Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1011.5 | ||
Root | \(0.601150 + 2.24352i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1011 |
Dual form | 1078.2.i.c.901.5 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −2.24749 | − | 1.29759i | −1.29759 | − | 0.749163i | −0.317602 | − | 0.948224i | \(-0.602877\pi\) |
−0.979987 | + | 0.199061i | \(0.936211\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.06486 | − | 1.76950i | 1.37065 | − | 0.791344i | 0.379638 | − | 0.925135i | \(-0.376049\pi\) |
0.991010 | + | 0.133791i | \(0.0427152\pi\) | |||||||
\(6\) | −2.59518 | −1.05948 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.86747 | + | 3.23456i | 0.622491 | + | 1.07819i | ||||
\(10\) | 1.76950 | − | 3.06486i | 0.559564 | − | 0.969194i | ||||
\(11\) | 3.22122 | − | 0.789769i | 0.971235 | − | 0.238124i | ||||
\(12\) | −2.24749 | + | 1.29759i | −0.648794 | + | 0.374582i | ||||
\(13\) | 5.01680 | 1.39141 | 0.695704 | − | 0.718328i | \(-0.255092\pi\) | ||||
0.695704 | + | 0.718328i | \(0.255092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.18432 | −2.37138 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.94681 | − | 3.37197i | 0.472171 | − | 0.817824i | −0.527322 | − | 0.849665i | \(-0.676804\pi\) |
0.999493 | + | 0.0318416i | \(0.0101372\pi\) | |||||||
\(18\) | 3.23456 | + | 1.86747i | 0.762393 | + | 0.440168i | ||||
\(19\) | 2.32819 | + | 4.03254i | 0.534123 | + | 0.925128i | 0.999205 | + | 0.0398605i | \(0.0126914\pi\) |
−0.465082 | + | 0.885267i | \(0.653975\pi\) | |||||||
\(20\) | − | 3.53900i | − | 0.791344i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39477 | − | 2.29457i | 0.510568 | − | 0.489204i | ||||
\(23\) | 0.779812 | + | 1.35067i | 0.162602 | + | 0.281635i | 0.935801 | − | 0.352528i | \(-0.114678\pi\) |
−0.773199 | + | 0.634163i | \(0.781345\pi\) | |||||||
\(24\) | −1.29759 | + | 2.24749i | −0.264869 | + | 0.458767i | ||||
\(25\) | 3.76225 | − | 6.51641i | 0.752450 | − | 1.30328i | ||||
\(26\) | 4.34467 | − | 2.50840i | 0.852060 | − | 0.491937i | ||||
\(27\) | − | 1.90732i | − | 0.367064i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.100205i | 0.0186075i | 0.999957 | + | 0.00930376i | \(0.00296152\pi\) | ||||
−0.999957 | + | 0.00930376i | \(0.997038\pi\) | |||||||
\(30\) | −7.95386 | + | 4.59216i | −1.45217 | + | 0.838410i | ||||
\(31\) | 0.242252 | + | 0.139864i | 0.0435098 | + | 0.0251204i | 0.521597 | − | 0.853192i | \(-0.325336\pi\) |
−0.478087 | + | 0.878312i | \(0.658670\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −8.26446 | − | 2.40482i | −1.43866 | − | 0.418626i | ||||
\(34\) | − | 3.89362i | − | 0.667750i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.73495 | 0.622491 | ||||||||
\(37\) | −0.352715 | − | 0.610920i | −0.0579860 | − | 0.100435i | 0.835575 | − | 0.549376i | \(-0.185135\pi\) |
−0.893561 | + | 0.448941i | \(0.851801\pi\) | |||||||
\(38\) | 4.03254 | + | 2.32819i | 0.654164 | + | 0.377682i | ||||
\(39\) | −11.2752 | − | 6.50974i | −1.80548 | − | 1.04239i | ||||
\(40\) | −1.76950 | − | 3.06486i | −0.279782 | − | 0.484597i | ||||
\(41\) | −2.94809 | −0.460415 | −0.230207 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230207 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.03556i | 1.37791i | 0.724804 | + | 0.688955i | \(0.241930\pi\) | ||||
−0.724804 | + | 0.688955i | \(0.758070\pi\) | |||||||
\(44\) | 0.926651 | − | 3.18454i | 0.139698 | − | 0.480088i | ||||
\(45\) | 11.4471 | + | 6.60898i | 1.70643 | + | 0.985209i | ||||
\(46\) | 1.35067 | + | 0.779812i | 0.199146 | + | 0.114977i | ||||
\(47\) | −5.68935 | + | 3.28475i | −0.829876 | + | 0.479129i | −0.853810 | − | 0.520584i | \(-0.825714\pi\) |
0.0239340 | + | 0.999714i | \(0.492381\pi\) | |||||||
\(48\) | 2.59518i | 0.374582i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 7.52450i | − | 1.06412i | ||||||
\(51\) | −8.75087 | + | 5.05232i | −1.22537 | + | 0.707466i | ||||
\(52\) | 2.50840 | − | 4.34467i | 0.347852 | − | 0.602498i | ||||
\(53\) | −2.77029 | + | 4.79828i | −0.380529 | + | 0.659095i | −0.991138 | − | 0.132837i | \(-0.957591\pi\) |
0.610609 | + | 0.791932i | \(0.290925\pi\) | |||||||
\(54\) | −0.953659 | − | 1.65179i | −0.129777 | − | 0.224780i | ||||
\(55\) | 8.47510 | − | 8.12048i | 1.14278 | − | 1.09496i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.0841i | − | 1.60058i | ||||||
\(58\) | 0.0501023 | + | 0.0867797i | 0.00657875 | + | 0.0113947i | ||||
\(59\) | −12.5871 | − | 7.26719i | −1.63871 | − | 0.946108i | −0.981279 | − | 0.192589i | \(-0.938312\pi\) |
−0.657427 | − | 0.753518i | \(-0.728355\pi\) | |||||||
\(60\) | −4.59216 | + | 7.95386i | −0.592846 | + | 1.02684i | ||||
\(61\) | −5.56360 | − | 9.63644i | −0.712346 | − | 1.23382i | −0.963974 | − | 0.265996i | \(-0.914299\pi\) |
0.251628 | − | 0.967824i | \(-0.419034\pi\) | |||||||
\(62\) | 0.279729 | 0.0355256 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 15.3758 | − | 8.87721i | 1.90713 | − | 1.10108i | ||||
\(66\) | −8.35964 | + | 2.04959i | −1.02900 | + | 0.252287i | ||||
\(67\) | −1.99196 | + | 3.45017i | −0.243356 | + | 0.421506i | −0.961668 | − | 0.274216i | \(-0.911582\pi\) |
0.718312 | + | 0.695721i | \(0.244915\pi\) | |||||||
\(68\) | −1.94681 | − | 3.37197i | −0.236085 | − | 0.408912i | ||||
\(69\) | − | 4.04750i | − | 0.487262i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.45381 | −1.00328 | −0.501641 | − | 0.865076i | \(-0.667270\pi\) | ||||
−0.501641 | + | 0.865076i | \(0.667270\pi\) | |||||||
\(72\) | 3.23456 | − | 1.86747i | 0.381196 | − | 0.220084i | ||||
\(73\) | −1.94885 | + | 3.37552i | −0.228096 | + | 0.395074i | −0.957244 | − | 0.289282i | \(-0.906583\pi\) |
0.729148 | + | 0.684356i | \(0.239917\pi\) | |||||||
\(74\) | −0.610920 | − | 0.352715i | −0.0710180 | − | 0.0410023i | ||||
\(75\) | −16.9112 | + | 9.76370i | −1.95274 | + | 1.12742i | ||||
\(76\) | 4.65637 | 0.534123 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0195 | −1.47417 | ||||||||
\(79\) | 6.66824 | − | 3.84991i | 0.750236 | − | 0.433149i | −0.0755434 | − | 0.997143i | \(-0.524069\pi\) |
0.825779 | + | 0.563994i | \(0.190736\pi\) | |||||||
\(80\) | −3.06486 | − | 1.76950i | −0.342662 | − | 0.197836i | ||||
\(81\) | 3.12751 | − | 5.41700i | 0.347501 | − | 0.601889i | ||||
\(82\) | −2.55312 | + | 1.47405i | −0.281945 | + | 0.162781i | ||||
\(83\) | −2.87320 | −0.315375 | −0.157687 | − | 0.987489i | \(-0.550404\pi\) | ||||
−0.157687 | + | 0.987489i | \(0.550404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.7795i | − | 1.49460i | ||||||
\(86\) | 4.51778 | + | 7.82503i | 0.487165 | + | 0.843794i | ||||
\(87\) | 0.130024 | − | 0.225209i | 0.0139401 | − | 0.0241449i | ||||
\(88\) | −0.789769 | − | 3.22122i | −0.0841896 | − | 0.343383i | ||||
\(89\) | 5.15200 | − | 2.97451i | 0.546111 | − | 0.315297i | −0.201441 | − | 0.979501i | \(-0.564562\pi\) |
0.747552 | + | 0.664203i | \(0.231229\pi\) | |||||||
\(90\) | 13.2180 | 1.39330 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.55962 | 0.162602 | ||||||||
\(93\) | −0.362973 | − | 0.628687i | −0.0376385 | − | 0.0651919i | ||||
\(94\) | −3.28475 | + | 5.68935i | −0.338796 | + | 0.586811i | ||||
\(95\) | 14.2711 | + | 8.23945i | 1.46419 | + | 0.845349i | ||||
\(96\) | 1.29759 | + | 2.24749i | 0.132435 | + | 0.229383i | ||||
\(97\) | 16.7587i | 1.70159i | 0.525502 | + | 0.850793i | \(0.323878\pi\) | ||||
−0.525502 | + | 0.850793i | \(0.676122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.57010 | + | 8.94436i | 0.861327 | + | 0.898942i | ||||
\(100\) | −3.76225 | − | 6.51641i | −0.376225 | − | 0.651641i | ||||
\(101\) | −0.701452 | + | 1.21495i | −0.0697971 | + | 0.120892i | −0.898812 | − | 0.438335i | \(-0.855569\pi\) |
0.829015 | + | 0.559227i | \(0.188902\pi\) | |||||||
\(102\) | −5.05232 | + | 8.75087i | −0.500254 | + | 0.866465i | ||||
\(103\) | −1.78653 | + | 1.03145i | −0.176032 | + | 0.101632i | −0.585427 | − | 0.810725i | \(-0.699073\pi\) |
0.409395 | + | 0.912357i | \(0.365740\pi\) | |||||||
\(104\) | − | 5.01680i | − | 0.491937i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.54058i | 0.538149i | ||||||||
\(107\) | −10.6222 | + | 6.13274i | −1.02689 | + | 0.592875i | −0.916092 | − | 0.400968i | \(-0.868674\pi\) |
−0.110797 | + | 0.993843i | \(0.535340\pi\) | |||||||
\(108\) | −1.65179 | − | 0.953659i | −0.158943 | − | 0.0917659i | ||||
\(109\) | 5.82394 | + | 3.36245i | 0.557832 | + | 0.322065i | 0.752275 | − | 0.658849i | \(-0.228957\pi\) |
−0.194443 | + | 0.980914i | \(0.562290\pi\) | |||||||
\(110\) | 3.27941 | − | 11.2701i | 0.312680 | − | 1.07456i | ||||
\(111\) | 1.83072i | 0.173764i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9900 | −1.12792 | −0.563960 | − | 0.825802i | \(-0.690723\pi\) | ||||
−0.563960 | + | 0.825802i | \(0.690723\pi\) | |||||||
\(114\) | −6.04206 | − | 10.4652i | −0.565891 | − | 0.980152i | ||||
\(115\) | 4.78003 | + | 2.75975i | 0.445740 | + | 0.257348i | ||||
\(116\) | 0.0867797 | + | 0.0501023i | 0.00805729 | + | 0.00465188i | ||||
\(117\) | 9.36873 | + | 16.2271i | 0.866140 | + | 1.50020i | ||||
\(118\) | −14.5344 | −1.33800 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.18432i | 0.838410i | ||||||||
