Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,2,Mod(26,125)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(125, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.d (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.998130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 125.26 |
Dual form | 125.2.d.a.101.1 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
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 | + | 1.53884i | 0.353553 | + | 1.08813i | 0.956844 | + | 0.290604i | \(0.0938561\pi\) |
−0.603290 | + | 0.797522i | \(0.706144\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | −0.329218 | − | 0.944254i | \(-0.606785\pi\) |
0.796305 | + | 0.604896i | \(0.206785\pi\) | |||||||
\(4\) | −0.500000 | + | 0.363271i | −0.250000 | + | 0.181636i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.30902 | + | 0.951057i | 0.534404 | + | 0.388267i | ||||
\(7\) | −0.618034 | −0.233595 | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||||
−0.116797 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(8\) | 1.80902 | + | 1.31433i | 0.639584 | + | 0.464685i | ||||
\(9\) | −0.618034 | + | 1.90211i | −0.206011 | + | 0.634038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61803 | − | 4.97980i | −0.487856 | − | 1.50147i | −0.827802 | − | 0.561020i | \(-0.810409\pi\) |
0.339946 | − | 0.940445i | \(-0.389591\pi\) | |||||||
\(12\) | −0.190983 | + | 0.587785i | −0.0551320 | + | 0.169679i | ||||
\(13\) | −0.572949 | + | 1.76336i | −0.158907 | + | 0.489067i | −0.998536 | − | 0.0540944i | \(-0.982773\pi\) |
0.839628 | + | 0.543161i | \(0.182773\pi\) | |||||||
\(14\) | −0.309017 | − | 0.951057i | −0.0825883 | − | 0.254181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 4.61653i | −0.375000 | + | 1.15413i | ||||
\(17\) | −4.23607 | − | 3.07768i | −1.02740 | − | 0.746448i | −0.0596113 | − | 0.998222i | \(-0.518986\pi\) |
−0.967786 | + | 0.251774i | \(0.918986\pi\) | |||||||
\(18\) | −3.23607 | −0.762749 | ||||||||
\(19\) | −0.690983 | − | 0.502029i | −0.158522 | − | 0.115173i | 0.505696 | − | 0.862712i | \(-0.331236\pi\) |
−0.664219 | + | 0.747538i | \(0.731236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 0.363271i | −0.109109 | + | 0.0792723i | ||||
\(22\) | 6.85410 | − | 4.97980i | 1.46130 | − | 1.06170i | ||||
\(23\) | −1.16312 | − | 3.57971i | −0.242527 | − | 0.746422i | −0.996033 | − | 0.0889808i | \(-0.971639\pi\) |
0.753506 | − | 0.657441i | \(-0.228361\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 1.54508 | + | 4.75528i | 0.297352 | + | 0.915155i | ||||
\(28\) | 0.309017 | − | 0.224514i | 0.0583987 | − | 0.0424292i | ||||
\(29\) | 2.92705 | − | 2.12663i | 0.543540 | − | 0.394905i | −0.281858 | − | 0.959456i | \(-0.590951\pi\) |
0.825398 | + | 0.564551i | \(0.190951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.42705 | + | 1.76336i | 0.435911 | + | 0.316708i | 0.784008 | − | 0.620750i | \(-0.213172\pi\) |
−0.348097 | + | 0.937459i | \(0.613172\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | −4.23607 | − | 3.07768i | −0.737405 | − | 0.535756i | ||||
\(34\) | 2.61803 | − | 8.05748i | 0.448989 | − | 1.38185i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.381966 | − | 1.17557i | −0.0636610 | − | 0.195928i | ||||
\(37\) | 0.0729490 | − | 0.224514i | 0.0119927 | − | 0.0369099i | −0.944881 | − | 0.327414i | \(-0.893823\pi\) |
0.956874 | + | 0.290504i | \(0.0938229\pi\) | |||||||
\(38\) | 0.427051 | − | 1.31433i | 0.0692768 | − | 0.213212i | ||||
\(39\) | 0.572949 | + | 1.76336i | 0.0917453 | + | 0.282363i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.236068 | + | 0.726543i | −0.0368676 | + | 0.113467i | −0.967797 | − | 0.251733i | \(-0.918999\pi\) |
0.930929 | + | 0.365200i | \(0.118999\pi\) | |||||||
\(42\) | −0.809017 | − | 0.587785i | −0.124834 | − | 0.0906972i | ||||
\(43\) | 4.85410 | 0.740244 | 0.370122 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370122 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(44\) | 2.61803 | + | 1.90211i | 0.394683 | + | 0.286754i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.92705 | − | 3.57971i | 0.726454 | − | 0.527800i | ||||
\(47\) | 0.500000 | − | 0.363271i | 0.0729325 | − | 0.0529886i | −0.550722 | − | 0.834689i | \(-0.685647\pi\) |
0.623654 | + | 0.781700i | \(0.285647\pi\) | |||||||
\(48\) | 1.50000 | + | 4.61653i | 0.216506 | + | 0.666338i | ||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23607 | −0.733196 | ||||||||
\(52\) | −0.354102 | − | 1.08981i | −0.0491051 | − | 0.151130i | ||||
\(53\) | −2.80902 | + | 2.04087i | −0.385848 | + | 0.280335i | −0.763752 | − | 0.645510i | \(-0.776645\pi\) |
0.377904 | + | 0.925845i | \(0.376645\pi\) | |||||||
\(54\) | −6.54508 | + | 4.75528i | −0.890673 | + | 0.647112i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.11803 | − | 0.812299i | −0.149404 | − | 0.108548i | ||||
\(57\) | −0.854102 | −0.113129 | ||||||||
\(58\) | 4.73607 | + | 3.44095i | 0.621876 | + | 0.451820i | ||||
\(59\) | −3.35410 | + | 10.3229i | −0.436667 | + | 1.34392i | 0.454702 | + | 0.890644i | \(0.349746\pi\) |
−0.891369 | + | 0.453279i | \(0.850254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69098 | + | 8.28199i | 0.344545 | + | 1.06040i | 0.961827 | + | 0.273659i | \(0.0882338\pi\) |
−0.617282 | + | 0.786742i | \(0.711766\pi\) | |||||||
\(62\) | −1.50000 | + | 4.61653i | −0.190500 | + | 0.586299i | ||||
\(63\) | 0.381966 | − | 1.17557i | 0.0481232 | − | 0.148108i | ||||
\(64\) | 1.30902 | + | 4.02874i | 0.163627 | + | 0.503593i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.61803 | − | 8.05748i | 0.322258 | − | 0.991807i | ||||
\(67\) | 3.85410 | + | 2.80017i | 0.470853 | + | 0.342095i | 0.797774 | − | 0.602957i | \(-0.206011\pi\) |
−0.326920 | + | 0.945052i | \(0.606011\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | −3.04508 | − | 2.21238i | −0.366585 | − | 0.266340i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.35410 | − | 3.88998i | 0.635415 | − | 0.461656i | −0.222857 | − | 0.974851i | \(-0.571538\pi\) |
0.858272 | + | 0.513195i | \(0.171538\pi\) | |||||||
\(72\) | −3.61803 | + | 2.62866i | −0.426389 | + | 0.309790i | ||||
\(73\) | 2.78115 | + | 8.55951i | 0.325509 | + | 1.00181i | 0.971210 | + | 0.238224i | \(0.0765653\pi\) |
−0.645701 | + | 0.763590i | \(0.723435\pi\) | |||||||
\(74\) | 0.381966 | 0.0444026 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.527864 | 0.0605502 | ||||||||
\(77\) | 1.00000 | + | 3.07768i | 0.113961 | + | 0.350735i | ||||
\(78\) | −2.42705 | + | 1.76336i | −0.274809 | + | 0.199661i | ||||
\(79\) | 6.54508 | − | 4.75528i | 0.736380 | − | 0.535011i | −0.155196 | − | 0.987884i | \(-0.549601\pi\) |
0.891575 | + | 0.452873i | \(0.149601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −1.23607 | −0.136501 | ||||||||
\(83\) | −5.04508 | − | 3.66547i | −0.553770 | − | 0.402337i | 0.275404 | − | 0.961329i | \(-0.411189\pi\) |
−0.829174 | + | 0.558991i | \(0.811189\pi\) | |||||||
\(84\) | 0.118034 | − | 0.363271i | 0.0128786 | − | 0.0396361i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.42705 | + | 7.46969i | 0.261716 | + | 0.805478i | ||||
\(87\) | 1.11803 | − | 3.44095i | 0.119866 | − | 0.368909i | ||||
\(88\) | 3.61803 | − | 11.1352i | 0.385684 | − | 1.18701i | ||||
\(89\) | −2.76393 | − | 8.50651i | −0.292976 | − | 0.901688i | −0.983894 | − | 0.178754i | \(-0.942793\pi\) |
0.690918 | − | 0.722934i | \(-0.257207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.354102 | − | 1.08981i | 0.0371200 | − | 0.114244i | ||||
\(92\) | 1.88197 | + | 1.36733i | 0.196209 | + | 0.142554i | ||||
\(93\) | 3.00000 | 0.311086 | ||||||||
\(94\) | 0.809017 | + | 0.587785i | 0.0834437 | + | 0.0606254i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.73607 | + | 1.98787i | −0.279249 | + | 0.202886i | ||||
\(97\) | −3.11803 | + | 2.26538i | −0.316588 | + | 0.230015i | −0.734718 | − | 0.678372i | \(-0.762686\pi\) |
0.418130 | + | 0.908387i | \(0.362686\pi\) | |||||||
\(98\) | −3.30902 | − | 10.1841i | −0.334261 | − | 1.02875i | ||||
\(99\) | 10.4721 | 1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | −2.61803 | − | 8.05748i | −0.259224 | − | 0.797809i | ||||
\(103\) | 6.92705 | − | 5.03280i | 0.682543 | − | 0.495896i | −0.191658 | − | 0.981462i | \(-0.561386\pi\) |
0.874200 | + | 0.485566i | \(0.161386\pi\) | |||||||
\(104\) | −3.35410 | + | 2.43690i | −0.328897 | + | 0.238957i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.54508 | − | 3.30220i | −0.441458 | − | 0.320738i | ||||
\(107\) | 16.4164 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(108\) | −2.50000 | − | 1.81636i | −0.240563 | − | 0.174779i | ||||
\(109\) | 3.09017 | − | 9.51057i | 0.295985 | − | 0.910947i | −0.686904 | − | 0.726748i | \(-0.741031\pi\) |
0.982889 | − | 0.184199i | \(-0.0589691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0729490 | − | 0.224514i | −0.00692401 | − | 0.0213099i | ||||
\(112\) | 0.927051 | − | 2.85317i | 0.0875981 | − | 0.269599i | ||||
\(113\) | −5.20820 | + | 16.0292i | −0.489947 | + | 1.50790i | 0.334740 | + | 0.942311i | \(0.391352\pi\) |
−0.824687 | + | 0.565590i | \(0.808648\pi\) | |||||||
\(114\) | −0.427051 | − | 1.31433i | −0.0399970 | − | 0.123098i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.690983 | + | 2.12663i | −0.0641562 | + | 0.197452i | ||||
