Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(91,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.n (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: | \(3.95259490005\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.2 | ||
Root | \(-0.227943 - 0.701538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.181 |
Dual form | 495.2.n.d.361.2 |
$q$-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 \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(397\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.359123 | − | 1.10527i | −0.253938 | − | 0.781542i | −0.994037 | − | 0.109044i | \(-0.965221\pi\) |
0.740098 | − | 0.672499i | \(-0.234779\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.525387 | − | 0.381716i | 0.262693 | − | 0.190858i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46813 | − | 2.51974i | 1.31083 | − | 0.952373i | 0.310831 | − | 0.950465i | \(-0.399393\pi\) |
0.999998 | − | 0.00190785i | \(-0.000607288\pi\) | |||||||
\(8\) | −2.49097 | − | 1.80980i | −0.880691 | − | 0.639860i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.16215 | −0.367503 | ||||||||
\(11\) | 3.15911 | − | 1.00996i | 0.952508 | − | 0.304514i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59676 | + | 4.91433i | 0.442863 | + | 1.36299i | 0.884811 | + | 0.465950i | \(0.154287\pi\) |
−0.441948 | + | 0.897040i | \(0.645713\pi\) | |||||||
\(14\) | −4.03048 | − | 2.92831i | −1.07719 | − | 0.782624i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.704384 | + | 2.16787i | −0.176096 | + | 0.541968i | ||||
\(17\) | −1.54508 | + | 4.75528i | −0.374738 | + | 1.15333i | 0.568917 | + | 0.822395i | \(0.307363\pi\) |
−0.943655 | + | 0.330930i | \(0.892637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.53048 | − | 3.29158i | −1.03936 | − | 0.755141i | −0.0692013 | − | 0.997603i | \(-0.522045\pi\) |
−0.970161 | + | 0.242462i | \(0.922045\pi\) | |||||||
\(20\) | −0.200680 | − | 0.617629i | −0.0448734 | − | 0.138106i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.25079 | − | 3.12896i | −0.479869 | − | 0.667097i | ||||
\(23\) | 0.219819 | 0.0458354 | 0.0229177 | − | 0.999737i | \(-0.492704\pi\) | ||||
0.0229177 | + | 0.999737i | \(0.492704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 4.85822 | − | 3.52970i | 0.952775 | − | 0.692232i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.860283 | − | 2.64768i | 0.162578 | − | 0.500364i | ||||
\(29\) | 5.19262 | − | 3.77266i | 0.964246 | − | 0.700566i | 0.0101128 | − | 0.999949i | \(-0.496781\pi\) |
0.954133 | + | 0.299383i | \(0.0967809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.874813 | − | 2.69240i | −0.157121 | − | 0.483569i | 0.841249 | − | 0.540649i | \(-0.181821\pi\) |
−0.998370 | + | 0.0570796i | \(0.981821\pi\) | |||||||
\(32\) | −3.50898 | −0.620306 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.81074 | 0.996533 | ||||||||
\(35\) | −1.32471 | − | 4.07703i | −0.223916 | − | 0.689144i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.17784 | + | 2.30883i | −0.522433 | + | 0.379570i | −0.817520 | − | 0.575901i | \(-0.804652\pi\) |
0.295087 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(38\) | −2.01108 | + | 6.18947i | −0.326240 | + | 1.00406i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.49097 | + | 1.80980i | −0.393857 | + | 0.286154i | ||||
\(41\) | 4.74165 | + | 3.44501i | 0.740521 | + | 0.538020i | 0.892874 | − | 0.450306i | \(-0.148685\pi\) |
−0.152353 | + | 0.988326i | \(0.548685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.90173 | −1.35750 | −0.678751 | − | 0.734369i | \(-0.737478\pi\) | ||||
−0.678751 | + | 0.734369i | \(0.737478\pi\) | |||||||
\(44\) | 1.27424 | − | 1.73650i | 0.192099 | − | 0.261788i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0789420 | − | 0.242959i | −0.0116394 | − | 0.0358223i | ||||
\(47\) | −0.192447 | − | 0.139821i | −0.0280713 | − | 0.0203950i | 0.573661 | − | 0.819093i | \(-0.305523\pi\) |
−0.601732 | + | 0.798698i | \(0.705523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.51569 | − | 10.8202i | 0.502241 | − | 1.54574i | ||||
\(50\) | −0.359123 | + | 1.10527i | −0.0507877 | + | 0.156308i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.71480 | + | 1.97242i | 0.376475 | + | 0.273525i | ||||
\(53\) | −0.783885 | − | 2.41255i | −0.107675 | − | 0.331389i | 0.882674 | − | 0.469986i | \(-0.155741\pi\) |
−0.990349 | + | 0.138596i | \(0.955741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0156899 | − | 3.31659i | 0.00211563 | − | 0.447209i | ||||
\(56\) | −13.1992 | −1.76382 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.03459 | − | 4.38439i | −0.792381 | − | 0.575698i | ||||
\(59\) | −6.36725 | + | 4.62608i | −0.828945 | + | 0.602264i | −0.919261 | − | 0.393649i | \(-0.871212\pi\) |
0.0903156 | + | 0.995913i | \(0.471212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50123 | + | 4.62030i | −0.192212 | + | 0.591569i | 0.807785 | + | 0.589477i | \(0.200666\pi\) |
−0.999998 | + | 0.00209225i | \(0.999334\pi\) | |||||||
\(62\) | −2.66165 | + | 1.93381i | −0.338031 | + | 0.245594i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.66892 | + | 8.21410i | 0.333615 | + | 1.02676i | ||||
\(65\) | 5.16724 | 0.640917 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1280 | 1.48167 | 0.740834 | − | 0.671688i | \(-0.234431\pi\) | ||||
0.740834 | + | 0.671688i | \(0.234431\pi\) | |||||||
\(68\) | 1.00340 | + | 3.08815i | 0.121680 | + | 0.374493i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.03048 | + | 2.92831i | −0.481734 | + | 0.350000i | ||||
\(71\) | 3.08459 | − | 9.49339i | 0.366073 | − | 1.12666i | −0.583233 | − | 0.812305i | \(-0.698212\pi\) |
0.949306 | − | 0.314353i | \(-0.101788\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7813 | + | 8.55964i | −1.37890 | + | 1.00183i | −0.381918 | + | 0.924196i | \(0.624736\pi\) |
−0.996982 | + | 0.0776335i | \(0.975264\pi\) | |||||||
\(74\) | 3.69311 | + | 2.68320i | 0.429316 | + | 0.311916i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.63670 | −0.417158 | ||||||||
\(77\) | 8.41136 | − | 11.4628i | 0.958564 | − | 1.30631i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.47274 | + | 7.61030i | 0.278205 | + | 0.856226i | 0.988354 | + | 0.152174i | \(0.0486275\pi\) |
−0.710149 | + | 0.704051i | \(0.751372\pi\) | |||||||
\(80\) | 1.84410 | + | 1.33982i | 0.206177 | + | 0.149796i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.10482 | − | 6.47797i | 0.232439 | − | 0.715373i | ||||
\(83\) | −3.87908 | + | 11.9386i | −0.425784 | + | 1.31043i | 0.476458 | + | 0.879197i | \(0.341921\pi\) |
−0.902242 | + | 0.431231i | \(0.858079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.04508 | + | 2.93893i | 0.438751 | + | 0.318771i | ||||
\(86\) | 3.19682 | + | 9.83880i | 0.344722 | + | 1.06094i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.69707 | − | 3.20157i | −1.03371 | − | 0.341288i | ||||
\(89\) | 2.56545 | 0.271937 | 0.135969 | − | 0.990713i | \(-0.456585\pi\) | ||||
0.135969 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.9206 | + | 13.0201i | 1.87859 | + | 1.36488i | ||||
\(92\) | 0.115490 | − | 0.0839083i | 0.0120407 | − | 0.00874805i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0854274 | + | 0.262919i | −0.00881116 | + | 0.0271180i | ||||
\(95\) | −4.53048 | + | 3.29158i | −0.464817 | + | 0.337709i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.621738 | + | 1.91351i | 0.0631279 | + | 0.194288i | 0.977646 | − | 0.210257i | \(-0.0674300\pi\) |
−0.914518 | + | 0.404545i | \(0.867430\pi\) | |||||||
\(98\) | −13.2218 | −1.33560 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.649414 | −0.0649414 | ||||||||
\(101\) | 2.34385 | + | 7.21362i | 0.233221 | + | 0.717782i | 0.997352 | + | 0.0727205i | \(0.0231681\pi\) |
−0.764131 | + | 0.645061i | \(0.776832\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6469 | − | 9.91508i | 1.34467 | − | 0.976962i | 0.345414 | − | 0.938450i | \(-0.387738\pi\) |
0.999258 | − | 0.0385116i | \(-0.0122617\pi\) | |||||||
\(104\) | 4.91645 | − | 15.1313i | 0.482098 | − | 1.48374i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.38500 | + | 1.73281i | −0.231652 | + | 0.168305i | ||||
\(107\) | 6.27928 | + | 4.56216i | 0.607041 | + | 0.441041i | 0.848371 | − | 0.529402i | \(-0.177584\pi\) |
−0.241330 | + | 0.970443i | \(0.577584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45671 | 0.426876 | 0.213438 | − | 0.976957i | \(-0.431534\pi\) | ||||
0.213438 | + | 0.976957i | \(0.431534\pi\) | |||||||
\(110\) | −3.67135 | + | 1.17372i | −0.350050 | + | 0.111910i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.01958 | + | 9.29332i | 0.285324 | + | 0.878136i | ||||
\(113\) | −6.23952 | − | 4.53327i | −0.586964 | − | 0.426455i | 0.254264 | − | 0.967135i | \(-0.418167\pi\) |