\(121\) | 9.75253 | − | 5.08804i | 0.886594 | − | 0.462549i | ||||
\(122\) | −9.63644 | − | 5.56360i | −0.872442 | − | 0.503705i | ||||
\(123\) | 6.62581 | + | 3.82541i | 0.597429 | + | 0.344926i | ||||
\(124\) | 0.242252 | − | 0.139864i | 0.0217549 | − | 0.0125602i | ||||
\(125\) | − | 8.93419i | − | 0.799098i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.2199i | − | 1.17308i | −0.809922 | − | 0.586538i | \(-0.800491\pi\) | ||
0.809922 | − | 0.586538i | \(-0.199509\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 11.7244 | − | 20.3073i | 1.03228 | − | 1.78796i | ||||
\(130\) | 8.87721 | − | 15.3758i | 0.778583 | − | 1.34855i | ||||
\(131\) | 8.24931 | + | 14.2882i | 0.720746 | + | 1.24837i | 0.960701 | + | 0.277584i | \(0.0895337\pi\) |
−0.239956 | + | 0.970784i | \(0.577133\pi\) | |||||||
\(132\) | −6.21487 | + | 5.95482i | −0.540935 | + | 0.518300i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.98392i | 0.344158i | ||||||||
\(135\) | −3.37500 | − | 5.84566i | −0.290473 | − | 0.503115i | ||||
\(136\) | −3.37197 | − | 1.94681i | −0.289144 | − | 0.166938i | ||||
\(137\) | −3.32187 | + | 5.75365i | −0.283807 | + | 0.491568i | −0.972319 | − | 0.233657i | \(-0.924931\pi\) |
0.688512 | + | 0.725225i | \(0.258264\pi\) | |||||||
\(138\) | −2.02375 | − | 3.50524i | −0.172273 | − | 0.298386i | ||||
\(139\) | 14.3533 | 1.21743 | 0.608716 | − | 0.793388i | \(-0.291685\pi\) | ||||
0.608716 | + | 0.793388i | \(0.291685\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0490 | 1.43578 | ||||||||
\(142\) | −7.32121 | + | 4.22690i | −0.614383 | + | 0.354714i | ||||
\(143\) | 16.1602 | − | 3.96211i | 1.35138 | − | 0.331328i | ||||
\(144\) | 1.86747 | − | 3.23456i | 0.155623 | − | 0.269547i | ||||
\(145\) | 0.177312 | + | 0.307113i | 0.0147249 | + | 0.0255044i | ||||
\(146\) | 3.89771i | 0.322577i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.705430 | −0.0579860 | ||||||||
\(149\) | −2.30871 | + | 1.33294i | −0.189137 | + | 0.109198i | −0.591579 | − | 0.806247i | \(-0.701495\pi\) |
0.402441 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(150\) | −9.76370 | + | 16.9112i | −0.797203 | + | 1.38080i | ||||
\(151\) | −8.99830 | − | 5.19517i | −0.732271 | − | 0.422777i | 0.0869812 | − | 0.996210i | \(-0.472278\pi\) |
−0.819253 | + | 0.573433i | \(0.805611\pi\) | |||||||
\(152\) | 4.03254 | − | 2.32819i | 0.327082 | − | 0.188841i | ||||
\(153\) | 14.5425 | 1.17569 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.989959 | 0.0795154 | ||||||||
\(156\) | −11.2752 | + | 6.50974i | −0.902738 | + | 0.521196i | ||||
\(157\) | −7.25273 | − | 4.18736i | −0.578831 | − | 0.334188i | 0.181838 | − | 0.983329i | \(-0.441795\pi\) |
−0.760669 | + | 0.649140i | \(0.775129\pi\) | |||||||
\(158\) | 3.84991 | − | 6.66824i | 0.306282 | − | 0.530497i | ||||
\(159\) | 12.4524 | − | 7.18940i | 0.987540 | − | 0.570156i | ||||
\(160\) | −3.53900 | −0.279782 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 6.25501i | − | 0.491440i | ||||||
\(163\) | −1.53254 | − | 2.65444i | −0.120038 | − | 0.207911i | 0.799745 | − | 0.600340i | \(-0.204968\pi\) |
−0.919782 | + | 0.392429i | \(0.871635\pi\) | |||||||
\(164\) | −1.47405 | + | 2.55312i | −0.115104 | + | 0.199365i | ||||
\(165\) | −29.5847 | + | 7.25349i | −2.30317 | + | 0.564684i | ||||
\(166\) | −2.48826 | + | 1.43660i | −0.193127 | + | 0.111502i | ||||
\(167\) | −10.0731 | −0.779482 | −0.389741 | − | 0.920925i | \(-0.627435\pi\) | ||||
−0.389741 | + | 0.920925i | \(0.627435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1682 | 0.936018 | ||||||||
\(170\) | −6.88975 | − | 11.9334i | −0.528420 | − | 0.915250i | ||||
\(171\) | −8.69566 | + | 15.0613i | −0.664973 | + | 1.15177i | ||||
\(172\) | 7.82503 | + | 4.51778i | 0.596653 | + | 0.344478i | ||||
\(173\) | 0.0383013 | + | 0.0663398i | 0.00291200 | + | 0.00504372i | 0.867478 | − | 0.497476i | \(-0.165740\pi\) |
−0.864566 | + | 0.502520i | \(0.832406\pi\) | |||||||
\(174\) | − | 0.260049i | − | 0.0197142i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.29457 | − | 2.39477i | −0.172960 | − | 0.180513i | ||||
\(177\) | 18.8596 | + | 32.6659i | 1.41758 | + | 2.45532i | ||||
\(178\) | 2.97451 | − | 5.15200i | 0.222949 | − | 0.386159i | ||||
\(179\) | 4.48746 | − | 7.77250i | 0.335408 | − | 0.580944i | −0.648155 | − | 0.761509i | \(-0.724459\pi\) |
0.983563 | + | 0.180564i | \(0.0577924\pi\) | |||||||
\(180\) | 11.4471 | − | 6.60898i | 0.853216 | − | 0.492604i | ||||
\(181\) | 15.1450i | 1.12572i | 0.826554 | + | 0.562858i | \(0.190298\pi\) | ||||
−0.826554 | + | 0.562858i | \(0.809702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.8771i | 2.13465i | ||||||||
\(184\) | 1.35067 | − | 0.779812i | 0.0995730 | − | 0.0574885i | ||||
\(185\) | −2.16204 | − | 1.24826i | −0.158957 | − | 0.0917736i | ||||
\(186\) | −0.628687 | − | 0.362973i | −0.0460976 | − | 0.0266145i | ||||
\(187\) | 3.60803 | − | 12.3994i | 0.263845 | − | 0.906734i | ||||
\(188\) | 6.56949i | 0.479129i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.4789 | 1.19550 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 2.24749 | + | 1.29759i | 0.162199 | + | 0.0936454i | ||||
\(193\) | 12.8415 | + | 7.41403i | 0.924350 | + | 0.533674i | 0.885020 | − | 0.465552i | \(-0.154144\pi\) |
0.0393299 | + | 0.999226i | \(0.487478\pi\) | |||||||
\(194\) | 8.37933 | + | 14.5134i | 0.601601 | + | 1.04200i | ||||
\(195\) | −46.0759 | −3.29956 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4745i | 1.03126i | 0.856811 | + | 0.515631i | \(0.172443\pi\) | ||||
−0.856811 | + | 0.515631i | \(0.827557\pi\) | |||||||
\(198\) | 11.8941 | + | 3.46099i | 0.845277 | + | 0.245962i | ||||
\(199\) | 9.72188 | + | 5.61293i | 0.689166 | + | 0.397890i | 0.803300 | − | 0.595575i | \(-0.203076\pi\) |
−0.114133 | + | 0.993465i | \(0.536409\pi\) | |||||||
\(200\) | −6.51641 | − | 3.76225i | −0.460779 | − | 0.266031i | ||||
\(201\) | 8.95381 | − | 5.16948i | 0.631553 | − | 0.364627i | ||||
\(202\) | 1.40290i | 0.0987080i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.1046i | 0.707466i | ||||||||
\(205\) | −9.03550 | + | 5.21665i | −0.631066 | + | 0.364346i | ||||
\(206\) | −1.03145 | + | 1.78653i | −0.0718647 | + | 0.124473i | ||||
\(207\) | −2.91256 | + | 5.04469i | −0.202437 | + | 0.350630i | ||||
\(208\) | −2.50840 | − | 4.34467i | −0.173926 | − | 0.301249i | ||||
\(209\) | 10.6844 | + | 11.1510i | 0.739054 | + | 0.771329i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.44038i | − | 0.443374i | −0.975118 | − | 0.221687i | \(-0.928844\pi\) | ||
0.975118 | − | 0.221687i | \(-0.0711563\pi\) | |||||||
\(212\) | 2.77029 | + | 4.79828i | 0.190264 | + | 0.329548i | ||||
\(213\) | 18.9999 | + | 10.9696i | 1.30185 | + | 0.751622i | ||||
\(214\) | −6.13274 | + | 10.6222i | −0.419226 | + | 0.726120i | ||||
\(215\) | 15.9884 | + | 27.6927i | 1.09040 | + | 1.88863i | ||||
\(216\) | −1.90732 | −0.129777 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.72491 | 0.455468 | ||||||||
\(219\) | 8.76006 | − | 5.05762i | 0.591950 | − | 0.341763i | ||||
\(220\) | −2.79499 | − | 11.3999i | −0.188438 | − | 0.768580i | ||||
\(221\) | 9.76675 | − | 16.9165i | 0.656983 | − | 1.13793i | ||||
\(222\) | 0.915358 | + | 1.58545i | 0.0614348 | + | 0.106408i | ||||
\(223\) | 4.01793i | 0.269061i | 0.990909 | + | 0.134530i | \(0.0429526\pi\) | ||||
−0.990909 | + | 0.134530i | \(0.957047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.1036 | 1.87357 | ||||||||
\(226\) | −10.3836 | + | 5.99498i | −0.690707 | + | 0.398780i | ||||
\(227\) | 6.36466 | − | 11.0239i | 0.422437 | − | 0.731682i | −0.573740 | − | 0.819037i | \(-0.694508\pi\) |
0.996177 | + | 0.0873549i | \(0.0278414\pi\) | |||||||
\(228\) | −10.4652 | − | 6.04206i | −0.693072 | − | 0.400145i | ||||
\(229\) | 5.20780 | − | 3.00672i | 0.344141 | − | 0.198690i | −0.317961 | − | 0.948104i | \(-0.602998\pi\) |
0.662102 | + | 0.749414i | \(0.269665\pi\) | |||||||
\(230\) | 5.51950 | 0.363945 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.100205 | 0.00657875 | ||||||||
\(233\) | −5.60053 | + | 3.23347i | −0.366903 | + | 0.211832i | −0.672105 | − | 0.740456i | \(-0.734609\pi\) |
0.305202 | + | 0.952288i | \(0.401276\pi\) | |||||||
\(234\) | 16.2271 | + | 9.36873i | 1.06080 | + | 0.612453i | ||||
\(235\) | −11.6247 | + | 20.1346i | −0.758312 | + | 1.31343i | ||||
\(236\) | −12.5871 | + | 7.26719i | −0.819353 | + | 0.473054i | ||||
\(237\) | −19.9824 | −1.29800 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.5775i | 1.00762i | 0.863813 | + | 0.503812i | \(0.168070\pi\) | ||||
−0.863813 | + | 0.503812i | \(0.831930\pi\) | |||||||
\(240\) | 4.59216 | + | 7.95386i | 0.296423 | + | 0.513419i | ||||
\(241\) | −11.7381 | + | 20.3310i | −0.756119 | + | 1.30964i | 0.188697 | + | 0.982035i | \(0.439573\pi\) |
−0.944816 | + | 0.327601i | \(0.893760\pi\) | |||||||
\(242\) | 5.90192 | − | 9.28264i | 0.379390 | − | 0.596710i | ||||
\(243\) | −19.0134 | + | 10.9774i | −1.21971 | + | 0.704201i | ||||
\(244\) | −11.1272 | −0.712346 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.65083 | 0.487799 | ||||||||
\(247\) | 11.6800 | + | 20.2304i | 0.743183 | + | 1.28723i | ||||
\(248\) | 0.139864 | − | 0.242252i | 0.00888140 | − | 0.0153830i | ||||
