Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(139,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("420.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.i (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.8 | ||
Character | \(\chi\) | \(=\) | 420.139 |
Dual form | 420.2.i.a.139.5 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33186 | + | 0.475542i | −0.941770 | + | 0.336259i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.54772 | − | 1.26671i | 0.773860 | − | 0.633356i | ||||
\(5\) | 2.22087 | − | 0.260295i | 0.993202 | − | 0.116407i | ||||
\(6\) | −0.475542 | − | 1.33186i | −0.194139 | − | 0.543731i | ||||
\(7\) | 1.17807 | + | 2.36900i | 0.445268 | + | 0.895397i | ||||
\(8\) | −1.45898 | + | 2.42309i | −0.515827 | + | 0.856693i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.83411 | + | 1.40279i | −0.896224 | + | 0.443602i | ||||
\(11\) | − | 0.365940i | − | 0.110335i | −0.998477 | − | 0.0551675i | \(-0.982431\pi\) | ||
0.998477 | − | 0.0551675i | \(-0.0175693\pi\) | |||||||
\(12\) | 1.26671 | + | 1.54772i | 0.365668 | + | 0.446788i | ||||
\(13\) | 1.72798 | 0.479254 | 0.239627 | − | 0.970865i | \(-0.422975\pi\) | ||||
0.239627 | + | 0.970865i | \(0.422975\pi\) | |||||||
\(14\) | −2.69558 | − | 2.59496i | −0.720425 | − | 0.693533i | ||||
\(15\) | 0.260295 | + | 2.22087i | 0.0672079 | + | 0.573425i | ||||
\(16\) | 0.790878 | − | 3.92103i | 0.197719 | − | 0.980259i | ||||
\(17\) | −0.146965 | −0.0356442 | −0.0178221 | − | 0.999841i | \(-0.505673\pi\) | ||||
−0.0178221 | + | 0.999841i | \(0.505673\pi\) | |||||||
\(18\) | 1.33186 | − | 0.475542i | 0.313923 | − | 0.112086i | ||||
\(19\) | 4.73636 | 1.08660 | 0.543298 | − | 0.839540i | \(-0.317175\pi\) | ||||
0.543298 | + | 0.839540i | \(0.317175\pi\) | |||||||
\(20\) | 3.10756 | − | 3.21606i | 0.694872 | − | 0.719134i | ||||
\(21\) | −2.36900 | + | 1.17807i | −0.516958 | + | 0.257075i | ||||
\(22\) | 0.174020 | + | 0.487382i | 0.0371011 | + | 0.103910i | ||||
\(23\) | −3.44964 | −0.719299 | −0.359650 | − | 0.933087i | \(-0.617104\pi\) | ||||
−0.359650 | + | 0.933087i | \(0.617104\pi\) | |||||||
\(24\) | −2.42309 | − | 1.45898i | −0.494612 | − | 0.297813i | ||||
\(25\) | 4.86449 | − | 1.15616i | 0.972899 | − | 0.231232i | ||||
\(26\) | −2.30143 | + | 0.821724i | −0.451347 | + | 0.161153i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 4.82416 | + | 2.17427i | 0.911681 | + | 0.410899i | ||||
\(29\) | −5.29049 | −0.982419 | −0.491209 | − | 0.871042i | \(-0.663445\pi\) | ||||
−0.491209 | + | 0.871042i | \(0.663445\pi\) | |||||||
\(30\) | −1.40279 | − | 2.83411i | −0.256114 | − | 0.517435i | ||||
\(31\) | 6.07392 | 1.09091 | 0.545454 | − | 0.838141i | \(-0.316357\pi\) | ||||
0.545454 | + | 0.838141i | \(0.316357\pi\) | |||||||
\(32\) | 0.811273 | + | 5.59838i | 0.143414 | + | 0.989663i | ||||
\(33\) | 0.365940 | 0.0637020 | ||||||||
\(34\) | 0.195737 | − | 0.0698879i | 0.0335686 | − | 0.0119857i | ||||
\(35\) | 3.23297 | + | 4.95458i | 0.546472 | + | 0.837478i | ||||
\(36\) | −1.54772 | + | 1.26671i | −0.257953 | + | 0.211119i | ||||
\(37\) | 7.52630i | 1.23732i | 0.785660 | + | 0.618658i | \(0.212323\pi\) | ||||
−0.785660 | + | 0.618658i | \(0.787677\pi\) | |||||||
\(38\) | −6.30819 | + | 2.25234i | −1.02332 | + | 0.365377i | ||||
\(39\) | 1.72798i | 0.276698i | ||||||||
\(40\) | −2.60948 | + | 5.76113i | −0.412594 | + | 0.910915i | ||||
\(41\) | 7.16300i | 1.11867i | 0.828941 | + | 0.559336i | \(0.188944\pi\) | ||||
−0.828941 | + | 0.559336i | \(0.811056\pi\) | |||||||
\(42\) | 2.59496 | − | 2.69558i | 0.400411 | − | 0.415937i | ||||
\(43\) | −8.65051 | −1.31919 | −0.659595 | − | 0.751621i | \(-0.729272\pi\) | ||||
−0.659595 | + | 0.751621i | \(0.729272\pi\) | |||||||
\(44\) | −0.463541 | − | 0.566373i | −0.0698814 | − | 0.0853839i | ||||
\(45\) | −2.22087 | + | 0.260295i | −0.331067 | + | 0.0388025i | ||||
\(46\) | 4.59445 | − | 1.64045i | 0.677414 | − | 0.241871i | ||||
\(47\) | 3.83760i | 0.559772i | 0.960033 | + | 0.279886i | \(0.0902967\pi\) | ||||
−0.960033 | + | 0.279886i | \(0.909703\pi\) | |||||||
\(48\) | 3.92103 | + | 0.790878i | 0.565953 | + | 0.114153i | ||||
\(49\) | −4.22431 | + | 5.58168i | −0.603473 | + | 0.797383i | ||||
\(50\) | −5.92904 | + | 3.85312i | −0.838493 | + | 0.544913i | ||||
\(51\) | − | 0.146965i | − | 0.0205792i | ||||||
\(52\) | 2.67442 | − | 2.18885i | 0.370876 | − | 0.303539i | ||||
\(53\) | − | 11.5549i | − | 1.58719i | −0.608447 | − | 0.793595i | \(-0.708207\pi\) | ||
0.608447 | − | 0.793595i | \(-0.291793\pi\) | |||||||
\(54\) | 0.475542 | + | 1.33186i | 0.0647130 | + | 0.181244i | ||||
\(55\) | −0.0952524 | − | 0.812704i | −0.0128438 | − | 0.109585i | ||||
\(56\) | −7.45908 | − | 0.601749i | −0.996762 | − | 0.0804120i | ||||
\(57\) | 4.73636i | 0.627346i | ||||||||
\(58\) | 7.04621 | − | 2.51585i | 0.925212 | − | 0.330347i | ||||
\(59\) | 6.18874 | 0.805706 | 0.402853 | − | 0.915265i | \(-0.368019\pi\) | ||||
0.402853 | + | 0.915265i | \(0.368019\pi\) | |||||||
\(60\) | 3.21606 | + | 3.10756i | 0.415192 | + | 0.401184i | ||||
\(61\) | − | 0.348039i | − | 0.0445619i | −0.999752 | − | 0.0222809i | \(-0.992907\pi\) | ||
0.999752 | − | 0.0222809i | \(-0.00709283\pi\) | |||||||
\(62\) | −8.08963 | + | 2.88840i | −1.02738 | + | 0.366827i | ||||
\(63\) | −1.17807 | − | 2.36900i | −0.148423 | − | 0.298466i | ||||
\(64\) | −3.74277 | − | 7.07048i | −0.467846 | − | 0.883810i | ||||
\(65\) | 3.83760 | − | 0.449783i | 0.475996 | − | 0.0557888i | ||||
\(66\) | −0.487382 | + | 0.174020i | −0.0599926 | + | 0.0214203i | ||||
\(67\) | 12.1623 | 1.48586 | 0.742929 | − | 0.669370i | \(-0.233436\pi\) | ||||
0.742929 | + | 0.669370i | \(0.233436\pi\) | |||||||
\(68\) | −0.227460 | + | 0.186162i | −0.0275836 | + | 0.0225755i | ||||
\(69\) | − | 3.44964i | − | 0.415288i | ||||||
\(70\) | −6.66198 | − | 5.06142i | −0.796259 | − | 0.604955i | ||||
\(71\) | 7.78061i | 0.923388i | 0.887039 | + | 0.461694i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461694i | \(0.847242\pi\) | |||||||
\(72\) | 1.45898 | − | 2.42309i | 0.171942 | − | 0.285564i | ||||
\(73\) | −4.55395 | −0.532999 | −0.266500 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266500 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(74\) | −3.57907 | − | 10.0240i | −0.416058 | − | 1.16527i | ||||
\(75\) | 1.15616 | + | 4.86449i | 0.133502 | + | 0.561703i | ||||
\(76\) | 7.33056 | − | 5.99961i | 0.840873 | − | 0.688202i | ||||
\(77\) | 0.866911 | − | 0.431102i | 0.0987937 | − | 0.0491286i | ||||
\(78\) | −0.821724 | − | 2.30143i | −0.0930419 | − | 0.260585i | ||||
\(79\) | − | 14.2442i | − | 1.60260i | −0.598261 | − | 0.801301i | \(-0.704141\pi\) | ||
0.598261 | − | 0.801301i | \(-0.295859\pi\) | |||||||
\(80\) | 0.735808 | − | 8.91395i | 0.0822658 | − | 0.996610i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.40630 | − | 9.54014i | −0.376163 | − | 1.05353i | ||||
\(83\) | − | 3.53810i | − | 0.388357i | −0.980966 | − | 0.194179i | \(-0.937796\pi\) | ||
0.980966 | − | 0.194179i | \(-0.0622042\pi\) | |||||||
\(84\) | −2.17427 | + | 4.82416i | −0.237233 | + | 0.526359i | ||||
\(85\) | −0.326389 | + | 0.0382542i | −0.0354019 | + | 0.00414925i | ||||
\(86\) | 11.5213 | − | 4.11367i | 1.24237 | − | 0.443589i | ||||
\(87\) | − | 5.29049i | − | 0.567200i | ||||||
\(88\) | 0.886707 | + | 0.533898i | 0.0945233 | + | 0.0569138i | ||||
\(89\) | − | 13.6498i | − | 1.44687i | −0.690390 | − | 0.723437i | \(-0.742561\pi\) | ||
0.690390 | − | 0.723437i | \(-0.257439\pi\) | |||||||
\(90\) | 2.83411 | − | 1.40279i | 0.298741 | − | 0.147867i | ||||
\(91\) | 2.03567 | + | 4.09357i | 0.213396 | + | 0.429123i | ||||
\(92\) | −5.33907 | + | 4.36970i | −0.556637 | + | 0.455573i | ||||
\(93\) | 6.07392i | 0.629836i | ||||||||
\(94\) | −1.82494 | − | 5.11116i | −0.188228 | − | 0.527176i | ||||
\(95\) | 10.5188 | − | 1.23285i | 1.07921 | − | 0.126488i | ||||
\(96\) | −5.59838 | + | 0.811273i | −0.571382 | + | 0.0828002i | ||||
\(97\) | −16.1970 | −1.64456 | −0.822280 | − | 0.569083i | \(-0.807298\pi\) | ||||
−0.822280 | + | 0.569083i | \(0.807298\pi\) | |||||||
\(98\) | 2.97189 | − | 9.44288i | 0.300206 | − | 0.953874i | ||||
\(99\) | 0.365940i | 0.0367784i | ||||||||
\(100\) | 6.06435 | − | 7.95133i | 0.606435 | − | 0.795133i | ||||
\(101\) | 4.41655i | 0.439463i | 0.975560 | + | 0.219732i | \(0.0705182\pi\) | ||||
−0.975560 | + | 0.219732i | \(0.929482\pi\) | |||||||
\(102\) | 0.0698879 | + | 0.195737i | 0.00691993 | + | 0.0193809i | ||||
\(103\) | − | 12.4670i | − | 1.22841i | −0.789147 | − | 0.614204i | \(-0.789477\pi\) | ||
0.789147 | − | 0.614204i | \(-0.210523\pi\) | |||||||
\(104\) | −2.52108 | + | 4.18705i | −0.247212 | + | 0.410574i | ||||
\(105\) | −4.95458 | + | 3.23297i | −0.483518 | + | 0.315506i | ||||
\(106\) | 5.49484 | + | 15.3896i | 0.533706 | + | 1.49477i | ||||
\(107\) | 6.16409 | 0.595905 | 0.297953 | − | 0.954581i | \(-0.403696\pi\) | ||||
0.297953 | + | 0.954581i | \(0.403696\pi\) | |||||||
\(108\) | −1.26671 | − | 1.54772i | −0.121889 | − | 0.148929i | ||||
\(109\) | −2.76468 | −0.264809 | −0.132404 | − | 0.991196i | \(-0.542270\pi\) | ||||
−0.132404 | + | 0.991196i | \(0.542270\pi\) | |||||||
\(110\) | 0.513337 | + | 1.03711i | 0.0489448 | + | 0.0988849i | ||||
\(111\) | −7.52630 | −0.714365 | ||||||||
\(112\) | 10.2206 | − | 2.74566i | 0.965759 | − | 0.259440i | ||||
\(113\) | − | 9.60538i | − | 0.903599i | −0.892120 | − | 0.451799i | \(-0.850782\pi\) | ||
0.892120 | − | 0.451799i | \(-0.149218\pi\) | |||||||
\(114\) | −2.25234 | − | 6.30819i | −0.210951 | − | 0.590816i | ||||
\(115\) | −7.66118 | + | 0.897923i | −0.714409 | + | 0.0837318i | ||||