\(117\) | −3.00000 | − | 2.17963i | −0.277350 | − | 0.201507i | ||||
\(118\) | −17.5623 | −1.61674 | ||||||||
\(119\) | 2.61803 | + | 1.90211i | 0.239995 | + | 0.174366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2812 | + | 9.64932i | −1.20738 | + | 0.877211i | ||||
\(122\) | −11.3992 | + | 8.28199i | −1.03203 | + | 0.749817i | ||||
\(123\) | 0.236068 | + | 0.726543i | 0.0212855 | + | 0.0655101i | ||||
\(124\) | −1.85410 | −0.166503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −6.14590 | − | 18.9151i | −0.545360 | − | 1.67845i | −0.720132 | − | 0.693837i | \(-0.755919\pi\) |
0.174772 | − | 0.984609i | \(-0.444081\pi\) | |||||||
\(128\) | −11.0172 | + | 8.00448i | −0.973794 | + | 0.707503i | ||||
\(129\) | 3.92705 | − | 2.85317i | 0.345758 | − | 0.251208i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.50000 | − | 3.99598i | −0.480537 | − | 0.349131i | 0.320996 | − | 0.947080i | \(-0.395982\pi\) |
−0.801534 | + | 0.597950i | \(0.795982\pi\) | |||||||
\(132\) | 3.23607 | 0.281664 | ||||||||
\(133\) | 0.427051 | + | 0.310271i | 0.0370300 | + | 0.0269039i | ||||
\(134\) | −2.38197 | + | 7.33094i | −0.205771 | + | 0.633297i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.61803 | − | 11.1352i | −0.310244 | − | 0.954832i | ||||
\(137\) | 3.69098 | − | 11.3597i | 0.315342 | − | 0.970523i | −0.660271 | − | 0.751027i | \(-0.729559\pi\) |
0.975613 | − | 0.219496i | \(-0.0704412\pi\) | |||||||
\(138\) | 1.88197 | − | 5.79210i | 0.160204 | − | 0.493056i | ||||
\(139\) | 1.54508 | + | 4.75528i | 0.131052 | + | 0.403338i | 0.994955 | − | 0.100321i | \(-0.0319869\pi\) |
−0.863903 | + | 0.503659i | \(0.831987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.190983 | − | 0.587785i | 0.0160837 | − | 0.0495004i | ||||
\(142\) | 8.66312 | + | 6.29412i | 0.726993 | + | 0.528191i | ||||
\(143\) | 9.70820 | 0.811841 | ||||||||
\(144\) | −7.85410 | − | 5.70634i | −0.654508 | − | 0.475528i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.7812 | + | 8.55951i | −0.975015 | + | 0.708390i | ||||
\(147\) | −5.35410 | + | 3.88998i | −0.441599 | + | 0.320840i | ||||
\(148\) | 0.0450850 | + | 0.138757i | 0.00370596 | + | 0.0114058i | ||||
\(149\) | −3.94427 | −0.323127 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5623 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298128\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298128\pi\) | |||||||
\(152\) | −0.590170 | − | 1.81636i | −0.0478691 | − | 0.147326i | ||||
\(153\) | 8.47214 | − | 6.15537i | 0.684932 | − | 0.497632i | ||||
\(154\) | −4.23607 | + | 3.07768i | −0.341352 | + | 0.248007i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.927051 | − | 0.673542i | −0.0742235 | − | 0.0539265i | ||||
\(157\) | −13.1803 | −1.05191 | −0.525953 | − | 0.850514i | \(-0.676291\pi\) | ||||
−0.525953 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(158\) | 10.5902 | + | 7.69421i | 0.842509 | + | 0.612118i | ||||
\(159\) | −1.07295 | + | 3.30220i | −0.0850904 | + | 0.261881i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.718847 | + | 2.21238i | 0.0566531 | + | 0.174360i | ||||
\(162\) | 0.500000 | − | 1.53884i | 0.0392837 | − | 0.120903i | ||||
\(163\) | −3.39919 | + | 10.4616i | −0.266245 | + | 0.819417i | 0.725159 | + | 0.688581i | \(0.241766\pi\) |
−0.991404 | + | 0.130836i | \(0.958234\pi\) | |||||||
\(164\) | −0.145898 | − | 0.449028i | −0.0113927 | − | 0.0350632i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.11803 | − | 9.59632i | 0.242006 | − | 0.744819i | ||||
\(167\) | 11.7812 | + | 8.55951i | 0.911653 | + | 0.662355i | 0.941432 | − | 0.337202i | \(-0.109480\pi\) |
−0.0297794 | + | 0.999556i | \(0.509480\pi\) | |||||||
\(168\) | −1.38197 | −0.106621 | ||||||||
\(169\) | 7.73607 | + | 5.62058i | 0.595082 | + | 0.432352i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.38197 | − | 1.00406i | 0.105682 | − | 0.0767822i | ||||
\(172\) | −2.42705 | + | 1.76336i | −0.185061 | + | 0.134455i | ||||
\(173\) | −5.83688 | − | 17.9641i | −0.443770 | − | 1.36578i | −0.883827 | − | 0.467813i | \(-0.845042\pi\) |
0.440057 | − | 0.897970i | \(-0.354958\pi\) | |||||||
\(174\) | 5.85410 | 0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.4164 | 1.91583 | ||||||||
\(177\) | 3.35410 | + | 10.3229i | 0.252110 | + | 0.775914i | ||||
\(178\) | 11.7082 | − | 8.50651i | 0.877567 | − | 0.637590i | ||||
\(179\) | 0.427051 | − | 0.310271i | 0.0319193 | − | 0.0231907i | −0.571711 | − | 0.820455i | \(-0.693720\pi\) |
0.603631 | + | 0.797264i | \(0.293720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.236068 | − | 0.171513i | −0.0175468 | − | 0.0127485i | 0.578977 | − | 0.815344i | \(-0.303452\pi\) |
−0.596524 | + | 0.802595i | \(0.703452\pi\) | |||||||
\(182\) | 1.85410 | 0.137435 | ||||||||
\(183\) | 7.04508 | + | 5.11855i | 0.520788 | + | 0.378374i | ||||
\(184\) | 2.60081 | − | 8.00448i | 0.191734 | − | 0.590098i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 4.61653i | 0.109985 | + | 0.338500i | ||||
\(187\) | −8.47214 | + | 26.0746i | −0.619544 | + | 1.90676i | ||||
\(188\) | −0.118034 | + | 0.363271i | −0.00860851 | + | 0.0264943i | ||||
\(189\) | −0.954915 | − | 2.93893i | −0.0694598 | − | 0.213775i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.562306 | + | 1.73060i | −0.0406870 | + | 0.125222i | −0.969337 | − | 0.245736i | \(-0.920970\pi\) |
0.928650 | + | 0.370958i | \(0.120970\pi\) | |||||||
\(192\) | 3.42705 | + | 2.48990i | 0.247326 | + | 0.179693i | ||||
\(193\) | −7.70820 | −0.554849 | −0.277424 | − | 0.960747i | \(-0.589481\pi\) | ||||
−0.277424 | + | 0.960747i | \(0.589481\pi\) | |||||||
\(194\) | −5.04508 | − | 3.66547i | −0.362216 | − | 0.263165i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30902 | − | 2.40414i | 0.236358 | − | 0.171724i | ||||
\(197\) | 3.00000 | − | 2.17963i | 0.213741 | − | 0.155292i | −0.475764 | − | 0.879573i | \(-0.657828\pi\) |
0.689505 | + | 0.724281i | \(0.257828\pi\) | |||||||
\(198\) | 5.23607 | + | 16.1150i | 0.372111 | + | 1.14524i | ||||
\(199\) | −17.5623 | −1.24496 | −0.622479 | − | 0.782636i | \(-0.713875\pi\) | ||||
−0.622479 | + | 0.782636i | \(0.713875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.76393 | 0.336022 | ||||||||
\(202\) | 0.736068 | + | 2.26538i | 0.0517896 | + | 0.159392i | ||||
\(203\) | −1.80902 | + | 1.31433i | −0.126968 | + | 0.0922477i | ||||
\(204\) | 2.61803 | − | 1.90211i | 0.183299 | − | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.2082 | + | 8.14324i | 0.780913 | + | 0.567366i | ||||
\(207\) | 7.52786 | 0.523223 | ||||||||
\(208\) | −7.28115 | − | 5.29007i | −0.504857 | − | 0.366800i | ||||
\(209\) | −1.38197 | + | 4.25325i | −0.0955926 | + | 0.294204i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.83688 | − | 8.73102i | −0.195299 | − | 0.601068i | −0.999973 | − | 0.00735149i | \(-0.997660\pi\) |
0.804674 | − | 0.593717i | \(-0.202340\pi\) | |||||||
\(212\) | 0.663119 | − | 2.04087i | 0.0455432 | − | 0.140168i | ||||
\(213\) | 2.04508 | − | 6.29412i | 0.140127 | − | 0.431266i | ||||
\(214\) | 8.20820 | + | 25.2623i | 0.561101 | + | 1.72689i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.45492 | + | 10.6331i | −0.235077 | + | 0.723493i | ||||
\(217\) | −1.50000 | − | 1.08981i | −0.101827 | − | 0.0739814i | ||||
\(218\) | 16.1803 | 1.09587 | ||||||||
\(219\) | 7.28115 | + | 5.29007i | 0.492015 | + | 0.357470i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.85410 | − | 5.70634i | 0.528324 | − | 0.383850i | ||||
\(222\) | 0.309017 | − | 0.224514i | 0.0207399 | − | 0.0150684i | ||||
\(223\) | 0.0557281 | + | 0.171513i | 0.00373183 | + | 0.0114854i | 0.952905 | − | 0.303269i | \(-0.0980780\pi\) |
−0.949173 | + | 0.314754i | \(0.898078\pi\) | |||||||
\(224\) | 2.09017 | 0.139655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2705 | −1.81401 | ||||||||
\(227\) | −4.56231 | − | 14.0413i | −0.302811 | − | 0.931956i | −0.980485 | − | 0.196594i | \(-0.937012\pi\) |
0.677674 | − | 0.735362i | \(-0.262988\pi\) | |||||||
\(228\) | 0.427051 | − | 0.310271i | 0.0282821 | − | 0.0205482i | ||||
\(229\) | −17.5623 | + | 12.7598i | −1.16055 | + | 0.843189i | −0.989847 | − | 0.142134i | \(-0.954604\pi\) |
−0.170702 | + | 0.985323i | \(0.554604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.61803 | + | 1.90211i | 0.172254 | + | 0.125150i | ||||
\(232\) | 8.09017 | 0.531146 | ||||||||
\(233\) | −2.38197 | − | 1.73060i | −0.156048 | − | 0.113375i | 0.507021 | − | 0.861933i | \(-0.330746\pi\) |
−0.663069 | + | 0.748558i | \(0.730746\pi\) | |||||||
\(234\) | 1.85410 | − | 5.70634i | 0.121206 | − | 0.373035i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.07295 | − | 6.37988i | −0.134937 | − | 0.415295i | ||||
\(237\) | 2.50000 | − | 7.69421i | 0.162392 | − | 0.499793i | ||||
\(238\) | −1.61803 | + | 4.97980i | −0.104882 | + | 0.322792i | ||||
\(239\) | −6.34346 | − | 19.5232i | −0.410324 | − | 1.26285i | −0.916367 | − | 0.400340i | \(-0.868892\pi\) |
0.506043 | − | 0.862508i | \(-0.331108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.781153 | − | 2.40414i | 0.0503185 | − | 0.154864i | −0.922740 | − | 0.385423i | \(-0.874055\pi\) |
0.973058 | + | 0.230559i | \(0.0740554\pi\) | |||||||
