26.2209 | −1.11402 | ||||||||
\(555\) | 1.20345 | − | 0.120879i | 0.0510838 | − | 0.00513101i | ||||
\(556\) | 0.181463 | 0.00769573 | ||||||||
\(557\) | − | 45.1321i | − | 1.91231i | −0.292867 | − | 0.956153i | \(-0.594609\pi\) | ||
0.292867 | − | 0.956153i | \(-0.405391\pi\) | |||||||
\(558\) | 12.5492i | 0.531251i | ||||||||
\(559\) | −10.5710 | −0.447104 | ||||||||
\(560\) | 0.877875 | + | 8.74004i | 0.0370970 | + | 0.369334i | ||||
\(561\) | −3.90149 | −0.164721 | ||||||||
\(562\) | − | 15.1895i | − | 0.640730i | ||||||
\(563\) | − | 21.8187i | − | 0.919549i | −0.888036 | − | 0.459774i | \(-0.847930\pi\) | ||
0.888036 | − | 0.459774i | \(-0.152070\pi\) | |||||||
\(564\) | −0.107117 | −0.00451044 | ||||||||
\(565\) | 0.510606 | + | 5.08354i | 0.0214813 | + | 0.213866i | ||||
\(566\) | 15.6865 | 0.659355 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 32.0688i | − | 1.34558i | ||||||
\(569\) | −13.9550 | −0.585022 | −0.292511 | − | 0.956262i | \(-0.594491\pi\) | ||||
−0.292511 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(570\) | −19.2178 | + | 1.93030i | −0.804947 | + | 0.0808512i | ||||
\(571\) | −38.6960 | −1.61938 | −0.809688 | − | 0.586860i | \(-0.800364\pi\) | ||||
−0.809688 | + | 0.586860i | \(0.800364\pi\) | |||||||
\(572\) | 0.0392530i | 0.00164125i | ||||||||
\(573\) | − | 12.3909i | − | 0.517636i | ||||||
\(574\) | 4.71984 | 0.197002 | ||||||||
\(575\) | 5.17288 | + | 25.4906i | 0.215724 | + | 1.06303i | ||||
\(576\) | 8.13585 | 0.338994 | ||||||||
\(577\) | − | 12.9243i | − | 0.538045i | −0.963134 | − | 0.269023i | \(-0.913299\pi\) | ||
0.963134 | − | 0.269023i | \(-0.0867006\pi\) | |||||||
\(578\) | − | 2.49272i | − | 0.103684i | ||||||
\(579\) | 16.1704 | 0.672021 | ||||||||
\(580\) | 0.660266 | − | 0.0663191i | 0.0274161 | − | 0.00275375i | ||||
\(581\) | 0.318582 | 0.0132170 | ||||||||
\(582\) | 1.26706i | 0.0525214i | ||||||||
\(583\) | 2.86404i | 0.118616i | ||||||||
\(584\) | −0.950540 | −0.0393336 | ||||||||
\(585\) | 0.249102 | + | 2.48004i | 0.0102991 | + | 0.102537i | ||||
\(586\) | 5.36705 | 0.221711 | ||||||||
\(587\) | 19.1803i | 0.791655i | 0.918325 | + | 0.395827i | \(0.129542\pi\) | ||||
−0.918325 | + | 0.395827i | \(0.870458\pi\) | |||||||
\(588\) | − | 0.0352144i | − | 0.00145222i | ||||||
\(589\) | 55.1698 | 2.27323 | ||||||||
\(590\) | 3.62129 | + | 36.0532i | 0.149086 | + | 1.48429i | ||||
\(591\) | 16.7925 | 0.690749 | ||||||||
\(592\) | − | 2.12487i | − | 0.0873317i | ||||||
\(593\) | − | 11.2804i | − | 0.463230i | −0.972807 | − | 0.231615i | \(-0.925599\pi\) | ||
0.972807 | − | 0.231615i | \(-0.0744010\pi\) | |||||||
\(594\) | −1.40171 | −0.0575128 | ||||||||
\(595\) | 8.68033 | − | 0.871878i | 0.355859 | − | 0.0357435i | ||||
\(596\) | 0.232377 | 0.00951852 | ||||||||
\(597\) | − | 24.1930i | − | 0.990154i | ||||||
\(598\) | 8.12799i | 0.332378i | ||||||||
\(599\) | −13.1199 | −0.536063 | −0.268032 | − | 0.963410i | \(-0.586373\pi\) | ||||
−0.268032 | + | 0.963410i | \(0.586373\pi\) | |||||||
\(600\) | 13.9789 | − | 2.83679i | 0.570688 | − | 0.115812i | ||||
\(601\) | 38.8284 | 1.58384 | 0.791922 | − | 0.610623i | \(-0.209081\pi\) | ||||
0.791922 | + | 0.610623i | \(0.209081\pi\) | |||||||
\(602\) | 13.2929i | 0.541777i | ||||||||
\(603\) | − | 5.35976i | − | 0.218266i | ||||||
\(604\) | −0.167068 | −0.00679789 | ||||||||
\(605\) | −2.22487 | + | 0.223473i | −0.0904540 | + | 0.00908546i | ||||
\(606\) | −0.211811 | −0.00860425 | ||||||||
\(607\) | 17.7809i | 0.721703i | 0.932623 | + | 0.360852i | \(0.117514\pi\) | ||||
−0.932623 | + | 0.360852i | \(0.882486\pi\) | |||||||
