Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,2,Mod(24,125)]
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([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.e (of order \(10\), 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: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(0.587785 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 125.99 |
Dual form | 125.2.e.a.24.1 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53884 | + | 0.500000i | −1.08813 | + | 0.353553i | −0.797522 | − | 0.603290i | \(-0.793856\pi\) |
−0.290604 | + | 0.956844i | \(0.593856\pi\) | |||||||
\(3\) | −0.587785 | − | 0.809017i | −0.339358 | − | 0.467086i | 0.604896 | − | 0.796305i | \(-0.293215\pi\) |
−0.944254 | + | 0.329218i | \(0.893215\pi\) | |||||||
\(4\) | 0.500000 | − | 0.363271i | 0.250000 | − | 0.181636i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.30902 | + | 0.951057i | 0.534404 | + | 0.388267i | ||||
\(7\) | − | 0.618034i | − | 0.233595i | −0.993156 | − | 0.116797i | \(-0.962737\pi\) | ||
0.993156 | − | 0.116797i | \(-0.0372628\pi\) | |||||||
\(8\) | 1.31433 | − | 1.80902i | 0.464685 | − | 0.639584i | ||||
\(9\) | 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 | \(-0.389591\pi\) | |||||||
\(12\) | −0.587785 | − | 0.190983i | −0.169679 | − | 0.0551320i | ||||
\(13\) | 1.76336 | + | 0.572949i | 0.489067 | + | 0.158907i | 0.543161 | − | 0.839628i | \(-0.317227\pi\) |
−0.0540944 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 4.61653i | −0.375000 | + | 1.15413i | ||||
\(17\) | 3.07768 | − | 4.23607i | 0.746448 | − | 1.02740i | −0.251774 | − | 0.967786i | \(-0.581014\pi\) |
0.998222 | − | 0.0596113i | \(-0.0189861\pi\) | |||||||
\(18\) | 3.23607i | 0.762749i | ||||||||
\(19\) | 0.690983 | + | 0.502029i | 0.158522 | + | 0.115173i | 0.664219 | − | 0.747538i | \(-0.268764\pi\) |
−0.505696 | + | 0.862712i | \(0.668764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 0.363271i | −0.109109 | + | 0.0792723i | ||||
\(22\) | 4.97980 | + | 6.85410i | 1.06170 | + | 1.46130i | ||||
\(23\) | −3.57971 | + | 1.16312i | −0.746422 | + | 0.242527i | −0.657441 | − | 0.753506i | \(-0.728361\pi\) |
−0.0889808 | + | 0.996033i | \(0.528361\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | −4.75528 | + | 1.54508i | −0.915155 | + | 0.297352i | ||||
\(28\) | −0.224514 | − | 0.309017i | −0.0424292 | − | 0.0583987i | ||||
\(29\) | −2.92705 | + | 2.12663i | −0.543540 | + | 0.394905i | −0.825398 | − | 0.564551i | \(-0.809049\pi\) |
0.281858 | + | 0.959456i | \(0.409049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.42705 | + | 1.76336i | 0.435911 | + | 0.316708i | 0.784008 | − | 0.620750i | \(-0.213172\pi\) |
−0.348097 | + | 0.937459i | \(0.613172\pi\) | |||||||
\(32\) | − | 3.38197i | − | 0.597853i | ||||||
\(33\) | −3.07768 | + | 4.23607i | −0.535756 | + | 0.737405i | ||||
\(34\) | −2.61803 | + | 8.05748i | −0.448989 | + | 1.38185i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.381966 | − | 1.17557i | −0.0636610 | − | 0.195928i | ||||
\(37\) | 0.224514 | + | 0.0729490i | 0.0369099 | + | 0.0119927i | 0.327414 | − | 0.944881i | \(-0.393823\pi\) |
−0.290504 | + | 0.956874i | \(0.593823\pi\) | |||||||
\(38\) | −1.31433 | − | 0.427051i | −0.213212 | − | 0.0692768i | ||||
\(39\) | −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 | \(0.118999\pi\) | |||||||
\(42\) | 0.587785 | − | 0.809017i | 0.0906972 | − | 0.124834i | ||||
\(43\) | − | 4.85410i | − | 0.740244i | −0.928983 | − | 0.370122i | \(-0.879316\pi\) | ||
0.928983 | − | 0.370122i | \(-0.120684\pi\) | |||||||
\(44\) | −2.61803 | − | 1.90211i | −0.394683 | − | 0.286754i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.92705 | − | 3.57971i | 0.726454 | − | 0.527800i | ||||
\(47\) | 0.363271 | + | 0.500000i | 0.0529886 | + | 0.0729325i | 0.834689 | − | 0.550722i | \(-0.185647\pi\) |
−0.781700 | + | 0.623654i | \(0.785647\pi\) | |||||||
\(48\) | 4.61653 | − | 1.50000i | 0.666338 | − | 0.216506i | ||||
\(49\) | 6.61803 | 0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23607 | −0.733196 | ||||||||
\(52\) | 1.08981 | − | 0.354102i | 0.151130 | − | 0.0491051i | ||||
\(53\) | 2.04087 | + | 2.80902i | 0.280335 | + | 0.385848i | 0.925845 | − | 0.377904i | \(-0.123355\pi\) |
−0.645510 | + | 0.763752i | \(0.723355\pi\) | |||||||
\(54\) | 6.54508 | − | 4.75528i | 0.890673 | − | 0.647112i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.11803 | − | 0.812299i | −0.149404 | − | 0.108548i | ||||
\(57\) | − | 0.854102i | − | 0.113129i | ||||||
\(58\) | 3.44095 | − | 4.73607i | 0.451820 | − | 0.621876i | ||||
\(59\) | 3.35410 | − | 10.3229i | 0.436667 | − | 1.34392i | −0.454702 | − | 0.890644i | \(-0.650254\pi\) |
0.891369 | − | 0.453279i | \(-0.149746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69098 | + | 8.28199i | 0.344545 | + | 1.06040i | 0.961827 | + | 0.273659i | \(0.0882338\pi\) |
−0.617282 | + | 0.786742i | \(0.711766\pi\) | |||||||
\(62\) | −4.61653 | − | 1.50000i | −0.586299 | − | 0.190500i | ||||
\(63\) | −1.17557 | − | 0.381966i | −0.148108 | − | 0.0481232i | ||||
\(64\) | −1.30902 | − | 4.02874i | −0.163627 | − | 0.503593i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.61803 | − | 8.05748i | 0.322258 | − | 0.991807i | ||||
\(67\) | −2.80017 | + | 3.85410i | −0.342095 | + | 0.470853i | −0.945052 | − | 0.326920i | \(-0.893989\pi\) |
0.602957 | + | 0.797774i | \(0.293989\pi\) | |||||||
\(68\) | − | 3.23607i | − | 0.392431i | ||||||
\(69\) | 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 | \(0.171538\pi\) | |||||||
\(72\) | −2.62866 | − | 3.61803i | −0.309790 | − | 0.426389i | ||||
\(73\) | 8.55951 | − | 2.78115i | 1.00181 | − | 0.325509i | 0.238224 | − | 0.971210i | \(-0.423435\pi\) |
0.763590 | + | 0.645701i | \(0.223435\pi\) | |||||||
\(74\) | −0.381966 | −0.0444026 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.527864 | 0.0605502 | ||||||||
\(77\) | −3.07768 | + | 1.00000i | −0.350735 | + | 0.113961i | ||||
\(78\) | 1.76336 | + | 2.42705i | 0.199661 | + | 0.274809i | ||||
\(79\) | −6.54508 | + | 4.75528i | −0.736380 | + | 0.535011i | −0.891575 | − | 0.452873i | \(-0.850399\pi\) |
0.155196 | + | 0.987884i | \(0.450399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | − | 1.23607i | − | 0.136501i | ||||||
\(83\) | −3.66547 | + | 5.04508i | −0.402337 | + | 0.553770i | −0.961329 | − | 0.275404i | \(-0.911189\pi\) |
0.558991 | + | 0.829174i | \(0.311189\pi\) | |||||||
\(84\) | −0.118034 | + | 0.363271i | −0.0128786 | + | 0.0396361i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.42705 | + | 7.46969i | 0.261716 | + | 0.805478i | ||||
\(87\) | 3.44095 | + | 1.11803i | 0.368909 | + | 0.119866i | ||||
\(88\) | −11.1352 | − | 3.61803i | −1.18701 | − | 0.385684i | ||||
\(89\) | 2.76393 | + | 8.50651i | 0.292976 | + | 0.901688i | 0.983894 | + | 0.178754i | \(0.0572068\pi\) |
−0.690918 | + | 0.722934i | \(0.742793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.354102 | − | 1.08981i | 0.0371200 | − | 0.114244i | ||||
\(92\) | −1.36733 | + | 1.88197i | −0.142554 | + | 0.196209i | ||||
\(93\) | − | 3.00000i | − | 0.311086i | ||||||
\(94\) | −0.809017 | − | 0.587785i | −0.0834437 | − | 0.0606254i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.73607 | + | 1.98787i | −0.279249 | + | 0.202886i | ||||
\(97\) | −2.26538 | − | 3.11803i | −0.230015 | − | 0.316588i | 0.678372 | − | 0.734718i | \(-0.262686\pi\) |
−0.908387 | + | 0.418130i | \(0.862686\pi\) | |||||||
\(98\) | −10.1841 | + | 3.30902i | −1.02875 | + | 0.334261i | ||||
\(99\) | −10.4721 | −1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | 8.05748 | − | 2.61803i | 0.797809 | − | 0.259224i | ||||
\(103\) | −5.03280 | − | 6.92705i | −0.495896 | − | 0.682543i | 0.485566 | − | 0.874200i | \(-0.338614\pi\) |
−0.981462 | + | 0.191658i | \(0.938614\pi\) | |||||||
\(104\) | 3.35410 | − | 2.43690i | 0.328897 | − | 0.238957i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.54508 | − | 3.30220i | −0.441458 | − | 0.320738i | ||||
\(107\) | 16.4164i | 1.58703i | 0.608548 | + | 0.793517i | \(0.291752\pi\) | ||||
−0.608548 | + | 0.793517i | \(0.708248\pi\) | |||||||
\(108\) | −1.81636 | + | 2.50000i | −0.174779 | + | 0.240563i | ||||
\(109\) | −3.09017 | + | 9.51057i | −0.295985 | + | 0.910947i | 0.686904 | + | 0.726748i | \(0.258969\pi\) |
−0.982889 | + | 0.184199i | \(0.941031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0729490 | − | 0.224514i | −0.00692401 | − | 0.0213099i | ||||
\(112\) | 2.85317 | + | 0.927051i | 0.269599 | + | 0.0875981i | ||||
\(113\) | 16.0292 | + | 5.20820i | 1.50790 | + | 0.489947i | 0.942311 | − | 0.334740i | \(-0.108648\pi\) |
0.565590 | + | 0.824687i | \(0.308648\pi\) | |||||||
\(114\) | 0.427051 | + | 1.31433i | 0.0399970 | + | 0.123098i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.690983 | + | 2.12663i | −0.0641562 | + | 0.197452i | ||||