−0.841228 | + | 0.540680i | \(0.818167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0679277 | − | 0.209060i | 0.00633429 | − | 0.0194950i | ||||
\(116\) | 1.28805 | − | 3.96421i | 0.119593 | − | 0.368068i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.39968 | + | 5.37618i | 0.681196 | + | 0.494918i | ||||
\(119\) | 6.62353 | + | 20.3851i | 0.607178 | + | 1.86870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.95996 | − | 6.38115i | 0.814542 | − | 0.580105i | ||||
\(122\) | 5.64579 | 0.511146 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.48735 | − | 1.08062i | −0.133568 | − | 0.0970426i | ||||
\(125\) | −0.809017 | + | 0.587785i | −0.0723607 | + | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.473149 | − | 1.45620i | 0.0419852 | − | 0.129217i | −0.927867 | − | 0.372912i | \(-0.878359\pi\) |
0.969852 | + | 0.243695i | \(0.0783594\pi\) | |||||||
\(128\) | 2.44266 | − | 1.77470i | 0.215903 | − | 0.156863i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.85567 | − | 5.71118i | −0.162753 | − | 0.500903i | ||||
\(131\) | −2.66108 | −0.232500 | −0.116250 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116250 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0062 | −2.08160 | ||||||||
\(134\) | −4.35544 | − | 13.4047i | −0.376252 | − | 1.15799i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4549 | − | 9.04898i | 1.06799 | − | 0.775944i | ||||
\(137\) | −3.16911 | + | 9.75352i | −0.270756 | + | 0.833300i | 0.719556 | + | 0.694435i | \(0.244345\pi\) |
−0.990311 | + | 0.138865i | \(0.955655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.28381 | − | 3.11237i | 0.363348 | − | 0.263987i | −0.391099 | − | 0.920348i | \(-0.627905\pi\) |
0.754447 | + | 0.656361i | \(0.227905\pi\) | |||||||
\(140\) | −2.25225 | − | 1.63636i | −0.190350 | − | 0.138297i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.6005 | −0.973491 | ||||||||
\(143\) | 10.0076 | + | 13.9123i | 0.836880 | + | 1.16340i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.98341 | − | 6.10429i | −0.164713 | − | 0.506934i | ||||
\(146\) | 13.6916 | + | 9.94756i | 1.13313 | + | 0.823266i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.788275 | + | 2.42606i | −0.0647958 | + | 0.199421i | ||||
\(149\) | −1.17068 | + | 3.60300i | −0.0959062 | + | 0.295169i | −0.987489 | − | 0.157689i | \(-0.949596\pi\) |
0.891583 | + | 0.452858i | \(0.149596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.78939 | + | 3.47969i | 0.389755 | + | 0.283173i | 0.765355 | − | 0.643608i | \(-0.222563\pi\) |
−0.375600 | + | 0.926782i | \(0.622563\pi\) | |||||||
\(152\) | 5.32819 | + | 16.3985i | 0.432173 | + | 1.33009i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.6902 | − | 5.18024i | −1.26435 | − | 0.417436i | ||||
\(155\) | −2.83095 | −0.227388 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.01026 | + | 4.36671i | 0.479671 | + | 0.348501i | 0.801198 | − | 0.598399i | \(-0.204196\pi\) |
−0.321528 | + | 0.946900i | \(0.604196\pi\) | |||||||
\(158\) | 7.52340 | − | 5.46607i | 0.598530 | − | 0.434857i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.08433 | + | 3.33724i | −0.0857242 | + | 0.263832i | ||||
\(161\) | 0.762360 | − | 0.553887i | 0.0600824 | − | 0.0436524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.64424 | + | 5.06044i | 0.128786 | + | 0.396364i | 0.994572 | − | 0.104051i | \(-0.0331807\pi\) |
−0.865785 | + | 0.500415i | \(0.833181\pi\) | |||||||
\(164\) | 3.80621 | 0.297215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5884 | 1.13228 | ||||||||
\(167\) | 0.609193 | + | 1.87490i | 0.0471407 | + | 0.145084i | 0.971856 | − | 0.235575i | \(-0.0756972\pi\) |
−0.924716 | + | 0.380659i | \(0.875697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0838 | + | 8.05285i | −0.852599 | + | 0.619450i | ||||
\(170\) | 1.79562 | − | 5.52634i | 0.137717 | − | 0.423851i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.67685 | + | 3.39793i | −0.356607 | + | 0.259090i | ||||
\(173\) | −1.59784 | − | 1.16090i | −0.121482 | − | 0.0882617i | 0.525385 | − | 0.850864i | \(-0.323921\pi\) |
−0.646867 | + | 0.762603i | \(0.723921\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.28684 | −0.324055 | ||||||||
\(176\) | −0.0357642 | + | 7.55994i | −0.00269583 | + | 0.569852i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.921313 | − | 2.83551i | −0.0690553 | − | 0.212530i | ||||
\(179\) | −1.63676 | − | 1.18918i | −0.122337 | − | 0.0888832i | 0.524934 | − | 0.851143i | \(-0.324090\pi\) |
−0.647271 | + | 0.762260i | \(0.724090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.22299 | − | 19.1524i | 0.462551 | − | 1.42359i | −0.399485 | − | 0.916740i | \(-0.630811\pi\) |
0.862036 | − | 0.506846i | \(-0.169189\pi\) | |||||||
\(182\) | 7.95498 | − | 24.4829i | 0.589662 | − | 1.81479i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.547562 | − | 0.397827i | −0.0403668 | − | 0.0293282i | ||||
\(185\) | 1.21383 | + | 3.73577i | 0.0892422 | + | 0.274659i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0784497 | + | 16.5829i | −0.00573681 | + | 1.21266i | ||||
\(188\) | −0.154481 | −0.0112667 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.26508 | + | 3.82530i | 0.381969 | + | 0.277517i | ||||
\(191\) | 10.2463 | − | 7.44439i | 0.741398 | − | 0.538657i | −0.151751 | − | 0.988419i | \(-0.548491\pi\) |
0.893149 | + | 0.449762i | \(0.148491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.30526 | + | 13.2502i | −0.309900 | + | 0.953773i | 0.667904 | + | 0.744248i | \(0.267192\pi\) |
−0.977803 | + | 0.209525i | \(0.932808\pi\) | |||||||
\(194\) | 1.89166 | − | 1.37437i | 0.135813 | − | 0.0986743i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.28314 | − | 7.02678i | −0.163081 | − | 0.501913i | ||||
\(197\) | −14.6060 | −1.04064 | −0.520319 | − | 0.853972i | \(-0.674187\pi\) | ||||
−0.520319 | + | 0.853972i | \(0.674187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8748 | −0.841784 | −0.420892 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420892 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(200\) | 0.951466 | + | 2.92831i | 0.0672788 | + | 0.207063i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.13125 | − | 5.18115i | 0.501753 | − | 0.364545i | ||||
\(203\) | 8.50254 | − | 26.1681i | 0.596762 | − | 1.83664i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.74165 | − | 3.44501i | 0.331171 | − | 0.240610i | ||||
\(206\) | −15.8597 | − | 11.5228i | −1.10500 | − | 0.802830i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.7784 | −0.816683 | ||||||||
\(209\) | −17.6366 | − | 5.82288i | −1.21995 | − | 0.402777i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.90710 | − | 21.2579i | −0.475504 | − | 1.46345i | −0.845277 | − | 0.534329i | \(-0.820564\pi\) |
0.369772 | − | 0.929122i | \(-0.379436\pi\) | |||||||
\(212\) | −1.33275 | − | 0.968301i | −0.0915338 | − | 0.0665032i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.78738 | − | 8.57866i | 0.190541 | − | 0.586425i | ||||
\(215\) | −2.75079 | + | 8.46605i | −0.187602 | + | 0.577380i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.81811 | − | 7.13328i | −0.666497 | − | 0.484238i | ||||
\(218\) | −1.60051 | − | 4.92586i | −0.108400 | − | 0.333621i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.25775 | − | 1.74848i | −0.0847976 | − | 0.117883i | ||||
\(221\) | −25.8362 | −1.73793 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4994 | + | 11.2610i | 1.03792 | + | 0.754091i | 0.969878 | − | 0.243592i | \(-0.0783258\pi\) |
0.0680388 | + | 0.997683i | \(0.478326\pi\) | |||||||
\(224\) | −12.1696 | + | 8.84173i | −0.813115 | + | 0.590763i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.76973 | + | 8.52434i | −0.184239 | + | 0.567031i | ||||
\(227\) | 12.4394 | − | 9.03772i | 0.825629 | − | 0.599855i | −0.0926901 | − | 0.995695i | \(-0.529547\pi\) |
0.918319 | + | 0.395840i | \(0.129547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.75064 | + | 8.46560i | 0.181767 | + | 0.559422i | 0.999878 | − | 0.0156388i | \(-0.00497820\pi\) |
−0.818110 | + | 0.575061i | \(0.804978\pi\) | |||||||
\(230\) | −0.255462 | −0.0168447 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.7624 | −1.29747 | ||||||||
\(233\) | −7.05677 | − | 21.7185i | −0.462304 | − | 1.42283i | −0.862342 | − | 0.506327i | \(-0.831003\pi\) |
0.400037 | − | 0.916499i | \(-0.368997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.192447 | + | 0.139821i | −0.0125539 | + | 0.00912092i | ||||
\(236\) | −1.57942 | + | 4.86096i | −0.102812 | + | 0.316422i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.1524 | − | 14.6416i | 1.30628 | − | 0.949071i | ||||
\(239\) | 13.6405 | + | 9.91037i | 0.882327 | + | 0.641048i | 0.933866 | − | 0.357623i | \(-0.116413\pi\) |