\(608\) | − | 1.22740i | − | 0.0497776i | ||||||
\(609\) | 8.42741 | 0.341496 | ||||||||
\(610\) | 3.25102 | + | 32.3668i | 0.131630 | + | 1.31049i | ||||
\(611\) | −3.39072 | −0.137174 | ||||||||
\(612\) | − | 0.137389i | − | 0.00555361i | ||||||
\(613\) | − | 31.1286i | − | 1.25727i | −0.777700 | − | 0.628636i | \(-0.783613\pi\) | ||
0.777700 | − | 0.628636i | \(-0.216387\pi\) | |||||||
\(614\) | −31.8755 | −1.28639 | ||||||||
\(615\) | −0.752479 | − | 7.49160i | −0.0303429 | − | 0.302091i | ||||
\(616\) | 2.85278 | 0.114942 | ||||||||
\(617\) | 6.29870i | 0.253576i | 0.991930 | + | 0.126788i | \(0.0404668\pi\) | ||||
−0.991930 | + | 0.126788i | \(0.959533\pi\) | |||||||
\(618\) | 22.6230i | 0.910030i | ||||||||
\(619\) | −34.5333 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(620\) | −0.701431 | + | 0.0704537i | −0.0281701 | + | 0.00282949i | ||||
\(621\) | 5.20203 | 0.208750 | ||||||||
\(622\) | − | 31.7454i | − | 1.27287i | ||||||
\(623\) | − | 6.02585i | − | 0.241421i | ||||||
\(624\) | 4.37886 | 0.175295 | ||||||||
\(625\) | 23.0223 | − | 9.74533i | 0.920894 | − | 0.389813i | ||||
\(626\) | 32.0756 | 1.28200 | ||||||||
\(627\) | 6.16229i | 0.246098i | ||||||||
\(628\) | 0.399250i | 0.0159318i | ||||||||
\(629\) | −2.11035 | −0.0841454 | ||||||||
\(630\) | 3.11862 | − | 0.313244i | 0.124249 | − | 0.0124799i | ||||
\(631\) | 23.4219 | 0.932410 | 0.466205 | − | 0.884677i | \(-0.345621\pi\) | ||||
0.466205 | + | 0.884677i | \(0.345621\pi\) | |||||||
\(632\) | 1.64250i | 0.0653353i | ||||||||
\(633\) | − | 4.37957i | − | 0.174072i | ||||||
\(634\) | 39.6591 | 1.57506 | ||||||||
\(635\) | 1.15731 | + | 11.5221i | 0.0459265 | + | 0.457240i | ||||
\(636\) | −0.100855 | −0.00399917 | ||||||||
\(637\) | − | 1.11469i | − | 0.0441655i | ||||||
\(638\) | 11.8128i | 0.467672i | ||||||||
\(639\) | −11.2413 | −0.444698 | ||||||||
\(640\) | −2.45948 | − | 24.4864i | −0.0972196 | − | 0.967908i | ||||
\(641\) | 25.0686 | 0.990149 | 0.495075 | − | 0.868850i | \(-0.335141\pi\) | ||||
0.495075 | + | 0.868850i | \(0.335141\pi\) | |||||||
\(642\) | − | 10.9554i | − | 0.432376i | ||||||
\(643\) | 5.79812i | 0.228656i | 0.993443 | + | 0.114328i | \(0.0364714\pi\) | ||||
−0.993443 | + | 0.114328i | \(0.963529\pi\) | |||||||
\(644\) | −0.183186 | −0.00721855 | ||||||||
\(645\) | 21.0992 | − | 2.11927i | 0.830781 | − | 0.0834461i | ||||
\(646\) | 33.7000 | 1.32591 | ||||||||
\(647\) | 3.48606i | 0.137051i | 0.997649 | + | 0.0685255i | \(0.0218295\pi\) | ||||
−0.997649 | + | 0.0685255i | \(0.978171\pi\) | |||||||
\(648\) | − | 2.85278i | − | 0.112068i | ||||||
\(649\) | 11.5606 | 0.453794 | ||||||||
\(650\) | 7.65627 | − | 1.55371i | 0.300304 | − | 0.0609416i | ||||
\(651\) | −8.95281 | −0.350888 | ||||||||
\(652\) | − | 0.707605i | − | 0.0277120i | ||||||
\(653\) | 46.4741i | 1.81867i | 0.416063 | + | 0.909336i | \(0.363409\pi\) | ||||
−0.416063 | + | 0.909336i | \(0.636591\pi\) | |||||||
\(654\) | −25.5520 | −0.999161 | ||||||||
\(655\) | 21.6365 | − | 2.17324i | 0.845409 | − | 0.0849154i | ||||
\(656\) | −13.2275 | −0.516447 | ||||||||
\(657\) | 0.333198i | 0.0129993i | ||||||||
\(658\) | 4.26379i | 0.166220i | ||||||||
\(659\) | 11.3280 | 0.441276 | 0.220638 | − | 0.975356i | \(-0.429186\pi\) | ||||
0.220638 | + | 0.975356i | \(0.429186\pi\) | |||||||
\(660\) | −0.00786945 | − | 0.0783475i | −0.000306318 | − | 0.00304967i | ||||
\(661\) | −15.9280 | −0.619529 | −0.309765 | − | 0.950813i | \(-0.600250\pi\) | ||||
−0.309765 | + | 0.950813i | \(0.600250\pi\) | |||||||
\(662\) | 2.10911i | 0.0819729i | ||||||||
