Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,2,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.75");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (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: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14453810176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.2 | ||
Root | \(-1.06789 + 0.927153i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.2.d.a.75.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.06789 | + | 0.927153i | −0.755112 | + | 0.655596i | ||||
\(3\) | 1.19935 | 0.692447 | 0.346223 | − | 0.938152i | \(-0.387464\pi\) | ||||
0.346223 | + | 0.938152i | \(0.387464\pi\) | |||||||
\(4\) | 0.280776 | − | 1.98019i | 0.140388 | − | 0.990097i | ||||
\(5\) | 1.56155 | 0.698348 | 0.349174 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349174 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(6\) | −1.28078 | + | 1.11198i | −0.522875 | + | 0.453965i | ||||
\(7\) | 0.868210i | 0.328153i | 0.986448 | + | 0.164076i | \(0.0524643\pi\) | ||||
−0.986448 | + | 0.164076i | \(0.947536\pi\) | |||||||
\(8\) | 1.53610 | + | 2.37495i | 0.543094 | + | 0.839672i | ||||
\(9\) | −1.56155 | −0.520518 | ||||||||
\(10\) | −1.66757 | + | 1.44780i | −0.527331 | + | 0.457834i | ||||
\(11\) | 3.09218i | 0.932326i | 0.884699 | + | 0.466163i | \(0.154364\pi\) | ||||
−0.884699 | + | 0.466163i | \(0.845636\pi\) | |||||||
\(12\) | 0.336750 | − | 2.37495i | 0.0972113 | − | 0.685589i | ||||
\(13\) | − | 4.74990i | − | 1.31739i | −0.752412 | − | 0.658693i | \(-0.771110\pi\) | ||
0.752412 | − | 0.658693i | \(-0.228890\pi\) | |||||||
\(14\) | −0.804963 | − | 0.927153i | −0.215135 | − | 0.247792i | ||||
\(15\) | 1.87285 | 0.483569 | ||||||||
\(16\) | −3.84233 | − | 1.11198i | −0.960582 | − | 0.277996i | ||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 1.66757 | − | 1.44780i | 0.393049 | − | 0.341249i | ||||
\(19\) | −3.07221 | − | 3.09218i | −0.704812 | − | 0.709394i | ||||
\(20\) | 0.438447 | − | 3.09218i | 0.0980398 | − | 0.691432i | ||||
\(21\) | 1.04129i | 0.227228i | ||||||||
\(22\) | −2.86692 | − | 3.30210i | −0.611229 | − | 0.704011i | ||||
\(23\) | − | 3.96039i | − | 0.825798i | −0.910777 | − | 0.412899i | \(-0.864516\pi\) | ||
0.910777 | − | 0.412899i | \(-0.135484\pi\) | |||||||
\(24\) | 1.84233 | + | 2.84840i | 0.376064 | + | 0.581428i | ||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 4.40388 | + | 5.07237i | 0.863672 | + | 0.994773i | ||||
\(27\) | −5.47091 | −1.05288 | ||||||||
\(28\) | 1.71922 | + | 0.243773i | 0.324903 | + | 0.0460687i | ||||
\(29\) | 8.45851i | 1.57071i | 0.619048 | + | 0.785353i | \(0.287519\pi\) | ||||
−0.619048 | + | 0.785353i | \(0.712481\pi\) | |||||||
\(30\) | −2.00000 | + | 1.73642i | −0.365148 | + | 0.317025i | ||||
\(31\) | 4.27156 | 0.767195 | 0.383597 | − | 0.923500i | \(-0.374685\pi\) | ||||
0.383597 | + | 0.923500i | \(0.374685\pi\) | |||||||
\(32\) | 5.13416 | − | 2.37495i | 0.907600 | − | 0.419836i | ||||
\(33\) | 3.70861i | 0.645586i | ||||||||
\(34\) | 1.06789 | − | 0.927153i | 0.183142 | − | 0.159005i | ||||
\(35\) | 1.35576i | 0.229165i | ||||||||
\(36\) | −0.438447 | + | 3.09218i | −0.0730745 | + | 0.515363i | ||||
\(37\) | − | 3.70861i | − | 0.609692i | −0.952402 | − | 0.304846i | \(-0.901395\pi\) | ||
0.952402 | − | 0.304846i | \(-0.0986050\pi\) | |||||||
\(38\) | 6.14770 | + | 0.453700i | 0.997288 | + | 0.0735998i | ||||
\(39\) | − | 5.69681i | − | 0.912219i | ||||||
\(40\) | 2.39871 | + | 3.70861i | 0.379269 | + | 0.586383i | ||||
\(41\) | 3.70861i | 0.579188i | 0.957150 | + | 0.289594i | \(0.0935202\pi\) | ||||
−0.957150 | + | 0.289594i | \(0.906480\pi\) | |||||||
\(42\) | −0.965435 | − | 1.11198i | −0.148970 | − | 0.171583i | ||||
\(43\) | 11.0129i | 1.67946i | 0.543005 | + | 0.839729i | \(0.317286\pi\) | ||||
−0.543005 | + | 0.839729i | \(0.682714\pi\) | |||||||
\(44\) | 6.12311 | + | 0.868210i | 0.923093 | + | 0.130888i | ||||
\(45\) | −2.43845 | −0.363502 | ||||||||
\(46\) | 3.67188 | + | 4.22926i | 0.541389 | + | 0.623570i | ||||
\(47\) | − | 9.27653i | − | 1.35312i | −0.736387 | − | 0.676560i | \(-0.763470\pi\) | ||
0.736387 | − | 0.676560i | \(-0.236530\pi\) | |||||||
\(48\) | −4.60831 | − | 1.33366i | −0.665152 | − | 0.192497i | ||||
\(49\) | 6.24621 | 0.892316 | ||||||||
\(50\) | 2.73546 | − | 2.37495i | 0.386852 | − | 0.335869i | ||||
\(51\) | −1.19935 | −0.167943 | ||||||||
\(52\) | −9.40572 | − | 1.33366i | −1.30434 | − | 0.184945i | ||||
\(53\) | − | 1.04129i | − | 0.143032i | −0.997439 | − | 0.0715161i | \(-0.977216\pi\) | ||
0.997439 | − | 0.0715161i | \(-0.0227837\pi\) | |||||||
\(54\) | 5.84233 | − | 5.07237i | 0.795040 | − | 0.690262i | ||||
\(55\) | 4.82860i | 0.651088i | ||||||||
\(56\) | −2.06196 | + | 1.33366i | −0.275540 | + | 0.178218i | ||||
\(57\) | −3.68466 | − | 3.70861i | −0.488045 | − | 0.491217i | ||||
\(58\) | −7.84233 | − | 9.03276i | −1.02975 | − | 1.18606i | ||||
\(59\) | −11.6153 | −1.51219 | −0.756093 | − | 0.654464i | \(-0.772894\pi\) | ||||
−0.756093 | + | 0.654464i | \(0.772894\pi\) | |||||||
\(60\) | 0.525853 | − | 3.70861i | 0.0678873 | − | 0.478780i | ||||
\(61\) | −0.684658 | −0.0876615 | −0.0438308 | − | 0.999039i | \(-0.513956\pi\) | ||||
−0.0438308 | + | 0.999039i | \(0.513956\pi\) | |||||||
\(62\) | −4.56155 | + | 3.96039i | −0.579318 | + | 0.502970i | ||||
\(63\) | − | 1.35576i | − | 0.170809i | ||||||
\(64\) | −3.28078 | + | 7.29634i | −0.410097 | + | 0.912042i | ||||
\(65\) | − | 7.41722i | − | 0.919993i | ||||||
\(66\) | −3.43845 | − | 3.96039i | −0.423244 | − | 0.487490i | ||||
\(67\) | 9.74247 | 1.19023 | 0.595116 | − | 0.803640i | \(-0.297106\pi\) | ||||
0.595116 | + | 0.803640i | \(0.297106\pi\) | |||||||
\(68\) | −0.280776 | + | 1.98019i | −0.0340491 | + | 0.240134i | ||||
\(69\) | − | 4.74990i | − | 0.571821i | ||||||
\(70\) | −1.25699 | − | 1.44780i | −0.150239 | − | 0.173045i | ||||
\(71\) | 10.9418 | 1.29856 | 0.649278 | − | 0.760551i | \(-0.275071\pi\) | ||||
0.649278 | + | 0.760551i | \(0.275071\pi\) | |||||||
\(72\) | −2.39871 | − | 3.70861i | −0.282690 | − | 0.437064i | ||||
\(73\) | 8.12311 | 0.950738 | 0.475369 | − | 0.879787i | \(-0.342315\pi\) | ||||
0.475369 | + | 0.879787i | \(0.342315\pi\) | |||||||
\(74\) | 3.43845 | + | 3.96039i | 0.399711 | + | 0.460386i | ||||
\(75\) | −3.07221 | −0.354748 | ||||||||
\(76\) | −6.98571 | + | 5.21535i | −0.801316 | + | 0.598242i | ||||
\(77\) | −2.68466 | −0.305945 | ||||||||
\(78\) | 5.28181 | + | 6.08356i | 0.598047 | + | 0.688828i | ||||
\(79\) | 8.01726 | 0.902013 | 0.451006 | − | 0.892521i | \(-0.351065\pi\) | ||||
0.451006 | + | 0.892521i | \(0.351065\pi\) | |||||||
\(80\) | −6.00000 | − | 1.73642i | −0.670820 | − | 0.194138i | ||||
\(81\) | −1.87689 | −0.208544 | ||||||||
\(82\) | −3.43845 | − | 3.96039i | −0.379713 | − | 0.437351i | ||||
\(83\) | 9.65719i | 1.06001i | 0.847993 | + | 0.530007i | \(0.177811\pi\) | ||||
−0.847993 | + | 0.530007i | \(0.822189\pi\) | |||||||
\(84\) | 2.06196 | + | 0.292370i | 0.224978 | + | 0.0319002i | ||||
\(85\) | −1.56155 | −0.169374 | ||||||||
\(86\) | −10.2107 | − | 11.7606i | −1.10105 | − | 1.26818i | ||||
\(87\) | 10.1447i | 1.08763i | ||||||||
\(88\) | −7.34376 | + | 4.74990i | −0.782848 | + | 0.506341i | ||||
\(89\) | 5.79119i | 0.613865i | 0.951731 | + | 0.306932i | \(0.0993026\pi\) | ||||
−0.951731 | + | 0.306932i | \(0.900697\pi\) | |||||||
\(90\) | 2.60399 | − | 2.26081i | 0.274485 | − | 0.238311i | ||||
\(91\) | 4.12391 | 0.432303 | ||||||||
\(92\) | −7.84233 | − | 1.11198i | −0.817619 | − | 0.115932i | ||||
\(93\) | 5.12311 | 0.531241 | ||||||||
\(94\) | 8.60076 | + | 9.90631i | 0.887100 | + | 1.02176i | ||||
\(95\) | −4.79741 | − | 4.82860i | −0.492204 | − | 0.495404i | ||||
\(96\) | 6.15767 | − | 2.84840i | 0.628465 | − | 0.290714i | ||||
\(97\) | − | 16.9170i | − | 1.71766i | −0.512258 | − | 0.858832i | \(-0.671191\pi\) | ||
0.512258 | − | 0.858832i | \(-0.328809\pi\) | |||||||
\(98\) | −6.67026 | + | 5.79119i | −0.673798 | + | 0.584999i | ||||
\(99\) | − | 4.82860i | − | 0.485292i | ||||||
\(100\) | −0.719224 | + | 5.07237i | −0.0719224 | + | 0.507237i | ||||
\(101\) | 8.24621 | 0.820529 | 0.410264 | − | 0.911967i | \(-0.365436\pi\) | ||||
0.410264 | + | 0.911967i | \(0.365436\pi\) | |||||||
\(102\) | 1.28078 | − | 1.11198i | 0.126816 | − | 0.110103i | ||||
\(103\) | −3.74571 | −0.369075 | −0.184538 | − | 0.982825i | \(-0.559079\pi\) | ||||
−0.184538 | + | 0.982825i | \(0.559079\pi\) | |||||||
\(104\) | 11.2808 | − | 7.29634i | 1.10617 | − | 0.715465i | ||||
\(105\) | 1.62603i | 0.158684i | ||||||||
\(106\) | 0.965435 | + | 1.11198i | 0.0937713 | + | 0.108005i | ||||
\(107\) | −7.86962 | −0.760785 | −0.380392 | − | 0.924825i | \(-0.624211\pi\) | ||||
−0.380392 | + | 0.924825i | \(0.624211\pi\) | |||||||
\(108\) | −1.53610 | + | 10.8335i | −0.147812 | + | 1.04245i | ||||
\(109\) | 15.8757i | 1.52062i | 0.649561 | + | 0.760310i | \(0.274953\pi\) | ||||
−0.649561 | + | 0.760310i | \(0.725047\pi\) | |||||||
\(110\) | −4.47685 | − | 5.15641i | −0.426850 | − | 0.491644i | ||||
\(111\) | − | 4.44793i | − | 0.422179i | ||||||
\(112\) | 0.965435 | − | 3.33595i | 0.0912250 | − | 0.315218i | ||||
\(113\) | − | 3.70861i | − | 0.348877i | −0.984668 | − | 0.174438i | \(-0.944189\pi\) | ||