\(242\) | −21.4894 | − | 15.6129i | −1.38139 | − | 1.00364i | ||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | −4.35410 | − | 3.16344i | −0.278743 | − | 0.202519i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.00000 | + | 0.726543i | −0.0637577 | + | 0.0463227i | ||||
\(247\) | 1.28115 | − | 0.930812i | 0.0815178 | − | 0.0592262i | ||||
\(248\) | 2.07295 | + | 6.37988i | 0.131632 | + | 0.405123i | ||||
\(249\) | −6.23607 | −0.395195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.1803 | −1.84185 | −0.920923 | − | 0.389744i | \(-0.872564\pi\) | ||||
−0.920923 | + | 0.389744i | \(0.872564\pi\) | |||||||
\(252\) | 0.236068 | + | 0.726543i | 0.0148709 | + | 0.0457679i | ||||
\(253\) | −15.9443 | + | 11.5842i | −1.00241 | + | 0.728292i | ||||
\(254\) | 26.0344 | − | 18.9151i | 1.63355 | − | 1.18684i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9721 | − | 7.97172i | −0.685758 | − | 0.498233i | ||||
\(257\) | −22.8541 | −1.42560 | −0.712800 | − | 0.701367i | \(-0.752573\pi\) | ||||
−0.712800 | + | 0.701367i | \(0.752573\pi\) | |||||||
\(258\) | 6.35410 | + | 4.61653i | 0.395589 | + | 0.287412i | ||||
\(259\) | −0.0450850 | + | 0.138757i | −0.00280144 | + | 0.00862196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23607 | + | 6.88191i | 0.138409 | + | 0.425980i | ||||
\(262\) | 3.39919 | − | 10.4616i | 0.210002 | − | 0.646321i | ||||
\(263\) | 3.37132 | − | 10.3759i | 0.207885 | − | 0.639803i | −0.791698 | − | 0.610913i | \(-0.790803\pi\) |
0.999583 | − | 0.0288905i | \(-0.00919740\pi\) | |||||||
\(264\) | −3.61803 | − | 11.1352i | −0.222675 | − | 0.685322i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.263932 | + | 0.812299i | −0.0161827 | + | 0.0498053i | ||||
\(267\) | −7.23607 | − | 5.25731i | −0.442840 | − | 0.321742i | ||||
\(268\) | −2.94427 | −0.179850 | ||||||||
\(269\) | 10.3262 | + | 7.50245i | 0.629602 | + | 0.457433i | 0.856262 | − | 0.516541i | \(-0.172781\pi\) |
−0.226660 | + | 0.973974i | \(0.572781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.47214 | − | 4.70228i | 0.393154 | − | 0.285643i | −0.373593 | − | 0.927593i | \(-0.621874\pi\) |
0.766747 | + | 0.641950i | \(0.221874\pi\) | |||||||
\(272\) | 20.5623 | − | 14.9394i | 1.24677 | − | 0.905834i | ||||
\(273\) | −0.354102 | − | 1.08981i | −0.0214312 | − | 0.0659585i | ||||
\(274\) | 19.3262 | 1.16754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.32624 | 0.140023 | ||||||||
\(277\) | 7.63525 | + | 23.4989i | 0.458758 | + | 1.41191i | 0.866666 | + | 0.498889i | \(0.166258\pi\) |
−0.407908 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(278\) | −6.54508 | + | 4.75528i | −0.392548 | + | 0.285203i | ||||
\(279\) | −4.85410 | + | 3.52671i | −0.290607 | + | 0.211139i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.16312 | − | 5.93085i | −0.486971 | − | 0.353805i | 0.317047 | − | 0.948410i | \(-0.397309\pi\) |
−0.804018 | + | 0.594605i | \(0.797309\pi\) | |||||||
\(282\) | 1.00000 | 0.0595491 | ||||||||
\(283\) | −24.1525 | − | 17.5478i | −1.43572 | − | 1.04311i | −0.988916 | − | 0.148474i | \(-0.952564\pi\) |
−0.446799 | − | 0.894634i | \(-0.647436\pi\) | |||||||
\(284\) | −1.26393 | + | 3.88998i | −0.0750006 | + | 0.230828i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.85410 | + | 14.9394i | 0.287029 | + | 0.883385i | ||||
\(287\) | 0.145898 | − | 0.449028i | 0.00861209 | − | 0.0265053i | ||||
\(288\) | 2.09017 | − | 6.43288i | 0.123164 | − | 0.379061i | ||||
\(289\) | 3.21885 | + | 9.90659i | 0.189344 | + | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.19098 | + | 3.66547i | −0.0698167 | + | 0.214874i | ||||
\(292\) | −4.50000 | − | 3.26944i | −0.263343 | − | 0.191330i | ||||
\(293\) | 19.5279 | 1.14083 | 0.570415 | − | 0.821357i | \(-0.306782\pi\) | ||||
0.570415 | + | 0.821357i | \(0.306782\pi\) | |||||||
\(294\) | −8.66312 | − | 6.29412i | −0.505243 | − | 0.367081i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.427051 | − | 0.310271i | 0.0248218 | − | 0.0180341i | ||||
\(297\) | 21.1803 | − | 15.3884i | 1.22901 | − | 0.892927i | ||||
\(298\) | −1.97214 | − | 6.06961i | −0.114243 | − | 0.351603i | ||||
\(299\) | 6.97871 | 0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 7.28115 | + | 22.4091i | 0.418983 | + | 1.28950i | ||||
\(303\) | 1.19098 | − | 0.865300i | 0.0684202 | − | 0.0497102i | ||||
\(304\) | 3.35410 | − | 2.43690i | 0.192371 | − | 0.139766i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.7082 | + | 9.95959i | 0.783646 | + | 0.569352i | ||||
\(307\) | −9.23607 | −0.527130 | −0.263565 | − | 0.964642i | \(-0.584898\pi\) | ||||
−0.263565 | + | 0.964642i | \(0.584898\pi\) | |||||||
\(308\) | −1.61803 | − | 1.17557i | −0.0921960 | − | 0.0669843i | ||||
\(309\) | 2.64590 | − | 8.14324i | 0.150520 | − | 0.463253i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.62868 | + | 8.09024i | 0.149059 | + | 0.458755i | 0.997511 | − | 0.0705172i | \(-0.0224650\pi\) |
−0.848452 | + | 0.529272i | \(0.822465\pi\) | |||||||
\(312\) | −1.28115 | + | 3.94298i | −0.0725310 | + | 0.223227i | ||||
\(313\) | 5.18034 | − | 15.9434i | 0.292810 | − | 0.901177i | −0.691138 | − | 0.722723i | \(-0.742890\pi\) |
0.983948 | − | 0.178454i | \(-0.0571096\pi\) | |||||||
\(314\) | −6.59017 | − | 20.2825i | −0.371905 | − | 1.14461i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.54508 | + | 4.75528i | −0.0869178 | + | 0.267506i | ||||
\(317\) | 6.19098 | + | 4.49801i | 0.347720 | + | 0.252634i | 0.747912 | − | 0.663798i | \(-0.231056\pi\) |
−0.400192 | + | 0.916431i | \(0.631056\pi\) | |||||||
\(318\) | −5.61803 | −0.315044 | ||||||||
\(319\) | −15.3262 | − | 11.1352i | −0.858105 | − | 0.623449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2812 | − | 9.64932i | 0.741282 | − | 0.538573i | ||||
\(322\) | −3.04508 | + | 2.21238i | −0.169696 | + | 0.123291i | ||||
\(323\) | 1.38197 | + | 4.25325i | 0.0768946 | + | 0.236657i | ||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.7984 | −0.985761 | ||||||||
\(327\) | −3.09017 | − | 9.51057i | −0.170887 | − | 0.525935i | ||||
\(328\) | −1.38197 | + | 1.00406i | −0.0763063 | + | 0.0554398i | ||||
\(329\) | −0.309017 | + | 0.224514i | −0.0170367 | + | 0.0123779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7082 | + | 13.5923i | 1.02830 | + | 0.747101i | 0.967967 | − | 0.251078i | \(-0.0807850\pi\) |
0.0603290 | + | 0.998179i | \(0.480785\pi\) | |||||||
\(332\) | 3.85410 | 0.211521 | ||||||||
\(333\) | 0.381966 | + | 0.277515i | 0.0209316 | + | 0.0152077i | ||||
\(334\) | −7.28115 | + | 22.4091i | −0.398407 | + | 1.22617i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.927051 | − | 2.85317i | −0.0505748 | − | 0.155653i | ||||
\(337\) | −2.42705 | + | 7.46969i | −0.132210 | + | 0.406900i | −0.995146 | − | 0.0984135i | \(-0.968623\pi\) |
0.862936 | + | 0.505314i | \(0.168623\pi\) | |||||||
\(338\) | −4.78115 | + | 14.7149i | −0.260060 | + | 0.800384i | ||||
\(339\) | 5.20820 | + | 16.0292i | 0.282871 | + | 0.870587i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.85410 | − | 14.9394i | 0.262864 | − | 0.809013i | ||||
\(342\) | 2.23607 | + | 1.62460i | 0.120913 | + | 0.0878482i | ||||
\(343\) | 8.41641 | 0.454443 | ||||||||
\(344\) | 8.78115 | + | 6.37988i | 0.473448 | + | 0.343980i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.7254 | − | 17.9641i | 1.32925 | − | 0.965755i | ||||
\(347\) | −16.1074 | + | 11.7027i | −0.864690 | + | 0.628234i | −0.929157 | − | 0.369686i | \(-0.879465\pi\) |
0.0644668 | + | 0.997920i | \(0.479465\pi\) | |||||||
\(348\) | 0.690983 | + | 2.12663i | 0.0370406 | + | 0.113999i | ||||
\(349\) | 21.7082 | 1.16201 | 0.581007 | − | 0.813899i | \(-0.302659\pi\) | ||||
0.581007 | + | 0.813899i | \(0.302659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.27051 | −0.494823 | ||||||||
\(352\) | 5.47214 | + | 16.8415i | 0.291666 | + | 0.897655i | ||||
\(353\) | 10.4443 | − | 7.58821i | 0.555893 | − | 0.403880i | −0.274061 | − | 0.961712i | \(-0.588367\pi\) |
0.829953 | + | 0.557833i | \(0.188367\pi\) | |||||||
\(354\) | −14.2082 | + | 10.3229i | −0.755158 | + | 0.548654i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.47214 | + | 3.24920i | 0.237023 | + | 0.172207i | ||||
\(357\) | 3.23607 | 0.171271 | ||||||||
\(358\) | 0.690983 | + | 0.502029i | 0.0365196 | + | 0.0265330i | ||||
\(359\) | 4.24671 | − | 13.0700i | 0.224133 | − | 0.689810i | −0.774246 | − | 0.632885i | \(-0.781870\pi\) |
0.998378 | − | 0.0569247i | \(-0.0181295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.64590 | − | 17.3763i | −0.297153 | − | 0.914541i | ||||
\(362\) | 0.145898 | − | 0.449028i | 0.00766823 | − | 0.0236004i | ||||
\(363\) | −5.07295 | + | 15.6129i | −0.266261 | + | 0.819466i | ||||
\(364\) | 0.218847 | + | 0.673542i | 0.0114707 | + | 0.0353032i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.35410 | + | 13.4005i | −0.227593 | + | 0.700458i | ||||
\(367\) | −20.6803 | − | 15.0251i | −1.07950 | − | 0.784306i | −0.101908 | − | 0.994794i | \(-0.532495\pi\) |
−0.977597 | + | 0.210488i | \(0.932495\pi\) | |||||||
\(368\) | 18.2705 | 0.952416 | ||||||||
\(369\) | −1.23607 | − | 0.898056i | −0.0643471 | − | 0.0467509i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73607 | − | 1.26133i | 0.0901322 | − | 0.0654848i | ||||
\(372\) | −1.50000 | + | 1.08981i | −0.0777714 | + | 0.0565042i | ||||
\(373\) | 8.73607 | + | 26.8869i | 0.452336 | + | 1.39215i | 0.874234 | + | 0.485505i | \(0.161364\pi\) |