\(249\) | 6.45748 | + | 3.72823i | 0.409226 | + | 0.236267i | ||||
\(250\) | −4.46709 | − | 7.73723i | −0.282524 | − | 0.489345i | ||||
\(251\) | − | 18.2818i | − | 1.15394i | −0.816766 | − | 0.576968i | \(-0.804236\pi\) | ||
0.816766 | − | 0.576968i | \(-0.195764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.57867 | + | 3.73495i | 0.224989 | + | 0.234814i | ||||
\(254\) | −6.60994 | − | 11.4488i | −0.414745 | − | 0.718359i | ||||
\(255\) | −17.8801 | + | 30.9693i | −1.11970 | + | 1.93937i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.33087 | − | 4.80983i | 0.519666 | − | 0.300029i | −0.217132 | − | 0.976142i | \(-0.569670\pi\) |
0.736798 | + | 0.676113i | \(0.236337\pi\) | |||||||
\(258\) | − | 23.4489i | − | 1.45986i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 17.7544i | − | 1.10108i | ||||||
\(261\) | −0.324118 | + | 0.187129i | −0.0200624 | + | 0.0115830i | ||||
\(262\) | 14.2882 | + | 8.24931i | 0.882729 | + | 0.509644i | ||||
\(263\) | −0.501139 | − | 0.289333i | −0.0309016 | − | 0.0178410i | 0.484470 | − | 0.874808i | \(-0.339013\pi\) |
−0.515371 | + | 0.856967i | \(0.672346\pi\) | |||||||
\(264\) | −2.40482 | + | 8.26446i | −0.148007 | + | 0.508642i | ||||
\(265\) | 19.6081i | 1.20452i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.4388 | −0.944837 | ||||||||
\(268\) | 1.99196 | + | 3.45017i | 0.121678 | + | 0.210753i | ||||
\(269\) | −19.1302 | − | 11.0448i | −1.16639 | − | 0.673413i | −0.213560 | − | 0.976930i | \(-0.568506\pi\) |
−0.952826 | + | 0.303517i | \(0.901839\pi\) | |||||||
\(270\) | −5.84566 | − | 3.37500i | −0.355756 | − | 0.205396i | ||||
\(271\) | 2.13111 | + | 3.69119i | 0.129456 | + | 0.224224i | 0.923466 | − | 0.383681i | \(-0.125344\pi\) |
−0.794010 | + | 0.607905i | \(0.792010\pi\) | |||||||
\(272\) | −3.89362 | −0.236085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.64374i | 0.401363i | ||||||||
\(275\) | 6.97258 | − | 23.9621i | 0.420462 | − | 1.44497i | ||||
\(276\) | −3.50524 | − | 2.02375i | −0.210991 | − | 0.121815i | ||||
\(277\) | 15.9048 | + | 9.18263i | 0.955626 | + | 0.551731i | 0.894824 | − | 0.446419i | \(-0.147301\pi\) |
0.0608016 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(278\) | 12.4303 | − | 7.17666i | 0.745522 | − | 0.430427i | ||||
\(279\) | 1.04477i | 0.0625489i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.72890i | 0.222448i | 0.993795 | + | 0.111224i | \(0.0354771\pi\) | ||||
−0.993795 | + | 0.111224i | \(0.964523\pi\) | |||||||
\(282\) | 14.7649 | − | 8.52450i | 0.879235 | − | 0.507626i | ||||
\(283\) | 6.36576 | − | 11.0258i | 0.378405 | − | 0.655417i | −0.612425 | − | 0.790529i | \(-0.709806\pi\) |
0.990830 | + | 0.135111i | \(0.0431392\pi\) | |||||||
\(284\) | −4.22690 | + | 7.32121i | −0.250821 | + | 0.434434i | ||||
\(285\) | −21.3828 | − | 37.0361i | −1.26661 | − | 2.19383i | ||||
\(286\) | 12.0141 | − | 11.5114i | 0.710408 | − | 0.680683i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 3.73495i | − | 0.220084i | ||||||
\(289\) | 0.919861 | + | 1.59325i | 0.0541094 | + | 0.0937203i | ||||
\(290\) | 0.307113 | + | 0.177312i | 0.0180343 | + | 0.0104121i | ||||
\(291\) | 21.7459 | − | 37.6649i | 1.27476 | − | 2.20796i | ||||
\(292\) | 1.94885 | + | 3.37552i | 0.114048 | + | 0.197537i | ||||
\(293\) | 26.2251 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −51.4371 | −2.99478 | ||||||||
\(296\) | −0.610920 | + | 0.352715i | −0.0355090 | + | 0.0205011i | ||||
\(297\) | −1.50634 | − | 6.14389i | −0.0874067 | − | 0.356505i | ||||
\(298\) | −1.33294 | + | 2.30871i | −0.0772149 | + | 0.133740i | ||||
\(299\) | 3.91216 | + | 6.77605i | 0.226246 | + | 0.391869i | ||||
\(300\) | 19.5274i | 1.12742i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.3903 | −0.597897 | ||||||||
\(303\) | 3.15301 | − | 1.82039i | 0.181136 | − | 0.104579i | ||||
\(304\) | 2.32819 | − | 4.03254i | 0.133531 | − | 0.231282i | ||||
\(305\) | −34.1033 | − | 19.6896i | −1.95275 | − | 1.12742i | ||||
\(306\) | 12.5941 | − | 7.27123i | 0.719959 | − | 0.415669i | ||||
\(307\) | −25.5942 | −1.46074 | −0.730369 | − | 0.683053i | \(-0.760652\pi\) | ||||
−0.730369 | + | 0.683053i | \(0.760652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.35360 | 0.304556 | ||||||||
\(310\) | 0.857330 | − | 0.494980i | 0.0486931 | − | 0.0281129i | ||||
\(311\) | 1.65385 | + | 0.954850i | 0.0937811 | + | 0.0541446i | 0.546157 | − | 0.837683i | \(-0.316090\pi\) |
−0.452376 | + | 0.891827i | \(0.649423\pi\) | |||||||
\(312\) | −6.50974 | + | 11.2752i | −0.368541 | + | 0.638332i | ||||
\(313\) | 26.3707 | − | 15.2251i | 1.49056 | − | 0.860576i | 0.490619 | − | 0.871374i | \(-0.336771\pi\) |
0.999942 | + | 0.0107985i | \(0.00343733\pi\) | |||||||
\(314\) | −8.37473 | −0.472613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 7.69982i | − | 0.433149i | ||||||
\(317\) | −17.1971 | − | 29.7862i | −0.965885 | − | 1.67296i | −0.707220 | − | 0.706994i | \(-0.750051\pi\) |
−0.258665 | − | 0.965967i | \(-0.583283\pi\) | |||||||
\(318\) | 7.18940 | − | 12.4524i | 0.403161 | − | 0.698296i | ||||
\(319\) | 0.0791385 | + | 0.322781i | 0.00443090 | + | 0.0180723i | ||||
\(320\) | −3.06486 | + | 1.76950i | −0.171331 | + | 0.0989180i | ||||
\(321\) | 31.8311 | 1.77664 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.1302 | 1.00879 | ||||||||
\(324\) | −3.12751 | − | 5.41700i | −0.173750 | − | 0.300944i | ||||
\(325\) | 18.8744 | − | 32.6915i | 1.04697 | − | 1.81340i | ||||
\(326\) | −2.65444 | − | 1.53254i | −0.147016 | − | 0.0848795i | ||||
\(327\) | −8.72616 | − | 15.1142i | −0.482558 | − | 0.835815i | ||||
\(328\) | 2.94809i | 0.162781i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −21.9944 | + | 21.0741i | −1.21075 | + | 1.16009i | ||||
\(331\) | −7.75642 | − | 13.4345i | −0.426332 | − | 0.738428i | 0.570212 | − | 0.821497i | \(-0.306861\pi\) |
−0.996544 | + | 0.0830696i | \(0.973528\pi\) | |||||||
\(332\) | −1.43660 | + | 2.48826i | −0.0788436 | + | 0.136561i | ||||
\(333\) | 1.31737 | − | 2.28175i | 0.0721915 | − | 0.125039i | ||||
\(334\) | −8.72358 | + | 5.03656i | −0.477333 | + | 0.275588i | ||||
\(335\) | 14.0991i | 0.770314i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.70882i | − | 0.419926i | −0.977709 | − | 0.209963i | \(-0.932666\pi\) | ||
0.977709 | − | 0.209963i | \(-0.0673344\pi\) | |||||||
\(338\) | 10.5380 | − | 6.08412i | 0.573192 | − | 0.330933i | ||||
\(339\) | 26.9473 | + | 15.5580i | 1.46358 | + | 0.844997i | ||||
\(340\) | −11.9334 | − | 6.88975i | −0.647180 | − | 0.373649i | ||||
\(341\) | 0.890808 | + | 0.259211i | 0.0482400 | + | 0.0140371i | ||||
\(342\) | 17.3913i | 0.940415i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.03556 | 0.487165 | ||||||||
\(345\) | −7.16204 | − | 12.4050i | −0.385591 | − | 0.667864i | ||||
\(346\) | 0.0663398 | + | 0.0383013i | 0.00356645 | + | 0.00205909i | ||||
\(347\) | −18.8285 | − | 10.8706i | −1.01077 | − | 0.583567i | −0.0993513 | − | 0.995052i | \(-0.531677\pi\) |
−0.911416 | + | 0.411485i | \(0.865010\pi\) | |||||||
\(348\) | −0.130024 | − | 0.225209i | −0.00697004 | − | 0.0120725i | ||||
\(349\) | −13.4565 | −0.720307 | −0.360154 | − | 0.932893i | \(-0.617276\pi\) | ||||
−0.360154 | + | 0.932893i | \(0.617276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.56862i | − | 0.510735i | ||||||
\(352\) | −3.18454 | − | 0.926651i | −0.169737 | − | 0.0493907i | ||||
\(353\) | −5.80903 | − | 3.35384i | −0.309183 | − | 0.178507i | 0.337378 | − | 0.941369i | \(-0.390460\pi\) |
−0.646561 | + | 0.762862i | \(0.723793\pi\) | |||||||
\(354\) | 32.6659 | + | 18.8596i | 1.73617 | + | 1.00238i | ||||
\(355\) | −25.9098 | + | 14.9590i | −1.37515 | + | 0.793941i | ||||
\(356\) | − | 5.94902i | − | 0.315297i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 8.97491i | − | 0.474339i | ||||||
\(359\) | 26.8869 | − | 15.5232i | 1.41904 | − | 0.819282i | 0.422823 | − | 0.906212i | \(-0.361039\pi\) |
0.996214 | + | 0.0869306i | \(0.0277058\pi\) | |||||||
\(360\) | 6.60898 | − | 11.4471i | 0.348324 | − | 0.603315i | ||||
\(361\) | −1.34091 | + | 2.32253i | −0.0705744 | + | 0.122238i | ||||
\(362\) | 7.57248 | + | 13.1159i | 0.398001 | + | 0.689358i | ||||
\(363\) | −28.5209 | − | 1.21946i | −1.49696 | − | 0.0640050i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.7940i | 0.722010i | ||||||||
\(366\) | 14.4385 | + | 25.0083i | 0.754714 | + | 1.30720i | ||||
\(367\) | −25.6770 | − | 14.8246i | −1.34033 | − | 0.773838i | −0.353471 | − | 0.935445i | \(-0.614999\pi\) |
−0.986855 | + | 0.161608i | \(0.948332\pi\) | |||||||
\(368\) | 0.779812 | − | 1.35067i | 0.0406505 | − | 0.0704087i | ||||
\(369\) | −5.50549 | − | 9.53578i | −0.286604 | − | 0.496413i | ||||
\(370\) | −2.49651 | −0.129788 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.725946 | −0.0376385 | ||||||||
\(373\) | −7.60418 | + | 4.39027i | −0.393729 | + | 0.227320i | −0.683775 | − | 0.729693i | \(-0.739663\pi\) |
0.290045 | + | 0.957013i | \(0.406330\pi\) | |||||||
\(374\) | −3.07506 | − | 12.5422i | −0.159008 | − | 0.648542i | ||||
\(375\) | −11.5929 | + | 20.0795i | −0.598655 | + | 1.03690i | ||||
\(376\) | 3.28475 | + | 5.68935i | 0.169398 | + | 0.293406i | ||||
