Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\), degree \(4\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 730.4 | ||
Character | \(\chi\) | \(=\) | 891.730 |
Dual form | 891.2.f.f.487.4 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.467460 | − | 0.339629i | −0.330544 | − | 0.240154i | 0.410117 | − | 0.912033i | \(-0.365488\pi\) |
−0.740661 | + | 0.671878i | \(0.765488\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.514863 | − | 1.58459i | −0.257432 | − | 0.792293i | ||||
\(5\) | −2.43063 | + | 1.76596i | −1.08701 | + | 0.789761i | −0.978892 | − | 0.204377i | \(-0.934483\pi\) |
−0.108120 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.359795 | − | 1.10733i | −0.135990 | − | 0.418533i | 0.859753 | − | 0.510710i | \(-0.170617\pi\) |
−0.995743 | + | 0.0921770i | \(0.970617\pi\) | |||||||
\(8\) | −0.654602 | + | 2.01466i | −0.231437 | + | 0.712289i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73599 | 0.548970 | ||||||||
\(11\) | 3.11301 | + | 1.14420i | 0.938607 | + | 0.344988i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.19252 | + | 2.31950i | 0.885446 | + | 0.643314i | 0.934687 | − | 0.355473i | \(-0.115680\pi\) |
−0.0492409 | + | 0.998787i | \(0.515680\pi\) | |||||||
\(14\) | −0.207894 | + | 0.639831i | −0.0555619 | + | 0.171002i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.70562 | + | 1.23921i | −0.426406 | + | 0.309802i | ||||
\(17\) | 0.254185 | − | 0.184677i | 0.0616490 | − | 0.0447906i | −0.556534 | − | 0.830825i | \(-0.687869\pi\) |
0.618183 | + | 0.786034i | \(0.287869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96794 | − | 6.05670i | 0.451477 | − | 1.38950i | −0.423746 | − | 0.905781i | \(-0.639285\pi\) |
0.875222 | − | 0.483721i | \(-0.160715\pi\) | |||||||
\(20\) | 4.04976 | + | 2.94232i | 0.905554 | + | 0.657923i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.06660 | − | 1.59213i | −0.227401 | − | 0.339444i | ||||
\(23\) | −0.0855002 | −0.0178280 | −0.00891401 | − | 0.999960i | \(-0.502837\pi\) | ||||
−0.00891401 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24428 | − | 3.82951i | 0.248857 | − | 0.765902i | ||||
\(26\) | −0.704604 | − | 2.16855i | −0.138184 | − | 0.425287i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.56942 | + | 1.14025i | −0.296593 | + | 0.215487i | ||||
\(29\) | −2.37938 | − | 7.32296i | −0.441839 | − | 1.35984i | −0.885914 | − | 0.463850i | \(-0.846468\pi\) |
0.444075 | − | 0.895990i | \(-0.353532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28194 | − | 3.83755i | −0.948664 | − | 0.689245i | 0.00182628 | − | 0.999998i | \(-0.499419\pi\) |
−0.950491 | + | 0.310753i | \(0.899419\pi\) | |||||||
\(32\) | 5.45485 | 0.964291 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.181543 | −0.0311344 | ||||||||
\(35\) | 2.83004 | + | 2.05614i | 0.478363 | + | 0.347551i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.92922 | − | 5.93753i | −0.317162 | − | 0.976124i | −0.974855 | − | 0.222838i | \(-0.928468\pi\) |
0.657694 | − | 0.753286i | \(-0.271532\pi\) | |||||||
\(38\) | −2.97697 | + | 2.16289i | −0.482928 | + | 0.350868i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.96670 | − | 6.05289i | −0.310963 | − | 0.957046i | ||||
\(41\) | 1.79510 | − | 5.52475i | 0.280348 | − | 0.862822i | −0.707407 | − | 0.706807i | \(-0.750135\pi\) |
0.987755 | − | 0.156015i | \(-0.0498649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.78458 | −1.03464 | −0.517320 | − | 0.855792i | \(-0.673070\pi\) | ||||
−0.517320 | + | 0.855792i | \(0.673070\pi\) | |||||||
\(44\) | 0.210303 | − | 5.52194i | 0.0317043 | − | 0.832463i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0399679 | + | 0.0290384i | 0.00589294 | + | 0.00428147i | ||||
\(47\) | −0.101276 | + | 0.311695i | −0.0147726 | + | 0.0454654i | −0.958171 | − | 0.286196i | \(-0.907609\pi\) |
0.943398 | + | 0.331661i | \(0.107609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.56638 | − | 3.31767i | 0.652340 | − | 0.473953i | ||||
\(50\) | −1.88227 | + | 1.36755i | −0.266193 | + | 0.193400i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.03174 | − | 6.25305i | 0.281752 | − | 0.867142i | ||||
\(53\) | 1.96000 | + | 1.42402i | 0.269227 | + | 0.195605i | 0.714205 | − | 0.699937i | \(-0.246789\pi\) |
−0.444978 | + | 0.895541i | \(0.646789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.58718 | + | 2.71632i | −1.29274 | + | 0.366269i | ||||
\(56\) | 2.46642 | 0.329589 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.37483 | + | 4.23130i | −0.180524 | + | 0.555596i | ||||
\(59\) | −0.709513 | − | 2.18366i | −0.0923707 | − | 0.284288i | 0.894189 | − | 0.447690i | \(-0.147753\pi\) |
−0.986560 | + | 0.163402i | \(0.947753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0732 | − | 8.04513i | 1.41778 | − | 1.03007i | 0.425641 | − | 0.904892i | \(-0.360049\pi\) |
0.992134 | − | 0.125182i | \(-0.0399515\pi\) | |||||||
\(62\) | 1.16575 | + | 3.58780i | 0.148050 | + | 0.455652i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.861321 | + | 0.625787i | 0.107665 | + | 0.0782233i | ||||
\(65\) | −11.8560 | −1.47055 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6798 | 1.42691 | 0.713456 | − | 0.700700i | \(-0.247129\pi\) | ||||
0.713456 | + | 0.700700i | \(0.247129\pi\) | |||||||
\(68\) | −0.423507 | − | 0.307696i | −0.0513578 | − | 0.0373136i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.624602 | − | 1.92233i | −0.0746542 | − | 0.229762i | ||||
\(71\) | −7.05272 | + | 5.12410i | −0.837004 | + | 0.608119i | −0.921532 | − | 0.388302i | \(-0.873062\pi\) |
0.0845279 | + | 0.996421i | \(0.473062\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.910538 | + | 2.80235i | 0.106570 | + | 0.327990i | 0.990096 | − | 0.140393i | \(-0.0448367\pi\) |
−0.883525 | + | 0.468383i | \(0.844837\pi\) | |||||||
\(74\) | −1.11473 | + | 3.43078i | −0.129584 | + | 0.398820i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.6106 | −1.21712 | ||||||||
\(77\) | 0.146963 | − | 3.85882i | 0.0167480 | − | 0.439753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.18989 | + | 5.22376i | 0.808926 | + | 0.587719i | 0.913519 | − | 0.406796i | \(-0.133354\pi\) |
−0.104593 | + | 0.994515i | \(0.533354\pi\) | |||||||
\(80\) | 1.95735 | − | 6.02412i | 0.218839 | − | 0.673517i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.71551 | + | 1.97293i | −0.299878 | + | 0.217874i | ||||
\(83\) | −4.01093 | + | 2.91411i | −0.440257 | + | 0.319865i | −0.785737 | − | 0.618561i | \(-0.787716\pi\) |
0.345480 | + | 0.938426i | \(0.387716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.291701 | + | 0.897762i | −0.0316394 | + | 0.0973760i | ||||
\(86\) | 3.17152 | + | 2.30424i | 0.341994 | + | 0.248473i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.34294 | + | 5.52265i | −0.462959 | + | 0.588717i | ||||
\(89\) | 2.12862 | 0.225634 | 0.112817 | − | 0.993616i | \(-0.464013\pi\) | ||||
0.112817 | + | 0.993616i | \(0.464013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41981 | − | 4.36973i | 0.148837 | − | 0.458072i | ||||
\(92\) | 0.0440209 | + | 0.135482i | 0.00458950 | + | 0.0141250i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.153203 | − | 0.111309i | 0.0158017 | − | 0.0114806i | ||||
\(95\) | 5.91254 | + | 18.1969i | 0.606613 | + | 1.86696i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0718724 | + | 0.0522184i | 0.00729754 | + | 0.00530197i | 0.591428 | − | 0.806358i | \(-0.298564\pi\) |
−0.584131 | + | 0.811660i | \(0.698564\pi\) | |||||||
\(98\) | −3.26138 | −0.329449 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.70883 | −0.670883 | ||||||||
\(101\) | 1.66373 | + | 1.20877i | 0.165547 | + | 0.120277i | 0.667474 | − | 0.744633i | \(-0.267375\pi\) |
−0.501927 | + | 0.864910i | \(0.667375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.932216 | − | 2.86907i | −0.0918540 | − | 0.282698i | 0.894567 | − | 0.446934i | \(-0.147484\pi\) |
−0.986421 | + | 0.164236i | \(0.947484\pi\) | |||||||
\(104\) | −6.76283 | + | 4.91348i | −0.663150 | + | 0.481807i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.432581 | − | 1.33135i | −0.0420160 | − | 0.129312i | ||||
\(107\) | 3.70600 | − | 11.4059i | 0.358272 | − | 1.10265i | −0.595815 | − | 0.803121i | \(-0.703171\pi\) |
0.954088 | − | 0.299527i | \(-0.0968290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.20013 | 0.498082 | 0.249041 | − | 0.968493i | \(-0.419885\pi\) | ||||
0.249041 | + | 0.968493i | \(0.419885\pi\) | |||||||
\(110\) | 5.40417 | + | 1.98632i | 0.515267 | + | 0.189388i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.98589 | + | 1.44283i | 0.187649 | + | 0.136335i | ||||
\(113\) | 5.94164 | − | 18.2865i | 0.558943 | − | 1.72025i | −0.126355 | − | 0.991985i | \(-0.540328\pi\) |
0.685298 | − | 0.728263i | \(-0.259672\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.207820 | − | 0.150990i | 0.0193793 | − | 0.0140799i | ||||
