Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(295,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.f (of order \(3\), degree \(2\), 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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.1 | ||
Root | \(1.01575 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.295 |
Dual form | 882.2.f.p.589.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.707107 | − | 1.58114i | −0.408248 | − | 0.912871i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.01575 | + | 1.75934i | 0.454259 | + | 0.786799i | 0.998645 | − | 0.0520355i | \(-0.0165709\pi\) |
−0.544387 | + | 0.838834i | \(0.683238\pi\) | |||||||
\(6\) | 1.72286 | + | 0.178197i | 0.703355 | + | 0.0727486i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(10\) | −2.03151 | −0.642419 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | −1.01575 | + | 1.40294i | −0.293223 | + | 0.404994i | ||||
\(13\) | −2.12132 | − | 3.67423i | −0.588348 | − | 1.01905i | −0.994449 | − | 0.105221i | \(-0.966445\pi\) |
0.406100 | − | 0.913828i | \(-0.366888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.06351 | − | 2.85008i | 0.532796 | − | 0.735889i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | −0.936492 | − | 2.85008i | −0.220733 | − | 0.671771i | ||||
\(19\) | 0.796921 | 0.182826 | 0.0914131 | − | 0.995813i | \(-0.470862\pi\) | ||||
0.0914131 | + | 0.995813i | \(0.470862\pi\) | |||||||
\(20\) | 1.01575 | − | 1.75934i | 0.227129 | − | 0.393399i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | − | 3.46410i | −0.426401 | − | 0.738549i | ||||
\(23\) | −3.37298 | − | 5.84218i | −0.703316 | − | 1.21818i | −0.967296 | − | 0.253650i | \(-0.918369\pi\) |
0.263980 | − | 0.964528i | \(-0.414965\pi\) | |||||||
\(24\) | −0.707107 | − | 1.58114i | −0.144338 | − | 0.322749i | ||||
\(25\) | 0.436492 | − | 0.756026i | 0.0872983 | − | 0.151205i | ||||
\(26\) | 4.24264 | 0.832050 | ||||||||
\(27\) | 4.94975 | + | 1.58114i | 0.952579 | + | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.43649 | + | 7.68423i | −0.823836 | + | 1.42693i | 0.0789700 | + | 0.996877i | \(0.474837\pi\) |
−0.902806 | + | 0.430049i | \(0.858496\pi\) | |||||||
\(30\) | 1.43649 | + | 3.21209i | 0.262266 | + | 0.586445i | ||||
\(31\) | −2.73861 | − | 4.74342i | −0.491869 | − | 0.851943i | 0.508087 | − | 0.861306i | \(-0.330353\pi\) |
−0.999956 | + | 0.00936313i | \(0.997020\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 6.89144 | + | 0.712788i | 1.19965 | + | 0.124080i | ||||
\(34\) | 0.707107 | − | 1.22474i | 0.121268 | − | 0.210042i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.93649 | + | 0.614017i | 0.489415 | + | 0.102336i | ||||
\(37\) | −9.74597 | −1.60223 | −0.801114 | − | 0.598512i | \(-0.795759\pi\) | ||||
−0.801114 | + | 0.598512i | \(0.795759\pi\) | |||||||
\(38\) | −0.398461 | + | 0.690154i | −0.0646388 | + | 0.111958i | ||||
\(39\) | −4.30948 | + | 5.95218i | −0.690068 | + | 0.953111i | ||||
\(40\) | 1.01575 | + | 1.75934i | 0.160605 | + | 0.278175i | ||||
\(41\) | 2.82843 | + | 4.89898i | 0.441726 | + | 0.765092i | 0.997818 | − | 0.0660290i | \(-0.0210330\pi\) |
−0.556092 | + | 0.831121i | \(0.687700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.43649 | + | 7.68423i | −0.676559 | + | 1.17183i | 0.299452 | + | 0.954111i | \(0.403196\pi\) |
−0.976011 | + | 0.217723i | \(0.930137\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −5.96550 | − | 1.24738i | −0.889284 | − | 0.185948i | ||||
\(46\) | 6.74597 | 0.994639 | ||||||||
\(47\) | 3.44572 | − | 5.96816i | 0.502610 | − | 0.870546i | −0.497386 | − | 0.867530i | \(-0.665707\pi\) |
0.999995 | − | 0.00301623i | \(-0.000960097\pi\) | |||||||
\(48\) | 1.72286 | + | 0.178197i | 0.248673 | + | 0.0257205i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.436492 | + | 0.756026i | 0.0617292 | + | 0.106918i | ||||
\(51\) | 1.00000 | + | 2.23607i | 0.140028 | + | 0.313112i | ||||
\(52\) | −2.12132 | + | 3.67423i | −0.294174 | + | 0.509525i | ||||
\(53\) | −10.6190 | −1.45862 | −0.729312 | − | 0.684181i | \(-0.760160\pi\) | ||||
−0.729312 | + | 0.684181i | \(0.760160\pi\) | |||||||
\(54\) | −3.84418 | + | 3.49604i | −0.523127 | + | 0.475750i | ||||
\(55\) | −8.12602 | −1.09571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.563508 | − | 1.26004i | −0.0746385 | − | 0.166897i | ||||
\(58\) | −4.43649 | − | 7.68423i | −0.582540 | − | 1.00899i | ||||
\(59\) | 1.32440 | + | 2.29393i | 0.172422 | + | 0.298644i | 0.939266 | − | 0.343190i | \(-0.111507\pi\) |
−0.766844 | + | 0.641833i | \(0.778174\pi\) | |||||||
\(60\) | −3.50000 | − | 0.362008i | −0.451848 | − | 0.0467351i | ||||
\(61\) | 0.398461 | − | 0.690154i | 0.0510176 | − | 0.0883652i | −0.839389 | − | 0.543531i | \(-0.817087\pi\) |
0.890406 | + | 0.455166i | \(0.150420\pi\) | |||||||
\(62\) | 5.47723 | 0.695608 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.30948 | − | 7.46423i | 0.534525 | − | 0.925824i | ||||
\(66\) | −4.06301 | + | 5.61177i | −0.500122 | + | 0.690761i | ||||
\(67\) | −0.436492 | − | 0.756026i | −0.0533259 | − | 0.0923632i | 0.838130 | − | 0.545470i | \(-0.183649\pi\) |
−0.891456 | + | 0.453107i | \(0.850316\pi\) | |||||||
\(68\) | 0.707107 | + | 1.22474i | 0.0857493 | + | 0.148522i | ||||
\(69\) | −6.85224 | + | 9.46420i | −0.824912 | + | 1.13936i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.12702 | −0.252430 | −0.126215 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126215 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(72\) | −2.00000 | + | 2.23607i | −0.235702 | + | 0.263523i | ||||
\(73\) | −15.3767 | −1.79971 | −0.899855 | − | 0.436190i | \(-0.856327\pi\) | ||||
−0.899855 | + | 0.436190i | \(0.856327\pi\) | |||||||
\(74\) | 4.87298 | − | 8.44025i | 0.566473 | − | 0.981160i | ||||
\(75\) | −1.50403 | − | 0.155563i | −0.173670 | − | 0.0179629i | ||||
\(76\) | −0.398461 | − | 0.690154i | −0.0457066 | − | 0.0791661i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | − | 6.70820i | −0.339683 | − | 0.759555i | ||||
\(79\) | −2.93649 | + | 5.08615i | −0.330381 | + | 0.572237i | −0.982587 | − | 0.185805i | \(-0.940511\pi\) |
0.652205 | + | 0.758042i | \(0.273844\pi\) | |||||||
\(80\) | −2.03151 | −0.227129 | ||||||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | −5.65685 | −0.624695 | ||||||||
\(83\) | 4.15283 | − | 7.19291i | 0.455832 | − | 0.789524i | −0.542904 | − | 0.839795i | \(-0.682675\pi\) |
0.998736 | + | 0.0502709i | \(0.0160085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.43649 | − | 2.48808i | −0.155809 | − | 0.269870i | ||||
\(86\) | −4.43649 | − | 7.68423i | −0.478399 | − | 0.828612i | ||||
\(87\) | 15.2869 | + | 1.58114i | 1.63893 | + | 0.169516i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | −7.07107 | −0.749532 | −0.374766 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374766 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(90\) | 4.06301 | − | 4.54259i | 0.428279 | − | 0.478831i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.37298 | + | 5.84218i | −0.351658 | + | 0.609089i | ||||
\(93\) | −5.56351 | + | 7.68423i | −0.576909 | + | 0.796817i | ||||
\(94\) | 3.44572 | + | 5.96816i | 0.355399 | + | 0.615569i | ||||
\(95\) | 0.809475 | + | 1.40205i | 0.0830504 | + | 0.143847i | ||||
\(96\) | −1.01575 | + | 1.40294i | −0.103670 | + | 0.143187i | ||||
\(97\) | −8.92295 | + | 15.4550i | −0.905988 | + | 1.56922i | −0.0864021 | + | 0.996260i | \(0.527537\pi\) |
−0.819586 | + | 0.572957i | \(0.805796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.74597 | − | 11.4003i | −0.376484 | − | 1.14578i | ||||
\(100\) | −0.872983 | −0.0872983 | ||||||||
\(101\) | −3.93399 | + | 6.81388i | −0.391447 | + | 0.678006i | −0.992641 | − | 0.121097i | \(-0.961359\pi\) |
0.601194 | + | 0.799103i | \(0.294692\pi\) | |||||||
\(102\) | −2.43649 | − | 0.252009i | −0.241249 | − | 0.0249526i | ||||
\(103\) | −9.01276 | − | 15.6106i | −0.888054 | − | 1.53815i | −0.842173 | − | 0.539207i | \(-0.818724\pi\) |
−0.0458803 | − | 0.998947i | \(-0.514609\pi\) | |||||||
\(104\) | −2.12132 | − | 3.67423i | −0.208013 | − | 0.360288i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30948 | − | 9.19628i | 0.515702 | − | 0.893222i | ||||
\(107\) | 15.7460 | 1.52222 | 0.761110 | − | 0.648623i | \(-0.224655\pi\) | ||||
0.761110 | + | 0.648623i | \(0.224655\pi\) | |||||||
\(108\) | −1.10557 | − | 5.07718i | −0.106383 | − | 0.488552i | ||||
\(109\) | 9.12702 | 0.874210 | 0.437105 | − | 0.899411i | \(-0.356004\pi\) | ||||
0.437105 | + | 0.899411i | \(0.356004\pi\) | |||||||
\(110\) | 4.06301 | − | 7.03734i | 0.387393 | − | 0.670984i | ||||
\(111\) | 6.89144 | + | 15.4097i | 0.654106 | + | 1.46263i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.93649 | + | 3.35410i | 0.182170 | + | 0.315527i | 0.942619 | − | 0.333870i | \(-0.108355\pi\) |
−0.760449 | + | 0.649397i | \(0.775021\pi\) | |||||||
\(114\) | 1.37298 | + | 0.142009i | 0.128592 | + | 0.0133004i | ||||
\(115\) | 6.85224 | − | 11.8684i | 0.638974 | − | 1.10674i | ||||
\(116\) | 8.87298 | 0.823836 | ||||||||
\(117\) | 12.4585 | + | 2.60505i | 1.15179 | + | 0.240837i | ||||
\(118\) | −2.64880 | −0.243842 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.06351 | − | 2.85008i | 0.188372 | − | 0.260176i | ||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0.398461 | + | 0.690154i | 0.0360749 | + | 0.0624836i | ||||
\(123\) | 5.74597 | − | 7.93624i | 0.518096 | − | 0.715586i | ||||