−0.421897 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(374\) | −44.3607 | −2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.38197 | 0.0712695 | ||||||||
\(377\) | 2.07295 | + | 6.37988i | 0.106762 | + | 0.328581i | ||||
\(378\) | 4.04508 | − | 2.93893i | 0.208057 | − | 0.151162i | ||||
\(379\) | −11.8090 | + | 8.57975i | −0.606588 | + | 0.440712i | −0.848211 | − | 0.529658i | \(-0.822320\pi\) |
0.241623 | + | 0.970370i | \(0.422320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0902 | − | 11.6902i | −0.824324 | − | 0.598907i | ||||
\(382\) | −2.94427 | −0.150642 | ||||||||
\(383\) | 26.9894 | + | 19.6089i | 1.37909 | + | 1.00197i | 0.996964 | + | 0.0778591i | \(0.0248084\pi\) |
0.382127 | + | 0.924110i | \(0.375192\pi\) | |||||||
\(384\) | −4.20820 | + | 12.9515i | −0.214749 | + | 0.660929i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.85410 | − | 11.8617i | −0.196169 | − | 0.603745i | ||||
\(387\) | −3.00000 | + | 9.23305i | −0.152499 | + | 0.469342i | ||||
\(388\) | 0.736068 | − | 2.26538i | 0.0373682 | − | 0.115007i | ||||
\(389\) | 4.63525 | + | 14.2658i | 0.235017 | + | 0.723307i | 0.997119 | + | 0.0758507i | \(0.0241672\pi\) |
−0.762102 | + | 0.647456i | \(0.775833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.09017 | + | 18.7436i | −0.307993 | + | 0.947905i | ||||
\(392\) | −11.9721 | − | 8.69827i | −0.604684 | − | 0.439329i | ||||
\(393\) | −6.79837 | −0.342933 | ||||||||
\(394\) | 4.85410 | + | 3.52671i | 0.244546 | + | 0.177673i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.23607 | + | 3.80423i | −0.263122 | + | 0.191170i | ||||
\(397\) | 23.4894 | − | 17.0660i | 1.17890 | − | 0.856519i | 0.186850 | − | 0.982388i | \(-0.440172\pi\) |
0.992047 | + | 0.125870i | \(0.0401721\pi\) | |||||||
\(398\) | −8.78115 | − | 27.0256i | −0.440159 | − | 1.35467i | ||||
\(399\) | 0.527864 | 0.0264263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5967 | 1.32818 | 0.664089 | − | 0.747653i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(402\) | 2.38197 | + | 7.33094i | 0.118802 | + | 0.365634i | ||||
\(403\) | −4.50000 | + | 3.26944i | −0.224161 | + | 0.162862i | ||||
\(404\) | −0.736068 | + | 0.534785i | −0.0366208 | + | 0.0266065i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.92705 | − | 2.12663i | −0.145267 | − | 0.105543i | ||||
\(407\) | −1.23607 | −0.0612696 | ||||||||
\(408\) | −9.47214 | − | 6.88191i | −0.468941 | − | 0.340705i | ||||
\(409\) | 0.489357 | − | 1.50609i | 0.0241971 | − | 0.0744711i | −0.938229 | − | 0.346016i | \(-0.887534\pi\) |
0.962426 | + | 0.271544i | \(0.0875344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.69098 | − | 11.3597i | −0.182063 | − | 0.560332i | ||||
\(412\) | −1.63525 | + | 5.03280i | −0.0805632 | + | 0.247948i | ||||
\(413\) | 2.07295 | − | 6.37988i | 0.102003 | − | 0.313933i | ||||
\(414\) | 3.76393 | + | 11.5842i | 0.184987 | + | 0.569332i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.93769 | − | 5.96361i | 0.0950033 | − | 0.292390i | ||||
\(417\) | 4.04508 | + | 2.93893i | 0.198089 | + | 0.143920i | ||||
\(418\) | −7.23607 | −0.353928 | ||||||||
\(419\) | 7.66312 | + | 5.56758i | 0.374368 | + | 0.271994i | 0.759020 | − | 0.651068i | \(-0.225679\pi\) |
−0.384652 | + | 0.923062i | \(0.625679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8885 | + | 18.8091i | −1.26173 | + | 0.916701i | −0.998841 | − | 0.0481252i | \(-0.984675\pi\) |
−0.262889 | + | 0.964826i | \(0.584675\pi\) | |||||||
\(422\) | 12.0172 | − | 8.73102i | 0.584989 | − | 0.425020i | ||||
\(423\) | 0.381966 | + | 1.17557i | 0.0185718 | + | 0.0571582i | ||||
\(424\) | −7.76393 | −0.377050 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7082 | 0.518814 | ||||||||
\(427\) | −1.66312 | − | 5.11855i | −0.0804840 | − | 0.247704i | ||||
\(428\) | −8.20820 | + | 5.96361i | −0.396759 | + | 0.288262i | ||||
\(429\) | 7.85410 | − | 5.70634i | 0.379200 | − | 0.275505i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.1353 | + | 17.5353i | 1.16255 | + | 0.844645i | 0.990099 | − | 0.140372i | \(-0.0448299\pi\) |
0.172456 | + | 0.985017i | \(0.444830\pi\) | |||||||
\(432\) | −24.2705 | −1.16772 | ||||||||
\(433\) | 21.7254 | + | 15.7844i | 1.04406 | + | 0.758552i | 0.971073 | − | 0.238781i | \(-0.0767478\pi\) |
0.0729839 | + | 0.997333i | \(0.476748\pi\) | |||||||
\(434\) | 0.927051 | − | 2.85317i | 0.0444999 | − | 0.136957i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.90983 | + | 5.87785i | 0.0914643 | + | 0.281498i | ||||
\(437\) | −0.993422 | + | 3.05744i | −0.0475218 | + | 0.146257i | ||||
\(438\) | −4.50000 | + | 13.8496i | −0.215018 | + | 0.661758i | ||||
\(439\) | −12.6631 | − | 38.9731i | −0.604378 | − | 1.86008i | −0.501013 | − | 0.865440i | \(-0.667039\pi\) |
−0.103365 | − | 0.994644i | \(-0.532961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.09017 | − | 12.5882i | 0.194770 | − | 0.599440i | ||||
\(442\) | 12.7082 | + | 9.23305i | 0.604468 | + | 0.439171i | ||||
\(443\) | −29.9443 | −1.42270 | −0.711348 | − | 0.702840i | \(-0.751915\pi\) | ||||
−0.711348 | + | 0.702840i | \(0.751915\pi\) | |||||||
\(444\) | 0.118034 | + | 0.0857567i | 0.00560165 | + | 0.00406983i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.236068 | + | 0.171513i | −0.0111781 | + | 0.00812140i | ||||
\(447\) | −3.19098 | + | 2.31838i | −0.150928 | + | 0.109656i | ||||
\(448\) | −0.809017 | − | 2.48990i | −0.0382225 | − | 0.117637i | ||||
\(449\) | 4.67376 | 0.220568 | 0.110284 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110284 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −3.21885 | − | 9.90659i | −0.151402 | − | 0.465967i | ||||
\(453\) | 11.7812 | − | 8.55951i | 0.553527 | − | 0.402161i | ||||
\(454\) | 19.3262 | − | 14.0413i | 0.907025 | − | 0.658992i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54508 | − | 1.12257i | −0.0723552 | − | 0.0525692i | ||||
\(457\) | 21.4164 | 1.00182 | 0.500909 | − | 0.865500i | \(-0.332999\pi\) | ||||
0.500909 | + | 0.865500i | \(0.332999\pi\) | |||||||
\(458\) | −28.4164 | − | 20.6457i | −1.32781 | − | 0.964712i | ||||
\(459\) | 8.09017 | − | 24.8990i | 0.377617 | − | 1.16218i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.253289 | + | 0.779543i | 0.0117968 | + | 0.0363069i | 0.956782 | − | 0.290807i | \(-0.0939238\pi\) |
−0.944985 | + | 0.327114i | \(0.893924\pi\) | |||||||
\(462\) | −1.61803 | + | 4.97980i | −0.0752778 | + | 0.231681i | ||||
\(463\) | 7.45492 | − | 22.9439i | 0.346459 | − | 1.06629i | −0.614339 | − | 0.789042i | \(-0.710577\pi\) |
0.960798 | − | 0.277250i | \(-0.0894229\pi\) | |||||||
\(464\) | 5.42705 | + | 16.7027i | 0.251945 | + | 0.775405i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.47214 | − | 4.53077i | 0.0681954 | − | 0.209884i | ||||
\(467\) | 22.2082 | + | 16.1352i | 1.02767 | + | 0.746648i | 0.967842 | − | 0.251560i | \(-0.0809437\pi\) |
0.0598315 | + | 0.998208i | \(0.480944\pi\) | |||||||
\(468\) | 2.29180 | 0.105938 | ||||||||
\(469\) | −2.38197 | − | 1.73060i | −0.109989 | − | 0.0799117i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6631 | + | 7.74721i | −0.491331 | + | 0.356973i | ||||
\(472\) | −19.6353 | + | 14.2658i | −0.903786 | + | 0.656639i | ||||
\(473\) | −7.85410 | − | 24.1724i | −0.361132 | − | 1.11145i | ||||
\(474\) | 13.0902 | 0.601251 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | −2.14590 | − | 6.60440i | −0.0982539 | − | 0.302394i | ||||
\(478\) | 26.8713 | − | 19.5232i | 1.22907 | − | 0.892969i | ||||
\(479\) | 8.78115 | − | 6.37988i | 0.401221 | − | 0.291504i | −0.368817 | − | 0.929502i | \(-0.620237\pi\) |
0.770038 | + | 0.637998i | \(0.220237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.354102 | + | 0.257270i | 0.0161457 | + | 0.0117305i | ||||
\(482\) | 4.09017 | 0.186302 | ||||||||
\(483\) | 1.88197 | + | 1.36733i | 0.0856324 | + | 0.0622156i | ||||
\(484\) | 3.13525 | − | 9.64932i | 0.142512 | − | 0.438606i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.00000 | − | 24.6215i | −0.362887 | − | 1.11685i | ||||
\(487\) | 11.2533 | − | 34.6341i | 0.509935 | − | 1.56942i | −0.282377 | − | 0.959303i | \(-0.591123\pi\) |
0.792312 | − | 0.610116i | \(-0.208877\pi\) | |||||||
\(488\) | −6.01722 | + | 18.5191i | −0.272387 | + | 0.838320i | ||||
\(489\) | 3.39919 | + | 10.4616i | 0.153717 | + | 0.473091i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3647 | + | 41.1325i | −0.603143 | + | 1.85628i | −0.0940550 | + | 0.995567i | \(0.529983\pi\) |
−0.509088 | + | 0.860715i | \(0.670017\pi\) | |||||||
\(492\) | −0.381966 | − | 0.277515i | −0.0172204 | − | 0.0125113i | ||||
\(493\) | −18.9443 | −0.853207 | ||||||||
\(494\) | 2.07295 | + | 1.50609i | 0.0932664 | + | 0.0677620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7812 | + | 8.55951i | −0.528989 | + | 0.384333i | ||||
\(497\) | −3.30902 | + | 2.40414i | −0.148430 | + | 0.107840i | ||||
\(498\) | −3.11803 | − | 9.59632i | −0.139722 | − | 0.430021i | ||||
\(499\) | 7.56231 | 0.338535 | 0.169268 | − | 0.985570i | \(-0.445860\pi\) | ||||
0.169268 | + | 0.985570i | \(0.445860\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | −14.5902 | − | 44.9039i | −0.651191 | − | 2.00416i | ||||
\(503\) | −30.2705 | + | 21.9928i | −1.34970 | + | 0.980611i | −0.350669 | + | 0.936500i | \(0.614046\pi\) |
−0.999027 | + | 0.0441115i | \(0.985954\pi\) | |||||||