\(116\) | −10.3788 | + | 7.54065i | −0.963649 | + | 0.700132i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.409965 | + | 1.26174i | −0.0377403 | + | 0.116153i | ||||
\(119\) | −0.295953 | − | 0.215023i | −0.0271300 | − | 0.0197111i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.38163 | + | 7.12378i | 0.761967 | + | 0.647616i | ||||
\(122\) | −7.90863 | −0.716014 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.36146 | + | 10.3455i | −0.301868 | + | 0.929054i | ||||
\(125\) | −0.903736 | − | 2.78141i | −0.0808326 | − | 0.248777i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6652 | − | 7.74873i | 0.946384 | − | 0.687588i | −0.00356461 | − | 0.999994i | \(-0.501135\pi\) |
0.949949 | + | 0.312405i | \(0.101135\pi\) | |||||||
\(128\) | −3.56138 | − | 10.9608i | −0.314785 | − | 0.968808i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.54220 | + | 4.02664i | 0.486083 | + | 0.353160i | ||||
\(131\) | −17.9718 | −1.57020 | −0.785100 | − | 0.619369i | \(-0.787389\pi\) | ||||
−0.785100 | + | 0.619369i | \(0.787389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.41484 | −0.642949 | ||||||||
\(134\) | −5.45983 | − | 3.96680i | −0.471657 | − | 0.342679i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.205670 | + | 0.632986i | 0.0176360 | + | 0.0542781i | ||||
\(137\) | 13.2693 | − | 9.64070i | 1.13367 | − | 0.823661i | 0.147447 | − | 0.989070i | \(-0.452895\pi\) |
0.986225 | + | 0.165409i | \(0.0528945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.67780 | − | 11.3191i | −0.311947 | − | 0.960073i | −0.976993 | − | 0.213271i | \(-0.931588\pi\) |
0.665046 | − | 0.746802i | \(-0.268412\pi\) | |||||||
\(140\) | 1.80105 | − | 5.54307i | 0.152217 | − | 0.468475i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.03716 | 0.422709 | ||||||||
\(143\) | 7.28438 | + | 10.8735i | 0.609150 | + | 0.909287i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7154 | + | 13.5976i | 1.55423 | + | 1.12922i | ||||
\(146\) | 0.526120 | − | 1.61923i | 0.0435420 | − | 0.134008i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.41525 | + | 6.11403i | −0.691729 | + | 0.502571i | ||||
\(149\) | 3.66623 | − | 2.66368i | 0.300350 | − | 0.218217i | −0.427395 | − | 0.904065i | \(-0.640569\pi\) |
0.727745 | + | 0.685848i | \(0.240569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.905687 | + | 2.78742i | −0.0737037 | + | 0.226837i | −0.981121 | − | 0.193393i | \(-0.938051\pi\) |
0.907418 | + | 0.420230i | \(0.138051\pi\) | |||||||
\(152\) | 10.9140 | + | 7.92945i | 0.885239 | + | 0.643164i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.37927 | + | 1.75393i | −0.111144 | + | 0.141336i | ||||
\(155\) | 19.6154 | 1.57555 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.57888 | + | 17.1700i | −0.445243 | + | 1.37032i | 0.436974 | + | 0.899474i | \(0.356050\pi\) |
−0.882217 | + | 0.470843i | \(0.843950\pi\) | |||||||
\(158\) | −1.58684 | − | 4.88380i | −0.126242 | − | 0.388534i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.2587 | + | 9.63304i | −1.04820 | + | 0.761559i | ||||
\(161\) | 0.0307625 | + | 0.0946773i | 0.00242443 | + | 0.00746161i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.71129 | + | 3.42295i | 0.369017 | + | 0.268106i | 0.756803 | − | 0.653643i | \(-0.226760\pi\) |
−0.387786 | + | 0.921749i | \(0.626760\pi\) | |||||||
\(164\) | −9.67868 | −0.755778 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.86467 | 0.222341 | ||||||||
\(167\) | 4.06266 | + | 2.95170i | 0.314378 | + | 0.228409i | 0.733773 | − | 0.679395i | \(-0.237758\pi\) |
−0.419395 | + | 0.907804i | \(0.637758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.794875 | + | 2.44637i | 0.0611442 | + | 0.188182i | ||||
\(170\) | 0.441265 | − | 0.320598i | 0.0338435 | − | 0.0245887i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.49313 | + | 10.7508i | 0.266349 | + | 0.819738i | ||||
\(173\) | −4.81753 | + | 14.8268i | −0.366270 | + | 1.12726i | 0.582912 | + | 0.812536i | \(0.301913\pi\) |
−0.949182 | + | 0.314728i | \(0.898087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.68824 | −0.354397 | ||||||||
\(176\) | −6.72751 | + | 1.90610i | −0.507105 | + | 0.143677i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.995046 | − | 0.722943i | −0.0745818 | − | 0.0541869i | ||||
\(179\) | 2.17822 | − | 6.70387i | 0.162808 | − | 0.501071i | −0.836060 | − | 0.548638i | \(-0.815147\pi\) |
0.998868 | + | 0.0475668i | \(0.0151467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.02068 | + | 1.46811i | −0.150196 | + | 0.109124i | −0.660345 | − | 0.750962i | \(-0.729590\pi\) |
0.510149 | + | 0.860086i | \(0.329590\pi\) | |||||||
\(182\) | −2.14779 | + | 1.56046i | −0.159205 | + | 0.115669i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0559686 | − | 0.172254i | 0.00412606 | − | 0.0126987i | ||||
\(185\) | 15.1747 | + | 11.0250i | 1.11566 | + | 0.810577i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00259 | − | 0.284062i | 0.0733165 | − | 0.0207727i | ||||
\(188\) | 0.546051 | 0.0398249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.41633 | − | 10.5144i | 0.247847 | − | 0.762795i | ||||
\(191\) | −3.65350 | − | 11.2443i | −0.264358 | − | 0.813611i | −0.991841 | − | 0.127484i | \(-0.959310\pi\) |
0.727483 | − | 0.686126i | \(-0.240690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.45816 | + | 3.96559i | −0.392887 | + | 0.285449i | −0.766637 | − | 0.642080i | \(-0.778072\pi\) |
0.373751 | + | 0.927529i | \(0.378072\pi\) | |||||||
\(194\) | −0.0158626 | − | 0.0488200i | −0.00113887 | − | 0.00350507i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.60820 | − | 5.52768i | −0.543443 | − | 0.394834i | ||||
\(197\) | −20.6474 | −1.47107 | −0.735534 | − | 0.677488i | \(-0.763069\pi\) | ||||
−0.735534 | + | 0.677488i | \(0.763069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2862 | −0.941832 | −0.470916 | − | 0.882178i | \(-0.656077\pi\) | ||||
−0.470916 | + | 0.882178i | \(0.656077\pi\) | |||||||
\(200\) | 6.90064 | + | 5.01361i | 0.487949 | + | 0.354516i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.367193 | − | 1.13010i | −0.0258356 | − | 0.0795138i | ||||
\(203\) | −7.25288 | + | 5.26953i | −0.509053 | + | 0.369848i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.39325 | + | 16.5987i | 0.376681 | + | 1.15931i | ||||
\(206\) | −0.538646 | + | 1.65778i | −0.0375292 | + | 0.115503i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.31958 | −0.576859 | ||||||||
\(209\) | 13.0563 | − | 16.6028i | 0.903120 | − | 1.14844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.75126 | + | 4.90508i | 0.464776 | + | 0.337680i | 0.795402 | − | 0.606082i | \(-0.207260\pi\) |
−0.330626 | + | 0.943762i | \(0.607260\pi\) | |||||||
\(212\) | 1.24736 | − | 3.83897i | 0.0856688 | − | 0.263661i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.60618 | + | 4.07313i | −0.383231 | + | 0.278433i | ||||
\(215\) | 16.4908 | − | 11.9813i | 1.12467 | − | 0.817117i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.34904 | + | 7.22960i | −0.159463 | + | 0.490778i | ||||
\(218\) | −2.43085 | − | 1.76612i | −0.164638 | − | 0.119616i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.24034 | + | 13.7932i | 0.622984 | + | 0.929936i | ||||
\(221\) | 1.23985 | 0.0834013 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.118556 | + | 0.364878i | −0.00793910 | + | 0.0244340i | −0.954948 | − | 0.296774i | \(-0.904089\pi\) |
0.947008 | + | 0.321209i | \(0.104089\pi\) | |||||||
\(224\) | −1.96263 | − | 6.04035i | −0.131134 | − | 0.403588i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.98811 | + | 6.53024i | −0.597880 | + | 0.434385i | ||||
\(227\) | 5.56664 | + | 17.1324i | 0.369471 | + | 1.13711i | 0.947134 | + | 0.320839i | \(0.103965\pi\) |
−0.577663 | + | 0.816276i | \(0.696035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.8634 | − | 7.89270i | −0.717872 | − | 0.521565i | 0.167832 | − | 0.985816i | \(-0.446324\pi\) |
−0.885704 | + | 0.464251i | \(0.846324\pi\) | |||||||
\(230\) | −0.148428 | −0.00978704 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.3108 | 1.07086 | ||||||||
\(233\) | 2.72611 | + | 1.98063i | 0.178593 | + | 0.129756i | 0.673490 | − | 0.739196i | \(-0.264794\pi\) |
−0.494897 | + | 0.868952i | \(0.664794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.304276 | − | 0.936466i | −0.0198488 | − | 0.0610883i | ||||
\(236\) | −3.09489 | + | 2.24857i | −0.201460 | + | 0.146369i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0653183 | + | 0.201029i | 0.00423395 | + | 0.0130308i | ||||
\(239\) | −7.16820 | + | 22.0615i | −0.463673 | + | 1.42704i | 0.396972 | + | 0.917831i | \(0.370061\pi\) |
−0.860644 | + | 0.509207i | \(0.829939\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1641 | 0.976807 | 0.488404 | − | 0.872618i | \(-0.337579\pi\) | ||||