\(116\) | −8.18820 | + | 6.70153i | −0.760255 | + | 0.622221i | ||||
\(117\) | −1.72798 | −0.159751 | ||||||||
\(118\) | −8.24256 | + | 2.94300i | −0.758789 | + | 0.270926i | ||||
\(119\) | −0.173135 | − | 0.348160i | −0.0158712 | − | 0.0319157i | ||||
\(120\) | −5.76113 | − | 2.60948i | −0.525917 | − | 0.238211i | ||||
\(121\) | 10.8661 | 0.987826 | ||||||||
\(122\) | 0.165507 | + | 0.463541i | 0.0149843 | + | 0.0419670i | ||||
\(123\) | −7.16300 | −0.645866 | ||||||||
\(124\) | 9.40073 | − | 7.69391i | 0.844210 | − | 0.690934i | ||||
\(125\) | 10.5024 | − | 3.83388i | 0.939367 | − | 0.342913i | ||||
\(126\) | 2.69558 | + | 2.59496i | 0.240142 | + | 0.231178i | ||||
\(127\) | −8.58236 | −0.761561 | −0.380781 | − | 0.924665i | \(-0.624345\pi\) | ||||
−0.380781 | + | 0.924665i | \(0.624345\pi\) | |||||||
\(128\) | 8.34716 | + | 7.63707i | 0.737792 | + | 0.675028i | ||||
\(129\) | − | 8.65051i | − | 0.761635i | ||||||
\(130\) | −4.89727 | + | 2.42399i | −0.429519 | + | 0.212598i | ||||
\(131\) | −18.6036 | −1.62540 | −0.812702 | − | 0.582680i | \(-0.802004\pi\) | ||||
−0.812702 | + | 0.582680i | \(0.802004\pi\) | |||||||
\(132\) | 0.566373 | − | 0.463541i | 0.0492964 | − | 0.0403460i | ||||
\(133\) | 5.57976 | + | 11.2204i | 0.483826 | + | 0.972935i | ||||
\(134\) | −16.1985 | + | 5.78367i | −1.39934 | + | 0.499633i | ||||
\(135\) | −0.260295 | − | 2.22087i | −0.0224026 | − | 0.191142i | ||||
\(136\) | 0.214418 | − | 0.356110i | 0.0183862 | − | 0.0305361i | ||||
\(137\) | − | 21.5809i | − | 1.84378i | −0.387447 | − | 0.921892i | \(-0.626643\pi\) | ||
0.387447 | − | 0.921892i | \(-0.373357\pi\) | |||||||
\(138\) | 1.64045 | + | 4.59445i | 0.139644 | + | 0.391105i | ||||
\(139\) | −13.1564 | −1.11591 | −0.557955 | − | 0.829871i | \(-0.688414\pi\) | ||||
−0.557955 | + | 0.829871i | \(0.688414\pi\) | |||||||
\(140\) | 11.2798 | + | 3.57307i | 0.953314 | + | 0.301979i | ||||
\(141\) | −3.83760 | −0.323184 | ||||||||
\(142\) | −3.70000 | − | 10.3627i | −0.310497 | − | 0.869619i | ||||
\(143\) | − | 0.632335i | − | 0.0528785i | ||||||
\(144\) | −0.790878 | + | 3.92103i | −0.0659065 | + | 0.326753i | ||||
\(145\) | −11.7495 | + | 1.37709i | −0.975740 | + | 0.114361i | ||||
\(146\) | 6.06523 | − | 2.16559i | 0.501962 | − | 0.179226i | ||||
\(147\) | −5.58168 | − | 4.22431i | −0.460369 | − | 0.348415i | ||||
\(148\) | 9.53366 | + | 11.6486i | 0.783662 | + | 0.957510i | ||||
\(149\) | 10.7665 | 0.882025 | 0.441012 | − | 0.897501i | \(-0.354620\pi\) | ||||
0.441012 | + | 0.897501i | \(0.354620\pi\) | |||||||
\(150\) | −3.85312 | − | 5.92904i | −0.314606 | − | 0.484104i | ||||
\(151\) | − | 3.34472i | − | 0.272190i | −0.990696 | − | 0.136095i | \(-0.956545\pi\) | ||
0.990696 | − | 0.136095i | \(-0.0434552\pi\) | |||||||
\(152\) | −6.91025 | + | 11.4766i | −0.560495 | + | 0.930879i | ||||
\(153\) | 0.146965 | 0.0118814 | ||||||||
\(154\) | −0.949601 | + | 0.986422i | −0.0765210 | + | 0.0794881i | ||||
\(155\) | 13.4894 | − | 1.58101i | 1.08349 | − | 0.126990i | ||||
\(156\) | 2.18885 | + | 2.67442i | 0.175248 | + | 0.214125i | ||||
\(157\) | 19.3169 | 1.54166 | 0.770830 | − | 0.637041i | \(-0.219842\pi\) | ||||
0.770830 | + | 0.637041i | \(0.219842\pi\) | |||||||
\(158\) | 6.77373 | + | 18.9714i | 0.538889 | + | 1.50928i | ||||
\(159\) | 11.5549 | 0.916364 | ||||||||
\(160\) | 3.25896 | + | 12.2221i | 0.257643 | + | 0.966240i | ||||
\(161\) | −4.06391 | − | 8.17219i | −0.320281 | − | 0.644059i | ||||
\(162\) | −1.33186 | + | 0.475542i | −0.104641 | + | 0.0373621i | ||||
\(163\) | −17.6321 | −1.38106 | −0.690528 | − | 0.723306i | \(-0.742622\pi\) | ||||
−0.690528 | + | 0.723306i | \(0.742622\pi\) | |||||||
\(164\) | 9.07346 | + | 11.0863i | 0.708518 | + | 0.865696i | ||||
\(165\) | 0.812704 | − | 0.0952524i | 0.0632689 | − | 0.00741539i | ||||
\(166\) | 1.68252 | + | 4.71227i | 0.130589 | + | 0.365743i | ||||
\(167\) | 16.7301i | 1.29461i | 0.762229 | + | 0.647307i | \(0.224105\pi\) | ||||
−0.762229 | + | 0.647307i | \(0.775895\pi\) | |||||||
\(168\) | 0.601749 | − | 7.45908i | 0.0464259 | − | 0.575481i | ||||
\(169\) | −10.0141 | −0.770315 | ||||||||
\(170\) | 0.416514 | − | 0.206161i | 0.0319452 | − | 0.0158118i | ||||
\(171\) | −4.73636 | −0.362199 | ||||||||
\(172\) | −13.3886 | + | 10.9577i | −1.02087 | + | 0.835517i | ||||
\(173\) | 17.5934 | 1.33760 | 0.668802 | − | 0.743441i | \(-0.266807\pi\) | ||||
0.668802 | + | 0.743441i | \(0.266807\pi\) | |||||||
\(174\) | 2.51585 | + | 7.04621i | 0.190726 | + | 0.534172i | ||||
\(175\) | 8.46965 | + | 10.1619i | 0.640245 | + | 0.768171i | ||||
\(176\) | −1.43486 | − | 0.289414i | −0.108157 | − | 0.0218154i | ||||
\(177\) | 6.18874i | 0.465175i | ||||||||
\(178\) | 6.49104 | + | 18.1796i | 0.486524 | + | 1.36262i | ||||
\(179\) | − | 7.52728i | − | 0.562615i | −0.959618 | − | 0.281308i | \(-0.909232\pi\) | ||
0.959618 | − | 0.281308i | \(-0.0907681\pi\) | |||||||
\(180\) | −3.10756 | + | 3.21606i | −0.231624 | + | 0.239711i | ||||
\(181\) | − | 3.83151i | − | 0.284794i | −0.989810 | − | 0.142397i | \(-0.954519\pi\) | ||
0.989810 | − | 0.142397i | \(-0.0454809\pi\) | |||||||
\(182\) | −4.65790 | − | 4.48403i | −0.345267 | − | 0.332379i | ||||
\(183\) | 0.348039 | 0.0257278 | ||||||||
\(184\) | 5.03294 | − | 8.35879i | 0.371034 | − | 0.616218i | ||||
\(185\) | 1.95906 | + | 16.7149i | 0.144033 | + | 1.22890i | ||||
\(186\) | −2.88840 | − | 8.08963i | −0.211788 | − | 0.593161i | ||||
\(187\) | 0.0537803i | 0.00393281i | ||||||||
\(188\) | 4.86114 | + | 5.93954i | 0.354535 | + | 0.433185i | ||||
\(189\) | 2.36900 | − | 1.17807i | 0.172319 | − | 0.0856918i | ||||
\(190\) | −13.4234 | + | 6.64413i | −0.973833 | + | 0.482016i | ||||
\(191\) | − | 20.1200i | − | 1.45583i | −0.685665 | − | 0.727917i | \(-0.740489\pi\) | ||
0.685665 | − | 0.727917i | \(-0.259511\pi\) | |||||||
\(192\) | 7.07048 | − | 3.74277i | 0.510268 | − | 0.270111i | ||||
\(193\) | − | 19.6683i | − | 1.41575i | −0.706336 | − | 0.707877i | \(-0.749653\pi\) | ||
0.706336 | − | 0.707877i | \(-0.250347\pi\) | |||||||
\(194\) | 21.5722 | − | 7.70237i | 1.54880 | − | 0.552998i | ||||
\(195\) | 0.449783 | + | 3.83760i | 0.0322097 | + | 0.274816i | ||||
\(196\) | 0.532333 | + | 13.9899i | 0.0380238 | + | 0.999277i | ||||
\(197\) | − | 5.44722i | − | 0.388098i | −0.980992 | − | 0.194049i | \(-0.937838\pi\) | ||
0.980992 | − | 0.194049i | \(-0.0621621\pi\) | |||||||
\(198\) | −0.174020 | − | 0.487382i | −0.0123670 | − | 0.0346367i | ||||
\(199\) | −6.66636 | −0.472566 | −0.236283 | − | 0.971684i | \(-0.575929\pi\) | ||||
−0.236283 | + | 0.971684i | \(0.575929\pi\) | |||||||
\(200\) | −4.29570 | + | 13.4739i | −0.303752 | + | 0.952751i | ||||
\(201\) | 12.1623i | 0.857861i | ||||||||
\(202\) | −2.10025 | − | 5.88225i | −0.147773 | − | 0.413873i | ||||
\(203\) | −6.23255 | − | 12.5332i | −0.437439 | − | 0.879655i | ||||
\(204\) | −0.186162 | − | 0.227460i | −0.0130340 | − | 0.0159254i | ||||
\(205\) | 1.86449 | + | 15.9081i | 0.130222 | + | 1.11107i | ||||
\(206\) | 5.92857 | + | 16.6043i | 0.413063 | + | 1.15688i | ||||
\(207\) | 3.44964 | 0.239766 | ||||||||
\(208\) | 1.36662 | − | 6.77545i | 0.0947579 | − | 0.469793i | ||||
\(209\) | − | 1.73322i | − | 0.119890i | ||||||
\(210\) | 5.06142 | − | 6.66198i | 0.349271 | − | 0.459721i | ||||
\(211\) | 8.81673i | 0.606969i | 0.952836 | + | 0.303484i | \(0.0981500\pi\) | ||||
−0.952836 | + | 0.303484i | \(0.901850\pi\) | |||||||
\(212\) | −14.6368 | − | 17.8838i | −1.00526 | − | 1.22826i | ||||
\(213\) | −7.78061 | −0.533118 | ||||||||
\(214\) | −8.20973 | + | 2.93128i | −0.561205 | + | 0.200378i | ||||
\(215\) | −19.2116 | + | 2.25168i | −1.31022 | + | 0.153564i | ||||
\(216\) | 2.42309 | + | 1.45898i | 0.164871 | + | 0.0992709i | ||||
\(217\) | 7.15549 | + | 14.3891i | 0.485746 | + | 0.976796i | ||||
\(218\) | 3.68218 | − | 1.31472i | 0.249389 | − | 0.0890442i | ||||
\(219\) | − | 4.55395i | − | 0.307727i | ||||||
\(220\) | −1.17689 | − | 1.13718i | −0.0793456 | − | 0.0766687i | ||||
\(221\) | −0.253952 | −0.0170826 | ||||||||
\(222\) | 10.0240 | − | 3.57907i | 0.672767 | − | 0.240211i | ||||
\(223\) | − | 7.18662i | − | 0.481252i | −0.970618 | − | 0.240626i | \(-0.922647\pi\) | ||
0.970618 | − | 0.240626i | \(-0.0773527\pi\) | |||||||
\(224\) | −12.3068 | + | 8.51717i | −0.822284 | + | 0.569078i | ||||
\(225\) | −4.86449 | + | 1.15616i | −0.324300 | + | 0.0770774i | ||||
\(226\) | 4.56776 | + | 12.7931i | 0.303843 | + | 0.850982i | ||||
\(227\) | 4.76468i | 0.316243i | 0.987420 | + | 0.158122i | \(0.0505438\pi\) | ||||
−0.987420 | + | 0.158122i | \(0.949456\pi\) | |||||||
\(228\) | 5.99961 | + | 7.33056i | 0.397334 | + | 0.485479i | ||||
\(229\) | 15.4673i | 1.02211i | 0.859548 | + | 0.511055i | \(0.170745\pi\) | ||||
−0.859548 | + | 0.511055i | \(0.829255\pi\) | |||||||
\(230\) | 9.77665 | − | 4.83912i | 0.644653 | − | 0.319082i | ||||
\(231\) | 0.431102 | + | 0.866911i | 0.0283644 | + | 0.0570386i | ||||
\(232\) | 7.71870 | − | 12.8193i | 0.506758 | − | 0.841631i | ||||
\(233\) | 13.7907i | 0.903461i | 0.892155 | + | 0.451730i | \(0.149193\pi\) | ||||
−0.892155 | + | 0.451730i | \(0.850807\pi\) | |||||||
\(234\) | 2.30143 | − | 0.821724i | 0.150449 | − | 0.0537178i | ||||
\(235\) | 0.998909 | + | 8.52280i | 0.0651616 | + | 0.555966i | ||||
\(236\) | 9.57845 | − | 7.83936i | 0.623504 | − | 0.510299i | ||||
\(237\) | 14.2442 | 0.925263 | ||||||||
\(238\) | 0.396156 | + | 0.381368i | 0.0256790 | + | 0.0247204i | ||||
\(239\) | 1.39679i | 0.0903506i | 0.998979 | + | 0.0451753i | \(0.0143846\pi\) | ||||
−0.998979 | + | 0.0451753i | \(0.985615\pi\) | |||||||
\(240\) | 8.91395 | + | 0.735808i | 0.575393 | + | 0.0474962i | ||||