\(117\) | 2.17963 | − | 3.00000i | 0.201507 | − | 0.277350i | ||||
\(118\) | 17.5623i | 1.61674i | ||||||||
\(119\) | −2.61803 | − | 1.90211i | −0.239995 | − | 0.174366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2812 | + | 9.64932i | −1.20738 | + | 0.877211i | ||||
\(122\) | −8.28199 | − | 11.3992i | −0.749817 | − | 1.03203i | ||||
\(123\) | 0.726543 | − | 0.236068i | 0.0655101 | − | 0.0212855i | ||||
\(124\) | 1.85410 | 0.166503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 18.9151 | − | 6.14590i | 1.67845 | − | 0.545360i | 0.693837 | − | 0.720132i | \(-0.255919\pi\) |
0.984609 | + | 0.174772i | \(0.0559187\pi\) | |||||||
\(128\) | 8.00448 | + | 11.0172i | 0.707503 | + | 0.973794i | ||||
\(129\) | −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 | \(0.795982\pi\) | |||||||
\(132\) | 3.23607i | 0.281664i | ||||||||
\(133\) | 0.310271 | − | 0.427051i | 0.0269039 | − | 0.0370300i | ||||
\(134\) | 2.38197 | − | 7.33094i | 0.205771 | − | 0.633297i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.61803 | − | 11.1352i | −0.310244 | − | 0.954832i | ||||
\(137\) | 11.3597 | + | 3.69098i | 0.970523 | + | 0.315342i | 0.751027 | − | 0.660271i | \(-0.229559\pi\) |
0.219496 | + | 0.975613i | \(0.429559\pi\) | |||||||
\(138\) | −5.79210 | − | 1.88197i | −0.493056 | − | 0.160204i | ||||
\(139\) | −1.54508 | − | 4.75528i | −0.131052 | − | 0.403338i | 0.863903 | − | 0.503659i | \(-0.168013\pi\) |
−0.994955 | + | 0.100321i | \(0.968013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.190983 | − | 0.587785i | 0.0160837 | − | 0.0495004i | ||||
\(142\) | −6.29412 | + | 8.66312i | −0.528191 | + | 0.726993i | ||||
\(143\) | − | 9.70820i | − | 0.811841i | ||||||
\(144\) | 7.85410 | + | 5.70634i | 0.654508 | + | 0.475528i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.7812 | + | 8.55951i | −0.975015 | + | 0.708390i | ||||
\(147\) | −3.88998 | − | 5.35410i | −0.320840 | − | 0.441599i | ||||
\(148\) | 0.138757 | − | 0.0450850i | 0.0114058 | − | 0.00370596i | ||||
\(149\) | 3.94427 | 0.323127 | 0.161564 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161564 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5623 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298128\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298128\pi\) | |||||||
\(152\) | 1.81636 | − | 0.590170i | 0.147326 | − | 0.0478691i | ||||
\(153\) | −6.15537 | − | 8.47214i | −0.497632 | − | 0.684932i | ||||
\(154\) | 4.23607 | − | 3.07768i | 0.341352 | − | 0.248007i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.927051 | − | 0.673542i | −0.0742235 | − | 0.0539265i | ||||
\(157\) | − | 13.1803i | − | 1.05191i | −0.850514 | − | 0.525953i | \(-0.823709\pi\) | ||
0.850514 | − | 0.525953i | \(-0.176291\pi\) | |||||||
\(158\) | 7.69421 | − | 10.5902i | 0.612118 | − | 0.842509i | ||||
\(159\) | 1.07295 | − | 3.30220i | 0.0850904 | − | 0.261881i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.718847 | + | 2.21238i | 0.0566531 | + | 0.174360i | ||||
\(162\) | 1.53884 | + | 0.500000i | 0.120903 | + | 0.0392837i | ||||
\(163\) | 10.4616 | + | 3.39919i | 0.819417 | + | 0.266245i | 0.688581 | − | 0.725159i | \(-0.258234\pi\) |
0.130836 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(164\) | 0.145898 | + | 0.449028i | 0.0113927 | + | 0.0350632i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.11803 | − | 9.59632i | 0.242006 | − | 0.744819i | ||||
\(167\) | −8.55951 | + | 11.7812i | −0.662355 | + | 0.911653i | −0.999556 | − | 0.0297794i | \(-0.990520\pi\) |
0.337202 | + | 0.941432i | \(0.390520\pi\) | |||||||
\(168\) | 1.38197i | 0.106621i | ||||||||
\(169\) | −7.73607 | − | 5.62058i | −0.595082 | − | 0.432352i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.38197 | − | 1.00406i | 0.105682 | − | 0.0767822i | ||||
\(172\) | −1.76336 | − | 2.42705i | −0.134455 | − | 0.185061i | ||||
\(173\) | −17.9641 | + | 5.83688i | −1.36578 | + | 0.443770i | −0.897970 | − | 0.440057i | \(-0.854958\pi\) |
−0.467813 | + | 0.883827i | \(0.654958\pi\) | |||||||
\(174\) | −5.85410 | −0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.4164 | 1.91583 | ||||||||
\(177\) | −10.3229 | + | 3.35410i | −0.775914 | + | 0.252110i | ||||
\(178\) | −8.50651 | − | 11.7082i | −0.637590 | − | 0.877567i | ||||
\(179\) | −0.427051 | + | 0.310271i | −0.0319193 | + | 0.0231907i | −0.603631 | − | 0.797264i | \(-0.706280\pi\) |
0.571711 | + | 0.820455i | \(0.306280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.236068 | − | 0.171513i | −0.0175468 | − | 0.0127485i | 0.578977 | − | 0.815344i | \(-0.303452\pi\) |
−0.596524 | + | 0.802595i | \(0.703452\pi\) | |||||||
\(182\) | 1.85410i | 0.137435i | ||||||||
\(183\) | 5.11855 | − | 7.04508i | 0.378374 | − | 0.520788i | ||||
\(184\) | −2.60081 | + | 8.00448i | −0.191734 | + | 0.590098i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 4.61653i | 0.109985 | + | 0.338500i | ||||
\(187\) | −26.0746 | − | 8.47214i | −1.90676 | − | 0.619544i | ||||
\(188\) | 0.363271 | + | 0.118034i | 0.0264943 | + | 0.00860851i | ||||
\(189\) | 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 | \(0.120970\pi\) | |||||||
\(192\) | −2.48990 | + | 3.42705i | −0.179693 | + | 0.247326i | ||||
\(193\) | 7.70820i | 0.554849i | 0.960747 | + | 0.277424i | \(0.0894808\pi\) | ||||
−0.960747 | + | 0.277424i | \(0.910519\pi\) | |||||||
\(194\) | 5.04508 | + | 3.66547i | 0.362216 | + | 0.263165i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30902 | − | 2.40414i | 0.236358 | − | 0.171724i | ||||
\(197\) | 2.17963 | + | 3.00000i | 0.155292 | + | 0.213741i | 0.879573 | − | 0.475764i | \(-0.157828\pi\) |
−0.724281 | + | 0.689505i | \(0.757828\pi\) | |||||||
\(198\) | 16.1150 | − | 5.23607i | 1.14524 | − | 0.372111i | ||||
\(199\) | 17.5623 | 1.24496 | 0.622479 | − | 0.782636i | \(-0.286125\pi\) | ||||
0.622479 | + | 0.782636i | \(0.286125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.76393 | 0.336022 | ||||||||
\(202\) | −2.26538 | + | 0.736068i | −0.159392 | + | 0.0517896i | ||||
\(203\) | 1.31433 | + | 1.80902i | 0.0922477 | + | 0.126968i | ||||
\(204\) | −2.61803 | + | 1.90211i | −0.183299 | + | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.2082 | + | 8.14324i | 0.780913 | + | 0.567366i | ||||
\(207\) | 7.52786i | 0.523223i | ||||||||
\(208\) | −5.29007 | + | 7.28115i | −0.366800 | + | 0.504857i | ||||
\(209\) | 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 | \(-0.202340\pi\) | |||||||
\(212\) | 2.04087 | + | 0.663119i | 0.140168 | + | 0.0455432i | ||||
\(213\) | −6.29412 | − | 2.04508i | −0.431266 | − | 0.140127i | ||||
\(214\) | −8.20820 | − | 25.2623i | −0.561101 | − | 1.72689i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.45492 | + | 10.6331i | −0.235077 | + | 0.723493i | ||||
\(217\) | 1.08981 | − | 1.50000i | 0.0739814 | − | 0.101827i | ||||
\(218\) | − | 16.1803i | − | 1.09587i | ||||||
\(219\) | −7.28115 | − | 5.29007i | −0.492015 | − | 0.357470i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.85410 | − | 5.70634i | 0.528324 | − | 0.383850i | ||||
\(222\) | 0.224514 | + | 0.309017i | 0.0150684 | + | 0.0207399i | ||||
\(223\) | 0.171513 | − | 0.0557281i | 0.0114854 | − | 0.00373183i | −0.303269 | − | 0.952905i | \(-0.598078\pi\) |
0.314754 | + | 0.949173i | \(0.398078\pi\) | |||||||
\(224\) | −2.09017 | −0.139655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2705 | −1.81401 | ||||||||
\(227\) | 14.0413 | − | 4.56231i | 0.931956 | − | 0.302811i | 0.196594 | − | 0.980485i | \(-0.437012\pi\) |
0.735362 | + | 0.677674i | \(0.237012\pi\) | |||||||
\(228\) | −0.310271 | − | 0.427051i | −0.0205482 | − | 0.0282821i | ||||
\(229\) | 17.5623 | − | 12.7598i | 1.16055 | − | 0.843189i | 0.170702 | − | 0.985323i | \(-0.445396\pi\) |
0.989847 | + | 0.142134i | \(0.0453963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.61803 | + | 1.90211i | 0.172254 | + | 0.125150i | ||||
\(232\) | 8.09017i | 0.531146i | ||||||||
\(233\) | −1.73060 | + | 2.38197i | −0.113375 | + | 0.156048i | −0.861933 | − | 0.507021i | \(-0.830746\pi\) |
0.748558 | + | 0.663069i | \(0.230746\pi\) | |||||||
\(234\) | −1.85410 | + | 5.70634i | −0.121206 | + | 0.373035i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.07295 | − | 6.37988i | −0.134937 | − | 0.415295i | ||||
\(237\) | 7.69421 | + | 2.50000i | 0.499793 | + | 0.162392i | ||||
\(238\) | 4.97980 | + | 1.61803i | 0.322792 | + | 0.104882i | ||||
\(239\) | 6.34346 | + | 19.5232i | 0.410324 | + | 1.26285i | 0.916367 | + | 0.400340i | \(0.131108\pi\) |
−0.506043 | + | 0.862508i | \(0.668892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.781153 | − | 2.40414i | 0.0503185 | − | 0.154864i | −0.922740 | − | 0.385423i | \(-0.874055\pi\) |
0.973058 | + | 0.230559i | \(0.0740554\pi\) | |||||||