\(124\) | −2.73861 | + | 4.74342i | −0.245935 | + | 0.425971i | ||||
\(125\) | 11.9310 | 1.06714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7460 | 1.30849 | 0.654246 | − | 0.756281i | \(-0.272986\pi\) | ||||
0.654246 | + | 0.756281i | \(0.272986\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 15.2869 | + | 1.58114i | 1.34594 | + | 0.139212i | ||||
\(130\) | 4.30948 | + | 7.46423i | 0.377966 | + | 0.654656i | ||||
\(131\) | 3.93399 | + | 6.81388i | 0.343715 | + | 0.595331i | 0.985119 | − | 0.171871i | \(-0.0549814\pi\) |
−0.641405 | + | 0.767203i | \(0.721648\pi\) | |||||||
\(132\) | −2.82843 | − | 6.32456i | −0.246183 | − | 0.550482i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.872983 | 0.0754143 | ||||||||
\(135\) | 2.24597 | + | 10.3143i | 0.193302 | + | 0.887715i | ||||
\(136\) | −1.41421 | −0.121268 | ||||||||
\(137\) | −7.74597 | + | 13.4164i | −0.661783 | + | 1.14624i | 0.318364 | + | 0.947968i | \(0.396866\pi\) |
−0.980147 | + | 0.198273i | \(0.936467\pi\) | |||||||
\(138\) | −4.77012 | − | 10.6663i | −0.406059 | − | 0.907977i | ||||
\(139\) | −9.23159 | − | 15.9896i | −0.783013 | − | 1.35622i | −0.930179 | − | 0.367107i | \(-0.880348\pi\) |
0.147165 | − | 0.989112i | \(-0.452985\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8730 | − | 1.22803i | −0.999886 | − | 0.103419i | ||||
\(142\) | 1.06351 | − | 1.84205i | 0.0892476 | − | 0.154581i | ||||
\(143\) | 16.9706 | 1.41915 | ||||||||
\(144\) | −0.936492 | − | 2.85008i | −0.0780410 | − | 0.237507i | ||||
\(145\) | −18.0255 | −1.49694 | ||||||||
\(146\) | 7.68836 | − | 13.3166i | 0.636293 | − | 1.10209i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.87298 | + | 8.44025i | 0.400557 | + | 0.693785i | ||||
\(149\) | 0.127017 | + | 0.219999i | 0.0104056 | + | 0.0180230i | 0.871181 | − | 0.490961i | \(-0.163354\pi\) |
−0.860776 | + | 0.508984i | \(0.830021\pi\) | |||||||
\(150\) | 0.886735 | − | 1.22474i | 0.0724016 | − | 0.100000i | ||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | 0.796921 | 0.0646388 | ||||||||
\(153\) | 2.82843 | − | 3.16228i | 0.228665 | − | 0.255655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.56351 | − | 9.63628i | 0.446872 | − | 0.774005i | ||||
\(156\) | 7.30948 | + | 0.756026i | 0.585226 | + | 0.0605305i | ||||
\(157\) | 3.22689 | + | 5.58913i | 0.257534 | + | 0.446061i | 0.965581 | − | 0.260104i | \(-0.0837568\pi\) |
−0.708047 | + | 0.706165i | \(0.750424\pi\) | |||||||
\(158\) | −2.93649 | − | 5.08615i | −0.233615 | − | 0.404633i | ||||
\(159\) | 7.50873 | + | 16.7900i | 0.595481 | + | 1.33154i | ||||
\(160\) | 1.01575 | − | 1.75934i | 0.0803023 | − | 0.139088i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.24597 | + | 3.60611i | 0.647864 | + | 0.283323i | ||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 2.82843 | − | 4.89898i | 0.220863 | − | 0.382546i | ||||
\(165\) | 5.74597 | + | 12.8484i | 0.447323 | + | 1.00024i | ||||
\(166\) | 4.15283 | + | 7.19291i | 0.322322 | + | 0.558278i | ||||
\(167\) | −6.18433 | − | 10.7116i | −0.478558 | − | 0.828887i | 0.521140 | − | 0.853471i | \(-0.325507\pi\) |
−0.999698 | + | 0.0245846i | \(0.992174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.50000 | + | 4.33013i | −0.192308 | + | 0.333087i | ||||
\(170\) | 2.87298 | 0.220348 | ||||||||
\(171\) | −1.59384 | + | 1.78197i | −0.121884 | + | 0.136271i | ||||
\(172\) | 8.87298 | 0.676559 | ||||||||
\(173\) | 6.36396 | − | 11.0227i | 0.483843 | − | 0.838041i | −0.515985 | − | 0.856598i | \(-0.672574\pi\) |
0.999828 | + | 0.0185571i | \(0.00590724\pi\) | |||||||
\(174\) | −9.01276 | + | 12.4483i | −0.683256 | + | 0.943702i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | − | 3.46410i | −0.150756 | − | 0.261116i | ||||
\(177\) | 2.69052 | − | 3.71611i | 0.202232 | − | 0.279320i | ||||
\(178\) | 3.53553 | − | 6.12372i | 0.264999 | − | 0.458993i | ||||
\(179\) | 0.872983 | 0.0652498 | 0.0326249 | − | 0.999468i | \(-0.489613\pi\) | ||||
0.0326249 | + | 0.999468i | \(0.489613\pi\) | |||||||
\(180\) | 1.90249 | + | 5.78996i | 0.141803 | + | 0.431558i | ||||
\(181\) | 7.86799 | 0.584823 | 0.292412 | − | 0.956293i | \(-0.405542\pi\) | ||||
0.292412 | + | 0.956293i | \(0.405542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.37298 | − | 0.142009i | −0.101494 | − | 0.0104976i | ||||
\(184\) | −3.37298 | − | 5.84218i | −0.248660 | − | 0.430691i | ||||
\(185\) | −9.89949 | − | 17.1464i | −0.727825 | − | 1.26063i | ||||
\(186\) | −3.87298 | − | 8.66025i | −0.283981 | − | 0.635001i | ||||
\(187\) | 2.82843 | − | 4.89898i | 0.206835 | − | 0.358249i | ||||
\(188\) | −6.89144 | −0.502610 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.61895 | −0.117451 | ||||||||
\(191\) | 6.93649 | − | 12.0144i | 0.501907 | − | 0.869328i | −0.498091 | − | 0.867125i | \(-0.665965\pi\) |
0.999998 | − | 0.00220333i | \(-0.000701341\pi\) | |||||||
\(192\) | −0.707107 | − | 1.58114i | −0.0510310 | − | 0.114109i | ||||
\(193\) | −8.06351 | − | 13.9664i | −0.580424 | − | 1.00532i | −0.995429 | − | 0.0955048i | \(-0.969553\pi\) |
0.415005 | − | 0.909819i | \(-0.363780\pi\) | |||||||
\(194\) | −8.92295 | − | 15.4550i | −0.640630 | − | 1.10960i | ||||
\(195\) | −14.8492 | − | 1.53587i | −1.06338 | − | 0.109986i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.61895 | −0.471581 | −0.235790 | − | 0.971804i | \(-0.575768\pi\) | ||||
−0.235790 | + | 0.971804i | \(0.575768\pi\) | |||||||
\(198\) | 11.7460 | + | 2.45607i | 0.834750 | + | 0.174545i | ||||
\(199\) | 20.6743 | 1.46556 | 0.732782 | − | 0.680464i | \(-0.238222\pi\) | ||||
0.732782 | + | 0.680464i | \(0.238222\pi\) | |||||||
\(200\) | 0.436492 | − | 0.756026i | 0.0308646 | − | 0.0534591i | ||||
\(201\) | −0.886735 | + | 1.22474i | −0.0625455 | + | 0.0863868i | ||||
\(202\) | −3.93399 | − | 6.81388i | −0.276795 | − | 0.479423i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.43649 | − | 1.98406i | 0.100575 | − | 0.138912i | ||||
\(205\) | −5.74597 | + | 9.95231i | −0.401316 | + | 0.695099i | ||||
\(206\) | 18.0255 | 1.25590 | ||||||||
\(207\) | 19.8095 | + | 4.14214i | 1.37685 | + | 0.287898i | ||||
\(208\) | 4.24264 | 0.294174 | ||||||||
\(209\) | −1.59384 | + | 2.76062i | −0.110248 | + | 0.190956i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.30948 | + | 2.26808i | 0.0901480 | + | 0.156141i | 0.907573 | − | 0.419894i | \(-0.137933\pi\) |
−0.817425 | + | 0.576035i | \(0.804599\pi\) | |||||||
\(212\) | 5.30948 | + | 9.19628i | 0.364656 | + | 0.631603i | ||||
\(213\) | 1.50403 | + | 3.36311i | 0.103054 | + | 0.230436i | ||||
\(214\) | −7.87298 | + | 13.6364i | −0.538186 | + | 0.932166i | ||||
\(215\) | −18.0255 | −1.22933 | ||||||||
\(216\) | 4.94975 | + | 1.58114i | 0.336788 | + | 0.107583i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.56351 | + | 7.90423i | −0.309080 | + | 0.535342i | ||||
\(219\) | 10.8730 | + | 24.3127i | 0.734728 | + | 1.64290i | ||||
\(220\) | 4.06301 | + | 7.03734i | 0.273928 | + | 0.474458i | ||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | −16.7909 | − | 1.73670i | −1.12693 | − | 0.116560i | ||||
\(223\) | −5.74667 | + | 9.95352i | −0.384825 | + | 0.666537i | −0.991745 | − | 0.128226i | \(-0.959072\pi\) |
0.606920 | + | 0.794763i | \(0.292405\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.817542 | + | 2.48808i | 0.0545028 | + | 0.165872i | ||||
\(226\) | −3.87298 | −0.257627 | ||||||||
\(227\) | −3.04726 | + | 5.27801i | −0.202254 | + | 0.350314i | −0.949254 | − | 0.314510i | \(-0.898160\pi\) |
0.747001 | + | 0.664823i | \(0.231493\pi\) | |||||||
\(228\) | −0.809475 | + | 1.11803i | −0.0536088 | + | 0.0740436i | ||||
\(229\) | 3.93399 | + | 6.81388i | 0.259966 | + | 0.450274i | 0.966232 | − | 0.257672i | \(-0.0829554\pi\) |
−0.706267 | + | 0.707946i | \(0.749622\pi\) | |||||||
\(230\) | 6.85224 | + | 11.8684i | 0.451823 | + | 0.782580i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.43649 | + | 7.68423i | −0.291270 | + | 0.504494i | ||||
\(233\) | 22.7460 | 1.49014 | 0.745069 | − | 0.666987i | \(-0.232417\pi\) | ||||
0.745069 | + | 0.666987i | \(0.232417\pi\) | |||||||
\(234\) | −8.48528 | + | 9.48683i | −0.554700 | + | 0.620174i | ||||
\(235\) | 14.0000 | 0.913259 | ||||||||
\(236\) | 1.32440 | − | 2.29393i | 0.0862110 | − | 0.149322i | ||||
\(237\) | 10.1183 | + | 1.04655i | 0.657256 | + | 0.0679806i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | 1.43649 | + | 3.21209i | 0.0927251 | + | 0.207340i | ||||
\(241\) | −0.886735 | + | 1.53587i | −0.0571197 | + | 0.0989341i | −0.893171 | − | 0.449717i | \(-0.851525\pi\) |
0.836052 | + | 0.548651i | \(0.184858\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | −13.4350 | + | 7.90569i | −0.861858 | + | 0.507151i | ||||
\(244\) | −0.796921 | −0.0510176 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.00000 | + | 8.94427i | 0.255031 | + | 0.570266i | ||||
\(247\) | −1.69052 | − | 2.92808i | −0.107566 | − | 0.186309i | ||||
\(248\) | −2.73861 | − | 4.74342i | −0.173902 | − | 0.301207i | ||||
\(249\) | −14.3095 | − | 1.48004i | −0.906826 | − | 0.0937939i | ||||
\(250\) | −5.96550 | + | 10.3325i | −0.377291 | + | 0.653488i | ||||
\(251\) | −25.8935 | −1.63438 | −0.817192 | − | 0.576366i | \(-0.804470\pi\) | ||||
−0.817192 | + | 0.576366i | \(0.804470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.9839 | 1.69646 | ||||||||
\(254\) | −7.37298 | + | 12.7704i | −0.462622 | + | 0.801285i | ||||