\(241\) | − | 18.9796i | − | 1.22258i | −0.791406 | − | 0.611290i | \(-0.790651\pi\) | ||
0.791406 | − | 0.611290i | \(-0.209349\pi\) | |||||||
\(242\) | −14.4721 | + | 5.16728i | −0.930305 | + | 0.332165i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.440866 | − | 0.538668i | −0.0282235 | − | 0.0344847i | ||||
\(245\) | −7.92875 | + | 13.4957i | −0.506549 | + | 0.862211i | ||||
\(246\) | 9.54014 | − | 3.40630i | 0.608257 | − | 0.217178i | ||||
\(247\) | 8.18432 | 0.520756 | ||||||||
\(248\) | −8.86171 | + | 14.7177i | −0.562719 | + | 0.934573i | ||||
\(249\) | 3.53810 | 0.224218 | ||||||||
\(250\) | −12.1647 | + | 10.1006i | −0.769360 | + | 0.638815i | ||||
\(251\) | 10.9949 | 0.693994 | 0.346997 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346997 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(252\) | −4.82416 | − | 2.17427i | −0.303894 | − | 0.136966i | ||||
\(253\) | 1.26236i | 0.0793639i | ||||||||
\(254\) | 11.4305 | − | 4.08127i | 0.717215 | − | 0.256081i | ||||
\(255\) | −0.0382542 | − | 0.326389i | −0.00239557 | − | 0.0204393i | ||||
\(256\) | −14.7490 | − | 6.20212i | −0.921814 | − | 0.387632i | ||||
\(257\) | −18.1739 | −1.13366 | −0.566828 | − | 0.823836i | \(-0.691830\pi\) | ||||
−0.566828 | + | 0.823836i | \(0.691830\pi\) | |||||||
\(258\) | 4.11367 | + | 11.5213i | 0.256106 | + | 0.717284i | ||||
\(259\) | −17.8298 | + | 8.86649i | −1.10789 | + | 0.550937i | ||||
\(260\) | 5.36979 | − | 5.55728i | 0.333020 | − | 0.344648i | ||||
\(261\) | 5.29049 | 0.327473 | ||||||||
\(262\) | 24.7775 | − | 8.84678i | 1.53076 | − | 0.546556i | ||||
\(263\) | −9.67183 | −0.596390 | −0.298195 | − | 0.954505i | \(-0.596385\pi\) | ||||
−0.298195 | + | 0.954505i | \(0.596385\pi\) | |||||||
\(264\) | −0.533898 | + | 0.886707i | −0.0328592 | + | 0.0545730i | ||||
\(265\) | −3.00769 | − | 25.6619i | −0.184761 | − | 1.57640i | ||||
\(266\) | −12.7673 | − | 12.2907i | −0.782811 | − | 0.753590i | ||||
\(267\) | 13.6498 | 0.835353 | ||||||||
\(268\) | 18.8238 | − | 15.4061i | 1.14985 | − | 0.941078i | ||||
\(269\) | 1.72109i | 0.104937i | 0.998623 | + | 0.0524684i | \(0.0167089\pi\) | ||||
−0.998623 | + | 0.0524684i | \(0.983291\pi\) | |||||||
\(270\) | 1.40279 | + | 2.83411i | 0.0853712 | + | 0.172478i | ||||
\(271\) | 8.11648 | 0.493041 | 0.246521 | − | 0.969138i | \(-0.420713\pi\) | ||||
0.246521 | + | 0.969138i | \(0.420713\pi\) | |||||||
\(272\) | −0.116231 | + | 0.576254i | −0.00704755 | + | 0.0349405i | ||||
\(273\) | −4.09357 | + | 2.03567i | −0.247754 | + | 0.123205i | ||||
\(274\) | 10.2626 | + | 28.7429i | 0.619988 | + | 1.73642i | ||||
\(275\) | −0.423085 | − | 1.78011i | −0.0255130 | − | 0.107345i | ||||
\(276\) | −4.36970 | − | 5.33907i | −0.263025 | − | 0.321375i | ||||
\(277\) | 1.12611i | 0.0676615i | 0.999428 | + | 0.0338307i | \(0.0107707\pi\) | ||||
−0.999428 | + | 0.0338307i | \(0.989229\pi\) | |||||||
\(278\) | 17.5225 | − | 6.25640i | 1.05093 | − | 0.375234i | ||||
\(279\) | −6.07392 | −0.363636 | ||||||||
\(280\) | −16.7223 | + | 0.605158i | −0.999346 | + | 0.0361651i | ||||
\(281\) | 14.3818 | 0.857944 | 0.428972 | − | 0.903318i | \(-0.358876\pi\) | ||||
0.428972 | + | 0.903318i | \(0.358876\pi\) | |||||||
\(282\) | 5.11116 | − | 1.82494i | 0.304365 | − | 0.108674i | ||||
\(283\) | 23.4832i | 1.39593i | 0.716132 | + | 0.697965i | \(0.245911\pi\) | ||||
−0.716132 | + | 0.697965i | \(0.754089\pi\) | |||||||
\(284\) | 9.85579 | + | 12.0422i | 0.584834 | + | 0.714573i | ||||
\(285\) | 1.23285 | + | 10.5188i | 0.0730278 | + | 0.623081i | ||||
\(286\) | 0.300702 | + | 0.842184i | 0.0177809 | + | 0.0497994i | ||||
\(287\) | −16.9691 | + | 8.43850i | −1.00166 | + | 0.498109i | ||||
\(288\) | −0.811273 | − | 5.59838i | −0.0478047 | − | 0.329888i | ||||
\(289\) | −16.9784 | −0.998729 | ||||||||
\(290\) | 14.9938 | − | 7.42145i | 0.880467 | − | 0.435803i | ||||
\(291\) | − | 16.1970i | − | 0.949487i | ||||||
\(292\) | −7.04824 | + | 5.76854i | −0.412467 | + | 0.337578i | ||||
\(293\) | 13.3608 | 0.780544 | 0.390272 | − | 0.920700i | \(-0.372381\pi\) | ||||
0.390272 | + | 0.920700i | \(0.372381\pi\) | |||||||
\(294\) | 9.44288 | + | 2.97189i | 0.550720 | + | 0.173324i | ||||
\(295\) | 13.7444 | − | 1.61090i | 0.800228 | − | 0.0937902i | ||||
\(296\) | −18.2369 | − | 10.9807i | −1.06000 | − | 0.638241i | ||||
\(297\) | −0.365940 | −0.0212340 | ||||||||
\(298\) | −14.3395 | + | 5.11991i | −0.830664 | + | 0.296588i | ||||
\(299\) | −5.96089 | −0.344727 | ||||||||
\(300\) | 7.95133 | + | 6.06435i | 0.459070 | + | 0.350126i | ||||
\(301\) | −10.1909 | − | 20.4930i | −0.587393 | − | 1.18120i | ||||
\(302\) | 1.59055 | + | 4.45471i | 0.0915261 | + | 0.256340i | ||||
\(303\) | −4.41655 | −0.253724 | ||||||||
\(304\) | 3.74588 | − | 18.5714i | 0.214841 | − | 1.06515i | ||||
\(305\) | −0.0905929 | − | 0.772949i | −0.00518733 | − | 0.0442589i | ||||
\(306\) | −0.195737 | + | 0.0698879i | −0.0111895 | + | 0.00399522i | ||||
\(307\) | − | 27.7860i | − | 1.58583i | −0.609333 | − | 0.792914i | \(-0.708563\pi\) | ||
0.609333 | − | 0.792914i | \(-0.291437\pi\) | |||||||
\(308\) | 0.795654 | − | 1.76535i | 0.0453366 | − | 0.100590i | ||||
\(309\) | 12.4670 | 0.709222 | ||||||||
\(310\) | −17.2142 | + | 8.52044i | −0.977698 | + | 0.483929i | ||||
\(311\) | −4.53917 | −0.257393 | −0.128696 | − | 0.991684i | \(-0.541079\pi\) | ||||
−0.128696 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(312\) | −4.18705 | − | 2.52108i | −0.237045 | − | 0.142728i | ||||
\(313\) | −2.86576 | −0.161982 | −0.0809911 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809911 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(314\) | −25.7275 | + | 9.18601i | −1.45189 | + | 0.518396i | ||||
\(315\) | −3.23297 | − | 4.95458i | −0.182157 | − | 0.279159i | ||||
\(316\) | −18.0434 | − | 22.0461i | −1.01502 | − | 1.24019i | ||||
\(317\) | 16.3518i | 0.918411i | 0.888330 | + | 0.459206i | \(0.151866\pi\) | ||||
−0.888330 | + | 0.459206i | \(0.848134\pi\) | |||||||
\(318\) | −15.3896 | + | 5.49484i | −0.863004 | + | 0.308135i | ||||
\(319\) | 1.93600i | 0.108395i | ||||||||
\(320\) | −10.1526 | − | 14.7284i | −0.567547 | − | 0.823341i | ||||
\(321\) | 6.16409i | 0.344046i | ||||||||
\(322\) | 9.29878 | + | 8.95168i | 0.518201 | + | 0.498858i | ||||
\(323\) | −0.696079 | −0.0387308 | ||||||||
\(324\) | 1.54772 | − | 1.26671i | 0.0859845 | − | 0.0703729i | ||||
\(325\) | 8.40573 | − | 1.99782i | 0.466266 | − | 0.110819i | ||||
\(326\) | 23.4836 | − | 8.38481i | 1.30064 | − | 0.464392i | ||||
\(327\) | − | 2.76468i | − | 0.152887i | ||||||
\(328\) | −17.3566 | − | 10.4507i | −0.958359 | − | 0.577041i | ||||
\(329\) | −9.09128 | + | 4.52096i | −0.501218 | + | 0.249248i | ||||
\(330\) | −1.03711 | + | 0.513337i | −0.0570912 | + | 0.0282583i | ||||
\(331\) | 16.4160i | 0.902306i | 0.892447 | + | 0.451153i | \(0.148987\pi\) | ||||
−0.892447 | + | 0.451153i | \(0.851013\pi\) | |||||||
\(332\) | −4.48176 | − | 5.47600i | −0.245969 | − | 0.300534i | ||||
\(333\) | − | 7.52630i | − | 0.412439i | ||||||
\(334\) | −7.95586 | − | 22.2822i | −0.435325 | − | 1.21923i | ||||
\(335\) | 27.0108 | − | 3.16578i | 1.47576 | − | 0.172965i | ||||
\(336\) | 2.74566 | + | 10.2206i | 0.149788 | + | 0.557581i | ||||
\(337\) | − | 35.3369i | − | 1.92492i | −0.271415 | − | 0.962462i | \(-0.587492\pi\) | ||
0.271415 | − | 0.962462i | \(-0.412508\pi\) | |||||||
\(338\) | 13.3374 | − | 4.76212i | 0.725460 | − | 0.259025i | ||||
\(339\) | 9.60538 | 0.521693 | ||||||||
\(340\) | −0.456702 | + | 0.472648i | −0.0247682 | + | 0.0256329i | ||||
\(341\) | − | 2.22269i | − | 0.120365i | ||||||
\(342\) | 6.30819 | − | 2.25234i | 0.341108 | − | 0.121792i | ||||
\(343\) | −18.1995 | − | 3.43179i | −0.982682 | − | 0.185299i | ||||
\(344\) | 12.6209 | − | 20.9610i | 0.680473 | − | 1.13014i | ||||
\(345\) | −0.897923 | − | 7.66118i | −0.0483426 | − | 0.412464i | ||||
\(346\) | −23.4321 | + | 8.36641i | −1.25971 | + | 0.449781i | ||||
\(347\) | 0.819726 | 0.0440052 | 0.0220026 | − | 0.999758i | \(-0.492996\pi\) | ||||
0.0220026 | + | 0.999758i | \(0.492996\pi\) | |||||||
\(348\) | −6.70153 | − | 8.18820i | −0.359240 | − | 0.438933i | ||||
\(349\) | 18.9508i | 1.01441i | 0.861825 | + | 0.507206i | \(0.169322\pi\) | ||||
−0.861825 | + | 0.507206i | \(0.830678\pi\) | |||||||
\(350\) | −16.1128 | − | 9.50665i | −0.861267 | − | 0.508152i | ||||
\(351\) | − | 1.72798i | − | 0.0922325i | ||||||
\(352\) | 2.04867 | − | 0.296877i | 0.109194 | − | 0.0158236i | ||||
\(353\) | −18.6922 | −0.994888 | −0.497444 | − | 0.867496i | \(-0.665728\pi\) | ||||
−0.497444 | + | 0.867496i | \(0.665728\pi\) | |||||||
\(354\) | −2.94300 | − | 8.24256i | −0.156419 | − | 0.438087i | ||||
\(355\) | 2.02525 | + | 17.2797i | 0.107489 | + | 0.917111i | ||||
\(356\) | −17.2904 | − | 21.1260i | −0.916387 | − | 1.11968i | ||||
\(357\) | 0.348160 | − | 0.173135i | 0.0184266 | − | 0.00916325i | ||||
\(358\) | 3.57953 | + | 10.0253i | 0.189184 | + | 0.529854i | ||||
\(359\) | 20.3800i | 1.07562i | 0.843067 | + | 0.537808i | \(0.180747\pi\) | ||||
−0.843067 | + | 0.537808i | \(0.819253\pi\) | |||||||
\(360\) | 2.60948 | − | 5.76113i | 0.137531 | − | 0.303638i | ||||
\(361\) | 3.43313 | 0.180691 | ||||||||
\(362\) | 1.82204 | + | 5.10305i | 0.0957644 | + | 0.268210i | ||||
\(363\) | 10.8661i | 0.570322i | ||||||||
\(364\) | 8.33603 | + | 3.75709i | 0.436927 | + | 0.196925i | ||||
\(365\) | −10.1137 | + | 1.18537i | −0.529375 | + | 0.0620451i | ||||
\(366\) | −0.463541 | + | 0.165507i | −0.0242297 | + | 0.00865120i | ||||
\(367\) | − | 2.16777i | − | 0.113157i | −0.998398 | − | 0.0565783i | \(-0.981981\pi\) | ||