0.984668 | − | 0.174438i | \(-0.0558110\pi\) | |||||||
\(114\) | 7.37326 | + | 0.544146i | 0.690569 | + | 0.0509639i | ||||
\(115\) | − | 6.18435i | − | 0.576694i | ||||||
\(116\) | 16.7495 | + | 2.37495i | 1.55515 | + | 0.220509i | ||||
\(117\) | 7.41722i | 0.685722i | ||||||||
\(118\) | 12.4039 | − | 10.7692i | 1.14187 | − | 0.991383i | ||||
\(119\) | − | 0.868210i | − | 0.0795887i | ||||||
\(120\) | 2.87689 | + | 4.44793i | 0.262623 | + | 0.406039i | ||||
\(121\) | 1.43845 | 0.130768 | ||||||||
\(122\) | 0.731140 | − | 0.634783i | 0.0661943 | − | 0.0574705i | ||||
\(123\) | 4.44793i | 0.401057i | ||||||||
\(124\) | 1.19935 | − | 8.45851i | 0.107705 | − | 0.759597i | ||||
\(125\) | −11.8078 | −1.05612 | ||||||||
\(126\) | 1.25699 | + | 1.44780i | 0.111982 | + | 0.128980i | ||||
\(127\) | −1.87285 | −0.166189 | −0.0830944 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830944 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(128\) | −3.26131 | − | 10.8335i | −0.288262 | − | 0.957552i | ||||
\(129\) | 13.2084i | 1.16294i | ||||||||
\(130\) | 6.87689 | + | 7.92077i | 0.603144 | + | 0.694698i | ||||
\(131\) | − | 4.82860i | − | 0.421876i | −0.977499 | − | 0.210938i | \(-0.932348\pi\) | ||
0.977499 | − | 0.210938i | \(-0.0676519\pi\) | |||||||
\(132\) | 7.34376 | + | 1.04129i | 0.639193 | + | 0.0906327i | ||||
\(133\) | 2.68466 | − | 2.66732i | 0.232789 | − | 0.231286i | ||||
\(134\) | −10.4039 | + | 9.03276i | −0.898759 | + | 0.780311i | ||||
\(135\) | −8.54312 | −0.735274 | ||||||||
\(136\) | −1.53610 | − | 2.37495i | −0.131720 | − | 0.203650i | ||||
\(137\) | −3.87689 | −0.331225 | −0.165613 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165613 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(138\) | 4.40388 | + | 5.07237i | 0.374883 | + | 0.431789i | ||||
\(139\) | − | 0.380664i | − | 0.0322875i | −0.999870 | − | 0.0161438i | \(-0.994861\pi\) | ||
0.999870 | − | 0.0161438i | \(-0.00513894\pi\) | |||||||
\(140\) | 2.68466 | + | 0.380664i | 0.226895 | + | 0.0321720i | ||||
\(141\) | − | 11.1258i | − | 0.936964i | ||||||
\(142\) | −11.6847 | + | 10.1447i | −0.980555 | + | 0.851328i | ||||
\(143\) | 14.6875 | 1.22823 | ||||||||
\(144\) | 6.00000 | + | 1.73642i | 0.500000 | + | 0.144702i | ||||
\(145\) | 13.2084i | 1.09690i | ||||||||
\(146\) | −8.67458 | + | 7.53136i | −0.717913 | + | 0.623300i | ||||
\(147\) | 7.49141 | 0.617881 | ||||||||
\(148\) | −7.34376 | − | 1.04129i | −0.603654 | − | 0.0855935i | ||||
\(149\) | −17.8078 | −1.45887 | −0.729434 | − | 0.684051i | \(-0.760217\pi\) | ||||
−0.729434 | + | 0.684051i | \(0.760217\pi\) | |||||||
\(150\) | 3.28078 | − | 2.84840i | 0.267874 | − | 0.232571i | ||||
\(151\) | −24.2824 | −1.97607 | −0.988035 | − | 0.154231i | \(-0.950710\pi\) | ||||
−0.988035 | + | 0.154231i | \(0.950710\pi\) | |||||||
\(152\) | 2.62454 | − | 12.0462i | 0.212878 | − | 0.977079i | ||||
\(153\) | 1.56155 | 0.126244 | ||||||||
\(154\) | 2.86692 | − | 2.48909i | 0.231023 | − | 0.200576i | ||||
\(155\) | 6.67026 | 0.535769 | ||||||||
\(156\) | −11.2808 | − | 1.59953i | −0.903185 | − | 0.128065i | ||||
\(157\) | 6.00000 | 0.478852 | 0.239426 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239426 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(158\) | −8.56155 | + | 7.43323i | −0.681121 | + | 0.591356i | ||||
\(159\) | − | 1.24887i | − | 0.0990422i | ||||||
\(160\) | 8.01726 | − | 3.70861i | 0.633820 | − | 0.293191i | ||||
\(161\) | 3.43845 | 0.270988 | ||||||||
\(162\) | 2.00432 | − | 1.74017i | 0.157474 | − | 0.136720i | ||||
\(163\) | − | 10.6323i | − | 0.832785i | −0.909185 | − | 0.416392i | \(-0.863294\pi\) | ||
0.909185 | − | 0.416392i | \(-0.136706\pi\) | |||||||
\(164\) | 7.34376 | + | 1.04129i | 0.573452 | + | 0.0813111i | ||||
\(165\) | 5.79119i | 0.450844i | ||||||||
\(166\) | −8.95369 | − | 10.3128i | −0.694941 | − | 0.800430i | ||||
\(167\) | −0.525853 | −0.0406917 | −0.0203459 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203459 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(168\) | −2.47301 | + | 1.59953i | −0.190797 | + | 0.123406i | ||||
\(169\) | −9.56155 | −0.735504 | ||||||||
\(170\) | 1.66757 | − | 1.44780i | 0.127896 | − | 0.111041i | ||||
\(171\) | 4.79741 | + | 4.82860i | 0.366867 | + | 0.369252i | ||||
\(172\) | 21.8078 | + | 3.09218i | 1.66283 | + | 0.235776i | ||||
\(173\) | − | 16.9170i | − | 1.28618i | −0.765792 | − | 0.643089i | \(-0.777653\pi\) | ||
0.765792 | − | 0.643089i | \(-0.222347\pi\) | |||||||
\(174\) | −9.40572 | − | 10.8335i | −0.713046 | − | 0.821283i | ||||
\(175\) | − | 2.22397i | − | 0.168116i | ||||||
\(176\) | 3.43845 | − | 11.8812i | 0.259183 | − | 0.895576i | ||||
\(177\) | −13.9309 | −1.04711 | ||||||||
\(178\) | −5.36932 | − | 6.18435i | −0.402447 | − | 0.463537i | ||||
\(179\) | −9.06897 | −0.677847 | −0.338923 | − | 0.940814i | \(-0.610063\pi\) | ||||
−0.338923 | + | 0.940814i | \(0.610063\pi\) | |||||||
\(180\) | −0.684658 | + | 4.82860i | −0.0510314 | + | 0.359902i | ||||
\(181\) | − | 2.08258i | − | 0.154797i | −0.997000 | − | 0.0773985i | \(-0.975339\pi\) | ||
0.997000 | − | 0.0773985i | \(-0.0246614\pi\) | |||||||
\(182\) | −4.40388 | + | 3.82349i | −0.326437 | + | 0.283416i | ||||
\(183\) | −0.821147 | −0.0607009 | ||||||||
\(184\) | 9.40572 | − | 6.08356i | 0.693399 | − | 0.448486i | ||||
\(185\) | − | 5.79119i | − | 0.425777i | ||||||
\(186\) | −5.47091 | + | 4.74990i | −0.401147 | + | 0.348280i | ||||
\(187\) | − | 3.09218i | − | 0.226122i | ||||||
\(188\) | −18.3693 | − | 2.60463i | −1.33972 | − | 0.189962i | ||||
\(189\) | − | 4.74990i | − | 0.345504i | ||||||
\(190\) | 9.59995 | + | 0.708476i | 0.696454 | + | 0.0513982i | ||||
\(191\) | 8.78898i | 0.635948i | 0.948099 | + | 0.317974i | \(0.103003\pi\) | ||||
−0.948099 | + | 0.317974i | \(0.896997\pi\) | |||||||
\(192\) | −3.93481 | + | 8.75088i | −0.283970 | + | 0.631540i | ||||
\(193\) | 3.70861i | 0.266952i | 0.991052 | + | 0.133476i | \(0.0426138\pi\) | ||||
−0.991052 | + | 0.133476i | \(0.957386\pi\) | |||||||
\(194\) | 15.6847 | + | 18.0655i | 1.12609 | + | 1.29703i | ||||
\(195\) | − | 8.89586i | − | 0.637046i | ||||||
\(196\) | 1.75379 | − | 12.3687i | 0.125271 | − | 0.883479i | ||||
\(197\) | 10.4924 | 0.747554 | 0.373777 | − | 0.927519i | \(-0.378063\pi\) | ||||
0.373777 | + | 0.927519i | \(0.378063\pi\) | |||||||
\(198\) | 4.47685 | + | 5.15641i | 0.318156 | + | 0.366450i | ||||
\(199\) | 13.2369i | 0.938340i | 0.883108 | + | 0.469170i | \(0.155447\pi\) | ||||
−0.883108 | + | 0.469170i | \(0.844553\pi\) | |||||||
\(200\) | −3.93481 | − | 6.08356i | −0.278233 | − | 0.430173i | ||||
\(201\) | 11.6847 | 0.824172 | ||||||||
\(202\) | −8.80604 | + | 7.64550i | −0.619591 | + | 0.537935i | ||||
\(203\) | −7.34376 | −0.515431 | ||||||||
\(204\) | −0.336750 | + | 2.37495i | −0.0235772 | + | 0.166280i | ||||
\(205\) | 5.79119i | 0.404474i | ||||||||
\(206\) | 4.00000 | − | 3.47284i | 0.278693 | − | 0.241964i | ||||
\(207\) | 6.18435i | 0.429842i | ||||||||
\(208\) | −5.28181 | + | 18.2507i | −0.366228 | + | 1.26546i | ||||
\(209\) | 9.56155 | − | 9.49980i | 0.661386 | − | 0.657115i | ||||
\(210\) | −1.50758 | − | 1.73642i | −0.104033 | − | 0.119824i | ||||
\(211\) | 2.02050 | 0.139097 | 0.0695485 | − | 0.997579i | \(-0.477844\pi\) | ||||
0.0695485 | + | 0.997579i | \(0.477844\pi\) | |||||||
\(212\) | −2.06196 | − | 0.292370i | −0.141616 | − | 0.0200800i | ||||
\(213\) | 13.1231 | 0.899180 | ||||||||
\(214\) | 8.40388 | − | 7.29634i | 0.574478 | − | 0.498767i | ||||
\(215\) | 17.1973i | 1.17285i | ||||||||
\(216\) | −8.40388 | − | 12.9931i | −0.571812 | − | 0.884071i | ||||
\(217\) | 3.70861i | 0.251757i | ||||||||
\(218\) | −14.7192 | − | 16.9535i | −0.996912 | − | 1.14824i | ||||
\(219\) | 9.74247 | 0.658335 | ||||||||
\(220\) | 9.56155 | + | 1.35576i | 0.644640 | + | 0.0914050i | ||||
\(221\) | 4.74990i | 0.319513i | ||||||||
\(222\) | 4.12391 | + | 4.74990i | 0.276779 | + | 0.318792i | ||||
\(223\) | 16.2651 | 1.08919 | 0.544595 | − | 0.838699i | \(-0.316683\pi\) | ||||
0.544595 | + | 0.838699i | \(0.316683\pi\) | |||||||
\(224\) | 2.06196 | + | 4.45753i | 0.137770 | + | 0.297831i | ||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 3.43845 | + | 3.96039i | 0.228722 | + | 0.263441i | ||||
\(227\) | 17.4644 | 1.15916 | 0.579578 | − | 0.814917i | \(-0.303217\pi\) | ||||
0.579578 | + | 0.814917i | \(0.303217\pi\) | |||||||
\(228\) | −8.37833 | + | 6.25504i | −0.554868 | + | 0.414250i | ||||
\(229\) | −2.43845 | −0.161137 | −0.0805686 | − | 0.996749i | \(-0.525674\pi\) | ||||
−0.0805686 | + | 0.996749i | \(0.525674\pi\) | |||||||
\(230\) | 5.73384 | + | 6.60421i | 0.378078 | + | 0.435468i | ||||
\(231\) | −3.21985 | −0.211851 | ||||||||
\(232\) | −20.0885 | + | 12.9931i | −1.31888 | + | 0.853042i | ||||
\(233\) | −9.80776 | −0.642528 | −0.321264 | − | 0.946990i | \(-0.604108\pi\) | ||||
−0.321264 | + | 0.946990i | \(0.604108\pi\) | |||||||
\(234\) | −6.87689 | − | 7.92077i | −0.449557 | − | 0.517797i | ||||
\(235\) | − | 14.4858i | − | 0.944949i | ||||||
\(236\) | −3.26131 | + | 23.0006i | −0.212293 | + | 1.49721i | ||||
\(237\) | 9.61553 | 0.624596 | ||||||||
\(238\) | 0.804963 | + | 0.927153i | 0.0521780 | + | 0.0600984i | ||||