−0.0515388 | + | 0.998671i | \(0.516413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9607 | −0.770459 | −0.385229 | − | 0.922821i | \(-0.625878\pi\) | ||||
−0.385229 | + | 0.922821i | \(0.625878\pi\) | |||||||
\(242\) | −10.2706 | − | 7.61154i | −0.660220 | − | 0.489288i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.974917 | + | 3.00049i | 0.0624127 | + | 0.192087i | ||||
\(245\) | −9.20420 | − | 6.68724i | −0.588034 | − | 0.427232i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94184 | − | 27.5201i | 0.568955 | − | 1.75106i | ||||
\(248\) | −2.69356 | + | 8.28992i | −0.171041 | + | 0.526410i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.940197 | + | 0.683093i | 0.0594633 | + | 0.0432026i | ||||
\(251\) | −4.94533 | − | 15.2201i | −0.312146 | − | 0.960687i | −0.976913 | − | 0.213637i | \(-0.931469\pi\) |
0.664767 | − | 0.747051i | \(-0.268531\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.694432 | − | 0.222008i | 0.0436586 | − | 0.0139575i | ||||
\(254\) | −1.77941 | −0.111650 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.1359 | + | 8.09073i | 0.695996 | + | 0.505671i | ||||
\(257\) | 4.42893 | − | 3.21780i | 0.276269 | − | 0.200721i | −0.441019 | − | 0.897498i | \(-0.645383\pi\) |
0.717288 | + | 0.696776i | \(0.245383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.20348 | + | 16.0147i | −0.323328 | + | 0.995103i | ||||
\(260\) | 2.71480 | − | 1.97242i | 0.168365 | − | 0.122324i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.955657 | + | 2.94121i | 0.0590407 | + | 0.181709i | ||||
\(263\) | −11.9841 | −0.738971 | −0.369486 | − | 0.929236i | \(-0.620466\pi\) | ||||
−0.369486 | + | 0.929236i | \(0.620466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53671 | −0.155829 | ||||||||
\(266\) | 8.62119 | + | 26.5333i | 0.528599 | + | 1.62686i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.37188 | − | 4.62944i | 0.389224 | − | 0.282788i | ||||
\(269\) | −4.21700 | + | 12.9786i | −0.257115 | + | 0.791318i | 0.736291 | + | 0.676665i | \(0.236576\pi\) |
−0.993406 | + | 0.114653i | \(0.963424\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.57702 | + | 6.95812i | −0.581763 | + | 0.422675i | −0.839359 | − | 0.543577i | \(-0.817070\pi\) |
0.257596 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(272\) | −9.22050 | − | 6.69909i | −0.559075 | − | 0.406192i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9184 | 0.720014 | ||||||||
\(275\) | −3.14941 | − | 1.03980i | −0.189917 | − | 0.0627025i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.17170 | + | 9.76148i | 0.190569 | + | 0.586511i | 1.00000 | 0.000704561i | \(-0.000224269\pi\) | |
−0.809431 | + | 0.587215i | \(0.800224\pi\) | |||||||
\(278\) | −4.97841 | − | 3.61703i | −0.298585 | − | 0.216935i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.07878 | + | 12.5532i | −0.243754 | + | 0.750198i | ||||
\(281\) | 0.908167 | − | 2.79505i | 0.0541767 | − | 0.166739i | −0.920307 | − | 0.391197i | \(-0.872061\pi\) |
0.974484 | + | 0.224458i | \(0.0720612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6592 | − | 12.8301i | −1.04973 | − | 0.762673i | −0.0775682 | − | 0.996987i | \(-0.524716\pi\) |
−0.972161 | + | 0.234314i | \(0.924716\pi\) | |||||||
\(284\) | −2.00318 | − | 6.16514i | −0.118867 | − | 0.365834i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7828 | − | 16.0573i | 0.696731 | − | 0.949490i | ||||
\(287\) | 25.1252 | 1.48309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.47214 | − | 4.70228i | −0.380714 | − | 0.276605i | ||||
\(290\) | −6.03459 | + | 4.38439i | −0.354363 | + | 0.257460i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.92241 | + | 8.99424i | −0.171021 | + | 0.526348i | ||||
\(293\) | −20.0365 | + | 14.5574i | −1.17055 | + | 0.850452i | −0.991074 | − | 0.133311i | \(-0.957439\pi\) |
−0.179473 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.43207 | + | 7.48515i | 0.141601 | + | 0.435802i | ||||
\(296\) | 12.0944 | 0.702974 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.40269 | 0.255041 | ||||||||
\(299\) | 0.350999 | + | 1.08026i | 0.0202988 | + | 0.0624732i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.8723 | + | 22.4301i | −1.77945 | + | 1.29285i | ||||
\(302\) | 2.12601 | − | 6.54319i | 0.122338 | − | 0.376518i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.3269 | − | 7.50295i | 0.592289 | − | 0.430323i | ||||
\(305\) | 3.93026 | + | 2.85550i | 0.225046 | + | 0.163506i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.94023 | −0.281954 | −0.140977 | − | 0.990013i | \(-0.545024\pi\) | ||||
−0.140977 | + | 0.990013i | \(0.545024\pi\) | |||||||
\(308\) | 0.0436798 | − | 9.23316i | 0.00248889 | − | 0.526108i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.01666 | + | 3.12896i | 0.0577425 | + | 0.177713i | ||||
\(311\) | −11.1722 | − | 8.11707i | −0.633517 | − | 0.460277i | 0.224100 | − | 0.974566i | \(-0.428056\pi\) |
−0.857617 | + | 0.514289i | \(0.828056\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.25750 | + | 3.87017i | −0.0710779 | + | 0.218755i | −0.980285 | − | 0.197589i | \(-0.936689\pi\) |
0.909207 | + | 0.416344i | \(0.136689\pi\) | |||||||
\(314\) | 2.66796 | − | 8.21113i | 0.150562 | − | 0.463381i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.20412 | + | 3.05447i | 0.236500 | + | 0.171827i | ||||
\(317\) | −7.97880 | − | 24.5562i | −0.448134 | − | 1.37921i | −0.879010 | − | 0.476803i | \(-0.841795\pi\) |
0.430876 | − | 0.902411i | \(-0.358205\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5938 | − | 17.1626i | 0.705119 | − | 0.960921i | ||||
\(320\) | 8.63682 | 0.482813 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.885974 | − | 0.643698i | −0.0493734 | − | 0.0358719i | ||||
\(323\) | 22.6524 | − | 16.4579i | 1.26041 | − | 0.915743i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.59676 | − | 4.91433i | 0.0885725 | − | 0.272598i | ||||
\(326\) | 5.00265 | − | 3.63464i | 0.277071 | − | 0.201304i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.57654 | − | 17.1628i | −0.307913 | − | 0.947659i | ||||
\(329\) | −1.01974 | −0.0562203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.35008 | −0.184137 | −0.0920684 | − | 0.995753i | \(-0.529348\pi\) | ||||
−0.0920684 | + | 0.995753i | \(0.529348\pi\) | |||||||
\(332\) | 2.51913 | + | 7.75307i | 0.138255 | + | 0.425505i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.85349 | − | 1.34664i | 0.101419 | − | 0.0736850i | ||||
\(335\) | 3.74775 | − | 11.5344i | 0.204761 | − | 0.630191i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.1669 | − | 16.1052i | 1.20751 | − | 0.877307i | 0.212507 | − | 0.977160i | \(-0.431837\pi\) |
0.995002 | + | 0.0998530i | \(0.0318372\pi\) | |||||||
\(338\) | 12.8810 | + | 9.35859i | 0.700634 | + | 0.509040i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.24707 | 0.176097 | ||||||||
\(341\) | −5.48285 | − | 7.62206i | −0.296913 | − | 0.412758i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.79826 | − | 17.8452i | −0.313076 | − | 0.963550i | ||||
\(344\) | 22.1739 | + | 16.1103i | 1.19554 | + | 0.868610i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.709284 | + | 2.18295i | −0.0381313 | + | 0.117356i | ||||
\(347\) | −4.89065 | + | 15.0519i | −0.262544 | + | 0.808027i | 0.729705 | + | 0.683762i | \(0.239657\pi\) |
−0.992249 | + | 0.124265i | \(0.960343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.96043 | + | 2.15088i | 0.158468 | + | 0.115134i | 0.664194 | − | 0.747561i | \(-0.268775\pi\) |
−0.505725 | + | 0.862695i | \(0.668775\pi\) | |||||||
\(350\) | 1.53950 | + | 4.73811i | 0.0822900 | + | 0.253263i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.0853 | + | 3.54393i | −0.590846 | + | 0.188892i | ||||
\(353\) | 27.4937 | 1.46334 | 0.731671 | − | 0.681658i | \(-0.238741\pi\) | ||||
0.731671 | + | 0.681658i | \(0.238741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.07556 | − | 5.86724i | −0.428606 | − | 0.311401i | ||||
\(356\) | 1.34785 | − | 0.979273i | 0.0714361 | − | 0.0519014i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.726559 | + | 2.23612i | −0.0383998 | + | 0.118183i | ||||
\(359\) | 0.387309 | − | 0.281397i | 0.0204414 | − | 0.0148515i | −0.577518 | − | 0.816378i | \(-0.695979\pi\) |
0.597959 | + | 0.801527i | \(0.295979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.81936 | + | 11.7548i | 0.201019 | + | 0.618673i | ||||
\(362\) | −23.4033 | −1.23005 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.3852 | 0.753992 | ||||||||
\(365\) | 4.50007 | + | 13.8498i | 0.235544 | + | 0.724931i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.5961 | − | 14.9639i | 1.07511 | − | 0.781111i | 0.0982843 | − | 0.995158i | \(-0.468665\pi\) |