\(663\) | − | 4.34894i | − | 0.168899i | ||||||
\(664\) | −0.908842 | −0.0352699 | ||||||||
\(665\) | −1.37710 | − | 13.7103i | −0.0534018 | − | 0.531663i | ||||
\(666\) | −0.758197 | −0.0293795 | ||||||||
\(667\) | − | 43.8396i | − | 1.69748i | ||||||
\(668\) | − | 0.714420i | − | 0.0276417i | ||||||
\(669\) | 15.7451 | 0.608742 | ||||||||
\(670\) | −16.7151 | + | 1.67891i | −0.645759 | + | 0.0648620i | ||||
\(671\) | 10.3786 | 0.400660 | ||||||||
\(672\) | 0.199179i | 0.00768351i | ||||||||
\(673\) | − | 16.8069i | − | 0.647859i | −0.946081 | − | 0.323929i | \(-0.894996\pi\) | ||
0.946081 | − | 0.323929i | \(-0.105004\pi\) | |||||||
\(674\) | 10.1795 | 0.392099 | ||||||||
\(675\) | −0.994397 | − | 4.90012i | −0.0382744 | − | 0.188606i | ||||
\(676\) | 0.414032 | 0.0159243 | ||||||||
\(677\) | 49.1818i | 1.89021i | 0.326768 | + | 0.945105i | \(0.394041\pi\) | ||||
−0.326768 | + | 0.945105i | \(0.605959\pi\) | |||||||
\(678\) | − | 3.20272i | − | 0.123000i | ||||||
\(679\) | −0.903942 | −0.0346901 | ||||||||
\(680\) | −24.7630 | + | 2.48727i | −0.949619 | + | 0.0953825i | ||||
\(681\) | −26.6766 | −1.02225 | ||||||||
\(682\) | − | 12.5492i | − | 0.480535i | ||||||
\(683\) | 4.52863i | 0.173283i | 0.996240 | + | 0.0866416i | \(0.0276135\pi\) | ||||
−0.996240 | + | 0.0866416i | \(0.972386\pi\) | |||||||
\(684\) | −0.217001 | −0.00829724 | ||||||||
\(685\) | 2.23886 | + | 22.2899i | 0.0855426 | + | 0.851653i | ||||
\(686\) | −1.40171 | −0.0535175 | ||||||||
\(687\) | − | 12.4550i | − | 0.475190i | ||||||
\(688\) | − | 37.2537i | − | 1.42028i | ||||||
\(689\) | −3.19250 | −0.121625 | ||||||||
\(690\) | −1.62950 | − | 16.2232i | −0.0620341 | − | 0.617606i | ||||
\(691\) | −27.8017 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(692\) | − | 0.0286303i | − | 0.00108836i | ||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | −17.0184 | −0.646008 | ||||||||
\(695\) | −11.4650 | + | 1.15157i | −0.434891 | + | 0.0436817i | ||||
\(696\) | −24.0415 | −0.911291 | ||||||||
\(697\) | 13.1371i | 0.497604i | ||||||||
\(698\) | 32.4118i | 1.22680i | ||||||||
\(699\) | −19.4102 | −0.734160 | ||||||||
\(700\) | 0.0350171 | + | 0.172555i | 0.00132352 | + | 0.00652195i | ||||
\(701\) | 14.7884 | 0.558551 | 0.279275 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279275 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(702\) | − | 1.56247i | − | 0.0589715i | ||||||
\(703\) | 3.33324i | 0.125715i | ||||||||
\(704\) | −8.13585 | −0.306632 | ||||||||
\(705\) | 6.76774 | − | 0.679772i | 0.254888 | − | 0.0256017i | ||||
\(706\) | 0.0454056 | 0.00170886 | ||||||||
\(707\) | − | 0.151109i | − | 0.00568305i | ||||||
\(708\) | 0.407100i | 0.0152997i | ||||||||
\(709\) | −17.0969 | −0.642088 | −0.321044 | − | 0.947064i | \(-0.604034\pi\) | ||||
−0.321044 | + | 0.947064i | \(0.604034\pi\) | |||||||
\(710\) | 3.52126 | + | 35.0573i | 0.132150 | + | 1.31568i | ||||
\(711\) | 0.575756 | 0.0215925 | ||||||||
\(712\) | 17.1904i | 0.644237i | ||||||||
\(713\) | 46.5728i | 1.74417i | ||||||||
\(714\) | −5.46876 | −0.204663 | ||||||||
\(715\) | −0.249102 | − | 2.48004i | −0.00931589 | − | 0.0927481i | ||||
\(716\) | 0.201399 | 0.00752664 | ||||||||
\(717\) | − | 15.8535i | − | 0.592061i | ||||||
\(718\) | 7.20840i | 0.269015i | ||||||||
\(719\) | −43.0029 | −1.60374 | −0.801869 | − | 0.597500i | \(-0.796161\pi\) | ||||
−0.801869 | + | 0.597500i | \(0.796161\pi\) | |||||||
\(720\) | −8.74004 | + | 0.877875i | −0.325722 | + | 0.0327165i | ||||
\(721\) | −16.1396 | −0.601069 | ||||||||
\(722\) | − | 26.5957i | − | 0.989789i | ||||||