0.488404 | + | 0.872618i | \(0.337579\pi\) | |||||||
\(242\) | −1.49863 | − | 6.17673i | −0.0963358 | − | 0.397055i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −18.4494 | − | 13.4043i | −1.18110 | − | 0.858120i | ||||
\(245\) | −5.24033 | + | 16.1281i | −0.334792 | + | 1.03039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.3312 | − | 14.7715i | 1.29364 | − | 0.939887i | ||||
\(248\) | 11.1889 | − | 8.12923i | 0.710497 | − | 0.516207i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.522189 | + | 1.60713i | −0.0330262 | + | 0.101644i | ||||
\(251\) | 0.471095 | + | 0.342271i | 0.0297353 | + | 0.0216039i | 0.602554 | − | 0.798078i | \(-0.294150\pi\) |
−0.572818 | + | 0.819682i | \(0.694150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.266163 | − | 0.0978289i | −0.0167335 | − | 0.00615045i | ||||
\(254\) | −7.61725 | −0.477949 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39982 | + | 4.30820i | −0.0874887 | + | 0.269263i | ||||
\(257\) | −3.39036 | − | 10.4344i | −0.211485 | − | 0.650883i | −0.999385 | − | 0.0350793i | \(-0.988832\pi\) |
0.787900 | − | 0.615803i | \(-0.211168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.88071 | + | 4.27258i | −0.365409 | + | 0.265485i | ||||
\(260\) | 6.10421 | + | 18.7868i | 0.378567 | + | 1.16511i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.40108 | + | 6.10374i | 0.519020 | + | 0.377090i | ||||
\(263\) | −14.3954 | −0.887656 | −0.443828 | − | 0.896112i | \(-0.646380\pi\) | ||||
−0.443828 | + | 0.896112i | \(0.646380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.27881 | −0.447134 | ||||||||
\(266\) | 3.46614 | + | 2.51830i | 0.212523 | + | 0.154407i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.01349 | − | 18.5076i | −0.367333 | − | 1.13053i | ||||
\(269\) | −0.395590 | + | 0.287413i | −0.0241195 | + | 0.0175239i | −0.599780 | − | 0.800165i | \(-0.704745\pi\) |
0.575660 | + | 0.817689i | \(0.304745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.77950 | + | 20.8652i | 0.411825 | + | 1.26747i | 0.915060 | + | 0.403318i | \(0.132143\pi\) |
−0.503234 | + | 0.864150i | \(0.667857\pi\) | |||||||
\(272\) | −0.204692 | + | 0.629977i | −0.0124113 | + | 0.0381980i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.47712 | −0.572534 | ||||||||
\(275\) | 8.25517 | − | 10.4976i | 0.497806 | − | 0.633029i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.32149 | − | 1.68666i | −0.139485 | − | 0.101342i | 0.515855 | − | 0.856676i | \(-0.327474\pi\) |
−0.655340 | + | 0.755334i | \(0.727474\pi\) | |||||||
\(278\) | −2.12508 | + | 6.54031i | −0.127454 | + | 0.392262i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.99497 | + | 4.35560i | −0.358268 | + | 0.260297i | ||||
\(281\) | −14.7064 | + | 10.6848i | −0.877308 | + | 0.637402i | −0.932538 | − | 0.361072i | \(-0.882411\pi\) |
0.0552299 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.34632 | + | 19.5320i | −0.377249 | + | 1.16105i | 0.564699 | + | 0.825297i | \(0.308992\pi\) |
−0.941949 | + | 0.335757i | \(0.891008\pi\) | |||||||
\(284\) | 11.7508 | + | 8.53744i | 0.697280 | + | 0.506604i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.287805 | − | 7.55691i | 0.0170183 | − | 0.446849i | ||||
\(287\) | −6.76362 | −0.399244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.22278 | + | 16.0741i | −0.307223 | + | 0.945534i | ||||
\(290\) | −4.13058 | − | 12.7126i | −0.242556 | − | 0.746511i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.97176 | − | 2.88565i | 0.232430 | − | 0.168870i | ||||
\(293\) | 0.265775 | + | 0.817972i | 0.0155268 | + | 0.0477864i | 0.958520 | − | 0.285026i | \(-0.0920023\pi\) |
−0.942993 | + | 0.332813i | \(0.892002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.58081 | + | 4.05470i | 0.324927 | + | 0.236074i | ||||
\(296\) | 13.2250 | 0.768685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.61848 | −0.151684 | ||||||||
\(299\) | −0.272961 | − | 0.198318i | −0.0157857 | − | 0.0114690i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.44106 | + | 7.51280i | 0.140700 | + | 0.433031i | ||||
\(302\) | 1.37006 | − | 0.995408i | 0.0788382 | − | 0.0572793i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.14894 | + | 12.7691i | 0.237958 | + | 0.732360i | ||||
\(305\) | −12.7075 | + | 39.1095i | −0.727627 | + | 2.23941i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48920 | 0.199139 | 0.0995696 | − | 0.995031i | \(-0.468253\pi\) | ||||
0.0995696 | + | 0.995031i | \(0.468253\pi\) | |||||||
\(308\) | −6.19029 | + | 1.75389i | −0.352725 | + | 0.0999370i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.16942 | − | 6.66197i | −0.520788 | − | 0.378375i | ||||
\(311\) | 3.35138 | − | 10.3145i | 0.190039 | − | 0.584881i | −0.809959 | − | 0.586486i | \(-0.800511\pi\) |
0.999999 | + | 0.00160485i | \(0.000510839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.8799 | − | 16.6232i | 1.29325 | − | 0.939598i | 0.293381 | − | 0.955996i | \(-0.405220\pi\) |
0.999866 | + | 0.0163974i | \(0.00521967\pi\) | |||||||
\(314\) | 8.43935 | − | 6.13155i | 0.476260 | − | 0.346023i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.57569 | − | 14.0825i | 0.257403 | − | 0.792204i | ||||
\(317\) | 0.900053 | + | 0.653927i | 0.0505520 | + | 0.0367282i | 0.612774 | − | 0.790258i | \(-0.290053\pi\) |
−0.562222 | + | 0.826986i | \(0.690053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.971887 | − | 25.5189i | 0.0544152 | − | 1.42878i | ||||
\(320\) | −3.19867 | −0.178811 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0177750 | − | 0.0547057i | 0.000990559 | − | 0.00304863i | ||||
\(323\) | −0.618308 | − | 1.90296i | −0.0344036 | − | 0.105883i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8550 | − | 9.33967i | 0.713065 | − | 0.518072i | ||||
\(326\) | −1.03980 | − | 3.20018i | −0.0575894 | − | 0.177242i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.95541 | + | 7.23303i | 0.549696 | + | 0.399377i | ||||
\(329\) | 0.381589 | 0.0210377 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3783 | −0.680373 | −0.340187 | − | 0.940358i | \(-0.610490\pi\) | ||||
−0.340187 | + | 0.940358i | \(0.610490\pi\) | |||||||
\(332\) | 6.68275 | + | 4.85530i | 0.366763 | + | 0.266469i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.896648 | − | 2.75960i | −0.0490624 | − | 0.150999i | ||||
\(335\) | −28.3893 | + | 20.6260i | −1.55107 | + | 1.12692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.16358 | + | 12.8142i | 0.226804 | + | 0.698032i | 0.998103 | + | 0.0615594i | \(0.0196074\pi\) |
−0.771299 | + | 0.636473i | \(0.780393\pi\) | |||||||
\(338\) | 0.459288 | − | 1.41354i | 0.0249820 | − | 0.0768866i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.57277 | 0.0852953 | ||||||||
\(341\) | −12.0518 | − | 17.9899i | −0.652642 | − | 0.974208i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9104 | − | 8.65342i | −0.643102 | − | 0.467241i | ||||
\(344\) | 4.44120 | − | 13.6686i | 0.239453 | − | 0.736962i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.28763 | − | 5.29478i | 0.391786 | − | 0.284649i | ||||
\(347\) | −7.87915 | + | 5.72454i | −0.422975 | + | 0.307309i | −0.778834 | − | 0.627230i | \(-0.784188\pi\) |
0.355859 | + | 0.934540i | \(0.384188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.37210 | + | 4.22288i | −0.0734466 | + | 0.226045i | −0.981040 | − | 0.193804i | \(-0.937917\pi\) |
0.907594 | + | 0.419850i | \(0.137917\pi\) | |||||||
\(350\) | 2.19156 | + | 1.59226i | 0.117144 | + | 0.0851100i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9810 | + | 6.24142i | 0.905090 | + | 0.332669i | ||||
\(353\) | 32.5235 | 1.73105 | 0.865527 | − | 0.500863i | \(-0.166984\pi\) | ||||
0.865527 | + | 0.500863i | \(0.166984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.09363 | − | 24.9096i | 0.429565 | − | 1.32207i | ||||
\(356\) | −1.09595 | − | 3.37299i | −0.0580852 | − | 0.178768i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.29506 | + | 2.39400i | −0.174149 | + | 0.126527i | ||||
\(359\) | −8.58143 | − | 26.4109i | −0.452911 | − | 1.39392i | −0.873571 | − | 0.486697i | \(-0.838201\pi\) |
0.420660 | − | 0.907218i | \(-0.361799\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4395 | − | 12.6705i | −0.917868 | − | 0.666870i | ||||
\(362\) | 1.44320 | 0.0758529 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.65523 | −0.401243 | ||||||||
\(365\) | −7.16201 | − | 5.20351i | −0.374877 | − | 0.272364i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.362229 | + | 1.11483i | 0.0189082 | + | 0.0581934i | 0.960065 | − | 0.279776i | \(-0.0902601\pi\) |
−0.941157 | + | 0.337969i | \(0.890260\pi\) | |||||||
\(368\) | 0.145831 | − | 0.105952i | 0.00760197 | − | 0.00552315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.34912 | − | 10.3075i | −0.174112 | − | 0.535862i | ||||