\(239\) | − | 19.4213i | − | 1.25626i | −0.778110 | − | 0.628129i | \(-0.783821\pi\) | ||
0.778110 | − | 0.628129i | \(-0.216179\pi\) | |||||||
\(240\) | −7.19612 | − | 2.08258i | −0.464507 | − | 0.134430i | ||||
\(241\) | − | 15.2910i | − | 0.984979i | −0.870318 | − | 0.492490i | \(-0.836087\pi\) | ||
0.870318 | − | 0.492490i | \(-0.163913\pi\) | |||||||
\(242\) | −1.53610 | + | 1.33366i | −0.0987444 | + | 0.0857309i | ||||
\(243\) | 14.1617 | 0.908472 | ||||||||
\(244\) | −0.192236 | + | 1.35576i | −0.0123066 | + | 0.0867934i | ||||
\(245\) | 9.75379 | 0.623147 | ||||||||
\(246\) | −4.12391 | − | 4.74990i | −0.262931 | − | 0.302843i | ||||
\(247\) | −14.6875 | + | 14.5927i | −0.934545 | + | 0.928509i | ||||
\(248\) | 6.56155 | + | 10.1447i | 0.416659 | + | 0.644192i | ||||
\(249\) | 11.5824i | 0.734004i | ||||||||
\(250\) | 12.6094 | − | 10.9476i | 0.797488 | − | 0.692387i | ||||
\(251\) | 22.4066i | 1.41429i | 0.707069 | + | 0.707145i | \(0.250017\pi\) | ||||
−0.707069 | + | 0.707145i | \(0.749983\pi\) | |||||||
\(252\) | −2.68466 | − | 0.380664i | −0.169118 | − | 0.0239796i | ||||
\(253\) | 12.2462 | 0.769913 | ||||||||
\(254\) | 2.00000 | − | 1.73642i | 0.125491 | − | 0.108953i | ||||
\(255\) | −1.87285 | −0.117283 | ||||||||
\(256\) | 13.5270 | + | 8.54521i | 0.845437 | + | 0.534076i | ||||
\(257\) | 18.9996i | 1.18516i | 0.805511 | + | 0.592581i | \(0.201891\pi\) | ||||
−0.805511 | + | 0.592581i | \(0.798109\pi\) | |||||||
\(258\) | −12.2462 | − | 14.1051i | −0.762416 | − | 0.878147i | ||||
\(259\) | 3.21985 | 0.200072 | ||||||||
\(260\) | −14.6875 | − | 2.08258i | −0.910882 | − | 0.129156i | ||||
\(261\) | − | 13.2084i | − | 0.817580i | ||||||
\(262\) | 4.47685 | + | 5.15641i | 0.276580 | + | 0.318564i | ||||
\(263\) | 6.56502i | 0.404816i | 0.979301 | + | 0.202408i | \(0.0648768\pi\) | ||||
−0.979301 | + | 0.202408i | \(0.935123\pi\) | |||||||
\(264\) | −8.80776 | + | 5.69681i | −0.542080 | + | 0.350614i | ||||
\(265\) | − | 1.62603i | − | 0.0998862i | ||||||
\(266\) | −0.393906 | + | 5.33749i | −0.0241520 | + | 0.327263i | ||||
\(267\) | 6.94568i | 0.425069i | ||||||||
\(268\) | 2.73546 | − | 19.2920i | 0.167095 | − | 1.17844i | ||||
\(269\) | 3.70861i | 0.226118i | 0.993588 | + | 0.113059i | \(0.0360649\pi\) | ||||
−0.993588 | + | 0.113059i | \(0.963935\pi\) | |||||||
\(270\) | 9.12311 | − | 7.92077i | 0.555215 | − | 0.482043i | ||||
\(271\) | − | 15.3540i | − | 0.932689i | −0.884603 | − | 0.466345i | \(-0.845571\pi\) | ||
0.884603 | − | 0.466345i | \(-0.154429\pi\) | |||||||
\(272\) | 3.84233 | + | 1.11198i | 0.232975 | + | 0.0674239i | ||||
\(273\) | 4.94602 | 0.299347 | ||||||||
\(274\) | 4.14010 | − | 3.59447i | 0.250112 | − | 0.217150i | ||||
\(275\) | − | 7.92077i | − | 0.477641i | ||||||
\(276\) | −9.40572 | − | 1.33366i | −0.566158 | − | 0.0802769i | ||||
\(277\) | −24.0540 | −1.44526 | −0.722632 | − | 0.691233i | \(-0.757068\pi\) | ||||
−0.722632 | + | 0.691233i | \(0.757068\pi\) | |||||||
\(278\) | 0.352934 | + | 0.406507i | 0.0211676 | + | 0.0243807i | ||||
\(279\) | −6.67026 | −0.399338 | ||||||||
\(280\) | −3.21985 | + | 2.08258i | −0.192423 | + | 0.124458i | ||||
\(281\) | − | 11.5824i | − | 0.690947i | −0.938429 | − | 0.345473i | \(-0.887718\pi\) | ||
0.938429 | − | 0.345473i | \(-0.112282\pi\) | |||||||
\(282\) | 10.3153 | + | 11.8812i | 0.614270 | + | 0.707513i | ||||
\(283\) | − | 4.82860i | − | 0.287030i | −0.989648 | − | 0.143515i | \(-0.954159\pi\) | ||
0.989648 | − | 0.143515i | \(-0.0458406\pi\) | |||||||
\(284\) | 3.07221 | − | 21.6669i | 0.182302 | − | 1.28570i | ||||
\(285\) | −5.75379 | − | 5.79119i | −0.340825 | − | 0.343041i | ||||
\(286\) | −15.6847 | + | 13.6176i | −0.927453 | + | 0.805224i | ||||
\(287\) | −3.21985 | −0.190062 | ||||||||
\(288\) | −8.01726 | + | 3.70861i | −0.472422 | + | 0.218532i | ||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −12.2462 | − | 14.1051i | −0.719122 | − | 0.828281i | ||||
\(291\) | − | 20.2895i | − | 1.18939i | ||||||
\(292\) | 2.28078 | − | 16.0853i | 0.133472 | − | 0.941322i | ||||
\(293\) | 4.74990i | 0.277492i | 0.990328 | + | 0.138746i | \(0.0443072\pi\) | ||||
−0.990328 | + | 0.138746i | \(0.955693\pi\) | |||||||
\(294\) | −8.00000 | + | 6.94568i | −0.466569 | + | 0.405080i | ||||
\(295\) | −18.1379 | −1.05603 | ||||||||
\(296\) | 8.80776 | − | 5.69681i | 0.511941 | − | 0.331120i | ||||
\(297\) | − | 16.9170i | − | 0.981625i | ||||||
\(298\) | 19.0167 | − | 16.5105i | 1.10161 | − | 0.956428i | ||||
\(299\) | −18.8114 | −1.08789 | ||||||||
\(300\) | −0.862603 | + | 6.08356i | −0.0498024 | + | 0.351235i | ||||
\(301\) | −9.56155 | −0.551119 | ||||||||
\(302\) | 25.9309 | − | 22.5134i | 1.49215 | − | 1.29550i | ||||
\(303\) | 9.89012 | 0.568172 | ||||||||
\(304\) | 8.36598 | + | 15.2974i | 0.479822 | + | 0.877366i | ||||
\(305\) | −1.06913 | −0.0612182 | ||||||||
\(306\) | −1.66757 | + | 1.44780i | −0.0953284 | + | 0.0827651i | ||||
\(307\) | 8.01726 | 0.457569 | 0.228785 | − | 0.973477i | \(-0.426525\pi\) | ||||
0.228785 | + | 0.973477i | \(0.426525\pi\) | |||||||
\(308\) | −0.753789 | + | 5.31614i | −0.0429511 | + | 0.302915i | ||||
\(309\) | −4.49242 | −0.255565 | ||||||||
\(310\) | −7.12311 | + | 6.18435i | −0.404565 | + | 0.351248i | ||||
\(311\) | 0.868210i | 0.0492317i | 0.999697 | + | 0.0246158i | \(0.00783626\pi\) | ||||
−0.999697 | + | 0.0246158i | \(0.992164\pi\) | |||||||
\(312\) | 13.5296 | − | 8.75088i | 0.765965 | − | 0.495421i | ||||
\(313\) | −4.56155 | −0.257834 | −0.128917 | − | 0.991655i | \(-0.541150\pi\) | ||||
−0.128917 | + | 0.991655i | \(0.541150\pi\) | |||||||
\(314\) | −6.40734 | + | 5.56292i | −0.361587 | + | 0.313933i | ||||
\(315\) | − | 2.11708i | − | 0.119284i | ||||||
\(316\) | 2.25106 | − | 15.8757i | 0.126632 | − | 0.893080i | ||||
\(317\) | − | 4.74990i | − | 0.266781i | −0.991064 | − | 0.133390i | \(-0.957414\pi\) | ||
0.991064 | − | 0.133390i | \(-0.0425864\pi\) | |||||||
\(318\) | 1.15790 | + | 1.33366i | 0.0649316 | + | 0.0747879i | ||||
\(319\) | −26.1552 | −1.46441 | ||||||||
\(320\) | −5.12311 | + | 11.3936i | −0.286390 | + | 0.636922i | ||||
\(321\) | −9.43845 | −0.526803 | ||||||||
\(322\) | −3.67188 | + | 3.18796i | −0.204626 | + | 0.177658i | ||||
\(323\) | 3.07221 | + | 3.09218i | 0.170942 | + | 0.172053i | ||||
\(324\) | −0.526988 | + | 3.71661i | −0.0292771 | + | 0.206479i | ||||
\(325\) | 12.1671i | 0.674910i | ||||||||
\(326\) | 9.85775 | + | 11.3541i | 0.545970 | + | 0.628846i | ||||
\(327\) | 19.0406i | 1.05295i | ||||||||
\(328\) | −8.80776 | + | 5.69681i | −0.486327 | + | 0.314554i | ||||
\(329\) | 8.05398 | 0.444030 | ||||||||
\(330\) | −5.36932 | − | 6.18435i | −0.295571 | − | 0.340437i | ||||
\(331\) | −2.25106 | −0.123729 | −0.0618647 | − | 0.998085i | \(-0.519705\pi\) | ||||
−0.0618647 | + | 0.998085i | \(0.519705\pi\) | |||||||
\(332\) | 19.1231 | + | 2.71151i | 1.04952 | + | 0.148814i | ||||
\(333\) | 5.79119i | 0.317355i | ||||||||
\(334\) | 0.561553 | − | 0.487546i | 0.0307268 | − | 0.0266773i | ||||
\(335\) | 15.2134 | 0.831196 | ||||||||
\(336\) | 1.15790 | − | 4.00098i | 0.0631685 | − | 0.218271i | ||||
\(337\) | 26.4168i | 1.43902i | 0.694484 | + | 0.719508i | \(0.255633\pi\) | ||||
−0.694484 | + | 0.719508i | \(0.744367\pi\) | |||||||
\(338\) | 10.2107 | − | 8.86502i | 0.555388 | − | 0.482193i | ||||
\(339\) | − | 4.44793i | − | 0.241579i | ||||||
\(340\) | −0.438447 | + | 3.09218i | −0.0237781 | + | 0.167697i | ||||
\(341\) | 13.2084i | 0.715276i | ||||||||
\(342\) | −9.59995 | − | 0.708476i | −0.519106 | − | 0.0383100i | ||||
\(343\) | 11.5005i | 0.620968i | ||||||||
\(344\) | −26.1552 | + | 16.9170i | −1.41019 | + | 0.912105i | ||||
\(345\) | − | 7.41722i | − | 0.399330i | ||||||
\(346\) | 15.6847 | + | 18.0655i | 0.843212 | + | 0.971208i | ||||
\(347\) | − | 24.1430i | − | 1.29606i | −0.761613 | − | 0.648032i | \(-0.775592\pi\) | ||
0.761613 | − | 0.648032i | \(-0.224408\pi\) | |||||||
\(348\) | 20.0885 | + | 2.84840i | 1.07686 | + | 0.152690i | ||||
\(349\) | −28.0540 | −1.50169 | −0.750847 | − | 0.660476i | \(-0.770355\pi\) | ||||
−0.750847 | + | 0.660476i | \(0.770355\pi\) | |||||||
\(350\) | 2.06196 | + | 2.37495i | 0.110216 | + | 0.126946i | ||||
\(351\) | 25.9863i | 1.38705i | ||||||||
\(352\) | 7.34376 | + | 15.8757i | 0.391424 | + | 0.846179i | ||||
\(353\) | 6.31534 | 0.336132 | 0.168066 | − | 0.985776i | \(-0.446248\pi\) | ||||
0.168066 | + | 0.985776i | \(0.446248\pi\) | |||||||
\(354\) | 14.8766 | − | 12.9160i | 0.790684 | − | 0.686480i | ||||
\(355\) | 17.0862 | 0.906843 | ||||||||
\(356\) | 11.4677 | + | 1.62603i | 0.607786 | + | 0.0861794i | ||||
\(357\) | − | 1.04129i | − | 0.0551109i | ||||||
\(358\) | 9.68466 | − | 8.40832i | 0.511850 | − | 0.444393i | ||||
\(359\) | − | 27.3420i | − | 1.44306i | −0.692384 | − | 0.721529i | \(-0.743440\pi\) | ||
0.692384 | − | 0.721529i | \(-0.256560\pi\) | |||||||
\(360\) | −3.74571 | − | 5.79119i | −0.197416 | − | 0.305223i | ||||
\(361\) | −0.123106 | + | 18.9996i | −0.00647924 | + | 0.999979i | ||||
\(362\) | 1.93087 | + | 2.22397i | 0.101484 | + | 0.116889i | ||||
\(363\) | 1.72521 | 0.0905498 | ||||||||
\(364\) | 1.15790 | − | 8.16614i | 0.0606903 | − | 0.428022i | ||||
\(365\) | 12.6847 | 0.663945 | ||||||||
\(366\) | 0.876894 | − | 0.761329i | 0.0458360 | − | 0.0397953i | ||||