\(723\) | 18.1106i | 0.673542i | ||||||||
\(724\) | −0.677515 | −0.0251796 | ||||||||
\(725\) | −41.2953 | + | 8.38019i | −1.53367 | + | 0.311232i | ||||
\(726\) | 1.40171 | 0.0520223 | ||||||||
\(727\) | − | 5.38547i | − | 0.199736i | −0.995001 | − | 0.0998680i | \(-0.968158\pi\) | ||
0.995001 | − | 0.0998680i | \(-0.0318420\pi\) | |||||||
\(728\) | 3.17995i | 0.117857i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 1.03912 | − | 0.104372i | 0.0384595 | − | 0.00386299i | ||||
\(731\) | −36.9992 | −1.36846 | ||||||||
\(732\) | 0.365475i | 0.0135083i | ||||||||
\(733\) | − | 5.19822i | − | 0.192001i | −0.995381 | − | 0.0960004i | \(-0.969395\pi\) | ||
0.995381 | − | 0.0960004i | \(-0.0306050\pi\) | |||||||
\(734\) | 36.3570 | 1.34196 | ||||||||
\(735\) | 0.223473 | + | 2.22487i | 0.00824292 | + | 0.0820657i | ||||
\(736\) | 1.03614 | 0.0381925 | ||||||||
\(737\) | 5.35976i | 0.197429i | ||||||||
\(738\) | 4.71984i | 0.173740i | ||||||||
\(739\) | 42.4649 | 1.56210 | 0.781048 | − | 0.624471i | \(-0.214686\pi\) | ||||
0.781048 | + | 0.624471i | \(0.214686\pi\) | |||||||
\(740\) | −0.00425666 | − | 0.0423789i | −0.000156478 | − | 0.00155788i | ||||
\(741\) | −6.86902 | −0.252340 | ||||||||
\(742\) | 4.01454i | 0.147379i | ||||||||
\(743\) | 35.8904i | 1.31669i | 0.752716 | + | 0.658346i | \(0.228743\pi\) | ||||
−0.752716 | + | 0.658346i | \(0.771257\pi\) | |||||||
\(744\) | 25.5404 | 0.936355 | ||||||||
\(745\) | −14.6818 | + | 1.47468i | −0.537898 | + | 0.0540280i | ||||
\(746\) | −37.0114 | −1.35508 | ||||||||
\(747\) | 0.318582i | 0.0116563i | ||||||||
\(748\) | 0.137389i | 0.00502343i | ||||||||
\(749\) | 7.81577 | 0.285582 | ||||||||
\(750\) | −14.9701 | + | 4.63608i | −0.546632 | + | 0.169286i | ||||
\(751\) | −10.6179 | −0.387453 | −0.193726 | − | 0.981056i | \(-0.562057\pi\) | ||||
−0.193726 | + | 0.981056i | \(0.562057\pi\) | |||||||
\(752\) | − | 11.9494i | − | 0.435750i | ||||||
\(753\) | − | 3.24386i | − | 0.118213i | ||||||
\(754\) | −13.1675 | −0.479533 | ||||||||
\(755\) | 10.5555 | − | 1.06022i | 0.384153 | − | 0.0385855i | ||||
\(756\) | 0.0352144 | 0.00128073 | ||||||||
\(757\) | − | 52.2844i | − | 1.90031i | −0.311779 | − | 0.950154i | \(-0.600925\pi\) | ||
0.311779 | − | 0.950154i | \(-0.399075\pi\) | |||||||
\(758\) | 11.1697i | 0.405701i | ||||||||
\(759\) | −5.20203 | −0.188822 | ||||||||
\(760\) | 3.92857 | + | 39.1124i | 0.142504 | + | 1.41876i | ||||
\(761\) | −3.51538 | −0.127433 | −0.0637163 | − | 0.997968i | \(-0.520295\pi\) | ||||
−0.0637163 | + | 0.997968i | \(0.520295\pi\) | |||||||
\(762\) | − | 7.25911i | − | 0.262970i | ||||||
\(763\) | − | 18.2292i | − | 0.659940i | ||||||
\(764\) | −0.436337 | −0.0157861 | ||||||||
\(765\) | 0.871878 | + | 8.68033i | 0.0315228 | + | 0.313838i | ||||
\(766\) | 0.0685270 | 0.00247598 | ||||||||
\(767\) | 12.8865i | 0.465303i | ||||||||
\(768\) | − | 0.844881i | − | 0.0304870i | ||||||
\(769\) | −0.982025 | −0.0354127 | −0.0177064 | − | 0.999843i | \(-0.505636\pi\) | ||||
−0.0177064 | + | 0.999843i | \(0.505636\pi\) | |||||||
\(770\) | −3.11862 | + | 0.313244i | −0.112387 | + | 0.0112885i | ||||
\(771\) | −23.6248 | −0.850826 | ||||||||
\(772\) | − | 0.569432i | − | 0.0204943i | ||||||
\(773\) | − | 20.2467i | − | 0.728224i | −0.931355 | − | 0.364112i | \(-0.881372\pi\) | ||
0.931355 | − | 0.364112i | \(-0.118628\pi\) | |||||||
\(774\) | −13.2929 | −0.477802 | ||||||||
\(775\) | 43.8699 | − | 8.90265i | 1.57585 | − | 0.319793i | ||||
\(776\) | 2.57874 | 0.0925715 | ||||||||
\(777\) | − | 0.540909i | − | 0.0194050i | ||||||