\(377\) | 0.502706i | 0.0258907i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.8135 | 1.58278 | 0.791391 | − | 0.611311i | \(-0.209358\pi\) | ||||
0.791391 | + | 0.611311i | \(0.209358\pi\) | |||||||
\(380\) | 14.2711 | − | 8.23945i | 0.732094 | − | 0.422675i | ||||
\(381\) | −17.1540 | + | 29.7116i | −0.878825 | + | 1.52217i | ||||
\(382\) | −5.19615 | − | 3.00000i | −0.265858 | − | 0.153493i | ||||
\(383\) | −4.58545 | + | 2.64741i | −0.234305 | + | 0.135276i | −0.612557 | − | 0.790427i | \(-0.709859\pi\) |
0.378251 | + | 0.925703i | \(0.376526\pi\) | |||||||
\(384\) | 2.59518 | 0.132435 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8281 | 0.754729 | ||||||||
\(387\) | −29.2261 | + | 16.8737i | −1.48564 | + | 0.857737i | ||||
\(388\) | 14.5134 | + | 8.37933i | 0.736808 | + | 0.425396i | ||||
\(389\) | −0.430119 | + | 0.744987i | −0.0218079 | + | 0.0377724i | −0.876723 | − | 0.480995i | \(-0.840276\pi\) |
0.854916 | + | 0.518767i | \(0.173609\pi\) | |||||||
\(390\) | −39.9029 | + | 23.0379i | −2.02056 | + | 1.16657i | ||||
\(391\) | 6.07258 | 0.307104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 42.8168i | − | 2.15982i | ||||||
\(394\) | 7.23723 | + | 12.5353i | 0.364606 | + | 0.631517i | ||||
\(395\) | 13.6248 | − | 23.5989i | 0.685539 | − | 1.18739i | ||||
\(396\) | 12.0311 | − | 2.94974i | 0.604585 | − | 0.148230i | ||||
\(397\) | −10.6931 | + | 6.17367i | −0.536672 | + | 0.309847i | −0.743729 | − | 0.668481i | \(-0.766945\pi\) |
0.207057 | + | 0.978329i | \(0.433611\pi\) | |||||||
\(398\) | 11.2259 | 0.562702 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.52450 | −0.376225 | ||||||||
\(401\) | −16.8626 | − | 29.2069i | −0.842078 | − | 1.45852i | −0.888134 | − | 0.459584i | \(-0.847999\pi\) |
0.0460561 | − | 0.998939i | \(-0.485335\pi\) | |||||||
\(402\) | 5.16948 | − | 8.95381i | 0.257830 | − | 0.446575i | ||||
\(403\) | 1.21533 | + | 0.701671i | 0.0605399 | + | 0.0349527i | ||||
\(404\) | 0.701452 | + | 1.21495i | 0.0348985 | + | 0.0604461i | ||||
\(405\) | − | 22.1365i | − | 1.09997i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.61866 | − | 1.68935i | −0.0802339 | − | 0.0837377i | ||||
\(408\) | 5.05232 | + | 8.75087i | 0.250127 | + | 0.433233i | ||||
\(409\) | −19.1846 | + | 33.2287i | −0.948616 | + | 1.64305i | −0.200273 | + | 0.979740i | \(0.564183\pi\) |
−0.748343 | + | 0.663312i | \(0.769150\pi\) | |||||||
\(410\) | −5.21665 | + | 9.03550i | −0.257632 | + | 0.446231i | ||||
\(411\) | 14.9317 | − | 8.62085i | 0.736529 | − | 0.425235i | ||||
\(412\) | 2.06291i | 0.101632i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.82511i | 0.286289i | ||||||||
\(415\) | −8.80595 | + | 5.08412i | −0.432267 | + | 0.249570i | ||||
\(416\) | −4.34467 | − | 2.50840i | −0.213015 | − | 0.122984i | ||||
\(417\) | −32.2589 | − | 18.6247i | −1.57973 | − | 0.912056i | ||||
\(418\) | 14.8284 | + | 4.31483i | 0.725282 | + | 0.211045i | ||||
\(419\) | − | 33.5023i | − | 1.63670i | −0.574723 | − | 0.818348i | \(-0.694890\pi\) | ||
0.574723 | − | 0.818348i | \(-0.305110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0155 | −1.12171 | −0.560853 | − | 0.827915i | \(-0.689527\pi\) | ||||
−0.560853 | + | 0.827915i | \(0.689527\pi\) | |||||||
\(422\) | −3.22019 | − | 5.57753i | −0.156756 | − | 0.271510i | ||||
\(423\) | −21.2494 | − | 12.2683i | −1.03318 | − | 0.596508i | ||||
\(424\) | 4.79828 | + | 2.77029i | 0.233025 | + | 0.134537i | ||||
\(425\) | −14.6488 | − | 25.3724i | −0.710570 | − | 1.23074i | ||||
\(426\) | 21.9391 | 1.06295 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.2655i | 0.592875i | ||||||||
\(429\) | −41.4611 | − | 12.0645i | −2.00176 | − | 0.582480i | ||||
\(430\) | 27.6927 | + | 15.9884i | 1.33546 | + | 0.771030i | ||||
\(431\) | 23.2425 | + | 13.4191i | 1.11955 | + | 0.646373i | 0.941286 | − | 0.337609i | \(-0.109618\pi\) |
0.178265 | + | 0.983983i | \(0.442952\pi\) | |||||||
\(432\) | −1.65179 | + | 0.953659i | −0.0794716 | + | 0.0458829i | ||||
\(433\) | − | 30.6912i | − | 1.47493i | −0.675387 | − | 0.737463i | \(-0.736024\pi\) | ||
0.675387 | − | 0.737463i | \(-0.263976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.920312i | − | 0.0441256i | ||||||
\(436\) | 5.82394 | − | 3.36245i | 0.278916 | − | 0.161032i | ||||
\(437\) | −3.63110 | + | 6.28924i | −0.173699 | + | 0.300855i | ||||
\(438\) | 5.05762 | − | 8.76006i | 0.241663 | − | 0.418572i | ||||
\(439\) | −8.42258 | − | 14.5883i | −0.401988 | − | 0.696263i | 0.591978 | − | 0.805954i | \(-0.298347\pi\) |
−0.993966 | + | 0.109691i | \(0.965014\pi\) | |||||||
\(440\) | −8.12048 | − | 8.47510i | −0.387129 | − | 0.404035i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 19.5335i | − | 0.929114i | ||||||
\(443\) | 0.395295 | + | 0.684671i | 0.0187810 | + | 0.0325297i | 0.875263 | − | 0.483647i | \(-0.160688\pi\) |
−0.856482 | + | 0.516177i | \(0.827355\pi\) | |||||||
\(444\) | 1.58545 | + | 0.915358i | 0.0752419 | + | 0.0434410i | ||||
\(445\) | 10.5268 | − | 18.2329i | 0.499017 | − | 0.864323i | ||||
\(446\) | 2.00897 | + | 3.47963i | 0.0951273 | + | 0.164765i | ||||
\(447\) | 6.91841 | 0.327230 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.9734 | 0.753833 | 0.376917 | − | 0.926247i | \(-0.376984\pi\) | ||||
0.376917 | + | 0.926247i | \(0.376984\pi\) | |||||||
\(450\) | 24.3384 | − | 14.0518i | 1.14732 | − | 0.662408i | ||||
\(451\) | −9.49646 | + | 2.32831i | −0.447171 | + | 0.109636i | ||||
\(452\) | −5.99498 | + | 10.3836i | −0.281980 | + | 0.488404i | ||||
\(453\) | 13.4824 | + | 23.3522i | 0.633458 | + | 1.09718i | ||||
\(454\) | − | 12.7293i | − | 0.597416i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0841 | −0.565891 | ||||||||
\(457\) | −30.2530 | + | 17.4666i | −1.41517 | + | 0.817052i | −0.995870 | − | 0.0907937i | \(-0.971060\pi\) |
−0.419305 | + | 0.907845i | \(0.637726\pi\) | |||||||
\(458\) | 3.00672 | − | 5.20780i | 0.140495 | − | 0.243344i | ||||
\(459\) | −6.43143 | − | 3.71319i | −0.300193 | − | 0.173317i | ||||
\(460\) | 4.78003 | − | 2.75975i | 0.222870 | − | 0.128674i | ||||
\(461\) | −20.8346 | −0.970364 | −0.485182 | − | 0.874413i | \(-0.661247\pi\) | ||||
−0.485182 | + | 0.874413i | \(0.661247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1724 | 0.612172 | 0.306086 | − | 0.952004i | \(-0.400981\pi\) | ||||
0.306086 | + | 0.952004i | \(0.400981\pi\) | |||||||
\(464\) | 0.0867797 | − | 0.0501023i | 0.00402865 | − | 0.00232594i | ||||
\(465\) | −2.22492 | − | 1.28456i | −0.103178 | − | 0.0595700i | ||||
\(466\) | −3.23347 | + | 5.60053i | −0.149788 | + | 0.259440i | ||||
\(467\) | 14.5651 | − | 8.40919i | 0.673995 | − | 0.389131i | −0.123594 | − | 0.992333i | \(-0.539442\pi\) |
0.797589 | + | 0.603202i | \(0.206109\pi\) | |||||||
\(468\) | 18.7375 | 0.866140 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 23.2494i | 1.07241i | ||||||||
\(471\) | 10.8670 | + | 18.8221i | 0.500723 | + | 0.867277i | ||||
\(472\) | −7.26719 | + | 12.5871i | −0.334500 | + | 0.579370i | ||||
\(473\) | 7.13600 | + | 29.1055i | 0.328114 | + | 1.33827i | ||||
\(474\) | −17.3053 | + | 9.99120i | −0.794857 | + | 0.458911i | ||||
\(475\) | 35.0369 | 1.60760 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.6938 | −0.947503 | ||||||||
\(478\) | 7.78874 | + | 13.4905i | 0.356249 | + | 0.617041i | ||||
\(479\) | −11.4291 | + | 19.7957i | −0.522208 | + | 0.904491i | 0.477458 | + | 0.878654i | \(0.341558\pi\) |
−0.999666 | + | 0.0258361i | \(0.991775\pi\) | |||||||
\(480\) | 7.95386 | + | 4.59216i | 0.363042 | + | 0.209603i | ||||
\(481\) | −1.76950 | − | 3.06486i | −0.0806822 | − | 0.139746i | ||||
\(482\) | 23.4762i | 1.06931i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.469894 | − | 10.9900i | 0.0213588 | − | 0.499544i | ||||
\(485\) | 29.6544 | + | 51.3630i | 1.34654 | + | 2.33227i | ||||
\(486\) | −10.9774 | + | 19.0134i | −0.497945 | + | 0.862467i | ||||
\(487\) | −15.6314 | + | 27.0744i | −0.708327 | + | 1.22686i | 0.257150 | + | 0.966371i | \(0.417217\pi\) |
−0.965477 | + | 0.260487i | \(0.916117\pi\) | |||||||
\(488\) | −9.63644 | + | 5.56360i | −0.436221 | + | 0.251852i | ||||
\(489\) | 7.95442i | 0.359711i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.4979i | − | 1.01532i | −0.861558 | − | 0.507659i | \(-0.830511\pi\) | ||
0.861558 | − | 0.507659i | \(-0.169489\pi\) | |||||||
\(492\) | 6.62581 | − | 3.82541i | 0.298715 | − | 0.172463i | ||||
\(493\) | 0.337887 | + | 0.195079i | 0.0152177 | + | 0.00878593i | ||||
\(494\) | 20.2304 | + | 11.6800i | 0.910210 | + | 0.525510i | ||||
\(495\) | 42.0932 | + | 12.2484i | 1.89195 | + | 0.550526i | ||||
\(496\) | − | 0.279729i | − | 0.0125602i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.45646 | 0.334132 | ||||||||
\(499\) | 15.9548 | + | 27.6346i | 0.714236 | + | 1.23709i | 0.963253 | + | 0.268595i | \(0.0865592\pi\) |
−0.249017 | + | 0.968499i | \(0.580107\pi\) | |||||||
\(500\) | −7.73723 | − | 4.46709i | −0.346020 | − | 0.199774i | ||||
\(501\) | 22.6392 | + | 13.0708i | 1.01145 | + | 0.583959i | ||||
\(502\) | −9.14090 | − | 15.8325i | −0.407978 | − | 0.706639i | ||||
\(503\) | 30.2687 | 1.34962 | 0.674808 | − | 0.737994i | \(-0.264227\pi\) | ||||
0.674808 | + | 0.737994i | \(0.264227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.96487i | 0.220934i | ||||||||