\(504\) | 2.23607 | − | 1.62460i | 0.0996024 | − | 0.0723654i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.7984 | − | 18.7436i | −1.14688 | − | 0.833255i | ||||
\(507\) | 9.56231 | 0.424677 | ||||||||
\(508\) | 9.94427 | + | 7.22494i | 0.441206 | + | 0.320555i | ||||
\(509\) | −6.28115 | + | 19.3314i | −0.278407 | + | 0.856849i | 0.709891 | + | 0.704312i | \(0.248744\pi\) |
−0.988298 | + | 0.152537i | \(0.951256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.71885 | − | 5.29007i | −0.0760373 | − | 0.234019i | ||||
\(512\) | −1.63525 | + | 5.03280i | −0.0722687 | + | 0.222420i | ||||
\(513\) | 1.31966 | − | 4.06150i | 0.0582644 | − | 0.179319i | ||||
\(514\) | −11.4271 | − | 35.1688i | −0.504026 | − | 1.55123i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.927051 | + | 2.85317i | −0.0408111 | + | 0.125604i | ||||
\(517\) | −2.61803 | − | 1.90211i | −0.115141 | − | 0.0836548i | ||||
\(518\) | −0.236068 | −0.0103722 | ||||||||
\(519\) | −15.2812 | − | 11.1024i | −0.670768 | − | 0.487342i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7533 | + | 17.2578i | −1.04065 | + | 0.756077i | −0.970412 | − | 0.241453i | \(-0.922376\pi\) |
−0.0702381 | + | 0.997530i | \(0.522376\pi\) | |||||||
\(522\) | −9.47214 | + | 6.88191i | −0.414584 | + | 0.301213i | ||||
\(523\) | 4.06231 | + | 12.5025i | 0.177632 | + | 0.546696i | 0.999744 | − | 0.0226305i | \(-0.00720412\pi\) |
−0.822112 | + | 0.569326i | \(0.807204\pi\) | |||||||
\(524\) | 4.20163 | 0.183549 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.6525 | 0.769685 | ||||||||
\(527\) | −4.85410 | − | 14.9394i | −0.211448 | − | 0.650770i | ||||
\(528\) | 20.5623 | − | 14.9394i | 0.894860 | − | 0.650153i | ||||
\(529\) | 7.14590 | − | 5.19180i | 0.310691 | − | 0.225730i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5623 | − | 12.7598i | −0.762139 | − | 0.553727i | ||||
\(532\) | −0.326238 | −0.0141442 | ||||||||
\(533\) | −1.14590 | − | 0.832544i | −0.0496344 | − | 0.0360615i | ||||
\(534\) | 4.47214 | − | 13.7638i | 0.193528 | − | 0.595619i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.29180 | + | 10.1311i | 0.142184 | + | 0.437597i | ||||
\(537\) | 0.163119 | − | 0.502029i | 0.00703910 | − | 0.0216641i | ||||
\(538\) | −6.38197 | + | 19.6417i | −0.275146 | + | 0.846813i | ||||
\(539\) | 10.7082 | + | 32.9565i | 0.461235 | + | 1.41954i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.38197 | − | 25.7970i | 0.360369 | − | 1.10910i | −0.592462 | − | 0.805599i | \(-0.701844\pi\) |
0.952831 | − | 0.303503i | \(-0.0981561\pi\) | |||||||
\(542\) | 10.4721 | + | 7.60845i | 0.449817 | + | 0.326811i | ||||
\(543\) | −0.291796 | −0.0125222 | ||||||||
\(544\) | 14.3262 | + | 10.4086i | 0.614232 | + | 0.446266i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | − | 1.08981i | 0.0641941 | − | 0.0466397i | ||||
\(547\) | −17.2254 | + | 12.5150i | −0.736506 | + | 0.535103i | −0.891615 | − | 0.452794i | \(-0.850427\pi\) |
0.155109 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(548\) | 2.28115 | + | 7.02067i | 0.0974460 | + | 0.299908i | ||||
\(549\) | −17.4164 | −0.743314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.09017 | −0.131646 | ||||||||
\(552\) | −2.60081 | − | 8.00448i | −0.110698 | − | 0.340693i | ||||
\(553\) | −4.04508 | + | 2.93893i | −0.172015 | + | 0.124976i | ||||
\(554\) | −32.3435 | + | 23.4989i | −1.37414 | + | 0.998373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 1.81636i | −0.106024 | − | 0.0770307i | ||||
\(557\) | −4.76393 | −0.201854 | −0.100927 | − | 0.994894i | \(-0.532181\pi\) | ||||
−0.100927 | + | 0.994894i | \(0.532181\pi\) | |||||||
\(558\) | −7.85410 | − | 5.70634i | −0.332491 | − | 0.241569i | ||||
\(559\) | −2.78115 | + | 8.55951i | −0.117630 | + | 0.362029i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.47214 | + | 26.0746i | 0.357694 | + | 1.10087i | ||||
\(562\) | 5.04508 | − | 15.5272i | 0.212814 | − | 0.654974i | ||||
\(563\) | −2.28115 | + | 7.02067i | −0.0961391 | + | 0.295886i | −0.987549 | − | 0.157312i | \(-0.949717\pi\) |
0.891410 | + | 0.453198i | \(0.149717\pi\) | |||||||
\(564\) | 0.118034 | + | 0.363271i | 0.00497013 | + | 0.0152965i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.9271 | − | 45.9407i | 0.627431 | − | 1.93103i | ||||
\(567\) | 0.500000 | + | 0.363271i | 0.0209980 | + | 0.0152560i | ||||
\(568\) | 14.7984 | 0.620926 | ||||||||
\(569\) | −16.6074 | − | 12.0660i | −0.696218 | − | 0.505832i | 0.182480 | − | 0.983210i | \(-0.441587\pi\) |
−0.878698 | + | 0.477377i | \(0.841587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.57295 | − | 4.77553i | 0.275069 | − | 0.199850i | −0.441695 | − | 0.897165i | \(-0.645623\pi\) |
0.716764 | + | 0.697316i | \(0.245623\pi\) | |||||||
\(572\) | −4.85410 | + | 3.52671i | −0.202960 | + | 0.147459i | ||||
\(573\) | 0.562306 | + | 1.73060i | 0.0234907 | + | 0.0722968i | ||||
\(574\) | 0.763932 | 0.0318859 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.47214 | −0.353006 | ||||||||
\(577\) | 10.4377 | + | 32.1239i | 0.434527 | + | 1.33734i | 0.893571 | + | 0.448923i | \(0.148192\pi\) |
−0.459044 | + | 0.888414i | \(0.651808\pi\) | |||||||
\(578\) | −13.6353 | + | 9.90659i | −0.567152 | + | 0.412060i | ||||
\(579\) | −6.23607 | + | 4.53077i | −0.259162 | + | 0.188292i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.11803 | + | 2.26538i | 0.129358 | + | 0.0939840i | ||||
\(582\) | −6.23607 | −0.258493 | ||||||||
\(583\) | 14.7082 | + | 10.6861i | 0.609152 | + | 0.442575i | ||||
\(584\) | −6.21885 | + | 19.1396i | −0.257338 | + | 0.792004i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.76393 | + | 30.0503i | 0.403344 | + | 1.24137i | ||||
\(587\) | −1.63525 | + | 5.03280i | −0.0674942 | + | 0.207726i | −0.979115 | − | 0.203306i | \(-0.934831\pi\) |
0.911621 | + | 0.411032i | \(0.134831\pi\) | |||||||
\(588\) | 1.26393 | − | 3.88998i | 0.0521237 | − | 0.160420i | ||||
\(589\) | −0.791796 | − | 2.43690i | −0.0326254 | − | 0.100411i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.14590 | − | 3.52671i | 0.0471359 | − | 0.145070i | ||||
\(592\) | 0.927051 | + | 0.673542i | 0.0381016 | + | 0.0276824i | ||||
\(593\) | 10.9098 | 0.448013 | 0.224007 | − | 0.974588i | \(-0.428086\pi\) | ||||
0.224007 | + | 0.974588i | \(0.428086\pi\) | |||||||
\(594\) | 34.2705 | + | 24.8990i | 1.40614 | + | 1.02162i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.97214 | − | 1.43284i | 0.0807818 | − | 0.0586914i | ||||
\(597\) | −14.2082 | + | 10.3229i | −0.581503 | + | 0.422487i | ||||
\(598\) | 3.48936 | + | 10.7391i | 0.142690 | + | 0.439156i | ||||
\(599\) | −9.47214 | −0.387021 | −0.193510 | − | 0.981098i | \(-0.561987\pi\) | ||||
−0.193510 | + | 0.981098i | \(0.561987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | −1.50000 | − | 4.61653i | −0.0611354 | − | 0.188156i | ||||
\(603\) | −7.70820 | + | 5.60034i | −0.313902 | + | 0.228063i | ||||
\(604\) | −7.28115 | + | 5.29007i | −0.296266 | + | 0.215250i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.92705 | + | 1.40008i | 0.0782811 | + | 0.0568745i | ||||
\(607\) | 35.5623 | 1.44343 | 0.721715 | − | 0.692191i | \(-0.243354\pi\) | ||||
0.721715 | + | 0.692191i | \(0.243354\pi\) | |||||||
\(608\) | 2.33688 | + | 1.69784i | 0.0947730 | + | 0.0688566i | ||||
\(609\) | −0.690983 | + | 2.12663i | −0.0280000 | + | 0.0861753i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.354102 | + | 1.08981i | 0.0143254 | + | 0.0440891i | ||||
\(612\) | −2.00000 | + | 6.15537i | −0.0808452 | + | 0.248816i | ||||
\(613\) | 4.62868 | − | 14.2456i | 0.186951 | − | 0.575374i | −0.813026 | − | 0.582227i | \(-0.802181\pi\) |
0.999977 | + | 0.00685287i | \(0.00218135\pi\) | |||||||
\(614\) | −4.61803 | − | 14.2128i | −0.186369 | − | 0.573584i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.23607 | + | 6.88191i | −0.0900937 | + | 0.277280i | ||||
\(617\) | 11.5172 | + | 8.36775i | 0.463666 | + | 0.336873i | 0.794968 | − | 0.606652i | \(-0.207488\pi\) |
−0.331302 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(618\) | 13.8541 | 0.557294 | ||||||||
\(619\) | −24.6976 | − | 17.9438i | −0.992679 | − | 0.721223i | −0.0321727 | − | 0.999482i | \(-0.510243\pi\) |
−0.960506 | + | 0.278259i | \(0.910243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2254 | − | 11.0619i | 0.610975 | − | 0.443900i | ||||
\(622\) | −11.1353 | + | 8.09024i | −0.446483 | + | 0.324389i | ||||
\(623\) | 1.70820 | + | 5.25731i | 0.0684377 | + | 0.210630i | ||||
\(624\) | −9.00000 | −0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.1246 | 1.08412 | ||||||||
\(627\) | 1.38197 | + | 4.25325i | 0.0551904 | + | 0.169859i | ||||
\(628\) | 6.59017 | − | 4.78804i | 0.262976 | − | 0.191064i | ||||
\(629\) | −1.00000 | + | 0.726543i | −0.0398726 | + | 0.0289691i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28115 | + | 6.01661i | 0.329667 | + | 0.239517i | 0.740290 | − | 0.672288i | \(-0.234688\pi\) |
−0.410622 | + | 0.911806i | \(0.634688\pi\) | |||||||
\(632\) | 18.0902 | 0.719588 | ||||||||
\(633\) | −7.42705 | − | 5.39607i | −0.295199 | − | 0.214474i | ||||
\(634\) | −3.82624 | + | 11.7759i | −0.151959 | + | 0.467683i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.663119 | − | 2.04087i | −0.0262944 | − | 0.0809258i | ||||
\(637\) | 3.79180 | − | 11.6699i | 0.150236 | − | 0.462380i | ||||