\(255\) | −2.91824 | + | 4.03063i | −0.182747 | + | 0.252408i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.98125 | + | 12.0919i | 0.435479 | + | 0.754271i | 0.997335 | − | 0.0729640i | \(-0.0232458\pi\) |
−0.561856 | + | 0.827235i | \(0.689912\pi\) | |||||||
\(258\) | −9.01276 | + | 12.4483i | −0.561110 | + | 0.774996i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.61895 | −0.534525 | ||||||||
\(261\) | −8.30948 | − | 25.2888i | −0.514344 | − | 1.56533i | ||||
\(262\) | −7.86799 | −0.486086 | ||||||||
\(263\) | −2.80948 | + | 4.86615i | −0.173240 | + | 0.300060i | −0.939551 | − | 0.342410i | \(-0.888757\pi\) |
0.766311 | + | 0.642470i | \(0.222090\pi\) | |||||||
\(264\) | 6.89144 | + | 0.712788i | 0.424139 | + | 0.0438691i | ||||
\(265\) | −10.7862 | − | 18.6823i | −0.662593 | − | 1.14764i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00000 | + | 11.1803i | 0.305995 | + | 0.684226i | ||||
\(268\) | −0.436492 | + | 0.756026i | −0.0266630 | + | 0.0461816i | ||||
\(269\) | −3.44572 | −0.210089 | −0.105045 | − | 0.994468i | \(-0.533499\pi\) | ||||
−0.105045 | + | 0.994468i | \(0.533499\pi\) | |||||||
\(270\) | −10.0554 | − | 3.21209i | −0.611955 | − | 0.195482i | ||||
\(271\) | −7.07107 | −0.429537 | −0.214768 | − | 0.976665i | \(-0.568900\pi\) | ||||
−0.214768 | + | 0.976665i | \(0.568900\pi\) | |||||||
\(272\) | 0.707107 | − | 1.22474i | 0.0428746 | − | 0.0742611i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.74597 | − | 13.4164i | −0.467951 | − | 0.810515i | ||||
\(275\) | 1.74597 | + | 3.02410i | 0.105286 | + | 0.182360i | ||||
\(276\) | 11.6224 | + | 1.20211i | 0.699584 | + | 0.0723586i | ||||
\(277\) | 12.1825 | − | 21.1006i | 0.731973 | − | 1.26781i | −0.224066 | − | 0.974574i | \(-0.571933\pi\) |
0.956039 | − | 0.293240i | \(-0.0947336\pi\) | |||||||
\(278\) | 18.4632 | 1.10735 | ||||||||
\(279\) | 16.0838 | + | 3.36311i | 0.962914 | + | 0.201344i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.37298 | − | 5.84218i | 0.201215 | − | 0.348515i | −0.747705 | − | 0.664031i | \(-0.768844\pi\) |
0.948920 | + | 0.315516i | \(0.102178\pi\) | |||||||
\(282\) | 7.00000 | − | 9.66829i | 0.416844 | − | 0.575738i | ||||
\(283\) | 5.25839 | + | 9.10781i | 0.312579 | + | 0.541403i | 0.978920 | − | 0.204244i | \(-0.0654737\pi\) |
−0.666341 | + | 0.745647i | \(0.732140\pi\) | |||||||
\(284\) | 1.06351 | + | 1.84205i | 0.0631076 | + | 0.109306i | ||||
\(285\) | 1.64445 | − | 2.27129i | 0.0974090 | − | 0.134540i | ||||
\(286\) | −8.48528 | + | 14.6969i | −0.501745 | + | 0.869048i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.93649 | + | 0.614017i | 0.173034 | + | 0.0361813i | ||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 9.01276 | − | 15.6106i | 0.529247 | − | 0.916683i | ||||
\(291\) | 30.7460 | + | 3.18008i | 1.80236 | + | 0.186420i | ||||
\(292\) | 7.68836 | + | 13.3166i | 0.449927 | + | 0.779297i | ||||
\(293\) | −3.13707 | − | 5.43357i | −0.183270 | − | 0.317433i | 0.759722 | − | 0.650248i | \(-0.225335\pi\) |
−0.942992 | + | 0.332815i | \(0.892002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.69052 | + | 4.66013i | −0.156648 | + | 0.271323i | ||||
\(296\) | −9.74597 | −0.566473 | ||||||||
\(297\) | −15.3767 | + | 13.9842i | −0.892248 | + | 0.811443i | ||||
\(298\) | −0.254033 | −0.0147158 | ||||||||
\(299\) | −14.3104 | + | 24.7863i | −0.827589 | + | 1.43343i | ||||
\(300\) | 0.617292 | + | 1.38031i | 0.0356394 | + | 0.0796921i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.50000 | − | 9.52628i | −0.316489 | − | 0.548176i | ||||
\(303\) | 13.5554 | + | 1.40205i | 0.778740 | + | 0.0805458i | ||||
\(304\) | −0.398461 | + | 0.690154i | −0.0228533 | + | 0.0395830i | ||||
\(305\) | 1.61895 | 0.0927008 | ||||||||
\(306\) | 1.32440 | + | 4.03063i | 0.0757109 | + | 0.230416i | ||||
\(307\) | 24.1200 | 1.37660 | 0.688302 | − | 0.725425i | \(-0.258357\pi\) | ||||
0.688302 | + | 0.725425i | \(0.258357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3095 | + | 25.2888i | −1.04159 | + | 1.43863i | ||||
\(310\) | 5.56351 | + | 9.63628i | 0.315986 | + | 0.547304i | ||||
\(311\) | −0.707107 | − | 1.22474i | −0.0400963 | − | 0.0694489i | 0.845281 | − | 0.534322i | \(-0.179433\pi\) |
−0.885377 | + | 0.464873i | \(0.846100\pi\) | |||||||
\(312\) | −4.30948 | + | 5.95218i | −0.243976 | + | 0.336976i | ||||
\(313\) | 13.3452 | − | 23.1146i | 0.754316 | − | 1.30651i | −0.191397 | − | 0.981513i | \(-0.561302\pi\) |
0.945714 | − | 0.325001i | \(-0.105365\pi\) | |||||||
\(314\) | −6.45378 | −0.364208 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.87298 | 0.330381 | ||||||||
\(317\) | −0.690525 | + | 1.19602i | −0.0387837 | + | 0.0671754i | −0.884766 | − | 0.466036i | \(-0.845682\pi\) |
0.845982 | + | 0.533212i | \(0.179015\pi\) | |||||||
\(318\) | −18.2950 | − | 1.89226i | −1.02593 | − | 0.106113i | ||||
\(319\) | −17.7460 | − | 30.7369i | −0.993583 | − | 1.72094i | ||||
\(320\) | 1.01575 | + | 1.75934i | 0.0567823 | + | 0.0983499i | ||||
\(321\) | −11.1341 | − | 24.8966i | −0.621444 | − | 1.38959i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.12702 | −0.0627089 | ||||||||
\(324\) | −7.24597 | + | 5.33816i | −0.402554 | + | 0.296565i | ||||
\(325\) | −3.70375 | −0.205447 | ||||||||
\(326\) | −5.00000 | + | 8.66025i | −0.276924 | + | 0.479647i | ||||
\(327\) | −6.45378 | − | 14.4311i | −0.356895 | − | 0.798041i | ||||
\(328\) | 2.82843 | + | 4.89898i | 0.156174 | + | 0.270501i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −14.0000 | − | 1.44803i | −0.770675 | − | 0.0797116i | ||||
\(331\) | 9.18246 | − | 15.9045i | 0.504714 | − | 0.874190i | −0.495272 | − | 0.868738i | \(-0.664931\pi\) |
0.999985 | − | 0.00545133i | \(-0.00173522\pi\) | |||||||
\(332\) | −8.30565 | −0.455832 | ||||||||
\(333\) | 19.4919 | − | 21.7926i | 1.06815 | − | 1.19423i | ||||
\(334\) | 12.3687 | 0.676783 | ||||||||
\(335\) | 0.886735 | − | 1.53587i | 0.0484475 | − | 0.0839136i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.127017 | − | 0.219999i | −0.00691904 | − | 0.0119841i | 0.862545 | − | 0.505980i | \(-0.168869\pi\) |
−0.869464 | + | 0.493996i | \(0.835536\pi\) | |||||||
\(338\) | −2.50000 | − | 4.33013i | −0.135982 | − | 0.235528i | ||||
\(339\) | 3.93399 | − | 5.43357i | 0.213665 | − | 0.295111i | ||||
\(340\) | −1.43649 | + | 2.48808i | −0.0779047 | + | 0.134935i | ||||
\(341\) | 21.9089 | 1.18643 | ||||||||
\(342\) | −0.746310 | − | 2.27129i | −0.0403558 | − | 0.122817i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.43649 | + | 7.68423i | −0.239200 | + | 0.414306i | ||||
\(345\) | −23.6109 | − | 2.44210i | −1.27117 | − | 0.131478i | ||||
\(346\) | 6.36396 | + | 11.0227i | 0.342129 | + | 0.592584i | ||||
\(347\) | 3.87298 | + | 6.70820i | 0.207913 | + | 0.360115i | 0.951057 | − | 0.309016i | \(-0.0999997\pi\) |
−0.743144 | + | 0.669131i | \(0.766666\pi\) | |||||||
\(348\) | −6.27415 | − | 14.0294i | −0.336330 | − | 0.752056i | ||||
\(349\) | 8.21584 | − | 14.2302i | 0.439784 | − | 0.761728i | −0.557889 | − | 0.829916i | \(-0.688388\pi\) |
0.997672 | + | 0.0681880i | \(0.0217218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.69052 | − | 21.5406i | −0.250362 | − | 1.14975i | ||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | −9.01276 | + | 15.6106i | −0.479701 | + | 0.830866i | −0.999729 | − | 0.0232830i | \(-0.992588\pi\) |
0.520028 | + | 0.854149i | \(0.325921\pi\) | |||||||
\(354\) | 1.87298 | + | 4.18812i | 0.0995479 | + | 0.222596i | ||||
\(355\) | −2.16052 | − | 3.74214i | −0.114669 | − | 0.198612i | ||||
\(356\) | 3.53553 | + | 6.12372i | 0.187383 | + | 0.324557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.436492 | + | 0.756026i | −0.0230693 | + | 0.0399572i | ||||
\(359\) | −28.2379 | −1.49034 | −0.745170 | − | 0.666875i | \(-0.767632\pi\) | ||||
−0.745170 | + | 0.666875i | \(0.767632\pi\) | |||||||
\(360\) | −5.96550 | − | 1.24738i | −0.314409 | − | 0.0657426i | ||||
\(361\) | −18.3649 | −0.966575 | ||||||||
\(362\) | −3.93399 | + | 6.81388i | −0.206766 | + | 0.358129i | ||||
\(363\) | −5.07877 | + | 7.01471i | −0.266566 | + | 0.368177i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6190 | − | 27.0528i | −0.817533 | − | 1.41601i | ||||
\(366\) | 0.809475 | − | 1.11803i | 0.0423119 | − | 0.0584406i | ||||
\(367\) | −2.03151 | + | 3.51867i | −0.106044 | + | 0.183673i | −0.914164 | − | 0.405344i | \(-0.867152\pi\) |
0.808120 | + | 0.589017i | \(0.200485\pi\) | |||||||
\(368\) | 6.74597 | 0.351658 | ||||||||
\(369\) | −16.6113 | − | 3.47340i | −0.864750 | − | 0.180818i | ||||
\(370\) | 19.7990 | 1.02930 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.43649 | + | 0.976025i | 0.489259 | + | 0.0506045i | ||||
\(373\) | 4.43649 | + | 7.68423i | 0.229713 | + | 0.397874i | 0.957723 | − | 0.287692i | \(-0.0928880\pi\) |
−0.728010 | + | 0.685566i | \(0.759555\pi\) | |||||||
\(374\) | 2.82843 | + | 4.89898i | 0.146254 | + | 0.253320i | ||||
\(375\) | −8.43649 | − | 18.8646i | −0.435659 | − | 0.974162i | ||||
\(376\) | 3.44572 | − | 5.96816i | 0.177699 | − | 0.307784i | ||||
\(377\) | 37.6449 | 1.93881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3649 | −0.635143 | −0.317572 | − | 0.948234i | \(-0.602867\pi\) | ||||
−0.317572 | + | 0.948234i | \(0.602867\pi\) | |||||||
\(380\) | 0.809475 | − | 1.40205i | 0.0415252 | − | 0.0719237i | ||||
\(381\) | −10.4270 | − | 23.3154i | −0.534190 | − | 1.19449i | ||||