\(506\) | 4.96669 | + | 1.44523i | 0.220796 | + | 0.0642481i | ||||
\(507\) | −27.3480 | − | 15.7894i | −1.21457 | − | 0.701231i | ||||
\(508\) | −11.4488 | − | 6.60994i | −0.507956 | − | 0.293269i | ||||
\(509\) | 19.9655 | − | 11.5271i | 0.884957 | − | 0.510930i | 0.0126676 | − | 0.999920i | \(-0.495968\pi\) |
0.872290 | + | 0.488989i | \(0.162634\pi\) | |||||||
\(510\) | 35.7603i | 1.58349i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 7.69133 | − | 4.44059i | 0.339581 | − | 0.196057i | ||||
\(514\) | 4.80983 | − | 8.33087i | 0.212153 | − | 0.367459i | ||||
\(515\) | −3.65031 | + | 6.32252i | −0.160852 | + | 0.278603i | ||||
\(516\) | −11.7244 | − | 20.3073i | −0.516140 | − | 0.893980i | ||||
\(517\) | −15.7325 | + | 15.0742i | −0.691912 | + | 0.662961i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.198797i | − | 0.00872624i | ||||||
\(520\) | −8.87721 | − | 15.3758i | −0.389291 | − | 0.674273i | ||||
\(521\) | 6.91351 | + | 3.99152i | 0.302886 | + | 0.174872i | 0.643739 | − | 0.765245i | \(-0.277382\pi\) |
−0.340852 | + | 0.940117i | \(0.610716\pi\) | |||||||
\(522\) | −0.187129 | + | 0.324118i | −0.00819043 | + | 0.0141862i | ||||
\(523\) | 2.79140 | + | 4.83485i | 0.122059 | + | 0.211413i | 0.920580 | − | 0.390555i | \(-0.127717\pi\) |
−0.798520 | + | 0.601968i | \(0.794383\pi\) | |||||||
\(524\) | 16.4986 | 0.720746 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.578666 | −0.0252310 | ||||||||
\(527\) | 0.943238 | − | 0.544579i | 0.0410881 | − | 0.0237222i | ||||
\(528\) | 2.04959 | + | 8.35964i | 0.0891970 | + | 0.363807i | ||||
\(529\) | 10.2838 | − | 17.8120i | 0.447121 | − | 0.774437i | ||||
\(530\) | 9.80405 | + | 16.9811i | 0.425861 | + | 0.737612i | ||||
\(531\) | − | 54.2851i | − | 2.35577i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7900 | −0.640625 | ||||||||
\(534\) | −13.3704 | + | 7.71938i | −0.578592 | + | 0.334050i | ||||
\(535\) | −21.7038 | + | 37.5920i | −0.938335 | + | 1.62524i | ||||
\(536\) | 3.45017 | + | 1.99196i | 0.149025 | + | 0.0860395i | ||||
\(537\) | −20.1710 | + | 11.6457i | −0.870444 | + | 0.502551i | ||||
\(538\) | −22.0896 | −0.952350 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.74999 | −0.290473 | ||||||||
\(541\) | −11.6066 | + | 6.70108i | −0.499007 | + | 0.288102i | −0.728304 | − | 0.685255i | \(-0.759691\pi\) |
0.229296 | + | 0.973357i | \(0.426358\pi\) | |||||||
\(542\) | 3.69119 | + | 2.13111i | 0.158550 | + | 0.0915390i | ||||
\(543\) | 19.6519 | − | 34.0381i | 0.843345 | − | 1.46072i | ||||
\(544\) | −3.37197 | + | 1.94681i | −0.144572 | + | 0.0834688i | ||||
\(545\) | 23.7994 | 1.01946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5161i | 1.04823i | 0.851647 | + | 0.524116i | \(0.175604\pi\) | ||||
−0.851647 | + | 0.524116i | \(0.824396\pi\) | |||||||
\(548\) | 3.32187 | + | 5.75365i | 0.141903 | + | 0.245784i | ||||
\(549\) | 20.7798 | − | 35.9916i | 0.886858 | − | 1.53608i | ||||
\(550\) | −5.94261 | − | 24.2381i | −0.253394 | − | 1.03351i | ||||
\(551\) | −0.404079 | + | 0.233295i | −0.0172143 | + | 0.00993870i | ||||
\(552\) | −4.04750 | −0.172273 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.3653 | 0.780265 | ||||||||
\(555\) | 3.23945 | + | 5.61089i | 0.137507 | + | 0.238169i | ||||
\(556\) | 7.17666 | − | 12.4303i | 0.304358 | − | 0.527164i | ||||
\(557\) | −3.12772 | − | 1.80579i | −0.132526 | − | 0.0765137i | 0.432271 | − | 0.901744i | \(-0.357712\pi\) |
−0.564797 | + | 0.825230i | \(0.691046\pi\) | |||||||
\(558\) | 0.522386 | + | 0.904799i | 0.0221144 | + | 0.0383032i | ||||
\(559\) | 45.3296i | 1.91724i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.1983 | + | 23.1858i | −1.02165 | + | 0.978905i | ||||
\(562\) | 1.86445 | + | 3.22933i | 0.0786472 | + | 0.136221i | ||||
\(563\) | 2.92902 | − | 5.07320i | 0.123443 | − | 0.213810i | −0.797680 | − | 0.603081i | \(-0.793940\pi\) |
0.921123 | + | 0.389271i | \(0.127273\pi\) | |||||||
\(564\) | 8.52450 | − | 14.7649i | 0.358946 | − | 0.621713i | ||||
\(565\) | −36.7476 | + | 21.2162i | −1.54598 | + | 0.892573i | ||||
\(566\) | − | 12.7315i | − | 0.535146i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.45381i | 0.354714i | ||||||||
\(569\) | 29.9772 | − | 17.3073i | 1.25671 | − | 0.725561i | 0.284275 | − | 0.958743i | \(-0.408247\pi\) |
0.972433 | + | 0.233182i | \(0.0749137\pi\) | |||||||
\(570\) | −37.0361 | − | 21.3828i | −1.55127 | − | 0.895628i | ||||
\(571\) | 6.89907 | + | 3.98318i | 0.288717 | + | 0.166691i | 0.637363 | − | 0.770564i | \(-0.280025\pi\) |
−0.348646 | + | 0.937254i | \(0.613358\pi\) | |||||||
\(572\) | 4.64882 | − | 15.9762i | 0.194377 | − | 0.667999i | ||||
\(573\) | 15.5711i | 0.650491i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.7354 | 0.489399 | ||||||||
\(576\) | −1.86747 | − | 3.23456i | −0.0778114 | − | 0.134773i | ||||
\(577\) | −15.9144 | − | 9.18819i | −0.662525 | − | 0.382509i | 0.130713 | − | 0.991420i | \(-0.458273\pi\) |
−0.793239 | + | 0.608911i | \(0.791607\pi\) | |||||||
\(578\) | 1.59325 | + | 0.919861i | 0.0662703 | + | 0.0382612i | ||||
\(579\) | −19.2407 | − | 33.3259i | −0.799618 | − | 1.38498i | ||||
\(580\) | 0.354624 | 0.0147249 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 43.4917i | − | 1.80279i | ||||||
\(583\) | −5.13418 | + | 17.6442i | −0.212636 | + | 0.730749i | ||||
\(584\) | 3.37552 | + | 1.94885i | 0.139680 | + | 0.0806442i | ||||
\(585\) | 57.4277 | + | 33.1559i | 2.37434 | + | 1.37083i | ||||
\(586\) | 22.7116 | − | 13.1126i | 0.938209 | − | 0.541675i | ||||
\(587\) | 17.2267i | 0.711021i | 0.934672 | + | 0.355511i | \(0.115693\pi\) | ||||
−0.934672 | + | 0.355511i | \(0.884307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.30252i | 0.0536695i | ||||||||
\(590\) | −44.5459 | + | 25.7186i | −1.83392 | + | 1.05882i | ||||
\(591\) | 18.7819 | − | 32.5312i | 0.772584 | − | 1.33816i | ||||
\(592\) | −0.352715 | + | 0.610920i | −0.0144965 | + | 0.0251087i | ||||
\(593\) | 20.6214 | + | 35.7172i | 0.846817 | + | 1.46673i | 0.884033 | + | 0.467424i | \(0.154818\pi\) |
−0.0372161 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(594\) | −4.37648 | − | 4.56760i | −0.179569 | − | 0.187411i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.66587i | 0.109198i | ||||||||
\(597\) | −14.5666 | − | 25.2300i | −0.596169 | − | 1.03260i | ||||
\(598\) | 6.77605 | + | 3.91216i | 0.277093 | + | 0.159980i | ||||
\(599\) | −4.97720 | + | 8.62076i | −0.203363 | + | 0.352235i | −0.949610 | − | 0.313434i | \(-0.898520\pi\) |
0.746247 | + | 0.665669i | \(0.231854\pi\) | |||||||
\(600\) | 9.76370 | + | 16.9112i | 0.398602 | + | 0.690398i | ||||
\(601\) | 4.76767 | 0.194477 | 0.0972386 | − | 0.995261i | \(-0.468999\pi\) | ||||
0.0972386 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8797 | −0.605949 | ||||||||
\(604\) | −8.99830 | + | 5.19517i | −0.366136 | + | 0.211389i | ||||
\(605\) | 20.8869 | − | 32.8512i | 0.849172 | − | 1.33559i | ||||
\(606\) | 1.82039 | − | 3.15301i | 0.0739484 | − | 0.128082i | ||||
\(607\) | −2.27672 | − | 3.94340i | −0.0924094 | − | 0.160058i | 0.816115 | − | 0.577889i | \(-0.196124\pi\) |
−0.908524 | + | 0.417832i | \(0.862790\pi\) | |||||||
\(608\) | − | 4.65637i | − | 0.188841i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.3791 | −1.59441 | ||||||||
\(611\) | −28.5423 | + | 16.4789i | −1.15470 | + | 0.666665i | ||||
\(612\) | 7.27123 | − | 12.5941i | 0.293922 | − | 0.509088i | ||||
\(613\) | −1.25482 | − | 0.724472i | −0.0506818 | − | 0.0292611i | 0.474445 | − | 0.880285i | \(-0.342649\pi\) |
−0.525127 | + | 0.851024i | \(0.675982\pi\) | |||||||
\(614\) | −22.1652 | + | 12.7971i | −0.894515 | + | 0.516449i | ||||
\(615\) | 27.0762 | 1.09182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.96752 | −0.119468 | −0.0597340 | − | 0.998214i | \(-0.519025\pi\) | ||||
−0.0597340 | + | 0.998214i | \(0.519025\pi\) | |||||||
\(618\) | 4.63636 | − | 2.67680i | 0.186502 | − | 0.107677i | ||||
\(619\) | 10.0004 | + | 5.77375i | 0.401951 | + | 0.232067i | 0.687326 | − | 0.726349i | \(-0.258785\pi\) |
−0.285374 | + | 0.958416i | \(0.592118\pi\) | |||||||
\(620\) | 0.494980 | − | 0.857330i | 0.0198789 | − | 0.0344312i | ||||
\(621\) | 2.57616 | − | 1.48735i | 0.103378 | − | 0.0596853i | ||||
\(622\) | 1.90970 | 0.0765720 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 13.0195i | 0.521196i | ||||||||
\(625\) | 3.00222 | + | 5.19999i | 0.120089 | + | 0.208000i | ||||
\(626\) | 15.2251 | − | 26.3707i | 0.608519 | − | 1.05399i | ||||
\(627\) | −9.54366 | − | 38.9256i | −0.381137 | − | 1.55454i | ||||
\(628\) | −7.25273 | + | 4.18736i | −0.289415 | + | 0.167094i | ||||
\(629\) | −2.74668 | −0.109517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5215 | −1.09562 | −0.547808 | − | 0.836604i | \(-0.684537\pi\) | ||||
−0.547808 | + | 0.836604i | \(0.684537\pi\) | |||||||
\(632\) | −3.84991 | − | 6.66824i | −0.153141 | − | 0.265248i | ||||
\(633\) | −8.35696 | + | 14.4747i | −0.332159 | + | 0.575317i | ||||
\(634\) | −29.7862 | − | 17.1971i | −1.18296 | − | 0.682983i | ||||
\(635\) | −23.3926 | − | 40.5171i | −0.928306 | − | 1.60787i | ||||