\(778\) | 18.0451i | 0.646949i | ||||||||
\(779\) | 20.7497 | 0.743434 | ||||||||
\(780\) | 0.0873329 | − | 0.00877198i | 0.00312702 | − | 0.000314087i | ||||
\(781\) | 11.2413 | 0.402244 | ||||||||
\(782\) | 28.4486i | 1.01732i | ||||||||
\(783\) | 8.42741i | 0.301171i | ||||||||
\(784\) | 3.92833 | 0.140298 | ||||||||
\(785\) | −2.53367 | − | 25.2250i | −0.0904305 | − | 0.900317i | ||||
\(786\) | −13.6314 | −0.486215 | ||||||||
\(787\) | 51.1899i | 1.82472i | 0.409385 | + | 0.912362i | \(0.365743\pi\) | ||||
−0.409385 | + | 0.912362i | \(0.634257\pi\) | |||||||
\(788\) | − | 0.591336i | − | 0.0210655i | ||||||
\(789\) | 3.88432 | 0.138285 | ||||||||
\(790\) | −0.180352 | − | 1.79557i | −0.00641663 | − | 0.0638834i | ||||
\(791\) | 2.28487 | 0.0812405 | ||||||||
\(792\) | 2.85278i | 0.101369i | ||||||||
\(793\) | 11.5689i | 0.410822i | ||||||||
\(794\) | 26.3497 | 0.935118 | ||||||||
\(795\) | 6.37212 | − | 0.640034i | 0.225996 | − | 0.0226997i | ||||
\(796\) | −0.851942 | −0.0301963 | ||||||||
\(797\) | − | 28.9089i | − | 1.02400i | −0.858984 | − | 0.512002i | \(-0.828904\pi\) | ||
0.858984 | − | 0.512002i | \(-0.171096\pi\) | |||||||
\(798\) | 8.63773i | 0.305772i | ||||||||
\(799\) | −11.8678 | −0.419852 | ||||||||
\(800\) | −0.198063 | − | 0.976002i | −0.00700260 | − | 0.0345069i | ||||
\(801\) | 6.02585 | 0.212913 | ||||||||
\(802\) | 36.5414i | 1.29032i | ||||||||
\(803\) | − | 0.333198i | − | 0.0117583i | ||||||
\(804\) | −0.188741 | −0.00665637 | ||||||||
\(805\) | 11.5739 | − | 1.16251i | 0.407925 | − | 0.0409732i | ||||
\(806\) | 13.9885 | 0.492723 | ||||||||
\(807\) | − | 0.573778i | − | 0.0201979i | ||||||
\(808\) | 0.431081i | 0.0151654i | ||||||||
\(809\) | −4.09282 | −0.143896 | −0.0719480 | − | 0.997408i | \(-0.522922\pi\) | ||||
−0.0719480 | + | 0.997408i | \(0.522922\pi\) | |||||||
\(810\) | 0.313244 | + | 3.11862i | 0.0110063 | + | 0.109577i | ||||
\(811\) | −34.4693 | −1.21038 | −0.605190 | − | 0.796081i | \(-0.706903\pi\) | ||||
−0.605190 | + | 0.796081i | \(0.706903\pi\) | |||||||
\(812\) | − | 0.296766i | − | 0.0104144i | ||||||
\(813\) | 24.9842i | 0.876235i | ||||||||
\(814\) | 0.758197 | 0.0265748 | ||||||||
\(815\) | 4.49051 | + | 44.7071i | 0.157296 | + | 1.56602i | ||||
\(816\) | 15.3264 | 0.536530 | ||||||||
\(817\) | 58.4391i | 2.04452i | ||||||||
\(818\) | 8.09285i | 0.282960i | ||||||||
\(819\) | 1.11469 | 0.0389503 | ||||||||
\(820\) | −0.263812 | + | 0.0264981i | −0.00921272 | + | 0.000925352i | ||||
\(821\) | −23.4118 | −0.817076 | −0.408538 | − | 0.912741i | \(-0.633961\pi\) | ||||
−0.408538 | + | 0.912741i | \(0.633961\pi\) | |||||||
\(822\) | − | 14.0430i | − | 0.489807i | ||||||
\(823\) | − | 7.79607i | − | 0.271754i | −0.990726 | − | 0.135877i | \(-0.956615\pi\) | ||
0.990726 | − | 0.135877i | \(-0.0433852\pi\) | |||||||
\(824\) | 46.0426 | 1.60397 | ||||||||
\(825\) | 0.994397 | + | 4.90012i | 0.0346205 | + | 0.170600i | ||||
\(826\) | 16.2046 | 0.563830 | ||||||||
\(827\) | 8.05371i | 0.280055i | 0.990148 | + | 0.140027i | \(0.0447191\pi\) | ||||
−0.990148 | + | 0.140027i | \(0.955281\pi\) | |||||||
\(828\) | − | 0.183186i | − | 0.00636616i | ||||||
\(829\) | 21.7570 | 0.755653 | 0.377827 | − | 0.925876i | \(-0.376672\pi\) | ||||
0.377827 | + | 0.925876i | \(0.376672\pi\) | |||||||
\(830\) | 0.993536 | − | 0.0997937i | 0.0344861 | − | 0.00346389i | ||||
\(831\) | 18.7064 | 0.648918 | ||||||||
\(832\) | − | 9.06893i | − | 0.314409i | ||||||
\(833\) | − | 3.90149i | − | 0.135179i | ||||||
\(834\) | 7.22312 | 0.250116 | ||||||||
\(835\) | 4.53376 | + | 45.1376i | 0.156897 | + | 1.56205i | ||||