\(242\) | 15.6129 | − | 21.4894i | 1.00364 | − | 1.38139i | ||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | 4.35410 | + | 3.16344i | 0.278743 | + | 0.202519i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.00000 | + | 0.726543i | −0.0637577 | + | 0.0463227i | ||||
\(247\) | 0.930812 | + | 1.28115i | 0.0592262 | + | 0.0815178i | ||||
\(248\) | 6.37988 | − | 2.07295i | 0.405123 | − | 0.131632i | ||||
\(249\) | 6.23607 | 0.395195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.1803 | −1.84185 | −0.920923 | − | 0.389744i | \(-0.872564\pi\) | ||||
−0.920923 | + | 0.389744i | \(0.872564\pi\) | |||||||
\(252\) | −0.726543 | + | 0.236068i | −0.0457679 | + | 0.0148709i | ||||
\(253\) | 11.5842 | + | 15.9443i | 0.728292 | + | 1.00241i | ||||
\(254\) | −26.0344 | + | 18.9151i | −1.63355 | + | 1.18684i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9721 | − | 7.97172i | −0.685758 | − | 0.498233i | ||||
\(257\) | − | 22.8541i | − | 1.42560i | −0.701367 | − | 0.712800i | \(-0.747427\pi\) | ||
0.701367 | − | 0.712800i | \(-0.252573\pi\) | |||||||
\(258\) | 4.61653 | − | 6.35410i | 0.287412 | − | 0.395589i | ||||
\(259\) | 0.0450850 | − | 0.138757i | 0.00280144 | − | 0.00862196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23607 | + | 6.88191i | 0.138409 | + | 0.425980i | ||||
\(262\) | 10.4616 | + | 3.39919i | 0.646321 | + | 0.210002i | ||||
\(263\) | −10.3759 | − | 3.37132i | −0.639803 | − | 0.207885i | −0.0288905 | − | 0.999583i | \(-0.509197\pi\) |
−0.610913 | + | 0.791698i | \(0.709197\pi\) | |||||||
\(264\) | 3.61803 | + | 11.1352i | 0.222675 | + | 0.685322i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.263932 | + | 0.812299i | −0.0161827 | + | 0.0498053i | ||||
\(267\) | 5.25731 | − | 7.23607i | 0.321742 | − | 0.442840i | ||||
\(268\) | 2.94427i | 0.179850i | ||||||||
\(269\) | −10.3262 | − | 7.50245i | −0.629602 | − | 0.457433i | 0.226660 | − | 0.973974i | \(-0.427219\pi\) |
−0.856262 | + | 0.516541i | \(0.827219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.47214 | − | 4.70228i | 0.393154 | − | 0.285643i | −0.373593 | − | 0.927593i | \(-0.621874\pi\) |
0.766747 | + | 0.641950i | \(0.221874\pi\) | |||||||
\(272\) | 14.9394 | + | 20.5623i | 0.905834 | + | 1.24677i | ||||
\(273\) | −1.08981 | + | 0.354102i | −0.0659585 | + | 0.0214312i | ||||
\(274\) | −19.3262 | −1.16754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.32624 | 0.140023 | ||||||||
\(277\) | −23.4989 | + | 7.63525i | −1.41191 | + | 0.458758i | −0.913023 | − | 0.407908i | \(-0.866258\pi\) |
−0.498889 | + | 0.866666i | \(0.666258\pi\) | |||||||
\(278\) | 4.75528 | + | 6.54508i | 0.285203 | + | 0.392548i | ||||
\(279\) | 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 | \(0.797309\pi\) | |||||||
\(282\) | 1.00000i | 0.0595491i | ||||||||
\(283\) | −17.5478 | + | 24.1525i | −1.04311 | + | 1.43572i | −0.148474 | + | 0.988916i | \(0.547436\pi\) |
−0.894634 | + | 0.446799i | \(0.852564\pi\) | |||||||
\(284\) | 1.26393 | − | 3.88998i | 0.0750006 | − | 0.230828i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.85410 | + | 14.9394i | 0.287029 | + | 0.883385i | ||||
\(287\) | 0.449028 | + | 0.145898i | 0.0265053 | + | 0.00861209i | ||||
\(288\) | −6.43288 | − | 2.09017i | −0.379061 | − | 0.123164i | ||||
\(289\) | −3.21885 | − | 9.90659i | −0.189344 | − | 0.582741i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.19098 | + | 3.66547i | −0.0698167 | + | 0.214874i | ||||
\(292\) | 3.26944 | − | 4.50000i | 0.191330 | − | 0.263343i | ||||
\(293\) | − | 19.5279i | − | 1.14083i | −0.821357 | − | 0.570415i | \(-0.806782\pi\) | ||
0.821357 | − | 0.570415i | \(-0.193218\pi\) | |||||||
\(294\) | 8.66312 | + | 6.29412i | 0.505243 | + | 0.367081i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.427051 | − | 0.310271i | 0.0248218 | − | 0.0180341i | ||||
\(297\) | 15.3884 | + | 21.1803i | 0.892927 | + | 1.22901i | ||||
\(298\) | −6.06961 | + | 1.97214i | −0.351603 | + | 0.114243i | ||||
\(299\) | −6.97871 | −0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | −22.4091 | + | 7.28115i | −1.28950 | + | 0.418983i | ||||
\(303\) | −0.865300 | − | 1.19098i | −0.0497102 | − | 0.0684202i | ||||
\(304\) | −3.35410 | + | 2.43690i | −0.192371 | + | 0.139766i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.7082 | + | 9.95959i | 0.783646 | + | 0.569352i | ||||
\(307\) | − | 9.23607i | − | 0.527130i | −0.964642 | − | 0.263565i | \(-0.915102\pi\) | ||
0.964642 | − | 0.263565i | \(-0.0848984\pi\) | |||||||
\(308\) | −1.17557 | + | 1.61803i | −0.0669843 | + | 0.0921960i | ||||
\(309\) | −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 | \(0.822465\pi\) | |||||||
\(312\) | −3.94298 | − | 1.28115i | −0.223227 | − | 0.0725310i | ||||
\(313\) | −15.9434 | − | 5.18034i | −0.901177 | − | 0.292810i | −0.178454 | − | 0.983948i | \(-0.557110\pi\) |
−0.722723 | + | 0.691138i | \(0.757110\pi\) | |||||||
\(314\) | 6.59017 | + | 20.2825i | 0.371905 | + | 1.14461i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.54508 | + | 4.75528i | −0.0869178 | + | 0.267506i | ||||
\(317\) | −4.49801 | + | 6.19098i | −0.252634 | + | 0.347720i | −0.916431 | − | 0.400192i | \(-0.868944\pi\) |
0.663798 | + | 0.747912i | \(0.268944\pi\) | |||||||
\(318\) | 5.61803i | 0.315044i | ||||||||
\(319\) | 15.3262 | + | 11.1352i | 0.858105 | + | 0.623449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2812 | − | 9.64932i | 0.741282 | − | 0.538573i | ||||
\(322\) | −2.21238 | − | 3.04508i | −0.123291 | − | 0.169696i | ||||
\(323\) | 4.25325 | − | 1.38197i | 0.236657 | − | 0.0768946i | ||||
\(324\) | −0.618034 | −0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.7984 | −0.985761 | ||||||||
\(327\) | 9.51057 | − | 3.09017i | 0.525935 | − | 0.170887i | ||||
\(328\) | 1.00406 | + | 1.38197i | 0.0554398 | + | 0.0763063i | ||||
\(329\) | 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 | \(0.480785\pi\) | |||||||
\(332\) | 3.85410i | 0.211521i | ||||||||
\(333\) | 0.277515 | − | 0.381966i | 0.0152077 | − | 0.0209316i | ||||
\(334\) | 7.28115 | − | 22.4091i | 0.398407 | − | 1.22617i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.927051 | − | 2.85317i | −0.0505748 | − | 0.155653i | ||||
\(337\) | −7.46969 | − | 2.42705i | −0.406900 | − | 0.132210i | 0.0984135 | − | 0.995146i | \(-0.468623\pi\) |
−0.505314 | + | 0.862936i | \(0.668623\pi\) | |||||||
\(338\) | 14.7149 | + | 4.78115i | 0.800384 | + | 0.260060i | ||||
\(339\) | −5.20820 | − | 16.0292i | −0.282871 | − | 0.870587i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.85410 | − | 14.9394i | 0.262864 | − | 0.809013i | ||||
\(342\) | −1.62460 | + | 2.23607i | −0.0878482 | + | 0.120913i | ||||
\(343\) | − | 8.41641i | − | 0.454443i | ||||||
\(344\) | −8.78115 | − | 6.37988i | −0.473448 | − | 0.343980i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.7254 | − | 17.9641i | 1.32925 | − | 0.965755i | ||||
\(347\) | −11.7027 | − | 16.1074i | −0.628234 | − | 0.864690i | 0.369686 | − | 0.929157i | \(-0.379465\pi\) |
−0.997920 | + | 0.0644668i | \(0.979465\pi\) | |||||||
\(348\) | 2.12663 | − | 0.690983i | 0.113999 | − | 0.0370406i | ||||
\(349\) | −21.7082 | −1.16201 | −0.581007 | − | 0.813899i | \(-0.697341\pi\) | ||||
−0.581007 | + | 0.813899i | \(0.697341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.27051 | −0.494823 | ||||||||
\(352\) | −16.8415 | + | 5.47214i | −0.897655 | + | 0.291666i | ||||
\(353\) | −7.58821 | − | 10.4443i | −0.403880 | − | 0.555893i | 0.557833 | − | 0.829953i | \(-0.311633\pi\) |
−0.961712 | + | 0.274061i | \(0.911633\pi\) | |||||||
\(354\) | 14.2082 | − | 10.3229i | 0.755158 | − | 0.548654i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.47214 | + | 3.24920i | 0.237023 | + | 0.172207i | ||||
\(357\) | 3.23607i | 0.171271i | ||||||||
\(358\) | 0.502029 | − | 0.690983i | 0.0265330 | − | 0.0365196i | ||||
\(359\) | −4.24671 | + | 13.0700i | −0.224133 | + | 0.689810i | 0.774246 | + | 0.632885i | \(0.218130\pi\) |
−0.998378 | + | 0.0569247i | \(0.981870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.64590 | − | 17.3763i | −0.297153 | − | 0.914541i | ||||
\(362\) | 0.449028 | + | 0.145898i | 0.0236004 | + | 0.00766823i | ||||
\(363\) | 15.6129 | + | 5.07295i | 0.819466 | + | 0.266261i | ||||
\(364\) | −0.218847 | − | 0.673542i | −0.0114707 | − | 0.0353032i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.35410 | + | 13.4005i | −0.227593 | + | 0.700458i | ||||
\(367\) | 15.0251 | − | 20.6803i | 0.784306 | − | 1.07950i | −0.210488 | − | 0.977597i | \(-0.567505\pi\) |
0.994794 | − | 0.101908i | \(-0.0324949\pi\) | |||||||
\(368\) | − | 18.2705i | − | 0.952416i | ||||||
\(369\) | 1.23607 | + | 0.898056i | 0.0643471 | + | 0.0467509i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73607 | − | 1.26133i | 0.0901322 | − | 0.0654848i | ||||
\(372\) | −1.08981 | − | 1.50000i | −0.0565042 | − | 0.0777714i | ||||