\(636\) | − | 14.3788i | − | 0.570156i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.229926 | + | 0.239967i | 0.00910288 | + | 0.00950040i | ||||
\(639\) | −15.7873 | − | 27.3443i | −0.624535 | − | 1.08173i | ||||
\(640\) | −1.76950 | + | 3.06486i | −0.0699456 | + | 0.121149i | ||||
\(641\) | −16.8273 | + | 29.1458i | −0.664639 | + | 1.15119i | 0.314744 | + | 0.949177i | \(0.398081\pi\) |
−0.979383 | + | 0.202013i | \(0.935252\pi\) | |||||||
\(642\) | 27.5666 | − | 15.9156i | 1.08797 | − | 0.628137i | ||||
\(643\) | − | 5.95261i | − | 0.234748i | −0.993088 | − | 0.117374i | \(-0.962552\pi\) | ||
0.993088 | − | 0.117374i | \(-0.0374476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 82.9855i | − | 3.26755i | ||||||
\(646\) | 15.7012 | − | 9.06508i | 0.617754 | − | 0.356661i | ||||
\(647\) | −10.1963 | − | 5.88686i | −0.400860 | − | 0.231437i | 0.285995 | − | 0.958231i | \(-0.407676\pi\) |
−0.686855 | + | 0.726795i | \(0.741009\pi\) | |||||||
\(648\) | −5.41700 | − | 3.12751i | −0.212800 | − | 0.122860i | ||||
\(649\) | −46.2854 | − | 13.4683i | −1.81686 | − | 0.528677i | ||||
\(650\) | − | 37.7489i | − | 1.48063i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.06508 | −0.120038 | ||||||||
\(653\) | −14.4335 | − | 24.9996i | −0.564827 | − | 0.978309i | −0.997066 | − | 0.0765498i | \(-0.975610\pi\) |
0.432239 | − | 0.901759i | \(-0.357724\pi\) | |||||||
\(654\) | −15.1142 | − | 8.72616i | −0.591010 | − | 0.341220i | ||||
\(655\) | 50.5660 | + | 29.1943i | 1.97578 | + | 1.14071i | ||||
\(656\) | 1.47405 | + | 2.55312i | 0.0575519 | + | 0.0996827i | ||||
\(657\) | −14.5577 | −0.567952 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 44.6812i | − | 1.74053i | −0.492581 | − | 0.870266i | \(-0.663947\pi\) | ||
0.492581 | − | 0.870266i | \(-0.336053\pi\) | |||||||
\(660\) | −8.51066 | + | 29.2479i | −0.331277 | + | 1.13847i | ||||
\(661\) | 34.3242 | + | 19.8171i | 1.33505 | + | 0.770794i | 0.986069 | − | 0.166334i | \(-0.0531929\pi\) |
0.348985 | + | 0.937128i | \(0.386526\pi\) | |||||||
\(662\) | −13.4345 | − | 7.75642i | −0.522147 | − | 0.301462i | ||||
\(663\) | −43.9013 | + | 25.3464i | −1.70499 | + | 0.984374i | ||||
\(664\) | 2.87320i | 0.111502i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 2.63474i | − | 0.102094i | ||||||
\(667\) | −0.135344 | + | 0.0781407i | −0.00524053 | + | 0.00302562i | ||||
\(668\) | −5.03656 | + | 8.72358i | −0.194870 | + | 0.337525i | ||||
\(669\) | 5.21362 | − | 9.03026i | 0.201570 | − | 0.349130i | ||||
\(670\) | 7.04953 | + | 12.2101i | 0.272347 | + | 0.471719i | ||||
\(671\) | −25.5321 | − | 26.6471i | −0.985657 | − | 1.02870i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.71886i | 0.104804i | 0.998626 | + | 0.0524022i | \(0.0166878\pi\) | ||||
−0.998626 | + | 0.0524022i | \(0.983312\pi\) | |||||||
\(674\) | −3.85441 | − | 6.67604i | −0.148466 | − | 0.257151i | ||||
\(675\) | −12.4289 | − | 7.17580i | −0.478387 | − | 0.276197i | ||||
\(676\) | 6.08412 | − | 10.5380i | 0.234005 | − | 0.405308i | ||||
\(677\) | −3.02973 | − | 5.24764i | −0.116442 | − | 0.201683i | 0.801913 | − | 0.597440i | \(-0.203816\pi\) |
−0.918355 | + | 0.395757i | \(0.870482\pi\) | |||||||
\(678\) | 31.1161 | 1.19501 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.7795 | −0.528420 | ||||||||
\(681\) | −28.6090 | + | 16.5174i | −1.09630 | + | 0.632949i | ||||
\(682\) | 0.901068 | − | 0.220921i | 0.0345037 | − | 0.00845950i | ||||
\(683\) | 3.01704 | − | 5.22567i | 0.115444 | − | 0.199955i | −0.802513 | − | 0.596634i | \(-0.796504\pi\) |
0.917957 | + | 0.396680i | \(0.129838\pi\) | |||||||
\(684\) | 8.69566 | + | 15.0613i | 0.332487 | + | 0.575884i | ||||
\(685\) | 23.5122i | 0.898354i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.6060 | −0.595405 | ||||||||
\(688\) | 7.82503 | − | 4.51778i | 0.298326 | − | 0.172239i | ||||
\(689\) | −13.8980 | + | 24.0720i | −0.529471 | + | 0.917071i | ||||
\(690\) | −12.4050 | − | 7.16204i | −0.472251 | − | 0.272654i | ||||
\(691\) | 17.1519 | − | 9.90263i | 0.652487 | − | 0.376714i | −0.136921 | − | 0.990582i | \(-0.543721\pi\) |
0.789409 | + | 0.613868i | \(0.210387\pi\) | |||||||
\(692\) | 0.0766026 | 0.00291200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7413 | −0.825288 | ||||||||
\(695\) | 43.9909 | − | 25.3982i | 1.66867 | − | 0.963407i | ||||
\(696\) | −0.225209 | − | 0.130024i | −0.00853652 | − | 0.00492856i | ||||
\(697\) | −5.73938 | + | 9.94090i | −0.217394 | + | 0.376538i | ||||
\(698\) | −11.6536 | + | 6.72823i | −0.441096 | + | 0.254667i | ||||
\(699\) | 16.7828 | 0.634786 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0155i | 0.982591i | 0.870993 | + | 0.491296i | \(0.163476\pi\) | ||||
−0.870993 | + | 0.491296i | \(0.836524\pi\) | |||||||
\(702\) | −4.78431 | − | 8.28667i | −0.180572 | − | 0.312760i | ||||
\(703\) | 1.64237 | − | 2.84467i | 0.0619433 | − | 0.107289i | ||||
\(704\) | −3.22122 | + | 0.789769i | −0.121404 | + | 0.0297655i | ||||
\(705\) | 52.2528 | − | 30.1682i | 1.96795 | − | 1.13620i | ||||
\(706\) | −6.70769 | −0.252447 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.7193 | 1.41758 | ||||||||
\(709\) | 12.4458 | + | 21.5568i | 0.467413 | + | 0.809583i | 0.999307 | − | 0.0372278i | \(-0.0118527\pi\) |
−0.531894 | + | 0.846811i | \(0.678519\pi\) | |||||||
\(710\) | −14.9590 | + | 25.9098i | −0.561401 | + | 0.972376i | ||||
\(711\) | 24.9055 | + | 14.3792i | 0.934030 | + | 0.539263i | ||||
\(712\) | −2.97451 | − | 5.15200i | −0.111474 | − | 0.193079i | ||||
\(713\) | 0.436271i | 0.0163385i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.5178 | − | 40.7388i | 1.59008 | − | 1.52354i | ||||
\(716\) | −4.48746 | − | 7.77250i | −0.167704 | − | 0.290472i | ||||
\(717\) | 20.2132 | − | 35.0102i | 0.754875 | − | 1.30748i | ||||
\(718\) | 15.5232 | − | 26.8869i | 0.579320 | − | 1.00341i | ||||
\(719\) | 11.5156 | − | 6.64851i | 0.429458 | − | 0.247948i | −0.269658 | − | 0.962956i | \(-0.586911\pi\) |
0.699116 | + | 0.715009i | \(0.253577\pi\) | |||||||
\(720\) | − | 13.2180i | − | 0.492604i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.68183i | 0.0998073i | ||||||||
\(723\) | 52.7626 | − | 30.4625i | 1.96226 | − | 1.13291i | ||||
\(724\) | 13.1159 | + | 7.57248i | 0.487449 | + | 0.281429i | ||||
\(725\) | 0.652974 | + | 0.376995i | 0.0242508 | + | 0.0140012i | ||||
\(726\) | −25.3095 | + | 13.2044i | −0.939325 | + | 0.490060i | ||||
\(727\) | − | 5.67083i | − | 0.210319i | −0.994455 | − | 0.105160i | \(-0.966465\pi\) | ||
0.994455 | − | 0.105160i | \(-0.0335354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.2116 | 1.41525 | ||||||||
\(730\) | 6.89699 | + | 11.9459i | 0.255269 | + | 0.442139i | ||||
\(731\) | 30.4677 | + | 17.5905i | 1.12689 | + | 0.650609i | ||||
\(732\) | 25.0083 | + | 14.4385i | 0.924332 | + | 0.533663i | ||||
\(733\) | 20.6879 | + | 35.8326i | 0.764127 | + | 1.32351i | 0.940707 | + | 0.339220i | \(0.110163\pi\) |
−0.176580 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(734\) | −29.6492 | −1.09437 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.55962i | − | 0.0574885i | ||||||
\(737\) | −3.69170 | + | 12.6870i | −0.135985 | + | 0.467330i | ||||
\(738\) | −9.53578 | − | 5.50549i | −0.351017 | − | 0.202660i | ||||
\(739\) | −35.9749 | − | 20.7701i | −1.32336 | − | 0.764042i | −0.339097 | − | 0.940752i | \(-0.610121\pi\) |
−0.984263 | + | 0.176710i | \(0.943455\pi\) | |||||||
\(740\) | −2.16204 | + | 1.24826i | −0.0794783 | + | 0.0458868i | ||||
\(741\) | − | 60.6236i | − | 2.22706i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7404i | 1.45793i | 0.684549 | + | 0.728967i | \(0.259999\pi\) | ||||
−0.684549 | + | 0.728967i | \(0.740001\pi\) | |||||||
\(744\) | −0.628687 | + | 0.362973i | −0.0230488 | + | 0.0133072i | ||||
\(745\) | −4.71725 | + | 8.17053i | −0.172827 | + | 0.299345i | ||||
\(746\) | −4.39027 | + | 7.60418i | −0.160739 | + | 0.278409i | ||||
\(747\) | −5.36562 | − | 9.29353i | −0.196318 | − | 0.340033i | ||||
\(748\) | −8.93419 | − | 9.32434i | −0.326666 | − | 0.340932i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 23.1858i | 0.846626i | ||||||||
\(751\) | −2.68263 | − | 4.64645i | −0.0978905 | − | 0.169551i | 0.812921 | − | 0.582374i | \(-0.197876\pi\) |
−0.910811 | + | 0.412823i | \(0.864543\pi\) | |||||||
\(752\) | 5.68935 | + | 3.28475i | 0.207469 | + | 0.119782i | ||||
\(753\) | −23.7223 | + | 41.0882i | −0.864487 | + | 1.49734i | ||||
\(754\) | 0.251353 | + | 0.435356i | 0.00915374 | + | 0.0158547i | ||||
\(755\) | −36.7714 | −1.33825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8962 | 0.941215 | 0.470607 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470607 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(758\) | 26.6852 | − | 15.4067i | 0.969251 | − | 0.559598i | ||||
\(759\) | −3.19659 | − | 13.0379i | −0.116029 | − | 0.473245i | ||||
\(760\) | 8.23945 | − | 14.2711i | 0.298876 | − | 0.517669i | ||||
\(761\) | −7.61030 | − | 13.1814i | −0.275873 | − | 0.477827i | 0.694482 | − | 0.719510i | \(-0.255634\pi\) |
−0.970355 | + | 0.241684i | \(0.922300\pi\) | |||||||
\(762\) | 34.3080i | 1.24285i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 44.5706 | − | 25.7329i | 1.61145 | − | 0.930374i | ||||