\(367\) | − | 14.1051i | − | 0.736282i | −0.929770 | − | 0.368141i | \(-0.879994\pi\) | ||
0.929770 | − | 0.368141i | \(-0.120006\pi\) | |||||||
\(368\) | −4.40388 | + | 15.2171i | −0.229568 | + | 0.793247i | ||||
\(369\) | − | 5.79119i | − | 0.301477i | ||||||
\(370\) | 5.36932 | + | 6.18435i | 0.279137 | + | 0.321509i | ||||
\(371\) | 0.904059 | 0.0469364 | ||||||||
\(372\) | 1.43845 | − | 10.1447i | 0.0745800 | − | 0.525980i | ||||
\(373\) | 12.1671i | 0.629990i | 0.949093 | + | 0.314995i | \(0.102003\pi\) | ||||
−0.949093 | + | 0.314995i | \(0.897997\pi\) | |||||||
\(374\) | 2.86692 | + | 3.30210i | 0.148245 | + | 0.170748i | ||||
\(375\) | −14.1617 | −0.731306 | ||||||||
\(376\) | 22.0313 | − | 14.2497i | 1.13618 | − | 0.734872i | ||||
\(377\) | 40.1771 | 2.06922 | ||||||||
\(378\) | 4.40388 | + | 5.07237i | 0.226511 | + | 0.260895i | ||||
\(379\) | −6.81791 | −0.350213 | −0.175106 | − | 0.984550i | \(-0.556027\pi\) | ||||
−0.175106 | + | 0.984550i | \(0.556027\pi\) | |||||||
\(380\) | −10.9086 | + | 8.14404i | −0.559597 | + | 0.417781i | ||||
\(381\) | −2.24621 | −0.115077 | ||||||||
\(382\) | −8.14873 | − | 9.38566i | −0.416925 | − | 0.480212i | ||||
\(383\) | −16.2651 | −0.831107 | −0.415554 | − | 0.909569i | \(-0.636412\pi\) | ||||
−0.415554 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(384\) | −3.91146 | − | 12.9931i | −0.199606 | − | 0.663053i | ||||
\(385\) | −4.19224 | −0.213656 | ||||||||
\(386\) | −3.43845 | − | 3.96039i | −0.175012 | − | 0.201578i | ||||
\(387\) | − | 17.1973i | − | 0.874188i | ||||||
\(388\) | −33.4990 | − | 4.74990i | −1.70065 | − | 0.241140i | ||||
\(389\) | −5.80776 | −0.294465 | −0.147233 | − | 0.989102i | \(-0.547037\pi\) | ||||
−0.147233 | + | 0.989102i | \(0.547037\pi\) | |||||||
\(390\) | 8.24782 | + | 9.49980i | 0.417645 | + | 0.481041i | ||||
\(391\) | 3.96039i | 0.200285i | ||||||||
\(392\) | 9.59482 | + | 14.8344i | 0.484612 | + | 0.749252i | ||||
\(393\) | − | 5.79119i | − | 0.292127i | ||||||
\(394\) | −11.2047 | + | 9.72808i | −0.564487 | + | 0.490093i | ||||
\(395\) | 12.5194 | 0.629918 | ||||||||
\(396\) | −9.56155 | − | 1.35576i | −0.480486 | − | 0.0681293i | ||||
\(397\) | 24.9309 | 1.25124 | 0.625622 | − | 0.780126i | \(-0.284845\pi\) | ||||
0.625622 | + | 0.780126i | \(0.284845\pi\) | |||||||
\(398\) | −12.2726 | − | 14.1356i | −0.615172 | − | 0.708552i | ||||
\(399\) | 3.21985 | − | 3.19906i | 0.161194 | − | 0.160153i | ||||
\(400\) | 9.84233 | + | 2.84840i | 0.492116 | + | 0.142420i | ||||
\(401\) | 20.6256i | 1.02999i | 0.857192 | + | 0.514997i | \(0.172207\pi\) | ||||
−0.857192 | + | 0.514997i | \(0.827793\pi\) | |||||||
\(402\) | −12.4779 | + | 10.8335i | −0.622342 | + | 0.540324i | ||||
\(403\) | − | 20.2895i | − | 1.01069i | ||||||
\(404\) | 2.31534 | − | 16.3291i | 0.115193 | − | 0.812403i | ||||
\(405\) | −2.93087 | −0.145636 | ||||||||
\(406\) | 7.84233 | − | 6.80879i | 0.389208 | − | 0.337915i | ||||
\(407\) | 11.4677 | 0.568432 | ||||||||
\(408\) | −1.84233 | − | 2.84840i | −0.0912089 | − | 0.141017i | ||||
\(409\) | − | 18.5431i | − | 0.916895i | −0.888722 | − | 0.458447i | \(-0.848406\pi\) | ||
0.888722 | − | 0.458447i | \(-0.151594\pi\) | |||||||
\(410\) | −5.36932 | − | 6.18435i | −0.265172 | − | 0.305423i | ||||
\(411\) | −4.64976 | −0.229356 | ||||||||
\(412\) | −1.05171 | + | 7.41722i | −0.0518138 | + | 0.365420i | ||||
\(413\) | − | 10.0845i | − | 0.496228i | ||||||
\(414\) | −5.73384 | − | 6.60421i | −0.281803 | − | 0.324579i | ||||
\(415\) | 15.0802i | 0.740259i | ||||||||
\(416\) | −11.2808 | − | 24.3868i | −0.553086 | − | 1.19566i | ||||
\(417\) | − | 0.456551i | − | 0.0223574i | ||||||
\(418\) | −1.40292 | + | 19.0098i | −0.0686190 | + | 0.929798i | ||||
\(419\) | 27.4489i | 1.34097i | 0.741924 | + | 0.670484i | \(0.233913\pi\) | ||||
−0.741924 | + | 0.670484i | \(0.766087\pi\) | |||||||
\(420\) | 3.21985 | + | 0.456551i | 0.157113 | + | 0.0222774i | ||||
\(421\) | − | 23.2930i | − | 1.13523i | −0.823294 | − | 0.567614i | \(-0.807866\pi\) | ||
0.823294 | − | 0.567614i | \(-0.192134\pi\) | |||||||
\(422\) | −2.15767 | + | 1.87331i | −0.105034 | + | 0.0911914i | ||||
\(423\) | 14.4858i | 0.704323i | ||||||||
\(424\) | 2.47301 | − | 1.59953i | 0.120100 | − | 0.0776800i | ||||
\(425\) | 2.56155 | 0.124254 | ||||||||
\(426\) | −14.0140 | + | 12.1671i | −0.678982 | + | 0.589499i | ||||
\(427\) | − | 0.594427i | − | 0.0287664i | ||||||
\(428\) | −2.20960 | + | 15.5834i | −0.106805 | + | 0.753250i | ||||
\(429\) | 17.6155 | 0.850486 | ||||||||
\(430\) | −15.9445 | − | 18.3648i | −0.768913 | − | 0.885630i | ||||
\(431\) | 17.0862 | 0.823015 | 0.411507 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411507 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(432\) | 21.0210 | + | 6.08356i | 1.01138 | + | 0.292695i | ||||
\(433\) | − | 28.0429i | − | 1.34765i | −0.738889 | − | 0.673827i | \(-0.764649\pi\) | ||
0.738889 | − | 0.673827i | \(-0.235351\pi\) | |||||||
\(434\) | −3.43845 | − | 3.96039i | −0.165051 | − | 0.190105i | ||||
\(435\) | 15.8415i | 0.759544i | ||||||||
\(436\) | 31.4370 | + | 4.45753i | 1.50556 | + | 0.213477i | ||||
\(437\) | −12.2462 | + | 12.1671i | −0.585816 | + | 0.582032i | ||||
\(438\) | −10.4039 | + | 9.03276i | −0.497117 | + | 0.431602i | ||||
\(439\) | 24.8082 | 1.18403 | 0.592015 | − | 0.805927i | \(-0.298332\pi\) | ||||
0.592015 | + | 0.805927i | \(0.298332\pi\) | |||||||
\(440\) | −11.4677 | + | 7.41722i | −0.546700 | + | 0.353602i | ||||
\(441\) | −9.75379 | −0.464466 | ||||||||
\(442\) | −4.40388 | − | 5.07237i | −0.209471 | − | 0.241268i | ||||
\(443\) | 34.7753i | 1.65222i | 0.563507 | + | 0.826111i | \(0.309452\pi\) | ||||
−0.563507 | + | 0.826111i | \(0.690548\pi\) | |||||||
\(444\) | −8.80776 | − | 1.24887i | −0.417998 | − | 0.0592690i | ||||
\(445\) | 9.04325i | 0.428691i | ||||||||
\(446\) | −17.3693 | + | 15.0802i | −0.822461 | + | 0.714069i | ||||
\(447\) | −21.3578 | −1.01019 | ||||||||
\(448\) | −6.33475 | − | 2.84840i | −0.299289 | − | 0.134574i | ||||
\(449\) | − | 35.9166i | − | 1.69501i | −0.530787 | − | 0.847505i | \(-0.678104\pi\) | ||
0.530787 | − | 0.847505i | \(-0.321896\pi\) | |||||||
\(450\) | −4.27156 | + | 3.70861i | −0.201363 | + | 0.174826i | ||||
\(451\) | −11.4677 | −0.539992 | ||||||||
\(452\) | −7.34376 | − | 1.04129i | −0.345422 | − | 0.0489782i | ||||
\(453\) | −29.1231 | −1.36832 | ||||||||
\(454\) | −18.6501 | + | 16.1922i | −0.875292 | + | 0.759938i | ||||
\(455\) | 6.43971 | 0.301898 | ||||||||
\(456\) | 3.14775 | − | 14.4477i | 0.147407 | − | 0.676575i | ||||
\(457\) | 12.1231 | 0.567095 | 0.283547 | − | 0.958958i | \(-0.408489\pi\) | ||||
0.283547 | + | 0.958958i | \(0.408489\pi\) | |||||||
\(458\) | 2.60399 | − | 2.26081i | 0.121677 | − | 0.105641i | ||||
\(459\) | 5.47091 | 0.255360 | ||||||||
\(460\) | −12.2462 | − | 1.73642i | −0.570983 | − | 0.0809610i | ||||
\(461\) | 19.3153 | 0.899605 | 0.449803 | − | 0.893128i | \(-0.351494\pi\) | ||||
0.449803 | + | 0.893128i | \(0.351494\pi\) | |||||||
\(462\) | 3.43845 | − | 2.98529i | 0.159971 | − | 0.138888i | ||||
\(463\) | − | 21.6452i | − | 1.00594i | −0.864304 | − | 0.502970i | \(-0.832241\pi\) | ||
0.864304 | − | 0.502970i | \(-0.167759\pi\) | |||||||
\(464\) | 9.40572 | − | 32.5004i | 0.436650 | − | 1.50879i | ||||
\(465\) | 8.00000 | 0.370991 | ||||||||
\(466\) | 10.4736 | − | 9.09329i | 0.485181 | − | 0.421239i | ||||
\(467\) | 3.09218i | 0.143089i | 0.997437 | + | 0.0715444i | \(0.0227928\pi\) | ||||
−0.997437 | + | 0.0715444i | \(0.977207\pi\) | |||||||
\(468\) | 14.6875 | + | 2.08258i | 0.678931 | + | 0.0962673i | ||||
\(469\) | 8.45851i | 0.390578i | ||||||||
\(470\) | 13.4305 | + | 15.4692i | 0.619504 | + | 0.713542i | ||||
\(471\) | 7.19612 | 0.331580 | ||||||||
\(472\) | −17.8423 | − | 27.5858i | −0.821260 | − | 1.26974i | ||||
\(473\) | −34.0540 | −1.56580 | ||||||||
\(474\) | −10.2683 | + | 8.91506i | −0.471640 | + | 0.409482i | ||||
\(475\) | 7.86962 | + | 7.92077i | 0.361083 | + | 0.363430i | ||||
\(476\) | −1.71922 | − | 0.243773i | −0.0788005 | − | 0.0111733i | ||||
\(477\) | 1.62603i | 0.0744508i | ||||||||
\(478\) | 18.0065 | + | 20.7398i | 0.823597 | + | 0.948615i | ||||
\(479\) | 8.68210i | 0.396695i | 0.980132 | + | 0.198348i | \(0.0635575\pi\) | ||||
−0.980132 | + | 0.198348i | \(0.936442\pi\) | |||||||
\(480\) | 9.61553 | − | 4.44793i | 0.438887 | − | 0.203019i | ||||
\(481\) | −17.6155 | −0.803199 | ||||||||
\(482\) | 14.1771 | + | 16.3291i | 0.645748 | + | 0.743770i | ||||
\(483\) | 4.12391 | 0.187644 | ||||||||
\(484\) | 0.403882 | − | 2.84840i | 0.0183583 | − | 0.129473i | ||||
\(485\) | − | 26.4168i | − | 1.19953i | ||||||
\(486\) | −15.1231 | + | 13.1300i | −0.685998 | + | 0.595590i | ||||
\(487\) | 9.59482 | 0.434783 | 0.217391 | − | 0.976085i | \(-0.430245\pi\) | ||||
0.217391 | + | 0.976085i | \(0.430245\pi\) | |||||||
\(488\) | −1.05171 | − | 1.62603i | −0.0476085 | − | 0.0736069i | ||||
\(489\) | − | 12.7519i | − | 0.576659i | ||||||
\(490\) | −10.4160 | + | 9.04325i | −0.470546 | + | 0.408532i | ||||
\(491\) | 2.71151i | 0.122369i | 0.998126 | + | 0.0611844i | \(0.0194878\pi\) | ||||
−0.998126 | + | 0.0611844i | \(0.980512\pi\) | |||||||
\(492\) | 8.80776 | + | 1.24887i | 0.397085 | + | 0.0563036i | ||||