\(382\) | 6.93649 | + | 12.0144i | 0.354902 | + | 0.614708i | ||||
\(383\) | −11.9310 | − | 20.6651i | −0.609646 | − | 1.05594i | −0.991299 | − | 0.131632i | \(-0.957978\pi\) |
0.381653 | − | 0.924306i | \(-0.375355\pi\) | |||||||
\(384\) | 1.72286 | + | 0.178197i | 0.0879193 | + | 0.00909358i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.1270 | 0.820844 | ||||||||
\(387\) | −8.30948 | − | 25.2888i | −0.422394 | − | 1.28550i | ||||
\(388\) | 17.8459 | 0.905988 | ||||||||
\(389\) | −10.4365 | + | 18.0765i | −0.529151 | + | 0.916517i | 0.470271 | + | 0.882522i | \(0.344156\pi\) |
−0.999422 | + | 0.0339945i | \(0.989177\pi\) | |||||||
\(390\) | 8.75472 | − | 12.0919i | 0.443313 | − | 0.612296i | ||||
\(391\) | 4.77012 | + | 8.26209i | 0.241235 | + | 0.417832i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.99193 | − | 11.0383i | 0.403140 | − | 0.556810i | ||||
\(394\) | 3.30948 | − | 5.73218i | 0.166729 | − | 0.288783i | ||||
\(395\) | −11.9310 | −0.600314 | ||||||||
\(396\) | −8.00000 | + | 8.94427i | −0.402015 | + | 0.449467i | ||||
\(397\) | −7.07107 | −0.354887 | −0.177443 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177443 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(398\) | −10.3372 | + | 17.9045i | −0.518155 | + | 0.897471i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.436492 | + | 0.756026i | 0.0218246 | + | 0.0378013i | ||||
\(401\) | −1.93649 | − | 3.35410i | −0.0967038 | − | 0.167496i | 0.813615 | − | 0.581405i | \(-0.197497\pi\) |
−0.910318 | + | 0.413909i | \(0.864163\pi\) | |||||||
\(402\) | −0.617292 | − | 1.38031i | −0.0307877 | − | 0.0688435i | ||||
\(403\) | −11.6190 | + | 20.1246i | −0.578781 | + | 1.00248i | ||||
\(404\) | 7.86799 | 0.391447 | ||||||||
\(405\) | 14.7202 | − | 10.8445i | 0.731454 | − | 0.538868i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4919 | − | 33.7610i | 0.966179 | − | 1.67347i | ||||
\(408\) | 1.00000 | + | 2.23607i | 0.0495074 | + | 0.110702i | ||||
\(409\) | −15.8144 | − | 27.3913i | −0.781971 | − | 1.35441i | −0.930792 | − | 0.365549i | \(-0.880881\pi\) |
0.148821 | − | 0.988864i | \(-0.452452\pi\) | |||||||
\(410\) | −5.74597 | − | 9.95231i | −0.283773 | − | 0.491509i | ||||
\(411\) | 26.6904 | + | 2.76062i | 1.31654 | + | 0.136171i | ||||
\(412\) | −9.01276 | + | 15.6106i | −0.444027 | + | 0.769077i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.4919 | + | 15.0844i | −0.663092 | + | 0.741360i | ||||
\(415\) | 16.8730 | 0.828262 | ||||||||
\(416\) | −2.12132 | + | 3.67423i | −0.104006 | + | 0.180144i | ||||
\(417\) | −18.7540 | + | 25.9028i | −0.918389 | + | 1.26846i | ||||
\(418\) | −1.59384 | − | 2.76062i | −0.0779574 | − | 0.135026i | ||||
\(419\) | −1.99230 | − | 3.45077i | −0.0973304 | − | 0.168581i | 0.813248 | − | 0.581917i | \(-0.197697\pi\) |
−0.910579 | + | 0.413335i | \(0.864364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.56351 | − | 4.44013i | 0.124938 | − | 0.216399i | −0.796771 | − | 0.604282i | \(-0.793460\pi\) |
0.921709 | + | 0.387883i | \(0.126794\pi\) | |||||||
\(422\) | −2.61895 | −0.127488 | ||||||||
\(423\) | 6.45378 | + | 19.6412i | 0.313793 | + | 0.954987i | ||||
\(424\) | −10.6190 | −0.515702 | ||||||||
\(425\) | −0.617292 | + | 1.06918i | −0.0299431 | + | 0.0518629i | ||||
\(426\) | −3.66455 | − | 0.379028i | −0.177548 | − | 0.0183640i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.87298 | − | 13.6364i | −0.380555 | − | 0.659141i | ||||
\(429\) | −12.0000 | − | 26.8328i | −0.579365 | − | 1.29550i | ||||
\(430\) | 9.01276 | − | 15.6106i | 0.434634 | − | 0.752808i | ||||
\(431\) | 9.49193 | 0.457210 | 0.228605 | − | 0.973519i | \(-0.426584\pi\) | ||||
0.228605 | + | 0.973519i | \(0.426584\pi\) | |||||||
\(432\) | −3.84418 | + | 3.49604i | −0.184953 | + | 0.168203i | ||||
\(433\) | 29.6985 | 1.42722 | 0.713609 | − | 0.700544i | \(-0.247059\pi\) | ||||
0.713609 | + | 0.700544i | \(0.247059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.7460 | + | 28.5008i | 0.611122 | + | 1.36651i | ||||
\(436\) | −4.56351 | − | 7.90423i | −0.218552 | − | 0.378544i | ||||
\(437\) | −2.68800 | − | 4.65576i | −0.128585 | − | 0.222715i | ||||
\(438\) | −26.4919 | − | 2.74009i | −1.26583 | − | 0.130926i | ||||
\(439\) | 5.47723 | − | 9.48683i | 0.261414 | − | 0.452782i | −0.705204 | − | 0.709004i | \(-0.749145\pi\) |
0.966618 | + | 0.256223i | \(0.0824780\pi\) | |||||||
\(440\) | −8.12602 | −0.387393 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −12.1825 | + | 21.1006i | −0.578806 | + | 1.00252i | 0.416811 | + | 0.908993i | \(0.363148\pi\) |
−0.995617 | + | 0.0935281i | \(0.970185\pi\) | |||||||
\(444\) | 9.89949 | − | 13.6730i | 0.469809 | − | 0.648893i | ||||
\(445\) | −7.18246 | − | 12.4404i | −0.340481 | − | 0.589731i | ||||
\(446\) | −5.74667 | − | 9.95352i | −0.272113 | − | 0.471313i | ||||
\(447\) | 0.258035 | − | 0.356394i | 0.0122046 | − | 0.0168569i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | −2.56351 | − | 0.536026i | −0.120845 | − | 0.0252685i | ||||
\(451\) | −22.6274 | −1.06548 | ||||||||
\(452\) | 1.93649 | − | 3.35410i | 0.0910849 | − | 0.157764i | ||||
\(453\) | 18.9515 | + | 1.96017i | 0.890417 | + | 0.0920967i | ||||
\(454\) | −3.04726 | − | 5.27801i | −0.143015 | − | 0.247709i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.563508 | − | 1.26004i | −0.0263887 | − | 0.0590069i | ||||
\(457\) | −16.9365 | + | 29.3349i | −0.792256 | + | 1.37223i | 0.132312 | + | 0.991208i | \(0.457760\pi\) |
−0.924567 | + | 0.381019i | \(0.875573\pi\) | |||||||
\(458\) | −7.86799 | −0.367647 | ||||||||
\(459\) | −7.00000 | − | 2.23607i | −0.326732 | − | 0.104371i | ||||
\(460\) | −13.7045 | −0.638974 | ||||||||
\(461\) | −4.98895 | + | 8.64112i | −0.232359 | + | 0.402457i | −0.958502 | − | 0.285087i | \(-0.907978\pi\) |
0.726143 | + | 0.687544i | \(0.241311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8095 | − | 18.7226i | −0.502359 | − | 0.870111i | −0.999996 | − | 0.00272598i | \(-0.999132\pi\) |
0.497637 | − | 0.867385i | \(-0.334201\pi\) | |||||||
\(464\) | −4.43649 | − | 7.68423i | −0.205959 | − | 0.356731i | ||||
\(465\) | −19.1703 | − | 1.98280i | −0.889001 | − | 0.0919502i | ||||
\(466\) | −11.3730 | + | 19.6986i | −0.526843 | + | 0.912519i | ||||
\(467\) | −39.0591 | −1.80744 | −0.903720 | − | 0.428125i | \(-0.859174\pi\) | ||||
−0.903720 | + | 0.428125i | \(0.859174\pi\) | |||||||
\(468\) | −3.97320 | − | 12.0919i | −0.183661 | − | 0.558948i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.00000 | + | 12.1244i | −0.322886 | + | 0.559255i | ||||
\(471\) | 6.55544 | − | 9.05427i | 0.302059 | − | 0.417199i | ||||
\(472\) | 1.32440 | + | 2.29393i | 0.0609604 | + | 0.105587i | ||||
\(473\) | −17.7460 | − | 30.7369i | −0.815960 | − | 1.41328i | ||||
\(474\) | −5.96550 | + | 8.23945i | −0.274005 | + | 0.378451i | ||||
\(475\) | 0.347849 | − | 0.602493i | 0.0159604 | − | 0.0276443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.2379 | − | 23.7447i | 0.972417 | − | 1.08719i | ||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | −9.01276 | + | 15.6106i | −0.411803 | + | 0.713265i | −0.995087 | − | 0.0990041i | \(-0.968434\pi\) |
0.583284 | + | 0.812269i | \(0.301768\pi\) | |||||||
\(480\) | −3.50000 | − | 0.362008i | −0.159752 | − | 0.0165233i | ||||
\(481\) | 20.6743 | + | 35.8090i | 0.942668 | + | 1.63275i | ||||
\(482\) | −0.886735 | − | 1.53587i | −0.0403897 | − | 0.0699570i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | −36.2540 | −1.64621 | ||||||||
\(486\) | −0.129018 | − | 15.5879i | −0.00585235 | − | 0.707083i | ||||
\(487\) | 30.4919 | 1.38172 | 0.690861 | − | 0.722988i | \(-0.257232\pi\) | ||||
0.690861 | + | 0.722988i | \(0.257232\pi\) | |||||||
\(488\) | 0.398461 | − | 0.690154i | 0.0180375 | − | 0.0312418i | ||||
\(489\) | −7.07107 | − | 15.8114i | −0.319765 | − | 0.715016i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.87298 | + | 11.9044i | 0.310173 | + | 0.537236i | 0.978400 | − | 0.206722i | \(-0.0662796\pi\) |
−0.668226 | + | 0.743958i | \(0.732946\pi\) | |||||||
\(492\) | −9.74597 | − | 1.00803i | −0.439382 | − | 0.0454457i | ||||
\(493\) | 6.27415 | − | 10.8671i | 0.282573 | − | 0.489431i | ||||
\(494\) | 3.38105 | 0.152121 | ||||||||
\(495\) | 16.2520 | − | 18.1703i | 0.730475 | − | 0.816696i | ||||
\(496\) | 5.47723 | 0.245935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.43649 | − | 11.6523i | 0.378048 | − | 0.522154i | ||||
\(499\) | 7.12702 | + | 12.3444i | 0.319049 | + | 0.552609i | 0.980290 | − | 0.197564i | \(-0.0633032\pi\) |
−0.661241 | + | 0.750174i | \(0.729970\pi\) | |||||||
\(500\) | −5.96550 | − | 10.3325i | −0.266785 | − | 0.462086i | ||||
\(501\) | −12.5635 | + | 17.3525i | −0.561296 | + | 0.775253i | ||||
\(502\) | 12.9468 | − | 22.4244i | 0.577842 | − | 1.00085i | ||||
\(503\) | −18.0255 | −0.803718 | −0.401859 | − | 0.915702i | \(-0.631636\pi\) | ||||
−0.401859 | + | 0.915702i | \(0.631636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9839 | −0.711273 | ||||||||
\(506\) | −13.4919 | + | 23.3687i | −0.599790 | + | 1.03887i | ||||
\(507\) | 8.61430 | + | 0.890985i | 0.382574 | + | 0.0395700i | ||||
\(508\) | −7.37298 | − | 12.7704i | −0.327123 | − | 0.566594i | ||||
\(509\) | 16.8807 | + | 29.2383i | 0.748226 | + | 1.29597i | 0.948672 | + | 0.316261i | \(0.102427\pi\) |
−0.200446 | + | 0.979705i | \(0.564239\pi\) | |||||||