\(373\) | 26.8869 | − | 8.73607i | 1.39215 | − | 0.452336i | 0.485505 | − | 0.874234i | \(-0.338636\pi\) |
0.906644 | + | 0.421897i | \(0.138636\pi\) | |||||||
\(374\) | 44.3607 | 2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.38197 | 0.0712695 | ||||||||
\(377\) | −6.37988 | + | 2.07295i | −0.328581 | + | 0.106762i | ||||
\(378\) | −2.93893 | − | 4.04508i | −0.151162 | − | 0.208057i | ||||
\(379\) | 11.8090 | − | 8.57975i | 0.606588 | − | 0.440712i | −0.241623 | − | 0.970370i | \(-0.577680\pi\) |
0.848211 | + | 0.529658i | \(0.177680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0902 | − | 11.6902i | −0.824324 | − | 0.598907i | ||||
\(382\) | − | 2.94427i | − | 0.150642i | ||||||
\(383\) | 19.6089 | − | 26.9894i | 1.00197 | − | 1.37909i | 0.0778591 | − | 0.996964i | \(-0.475192\pi\) |
0.924110 | − | 0.382127i | \(-0.124808\pi\) | |||||||
\(384\) | 4.20820 | − | 12.9515i | 0.214749 | − | 0.660929i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.85410 | − | 11.8617i | −0.196169 | − | 0.603745i | ||||
\(387\) | −9.23305 | − | 3.00000i | −0.469342 | − | 0.152499i | ||||
\(388\) | −2.26538 | − | 0.736068i | −0.115007 | − | 0.0373682i | ||||
\(389\) | −4.63525 | − | 14.2658i | −0.235017 | − | 0.723307i | −0.997119 | − | 0.0758507i | \(-0.975833\pi\) |
0.762102 | − | 0.647456i | \(-0.224167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.09017 | + | 18.7436i | −0.307993 | + | 0.947905i | ||||
\(392\) | 8.69827 | − | 11.9721i | 0.439329 | − | 0.604684i | ||||
\(393\) | 6.79837i | 0.342933i | ||||||||
\(394\) | −4.85410 | − | 3.52671i | −0.244546 | − | 0.177673i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.23607 | + | 3.80423i | −0.263122 | + | 0.191170i | ||||
\(397\) | 17.0660 | + | 23.4894i | 0.856519 | + | 1.17890i | 0.982388 | + | 0.186850i | \(0.0598279\pi\) |
−0.125870 | + | 0.992047i | \(0.540172\pi\) | |||||||
\(398\) | −27.0256 | + | 8.78115i | −1.35467 | + | 0.440159i | ||||
\(399\) | −0.527864 | −0.0264263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5967 | 1.32818 | 0.664089 | − | 0.747653i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(402\) | −7.33094 | + | 2.38197i | −0.365634 | + | 0.118802i | ||||
\(403\) | 3.26944 | + | 4.50000i | 0.162862 | + | 0.224161i | ||||
\(404\) | 0.736068 | − | 0.534785i | 0.0366208 | − | 0.0266065i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.92705 | − | 2.12663i | −0.145267 | − | 0.105543i | ||||
\(407\) | − | 1.23607i | − | 0.0612696i | ||||||
\(408\) | −6.88191 | + | 9.47214i | −0.340705 | + | 0.468941i | ||||
\(409\) | −0.489357 | + | 1.50609i | −0.0241971 | + | 0.0744711i | −0.962426 | − | 0.271544i | \(-0.912466\pi\) |
0.938229 | + | 0.346016i | \(0.112466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.69098 | − | 11.3597i | −0.182063 | − | 0.560332i | ||||
\(412\) | −5.03280 | − | 1.63525i | −0.247948 | − | 0.0805632i | ||||
\(413\) | −6.37988 | − | 2.07295i | −0.313933 | − | 0.102003i | ||||
\(414\) | −3.76393 | − | 11.5842i | −0.184987 | − | 0.569332i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.93769 | − | 5.96361i | 0.0950033 | − | 0.292390i | ||||
\(417\) | −2.93893 | + | 4.04508i | −0.143920 | + | 0.198089i | ||||
\(418\) | 7.23607i | 0.353928i | ||||||||
\(419\) | −7.66312 | − | 5.56758i | −0.374368 | − | 0.271994i | 0.384652 | − | 0.923062i | \(-0.374321\pi\) |
−0.759020 | + | 0.651068i | \(0.774321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8885 | + | 18.8091i | −1.26173 | + | 0.916701i | −0.998841 | − | 0.0481252i | \(-0.984675\pi\) |
−0.262889 | + | 0.964826i | \(0.584675\pi\) | |||||||
\(422\) | 8.73102 | + | 12.0172i | 0.425020 | + | 0.584989i | ||||
\(423\) | 1.17557 | − | 0.381966i | 0.0571582 | − | 0.0185718i | ||||
\(424\) | 7.76393 | 0.377050 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7082 | 0.518814 | ||||||||
\(427\) | 5.11855 | − | 1.66312i | 0.247704 | − | 0.0804840i | ||||
\(428\) | 5.96361 | + | 8.20820i | 0.288262 | + | 0.396759i | ||||
\(429\) | −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 | \(0.444830\pi\) | |||||||
\(432\) | − | 24.2705i | − | 1.16772i | ||||||
\(433\) | 15.7844 | − | 21.7254i | 0.758552 | − | 1.04406i | −0.238781 | − | 0.971073i | \(-0.576748\pi\) |
0.997333 | − | 0.0729839i | \(-0.0232522\pi\) | |||||||
\(434\) | −0.927051 | + | 2.85317i | −0.0444999 | + | 0.136957i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.90983 | + | 5.87785i | 0.0914643 | + | 0.281498i | ||||
\(437\) | −3.05744 | − | 0.993422i | −0.146257 | − | 0.0475218i | ||||
\(438\) | 13.8496 | + | 4.50000i | 0.661758 | + | 0.215018i | ||||
\(439\) | 12.6631 | + | 38.9731i | 0.604378 | + | 1.86008i | 0.501013 | + | 0.865440i | \(0.332961\pi\) |
0.103365 | + | 0.994644i | \(0.467039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.09017 | − | 12.5882i | 0.194770 | − | 0.599440i | ||||
\(442\) | −9.23305 | + | 12.7082i | −0.439171 | + | 0.604468i | ||||
\(443\) | 29.9443i | 1.42270i | 0.702840 | + | 0.711348i | \(0.251915\pi\) | ||||
−0.702840 | + | 0.711348i | \(0.748085\pi\) | |||||||
\(444\) | −0.118034 | − | 0.0857567i | −0.00560165 | − | 0.00406983i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.236068 | + | 0.171513i | −0.0111781 | + | 0.00812140i | ||||
\(447\) | −2.31838 | − | 3.19098i | −0.109656 | − | 0.150928i | ||||
\(448\) | −2.48990 | + | 0.809017i | −0.117637 | + | 0.0382225i | ||||
\(449\) | −4.67376 | −0.220568 | −0.110284 | − | 0.993900i | \(-0.535176\pi\) | ||||
−0.110284 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 9.90659 | − | 3.21885i | 0.465967 | − | 0.151402i | ||||
\(453\) | −8.55951 | − | 11.7812i | −0.402161 | − | 0.553527i | ||||
\(454\) | −19.3262 | + | 14.0413i | −0.907025 | + | 0.658992i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54508 | − | 1.12257i | −0.0723552 | − | 0.0525692i | ||||
\(457\) | 21.4164i | 1.00182i | 0.865500 | + | 0.500909i | \(0.167001\pi\) | ||||
−0.865500 | + | 0.500909i | \(0.832999\pi\) | |||||||
\(458\) | −20.6457 | + | 28.4164i | −0.964712 | + | 1.32781i | ||||
\(459\) | −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 | \(0.893924\pi\) | |||||||
\(462\) | −4.97980 | − | 1.61803i | −0.231681 | − | 0.0752778i | ||||
\(463\) | −22.9439 | − | 7.45492i | −1.06629 | − | 0.346459i | −0.277250 | − | 0.960798i | \(-0.589423\pi\) |
−0.789042 | + | 0.614339i | \(0.789423\pi\) | |||||||
\(464\) | −5.42705 | − | 16.7027i | −0.251945 | − | 0.775405i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.47214 | − | 4.53077i | 0.0681954 | − | 0.209884i | ||||
\(467\) | −16.1352 | + | 22.2082i | −0.746648 | + | 1.02767i | 0.251560 | + | 0.967842i | \(0.419056\pi\) |
−0.998208 | + | 0.0598315i | \(0.980944\pi\) | |||||||
\(468\) | − | 2.29180i | − | 0.105938i | ||||||
\(469\) | 2.38197 | + | 1.73060i | 0.109989 | + | 0.0799117i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6631 | + | 7.74721i | −0.491331 | + | 0.356973i | ||||
\(472\) | −14.2658 | − | 19.6353i | −0.656639 | − | 0.903786i | ||||
\(473\) | −24.1724 | + | 7.85410i | −1.11145 | + | 0.361132i | ||||
\(474\) | −13.0902 | −0.601251 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 6.60440 | − | 2.14590i | 0.302394 | − | 0.0982539i | ||||
\(478\) | −19.5232 | − | 26.8713i | −0.892969 | − | 1.22907i | ||||
\(479\) | −8.78115 | + | 6.37988i | −0.401221 | + | 0.291504i | −0.770038 | − | 0.637998i | \(-0.779763\pi\) |
0.368817 | + | 0.929502i | \(0.379763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.354102 | + | 0.257270i | 0.0161457 | + | 0.0117305i | ||||
\(482\) | 4.09017i | 0.186302i | ||||||||
\(483\) | 1.36733 | − | 1.88197i | 0.0622156 | − | 0.0856324i | ||||
\(484\) | −3.13525 | + | 9.64932i | −0.142512 | + | 0.438606i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.00000 | − | 24.6215i | −0.362887 | − | 1.11685i | ||||
\(487\) | 34.6341 | + | 11.2533i | 1.56942 | + | 0.509935i | 0.959303 | − | 0.282377i | \(-0.0911230\pi\) |
0.610116 | + | 0.792312i | \(0.291123\pi\) | |||||||
\(488\) | 18.5191 | + | 6.01722i | 0.838320 | + | 0.272387i | ||||
\(489\) | −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 | \(0.670017\pi\) | |||||||
\(492\) | 0.277515 | − | 0.381966i | 0.0125113 | − | 0.0172204i | ||||
\(493\) | 18.9443i | 0.853207i | ||||||||
\(494\) | −2.07295 | − | 1.50609i | −0.0932664 | − | 0.0677620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7812 | + | 8.55951i | −0.528989 | + | 0.384333i | ||||
\(497\) | −2.40414 | − | 3.30902i | −0.107840 | − | 0.148430i | ||||
\(498\) | −9.59632 | + | 3.11803i | −0.430021 | + | 0.139722i | ||||
\(499\) | −7.56231 | −0.338535 | −0.169268 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169268 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | 44.9039 | − | 14.5902i | 2.00416 | − | 0.651191i | ||||
\(503\) | 21.9928 | + | 30.2705i | 0.980611 | + | 1.34970i | 0.936500 | + | 0.350669i | \(0.114046\pi\) |