\(493\) | − | 8.45851i | − | 0.380952i | ||||||
\(494\) | 2.15503 | − | 29.2009i | 0.0969593 | − | 1.31381i | ||||
\(495\) | − | 7.54011i | − | 0.338903i | ||||||
\(496\) | −16.4127 | − | 4.74990i | −0.736953 | − | 0.213277i | ||||
\(497\) | 9.49980i | 0.426124i | ||||||||
\(498\) | −10.7386 | − | 12.3687i | −0.481210 | − | 0.554255i | ||||
\(499\) | 11.0129i | 0.493007i | 0.969142 | + | 0.246504i | \(0.0792817\pi\) | ||||
−0.969142 | + | 0.246504i | \(0.920718\pi\) | |||||||
\(500\) | −3.31534 | + | 23.3817i | −0.148267 | + | 1.04566i | ||||
\(501\) | −0.630683 | −0.0281768 | ||||||||
\(502\) | −20.7743 | − | 23.9277i | −0.927202 | − | 1.06795i | ||||
\(503\) | − | 35.6435i | − | 1.58926i | −0.607091 | − | 0.794632i | \(-0.707664\pi\) | ||
0.607091 | − | 0.794632i | \(-0.292336\pi\) | |||||||
\(504\) | 3.21985 | − | 2.08258i | 0.143424 | − | 0.0927655i | ||||
\(505\) | 12.8769 | 0.573014 | ||||||||
\(506\) | −13.0776 | + | 11.3541i | −0.581370 | + | 0.504752i | ||||
\(507\) | −11.4677 | −0.509297 | ||||||||
\(508\) | −0.525853 | + | 3.70861i | −0.0233309 | + | 0.164543i | ||||
\(509\) | 9.49980i | 0.421071i | 0.977586 | + | 0.210536i | \(0.0675208\pi\) | ||||
−0.977586 | + | 0.210536i | \(0.932479\pi\) | |||||||
\(510\) | 2.00000 | − | 1.73642i | 0.0885615 | − | 0.0768900i | ||||
\(511\) | 7.05256i | 0.311987i | ||||||||
\(512\) | −22.3680 | + | 3.41624i | −0.988537 | + | 0.150978i | ||||
\(513\) | 16.8078 | + | 16.9170i | 0.742081 | + | 0.746905i | ||||
\(514\) | −17.6155 | − | 20.2895i | −0.776988 | − | 0.894930i | ||||
\(515\) | −5.84912 | −0.257743 | ||||||||
\(516\) | 26.1552 | + | 3.70861i | 1.15142 | + | 0.163262i | ||||
\(517\) | 28.6847 | 1.26155 | ||||||||
\(518\) | −3.43845 | + | 2.98529i | −0.151077 | + | 0.131166i | ||||
\(519\) | − | 20.2895i | − | 0.890609i | ||||||
\(520\) | 17.6155 | − | 11.3936i | 0.772492 | − | 0.499643i | ||||
\(521\) | 15.2910i | 0.669910i | 0.942234 | + | 0.334955i | \(0.108721\pi\) | ||||
−0.942234 | + | 0.334955i | \(0.891279\pi\) | |||||||
\(522\) | 12.2462 | + | 14.1051i | 0.536002 | + | 0.617365i | ||||
\(523\) | −33.4990 | −1.46481 | −0.732404 | − | 0.680871i | \(-0.761602\pi\) | ||||
−0.732404 | + | 0.680871i | \(0.761602\pi\) | |||||||
\(524\) | −9.56155 | − | 1.35576i | −0.417698 | − | 0.0592265i | ||||
\(525\) | − | 2.66732i | − | 0.116411i | ||||||
\(526\) | −6.08677 | − | 7.01071i | −0.265396 | − | 0.305682i | ||||
\(527\) | −4.27156 | −0.186072 | ||||||||
\(528\) | 4.12391 | − | 14.2497i | 0.179470 | − | 0.620139i | ||||
\(529\) | 7.31534 | 0.318058 | ||||||||
\(530\) | 1.50758 | + | 1.73642i | 0.0654850 | + | 0.0754253i | ||||
\(531\) | 18.1379 | 0.787120 | ||||||||
\(532\) | −4.52802 | − | 6.06506i | −0.196315 | − | 0.262954i | ||||
\(533\) | 17.6155 | 0.763013 | ||||||||
\(534\) | −6.43971 | − | 7.41722i | −0.278673 | − | 0.320975i | ||||
\(535\) | −12.2888 | −0.531292 | ||||||||
\(536\) | 14.9654 | + | 23.1379i | 0.646408 | + | 0.999404i | ||||
\(537\) | −10.8769 | −0.469373 | ||||||||
\(538\) | −3.43845 | − | 3.96039i | −0.148242 | − | 0.170744i | ||||
\(539\) | 19.3144i | 0.831929i | ||||||||
\(540\) | −2.39871 | + | 16.9170i | −0.103224 | + | 0.727993i | ||||
\(541\) | −12.1922 | −0.524185 | −0.262093 | − | 0.965043i | \(-0.584413\pi\) | ||||
−0.262093 | + | 0.965043i | \(0.584413\pi\) | |||||||
\(542\) | 14.2355 | + | 16.3964i | 0.611467 | + | 0.704285i | ||||
\(543\) | − | 2.49775i | − | 0.107189i | ||||||
\(544\) | −5.13416 | + | 2.37495i | −0.220125 | + | 0.101825i | ||||
\(545\) | 24.7908i | 1.06192i | ||||||||
\(546\) | −5.28181 | + | 4.58572i | −0.226041 | + | 0.196251i | ||||
\(547\) | −19.4849 | −0.833116 | −0.416558 | − | 0.909109i | \(-0.636764\pi\) | ||||
−0.416558 | + | 0.909109i | \(0.636764\pi\) | |||||||
\(548\) | −1.08854 | + | 7.67700i | −0.0465001 | + | 0.327945i | ||||
\(549\) | 1.06913 | 0.0456294 | ||||||||
\(550\) | 7.34376 | + | 8.45851i | 0.313139 | + | 0.360672i | ||||
\(551\) | 26.1552 | − | 25.9863i | 1.11425 | − | 1.10705i | ||||
\(552\) | 11.2808 | − | 7.29634i | 0.480142 | − | 0.310553i | ||||
\(553\) | 6.96067i | 0.295998i | ||||||||
\(554\) | 25.6870 | − | 22.3017i | 1.09134 | − | 0.947509i | ||||
\(555\) | − | 6.94568i | − | 0.294828i | ||||||
\(556\) | −0.753789 | − | 0.106882i | −0.0319678 | − | 0.00453279i | ||||
\(557\) | −18.9309 | −0.802127 | −0.401063 | − | 0.916050i | \(-0.631359\pi\) | ||||
−0.401063 | + | 0.916050i | \(0.631359\pi\) | |||||||
\(558\) | 7.12311 | − | 6.18435i | 0.301545 | − | 0.261805i | ||||
\(559\) | 52.3104 | 2.21249 | ||||||||
\(560\) | 1.50758 | − | 5.20926i | 0.0637068 | − | 0.220131i | ||||
\(561\) | − | 3.70861i | − | 0.156578i | ||||||
\(562\) | 10.7386 | + | 12.3687i | 0.452982 | + | 0.521742i | ||||
\(563\) | −33.6466 | −1.41804 | −0.709018 | − | 0.705191i | \(-0.750861\pi\) | ||||
−0.709018 | + | 0.705191i | \(0.750861\pi\) | |||||||
\(564\) | −22.0313 | − | 3.12387i | −0.927685 | − | 0.131539i | ||||
\(565\) | − | 5.79119i | − | 0.243637i | ||||||
\(566\) | 4.47685 | + | 5.15641i | 0.188176 | + | 0.216740i | ||||
\(567\) | − | 1.62954i | − | 0.0684342i | ||||||
\(568\) | 16.8078 | + | 25.9863i | 0.705238 | + | 1.09036i | ||||
\(569\) | 12.7519i | 0.534586i | 0.963615 | + | 0.267293i | \(0.0861291\pi\) | ||||
−0.963615 | + | 0.267293i | \(0.913871\pi\) | |||||||
\(570\) | 11.5137 | + | 0.849712i | 0.482257 | + | 0.0355905i | ||||
\(571\) | − | 17.5780i | − | 0.735615i | −0.929902 | − | 0.367807i | \(-0.880109\pi\) | ||
0.929902 | − | 0.367807i | \(-0.119891\pi\) | |||||||
\(572\) | 4.12391 | − | 29.0841i | 0.172429 | − | 1.21607i | ||||
\(573\) | 10.5411i | 0.440360i | ||||||||
\(574\) | 3.43845 | − | 2.98529i | 0.143518 | − | 0.124604i | ||||
\(575\) | 10.1447i | 0.423065i | ||||||||
\(576\) | 5.12311 | − | 11.3936i | 0.213463 | − | 0.474734i | ||||
\(577\) | 27.0000 | 1.12402 | 0.562012 | − | 0.827129i | \(-0.310027\pi\) | ||||
0.562012 | + | 0.827129i | \(0.310027\pi\) | |||||||
\(578\) | 17.0862 | − | 14.8344i | 0.710694 | − | 0.617031i | ||||
\(579\) | 4.44793i | 0.184850i | ||||||||
\(580\) | 26.1552 | + | 3.70861i | 1.08604 | + | 0.153992i | ||||
\(581\) | −8.38447 | −0.347847 | ||||||||
\(582\) | 18.8114 | + | 21.6669i | 0.779759 | + | 0.898123i | ||||
\(583\) | 3.21985 | 0.133353 | ||||||||
\(584\) | 12.4779 | + | 19.2920i | 0.516340 | + | 0.798307i | ||||
\(585\) | 11.5824i | 0.478873i | ||||||||
\(586\) | −4.40388 | − | 5.07237i | −0.181923 | − | 0.209538i | ||||
\(587\) | − | 4.82860i | − | 0.199297i | −0.995023 | − | 0.0996487i | \(-0.968228\pi\) | ||
0.995023 | − | 0.0996487i | \(-0.0317719\pi\) | |||||||
\(588\) | 2.10341 | − | 14.8344i | 0.0867432 | − | 0.611762i | ||||
\(589\) | −13.1231 | − | 13.2084i | −0.540728 | − | 0.544243i | ||||
\(590\) | 19.3693 | − | 16.8166i | 0.797422 | − | 0.692330i | ||||
\(591\) | 12.5841 | 0.517641 | ||||||||
\(592\) | −4.12391 | + | 14.2497i | −0.169492 | + | 0.585659i | ||||
\(593\) | −36.7386 | −1.50867 | −0.754337 | − | 0.656487i | \(-0.772042\pi\) | ||||
−0.754337 | + | 0.656487i | \(0.772042\pi\) | |||||||
\(594\) | 15.6847 | + | 18.0655i | 0.643549 | + | 0.741237i | ||||
\(595\) | − | 1.35576i | − | 0.0555806i | ||||||
\(596\) | −5.00000 | + | 35.2628i | −0.204808 | + | 1.44442i | ||||
\(597\) | 15.8757i | 0.649750i | ||||||||
\(598\) | 20.0885 | − | 17.4411i | 0.821482 | − | 0.713219i | ||||
\(599\) | −7.72197 | −0.315511 | −0.157756 | − | 0.987478i | \(-0.550426\pi\) | ||||
−0.157756 | + | 0.987478i | \(0.550426\pi\) | |||||||
\(600\) | −4.71922 | − | 7.29634i | −0.192661 | − | 0.297872i | ||||
\(601\) | 39.1687i | 1.59772i | 0.601514 | + | 0.798862i | \(0.294564\pi\) | ||||
−0.601514 | + | 0.798862i | \(0.705436\pi\) | |||||||
\(602\) | 10.2107 | − | 8.86502i | 0.416156 | − | 0.361311i | ||||
\(603\) | −15.2134 | −0.619537 | ||||||||
\(604\) | −6.81791 | + | 48.0837i | −0.277417 | + | 1.95650i | ||||
\(605\) | 2.24621 | 0.0913215 | ||||||||
\(606\) | −10.5616 | + | 9.16965i | −0.429034 | + | 0.372491i | ||||
\(607\) | −13.6358 | −0.553461 | −0.276730 | − | 0.960948i | \(-0.589251\pi\) | ||||
−0.276730 | + | 0.960948i | \(0.589251\pi\) | |||||||
\(608\) | −23.1170 | − | 8.57940i | −0.937517 | − | 0.347940i | ||||
\(609\) | −8.80776 | −0.356909 | ||||||||
\(610\) | 1.14171 | − | 0.991247i | 0.0462266 | − | 0.0401344i | ||||
\(611\) | −44.0626 | −1.78258 | ||||||||
\(612\) | 0.438447 | − | 3.09218i | 0.0177232 | − | 0.124994i | ||||
\(613\) | 24.3002 | 0.981475 | 0.490738 | − | 0.871307i | \(-0.336727\pi\) | ||||
0.490738 | + | 0.871307i | \(0.336727\pi\) | |||||||
\(614\) | −8.56155 | + | 7.43323i | −0.345516 | + | 0.299981i | ||||
\(615\) | 6.94568i | 0.280077i | ||||||||
\(616\) | −4.12391 | − | 6.37593i | −0.166157 | − | 0.256894i | ||||
\(617\) | −28.5464 | −1.14923 | −0.574617 | − | 0.818422i | \(-0.694849\pi\) | ||||
−0.574617 | + | 0.818422i | \(0.694849\pi\) | |||||||
\(618\) | 4.79741 | − | 4.16516i | 0.192980 | − | 0.167547i | ||||
\(619\) | 34.3946i | 1.38244i | 0.722646 | + | 0.691218i | \(0.242926\pi\) | ||||
−0.722646 | + | 0.691218i | \(0.757074\pi\) | |||||||
\(620\) | 1.87285 | − | 13.2084i | 0.0752156 | − | 0.530463i | ||||
\(621\) | 21.6669i | 0.869464i | ||||||||
\(622\) | −0.804963 | − | 0.927153i | −0.0322761 | − | 0.0371754i | ||||