\(510\) | −2.03151 | − | 4.54259i | −0.0899566 | − | 0.201149i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.94456 | + | 1.26004i | 0.174157 | + | 0.0556323i | ||||
\(514\) | −13.9625 | −0.615860 | ||||||||
\(515\) | 18.3095 | − | 31.7129i | 0.806812 | − | 1.39744i | ||||
\(516\) | −6.27415 | − | 14.0294i | −0.276204 | − | 0.617611i | ||||
\(517\) | 13.7829 | + | 23.8726i | 0.606170 | + | 1.04992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.9284 | − | 2.26808i | −0.962551 | − | 0.0995575i | ||||
\(520\) | 4.30948 | − | 7.46423i | 0.188983 | − | 0.327328i | ||||
\(521\) | −1.41421 | −0.0619578 | −0.0309789 | − | 0.999520i | \(-0.509862\pi\) | ||||
−0.0309789 | + | 0.999520i | \(0.509862\pi\) | |||||||
\(522\) | 26.0554 | + | 5.44816i | 1.14042 | + | 0.238460i | ||||
\(523\) | 31.0115 | 1.35604 | 0.678019 | − | 0.735045i | \(-0.262839\pi\) | ||||
0.678019 | + | 0.735045i | \(0.262839\pi\) | |||||||
\(524\) | 3.93399 | − | 6.81388i | 0.171857 | − | 0.297666i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.80948 | − | 4.86615i | −0.122499 | − | 0.212174i | ||||
\(527\) | 3.87298 | + | 6.70820i | 0.168710 | + | 0.292214i | ||||
\(528\) | −4.06301 | + | 5.61177i | −0.176820 | + | 0.244221i | ||||
\(529\) | −11.2540 | + | 19.4926i | −0.489306 | + | 0.847502i | ||||
\(530\) | 21.5725 | 0.937048 | ||||||||
\(531\) | −7.77817 | − | 1.62641i | −0.337544 | − | 0.0705800i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | − | 20.7846i | 0.519778 | − | 0.900281i | ||||
\(534\) | −12.1825 | − | 1.26004i | −0.527187 | − | 0.0545274i | ||||
\(535\) | 15.9940 | + | 27.7024i | 0.691481 | + | 1.19768i | ||||
\(536\) | −0.436492 | − | 0.756026i | −0.0188536 | − | 0.0326553i | ||||
\(537\) | −0.617292 | − | 1.38031i | −0.0266381 | − | 0.0595647i | ||||
\(538\) | 1.72286 | − | 2.98408i | 0.0742778 | − | 0.128653i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.80948 | − | 7.10222i | 0.336066 | − | 0.305631i | ||||
\(541\) | 16.1109 | 0.692661 | 0.346330 | − | 0.938113i | \(-0.387428\pi\) | ||||
0.346330 | + | 0.938113i | \(0.387428\pi\) | |||||||
\(542\) | 3.53553 | − | 6.12372i | 0.151864 | − | 0.263036i | ||||
\(543\) | −5.56351 | − | 12.4404i | −0.238753 | − | 0.533868i | ||||
\(544\) | 0.707107 | + | 1.22474i | 0.0303170 | + | 0.0525105i | ||||
\(545\) | 9.27079 | + | 16.0575i | 0.397117 | + | 0.687827i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.4919 | + | 25.1008i | −0.619630 | + | 1.07323i | 0.369923 | + | 0.929062i | \(0.379384\pi\) |
−0.989553 | + | 0.144169i | \(0.953949\pi\) | |||||||
\(548\) | 15.4919 | 0.661783 | ||||||||
\(549\) | 0.746310 | + | 2.27129i | 0.0318517 | + | 0.0969364i | ||||
\(550\) | −3.49193 | −0.148897 | ||||||||
\(551\) | −3.53553 | + | 6.12372i | −0.150619 | + | 0.260879i | ||||
\(552\) | −6.85224 | + | 9.46420i | −0.291651 | + | 0.402823i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.1825 | + | 21.1006i | 0.517583 | + | 0.896480i | ||||
\(555\) | −20.1109 | + | 27.7768i | −0.853659 | + | 1.17906i | ||||
\(556\) | −9.23159 | + | 15.9896i | −0.391507 | + | 0.678109i | ||||
\(557\) | 3.38105 | 0.143260 | 0.0716298 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716298 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(558\) | −10.9545 | + | 12.2474i | −0.463739 | + | 0.518476i | ||||
\(559\) | 37.6449 | 1.59221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.74597 | − | 1.00803i | −0.411475 | − | 0.0425592i | ||||
\(562\) | 3.37298 | + | 5.84218i | 0.142281 | + | 0.246437i | ||||
\(563\) | −2.60960 | − | 4.51995i | −0.109981 | − | 0.190493i | 0.805781 | − | 0.592213i | \(-0.201746\pi\) |
−0.915762 | + | 0.401720i | \(0.868412\pi\) | |||||||
\(564\) | 4.87298 | + | 10.8963i | 0.205190 | + | 0.458818i | ||||
\(565\) | −3.93399 | + | 6.81388i | −0.165504 | + | 0.286662i | ||||
\(566\) | −10.5168 | −0.442054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.12702 | −0.0892476 | ||||||||
\(569\) | −3.74597 | + | 6.48820i | −0.157039 | + | 0.272000i | −0.933800 | − | 0.357796i | \(-0.883528\pi\) |
0.776761 | + | 0.629796i | \(0.216862\pi\) | |||||||
\(570\) | 1.14477 | + | 2.55978i | 0.0479492 | + | 0.107218i | ||||
\(571\) | −0.254033 | − | 0.439999i | −0.0106310 | − | 0.0184134i | 0.860661 | − | 0.509178i | \(-0.170051\pi\) |
−0.871292 | + | 0.490765i | \(0.836717\pi\) | |||||||
\(572\) | −8.48528 | − | 14.6969i | −0.354787 | − | 0.614510i | ||||
\(573\) | −23.9012 | − | 2.47212i | −0.998487 | − | 0.103274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.88912 | −0.245593 | ||||||||
\(576\) | −2.00000 | + | 2.23607i | −0.0833333 | + | 0.0931695i | ||||
\(577\) | −35.1757 | −1.46438 | −0.732192 | − | 0.681098i | \(-0.761503\pi\) | ||||
−0.732192 | + | 0.681098i | \(0.761503\pi\) | |||||||
\(578\) | 7.50000 | − | 12.9904i | 0.311959 | − | 0.540329i | ||||
\(579\) | −16.3811 | + | 22.6253i | −0.680774 | + | 0.940274i | ||||
\(580\) | 9.01276 | + | 15.6106i | 0.374234 | + | 0.648193i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.1270 | + | 25.0367i | −0.751389 | + | 1.03781i | ||||
\(583\) | 21.2379 | − | 36.7851i | 0.879584 | − | 1.52348i | ||||
\(584\) | −15.3767 | −0.636293 | ||||||||
\(585\) | 8.07157 | + | 24.5647i | 0.333719 | + | 1.01563i | ||||
\(586\) | 6.27415 | 0.259183 | ||||||||
\(587\) | −14.8884 | + | 25.7875i | −0.614512 | + | 1.06437i | 0.375958 | + | 0.926637i | \(0.377314\pi\) |
−0.990470 | + | 0.137729i | \(0.956020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.18246 | − | 3.78013i | −0.0899266 | − | 0.155757i | ||||
\(590\) | −2.69052 | − | 4.66013i | −0.110767 | − | 0.191854i | ||||
\(591\) | 4.68030 | + | 10.4655i | 0.192522 | + | 0.430492i | ||||
\(592\) | 4.87298 | − | 8.44025i | 0.200278 | − | 0.346892i | ||||
\(593\) | −22.8070 | −0.936573 | −0.468287 | − | 0.883577i | \(-0.655129\pi\) | ||||
−0.468287 | + | 0.883577i | \(0.655129\pi\) | |||||||
\(594\) | −4.42227 | − | 20.3087i | −0.181448 | − | 0.833276i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.127017 | − | 0.219999i | 0.00520280 | − | 0.00901152i | ||||
\(597\) | −14.6190 | − | 32.6890i | −0.598314 | − | 1.33787i | ||||
\(598\) | −14.3104 | − | 24.7863i | −0.585194 | − | 1.01359i | ||||
\(599\) | −0.618950 | − | 1.07205i | −0.0252896 | − | 0.0438029i | 0.853104 | − | 0.521742i | \(-0.174717\pi\) |
−0.878393 | + | 0.477939i | \(0.841384\pi\) | |||||||
\(600\) | −1.50403 | − | 0.155563i | −0.0614017 | − | 0.00635083i | ||||
\(601\) | −18.8224 | + | 32.6014i | −0.767783 | + | 1.32984i | 0.170979 | + | 0.985275i | \(0.445307\pi\) |
−0.938762 | + | 0.344565i | \(0.888026\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.56351 | + | 0.536026i | 0.104394 | + | 0.0218287i | ||||
\(604\) | 11.0000 | 0.447584 | ||||||||
\(605\) | 5.07877 | − | 8.79668i | 0.206481 | − | 0.357636i | ||||
\(606\) | −7.99193 | + | 11.0383i | −0.324650 | + | 0.448402i | ||||
\(607\) | 7.86799 | + | 13.6278i | 0.319352 | + | 0.553134i | 0.980353 | − | 0.197251i | \(-0.0632015\pi\) |
−0.661001 | + | 0.750385i | \(0.729868\pi\) | |||||||
\(608\) | −0.398461 | − | 0.690154i | −0.0161597 | − | 0.0279894i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.809475 | + | 1.40205i | −0.0327747 | + | 0.0567674i | ||||
\(611\) | −29.2379 | −1.18284 | ||||||||
\(612\) | −4.15283 | − | 0.868351i | −0.167868 | − | 0.0351010i | ||||
\(613\) | 3.38105 | 0.136559 | 0.0682797 | − | 0.997666i | \(-0.478249\pi\) | ||||
0.0682797 | + | 0.997666i | \(0.478249\pi\) | |||||||
\(614\) | −12.0600 | + | 20.8886i | −0.486703 | + | 0.842994i | ||||
\(615\) | 19.7990 | + | 2.04783i | 0.798372 | + | 0.0825764i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8730 | + | 24.0287i | 0.558505 | + | 0.967360i | 0.997622 | + | 0.0689293i | \(0.0219583\pi\) |
−0.439116 | + | 0.898430i | \(0.644708\pi\) | |||||||
\(618\) | −12.7460 | − | 28.5008i | −0.512718 | − | 1.14647i | ||||
\(619\) | 11.1733 | − | 19.3527i | 0.449092 | − | 0.777850i | −0.549235 | − | 0.835668i | \(-0.685081\pi\) |
0.998327 | + | 0.0578175i | \(0.0184142\pi\) | |||||||
\(620\) | −11.1270 | −0.446872 | ||||||||
\(621\) | −7.45812 | − | 34.2505i | −0.299284 | − | 1.37442i | ||||
\(622\) | 1.41421 | 0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | − | 6.70820i | −0.120096 | − | 0.268543i | ||||
\(625\) | 9.93649 | + | 17.2105i | 0.397460 | + | 0.688420i | ||||
\(626\) | 13.3452 | + | 23.1146i | 0.533382 | + | 0.923845i | ||||
\(627\) | 5.49193 | + | 0.568036i | 0.219327 | + | 0.0226852i | ||||
\(628\) | 3.22689 | − | 5.58913i | 0.128767 | − | 0.223031i | ||||
\(629\) | 13.7829 | 0.549559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6190 | −1.09949 | −0.549747 | − | 0.835332i | \(-0.685276\pi\) | ||||
−0.549747 | + | 0.835332i | \(0.685276\pi\) | |||||||
\(632\) | −2.93649 | + | 5.08615i | −0.116807 | + | 0.202316i | ||||
\(633\) | 2.66021 | − | 3.67423i | 0.105734 | − | 0.146038i | ||||
\(634\) | −0.690525 | − | 1.19602i | −0.0274243 | − | 0.0475002i | ||||
\(635\) | 14.9783 | + | 25.9431i | 0.594394 | + | 1.02952i | ||||
\(636\) | 10.7862 | − | 14.8978i | 0.427702 | − | 0.590735i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 35.4919 | 1.40514 | ||||||||
\(639\) | 4.25403 | − | 4.75615i | 0.168287 | − | 0.188151i | ||||
\(640\) | −2.03151 | −0.0803023 | ||||||||
\(641\) | 18.5554 | − | 32.1390i | 0.732896 | − | 1.26941i | −0.222744 | − | 0.974877i | \(-0.571502\pi\) |
0.955640 | − | 0.294536i | \(-0.0951651\pi\) | |||||||