\(766\) | −2.64741 | + | 4.58545i | −0.0956548 | + | 0.165679i | ||||
\(767\) | −63.1471 | − | 36.4580i | −2.28011 | − | 1.31642i | ||||
\(768\) | 2.24749 | − | 1.29759i | 0.0810993 | − | 0.0468227i | ||||
\(769\) | 22.5146 | 0.811898 | 0.405949 | − | 0.913896i | \(-0.366941\pi\) | ||||
0.405949 | + | 0.913896i | \(0.366941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9647 | −0.899083 | ||||||||
\(772\) | 12.8415 | − | 7.41403i | 0.462175 | − | 0.266837i | ||||
\(773\) | −24.2776 | − | 14.0167i | −0.873204 | − | 0.504144i | −0.00479213 | − | 0.999989i | \(-0.501525\pi\) |
−0.868412 | + | 0.495844i | \(0.834859\pi\) | |||||||
\(774\) | −16.8737 | + | 29.2261i | −0.606512 | + | 1.05051i | ||||
\(775\) | 1.82283 | − | 1.05241i | 0.0654778 | − | 0.0378036i | ||||
\(776\) | 16.7587 | 0.601601 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.860237i | 0.0308410i | ||||||||
\(779\) | −6.86371 | − | 11.8883i | −0.245918 | − | 0.425943i | ||||
\(780\) | −23.0379 | + | 39.9029i | −0.824891 | + | 1.42875i | ||||
\(781\) | −27.2316 | + | 6.67655i | −0.974423 | + | 0.238906i | ||||
\(782\) | 5.25901 | − | 3.03629i | 0.188062 | − | 0.108578i | ||||
\(783\) | 0.191122 | 0.00683014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.6381 | −1.05783 | ||||||||
\(786\) | −21.4084 | − | 37.0805i | −0.763613 | − | 1.32262i | ||||
\(787\) | −6.37160 | + | 11.0359i | −0.227123 | + | 0.393388i | −0.956954 | − | 0.290239i | \(-0.906265\pi\) |
0.729831 | + | 0.683627i | \(0.239599\pi\) | |||||||
\(788\) | 12.5353 | + | 7.23723i | 0.446550 | + | 0.257816i | ||||
\(789\) | 0.750870 | + | 1.30054i | 0.0267317 | + | 0.0463006i | ||||
\(790\) | − | 27.2496i | − | 0.969499i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.94436 | − | 8.57010i | 0.317824 | − | 0.304525i | ||||
\(793\) | −27.9114 | − | 48.3440i | −0.991165 | − | 1.71675i | ||||
\(794\) | −6.17367 | + | 10.6931i | −0.219095 | + | 0.379484i | ||||
\(795\) | 25.4432 | − | 44.0690i | 0.902379 | − | 1.56297i | ||||
\(796\) | 9.72188 | − | 5.61293i | 0.344583 | − | 0.198945i | ||||
\(797\) | − | 5.63488i | − | 0.199598i | −0.995008 | − | 0.0997989i | \(-0.968180\pi\) | ||
0.995008 | − | 0.0997989i | \(-0.0318199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.5791i | 0.904923i | ||||||||
\(800\) | −6.51641 | + | 3.76225i | −0.230390 | + | 0.133016i | ||||
\(801\) | 19.2425 | + | 11.1096i | 0.679899 | + | 0.392540i | ||||
\(802\) | −29.2069 | − | 16.8626i | −1.03133 | − | 0.595439i | ||||
\(803\) | −3.61182 | + | 12.4124i | −0.127458 | + | 0.438025i | ||||
\(804\) | − | 10.3390i | − | 0.364627i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.40334 | 0.0494306 | ||||||||
\(807\) | 28.6632 | + | 49.6462i | 1.00899 | + | 1.74763i | ||||
\(808\) | 1.21495 | + | 0.701452i | 0.0427418 | + | 0.0246770i | ||||
\(809\) | 14.7572 | + | 8.52007i | 0.518835 | + | 0.299550i | 0.736458 | − | 0.676483i | \(-0.236497\pi\) |
−0.217623 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(810\) | −11.0682 | − | 19.1707i | −0.388898 | − | 0.673591i | ||||
\(811\) | 0.332109 | 0.0116619 | 0.00583097 | − | 0.999983i | \(-0.498144\pi\) | ||||
0.00583097 | + | 0.999983i | \(0.498144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.0612i | − | 0.387934i | ||||||
\(814\) | −2.24647 | − | 0.653687i | −0.0787388 | − | 0.0229117i | ||||
\(815\) | −9.39404 | − | 5.42365i | −0.329059 | − | 0.189982i | ||||
\(816\) | 8.75087 | + | 5.05232i | 0.306342 | + | 0.176867i | ||||
\(817\) | −36.4363 | + | 21.0365i | −1.27474 | + | 0.735973i | ||||
\(818\) | 38.3692i | 1.34155i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4333i | 0.364346i | ||||||||
\(821\) | 1.97706 | − | 1.14146i | 0.0690000 | − | 0.0398372i | −0.465103 | − | 0.885257i | \(-0.653983\pi\) |
0.534103 | + | 0.845419i | \(0.320649\pi\) | |||||||
\(822\) | 8.62085 | − | 14.9317i | 0.300687 | − | 0.520804i | ||||
\(823\) | −5.04228 | + | 8.73348i | −0.175763 | + | 0.304430i | −0.940425 | − | 0.340001i | \(-0.889572\pi\) |
0.764662 | + | 0.644431i | \(0.222906\pi\) | |||||||
\(824\) | 1.03145 | + | 1.78653i | 0.0359324 | + | 0.0622367i | ||||
\(825\) | −46.7637 | + | 44.8070i | −1.62810 | + | 1.55998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.9337i | 0.380204i | 0.981764 | + | 0.190102i | \(0.0608818\pi\) | ||||
−0.981764 | + | 0.190102i | \(0.939118\pi\) | |||||||
\(828\) | 2.91256 | + | 5.04469i | 0.101218 | + | 0.175315i | ||||
\(829\) | 10.0682 | + | 5.81287i | 0.349683 | + | 0.201889i | 0.664545 | − | 0.747248i | \(-0.268625\pi\) |
−0.314863 | + | 0.949137i | \(0.601959\pi\) | |||||||
\(830\) | −5.08412 | + | 8.80595i | −0.176472 | + | 0.305659i | ||||
\(831\) | −23.8306 | − | 41.2757i | −0.826673 | − | 1.43184i | ||||
\(832\) | −5.01680 | −0.173926 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.2494 | −1.28984 | ||||||||
\(835\) | −30.8727 | + | 17.8244i | −1.06839 | + | 0.616838i | ||||
\(836\) | 14.9992 | − | 3.67746i | 0.518759 | − | 0.127188i | ||||
\(837\) | 0.266766 | − | 0.462052i | 0.00922078 | − | 0.0159709i | ||||
\(838\) | −16.7512 | − | 29.0139i | −0.578659 | − | 1.00227i | ||||
\(839\) | − | 23.4571i | − | 0.809828i | −0.914355 | − | 0.404914i | \(-0.867301\pi\) | ||
0.914355 | − | 0.404914i | \(-0.132699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9900 | 0.999654 | ||||||||
\(842\) | −19.9320 | + | 11.5077i | −0.686902 | + | 0.396583i | ||||
\(843\) | 4.83858 | − | 8.38067i | 0.166650 | − | 0.288646i | ||||
\(844\) | −5.57753 | − | 3.22019i | −0.191986 | − | 0.110843i | ||||
\(845\) | 37.2940 | − | 21.5317i | 1.28295 | − | 0.740712i | ||||
\(846\) | −24.5367 | −0.843589 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.54058 | 0.190264 | ||||||||
\(849\) | −28.6140 | + | 16.5203i | −0.982029 | + | 0.566975i | ||||
\(850\) | −25.3724 | − | 14.6488i | −0.870266 | − | 0.502449i | ||||
\(851\) | 0.550102 | − | 0.952805i | 0.0188573 | − | 0.0326617i | ||||
\(852\) | 18.9999 | − | 10.9696i | 0.650924 | − | 0.375811i | ||||
\(853\) | 38.5870 | 1.32119 | 0.660597 | − | 0.750741i | \(-0.270303\pi\) | ||||
0.660597 | + | 0.750741i | \(0.270303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 61.5478i | 2.10489i | ||||||||
\(856\) | 6.13274 | + | 10.6222i | 0.209613 | + | 0.363060i | ||||
\(857\) | 21.3007 | − | 36.8938i | 0.727617 | − | 1.26027i | −0.230271 | − | 0.973126i | \(-0.573961\pi\) |
0.957888 | − | 0.287142i | \(-0.0927053\pi\) | |||||||
\(858\) | −41.9386 | + | 10.2824i | −1.43176 | + | 0.351035i | ||||
\(859\) | −10.7344 | + | 6.19752i | −0.366254 | + | 0.211457i | −0.671821 | − | 0.740714i | \(-0.734487\pi\) |
0.305567 | + | 0.952171i | \(0.401154\pi\) | |||||||
\(860\) | 31.9768 | 1.09040 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.8381 | 0.914110 | ||||||||
\(863\) | 19.6374 | + | 34.0130i | 0.668465 | + | 1.15781i | 0.978333 | + | 0.207036i | \(0.0663816\pi\) |
−0.309869 | + | 0.950779i | \(0.600285\pi\) | |||||||
\(864\) | −0.953659 | + | 1.65179i | −0.0324441 | + | 0.0561949i | ||||
\(865\) | 0.234776 | + | 0.135548i | 0.00798264 | + | 0.00460878i | ||||
\(866\) | −15.3456 | − | 26.5794i | −0.521465 | − | 0.903204i | ||||
\(867\) | − | 4.77440i | − | 0.162147i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.4393 | − | 17.6678i | 0.625512 | − | 0.599338i | ||||
\(870\) | −0.460156 | − | 0.797013i | −0.0156007 | − | 0.0270213i | ||||
\(871\) | −9.99325 | + | 17.3088i | −0.338608 | + | 0.586487i | ||||
\(872\) | 3.36245 | − | 5.82394i | 0.113867 | − | 0.197223i | ||||
\(873\) | −54.2069 | + | 31.2964i | −1.83463 | + | 1.05922i | ||||
\(874\) | 7.26219i | 0.245647i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 10.1152i | − | 0.341763i | ||||||
\(877\) | 39.9403 | − | 23.0595i | 1.34869 | − | 0.778665i | 0.360624 | − | 0.932711i | \(-0.382564\pi\) |
0.988064 | + | 0.154046i | \(0.0492304\pi\) | |||||||
\(878\) | −14.5883 | − | 8.42258i | −0.492332 | − | 0.284248i | ||||
\(879\) | −58.9407 | − | 34.0294i | −1.98802 | − | 1.14778i | ||||
\(880\) | −11.2701 | − | 3.27941i | −0.379915 | − | 0.110549i | ||||
\(881\) | 14.9583i | 0.503957i | 0.967733 | + | 0.251978i | \(0.0810812\pi\) | ||||
−0.967733 | + | 0.251978i | \(0.918919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.42386 | −0.283485 | −0.141743 | − | 0.989904i | \(-0.545271\pi\) | ||||
−0.141743 | + | 0.989904i | \(0.545271\pi\) | |||||||
\(884\) | −9.76675 | − | 16.9165i | −0.328491 | − | 0.568964i | ||||
\(885\) | 115.604 | + | 66.7442i | 3.88600 | + | 2.24358i | ||||
\(886\) | 0.684671 | + | 0.395295i | 0.0230020 | + | 0.0132802i | ||||
\(887\) | 5.66022 | + | 9.80379i | 0.190052 | + | 0.329179i | 0.945267 | − | 0.326298i | \(-0.105801\pi\) |
−0.755216 | + | 0.655477i | \(0.772468\pi\) | |||||||
\(888\) | 1.83072 | 0.0614348 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 21.0536i | − | 0.705717i | ||||||
\(891\) | 5.79621 | − | 19.9194i | 0.194180 | − | 0.667324i | ||||
\(892\) | 3.47963 | + | 2.00897i | 0.116507 | + | 0.0672652i | ||||
\(893\) | −26.4917 | − | 15.2950i | −0.886512 | − | 0.511828i | ||||
\(894\) | 5.99152 | − | 3.45920i | 0.200386 | − | 0.115693i | ||||
\(895\) | − | 31.7622i | − | 1.06169i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 20.3055i | − | 0.677980i | ||||||