\(623\) | −5.02797 | −0.201441 | ||||||||
\(624\) | −6.33475 | + | 21.8890i | −0.253593 | + | 0.876262i | ||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 4.87123 | − | 4.22926i | 0.194694 | − | 0.169035i | ||||
\(627\) | 11.4677 | − | 11.3936i | 0.457975 | − | 0.455017i | ||||
\(628\) | 1.68466 | − | 11.8812i | 0.0672252 | − | 0.474110i | ||||
\(629\) | 3.70861i | 0.147872i | ||||||||
\(630\) | 1.96286 | + | 2.26081i | 0.0782022 | + | 0.0900729i | ||||
\(631\) | − | 12.7494i | − | 0.507544i | −0.967264 | − | 0.253772i | \(-0.918329\pi\) | ||
0.967264 | − | 0.253772i | \(-0.0816713\pi\) | |||||||
\(632\) | 12.3153 | + | 19.0406i | 0.489878 | + | 0.757394i | ||||
\(633\) | 2.42329 | 0.0963172 | ||||||||
\(634\) | 4.40388 | + | 5.07237i | 0.174900 | + | 0.201450i | ||||
\(635\) | −2.92456 | −0.116058 | ||||||||
\(636\) | −2.47301 | − | 0.350654i | −0.0980613 | − | 0.0139044i | ||||
\(637\) | − | 29.6689i | − | 1.17552i | ||||||
\(638\) | 27.9309 | − | 24.2499i | 1.10579 | − | 0.960061i | ||||
\(639\) | −17.0862 | −0.675921 | ||||||||
\(640\) | −5.09271 | − | 16.9170i | −0.201307 | − | 0.668704i | ||||
\(641\) | − | 48.6685i | − | 1.92229i | −0.276045 | − | 0.961145i | \(-0.589024\pi\) | ||
0.276045 | − | 0.961145i | \(-0.410976\pi\) | |||||||
\(642\) | 10.0792 | − | 8.75088i | 0.397795 | − | 0.345370i | ||||
\(643\) | 6.56502i | 0.258899i | 0.991586 | + | 0.129449i | \(0.0413210\pi\) | ||||
−0.991586 | + | 0.129449i | \(0.958679\pi\) | |||||||
\(644\) | 0.965435 | − | 6.80879i | 0.0380435 | − | 0.268304i | ||||
\(645\) | 20.6256i | 0.812133i | ||||||||
\(646\) | −6.14770 | − | 0.453700i | −0.241878 | − | 0.0178506i | ||||
\(647\) | − | 36.2379i | − | 1.42466i | −0.701845 | − | 0.712329i | \(-0.747640\pi\) | ||
0.701845 | − | 0.712329i | \(-0.252360\pi\) | |||||||
\(648\) | −2.88310 | − | 4.45753i | −0.113259 | − | 0.175108i | ||||
\(649\) | − | 35.9166i | − | 1.40985i | ||||||
\(650\) | −11.2808 | − | 12.9931i | −0.442468 | − | 0.509633i | ||||
\(651\) | 4.44793i | 0.174328i | ||||||||
\(652\) | −21.0540 | − | 2.98529i | −0.824537 | − | 0.116913i | ||||
\(653\) | −45.8078 | −1.79260 | −0.896298 | − | 0.443452i | \(-0.853754\pi\) | ||||
−0.896298 | + | 0.443452i | \(0.853754\pi\) | |||||||
\(654\) | −17.6535 | − | 20.3333i | −0.690308 | − | 0.795093i | ||||
\(655\) | − | 7.54011i | − | 0.294616i | ||||||
\(656\) | 4.12391 | − | 14.2497i | 0.161012 | − | 0.556357i | ||||
\(657\) | −12.6847 | −0.494876 | ||||||||
\(658\) | −8.60076 | + | 7.46726i | −0.335292 | + | 0.291104i | ||||
\(659\) | −3.36750 | −0.131179 | −0.0655896 | − | 0.997847i | \(-0.520893\pi\) | ||||
−0.0655896 | + | 0.997847i | \(0.520893\pi\) | |||||||
\(660\) | 11.4677 | + | 1.62603i | 0.446379 | + | 0.0632931i | ||||
\(661\) | − | 17.5018i | − | 0.680740i | −0.940292 | − | 0.340370i | \(-0.889448\pi\) | ||
0.940292 | − | 0.340370i | \(-0.110552\pi\) | |||||||
\(662\) | 2.40388 | − | 2.08707i | 0.0934295 | − | 0.0811165i | ||||
\(663\) | 5.69681i | 0.221246i | ||||||||
\(664\) | −22.9354 | + | 14.8344i | −0.890064 | + | 0.575688i | ||||
\(665\) | 4.19224 | − | 4.16516i | 0.162568 | − | 0.161518i | ||||
\(666\) | −5.36932 | − | 6.18435i | −0.208057 | − | 0.239639i | ||||
\(667\) | 33.4990 | 1.29709 | ||||||||
\(668\) | −0.147647 | + | 1.04129i | −0.00571264 | + | 0.0402887i | ||||
\(669\) | 19.5076 | 0.754207 | ||||||||
\(670\) | −16.2462 | + | 14.1051i | −0.627646 | + | 0.544928i | ||||
\(671\) | − | 2.11708i | − | 0.0817291i | ||||||
\(672\) | 2.47301 | + | 5.34615i | 0.0953985 | + | 0.206232i | ||||
\(673\) | 31.7515i | 1.22393i | 0.790885 | + | 0.611964i | \(0.209620\pi\) | ||||
−0.790885 | + | 0.611964i | \(0.790380\pi\) | |||||||
\(674\) | −24.4924 | − | 28.2102i | −0.943413 | − | 1.08662i | ||||
\(675\) | 14.0140 | 0.539400 | ||||||||
\(676\) | −2.68466 | + | 18.9337i | −0.103256 | + | 0.728220i | ||||
\(677\) | − | 4.29335i | − | 0.165007i | −0.996591 | − | 0.0825034i | \(-0.973708\pi\) | ||
0.996591 | − | 0.0825034i | \(-0.0262915\pi\) | |||||||
\(678\) | 4.12391 | + | 4.74990i | 0.158378 | + | 0.182419i | ||||
\(679\) | 14.6875 | 0.563656 | ||||||||
\(680\) | −2.39871 | − | 3.70861i | −0.0919862 | − | 0.142219i | ||||
\(681\) | 20.9460 | 0.802653 | ||||||||
\(682\) | −12.2462 | − | 14.1051i | −0.468932 | − | 0.540113i | ||||
\(683\) | 13.6358 | 0.521760 | 0.260880 | − | 0.965371i | \(-0.415987\pi\) | ||||
0.260880 | + | 0.965371i | \(0.415987\pi\) | |||||||
\(684\) | 10.9086 | − | 8.14404i | 0.417099 | − | 0.311395i | ||||
\(685\) | −6.05398 | −0.231311 | ||||||||
\(686\) | −10.6627 | − | 12.2813i | −0.407104 | − | 0.468901i | ||||
\(687\) | −2.92456 | −0.111579 | ||||||||
\(688\) | 12.2462 | − | 42.3154i | 0.466882 | − | 1.61326i | ||||
\(689\) | −4.94602 | −0.188429 | ||||||||
\(690\) | 6.87689 | + | 7.92077i | 0.261799 | + | 0.301539i | ||||
\(691\) | 23.3817i | 0.889480i | 0.895660 | + | 0.444740i | \(0.146704\pi\) | ||||
−0.895660 | + | 0.444740i | \(0.853296\pi\) | |||||||
\(692\) | −33.4990 | − | 4.74990i | −1.27344 | − | 0.180564i | ||||
\(693\) | 4.19224 | 0.159250 | ||||||||
\(694\) | 22.3842 | + | 25.7820i | 0.849694 | + | 0.978673i | ||||
\(695\) | − | 0.594427i | − | 0.0225479i | ||||||
\(696\) | −24.0932 | + | 15.5834i | −0.913252 | + | 0.590686i | ||||
\(697\) | − | 3.70861i | − | 0.140474i | ||||||
\(698\) | 29.9585 | − | 26.0103i | 1.13395 | − | 0.984505i | ||||
\(699\) | −11.7630 | −0.444916 | ||||||||
\(700\) | −4.40388 | − | 0.624437i | −0.166451 | − | 0.0236015i | ||||
\(701\) | 29.3693 | 1.10926 | 0.554632 | − | 0.832096i | \(-0.312859\pi\) | ||||
0.554632 | + | 0.832096i | \(0.312859\pi\) | |||||||
\(702\) | −24.0932 | − | 27.7505i | −0.909341 | − | 1.04737i | ||||
\(703\) | −11.4677 | + | 11.3936i | −0.432512 | + | 0.429718i | ||||
\(704\) | −22.5616 | − | 10.1447i | −0.850321 | − | 0.382344i | ||||
\(705\) | − | 17.3736i | − | 0.654327i | ||||||
\(706\) | −6.74409 | + | 5.85528i | −0.253817 | + | 0.220367i | ||||
\(707\) | 7.15944i | 0.269259i | ||||||||
\(708\) | −3.91146 | + | 27.5858i | −0.147002 | + | 1.03674i | ||||
\(709\) | 37.3693 | 1.40343 | 0.701717 | − | 0.712456i | \(-0.252417\pi\) | ||||
0.701717 | + | 0.712456i | \(0.252417\pi\) | |||||||
\(710\) | −18.2462 | + | 15.8415i | −0.684768 | + | 0.594523i | ||||
\(711\) | −12.5194 | −0.469513 | ||||||||
\(712\) | −13.7538 | + | 8.89586i | −0.515445 | + | 0.333387i | ||||
\(713\) | − | 16.9170i | − | 0.633547i | ||||||
\(714\) | 0.965435 | + | 1.11198i | 0.0361305 | + | 0.0416149i | ||||
\(715\) | 22.9354 | 0.857733 | ||||||||
\(716\) | −2.54635 | + | 17.9583i | −0.0951617 | + | 0.671134i | ||||
\(717\) | − | 23.2930i | − | 0.869891i | ||||||
\(718\) | 25.3502 | + | 29.1983i | 0.946063 | + | 1.08967i | ||||
\(719\) | − | 15.9484i | − | 0.594776i | −0.954757 | − | 0.297388i | \(-0.903885\pi\) | ||
0.954757 | − | 0.297388i | \(-0.0961155\pi\) | |||||||
\(720\) | 9.36932 | + | 2.71151i | 0.349174 | + | 0.101052i | ||||
\(721\) | − | 3.25206i | − | 0.121113i | ||||||
\(722\) | −17.4841 | − | 20.4036i | −0.650690 | − | 0.759344i | ||||
\(723\) | − | 18.3393i | − | 0.682046i | ||||||
\(724\) | −4.12391 | − | 0.584739i | −0.153264 | − | 0.0217317i | ||||
\(725\) | − | 21.6669i | − | 0.804689i | ||||||
\(726\) | −1.84233 | + | 1.59953i | −0.0683753 | + | 0.0593641i | ||||
\(727\) | 23.6554i | 0.877332i | 0.898650 | + | 0.438666i | \(0.144549\pi\) | ||||
−0.898650 | + | 0.438666i | \(0.855451\pi\) | |||||||
\(728\) | 6.33475 | + | 9.79408i | 0.234782 | + | 0.362993i | ||||
\(729\) | 22.6155 | 0.837612 | ||||||||
\(730\) | −13.5458 | + | 11.7606i | −0.501353 | + | 0.435280i | ||||
\(731\) | − | 11.0129i | − | 0.407329i | ||||||
\(732\) | −0.230559 | + | 1.62603i | −0.00852170 | + | 0.0600998i | ||||
\(733\) | 3.12311 | 0.115355 | 0.0576773 | − | 0.998335i | \(-0.481631\pi\) | ||||
0.0576773 | + | 0.998335i | \(0.481631\pi\) | |||||||
\(734\) | 13.0776 | + | 15.0627i | 0.482703 | + | 0.555975i | ||||
\(735\) | 11.6982 | 0.431496 | ||||||||
\(736\) | −9.40572 | − | 20.3333i | −0.346699 | − | 0.749494i | ||||
\(737\) | 30.1254i | 1.10968i | ||||||||
\(738\) | 5.36932 | + | 6.18435i | 0.197647 | + | 0.227649i | ||||
\(739\) | 30.3273i | 1.11561i | 0.829972 | + | 0.557804i | \(0.188356\pi\) | ||||
−0.829972 | + | 0.557804i | \(0.811644\pi\) | |||||||
\(740\) | −11.4677 | − | 1.62603i | −0.421560 | − | 0.0597740i | ||||
\(741\) | −17.6155 | + | 17.5018i | −0.647123 | + | 0.642943i | ||||
\(742\) | −0.965435 | + | 0.838200i | −0.0354422 | + | 0.0307713i | ||||
\(743\) | 38.4440 | 1.41037 | 0.705187 | − | 0.709021i | \(-0.250863\pi\) | ||||
0.705187 | + | 0.709021i | \(0.250863\pi\) | |||||||
\(744\) | 7.86962 | + | 12.1671i | 0.288514 | + | 0.446068i | ||||
\(745\) | −27.8078 | −1.01880 | ||||||||
\(746\) | −11.2808 | − | 12.9931i | −0.413019 | − | 0.475713i | ||||
\(747\) | − | 15.0802i | − | 0.551756i | ||||||
\(748\) | −6.12311 | − | 0.868210i | −0.223883 | − | 0.0317449i | ||||
\(749\) | − | 6.83248i | − | 0.249653i | ||||||
\(750\) | 15.1231 | − | 13.1300i | 0.552218 | − | 0.479441i | ||||
\(751\) | 8.24782 | 0.300967 | 0.150484 | − | 0.988612i | \(-0.451917\pi\) | ||||
0.150484 | + | 0.988612i | \(0.451917\pi\) | |||||||
\(752\) | −10.3153 | + | 35.6435i | −0.376162 | + | 1.29978i | ||||