\(371\) | 0.871672 | − | 2.68273i | 0.0452550 | − | 0.139280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.7668 | 1.12704 | 0.563520 | − | 0.826102i | \(-0.309447\pi\) | ||||
0.563520 | + | 0.826102i | \(0.309447\pi\) | |||||||
\(374\) | −0.565145 | − | 0.207721i | −0.0292230 | − | 0.0107410i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.561664 | − | 0.408072i | −0.0289656 | − | 0.0210447i | ||||
\(377\) | 9.38942 | − | 28.8977i | 0.483580 | − | 1.48831i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1440 | − | 9.54967i | 0.675161 | − | 0.490533i | −0.196588 | − | 0.980486i | \(-0.562986\pi\) |
0.871749 | + | 0.489953i | \(0.162986\pi\) | |||||||
\(380\) | 25.7904 | − | 18.7379i | 1.32302 | − | 0.961232i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.11104 | + | 6.49710i | −0.108010 | + | 0.332421i | ||||
\(383\) | −5.01052 | − | 3.64036i | −0.256026 | − | 0.186014i | 0.452367 | − | 0.891832i | \(-0.350580\pi\) |
−0.708393 | + | 0.705818i | \(0.750580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.45730 | + | 9.63890i | 0.329094 | + | 0.491244i | ||||
\(386\) | 3.89830 | 0.198418 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0457401 | − | 0.140773i | 0.00232210 | − | 0.00714669i | ||||
\(389\) | −0.223485 | − | 0.687817i | −0.0113312 | − | 0.0348737i | 0.945231 | − | 0.326402i | \(-0.105836\pi\) |
−0.956562 | + | 0.291528i | \(0.905836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0217329 | + | 0.0157899i | −0.00109908 | + | 0.000798528i | ||||
\(392\) | 3.69481 | + | 11.3714i | 0.186616 | + | 0.574345i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.65184 | + | 7.01247i | 0.486253 | + | 0.353283i | ||||
\(395\) | −26.7009 | −1.34347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.08994 | 0.205268 | 0.102634 | − | 0.994719i | \(-0.467273\pi\) | ||||
0.102634 | + | 0.994719i | \(0.467273\pi\) | |||||||
\(398\) | 6.21075 | + | 4.51238i | 0.311317 | + | 0.226185i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.62328 | + | 8.07363i | 0.131164 | + | 0.403681i | ||||
\(401\) | 4.56793 | − | 3.31879i | 0.228111 | − | 0.165733i | −0.467859 | − | 0.883803i | \(-0.654974\pi\) |
0.695970 | + | 0.718071i | \(0.254974\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.96148 | − | 24.5029i | −0.396590 | − | 1.22058i | ||||
\(404\) | 1.05881 | − | 3.25868i | 0.0526777 | − | 0.162125i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.18012 | 0.257085 | ||||||||
\(407\) | 0.788016 | − | 20.6910i | 0.0390605 | − | 1.02561i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.64422 | − | 5.55385i | −0.377982 | − | 0.274620i | 0.382531 | − | 0.923943i | \(-0.375053\pi\) |
−0.760513 | + | 0.649323i | \(0.775053\pi\) | |||||||
\(410\) | 3.11629 | − | 9.59094i | 0.153902 | − | 0.473663i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.06632 | + | 2.95436i | −0.200333 | + | 0.145551i | ||||
\(413\) | −2.16276 | + | 1.57134i | −0.106422 | + | 0.0773204i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.60290 | − | 14.1663i | 0.225948 | − | 0.695395i | ||||
\(416\) | 17.4147 | + | 12.6525i | 0.853827 | + | 0.620342i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.7421 | + | 3.32687i | −0.574324 | + | 0.162723i | ||||
\(419\) | 0.151564 | 0.00740438 | 0.00370219 | − | 0.999993i | \(-0.498822\pi\) | ||||
0.00370219 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.24605 | − | 16.1457i | 0.255677 | − | 0.786892i | −0.738019 | − | 0.674780i | \(-0.764239\pi\) |
0.993696 | − | 0.112112i | \(-0.0357615\pi\) | |||||||
\(422\) | −1.49003 | − | 4.58585i | −0.0725337 | − | 0.223236i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.15194 | + | 3.01656i | −0.201636 | + | 0.146497i | ||||
\(425\) | −0.390942 | − | 1.20320i | −0.0189635 | − | 0.0583636i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8927 | − | 9.36711i | −0.623923 | − | 0.453306i | ||||
\(428\) | −19.9817 | −0.965852 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.7780 | −0.567986 | ||||||||
\(431\) | 20.5242 | + | 14.9117i | 0.988618 | + | 0.718273i | 0.959618 | − | 0.281307i | \(-0.0907678\pi\) |
0.0289998 | + | 0.999579i | \(0.490768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.10950 | + | 15.7254i | 0.245547 | + | 0.755716i | 0.995546 | + | 0.0942769i | \(0.0300539\pi\) |
−0.749999 | + | 0.661439i | \(0.769946\pi\) | |||||||
\(434\) | 3.55347 | − | 2.58175i | 0.170572 | − | 0.123928i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.67736 | − | 8.24005i | −0.128222 | − | 0.394627i | ||||
\(437\) | −0.168259 | + | 0.517849i | −0.00804893 | + | 0.0247721i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.2413 | −1.87289 | −0.936443 | − | 0.350819i | \(-0.885903\pi\) | ||||
−0.936443 | + | 0.350819i | \(0.885903\pi\) | |||||||
\(440\) | 0.803326 | − | 21.0930i | 0.0382971 | − | 1.00557i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.579580 | − | 0.421089i | −0.0275678 | − | 0.0200292i | ||||
\(443\) | 9.94706 | − | 30.6139i | 0.472599 | − | 1.45451i | −0.376570 | − | 0.926388i | \(-0.622896\pi\) |
0.849169 | − | 0.528122i | \(-0.177104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.17390 | + | 3.75906i | −0.245266 | + | 0.178197i | ||||
\(446\) | 0.179344 | − | 0.130301i | 0.00849216 | − | 0.00616992i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.383056 | − | 1.17893i | 0.0180977 | − | 0.0556990i | ||||
\(449\) | 20.9085 | + | 15.1909i | 0.986731 | + | 0.716902i | 0.959203 | − | 0.282719i | \(-0.0912364\pi\) |
0.0275281 | + | 0.999621i | \(0.491236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9096 | − | 15.1447i | 0.560799 | − | 0.713134i | ||||
\(452\) | −32.0357 | −1.50683 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.21647 | − | 9.89928i | 0.150957 | − | 0.464596i | ||||
\(455\) | 4.26572 | + | 13.1285i | 0.199980 | + | 0.615476i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2877 | − | 7.47444i | 0.481238 | − | 0.349640i | −0.320567 | − | 0.947226i | \(-0.603873\pi\) |
0.801805 | + | 0.597586i | \(0.203873\pi\) | |||||||
\(458\) | 2.39760 | + | 7.37904i | 0.112032 | + | 0.344800i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.346255 | − | 0.251569i | −0.0161442 | − | 0.0117295i | ||||
\(461\) | −19.0217 | −0.885931 | −0.442965 | − | 0.896539i | \(-0.646073\pi\) | ||||
−0.442965 | + | 0.896539i | \(0.646073\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8667 | −1.06271 | −0.531353 | − | 0.847150i | \(-0.678316\pi\) | ||||
−0.531353 | + | 0.847150i | \(0.678316\pi\) | |||||||
\(464\) | 13.1330 | + | 9.54168i | 0.609684 | + | 0.442961i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.601664 | − | 1.85173i | −0.0278716 | − | 0.0857798i | ||||
\(467\) | −12.8819 | + | 9.35921i | −0.596101 | + | 0.433093i | −0.844493 | − | 0.535567i | \(-0.820098\pi\) |
0.248392 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.20232 | − | 12.9334i | −0.194045 | − | 0.597210i | ||||
\(470\) | −0.175814 | + | 0.541101i | −0.00810971 | + | 0.0249591i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.86377 | 0.223873 | ||||||||
\(473\) | −21.1205 | − | 7.76289i | −0.971120 | − | 0.356938i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7455 | − | 15.0725i | −0.951870 | − | 0.691574i | ||||
\(476\) | −0.188347 | + | 0.579671i | −0.00863285 | + | 0.0265692i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.8436 | − | 7.87832i | 0.495973 | − | 0.360346i | ||||
\(479\) | 13.2598 | − | 9.63378i | 0.605854 | − | 0.440179i | −0.242098 | − | 0.970252i | \(-0.577836\pi\) |
0.847952 | + | 0.530073i | \(0.177836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.61303 | − | 23.4305i | 0.347124 | − | 1.06834i | ||||
\(482\) | −7.08862 | − | 5.15018i | −0.322878 | − | 0.234584i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.97285 | − | 16.9492i | 0.316948 | − | 0.770418i | ||||
\(485\) | −0.266911 | −0.0121198 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.04142 | − | 21.6713i | 0.319077 | − | 0.982019i | −0.654966 | − | 0.755658i | \(-0.727317\pi\) |
0.974044 | − | 0.226361i | \(-0.0726828\pi\) | |||||||
\(488\) | 8.95967 | + | 27.5750i | 0.405585 | + | 1.24826i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.92722 | − | 5.75946i | 0.358115 | − | 0.260186i | ||||
\(491\) | −13.4864 | − | 41.5070i | −0.608634 | − | 1.87318i | −0.469558 | − | 0.882901i | \(-0.655587\pi\) |
−0.139076 | − | 0.990282i | \(-0.544413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.95718 | − | 1.42198i | −0.0881471 | − | 0.0640426i | ||||
\(494\) | −14.5209 | −0.653324 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.7645 | 0.618045 | ||||||||
\(497\) | 8.21163 | + | 5.96610i | 0.368342 | + | 0.267616i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.21233 | − | 19.1196i | −0.278102 | − | 0.855910i | −0.988382 | − | 0.151991i | \(-0.951432\pi\) |
0.710280 | − | 0.703919i | \(-0.248568\pi\) | |||||||