\(642\) | 27.1281 | + | 2.80588i | 1.07066 | + | 0.110739i | ||||
\(643\) | −20.1468 | − | 34.8953i | −0.794514 | − | 1.37614i | −0.923147 | − | 0.384446i | \(-0.874392\pi\) |
0.128634 | − | 0.991692i | \(-0.458941\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.7460 | + | 28.5008i | 0.501872 | + | 1.12222i | ||||
\(646\) | 0.563508 | − | 0.976025i | 0.0221709 | − | 0.0384012i | ||||
\(647\) | −5.47723 | −0.215332 | −0.107666 | − | 0.994187i | \(-0.534338\pi\) | ||||
−0.107666 | + | 0.994187i | \(0.534338\pi\) | |||||||
\(648\) | −1.00000 | − | 8.94427i | −0.0392837 | − | 0.351364i | ||||
\(649\) | −10.5952 | −0.415898 | ||||||||
\(650\) | 1.85188 | − | 3.20755i | 0.0726366 | − | 0.125810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00000 | − | 8.66025i | −0.195815 | − | 0.339162i | ||||
\(653\) | 22.7460 | + | 39.3972i | 0.890118 | + | 1.54173i | 0.839732 | + | 0.543001i | \(0.182712\pi\) |
0.0503861 | + | 0.998730i | \(0.483955\pi\) | |||||||
\(654\) | 15.7246 | + | 1.62641i | 0.614879 | + | 0.0635975i | ||||
\(655\) | −7.99193 | + | 13.8424i | −0.312271 | + | 0.540869i | ||||
\(656\) | −5.65685 | −0.220863 | ||||||||
\(657\) | 30.7534 | − | 34.3834i | 1.19981 | − | 1.34142i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.4365 | + | 31.9329i | −0.718184 | + | 1.24393i | 0.243535 | + | 0.969892i | \(0.421693\pi\) |
−0.961719 | + | 0.274039i | \(0.911640\pi\) | |||||||
\(660\) | 8.25403 | − | 11.4003i | 0.321288 | − | 0.443758i | ||||
\(661\) | 12.4977 | + | 21.6466i | 0.486104 | + | 0.841956i | 0.999872 | − | 0.0159726i | \(-0.00508447\pi\) |
−0.513769 | + | 0.857929i | \(0.671751\pi\) | |||||||
\(662\) | 9.18246 | + | 15.9045i | 0.356886 | + | 0.618145i | ||||
\(663\) | 6.09452 | − | 8.41765i | 0.236691 | − | 0.326914i | ||||
\(664\) | 4.15283 | − | 7.19291i | 0.161161 | − | 0.279139i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.12702 | + | 27.7768i | 0.353665 | + | 1.07633i | ||||
\(667\) | 59.8569 | 2.31767 | ||||||||
\(668\) | −6.18433 | + | 10.7116i | −0.239279 | + | 0.414443i | ||||
\(669\) | 19.8014 | + | 2.04808i | 0.765567 | + | 0.0791833i | ||||
\(670\) | 0.886735 | + | 1.53587i | 0.0342576 | + | 0.0593359i | ||||
\(671\) | 1.59384 | + | 2.76062i | 0.0615296 | + | 0.106572i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1190 | − | 27.9188i | 0.621340 | − | 1.07619i | −0.367897 | − | 0.929867i | \(-0.619922\pi\) |
0.989236 | − | 0.146326i | \(-0.0467447\pi\) | |||||||
\(674\) | 0.254033 | 0.00978500 | ||||||||
\(675\) | 3.35591 | − | 3.05198i | 0.129169 | − | 0.117471i | ||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 6.36396 | − | 11.0227i | 0.244587 | − | 0.423637i | −0.717428 | − | 0.696632i | \(-0.754681\pi\) |
0.962015 | + | 0.272995i | \(0.0880143\pi\) | |||||||
\(678\) | 2.73861 | + | 6.12372i | 0.105176 | + | 0.235180i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.43649 | − | 2.48808i | −0.0550869 | − | 0.0954134i | ||||
\(681\) | 10.5000 | + | 1.08602i | 0.402361 | + | 0.0416166i | ||||
\(682\) | −10.9545 | + | 18.9737i | −0.419468 | + | 0.726539i | ||||
\(683\) | −7.74597 | −0.296391 | −0.148196 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148196 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(684\) | 2.34015 | + | 0.489323i | 0.0894780 | + | 0.0187097i | ||||
\(685\) | −31.4720 | −1.20248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.99193 | − | 11.0383i | 0.304911 | − | 0.421139i | ||||
\(688\) | −4.43649 | − | 7.68423i | −0.169140 | − | 0.292958i | ||||
\(689\) | 22.5262 | + | 39.0165i | 0.858180 | + | 1.48641i | ||||
\(690\) | 13.9204 | − | 19.2266i | 0.529939 | − | 0.731943i | ||||
\(691\) | −10.6458 | + | 18.4391i | −0.404986 | + | 0.701455i | −0.994320 | − | 0.106434i | \(-0.966057\pi\) |
0.589334 | + | 0.807889i | \(0.299390\pi\) | |||||||
\(692\) | −12.7279 | −0.483843 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.74597 | −0.294033 | ||||||||
\(695\) | 18.7540 | − | 32.4829i | 0.711381 | − | 1.23215i | ||||
\(696\) | 15.2869 | + | 1.58114i | 0.579449 | + | 0.0599329i | ||||
\(697\) | −4.00000 | − | 6.92820i | −0.151511 | − | 0.262424i | ||||
\(698\) | 8.21584 | + | 14.2302i | 0.310974 | + | 0.538623i | ||||
\(699\) | −16.0838 | − | 35.9645i | −0.608346 | − | 1.36030i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.7460 | −1.19903 | −0.599514 | − | 0.800364i | \(-0.704640\pi\) | ||||
−0.599514 | + | 0.800364i | \(0.704640\pi\) | |||||||
\(702\) | 21.0000 | + | 6.70820i | 0.792594 | + | 0.253185i | ||||
\(703\) | −7.76677 | −0.292929 | ||||||||
\(704\) | −2.00000 | + | 3.46410i | −0.0753778 | + | 0.130558i | ||||
\(705\) | −9.89949 | − | 22.1359i | −0.372837 | − | 0.833688i | ||||
\(706\) | −9.01276 | − | 15.6106i | −0.339200 | − | 0.587511i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.56351 | − | 0.472008i | −0.171507 | − | 0.0177391i | ||||
\(709\) | −12.3649 | + | 21.4167i | −0.464374 | + | 0.804320i | −0.999173 | − | 0.0406597i | \(-0.987054\pi\) |
0.534799 | + | 0.844979i | \(0.320387\pi\) | |||||||
\(710\) | 4.32105 | 0.162166 | ||||||||
\(711\) | −5.50000 | − | 16.7385i | −0.206266 | − | 0.627743i | ||||
\(712\) | −7.07107 | −0.264999 | ||||||||
\(713\) | −18.4746 | + | 31.9989i | −0.691879 | + | 1.19837i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.2379 | + | 29.8569i | 0.644661 | + | 1.11659i | ||||
\(716\) | −0.436492 | − | 0.756026i | −0.0163125 | − | 0.0282540i | ||||
\(717\) | 15.2363 | − | 21.0441i | 0.569010 | − | 0.785907i | ||||
\(718\) | 14.1190 | − | 24.4547i | 0.526915 | − | 0.912643i | ||||
\(719\) | −9.36061 | −0.349092 | −0.174546 | − | 0.984649i | \(-0.555846\pi\) | ||||
−0.174546 | + | 0.984649i | \(0.555846\pi\) | |||||||
\(720\) | 4.06301 | − | 4.54259i | 0.151420 | − | 0.169292i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.18246 | − | 15.9045i | 0.341736 | − | 0.591904i | ||||
\(723\) | 3.05544 | + | 0.316027i | 0.113633 | + | 0.0117532i | ||||
\(724\) | −3.93399 | − | 6.81388i | −0.146206 | − | 0.253236i | ||||
\(725\) | 3.87298 | + | 6.70820i | 0.143839 | + | 0.249136i | ||||
\(726\) | −3.53553 | − | 7.90569i | −0.131216 | − | 0.293408i | ||||
\(727\) | 18.1153 | − | 31.3767i | 0.671861 | − | 1.16370i | −0.305515 | − | 0.952187i | \(-0.598829\pi\) |
0.977376 | − | 0.211509i | \(-0.0678379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 31.2379 | 1.15617 | ||||||||
\(731\) | 6.27415 | − | 10.8671i | 0.232058 | − | 0.401936i | ||||
\(732\) | 0.563508 | + | 1.26004i | 0.0208279 | + | 0.0465725i | ||||
\(733\) | −4.82073 | − | 8.34975i | −0.178058 | − | 0.308405i | 0.763157 | − | 0.646213i | \(-0.223648\pi\) |
−0.941215 | + | 0.337808i | \(0.890315\pi\) | |||||||
\(734\) | −2.03151 | − | 3.51867i | −0.0749843 | − | 0.129877i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.37298 | + | 5.84218i | −0.124330 | + | 0.215346i | ||||
\(737\) | 3.49193 | 0.128627 | ||||||||
\(738\) | 11.3137 | − | 12.6491i | 0.416463 | − | 0.465620i | ||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | −9.89949 | + | 17.1464i | −0.363913 | + | 0.630315i | ||||
\(741\) | −3.43431 | + | 4.74342i | −0.126163 | + | 0.174254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.8730 | + | 24.0287i | 0.508950 | + | 0.881528i | 0.999946 | + | 0.0103660i | \(0.00329968\pi\) |
−0.490996 | + | 0.871162i | \(0.663367\pi\) | |||||||
\(744\) | −5.56351 | + | 7.68423i | −0.203968 | + | 0.281718i | ||||
\(745\) | −0.258035 | + | 0.446930i | −0.00945367 | + | 0.0163742i | ||||
\(746\) | −8.87298 | −0.324863 | ||||||||
\(747\) | 7.77817 | + | 23.6718i | 0.284589 | + | 0.866106i | ||||
\(748\) | −5.65685 | −0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 20.5554 | + | 2.12607i | 0.750579 | + | 0.0776330i | ||||
\(751\) | 6.50000 | + | 11.2583i | 0.237188 | + | 0.410822i | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | 3.44572 | + | 5.96816i | 0.125652 | + | 0.217636i | ||||
\(753\) | 18.3095 | + | 40.9412i | 0.667234 | + | 1.49198i | ||||
\(754\) | −18.8224 | + | 32.6014i | −0.685473 | + | 1.18727i | ||||
\(755\) | −22.3466 | −0.813275 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2379 | −0.553831 | −0.276915 | − | 0.960894i | \(-0.589312\pi\) | ||||
−0.276915 | + | 0.960894i | \(0.589312\pi\) | |||||||
\(758\) | 6.18246 | − | 10.7083i | 0.224557 | − | 0.388944i | ||||
\(759\) | −19.0805 | − | 42.6652i | −0.692577 | − | 1.54865i | ||||
\(760\) | 0.809475 | + | 1.40205i | 0.0293627 | + | 0.0508578i | ||||
\(761\) | 1.14477 | + | 1.98280i | 0.0414979 | + | 0.0718765i | 0.886028 | − | 0.463631i | \(-0.153454\pi\) |
−0.844530 | + | 0.535508i | \(0.820120\pi\) | |||||||
\(762\) | 25.4052 | + | 2.62769i | 0.920334 | + | 0.0951910i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.8730 | −0.501907 | ||||||||
\(765\) | 8.43649 | + | 1.76406i | 0.305022 | + | 0.0637797i | ||||
\(766\) | 23.8620 | 0.862169 | ||||||||
\(767\) | 5.61895 | − | 9.73231i | 0.202889 | − | 0.351413i | ||||
\(768\) | −1.01575 | + | 1.40294i | −0.0366528 | + | 0.0506243i | ||||
\(769\) | 4.85993 | + | 8.41765i | 0.175254 | + | 0.303548i | 0.940249 | − | 0.340488i | \(-0.110592\pi\) |
−0.764995 | + | 0.644036i | \(0.777259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1825 | − | 19.5886i | 0.510769 | − | 0.705466i | ||||
\(772\) | −8.06351 | + | 13.9664i | −0.290212 | + | 0.502662i | ||||
\(773\) | −3.44572 | −0.123934 | −0.0619670 | − | 0.998078i | \(-0.519737\pi\) | ||||