\(836\) | 0.217001 | 0.00750514 | ||||||||
\(837\) | − | 8.95281i | − | 0.309454i | ||||||
\(838\) | − | 29.0299i | − | 1.00282i | ||||||
\(839\) | 24.1712 | 0.834481 | 0.417241 | − | 0.908796i | \(-0.362997\pi\) | ||||
0.417241 | + | 0.908796i | \(0.362997\pi\) | |||||||
\(840\) | −0.637518 | − | 6.34707i | −0.0219965 | − | 0.218995i | ||||
\(841\) | 42.0212 | 1.44901 | ||||||||
\(842\) | − | 30.9293i | − | 1.06590i | ||||||
\(843\) | 10.8364i | 0.373226i | ||||||||
\(844\) | −0.154224 | −0.00530860 | ||||||||
\(845\) | −26.1589 | + | 2.62748i | −0.899893 | + | 0.0903879i | ||||
\(846\) | −4.26379 | −0.146592 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | − | 11.2509i | − | 0.386357i | ||||||
\(849\) | −11.1910 | −0.384075 | ||||||||
\(850\) | 26.7976 | − | 5.43812i | 0.919149 | − | 0.186526i | ||||
\(851\) | −2.81383 | −0.0964568 | ||||||||
\(852\) | 0.395854i | 0.0135617i | ||||||||
\(853\) | − | 30.5632i | − | 1.04646i | −0.852191 | − | 0.523231i | \(-0.824726\pi\) | ||
0.852191 | − | 0.523231i | \(-0.175274\pi\) | |||||||
\(854\) | 14.5477 | 0.497813 | ||||||||
\(855\) | 13.7103 | − | 1.37710i | 0.468883 | − | 0.0470959i | ||||
\(856\) | −22.2966 | −0.762084 | ||||||||
\(857\) | − | 0.795673i | − | 0.0271797i | −0.999908 | − | 0.0135898i | \(-0.995674\pi\) | ||
0.999908 | − | 0.0135898i | \(-0.00432591\pi\) | |||||||
\(858\) | 1.56247i | 0.0533417i | ||||||||
\(859\) | −4.10327 | −0.140002 | −0.0700008 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0700008 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(860\) | −0.0746287 | − | 0.742996i | −0.00254482 | − | 0.0253360i | ||||
\(861\) | −3.36720 | −0.114754 | ||||||||
\(862\) | − | 7.11391i | − | 0.242301i | ||||||
\(863\) | 45.3489i | 1.54369i | 0.635808 | + | 0.771847i | \(0.280667\pi\) | ||||
−0.635808 | + | 0.771847i | \(0.719333\pi\) | |||||||
\(864\) | −0.199179 | −0.00677622 | ||||||||
\(865\) | 0.181690 | + | 1.80888i | 0.00617764 | + | 0.0615039i | ||||
\(866\) | −51.6179 | −1.75405 | ||||||||
\(867\) | 1.77835i | 0.0603958i | ||||||||
\(868\) | 0.315268i | 0.0107009i | ||||||||
\(869\) | −0.575756 | −0.0195312 | ||||||||
\(870\) | 26.2819 | − | 2.63983i | 0.891040 | − | 0.0894987i | ||||
\(871\) | −5.97445 | −0.202437 | ||||||||
\(872\) | 52.0037i | 1.76107i | ||||||||
\(873\) | − | 0.903942i | − | 0.0305938i | ||||||
\(874\) | 44.9337 | 1.51991 | ||||||||
\(875\) | −3.30745 | − | 10.6799i | −0.111812 | − | 0.361047i | ||||
\(876\) | 0.0117334 | 0.000396434 | ||||||||
\(877\) | 21.8578i | 0.738084i | 0.929413 | + | 0.369042i | \(0.120314\pi\) | ||||
−0.929413 | + | 0.369042i | \(0.879686\pi\) | |||||||
\(878\) | − | 31.5282i | − | 1.06402i | ||||||
\(879\) | −3.82893 | −0.129147 | ||||||||
\(880\) | 8.74004 | − | 0.877875i | 0.294627 | − | 0.0295932i | ||||
\(881\) | 17.3075 | 0.583105 | 0.291553 | − | 0.956555i | \(-0.405828\pi\) | ||||
0.291553 | + | 0.956555i | \(0.405828\pi\) | |||||||
\(882\) | − | 1.40171i | − | 0.0471980i | ||||||
\(883\) | − | 42.4935i | − | 1.43002i | −0.699115 | − | 0.715009i | \(-0.746422\pi\) | ||
0.699115 | − | 0.715009i | \(-0.253578\pi\) | |||||||
\(884\) | −0.153145 | −0.00515084 | ||||||||
\(885\) | −2.58348 | − | 25.7209i | −0.0868428 | − | 0.864598i | ||||
\(886\) | −14.8760 | −0.499770 | ||||||||
\(887\) | − | 20.4211i | − | 0.685673i | −0.939395 | − | 0.342837i | \(-0.888612\pi\) | ||
0.939395 | − | 0.342837i | \(-0.111388\pi\) | |||||||
\(888\) | 1.54309i | 0.0517828i | ||||||||
\(889\) | 5.17876 | 0.173690 | ||||||||