\(753\) | 26.8734i | 0.979320i | ||||||||
\(754\) | −42.9047 | + | 37.2503i | −1.56250 | + | 1.35658i | ||||
\(755\) | −37.9182 | −1.37998 | ||||||||
\(756\) | −9.40572 | − | 1.33366i | −0.342083 | − | 0.0485047i | ||||
\(757\) | −24.1922 | −0.879282 | −0.439641 | − | 0.898174i | \(-0.644894\pi\) | ||||
−0.439641 | + | 0.898174i | \(0.644894\pi\) | |||||||
\(758\) | 7.28078 | − | 6.32124i | 0.264450 | − | 0.229598i | ||||
\(759\) | 14.6875 | 0.533123 | ||||||||
\(760\) | 4.09836 | − | 18.8108i | 0.148663 | − | 0.682341i | ||||
\(761\) | −10.6155 | −0.384813 | −0.192406 | − | 0.981315i | \(-0.561629\pi\) | ||||
−0.192406 | + | 0.981315i | \(0.561629\pi\) | |||||||
\(762\) | 2.39871 | − | 2.08258i | 0.0868959 | − | 0.0754439i | ||||
\(763\) | −13.7835 | −0.498995 | ||||||||
\(764\) | 17.4039 | + | 2.46774i | 0.629650 | + | 0.0892797i | ||||
\(765\) | 2.43845 | 0.0881622 | ||||||||
\(766\) | 17.3693 | − | 15.0802i | 0.627579 | − | 0.544870i | ||||
\(767\) | 55.1716i | 1.99213i | ||||||||
\(768\) | 16.2236 | + | 10.2487i | 0.585420 | + | 0.369819i | ||||
\(769\) | 54.2311 | 1.95562 | 0.977811 | − | 0.209489i | \(-0.0671801\pi\) | ||||
0.977811 | + | 0.209489i | \(0.0671801\pi\) | |||||||
\(770\) | 4.47685 | − | 3.88684i | 0.161334 | − | 0.140072i | ||||
\(771\) | 22.7872i | 0.820662i | ||||||||
\(772\) | 7.34376 | + | 1.04129i | 0.264308 | + | 0.0374769i | ||||
\(773\) | − | 25.8321i | − | 0.929115i | −0.885543 | − | 0.464558i | \(-0.846213\pi\) | ||
0.885543 | − | 0.464558i | \(-0.153787\pi\) | |||||||
\(774\) | 15.9445 | + | 18.3648i | 0.573114 | + | 0.660110i | ||||
\(775\) | −10.9418 | −0.393042 | ||||||||
\(776\) | 40.1771 | − | 25.9863i | 1.44227 | − | 0.932853i | ||||
\(777\) | 3.86174 | 0.138539 | ||||||||
\(778\) | 6.20205 | − | 5.38468i | 0.222354 | − | 0.193050i | ||||
\(779\) | 11.4677 | − | 11.3936i | 0.410872 | − | 0.408219i | ||||
\(780\) | −17.6155 | − | 2.49775i | −0.630737 | − | 0.0894337i | ||||
\(781\) | 33.8340i | 1.21068i | ||||||||
\(782\) | −3.67188 | − | 4.22926i | −0.131306 | − | 0.151238i | ||||
\(783\) | − | 46.2758i | − | 1.65376i | ||||||
\(784\) | −24.0000 | − | 6.94568i | −0.857143 | − | 0.248060i | ||||
\(785\) | 9.36932 | 0.334405 | ||||||||
\(786\) | 5.36932 | + | 6.18435i | 0.191517 | + | 0.220589i | ||||
\(787\) | 40.9904 | 1.46115 | 0.730575 | − | 0.682833i | \(-0.239252\pi\) | ||||
0.730575 | + | 0.682833i | \(0.239252\pi\) | |||||||
\(788\) | 2.94602 | − | 20.7770i | 0.104948 | − | 0.740151i | ||||
\(789\) | 7.87377i | 0.280314i | ||||||||
\(790\) | −13.3693 | + | 11.6074i | −0.475659 | + | 0.412972i | ||||
\(791\) | 3.21985 | 0.114485 | ||||||||
\(792\) | 11.4677 | − | 7.41722i | 0.407486 | − | 0.263559i | ||||
\(793\) | 3.25206i | 0.115484i | ||||||||
\(794\) | −26.6234 | + | 23.1147i | −0.944830 | + | 0.820311i | ||||
\(795\) | − | 1.95018i | − | 0.0691659i | ||||||
\(796\) | 26.2116 | + | 3.71661i | 0.929047 | + | 0.131732i | ||||
\(797\) | 23.2930i | 0.825079i | 0.910940 | + | 0.412539i | \(0.135358\pi\) | ||||
−0.910940 | + | 0.412539i | \(0.864642\pi\) | |||||||
\(798\) | −0.472433 | + | 6.40153i | −0.0167239 | + | 0.226612i | ||||
\(799\) | 9.27653i | 0.328180i | ||||||||
\(800\) | −13.1514 | + | 6.08356i | −0.464973 | + | 0.215086i | ||||
\(801\) | − | 9.04325i | − | 0.319528i | ||||||
\(802\) | −19.1231 | − | 22.0259i | −0.675260 | − | 0.777761i | ||||
\(803\) | 25.1181i | 0.886398i | ||||||||
\(804\) | 3.28078 | − | 23.1379i | 0.115704 | − | 0.816010i | ||||
\(805\) | 5.36932 | 0.189244 | ||||||||
\(806\) | 18.8114 | + | 21.6669i | 0.662605 | + | 0.763185i | ||||
\(807\) | 4.44793i | 0.156575i | ||||||||
\(808\) | 12.6670 | + | 19.5843i | 0.445624 | + | 0.688975i | ||||
\(809\) | 19.6307 | 0.690178 | 0.345089 | − | 0.938570i | \(-0.387849\pi\) | ||||
0.345089 | + | 0.938570i | \(0.387849\pi\) | |||||||
\(810\) | 3.12985 | − | 2.71736i | 0.109972 | − | 0.0954784i | ||||
\(811\) | −0.378206 | −0.0132806 | −0.00664030 | − | 0.999978i | \(-0.502114\pi\) | ||||
−0.00664030 | + | 0.999978i | \(0.502114\pi\) | |||||||
\(812\) | −2.06196 | + | 14.5421i | −0.0723605 | + | 0.510327i | ||||
\(813\) | − | 18.4149i | − | 0.645837i | ||||||
\(814\) | −12.2462 | + | 10.6323i | −0.429229 | + | 0.372661i | ||||
\(815\) | − | 16.6029i | − | 0.581573i | ||||||
\(816\) | 4.60831 | + | 1.33366i | 0.161323 | + | 0.0466874i | ||||
\(817\) | 34.0540 | − | 33.8340i | 1.19140 | − | 1.18370i | ||||
\(818\) | 17.1922 | + | 19.8019i | 0.601112 | + | 0.692358i | ||||
\(819\) | −6.43971 | −0.225022 | ||||||||
\(820\) | 11.4677 | + | 1.62603i | 0.400469 | + | 0.0567834i | ||||
\(821\) | 33.4233 | 1.16648 | 0.583240 | − | 0.812300i | \(-0.301785\pi\) | ||||
0.583240 | + | 0.812300i | \(0.301785\pi\) | |||||||
\(822\) | 4.96543 | − | 4.31104i | 0.173189 | − | 0.150365i | ||||
\(823\) | 22.1328i | 0.771500i | 0.922603 | + | 0.385750i | \(0.126057\pi\) | ||||
−0.922603 | + | 0.385750i | \(0.873943\pi\) | |||||||
\(824\) | −5.75379 | − | 8.89586i | −0.200443 | − | 0.309902i | ||||
\(825\) | − | 9.49980i | − | 0.330741i | ||||||
\(826\) | 9.34991 | + | 10.7692i | 0.325325 | + | 0.374708i | ||||
\(827\) | −25.1864 | −0.875817 | −0.437909 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437909 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(828\) | 12.2462 | + | 1.73642i | 0.425585 | + | 0.0603448i | ||||
\(829\) | − | 8.91506i | − | 0.309633i | −0.987943 | − | 0.154816i | \(-0.950521\pi\) | ||
0.987943 | − | 0.154816i | \(-0.0494786\pi\) | |||||||
\(830\) | −13.9817 | − | 16.1040i | −0.485311 | − | 0.558978i | ||||
\(831\) | −28.8492 | −1.00077 | ||||||||
\(832\) | 34.6569 | + | 15.5834i | 1.20151 | + | 0.540256i | ||||
\(833\) | −6.24621 | −0.216418 | ||||||||
\(834\) | 0.423292 | + | 0.487546i | 0.0146574 | + | 0.0168823i | ||||
\(835\) | −0.821147 | −0.0284170 | ||||||||
\(836\) | −16.1268 | − | 21.6010i | −0.557756 | − | 0.747088i | ||||
\(837\) | −23.3693 | −0.807762 | ||||||||
\(838\) | −25.4493 | − | 29.3124i | −0.879133 | − | 1.01258i | ||||
\(839\) | 51.2587 | 1.76965 | 0.884823 | − | 0.465926i | \(-0.154279\pi\) | ||||
0.884823 | + | 0.465926i | \(0.154279\pi\) | |||||||
\(840\) | −3.86174 | + | 2.49775i | −0.133243 | + | 0.0861805i | ||||
\(841\) | −42.5464 | −1.46712 | ||||||||
\(842\) | 21.5961 | + | 24.8743i | 0.744251 | + | 0.857225i | ||||
\(843\) | − | 13.8914i | − | 0.478444i | ||||||
\(844\) | 0.567309 | − | 4.00098i | 0.0195276 | − | 0.137719i | ||||
\(845\) | −14.9309 | −0.513638 | ||||||||
\(846\) | −13.4305 | − | 15.4692i | −0.461751 | − | 0.531843i | ||||
\(847\) | 1.24887i | 0.0429118i | ||||||||
\(848\) | −1.15790 | + | 4.00098i | −0.0397623 | + | 0.137394i | ||||
\(849\) | − | 5.79119i | − | 0.198753i | ||||||
\(850\) | −2.73546 | + | 2.37495i | −0.0938254 | + | 0.0814601i | ||||
\(851\) | −14.6875 | −0.503482 | ||||||||
\(852\) | 3.68466 | − | 25.9863i | 0.126234 | − | 0.890275i | ||||
\(853\) | 6.63068 | 0.227030 | 0.113515 | − | 0.993536i | \(-0.463789\pi\) | ||||
0.113515 | + | 0.993536i | \(0.463789\pi\) | |||||||
\(854\) | 0.551125 | + | 0.634783i | 0.0188591 | + | 0.0217218i | ||||
\(855\) | 7.49141 | + | 7.54011i | 0.256201 | + | 0.257866i | ||||
\(856\) | −12.0885 | − | 18.6899i | −0.413178 | − | 0.638809i | ||||
\(857\) | 4.16516i | 0.142279i | 0.997466 | + | 0.0711396i | \(0.0226636\pi\) | ||||
−0.997466 | + | 0.0711396i | \(0.977336\pi\) | |||||||
\(858\) | −18.8114 | + | 16.3323i | −0.642212 | + | 0.557575i | ||||
\(859\) | − | 22.6203i | − | 0.771795i | −0.922542 | − | 0.385898i | \(-0.873892\pi\) | ||
0.922542 | − | 0.385898i | \(-0.126108\pi\) | |||||||
\(860\) | 34.0540 | + | 4.82860i | 1.16123 | + | 0.164654i | ||||
\(861\) | −3.86174 | −0.131608 | ||||||||
\(862\) | −18.2462 | + | 15.8415i | −0.621468 | + | 0.539565i | ||||
\(863\) | −22.7048 | −0.772880 | −0.386440 | − | 0.922315i | \(-0.626295\pi\) | ||||
−0.386440 | + | 0.922315i | \(0.626295\pi\) | |||||||
\(864\) | −28.0885 | + | 12.9931i | −0.955592 | + | 0.442036i | ||||
\(865\) | − | 26.4168i | − | 0.898199i | ||||||
\(866\) | 26.0000 | + | 29.9467i | 0.883516 | + | 1.01763i | ||||
\(867\) | −19.1896 | −0.651715 | ||||||||
\(868\) | 7.34376 | + | 1.04129i | 0.249264 | + | 0.0353437i | ||||
\(869\) | 24.7908i | 0.840970i | ||||||||
\(870\) | −14.6875 | − | 16.9170i | −0.497954 | − | 0.573541i | ||||
\(871\) | − | 46.2758i | − | 1.56799i | ||||||
\(872\) | −37.7041 | + | 24.3868i | −1.27682 | + | 0.825840i | ||||
\(873\) | 26.4168i | 0.894074i | ||||||||
\(874\) | 1.79683 | − | 24.3472i | 0.0607785 | − | 0.823558i | ||||
\(875\) | − | 10.2516i | − | 0.346568i | ||||||
\(876\) | 2.73546 | − | 19.2920i | 0.0924225 | − | 0.651815i | ||||
\(877\) | 14.2497i | 0.481178i | 0.970627 | + | 0.240589i | \(0.0773406\pi\) | ||||
−0.970627 | + | 0.240589i | \(0.922659\pi\) | |||||||
\(878\) | −26.4924 | + | 23.0010i | −0.894076 | + | 0.776246i | ||||
\(879\) | 5.69681i | 0.192149i | ||||||||
\(880\) | 5.36932 | − | 18.5531i | 0.181000 | − | 0.625423i | ||||
\(881\) | 35.1771 | 1.18515 | 0.592573 | − | 0.805517i | \(-0.298112\pi\) | ||||
0.592573 | + | 0.805517i | \(0.298112\pi\) | |||||||
\(882\) | 10.4160 | − | 9.04325i | 0.350724 | − | 0.304502i | ||||
\(883\) | 0.594427i | 0.0200041i | 0.999950 | + | 0.0100020i | \(0.00318380\pi\) | ||||