\(500\) | −3.94209 | + | 2.86410i | −0.176296 | + | 0.128086i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.103973 | − | 0.319996i | −0.00464054 | − | 0.0142821i | ||||
\(503\) | −3.27815 | + | 10.0891i | −0.146165 | + | 0.449850i | −0.997159 | − | 0.0753254i | \(-0.976000\pi\) |
0.850994 | + | 0.525176i | \(0.176000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.17856 | −0.274942 | ||||||||
\(506\) | 0.0911948 | + | 0.136128i | 0.00405410 | + | 0.00605162i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7697 | − | 12.9104i | −0.788401 | − | 0.572807i | ||||
\(509\) | −13.7415 | + | 42.2919i | −0.609080 | + | 1.87456i | −0.143240 | + | 0.989688i | \(0.545752\pi\) |
−0.465840 | + | 0.884869i | \(0.654248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.77553 | − | 2.01654i | 0.122782 | − | 0.0892064i | ||||
\(512\) | −16.5301 | + | 12.0098i | −0.730534 | + | 0.530764i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.95899 | + | 6.02915i | −0.0864073 | + | 0.265934i | ||||
\(515\) | 7.33253 | + | 5.32739i | 0.323110 | + | 0.234753i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.671913 | + | 0.854430i | −0.0295507 | + | 0.0375778i | ||||
\(518\) | 4.20009 | 0.184541 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.76095 | − | 23.8858i | 0.340340 | − | 1.04746i | ||||
\(521\) | 5.23819 | + | 16.1215i | 0.229489 | + | 0.706296i | 0.997805 | + | 0.0662243i | \(0.0210953\pi\) |
−0.768315 | + | 0.640071i | \(0.778905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4438 | + | 17.7595i | −1.06885 | + | 0.776567i | −0.975706 | − | 0.219085i | \(-0.929693\pi\) |
−0.0931472 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(524\) | 9.25301 | + | 28.4778i | 0.404219 | + | 1.24406i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.72925 | + | 4.88909i | 0.293409 | + | 0.213174i | ||||
\(527\) | −2.05130 | −0.0893560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9927 | −0.999682 | ||||||||
\(530\) | 3.40255 | + | 2.47210i | 0.147797 | + | 0.107381i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.81763 | + | 11.7495i | 0.165515 | + | 0.509404i | ||||
\(533\) | 18.5456 | − | 13.4741i | 0.803298 | − | 0.583630i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1344 | + | 34.2682i | 0.481382 | + | 1.48154i | ||||
\(536\) | −7.64561 | + | 23.5308i | −0.330240 | + | 1.01637i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.282536 | 0.0121810 | ||||||||
\(539\) | 18.0112 | − | 5.10310i | 0.775799 | − | 0.219806i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.57164 | − | 6.95421i | −0.411517 | − | 0.298985i | 0.362699 | − | 0.931906i | \(-0.381855\pi\) |
−0.774216 | + | 0.632922i | \(0.781855\pi\) | |||||||
\(542\) | 3.91728 | − | 12.0561i | 0.168262 | − | 0.517856i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.38654 | − | 1.00738i | 0.0594476 | − | 0.0431912i | ||||
\(545\) | −12.6396 | + | 9.18321i | −0.541421 | + | 0.393365i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.786698 | − | 2.42121i | 0.0336368 | − | 0.103523i | −0.932828 | − | 0.360321i | \(-0.882667\pi\) |
0.966465 | + | 0.256797i | \(0.0826673\pi\) | |||||||
\(548\) | −22.1084 | − | 16.0627i | −0.944424 | − | 0.686164i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.42425 | + | 2.10350i | −0.316571 | + | 0.0896937i | ||||
\(551\) | −49.0355 | −2.08898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.19757 | − | 9.84109i | 0.135974 | − | 0.418486i | ||||
\(554\) | 0.512364 | + | 1.57690i | 0.0217683 | + | 0.0669959i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0425 | + | 11.6556i | −0.680355 | + | 0.494307i | ||||
\(557\) | 2.98987 | + | 9.20189i | 0.126685 | + | 0.389896i | 0.994204 | − | 0.107507i | \(-0.0342868\pi\) |
−0.867519 | + | 0.497404i | \(0.834287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6599 | − | 15.7368i | −0.916117 | − | 0.665598i | ||||
\(560\) | −7.37496 | −0.311649 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.5035 | 0.443064 | ||||||||
\(563\) | 19.4061 | + | 14.0993i | 0.817868 | + | 0.594216i | 0.916101 | − | 0.400947i | \(-0.131319\pi\) |
−0.0982327 | + | 0.995163i | \(0.531319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.8512 | + | 54.9404i | 0.751007 | + | 2.31136i | ||||
\(566\) | 9.60027 | − | 6.97501i | 0.403530 | − | 0.293181i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.70659 | − | 17.5631i | −0.239443 | − | 0.736930i | ||||
\(569\) | −11.6249 | + | 35.7779i | −0.487343 | + | 1.49989i | 0.341215 | + | 0.939985i | \(0.389162\pi\) |
−0.828558 | + | 0.559903i | \(0.810838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.7548 | −0.617469 | −0.308735 | − | 0.951148i | \(-0.599905\pi\) | ||||
−0.308735 | + | 0.951148i | \(0.599905\pi\) | |||||||
\(572\) | 13.4795 | − | 17.1411i | 0.563608 | − | 0.716705i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.16172 | + | 2.29712i | 0.131968 | + | 0.0958801i | ||||
\(575\) | −0.106386 | + | 0.327424i | −0.00443662 | + | 0.0136545i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0466 | − | 13.1116i | 0.751289 | − | 0.545843i | −0.144937 | − | 0.989441i | \(-0.546298\pi\) |
0.896226 | + | 0.443598i | \(0.146298\pi\) | |||||||
\(578\) | 7.90067 | − | 5.74017i | 0.328625 | − | 0.238760i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.9106 | − | 36.6571i | 0.494562 | − | 1.52210i | ||||
\(581\) | 4.67001 | + | 3.39296i | 0.193745 | + | 0.140764i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.47213 | + | 6.67562i | 0.185217 | + | 0.276476i | ||||
\(584\) | −6.24181 | −0.258288 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.153568 | − | 0.472634i | 0.00634384 | − | 0.0195243i | ||||
\(587\) | −0.772594 | − | 2.37780i | −0.0318884 | − | 0.0981424i | 0.933846 | − | 0.357677i | \(-0.116431\pi\) |
−0.965734 | + | 0.259534i | \(0.916431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6374 | + | 24.4390i | −1.38601 | + | 1.00699i | ||||
\(590\) | −1.23171 | − | 3.79081i | −0.0507087 | − | 0.156065i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.6484 | + | 7.73648i | 0.437645 | + | 0.317968i | ||||
\(593\) | −10.8953 | −0.447417 | −0.223708 | − | 0.974656i | \(-0.571816\pi\) | ||||
−0.223708 | + | 0.974656i | \(0.571816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.09907 | 0.0450577 | ||||||||
\(596\) | −6.10843 | − | 4.43804i | −0.250211 | − | 0.181789i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0602437 | + | 0.185411i | 0.00246355 | + | 0.00758203i | ||||
\(599\) | 29.8026 | − | 21.6529i | 1.21770 | − | 0.884713i | 0.221796 | − | 0.975093i | \(-0.428808\pi\) |
0.995907 | + | 0.0903802i | \(0.0288082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.77564 | − | 14.6979i | −0.194802 | − | 0.599540i | −0.999979 | − | 0.00650456i | \(-0.997930\pi\) |
0.805177 | − | 0.593035i | \(-0.202070\pi\) | |||||||
\(602\) | 1.41047 | − | 4.34099i | 0.0574866 | − | 0.176925i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.88321 | 0.198695 | ||||||||
\(605\) | −32.9530 | − | 2.51367i | −1.33973 | − | 0.102195i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.6112 | + | 14.9749i | 0.836585 | + | 0.607814i | 0.921415 | − | 0.388581i | \(-0.127035\pi\) |
−0.0848299 | + | 0.996395i | \(0.527035\pi\) | |||||||
\(608\) | 10.7348 | − | 33.0384i | 0.435355 | − | 1.33988i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.2230 | − | 13.9663i | 0.778316 | − | 0.565479i | ||||
\(611\) | −1.04630 | + | 0.760183i | −0.0423289 | + | 0.0307537i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6728 | + | 35.9252i | −0.471461 | + | 1.45101i | 0.379211 | + | 0.925310i | \(0.376195\pi\) |
−0.850672 | + | 0.525697i | \(0.823805\pi\) | |||||||
\(614\) | −1.63106 | − | 1.18503i | −0.0658243 | − | 0.0478241i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.67799 | + | 2.82207i | 0.309355 | + | 0.113704i | ||||
\(617\) | 41.8928 | 1.68654 | 0.843271 | − | 0.537489i | \(-0.180627\pi\) | ||||
0.843271 | + | 0.537489i | \(0.180627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.85089 | + | 5.69646i | −0.0743936 | + | 0.228960i | −0.981338 | − | 0.192290i | \(-0.938409\pi\) |
0.906945 | + | 0.421250i | \(0.138409\pi\) | |||||||
\(620\) | −10.0993 | − | 31.0823i | −0.405596 | − | 1.24830i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.06974 | + | 3.68338i | −0.203278 | + | 0.147690i | ||||
\(623\) | −0.765867 | − | 2.35710i | −0.0306838 | − | 0.0944351i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3964 | + | 16.9985i | 0.935856 | + | 0.679939i | ||||
\(626\) | −16.3411 | −0.653123 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.0798 | 1.20031 | ||||||||
\(629\) | −1.58690 | − | 1.15295i | −0.0632739 | − | 0.0459712i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.64368 | − | 20.4471i | −0.264481 | − | 0.813988i | −0.991813 | − | 0.127702i | \(-0.959240\pi\) |