0.0441115 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(504\) | −2.23607 | + | 1.62460i | −0.0996024 | + | 0.0723654i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.7984 | − | 18.7436i | −1.14688 | − | 0.833255i | ||||
\(507\) | 9.56231i | 0.424677i | ||||||||
\(508\) | 7.22494 | − | 9.94427i | 0.320555 | − | 0.441206i | ||||
\(509\) | 6.28115 | − | 19.3314i | 0.278407 | − | 0.856849i | −0.709891 | − | 0.704312i | \(-0.751256\pi\) |
0.988298 | − | 0.152537i | \(-0.0487444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.71885 | − | 5.29007i | −0.0760373 | − | 0.234019i | ||||
\(512\) | −5.03280 | − | 1.63525i | −0.222420 | − | 0.0722687i | ||||
\(513\) | −4.06150 | − | 1.31966i | −0.179319 | − | 0.0582644i | ||||
\(514\) | 11.4271 | + | 35.1688i | 0.504026 | + | 1.55123i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.927051 | + | 2.85317i | −0.0408111 | + | 0.125604i | ||||
\(517\) | 1.90211 | − | 2.61803i | 0.0836548 | − | 0.115141i | ||||
\(518\) | 0.236068i | 0.0103722i | ||||||||
\(519\) | 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 | \(0.522376\pi\) | |||||||
\(522\) | −6.88191 | − | 9.47214i | −0.301213 | − | 0.414584i | ||||
\(523\) | 12.5025 | − | 4.06231i | 0.546696 | − | 0.177632i | −0.0226305 | − | 0.999744i | \(-0.507204\pi\) |
0.569326 | + | 0.822112i | \(0.307204\pi\) | |||||||
\(524\) | −4.20163 | −0.183549 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.6525 | 0.769685 | ||||||||
\(527\) | 14.9394 | − | 4.85410i | 0.650770 | − | 0.211448i | ||||
\(528\) | −14.9394 | − | 20.5623i | −0.650153 | − | 0.894860i | ||||
\(529\) | −7.14590 | + | 5.19180i | −0.310691 | + | 0.225730i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5623 | − | 12.7598i | −0.762139 | − | 0.553727i | ||||
\(532\) | − | 0.326238i | − | 0.0141442i | ||||||
\(533\) | −0.832544 | + | 1.14590i | −0.0360615 | + | 0.0496344i | ||||
\(534\) | −4.47214 | + | 13.7638i | −0.193528 | + | 0.595619i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.29180 | + | 10.1311i | 0.142184 | + | 0.437597i | ||||
\(537\) | 0.502029 | + | 0.163119i | 0.0216641 | + | 0.00703910i | ||||
\(538\) | 19.6417 | + | 6.38197i | 0.846813 | + | 0.275146i | ||||
\(539\) | −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 | \(-0.0981561\pi\) | |||||||
\(542\) | −7.60845 | + | 10.4721i | −0.326811 | + | 0.449817i | ||||
\(543\) | 0.291796i | 0.0125222i | ||||||||
\(544\) | −14.3262 | − | 10.4086i | −0.614232 | − | 0.446266i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | − | 1.08981i | 0.0641941 | − | 0.0466397i | ||||
\(547\) | −12.5150 | − | 17.2254i | −0.535103 | − | 0.736506i | 0.452794 | − | 0.891615i | \(-0.350427\pi\) |
−0.987897 | + | 0.155109i | \(0.950427\pi\) | |||||||
\(548\) | 7.02067 | − | 2.28115i | 0.299908 | − | 0.0974460i | ||||
\(549\) | 17.4164 | 0.743314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.09017 | −0.131646 | ||||||||
\(552\) | 8.00448 | − | 2.60081i | 0.340693 | − | 0.110698i | ||||
\(553\) | 2.93893 | + | 4.04508i | 0.124976 | + | 0.172015i | ||||
\(554\) | 32.3435 | − | 23.4989i | 1.37414 | − | 0.998373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 1.81636i | −0.106024 | − | 0.0770307i | ||||
\(557\) | − | 4.76393i | − | 0.201854i | −0.994894 | − | 0.100927i | \(-0.967819\pi\) | ||
0.994894 | − | 0.100927i | \(-0.0321809\pi\) | |||||||
\(558\) | −5.70634 | + | 7.85410i | −0.241569 | + | 0.332491i | ||||
\(559\) | 2.78115 | − | 8.55951i | 0.117630 | − | 0.362029i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.47214 | + | 26.0746i | 0.357694 | + | 1.10087i | ||||
\(562\) | 15.5272 | + | 5.04508i | 0.654974 | + | 0.212814i | ||||
\(563\) | 7.02067 | + | 2.28115i | 0.295886 | + | 0.0961391i | 0.453198 | − | 0.891410i | \(-0.350283\pi\) |
−0.157312 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(564\) | −0.118034 | − | 0.363271i | −0.00497013 | − | 0.0152965i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.9271 | − | 45.9407i | 0.627431 | − | 1.93103i | ||||
\(567\) | −0.363271 | + | 0.500000i | −0.0152560 | + | 0.0209980i | ||||
\(568\) | − | 14.7984i | − | 0.620926i | ||||||
\(569\) | 16.6074 | + | 12.0660i | 0.696218 | + | 0.505832i | 0.878698 | − | 0.477377i | \(-0.158413\pi\) |
−0.182480 | + | 0.983210i | \(0.558413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.57295 | − | 4.77553i | 0.275069 | − | 0.199850i | −0.441695 | − | 0.897165i | \(-0.645623\pi\) |
0.716764 | + | 0.697316i | \(0.245623\pi\) | |||||||
\(572\) | −3.52671 | − | 4.85410i | −0.147459 | − | 0.202960i | ||||
\(573\) | 1.73060 | − | 0.562306i | 0.0722968 | − | 0.0234907i | ||||
\(574\) | −0.763932 | −0.0318859 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.47214 | −0.353006 | ||||||||
\(577\) | −32.1239 | + | 10.4377i | −1.33734 | + | 0.434527i | −0.888414 | − | 0.459044i | \(-0.848192\pi\) |
−0.448923 | + | 0.893571i | \(0.648192\pi\) | |||||||
\(578\) | 9.90659 | + | 13.6353i | 0.412060 | + | 0.567152i | ||||
\(579\) | 6.23607 | − | 4.53077i | 0.259162 | − | 0.188292i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.11803 | + | 2.26538i | 0.129358 | + | 0.0939840i | ||||
\(582\) | − | 6.23607i | − | 0.258493i | ||||||
\(583\) | 10.6861 | − | 14.7082i | 0.442575 | − | 0.609152i | ||||
\(584\) | 6.21885 | − | 19.1396i | 0.257338 | − | 0.792004i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.76393 | + | 30.0503i | 0.403344 | + | 1.24137i | ||||
\(587\) | −5.03280 | − | 1.63525i | −0.207726 | − | 0.0674942i | 0.203306 | − | 0.979115i | \(-0.434831\pi\) |
−0.411032 | + | 0.911621i | \(0.634831\pi\) | |||||||
\(588\) | −3.88998 | − | 1.26393i | −0.160420 | − | 0.0521237i | ||||
\(589\) | 0.791796 | + | 2.43690i | 0.0326254 | + | 0.100411i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.14590 | − | 3.52671i | 0.0471359 | − | 0.145070i | ||||
\(592\) | −0.673542 | + | 0.927051i | −0.0276824 | + | 0.0381016i | ||||
\(593\) | − | 10.9098i | − | 0.448013i | −0.974588 | − | 0.224007i | \(-0.928086\pi\) | ||
0.974588 | − | 0.224007i | \(-0.0719137\pi\) | |||||||
\(594\) | −34.2705 | − | 24.8990i | −1.40614 | − | 1.02162i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.97214 | − | 1.43284i | 0.0807818 | − | 0.0586914i | ||||
\(597\) | −10.3229 | − | 14.2082i | −0.422487 | − | 0.581503i | ||||
\(598\) | 10.7391 | − | 3.48936i | 0.439156 | − | 0.142690i | ||||
\(599\) | 9.47214 | 0.387021 | 0.193510 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193510 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | 4.61653 | − | 1.50000i | 0.188156 | − | 0.0611354i | ||||
\(603\) | 5.60034 | + | 7.70820i | 0.228063 | + | 0.313902i | ||||
\(604\) | 7.28115 | − | 5.29007i | 0.296266 | − | 0.215250i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.92705 | + | 1.40008i | 0.0782811 | + | 0.0568745i | ||||
\(607\) | 35.5623i | 1.44343i | 0.692191 | + | 0.721715i | \(0.256646\pi\) | ||||
−0.692191 | + | 0.721715i | \(0.743354\pi\) | |||||||
\(608\) | 1.69784 | − | 2.33688i | 0.0688566 | − | 0.0947730i | ||||
\(609\) | 0.690983 | − | 2.12663i | 0.0280000 | − | 0.0861753i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.354102 | + | 1.08981i | 0.0143254 | + | 0.0440891i | ||||
\(612\) | −6.15537 | − | 2.00000i | −0.248816 | − | 0.0808452i | ||||
\(613\) | −14.2456 | − | 4.62868i | −0.575374 | − | 0.186951i | 0.00685287 | − | 0.999977i | \(-0.497819\pi\) |
−0.582227 | + | 0.813026i | \(0.697819\pi\) | |||||||
\(614\) | 4.61803 | + | 14.2128i | 0.186369 | + | 0.573584i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.23607 | + | 6.88191i | −0.0900937 | + | 0.277280i | ||||
\(617\) | −8.36775 | + | 11.5172i | −0.336873 | + | 0.463666i | −0.943525 | − | 0.331302i | \(-0.892512\pi\) |
0.606652 | + | 0.794968i | \(0.292512\pi\) | |||||||
\(618\) | − | 13.8541i | − | 0.557294i | ||||||
\(619\) | 24.6976 | + | 17.9438i | 0.992679 | + | 0.721223i | 0.960506 | − | 0.278259i | \(-0.0897573\pi\) |
0.0321727 | + | 0.999482i | \(0.489757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2254 | − | 11.0619i | 0.610975 | − | 0.443900i | ||||
\(622\) | −8.09024 | − | 11.1353i | −0.324389 | − | 0.446483i | ||||
\(623\) | 5.25731 | − | 1.70820i | 0.210630 | − | 0.0684377i | ||||
\(624\) | 9.00000 | 0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.1246 | 1.08412 | ||||||||
\(627\) | −4.25325 | + | 1.38197i | −0.169859 | + | 0.0551904i | ||||
\(628\) | −4.78804 | − | 6.59017i | −0.191064 | − | 0.262976i | ||||
\(629\) | 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 | \(0.634688\pi\) | |||||||
\(632\) | 18.0902i | 0.719588i | ||||||||
\(633\) | −5.39607 | + | 7.42705i | −0.214474 | + | 0.295199i | ||||
\(634\) | 3.82624 | − | 11.7759i | 0.151959 | − | 0.467683i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.663119 | − | 2.04087i | −0.0262944 | − | 0.0809258i | ||||
\(637\) | 11.6699 | + | 3.79180i | 0.462380 | + | 0.150236i | ||||