\(890\) | −1.88756 | − | 18.7923i | −0.0632711 | − | 0.629921i | ||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − | 0.554455i | − | 0.0185645i | ||||||
\(893\) | 18.7448i | 0.627270i | ||||||||
\(894\) | 9.24975 | 0.309358 | ||||||||
\(895\) | −12.7246 | + | 1.27809i | −0.425336 | + | 0.0427220i | ||||
\(896\) | −11.0057 | −0.367676 | ||||||||
\(897\) | − | 5.79864i | − | 0.193611i | ||||||
\(898\) | − | 30.4224i | − | 1.01521i | ||||||
\(899\) | −75.4490 | −2.51636 | ||||||||
\(900\) | −0.172555 | + | 0.0350171i | −0.00575182 | + | 0.00116724i | ||||
\(901\) | −11.1740 | −0.372261 | ||||||||
\(902\) | − | 4.71984i | − | 0.157153i | ||||||
\(903\) | − | 9.48334i | − | 0.315586i | ||||||
\(904\) | −6.51821 | −0.216793 | ||||||||
\(905\) | 42.8059 | − | 4.29955i | 1.42292 | − | 0.142922i | ||||
\(906\) | −6.65013 | −0.220936 | ||||||||
\(907\) | 31.1605i | 1.03467i | 0.855784 | + | 0.517334i | \(0.173075\pi\) | ||||
−0.855784 | + | 0.517334i | \(0.826925\pi\) | |||||||
\(908\) | 0.939400i | 0.0311751i | ||||||||
\(909\) | 0.151109 | 0.00501198 | ||||||||
\(910\) | −0.349169 | − | 3.47629i | −0.0115748 | − | 0.115238i | ||||
\(911\) | 35.4090 | 1.17315 | 0.586576 | − | 0.809894i | \(-0.300476\pi\) | ||||
0.586576 | + | 0.809894i | \(0.300476\pi\) | |||||||
\(912\) | − | 24.2075i | − | 0.801591i | ||||||
\(913\) | − | 0.318582i | − | 0.0105435i | ||||||
\(914\) | −26.3692 | −0.872217 | ||||||||
\(915\) | −2.31933 | − | 23.0910i | −0.0766746 | − | 0.763365i | ||||
\(916\) | −0.438597 | −0.0144916 | ||||||||
\(917\) | − | 9.72484i | − | 0.321142i | ||||||
\(918\) | − | 5.46876i | − | 0.180496i | ||||||
\(919\) | −3.15738 | −0.104153 | −0.0520763 | − | 0.998643i | \(-0.516584\pi\) | ||||
−0.0520763 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(920\) | −33.0176 | + | 3.31639i | −1.08856 | + | 0.109338i | ||||
\(921\) | 22.7405 | 0.749325 | ||||||||
\(922\) | − | 16.6313i | − | 0.547723i | ||||||
\(923\) | 12.5305i | 0.412446i | ||||||||
\(924\) | −0.0352144 | −0.00115847 | ||||||||
\(925\) | 0.537879 | + | 2.65052i | 0.0176853 | + | 0.0871486i | ||||
\(926\) | −29.9150 | −0.983069 | ||||||||
\(927\) | − | 16.1396i | − | 0.530093i | ||||||
\(928\) | 1.67856i | 0.0551016i | ||||||||
\(929\) | 23.3245 | 0.765253 | 0.382627 | − | 0.923903i | \(-0.375020\pi\) | ||||
0.382627 | + | 0.923903i | \(0.375020\pi\) | |||||||
\(930\) | −27.9204 | + | 2.80441i | −0.915547 | + | 0.0919603i | ||||
\(931\) | −6.16229 | −0.201961 | ||||||||
\(932\) | 0.683517i | 0.0223893i | ||||||||
\(933\) | 22.6476i | 0.741451i | ||||||||
\(934\) | −51.7416 | −1.69304 | ||||||||
\(935\) | −0.871878 | − | 8.68033i | −0.0285135 | − | 0.283877i | ||||
\(936\) | −3.17995 | −0.103940 | ||||||||
\(937\) | − | 20.7414i | − | 0.677594i | −0.940860 | − | 0.338797i | \(-0.889980\pi\) | ||
0.940860 | − | 0.338797i | \(-0.110020\pi\) | |||||||
\(938\) | 7.51282i | 0.245302i | ||||||||
\(939\) | −22.8832 | −0.746766 | ||||||||
\(940\) | −0.0239377 | − | 0.238322i | −0.000780763 | − | 0.00777320i | ||||
\(941\) | 19.2141 | 0.626361 | 0.313180 | − | 0.949694i | \(-0.398606\pi\) | ||||
0.313180 | + | 0.949694i | \(0.398606\pi\) | |||||||
\(942\) | 15.8922i | 0.517794i | ||||||||
\(943\) | 17.5163i | 0.570409i | ||||||||
\(944\) | −45.4139 | −1.47810 | ||||||||
\(945\) | −2.22487 | + | 0.223473i | −0.0723751 | + | 0.00726957i | ||||
\(946\) | 13.2929 | 0.432189 | ||||||||
\(947\) | − | 30.5000i | − | 0.991115i | −0.868575 | − | 0.495558i | \(-0.834964\pi\) | ||
0.868575 | − | 0.495558i | \(-0.165036\pi\) | |||||||
\(948\) | − | 0.0202749i | − | 0.000658498i | ||||||
\(949\) | 0.371412 | 0.0120565 | ||||||||