−0.999950 | + | 0.0100020i | \(0.996816\pi\) | |||||||
\(884\) | 9.40572 | + | 1.33366i | 0.316349 | + | 0.0448558i | ||||
\(885\) | −21.7538 | −0.731246 | ||||||||
\(886\) | −32.2420 | − | 37.1361i | −1.08319 | − | 1.24761i | ||||
\(887\) | −31.4785 | −1.05694 | −0.528472 | − | 0.848951i | \(-0.677235\pi\) | ||||
−0.528472 | + | 0.848951i | \(0.677235\pi\) | |||||||
\(888\) | 10.5636 | − | 6.83248i | 0.354492 | − | 0.229283i | ||||
\(889\) | − | 1.62603i | − | 0.0545353i | ||||||
\(890\) | −8.38447 | − | 9.65719i | −0.281048 | − | 0.323710i | ||||
\(891\) | − | 5.80369i | − | 0.194431i | ||||||
\(892\) | 4.56685 | − | 32.2080i | 0.152910 | − | 1.07840i | ||||
\(893\) | −28.6847 | + | 28.4994i | −0.959895 | + | 0.953696i | ||||
\(894\) | 22.8078 | − | 19.8019i | 0.762806 | − | 0.662276i | ||||
\(895\) | −14.1617 | −0.473373 | ||||||||
\(896\) | 9.40572 | − | 2.83150i | 0.314223 | − | 0.0945938i | ||||
\(897\) | −22.5616 | −0.753308 | ||||||||
\(898\) | 33.3002 | + | 38.3550i | 1.11124 | + | 1.27992i | ||||
\(899\) | 36.1310i | 1.20504i | ||||||||
\(900\) | 1.12311 | − | 7.92077i | 0.0374369 | − | 0.264026i | ||||
\(901\) | 1.04129i | 0.0346904i | ||||||||
\(902\) | 12.2462 | − | 10.6323i | 0.407754 | − | 0.354016i | ||||
\(903\) | −11.4677 | −0.381620 | ||||||||
\(904\) | 8.80776 | − | 5.69681i | 0.292942 | − | 0.189473i | ||||
\(905\) | − | 3.25206i | − | 0.108102i | ||||||
\(906\) | 31.1003 | − | 27.0016i | 1.03324 | − | 0.897067i | ||||
\(907\) | 36.7188 | 1.21923 | 0.609614 | − | 0.792698i | \(-0.291324\pi\) | ||||
0.609614 | + | 0.792698i | \(0.291324\pi\) | |||||||
\(908\) | 4.90360 | − | 34.5830i | 0.162732 | − | 1.14768i | ||||
\(909\) | −12.8769 | −0.427100 | ||||||||
\(910\) | −6.87689 | + | 5.97059i | −0.227967 | + | 0.197923i | ||||
\(911\) | 10.6465 | 0.352735 | 0.176368 | − | 0.984324i | \(-0.443565\pi\) | ||||
0.176368 | + | 0.984324i | \(0.443565\pi\) | |||||||
\(912\) | 10.0338 | + | 18.3470i | 0.332251 | + | 0.607529i | ||||
\(913\) | −29.8617 | −0.988279 | ||||||||
\(914\) | −12.9461 | + | 11.2400i | −0.428220 | + | 0.371785i | ||||
\(915\) | −1.28226 | −0.0423904 | ||||||||
\(916\) | −0.684658 | + | 4.82860i | −0.0226218 | + | 0.159541i | ||||
\(917\) | 4.19224 | 0.138440 | ||||||||
\(918\) | −5.84233 | + | 5.07237i | −0.192826 | + | 0.167413i | ||||
\(919\) | − | 12.8563i | − | 0.424089i | −0.977260 | − | 0.212044i | \(-0.931988\pi\) | ||
0.977260 | − | 0.212044i | \(-0.0680121\pi\) | |||||||
\(920\) | 14.6875 | − | 9.49980i | 0.484233 | − | 0.313199i | ||||
\(921\) | 9.61553 | 0.316842 | ||||||||
\(922\) | −20.6267 | + | 17.9083i | −0.679303 | + | 0.589777i | ||||
\(923\) | − | 51.9726i | − | 1.71070i | ||||||
\(924\) | −0.904059 | + | 6.37593i | −0.0297413 | + | 0.209753i | ||||
\(925\) | 9.49980i | 0.312352i | ||||||||
\(926\) | 20.0684 | + | 23.1147i | 0.659490 | + | 0.759597i | ||||
\(927\) | 5.84912 | 0.192110 | ||||||||
\(928\) | 20.0885 | + | 43.4274i | 0.659439 | + | 1.42557i | ||||
\(929\) | −25.6847 | −0.842686 | −0.421343 | − | 0.906901i | \(-0.638441\pi\) | ||||
−0.421343 | + | 0.906901i | \(0.638441\pi\) | |||||||
\(930\) | −8.54312 | + | 7.41722i | −0.280140 | + | 0.243220i | ||||
\(931\) | −19.1896 | − | 19.3144i | −0.628915 | − | 0.633003i | ||||
\(932\) | −2.75379 | + | 19.4213i | −0.0902033 | + | 0.636165i | ||||
\(933\) | 1.04129i | 0.0340903i | ||||||||
\(934\) | −2.86692 | − | 3.30210i | −0.0938084 | − | 0.108048i | ||||
\(935\) | − | 4.82860i | − | 0.157912i | ||||||
\(936\) | −17.6155 | + | 11.3936i | −0.575782 | + | 0.372412i | ||||
\(937\) | −22.1231 | −0.722730 | −0.361365 | − | 0.932424i | \(-0.617689\pi\) | ||||
−0.361365 | + | 0.932424i | \(0.617689\pi\) | |||||||
\(938\) | −7.84233 | − | 9.03276i | −0.256061 | − | 0.294930i | ||||
\(939\) | −5.47091 | −0.178536 | ||||||||
\(940\) | −28.6847 | − | 4.06727i | −0.935590 | − | 0.132660i | ||||
\(941\) | 24.9190i | 0.812336i | 0.913799 | + | 0.406168i | \(0.133135\pi\) | ||||
−0.913799 | + | 0.406168i | \(0.866865\pi\) | |||||||
\(942\) | −7.68466 | + | 6.67190i | −0.250380 | + | 0.217382i | ||||
\(943\) | 14.6875 | 0.478292 | ||||||||
\(944\) | 44.6299 | + | 12.9160i | 1.45258 | + | 0.420381i | ||||
\(945\) | − | 7.41722i | − | 0.241282i | ||||||
\(946\) | 36.3659 | − | 31.5732i | 1.18236 | − | 1.02653i | ||||
\(947\) | 2.71151i | 0.0881123i | 0.999029 | + | 0.0440561i | \(0.0140280\pi\) | ||||
−0.999029 | + | 0.0440561i | \(0.985972\pi\) | |||||||
\(948\) | 2.69981 | − | 19.0406i | 0.0876859 | − | 0.618410i | ||||
\(949\) | − | 38.5839i | − | 1.25249i | ||||||
\(950\) | −15.7476 | − | 1.16218i | −0.510921 | − | 0.0377059i | ||||
\(951\) | − | 5.69681i | − | 0.184732i | ||||||
\(952\) | 2.06196 | − | 1.33366i | 0.0668284 | − | 0.0432242i | ||||
\(953\) | 24.7908i | 0.803053i | 0.915848 | + | 0.401526i | \(0.131520\pi\) | ||||
−0.915848 | + | 0.401526i | \(0.868480\pi\) | |||||||
\(954\) | −1.50758 | − | 1.73642i | −0.0488096 | − | 0.0562187i | ||||
\(955\) | 13.7245i | 0.444113i | ||||||||
\(956\) | −38.4579 | − | 5.45303i | −1.24382 | − | 0.176364i | ||||
\(957\) | −31.3693 | −1.01403 | ||||||||
\(958\) | −8.04963 | − | 9.27153i | −0.260072 | − | 0.299549i | ||||
\(959\) | − | 3.36596i | − | 0.108692i | ||||||
\(960\) | −6.14441 | + | 13.6650i | −0.198310 | + | 0.441035i | ||||
\(961\) | −12.7538 | −0.411413 | ||||||||
\(962\) | 18.8114 | − | 16.3323i | 0.606505 | − | 0.526574i | ||||
\(963\) | 12.2888 | 0.396002 | ||||||||
\(964\) | −30.2791 | − | 4.29335i | −0.975225 | − | 0.138279i | ||||
\(965\) | 5.79119i | 0.186425i | ||||||||
\(966\) | −4.40388 | + | 3.82349i | −0.141693 | + | 0.123019i | ||||
\(967\) | 26.4738i | 0.851341i | 0.904878 | + | 0.425670i | \(0.139962\pi\) | ||||
−0.904878 | + | 0.425670i | \(0.860038\pi\) | |||||||
\(968\) | 2.20960 | + | 3.41624i | 0.0710193 | + | 0.109802i | ||||
\(969\) | 3.68466 | + | 3.70861i | 0.118368 | + | 0.119138i | ||||
\(970\) | 24.4924 | + | 28.2102i | 0.786404 | + | 0.905777i | ||||
\(971\) | 19.4849 | 0.625301 | 0.312651 | − | 0.949868i | \(-0.398783\pi\) | ||||
0.312651 | + | 0.949868i | \(0.398783\pi\) | |||||||
\(972\) | 3.97626 | − | 28.0429i | 0.127539 | − | 0.899475i | ||||
\(973\) | 0.330497 | 0.0105952 | ||||||||
\(974\) | −10.2462 | + | 8.89586i | −0.328310 | + | 0.285042i | ||||
\(975\) | 14.5927i | 0.467339i | ||||||||
\(976\) | 2.63068 | + | 0.761329i | 0.0842061 | + | 0.0243695i | ||||
\(977\) | − | 26.8734i | − | 0.859755i | −0.902887 | − | 0.429878i | \(-0.858557\pi\) | ||
0.902887 | − | 0.429878i | \(-0.141443\pi\) | |||||||
\(978\) | 11.8229 | + | 13.6176i | 0.378055 | + | 0.435442i | ||||
\(979\) | −17.9074 | −0.572322 | ||||||||
\(980\) | 2.73863 | − | 19.3144i | 0.0874824 | − | 0.616975i | ||||
\(981\) | − | 24.7908i | − | 0.791509i | ||||||
\(982\) | −2.51398 | − | 2.89560i | −0.0802245 | − | 0.0924022i | ||||
\(983\) | −13.3405 | −0.425497 | −0.212748 | − | 0.977107i | \(-0.568241\pi\) | ||||
−0.212748 | + | 0.977107i | \(0.568241\pi\) | |||||||
\(984\) | −10.5636 | + | 6.83248i | −0.336756 | + | 0.217812i | ||||
\(985\) | 16.3845 | 0.522053 | ||||||||
\(986\) | 7.84233 | + | 9.03276i | 0.249751 | + | 0.287662i | ||||
\(987\) | 9.65956 | 0.307467 | ||||||||
\(988\) | 24.7724 | + | 33.1814i | 0.788115 | + | 1.05564i | ||||
\(989\) | 43.6155 | 1.38689 | ||||||||
\(990\) | 6.99083 | + | 8.05200i | 0.222183 | + | 0.255909i | ||||
\(991\) | −54.1833 | −1.72119 | −0.860594 | − | 0.509292i | \(-0.829907\pi\) | ||||
−0.860594 | + | 0.509292i | \(0.829907\pi\) | |||||||
\(992\) | 21.9309 | − | 10.1447i | 0.696306 | − | 0.322096i | ||||
\(993\) | −2.69981 | −0.0856760 | ||||||||
\(994\) | −8.80776 | − | 10.1447i | −0.279365 | − | 0.321772i | ||||
\(995\) | 20.6701i | 0.655288i | ||||||||
\(996\) | 22.9354 | + | 3.25206i | 0.726734 | + | 0.103045i | ||||
\(997\) | −28.5464 | −0.904073 | −0.452037 | − | 0.891999i | \(-0.649302\pi\) | ||||
−0.452037 | + | 0.891999i | \(0.649302\pi\) | |||||||
\(998\) | −10.2107 | − | 11.7606i | −0.323214 | − | 0.372276i | ||||
\(999\) | 20.2895i | 0.641931i |
(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 | 76.2.d.a.75.2 | yes | 8 | |
3.2 | odd | 2 | 684.2.f.b.379.7 | 8 | |||
4.3 | odd | 2 | inner | 76.2.d.a.75.8 | yes | 8 | |
8.3 | odd | 2 | 1216.2.h.d.1215.5 | 8 | |||
8.5 | even | 2 | 1216.2.h.d.1215.4 | 8 | |||
12.11 | even | 2 | 684.2.f.b.379.1 | 8 | |||
19.18 | odd | 2 | inner | 76.2.d.a.75.7 | yes | 8 | |
57.56 | even | 2 | 684.2.f.b.379.2 | 8 | |||
76.75 | even | 2 | inner | 76.2.d.a.75.1 | ✓ | 8 | |
152.37 | odd | 2 | 1216.2.h.d.1215.6 | 8 | |||
152.75 | even | 2 | 1216.2.h.d.1215.3 | 8 | |||
228.227 | odd | 2 | 684.2.f.b.379.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.d.a.75.1 | ✓ | 8 | 76.75 | even | 2 | inner | |
76.2.d.a.75.2 | yes | 8 | 1.1 | even | 1 | trivial | |
76.2.d.a.75.7 | yes | 8 | 19.18 | odd | 2 | inner | |
76.2.d.a.75.8 | yes | 8 | 4.3 | odd | 2 | inner | |
684.2.f.b.379.1 | 8 | 12.11 | even | 2 | |||
684.2.f.b.379.2 | 8 | 57.56 | even | 2 | |||
684.2.f.b.379.7 | 8 | 3.2 | odd | 2 | |||
684.2.f.b.379.8 | 8 | 228.227 | odd | 2 | |||
1216.2.h.d.1215.3 | 8 | 152.75 | even | 2 | |||
1216.2.h.d.1215.4 | 8 | 8.5 | even | 2 | |||
1216.2.h.d.1215.5 | 8 | 8.3 | odd | 2 | |||
1216.2.h.d.1215.6 | 8 | 152.37 | odd | 2 |