0.976823 | + | 0.214047i | \(0.0686645\pi\) | |||||||
\(368\) | −0.154837 | + | 0.476539i | −0.00807143 | + | 0.0248413i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.69311 | − | 2.68320i | 0.191996 | − | 0.139493i | ||||
\(371\) | −8.79762 | − | 6.39184i | −0.456750 | − | 0.331848i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.75967 | −0.142890 | −0.0714451 | − | 0.997445i | \(-0.522761\pi\) | ||||
−0.0714451 | + | 0.997445i | \(0.522761\pi\) | |||||||
\(374\) | 18.3568 | − | 5.86861i | 0.949205 | − | 0.303459i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.226333 | + | 0.696580i | 0.0116722 | + | 0.0359234i | ||||
\(377\) | 26.8315 | + | 19.4942i | 1.38189 | + | 1.00400i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.69130 | + | 20.5937i | −0.343709 | + | 1.05783i | 0.618562 | + | 0.785736i | \(0.287716\pi\) |
−0.962271 | + | 0.272092i | \(0.912284\pi\) | |||||||
\(380\) | −1.12380 | + | 3.45871i | −0.0576499 | + | 0.177428i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9077 | − | 8.65148i | −0.609253 | − | 0.442648i | ||||
\(383\) | −5.01518 | − | 15.4351i | −0.256264 | − | 0.788699i | −0.993578 | − | 0.113149i | \(-0.963906\pi\) |
0.737314 | − | 0.675550i | \(-0.236094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.30253 | − | 11.5419i | −0.423136 | − | 0.588229i | ||||
\(386\) | 16.1912 | 0.824109 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.05707 | + | 0.768007i | 0.0536647 | + | 0.0389897i | ||||
\(389\) | −13.1802 | + | 9.57598i | −0.668263 | + | 0.485522i | −0.869443 | − | 0.494033i | \(-0.835522\pi\) |
0.201180 | + | 0.979554i | \(0.435522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.339639 | + | 1.04530i | −0.0171763 | + | 0.0528631i | ||||
\(392\) | −28.3398 | + | 20.5901i | −1.43138 | + | 1.03996i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.24537 | + | 16.1436i | 0.264258 | + | 0.813302i | ||||
\(395\) | 8.00194 | 0.402621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.9673 | −1.00213 | −0.501064 | − | 0.865410i | \(-0.667058\pi\) | ||||
−0.501064 | + | 0.865410i | \(0.667058\pi\) | |||||||
\(398\) | 4.26453 | + | 13.1249i | 0.213761 | + | 0.657890i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.84410 | − | 1.33982i | 0.0922050 | − | 0.0669909i | ||||
\(401\) | 8.44448 | − | 25.9894i | 0.421697 | − | 1.29785i | −0.484425 | − | 0.874833i | \(-0.660971\pi\) |
0.906122 | − | 0.423017i | \(-0.139029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8345 | − | 8.59825i | 0.589517 | − | 0.428309i | ||||
\(404\) | 3.98498 | + | 2.89526i | 0.198260 | + | 0.144044i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −31.9763 | −1.58696 | ||||||||
\(407\) | −7.70731 | + | 10.5034i | −0.382037 | + | 0.520632i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.70626 | + | 23.7174i | 0.381050 | + | 1.17275i | 0.939305 | + | 0.343082i | \(0.111471\pi\) |
−0.558255 | + | 0.829669i | \(0.688529\pi\) | |||||||
\(410\) | −5.51049 | − | 4.00361i | −0.272144 | − | 0.197724i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.38518 | − | 10.4185i | 0.166776 | − | 0.513283i | ||||
\(413\) | −10.4259 | + | 32.0876i | −0.513025 | + | 1.57893i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1556 | + | 7.37844i | 0.498517 | + | 0.362193i | ||||
\(416\) | −5.60301 | − | 17.2443i | −0.274710 | − | 0.845471i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.102110 | + | 21.5843i | −0.00499437 | + | 1.05572i | ||||
\(419\) | −16.8256 | −0.821986 | −0.410993 | − | 0.911639i | \(-0.634818\pi\) | ||||
−0.410993 | + | 0.911639i | \(0.634818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0933 | − | 13.8721i | −0.930551 | − | 0.676085i | 0.0155763 | − | 0.999879i | \(-0.495042\pi\) |
−0.946128 | + | 0.323793i | \(0.895042\pi\) | |||||||
\(422\) | −21.0151 | + | 15.2684i | −1.02300 | + | 0.743253i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.41359 | + | 7.42826i | −0.117214 | + | 0.360748i | ||||
\(425\) | 4.04508 | − | 2.93893i | 0.196215 | − | 0.142559i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.43552 | + | 19.8065i | 0.311437 | + | 0.958504i | ||||
\(428\) | 5.04050 | 0.243642 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.3451 | 0.498886 | ||||||||
\(431\) | 11.6362 | + | 35.8126i | 0.560497 | + | 1.72503i | 0.680966 | + | 0.732315i | \(0.261560\pi\) |
−0.120469 | + | 0.992717i | \(0.538440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0594 | − | 18.2068i | 1.20428 | − | 0.874961i | 0.209581 | − | 0.977791i | \(-0.432790\pi\) |
0.994699 | + | 0.102831i | \(0.0327900\pi\) | |||||||
\(434\) | −4.35827 | + | 13.4134i | −0.209204 | + | 0.643862i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.34150 | − | 1.70120i | 0.112137 | − | 0.0814726i | ||||
\(437\) | −0.995884 | − | 0.723552i | −0.0476396 | − | 0.0346122i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.2131 | −1.34654 | −0.673268 | − | 0.739399i | \(-0.735110\pi\) | ||||
−0.673268 | + | 0.739399i | \(0.735110\pi\) | |||||||
\(440\) | −6.04143 | + | 8.23313i | −0.288014 | + | 0.392499i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.27837 | + | 28.5559i | 0.441327 | + | 1.35827i | ||||
\(443\) | 11.8456 | + | 8.60636i | 0.562803 | + | 0.408900i | 0.832484 | − | 0.554050i | \(-0.186918\pi\) |
−0.269681 | + | 0.962950i | \(0.586918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.792768 | − | 2.43989i | 0.0375808 | − | 0.115662i | ||||
\(446\) | 6.88019 | − | 21.1751i | 0.325787 | − | 1.00267i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.9536 | + | 21.7626i | 1.41517 | + | 1.02818i | ||||
\(449\) | −3.70749 | − | 11.4105i | −0.174967 | − | 0.538493i | 0.824665 | − | 0.565622i | \(-0.191364\pi\) |
−0.999632 | + | 0.0271282i | \(0.991364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.4587 | + | 6.09429i | 0.869187 | + | 0.286969i | ||||
\(452\) | −5.00858 | −0.235584 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.4564 | − | 10.5032i | −0.678471 | − | 0.492938i | ||||
\(455\) | 17.9206 | − | 13.0201i | 0.840132 | − | 0.610392i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10367 | − | 9.55211i | 0.145183 | − | 0.446829i | −0.851851 | − | 0.523784i | \(-0.824520\pi\) |
0.997035 | + | 0.0769553i | \(0.0245199\pi\) | |||||||
\(458\) | 8.36893 | − | 6.08039i | 0.391055 | − | 0.284118i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0441132 | − | 0.135767i | −0.00205679 | − | 0.00633015i | ||||
\(461\) | 13.4491 | 0.626386 | 0.313193 | − | 0.949689i | \(-0.398601\pi\) | ||||
0.313193 | + | 0.949689i | \(0.398601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7836 | 0.872946 | 0.436473 | − | 0.899717i | \(-0.356227\pi\) | ||||
0.436473 | + | 0.899717i | \(0.356227\pi\) | |||||||
\(464\) | 4.52104 | + | 13.9143i | 0.209884 | + | 0.645957i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.4705 | + | 15.5992i | −0.994602 | + | 0.722620i | ||||
\(467\) | −8.20470 | + | 25.2515i | −0.379668 | + | 1.16850i | 0.560607 | + | 0.828082i | \(0.310568\pi\) |
−0.940275 | + | 0.340416i | \(0.889432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.0614 | − | 30.5594i | 1.94221 | − | 1.41110i | ||||
\(470\) | 0.223652 | + | 0.162493i | 0.0103163 | + | 0.00749522i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.2329 | 1.11541 | ||||||||
\(473\) | −28.1216 | + | 8.99039i | −1.29303 | + | 0.413379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.73049 | + | 5.32589i | 0.0794002 | + | 0.244369i | ||||
\(476\) | 11.2613 | + | 8.18178i | 0.516159 | + | 0.375011i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.05501 | − | 18.6354i | 0.276950 | − | 0.852363i | ||||
\(479\) | −3.33214 | + | 10.2553i | −0.152249 | + | 0.468575i | −0.997872 | − | 0.0652062i | \(-0.979229\pi\) |
0.845623 | + | 0.533781i | \(0.179229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4206 | − | 11.9303i | −0.748716 | − | 0.543974i | ||||
\(482\) | 4.29538 | + | 13.2198i | 0.195649 | + | 0.602146i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.27166 | − | 6.77273i | 0.103257 | − | 0.307851i | ||||
\(485\) | 2.01199 | 0.0913596 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.51018 | − | 4.00338i | −0.249690 | − | 0.181410i | 0.455899 | − | 0.890031i | \(-0.349318\pi\) |
−0.705589 | + | 0.708621i | \(0.749318\pi\) | |||||||
\(488\) | 12.1013 | − | 8.79212i | 0.547801 | − | 0.398001i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.08575 | + | 12.5746i | −0.184575 | + | 0.568064i | ||||
\(491\) | 21.1116 | − | 15.3385i | 0.952754 | − | 0.692216i | 0.00129727 | − | 0.999999i | \(-0.499587\pi\) |
0.951457 | + | 0.307783i | \(0.0995871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.91703 | + | 30.5215i | 0.446640 | + | 1.37462i | ||||