−0.0619670 | + | 0.998078i | \(0.519737\pi\) | |||||||
\(774\) | 26.0554 | + | 5.44816i | 0.936544 | + | 0.195830i | ||||
\(775\) | −4.78153 | −0.171758 | ||||||||
\(776\) | −8.92295 | + | 15.4550i | −0.320315 | + | 0.554802i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.4365 | − | 18.0765i | −0.374166 | − | 0.648075i | ||||
\(779\) | 2.25403 | + | 3.90410i | 0.0807591 | + | 0.139879i | ||||
\(780\) | 6.09452 | + | 13.6278i | 0.218219 | + | 0.487952i | ||||
\(781\) | 4.25403 | − | 7.36820i | 0.152221 | − | 0.263655i | ||||
\(782\) | −9.54024 | −0.341158 | ||||||||
\(783\) | −34.1093 | + | 31.0203i | −1.21897 | + | 1.10857i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.55544 | + | 11.3544i | −0.233974 | + | 0.405254i | ||||
\(786\) | 5.56351 | + | 12.4404i | 0.198444 | + | 0.443734i | ||||
\(787\) | −4.77012 | − | 8.26209i | −0.170036 | − | 0.294512i | 0.768396 | − | 0.639975i | \(-0.221055\pi\) |
−0.938432 | + | 0.345463i | \(0.887722\pi\) | |||||||
\(788\) | 3.30948 | + | 5.73218i | 0.117895 | + | 0.204200i | ||||
\(789\) | 9.68066 | + | 1.00128i | 0.344641 | + | 0.0356465i | ||||
\(790\) | 5.96550 | − | 10.3325i | 0.212243 | − | 0.367616i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.74597 | − | 11.4003i | −0.133107 | − | 0.405093i | ||||
\(793\) | −3.38105 | −0.120065 | ||||||||
\(794\) | 3.53553 | − | 6.12372i | 0.125471 | − | 0.217323i | ||||
\(795\) | −21.9123 | + | 30.2649i | −0.777149 | + | 1.07339i | ||||
\(796\) | −10.3372 | − | 17.9045i | −0.366391 | − | 0.634608i | ||||
\(797\) | −13.0366 | − | 22.5800i | −0.461779 | − | 0.799825i | 0.537271 | − | 0.843410i | \(-0.319455\pi\) |
−0.999050 | + | 0.0435852i | \(0.986122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.87298 | + | 8.44025i | −0.172394 | + | 0.298595i | ||||
\(800\) | −0.872983 | −0.0308646 | ||||||||
\(801\) | 14.1421 | − | 15.8114i | 0.499688 | − | 0.558668i | ||||
\(802\) | 3.87298 | 0.136760 | ||||||||
\(803\) | 30.7534 | − | 53.2665i | 1.08527 | − | 1.87973i | ||||
\(804\) | 1.50403 | + | 0.155563i | 0.0530430 | + | 0.00548628i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.6190 | − | 20.1246i | −0.409260 | − | 0.708859i | ||||
\(807\) | 2.43649 | + | 5.44816i | 0.0857686 | + | 0.191784i | ||||
\(808\) | −3.93399 | + | 6.81388i | −0.138397 | + | 0.239711i | ||||
\(809\) | −30.7298 | −1.08040 | −0.540202 | − | 0.841536i | \(-0.681652\pi\) | ||||
−0.540202 | + | 0.841536i | \(0.681652\pi\) | |||||||
\(810\) | 2.03151 | + | 18.1703i | 0.0713798 | + | 0.638441i | ||||
\(811\) | 13.9625 | 0.490290 | 0.245145 | − | 0.969486i | \(-0.421164\pi\) | ||||
0.245145 | + | 0.969486i | \(0.421164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.00000 | + | 11.1803i | 0.175358 | + | 0.392112i | ||||
\(814\) | 19.4919 | + | 33.7610i | 0.683192 | + | 1.18332i | ||||
\(815\) | 10.1575 | + | 17.5934i | 0.355803 | + | 0.616268i | ||||
\(816\) | −2.43649 | − | 0.252009i | −0.0852943 | − | 0.00882207i | ||||
\(817\) | −3.53553 | + | 6.12372i | −0.123693 | + | 0.214242i | ||||
\(818\) | 31.6288 | 1.10587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.4919 | 0.401316 | ||||||||
\(821\) | −10.7460 | + | 18.6126i | −0.375037 | + | 0.649583i | −0.990333 | − | 0.138714i | \(-0.955703\pi\) |
0.615296 | + | 0.788296i | \(0.289037\pi\) | |||||||
\(822\) | −15.7360 | + | 21.7343i | −0.548855 | + | 0.758070i | ||||
\(823\) | 10.8730 | + | 18.8326i | 0.379008 | + | 0.656462i | 0.990918 | − | 0.134466i | \(-0.0429318\pi\) |
−0.611910 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(824\) | −9.01276 | − | 15.6106i | −0.313974 | − | 0.543820i | ||||
\(825\) | 3.54694 | − | 4.89898i | 0.123489 | − | 0.170561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.1270 | 1.43013 | 0.715063 | − | 0.699060i | \(-0.246398\pi\) | ||||
0.715063 | + | 0.699060i | \(0.246398\pi\) | |||||||
\(828\) | −6.31754 | − | 19.2266i | −0.219550 | − | 0.668170i | ||||
\(829\) | 54.4358 | 1.89063 | 0.945317 | − | 0.326153i | \(-0.105752\pi\) | ||||
0.945317 | + | 0.326153i | \(0.105752\pi\) | |||||||
\(830\) | −8.43649 | + | 14.6124i | −0.292835 | + | 0.507205i | ||||
\(831\) | −41.9773 | − | 4.34175i | −1.45618 | − | 0.150614i | ||||
\(832\) | −2.12132 | − | 3.67423i | −0.0735436 | − | 0.127381i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.0554 | − | 29.1929i | −0.452073 | − | 1.01087i | ||||
\(835\) | 12.5635 | − | 21.7606i | 0.434778 | − | 0.753058i | ||||
\(836\) | 3.18768 | 0.110248 | ||||||||
\(837\) | −6.05544 | − | 27.8088i | −0.209307 | − | 0.961214i | ||||
\(838\) | 3.98461 | 0.137646 | ||||||||
\(839\) | −19.9672 | + | 34.5842i | −0.689345 | + | 1.19398i | 0.282706 | + | 0.959207i | \(0.408768\pi\) |
−0.972050 | + | 0.234773i | \(0.924565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8649 | − | 43.0673i | −0.857411 | − | 1.48508i | ||||
\(842\) | 2.56351 | + | 4.44013i | 0.0883443 | + | 0.153017i | ||||
\(843\) | −11.6224 | − | 1.20211i | −0.400295 | − | 0.0414029i | ||||
\(844\) | 1.30948 | − | 2.26808i | 0.0450740 | − | 0.0780704i | ||||
\(845\) | −10.1575 | −0.349430 | ||||||||
\(846\) | −20.2367 | − | 4.23146i | −0.695750 | − | 0.145481i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.30948 | − | 9.19628i | 0.182328 | − | 0.315802i | ||||
\(849\) | 10.6825 | − | 14.7544i | 0.366621 | − | 0.506371i | ||||
\(850\) | −0.617292 | − | 1.06918i | −0.0211730 | − | 0.0366726i | ||||
\(851\) | 32.8730 | + | 56.9377i | 1.12687 | + | 1.95180i | ||||
\(852\) | 2.16052 | − | 2.98408i | 0.0740183 | − | 0.102233i | ||||
\(853\) | −22.7564 | + | 39.4153i | −0.779165 | + | 1.34955i | 0.153258 | + | 0.988186i | \(0.451024\pi\) |
−0.932423 | + | 0.361368i | \(0.882310\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.75403 | − | 0.994063i | −0.162585 | − | 0.0339962i | ||||
\(856\) | 15.7460 | 0.538186 | ||||||||
\(857\) | 23.8620 | − | 41.3302i | 0.815110 | − | 1.41181i | −0.0941381 | − | 0.995559i | \(-0.530010\pi\) |
0.909249 | − | 0.416254i | \(-0.136657\pi\) | |||||||
\(858\) | 29.2379 | + | 3.02410i | 0.998165 | + | 0.103241i | ||||
\(859\) | −1.14477 | − | 1.98280i | −0.0390591 | − | 0.0676523i | 0.845835 | − | 0.533445i | \(-0.179103\pi\) |
−0.884894 | + | 0.465792i | \(0.845769\pi\) | |||||||
\(860\) | 9.01276 | + | 15.6106i | 0.307333 | + | 0.532316i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.74597 | + | 8.22026i | −0.161648 | + | 0.279983i | ||||
\(863\) | −36.1270 | −1.22978 | −0.614889 | − | 0.788614i | \(-0.710799\pi\) | ||||
−0.614889 | + | 0.788614i | \(0.710799\pi\) | |||||||
\(864\) | −1.10557 | − | 5.07718i | −0.0376122 | − | 0.172729i | ||||
\(865\) | 25.8569 | 0.879159 | ||||||||
\(866\) | −14.8492 | + | 25.7196i | −0.504598 | + | 0.873989i | ||||
\(867\) | 10.6066 | + | 23.7171i | 0.360219 | + | 0.805474i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7460 | − | 20.3446i | −0.398455 | − | 0.690144i | ||||
\(870\) | −31.0554 | − | 3.21209i | −1.05288 | − | 0.108900i | ||||
\(871\) | −1.85188 | + | 3.20755i | −0.0627485 | + | 0.108684i | ||||
\(872\) | 9.12702 | 0.309080 | ||||||||
\(873\) | −16.7125 | − | 50.8623i | −0.565633 | − | 1.72143i | ||||
\(874\) | 5.37600 | 0.181846 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.6190 | − | 21.5726i | 0.527715 | − | 0.728872i | ||||
\(877\) | −19.4365 | − | 33.6650i | −0.656324 | − | 1.13679i | −0.981560 | − | 0.191153i | \(-0.938777\pi\) |
0.325237 | − | 0.945633i | \(-0.394556\pi\) | |||||||
\(878\) | 5.47723 | + | 9.48683i | 0.184847 | + | 0.320165i | ||||
\(879\) | −6.37298 | + | 8.80226i | −0.214955 | + | 0.296893i | ||||
\(880\) | 4.06301 | − | 7.03734i | 0.136964 | − | 0.237229i | ||||
\(881\) | −15.7360 | −0.530159 | −0.265079 | − | 0.964227i | \(-0.585398\pi\) | ||||
−0.265079 | + | 0.964227i | \(0.585398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.50807 | 0.151709 | 0.0758543 | − | 0.997119i | \(-0.475832\pi\) | ||||
0.0758543 | + | 0.997119i | \(0.475832\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 9.27079 | + | 0.958887i | 0.311634 | + | 0.0322326i | ||||
\(886\) | −12.1825 | − | 21.1006i | −0.409278 | − | 0.708890i | ||||
\(887\) | −18.0255 | − | 31.2211i | −0.605238 | − | 1.04830i | −0.992014 | − | 0.126129i | \(-0.959745\pi\) |
0.386776 | − | 0.922174i | \(-0.373589\pi\) | |||||||
\(888\) | 6.89144 | + | 15.4097i | 0.231262 | + | 0.517117i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.3649 | 0.481513 | ||||||||
\(891\) | 32.9839 | + | 14.4244i | 1.10500 | + | 0.483237i | ||||
\(892\) | 11.4933 | 0.384825 | ||||||||
\(893\) | 2.74597 | − | 4.75615i | 0.0918903 | − | 0.159159i | ||||
\(894\) | 0.179629 | + | 0.401662i | 0.00600768 | + | 0.0134336i | ||||
\(895\) | 0.886735 | + | 1.53587i | 0.0296403 | + | 0.0513385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.3095 | + | 5.10012i | 1.64640 | + | 0.170288i | ||||
\(898\) | −4.50000 | + | 7.79423i | −0.150167 | + | 0.260097i | ||||
\(899\) | 48.5993 | 1.62088 | ||||||||
\(900\) | 1.74597 | − | 1.95205i | 0.0581989 | − | 0.0650683i | ||||
\(901\) | 15.0175 | 0.500304 | ||||||||
\(902\) | 11.3137 | − | 19.5959i | 0.376705 | − | 0.652473i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.93649 | + | 3.35410i | 0.0644068 | + | 0.111556i | ||||
\(905\) | 7.99193 | + | 13.8424i | 0.265661 | + | 0.460138i | ||||
\(906\) | −11.1733 | + | 15.4324i | −0.371207 | + | 0.512706i | ||||