\(950\) | −8.58933 | − | 42.3259i | −0.278675 | − | 1.37323i | ||||
\(951\) | −28.2934 | −0.917476 | ||||||||
\(952\) | 11.1301i | 0.360728i | ||||||||
\(953\) | 12.0030i | 0.388814i | 0.980921 | + | 0.194407i | \(0.0622783\pi\) | ||||
−0.980921 | + | 0.194407i | \(0.937722\pi\) | |||||||
\(954\) | −4.01454 | −0.129976 | ||||||||
\(955\) | 27.5681 | − | 2.76902i | 0.892083 | − | 0.0896035i | ||||
\(956\) | −0.558272 | −0.0180558 | ||||||||
\(957\) | − | 8.42741i | − | 0.272419i | ||||||
\(958\) | 29.8802i | 0.965385i | ||||||||
\(959\) | 10.0185 | 0.323514 | ||||||||
\(960\) | 1.81814 | + | 18.1012i | 0.0586803 | + | 0.584215i | ||||
\(961\) | 49.1528 | 1.58558 | ||||||||
\(962\) | 0.845152i | 0.0272488i | ||||||||
\(963\) | 7.81577i | 0.251860i | ||||||||
\(964\) | 0.637755 | 0.0205407 | ||||||||
\(965\) | 3.61365 | + | 35.9772i | 0.116328 | + | 1.15815i | ||||
\(966\) | −7.29173 | −0.234608 | ||||||||
\(967\) | 61.6054i | 1.98110i | 0.137163 | + | 0.990549i | \(0.456202\pi\) | ||||
−0.137163 | + | 0.990549i | \(0.543798\pi\) | |||||||
\(968\) | − | 2.85278i | − | 0.0916917i | ||||||
\(969\) | −24.0421 | −0.772344 | ||||||||
\(970\) | −2.81905 | + | 0.283154i | −0.0905143 | + | 0.00909153i | ||||
\(971\) | 14.7208 | 0.472414 | 0.236207 | − | 0.971703i | \(-0.424096\pi\) | ||||
0.236207 | + | 0.971703i | \(0.424096\pi\) | |||||||
\(972\) | 0.0352144i | 0.00112950i | ||||||||
\(973\) | 5.15308i | 0.165200i | ||||||||
\(974\) | 57.0356 | 1.82754 | ||||||||
\(975\) | −5.46210 | + | 1.10844i | −0.174927 | + | 0.0354985i | ||||
\(976\) | −40.7705 | −1.30503 | ||||||||
\(977\) | 54.5153i | 1.74410i | 0.489418 | + | 0.872049i | \(0.337209\pi\) | ||||
−0.489418 | + | 0.872049i | \(0.662791\pi\) | |||||||
\(978\) | − | 28.1662i | − | 0.900656i | ||||||
\(979\) | −6.02585 | −0.192587 | ||||||||
\(980\) | 0.0783475 | − | 0.00786945i | 0.00250272 | − | 0.000251381i | ||||
\(981\) | 18.2292 | 0.582012 | ||||||||
\(982\) | − | 51.9048i | − | 1.65635i | ||||||
\(983\) | − | 5.98139i | − | 0.190777i | −0.995440 | − | 0.0953884i | \(-0.969591\pi\) | ||
0.995440 | − | 0.0953884i | \(-0.0304093\pi\) | |||||||
\(984\) | 9.60588 | 0.306224 | ||||||||
\(985\) | 3.75266 | + | 37.3611i | 0.119570 | + | 1.19042i | ||||
\(986\) | −46.0874 | −1.46772 | ||||||||
\(987\) | − | 3.04186i | − | 0.0968233i | ||||||
\(988\) | 0.241888i | 0.00769549i | ||||||||
\(989\) | −49.3326 | −1.56869 | ||||||||
\(990\) | −0.313244 | − | 3.11862i | −0.00995554 | − | 0.0991163i | ||||
\(991\) | −16.8699 | −0.535891 | −0.267945 | − | 0.963434i | \(-0.586345\pi\) | ||||
−0.267945 | + | 0.963434i | \(0.586345\pi\) | |||||||
\(992\) | − | 1.78321i | − | 0.0566171i | ||||||
\(993\) | − | 1.50467i | − | 0.0477493i | ||||||
\(994\) | 15.7570 | 0.499781 | ||||||||
\(995\) | 53.8264 | − | 5.40648i | 1.70641 | − | 0.171397i | ||||
\(996\) | 0.0112187 | 0.000355477 | ||||||||
\(997\) | 14.6712i | 0.464642i | 0.972639 | + | 0.232321i | \(0.0746320\pi\) | ||||
−0.972639 | + | 0.232321i | \(0.925368\pi\) | |||||||
\(998\) | 15.3229i | 0.485039i | ||||||||
\(999\) | 0.540909 | 0.0171136 |
(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 | 1155.2.c.f.694.6 | ✓ | 20 | |
5.2 | odd | 4 | 5775.2.a.co.1.7 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cn.1.4 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.f.694.15 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.f.694.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1155.2.c.f.694.15 | yes | 20 | 5.4 | even | 2 | inner | |
5775.2.a.cn.1.4 | 10 | 5.3 | odd | 4 | |||
5775.2.a.co.1.7 | 10 | 5.2 | odd | 4 |