\(494\) | −33.6283 | −1.51301 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.45297 | 0.289747 | ||||||||
\(497\) | −13.2231 | − | 40.6967i | −0.593139 | − | 1.82549i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6815 | + | 11.3933i | −0.702000 | + | 0.510033i | −0.880583 | − | 0.473892i | \(-0.842849\pi\) |
0.178583 | + | 0.983925i | \(0.442849\pi\) | |||||||
\(500\) | −0.200680 | + | 0.617629i | −0.00897468 | + | 0.0276212i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.0464 | + | 10.9318i | −0.671552 | + | 0.487911i | ||||
\(503\) | 15.2437 | + | 11.0752i | 0.679683 | + | 0.493819i | 0.873253 | − | 0.487268i | \(-0.162007\pi\) |
−0.193570 | + | 0.981087i | \(0.562007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.58484 | 0.337521 | ||||||||
\(506\) | −0.494765 | − | 0.687805i | −0.0219950 | − | 0.0305767i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.307270 | − | 0.945678i | −0.0136329 | − | 0.0419577i | ||||
\(509\) | −4.16741 | − | 3.02780i | −0.184717 | − | 0.134205i | 0.491584 | − | 0.870830i | \(-0.336418\pi\) |
−0.676301 | + | 0.736625i | \(0.736418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.2911 | + | 59.3718i | −0.853387 | + | 2.62645i | ||||
\(512\) | 6.80928 | − | 20.9568i | 0.300930 | − | 0.926168i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.14707 | − | 3.73956i | −0.227027 | − | 0.164945i | ||||
\(515\) | −5.21267 | − | 16.0429i | −0.229698 | − | 0.706936i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.749175 | − | 0.247346i | −0.0329487 | − | 0.0108783i | ||||
\(518\) | 19.5692 | 0.859820 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.8714 | − | 9.35164i | −0.564450 | − | 0.410097i | ||||
\(521\) | −33.5759 | + | 24.3944i | −1.47099 | + | 1.06874i | −0.490663 | + | 0.871349i | \(0.663246\pi\) |
−0.980326 | + | 0.197387i | \(0.936754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.13926 | + | 6.58397i | −0.0935434 | + | 0.287897i | −0.986871 | − | 0.161508i | \(-0.948364\pi\) |
0.893328 | + | 0.449405i | \(0.148364\pi\) | |||||||
\(524\) | −1.39810 | + | 1.01578i | −0.0610762 | + | 0.0443745i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.30377 | + | 13.2456i | 0.187653 | + | 0.577537i | ||||
\(527\) | 14.1548 | 0.616592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9517 | −0.997899 | ||||||||
\(530\) | 0.910990 | + | 2.80374i | 0.0395709 | + | 0.121787i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.6125 | + | 9.16355i | −0.546823 | + | 0.397290i | ||||
\(533\) | −9.35863 | + | 28.8029i | −0.405367 | + | 1.24759i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.27928 | − | 4.56216i | 0.271477 | − | 0.197239i | ||||
\(536\) | −30.2104 | − | 21.9492i | −1.30489 | − | 0.948059i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.8592 | 0.683740 | ||||||||
\(539\) | 0.178505 | − | 37.7329i | 0.00768874 | − | 1.62527i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.78173 | − | 27.0274i | −0.377556 | − | 1.16200i | −0.941738 | − | 0.336348i | \(-0.890808\pi\) |
0.564182 | − | 0.825651i | \(-0.309192\pi\) | |||||||
\(542\) | 11.1299 | + | 8.08635i | 0.478071 | + | 0.347339i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.42167 | − | 16.6862i | 0.232452 | − | 0.715415i | ||||
\(545\) | 1.37720 | − | 4.23858i | 0.0589928 | − | 0.181561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9205 | − | 15.1996i | −0.894496 | − | 0.649889i | 0.0425503 | − | 0.999094i | \(-0.486452\pi\) |
−0.937046 | + | 0.349205i | \(0.886452\pi\) | |||||||
\(548\) | 2.05807 | + | 6.33407i | 0.0879162 | + | 0.270578i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0182340 | + | 3.85436i | −0.000777501 | + | 0.164351i | ||||
\(551\) | −35.9431 | −1.53123 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.7518 | + | 20.1628i | 1.18012 | + | 0.857411i | ||||
\(554\) | 9.65002 | − | 7.01115i | 0.409990 | − | 0.297875i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.06262 | − | 3.27039i | 0.0450649 | − | 0.138696i | ||||
\(557\) | −6.52399 | + | 4.73996i | −0.276430 | + | 0.200838i | −0.717359 | − | 0.696704i | \(-0.754649\pi\) |
0.440929 | + | 0.897542i | \(0.354649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2140 | − | 43.7461i | −0.601186 | − | 1.85026i | ||||
\(560\) | 9.77157 | 0.412924 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.41542 | −0.144071 | ||||||||
\(563\) | −9.16284 | − | 28.2003i | −0.386168 | − | 1.18850i | −0.935630 | − | 0.352983i | \(-0.885167\pi\) |
0.549462 | − | 0.835519i | \(-0.314833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.23952 | + | 4.53327i | −0.262498 | + | 0.190716i | ||||
\(566\) | −7.83892 | + | 24.1257i | −0.329494 | + | 1.01408i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.8647 | + | 18.0653i | −1.04330 | + | 0.758002i | ||||
\(569\) | −34.0618 | − | 24.7473i | −1.42794 | − | 1.03746i | −0.990395 | − | 0.138266i | \(-0.955847\pi\) |
−0.437548 | − | 0.899195i | \(-0.644153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6823 | −1.11662 | −0.558311 | − | 0.829632i | \(-0.688550\pi\) | ||||
−0.558311 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(572\) | 10.5684 | + | 3.48924i | 0.441887 | + | 0.145893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.02304 | − | 27.7700i | −0.376614 | − | 1.15910i | ||||
\(575\) | −0.177837 | − | 0.129206i | −0.00741632 | − | 0.00538827i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.02228 | + | 3.14627i | −0.0425582 | + | 0.130981i | −0.970078 | − | 0.242793i | \(-0.921936\pi\) |
0.927520 | + | 0.373774i | \(0.121936\pi\) | |||||||
\(578\) | −2.87299 | + | 8.84214i | −0.119500 | + | 0.367785i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.37216 | − | 2.45002i | −0.140021 | − | 0.101731i | ||||
\(581\) | 16.6290 | + | 51.1788i | 0.689887 | + | 2.12325i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.91296 | − | 6.82982i | −0.203474 | − | 0.282862i | ||||
\(584\) | 44.8381 | 1.85542 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2854 | + | 16.9178i | 0.961911 | + | 0.698869i | ||||
\(587\) | −6.89906 | + | 5.01246i | −0.284755 | + | 0.206886i | −0.720989 | − | 0.692947i | \(-0.756312\pi\) |
0.436234 | + | 0.899833i | \(0.356312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.89893 | + | 15.0774i | −0.201857 | + | 0.621252i | ||||
\(590\) | 7.39968 | − | 5.37618i | 0.304640 | − | 0.221334i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.76684 | − | 8.51544i | −0.113716 | − | 0.349983i | ||||
\(593\) | 23.4343 | 0.962333 | 0.481167 | − | 0.876629i | \(-0.340213\pi\) | ||||
0.481167 | + | 0.876629i | \(0.340213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4342 | 0.878717 | ||||||||
\(596\) | 0.760259 | + | 2.33984i | 0.0311414 | + | 0.0958434i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.06793 | − | 0.775895i | 0.0436708 | − | 0.0317287i | ||||
\(599\) | −5.82017 | + | 17.9126i | −0.237805 | + | 0.731890i | 0.758931 | + | 0.651171i | \(0.225722\pi\) |
−0.996737 | + | 0.0807194i | \(0.974278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4664 | − | 22.1351i | 1.24275 | − | 0.902911i | 0.244971 | − | 0.969530i | \(-0.421221\pi\) |
0.997778 | + | 0.0666198i | \(0.0212214\pi\) | |||||||
\(602\) | 35.8782 | + | 26.0670i | 1.46229 | + | 1.06241i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.84453 | 0.156432 | ||||||||
\(605\) | −3.30005 | − | 10.4933i | −0.134166 | − | 0.426614i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.07520 | − | 27.9306i | −0.368351 | − | 1.13367i | −0.947856 | − | 0.318699i | \(-0.896754\pi\) |
0.579505 | − | 0.814969i | \(-0.303246\pi\) | |||||||
\(608\) | 15.8973 | + | 11.5501i | 0.644723 | + | 0.468418i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.74465 | − | 5.36947i | 0.0706387 | − | 0.217403i | ||||
\(611\) | 0.379834 | − | 1.16901i | 0.0153665 | − | 0.0472931i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4453 | + | 7.58894i | 0.421881 | + | 0.306515i | 0.778394 | − | 0.627776i | \(-0.216035\pi\) |
−0.356513 | + | 0.934290i | \(0.616035\pi\) | |||||||
\(614\) | 1.77415 | + | 5.46027i | 0.0715989 | + | 0.220359i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −41.6978 | + | 13.3307i | −1.68005 | + | 0.537109i | ||||
\(617\) | −41.6041 | −1.67492 | −0.837459 | − | 0.546500i | \(-0.815960\pi\) | ||||
−0.837459 | + | 0.546500i | \(0.815960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.45545 | − | 2.51053i | −0.138886 | − | 0.100907i | 0.516173 | − | 0.856484i | \(-0.327356\pi\) |
−0.655059 | + | 0.755578i | \(0.727356\pi\) | |||||||
\(620\) | −1.48735 | + | 1.08062i | −0.0597333 | + | 0.0433988i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.95935 | + | 15.2633i | −0.198852 | + | 0.612002i | ||||