0.998398 | − | 0.0565783i | \(-0.0180191\pi\) | |||||||
\(368\) | −2.72824 | + | 13.5261i | −0.142219 | + | 0.705099i | ||||
\(369\) | − | 7.16300i | − | 0.372891i | ||||||
\(370\) | −10.5578 | − | 21.3304i | −0.548876 | − | 1.10891i | ||||
\(371\) | 27.3736 | − | 13.6125i | 1.42117 | − | 0.706724i | ||||
\(372\) | 7.69391 | + | 9.40073i | 0.398911 | + | 0.487405i | ||||
\(373\) | − | 9.91788i | − | 0.513528i | −0.966474 | − | 0.256764i | \(-0.917344\pi\) | ||
0.966474 | − | 0.256764i | \(-0.0826564\pi\) | |||||||
\(374\) | −0.0255748 | − | 0.0716280i | −0.00132244 | − | 0.00370380i | ||||
\(375\) | 3.83388 | + | 10.5024i | 0.197981 | + | 0.542344i | ||||
\(376\) | −9.29887 | − | 5.59898i | −0.479553 | − | 0.288745i | ||||
\(377\) | −9.14183 | −0.470828 | ||||||||
\(378\) | −2.59496 | + | 2.69558i | −0.133470 | + | 0.138646i | ||||
\(379\) | − | 0.146790i | − | 0.00754011i | −0.999993 | − | 0.00377005i | \(-0.998800\pi\) | ||
0.999993 | − | 0.00377005i | \(-0.00120005\pi\) | |||||||
\(380\) | 14.7185 | − | 15.2324i | 0.755045 | − | 0.781408i | ||||
\(381\) | − | 8.58236i | − | 0.439688i | ||||||
\(382\) | 9.56791 | + | 26.7971i | 0.489537 | + | 1.37106i | ||||
\(383\) | − | 34.9127i | − | 1.78395i | −0.452081 | − | 0.891977i | \(-0.649318\pi\) | ||
0.452081 | − | 0.891977i | \(-0.350682\pi\) | |||||||
\(384\) | −7.63707 | + | 8.34716i | −0.389728 | + | 0.425964i | ||||
\(385\) | 1.81308 | − | 1.18307i | 0.0924031 | − | 0.0602950i | ||||
\(386\) | 9.35309 | + | 26.1955i | 0.476060 | + | 1.33331i | ||||
\(387\) | 8.65051 | 0.439730 | ||||||||
\(388\) | −25.0685 | + | 20.5170i | −1.27266 | + | 1.04159i | ||||
\(389\) | 27.6435 | 1.40158 | 0.700790 | − | 0.713368i | \(-0.252831\pi\) | ||||
0.700790 | + | 0.713368i | \(0.252831\pi\) | |||||||
\(390\) | −2.42399 | − | 4.89727i | −0.122743 | − | 0.247983i | ||||
\(391\) | 0.506975 | 0.0256388 | ||||||||
\(392\) | −7.36176 | − | 18.3795i | −0.371825 | − | 0.928303i | ||||
\(393\) | − | 18.6036i | − | 0.938427i | ||||||
\(394\) | 2.59038 | + | 7.25495i | 0.130501 | + | 0.365499i | ||||
\(395\) | −3.70771 | − | 31.6346i | −0.186555 | − | 1.59171i | ||||
\(396\) | 0.463541 | + | 0.566373i | 0.0232938 | + | 0.0284613i | ||||
\(397\) | 9.62119 | 0.482874 | 0.241437 | − | 0.970417i | \(-0.422381\pi\) | ||||
0.241437 | + | 0.970417i | \(0.422381\pi\) | |||||||
\(398\) | 8.87869 | − | 3.17013i | 0.445048 | − | 0.158904i | ||||
\(399\) | −11.2204 | + | 5.57976i | −0.561724 | + | 0.279337i | ||||
\(400\) | −0.686127 | − | 19.9882i | −0.0343063 | − | 0.999411i | ||||
\(401\) | −21.8030 | −1.08879 | −0.544395 | − | 0.838829i | \(-0.683241\pi\) | ||||
−0.544395 | + | 0.838829i | \(0.683241\pi\) | |||||||
\(402\) | −5.78367 | − | 16.1985i | −0.288463 | − | 0.807907i | ||||
\(403\) | 10.4956 | 0.522822 | ||||||||
\(404\) | 5.59450 | + | 6.83559i | 0.278337 | + | 0.340083i | ||||
\(405\) | 2.22087 | − | 0.260295i | 0.110356 | − | 0.0129342i | ||||
\(406\) | 14.2609 | + | 13.7286i | 0.707759 | + | 0.681340i | ||||
\(407\) | 2.75417 | 0.136519 | ||||||||
\(408\) | 0.356110 | + | 0.214418i | 0.0176300 | + | 0.0106153i | ||||
\(409\) | 30.1429i | 1.49047i | 0.666801 | + | 0.745236i | \(0.267663\pi\) | ||||
−0.666801 | + | 0.745236i | \(0.732337\pi\) | |||||||
\(410\) | −10.0482 | − | 20.3007i | −0.496245 | − | 1.00258i | ||||
\(411\) | 21.5809 | 1.06451 | ||||||||
\(412\) | −15.7921 | − | 19.2954i | −0.778020 | − | 0.950616i | ||||
\(413\) | 7.29076 | + | 14.6611i | 0.358755 | + | 0.721427i | ||||
\(414\) | −4.59445 | + | 1.64045i | −0.225805 | + | 0.0806235i | ||||
\(415\) | −0.920951 | − | 7.85766i | −0.0452077 | − | 0.385717i | ||||
\(416\) | 1.40186 | + | 9.67386i | 0.0687319 | + | 0.474300i | ||||
\(417\) | − | 13.1564i | − | 0.644271i | ||||||
\(418\) | 0.824220 | + | 2.30842i | 0.0403139 | + | 0.112908i | ||||
\(419\) | 24.2208 | 1.18327 | 0.591633 | − | 0.806208i | \(-0.298484\pi\) | ||||
0.591633 | + | 0.806208i | \(0.298484\pi\) | |||||||
\(420\) | −3.57307 | + | 11.2798i | −0.174348 | + | 0.550396i | ||||
\(421\) | 5.72899 | 0.279214 | 0.139607 | − | 0.990207i | \(-0.455416\pi\) | ||||
0.139607 | + | 0.990207i | \(0.455416\pi\) | |||||||
\(422\) | −4.19272 | − | 11.7427i | −0.204099 | − | 0.571625i | ||||
\(423\) | − | 3.83760i | − | 0.186591i | ||||||
\(424\) | 27.9986 | + | 16.8584i | 1.35973 | + | 0.818715i | ||||
\(425\) | −0.714909 | + | 0.169915i | −0.0346782 | + | 0.00824209i | ||||
\(426\) | 10.3627 | − | 3.70000i | 0.502075 | − | 0.179266i | ||||
\(427\) | 0.824505 | − | 0.410014i | 0.0399006 | − | 0.0198420i | ||||
\(428\) | 9.54029 | − | 7.80813i | 0.461147 | − | 0.377420i | ||||
\(429\) | 0.632335 | 0.0305294 | ||||||||
\(430\) | 24.5165 | − | 12.1349i | 1.18229 | − | 0.585195i | ||||
\(431\) | 34.1933i | 1.64703i | 0.567293 | + | 0.823516i | \(0.307991\pi\) | ||||
−0.567293 | + | 0.823516i | \(0.692009\pi\) | |||||||
\(432\) | −3.92103 | − | 0.790878i | −0.188651 | − | 0.0380511i | ||||
\(433\) | −32.7841 | −1.57550 | −0.787751 | − | 0.615994i | \(-0.788755\pi\) | ||||
−0.787751 | + | 0.615994i | \(0.788755\pi\) | |||||||
\(434\) | −16.3728 | − | 15.7616i | −0.785917 | − | 0.756581i | ||||
\(435\) | −1.37709 | − | 11.7495i | −0.0660263 | − | 0.563344i | ||||
\(436\) | −4.27896 | + | 3.50206i | −0.204925 | + | 0.167718i | ||||
\(437\) | −16.3387 | −0.781587 | ||||||||
\(438\) | 2.16559 | + | 6.06523i | 0.103476 | + | 0.289808i | ||||
\(439\) | 32.1286 | 1.53342 | 0.766708 | − | 0.641996i | \(-0.221894\pi\) | ||||
0.766708 | + | 0.641996i | \(0.221894\pi\) | |||||||
\(440\) | 2.10823 | + | 0.954911i | 0.100506 | + | 0.0455236i | ||||
\(441\) | 4.22431 | − | 5.58168i | 0.201158 | − | 0.265794i | ||||
\(442\) | 0.338229 | − | 0.120765i | 0.0160879 | − | 0.00574418i | ||||
\(443\) | −12.4260 | −0.590377 | −0.295189 | − | 0.955439i | \(-0.595382\pi\) | ||||
−0.295189 | + | 0.955439i | \(0.595382\pi\) | |||||||
\(444\) | −11.6486 | + | 9.53366i | −0.552819 | + | 0.452448i | ||||
\(445\) | −3.55297 | − | 30.3143i | −0.168427 | − | 1.43704i | ||||
\(446\) | 3.41754 | + | 9.57160i | 0.161825 | + | 0.453228i | ||||
\(447\) | 10.7665i | 0.509237i | ||||||||
\(448\) | 12.3407 | − | 17.1961i | 0.583045 | − | 0.812440i | ||||
\(449\) | 3.27542 | 0.154577 | 0.0772883 | − | 0.997009i | \(-0.475374\pi\) | ||||
0.0772883 | + | 0.997009i | \(0.475374\pi\) | |||||||
\(450\) | 5.92904 | − | 3.85312i | 0.279498 | − | 0.181638i | ||||
\(451\) | 2.62123 | 0.123429 | ||||||||
\(452\) | −12.1673 | − | 14.8665i | −0.572300 | − | 0.699259i | ||||
\(453\) | 3.34472 | 0.157149 | ||||||||
\(454\) | −2.26581 | − | 6.34591i | −0.106340 | − | 0.297828i | ||||
\(455\) | 5.58649 | + | 8.56140i | 0.261899 | + | 0.401365i | ||||
\(456\) | −11.4766 | − | 6.91025i | −0.537443 | − | 0.323602i | ||||
\(457\) | 17.9017i | 0.837406i | 0.908123 | + | 0.418703i | \(0.137515\pi\) | ||||
−0.908123 | + | 0.418703i | \(0.862485\pi\) | |||||||
\(458\) | −7.35535 | − | 20.6004i | −0.343693 | − | 0.962591i | ||||
\(459\) | 0.146965i | 0.00685973i | ||||||||
\(460\) | −10.7200 | + | 11.0943i | −0.499821 | + | 0.517272i | ||||
\(461\) | 40.2381i | 1.87408i | 0.349226 | + | 0.937039i | \(0.386445\pi\) | ||||
−0.349226 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(462\) | −0.986422 | − | 0.949601i | −0.0458925 | − | 0.0441794i | ||||
\(463\) | 25.8834 | 1.20290 | 0.601451 | − | 0.798910i | \(-0.294589\pi\) | ||||
0.601451 | + | 0.798910i | \(0.294589\pi\) | |||||||
\(464\) | −4.18413 | + | 20.7442i | −0.194243 | + | 0.963025i | ||||
\(465\) | 1.58101 | + | 13.4894i | 0.0733176 | + | 0.625554i | ||||
\(466\) | −6.55806 | − | 18.3674i | −0.303796 | − | 0.850852i | ||||
\(467\) | 20.8217i | 0.963511i | 0.876306 | + | 0.481756i | \(0.160001\pi\) | ||||
−0.876306 | + | 0.481756i | \(0.839999\pi\) | |||||||
\(468\) | −2.67442 | + | 2.18885i | −0.123625 | + | 0.101180i | ||||
\(469\) | 14.3280 | + | 28.8124i | 0.661605 | + | 1.33043i | ||||
\(470\) | −5.38336 | − | 10.8762i | −0.248316 | − | 0.501681i | ||||
\(471\) | 19.3169i | 0.890078i | ||||||||
\(472\) | −9.02924 | + | 14.9959i | −0.415605 | + | 0.690243i | ||||
\(473\) | 3.16557i | 0.145553i | ||||||||
\(474\) | −18.9714 | + | 6.77373i | −0.871385 | + | 0.311128i | ||||
\(475\) | 23.0400 | − | 5.47600i | 1.05715 | − | 0.251256i | ||||
\(476\) | −0.708982 | − | 0.319542i | −0.0324961 | − | 0.0146462i | ||||
\(477\) | 11.5549i | 0.529063i | ||||||||
\(478\) | −0.664230 | − | 1.86033i | −0.0303812 | − | 0.0850895i | ||||
\(479\) | −6.30716 | −0.288181 | −0.144091 | − | 0.989564i | \(-0.546026\pi\) | ||||
−0.144091 | + | 0.989564i | \(0.546026\pi\) | |||||||
\(480\) | −12.2221 | + | 3.25896i | −0.557859 | + | 0.148750i | ||||
\(481\) | 13.0053i | 0.592989i | ||||||||
\(482\) | 9.02557 | + | 25.2782i | 0.411103 | + | 1.15139i | ||||
\(483\) | 8.17219 | − | 4.06391i | 0.371847 | − | 0.184914i | ||||
\(484\) | 16.8177 | − | 13.7642i | 0.764439 | − | 0.625646i | ||||
\(485\) | −35.9715 | + | 4.21601i | −1.63338 | + | 0.191439i | ||||
\(486\) | −0.475542 | − | 1.33186i | −0.0215710 | − | 0.0604146i | ||||
\(487\) | 2.04829 | 0.0928167 | 0.0464083 | − | 0.998923i | \(-0.485222\pi\) | ||||
0.0464083 | + | 0.998923i | \(0.485222\pi\) | |||||||
\(488\) | 0.843332 | + | 0.507782i | 0.0381758 | + | 0.0229862i | ||||
\(489\) | − | 17.6321i | − | 0.797353i | ||||||
\(490\) | 4.14223 | − | 21.7449i | 0.187127 | − | 0.982336i | ||||
\(491\) | − | 2.63143i | − | 0.118755i | −0.998236 | − | 0.0593774i | \(-0.981088\pi\) | ||
0.998236 | − | 0.0593774i | \(-0.0189115\pi\) | |||||||
\(492\) | −11.0863 | + | 9.07346i | −0.499810 | + | 0.409063i | ||||
\(493\) | 0.777515 | 0.0350175 | ||||||||