\(898\) | 13.8334 | − | 7.98672i | 0.461627 | − | 0.266520i | ||||
\(899\) | −0.0140151 | + | 0.0242748i | −0.000467428 | + | 0.000809609i | ||||
\(900\) | 14.0518 | − | 24.3384i | 0.468393 | − | 0.811281i | ||||
\(901\) | 10.7865 | + | 18.6827i | 0.359349 | + | 0.622411i | ||||
\(902\) | −7.06002 | + | 6.76461i | −0.235073 | + | 0.225237i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.9900i | 0.398780i | ||||||||
\(905\) | 26.7990 | + | 46.4172i | 0.890828 | + | 1.54296i | ||||
\(906\) | 23.3522 | + | 13.4824i | 0.775825 | + | 0.447923i | ||||
\(907\) | −27.4033 | + | 47.4638i | −0.909910 | + | 1.57601i | −0.0957232 | + | 0.995408i | \(0.530516\pi\) |
−0.814187 | + | 0.580603i | \(0.802817\pi\) | |||||||
\(908\) | −6.36466 | − | 11.0239i | −0.211219 | − | 0.365841i | ||||
\(909\) | −5.23977 | −0.173792 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.5914 | 1.54364 | 0.771820 | − | 0.635841i | \(-0.219347\pi\) | ||||
0.771820 | + | 0.635841i | \(0.219347\pi\) | |||||||
\(912\) | −10.4652 | + | 6.04206i | −0.346536 | + | 0.200073i | ||||
\(913\) | −9.25521 | + | 2.26916i | −0.306303 | + | 0.0750983i | ||||
\(914\) | −17.4666 | + | 30.2530i | −0.577743 | + | 1.00068i | ||||
\(915\) | 51.0979 | + | 88.5042i | 1.68924 | + | 2.92586i | ||||
\(916\) | − | 6.01345i | − | 0.198690i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.42637 | −0.245107 | ||||||||
\(919\) | 47.0315 | − | 27.1536i | 1.55142 | − | 0.895716i | 0.553399 | − | 0.832916i | \(-0.313331\pi\) |
0.998026 | − | 0.0627991i | \(-0.0200028\pi\) | |||||||
\(920\) | 2.75975 | − | 4.78003i | 0.0909863 | − | 0.157593i | ||||
\(921\) | 57.5227 | + | 33.2107i | 1.89544 | + | 1.09433i | ||||
\(922\) | −18.0433 | + | 10.4173i | −0.594224 | + | 0.343076i | ||||
\(923\) | −42.4110 | −1.39598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.30800 | −0.174526 | ||||||||
\(926\) | 11.4076 | − | 6.58618i | 0.374877 | − | 0.216435i | ||||
\(927\) | −6.67259 | − | 3.85242i | −0.219157 | − | 0.126530i | ||||
\(928\) | 0.0501023 | − | 0.0867797i | 0.00164469 | − | 0.00284868i | ||||
\(929\) | 18.6550 | − | 10.7704i | 0.612049 | − | 0.353367i | −0.161718 | − | 0.986837i | \(-0.551703\pi\) |
0.773767 | + | 0.633470i | \(0.218370\pi\) | |||||||
\(930\) | −2.56912 | −0.0842447 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.46694i | 0.211832i | ||||||||
\(933\) | −2.47801 | − | 4.29203i | −0.0811262 | − | 0.140515i | ||||
\(934\) | 8.40919 | − | 14.5651i | 0.275157 | − | 0.476586i | ||||
\(935\) | −10.8826 | − | 44.3868i | −0.355900 | − | 1.45161i | ||||
\(936\) | 16.2271 | − | 9.36873i | 0.530400 | − | 0.306227i | ||||
\(937\) | −15.2663 | −0.498729 | −0.249364 | − | 0.968410i | \(-0.580222\pi\) | ||||
−0.249364 | + | 0.968410i | \(0.580222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −79.0239 | −2.57885 | ||||||||
\(940\) | 11.6247 | + | 20.1346i | 0.379156 | + | 0.656717i | ||||
\(941\) | −18.0945 | + | 31.3405i | −0.589863 | + | 1.02167i | 0.404387 | + | 0.914588i | \(0.367485\pi\) |
−0.994250 | + | 0.107085i | \(0.965848\pi\) | |||||||
\(942\) | 18.8221 | + | 10.8670i | 0.613258 | + | 0.354064i | ||||
\(943\) | −2.29896 | − | 3.98191i | −0.0748644 | − | 0.129669i | ||||
\(944\) | 14.5344i | 0.473054i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.7327 | + | 21.6381i | 0.674079 | + | 0.703516i | ||||
\(947\) | −19.9609 | − | 34.5733i | −0.648641 | − | 1.12348i | −0.983448 | − | 0.181193i | \(-0.942004\pi\) |
0.334806 | − | 0.942287i | \(-0.391329\pi\) | |||||||
\(948\) | −9.99120 | + | 17.3053i | −0.324499 | + | 0.562049i | ||||
\(949\) | −9.77701 | + | 16.9343i | −0.317375 | + | 0.549710i | ||||
\(950\) | 30.3428 | − | 17.5184i | 0.984451 | − | 0.568373i | ||||
\(951\) | 89.2590i | 2.89442i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.97831i | 0.290836i | 0.989370 | + | 0.145418i | \(0.0464527\pi\) | ||||
−0.989370 | + | 0.145418i | \(0.953547\pi\) | |||||||
\(954\) | −17.9213 | + | 10.3469i | −0.580225 | + | 0.334993i | ||||
\(955\) | −18.3892 | − | 10.6170i | −0.595059 | − | 0.343558i | ||||
\(956\) | 13.4905 | + | 7.78874i | 0.436314 | + | 0.251906i | ||||
\(957\) | 0.240974 | − | 0.828136i | 0.00778959 | − | 0.0267699i | ||||
\(958\) | 22.8582i | 0.738513i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.18432 | 0.296423 | ||||||||
\(961\) | −15.4609 | − | 26.7790i | −0.498738 | − | 0.863839i | ||||
\(962\) | −3.06486 | − | 1.76950i | −0.0988151 | − | 0.0570509i | ||||
\(963\) | −39.6734 | − | 22.9055i | −1.27846 | − | 0.738119i | ||||
\(964\) | 11.7381 | + | 20.3310i | 0.378059 | + | 0.654818i | ||||
\(965\) | 52.4765 | 1.68928 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.5738i | 1.65850i | 0.558877 | + | 0.829251i | \(0.311232\pi\) | ||||
−0.558877 | + | 0.829251i | \(0.688768\pi\) | |||||||
\(968\) | −5.08804 | − | 9.75253i | −0.163536 | − | 0.313458i | ||||
\(969\) | −40.7473 | − | 23.5255i | −1.30899 | − | 0.755748i | ||||
\(970\) | 51.3630 | + | 29.6544i | 1.64917 | + | 0.952147i | ||||
\(971\) | 29.0721 | − | 16.7848i | 0.932967 | − | 0.538649i | 0.0452186 | − | 0.998977i | \(-0.485602\pi\) |
0.887749 | + | 0.460328i | \(0.152268\pi\) | |||||||
\(972\) | 21.9548i | 0.704201i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.2628i | 1.00173i | ||||||||
\(975\) | −84.8402 | + | 48.9825i | −2.71706 | + | 1.56870i | ||||
\(976\) | −5.56360 | + | 9.63644i | −0.178087 | + | 0.308455i | ||||
\(977\) | 0.576295 | − | 0.998172i | 0.0184373 | − | 0.0319344i | −0.856660 | − | 0.515882i | \(-0.827464\pi\) |
0.875097 | + | 0.483948i | \(0.160798\pi\) | |||||||
\(978\) | 3.97721 | + | 6.88873i | 0.127177 | + | 0.220277i | ||||
\(979\) | 14.2466 | − | 13.6504i | 0.455322 | − | 0.436270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.1172i | 0.801929i | ||||||||
\(982\) | −11.2490 | − | 19.4838i | −0.358969 | − | 0.621753i | ||||
\(983\) | 14.3846 | + | 8.30496i | 0.458798 | + | 0.264887i | 0.711539 | − | 0.702647i | \(-0.247999\pi\) |
−0.252741 | + | 0.967534i | \(0.581332\pi\) | |||||||
\(984\) | 3.82541 | − | 6.62581i | 0.121950 | − | 0.211223i | ||||
\(985\) | 25.6125 | + | 44.3622i | 0.816083 | + | 1.41350i | ||||
\(986\) | 0.390159 | 0.0124252 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.3601 | 0.743183 | ||||||||
\(989\) | −12.2041 | + | 7.04604i | −0.388068 | + | 0.224051i | ||||
\(990\) | 42.5780 | − | 10.4391i | 1.35322 | − | 0.331777i | ||||
\(991\) | 9.24571 | − | 16.0140i | 0.293700 | − | 0.508703i | −0.680982 | − | 0.732300i | \(-0.738447\pi\) |
0.974682 | + | 0.223598i | \(0.0717801\pi\) | |||||||
\(992\) | −0.139864 | − | 0.242252i | −0.00444070 | − | 0.00769151i | ||||
\(993\) | 40.2586i | 1.27757i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.7283 | 1.25947 | ||||||||
\(996\) | 6.45748 | − | 3.72823i | 0.204613 | − | 0.118134i | ||||
\(997\) | 10.5865 | − | 18.3363i | 0.335277 | − | 0.580717i | −0.648261 | − | 0.761418i | \(-0.724503\pi\) |
0.983538 | + | 0.180701i | \(0.0578367\pi\) | |||||||
\(998\) | 27.6346 | + | 15.9548i | 0.874757 | + | 0.505041i | ||||
\(999\) | −1.16522 | + | 0.672739i | −0.0368659 | + | 0.0212845i |
(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 | 1078.2.i.c.1011.5 | 16 | ||
7.2 | even | 3 | 154.2.i.a.131.4 | yes | 16 | ||
7.3 | odd | 6 | 1078.2.c.b.1077.10 | 16 | |||
7.4 | even | 3 | 1078.2.c.b.1077.15 | 16 | |||
7.5 | odd | 6 | inner | 1078.2.i.c.901.1 | 16 | ||
7.6 | odd | 2 | 154.2.i.a.87.8 | yes | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.c.1011.1 | 16 | ||
21.2 | odd | 6 | 1386.2.bk.c.901.8 | 16 | |||
21.20 | even | 2 | 1386.2.bk.c.703.4 | 16 | |||
28.23 | odd | 6 | 1232.2.bn.b.593.2 | 16 | |||
28.27 | even | 2 | 1232.2.bn.b.241.1 | 16 | |||
77.10 | even | 6 | 1078.2.c.b.1077.2 | 16 | |||
77.32 | odd | 6 | 1078.2.c.b.1077.7 | 16 | |||
77.54 | even | 6 | inner | 1078.2.i.c.901.5 | 16 | ||
77.65 | odd | 6 | 154.2.i.a.131.8 | yes | 16 | ||
77.76 | even | 2 | 154.2.i.a.87.4 | ✓ | 16 | ||
231.65 | even | 6 | 1386.2.bk.c.901.4 | 16 | |||
231.230 | odd | 2 | 1386.2.bk.c.703.8 | 16 | |||
308.219 | even | 6 | 1232.2.bn.b.593.1 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.b.241.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.4 | ✓ | 16 | 77.76 | even | 2 | ||
154.2.i.a.87.8 | yes | 16 | 7.6 | odd | 2 | ||
154.2.i.a.131.4 | yes | 16 | 7.2 | even | 3 | ||
154.2.i.a.131.8 | yes | 16 | 77.65 | odd | 6 | ||
1078.2.c.b.1077.2 | 16 | 77.10 | even | 6 | |||
1078.2.c.b.1077.7 | 16 | 77.32 | odd | 6 | |||
1078.2.c.b.1077.10 | 16 | 7.3 | odd | 6 | |||
1078.2.c.b.1077.15 | 16 | 7.4 | even | 3 | |||
1078.2.i.c.901.1 | 16 | 7.5 | odd | 6 | inner | ||
1078.2.i.c.901.5 | 16 | 77.54 | even | 6 | inner | ||
1078.2.i.c.1011.1 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.c.1011.5 | 16 | 1.1 | even | 1 | trivial | ||
1232.2.bn.b.241.1 | 16 | 28.27 | even | 2 | |||
1232.2.bn.b.241.2 | 16 | 308.307 | odd | 2 | |||
1232.2.bn.b.593.1 | 16 | 308.219 | even | 6 | |||
1232.2.bn.b.593.2 | 16 | 28.23 | odd | 6 | |||
1386.2.bk.c.703.4 | 16 | 21.20 | even | 2 | |||
1386.2.bk.c.703.8 | 16 | 231.230 | odd | 2 | |||
1386.2.bk.c.901.4 | 16 | 231.65 | even | 6 | |||
1386.2.bk.c.901.8 | 16 | 21.2 | odd | 6 |