\(623\) | 8.89731 | − | 6.46427i | 0.356463 | − | 0.258986i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 4.72918 | 0.189016 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.82455 | 0.192521 | ||||||||
\(629\) | −6.06913 | − | 18.6789i | −0.241992 | − | 0.744775i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2892 | − | 16.1941i | 0.887319 | − | 0.644675i | −0.0478586 | − | 0.998854i | \(-0.515240\pi\) |
0.935178 | + | 0.354179i | \(0.115240\pi\) | |||||||
\(632\) | 7.61358 | − | 23.4322i | 0.302852 | − | 0.932082i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.2758 | + | 17.6374i | −0.964116 | + | 0.700471i | ||||
\(635\) | −1.23872 | − | 0.899983i | −0.0491571 | − | 0.0357147i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 58.7877 | 2.32925 | ||||||||
\(638\) | −23.4920 | − | 7.75607i | −0.930057 | − | 0.307066i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.933014 | − | 2.87152i | −0.0368806 | − | 0.113507i | ||||
\(641\) | 7.41712 | + | 5.38885i | 0.292958 | + | 0.212847i | 0.724550 | − | 0.689222i | \(-0.242048\pi\) |
−0.431591 | + | 0.902069i | \(0.642048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.05346 | + | 3.24223i | −0.0415446 | + | 0.127861i | −0.969678 | − | 0.244387i | \(-0.921413\pi\) |
0.928133 | + | 0.372249i | \(0.121413\pi\) | |||||||
\(644\) | 0.189106 | − | 0.582010i | 0.00745184 | − | 0.0229344i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.3254 | − | 19.1265i | −1.03576 | − | 0.752523i | ||||
\(647\) | −6.90986 | − | 21.2663i | −0.271654 | − | 0.836066i | −0.990085 | − | 0.140468i | \(-0.955139\pi\) |
0.718431 | − | 0.695598i | \(-0.244861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4427 | + | 21.0450i | −0.606179 | + | 0.826087i | ||||
\(650\) | −6.00509 | −0.235539 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.79551 | + | 2.03106i | 0.109481 | + | 0.0795423i | ||||
\(653\) | −11.9699 | + | 8.69667i | −0.468420 | + | 0.340327i | −0.796825 | − | 0.604210i | \(-0.793489\pi\) |
0.328405 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.822320 | + | 2.53084i | −0.0321307 | + | 0.0988882i | ||||
\(656\) | −10.8083 | + | 7.85267i | −0.421992 | + | 0.306595i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.366214 | + | 1.12709i | 0.0142765 | + | 0.0439385i | ||||
\(659\) | 47.4724 | 1.84926 | 0.924631 | − | 0.380864i | \(-0.124373\pi\) | ||||
0.924631 | + | 0.380864i | \(0.124373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | 1.20309 | + | 3.70273i | 0.0467594 | + | 0.143911i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.2690 | − | 22.7183i | 1.21347 | − | 0.881641i | ||||
\(665\) | −7.41833 | + | 22.8313i | −0.287670 | + | 0.885358i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.14144 | − | 0.829302i | 0.0441966 | − | 0.0321107i | ||||
\(668\) | 1.03574 | + | 0.752510i | 0.0400740 | + | 0.0291155i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.0945 | −0.544518 | ||||||||
\(671\) | −0.0762228 | + | 16.1122i | −0.00294255 | + | 0.622005i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8639 | − | 36.5133i | −0.457319 | − | 1.40748i | −0.868391 | − | 0.495880i | \(-0.834846\pi\) |
0.411072 | − | 0.911603i | \(-0.365154\pi\) | |||||||
\(674\) | −25.7612 | − | 18.7166i | −0.992285 | − | 0.720937i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.74938 | + | 8.46172i | −0.105745 | + | 0.325451i | ||||
\(677\) | 7.08677 | − | 21.8108i | 0.272367 | − | 0.838259i | −0.717537 | − | 0.696520i | \(-0.754731\pi\) |
0.989904 | − | 0.141739i | \(-0.0452693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.97782 | + | 5.06969i | 0.267784 | + | 0.194557i | ||||
\(680\) | −4.75733 | − | 14.6416i | −0.182435 | − | 0.561478i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.45540 | + | 8.79727i | −0.247190 | + | 0.336865i | ||||
\(683\) | −25.9084 | −0.991359 | −0.495680 | − | 0.868505i | \(-0.665081\pi\) | ||||
−0.495680 | + | 0.868505i | \(0.665081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.29684 | + | 6.02801i | 0.317006 | + | 0.230318i | ||||
\(686\) | −17.6414 | + | 12.8173i | −0.673553 | + | 0.489365i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.27024 | − | 19.2978i | 0.239050 | − | 0.735722i | ||||
\(689\) | 10.6044 | − | 7.70454i | 0.403995 | − | 0.293520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.57824 | + | 14.0904i | 0.174165 | + | 0.536023i | 0.999594 | − | 0.0284814i | \(-0.00906715\pi\) |
−0.825430 | + | 0.564505i | \(0.809067\pi\) | |||||||
\(692\) | −1.28262 | −0.0487579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.3927 | 0.698177 | ||||||||
\(695\) | −1.63627 | − | 5.03592i | −0.0620672 | − | 0.191023i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.7082 | + | 17.2250i | −0.898014 | + | 0.652445i | ||||
\(698\) | 1.31414 | − | 4.04450i | 0.0497409 | − | 0.153087i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.25225 | + | 1.63636i | −0.0851271 | + | 0.0618484i | ||||
\(701\) | 4.45471 | + | 3.23653i | 0.168252 | + | 0.122242i | 0.668725 | − | 0.743510i | \(-0.266840\pi\) |
−0.500473 | + | 0.865752i | \(0.666840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.9968 | 0.829626 | ||||||||
\(704\) | 16.7273 | + | 23.2538i | 0.630435 | + | 0.876409i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.87362 | − | 30.3879i | −0.371599 | − | 1.14366i | ||||
\(707\) | 26.3052 | + | 19.1119i | 0.989309 | + | 0.718775i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.53161 | + | 17.0245i | −0.207744 | + | 0.639370i | 0.791846 | + | 0.610721i | \(0.209120\pi\) |
−0.999590 | + | 0.0286488i | \(0.990880\pi\) | |||||||
\(710\) | −3.58475 | + | 11.0327i | −0.134533 | + | 0.414050i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.39046 | − | 4.64294i | −0.239493 | − | 0.174002i | ||||
\(713\) | −0.192300 | − | 0.591840i | −0.00720171 | − | 0.0221646i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3239 | − | 5.21870i | 0.610478 | − | 0.195168i | ||||
\(716\) | −1.31386 | −0.0491012 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.450110 | − | 0.327024i | −0.0167980 | − | 0.0122044i | ||||
\(719\) | 26.3673 | − | 19.1570i | 0.983334 | − | 0.714434i | 0.0248831 | − | 0.999690i | \(-0.492079\pi\) |
0.958451 | + | 0.285256i | \(0.0920786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.3459 | − | 68.7735i | 0.832204 | − | 2.56126i | ||||
\(722\) | 11.6206 | − | 8.44284i | 0.432473 | − | 0.314210i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.04130 | − | 12.4378i | −0.150194 | − | 0.462248i | ||||
\(725\) | −6.41843 | −0.238375 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.0199 | −1.59552 | −0.797759 | − | 0.602976i | \(-0.793982\pi\) | ||||
−0.797759 | + | 0.602976i | \(0.793982\pi\) | |||||||
\(728\) | −21.0760 | − | 64.8654i | −0.781130 | − | 2.40407i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.6916 | − | 9.94756i | 0.506750 | − | 0.368176i | ||||
\(731\) | 13.7539 | − | 42.3302i | 0.508708 | − | 1.56564i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.9323 | + | 23.9267i | −1.21638 | + | 0.883755i | −0.995795 | − | 0.0916123i | \(-0.970798\pi\) |
−0.220589 | + | 0.975367i | \(0.570798\pi\) | |||||||
\(734\) | −23.9357 | − | 17.3903i | −0.883483 | − | 0.641888i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.771340 | −0.0284320 | ||||||||
\(737\) | 38.3136 | − | 12.2488i | 1.41130 | − | 0.451189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7810 | + | 36.2581i | 0.433370 | + | 1.33377i | 0.894748 | + | 0.446571i | \(0.147355\pi\) |
−0.461379 | + | 0.887203i | \(0.652645\pi\) | |||||||
\(740\) | 2.06373 | + | 1.49939i | 0.0758643 | + | 0.0551186i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.90527 | + | 12.0192i | −0.143367 | + | 0.441238i | ||||
\(743\) | 5.57409 | − | 17.1553i | 0.204493 | − | 0.629366i | −0.795240 | − | 0.606294i | \(-0.792655\pi\) |
0.999734 | − | 0.0230717i | \(-0.00734459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.06489 | + | 2.22677i | 0.112289 | + | 0.0815827i | ||||
\(746\) | 0.991061 | + | 3.05017i | 0.0362853 | + | 0.111675i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.28875 | + | 8.74240i | 0.229940 | + | 0.319654i | ||||
\(749\) | 33.2728 | 1.21576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1861 | + | 10.3068i | 0.517657 | + | 0.376100i | 0.815720 | − | 0.578446i | \(-0.196341\pi\) |
−0.298064 | + | 0.954546i | \(0.596341\pi\) | |||||||
\(752\) | 0.438670 | − | 0.318713i | 0.0159967 | − | 0.0116223i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.9105 | − | 36.6568i | 0.433756 | − | 1.33496i | ||||
\(755\) | 4.78939 | − | 3.47969i | 0.174304 | − | 0.126639i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.02236 | − | 24.6903i | −0.291578 | − | 0.897383i | −0.984350 | − | 0.176227i | \(-0.943611\pi\) |
0.692772 | − | 0.721157i | \(-0.256389\pi\) | |||||||