\(907\) | 2.30948 | − | 4.00013i | 0.0766849 | − | 0.132822i | −0.825133 | − | 0.564939i | \(-0.808900\pi\) |
0.901818 | + | 0.432117i | \(0.142233\pi\) | |||||||
\(908\) | 6.09452 | 0.202254 | ||||||||
\(909\) | −7.36831 | − | 22.4244i | −0.244391 | − | 0.743772i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6270 | − | 20.1386i | 0.385220 | − | 0.667221i | −0.606579 | − | 0.795023i | \(-0.707459\pi\) |
0.991800 | + | 0.127802i | \(0.0407921\pi\) | |||||||
\(912\) | 1.37298 | + | 0.142009i | 0.0454640 | + | 0.00470239i | ||||
\(913\) | 16.6113 | + | 28.7716i | 0.549754 | + | 0.952202i | ||||
\(914\) | −16.9365 | − | 29.3349i | −0.560209 | − | 0.970311i | ||||
\(915\) | −1.14477 | − | 2.55978i | −0.0378449 | − | 0.0846239i | ||||
\(916\) | 3.93399 | − | 6.81388i | 0.129983 | − | 0.225137i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.43649 | − | 4.94414i | 0.179431 | − | 0.163181i | ||||
\(919\) | −39.3649 | −1.29853 | −0.649264 | − | 0.760563i | \(-0.724923\pi\) | ||||
−0.649264 | + | 0.760563i | \(0.724923\pi\) | |||||||
\(920\) | 6.85224 | − | 11.8684i | 0.225912 | − | 0.391290i | ||||
\(921\) | −17.0554 | − | 38.1371i | −0.561996 | − | 1.25666i | ||||
\(922\) | −4.98895 | − | 8.64112i | −0.164302 | − | 0.284580i | ||||
\(923\) | 4.51208 | + | 7.81516i | 0.148517 | + | 0.257239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.25403 | + | 7.36820i | −0.139872 | + | 0.242265i | ||||
\(926\) | 21.6190 | 0.710443 | ||||||||
\(927\) | 52.9318 | + | 11.0680i | 1.73851 | + | 0.363520i | ||||
\(928\) | 8.87298 | 0.291270 | ||||||||
\(929\) | −5.30900 | + | 9.19547i | −0.174183 | + | 0.301693i | −0.939878 | − | 0.341510i | \(-0.889062\pi\) |
0.765695 | + | 0.643203i | \(0.222395\pi\) | |||||||
\(930\) | 11.3023 | − | 15.6106i | 0.370617 | − | 0.511890i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.3730 | − | 19.6986i | −0.372534 | − | 0.645249i | ||||
\(933\) | −1.43649 | + | 1.98406i | −0.0470286 | + | 0.0649552i | ||||
\(934\) | 19.5295 | − | 33.8262i | 0.639026 | − | 1.10683i | ||||
\(935\) | 11.4919 | 0.375826 | ||||||||
\(936\) | 12.4585 | + | 2.60505i | 0.407218 | + | 0.0851488i | ||||
\(937\) | −42.4036 | −1.38526 | −0.692632 | − | 0.721291i | \(-0.743549\pi\) | ||||
−0.692632 | + | 0.721291i | \(0.743549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −45.9839 | − | 4.75615i | −1.50063 | − | 0.155211i | ||||
\(940\) | −7.00000 | − | 12.1244i | −0.228315 | − | 0.395453i | ||||
\(941\) | −0.836124 | − | 1.44821i | −0.0272569 | − | 0.0472103i | 0.852075 | − | 0.523419i | \(-0.175344\pi\) |
−0.879332 | + | 0.476209i | \(0.842011\pi\) | |||||||
\(942\) | 4.56351 | + | 10.2043i | 0.148687 | + | 0.332475i | ||||
\(943\) | 19.0805 | − | 33.0484i | 0.621346 | − | 1.07620i | ||||
\(944\) | −2.64880 | −0.0862110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.4919 | 1.15394 | ||||||||
\(947\) | −13.8014 | + | 23.9047i | −0.448486 | + | 0.776800i | −0.998288 | − | 0.0584952i | \(-0.981370\pi\) |
0.549802 | + | 0.835295i | \(0.314703\pi\) | |||||||
\(948\) | −4.15283 | − | 9.28600i | −0.134878 | − | 0.301595i | ||||
\(949\) | 32.6190 | + | 56.4977i | 1.05886 | + | 1.83399i | ||||
\(950\) | 0.347849 | + | 0.602493i | 0.0112857 | + | 0.0195475i | ||||
\(951\) | 2.37936 | + | 0.246099i | 0.0771559 | + | 0.00798030i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.5081 | −0.923467 | −0.461733 | − | 0.887019i | \(-0.652772\pi\) | ||||
−0.461733 | + | 0.887019i | \(0.652772\pi\) | |||||||
\(954\) | 9.94456 | + | 30.2649i | 0.321967 | + | 0.979863i | ||||
\(955\) | 28.1830 | 0.911982 | ||||||||
\(956\) | 7.50000 | − | 12.9904i | 0.242567 | − | 0.420139i | ||||
\(957\) | −36.0510 | + | 49.7931i | −1.16536 | + | 1.60958i | ||||
\(958\) | −9.01276 | − | 15.6106i | −0.291189 | − | 0.504354i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.06351 | − | 2.85008i | 0.0665994 | − | 0.0919861i | ||||
\(961\) | 0.500000 | − | 0.866025i | 0.0161290 | − | 0.0279363i | ||||
\(962\) | −41.3486 | −1.33313 | ||||||||
\(963\) | −31.4919 | + | 35.2091i | −1.01481 | + | 1.13460i | ||||
\(964\) | 1.77347 | 0.0571197 | ||||||||
\(965\) | 16.3811 | − | 28.3728i | 0.527325 | − | 0.913354i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.7540 | − | 25.5547i | −0.474458 | − | 0.821785i | 0.525114 | − | 0.851032i | \(-0.324022\pi\) |
−0.999572 | + | 0.0292467i | \(0.990689\pi\) | |||||||
\(968\) | −2.50000 | − | 4.33013i | −0.0803530 | − | 0.139176i | ||||
\(969\) | 0.796921 | + | 1.78197i | 0.0256008 | + | 0.0572451i | ||||
\(970\) | 18.1270 | − | 31.3969i | 0.582023 | − | 1.00809i | ||||
\(971\) | 36.8480 | 1.18251 | 0.591254 | − | 0.806486i | \(-0.298633\pi\) | ||||
0.591254 | + | 0.806486i | \(0.298633\pi\) | |||||||
\(972\) | 13.5640 | + | 7.68223i | 0.435067 | + | 0.246408i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −15.2460 | + | 26.4068i | −0.488512 | + | 0.846128i | ||||
\(975\) | 2.61895 | + | 5.85615i | 0.0838735 | + | 0.187547i | ||||
\(976\) | 0.398461 | + | 0.690154i | 0.0127544 | + | 0.0220913i | ||||
\(977\) | −7.25403 | − | 12.5644i | −0.232077 | − | 0.401969i | 0.726342 | − | 0.687333i | \(-0.241219\pi\) |
−0.958419 | + | 0.285364i | \(0.907885\pi\) | |||||||
\(978\) | 17.2286 | + | 1.78197i | 0.550910 | + | 0.0569811i | ||||
\(979\) | 14.1421 | − | 24.4949i | 0.451985 | − | 0.782860i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.2540 | + | 20.4086i | −0.582806 | + | 0.651597i | ||||
\(982\) | −13.7460 | −0.438651 | ||||||||
\(983\) | −4.94975 | + | 8.57321i | −0.157872 | + | 0.273443i | −0.934101 | − | 0.357008i | \(-0.883797\pi\) |
0.776229 | + | 0.630451i | \(0.217130\pi\) | |||||||
\(984\) | 5.74597 | − | 7.93624i | 0.183175 | − | 0.252998i | ||||
\(985\) | −6.72322 | − | 11.6450i | −0.214220 | − | 0.371039i | ||||
\(986\) | 6.27415 | + | 10.8671i | 0.199810 | + | 0.346080i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.69052 | + | 2.92808i | −0.0537828 | + | 0.0931545i | ||||
\(989\) | 59.8569 | 1.90334 | ||||||||
\(990\) | 7.60995 | + | 23.1599i | 0.241860 | + | 0.736069i | ||||
\(991\) | 3.74597 | 0.118995 | 0.0594973 | − | 0.998228i | \(-0.481050\pi\) | ||||
0.0594973 | + | 0.998228i | \(0.481050\pi\) | |||||||
\(992\) | −2.73861 | + | 4.74342i | −0.0869510 | + | 0.150604i | ||||
\(993\) | −31.6402 | − | 3.27257i | −1.00407 | − | 0.103852i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0000 | + | 36.3731i | 0.665745 | + | 1.15310i | ||||
\(996\) | 5.87298 | + | 13.1324i | 0.186093 | + | 0.416116i | ||||
\(997\) | 0.129018 | − | 0.223465i | 0.00408603 | − | 0.00707721i | −0.863975 | − | 0.503534i | \(-0.832033\pi\) |
0.868061 | + | 0.496457i | \(0.165366\pi\) | |||||||
\(998\) | −14.2540 | −0.451204 | ||||||||
\(999\) | −48.2401 | − | 15.4097i | −1.52625 | − | 0.487542i |
(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 | 882.2.f.p.295.1 | ✓ | 8 | |
3.2 | odd | 2 | 2646.2.f.s.883.2 | 8 | |||
7.2 | even | 3 | 882.2.e.t.655.4 | 8 | |||
7.3 | odd | 6 | 882.2.h.r.79.3 | 8 | |||
7.4 | even | 3 | 882.2.h.r.79.2 | 8 | |||
7.5 | odd | 6 | 882.2.e.t.655.1 | 8 | |||
7.6 | odd | 2 | inner | 882.2.f.p.295.4 | yes | 8 | |
9.2 | odd | 6 | 7938.2.a.cd.1.3 | 4 | |||
9.4 | even | 3 | inner | 882.2.f.p.589.2 | yes | 8 | |
9.5 | odd | 6 | 2646.2.f.s.1765.2 | 8 | |||
9.7 | even | 3 | 7938.2.a.cu.1.2 | 4 | |||
21.2 | odd | 6 | 2646.2.e.r.2125.2 | 8 | |||
21.5 | even | 6 | 2646.2.e.r.2125.3 | 8 | |||
21.11 | odd | 6 | 2646.2.h.s.667.3 | 8 | |||
21.17 | even | 6 | 2646.2.h.s.667.2 | 8 | |||
21.20 | even | 2 | 2646.2.f.s.883.3 | 8 | |||
63.4 | even | 3 | 882.2.e.t.373.4 | 8 | |||
63.5 | even | 6 | 2646.2.h.s.361.2 | 8 | |||
63.13 | odd | 6 | inner | 882.2.f.p.589.3 | yes | 8 | |
63.20 | even | 6 | 7938.2.a.cd.1.2 | 4 | |||
63.23 | odd | 6 | 2646.2.h.s.361.3 | 8 | |||
63.31 | odd | 6 | 882.2.e.t.373.1 | 8 | |||
63.32 | odd | 6 | 2646.2.e.r.1549.2 | 8 | |||
63.34 | odd | 6 | 7938.2.a.cu.1.3 | 4 | |||
63.40 | odd | 6 | 882.2.h.r.67.3 | 8 | |||
63.41 | even | 6 | 2646.2.f.s.1765.3 | 8 | |||
63.58 | even | 3 | 882.2.h.r.67.2 | 8 | |||
63.59 | even | 6 | 2646.2.e.r.1549.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.t.373.1 | 8 | 63.31 | odd | 6 | |||
882.2.e.t.373.4 | 8 | 63.4 | even | 3 | |||
882.2.e.t.655.1 | 8 | 7.5 | odd | 6 | |||
882.2.e.t.655.4 | 8 | 7.2 | even | 3 | |||
882.2.f.p.295.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
882.2.f.p.295.4 | yes | 8 | 7.6 | odd | 2 | inner | |
882.2.f.p.589.2 | yes | 8 | 9.4 | even | 3 | inner | |
882.2.f.p.589.3 | yes | 8 | 63.13 | odd | 6 | inner | |
882.2.h.r.67.2 | 8 | 63.58 | even | 3 | |||
882.2.h.r.67.3 | 8 | 63.40 | odd | 6 | |||
882.2.h.r.79.2 | 8 | 7.4 | even | 3 | |||
882.2.h.r.79.3 | 8 | 7.3 | odd | 6 | |||
2646.2.e.r.1549.2 | 8 | 63.32 | odd | 6 | |||
2646.2.e.r.1549.3 | 8 | 63.59 | even | 6 | |||
2646.2.e.r.2125.2 | 8 | 21.2 | odd | 6 | |||
2646.2.e.r.2125.3 | 8 | 21.5 | even | 6 | |||
2646.2.f.s.883.2 | 8 | 3.2 | odd | 2 | |||
2646.2.f.s.883.3 | 8 | 21.20 | even | 2 | |||
2646.2.f.s.1765.2 | 8 | 9.5 | odd | 6 | |||
2646.2.f.s.1765.3 | 8 | 63.41 | even | 6 | |||
2646.2.h.s.361.2 | 8 | 63.5 | even | 6 | |||
2646.2.h.s.361.3 | 8 | 63.23 | odd | 6 | |||
2646.2.h.s.667.2 | 8 | 21.17 | even | 6 | |||
2646.2.h.s.667.3 | 8 | 21.11 | odd | 6 | |||
7938.2.a.cd.1.2 | 4 | 63.20 | even | 6 | |||
7938.2.a.cd.1.3 | 4 | 9.2 | odd | 6 | |||
7938.2.a.cu.1.2 | 4 | 9.7 | even | 3 | |||
7938.2.a.cu.1.3 | 4 | 63.34 | odd | 6 |