\(494\) | −10.9004 | + | 3.89198i | −0.490432 | + | 0.175109i | ||||
\(495\) | 0.0952524 | + | 0.812704i | 0.00428127 | + | 0.0365283i | ||||
\(496\) | 4.80373 | − | 23.8160i | 0.215694 | − | 1.06937i | ||||
\(497\) | −18.4323 | + | 9.16608i | −0.826799 | + | 0.411155i | ||||
\(498\) | −4.71227 | + | 1.68252i | −0.211162 | + | 0.0753953i | ||||
\(499\) | 26.3951i | 1.18161i | 0.806815 | + | 0.590804i | \(0.201190\pi\) | ||||
−0.806815 | + | 0.590804i | \(0.798810\pi\) | |||||||
\(500\) | 11.3984 | − | 19.2374i | 0.509753 | − | 0.860321i | ||||
\(501\) | −16.7301 | −0.747446 | ||||||||
\(502\) | −14.6437 | + | 5.22855i | −0.653582 | + | 0.233361i | ||||
\(503\) | 25.3043i | 1.12826i | 0.825685 | + | 0.564132i | \(0.190789\pi\) | ||||
−0.825685 | + | 0.564132i | \(0.809211\pi\) | |||||||
\(504\) | 7.45908 | + | 0.601749i | 0.332254 | + | 0.0268040i | ||||
\(505\) | 1.14961 | + | 9.80857i | 0.0511568 | + | 0.436476i | ||||
\(506\) | −0.600305 | − | 1.68129i | −0.0266868 | − | 0.0747425i | ||||
\(507\) | − | 10.0141i | − | 0.444742i | ||||||
\(508\) | −13.2831 | + | 10.8714i | −0.589342 | + | 0.482340i | ||||
\(509\) | − | 32.2172i | − | 1.42800i | −0.700145 | − | 0.714001i | \(-0.746881\pi\) | ||
0.700145 | − | 0.714001i | \(-0.253119\pi\) | |||||||
\(510\) | 0.206161 | + | 0.416514i | 0.00912896 | + | 0.0184436i | ||||
\(511\) | −5.36486 | − | 10.7883i | −0.237327 | − | 0.477246i | ||||
\(512\) | 22.5931 | + | 1.24660i | 0.998481 | + | 0.0550925i | ||||
\(513\) | − | 4.73636i | − | 0.209115i | ||||||
\(514\) | 24.2051 | − | 8.64244i | 1.06764 | − | 0.381201i | ||||
\(515\) | −3.24509 | − | 27.6875i | −0.142996 | − | 1.22006i | ||||
\(516\) | −10.9577 | − | 13.3886i | −0.482386 | − | 0.589399i | ||||
\(517\) | 1.40433 | 0.0617625 | ||||||||
\(518\) | 19.5305 | − | 20.2878i | 0.858120 | − | 0.891393i | ||||
\(519\) | 17.5934i | 0.772266i | ||||||||
\(520\) | −4.50911 | + | 9.95510i | −0.197738 | + | 0.436560i | ||||
\(521\) | − | 31.1683i | − | 1.36551i | −0.730649 | − | 0.682753i | \(-0.760782\pi\) | ||
0.730649 | − | 0.682753i | \(-0.239218\pi\) | |||||||
\(522\) | −7.04621 | + | 2.51585i | −0.308404 | + | 0.110116i | ||||
\(523\) | 6.94386i | 0.303634i | 0.988409 | + | 0.151817i | \(0.0485124\pi\) | ||||
−0.988409 | + | 0.151817i | \(0.951488\pi\) | |||||||
\(524\) | −28.7932 | + | 23.5654i | −1.25784 | + | 1.02946i | ||||
\(525\) | −10.1619 | + | 8.46965i | −0.443504 | + | 0.369646i | ||||
\(526\) | 12.8816 | − | 4.59935i | 0.561662 | − | 0.200541i | ||||
\(527\) | −0.892652 | −0.0388846 | ||||||||
\(528\) | 0.289414 | − | 1.43486i | 0.0125951 | − | 0.0624444i | ||||
\(529\) | −11.1000 | −0.482609 | ||||||||
\(530\) | 16.2091 | + | 32.7479i | 0.704080 | + | 1.42248i | ||||
\(531\) | −6.18874 | −0.268569 | ||||||||
\(532\) | 22.8490 | + | 10.2982i | 0.990629 | + | 0.446482i | ||||
\(533\) | 12.3775i | 0.536129i | ||||||||
\(534\) | −18.1796 | + | 6.49104i | −0.786710 | + | 0.280895i | ||||
\(535\) | 13.6896 | − | 1.60448i | 0.591854 | − | 0.0693678i | ||||
\(536\) | −17.7445 | + | 29.4703i | −0.766445 | + | 1.27292i | ||||
\(537\) | 7.52728 | 0.324826 | ||||||||
\(538\) | −0.818451 | − | 2.29226i | −0.0352859 | − | 0.0988263i | ||||
\(539\) | 2.04256 | + | 1.54584i | 0.0879793 | + | 0.0665843i | ||||
\(540\) | −3.21606 | − | 3.10756i | −0.138397 | − | 0.133728i | ||||
\(541\) | −14.0032 | −0.602044 | −0.301022 | − | 0.953617i | \(-0.597328\pi\) | ||||
−0.301022 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(542\) | −10.8100 | + | 3.85972i | −0.464331 | + | 0.165789i | ||||
\(543\) | 3.83151 | 0.164426 | ||||||||
\(544\) | −0.119229 | − | 0.822765i | −0.00511189 | − | 0.0352757i | ||||
\(545\) | −6.13999 | + | 0.719634i | −0.263008 | + | 0.0308257i | ||||
\(546\) | 4.48403 | − | 4.65790i | 0.191899 | − | 0.199340i | ||||
\(547\) | −15.3265 | −0.655313 | −0.327656 | − | 0.944797i | \(-0.606259\pi\) | ||||
−0.327656 | + | 0.944797i | \(0.606259\pi\) | |||||||
\(548\) | −27.3368 | − | 33.4013i | −1.16777 | − | 1.42683i | ||||
\(549\) | 0.348039i | 0.0148540i | ||||||||
\(550\) | 1.41001 | + | 2.16967i | 0.0601230 | + | 0.0925151i | ||||
\(551\) | −25.0577 | −1.06749 | ||||||||
\(552\) | 8.35879 | + | 5.03294i | 0.355774 | + | 0.214216i | ||||
\(553\) | 33.7446 | − | 16.7807i | 1.43497 | − | 0.713587i | ||||
\(554\) | −0.535513 | − | 1.49983i | −0.0227517 | − | 0.0637215i | ||||
\(555\) | −16.7149 | + | 1.95906i | −0.709508 | + | 0.0831574i | ||||
\(556\) | −20.3624 | + | 16.6654i | −0.863558 | + | 0.706768i | ||||
\(557\) | 14.6903i | 0.622448i | 0.950337 | + | 0.311224i | \(0.100739\pi\) | ||||
−0.950337 | + | 0.311224i | \(0.899261\pi\) | |||||||
\(558\) | 8.08963 | − | 2.88840i | 0.342461 | − | 0.122276i | ||||
\(559\) | −14.9479 | −0.632227 | ||||||||
\(560\) | 21.9840 | − | 8.75811i | 0.928993 | − | 0.370098i | ||||
\(561\) | −0.0537803 | −0.00227061 | ||||||||
\(562\) | −19.1545 | + | 6.83913i | −0.807986 | + | 0.288491i | ||||
\(563\) | 25.5127i | 1.07523i | 0.843190 | + | 0.537616i | \(0.180675\pi\) | ||||
−0.843190 | + | 0.537616i | \(0.819325\pi\) | |||||||
\(564\) | −5.93954 | + | 4.86114i | −0.250100 | + | 0.204691i | ||||
\(565\) | −2.50023 | − | 21.3323i | −0.105186 | − | 0.897456i | ||||
\(566\) | −11.1672 | − | 31.2764i | −0.469393 | − | 1.31464i | ||||
\(567\) | 1.17807 | + | 2.36900i | 0.0494742 | + | 0.0994886i | ||||
\(568\) | −18.8531 | − | 11.3517i | −0.791060 | − | 0.476308i | ||||
\(569\) | 18.8877 | 0.791815 | 0.395908 | − | 0.918290i | \(-0.370430\pi\) | ||||
0.395908 | + | 0.918290i | \(0.370430\pi\) | |||||||
\(570\) | −6.64413 | − | 13.4234i | −0.278292 | − | 0.562243i | ||||
\(571\) | − | 16.5940i | − | 0.694436i | −0.937784 | − | 0.347218i | \(-0.887126\pi\) | ||
0.937784 | − | 0.347218i | \(-0.112874\pi\) | |||||||
\(572\) | −0.800987 | − | 0.978679i | −0.0334910 | − | 0.0409206i | ||||
\(573\) | 20.1200 | 0.840526 | ||||||||
\(574\) | 18.5877 | − | 19.3085i | 0.775836 | − | 0.805919i | ||||
\(575\) | −16.7807 | + | 3.98834i | −0.699805 | + | 0.166325i | ||||
\(576\) | 3.74277 | + | 7.07048i | 0.155949 | + | 0.294603i | ||||
\(577\) | 12.4355 | 0.517695 | 0.258848 | − | 0.965918i | \(-0.416657\pi\) | ||||
0.258848 | + | 0.965918i | \(0.416657\pi\) | |||||||
\(578\) | 22.6129 | − | 8.07393i | 0.940573 | − | 0.335831i | ||||
\(579\) | 19.6683 | 0.817386 | ||||||||
\(580\) | −16.4405 | + | 17.0145i | −0.682655 | + | 0.706490i | ||||
\(581\) | 8.38176 | − | 4.16813i | 0.347734 | − | 0.172923i | ||||
\(582\) | 7.70237 | + | 21.5722i | 0.319273 | + | 0.894199i | ||||
\(583\) | −4.22840 | −0.175123 | ||||||||
\(584\) | 6.64411 | − | 11.0346i | 0.274935 | − | 0.456617i | ||||
\(585\) | −3.83760 | + | 0.449783i | −0.158665 | + | 0.0185963i | ||||
\(586\) | −17.7947 | + | 6.35359i | −0.735092 | + | 0.262465i | ||||
\(587\) | 6.89502i | 0.284588i | 0.989824 | + | 0.142294i | \(0.0454478\pi\) | ||||
−0.989824 | + | 0.142294i | \(0.954552\pi\) | |||||||
\(588\) | −13.9899 | + | 0.532333i | −0.576933 | + | 0.0219531i | ||||
\(589\) | 28.7683 | 1.18538 | ||||||||
\(590\) | −17.5396 | + | 8.68152i | −0.722093 | + | 0.357412i | ||||
\(591\) | 5.44722 | 0.224069 | ||||||||
\(592\) | 29.5109 | + | 5.95239i | 1.21289 | + | 0.244642i | ||||
\(593\) | 7.25097 | 0.297762 | 0.148881 | − | 0.988855i | \(-0.452433\pi\) | ||||
0.148881 | + | 0.988855i | \(0.452433\pi\) | |||||||
\(594\) | 0.487382 | − | 0.174020i | 0.0199975 | − | 0.00714011i | ||||
\(595\) | −0.475133 | − | 0.728150i | −0.0194785 | − | 0.0298512i | ||||
\(596\) | 16.6635 | − | 13.6380i | 0.682564 | − | 0.558636i | ||||
\(597\) | − | 6.66636i | − | 0.272836i | ||||||
\(598\) | 7.93909 | − | 2.83465i | 0.324654 | − | 0.115917i | ||||
\(599\) | 30.0293i | 1.22696i | 0.789709 | + | 0.613482i | \(0.210232\pi\) | ||||
−0.789709 | + | 0.613482i | \(0.789768\pi\) | |||||||
\(600\) | −13.4739 | − | 4.29570i | −0.550071 | − | 0.175371i | ||||
\(601\) | 36.6770i | 1.49609i | 0.663650 | + | 0.748043i | \(0.269006\pi\) | ||||
−0.663650 | + | 0.748043i | \(0.730994\pi\) | |||||||
\(602\) | 23.3182 | + | 22.4477i | 0.950377 | + | 0.914902i | ||||
\(603\) | −12.1623 | −0.495286 | ||||||||
\(604\) | −4.23680 | − | 5.17670i | −0.172393 | − | 0.210637i | ||||
\(605\) | 24.1321 | − | 2.82839i | 0.981110 | − | 0.114990i | ||||
\(606\) | 5.88225 | − | 2.10025i | 0.238950 | − | 0.0853170i | ||||
\(607\) | 13.3370i | 0.541332i | 0.962673 | + | 0.270666i | \(0.0872439\pi\) | ||||
−0.962673 | + | 0.270666i | \(0.912756\pi\) | |||||||
\(608\) | 3.84248 | + | 26.5159i | 0.155833 | + | 1.07536i | ||||
\(609\) | 12.5332 | − | 6.23255i | 0.507869 | − | 0.252556i | ||||
\(610\) | 0.488227 | + | 0.986381i | 0.0197677 | + | 0.0399374i | ||||
\(611\) | 6.63128i | 0.268273i | ||||||||
\(612\) | 0.227460 | − | 0.186162i | 0.00919454 | − | 0.00752516i | ||||
\(613\) | 1.93442i | 0.0781304i | 0.999237 | + | 0.0390652i | \(0.0124380\pi\) | ||||
−0.999237 | + | 0.0390652i | \(0.987562\pi\) | |||||||
\(614\) | 13.2134 | + | 37.0071i | 0.533248 | + | 1.49348i | ||||
\(615\) | −15.9081 | + | 1.86449i | −0.641475 | + | 0.0751836i | ||||
\(616\) | −0.220204 | + | 2.72958i | −0.00887227 | + | 0.109978i | ||||
\(617\) | 25.8246i | 1.03966i | 0.854270 | + | 0.519829i | \(0.174004\pi\) | ||||
−0.854270 | + | 0.519829i | \(0.825996\pi\) | |||||||
\(618\) | −16.6043 | + | 5.92857i | −0.667924 | + | 0.238482i | ||||
\(619\) | −7.45062 | −0.299466 | −0.149733 | − | 0.988726i | \(-0.547841\pi\) | ||||
−0.149733 | + | 0.988726i | \(0.547841\pi\) | |||||||
\(620\) | 18.8751 | − | 19.5341i | 0.758041 | − | 0.784509i | ||||
\(621\) | 3.44964i | 0.138429i | ||||||||
\(622\) | 6.04556 | − | 2.15857i | 0.242405 | − | 0.0865506i | ||||