\(638\) | −29.1522 | − | 9.47214i | −1.15415 | − | 0.375005i | ||||
\(639\) | −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 | \(0.106854\pi\) | |||||||
\(642\) | −15.6129 | + | 21.4894i | −0.616193 | + | 0.848117i | ||||
\(643\) | − | 30.8328i | − | 1.21593i | −0.793965 | − | 0.607964i | \(-0.791987\pi\) | ||
0.793965 | − | 0.607964i | \(-0.208013\pi\) | |||||||
\(644\) | 1.16312 | + | 0.845055i | 0.0458333 | + | 0.0332998i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.85410 | + | 4.25325i | −0.230327 | + | 0.167342i | ||||
\(647\) | −21.4783 | − | 29.5623i | −0.844398 | − | 1.16221i | −0.985069 | − | 0.172158i | \(-0.944926\pi\) |
0.140671 | − | 0.990056i | \(-0.455074\pi\) | |||||||
\(648\) | −2.12663 | + | 0.690983i | −0.0835418 | + | 0.0271444i | ||||
\(649\) | −56.8328 | −2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.85410 | −0.0726680 | ||||||||
\(652\) | 6.46564 | − | 2.10081i | 0.253214 | − | 0.0822742i | ||||
\(653\) | −11.2209 | − | 15.4443i | −0.439109 | − | 0.604381i | 0.530905 | − | 0.847431i | \(-0.321852\pi\) |
−0.970014 | + | 0.243050i | \(0.921852\pi\) | |||||||
\(654\) | −13.0902 | + | 9.51057i | −0.511866 | + | 0.371893i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 2.17963i | −0.117130 | − | 0.0851002i | ||||
\(657\) | − | 18.0000i | − | 0.702247i | ||||||
\(658\) | −0.363271 | + | 0.500000i | −0.0141618 | + | 0.0194920i | ||||
\(659\) | −4.79837 | + | 14.7679i | −0.186918 | + | 0.575275i | −0.999976 | − | 0.00690786i | \(-0.997801\pi\) |
0.813058 | + | 0.582183i | \(0.197801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.08359 | + | 18.7234i | 0.236624 | + | 0.728255i | 0.996902 | + | 0.0786563i | \(0.0250630\pi\) |
−0.760277 | + | 0.649598i | \(0.774937\pi\) | |||||||
\(662\) | −35.5851 | − | 11.5623i | −1.38305 | − | 0.449382i | ||||
\(663\) | −9.23305 | − | 3.00000i | −0.358582 | − | 0.116510i | ||||
\(664\) | 4.30902 | + | 13.2618i | 0.167222 | + | 0.514657i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.236068 | + | 0.726543i | −0.00914745 | + | 0.0281530i | ||||
\(667\) | 8.00448 | − | 11.0172i | 0.309935 | − | 0.426588i | ||||
\(668\) | 9.00000i | 0.348220i | ||||||||
\(669\) | −0.145898 | − | 0.106001i | −0.00564074 | − | 0.00409824i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.8885 | − | 26.8011i | 1.42407 | − | 1.03464i | ||||
\(672\) | 1.22857 | + | 1.69098i | 0.0473932 | + | 0.0652311i | ||||
\(673\) | −11.5842 | + | 3.76393i | −0.446538 | + | 0.145089i | −0.523650 | − | 0.851934i | \(-0.675430\pi\) |
0.0771122 | + | 0.997022i | \(0.475430\pi\) | |||||||
\(674\) | 12.7082 | 0.489502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | 10.0984 | − | 3.28115i | 0.388111 | − | 0.126105i | −0.108460 | − | 0.994101i | \(-0.534592\pi\) |
0.496571 | + | 0.867996i | \(0.334592\pi\) | |||||||
\(678\) | 16.0292 | + | 22.0623i | 0.615598 | + | 0.847298i | ||||
\(679\) | −1.92705 | + | 1.40008i | −0.0739534 | + | 0.0537303i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9443 | − | 8.67802i | −0.457705 | − | 0.332543i | ||||
\(682\) | 25.4164i | 0.973245i | ||||||||
\(683\) | −7.91872 | + | 10.8992i | −0.303002 | + | 0.417046i | −0.933183 | − | 0.359402i | \(-0.882981\pi\) |
0.630181 | + | 0.776448i | \(0.282981\pi\) | |||||||
\(684\) | 0.326238 | − | 1.00406i | 0.0124740 | − | 0.0383911i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.20820 | + | 12.9515i | 0.160670 | + | 0.494491i | ||||
\(687\) | −20.6457 | − | 6.70820i | −0.787684 | − | 0.255934i | ||||
\(688\) | 22.4091 | + | 7.28115i | 0.854338 | + | 0.277591i | ||||
\(689\) | 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 | \(-0.142344\pi\) | |||||||
\(692\) | −6.86167 | + | 9.44427i | −0.260841 | + | 0.359017i | ||||
\(693\) | 6.47214i | 0.245856i | ||||||||
\(694\) | 26.0623 | + | 18.9354i | 0.989312 | + | 0.718777i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.54508 | − | 4.75528i | 0.248091 | − | 0.180249i | ||||
\(697\) | 2.35114 | + | 3.23607i | 0.0890558 | + | 0.122575i | ||||
\(698\) | 33.4055 | − | 10.8541i | 1.26442 | − | 0.410834i | ||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0132 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(702\) | 14.2658 | − | 4.63525i | 0.538430 | − | 0.174946i | ||||
\(703\) | 0.118513 | + | 0.163119i | 0.00446980 | + | 0.00615215i | ||||
\(704\) | −17.9443 | + | 13.0373i | −0.676300 | + | 0.491361i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.8992 | + | 12.2780i | 0.636009 | + | 0.462088i | ||||
\(707\) | − | 0.909830i | − | 0.0342177i | ||||||
\(708\) | −3.94298 | + | 5.42705i | −0.148186 | + | 0.203961i | ||||
\(709\) | 10.3647 | − | 31.8994i | 0.389256 | − | 1.19801i | −0.544089 | − | 0.839027i | \(-0.683125\pi\) |
0.933345 | − | 0.358980i | \(-0.116875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | + | 15.3884i | 0.187515 | + | 0.577111i | ||||
\(712\) | 19.0211 | + | 6.18034i | 0.712847 | + | 0.231618i | ||||
\(713\) | −10.7391 | − | 3.48936i | −0.402184 | − | 0.130677i | ||||
\(714\) | −1.61803 | − | 4.97980i | −0.0605534 | − | 0.186364i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.100813 | + | 0.310271i | −0.00376756 | + | 0.0115954i | ||||
\(717\) | 12.0660 | − | 16.6074i | 0.450612 | − | 0.620214i | ||||
\(718\) | − | 22.2361i | − | 0.829843i | ||||||
\(719\) | −18.8435 | − | 13.6906i | −0.702742 | − | 0.510572i | 0.178082 | − | 0.984016i | \(-0.443011\pi\) |
−0.880824 | + | 0.473443i | \(0.843011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28115 | + | 3.11044i | −0.159438 | + | 0.115839i | ||||
\(722\) | 17.3763 | + | 23.9164i | 0.646678 | + | 0.890077i | ||||
\(723\) | −2.40414 | + | 0.781153i | −0.0894110 | + | 0.0290514i | ||||
\(724\) | −0.180340 | −0.00670228 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.5623 | −0.985820 | ||||||||
\(727\) | 23.3601 | − | 7.59017i | 0.866380 | − | 0.281504i | 0.158089 | − | 0.987425i | \(-0.449467\pi\) |
0.708291 | + | 0.705921i | \(0.249467\pi\) | |||||||
\(728\) | −1.50609 | − | 2.07295i | −0.0558192 | − | 0.0768286i | ||||
\(729\) | 10.5172 | − | 7.64121i | 0.389527 | − | 0.283008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.5623 | − | 14.9394i | −0.760524 | − | 0.552553i | ||||
\(732\) | − | 5.38197i | − | 0.198923i | ||||||
\(733\) | −11.7432 | + | 16.1631i | −0.433745 | + | 0.596998i | −0.968808 | − | 0.247814i | \(-0.920288\pi\) |
0.535063 | + | 0.844812i | \(0.320288\pi\) | |||||||
\(734\) | −12.7812 | + | 39.3363i | −0.471761 | + | 1.45193i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.93363 | + | 12.1065i | 0.144995 | + | 0.446250i | ||||
\(737\) | 23.7234 | + | 7.70820i | 0.873863 | + | 0.283935i | ||||
\(738\) | −2.35114 | − | 0.763932i | −0.0865467 | − | 0.0281207i | ||||
\(739\) | −4.93769 | − | 15.1967i | −0.181636 | − | 0.559018i | 0.818238 | − | 0.574879i | \(-0.194951\pi\) |
−0.999874 | + | 0.0158612i | \(0.994951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.489357 | − | 1.50609i | 0.0179770 | − | 0.0553274i | ||||
\(742\) | −2.04087 | + | 2.80902i | −0.0749227 | + | 0.103122i | ||||
\(743\) | 28.3607i | 1.04045i | 0.854029 | + | 0.520226i | \(0.174152\pi\) | ||||
−0.854029 | + | 0.520226i | \(0.825848\pi\) | |||||||
\(744\) | −5.42705 | − | 3.94298i | −0.198965 | − | 0.144557i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −37.0066 | + | 26.8869i | −1.35491 | + | 0.984398i | ||||
\(747\) | 7.33094 | + | 10.0902i | 0.268225 | + | 0.369180i | ||||
\(748\) | −16.1150 | + | 5.23607i | −0.589221 | + | 0.191450i | ||||
\(749\) | 10.1459 | 0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.11146 | −0.186520 | −0.0932598 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932598 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(752\) | −2.85317 | + | 0.927051i | −0.104044 | + | 0.0338061i | ||||
\(753\) | 17.1518 | + | 23.6074i | 0.625045 | + | 0.860301i | ||||
\(754\) | 8.78115 | − | 6.37988i | 0.319791 | − | 0.232342i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.54508 | + | 1.12257i | 0.0561942 | + | 0.0408275i | ||||
\(757\) | − | 30.4164i | − | 1.10550i | −0.833346 | − | 0.552752i | \(-0.813578\pi\) | ||
0.833346 | − | 0.552752i | \(-0.186422\pi\) | |||||||
\(758\) | −13.8823 | + | 19.1074i | −0.504229 | + | 0.694012i | ||||
\(759\) | 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 | \(-0.208541\pi\) | |||||||
\(762\) | 30.6053 | + | 9.94427i | 1.10871 | + | 0.360243i | ||||
\(763\) | 5.87785 | + | 1.90983i | 0.212793 | + | 0.0691405i | ||||
\(764\) | 0.347524 | + | 1.06957i | 0.0125730 | + | 0.0386957i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6803 | + | 51.3368i | −0.602685 | + | 1.85487i | ||||
\(767\) | 11.8290 | − | 16.2812i | 0.427119 | − | 0.587878i | ||||
\(768\) | 13.5623i | 0.489388i | ||||||||