0.727332 | − | 0.686286i | \(-0.240760\pi\) | |||||||
\(632\) | −15.2306 | + | 11.0657i | −0.605841 | + | 0.440169i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.198646 | − | 0.611369i | −0.00788923 | − | 0.0242806i | ||||
\(635\) | −12.2393 | + | 37.6686i | −0.485701 | + | 1.49483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.2736 | 0.882512 | ||||||||
\(638\) | −9.12129 | + | 11.5990i | −0.361115 | + | 0.459208i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 28.0127 | + | 20.3525i | 1.10730 | + | 0.804501i | ||||
\(641\) | 3.96685 | − | 12.2087i | 0.156681 | − | 0.482215i | −0.841646 | − | 0.540029i | \(-0.818413\pi\) |
0.998327 | + | 0.0578142i | \(0.0184131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9401 | + | 16.6670i | −0.904671 | + | 0.657282i | −0.939661 | − | 0.342106i | \(-0.888860\pi\) |
0.0349907 | + | 0.999388i | \(0.488860\pi\) | |||||||
\(644\) | 0.134186 | − | 0.0974917i | 0.00528766 | − | 0.00384171i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.357266 | + | 1.09955i | −0.0140564 | + | 0.0432613i | ||||
\(647\) | 14.1536 | + | 10.2832i | 0.556436 | + | 0.404274i | 0.830153 | − | 0.557536i | \(-0.188253\pi\) |
−0.273717 | + | 0.961810i | \(0.588253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.289810 | − | 7.60956i | 0.0113760 | − | 0.298701i | ||||
\(650\) | −9.18120 | −0.360116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.99829 | − | 9.22780i | 0.117422 | − | 0.361389i | ||||
\(653\) | −9.05488 | − | 27.8681i | −0.354345 | − | 1.09056i | −0.956388 | − | 0.292098i | \(-0.905647\pi\) |
0.602043 | − | 0.798463i | \(-0.294353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.6828 | − | 31.7374i | 1.70683 | − | 1.24008i | ||||
\(656\) | 3.78455 | + | 11.6477i | 0.147762 | + | 0.454764i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.178378 | − | 0.129599i | −0.00695388 | − | 0.00505229i | ||||
\(659\) | 27.5870 | 1.07464 | 0.537319 | − | 0.843379i | \(-0.319437\pi\) | ||||
0.537319 | + | 0.843379i | \(0.319437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7552 | 1.15734 | 0.578672 | − | 0.815560i | \(-0.303571\pi\) | ||||
0.578672 | + | 0.815560i | \(0.303571\pi\) | |||||||
\(662\) | 5.78636 | + | 4.20404i | 0.224893 | + | 0.163395i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.24537 | − | 9.98823i | −0.125945 | − | 0.387619i | ||||
\(665\) | 18.0228 | − | 13.0943i | 0.698893 | − | 0.507775i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.203437 | + | 0.626115i | 0.00787711 | + | 0.0242433i | ||||
\(668\) | 2.58550 | − | 7.95736i | 0.100036 | − | 0.307880i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.2760 | 0.783332 | ||||||||
\(671\) | 43.6761 | − | 12.3747i | 1.68610 | − | 0.477720i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.80999 | − | 5.67429i | −0.301053 | − | 0.218728i | 0.426995 | − | 0.904254i | \(-0.359572\pi\) |
−0.728048 | + | 0.685526i | \(0.759572\pi\) | |||||||
\(674\) | 2.40577 | − | 7.40418i | 0.0926666 | − | 0.285198i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.46724 | − | 2.51910i | 0.133355 | − | 0.0968883i | ||||
\(677\) | 0.0793768 | − | 0.0576706i | 0.00305070 | − | 0.00221646i | −0.586259 | − | 0.810124i | \(-0.699400\pi\) |
0.589310 | + | 0.807907i | \(0.299400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0319639 | − | 0.0983747i | 0.00122666 | − | 0.00377528i | ||||
\(680\) | −1.61774 | − | 1.17535i | −0.0620373 | − | 0.0450727i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.476165 | + | 12.5027i | −0.0182333 | + | 0.478753i | ||||
\(683\) | 30.5246 | 1.16799 | 0.583996 | − | 0.811756i | \(-0.301488\pi\) | ||||
0.583996 | + | 0.811756i | \(0.301488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2277 | + | 46.8660i | −0.581820 | + | 1.79066i | ||||
\(686\) | 2.62868 | + | 8.09025i | 0.100364 | + | 0.308887i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.5719 | − | 8.40751i | 0.441176 | − | 0.320533i | ||||
\(689\) | 2.95431 | + | 9.09244i | 0.112550 | + | 0.346395i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.5371 | − | 19.2804i | −1.00952 | − | 0.733459i | −0.0454115 | − | 0.998968i | \(-0.514460\pi\) |
−0.964108 | + | 0.265509i | \(0.914460\pi\) | |||||||
\(692\) | 25.9748 | 0.987413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.62741 | 0.213614 | ||||||||
\(695\) | 28.9284 | + | 21.0177i | 1.09732 | + | 0.797248i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.564004 | − | 1.73583i | −0.0213632 | − | 0.0657491i | ||||
\(698\) | 2.07561 | − | 1.50802i | 0.0785631 | − | 0.0570794i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.41380 | + | 7.42892i | 0.0912331 | + | 0.280787i | ||||
\(701\) | −2.70365 | + | 8.32098i | −0.102115 | + | 0.314279i | −0.989043 | − | 0.147630i | \(-0.952835\pi\) |
0.886927 | + | 0.461909i | \(0.152835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.7584 | −1.49952 | ||||||||
\(704\) | 1.96528 | + | 2.93360i | 0.0740692 | + | 0.110564i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.2034 | − | 11.0460i | −0.572189 | − | 0.415720i | ||||
\(707\) | 0.739912 | − | 2.27721i | 0.0278273 | − | 0.0856435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.6621 | + | 15.7385i | −0.813539 | + | 0.591071i | −0.914854 | − | 0.403784i | \(-0.867695\pi\) |
0.101316 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(710\) | −12.2435 | + | 8.89542i | −0.459490 | + | 0.333839i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.39340 | + | 4.28845i | −0.0522199 | + | 0.160716i | ||||
\(713\) | 0.451607 | + | 0.328111i | 0.0169128 | + | 0.0122879i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.9078 | − | 13.5656i | −1.38027 | − | 0.507323i | ||||
\(716\) | −11.7443 | −0.438907 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.95846 | + | 15.2606i | −0.185048 | + | 0.569519i | ||||
\(719\) | −4.63672 | − | 14.2703i | −0.172920 | − | 0.532194i | 0.826612 | − | 0.562772i | \(-0.190265\pi\) |
−0.999532 | + | 0.0305782i | \(0.990265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.84161 | + | 2.06455i | −0.105827 | + | 0.0768879i | ||||
\(722\) | 3.84897 | + | 11.8459i | 0.143244 | + | 0.440860i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.36672 | + | 2.44607i | 0.125123 | + | 0.0909073i | ||||
\(725\) | −31.0040 | −1.15146 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.5325 | 1.02112 | 0.510562 | − | 0.859841i | \(-0.329437\pi\) | ||||
0.510562 | + | 0.859841i | \(0.329437\pi\) | |||||||
\(728\) | 7.87410 | + | 5.72087i | 0.291834 | + | 0.212029i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.58069 | + | 4.86486i | 0.0585039 | + | 0.180057i | ||||
\(731\) | −1.72454 | + | 1.25295i | −0.0637845 | + | 0.0463422i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7524 | + | 45.4031i | 0.544891 | + | 1.67700i | 0.721248 | + | 0.692677i | \(0.243569\pi\) |
−0.176357 | + | 0.984326i | \(0.556431\pi\) | |||||||
\(734\) | 0.209300 | − | 0.644160i | 0.00772541 | − | 0.0237764i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.466391 | −0.0171914 | ||||||||
\(737\) | 36.3593 | + | 13.3640i | 1.33931 | + | 0.492267i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.20421 | − | 0.874910i | −0.0442976 | − | 0.0321841i | 0.565416 | − | 0.824806i | \(-0.308716\pi\) |
−0.609714 | + | 0.792622i | \(0.708716\pi\) | |||||||
\(740\) | 9.65725 | − | 29.7220i | 0.355007 | − | 1.09260i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.31861 | + | 0.958023i | −0.0484076 | + | 0.0351701i | ||||
\(743\) | 14.6919 | − | 10.6743i | 0.538993 | − | 0.391601i | −0.284718 | − | 0.958611i | \(-0.591900\pi\) |
0.823711 | + | 0.567010i | \(0.191900\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.20733 | + | 12.9488i | −0.154145 | + | 0.474409i | ||||
\(746\) | −10.1751 | − | 7.39264i | −0.372537 | − | 0.270664i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.966316 | − | 1.44243i | −0.0353320 | − | 0.0527406i | ||||
\(749\) | −13.9635 | −0.510216 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.35802 | + | 4.17956i | −0.0495550 | + | 0.152514i | −0.972772 | − | 0.231765i | \(-0.925550\pi\) |
0.923217 | + | 0.384279i | \(0.125550\pi\) | |||||||
\(752\) | −0.213517 | − | 0.657136i | −0.00778615 | − | 0.0239633i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.2037 | + | 10.3196i | −0.517267 | + | 0.375817i | ||||
\(755\) | −2.72107 | − | 8.37459i | −0.0990299 | − | 0.304783i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1369 | + | 8.09140i | 0.404776 | + | 0.294087i | 0.771483 | − | 0.636249i | \(-0.219515\pi\) |
−0.366708 | + | 0.930336i | \(0.619515\pi\) | |||||||
\(758\) | −9.38763 | −0.340974 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −40.5309 | −1.47021 | ||||||||
\(761\) | 25.1654 | + | 18.2837i | 0.912244 | + | 0.662784i | 0.941581 | − | 0.336786i | \(-0.109340\pi\) |