\(758\) | 25.1646 | 0.914019 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.2424 | 0.625447 | ||||||||
\(761\) | −8.65430 | − | 26.6352i | −0.313718 | − | 0.965525i | −0.976279 | − | 0.216517i | \(-0.930530\pi\) |
0.662561 | − | 0.749008i | \(-0.269470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4564 | − | 11.2298i | 0.559561 | − | 0.406545i | ||||
\(764\) | 2.54164 | − | 7.82237i | 0.0919534 | − | 0.283003i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.2589 | + | 11.0862i | −0.551326 | + | 0.400562i | ||||
\(767\) | −32.9011 | − | 23.9040i | −1.18799 | − | 0.863124i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9537 | 0.827732 | 0.413866 | − | 0.910338i | \(-0.364178\pi\) | ||||
0.413866 | + | 0.910338i | \(0.364178\pi\) | |||||||
\(770\) | −9.77524 | + | 13.3215i | −0.352275 | + | 0.480073i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.79590 | + | 8.60489i | 0.100627 | + | 0.309697i | ||||
\(773\) | −19.0347 | − | 13.8295i | −0.684631 | − | 0.497414i | 0.190259 | − | 0.981734i | \(-0.439067\pi\) |
−0.874891 | + | 0.484320i | \(0.839067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.874813 | + | 2.69240i | −0.0314242 | + | 0.0967138i | ||||
\(776\) | 1.91434 | − | 5.89172i | 0.0687207 | − | 0.211500i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.3173 | + | 11.1287i | 0.549153 | + | 0.398983i | ||||
\(779\) | −10.1424 | − | 31.2151i | −0.363389 | − | 1.11840i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.156616 | − | 33.1060i | 0.00560416 | − | 1.18463i | ||||
\(782\) | 1.27731 | 0.0456765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.9804 | + | 15.2431i | 0.749298 | + | 0.544397i | ||||
\(785\) | 6.01026 | − | 4.36671i | 0.214515 | − | 0.155854i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.80964 | + | 24.0356i | −0.278384 | + | 0.856777i | 0.709921 | + | 0.704282i | \(0.248731\pi\) |
−0.988304 | + | 0.152495i | \(0.951269\pi\) | |||||||
\(788\) | −7.67383 | + | 5.57536i | −0.273369 | + | 0.198614i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.87368 | − | 8.84429i | −0.102241 | − | 0.314666i | ||||
\(791\) | −33.0621 | −1.17555 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.1028 | −0.891427 | ||||||||
\(794\) | 7.17071 | + | 22.0692i | 0.254479 | + | 0.783205i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.23888 | + | 4.53281i | −0.221131 | + | 0.160661i | ||||
\(797\) | −2.67499 | + | 8.23277i | −0.0947530 | + | 0.291620i | −0.987189 | − | 0.159554i | \(-0.948994\pi\) |
0.892436 | + | 0.451173i | \(0.148994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.962236 | − | 0.699105i | 0.0340414 | − | 0.0247326i | ||||
\(800\) | 2.83882 | + | 2.06253i | 0.100368 | + | 0.0729213i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.7579 | −1.12141 | ||||||||
\(803\) | −28.5736 | + | 38.9395i | −1.00834 | + | 1.37415i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.291195 | − | 0.896208i | −0.0102633 | − | 0.0315872i | ||||
\(806\) | −13.7534 | − | 9.99243i | −0.484443 | − | 0.351968i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.21672 | − | 22.2108i | 0.253883 | − | 0.781373i | ||||
\(809\) | 3.15582 | − | 9.71261i | 0.110953 | − | 0.341477i | −0.880129 | − | 0.474735i | \(-0.842544\pi\) |
0.991081 | + | 0.133258i | \(0.0425438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.5273 | + | 27.9917i | 1.35288 | + | 0.982923i | 0.998862 | + | 0.0476835i | \(0.0151839\pi\) |
0.354015 | + | 0.935240i | \(0.384816\pi\) | |||||||
\(812\) | −5.52167 | − | 16.9940i | −0.193773 | − | 0.596371i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.3769 | + | 4.74664i | 0.503910 | + | 0.166370i | ||||
\(815\) | 5.32086 | 0.186381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.3291 | + | 29.3008i | 1.41094 | + | 1.02510i | ||||
\(818\) | 23.4466 | − | 17.0350i | 0.819792 | − | 0.595613i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.17618 | − | 3.61993i | 0.0410742 | − | 0.126413i | ||||
\(821\) | −38.4767 | + | 27.9550i | −1.34285 | + | 0.975635i | −0.343512 | + | 0.939148i | \(0.611617\pi\) |
−0.999334 | + | 0.0364868i | \(0.988383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.64384 | − | 23.5253i | −0.266448 | − | 0.820041i | −0.991356 | − | 0.131196i | \(-0.958118\pi\) |
0.724909 | − | 0.688845i | \(-0.241882\pi\) | |||||||
\(824\) | −51.9384 | −1.80936 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39.2096 | 1.36428 | ||||||||
\(827\) | 0.482580 | + | 1.48523i | 0.0167810 | + | 0.0516465i | 0.959096 | − | 0.283080i | \(-0.0913561\pi\) |
−0.942315 | + | 0.334726i | \(0.891356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.1365 | + | 24.8016i | −1.18561 | + | 0.861396i | −0.992793 | − | 0.119839i | \(-0.961762\pi\) |
−0.192817 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(830\) | 4.50806 | − | 13.8744i | 0.156477 | − | 0.481587i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36.1052 | + | 26.2320i | −1.25172 | + | 0.909430i | ||||
\(833\) | 46.0210 | + | 33.4362i | 1.59453 | + | 1.15850i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.97139 | 0.0682227 | ||||||||
\(836\) | −11.4887 | + | 3.67292i | −0.397346 | + | 0.127031i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.04247 | + | 18.5968i | 0.208734 | + | 0.642416i | ||||
\(839\) | −5.09236 | − | 3.69982i | −0.175808 | − | 0.127732i | 0.496401 | − | 0.868093i | \(-0.334654\pi\) |
−0.672209 | + | 0.740361i | \(0.734654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.76886 | − | 11.5994i | 0.129961 | − | 0.399978i | ||||
\(842\) | −8.47554 | + | 26.0850i | −0.292086 | + | 0.898949i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.7434 | − | 8.53205i | −0.404223 | − | 0.293685i | ||||
\(845\) | 4.23363 | + | 13.0298i | 0.145641 | + | 0.448238i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.9954 | − | 44.7074i | 0.515249 | − | 1.53617i | ||||
\(848\) | 5.78225 | 0.198563 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.70098 | − | 3.41546i | −0.161242 | − | 0.117149i | ||||
\(851\) | −0.698548 | + | 0.507525i | −0.0239459 | + | 0.0173977i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.24692 | + | 6.91532i | −0.0769332 | + | 0.236776i | −0.982126 | − | 0.188225i | \(-0.939726\pi\) |
0.905193 | + | 0.425002i | \(0.139726\pi\) | |||||||
\(854\) | 19.5803 | − | 14.2259i | 0.670025 | − | 0.486802i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.38491 | − | 22.7284i | −0.252411 | − | 0.776841i | ||||
\(857\) | −39.8590 | −1.36156 | −0.680779 | − | 0.732489i | \(-0.738359\pi\) | ||||
−0.680779 | + | 0.732489i | \(0.738359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5278 | 0.461564 | 0.230782 | − | 0.973006i | \(-0.425872\pi\) | ||||
0.230782 | + | 0.973006i | \(0.425872\pi\) | |||||||
\(860\) | 1.78640 | + | 5.49797i | 0.0609157 | + | 0.187479i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.4037 | − | 25.7223i | 1.20585 | − | 0.876104i | ||||
\(863\) | −15.5472 | + | 47.8493i | −0.529232 | + | 1.62881i | 0.226560 | + | 0.973997i | \(0.427252\pi\) |
−0.755792 | + | 0.654812i | \(0.772748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.59784 | + | 1.16090i | −0.0543283 | + | 0.0394718i | ||||
\(866\) | −29.1228 | − | 21.1589i | −0.989632 | − | 0.719010i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.88119 | −0.267505 | ||||||||
\(869\) | 15.4977 | + | 21.5444i | 0.525725 | + | 0.730844i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3655 | + | 59.6009i | 0.656175 | + | 2.01950i | ||||
\(872\) | −11.1015 | − | 8.06574i | −0.375946 | − | 0.273140i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.442073 | + | 1.36056i | −0.0149534 | + | 0.0460217i | ||||
\(875\) | −1.32471 | + | 4.07703i | −0.0447833 | + | 0.137829i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.976773 | + | 0.709667i | 0.0329833 | + | 0.0239638i | 0.604155 | − | 0.796867i | \(-0.293511\pi\) |
−0.571171 | + | 0.820831i | \(0.693511\pi\) | |||||||
\(878\) | 10.1320 | + | 31.1830i | 0.341937 | + | 1.05237i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.17888 | + | 2.37016i | 0.242000 | + | 0.0798982i | ||||
\(881\) | −1.91816 | −0.0646245 | −0.0323123 | − | 0.999478i | \(-0.510287\pi\) | ||||
−0.0323123 | + | 0.999478i | \(0.510287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.9950 | − | 34.1439i | −1.58151 | − | 1.14903i | −0.914941 | − | 0.403587i | \(-0.867763\pi\) |
−0.666566 | − | 0.745446i | \(-0.732237\pi\) | |||||||
\(884\) | −13.5740 | + | 9.86208i | −0.456543 | + | 0.331698i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.25828 | − | 16.1833i | 0.176656 | − | 0.543690i | ||||
\(887\) | 24.4668 | − | 17.7762i | 0.821516 | − | 0.596866i | −0.0956306 | − | 0.995417i | \(-0.530487\pi\) |