\(638\) | 9.47214 | − | 29.1522i | 0.375005 | − | 1.15415i | ||||
\(639\) | 4.09017 | + | 12.5882i | 0.161805 | + | 0.497983i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.336881 | + | 1.03681i | −0.0133060 | + | 0.0409517i | −0.957489 | − | 0.288470i | \(-0.906854\pi\) |
0.944183 | + | 0.329421i | \(0.106854\pi\) | |||||||
\(642\) | 21.4894 | + | 15.6129i | 0.848117 | + | 0.616193i | ||||
\(643\) | 30.8328 | 1.21593 | 0.607964 | − | 0.793965i | \(-0.291987\pi\) | ||||
0.607964 | + | 0.793965i | \(0.291987\pi\) | |||||||
\(644\) | −1.16312 | − | 0.845055i | −0.0458333 | − | 0.0332998i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.85410 | + | 4.25325i | −0.230327 | + | 0.167342i | ||||
\(647\) | −29.5623 | + | 21.4783i | −1.16221 | + | 0.844398i | −0.990056 | − | 0.140671i | \(-0.955074\pi\) |
−0.172158 | + | 0.985069i | \(0.555074\pi\) | |||||||
\(648\) | −0.690983 | − | 2.12663i | −0.0271444 | − | 0.0835418i | ||||
\(649\) | 56.8328 | 2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.85410 | −0.0726680 | ||||||||
\(652\) | −2.10081 | − | 6.46564i | −0.0822742 | − | 0.253214i | ||||
\(653\) | 15.4443 | − | 11.2209i | 0.604381 | − | 0.439109i | −0.243050 | − | 0.970014i | \(-0.578148\pi\) |
0.847431 | + | 0.530905i | \(0.178148\pi\) | |||||||
\(654\) | 13.0902 | − | 9.51057i | 0.511866 | − | 0.371893i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 2.17963i | −0.117130 | − | 0.0851002i | ||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | −0.500000 | − | 0.363271i | −0.0194920 | − | 0.0141618i | ||||
\(659\) | 4.79837 | − | 14.7679i | 0.186918 | − | 0.575275i | −0.813058 | − | 0.582183i | \(-0.802199\pi\) |
0.999976 | + | 0.00690786i | \(0.00219886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.08359 | + | 18.7234i | 0.236624 | + | 0.728255i | 0.996902 | + | 0.0786563i | \(0.0250630\pi\) |
−0.760277 | + | 0.649598i | \(0.774937\pi\) | |||||||
\(662\) | −11.5623 | + | 35.5851i | −0.449382 | + | 1.38305i | ||||
\(663\) | 3.00000 | − | 9.23305i | 0.116510 | − | 0.358582i | ||||
\(664\) | −4.30902 | − | 13.2618i | −0.167222 | − | 0.514657i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.236068 | + | 0.726543i | −0.00914745 | + | 0.0281530i | ||||
\(667\) | −11.0172 | − | 8.00448i | −0.426588 | − | 0.309935i | ||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 0.145898 | + | 0.106001i | 0.00564074 | + | 0.00409824i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.8885 | − | 26.8011i | 1.42407 | − | 1.03464i | ||||
\(672\) | 1.69098 | − | 1.22857i | 0.0652311 | − | 0.0473932i | ||||
\(673\) | −3.76393 | − | 11.5842i | −0.145089 | − | 0.446538i | 0.851934 | − | 0.523650i | \(-0.175430\pi\) |
−0.997022 | + | 0.0771122i | \(0.975430\pi\) | |||||||
\(674\) | −12.7082 | −0.489502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | −3.28115 | − | 10.0984i | −0.126105 | − | 0.388111i | 0.867996 | − | 0.496571i | \(-0.165408\pi\) |
−0.994101 | + | 0.108460i | \(0.965408\pi\) | |||||||
\(678\) | −22.0623 | + | 16.0292i | −0.847298 | + | 0.615598i | ||||
\(679\) | 1.92705 | − | 1.40008i | 0.0739534 | − | 0.0537303i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9443 | − | 8.67802i | −0.457705 | − | 0.332543i | ||||
\(682\) | 25.4164 | 0.973245 | ||||||||
\(683\) | −10.8992 | − | 7.91872i | −0.417046 | − | 0.303002i | 0.359402 | − | 0.933183i | \(-0.382981\pi\) |
−0.776448 | + | 0.630181i | \(0.782981\pi\) | |||||||
\(684\) | −0.326238 | + | 1.00406i | −0.0124740 | + | 0.0383911i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.20820 | + | 12.9515i | 0.160670 | + | 0.494491i | ||||
\(687\) | −6.70820 | + | 20.6457i | −0.255934 | + | 0.787684i | ||||
\(688\) | −7.28115 | + | 22.4091i | −0.277591 | + | 0.854338i | ||||
\(689\) | −1.98936 | − | 6.12261i | −0.0757885 | − | 0.233253i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.2082 | − | 34.4953i | 0.426380 | − | 1.31226i | −0.475286 | − | 0.879831i | \(-0.657656\pi\) |
0.901667 | − | 0.432432i | \(-0.142344\pi\) | |||||||
\(692\) | 9.44427 | + | 6.86167i | 0.359017 | + | 0.260841i | ||||
\(693\) | −6.47214 | −0.245856 | ||||||||
\(694\) | −26.0623 | − | 18.9354i | −0.989312 | − | 0.718777i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.54508 | − | 4.75528i | 0.248091 | − | 0.180249i | ||||
\(697\) | 3.23607 | − | 2.35114i | 0.122575 | − | 0.0890558i | ||||
\(698\) | 10.8541 | + | 33.4055i | 0.410834 | + | 1.26442i | ||||
\(699\) | −2.94427 | −0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0132 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(702\) | −4.63525 | − | 14.2658i | −0.174946 | − | 0.538430i | ||||
\(703\) | −0.163119 | + | 0.118513i | −0.00615215 | + | 0.00446980i | ||||
\(704\) | 17.9443 | − | 13.0373i | 0.676300 | − | 0.491361i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.8992 | + | 12.2780i | 0.636009 | + | 0.462088i | ||||
\(707\) | −0.909830 | −0.0342177 | ||||||||
\(708\) | −5.42705 | − | 3.94298i | −0.203961 | − | 0.148186i | ||||
\(709\) | −10.3647 | + | 31.8994i | −0.389256 | + | 1.19801i | 0.544089 | + | 0.839027i | \(0.316875\pi\) |
−0.933345 | + | 0.358980i | \(0.883125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | + | 15.3884i | 0.187515 | + | 0.577111i | ||||
\(712\) | 6.18034 | − | 19.0211i | 0.231618 | − | 0.712847i | ||||
\(713\) | 3.48936 | − | 10.7391i | 0.130677 | − | 0.402184i | ||||
\(714\) | 1.61803 | + | 4.97980i | 0.0605534 | + | 0.186364i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.100813 | + | 0.310271i | −0.00376756 | + | 0.0115954i | ||||
\(717\) | −16.6074 | − | 12.0660i | −0.620214 | − | 0.450612i | ||||
\(718\) | 22.2361 | 0.829843 | ||||||||
\(719\) | 18.8435 | + | 13.6906i | 0.702742 | + | 0.510572i | 0.880824 | − | 0.473443i | \(-0.156989\pi\) |
−0.178082 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28115 | + | 3.11044i | −0.159438 | + | 0.115839i | ||||
\(722\) | 23.9164 | − | 17.3763i | 0.890077 | − | 0.646678i | ||||
\(723\) | −0.781153 | − | 2.40414i | −0.0290514 | − | 0.0894110i | ||||
\(724\) | 0.180340 | 0.00670228 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.5623 | −0.985820 | ||||||||
\(727\) | −7.59017 | − | 23.3601i | −0.281504 | − | 0.866380i | −0.987425 | − | 0.158089i | \(-0.949467\pi\) |
0.705921 | − | 0.708291i | \(-0.250533\pi\) | |||||||
\(728\) | 2.07295 | − | 1.50609i | 0.0768286 | − | 0.0558192i | ||||
\(729\) | −10.5172 | + | 7.64121i | −0.389527 | + | 0.283008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.5623 | − | 14.9394i | −0.760524 | − | 0.552553i | ||||
\(732\) | −5.38197 | −0.198923 | ||||||||
\(733\) | −16.1631 | − | 11.7432i | −0.596998 | − | 0.433745i | 0.247814 | − | 0.968808i | \(-0.420288\pi\) |
−0.844812 | + | 0.535063i | \(0.820288\pi\) | |||||||
\(734\) | 12.7812 | − | 39.3363i | 0.471761 | − | 1.45193i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.93363 | + | 12.1065i | 0.144995 | + | 0.446250i | ||||
\(737\) | 7.70820 | − | 23.7234i | 0.283935 | − | 0.873863i | ||||
\(738\) | 0.763932 | − | 2.35114i | 0.0281207 | − | 0.0865467i | ||||
\(739\) | 4.93769 | + | 15.1967i | 0.181636 | + | 0.559018i | 0.999874 | − | 0.0158612i | \(-0.00504898\pi\) |
−0.818238 | + | 0.574879i | \(0.805049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.489357 | − | 1.50609i | 0.0179770 | − | 0.0553274i | ||||
\(742\) | 2.80902 | + | 2.04087i | 0.103122 | + | 0.0749227i | ||||
\(743\) | −28.3607 | −1.04045 | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(744\) | 5.42705 | + | 3.94298i | 0.198965 | + | 0.144557i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −37.0066 | + | 26.8869i | −1.35491 | + | 0.984398i | ||||
\(747\) | 10.0902 | − | 7.33094i | 0.369180 | − | 0.268225i | ||||
\(748\) | −5.23607 | − | 16.1150i | −0.191450 | − | 0.589221i | ||||
\(749\) | −10.1459 | −0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.11146 | −0.186520 | −0.0932598 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932598 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(752\) | 0.927051 | + | 2.85317i | 0.0338061 | + | 0.104044i | ||||
\(753\) | −23.6074 | + | 17.1518i | −0.860301 | + | 0.625045i | ||||
\(754\) | −8.78115 | + | 6.37988i | −0.319791 | + | 0.232342i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.54508 | + | 1.12257i | 0.0561942 | + | 0.0408275i | ||||
\(757\) | −30.4164 | −1.10550 | −0.552752 | − | 0.833346i | \(-0.686422\pi\) | ||||
−0.552752 | + | 0.833346i | \(0.686422\pi\) | |||||||
\(758\) | −19.1074 | − | 13.8823i | −0.694012 | − | 0.504229i | ||||
\(759\) | −6.09017 | + | 18.7436i | −0.221059 | + | 0.680350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.70163 | − | 17.5478i | −0.206684 | − | 0.636107i | −0.999640 | − | 0.0268287i | \(-0.991459\pi\) |
0.792956 | − | 0.609279i | \(-0.208541\pi\) | |||||||
\(762\) | 9.94427 | − | 30.6053i | 0.360243 | − | 1.10871i | ||||
\(763\) | −1.90983 | + | 5.87785i | −0.0691405 | + | 0.212793i | ||||
\(764\) | −0.347524 | − | 1.06957i | −0.0125730 | − | 0.0386957i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6803 | + | 51.3368i | −0.602685 | + | 1.85487i | ||||
\(767\) | −16.2812 | − | 11.8290i | −0.587878 | − | 0.427119i | ||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −10.8541 | − | 7.88597i | −0.391409 | − | 0.284375i | 0.374624 | − | 0.927177i | \(-0.377772\pi\) |