−0.0293374 | + | 0.999570i | \(0.509340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.87098 | − | 5.75828i | −0.0677340 | − | 0.208464i | ||||
\(764\) | −15.9365 | + | 11.5786i | −0.576564 | + | 0.418898i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.10585 | + | 3.40344i | 0.0399558 | + | 0.122971i | ||||
\(767\) | 2.79986 | − | 8.61708i | 0.101097 | − | 0.311145i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.9353 | 0.791009 | 0.395504 | − | 0.918464i | \(-0.370570\pi\) | ||||
0.395504 | + | 0.918464i | \(0.370570\pi\) | |||||||
\(770\) | 0.255127 | − | 6.69888i | 0.00919413 | − | 0.241411i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.09402 | + | 6.60719i | 0.327301 | + | 0.237798i | ||||
\(773\) | −3.92965 | + | 12.0942i | −0.141340 | + | 0.434999i | −0.996522 | − | 0.0833281i | \(-0.973445\pi\) |
0.855182 | + | 0.518327i | \(0.173445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.2682 | + | 15.4522i | −0.763976 | + | 0.555061i | ||||
\(776\) | −0.152250 | + | 0.110616i | −0.00546546 | + | 0.00397089i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.129132 | + | 0.397429i | −0.00462962 | + | 0.0142485i | ||||
\(779\) | −29.9291 | − | 21.7448i | −1.07232 | − | 0.779087i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.8182 | + | 7.88168i | −0.995412 | + | 0.282029i | ||||
\(782\) | 0.0155220 | 0.000555064 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.67724 | + | 11.3174i | −0.131330 | + | 0.404193i | ||||
\(785\) | −16.7613 | − | 51.5861i | −0.598238 | − | 1.84119i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9650 | − | 10.1461i | 0.497797 | − | 0.361671i | −0.310378 | − | 0.950613i | \(-0.600455\pi\) |
0.808175 | + | 0.588942i | \(0.200455\pi\) | |||||||
\(788\) | 10.6306 | + | 32.7176i | 0.378700 | + | 1.16552i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.4816 | + | 9.06842i | 0.444076 | + | 0.322640i | ||||
\(791\) | −22.3870 | −0.795991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0120 | 1.91802 | ||||||||
\(794\) | −1.91188 | − | 1.38906i | −0.0678501 | − | 0.0492960i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.84057 | + | 21.0531i | 0.242457 | + | 0.746207i | ||||
\(797\) | −28.4786 | + | 20.6909i | −1.00876 | + | 0.732910i | −0.963950 | − | 0.266085i | \(-0.914270\pi\) |
−0.0448149 | + | 0.998995i | \(0.514270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0318199 | + | 0.0979317i | 0.00112571 | + | 0.00346457i | ||||
\(800\) | 6.78739 | − | 20.8894i | 0.239970 | − | 0.738553i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.26248 | −0.115202 | ||||||||
\(803\) | −0.371921 | + | 9.76556i | −0.0131248 | + | 0.344619i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.241968 | − | 0.175800i | −0.00852827 | − | 0.00619615i | ||||
\(806\) | −4.60024 | + | 14.1581i | −0.162037 | + | 0.498697i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.52434 | + | 2.56058i | −0.123986 | + | 0.0900810i | ||||
\(809\) | 15.4367 | − | 11.2154i | 0.542725 | − | 0.394313i | −0.282371 | − | 0.959305i | \(-0.591121\pi\) |
0.825096 | + | 0.564992i | \(0.191121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.59769 | + | 29.5387i | −0.337020 | + | 1.03724i | 0.628698 | + | 0.777650i | \(0.283588\pi\) |
−0.965718 | + | 0.259593i | \(0.916412\pi\) | |||||||
\(812\) | 12.0843 | + | 8.77973i | 0.424075 | + | 0.308108i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.39563 | + | 9.40457i | −0.259217 | + | 0.329630i | ||||
\(815\) | −17.4962 | −0.612865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.3517 | + | 41.0922i | −0.467115 | + | 1.43763i | ||||
\(818\) | 1.68711 | + | 5.19240i | 0.0589885 | + | 0.181548i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.5253 | − | 17.0922i | 0.821540 | − | 0.596884i | ||||
\(821\) | 10.5092 | + | 32.3440i | 0.366774 | + | 1.12881i | 0.948863 | + | 0.315689i | \(0.102236\pi\) |
−0.582089 | + | 0.813125i | \(0.697764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5851 | − | 9.14359i | −0.438688 | − | 0.318726i | 0.346425 | − | 0.938078i | \(-0.387395\pi\) |
−0.785113 | + | 0.619352i | \(0.787395\pi\) | |||||||
\(824\) | 6.39042 | 0.222621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.54467 | 0.0537461 | ||||||||
\(827\) | −12.9667 | − | 9.42084i | −0.450895 | − | 0.327595i | 0.339054 | − | 0.940767i | \(-0.389893\pi\) |
−0.789949 | + | 0.613172i | \(0.789893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.90205 | + | 18.1646i | 0.204987 | + | 0.630884i | 0.999714 | + | 0.0239173i | \(0.00761382\pi\) |
−0.794727 | + | 0.606967i | \(0.792386\pi\) | |||||||
\(830\) | −6.96296 | + | 5.05888i | −0.241688 | + | 0.175596i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.29827 | + | 3.99567i | 0.0450095 | + | 0.138525i | ||||
\(833\) | 0.548012 | − | 1.68661i | 0.0189875 | − | 0.0584375i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0874 | −0.522122 | ||||||||
\(836\) | −33.0308 | − | 12.1406i | −1.14240 | − | 0.419891i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.0708501 | − | 0.0514756i | −0.00244747 | − | 0.00177819i | ||||
\(839\) | 0.459793 | − | 1.41510i | 0.0158738 | − | 0.0488545i | −0.942806 | − | 0.333342i | \(-0.891824\pi\) |
0.958680 | + | 0.284488i | \(0.0918235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5029 | + | 17.8024i | −0.844927 | + | 0.613875i | ||||
\(842\) | −7.93586 | + | 5.76574i | −0.273488 | + | 0.198700i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.29654 | − | 13.2234i | 0.147893 | − | 0.455168i | ||||
\(845\) | −6.25224 | − | 4.54252i | −0.215084 | − | 0.156267i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.87274 | − | 11.8444i | 0.167429 | − | 0.406977i | ||||
\(848\) | −5.10768 | −0.175399 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.225891 | + | 0.695221i | −0.00774800 | + | 0.0238459i | ||||
\(851\) | 0.164949 | + | 0.507660i | 0.00565437 | + | 0.0174024i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.5825 | + | 22.2195i | −1.04713 | + | 0.760781i | −0.971664 | − | 0.236367i | \(-0.924043\pi\) |
−0.0754620 | + | 0.997149i | \(0.524043\pi\) | |||||||
\(854\) | 2.84548 | + | 8.75750i | 0.0973704 | + | 0.299675i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5530 | + | 14.9326i | 0.702487 | + | 0.510387i | ||||
\(857\) | 19.8270 | 0.677276 | 0.338638 | − | 0.940917i | \(-0.390034\pi\) | ||||
0.338638 | + | 0.940917i | \(0.390034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7153 | −0.536199 | −0.268099 | − | 0.963391i | \(-0.586396\pi\) | ||||
−0.268099 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(860\) | −27.4759 | − | 19.9624i | −0.936921 | − | 0.680713i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.52979 | − | 13.9413i | −0.154285 | − | 0.474842i | ||||
\(863\) | −6.57548 | + | 4.77736i | −0.223832 | + | 0.162623i | −0.694050 | − | 0.719927i | \(-0.744175\pi\) |
0.470218 | + | 0.882550i | \(0.344175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4739 | − | 44.5462i | −0.492128 | − | 1.51462i | ||||
\(866\) | 2.95233 | − | 9.08634i | 0.100324 | − | 0.308766i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.6654 | 0.429891 | ||||||||
\(869\) | 16.4052 | + | 24.4882i | 0.556508 | + | 0.830707i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.2879 | + | 27.0913i | 1.26345 | + | 0.917953i | ||||
\(872\) | −3.40401 | + | 10.4765i | −0.115274 | + | 0.354778i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.254531 | − | 0.184928i | 0.00860964 | − | 0.00625527i | ||||
\(875\) | −2.75479 | + | 2.00148i | −0.0931290 | + | 0.0676622i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.782904 | + | 2.40953i | −0.0264368 | + | 0.0813640i | −0.963404 | − | 0.268052i | \(-0.913620\pi\) |
0.936968 | + | 0.349416i | \(0.113620\pi\) | |||||||
\(878\) | 18.3437 | + | 13.3275i | 0.619071 | + | 0.449782i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.9860 | − | 16.5135i | 0.437759 | − | 0.556671i | ||||
\(881\) | −47.4109 | −1.59731 | −0.798657 | − | 0.601786i | \(-0.794456\pi\) | ||||
−0.798657 | + | 0.601786i | \(0.794456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.19295 | − | 25.2153i | 0.275715 | − | 0.848563i | −0.713315 | − | 0.700844i | \(-0.752807\pi\) |
0.989029 | − | 0.147719i | \(-0.0471930\pi\) | |||||||
\(884\) | −0.638353 | − | 1.96465i | −0.0214701 | − | 0.0660783i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0472 | + | 10.9325i | −0.505522 | + | 0.367283i | ||||
\(887\) | −14.7801 | − | 45.4884i | −0.496266 | − | 1.52735i | −0.814974 | − | 0.579498i | \(-0.803249\pi\) |
0.318707 | − | 0.947853i | \(-0.396751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4177 | − | 9.02200i | −0.416477 | − | 0.302588i | ||||
\(890\) | 3.69528 | 0.123866 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.639221 | 0.0214027 | ||||||||