0.917146 | + | 0.398551i | \(0.130487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.02832 | − | 6.24251i | −0.0680275 | − | 0.209367i | ||||
\(890\) | −2.98143 | −0.0999378 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.4417 | 0.416578 | ||||||||
\(893\) | 0.411644 | + | 1.26691i | 0.0137752 | + | 0.0423956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.63676 | + | 1.18918i | −0.0547109 | + | 0.0397498i | ||||
\(896\) | 3.99968 | − | 12.3098i | 0.133620 | − | 0.411240i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.2802 | + | 8.19553i | −0.376425 | + | 0.273488i | ||||
\(899\) | −14.7001 | − | 10.6802i | −0.490275 | − | 0.356206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6835 | 0.422550 | ||||||||
\(902\) | 0.106870 | − | 22.5904i | 0.00355837 | − | 0.752179i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.33815 | + | 22.5845i | 0.244063 | + | 0.751149i | ||||
\(905\) | −16.2920 | − | 11.8368i | −0.541564 | − | 0.393469i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.87830 | + | 30.4023i | −0.328004 | + | 1.00949i | 0.642063 | + | 0.766652i | \(0.278079\pi\) |
−0.970066 | + | 0.242839i | \(0.921921\pi\) | |||||||
\(908\) | 3.08563 | − | 9.49660i | 0.102400 | − | 0.315156i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.8264 | − | 15.1313i | −0.690389 | − | 0.501597i | ||||
\(911\) | 16.0211 | + | 49.3079i | 0.530803 | + | 1.63364i | 0.752547 | + | 0.658538i | \(0.228825\pi\) |
−0.221745 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.196955 | + | 41.6330i | −0.00651826 | + | 1.37785i | ||||
\(914\) | −11.6722 | −0.386083 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.67660 | + | 3.39775i | 0.154519 | + | 0.112265i | ||||
\(917\) | −9.22898 | + | 6.70525i | −0.304768 | + | 0.221427i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5710 | + | 32.5341i | −0.348704 | + | 1.07320i | 0.610866 | + | 0.791734i | \(0.290821\pi\) |
−0.959571 | + | 0.281468i | \(0.909179\pi\) | |||||||
\(920\) | −0.547562 | + | 0.397827i | −0.0180526 | + | 0.0131160i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.82988 | − | 14.8648i | −0.159064 | − | 0.489547i | ||||
\(923\) | 51.5790 | 1.69774 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.92802 | 0.129153 | ||||||||
\(926\) | −6.74561 | − | 20.7609i | −0.221675 | − | 0.682244i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.2208 | + | 13.2382i | −0.598127 | + | 0.434565i | ||||
\(929\) | −5.66990 | + | 17.4502i | −0.186023 | + | 0.572521i | −0.999964 | − | 0.00842624i | \(-0.997318\pi\) |
0.813941 | + | 0.580947i | \(0.197318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51.5433 | + | 37.4484i | −1.68926 | + | 1.22732i | ||||
\(932\) | −11.9978 | − | 8.71693i | −0.393002 | − | 0.285533i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.8561 | 1.00964 | ||||||||
\(935\) | 15.7471 | + | 5.19902i | 0.514984 | + | 0.170026i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.04576 | + | 3.21852i | 0.0341635 | + | 0.105144i | 0.966684 | − | 0.255972i | \(-0.0823956\pi\) |
−0.932521 | + | 0.361117i | \(0.882396\pi\) | |||||||
\(938\) | −48.8815 | − | 35.5145i | −1.59604 | − | 1.15959i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0477373 | + | 0.146920i | −0.00155702 | + | 0.00479201i | ||||
\(941\) | 10.8465 | − | 33.3822i | 0.353587 | − | 1.08823i | −0.603237 | − | 0.797562i | \(-0.706123\pi\) |
0.956824 | − | 0.290668i | \(-0.0938774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04230 | + | 0.757278i | 0.0339421 | + | 0.0246604i | ||||
\(944\) | −5.54375 | − | 17.0619i | −0.180434 | − | 0.555318i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.0359 | + | 27.8532i | 0.651423 | + | 0.905585i | ||||
\(947\) | 39.0512 | 1.26899 | 0.634497 | − | 0.772925i | \(-0.281207\pi\) | ||||
0.634497 | + | 0.772925i | \(0.281207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.8769 | − | 44.2297i | −1.97615 | − | 1.43576i | ||||
\(950\) | 5.26508 | − | 3.82530i | 0.170822 | − | 0.124109i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20.3939 | − | 62.7660i | 0.660971 | − | 2.03426i | ||||
\(953\) | 19.9652 | − | 14.5055i | 0.646735 | − | 0.469881i | −0.215422 | − | 0.976521i | \(-0.569113\pi\) |
0.862158 | + | 0.506640i | \(0.169113\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.91375 | − | 12.0453i | −0.126646 | − | 0.389776i | ||||
\(956\) | 10.9495 | 0.354131 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.5315 | 0.404873 | ||||||||
\(959\) | 13.5855 | + | 41.8118i | 0.438698 | + | 1.35017i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5958 | − | 13.5107i | 0.599865 | − | 0.435827i | ||||
\(962\) | −7.28913 | + | 22.4336i | −0.235011 | + | 0.723290i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.28401 | + | 4.56560i | −0.202394 | + | 0.147048i | ||||
\(965\) | 11.2713 | + | 8.18910i | 0.362837 | + | 0.263616i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.20724 | 0.0388222 | 0.0194111 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194111 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(968\) | −33.8676 | − | 0.320445i | −1.08855 | − | 0.0102995i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.722551 | − | 2.22378i | −0.0231997 | − | 0.0714014i | ||||
\(971\) | 40.7599 | + | 29.6138i | 1.30805 | + | 0.950353i | 0.999999 | − | 0.00101751i | \(-0.000323883\pi\) |
0.308049 | + | 0.951370i | \(0.400324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.01442 | − | 21.5882i | 0.224872 | − | 0.692085i | ||||
\(974\) | −2.44597 | + | 7.52793i | −0.0783740 | + | 0.241210i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.95877 | − | 6.50893i | −0.286763 | − | 0.208346i | ||||
\(977\) | 1.81804 | + | 5.59535i | 0.0581642 | + | 0.179011i | 0.975917 | − | 0.218140i | \(-0.0699989\pi\) |
−0.917753 | + | 0.397151i | \(0.869999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.10454 | − | 2.59100i | 0.259022 | − | 0.0828088i | ||||
\(980\) | −7.38839 | −0.236013 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.5348 | − | 17.8256i | −0.782937 | − | 0.568837i | ||||
\(983\) | 29.5210 | − | 21.4482i | 0.941573 | − | 0.684093i | −0.00722580 | − | 0.999974i | \(-0.502300\pi\) |
0.948799 | + | 0.315881i | \(0.102300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.51352 | + | 13.8912i | −0.143813 | + | 0.442610i | ||||
\(986\) | 30.1730 | − | 21.9219i | 0.960903 | − | 0.698137i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.80695 | − | 17.8720i | −0.184744 | − | 0.568583i | ||||
\(989\) | −1.95677 | −0.0622216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8404 | −1.17027 | −0.585137 | − | 0.810934i | \(-0.698959\pi\) | ||||
−0.585137 | + | 0.810934i | \(0.698959\pi\) | |||||||
\(992\) | 3.06970 | + | 9.44757i | 0.0974631 | + | 0.299961i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −40.2320 | + | 29.2302i | −1.27608 | + | 0.927127i | ||||
\(995\) | −3.66952 | + | 11.2936i | −0.116332 | + | 0.358032i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2099 | + | 20.4957i | −0.893417 | + | 0.649105i | −0.936767 | − | 0.349955i | \(-0.886197\pi\) |
0.0433498 | + | 0.999060i | \(0.486197\pi\) | |||||||
\(998\) | 18.2242 | + | 13.2406i | 0.576877 | + | 0.419125i | ||||
\(999\) | 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 | 495.2.n.d.181.2 | 8 | ||
3.2 | odd | 2 | 165.2.m.a.16.1 | ✓ | 8 | ||
11.3 | even | 5 | 5445.2.a.be.1.3 | 4 | |||
11.8 | odd | 10 | 5445.2.a.bv.1.2 | 4 | |||
11.9 | even | 5 | inner | 495.2.n.d.361.2 | 8 | ||
15.2 | even | 4 | 825.2.bx.h.49.2 | 16 | |||
15.8 | even | 4 | 825.2.bx.h.49.3 | 16 | |||
15.14 | odd | 2 | 825.2.n.k.676.2 | 8 | |||
33.8 | even | 10 | 1815.2.a.o.1.3 | 4 | |||
33.14 | odd | 10 | 1815.2.a.x.1.2 | 4 | |||
33.20 | odd | 10 | 165.2.m.a.31.1 | yes | 8 | ||
165.14 | odd | 10 | 9075.2.a.cl.1.3 | 4 | |||
165.53 | even | 20 | 825.2.bx.h.724.2 | 16 | |||
165.74 | even | 10 | 9075.2.a.dj.1.2 | 4 | |||
165.119 | odd | 10 | 825.2.n.k.526.2 | 8 | |||
165.152 | even | 20 | 825.2.bx.h.724.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.1 | ✓ | 8 | 3.2 | odd | 2 | ||
165.2.m.a.31.1 | yes | 8 | 33.20 | odd | 10 | ||
495.2.n.d.181.2 | 8 | 1.1 | even | 1 | trivial | ||
495.2.n.d.361.2 | 8 | 11.9 | even | 5 | inner | ||
825.2.n.k.526.2 | 8 | 165.119 | odd | 10 | |||
825.2.n.k.676.2 | 8 | 15.14 | odd | 2 | |||
825.2.bx.h.49.2 | 16 | 15.2 | even | 4 | |||
825.2.bx.h.49.3 | 16 | 15.8 | even | 4 | |||
825.2.bx.h.724.2 | 16 | 165.53 | even | 20 | |||
825.2.bx.h.724.3 | 16 | 165.152 | even | 20 | |||
1815.2.a.o.1.3 | 4 | 33.8 | even | 10 | |||
1815.2.a.x.1.2 | 4 | 33.14 | odd | 10 | |||
5445.2.a.be.1.3 | 4 | 11.3 | even | 5 | |||
5445.2.a.bv.1.2 | 4 | 11.8 | odd | 10 | |||
9075.2.a.cl.1.3 | 4 | 165.14 | odd | 10 | |||
9075.2.a.dj.1.2 | 4 | 165.74 | even | 10 |