−0.766033 | + | 0.642802i | \(0.777772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4894 | + | 13.4333i | −0.665878 | + | 0.483789i | ||||
\(772\) | 3.85410 | − | 2.80017i | 0.138712 | − | 0.100780i | ||||
\(773\) | 11.1738 | + | 34.3893i | 0.401892 | + | 1.23690i | 0.923462 | + | 0.383689i | \(0.125346\pi\) |
−0.521570 | + | 0.853208i | \(0.674654\pi\) | |||||||
\(774\) | −15.7082 | −0.564620 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.61803 | −0.309369 | ||||||||
\(777\) | 0.0450850 | + | 0.138757i | 0.00161741 | + | 0.00497789i | ||||
\(778\) | −19.6353 | + | 14.2658i | −0.703958 | + | 0.511455i | ||||
\(779\) | 0.527864 | − | 0.383516i | 0.0189127 | − | 0.0137409i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0344 | − | 20.3682i | −1.00315 | − | 0.728832i | ||||
\(782\) | −31.8885 | −1.14033 | ||||||||
\(783\) | 14.6353 | + | 10.6331i | 0.523021 | + | 0.379997i | ||||
\(784\) | 9.92705 | − | 30.5523i | 0.354538 | − | 1.09115i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.39919 | − | 10.4616i | −0.121245 | − | 0.373154i | ||||
\(787\) | 3.65248 | − | 11.2412i | 0.130197 | − | 0.400704i | −0.864615 | − | 0.502434i | \(-0.832438\pi\) |
0.994812 | + | 0.101730i | \(0.0324378\pi\) | |||||||
\(788\) | −0.708204 | + | 2.17963i | −0.0252287 | + | 0.0776460i | ||||
\(789\) | −3.37132 | − | 10.3759i | −0.120022 | − | 0.369391i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.21885 | − | 9.90659i | 0.114449 | − | 0.352238i | ||||
\(792\) | 18.9443 | + | 13.7638i | 0.673155 | + | 0.489076i | ||||
\(793\) | −16.1459 | −0.573358 | ||||||||
\(794\) | 38.0066 | + | 27.6134i | 1.34880 | + | 0.979963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.78115 | − | 6.37988i | 0.311240 | − | 0.226129i | ||||
\(797\) | 7.89919 | − | 5.73910i | 0.279804 | − | 0.203289i | −0.439028 | − | 0.898473i | \(-0.644677\pi\) |
0.718832 | + | 0.695184i | \(0.244677\pi\) | |||||||
\(798\) | 0.263932 | + | 0.812299i | 0.00934309 | + | 0.0287551i | ||||
\(799\) | −3.23607 | −0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8885 | 0.632061 | ||||||||
\(802\) | 13.2984 | + | 40.9282i | 0.469582 | + | 1.44522i | ||||
\(803\) | 38.1246 | − | 27.6992i | 1.34539 | − | 0.977482i | ||||
\(804\) | −2.38197 | + | 1.73060i | −0.0840055 | + | 0.0610335i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.28115 | − | 5.29007i | −0.256468 | − | 0.186335i | ||||
\(807\) | 12.7639 | 0.449312 | ||||||||
\(808\) | 2.66312 | + | 1.93487i | 0.0936882 | + | 0.0680685i | ||||
\(809\) | 9.57295 | − | 29.4625i | 0.336567 | − | 1.03585i | −0.629378 | − | 0.777099i | \(-0.716690\pi\) |
0.965945 | − | 0.258747i | \(-0.0833097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.54508 | − | 13.9883i | −0.159600 | − | 0.491197i | 0.838998 | − | 0.544134i | \(-0.183142\pi\) |
−0.998598 | + | 0.0529372i | \(0.983142\pi\) | |||||||
\(812\) | 0.427051 | − | 1.31433i | 0.0149866 | − | 0.0461239i | ||||
\(813\) | 2.47214 | − | 7.60845i | 0.0867016 | − | 0.266840i | ||||
\(814\) | −0.618034 | − | 1.90211i | −0.0216621 | − | 0.0666690i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.85410 | − | 24.1724i | 0.274949 | − | 0.846205i | ||||
\(817\) | −3.35410 | − | 2.43690i | −0.117345 | − | 0.0852563i | ||||
\(818\) | 2.56231 | 0.0895889 | ||||||||
\(819\) | 1.85410 | + | 1.34708i | 0.0647876 | + | 0.0470709i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9164 | − | 23.9152i | 1.14879 | − | 0.834645i | 0.160471 | − | 0.987041i | \(-0.448699\pi\) |
0.988320 | + | 0.152395i | \(0.0486987\pi\) | |||||||
\(822\) | 15.6353 | − | 11.3597i | 0.545342 | − | 0.396214i | ||||
\(823\) | −14.7426 | − | 45.3732i | −0.513896 | − | 1.58161i | −0.785281 | − | 0.619139i | \(-0.787482\pi\) |
0.271385 | − | 0.962471i | \(-0.412518\pi\) | |||||||
\(824\) | 19.1459 | 0.666979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8541 | 0.377663 | ||||||||
\(827\) | 0.298374 | + | 0.918300i | 0.0103755 | + | 0.0319324i | 0.956110 | − | 0.293007i | \(-0.0946560\pi\) |
−0.945735 | + | 0.324940i | \(0.894656\pi\) | |||||||
\(828\) | −3.76393 | + | 2.73466i | −0.130806 | + | 0.0950359i | ||||
\(829\) | 29.0066 | − | 21.0745i | 1.00744 | − | 0.731948i | 0.0437695 | − | 0.999042i | \(-0.486063\pi\) |
0.963671 | + | 0.267094i | \(0.0860633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.9894 | + | 14.5231i | 0.693423 | + | 0.503801i | ||||
\(832\) | −7.85410 | −0.272292 | ||||||||
\(833\) | 28.0344 | + | 20.3682i | 0.971336 | + | 0.705717i | ||||
\(834\) | −2.50000 | + | 7.69421i | −0.0865679 | + | 0.266429i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.854102 | − | 2.62866i | −0.0295397 | − | 0.0909140i | ||||
\(837\) | −4.63525 | + | 14.2658i | −0.160218 | + | 0.493100i | ||||
\(838\) | −4.73607 | + | 14.5761i | −0.163605 | + | 0.503524i | ||||
\(839\) | 3.35410 | + | 10.3229i | 0.115796 | + | 0.356385i | 0.992112 | − | 0.125352i | \(-0.0400061\pi\) |
−0.876316 | + | 0.481737i | \(0.840006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.91641 | + | 15.1311i | −0.169531 | + | 0.521764i | ||||
\(842\) | −41.8885 | − | 30.4338i | −1.44357 | − | 1.04882i | ||||
\(843\) | −10.0902 | −0.347524 | ||||||||
\(844\) | 4.59017 | + | 3.33495i | 0.158000 | + | 0.114794i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.61803 | + | 1.17557i | −0.0556292 | + | 0.0404169i | ||||
\(847\) | 8.20820 | − | 5.96361i | 0.282037 | − | 0.204912i | ||||
\(848\) | −5.20820 | − | 16.0292i | −0.178850 | − | 0.550445i | ||||
\(849\) | −29.8541 | −1.02459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.888544 | −0.0304589 | ||||||||
\(852\) | 1.26393 | + | 3.88998i | 0.0433016 | + | 0.133269i | ||||
\(853\) | −12.3820 | + | 8.99602i | −0.423950 | + | 0.308018i | −0.779225 | − | 0.626744i | \(-0.784387\pi\) |
0.355275 | + | 0.934762i | \(0.384387\pi\) | |||||||
\(854\) | 7.04508 | − | 5.11855i | 0.241078 | − | 0.175153i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6976 | + | 21.5765i | 1.01504 | + | 0.737471i | ||||
\(857\) | −19.6869 | −0.672492 | −0.336246 | − | 0.941774i | \(-0.609157\pi\) | ||||
−0.336246 | + | 0.941774i | \(0.609157\pi\) | |||||||
\(858\) | 12.7082 | + | 9.23305i | 0.433851 | + | 0.315211i | ||||
\(859\) | −0.489357 | + | 1.50609i | −0.0166966 | + | 0.0513870i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.942361 | + | 0.334598i | \(0.108600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.145898 | − | 0.449028i | −0.00497219 | − | 0.0153028i | ||||
\(862\) | −14.9164 | + | 45.9080i | −0.508055 | + | 1.56363i | ||||
\(863\) | 6.62461 | − | 20.3885i | 0.225504 | − | 0.694031i | −0.772736 | − | 0.634728i | \(-0.781112\pi\) |
0.998240 | − | 0.0593032i | \(-0.0188879\pi\) | |||||||
\(864\) | −5.22542 | − | 16.0822i | −0.177773 | − | 0.547128i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.4271 | + | 41.3242i | −0.456270 | + | 1.40425i | ||||
\(867\) | 8.42705 | + | 6.12261i | 0.286198 | + | 0.207935i | ||||
\(868\) | 1.14590 | 0.0388943 | ||||||||
\(869\) | −34.2705 | − | 24.8990i | −1.16255 | − | 0.844640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.14590 | + | 5.19180i | −0.242130 | + | 0.175917i | ||||
\(872\) | 18.0902 | − | 13.1433i | 0.612610 | − | 0.445088i | ||||
\(873\) | −2.38197 | − | 7.33094i | −0.0806173 | − | 0.248115i | ||||
\(874\) | −5.20163 | −0.175948 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.56231 | −0.187933 | ||||||||
\(877\) | 11.2918 | + | 34.7526i | 0.381297 | + | 1.17351i | 0.939131 | + | 0.343559i | \(0.111632\pi\) |
−0.557834 | + | 0.829952i | \(0.688368\pi\) | |||||||
\(878\) | 53.6418 | − | 38.9731i | 1.81032 | − | 1.31528i | ||||
\(879\) | 15.7984 | − | 11.4782i | 0.532866 | − | 0.387150i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6525 | + | 23.7234i | 1.10009 | + | 0.799262i | 0.981075 | − | 0.193630i | \(-0.0620262\pi\) |
0.119015 | + | 0.992892i | \(0.462026\pi\) | |||||||
\(882\) | 21.4164 | 0.721128 | ||||||||
\(883\) | −16.6525 | − | 12.0987i | −0.560400 | − | 0.407155i | 0.271205 | − | 0.962522i | \(-0.412578\pi\) |
−0.831605 | + | 0.555367i | \(0.812578\pi\) | |||||||
\(884\) | −1.85410 | + | 5.70634i | −0.0623602 | + | 0.191925i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.9721 | − | 46.0795i | −0.502999 | − | 1.54807i | ||||
\(887\) | −9.23607 | + | 28.4257i | −0.310117 | + | 0.954441i | 0.667601 | + | 0.744519i | \(0.267321\pi\) |
−0.977718 | + | 0.209922i | \(0.932679\pi\) | |||||||
\(888\) | 0.163119 | − | 0.502029i | 0.00547391 | − | 0.0168470i | ||||
\(889\) | 3.79837 | + | 11.6902i | 0.127393 | + | 0.392076i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61803 | + | 4.97980i | −0.0542062 | + | 0.166829i | ||||
\(892\) | −0.0901699 | − | 0.0655123i | −0.00301911 | − | 0.00219351i | ||||
\(893\) | −0.527864 | −0.0176643 | ||||||||
\(894\) | −5.16312 | − | 3.75123i | −0.172681 | − | 0.125460i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.80902 | − | 4.94704i | 0.227473 | − | 0.165269i | ||||
\(897\) | 5.64590 | − | 4.10199i | 0.188511 | − | 0.136961i | ||||
\(898\) | 2.33688 | + | 7.19218i | 0.0779827 | + | 0.240006i | ||||
\(899\) | 10.8541 | 0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | 2.00000 | + | 6.15537i | 0.0665927 | + | 0.204951i | ||||
\(903\) | −2.42705 | + | 1.76336i | −0.0807672 | + | 0.0586808i | ||||