\(769\) | 10.8541 | + | 7.88597i | 0.391409 | + | 0.284375i | 0.766033 | − | 0.642802i | \(-0.222228\pi\) |
−0.374624 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4894 | + | 13.4333i | −0.665878 | + | 0.483789i | ||||
\(772\) | 2.80017 | + | 3.85410i | 0.100780 | + | 0.138712i | ||||
\(773\) | 34.3893 | − | 11.1738i | 1.23690 | − | 0.401892i | 0.383689 | − | 0.923462i | \(-0.374654\pi\) |
0.853208 | + | 0.521570i | \(0.174654\pi\) | |||||||
\(774\) | 15.7082 | 0.564620 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.61803 | −0.309369 | ||||||||
\(777\) | −0.138757 | + | 0.0450850i | −0.00497789 | + | 0.00161741i | ||||
\(778\) | 14.2658 | + | 19.6353i | 0.511455 | + | 0.703958i | ||||
\(779\) | −0.527864 | + | 0.383516i | −0.0189127 | + | 0.0137409i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0344 | − | 20.3682i | −1.00315 | − | 0.728832i | ||||
\(782\) | − | 31.8885i | − | 1.14033i | ||||||
\(783\) | 10.6331 | − | 14.6353i | 0.379997 | − | 0.523021i | ||||
\(784\) | −9.92705 | + | 30.5523i | −0.354538 | + | 1.09115i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.39919 | − | 10.4616i | −0.121245 | − | 0.373154i | ||||
\(787\) | 11.2412 | + | 3.65248i | 0.400704 | + | 0.130197i | 0.502434 | − | 0.864615i | \(-0.332438\pi\) |
−0.101730 | + | 0.994812i | \(0.532438\pi\) | |||||||
\(788\) | 2.17963 | + | 0.708204i | 0.0776460 | + | 0.0252287i | ||||
\(789\) | 3.37132 | + | 10.3759i | 0.120022 | + | 0.369391i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.21885 | − | 9.90659i | 0.114449 | − | 0.352238i | ||||
\(792\) | −13.7638 | + | 18.9443i | −0.489076 | + | 0.673155i | ||||
\(793\) | 16.1459i | 0.573358i | ||||||||
\(794\) | −38.0066 | − | 27.6134i | −1.34880 | − | 0.979963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.78115 | − | 6.37988i | 0.311240 | − | 0.226129i | ||||
\(797\) | 5.73910 | + | 7.89919i | 0.203289 | + | 0.279804i | 0.898473 | − | 0.439028i | \(-0.144677\pi\) |
−0.695184 | + | 0.718832i | \(0.744677\pi\) | |||||||
\(798\) | 0.812299 | − | 0.263932i | 0.0287551 | − | 0.00934309i | ||||
\(799\) | 3.23607 | 0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8885 | 0.632061 | ||||||||
\(802\) | −40.9282 | + | 13.2984i | −1.44522 | + | 0.469582i | ||||
\(803\) | −27.6992 | − | 38.1246i | −0.977482 | − | 1.34539i | ||||
\(804\) | 2.38197 | − | 1.73060i | 0.0840055 | − | 0.0610335i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.28115 | − | 5.29007i | −0.256468 | − | 0.186335i | ||||
\(807\) | 12.7639i | 0.449312i | ||||||||
\(808\) | 1.93487 | − | 2.66312i | 0.0680685 | − | 0.0936882i | ||||
\(809\) | −9.57295 | + | 29.4625i | −0.336567 | + | 1.03585i | 0.629378 | + | 0.777099i | \(0.283310\pi\) |
−0.965945 | + | 0.258747i | \(0.916690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.54508 | − | 13.9883i | −0.159600 | − | 0.491197i | 0.838998 | − | 0.544134i | \(-0.183142\pi\) |
−0.998598 | + | 0.0529372i | \(0.983142\pi\) | |||||||
\(812\) | 1.31433 | + | 0.427051i | 0.0461239 | + | 0.0149866i | ||||
\(813\) | −7.60845 | − | 2.47214i | −0.266840 | − | 0.0867016i | ||||
\(814\) | 0.618034 | + | 1.90211i | 0.0216621 | + | 0.0666690i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.85410 | − | 24.1724i | 0.274949 | − | 0.846205i | ||||
\(817\) | 2.43690 | − | 3.35410i | 0.0852563 | − | 0.117345i | ||||
\(818\) | − | 2.56231i | − | 0.0895889i | ||||||
\(819\) | −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 | \(0.0486987\pi\) | |||||||
\(822\) | 11.3597 | + | 15.6353i | 0.396214 | + | 0.545342i | ||||
\(823\) | −45.3732 | + | 14.7426i | −1.58161 | + | 0.513896i | −0.962471 | − | 0.271385i | \(-0.912518\pi\) |
−0.619139 | + | 0.785281i | \(0.712518\pi\) | |||||||
\(824\) | −19.1459 | −0.666979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8541 | 0.377663 | ||||||||
\(827\) | −0.918300 | + | 0.298374i | −0.0319324 | + | 0.0103755i | −0.324940 | − | 0.945735i | \(-0.605344\pi\) |
0.293007 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(828\) | 2.73466 | + | 3.76393i | 0.0950359 | + | 0.130806i | ||||
\(829\) | −29.0066 | + | 21.0745i | −1.00744 | + | 0.731948i | −0.963671 | − | 0.267094i | \(-0.913937\pi\) |
−0.0437695 | + | 0.999042i | \(0.513937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.9894 | + | 14.5231i | 0.693423 | + | 0.503801i | ||||
\(832\) | − | 7.85410i | − | 0.272292i | ||||||
\(833\) | 20.3682 | − | 28.0344i | 0.705717 | − | 0.971336i | ||||
\(834\) | 2.50000 | − | 7.69421i | 0.0865679 | − | 0.266429i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.854102 | − | 2.62866i | −0.0295397 | − | 0.0909140i | ||||
\(837\) | −14.2658 | − | 4.63525i | −0.493100 | − | 0.160218i | ||||
\(838\) | 14.5761 | + | 4.73607i | 0.503524 | + | 0.163605i | ||||
\(839\) | −3.35410 | − | 10.3229i | −0.115796 | − | 0.356385i | 0.876316 | − | 0.481737i | \(-0.159994\pi\) |
−0.992112 | + | 0.125352i | \(0.959994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.91641 | + | 15.1311i | −0.169531 | + | 0.521764i | ||||
\(842\) | 30.4338 | − | 41.8885i | 1.04882 | − | 1.44357i | ||||
\(843\) | 10.0902i | 0.347524i | ||||||||
\(844\) | −4.59017 | − | 3.33495i | −0.158000 | − | 0.114794i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.61803 | + | 1.17557i | −0.0556292 | + | 0.0404169i | ||||
\(847\) | 5.96361 | + | 8.20820i | 0.204912 | + | 0.282037i | ||||
\(848\) | −16.0292 | + | 5.20820i | −0.550445 | + | 0.178850i | ||||
\(849\) | 29.8541 | 1.02459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.888544 | −0.0304589 | ||||||||
\(852\) | −3.88998 | + | 1.26393i | −0.133269 | + | 0.0433016i | ||||
\(853\) | 8.99602 | + | 12.3820i | 0.308018 | + | 0.423950i | 0.934762 | − | 0.355275i | \(-0.115613\pi\) |
−0.626744 | + | 0.779225i | \(0.715613\pi\) | |||||||
\(854\) | −7.04508 | + | 5.11855i | −0.241078 | + | 0.175153i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6976 | + | 21.5765i | 1.01504 | + | 0.737471i | ||||
\(857\) | − | 19.6869i | − | 0.672492i | −0.941774 | − | 0.336246i | \(-0.890843\pi\) | ||
0.941774 | − | 0.336246i | \(-0.109157\pi\) | |||||||
\(858\) | 9.23305 | − | 12.7082i | 0.315211 | − | 0.433851i | ||||
\(859\) | 0.489357 | − | 1.50609i | 0.0166966 | − | 0.0513870i | −0.942361 | − | 0.334598i | \(-0.891400\pi\) |
0.959058 | + | 0.283211i | \(0.0913996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.145898 | − | 0.449028i | −0.00497219 | − | 0.0153028i | ||||
\(862\) | −45.9080 | − | 14.9164i | −1.56363 | − | 0.508055i | ||||
\(863\) | −20.3885 | − | 6.62461i | −0.694031 | − | 0.225504i | −0.0593032 | − | 0.998240i | \(-0.518888\pi\) |
−0.634728 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(864\) | 5.22542 | + | 16.0822i | 0.177773 | + | 0.547128i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.4271 | + | 41.3242i | −0.456270 | + | 1.40425i | ||||
\(867\) | −6.12261 | + | 8.42705i | −0.207935 | + | 0.286198i | ||||
\(868\) | − | 1.14590i | − | 0.0388943i | ||||||
\(869\) | 34.2705 | + | 24.8990i | 1.16255 | + | 0.844640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.14590 | + | 5.19180i | −0.242130 | + | 0.175917i | ||||
\(872\) | 13.1433 | + | 18.0902i | 0.445088 | + | 0.612610i | ||||
\(873\) | −7.33094 | + | 2.38197i | −0.248115 | + | 0.0806173i | ||||
\(874\) | 5.20163 | 0.175948 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.56231 | −0.187933 | ||||||||
\(877\) | −34.7526 | + | 11.2918i | −1.17351 | + | 0.381297i | −0.829952 | − | 0.557834i | \(-0.811632\pi\) |
−0.343559 | + | 0.939131i | \(0.611632\pi\) | |||||||
\(878\) | −38.9731 | − | 53.6418i | −1.31528 | − | 1.81032i | ||||
\(879\) | −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 | \(0.462026\pi\) | |||||||
\(882\) | 21.4164i | 0.721128i | ||||||||
\(883\) | −12.0987 | + | 16.6525i | −0.407155 | + | 0.560400i | −0.962522 | − | 0.271205i | \(-0.912578\pi\) |
0.555367 | + | 0.831605i | \(0.312578\pi\) | |||||||
\(884\) | 1.85410 | − | 5.70634i | 0.0623602 | − | 0.191925i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.9721 | − | 46.0795i | −0.502999 | − | 1.54807i | ||||
\(887\) | −28.4257 | − | 9.23607i | −0.954441 | − | 0.310117i | −0.209922 | − | 0.977718i | \(-0.567321\pi\) |
−0.744519 | + | 0.667601i | \(0.767321\pi\) | |||||||
\(888\) | −0.502029 | − | 0.163119i | −0.0168470 | − | 0.00547391i | ||||
\(889\) | −3.79837 | − | 11.6902i | −0.127393 | − | 0.392076i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61803 | + | 4.97980i | −0.0542062 | + | 0.166829i | ||||
\(892\) | 0.0655123 | − | 0.0901699i | 0.00219351 | − | 0.00301911i | ||||
\(893\) | 0.527864i | 0.0176643i | ||||||||
\(894\) | 5.16312 | + | 3.75123i | 0.172681 | + | 0.125460i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.80902 | − | 4.94704i | 0.227473 | − | 0.165269i | ||||
\(897\) | 4.10199 | + | 5.64590i | 0.136961 | + | 0.188511i | ||||