\(893\) | 1.68854 | + | 1.22680i | 0.0565048 | + | 0.0410531i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.54430 | + | 20.1413i | 0.218752 | + | 0.673249i | ||||
\(896\) | −10.8559 | + | 7.88728i | −0.362671 | + | 0.263496i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.61459 | − | 14.2023i | −0.153991 | − | 0.473935i | ||||
\(899\) | −15.5345 | + | 47.8104i | −0.518106 | + | 1.59457i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.761187 | 0.0253588 | ||||||||
\(902\) | −10.7108 | + | 3.03468i | −0.356631 | + | 0.101044i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.9516 | + | 23.9407i | 1.09595 | + | 0.796257i | ||||
\(905\) | 2.31891 | − | 7.13687i | 0.0770832 | − | 0.237238i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.3946 | + | 27.8953i | −1.27487 | + | 0.926249i | −0.999385 | − | 0.0350562i | \(-0.988839\pi\) |
−0.275487 | + | 0.961305i | \(0.588839\pi\) | |||||||
\(908\) | 24.2817 | − | 17.6417i | 0.805815 | − | 0.585459i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.46479 | − | 7.58583i | 0.0817068 | − | 0.251468i | ||||
\(911\) | 23.0022 | + | 16.7120i | 0.762095 | + | 0.553695i | 0.899552 | − | 0.436813i | \(-0.143893\pi\) |
−0.137457 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.8204 | + | 4.48236i | −0.523578 | + | 0.148345i | ||||
\(914\) | −7.34762 | −0.243038 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.91352 | + | 21.2776i | −0.228429 | + | 0.703032i | ||||
\(917\) | 6.46615 | + | 19.9008i | 0.213531 | + | 0.657181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.0442 | + | 22.5550i | −1.02406 | + | 0.744020i | −0.967110 | − | 0.254358i | \(-0.918136\pi\) |
−0.0569449 | + | 0.998377i | \(0.518136\pi\) | |||||||
\(920\) | 0.168154 | + | 0.517523i | 0.00554386 | + | 0.0170622i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.89190 | + | 6.46034i | 0.292839 | + | 0.212760i | ||||
\(923\) | −34.4013 | −1.13233 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.1383 | −0.826543 | ||||||||
\(926\) | 10.6893 | + | 7.76621i | 0.351271 | + | 0.255214i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.9791 | − | 39.9457i | −0.426061 | − | 1.31128i | ||||
\(929\) | −10.8309 | + | 7.86907i | −0.355349 | + | 0.258176i | −0.751109 | − | 0.660178i | \(-0.770481\pi\) |
0.395761 | + | 0.918354i | \(0.370481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1078 | − | 34.1862i | −0.364042 | − | 1.12041i | ||||
\(932\) | 1.73491 | − | 5.33951i | 0.0568289 | − | 0.174901i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.20041 | 0.301047 | ||||||||
\(935\) | −1.93528 | + | 2.46098i | −0.0632905 | + | 0.0804826i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9588 | + | 14.5010i | 0.652027 | + | 0.473725i | 0.863961 | − | 0.503559i | \(-0.167976\pi\) |
−0.211934 | + | 0.977284i | \(0.567976\pi\) | |||||||
\(938\) | −2.42815 | + | 7.47309i | −0.0792820 | + | 0.244005i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.32725 | + | 0.964304i | −0.0432901 | + | 0.0314521i | ||||
\(941\) | −6.71670 | + | 4.87997i | −0.218958 | + | 0.159082i | −0.691858 | − | 0.722034i | \(-0.743207\pi\) |
0.472899 | + | 0.881116i | \(0.343207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.153481 | + | 0.472367i | −0.00499804 | + | 0.0153824i | ||||
\(944\) | 3.91616 | + | 2.84526i | 0.127460 | + | 0.0926053i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.23646 | + | 10.8020i | 0.235278 | + | 0.351202i | ||||
\(947\) | 37.9496 | 1.23320 | 0.616598 | − | 0.787278i | \(-0.288510\pi\) | ||||
0.616598 | + | 0.787278i | \(0.288510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.59314 | + | 11.0585i | −0.116638 | + | 0.358975i | ||||
\(950\) | 4.57863 | + | 14.0916i | 0.148550 | + | 0.457191i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.626929 | − | 0.455490i | 0.0203189 | − | 0.0147625i | ||||
\(953\) | −15.0400 | − | 46.2884i | −0.487194 | − | 1.49943i | −0.828778 | − | 0.559578i | \(-0.810963\pi\) |
0.341583 | − | 0.939852i | \(-0.389037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.7373 | + | 20.8789i | 0.929918 | + | 0.675625i | ||||
\(956\) | 38.6490 | 1.25000 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.47032 | −0.305972 | ||||||||
\(959\) | −15.4497 | − | 11.2249i | −0.498897 | − | 0.362470i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.59254 | + | 11.0567i | 0.115888 | + | 0.356668i | ||||
\(962\) | −11.5165 | + | 8.36721i | −0.371306 | + | 0.269770i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.80746 | − | 24.0289i | −0.251461 | − | 0.773918i | ||||
\(965\) | 6.26373 | − | 19.2778i | 0.201636 | − | 0.620573i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9780 | 0.353029 | 0.176515 | − | 0.984298i | \(-0.443518\pi\) | ||||
0.176515 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(968\) | −19.8386 | + | 12.2229i | −0.637637 | + | 0.392858i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.124770 | + | 0.0906508i | 0.00400613 | + | 0.00291062i | ||||
\(971\) | 4.03687 | − | 12.4242i | 0.129549 | − | 0.398712i | −0.865153 | − | 0.501508i | \(-0.832779\pi\) |
0.994702 | + | 0.102796i | \(0.0327789\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2108 | + | 8.14510i | −0.359401 | + | 0.261120i | ||||
\(974\) | −10.6518 | + | 7.73897i | −0.341305 | + | 0.247973i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.91708 | + | 27.4439i | −0.285429 | + | 0.878459i | ||||
\(977\) | 8.96092 | + | 6.51049i | 0.286685 | + | 0.208289i | 0.721828 | − | 0.692072i | \(-0.243302\pi\) |
−0.435143 | + | 0.900361i | \(0.643302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.62642 | + | 2.43556i | 0.211781 | + | 0.0778409i | ||||
\(980\) | 28.2544 | 0.902554 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.79262 | + | 23.9832i | −0.248673 | + | 0.765336i | ||||
\(983\) | −8.16778 | − | 25.1378i | −0.260512 | − | 0.801772i | −0.992693 | − | 0.120663i | \(-0.961498\pi\) |
0.732182 | − | 0.681109i | \(-0.238502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.1863 | − | 36.4625i | 1.59907 | − | 1.16179i | ||||
\(986\) | 0.431959 | + | 1.32943i | 0.0137564 | + | 0.0423378i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.8745 | − | 24.6113i | −1.07769 | − | 0.782989i | ||||
\(989\) | 0.580083 | 0.0184456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9911 | −0.603272 | −0.301636 | − | 0.953423i | \(-0.597533\pi\) | ||||
−0.301636 | + | 0.953423i | \(0.597533\pi\) | |||||||
\(992\) | −28.8122 | − | 20.9333i | −0.914788 | − | 0.664633i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.81234 | − | 5.57782i | −0.0574841 | − | 0.176918i | ||||
\(995\) | 32.2938 | − | 23.4628i | 1.02378 | − | 0.743822i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.83334 | + | 21.0309i | 0.216414 | + | 0.666054i | 0.999050 | + | 0.0435746i | \(0.0138746\pi\) |
−0.782636 | + | 0.622480i | \(0.786125\pi\) | |||||||
\(998\) | −3.58956 | + | 11.0475i | −0.113625 | + | 0.349703i | ||||
\(999\) | 0 | 0 |
(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 | 891.2.f.f.730.4 | 36 | ||
3.2 | odd | 2 | 891.2.f.e.730.6 | 36 | |||
9.2 | odd | 6 | 297.2.n.b.37.6 | 72 | |||
9.4 | even | 3 | 99.2.m.b.70.6 | yes | 72 | ||
9.5 | odd | 6 | 297.2.n.b.235.4 | 72 | |||
9.7 | even | 3 | 99.2.m.b.4.4 | ✓ | 72 | ||
11.3 | even | 5 | inner | 891.2.f.f.487.4 | 36 | ||
11.5 | even | 5 | 9801.2.a.cm.1.11 | 18 | |||
11.6 | odd | 10 | 9801.2.a.co.1.8 | 18 | |||
33.5 | odd | 10 | 9801.2.a.cp.1.8 | 18 | |||
33.14 | odd | 10 | 891.2.f.e.487.6 | 36 | |||
33.17 | even | 10 | 9801.2.a.cn.1.11 | 18 | |||
99.14 | odd | 30 | 297.2.n.b.289.6 | 72 | |||
99.16 | even | 15 | 1089.2.e.p.364.8 | 36 | |||
99.25 | even | 15 | 99.2.m.b.58.6 | yes | 72 | ||
99.47 | odd | 30 | 297.2.n.b.91.4 | 72 | |||
99.49 | even | 15 | 1089.2.e.p.727.8 | 36 | |||
99.58 | even | 15 | 99.2.m.b.25.4 | yes | 72 | ||
99.61 | odd | 30 | 1089.2.e.o.364.11 | 36 | |||
99.94 | odd | 30 | 1089.2.e.o.727.11 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.4 | ✓ | 72 | 9.7 | even | 3 | ||
99.2.m.b.25.4 | yes | 72 | 99.58 | even | 15 | ||
99.2.m.b.58.6 | yes | 72 | 99.25 | even | 15 | ||
99.2.m.b.70.6 | yes | 72 | 9.4 | even | 3 | ||
297.2.n.b.37.6 | 72 | 9.2 | odd | 6 | |||
297.2.n.b.91.4 | 72 | 99.47 | odd | 30 | |||
297.2.n.b.235.4 | 72 | 9.5 | odd | 6 | |||
297.2.n.b.289.6 | 72 | 99.14 | odd | 30 | |||
891.2.f.e.487.6 | 36 | 33.14 | odd | 10 | |||
891.2.f.e.730.6 | 36 | 3.2 | odd | 2 | |||
891.2.f.f.487.4 | 36 | 11.3 | even | 5 | inner | ||
891.2.f.f.730.4 | 36 | 1.1 | even | 1 | trivial | ||
1089.2.e.o.364.11 | 36 | 99.61 | odd | 30 | |||
1089.2.e.o.727.11 | 36 | 99.94 | odd | 30 | |||
1089.2.e.p.364.8 | 36 | 99.16 | even | 15 | |||
1089.2.e.p.727.8 | 36 | 99.49 | even | 15 | |||
9801.2.a.cm.1.11 | 18 | 11.5 | even | 5 | |||
9801.2.a.cn.1.11 | 18 | 33.17 | even | 10 | |||
9801.2.a.co.1.8 | 18 | 11.6 | odd | 10 | |||
9801.2.a.cp.1.8 | 18 | 33.5 | odd | 10 |