\(623\) | 32.3363 | − | 16.0804i | 1.29553 | − | 0.644246i | ||||
\(624\) | 6.77545 | + | 1.36662i | 0.271235 | + | 0.0547085i | ||||
\(625\) | 22.3266 | − | 11.2483i | 0.893063 | − | 0.449931i | ||||
\(626\) | 3.81680 | − | 1.36279i | 0.152550 | − | 0.0544679i | ||||
\(627\) | 1.73322 | 0.0692183 | ||||||||
\(628\) | 29.8972 | − | 24.4690i | 1.19303 | − | 0.976420i | ||||
\(629\) | − | 1.10610i | − | 0.0441032i | ||||||
\(630\) | 6.66198 | + | 5.06142i | 0.265420 | + | 0.201652i | ||||
\(631\) | − | 33.3176i | − | 1.32635i | −0.748463 | − | 0.663176i | \(-0.769208\pi\) | ||
0.748463 | − | 0.663176i | \(-0.230792\pi\) | |||||||
\(632\) | 34.5151 | + | 20.7820i | 1.37294 | + | 0.826665i | ||||
\(633\) | −8.81673 | −0.350434 | ||||||||
\(634\) | −7.77598 | − | 21.7784i | −0.308824 | − | 0.864932i | ||||
\(635\) | −19.0603 | + | 2.23394i | −0.756384 | + | 0.0886514i | ||||
\(636\) | 17.8838 | − | 14.6368i | 0.709138 | − | 0.580385i | ||||
\(637\) | −7.29951 | + | 9.64501i | −0.289217 | + | 0.382149i | ||||
\(638\) | −0.920649 | − | 2.57849i | −0.0364488 | − | 0.102083i | ||||
\(639\) | − | 7.78061i | − | 0.307796i | ||||||
\(640\) | 20.5258 | + | 14.7882i | 0.811354 | + | 0.584555i | ||||
\(641\) | −7.97123 | −0.314845 | −0.157422 | − | 0.987531i | \(-0.550318\pi\) | ||||
−0.157422 | + | 0.987531i | \(0.550318\pi\) | |||||||
\(642\) | −2.93128 | − | 8.20973i | −0.115688 | − | 0.324012i | ||||
\(643\) | − | 17.9282i | − | 0.707019i | −0.935431 | − | 0.353510i | \(-0.884988\pi\) | ||
0.935431 | − | 0.353510i | \(-0.115012\pi\) | |||||||
\(644\) | −16.6416 | − | 7.50046i | −0.655771 | − | 0.295560i | ||||
\(645\) | −2.25168 | − | 19.2116i | −0.0886600 | − | 0.756457i | ||||
\(646\) | 0.927082 | − | 0.331014i | 0.0364755 | − | 0.0130236i | ||||
\(647\) | − | 32.2608i | − | 1.26830i | −0.773208 | − | 0.634152i | \(-0.781349\pi\) | ||
0.773208 | − | 0.634152i | \(-0.218651\pi\) | |||||||
\(648\) | −1.45898 | + | 2.42309i | −0.0573141 | + | 0.0951881i | ||||
\(649\) | − | 2.26471i | − | 0.0888976i | ||||||
\(650\) | −10.2452 | + | 6.65809i | −0.401851 | + | 0.261152i | ||||
\(651\) | −14.3891 | + | 7.15549i | −0.563954 | + | 0.280446i | ||||
\(652\) | −27.2896 | + | 22.3349i | −1.06874 | + | 0.874700i | ||||
\(653\) | 8.09685i | 0.316854i | 0.987371 | + | 0.158427i | \(0.0506423\pi\) | ||||
−0.987371 | + | 0.158427i | \(0.949358\pi\) | |||||||
\(654\) | 1.31472 | + | 3.68218i | 0.0514097 | + | 0.143985i | ||||
\(655\) | −41.3161 | + | 4.84242i | −1.61435 | + | 0.189209i | ||||
\(656\) | 28.0864 | + | 5.66506i | 1.09659 | + | 0.221183i | ||||
\(657\) | 4.55395 | 0.177666 | ||||||||
\(658\) | 9.95844 | − | 10.3446i | 0.388220 | − | 0.403274i | ||||
\(659\) | − | 39.2582i | − | 1.52928i | −0.644456 | − | 0.764641i | \(-0.722916\pi\) | ||
0.644456 | − | 0.764641i | \(-0.277084\pi\) | |||||||
\(660\) | 1.13718 | − | 1.17689i | 0.0442647 | − | 0.0458102i | ||||
\(661\) | − | 14.5952i | − | 0.567688i | −0.958870 | − | 0.283844i | \(-0.908390\pi\) | ||
0.958870 | − | 0.283844i | \(-0.0916099\pi\) | |||||||
\(662\) | −7.80650 | − | 21.8639i | −0.303408 | − | 0.849764i | ||||
\(663\) | − | 0.253952i | − | 0.00986266i | ||||||
\(664\) | 8.57316 | + | 5.16202i | 0.332703 | + | 0.200325i | ||||
\(665\) | 15.3125 | + | 23.4667i | 0.593794 | + | 0.910000i | ||||
\(666\) | 3.57907 | + | 10.0240i | 0.138686 | + | 0.388422i | ||||
\(667\) | 18.2503 | 0.706653 | ||||||||
\(668\) | 21.1922 | + | 25.8935i | 0.819952 | + | 1.00185i | ||||
\(669\) | 7.18662 | 0.277851 | ||||||||
\(670\) | −34.4692 | + | 17.0611i | −1.33166 | + | 0.659129i | ||||
\(671\) | −0.127361 | −0.00491674 | ||||||||
\(672\) | −8.51717 | − | 12.3068i | −0.328557 | − | 0.474746i | ||||
\(673\) | 32.3547i | 1.24718i | 0.781751 | + | 0.623591i | \(0.214327\pi\) | ||||
−0.781751 | + | 0.623591i | \(0.785673\pi\) | |||||||
\(674\) | 16.8042 | + | 47.0640i | 0.647273 | + | 1.81284i | ||||
\(675\) | −1.15616 | − | 4.86449i | −0.0445006 | − | 0.187234i | ||||
\(676\) | −15.4990 | + | 12.6850i | −0.596116 | + | 0.487884i | ||||
\(677\) | 6.45779 | 0.248193 | 0.124097 | − | 0.992270i | \(-0.460397\pi\) | ||||
0.124097 | + | 0.992270i | \(0.460397\pi\) | |||||||
\(678\) | −12.7931 | + | 4.56776i | −0.491315 | + | 0.175424i | ||||
\(679\) | −19.0812 | − | 38.3708i | −0.732270 | − | 1.47254i | ||||
\(680\) | 0.383501 | − | 0.846684i | 0.0147066 | − | 0.0324688i | ||||
\(681\) | −4.76468 | −0.182583 | ||||||||
\(682\) | 1.05698 | + | 2.96032i | 0.0404739 | + | 0.113356i | ||||
\(683\) | 16.8904 | 0.646292 | 0.323146 | − | 0.946349i | \(-0.395259\pi\) | ||||
0.323146 | + | 0.946349i | \(0.395259\pi\) | |||||||
\(684\) | −7.33056 | + | 5.99961i | −0.280291 | + | 0.229401i | ||||
\(685\) | −5.61741 | − | 47.9284i | −0.214630 | − | 1.83125i | ||||
\(686\) | 25.8712 | − | 4.08395i | 0.987769 | − | 0.155926i | ||||
\(687\) | −15.4673 | −0.590115 | ||||||||
\(688\) | −6.84149 | + | 33.9189i | −0.260829 | + | 1.29315i | ||||
\(689\) | − | 19.9666i | − | 0.760667i | ||||||
\(690\) | 4.83912 | + | 9.77665i | 0.184222 | + | 0.372191i | ||||
\(691\) | −0.330330 | −0.0125663 | −0.00628317 | − | 0.999980i | \(-0.502000\pi\) | ||||
−0.00628317 | + | 0.999980i | \(0.502000\pi\) | |||||||
\(692\) | 27.2297 | − | 22.2858i | 1.03512 | − | 0.847180i | ||||
\(693\) | −0.866911 | + | 0.431102i | −0.0329312 | + | 0.0163762i | ||||
\(694\) | −1.09176 | + | 0.389814i | −0.0414428 | + | 0.0147971i | ||||
\(695\) | −29.2186 | + | 3.42454i | −1.10832 | + | 0.129900i | ||||
\(696\) | 12.8193 | + | 7.71870i | 0.485916 | + | 0.292577i | ||||
\(697\) | − | 1.05271i | − | 0.0398742i | ||||||
\(698\) | −9.01189 | − | 25.2399i | −0.341105 | − | 0.955343i | ||||
\(699\) | −13.7907 | −0.521613 | ||||||||
\(700\) | 25.9809 | + | 4.99924i | 0.981986 | + | 0.188954i | ||||
\(701\) | −22.4214 | −0.846846 | −0.423423 | − | 0.905932i | \(-0.639172\pi\) | ||||
−0.423423 | + | 0.905932i | \(0.639172\pi\) | |||||||
\(702\) | 0.821724 | + | 2.30143i | 0.0310140 | + | 0.0868618i | ||||
\(703\) | 35.6473i | 1.34446i | ||||||||
\(704\) | −2.58737 | + | 1.36963i | −0.0975152 | + | 0.0516198i | ||||
\(705\) | −8.52280 | + | 0.998909i | −0.320987 | + | 0.0376211i | ||||
\(706\) | 24.8955 | − | 8.88894i | 0.936955 | − | 0.334540i | ||||
\(707\) | −10.4628 | + | 5.20300i | −0.393494 | + | 0.195679i | ||||
\(708\) | 7.83936 | + | 9.57845i | 0.294621 | + | 0.359980i | ||||
\(709\) | −15.6572 | −0.588018 | −0.294009 | − | 0.955803i | \(-0.594990\pi\) | ||||
−0.294009 | + | 0.955803i | \(0.594990\pi\) | |||||||
\(710\) | −10.9146 | − | 22.0511i | −0.409616 | − | 0.827563i | ||||
\(711\) | 14.2442i | 0.534201i | ||||||||
\(712\) | 33.0747 | + | 19.9147i | 1.23953 | + | 0.746336i | ||||
\(713\) | −20.9528 | −0.784689 | ||||||||
\(714\) | −0.381368 | + | 0.396156i | −0.0142723 | + | 0.0148258i | ||||
\(715\) | −0.164594 | − | 1.40433i | −0.00615546 | − | 0.0525191i | ||||
\(716\) | −9.53490 | − | 11.6501i | −0.356336 | − | 0.435385i | ||||
\(717\) | −1.39679 | −0.0521640 | ||||||||
\(718\) | −9.69154 | − | 27.1434i | −0.361685 | − | 1.01298i | ||||
\(719\) | −32.0066 | −1.19365 | −0.596823 | − | 0.802373i | \(-0.703571\pi\) | ||||
−0.596823 | + | 0.802373i | \(0.703571\pi\) | |||||||
\(720\) | −0.735808 | + | 8.91395i | −0.0274219 | + | 0.332203i | ||||
\(721\) | 29.5343 | − | 14.6870i | 1.09991 | − | 0.546971i | ||||
\(722\) | −4.57245 | + | 1.63259i | −0.170169 | + | 0.0607588i | ||||
\(723\) | 18.9796 | 0.705857 | ||||||||
\(724\) | −4.85342 | − | 5.93011i | −0.180376 | − | 0.220391i | ||||
\(725\) | −25.7355 | + | 6.11665i | −0.955794 | + | 0.227167i | ||||
\(726\) | −5.16728 | − | 14.4721i | −0.191776 | − | 0.537112i | ||||
\(727\) | − | 3.20369i | − | 0.118818i | −0.998234 | − | 0.0594091i | \(-0.981078\pi\) | ||
0.998234 | − | 0.0594091i | \(-0.0189216\pi\) | |||||||
\(728\) | −12.8891 | − | 1.03981i | −0.477702 | − | 0.0385378i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 12.9064 | − | 6.38824i | 0.477687 | − | 0.236439i | ||||
\(731\) | 1.27132 | 0.0470215 | ||||||||
\(732\) | 0.538668 | − | 0.440866i | 0.0199097 | − | 0.0162949i | ||||
\(733\) | 32.3886 | 1.19630 | 0.598150 | − | 0.801384i | \(-0.295903\pi\) | ||||
0.598150 | + | 0.801384i | \(0.295903\pi\) | |||||||
\(734\) | 1.03086 | + | 2.88717i | 0.0380499 | + | 0.106568i | ||||
\(735\) | −13.4957 | − | 7.92875i | −0.497798 | − | 0.292456i | ||||
\(736\) | −2.79860 | − | 19.3124i | −0.103158 | − | 0.711863i | ||||
\(737\) | − | 4.45066i | − | 0.163942i | ||||||
\(738\) | 3.40630 | + | 9.54014i | 0.125388 | + | 0.351177i | ||||
\(739\) | − | 4.75067i | − | 0.174756i | −0.996175 | − | 0.0873781i | \(-0.972151\pi\) | ||
0.996175 | − | 0.0873781i | \(-0.0278488\pi\) | |||||||
\(740\) | 24.2051 | + | 23.3884i | 0.889796 | + | 0.859776i | ||||
\(741\) | 8.18432i | 0.300658i | ||||||||
\(742\) | −29.9846 | + | 31.1472i | −1.10077 | + | 1.14345i | ||||
\(743\) | −12.4260 | −0.455866 | −0.227933 | − | 0.973677i | \(-0.573197\pi\) | ||||
−0.227933 | + | 0.973677i | \(0.573197\pi\) | |||||||
\(744\) | −14.7177 | − | 8.86171i | −0.539576 | − | 0.324886i | ||||
\(745\) | 23.9109 | − | 2.80246i | 0.876028 | − | 0.102674i | ||||
\(746\) | 4.71636 | + | 13.2093i | 0.172678 | + | 0.483625i | ||||
\(747\) | 3.53810i | 0.129452i | ||||||||
\(748\) | 0.0681242 | + | 0.0832369i | 0.00249087 | + | 0.00304344i | ||||
\(749\) | 7.26172 | + | 14.6027i | 0.265337 | + | 0.533572i | ||||
\(750\) | −10.1006 | − | 12.1647i | −0.368820 | − | 0.444190i | ||||
\(751\) | − | 15.8621i | − | 0.578816i | −0.957206 | − | 0.289408i | \(-0.906542\pi\) | ||
0.957206 | − | 0.289408i | \(-0.0934585\pi\) | |||||||