\(904\) | −30.4894 | + | 22.1518i | −1.01406 | + | 0.736758i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.0623 | + | 13.8496i | 0.633303 | + | 0.460121i | ||||
\(907\) | 33.2492 | 1.10402 | 0.552011 | − | 0.833837i | \(-0.313861\pi\) | ||||
0.552011 | + | 0.833837i | \(0.313861\pi\) | |||||||
\(908\) | 7.38197 | + | 5.36331i | 0.244979 | + | 0.177988i | ||||
\(909\) | −0.909830 | + | 2.80017i | −0.0301772 | + | 0.0928757i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.4336 | − | 38.2668i | −0.411944 | − | 1.26783i | −0.914955 | − | 0.403555i | \(-0.867774\pi\) |
0.503011 | − | 0.864280i | \(-0.332226\pi\) | |||||||
\(912\) | 1.28115 | − | 3.94298i | 0.0424232 | − | 0.130565i | ||||
\(913\) | −10.0902 | + | 31.0543i | −0.333936 | + | 1.02775i | ||||
\(914\) | 10.7082 | + | 32.9565i | 0.354196 | + | 1.09010i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.14590 | − | 12.7598i | 0.136984 | − | 0.421594i | ||||
\(917\) | 3.39919 | + | 2.46965i | 0.112251 | + | 0.0815552i | ||||
\(918\) | 42.3607 | 1.39811 | ||||||||
\(919\) | 43.0517 | + | 31.2789i | 1.42014 | + | 1.03179i | 0.991748 | + | 0.128203i | \(0.0409209\pi\) |
0.428395 | + | 0.903591i | \(0.359079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.47214 | + | 5.42882i | −0.246215 | + | 0.178886i | ||||
\(922\) | −1.07295 | + | 0.779543i | −0.0353357 | + | 0.0256729i | ||||
\(923\) | 3.79180 | + | 11.6699i | 0.124808 | + | 0.384121i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.0344 | 1.28275 | ||||||||
\(927\) | 5.29180 | + | 16.2865i | 0.173805 | + | 0.534918i | ||||
\(928\) | −9.89919 | + | 7.19218i | −0.324957 | + | 0.236095i | ||||
\(929\) | −33.6803 | + | 24.4702i | −1.10502 | + | 0.802841i | −0.981872 | − | 0.189548i | \(-0.939298\pi\) |
−0.123145 | + | 0.992389i | \(0.539298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.57295 | + | 3.32244i | 0.149872 | + | 0.108889i | ||||
\(932\) | 1.81966 | 0.0596049 | ||||||||
\(933\) | 6.88197 | + | 5.00004i | 0.225305 | + | 0.163694i | ||||
\(934\) | −13.7254 | + | 42.2425i | −0.449110 | + | 1.38222i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.56231 | − | 7.88597i | −0.0837516 | − | 0.257761i | ||||
\(937\) | −5.47871 | + | 16.8617i | −0.178982 | + | 0.550849i | −0.999793 | − | 0.0203504i | \(-0.993522\pi\) |
0.820811 | + | 0.571200i | \(0.193522\pi\) | |||||||
\(938\) | 1.47214 | − | 4.53077i | 0.0480669 | − | 0.147935i | ||||
\(939\) | −5.18034 | − | 15.9434i | −0.169054 | − | 0.520295i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3435 | + | 44.1446i | −0.467583 | + | 1.43907i | 0.388121 | + | 0.921608i | \(0.373124\pi\) |
−0.855704 | + | 0.517465i | \(0.826876\pi\) | |||||||
\(942\) | −17.2533 | − | 12.5352i | −0.562143 | − | 0.408420i | ||||
\(943\) | 2.87539 | 0.0936355 | ||||||||
\(944\) | −42.6246 | − | 30.9686i | −1.38731 | − | 1.00794i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.2705 | − | 24.1724i | 1.08172 | − | 0.785914i | ||||
\(947\) | 2.14590 | − | 1.55909i | 0.0697323 | − | 0.0506635i | −0.552373 | − | 0.833597i | \(-0.686278\pi\) |
0.622105 | + | 0.782934i | \(0.286278\pi\) | |||||||
\(948\) | 1.54508 | + | 4.75528i | 0.0501820 | + | 0.154444i | ||||
\(949\) | −16.6869 | −0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.65248 | 0.248149 | ||||||||
\(952\) | 2.23607 | + | 6.88191i | 0.0724714 | + | 0.223044i | ||||
\(953\) | −6.26393 | + | 4.55101i | −0.202909 | + | 0.147422i | −0.684599 | − | 0.728919i | \(-0.740023\pi\) |
0.481691 | + | 0.876341i | \(0.340023\pi\) | |||||||
\(954\) | 9.09017 | − | 6.60440i | 0.294305 | − | 0.213825i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.2639 | + | 7.45718i | 0.331959 | + | 0.241183i | ||||
\(957\) | −18.9443 | −0.612381 | ||||||||
\(958\) | 14.2082 | + | 10.3229i | 0.459046 | + | 0.333517i | ||||
\(959\) | −2.28115 | + | 7.02067i | −0.0736623 | + | 0.226709i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.79837 | − | 20.9232i | −0.219302 | − | 0.674943i | ||||
\(962\) | −0.218847 | + | 0.673542i | −0.00705591 | + | 0.0217159i | ||||
\(963\) | −10.1459 | + | 31.2259i | −0.326947 | + | 1.00624i | ||||
\(964\) | 0.482779 | + | 1.48584i | 0.0155493 | + | 0.0478557i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.16312 | + | 3.57971i | −0.0374227 | + | 0.115175i | ||||
\(967\) | 3.32624 | + | 2.41665i | 0.106965 | + | 0.0777143i | 0.639982 | − | 0.768390i | \(-0.278942\pi\) |
−0.533017 | + | 0.846104i | \(0.678942\pi\) | |||||||
\(968\) | −36.7082 | −1.17985 | ||||||||
\(969\) | 3.61803 | + | 2.62866i | 0.116228 | + | 0.0844446i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.54508 | + | 3.30220i | −0.145859 | + | 0.105973i | −0.658321 | − | 0.752737i | \(-0.728733\pi\) |
0.512463 | + | 0.858709i | \(0.328733\pi\) | |||||||
\(972\) | 8.00000 | − | 5.81234i | 0.256600 | − | 0.186431i | ||||
\(973\) | −0.954915 | − | 2.93893i | −0.0306132 | − | 0.0942177i | ||||
\(974\) | 58.9230 | 1.88801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | 0.725425 | + | 2.23263i | 0.0232084 | + | 0.0714281i | 0.961990 | − | 0.273085i | \(-0.0880440\pi\) |
−0.938782 | + | 0.344513i | \(0.888044\pi\) | |||||||
\(978\) | −14.3992 | + | 10.4616i | −0.460435 | + | 0.334526i | ||||
\(979\) | −37.8885 | + | 27.5276i | −1.21092 | + | 0.879787i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1803 | + | 11.7557i | 0.516598 | + | 0.375331i | ||||
\(982\) | −69.9787 | −2.23311 | ||||||||
\(983\) | 7.78115 | + | 5.65334i | 0.248180 | + | 0.180313i | 0.704920 | − | 0.709287i | \(-0.250983\pi\) |
−0.456740 | + | 0.889600i | \(0.650983\pi\) | |||||||
\(984\) | −0.527864 | + | 1.62460i | −0.0168277 | + | 0.0517903i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.47214 | − | 29.1522i | −0.301654 | − | 0.928396i | ||||
\(987\) | −0.118034 | + | 0.363271i | −0.00375706 | + | 0.0115631i | ||||
\(988\) | −0.302439 | + | 0.930812i | −0.00962187 | + | 0.0296131i | ||||
\(989\) | −5.64590 | − | 17.3763i | −0.179529 | − | 0.552534i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.74671 | + | 14.6089i | −0.150784 | + | 0.464066i | −0.997709 | − | 0.0676459i | \(-0.978451\pi\) |
0.846925 | + | 0.531712i | \(0.178451\pi\) | |||||||
\(992\) | −8.20820 | − | 5.96361i | −0.260611 | − | 0.189345i | ||||
\(993\) | 23.1246 | 0.733837 | ||||||||
\(994\) | −5.35410 | − | 3.88998i | −0.169822 | − | 0.123383i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.11803 | − | 2.26538i | 0.0987987 | − | 0.0717814i | ||||
\(997\) | 20.1353 | − | 14.6291i | 0.637690 | − | 0.463309i | −0.221366 | − | 0.975191i | \(-0.571051\pi\) |
0.859056 | + | 0.511882i | \(0.171051\pi\) | |||||||
\(998\) | 3.78115 | + | 11.6372i | 0.119690 | + | 0.368369i | ||||
\(999\) | 1.18034 | 0.0373443 |
(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 | 125.2.d.a.26.1 | 4 | ||
5.2 | odd | 4 | 125.2.e.a.99.1 | 8 | |||
5.3 | odd | 4 | 125.2.e.a.99.2 | 8 | |||
5.4 | even | 2 | 25.2.d.a.6.1 | ✓ | 4 | ||
15.14 | odd | 2 | 225.2.h.b.181.1 | 4 | |||
20.19 | odd | 2 | 400.2.u.b.81.1 | 4 | |||
25.2 | odd | 20 | 625.2.b.a.624.4 | 4 | |||
25.3 | odd | 20 | 125.2.e.a.24.1 | 8 | |||
25.4 | even | 10 | 25.2.d.a.21.1 | yes | 4 | ||
25.6 | even | 5 | 625.2.d.b.376.1 | 4 | |||
25.8 | odd | 20 | 625.2.e.c.249.1 | 8 | |||
25.9 | even | 10 | 625.2.d.h.251.1 | 4 | |||
25.11 | even | 5 | 625.2.a.c.1.2 | 2 | |||
25.12 | odd | 20 | 625.2.e.c.374.1 | 8 | |||
25.13 | odd | 20 | 625.2.e.c.374.2 | 8 | |||
25.14 | even | 10 | 625.2.a.b.1.1 | 2 | |||
25.16 | even | 5 | 625.2.d.b.251.1 | 4 | |||
25.17 | odd | 20 | 625.2.e.c.249.2 | 8 | |||
25.19 | even | 10 | 625.2.d.h.376.1 | 4 | |||
25.21 | even | 5 | inner | 125.2.d.a.101.1 | 4 | ||
25.22 | odd | 20 | 125.2.e.a.24.2 | 8 | |||
25.23 | odd | 20 | 625.2.b.a.624.1 | 4 | |||
75.11 | odd | 10 | 5625.2.a.d.1.1 | 2 | |||
75.14 | odd | 10 | 5625.2.a.f.1.2 | 2 | |||
75.29 | odd | 10 | 225.2.h.b.46.1 | 4 | |||
100.11 | odd | 10 | 10000.2.a.l.1.2 | 2 | |||
100.39 | odd | 10 | 10000.2.a.c.1.1 | 2 | |||
100.79 | odd | 10 | 400.2.u.b.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 5.4 | even | 2 | ||
25.2.d.a.21.1 | yes | 4 | 25.4 | even | 10 | ||
125.2.d.a.26.1 | 4 | 1.1 | even | 1 | trivial | ||
125.2.d.a.101.1 | 4 | 25.21 | even | 5 | inner | ||
125.2.e.a.24.1 | 8 | 25.3 | odd | 20 | |||
125.2.e.a.24.2 | 8 | 25.22 | odd | 20 | |||
125.2.e.a.99.1 | 8 | 5.2 | odd | 4 | |||
125.2.e.a.99.2 | 8 | 5.3 | odd | 4 | |||
225.2.h.b.46.1 | 4 | 75.29 | odd | 10 | |||
225.2.h.b.181.1 | 4 | 15.14 | odd | 2 | |||
400.2.u.b.81.1 | 4 | 20.19 | odd | 2 | |||
400.2.u.b.321.1 | 4 | 100.79 | odd | 10 | |||
625.2.a.b.1.1 | 2 | 25.14 | even | 10 | |||
625.2.a.c.1.2 | 2 | 25.11 | even | 5 | |||
625.2.b.a.624.1 | 4 | 25.23 | odd | 20 | |||
625.2.b.a.624.4 | 4 | 25.2 | odd | 20 | |||
625.2.d.b.251.1 | 4 | 25.16 | even | 5 | |||
625.2.d.b.376.1 | 4 | 25.6 | even | 5 | |||
625.2.d.h.251.1 | 4 | 25.9 | even | 10 | |||
625.2.d.h.376.1 | 4 | 25.19 | even | 10 | |||
625.2.e.c.249.1 | 8 | 25.8 | odd | 20 | |||
625.2.e.c.249.2 | 8 | 25.17 | odd | 20 | |||
625.2.e.c.374.1 | 8 | 25.12 | odd | 20 | |||
625.2.e.c.374.2 | 8 | 25.13 | odd | 20 | |||
5625.2.a.d.1.1 | 2 | 75.11 | odd | 10 | |||
5625.2.a.f.1.2 | 2 | 75.14 | odd | 10 | |||
10000.2.a.c.1.1 | 2 | 100.39 | odd | 10 | |||
10000.2.a.l.1.2 | 2 | 100.11 | odd | 10 |