\(898\) | 7.19218 | − | 2.33688i | 0.240006 | − | 0.0779827i | ||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | −6.15537 | + | 2.00000i | −0.204951 | + | 0.0665927i | ||||
\(903\) | 1.76336 | + | 2.42705i | 0.0586808 | + | 0.0807672i | ||||
\(904\) | 30.4894 | − | 22.1518i | 1.01406 | − | 0.736758i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.0623 | + | 13.8496i | 0.633303 | + | 0.460121i | ||||
\(907\) | 33.2492i | 1.10402i | 0.833837 | + | 0.552011i | \(0.186139\pi\) | ||||
−0.833837 | + | 0.552011i | \(0.813861\pi\) | |||||||
\(908\) | 5.36331 | − | 7.38197i | 0.177988 | − | 0.244979i | ||||
\(909\) | 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 | \(-0.332226\pi\) | |||||||
\(912\) | 3.94298 | + | 1.28115i | 0.130565 | + | 0.0424232i | ||||
\(913\) | 31.0543 | + | 10.0902i | 1.02775 | + | 0.333936i | ||||
\(914\) | −10.7082 | − | 32.9565i | −0.354196 | − | 1.09010i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.14590 | − | 12.7598i | 0.136984 | − | 0.421594i | ||||
\(917\) | −2.46965 | + | 3.39919i | −0.0815552 | + | 0.112251i | ||||
\(918\) | − | 42.3607i | − | 1.39811i | ||||||
\(919\) | −43.0517 | − | 31.2789i | −1.42014 | − | 1.03179i | −0.991748 | − | 0.128203i | \(-0.959079\pi\) |
−0.428395 | − | 0.903591i | \(-0.640921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.47214 | + | 5.42882i | −0.246215 | + | 0.178886i | ||||
\(922\) | −0.779543 | − | 1.07295i | −0.0256729 | − | 0.0353357i | ||||
\(923\) | 11.6699 | − | 3.79180i | 0.384121 | − | 0.124808i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.0344 | 1.28275 | ||||||||
\(927\) | −16.2865 | + | 5.29180i | −0.534918 | + | 0.173805i | ||||
\(928\) | 7.19218 | + | 9.89919i | 0.236095 | + | 0.324957i | ||||
\(929\) | 33.6803 | − | 24.4702i | 1.10502 | − | 0.802841i | 0.123145 | − | 0.992389i | \(-0.460702\pi\) |
0.981872 | + | 0.189548i | \(0.0607021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.57295 | + | 3.32244i | 0.149872 | + | 0.108889i | ||||
\(932\) | 1.81966i | 0.0596049i | ||||||||
\(933\) | 5.00004 | − | 6.88197i | 0.163694 | − | 0.225305i | ||||
\(934\) | 13.7254 | − | 42.2425i | 0.449110 | − | 1.38222i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.56231 | − | 7.88597i | −0.0837516 | − | 0.257761i | ||||
\(937\) | −16.8617 | − | 5.47871i | −0.550849 | − | 0.178982i | 0.0203504 | − | 0.999793i | \(-0.493522\pi\) |
−0.571200 | + | 0.820811i | \(0.693522\pi\) | |||||||
\(938\) | −4.53077 | − | 1.47214i | −0.147935 | − | 0.0480669i | ||||
\(939\) | 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 | \(0.826876\pi\) | |||||||
\(942\) | 12.5352 | − | 17.2533i | 0.408420 | − | 0.562143i | ||||
\(943\) | − | 2.87539i | − | 0.0936355i | ||||||
\(944\) | 42.6246 | + | 30.9686i | 1.38731 | + | 1.00794i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.2705 | − | 24.1724i | 1.08172 | − | 0.785914i | ||||
\(947\) | 1.55909 | + | 2.14590i | 0.0506635 | + | 0.0697323i | 0.833597 | − | 0.552373i | \(-0.186278\pi\) |
−0.782934 | + | 0.622105i | \(0.786278\pi\) | |||||||
\(948\) | 4.75528 | − | 1.54508i | 0.154444 | − | 0.0501820i | ||||
\(949\) | 16.6869 | 0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.65248 | 0.248149 | ||||||||
\(952\) | −6.88191 | + | 2.23607i | −0.223044 | + | 0.0724714i | ||||
\(953\) | 4.55101 | + | 6.26393i | 0.147422 | + | 0.202909i | 0.876341 | − | 0.481691i | \(-0.159977\pi\) |
−0.728919 | + | 0.684599i | \(0.759977\pi\) | |||||||
\(954\) | −9.09017 | + | 6.60440i | −0.294305 | + | 0.213825i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.2639 | + | 7.45718i | 0.331959 | + | 0.241183i | ||||
\(957\) | − | 18.9443i | − | 0.612381i | ||||||
\(958\) | 10.3229 | − | 14.2082i | 0.333517 | − | 0.459046i | ||||
\(959\) | 2.28115 | − | 7.02067i | 0.0736623 | − | 0.226709i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.79837 | − | 20.9232i | −0.219302 | − | 0.674943i | ||||
\(962\) | −0.673542 | − | 0.218847i | −0.0217159 | − | 0.00705591i | ||||
\(963\) | 31.2259 | + | 10.1459i | 1.00624 | + | 0.326947i | ||||
\(964\) | −0.482779 | − | 1.48584i | −0.0155493 | − | 0.0478557i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.16312 | + | 3.57971i | −0.0374227 | + | 0.115175i | ||||
\(967\) | −2.41665 | + | 3.32624i | −0.0777143 | + | 0.106965i | −0.846104 | − | 0.533017i | \(-0.821058\pi\) |
0.768390 | + | 0.639982i | \(0.221058\pi\) | |||||||
\(968\) | 36.7082i | 1.17985i | ||||||||
\(969\) | −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 | \(0.328733\pi\) | |||||||
\(972\) | 5.81234 | + | 8.00000i | 0.186431 | + | 0.256600i | ||||
\(973\) | −2.93893 | + | 0.954915i | −0.0942177 | + | 0.0306132i | ||||
\(974\) | −58.9230 | −1.88801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | −2.23263 | + | 0.725425i | −0.0714281 | + | 0.0232084i | −0.344513 | − | 0.938782i | \(-0.611956\pi\) |
0.273085 | + | 0.961990i | \(0.411956\pi\) | |||||||
\(978\) | 10.4616 | + | 14.3992i | 0.334526 | + | 0.460435i | ||||
\(979\) | 37.8885 | − | 27.5276i | 1.21092 | − | 0.879787i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1803 | + | 11.7557i | 0.516598 | + | 0.375331i | ||||
\(982\) | − | 69.9787i | − | 2.23311i | ||||||
\(983\) | 5.65334 | − | 7.78115i | 0.180313 | − | 0.248180i | −0.709287 | − | 0.704920i | \(-0.750983\pi\) |
0.889600 | + | 0.456740i | \(0.150983\pi\) | |||||||
\(984\) | 0.527864 | − | 1.62460i | 0.0168277 | − | 0.0517903i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.47214 | − | 29.1522i | −0.301654 | − | 0.928396i | ||||
\(987\) | −0.363271 | − | 0.118034i | −0.0115631 | − | 0.00375706i | ||||
\(988\) | 0.930812 | + | 0.302439i | 0.0296131 | + | 0.00962187i | ||||
\(989\) | 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 | \(0.178451\pi\) | |||||||
\(992\) | 5.96361 | − | 8.20820i | 0.189345 | − | 0.260611i | ||||
\(993\) | − | 23.1246i | − | 0.733837i | ||||||
\(994\) | 5.35410 | + | 3.88998i | 0.169822 | + | 0.123383i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.11803 | − | 2.26538i | 0.0987987 | − | 0.0717814i | ||||
\(997\) | 14.6291 | + | 20.1353i | 0.463309 | + | 0.637690i | 0.975191 | − | 0.221366i | \(-0.0710515\pi\) |
−0.511882 | + | 0.859056i | \(0.671051\pi\) | |||||||
\(998\) | 11.6372 | − | 3.78115i | 0.368369 | − | 0.119690i | ||||
\(999\) | −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.e.a.99.1 | 8 | ||
5.2 | odd | 4 | 25.2.d.a.6.1 | ✓ | 4 | ||
5.3 | odd | 4 | 125.2.d.a.26.1 | 4 | |||
5.4 | even | 2 | inner | 125.2.e.a.99.2 | 8 | ||
15.2 | even | 4 | 225.2.h.b.181.1 | 4 | |||
20.7 | even | 4 | 400.2.u.b.81.1 | 4 | |||
25.2 | odd | 20 | 625.2.a.b.1.1 | 2 | |||
25.3 | odd | 20 | 125.2.d.a.101.1 | 4 | |||
25.4 | even | 10 | inner | 125.2.e.a.24.1 | 8 | ||
25.6 | even | 5 | 625.2.e.c.249.2 | 8 | |||
25.8 | odd | 20 | 625.2.d.b.376.1 | 4 | |||
25.9 | even | 10 | 625.2.e.c.374.2 | 8 | |||
25.11 | even | 5 | 625.2.b.a.624.4 | 4 | |||
25.12 | odd | 20 | 625.2.d.h.251.1 | 4 | |||
25.13 | odd | 20 | 625.2.d.b.251.1 | 4 | |||
25.14 | even | 10 | 625.2.b.a.624.1 | 4 | |||
25.16 | even | 5 | 625.2.e.c.374.1 | 8 | |||
25.17 | odd | 20 | 625.2.d.h.376.1 | 4 | |||
25.19 | even | 10 | 625.2.e.c.249.1 | 8 | |||
25.21 | even | 5 | inner | 125.2.e.a.24.2 | 8 | ||
25.22 | odd | 20 | 25.2.d.a.21.1 | yes | 4 | ||
25.23 | odd | 20 | 625.2.a.c.1.2 | 2 | |||
75.2 | even | 20 | 5625.2.a.f.1.2 | 2 | |||
75.23 | even | 20 | 5625.2.a.d.1.1 | 2 | |||
75.47 | even | 20 | 225.2.h.b.46.1 | 4 | |||
100.23 | even | 20 | 10000.2.a.l.1.2 | 2 | |||
100.27 | even | 20 | 10000.2.a.c.1.1 | 2 | |||
100.47 | even | 20 | 400.2.u.b.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 5.2 | odd | 4 | ||
25.2.d.a.21.1 | yes | 4 | 25.22 | odd | 20 | ||
125.2.d.a.26.1 | 4 | 5.3 | odd | 4 | |||
125.2.d.a.101.1 | 4 | 25.3 | odd | 20 | |||
125.2.e.a.24.1 | 8 | 25.4 | even | 10 | inner | ||
125.2.e.a.24.2 | 8 | 25.21 | even | 5 | inner | ||
125.2.e.a.99.1 | 8 | 1.1 | even | 1 | trivial | ||
125.2.e.a.99.2 | 8 | 5.4 | even | 2 | inner | ||
225.2.h.b.46.1 | 4 | 75.47 | even | 20 | |||
225.2.h.b.181.1 | 4 | 15.2 | even | 4 | |||
400.2.u.b.81.1 | 4 | 20.7 | even | 4 | |||
400.2.u.b.321.1 | 4 | 100.47 | even | 20 | |||
625.2.a.b.1.1 | 2 | 25.2 | odd | 20 | |||
625.2.a.c.1.2 | 2 | 25.23 | odd | 20 | |||
625.2.b.a.624.1 | 4 | 25.14 | even | 10 | |||
625.2.b.a.624.4 | 4 | 25.11 | even | 5 | |||
625.2.d.b.251.1 | 4 | 25.13 | odd | 20 | |||
625.2.d.b.376.1 | 4 | 25.8 | odd | 20 | |||
625.2.d.h.251.1 | 4 | 25.12 | odd | 20 | |||
625.2.d.h.376.1 | 4 | 25.17 | odd | 20 | |||
625.2.e.c.249.1 | 8 | 25.19 | even | 10 | |||
625.2.e.c.249.2 | 8 | 25.6 | even | 5 | |||
625.2.e.c.374.1 | 8 | 25.16 | even | 5 | |||
625.2.e.c.374.2 | 8 | 25.9 | even | 10 | |||
5625.2.a.d.1.1 | 2 | 75.23 | even | 20 | |||
5625.2.a.f.1.2 | 2 | 75.2 | even | 20 | |||
10000.2.a.c.1.1 | 2 | 100.27 | even | 20 | |||
10000.2.a.l.1.2 | 2 | 100.23 | even | 20 |