\(752\) | 15.0474 | + | 3.03507i | 0.548721 | + | 0.110678i | ||||
\(753\) | 10.9949i | 0.400678i | ||||||||
\(754\) | 12.1757 | − | 4.34732i | 0.443412 | − | 0.158320i | ||||
\(755\) | −0.870615 | − | 7.42818i | −0.0316849 | − | 0.270339i | ||||
\(756\) | 2.17427 | − | 4.82416i | 0.0790776 | − | 0.175453i | ||||
\(757\) | − | 9.98543i | − | 0.362927i | −0.983398 | − | 0.181463i | \(-0.941917\pi\) | ||
0.983398 | − | 0.181463i | \(-0.0580834\pi\) | |||||||
\(758\) | 0.0698048 | + | 0.195504i | 0.00253543 | + | 0.00710104i | ||||
\(759\) | −1.26236 | −0.0458208 | ||||||||
\(760\) | −12.3594 | + | 27.2868i | −0.448323 | + | 0.989796i | ||||
\(761\) | 8.89622i | 0.322488i | 0.986915 | + | 0.161244i | \(0.0515506\pi\) | ||||
−0.986915 | + | 0.161244i | \(0.948449\pi\) | |||||||
\(762\) | 4.08127 | + | 11.4305i | 0.147849 | + | 0.414084i | ||||
\(763\) | −3.25699 | − | 6.54953i | −0.117911 | − | 0.237109i | ||||
\(764\) | −25.4863 | − | 31.1402i | −0.922062 | − | 1.12661i | ||||
\(765\) | 0.326389 | − | 0.0382542i | 0.0118006 | − | 0.00138308i | ||||
\(766\) | 16.6024 | + | 46.4989i | 0.599870 | + | 1.68007i | ||||
\(767\) | 10.6940 | 0.386138 | ||||||||
\(768\) | 6.20212 | − | 14.7490i | 0.223800 | − | 0.532210i | ||||
\(769\) | − | 10.0175i | − | 0.361242i | −0.983553 | − | 0.180621i | \(-0.942189\pi\) | ||
0.983553 | − | 0.180621i | \(-0.0578107\pi\) | |||||||
\(770\) | −1.85218 | + | 2.43789i | −0.0667478 | + | 0.0878553i | ||||
\(771\) | − | 18.1739i | − | 0.654516i | ||||||
\(772\) | −24.9141 | − | 30.4410i | −0.896677 | − | 1.09560i | ||||
\(773\) | −41.9683 | −1.50949 | −0.754747 | − | 0.656016i | \(-0.772240\pi\) | ||||
−0.754747 | + | 0.656016i | \(0.772240\pi\) | |||||||
\(774\) | −11.5213 | + | 4.11367i | −0.414124 | + | 0.147863i | ||||
\(775\) | 29.5465 | − | 7.02243i | 1.06134 | − | 0.252253i | ||||
\(776\) | 23.6311 | − | 39.2470i | 0.848308 | − | 1.40888i | ||||
\(777\) | −8.86649 | − | 17.8298i | −0.318084 | − | 0.639641i | ||||
\(778\) | −36.8173 | + | 13.1456i | −1.31997 | + | 0.471293i | ||||
\(779\) | 33.9266i | 1.21555i | ||||||||
\(780\) | 5.55728 | + | 5.36979i | 0.198983 | + | 0.192269i | ||||
\(781\) | 2.84724 | 0.101882 | ||||||||
\(782\) | −0.675222 | + | 0.241088i | −0.0241459 | + | 0.00862128i | ||||
\(783\) | 5.29049i | 0.189067i | ||||||||
\(784\) | 18.5451 | + | 20.9781i | 0.662323 | + | 0.749218i | ||||
\(785\) | 42.9003 | − | 5.02810i | 1.53118 | − | 0.179461i | ||||
\(786\) | 8.84678 | + | 24.7775i | 0.315554 | + | 0.883782i | ||||
\(787\) | − | 0.375554i | − | 0.0133871i | −0.999978 | − | 0.00669353i | \(-0.997869\pi\) | ||
0.999978 | − | 0.00669353i | \(-0.00213063\pi\) | |||||||
\(788\) | −6.90006 | − | 8.43077i | −0.245805 | − | 0.300334i | ||||
\(789\) | − | 9.67183i | − | 0.344326i | ||||||
\(790\) | 19.9817 | + | 40.3697i | 0.710917 | + | 1.43629i | ||||
\(791\) | 22.7551 | − | 11.3158i | 0.809080 | − | 0.402343i | ||||
\(792\) | −0.886707 | − | 0.533898i | −0.0315078 | − | 0.0189713i | ||||
\(793\) | − | 0.601403i | − | 0.0213565i | ||||||
\(794\) | −12.8141 | + | 4.57528i | −0.454756 | + | 0.162370i | ||||
\(795\) | 25.6619 | − | 3.00769i | 0.910134 | − | 0.106672i | ||||
\(796\) | −10.3177 | + | 8.44437i | −0.365700 | + | 0.299303i | ||||
\(797\) | 42.5573 | 1.50746 | 0.753728 | − | 0.657187i | \(-0.228254\pi\) | ||||
0.753728 | + | 0.657187i | \(0.228254\pi\) | |||||||
\(798\) | 12.2907 | − | 12.7673i | 0.435086 | − | 0.451956i | ||||
\(799\) | − | 0.563993i | − | 0.0199526i | ||||||
\(800\) | 10.4191 | + | 26.2953i | 0.368369 | + | 0.929680i | ||||
\(801\) | 13.6498i | 0.482291i | ||||||||
\(802\) | 29.0386 | − | 10.3682i | 1.02539 | − | 0.366115i | ||||
\(803\) | 1.66647i | 0.0588085i | ||||||||
\(804\) | 15.4061 | + | 18.8238i | 0.543332 | + | 0.663864i | ||||
\(805\) | −11.1526 | − | 17.0915i | −0.393077 | − | 0.602397i | ||||
\(806\) | −13.9787 | + | 4.99109i | −0.492378 | + | 0.175804i | ||||
\(807\) | −1.72109 | −0.0605853 | ||||||||
\(808\) | −10.7017 | − | 6.44365i | −0.376485 | − | 0.226687i | ||||
\(809\) | −46.6092 | −1.63869 | −0.819346 | − | 0.573300i | \(-0.805663\pi\) | ||||
−0.819346 | + | 0.573300i | \(0.805663\pi\) | |||||||
\(810\) | −2.83411 | + | 1.40279i | −0.0995805 | + | 0.0492891i | ||||
\(811\) | −55.4019 | −1.94542 | −0.972711 | − | 0.232019i | \(-0.925467\pi\) | ||||
−0.972711 | + | 0.232019i | \(0.925467\pi\) | |||||||
\(812\) | −25.5222 | − | 11.5030i | −0.895652 | − | 0.403675i | ||||
\(813\) | 8.11648i | 0.284657i | ||||||||
\(814\) | −3.66818 | + | 1.30972i | −0.128570 | + | 0.0459058i | ||||
\(815\) | −39.1586 | + | 4.58956i | −1.37167 | + | 0.160765i | ||||
\(816\) | −0.576254 | − | 0.116231i | −0.0201729 | − | 0.00406891i | ||||
\(817\) | −40.9719 | −1.43343 | ||||||||
\(818\) | −14.3342 | − | 40.1463i | −0.501184 | − | 1.40368i | ||||
\(819\) | −2.03567 | − | 4.09357i | −0.0711322 | − | 0.143041i | ||||
\(820\) | 23.0367 | + | 22.2595i | 0.804475 | + | 0.777334i | ||||
\(821\) | 1.12596 | 0.0392961 | 0.0196481 | − | 0.999807i | \(-0.493745\pi\) | ||||
0.0196481 | + | 0.999807i | \(0.493745\pi\) | |||||||
\(822\) | −28.7429 | + | 10.2626i | −1.00252 | + | 0.357950i | ||||
\(823\) | 44.2302 | 1.54177 | 0.770884 | − | 0.636976i | \(-0.219815\pi\) | ||||
0.770884 | + | 0.636976i | \(0.219815\pi\) | |||||||
\(824\) | 30.2087 | + | 18.1891i | 1.05237 | + | 0.633646i | ||||
\(825\) | 1.78011 | − | 0.423085i | 0.0619756 | − | 0.0147299i | ||||
\(826\) | −16.6823 | − | 16.0596i | −0.580451 | − | 0.558784i | ||||
\(827\) | −28.2414 | −0.982048 | −0.491024 | − | 0.871146i | \(-0.663377\pi\) | ||||
−0.491024 | + | 0.871146i | \(0.663377\pi\) | |||||||
\(828\) | 5.33907 | − | 4.36970i | 0.185546 | − | 0.151858i | ||||
\(829\) | 38.0736i | 1.32235i | 0.750231 | + | 0.661175i | \(0.229942\pi\) | ||||
−0.750231 | + | 0.661175i | \(0.770058\pi\) | |||||||
\(830\) | 4.96322 | + | 10.0274i | 0.172276 | + | 0.348055i | ||||
\(831\) | −1.12611 | −0.0390644 | ||||||||
\(832\) | −6.46741 | − | 12.2176i | −0.224217 | − | 0.423570i | ||||
\(833\) | 0.620825 | − | 0.820311i | 0.0215103 | − | 0.0284221i | ||||
\(834\) | 6.25640 | + | 17.5225i | 0.216642 | + | 0.606754i | ||||
\(835\) | 4.35476 | + | 37.1553i | 0.150703 | + | 1.28581i | ||||
\(836\) | −2.19550 | − | 2.68255i | −0.0759329 | − | 0.0927778i | ||||
\(837\) | − | 6.07392i | − | 0.209945i | ||||||
\(838\) | −32.2589 | + | 11.5180i | −1.11436 | + | 0.397883i | ||||
\(839\) | 10.9246 | 0.377160 | 0.188580 | − | 0.982058i | \(-0.439612\pi\) | ||||
0.188580 | + | 0.982058i | \(0.439612\pi\) | |||||||
\(840\) | −0.605158 | − | 16.7223i | −0.0208800 | − | 0.576973i | ||||
\(841\) | −1.01075 | −0.0348533 | ||||||||
\(842\) | −7.63023 | + | 2.72437i | −0.262955 | + | 0.0938880i | ||||
\(843\) | 14.3818i | 0.495334i | ||||||||
\(844\) | 11.1683 | + | 13.6458i | 0.384428 | + | 0.469709i | ||||
\(845\) | −22.2400 | + | 2.60662i | −0.765078 | + | 0.0896705i | ||||
\(846\) | 1.82494 | + | 5.11116i | 0.0627427 | + | 0.175725i | ||||
\(847\) | 12.8010 | + | 25.7418i | 0.439847 | + | 0.884497i | ||||
\(848\) | −45.3072 | − | 9.13852i | −1.55586 | − | 0.313818i | ||||
\(849\) | −23.4832 | −0.805940 | ||||||||
\(850\) | 0.871360 | − | 0.566273i | 0.0298874 | − | 0.0194230i | ||||
\(851\) | − | 25.9630i | − | 0.890001i | ||||||
\(852\) | −12.0422 | + | 9.85579i | −0.412559 | + | 0.337654i | ||||
\(853\) | −23.7748 | −0.814035 | −0.407017 | − | 0.913420i | \(-0.633431\pi\) | ||||
−0.407017 | + | 0.913420i | \(0.633431\pi\) | |||||||
\(854\) | −0.903149 | + | 0.938169i | −0.0309051 | + | 0.0321035i | ||||
\(855\) | −10.5188 | + | 1.23285i | −0.359736 | + | 0.0421626i | ||||
\(856\) | −8.99327 | + | 14.9362i | −0.307384 | + | 0.510508i | ||||
\(857\) | 19.0201 | 0.649715 | 0.324857 | − | 0.945763i | \(-0.394684\pi\) | ||||
0.324857 | + | 0.945763i | \(0.394684\pi\) | |||||||
\(858\) | −0.842184 | + | 0.300702i | −0.0287517 | + | 0.0102658i | ||||
\(859\) | −12.9659 | −0.442390 | −0.221195 | − | 0.975230i | \(-0.570996\pi\) | ||||
−0.221195 | + | 0.975230i | \(0.570996\pi\) | |||||||
\(860\) | −26.8820 | + | 27.8206i | −0.916668 | + | 0.948674i | ||||
\(861\) | −8.43850 | − | 16.9691i | −0.287583 | − | 0.578307i | ||||
\(862\) | −16.2603 | − | 45.5408i | −0.553829 | − | 1.55112i | ||||
\(863\) | 39.2414 | 1.33579 | 0.667896 | − | 0.744255i | \(-0.267195\pi\) | ||||
0.667896 | + | 0.744255i | \(0.267195\pi\) | |||||||
\(864\) | 5.59838 | − | 0.811273i | 0.190461 | − | 0.0276001i | ||||
\(865\) | 39.0727 | − | 4.57948i | 1.32851 | − | 0.155707i | ||||
\(866\) | 43.6639 | − | 15.5902i | 1.48376 | − | 0.529776i | ||||
\(867\) | − | 16.9784i | − | 0.576617i | ||||||
\(868\) | 29.3016 | + | 13.2064i | 0.994560 | + | 0.448253i | ||||
\(869\) | −5.21254 | −0.176823 | ||||||||
\(870\) | 7.42145 | + | 14.9938i | 0.251611 | + | 0.508338i | ||||
\(871\) | 21.0161 | 0.712104 | ||||||||
\(872\) | 4.03361 | − | 6.69909i | 0.136595 | − | 0.226860i | ||||
\(873\) | 16.1970 | 0.548187 | ||||||||
\(874\) | 21.7610 | − | 7.76974i | 0.736075 | − | 0.262816i | ||||
\(875\) | 21.4551 | + | 20.3637i | 0.725313 | + | 0.688419i | ||||
\(876\) | −5.76854 | − | 7.04824i | −0.194901 | − | 0.238138i | ||||
\(877\) | − | 46.1400i | − | 1.55804i | −0.627000 | − | 0.779019i | \(-0.715717\pi\) | ||
0.627000 | − | 0.779019i | \(-0.284283\pi\) | |||||||
\(878\) | −42.7909 | + | 15.2785i | −1.44412 | + | 0.515624i | ||||
\(879\) | 13.3608i | 0.450647i | ||||||||
\(880\) | −3.26197 | − | 0.269262i | −0.109961 | − | 0.00907681i | ||||
\(881\) | 25.7227i | 0.866619i | 0.901245 | + | 0.433309i | \(0.142654\pi\) | ||||
−0.901245 | + | 0.433309i | \(0.857346\pi\) | |||||||
\(882\) | −2.97189 | + | 9.44288i | −0.100069 | + | 0.317958i | ||||
\(883\) | 48.0270 | 1.61624 | 0.808119 | − | 0.589020i | \(-0.200486\pi\) | ||||
0.808119 | + | 0.589020i | \(0.200486\pi\) | |||||||
\(884\) | −0.393046 | + | 0.321684i | −0.0132196 | + | 0.0108194i | ||||
\(885\) | 1.61090 | + | 13.7444i | 0.0541498 | + | 0.462012i | ||||
\(886\) | 16.5497 | − | 5.90908i | 0.555999 | − | 0.198519i | ||||
\(887\) | − | 40.6595i | − | 1.36521i | −0.730787 | − | 0.682606i | \(-0.760847\pi\) | ||
0.730787 | − | 0.682606i | \(-0.239153\pi\) | |||||||
\(888\) | 10.9807 | − | 18.2369i | 0.368488 | − | 0.611991i | ||||
\(889\) | −10.1106 | − | 20.3316i | −0.339099 | − | 0.681900i | ||||
\(890\) | 19.1478 | + | 38.6850i | 0.641836 | + | 1.29672i | ||||
\(891\) | − | 0.365940i | − | 0.0122595i | ||||||
\(892\) | −9.10339 | − | 11.1229i | −0.304804 | − | 0.372422i | ||||
\(893\) | 18.1763i | 0.608246i | ||||||||
\(894\) | −5.11991 | − | 14.3395i | −0.171235 | − | 0.479584i | ||||
\(895\) | −1.95931 | − | 16.7171i | −0.0654926 | − | 0.558790i | ||||
\(896\) | −8.25870 | + | 28.7714i | −0.275904 | + | 0.961185i | ||||
\(897\) | − | 5.96089i | − | 0.199028i | ||||||
\(898\) | −4.36241 | + | 1.55760i | −0.145575 | + | 0.0519777i | ||||
\(899\) | −32.1340 | −1.07173 | ||||||||
\(900\) | −6.06435 | + | 7.95133i | −0.202145 | + | 0.265044i | ||||
\(901\) | 1.69817i | 0.0565741i | ||||||||
\(902\) | −3.49112 | + | 1.24650i | −0.116242 | + | 0.0415040i | ||||
\(903\) | 20.4930 | − | 10.1909i | 0.681966 | − | 0.339131i | ||||
\(904\) | 23.2747 | + | 14.0140i | 0.774107 | + | 0.466100i | ||||
\(905\) | −0.997323 | − | 8.50927i | −0.0331521 | − | 0.282858i | ||||
\(906\) | −4.45471 | + | 1.59055i | −0.147998 | + | 0.0528426i | ||||
\(907\) | −28.5510 | −0.948021 | −0.474010 | − | 0.880519i | \(-0.657194\pi\) | ||||
−0.474010 | + | 0.880519i | \(0.657194\pi\) | |||||||
\(908\) | 6.03549 | + | 7.37440i | 0.200295 | + | 0.244728i | ||||
\(909\) | − | 4.41655i | − | 0.146488i | ||||||
\(910\) | −11.5117 | − | 8.74601i | −0.381611 | − | 0.289927i | ||||
\(911\) | 11.7799i | 0.390286i | 0.980775 | + | 0.195143i | \(0.0625171\pi\) | ||||
−0.980775 | + | 0.195143i | \(0.937483\pi\) | |||||||
\(912\) | 18.5714 | + | 3.74588i | 0.614962 | + | 0.124039i | ||||
\(913\) | −1.29473 | −0.0428494 | ||||||||
\(914\) | −8.51300 | − | 23.8426i | −0.281585 | − | 0.788644i | ||||
\(915\) | 0.772949 | − | 0.0905929i | 0.0255529 | − | 0.00299491i | ||||
\(916\) | 19.5926 | + | 23.9391i | 0.647359 | + | 0.790970i | ||||
\(917\) | −21.9163 | − | 44.0719i | −0.723740 | − | 1.45538i | ||||
\(918\) | −0.0698879 | − | 0.195737i | −0.00230664 | − | 0.00646029i | ||||
\(919\) | − | 50.9066i | − | 1.67925i | −0.543164 | − | 0.839626i | \(-0.682774\pi\) | ||
0.543164 | − | 0.839626i | \(-0.317226\pi\) | |||||||
\(920\) | 9.00174 | − | 19.8738i | 0.296779 | − | 0.655220i | ||||
\(921\) | 27.7860 | 0.915578 | ||||||||
\(922\) | −19.1349 | − | 53.5917i | −0.630175 | − | 1.76495i | ||||
\(923\) | 13.4447i | 0.442538i | ||||||||
\(924\) | 1.76535 | + | 0.795654i | 0.0580759 | + | 0.0261751i | ||||
\(925\) | 8.70162 | + | 36.6116i | 0.286107 | + | 1.20378i | ||||
\(926\) | −34.4731 | + | 12.3086i | −1.13286 | + | 0.404486i | ||||
\(927\) | 12.4670i | 0.409469i | ||||||||
\(928\) | −4.29203 | − | 29.6181i | −0.140893 | − | 0.972263i | ||||
\(929\) | − | 7.20396i | − | 0.236354i | −0.992993 | − | 0.118177i | \(-0.962295\pi\) | ||
0.992993 | − | 0.118177i | \(-0.0377051\pi\) | |||||||
\(930\) | −8.52044 | − | 17.2142i | −0.279396 | − | 0.564474i | ||||
\(931\) | −20.0079 | + | 26.4369i | −0.655732 | + | 0.866433i | ||||
\(932\) | 17.4689 | + | 21.3442i | 0.572212 | + | 0.699152i | ||||
\(933\) | − | 4.53917i | − | 0.148606i | ||||||
\(934\) | −9.90156 | − | 27.7316i | −0.323989 | − | 0.907406i | ||||
\(935\) | 0.0139987 | + | 0.119439i | 0.000457808 | + | 0.00390607i | ||||
\(936\) | 2.52108 | − | 4.18705i | 0.0824040 | − | 0.136858i | ||||
\(937\) | 43.7398 | 1.42892 | 0.714458 | − | 0.699678i | \(-0.246673\pi\) | ||||
0.714458 | + | 0.699678i | \(0.246673\pi\) | |||||||
\(938\) | −32.7844 | − | 31.5607i | −1.07045 | − | 1.03049i | ||||
\(939\) | − | 2.86576i | − | 0.0935205i | ||||||
\(940\) | 12.3420 | + | 11.9256i | 0.402551 | + | 0.388970i | ||||
\(941\) | − | 44.8849i | − | 1.46320i | −0.681732 | − | 0.731602i | \(-0.738773\pi\) | ||
0.681732 | − | 0.731602i | \(-0.261227\pi\) | |||||||
\(942\) | −9.18601 | − | 25.7275i | −0.299296 | − | 0.838248i | ||||
\(943\) | − | 24.7097i | − | 0.804660i | ||||||
\(944\) | 4.89454 | − | 24.2663i | 0.159304 | − | 0.789800i | ||||
\(945\) | 4.95458 | − | 3.23297i | 0.161173 | − | 0.105169i | ||||
\(946\) | −1.50536 | − | 4.21610i | −0.0489434 | − | 0.137077i | ||||
\(947\) | −25.8593 | −0.840316 | −0.420158 | − | 0.907451i | \(-0.638025\pi\) | ||||
−0.420158 | + | 0.907451i | \(0.638025\pi\) | |||||||
\(948\) | 22.0461 | − | 18.0434i | 0.716024 | − | 0.586021i | ||||
\(949\) | −7.86911 | −0.255442 | ||||||||
\(950\) | −28.0821 | + | 18.2498i | −0.911103 | + | 0.592100i | ||||
\(951\) | −16.3518 | −0.530245 | ||||||||
\(952\) | 1.09622 | + | 0.0884359i | 0.0355288 | + | 0.00286622i | ||||
\(953\) | 3.07479i | 0.0996022i | 0.998759 | + | 0.0498011i | \(0.0158587\pi\) | ||||
−0.998759 | + | 0.0498011i | \(0.984141\pi\) | |||||||
\(954\) | −5.49484 | − | 15.3896i | −0.177902 | − | 0.498256i | ||||
\(955\) | −5.23714 | − | 44.6839i | −0.169470 | − | 1.44594i | ||||
\(956\) | 1.76933 | + | 2.16184i | 0.0572241 | + | 0.0699188i | ||||
\(957\) | −1.93600 | −0.0625820 | ||||||||
\(958\) | 8.40027 | − | 2.99932i | 0.271401 | − | 0.0969035i | ||||
\(959\) | 51.1252 | − | 25.4238i | 1.65092 | − | 0.820977i | ||||
\(960\) | 14.7284 | − | 10.1526i | 0.475356 | − | 0.327674i | ||||
\(961\) | 5.89250 | 0.190081 | ||||||||
\(962\) | −6.18454 | − | 17.3212i | −0.199398 | − | 0.558459i | ||||
\(963\) | −6.16409 | −0.198635 | ||||||||
\(964\) | −24.0416 | − | 29.3750i | −0.774329 | − | 0.946107i | ||||
\(965\) | −5.11956 | − | 43.6806i | −0.164804 | − | 1.40613i | ||||
\(966\) | −8.95168 | + | 9.29878i | −0.288016 | + | 0.299183i | ||||
\(967\) | −20.0103 | −0.643488 | −0.321744 | − | 0.946827i | \(-0.604269\pi\) | ||||
−0.321744 | + | 0.946827i | \(0.604269\pi\) | |||||||
\(968\) | −15.8534 | + | 26.3295i | −0.509547 | + | 0.846264i | ||||
\(969\) | − | 0.696079i | − | 0.0223613i | ||||||
\(970\) | 45.9042 | − | 22.7211i | 1.47389 | − | 0.729530i | ||||
\(971\) | −40.3382 | −1.29451 | −0.647257 | − | 0.762272i | \(-0.724084\pi\) | ||||
−0.647257 | + | 0.762272i | \(0.724084\pi\) | |||||||
\(972\) | 1.26671 | + | 1.54772i | 0.0406298 | + | 0.0496432i | ||||
\(973\) | −15.4991 | − | 31.1674i | −0.496878 | − | 0.999182i | ||||
\(974\) | −2.72804 | + | 0.974045i | −0.0874119 | + | 0.0312104i | ||||
\(975\) | 1.99782 | + | 8.40573i | 0.0639814 | + | 0.269199i | ||||
\(976\) | −1.36467 | − | 0.275257i | −0.0436822 | − | 0.00881075i | ||||
\(977\) | 2.19619i | 0.0702622i | 0.999383 | + | 0.0351311i | \(0.0111849\pi\) | ||||
−0.999383 | + | 0.0351311i | \(0.988815\pi\) | |||||||
\(978\) | 8.38481 | + | 23.4836i | 0.268117 | + | 0.750923i | ||||
\(979\) | −4.99500 | −0.159641 | ||||||||
\(980\) | 4.82374 | + | 30.9311i | 0.154089 | + | 0.988057i | ||||
\(981\) | 2.76468 | 0.0882696 | ||||||||
\(982\) | 1.25135 | + | 3.50471i | 0.0399323 | + | 0.111840i | ||||
\(983\) | 20.0116i | 0.638272i | 0.947709 | + | 0.319136i | \(0.103393\pi\) | ||||
−0.947709 | + | 0.319136i | \(0.896607\pi\) | |||||||
\(984\) | 10.4507 | − | 17.3566i | 0.333155 | − | 0.553309i | ||||
\(985\) | −1.41788 | − | 12.0975i | −0.0451775 | − | 0.385460i | ||||
\(986\) | −1.03554 | + | 0.369741i | −0.0329785 | + | 0.0117749i | ||||
\(987\) | −4.52096 | − | 9.09128i | −0.143904 | − | 0.289379i | ||||
\(988\) | 12.6670 | − | 10.3672i | 0.402992 | − | 0.329824i | ||||
\(989\) | 29.8411 | 0.948892 | ||||||||
\(990\) | −0.513337 | − | 1.03711i | −0.0163149 | − | 0.0329616i | ||||
\(991\) | 17.3259i | 0.550374i | 0.961391 | + | 0.275187i | \(0.0887398\pi\) | ||||
−0.961391 | + | 0.275187i | \(0.911260\pi\) | |||||||
\(992\) | 4.92761 | + | 34.0041i | 0.156452 | + | 1.07963i | ||||
\(993\) | −16.4160 | −0.520947 | ||||||||
\(994\) | 20.1904 | − | 20.9733i | 0.640400 | − | 0.665232i | ||||
\(995\) | −14.8051 | + | 1.73522i | −0.469353 | + | 0.0550102i | ||||
\(996\) | 5.47600 | − | 4.48176i | 0.173514 | − | 0.142010i | ||||
\(997\) | −38.4882 | −1.21893 | −0.609467 | − | 0.792812i | \(-0.708616\pi\) | ||||
−0.609467 | + | 0.792812i | \(0.708616\pi\) | |||||||
\(998\) | −12.5520 | − | 35.1547i | −0.397326 | − | 1.11280i | ||||
\(999\) | 7.52630 | 0.238122 |
(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 | 420.2.i.a.139.8 | yes | 48 | |
4.3 | odd | 2 | inner | 420.2.i.a.139.43 | yes | 48 | |
5.4 | even | 2 | inner | 420.2.i.a.139.41 | yes | 48 | |
7.6 | odd | 2 | inner | 420.2.i.a.139.7 | yes | 48 | |
20.19 | odd | 2 | inner | 420.2.i.a.139.6 | yes | 48 | |
28.27 | even | 2 | inner | 420.2.i.a.139.44 | yes | 48 | |
35.34 | odd | 2 | inner | 420.2.i.a.139.42 | yes | 48 | |
140.139 | even | 2 | inner | 420.2.i.a.139.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.i.a.139.5 | ✓ | 48 | 140.139 | even | 2 | inner | |
420.2.i.a.139.6 | yes | 48 | 20.19 | odd | 2 | inner | |
420.2.i.a.139.7 | yes | 48 | 7.6 | odd | 2 | inner | |
420.2.i.a.139.8 | yes | 48 | 1.1 | even | 1 | trivial | |
420.2.i.a.139.41 | yes | 48 | 5.4 | even | 2 | inner | |
420.2.i.a.139.42 | yes | 48 | 35.34 | odd | 2 | inner | |
420.2.i.a.139.43 | yes | 48 | 4.3 | odd | 2 | inner | |
420.2.i.a.139.44 | yes | 48 | 28.27 | even | 2 | inner |